/*
    Copyright (C) 2019 Alessandro Languasco
*/

/****************   	A. LANGUASCO  		******************** 
************* COMPUTATION OF THE max_chi |L(1,chi)| MOD q(PRIME) *******/ 

/*************************  Building the  S approach ****************/

\\ Global variables:

  
global(log_gamma_matrix);
global(ak_matrix); 
global(tab);   \\global variable used to initialise sumnum
global(phir);
global(phirhalf);
global(pir); 
global(defaultprecision);

 /************* COMPUTATION OF THE max_chi |L(1,chi)| MOD q(PRIME) ******* 
*************                   FOR r1<=q<=r2                        *************
*************          Using the loggamma-function       ********************/

  
{maxL_logGamma(r1,r2,defaultprecision)=local(minutes, millisec, seconds, rows,
columns, elaptimefinalcomp, elaptimeprecomp, M, Lvalue, evenresult,oddresult,
qminusone, qminustwo, correctionLvalue, logtwopi, qminusonehalf, qminusonehalfminusone,
twoPi, twoPiI, u, conjv, chi, aux, numer, i
);

 
\\ minutes,millisec,seconds: used just to compute the elapsed computation time; local variables

\\ defaultprecision: used to fix the precision used in the computations; global variable


print("************ A. LANGUASCO *************");
print("********* COMPUTATION OF THE MAX |L(1,chi)|**********");
 print("******* FOR q IN ONE INTERVAL ********");
 print("********* with the logGamma-FUNCTION   **********");
 
\\ precision setting

default(realprecision,defaultprecision);       


r1=nextprime(r1);
r2=precprime(r2);
if (r1>r2, print("error: no odd primes in this interval. END PROGRAM");return);
if (r1 < 3, r1=3);
print("Interval=[",r1,",",r2,"]");
phir=r2-1;
phirhalf=phir/2;
pir=primepi(r2)-primepi(r1)+1; 


gettime(); 
print("Performing precomputations of log(Gamma(a/q)");
print(" for this interval");

precomplogGamma(r1,r2);

elaptimeprecomp=gettime();

twoPi=2*Pi;
logtwopi=log(twoPi);
twoPiI=twoPi*I;
 
MaxLfile = fileopen("maxL-values.tex", "w");
i=0;

gettime();
print("Starting computation of max_q");
forprime(q=r1,r2,
	i+=1; 
	qminusone=q-1; 
	qminustwo=qminusone-1;
	qminusonehalf=qminusone/2;   
	qminusonehalfminusone=qminusonehalf-1;
	correctionLvalue= 2/sqrt(q);
 	
	u=twoPiI/qminusone;  
	
	M=0;Lvalue=0;
	\\ even characters
	for (m=1, qminusonehalfminusone, 
					numer=0; 
					aux=0;  
			        \\ v=exp(u*2*m);  \\ j=2m+1; j-1 even (j odd) means an even character
			        conjv=  exp(-u*2*m); \\ conjugate of v
			        chi=1; \\ k=0 ; chi = v^0 
			        for (k=0,qminustwo,   \\chi=v^(-k) built via subsequent products 					 
 						aux += chi * log_gamma_matrix[i,k+1]; \\log(gamma(g^k%q/q))
 						chi= chi * conjv;
						); 
					Lvalue=abs(correctionLvalue*aux);
					if (Lvalue>M, M=Lvalue);
			);
	evenresult= M;
	\\print("max_{chi even}|L(1,chi)|(",q")  = ",   evenresult); 
	
	M=0;Lvalue=0;
	\\ odd characters
	correctionLvalue= Pi/(q^(1.5)); 
	for(m=1, qminusonehalf, 
					numer=0; 
					aux=0;  
					\\ v=exp(u*(2*m-1));  \\ j=2m; j-1 odd (j even) means an odd character  
					conjv=  exp(-u*(2*m-1));\\ conjugate of v
					chi = 1; 	\\ k=0 ; chi = v^0	
					 for (k=0,qminustwo,   \\chi=v^(-k) built via subsequent products
						aux += chi * ak_matrix[i,k+1]; \\ a= g^k%q
						chi= chi * conjv;
						\\print(numer); print(aux);
	 					); 
					Lvalue=abs(correctionLvalue*aux);
					if (Lvalue>M, M=Lvalue);
			);
	oddresult=M;
	\\print("max_{chi odd}|L(1,chi)|(",q")  = ", oddresult); 
	\\print("max_{chi}|L(1,chi)|(",q")  = ", max(oddresult,evenresult)); 
	

	filewrite1(MaxLfile, "$");
	filewrite1(MaxLfile,q);
	filewrite1(MaxLfile,"$ & $");
	filewrite1(MaxLfile, max(oddresult,evenresult));
	filewrite(MaxLfile,"\\dotsc$ \\\\");

	print("$",q,"$ & $", max(oddresult,evenresult), "\\dotsc$ \\\\");
 
);

fileclose(MaxLfile);  
elaptimefinalcomp=gettime();

seconds=floor(elaptimeprecomp/1000)%60;
minutes=floor(elaptimeprecomp/60000);
millisec=elaptimeprecomp- minutes*60000 - seconds*1000;
\\print(elaptimeprecomp); 
print("Precomputation time: ", minutes, " min, ", seconds, " sec, ", millisec, " millisec");

\\print(elaptimefinalcomp);
seconds=floor(elaptimefinalcomp/1000)%60;
minutes=floor(elaptimefinalcomp/60000);
millisec=elaptimefinalcomp- minutes*60000 - seconds*1000;
 
print("Final step max computation time (output time included): ", minutes, " min, ", seconds, " sec, ", millisec, " millisec");

seconds=floor((elaptimefinalcomp+elaptimeprecomp)/1000)%60;
minutes=floor((elaptimefinalcomp+elaptimeprecomp)/60000);
millisec=(elaptimefinalcomp+elaptimeprecomp)- minutes*60000 - seconds*1000;

print("Total elapsed time: ", minutes, " min, ", seconds, " sec, ", millisec, " millisec");

print("******  END PROGRAM   ********"); 
}
 
 
 

/*****************   for precomputations    ****************/

{precomplogGamma(r1,r2)= local(rows, columns, i, aoverq, g, g1, a, nhalf,logpi); 
 

ak_matrix=matrix(pir,phir+1,rows,columns,0); 
log_gamma_matrix=matrix(pir,phir+1,rows,columns,0);

 logpi = log(Pi);
i=0;
forprime(q=r1,r2,
			print("Precomputation for q = ",q);
			g1=znprimroot(q);  \\ needed here to sort the sequences log(Gamma(a/q)) using a=a=g^k%q
			g=lift(g1);  
			i+=1;  
			ak_matrix[i,phir+1]=q;
            log_gamma_matrix[i,phir+1]=q;
            
			a=1;  
			nhalf= (q-1)/2;
			for(k=0, nhalf-1, aoverq = a/q; \\ already sorted for the final summation 
				log_gamma_matrix[i,k+1] = log(gamma(aoverq));  \\ using lngamma is slower !!
				log_gamma_matrix[i,k+nhalf+1] = -log_gamma_matrix[i,k+1] + logpi - log(sin(Pi* aoverq));	 
				ak_matrix[i,k+1]= a;	
				ak_matrix[i,k+nhalf+1]= q-a;	\\ g^(k+m)= g^k(q-1) \equiv - g^k \equiv q-g^k 
				a=(a*g)%q; \\a=g^(k+1)%q
				);

		);
 

}

 
 
/**** RESULTS ****

 gp2.11.2 and gp2c0.0.11 compiled by myself, see below 

*******************
 gp 2.11.2  on macmini
 
languasc-macmini:gp_scripts languasc$ gp2c-run -pmy_ -g -W  MaxL-loggamma-final.gp

Reading GPRC: /Users/languasc/.gprc ...Done.

