/*
    Copyright (C) 2019 Alessandro Languasco
*/

/****************   	A. LANGUASCO  		******************** 
************* COMPUTATION OF THE EULER KRONECKER CONSTANTS MOD q(PRIME) *******/

/******* Direct use of the pari/gp lfun functions  *****/

{max_direct(r1,r2,defaultprecision)=local(minutes, millisec, seconds, rows,
n,m,L,evenmax,oddmax,q, G, chi, elaptimecomp,absderlog);
default(realprecision,defaultprecision);  

print("************ A. LANGUASCO  *************");
print("********* COMPUTATION OF THE MAX |L'/L|**********");
 print("******* FOR q IN ONE INTERVAL ********");
print("********* direct use of the lfun command  **********");

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,"]");
gettime(); 

forprime(q=r1,r2,
			oddmax=0;
			evenmax=0; 
			G= znstar(q, 1);
			for(m=2, q-1, chi=znconreychar(G,m); L=lfuncreate(Mod(m,q));  \\ defines L as the Dirichlet L-function associated with a non-trivial Dirichlet character (Conrey notation)
						absderlog=abs(lfun(L,1,1)/lfun(L,1)); \\ computes the absolute value logarithmic derivative of L at 1
						if (zncharisodd(G,chi), 
						              if(absderlog>oddmax, oddmax=absderlog),  
						              if(absderlog>evenmax, evenmax=absderlog));
				);
			print("max_{chi even}|L'/L(1,chi)|(",q")  = ",   evenmax); 
			print("max_{chi odd}|L'/L(1,chi)|(",q")  = ", oddmax); 
			print("max_{chi}|L'/L(1,chi)|(",q")  = ", max(oddmax,evenmax)); 
			);
			
elaptimecomp=gettime();
seconds=floor(elaptimecomp/1000)%60;
minutes=floor(elaptimecomp/60000);
millisec=elaptimecomp- minutes*60000 - seconds*1000; 
print("Total computation time: ", minutes, " min, ", seconds, " sec, ", millisec, " millisec");
print("******  END PROGRAM   ********"); 
}

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

*******************
 gp 2.11.2  on macmini

languasc@languasco1:~/Desktop/EK$ gp2c-run -pmy_ -g -W Max-direct-final.gp
 

                  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


***************  Directly  ************

 

