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lfunc_lfunctions • Show schema
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{'Lhash': '3022765090016417198594284346952', 'a10': [-1.1847925309040954, 0.0], 'a2': [0.8793852415718167, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.2266815969056775, 0.0], 'a5': [-1.3472963553338606, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [-2.8374961755702346, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.5275177946066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 7], 'central_character': '567.1', 'coefficient_field': 'CDF', 'conductor': 567, 'conductor_radical': 21, 'conjugate': '3022765090016417198594284346952', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8793852415718167, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.3472963553338606, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.6527036446661394, 0], [11.0, 0]], [[1.0, 0], [3.369585061808191, 0], [13.0, 0]], [[1.0, 0], [0.4679111137620439, 0], [17.0, 0]], [[1.0, 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'5.46011383056055644730047054973876', '6.50057767771042358522708295707264', '7.913953997702209406289956428163234', '8.245839697179878784779077894000407', '9.572310937334592632146804226006193', '10.18353691824275963884012225753495'], 'prelabel': '2-567-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.38454120518082410602072645616', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.80709206323046140474176002180', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.53132672795117656662485945350', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.5275177946066, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 567, 'conductor_radical': 21, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/567/2/a/c/1/3'], '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': '2-567-1.1-c1-0-21', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-567-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.38454120518082410602072645616', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3022765090016417198594284346952', 'Lhash_array': ['3022765090016417198594284346952'], 'label': '2-567-1.1-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/567/2/a/c/1/3'}