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lfunc_lfunctions • Show schema
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{'Lhash': '1587567563940657641462441556035', 'a10': 0, 'a2': 0, 'a3': -7, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 7, 'a8': 0, 'a9': 22, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.30133700401845, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1, -7]]], 'bad_primes': [2, 5, 7], 'central_character': '700.1', 'coefficient_field': '1.1.1.1', 'conductor': 700, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[1], [1, 7, 27], [1], [1, -7], [1, 7, 1331], [1, 3, 2197], [1, 61, 4913], [1, -48, 6859], [1, 58, 12167], [1, -219, 24389], [1, -298, 29791], [1, -170, 50653], [1, -50, 68921], [1, 484, 79507], [1, 131, 103823], [1, 210, 148877], [1, 782, 205379], [1, -488, 226981], [1, 494, 300763], [1, 240, 357911], [1, 58, 389017], [1, 1065, 493039], [1, 1036, 571787], [1, -608, 704969], [1, -1339, 912673], [1, 1076, 1030301], [1, -229, 1092727], [1, -1608, 1225043], [1, 371, 1295029], [1, 978, 1442897]], 'euler_factors_factorization': [[1], [[[1, 7, 27], 1]], [1], [[[1, -7], 1]], [[[1, 7, 1331], 1]], [[[1, 3, 2197], 1]], [[[1, 61, 4913], 1]], [[[1, -48, 6859], 1]], [[[1, 58, 12167], 1]], [[[1, -219, 24389], 1]], [[[1, -298, 29791], 1]], [[[1, -170, 50653], 1]], [[[1, -50, 68921], 1]], [[[1, 484, 79507], 1]], [[[1, 131, 103823], 1]], [[[1, 210, 148877], 1]], [[[1, 782, 205379], 1]], [[[1, -488, 226981], 1]], [[[1, 494, 300763], 1]], [[[1, 240, 357911], 1]], [[[1, 58, 389017], 1]], [[[1, 1065, 493039], 1]], [[[1, 1036, 571787], 1]], [[[1, -608, 704969], 1]], [[[1, -1339, 912673], 1]], [[[1, 1076, 1030301], 1]], [[[1, -229, 1092727], 1]], [[[1, -1608, 1225043], 1]], [[[1, 371, 1295029], 1]], [[[1, 978, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 16, 'label': '2-700-1.1-c3-0-16', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 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{'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 380506571210517145, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.25236998558974372685885174302', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.80702106357602276264079818460', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.44064820003552335328788621536', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41.30133700401845, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 700, 'conductor_radical': 70, 'degree': 2, 'dirichlet_coefficients': [1, 0, -7, 0, 0, 0, 7, 0, 22, 0, -7, 0, -3, 0, 0, 0, -61, 0, 48, 0, -49, 0, -58, 0, 0, 0, 35, 0, 219, 0, 298, 0, 49, 0, 0, 0, 170, 0, 21, 0, 50, 0, -484, 0, 0, 0, -131, 0, 49, 0, 427, 0, -210, 0, 0, 0, -336, 0, -782, 0, 488, 0, 154, 0, 0, 0, -494, 0, 406, 0, -240, 0, -58, 0, 0, 0, -49, 0, -1065, 0, -839, 0, -1036, 0, 0, 0, -1533, 0, 608, 0, -21, 0, -2086, 0, 0, 0, 1339, 0, -154, 0], 'euler11': [1, 7, 1331], 'euler13': [1, 3, 2197], 'euler17': [1, 61, 4913], 'euler19': [1, -48, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 58, 12167], 'euler29': [1, -219, 24389], 'euler3': [1, 7, 27], 'euler31': [1, -298, 29791], 'euler37': [1, -170, 50653], 'euler41': [1, -50, 68921], 'euler43': [1, 484, 79507], 'euler47': [1, 131, 103823], 'euler5': [1, 0, 0], 'euler53': [1, 210, 148877], 'euler59': [1, 782, 205379], 'euler61': [1, -488, 226981], 'euler67': [1, 494, 300763], 'euler7': [1, -7, 0], 'euler71': [1, 240, 357911], 'euler73': [1, 58, 389017], 'euler79': [1, 1065, 493039], 'euler83': [1, 1036, 571787], 'euler89': [1, -608, 704969], 'euler97': [1, -1339, 912673], 'euler_factors': [[1, 0, 0], [1, 7, 27], [1, 0, 0], [1, -7, 0], [1, 7, 1331], [1, 3, 2197], [1, 61, 4913], [1, -48, 6859], [1, 58, 12167], [1, -219, 24389], [1, -298, 29791], [1, -170, 50653], [1, -50, 68921], [1, 484, 79507], [1, 131, 103823], [1, 210, 148877], [1, 782, 205379], [1, -488, 226981], [1, 494, 300763], [1, 240, 357911], [1, 58, 389017], [1, 1065, 493039], [1, 1036, 571787], [1, -608, 704969], [1, -1339, 912673]], 'index': 16, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/700/4/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/700/4/a/c'], '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': '2-700-1.1-c3-0-16', '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': '2-700-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.426611626978749, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 380506571210517145, 'z1': {'__RealLiteral__': 0, 'data': '1.25236998558974372685885174302', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20423957
{'Lhash': '1587567563940657641462441556035', 'Lhash_array': ['1587567563940657641462441556035'], 'factors': ['2-700-1.1-c3-0-16'], 'label': '2-700-1.1-c3-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/700/4/a/c'}
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id: 24569175
{'Lhash': '1587567563940657641462441556035', 'Lhash_array': ['1587567563940657641462441556035'], 'factors': ['2-700-1.1-c3-0-16'], 'label': '2-700-1.1-c3-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/700/4/a/c/1/1'}