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lfunc_lfunctions • Show schema
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{'Lhash': '4013277909246125565112276793281', 'a10': [-41.95668014855118, 16.44968304371583], 'a2': [1.131981083497324, -2.592029866071034], 'a3': [5.070627768084831, 1.1352242234585384], 'a4': [-5.437237653208449, -5.8682575525050265], 'a5': [-11.266529748902666, -11.266529748902666], 'a6': [8.682389806820115, -11.85816626812199], 'a7': [30.212070392050382, 0.0], 'a8': [-21.365549007801288, 7.450725843516285], 'a9': [24.42253192494592, 11.512598940942809], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8320916802755507, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.131981083497324, 2.592029866071034]]], [3, [[1.0, 0], [-5.070627768084831, -1.1352242234585384]]]], 'bad_primes': [2, 3], 'central_character': '48.35', 'coefficient_field': 'CDF', 'conductor': 48, 'conductor_radical': 6, 'conjugate': '2190618506049837915025256399808', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.131981083497324, 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[[1.0, 0], [352.52060108088494, 352.52060108088494], [0, 226981.0]], [[1.0, 0], [228.4547658078833, -228.4547658078833], [0, -300763.0]], [[1.0, 0], [0, -524.7527809615522], [-357911.0, 0]], [[1.0, 0], [0, -578.8015377480751], [-389017.0, 0]], [[1.0, 0], [0, 745.2292873875256], [-493039.0, 0]], [[1.0, 0], [-286.23701522740487, -286.23701522740487], [0, 571787.0]], [[1.0, 0], [203.12788053721712, 0], [704969.0, 0]], [[1.0, 0], [39.424396279765396, 0], [912673.0, 0]], [[1.0, 0], [477.0634968816435, 477.0634968816435], [0, 1030301.0]], [[1.0, 0], [1080.9238524929406, 0], [1092727.0, 0]], [[1.0, 0], [-1267.2090607816708, 1267.2090607816708], [0, -1225043.0]], [[1.0, 0], [-1252.2687479013007, -1252.2687479013007], [0, 1295029.0]], [[1.0, 0], [0, -644.8772635582567], [-1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-48-48.35-c3-0-15', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 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'root_analytic_conductor': 1.6828819567264814, 'root_angle': 0.46936714835625676, 'root_number': '0.09608746456059847 + 0.9953728945246177*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.234683574178', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.16591804439138827737960065382', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.74116660450628918308283819244', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.99834432676598443049783402594', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.8320916802755507, 'bad_primes': [2, 3], 'central_character': '48.35', 'conductor': 48, 'conductor_radical': 6, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/48/4/k/a/35/15'], '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': '2-48-48.35-c3-0-15', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-48-48.35-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6828819567264814, 'root_angle': 0.23468357417812838, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '3.16591804439138827737960065382', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4013277909246125565112276793281', 'Lhash_array': ['4013277909246125565112276793281'], 'label': '2-48-48.35-c3-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/48/4/k/a/35/15'}