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lfunc_lfunctions • Show schema
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{'Lhash': '443598806487613373793999952724', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0.9238795325112867, 1.6002062903825311], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.171221833107733, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '3528.521', 'coefficient_field': 'CDF', 'conductor': 3528, 'conductor_radical': 42, 'conjugate': '2150697107368723946782705449274', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.9238795325112867, -1.6002062903825311], [-2.5, 4.330127018922194]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.7320508075688772, -1.0], [5.5, 9.526279441628825]], [[1.0, 0], [0, -5.543277195067721], [-13.0, 0]], [[1.0, 0], [2.230442497387663, -3.8632397288362457], [-8.5, 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-0.8345875397143943, 'root_number': '-0.86798877885446785075579661516950215348299239531842555433 - 0.49658380942468281809597686178669211849429857632890836967*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4172937698571971', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.34993775604077913044155352832', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.45598028537839043050867619476', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.62848966950346826030762445142', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.171221833107733, 'bad_primes': [2, 3, 7], 'central_character': '21.17', 'conductor': 3528, 'conductor_radical': 42, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3528/2/bl/c/521/8'], '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': '2-3528-21.17-c1-0-7', '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': '2-3528-21.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.307656906122299, 'root_angle': -0.4172937698571971, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.34993775604077913044155352832', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '443598806487613373793999952724', 'Lhash_array': ['443598806487613373793999952724'], 'label': '2-3528-21.17-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3528/2/bl/c/521/8'}