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lfunc_lfunctions • Show schema
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{'Lhash': '1476578493107157148344413103332', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.30901699437494745, 0.9510565162951535], 'a4': [0.0, 0.0], 'a5': [1.3090169943749475, -0.9510565162951535], 'a6': [0.0, 0.0], 'a7': [-0.07294901687515773, -0.2245139882897927], 'a8': [0.0, 0.0], 'a9': [-0.8090169943749475, -0.5877852522924731], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.216101226723606, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.30901699437494745, -0.9510565162951535]]], [11, [[1.0, 0], [-0.8090169943749475, -3.216440812888141]]]], 'bad_primes': [2, 3, 11], 'central_character': '528.433', 'coefficient_field': 'CDF', 'conductor': 528, 'conductor_radical': 66, 'conjugate': '1832817956063081299740942504715', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [-1.3090169943749475, 0.9510565162951535], 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-1.6505272898925072, -3.256104384235138], 'positive_zeros': ['1.16481504670238952861393537665702', '2.70706353928177007759572660854407', '3.82820204515274875978879110039910', '5.64098103540692299657699111564359', '5.96934643472988870647415420070925', '7.06121320135829142292749847951622', '8.131299794303231184660347493952848', '8.847206689438132349695702323911114', '10.08124489331243158531221118454486', '10.73547275145947364181234771048762'], 'prelabel': '2-528-11.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.053314692569945, 'root_angle': -0.18600346868711404, 'root_number': '0.8340724221671884 - 0.5516549597168138*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0930017343436', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.16481504670238952861393537666', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.70706353928177007759572660854', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.82820204515274875978879110040', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.216101226723606, 'bad_primes': [2, 3, 11], 'central_character': '11.4', 'conductor': 528, 'conductor_radical': 66, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/528/2/y/i/433/1'], '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': '2-528-11.4-c1-0-2', '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': '2-528-11.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.053314692569945, 'root_angle': -0.09300173434355702, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16481504670238952861393537666', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1476578493107157148344413103332', 'Lhash_array': ['1476578493107157148344413103332'], 'label': '2-528-11.4-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/528/2/y/i/433/1'}