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{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e4-0', 'trace_hash': 1197133602664870614, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.69209541322626166937473202695', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.15600757047971530270336309326', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.20749128807090368073365284731', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.0246855420925831, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 16518176833536, 'conductor_radical': 42, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, 2, 0, 2, 0, 2, 0, 1], 'euler13': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'euler17': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler19': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'euler2': [1, 0, 0, 0, 1, 0, 0, 0, 0], 'euler23': [1, -4, 8, -12, 14, -12, 8, -4, 1], 'euler29': [1, 0, 2, 0, 2, 0, 2, 0, 1], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler37': [1, 0, 2, 0, 2, 0, 2, 0, 1], 'euler41': [1, 0, 0, 0, 2, 0, 0, 0, 1], 'euler43': [1, 4, 6, 4, 2, 4, 6, 4, 1], 'euler47': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'euler53': [1, -4, 6, -4, 2, -4, 6, -4, 1], 'euler59': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'euler61': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'euler67': [1, -4, 6, -4, 2, -4, 6, -4, 1], 'euler7': [1, 0, 0, 0, 1, 0, 0, 0, 0], 'euler71': [1, 0, 0, 0, 2, 0, 0, 0, 1], 'euler73': [1, 0, 0, 0, 2, 0, 0, 0, 1], 'euler79': [1, 0, 0, 0, 2, 0, 0, 0, 1], 'euler83': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'euler89': [1, 0, 0, 0, 2, 0, 0, 0, 1], 'euler97': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler_factors': [[1, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 2, 0, 2, 0, 2, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 1], [1, -4, 8, -12, 14, -12, 8, -4, 1], [1, 0, 2, 0, 2, 0, 2, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, 2, 0, 2, 0, 2, 0, 1], [1, 0, 0, 0, 2, 0, 0, 0, 1], [1, 4, 6, 4, 2, 4, 6, 4, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, -4, 6, -4, 2, -4, 6, -4, 1], [1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 1], [1, -4, 6, -4, 2, -4, 6, -4, 1], [1, 0, 0, 0, 2, 0, 0, 0, 1], [1, 0, 0, 0, 2, 0, 0, 0, 1], [1, 0, 0, 0, 2, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 2, 0, 0, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2016/1/dp/b'], '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': '8-2016e4-1.1-c0e4-0-7', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0, 0, 0], 'order_of_vanishing': 0, 'prelabel': '8-2016e4-1.1-c0e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.0030528727181498, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e4-0', 'trace_hash': 1197133602664870614, 'z1': {'__RealLiteral__': 0, 'data': '0.69209541322626166937473202695', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '877335165991475062879123867251,1465413690586988307237343219069,1530677056093438907413129057920,2367071935873319220039769239084', 'Lhash_array': ['877335165991475062879123867251', '1465413690586988307237343219069', '1530677056093438907413129057920', '2367071935873319220039769239084'], 'factors': ['2-2016-224.69-c0-0-0', '2-2016-224.181-c0-0-0', '2-2016-224.13-c0-0-0', '2-2016-224.125-c0-0-2'], 'label': '8-2016e4-1.1-c0e4-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2016/1/dp/b'}