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lfunc_lfunctions • Show schema
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{'Lhash': '2137312811566781831176866083080', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.5, -0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.5, -0.8660254037844386], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7860273948969788, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.5, 0.8660254037844386]]]], 'bad_primes': [3, 5, 7], 'central_character': '1575.451', 'coefficient_field': 'CDF', 'conductor': 1575, 'conductor_radical': 105, 'conjugate': '1524099812195066583483549597596', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, -1.7320508075688772], [-1.0, 0]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 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'3.43807187385475128884232854566930', '4.91471620087078538433950296498007', '5.60313709408012586111736879051437', '6.51519360316686909037643447562189', '7.65024385460216583404467428725106', '8.010216691182826770194000175682488', '8.715781220519617269067992459066652', '9.759633078010087114845882513776792'], 'prelabel': '2-1575-7.3-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8865818602345633, 'root_angle': 0.2929874272254411, 'root_number': '0.60546434364936736350712946050774 + 0.79587243234656694719841781696280*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.14649371361272054', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.68604251927303734649373186138', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.96215741090627392784972702705', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43807187385475128884232854567', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7860273948969788, 'bad_primes': [3, 5, 7], 'central_character': '7.3', 'conductor': 1575, 'conductor_radical': 105, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1575/1/x/b/451/1'], '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': '2-1575-7.3-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1575-7.3-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8865818602345633, 'root_angle': 0.14649371361272054, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.68604251927303734649373186138', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2137312811566781831176866083080', 'Lhash_array': ['2137312811566781831176866083080'], 'label': '2-1575-7.3-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1575/1/x/b/451/1'}