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lfunc_lfunctions • Show schema
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{'Lhash': '2064276638614639087701656801429', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, -1.9318516525781366], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.630445396272019, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '3267.2782', 'coefficient_field': 'CDF', 'conductor': 3267, 'conductor_radical': 33, 'conjugate': '1251287253874415730607231709267', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 1.9318516525781366], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0.5176380902050415], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, -1.4142135623730951], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 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1.27688895220846, 'root_angle': 0.32509914385947863, 'root_number': '0.52223296786709351453187376983832 + 0.85280286542244173719375092973546*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1625495719297393', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.62842713776413164374217909733', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.58563405145722755519026087337', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.94873373982252916440742829324', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.630445396272019, 'bad_primes': [3, 11], 'central_character': '11.10', 'conductor': 3267, 'conductor_radical': 33, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3267/1/c/a/2782/1'], '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': '2-3267-11.10-c0-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3267-11.10-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.27688895220846, 'root_angle': 0.16254957192973932, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.62842713776413164374217909733', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2064276638614639087701656801429', 'Lhash_array': ['2064276638614639087701656801429'], 'label': '2-3267-11.10-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3267/1/c/a/2782/1'}