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lfunc_lfunctions • Show schema
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{'Lhash': '1223789942935989924179969506451', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 5, 'a6': 0, 'a7': 18, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.481375204133265, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -5]]], 'bad_primes': [2, 3, 5], 'central_character': '720.1', 'coefficient_field': '1.1.1.1', 'conductor': 720, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1, -5], [1, -18, 343], [1, 16, 1331], [1, 6, 2197], [1, -6, 4913], [1, -124, 6859], [1, -42, 12167], [1, 142, 24389], [1, -188, 29791], [1, -202, 50653], [1, 54, 68921], [1, 66, 79507], [1, -38, 103823], [1, 738, 148877], [1, -564, 205379], [1, 262, 226981], [1, -554, 300763], [1, -140, 357911], [1, -882, 389017], [1, -1160, 493039], [1, -642, 571787], [1, -854, 704969], [1, 478, 912673], [1, -1794, 1030301], [1, 642, 1092727], [1, 850, 1225043], [1, -666, 1295029], [1, -1446, 1442897]], 'euler_factors_factorization': [[1], [1], [[[1, -5], 1]], [[[1, -18, 343], 1]], [[[1, 16, 1331], 1]], [[[1, 6, 2197], 1]], [[[1, -6, 4913], 1]], [[[1, -124, 6859], 1]], [[[1, -42, 12167], 1]], [[[1, 142, 24389], 1]], [[[1, -188, 29791], 1]], [[[1, -202, 50653], 1]], [[[1, 54, 68921], 1]], [[[1, 66, 79507], 1]], [[[1, -38, 103823], 1]], [[[1, 738, 148877], 1]], [[[1, -564, 205379], 1]], [[[1, 262, 226981], 1]], [[[1, -554, 300763], 1]], [[[1, -140, 357911], 1]], [[[1, -882, 389017], 1]], [[[1, -1160, 493039], 1]], [[[1, -642, 571787], 1]], [[[1, -854, 704969], 1]], [[[1, 478, 912673], 1]], [[[1, -1794, 1030301], 1]], [[[1, 642, 1092727], 1]], [[[1, 850, 1225043], 1]], [[[1, -666, 1295029], 1]], [[[1, -1446, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-720-1.1-c3-0-12', 'leading_term': '2.56703031447414847914397321109720000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 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True, 'root_analytic_conductor': 6.517773792034613, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 1724835619556034651, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.965400042184855393392491537749', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.15682645795474749058403339358', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.35635530913369842802878880504', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 42.481375204133265, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 720, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 5, 0, 18, 0, 0, 0, -16, 0, -6, 0, 0, 0, 6, 0, 124, 0, 0, 0, 42, 0, 25, 0, 0, 0, -142, 0, 188, 0, 0, 0, 90, 0, 202, 0, 0, 0, -54, 0, -66, 0, 0, 0, 38, 0, -19, 0, 0, 0, -738, 0, -80, 0, 0, 0, 564, 0, -262, 0, 0, 0, -30, 0, 554, 0, 0, 0, 140, 0, 882, 0, 0, 0, -288, 0, 1160, 0, 0, 0, 642, 0, 30, 0, 0, 0, 854, 0, -108, 0, 0, 0, 620, 0, -478, 0, 0, 0], 'euler11': [1, 16, 1331], 'euler13': [1, 6, 2197], 'euler17': [1, -6, 4913], 'euler19': [1, -124, 6859], 'euler2': [1, 0, 0], 'euler23': [1, -42, 12167], 'euler29': [1, 142, 24389], 'euler3': [1, 0, 0], 'euler31': [1, -188, 29791], 'euler37': [1, -202, 50653], 'euler41': [1, 54, 68921], 'euler43': [1, 66, 79507], 'euler47': [1, -38, 103823], 'euler5': [1, -5, 0], 'euler53': [1, 738, 148877], 'euler59': [1, -564, 205379], 'euler61': [1, 262, 226981], 'euler67': [1, -554, 300763], 'euler7': [1, -18, 343], 'euler71': [1, -140, 357911], 'euler73': [1, -882, 389017], 'euler79': [1, -1160, 493039], 'euler83': [1, -642, 571787], 'euler89': [1, -854, 704969], 'euler97': [1, 478, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -5, 0], [1, -18, 343], [1, 16, 1331], [1, 6, 2197], [1, -6, 4913], [1, -124, 6859], [1, -42, 12167], [1, 142, 24389], [1, -188, 29791], [1, -202, 50653], [1, 54, 68921], [1, 66, 79507], [1, -38, 103823], [1, 738, 148877], [1, -564, 205379], [1, 262, 226981], [1, -554, 300763], [1, -140, 357911], [1, -882, 389017], [1, -1160, 493039], [1, -642, 571787], [1, -854, 704969], [1, 478, 912673]], 'index': 12, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/720/4/a/ba/1/1', 'ModularForm/GL2/Q/holomorphic/720/4/a/ba'], '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': '2-720-1.1-c3-0-12', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-720-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.517773792034613, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1724835619556034651, 'z1': {'__RealLiteral__': 0, 'data': '0.965400042184855393392491537749', 'prec': 107}}
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lfunc_instances • Show schema
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id: 20487560
{'Lhash': '1223789942935989924179969506451', 'Lhash_array': ['1223789942935989924179969506451'], 'label': '2-720-1.1-c3-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/ba'}
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id: 24569834
{'Lhash': '1223789942935989924179969506451', 'Lhash_array': ['1223789942935989924179969506451'], 'label': '2-720-1.1-c3-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/ba/1/1'}