LMFDB - Embedded newform 1.114.a.a.1.4

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			1.4
Root			$-1.42245e15$ 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)

$f(q)$	$=$	$q-6.77248e16 q^{2} -4.98640e26 q^{3} -5.79795e33 q^{4} -2.60538e39 q^{5} +3.37703e43 q^{6} +3.08065e47 q^{7} +1.09596e51 q^{8} -5.73036e53 q^{9} +O(q^{10})$	\(q-6.77248e16 q^{2} -4.98640e26 q^{3} -5.79795e33 q^{4} -2.60538e39 q^{5} +3.37703e43 q^{6} +3.08065e47 q^{7} +1.09596e51 q^{8} -5.73036e53 q^{9} +1.76449e56 q^{10} -1.29301e59 q^{11} +2.89109e60 q^{12} -3.41279e62 q^{13} -2.08637e64 q^{14} +1.29915e66 q^{15} -1.40142e67 q^{16} +4.55013e69 q^{17} +3.88088e70 q^{18} -6.83408e71 q^{19} +1.51059e73 q^{20} -1.53614e74 q^{21} +8.75687e75 q^{22} +3.21328e76 q^{23} -5.46489e77 q^{24} -2.84164e78 q^{25} +2.31131e79 q^{26} +6.95460e80 q^{27} -1.78615e81 q^{28} +5.81756e82 q^{29} -8.79845e82 q^{30} +8.62588e83 q^{31} -1.04320e85 q^{32} +6.44745e85 q^{33} -3.08157e86 q^{34} -8.02628e86 q^{35} +3.32244e87 q^{36} +3.36802e88 q^{37} +4.62836e88 q^{38} +1.70176e89 q^{39} -2.85539e90 q^{40} +1.91039e91 q^{41} +1.04035e91 q^{42} +9.11497e91 q^{43} +7.49679e92 q^{44} +1.49298e93 q^{45} -2.17619e93 q^{46} +4.23475e92 q^{47} +6.98806e93 q^{48} -2.18481e95 q^{49} +1.92449e95 q^{50} -2.26888e96 q^{51} +1.97872e96 q^{52} -1.29781e97 q^{53} -4.70999e97 q^{54} +3.36878e98 q^{55} +3.37627e98 q^{56} +3.40774e98 q^{57} -3.93993e99 q^{58} +8.79283e98 q^{59} -7.53239e99 q^{60} +1.49190e99 q^{61} -5.84186e100 q^{62} -1.76533e101 q^{63} +8.52036e101 q^{64} +8.89163e101 q^{65} -4.36652e102 q^{66} +1.91959e103 q^{67} -2.63814e103 q^{68} -1.60227e103 q^{69} +5.43578e103 q^{70} -4.73462e104 q^{71} -6.28024e104 q^{72} +3.08550e105 q^{73} -2.28099e105 q^{74} +1.41695e105 q^{75} +3.96236e105 q^{76} -3.98331e106 q^{77} -1.15251e106 q^{78} -2.94658e107 q^{79} +3.65124e106 q^{80} +1.24067e107 q^{81} -1.29381e108 q^{82} -3.83926e108 q^{83} +8.90644e107 q^{84} -1.18548e109 q^{85} -6.17309e108 q^{86} -2.90087e109 q^{87} -1.41708e110 q^{88} -1.59303e110 q^{89} -1.01112e110 q^{90} -1.05136e110 q^{91} -1.86305e110 q^{92} -4.30121e110 q^{93} -2.86797e109 q^{94} +1.78054e111 q^{95} +5.20180e111 q^{96} -1.90148e112 q^{97} +1.47966e112 q^{98} +7.40941e112 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−6.77248e16	−0.664589	−0.332294	−	0.943176i	$-0.607823\pi$
$2$	−6.77248e16	−0.664589	−0.332294	+	0.943176i	$0.607823\pi$
$3$	−4.98640e26	−0.550093	−0.275047	−	0.961431i	$-0.588693\pi$
$3$	−4.98640e26	−0.550093	−0.275047	+	0.961431i	$0.588693\pi$
$4$	−5.79795e33	−0.558322
$5$	−2.60538e39	−0.839588	−0.419794	−	0.907619i	$-0.637898\pi$
$5$	−2.60538e39	−0.839588	−0.419794	+	0.907619i	$0.637898\pi$
$6$	3.37703e43	0.365586
$7$	3.08065e47	0.550305	0.275153	−	0.961401i	$-0.411272\pi$
$7$	3.08065e47	0.550305	0.275153	+	0.961401i	$0.411272\pi$
$8$	1.09596e51	1.03564
$9$	−5.73036e53	−0.697398
$10$	1.76449e56	0.557980
$11$	−1.29301e59	−1.87463	−0.937313	−	0.348490i	$-0.886695\pi$
$11$	−1.29301e59	−1.87463	−0.937313	+	0.348490i	$0.886695\pi$
$12$	2.89109e60	0.307129
$13$	−3.41279e62	−0.393832	−0.196916	−	0.980420i	$-0.563093\pi$
$13$	−3.41279e62	−0.393832	−0.196916	+	0.980420i	$0.563093\pi$
$14$	−2.08637e64	−0.365726
$15$	1.29915e66	0.461851
$16$	−1.40142e67	−0.129954
$17$	4.55013e69	1.37297	0.686484	−	0.727145i	$-0.259153\pi$
$17$	4.55013e69	1.37297	0.686484	+	0.727145i	$0.259153\pi$
$18$	3.88088e70	0.463482
$19$	−6.83408e71	−0.384682	−0.192341	−	0.981328i	$-0.561608\pi$
$19$	−6.83408e71	−0.384682	−0.192341	+	0.981328i	$0.561608\pi$
$20$	1.51059e73	0.468760
$21$	−1.53614e74	−0.302719
$22$	8.75687e75	1.24585
$23$	3.21328e76	0.370959	0.185480	−	0.982648i	$-0.440616\pi$
$23$	3.21328e76	0.370959	0.185480	+	0.982648i	$0.440616\pi$
$24$	−5.46489e77	−0.569700
$25$	−2.84164e78	−0.295092
$26$	2.31131e79	0.261736
$27$	6.95460e80	0.933727
$28$	−1.78615e81	−0.307247
$29$	5.81756e82	1.37801	0.689007	−	0.724755i	$-0.258047\pi$
$29$	5.81756e82	1.37801	0.689007	+	0.724755i	$0.258047\pi$
$30$	−8.79845e82	−0.306941
$31$	8.62588e83	0.471919	0.235960	−	0.971763i	$-0.424177\pi$
$31$	8.62588e83	0.471919	0.235960	+	0.971763i	$0.424177\pi$
$32$	−1.04320e85	−0.949277
$33$	6.44745e85	1.03122
$34$	−3.08157e86	−0.912458
$35$	−8.02628e86	−0.462029
$36$	3.32244e87	0.389373
$37$	3.36802e88	0.839417	0.419708	−	0.907659i	$-0.362132\pi$
$37$	3.36802e88	0.839417	0.419708	+	0.907659i	$0.362132\pi$
$38$	4.62836e88	0.255655
$39$	1.70176e89	0.216644
$40$	−2.85539e90	−0.869513
$41$	1.91039e91	1.44156	0.720781	−	0.693162i	$-0.243783\pi$
$41$	1.91039e91	1.44156	0.720781	+	0.693162i	$0.243783\pi$
$42$	1.04035e91	0.201184
$43$	9.11497e91	0.466431	0.233216	−	0.972425i	$-0.425075\pi$
$43$	9.11497e91	0.466431	0.233216	+	0.972425i	$0.425075\pi$
$44$	7.49679e92	1.04664
$45$	1.49298e93	0.585526
$46$	−2.17619e93	−0.246535
$47$	4.23475e92	0.0142331	0.00711653	−	0.999975i	$-0.497735\pi$
$47$	4.23475e92	0.0142331	0.00711653	+	0.999975i	$0.497735\pi$
$48$	6.98806e93	0.0714870
$49$	−2.18481e95	−0.697164
$50$	1.92449e95	0.196115
$51$	−2.26888e96	−0.755260
$52$	1.97872e96	0.219885
$53$	−1.29781e97	−0.491613	−0.245807	−	0.969319i	$-0.579053\pi$
$53$	−1.29781e97	−0.491613	−0.245807	+	0.969319i	$0.579053\pi$
$54$	−4.70999e97	−0.620544
$55$	3.36878e98	1.57391
$56$	3.37627e98	0.569920
$57$	3.40774e98	0.211611
$58$	−3.93993e99	−0.915812
$59$	8.79283e98	0.0778019	0.0389009	−	0.999243i	$-0.487614\pi$
$59$	8.79283e98	0.0778019	0.0389009	+	0.999243i	$0.487614\pi$
$60$	−7.53239e99	−0.257862
$61$	1.49190e99	0.0200726	0.0100363	−	0.999950i	$-0.496805\pi$
$61$	1.49190e99	0.0200726	0.0100363	+	0.999950i	$0.496805\pi$
$62$	−5.84186e100	−0.313632
$63$	−1.76533e101	−0.383781
$64$	8.52036e101	0.760833
$65$	8.89163e101	0.330656
$66$	−4.36652e102	−0.685336
$67$	1.91959e103	1.28820	0.644100	−	0.764941i	$-0.277232\pi$
$67$	1.91959e103	1.28820	0.644100	+	0.764941i	$0.277232\pi$
$68$	−2.63814e103	−0.766558
$69$	−1.60227e103	−0.204062
$70$	5.43578e103	0.307059
$71$	−4.73462e104	−1.20002	−0.600010	−	0.799992i	$-0.704837\pi$
$71$	−4.73462e104	−1.20002	−0.600010	+	0.799992i	$0.704837\pi$
$72$	−6.28024e104	−0.722255
$73$	3.08550e105	1.62774	0.813869	−	0.581049i	$-0.197357\pi$
