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lfunc_lfunctions • Show schema
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{'Lhash': '2388575487813548994911259422689', 'a10': 2, 'a2': 1, 'a3': 1, 'a4': 1, 'a5': 2, 'a6': 1, 'a7': -1, 'a8': 1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.6890885733831555, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1]], [7, [1, 1]], [11, [1, -1]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '462.1', 'coefficient_field': '1.1.1.1', 'conductor': 462, 'conductor_radical': 462, 'degree': 2, 'euler_factors': [[1, -1], [1, -1], [1, -2, 5], [1, 1], [1, -1], [1, 2, 13], [1, 2, 17], [1, 0, 19], [1, 0, 23], [1, 2, 29], [1, -4, 31], [1, 2, 37], [1, 10, 41], [1, -4, 43], [1, -4, 47], [1, 2, 53], [1, 12, 59], [1, 2, 61], [1, -12, 67], [1, -8, 71], [1, -6, 73], [1, 8, 79], [1, 8, 83], [1, 14, 89], [1, 14, 97], [1, 10, 101], [1, -4, 103], [1, 12, 107], [1, -14, 109], [1, -18, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, -1], 1]], [[[1, -2, 5], 1]], [[[1, 1], 1]], [[[1, -1], 1]], [[[1, 2, 13], 1]], [[[1, 2, 17], 1]], [[[1, 0, 19], 1]], [[[1, 0, 23], 1]], [[[1, 2, 29], 1]], [[[1, -4, 31], 1]], [[[1, 2, 37], 1]], [[[1, 10, 41], 1]], [[[1, -4, 43], 1]], [[[1, -4, 47], 1]], [[[1, 2, 53], 1]], [[[1, 12, 59], 1]], [[[1, 2, 61], 1]], [[[1, -12, 67], 1]], [[[1, -8, 71], 1]], [[[1, -6, 73], 1]], [[[1, 8, 79], 1]], [[[1, 8, 83], 1]], [[[1, 14, 89], 1]], [[[1, 14, 97], 1]], [[[1, 10, 101], 1]], [[[1, -4, 103], 1]], [[[1, 12, 107], 1]], [[[1, -14, 109], 1]], [[[1, -18, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-462-1.1-c1-0-6', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/462/2/a/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.757859414027748, 2.7627190783017515, 2.7748457818007615, 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1.75905282868817, 1.0703004452012943, 0.1344067466395208, -0.7559947605672037, -1.332040370770986, -1.4392525410724863, -1.0871115897423969, -0.4407196357932417, 0.24201839383549503, 0.705123979826287], 'positive_zeros': ['1.88425382150531611231140922836060', '2.96523175330119569799799482797290', '4.18774926881798203669654007782830', '5.33211397644666962563070735993907', '6.34557563328331303195978146207690', '7.16036475066804637810786253711636', '8.354764684441443853355726283696959', '9.432611216215457888567824586169575', '10.02727748724745217892398596458490', '11.07234697320449720415471226055324'], 'prelabel': '2-462-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.9207000217064496, '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': 661039448796501051, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.88425382150531611231140922836', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.96523175330119569799799482797', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.18774926881798203669654007783', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.6890885733831555, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 462, 'conductor_radical': 462, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, 1, 2, 1, -1, 1, 1, 2, 1, 1, -2, -1, 2, 1, -2, 1, 0, 2, -1, 1, 0, 1, -1, -2, 1, -1, -2, 2, 4, 1, 1, -2, -2, 1, -2, 0, -2, 2, -10, -1, 4, 1, 2, 0, 4, 1, 1, -1, -2, -2, -2, 1, 2, -1, 0, -2, -12, 2, -2, 4, -1, 1, -4, 1, 12, -2, 0, -2, 8, 1, 6, -2, -1, 0, -1, -2, -8, 2, 1, -10, -8, -1, -4, 4, -2, 1, -14, 2, 2, 0, 4, 4, 0, 1, -14, 1, 1, -1], 'euler11': [1, -1, 0], 'euler13': [1, 2, 13], 'euler17': [1, 2, 17], 'euler19': [1, 0, 19], 'euler2': [1, -1, 0], 'euler23': [1, 0, 23], 'euler29': [1, 2, 29], 'euler3': [1, -1, 0], 'euler31': [1, -4, 31], 'euler37': [1, 2, 37], 'euler41': [1, 10, 41], 'euler43': [1, -4, 43], 'euler47': [1, -4, 47], 'euler5': [1, -2, 5], 'euler53': [1, 2, 53], 'euler59': [1, 12, 59], 'euler61': [1, 2, 61], 'euler67': [1, -12, 67], 'euler7': [1, 1, 0], 'euler71': [1, -8, 71], 'euler73': [1, -6, 73], 'euler79': [1, 8, 79], 'euler83': [1, 8, 83], 'euler89': [1, 14, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, -1, 0], [1, -1, 0], [1, -2, 5], [1, 1, 0], [1, -1, 0], [1, 2, 13], [1, 2, 17], [1, 0, 19], [1, 0, 23], [1, 2, 29], [1, -4, 31], [1, 2, 37], [1, 10, 41], [1, -4, 43], [1, -4, 47], [1, 2, 53], [1, 12, 59], [1, 2, 61], [1, -12, 67], [1, -8, 71], [1, -6, 73], [1, 8, 79], [1, 8, 83], [1, 14, 89], [1, 14, 97]], 'index': 6, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/462/g', 'ModularForm/GL2/Q/holomorphic/462/2/a/g/1/1', 'ModularForm/GL2/Q/holomorphic/462/2/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': '2-462-1.1-c1-0-6', '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': '2-462-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.9207000217064496, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 661039448796501051, 'z1': {'__RealLiteral__': 0, 'data': '1.88425382150531611231140922836', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10912756
{'Lhash': '2388575487813548994911259422689', 'Lhash_array': ['2388575487813548994911259422689'], 'label': '2-462-1.1-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/462/2/a/g'}
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id: 24549432
{'Lhash': '2388575487813548994911259422689', 'Lhash_array': ['2388575487813548994911259422689'], 'label': '2-462-1.1-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/462/2/a/g/1/1'}
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id: 91263
{'Lhash': '661039448796501051', 'Lhash_array': ['661039448796501051'], 'label': '2-462-1.1-c1-0-6', 'type': 'ECQ', 'url': 'EllipticCurve/Q/462/g'}