Table lfunc_lfunctions
L-functions
{'Lhash': '4035917043592029811065058241783', 'a10': [-195.61648267796608, 0.0], 'a2': [7.824659307118643, 0.0], 'a3': [-16.304359454920966, 0.0], 'a4': [29.225293272478403, 0.0], 'a5': [-25.0, 0.0], 'a6': [-127.57605795555519, 0.0], 'a7': [-125.43559474062279, 0.0], 'a8': [-21.71113482002659, 0.0], 'a9': [22.832137235270746, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.821110089713937, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 7}, 'bad_lfactors': [[5, [[1.0, 0], [25.0, 0]]], [11, [[1.0, 0], [121.0, 0]]]], 'bad_primes': [5, 11], 'central_character': '55.1', 'coefficient_field': 'CDF', 'conductor': 55, 'conductor_radical': 55, 'conjugate': '4035917043592029811065058241783', 'degree': 2, 'euler_factors': [[[1.0, 0], [-7.824659307118643, 0], [32.0, 0]], [[1.0, 0], [16.304359454920966, 0], [243.0, 0]], [[1.0, 0], [25.0, 0]], [[1.0, 0], [125.43559474062279, 0], [16807.0, 0]], [[1.0, 0], [121.0, 0]], [[1.0, 0], [-532.2996971007925, 0], [371293.0, 0]], [[1.0, 0], [1373.0919177848932, 0], [1419857.0, 0]], [[1.0, 0], [554.6394116303316, 0], [2476099.0, 0]], [[1.0, 0], [-4250.715049258318, 0], [6436343.0, 0]], [[1.0, 0], [6973.398118007846, 0], [20511149.0, 0]], [[1.0, 0], [-3130.0347973757666, 0], [28629151.0, 0]], [[1.0, 0], [-1384.7003093610635, 0], [69343957.0, 0]], [[1.0, 0], [-679.3852837687172, 0], [115856201.0, 0]], [[1.0, 0], [1721.0570116362862, 0], [147008443.0, 0]], [[1.0, 0], [15143.301716580034, 0], [229345007.0, 0]], [[1.0, 0], [9544.435698499288, 0], [418195493.0, 0]], [[1.0, 0], [-27582.671776342628, 0], [714924299.0, 0]], [[1.0, 0], [40527.51374990546, 0], [844596301.0, 0]], [[1.0, 0], [58726.524917521, 0], [1350125107.0, 0]], [[1.0, 0], [42527.77676761923, 0], [1804229351.0, 0]], [[1.0, 0], [-23753.048367071096, 0], [2073071593.0, 0]], [[1.0, 0], [78690.07273066152, 0], [3077056399.0, 0]], [[1.0, 0], [-52252.054807988745, 0], [3939040643.0, 0]], [[1.0, 0], [-8156.089190666574, 0], [5584059449.0, 0]], [[1.0, 0], [-79010.07495555452, 0], [8587340257.0, 0]], [[1.0, 0], [116968.2942065878, 0], [10510100501.0, 0]], [[1.0, 0], [-99313.27613697077, 0], [11592740743.0, 0]], [[1.0, 0], [-122146.06067739744, 0], [14025517307.0, 0]], [[1.0, 0], [68840.4043713693, 0], [15386239549.0, 0]], [[1.0, 0], [65961.5284056253, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 10762885, 'index': 17, 'label': '2-55-1.1-c5-0-17', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/55/6/a/b/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [-3.099162808575247e-120, 0.36945551559352147, 0.7346139317974345, 1.0911355335544182, 1.4346027744387264, 1.7604994873921922, 2.0642108120504035, 2.341049049829363, 2.5863092641101417, 2.7953567681962466, 2.963746728244114, 3.087373999664047, 3.162649071944879, 3.186693691889297, 3.157547461416105, 3.0743745778303055, 2.937658038341328, 2.74936722219464, 2.5130839607507447, 2.2340721772635384, 1.9192770802805148, 1.5772418542488056, 1.2179328869044033, 0.8524688178669465, 0.4927540159435012, 0.15102332689300438, -0.16068819255887634, -0.43112970101862014, -0.6504453768207817, -0.8107776484372151, -0.9068240860406886, -0.9363063401598982, -0.9003091936808543, -0.8034504734039242, -0.6538485631144331, -0.46286367765287767, -0.24460174380446645, -0.015185241652504589, 0.20818706834274758, 0.40835103136369527, 0.569399840033304, 0.6779434590300458, 0.7243166037358403, 0.7036392412928256, 0.6166321550113641, 0.4700962582976532, 0.2769786828237263, 0.05597120818328096, -0.16938335219761674, -0.3720651003967524, -0.5233796963886, -0.5950971468530638, -0.561795690293238, -0.4032472668450063, -0.10665825653910856, 0.33143072728113027, 0.9037766604038272, 1.5917657611472826, 2.365573689732561, 3.1852278753147676, 4.002577813742099, 4.764103408398494, 5.414413508285315, 5.900213532563144, 6.174459636552287, 6.200374176232696, 5.9549791941510275, 5.4318155303944415, 4.6425569150609025, 3.6173002253715505, 2.4034112014456546, 1.062922570257897, -0.331390610691364, -1.7010067850918105, -2.967359848172548, -4.057794169369353, -4.911267820981089, -5.483291540481427, -5.749631844108338, -5.708395802061906, -5.380247008701662, -4.806667077331261, -4.046360152838893, -3.1700819776876443, -2.254341013815089, -1.3745485322319488, -0.5982714870850525, 