-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1312132210919591348692756235231,3313798644545096993965525672638', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.2278938933735533, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '225.1', 'coefficient_field': '1.1.1.1', 'conductor': 50625, 'conductor_radical': 15, 'degree': 4, 'euler_factors': [[1, 0, 0, 0, 4], [1], [1], [1, 0, -5, 0, 49], [1, 4, 26, 44, 121], [1, 0, -25, 0, 169], [1, 0, -30, 0, 289], [1, -10, 63, -190, 361], [1, 0, -10, 0, 529], [1, -20, 158, -580, 841], [1, 6, 71, 186, 961], [1, 0, -70, 0, 1369], [1, -16, 146, -656, 1681], [1, 0, -85, 0, 1849], [1, 0, -90, 0, 2209], [1, 0, -90, 0, 2809], [1, 20, 218, 1180, 3481], [1, -14, 171, -854, 3721], [1, 0, -125, 0, 4489], [1, -16, 206, -1136, 5041], [1, 0, 50, 0, 5329], [1, 0, 158, 0, 6241], [1, 0, -130, 0, 6889], [1, 0, 178, 0, 7921], [1, 0, 95, 0, 9409], [1, 24, 346, 2424, 10201], [1, 0, -190, 0, 10609], [1, 0, -70, 0, 11449], [1, 10, 243, 1090, 11881], [1, 0, -210, 0, 12769]], 'euler_factors_factorization': [[[[1, -2, 2], 1], [[1, 2, 2], 1]], [1], [1], [[[1, 0, -5, 0, 49], 1]], [[[1, 2, 11], 2]], [[[1, 0, -25, 0, 169], 1]], [[[1, -8, 17], 1], [[1, 8, 17], 1]], [[[1, -5, 19], 2]], [[[1, 0, -10, 0, 529], 1]], [[[1, -10, 29], 2]], [[[1, 3, 31], 2]], [[[1, -12, 37], 1], [[1, 12, 37], 1]], [[[1, -8, 41], 2]], [[[1, 0, -85, 0, 1849], 1]], [[[1, 0, -90, 0, 2209], 1]], [[[1, -14, 53], 1], [[1, 14, 53], 1]], [[[1, 10, 59], 2]], [[[1, -7, 61], 2]], [[[1, 0, -125, 0, 4489], 1]], [[[1, -8, 71], 2]], [[[1, 0, 50, 0, 5329], 1]], [[[1, 0, 79], 2]], [[[1, 0, -130, 0, 6889], 1]], [[[1, 0, 89], 2]], [[[1, 0, 95, 0, 9409], 1]], [[[1, 12, 101], 2]], [[[1, 0, -190, 0, 10609], 1]], [[[1, 0, -70, 0, 11449], 1]], [[[1, 5, 109], 2]], [[[1, 0, -210, 0, 12769], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 0, 'label': '4-15e4-1.1-c1e2-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/225/2/b/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.3114121892678139, 1.3122609657409596, 1.3085506053845417, 1.3036881145089922, 1.2962070009284385, 1.2834356263295659, 1.2634639029200663, 1.2343024087614616, 1.1933818379946344, 1.137887273437147, 1.0650614217370804, 0.9721859329113326, 0.8567815936796686, 0.7166572660773208, 0.5502406875438205, 0.3565714826780312, 0.13566219200613905, -0.11155252619762036, -0.38285322629744206, -0.6748660645701777, -0.9827690367373229, -1.3005236973956997, -1.6207250397845347, -1.934944037163864, -2.2337946530534505, -2.507367013945131, -2.745560878174568, -2.938550476684841, -3.0773874910473786, -3.154397191657259, -3.163989486794183, -3.1028546758729405, -2.9708516226940858, -2.770864852405016, -2.50958453677737, -2.196917885214901, -1.846459748848519, -1.47442619031299, -1.0996564658129848, -0.7421486700007438, -0.4225404226812195, -0.16045327625444478, 0.02644257612293482, 0.12396333635589554, 0.12248408056054694, 0.018001056856902144, -0.1870725819904161, -0.48360879283699537, -0.8556983306579581, -1.2812336672152445, -1.7329250891396513, -2.179614830443402, -2.588485736300005, -2.926663292421767, -3.164387504725828, -3.276233323110853, -3.2446760209816836, -3.0602015022183036, -2.7244770911881218, -2.2487992839159006, -1.6560950168399136, -0.9775653767357396, -0.2530359749573595, 