LMFDB - Embedded newform 1.114.a.a.1.3

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			1.3
Root			$-2.30101e15$ 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)

$f(q)$	$=$	$q-1.09896e17 q^{2} +1.02220e27 q^{3} +1.69249e33 q^{4} +3.22293e39 q^{5} -1.12336e44 q^{6} -9.90814e46 q^{7} +9.55225e50 q^{8} +2.23221e53 q^{9} +O(q^{10})$	\(q-1.09896e17 q^{2} +1.02220e27 q^{3} +1.69249e33 q^{4} +3.22293e39 q^{5} -1.12336e44 q^{6} -9.90814e46 q^{7} +9.55225e50 q^{8} +2.23221e53 q^{9} -3.54186e56 q^{10} -1.44891e58 q^{11} +1.73007e60 q^{12} +9.01779e62 q^{13} +1.08886e64 q^{14} +3.29449e66 q^{15} -1.22551e68 q^{16} -4.96013e69 q^{17} -2.45311e70 q^{18} +6.55757e71 q^{19} +5.45479e72 q^{20} -1.01281e74 q^{21} +1.59229e75 q^{22} -1.18742e77 q^{23} +9.76435e77 q^{24} +7.57620e77 q^{25} -9.91017e79 q^{26} -6.11745e80 q^{27} -1.67695e80 q^{28} -6.34527e82 q^{29} -3.62050e83 q^{30} +9.38310e83 q^{31} +3.54823e84 q^{32} -1.48108e85 q^{33} +5.45098e86 q^{34} -3.19332e86 q^{35} +3.77801e86 q^{36} -3.13178e88 q^{37} -7.20650e88 q^{38} +9.21801e89 q^{39} +3.07862e90 q^{40} +1.61740e91 q^{41} +1.11304e91 q^{42} +2.72347e92 q^{43} -2.45227e91 q^{44} +7.19427e92 q^{45} +1.30492e94 q^{46} +3.25015e94 q^{47} -1.25272e95 q^{48} -3.03568e95 q^{49} -8.32593e94 q^{50} -5.07027e96 q^{51} +1.52625e96 q^{52} +1.52716e97 q^{53} +6.72282e97 q^{54} -4.66973e97 q^{55} -9.46451e97 q^{56} +6.70317e98 q^{57} +6.97318e99 q^{58} -1.63496e100 q^{59} +5.57590e99 q^{60} -8.94794e100 q^{61} -1.03116e101 q^{62} -2.21171e100 q^{63} +8.82708e101 q^{64} +2.90637e102 q^{65} +1.62764e102 q^{66} -2.77481e101 q^{67} -8.39500e102 q^{68} -1.21378e104 q^{69} +3.50933e103 q^{70} +1.17940e104 q^{71} +2.13227e104 q^{72} -2.38294e105 q^{73} +3.44170e105 q^{74} +7.74442e104 q^{75} +1.10986e105 q^{76} +1.43560e105 q^{77} -1.01302e107 q^{78} -5.15904e106 q^{79} -3.94973e107 q^{80} -8.08744e107 q^{81} -1.77746e108 q^{82} +4.82692e108 q^{83} -1.71418e107 q^{84} -1.59862e109 q^{85} -2.99298e109 q^{86} -6.48615e109 q^{87} -1.38403e109 q^{88} -2.35607e110 q^{89} -7.90620e109 q^{90} -8.93495e109 q^{91} -2.00970e110 q^{92} +9.59143e110 q^{93} -3.57178e111 q^{94} +2.11346e111 q^{95} +3.62701e111 q^{96} -3.11349e111 q^{97} +3.33609e112 q^{98} -3.23427e111 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.09896e17	−1.07842	−0.539208	−	0.842173i	$-0.681276\pi$
$2$	−1.09896e17	−1.07842	−0.539208	+	0.842173i	$0.681276\pi$
$3$	1.02220e27	1.12768	0.563841	−	0.825884i	$-0.309323\pi$
$3$	1.02220e27	1.12768	0.563841	+	0.825884i	$0.309323\pi$
$4$	1.69249e33	0.162981
$5$	3.22293e39	1.03859	0.519297	−	0.854594i	$-0.326194\pi$
$5$	3.22293e39	1.03859	0.519297	+	0.854594i	$0.326194\pi$
$6$	−1.12336e44	−1.21611
$7$	−9.90814e46	−0.176992	−0.0884958	−	0.996077i	$-0.528206\pi$
$7$	−9.90814e46	−0.176992	−0.0884958	+	0.996077i	$0.528206\pi$
$8$	9.55225e50	0.902655
$9$	2.23221e53	0.271665
$10$	−3.54186e56	−1.12004
$11$	−1.44891e58	−0.210065	−0.105033	−	0.994469i	$-0.533495\pi$
$11$	−1.44891e58	−0.210065	−0.105033	+	0.994469i	$0.533495\pi$
$12$	1.73007e60	0.183791
$13$	9.01779e62	1.04064	0.520320	−	0.853971i	$-0.325813\pi$
$13$	9.01779e62	1.04064	0.520320	+	0.853971i	$0.325813\pi$
$14$	1.08886e64	0.190871
$15$	3.29449e66	1.17120
$16$	−1.22551e68	−1.13642
$17$	−4.96013e69	−1.49668	−0.748341	−	0.663314i	$-0.769149\pi$
$17$	−4.96013e69	−1.49668	−0.748341	+	0.663314i	$0.769149\pi$
$18$	−2.45311e70	−0.292968
$19$	6.55757e71	0.369117	0.184559	−	0.982821i	$-0.440914\pi$
$19$	6.55757e71	0.369117	0.184559	+	0.982821i	$0.440914\pi$
$20$	5.45479e72	0.169271
$21$	−1.01281e74	−0.199590
$22$	1.59229e75	0.226538
$23$	−1.18742e77	−1.37082	−0.685411	−	0.728156i	$-0.740378\pi$
$23$	−1.18742e77	−1.37082	−0.685411	+	0.728156i	$0.740378\pi$
$24$	9.76435e77	1.01791
$25$	7.57620e77	0.0786758
$26$	−9.91017e79	−1.12224
$27$	−6.11745e80	−0.821329
$28$	−1.67695e80	−0.0288463
$29$	−6.34527e82	−1.50301	−0.751507	−	0.659725i	$-0.770673\pi$
$29$	−6.34527e82	−1.50301	−0.751507	+	0.659725i	$0.770673\pi$
$30$	−3.62050e83	−1.26304
$31$	9.38310e83	0.513346	0.256673	−	0.966498i	$-0.417374\pi$
$31$	9.38310e83	0.513346	0.256673	+	0.966498i	$0.417374\pi$
$32$	3.54823e84	0.322877
$33$	−1.48108e85	−0.236887
$34$	5.45098e86	1.61405
$35$	−3.19332e86	−0.183822
$36$	3.77801e86	0.0442763
$37$	−3.13178e88	−0.780538	−0.390269	−	0.920701i	$-0.627618\pi$
$37$	−3.13178e88	−0.780538	−0.390269	+	0.920701i	$0.627618\pi$
$38$	−7.20650e88	−0.398062
$39$	9.21801e89	1.17351
$40$	3.07862e90	0.937491
$41$	1.61740e91	1.22048	0.610239	−	0.792218i	$-0.291074\pi$
$41$	1.61740e91	1.22048	0.610239	+	0.792218i	$0.291074\pi$
$42$	1.11304e91	0.215241
$43$	2.72347e92	1.39366	0.696828	−	0.717238i	$-0.254594\pi$
$43$	2.72347e92	1.39366	0.696828	+	0.717238i	$0.254594\pi$
$44$	−2.45227e91	−0.0342367
$45$	7.19427e92	0.282150
$46$	1.30492e94	1.47832
$47$	3.25015e94	1.09238	0.546191	−	0.837660i	$-0.316077\pi$
$47$	3.25015e94	1.09238	0.546191	+	0.837660i	$0.316077\pi$
$48$	−1.25272e95	−1.28152
$49$	−3.03568e95	−0.968674
$50$	−8.32593e94	−0.0848452
$51$	−5.07027e96	−1.68778
$52$	1.52625e96	0.169605
$53$	1.52716e97	0.578492	0.289246	−	0.957255i	$-0.406595\pi$
$53$	1.52716e97	0.578492	0.289246	+	0.957255i	$0.406595\pi$
$54$	6.72282e97	0.885735
$55$	−4.66973e97	−0.218172
$56$	−9.46451e97	−0.159762
$57$	6.70317e98	0.416247
$58$	6.97318e99	1.62087
$59$	−1.63496e100	−1.44667	−0.723333	−	0.690499i	$-0.757391\pi$
$59$	−1.63496e100	−1.44667	−0.723333	+	0.690499i	$0.757391\pi$
$60$	5.57590e99	0.190884
$61$	−8.94794e100	−1.20389	−0.601946	−	0.798537i	$-0.705608\pi$
$61$	−8.94794e100	−1.20389	−0.601946	+	0.798537i	$0.705608\pi$
$62$	−1.03116e101	−0.553601
$63$	−2.21171e100	−0.0480825
$64$	8.82708e101	0.788222
$65$	2.90637e102	1.08080
$66$	1.62764e102	0.255462
$67$	−2.77481e101	−0.0186212	−0.00931060	−	0.999957i	$-0.502964\pi$
$67$	−2.77481e101	−0.0186212	−0.00931060	+	0.999957i	$0.502964\pi$
$68$	−8.39500e102	−0.243931
$69$	−1.21378e104	−1.54585
$70$	3.50933e103	0.198237
$71$	1.17940e104	0.298926	0.149463	−	0.988767i	$-0.452245\pi$
$71$	1.17940e104	0.298926	0.149463	+	0.988767i	$0.452245\pi$
$72$	2.13227e104	0.245220
$73$	−2.38294e105	−1.25710	−0.628552	−	0.777768i	$-0.716352\pi$
