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lfunc_lfunctions • Show schema
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{'Lhash': '183161832713649527041617692772', 'a10': [-56.0, 0], 'a2': [-4.0, 0], 'a3': [0, 0], 'a4': [16.0, 0], 'a5': [14.0, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [-64.0, 0], 'a9': [-81.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.952673945750476, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [4.0, 0]]], [41, [[1.0, 0], [1519.0, 720.0]]]], 'bad_primes': [2, 41], 'central_character': '164.163', 'coefficient_field': 'CDF', 'conductor': 164, 'conductor_radical': 82, 'conjugate': '2174828984032517538507923626715', 'degree': 2, 'euler_factors': [[[1.0, 0], [4.0, 0]], [[1.0, 0], [0, 0], [81.0, 0]], [[1.0, 0], [-14.0, 0], [625.0, 0]], [[1.0, 0], [0, 0], [2401.0, 0]], [[1.0, 0], [0, 0], [14641.0, 0]], [[1.0, 0], [0, -240.0], [-28561.0, 0]], [[1.0, 0], [0, 480.0], [-83521.0, 0]], [[1.0, 0], [0, 0], [130321.0, 0]], [[1.0, 0], [0, 0], [-279841.0, 0]], [[1.0, 0], [0, -1680.0], [-707281.0, 0]], [[1.0, 0], [0, 0], 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'2-164-164.163-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.117362498705996, 'root_angle': -0.42955342504544547, 'root_number': '-0.903628792385484830458060678167757287328970850684116598 - 0.428316478286734086853063652587745389649018441403926235*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.42955342504544547', 'prec': 67}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.14448920915642909908543719449', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.91142141695570175259475171900', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.30137606874165206178683922708', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.952673945750476, 'bad_primes': [2, 41], 'central_character': '164.163', 'conductor': 164, 'conductor_radical': 82, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/164/5/d/b/163/2'], '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': '2-164-164.163-c4-0-6', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-164-164.163-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.117362498705996, 'root_angle': -0.42955342504544547, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '0.14448920915642909908543719449', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '183161832713649527041617692772', 'Lhash_array': ['183161832713649527041617692772'], 'factors': ['2-164-164.163-c4-0-6'], 'label': '2-164-164.163-c4-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/164/5/d/b/163/2'}