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{'Lhash': '150431085669840716302559975526,687919871999396479463472457481,1964240573095847222862132723289,2538238567344599457788806273998', 'a10': 0, 'a2': 0, 'a3': 4, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 46599.33510715295, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 0, 4, 0, 25]], [23, [1, 12, 82, 276, 529]]], 'bad_primes': [2, 5, 23], 'central_character': '1840.1', 'coefficient_field': '1.1.1.1', 'conductor': 11462287360000, 'conductor_radical': 230, 'degree': 8, 'euler_factors': [[1], [1, -4, 18, -40, 91, -120, 162, -108, 81], [1, 0, 4, 0, 25], [1, 0, -28, 0, 294, 0, -1372, 0, 2401], [1, 0, -4, 0, 246, 0, -484, 0, 14641], [1, 0, -10, 0, 363, 0, -1690, 0, 28561], [1, 0, 56, 0, 1362, 0, 16184, 0, 83521], [1, 0, 64, 0, 1746, 0, 23104, 0, 130321], [1, 12, 82, 276, 529], [1, 12, 170, 1152, 8259, 33408, 142970, 292668, 707281], [1, 0, -82, 0, 3603, 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'euler_factors_factorization': [[1], [[[1, -1, 3], 4]], [[[1, 0, 4, 0, 25], 1]], [[[1, 0, -7], 4]], [[[1, 0, -2, 0, 121], 2]], [[[1, 0, -5, 0, 169], 2]], [[[1, 0, 28, 0, 289], 2]], [[[1, 0, 32, 0, 361], 2]], [[[1, 6, 23], 2]], [[[1, 3, 29], 4]], [[[1, 0, -41, 0, 961], 2]], [[[1, 0, 50, 0, 1369], 2]], [[[1, 3, 41], 4]], [[[1, 0, 40, 0, 1849], 2]], [[[1, 9, 47], 4]], [[[1, 0, 82, 0, 2809], 2]], [[[1, 0, -34, 0, 3481], 2]], [[[1, 0, 4, 0, 3721], 2]], [[[1, 0, -67], 4]], [[[1, 0, 47, 0, 5041], 2]], [[[1, 0, -125, 0, 5329], 2]], [[[1, 0, 104, 0, 6241], 2]], [[[1, 0, -152, 0, 6889], 2]], [[[1, 0, -164, 0, 7921], 2]], [[[1, 0, 98, 0, 9409], 2]], [[[1, -12, 101], 4]], [[[1, 0, -80, 0, 10609], 2]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '8-1840e4-1.1-c1e4-0-0', 'leading_term': '0.39850070681149674745955092096004702204864176354167647157297427484631124793463428545992568', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': 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'8.308678797095548808501712471759508', '8.369471043430888707803548604073231', '8.715694221292644285687249893231139', '8.760914035027131734209386337845569', '8.789598801437329937897341846001850', '8.894035635666149981426830181726768', '9.403053071224399953500961090180723', '9.710435337968110491174930506724162'], 'prelabel': '8-1840e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.833076306560515, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e4-0', 'trace_hash': 425318843339091544, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.11866920241489012450222362196', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.54267309294496647913256063402', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.54951259656422904729164029608', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 46599.33510715295, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 11462287360000, 'conductor_radical': 230, 'degree': 8, 'dirichlet_coefficients': [1, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, -4, 0, -40, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, -36, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, -55, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -4, 0, 246, 0, -484, 0, 14641], 'euler13': [1, 0, -10, 0, 363, 0, -1690, 0, 28561], 'euler17': [1, 0, 56, 0, 1362, 0, 16184, 0, 83521], 'euler19': [1, 0, 64, 0, 1746, 0, 23104, 0, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 12, 82, 276, 529, 0, 0, 0, 0], 'euler29': [1, 12, 170, 1152, 8259, 33408, 142970, 292668, 707281], 'euler3': [1, -4, 18, -40, 91, -120, 162, -108, 81], 'euler31': [1, 0, -82, 0, 3603, 0, -78802, 0, 923521], 'euler37': [1, 0, 100, 0, 5238, 0, 136900, 0, 1874161], 'euler41': [1, 12, 218, 1584, 14595, 64944, 366458, 827052, 2825761], 'euler43': [1, 0, 80, 0, 5298, 0, 147920, 0, 3418801], 'euler47': [1, 36, 674, 7992, 65499, 375624, 1488866, 3737628, 4879681], 'euler5': [1, 0, 4, 0, 25, 0, 0, 0, 0], 'euler53': [1, 0, 164, 0, 12342, 0, 460676, 0, 7890481], 'euler59': [1, 0, -68, 0, 8118, 0, -236708, 0, 12117361], 'euler61': [1, 0, 8, 0, 7458, 0, 29768, 0, 13845841], 'euler67': [1, 0, -268, 0, 26934, 0, -1203052, 0, 20151121], 'euler7': [1, 0, -28, 0, 294, 0, -1372, 0, 2401], 'euler71': [1, 0, 94, 0, 12291, 0, 473854, 0, 25411681], 'euler73': [1, 0, -250, 0, 26283, 0, -1332250, 0, 28398241], 'euler79': [1, 0, 208, 0, 23298, 0, 1298128, 0, 38950081], 'euler83': [1, 0, -304, 0, 36882, 0, -2094256, 0, 47458321], 'euler89': [1, 0, -328, 0, 42738, 0, -2598088, 0, 62742241], 'euler97': [1, 0, 196, 0, 28422, 0, 1844164, 0, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -4, 18, -40, 91, -120, 162, -108, 81], [1, 0, 4, 0, 25, 0, 0, 0, 0], [1, 0, -28, 0, 294, 0, -1372, 0, 2401], [1, 0, -4, 0, 246, 0, -484, 0, 14641], [1, 0, -10, 0, 363, 0, -1690, 0, 28561], [1, 0, 56, 0, 1362, 0, 16184, 0, 83521], [1, 0, 64, 0, 1746, 0, 23104, 0, 130321], [1, 12, 82, 276, 529, 0, 0, 0, 0], [1, 12, 170, 1152, 8259, 33408, 142970, 292668, 707281], [1, 0, -82, 0, 3603, 0, -78802, 0, 923521], [1, 0, 100, 0, 5238, 0, 136900, 0, 1874161], [1, 12, 218, 1584, 14595, 64944, 366458, 827052, 2825761], [1, 0, 80, 0, 5298, 0, 147920, 0, 3418801], [1, 36, 674, 7992, 65499, 375624, 1488866, 3737628, 4879681], [1, 0, 164, 0, 12342, 0, 460676, 0, 7890481], [1, 0, -68, 0, 8118, 0, -236708, 0, 12117361], [1, 0, 8, 0, 7458, 0, 29768, 0, 13845841], [1, 0, -268, 0, 26934, 0, -1203052, 0, 20151121], [1, 0, 94, 0, 12291, 0, 473854, 0, 25411681], [1, 0, -250, 0, 26283, 0, -1332250, 0, 28398241], [1, 0, 208, 0, 23298, 0, 1298128, 0, 38950081], [1, 0, -304, 0, 36882, 0, -2094256, 0, 47458321], [1, 0, -328, 0, 42738, 0, -2598088, 0, 62742241], [1, 0, 196, 0, 28422, 0, 1844164, 0, 88529281]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1840/2/m/d'], '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': '8-1840e4-1.1-c1e4-0-0', '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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-1840e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.833076306560515, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 425318843339091544, 'z1': {'__RealLiteral__': 0, 'data': '0.11866920241489012450222362196', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '150431085669840716302559975526,687919871999396479463472457481,1964240573095847222862132723289,2538238567344599457788806273998', 'Lhash_array': ['150431085669840716302559975526', '687919871999396479463472457481', '1964240573095847222862132723289', '2538238567344599457788806273998'], 'factors': ['2-1840-460.459-c1-0-2', '2-1840-460.459-c1-0-18', '2-1840-460.459-c1-0-57', '2-1840-460.459-c1-0-68'], 'label': '8-1840e4-1.1-c1e4-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1840/2/m/d'}