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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': 1, 'A3': 1, 'A4': 1, 'A5': 1, 'A6': 1, 'A7': 1, 'A8': 1, 'A9': 1, 'Lhash': '546066596270975915', 'a10': [0.31622776601683794, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.4082482904638631, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 258.47575134288473, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1]], [5, [1, -1]], [13, [1, -1]], [83, [1, 1]]], 'bad_primes': [2, 3, 5, 13, 83], 'central_character': '32370.1', 'coefficient_field': '1.1.1.1', 'conductor': 32370, 'conductor_radical': 32370, 'degree': 2, 'euler_factors': [[1, -1], [1, -1], [1, -1], [1, -1, 7], [1, 2, 11], [1, -1], [1, 3, 17], [1, 8, 19], [1, -3, 23], [1, -2, 29], [1, -4, 31], [1, 4, 37], [1, 7, 41], [1, -2, 43], [1, 1, 47], [1, 9, 53], [1, -4, 59], [1, 8, 61], [1, 9, 67], [1, -2, 71], [1, -4, 73], [1, 4, 79], [1, 1], [1, 8, 89], [1, 0, 97]], 'gamma_factors': [[], [0]], 'index': 36, 'label': '2-32370-1.1-c1-0-36', 'leading_term': '11.3608168406', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/32370/bk', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 2.720426588139664, 4.687241514584819, 5.145449238198414, 3.8094746398942, 1.387046890001544, -0.6285329488365425, -1.036790691926512, -0.007484199352870614, 1.020312451829487, 0.7812032168699677, -0.4103909934521726, -0.9521297357842471, 0.1405343663034466, 1.864599067752754, 2.252865691729452, 0.8008330234638633, -0.7642765661442554, -0.6497680265767832, 0.544204979250097, 0.5428490182538493, -1.333311146271143, -2.84560137633617, -1.742019694258966, 0.8863524006019993, 1.846837358285022, 0.4057652140671751, -0.4467670462797393, 1.585913964473604, 4.253337298675049, 3.659460817229371, 0.1497712733971676, -1.822625425601562, -0.2366003897503589, 1.428296142311176, -0.2037860627061603, -2.613552898203723, -0.9976512975572159, 3.807233166954968, 5.826220922460558, 2.785851732986737, -0.5021439287367307, 0.2124509248914556, 2.207740332610038, 1.004954194829093, -1.660156173699233, -0.6636087265592054, 3.585474433511556, 5.333538699256493, 2.572310901285289, -0.2357873635004206, 0.1364118068815442, 1.15864867779562, 0.1996863979835298, -0.832216122842716, 0.02824869380418389, 0.6378563808189858, -0.8708379322863546, -2.032843562895631, -0.7339108846480542, 0.4928477201966874, -0.4509538215712095, -0.6506495310952761, 1.854400446367819, 2.752114695592991, -1.157439194926626, -4.568133736633193, -1.824320806366547, 2.624293263363522, 1.535227747365696, -2.077060374285433, -0.4442570920041576, 4.246145483634856, 3.357340444646185, -2.394535942397892, -4.103495215157445, -0.5740646423604253, 0.5969988578488414, -2.22102822234698, -2.460381162807337, 1.334189060730428, 3.018781109738809, 0.7843073365724951, -0.5509167424486544, 0.2687942725562442, -0.1223462505422066, -1.131934199220239, 0.3740509913327088, 1.93981919410052, -0.3619676978073839, -3.043985060816967, -1.161063003102757, 1.790433474168025, 0.5802830267584522, -1.627539293105849, -0.2899630256194973, 1.291674561379097, -0.342137422388781, -1.173779242680972, 1.391169416870977, 2.612810054382492, 0.5790969718115084, 0.1365955853688851, 1.74322045053301, 0.366308919270497, -2.09970763039841, 0.7207542428623849, 5.076428827673618, 2.736347598291176, -1.739927549052639, 1.185152390519874, 