$73$	3.08550e105	1.62774	0.813869	+	0.581049i	$0.197357\pi$
$74$	−2.28099e105	−0.557867
$75$	1.41695e105	0.162328
$76$	3.96236e105	0.214776
$77$	−3.98331e106	−1.03162
$78$	−1.15251e106	−0.143979
$79$	−2.94658e107	−1.79220	−0.896101	−	0.443850i	$-0.853612\pi$
$79$	−2.94658e107	−1.79220	−0.896101	+	0.443850i	$0.853612\pi$
$80$	3.65124e106	0.109108
$81$	1.24067e107	0.183761
$82$	−1.29381e108	−0.958046
$83$	−3.83926e108	−1.43329	−0.716647	−	0.697436i	$-0.754324\pi$
$83$	−3.83926e108	−1.43329	−0.716647	+	0.697436i	$0.754324\pi$
$84$	8.90644e107	0.169015
$85$	−1.18548e109	−1.15273
$86$	−6.17309e108	−0.309985
$87$	−2.90087e109	−0.758036
$88$	−1.41708e110	−1.94144
$89$	−1.59303e110	−1.15263	−0.576315	−	0.817228i	$-0.695510\pi$
$89$	−1.59303e110	−1.15263	−0.576315	+	0.817228i	$0.695510\pi$
$90$	−1.01112e110	−0.389134
$91$	−1.05136e110	−0.216728
$92$	−1.86305e110	−0.207115
$93$	−4.30121e110	−0.259599
$94$	−2.86797e109	−0.00945913
$95$	1.78054e111	0.322974
$96$	5.20180e111	0.522191
$97$	−1.90148e112	−1.06289	−0.531445	−	0.847093i	$-0.678351\pi$
$97$	−1.90148e112	−1.06289	−0.531445	+	0.847093i	$0.678351\pi$
$98$	1.47966e112	0.463327
$99$	7.40941e112	1.30736
$100$	1.64757e112	0.164757
$101$	3.22156e113	1.83615	0.918076	−	0.396403i	$-0.129742\pi$
$101$	3.22156e113	1.83615	0.918076	+	0.396403i	$0.129742\pi$
$102$	1.53659e113	0.501937
$103$	2.97045e113	0.559138	0.279569	−	0.960126i	$-0.409808\pi$
$103$	2.97045e113	0.559138	0.279569	+	0.960126i	$0.409808\pi$
$104$	−3.74028e113	−0.407869
$105$	4.00222e113	0.254159
$106$	8.78937e113	0.326721
$107$	−2.97733e114	−0.651093	−0.325546	−	0.945526i	$-0.605548\pi$
$107$	−2.97733e114	−0.651093	−0.325546	+	0.945526i	$0.605548\pi$
$108$	−4.03224e114	−0.521320
$109$	1.44709e114	0.111147	0.0555734	−	0.998455i	$-0.482301\pi$
$109$	1.44709e114	0.111147	0.0555734	+	0.998455i	$0.482301\pi$
$110$	−2.28150e115	−1.04600
$111$	−1.67943e115	−0.461757
$112$	−4.31730e114	−0.0715145
$113$	−5.84545e115	−0.585984	−0.292992	−	0.956115i	$-0.594651\pi$
$113$	−5.84545e115	−0.585984	−0.292992	+	0.956115i	$0.594651\pi$
$114$	−2.30789e115	−0.140634
$115$	−8.37183e115	−0.311453
$116$	−3.37299e116	−0.769376
$117$	1.95565e116	0.274657
$118$	−5.95493e115	−0.0517062
$119$	1.40174e117	0.755551
$120$	1.42381e117	0.478313
$121$	1.19613e118	2.51422
$122$	−1.01038e116	−0.0133400
$123$	−9.52596e117	−0.792994
$124$	−5.00124e117	−0.263483
$125$	3.24925e118	1.08734
$126$	1.19556e118	0.255057
$127$	−1.33608e119	−1.82357	−0.911786	−	0.410665i	$-0.865297\pi$
$127$	−1.33608e119	−1.82357	−0.911786	+	0.410665i	$0.865297\pi$
$128$	5.06279e118	0.443636
$129$	−4.54509e118	−0.256580
$130$	−6.02184e118	−0.219750
$131$	−1.30956e119	−0.309953	−0.154976	−	0.987918i	$-0.549530\pi$
$131$	−1.30956e119	−0.309953	−0.154976	+	0.987918i	$0.549530\pi$
$132$	−3.73820e119	−0.575752
$133$	−2.10534e119	−0.211692
$134$	−1.30004e120	−0.856123
$135$	−1.81194e120	−0.783945
$136$	4.98676e120	1.42190
$137$	1.10790e120	0.208828	0.104414	−	0.994534i	$-0.466703\pi$
$137$	1.10790e120	0.208828	0.104414	+	0.994534i	$0.466703\pi$
$138$	1.08513e120	0.135617
$139$	1.30193e121	1.08206	0.541031	−	0.841003i	$-0.318034\pi$
$139$	1.30193e121	1.08206	0.541031	+	0.841003i	$0.318034\pi$
$140$	4.65359e120	0.257961
$141$	−2.11161e119	−0.00782951
$142$	3.20651e121	0.797520
$143$	4.41277e121	0.738287
$144$	8.03067e120	0.0906298
$145$	−1.51570e122	−1.15696
$146$	−2.08965e122	−1.08178
$147$	1.08943e122	0.383505
$148$	−1.95276e122	−0.468665
$149$	−4.81206e122	−0.789417	−0.394708	−	0.918806i	$-0.629154\pi$
$149$	−4.81206e122	−0.789417	−0.394708	+	0.918806i	$0.629154\pi$
$150$	−9.59629e121	−0.107882
$151$	1.11299e123	0.859594	0.429797	−	0.902925i	$-0.358585\pi$
$151$	1.11299e123	0.859594	0.429797	+	0.902925i	$0.358585\pi$
$152$	−7.48987e122	−0.398393
$153$	−2.60739e123	−0.957504
$154$	2.69769e123	0.685600
$155$	−2.24737e123	−0.396218
$156$	−9.86669e122	−0.120957
$157$	8.46497e123	0.723261	0.361631	−	0.932321i	$-0.382220\pi$
$157$	8.46497e123	0.723261	0.361631	+	0.932321i	$0.382220\pi$
$158$	1.99556e124	1.19108
$159$	6.47139e123	0.270433
$160$	2.71793e124	0.797001
$161$	9.89901e123	0.204141
$162$	−8.40242e123	−0.122125
$163$	−3.21901e124	−0.330463	−0.165232	−	0.986255i	$-0.552837\pi$
$163$	−3.21901e124	−0.330463	−0.165232	+	0.986255i	$0.552837\pi$
$164$	−1.10763e125	−0.804856
$165$	−1.67981e125	−0.865798
$166$	2.60013e125	0.952550
$167$	−5.20813e125	−1.35894	−0.679472	−	0.733702i	$-0.737791\pi$
$167$	−5.20813e125	−1.35894	−0.679472	+	0.733702i	$0.737791\pi$
$168$	−1.68354e125	−0.313509
$169$	−6.34457e125	−0.844897
$170$	8.02866e125	0.766089
$171$	3.91617e125	0.268276
$172$	−5.28481e125	−0.260419
$173$	1.77434e126	0.630131	0.315066	−	0.949070i	$-0.397974\pi$
$173$	1.77434e126	0.630131	0.315066	+	0.949070i	$0.397974\pi$
$174$	1.96460e126	0.503782
$175$	−8.75410e125	−0.162391
$176$	1.81205e126	0.243616
$177$	−4.38446e125	−0.0427983
$178$	1.07888e127	0.766024
$179$	1.96694e127	1.01764	0.508821	−	0.860872i	$-0.330082\pi$
$179$	1.96694e127	1.01764	0.508821	+	0.860872i	$0.330082\pi$
$180$	−8.65621e126	−0.326912
$181$	−4.15323e127	−1.14696	−0.573478	−	0.819221i	$-0.694406\pi$
$181$	−4.15323e127	−1.14696	−0.573478	+	0.819221i	$0.694406\pi$
$182$	7.12033e126	0.144035
$183$	−7.43919e125	−0.0110418
$184$	3.52163e127	0.384181
$185$	−8.77498e127	−0.704764
$186$	2.91298e127	0.172527
$187$	−5.88336e128	−2.57380
$188$	−2.45528e126	−0.00794664
$189$	2.14247e128	0.513835
$190$	−1.20587e128	−0.214645
$191$	1.27905e129	1.69240	0.846199	−	0.532867i	$-0.178885\pi$
$191$	1.27905e129	1.69240	0.846199	+	0.532867i	$0.178885\pi$
$192$	−4.24859e128	−0.418529
$193$	1.57190e129	1.15462	0.577308	−	0.816526i	$-0.304103\pi$
$193$	1.57190e129	1.15462	0.577308	+	0.816526i	$0.304103\pi$
$194$	1.28777e129	0.706384
$195$	−4.43372e128	−0.181892
$196$	1.26674e129	0.389242
$197$	−3.31452e129	−0.763976	−0.381988	−	0.924167i	$-0.624760\pi$
$197$	−3.31452e129	−0.763976	−0.381988	+	0.924167i	$0.624760\pi$
$198$	−5.01800e129	−0.868856
$199$	1.27446e130	1.66007	0.830037	−	0.557708i	$-0.188319\pi$
$199$	1.27446e130	1.66007	0.830037	+	0.557708i	$0.188319\pi$
$200$	−3.11432e129	−0.305610
$201$	−9.57187e129	−0.708630
$202$	−2.18180e130	−1.22029
$203$	1.79219e130	0.758328
$204$	1.31548e130	0.421678
