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lfunc_lfunctions • Show schema
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{'Lhash': '340344665796604548701450124404', 'a10': [0.5, -0.36327126400268045], 'a2': [0.5, -0.36327126400268045], 'a3': [-1.0, -0.7265425280053609], 'a4': [-0.5, 1.5388417685876268], 'a5': [1.0, 0.0], 'a6': [-0.7639320225002103, 0.0], 'a7': [-1.3090169943749475, 4.028740053470407], 'a8': [0.6909830056250525, 2.1266270208801], 'a9': [-0.45491502812526285, -1.400084492874739], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.673623634245049, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[31, [[1.0, 0], [0, 0]]]], 'bad_primes': [31], 'central_character': '961.388', 'coefficient_field': 'CDF', 'conductor': 961, 'conductor_radical': 31, 'conjugate': '2493379287346810081471627363669', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, 0.36327126400268045], [0.6180339887498949, -1.902113032590307]], [[1.0, 0], [1.0, 0.7265425280053609], [0.9270509831248422, 2.853169548885461]], [[1.0, 0], [-1.0, 0], [5.0, 0]], [[1.0, 0], 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-1.363929210825883, -0.2050659909517438, 0.7213089065618978], 'positive_zeros': ['0.26848460114745219926570147507951', '1.85899991109499497841123718049249', '3.72088972374755990463734373784698', '4.51702101260879024026853345430226', '5.31965735447978908765507505357551', '6.08057523351771029454983859615196', '7.09564495753994854094487202707922', '7.63747526276266042585125793828634', '9.415633351676881190578847180080967', '9.742494216546238320127615463036400'], 'prelabel': '2-31e2-31.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.77013061682027, 'root_angle': -0.7759769215508943, 'root_number': '-0.7623955954533875 - 0.6471112393037804*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.387988460775', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.26848460114745219926570147508', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.85899991109499497841123718049', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.72088972374755990463734373785', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.673623634245049, 'bad_primes': [31], 'central_character': '31.16', 'conductor': 961, 'conductor_radical': 31, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/961/2/d/d/388/1'], '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': '2-31e2-31.16-c1-0-8', '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': '2-31e2-31.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.77013061682027, 'root_angle': -0.38798846077544713, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.26848460114745219926570147508', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '340344665796604548701450124404', 'Lhash_array': ['340344665796604548701450124404'], 'label': '2-31e2-31.16-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/961/2/d/d/388/1'}