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lfunc_lfunctions • Show schema
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{'Lhash': '2492106817520274441297674633151', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.340460544584857, -1.6982598792826094], 'a4': [0.0, 0.0], 'a5': [1.6819537219399772, -0.2965738214810412], 'a6': [0.0, 0.0], 'a7': [0.981328154857081, -1.1695013540647734], 'a8': [0.0, 0.0], 'a9': [-2.768173235161965, 1.1563809666943412], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.4495373673193144, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.340460544584857, 1.6982598792826094]]]], 'bad_primes': [2, 3], 'central_character': '432.47', 'coefficient_field': 'CDF', 'conductor': 432, 'conductor_radical': 6, 'conjugate': '1321223697813943396864084803455', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.340460544584857, 1.6982598792826094]], [[1.0, 0], [-1.6819537219399772, 0.2965738214810412], [4.698463103929542, -1.7101007166283437]], [[1.0, 0], [-0.981328154857081, 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-4.41044923347054, -3.9299802985675796], 'positive_zeros': ['1.96592563997649857862948602837868', '3.46462158698988188675575966935307', '4.66993994718515951238018686145514', '5.59507304460713143461182436626864', '6.41996233102795307131463508108306', '7.83487471846865612576429592335228', '8.979280390994537421634090480265239', '9.552713683626075188486441734936685', '10.50683879584220664449616937334916', '11.10196711257154594764926864187325'], 'prelabel': '2-432-108.47-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.857293021394124, 'root_angle': 0.4962491801872762, 'root_number': '0.011783275275612976 + 0.9999305748019605*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.248124590094', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.96592563997649857862948602838', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.46462158698988188675575966935', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.66993994718515951238018686146', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.4495373673193144, 'bad_primes': [2, 3], 'central_character': '108.47', 'conductor': 432, 'conductor_radical': 6, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/432/2/be/a/47/3'], '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': '2-432-108.47-c1-0-14', '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': '2-432-108.47-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.857293021394124, 'root_angle': 0.2481245900936381, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.96592563997649857862948602838', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2492106817520274441297674633151', 'Lhash_array': ['2492106817520274441297674633151'], 'label': '2-432-108.47-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/432/2/be/a/47/3'}