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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': -1, 'A6': 0, 'A7': 0, 'A8': -1, 'A9': 0, 'Lhash': '943754031939761683', 'a10': [0.31622776601683794, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 809.9226277018473, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [5, [1, 1]], [7, [1]], [23, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '101430.1', 'coefficient_field': '1.1.1.1', 'conductor': 101430, 'conductor_radical': 4830, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, 1], [1], [1, -4, 11], [1, -2, 13], [1, -6, 17], [1, -4, 19], [1, -1], [1, 2, 29], [1, 4, 31], [1, 6, 37], [1, -10, 41], [1, -4, 43], [1, 12, 47], [1, -6, 53], [1, 4, 59], [1, -14, 61], [1, 12, 67], [1, -12, 71], [1, 10, 73], [1, 8, 79], [1, 4, 83], [1, 6, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 36, 'label': '2-101430-1.1-c1-0-36', 'leading_term': '2.03621782068', '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': 0, 'origin': 'EllipticCurve/Q/101430/bg', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.036217820677184, 1.527130278074434, 0.3046203421757742, -0.7785277777127086, -0.842610639556075, 0.02586165585681765, 0.4611910982088844, -0.843837386592466, -3.231268251838523, -4.167280574099408, -2.053298947000959, 1.354170134666004, 2.585942285236943, 0.8542952787740125, -0.6947329791785744, 0.5870500994049308, 2.52073891222846, 0.7998015346790887, -4.201817002456287, -6.737900639289569, -3.413714194163853, 1.579293752083648, 2.203853455011339, -0.7777630006951032, -1.530365625412054, 1.460167757512515, 3.37956289440102, 1.379912438047722, -0.9944390982000713, -0.3994542718671144, 0.750899940894406, -0.5729194153152452, -2.156807244131926, -0.9457228426571057, 0.8874691542102501, 0.0302765028035342, -1.593850739371995, -0.7361960315492471, 0.6294807763548724, -0.5903379841645446, -1.856995955260512, 0.2393767636326893, 2.585712216266444, 0.9478260704907882, -1.730303944042927, -0.9475033284973428, 0.7069914840777409, -0.444469559944458, -1.003660871731146, 1.925648664580811, 2.986875918276264, -0.9269983943732845, -2.055168538882835, 4.522647826653637, 9.631128384265073, 5.241462878082559, -1.280305529640475, -1.278637167301047, 0.4082404526486881, -2.168006266661608, -3.612696095916812, 0.3451518915437849, 3.078216809268553, 0.4072330347072904, -1.710938651947542, -0.2889749553063286, -0.06612154876757732, -1.407701767103957, 0.1882504635967111, 2.648587813092456, 1.182793129977652, -0.8480547447851717, 0.806338119356234, 1.914589844265552, -0.5187746743476657, -1.634577385211811, 0.03102212379660085, -0.2221727638536942, -1.689788278932089, -0.3545432163448354, 0.4836388831943188, -2.239794955644938, -2.817516432139329, 0.552920187207455, 0.8098760735605495, -1.160703540380552, 3.013492194330177, 8.947594673565918, 6.04179283829121, -0.02496254383081848, 1.286937516782464, 3.997744767854262, 1.014894716952229, 0.380855753285049, 5.604130438438937, 6.24236183081633, 0.7871058760334237, -0.5065043891177528, 1.845821469310533, 0.2935290196434295, -1.445967168943435, 1.343076736459656, 2.50956910644118, -0.00509824004826558, 0.2172346871067356, 1.911126092825879, -0.3745588503962205, -2.330827614808116, -0.003074630527974755, 1.188159154322555, -0.2596119240454508, 0.003641938981124096, 0.2389660791201334, -1.067888118185806, 1.323230725724714, 5.496094231684231, 3.46032913884214, -0.6933447496956956, 0.4730289130667886, 1.392385035376284, -1.15039634929188], 'positive_zeros': ['0.5584991928536916', '1.243202588622378', '1.633370397685812', '2.644978277644576', '3.348032569531419', '3.683220506463055', '4.295884306685512', '5.157285266893387', '5.686218798519551', '6.145922088701930', '6.866516397011782', '7.310052546161524', '7.681300958837512', '8.353178311974988', '8.753808717738787', '9.349437007775974', '9.675878102683762', '10.23137947883786', '10.82222311634626', '11.35810694287795', '11.69068323473766', '12.10848450315127', '12.69892433760097', '13.10379556077776', '13.93162932677023', '14.37963915143480', '14.57896971768782', '15.23255170223481', '15.77804695904616', '16.29972318354685', '16.48654118144701', '16.98457466719956', '17.60411659651791', '17.91956118918136', '18.45525704848647', '18.99448717444607', '19.21477496818346', '19.79191752265101'], 'prelabel': '2-101430-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 28.45913961633147, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 943754031939761683, 'z1': {'__RealLiteral__': 0, 'data': '0.5584991928536916', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.243202588622378', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.633370397685812', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 809.9226277018473, 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '1.1', 'conductor': 101430, 'conductor_radical': 4830, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, -1, 0, 0, -1, 0, 1, 4, 0, 2, 0, 0, 1, 6, 0, 4, -1, 0, -4, 1, 0, 1, -2, 0, 0, -2, 0, -4, -1, 0, -6, 0, 0, -6, -4, 0, 1, 10, 0, 4, 4, 0, -1, -12, 0, 0, -1, 0, 2, 6, 0, -4, 0, 0, 2, -4, 0, 14, 4, 0, 1, -2, 0, -12, 6, 0, 0, 12, 0, -10, 6, 0, 4, 0, 0, -8, -1, 0, -10, -4, 0, -6, -4, 0, -4, -6, 0, 0, 1, 0, 12, -4, 0, -2, 0, 0, 1], 'euler11': [1, -4, 11], 'euler13': [1, -2, 13], 'euler17': [1, -6, 17], 'euler19': [1, -4, 19], 'euler2': [1, 1, 0], 'euler23': [1, -1, 0], 'euler29': [1, 2, 29], 'euler3': [1, 0, 0], 'euler31': [1, 4, 31], 'euler37': [1, 6, 37], 'euler41': [1, -10, 41], 'euler43': [1, -4, 43], 'euler47': [1, 12, 47], 'euler5': [1, 1, 0], 'euler53': [1, -6, 53], 'euler59': [1, 4, 59], 'euler61': [1, -14, 61], 'euler67': [1, 12, 67], 'euler7': [1, 0, 0], 'euler71': [1, -12, 71], 'euler73': [1, 10, 73], 'euler79': [1, 8, 79], 'euler83': [1, 4, 83], 'euler89': [1, 6, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 1, 0], [1, 0, 0], [1, -4, 11], [1, -2, 13], [1, -6, 17], [1, -4, 19], [1, -1, 0], [1, 2, 29], [1, 4, 31], [1, 6, 37], [1, -10, 41], [1, -4, 43], [1, 12, 47], [1, -6, 53], [1, 4, 59], [1, -14, 61], [1, 12, 67], [1, -12, 71], [1, 10, 73], [1, 8, 79], [1, 4, 83], [1, 6, 89], [1, 2, 97]], 'index': 36, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/101430/bg'], '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': '2-101430-1.1-c1-0-36', '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': '2-101430-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 28.45913961633147, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 943754031939761683, 'z1': {'__RealLiteral__': 0, 'data': '0.5584991928536916', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '943754031939761683', 'Lhash_array': ['943754031939761683'], 'label': '2-101430-1.1-c1-0-36', 'type': 'ECQ', 'url': 'EllipticCurve/Q/101430/bg'}