0.4737877686497473, 1.1565768366862905, 1.751560900910085, 2.2197410056861493, 2.531247891144382, 2.6673955816688566, 2.6230335932975226, 2.407215533608137, 2.0428842115082615, 1.5652915186735732, 1.0192069079557322, 0.45500578144881093, -0.07549431145515217, -0.5244022705916583, -0.851557290843355, -1.029716343683252, -1.046223687867881, -0.9061738329948269, -0.6308282108431814, -0.2574600912906771, 0.1654092867939367, 0.5815672304866353, 0.9336788580828081, 1.1688637439774925, 1.244826725199317, 1.134951005074444, 0.8317595171774782, 0.34879477239724666, -0.2797996638552679, -1.002423535853801, -1.7538136536963056, -2.46318897170717, -3.059191631016141, -3.48094517533826, -3.6809864065833278, -3.635755535098759, -3.3437865097616184, -2.8321480773499337, -2.1489396648293164, -1.3637683702733243, -0.5560845352305192, 0.18963669966381155, 0.7960801398562117, 1.200044500415962, 1.3608479311311956, 1.2650652495519346, 0.9281508831732117, 0.39343007418045084, -0.2731975239299268, -0.9909056204471458, -1.6730745682081267, -2.239162066472539, -2.622569894687691, -2.7819563973404975, -2.703046714943953, -2.404498750461773, -1.931593953600055, -1.3542030782329604, -0.7542784458302618, -0.21741710985518006, 0.18062439414997164, 0.38375031011573196, 0.36394233191046305, 0.12628174705501916, -0.29143479253867494, -0.8225945604878745, -1.3801896610871678, -1.8692849698018896, -2.198275031309796, -2.294886973567245, -2.1131388142324723, -1.6455069897210866, -0.9203292953917191, -0.0042663798612307385, 1.0101000397724964, 2.012566590145892, 2.892133669582335, 3.551434534618127, 3.9194552204459745, 3.9640683205646563, 3.6934483377341794, 3.159703421065581, 2.4472243605093125, 1.6655731690611437, 0.9297933692021031, 0.3473007157829445, -0.0004392603069130374, -0.06807559147016323, 0.1453847361021897, 0.5973890983130028, 1.2067262537865846, 1.8674394878820262, 2.4623141826994823, 2.8842575779443176, 3.0487570831495088, 2.9120318756677883, 2.4734189664903403, 1.7805358149752986, 0.918781558090136, 0.0005810387789466406, -0.8524602870718717, -1.5301637458206212, -1.9480478600271005, -2.065918191129806, -1.8888200053788449, -1.4729121464008608, -0.9108043689685144, -0.32185364216352125, 0.17100130386473597, 0.4593969425895127, 0.468607979704671, 0.1710774649207878, -0.40900080457368493, -1.1977715369514077, -2.0829528167708946, -2.9332985383960444, -3.6165297333883033, -4.027102276100229, -4.096558208045615, -3.815065081443017, -3.223785152653723, -2.4193935667462014, -1.529017730615476, -0.6979000728189795, -0.05873123251552078, 0.2860955476990788, 0.28477605594363603, -0.05628933736234031, -0.6724253563110099, -1.4525201045231968, -2.2560981658592767, -2.9410899770624814, -3.38353721994876, -3.506691947992691, -3.2866602496289627, -2.7665982871233283, -2.040587269104659, -1.2461411287106128, -0.5331598873317076, -0.042570704108158254, 0.1224028033932243, -0.0862966946989481, -0.6512407657686715, -1.491870722679553, -2.4762747968070173, -3.4463945701503196, -4.24007260373487, -4.726713664188146, -4.819945059467321, -4.504060657910856, -3.8234097528170126, -2.8862152787478603, -1.832766952367064, -0.8189566446650811, 0.01935170714198305, 0.5865412407828883, 0.8456080835553944, 0.8233789975545703, 0.6015341490170596, 0.29988244004401554, 