LMFDB - Embedded newform 1.114.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,114,Mod(1,1)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1, base_ring=CyclotomicField(1))

chi = DirichletCharacter(H, H._module([]))

N = Newforms(chi, 114, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 114);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 114 $
Character orbit:	$[\chi]$	$=$	1.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$80.8627478904$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} + \cdots - 66\!\cdots\!92 $ x^9 - x^8 - 32682013255644323754097819016304x^7 + 3915698636477556878976050211633151956990251264x^6 + 353548693607679711817279775814730428221926651961620009306114816x^5 - 67347657276227442467062695667670606469875246411798474590267077430986506414592x^4 - 1404195077646744215271916828405070669439443799283417428536494521425469742524325549320410124288x^3 + 317204131957055445253658481392625730341583630885680673395034283308448625427940239436992319045128764571680768x^2 + 1463442847701866442854533797255908842623728744878458229284167663408905230284437690341635050772170732679489447467116524470272*x - 660672734451343435665026023023017387967005158347281097502776856012295795980523499522586291466258570283417285019173682023212237580061704192
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{144}\cdot 3^{48}\cdot 5^{19}\cdot 7^{7}\cdot 11^{2}\cdot 13^{2}\cdot 19^{3}\cdot 23 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.94089e15$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.88610e17 q^{2} +4.27041e26 q^{3} +2.51891e34 q^{4} -5.60099e39 q^{5} -8.05442e43 q^{6} -6.14078e47 q^{7} -2.79228e51 q^{8} -6.39314e53 q^{9} +O(q^{10})$	\(q-1.88610e17 q^{2} +4.27041e26 q^{3} +2.51891e34 q^{4} -5.60099e39 q^{5} -8.05442e43 q^{6} -6.14078e47 q^{7} -2.79228e51 q^{8} -6.39314e53 q^{9} +1.05640e57 q^{10} +8.11533e58 q^{11} +1.07568e61 q^{12} -4.04092e62 q^{13} +1.15821e65 q^{14} -2.39186e66 q^{15} +2.65072e68 q^{16} -4.66247e68 q^{17} +1.20581e71 q^{18} +7.05627e71 q^{19} -1.41084e74 q^{20} -2.62237e74 q^{21} -1.53063e76 q^{22} +7.73306e75 q^{23} -1.19242e78 q^{24} +2.17415e79 q^{25} +7.62157e79 q^{26} -6.23904e80 q^{27} -1.54681e82 q^{28} -7.64722e81 q^{29} +4.51128e83 q^{30} +8.29513e83 q^{31} -2.09986e85 q^{32} +3.46558e85 q^{33} +8.79388e85 q^{34} +3.43945e87 q^{35} -1.61037e88 q^{36} +4.92250e88 q^{37} -1.33088e89 q^{38} -1.72564e89 q^{39} +1.56395e91 q^{40} -1.22301e91 q^{41} +4.94605e91 q^{42} +2.60913e92 q^{43} +2.04418e93 q^{44} +3.58079e93 q^{45} -1.45853e93 q^{46} -1.88787e94 q^{47} +1.13197e95 q^{48} +6.37069e94 q^{49} -4.10066e96 q^{50} -1.99107e95 q^{51} -1.01787e97 q^{52} +3.65886e97 q^{53} +1.17674e98 q^{54} -4.54539e98 q^{55} +1.71468e99 q^{56} +3.01332e98 q^{57} +1.44234e99 q^{58} +1.85825e99 q^{59} -6.02487e100 q^{60} -7.04144e100 q^{61} -1.56454e101 q^{62} +3.92589e101 q^{63} +1.20788e102 q^{64} +2.26332e102 q^{65} -6.53643e102 q^{66} +2.94156e103 q^{67} -1.17443e103 q^{68} +3.30234e102 q^{69} -6.48714e104 q^{70} -1.56426e104 q^{71} +1.78514e105 q^{72} +2.45574e105 q^{73} -9.28432e105 q^{74} +9.28451e105 q^{75} +1.77741e106 q^{76} -4.98345e106 q^{77} +3.25473e106 q^{78} -1.45426e107 q^{79} -1.48467e108 q^{80} +2.58878e107 q^{81} +2.30671e108 q^{82} -2.11361e106 q^{83} -6.60551e108 q^{84} +2.61145e108 q^{85} -4.92107e109 q^{86} -3.26568e108 q^{87} -2.26603e110 q^{88} +1.20430e110 q^{89} -6.75373e110 q^{90} +2.48144e110 q^{91} +1.94789e110 q^{92} +3.54236e110 q^{93} +3.56070e111 q^{94} -3.95221e111 q^{95} -8.96727e111 q^{96} +5.43087e111 q^{97} -1.20158e112 q^{98} -5.18825e112 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 49\!\cdots\!32 q^{2}+ \cdots + 55\!\cdots\!77 q^{9}+O(q^{10}) $ 9 * q + 4973724357874032 * q^2 - 1047822666262699970761104924 * q^3 + 57140122287714158706660944854495488 * q^4 - 3116148576934475303759287082847998426250 * q^5 - 8679197271676415971774420800017032303605312 * q^6 - 175592521264923853936268390919613238158926276408 * q^7 - 1152754689437068715781677022006928573086863264747520 * q^8 + 551049940125998155825143115188713609620516409643418677 * q^9	$ 9 q + 49\!\cdots\!32 q^{2}+ \cdots + 32\!\cdots\!64 q^{99}+O(q^{100}) $ 9 * q + 4973724357874032 * q^2 - 1047822666262699970761104924 * q^3 + 57140122287714158706660944854495488 * q^4 - 3116148576934475303759287082847998426250 * q^5 - 8679197271676415971774420800017032303605312 * q^6 - 175592521264923853936268390919613238158926276408 * q^7 - 1152754689437068715781677022006928573086863264747520 * q^8 + 551049940125998155825143115188713609620516409643418677 * q^9 - 153264347969576737314363653067831776074945972002322140000 * q^10 + 124303845165751869554468963179928310347446325358753066991788 * q^11 - 4766393536299397973462835582969587848650683059861216359840768 * q^12 + 118066950692074908165278563837084569941718111528864100316810046 * q^13 + 23370095428037254282484566813709955199818716752021690625741210496 * q^14 - 801369990352485680694849420185298838396866837392656002948893145000 * q^15 + 109009769902909383382120055717425408918319663897461125806267782201344 * q^16 + 1031208472354491758575110721181756882175051278670426497304478795027362 * q^17 + 21853761778376511004199260652941739695840479087427332697148033133176496 * q^18 - 2054770397164032300993860357285529834117448193071848654506031346813189260 * q^19 - 128965280615606341221181395517996603639092921677759187360515198160536640000 * q^20 - 2051981423257402292087521454906945230917134727108225442350522950612144271072 * q^21 - 31233703450481121590220064319836416371256690633810598891839492722859409642176 * q^22 - 167806258064059379045373533912927060845638327737895149615950186261514952182184 * q^23 + 837647327683589821169163577629460913691878109446800095361456758053616583557120 * q^24 + 36110808046585671891862329281725549351642982282250931138010564349682541171484375 * q^25 + 273284118611845700597932385482119882778869175349924218776704957190525454972143648 * q^26 - 1293409658858973603349494974301711616276027502548100865754773226934344693652580120 * q^27 - 12449742560521692406151296738508394024549837700960492852336353346600639157797779456 * q^28 + 16393803312375561825707281499219064392567318107169713827635118635692166495008904910 * q^29 + 1444554724925215896891120206778115916774229741452396468041800381952830143736681360000 * q^30 + 1314403569804018815618492241812394006579677928452900483535632508652944766037998410528 * q^31 - 21448902248775261233416755741924844958908937761160756654268584846741870841621352808448 * q^32 - 211847819746714833550323551974005344232426451287015334370441057211901425852772059609168 * q^33 + 319367478280300365454292314290661290493902375851140946818660251269274780967076833561056 * q^34 + 3439596420817236254046899424410940097643944233598368039111722250253904941775326256910000 * q^35 + 2704504833410501582895107271001450900815653199167021310209481973200374905160451231300864 * q^36 - 59867320490204404665587120670290466524223984034118562335350833430431530376567774885723498 * q^37 - 82453523727277361450274687052865709436318494611960850831592535368825105943678502733442880 * q^38 + 871232822588974033828162396761465282346428529310140460376676860192325312944522604565747064 * q^39 + 6827166757827354756060064429590450961456578801730020944860911233033409499443258590438400000 * q^40 - 34550149215769251780094496181290849916810545798144119670305052821692690196704735942577072902 * q^41 - 106065652173490837329551409984862217118049589651335199831107089722564993162529690865908896256 * q^42 + 207231754793163377176542763271534728167453514398489730764515211376339059665627233099893879756 * q^43 + 2312703333865421082227940066456566870684549523781445620538452769155749838714861346004252527616 * q^44 + 256198961065429853532686454584243663537866293764106258783025404071252757628746328749329658750 * q^45 - 28138310036672836977617659816100322616155099852864640775866866896982035999177616032492961297792 * q^46 - 49338615100567586008533951288135845393852650707485360531368204467394665532910688983139358306128 * q^47 + 244064292546444123908052536984208158793401136481260186300744503278739285380247288265778682658816 * q^48 + 752433840599750193271015544145910422089938845099283047668758541087980882087499887025758157789313 * q^49 - 1756648703190643407679915187540746659445068152182448123783254139837888034842840604352884543750000 * q^50 - 4186453060070964308543321243867301742071184523159619262981910395937624269639977914668070815961592 * q^51 - 299921527358232778097628046170322710643014254923572622961503877233695051976123243837021461385728 * q^52 + 45439534345102239290843163912544095765806982832307502313849525819073728936151813167470772365925926 * q^53 + 38680516880674041302480509047884889106404603448054948500904779898349149372610056782201281117946240 * q^54 - 432576867358466335617986215621945887405045763707273014611343529132044150112466209509767824829515000 * q^55 - 