-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1336779381936000765812307819259', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 35.13417688936339, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [11, [1, -1]]], 'bad_primes': [2, 5, 11], 'central_character': '4400.1', 'coefficient_field': '1.1.1.1', 'conductor': 4400, 'conductor_radical': 110, 'degree': 2, 'euler_factors': [[1], [1, 2, 3], [1], [1, 4, 7], [1, -1], [1, -4, 13], [1, 0, 17], [1, -4, 19], [1, 6, 23], [1, 6, 29], [1, 8, 31], [1, 2, 37], [1, -6, 41], [1, -8, 43], [1, -6, 47], [1, -6, 53], [1, -12, 59], [1, -2, 61], [1, 10, 67], [1, -12, 71], [1, -16, 73], [1, 8, 79], [1, 0, 83], [1, -6, 89], [1, 14, 97], [1, 18, 101], [1, -14, 103], [1, 12, 107], [1, 10, 109], [1, 6, 113]], 'euler_factors_factorization': [[1], [[[1, 2, 3], 1]], [1], [[[1, 4, 7], 1]], [[[1, -1], 1]], [[[1, -4, 13], 1]], [[[1, 0, 17], 1]], [[[1, -4, 19], 1]], [[[1, 6, 23], 1]], [[[1, 6, 29], 1]], [[[1, 8, 31], 1]], [[[1, 2, 37], 1]], [[[1, -6, 41], 1]], [[[1, -8, 43], 1]], [[[1, -6, 47], 1]], [[[1, -6, 53], 1]], [[[1, -12, 59], 1]], [[[1, -2, 61], 1]], [[[1, 10, 67], 1]], [[[1, -12, 71], 1]], [[[1, -16, 73], 1]], [[[1, 8, 79], 1]], [[[1, 0, 83], 1]], [[[1, -6, 89], 1]], [[[1, 14, 97], 1]], [[[1, 18, 101], 1]], [[[1, -14, 103], 1]], [[[1, 12, 107], 1]], [[[1, 10, 109], 1]], [[[1, 6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 44, 'label': '2-4400-1.1-c1-0-44', 'load_key': 'CMFs-workshop', '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': 'ModularForm/GL2/Q/holomorphic/4400/2/a/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-3.318131193078304e-61, 0.10548588916092717, 0.2099737702260983, 0.31243924803072864, 0.4118071299244213, 0.5069308350181835, 0.5965772156741488, 0.6794180465839333, 0.7540290496158374, 0.8188969223003839, 0.8724344552409903, 0.9130034803344352, 0.9389450986327086, 0.9486163961780893, 0.9404326640544768, 0.9129139877125575, 0.8647349521048631, 0.7947761162343197, 0.7021758385347746, 0.5863809808031343, 0.4471949833357361, 0.2848217895525156, 0.09990410808295282, -0.1064454619485148, -0.33262184678691864, -0.5765147537127683, -0.835506920891402, -1.1064843313183472, -1.3858591358695322, -1.669605766437369, -1.9533104199275348, -2.2322337621143373, -2.5013863432432673, -2.755615842609564, -2.989704876313633, -3.1984777213841933, -3.376913941809194, -3.5202665597215357, -3.624182110366085, -3.684819664778349, -3.698965711115457, -3.6641416651830006, -3.578700742455806, -3.441910975604236, -3.254021308863929, -3.0163079466616622, -2.731098479039288, -2.4017717478344127, -2.0327319492794844, -1.6293560813683885, -1.1979145254477628, -0.7454652853445047, -0.27972317542380476, 0.1910939696918068, 0.6584392193574453, 1.113627023027787, 1.5480359774388515, 1.9533190290211786, 2.321615768368165, 2.6457611159848384, 2.9194844901279686, 3.137593504258361, 3.296136375130246, 3.3925375395551165, 3.4257014795923637, 3.396080437596767, 3.305702553280679, 3.158157957599919, 2.9585414896769646, 2.7133519343130295, 2.430348975057806, 2.118370383247298, 1.787113275666151, 1.4468845293704036, 1.1083265979597114, 0.7821259863361312, 0.47871247026402414, 0.20795775634377267, -0.02111736372268718, -0.20061822766533513, -0.32402495738414505, -0.38640613195802553, -0.38458985912895505, -0.31728570989844895, -0.18515232400429235, 0.00919293786504819, 0.2612241694394543, 0.56461691626353, 