 ?  init_Max_direct_final();max_direct(3,300,30)            
 ************ A. LANGUASCO  *************
********* COMPUTATION OF THE MAX |L'/L|**********
******* FOR q IN ONE INTERVAL ********
********* direct use of the lfun command  **********
Interval=[3,293]
max_{chi even}|L'/L(1,chi)|(3)  = 0
max_{chi odd}|L'/L(1,chi)|(3)  = 0.368281615970147842633237904076
max_{chi}|L'/L(1,chi)|(3)  = 0.368281615970147842633237904076
max_{chi even}|L'/L(1,chi)|(5)  = 0.827679476715504887991046989677
max_{chi odd}|L'/L(1,chi)|(5)  = 0.180899098585657908884214228728
max_{chi}|L'/L(1,chi)|(5)  = 0.827679476715504887991046989677
max_{chi even}|L'/L(1,chi)|(7)  = 0.693743252999179022242316373933
max_{chi odd}|L'/L(1,chi)|(7)  = 0.251084483958898199841792124425
max_{chi}|L'/L(1,chi)|(7)  = 0.693743252999179022242316373933
max_{chi even}|L'/L(1,chi)|(11)  = 0.566852343328803197958852026226
max_{chi odd}|L'/L(1,chi)|(11)  = 0.649609999423979953636904530776
max_{chi}|L'/L(1,chi)|(11)  = 0.649609999423979953636904530776
max_{chi even}|L'/L(1,chi)|(13)  = 0.565582635433404890770098107244
max_{chi odd}|L'/L(1,chi)|(13)  = 0.696309862992037155840892183520
max_{chi}|L'/L(1,chi)|(13)  = 0.696309862992037155840892183520
max_{chi even}|L'/L(1,chi)|(17)  = 0.510627102336359538761550412731
max_{chi odd}|L'/L(1,chi)|(17)  = 1.36293176857311326439833395890
max_{chi}|L'/L(1,chi)|(17)  = 1.36293176857311326439833395890
max_{chi even}|L'/L(1,chi)|(19)  = 0.644329999573610570346026468705
max_{chi odd}|L'/L(1,chi)|(19)  = 1.56821936415476775304938942269
max_{chi}|L'/L(1,chi)|(19)  = 1.56821936415476775304938942269
max_{chi even}|L'/L(1,chi)|(23)  = 0.617943642128736392603203757765
max_{chi odd}|L'/L(1,chi)|(23)  = 1.07370241439895666993863022504
max_{chi}|L'/L(1,chi)|(23)  = 1.07370241439895666993863022504
max_{chi even}|L'/L(1,chi)|(29)  = 0.908711562024443188256150455943
max_{chi odd}|L'/L(1,chi)|(29)  = 1.37173438584080190328583030799
max_{chi}|L'/L(1,chi)|(29)  = 1.37173438584080190328583030799
max_{chi even}|L'/L(1,chi)|(31)  = 0.791265179022304116114210355804
max_{chi odd}|L'/L(1,chi)|(31)  = 1.41315141911004437078399808370
max_{chi}|L'/L(1,chi)|(31)  = 1.41315141911004437078399808370
max_{chi even}|L'/L(1,chi)|(37)  = 0.733183107188977342750203978087
max_{chi odd}|L'/L(1,chi)|(37)  = 1.29518958101078356915278401821
max_{chi}|L'/L(1,chi)|(37)  = 1.29518958101078356915278401821
max_{chi even}|L'/L(1,chi)|(41)  = 0.916079374735210610265214032861
max_{chi odd}|L'/L(1,chi)|(41)  = 1.29673609198958173353796568380
max_{chi}|L'/L(1,chi)|(41)  = 1.29673609198958173353796568380
max_{chi even}|L'/L(1,chi)|(43)  = 1.39288786688690318884121465229
max_{chi odd}|L'/L(1,chi)|(43)  = 1.41176882240051173489451389181
max_{chi}|L'/L(1,chi)|(43)  = 1.41176882240051173489451389181
max_{chi even}|L'/L(1,chi)|(47)  = 1.35156929889543656315617537620
max_{chi odd}|L'/L(1,chi)|(47)  = 1.39567565425273602292102717603
max_{chi}|L'/L(1,chi)|(47)  = 1.39567565425273602292102717603
max_{chi even}|L'/L(1,chi)|(53)  = 1.00112944067413655687127416377
max_{chi odd}|L'/L(1,chi)|(53)  = 1.30627572903790815149667975264
