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lfunc_lfunctions • Show schema
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{'Lhash': '2371642470788244581152486895854', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.776064323404867, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '1600.1', 'coefficient_field': '1.1.1.1', 'conductor': 1600, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[1], [1, -1, 3], [1], [1, 2, 7], [1, 3, 11], [1, -4, 13], [1, 3, 17], [1, -5, 19], [1, 6, 23], [1, 0, 29], [1, 2, 31], [1, 2, 37], [1, 3, 41], [1, 4, 43], [1, 12, 47], [1, 6, 53], [1, 0, 59], [1, 2, 61], [1, 13, 67], [1, 12, 71], [1, -11, 73], [1, -10, 79], [1, 9, 83], [1, -15, 89], [1, -2, 97], [1, -18, 101], [1, -4, 103], [1, 3, 107], [1, -10, 109], [1, 9, 113]], 'euler_factors_factorization': [[1], [[[1, -1, 3], 1]], [1], [[[1, 2, 7], 1]], [[[1, 3, 11], 1]], [[[1, -4, 13], 1]], [[[1, 3, 17], 1]], [[[1, -5, 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-3.2240568789747823, -2.7967411762182515, -2.3255183256814607, -1.8323704947633461, -1.3396157033205314, -0.8688095995564538, -0.439692277533455, -0.0692328910096991], 'positive_zeros': ['1.87089602636661166790933941518737', '3.06686786928646871283577398078698', '3.55969126432596148811318362766381', '4.87231762597053926583262812281120', '5.85608845646892265745636218717516', '6.48281153851554012248969831428275', '7.62075816029599842618575360070381', '8.242137217807967407949530158729158', '8.972823812527392717881630254408949'], 'prelabel': '2-40e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.5743620862197027, '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': 241942744924766728, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.87089602636661166790933941519', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.06686786928646871283577398079', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.55969126432596148811318362766', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.776064323404867, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 1600, 'conductor_radical': 10, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, -2, 0, -2, 0, -3, 0, 4, 0, 0, 0, -3, 0, 5, 0, -2, 0, -6, 0, 0, 0, -5, 0, 0, 0, -2, 0, -3, 0, 0, 0, -2, 0, 4, 0, -3, 0, -4, 0, 0, 0, -12, 0, -3, 0, -3, 0, -6, 0, 0, 0, 5, 0, 0, 0, -2, 0, 4, 0, 0, 0, -13, 0, -6, 0, -12, 0, 11, 0, 0, 0, 6, 0, 10, 0, 1, 0, -9, 0, 0, 0, 0, 0, 15, 0, -8, 0, -2, 0, 0, 0, 2, 0, 6, 0], 'euler11': [1, 3, 11], 'euler13': [1, -4, 13], 'euler17': [1, 3, 17], 'euler19': [1, -5, 19], 'euler2': [1, 0, 0], 'euler23': [1, 6, 23], 'euler29': [1, 0, 29], 'euler3': [1, -1, 3], 'euler31': [1, 2, 31], 'euler37': [1, 2, 37], 'euler41': [1, 3, 41], 'euler43': [1, 4, 43], 'euler47': [1, 12, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, 0, 59], 'euler61': [1, 2, 61], 'euler67': [1, 13, 67], 'euler7': [1, 2, 7], 'euler71': [1, 12, 71], 'euler73': [1, -11, 73], 'euler79': [1, -10, 79], 'euler83': [1, 9, 83], 'euler89': [1, -15, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, -1, 3], [1, 0, 0], [1, 2, 7], [1, 3, 11], [1, -4, 13], [1, 3, 17], [1, -5, 19], [1, 6, 23], [1, 0, 29], [1, 2, 31], [1, 2, 37], [1, 3, 41], [1, 4, 43], [1, 12, 47], [1, 6, 53], [1, 0, 59], [1, 2, 61], [1, 13, 67], [1, 12, 71], [1, -11, 73], [1, -10, 79], [1, 9, 83], [1, -15, 89], [1, -2, 97]], 'index': 28, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1600/p', 'ModularForm/GL2/Q/holomorphic/1600/2/a/p/1/1', 'ModularForm/GL2/Q/holomorphic/1600/2/a/p'], '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': '2-40e2-1.1-c1-0-28', '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': '2-40e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.5743620862197027, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 241942744924766728, 'z1': {'__RealLiteral__': 0, 'data': '1.87089602636661166790933941519', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20578109
{'Lhash': '2371642470788244581152486895854', 'Lhash_array': ['2371642470788244581152486895854'], 'label': '2-40e2-1.1-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1600/2/a/p'}
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id: 24553771
{'Lhash': '2371642470788244581152486895854', 'Lhash_array': ['2371642470788244581152486895854'], 'label': '2-40e2-1.1-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1600/2/a/p/1/1'}
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id: 33038
{'Lhash': '241942744924766728', 'Lhash_array': ['241942744924766728'], 'label': '2-40e2-1.1-c1-0-28', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1600/p'}