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lfunc_lfunctions • Show schema
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{'Lhash': '1946797243581790880595227661784', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, -0.5293165801288394], 'a4': [0.0, 0.0], 'a5': [-2.778457118258389, 0.0], 'a6': [0.0, 0.0], 'a7': [3.18076505270593, 0.0], 'a8': [0.0, 0.0], 'a9': [2.7198239580007098, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.810734151149071, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-0.6656468759659453, -3.2491405381295495]]]], 'bad_primes': [2, 11], 'central_character': '352.351', 'coefficient_field': 'CDF', 'conductor': 352, 'conductor_radical': 22, 'conjugate': '1480002846578126061503810409730', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0.5293165801288394], [-3.0, 0]], [[1.0, 0], [2.778457118258389, 0], [5.0, 0]], [[1.0, 0], [-3.18076505270593, 0], [7.0, 0]], [[1.0, 0], [-0.6656468759659453, -3.2491405381295495]], [[1.0, 0], [0, 6.00919217745212], [-13.0, 0]], [[1.0, 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'4.27225032014185792324947059741428', '5.53893932507849803931166704769244', '7.06398011960465920630869206297308', '7.79415019637989975101379066571751', '8.671129086187156632144687214532312', '9.682541172027293157331795376934084', '10.92221180764582702954265060676230', '11.62124500138722377379424774724370'], 'prelabel': '2-352-44.43-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6765244260520247, 'root_angle': 0.18567832749619878, 'root_number': '0.8346354810650872 + 0.5508026994734598*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0928391637481', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.53575223585370216916168653561', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.74233511904721328525009843824', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.27225032014185792324947059741', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.810734151149071, 'bad_primes': [2, 11], 'central_character': '44.43', 'conductor': 352, 'conductor_radical': 22, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/352/2/e/a/351/6'], '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': '2-352-44.43-c1-0-6', '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': '2-352-44.43-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6765244260520247, 'root_angle': 0.09283916374809939, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.53575223585370216916168653561', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1946797243581790880595227661784', 'Lhash_array': ['1946797243581790880595227661784'], 'label': '2-352-44.43-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/352/2/e/a/351/6'}