max_{chi}|L'/L(1,chi)|(53)  = 1.30627572903790815149667975264
max_{chi even}|L'/L(1,chi)|(59)  = 1.81899383678937843989348366929
max_{chi odd}|L'/L(1,chi)|(59)  = 1.32353200689013556740700834632
max_{chi}|L'/L(1,chi)|(59)  = 1.81899383678937843989348366929
max_{chi even}|L'/L(1,chi)|(61)  = 1.41809980889441627035459190983
max_{chi odd}|L'/L(1,chi)|(61)  = 1.29707099312546569340773776449
max_{chi}|L'/L(1,chi)|(61)  = 1.41809980889441627035459190983
max_{chi even}|L'/L(1,chi)|(67)  = 1.67019193303154369921782607634
max_{chi odd}|L'/L(1,chi)|(67)  = 1.40107639865766134900254448893
max_{chi}|L'/L(1,chi)|(67)  = 1.67019193303154369921782607634
max_{chi even}|L'/L(1,chi)|(71)  = 1.47455511100236771011015896767
max_{chi odd}|L'/L(1,chi)|(71)  = 1.23112352788523565627982472042
max_{chi}|L'/L(1,chi)|(71)  = 1.47455511100236771011015896767
max_{chi even}|L'/L(1,chi)|(73)  = 1.78248970799598673447282517891
max_{chi odd}|L'/L(1,chi)|(73)  = 1.48272839696663020051708640270
max_{chi}|L'/L(1,chi)|(73)  = 1.78248970799598673447282517891
max_{chi even}|L'/L(1,chi)|(79)  = 1.27095088466385163871005360770
max_{chi odd}|L'/L(1,chi)|(79)  = 1.34616837027813468918588610688
max_{chi}|L'/L(1,chi)|(79)  = 1.34616837027813468918588610688
max_{chi even}|L'/L(1,chi)|(83)  = 1.16333003167253880184592380510
max_{chi odd}|L'/L(1,chi)|(83)  = 1.34527786237910789501875868023
max_{chi}|L'/L(1,chi)|(83)  = 1.34527786237910789501875868023
max_{chi even}|L'/L(1,chi)|(89)  = 1.61654649274126300156782088673
max_{chi odd}|L'/L(1,chi)|(89)  = 1.27381998100989573937802515309
max_{chi}|L'/L(1,chi)|(89)  = 1.61654649274126300156782088673
max_{chi even}|L'/L(1,chi)|(97)  = 1.60286118570076458480362218799
max_{chi odd}|L'/L(1,chi)|(97)  = 1.47070211417034258063739679739
max_{chi}|L'/L(1,chi)|(97)  = 1.60286118570076458480362218799
max_{chi even}|L'/L(1,chi)|(101)  = 1.51871979857079618912367283335
max_{chi odd}|L'/L(1,chi)|(101)  = 1.27994704538217415996880600332
max_{chi}|L'/L(1,chi)|(101)  = 1.51871979857079618912367283335
max_{chi even}|L'/L(1,chi)|(103)  = 1.56072764165486011343921965820
max_{chi odd}|L'/L(1,chi)|(103)  = 1.33555360325105672672035007620
max_{chi}|L'/L(1,chi)|(103)  = 1.56072764165486011343921965820
max_{chi even}|L'/L(1,chi)|(107)  = 1.51176315288720940464356960246
max_{chi odd}|L'/L(1,chi)|(107)  = 1.55529418086936504978552066530
max_{chi}|L'/L(1,chi)|(107)  = 1.55529418086936504978552066530
max_{chi even}|L'/L(1,chi)|(109)  = 1.64357129023277185742674081202
max_{chi odd}|L'/L(1,chi)|(109)  = 1.65357828827908326582841136643
max_{chi}|L'/L(1,chi)|(109)  = 1.65357828827908326582841136643
max_{chi even}|L'/L(1,chi)|(113)  = 1.51486982889352164427060492878
max_{chi odd}|L'/L(1,chi)|(113)  = 1.24748116143699351889256349382
max_{chi}|L'/L(1,chi)|(113)  = 1.51486982889352164427060492878
max_{chi even}|L'/L(1,chi)|(127)  = 1.55590143040596443193792941854
max_{chi odd}|L'/L(1,chi)|(127)  = 1.48849928643174274996361403061
max_{chi}|L'/L(1,chi)|(127)  = 1.55590143040596443193792941854
max_{chi even}|L'/L(1,chi)|(131)  = 1.43797882292531602089564238879
