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lfunc_lfunctions • Show schema
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{'Lhash': '2355759459226810899214303230790', 'a10': [2.9270509831248424, 2.1266270208801], 'a2': [1.3090169943749475, 0.9510565162951535], 'a3': [-0.30901699437494745, -0.9510565162951535], 'a4': [0.19098300562505258, 0.5877852522924731], 'a5': [2.23606797749979, 0.0], 'a6': [0.5, -1.5388417685876268], 'a7': [-1.0, 0.0], 'a8': [0.6909830056250525, -2.1266270208801], 'a9': [-0.8090169943749475, 0.5877852522924731], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.192146106117222, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.30901699437494745, 0.9510565162951535]]], [5, [[1.0, 0], [-2.23606797749979, 0]]], [7, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 7], 'central_character': '525.316', 'coefficient_field': 'CDF', 'conductor': 525, 'conductor_radical': 105, 'conjugate': '1724585621817636137162045265492', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3090169943749475, -0.9510565162951535], 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[12.669696769372845, -38.9933171681013]], [[1.0, 0], [-1.0, 0], [43.0, 0]], [[1.0, 0], [-3.708203932499369, -11.412678195541844], [-38.02379873562253, 27.625906857746237]], [[1.0, 0], [-1.2639320225002102, -3.889982777757519], [-42.877900701872214, 31.152618371501077]], [[1.0, 0], [8.354101966249685, -6.069610361773602], [18.232002668121897, -56.11233446141406]], [[1.0, 0], [0.2360679774997897, 0.17151342515380985], [18.850036656871794, 58.014447494004365]], [[1.0, 0], [1.7811529493745268, -5.481825109481129], [-54.20413862312148, -39.3816119035957]], [[1.0, 0], [-0.45491502812526285, -1.400084492874739], [-57.440206600621266, 41.73275291276559]], [[1.0, 0], [11.399186938124421, 8.281994095230607], [22.558240589371163, 69.42712568954622]], [[1.0, 0], [2.336881039375368, 7.192180303222566], [-63.912342555620846, 46.43503493110538]], [[1.0, 0], [4.0, -12.310734148701014], [-67.14841053312064, -48.78617594027527]], [[1.0, 0], [3.618033988749895, 2.628655560595668], [27.502512499370322, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.192146106117222, 'bad_primes': [3, 5, 7], 'central_character': '25.16', 'conductor': 525, 'conductor_radical': 105, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/525/2/n/a/316/1'], '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': '2-525-25.16-c1-0-20', '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': '2-525-25.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0474731026602577, 'root_angle': 0.02, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.85836653948862329741753387911', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2355759459226810899214303230790', 'Lhash_array': ['2355759459226810899214303230790'], 'label': '2-525-25.16-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/525/2/n/a/316/1'}