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{'Lhash': '1552201016987226405552524757883,1917584557174842843751747224228,2712990196941329149978500293779,3142400952850168618390038482309', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.002346296297611515, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '441.1', 'coefficient_field': '1.1.1.1', 'conductor': 37822859361, 'conductor_radical': 21, 'degree': 8, 'euler_factors': [[1, 0, 0, 0, -1, 0, 0, 0, 1], [1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1], [1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 0, 0, 2, 0, 0, 0, 1], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 0, 0, 0, -1, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.002346296297611515, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 37822859361, 'conductor_radical': 21, '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, 0, 0, -2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 4, 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], 'euler11': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'euler13': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler17': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler19': [1, 0, -2, 0, 3, 0, -2, 0, 1], 'euler2': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'euler23': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'euler29': [1, 0, 0, 0, 2, 0, 0, 0, 1], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 0, -2, 0, 3, 0, -2, 0, 1], 'euler37': [1, 0, -2, 0, 3, 0, -2, 0, 1], 'euler41': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler43': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler47': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler5': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler53': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'euler59': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler61': [1, 0, -2, 0, 3, 0, -2, 0, 1], 'euler67': [1, -4, 10, -16, 19, -16, 10, -4, 1], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, 0, 0, 0, 2, 0, 0, 0, 1], 'euler73': [1, 0, -2, 0, 3, 0, -2, 0, 1], 'euler79': [1, 4, 10, 16, 19, 16, 10, 4, 1], 'euler83': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler89': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler97': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler_factors': [[1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 0, 0, 2, 0, 0, 0, 1], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, -4, 10, -16, 19, -16, 10, -4, 1], [1, 0, 0, 0, 2, 0, 0, 0, 1], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, 4, 10, 16, 19, 16, 10, 4, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/1/q/a'], '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': '8-21e8-1.1-c0e4-0-0', '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': '8-21e8-1.1-c0e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.4691350238163359, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e4-0', 'trace_hash': 2245895948794607465, 'z1': {'__RealLiteral__': 0, 'data': '1.22447069934551854485032977313', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1552201016987226405552524757883,1917584557174842843751747224228,2712990196941329149978500293779,3142400952850168618390038482309', 'Lhash_array': ['1552201016987226405552524757883', '1917584557174842843751747224228', '2712990196941329149978500293779', '3142400952850168618390038482309'], 'label': '8-21e8-1.1-c0e4-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/1/q/a'}