max_{chi odd}|L'/L(1,chi)|(131)  = 1.27572700301367543915138664345
max_{chi}|L'/L(1,chi)|(131)  = 1.43797882292531602089564238879
max_{chi even}|L'/L(1,chi)|(137)  = 1.53929870904867707257469538680
max_{chi odd}|L'/L(1,chi)|(137)  = 1.36270081382481387074802450457
max_{chi}|L'/L(1,chi)|(137)  = 1.53929870904867707257469538680
max_{chi even}|L'/L(1,chi)|(139)  = 1.58828875478913218915240825692
max_{chi odd}|L'/L(1,chi)|(139)  = 1.46843197510913207331559965477
max_{chi}|L'/L(1,chi)|(139)  = 1.58828875478913218915240825692
max_{chi even}|L'/L(1,chi)|(149)  = 1.55933423387754689170927007457
max_{chi odd}|L'/L(1,chi)|(149)  = 1.49066249516909038748573912245
max_{chi}|L'/L(1,chi)|(149)  = 1.55933423387754689170927007457
max_{chi even}|L'/L(1,chi)|(151)  = 1.48171078244888795642226012230
max_{chi odd}|L'/L(1,chi)|(151)  = 1.21630093914275672755098193481
max_{chi}|L'/L(1,chi)|(151)  = 1.48171078244888795642226012230
max_{chi even}|L'/L(1,chi)|(157)  = 1.52915091159611605159149879696
max_{chi odd}|L'/L(1,chi)|(157)  = 1.47930592186725803914452237782
max_{chi}|L'/L(1,chi)|(157)  = 1.52915091159611605159149879696
max_{chi even}|L'/L(1,chi)|(163)  = 1.57513694273693708178977104660
max_{chi odd}|L'/L(1,chi)|(163)  = 2.16832712928352380386400324642
max_{chi}|L'/L(1,chi)|(163)  = 2.16832712928352380386400324642
max_{chi even}|L'/L(1,chi)|(167)  = 1.56607236656750344030293511154
max_{chi odd}|L'/L(1,chi)|(167)  = 1.35615244416151765582440171259
max_{chi}|L'/L(1,chi)|(167)  = 1.56607236656750344030293511154
max_{chi even}|L'/L(1,chi)|(173)  = 1.54242401828716131644723995819
max_{chi odd}|L'/L(1,chi)|(173)  = 1.43963149697994500743617408030
max_{chi}|L'/L(1,chi)|(173)  = 1.54242401828716131644723995819
max_{chi even}|L'/L(1,chi)|(179)  = 1.60085064594072009293300914735
max_{chi odd}|L'/L(1,chi)|(179)  = 1.39782757591912800423472060801
max_{chi}|L'/L(1,chi)|(179)  = 1.60085064594072009293300914735
max_{chi even}|L'/L(1,chi)|(181)  = 1.50955704471891625386577768178
max_{chi odd}|L'/L(1,chi)|(181)  = 1.65656567095010010041093792977
max_{chi}|L'/L(1,chi)|(181)  = 1.65656567095010010041093792977
max_{chi even}|L'/L(1,chi)|(191)  = 1.69400806335478035992195123369
max_{chi odd}|L'/L(1,chi)|(191)  = 1.51238257796640956592393446369
max_{chi}|L'/L(1,chi)|(191)  = 1.69400806335478035992195123369
max_{chi even}|L'/L(1,chi)|(193)  = 1.72106839151430000218016220949
max_{chi odd}|L'/L(1,chi)|(193)  = 1.42940396032541735361413928822
max_{chi}|L'/L(1,chi)|(193)  = 1.72106839151430000218016220949
max_{chi even}|L'/L(1,chi)|(197)  = 1.58142886014710250392544294033
max_{chi odd}|L'/L(1,chi)|(197)  = 1.58425224704856913591906318269
max_{chi}|L'/L(1,chi)|(197)  = 1.58425224704856913591906318269
max_{chi even}|L'/L(1,chi)|(199)  = 1.43355422198296835867339511842
max_{chi odd}|L'/L(1,chi)|(199)  = 1.52055512030192431037107983792
max_{chi}|L'/L(1,chi)|(199)  = 1.52055512030192431037107983792
max_{chi even}|L'/L(1,chi)|(211)  = 1.42636194836883457299103667906
max_{chi odd}|L'/L(1,chi)|(211)  = 1.58887689723521687477342354947
max_{chi}|L'/L(1,chi)|(211)  = 1.58887689723521687477342354947
