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lfunc_lfunctions • Show schema
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{'Lhash': '3278934640296184619057978709813', 'a10': [-15.788577656827325, 0.0], 'a2': [3.1529176910225427, 0.0], 'a3': [1.9913819743416703, 0.0], 'a4': [1.9408899663629233, 0.0], 'a5': [-5.007608572143484, 0.0], 'a6': [6.278663456485252, 0.0], 'a7': [2.7851649379395647, 0.0], 'a8': [-19.103875216906534, 0.0], 'a9': [-23.03439783226707, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.051551991659046, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [0, 0]]]], 'bad_primes': [17], 'central_character': '289.1', 'coefficient_field': 'CDF', 'conductor': 289, 'conductor_radical': 17, 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.1529176910225427, 0], [8.0, 0]], [[1.0, 0], [-1.9913819743416703, 0], [27.0, 0]], [[1.0, 0], [5.007608572143484, 0], [125.0, 0]], [[1.0, 0], [-2.7851649379395647, 0], [343.0, 0]], [[1.0, 0], [27.245347886344927, 0], [1331.0, 0]], [[1.0, 0], [59.73516549017607, 0], [2197.0, 0]], [[1.0, 0], 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'4.83525916146163783885984894187043', '5.41759693288690233451686978425964', '6.85302170543855950139595440634423', '7.964466508431045695325469645967698', '8.902689968101943823630969475237151', '9.946745493332234891950591065366445', '11.30851947879964036174815772890502'], 'prelabel': '2-17e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.129352490604193, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.58662334850458093131607388487', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.43103592106447743886612754842', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.83525916146163783885984894187', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.051551991659046, 'bad_primes': [17], 'central_character': '1.1', 'conductor': 289, 'conductor_radical': 17, 'degree': 2, 'index': 54, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/289/4/a/g/1/12'], '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': '2-17e2-1.1-c3-0-54', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-17e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.129352490604193, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.58662334850458093131607388487', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3278934640296184619057978709813', 'Lhash_array': ['3278934640296184619057978709813'], 'label': '2-17e2-1.1-c3-0-54', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/289/4/a/g/1/12'}