$73$	−2.38294e105	−1.25710	−0.628552	+	0.777768i	$0.716352\pi$
$74$	3.44170e105	0.841744
$75$	7.74442e104	0.0887212
$76$	1.10986e105	0.0601592
$77$	1.43560e105	0.0371798
$78$	−1.01302e107	−1.26553
$79$	−5.15904e106	−0.313790	−0.156895	−	0.987615i	$-0.550148\pi$
$79$	−5.15904e106	−0.313790	−0.156895	+	0.987615i	$0.550148\pi$
$80$	−3.94973e107	−1.18028
$81$	−8.08744e107	−1.19786
$82$	−1.77746e108	−1.31618
$83$	4.82692e108	1.80201	0.901006	−	0.433806i	$-0.142830\pi$
$83$	4.82692e108	1.80201	0.901006	+	0.433806i	$0.142830\pi$
$84$	−1.71418e107	−0.0325295
$85$	−1.59862e109	−1.55444
$86$	−2.99298e109	−1.50294
$87$	−6.48615e109	−1.69492
$88$	−1.38403e109	−0.189616
$89$	−2.35607e110	−1.70472	−0.852359	−	0.522957i	$-0.824829\pi$
$89$	−2.35607e110	−1.70472	−0.852359	+	0.522957i	$0.824829\pi$
$90$	−7.90620e109	−0.304275
$91$	−8.93495e109	−0.184185
$92$	−2.00970e110	−0.223418
$93$	9.59143e110	0.578891
$94$	−3.57178e111	−1.17804
$95$	2.11346e111	0.383363
$96$	3.62701e111	0.364103
$97$	−3.11349e111	−0.174038	−0.0870191	−	0.996207i	$-0.527734\pi$
$97$	−3.11349e111	−0.174038	−0.0870191	+	0.996207i	$0.527734\pi$
$98$	3.33609e112	1.04463
$99$	−3.23427e111	−0.0570674
$100$	1.28227e111	0.0128227
$101$	2.24849e113	1.28155	0.640773	−	0.767730i	$-0.278614\pi$
$101$	2.24849e113	1.28155	0.640773	+	0.767730i	$0.278614\pi$
$102$	5.57201e113	1.82013
$103$	1.20858e113	0.227495	0.113747	−	0.993510i	$-0.463715\pi$
$103$	1.20858e113	0.227495	0.113747	+	0.993510i	$0.463715\pi$
$104$	8.61402e113	0.939338
$105$	−3.26423e113	−0.207293
$106$	−1.67828e114	−0.623855
$107$	−7.64190e114	−1.67116	−0.835579	−	0.549370i	$-0.814868\pi$
$107$	−7.64190e114	−1.67116	−0.835579	+	0.549370i	$0.814868\pi$
$108$	−1.03537e114	−0.133861
$109$	4.79096e114	0.367981	0.183991	−	0.982928i	$-0.441098\pi$
$109$	4.79096e114	0.367981	0.183991	+	0.982928i	$0.441098\pi$
$110$	5.13183e114	0.235280
$111$	−3.20132e115	−0.880198
$112$	1.21425e115	0.201137
$113$	−8.45524e115	−0.847606	−0.423803	−	0.905754i	$-0.639305\pi$
$113$	−8.45524e115	−0.847606	−0.423803	+	0.905754i	$0.639305\pi$
$114$	−7.36650e115	−0.448887
$115$	−3.82697e116	−1.42373
$116$	−1.07393e116	−0.244963
$117$	2.01296e116	0.282706
$118$	1.79675e117	1.56011
$119$	4.91457e116	0.264900
$120$	3.14698e117	1.05719
$121$	−4.54751e117	−0.955873
$122$	9.83341e117	1.29830
$123$	1.65331e118	1.37631
$124$	1.58808e117	0.0836658
$125$	−2.85939e118	−0.956881
$126$	2.43058e117	0.0518529
$127$	−4.50572e118	−0.614971	−0.307485	−	0.951553i	$-0.599487\pi$
$127$	−4.50572e118	−0.614971	−0.307485	+	0.951553i	$0.599487\pi$
$128$	−1.33853e119	−1.17291
$129$	2.78394e119	1.57160
$130$	−3.19398e119	−1.16555
$131$	−1.94923e119	−0.461355	−0.230677	−	0.973030i	$-0.574094\pi$
$131$	−1.94923e119	−0.461355	−0.230677	+	0.973030i	$0.574094\pi$
$132$	−2.50672e118	−0.0386081
$133$	−6.49733e118	−0.0653307
$134$	3.04940e118	0.0200814
$135$	−1.97161e120	−0.853027
$136$	−4.73805e120	−1.35099
$137$	7.58755e119	0.143018	0.0715088	−	0.997440i	$-0.477219\pi$
$137$	7.58755e119	0.143018	0.0715088	+	0.997440i	$0.477219\pi$
$138$	1.33390e121	1.66707
$139$	2.28981e121	1.90310	0.951552	−	0.307489i	$-0.0994887\pi$
$139$	2.28981e121	1.90310	0.951552	+	0.307489i	$0.0994887\pi$
$140$	−5.40468e119	−0.0299596
$141$	3.32232e121	1.23186
$142$	−1.29611e121	−0.322367
$143$	−1.30659e121	−0.218602
$144$	−2.73560e121	−0.308725
$145$	−2.04503e122	−1.56102
$146$	2.61875e122	1.35568
$147$	−3.10308e122	−1.09236
$148$	−5.30052e121	−0.127213
$149$	1.83806e121	0.0301534	0.0150767	−	0.999886i	$-0.495201\pi$
$149$	1.83806e121	0.0301534	0.0150767	+	0.999886i	$0.495201\pi$
$150$	−8.51079e121	−0.0956784
$151$	−1.34553e123	−1.03919	−0.519596	−	0.854412i	$-0.673918\pi$
$151$	−1.34553e123	−1.03919	−0.519596	+	0.854412i	$0.673918\pi$
$152$	6.26396e122	0.333186
$153$	−1.10721e123	−0.406596
$154$	−1.57766e122	−0.0400953
$155$	3.02411e123	0.533158
$156$	1.56014e123	0.191260
$157$	3.31978e123	0.283648	0.141824	−	0.989892i	$-0.454703\pi$
$157$	3.31978e123	0.283648	0.141824	+	0.989892i	$0.454703\pi$
$158$	5.66957e123	0.338396
$159$	1.56107e124	0.652354
$160$	1.14357e124	0.335338
$161$	1.17651e124	0.242624
$162$	8.88775e124	1.29179
$163$	−1.09702e125	−1.12620	−0.563099	−	0.826390i	$-0.690391\pi$
$163$	−1.09702e125	−1.12620	−0.563099	+	0.826390i	$0.690391\pi$
$164$	2.73744e124	0.198915
$165$	−4.77341e124	−0.246029
$166$	−5.30458e125	−1.94332
$167$	−4.94497e125	−1.29028	−0.645139	−	0.764065i	$-0.723200\pi$
$167$	−4.94497e125	−1.29028	−0.645139	+	0.764065i	$0.723200\pi$
$168$	−9.67465e124	−0.180161
$169$	6.22756e124	0.0829314
$170$	1.75681e126	1.67634
$171$	1.46379e125	0.100276
$172$	4.60946e125	0.227140
$173$	−4.28581e126	−1.52205	−0.761023	−	0.648725i	$-0.775303\pi$
$173$	−4.28581e126	−1.52205	−0.761023	+	0.648725i	$0.775303\pi$
$174$	7.12801e126	1.82783
$175$	−7.50661e124	−0.0139250
$176$	1.77565e126	0.238722
$177$	−1.67126e127	−1.63138
$178$	2.58922e127	1.83839
$179$	−1.38227e126	−0.0715151	−0.0357576	−	0.999360i	$-0.511384\pi$
$179$	−1.38227e126	−0.0715151	−0.0357576	+	0.999360i	$0.511384\pi$
$180$	1.21763e126	0.0459851
$181$	5.55145e127	1.53309	0.766544	−	0.642192i	$-0.221975\pi$
$181$	5.55145e127	1.53309	0.766544	+	0.642192i	$0.221975\pi$
$182$	9.81913e126	0.198628
$183$	−9.14661e127	−1.35761
$184$	−1.13425e128	−1.23738
$185$	−1.00935e128	−0.810661
$186$	−1.05406e128	−0.624286
$187$	7.18678e127	0.314401
$188$	5.50086e127	0.178038
$189$	6.06125e127	0.145368
$190$	−2.32260e128	−0.413425
$191$	−1.26256e128	−0.167058	−0.0835288	−	0.996505i	$-0.526619\pi$
$191$	−1.26256e128	−0.167058	−0.0835288	+	0.996505i	$0.526619\pi$
$192$	9.02308e128	0.888864
$193$	1.25975e129	0.925330	0.462665	−	0.886533i	$-0.346893\pi$
$193$	1.25975e129	0.925330	0.462665	+	0.886533i	$0.346893\pi$
$194$	3.42160e128	0.187686
$195$	2.97090e129	1.21880
$196$	−5.13787e128	−0.157876
$197$	−1.67043e129	−0.385022	−0.192511	−	0.981295i	$-0.561663\pi$
$197$	−1.67043e129	−0.385022	−0.192511	+	0.981295i	$0.561663\pi$
$198$	3.55433e128	0.0615424
$199$	−5.90848e129	−0.769621	−0.384810	−	0.922996i	$-0.625733\pi$
$199$	−5.90848e129	−0.769621	−0.384810	+	0.922996i	$0.625733\pi$
$200$	7.23698e128	0.0710170
$201$	−2.83642e128	−0.0209988
$202$	−2.47100e130	−1.38204
$203$	6.28698e129	0.266021
