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lfunc_lfunctions • Show schema
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{'Lhash': '6383131026422173735721802768626,7849080437124977575698556684885', 'a10': 0, 'a2': -2, 'a3': -4, 'a4': 2, 'a5': 0, 'a6': 8, 'a7': 4, 'a8': 0, 'a9': 8, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.0742454944658573, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 2]], [5, [1, 0, 25]]], 'bad_primes': [2, 5], 'central_character': '10.1', 'coefficient_field': '1.1.1.1', 'conductor': 100, 'conductor_radical': 10, 'degree': 4, 'euler_factors': [[1, 2, 2], [1, 4, 8, 36, 81], [1, 0, 25], [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, 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'19.62802241243125925268870039984091', '20.91840880760687132371699108974280', '20.97670027424001189851460753413717'], 'prelabel': '4-10e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.5219964217887867, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c2e2-0', 'trace_hash': 96314964279579797, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '5.03540251964772219755791684917', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.19183269878294484670114036539', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.67558497356483516574264525363', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 0.0742454944658573, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 100, 'conductor_radical': 10, 'degree': 4, 'dirichlet_coefficients': [1, -2, -4, 2, 0, 8, 4, 0, 8, 0, -16, -8, 6, -8, 0, -4, 14, -16, 0, 0, -16, 32, -4, 0, -25, -12, -36, 8, 0, 0, 104, 8, 64, -28, 0, 16, -6, 0, -24, 0, -16, 32, -84, -32, 0, 8, -36, 16, 8, 50, -56, 12, 106, 72, 0, 0, 0, 0, 0, 0, -96, -208, 32, -8, 0, -128, 124, 28, 16, 0, -56, 0, -94, 12, 100, 0, -64, 48, 0, 0, 143, 32, 36, -32, 0, 168, 0, 0, 0, 0, 24, -8, -416, 72, 0, -32, -126, -16, -128, -50], '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, 4, 8, 36, 81], '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, 25, 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, 4, 8, 36, 81], [1, 0, 25, 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': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/10/3/c/a'], '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': '4-10e2-1.1-c2e2-0-0', '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': '4-10e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.5219964217887867, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e2-0', 'trace_hash': 96314964279579797, 'z1': {'__RealLiteral__': 0, 'data': '5.03540251964772219755791684917', 'prec': 103}}
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{'Lhash': '6383131026422173735721802768626,7849080437124977575698556684885', 'Lhash_array': ['6383131026422173735721802768626', '7849080437124977575698556684885'], 'label': '4-10e2-1.1-c2e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/10/3/c/a'}