6.53117860476894, 3.723259307075595, -2.765826132056899, -2.465524872925326, 1.155672102582491, -0.3953104330373114, -3.366919325665222, -1.189493381449097, 1.846610884930488, 0.83931178560494], 'positive_zeros': ['1.403845887990044', '2.001422164035049', '2.667179615698110', '3.229334218050568', '4.107827099971517', '4.634486531222210', '5.092219633711704', '5.912600471514018', '6.560669735560193', '6.844454514202677', '7.760745625112519', '8.273838078664770', '8.732305401984239', '9.306858674847095', '10.18783745910744', '10.47611143676015', '11.08351700877180', '11.54487525624039', '12.46129603900350', '12.72524528499919', '13.28183090848415', '13.74466669468632', '14.13670096695456', '14.85244211015617', '15.16697744593878', '15.58483732933549', '16.19273566069412', '16.83649010435247', '17.34263551137309', '17.77331441343249', '18.39652944035203', '19.04361897020366', '19.31859832450575', '19.91875689649051'], 'prelabel': '2-32370-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.0771810757634, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 546066596270975915, 'z1': {'__RealLiteral__': 0, 'data': '1.403845887990044', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.001422164035049', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.667179615698110', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 258.47575134288473, 'bad_primes': [2, 3, 5, 13, 83], 'central_character': '1.1', 'conductor': 32370, 'conductor_radical': 32370, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1, 1, -3, 1, -8, 1, 1, -2, 3, 1, 1, 1, 1, 1, 2, 1, 4, 1, -2, -3, 1, 1, -4, -8, 1, 1, -7, 1, 2, -2, 1, 3, -1, 1, -6, 1, -3, 1, -9, 1, -2, 1, -8, 2, 4, 1, -8, 4, 1, 1, 1, -2, -9, -3, 3, 1, 2, 1, 4, -4, 1, -8, -2, 1, -4, 1, 1, -7, -1, 1, -3, 2, 2, -2, -8, 1, 1, 3, 4, -1, -8, 1, 0, -6, -2, 1], 'euler11': [1, 2, 11], 'euler13': [1, -1, 0], 'euler17': [1, 3, 17], 'euler19': [1, 8, 19], 'euler2': [1, -1, 0], 'euler23': [1, -3, 23], 'euler29': [1, -2, 29], 'euler3': [1, -1, 0], 'euler31': [1, -4, 31], 'euler37': [1, 4, 37], 'euler41': [1, 7, 41], 'euler43': [1, -2, 43], 'euler47': [1, 1, 47], 'euler5': [1, -1, 0], 'euler53': [1, 9, 53], 'euler59': [1, -4, 59], 'euler61': [1, 8, 61], 'euler67': [1, 9, 67], 'euler7': [1, -1, 7], 'euler71': [1, -2, 71], 'euler73': [1, -4, 73], 'euler79': [1, 4, 79], 'euler83': [1, 1, 0], 'euler89': [1, 8, 89], 'euler97': [1, 0, 97], 'euler_factors': [[1, -1, 0], [1, -1, 0], [1, -1, 0], [1, -1, 7], [1, 2, 11], [1, -1, 0], [1, 3, 17], [1, 8, 19], [1, -3, 23], [1, -2, 29], [1, -4, 31], [1, 4, 37], [1, 7, 41], [1, -2, 43], [1, 1, 47], [1, 9, 53], [1, -4, 59], [1, 8, 61], [1, 9, 67], [1, -2, 71], [1, -4, 73], [1, 4, 79], [1, 1, 0], [1, 8, 89], [1, 0, 97]], 'index': 36, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/32370/bk'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-32370-1.1-c1-0-36', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-32370-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.0771810757634, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 546066596270975915, 'z1': {'__RealLiteral__': 0, 'data': '1.403845887990044', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '546066596270975915', 'Lhash_array': ['546066596270975915'], 'factors': ['2-32370-1.1-c1-0-36'], 'label': '2-32370-1.1-c1-0-36', 'type': 'ECQ', 'url': 'EllipticCurve/Q/32370/bk'}