159465105485502254328469891445580976480576866382179762995668936857815143816140668281747609575260160 * q^56 + 1990014681911564315630720992224179214491287391034406566984522978256103716439101105615294767535358160 * q^57 + 4618158171946557697639499111957754813666889826993148515766803610504911213619043847144587412863790880 * q^58 - 7994556888742389963754891914386272086617532494092324481666622701281195647537712229818800059078242980 * q^59 - 51547668272403014021235031153713789291688796805654426950141340288411508848106756189101821863952640000 * q^60 - 20010787184525995584720289117304568167948599723976550204852777948468547299349907237396329738847967762 * q^61 + 292035427959193157957119307134870542698832076716753725989233844815905689373991776544712306185499282944 * q^62 + 1084750421819290453616791018398299860321649524662704337157840276934678472457615663242574941575258587176 * q^63 - 2173182954777058552426966649041133062639998025794768537871770595713126062249675532560302339710750031872 * q^64 - 6050492601584073293182223610830486690452314196108303412288731430157341922477676622337759152417832607500 * q^65 - 2811384209515387361103707894564511021023407746835224054361358951726305534503884893008505470528471177984 * q^66 + 24573799368134891916564011470928671317077382485972351268274803174871528123414635568434858147580241074212 * q^67 + 63690775145054712155234191070401247673413728435364958188409307863633237295553890585548320729107243037184 * q^68 - 24003285462463676531332362285165839175525050544235078632804235222118832623175439122841457438544940522656 * q^69 - 863169709419813836575212169649584339603968815833753646438175375944308193587969610263821675032671814880000 * q^70 + 91658679156386468719245489455910792073607873475232020252166152112986794966382882952820365384103518048008 * q^71 + 873882756027094209986251517892994706349418254125301044053004437567652817562627690659257226446504466493440 * q^72 + 541694808507779980546116004112644787310665887489575442433845489271276265038276918082847569639076524144666 * q^73 - 9378706212502591696314586127924566164346165127102664760442762960199173362938872227498081812178947973840224 * q^74 - 29348285812521570443266953567594350343794068770628558899049305240540166160078653563092442717138745889062500 * q^75 - 60564820012723729139203913493989896690950347961424832880261930310236667425867853870924430511072293881605120 * q^76 + 1068940833620544673782151517761484277047755630607342022951044010736792743275783369575718784146165485947744 * q^77 - 286969622560772923408733006352532687901626912195145659167094759389964370273396505496077341678419418050144128 * q^78 - 596276255135400928959400589889218117555952939149585650758445593510201386502571903994653015956197756762453040 * q^79 - 2420836681564557797101060397107174542916086634827557275495079675925079838120631425602247114230349809336320000 * q^80 - 3030606522373897290470630089608148759339991046893156580144516813393469703984963913807719049058860501442725951 * q^81 - 6936458118821589036700513874923262497738432667781968228952468701667638701536840125370171023576003636856609696 * q^82 - 11004287102773590749349691331049602909161139219297045772286679604418555775574362523281340925221936593079346764 * q^83 - 57855325032373861757970130314922242695268575192193159587088758458166711077597077741056893950844377121225826304 * q^84 - 64354197775882201370863569029422599518759619010400232504975477030343845397959668657595763753959731762134552500 * q^85 - 210819753145942403520859363592361681829074054483701088761378978430433240411156075153802810720648226504181908672 * q^86 - 154008309759204716022098762324487951847505839469072421264586325306012373529922474900817730928920322507018969160 * q^87 - 609999238537345062842609214560983373867364799260253404096252032888004927138583268244389069934087697492178288640 * q^88 - 654568028165810774739876366172819409302687924287909841936841472021672950876376689746932135695962343969713322070 * q^89 - 2734380769439054007162335818387627599332566037560181838266985769883367234594498859125630424774118397399333420000 * q^90 - 2323627076132845640660102608242767489368371452521120033992540027246745766005131800187294415915449799674836938512 * q^91 - 4256037231999230829372236189816770749190987971335840398392358871486563229805945773322404171318956972524277721088 * q^92 + 154296866852621529872615733195411660158426537898618117528867810834868770230718469048319703695743778039088292992 * q^93 + 1827384388290191849012043193156273334448650299359011463985703887856827570148696897626054924182121847958990279936 * q^94 - 4096663912916778389991331111354003035604483111168308740332618943380051360421354423075027168404452962459195325000 * q^95 + 8457146062137046129332319587633700387597377410609689871416901579530268721609757152896450994557102813871989587968 * q^96 + 36807391546013154433957869141705553075329468371786108764367006729276625672848917612484272062474831101244619876722 * q^97 + 225562248663489353389248034966442578767140826293081704735030344217680122252159170139356951685061050587472992483824 * q^98 + 321571830004348537474522583988170945954403617464147621640077047560490989900478751999197984675098698758537853855164 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.88610e17	−1.85084	−0.925422	−	0.378939i	$-0.876289\pi$
$2$	−1.88610e17	−1.85084	−0.925422	+	0.378939i	$0.876289\pi$
$3$	4.27041e26	0.471106	0.235553	−	0.971861i	$-0.424310\pi$
$3$	4.27041e26	0.471106	0.235553	+	0.971861i	$0.424310\pi$
$4$	2.51891e34	2.42562
$5$	−5.60099e39	−1.80493	−0.902464	−	0.430766i	$-0.858244\pi$
$5$	−5.60099e39	−1.80493	−0.902464	+	0.430766i	$0.858244\pi$
$6$	−8.05442e43	−0.871944
$7$	−6.14078e47	−1.09694	−0.548472	−	0.836169i	$-0.684790\pi$
$7$	−6.14078e47	−1.09694	−0.548472	+	0.836169i	$0.684790\pi$
$8$	−2.79228e51	−2.63860
$9$	−6.39314e53	−0.778059
$10$	1.05640e57	3.34064
$11$	8.11533e58	1.17658	0.588288	−	0.808652i	$-0.299802\pi$
$11$	8.11533e58	1.17658	0.588288	+	0.808652i	$0.299802\pi$
$12$	1.07568e61	1.14273
$13$	−4.04092e62	−0.466317	−0.233158	−	0.972439i	$-0.574906\pi$
$13$	−4.04092e62	−0.466317	−0.233158	+	0.972439i	$0.574906\pi$
$14$	1.15821e65	2.03027
$15$	−2.39186e66	−0.850313
$16$	2.65072e68	2.45802
$17$	−4.66247e68	−0.140686	−0.0703431	−	0.997523i	$-0.522409\pi$
$17$	−4.66247e68	−0.140686	−0.0703431	+	0.997523i	$0.522409\pi$
$18$	1.20581e71	1.44006
$19$	7.05627e71	0.397189	0.198594	−	0.980082i	$-0.436362\pi$
$19$	7.05627e71	0.397189	0.198594	+	0.980082i	$0.436362\pi$
$20$	−1.41084e74	−4.37807
$21$	−2.62237e74	−0.516777
$22$	−1.53063e76	−2.17766
$23$	7.73306e75	0.0892747	0.0446374	−	0.999003i	$-0.485787\pi$
$23$	7.73306e75	0.0892747	0.0446374	+	0.999003i	$0.485787\pi$
$24$	−1.19242e78	−1.24306
$25$	2.17415e79	2.25776
$26$	7.62157e79	0.863079
$27$	−6.23904e80	−0.837655
$28$	−1.54681e82	−2.66077
$29$	−7.64722e81	−0.181141	−0.0905705	−	0.995890i	$-0.528869\pi$
$29$	−7.64722e81	−0.181141	−0.0905705	+	0.995890i	$0.528869\pi$
$30$	4.51128e83	1.57380
$31$	8.29513e83	0.453824	0.226912	−	0.973915i	$-0.427137\pi$
$31$	8.29513e83	0.453824	0.226912	+	0.973915i	$0.427137\pi$
$32$	−2.09986e85	−1.91081
$33$	3.46558e85	0.554292
$34$	8.79388e85	0.260388
$35$	3.43945e87	1.97990
$36$	−1.61037e88	−1.88728
$37$	4.92250e88	1.22684	0.613420	−	0.789757i	$-0.289793\pi$
$37$	4.92250e88	1.22684	0.613420	+	0.789757i	$0.289793\pi$
$38$	−1.33088e89	−0.735134
$39$	−1.72564e89	−0.219685
$40$	1.56395e91	4.76249
$41$	−1.22301e91	−0.922871	−0.461435	−	0.887174i	$-0.652665\pi$
$41$	−1.22301e91	−0.922871	−0.461435	+	0.887174i	$0.652665\pi$
$42$	4.94605e91	0.956474
$43$	2.60913e92	1.33514	0.667571	−	0.744546i	$-0.267334\pi$
$43$	2.60913e92	1.33514	0.667571	+	0.744546i	$0.267334\pi$
$44$	2.04418e93	2.85393
$45$	3.58079e93	1.40434
$46$	−1.45853e93	−0.165234
$47$	−1.88787e94	−0.634515	−0.317258	−	0.948339i	$-0.602762\pi$
$47$	−1.88787e94	−0.634515	−0.317258	+	0.948339i	$0.602762\pi$
$48$	1.13197e95	1.15799
$49$	6.37069e94	0.203286
$50$	−4.10066e96	−4.17877
$51$	−1.99107e95	−0.0662782
$52$	−1.01787e97	−1.13111
$53$	3.65886e97	1.38599	0.692993	−	0.720945i	$-0.256292\pi$
$53$	3.65886e97	1.38599	0.692993	+	0.720945i	$0.256292\pi$
$54$	1.17674e98	1.55037
$55$	−4.54539e98	−2.12363
$56$	1.71468e99	2.89440
$57$	3.01332e98	0.187118
$58$	1.44234e99	0.335264
$59$	1.85825e99	0.164425	0.0822123	−	0.996615i	$-0.473801\pi$
$59$	1.85825e99	0.164425	0.0822123	+	0.996615i	$0.473801\pi$
$60$	−6.02487e100	−2.06254
$61$	−7.04144e100	−0.947384	−0.473692	−	0.880691i	$-0.657079\pi$
$61$	−7.04144e100	−0.947384	−0.473692	+	0.880691i	$0.657079\pi$
$62$	−1.56454e101	−0.839957
$63$	3.92589e101	0.853487
$64$	1.20788e102	1.07858
$65$	2.26332e102	0.841668
$66$	−6.53643e102	−1.02591
$67$	2.94156e103	1.97402	0.987009	−	0.160667i	$-0.0513644\pi$
$67$	2.94156e103	1.97402	0.987009	+	0.160667i	$0.0513644\pi$
$68$	−1.17443e103	−0.341252
$69$	3.30234e102	0.0420579
$70$	−6.48714e104	−3.66449
$71$	−1.56426e104	−0.396472	−0.198236	−	0.980154i	$-0.563521\pi$
