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lfunc_lfunctions • Show schema
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{'Lhash': '455736792362764227625434802193', 'a10': [0, 0], 'a2': [-5.12783728193508, -5.12783728193508], 'a3': [-10.337226029966937, 10.337226029966937], 'a4': [0, 36.58943038000669], 'a5': [0, 0], 'a6': [106.01522605650841, 0], 'a7': [-13.095800853708795, -13.095800853708795], 'a8': [105.57924871640508, -105.57924871640508], 'a9': [0, -132.71648398925197], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.089743539672764, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [13.095800853708795, 13.095800853708795]]]], 'bad_primes': [5, 7], 'central_character': '175.57', 'coefficient_field': 'CDF', 'conductor': 175, 'conductor_radical': 35, 'conjugate': '770946574388243224428961968872', 'degree': 2, 'euler_factors': [[[1.0, 0], [5.12783728193508, 5.12783728193508], [0, 16.0]], [[1.0, 0], [10.337226029966937, -10.337226029966937], [0, -81.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [13.095800853708795, 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'root_number': '0.9732489894677301637880577483081525807410411271519101104 - 0.2297529205473611835239373693814627187159909372855097264*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.036895904412608316', 'prec': 70}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.35951293856581048817887109148', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.79461738554919540284805983793', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.18233503787510218057695002952', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.089743539672764, 'bad_primes': [5, 7], 'central_character': '5.2', 'conductor': 175, 'conductor_radical': 35, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/175/5/g/c/57/1'], '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': '2-175-5.2-c4-0-7', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-175-5.2-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.25320391465925, 'root_angle': -0.036895904412608316, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '0.35951293856581048817887109148', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '455736792362764227625434802193', 'Lhash_array': ['455736792362764227625434802193'], 'label': '2-175-5.2-c4-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/175/5/g/c/57/1'}