max_{chi even}|L'/L(1,chi)|(223)  = 1.57809439787964273689310796956
max_{chi odd}|L'/L(1,chi)|(223)  = 1.55303288836237605943021818591
max_{chi}|L'/L(1,chi)|(223)  = 1.57809439787964273689310796956
max_{chi even}|L'/L(1,chi)|(227)  = 1.61440476278289514090073256762
max_{chi odd}|L'/L(1,chi)|(227)  = 1.50389687420786831791141229315
max_{chi}|L'/L(1,chi)|(227)  = 1.61440476278289514090073256762
max_{chi even}|L'/L(1,chi)|(229)  = 1.64147596839111917230029367252
max_{chi odd}|L'/L(1,chi)|(229)  = 1.64391627222705529854073112016
max_{chi}|L'/L(1,chi)|(229)  = 1.64391627222705529854073112016
max_{chi even}|L'/L(1,chi)|(233)  = 1.34601818744675837966996822954
max_{chi odd}|L'/L(1,chi)|(233)  = 1.56534808865669695863593307680
max_{chi}|L'/L(1,chi)|(233)  = 1.56534808865669695863593307680
max_{chi even}|L'/L(1,chi)|(239)  = 1.62409294223527640292514612201
max_{chi odd}|L'/L(1,chi)|(239)  = 1.83593237895342242137799671838
max_{chi}|L'/L(1,chi)|(239)  = 1.83593237895342242137799671838
max_{chi even}|L'/L(1,chi)|(241)  = 1.52053007064284698420889751143
max_{chi odd}|L'/L(1,chi)|(241)  = 1.74483502309356231328685290592
max_{chi}|L'/L(1,chi)|(241)  = 1.74483502309356231328685290592
max_{chi even}|L'/L(1,chi)|(251)  = 1.48698867799867919284125336441
max_{chi odd}|L'/L(1,chi)|(251)  = 1.60634233356394595761434310531
max_{chi}|L'/L(1,chi)|(251)  = 1.60634233356394595761434310531
max_{chi even}|L'/L(1,chi)|(257)  = 1.52986363395322517571321794433
max_{chi odd}|L'/L(1,chi)|(257)  = 1.44048311367778018043569879961
max_{chi}|L'/L(1,chi)|(257)  = 1.52986363395322517571321794433
max_{chi even}|L'/L(1,chi)|(263)  = 1.47652133868945448396166271321
max_{chi odd}|L'/L(1,chi)|(263)  = 1.61873689910065712561008039262
max_{chi}|L'/L(1,chi)|(263)  = 1.61873689910065712561008039262
max_{chi even}|L'/L(1,chi)|(269)  = 1.58662353583078976012953348699
max_{chi odd}|L'/L(1,chi)|(269)  = 1.50439156819694711118224374474
max_{chi}|L'/L(1,chi)|(269)  = 1.58662353583078976012953348699
max_{chi even}|L'/L(1,chi)|(271)  = 1.46458989230894491096657135270
max_{chi odd}|L'/L(1,chi)|(271)  = 1.51145118046000075647340279932
max_{chi}|L'/L(1,chi)|(271)  = 1.51145118046000075647340279932
max_{chi even}|L'/L(1,chi)|(277)  = 1.60164832656696765575321238671
max_{chi odd}|L'/L(1,chi)|(277)  = 1.72974155675277125427451583060
max_{chi}|L'/L(1,chi)|(277)  = 1.72974155675277125427451583060
max_{chi even}|L'/L(1,chi)|(281)  = 1.49191529286515462825136060300
max_{chi odd}|L'/L(1,chi)|(281)  = 1.60536366070704717918242357661
max_{chi}|L'/L(1,chi)|(281)  = 1.60536366070704717918242357661
max_{chi even}|L'/L(1,chi)|(283)  = 1.55609186296142373233316514603
max_{chi odd}|L'/L(1,chi)|(283)  = 1.49992248252889901008064735773
max_{chi}|L'/L(1,chi)|(283)  = 1.55609186296142373233316514603
max_{chi even}|L'/L(1,chi)|(293)  = 1.41713157874130820443673390762
max_{chi odd}|L'/L(1,chi)|(293)  = 1.58515317244284064528356780036
max_{chi}|L'/L(1,chi)|(293)  = 1.58515317244284064528356780036
Total computation time: 0 min, 41 sec, 837 millisec
******  END PROGRAM   ********