GP/PARI CALCULATOR Version 2.11.2 (released)
i386 running darwin (x86-64/GMP-6.1.2 kernel) 64-bit version
compiled: Aug  3 2019, Apple LLVM version 10.0.1 (clang-1001.0.46.4)
threading engine: single
(readline v8.0 enabled, extended help enabled)
Copyright (C) 2000-2018 The PARI Group
PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER.
Type ? for help, \q to quit.
Type ?17 for how to get moral (and possibly technical) support.

parisizemax = 400003072, primelimit = 500000


 ?  init_MaxL_loggamma_final();maxL_logGamma(3,1000,30)
************ A. LANGUASCO *************
********* COMPUTATION OF THE MAX |L(1,chi)|**********
******* FOR q IN ONE INTERVAL ********
********* with the logGamma-FUNCTION   **********
Interval=[3,997]
Performing precomputations of log(Gamma(a/q)
 for this interval 
Starting computation of max_q
max_{chi even}|L(1,chi)|(3)  = 0
max_{chi odd}|L(1,chi)|(3)  = 0.604599788078072616864692752547
max_{chi}|L(1,chi)|(3)  = 0.604599788078072616864692752547
max_{chi even}|L(1,chi)|(5)  = 0.430408940964004038889433232951
max_{chi odd}|L(1,chi)|(5)  = 0.888576587631673249403176198012
max_{chi}|L(1,chi)|(5)  = 0.888576587631673249403176198012
max_{chi even}|L(1,chi)|(7)  = 0.547959686797993973084485988763
max_{chi odd}|L(1,chi)|(7)  = 1.18741041172372594878462529795
max_{chi}|L(1,chi)|(7)  = 1.18741041172372594878462529795
max_{chi even}|L(1,chi)|(11)  = 0.752112192485773472880260688464
max_{chi odd}|L(1,chi)|(11)  = 1.42640418224108352050983157388
max_{chi}|L(1,chi)|(11)  = 1.42640418224108352050983157388
max_{chi even}|L(1,chi)|(13)  = 0.843864875218394067306390474312
max_{chi odd}|L(1,chi)|(13)  = 1.40613477980703732992641904009
max_{chi}|L(1,chi)|(13)  = 1.40613477980703732992641904009
max_{chi even}|L(1,chi)|(17)  = 1.01608483384284075219467141262
max_{chi odd}|L(1,chi)|(17)  = 1.64849370699838393605712538480
max_{chi}|L(1,chi)|(17)  = 1.64849370699838393605712538480
max_{chi even}|L(1,chi)|(19)  = 0.987263992553171680874829941504
max_{chi odd}|L(1,chi)|(19)  = 1.66331503401599345646761861198
max_{chi}|L(1,chi)|(19)  = 1.66331503401599345646761861198
max_{chi even}|L(1,chi)|(23)  = 1.13377009642762552184987116509
max_{chi odd}|L(1,chi)|(23)  = 1.96520205410785916590276700512
max_{chi}|L(1,chi)|(23)  = 1.96520205410785916590276700512
max_{chi even}|L(1,chi)|(29)  = 1.15662389061773581611732794799
max_{chi odd}|L(1,chi)|(29)  = 1.94760835256298812067787472221
max_{chi}|L(1,chi)|(29)  = 1.94760835256298812067787472221
max_{chi even}|L(1,chi)|(31)  = 1.25445178426408074704957929787
max_{chi odd}|L(1,chi)|(31)  = 1.95460789577555396208826644691
max_{chi}|L(1,chi)|(31)  = 1.95460789577555396208826644691
max_{chi even}|L(1,chi)|(37)  = 1.36669974524631951032595910079
max_{chi odd}|L(1,chi)|(37)  = 1.99550481523309639952094476513
max_{chi}|L(1,chi)|(37)  = 1.99550481523309639952094476513
max_{chi even}|L(1,chi)|(41)  = 1.32329565691781381530043001685
max_{chi odd}|L(1,chi)|(41)  = 2.11431182971789691740711719452
max_{chi}|L(1,chi)|(41)  = 2.11431182971789691740711719452
max_{chi even}|L(1,chi)|(43)  = 1.32671527878855168858017050168
max_{chi odd}|L(1,chi)|(43)  = 2.15300367350566872872181166589
max_{chi}|L(1,chi)|(43)  = 2.15300367350566872872181166589
max_{chi even}|L(1,chi)|(47)  = 1.50891967744749119466846565048
max_{chi odd}|L(1,chi)|(47)  = 2.29124192852861593669991478644
max_{chi}|L(1,chi)|(47)  = 2.29124192852861593669991478644
max_{chi even}|L(1,chi)|(53)  = 1.50188081711004916245133290002
max_{chi odd}|L(1,chi)|(53)  = 2.30607194293623581454960238070
max_{chi}|L(1,chi)|(53)  = 2.30607194293623581454960238070
max_{chi even}|L(1,chi)|(59)  = 1.51084650592499030430887079909
max_{chi odd}|L(1,chi)|(59)  = 2.37483432765382947109503698217
max_{chi}|L(1,chi)|(59)  = 2.37483432765382947109503698217
max_{chi even}|L(1,chi)|(61)  = 1.60648635177149834778810520610
max_{chi odd}|L(1,chi)|(61)  = 2.27383316907813941451707465286
max_{chi}|L(1,chi)|(61)  = 2.27383316907813941451707465286
max_{chi even}|L(1,chi)|(67)  = 1.60312732811278016588663157359
max_{chi odd}|L(1,chi)|(67)  = 2.40177874951129444901523775053
max_{chi}|L(1,chi)|(67)  = 2.40177874951129444901523775053
max_{chi even}|L(1,chi)|(71)  = 1.71525787937029529648590017753
max_{chi odd}|L(1,chi)|(71)  = 2.60986917715784586434512887899
max_{chi}|L(1,chi)|(71)  = 2.60986917715784586434512887899
max_{chi even}|L(1,chi)|(73)  = 1.79463648373514640544187424855
max_{chi odd}|L(1,chi)|(73)  = 2.22099352575696724500691589494
max_{chi}|L(1,chi)|(73)  = 2.22099352575696724500691589494
max_{chi even}|L(1,chi)|(79)  = 1.65795561190294060018050468104
max_{chi odd}|L(1,chi)|(79)  = 2.49865862902662621045751915333
max_{chi}|L(1,chi)|(79)  = 2.49865862902662621045751915333
max_{chi even}|L(1,chi)|(83)  = 1.72783651635434799362045793049
max_{chi odd}|L(1,chi)|(83)  = 2.40279523907172221214735958325
max_{chi}|L(1,chi)|(83)  = 2.40279523907172221214735958325
max_{chi even}|L(1,chi)|(89)  = 1.77900323151629955192781372977
max_{chi odd}|L(1,chi)|(89)  = 2.48752834330666367191078756009
max_{chi}|L(1,chi)|(89)  = 2.48752834330666367191078756009
max_{chi even}|L(1,chi)|(97)  = 1.89349532374748011332010330921
max_{chi odd}|L(1,chi)|(97)  = 2.42085614235917869433795064647
max_{chi}|L(1,chi)|(97)  = 2.42085614235917869433795064647
max_{chi even}|L(1,chi)|(101)  = 1.75704723200287824039102981981
max_{chi odd}|L(1,chi)|(101)  = 2.49348309598992905601857403054
max_{chi}|L(1,chi)|(101)  = 2.49348309598992905601857403054
max_{chi even}|L(1,chi)|(103)  = 1.78695317263936534037653310106
max_{chi odd}|L(1,chi)|(103)  = 2.58872219777793564220546520282
max_{chi}|L(1,chi)|(103)  = 2.58872219777793564220546520282
max_{chi even}|L(1,chi)|(107)  = 1.89183652794600128156221974075
max_{chi odd}|L(1,chi)|(107)  = 2.54845309686851323582504835532
max_{chi}|L(1,chi)|(107)  = 2.54845309686851323582504835532
max_{chi even}|L(1,chi)|(109)  = 1.89386750154832965285535696848
max_{chi odd}|L(1,chi)|(109)  = 2.43977808110771365276355432077
max_{chi}|L(1,chi)|(109)  = 2.43977808110771365276355432077
max_{chi even}|L(1,chi)|(113)  = 1.79187977151032621676917779946
max_{chi odd}|L(1,chi)|(113)  = 2.37003547987807971651823457293
max_{chi}|L(1,chi)|(113)  = 2.37003547987807971651823457293
max_{chi even}|L(1,chi)|(127)  = 1.97340559832169904917449332077
max_{chi odd}|L(1,chi)|(127)  = 2.72368730766675765849410753531
max_{chi}|L(1,chi)|(127)  = 2.72368730766675765849410753531
max_{chi even}|L(1,chi)|(131)  = 1.97373935704917183641121699938
max_{chi odd}|L(1,chi)|(131)  = 2.57848536120487307251550163471
