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lfunc_lfunctions • Show schema
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{'Lhash': '1492572801424614393899619623035', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.5, 0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.5, 0.8660254037844386], 'a8': [0.0, 0.0], 'a9': [1.0, 1.7320508075688772], '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], [-1.0, 0]]], [13, [[1.0, 0], [-1.0, 3.4641016151377544]]]], 'bad_primes': [2, 5, 13], 'central_character': '260.61', 'coefficient_field': 'CDF', 'conductor': 260, 'conductor_radical': 130, 'conjugate': '2507979299650470274712346766042', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.5, -0.8660254037844386], [-1.5, -2.598076211353316]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.5, -0.8660254037844386], [-3.5, 6.06217782649107]], [[1.0, 0], [1.5, -2.598076211353316], [-5.5, -9.526279441628825]], [[1.0, 0], [-1.0, 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-0.8481181199495516, -1.9650742378039525, -2.527676725973397, -2.3891789795594347], 'positive_zeros': ['1.17743233124008280959897587171855', '3.04107735360159192429699392408680', '4.62920393158057106026919346180767', '5.88413821826063427914267247536010', '6.83210411564571409047157481952647', '7.73438706040159902965256644242276', '9.121818417072777770932432991858400', '9.775142104213168411996169639241613', '11.25450457241074693523981802723745', '11.57063720767422974062168494641183'], 'prelabel': '2-260-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': -0.32516952776306657, 'root_number': '0.5220443854178448 - 0.8529183194501714*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.162584763882', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.17743233124008280959897587172', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.04107735360159192429699392409', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.62920393158057106026919346181', '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': '13.9', 'conductor': 260, 'conductor_radical': 130, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/260/2/i/b/61/1'], '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': '2-260-13.9-c1-0-1', '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': '2-260-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': -0.16258476388153328, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17743233124008280959897587172', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1492572801424614393899619623035', 'Lhash_array': ['1492572801424614393899619623035'], 'label': '2-260-13.9-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/260/2/i/b/61/1'}