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lfunc_lfunctions • Show schema
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{'Lhash': '1922565960609834711847411216811', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.1325108752343365, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]]], 'bad_primes': [2, 3], 'central_character': '768.1', 'coefficient_field': '1.1.1.1', 'conductor': 768, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, -2, 5], [1, -2, 7], [1, 0, 11], [1, -4, 13], [1, 2, 17], [1, 4, 19], [1, 4, 23], [1, -6, 29], [1, -2, 31], [1, -8, 37], [1, 2, 41], [1, 4, 43], [1, 12, 47], [1, -6, 53], [1, -4, 59], [1, 0, 61], [1, -12, 67], [1, 12, 71], [1, -6, 73], [1, -10, 79], [1, 16, 83], [1, -10, 89], [1, 2, 97], [1, 10, 101], [1, -6, 103], [1, 12, 107], [1, 4, 109], [1, 6, 113]], 'euler_factors_factorization': [[1], [[[1, -1], 1]], [[[1, -2, 5], 1]], [[[1, -2, 7], 1]], [[[1, 0, 11], 1]], [[[1, -4, 13], 1]], [[[1, 2, 17], 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1.504789884486054, 2.799445333976151, 3.6042885712319124, 3.656888911941637, 2.9461674424501085, 1.7183958130925163], 'positive_zeros': ['1.51663712403377833666587682944114', '2.47902910741521785662962015803201', '3.87678607648250663694375372790412', '4.84641162437662246944769643987818', '6.03168549170604009889878923550468', '6.68785915312412950432661260762243', '8.137356992201587112320496664394305', '8.420702100846206882694460804855721', '9.497476761258686531860854084972917', '10.21776117870948491031897964138770'], 'prelabel': '2-768-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.4763906951921655, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 2016428330863064073, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.51663712403377833666587682944', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.47902910741521785662962015803', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.87678607648250663694375372790', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.1325108752343365, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 768, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 2, 0, 2, 0, 1, 0, 0, 0, 4, 0, 2, 0, -2, 0, -4, 0, 2, 0, -4, 0, -1, 0, 1, 0, 6, 0, 2, 0, 0, 0, 4, 0, 8, 0, 4, 0, -2, 0, -4, 0, 2, 0, -12, 0, -3, 0, -2, 0, 6, 0, 0, 0, -4, 0, 4, 0, 0, 0, 2, 0, 8, 0, 12, 0, -4, 0, -12, 0, 6, 0, -1, 0, 0, 0, 10, 0, 1, 0, -16, 0, -4, 0, 6, 0, 10, 0, 8, 0, 2, 0, -8, 0, -2, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -4, 13], 'euler17': [1, 2, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, -2, 31], 'euler37': [1, -8, 37], 'euler41': [1, 2, 41], 'euler43': [1, 4, 43], 'euler47': [1, 12, 47], 'euler5': [1, -2, 5], 'euler53': [1, -6, 53], 'euler59': [1, -4, 59], 'euler61': [1, 0, 61], 'euler67': [1, -12, 67], 'euler7': [1, -2, 7], 'euler71': [1, 12, 71], 'euler73': [1, -6, 73], 'euler79': [1, -10, 79], 'euler83': [1, 16, 83], 'euler89': [1, -10, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, -2, 5], [1, -2, 7], [1, 0, 11], [1, -4, 13], [1, 2, 17], [1, 4, 19], [1, 4, 23], [1, -6, 29], [1, -2, 31], [1, -8, 37], [1, 2, 41], [1, 4, 43], [1, 12, 47], [1, -6, 53], [1, -4, 59], [1, 0, 61], [1, -12, 67], [1, 12, 71], [1, -6, 73], [1, -10, 79], [1, 16, 83], [1, -10, 89], [1, 2, 97]], 'index': 8, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/768/h', 'ModularForm/GL2/Q/holomorphic/768/2/a/h/1/1', 'ModularForm/GL2/Q/holomorphic/768/2/a/h'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, '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': '2-768-1.1-c1-0-8', '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': '2-768-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.4763906951921655, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2016428330863064073, 'z1': {'__RealLiteral__': 0, 'data': '1.51663712403377833666587682944', 'prec': 103}}
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lfunc_instances • Show schema
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id: 14399310
{'Lhash': '1922565960609834711847411216811', 'Lhash_array': ['1922565960609834711847411216811'], 'label': '2-768-1.1-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/768/2/a/h'}
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id: 24550473
{'Lhash': '1922565960609834711847411216811', 'Lhash_array': ['1922565960609834711847411216811'], 'label': '2-768-1.1-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/768/2/a/h/1/1'}
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id: 32223
{'Lhash': '2016428330863064073', 'Lhash_array': ['2016428330863064073'], 'label': '2-768-1.1-c1-0-8', 'type': 'ECQ', 'url': 'EllipticCurve/Q/768/h'}