max_{chi}|L(1,chi)|(131)  = 2.57848536120487307251550163471
max_{chi even}|L(1,chi)|(137)  = 1.99198097840533428024815599276
max_{chi odd}|L(1,chi)|(137)  = 2.72051117298997095021332225039
max_{chi}|L(1,chi)|(137)  = 2.72051117298997095021332225039
max_{chi even}|L(1,chi)|(139)  = 1.98709657583106073618587147388
max_{chi odd}|L(1,chi)|(139)  = 2.78392266035840572927430273739
max_{chi}|L(1,chi)|(139)  = 2.78392266035840572927430273739
max_{chi even}|L(1,chi)|(149)  = 2.02938296907160492831101373856
max_{chi odd}|L(1,chi)|(149)  = 2.68631183937556722239373025709
max_{chi}|L(1,chi)|(149)  = 2.68631183937556722239373025709
max_{chi even}|L(1,chi)|(151)  = 2.00479938942436303653435753005
max_{chi odd}|L(1,chi)|(151)  = 2.62352855587439821150270052709
max_{chi}|L(1,chi)|(151)  = 2.62352855587439821150270052709
max_{chi even}|L(1,chi)|(157)  = 2.04329000587466161979123385231
max_{chi odd}|L(1,chi)|(157)  = 2.91562362895517732081839286279
max_{chi}|L(1,chi)|(157)  = 2.91562362895517732081839286279
max_{chi even}|L(1,chi)|(163)  = 2.08908788594361630850393279524
max_{chi odd}|L(1,chi)|(163)  = 2.69099736683125370993373921388
max_{chi}|L(1,chi)|(163)  = 2.69099736683125370993373921388
max_{chi even}|L(1,chi)|(167)  = 1.96831025301155479114817195426
max_{chi odd}|L(1,chi)|(167)  = 2.74644085264695532114443109623
max_{chi}|L(1,chi)|(167)  = 2.74644085264695532114443109623
max_{chi even}|L(1,chi)|(173)  = 2.04803162793802224505487997172
max_{chi odd}|L(1,chi)|(173)  = 2.83083393377236324187600452713
max_{chi}|L(1,chi)|(173)  = 2.83083393377236324187600452713
max_{chi even}|L(1,chi)|(179)  = 2.08626159325560635433236885427
max_{chi odd}|L(1,chi)|(179)  = 2.95215347090837063371989208638
max_{chi}|L(1,chi)|(179)  = 2.95215347090837063371989208638
max_{chi even}|L(1,chi)|(181)  = 2.09124043729391132703882025411
max_{chi odd}|L(1,chi)|(181)  = 2.55866549759635341623707612755
max_{chi}|L(1,chi)|(181)  = 2.55866549759635341623707612755
max_{chi even}|L(1,chi)|(191)  = 2.12965711900231590486569597077
max_{chi odd}|L(1,chi)|(191)  = 2.95512966360404799352636309788
max_{chi}|L(1,chi)|(191)  = 2.95512966360404799352636309788
max_{chi even}|L(1,chi)|(193)  = 2.17043401934037005992664395072
max_{chi odd}|L(1,chi)|(193)  = 2.60255291569166233786515416685
max_{chi}|L(1,chi)|(193)  = 2.60255291569166233786515416685
max_{chi even}|L(1,chi)|(197)  = 2.13260507788168759502205534752
max_{chi odd}|L(1,chi)|(197)  = 2.81468933588096728324501080140
max_{chi}|L(1,chi)|(197)  = 2.81468933588096728324501080140
max_{chi even}|L(1,chi)|(199)  = 2.03713743437672601621173688041
max_{chi odd}|L(1,chi)|(199)  = 2.79249308566493928174043020396
max_{chi}|L(1,chi)|(199)  = 2.79249308566493928174043020396
max_{chi even}|L(1,chi)|(211)  = 2.12312102700473174671488732238
max_{chi odd}|L(1,chi)|(211)  = 2.89594376660833329272394923676
max_{chi}|L(1,chi)|(211)  = 2.89594376660833329272394923676
max_{chi even}|L(1,chi)|(223)  = 2.13839450221210714707074389760
max_{chi odd}|L(1,chi)|(223)  = 2.92740993747063127172267612416
max_{chi}|L(1,chi)|(223)  = 2.92740993747063127172267612416
max_{chi even}|L(1,chi)|(227)  = 2.14096907656493924441168287635
max_{chi odd}|L(1,chi)|(227)  = 2.68264264675366168697033571053
max_{chi}|L(1,chi)|(227)  = 2.68264264675366168697033571053
max_{chi even}|L(1,chi)|(229)  = 2.15274858041007989408327527653
max_{chi odd}|L(1,chi)|(229)  = 2.87581890996867882018490166417
max_{chi}|L(1,chi)|(229)  = 2.87581890996867882018490166417
max_{chi even}|L(1,chi)|(233)  = 2.13861665134383118790365795278
max_{chi odd}|L(1,chi)|(233)  = 2.91527084775689862127414734394
max_{chi}|L(1,chi)|(233)  = 2.91527084775689862127414734394
max_{chi even}|L(1,chi)|(239)  = 2.28132279961623533554423924316
max_{chi odd}|L(1,chi)|(239)  = 3.04819103378239805449031098106
max_{chi}|L(1,chi)|(239)  = 3.04819103378239805449031098106
max_{chi even}|L(1,chi)|(241)  = 2.41835638390008713223221533366
max_{chi odd}|L(1,chi)|(241)  = 2.77830595707238913568405847443
max_{chi}|L(1,chi)|(241)  = 2.77830595707238913568405847443
max_{chi even}|L(1,chi)|(251)  = 2.26113300249620187746611325272
max_{chi odd}|L(1,chi)|(251)  = 2.96609382990202814045159294394
max_{chi}|L(1,chi)|(251)  = 2.96609382990202814045159294394
max_{chi even}|L(1,chi)|(257)  = 2.26917391099642932433615802602
max_{chi odd}|L(1,chi)|(257)  = 2.90271693301413614997407956341
max_{chi}|L(1,chi)|(257)  = 2.90271693301413614997407956341
max_{chi even}|L(1,chi)|(263)  = 2.13636417384364698945009270248
max_{chi odd}|L(1,chi)|(263)  = 2.93609043858561342569242914697
max_{chi}|L(1,chi)|(263)  = 2.93609043858561342569242914697
max_{chi even}|L(1,chi)|(269)  = 2.26557554046803297908883743769
max_{chi odd}|L(1,chi)|(269)  = 2.95235925085763617694817528815
max_{chi}|L(1,chi)|(269)  = 2.95235925085763617694817528815
max_{chi even}|L(1,chi)|(271)  = 2.33458036541744010955629484969
max_{chi odd}|L(1,chi)|(271)  = 2.86925767656885353188813607888
max_{chi}|L(1,chi)|(271)  = 2.86925767656885353188813607888
max_{chi even}|L(1,chi)|(277)  = 2.24322637710593016107029401060
max_{chi odd}|L(1,chi)|(277)  = 3.01622855659087525191859838663
max_{chi}|L(1,chi)|(277)  = 3.01622855659087525191859838663
max_{chi even}|L(1,chi)|(281)  = 2.23054560743963256874827429883
max_{chi odd}|L(1,chi)|(281)  = 2.80321128554057954903648560934
max_{chi}|L(1,chi)|(281)  = 2.80321128554057954903648560934
max_{chi even}|L(1,chi)|(283)  = 2.37259028300440742457175743441
max_{chi odd}|L(1,chi)|(283)  = 2.94572301912315375394664649007
max_{chi}|L(1,chi)|(283)  = 2.94572301912315375394664649007
max_{chi even}|L(1,chi)|(293)  = 2.32688123956902918586823666343
max_{chi odd}|L(1,chi)|(293)  = 3.11291787542876229268348893252
max_{chi}|L(1,chi)|(293)  = 3.11291787542876229268348893252
max_{chi even}|L(1,chi)|(307)  = 2.26835201825713419933085424521
max_{chi odd}|L(1,chi)|(307)  = 3.02482538363473232115657507118
max_{chi}|L(1,chi)|(307)  = 3.02482538363473232115657507118
max_{chi even}|L(1,chi)|(311)  = 2.29501674932209347216210705252
max_{chi odd}|L(1,chi)|(311)  = 3.38472414241331604469710895130
max_{chi}|L(1,chi)|(311)  = 3.38472414241331604469710895130
max_{chi even}|L(1,chi)|(313)  = 2.32038245028909348427277238440
max_{chi odd}|L(1,chi)|(313)  = 3.10929623072433076283321530583
max_{chi}|L(1,chi)|(313)  = 3.10929623072433076283321530583
max_{chi even}|L(1,chi)|(317)  = 2.38990544814360127720244887363
max_{chi odd}|L(1,chi)|(317)  = 2.95307987036615177805014754274
max_{chi}|L(1,chi)|(317)  = 2.95307987036615177805014754274