$71$	−1.56426e104	−0.396472	−0.198236	+	0.980154i	$0.563521\pi$
$72$	1.78514e105	2.05299
$73$	2.45574e105	1.29551	0.647754	−	0.761849i	$-0.275708\pi$
$73$	2.45574e105	1.29551	0.647754	+	0.761849i	$0.275708\pi$
$74$	−9.28432e105	−2.27069
$75$	9.28451e105	1.06365
$76$	1.77741e106	0.963430
$77$	−4.98345e106	−1.29064
$78$	3.25473e106	0.406602
$79$	−1.45426e107	−0.884526	−0.442263	−	0.896885i	$-0.645824\pi$
$79$	−1.45426e107	−0.884526	−0.442263	+	0.896885i	$0.645824\pi$
$80$	−1.48467e108	−4.43655
$81$	2.58878e107	0.383434
$82$	2.30671e108	1.70809
$83$	−2.11361e106	−0.00789064	−0.00394532	−	0.999992i	$-0.501256\pi$
$83$	−2.11361e106	−0.00789064	−0.00394532	+	0.999992i	$0.501256\pi$
$84$	−6.60551e108	−1.25351
$85$	2.61145e108	0.253929
$86$	−4.92107e109	−2.47114
$87$	−3.26568e108	−0.0853367
$88$	−2.26603e110	−3.10451
$89$	1.20430e110	0.871360	0.435680	−	0.900102i	$-0.356508\pi$
$89$	1.20430e110	0.871360	0.435680	+	0.900102i	$0.356508\pi$
$90$	−6.75373e110	−2.59921
$91$	2.48144e110	0.511523
$92$	1.94789e110	0.216547
$93$	3.54236e110	0.213799
$94$	3.56070e111	1.17439
$95$	−3.95221e111	−0.716897
$96$	−8.96727e111	−0.900193
$97$	5.43087e111	0.303575	0.151788	−	0.988413i	$-0.451497\pi$
$97$	5.43087e111	0.303575	0.151788	+	0.988413i	$0.451497\pi$
$98$	−1.20158e112	−0.376251
$99$	−5.18825e112	−0.915445
$100$	5.47648e113	5.47648
$101$	−2.71283e113	−1.54620	−0.773099	−	0.634285i	$-0.781294\pi$
$101$	−2.71283e113	−1.54620	−0.773099	+	0.634285i	$0.781294\pi$
$102$	3.75535e112	0.122671
$103$	7.73280e113	1.45557	0.727785	−	0.685805i	$-0.240550\pi$
$103$	7.73280e113	1.45557	0.727785	+	0.685805i	$0.240550\pi$
$104$	1.12834e114	1.23042
$105$	1.46879e114	0.932746
$106$	−6.90096e114	−2.56524
$107$	−1.12023e114	−0.244975	−0.122488	−	0.992470i	$-0.539087\pi$
$107$	−1.12023e114	−0.244975	−0.122488	+	0.992470i	$0.539087\pi$
$108$	−1.57156e115	−2.03183
$109$	−1.55499e115	−1.19435	−0.597174	−	0.802112i	$-0.703710\pi$
$109$	−1.55499e115	−1.19435	−0.597174	+	0.802112i	$0.703710\pi$
$110$	8.57306e115	3.93051
$111$	2.10211e115	0.577972
$112$	−1.62775e116	−2.69631
$113$	−1.15115e116	−1.15398	−0.576991	−	0.816750i	$-0.695773\pi$
$113$	−1.15115e116	−1.15398	−0.576991	+	0.816750i	$0.695773\pi$
$114$	−5.68342e115	−0.346326
$115$	−4.33128e115	−0.161134
$116$	−1.92627e116	−0.439380
$117$	2.58342e116	0.362822
$118$	−3.50485e116	−0.304324
$119$	2.86312e116	0.154325
$120$	6.67872e117	2.24364
$121$	1.82842e117	0.384329
$122$	1.32809e118	1.75346
$123$	−5.22274e117	−0.434770
$124$	2.08947e118	1.10081
$125$	−6.78383e118	−2.27017
$126$	−7.40461e118	−1.57967
$127$	1.08958e119	1.48713	0.743566	−	0.668663i	$-0.233133\pi$
$127$	1.08958e119	1.48713	0.743566	+	0.668663i	$0.233133\pi$
$128$	−9.75550e117	−0.0854842
$129$	1.11421e119	0.628994
$130$	−4.26884e119	−1.55779
$131$	−7.59197e118	−0.179691	−0.0898455	−	0.995956i	$-0.528637\pi$
$131$	−7.59197e118	−0.179691	−0.0898455	+	0.995956i	$0.528637\pi$
$132$	8.72949e119	1.34450
$133$	−4.33310e119	−0.435694
$134$	−5.54807e120	−3.65360
$135$	3.49448e120	1.51191
$136$	1.30189e120	0.371215
$137$	−7.95954e119	−0.150029	−0.0750146	−	0.997182i	$-0.523900\pi$
$137$	−7.95954e119	−0.150029	−0.0750146	+	0.997182i	$0.523900\pi$
$138$	−6.22853e119	−0.0778426
$139$	−7.52424e120	−0.625355	−0.312677	−	0.949859i	$-0.601226\pi$
$139$	−7.52424e120	−0.625355	−0.312677	+	0.949859i	$0.601226\pi$
$140$	8.66366e121	4.80250
$141$	−8.06197e120	−0.298924
$142$	2.95035e121	0.733808
$143$	−3.27934e121	−0.548656
$144$	−1.69464e122	−1.91248
$145$	4.28320e121	0.326947
$146$	−4.63176e122	−2.39778
$147$	2.72055e121	0.0957695
$148$	1.23993e123	2.97585
$149$	−2.95164e122	−0.484216	−0.242108	−	0.970249i	$-0.577839\pi$
$149$	−2.95164e122	−0.484216	−0.242108	+	0.970249i	$0.577839\pi$
$150$	−1.75115e123	−1.96864
$151$	1.62350e122	0.125388	0.0626938	−	0.998033i	$-0.480031\pi$
$151$	1.62350e122	0.125388	0.0626938	+	0.998033i	$0.480031\pi$
$152$	−1.97031e123	−1.04802
$153$	2.98078e122	0.109462
$154$	9.39928e123	2.38877
$155$	−4.64610e123	−0.819120
$156$	−4.34673e123	−0.532872
$157$	−2.33358e124	−1.99385	−0.996926	−	0.0783427i	$-0.975037\pi$
$157$	−2.33358e124	−1.99385	−0.996926	+	0.0783427i	$0.975037\pi$
$158$	2.74287e124	1.63712
$159$	1.56248e124	0.652947
$160$	1.17613e125	3.44887
$161$	−4.74870e123	−0.0979294
$162$	−4.88269e124	−0.709677
$163$	3.70963e124	0.380830	0.190415	−	0.981704i	$-0.439017\pi$
$163$	3.70963e124	0.380830	0.190415	+	0.981704i	$0.439017\pi$
$164$	−3.08064e125	−2.23854
$165$	−1.94107e125	−1.00046
$166$	3.98647e123	0.0146043
$167$	−4.86304e125	−1.26890	−0.634450	−	0.772964i	$-0.718773\pi$
$167$	−4.86304e125	−1.26890	−0.634450	+	0.772964i	$0.718773\pi$
$168$	7.32238e125	1.36357
$169$	−5.87639e125	−0.782549
$170$	−4.92544e125	−0.469982
$171$	−4.51117e125	−0.309036
$172$	6.57216e126	3.23855
$173$	−2.01197e126	−0.714524	−0.357262	−	0.934004i	$-0.616290\pi$
$173$	−2.01197e126	−0.714524	−0.357262	+	0.934004i	$0.616290\pi$
$174$	6.15940e125	0.157945
$175$	−1.33510e127	−2.47664
$176$	2.15115e127	2.89204
$177$	7.93552e125	0.0774614
$178$	−2.27142e127	−1.61275
$179$	−2.78372e127	−1.44022	−0.720110	−	0.693860i	$-0.755909\pi$
$179$	−2.78372e127	−1.44022	−0.720110	+	0.693860i	$0.755909\pi$
$180$	9.01969e127	3.40640
$181$	5.39204e127	1.48907	0.744533	−	0.667586i	$-0.232672\pi$
$181$	5.39204e127	1.48907	0.744533	+	0.667586i	$0.232672\pi$
$182$	−4.68024e127	−0.946749
$183$	−3.00699e127	−0.446318
$184$	−2.15928e127	−0.235561
$185$	−2.75709e128	−2.21436
$186$	−6.68125e127	−0.395709
$187$	−3.78375e127	−0.165528
$188$	−4.75536e128	−1.53909
$189$	3.83126e128	0.918861
$190$	7.45427e128	1.32686
$191$	1.20920e126	0.00159997	0.000799986	−	1.00000i	$-0.499745\pi$
$191$	1.20920e126	0.00159997	0.000799986		1.00000i	$0.499745\pi$
$192$	5.15813e128	0.508128
$193$	1.64872e129	1.21104	0.605520	−	0.795830i	$-0.292965\pi$
$193$	1.64872e129	1.21104	0.605520	+	0.795830i	$0.292965\pi$
$194$	−1.02432e129	−0.561871
$195$	9.66530e128	0.396515
$196$	1.60472e129	0.493096
$197$	1.28686e128	0.0296612	0.0148306	−	0.999890i	$-0.495279\pi$
$197$	1.28686e128	0.0296612	0.0148306	+	0.999890i	$0.495279\pi$
$198$	9.78555e129	1.69434
$199$	−3.88721e129	−0.506336	−0.253168	−	0.967422i	$-0.581473\pi$
$199$	−3.88721e129	−0.506336	−0.253168	+	0.967422i	$0.581473\pi$
$200$	−6.07082e130	−5.95734
$201$	1.25617e130	0.929972
$202$	5.11667e130	2.86177
$203$	4.69599e129	0.198702
$204$	−5.01532e129	−0.160766
$205$	6.85005e130	1.66571
$206$	−1.45848e131	−2.69403
$207$	−4.94385e129	−0.0694610
$208$	−1.07114e131	−1.14621
$209$	5.72640e130	0.467322
$210$	−2.77028e131	−1.72637
$211$	2.62269e131	1.24965	0.624826	−	0.780764i	$-0.285170\pi$
$211$	2.62269e131	1.24965	0.624826	+	0.780764i	$0.285170\pi$
$212$	9.21633e131	3.36188
$213$	−6.68005e130	−0.186781
$214$	2.11286e131	0.453411
$215$	−1.46137e132	−2.40984
$216$	1.74211e132	2.21024
$217$	−5.09386e131	−0.497820
$218$	2.93287e132	2.21055
$219$	1.04870e132	0.610322
$220$	−1.14494e133	−5.15113
$221$	1.88407e131	0.0656043
$222$	−3.96479e132	−1.06974
$223$	−2.19034e132	−0.458445	−0.229223	−	0.973374i	$-0.573618\pi$
$223$	−2.19034e132	−0.458445	−0.229223	+	0.973374i	$0.573618\pi$
$224$	1.28948e133	2.09605
$225$	−1.38996e133	−1.75667
$226$	2.17118e133	2.13584
$227$	8.43566e132	0.646633	0.323317	−	0.946291i	$-0.395202\pi$
$227$	8.43566e132	0.646633	0.323317	+	0.946291i	$0.395202\pi$
$228$	7.59028e132	0.453878
$229$	−1.68499e133	−0.786851	−0.393425	−	0.919357i	$-0.628710\pi$
$229$	−1.68499e133	−0.786851	−0.393425	+	0.919357i	$0.628710\pi$
$230$	8.16922e132	0.298235
$231$	−2.12814e133	−0.608028
$232$	2.13532e133	0.477959
$233$	7.75558e132	0.136146	0.0680729	−	0.997680i	$-0.478315\pi$
$233$	7.75558e132	0.136146	0.0680729	+	0.997680i	$0.478315\pi$
$234$	−4.87258e133	−0.671526
$235$	1.05739e134	1.14525
$236$	4.68078e133	0.398832
$237$	−6.21028e133	−0.416706
$238$	−5.40013e133	−0.285631
$239$	2.42909e134	1.01382	0.506911	−	0.861998i	$-0.330787\pi$
$239$	2.42909e134	1.01382	0.506911	+	0.861998i	$0.330787\pi$
$240$	−6.34015e134	−2.09009
$241$	3.26379e134	0.850668	0.425334	−	0.905037i	$-0.360157\pi$
$241$	3.26379e134	0.850668	0.425334	+	0.905037i	$0.360157\pi$
$242$	−3.44859e134	−0.711333
$243$	6.23200e134	1.01829
$244$	−1.77368e135	−2.29799
$245$	−3.56822e134	−0.366917
$246$	9.85061e134	0.804692
$247$	−2.85138e134	−0.185216
$248$	−2.31623e135	−1.19746
$249$	−9.02598e132	−0.00371733
$250$	1.27950e136	4.20174
$251$	−1.26945e134	−0.0332698	−0.0166349	−	0.999862i	$-0.505295\pi$
$251$	−1.26945e134	−0.0332698	−0.0166349	+	0.999862i	$0.505295\pi$
$252$	9.88896e135	2.07024
$253$	6.27564e134	0.105038
$254$	−2.05506e136	−2.75245
$255$	1.11520e135	0.119627
$256$	−1.07033e136	−0.920366
$257$	−2.94200e135	−0.202965	−0.101482	−	0.994837i	$-0.532359\pi$
$257$	−2.94200e135	−0.202965	−0.101482	+	0.994837i	$0.532359\pi$
$258$	−2.10150e136	−1.16417
$259$	−3.02280e136	−1.34578
$260$	5.70109e136	2.04157
$261$	4.88898e135	0.140938
$262$	1.43192e136	0.332580
$263$	7.20351e136	1.34910	0.674551	−	0.738228i	$-0.264337\pi$