0.9114160383522272, 1.292257522815473, 1.69663843262538, 2.113227407453227, 2.530206557434252, 2.9356342737956904, 3.3178174780688097, 3.6656811918700236, 3.969123068781361, 4.2193407126384725, 4.409120222151886, 4.533075444475983, 4.587828868454998, 4.572126904369346, 4.486884428510104, 4.335155851423034, 4.122032519834327, 3.8544688962261193, 3.5410425822933083, 3.19165576530883, 2.817187972271298, 2.4291120221694795, 2.0390866861460535, 1.6585407245990278, 1.2982636099466058, 0.9680183222536998, 0.6761911006218531, 0.42949194639269, 0.23271802767773214, 0.08858997405787025, -0.002331557142899335, -0.04164462842318288, -0.033018890368396454, 0.017975265094828947, 0.10411573708403371, 0.21684716497912043, 0.3466570449432769, 0.483495169695184, 0.6172199556944737, 0.7380537332799977, 0.8370282694620695, 0.9064017247769671, 0.9400289415727141, 0.9336684177928068, 0.8852115030049317, 0.7948221963316062, 0.6649793338605385, 0.5004168041808438, 0.3079615804423878, 0.09627364385271428, -0.1245038764750725, -0.34317198677898236, -0.5479645283536277, -0.7270791954774051, -0.8692293838927877, -0.9641938181741727, -1.00334026072147, -0.9800999354903644, -0.8903706243733817, -0.7328286905382435, -0.5091334863491476, -0.2240116085078922, 0.11478687302068456, 0.4966629384544128, 0.9084711915484648, 1.334942291200247, 1.7592117305759147, 2.163436535193849, 2.5294771563989933, 2.839618366738045, 3.077300492420609, 3.22783098167742, 3.279046198457349, 3.2218944908472262, 3.050914001945716, 2.7645823022914264, 2.365519608554375, 1.8605329443214045, 1.2604948825272884, 0.5800572361981653, -0.16279304106676656, -0.9473217121017582, -1.7507584840469224, -2.549105568430711, -3.3180128463590153, -4.033685413895475, -4.673787156858877, -5.218303376629393, -5.650326423226488, -5.956730786204957, -6.1287080766128454, -6.16213766594549, -6.05777522941086, -5.821248813998035, -5.46286001432922, -4.99719605534313, -4.442566695710172, -3.8202875211037917, -3.1538380460403697, -2.467928769244853, -1.7875156560212027, -1.1368032342995429, -0.5382784392623278, -0.011816451432924476, 0.4261029470179058, 0.7630344321981296, 0.9910335757877509, 1.1069299689268073, 1.1123947005834693, 1.0137988648237743, 0.8218690269367569, 0.5511546655199563, 0.2193311095014676, -0.1536309913702384, -0.5463924450802051, -0.937226791131383, -1.30501165261317, -1.6301851065621453, -1.8956234444075084, -2.08740015919717, -2.1953913563541696, -2.213699810480275, -2.1408782705594986, -1.979941969356165, -1.7381701875381594, -1.4267066947343634, -1.0599784637194036, -0.6549607679746051, -0.23032419970727885, 0.1944950860495197, 0.6002567812727166, 0.968862713591889, 1.2842418453604034, 1.5331306770208277, 1.7057107494117705, 1.796071855411317, 1.8024780811305814, 1.72742349682204, 1.5774747394502109, 1.3629083620553195, 1.0971611418138871, 0.7961210199606154, 0.4772945082242403, 0.15889281360611504, -0.14111673629338992, -0.4059453834435586, -0.6208556152565042, -0.7739266109009594, -0.8566724970302177, -0.8644808041918284, -0.7968476132130481, -0.6573962778048502, -0.45367778553062277, -0.19676220650169657, 0.09935830920884349, 0.4185244646098114, 0.7432835859884026, 1.055836518295653, 1.3390076409025147, 1.5771862883750127, 1.7571888583719872, 1.8689945801637853, 1.9063141470922675, 1.866958893173675, 1.7529885035921577, 1.5706268731533348, 1.3299480698280126, 1.0443467780945848, 0.7298194295719471], 