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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -2, 'Lhash': '950481803756800917669786521883', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896257, 0], 'a4': [0.0, 0], 'a5': [-0.447213595499958, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 210.04264219058754, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1, 3]], [5, [1, 1, 5]], [11, [1]]], 'bad_primes': [3, 5, 11], 'central_character': '3294225.1', 'coefficient_field': '1.1.1.1', 'conductor': 3294225, 'conductor_radical': 165, 'degree': 4, 'euler_factors': [[1, 0, 0, 0, 4], [1, 1, 3], [1, 1, 5], [1, 0, 10, 0, 49], [1], [1, 0, 10, 0, 169], [1, 0, -30, 0, 289], [1, 0, -38, 0, 361], [1, 2, 47, 46, 529], [1, 0, 58, 0, 841], [1, -14, 111, -434, 961], [1, 0, 65, 0, 1369], [1, 0, 18, 0, 1681], [1, 0, 50, 0, 1849], [1, 16, 158, 752, 2209], [1, -12, 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-0.8807737012445158, -1.2382843749574428], 'positive_zeros': ['0.74979793610769007127710514803746', '1.65668244707724998022653476825413', '2.32159156072485424081104661543763', '2.82767102164583012351673409928864', '3.33733559656066460416950662825812', '3.84792502687481147981679237100368', '4.50304996929188052023847279146938', '4.71920964949621529052226248223836', '5.10459545607334527318352567687165', '5.73628449711830132991006753856055', '6.15517988443792192476449132837080', '6.36653146481970975334128540406398', '6.89527691908007437702093531710145', '7.14519786679342819384976248425481'], 'prelabel': '4-1815e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.80694732914213, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1610627823245362465, 'z1': {'__RealLiteral__': 0, 'data': '0.74979793610769007127710514803746', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.65668244707724998022653476825413', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.32159156072485424081104661543763', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 210.04264219058754, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 3294225, 'conductor_radical': 165, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, -4, 0, 0, 0, 0, 0, 0, -2, 0, -4, 0, 5, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -16, 4, -10, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, 0, 0, 0], 'euler13': [1, 0, 10, 0, 169], 'euler17': [1, 0, -30, 0, 289], 'euler19': [1, 0, -38, 0, 361], 'euler2': [1, 0, 0, 0, 4], 'euler23': [1, 2, 47, 46, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, 1, 3, 0, 0], 'euler31': [1, -14, 111, -434, 961], 'euler37': [1, 0, 65, 0, 1369], 'euler41': [1, 0, 18, 0, 1681], 'euler43': [1, 0, 50, 0, 1849], 'euler47': [1, 16, 158, 752, 2209], 'euler5': [1, 1, 5, 0, 0], 'euler53': [1, -12, 142, -636, 2809], 'euler59': [1, 0, 93, 0, 3481], 'euler61': [1, 0, 22, 0, 3721], 'euler67': [1, 0, 85, 0, 4489], 'euler7': [1, 0, 10, 0, 49], 'euler71': [1, 0, 133, 0, 5041], 'euler73': [1, 0, 130, 0, 5329], 'euler79': [1, 0, -58, 0, 6241], 'euler83': [1, 0, -130, 0, 6889], 'euler89': [1, 0, -47, 0, 7921], 'euler97': [1, 0, 145, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 4], [1, 1, 3, 0, 0], [1, 1, 5, 0, 0], [1, 0, 10, 0, 49], [1, 0, 0, 0, 0], [1, 0, 10, 0, 169], [1, 0, -30, 0, 289], [1, 0, -38, 0, 361], [1, 2, 47, 46, 529], [1, 0, 58, 0, 841], [1, -14, 111, -434, 961], [1, 0, 65, 0, 1369], [1, 0, 18, 0, 1681], [1, 0, 50, 0, 1849], [1, 16, 158, 752, 2209], [1, -12, 142, -636, 2809], [1, 0, 93, 0, 3481], [1, 0, 22, 0, 3721], [1, 0, 85, 0, 4489], [1, 0, 133, 0, 5041], [1, 0, 130, 0, 5329], [1, 0, -58, 0, 6241], [1, 0, -130, 0, 6889], [1, 0, -47, 0, 7921], [1, 0, 145, 0, 9409]], 'index': 17, 'instance_types': ['ECNF', 'ECNF', 'BMF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.11.1/27225.9/c', 'EllipticCurve/2.0.11.1/27225.1/c', 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/27225.1/c', 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/27225.9/c'], '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': '4-1815e2-1.1-c1e2-0-17', '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': '4-1815e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.80694732914213, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1610627823245362465, 'z1': {'__RealLiteral__': 0, 'data': '0.74979793610769007127710514803746', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9912038
{'Lhash': '950481803756800917669786521883', 'Lhash_array': ['950481803756800917669786521883'], 'label': '4-1815e2-1.1-c1e2-0-17', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/27225.9/c'}
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id: 9912028
{'Lhash': '950481803756800917669786521883', 'Lhash_array': ['950481803756800917669786521883'], 'label': '4-1815e2-1.1-c1e2-0-17', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/27225.1/c'}
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id: 9911948
{'Lhash': '950481803756800917669786521883', 'Lhash_array': ['950481803756800917669786521883'], 'label': '4-1815e2-1.1-c1e2-0-17', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.11.1/27225.1/c'}
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id: 9911611
{'Lhash': '950481803756800917669786521883', 'Lhash_array': ['950481803756800917669786521883'], 'label': '4-1815e2-1.1-c1e2-0-17', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.11.1/27225.9/c'}