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lfunc_lfunctions • Show schema
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{'Lhash': '1284199986170876257900991588320', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.7071067811865476, 0.7071067811865476], 'a4': [0.0, 0.0], 'a5': [-0.7071067811865476, 0.7071067811865476], 'a6': [0.0, 0.0], 'a7': [0.7071067811865476, 0.7071067811865476], 'a8': [0.0, 0.0], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6768584424468882, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [5, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [7, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '3360.3233', 'coefficient_field': 'CDF', 'conductor': 3360, 'conductor_radical': 210, 'conjugate': '1292596303790931072933689159622', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0.7071067811865476, 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0], [0, -1.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-3360-105.83-c0-0-3', 'leading_term': '1.0361901019517196740321947027529', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3360/1/bn/c/3233/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.0361901019517197, 1.0185666603991534, 1.004670670061898, 0.9932910597452809, 0.9827939518661983, 0.9713082190208601, 0.9569042140113294, 0.9377440983444285, 0.9121958968791746, 0.8789135409921675, 0.8368899743111926, 0.7854910651562406, 0.7244765777659625, 0.6540123370878654, 0.5746758014709422, 0.48745582530860426, 0.39374646205274805, 0.2953341354507669, 0.19437728613445818, 0.09337759226231762, -0.004857998774434459, -0.09726495087393415, -0.1805787453129545, -0.25140226773081303, 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'5.46862014067402229555304726118439', '6.46960342381366116494048825295226', '7.48864980641307776032480220716490', '7.77997601204845604305511038231737', '8.299542090261446822770517052834467'], 'prelabel': '2-3360-105.83-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2949356904676341, 'root_angle': -0.32379180882521663, 'root_number': '0.52573111211913360602566908484825 - 0.85065080835203993218154049706283*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.16189590441260832', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.01305516357556828690413184279', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.56896874111692806635903628188', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.25344723551540963051324191330', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6768584424468882, 'bad_primes': [2, 3, 5, 7], 'central_character': '105.83', 'conductor': 3360, 'conductor_radical': 210, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3360/1/bn/c/3233/1'], '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': '2-3360-105.83-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': '2-3360-105.83-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2949356904676341, 'root_angle': -0.16189590441260832, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.01305516357556828690413184279', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1284199986170876257900991588320', 'Lhash_array': ['1284199986170876257900991588320'], 'label': '2-3360-105.83-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3360/1/bn/c/3233/1'}