-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_151.123', 'a10': [0.5358267949789967, 0.8443279255020151], 'a2': [-0.8090169943749475, -0.5877852522924731], 'a3': [-0.18738131458572463, 0.9822872507286887], 'a4': [0.30901699437494745, 0.9510565162951535], 'a5': [-0.9297764858882515, -0.368124552684678], 'a6': [0.7289686274214116, -0.6845471059286887], 'a7': [0.9685831611286311, -0.2486898871648548], 'a8': [0.30901699437494745, -0.9510565162951535], 'a9': [-0.9297764858882515, -0.368124552684678], 'algebraic': True, 'analytic_conductor': 0.701241051920901, 'analytic_normalization': 0, 'bad_lfactors': [[151, [1]]], 'bad_primes': [151], 'central_character': '151.123', 'coeff_info': ['x^25 - 1', '0.968583161128631 + 0.248689887164855*I', '\\\\zeta_{25}'], 'conductor': 151, 'conductor_radical': 151, 'conjugate': 'dirichlet_L_151.124', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^15', 'a^7', 'a^5', 'a^14', 'a^22', 'a^24', 'a^20', 'a^14', 'a^4', 'a^18', 'a^12', 'a^2', 'a^14', 'a^21', 'a^10', 'a^1', 'a^4', 'a^5', 'a^19', 'a^6', 'a^8', 'a^5', 'a^2', 'a^3', 'a^17', 'a^21', 'a^4', 'a^8', 'a^11', 'a^16', 'a^0', 'a^0', 'a^16', 'a^13', 'a^19', 'a^2', 'a^20', 'a^9', 'a^9', 'a^22', 'a^21', 'a^1', 'a^23', 'a^3', 'a^20', 'a^22', 'a^17', 'a^23', 'a^18', 'a^8', 'a^7', 'a^13', 'a^11', 'a^7', 'a^19', 'a^12', 'a^23', 'a^10', 'a^1', 'a^18', 'a^6', 'a^13', 'a^15', 'a^16', 'a^15', 'a^11', 'a^6', 'a^12', 'a^3', 'a^24', 'a^9', 'a^24', 'a^17', 'a^10', 'a^10', 'a^17', 'a^24', 'a^9', 'a^24', 'a^3', 'a^12', 'a^6', 'a^11', 'a^15', 'a^16', 'a^15', 'a^13', 'a^6', 'a^18', 'a^1', 'a^10', 'a^23', 'a^12', 'a^19', 'a^7', 'a^11', 'a^13', 'a^7', 'a^8'], 'euler_factors': [[1, 'a^15'], [1, 'a^7'], [1, 'a^14'], [1, 'a^24'], [1, 'a^18'], [1, 'a^2'], [1, 'a^1'], [1, 'a^5'], [1, 'a^5'], [1, 'a^8'], [1, 'a^16'], [1, 'a^2'], [1, 'a^22'], [1, 'a^1'], [1, 'a^22'], [1, 'a^13'], [1, 'a^10'], [1, 'a^18'], [1, 'a^11'], [1, 'a^24'], [1, 'a^24'], [1, 'a^9'], [1, 'a^6'], [1, 'a^6'], [1, 'a^11'], [1, 'a^18']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-151-151.123-r0-0-0', 'leading_term': '0.666231409557827573340254743873+0.0749292888761344088762200477844*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/151/123', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.6704317186805028, 0.7603604047989538, 0.7865600789562464, 0.5054747897863772, -0.17349411436173953, -1.143578191414503, -2.123081265740273, -2.749325397957321, -2.7347672782157937, -2.0278749896926564, -0.893616209517314, 0.15473660818408658, 0.5757418252821945, 0.08746372611041109, -1.12405714592972, -2.4130426186253344, -2.941699958777738, -2.106912747516448, 0.08891220031344473, 2.945060838145686, 5.343453726534699, 6.291858399798489, 5.446379646910783, 3.3089038867154095, 0.9603627180271413, -0.5381094895610642, -0.729480229891587, 0.026880767446895777, 0.8511932029446778, 0.9574403038650193, 0.1775563116534557, -0.9621506030132193, -1.6656483487766138, -1.4864322701456127, -0.6782552554150377, 0.006224632453584801, -0.0571109568426297, -0.78386088018195, -1.3324276125104375, -0.6993872348083455, 1.4323447162263496, 4.23941200052423, 6.121509031562166, 5.722942973911898, 2.9253150034079054, -0.9303120805285633, -3.825157686256139, -4.3519494516108805, -2.6087494485795277, -0.04787225371925479, 1.6117913260158812, 1.5995384248794624, 0.5287190007422746, -0.24797416430752273, 0.1809427327123712, 1.5317986752017592, 2.603890027775768, 2.3409800138809826, 0.7733671298063248, -0.9654168238914602, -1.5712382602000454, -0.6595539725119112, 0.9263624904388704, 1.8614855000224393, 1.4895761690138114, 0.3580442108910121, -0.350900085678026, 