$204$	−8.58139e129	−0.275076
$205$	5.21277e130	1.26758
$206$	−1.32818e130	−0.245334
$207$	−2.65057e130	−0.372405
$208$	−1.10514e131	−1.18260
$209$	−9.50132e129	−0.0775387
$210$	3.58725e130	0.223548
$211$	7.76482e130	0.369975	0.184988	−	0.982741i	$-0.440776\pi$
$211$	7.76482e130	0.369975	0.184988	+	0.982741i	$0.440776\pi$
$212$	2.58470e130	0.0942833
$213$	1.20559e131	0.337094
$214$	8.39812e131	1.80220
$215$	8.77756e131	1.44744
$216$	−5.84354e131	−0.741377
$217$	−9.29690e130	−0.0908580
$218$	−5.26507e131	−0.396837
$219$	−2.43585e132	−1.41761
$220$	−7.90348e130	−0.0355580
$221$	−4.47294e132	−1.55751
$222$	3.51811e132	0.949220
$223$	−3.31237e132	−0.693288	−0.346644	−	0.937997i	$-0.612679\pi$
$223$	−3.31237e132	−0.693288	−0.346644	+	0.937997i	$0.612679\pi$
$224$	−3.51563e131	−0.0571466
$225$	1.69117e131	0.0213735
$226$	9.29195e132	0.914072
$227$	−4.94248e132	−0.378864	−0.189432	−	0.981894i	$-0.560665\pi$
$227$	−4.94248e132	−0.378864	−0.189432	+	0.981894i	$0.560665\pi$
$228$	1.13451e132	0.0678404
$229$	−1.00433e132	−0.0468998	−0.0234499	−	0.999725i	$-0.507465\pi$
$229$	−1.00433e132	−0.0468998	−0.0234499	+	0.999725i	$0.507465\pi$
$230$	4.20568e133	1.53537
$231$	1.46747e132	0.0419270
$232$	−6.06116e133	−1.35670
$233$	6.53648e133	1.14745	0.573726	−	0.819047i	$-0.305497\pi$
$233$	6.53648e133	1.14745	0.573726	+	0.819047i	$0.305497\pi$
$234$	−2.21216e133	−0.304874
$235$	1.04750e134	1.13454
$236$	−2.76716e133	−0.235779
$237$	−5.27359e133	−0.353855
$238$	−5.40091e133	−0.285673
$239$	−5.72257e133	−0.238842	−0.119421	−	0.992844i	$-0.538104\pi$
$239$	−5.72257e133	−0.238842	−0.119421	+	0.992844i	$0.538104\pi$
$240$	−4.03743e134	−1.33098
$241$	1.53134e134	0.399126	0.199563	−	0.979885i	$-0.436048\pi$
$241$	1.53134e134	0.399126	0.199563	+	0.979885i	$0.436048\pi$
$242$	4.99752e134	1.03083
$243$	−3.24043e134	−0.529479
$244$	−1.51443e134	−0.196212
$245$	−9.78378e134	−1.00606
$246$	−1.81692e135	−1.48423
$247$	5.91348e134	0.384118
$248$	8.96297e134	0.463374
$249$	4.93409e135	2.03210
$250$	3.14235e135	1.03192
$251$	1.06766e135	0.279812	0.139906	−	0.990165i	$-0.455320\pi$
$251$	1.06766e135	0.279812	0.139906	+	0.990165i	$0.455320\pi$
$252$	−3.74330e133	−0.00783654
$253$	1.72046e135	0.287962
$254$	4.95160e135	0.663194
$255$	−1.63411e136	−1.75292
$256$	5.54330e135	0.476661
$257$	−8.75848e135	−0.604237	−0.302118	−	0.953270i	$-0.597694\pi$
$257$	−8.75848e135	−0.604237	−0.302118	+	0.953270i	$0.597694\pi$
$258$	−3.05944e136	−1.69484
$259$	3.10301e135	0.138149
$260$	4.91901e135	0.176150
$261$	−1.41640e136	−0.408317
$262$	2.14212e136	0.497533
$263$	3.38428e136	0.633820	0.316910	−	0.948456i	$-0.397355\pi$
$263$	3.38428e136	0.633820	0.316910	+	0.948456i	$0.397355\pi$
$264$	−1.41476e136	−0.213827
$265$	4.92192e136	0.600818
$266$	7.14030e135	0.0704537
$267$	−2.40838e137	−1.92238
$268$	−4.69635e134	−0.00303490
$269$	2.32178e137	1.21568	0.607838	−	0.794061i	$-0.292037\pi$
$269$	2.32178e137	1.21568	0.607838	+	0.794061i	$0.292037\pi$
$270$	2.16672e137	0.919918
$271$	−2.07635e137	−0.715379	−0.357690	−	0.933841i	$-0.616435\pi$
$271$	−2.07635e137	−0.715379	−0.357690	+	0.933841i	$0.616435\pi$
$272$	6.07870e137	1.70086
$273$	−9.13333e136	−0.207702
$274$	−8.33840e136	−0.154233
$275$	−1.09772e136	−0.0165270
$276$	−2.05432e137	−0.251945
$277$	8.77859e137	0.877643	0.438822	−	0.898574i	$-0.355396\pi$
$277$	8.77859e137	0.877643	0.438822	+	0.898574i	$0.355396\pi$
$278$	−2.51640e138	−2.05234
$279$	2.09451e137	0.139458
$280$	−3.05034e137	−0.165928
$281$	5.38805e136	0.0239621	0.0119810	−	0.999928i	$-0.496186\pi$
$281$	5.38805e136	0.0239621	0.0119810	+	0.999928i	$0.496186\pi$
$282$	−3.65109e138	−1.32846
$283$	9.40247e136	0.0280097	0.0140049	−	0.999902i	$-0.495542\pi$
$283$	9.40247e136	0.0280097	0.0140049	+	0.999902i	$0.495542\pi$
$284$	1.99613e137	0.0487194
$285$	2.16038e138	0.432311
$286$	1.43589e138	0.235744
$287$	−1.60254e138	−0.216014
$288$	7.92040e137	0.0877145
$289$	1.36198e139	1.24006
$290$	2.24741e139	1.68343
$291$	−3.18262e138	−0.196260
$292$	−4.03311e138	−0.204884
$293$	−1.34822e139	−0.564598	−0.282299	−	0.959326i	$-0.591097\pi$
$293$	−1.34822e139	−0.564598	−0.282299	+	0.959326i	$0.591097\pi$
$294$	3.41016e139	1.17801
$295$	−5.26936e139	−1.50250
$296$	−2.99156e139	−0.704556
$297$	8.86361e138	0.172533
$298$	−2.01995e138	−0.0325179
$299$	−1.07079e140	−1.42653
$300$	1.31074e138	0.0144599
$301$	−2.69846e139	−0.246665
$302$	1.47868e140	1.12068
$303$	2.29842e140	1.44518
$304$	−8.03638e139	−0.419472
$305$	−2.88386e140	−1.25035
$306$	1.21678e140	0.438480
$307$	−2.83431e140	−0.849432	−0.424716	−	0.905327i	$-0.639626\pi$
$307$	−2.83431e140	−0.849432	−0.424716	+	0.905327i	$0.639626\pi$
$308$	2.42974e138	0.00605961
$309$	1.23541e140	0.256542
$310$	−3.32336e140	−0.574966
$311$	8.38794e140	1.20974	0.604872	−	0.796323i	$-0.293224\pi$
$311$	8.38794e140	1.20974	0.604872	+	0.796323i	$0.293224\pi$
$312$	8.80528e140	1.05927
$313$	1.50310e141	1.50915	0.754575	−	0.656214i	$-0.227843\pi$
$313$	1.50310e141	1.50915	0.754575	+	0.656214i	$0.227843\pi$
$314$	−3.64830e140	−0.305890
$315$	−7.12818e139	−0.0499382
$316$	−8.73165e139	−0.0511418
$317$	−3.24738e141	−1.59105	−0.795526	−	0.605919i	$-0.792806\pi$
$317$	−3.24738e141	−1.59105	−0.795526	+	0.605919i	$0.792806\pi$
$318$	−1.71555e141	−0.703509
$319$	9.19371e140	0.315731
$320$	2.84491e141	0.818642
$321$	−7.81157e141	−1.88453
$322$	−1.29294e141	−0.261650
$323$	−3.25264e141	−0.552451
$324$	−1.36879e141	−0.195229
$325$	6.83206e140	0.0818731
$326$	1.20558e142	1.21451
$327$	4.89734e141	0.414966
$328$	1.54498e142	1.10167
$329$	−3.22030e141	−0.193343
$330$	5.24578e141	0.265321
$331$	−1.44856e142	−0.617527	−0.308764	−	0.951139i	$-0.599915\pi$
$331$	−1.44856e142	−0.617527	−0.308764	+	0.951139i	$0.599915\pi$
$332$	8.16953e141	0.293694
$333$	−6.99081e141	−0.212045
$334$	5.43432e142	1.39146
$335$	−8.94303e140	−0.0193398
$336$	1.24121e142	0.226818
$337$	−8.96357e142	−1.38481	−0.692407	−	0.721507i	$-0.743450\pi$
$337$	−8.96357e142	−1.38481	−0.692407	+	0.721507i	$0.743450\pi$
$338$	−6.84383e141	−0.0894346
$339$	−8.64297e142	−0.955829
$340$	−2.70565e142	−0.253345
$341$	−1.35952e142	−0.107836
$342$	−1.60864e142	−0.108140
$343$	6.11286e142	0.348439
$344$	2.60153e143	1.25799
