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lfunc_lfunctions • Show schema
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{'Lhash': '873553247810456690364555525783', 'a10': [0, 0], 'a2': [-0.8660254037844386, 0.5], 'a3': [0.5, 0.8660254037844386], 'a4': [0.5, -0.8660254037844386], 'a5': [0, 0], 'a6': [-0.8660254037844386, -0.5], 'a7': [-4.442899129212303, -2.565109008233077], 'a8': [0, 1.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.570828394149682, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, -0.5]]], [3, [[1.0, 0], [-0.5, -0.8660254037844386]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-3.190762614372047, 1.6789978971772597]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1950.751', 'coefficient_field': 'CDF', 'conductor': 1950, 'conductor_radical': 390, 'conjugate': '806684711956951936953603114890', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.442899129212303, 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'8.418161811036620022814267845399017', '9.348162960551470833428799171107923'], 'prelabel': '2-1950-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': -0.15010480225812833, 'root_number': '0.8908570013392183082830597280018735053874407352458499059 - 0.4542838354651153436550505474611195174799210145714719599*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07505240112906417', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68911200582651171364615620842', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.32196292710966639777897488221', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.98862037642182803206450703838', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.570828394149682, 'bad_primes': [2, 3, 5, 13], 'central_character': '13.10', 'conductor': 1950, 'conductor_radical': 390, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1950/2/bc/k/751/1'], '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': '2-1950-13.10-c1-0-15', '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': '2-1950-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': -0.07505240112906417, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.68911200582651171364615620842', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '873553247810456690364555525783', 'Lhash_array': ['873553247810456690364555525783'], 'label': '2-1950-13.10-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1950/2/bc/k/751/1'}