LMFDB - Embedded newform 1.108.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,108,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, 108, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 108);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 108 $
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:	$72.5037502298$
Analytic rank:	$0$
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} - 4 x^{8} + \cdots + 27\!\cdots\!52 $ x^9 - 4x^8 - 1821920358703753620268152338564x^7 - 73610452992619178855916817548457004116206104x^6 + 1042927933110487260237221890240470544935357005162429842147046x^5 + 37285327276878712774794751452846309004234687688262114577783522497342862192x^4 - 218672290124818314716153768032496183184282019511769799142310101749410545149517793316218948x^3 - 4552285969041146724473022504964060810600176627997038494887972653349745683436300456342246069993967618888x^2 + 13787038069926754539844292446554405975460560959925593369765930486571095483376487264340523168734579760333319466810117217x + 277748822013850248516050532972247539400431679963024154714012464502371488213901308745686995951512635653307279617190020931289801256052
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{143}\cdot 3^{48}\cdot 5^{18}\cdot 7^{8}\cdot 11^{2}\cdot 13^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$3.47594e14$ 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)

$f(q)$	$=$	$q-7.73495e15 q^{2} +6.57221e25 q^{3} -1.02430e32 q^{4} +3.43777e37 q^{5} -5.08357e41 q^{6} +9.22106e44 q^{7} +2.04736e48 q^{8} +3.19227e51 q^{9} +O(q^{10})$	\(q-7.73495e15 q^{2} +6.57221e25 q^{3} -1.02430e32 q^{4} +3.43777e37 q^{5} -5.08357e41 q^{6} +9.22106e44 q^{7} +2.04736e48 q^{8} +3.19227e51 q^{9} -2.65909e53 q^{10} +5.28808e55 q^{11} -6.73191e57 q^{12} -1.89047e59 q^{13} -7.13244e60 q^{14} +2.25937e63 q^{15} +7.84008e62 q^{16} +2.07360e65 q^{17} -2.46920e67 q^{18} +3.96161e67 q^{19} -3.52130e69 q^{20} +6.06028e70 q^{21} -4.09030e71 q^{22} +7.68335e72 q^{23} +1.34557e74 q^{24} +5.65526e74 q^{25} +1.46227e75 q^{26} +1.35725e77 q^{27} -9.44512e76 q^{28} -1.37014e78 q^{29} -1.74761e79 q^{30} -8.63725e78 q^{31} -3.38267e80 q^{32} +3.47544e81 q^{33} -1.60392e81 q^{34} +3.16998e82 q^{35} -3.26984e83 q^{36} -9.81590e83 q^{37} -3.06428e83 q^{38} -1.24246e85 q^{39} +7.03833e85 q^{40} -9.94685e85 q^{41} -4.68759e86 q^{42} -2.93719e87 q^{43} -5.41658e87 q^{44} +1.09743e89 q^{45} -5.94303e88 q^{46} -1.38601e89 q^{47} +5.15267e88 q^{48} -1.81345e90 q^{49} -4.37431e90 q^{50} +1.36281e91 q^{51} +1.93641e91 q^{52} +6.72527e91 q^{53} -1.04983e93 q^{54} +1.81792e93 q^{55} +1.88788e93 q^{56} +2.60365e93 q^{57} +1.05980e94 q^{58} -3.97826e94 q^{59} -2.31427e95 q^{60} +1.68274e95 q^{61} +6.68086e94 q^{62} +2.94361e96 q^{63} +2.48926e96 q^{64} -6.49900e96 q^{65} -2.68823e97 q^{66} +4.95750e97 q^{67} -2.12399e97 q^{68} +5.04966e98 q^{69} -2.45197e98 q^{70} -1.97010e99 q^{71} +6.53571e99 q^{72} +1.51394e99 q^{73} +7.59255e99 q^{74} +3.71676e100 q^{75} -4.05787e99 q^{76} +4.87617e100 q^{77} +9.61034e100 q^{78} +1.53975e101 q^{79} +2.69524e100 q^{80} +5.32205e102 q^{81} +7.69384e101 q^{82} -5.40827e102 q^{83} -6.20753e102 q^{84} +7.12855e102 q^{85} +2.27190e103 q^{86} -9.00485e103 q^{87} +1.08266e104 q^{88} -1.73192e103 q^{89} -8.48854e104 q^{90} -1.74321e104 q^{91} -7.87005e104 q^{92} -5.67658e104 q^{93} +1.07207e105 q^{94} +1.36191e105 q^{95} -2.22316e106 q^{96} +2.04081e105 q^{97} +1.40269e106 q^{98} +1.68810e107 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 54\!