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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -3, 'A4': -1, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 6, 'Lhash': '780585599058355377444180827554', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.7320508075688772, 0], 'a4': [-0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [2.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 57.47430058395051, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 1]], [3, [1, 3, 3]], [7, [1, 1]], [73, [1, -1, 71, 73]]], 'bad_primes': [2, 3, 7, 73], 'central_character': '901404.1', 'coefficient_field': '1.1.1.1', 'conductor': 901404, 'conductor_radical': 3066, 'degree': 4, 'euler_factors': [[1, 0, 1], [1, 3, 3], [1, 0, 1, 0, 25], [1, 1], [1, 0, -13, 0, 121], [1, -3, 28, -39, 169], [1, 0, -11, 0, 289], [1, 0, 34, 0, 361], [1, 0, -10, 0, 529], [1, 0, 14, 0, 841], [1, -9, 82, -279, 961], [1, -5, 60, -185, 1369], [1, 0, 64, 0, 1681], [1, -8, 102, -344, 1849], [1, 0, 58, 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-0.3362144819990938, -0.41824394152103, -0.2919327806282847, 0.02324252381051891, 0.47234688619414356], 'positive_zeros': ['0.61577346227566000338851588568899', '1.12106303563957554716196069464350', '2.11105866831813092685590283972153', '2.95429116618460432717681410796440', '3.63784553140918674542066302688280', '4.19938866623469113746777941570832', '4.56134135438064287025250025384075', '5.01077757322795603322785085211459', '5.61239355675081315079617672569960', '5.94468201904435523015631772119684', '6.31635538667819651049251483208778', '6.60638182693326161618251056166492', '7.35156564777050085522577847765002', '7.48245353184456152941549350212960', '8.318008438991289993315007888665717'], 'prelabel': '4-901404-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.75339439335373, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 662087962691239813, 'z1': {'__RealLiteral__': 0, 'data': '0.61577346227566000338851588568899', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.12106303563957554716196069464350', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.11105866831813092685590283972153', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 57.47430058395051, 'bad_primes': [2, 3, 7, 73], 'central_character': '1.1', 'conductor': 901404, 'conductor_radical': 3066, 'degree': 4, 'dirichlet_coefficients': [1, 0, -3, -1, 0, 0, -1, 0, 6, 0, 0, 3, 3, 0, 0, 1, 0, 0, 0, 0, 3, 0, 0, 0, -1, 0, -9, 1, 0, 0, 9, 0, 0, 0, 0, -6, 5, 0, -9, 0, 0, 0, 8, 0, 0, 0, 0, -3, 1, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, -6, -1, 0, 0, -5, 0, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, 4, 0, 9, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, 0, -27, 0, 0, 0, -9, 0, 0, 1], 'euler11': [1, 0, -13, 0, 121], 'euler13': [1, -3, 28, -39, 169], 'euler17': [1, 0, -11, 0, 289], 'euler19': [1, 0, 34, 0, 361], 'euler2': [1, 0, 1, 0, 0], 'euler23': [1, 0, -10, 0, 529], 'euler29': [1, 0, 14, 0, 841], 'euler3': [1, 3, 3, 0, 0], 'euler31': [1, -9, 82, -279, 961], 'euler37': [1, -5, 60, -185, 1369], 'euler41': [1, 0, 64, 0, 1681], 'euler43': [1, -8, 102, -344, 1849], 'euler47': [1, 0, 58, 0, 2209], 'euler5': [1, 0, 1, 0, 25], 'euler53': [1, 0, -70, 0, 2809], 'euler59': [1, 0, -26, 0, 3481], 'euler61': [1, -9, 136, -549, 3721], 'euler67': [1, 5, 120, 335, 4489], 'euler7': [1, 1, 0, 0, 0], 'euler71': [1, 0, -16, 0, 5041], 'euler73': [1, -1, 71, 73, 0], 'euler79': [1, -4, 126, -316, 6241], 'euler83': [1, 0, 76, 0, 6889], 'euler89': [1, 0, -92, 0, 7921], 'euler97': [1, 9, 202, 873, 9409], 'euler_factors': [[1, 0, 1, 0, 0], [1, 3, 3, 0, 0], [1, 0, 1, 0, 25], [1, 1, 0, 0, 0], [1, 0, -13, 0, 121], [1, -3, 28, -39, 169], [1, 0, -11, 0, 289], [1, 0, 34, 0, 361], [1, 0, -10, 0, 529], [1, 0, 14, 0, 841], [1, -9, 82, -279, 961], [1, -5, 60, -185, 1369], [1, 0, 64, 0, 1681], [1, -8, 102, -344, 1849], [1, 0, 58, 0, 2209], [1, 0, -70, 0, 2809], [1, 0, -26, 0, 3481], [1, -9, 136, -549, 3721], [1, 5, 120, 335, 4489], [1, 0, -16, 0, 5041], [1, -1, 71, 73, 0], [1, -4, 126, -316, 6241], [1, 0, 76, 0, 6889], [1, 0, -92, 0, 7921], [1, 9, 202, 873, 9409]], 'index': 2, 'instance_types': ['ECNF', 'ECNF', 'BMF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.3.1/100156.6/a', 'EllipticCurve/2.0.3.1/100156.3/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/100156.6/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/100156.3/a'], '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': '4-901404-1.1-c1e2-0-2', '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': '4-901404-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.75339439335373, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 662087962691239813, 'z1': {'__RealLiteral__': 0, 'data': '0.61577346227566000338851588568899', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9670948
{'Lhash': '780585599058355377444180827554', 'Lhash_array': ['780585599058355377444180827554'], 'label': '4-901404-1.1-c1e2-0-2', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/100156.3/a'}
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id: 9670942
{'Lhash': '780585599058355377444180827554', 'Lhash_array': ['780585599058355377444180827554'], 'label': '4-901404-1.1-c1e2-0-2', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/100156.6/a'}
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id: 9670735
{'Lhash': '780585599058355377444180827554', 'Lhash_array': ['780585599058355377444180827554'], 'label': '4-901404-1.1-c1e2-0-2', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/100156.3/a'}
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id: 9670363
{'Lhash': '780585599058355377444180827554', 'Lhash_array': ['780585599058355377444180827554'], 'label': '4-901404-1.1-c1e2-0-2', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/100156.6/a'}