-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_3024.2795', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.6427876096865394, -0.766044443118978], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 14.04339696032321, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1]]], 'bad_primes': [2, 3, 7], 'central_character': '3024.2795', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 3024, 'conductor_radical': 42, 'conjugate': 'dirichlet_L_3024.515', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^23', 0, 0, 0, 0, 0, 'a^49', 0, 'a^47', 0, 0, 0, 'a^18', 0, 'a^9', 0, 0, 0, 'a^2', 0, 'a^46', 0, 0, 0, 'a^61', 0, 'a^26', 0, 0, 0, 0, 0, 'a^21', 0, 0, 0, 'a^20', 0, 'a^55', 0, 0, 0, 'a^28', 0, 0, 0, 0, 0, 'a^39', 0, 'a^0', 0, 0, 0, 'a^29', 0, 'a^55', 0, 0, 0, 'a^34', 0, 'a^41', 0, 0, 0, 'a^6', 0, 'a^42', 0, 0, 0, 0, 0, 'a^22', 0, 0, 0, 'a^43', 0, 'a^41', 0, 0, 0, 'a^0', 0, 0, 0, 0, 0, 'a^32', 0, 'a^28', 0, 0, 0], 'euler_factors': [[0], [0], [1, 'a^23'], [0], [1, 'a^49'], [1, 'a^47'], [1, 'a^18'], [1, 'a^9'], [1, 'a^2'], [1, 'a^61'], [1, 'a^26'], [1, 'a^21'], [1, 'a^20'], [1, 'a^55'], [1, 'a^28'], [1, 'a^39'], [1, 'a^29'], [1, 'a^55'], [1, 'a^41'], [1, 'a^6'], [1, 'a^42'], [1, 'a^22'], [1, 'a^43'], [1, 'a^0'], [1, 'a^28'], [1, 'a^43']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-3024-3024.2795-r0-0-0', 'leading_term': '0.599117709890680715468084233347-0.464183736290294794346186916127*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/3024/2795', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.7578974675647565, 0.0006349657834209353, -1.3358164279883515, -2.53242681683398, -2.3905674820815794, -0.7935701321741324, 0.7433770082873674, 0.4129307777547274, -1.8430743951451785, -3.9234394009401403, -3.6396750963421214, -1.1926315499669549, 0.9202005386516849, 0.7578585539365118, -0.768686908289555, -1.1443857588473663, 0.3389451891734667, 1.4479261553099299, -0.06706582353383428, -3.1578733735875355, -4.404167282552452, -2.34585421194425, 0.4867470150854068, 0.8180259742649553, -1.076867968156114, -1.9593371987728203, -0.33856007854529685, 1.4099898548323, 0.65590155493548, -1.4128264024500725, -1.4504803065020908, 0.8904826144864855, 2.083113934836472, -0.1758460952872132, -3.3180994335078324, -3.3802816060715455, -0.6708385577844933, 0.8399195297117755, -0.5012880113409077, -1.8223647495651945, -0.6029683243178277, 1.1849700113613215, 0.3920122257265211, -1.806336166022927, -1.3404309227688889, 2.231550345004707, 4.509067868660756, 2.696787357091517, -0.24505932123283763, -0.33634138293201277, 1.3500757386158249, 0.9467558420955811, -1.563386476122368, -2.4208605862707158, -0.6997690002128586, -0.1397511884261868, -2.7752205462827413, -5.013898065800529, -3.1820320038064436, 0.34510702227800527, 0.7556419271507135, -1.5888699752321527, -2.0921492753876394, 0.30765327981214785, 1.677128773001094, 0.15116344666714693, -0.9183095429664293, 0.775277839075613, 1.9844027377427957, -0.49305995121821733, -3.6311118251960113, -2.5920253139087355, 1.2950443760814774, 2.6312463999812286, 0.6822148762977988, -0.07459644115351514, 1.890654614981952, 2.8190612905086168, 0.9774307569800099, 0.08348795849806488, 2.3848436882149, 3.955944343085986, 1.265456489445971, -2.3083568680854873, -1.8923630806261302, 0.7120218881963831, 0.4427557832298687, -2.1367162866054423, -2.223913221894121, 0.39221841288967507, 1.1515552999310539, -0.7721561181235095, -1.2021375994965275, 0.7096285010585819, 0.3470135100651258, -3.697623395250777, -5.973908646978382, -2.9663862959862732, 0.9489342068915136, 0.9777846121324012, -0.6264831531084719, -0.05142105504932644, 0.6271860059392107, -1.9364332864282294, -4.878032803303464, -3.6277597752484083, -0.3925587387722723, -0.40642288189646525, -2.416258774684539, -1.1220583354577276, 2.714718423140704, 3.274816831654153, 0.057730251535089955, -1.5040973753722047, 0.02873801068030675, 0.35528769931728316, -1.4697414697264517, -1.1593331011539791, 1.731648635217237, 1.8284072447160096, -2.1346430075250433, -4.128609541930208, -1.1717072473416346, 