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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': -1, 'A5': -1, 'A6': 0, 'A7': -3, 'A8': 2, 'A9': -2, 'Lhash': '2288656461122876809', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.010309278350515464, 0.0], 'a4': [-0.010309278350515464, 0.0], 'a5': [-0.010309278350515464, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.030927835051546393, 0.0], 'a8': [0.020618556701030927, 0.0], 'a9': [-0.020618556701030927, 0.0], 'algebraic': True, 'analytic_conductor': 0.05317656310268728, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[2, [1, 0, 1, -2]], [3, [1, 1, 3, 3]], [139, [1, -13, 151, -139]]], 'bad_primes': [2, 3, 139], 'central_character': '834.1', 'coefficient_field': '1.1.1.1', 'conductor': 834, 'conductor_radical': 834, 'degree': 4, 'euler_factors': [[1, 0, 1, -2], [1, 1, 3, 3], [1, 1, 0, 5, 25], [1, 3, 6, 21, 49], [1, -5, 18, -55, 121], [1, 3, 12, 39, 169], [1, 2, -6, 34, 289], [1, 0, -10, 0, 361], [1, -8, 46, -184, 529], [1, -1, -12, -29, 841], [1, 1, 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-2.972239917151478, 0.2134985118877699], 'positive_zeros': [3.380791527308811, 4.534727040759649, 5.522461614895254, 6.713431960464213, 7.080821526266834, 8.394293563409523, 9.118384206900108, 9.665996402363403, 10.60469362829825, 11.21838482337726, 12.01702642059916, 12.38087809046147, 13.32136544650794, 13.67182382040067, 14.68185679708366, 14.89888803240158, 15.87549417918701, 16.52768797097978, 17.01875430819314, 17.19494056843468, 17.9344929515315, 18.87475561039471, 19.34358426295987, 19.54983103116121], 'prelabel': '4-834-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.48020874666997304, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 2288656461122876809, 'z1': {'__RealLiteral__': 0, 'data': '3.38079152731', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.53472704076', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.5224616149', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.05317656310268728, 'bad_primes': [2, 3, 139], 'central_character': '1.1', 'conductor': 834, 'conductor_radical': 834, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, -1, -1, 0, -3, 2, -2, 0, 5, 1, -3, 0, 1, 1, -2, 0, 0, 1, 3, 0, 8, -2, 1, 0, 2, 3, 1, 0, -1, -4, -5, 0, 3, 2, -4, 0, 3, -2, -8, 0, -2, -5, 2, 0, 4, -1, 3, 0, 2, 3, 0, 0, -5, -6, 0, 0, 2, -1, 8, 0, 6, 3, 3, 0, -15, 2, -8, 0, 3, -4, -4, 0, -1, 0, -15, 0, 9, -1, 7, 0, 7, -3, 2, 0, -1, 10, -11, 0, 9, -8, 1, 0, 0, 4, -4, 0, -10, -1], 'euler11': [1, -5, 18, -55, 121], 'euler13': [1, 3, 12, 39, 169], 'euler17': [1, 2, -6, 34, 289], 'euler19': [1, 0, -10, 0, 361], 'euler2': [1, 0, 1, -2, 0], 'euler23': [1, -8, 46, -184, 529], 'euler29': [1, -1, -12, -29, 841], 'euler3': [1, 1, 3, 3, 0], 'euler31': [1, 1, 14, 31, 961], 'euler37': [1, 4, 14, 148, 1369], 'euler41': [1, 8, 30, 328, 1681], 'euler43': [1, 2, 46, 86, 1849], 'euler47': [1, -4, 30, -188, 2209], 'euler5': [1, 1, 0, 5, 25], 'euler53': [1, 0, -58, 0, 2809], 'euler59': [1, -2, 62, -118, 3481], 'euler61': [1, -8, 102, -488, 3721], 'euler67': [1, 15, 186, 1005, 4489], 'euler7': [1, 3, 6, 21, 49], 'euler71': [1, -3, 70, -213, 5041], 'euler73': [1, 4, 6, 292, 5329], 'euler79': [1, -9, 30, -711, 6241], 'euler83': [1, -7, 18, -581, 6889], 'euler89': [1, 11, 112, 979, 7921], 'euler97': [1, 4, 54, 388, 9409], 'euler_factors': [[1, 0, 1, -2, 0], [1, 1, 3, 3, 0], [1, 1, 0, 5, 25], [1, 3, 6, 21, 49], [1, -5, 18, -55, 121], [1, 3, 12, 39, 169], [1, 2, -6, 34, 289], [1, 0, -10, 0, 361], [1, -8, 46, -184, 529], [1, -1, -12, -29, 841], [1, 1, 14, 31, 961], [1, 4, 14, 148, 1369], [1, 8, 30, 328, 1681], [1, 2, 46, 86, 1849], [1, -4, 30, -188, 2209], [1, 0, -58, 0, 2809], [1, -2, 62, -118, 3481], [1, -8, 102, -488, 3721], [1, 15, 186, 1005, 4489], [1, -3, 70, -213, 5041], [1, 4, 6, 292, 5329], [1, -9, 30, -711, 6241], [1, -7, 18, -581, 6889], [1, 11, 112, 979, 7921], [1, 4, 54, 388, 9409]], 'index': 0, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/834/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-834-1.1-c1e2-0-0', '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': '4-834-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.48020874666997304, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2288656461122876809, 'z1': {'__RealLiteral__': 0, 'data': '3.38079152731', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': '2288656461122876809', 'Lhash_array': ['2288656461122876809'], 'factors': ['4-834-1.1-c1e2-0-0'], 'label': '4-834-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/834/a'}