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'prelabel': '8-5408e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.571384740913323, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e4-0', 'trace_hash': 1479051018772605138, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.38803538483078496095530353821', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.57456093185557302966688042000', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.67253584796936636256325940460', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3477404.0836117985, 'bad_primes': [2, 13], 'central_character': '1.1', 'conductor': 855355656503296, 'conductor_radical': 26, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, -5, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 16, 0, 0, 0, -18, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0], 'euler11': [1, 0, 13, 0, 76, 0, 1573, 0, 14641], 'euler13': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler17': [1, -8, 58, -304, 1563, -5168, 16762, -39304, 83521], 'euler19': [1, 0, -3, 0, 516, 0, -1083, 0, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, 29, 0, 924, 0, 15341, 0, 279841], 'euler29': [1, 20, 266, 2240, 14371, 64960, 223706, 487780, 707281], 'euler3': [1, 0, 5, 0, 20, 0, 45, 0, 81], 'euler31': [1, 0, 68, 0, 2806, 0, 65348, 0, 923521], 'euler37': [1, -8, 138, -784, 7643, -29008, 188922, -405224, 1874161], 'euler41': [1, 0, 130, 0, 7587, 0, 218530, 0, 2825761], 'euler43': [1, 0, 101, 0, 5020, 0, 186749, 0, 3418801], 'euler47': [1, 0, 72, 0, 2382, 0, 159048, 0, 4879681], 'euler5': [1, -2, 13, -22, 96, -110, 325, -250, 625], 'euler53': [1, 2, 205, 310, 16128, 16430, 575845, 297754, 7890481], 'euler59': [1, 0, 21, 0, 7068, 0, 73101, 0, 12117361], 'euler61': [1, 12, 162, 1488, 15803, 90768, 602802, 2723772, 13845841], 'euler67': [1, 0, 149, 0, 13300, 0, 668861, 0, 20151121], 'euler7': [1, 0, 5, 0, 100, 0, 245, 0, 2401], 'euler71': [1, 0, 205, 0, 20380, 0, 1033405, 0, 25411681], 'euler73': [1, -42, 877, -12222, 122568, -892206, 4673533, -16338714, 28398241], 'euler79': [1, 0, -64, 0, 10174, 0, -399424, 0, 38950081], 'euler83': [1, 0, 252, 0, 28566, 0, 1736028, 0, 47458321], 'euler89': [1, 18, 401, 4482, 55860, 398898, 3176321, 12689442, 62742241], 'euler97': [1, 2, 177, 370, 26756, 35890, 1665393, 1825346, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 5, 0, 20, 0, 45, 0, 81], [1, -2, 13, -22, 96, -110, 325, -250, 625], [1, 0, 5, 0, 100, 0, 245, 0, 2401], [1, 0, 13, 0, 76, 0, 1573, 0, 14641], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -8, 58, -304, 1563, -5168, 16762, -39304, 83521], [1, 0, -3, 0, 516, 0, -1083, 0, 130321], [1, 0, 29, 0, 924, 0, 15341, 0, 279841], [1, 20, 266, 2240, 14371, 64960, 223706, 487780, 707281], [1, 0, 68, 0, 2806, 0, 65348, 0, 923521], [1, -8, 138, -784, 7643, -29008, 188922, -405224, 1874161], [1, 0, 130, 0, 7587, 0, 218530, 0, 2825761], [1, 0, 101, 0, 5020, 0, 186749, 0, 3418801], [1, 0, 72, 0, 2382, 0, 159048, 0, 4879681], [1, 2, 205, 310, 16128, 16430, 575845, 297754, 7890481], [1, 0, 21, 0, 7068, 0, 73101, 0, 12117361], [1, 12, 162, 1488, 15803, 90768, 602802, 2723772, 13845841], [1, 0, 149, 0, 13300, 0, 668861, 0, 20151121], [1, 0, 205, 0, 20380, 0, 1033405, 0, 25411681], [1, -42, 877, -12222, 122568, -892206, 4673533, -16338714, 28398241], [1, 0, -64, 0, 10174, 0, -399424, 0, 38950081], [1, 0, 252, 0, 28566, 0, 1736028, 0, 47458321], [1, 18, 401, 4482, 55860, 398898, 3176321, 12689442, 62742241], [1, 2, 177, 370, 26756, 35890, 1665393, 1825346, 88529281]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5408/2/a/bi'], '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': '8-5408e4-1.1-c1e4-0-1', '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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-5408e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.571384740913323, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1479051018772605138, 'z1': {'__RealLiteral__': 0, 'data': '0.38803538483078496095530353821', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '491893288490536537865440060834,728342510134407962001824272156,852540471353368505190259584889,1710307654540408254984810495224', 'Lhash_array': ['491893288490536537865440060834', '728342510134407962001824272156', '852540471353368505190259584889', '1710307654540408254984810495224'], 'factors': ['2-5408-1.1-c1-0-13', '2-5408-1.1-c1-0-24', '2-5408-1.1-c1-0-37', '2-5408-1.1-c1-0-113'], 'label': '8-5408e4-1.1-c1e4-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5408/2/a/bi'}