$345$	−3.91194e143	−1.60551
$346$	4.70992e143	1.64140
$347$	−5.61968e143	−1.66378	−0.831890	−	0.554941i	$-0.812741\pi$
$347$	−5.61968e143	−1.66378	−0.831890	+	0.554941i	$0.812741\pi$
$348$	−1.09778e143	−0.276240
$349$	5.89742e143	1.26190	0.630950	−	0.775823i	$-0.282665\pi$
$349$	5.89742e143	1.26190	0.630950	+	0.775823i	$0.282665\pi$
$350$	8.24944e141	0.0150169
$351$	−5.51658e143	−0.854708
$352$	−5.14105e142	−0.0678253
$353$	3.96686e143	0.445837	0.222919	−	0.974837i	$-0.428442\pi$
$353$	3.96686e143	0.445837	0.222919	+	0.974837i	$0.428442\pi$
$354$	1.83665e144	1.75931
$355$	3.80112e143	0.310463
$356$	−3.98763e143	−0.277837
$357$	5.02369e143	0.298723
$358$	1.51906e143	0.0771231
$359$	1.80362e143	0.0782185	0.0391093	−	0.999235i	$-0.487548\pi$
$359$	1.80362e143	0.0782185	0.0391093	+	0.999235i	$0.487548\pi$
$360$	6.87215e143	0.254684
$361$	−2.72613e144	−0.863752
$362$	−6.10081e144	−1.65331
$363$	−4.64848e144	−1.07792
$364$	−1.51223e143	−0.0300186
$365$	−7.68004e144	−1.30562
$366$	1.00517e145	1.46406
$367$	−6.91439e144	−0.863220	−0.431610	−	0.902060i	$-0.642054\pi$
$367$	−6.91439e144	−0.863220	−0.431610	+	0.902060i	$0.642054\pi$
$368$	1.45520e145	1.55783
$369$	3.61039e144	0.331561
$370$	1.10923e145	0.874230
$371$	−1.51313e144	−0.102388
$372$	1.62334e144	0.0943484
$373$	2.65829e145	1.32756	0.663778	−	0.747929i	$-0.268952\pi$
$373$	2.65829e145	1.32756	0.663778	+	0.747929i	$0.268952\pi$
$374$	−7.89797e144	−0.339055
$375$	−2.92288e145	−1.07906
$376$	3.10463e145	0.986044
$377$	−5.72203e145	−1.56410
$378$	−6.66106e144	−0.156768
$379$	7.49619e145	1.51959	0.759793	−	0.650165i	$-0.225300\pi$
$379$	7.49619e145	1.51959	0.759793	+	0.650165i	$0.225300\pi$
$380$	3.57701e144	0.0624809
$381$	−4.60577e145	−0.693491
$382$	1.38750e145	0.180157
$383$	2.05336e145	0.230004	0.115002	−	0.993365i	$-0.463313\pi$
$383$	2.05336e145	0.230004	0.115002	+	0.993365i	$0.463313\pi$
$384$	−1.36825e146	−1.32267
$385$	4.62683e144	0.0386147
$386$	−1.38441e146	−0.997890
$387$	6.07938e145	0.378608
$388$	−5.26956e144	−0.0283649
$389$	1.80014e146	0.837824	0.418912	−	0.908027i	$-0.362412\pi$
$389$	1.80014e146	0.837824	0.418912	+	0.908027i	$0.362412\pi$
$390$	−3.26489e146	−1.31437
$391$	5.88976e146	2.05168
$392$	−2.89976e146	−0.874378
$393$	−1.99251e146	−0.520261
$394$	1.83573e146	0.415214
$395$	−1.66272e146	−0.325900
$396$	−5.47399e144	−0.00930092
$397$	1.09803e147	1.61790	0.808950	−	0.587878i	$-0.200036\pi$
$397$	1.09803e147	1.61790	0.808950	+	0.587878i	$0.200036\pi$
$398$	6.49317e146	0.829971
$399$	−6.64160e145	−0.0736722
$400$	−9.28472e145	−0.0894086
$401$	−7.71584e146	−0.645247	−0.322623	−	0.946527i	$-0.604565\pi$
$401$	−7.71584e146	−0.645247	−0.322623	+	0.946527i	$0.604565\pi$
$402$	3.11711e145	0.0226454
$403$	8.46148e146	0.534209
$404$	3.80556e146	0.208868
$405$	−2.60652e147	−1.24409
$406$	−6.90913e146	−0.286881
$407$	4.53766e146	0.163964
$408$	−4.84325e147	−1.52348
$409$	8.04403e146	0.220347	0.110173	−	0.993912i	$-0.464859\pi$
$409$	8.04403e146	0.220347	0.110173	+	0.993912i	$0.464859\pi$
$410$	−5.72861e147	−1.36698
$411$	7.75602e146	0.161278
$412$	2.04551e146	0.0370774
$413$	1.61994e147	0.256048
$414$	2.91287e147	0.401607
$415$	1.55568e148	1.87156
$416$	3.19971e147	0.335999
$417$	2.34065e148	2.14609
$418$	1.04415e147	0.0836190
$419$	−2.75490e148	−1.92759	−0.963793	−	0.266653i	$-0.914082\pi$
$419$	−2.75490e148	−1.92759	−0.963793	+	0.266653i	$0.914082\pi$
$420$	−5.52468e146	−0.0337849
$421$	−1.26392e148	−0.675742	−0.337871	−	0.941192i	$-0.609707\pi$
$421$	−1.26392e148	−0.675742	−0.337871	+	0.941192i	$0.609707\pi$
$422$	−8.53321e147	−0.398987
$423$	7.25504e147	0.296762
$424$	1.45878e148	0.522178
$425$	−3.75790e147	−0.117753
$426$	−1.32489e148	−0.363527
$427$	8.86574e147	0.213079
$428$	−1.29339e148	−0.272367
$429$	−1.33560e148	−0.246514
$430$	−9.64617e148	−1.56094
$431$	1.34529e149	1.90920	0.954600	−	0.297890i	$-0.0962829\pi$
$431$	1.34529e149	1.90920	0.954600	+	0.297890i	$0.0962829\pi$
$432$	7.49700e148	0.933374
$433$	−1.10710e149	−1.20954	−0.604770	−	0.796400i	$-0.706735\pi$
$433$	−1.10710e149	−1.20954	−0.604770	+	0.796400i	$0.706735\pi$
$434$	1.02169e148	0.0979828
$435$	−2.09044e149	−1.76033
$436$	8.10867e147	0.0599740
$437$	−7.78658e148	−0.505995
$438$	2.67689e149	1.52878
$439$	2.97638e148	0.149432	0.0747160	−	0.997205i	$-0.476195\pi$
$439$	2.97638e148	0.149432	0.0747160	+	0.997205i	$0.476195\pi$
$440$	−4.46064e148	−0.196934
$441$	−6.77629e148	−0.263155
$442$	4.91558e149	1.67964
$443$	5.95192e149	1.78997	0.894987	−	0.446093i	$-0.147185\pi$
$443$	5.95192e149	1.78997	0.894987	+	0.446093i	$0.147185\pi$
$444$	−5.41821e148	−0.143456
$445$	−7.59344e149	−1.77051
$446$	3.64015e149	0.747653
$447$	1.87887e148	0.0340034
$448$	−8.74600e148	−0.139509
$449$	−4.89256e149	−0.688047	−0.344023	−	0.938961i	$-0.611790\pi$
$449$	−4.89256e149	−0.688047	−0.344023	+	0.938961i	$0.611790\pi$
$450$	−1.85853e148	−0.0230495
$451$	−2.34346e149	−0.256380
$452$	−1.43104e149	−0.138144
$453$	−1.37541e150	−1.17188
$454$	5.43157e149	0.408573
$455$	−2.87967e149	−0.191293
$456$	6.40304e149	0.375727
$457$	−3.60405e150	−1.86864	−0.934319	−	0.356439i	$-0.883991\pi$
$457$	−3.60405e150	−1.86864	−0.934319	+	0.356439i	$0.883991\pi$
$458$	1.10371e149	0.0505775
$459$	3.03434e150	1.22927
$460$	−6.47712e149	−0.232041
$461$	1.17618e150	0.372711	0.186356	−	0.982482i	$-0.440332\pi$
$461$	1.17618e150	0.372711	0.186356	+	0.982482i	$0.440332\pi$
$462$	−1.61269e149	−0.0452147
$463$	3.85891e150	0.957499	0.478749	−	0.877952i	$-0.341090\pi$
$463$	3.85891e150	0.957499	0.478749	+	0.877952i	$0.341090\pi$
$464$	7.77620e150	1.70805
$465$	3.09125e150	0.601232
$466$	−7.18332e150	−1.23743
$467$	3.34795e150	0.510947	0.255473	−	0.966816i	$-0.417769\pi$
$467$	3.34795e150	0.510947	0.255473	+	0.966816i	$0.417769\pi$
$468$	3.40693e149	0.0460757
$469$	2.74932e148	0.00329580
$470$	−1.15116e151	−1.22351
$471$	3.39349e150	0.319864
$472$	−1.56176e151	−1.30584
$473$	−3.94606e150	−0.292759
$474$	5.79546e150	0.381603
$475$	4.96815e149	0.0290406
$476$	8.31788e149	0.0431737
$477$	3.40894e150	0.157156
$478$	6.28887e150	0.257571
$479$	−2.92545e150	−0.106472	−0.0532361	−	0.998582i	$-0.516954\pi$
$479$	−2.92545e150	−0.106472	−0.0532361	+	0.998582i	$0.516954\pi$
