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lfunc_lfunctions • Show schema
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{'Lhash': '1453837686183917434514019531625', 'a10': [0.0, 0.0], 'a2': [-0.7071067811865476, 0.7071067811865476], 'a3': [0.2928932188134525, 0.7071067811865476], 'a4': [0.0, -1.0], 'a5': [0.0, 0.0], 'a6': [-0.7071067811865476, -0.2928932188134525], 'a7': [0.0, 0.0], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [0.2928932188134525, -0.2928932188134525], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6968210429522081, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [5, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [2, 5, 17], 'central_character': '3400.699', 'coefficient_field': 'CDF', 'conductor': 3400, 'conductor_radical': 170, 'conjugate': '957678159654875493565130797607', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [-0.2928932188134525, 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'root_number': '0.91426058789564978341621899798133 - 0.40512661899793851577639326005298*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.06638628328043013', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.14687571316746639563512534176', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.23577996918959042715700732826', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.70258654741254937678507315889', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6968210429522081, 'bad_primes': [2, 5, 17], 'central_character': '680.19', 'conductor': 3400, 'conductor_radical': 170, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3400/1/br/b/699/1'], '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': '2-3400-680.19-c0-0-3', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3400-680.19-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3026208362191234, 'root_angle': -0.06638628328043011, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.14687571316746639563512534176', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1453837686183917434514019531625', 'Lhash_array': ['1453837686183917434514019531625'], 'label': '2-3400-680.19-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3400/1/br/b/699/1'}