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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 0, 'Lhash': '954524985325975680048980467693', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 81.99366952191765, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -1]], [3, [1]], [7, [1, 1, 7]]], 'bad_primes': [2, 3, 7], 'central_character': '1285956.1', 'coefficient_field': '1.1.1.1', 'conductor': 1285956, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1, 0, -1], [1], [1, 0, -2, 0, 25], [1, 1, 7], [1, 3, 22, 33, 121], [1, 0, -20, 0, 169], [1, 0, -5, 0, 289], [1, 0, 4, 0, 361], [1, -12, 82, -276, 529], [1, -15, 112, -435, 841], [1, 0, 19, 0, 961], [1, -10, 90, -370, 1369], [1, 0, -2, 0, 1681], [1, -4, 54, -172, 1849], [1, 0, -53, 0, 2209], [1, 12, 142, 636, 2809], [1, 0, 34, 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5.80324583552435, 5.003071668807729, 3.9565504441718318, 2.7842096638993308, 1.6197083764782538], 'positive_zeros': ['0.75298744398032218528892677724019', '1.34368249999935027421367604738381', '2.43283859455065084464030378882623', '2.88276004118655470913758768232476', '3.00552827782712402555254810799560', '3.79780945628844250931626369812712', '4.56462103439396064097144180854119', '4.93397766641927861829630882996787', '5.15048987579808129503776929128553', '5.91640674141710362447095436090514', '6.36862857855936098839709322412322', '6.70560784798031940089390938489756', '6.95750116187864916688740652005353', '7.68218133483775864024233892448702', '7.937391776862262487108348805361589'], 'prelabel': '4-1134e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.00915861815445, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1672142788656099832, 'z1': {'__RealLiteral__': 0, 'data': '0.75298744398032218528892677724019', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.34368249999935027421367604738381', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.43283859455065084464030378882623', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 81.99366952191765, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 1285956, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 1, 0, 0, -1, 0, 0, 0, -3, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 12, 0, 2, 0, 0, -1, 15, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 4, -3, 0, 0, 0, 0, -6, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -5, 0, 0, 0, 12, 0, 0, 0, 0, 0, 3, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 2], 'euler11': [1, 3, 22, 33, 121], 'euler13': [1, 0, -20, 0, 169], 'euler17': [1, 0, -5, 0, 289], 'euler19': [1, 0, 4, 0, 361], 'euler2': [1, 0, -1, 0, 0], 'euler23': [1, -12, 82, -276, 529], 'euler29': [1, -15, 112, -435, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 19, 0, 961], 'euler37': [1, -10, 90, -370, 1369], 'euler41': [1, 0, -2, 0, 1681], 'euler43': [1, -4, 54, -172, 1849], 'euler47': [1, 0, -53, 0, 2209], 'euler5': [1, 0, -2, 0, 25], 'euler53': [1, 12, 142, 636, 2809], 'euler59': [1, 0, 34, 0, 3481], 'euler61': [1, 0, -56, 0, 3721], 'euler67': [1, 5, 120, 335, 4489], 'euler7': [1, 1, 7, 0, 0], 'euler71': [1, -12, 169, -852, 5041], 'euler73': [1, 0, 109, 0, 5329], 'euler79': [1, -10, 147, -790, 6241], 'euler83': [1, 0, -8, 0, 6889], 'euler89': [1, 0, 34, 0, 7921], 'euler97': [1, 0, -53, 0, 9409], 'euler_factors': [[1, 0, -1, 0, 0], [1, 0, 0, 0, 0], [1, 0, -2, 0, 25], [1, 1, 7, 0, 0], [1, 3, 22, 33, 121], [1, 0, -20, 0, 169], [1, 0, -5, 0, 289], [1, 0, 4, 0, 361], [1, -12, 82, -276, 529], [1, -15, 112, -435, 841], [1, 0, 19, 0, 961], [1, -10, 90, -370, 1369], [1, 0, -2, 0, 1681], [1, -4, 54, -172, 1849], [1, 0, -53, 0, 2209], [1, 12, 142, 636, 2809], [1, 0, 34, 0, 3481], [1, 0, -56, 0, 3721], [1, 5, 120, 335, 4489], [1, -12, 169, -852, 5041], [1, 0, 109, 0, 5329], [1, -10, 147, -790, 6241], [1, 0, -8, 0, 6889], [1, 0, 34, 0, 7921], [1, 0, -53, 0, 9409]], 'index': 34, 'instance_types': ['ECNF', 'ECNF', 'BMF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.7.1/26244.2/c', 'EllipticCurve/2.0.7.1/26244.2/g', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/26244.2/c', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/26244.2/g'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, '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': '4-1134e2-1.1-c1e2-0-34', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-1134e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.00915861815445, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1672142788656099832, 'z1': {'__RealLiteral__': 0, 'data': '0.75298744398032218528892677724019', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9617322
{'Lhash': '954524985325975680048980467693', 'Lhash_array': ['954524985325975680048980467693'], 'label': '4-1134e2-1.1-c1e2-0-34', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/26244.2/g'}
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id: 9617190
{'Lhash': '954524985325975680048980467693', 'Lhash_array': ['954524985325975680048980467693'], 'label': '4-1134e2-1.1-c1e2-0-34', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/26244.2/c'}
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id: 9616667
{'Lhash': '954524985325975680048980467693', 'Lhash_array': ['954524985325975680048980467693'], 'label': '4-1134e2-1.1-c1e2-0-34', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/26244.2/g'}
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id: 9616666
{'Lhash': '954524985325975680048980467693', 'Lhash_array': ['954524985325975680048980467693'], 'label': '4-1134e2-1.1-c1e2-0-34', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/26244.2/c'}