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lfunc_lfunctions • Show schema
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{'Lhash': '2631475412914276460384647246831', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.8793852415718167, 0.0], 'a4': [0.0, 0.0], 'a5': [-0.6945927106677214, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.2266815969056775, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.166826152042992, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [41, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 7, 41], 'central_character': '1148.1', 'coefficient_field': 'CDF', 'conductor': 1148, 'conductor_radical': 574, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.8793852415718167, 0], [3.0, 0]], [[1.0, 0], [0.6945927106677214, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [4.36958506180819, 0], [11.0, 0]], [[1.0, 0], [3.7168814171420514, 0], [13.0, 0]], [[1.0, 0], [-2.5320888862379562, 0], [17.0, 0]], [[1.0, 0], [-2.2908593693815895, 0], [19.0, 0]], 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'7.32734396084236862853926910226005', '7.69247962891737510788504612030337', '8.480826330939252212195663794203190', '9.332584409533458254803556527133207'], 'prelabel': '2-1148-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0276766921259926, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.07586807629839194786398762236', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.96235071489821099263400895465', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.00607624713069490703381911459', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.166826152042992, 'bad_primes': [2, 7, 41], 'central_character': '1.1', 'conductor': 1148, 'conductor_radical': 574, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1148/2/a/b/1/3'], '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': '2-1148-1.1-c1-0-16', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1148-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0276766921259926, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.07586807629839194786398762236', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2631475412914276460384647246831', 'Lhash_array': ['2631475412914276460384647246831'], 'label': '2-1148-1.1-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1148/2/a/b/1/3'}