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lfunc_lfunctions • Show schema
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{'Lhash': '2057667365139486700975187179967', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -3, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.62621853429843, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, -1]], [13, [1, 1]]], 'bad_primes': [2, 7, 13], 'central_character': '1456.1', 'coefficient_field': '1.1.1.1', 'conductor': 1456, 'conductor_radical': 182, 'degree': 2, 'euler_factors': [[1], [1, 0, 3], [1, 3, 5], [1, -1], [1, -6, 11], [1, 1], [1, -4, 17], [1, 5, 19], [1, 3, 23], [1, 5, 29], [1, -3, 31], [1, 4, 37], [1, 6, 41], [1, -1, 43], [1, 7, 47], [1, 9, 53], [1, 8, 59], [1, 10, 61], [1, -6, 67], [1, -8, 71], [1, 13, 73], [1, 3, 79], [1, 15, 83], [1, -3, 89], [1, -7, 97], [1, 14, 101], [1, -4, 103], [1, -4, 107], [1, 2, 109], [1, 3, 113]], 'euler_factors_factorization': [[1], [[[1, 0, 3], 1]], [[[1, 3, 5], 1]], [[[1, -1], 1]], [[[1, -6, 11], 1]], [[[1, 1], 1]], [[[1, 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0.627434270657657, 1.1847024509160828, 1.8053889829456986, 2.4707962544151325, 3.1592653517433145, 3.8470649571758737, 4.5094000935816085, 5.121494582326771, 5.659696701634859], 'positive_zeros': ['1.62321334030766970947302300596728', '3.20361346457630305584783093767369', '3.91316951599567757387300319070502', '4.71772169836810783436044308639554', '5.91107970337180073579003850586233', '6.69324481208496363874135514467267', '7.65856427227425769928738953272318', '8.306653899443735547493881784402036', '8.920719672465111957084037828236432'], 'prelabel': '2-1456-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.4097241141034313, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1858666166202072444, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.62321334030766970947302300597', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.20361346457630305584783093767', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.91316951599567757387300319071', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.62621853429843, 'bad_primes': [2, 7, 13], 'central_character': '1.1', 'conductor': 1456, 'conductor_radical': 182, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -3, 0, 1, 0, -3, 0, 6, 0, -1, 0, 0, 0, 4, 0, -5, 0, 0, 0, -3, 0, 4, 0, 0, 0, -5, 0, 3, 0, 0, 0, -3, 0, -4, 0, 0, 0, -6, 0, 1, 0, 9, 0, -7, 0, 1, 0, 0, 0, -9, 0, -18, 0, 0, 0, -8, 0, -10, 0, -3, 0, 3, 0, 6, 0, 0, 0, 8, 0, -13, 0, 0, 0, 6, 0, -3, 0, 9, 0, -15, 0, -12, 0, 0, 0, 3, 0, -1, 0, 0, 0, 15, 0, 7, 0, -18, 0], 'euler11': [1, -6, 11], 'euler13': [1, 1, 0], 'euler17': [1, -4, 17], 'euler19': [1, 5, 19], 'euler2': [1, 0, 0], 'euler23': [1, 3, 23], 'euler29': [1, 5, 29], 'euler3': [1, 0, 3], 'euler31': [1, -3, 31], 'euler37': [1, 4, 37], 'euler41': [1, 6, 41], 'euler43': [1, -1, 43], 'euler47': [1, 7, 47], 'euler5': [1, 3, 5], 'euler53': [1, 9, 53], 'euler59': [1, 8, 59], 'euler61': [1, 10, 61], 'euler67': [1, -6, 67], 'euler7': [1, -1, 0], 'euler71': [1, -8, 71], 'euler73': [1, 13, 73], 'euler79': [1, 3, 79], 'euler83': [1, 15, 83], 'euler89': [1, -3, 89], 'euler97': [1, -7, 97], 'euler_factors': [[1, 0, 0], [1, 0, 3], [1, 3, 5], [1, -1, 0], [1, -6, 11], [1, 1, 0], [1, -4, 17], [1, 5, 19], [1, 3, 23], [1, 5, 29], [1, -3, 31], [1, 4, 37], [1, 6, 41], [1, -1, 43], [1, 7, 47], [1, 9, 53], [1, 8, 59], [1, 10, 61], [1, -6, 67], [1, -8, 71], [1, 13, 73], [1, 3, 79], [1, 15, 83], [1, -3, 89], [1, -7, 97]], 'index': 25, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1456/g', 'ModularForm/GL2/Q/holomorphic/1456/2/a/g/1/1', 'ModularForm/GL2/Q/holomorphic/1456/2/a/g'], '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': '2-1456-1.1-c1-0-25', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1456-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.4097241141034313, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1858666166202072444, 'z1': {'__RealLiteral__': 0, 'data': '1.62321334030766970947302300597', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20713403
{'Lhash': '2057667365139486700975187179967', 'Lhash_array': ['2057667365139486700975187179967'], 'label': '2-1456-1.1-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1456/2/a/g'}
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id: 24553213
{'Lhash': '2057667365139486700975187179967', 'Lhash_array': ['2057667365139486700975187179967'], 'label': '2-1456-1.1-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1456/2/a/g/1/1'}
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id: 39862
{'Lhash': '1858666166202072444', 'Lhash_array': ['1858666166202072444'], 'label': '2-1456-1.1-c1-0-25', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1456/g'}