$205$	−4.97729e130	−1.21032
$206$	−2.01173e130	−0.371597
$207$	−1.84133e130	−0.258706
$208$	4.78277e129	0.0511801
$209$	8.83652e130	0.721134
$210$	−2.71050e130	−0.168911
$211$	9.19315e130	0.438032	0.219016	−	0.975721i	$-0.429715\pi$
$211$	9.19315e130	0.438032	0.219016	+	0.975721i	$0.429715\pi$
$212$	7.52462e130	0.274479
$213$	2.36087e131	0.660123
$214$	2.01639e131	0.432709
$215$	−2.37480e131	−0.391610
$216$	7.62196e131	0.967007
$217$	2.65733e131	0.259699
$218$	−9.80035e130	−0.0738669
$219$	−1.53855e132	−0.895407
$220$	−1.95320e132	−0.878750
$221$	−1.55287e132	−0.540718
$222$	1.13739e132	0.306879
$223$	−4.44142e132	−0.929601	−0.464801	−	0.885415i	$-0.653874\pi$
$223$	−4.44142e132	−0.929601	−0.464801	+	0.885415i	$0.653874\pi$
$224$	−3.21373e132	−0.522392
$225$	1.62836e132	0.205797
$226$	3.95882e132	0.389438
$227$	1.05003e133	0.804899	0.402449	−	0.915442i	$-0.368159\pi$
$227$	1.05003e133	0.804899	0.402449	+	0.915442i	$0.368159\pi$
$228$	−1.97579e132	−0.118147
$229$	1.84432e132	0.0861253	0.0430627	−	0.999072i	$-0.486288\pi$
$229$	1.84432e132	0.0861253	0.0430627	+	0.999072i	$0.486288\pi$
$230$	5.66980e132	0.206988
$231$	1.98624e133	0.567485
$232$	6.37580e133	1.42713
$233$	−7.61847e133	−1.33739	−0.668695	−	0.743537i	$-0.733147\pi$
$233$	−7.61847e133	−1.33739	−0.668695	+	0.743537i	$0.733147\pi$
$234$	−1.32446e133	−0.182534
$235$	−1.10331e132	−0.0119499
$236$	−5.09804e132	−0.0434385
$237$	1.46928e134	0.985878
$238$	−9.49324e133	−0.502130
$239$	4.12738e133	0.172263	0.0861316	−	0.996284i	$-0.472549\pi$
$239$	4.12738e133	0.172263	0.0861316	+	0.996284i	$0.472549\pi$
$240$	−1.82066e133	−0.0600196
$241$	−8.68682e133	−0.226411	−0.113206	−	0.993572i	$-0.536112\pi$
$241$	−8.68682e133	−0.226411	−0.113206	+	0.993572i	$0.536112\pi$
$242$	−8.10073e134	−1.67092
$243$	−6.33310e134	−1.03481
$244$	−8.64993e132	−0.0112070
$245$	5.69226e134	0.585331
$246$	6.45143e134	0.527015
$247$	2.33233e134	0.151500
$248$	9.45361e134	0.488740
$249$	1.91441e135	0.788445
$250$	−2.20054e135	−0.722636
$251$	4.61976e135	1.21075	0.605375	−	0.795940i	$-0.293023\pi$
$251$	4.61976e135	1.21075	0.605375	+	0.795940i	$0.293023\pi$
$252$	1.02353e135	0.214274
$253$	−4.15480e135	−0.695410
$254$	9.04859e135	1.21193
$255$	5.91129e135	0.634107
$256$	−1.22768e136	−1.05567
$257$	−2.64024e136	−1.82147	−0.910735	−	0.412990i	$-0.864484\pi$
$257$	−2.64024e136	−1.82147	−0.910735	+	0.412990i	$0.864484\pi$
$258$	3.07815e135	0.170520
$259$	1.03757e136	0.461935
$260$	−5.15532e135	−0.184613
$261$	−3.33367e136	−0.961024
$262$	8.86893e135	0.205991
$263$	−5.89594e136	−1.10421	−0.552107	−	0.833773i	$-0.686176\pi$
$263$	−5.89594e136	−1.10421	−0.552107	+	0.833773i	$0.686176\pi$
$264$	7.06615e136	1.06797
$265$	3.38128e136	0.412753
$266$	1.42584e136	0.140688
$267$	7.94351e136	0.634054
$268$	−1.11297e137	−0.719230
$269$	2.45192e135	0.0128381	0.00641907	−	0.999979i	$-0.497957\pi$
$269$	2.45192e135	0.0128381	0.00641907	+	0.999979i	$0.497957\pi$
$270$	1.22713e137	0.521001
$271$	2.07600e137	0.715256	0.357628	−	0.933864i	$-0.383586\pi$
$271$	2.07600e137	0.715256	0.357628	+	0.933864i	$0.383586\pi$
$272$	−6.37667e136	−0.178423
$273$	5.24252e136	0.119220
$274$	−7.50325e136	−0.138785
$275$	3.67426e137	0.553188
$276$	9.28989e136	0.113932
$277$	8.20124e136	0.0819923	0.0409961	−	0.999159i	$-0.486947\pi$
$277$	8.20124e136	0.0819923	0.0409961	+	0.999159i	$0.486947\pi$
$278$	−8.81730e137	−0.719126
$279$	−4.94294e137	−0.329115
$280$	−8.79647e137	−0.478497
$281$	−3.33997e138	−1.48537	−0.742686	−	0.669639i	$-0.766449\pi$
$281$	−3.33997e138	−1.48537	−0.742686	+	0.669639i	$0.766449\pi$
$282$	1.43009e136	0.00520340
$283$	7.49959e136	0.0223411	0.0111705	−	0.999938i	$-0.496444\pi$
$283$	7.49959e136	0.0223411	0.0111705	+	0.999938i	$0.496444\pi$
$284$	2.74511e138	0.669998
$285$	−8.87847e137	−0.177666
$286$	−2.98854e138	−0.490657
$287$	5.88524e138	0.793299
$288$	5.97790e138	0.662023
$289$	9.72054e138	0.885038
$290$	1.02650e139	0.768905
$291$	9.48152e138	0.584688
$292$	−1.78896e139	−0.908802
$293$	−1.09218e139	−0.457378	−0.228689	−	0.973500i	$-0.573444\pi$
$293$	−1.09218e139	−0.457378	−0.228689	+	0.973500i	$0.573444\pi$
$294$	−7.37816e138	−0.254873
$295$	−2.29087e138	−0.0653215
$296$	3.69121e139	0.869336
$297$	−8.99236e139	−1.75039
$298$	3.25895e139	0.524637
$299$	−1.09663e139	−0.146096
$300$	−8.21543e138	−0.0906315
$301$	2.80801e139	0.256679
$302$	−7.53770e139	−0.571277
$303$	−1.60640e140	−1.01006
$304$	9.57744e138	0.0499910
$305$	−3.88696e138	−0.0168527
$306$	1.76585e140	0.636346
$307$	2.14827e140	0.643828	0.321914	−	0.946769i	$-0.395674\pi$
$307$	2.14827e140	0.643828	0.321914	+	0.946769i	$0.395674\pi$
$308$	2.30950e140	0.575974
$309$	−1.48119e140	−0.307578
$310$	1.52203e140	0.263322
$311$	7.31121e139	0.105445	0.0527227	−	0.998609i	$-0.483210\pi$
$311$	7.31121e139	0.105445	0.0527227	+	0.998609i	$0.483210\pi$
$312$	1.86505e140	0.224366
$313$	1.31379e140	0.131908	0.0659540	−	0.997823i	$-0.478991\pi$
$313$	1.31379e140	0.131908	0.0659540	+	0.997823i	$0.478991\pi$
$314$	−5.73288e140	−0.480671
$315$	4.59935e140	0.322218
$316$	1.70841e141	1.00063
$317$	1.20234e141	0.589086	0.294543	−	0.955638i	$-0.404833\pi$
$317$	1.20234e141	0.589086	0.294543	+	0.955638i	$0.404833\pi$
$318$	−4.38273e140	−0.179727
$319$	−7.52215e141	−2.58326
$320$	−2.21988e141	−0.638786
$321$	1.48461e141	0.358162
$322$	−6.70408e140	−0.135670
$323$	−3.10960e141	−0.528155
$324$	−7.19335e140	−0.102598
$325$	9.69792e140	0.116217
$326$	2.18007e141	0.219622
$327$	−7.21575e140	−0.0611411
$328$	2.09371e142	1.49294
$329$	1.30458e140	0.00783253
$330$	1.13765e142	0.575400
$331$	−1.50465e140	−0.00641435	−0.00320718	−	0.999995i	$-0.501021\pi$
$331$	−1.50465e140	−0.00641435	−0.00320718	+	0.999995i	$0.501021\pi$
$332$	2.22598e142	0.800239
$333$	−1.93000e142	−0.585407
$334$	3.52720e142	0.903138
$335$	−5.00128e142	−1.08156
$336$	2.15278e141	0.0393396
$337$	−1.00091e143	−1.54634	−0.773170	−	0.634199i	$-0.781330\pi$
$337$	−1.00091e143	−1.54634	−0.773170	+	0.634199i	$0.781330\pi$
$338$	4.29685e142	0.561509
$339$	2.91478e142	0.322346
$340$	6.87337e142	0.643593
$341$	−1.11533e143	−0.884672
$342$	−2.65222e142	−0.178293
$343$	−1.63850e143	−0.933958
$344$	9.98963e142	0.483056
$345$	4.17453e142	0.171328
