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lfunc_lfunctions • Show schema
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{'Lhash': '4305630549156711000172639528046', 'a10': [-1.5376480923941345, 4.508684327502959], 'a2': [0.6455722569021558, -1.8929438610582874], 'a3': [0.0, -0.8204565834207993], 'a4': [-3.166472922236514, -2.4440640811449588], 'a5': [-2.3818373171311533, 0.0], 'a6': [-1.5530782528512588, -0.5296640082491972], 'a7': [0.0, -12.376445907119905], 'a8': [-6.670663169264205, 4.41613551447666], 'a9': [8.326850994721468, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.0708500091382565, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.6455722569021558, 1.8929438610582874]]], [19, [[1.0, 0], [0, -4.358898943540674]]]], 'bad_primes': [2, 19], 'central_character': '76.39', 'coefficient_field': 'CDF', 'conductor': 76, 'conductor_radical': 38, 'conjugate': '1511976188797893778485224131625', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6455722569021558, 1.8929438610582874]], [[1.0, 0], [0, 0.8204565834207993], [-9.0, 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103}, 'z3': {'__RealLiteral__': 0, 'data': '6.14846673263707563468663741264', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.0708500091382565, 'bad_primes': [2, 19], 'central_character': '4.3', 'conductor': 76, 'conductor_radical': 38, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/76/3/b/b/39/7'], '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-c2-0-14', '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': '2-76-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4390448252706574, 'root_angle': 0.35461945599241124, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '3.39654361255500520752466058899', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4305630549156711000172639528046', 'Lhash_array': ['4305630549156711000172639528046'], 'label': '2-76-4.3-c2-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/76/3/b/b/39/7'}