max_{chi even}|L(1,chi)|(331)  = 2.31385061805176110341904614000
max_{chi odd}|L(1,chi)|(331)  = 2.95426729345152158301122222583
max_{chi}|L(1,chi)|(331)  = 2.95426729345152158301122222583
max_{chi even}|L(1,chi)|(337)  = 2.36205323884793501238859395259
max_{chi odd}|L(1,chi)|(337)  = 3.01307766294270421990892299882
max_{chi}|L(1,chi)|(337)  = 3.01307766294270421990892299882
max_{chi even}|L(1,chi)|(347)  = 2.37780177073113017469407745863
max_{chi odd}|L(1,chi)|(347)  = 3.10750424169246830621098007832
max_{chi}|L(1,chi)|(347)  = 3.10750424169246830621098007832
max_{chi even}|L(1,chi)|(349)  = 2.34692483691765879171802146030
max_{chi odd}|L(1,chi)|(349)  = 3.24312632555570194704840092849
max_{chi}|L(1,chi)|(349)  = 3.24312632555570194704840092849
max_{chi even}|L(1,chi)|(353)  = 2.33602647560377812208188125373
max_{chi odd}|L(1,chi)|(353)  = 2.96318053008948669143319019321
max_{chi}|L(1,chi)|(353)  = 2.96318053008948669143319019321
max_{chi even}|L(1,chi)|(359)  = 2.51189976010171382187245703886
max_{chi odd}|L(1,chi)|(359)  = 3.15033145392974552469052671095
max_{chi}|L(1,chi)|(359)  = 3.15033145392974552469052671095
max_{chi even}|L(1,chi)|(367)  = 2.32559167906433445299387381229
max_{chi odd}|L(1,chi)|(367)  = 2.94003500276564543524572051749
max_{chi}|L(1,chi)|(367)  = 2.94003500276564543524572051749
max_{chi even}|L(1,chi)|(373)  = 2.42517770788435555122336390950
max_{chi odd}|L(1,chi)|(373)  = 3.32946093758130126984874928456
max_{chi}|L(1,chi)|(373)  = 3.32946093758130126984874928456
max_{chi even}|L(1,chi)|(379)  = 2.50032774454924842445339647023
max_{chi odd}|L(1,chi)|(379)  = 2.98417634686154821282891886779
max_{chi}|L(1,chi)|(379)  = 2.98417634686154821282891886779
max_{chi even}|L(1,chi)|(383)  = 2.44290543637279045569350099626
max_{chi odd}|L(1,chi)|(383)  = 3.15698301880900757107584482170
max_{chi}|L(1,chi)|(383)  = 3.15698301880900757107584482170
max_{chi even}|L(1,chi)|(389)  = 2.44938989026768349271142802216
max_{chi odd}|L(1,chi)|(389)  = 3.13576641023433071248884490813
max_{chi}|L(1,chi)|(389)  = 3.13576641023433071248884490813
max_{chi even}|L(1,chi)|(397)  = 2.49906007676213685856872758837
max_{chi odd}|L(1,chi)|(397)  = 3.22908440562028461328032006458
max_{chi}|L(1,chi)|(397)  = 3.22908440562028461328032006458
max_{chi even}|L(1,chi)|(401)  = 2.51597590610115638884396738622
max_{chi odd}|L(1,chi)|(401)  = 3.02531335084626851927421904169
max_{chi}|L(1,chi)|(401)  = 3.02531335084626851927421904169
max_{chi even}|L(1,chi)|(409)  = 2.58450736883986784592907409547
max_{chi odd}|L(1,chi)|(409)  = 2.97468553326599915860870900047
max_{chi}|L(1,chi)|(409)  = 2.97468553326599915860870900047
max_{chi even}|L(1,chi)|(419)  = 2.49907780559251470258506809851
max_{chi odd}|L(1,chi)|(419)  = 3.15638028965444731073868407588
max_{chi}|L(1,chi)|(419)  = 3.15638028965444731073868407588
max_{chi even}|L(1,chi)|(421)  = 2.51544464593959402653418042342
max_{chi odd}|L(1,chi)|(421)  = 2.89771782676987997033822961589
max_{chi}|L(1,chi)|(421)  = 2.89771782676987997033822961589
max_{chi even}|L(1,chi)|(431)  = 2.51861144511280328428786055488
max_{chi odd}|L(1,chi)|(431)  = 3.27666788721708595129425883251
max_{chi}|L(1,chi)|(431)  = 3.27666788721708595129425883251
max_{chi even}|L(1,chi)|(433)  = 2.49208695955740632425483658902
max_{chi odd}|L(1,chi)|(433)  = 3.14357057349630992081515342345
max_{chi}|L(1,chi)|(433)  = 3.14357057349630992081515342345
max_{chi even}|L(1,chi)|(439)  = 2.50332038170787208662697790895
max_{chi odd}|L(1,chi)|(439)  = 3.22131456032260084903381293645
max_{chi}|L(1,chi)|(439)  = 3.22131456032260084903381293645
max_{chi even}|L(1,chi)|(443)  = 2.48380906948580810006622141655
max_{chi odd}|L(1,chi)|(443)  = 3.28708635670026587878865275729
max_{chi}|L(1,chi)|(443)  = 3.28708635670026587878865275729
max_{chi even}|L(1,chi)|(449)  = 2.51283734884048118141820928565
max_{chi odd}|L(1,chi)|(449)  = 3.14374861185339258666718155942
max_{chi}|L(1,chi)|(449)  = 3.14374861185339258666718155942
max_{chi even}|L(1,chi)|(457)  = 2.48110861607980520133045734315
max_{chi odd}|L(1,chi)|(457)  = 3.01805880291502467267265047463
max_{chi}|L(1,chi)|(457)  = 3.01805880291502467267265047463
max_{chi even}|L(1,chi)|(461)  = 2.38561842579239861477049438058
max_{chi odd}|L(1,chi)|(461)  = 2.99061762375575687939818599075
max_{chi}|L(1,chi)|(461)  = 2.99061762375575687939818599075
max_{chi even}|L(1,chi)|(463)  = 2.45439131257117153089977840950
max_{chi odd}|L(1,chi)|(463)  = 3.02557292452165996572378279291
max_{chi}|L(1,chi)|(463)  = 3.02557292452165996572378279291
max_{chi even}|L(1,chi)|(467)  = 2.50061417555450327878689145562
max_{chi odd}|L(1,chi)|(467)  = 3.17549334417045753275838551244
max_{chi}|L(1,chi)|(467)  = 3.17549334417045753275838551244
max_{chi even}|L(1,chi)|(479)  = 2.56247053250039190346996964944
max_{chi odd}|L(1,chi)|(479)  = 3.58857580472017716180065757364
max_{chi}|L(1,chi)|(479)  = 3.58857580472017716180065757364
max_{chi even}|L(1,chi)|(487)  = 2.49965102976096190206653545749
max_{chi odd}|L(1,chi)|(487)  = 3.02150659065323210851247532813
max_{chi}|L(1,chi)|(487)  = 3.02150659065323210851247532813
max_{chi even}|L(1,chi)|(491)  = 2.54019642548797276275131673193
max_{chi odd}|L(1,chi)|(491)  = 3.08880305445418175347931846454
max_{chi}|L(1,chi)|(491)  = 3.08880305445418175347931846454
max_{chi even}|L(1,chi)|(499)  = 2.55530399132386022811507854110
max_{chi odd}|L(1,chi)|(499)  = 3.33310237076133842063983002611
max_{chi}|L(1,chi)|(499)  = 3.33310237076133842063983002611
max_{chi even}|L(1,chi)|(503)  = 2.60121683211412492779005394307
max_{chi odd}|L(1,chi)|(503)  = 3.23862981619088362793681328519
max_{chi}|L(1,chi)|(503)  = 3.23862981619088362793681328519
max_{chi even}|L(1,chi)|(509)  = 2.63659083622767178666121112587
max_{chi odd}|L(1,chi)|(509)  = 3.18790240372285890369329278804
max_{chi}|L(1,chi)|(509)  = 3.18790240372285890369329278804
max_{chi even}|L(1,chi)|(521)  = 2.52662844150389963872729785664
max_{chi odd}|L(1,chi)|(521)  = 3.32391248073785183118435027656
max_{chi}|L(1,chi)|(521)  = 3.32391248073785183118435027656
max_{chi even}|L(1,chi)|(523)  = 2.48086894861614523482907980722
max_{chi odd}|L(1,chi)|(523)  = 3.39266087785391065974002131993
max_{chi}|L(1,chi)|(523)  = 3.39266087785391065974002131993
max_{chi even}|L(1,chi)|(541)  = 2.60301281032093459349658700670
max_{chi odd}|L(1,chi)|(541)  = 3.08990995669354475231608583966
max_{chi}|L(1,chi)|(541)  = 3.08990995669354475231608583966
max_{chi even}|L(1,chi)|(547)  = 2.50667895278262316090421620880