\cdots\!96 q^{2}+ \cdots + 36\!\cdots\!13 q^{9}+O(q^{10}) $ 9 * q + 5465779613435496 * q^2 + 15983866788128062714366812 * q^3 + 641838178072986908923140040636992 * q^4 + 24730262360170403173006735448079708750 * q^5 - 120659696701040014765473752948751733206432 * q^6 - 935936272579440558945885185297012359442693544 * q^7 - 1000549071290096181876510601182828415482105239040 * q^8 + 3695400441386851970702053152997489358579707799946813 * q^9	$ 9 q + 54\!\cdots\!96 q^{2}+ \cdots + 21\!\cdots\!36 q^{99}+O(q^{100}) $ 9 * q + 5465779613435496 * q^2 + 15983866788128062714366812 * q^3 + 641838178072986908923140040636992 * q^4 + 24730262360170403173006735448079708750 * q^5 - 120659696701040014765473752948751733206432 * q^6 - 935936272579440558945885185297012359442693544 * q^7 - 1000549071290096181876510601182828415482105239040 * q^8 + 3695400441386851970702053152997489358579707799946813 * q^9 - 1051865624814321749095840304599907252969934693398466000 * q^10 + 75371386674400378520973626363253224857093312063724664948 * q^11 - 7994600333787230851514661173029738426135745580020653426944 * q^12 + 386688410581830829569835770029121092890073212075170355706982 * q^13 - 7425120169660057221925189838061614099801999208262592119204416 * q^14 + 1114849595057357604173216029035423209082636701646415622289453000 * q^15 + 29408614076374287218252370499930154042728180304312580290885259264 * q^16 + 557190110555184717584150469172018747011155217501263013200292053826 * q^17 + 23686310065847344603267400477778156225688961326793890396260803764872 * q^18 + 858726527367010511176780653766124295103204700130810063275302960078860 * q^19 + 13293825016749054587175558577837356326662860013460552585283415249200000 * q^20 + 98208620574357072907810930779441373553105765539483211558155794396236448 * q^21 - 2120482037145318757833662337561674615184814159100624269907546121294686688 * q^22 - 10034721240753129475726648205629192527604953514063764213610508652545603448 * q^23 - 2941281585435310612767332425157841570788095859273373502643916660565125120 * q^24 + 2090668146509277585662418878235593338432069837730236508072952837108480609375 * q^25 + 297618678938898468541825094241452097503242676900281081118135240117081112048 * q^26 + 12010637132277372007849219431146961646841705965134800444369356096651346807640 * q^27 - 772836919356016231875276488741314175452898152873144799220188421863529684675072 * q^28 + 3591314969861592690040264647853795847194812597017039069680951706167032656423190 * q^29 + 1723952423459255307102435810928767115448833503290363214135969710252703496200000 * q^30 + 80089747856260124585510286878769275145759211608657844798932602922226546761434208 * q^31 - 1446206593191149472500309116447393072011146060673364310104554905463216959190564864 * q^32 + 3945091609919542459300423121384432970721444207912781947382890849249898482566767664 * q^33 + 11119656315304296004606294411853238631199272487238804497227126821893639468830096464 * q^34 + 49067962462953733482940013097788952961901858200557588372758479947688558453676754000 * q^35 - 471823079431745456450508655131148234440317478341437039102283657625130709182178187456 * q^36 - 211704323021230989692835910298149365559694037564054725936839839132550744753936919634 * q^37 + 8222885444046313840674570479741432975521521666418514540085950022601909450574547779040 * q^38 + 12361178896398609619161562511793017908827480821637222996756699411815138902405469354856 * q^39 - 46215645594071398383759344185895857310354869228136299740138569713991972194487637120000 * q^40 - 152723040798290839871602016171161581257438821965138798374317736485575056512069694567862 * q^41 + 1126972287891090202493176150041627427283154361091115578522922093800965746370272835782912 * q^42 + 588069515895858848125340008029591292900452115124091837264351724714905019444084944743892 * q^43 - 6139643207231705808426527030461811499402203060055049552369302116418471883341886274962176 * q^44 - 31911427383192526363701563735501578120849438309590564668521639113629216238459194946116250 * q^45 - 18263182784420532146882371818610257236316553965008962373113458516888555657572617999188672 * q^46 + 411127412634686500562199358253262979305374320422388983156864942033640143172424484152539536 * q^47 + 143930370214090114738516122425367964462847873560413052946256979092891611198246163544522752 * q^48 - 4997644842464582200845249613678276624838382931152181846690817178995051025280570789312693263 * q^49 - 327953810706856692980141167207241667907351028782006717494410015078645777795786692667625000 * q^50 + 42691516908125956684809245526355840553570893389914391645941980034335859681366662250925257208 * q^51 + 59364881289634100249284358230824565528876555321811374467351490113119501371198417490401094016 * q^52 - 53335374129204409504769785775612138052491162110126476217063770562215392060493506708504818338 * q^53 - 1554605781923117836337527850943594545571965959146902578434980467357667330247224121116945547840 * q^54 + 1474216898342963983363455770095216024051493885851745466905891181181387017915931645476666255000 * q^55 + 7453692229427932770491342947786818133880887558034867118652861854414844393630476278780284170240 * q^56 - 9382173343921294589567308072318971089362548602163794938031557584052656917238640814769133635120 * q^57 - 14675317362256339836240584983997175224307357531571668080947702647986363061369632064127758276240 * q^58 - 17201443369933521380448054479438020840215748691907958949057650623559478137031846309102734186620 * q^59 + 119942427235571024011403351926139340364016919293031353278124824892037701815579444998816654144000 * q^60 + 996825825169496808828278558344476432289838610202339535134269176536499940712988317319113083438198 * q^61 - 1806664642208894952880819938644089164868010113998872083788864908221482430118942433714202980872448 * q^62 - 525131716387364530569619107989883435883820178537003544594931993029001820968120281192738395294408 * q^63 + 8859800242100397923173345055025991374254635563298611761326132852774863587391298255452246238298112 * q^64 + 3354685369129755322181059460881157417967535549386685974710181837734684369198862379954288278640500 * q^65 + 57953332747637118130796913061247956114095776689582635716826448321044474448975464944502438440474496 * q^66 + 