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lfunc_lfunctions • Show schema
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{'Lhash': '878186183045540683841820111620', 'a10': [6.196152422706632, 0.0], 'a2': [-1.5059711791502262, 0.0], 'a3': [0.0, 0.0], 'a4': [0.2679491924311227, 0.0], 'a5': [-4.11438977617283, 0.0], 'a6': [0.0, 0.0], 'a7': [1.2679491924311228, 0.0], 'a8': [2.6084185970226037, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.096325623691686, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 19], 'central_character': '513.1', 'coefficient_field': 'CDF', 'conductor': 513, 'conductor_radical': 57, 'conjugate': '878186183045540683841820111620', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.5059711791502262, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.11438977617283, 0], [5.0, 0]], [[1.0, 0], [-1.2679491924311228, 0], [7.0, 0]], [[1.0, 0], [2.6084185970226037, 0], [11.0, 0]], [[1.0, 0], [3.4641016151377544, 0], [13.0, 0]], [[1.0, 0], [0, 0], 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'6.80937700929445157621554083749389', '7.77929548412915820872467677190271', '8.053880533120333836213770181474029', '8.880392718537877590783725694658806', '10.09609118664483115865985302066836', '10.72291061228862111609064919061183'], 'prelabel': '2-513-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.023938147200078, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.69276674730989039387230677103', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.77718809648189492186415541501', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.35154857519092802021017535351', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.096325623691686, 'bad_primes': [3, 19], 'central_character': '1.1', 'conductor': 513, 'conductor_radical': 57, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/513/2/a/i/1/2'], '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': '2-513-1.1-c1-0-0', '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': '2-513-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.023938147200078, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.69276674730989039387230677103', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '878186183045540683841820111620', 'Lhash_array': ['878186183045540683841820111620'], 'factors': ['2-513-1.1-c1-0-0'], 'label': '2-513-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/513/2/a/i/1/2'}