$480$	1.16896e151	0.378155
$481$	−2.82417e151	−0.812259
$482$	−1.68288e151	−0.430423
$483$	1.20263e151	0.273603
$484$	−7.69663e150	−0.155789
$485$	−1.00346e151	−0.180755
$486$	3.56110e151	0.570998
$487$	6.06381e151	0.865684	0.432842	−	0.901470i	$-0.357511\pi$
$487$	6.06381e151	0.865684	0.432842	+	0.901470i	$0.357511\pi$
$488$	−8.54730e151	−1.08670
$489$	−1.12138e152	−1.26999
$490$	1.07520e152	1.08495
$491$	1.63043e152	1.46622	0.733110	−	0.680110i	$-0.238068\pi$
$491$	1.63043e152	1.46622	0.733110	+	0.680110i	$0.238068\pi$
$492$	2.79822e151	0.224313
$493$	3.14734e152	2.24953
$494$	−6.49866e151	−0.414239
$495$	−1.04238e151	−0.0592698
$496$	−1.14991e152	−0.583376
$497$	−1.16857e151	−0.0529075
$498$	−5.42236e152	−2.19144
$499$	−4.84545e150	−0.0174845	−0.00874224	−	0.999962i	$-0.502783\pi$
$499$	−4.84545e150	−0.0174845	−0.00874224	+	0.999962i	$0.502783\pi$
$500$	−4.83950e151	−0.155954
$501$	−5.05477e152	−1.45502
$502$	−1.17331e152	−0.301753
$503$	1.82127e152	0.418584	0.209292	−	0.977853i	$-0.432884\pi$
$503$	1.82127e152	0.418584	0.209292	+	0.977853i	$0.432884\pi$
$504$	−2.11268e151	−0.0434019
$505$	7.24674e152	1.33100
$506$	−1.89071e152	−0.310543
$507$	6.36583e151	0.0935202
$508$	−7.62591e151	−0.100229
$509$	−9.87916e152	−1.16189	−0.580946	−	0.813942i	$-0.697317\pi$
$509$	−9.87916e152	−1.16189	−0.580946	+	0.813942i	$0.697317\pi$
$510$	1.79582e153	1.89037
$511$	2.36105e152	0.222497
$512$	7.80822e152	0.658870
$513$	−4.01156e152	−0.303167
$514$	9.62520e152	0.651619
$515$	3.89516e152	0.236274
$516$	4.71181e152	0.256141
$517$	−4.70917e152	−0.229472
$518$	−3.41008e152	−0.148982
$519$	−4.38097e153	−1.71638
$520$	2.77624e153	0.975590
$521$	−9.21635e152	−0.290555	−0.145277	−	0.989391i	$-0.546407\pi$
$521$	−9.21635e152	−0.290555	−0.145277	+	0.989391i	$0.546407\pi$
$522$	1.55656e153	0.440335
$523$	−2.65235e153	−0.673420	−0.336710	−	0.941608i	$-0.609314\pi$
$523$	−2.65235e153	−0.673420	−0.336710	+	0.941608i	$0.609314\pi$
$524$	−3.29906e152	−0.0751922
$525$	−7.67328e151	−0.0157029
$526$	−3.71918e153	−0.683522
$527$	−4.65414e153	−0.768316
$528$	1.81508e153	0.269202
$529$	6.59645e153	0.879154
$530$	−5.40898e153	−0.647931
$531$	−3.64958e153	−0.393009
$532$	−1.09967e152	−0.0106477
$533$	1.45854e154	1.27008
$534$	2.64671e154	2.07312
$535$	−2.46293e154	−1.73565
$536$	−2.65057e152	−0.0168085
$537$	−1.41297e153	−0.0806463
$538$	−2.55154e154	−1.31100
$539$	4.39842e153	0.203485
$540$	−3.33694e153	−0.139027
$541$	2.64425e154	0.992333	0.496166	−	0.868227i	$-0.334741\pi$
$541$	2.64425e154	0.992333	0.496166	+	0.868227i	$0.334741\pi$
$542$	2.28182e154	0.771476
$543$	5.67471e154	1.72883
$544$	−1.75997e154	−0.483244
$545$	1.54409e154	0.382183
$546$	1.00371e154	0.223989
$547$	−8.15592e154	−1.64130	−0.820652	−	0.571428i	$-0.806390\pi$
$547$	−8.15592e154	−1.64130	−0.820652	+	0.571428i	$0.806390\pi$
$548$	1.28419e153	0.0233092
$549$	−1.99737e154	−0.327055
$550$	1.20635e153	0.0178230
$551$	−4.16096e154	−0.554789
$552$	−1.15944e155	−1.39537
$553$	5.11165e153	0.0555382
$554$	−9.64731e154	−0.946465
$555$	−1.03176e155	−0.914168
$556$	3.87548e154	0.310170
$557$	2.06136e155	1.49051	0.745257	−	0.666778i	$-0.232327\pi$
$557$	2.06136e155	1.49051	0.745257	+	0.666778i	$0.232327\pi$
$558$	−2.30178e154	−0.150394
$559$	2.45597e155	1.45029
$560$	3.91345e154	0.208899
$561$	7.34635e154	0.354544
$562$	−5.92124e153	−0.0258411
$563$	3.49398e155	1.37910	0.689551	−	0.724237i	$-0.257808\pi$
$563$	3.49398e155	1.37910	0.689551	+	0.724237i	$0.257808\pi$
$564$	5.62300e154	0.200770
$565$	−2.72506e155	−0.880317
$566$	−1.03329e154	−0.0302061
$567$	8.01314e154	0.212012
$568$	1.12659e155	0.269827
$569$	−3.14953e155	−0.682972	−0.341486	−	0.939887i	$-0.610930\pi$
$569$	−3.14953e155	−0.682972	−0.341486	+	0.939887i	$0.610930\pi$
$570$	−2.37417e155	−0.466211
$571$	−3.77989e155	−0.672264	−0.336132	−	0.941815i	$-0.609119\pi$
$571$	−3.77989e155	−0.672264	−0.336132	+	0.941815i	$0.609119\pi$
$572$	−2.21140e154	−0.0356280
$573$	−1.29059e155	−0.188388
$574$	1.76113e155	0.232953
$575$	−8.99612e154	−0.107851
$576$	1.97039e155	0.214133
$577$	3.28632e155	0.323800	0.161900	−	0.986807i	$-0.448238\pi$
$577$	3.28632e155	0.323800	0.161900	+	0.986807i	$0.448238\pi$
$578$	−1.49675e156	−1.33730
$579$	1.28772e156	1.04348
$580$	−3.46121e155	−0.254417
$581$	−4.78258e155	−0.318941
$582$	3.49757e155	0.211650
$583$	−2.21271e155	−0.121521
$584$	−2.27624e156	−1.13473
$585$	6.48764e155	0.293616
$586$	1.48163e156	0.608872
$587$	1.61595e156	0.603080	0.301540	−	0.953454i	$-0.402499\pi$
$587$	1.61595e156	0.603080	0.301540	+	0.953454i	$0.402499\pi$
$588$	−5.25195e155	−0.178033
$589$	6.15303e155	0.189485
$590$	5.79080e156	1.62032
$591$	−1.70752e156	−0.434182
$592$	3.83803e156	0.887017
$593$	−5.53946e156	−1.16380	−0.581899	−	0.813261i	$-0.697690\pi$
$593$	−5.53946e156	−1.16380	−0.581899	+	0.813261i	$0.697690\pi$
$594$	−9.74074e155	−0.186062
$595$	1.58393e156	0.275124
$596$	3.11091e154	0.00491443
$597$	−6.03967e156	−0.867887
$598$	1.17675e157	1.53840
$599$	−8.37445e156	−0.996186	−0.498093	−	0.867124i	$-0.665966\pi$
$599$	−8.37445e156	−0.996186	−0.498093	+	0.867124i	$0.665966\pi$
$600$	7.39766e155	0.0800846
$601$	−6.56949e155	−0.0647327	−0.0323664	−	0.999476i	$-0.510304\pi$
$601$	−6.56949e155	−0.0647327	−0.0323664	+	0.999476i	$0.510304\pi$
$602$	2.96549e156	0.266008
$603$	−6.19398e154	−0.00505873
$604$	−2.27730e156	−0.169369
$605$	−1.46563e157	−0.992763
$606$	−2.52587e157	−1.55850
$607$	−1.95966e157	−1.10159	−0.550795	−	0.834641i	$-0.685675\pi$
$607$	−1.95966e157	−1.10159	−0.550795	+	0.834641i	$0.685675\pi$
$608$	2.32677e156	0.119180
$609$	6.42657e156	0.299987
$610$	3.16924e157	1.34840
$611$	2.93092e157	1.13678
$612$	−1.87394e156	−0.0662676
$613$	−3.39218e157	−1.09386	−0.546930	−	0.837178i	$-0.684204\pi$
$613$	−3.39218e157	−1.09386	−0.546930	+	0.837178i	$0.684204\pi$
$614$	3.11479e157	0.916041
$615$	5.32851e157	1.42943
$616$	1.37132e156	0.0335605
$617$	2.40775e157	0.537650	0.268825	−	0.963189i	$-0.413365\pi$
$617$	2.40775e157	0.537650	0.268825	+	0.963189i	$0.413365\pi$
$618$	−1.35767e157	−0.276658
$619$	2.69300e157	0.500859	0.250429	−	0.968135i	$-0.419428\pi$
$619$	2.69300e157	0.500859	0.250429	+	0.968135i	$0.419428\pi$
$620$	5.11828e156	0.0868947
