-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2479186792202273735110721882136', 'a10': [0, 0], 'a2': [0, -1.0], 'a3': [0, 0], 'a4': [1.0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -4.0], 'a8': [0, -3.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.356242591224525, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [3, 5, 13], 'central_character': '2925.2224', 'coefficient_field': 'CDF', 'conductor': 2925, 'conductor_radical': 195, 'conjugate': '435720536085507032298522839596', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0], [-2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 4.0], [-7.0, 0]], [[1.0, 0], [4.0, 0], [11.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 2.0], [-17.0, 0]], [[1.0, 0], [0, 0], [19.0, 0]], [[1.0, 0], [0, 0], [-23.0, 0]], [[1.0, 0], [10.0, 0], [29.0, 0]], [[1.0, 0], [-4.0, 0], [31.0, 0]], [[1.0, 0], [0, 2.0], [-37.0, 0]], [[1.0, 0], [6.0, 0], [41.0, 0]], [[1.0, 0], [0, -12.0], [-43.0, 0]], [[1.0, 0], [0, 0], [-47.0, 0]], [[1.0, 0], [0, -6.0], [-53.0, 0]], [[1.0, 0], [-12.0, 0], [59.0, 0]], [[1.0, 0], [2.0, 0], [61.0, 0]], [[1.0, 0], [0, 8.0], [-67.0, 0]], [[1.0, 0], [0, 0], [71.0, 0]], [[1.0, 0], [0, 2.0], [-73.0, 0]], [[1.0, 0], [8.0, 0], [79.0, 0]], [[1.0, 0], [0, -4.0], [-83.0, 0]], [[1.0, 0], [2.0, 0], [89.0, 0]], [[1.0, 0], [0, -10.0], [-97.0, 0]], [[1.0, 0], [-18.0, 0], [101.0, 0]], [[1.0, 0], [0, 0], [-103.0, 0]], [[1.0, 0], [0, 12.0], [-107.0, 0]], [[1.0, 0], [-2.0, 0], [109.0, 0]], [[1.0, 0], [0, 6.0], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 86, 'label': '2-2925-5.4-c1-0-86', 'leading_term': '1.2074548902114016631839751975698011287102627233560021955', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2925/2/c/e/2224/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.2074548902114017, 1.4023059299551384, 1.6004462681792258, 1.8014510232294743, 2.004749194642807, 2.209581573243717, 2.4149668316316726, 2.619677594711462, 2.8222276673952886, 3.0208709974670898, 3.213612427544215, 3.3982298670534083, 3.5723071954537597, 3.733276976888747, 3.8784719005424084, 4.0051837352648425, 4.110728480274615, 4.192516291115765, 4.248124653833408, 4.275373169281609, 4.272398197449913, 4.237725506114475, 4.170338978518546, 4.06974337157849, 3.9360190896196117, 3.7698669583671185, 3.5726410579654835, 3.346367808490004, 3.0937497009498527, 2.818152333014184, 2.5235737409504235, 2.214595414241065, 1.8963148310547784, 1.5742598525429798, 1.2542858506078518, 0.9424570037581518, 0.6449137632437724, 0.36772904940051065, 0.11675626730572007, -0.10252728806094547, -0.285177653606315, -0.4269377368716768, -0.5243826401642694, -0.5750521377846507, -0.5775657075715096, -0.5317156957005227, -0.4385345215768531, -0.30033230917826403, -0.12070195876982778, 0.09551056033717183, 0.3422720236527709, 0.6124642027643521, 0.8980218073556373, 1.1901042429302915, 1.4792981631324167, 1.7558466684473453, 2.009899933531701, 2.231781072960238, 2.4122602188109026, 2.542829120356214, 2.6159681199301272, 2.625397138701857, 2.566302344291821, 2.4355304840972463, 2.23174346046883, 1.955526593690921, 1.609445153293062, 1.1980451146003557, 0.727795682615545, 0.20697287681751397, -0.35451466280800903, -0.9453545645315067, -1.5531093077463731, -2.1645376568881343, -2.765950404021957, -3.3435903888588654, -3.884025550211716, -4.374542879445482, -4.803530642519358, -5.1608361496346555, -5.438086703774202, -5.628962159969658, -5.729408768147774, -5.737785629215882, -5.654937125136204, -5.484187031421043, -5.231252612249462, -4.904079748950654, -4.512602966449283, -4.0684369969903225, -3.584509150314931, -3.074644139389079, -2.5531150406060066, -2.034175655988139, -1.531590614357089, -1.0581800376872832, -0.6253954670518883, -0.24294297163614417, 0.08153203924710947, 0.3426857853529672, 0.537632897523342, 0.6660120532575354, 0.7299568739297347, 0.7339720952405027, 0.6847187255345795, 0.5907155632250698, 0.46196790498890944, 0.30953739323425117, 0.14506958580233567, -0.019702140999889105, -0.17345642639578954, -0.30576703489076257, -0.4075490828025435, -0.47144937226982836, -0.49216379843764746, -0.4666675377765147, -0.394347142004352, -0.27702762752988386, -0.1188920112690153, 0.07370467589975029, 0.2925202585954472, 0.5277980935308327, 0.768712411971133, 1.0038676816648362, 1.221830568401471, 1.4116711802500121, 1.5634893673854362, 1.6689019974676804, 1.7214683559950759, 