0.012337691764862591, 0.8784727393216663, 0.941792104754016, -0.5583519481881546, -2.917428579256078, -4.339489864170218, -3.4199783136922237, -0.5025144999444909, 2.340087336752645, 2.833144229091898, 0.34380889918340535, -3.5096911313306336, -6.0526341337632, -5.604760619033918, -2.7035491631126267, 0.47761902116746086, 1.9499398185171195, 1.3795501722784806, 0.014402382362302906, -0.697371773436615, -0.42018204756781063, 0.022392218429754078, -0.22737785132427207, -1.0028986520677319, -1.2481890804562108, -0.22300839781344634, 1.4898468312753366, 2.3145284867550053, 1.1615074310910032, -1.3640170612596325, -3.3120563877577167, -3.11958063983697, -1.1355917487682954, 0.5832983085719706, 0.1440982041368764, -2.3429112777720738, -4.73009643343817, -4.730815354381465, -2.0291670829087596, 1.3804820552846713, 2.971147770923401, 1.9244704433315858, -0.258638120424594, -1.3080313079787915, -0.35986095019618525, 1.3384648988702066, 1.8086448370190225, 0.37071636129598967, -1.7065273045755047, -2.5283829339557387, -1.4729508930365773, 0.2671583515025156, 0.9934595413451746, 0.24379670907889342, -0.85123259130339, -0.9102503068683551, 0.16083393683417274, 1.1257307000776282, 0.9060100355013085, -0.09221492671570045, -0.4040715324257308, 0.6384179826863651, 1.653585214808653, 0.1760448765779896, -4.81909004886975, -11.31425349162169, -15.408205247765668, -14.438175999642205, -9.237788359199074, -3.395378146967833, -0.20049271269238927, -0.13863512335276063, -1.1531985089403716, -1.1197709865503833, 0.09857516046021145, 0.9702539720079659, 0.34179424219741644, -1.1733697793258508, -1.9465115133967625, -1.2542045280557759, -0.11890603114139507, -0.09847627735637837, -1.422019912859312, -2.6505457686854332, -2.3258101581123167, -0.7636054919814014, 0.12300198087919638, -1.077769546343359, -3.538183125952041, -4.847996723775392, -3.5161117903207106, -0.6428936883049226, 1.1491013739197127, 0.4917573232716097, -1.2265694237273395, -1.3470783036492129, 1.0930694572713073, 4.115106631628336, 4.718835552189405, 2.020570085480411, -1.710357690320881, -3.2537489064140575, -1.5952074344842744, 1.2289891784767422, 2.369719661685049, 1.0150425000717784, -1.1115141807480708, -1.8851794129768487, -1.013057841327599, 0.03596304481578191, 0.03699525354948358, -0.5736895615904265, -0.5054457181021602, 0.500528350138861, 1.1727707670474194, 0.33535187946980816, -1.3252027411299916, -1.7143737210157997, 0.21612472212519157, 2.8199365036878237, 3.123710834618036, 0.06046284866089763, -3.9494324685782543, -5.081808724003211, -1.921613776765703, 2.9799226659743185, 5.533601131042128, 4.043156700114628, 0.5833532999553326, -1.436813375598205, -0.7309945803017596, 1.0475826745157202, 1.6493650584942634, 0.7748754790680411, -0.04857619117712667, 0.21001802597522937, 0.605461032666524, -0.5572830993635878, -3.335749061723084, -5.634819640957921, -5.360450068479556, -2.7728186466197964, -0.2361573188809674, 0.3817732167208202, -0.39122389371862104, -0.634021170923374, 0.384601273384526, 1.296535771816333, 0.5881732934419175, -1.023446434595297, -0.9654487276123888, 2.142812419689992, 6.294353061295709, 7.658302109149041, 4.561179230994643, -0.46665938143928515, -3.0395784535173305, -1.2856209593955612, 2.4361766954950834, 4.228793248420869, 2.6856925384467347, -0.0999127616690432, -1.3007122971757736, -0.4539871954138768, 0.5547244898101312, 0.16051883777599651, -1.036156037275805, -1.3627944793371012, -0.41916517388937535, 0.45735160062450314, 0.13321396642279162, -0.661050769505351, -0.2993863346522292, 1.3019837599961799, 2.089954694375353, 0.2862395056590179, -2.9781607124397658, -4.307192378341027, -1.7073901237468305, 