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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '1798494989268718059534021883725', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.053633468145186, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 0, 1]]], 'bad_primes': [2, 3, 5], 'central_character': '518400.1', 'coefficient_field': '1.1.1.1', 'conductor': 518400, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, 1], [1, 0, 14, 0, 49], [1, 0, 6, 0, 121], [1, -4, 30, -52, 169], [1, 0, -30, 0, 289], [1, 0, 22, 0, 361], [1, 0, 46, 0, 529], [1, 0, -54, 0, 841], [1, 0, 62, 0, 961], [1, 20, 174, 740, 1369], [1, 0, 18, 0, 1681], [1, 0, 70, 0, 1849], [1, 0, 30, 0, 2209], [1, 0, -6, 0, 2809], [1, 0, 102, 0, 3481], [1, 4, 126, 244, 3721], [1, 0, -10, 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1.367749665003821], 'positive_zeros': ['1.41876238526997484123607915145871', '1.81991023625961983556535330642722', '2.87445137306150751096040290970115', '3.32610394212435362066123978913857', '3.86241021712481235839964797971550', '4.39117257263834992607303650661887', '5.09830612026592740154687510675048', '5.39489464443801167560551597461112', '6.02009612668076545860354253983507', '6.43621806851354041530494644572807', '6.92675645169101568379566659877011', '7.26814634263702574100977849522975', '7.947795733903779918243166070632418', '8.301112225349946279204968725534980'], 'prelabel': '4-720e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.397754980295566, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1095876811112003595, 'z1': {'__RealLiteral__': 0, 'data': '1.41876238526997484123607915145871', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.81991023625961983556535330642722', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.87445137306150751096040290970115', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 33.053633468145186, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 518400, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0], 'euler11': [1, 0, 6, 0, 121], 'euler13': [1, -4, 30, -52, 169], 'euler17': [1, 0, -30, 0, 289], 'euler19': [1, 0, 22, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, -54, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 62, 0, 961], 'euler37': [1, 20, 174, 740, 1369], 'euler41': [1, 0, 18, 0, 1681], 'euler43': [1, 0, 70, 0, 1849], 'euler47': [1, 0, 30, 0, 2209], 'euler5': [1, 0, 1, 0, 0], 'euler53': [1, 0, -6, 0, 2809], 'euler59': [1, 0, 102, 0, 3481], 'euler61': [1, 4, 126, 244, 3721], 'euler67': [1, 0, -10, 0, 4489], 'euler7': [1, 0, 14, 0, 49], 'euler71': [1, 0, 78, 0, 5041], 'euler73': [1, 20, 246, 1460, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, 0, -142, 0, 7921], 'euler97': [1, 4, 198, 388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 1, 0, 0], [1, 0, 14, 0, 49], [1, 0, 6, 0, 121], [1, -4, 30, -52, 169], [1, 0, -30, 0, 289], [1, 0, 22, 0, 361], [1, 0, 46, 0, 529], [1, 0, -54, 0, 841], [1, 0, 62, 0, 961], [1, 20, 174, 740, 1369], [1, 0, 18, 0, 1681], [1, 0, 70, 0, 1849], [1, 0, 30, 0, 2209], [1, 0, -6, 0, 2809], [1, 0, 102, 0, 3481], [1, 4, 126, 244, 3721], [1, 0, -10, 0, 4489], [1, 0, 78, 0, 5041], [1, 20, 246, 1460, 5329], [1, 0, 158, 0, 6241], [1, 0, 22, 0, 6889], [1, 0, -142, 0, 7921], [1, 4, 198, 388, 9409]], 'index': 81, 'instance_types': ['HMF', 'ECNF', 'HMF', 'ECNF', 'ECNF', 'ECNF', 'BMF', 'BMF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-3600.1-d', 'EllipticCurve/2.2.12.1/3600.1/j', 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-3600.1-j', 'EllipticCurve/2.2.12.1/3600.1/d', 'EllipticCurve/2.0.3.1/57600.1/j', 'EllipticCurve/2.0.3.1/57600.1/k', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/57600.1/k', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/57600.1/j'], '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': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-720e2-1.1-c1e2-0-81', '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': 1, 'prelabel': '4-720e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.397754980295566, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1095876811112003595, 'z1': {'__RealLiteral__': 0, 'data': '1.41876238526997484123607915145871', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9787121
{'Lhash': '1798494989268718059534021883725', 'Lhash_array': ['1798494989268718059534021883725'], 'label': '4-720e2-1.1-c1e2-0-81', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/57600.1/j'}
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id: 9786877
{'Lhash': '1798494989268718059534021883725', 'Lhash_array': ['1798494989268718059534021883725'], 'label': '4-720e2-1.1-c1e2-0-81', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/57600.1/k'}
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id: 9786594
{'Lhash': '1798494989268718059534021883725', 'Lhash_array': ['1798494989268718059534021883725'], 'label': '4-720e2-1.1-c1e2-0-81', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/57600.1/k'}
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id: 9786433
{'Lhash': '1798494989268718059534021883725', 'Lhash_array': ['1798494989268718059534021883725'], 'label': '4-720e2-1.1-c1e2-0-81', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/57600.1/j'}
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id: 9581005
{'Lhash': '1798494989268718059534021883725', 'Lhash_array': ['1798494989268718059534021883725'], 'label': '4-720e2-1.1-c1e2-0-81', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.12.1/3600.1/d'}
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id: 9580855
{'Lhash': '1798494989268718059534021883725', 'Lhash_array': ['1798494989268718059534021883725'], 'label': '4-720e2-1.1-c1e2-0-81', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-3600.1-j'}
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id: 9580272
{'Lhash': '1798494989268718059534021883725', 'Lhash_array': ['1798494989268718059534021883725'], 'label': '4-720e2-1.1-c1e2-0-81', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.12.1/3600.1/j'}
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id: 9580213
{'Lhash': '1798494989268718059534021883725', 'Lhash_array': ['1798494989268718059534021883725'], 'label': '4-720e2-1.1-c1e2-0-81', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-3600.1-d'}