$263$	7.20351e136	1.34910	0.674551	+	0.738228i	$0.264337\pi$
$264$	−9.67686e136	−1.46256
$265$	−2.04932e137	−2.50160
$266$	8.17266e136	0.806401
$267$	5.14284e136	0.410503
$268$	7.40952e137	4.78822
$269$	−3.56928e137	−1.86886	−0.934431	−	0.356144i	$-0.884091\pi$
$269$	−3.56928e137	−1.86886	−0.934431	+	0.356144i	$0.884091\pi$
$270$	−6.59094e137	−2.79830
$271$	2.73335e137	0.941737	0.470868	−	0.882203i	$-0.343941\pi$
$271$	2.73335e137	0.941737	0.470868	+	0.882203i	$0.343941\pi$
$272$	−1.23589e137	−0.345810
$273$	1.05968e137	0.240982
$274$	1.50125e137	0.277681
$275$	1.76439e138	2.65643
$276$	8.31829e136	0.102017
$277$	−1.06832e138	−1.06806	−0.534028	−	0.845466i	$-0.679322\pi$
$277$	−1.06832e138	−1.06806	−0.534028	+	0.845466i	$0.679322\pi$
$278$	1.41915e138	1.15743
$279$	−5.30319e137	−0.353102
$280$	−9.60389e138	−5.22418
$281$	4.71188e137	0.209550	0.104775	−	0.994496i	$-0.466588\pi$
$281$	4.71188e137	0.209550	0.104775	+	0.994496i	$0.466588\pi$
$282$	1.52057e138	0.553262
$283$	4.53189e138	1.35004	0.675019	−	0.737800i	$-0.264135\pi$
$283$	4.53189e138	1.35004	0.675019	+	0.737800i	$0.264135\pi$
$284$	−3.94024e138	−0.961692
$285$	−1.68776e138	−0.337735
$286$	6.18516e138	1.01548
$287$	7.51022e138	1.01234
$288$	1.34247e139	1.48672
$289$	−1.07658e139	−0.980207
$290$	−8.07855e138	−0.605127
$291$	2.31921e138	0.143016
$292$	6.18578e139	3.14241
$293$	−1.58351e139	−0.663133	−0.331566	−	0.943432i	$-0.607577\pi$
$293$	−1.58351e139	−0.663133	−0.331566	+	0.943432i	$0.607577\pi$
$294$	−5.13123e138	−0.177254
$295$	−1.04081e139	−0.296774
$296$	−1.37450e140	−3.23714
$297$	−5.06319e139	−0.985564
$298$	5.56708e139	0.896207
$299$	−3.12487e138	−0.0416303
$300$	2.33868e140	2.58001
$301$	−1.60221e140	−1.46458
$302$	−3.06208e139	−0.232073
$303$	−1.15849e140	−0.728424
$304$	1.87042e140	0.976297
$305$	3.94391e140	1.70996
$306$	−5.62205e139	−0.202597
$307$	−4.45428e140	−1.33493	−0.667466	−	0.744640i	$-0.732621\pi$
$307$	−4.45428e140	−1.33493	−0.667466	+	0.744640i	$0.732621\pi$
$308$	−1.25529e141	−3.13060
$309$	3.30222e140	0.685729
$310$	8.76300e140	1.51606
$311$	8.96108e140	1.29240	0.646202	−	0.763167i	$-0.276356\pi$
$311$	8.96108e140	1.29240	0.646202	+	0.763167i	$0.276356\pi$
$312$	4.81846e140	0.579661
$313$	−4.73362e140	−0.475268	−0.237634	−	0.971355i	$-0.576372\pi$
$313$	−4.73362e140	−0.475268	−0.237634	+	0.971355i	$0.576372\pi$
$314$	4.40137e141	3.69031
$315$	−2.19889e141	−1.54048
$316$	−3.66314e141	−2.14553
$317$	3.23780e141	1.58636	0.793180	−	0.608987i	$-0.208424\pi$
$317$	3.23780e141	1.58636	0.793180	+	0.608987i	$0.208424\pi$
$318$	−2.94700e141	−1.20850
$319$	−6.20598e140	−0.213126
$320$	−6.76531e141	−1.94677
$321$	−4.78383e140	−0.115409
$322$	8.95653e140	0.181252
$323$	−3.28996e140	−0.0558790
$324$	6.52089e141	0.930066
$325$	−8.78556e141	−1.05283
$326$	−6.99673e141	−0.704856
$327$	−6.64045e141	−0.562665
$328$	3.41497e142	2.43509
$329$	1.15930e142	0.696028
$330$	3.66105e142	1.85169
$331$	−2.18352e141	−0.0930842	−0.0465421	−	0.998916i	$-0.514820\pi$
$331$	−2.18352e141	−0.0930842	−0.0465421	+	0.998916i	$0.514820\pi$
$332$	−5.32399e140	−0.0191397
$333$	−3.14702e142	−0.954554
$334$	9.17217e142	2.34853
$335$	−1.64756e143	−3.56296
$336$	−6.95117e142	−1.27025
$337$	−1.67134e142	−0.258211	−0.129106	−	0.991631i	$-0.541211\pi$
$337$	−1.67134e142	−0.258211	−0.129106	+	0.991631i	$0.541211\pi$
$338$	1.10834e143	1.44838
$339$	−4.91588e142	−0.543649
$340$	6.57799e142	0.615935
$341$	6.73178e142	0.533958
$342$	8.50852e142	0.571978
$343$	1.53322e143	0.873950
$344$	−7.28540e143	−3.52291
$345$	−1.84964e142	−0.0759115
$346$	3.79478e143	1.32247
$347$	−2.35610e143	−0.697554	−0.348777	−	0.937206i	$-0.613403\pi$
$347$	−2.35610e143	−0.697554	−0.348777	+	0.937206i	$0.613403\pi$
$348$	−8.22595e142	−0.206995
$349$	−7.28421e143	−1.55864	−0.779320	−	0.626626i	$-0.784436\pi$
$349$	−7.28421e143	−1.55864	−0.779320	+	0.626626i	$0.784436\pi$
$350$	2.51812e144	4.58387
$351$	2.52115e143	0.390612
$352$	−1.70411e144	−2.24821
$353$	−1.06859e144	−1.20099	−0.600497	−	0.799627i	$-0.705030\pi$
$353$	−1.06859e144	−1.20099	−0.600497	+	0.799627i	$0.705030\pi$
$354$	−1.49672e143	−0.143369
$355$	8.76142e143	0.715604
$356$	3.03351e144	2.11359
$357$	1.22267e143	0.0727035
$358$	5.25037e144	2.66562
$359$	2.26995e144	0.984418	0.492209	−	0.870477i	$-0.336189\pi$
$359$	2.26995e144	0.984418	0.492209	+	0.870477i	$0.336189\pi$
$360$	−9.99856e144	−3.70549
$361$	−2.65823e144	−0.842241
$362$	−1.01699e145	−2.75603
$363$	7.80813e143	0.181060
$364$	6.25053e144	1.24076
$365$	−1.37546e145	−2.33830
$366$	5.67147e144	0.826066
$367$	−5.89132e143	−0.0735495	−0.0367748	−	0.999324i	$-0.511708\pi$
$367$	−5.89132e143	−0.0735495	−0.0367748	+	0.999324i	$0.511708\pi$
$368$	2.04982e144	0.219439
$369$	7.81885e144	0.718048
$370$	5.20014e145	4.09843
$371$	−2.24682e145	−1.52035
$372$	8.92290e144	0.518597
$373$	−2.25384e145	−1.12558	−0.562788	−	0.826601i	$-0.690271\pi$
$373$	−2.25384e145	−1.12558	−0.562788	+	0.826601i	$0.690271\pi$
$374$	7.13652e144	0.306366
$375$	−2.89697e145	−1.06949
$376$	5.27144e145	1.67423
$377$	3.09018e144	0.0844691
$378$	−7.22613e145	−1.70067
$379$	6.61220e145	1.34039	0.670194	−	0.742186i	$-0.266211\pi$
$379$	6.61220e145	1.34039	0.670194	+	0.742186i	$0.266211\pi$
$380$	−9.95527e145	−1.73892
$381$	4.65296e145	0.700597
$382$	−2.28067e143	−0.00296130
$383$	−6.68934e145	−0.749294	−0.374647	−	0.927167i	$-0.622236\pi$
$383$	−6.68934e145	−0.749294	−0.374647	+	0.927167i	$0.622236\pi$
$384$	−4.16600e144	−0.0402722
$385$	2.79123e146	2.32951
$386$	−3.10965e146	−2.24145
$387$	−1.66805e146	−1.03882
$388$	1.36799e146	0.736359
$389$	2.85514e146	1.32885	0.664424	−	0.747356i	$-0.268677\pi$
$389$	2.85514e146	1.32885	0.664424	+	0.747356i	$0.268677\pi$
$390$	−1.82297e146	−0.733887
$391$	−3.60551e144	−0.0125597
$392$	−1.77887e146	−0.536392
$393$	−3.24209e145	−0.0846536
$394$	−2.42714e145	−0.0548983
$395$	8.14529e146	1.59651
$396$	−1.30687e147	−2.22052
$397$	7.01748e145	0.103399	0.0516996	−	0.998663i	$-0.483536\pi$
$397$	7.01748e145	0.103399	0.0516996	+	0.998663i	$0.483536\pi$
$398$	7.33166e146	0.937149
$399$	−1.85041e146	−0.205258
$400$	5.76306e147	5.54963
$401$	9.52208e145	0.0796297	0.0398148	−	0.999207i	$-0.487323\pi$
$401$	9.52208e145	0.0796297	0.0398148	+	0.999207i	$0.487323\pi$
$402$	−2.36925e147	−1.72123
$403$	−3.35200e146	−0.211626
$404$	−6.83338e147	−3.75049
$405$	−1.44997e147	−0.692071
$406$	−8.85711e146	−0.367766
$407$	3.99477e147	1.44347
$408$	5.55961e146	0.174882
$409$	−1.06009e147	−0.290386	−0.145193	−	0.989403i	$-0.546380\pi$
$409$	−1.06009e147	−0.290386	−0.145193	+	0.989403i	$0.546380\pi$
$410$	−1.29199e148	−3.08298
$411$	−3.39905e146	−0.0706798
$412$	1.94782e148	3.53066
$413$	−1.14111e147	−0.180364
$414$	9.32459e146	0.128561
$415$	1.18383e146	0.0142420
$416$	8.48537e147	0.891041
$417$	−3.21316e147	−0.294609
$418$	−1.08006e148	−0.864941
$419$	1.80384e148	1.26214	0.631068	−	0.775728i	$-0.282617\pi$
$419$	1.80384e148	1.26214	0.631068	+	0.775728i	$0.282617\pi$
$420$	3.69974e148	2.26249
$421$	1.37652e148	0.735944	0.367972	−	0.929837i	$-0.380052\pi$
$421$	1.37652e148	0.735944	0.367972	+	0.929837i	$0.380052\pi$
$422$	−4.94666e148	−2.31291
$423$	1.20694e148	0.493690
$424$	−1.02165e149	−3.65706
$425$	−1.01369e148	−0.317636
$426$	1.25992e148	0.345702
$427$	4.32400e148	1.03923
$428$	−2.82175e148	−0.594218
$429$	−1.40041e148	−0.258476
$430$	2.75629e149	4.46023
$431$	−4.95499e148	−0.703197	−0.351599	−	0.936151i	$-0.614362\pi$
$431$	−4.95499e148	−0.703197	−0.351599	+	0.936151i	$0.614362\pi$
$432$	−1.65380e149	−2.05897
$433$	−6.91318e148	−0.755287	−0.377643	−	0.925951i	$-0.623265\pi$
$433$	−6.91318e148	−0.755287	−0.377643	+	0.925951i	$0.623265\pi$
$434$	9.60752e148	0.921386
$435$	1.82911e148	0.154027
$436$	−3.91688e149	−2.89704
$437$	5.45666e147	0.0354589
$438$	−1.97795e149	−1.12961
$439$	−9.70418e148	−0.487207	−0.243604	−	0.969875i	$-0.578330\pi$
$439$	−9.70418e148	−0.487207	−0.243604	+	0.969875i	$0.578330\pi$
$440$	1.26920e150	5.60342
$441$	−4.07287e148	−0.158169
$442$	−3.55353e148	−0.121423
$443$	−2.25370e149	−0.677776	−0.338888	−	0.940827i	$-0.610051\pi$
$443$	−2.25370e149	−0.677776	−0.338888	+	0.940827i	$0.610051\pi$
$444$	5.29502e149	1.40194
$445$	−6.74525e149	−1.57274
$446$	4.13120e149	0.848510
$447$	−1.26047e149	−0.228117
$448$	−7.41731e149	−1.18315
$449$	2.06820e149	0.290853	0.145427	−	0.989369i	$-0.453544\pi$
$449$	2.06820e149	0.290853	0.145427	+	0.989369i	$0.453544\pi$
$450$	2.62161e150	3.25133
$451$	−9.92511e149	−1.08583
$452$	−2.89964e150	−2.79913
$453$	6.93301e148	0.0590709
$454$	−1.59105e150	−1.19682
$455$	−1.38985e150	−0.923262
$456$	−8.41402e149	−0.493730
$457$	1.36171e149	0.0706022	0.0353011	−	0.999377i	$-0.488761\pi$
$457$	1.36171e149	0.0706022	0.0353011	+	0.999377i	$0.488761\pi$
$458$	3.17806e150	1.45634
$459$	2.90893e149	0.117847
$460$	−1.09101e150	−0.390851
$461$	3.09004e150	0.979178	0.489589	−	0.871953i	$-0.337147\pi$
$461$	3.09004e150	0.979178	0.489589	+	0.871953i	$0.337147\pi$
$462$	4.01388e150	1.12536
