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lfunc_lfunctions • Show schema
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{'Lhash': '1267104790794512495347185257516', 'a10': [1.6894881501748442, -3.69946301667335], 'a2': [-1.9054922156430456, -0.5595029966006254], 'a3': [-0.6548607339452851, 0.7557495743542583], 'a4': [1.635349915008801, 1.050975574391703], 'a5': [-0.2914457762111592, 2.0270498982367156], 'a6': [1.670676182393887, -1.0736783879091123], 'a7': [1.342486253542133, 2.9396348502695946], 'a8': [0.07290125180645216, 0.08413252950851399], 'a9': [-0.14231483827328514, -0.9898214418809327], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5509677739468349, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.6548607339452851, -0.7557495743542583]]], [23, [[1.0, 0], [-1.3737459673541872, -4.594869096849018]]]], 'bad_primes': [3, 23], 'central_character': '69.64', 'coefficient_field': 'CDF', 'conductor': 69, 'conductor_radical': 69, 'conjugate': '3228185590449516012698574186952', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[-2.182539617349447, -15.179896469113421], [-79.63791681000329, 23.383802217838664]], [[1.0, 0], [-1.710600897028414, 1.9741386722497414], [-12.666020606322377, -88.094108327403]], [[1.0, 0], [0.17289301774720484, -1.2024973516047521], [-93.07081844060625, -27.32805801361868]], [[1.0, 0], [1.0835152250313898, 7.536013920635829], [-96.90879033506424, 28.4549882409844]], [[1.0, 0], [10.404006611220701, -3.054891973760316], [86.64911388161165, -55.68600419792655]], [[1.0, 0], [3.007737304313762, 3.4711138867801954], [-15.22768769524151, 105.9108942812598]], [[1.0, 0], [-0.7102740786824542, 0.45646543346340207], [45.28023641720562, -99.1498874936425]], [[1.0, 0], [10.680181341096205, 3.1359841911318607], [95.06164920992347, 61.09241237248253]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-69-23.18-c1-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': 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0.7422720350025555, 'root_angle': -0.37254477039862854, 'root_number': '0.389798166687661 - 0.9209003145004016*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.186272385199', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.999569432276039913572734679715', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '4.63021087335897201584213693447', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.48737565548604064164791349203', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5509677739468349, 'bad_primes': [3, 23], 'central_character': '23.18', 'conductor': 69, 'conductor_radical': 69, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/69/2/e/c/64/1'], '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': '2-69-23.18-c1-0-0', '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': '2-69-23.18-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7422720350025555, 'root_angle': -0.18627238519931427, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.999569432276039913572734679715', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1267104790794512495347185257516', 'Lhash_array': ['1267104790794512495347185257516'], 'label': '2-69-23.18-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/69/2/e/c/64/1'}