Table lfunc_lfunctions
L-functions
{'Lhash': '2784837071304493377235045392519', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, -63.91996797437437], 'a4': [0.0, 0.0], 'a5': [217.6798718974975, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, -1726.2392954362363], 'a8': [0.0, 0.0], 'a9': [2475.2376941549546, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.036115521956075, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]]], 'bad_primes': [2], 'central_character': '32.31', 'coefficient_field': 'CDF', 'conductor': 32, 'conductor_radical': 2, 'conjugate': '725732577098509208744950270479', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 63.91996797437437], [-6561.0, 0]], [[1.0, 0], [-217.6798718974975, 0], [390625.0, 0]], [[1.0, 0], [0, 1726.2392954362363], [-5764801.0, 0]], [[1.0, 0], [0, 5955.281313050651], [-214358881.0, 0]], [[1.0, 0], [49121.18526821221, 0], [815730721.0, 0]], [[1.0, 0], [55631.93357886527, 0], [6975757441.0, 0]], [[1.0, 0], [0, 202658.78831064663], [-16983563041.0, 0]], [[1.0, 0], [0, 209565.21485987748], [-78310985281.0, 0]], [[1.0, 0], [-3082.262481976371, 0], [500246412961.0, 0]], [[1.0, 0], [0, -1360349.8614571306], [-852891037441.0, 0]], [[1.0, 0], [-1314199.0547958263, 0], [3512479453921.0, 0]], [[1.0, 0], [-4544889.099951766, 0], [7984925229121.0, 0]], [[1.0, 0], [0, 3487604.478046219], [-11688200277601.0, 0]], [[1.0, 0], [0, -7233606.08217764], [-23811286661761.0, 0]], [[1.0, 0], [2485572.604067184, 0], [62259690411361.0, 0]], [[1.0, 0], [0, 14879049.567173157], [-146830437604321.0, 0]], [[1.0, 0], [-4136479.3763323384, 0], [191707312997281.0, 0]], [[1.0, 0], [0, 6044808.088806714], [-406067677556641.0, 0]], [[1.0, 0], [0, 42024188.98132784], [-645753531245761.0, 0]], [[1.0, 0], [-9004995.759358948, 0], [806460091894081.0, 0]], [[1.0, 0], [0, 6817411.651305783], [-1517108809906561.0, 0]], [[1.0, 0], [0, -58177950.822705194], [-2252292232139041.0, 0]], [[1.0, 0], [-78249856.34875669, 0], [3936588805702081.0, 0]], [[1.0, 0], [-60142348.84643479, 0], [7837433594376961.0, 0]], [[1.0, 0], [-1923490.6485797907, 0], [10828567056280800, 0]], [[1.0, 0], [0, -99598182.0421424], [-12667700813876160, 0]], [[1.0, 0], [0, -29036858.83583134], [-17181861798319200, 0]], [[1.0, 0], [-89760645.71023473, 0], [19925626416901920, 0]], [[1.0, 0], [283785710.92079246, 0], [26584441929064320, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 12243574, 'index': 6, 'label': '2-2e5-4.3-c8-0-6', 'load_key': 'CMFs-workshop', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/32/9/c/a/31/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [1.3944492675509876, 1.6692119068728672, 1.9168464586322533, 2.1307365038432984, 2.304970250287668, 2.434466920103951, 2.5150973619987473, 2.5437973783524264, 2.51867145019611, 2.439083719769403, 2.30573231341233, 2.1207024227390145, 1.8874930764735087, 1.611012294605165, 1.2975353815943815, 0.9546215389469206, 0.5909848001383441, 0.21631653689223565, -0.1589415409289606, -0.5238728894756269, -0.8674066978043662, -1.1786773562311736, -1.4474137725573146, -1.6643465567373452, -1.821618301178603, -1.9131797109230437, -1.9351523876554577, -1.8861378499238493, -1.767452076589608, -1.5832656656177257, -1.3406317412459108, -1.0493870997609867, -0.7219167677649965, -0.3727780837094484, -0.018187437211070284, 0.3246193532581039, 0.6381337366505039, 0.9054005936942262, 1.1108884559152459, 1.241361638762793, 1.2867070865360024, 1.2406658922964817, 1.101419343480844, 0.8719823353972466, 0.5603633140836787, 0.1794595824446559, -0.2533303761209126, -0.7167803897284158, -1.1867812429844535, -1.6375232808393916, -2.042865359697857, -2.3778215246093053, -2.6200825509712757, -2.751479352172592, -2.759290422451549, -2.6372969152149985, -2.3864972594862537, -2.0154085557954255, -1.5399040181756916, -0.9825635385794286, -0.371546590129174, 0.2609688020821949, 0.880702777022859, 1.4534359087728788, 1.9472803659620752, 2.334904702618983, 2.5955486141374804, 2.7166674165707865, 2.695062129635378, 2.537379776374798, 2.2599087177626687, 1.8876433111981819, 1.452647712806369, 0.9918062005662558, 0.5441023768757357, 0.1476171879188441, -0.1635287792119129, -0.3620438403531302, -0.42989942295733646, -0.36010521693530295, -0.15764168454423153, 0.16057373493025637, 0.5667354490420294, 1.0241777658647169, 1.49025905819378, 1.9198964213113314, 2.2694753593525747, 2.500809153559628, 