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lfunc_lfunctions • Show schema
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{'Lhash': '2254271038458975098774866114883', 'a10': [-0.2928932188134525, 0.7071067811865476], 'a2': [0.541196100146197, 0.541196100146197], 'a3': [0.0, 0.0], 'a4': [0.0, -0.41421356237309503], 'a5': [0.3826834323650898, 0.9238795325112867], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.7653668647301796, -0.7653668647301796], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.2919530323903064, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.3826834323650898, -0.9238795325112867]]], [13, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.298', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '2504315980251187599570521443124', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.541196100146197, -0.541196100146197], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.3826834323650898, 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'4.99551464274868561556390286451607', '6.06539481906566001520305560184223', '7.36271585030668874097225486716249', '8.312036772387671408730363858141593', '9.043279315929973620732128078036335', '9.987524839695992137949128078262055', '11.10537437956690019417148919380867'], 'prelabel': '2-585-65.38-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5403267829659255, 'root_angle': -0.19879180882521663, 'root_number': '0.81124218517556085398167691672200 - 0.58471028466376494325476189408372*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.09939590441260832', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.77830629201225741388919556009', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.04133990223048461664853622844', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.26182268001566047566648137340', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.2919530323903064, 'bad_primes': [3, 5, 13], 'central_character': '65.38', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/1/o/a/298/3'], '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': '2-585-65.38-c0-0-2', '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': '2-585-65.38-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5403267829659255, 'root_angle': -0.09939590441260832, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.77830629201225741388919556009', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2254271038458975098774866114883', 'Lhash_array': ['2254271038458975098774866114883'], 'label': '2-585-65.38-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/1/o/a/298/3'}