1.5911395990662736, 0.34429930156293465, -1.1697705557373366, 0.26919276691913563, 1.2022947228234273, -0.9936843113291701, -2.2511817101193596, 0.33897617856753653, 2.2639208687717463, -0.20562144706213106, -2.7359288748750314, -0.9243225143420999, 1.4081270262207852, -0.48888404636823235, -3.3535866563933907, -2.2835541873549716, 0.2081228959717145, -0.2582799497416551, -1.3860555854561047, 0.31097924683750483, 1.464975891838356, -1.7897312793988904, -5.137285775296911, -2.9815416278400444, 1.361592364759555, 1.6459981510184913, -0.4702918020410466, -0.00434911101544039, 1.316534808277108, -0.6124101446099262, -3.0694777231325, -1.5421390276585143, 1.0464970522535721, -0.041528482817457045, -1.7354935177071429, 0.8644193947589628, 4.259449813191022, 2.5761620274887687, -1.4542067642482417, -1.7934559391271168, -0.02576281507417934, -0.8254353759093738, -2.127088123535861, -0.06658719103685905, 2.062605048839105, 0.005247640653800441, -2.348319079945389, -0.1404282080980995, 2.6171146138580763, 0.48395050599149014, -2.909199988160835, -1.8823975030357998, 0.7906607178131494, 0.2612293474219596, -0.9087476566271983, 0.7675785450637521, 1.6134766564384544, -1.4405000692849073, -3.326043834893421, -0.14219978176276907, 2.813974143875284, 0.9757188672949606, -0.9535412012067793, 1.272229143827953, 3.1334081951067905, 0.8044424373601307, -1.3509395366399506, -0.17600811529837038, 0.05629265021369866, -2.560211365846274, -2.8378148782080057, 0.5278460737801252, 1.1514761692852291, -2.6334356516415376, -3.9332179281590984, -0.3546923738495089, 1.8282886754473888, 0.19283387528003998, -0.17599957821625223, 1.8221772931178302, 1.427383195987209, -0.8129475482720178, 0.5488276967202901, 3.914859248265558, 2.6842742178577397, -1.626929995372444, -1.9569097070434465, 0.7578994894520876, 0.28013244062035225, -2.05549027603318, -0.743602595669642, 2.038445333566495, 1.0468538636788667, -1.1739479854835908, -0.29163051342311286, 0.15347670281238476, -3.3238402424851285, -5.278132424942459, -1.4318125300455573, 2.175458605871106, 0.2697050609765141, -2.2682258431641444, -1.0008012712812029, -0.007429042131753245, -1.755551610652327, -1.7072411923490467, 0.824021511080181, -0.0374338957672989, -4.159758981895022, -4.291088231718128, -0.11186684710750933, 1.2726234096220526, -0.4301089805855761, 0.9130663205083873, 4.277254691687789, 3.4627740256129798, 0.06008371208674565, -0.07001644121882228, 1.3148123552081985, 0.05667466869904041, -0.24159818205045408, 3.813485550786108, 6.207563699951971, 2.330460024484669, -1.5001153117574009, 0.07272156734320674, 2.04050213036284, 0.40401513385303955, -0.4454586287204433, 1.2094757916750232, 0.33609599780498656, -2.9266774164776272, -2.2630827954503534, 1.4747421583955618, 1.3737049249374875, -1.3262717382772622, 0.05619980845117506, 3.4240885240893286, 2.1902554982384594, -1.081398375840951, -0.3487339947755035, 1.6302527966245162, 0.30389174387885187, -0.7435061657304689, 1.254564422629798, 0.9844835960529391, -3.295685137122189, -4.4006455006913985, -0.3178193564806371, 1.385648204437646, -1.3877830824894963, -1.9189126324866743, 0.8596075215170894, 1.1136198761721887, -0.66362704566087, 0.49170270364925, 1.9807460687701608, -0.8604256129355861, -3.4160525290122346, -0.5970436290072288, 2.1221205437952824, -0.3444942514668043, -2.4422556109586986, 0.007042454194159534, 1.3737645719404226, -1.1952845684589108, -2.024099012697138, 0.20205388713571287, -0.048823750981495995, -2.179067655838857, -0.7332777071005201, 1.4250193202918542, -1.8474189194834987, -6.195003074303942, -4.426518981080983, -0.42625043337227164, -0.43853520019747827, -0.9625291343265914, 1.6621010805313003, 2.582511575938074, -0.2963617831913712, -1.1878918027542424, 0.615273243186885, -0.912324328264497, -4.240819119933672, -2.0552756316284846, 3.187905237788112, 3.3370512090605766, 0.17509802813209646, 0.042520401443188804, 0.48973778821320485, -2.282777444739265, -3.4611516699705485, -0.11469233435371672, 1.7239051331562858, -0.017321027872757296, 