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lfunc_lfunctions • Show schema
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{'Lhash': '2399046771831570588680279206021', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.8632039700232084, 1.6530715828377047], 'a4': [0.0, 0.0], 'a5': [-0.8772357852101692, -2.056807569304114], 'a6': [0.0, 0.0], 'a7': [0.5170631895759412, 0.8955797150691486], 'a8': [0.0, 0.0], 'a9': [3.9652913159711085, 6.868086026073614], '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], [0.8772357852101692, 2.056807569304114]]], [13, [[1.0, 0], [-3.576723722706811, 0.4550246272745375]]]], 'bad_primes': [2, 5, 13], 'central_character': '260.69', 'coefficient_field': 'CDF', 'conductor': 260, 'conductor_radical': 130, 'conjugate': '2805355871676564653548663965968', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.8632039700232084, -1.6530715828377047], [1.5, 2.598076211353316]], [[1.0, 0], [0.8772357852101692, 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'10.85594063465423350708041407339103', '12.17865437017321543925267380793883'], 'prelabel': '2-260-65.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': -0.1726849342325902, 'root_number': '0.8564177088595183 - 0.5162835538265899*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0863424671163', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.89251420809459894046738246732', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.07774402082743044644036825962', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.07497959922960651495558330575', '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': '65.4', 'conductor': 260, 'conductor_radical': 130, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/260/2/z/a/69/8'], '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': '2-260-65.4-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': '2-260-65.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': -0.0863424671162951, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.89251420809459894046738246732', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2399046771831570588680279206021', 'Lhash_array': ['2399046771831570588680279206021'], 'label': '2-260-65.4-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/260/2/z/a/69/8'}