'positive_zeros': ['1.05453299331481824083824038719691', '2.46535642408448141031036689968604', '3.65149113231465708944230333700347', '3.98244178628333179220455849881635', '5.52958383648087111826963240905637', '5.65889433188227421033845679887479', '6.44241690116309043090441361867350', '7.01609870378475161743947583743085', '7.86499496632861719392953609421368'], 'prelabel': '2-4400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.927408952431357, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 521309441253088293, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05453299331481824083824038720', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.46535642408448141031036689969', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.65149113231465708944230333700', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 35.13417688936339, 'bad_primes': [2, 5, 11], 'central_character': '1.1', 'conductor': 4400, 'conductor_radical': 110, 'degree': 2, 'dirichlet_coefficients': [1, 0, -2, 0, 0, 0, -4, 0, 1, 0, 1, 0, 4, 0, 0, 0, 0, 0, 4, 0, 8, 0, -6, 0, 0, 0, 4, 0, -6, 0, -8, 0, -2, 0, 0, 0, -2, 0, -8, 0, 6, 0, 8, 0, 0, 0, 6, 0, 9, 0, 0, 0, 6, 0, 0, 0, -8, 0, 12, 0, 2, 0, -4, 0, 0, 0, -10, 0, 12, 0, 12, 0, 16, 0, 0, 0, -4, 0, -8, 0, -11, 0, 0, 0, 0, 0, 12, 0, 6, 0, -16, 0, 16, 0, 0, 0, -14, 0, 1, 0], 'euler11': [1, -1, 0], 'euler13': [1, -4, 13], 'euler17': [1, 0, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 6, 23], 'euler29': [1, 6, 29], 'euler3': [1, 2, 3], 'euler31': [1, 8, 31], 'euler37': [1, 2, 37], 'euler41': [1, -6, 41], 'euler43': [1, -8, 43], 'euler47': [1, -6, 47], 'euler5': [1, 0, 0], 'euler53': [1, -6, 53], 'euler59': [1, -12, 59], 'euler61': [1, -2, 61], 'euler67': [1, 10, 67], 'euler7': [1, 4, 7], 'euler71': [1, -12, 71], 'euler73': [1, -16, 73], 'euler79': [1, 8, 79], 'euler83': [1, 0, 83], 'euler89': [1, -6, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 0, 0], [1, 2, 3], [1, 0, 0], [1, 4, 7], [1, -1, 0], [1, -4, 13], [1, 0, 17], [1, -4, 19], [1, 6, 23], [1, 6, 29], [1, 8, 31], [1, 2, 37], [1, -6, 41], [1, -8, 43], [1, -6, 47], [1, -6, 53], [1, -12, 59], [1, -2, 61], [1, 10, 67], [1, -12, 71], [1, -16, 73], [1, 8, 79], [1, 0, 83], [1, -6, 89], [1, 14, 97]], 'index': 44, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/4400/e', 'ModularForm/GL2/Q/holomorphic/4400/2/a/e/1/1', 'ModularForm/GL2/Q/holomorphic/4400/2/a/e'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, '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': '2-4400-1.1-c1-0-44', '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': '2-4400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.927408952431357, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 521309441253088293, 'z1': {'__RealLiteral__': 0, 'data': '1.05453299331481824083824038720', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20243626
{'Lhash': '1336779381936000765812307819259', 'Lhash_array': ['1336779381936000765812307819259'], 'label': '2-4400-1.1-c1-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4400/2/a/e'}
-
id: 24565752
{'Lhash': '1336779381936000765812307819259', 'Lhash_array': ['1336779381936000765812307819259'], 'label': '2-4400-1.1-c1-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4400/2/a/e/1/1'}
-
id: 90959
{'Lhash': '521309441253088293', 'Lhash_array': ['521309441253088293'], 'label': '2-4400-1.1-c1-0-44', 'type': 'ECQ', 'url': 'EllipticCurve/Q/4400/e'}