max_{chi odd}|L(1,chi)|(547)  = 3.21177134746313664845285051418
max_{chi}|L(1,chi)|(547)  = 3.21177134746313664845285051418
max_{chi even}|L(1,chi)|(557)  = 2.61303855112484520002564687660
max_{chi odd}|L(1,chi)|(557)  = 3.36888198211914580127389042801
max_{chi}|L(1,chi)|(557)  = 3.36888198211914580127389042801
max_{chi even}|L(1,chi)|(563)  = 2.64110830077429048758423730598
max_{chi odd}|L(1,chi)|(563)  = 3.19827255926659391012489648438
max_{chi}|L(1,chi)|(563)  = 3.19827255926659391012489648438
max_{chi even}|L(1,chi)|(569)  = 2.69805822188443505913000689019
max_{chi odd}|L(1,chi)|(569)  = 3.19231644611870880739554354757
max_{chi}|L(1,chi)|(569)  = 3.19231644611870880739554354757
max_{chi even}|L(1,chi)|(571)  = 2.60679202654447870509438980422
max_{chi odd}|L(1,chi)|(571)  = 3.29737963928860833400612713236
max_{chi}|L(1,chi)|(571)  = 3.29737963928860833400612713236
max_{chi even}|L(1,chi)|(577)  = 2.61946411441987326583427779147
max_{chi odd}|L(1,chi)|(577)  = 3.10129116198243754093122394033
max_{chi}|L(1,chi)|(577)  = 3.10129116198243754093122394033
max_{chi even}|L(1,chi)|(587)  = 2.56454946443907554395759952362
max_{chi odd}|L(1,chi)|(587)  = 3.17339593032303497730382120451
max_{chi}|L(1,chi)|(587)  = 3.17339593032303497730382120451
max_{chi even}|L(1,chi)|(593)  = 2.54061391075566391687697376596
max_{chi odd}|L(1,chi)|(593)  = 3.32734104110339616101985098272
max_{chi}|L(1,chi)|(593)  = 3.32734104110339616101985098272
max_{chi even}|L(1,chi)|(599)  = 2.60622892459659697025012756327
max_{chi odd}|L(1,chi)|(599)  = 3.20904989883664076353720703220
max_{chi}|L(1,chi)|(599)  = 3.20904989883664076353720703220
max_{chi even}|L(1,chi)|(601)  = 2.71357102171217499608328546243
max_{chi odd}|L(1,chi)|(601)  = 3.03462372828981497636351602452
max_{chi}|L(1,chi)|(601)  = 3.03462372828981497636351602452
max_{chi even}|L(1,chi)|(607)  = 2.58428728184283876414408569702
max_{chi odd}|L(1,chi)|(607)  = 3.22334095612061763642992301825
max_{chi}|L(1,chi)|(607)  = 3.22334095612061763642992301825
max_{chi even}|L(1,chi)|(613)  = 2.55879097753330779863214575042
max_{chi odd}|L(1,chi)|(613)  = 3.30461730437919519650689110196
max_{chi}|L(1,chi)|(613)  = 3.30461730437919519650689110196
max_{chi even}|L(1,chi)|(617)  = 2.55599400896083070946484809548
max_{chi odd}|L(1,chi)|(617)  = 3.21110531139170629353622676966
max_{chi}|L(1,chi)|(617)  = 3.21110531139170629353622676966
max_{chi even}|L(1,chi)|(619)  = 2.48989158941568611793628412626
max_{chi odd}|L(1,chi)|(619)  = 3.37069356094491605525491036082
max_{chi}|L(1,chi)|(619)  = 3.37069356094491605525491036082
max_{chi even}|L(1,chi)|(631)  = 2.70274764561013412176302261790
max_{chi odd}|L(1,chi)|(631)  = 3.13208638787415093755171585220
max_{chi}|L(1,chi)|(631)  = 3.13208638787415093755171585220
max_{chi even}|L(1,chi)|(641)  = 2.63364710368729533814282510215
max_{chi odd}|L(1,chi)|(641)  = 3.23211518539269050934542501919
max_{chi}|L(1,chi)|(641)  = 3.23211518539269050934542501919
max_{chi even}|L(1,chi)|(643)  = 2.78266716831593830452176180073
max_{chi odd}|L(1,chi)|(643)  = 3.18685340027257900687187281884
max_{chi}|L(1,chi)|(643)  = 3.18685340027257900687187281884
max_{chi even}|L(1,chi)|(647)  = 2.74376739278925287558646435668
max_{chi odd}|L(1,chi)|(647)  = 3.38314148149622511105230281091
max_{chi}|L(1,chi)|(647)  = 3.38314148149622511105230281091
max_{chi even}|L(1,chi)|(653)  = 2.58514619899027084727159558537
max_{chi odd}|L(1,chi)|(653)  = 3.43910390260448591467634183370
max_{chi}|L(1,chi)|(653)  = 3.43910390260448591467634183370
max_{chi even}|L(1,chi)|(659)  = 2.71175188703471301110076550186
max_{chi odd}|L(1,chi)|(659)  = 3.40474114893667565054038830288
max_{chi}|L(1,chi)|(659)  = 3.40474114893667565054038830288
max_{chi even}|L(1,chi)|(661)  = 2.68101272512553485861543720210
max_{chi odd}|L(1,chi)|(661)  = 3.19707359599057009574455632193
max_{chi}|L(1,chi)|(661)  = 3.19707359599057009574455632193
max_{chi even}|L(1,chi)|(673)  = 2.80529255651737708379881665923
max_{chi odd}|L(1,chi)|(673)  = 3.29524177279177739366473959234
max_{chi}|L(1,chi)|(673)  = 3.29524177279177739366473959234
max_{chi even}|L(1,chi)|(677)  = 2.68255872720155998788306352413
max_{chi odd}|L(1,chi)|(677)  = 3.14203413621204495006097125621
max_{chi}|L(1,chi)|(677)  = 3.14203413621204495006097125621
max_{chi even}|L(1,chi)|(683)  = 2.66700701750622649993607409797
max_{chi odd}|L(1,chi)|(683)  = 3.10413178955563308313872650724
max_{chi}|L(1,chi)|(683)  = 3.10413178955563308313872650724
max_{chi even}|L(1,chi)|(691)  = 2.71791512017844219406841975455
max_{chi odd}|L(1,chi)|(691)  = 3.51698989024002615984946445256
max_{chi}|L(1,chi)|(691)  = 3.51698989024002615984946445256
max_{chi even}|L(1,chi)|(701)  = 2.62735452968571327525501456042
max_{chi odd}|L(1,chi)|(701)  = 3.35085324504731590551613080436
max_{chi}|L(1,chi)|(701)  = 3.35085324504731590551613080436
max_{chi even}|L(1,chi)|(709)  = 2.68638329107474129689140337721
max_{chi odd}|L(1,chi)|(709)  = 3.18491137055861253375845988616
max_{chi}|L(1,chi)|(709)  = 3.18491137055861253375845988616
max_{chi even}|L(1,chi)|(719)  = 2.74270351969899274873970301412
max_{chi odd}|L(1,chi)|(719)  = 3.63201071708524524489955813645
max_{chi}|L(1,chi)|(719)  = 3.63201071708524524489955813645
max_{chi even}|L(1,chi)|(727)  = 2.81558780259686487088417483146
max_{chi odd}|L(1,chi)|(727)  = 3.19488076113527166415118327181
max_{chi}|L(1,chi)|(727)  = 3.19488076113527166415118327181
max_{chi even}|L(1,chi)|(733)  = 2.66965723382888750230298133638
max_{chi odd}|L(1,chi)|(733)  = 3.45685741198240493832871170689
max_{chi}|L(1,chi)|(733)  = 3.45685741198240493832871170689
max_{chi even}|L(1,chi)|(739)  = 2.61407070091648200098444243326
max_{chi odd}|L(1,chi)|(739)  = 3.29109339411323807636519499288
max_{chi}|L(1,chi)|(739)  = 3.29109339411323807636519499288
max_{chi even}|L(1,chi)|(743)  = 2.63353802705060439070762180062
max_{chi odd}|L(1,chi)|(743)  = 3.36194027636618645067801019522
max_{chi}|L(1,chi)|(743)  = 3.36194027636618645067801019522
max_{chi even}|L(1,chi)|(751)  = 2.77109054521903303438781028069
max_{chi odd}|L(1,chi)|(751)  = 3.37121298850114852069195462707
max_{chi}|L(1,chi)|(751)  = 3.37121298850114852069195462707
max_{chi even}|L(1,chi)|(757)  = 2.71418714293171265037702045286
max_{chi odd}|L(1,chi)|(757)  = 3.29522003757629360256760087960
max_{chi}|L(1,chi)|(757)  = 3.29522003757629360256760087960
max_{chi even}|L(1,chi)|(761)  = 2.76233967094401308817813041399
max_{chi odd}|L(1,chi)|(761)  = 3.39036396026169168862024302997
