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lfunc_lfunctions • Show schema
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{'Lhash': '5632573810890632038445148276819', 'a10': [0.0, 0.0], 'a2': [0.6180339887498949, 0.0], 'a3': [-1.618033988749895, 0.0], 'a4': [-0.6180339887498949, 0.0], 'a5': [0.0, 0.0], 'a6': [-1.0, 0.0], 'a7': [0.6180339887498949, 0.0], 'a8': [-1.0, 0.0], 'a9': [1.618033988749895, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.023456055593751114, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[47, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [47], 'central_character': '47.46', 'coefficient_field': 'CDF', 'conductor': 47, 'conductor_radical': 47, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6180339887498949, 0], [1.0, 0]], [[1.0, 0], [1.618033988749895, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.6180339887498949, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.618033988749895, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 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'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/47/1/b/a/46/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.09765625', 'prec': 34}, 'plot_values': [0.3597283851876741, 0.3673492375902876, 0.3896576324364829, 0.4252755390334226, 0.47258387195974055, 0.530167126343632, 0.5969730137888365, 0.6722801409452726, 0.7555946002149264, 0.8465421819635782, 0.9447789223712488, 1.04992255634265, 1.1615012483541076, 1.2789153569202338, 1.401408994619405, 1.5280493321845396, 1.657712555033553, 1.7890760608273615, 1.920616930352245, 2.0506169660196094, 2.1771747166896174, 2.2982249253939417, 2.411565768622433, 2.51489411610761, 2.605848838541062, 2.6820619356996382, 2.7412169571658356, 2.7811138511869493, 2.799739014789269, 2.795338942574076, 2.7664954973223956, 2.7122004693336557, 2.631926771813128, 2.525693356415326, 2.3941207467209478, 2.238473998290258, 2.0606899211802983, 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'rational': False, 'root_analytic_conductor': 0.15315369924931985, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.44331727518334815292959324093', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.40411667131609441039217306830', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.73380655474091416962152422615', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.023456055593751114, 'bad_primes': [47], 'central_character': '47.46', 'conductor': 47, 'conductor_radical': 47, 'degree': 2, 'index': 1, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/47/1/b/a/46/2', 'ArtinRepresentation/2.47.5t2.a.b'], 'is_instance_Artin': True, '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': '2-47-47.46-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': '2-47-47.46-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.15315369924931985, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '4.44331727518334815292959324093', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24596348
{'Lhash': '5632573810890632038445148276819', 'Lhash_array': ['5632573810890632038445148276819'], 'label': '2-47-47.46-c0-0-1', 'type': 'Artin', 'url': 'ArtinRepresentation/2.47.5t2.a.b'}
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id: 19803896
{'Lhash': '5632573810890632038445148276819', 'Lhash_array': ['5632573810890632038445148276819'], 'label': '2-47-47.46-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/47/1/b/a/46/2'}