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lfunc_lfunctions • Show schema
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{'Lhash': '959808689299862023758497842237', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-3.3104562314729598, 0], 'a4': [0, 0], 'a5': [0, -3.9962857267613767], 'a6': [0, 0], 'a7': [-2.0843118689501168, 1.6296146884934708], 'a8': [0, 0], 'a9': [7.95912046049815, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.837569529021748, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.0843118689501168, -1.6296146884934708]]], [11, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 7, 11], 'central_character': '1232.111', 'coefficient_field': 'CDF', 'conductor': 1232, 'conductor_radical': 154, 'conjugate': '781490765631741555015330168500', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [3.3104562314729598, 0], [3.0, 0]], [[1.0, 0], [0, 3.9962857267613767], [-5.0, 0]], [[1.0, 0], [2.0843118689501168, -1.6296146884934708]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, -3.138118220334103], [-13.0, 0]], [[1.0, 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['0.75715555148008202370928745598083', '2.74052189414249944823428233809062', '3.73925838352416533023573313914875', '4.91891405117007941942647008716727', '5.83564311175047286750868092264454', '6.52966991829273651678186471925214', '7.13442072182812434509178126970018', '7.57607167887713097381476719558694', '9.620967923613126484353123294169964', '10.18331873241958029274308891807456'], 'prelabel': '2-1232-28.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.13649000142225, 'root_angle': 0.288777797378761, 'root_number': '0.61593645694453065985116539549709586633475761193147101 + 0.78779583713460832724964363355193495979164818306830642*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1443888986893805', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.75715555148008202370928745598', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.74052189414249944823428233809', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.73925838352416533023573313915', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.837569529021748, 'bad_primes': [2, 7, 11], 'central_character': '28.27', 'conductor': 1232, 'conductor_radical': 154, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1232/2/j/a/111/1'], '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': '2-1232-28.27-c1-0-13', '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': '2-1232-28.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.13649000142225, 'root_angle': 0.1443888986893805, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.75715555148008202370928745598', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '959808689299862023758497842237', 'Lhash_array': ['959808689299862023758497842237'], 'label': '2-1232-28.27-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1232/2/j/a/111/1'}