max_{chi}|L(1,chi)|(761)  = 3.39036396026169168862024302997
max_{chi even}|L(1,chi)|(769)  = 2.74259278564652916003832476429
max_{chi odd}|L(1,chi)|(769)  = 3.37966794694746138163416821630
max_{chi}|L(1,chi)|(769)  = 3.37966794694746138163416821630
max_{chi even}|L(1,chi)|(773)  = 2.73066472498037859042960271546
max_{chi odd}|L(1,chi)|(773)  = 3.32182777438635162483294645420
max_{chi}|L(1,chi)|(773)  = 3.32182777438635162483294645420
max_{chi even}|L(1,chi)|(787)  = 2.71402958746057909424718261535
max_{chi odd}|L(1,chi)|(787)  = 3.41806860456589489290488883781
max_{chi}|L(1,chi)|(787)  = 3.41806860456589489290488883781
max_{chi even}|L(1,chi)|(797)  = 2.73379764469991462172141385405
max_{chi odd}|L(1,chi)|(797)  = 3.41332527420052976238715906739
max_{chi}|L(1,chi)|(797)  = 3.41332527420052976238715906739
max_{chi even}|L(1,chi)|(809)  = 2.79098505490225675471611896142
max_{chi odd}|L(1,chi)|(809)  = 3.33399463072530149065220868852
max_{chi}|L(1,chi)|(809)  = 3.33399463072530149065220868852
max_{chi even}|L(1,chi)|(811)  = 2.66608483563176971600872520187
max_{chi odd}|L(1,chi)|(811)  = 3.41748712961750993035612332531
max_{chi}|L(1,chi)|(811)  = 3.41748712961750993035612332531
max_{chi even}|L(1,chi)|(821)  = 2.71679906114050689421942977852
max_{chi odd}|L(1,chi)|(821)  = 3.32756221988730824824951614294
max_{chi}|L(1,chi)|(821)  = 3.32756221988730824824951614294
max_{chi even}|L(1,chi)|(823)  = 2.69381168019125700635221901460
max_{chi odd}|L(1,chi)|(823)  = 3.37960627332789369390005691334
max_{chi}|L(1,chi)|(823)  = 3.37960627332789369390005691334
max_{chi even}|L(1,chi)|(827)  = 2.77331466078360761854018596217
max_{chi odd}|L(1,chi)|(827)  = 3.40849620130058074419186199017
max_{chi}|L(1,chi)|(827)  = 3.40849620130058074419186199017
max_{chi even}|L(1,chi)|(829)  = 2.67202611221790528293470441621
max_{chi odd}|L(1,chi)|(829)  = 3.37089500117347869458163604211
max_{chi}|L(1,chi)|(829)  = 3.37089500117347869458163604211
max_{chi even}|L(1,chi)|(839)  = 2.80323061355797552968813924643
max_{chi odd}|L(1,chi)|(839)  = 3.57917416660357193379948511931
max_{chi}|L(1,chi)|(839)  = 3.57917416660357193379948511931
max_{chi even}|L(1,chi)|(853)  = 2.76456871825731969503579945794
max_{chi odd}|L(1,chi)|(853)  = 3.38016417685190138464013883123
max_{chi}|L(1,chi)|(853)  = 3.38016417685190138464013883123
max_{chi even}|L(1,chi)|(857)  = 2.73641055061407481774418078910
max_{chi odd}|L(1,chi)|(857)  = 3.57544465806174330360312716184
max_{chi}|L(1,chi)|(857)  = 3.57544465806174330360312716184
max_{chi even}|L(1,chi)|(859)  = 2.77186923381296189108701439155
max_{chi odd}|L(1,chi)|(859)  = 3.50541693805340088235348934788
max_{chi}|L(1,chi)|(859)  = 3.50541693805340088235348934788
max_{chi even}|L(1,chi)|(863)  = 2.81783764647980254382181533159
max_{chi odd}|L(1,chi)|(863)  = 3.50825623636559589065557628386
max_{chi}|L(1,chi)|(863)  = 3.50825623636559589065557628386
max_{chi even}|L(1,chi)|(877)  = 2.74907131045016489055520930608
max_{chi odd}|L(1,chi)|(877)  = 3.49769275741261662405276790520
max_{chi}|L(1,chi)|(877)  = 3.49769275741261662405276790520
max_{chi even}|L(1,chi)|(881)  = 2.87439419284218465206987575641
max_{chi odd}|L(1,chi)|(881)  = 3.39897242344112875811946433945
max_{chi}|L(1,chi)|(881)  = 3.39897242344112875811946433945
max_{chi even}|L(1,chi)|(883)  = 2.71938478618813610977513166888
max_{chi odd}|L(1,chi)|(883)  = 3.34652632278953040018003375892
max_{chi}|L(1,chi)|(883)  = 3.34652632278953040018003375892
max_{chi even}|L(1,chi)|(887)  = 2.74151587441709188927509996554
max_{chi odd}|L(1,chi)|(887)  = 3.34968741972912759452502545654
max_{chi}|L(1,chi)|(887)  = 3.34968741972912759452502545654
max_{chi even}|L(1,chi)|(907)  = 2.81643010808340974214421038261
max_{chi odd}|L(1,chi)|(907)  = 3.39778872837837091734236419151
max_{chi}|L(1,chi)|(907)  = 3.39778872837837091734236419151
max_{chi even}|L(1,chi)|(911)  = 2.75477185676203650566859655348
max_{chi odd}|L(1,chi)|(911)  = 3.37032660476473849985853056954
max_{chi}|L(1,chi)|(911)  = 3.37032660476473849985853056954
max_{chi even}|L(1,chi)|(919)  = 2.65883886926116939475989073826
max_{chi odd}|L(1,chi)|(919)  = 3.35063473135683107552976812180
max_{chi}|L(1,chi)|(919)  = 3.35063473135683107552976812180
max_{chi even}|L(1,chi)|(929)  = 2.77027568478944768686838662943
max_{chi odd}|L(1,chi)|(929)  = 3.53321177004124872239874436148
max_{chi}|L(1,chi)|(929)  = 3.53321177004124872239874436148
max_{chi even}|L(1,chi)|(937)  = 2.79485854549170939115346880065
max_{chi odd}|L(1,chi)|(937)  = 3.56404261890133745461623907397
max_{chi}|L(1,chi)|(937)  = 3.56404261890133745461623907397
max_{chi even}|L(1,chi)|(941)  = 2.83704282163697061242559319581
max_{chi odd}|L(1,chi)|(941)  = 3.36178737964711744410945269493
max_{chi}|L(1,chi)|(941)  = 3.36178737964711744410945269493
max_{chi even}|L(1,chi)|(947)  = 2.81007465375019053333120444524
max_{chi odd}|L(1,chi)|(947)  = 3.35241151685426146046317817853
max_{chi}|L(1,chi)|(947)  = 3.35241151685426146046317817853
max_{chi even}|L(1,chi)|(953)  = 2.93198180573692665691215347913
max_{chi odd}|L(1,chi)|(953)  = 3.49561078035208420652588273363
max_{chi}|L(1,chi)|(953)  = 3.49561078035208420652588273363
max_{chi even}|L(1,chi)|(967)  = 2.82035064753059530303789180235
max_{chi odd}|L(1,chi)|(967)  = 3.34475180524849073411075928718
max_{chi}|L(1,chi)|(967)  = 3.34475180524849073411075928718
max_{chi even}|L(1,chi)|(971)  = 2.86245005292327967136583134318
max_{chi odd}|L(1,chi)|(971)  = 3.50133666092278415387426395493
max_{chi}|L(1,chi)|(971)  = 3.50133666092278415387426395493
max_{chi even}|L(1,chi)|(977)  = 2.92217104043674254033970895522
max_{chi odd}|L(1,chi)|(977)  = 3.46323541639460242041962117061
max_{chi}|L(1,chi)|(977)  = 3.46323541639460242041962117061
max_{chi even}|L(1,chi)|(983)  = 2.79862512965123919287543540620
max_{chi odd}|L(1,chi)|(983)  = 3.38200836946693885301545542710
max_{chi}|L(1,chi)|(983)  = 3.38200836946693885301545542710
max_{chi even}|L(1,chi)|(991)  = 2.84300155185673750284839238999
max_{chi odd}|L(1,chi)|(991)  = 3.47683493471726594626831378059
max_{chi}|L(1,chi)|(991)  = 3.47683493471726594626831378059
max_{chi even}|L(1,chi)|(997)  = 2.87606235754361659587787338819
max_{chi odd}|L(1,chi)|(997)  = 3.49595691818271364657373564526
max_{chi}|L(1,chi)|(997)  = 3.49595691818271364657373564526
Precomputation time: 0 min, 0 sec, 958 millisec
Final step max computation time (output time included): 0 min, 15 sec, 581 millisec
Total elapsed time: 0 min, 16 sec, 539 millisec
******  END PROGRAM   ******** 