0.7181996096048613, 3.709748369899774, 1.7719825404961962, -3.450656616167931, -3.625621528558558, -0.05801472835951389, 0.14096979824741904, -1.4128831825487456, -0.2190190823458292, 0.21162519238700273, -2.4753764861283605, -2.293486561454681, 2.0523829072132767, 2.692631979391131, -1.5437661847196553, -2.610985611187844, 0.20329531270048531, 0.11925461123048066, -1.7320581228622902, 0.42627931442381173, 3.3684056143922256, 1.750490870084605, -0.38804389652124377, 0.5465161282907751, -0.5377496730689029, -4.716756277860845, -4.559716838609068, 0.22498296041041235, 1.1353169737614501, -2.001986667836638, -1.5890950809532582, 1.5071268243551819, 1.2027957585245697, -0.25254395980659844, 0.9803745596660572, 0.4156237831107716, -3.8228463862597972, -4.518253175280147, -0.21317232348973278, 0.8381817921765897, -2.453817314774907, -2.4899806039352415, 0.44083856909989605, -0.06885385927651037, -1.7138245686076965, 0.7651703594346136, 3.1048275183736562, 0.9888719768530959, -0.4671947975675442, 1.003676924508508, -0.5514972387894581, -4.546288217634011, -2.952232144684328, 2.619978250961587, 3.166146391319024, -0.19956535886491594, -0.505344680113511, 0.36024421759121344, -1.3155402253508628, -1.0905372279709005, 2.498796138631484, 2.4347083430988588, -1.8006289911395572, -2.249247501962726, 0.6495138832053098, -0.5284355558493989, -3.544940437076667, -1.6374383614200367, 1.445791080642174, -0.004596565446099316, -1.5325367471487839, 0.3361823491108486, 0.41909539055674044, -1.8570779679081628, -0.19151010938586438, 3.4749051337170784, 1.874497147967721, -1.431800864275879, 0.8912865287867644, 4.321275824404069, 2.3951380592686626, -0.248274533122643, 0.4408812035184039, -0.32109966509905175, -3.025858310956373, -1.6964882337490828, 1.5501373265119613, 0.03748000102696807, -2.34885380297223, 0.5978528005368849, 3.2747275109168617, 0.1810454984882889, -2.354120125271038, -0.2555785133926972, 0.5124963388090198, -1.3364502788188288, -0.13110693404404156, 2.276468503252281, 0.31541893824857203, -1.7337302295306483, 0.9475997525114735, 2.055396977008412, -2.1218140657094624, -3.8631827461016153, -0.4869835738181355, 0.3617109984809749, -2.2611383111040464, -1.741720822492566, 0.5906487713552286, -0.20832699460464618, -0.30568095607808976, 3.031007784128595, 2.895187121789709, -2.239818241549259, -3.528649583009938, 0.15711945814211775, 0.6088411701319286, -1.6870187122608824, -0.10949317619381913, 2.455195917708345, 0.9269410525629503, -0.07663473461519936, 2.198332809675107, 1.6376396297428113, -1.9164493376657583, -1.154464125296411, 1.939050151096531, -0.12263511501171774, -3.4496362031275747, -1.1440959670211663, 1.7165167680936269, -0.17879947768436547, -1.343091576610896, 0.8172083172892889, 0.7875128050558912, -0.6650524270762962, 1.6957781168597466, 3.310137582192481, -1.3615143216429297, -5.1286234742451, -1.9148010228297652, 1.2815400588322958, 0.13068168676735314, 0.49131766426514517, 2.748352659102606, 1.0286641580610238, -1.7654239694034168, 0.1310217804527032, 1.9614073149468068, -0.4484741387658345, -0.9855383857681345, 1.7729712787425453, 0.17129193073693483, -4.674062625699009, -3.77218459462049, 0.8990023246221677, 1.327506968421787, -0.14251959115335688, 0.8519063235142974, 0.21159971658801596, -2.3921258496081887, -0.25226506463044446, 4.237258148439522, 2.529278167309266, -1.961456121902952, -1.285386531503281, 0.47937641679072307, -1.7766127593066001, -2.3393682526553636, 1.1091148148904924, 1.6138206037089633, -1.0275254411740777, -0.5838236838107704, 0.365180749706364, -2.6564409992948557, -3.5681628532788014, 0.9331889077519969, 2.428840248633722, -1.4939049271590696, -2.3584537515549773, 0.3673037433728054, -0.505039734257228, -2.867691589356699, -1.194503828983221, 0.526485998355193, -0.17638578618695613, 2.5806456955168153, 7.489218377327331, 5.824507465403461, 0.220134988465012, -0.20487182329625023, 1.6653319945355325, -0.27195420546194754, -1.2178752844455567, 1.8185183513795076, 2.188904175432566, -0.7024076509535924, -0.11373154008217798, 