******  END PROGRAM   ********

   
? for(n=1,10,m=nextprime(n*10^3); init_Max_direct_final();max_direct(m,m,30))
************ A. LANGUASCO  *************
********* COMPUTATION OF THE MAX |L'/L|**********
******* FOR q IN ONE INTERVAL ********
********* direct use of the lfun command  **********
Interval=[1009,1009]
max_{chi even}|L'/L(1,chi)|(1009)  = 1.66163071579662920308405512837
max_{chi odd}|L'/L(1,chi)|(1009)  = 1.91905070366722993140044134955
max_{chi}|L'/L(1,chi)|(1009)  = 1.91905070366722993140044134955
Total computation time: 0 min, 11 sec, 540 millisec
******  END PROGRAM   ********
************ A. LANGUASCO  *************
********* COMPUTATION OF THE MAX |L'/L|**********
******* FOR q IN ONE INTERVAL ********
********* direct use of the lfun command  **********
Interval=[2003,2003]
max_{chi even}|L'/L(1,chi)|(2003)  = 1.87590052118752805867444411545
max_{chi odd}|L'/L(1,chi)|(2003)  = 1.93559000482102812476860401386
max_{chi}|L'/L(1,chi)|(2003)  = 1.93559000482102812476860401386
Total computation time: 0 min, 32 sec, 532 millisec
******  END PROGRAM   ********
************ A. LANGUASCO  *************
********* COMPUTATION OF THE MAX |L'/L|**********
******* FOR q IN ONE INTERVAL ********
********* direct use of the lfun command  **********
Interval=[3001,3001]
max_{chi even}|L'/L(1,chi)|(3001)  = 1.85170875270322364850217009333
max_{chi odd}|L'/L(1,chi)|(3001)  = 2.02047653064549796546951465975
max_{chi}|L'/L(1,chi)|(3001)  = 2.02047653064549796546951465975
Total computation time: 0 min, 59 sec, 101 millisec
******  END PROGRAM   ********
************ A. LANGUASCO  *************
********* COMPUTATION OF THE MAX |L'/L|**********
******* FOR q IN ONE INTERVAL ********
********* direct use of the lfun command  **********
Interval=[4001,4001]
max_{chi even}|L'/L(1,chi)|(4001)  = 1.92493112516329229196301756391
max_{chi odd}|L'/L(1,chi)|(4001)  = 1.98111048196548026386404591492
max_{chi}|L'/L(1,chi)|(4001)  = 1.98111048196548026386404591492
Total computation time: 1 min, 29 sec, 930 millisec
******  END PROGRAM   ********
************ A. LANGUASCO  *************
********* COMPUTATION OF THE MAX |L'/L|**********
******* FOR q IN ONE INTERVAL ********
********* direct use of the lfun command  **********
Interval=[5003,5003]
max_{chi even}|L'/L(1,chi)|(5003)  = 2.16914336482541724701723239482
max_{chi odd}|L'/L(1,chi)|(5003)  = 2.09085309222589149130565282238
max_{chi}|L'/L(1,chi)|(5003)  = 2.16914336482541724701723239482
Total computation time: 2 min, 9 sec, 845 millisec
******  END PROGRAM   ********
************ A. LANGUASCO  *************
********* COMPUTATION OF THE MAX |L'/L|**********
******* FOR q IN ONE INTERVAL ********
********* direct use of the lfun command  **********
Interval=[6007,6007]
max_{chi even}|L'/L(1,chi)|(6007)  = 2.19761938716235219714332977972
max_{chi odd}|L'/L(1,chi)|(6007)  = 2.27649543589754496157793572989
max_{chi}|L'/L(1,chi)|(6007)  = 2.27649543589754496157793572989
Total computation time: 2 min, 48 sec, 659 millisec
******  END PROGRAM   ********
************ A. LANGUASCO  *************
********* COMPUTATION OF THE MAX |L'/L|**********
******* FOR q IN ONE INTERVAL ********
********* direct use of the lfun command  **********
Interval=[7001,7001]
max_{chi even}|L'/L(1,chi)|(7001)  = 2.16381618373619426178026988823
max_{chi odd}|L'/L(1,chi)|(7001)  = 2.08777770385597106873908214147
max_{chi}|L'/L(1,chi)|(7001)  = 2.16381618373619426178026988823
Total computation time: 3 min, 28 sec, 160 millisec
******  END PROGRAM   ********
************ A. LANGUASCO  *************
********* COMPUTATION OF THE MAX |L'/L|**********
******* FOR q IN ONE INTERVAL ********
********* direct use of the lfun command  **********
Interval=[8009,8009]
max_{chi even}|L'/L(1,chi)|(8009)  = 2.08775398337120103585896611130
max_{chi odd}|L'/L(1,chi)|(8009)  = 2.15077860002341223830865273302
max_{chi}|L'/L(1,chi)|(8009)  = 2.15077860002341223830865273302
Total computation time: 4 min, 14 sec, 597 millisec
******  END PROGRAM   ********
************ A. LANGUASCO  *************
********* COMPUTATION OF THE MAX |L'/L|**********
******* FOR q IN ONE INTERVAL ********
********* direct use of the lfun command  **********
Interval=[9001,9001]
max_{chi even}|L'/L(1,chi)|(9001)  = 2.16225139707852719114127441722
max_{chi odd}|L'/L(1,chi)|(9001)  = 1.99923255049969643889532283355
max_{chi}|L'/L(1,chi)|(9001)  = 2.16225139707852719114127441722
Total computation time: 5 min, 2 sec, 395 millisec
******  END PROGRAM   ********
************ A. LANGUASCO  *************
********* COMPUTATION OF THE MAX |L'/L|**********
******* FOR q IN ONE INTERVAL ********
********* direct use of the lfun command  **********
Interval=[10007,10007]
max_{chi even}|L'/L(1,chi)|(10007)  = 2.02551416039253687835130081402
max_{chi odd}|L'/L(1,chi)|(10007)  = 2.17148657398748131199086566182
max_{chi}|L'/L(1,chi)|(10007)  = 2.17148657398748131199086566182
Total computation time: 6 min, 10 sec, 843 millisec
******  END PROGRAM   ********
 

