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lfunc_lfunctions • Show schema
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{'Lhash': '2214059804136510892353862064877', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.989435883192783, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -1]], [13, [1]]], 'bad_primes': [2, 5, 13], 'central_character': '3380.1', 'coefficient_field': '1.1.1.1', 'conductor': 3380, 'conductor_radical': 130, 'degree': 2, 'euler_factors': [[1], [1, -1, 3], [1, -1], [1, -1, 7], [1, 3, 11], [1], [1, 3, 17], [1, 5, 19], [1, -9, 23], [1, 9, 29], [1, 8, 31], [1, -7, 37], [1, 3, 41], [1, 1, 43], [1, 0, 47], [1, -6, 53], [1, 9, 59], [1, 1, 61], [1, 5, 67], [1, 9, 71], [1, 2, 73], [1, -8, 79], [1, 0, 83], [1, 3, 89], [1, 17, 97], [1, -15, 101], [1, -8, 103], [1, 3, 107], [1, 14, 109], [1, 15, 113]], 'euler_factors_factorization': [[1], [[[1, -1, 3], 1]], [[[1, -1], 1]], [[[1, -1, 7], 1]], [[[1, 3, 11], 1]], [1], [[[1, 3, 17], 1]], [[[1, 5, 19], 1]], [[[1, -9, 23], 1]], [[[1, 9, 29], 1]], [[[1, 8, 31], 1]], [[[1, -7, 37], 1]], [[[1, 3, 41], 1]], [[[1, 1, 43], 1]], [[[1, 0, 47], 1]], [[[1, -6, 53], 1]], [[[1, 9, 59], 1]], [[[1, 1, 61], 1]], [[[1, 5, 67], 1]], [[[1, 9, 71], 1]], [[[1, 2, 73], 1]], [[[1, -8, 79], 1]], [[[1, 0, 83], 1]], [[[1, 3, 89], 1]], [[[1, 17, 97], 1]], [[[1, -15, 101], 1]], [[[1, -8, 103], 1]], [[[1, 3, 107], 1]], [[[1, 14, 109], 1]], [[[1, 15, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 46, 'label': '2-3380-1.1-c1-0-46', '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/3380/2/a/i', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.1084745963690159e-60, 0.21100919281933794, 0.42160178078119875, 0.6313056617660558, 0.8395412318416481, 1.045576082132127, 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-0.05123933446036369, -0.4404314783465912, -0.7112286512281456, -0.863598050809984, -0.9043549469443974, -0.8465906303169505, -0.7087426210067648], 'positive_zeros': ['1.74658522130458408068637361407274', '2.52066163535597727617330327108411', '3.31037755216008297415525778188057', '4.39734458848774032252717107221060', '5.25511784388449709238563954834285', '5.86288535521223664989873065993456', '6.84469943386060810528121144721035', '7.60757322588473593410243954858148', '8.294167744689612160953219268944275'], 'prelabel': '2-3380-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.195135790640393, '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': 761229689085583191, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.74658522130458408068637361407', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.52066163535597727617330327108', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.31037755216008297415525778188', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.989435883192783, 'bad_primes': [2, 5, 13], 'central_character': '1.1', 'conductor': 3380, 'conductor_radical': 130, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, 1, 0, -2, 0, -3, 0, 0, 0, 1, 0, -3, 0, -5, 0, 1, 0, 9, 0, 1, 0, -5, 0, -9, 0, -8, 0, -3, 0, 1, 0, 7, 0, 0, 0, -3, 0, -1, 0, -2, 0, 0, 0, -6, 0, -3, 0, 6, 0, -3, 0, -5, 0, -9, 0, -1, 0, -2, 0, 0, 0, -5, 0, 9, 0, -9, 0, -2, 0, 1, 0, -3, 0, 8, 0, 1, 0, 0, 0, -3, 0, -9, 0, -3, 0, 0, 0, -8, 0, -5, 0, -17, 0, 6, 0], 'euler11': [1, 3, 11], 'euler13': [1, 0, 0], 'euler17': [1, 3, 17], 'euler19': [1, 5, 19], 'euler2': [1, 0, 0], 'euler23': [1, -9, 23], 'euler29': [1, 9, 29], 'euler3': [1, -1, 3], 'euler31': [1, 8, 31], 'euler37': [1, -7, 37], 'euler41': [1, 3, 41], 'euler43': [1, 1, 43], 'euler47': [1, 0, 47], 'euler5': [1, -1, 0], 'euler53': [1, -6, 53], 'euler59': [1, 9, 59], 'euler61': [1, 1, 61], 'euler67': [1, 5, 67], 'euler7': [1, -1, 7], 'euler71': [1, 9, 71], 'euler73': [1, 2, 73], 'euler79': [1, -8, 79], 'euler83': [1, 0, 83], 'euler89': [1, 3, 89], 'euler97': [1, 17, 97], 'euler_factors': [[1, 0, 0], [1, -1, 3], [1, -1, 0], [1, -1, 7], [1, 3, 11], [1, 0, 0], [1, 3, 17], [1, 5, 19], [1, -9, 23], [1, 9, 29], [1, 8, 31], [1, -7, 37], [1, 3, 41], [1, 1, 43], [1, 0, 47], [1, -6, 53], [1, 9, 59], [1, 1, 61], [1, 5, 67], [1, 9, 71], [1, 2, 73], [1, -8, 79], [1, 0, 83], [1, 3, 89], [1, 17, 97]], 'index': 46, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/3380/i', 'ModularForm/GL2/Q/holomorphic/3380/2/a/i/1/1', 'ModularForm/GL2/Q/holomorphic/3380/2/a/i'], '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': '2-3380-1.1-c1-0-46', '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': '2-3380-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.195135790640393, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 761229689085583191, 'z1': {'__RealLiteral__': 0, 'data': '1.74658522130458408068637361407', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20039501
{'Lhash': '2214059804136510892353862064877', 'Lhash_array': ['2214059804136510892353862064877'], 'label': '2-3380-1.1-c1-0-46', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3380/2/a/i'}
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id: 24561327
{'Lhash': '2214059804136510892353862064877', 'Lhash_array': ['2214059804136510892353862064877'], 'label': '2-3380-1.1-c1-0-46', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3380/2/a/i/1/1'}
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id: 38760
{'Lhash': '761229689085583191', 'Lhash_array': ['761229689085583191'], 'label': '2-3380-1.1-c1-0-46', 'type': 'ECQ', 'url': 'EllipticCurve/Q/3380/i'}