/* Copyright (C) 2019 Alessandro Languasco */ /**************** A. LANGUASCO ******************** ************* COMPUTATION OF THE EULER KRONECKER CONSTANTS MOD q(PRIME) *******/ /******* Direct use of the pari/gp lfun functions *****/ {maxL_direct(r1,r2,defaultprecision)=local(minutes, millisec, seconds, rows, n,m,L,evenmax,oddmax,q, G, chi, elaptimecomp,absL); default(realprecision,defaultprecision); print("************ A. LANGUASCO *************"); print("********* COMPUTATION OF THE MAX |L(1,chi)|**********"); 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) absL=abs(lfun(L,1)); \\ computes the absolute value of L at 1 if (zncharisodd(G,chi), if(absL>oddmax, oddmax=absL), if(absL>evenmax, evenmax=absL)); ); print("max_{chi even}|L(1,chi)|(",q") = ", evenmax); print("max_{chi odd}|L(1,chi)|(",q") = ", oddmax); print("max_{chi}|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/MaxL$ gp2c-run -pmy_ -g -W MaxL-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_MaxL_direct_final();maxL_direct(3,300,30) ************ A. LANGUASCO ************* ********* COMPUTATION OF THE MAX |L(1,chi)|********** ******* FOR q IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[3,293] 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 Total computation time: 0 min, 19 sec, 673 millisec ****** END PROGRAM ******** ****** END PROGRAM ******** ? for(n=1,10,m=nextprime(n*10^3); init_MaxL_direct_final();maxL_direct(m,m,30)) ************ A. LANGUASCO ************* ********* COMPUTATION OF THE MAX |L(1,chi)|********** ******* FOR q IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[1009,1009] 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 Total computation time: 0 min, 5 sec, 595 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE MAX |L(1,chi)|********** ******* FOR q IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[2003,2003] 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 Total computation time: 0 min, 15 sec, 869 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE MAX |L(1,chi)|********** ******* FOR q IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[3001,3001] 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 Total computation time: 0 min, 29 sec, 255 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE MAX |L(1,chi)|********** ******* FOR q IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[4001,4001] 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 Total computation time: 0 min, 44 sec, 211 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE MAX |L(1,chi)|********** ******* FOR q IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[5003,5003] 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 Total computation time: 1 min, 3 sec, 833 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE MAX |L(1,chi)|********** ******* FOR q IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[6007,6007] 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 Total computation time: 1 min, 23 sec, 324 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE MAX |L(1,chi)|********** ******* FOR q IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[7001,7001] 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 Total computation time: 1 min, 43 sec, 262 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE MAX |L(1,chi)|********** ******* FOR q IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[8009,8009] 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 Total computation time: 2 min, 5 sec, 648 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE MAX |L(1,chi)|********** ******* FOR q IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[9001,9001] 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 Total computation time: 2 min, 29 sec, 701 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE MAX |L(1,chi)|********** ******* FOR q IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[10007,10007] 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 Total computation time: 3 min, 4 sec, 184 millisec ****** END PROGRAM ******** ****************** larger q's ********************** ? init_MaxL_direct_final();maxL_direct(20011,20011,30) ************ A. LANGUASCO ************* ********* COMPUTATION OF THE MAX |L(1,chi)|********** ******* FOR q IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[20011,20011] 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 Total computation time: 8 min, 34 sec, 228 millisec ****** END PROGRAM ******** ? init_MaxL_direct_final();maxL_direct(30011,30011,30) ************ A. LANGUASCO ************* ********* COMPUTATION OF THE MAX |L(1,chi)|********** ******* FOR q IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[30011,30011] 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 Total computation time: 16 min, 1 sec, 769 millisec ****** END PROGRAM ******** *******/