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lfunc_lfunctions • Show schema
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{'Lhash': '1918799671484282766127157689456', 'a10': 0, 'a2': 1, 'a3': -3, 'a4': 1, 'a5': 0, 'a6': -3, 'a7': 0, 'a8': 1, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.772324373936879, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [5, [1]], [37, [1, -1]]], 'bad_primes': [2, 5, 37], 'central_character': '1850.1', 'coefficient_field': '1.1.1.1', 'conductor': 1850, 'conductor_radical': 370, 'degree': 2, 'euler_factors': [[1, -1], [1, 3, 3], [1], [1, 0, 7], [1, 1, 11], [1, 2, 13], [1, 7, 17], [1, -5, 19], [1, -6, 23], [1, 0, 29], [1, 4, 31], [1, -1], [1, 3, 41], [1, 4, 43], [1, 4, 47], [1, -2, 53], [1, -4, 59], [1, 8, 61], [1, 13, 67], [1, 6, 71], [1, 7, 73], [1, -14, 79], [1, -3, 83], [1, 7, 89], [1, 18, 97], [1, -6, 101], [1, 18, 103], [1, -5, 107], [1, 6, 109], [1, 17, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, 3, 3], 1]], [1], [[[1, 0, 7], 1]], [[[1, 1, 11], 1]], [[[1, 2, 13], 1]], [[[1, 7, 17], 1]], [[[1, -5, 19], 1]], [[[1, -6, 23], 1]], [[[1, 0, 29], 1]], [[[1, 4, 31], 1]], [[[1, -1], 1]], [[[1, 3, 41], 1]], [[[1, 4, 43], 1]], [[[1, 4, 47], 1]], [[[1, -2, 53], 1]], [[[1, -4, 59], 1]], [[[1, 8, 61], 1]], [[[1, 13, 67], 1]], [[[1, 6, 71], 1]], [[[1, 7, 73], 1]], [[[1, -14, 79], 1]], [[[1, -3, 83], 1]], [[[1, 7, 89], 1]], [[[1, 18, 97], 1]], [[[1, -6, 101], 1]], [[[1, 18, 103], 1]], [[[1, -5, 107], 1]], [[[1, 6, 109], 1]], [[[1, 17, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 41, 'label': '2-1850-1.1-c1-0-41', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1850/2/a/h', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-6.855040267018914e-61, 0.1601134133969056, 0.31983260047514406, 0.4786813949780492, 0.6360254843474994, 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3.1869290983935175, 2.278803877111708, 1.3975219544201438, 0.5885742821193207, -0.10791280886721723, -0.6596981937565479, -1.0444085867223198, -1.2508444217307284], 'positive_zeros': ['1.51366604578487137578114595905943', '2.91348169870031232108756983592837', '4.22473947000803998945761355946705', '4.99317541960821719676613529042238', '5.39344798256389985367504415125236', '6.41920364978516898967942841242380', '6.90390686229064882950913520290343', '7.65898904963165500718515206931291', '9.006497938916409149052258052202843'], 'prelabel': '2-1850-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.8434781609808684, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 34201878056111880, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.51366604578487137578114595906', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.91348169870031232108756983593', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.22473947000803998945761355947', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.772324373936879, 'bad_primes': [2, 5, 37], 'central_character': '1.1', 'conductor': 1850, 'conductor_radical': 370, 'degree': 2, 'dirichlet_coefficients': [1, 1, -3, 1, 0, -3, 0, 1, 6, 0, -1, -3, -2, 0, 0, 1, -7, 6, 5, 0, 0, -1, 6, -3, 0, -2, -9, 0, 0, 0, -4, 1, 3, -7, 0, 6, 1, 5, 6, 0, -3, 0, -4, -1, 0, 6, -4, -3, -7, 0, 21, -2, 2, -9, 0, 0, -15, 0, 4, 0, -8, -4, 0, 1, 0, 3, -13, -7, -18, 0, -6, 6, -7, 1, 0, 5, 0, 6, 14, 0, 9, -3, 3, 0, 0, -4, 0, -1, -7, 0, 0, 6, 12, -4, 0, -3, -18, -7, -6, 0], 'euler11': [1, 1, 11], 'euler13': [1, 2, 13], 'euler17': [1, 7, 17], 'euler19': [1, -5, 19], 'euler2': [1, -1, 0], 'euler23': [1, -6, 23], 'euler29': [1, 0, 29], 'euler3': [1, 3, 3], 'euler31': [1, 4, 31], 'euler37': [1, -1, 0], 'euler41': [1, 3, 41], 'euler43': [1, 4, 43], 'euler47': [1, 4, 47], 'euler5': [1, 0, 0], 'euler53': [1, -2, 53], 'euler59': [1, -4, 59], 'euler61': [1, 8, 61], 'euler67': [1, 13, 67], 'euler7': [1, 0, 7], 'euler71': [1, 6, 71], 'euler73': [1, 7, 73], 'euler79': [1, -14, 79], 'euler83': [1, -3, 83], 'euler89': [1, 7, 89], 'euler97': [1, 18, 97], 'euler_factors': [[1, -1, 0], [1, 3, 3], [1, 0, 0], [1, 0, 7], [1, 1, 11], [1, 2, 13], [1, 7, 17], [1, -5, 19], [1, -6, 23], [1, 0, 29], [1, 4, 31], [1, -1, 0], [1, 3, 41], [1, 4, 43], [1, 4, 47], [1, -2, 53], [1, -4, 59], [1, 8, 61], [1, 13, 67], [1, 6, 71], [1, 7, 73], [1, -14, 79], [1, -3, 83], [1, 7, 89], [1, 18, 97]], 'index': 41, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1850/h', 'ModularForm/GL2/Q/holomorphic/1850/2/a/h/1/1', 'ModularForm/GL2/Q/holomorphic/1850/2/a/h'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-1850-1.1-c1-0-41', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1850-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.8434781609808684, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 34201878056111880, 'z1': {'__RealLiteral__': 0, 'data': '1.51366604578487137578114595906', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20590951
{'Lhash': '1918799671484282766127157689456', 'Lhash_array': ['1918799671484282766127157689456'], 'label': '2-1850-1.1-c1-0-41', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1850/2/a/h'}
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id: 24554800
{'Lhash': '1918799671484282766127157689456', 'Lhash_array': ['1918799671484282766127157689456'], 'label': '2-1850-1.1-c1-0-41', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1850/2/a/h/1/1'}
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id: 31200
{'Lhash': '34201878056111880', 'Lhash_array': ['34201878056111880'], 'label': '2-1850-1.1-c1-0-41', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1850/h'}