$346$	−1.20166e143	−0.418778
$347$	−7.82894e142	−0.231786	−0.115893	−	0.993262i	$-0.536973\pi$
$347$	−7.82894e142	−0.231786	−0.115893	+	0.993262i	$0.536973\pi$
$348$	1.68191e143	0.423228
$349$	4.38437e142	0.0938147	0.0469074	−	0.998899i	$-0.485063\pi$
$349$	4.38437e142	0.0938147	0.0469074	+	0.998899i	$0.485063\pi$
$350$	5.92869e142	0.107923
$351$	−2.37346e143	−0.367731
$352$	1.34886e144	1.77954
$353$	−3.31053e143	−0.372071	−0.186036	−	0.982543i	$-0.559564\pi$
$353$	−3.31053e143	−0.372071	−0.186036	+	0.982543i	$0.559564\pi$
$354$	2.96936e142	0.0284432
$355$	1.23355e144	1.00752
$356$	9.23633e143	0.643539
$357$	−6.98963e143	−0.415623
$358$	−1.33211e144	−0.676313
$359$	−2.35286e144	−1.02037	−0.510187	−	0.860064i	$-0.670424\pi$
$359$	−2.35286e144	−1.02037	−0.510187	+	0.860064i	$0.670424\pi$
$360$	1.63624e144	0.606396
$361$	−2.68910e144	−0.852020
$362$	2.81277e144	0.762254
$363$	−5.96436e144	−1.38306
$364$	6.09575e143	0.121004
$365$	−8.03891e144	−1.36663
$366$	5.03817e142	0.00733824
$367$	1.41695e145	1.76898	0.884490	−	0.466559i	$-0.154507\pi$
$367$	1.41695e145	1.76898	0.884490	+	0.466559i	$0.154507\pi$
$368$	−4.50317e143	−0.0482078
$369$	−1.09472e145	−1.00534
$370$	5.94284e144	0.468378
$371$	−3.99809e144	−0.270537
$372$	2.49382e144	0.144940
$373$	3.38666e145	1.69131	0.845654	−	0.533731i	$-0.179211\pi$
$373$	3.38666e145	1.69131	0.845654	+	0.533731i	$0.179211\pi$
$374$	3.98449e145	1.71052
$375$	−1.62020e145	−0.598140
$376$	4.64111e143	0.0147404
$377$	−1.98541e145	−0.542706
$378$	−1.45098e145	−0.341489
$379$	−5.37146e145	−1.08887	−0.544436	−	0.838802i	$-0.683256\pi$
$379$	−5.37146e145	−1.08887	−0.544436	+	0.838802i	$0.683256\pi$
$380$	−1.03235e145	−0.180323
$381$	6.66224e145	1.00313
$382$	−8.66234e145	−1.12475
$383$	2.61667e145	0.293102	0.146551	−	0.989203i	$-0.453183\pi$
$383$	2.61667e145	0.293102	0.146551	+	0.989203i	$0.453183\pi$
$384$	−2.52451e145	−0.244041
$385$	1.03780e146	0.866132
$386$	−1.06457e146	−0.767344
$387$	−5.22321e145	−0.325288
$388$	1.10247e146	0.593435
$389$	−2.76110e146	−1.28508	−0.642539	−	0.766253i	$-0.722119\pi$
$389$	−2.76110e146	−1.28508	−0.642539	+	0.766253i	$0.722119\pi$
$390$	3.00273e145	0.120883
$391$	1.46209e146	0.509315
$392$	−2.39446e146	−0.722013
$393$	6.52997e145	0.170503
$394$	2.24475e146	0.507729
$395$	7.67695e146	1.50471
$396$	−4.29594e146	−0.729928
$397$	1.19431e147	1.75976	0.879880	−	0.475196i	$-0.157623\pi$
$397$	1.19431e147	1.75976	0.879880	+	0.475196i	$0.157623\pi$
$398$	−8.63125e146	−1.10327
$399$	1.04981e146	0.116450
$400$	3.98234e145	0.0383485
$401$	6.70688e146	0.560872	0.280436	−	0.959873i	$-0.409521\pi$
$401$	6.70688e146	0.560872	0.280436	+	0.959873i	$0.409521\pi$
$402$	6.48252e146	0.470947
$403$	−2.94383e146	−0.185857
$404$	−1.86784e147	−1.02516
$405$	−3.23242e146	−0.154283
$406$	−1.21375e147	−0.503976
$407$	−4.35488e147	−1.57359
$408$	−2.48660e147	−0.782179
$409$	2.86067e147	0.783611	0.391806	−	0.920048i	$-0.371851\pi$
$409$	2.86067e147	0.783611	0.391806	+	0.920048i	$0.371851\pi$
$410$	3.37086e147	0.804364
$411$	−5.52445e146	−0.114875
$412$	−1.72225e147	−0.312179
$413$	2.70877e146	0.0428148
$414$	1.24704e147	0.171933
$415$	1.00027e148	1.20338
$416$	3.56022e147	0.373855
$417$	−6.49195e147	−0.595234
$418$	−5.98451e147	−0.479257
$419$	2.40950e148	1.68591	0.842954	−	0.537985i	$-0.180814\pi$
$419$	2.40950e148	1.68591	0.842954	+	0.537985i	$0.180814\pi$
$420$	−2.32047e147	−0.141903
$421$	9.14893e147	0.489139	0.244569	−	0.969632i	$-0.421353\pi$
$421$	9.14893e147	0.489139	0.244569	+	0.969632i	$0.421353\pi$
$422$	−6.22604e147	−0.291111
$423$	−2.42666e146	−0.00992611
$424$	−1.42234e148	−0.509136
$425$	−1.29298e148	−0.405152
$426$	−1.59890e148	−0.438710
$427$	4.59601e146	0.0110460
$428$	1.72624e148	0.363520
$429$	−2.20038e148	−0.406126
$430$	1.60833e148	0.260259
$431$	−9.34136e148	−1.32570	−0.662849	−	0.748754i	$-0.730653\pi$
$431$	−9.34136e148	−1.32570	−0.662849	+	0.748754i	$0.730653\pi$
$432$	−9.74635e147	−0.121342
$433$	3.81861e148	0.417196	0.208598	−	0.978002i	$-0.433110\pi$
$433$	3.81861e148	0.417196	0.208598	+	0.978002i	$0.433110\pi$
$434$	−1.79967e148	−0.172593
$435$	7.55786e148	0.636438
$436$	−8.39013e147	−0.0620557
$437$	−2.19598e148	−0.142701
$438$	1.04198e149	0.595077
$439$	−3.16295e149	−1.58799	−0.793994	−	0.607925i	$-0.792002\pi$
$439$	−3.16295e149	−1.58799	−0.793994	+	0.607925i	$0.792002\pi$
$440$	3.69204e149	1.63001
$441$	1.25198e149	0.486201
$442$	1.05168e149	0.359355
$443$	−3.87339e149	−1.16488	−0.582439	−	0.812875i	$-0.697901\pi$
$443$	−3.87339e149	−1.16488	−0.582439	+	0.812875i	$0.697901\pi$
$444$	9.73725e148	0.257809
$445$	4.15046e149	0.967734
$446$	3.00794e149	0.617802
$447$	2.39948e149	0.434253
$448$	2.62483e149	0.418690
$449$	−3.24391e149	−0.456195	−0.228097	−	0.973638i	$-0.573250\pi$
$449$	−3.24391e149	−0.456195	−0.228097	+	0.973638i	$0.573250\pi$
$450$	−1.10280e149	−0.136770
$451$	−2.47015e150	−2.70239
$452$	3.38916e149	0.327168
$453$	−5.54981e149	−0.472857
$454$	−7.11131e149	−0.534926
$455$	2.73920e149	0.181962
$456$	3.73475e149	0.219153
$457$	−1.75774e150	−0.911359	−0.455679	−	0.890144i	$-0.650604\pi$
$457$	−1.75774e150	−0.911359	−0.455679	+	0.890144i	$0.650604\pi$
$458$	−1.24906e149	−0.0572379
$459$	3.16444e150	1.28198
$460$	4.85394e149	0.173891
$461$	5.65178e150	1.79095	0.895475	−	0.445113i	$-0.146836\pi$
$461$	5.65178e150	1.79095	0.895475	+	0.445113i	$0.146836\pi$
$462$	−1.34517e150	−0.377144
$463$	−2.16026e150	−0.536020	−0.268010	−	0.963416i	$-0.586366\pi$
$463$	−2.16026e150	−0.536020	−0.268010	+	0.963416i	$0.586366\pi$
$464$	−8.15286e149	−0.179079
$465$	1.12063e150	0.217957
$466$	5.15959e150	0.888814
$467$	−1.87974e150	−0.286875	−0.143438	−	0.989659i	$-0.545816\pi$
$467$	−1.87974e150	−0.286875	−0.143438	+	0.989659i	$0.545816\pi$
$468$	−1.13388e150	−0.153347
$469$	5.91360e150	0.708903
$470$	7.47216e148	0.00794177
$471$	−4.22097e150	−0.397861
$472$	9.63658e149	0.0805750
$473$	−1.17857e151	−0.874383
$474$	−9.95067e150	−0.655203
$475$	1.94200e150	0.113517
$476$	−8.12721e150	−0.421841
$477$	7.43691e150	0.342850
$478$	−2.79526e150	−0.114484
$479$	1.36596e151	0.497145	0.248572	−	0.968613i	$-0.420039\pi$
$479$	1.36596e151	0.497145	0.248572	+	0.968613i	$0.420039\pi$
$480$	−1.35527e151	−0.438425
