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lfunc_lfunctions • Show schema
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{'Lhash': '1313668062344983344177463905318', 'a10': [-0.7071067811865476, 0.7071067811865476], 'a2': [0, -1.0], 'a3': [2.234800592983976, 2.234800592983976], 'a4': [-1.0, 0], 'a5': [-0.7071067811865476, -0.7071067811865476], 'a6': [2.234800592983976, -2.234800592983976], 'a7': [-0.7071067811865476, 0.7071067811865476], 'a8': [0, 1.0], 'a9': [0, 6.98866738080306], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.50219784053237, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]], [7, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [17, [[1.0, 0], [-1.2983600478274375, 3.913343990272965]]]], 'bad_primes': [2, 5, 7, 17], 'central_character': '1190.421', 'coefficient_field': 'CDF', 'conductor': 1190, 'conductor_radical': 1190, 'conjugate': '1891722090480862328602371696684', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], 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'root_number': '0.83230807866892081308292267088325513188640285808298027492 - 0.5543133249187227711001261896743162950507083719773220040*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.09350953145627913', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03630137682139613326835262511', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.28258553686024004487393287011', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.57383601920084108656200320363', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.50219784053237, 'bad_primes': [2, 5, 7, 17], 'central_character': '17.13', 'conductor': 1190, 'conductor_radical': 1190, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1190/2/p/e/421/12'], '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': '2-1190-17.13-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': 0, 'prelabel': '2-1190-17.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0825635176801094, 'root_angle': -0.09350953145627913, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03630137682139613326835262511', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1313668062344983344177463905318', 'Lhash_array': ['1313668062344983344177463905318'], 'label': '2-1190-17.13-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1190/2/p/e/421/12'}