$463$	6.48700e150	1.60960	0.804800	−	0.593546i	$-0.202273\pi$
$463$	6.48700e150	1.60960	0.804800	+	0.593546i	$0.202273\pi$
$464$	−2.02707e150	−0.445248
$465$	−1.98408e150	−0.385893
$466$	−1.46278e150	−0.251985
$467$	1.02630e151	1.56628	0.783140	−	0.621846i	$-0.213617\pi$
$467$	1.02630e151	1.56628	0.783140	+	0.621846i	$0.213617\pi$
$468$	6.50739e150	0.880068
$469$	−1.80635e151	−2.16539
$470$	−1.99435e151	−2.11969
$471$	−9.96537e150	−0.939317
$472$	−5.18876e150	−0.433851
$473$	2.11739e151	1.57090
$474$	1.17132e151	0.771258
$475$	1.53414e151	0.896758
$476$	7.21194e150	0.374334
$477$	−2.33916e151	−1.07838
$478$	−4.58150e151	−1.87643
$479$	2.66875e151	0.971297	0.485649	−	0.874154i	$-0.338583\pi$
$479$	2.66875e151	0.971297	0.485649	+	0.874154i	$0.338583\pi$
$480$	5.02256e151	1.62478
$481$	−1.98914e151	−0.572096
$482$	−6.15584e151	−1.57445
$483$	−2.02789e150	−0.0461352
$484$	4.60564e151	0.932238
$485$	−3.04183e151	−0.547932
$486$	−1.17542e152	−1.88470
$487$	5.98006e151	0.853727	0.426864	−	0.904316i	$-0.359618\pi$
$487$	5.98006e151	0.853727	0.426864	+	0.904316i	$0.359618\pi$
$488$	1.96616e152	2.49977
$489$	1.58416e151	0.179411
$490$	6.73002e151	0.679106
$491$	−9.12641e151	−0.820721	−0.410361	−	0.911923i	$-0.634597\pi$
$491$	−9.12641e151	−0.820721	−0.410361	+	0.911923i	$0.634597\pi$
$492$	−1.31556e152	−1.05459
$493$	3.56549e150	0.0254841
$494$	5.37799e151	0.342805
$495$	2.90593e152	1.65231
$496$	2.19881e152	1.11551
$497$	9.60580e151	0.434908
$498$	1.70239e150	0.00688020
$499$	2.14934e152	0.775575	0.387787	−	0.921749i	$-0.373239\pi$
$499$	2.14934e152	0.775575	0.387787	+	0.921749i	$0.373239\pi$
$500$	−1.70878e153	−5.50658
$501$	−2.07672e152	−0.597787
$502$	2.39431e151	0.0615772
$503$	−2.67799e152	−0.615485	−0.307743	−	0.951470i	$-0.599574\pi$
$503$	−2.67799e152	−0.615485	−0.307743	+	0.951470i	$0.599574\pi$
$504$	−1.09622e153	−2.25201
$505$	1.51945e153	2.79078
$506$	−1.18365e152	−0.194410
$507$	−2.50946e152	−0.368664
$508$	2.74456e153	3.60722
$509$	5.42874e152	0.638476	0.319238	−	0.947675i	$-0.396573\pi$
$509$	5.42874e152	0.638476	0.319238	+	0.947675i	$0.396573\pi$
$510$	−2.10337e152	−0.221412
$511$	−1.50801e153	−1.42110
$512$	2.12006e153	1.78894
$513$	−4.40244e152	−0.332707
$514$	5.54890e152	0.375656
$515$	−4.33113e153	−2.62720
$516$	2.80658e153	1.52570
$517$	−1.53207e153	−0.746555
$518$	5.70130e153	2.49082
$519$	−8.59195e152	−0.336617
$520$	−6.31980e153	−2.22083
$521$	−5.49950e152	−0.173377	−0.0866885	−	0.996235i	$-0.527628\pi$
$521$	−5.49950e152	−0.173377	−0.0866885	+	0.996235i	$0.527628\pi$
$522$	−9.22109e152	−0.260855
$523$	7.46759e153	1.89599	0.947993	−	0.318292i	$-0.103109\pi$
$523$	7.46759e153	1.89599	0.947993	+	0.318292i	$0.103109\pi$
$524$	−1.91235e153	−0.435863
$525$	−5.70142e153	−1.16676
$526$	−1.35865e154	−2.49698
$527$	−3.86758e152	−0.0638468
$528$	9.18630e153	1.36246
$529$	−7.44338e153	−0.992030
$530$	3.86522e154	4.63008
$531$	−1.18801e153	−0.127932
$532$	−1.09147e154	−1.05683
$533$	4.94207e153	0.430350
$534$	−9.69990e153	−0.759777
$535$	6.27438e153	0.442163
$536$	−8.21364e154	−5.20865
$537$	−1.18876e154	−0.678497
$538$	6.73202e154	3.45897
$539$	5.17003e153	0.239182
$540$	8.80229e154	3.66731
$541$	−1.69092e154	−0.634567	−0.317283	−	0.948331i	$-0.602771\pi$
$541$	−1.69092e154	−0.634567	−0.317283	+	0.948331i	$0.602771\pi$
$542$	−5.15536e154	−1.74301
$543$	2.30263e154	0.701509
$544$	9.79053e153	0.268824
$545$	8.70949e154	2.15571
$546$	−1.99866e154	−0.446020
$547$	−3.56944e154	−0.718318	−0.359159	−	0.933276i	$-0.616936\pi$
$547$	−3.56944e154	−0.718318	−0.359159	+	0.933276i	$0.616936\pi$
$548$	−2.00494e154	−0.363914
$549$	4.50169e154	0.737120
$550$	−3.32782e155	−4.91663
$551$	−5.39609e153	−0.0719472
$552$	−9.22103e153	−0.110974
$553$	8.93028e154	0.970276
$554$	2.01496e155	1.97681
$555$	−1.17739e155	−1.04320
$556$	−1.89529e155	−1.51687
$557$	−1.60713e155	−1.16207	−0.581034	−	0.813880i	$-0.697352\pi$
$557$	−1.60713e155	−1.16207	−0.581034	+	0.813880i	$0.697352\pi$
$558$	1.00023e155	0.653536
$559$	−1.05433e155	−0.622599
$560$	9.11702e155	4.86664
$561$	−1.61582e154	−0.0779813
$562$	−8.88706e154	−0.387843
$563$	2.24616e155	0.886576	0.443288	−	0.896379i	$-0.353812\pi$
$563$	2.24616e155	0.886576	0.443288	+	0.896379i	$0.353812\pi$
$564$	−2.03074e155	−0.725077
$565$	6.44758e155	2.08286
$566$	−8.54760e155	−2.49871
$567$	−1.58971e155	−0.420606
$568$	4.36785e155	1.04613
$569$	−3.25218e155	−0.705230	−0.352615	−	0.935768i	$-0.614708\pi$
$569$	−3.25218e155	−0.705230	−0.352615	+	0.935768i	$0.614708\pi$
$570$	3.18328e155	0.625094
$571$	1.54543e154	0.0274858	0.0137429	−	0.999906i	$-0.495625\pi$
$571$	1.54543e154	0.0274858	0.0137429	+	0.999906i	$0.495625\pi$
$572$	−8.26036e155	−1.33083
$573$	5.16378e152	0.000753757 0
$574$	−1.41650e156	−1.87368
$575$	1.68128e155	0.201561
$576$	−7.72212e155	−0.839202
$577$	2.31899e155	0.228489	0.114244	−	0.993453i	$-0.463555\pi$
$577$	2.31899e155	0.228489	0.114244	+	0.993453i	$0.463555\pi$
$578$	2.03054e156	1.81421
$579$	7.04071e155	0.570529
$580$	1.07890e156	0.793049
$581$	1.29792e154	0.00865559
$582$	−4.37425e155	−0.264701
$583$	2.96928e156	1.63072
$584$	−6.85709e156	−3.41833
$585$	−1.44697e156	−0.654867
$586$	2.98666e156	1.22736
$587$	−3.21119e156	−1.19843	−0.599216	−	0.800587i	$-0.704521\pi$
$587$	−3.21119e156	−1.19843	−0.599216	+	0.800587i	$0.704521\pi$
$588$	6.85282e155	0.232301
$589$	5.85327e155	0.180254
$590$	1.96307e156	0.549283
$591$	5.49542e154	0.0139736
$592$	1.30482e157	3.01560
$593$	−7.20857e156	−1.51446	−0.757232	−	0.653146i	$-0.773449\pi$
$593$	−7.20857e156	−1.51446	−0.757232	+	0.653146i	$0.773449\pi$
$594$	9.54968e156	1.82412
$595$	−1.60363e156	−0.278545
$596$	−7.43491e156	−1.17452
$597$	−1.66000e156	−0.238538
$598$	5.89381e155	0.0770511
$599$	1.34878e157	1.60445	0.802225	−	0.597022i	$-0.203649\pi$
$599$	1.34878e157	1.60445	0.802225	+	0.597022i	$0.203649\pi$
$600$	−2.59249e157	−2.80654
$601$	−1.50334e157	−1.48133	−0.740663	−	0.671876i	$-0.765489\pi$
$601$	−1.50334e157	−1.48133	−0.740663	+	0.671876i	$0.765489\pi$
$602$	3.02192e157	2.71070
$603$	−1.88058e157	−1.53590
$604$	4.08945e156	0.304143
$605$	−1.02410e157	−0.693687
$606$	2.18503e157	1.34820
$607$	−1.53659e157	−0.863765	−0.431883	−	0.901930i	$-0.642150\pi$
$607$	−1.53659e157	−0.863765	−0.431883	+	0.901930i	$0.642150\pi$
$608$	−1.48172e157	−0.758951
$609$	2.00538e156	0.0936096
$610$	−7.43860e157	−3.16487
$611$	7.62871e156	0.295885
$612$	7.50832e156	0.265514
$613$	4.67591e157	1.50782	0.753909	−	0.656979i	$-0.228166\pi$
$613$	4.67591e157	1.50782	0.753909	+	0.656979i	$0.228166\pi$
$614$	8.40121e157	2.47075
$615$	2.92525e157	0.784729
$616$	1.39152e158	3.40548
$617$	−3.06073e156	−0.0683460	−0.0341730	−	0.999416i	$-0.510880\pi$
$617$	−3.06073e156	−0.0683460	−0.0341730	+	0.999416i	$0.510880\pi$
$618$	−6.22832e157	−1.26918
$619$	4.87027e157	0.905799	0.452899	−	0.891562i	$-0.350390\pi$
$619$	4.87027e157	0.905799	0.452899	+	0.891562i	$0.350390\pi$
$620$	−1.17031e158	−1.98687
$621$	−4.82469e156	−0.0747814
$622$	−1.69015e158	−2.39204
$623$	−7.39532e157	−0.955833
$624$	−4.57419e157	−0.539989
$625$	1.70599e158	1.83973
$626$	8.92808e157	0.879647
$627$	2.44541e157	0.220159
$628$	−5.87809e158	−4.83633
$629$	−2.29510e157	−0.172600
$630$	4.14732e158	2.85119
$631$	1.91122e158	1.20130	0.600651	−	0.799511i	$-0.294908\pi$
$631$	1.91122e158	1.20130	0.600651	+	0.799511i	$0.294908\pi$
$632$	4.06069e158	2.33391
$633$	1.12000e158	0.588719
$634$	−6.10681e158	−2.93610
$635$	−6.10274e158	−2.68416
$636$	3.93575e158	1.58380
$637$	−2.57435e157	−0.0947958
$638$	1.17051e158	0.394463
$639$	1.00005e158	0.308479
$640$	5.46405e157	0.154293
$641$	2.92098e158	0.755180	0.377590	−	0.925973i	$-0.376753\pi$
$641$	2.92098e158	0.755180	0.377590	+	0.925973i	$0.376753\pi$
$642$	9.02278e157	0.213605
$643$	2.10479e158	0.456340	0.228170	−	0.973621i	$-0.426726\pi$
$643$	2.10479e158	0.456340	0.228170	+	0.973621i	$0.426726\pi$
$644$	−1.19616e158	−0.237540
$645$	−6.24066e158	−1.13529
$646$	6.20520e157	0.103423
$647$	2.00894e158	0.306814	0.153407	−	0.988163i	$-0.450975\pi$
$647$	2.00894e158	0.306814	0.153407	+	0.988163i	$0.450975\pi$
$648$	−7.22857e158	−1.01173
$649$	1.50804e158	0.193458
$650$	1.65704e159	1.94863
$651$	−2.17529e158	−0.234526
$652$	9.34422e158	0.923749
$653$	−4.92692e158	−0.446664	−0.223332	−	0.974742i	$-0.571693\pi$
$653$	−4.92692e158	−0.446664	−0.223332	+	0.974742i	$0.571693\pi$
$654$	1.25246e159	1.04140
$655$	4.25226e158	0.324329
$656$	−3.24185e159	−2.26843
$657$	−1.56999e159	−1.00798
$658$	−2.18655e159	−1.28824
$659$	2.50748e159	1.35585	0.677924	−	0.735132i	$-0.262880\pi$
$659$	2.50748e159	1.35585	0.677924	+	0.735132i	$0.262880\pi$
$660$	−4.88938e159	−2.42673
$661$	4.71683e158	0.214915	0.107458	−	0.994210i	$-0.465729\pi$
$661$	4.71683e158	0.214915	0.107458	+	0.994210i	$0.465729\pi$
$662$	4.11834e158	0.172284
$663$	8.04574e157	0.0309066
$664$	5.90177e157	0.0208203
$665$	2.42697e159	0.786396
$666$	5.93559e159	1.76673
$667$	−5.91364e157	−0.0161713
$668$	−1.22496e160	−3.07787
$669$	−9.35367e158	−0.215976
