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lfunc_lfunctions • Show schema
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{'Lhash': '2432672026916928818843118404062', 'a10': [-2.5320888862379562, 0.0], 'a2': [1.0, 0.0], 'a3': [0.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-2.5320888862379562, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.3472963553338606, 0.0], 'a8': [1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.642188614702686, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1458.1', 'coefficient_field': 'CDF', 'conductor': 1458, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.5320888862379562, 0], [5.0, 0]], [[1.0, 0], [2.3472963553338606, 0], [7.0, 0]], [[1.0, 0], [-4.2908593693815895, 0], [11.0, 0]], [[1.0, 0], [-0.7587704831436335, 0], [13.0, 0]], [[1.0, 0], [4.921274307573399, 0], [17.0, 0]], [[1.0, 0], [7.248970303380007, 0], [19.0, 0]], [[1.0, 0], [-0.3054072893322786, 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'6.72839680947481487061195827407690', '7.12747836562599051746916660154210', '8.456067403753439941289777231534553', '8.892080039554351731487902639479371'], 'prelabel': '2-1458-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4120651539357634, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.91903985725952206449668302401', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.31615700978255030754866748572', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.95604132269624399904265074776', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.642188614702686, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 1458, 'conductor_radical': 6, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1458/2/a/d/1/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-1458-1.1-c1-0-30', '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': '2-1458-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4120651539357634, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.91903985725952206449668302401', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2432672026916928818843118404062', 'Lhash_array': ['2432672026916928818843118404062'], 'factors': ['2-1458-1.1-c1-0-30'], 'label': '2-1458-1.1-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1458/2/a/d/1/1'}