$481$	−1.14944e151	−0.330589
$482$	5.88313e150	0.150470
$483$	−4.93604e150	−0.112296
$484$	−6.93507e151	−1.40374
$485$	4.95407e151	0.892389
$486$	4.28907e151	0.687724
$487$	8.12555e151	1.16002	0.580012	−	0.814608i	$-0.303048\pi$
$487$	8.12555e151	1.16002	0.580012	+	0.814608i	$0.303048\pi$
$488$	1.63506e150	0.0207880
$489$	1.60513e151	0.181786
$490$	−3.85507e151	−0.389004
$491$	−4.72472e151	−0.424885	−0.212442	−	0.977174i	$-0.568142\pi$
$491$	−4.72472e151	−0.424885	−0.212442	+	0.977174i	$0.568142\pi$
$492$	5.52310e151	0.442746
$493$	2.64707e152	1.89197
$494$	−1.57956e151	−0.100685
$495$	−1.93043e152	−1.09764
$496$	−1.20885e151	−0.0613279
$497$	−1.45857e152	−0.660377
$498$	−1.29653e152	−0.523991
$499$	1.93976e152	0.699951	0.349975	−	0.936759i	$-0.386190\pi$
$499$	1.93976e152	0.699951	0.349975	+	0.936759i	$0.386190\pi$
$500$	−1.88390e152	−0.607088
$501$	2.59698e152	0.747545
$502$	−3.12872e152	−0.804650
$503$	−3.80346e152	−0.874153	−0.437077	−	0.899424i	$-0.643986\pi$
$503$	−3.80346e152	−0.874153	−0.437077	+	0.899424i	$0.643986\pi$
$504$	−1.93473e152	−0.397461
$505$	−8.39340e152	−1.54161
$506$	2.81383e152	0.462161
$507$	3.16366e152	0.464772
$508$	7.74654e152	1.01814
$509$	9.31167e152	1.09515	0.547574	−	0.836757i	$-0.315551\pi$
$509$	9.31167e152	1.09515	0.547574	+	0.836757i	$0.315551\pi$
$510$	−4.00341e152	−0.421420
$511$	9.50536e152	0.895752
$512$	3.05694e152	0.257949
$513$	−4.75283e152	−0.359187
$514$	1.78810e153	1.21053
$515$	−7.73916e152	−0.469446
$516$	2.63522e152	0.143255
$517$	−5.47556e151	−0.0266817
$518$	−7.02692e152	−0.306997
$519$	−8.84754e152	−0.346631
$520$	9.74486e152	0.342442
$521$	−3.31452e153	−1.04493	−0.522467	−	0.852660i	$-0.674988\pi$
$521$	−3.31452e153	−1.04493	−0.522467	+	0.852660i	$0.674988\pi$
$522$	2.25772e153	0.638685
$523$	−7.03975e153	−1.78736	−0.893679	−	0.448706i	$-0.851885\pi$
$523$	−7.03975e153	−1.78736	−0.893679	+	0.448706i	$0.851885\pi$
$524$	7.59273e152	0.173054
$525$	4.36514e152	0.0893301
$526$	3.99302e153	0.733849
$527$	3.92489e153	0.647929
$528$	−9.03562e152	−0.134011
$529$	−6.47066e153	−0.862389
$530$	−2.28997e153	−0.274311
$531$	−5.03861e152	−0.0542588
$532$	1.22067e153	0.118192
$533$	−6.51976e153	−0.567733
$534$	−5.37972e153	−0.421385
$535$	7.75707e153	0.546650
$536$	2.10380e154	1.33411
$537$	−9.80795e153	−0.559798
$538$	−1.66056e152	−0.00853209
$539$	2.82498e154	1.30692
$540$	1.05055e154	0.437694
$541$	1.33157e154	0.499712	0.249856	−	0.968283i	$-0.419617\pi$
$541$	1.33157e154	0.499712	0.249856	+	0.968283i	$0.419617\pi$
$542$	−1.40596e154	−0.475351
$543$	2.07097e154	0.630932
$544$	−4.74669e154	−1.30333
$545$	−3.77021e153	−0.0933175
$546$	−3.55048e153	−0.0792325
$547$	9.14885e153	0.184112	0.0920561	−	0.995754i	$-0.470656\pi$
$547$	9.14885e153	0.184112	0.0920561	+	0.995754i	$0.470656\pi$
$548$	−6.42356e153	−0.116594
$549$	−8.54911e152	−0.0139986
$550$	−2.48838e154	−0.367642
$551$	−3.97576e154	−0.530097
$552$	−1.75602e154	−0.211336
$553$	−9.07738e154	−0.986258
$554$	−5.55427e153	−0.0544911
$555$	4.37556e154	0.387686
$556$	−7.54853e154	−0.604139
$557$	5.43636e154	0.393088	0.196544	−	0.980495i	$-0.437028\pi$
$557$	5.43636e154	0.393088	0.196544	+	0.980495i	$0.437028\pi$
$558$	3.34760e154	0.218726
$559$	−3.11075e154	−0.183695
$560$	1.12482e154	0.0600427
$561$	2.93368e155	1.41583
$562$	2.26199e155	0.987162
$563$	−1.72693e154	−0.0681633	−0.0340817	−	0.999419i	$-0.510851\pi$
$563$	−1.72693e154	−0.0681633	−0.0340817	+	0.999419i	$0.510851\pi$
$564$	1.22430e153	0.00437139
$565$	1.52296e155	0.491985
$566$	−5.07908e153	−0.0148476
$567$	3.82208e154	0.101125
$568$	−5.18895e155	−1.24279
$569$	2.07631e155	0.450246	0.225123	−	0.974330i	$-0.427722\pi$
$569$	2.07631e155	0.450246	0.225123	+	0.974330i	$0.427722\pi$
$570$	6.01293e154	0.118075
$571$	2.40317e155	0.427409	0.213705	−	0.976898i	$-0.431447\pi$
$571$	2.40317e155	0.427409	0.213705	+	0.976898i	$0.431447\pi$
$572$	−2.55850e155	−0.412202
$573$	−6.37786e155	−0.930977
$574$	−3.98577e155	−0.527218
$575$	−9.13099e154	−0.109467
$576$	−4.88247e155	−0.530603
$577$	1.09131e156	1.07527	0.537633	−	0.843179i	$-0.319319\pi$
$577$	1.09131e156	1.07527	0.537633	+	0.843179i	$0.319319\pi$
$578$	−6.58321e155	−0.588186
$579$	−7.83813e155	−0.635146
$580$	8.78792e155	0.645958
$581$	−1.18274e156	−0.788749
$582$	−6.42134e155	−0.388577
$583$	1.67808e156	0.921591
$584$	3.38158e156	1.68575
$585$	−5.09523e155	−0.230599
$586$	7.39679e155	0.303968
$587$	−3.12729e156	−1.16712	−0.583560	−	0.812070i	$-0.698341\pi$
$587$	−3.12729e156	−1.16712	−0.583560	+	0.812070i	$0.698341\pi$
$588$	−6.31648e155	−0.214119
$589$	−5.89499e155	−0.181539
$590$	1.55149e155	0.0434119
$591$	1.65275e156	0.420258
$592$	−4.72003e155	−0.109086
$593$	6.86537e156	1.44236	0.721181	−	0.692747i	$-0.243600\pi$
$593$	6.86537e156	1.44236	0.721181	+	0.692747i	$0.243600\pi$
$594$	6.09006e156	1.16329
$595$	−3.65206e156	−0.634351
$596$	2.79000e156	0.440749
$597$	−6.35497e156	−0.913195
$598$	7.42688e155	0.0970934
$599$	−6.19882e156	−0.737384	−0.368692	−	0.929552i	$-0.620194\pi$
$599$	−6.19882e156	−0.737384	−0.368692	+	0.929552i	$0.620194\pi$
$600$	1.55292e156	0.168114
$601$	−6.47180e154	−0.00637702	−0.00318851	−	0.999995i	$-0.501015\pi$
$601$	−6.47180e154	−0.00637702	−0.00318851	+	0.999995i	$0.501015\pi$
$602$	−1.90172e156	−0.170586
$603$	−1.10000e157	−0.898387
$604$	−6.45306e156	−0.479931
$605$	−3.11636e157	−2.11091
$606$	1.08793e157	0.671271
$607$	1.87109e157	1.05180	0.525900	−	0.850547i	$-0.323729\pi$
$607$	1.87109e157	1.05180	0.525900	+	0.850547i	$0.323729\pi$
$608$	7.12929e156	0.365169
$609$	−8.93656e156	−0.417151
$610$	2.63243e155	0.0112001
$611$	−1.44523e155	−0.00560543
$612$	1.51175e157	0.534596
$613$	4.92361e157	1.58769	0.793847	−	0.608117i	$-0.208075\pi$
$613$	4.92361e157	1.58769	0.793847	+	0.608117i	$0.208075\pi$
$614$	−1.45491e157	−0.427881
$615$	2.48187e157	0.665788
$616$	−4.36554e157	−1.06839
$617$	6.61199e157	1.47645	0.738227	−	0.674552i	$-0.235663\pi$
$617$	6.61199e157	1.47645	0.738227	+	0.674552i	$0.235663\pi$
$618$	1.00313e157	0.204413
$619$	−4.05110e157	−0.753444	−0.376722	−	0.926326i	$-0.622949\pi$
$619$	−4.05110e157	−0.753444	−0.376722	+	0.926326i	$0.622949\pi$
$620$	1.30301e157	0.221217
$621$	2.23471e157	0.346375
$622$	−4.95150e156	−0.0700778