1.9937563625602792, 0.41692805511100856, 0.35825564539962207, 5.11331439741658, 6.116026498054481, 0.6644095731207051, -2.0137492213702672, -0.15050689649047136, -0.6319636030461584, -1.9304028879474902, 0.5992541539746323, 2.0278675495463134, -0.42205587750375756, -0.08640944862167169, 2.9268400354159225, 0.8101896419823205, -3.5724541619354446, -2.0700499156136174, 0.8821340569365367, -1.2887178750502577, -3.021968416272304, -0.5038514632768654, 0.30369924066161236, -0.8912410316086117, 1.4420990391501467, 3.5001238921651012, 0.07296276441966003, -2.1996973548347136, 0.8370277748867819, 1.3877598283990742, -2.241029330705387, -1.8129423267533742, 1.7619882486552547, 0.8911223336111836, -1.5060035144511832, -0.18386823628291582, 0.22465650817260502, -1.9174910395588436, -0.3694251138186538, 2.7162169022081284, -0.13939174886139985, -3.9388173798842008, -0.9632798397259069, 2.6562251654696367, 0.8905831601311972, -0.34751649027935655, 1.0946083597663565, -0.45971922324345027, -2.7182409704834343, -0.015298608468550735, 2.3932227382741926, 0.09949888414409781, -0.09596068265012594, 3.1781603592452887, 1.7206767466713193, -2.9462282643911277, -2.121441310067002, 1.0696429160997125, -0.12395689501484486, -1.1309932341557118, 1.3431771041869243, 1.3891527623657527, -0.7850160846792382, 0.6302946140857578, 1.3595915299247776, -3.7462070105164393, -6.569970592603793, -1.8682176122693779, 1.6410910976191184, 0.15577266254604769, 0.24136695951931575, 1.3001925364657558, -1.5757034919041935, -3.367587129278992, -0.19690885518682674, 0.9372229430311493, -1.494580047272338, -0.22715089592496565, 2.5256122278732858, -0.43101129688701756, -3.6718650397712493, -0.6992521060460677, 1.6608787925474904, -0.8443471003636573, -1.4629699847776998, 0.5846131493377216, -0.23481792384119743, -0.7391959018012868, 2.4612508504495993, 2.1315387468937823, -3.2278016281174926, -3.698182025854609, 1.1025934893883291, 1.6749425635958697, -0.8612002312315257, -0.2315466187972227, -0.39180105384187, -3.8389692420361654, -3.610417010348923, 0.24147454103515448, 0.29314648204172356, -0.8265805067107845, 2.2328364008916783, 3.182950955854164, -1.201518177100714, -1.913180334082818, 2.5759776013329336, 3.0743421451986093, -0.05842869502017363, -0.07083076001374801, 0.12967244779591036, -2.223249254798694, -1.184609338145135, 2.2723756581563506, 0.11025083154796389, -3.939813499119327, -1.8022613712148599, 1.014326632665036, -1.2675825781202, -1.801175519692714, 1.7670318411286832, 1.9755097855200079, -0.516004710610447, 0.10676668048613643], 'positive_zeros': ['0.31268663361090333727204925575', '1.69717037879534096925959785763', '2.26180050447112487157086533299', '3.58256336727698593932449582685', '4.21985337452598380712369059095', '4.942133894726969899815265356942', '5.61744195557400000182624379400', '6.80638497355860620357746315658', '7.338650609405828892909757745913', '8.17124191495593058673470473802', '8.8460359538982542812788447861', '9.580274482790132791655618014912', '10.29652910742195364174201820279', '11.33238670873270591421886494663', '11.79550481990384955421364186296', '12.58572389145284314155997642114', '13.179199688678599880103766528620', '13.88337968552959419931040280686', '14.9626832838774484031096247452', '15.37714264408165354335602288419', '16.06327283388809953193844229921', '17.039117705285957738908921355403', '17.139343249190463653241409786688', '18.39807567389047719470876828440', '18.8630633502343440183135326728', '19.65194853704832394710726076410', '20.33567429637041463856474122867', '20.83120490191731141445194283831', '21.52100697673225909997217128722', '22.39308424937651565069714448666', '23.24995940770322993969573355257', '23.45975876550023058954686570617', '24.58883881141327320858785107487', '24.64559738275429803639288409855', '25.71831928181537482695195274740', '26.46268516493737184190160701223', '26.933015947108273252423312592704', '27.76474923196481617827213540795', '28.32373327032059458214036771080', '28.94969099820521532814871376676', '29.412040574956903