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lfunc_lfunctions • Show schema
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{'Lhash': '2142310321944752937473940070606', 'a10': -10, 'a2': 2, 'a3': 3, 'a4': 4, 'a5': -5, 'a6': 6, 'a7': 0, 'a8': 8, 'a9': 9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 86.73280770843874, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2]], [3, [1, -3]], [5, [1, 5]], [7, [1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1470.1', 'coefficient_field': '1.1.1.1', 'conductor': 1470, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1, -2], [1, -3], [1, 5], [1], [1, -16, 1331], [1, 58, 2197], [1, 34, 4913], [1, 64, 6859], [1, 16, 12167], [1, -62, 24389], [1, 60, 29791], [1, -150, 50653], [1, 474, 68921], [1, 292, 79507], [1, 240, 103823], [1, 662, 148877], [1, -324, 205379], [1, -514, 226981], [1, 372, 300763], [1, 412, 357911], [1, -770, 389017], [1, 560, 493039], [1, -852, 571787], [1, 1466, 704969], [1, -178, 912673], [1, 1278, 1030301], [1, -296, 1092727], [1, -1164, 1225043], [1, 778, 1295029], [1, 42, 1442897]], 'euler_factors_factorization': [[[[1, -2], 1]], [[[1, -3], 1]], [[[1, 5], 1]], [1], [[[1, -16, 1331], 1]], [[[1, 58, 2197], 1]], [[[1, 34, 4913], 1]], [[[1, 64, 6859], 1]], [[[1, 16, 12167], 1]], [[[1, -62, 24389], 1]], [[[1, 60, 29791], 1]], [[[1, -150, 50653], 1]], [[[1, 474, 68921], 1]], [[[1, 292, 79507], 1]], [[[1, 240, 103823], 1]], [[[1, 662, 148877], 1]], [[[1, -324, 205379], 1]], [[[1, -514, 226981], 1]], [[[1, 372, 300763], 1]], [[[1, 412, 357911], 1]], [[[1, -770, 389017], 1]], [[[1, 560, 493039], 1]], [[[1, -852, 571787], 1]], [[[1, 1466, 704969], 1]], [[[1, -178, 912673], 1]], [[[1, 1278, 1030301], 1]], [[[1, -296, 1092727], 1]], [[[1, -1164, 1225043], 1]], [[[1, 778, 1295029], 1]], [[[1, 42, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 77, 'label': '2-1470-1.1-c3-0-77', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': 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'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 881825251048302894, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.68998485983365503426229209025', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.66012898788104673699929867276', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.59471501376483369452689650355', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 86.73280770843874, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 1470, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 2, 3, 4, -5, 6, 0, 8, 9, -10, 16, 12, -58, 0, -15, 16, -34, 18, -64, -20, 0, 32, -16, 24, 25, -116, 27, 0, 62, -30, -60, 32, 48, -68, 0, 36, 150, -128, -174, -40, -474, 0, -292, 64, -45, -32, -240, 48, 0, 50, -102, -232, -662, 54, -80, 0, -192, 124, 324, -60, 514, -120, 0, 64, 290, 96, -372, -136, -48, 0, -412, 72, 770, 300, 75, -256, 0, -348, -560, -80, 81, -948, 852, 0, 170, -584, 186, 128, -1466, -90, 0, -64, -180, -480, 320, 96, 178, 0, 144, 100], 'euler11': [1, -16, 1331], 'euler13': [1, 58, 2197], 'euler17': [1, 34, 4913], 'euler19': [1, 64, 6859], 'euler2': [1, -2, 0], 'euler23': [1, 16, 12167], 'euler29': [1, -62, 24389], 'euler3': [1, -3, 0], 'euler31': [1, 60, 29791], 'euler37': [1, -150, 50653], 'euler41': [1, 474, 68921], 'euler43': [1, 292, 79507], 'euler47': [1, 240, 103823], 'euler5': [1, 5, 0], 'euler53': [1, 662, 148877], 'euler59': [1, -324, 205379], 'euler61': [1, -514, 226981], 'euler67': [1, 372, 300763], 'euler7': [1, 0, 0], 'euler71': [1, 412, 357911], 'euler73': [1, -770, 389017], 'euler79': [1, 560, 493039], 'euler83': [1, -852, 571787], 'euler89': [1, 1466, 704969], 'euler97': [1, -178, 912673], 'euler_factors': [[1, -2, 0], [1, -3, 0], [1, 5, 0], [1, 0, 0], [1, -16, 1331], [1, 58, 2197], [1, 34, 4913], [1, 64, 6859], [1, 16, 12167], [1, -62, 24389], [1, 60, 29791], [1, -150, 50653], [1, 474, 68921], [1, 292, 79507], [1, 240, 103823], [1, 662, 148877], [1, -324, 205379], [1, -514, 226981], [1, 372, 300763], [1, 412, 357911], [1, -770, 389017], [1, 560, 493039], [1, -852, 571787], [1, 1466, 704969], [1, -178, 912673]], 'index': 77, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1470/4/a/z/1/1', 'ModularForm/GL2/Q/holomorphic/1470/4/a/z'], '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': '2-1470-1.1-c3-0-77', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-1470-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.313045028799053, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 881825251048302894, 'z1': {'__RealLiteral__': 0, 'data': '1.68998485983365503426229209025', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21229139
{'Lhash': '2142310321944752937473940070606', 'Lhash_array': ['2142310321944752937473940070606'], 'factors': ['2-1470-1.1-c3-0-77'], 'label': '2-1470-1.1-c3-0-77', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1470/4/a/z'}
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id: 24591403
{'Lhash': '2142310321944752937473940070606', 'Lhash_array': ['2142310321944752937473940070606'], 'factors': ['2-1470-1.1-c3-0-77'], 'label': '2-1470-1.1-c3-0-77', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1470/4/a/z/1/1'}