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lfunc_lfunctions • Show schema
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{'Lhash': '1536115619846686318125092115964', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-4.981362280893904, -0.4313117509267221], 'a6': [0, 0], 'a7': [6.195880593721209, 3.577193328651718], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.1418028263681, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [4.981362280893904, 0.4313117509267221]]]], 'bad_primes': [2, 3, 5], 'central_character': '1620.269', 'coefficient_field': 'CDF', 'conductor': 1620, 'conductor_radical': 30, 'conjugate': '159053702989367968607805251289', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.981362280893904, 0.4313117509267221]], [[1.0, 0], [-6.195880593721209, -3.577193328651718], [24.5, 42.4352447854375]], [[1.0, 0], [-4.390608804988488, -2.5349191754664444], [60.5, 104.78907385791707]], [[1.0, 0], 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'root_analytic_conductor': 6.643929772835358, 'root_angle': 0.7497145492058324, 'root_number': '-0.7064723847135625362023016588425898947863254248080215135 + 0.7077406090066699650994106656346698701154451697965805208*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3748572746029162', 'prec': 60}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21178155839639261663075071651', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.51309077277415345768404518314', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.86629491812680110806226787298', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 44.1418028263681, 'bad_primes': [2, 3, 5], 'central_character': '45.29', 'conductor': 1620, 'conductor_radical': 30, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1620/3/t/d/269/1'], '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': '2-1620-45.29-c2-0-38', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-1620-45.29-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.643929772835358, 'root_angle': 0.3748572746029162, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21178155839639261663075071651', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1536115619846686318125092115964', 'Lhash_array': ['1536115619846686318125092115964'], 'label': '2-1620-45.29-c2-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1620/3/t/d/269/1'}