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lfunc_lfunctions • Show schema
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{'Lhash': '1545388468700319203501121614222', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.965330172255797, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [13, [1, -1]]], 'bad_primes': [2, 3, 13], 'central_character': '1248.1', 'coefficient_field': '1.1.1.1', 'conductor': 1248, 'conductor_radical': 78, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 0, 5], [1, -2, 7], [1, 0, 11], [1, -1], [1, -2, 17], [1, 2, 19], [1, -8, 23], [1, -6, 29], [1, -2, 31], [1, 6, 37], [1, 0, 41], [1, -4, 43], [1, -8, 47], [1, 6, 53], [1, -4, 59], [1, -2, 61], [1, -2, 67], [1, -4, 71], [1, 2, 73], [1, -12, 79], [1, 12, 83], [1, -12, 89], [1, 18, 97], [1, 2, 101], [1, -12, 103], [1, 4, 107], [1, 2, 109], [1, 2, 113]], 'euler_factors_factorization': [[1], [[[1, -1], 1]], [[[1, 0, 5], 1]], [[[1, -2, 7], 1]], [[[1, 0, 11], 1]], [[[1, -1], 1]], 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0.5155725725133479, 0.8490790664747718, 1.1363733956293753, 1.3543572339013177, 1.4850636381373339, 1.5169785742464494, 1.4459173958993266, 1.2753903201505425, 1.0164252766323254, 0.6868535204115038, 0.31010061224842583, -0.08643975608680866, -0.47334150659725366, -0.8212607108105319], 'positive_zeros': ['1.21909654633704707619269809337472', '2.43766757243998842407464205466746', '3.51100966248523097859158706460666', '4.53138639637399252599647393052485', '5.36708441859909895042575363131990', '6.48798103863965861426704983959485', '7.37444340174235339103368042804519', '8.170210140292499884928170378645734', '8.772746136966357733511362932356812', '9.614324717724064020306346133932790'], 'prelabel': '2-1248-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.1567911195161136, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1776776780096203195, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21909654633704707619269809337', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.43766757243998842407464205467', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.51100966248523097859158706461', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.965330172255797, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 1248, 'conductor_radical': 78, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, -2, 0, 2, 0, 8, 0, -5, 0, 1, 0, 6, 0, 2, 0, 0, 0, 0, 0, -6, 0, 1, 0, 0, 0, 4, 0, 0, 0, 8, 0, -3, 0, 2, 0, -6, 0, 0, 0, -2, 0, 4, 0, 2, 0, 2, 0, 0, 0, 2, 0, 8, 0, 4, 0, -2, 0, -5, 0, 0, 0, 12, 0, 1, 0, -12, 0, 0, 0, 6, 0, 12, 0, 2, 0, 2, 0, 0, 0, -18, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -1, 0], 'euler17': [1, -2, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, -8, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, -2, 31], 'euler37': [1, 6, 37], 'euler41': [1, 0, 41], 'euler43': [1, -4, 43], 'euler47': [1, -8, 47], 'euler5': [1, 0, 5], 'euler53': [1, 6, 53], 'euler59': [1, -4, 59], 'euler61': [1, -2, 61], 'euler67': [1, -2, 67], 'euler7': [1, -2, 7], 'euler71': [1, -4, 71], 'euler73': [1, 2, 73], 'euler79': [1, -12, 79], 'euler83': [1, 12, 83], 'euler89': [1, -12, 89], 'euler97': [1, 18, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 5], [1, -2, 7], [1, 0, 11], [1, -1, 0], [1, -2, 17], [1, 2, 19], [1, -8, 23], [1, -6, 29], [1, -2, 31], [1, 6, 37], [1, 0, 41], [1, -4, 43], [1, -8, 47], [1, 6, 53], [1, -4, 59], [1, -2, 61], [1, -2, 67], [1, -4, 71], [1, 2, 73], [1, -12, 79], [1, 12, 83], [1, -12, 89], [1, 18, 97]], 'index': 7, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1248/i', 'ModularForm/GL2/Q/holomorphic/1248/2/a/i/1/1', 'ModularForm/GL2/Q/holomorphic/1248/2/a/i'], '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': '2-1248-1.1-c1-0-7', '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': '2-1248-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.1567911195161136, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1776776780096203195, 'z1': {'__RealLiteral__': 0, 'data': '1.21909654633704707619269809337', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20593992
{'Lhash': '1545388468700319203501121614222', 'Lhash_array': ['1545388468700319203501121614222'], 'label': '2-1248-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1248/2/a/i'}
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id: 24552372
{'Lhash': '1545388468700319203501121614222', 'Lhash_array': ['1545388468700319203501121614222'], 'label': '2-1248-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1248/2/a/i/1/1'}
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id: 92778
{'Lhash': '1776776780096203195', 'Lhash_array': ['1776776780096203195'], 'label': '2-1248-1.1-c1-0-7', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1248/i'}