648909708796068', '30.52416084358821018394970290098', '31.10195925236263089554284646824', '31.573706352619281656188928874746', '31.99827098974006360539476783662', '33.19982996435595632537358333649', '33.35340192491030274162811568133', '34.15475381975003588043852354568', '35.00551580947812734809195776475', '35.61972185723683100738710939291', '36.01026258570879615193225573712', '36.693510156657721530442502695768', '37.348327566400358915405886529964', '38.21946104186089598416033249452', '38.79547856019241895003839674268', '39.33519615707531652486866267915', '39.88781707984202698895876928003', '40.59398614160521998520135366594', '41.232576632640119276119348259089', '41.9643434841387830880472139344', '42.4550824190222275508770568634', '43.39479473611334438312612674896', '43.69951191501006055128749349704', '44.33584706524029130190911388618', '44.87053022920221634990789303679', '45.82182539495435287688138711583', '46.47516384409388982937069451460', '46.87575729641858953271079774347', '47.43838963818286501574838410893', '48.277382874701734524903654625646', '48.7448572790573415746327438961', '49.30904277541167458424404397238', '50.184138473314191457441161307507', '50.947721515280687071237334003248', '51.07532432545638041753730349380', '51.88152651541538918332498245247', '52.50047710664808643570880760591', '53.13652921305355648261340514359', '53.78668156825806005930665296220', '54.56743281751832008448840720146', '55.04432243054960044123132439993', '55.521355283501529031607993021902', '56.130687103272490970705536198367', '56.88502920727840236754464973009', '57.60084896144642138261822292792', '57.99751698981367347556859913195', '58.827731755889504398630457597314', '59.40946563117501889562763057439', '59.697788534693032376382234816273', '60.57619939364997483857325890501', '61.051970344932608527805756061656', '61.9027639629733379783925662180', '62.53299085875295555754519750896', '62.84724323575713132931482256423', '63.61420204197859078293091657262', '64.00956334880602556683889398572', '64.872016409475929130634632130201', '65.52505195040215976120524782366', '65.97158810714344364638148784518', '66.63305720248591119567821409475', '67.30551810888474268937098068295', '67.86591507637037800461739460223', '68.1503108315234979669957606875', '69.15027600452893611856863636977', '69.7110425540144876472588509638', '70.50735774010491361549270378402', '70.62174398506545658407279892500', '71.45198189947454785212995284374', '71.87162567475304188439971116311', '72.821788931694472726833013738922', '73.34493771891424824639588098169', '73.65168796258560130785954147173', '74.69582599765524776353956716582', '75.013175251625821516882220297103', '75.63433415477466694210522921432', '75.969075664522805713576597326857', '77.018978643501014007069979047846', '77.492668055749942608326395165751', '78.18523372665213526239515275848', '78.53728527067799721484297167156', '79.09592139932931534105868843549', '79.86715430120675742214063019869', '80.45465309739191710006481420970', '80.93267415393894283251207136794', '81.74609373416797638974428801055', '82.22955525869068382781699125434', '82.855509004232075939858561295517', '83.26887341911275643192915235076', '83.83533452430666975850452848846', '84.71151912579384530258827668598', '85.1751826875824117749209044169', '85.8395365129073248727979327426', '86.42103510478146515858501748077', '86.80977139513991381666837122140', '87.434129521904430875377354287458', '88.168739315552286247566012400030', '88.7212671997285974939272700097', '89.37431253293104680787184577762', '89.87654471646407120732993968913', '90.59264076696355923937440170515', '90.930361896173920765640394233533', '91.63430235184332134318825449710', '92.07030776116128724140828956241', '93.21088516221614334329829093839', '93.32217750164603086533573861042', '93.89263292273085173707158688846', '94.65698690865593038622745596604', '95.1917276072636496947948662871', '95.53703272180530536579395929263', '96.36363432897936960387844310789', '97.21556939808642227084547977002', '97.48941303430480966118678238178', '97.896