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lfunc_lfunctions • Show schema
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{'Lhash': '2213700147517014079802788693193', 'a10': -2, 'a2': -1, 'a3': 1, 'a4': -1, 'a5': 2, 'a6': -1, 'a7': 0, 'a8': 3, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.125890668500054, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -1]], [47, [1, 1]]], 'bad_primes': [3, 47], 'central_character': '141.1', 'coefficient_field': '1.1.1.1', 'conductor': 141, 'conductor_radical': 141, 'degree': 2, 'euler_factors': [[1, 1, 2], [1, -1], [1, -2, 5], [1, 0, 7], [1, -4, 11], [1, 2, 13], [1, -2, 17], [1, 0, 19], [1, 0, 23], [1, 6, 29], [1, 4, 31], [1, 10, 37], [1, 2, 41], [1, -8, 43], [1, 1], [1, 2, 53], [1, 4, 59], [1, -14, 61], [1, 8, 67], [1, -16, 71], [1, -2, 73], [1, -8, 79], [1, 4, 83], [1, -18, 89], [1, 14, 97], [1, 10, 101], [1, 16, 103], [1, 4, 107], [1, 18, 109], [1, 10, 113]], 'euler_factors_factorization': [[[[1, 1, 2], 1]], [[[1, -1], 1]], [[[1, -2, 5], 1]], [[[1, 0, 7], 1]], [[[1, -4, 11], 1]], [[[1, 2, 13], 1]], [[[1, -2, 17], 1]], [[[1, 0, 19], 1]], [[[1, 0, 23], 1]], [[[1, 6, 29], 1]], [[[1, 4, 31], 1]], [[[1, 10, 37], 1]], [[[1, 2, 41], 1]], [[[1, -8, 43], 1]], [[[1, 1], 1]], [[[1, 2, 53], 1]], [[[1, 4, 59], 1]], [[[1, -14, 61], 1]], [[[1, 8, 67], 1]], [[[1, -16, 71], 1]], [[[1, -2, 73], 1]], [[[1, -8, 79], 1]], [[[1, 4, 83], 1]], [[[1, -18, 89], 1]], [[[1, 14, 97], 1]], [[[1, 10, 101], 1]], [[[1, 16, 103], 1]], [[[1, 4, 107], 1]], [[[1, 18, 109], 1]], [[[1, 10, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-141-1.1-c1-0-2', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/141/2/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9624779691206062, 0.9656083203125829, 0.9741577673173464, 0.9857072432421804, 0.9965365450175953, 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-1.4664149570892848, -1.8528246879546968, -1.626180163916416, -0.8796852610576733, 0.17151567330405001, 1.245826327542833, 2.0672848144874916], 'positive_zeros': ['1.74630150225815909613391524572710', '3.82986653803997716904500612795942', '5.36270443497112201719182264502865', '6.91995908324451733419004550128748', '8.104359289936234206684837124367328', '9.310688144069273468867229042448851', '9.575443434008070535852551553455062', '10.75662405333874085581848740520407', '12.25269126968811006373592111534666', '13.33645536469427920089901573537019'], 'prelabel': '2-141-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.0610799538677818, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 702837145351259199, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.74630150225815909613391524573', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.82986653803997716904500612796', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.36270443497112201719182264503', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.125890668500054, 'bad_primes': [3, 47], 'central_character': '1.1', 'conductor': 141, 'conductor_radical': 141, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, -1, 2, -1, 0, 3, 1, -2, 4, -1, -2, 0, 2, -1, 2, -1, 0, -2, 0, -4, 0, 3, -1, 2, 1, 0, -6, -2, -4, -5, 4, -2, 0, -1, -10, 0, -2, 6, -2, 0, 8, -4, 2, 0, -1, -1, -7, 1, 2, 2, -2, -1, 8, 0, 0, 6, -4, -2, 14, 4, 0, 7, -4, -4, -8, -2, 0, 0, 16, 3, 2, 10, -1, 0, 0, 2, 8, -2, 1, 2, -4, 0, 4, -8, -6, 12, 18, -2, 0, 0, -4, 1, 0, -5, -14, 7, 4, 1], 'euler11': [1, -4, 11], 'euler13': [1, 2, 13], 'euler17': [1, -2, 17], 'euler19': [1, 0, 19], 'euler2': [1, 1, 2], 'euler23': [1, 0, 23], 'euler29': [1, 6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 4, 31], 'euler37': [1, 10, 37], 'euler41': [1, 2, 41], 'euler43': [1, -8, 43], 'euler47': [1, 1, 0], 'euler5': [1, -2, 5], 'euler53': [1, 2, 53], 'euler59': [1, 4, 59], 'euler61': [1, -14, 61], 'euler67': [1, 8, 67], 'euler7': [1, 0, 7], 'euler71': [1, -16, 71], 'euler73': [1, -2, 73], 'euler79': [1, -8, 79], 'euler83': [1, 4, 83], 'euler89': [1, -18, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 1, 2], [1, -1, 0], [1, -2, 5], [1, 0, 7], [1, -4, 11], [1, 2, 13], [1, -2, 17], [1, 0, 19], [1, 0, 23], [1, 6, 29], [1, 4, 31], [1, 10, 37], [1, 2, 41], [1, -8, 43], [1, 1, 0], [1, 2, 53], [1, 4, 59], [1, -14, 61], [1, 8, 67], [1, -16, 71], [1, -2, 73], [1, -8, 79], [1, 4, 83], [1, -18, 89], [1, 14, 97]], 'index': 2, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/141/c', 'ModularForm/GL2/Q/holomorphic/141/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/141/2/a/c'], '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': '2-141-1.1-c1-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-141-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.0610799538677818, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 702837145351259199, 'z1': {'__RealLiteral__': 0, 'data': '1.74630150225815909613391524573', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9981364
{'Lhash': '2213700147517014079802788693193', 'Lhash_array': ['2213700147517014079802788693193'], 'label': '2-141-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/141/2/a/c'}
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id: 24547224
{'Lhash': '2213700147517014079802788693193', 'Lhash_array': ['2213700147517014079802788693193'], 'label': '2-141-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/141/2/a/c/1/1'}
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id: 22107
{'Lhash': '702837145351259199', 'Lhash_array': ['702837145351259199'], 'label': '2-141-1.1-c1-0-2', 'type': 'ECQ', 'url': 'EllipticCurve/Q/141/c'}