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{'algebraic': True, 'analytic_conductor': 23.250869755659934, 'bad_primes': [5, 11], 'central_character': '1.1', 'conductor': 5719140625, 'conductor_radical': 55, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 2, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 24, 0, 0, 8, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 8, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, -6, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0], 'euler11': [1, -4, 6, -4, 1, 0, 0, 0, 0], 'euler13': [1, 0, -4, 0, -170, 0, -676, 0, 28561], 'euler17': [1, 0, -20, 0, 166, 0, -5780, 0, 83521], 'euler19': [1, 0, 76, 0, 2166, 0, 27436, 0, 130321], 'euler2': [1, 0, -2, 0, 1, 0, -8, 0, 16], 'euler23': [1, 0, -76, 0, 2502, 0, -40204, 0, 279841], 'euler29': [1, 8, 76, 472, 3510, 13688, 63916, 195112, 707281], 'euler3': [1, 0, 4, 0, 22, 0, 36, 0, 81], 'euler31': [1, 0, 124, 0, 5766, 0, 119164, 0, 923521], 'euler37': [1, 0, -76, 0, 3670, 0, -104044, 0, 1874161], 'euler41': [1, -24, 380, -3816, 29094, -156456, 638780, -1654104, 2825761], 'euler43': [1, 0, -100, 0, 6198, 0, -184900, 0, 3418801], 'euler47': [1, 0, -172, 0, 11814, 0, -379948, 0, 4879681], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 0, -76, 0, 2454, 0, -213484, 0, 7890481], 'euler59': [1, -16, 268, -2576, 24918, -151984, 932908, -3286064, 12117361], 'euler61': [1, -8, 12, -472, 9398, -28792, 44652, -1815848, 13845841], 'euler67': [1, 0, -92, 0, 6486, 0, -412988, 0, 20151121], 'euler7': [1, 0, -20, 0, 198, 0, -980, 0, 2401], 'euler71': [1, 0, 28, 0, 10278, 0, 141148, 0, 25411681], 'euler73': [1, 0, -244, 0, 25030, 0, -1300276, 0, 28398241], 'euler79': [1, 16, 412, 4048, 52870, 319792, 2571292, 7888624, 38950081], 'euler83': [1, 0, -260, 0, 30678, 0, -1791140, 0, 47458321], 'euler89': [1, -8, 124, -1144, 21606, -101816, 982204, -5639752, 62742241], 'euler97': [1, 0, -316, 0, 43270, 0, -2973244, 0, 88529281], 'euler_factors': [[1, 0, -2, 0, 1, 0, -8, 0, 16], [1, 0, 4, 0, 22, 0, 36, 0, 81], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -20, 0, 198, 0, -980, 0, 2401], [1, -4, 6, -4, 1, 0, 0, 0, 0], [1, 0, -4, 0, -170, 0, -676, 0, 28561], [1, 0, -20, 0, 166, 0, -5780, 0, 83521], [1, 0, 76, 0, 2166, 0, 27436, 0, 130321], [1, 0, -76, 0, 2502, 0, -40204, 0, 279841], [1, 8, 76, 472, 3510, 13688, 63916, 195112, 707281], [1, 0, 124, 0, 5766, 0, 119164, 0, 923521], [1, 0, -76, 0, 3670, 0, -104044, 0, 1874161], [1, -24, 380, -3816, 29094, -156456, 638780, -1654104, 2825761], [1, 0, -100, 0, 6198, 0, -184900, 0, 3418801], [1, 0, -172, 0, 11814, 0, -379948, 0, 4879681], [1, 0, -76, 0, 2454, 0, -213484, 0, 7890481], [1, -16, 268, -2576, 24918, -151984, 932908, -3286064, 12117361], [1, -8, 12, -472, 9398, -28792, 44652, -1815848, 13845841], [1, 0, -92, 0, 6486, 0, -412988, 0, 20151121], [1, 0, 28, 0, 10278, 0, 141148, 0, 25411681], [1, 0, -244, 0, 25030, 0, -1300276, 0, 28398241], [1, 16, 412, 4048, 52870, 319792, 2571292, 7888624, 38950081], [1, 0, -260, 0, 30678, 0, -1791140, 0, 47458321], [1, -8, 124, -1144, 21606, -101816, 982204, -5639752, 62742241], [1, 0, -316, 0, 43270, 0, -2973244, 0, 88529281]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/275/2/b/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': '8-275e4-1.1-c1e4-0-3', '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': '8-275e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.481852238107839, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1706043358263505286, 'z1': {'__RealLiteral__': 0, 'data': '0.824723059246608476425168087687', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1045460681076024833317833732389,1695098127390482797993170379186,3390514462241935472179219710637,4818660800468690872904183286682', 'Lhash_array': ['1045460681076024833317833732389', '1695098127390482797993170379186', '3390514462241935472179219710637', '4818660800468690872904183286682'], 'label': '8-275e4-1.1-c1e4-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/275/2/b/d'}