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lfunc_lfunctions • Show schema
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{'Lhash': '2100239216507175808422741770089', 'a10': [1.1978186211170925, -8.331011502744426], 'a2': [-0.8308300260037729, -1.8192639907090367], 'a3': [-2.878478920843492, 0.8451976705242891], 'a4': [-2.6194429357811404, 3.022998297417033], 'a5': [3.5402813892487988, 2.2752006970654897], 'a6': [3.9291644036717104, 4.53449744612555], 'a7': [-0.4843899068948747, -3.3690058035589825], 'a8': [7.675943788915979, 2.2538604547314374], 'a9': [7.571281795480631, -4.8657673571003786], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.142263580792209, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8308300260037729, 1.8192639907090367]]], [3, [[1.0, 0], [2.878478920843492, -0.8451976705242891]]], [23, [[1.0, 0], [98.82475473121879, 48.99661062067916]]]], 'bad_primes': [2, 3, 23], 'central_character': '138.73', 'coefficient_field': 'CDF', 'conductor': 138, 'conductor_radical': 138, 'conjugate': 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0.6999416771683522, 'root_number': '-0.5876370090101561 + 0.8091246786754175*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.349970838584', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.65679660951451930826323589557', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.19447521818929388578458520030', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.59609861029680266945397489595', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.142263580792209, 'bad_primes': [2, 3, 23], 'central_character': '23.4', 'conductor': 138, 'conductor_radical': 138, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/138/4/e/c/73/3'], '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': '2-138-23.4-c3-0-6', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-138-23.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8534651882916338, 'root_angle': 0.3499708385841761, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.65679660951451930826323589557', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2100239216507175808422741770089', 'Lhash_array': ['2100239216507175808422741770089'], 'label': '2-138-23.4-c3-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/138/4/e/c/73/3'}