2.8328225642923197, 5.081849262142431, 2.955540275115506, -1.311348657109578, -3.672303642509334, -2.583048496771638, -0.24834429886919188, 0.3930488228799708, -0.8246614254806566, -1.431996844532012, 0.29720304356081084, 3.0082862874374556, 3.824549854681814, 1.8098291460351414, -0.9322861527818576, -1.7859138553749778, -0.586223368101506, 0.5611671733703074, 0.15626739064342324, -0.8771645329259721, -0.6579187716745044, 0.9691579505850024, 2.1213421136254627, 1.3533833027434077, -0.38281499918566475, -0.9733281934634763, -0.013014851785060729, 0.5758636169195891, -0.7406982601185294, -2.4930724154934363, -1.4356244204646549, 3.3357691060155394, 8.327777600834894, 8.6574557439399, 3.1867011910766267, -3.9762307737645934, -7.454003885408725, -5.723564718056573, -1.888457679313165, 0.26409764553083326, 0.06812752089317602, -0.43592560645960343, 0.1756117377125397, 0.992674755940828, 0.5242883701354007, -0.8994399852730058, -1.5010625463961995, -0.6248226303914828, 0.17866429666330638, -0.7609507832126065, -2.702303343463844, -3.088827909862528, -0.797394453825753, 2.127346332248607, 2.7267761740515533, 0.7113122560926838, -1.2174694432391524, -0.8808176842573474, 0.44628409459425816, -0.42022836860345636, -4.297019434383328, -8.033075622055875, -7.8613497696517936, -3.7949810169177884, 0.30048601080840187, 1.1024070893735385, -0.6154337771056517, -1.4583880047662081, 0.14896048476034776, 2.1492623452133364, 1.7408060785879265, -0.9080315192908613, -2.8417106360448883, -1.997772480419746, 0.3935418116400985, 1.586256555178967, 0.7247703066555793, -0.5198370505342376, -0.5499434943680039, 0.11565849067072427, 0.0659357396837586, -0.5493325749657132, -0.13642844932185993, 1.6032387441128315, 2.3448275936132195, -0.23681131982625356, -4.838282533316554, -6.9355548740309665, -3.596502036212451, 2.7834031916702617, 6.61863623819396, 5.040499901169172, 0.7795658030029731, -1.259988301469474, 0.4829687875933255, 3.0876202548796385, 3.240586411926362, 1.1307133187733804, -0.45955905432691513, -0.07180864059910835, 0.8442493832684954, 0.42771241515700226, -0.8242122064967274, -0.8953552785641355, 0.6350391328284989, 1.7362847333782079, 0.6742597861954929, -1.4143715405926707, -1.823458814581958, 0.1322062900916237, 2.103071524282995, 1.7768669917926796, -0.029381884324135264, -0.4927907363319066, 1.3044157449097797, 3.007098624071764, 2.1830293335574127, -0.16163310291342803, -0.7022818064375049, 1.6120146018899548, 3.5893917852909, 1.4804458659703172, -4.038157897067989, -7.99940319487464, -6.588285811526218, -1.3938600085213566, 2.591632470276115, 2.5798181192542424, 0.4007050385432492, -0.6368309664156664, 0.14339332137721628, 0.8179790179177846, 0.18796134376936616, -0.6020706639174802, -0.16836368251132044, 0.7366963524942922, 0.24196644504143114, -1.7000501658513354, -2.890096392353335, -1.857901182524769, -0.03094551641418493, 0.28081460568014915, -0.48830642975719435, 0.7514977397733829, 5.395315901515084, 10.168748652074553, 10.077022501664384, 4.2597362115674, -2.496289557127142, -4.791773645222303, -2.2686393470362325, 0.7970783416511217, 1.0148929035255918, -0.5752321709579623, -0.9203967415704363, 0.5645628263601802, 1.5582157321393586, 0.5653996296668776, -0.7467291413266663, 0.06992054973379397, 2.5911880609403384, 3.831994265682348, 2.1871163580107065, -0.4122455811147432, -1.0654874719358545, 0.3803791146479222, 1.5031936271109554, 0.8765079991862386, -0.13342439245274534, 0.21813320906330003, 1.1663294295286142, 0.5217236559380017, -1.7225899412595045, -2.7611716137732336, -0.868950518086506, 1.3886676383460763, -0.32494563244940844, -6.394473782715531, -11.76458955645256, -11.240276450973882, -5.384286237254524, 