$621$	7.26397e157	1.12590
$622$	−9.21800e157	−1.30461
$623$	2.33442e157	0.301721
$624$	−1.12968e158	−1.33360
$625$	−9.94518e157	−1.07249
$626$	−1.65184e158	−1.62749
$627$	−9.71228e156	−0.0874390
$628$	5.61871e156	0.0462293
$629$	1.55341e158	1.16822
$630$	7.83357e156	0.0538541
$631$	2.09348e157	0.131586	0.0657931	−	0.997833i	$-0.479042\pi$
$631$	2.09348e157	0.131586	0.0657931	+	0.997833i	$0.479042\pi$
$632$	−4.92805e157	−0.283244
$633$	7.93722e157	0.417214
$634$	3.56873e158	1.71582
$635$	−1.45216e158	−0.638704
$636$	2.64209e157	0.106321
$637$	−2.73751e158	−1.00804
$638$	−1.01035e158	−0.340489
$639$	2.63267e157	0.0812079
$640$	−4.31398e158	−1.21818
$641$	1.89913e158	0.490995	0.245497	−	0.969397i	$-0.421049\pi$
$641$	1.89913e158	0.490995	0.245497	+	0.969397i	$0.421049\pi$
$642$	8.58459e158	2.03231
$643$	−5.66857e158	−1.22901	−0.614503	−	0.788915i	$-0.710643\pi$
$643$	−5.66857e158	−1.22901	−0.614503	+	0.788915i	$0.710643\pi$
$644$	1.99124e157	0.0395432
$645$	8.97246e158	1.63225
$646$	3.57452e158	0.595772
$647$	6.31159e157	0.0963933	0.0481967	−	0.998838i	$-0.484653\pi$
$647$	6.31159e157	0.0963933	0.0481967	+	0.998838i	$0.484653\pi$
$648$	−7.72532e158	−1.08126
$649$	2.36891e158	0.303894
$650$	−7.50814e157	−0.0882933
$651$	−9.50333e157	−0.102459
$652$	−1.85670e158	−0.183549
$653$	1.24551e159	1.12916	0.564578	−	0.825380i	$-0.309039\pi$
$653$	1.24551e159	1.12916	0.564578	+	0.825380i	$0.309039\pi$
$654$	−5.38197e158	−0.447506
$655$	−6.28223e158	−0.479160
$656$	−1.98214e159	−1.38697
$657$	−5.31923e158	−0.341511
$658$	3.53897e158	0.208504
$659$	−1.80162e159	−0.974173	−0.487087	−	0.873354i	$-0.661940\pi$
$659$	−1.80162e159	−0.974173	−0.487087	+	0.873354i	$0.661940\pi$
$660$	−8.07897e157	−0.0400981
$661$	−4.94704e157	−0.0225405	−0.0112702	−	0.999936i	$-0.503588\pi$
$661$	−4.94704e157	−0.0225405	−0.0112702	+	0.999936i	$0.503588\pi$
$662$	1.59191e159	0.665951
$663$	−4.57226e159	−1.75637
$664$	4.61080e159	1.62659
$665$	−2.09404e158	−0.0678520
$666$	7.68260e158	0.228673
$667$	7.53449e159	2.06037
$668$	−8.36933e158	−0.210291
$669$	−3.38591e159	−0.781808
$670$	9.82801e157	0.0208564
$671$	1.29647e159	0.252896
$672$	−3.59369e158	−0.0644431
$673$	4.25617e159	0.701727	0.350863	−	0.936427i	$-0.385888\pi$
$673$	4.25617e159	0.701727	0.350863	+	0.936427i	$0.385888\pi$
$674$	9.85059e159	1.49341
$675$	−4.63470e158	−0.0646187
$676$	1.05401e158	0.0135163
$677$	−1.65116e160	−1.94774	−0.973868	−	0.227113i	$-0.927071\pi$
$677$	−1.65116e160	−1.94774	−0.973868	+	0.227113i	$0.927071\pi$
$678$	9.49827e159	1.03078
$679$	3.08489e158	0.0308033
$680$	−1.52704e160	−1.40313
$681$	−5.05222e159	−0.427238
$682$	1.49406e159	0.116292
$683$	−1.30969e160	−0.938425	−0.469213	−	0.883085i	$-0.655462\pi$
$683$	−1.30969e160	−0.938425	−0.469213	+	0.883085i	$0.655462\pi$
$684$	2.47746e158	0.0163432
$685$	2.44541e159	0.148537
$686$	−6.71778e159	−0.375762
$687$	−1.02663e159	−0.0528880
$688$	−3.33765e160	−1.58378
$689$	1.37716e160	0.602002
$690$	4.29906e160	1.73141
$691$	1.18046e160	0.438067	0.219034	−	0.975717i	$-0.429710\pi$
$691$	1.18046e160	0.438067	0.219034	+	0.975717i	$0.429710\pi$
$692$	−7.25370e159	−0.248065
$693$	3.20456e158	0.0101005
$694$	6.17579e160	1.79425
$695$	7.37988e160	1.97655
$696$	−6.19574e160	−1.52993
$697$	−8.02253e160	−1.82667
$698$	−6.48101e160	−1.36085
$699$	6.68162e160	1.29396
$700$	−1.27049e158	−0.00226951
$701$	−2.07630e160	−0.342154	−0.171077	−	0.985258i	$-0.554725\pi$
$701$	−2.07630e160	−0.342154	−0.171077	+	0.985258i	$0.554725\pi$
$702$	6.06249e160	0.921731
$703$	−2.05369e160	−0.288110
$704$	−1.27896e160	−0.165578
$705$	1.07076e161	1.27940
$706$	−4.35942e160	−0.480798
$707$	−2.22784e160	−0.226823
$708$	−2.82860e160	−0.265884
$709$	1.98807e161	1.72552	0.862760	−	0.505614i	$-0.168734\pi$
$709$	1.98807e161	1.72552	0.862760	+	0.505614i	$0.168734\pi$
$710$	−4.17727e160	−0.334808
$711$	−1.15161e160	−0.0852458
$712$	−2.25058e161	−1.53877
$713$	−1.11417e161	−0.703707
$714$	−5.52083e160	−0.322148
$715$	−4.21106e160	−0.227039
$716$	−2.33949e159	−0.0116556
$717$	−5.84963e160	−0.269337
$718$	−1.98211e160	−0.0843521
$719$	−9.33119e160	−0.367075	−0.183538	−	0.983013i	$-0.558755\pi$
$719$	−9.33119e160	−0.367075	−0.183538	+	0.983013i	$0.558755\pi$
$720$	−8.81666e160	−0.320640
$721$	−1.19748e160	−0.0402647
$722$	2.99590e161	0.931484
$723$	1.56534e161	0.450086
$724$	9.39579e160	0.249864
$725$	−4.80730e160	−0.118251
$726$	5.10848e161	1.16245
$727$	7.89963e161	1.66308	0.831538	−	0.555467i	$-0.187461\pi$
$727$	7.89963e161	1.66308	0.831538	+	0.555467i	$0.187461\pi$
$728$	−8.53489e160	−0.166255
$729$	3.33289e161	0.600780
$730$	8.44004e161	1.40800
$731$	−1.35088e162	−2.08586
$732$	−1.54806e161	−0.221264
$733$	−1.06829e162	−1.41356	−0.706779	−	0.707435i	$-0.749852\pi$
$733$	−1.06829e162	−1.41356	−0.706779	+	0.707435i	$0.749852\pi$
$734$	7.59863e161	0.930910
$735$	−1.00010e162	−1.13451
$736$	−4.21323e161	−0.442607
$737$	4.02045e159	0.00391166
$738$	−3.96766e161	−0.357561
$739$	7.09444e161	0.592253	0.296127	−	0.955149i	$-0.404305\pi$
$739$	7.09444e161	0.592253	0.296127	+	0.955149i	$0.404305\pi$
$740$	−1.70832e161	−0.132123
$741$	6.04478e161	0.433163
$742$	1.66286e161	0.110417
$743$	−2.82546e162	−1.73869	−0.869344	−	0.494207i	$-0.835458\pi$
$743$	−2.82546e162	−1.73869	−0.869344	+	0.494207i	$0.835458\pi$
$744$	9.16198e161	0.522539
$745$	5.92394e160	0.0313171
$746$	−2.92135e162	−1.43166
$747$	1.07747e162	0.489544
$748$	1.21636e161	0.0512414
$749$	7.57170e161	0.295781
$750$	3.21212e162	1.16367
$751$	5.02526e162	1.68850	0.844252	−	0.535947i	$-0.180045\pi$
$751$	5.02526e162	1.68850	0.844252	+	0.535947i	$0.180045\pi$
$752$	−3.98310e162	−1.24140
$753$	1.09136e162	0.315538
$754$	6.28827e162	1.68675
$755$	−4.33655e162	−1.07930
$756$	1.02586e161	0.0236923
$757$	1.99165e162	0.426870	0.213435	−	0.976957i	$-0.431535\pi$
$757$	1.99165e162	0.426870	0.213435	+	0.976957i	$0.431535\pi$
$758$	−8.23800e162	−1.63875
$759$	1.75866e162	0.324729
$760$	2.01883e162	0.346044
$761$	−3.82252e161	−0.0608299	−0.0304150	−	0.999537i	$-0.509683\pi$
$761$	−3.82252e161	−0.0608299	−0.0304150	+	0.999537i	$0.509683\pi$
$762$	5.06154e162	0.747872
$763$	−4.74695e161	−0.0651296
$764$	−2.13687e161	−0.0272272
$765$	−3.56845e162	−0.422288