$670$	3.10747e160	6.59448
$671$	−5.71436e159	−1.11467
$672$	5.50661e159	0.987462
$673$	−8.68697e158	−0.143225	−0.0716123	−	0.997433i	$-0.522814\pi$
$673$	−8.68697e158	−0.143225	−0.0716123	+	0.997433i	$0.522814\pi$
$674$	3.15231e159	0.477908
$675$	−1.35646e160	−1.89123
$676$	−1.48021e160	−1.89817
$677$	−1.83601e159	−0.216578	−0.108289	−	0.994119i	$-0.534537\pi$
$677$	−1.83601e159	−0.216578	−0.108289	+	0.994119i	$0.534537\pi$
$678$	9.27184e159	1.00621
$679$	−3.33498e159	−0.333005
$680$	−7.29187e159	−0.670017
$681$	3.60238e159	0.304633
$682$	−1.26968e160	−0.988273
$683$	7.21473e159	0.516952	0.258476	−	0.966018i	$-0.416780\pi$
$683$	7.21473e159	0.516952	0.258476	+	0.966018i	$0.416780\pi$
$684$	−1.13632e160	−0.749605
$685$	4.45813e159	0.270792
$686$	−2.89180e160	−1.61755
$687$	−7.19560e159	−0.370690
$688$	6.91607e160	3.28181
$689$	−1.47851e160	−0.646308
$690$	3.48860e159	0.140500
$691$	−1.03343e160	−0.383506	−0.191753	−	0.981443i	$-0.561417\pi$
$691$	−1.03343e160	−0.383506	−0.191753	+	0.981443i	$0.561417\pi$
$692$	−5.06797e160	−1.73316
$693$	3.18599e160	1.00419
$694$	4.44383e160	1.29106
$695$	4.21432e160	1.12872
$696$	9.11868e159	0.225170
$697$	5.70223e159	0.129835
$698$	1.37387e161	2.88480
$699$	3.31195e159	0.0641392
$700$	−3.36299e161	−6.00739
$701$	−5.97024e160	−0.983838	−0.491919	−	0.870641i	$-0.663704\pi$
$701$	−5.97024e160	−0.983838	−0.491919	+	0.870641i	$0.663704\pi$
$702$	−4.75513e160	−0.722962
$703$	3.47345e160	0.487287
$704$	9.80232e160	1.26904
$705$	4.51550e160	0.539537
$706$	2.01547e161	2.22285
$707$	1.66589e161	1.69609
$708$	1.99888e160	0.187892
$709$	−3.32929e160	−0.288961	−0.144481	−	0.989508i	$-0.546151\pi$
$709$	−3.32929e160	−0.288961	−0.144481	+	0.989508i	$0.546151\pi$
$710$	−1.65249e161	−1.32447
$711$	9.29727e160	0.688213
$712$	−3.36272e161	−2.29917
$713$	6.41467e159	0.0405150
$714$	−2.30608e160	−0.134563
$715$	1.83676e161	0.990285
$716$	−7.01193e161	−3.49343
$717$	1.03732e161	0.477618
$718$	−4.28135e161	−1.82200
$719$	−1.76641e161	−0.694878	−0.347439	−	0.937703i	$-0.612949\pi$
$719$	−1.76641e161	−0.694878	−0.347439	+	0.937703i	$0.612949\pi$
$720$	9.49169e161	3.45189
$721$	−4.74854e161	−1.59668
$722$	5.01369e161	1.55886
$723$	1.39378e161	0.400755
$724$	1.35821e162	3.61191
$725$	−1.66262e161	−0.408974
$726$	−1.47269e161	−0.335114
$727$	−9.04926e161	−1.90511	−0.952553	−	0.304373i	$-0.901553\pi$
$727$	−9.04926e161	−1.90511	−0.952553	+	0.304373i	$0.901553\pi$
$728$	−6.92887e161	−1.34971
$729$	5.34181e160	0.0962904
$730$	2.59425e162	4.32783
$731$	−1.21650e161	−0.187836
$732$	−7.57433e161	−1.08260
$733$	−4.47247e161	−0.591797	−0.295898	−	0.955219i	$-0.595619\pi$
$733$	−4.47247e161	−0.591797	−0.295898	+	0.955219i	$0.595619\pi$
$734$	1.11116e161	0.136129
$735$	−1.52378e161	−0.172857
$736$	−1.62383e161	−0.170587
$737$	2.38717e162	2.32258
$738$	−1.47471e162	−1.32899
$739$	−1.79324e162	−1.49702	−0.748509	−	0.663125i	$-0.769230\pi$
$739$	−1.79324e162	−1.49702	−0.748509	+	0.663125i	$0.769230\pi$
$740$	−6.94485e162	−5.37119
$741$	−1.21766e161	−0.0872563
$742$	4.23773e162	2.81393
$743$	−6.25908e161	−0.385161	−0.192581	−	0.981281i	$-0.561686\pi$
$743$	−6.25908e161	−0.385161	−0.192581	+	0.981281i	$0.561686\pi$
$744$	−9.89126e161	−0.564132
$745$	1.65321e162	0.873974
$746$	4.25097e162	2.08327
$747$	1.35126e160	0.00613938
$748$	−9.53092e161	−0.401508
$749$	6.87907e161	0.268724
$750$	5.46398e162	1.97946
$751$	6.40883e161	0.215339	0.107669	−	0.994187i	$-0.465661\pi$
$751$	6.40883e161	0.215339	0.107669	+	0.994187i	$0.465661\pi$
$752$	−5.00421e162	−1.55965
$753$	−5.42107e160	−0.0156736
$754$	−5.82839e161	−0.156339
$755$	−9.09320e161	−0.226315
$756$	9.65060e162	2.22881
$757$	−5.75127e162	−1.23267	−0.616335	−	0.787484i	$-0.711383\pi$
$757$	−5.75127e162	−1.23267	−0.616335	+	0.787484i	$0.711383\pi$
$758$	−1.24713e163	−2.48085
$759$	2.67996e161	0.0494843
$760$	1.10357e163	1.89161
$761$	4.81040e161	0.0765505	0.0382752	−	0.999267i	$-0.487814\pi$
$761$	4.81040e161	0.0765505	0.0382752	+	0.999267i	$0.487814\pi$
$762$	−8.77594e162	−1.29670
$763$	9.54886e162	1.31013
$764$	3.04586e160	0.00388093
$765$	−1.66953e162	−0.197571
$766$	1.26168e163	1.38683
$767$	−7.50906e161	−0.0766739
$768$	−4.57076e162	−0.433590
$769$	4.24427e162	0.374080	0.187040	−	0.982352i	$-0.440111\pi$
$769$	4.24427e162	0.374080	0.187040	+	0.982352i	$0.440111\pi$
$770$	−5.26453e163	−4.31155
$771$	−1.25636e162	−0.0956181
$772$	4.15297e163	2.93753
$773$	−2.52938e163	−1.66293	−0.831463	−	0.555580i	$-0.812496\pi$
$773$	−2.52938e163	−1.66293	−0.831463	+	0.555580i	$0.812496\pi$
$774$	3.14611e163	1.92269
$775$	1.80348e163	1.02463
$776$	−1.51645e163	−0.801015
$777$	−1.29086e163	−0.634003
$778$	−5.38508e163	−2.45949
$779$	−8.62987e162	−0.366554
$780$	2.43460e163	0.961795
$781$	−1.26945e163	−0.466480
$782$	6.80036e161	0.0232461
$783$	4.77113e162	0.151734
$784$	1.68869e163	0.499682
$785$	1.30704e164	3.59876
$786$	6.11490e162	0.156681
$787$	−1.44493e163	−0.344567	−0.172283	−	0.985047i	$-0.555114\pi$
$787$	−1.44493e163	−0.344567	−0.172283	+	0.985047i	$0.555114\pi$
$788$	3.24148e162	0.0719469
$789$	3.07620e163	0.635570
$790$	−1.53628e164	−2.95488
$791$	7.06895e163	1.26585
$792$	1.44870e164	2.41549
$793$	2.84539e163	0.441781
$794$	−1.32357e163	−0.191376
$795$	−8.75145e163	−1.17852
$796$	−9.79152e163	−1.22818
$797$	−1.29295e164	−1.51073	−0.755367	−	0.655302i	$-0.772541\pi$
$797$	−1.29295e164	−1.51073	−0.755367	+	0.655302i	$0.772541\pi$
$798$	3.49006e163	0.379901
$799$	8.80211e162	0.0892676
$800$	−4.56541e164	−4.31415
$801$	−7.69923e163	−0.677969
$802$	−1.79596e163	−0.147382
$803$	1.99291e164	1.52426
$804$	3.16417e164	2.25576
$805$	2.65975e163	0.176755
$806$	6.32220e163	0.391686
$807$	−1.52423e164	−0.880433
$808$	7.57497e164	4.07980
$809$	−2.69985e164	−1.35596	−0.677981	−	0.735079i	$-0.737145\pi$
$809$	−2.69985e164	−1.35596	−0.677981	+	0.735079i	$0.737145\pi$
$810$	2.73479e164	1.28091
$811$	−2.31814e164	−1.01266	−0.506328	−	0.862341i	$-0.668998\pi$
$811$	−2.31814e164	−1.01266	−0.506328	+	0.862341i	$0.668998\pi$
$812$	1.18288e164	0.481975
$813$	1.16725e164	0.443658
$814$	−7.53453e164	−2.67164
$815$	−2.07776e164	−0.687370
$816$	−5.27777e163	−0.162913
$817$	1.84107e164	0.530303
$818$	1.99943e164	0.537459
$819$	−1.58642e164	−0.397995
$820$	1.72547e165	4.04039
$821$	−8.11621e164	−1.77405	−0.887023	−	0.461726i	$-0.847230\pi$
$821$	−8.11621e164	−1.77405	−0.887023	+	0.461726i	$0.847230\pi$
$822$	6.41095e163	0.130817
$823$	3.00960e164	0.573347	0.286673	−	0.958028i	$-0.407451\pi$
$823$	3.00960e164	0.573347	0.286673	+	0.958028i	$0.407451\pi$
$824$	−2.15921e165	−3.84067
$825$	7.53469e164	1.25146
$826$	2.15225e164	0.333826
$827$	−6.19688e164	−0.897659	−0.448830	−	0.893617i	$-0.648159\pi$
$827$	−6.19688e164	−0.897659	−0.448830	+	0.893617i	$0.648159\pi$
$828$	−1.24531e164	−0.168486
$829$	3.93187e164	0.496899	0.248449	−	0.968645i	$-0.420079\pi$
$829$	3.93187e164	0.496899	0.248449	+	0.968645i	$0.420079\pi$
$830$	−2.23282e163	−0.0263598
$831$	−4.56217e164	−0.503168
$832$	−4.88093e164	−0.502962
$833$	−2.97032e163	−0.0285996
$834$	6.06034e164	0.545274
$835$	2.72378e165	2.29027
$836$	1.44243e165	1.13355
$837$	−5.17537e164	−0.380148
$838$	−3.40222e165	−2.33602
$839$	1.28568e165	0.825246	0.412623	−	0.910902i	$-0.364613\pi$
$839$	1.28568e165	0.825246	0.412623	+	0.910902i	$0.364613\pi$
$840$	−4.10126e165	−2.46115
$841$	−1.72379e165	−0.967188
$842$	−2.59626e165	−1.36212
$843$	2.01217e164	0.0987201
$844$	6.60633e165	3.03118
$845$	3.29136e165	1.41244
$846$	−2.27641e165	−0.913743
$847$	−1.12280e165	−0.421588
$848$	9.69861e165	3.40678
$849$	1.93531e165	0.636012
$850$	1.91192e165	0.587895
$851$	3.80660e164	0.109526
$852$	−1.68264e165	−0.453059
$853$	−5.93734e165	−1.49614	−0.748069	−	0.663621i	$-0.769019\pi$
$853$	−5.93734e165	−1.49614	−0.748069	+	0.663621i	$0.769019\pi$
$854$	−8.15548e165	−1.92345
$855$	2.52670e165	0.557788
$856$	3.12798e165	0.646393
$857$	5.78001e165	1.11818	0.559090	−	0.829107i	$-0.311150\pi$
$857$	5.78001e165	1.11818	0.559090	+	0.829107i	$0.311150\pi$
$858$	2.64132e165	0.478398
$859$	−7.84865e165	−1.33101	−0.665505	−	0.746393i	$-0.731784\pi$
$859$	−7.84865e165	−1.33101	−0.665505	+	0.746393i	$0.731784\pi$
$860$	−3.68106e166	−5.84535
$861$	3.20717e165	0.476919
$862$	9.34561e165	1.30151
$863$	−6.71487e165	−0.875846	−0.437923	−	0.899013i	$-0.644286\pi$
$863$	−6.71487e165	−0.875846	−0.437923	+	0.899013i	$0.644286\pi$
$864$	1.31011e166	1.60060
$865$	1.12690e166	1.28966
$866$	1.30389e166	1.39792
$867$	−4.59744e165	−0.461782
$868$	−1.28310e166	−1.20752
$869$	−1.18018e166	−1.04071
$870$	−3.44987e165	−0.285079
$871$	−1.18866e166	−0.920517
$872$	4.34196e166	3.15141
$873$	−3.47203e165	−0.236199
$874$	−1.02918e165	−0.0656289
$875$	4.16580e166	2.49025
$876$	2.64158e166	1.48041
$877$	5.59481e165	0.293974	0.146987	−	0.989138i	$-0.453042\pi$
$877$	5.59481e165	0.293974	0.146987	+	0.989138i	$0.453042\pi$
$878$	1.83030e166	0.901744
$879$	−6.76225e165	−0.312406
$880$	−1.20486e167	−5.21993
$881$	1.57365e166	0.639395	0.319697	−	0.947520i	$-0.396419\pi$
