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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': -1, 'A5': -2, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '991529464469543247171832489674', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [-0.5, 0], 'a5': [-0.894427190999916, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 210.04264219058754, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 0, -1]], [5, [1, 2, 1]], [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, 1, 0, 4], [1, 0, -1], [1, 2, 1], [1, 0, -2, 0, 49], [1], [1, 0, 10, 0, 169], [1, 0, -14, 0, 289], [1, 0, -26, 0, 361], [1, 4, 46, 92, 529], [1, 0, 46, 0, 841], [1, 4, 62, 124, 961], [1, -8, 86, -296, 1369], [1, 0, -58, 0, 1681], [1, 0, -34, 0, 1849], [1, 12, 126, 564, 2209], [1, -8, 86, -424, 2809], 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-1.0865023670361975, -1.6911826837607742, -2.027304361342137, -2.0774512932259], 'positive_zeros': ['0.78217883089474894796194859273730', '1.68018573414219972802205623813826', '2.25388240613840196989583496895827', '2.89966866495590632789433482853132', '3.46758282411430900411106446660498', '3.89874688556222838492530649439904', '4.33618876115865514319167125330269', '4.60520906272607113551819173000877', '5.15406160164655127727102809387732', '5.53046691433963606696513728450343', '6.18854804423263531608405590789368', '6.48514474486789088379505720379329', '6.91538408819636718866488331109190', '7.40464040898396316573413502921739'], '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': 1263222732576447350, 'z1': {'__RealLiteral__': 0, 'data': '0.78217883089474894796194859273730', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.68018573414219972802205623813826', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.25388240613840196989583496895827', '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, 0, -1, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 2, 0, 0, -4, 0, 3, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -1, 8, 0, 0, 0, 0, 0, 0, 0, -2, 0, -12, 0, 2, 0, 0, 0, 8, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 7, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 1, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, -3], 'euler11': [1, 0, 0, 0, 0], 'euler13': [1, 0, 10, 0, 169], 'euler17': [1, 0, -14, 0, 289], 'euler19': [1, 0, -26, 0, 361], 'euler2': [1, 0, 1, 0, 4], 'euler23': [1, 4, 46, 92, 529], 'euler29': [1, 0, 46, 0, 841], 'euler3': [1, 0, -1, 0, 0], 'euler31': [1, 4, 62, 124, 961], 'euler37': [1, -8, 86, -296, 1369], 'euler41': [1, 0, -58, 0, 1681], 'euler43': [1, 0, -34, 0, 1849], 'euler47': [1, 12, 126, 564, 2209], 'euler5': [1, 2, 1, 0, 0], 'euler53': [1, -8, 86, -424, 2809], 'euler59': [1, 12, 150, 708, 3481], 'euler61': [1, 0, 26, 0, 3721], 'euler67': [1, -8, 150, -536, 4489], 'euler7': [1, 0, -2, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, 18, 0, 5329], 'euler79': [1, 0, -42, 0, 6241], 'euler83': [1, 0, 114, 0, 6889], 'euler89': [1, -8, 190, -712, 7921], 'euler97': [1, 4, 134, 388, 9409], 'euler_factors': [[1, 0, 1, 0, 4], [1, 0, -1, 0, 0], [1, 2, 1, 0, 0], [1, 0, -2, 0, 49], [1, 0, 0, 0, 0], [1, 0, 10, 0, 169], [1, 0, -14, 0, 289], [1, 0, -26, 0, 361], [1, 4, 46, 92, 529], [1, 0, 46, 0, 841], [1, 4, 62, 124, 961], [1, -8, 86, -296, 1369], [1, 0, -58, 0, 1681], [1, 0, -34, 0, 1849], [1, 12, 126, 564, 2209], [1, -8, 86, -424, 2809], [1, 12, 150, 708, 3481], [1, 0, 26, 0, 3721], [1, -8, 150, -536, 4489], [1, 0, 142, 0, 5041], [1, 0, 18, 0, 5329], [1, 0, -42, 0, 6241], [1, 0, 114, 0, 6889], [1, -8, 190, -712, 7921], [1, 4, 134, 388, 9409]], 'index': 20, 'instance_types': ['BMF', 'ECNF', 'ECNF', 'BMF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/27225.5/j', 'EllipticCurve/2.0.11.1/27225.5/j', 'EllipticCurve/2.0.11.1/27225.5/h', 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/27225.5/h'], '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-c1e2-0-20', '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': 1263222732576447350, 'z1': {'__RealLiteral__': 0, 'data': '0.78217883089474894796194859273730', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9912036
{'Lhash': '991529464469543247171832489674', 'Lhash_array': ['991529464469543247171832489674'], 'label': '4-1815e2-1.1-c1e2-0-20', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/27225.5/h'}
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id: 9911724
{'Lhash': '991529464469543247171832489674', 'Lhash_array': ['991529464469543247171832489674'], 'label': '4-1815e2-1.1-c1e2-0-20', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.11.1/27225.5/h'}
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id: 9911363
{'Lhash': '991529464469543247171832489674', 'Lhash_array': ['991529464469543247171832489674'], 'label': '4-1815e2-1.1-c1e2-0-20', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.11.1/27225.5/j'}
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id: 9911240
{'Lhash': '991529464469543247171832489674', 'Lhash_array': ['991529464469543247171832489674'], 'label': '4-1815e2-1.1-c1e2-0-20', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/27225.5/j'}