67272594646508937763531278535250984988721264552212406692490519409868542593541008988303512955099676 * q^67 - 5271355091203561642375555737902479878900668615857946963901492781607485228195805621489749763440512 * q^68 + 1211310643069343900708768635208063407543461033111793008132153244460934861341593025873966799465486816 * q^69 + 3012778566653438568685732696962102874663629250451589330912197198332559170935750394136926553795280000 * q^70 + 557606230265736297562017362716168472788611890356025926095319973789617215901574196175404049892853528 * q^71 + 16960010475120540092713267652235654327415255109531175122804202418279614126703951005828887393908830720 * q^72 + 13389828619022747318968894782762272535480348540089259518080823938522165418472525950139881426529375402 * q^73 + 72532783100036668116960948230568216484424073462645933664305672446671831241015488437308573521198008624 * q^74 + 181746227987304022931719943233189267636401541776890365701313509214346868335764760358972397994607562500 * q^75 + 369203366658532984115827909838760339113448992029578983924004973867253851696995490992782273693567066880 * q^76 + 388491114360440288787870394325327319503105866790556270795138762844335429572119358188629406545039198432 * q^77 + 1684225666426130585491319943814839912966891568955799622030995821490516792520001316121300784238905446464 * q^78 + 1767099872706468468805139692411742252367926917059947532799767578463589430448822266501638541217663494640 * q^79 + 6734051899360870505834986379536968461908477509814468240268598557190207937484585956747946194493844480000 * q^80 + 8587274871353378729934471647154494323432295856816917259751843692725713832863430007711361770205995287889 * q^81 + 8604324829509629266993327118230721908083540408244010940656031675054140623869235247377840945490064899472 * q^82 + 10573584024255166860785482858544789933175527426032260694531283318949407366175819470225352840720947271372 * q^83 + 29398865778509538549966771421066766907861809604721299372151512034272864117018289488710440505099182516224 * q^84 + 28217101873426464307527276596170727373321741101882319418731811087750656251683841267824081156479505981500 * q^85 - 5660340715902714082316421136856625160042953949488572010019823412763437338500312808862231168781884748512 * q^86 - 238801934255165782785740400186129085029676437910074769136670805304976544209174607407124977464878965608280 * q^87 - 649669481755409892912473717222108679378769149016402953512733477402495574055782427323588758822348679034880 * q^88 - 887044331989597087426634052611019082958734414422732136340380168408138968025139915003605988823387508725030 * q^89 - 2358060024132454293950038004387227695091155243819311445899211024200212376406755931436993187026324923882000 * q^90 - 2028610692814038362284016228595385975371756633777610476239575578728190535138139517202725484712408010671472 * q^91 - 9605953523619230804079170889956757296920712871591046684448269611692869761363895640295324681873778639117824 * q^92 - 10277229372847627124269654885108201819576328825280371977906378287406641199658335902623697673880879481373056 * q^93 - 13250229074063549042347396359745980974584115253516850536254551366146505318484654226001161612613989202932096 * q^94 + 1932498314000384011251898358613786886453409028619258552182745516014729315280931175089689966876445460945000 * q^95 + 8188689385662642160607934226103033776391463701323345460407294147322816918802843383187307295905239187980288 * q^96 + 18319527847032942156630290559559475585838161401404427251154943474039162663641018432069269659324962153774386 * q^97 + 91489091329550984599525415507771543780042234198589939082127267861983786873859650920519076378970080872245928 * q^98 + 211118154688143874137117803870035099572707397285369760168480766428388700807018832202269547436760962791157636 * 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 $

$2$	−7.73495e15	−0.607229	−0.303615	−	0.952795i	$-0.598193\pi$
$2$	−7.73495e15	−0.607229	−0.303615	+	0.952795i	$0.598193\pi$
$3$	6.57221e25	1.95760	0.978801	−	0.204812i	$-0.0656584\pi$
$3$	6.57221e25	1.95760	0.978801	+	0.204812i	$0.0656584\pi$
$4$	−1.02430e32	−0.631273
$5$	3.43777e37	1.38478	0.692391	−	0.721523i	$-0.256558\pi$
$5$	3.43777e37	1.38478	0.692391	+	0.721523i	$0.256558\pi$
$6$	−5.08357e41	−1.18871
$7$	9.22106e44	0.564983	0.282492	−	0.959270i	$-0.408839\pi$
$7$	9.22106e44	0.564983	0.282492	+	0.959270i	$0.408839\pi$
$8$	2.04736e48	0.990556
$9$	3.19227e51	2.83221
$10$	−2.65909e53	−0.840879
$11$	5.28808e55	1.02044	0.510222	−	0.860042i	$-0.329563\pi$
$11$	5.28808e55	1.02044	0.510222	+	0.860042i	$0.329563\pi$
$12$	−6.73191e57	−1.23578
$13$	−1.89047e59	−0.479293	−0.239646	−	0.970860i	$-0.577031\pi$
$13$	−1.89047e59	−0.479293	−0.239646	+	0.970860i	$0.577031\pi$
$14$	−7.13244e60	−0.343074
$15$	2.25937e63	2.71085
$16$	7.84008e62	0.0297784
$17$	2.07360e65	0.307403	0.153701	−	0.988117i	$-0.450881\pi$
$17$	2.07360e65	0.307403	0.153701	+	0.988117i	$0.450881\pi$
$18$	−2.46920e67	−1.71980
$19$	3.96161e67	0.152952	0.0764758	−	0.997071i	$-0.475633\pi$
$19$	3.96161e67	0.152952	0.0764758	+	0.997071i	$0.475633\pi$
$20$	−3.52130e69	−0.874175
$21$	6.06028e70	1.10601
$22$	−4.09030e71	−0.619644
$23$	7.68335e72	1.07922	0.539612	−	0.841914i	$-0.318571\pi$
$23$	7.68335e72	1.07922	0.539612	+	0.841914i	$0.318571\pi$
$24$	1.34557e74	1.93912
$25$	5.65526e74	0.917619
$26$	1.46227e75	0.291040
$27$	1.35725e77	3.58673
$28$	−9.44512e76	−0.356659
$29$	−1.37014e78	−0.791538	−0.395769	−	0.918350i	$-0.629522\pi$
$29$	−1.37014e78	−0.791538	−0.395769	+	0.918350i	$0.629522\pi$
$30$	−1.74761e79	−1.64611
$31$	−8.63725e78	−0.140775	−0.0703874	−	0.997520i	$-0.522424\pi$
$31$	−8.63725e78	−0.140775	−0.0703874	+	0.997520i	$0.522424\pi$
$32$	−3.38267e80	−1.00864
$33$	3.47544e81	1.99763
$34$	−1.60392e81	−0.186664
$35$	3.16998e82	0.782378
$36$	−3.26984e83	−1.78790
$37$	−9.81590e83	−1.23919	−0.619595	−	0.784922i	$-0.712703\pi$
$37$	−9.81590e83	−1.23919	−0.619595	+	0.784922i	$0.712703\pi$
$38$	−3.06428e83	−0.0928767
$39$	−1.24246e85	−0.938264
$40$	7.03833e85	1.37170
$41$	−9.94685e85	−0.517308	−0.258654	−	0.965970i	$-0.583279\pi$
$41$	−9.94685e85	−0.517308	−0.258654	+	0.965970i	$0.583279\pi$
$42$	−4.68759e86	−0.671603
$43$	−2.93719e87	−1.19500	−0.597501	−	0.801868i	$-0.703840\pi$
$43$	−2.93719e87	−1.19500	−0.597501	+	0.801868i	$0.703840\pi$
$44$	−5.41658e87	−0.644179
$45$	1.09743e89	3.92199
$46$	−5.94303e88	−0.655336
$47$	−1.38601e89	−0.483648	−0.241824	−	0.970320i	$-0.577746\pi$
$47$	−1.38601e89	−0.483648	−0.241824	+	0.970320i	$0.577746\pi$
$48$	5.15267e88	0.0582943
$49$	−1.81345e90	−0.680794
