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lfunc_lfunctions • Show schema
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{'Lhash': '1173992803524340524592171434784', 'a10': [-0.028105072114172947, 2.2358913446143704], 'a2': [0.7071067811865476, 0.7071067811865476], 'a3': [-1.7272516532760278, 0.12884768626261212], 'a4': [0.0, 1.0], 'a5': [1.5611406446954605, 1.6008872188507977], 'a6': [-1.3124604295436444, -1.130242284150665], 'a7': [0.23646184648641466, -0.23646184648641466], 'a8': [-0.7071067811865476, 0.7071067811865476], 'a9': [2.966796547489543, -0.4451047582357754], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]], [3, [[1.0, 0], [1.7272516532760278, -0.12884768626261212]]], [5, [[1.0, 0], [-1.5611406446954605, -1.6008872188507977]]], [13, [[1.0, 0], [0.9657013995508252, -3.4738193399924495]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '390.77', 'coefficient_field': 'CDF', 'conductor': 390, 'conductor_radical': 390, 'conjugate': '2567275659560580934249924164873', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [1.7272516532760278, -0.12884768626261212]], [[1.0, 0], [-1.5611406446954605, -1.6008872188507977]], [[1.0, 0], [-0.23646184648641466, 0.23646184648641466], [0, -7.0]], [[1.0, 0], [-2.012255690450383, 0], [11.0, 0]], [[1.0, 0], [0.9657013995508252, -3.4738193399924495]], [[1.0, 0], [2.6919744413235116, -2.6919744413235116], [0, -17.0]], [[1.0, 0], [8.016002233238334, 0], [19.0, 0]], [[1.0, 0], [-6.23030732592187, -6.23030732592187], [0, 23.0]], [[1.0, 0], [-4.555801966186678, 0], [29.0, 0]], [[1.0, 0], [0, 7.052928308664435], [-31.0, 0]], [[1.0, 0], [-1.1974157422186915, 1.1974157422186915], [0, -37.0]], [[1.0, 0], [-7.901813102632353, 0], [41.0, 0]], [[1.0, 0], [-2.7644045947702107, 2.7644045947702107], [0, -43.0]], [[1.0, 0], [2.0436867481469263, 2.0436867481469263], [0, 47.0]], [[1.0, 0], [6.830138434056493, 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'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': -0.6095993108011061, 'root_number': '-0.33755326935599245 - 0.9413064274438376*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.304799655401', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.926117025711164724805246347381', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.48136402445213401696885200472', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.43264975702110278365587076159', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'bad_primes': [2, 3, 5, 13], 'central_character': '195.77', 'conductor': 390, 'conductor_radical': 390, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/s/c/77/7'], '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': '2-390-195.77-c1-0-7', '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': '2-390-195.77-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': -0.30479965540055304, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.926117025711164724805246347381', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1173992803524340524592171434784', 'Lhash_array': ['1173992803524340524592171434784'], 'label': '2-390-195.77-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/s/c/77/7'}