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lfunc_lfunctions • Show schema
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{'Lhash': '2373726589587269914437615188908', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.076110452553291, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 1]], [13, [1, 1]]], 'bad_primes': [2, 5, 13], 'central_character': '260.1', 'coefficient_field': '1.1.1.1', 'conductor': 260, 'conductor_radical': 130, 'degree': 2, 'euler_factors': [[1], [1, -2, 3], [1, 1], [1, -2, 7], [1, -4, 11], [1, 1], [1, -2, 17], [1, 0, 19], [1, 6, 23], [1, 10, 29], [1, 0, 31], [1, -10, 37], [1, 2, 41], [1, -2, 43], [1, 6, 47], [1, -2, 53], [1, 8, 59], [1, -2, 61], [1, 6, 67], [1, 8, 71], [1, -10, 73], [1, 16, 79], [1, -6, 83], [1, -10, 89], [1, -2, 97], [1, 10, 101], [1, -18, 103], [1, -6, 107], [1, -18, 109], [1, -2, 113]], 'euler_factors_factorization': [[1], [[[1, -2, 3], 1]], [[[1, 1], 1]], [[[1, -2, 7], 1]], [[[1, -4, 11], 1]], [[[1, 1], 1]], [[[1, -2, 17], 1]], [[[1, 0, 19], 1]], [[[1, 6, 23], 1]], [[[1, 10, 29], 1]], [[[1, 0, 31], 1]], [[[1, -10, 37], 1]], [[[1, 2, 41], 1]], [[[1, -2, 43], 1]], [[[1, 6, 47], 1]], [[[1, -2, 53], 1]], [[[1, 8, 59], 1]], [[[1, -2, 61], 1]], [[[1, 6, 67], 1]], [[[1, 8, 71], 1]], [[[1, -10, 73], 1]], [[[1, 16, 79], 1]], [[[1, -6, 83], 1]], [[[1, -10, 89], 1]], [[[1, -2, 97], 1]], [[[1, 10, 101], 1]], [[[1, -18, 103], 1]], [[[1, -6, 107], 1]], [[[1, -18, 109], 1]], [[[1, -2, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-260-1.1-c1-0-1', '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/260/2/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.7644191645458749, 1.7694309697107853, 1.7829568961265574, 1.8006944313999294, 1.816144313756169, 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0.14878411367334599, 0.825001949151623, 1.2476991025813393, 1.2914361157303824, 0.9577466300870039, 0.376178587446827, -0.23710275604980385, -0.6505515997562786, -0.6960538054891922], 'positive_zeros': ['1.87254010620899892030103745588013', '3.41867360196891109068838701089295', '4.38508404435448495799335874606981', '5.95797413547964079007979268211989', '7.44804443925374277002602322353151', '8.075719677783827392213832045836116', '9.029007054104177535540216852388142', '9.804097713553654747996703799712865', '11.24644254703426645988179324296525', '11.86211802977140750906415972759882'], 'prelabel': '2-260-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.4408714212424685, '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': 1177932749422427696, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.87254010620899892030103745588', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.41867360196891109068838701089', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.38508404435448495799335874607', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.076110452553291, 'bad_primes': [2, 5, 13], 'central_character': '1.1', 'conductor': 260, 'conductor_radical': 130, 'degree': 2, 'dirichlet_coefficients': [1, 0, 2, 0, -1, 0, 2, 0, 1, 0, 4, 0, -1, 0, -2, 0, 2, 0, 0, 0, 4, 0, -6, 0, 1, 0, -4, 0, -10, 0, 0, 0, 8, 0, -2, 0, 10, 0, -2, 0, -2, 0, 2, 0, -1, 0, -6, 0, -3, 0, 4, 0, 2, 0, -4, 0, 0, 0, -8, 0, 2, 0, 2, 0, 1, 0, -6, 0, -12, 0, -8, 0, 10, 0, 2, 0, 8, 0, -16, 0, -11, 0, 6, 0, -2, 0, -20, 0, 10, 0, -2, 0, 0, 0, 0, 0, 2, 0, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, 1, 0], 'euler17': [1, -2, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 6, 23], 'euler29': [1, 10, 29], 'euler3': [1, -2, 3], 'euler31': [1, 0, 31], 'euler37': [1, -10, 37], 'euler41': [1, 2, 41], 'euler43': [1, -2, 43], 'euler47': [1, 6, 47], 'euler5': [1, 1, 0], 'euler53': [1, -2, 53], 'euler59': [1, 8, 59], 'euler61': [1, -2, 61], 'euler67': [1, 6, 67], 'euler7': [1, -2, 7], 'euler71': [1, 8, 71], 'euler73': [1, -10, 73], 'euler79': [1, 16, 79], 'euler83': [1, -6, 83], 'euler89': [1, -10, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, -2, 3], [1, 1, 0], [1, -2, 7], [1, -4, 11], [1, 1, 0], [1, -2, 17], [1, 0, 19], [1, 6, 23], [1, 10, 29], [1, 0, 31], [1, -10, 37], [1, 2, 41], [1, -2, 43], [1, 6, 47], [1, -2, 53], [1, 8, 59], [1, -2, 61], [1, 6, 67], [1, 8, 71], [1, -10, 73], [1, 16, 79], [1, -6, 83], [1, -10, 89], [1, -2, 97]], 'index': 1, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/260/a', 'ModularForm/GL2/Q/holomorphic/260/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/260/2/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': '2-260-1.1-c1-0-1', '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': '2-260-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1177932749422427696, 'z1': {'__RealLiteral__': 0, 'data': '1.87254010620899892030103745588', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10124009
{'Lhash': '2373726589587269914437615188908', 'Lhash_array': ['2373726589587269914437615188908'], 'label': '2-260-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/260/2/a/a'}
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id: 24548827
{'Lhash': '2373726589587269914437615188908', 'Lhash_array': ['2373726589587269914437615188908'], 'label': '2-260-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/260/2/a/a/1/1'}
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id: 22962
{'Lhash': '1177932749422427696', 'Lhash_array': ['1177932749422427696'], 'label': '2-260-1.1-c1-0-1', 'type': 'ECQ', 'url': 'EllipticCurve/Q/260/a'}