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lfunc_lfunctions • Show schema
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{'Lhash': '2088461349119966435909242211860', 'a10': [0.0, 0.0], 'a2': [0.0, 2.4892885718100786], 'a3': [0.0, -1.0], 'a4': [-4.196557593744262, 0.0], 'a5': [0.0, 0.0], 'a6': [2.4892885718100786, 0.0], 'a7': [0.0, 1.1965575937442616], 'a8': [0.0, -5.467865715430237], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.785414197074841, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [3, 5, 13], 'central_character': '975.274', 'coefficient_field': 'CDF', 'conductor': 975, 'conductor_radical': 195, 'conjugate': '74661130432970046925939252966', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -2.4892885718100786], [-2.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.1965575937442616], [-7.0, 0]], [[1.0, 0], [1.1965575937442616, 0], [11.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 6.175134737364419], [-17.0, 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'4.33745900979908265966801562894323', '5.44908867718064415994054435779144', '6.65739091274957298006745735863861', '8.269399661457781007960468908097166', '8.616077350901613521496146708987514', '9.841532883010060604669376265917601', '10.23747172699111496466814559363045'], 'prelabel': '2-975-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.790235509249146, 'root_angle': 0.35241638234956674, 'root_number': '0.44721359549995804 + 0.8944271909999159*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.176208191175', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.64750551038587228950260744757', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.74589052912346347466346002477', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.85096843753709715796561504672', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.785414197074841, 'bad_primes': [3, 5, 13], 'central_character': '5.4', 'conductor': 975, 'conductor_radical': 195, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/975/2/c/i/274/5'], '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': '2-975-5.4-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': '2-975-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.790235509249146, 'root_angle': 0.17620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.64750551038587228950260744757', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2088461349119966435909242211860', 'Lhash_array': ['2088461349119966435909242211860'], 'label': '2-975-5.4-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/975/2/c/i/274/5'}