1.7170331102217484, 1.653969552752212, 1.5333099882136887, 1.3587549812737172, 1.136558546744514, 0.8752920026153992, 0.5854948740745067, 0.2792266707065633, -0.03046169813711967, -0.33011389746149156, -0.6064853042302049, -0.8471629634913983, -1.041159167976118, -1.1794499640041944, -1.255431750810002, -1.2652723256773581, -1.2081371241744157, -1.0862768428117535, -0.9049688848852756, -0.6723118669127849, -0.3988794555832874, -0.09724674446499298, 0.218591109874603, 0.5338825177128659, 0.8338351790506234, 1.1043503454297714, 1.332740208222857, 1.5083928042410686, 1.6233503574933048, 1.6727702098914505, 1.6552423312492799, 1.5729436560066379, 1.4316169110979402, 1.2403698511171615, 1.0112995263656972, 0.7589549642782425, 0.4996600167563475, 0.2507256911868744, 0.029587642998372927, -0.14709068974944428, -0.2643058711267049, -0.3095488246432206, -0.273542668777732, -0.15084435679225236, 0.0597240648788427, 0.35484141544485737, 0.7266684853798677, 1.1630521488960701, 1.6479495739612737, 2.162058664791304, 2.6836302687040647, 3.1894279675155945, 3.655792964306737, 4.059765126179768, 4.380207030336703, 4.598876161612866, 4.701391383833028, 4.6780434847486125, 4.524405869391901, 4.241710109911133, 3.8369616857405218, 3.322783389384619, 2.7169869627736603, 2.0418869354144107, 1.3233836927803644, 0.5898548449277387, -0.12909564236968796, -0.8039729156962793, -1.4067481730080498, -1.9121714866061046, -2.2989756954339606, -2.550910595297124, -2.657553843215492, -2.6148550332332916, -2.425381850998626, -2.098251493823756, -1.6487459639416964, -1.09762564202075, -0.4701709247085728, 0.20500413388935346, 0.897310054545546, 1.575646376271878, 2.2099002949789, 2.772404708353068, 3.2392818980251707, 3.5916039141444895, 3.816309196638179, 3.906826698632351, 3.8633732185886753, 3.6929060926326187, 3.408731021393962, 3.0297827018556687, 2.579613167365782, 2.0851383882403236, 1.5752068978590559, 1.0790642449164427, 0.6247933471322502, 0.23781294092494004, -0.06048589386482325, -0.25389165517720014, -0.3322498105800473, -0.2920166905555224, -0.13645772358639194, 0.1245233958130005, 0.4749183049098634, 0.893484416276927, 1.3549078220358033, 1.8311979806313492, 2.2932403021996053, 2.712423392257443, 3.0622527701167552, 3.3198626788673766, 3.4673422236524853, 3.4928013263243516, 3.391115421768084, 3.1643047612372803, 2.821523744601219, 2.378656832634567, 1.8575391466259874, 1.2848406601576559, 0.690671767234821, 0.10698390335746871, -0.43414911482972, -0.9022759905906668, -1.270243748825282, -1.5157120583688177, -1.622421804772818, -1.5811465038961872], 'positive_zeros': ['1.95573353710866215063471080346750', '2.46681253267662140395938145967146', '3.52300394618510796945620991643852', '4.96285408740251922171154036978216', '5.52897037324362149421164876483023', '6.02446013151447915170303196879540', '6.95199897208198663300635311658999', '7.63295805216301077889711192274894', '8.488049936849601662791879763475562', '8.772690652692617962106754501794925'], 'prelabel': '2-2925-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.832829667102341, 'root_angle': -0.8524163823495667, 'root_number': '-0.89442719099991587856366946749251049417624734384461028971 - 0.44721359549995793928183473374625524708812367192230514485*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.42620819117478337', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.95573353710866215063471080347', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.46681253267662140395938145967', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52300394618510796945620991644', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 23.356242591224525, 'bad_primes': [3, 5, 13], 'central_character': '5.4', 'conductor': 2925, 'conductor_radical': 195, 'degree': 2, 'index': 86, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2925/2/c/e/2224/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-2925-5.4-c1-0-86', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-2925-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.832829667102341, 'root_angle': -0.42620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.95573353710866215063471080347', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2479186792202273735110721882136', 'Lhash_array': ['2479186792202273735110721882136'], 'label': '2-2925-5.4-c1-0-86', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2925/2/c/e/2224/1'}