0.04839147895495702, -0.040788135468095066, 0.10095083398479807, 0.4805416092496333, 1.038900217171313, 1.6584769419090029, 2.1835307633952707, 2.4510568619041027, 2.3206102817097305, 1.707935640816371, 0.6022032919785386, -0.9232092746001733, -2.718290978742143, -4.580816468139625, -6.2809145930181325, -7.610296799138196, -8.400768282815156, -8.571601462119387, -8.120559074211585, -7.144886275455968, -5.801731229826272, -4.297534356636287, -2.836807943509837, -1.5971673671016267, -0.6947702329559411, -0.171215528018542, 0.007063641512382351, -0.06497008056954344, -0.2577935413148277, -0.4402023962741991, -0.5080594536013957, -0.41202650989722367, -0.16294367992263795, 0.16673012673356152, 0.46665310965143814, 0.6137060183387963, 0.5067634555948518, 0.09611879903495009, -0.5981063688257584, -1.4802461149333013, -2.39139121250442, -3.1387280747349062, -3.5272970075720593, -3.408555819408456, -2.7025937166442198, -1.4335307895046587, 0.28165080011346727, 2.2354247779358385, 4.172786584783976, 5.828594313080867, 6.974849234761617, 7.464344957725255, 7.248513334618294, 6.394316083556775, 5.059214018489585, 3.469394540419817, 1.8700307414237105, 0.48318673062979284, -0.5299850123979868, -1.0980265806230642, -1.2379405041223597, -1.0490511633300104, -0.6761161558690915, -0.2762523123030529, 0.022864613911264226, 0.15226859426629058, 0.11534661966800021, -0.014125051927589215, -0.11504878031130333, -0.0524525763504467, 0.28527855105193983, 0.9497416430750871, 1.9153479850932442, 3.073050719731201, 4.249583846625648, 5.24157079331415, 5.854789840577551, 5.954880188910043, 5.4905550404071555, 4.521604077799463, 3.2009816764834076, 1.7577784760998434, 0.44676958543261314, -0.4993197749484844, -0.9158429101577041, -0.7442078835921528, -0.03805464359812252, 1.042039724243834, 2.2662135048776646, 3.3819967046184125, 4.164069331224757, 4.465557884809562, 4.238493167864082, 3.5480782349120763, 2.547753298654375, 1.4446282355949718, 0.4525454111324264, -0.26333855067246925, -0.6120792010620969, -0.6092861740315102, -0.35495229732220485, -0.02056426297959615, 0.20690890462553543, 0.1643692875097829, -0.24001579654232696, -1.0042791006192433, -2.0281028251456115, -3.136709825399012, -4.1148311754654, -4.766255612509532, -4.946637097072248, -4.616268537980264, -3.831512375681801, -2.7538567415412083, -1.5955291763928519, -0.5864422697085164, 0.08929552339477392, 0.32922791346938435, 0.13866042626081843, -0.37281523124005855, -1.0176603931492545, -1.5797149878907601, -1.86234507290249, -1.7474243049301998, -1.2152215731973668, -0.365801679078373, 0.614443902851079, 1.484265433867936, 2.0115439364156504, 2.025447063468498, 1.4600126891508896, 0.3744228710406881, -1.0570091065532783, -2.5828910914774506, -3.9229952688468006, -4.840662251606145, -5.17804776373944, -4.909067713406535, -4.1203779956762006, -3.008991288935079, -1.815608315705474, -0.7809449311164309, -0.08106632496678097, 0.20696395826650732, 0.11924052046176983, -0.21011294000751432, -0.5888621149955074, -0.8233176032606682, -0.7677772372776108, -0.37367461087106935, 0.30315942527429035, 1.1048565824818046, 1.8175491327071651, 2.221489724683668, 2.150797446326369, 1.541048631070979, 