0.020745047221553924, 0.4471753689361234, 0.6668436237823684, 0.6872816211598813, 0.5360307669045492, 0.2568460250347062, -0.09580630988643636, -0.4633654930519209, -0.79017531214255, -1.0300696970334684, -1.1517760339689125, -1.1424847967219511, -1.0091333622182779, -0.7772131930806211, -0.4872045642408406, -0.18903747206448038, 0.06476491751395476, 0.2264167789662152, 0.25974105666847735, 0.14567322355641849, -0.11436988438123402, -0.4977770282303888, -0.9628808212285632, -1.45377627619657, -1.9072865185503425, -2.2612325136365405, -2.462949526271978, -2.4769085989630284, -2.290365253223482, -1.9161698695473686, -1.392214853771401, -0.7774242559979679, -0.14465888675692823, 0.4286472592692006, 0.8709472564253375, 1.1267505213782507, 1.1650764707707473, 0.9849254839640278, 0.6168421555158651, 0.12013614161879602, -0.4240946739074369, -0.9234007379293608, -1.2866140480409325, -1.4370354804805694, -1.3243616397914288, -0.9336085292361701, -0.2896094404162128, 0.5437977273624766, 1.4700861168617536, 2.371292744852159, 3.122922064497801, 3.610634600259212, 3.746506937780696, 3.482594152547956, 2.819786664491717, 1.8105097465324274, 0.5546012796083849, -0.8113788894310778, -2.1302310211290947, -3.2436140602692705, -4.012433072852617, -4.335370043466932, -4.1629745658422035, -3.5052645965281544, -2.4316298567725396, -1.0628711494690612, 0.44369605931442285, 1.9141531691085318, 3.1802426065129814, 4.100946240266503, 4.580394570047303, 4.579611440933479, 4.120458241401093, 3.2812517760828834, 2.1847302044319328, 0.9801528945136707, -0.17782652924488582, -1.1504125767785263, -1.8329491358800871, -2.1676089771681553, -2.1487487594925283, -1.8203325127912258, -1.2660615677432163, -0.5939774328448283, 0.0818553112828141, 0.6595638192338555, 1.0646371174414284, 1.2596733173779504, 1.2472824027206408, 1.0659137206486329, 0.7796011253491089, 0.4636661610975151, 0.1891079081355384, 0.008613190704366377, -0.05319932159102151, -0.003483651060978262, 0.1218605566711666, 0.26734747977267875, 0.37140583755276774, 0.38154631861011706, 0.26811814439742115, 0.03374510810067219, -0.283740148469822, -0.6158693800612743, -0.8752028879131558, -0.9722528706843889, -0.8346908313056932, -0.4252189139805648, 0.24551530280930314, 1.1139017239598106, 2.0679184788880307, 2.9612586712179256, 3.6352713843736066, 3.9453947221982495, 3.787703777407603, 3.120867019381189, 1.9793006841652296, 0.4745883939278998, -1.2158945592171413, -2.8720492256095382, -4.2626254205039995, -5.180478125363164, -5.475817025421818, -5.081837632227712, -4.028177776842293, -2.4395283354283777, -0.5191422779348612, 1.4804734383592995, 3.2951744175329925, 4.689087005803979, 5.490284198896044, 5.616314212713665, 5.085310460116234, 4.010822502436275, 2.5812738343573964, 1.0275898664923047, -0.41542249393875, -1.5472947254792282, -2.2331714775630402, -2.422863473701647, -2.1546120929089696, -1.5432560168219207, -0.7552928214229526, 0.02433743893371928, 0.6274851048644723, 0.9335105506068332, 0.8899088646147707, 0.519242772131291, -0.08856766088783158, -0.7967483265077403, -1.4506953057495762, -1.9096710808316886, -2.074895200004693, -1.908552521298923, -1.4401126943008458, -0.7589244319153168, 0.00519304945984833, 0.7092415867502185, 1.2265434691337416, 1.4723744779157055, 1.4204960752568352, 1.1072622968214931, 0.6225693050886918, 0.08965930881763667, -0.36188132699894965, -0.6241641339520011, -0.6340961303914167, -0.3865925863176159, 0.06493543895124909, 0.620936136679509], 'positive_zeros': ['3.18377717240491839984000138460643', '4.63328584143517183668702116174501', '5.90571861093459695816930268547476', '6.78443238236780676041348362222860', '8.970357153050841115564913238363604', '10.87011372956552610271840328523794', '11.59239281058810462992628757456809', '12.83942875742554205581132419048341', '13.32779602285801649924992840540918'], 'prelabel': '2-55-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.970035368428116, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.18377717240491839984000138461', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '4.63328584143517183668702116175', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '5.90571861093459695816930268547', 'prec': 100}}