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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 4, 'A8': 0, 'A9': 0, 'Lhash': '1019325760818065925', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 247.2168446578842, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -1]], [43, [1, -1]]], 'bad_primes': [2, 3, 5, 43], 'central_character': '30960.1', 'coefficient_field': '1.1.1.1', 'conductor': 30960, 'conductor_radical': 1290, 'degree': 2, 'euler_factors': [[1], [1], [1, -1], [1, -4, 7], [1, 4, 11], [1, -4, 13], [1, 4, 17], [1, 4, 19], [1, -8, 23], [1, 6, 29], [1, -4, 31], [1, -2, 37], [1, 10, 41], [1, -1], [1, -4, 47], [1, -2, 53], [1, 12, 59], [1, 0, 61], [1, 8, 67], [1, 12, 71], [1, 14, 73], [1, 8, 79], [1, -6, 83], [1, -4, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 49, 'label': '2-30960-1.1-c1-0-49', 'leading_term': '6.9603841992', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/30960/bz', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.64555765206865, 2.714614276386444, 2.704841372099663, 1.568142408435196, 0.0305377109971209, -0.7432847194855359, -0.1317307363259161, 1.178984202490245, 1.642276155042986, 0.4259567630417801, -1.402314799684728, -1.646931299974835, 0.6671837078743917, 3.851163603949597, 5.006343693669796, 3.153377048748521, 0.4335539843909227, -0.349973246831731, 0.9323460813135928, 1.788222169369309, 0.6505652123427582, -0.8164189003641417, -0.06954802754119666, 2.355102729160138, 3.100913777596975, 0.6499655436483737, -2.121282133145392, -1.625120926336259, 1.382963748404244, 2.798432366890613, 1.038110939941636, -0.861369038026439, -0.1066734910569814, 1.603620667100881, 1.235805953804643, -0.09497295430135469, 1.408867205817667, 5.633919976968637, 7.652510957562325, 4.759748024609537, 0.5673923000550227, -0.5281903938017446, 0.3945414567356465, -0.1572089565419648, -1.470942354214235, -0.2577615858661842, 2.343086506235823, 1.42949227393274, -3.36000605162304, -6.195166852775828, -3.819996066726729, -0.3102398134223913, 0.1759829631347756, -0.1000417489334785, 2.156860507076891, 4.376198029181899, 2.669680782506271, -0.600120859704213, -0.6359706301656741, 1.365736561025673, 0.9933738150818513, -0.5301504295547088, 1.436098734222754, 5.276938650955819, 4.69006606071589, -0.2162784390472745, -2.610824888370364, -0.4764566139763732, 0.866371849579921, -0.8537342226013183, -1.532452189782737, 0.2364896271690079, 0.4745311694958002, -1.394920535897494, -1.016782234937612, 1.084598198683685, -1.267583214363116, -7.834407631937646, -10.13162295669881, -5.228898129404513, -0.3433473995443055, -0.1176191857405086, -0.6035491972602381, 0.741473768423273, 0.7810053838592114, -0.490705230346514, 1.167198213303279, 4.103796822685721, 1.888260971509511, -3.880829435244576, -4.848293217230924, -0.6421307684813139, 1.173811734772191, -0.512323114794532, -0.0854157232519104, 2.095468607829421, 1.034821530643384, -1.341934516079563, 0.0617071569285163, 2.303218890545716, 0.351014797681468, -1.926262422092729, 0.3873292007334836, 2.673238447443224, 0.2145820066612104, -2.03156002933276, -0.1172256139792034, 0.6053110381488879, -2.640622327081905, -3.732818131014885, -0.6649378381480453, 0.2755540654877392, -1.856652584237443, -1.07983307402793, 1.778559005491638, 0.7251226065647741, -1.646833643529974, 0.8462569988073981, 4.226103336773955, 2.027366510441986], 'positive_zeros': ['1.255727938678685', '1.776843263210540', '2.555422519113520', '3.196199217105689', '4.310604716839754', '4.594983342024729', '5.339942111119706', '5.758455459159680', '6.548239288904613', '7.139938141099991', '7.856766182821188', '8.264187848849934', '8.963261274437155', '9.093592006945853', '10.30503455742277', '10.63881458531797', '10.97265485238109', '11.52368901145783', '12.08567165085941', '13.04160471982081', '13.30819925287600', '13.52451174666502', '14.44103250115402', '14.82711768633896', '15.38051325301860', '15.63638039541242', '16.48883171620018', '17.04552360676599', '17.39975557273104', '17.96752060607184', '18.32000781704481', '18.85519716240642', '19.18317569512801'], 'prelabel': '2-30960-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.72313087962713, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1019325760818065925, 'z1': {'__RealLiteral__': 0, 'data': '1.255727938678685', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.776843263210540', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.555422519113520', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 247.2168446578842, 'bad_primes': [2, 3, 5, 43], 'central_character': '1.1', 'conductor': 30960, 'conductor_radical': 1290, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, 4, 0, 0, 0, -4, 0, 4, 0, 0, 0, -4, 0, -4, 0, 0, 0, 8, 0, 1, 0, 0, 0, -6, 0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 0, -10, 0, 1, 0, 0, 0, 4, 0, 9, 0, 0, 0, 2, 0, -4, 0, 0, 0, -12, 0, 0, 0, 0, 0, 4, 0, -8, 0, 0, 0, -12, 0, -14, 0, 0, 0, -16, 0, -8, 0, 0, 0, 6, 0, -4, 0, 0, 0, 4, 0, 16, 0, 0, 0, -4, 0, 2, 0, 0, 0], 'euler11': [1, 4, 11], 'euler13': [1, -4, 13], 'euler17': [1, 4, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -8, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, -2, 37], 'euler41': [1, 10, 41], 'euler43': [1, -1, 0], 'euler47': [1, -4, 47], 'euler5': [1, -1, 0], 'euler53': [1, -2, 53], 'euler59': [1, 12, 59], 'euler61': [1, 0, 61], 'euler67': [1, 8, 67], 'euler7': [1, -4, 7], 'euler71': [1, 12, 71], 'euler73': [1, 14, 73], 'euler79': [1, 8, 79], 'euler83': [1, -6, 83], 'euler89': [1, -4, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -1, 0], [1, -4, 7], [1, 4, 11], [1, -4, 13], [1, 4, 17], [1, 4, 19], [1, -8, 23], [1, 6, 29], [1, -4, 31], [1, -2, 37], [1, 10, 41], [1, -1, 0], [1, -4, 47], [1, -2, 53], [1, 12, 59], [1, 0, 61], [1, 8, 67], [1, 12, 71], [1, 14, 73], [1, 8, 79], [1, -6, 83], [1, -4, 89], [1, -2, 97]], 'index': 49, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/30960/bz'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-30960-1.1-c1-0-49', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-30960-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.72313087962713, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1019325760818065925, 'z1': {'__RealLiteral__': 0, 'data': '1.255727938678685', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1019325760818065925', 'Lhash_array': ['1019325760818065925'], 'label': '2-30960-1.1-c1-0-49', 'type': 'ECQ', 'url': 'EllipticCurve/Q/30960/bz'}