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lfunc_lfunctions • Show schema
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{'Lhash': '2075226589217806487661392120986', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.7071067811865476, 0.7071067811865476], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.7071067811865476, -0.7071067811865476], 'a8': [0.0, 0.0], 'a9': [0.0, 1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5988780151596029, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1200.1007', 'coefficient_field': 'CDF', 'conductor': 1200, 'conductor_radical': 30, 'conjugate': '2022201771710975763903062907527', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.7071067811865476, 0.7071067811865476], [0, -1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [-1.224744871391589, 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'7.58503914190711347193697991637057', '8.422264989579997865737134093846591', '8.813374709990459824199219602286632', '9.616820441958502558689855416076810'], 'prelabel': '2-1200-60.47-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7738720922475515, 'root_angle': -0.1249219662659375, 'root_number': '0.92397331967055129062313806981359 - 0.38245693161058178870336896159674*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.062460983132968745', 'prec': 70}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.63706512570907164309288813831', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.36489843690771134487902723627', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.73483921743346343209832230530', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5988780151596029, 'bad_primes': [2, 3, 5], 'central_character': '60.47', 'conductor': 1200, 'conductor_radical': 30, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1200/1/bj/b/1007/4'], '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': '2-1200-60.47-c0-0-4', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1200-60.47-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7738720922475515, 'root_angle': -0.06246098313296875, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.63706512570907164309288813831', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2075226589217806487661392120986', 'Lhash_array': ['2075226589217806487661392120986'], 'label': '2-1200-60.47-c0-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1200/1/bj/b/1007/4'}