0.2515962890049188, 1.5500859221875838, -0.05533016543356193, -0.4340953514212221, 1.709327224421115, 3.763192593276359, 3.2628403922354576, 1.105482326297289, -0.14517869391396188, 0.14381202206410543, 0.37812415143884426, -0.3326098696246423, -0.7935619944260489, -0.01620652997231336, 0.5464271815090064, -1.2719352717654981, -4.7551514743869685, -6.301864923352139, -3.800585868223334, 0.29644360383333357, 1.719613118900221, -0.3168660663164359, -2.295947174069852, -1.272139687973046, 1.1009268504247274, 0.9071641481472758, -2.456842842782717, -5.104750413080594, -3.6162656632502994, 0.47868478310987894, 2.6816757498108763, 1.253586631464788, -0.94549948528123, -0.6773473138038272, 1.3825673142592363, 1.9974743838984361, 0.09952204667002681, -1.8159831408457046, -1.335547071440638, 0.5645396320718239, 1.1317332178828248, -0.2140230209650483, -1.3206682548973347, -0.6788735765378746, 0.4454525136355374, 0.2221698140868144, -0.7341344183325754, -0.3397764328465185, 1.363509412871693, 1.7319589508693733, -0.4355860311974967, -2.061127185863981, 0.8964369606370434, 7.548122565582712, 11.691523456487957, 8.473915839595936, 0.21506550129653812, -5.98178160075668, -5.975855200117381, -2.270097322168919, 0.19441309795285222, -0.04299341121527306, -0.695634793925052, -0.1318552515382355, 0.4214975745881562, -0.45894147052924616, -1.599230405111586, -0.8288602483297857, 1.4931828664583795, 2.5889653805861945, 1.1395396733621497, -0.7378590621003229, -0.47852418650924367, 1.2338407340952087, 1.5232950097031555, -0.33266041102754346, -1.7100175503343977, -0.5591979305305859, 1.2412713007988196, 0.30424665619432256, -3.191780271248849, -5.137595517813904, -2.8435007051248293, 1.1430634946634677, 2.251250584404545, -0.07311530558144921, -1.8094834190731357, -0.11096387447777813, 2.586052338961844, 1.8153253590808767, -2.7439115787976647, -6.587538678453709, -6.013416366590986, -2.409049083422781, 0.18099670791501732, 0.27774277736132946, -0.14328710709742148, 0.5570654789706114, 1.3129356312081657, 0.5921350029443824, -0.8000005377075745, -0.9282128925627432, 0.08481600776159927, 0.2263036593736371, -0.8351548440945846, -0.5094947431260199, 2.935516195753959, 6.7927912373523975, 6.48357433876527, 1.6937715482308948, -2.3623522843181246, -1.0652475021639272, 3.7671668046717244, 6.1278477611333395, 3.333588450883374, -1.0101750640438139, -2.138871172748502, -0.10233699713192376, 1.2055752892423042, -0.17518296139160022, -2.0196377775618197, -1.7674572049191866, -0.2736052940137975, -0.06574937036536581, -1.2327151491971482, -1.4011333033877376, 0.26662071407706023, 1.3826882596722532, -0.21193042335541246, -2.9456147812751583, -3.3860922541061647, -0.9733170904612289, 1.249742898829381, 0.9460058422525, -0.5256015510866549, -0.6908328960539052, 0.11683445769127063, -0.26610770742024403, -1.4217869896838582, 0.2040957166717038, 6.0895104046031, 11.905900589069768, 11.589932964216821, 4.816779528193188, -2.0250319976238136, -3.127136097142746, 0.38244235985487757, 2.8926939423607143, 1.6860428832732783, -0.5968709573514515, -0.7082938670310908, 0.7181375192151093, 0.9330699460510463, -0.4552165356364773, -1.1959307404289972, -0.19846030334061243, 0.8214470093185415, 0.273271185447185, -0.7311045171352204, -0.3957485927048628, 0.44076812611479, -0.6470155142428873, -3.46151017496886, -4.562337586847926, -2.0538316088086206, 0.9737420059900885, 0.06265040465928855, -4.318071060549575, -6.763130707853484, -3.8328409941719714, 1.3553035803147673, 3.181603931476811, 0.6748898840937148, -1.9107527193501839, -1.363155941198117, 0.4823293320210708, 