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{'Lhash': '410982295887889919944154851174,856366756447217521789146495085,1219653799148521035188913596516', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': -3, 'a6': 0, 'a7': -3, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 234980.95324300366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -3, 3, -1]], [7, [1, 3, 3, 1]], [23, [1, 3, 3, 1]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '7728.1', 'coefficient_field': '1.1.1.1', 'conductor': 461531492352, 'conductor_radical': 966, 'degree': 6, 'euler_factors': [[1], [1, -3, 3, -1], [1, 3, 0, -16, 0, 75, 125], [1, 3, 3, 1], [1, -6, 18, -48, 198, -726, 1331], [1, 9, 30, 70, 390, 1521, 2197], [1, 0, 42, 4, 714, 0, 4913], [1, 6, 60, 222, 1140, 2166, 6859], [1, 3, 3, 1], [1, 6, 18, 86, 522, 5046, 24389], [1, 0, 54, -74, 1674, 0, 29791], [1, 0, 72, 74, 2664, 0, 50653], [1, -12, 132, -966, 5412, -20172, 68921], [1, -9, 102, -558, 4386, -16641, 79507], 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'5.86061346501011050985462171864456', '6.12477993822057657532343594794853', '6.36971393201773100983475775651186', '6.56424004893800812947655026009171', '6.82096482588298673040405124893871', '7.14007549500221363358999757181552', '7.29602799138631328215052231154771', '7.36475129666248187744644476244222', '7.61701691928292059128225816506302', '7.82713227222982077365012894613231', '8.024580538701320346578820748018727'], 'prelabel': '6-7728e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.8554688390983705, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e3-0', 'trace_hash': 2005505606119775454, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.32420786596393055999396332525', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.67555425469213376190742891100', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.962137200052548421357751631647', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 234980.95324300366, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 461531492352, 'conductor_radical': 966, 'degree': 6, 'dirichlet_coefficients': [1, 0, 3, 0, -3, 0, -3, 0, 6, 0, 6, 0, -9, 0, -9, 0, 0, 0, -6, 0, -9, 0, -3, 0, 9, 0, 10, 0, -6, 0, 0, 0, 18, 0, 9, 0, 0, 0, -27, 0, 12, 0, 9, 0, -18, 0, 0, 0, 6, 0, 0, 0, -9, 0, -18, 0, -18, 0, 27, 0, -33, 0, -18, 0, 27, 0, -15, 0, -9, 0, -3, 0, 18, 0, 27, 0, -18, 0, 0, 0, 15, 0, 12, 0, 0, 0, -18, 0, 3, 0, 27, 0, 0, 0, 18, 0, 6, 0, 36, 0], 'euler11': [1, -6, 18, -48, 198, -726, 1331], 'euler13': [1, 9, 30, 70, 390, 1521, 2197], 'euler17': [1, 0, 42, 4, 714, 0, 4913], 'euler19': [1, 6, 60, 222, 1140, 2166, 6859], 'euler2': [1, 0, 0, 0, 0, 0, 0], 'euler23': [1, 3, 3, 1, 0, 0, 0], 'euler29': [1, 6, 18, 86, 522, 5046, 24389], 'euler3': [1, -3, 3, -1, 0, 0, 0], 'euler31': [1, 0, 54, -74, 1674, 0, 29791], 'euler37': [1, 0, 72, 74, 2664, 0, 50653], 'euler41': [1, -12, 132, -966, 5412, -20172, 68921], 'euler43': [1, -9, 102, -558, 4386, -16641, 79507], 'euler47': [1, 0, 69, -232, 3243, 0, 103823], 'euler5': [1, 3, 0, -16, 0, 75, 125], 'euler53': [1, 9, 174, 952, 9222, 25281, 148877], 'euler59': [1, -27, 408, -3814, 24072, -93987, 205379], 'euler61': [1, 33, 540, 5288, 32940, 122793, 226981], 'euler67': [1, 15, 264, 2082, 17688, 67335, 300763], 'euler7': [1, 3, 3, 1, 0, 0, 0], 'euler71': [1, 3, 60, -402, 4260, 15123, 357911], 'euler73': [1, -18, 234, -1942, 17082, -95922, 389017], 'euler79': [1, 0, 144, 344, 11376, 0, 493039], 'euler83': [1, -12, 270, -1910, 22410, -82668, 571787], 'euler89': [1, -3, 108, -510, 9612, -23763, 704969], 'euler97': [1, -6, 84, 492, 8148, -56454, 912673], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0], [1, -3, 3, -1, 0, 0, 0], [1, 3, 0, -16, 0, 75, 125], [1, 3, 3, 1, 0, 0, 0], [1, -6, 18, -48, 198, -726, 1331], [1, 9, 30, 70, 390, 1521, 2197], [1, 0, 42, 4, 714, 0, 4913], [1, 6, 60, 222, 1140, 2166, 6859], [1, 3, 3, 1, 0, 0, 0], [1, 6, 18, 86, 522, 5046, 24389], [1, 0, 54, -74, 1674, 0, 29791], [1, 0, 72, 74, 2664, 0, 50653], [1, -12, 132, -966, 5412, -20172, 68921], [1, -9, 102, -558, 4386, -16641, 79507], [1, 0, 69, -232, 3243, 0, 103823], [1, 9, 174, 952, 9222, 25281, 148877], [1, -27, 408, -3814, 24072, -93987, 205379], [1, 33, 540, 5288, 32940, 122793, 226981], [1, 15, 264, 2082, 17688, 67335, 300763], [1, 3, 60, -402, 4260, 15123, 357911], [1, -18, 234, -1942, 17082, -95922, 389017], [1, 0, 144, 344, 11376, 0, 493039], [1, -12, 270, -1910, 22410, -82668, 571787], [1, -3, 108, -510, 9612, -23763, 704969], [1, -6, 84, 492, 8148, -56454, 912673]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7728/2/a/bu'], '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': '6-7728e3-1.1-c1e3-0-1', 'motivic_weight': 1, '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}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '6-7728e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.8554688390983705, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 2005505606119775454, 'z1': {'__RealLiteral__': 0, 'data': '0.32420786596393055999396332525', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '410982295887889919944154851174,856366756447217521789146495085,1219653799148521035188913596516', 'Lhash_array': ['410982295887889919944154851174', '856366756447217521789146495085', '1219653799148521035188913596516'], 'label': '6-7728e3-1.1-c1e3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7728/2/a/bu'}