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lfunc_lfunctions • Show schema
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{'Lhash': '2163262594851962387774998037866', 'a10': [-3.1621567958667436, -0.027647754949923553], 'a2': [-0.6213722571933793, -1.270392269336682], 'a3': [1.7277930359808098, 0.12137225719337925], 'a4': [-1.2277930359808098, 1.578773023837507], 'a5': [1.0, -2.0], 'a6': [-0.9194122814799849, -2.270392269336682], 'a7': [1.0, 0.0], 'a8': [2.768577574654174, 0.5787730238375071], 'a9': [2.9705375503675686, 0.4194122814799849], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.3537168848937777, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.6213722571933793, 1.270392269336682]]], [3, [[1.0, 0], [-1.7277930359808098, -0.12137225719337925]]], [5, [[1.0, 0], [-1.0, 2.0]]], [7, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '420.239', 'coefficient_field': 'CDF', 'conductor': 420, 'conductor_radical': 210, 'conjugate': '1885029106139202830817808531910', 'degree': 2, 'euler_factors': [[[1.0, 0], 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-2.4530680176354895, -3.4085090525331085, -3.6664144572672153], 'positive_zeros': ['1.70651328880567396191403880814678', '3.25991482964941801418624682659089', '4.59884925978968579407595531668447', '5.98655374117242715846154090888464', '6.91602830983979071661029809374057', '7.59237888891814503443928691959447', '8.714604647195644652880670203630661', '9.208707060766649844772330213309937', '10.37647187539469739660922524985367', '10.84532164760799796450634542704187'], 'prelabel': '2-420-60.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8313156158602968, 'root_angle': 0.38030605149882396, 'root_number': '0.36723041266985607 + 0.9301300038222222*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.190153025749', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.70651328880567396191403880815', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.25991482964941801418624682659', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.59884925978968579407595531668', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.3537168848937777, 'bad_primes': [2, 3, 5, 7], 'central_character': '60.59', 'conductor': 420, 'conductor_radical': 210, 'degree': 2, 'index': 47, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/420/2/l/f/239/3'], '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': '2-420-60.59-c1-0-47', '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': '2-420-60.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8313156158602968, 'root_angle': 0.19015302574941198, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.70651328880567396191403880815', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2163262594851962387774998037866', 'Lhash_array': ['2163262594851962387774998037866'], 'label': '2-420-60.59-c1-0-47', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/420/2/l/f/239/3'}