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lfunc_lfunctions • Show schema
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{'Lhash': '2290737795470392101466292218944', 'a10': [7.2080992435478315, 12.484794115823634], 'a2': [-0.5, 0.8660254037844386], 'a3': [-3.7080992435478315, 6.422616289332565], 'a4': [3.5, 6.06217782649107], 'a5': [7.2080992435478315, -12.484794115823634], 'a6': [-3.7080992435478315, -6.422616289332565], 'a7': [0.41619848709566293, 0.0], 'a8': [-15.0, 0.0], 'a9': [-14.0, -24.24871130596428], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1210362901090722, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[19, [[1.0, 0], [82.37289319193049, -8.585247066381529]]]], 'bad_primes': [19], 'central_character': '19.11', 'coefficient_field': 'CDF', 'conductor': 19, 'conductor_radical': 19, 'conjugate': '5519266464084512550061240572246', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386], [-4.0, -6.928203230275509]], [[1.0, 0], [3.7080992435478315, -6.422616289332565], [-13.5, -23.382685902179844]], [[1.0, 0], 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'11.18219070282663027290289746649133', '12.02385442510357635313138596982616', '13.90417977939677390310978154853181', '14.82549206667388121647402799031973', '16.98634599910734003893039707090675', '17.97252127723841563049350418387586'], 'prelabel': '2-19-19.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0587900122824507, 'root_angle': -0.21707142961268494, 'root_number': '0.20542339556641942 - 0.9786731980359749*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.217071429613', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.80707349095875850976934547520', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.28325877538933314029638690587', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.79355637724893168100621851114', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.1210362901090722, 'bad_primes': [19], 'central_character': '19.11', 'conductor': 19, 'conductor_radical': 19, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/19/4/c/a/11/1'], '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': '2-19-19.11-c3-0-1', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-19-19.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0587900122824507, 'root_angle': -0.21707142961268494, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.80707349095875850976934547520', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2290737795470392101466292218944', 'Lhash_array': ['2290737795470392101466292218944'], 'factors': ['2-19-19.11-c3-0-1'], 'label': '2-19-19.11-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/19/4/c/a/11/1'}