$50$	−4.37431e90	−0.557205
$51$	1.36281e91	0.601772
$52$	1.93641e91	0.302564
$53$	6.72527e91	0.379272	0.189636	−	0.981854i	$-0.439269\pi$
$53$	6.72527e91	0.379272	0.189636	+	0.981854i	$0.439269\pi$
$54$	−1.04983e93	−2.17797
$55$	1.81792e93	1.41309
$56$	1.88788e93	0.559648
$57$	2.60365e93	0.299419
$58$	1.05980e94	0.480645
$59$	−3.97826e94	−0.722953	−0.361477	−	0.932381i	$-0.617727\pi$
$59$	−3.97826e94	−0.722953	−0.361477	+	0.932381i	$0.617727\pi$
$60$	−2.31427e95	−1.71129
$61$	1.68274e95	0.513892	0.256946	−	0.966426i	$-0.417284\pi$
$61$	1.68274e95	0.513892	0.256946	+	0.966426i	$0.417284\pi$
$62$	6.68086e94	0.0854825
$63$	2.94361e96	1.60015
$64$	2.48926e96	0.582696
$65$	−6.49900e96	−0.663715
$66$	−2.68823e97	−1.21302
$67$	4.95750e97	1.00060	0.500300	−	0.865852i	$-0.333223\pi$
$67$	4.95750e97	1.00060	0.500300	+	0.865852i	$0.333223\pi$
$68$	−2.12399e97	−0.194055
$69$	5.04966e98	2.11269
$70$	−2.45197e98	−0.475083
$71$	−1.97010e99	−1.78718	−0.893588	−	0.448889i	$-0.851820\pi$
$71$	−1.97010e99	−1.78718	−0.893588	+	0.448889i	$0.851820\pi$
$72$	6.53571e99	2.80546
$73$	1.51394e99	0.310697	0.155349	−	0.987860i	$-0.450350\pi$
$73$	1.51394e99	0.310697	0.155349	+	0.987860i	$0.450350\pi$
$74$	7.59255e99	0.752472
$75$	3.71676e100	1.79633
$76$	−4.05787e99	−0.0965542
$77$	4.87617e100	0.576534
$78$	9.61034e100	0.569741
$79$	1.53975e101	0.461745	0.230872	−	0.972984i	$-0.425842\pi$
$79$	1.53975e101	0.461745	0.230872	+	0.972984i	$0.425842\pi$
$80$	2.69524e100	0.0412366
$81$	5.32205e102	4.18919
$82$	7.69384e101	0.314125
$83$	−5.40827e102	−1.15446	−0.577232	−	0.816580i	$-0.695867\pi$
$83$	−5.40827e102	−1.15446	−0.577232	+	0.816580i	$0.695867\pi$
$84$	−6.20753e102	−0.698196
$85$	7.12855e102	0.425685
$86$	2.27190e103	0.725640
$87$	−9.00485e103	−1.54952
$88$	1.08266e104	1.01081
$89$	−1.73192e103	−0.0883408	−0.0441704	−	0.999024i	$-0.514064\pi$
$89$	−1.73192e103	−0.0883408	−0.0441704	+	0.999024i	$0.514064\pi$
$90$	−8.48854e104	−2.38154
$91$	−1.74321e104	−0.270792
$92$	−7.87005e104	−0.681285
$93$	−5.67658e104	−0.275581
$94$	1.07207e105	0.293685
$95$	1.36191e105	0.211805
$96$	−2.22316e106	−1.97451
$97$	2.04081e105	0.104116	0.0520578	−	0.998644i	$-0.483422\pi$
$97$	2.04081e105	0.104116	0.0520578	+	0.998644i	$0.483422\pi$
$98$	1.40269e106	0.413398
$99$	1.68810e107	2.89011
$100$	−5.79268e106	−0.579268
$101$	2.98214e107	1.75120	0.875599	−	0.483039i	$-0.160467\pi$
$101$	2.98214e107	1.75120	0.875599	+	0.483039i	$0.160467\pi$
$102$	−1.05413e107	−0.365413
$103$	−3.48209e107	−0.716224	−0.358112	−	0.933679i	$-0.616579\pi$
$103$	−3.48209e107	−0.716224	−0.358112	+	0.933679i	$0.616579\pi$
$104$	−3.87047e107	−0.474766
$105$	2.08338e108	1.53159
$106$	−5.20196e107	−0.230305
$107$	4.28695e108	1.14846	0.574231	−	0.818693i	$-0.305301\pi$
$107$	4.28695e108	1.14846	0.574231	+	0.818693i	$0.305301\pi$
$108$	−1.39023e109	−2.26421
$109$	1.04704e109	1.04146	0.520732	−	0.853721i	$-0.325659\pi$
$109$	1.04704e109	1.04146	0.520732	+	0.853721i	$0.325659\pi$
$110$	−1.40615e109	−0.858071
$111$	−6.45122e109	−2.42584
$112$	7.22939e107	0.0168243
$113$	1.09349e109	0.158168	0.0790840	−	0.996868i	$-0.474800\pi$
$113$	1.09349e109	0.158168	0.0790840	+	0.996868i	$0.474800\pi$
$114$	−2.01391e109	−0.181816
$115$	2.64136e110	1.49449
$116$	1.40343e110	0.499677
