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lfunc_lfunctions • Show schema
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{'Lhash': '1162606366159368423656727977420', 'a10': [0, 0], 'a2': [2.8284271247461903, 2.8284271247461903], 'a3': [0, 0], 'a4': [0, 16.0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-158.6754164286555, 158.6754164286555], 'a8': [-45.254833995939045, 45.254833995939045], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 72.1727189158413, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-2.8284271247461903, -2.8284271247461903]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '450.143', 'coefficient_field': 'CDF', 'conductor': 450, 'conductor_radical': 30, 'conjugate': '307580823833999151970813290067', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.8284271247461903, -2.8284271247461903]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [158.6754164286555, -158.6754164286555], [0, -16807.0]], [[1.0, 0], [0, -147.07101663251854], [-161051.0, 0]], [[1.0, 0], 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'0.81224028910836476911821283818300689126907496148305892995 + 0.5833229917885630677931177439465194247143706325466365089*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.09912390336749613', 'prec': 64}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.917134710424190480882321025706', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.40342139258418503307483616178', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.59326297444736901753476802862', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 72.1727189158413, 'bad_primes': [2, 3, 5], 'central_character': '15.8', 'conductor': 450, 'conductor_radical': 30, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/450/6/f/f/143/5'], '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': '2-450-15.8-c5-0-21', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-450-15.8-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.495452837597375, 'root_angle': 0.09912390336749613, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.917134710424190480882321025706', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1162606366159368423656727977420', 'Lhash_array': ['1162606366159368423656727977420'], 'label': '2-450-15.8-c5-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/450/6/f/f/143/5'}