0.4499625627807169, -0.9489053383988091, -2.3998796480162423, -3.629605790712519, -4.397135529265204, -4.568106233393547, -4.124538459885524, -3.1914540073847006, -1.9847825995575348, -0.7773124955516032, 0.17995075572412622, 0.708817139955575, 0.7485485403576825, 0.3641198670030713, -0.2723418008474765, -0.9353563530927962, -1.3976767699228918, -1.5060768423684652, -1.2045217918960511, -0.5700433286369175, 0.22659623469798473, 0.9495233125205046, 1.3728544208956257, 1.3366847351553073, 0.7949852662434417, -0.1652365085405367, -1.342049265632048, -2.465964495152942, -3.2601341472798664, -3.519815778841082, -3.1493652030924255, -2.2068985309837994, -0.8736968045191712, 0.5717267414803707, 1.8314711057870323, 2.654880959901124, 2.896308584806989, 2.5552366251553305, 1.7632626627460584, 0.7577818305383021, -0.1870475533168704, -0.8273509862580055, -1.00803543084106, -0.7047840194898494, -0.01750320300920543, 0.8537148843056345, 1.6701681822943624, 2.22039320622407, 2.3724200324733857, 2.1165306883080213, 1.5529756211693169, 0.8718369470625517, 0.28464736208861185, -0.031927321325504916, 0.003024540379622288, 0.3497252081609505, 0.8493748604865411, 1.2701152191989904, 1.3621554360265873, 0.942532131894962, -0.060786077681231496, -1.5618091347318168, -3.3375745182742267, -5.065818910100123, -6.397662574762292, -7.049683588287498, -6.857011402170411, -5.838574038477614, -4.171301973971347, -2.173527118794275, -0.21389757174864432, 1.3634462192355117, 2.3183053481093747, 2.569478166047532, 2.195004693003163, 1.4124468410325606, 0.5067111454673134, -0.24293200393270967, -0.6338974396060619, -0.5921911299033923, -0.17487568301980286, 0.449604375547358, 1.0633876427300157, 1.4656917839858312, 1.5308949042872173, 1.248429089851351, 0.7166957679903253, 0.1117715734813233, -0.37246923748969196, -0.5945549102862764, -0.5097306799150818, -0.20261059089574304, 0.13835150022210219, 0.26498606500448363, -0.05507808011470409, -0.9613874077794518, -2.450002723457178, -4.350855863985221, -6.352157042245629, -8.075159520785151, -9.141778173024807, -9.298863767310644, -8.442379340448998, -6.6962452045258765, -4.3394133624164, -1.7893226262339037, 0.5295069756074441, 2.2549882255705263, 3.1787588007910546, 3.2793519827693087, 2.709146339177151, 1.746642099861839, 0.7111573045246318, -0.12212184368042237, -0.5848632030866864, -0.6549313385509234, -0.43405733098784094, -0.10885865579514659, 0.12719449660917356, 0.13882086649249953, -0.10219400042498535, -0.5063198772514825, -0.8942254441286382, -1.0613039788343326, -0.8422506088122421, -0.1853408352561802, 0.8271031084479261, 1.9701726624815932, 2.9448006116808854, 3.4550535504022855, 3.270890507833358, 2.315807915243386, 0.7345691649348793], 'positive_zeros': ['1.03508980367567642243416015716894', '2.61412619845600714917427497300894', '2.81947525310129657968705132066671', '3.89658176012304504172302630337473', '4.67811541254359204024988961648038', '5.16340751709186156363692836859870', '5.66114704444160969580464941269834', '6.48321588953719438989821492717254', '6.91289580859699725719709395531452', '7.65577345363067892628210313770487', '7.896509426078001001688218766754464', '8.500271287471624913381000410190823', '9.312389168373981811178736766398945', '9.404709123413616119375007601467347', '10.12504009504936354468855500210780', '10.66342157981520354662097079041954', '10.89657133502083882389003808699727', '11.69505015980260670220668210358890', '11.86762722550013622798387474922067', '12.73460214203850642110915677933257'], 