$766$	−2.25656e162	−0.248040
$767$	−1.47437e163	−1.50546
$768$	5.66638e162	0.537522
$769$	9.53402e162	0.840307	0.420153	−	0.907453i	$-0.361976\pi$
$769$	9.53402e162	0.840307	0.420153	+	0.907453i	$0.361976\pi$
$770$	−5.08469e161	−0.0416427
$771$	−8.95294e162	−0.681386
$772$	2.13212e162	0.150811
$773$	2.88639e162	0.189764	0.0948820	−	0.995489i	$-0.469753\pi$
$773$	2.88639e162	0.189764	0.0948820	+	0.995489i	$0.469753\pi$
$774$	−6.68098e162	−0.408297
$775$	7.10882e161	0.0403879
$776$	−2.97408e162	−0.157096
$777$	3.17191e162	0.155788
$778$	−1.97827e163	−0.903523
$779$	1.06062e163	0.450500
$780$	5.02823e162	0.198641
$781$	−1.70884e162	−0.0627940
$782$	−6.47260e163	−2.21257
$783$	3.88168e163	1.23447
$784$	3.72026e163	1.10082
$785$	1.06994e163	0.294595
$786$	2.18969e163	0.561058
$787$	7.73372e163	1.84423	0.922117	−	0.386911i	$-0.126458\pi$
$787$	7.73372e163	1.84423	0.922117	+	0.386911i	$0.126458\pi$
$788$	−2.82719e162	−0.0627514
$789$	3.45942e163	0.714747
$790$	1.82726e163	0.351456
$791$	8.37757e162	0.150019
$792$	−3.08946e162	−0.0515122
$793$	−8.06906e163	−1.25282
$794$	−1.20669e164	−1.74477
$795$	5.03120e163	0.677531
$796$	−1.00001e163	−0.125434
$797$	−1.05260e164	−1.22990	−0.614949	−	0.788567i	$-0.710823\pi$
$797$	−1.05260e164	−1.22990	−0.614949	+	0.788567i	$0.710823\pi$
$798$	7.29884e162	0.0794493
$799$	−1.61212e164	−1.63495
$800$	2.68821e162	0.0254026
$801$	−5.25925e163	−0.463113
$802$	8.47938e163	0.695845
$803$	3.45266e163	0.264074
$804$	−4.80063e161	−0.00342240
$805$	3.79181e163	0.251988
$806$	−9.29881e163	−0.576099
$807$	2.37333e164	1.37089
$808$	2.14782e164	1.15679
$809$	−1.15712e164	−0.581150	−0.290575	−	0.956852i	$-0.593847\pi$
$809$	−1.15712e164	−0.581150	−0.290575	+	0.956852i	$0.593847\pi$
$810$	2.86446e164	1.34165
$811$	−8.38601e163	−0.366334	−0.183167	−	0.983082i	$-0.558635\pi$
$811$	−8.38601e163	−0.366334	−0.183167	+	0.983082i	$0.558635\pi$
$812$	1.06407e163	0.0433564
$813$	−2.12245e164	−0.806720
$814$	−4.98670e163	−0.176821
$815$	−3.53561e164	−1.16966
$816$	6.21367e164	1.91802
$817$	1.78594e164	0.514423
$818$	−8.84005e163	−0.237625
$819$	−1.99447e163	−0.0500366
$820$	8.82258e163	0.206592
$821$	−4.22560e164	−0.923634	−0.461817	−	0.886975i	$-0.652802\pi$
$821$	−4.22560e164	−0.923634	−0.461817	+	0.886975i	$0.652802\pi$
$822$	−8.52354e163	−0.173925
$823$	3.19969e164	0.609562	0.304781	−	0.952422i	$-0.401417\pi$
$823$	3.19969e164	0.609562	0.304781	+	0.952422i	$0.401417\pi$
$824$	1.15446e164	0.205349
$825$	−1.12209e163	−0.0186372
$826$	−1.78025e164	−0.276126
$827$	−8.20903e164	−1.18913	−0.594567	−	0.804046i	$-0.702676\pi$
$827$	−8.20903e164	−1.18913	−0.594567	+	0.804046i	$0.702676\pi$
$828$	−4.48608e163	−0.0606950
$829$	7.67894e164	0.970443	0.485222	−	0.874391i	$-0.338739\pi$
$829$	7.67894e164	0.970443	0.485222	+	0.874391i	$0.338739\pi$
$830$	−1.70963e165	−2.01832
$831$	8.97351e164	0.989702
$832$	7.96007e164	0.820256
$833$	1.50574e165	1.44980
$834$	−2.57227e165	−2.31438
$835$	−1.59373e165	−1.34007
$836$	−1.60809e163	−0.0126374
$837$	−5.74006e164	−0.421627
$838$	3.02752e165	2.07874
$839$	−1.35873e165	−0.872131	−0.436066	−	0.899915i	$-0.643628\pi$
$839$	−1.35873e165	−0.872131	−0.436066	+	0.899915i	$0.643628\pi$
$840$	−3.11807e164	−0.187114
$841$	2.24397e165	1.25905
$842$	1.38899e165	0.728731
$843$	5.50768e163	0.0270216
$844$	1.31419e164	0.0602990
$845$	2.00710e164	0.0861320
$846$	−7.97298e164	−0.320033
$847$	4.50573e164	0.169181
$848$	−1.87155e165	−0.657409
$849$	9.61124e163	0.0315860
$850$	4.12977e164	0.126986
$851$	3.71874e165	1.06998
$852$	2.04045e164	0.0549399
$853$	5.97925e165	1.50670	0.753350	−	0.657620i	$-0.228437\pi$
$853$	5.97925e165	1.50670	0.753350	+	0.657620i	$0.228437\pi$
$854$	−9.74308e164	−0.229787
$855$	4.71769e164	0.104146
$856$	−7.29973e165	−1.50848
$857$	−3.15799e165	−0.610934	−0.305467	−	0.952203i	$-0.598813\pi$
$857$	−3.15799e165	−0.610934	−0.305467	+	0.952203i	$0.598813\pi$
$858$	1.46777e165	0.265844
$859$	−3.52881e165	−0.598432	−0.299216	−	0.954185i	$-0.596725\pi$
$859$	−3.52881e165	−0.598432	−0.299216	+	0.954185i	$0.596725\pi$
$860$	1.48560e165	0.235906
$861$	−1.63813e165	−0.243595
$862$	−1.47842e166	−2.05891
$863$	−3.69460e165	−0.481900	−0.240950	−	0.970537i	$-0.577459\pi$
$863$	−3.69460e165	−0.481900	−0.240950	+	0.970537i	$0.577459\pi$
$864$	−2.17061e165	−0.265189
$865$	−1.38129e166	−1.58079
$866$	1.21666e166	1.30439
$867$	1.39222e166	1.39839
$868$	−1.57349e164	−0.0148082
$869$	7.47498e164	0.0659163
$870$	2.29731e166	1.89837
$871$	−2.50227e164	−0.0193780
$872$	4.57645e165	0.332160
$873$	−6.94998e164	−0.0472801
$874$	8.55713e165	0.545673
$875$	2.83313e165	0.169360
$876$	−4.12265e165	−0.231044
$877$	1.08383e166	0.569487	0.284744	−	0.958604i	$-0.408092\pi$
$877$	1.08383e166	0.569487	0.284744	+	0.958604i	$0.408092\pi$
$878$	−3.27092e165	−0.161150
$879$	−1.37815e166	−0.636687
$880$	5.72280e165	0.247935
$881$	1.71506e166	0.696853	0.348426	−	0.937336i	$-0.386716\pi$
$881$	1.71506e166	0.696853	0.348426	+	0.937336i	$0.386716\pi$
$882$	7.44686e165	0.283791
$883$	−1.73570e166	−0.620434	−0.310217	−	0.950666i	$-0.600402\pi$
$883$	−1.73570e166	−0.620434	−0.310217	+	0.950666i	$0.600402\pi$
$884$	−7.57043e165	−0.253844
$885$	−5.38636e166	−1.69434
$886$	−6.54091e166	−1.93034
$887$	4.29233e166	1.18853	0.594263	−	0.804271i	$-0.297444\pi$
$887$	4.29233e166	1.18853	0.594263	+	0.804271i	$0.297444\pi$
$888$	−3.05798e166	−0.794515
$889$	4.46433e165	0.108845
$890$	8.34487e166	1.90934
$891$	1.17179e166	0.251629
$892$	−5.60616e165	−0.112993
$893$	2.13131e166	0.403218
$894$	−2.06480e165	−0.0366698
$895$	−4.45497e165	−0.0742751
$896$	1.32623e166	0.207595
$897$	−1.09456e167	−1.60867
$898$	5.37672e166	0.742000
$899$	−5.95383e166	−0.771567
$900$	2.86230e164	0.00348347
$901$	−7.57491e166	−0.865818
$902$	2.57537e166	0.276484
$903$	−2.75837e166	−0.278160
$904$	−8.07666e166	−0.765095
$905$	1.78919e167	1.59225
$906$	1.51151e167	1.26377
$907$	1.05549e167	0.829167	0.414584	−	0.910011i	$-0.363927\pi$
$907$	1.05549e167	0.829167	0.414584	+	0.910011i	$0.363927\pi$
$908$	−8.36511e165	−0.0617478
$909$	5.01912e166	0.348152
$910$	3.16464e166	0.206293
$911$	−1.51221e166	−0.0926452	−0.0463226	−	0.998927i	$-0.514750\pi$