$117$	−6.03489e110	−1.35746
$118$	3.07716e110	0.438998
$119$	1.91208e110	0.173677
$120$	4.62574e111	2.68525
$121$	1.10930e110	0.0413079
$122$	−1.30159e111	−0.312050
$123$	−6.53728e111	−1.01268
$124$	8.84712e110	0.0888673
$125$	−1.74540e111	−0.114080
$126$	−2.27687e112	−0.971658
$127$	2.73604e112	0.764933	0.382467	−	0.923969i	$-0.375075\pi$
$127$	2.73604e112	0.764933	0.382467	+	0.923969i	$0.375075\pi$
$128$	3.56326e112	0.654809
$129$	−1.93038e113	−2.33934
$130$	5.02694e112	0.403027
$131$	−5.72197e112	−0.304461	−0.152230	−	0.988345i	$-0.548646\pi$
$131$	−5.72197e112	−0.304461	−0.152230	+	0.988345i	$0.548646\pi$
$132$	−3.55989e113	−1.26105
$133$	3.65302e112	0.0864151
$134$	−3.83460e113	−0.607594
$135$	4.66592e114	4.96684
$136$	4.24540e113	0.304500
$137$	−2.83070e114	−1.37197	−0.685983	−	0.727617i	$-0.740628\pi$
$137$	−2.83070e114	−1.37197	−0.685983	+	0.727617i	$0.740628\pi$
$138$	−3.90589e114	−1.28289
$139$	7.98261e114	1.78178	0.890888	−	0.454223i	$-0.150083\pi$
$139$	7.98261e114	1.78178	0.890888	+	0.454223i	$0.150083\pi$
$140$	−3.24701e114	−0.493894
$141$	−9.10913e114	−0.946791
$142$	1.52386e115	1.08522
$143$	−9.99697e114	−0.489092
$144$	2.50276e114	0.0843386
$145$	−4.71022e115	−1.09611
$146$	−1.17103e115	−0.188664
$147$	−1.19184e116	−1.33272
$148$	1.00544e116	0.782267
$149$	2.88218e115	0.156407	0.0782035	−	0.996937i	$-0.475082\pi$
$149$	2.88218e115	0.156407	0.0782035	+	0.996937i	$0.475082\pi$
$150$	−2.87489e116	−1.09079
$151$	6.67733e116	1.77556	0.887781	−	0.460265i	$-0.152246\pi$
$151$	6.67733e116	1.77556	0.887781	+	0.460265i	$0.152246\pi$
$152$	8.11083e115	0.151507
$153$	6.61948e116	0.870628
$154$	−3.77169e116	−0.350088
$155$	−2.96928e116	−0.194942
$156$	1.27265e117	0.592301
$157$	2.20426e117	0.728837	0.364419	−	0.931235i	$-0.381268\pi$
$157$	2.20426e117	0.728837	0.364419	+	0.931235i	$0.381268\pi$
$158$	−1.19099e117	−0.280385
$159$	4.41999e117	0.742463
$160$	−1.16288e118	−1.39674
$161$	7.08486e117	0.609743
$162$	−4.11658e118	−2.54380
$163$	−3.93298e118	−1.74858	−0.874290	−	0.485405i	$-0.838672\pi$
$163$	−3.93298e118	−1.74858	−0.874290	+	0.485405i	$0.838672\pi$
$164$	1.01885e118	0.326563
$165$	1.19478e119	2.76627
$166$	4.18327e118	0.701024
$167$	−1.23802e119	−1.50452	−0.752259	−	0.658867i	$-0.771036\pi$
$167$	−1.23802e119	−1.50452	−0.752259	+	0.658867i	$0.771036\pi$
$168$	1.24075e119	1.09557
$169$	−1.19836e119	−0.770279
$170$	−5.51389e118	−0.258488
$171$	1.26465e119	0.433191
$172$	3.00856e119	0.754373
$173$	6.47259e117	0.0119018	0.00595088	−	0.999982i	$-0.498106\pi$
$173$	6.47259e117	0.0119018	0.00595088	+	0.999982i	$0.498106\pi$
$174$	6.96520e119	0.940912
$175$	5.21475e119	0.518439
$176$	4.14590e118	0.0303872
$177$	−2.61460e120	−1.41526
$178$	1.33963e119	0.0536431
$179$	−2.20280e120	−0.653639	−0.326819	−	0.945087i	$-0.605977\pi$
$179$	−2.20280e120	−0.653639	−0.326819	+	0.945087i	$0.605977\pi$
$180$	−1.12409e121	−2.47584
$181$	5.39860e120	0.884052	0.442026	−	0.897002i	$-0.354260\pi$
$181$	5.39860e120	0.884052	0.442026	+	0.897002i	$0.354260\pi$
$182$	1.34837e120	0.164433
$183$	1.10594e121	1.00600
$184$	1.57306e121	1.06903
$185$	−3.37448e121	−1.71601
$186$	4.39081e120	0.167341
$187$	1.09654e121	0.313687
$188$	1.41968e121	0.305314
$189$	1.25153e122	2.02645
