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lfunc_lfunctions • Show schema
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{'Lhash': '1759681393927780714633907829156', 'a10': [0.8202492506530019, 0.0], 'a2': [0.8202492506530019, 0.0], 'a3': [-2.327191166803189, 0.0], 'a4': [-1.3271911668031888, 0.0], 'a5': [1.0, 0.0], 'a6': [-1.9088768106966008, 0.0], 'a7': [-0.5617167605971033, 0.0], 'a8': [-2.7291260613496027, 0.0], 'a9': [2.415818726846788, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.412997564841117, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 19], 'central_character': '1805.1', 'coefficient_field': 'CDF', 'conductor': 1805, 'conductor_radical': 95, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8202492506530019, 0], [2.0, 0]], [[1.0, 0], [2.327191166803189, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.5617167605971033, 0], [7.0, 0]], [[1.0, 0], [0.11109207259970781, 0], [11.0, 0]], [[1.0, 0], [-6.890450311106168, 0], [13.0, 0]], [[1.0, 0], 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'5.67789132021935583309302244838270', '6.26082470991179082995167469002609', '6.73437144441975477482652207910331', '8.394665759903286237497965982255030', '8.727390608412425507723086983088549'], 'prelabel': '2-1805-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7964453854679796, 'root_angle': 1.0, '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': '1.38814385731444096100905722486', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.10581063877843075820460278495', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.10708829601966542975994261094', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.412997564841117, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 1805, 'conductor_radical': 95, 'degree': 2, 'index': 65, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1805/2/a/j/1/3'], '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': '2-1805-1.1-c1-0-65', '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': '2-1805-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7964453854679796, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.38814385731444096100905722486', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1759681393927780714633907829156', 'Lhash_array': ['1759681393927780714633907829156'], 'label': '2-1805-1.1-c1-0-65', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1805/2/a/j/1/3'}