 

? for(n=1,10,m=nextprime(n*10^3);init_MaxL_loggamma_final();maxL_logGamma(m,m,30))
************ A. LANGUASCO *************
********* COMPUTATION OF THE MAX |L(1,chi)|**********
******* FOR q IN ONE INTERVAL ********
********* with the logGamma-FUNCTION   **********
Interval=[1009,1009]
Performing precomputations of log(Gamma(a/q)
 for this interval
Precomputation for q = 1009
Starting computation of max_q
max_{chi even}|L(1,chi)|(1009)  = 3.07844414412170961719810195366
max_{chi odd}|L(1,chi)|(1009)  = 3.31985248810176999898574237090
max_{chi}|L(1,chi)|(1009)  = 3.31985248810176999898574237090
Precomputation time: 0 min, 0 sec, 14 millisec
Final step max computation time (output time included): 0 min, 0 sec, 303 millisec
Total elapsed time: 0 min, 0 sec, 317 millisec
******  END PROGRAM   ********
************ A. LANGUASCO *************
********* COMPUTATION OF THE MAX |L(1,chi)|**********
******* FOR q IN ONE INTERVAL ********
********* with the logGamma-FUNCTION   **********
Interval=[2003,2003]
Performing precomputations of log(Gamma(a/q)
 for this interval
Precomputation for q = 2003
Starting computation of max_q
max_{chi even}|L(1,chi)|(2003)  = 3.09573263454819572676883180756
max_{chi odd}|L(1,chi)|(2003)  = 3.67048113521803722214602616933
max_{chi}|L(1,chi)|(2003)  = 3.67048113521803722214602616933
Precomputation time: 0 min, 0 sec, 25 millisec
Final step max computation time (output time included): 0 min, 1 sec, 196 millisec
Total elapsed time: 0 min, 1 sec, 221 millisec
******  END PROGRAM   ********
************ A. LANGUASCO *************
********* COMPUTATION OF THE MAX |L(1,chi)|**********
******* FOR q IN ONE INTERVAL ********
********* with the logGamma-FUNCTION   **********
Interval=[3001,3001]
Performing precomputations of log(Gamma(a/q)
 for this interval
Precomputation for q = 3001
Starting computation of max_q
max_{chi even}|L(1,chi)|(3001)  = 3.23392205274886827945920887811
max_{chi odd}|L(1,chi)|(3001)  = 3.99093817820114176775045157700
max_{chi}|L(1,chi)|(3001)  = 3.99093817820114176775045157700
Precomputation time: 0 min, 0 sec, 38 millisec
Final step max computation time (output time included): 0 min, 2 sec, 778 millisec
Total elapsed time: 0 min, 2 sec, 816 millisec
******  END PROGRAM   ********
************ A. LANGUASCO *************
********* COMPUTATION OF THE MAX |L(1,chi)|**********
******* FOR q IN ONE INTERVAL ********
********* with the logGamma-FUNCTION   **********
Interval=[4001,4001]
Performing precomputations of log(Gamma(a/q)
 for this interval
Precomputation for q = 4001
Starting computation of max_q
max_{chi even}|L(1,chi)|(4001)  = 3.39232881271850885094408636309
max_{chi odd}|L(1,chi)|(4001)  = 3.89683090185312661986055638166
max_{chi}|L(1,chi)|(4001)  = 3.89683090185312661986055638166
Precomputation time: 0 min, 0 sec, 62 millisec
Final step max computation time (output time included): 0 min, 5 sec, 20 millisec
Total elapsed time: 0 min, 5 sec, 82 millisec
******  END PROGRAM   ********
************ A. LANGUASCO *************
********* COMPUTATION OF THE MAX |L(1,chi)|**********
******* FOR q IN ONE INTERVAL ********
********* with the logGamma-FUNCTION   **********
Interval=[5003,5003]
Performing precomputations of log(Gamma(a/q)
 for this interval
Precomputation for q = 5003
Starting computation of max_q
max_{chi even}|L(1,chi)|(5003)  = 3.57249105429399751903272365618
max_{chi odd}|L(1,chi)|(5003)  = 3.80289711660932882267432296113
max_{chi}|L(1,chi)|(5003)  = 3.80289711660932882267432296113
Precomputation time: 0 min, 0 sec, 62 millisec
Final step max computation time (output time included): 0 min, 7 sec, 404 millisec
Total elapsed time: 0 min, 7 sec, 466 millisec
******  END PROGRAM   ********
************ A. LANGUASCO *************
********* COMPUTATION OF THE MAX |L(1,chi)|**********
******* FOR q IN ONE INTERVAL ********
********* with the logGamma-FUNCTION   **********
Interval=[6007,6007]
Performing precomputations of log(Gamma(a/q)
 for this interval
Precomputation for q = 6007
Starting computation of max_q
max_{chi even}|L(1,chi)|(6007)  = 3.52283811295713078751457042169
max_{chi odd}|L(1,chi)|(6007)  = 3.76152460205695944560206379691
max_{chi}|L(1,chi)|(6007)  = 3.76152460205695944560206379691
Precomputation time: 0 min, 0 sec, 75 millisec
Final step max computation time (output time included): 0 min, 11 sec, 65 millisec
Total elapsed time: 0 min, 11 sec, 140 millisec
******  END PROGRAM   ********
************ A. LANGUASCO *************
********* COMPUTATION OF THE MAX |L(1,chi)|**********
******* FOR q IN ONE INTERVAL ********
********* with the logGamma-FUNCTION   **********
Interval=[7001,7001]
Performing precomputations of log(Gamma(a/q)
 for this interval
Precomputation for q = 7001
Starting computation of max_q
max_{chi even}|L(1,chi)|(7001)  = 3.68513594948439055894091803485
max_{chi odd}|L(1,chi)|(7001)  = 3.91641550003990993080207866831
max_{chi}|L(1,chi)|(7001)  = 3.91641550003990993080207866831
Precomputation time: 0 min, 0 sec, 88 millisec
Final step max computation time (output time included): 0 min, 14 sec, 942 millisec
Total elapsed time: 0 min, 15 sec, 30 millisec
******  END PROGRAM   ********
************ A. LANGUASCO *************
********* COMPUTATION OF THE MAX |L(1,chi)|**********
******* FOR q IN ONE INTERVAL ********
********* with the logGamma-FUNCTION   **********
Interval=[8009,8009]
Performing precomputations of log(Gamma(a/q)
 for this interval
Precomputation for q = 8009
Starting computation of max_q
max_{chi even}|L(1,chi)|(8009)  = 3.70791212649663265579022237853
max_{chi odd}|L(1,chi)|(8009)  = 4.06237865608944822288068728281
max_{chi}|L(1,chi)|(8009)  = 4.06237865608944822288068728281
Precomputation time: 0 min, 0 sec, 101 millisec
Final step max computation time (output time included): 0 min, 19 sec, 449 millisec
Total elapsed time: 0 min, 19 sec, 550 millisec
******  END PROGRAM   ********
************ A. LANGUASCO *************
********* COMPUTATION OF THE MAX |L(1,chi)|**********
******* FOR q IN ONE INTERVAL ********
********* with the logGamma-FUNCTION   **********
Interval=[9001,9001]
Performing precomputations of log(Gamma(a/q)
 for this interval
Precomputation for q = 9001
Starting computation of max_q
max_{chi even}|L(1,chi)|(9001)  = 3.76280785149141863067460917398
max_{chi odd}|L(1,chi)|(9001)  = 4.20018736096114017392758494824
max_{chi}|L(1,chi)|(9001)  = 4.20018736096114017392758494824
Precomputation time: 0 min, 0 sec, 112 millisec
Final step max computation time (output time included): 0 min, 24 sec, 327 millisec
Total elapsed time: 0 min, 24 sec, 439 millisec
******  END PROGRAM   ********
************ A. LANGUASCO *************
********* COMPUTATION OF THE MAX |L(1,chi)|**********
******* FOR q IN ONE INTERVAL ********
********* with the logGamma-FUNCTION   **********
Interval=[10007,10007]
Performing precomputations of log(Gamma(a/q)
 for this interval
Precomputation for q = 10007
Starting computation of max_q
max_{chi even}|L(1,chi)|(10007)  = 3.70673473502913528850646529400
max_{chi odd}|L(1,chi)|(10007)  = 4.10274923910993064789781835831
max_{chi}|L(1,chi)|(10007)  = 4.10274923910993064789781835831
Precomputation time: 0 min, 0 sec, 125 millisec
Final step max computation time (output time included): 0 min, 30 sec, 215 millisec
Total elapsed time: 0 min, 30 sec, 340 millisec
******  END PROGRAM   ********
 

