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lfunc_lfunctions • Show schema
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{'Lhash': '816298631257151857015569915043', 'a10': [0.9866234245176569, 1.7088818992021788], 'a2': [1.2701964185771195, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.3866010582338592, 0.0], 'a5': [0.7767487060173556, 1.3453682235354412], 'a6': [0.0, 0.0], 'a7': [-1.1520676944185118, 2.381751462154944], 'a8': [-3.0314521167410113, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.5275177946066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.1520676944185118, -2.381751462154944]]]], 'bad_primes': [3, 7], 'central_character': '567.352', 'coefficient_field': 'CDF', 'conductor': 567, 'conductor_radical': 21, 'conjugate': '3022222649695648622929892810538', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.2701964185771195, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.7767487060173556, -1.3453682235354412], [-2.5, 4.330127018922194]], [[1.0, 0], [1.1520676944185118, 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'10.32095337098512118446194818438243'], 'prelabel': '2-567-63.58-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': -0.5989877474613642, 'root_number': '-0.3059909962447576 - 0.95203440600492*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.299493873731', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.64394607718418973589699909764', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.86665925370199198450550043602', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.81161482455803746970223417114', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.5275177946066, 'bad_primes': [3, 7], 'central_character': '63.58', 'conductor': 567, 'conductor_radical': 21, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/567/2/h/l/352/6'], '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': '2-567-63.58-c1-0-5', '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': '2-567-63.58-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': -0.2994938737306821, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.64394607718418973589699909764', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '816298631257151857015569915043', 'Lhash_array': ['816298631257151857015569915043'], 'label': '2-567-63.58-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/567/2/h/l/352/6'}