0.25249378693105196, -1.6962696264738064, -2.0927555244286076, -0.07732826251397239, 1.2009723722481862, -0.8231049069579307, -4.2009136381438905, -5.018896022638874, -2.6519945352086522, -0.18380610965066707, 0.16492650739750528, -0.4024275311595305, -0.08107732244153384, 0.34718936629951863, -0.8631063558277192, -2.840356414481398, -2.789348780965476, -0.36616861274111234, 1.239436958224957, -0.08270375778539685, -1.7589677947626083, -0.01704969537612697, 3.9295938947239604, 4.324071409519895, -1.5870055588744516, -8.979008381597446, -10.636383979503307, -5.490624828604298, 0.5718089750717293, 2.249246061736787, 0.4602954502469118, -0.6007148232158009, 0.39790727970929757, 1.2327942716400935, 0.5045788617639796, -0.3531776654681018, -0.05678869473869124, 0.10947021119066147], 'positive_zeros': ['1.18428572809159518535954617387', '3.38179266961204616877504589068', '4.091023129158483513509587493644', '5.61463666730587429269229911827', '7.66820293422985354986191411155', '8.42866121745876543532005708769', '9.42464260980011550237810565510', '10.932318154931076886846772424851', '11.20872559047300295399673310343', '12.31345241019964797644046015144', '13.98614107900512091418949188611', '15.31889251595949299557896737600', '16.41522455628681121947309721860', '16.81472607046274094124548341940', '18.252665909641683839842012619589', '19.193172002017237093315763879975', '20.4240704372441223002281882778', '20.93269613795411747521667862604', '21.78878242917678026276107513317', '23.172644126386081701495969431046', '24.091858056230531032118755765138', '25.569822510898469405287754502097', '26.566219297081268714601753916093', '27.46737763433503510938699114804', '27.66010679436649563852161692306', '28.79261112757388889556295500338', '29.83938134882666546611242636227', '31.110330942310839242946214708530', '31.587817235261445841951589760283', '32.98995126821071843508403986912', '34.022361716769758819676230316212', '34.752353156928351993050210289530', '35.67913020021749827734811434821', '36.82109330214032067392201740330', '37.56245175141998088138604111772', '38.3981309279375543314678663990', '39.34423227045488549945527386822', '39.84784556917410993495699983086', '40.64115830384133735968659253261', '42.866998975798845378947085630608', '43.0719463848737081784422619124', '44.03979317501131633893968231787', '44.76264316954538731245686785157', '45.99406468595891488375529951898', '46.20381608505400123856202340945', '47.69598356024621341340161865133', '47.903442102478149956403474029835', '49.45280872490979588554920187669', '50.087790209666316165344746789631', '50.82607251910758501009759971564', '52.0363954241818146634274960912', '52.98258932169409713397895633403', '53.891060517348505704229480048382', '54.982362910711706287848961767768', '55.33412964109098159738898909949', '56.11246608555492307688564777069', '56.93932429192170661993866801678', '57.78762525059583073991712786327', '58.75450879970738353351111804828', '59.80823356350853087330856811455', '60.99734933450135062620067180201', '61.687559176912746140569571972134', '62.77228227386501884325688575006', '63.00389941070431704115984799106', '63.657851026061166952606684172421', '65.36042101149785494140512036908', '65.799424030185686221794695107517', '66.46903206672926608501739317132', '67.29874692830404461406080593971', '67.94328195896484787091612470712', '69.34318755490038865244372699431', '70.108981249526180015950615567948', '71.23682814473424428497099045291', '71.98507033957669898483224992674', '72.54458030056342623464639746936', '73.55200517058019701431511668303', '74.110308691641433114898406429029', '74.75758444868564491578161573727', '75.6540