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  • lfunc_lfunctions • Show schema
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'8.575130633473291541202372990910825', '8.845318237055460923773589267055141', '8.851083345425172667655821260988262'], 'prelabel': '8-3312e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.142611510647881, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e4-0', 'trace_hash': 756556063571677276, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.35710540578101969505754034865', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '0.880996477802219952126540561766', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '1.00196158267255976486742537928', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 489181.1802208488, 'bad_primes': [2, 3, 23], 'central_character': '1.1', 'conductor': 120326507790336, 'conductor_radical': 138, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 4, 0, -2, 0, 0, 0, -2, 0, 4, 0, 0, 0, 2, 0, -8, 0, 0, 0, 4, 0, 4, 0, 0, 0, 12, 0, -12, 0, 0, 0, -8, 0, 14, 0, 0, 0, 4, 0, -4, 0, 0, 0, 12, 0, 2, 0, 0, 0, 8, 0, -8, 0, 0, 0, 16, 0, 6, 0, 0, 0, 16, 0, -8, 0, 0, 0, 12, 0, 16, 0, 0, 0, 4, 0, -10, 0, 0, 0, 14, 0, 8, 0, 0, 0, 14, 0, -8, 0, 0, 0, -32, 0, 4, 0, 0, 0], 'euler11': [1, 2, 22, -6, 194, -66, 2662, 2662, 14641], 'euler13': [1, -4, 32, -108, 526, -1404, 5408, -8788, 28561], 'euler17': [1, -2, 46, -30, 938, -510, 13294, -9826, 83521], 'euler19': [1, 8, 60, 216, 1114, 4104, 21660, 54872, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -4, 6, -4, 1, 0, 0, 0, 0], 'euler29': [1, -12, 144, -996, 6574, -28884, 121104, -292668, 707281], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 12, 152, 1068, 7406, 33108, 146072, 357492, 923521], 'euler37': [1, -14, 138, -938, 5882, -34706, 188922, -709142, 1874161], 'euler41': [1, -4, 88, -108, 3662, -4428, 147928, -275684, 2825761], 'euler43': [1, 4, 28, 220, 3178, 9460, 51772, 318028, 3418801], 'euler47': [1, -12, 132, -972, 8006, -45684, 291588, -1245876, 4879681], 'euler5': [1, -4, 12, -36, 106, -180, 300, -500, 625], 'euler53': [1, -8, 140, -920, 10906, -48760, 393260, -1191016, 7890481], 'euler59': [1, -16, 144, -912, 5166, -53808, 501264, -3286064, 12117361], 'euler61': [1, -6, 234, -1090, 21114, -66490, 870714, -1361886, 13845841], 'euler67': [1, 8, 140, 696, 10906, 46632, 628460, 2406104, 20151121], 'euler7': [1, 2, 2, -6, 2, -42, 98, 686, 2401], 'euler71': [1, -12, 256, -2396, 26398, -170116, 1290496, -4294932, 25411681], 'euler73': [1, -16, 224, -2112, 21950, -154176, 1193696, -6224272, 28398241], 'euler79': [1, 10, 282, 2082, 32722, 164478, 1759962, 4930390, 38950081], 'euler83': [1, -14, 382, -3542, 49650, -293986, 2631598, -8005018, 47458321], 'euler89': [1, -14, 230, -2954, 28234, -262906, 1821830, -9869566, 62742241], 'euler97': [1, -4, 284, -1116, 37766, -108252, 2672156, -3650692, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -4, 12, -36, 106, -180, 300, -500, 625], [1, 2, 2, -6, 2, -42, 98, 686, 2401], [1, 2, 22, -6, 194, -66, 2662, 2662, 14641], [1, -4, 32, -108, 526, -1404, 5408, -8788, 28561], [1, -2, 46, -30, 938, -510, 13294, -9826, 83521], [1, 8, 60, 216, 1114, 4104, 21660, 54872, 130321], [1, -4, 6, -4, 1, 0, 0, 0, 0], [1, -12, 144, -996, 6574, -28884, 121104, -292668, 707281], [1, 12, 152, 1068, 7406, 33108, 146072, 357492, 923521], [1, -14, 138, -938, 5882, -34706, 188922, -709142, 1874161], [1, -4, 88, -108, 3662, -4428, 147928, -275684, 2825761], [1, 4, 28, 220, 3178, 9460, 51772, 318028, 3418801], [1, -12, 132, -972, 8006, -45684, 291588, -1245876, 4879681], [1, -8, 140, -920, 10906, -48760, 393260, -1191016, 7890481], [1, -16, 144, -912, 5166, -53808, 501264, -3286064, 12117361], [1, -6, 234, -1090, 21114, -66490, 870714, -1361886, 13845841], [1, 8, 140, 696, 10906, 46632, 628460, 2406104, 20151121], [1, -12, 256, -2396, 26398, -170116, 1290496, -4294932, 25411681], [1, -16, 224, -2112, 21950, -154176, 1193696, -6224272, 28398241], [1, 10, 282, 2082, 32722, 164478, 1759962, 4930390, 38950081], [1, -14, 382, -3542, 49650, -293986, 2631598, -8005018, 47458321], [1, -14, 230, -2954, 28234, -262906, 1821830, -9869566, 62742241], [1, -4, 284, -1116, 37766, -108252, 2672156, -3650692, 88529281]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3312/2/a/bh'], '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': '8-3312e4-1.1-c1e4-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-3312e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.142611510647881, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 756556063571677276, 'z1': {'__RealLiteral__': 0, 'data': '0.35710540578101969505754034865', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '452684881983055038084147519376,1116795713884940102494684649640,1270137201680497081806098526554,1415778504655405854653027490586', 'Lhash_array': ['452684881983055038084147519376', '1116795713884940102494684649640', '1270137201680497081806098526554', '1415778504655405854653027490586'], 'factors': ['2-3312-1.1-c1-0-2', '2-3312-1.1-c1-0-15', '2-3312-1.1-c1-0-18', '2-3312-1.1-c1-0-23'], 'label': '8-3312e4-1.1-c1e4-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3312/2/a/bh'}