'prelabel': '4-15e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 2068601627827422906, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03508980367567642243416015717', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.61412619845600714917427497301', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.81947525310129657968705132067', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.2278938933735533, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 50625, 'conductor_radical': 15, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 4, 26, 44, 121], 'euler13': [1, 0, -25, 0, 169], 'euler17': [1, 0, -30, 0, 289], 'euler19': [1, -10, 63, -190, 361], 'euler2': [1, 0, 0, 0, 4], 'euler23': [1, 0, -10, 0, 529], 'euler29': [1, -20, 158, -580, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 6, 71, 186, 961], 'euler37': [1, 0, -70, 0, 1369], 'euler41': [1, -16, 146, -656, 1681], 'euler43': [1, 0, -85, 0, 1849], 'euler47': [1, 0, -90, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -90, 0, 2809], 'euler59': [1, 20, 218, 1180, 3481], 'euler61': [1, -14, 171, -854, 3721], 'euler67': [1, 0, -125, 0, 4489], 'euler7': [1, 0, -5, 0, 49], 'euler71': [1, -16, 206, -1136, 5041], 'euler73': [1, 0, 50, 0, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, 0, -130, 0, 6889], 'euler89': [1, 0, 178, 0, 7921], 'euler97': [1, 0, 95, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 4], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -5, 0, 49], [1, 4, 26, 44, 121], [1, 0, -25, 0, 169], [1, 0, -30, 0, 289], [1, -10, 63, -190, 361], [1, 0, -10, 0, 529], [1, -20, 158, -580, 841], [1, 6, 71, 186, 961], [1, 0, -70, 0, 1369], [1, -16, 146, -656, 1681], [1, 0, -85, 0, 1849], [1, 0, -90, 0, 2209], [1, 0, -90, 0, 2809], [1, 20, 218, 1180, 3481], [1, -14, 171, -854, 3721], [1, 0, -125, 0, 4489], [1, -16, 206, -1136, 5041], [1, 0, 50, 0, 5329], [1, 0, 158, 0, 6241], [1, 0, -130, 0, 6889], [1, 0, 178, 0, 7921], [1, 0, 95, 0, 9409]], 'index': 0, 'instance_types': ['HMF', 'ECNF', 'CMF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-2025.1-f', 'EllipticCurve/2.2.5.1/2025.1/f', 'ModularForm/GL2/Q/holomorphic/225/2/b/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-15e4-1.1-c1e2-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-15e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2068601627827422906, 'z1': {'__RealLiteral__': 0, 'data': '1.03508980367567642243416015717', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 10063442
{'Lhash': '1312132210919591348692756235231,3313798644545096993965525672638', 'Lhash_array': ['1312132210919591348692756235231', '3313798644545096993965525672638'], 'label': '4-15e4-1.1-c1e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/2/b/a'}
-
id: 9517632
{'Lhash': '_1312132210919591348692756235231', 'Lhash_array': ['_1312132210919591348692756235231'], 'label': '4-15e4-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.5.1/2025.1/f'}
-
id: 9517135
{'Lhash': '_1312132210919591348692756235231', 'Lhash_array': ['_1312132210919591348692756235231'], 'label': '4-15e4-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-2025.1-f'}