$911$	−1.51221e166	−0.0926452	−0.0463226	+	0.998927i	$0.514750\pi$
$912$	−8.21481e166	−0.473031
$913$	−6.99376e166	−0.378540
$914$	3.96069e167	2.01517
$915$	−2.94789e167	−1.41000
$916$	−1.69982e165	−0.00764378
$917$	1.93133e166	0.0816560
$918$	−3.33461e167	−1.32566
$919$	4.78265e167	1.78790	0.893949	−	0.448169i	$-0.147924\pi$
$919$	4.78265e167	1.78790	0.893949	+	0.448169i	$0.147924\pi$
$920$	−3.65562e167	−1.28513
$921$	−2.89724e167	−0.957889
$922$	−1.29258e167	−0.401938
$923$	1.06356e167	0.311075
$924$	2.48369e165	0.00683330
$925$	−2.37270e166	−0.0614094
$926$	−4.24078e167	−1.03258
$927$	2.69780e166	0.0618024
$928$	−2.25144e167	−0.485289
$929$	5.46657e167	1.10873	0.554367	−	0.832273i	$-0.312961\pi$
$929$	5.46657e167	1.10873	0.554367	+	0.832273i	$0.312961\pi$
$930$	−3.39715e167	−0.648379
$931$	−1.99067e167	−0.357554
$932$	1.10630e167	0.187013
$933$	8.57418e167	1.36421
$934$	−3.67926e167	−0.551013
$935$	2.31625e167	0.326534
$936$	1.92283e167	0.255186
$937$	2.46242e167	0.307663	0.153832	−	0.988097i	$-0.450839\pi$
$937$	2.46242e167	0.307663	0.153832	+	0.988097i	$0.450839\pi$
$938$	−3.02139e165	−0.00355424
$939$	1.53647e168	1.70184
$940$	1.77289e167	0.184909
$941$	5.12082e167	0.502951	0.251476	−	0.967864i	$-0.419084\pi$
$941$	5.12082e167	0.502951	0.251476	+	0.967864i	$0.419084\pi$
$942$	−3.72931e167	−0.344947
$943$	−1.92053e168	−1.67306
$944$	2.00366e168	1.64402
$945$	1.95350e167	0.150979
$946$	4.33656e167	0.315716
$947$	−9.73436e167	−0.667626	−0.333813	−	0.942639i	$-0.608335\pi$
$947$	−9.73436e167	−0.667626	−0.333813	+	0.942639i	$0.608335\pi$
$948$	−8.92552e166	−0.0576717
$949$	−2.14888e168	−1.30819
$950$	−5.45979e166	−0.0313178
$951$	−3.31948e168	−1.79420
$952$	4.69452e167	0.239113
$953$	−3.20059e166	−0.0153632	−0.00768160	−	0.999970i	$-0.502445\pi$
$953$	−3.20059e166	−0.0153632	−0.00768160	+	0.999970i	$0.502445\pi$
$954$	−3.74629e167	−0.169480
$955$	−4.06913e167	−0.173505
$956$	−9.68542e166	−0.0389267
$957$	9.39784e167	0.356044
$958$	3.21494e167	0.114821
$959$	−7.51785e166	−0.0253129
$960$	2.90807e168	0.923168
$961$	−2.46054e168	−0.736475
$962$	3.10365e168	0.875953
$963$	−1.70584e168	−0.453996
$964$	2.59179e167	0.0650500
$965$	4.06008e168	0.961041
$966$	−1.32164e168	−0.295058
$967$	7.08704e168	1.49235	0.746173	−	0.665752i	$-0.231889\pi$
$967$	7.08704e168	1.49235	0.746173	+	0.665752i	$0.231889\pi$
$968$	−4.34389e168	−0.862823
$969$	−3.32486e168	−0.622989
$970$	1.10276e168	0.194929
$971$	−4.01279e168	−0.669206	−0.334603	−	0.942359i	$-0.608602\pi$
$971$	−4.01279e168	−0.669206	−0.334603	+	0.942359i	$0.608602\pi$
$972$	−5.48441e167	−0.0862951
$973$	−2.26877e168	−0.336833
$974$	−6.66388e168	−0.933568
$975$	6.98375e167	0.0923268
$976$	1.09658e169	1.36812
$977$	7.28925e168	0.858302	0.429151	−	0.903233i	$-0.358813\pi$
$977$	7.28925e168	0.858302	0.429151	+	0.903233i	$0.358813\pi$
$978$	1.23235e169	1.36958
$979$	3.41373e168	0.358102
$980$	−1.65590e168	−0.163969
$981$	1.06945e168	0.0999677
$982$	−1.79178e169	−1.58119
$983$	6.74748e168	0.562171	0.281085	−	0.959683i	$-0.409306\pi$
$983$	6.74748e168	0.562171	0.281085	+	0.959683i	$0.409306\pi$
$984$	1.57929e169	1.24233
$985$	−5.38367e168	−0.399881
$986$	−3.45879e169	−2.42593
$987$	−3.29180e168	−0.218029
$988$	1.00085e168	0.0626041
$989$	−3.23390e169	−1.91045
$990$	1.14554e168	0.0639175
$991$	2.21026e169	1.16488	0.582441	−	0.812873i	$-0.302098\pi$
$991$	2.21026e169	1.16488	0.582441	+	0.812873i	$0.302098\pi$
$992$	3.32933e168	0.165748
$993$	−1.48073e169	−0.696374
$994$	1.28420e168	0.0570563
$995$	−1.90426e169	−0.799323
$996$	8.35092e168	0.331193
$997$	1.66103e169	0.622447	0.311223	−	0.950337i	$-0.399261\pi$
$997$	1.66103e169	0.622447	0.311223	+	0.950337i	$0.399261\pi$
$998$	5.32494e167	0.0188556
$999$	1.91585e169	0.641079

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.114.a.a.1.3	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.114.a.a.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-1.09896e17 q^{2} +1.02220e27 q^{3} +1.69249e33 q^{4} +3.22293e39 q^{5} -1.12336e44 q^{6} -9.90814e46 q^{7} +9.55225e50 q^{8} +2.23221e53 q^{9} +O(q^{10})\)	\(q-1.09896e17 q^{2} +1.02220e27 q^{3} +1.69249e33 q^{4} +3.22293e39 q^{5} -1.12336e44 q^{6} -9.90814e46 q^{7} +9.55225e50 q^{8} +2.23221e53 q^{9} -3.54186e56 q^{10} -1.44891e58 q^{11} +1.73007e60 q^{12} +9.01779e62 q^{13} +1.08886e64 q^{14} +3.29449e66 q^{15} -1.22551e68 q^{16} -4.96013e69 q^{17} -2.45311e70 q^{18} +6.55757e71 q^{19} +5.45479e72 q^{20} -1.01281e74 q^{21} +1.59229e75 q^{22} -1.18742e77 q^{23} +9.76435e77 q^{24} +7.57620e77 q^{25} -9.91017e79 q^{26} -6.11745e80 q^{27} -1.67695e80 q^{28} -6.34527e82 q^{29} -3.62050e83 q^{30} +9.38310e83 q^{31} +3.54823e84 q^{32} -1.48108e85 q^{33} +5.45098e86 q^{34} -3.19332e86 q^{35} +3.77801e86 q^{36} -3.13178e88 q^{37} -7.20650e88 q^{38} +9.21801e89 q^{39} +3.07862e90 q^{40} +1.61740e91 q^{41} +1.11304e91 q^{42} +2.72347e92 q^{43} -2.45227e91 q^{44} +7.19427e92 q^{45} +1.30492e94 q^{46} +3.25015e94 q^{47} -1.25272e95 q^{48} -3.03568e95 q^{49} -8.32593e94 q^{50} -5.07027e96 q^{51} +1.52625e96 q^{52} +1.52716e97 q^{53} +6.72282e97 q^{54} -4.66973e97 q^{55} -9.46451e97 q^{56} +6.70317e98 q^{57} +6.97318e99 q^{58} -1.63496e100 q^{59} +5.57590e99 q^{60} -8.94794e100 q^{61} -1.03116e101 q^{62} -2.21171e100 q^{63} +8.82708e101 q^{64} +2.90637e102 q^{65} +1.62764e102 q^{66} -2.77481e101 q^{67} -8.39500e102 q^{68} -1.21378e104 q^{69} +3.50933e103 q^{70} +1.17940e104 q^{71} +2.13227e104 q^{72} -2.38294e105 q^{73} +3.44170e105 q^{74} +7.74442e104 q^{75} +1.10986e105 q^{76} +1.43560e105 q^{77} -1.01302e107 q^{78} -5.15904e106 q^{79} -3.94973e107 q^{80} -8.08744e107 q^{81} -1.77746e108 q^{82} +4.82692e108 q^{83} -1.71418e107 q^{84} -1.59862e109 q^{85} -2.99298e109 q^{86} -6.48615e109 q^{87} -1.38403e109 q^{88} -2.35607e110 q^{89} -7.90620e109 q^{90} -8.93495e109 q^{91} -2.00970e110 q^{92} +9.59143e110 q^{93} -3.57178e111 q^{94} +2.11346e111 q^{95} +3.62701e111 q^{96} -3.11349e111 q^{97} +3.33609e112 q^{98} -3.23427e111 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 49\!\cdots\!32 q^{2}+ \cdots + 55\!\cdots\!77 q^{9}+O(q^{10}) \) 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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