******************  larger q's **********************

? init_Max_direct_final();max_direct(20011,20011,30)
************ A. LANGUASCO  *************
********* COMPUTATION OF THE MAX |L'/L|**********
******* FOR q IN ONE INTERVAL ********
********* direct use of the lfun command  **********
Interval=[20011,20011]
max_{chi even}|L'/L(1,chi)|(20011)  = 2.28807406721414248609296533589
max_{chi odd}|L'/L(1,chi)|(20011)  = 2.34670358729048423962840680872
max_{chi}|L'/L(1,chi)|(20011)  = 2.34670358729048423962840680872
Total computation time: 17 min, 6 sec, 42 millisec
******  END PROGRAM   ******** 
 
? init_Max_direct_final();max_direct(30011,30011,30)
************ A. LANGUASCO  *************
********* COMPUTATION OF THE MAX |L'/L|**********
******* FOR q IN ONE INTERVAL ********
********* direct use of the lfun command  **********
Interval=[30011,30011]
max_{chi even}|L'/L(1,chi)|(30011)  = 2.18119895632481240565959034653
max_{chi odd}|L'/L(1,chi)|(30011)  = 2.28268986824865518173486616741
max_{chi}|L'/L(1,chi)|(30011)  = 2.28268986824865518173486616741
Total computation time: 32 min, 3 sec, 791 millisec
******  END PROGRAM   ********
 
******  END PROGRAM  
 
 

 

*******/