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lfunc_lfunctions • Show schema
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{'Lhash': '2094850439919196711874555399769', 'a10': 0, 'a2': -1, 'a3': -1, 'a4': 1, 'a5': 0, 'a6': 1, 'a7': 4, 'a8': -1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [19, [1, -1]]], 'bad_primes': [2, 3, 19], 'central_character': '114.1', 'coefficient_field': '1.1.1.1', 'conductor': 114, 'conductor_radical': 114, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1, 0, 5], [1, -4, 7], [1, -4, 11], [1, 0, 13], [1, 2, 17], [1, -1], [1, 2, 23], [1, 6, 29], [1, -6, 31], [1, 8, 37], [1, -10, 41], [1, 12, 43], [1, -10, 47], [1, -2, 53], [1, -4, 59], [1, 10, 61], [1, 0, 67], [1, 16, 71], [1, 2, 73], [1, -10, 79], [1, 16, 83], [1, 2, 89], [1, 10, 97], [1, -8, 101], [1, 6, 103], [1, 4, 107], [1, 4, 109], [1, 14, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, 1], 1]], [[[1, 0, 5], 1]], [[[1, -4, 7], 1]], [[[1, -4, 11], 1]], [[[1, 0, 13], 1]], [[[1, 2, 17], 1]], [[[1, -1], 1]], [[[1, 2, 23], 1]], [[[1, 6, 29], 1]], [[[1, -6, 31], 1]], [[[1, 8, 37], 1]], [[[1, -10, 41], 1]], [[[1, 12, 43], 1]], [[[1, -10, 47], 1]], [[[1, -2, 53], 1]], [[[1, -4, 59], 1]], [[[1, 10, 61], 1]], [[[1, 0, 67], 1]], [[[1, 16, 71], 1]], [[[1, 2, 73], 1]], [[[1, -10, 79], 1]], [[[1, 16, 83], 1]], [[[1, 2, 89], 1]], [[[1, 10, 97], 1]], [[[1, -8, 101], 1]], [[[1, 6, 103], 1]], [[[1, 4, 107], 1]], [[[1, 4, 109], 1]], [[[1, 14, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-114-1.1-c1-0-0', '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/114/2/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7635720565155919, 0.7659227967841661, 0.7722742391013558, 0.7806041471145164, 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3.0090772855868835, 4.188189462757731, 4.784637847278235, 4.594725293707516, 3.5586077855734617, 1.7801767766459629, -0.4879694362805767, -2.8919581183255976, -5.046569793723306], 'positive_zeros': ['1.65254561433729232279648150468581', '4.27018118796272972112253469343045', '5.74836164136915456195765077676489', '7.09437019996928771238631970369177', '8.207396006533562213635154307094094', '9.298664195949931722300659185452242', '10.56257717710158856411860996176629', '11.52937511132746201935826257993487', '12.01124919433445646031830085268382', '13.70872882601071417023000094865518'], 'prelabel': '2-114-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.9540935923915415, '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': 680862519249031396, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.65254561433729232279648150469', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.27018118796272972112253469343', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.74836164136915456195765077676', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 114, 'conductor_radical': 114, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, 0, 1, 4, -1, 1, 0, 4, -1, 0, -4, 0, 1, -2, -1, 1, 0, -4, -4, -2, 1, -5, 0, -1, 4, -6, 0, 6, -1, -4, 2, 0, 1, -8, -1, 0, 0, 10, 4, -12, 4, 0, 2, 10, -1, 9, 5, 2, 0, 2, 1, 0, -4, -1, 6, 4, 0, -10, -6, 4, 1, 0, 4, 0, -2, 2, 0, -16, -1, -2, 8, 5, 1, 16, 0, 10, 0, 1, -10, -16, -4, 0, 12, 6, -4, -2, 0, 0, -2, -6, -10, 0, 1, -10, -9, 4, -5], 'euler11': [1, -4, 11], 'euler13': [1, 0, 13], 'euler17': [1, 2, 17], 'euler19': [1, -1, 0], 'euler2': [1, 1, 0], 'euler23': [1, 2, 23], 'euler29': [1, 6, 29], 'euler3': [1, 1, 0], 'euler31': [1, -6, 31], 'euler37': [1, 8, 37], 'euler41': [1, -10, 41], 'euler43': [1, 12, 43], 'euler47': [1, -10, 47], 'euler5': [1, 0, 5], 'euler53': [1, -2, 53], 'euler59': [1, -4, 59], 'euler61': [1, 10, 61], 'euler67': [1, 0, 67], 'euler7': [1, -4, 7], 'euler71': [1, 16, 71], 'euler73': [1, 2, 73], 'euler79': [1, -10, 79], 'euler83': [1, 16, 83], 'euler89': [1, 2, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, 0, 5], [1, -4, 7], [1, -4, 11], [1, 0, 13], [1, 2, 17], [1, -1, 0], [1, 2, 23], [1, 6, 29], [1, -6, 31], [1, 8, 37], [1, -10, 41], [1, 12, 43], [1, -10, 47], [1, -2, 53], [1, -4, 59], [1, 10, 61], [1, 0, 67], [1, 16, 71], [1, 2, 73], [1, -10, 79], [1, 16, 83], [1, 2, 89], [1, 10, 97]], 'index': 0, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/114/a', 'ModularForm/GL2/Q/holomorphic/114/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/114/2/a/a'], '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': '2-114-1.1-c1-0-0', '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': '2-114-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 680862519249031396, 'z1': {'__RealLiteral__': 0, 'data': '1.65254561433729232279648150469', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9969080
{'Lhash': '2094850439919196711874555399769', 'Lhash_array': ['2094850439919196711874555399769'], 'label': '2-114-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/2/a/a'}
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id: 24546873
{'Lhash': '2094850439919196711874555399769', 'Lhash_array': ['2094850439919196711874555399769'], 'label': '2-114-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/2/a/a/1/1'}
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id: 22007
{'Lhash': '680862519249031396', 'Lhash_array': ['680862519249031396'], 'label': '2-114-1.1-c1-0-0', 'type': 'ECQ', 'url': 'EllipticCurve/Q/114/a'}