$623$	−4.90759e157	−0.634298
$624$	−2.38488e156	−0.0281538
$625$	−5.72913e157	−0.617828
$626$	−8.89762e156	−0.0876645
$627$	−4.40624e157	−0.396691
$628$	−4.90795e157	−0.403813
$629$	1.53250e158	1.15249
$630$	−3.11490e157	−0.214142
$631$	−3.83850e157	−0.241270	−0.120635	−	0.992697i	$-0.538493\pi$
$631$	−3.83850e157	−0.241270	−0.120635	+	0.992697i	$0.538493\pi$
$632$	−3.22933e158	−1.85608
$633$	−4.58407e157	−0.240958
$634$	−8.14282e157	−0.391500
$635$	3.48101e158	1.53105
$636$	−3.75208e157	−0.150989
$637$	7.45631e157	0.274565
$638$	5.09436e158	1.71680
$639$	2.71311e158	0.836891
$640$	−1.31905e158	−0.372471
$641$	−6.31333e158	−1.63222	−0.816112	−	0.577893i	$-0.803875\pi$
$641$	−6.31333e158	−1.63222	−0.816112	+	0.577893i	$0.803875\pi$
$642$	−1.00545e158	−0.238030
$643$	2.52196e158	0.546787	0.273393	−	0.961902i	$-0.411854\pi$
$643$	2.52196e158	0.546787	0.273393	+	0.961902i	$0.411854\pi$
$644$	−5.73940e157	−0.113976
$645$	1.18417e158	0.215422
$646$	2.10597e158	0.351006
$647$	4.97844e158	0.760328	0.380164	−	0.924919i	$-0.375868\pi$
$647$	4.97844e158	0.760328	0.380164	+	0.924919i	$0.375868\pi$
$648$	1.35973e158	0.190311
$649$	−1.13692e158	−0.145849
$650$	−6.56789e157	−0.0772363
$651$	−1.32505e158	−0.142859
$652$	1.86637e158	0.184505
$653$	−7.76519e158	−0.703975	−0.351988	−	0.936005i	$-0.614494\pi$
$653$	−7.76519e158	−0.703975	−0.351988	+	0.936005i	$0.614494\pi$
$654$	4.88685e157	0.0406337
$655$	3.41189e158	0.260233
$656$	−2.67726e158	−0.187337
$657$	−1.76811e159	−1.13518
$658$	−8.83523e156	−0.00520541
$659$	−3.51623e159	−1.90130	−0.950650	−	0.310265i	$-0.899582\pi$
$659$	−3.51623e159	−1.90130	−0.950650	+	0.310265i	$0.899582\pi$
$660$	9.73944e158	0.483394
$661$	2.58685e159	1.17866	0.589331	−	0.807891i	$-0.299391\pi$
$661$	2.58685e159	1.17866	0.589331	+	0.807891i	$0.299391\pi$
$662$	1.01902e157	0.00426291
$663$	7.74321e158	0.297445
$664$	−4.20767e159	−1.48438
$665$	5.48522e158	0.177734
$666$	1.30709e159	0.389055
$667$	1.86935e159	0.511187
$668$	3.01965e159	0.758728
$669$	2.21467e159	0.511367
$670$	3.38710e159	0.718790
$671$	−1.92903e158	−0.0376285
$672$	1.60249e159	0.287364
$673$	−2.20407e158	−0.0363391	−0.0181695	−	0.999835i	$-0.505784\pi$
$673$	−2.20407e158	−0.0363391	−0.0181695	+	0.999835i	$0.505784\pi$
$674$	6.77863e159	1.02768
$675$	−1.97625e159	−0.275536
$676$	3.67855e159	0.471724
$677$	−1.05943e160	−1.24972	−0.624862	−	0.780736i	$-0.714845\pi$
$677$	−1.05943e160	−1.24972	−0.624862	+	0.780736i	$0.714845\pi$
$678$	−1.97403e159	−0.214227
$679$	−5.85779e159	−0.584913
$680$	−1.29924e160	−1.19381
$681$	−5.23587e159	−0.442769
$682$	7.55357e159	0.587943
$683$	−4.47223e159	−0.320446	−0.160223	−	0.987081i	$-0.551221\pi$
$683$	−4.47223e159	−0.320446	−0.160223	+	0.987081i	$0.551221\pi$
$684$	−2.27058e159	−0.149784
$685$	−2.88651e159	−0.175330
$686$	1.10967e160	0.620698
$687$	−9.19650e158	−0.0473770
$688$	−1.27739e159	−0.0606147
$689$	4.42915e159	0.193613
$690$	−2.82719e159	−0.113863
$691$	3.15672e159	0.117146	0.0585729	−	0.998283i	$-0.481345\pi$
$691$	3.15672e159	0.117146	0.0585729	+	0.998283i	$0.481345\pi$
$692$	−1.02875e160	−0.351816
$693$	2.28258e160	0.719446
$694$	5.30213e159	0.154042
$695$	−3.39203e160	−0.908485
$696$	−3.17923e160	−0.785055
$697$	8.69252e160	1.97922
$698$	−2.96931e159	−0.0623482
$699$	3.79887e160	0.735689
$700$	5.07558e159	0.0906664
$701$	3.50508e160	0.577604	0.288802	−	0.957389i	$-0.406743\pi$
$701$	3.50508e160	0.577604	0.288802	+	0.957389i	$0.406743\pi$
$702$	1.60742e160	0.244390
$703$	−2.30173e160	−0.322908
$704$	−1.10169e161	−1.42628
$705$	5.50156e158	0.00657356
$706$	2.24205e160	0.247274
$707$	9.92451e160	1.01044
$708$	2.54209e159	0.0238952
$709$	−1.59516e161	−1.38450	−0.692249	−	0.721659i	$-0.743380\pi$
$709$	−1.59516e161	−1.38450	−0.692249	+	0.721659i	$0.743380\pi$
$710$	−8.35419e160	−0.669588
$711$	1.68850e161	1.24988
$712$	−1.74590e161	−1.19371
$713$	2.77174e160	0.175063
$714$	4.73371e160	0.276218
$715$	−1.14969e161	−0.619856
$716$	−1.14042e161	−0.568172
$717$	−2.05808e160	−0.0947608
$718$	1.59347e161	0.678128
$719$	−2.07400e161	−0.815882	−0.407941	−	0.913008i	$-0.633753\pi$
$719$	−2.07400e161	−0.815882	−0.407941	+	0.913008i	$0.633753\pi$
$720$	−2.09230e160	−0.0760917
$721$	9.15093e160	0.307697
$722$	1.82119e161	0.566243
$723$	4.33160e160	0.124547
$724$	2.40802e161	0.640371
$725$	−1.65314e161	−0.406642
$726$	4.03935e161	0.919163
$727$	−3.96258e160	−0.0834226	−0.0417113	−	0.999130i	$-0.513281\pi$
$727$	−3.96258e160	−0.0834226	−0.0417113	+	0.999130i	$0.513281\pi$
$728$	−1.15225e161	−0.224452
$729$	2.13850e161	0.385482
$730$	5.44433e161	0.908245
$731$	4.14743e161	0.640394
$732$	4.31320e159	0.00616487
$733$	7.21127e161	0.954195	0.477097	−	0.878850i	$-0.341689\pi$
$733$	7.21127e161	0.954195	0.477097	+	0.878850i	$0.341689\pi$
$734$	−9.59628e161	−1.17564
$735$	−2.83839e161	−0.321986
$736$	−3.35209e161	−0.352143
$737$	−2.48205e162	−2.41489
$738$	7.41398e161	0.668139
$739$	−9.97899e161	−0.833059	−0.416529	−	0.909122i	$-0.636754\pi$
$739$	−9.97899e161	−0.833059	−0.416529	+	0.909122i	$0.636754\pi$
$740$	5.08769e161	0.393485
$741$	−1.16299e161	−0.0833390
$742$	2.70770e161	0.179796
$743$	−1.13938e162	−0.701130	−0.350565	−	0.936538i	$-0.614010\pi$
$743$	−1.13938e162	−0.701130	−0.350565	+	0.936538i	$0.614010\pi$
$744$	−4.71395e161	−0.268852
$745$	1.25372e162	0.662785
$746$	−2.29361e162	−1.12402
$747$	2.20003e162	0.999575
$748$	3.41114e162	1.43701
$749$	−9.17211e161	−0.358300
$750$	1.09728e162	0.397517
$751$	1.03046e162	0.346237	0.173119	−	0.984901i	$-0.444616\pi$
$751$	1.03046e162	0.346237	0.173119	+	0.984901i	$0.444616\pi$
$752$	−5.93468e159	−0.00184965
$753$	−2.30360e162	−0.666025
$754$	1.34462e162	0.360676
$755$	−2.89976e162	−0.721705
$756$	−1.24219e162	−0.286885
$757$	6.88017e162	1.47463	0.737313	−	0.675552i	$-0.236094\pi$
$757$	6.88017e162	1.47463	0.737313	+	0.675552i	$0.236094\pi$
$758$	3.63781e162	0.723652
$759$	2.07175e162	0.382540
$760$	1.95140e162	0.334486
$761$	−6.93158e162	−1.10306	−0.551530	−	0.834155i	$-0.685956\pi$
$761$	−6.93158e162	−1.10306	−0.551530	+	0.834155i	$0.685956\pi$
$762$	−4.51199e162	−0.666672
$763$	4.45797e161	0.0611647
$764$	−7.41587e162	−0.944904
$765$	6.79325e162	0.803909
$766$	−1.77214e162	−0.194792