439861061614459787447769673', '98.75942460808793944194357608559', '99.37142508637427173213790609854', '99.59332345072630768019842624258', '100.413729633002736465671538255267', '101.257136472996630780992286689295', '101.58647684489611024449106008790', '102.22549911009891341104170693773', '102.53610078358471650812385689885', '103.29525873690218308153451350471', '103.953442965986756225896022714876', '104.66080733271921307884981730030', '105.01715165128738438424560821422', '105.589958921546436713655126963817', '106.45128357289376580932185973366', '106.74474587184870748490596632173', '107.133548116015568782081050115495', '108.108325592550919976322584173746', '108.55559104264690198693293103665', '109.210160094848961021747560558588', '109.88698599190723274358183923799', '110.12137292737385081762966061903', '110.66350276538975660383926711127', '111.579467899959204617190422637006', '111.96737685145726917705757545724', '112.751437457210429529094417847103', '113.115661102211935693962816865455', '113.68561291833183657475923587353', '114.49246720226228618781702907860', '114.80529618254987494923842299068', '115.266130346661122712275225645457', '116.095574799804281769535314988521', '116.851299297531975272216822006002', '117.2973868591660621480140075056', '117.60459699579917506594311654346', '118.22877604357203471173629660257', '118.9294190376421257782162952440', '119.599948304245689792343278877297', '119.949688822953398414441423324545', '120.75383589571349604765384691071', '121.24948627894273346691866537888', '121.82638114890898771307838977504', '122.24534881938475116569804940635', '122.82706595456883797212382811469', '123.57730081435522673046942143888', '123.99812153492635519109498040843', '124.93491461069546319261143141340', '125.19277443779479576248235661346', '125.583412973721609528233342884779', '126.38696766315582023600872778943', '126.87831776404269814196197667601', '127.458425523225629876428717061660', '128.13791720828375940641490931032', '128.78194119704553444399873886039', '129.15325824491383175645731422458', '129.70088626917666508597191234140', '130.340924225125682261079093431316', '130.85517865150988846410338648359', '131.42551139768871658478140953300', '132.2364577231925446044196544094', '132.55120168943186112697636721025', '133.32638676711322525843796551918', '133.71132652682067148194193758581', '134.10175937789570690141457173640', '134.869442364316855906709409288202', '135.61015314732272481579650964844', '136.014083899157145733303971999077', '136.57247613753696393704794903215', '137.32548431475248426282215704562', '137.51832828881931740114756573103', '138.26171984306060441820616982148', '138.8475648703852606925479217969', '139.36617515542933948664574452805', '140.08619453214993223504990008807', '140.60563675339331203933703158386', '141.13957132205504681633782361661', '141.68553042431903300736240993425', '142.02516740479340798792415595959', '142.743507895634546513997665566', '143.57052672309118270914195005864', '144.09241767707963694406642042848', '144.29217635389431618733239861534', '145.08627715766169460956288882504', '145.612713005956089774180447263994', '146.20224611158267062256073655419', '146.67624476379633584241564850767', '147.19869069329676977746761438712', '148.0519579700326111605247647282', '148.67552766998050494970262249970', '148.857832632444137232270073480126', '149.39962647266357215937522353468', '150.01582746417236505169741121561', '150.77828376273368998569779009738', '151.4020966542642115481423115222', '151.67592800721120893115906734667', '152.402955126692022579665307064986', '152.99286600496052005540490027242', '153.53066374525746301054942508900', '153.81639108792830061440869872917', '154.628456344440878698417635682665', '155.202818974248577593992372287025', '155.88282182609752646495682469192', '156.191729921543901881514399783797', '157.01952652265119503083843703424', '157.3952122786123918658905002194', '157.580731643419630045829900855364', '158.768963748295629813728730387938', '159.089542944878218295655865058732', '159.65786865235752551543