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lfunc_lfunctions • Show schema
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{'Lhash': '2180193245323741586300959021961', 'a10': [3.47096985741235, 6.011896144578292], 'a2': [-1.5595672009699089, 0.6943640545381461], 'a3': [-2.2414781090912843, 0.4764408799270662], 'a4': [0.6118472013887458, -0.6795251590255587], 'a5': [-0.42505142156766934, -4.044094136580212], 'a6': [3.1649123194969384, -2.2994433975226163], 'a7': [0.0, 0.0], 'a8': [0.5727032027202588, -1.7625992186996822], 'a9': [2.05659182854196, -0.9156536760380152], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.303936668947014, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-3.118729456633955, 1.1285063474893156]]]], 'bad_primes': [7, 11], 'central_character': '539.422', 'coefficient_field': 'CDF', 'conductor': 539, 'conductor_radical': 77, 'conjugate': '212165058801762258195333139400', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.5595672009699089, -0.6943640545381461], [1.3382612127177165, 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'data': '0.46113210186', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.71986921706282225105096591071', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.09839007628684410904633983042', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.73259149703252156345648859581', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.303936668947014, 'bad_primes': [7, 11], 'central_character': '77.37', 'conductor': 539, 'conductor_radical': 77, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/539/2/q/g/422/1'], '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': '2-539-77.37-c1-0-25', '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': '2-539-77.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0745931333509744, 'root_angle': 0.4611321018596083, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.71986921706282225105096591071', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2180193245323741586300959021961', 'Lhash_array': ['2180193245323741586300959021961'], 'label': '2-539-77.37-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/539/2/q/g/422/1'}