$767$	−3.00081e161	−0.0306408
$768$	6.12171e162	0.580716
$769$	−2.68294e162	−0.236468	−0.118234	−	0.992986i	$-0.537723\pi$
$769$	−2.68294e162	−0.236468	−0.118234	+	0.992986i	$0.537723\pi$
$770$	−7.02850e162	−0.575621
$771$	1.31653e163	1.00198
$772$	−9.11381e162	−0.644648
$773$	−2.05053e163	−1.34811	−0.674053	−	0.738683i	$-0.735448\pi$
$773$	−2.05053e163	−1.34811	−0.674053	+	0.738683i	$0.735448\pi$
$774$	3.53741e162	0.216183
$775$	−2.45116e162	−0.139260
$776$	−2.08394e163	−1.10077
$777$	−5.17374e162	−0.254107
$778$	1.86995e163	0.854049
$779$	−1.30557e163	−0.554543
$780$	2.57065e162	0.101554
$781$	6.12190e163	2.24959
$782$	−9.90195e162	−0.338485
$783$	4.04588e163	1.28669
$784$	3.06185e162	0.0905995
$785$	−2.20545e163	−0.607241
$786$	−4.42240e162	−0.113314
$787$	1.49582e163	0.356704	0.178352	−	0.983967i	$-0.442923\pi$
$787$	1.49582e163	0.356704	0.178352	+	0.983967i	$0.442923\pi$
$788$	1.92174e163	0.426544
$789$	2.93995e163	0.607421
$790$	−5.19920e163	−1.00001
$791$	−1.80078e163	−0.322470
$792$	8.12041e163	1.35396
$793$	−5.09153e161	−0.00790521
$794$	−8.08844e163	−1.16952
$795$	−1.68604e163	−0.227052
$796$	−7.38926e163	−0.926856
$797$	−3.86378e162	−0.0451457	−0.0225729	−	0.999745i	$-0.507186\pi$
$797$	−3.86378e162	−0.0451457	−0.0225729	+	0.999745i	$0.507186\pi$
$798$	−7.10980e162	−0.0773916
$799$	1.92687e162	0.0195415
$800$	2.96439e163	0.280124
$801$	9.12867e163	0.803841
$802$	−4.54222e163	−0.372749
$803$	−3.98958e164	−3.05140
$804$	5.54972e163	0.395644
$805$	−2.57907e163	−0.171394
$806$	1.99370e163	0.123518
$807$	−1.22262e162	−0.00706218
$808$	3.53070e164	1.90160
$809$	1.10161e164	0.553269	0.276635	−	0.960975i	$-0.410781\pi$
$809$	1.10161e164	0.553269	0.276635	+	0.960975i	$0.410781\pi$
$810$	2.18915e163	0.102535
$811$	1.93566e164	0.845574	0.422787	−	0.906229i	$-0.361052\pi$
$811$	1.93566e164	0.845574	0.422787	+	0.906229i	$0.361052\pi$
$812$	−1.03910e164	−0.423391
$813$	−1.03517e164	−0.393458
$814$	2.94933e164	1.04579
$815$	8.38676e163	0.277453
$816$	3.17966e163	0.0981492
$817$	−6.22924e163	−0.179427
$818$	−1.93738e164	−0.520779
$819$	6.02469e163	0.151145
$820$	2.88581e164	0.675748
$821$	−6.87625e164	−1.50302	−0.751508	−	0.659724i	$-0.770673\pi$
$821$	−6.87625e164	−1.50302	−0.751508	+	0.659724i	$0.770673\pi$
$822$	3.74142e163	0.0763447
$823$	−2.64784e164	−0.504431	−0.252215	−	0.967671i	$-0.581159\pi$
$823$	−2.64784e164	−0.504431	−0.252215	+	0.967671i	$0.581159\pi$
$824$	3.25549e164	0.579068
$825$	−1.83213e164	−0.304305
$826$	−1.83451e163	−0.0284542
$827$	3.57582e163	0.0517981	0.0258991	−	0.999665i	$-0.491755\pi$
$827$	3.57582e163	0.0517981	0.0258991	+	0.999665i	$0.491755\pi$
$828$	1.06759e164	0.144441
$829$	2.64360e164	0.334091	0.167045	−	0.985949i	$-0.446577\pi$
$829$	2.64360e164	0.334091	0.167045	+	0.985949i	$0.446577\pi$
$830$	−6.77433e164	−0.799749
$831$	−4.08947e163	−0.0451034
$832$	−2.90782e164	−0.299640
$833$	−9.94118e164	−0.957184
$834$	4.39666e164	0.395586
$835$	1.35692e165	1.14095
$836$	−5.12337e164	−0.402625
$837$	5.99896e164	0.440643
$838$	−1.63183e165	−1.12044
$839$	−1.25242e165	−0.803897	−0.401948	−	0.915662i	$-0.631667\pi$
$839$	−1.25242e165	−0.803897	−0.401948	+	0.915662i	$0.631667\pi$
$840$	4.38627e164	0.263218
$841$	1.60212e165	0.898923
$842$	−6.19609e164	−0.325076
$843$	1.66544e165	0.817093
$844$	−5.33014e164	−0.244563
$845$	1.65300e165	0.709365
$846$	1.64345e163	0.00659678
$847$	3.68485e165	1.38359
$848$	1.81878e164	0.0638873
$849$	−3.73960e163	−0.0122897
$850$	8.75670e164	0.269260
$851$	1.08224e165	0.311389
$852$	−1.36882e165	−0.368561
$853$	−1.86577e165	−0.470152	−0.235076	−	0.971977i	$-0.575534\pi$
$853$	−1.86577e165	−0.470152	−0.235076	+	0.971977i	$0.575534\pi$
$854$	−3.11264e163	−0.00734107
$855$	−1.02031e165	−0.225241
$856$	−3.26303e165	−0.674300
$857$	−5.24157e165	−1.01402	−0.507008	−	0.861941i	$-0.669248\pi$
$857$	−5.24157e165	−1.01402	−0.507008	+	0.861941i	$0.669248\pi$
$858$	1.49020e165	0.269907
$859$	−3.57472e165	−0.606218	−0.303109	−	0.952956i	$-0.598025\pi$
$859$	−3.57472e165	−0.606218	−0.303109	+	0.952956i	$0.598025\pi$
$860$	1.37690e165	0.218644
$861$	−2.93462e165	−0.436388
$862$	6.32641e165	0.881043
$863$	−2.23901e165	−0.292043	−0.146022	−	0.989281i	$-0.546647\pi$
$863$	−2.23901e165	−0.292043	−0.146022	+	0.989281i	$0.546647\pi$
$864$	−7.25503e165	−0.886365
$865$	−4.62282e165	−0.529050
$866$	−2.58615e165	−0.277263
$867$	−4.84705e165	−0.486854
$868$	−1.54071e165	−0.144996
$869$	3.80995e166	3.35971
$870$	−5.11854e165	−0.422969
$871$	−6.55118e165	−0.507334
$872$	1.58595e165	0.115108
$873$	1.08962e166	0.741257
$874$	1.48722e165	0.0948376
$875$	1.00098e166	0.598371
$876$	8.92046e165	0.499926
$877$	−2.28147e166	−1.19878	−0.599389	−	0.800458i	$-0.704590\pi$
$877$	−2.28147e166	−1.19878	−0.599389	+	0.800458i	$0.704590\pi$
$878$	2.14210e166	1.05536
$879$	5.44607e165	0.251601
$880$	−4.72109e165	−0.204537
$881$	−1.80145e166	−0.731954	−0.365977	−	0.930624i	$-0.619265\pi$
$881$	−1.80145e166	−0.731954	−0.365977	+	0.930624i	$0.619265\pi$
$882$	−8.47898e165	−0.323123
$883$	−1.36757e166	−0.488844	−0.244422	−	0.969669i	$-0.578598\pi$
$883$	−1.36757e166	−0.488844	−0.244422	+	0.969669i	$0.578598\pi$
$884$	9.00344e165	0.301895
$885$	1.14232e165	0.0359329
$886$	2.62324e166	0.774164
$887$	8.22825e165	0.227836	0.113918	−	0.993490i	$-0.463660\pi$
$887$	8.22825e165	0.227836	0.113918	+	0.993490i	$0.463660\pi$
$888$	−1.84059e166	−0.478216
$889$	−4.11601e166	−1.00352
$890$	−2.81089e166	−0.643145
$891$	−1.60420e166	−0.344483
$892$	2.57511e166	0.519017
$893$	−2.89406e164	−0.00547520
$894$	−1.62504e166	−0.288599
$895$	−5.12463e166	−0.854399
$896$	1.55967e166	0.244135
$897$	5.46822e165	0.0803661
$898$	2.19693e166	0.303182
$899$	5.01815e166	0.650311
$900$	−9.44116e165	−0.114901
$901$	−5.90520e166	−0.674969
$902$	1.67290e167	1.79598
$903$	−1.40018e166	−0.141198
$904$	−6.40638e166	−0.606871
$905$	1.08208e167	0.962970
$906$	3.75860e166	0.314255
$907$	−3.24391e166	−0.254834	−0.127417	−	0.991849i	$-0.540669\pi$
$907$	−3.24391e166	−0.254834	−0.127417	+	0.991849i	$0.540669\pi$
$908$	−6.08803e166	−0.449393
$909$	−1.84607e167	−1.28053
$910$	−1.85512e166	−0.120930
$911$	5.14709e166	0.315336	0.157668	−	0.987492i	$-0.449602\pi$
$911$	5.14709e166	0.315336	0.157668	+	0.987492i	$0.449602\pi$
