In my second example there were not enough coefficients defined in
pari_precode. Even though SAGE indicates the need of 72 of them I had
to give about 150. It works now and the result coincides with direct
summation of the L-series.
sage: L = Dokchitser(conductor=1, gammaV=[-11,-10,0,1], weight=31,
eps=1)
sage: print "\n", L
sage: print "Need", L.num_coeffs(), "coefficients"
sage: pari_precode = 'a(n)=A = [1, -10944, 12764304, 1539411968,
-11482890300, -139692542976,283267356736, -44134904365056,
46408678295058, 125668751443200,-8667187482096, 19649522340790272,
-29130483042689756,-3100077952118784, -146571102587851200,
1644106253837795328,-1554319252561868604, -507896575261114752,
-18233998180128777200,-17676898755051110400, 3615710654654751744,
94853699804058624,261686936006403269184, -563351336326501761024,
1273558077534900496250,318804006419196689664, 1733150370907327062096,
436065159103123816448,146105592452920851300, 1604074146721443532800,
5528815804645196514304,-86120915270310442303488,
-110630615846467901184,17010469900037090002176,
-3252727982970454060800,71442074786474120454144,
30865537336368838888516,199552876083329337676800,
-371830341223737023269824,506796265224929201356800,
-1019873964356065152450396,-39570337404541603086336,
-19316317801594343492336,-13342372138838368124928,
-532905761830142046137400,-2863901827654077377949696,
9402210025740654399518976,20985872032286786256371712,
41397191784780224333528098,-13937819600541951030960000,
-19839803452752469669511616,-44843814229537665297399808,
-47811913909986066768860796,-18967597659209787367578624,
99524363066441582068800,-12501977699285561524617216,
-232744295906610471329068800,-1598979603804765796627200,
-303004859031494257683250800,-225633309486693908683161600,
162598541877744568752031204,-60507360166037030652542976,
13146063630252454751810688,2020357112729589723468660736,
334502141165216685081766800,1210741459823744710557696,
3175361774024202560623447696,-2392737659486555189441052672,
3340251604014277274458407936,35597855045628649241395200,
-1741928161061823329619112896,-2048242578261034968112693248,
438923353770530901091061284,-337792440609220572795919104,
16256082463311040543885860000,-28069635022980459402885529600,
-2455131288388681244998656,4069311254352577982664953856,
-3515405762534580567251859200,-18879091754363357745276518400,
7869135928450504713662605203,11161500665912777028417133824,
-35452724179555767981578670576,5566068254600639742782472192,
17848077468345931142746141200,211397782020648495180125184,
1864936198169187433931995200,382525490636317472248037376,
-109249069070044747176364086300,5832120657469074552927705600,
-8251714931945597829824796416,402844001157507317216175194112,
70571485690495900448316604416,-102897786521705721748335673344,
209379000832818388460741160000,-1099273543268484659936181092352,
-47634607872499886285012051324,-453050866892634775106131504512,
-402232715579547033180281568,1960530546500297761616389120000,
-1162808714917392687418076881596,217126808986923028063135125504,
-1107846872750651745406597762496,1285671083196997900475575566336,
-41518808803941698650085683200,523253585830887514718412551424,
2388011350427463221803191653136,2668032423318378298280861564928,
-1353387698245376319875092670300,-1089194629399136674160947200,
393977101684762115700040332864,465721632717759338256330129408,
-2191859217894400283775903367356,2547153574401944998225328947200,
-3004922379104648837601242515200,224916697613756835047968358400,
-1351907216107831205712522025848,3316085177240673156085496755200,
-440287906197075715760026316544,6468901595395624704595407667200,
17418925606006459225002822869810,-1779478442310036560422229496576,
-13017981322725979849683199464384,8511125218538365507831460790272,
-38428433527137866970367006687500,-143870520369482864803816169472,
-23138036526704545438714845446144,-112807418472440250565409648934912,
-246559352580161885016598374144,-3660791432912131401534855859200,
45425161794085346769947063285904,-170306094061263137610490970112,
-5165096467214113117531863219200,-34751159254920872823463011585024,
-19901575582533148120269656068800,68599731564583393961379521101824,
87800288301206959073246211559716,-36555713554332250491672816451584,
82642925867275339252478377373200,-5007288385633217171589719654400,
120012667040401537914397663432704,19063661794660594519351571533824,
252479357975010451184932608576,76300798217251210651928597889024,
-1677714490353398050060512390000,-4803577183664690181540574692096,
528406340687237356581350035413792,47514777574357032247245348159488,
296728983438293492141383117642500,-177906566478476027712286851840000];return(A[n]);'
sage: L.init_coeffs('a(k)', pari_precode=pari_precode)
sage: print "L(19,Delta \otimes g_20) :\n\t",L(19)
Dokchitser L-series of conductor 1 and weight 31
Need 72 coefficients
L(19,Delta \otimes g_20) :
verbose -1 (309: dokchitser.py, __call__) Warning: Loss of 2 decimal
digits due to cancellation
0.994683426196919
I still could not figure out if I can give the list of coefficient to
init_coeffs function directly without pari_precode variable.
Kirill
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