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lfunc_lfunctions • Show schema
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{'Lhash': '3674723838143907594412386655886', 'a10': [-4.354248688935409, -0.9372539331937718], 'a2': [1.680141558182612, -1.0849536139705258], 'a3': [0.7379220415617695, 2.907829269502821], 'a4': [1.6457513110645905, -3.6457513110645907], 'a5': [-1.5747192837289654, -1.5747192837289654], 'a6': [4.394673363483245, 4.084953613970526], 'a7': [0.0, 3.6457513110645907], 'a8': [-1.1903758884241724, -7.91094212115462], 'a9': [-7.91094212115462, 4.291502622129181], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3079052689294253, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.680141558182612, 1.0849536139705258]]], [3, [[1.0, 0], [-0.7379220415617695, -2.907829269502821]]]], 'bad_primes': [2, 3], 'central_character': '48.29', 'coefficient_field': 'CDF', 'conductor': 48, 'conductor_radical': 6, 'conjugate': '3779537942359588198930686214480', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.680141558182612, 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0.06583875374309987, 'root_number': '0.9786850625958881 + 0.2053668625939507*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0329193768715', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.89884597339543381502222992146', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.95915352064354997919134315054', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.04628767577453036506155257882', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3079052689294253, 'bad_primes': [2, 3], 'central_character': '48.29', 'conductor': 48, 'conductor_radical': 6, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/48/3/i/a/29/4'], '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': '2-48-48.29-c2-0-7', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-48-48.29-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1436368606027987, 'root_angle': 0.03291937687154994, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.89884597339543381502222992146', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3674723838143907594412386655886', 'Lhash_array': ['3674723838143907594412386655886'], 'label': '2-48-48.29-c2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/48/3/i/a/29/4'}