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lfunc_lfunctions • Show schema
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{'Lhash': '2322746056809854722432490410761', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.5, 0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [0.5, -0.8660254037844386], 'a6': [0.0, 0.0], 'a7': [0.5, -2.598076211353316], 'a8': [0.0, 0.0], 'a9': [1.0, -1.7320508075688772], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.2358112565958517, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.5, 0.8660254037844386]]], [7, [[1.0, 0], [-0.5, 2.598076211353316]]]], 'bad_primes': [2, 5, 7], 'central_character': '280.121', 'coefficient_field': 'CDF', 'conductor': 280, 'conductor_radical': 70, 'conjugate': '1878868550075835172924223726499', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.5, -0.8660254037844386], [-1.5, 2.598076211353316]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [-0.5, 2.598076211353316]], [[1.0, 0], [-1.0, -1.7320508075688772], [-5.5, 9.526279441628825]], 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-2.508230925082804, -3.2415289816798993, -3.399547571735041, -2.916941902124804, -1.9106486378747436], 'positive_zeros': ['1.83232355697355770878513762231589', '3.08037391997683798988042195968070', '4.75173078951368002675729806367878', '6.06103251015962913007064911156938', '6.85581568554923371841397739720236', '8.254349299597378995482278508417808', '8.723048765687327553149368847022885', '10.01621194868901967206026104277176', '11.08944934396701605930796412373375', '11.75937320688817184309430848930968'], 'prelabel': '2-280-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4952629389494851, 'root_angle': 0.04034590610789225, 'root_number': '0.9919779164085226 + 0.12641128651274003*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0201729530539', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.83232355697355770878513762232', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.08037391997683798988042195968', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.75173078951368002675729806368', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.2358112565958517, 'bad_primes': [2, 5, 7], 'central_character': '7.2', 'conductor': 280, 'conductor_radical': 70, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/280/2/q/b/121/1'], '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': '2-280-7.2-c1-0-5', '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': '2-280-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4952629389494851, 'root_angle': 0.020172953053946126, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.83232355697355770878513762232', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2322746056809854722432490410761', 'Lhash_array': ['2322746056809854722432490410761'], 'label': '2-280-7.2-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/280/2/q/b/121/1'}