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lfunc_lfunctions • Show schema
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{'Lhash': '2488129902936807193339557182137', 'a10': 0, 'a2': -1, 'a3': 0, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': -1, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.318036774617276, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [37, [1, -1]]], 'bad_primes': [2, 3, 37], 'central_character': '666.1', 'coefficient_field': '1.1.1.1', 'conductor': 666, 'conductor_radical': 222, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, 0, 5], [1, 1, 7], [1, 3, 11], [1, 1, 13], [1, -3, 17], [1, 7, 19], [1, 3, 23], [1, 0, 29], [1, -2, 31], [1, -1], [1, -6, 41], [1, 4, 43], [1, 6, 47], [1, 9, 53], [1, 0, 59], [1, 10, 61], [1, -2, 67], [1, 12, 71], [1, -5, 73], [1, -2, 79], [1, 3, 83], [1, -3, 89], [1, -2, 97], [1, 6, 101], [1, -14, 103], [1, 9, 107], [1, -5, 109], [1, -6, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [1], [[[1, 0, 5], 1]], [[[1, 1, 7], 1]], [[[1, 3, 11], 1]], [[[1, 1, 13], 1]], [[[1, -3, 17], 1]], [[[1, 7, 19], 1]], [[[1, 3, 23], 1]], [[[1, 0, 29], 1]], [[[1, -2, 31], 1]], [[[1, -1], 1]], [[[1, -6, 41], 1]], [[[1, 4, 43], 1]], [[[1, 6, 47], 1]], [[[1, 9, 53], 1]], [[[1, 0, 59], 1]], [[[1, 10, 61], 1]], [[[1, -2, 67], 1]], [[[1, 12, 71], 1]], [[[1, -5, 73], 1]], [[[1, -2, 79], 1]], [[[1, 3, 83], 1]], [[[1, -3, 89], 1]], [[[1, -2, 97], 1]], [[[1, 6, 101], 1]], [[[1, -14, 103], 1]], [[[1, 9, 107], 1]], [[[1, -5, 109], 1]], [[[1, -6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-666-1.1-c1-0-12', '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/666/2/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [-3.62791360638917e-120, 0.2034084482647344, 0.40945235955882836, 0.619127455810584, 0.8305104809035208, 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1.237562422366505, 3.1966994086367455, 4.379489944587269, 4.497079384827651, 3.5888802965193993, 2.0112885414178594, 0.32101390431700716, -0.9092364962929979, -1.2812731225890053, -0.7037453790099908], 'positive_zeros': ['1.96278840753819796229532576491017', '3.14043362082132550386338477309736', '4.49624163661933276807437922670005', '5.78215828046120660270620191901984', '6.55620004019545166157451145996701', '7.73927537740876447103082520862615', '8.208412645914458611430202370846816', '9.339371053419225859875408435924510', '10.06815972051721250592457118805347'], 'prelabel': '2-666-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.3060868965885213, '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': 981830034755708329, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.96278840753819796229532576491', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.14043362082132550386338477310', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.49624163661933276807437922670', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.318036774617276, 'bad_primes': [2, 3, 37], 'central_character': '1.1', 'conductor': 666, 'conductor_radical': 222, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 0, 0, -1, -1, 0, 0, -3, 0, -1, 1, 0, 1, 3, 0, -7, 0, 0, 3, -3, 0, -5, 1, 0, -1, 0, 0, 2, -1, 0, -3, 0, 0, 1, 7, 0, 0, 6, 0, -4, -3, 0, 3, -6, 0, -6, 5, 0, -1, -9, 0, 0, 1, 0, 0, 0, 0, -10, -2, 0, 1, 0, 0, 2, 3, 0, 0, -12, 0, 5, -1, 0, -7, 3, 0, 2, 0, 0, -6, -3, 0, 0, 4, 0, 3, 3, 0, 1, -3, 0, 6, 0, 0, 2, 6, 0, -5], 'euler11': [1, 3, 11], 'euler13': [1, 1, 13], 'euler17': [1, -3, 17], 'euler19': [1, 7, 19], 'euler2': [1, 1, 0], 'euler23': [1, 3, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, -2, 31], 'euler37': [1, -1, 0], 'euler41': [1, -6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 6, 47], 'euler5': [1, 0, 5], 'euler53': [1, 9, 53], 'euler59': [1, 0, 59], 'euler61': [1, 10, 61], 'euler67': [1, -2, 67], 'euler7': [1, 1, 7], 'euler71': [1, 12, 71], 'euler73': [1, -5, 73], 'euler79': [1, -2, 79], 'euler83': [1, 3, 83], 'euler89': [1, -3, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 0, 5], [1, 1, 7], [1, 3, 11], [1, 1, 13], [1, -3, 17], [1, 7, 19], [1, 3, 23], [1, 0, 29], [1, -2, 31], [1, -1, 0], [1, -6, 41], [1, 4, 43], [1, 6, 47], [1, 9, 53], [1, 0, 59], [1, 10, 61], [1, -2, 67], [1, 12, 71], [1, -5, 73], [1, -2, 79], [1, 3, 83], [1, -3, 89], [1, -2, 97]], 'index': 12, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/666/a', 'ModularForm/GL2/Q/holomorphic/666/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/666/2/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': '2-666-1.1-c1-0-12', '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': '2-666-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.3060868965885213, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 981830034755708329, 'z1': {'__RealLiteral__': 0, 'data': '1.96278840753819796229532576491', 'prec': 103}}
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lfunc_instances • Show schema
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id: 12842545
{'Lhash': '2488129902936807193339557182137', 'Lhash_array': ['2488129902936807193339557182137'], 'label': '2-666-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/666/2/a/a'}
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id: 24550117
{'Lhash': '2488129902936807193339557182137', 'Lhash_array': ['2488129902936807193339557182137'], 'label': '2-666-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/666/2/a/a/1/1'}
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id: 40173
{'Lhash': '981830034755708329', 'Lhash_array': ['981830034755708329'], 'label': '2-666-1.1-c1-0-12', 'type': 'ECQ', 'url': 'EllipticCurve/Q/666/a'}