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lfunc_lfunctions • Show schema
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{'Lhash': '870487210642650419612058473067', 'a10': [0.30901699437494745, -0.5352331346596348], 'a2': [-0.30901699437494745, 0.5352331346596348], 'a3': [-1.118033988749895, 1.9364916731037085], 'a4': [0.8090169943749475, 1.4012585384440734], 'a5': [-1.0, 0.0], 'a6': [-0.6909830056250525, -1.1968176729092423], 'a7': [2.118033988749895, 3.6685424806725857], 'a8': [-2.23606797749979, 0.0], 'a9': [-1.0, -1.7320508075688772], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.747358970798196, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 13], 'central_character': '845.191', 'coefficient_field': 'CDF', 'conductor': 845, 'conductor_radical': 65, 'conjugate': '2802540150195354343771380986095', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.30901699437494745, -0.5352331346596348], [-1.0, -1.7320508075688772]], [[1.0, 0], [1.118033988749895, -1.9364916731037085], [-1.5, 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False, 'root_analytic_conductor': 2.5975678953201964, 'root_angle': 0.8292514305481999, 'root_number': '-0.8595425350987748 + 0.5110642135348273*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.414625715274', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68669332897087479162575002553', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.31506866949456603414308599452', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.79672712140483236028118505322', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.747358970798196, 'bad_primes': [5, 13], 'central_character': '13.9', 'conductor': 845, 'conductor_radical': 65, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/845/2/e/g/191/1'], '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': '2-845-13.9-c1-0-11', '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': '2-845-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5975678953201964, 'root_angle': 0.41462571527409997, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.68669332897087479162575002553', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '870487210642650419612058473067', 'Lhash_array': ['870487210642650419612058473067'], 'label': '2-845-13.9-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/845/2/e/g/191/1'}