******************  larger q's **********************
  
? init_MaxL_loggamma_final();maxL_logGamma(20011,20011,30) 
************ A. LANGUASCO *************
********* COMPUTATION OF THE MAX |L(1,chi)|**********
******* FOR q IN ONE INTERVAL ********
********* with the logGamma-FUNCTION   **********
Interval=[20011,20011]
Performing precomputations of log(Gamma(a/q)
 for this interval
Precomputation for q = 20011
Starting computation of max_q
max_{chi even}|L(1,chi)|(20011)  = 4.05535886576636521794366566036
max_{chi odd}|L(1,chi)|(20011)  = 4.33280353731415736232872405408
max_{chi}|L(1,chi)|(20011)  = 4.33280353731415736232872405408
Precomputation time: 0 min, 0 sec, 250 millisec
Final step max computation time (output time included): 2 min, 0 sec, 688 millisec
Total elapsed time: 2 min, 0 sec, 938 millisec
******  END PROGRAM   ********
  
? init_MaxL_loggamma_final();maxL_logGamma(30011,30011,30)
************ A. LANGUASCO *************
********* COMPUTATION OF THE MAX |L(1,chi)|**********
******* FOR q IN ONE INTERVAL ********
********* with the logGamma-FUNCTION   **********
Interval=[30011,30011]
Performing precomputations of log(Gamma(a/q)
 for this interval
Precomputation for q = 30011
Starting computation of max_q
max_{chi even}|L(1,chi)|(30011)  = 4.02457758035036861843291902838
max_{chi odd}|L(1,chi)|(30011)  = 4.34820667944694742386439105974
max_{chi}|L(1,chi)|(30011)  = 4.34820667944694742386439105974
Precomputation time: 0 min, 0 sec, 378 millisec
Final step max computation time (output time included): 4 min, 29 sec, 698 millisec
Total elapsed time: 4 min, 30 sec, 76 millisec
******  END PROGRAM   ********
 
 
?  init_MaxL_loggamma_final();maxL_logGamma(83089,83089,10)
************ A. LANGUASCO *************
********* COMPUTATION OF THE MAX |L(1,chi)|**********
******* FOR q IN ONE INTERVAL ********
********* with the logGamma-FUNCTION   **********
Interval=[83089,83089]
Performing precomputations of log(Gamma(a/q)
 for this interval
Precomputation for q = 83089
Starting computation of max_q
max_{chi even}|L(1,chi)|(83089)  = 4.279852323
max_{chi odd}|L(1,chi)|(83089)  = 4.956128332
max_{chi}|L(1,chi)|(83089)  = 4.956128332
Precomputation time: 0 min, 0 sec, 782 millisec
Final step max computation time (output time included): 26 min, 35 sec, 147 millisec
Total elapsed time: 26 min, 35 sec, 929 millisec
******  END PROGRAM   ********
 
 
 
 

 
*******/