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lfunc_lfunctions • Show schema
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{'Lhash': '3609312183015579899004516048882', 'a10': [0.0, 0.0], 'a2': [2.7152478256666988, 2.7152478256666988], 'a3': [16.98471565962474, -16.98471565962474], 'a4': [0.0, -49.25485849042453], 'a5': [0.0, 0.0], 'a6': [92.23542452872641, -1.6897028702303112e-60], 'a7': [-383.5996143778139, -383.5996143778139], 'a8': [307.5150082623149, -307.5150082623149], 'a9': [0.0, 152.03886792339623], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.751352090496276, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]]], 'bad_primes': [5], 'central_character': '25.7', 'coefficient_field': 'CDF', 'conductor': 25, 'conductor_radical': 5, 'conjugate': '1586657077069825823383129922104', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.7152478256666988, -2.7152478256666988], [0, 64.0]], [[1.0, 0], [-16.98471565962474, 16.98471565962474], [0, -729.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [383.5996143778139, 383.5996143778139], [0, 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'root_number': '0.43757086043056154 + 0.8991839311854155*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.177919458625', 'prec': 47}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.84724527591889659009133171278', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.06497223377640138429993403034', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.52225920956419586112800239273', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.751352090496276, 'bad_primes': [5], 'central_character': '5.2', 'conductor': 25, 'conductor_radical': 5, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/25/7/c/d/7/3'], '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': '2-5e2-5.2-c6-0-5', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-5e2-5.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.39819767544218, 'root_angle': 0.17791945862485206, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '2.84724527591889659009133171278', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3609312183015579899004516048882', 'Lhash_array': ['3609312183015579899004516048882'], 'label': '2-5e2-5.2-c6-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/25/7/c/d/7/3'}