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lfunc_lfunctions • Show schema
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{'Lhash': '906584725179414509629954663471,1534292947802543504214387310112', 'a10': 0, 'a2': -2, 'a3': 0, 'a4': 2, 'a5': 0, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 150.34712629336104, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 2]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '450.1', 'coefficient_field': '1.1.1.1', 'conductor': 202500, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, 2, 2], [1], [1], [1, 4, 8, 196, 2401], [1, -16, 306, -1936, 14641], [1, 6, 18, 1014, 28561], [1, -14, 98, -4046, 83521], [1, 0, -322, 0, 130321], [1, 4, 8, 2116, 279841], [1, 0, -82, 0, 707281], [1, -104, 4626, -99944, 923521], [1, -6, 18, -8214, 1874161], [1, -16, 3426, -26896, 2825761], [1, -84, 3528, -155316, 3418801], [1, 36, 648, 79524, 4879681], [1, -106, 5618, -297754, 7890481], [1, 0, -6562, 0, 12117361], [1, 96, 9746, 357216, 13845841], [1, 124, 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{'algebraic': True, 'analytic_conductor': 150.34712629336104, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 202500, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, -2, 0, 2, 0, 0, -4, 0, 0, 0, 16, 0, -6, 8, 0, -4, 14, 0, 0, 0, 0, -32, -4, 0, 0, 12, 0, -8, 0, 0, 104, 8, 0, -28, 0, 0, 6, 0, 0, 0, 16, 0, 84, 32, 0, 8, -36, 0, 8, 0, 0, -12, 106, 0, 0, 0, 0, 0, 0, 0, -96, -208, 0, -8, 0, 0, -124, 28, 0, 0, 56, 0, 94, -12, 0, 0, -64, 0, 0, 0, 0, -32, 36, 0, 0, -168, 0, 0, 0, 0, 24, -8, 0, 72, 0, 0, 126, -16, 0, 0], 'euler11': [1, -16, 306, -1936, 14641], 'euler13': [1, 6, 18, 1014, 28561], 'euler17': [1, -14, 98, -4046, 83521], 'euler19': [1, 0, -322, 0, 130321], 'euler2': [1, 2, 2, 0, 0], 'euler23': [1, 4, 8, 2116, 279841], 'euler29': [1, 0, -82, 0, 707281], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -104, 4626, -99944, 923521], 'euler37': [1, -6, 18, -8214, 1874161], 'euler41': [1, -16, 3426, -26896, 2825761], 'euler43': [1, -84, 3528, -155316, 3418801], 'euler47': [1, 36, 648, 79524, 4879681], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, -106, 5618, -297754, 7890481], 'euler59': [1, 0, -6562, 0, 12117361], 'euler61': [1, 96, 9746, 357216, 13845841], 'euler67': [1, 124, 7688, 556636, 20151121], 'euler7': [1, 4, 8, 196, 2401], 'euler71': [1, -56, 10866, -282296, 25411681], 'euler73': [1, -94, 4418, -500926, 28398241], 'euler79': [1, 0, -12482, 0, 38950081], 'euler83': [1, -36, 648, -248004, 47458321], 'euler89': [1, 0, -9442, 0, 62742241], 'euler97': [1, -126, 7938, -1185534, 88529281], 'euler_factors': [[1, 2, 2, 0, 0], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 4, 8, 196, 2401], [1, -16, 306, -1936, 14641], [1, 6, 18, 1014, 28561], [1, -14, 98, -4046, 83521], [1, 0, -322, 0, 130321], [1, 4, 8, 2116, 279841], [1, 0, -82, 0, 707281], [1, -104, 4626, -99944, 923521], [1, -6, 18, -8214, 1874161], [1, -16, 3426, -26896, 2825761], [1, -84, 3528, -155316, 3418801], [1, 36, 648, 79524, 4879681], [1, -106, 5618, -297754, 7890481], [1, 0, -6562, 0, 12117361], [1, 96, 9746, 357216, 13845841], [1, 124, 7688, 556636, 20151121], [1, -56, 10866, -282296, 25411681], [1, -94, 4418, -500926, 28398241], [1, 0, -12482, 0, 38950081], [1, -36, 648, -248004, 47458321], [1, 0, -9442, 0, 62742241], [1, -126, 7938, -1185534, 88529281]], 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/450/3/g/b'], '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': '4-450e2-1.1-c2e2-0-8', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'prelabel': '4-450e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.5016584493941383, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e2-0', 'trace_hash': 1799912960418996163, 'z1': {'__RealLiteral__': 0, 'data': '0.71516924696457514430741542876', 'prec': 103}}
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{'Lhash': '906584725179414509629954663471,1534292947802543504214387310112', 'Lhash_array': ['906584725179414509629954663471', '1534292947802543504214387310112'], 'factors': ['2-450-5.3-c2-0-4', '2-450-5.2-c2-0-9'], 'label': '4-450e2-1.1-c2e2-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/450/3/g/b'}