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lfunc_lfunctions • Show schema
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{'Lhash': '2487562765340713106115890064125', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.6016791318831545, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, -1.0], 'a6': [0.0, 0.0], 'a7': [0.0, 2.768734305276283], 'a8': [0.0, 0.0], 'a9': [3.768734305276283, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.076110452553291, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 1.0]]], [13, [[1.0, 0], [0.1670551733931289, 3.6016791318831545]]]], 'bad_primes': [2, 5, 13], 'central_character': '260.181', 'coefficient_field': 'CDF', 'conductor': 260, 'conductor_radical': 130, 'conjugate': '2667643460856862447054634616635', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.6016791318831545, 0], [3.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, -2.768734305276283], [-7.0, 0]], [[1.0, 0], [0, -2.1670551733931287], [-11.0, 0]], [[1.0, 0], [0.1670551733931289, 3.6016791318831545]], [[1.0, 0], 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'6.13715016848265939728381532285686', '7.37797870919718603160532688692848', '8.008731783985377883890187855713480', '9.081145924994609554438741163390406', '9.939604970373444136465959354113587', '10.85060556579051053459800402540234', '12.01059085311433131513018270971886'], 'prelabel': '2-260-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': -0.01475346016023625, 'root_number': '0.9989260605979493 - 0.04633276873080413*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00737673008012', 'prec': 57}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.96234101486075831207888516286', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.44543364396445653262921987706', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.15705663020660915758076541043', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.076110452553291, 'bad_primes': [2, 5, 13], 'central_character': '13.12', 'conductor': 260, 'conductor_radical': 130, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/260/2/f/a/181/5'], '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': '2-260-13.12-c1-0-3', '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': '2-260-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': -0.007376730080118125, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.96234101486075831207888516286', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2487562765340713106115890064125', 'Lhash_array': ['2487562765340713106115890064125'], 'label': '2-260-13.12-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/260/2/f/a/181/5'}