$881$	1.57365e166	0.639395	0.319697	+	0.947520i	$0.396419\pi$
$882$	7.68184e165	0.292746
$883$	−2.60757e166	−0.932085	−0.466042	−	0.884762i	$-0.654321\pi$
$883$	−2.60757e166	−0.932085	−0.466042	+	0.884762i	$0.654321\pi$
$884$	4.74579e165	0.159131
$885$	−4.44468e165	−0.139812
$886$	4.25070e166	1.25446
$887$	−2.21821e166	−0.614211	−0.307106	−	0.951675i	$-0.599360\pi$
$887$	−2.21821e166	−0.614211	−0.307106	+	0.951675i	$0.599360\pi$
$888$	−5.86967e166	−1.52504
$889$	−6.69088e166	−1.63130
$890$	1.27222e167	2.91090
$891$	2.10088e166	0.451139
$892$	−5.51728e166	−1.11201
$893$	−1.33213e166	−0.252022
$894$	2.37737e166	0.422209
$895$	1.55916e167	2.59949
$896$	5.99064e165	0.0937714
$897$	−1.33445e165	−0.0196123
$898$	−3.90083e166	−0.538324
$899$	−6.34347e165	−0.0822062
$900$	−3.50119e167	−4.26102
$901$	−1.70593e166	−0.194989
$902$	1.87197e167	2.00970
$903$	−6.84209e166	−0.689971
$904$	3.21432e167	3.04490
$905$	−3.02008e167	−2.68766
$906$	−1.30763e166	−0.109331
$907$	−1.04700e167	−0.822501	−0.411251	−	0.911522i	$-0.634908\pi$
$907$	−1.04700e167	−0.822501	−0.411251	+	0.911522i	$0.634908\pi$
$908$	2.12487e167	1.56849
$909$	1.73435e167	1.20303
$910$	2.62140e167	1.70881
$911$	−5.21549e166	−0.319527	−0.159763	−	0.987155i	$-0.551073\pi$
$911$	−5.21549e166	−0.319527	−0.159763	+	0.987155i	$0.551073\pi$
$912$	7.98748e166	0.459940
$913$	−1.71526e165	−0.00928393
$914$	−2.56831e166	−0.130674
$915$	1.68421e167	0.805573
$916$	−4.24434e167	−1.90860
$917$	4.66207e166	0.197111
$918$	−5.48653e166	−0.218116
$919$	7.35016e166	0.274771	0.137385	−	0.990518i	$-0.456130\pi$
$919$	7.35016e166	0.274771	0.137385	+	0.990518i	$0.456130\pi$
$920$	1.20941e167	0.425170
$921$	−1.90216e167	−0.628895
$922$	−5.82812e167	−1.81230
$923$	6.32106e166	0.184882
$924$	−5.36059e167	−1.47484
$925$	1.07022e168	2.76992
$926$	−1.22351e168	−2.97912
$927$	−4.94368e167	−1.13252
$928$	1.60581e167	0.346125
$929$	9.04723e167	1.83496	0.917482	−	0.397777i	$-0.130218\pi$
$929$	9.04723e167	1.83496	0.917482	+	0.397777i	$0.130218\pi$
$930$	3.74216e167	0.714227
$931$	4.49533e166	0.0807430
$932$	1.95356e167	0.330238
$933$	3.82675e167	0.608860
$934$	−1.93570e168	−2.89894
$935$	2.11928e167	0.298766
$936$	−7.21361e167	−0.957342
$937$	3.14655e166	0.0393140	0.0196570	−	0.999807i	$-0.493743\pi$
$937$	3.14655e166	0.0393140	0.0196570	+	0.999807i	$0.493743\pi$
$938$	3.40695e168	4.00779
$939$	−2.02145e167	−0.223902
$940$	2.66348e168	2.77795
$941$	−1.85910e167	−0.182595	−0.0912977	−	0.995824i	$-0.529101\pi$
$941$	−1.85910e167	−0.182595	−0.0912977	+	0.995824i	$0.529101\pi$
$942$	1.87957e168	1.73853
$943$	−9.45758e166	−0.0823890
$944$	4.92572e167	0.404159
$945$	−2.14589e168	−1.65848
$946$	−3.99361e168	−2.90748
$947$	−1.39856e168	−0.959195	−0.479598	−	0.877489i	$-0.659217\pi$
$947$	−1.39856e168	−0.959195	−0.479598	+	0.877489i	$0.659217\pi$
$948$	−1.56431e168	−1.01077
$949$	−9.92343e167	−0.604117
$950$	−2.89354e168	−1.65976
$951$	1.38268e168	0.747345
$952$	−7.99462e167	−0.407202
$953$	1.02353e168	0.491307	0.245654	−	0.969358i	$-0.420997\pi$
$953$	1.02353e168	0.491307	0.245654	+	0.969358i	$0.420997\pi$
$954$	4.41188e168	1.99591
$955$	−6.77271e165	−0.00288783
$956$	6.11865e168	2.45915
$957$	−2.65021e167	−0.100405
$958$	−5.03354e168	−1.79772
$959$	4.88778e167	0.164574
$960$	−2.88907e168	−0.917134
$961$	−2.65287e168	−0.794044
$962$	3.75172e168	1.05886
$963$	7.16176e167	0.190605
$964$	8.22120e168	2.06340
$965$	−9.23446e168	−2.18584
$966$	3.82481e167	0.0853890
$967$	−1.33262e168	−0.280615	−0.140307	−	0.990108i	$-0.544809\pi$
$967$	−1.33262e168	−0.280615	−0.140307	+	0.990108i	$0.544809\pi$
$968$	−5.10546e168	−1.01409
$969$	−1.40495e167	−0.0263250
$970$	5.73719e168	1.01414
$971$	3.23269e168	0.539111	0.269556	−	0.962985i	$-0.413123\pi$
$971$	3.23269e168	0.539111	0.269556	+	0.962985i	$0.413123\pi$
$972$	1.56978e169	2.46999
$973$	4.62047e168	0.685979
$974$	−1.12790e169	−1.58012
$975$	−3.75180e168	−0.495996
$976$	−1.86649e169	−2.32869
$977$	9.05296e168	1.06598	0.532989	−	0.846122i	$-0.321069\pi$
$977$	9.05296e168	1.06598	0.532989	+	0.846122i	$0.321069\pi$
$978$	−2.98789e168	−0.332062
$979$	9.77326e168	1.02522
$980$	−8.98803e168	−0.890002
$981$	9.94127e168	0.929273
$982$	1.72133e169	1.51903
$983$	−1.31699e169	−1.09726	−0.548628	−	0.836067i	$-0.684850\pi$
$983$	−1.31699e169	−1.09726	−0.548628	+	0.836067i	$0.684850\pi$
$984$	1.45833e169	1.14719
$985$	−7.20768e167	−0.0535363
$986$	−6.72487e167	−0.0471670
$987$	4.95068e168	0.327903
$988$	−7.18238e168	−0.449263
$989$	2.01765e168	0.119194
$990$	−5.48088e169	−3.05817
$991$	−1.13676e169	−0.599112	−0.299556	−	0.954079i	$-0.596839\pi$
$991$	−1.13676e169	−0.599112	−0.299556	+	0.954079i	$0.596839\pi$
$992$	−1.74186e169	−0.867170
$993$	−9.32455e167	−0.0438526
$994$	−1.81175e169	−0.804947
$995$	2.17722e169	0.913900
$996$	−2.27356e167	−0.00901684
$997$	−4.94638e168	−0.185358	−0.0926790	−	0.995696i	$-0.529543\pi$
$997$	−4.94638e168	−0.185358	−0.0926790	+	0.995696i	$0.529543\pi$
$998$	−4.05386e169	−1.43547
$999$	−3.07117e169	−1.02767

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.114.a.a.1.1	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.114.a.a.1.1	✓	9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 114 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-1.88610e17 q^{2} +4.27041e26 q^{3} +2.51891e34 q^{4} -5.60099e39 q^{5} -8.05442e43 q^{6} -6.14078e47 q^{7} -2.79228e51 q^{8} -6.39314e53 q^{9} +O(q^{10})\)	\(q-1.88610e17 q^{2} +4.27041e26 q^{3} +2.51891e34 q^{4} -5.60099e39 q^{5} -8.05442e43 q^{6} -6.14078e47 q^{7} -2.79228e51 q^{8} -6.39314e53 q^{9} +1.05640e57 q^{10} +8.11533e58 q^{11} +1.07568e61 q^{12} -4.04092e62 q^{13} +1.15821e65 q^{14} -2.39186e66 q^{15} +2.65072e68 q^{16} -4.66247e68 q^{17} +1.20581e71 q^{18} +7.05627e71 q^{19} -1.41084e74 q^{20} -2.62237e74 q^{21} -1.53063e76 q^{22} +7.73306e75 q^{23} -1.19242e78 q^{24} +2.17415e79 q^{25} +7.62157e79 q^{26} -6.23904e80 q^{27} -1.54681e82 q^{28} -7.64722e81 q^{29} +4.51128e83 q^{30} +8.29513e83 q^{31} -2.09986e85 q^{32} +3.46558e85 q^{33} +8.79388e85 q^{34} +3.43945e87 q^{35} -1.61037e88 q^{36} +4.92250e88 q^{37} -1.33088e89 q^{38} -1.72564e89 q^{39} +1.56395e91 q^{40} -1.22301e91 q^{41} +4.94605e91 q^{42} +2.60913e92 q^{43} +2.04418e93 q^{44} +3.58079e93 q^{45} -1.45853e93 q^{46} -1.88787e94 q^{47} +1.13197e95 q^{48} +6.37069e94 q^{49} -4.10066e96 q^{50} -1.99107e95 q^{51} -1.01787e97 q^{52} +3.65886e97 q^{53} +1.17674e98 q^{54} -4.54539e98 q^{55} +1.71468e99 q^{56} +3.01332e98 q^{57} +1.44234e99 q^{58} +1.85825e99 q^{59} -6.02487e100 q^{60} -7.04144e100 q^{61} -1.56454e101 q^{62} +3.92589e101 q^{63} +1.20788e102 q^{64} +2.26332e102 q^{65} -6.53643e102 q^{66} +2.94156e103 q^{67} -1.17443e103 q^{68} +3.30234e102 q^{69} -6.48714e104 q^{70} -1.56426e104 q^{71} +1.78514e105 q^{72} +2.45574e105 q^{73} -9.28432e105 q^{74} +9.28451e105 q^{75} +1.77741e106 q^{76} -4.98345e106 q^{77} +3.25473e106 q^{78} -1.45426e107 q^{79} -1.48467e108 q^{80} +2.58878e107 q^{81} +2.30671e108 q^{82} -2.11361e106 q^{83} -6.60551e108 q^{84} +2.61145e108 q^{85} -4.92107e109 q^{86} -3.26568e108 q^{87} -2.26603e110 q^{88} +1.20430e110 q^{89} -6.75373e110 q^{90} +2.48144e110 q^{91} +1.94789e110 q^{92} +3.54236e110 q^{93} +3.56070e111 q^{94} -3.95221e111 q^{95} -8.96727e111 q^{96} +5.43087e111 q^{97} -1.20158e112 q^{98} -5.18825e112 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 49\!\cdots\!32 q^{2}+ \cdots + 55\!\cdots\!77 q^{9}+O(q^{10}) \) 9 * q + 4973724357874032 * q^2 - 1047822666262699970761104924 * q^3 + 57140122287714158706660944854495488 * q^4 - 3116148576934475303759287082847998426250 * q^5 - 8679197271676415971774420800017032303605312 * q^6 - 175592521264923853936268390919613238158926276408 * q^7 - 1152754689437068715781677022006928573086863264747520 * q^8 + 551049940125998155825143115188713609620516409643418677 * q^9	\( 9 q + 49\!\cdots\!32 q^{2}+ \cdots + 32\!