610949721289018578493084', '76.68037767708766962834974128871', '77.71435452894969342680034913924', '78.796574844488926290915982483530', '79.19267423321548565243525954947', '79.96450690837546027027965613273', '81.13091497749613861666495418470', '81.997611349685412628179394249071', '82.54459754833942470917455129740', '83.26830174503923015313494428087', '84.30003374620958646913515465167', '85.003431912526302564481386682', '85.49906031656748420609877990173', '86.36590496498811028688497334143', '87.63277896450041219642473666132', '88.98730227398423557251754214299', '89.40297074731121640646983754447', '89.944114558131839792954296977101', '90.74526982123821782437803229548', '91.74650703343871595974718533994', '92.014231915277562788209601039000', '93.20257938760639698777745005972', '94.15290531032932166720185924392', '94.87337841952014984381335298663', '95.25495592481276388932423609053', '96.842565140875772379968801752595', '97.400997729780291043728741475551', '98.10514700741189767699331653940', '98.96518871659411311773621480438', '99.94631666188589898359435015003', '100.78383763639709040976711127445', '101.49747180541126141561924618693', '101.91032082772763342602717587647', '102.53167047504470677349399085597', '103.41953156076561051660022653157', '104.55219556796441922089851524608', '105.694247199217974014275736954564', '106.1956369848011629141842761990', '107.36474045667830458023376684882', '107.83342531612316330313862857707', '108.54297271562476919714581111627', '109.26334903351344508999717111752', '110.09807231174403477743160693788', '110.92094169598601424244161177098', '111.86921290974431920628707148613', '112.30691438195658226531888117138', '113.4127412331066347578782332043', '113.877664718823824015455726880081', '114.781474364009348129321805243228', '116.0218896794099921022953046664', '116.94246570940182318964045382957', '117.45968606061596067993205344784', '118.18157885088550346413738999685', '118.80135345189853098728964579879', '119.42286683414899960714470591464', '120.632470065987944237264614295128', '121.046885381166963781154245530623', '121.46854844613748134986613360690', '122.99551330408865431776461800990', '123.957661431641263700443257416294', '124.57459519676781100702998023513', '125.211358362717532220712322830674', '126.044797395459042131166996703810', '126.55167925146304773302024273317', '127.75290999762485869557815588291', '128.36988029387615350636853639205', '129.3081534620587082006481821987', '129.611499837321675394490716127060', '130.39504925204986066850586539530', '131.34547677046656932976889629268', '131.85063284952518103656333792769', '133.41718637542218997426029197816', '134.05181473164676761732580143749', '134.46687469821026082299934430976', '135.85737884087279697302939116608', '136.17150206213288509844289446831', '136.75797177292581367066546641139', '137.50460914388109161950101255258', '137.96634975492372556745399606261', '139.34816201837772274485918245749', '139.964027469459864516937631302808', '140.78044087391089392713464203488', '141.35506043577865428393089424614', '142.46227571914670557195306875411', '143.27945595731449320639194951944', '143.8596715207302588863430720660', '144.70002473233968791931429396917', '145.52799088241570628282658460594', '146.21017625644718677466055570787', '147.03871785352702939232101425580', '147.56885790759882901698958145392', '148.195140789503746863763477653455', '149.01234490671625297216622226920', '149.6329925468974557972684156491', '150.94551020081082169089640512180', '152.13641363943764126823185111755', '152.48543449945300042595855103856', '153.17014422655593830317114203900', '153.6396999092452127148446181232', '154.49357