2.5847987197535387, 2.5044500867528408, 2.256944755553049, 1.8545268869944274, 1.3240662631962217, 0.7052701739407464, 0.04764129306785366, -0.5935989357118343, -1.1622927594006485, -1.6064214350391903, -1.8830107145420758, -1.9623958789264726, -1.8314130634509929, -1.495165464538482, -0.9771340345102493, -0.3175527879416063, 0.42986446756353236, 1.2025921947027498, 1.934951938544794, 2.5642406607796433, 3.0367372738991274, 3.3129830188048905, 3.3717799600077347, 3.2124605321747035, 2.8551416306162016, 2.338875009163553, 1.717822620307145, 1.055798728087918, 0.41970694027100225, -0.12746188741694794, -0.5333331801388046, -0.7618214923831713, -0.7971267691840853, -0.645569417317523, -0.335001702414273, 0.08820603098043818, 0.5643335571403102, 1.027109463778302, 1.4114122035758168, 1.6610158931264505, 1.7354870538726215, 1.6154042106053617, 1.3052370706826073, 0.8334712686086355, 0.24987300169084567, -0.3798783973708774, -0.9816412652338049, -1.4815284018047392, -1.814890281661141, -1.9344953210829974, -1.8168939791042908, -1.466134417504709, -0.9142867605430725, -0.21860014214034046, 0.5444798974998564, 1.2878145787378128, 1.9236457351280158, 2.374064029175757, 2.580605692572145, 2.5117762511917365, 2.167516073986421, 1.5799699886140302, 0.8103630045821066, -0.057735726944060074, -0.9280177249918142, -1.7027837245269766, -2.294659628565346, -2.637220177766929, -2.693162084245801, -2.4589480393678964, -1.965270701436913, -1.273210623149614, -0.4665183804064167, 0.3590335171837077, 1.1078787638152834, 1.6968789841236411, 2.065921716911961, 2.1854626327047004, 2.059963306259369, 1.7267114649189914, 1.2501302123818294, 0.7123039888512236, 0.20098645716161997, -0.20326790248943835, -0.4390483736711662, -0.47339760569847733, -0.30710676769546846, 0.02484766858077037, 0.4578990743104037, 0.9069767268165028, 1.2788831718281382, 1.4862564039955495, 1.461132790865522, 1.166125750196188, 0.6015202474511046, -0.19287743661781254, -1.14157109134861, -2.1425135305166494, -3.0803985008991557, -3.8423135456309048, -4.333565755306628, -4.4914032713161065, -4.294596162039567, -3.767385889233659, -2.9770921790017266, -2.025571874222348, -1.0356261766674382, -0.13421686602326308, 0.5651388418600405, 0.978254147978001, 1.0621005281947065, 0.8207935753203249, 0.30478622966183144, -0.3966873865326075, -1.1688662459587258, -1.8884936634119094, -2.4421083820856775, -2.7428536968361454, -2.7432524944104113, -2.4419804049039366, -1.883566870161327, -1.1510326901023427, -0.3525686488785368, 0.39569768241601344, 0.9881620745665168, 1.346519764045483, 1.432177050139794, 1.2522781570778294, 0.85832167626833, 0.3375180872316224, -0.2017850578630217, -0.6482999475683822, -0.9066778980107841, -0.9139677346946546, -0.6508881242566817, -0.1459470079646051, 0.5284200220465122, 1.2672194687728182, 1.950050931532329, 2.461313284120405, 2.7101667847047395, 2.646910498164138, 2.272945578556954, 1.6424884638319925, 0.8555216926616017, 0.042912602585051335, -0.6540452526787655, -1.1064301820062363, -1.219123498831561, -0.9473042188984755, -0.3051725503167014, 0.6347082950657718, 1.7515419397013297, 2.8944217051067342, 3.9056136058916633, 4.645259242298433, 5.013460516213622, 4.9660827326403805, 4.521609914969391, 3.757849039209815, 2.798968433135075, 1.7949860910362532, 0.8971164473662018, 0.23311193307781558, -0.11323597374616795, -0.11495850998872184, 0.19504889622755725, 0.7313020185751201, 1.372026408865159], 'positive_zeros': ['2.19684909296229404503866106388640', '4.25647132429671964340172265985224', '5.67833114888102104889711452203173', '7.57351118866909932846050249272001', '9.429371226119558077918527099296238', '10.06697530192770405285114237440900', '11.75904704586608793154475359204921', '12.92932269742977209774518869250649', '14.59324131368081621807407851194023', '15.35075822714166116392084292963938'], 'prelabel': '2-2e5-4.3-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6105561236402455, 'root_angle': 0.375, 'root_number': '-0.7071067811865475 + 0.7071067811865476*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.375', 'prec': 10}, 'spectral_label': 'c8-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.19684909296229404503866106389', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '4.25647132429671964340172265985', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '5.67833114888102104889711452203', 'prec': 100}}