$912$	−4.77569e165	−0.0274997
$913$	4.96419e167	2.68689
$914$	1.19043e167	0.605678
$915$	1.93819e165	0.00927054
$916$	−1.06933e166	−0.0480857
$917$	−4.03428e166	−0.170569
$918$	−2.14311e167	−0.851986
$919$	−1.92419e167	−0.719318	−0.359659	−	0.933084i	$-0.617107\pi$
$919$	−1.92419e167	−0.719318	−0.359659	+	0.933084i	$0.617107\pi$
$920$	−9.17518e166	−0.322554
$921$	−1.07121e167	−0.354166
$922$	−3.82766e167	−1.19024
$923$	1.61583e167	0.472606
$924$	−1.15161e167	−0.316839
$925$	−9.57070e166	−0.247706
$926$	1.46303e167	0.356232
$927$	−1.70218e167	−0.389942
$928$	−6.06886e167	−1.30812
$929$	1.68288e167	0.341324	0.170662	−	0.985330i	$-0.445409\pi$
$929$	1.68288e167	0.341324	0.170662	+	0.985330i	$0.445409\pi$
$930$	−7.58943e166	−0.144851
$931$	1.49312e167	0.268186
$932$	4.41715e167	0.746695
$933$	−3.64566e166	−0.0580048
$934$	1.27305e167	0.190654
$935$	1.53284e168	2.16093
$936$	2.14332e167	0.284447
$937$	2.76919e167	0.345991	0.172996	−	0.984923i	$-0.444655\pi$
$937$	2.76919e167	0.345991	0.172996	+	0.984923i	$0.444655\pi$
$938$	−4.00498e167	−0.471129
$939$	−6.55109e166	−0.0725617
$940$	6.39695e165	0.00667190
$941$	−2.66300e167	−0.261552	−0.130776	−	0.991412i	$-0.541747\pi$
$941$	−2.66300e167	−0.261552	−0.130776	+	0.991412i	$0.541747\pi$
$942$	2.85864e167	0.264414
$943$	6.13862e167	0.534761
$944$	−1.23225e166	−0.0101107
$945$	−5.58196e167	−0.431409
$946$	7.98186e167	0.581105
$947$	−8.14913e167	−0.558904	−0.279452	−	0.960160i	$-0.590153\pi$
$947$	−8.14913e167	−0.558904	−0.279452	+	0.960160i	$0.590153\pi$
$948$	−8.51881e167	−0.550437
$949$	−1.05302e168	−0.641054
$950$	−1.31521e167	−0.0754419
$951$	−5.99535e167	−0.324052
$952$	1.53625e168	0.782481
$953$	−9.73279e167	−0.467184	−0.233592	−	0.972335i	$-0.575048\pi$
$953$	−9.73279e167	−0.467184	−0.233592	+	0.972335i	$0.575048\pi$
$954$	−5.03663e167	−0.227854
$955$	−3.33242e168	−1.42092
$956$	−2.39303e167	−0.0961784
$957$	3.75084e168	1.42103
$958$	−9.25097e167	−0.330397
$959$	3.41306e167	0.114919
$960$	1.10692e168	0.351392
$961$	−2.59690e168	−0.777292
$962$	7.78453e167	0.219705
$963$	1.70612e168	0.454071
$964$	5.03658e167	0.126410
$965$	−4.09540e168	−0.969401
$966$	3.34292e167	0.0746309
$967$	−4.82685e168	−1.01641	−0.508204	−	0.861237i	$-0.669690\pi$
$967$	−4.82685e168	−1.01641	−0.508204	+	0.861237i	$0.669690\pi$
$968$	1.31090e169	2.60383
$969$	1.55057e168	0.290534
$970$	−3.35513e168	−0.593071
$971$	2.67055e168	0.445363	0.222682	−	0.974891i	$-0.428519\pi$
$971$	2.67055e168	0.445363	0.222682	+	0.974891i	$0.428519\pi$
$972$	3.67190e168	0.577759
$973$	4.01080e168	0.595464
$974$	−5.50301e168	−0.770938
$975$	−4.83577e167	−0.0639300
$976$	−2.09078e166	−0.00260852
$977$	−9.63171e168	−1.13412	−0.567062	−	0.823675i	$-0.691920\pi$
$977$	−9.63171e168	−1.13412	−0.567062	+	0.823675i	$0.691920\pi$
$978$	−1.08707e168	−0.120813
$979$	2.05981e169	2.16075
$980$	−3.30035e168	−0.326803
$981$	−8.29233e167	−0.0775135
$982$	3.19980e168	0.282374
$983$	−9.57558e168	−0.797795	−0.398897	−	0.916996i	$-0.630607\pi$
$983$	−9.57558e168	−0.797795	−0.398897	+	0.916996i	$0.630607\pi$
$984$	−1.04401e169	−0.821258
$985$	8.63560e168	0.641424
$986$	−1.79272e169	−1.25738
$987$	−6.50515e166	−0.00430862
$988$	−1.35227e168	−0.0845857
$989$	2.92890e168	0.173027
$990$	1.30738e169	0.729481
$991$	−2.56102e169	−1.34974	−0.674872	−	0.737935i	$-0.735801\pi$
$991$	−2.56102e169	−1.34974	−0.674872	+	0.737935i	$0.735801\pi$
$992$	−8.99850e168	−0.447982
$993$	7.50277e166	0.00352849
$994$	9.87815e168	0.438879
$995$	−3.32046e169	−1.39378
$996$	−1.10996e169	−0.440206
$997$	5.08703e169	1.90629	0.953143	−	0.302521i	$-0.0978283\pi$
$997$	5.08703e169	1.90629	0.953143	+	0.302521i	$0.0978283\pi$
$998$	−1.31370e169	−0.465179
$999$	2.34233e169	0.783786

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.114.a.a.1.4	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.114.a.a.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-6.77248e16 q^{2} -4.98640e26 q^{3} -5.79795e33 q^{4} -2.60538e39 q^{5} +3.37703e43 q^{6} +3.08065e47 q^{7} +1.09596e51 q^{8} -5.73036e53 q^{9} +O(q^{10})\)	\(q-6.77248e16 q^{2} -4.98640e26 q^{3} -5.79795e33 q^{4} -2.60538e39 q^{5} +3.37703e43 q^{6} +3.08065e47 q^{7} +1.09596e51 q^{8} -5.73036e53 q^{9} +1.76449e56 q^{10} -1.29301e59 q^{11} +2.89109e60 q^{12} -3.41279e62 q^{13} -2.08637e64 q^{14} +1.29915e66 q^{15} -1.40142e67 q^{16} +4.55013e69 q^{17} +3.88088e70 q^{18} -6.83408e71 q^{19} +1.51059e73 q^{20} -1.53614e74 q^{21} +8.75687e75 q^{22} +3.21328e76 q^{23} -5.46489e77 q^{24} -2.84164e78 q^{25} +2.31131e79 q^{26} +6.95460e80 q^{27} -1.78615e81 q^{28} +5.81756e82 q^{29} -8.79845e82 q^{30} +8.62588e83 q^{31} -1.04320e85 q^{32} +6.44745e85 q^{33} -3.08157e86 q^{34} -8.02628e86 q^{35} +3.32244e87 q^{36} +3.36802e88 q^{37} +4.62836e88 q^{38} +1.70176e89 q^{39} -2.85539e90 q^{40} +1.91039e91 q^{41} +1.04035e91 q^{42} +9.11497e91 q^{43} +7.49679e92 q^{44} +1.49298e93 q^{45} -2.17619e93 q^{46} +4.23475e92 q^{47} +6.98806e93 q^{48} -2.18481e95 q^{49} +1.92449e95 q^{50} -2.26888e96 q^{51} +1.97872e96 q^{52} -1.29781e97 q^{53} -4.70999e97 q^{54} +3.36878e98 q^{55} +3.37627e98 q^{56} +3.40774e98 q^{57} -3.93993e99 q^{58} +8.79283e98 q^{59} -7.53239e99 q^{60} +1.49190e99 q^{61} -5.84186e100 q^{62} -1.76533e101 q^{63} +8.52036e101 q^{64} +8.89163e101 q^{65} -4.36652e102 q^{66} +1.91959e103 q^{67} -2.63814e103 q^{68} -1.60227e103 q^{69} +5.43578e103 q^{70} -4.73462e104 q^{71} -6.28024e104 q^{72} +3.08550e105 q^{73} -2.28099e105 q^{74} +1.41695e105 q^{75} +3.96236e105 q^{76} -3.98331e106 q^{77} -1.15251e106 q^{78} -2.94658e107 q^{79} +3.65124e106 q^{80} +1.24067e107 q^{81} -1.29381e108 q^{82} -3.83926e108 q^{83} +8.90644e107 q^{84} -1.18548e109 q^{85} -6.17309e108 q^{86} -2.90087e109 q^{87} -1.41708e110 q^{88} -1.59303e110 q^{89} -1.01112e110 q^{90} -1.05136e110 q^{91} -1.86305e110 q^{92} -4.30121e110 q^{93} -2.86797e109 q^{94} +1.78054e111 q^{95} +5.20180e111 q^{96} -1.90148e112 q^{97} +1.47966e112 q^{98} +7.40941e112 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 49\!\cdots\!32 q^{2}+ \cdots + 55\!\cdots\!77 q^{9}+O(q^{10}) \) 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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