193375421', '160.14440845352600019735084007733', '160.8494864630164983387260490142', '161.26329279597870113002059361589', '161.93799370559774075982012477421', '162.14376010715212088333917769339', '163.16350459582244242868848810974', '163.78582264222757764077865530373', '163.94351891659960113226518202489', '164.632294703657236746301915357871', '165.25963384368182432223242625704', '165.63409203396777824503939204101', '166.2993520035660289204061467', '167.04265811927496149176842909714', '167.38035488473192770271115173771', '168.18936801056479545348977899358', '168.50403330495719068365642487895', '168.93038811438754061427804200418', '169.692501359802537978350867351625', '170.24006617905454227603484644942', '170.75026127052513080054924911843', '171.393782255500966925801975671262', '171.962738811864882876408341846896', '172.528937749001790430900079728209', '172.85031330299228303682101956578', '173.46699305084660530022989596738', '174.05419644098089109062534825397', '174.745802913737060456328318293128', '175.424063547749744475903490588982', '175.70978570564003953910193025901', '176.20420633117294051343570313764', '176.87615244827684612277419641140', '177.51190086367299077863656122509', '177.82359287749818137412489450363', '178.5425411070843964412395005452', '179.23613465440612871900319829240', '179.672058109669501642109602067146', '180.16016017292847205122281825013', '180.79594804113342020880140152858', '181.175112894722089933027926310203', '181.67607691043770752636443636193', '182.608125010579759989887571640541', '183.156045690017309832069058271663', '183.38842473224365703373759505235', '183.932406841421728928349855533589', '184.70512722155645637133649407252', '185.1237737687645811654334662523', '185.644583542211014484956643451171', '186.22278172660421241727285643009', '186.92589031148182019271400697160', '187.41363975185948063554760815480', '188.016294081741799290312141781236', '188.39963632490348594619891265166', '188.84235648853876918429072235028', '189.50565538815651345318997274001', '190.23530094480191103255054419595', '190.80803077168462217476176736518', '191.301797329070275061993436516471', '191.50159704077914661036405447427', '192.47423376327707939404073508777', '192.85691552886450031728857272658', '193.248221653744648574450344611592', '193.98210292670276945661564063112', '194.51574724230193093544111986206', '195.303965300799054160047252834928', '195.64215793878962654568524441693', '195.960946277265299085323490824709', '196.65548744194379254759770876611', '197.19441464760313558401754701299', '197.95078761155036961789122701865', '198.310907120065114368401921816609', '198.91324005149827586541743982848', '199.598945808526652295629695960696', '199.97844710201263981173547045314'], 'prelabel': '1-3024-3024.2795-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 14.04339696032321, 'root_angle': -0.41964186176086865, 'root_number': '0.249779506133175673975487553464-0.968302741045313191397122297374*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.779100421978895567487232354238-0.0603628799969149050601038622231*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.312686633611', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.6971703788', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.26180050447', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 14.04339696032321, 'bad_primes': [2, 3, 7], 'central_character': '3024.2795', 'conductor': 3024, 'conductor_radical': 42, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3024/2795'], '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': '1-3024-3024.2795-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': '1-3024-3024.2795-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 14.04339696032321, 'root_angle': -0.20982093088043433, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.312686633611', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_3024.2795', 'Lhash_array': ['dirichlet_L_3024.2795'], 'label': '1-3024-3024.2795-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3024/2795'}