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lfunc_lfunctions • Show schema
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{'Lhash': '1390454032915211521614735979025', 'a10': [0, 0], 'a2': [0, 0], 'a3': [9.0, -9.0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [29.0, 29.0], 'a8': [0, 0], 'a9': [0, -81.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.34798523353774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '400.257', 'coefficient_field': 'CDF', 'conductor': 400, 'conductor_radical': 10, 'conjugate': '1480422313244370279335629153172', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-9.0, 9.0], [0, -81.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-29.0, -29.0], [0, 2401.0]], [[1.0, 0], [-118.0, 0], [14641.0, 0]], [[1.0, 0], [69.0, -69.0], [0, -28561.0]], [[1.0, 0], [-271.0, -271.0], [0, 83521.0]], [[1.0, 0], [0, 280.0], [-130321.0, 0]], [[1.0, 0], [-269.0, 269.0], [0, -279841.0]], [[1.0, 0], [0, -680.0], [-707281.0, 0]], [[1.0, 0], [202.0, 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'9.672282478832618001564081507823945', '10.51900781567236392780749389872874'], 'prelabel': '2-20e2-5.2-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.430239904819861, 'root_angle': 0.0881040955873917, 'root_number': '0.85065080835203993218154049706301107224040140376481688184 + 0.5257311121191336060256690848478766072854979322433417816*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.08810409558739168', 'prec': 64}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09687482707370030536403764016', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.72454516198388418838598037543', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.79047159861015481394913400203', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41.34798523353774, 'bad_primes': [2, 5], 'central_character': '5.2', 'conductor': 400, 'conductor_radical': 10, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/400/5/p/c/257/1'], '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': '2-20e2-5.2-c4-0-24', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-20e2-5.2-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.430239904819861, 'root_angle': 0.0881040955873917, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09687482707370030536403764016', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1390454032915211521614735979025', 'Lhash_array': ['1390454032915211521614735979025'], 'factors': ['2-20e2-5.2-c4-0-24'], 'label': '2-20e2-5.2-c4-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/400/5/p/c/257/1'}