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lfunc_lfunctions • Show schema
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{'Lhash': '1119420322335380428989940666352', 'a10': [0.349288488464753, -0.604985408519888], 'a2': [2.127743056259473, 1.2284530262977635], 'a3': [-0.5, 0.8660254037844386], 'a4': [2.0181936756402674, 3.4956139857231263], 'a5': [0.0, -0.28433198582889024], 'a6': [-2.127743056259473, 1.2284530262977635], 'a7': [-4.073062635629972, 2.3515838091071712], 'a8': [0.0, 5.00321240879012], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.294081654010892, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.5, -0.8660254037844386]]], [13, [[1.0, 0], [-2.085590770293158, -2.941141128689338]]], [17, [[1.0, 0], [0.5, 0.8660254037844386]]]], 'bad_primes': [3, 13, 17], 'central_character': '663.511', 'coefficient_field': 'CDF', 'conductor': 663, 'conductor_radical': 663, 'conjugate': '3436935333647168600775080991746', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.127743056259473, 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'6.89785383650877045135082029162031', '8.373133274204966017334121227411898', '9.774697949830794700348394526351615', '10.71623034158369975656515351466494'], 'prelabel': '2-663-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.300887144996662, 'root_angle': -0.8670864096581682, 'root_number': '-0.9140810111709794 - 0.4055316325721581*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.433543204829', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.883066928800285025186214397191', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.61418884024243244603527187308', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.44515386172925533751508575577', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.294081654010892, 'bad_primes': [3, 13, 17], 'central_character': '13.4', 'conductor': 663, 'conductor_radical': 663, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/663/2/z/d/511/8'], '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': '2-663-13.4-c1-0-9', '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': '2-663-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.300887144996662, 'root_angle': -0.4335432048290841, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.883066928800285025186214397191', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1119420322335380428989940666352', 'Lhash_array': ['1119420322335380428989940666352'], 'label': '2-663-13.4-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/663/2/z/d/511/8'}