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lfunc_lfunctions • Show schema
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{'Lhash': '1716763046829368815425534798337', 'a10': [-1173.7011661633144, 830.9913007620821], 'a2': [-6.529193716934094, 4.622729648892347], 'a3': [0.0, -11.85189992490571], 'a4': [21.26074118650329, -60.36539475726571], 'a5': [179.762037557441, 0.0], 'a6': [54.7881291785666, 77.38335052342602], 'a7': [0.0, -39.467652220658216], 'a8': [140.23740233922362, 492.420014809661], 'a9': [588.53246817002, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.484110355108676, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [6.529193716934094, -4.622729648892347]]], [19, [[1.0, 0], [0, 1573.562518618183]]]], 'bad_primes': [2, 19], 'central_character': '76.39', 'coefficient_field': 'CDF', 'conductor': 76, 'conductor_radical': 38, 'conjugate': '1249827357955213046112419686344', 'degree': 2, 'euler_factors': [[[1.0, 0], [6.529193716934094, -4.622729648892347]], [[1.0, 0], [0, 11.85189992490571], [-729.0, 0]], [[1.0, 0], 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'prec': 50}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.35428725117179816475926405623', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.65611172047539342893377116739', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.58122202180303281987179781111', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.484110355108676, 'bad_primes': [2, 19], 'central_character': '4.3', 'conductor': 76, 'conductor_radical': 38, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/76/7/b/a/39/12'], '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': '2-76-4.3-c6-0-31', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-76-4.3-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.181400525554647, 'root_angle': 0.053895292295771016, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '1.35428725117179816475926405623', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1716763046829368815425534798337', 'Lhash_array': ['1716763046829368815425534798337'], 'label': '2-76-4.3-c6-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/76/7/b/a/39/12'}