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lfunc_lfunctions • Show schema
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{'Lhash': '1229042326076679671999262957992', 'a10': 25, 'a2': -5, 'a3': -1, 'a4': 17, 'a5': -5, 'a6': 5, 'a7': -2, 'a8': -45, 'a9': -26, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 61.65699595599897, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [1, 5]], [11, [1, 11]], [19, [1, -19]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.1', 'coefficient_field': '1.1.1.1', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 2, 'euler_factors': [[1, 5, 8], [1, 1, 27], [1, 5], [1, 2, 343], [1, 11], [1, 7, 2197], [1, -14, 4913], [1, -19], [1, -55, 12167], [1, 26, 24389], [1, -261, 29791], [1, 126, 50653], [1, 381, 68921], [1, -387, 79507], [1, -189, 103823], [1, 404, 148877], [1, -746, 205379], [1, -79, 226981], [1, -537, 300763], [1, 824, 357911], [1, -169, 389017], [1, 338, 493039], [1, -601, 571787], [1, 762, 704969], [1, -866, 912673], [1, -1006, 1030301], [1, -2002, 1092727], [1, -1144, 1225043], [1, -766, 1295029], [1, 2042, 1442897]], 'euler_factors_factorization': [[[[1, 5, 8], 1]], [[[1, 1, 27], 1]], [[[1, 5], 1]], [[[1, 2, 343], 1]], [[[1, 11], 1]], [[[1, 7, 2197], 1]], [[[1, -14, 4913], 1]], [[[1, -19], 1]], [[[1, -55, 12167], 1]], [[[1, 26, 24389], 1]], [[[1, -261, 29791], 1]], [[[1, 126, 50653], 1]], [[[1, 381, 68921], 1]], [[[1, -387, 79507], 1]], [[[1, -189, 103823], 1]], [[[1, 404, 148877], 1]], [[[1, -746, 205379], 1]], [[[1, -79, 226981], 1]], [[[1, -537, 300763], 1]], [[[1, 824, 357911], 1]], [[[1, -169, 389017], 1]], [[[1, 338, 493039], 1]], [[[1, -601, 571787], 1]], [[[1, 762, 704969], 1]], [[[1, -866, 912673], 1]], [[[1, -1006, 1030301], 1]], [[[1, -2002, 1092727], 1]], [[[1, -1144, 1225043], 1]], [[[1, -766, 1295029], 1]], [[[1, 2042, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 88, 'label': '2-1045-1.1-c3-0-88', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 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'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 898936869737437533, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.969543441903787488862079112677', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.36635898609352705579425547933', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.29836247110109601722925020108', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 61.65699595599897, 'bad_primes': [5, 11, 19], 'central_character': '1.1', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 2, 'dirichlet_coefficients': [1, -5, -1, 17, -5, 5, -2, -45, -26, 25, -11, -17, -7, 10, 5, 89, 14, 130, 19, -85, 2, 55, 55, 45, 25, 35, 53, -34, -26, -25, 261, -85, 11, -70, 10, -442, -126, -95, 7, 225, -381, -10, 387, -187, 130, -275, 189, -89, -339, -125, -14, -119, -404, -265, 55, 90, -19, 130, 746, 85, 79, -1305, 52, -287, 35, -55, 537, 238, -55, -50, -824, 1170, 169, 630, -25, 323, 22, -35, -338, -445, 649, 1905, 601, 34, -70, -1935, 26, 495, -762, -650, 14, 935, -261, -945, -95, 85, 866, 1695, 286, 425], 'euler11': [1, 11, 0], 'euler13': [1, 7, 2197], 'euler17': [1, -14, 4913], 'euler19': [1, -19, 0], 'euler2': [1, 5, 8], 'euler23': [1, -55, 12167], 'euler29': [1, 26, 24389], 'euler3': [1, 1, 27], 'euler31': [1, -261, 29791], 'euler37': [1, 126, 50653], 'euler41': [1, 381, 68921], 'euler43': [1, -387, 79507], 'euler47': [1, -189, 103823], 'euler5': [1, 5, 0], 'euler53': [1, 404, 148877], 'euler59': [1, -746, 205379], 'euler61': [1, -79, 226981], 'euler67': [1, -537, 300763], 'euler7': [1, 2, 343], 'euler71': [1, 824, 357911], 'euler73': [1, -169, 389017], 'euler79': [1, 338, 493039], 'euler83': [1, -601, 571787], 'euler89': [1, 762, 704969], 'euler97': [1, -866, 912673], 'euler_factors': [[1, 5, 8], [1, 1, 27], [1, 5, 0], [1, 2, 343], [1, 11, 0], [1, 7, 2197], [1, -14, 4913], [1, -19, 0], [1, -55, 12167], [1, 26, 24389], [1, -261, 29791], [1, 126, 50653], [1, 381, 68921], [1, -387, 79507], [1, -189, 103823], [1, 404, 148877], [1, -746, 205379], [1, -79, 226981], [1, -537, 300763], [1, 824, 357911], [1, -169, 389017], [1, 338, 493039], [1, -601, 571787], [1, 762, 704969], [1, -866, 912673]], 'index': 88, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1045/4/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/1045/4/a/a'], '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': '2-1045-1.1-c3-0-88', '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': '2-1045-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.85219688724111, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 898936869737437533, 'z1': {'__RealLiteral__': 0, 'data': '0.969543441903787488862079112677', 'prec': 107}}
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lfunc_instances • Show schema
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id: 20042524
{'Lhash': '1229042326076679671999262957992', 'Lhash_array': ['1229042326076679671999262957992'], 'label': '2-1045-1.1-c3-0-88', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1045/4/a/a'}
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id: 24580813
{'Lhash': '1229042326076679671999262957992', 'Lhash_array': ['1229042326076679671999262957992'], 'label': '2-1045-1.1-c3-0-88', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1045/4/a/a/1/1'}