271940265255034552753427', '155.47610211675352356946418125941', '156.02983799646003311179471981073', '156.82798714304946697423136268546', '157.58115360384187229754467998569', '158.158460981122930010294229343580', '159.27539398954495784435389159565', '159.991972859737290577074056468359', '160.63649015502383302380958919433', '161.392494622738271804879735501144', '162.77228415019731207693980987999', '163.2638550755518363215234358688', '163.559015932115016187907409479992', '164.4988327018563161006687970109', '165.28441227015176774923366575556', '165.7055469455601727554474109920', '166.31867897843439355905186458823', '167.60033289796414067092758468003', '168.201212665853359490001313019549', '169.28973473997661989052891505958', '170.0137363059198918493544521513', '170.59984555498165870564486184482', '171.65627126346066521171411815461', '171.84523811821338767062208732525', '172.77022695491687477053116464957', '173.41283048895464443572129116500', '174.48284915174155251681324395794', '175.18971390450360242806490789559', '175.878386921526095144417925789128', '176.16941729823282188564567682922', '176.85846399101563277632593086600', '178.32327330836934680576929566492', '179.03249653909189478934958896366', '179.89921833082574874680425417425', '180.46988480901322918945529363099', '181.15848181669398525518629343702', '181.918715808252709404778140648740', '182.57141203825197780185870340679', '183.24280540089074278965800962696', '183.647230580384383900698090185377', '184.87085202438283444530767811779', '185.31837736123928895589593259541', '186.47274339111734164492524255522', '187.25001297548274884296659570056', '188.02547488627568896751457009279', '188.484261081965438697607338502589', '189.38542022092781382188999952630', '189.91773966760502172962781437633', '191.29410350919179893450167409276', '191.64642469274049300912460511766', '192.2221995632186702227872269335', '192.650167878533482526107954002523', '193.794297523218353442285188891', '194.363517019776670323375906395181', '195.00147477275990150059006719421', '195.873412212782290909673747845184', '197.14856532369888954926106538800', '197.88922999886152541078243009196', '198.34705853378327457167994898054', '199.20509852662121489715511854034', '199.71706509028630168464470195185'], 'prelabel': '1-151-151.123-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.701241051920901, 'root_angle': 0.07129933394762891, 'root_number': '0.975018177885956278737794047900+0.222125083662223341033678064142*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0356496669738', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(25)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.685178297380968873246732017916+0.0177482359904618004403791377710*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.18428572809', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.38179266961', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.09102312916', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.701241051920901, 'bad_primes': [151], 'central_character': '151.123', 'conductor': 151, 'conductor_radical': 151, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/151/123'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-151-151.123-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-151-151.123-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.701241051920901, 'root_angle': 0.035649666973814456, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.18428572809', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_151.123', 'Lhash_array': ['dirichlet_L_151.123'], 'label': '1-151-151.123-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/151/123'}