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lfunc_lfunctions • Show schema
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{'Lhash': '1827309643528021412956889116268', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [3.4641016151377544, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.599383156425752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '576.289', 'coefficient_field': 'CDF', 'conductor': 576, 'conductor_radical': 6, 'conjugate': '1543036818334516903998506258070', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-5.0, 0]], [[1.0, 0], [-3.4641016151377544, 0], [7.0, 0]], [[1.0, 0], [0, 0], [-11.0, 0]], [[1.0, 0], [0, 6.928203230275509], [-13.0, 0]], [[1.0, 0], [0, 0], [17.0, 0]], [[1.0, 0], [0, -8.0], [-19.0, 0]], [[1.0, 0], [0, 0], [23.0, 0]], [[1.0, 0], [0, 0], [-29.0, 0]], [[1.0, 0], 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0.08333333333333333, 'root_number': '0.9659258262890683 + 0.25881904510252074*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0416666666667', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.44149313951259936804694043266', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.74081942433013216509787079475', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.57432985796372147118514508149', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.599383156425752, 'bad_primes': [2, 3], 'central_character': '8.5', 'conductor': 576, 'conductor_radical': 6, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/576/2/d/c/289/3'], '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': '2-24e2-8.5-c1-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-24e2-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.144617251731822, 'root_angle': 0.041666666666666664, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.44149313951259936804694043266', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1827309643528021412956889116268', 'Lhash_array': ['1827309643528021412956889116268'], 'label': '2-24e2-8.5-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/576/2/d/c/289/3'}