\cdots\!64 q^{99}+O(q^{100}) \) 9 * q + 4973724357874032 * q^2 - 1047822666262699970761104924 * q^3 + 57140122287714158706660944854495488 * q^4 - 3116148576934475303759287082847998426250 * q^5 - 8679197271676415971774420800017032303605312 * q^6 - 175592521264923853936268390919613238158926276408 * q^7 - 1152754689437068715781677022006928573086863264747520 * q^8 + 551049940125998155825143115188713609620516409643418677 * q^9 - 153264347969576737314363653067831776074945972002322140000 * q^10 + 124303845165751869554468963179928310347446325358753066991788 * q^11 - 4766393536299397973462835582969587848650683059861216359840768 * q^12 + 118066950692074908165278563837084569941718111528864100316810046 * q^13 + 23370095428037254282484566813709955199818716752021690625741210496 * q^14 - 801369990352485680694849420185298838396866837392656002948893145000 * q^15 + 109009769902909383382120055717425408918319663897461125806267782201344 * q^16 + 1031208472354491758575110721181756882175051278670426497304478795027362 * q^17 + 21853761778376511004199260652941739695840479087427332697148033133176496 * q^18 - 2054770397164032300993860357285529834117448193071848654506031346813189260 * q^19 - 128965280615606341221181395517996603639092921677759187360515198160536640000 * q^20 - 2051981423257402292087521454906945230917134727108225442350522950612144271072 * q^21 - 31233703450481121590220064319836416371256690633810598891839492722859409642176 * q^22 - 167806258064059379045373533912927060845638327737895149615950186261514952182184 * q^23 + 837647327683589821169163577629460913691878109446800095361456758053616583557120 * q^24 + 36110808046585671891862329281725549351642982282250931138010564349682541171484375 * q^25 + 273284118611845700597932385482119882778869175349924218776704957190525454972143648 * q^26 - 1293409658858973603349494974301711616276027502548100865754773226934344693652580120 * q^27 - 12449742560521692406151296738508394024549837700960492852336353346600639157797779456 * q^28 + 16393803312375561825707281499219064392567318107169713827635118635692166495008904910 * q^29 + 1444554724925215896891120206778115916774229741452396468041800381952830143736681360000 * q^30 + 1314403569804018815618492241812394006579677928452900483535632508652944766037998410528 * q^31 - 21448902248775261233416755741924844958908937761160756654268584846741870841621352808448 * q^32 - 211847819746714833550323551974005344232426451287015334370441057211901425852772059609168 * q^33 + 319367478280300365454292314290661290493902375851140946818660251269274780967076833561056 * q^34 + 3439596420817236254046899424410940097643944233598368039111722250253904941775326256910000 * q^35 + 2704504833410501582895107271001450900815653199167021310209481973200374905160451231300864 * q^36 - 59867320490204404665587120670290466524223984034118562335350833430431530376567774885723498 * q^37 - 82453523727277361450274687052865709436318494611960850831592535368825105943678502733442880 * q^38 + 871232822588974033828162396761465282346428529310140460376676860192325312944522604565747064 * q^39 + 6827166757827354756060064429590450961456578801730020944860911233033409499443258590438400000 * q^40 - 34550149215769251780094496181290849916810545798144119670305052821692690196704735942577072902 * q^41 - 106065652173490837329551409984862217118049589651335199831107089722564993162529690865908896256 * q^42 + 207231754793163377176542763271534728167453514398489730764515211376339059665627233099893879756 * q^43 + 2312703333865421082227940066456566870684549523781445620538452769155749838714861346004252527616 * q^44 + 256198961065429853532686454584243663537866293764106258783025404071252757628746328749329658750 * q^45 - 28138310036672836977617659816100322616155099852864640775866866896982035999177616032492961297792 * q^46 - 49338615100567586008533951288135845393852650707485360531368204467394665532910688983139358306128 * q^47 + 244064292546444123908052536984208158793401136481260186300744503278739285380247288265778682658816 * q^48 + 752433840599750193271015544145910422089938845099283047668758541087980882087499887025758157789313 * q^49 - 1756648703190643407679915187540746659445068152182448123783254139837888034842840604352884543750000 * q^50 - 4186453060070964308543321243867301742071184523159619262981910395937624269639977914668070815961592 * q^51 - 299921527358232778097628046170322710643014254923572622961503877233695051976123243837021461385728 * q^52 + 45439534345102239290843163912544095765806982832307502313849525819073728936151813167470772365925926 * q^53 + 38680516880674041302480509047884889106404603448054948500904779898349149372610056782201281117946240 * q^54 - 432576867358466335617986215621945887405045763707273014611343529132044150112466209509767824829515000 * q^55 - 159465105485502254328469891445580976480576866382179762995668936857815143816140668281747609575260160 * q^56 + 1990014681911564315630720992224179214491287391034406566984522978256103716439101105615294767535358160 * q^57 + 4618158171946557697639499111957754813666889826993148515766803610504911213619043847144587412863790880 * q^58 - 7994556888742389963754891914386272086617532494092324481666622701281195647537712229818800059078242980 * q^59 - 51547668272403014021235031153713789291688796805654426950141340288411508848106756189101821863952640000 * q^60 - 20010787184525995584720289117304568167948599723976550204852777948468547299349907237396329738847967762 * q^61 + 292035427959193157957119307134870542698832076716753725989233844815905689373991776544712306185499282944 * q^62 + 1084750421819290453616791018398299860321649524662704337157840276934678472457615663242574941575258587176 * q^63 - 2173182954777058552426966649041133062639998025794768537871770595713126062249675532560302339710750031872 * q^64 - 6050492601584073293182223610830486690452314196108303412288731430157341922477676622337759152417832607500 * q^65 - 2811384209515387361103707894564511021023407746835224054361358951726305534503884893008505470528471177984 * q^66 + 24573799368134891916564011470928671317077382485972351268274803174871528123414635568434858147580241074212 * q^67 + 63690775145054712155234191070401247673413728435364958188409307863633237295553890585548320729107243037184 * q^68 - 24003285462463676531332362285165839175525050544235078632804235222118832623175439122841457438544940522656 * q^69 - 863169709419813836575212169649584339603968815833753646438175375944308193587969610263821675032671814880000 * q^70 + 91658679156386468719245489455910792073607873475232020252166152112986794966382882952820365384103518048008 * q^71 + 873882756027094209986251517892994706349418254125301044053004437567652817562627690659257226446504466493440 * q^72 + 541694808507779980546116004112644787310665887489575442433845489271276265038276918082847569639076524144666 * q^73 - 9378706212502591696314586127924566164346165127102664760442762960199173362938872227498081812178947973840224 * q^74 - 29348285812521570443266953567594350343794068770628558899049305240540166160078653563092442717138745889062500 * q^75 - 60564820012723729139203913493989896690950347961424832880261930310236667425867853870924430511072293881605120 * q^76 + 1068940833620544673782151517761484277047755630607342022951044010736792743275783369575718784146165485947744 * q^77 - 286969622560772923408733006352532687901626912195145659167094759389964370273396505496077341678419418050144128 * q^78 - 596276255135400928959400589889218117555952939149585650758445593510201386502571903994653015956197756762453040 * q^79 - 2420836681564557797101060397107174542916086634827557275495079675925079838120631425602247114230349809336320000 * q^80 - 3030606522373897290470630089608148759339991046893156580144516813393469703984963913807719049058860501442725951 * q^81 - 6936458118821589036700513874923262497738432667781968228952468701667638701536840125370171023576003636856609696 * q^82 - 11004287102773590749349691331049602909161139219297045772286679604418555775574362523281340925221936593079346764 * q^83 - 57855325032373861757970130314922242695268575192193159587088758458166711077597077741056893950844377121225826304 * q^84 - 64354197775882201370863569029422599518759619010400232504975477030343845397959668657595763753959731762134552500 * q^85 - 210819753145942403520859363592361681829074054483701088761378978430433240411156075153802810720648226504181908672 * q^86 - 154008309759204716022098762324487951847505839469072421264586325306012373529922474900817730928920322507018969160 * q^87 - 609999238537345062842609214560983373867364799260253404096252032888004927138583268244389069934087697492178288640 * q^88 - 654568028165810774739876366172819409302687924287909841936841472021672950876376689746932135695962343969713322070 * q^89 - 2734380769439054007162335818387627599332566037560181838266985769883367234594498859125630424774118397399333420000 * q^90 - 2323627076132845640660102608242767489368371452521120033992540027246745766005131800187294415915449799674836938512 * q^91 - 4256037231999230829372236189816770749190987971335840398392358871486563229805945773322404171318956972524277721088 * q^92 + 154296866852621529872615733195411660158426537898618117528867810834868770230718469048319703695743778039088292992 * q^93 + 1827384388290191849012043193156273334448650299359011463985703887856827570148696897626054924182121847958990279936 * q^94 - 4096663912916778389991331111354003035604483111168308740332618943380051360421354423075027168404452962459195325000 * q^95 + 8457146062137046129332319587633700387597377410609689871416901579530268721609757152896450994557102813871989587968 * q^96 + 36807391546013154433957869141705553075329468371786108764367006729276625672848917612484272062474831101244619876722 * q^97 + 225562248663489353389248034966442578767140826293081704735030344217680122252159170139356951685061050587472992483824 * q^98 + 321571830004348537474522583988170945954403617464147621640077047560490989900478751999197984675098698758537853855164 * q^99

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