$190$	−1.05343e121	−0.128614
$191$	−6.77853e121	−0.624957	−0.312479	−	0.949925i	$-0.601159\pi$
$191$	−6.77853e121	−0.624957	−0.312479	+	0.949925i	$0.601159\pi$
$192$	1.63600e122	1.14069
$193$	−2.82491e122	−1.49172	−0.745862	−	0.666100i	$-0.767962\pi$
$193$	−2.82491e122	−1.49172	−0.745862	+	0.666100i	$0.767962\pi$
$194$	−1.57856e121	−0.0632220
$195$	−4.27128e122	−1.29929
$196$	1.85752e122	0.429767
$197$	4.89633e122	0.862835	0.431417	−	0.902152i	$-0.358014\pi$
$197$	4.89633e122	0.862835	0.431417	+	0.902152i	$0.358014\pi$
$198$	−1.30573e123	−1.75496
$199$	−7.15013e122	−0.733964	−0.366982	−	0.930228i	$-0.619609\pi$
$199$	−7.15013e122	−0.733964	−0.366982	+	0.930228i	$0.619609\pi$
$200$	1.15783e123	0.908953
$201$	3.25817e123	1.95878
$202$	−2.30667e123	−1.06338
$203$	−1.26341e123	−0.447206
$204$	−1.39593e123	−0.379882
$205$	−3.41950e123	−0.716359
$206$	2.69338e123	0.434912
$207$	2.45273e124	3.05658
$208$	−1.48214e122	−0.0142726
$209$	2.09493e123	0.156079
$210$	−1.61148e124	−0.930023
$211$	3.58398e124	1.60418	0.802092	−	0.597200i	$-0.203720\pi$
$211$	3.58398e124	1.60418	0.802092	+	0.597200i	$0.203720\pi$
$212$	−6.88868e123	−0.239424
$213$	−1.29479e125	−3.49858
$214$	−3.31593e124	−0.697379
$215$	−1.00974e125	−1.65482
$216$	2.77878e125	3.55286
$217$	−7.96446e123	−0.0795354
$218$	−8.09876e124	−0.632407
$219$	9.94997e124	0.608221
$220$	−1.86209e125	−0.892047
$221$	−3.92008e124	−0.147336
$222$	4.98998e125	1.47304
$223$	−3.82169e125	−0.887045	−0.443522	−	0.896263i	$-0.646271\pi$
$223$	−3.82169e125	−0.887045	−0.443522	+	0.896263i	$0.646271\pi$
$224$	−3.11918e125	−0.569864
$225$	1.80531e126	2.59889
$226$	−8.45809e124	−0.0960442
$227$	4.59984e124	0.0412439	0.0206219	−	0.999787i	$-0.493435\pi$
$227$	4.59984e124	0.0412439	0.0206219	+	0.999787i	$0.493435\pi$
$228$	−2.66692e125	−0.189015
$229$	−8.92992e125	−0.500783	−0.250391	−	0.968145i	$-0.580559\pi$
$229$	−8.92992e125	−0.500783	−0.250391	+	0.968145i	$0.580559\pi$
$230$	−2.04307e126	−0.907497
$231$	3.20472e126	1.12863
$232$	−2.80516e126	−0.784063
$233$	−7.80293e126	−1.73267	−0.866335	−	0.499463i	$-0.833531\pi$
$233$	−7.80293e126	−1.73267	−0.866335	+	0.499463i	$0.833531\pi$
$234$	4.66795e126	0.824287
$235$	−4.76477e126	−0.669747
$236$	4.07492e126	0.456381
$237$	1.01196e127	0.903913
$238$	−1.47898e126	−0.105462
$239$	−1.21238e127	−0.690797	−0.345399	−	0.938456i	$-0.612256\pi$
$239$	−1.21238e127	−0.690797	−0.345399	+	0.938456i	$0.612256\pi$
$240$	1.77137e126	0.0807248
$241$	−3.75235e127	−1.36896	−0.684482	−	0.729030i	$-0.739972\pi$
$241$	−3.75235e127	−1.36896	−0.684482	+	0.729030i	$0.739972\pi$
$242$	−8.58039e125	−0.0250833
$243$	1.96796e128	4.61404
$244$	−1.72363e127	−0.324406
$245$	−6.23422e127	−0.942750
$246$	5.05655e127	0.614931
$247$	−7.48931e126	−0.0733086
$248$	−1.76835e127	−0.139445
$249$	−3.55443e128	−2.25998
$250$	1.35006e127	0.0692727
$251$	−6.69715e127	−0.277553	−0.138776	−	0.990324i	$-0.544317\pi$
$251$	−6.69715e127	−0.277553	−0.138776	+	0.990324i	$0.544317\pi$
$252$	−3.01514e128	−1.01013
$253$	4.06302e128	1.10129
$254$	−2.11631e128	−0.464490
$255$	4.68503e128	0.833323
$256$	−6.79522e128	−0.980315
$257$	8.21762e128	0.962330	0.481165	−	0.876630i	$-0.340214\pi$
$257$	8.21762e128	0.962330	0.481165	+	0.876630i	$0.340214\pi$
$258$	1.49314e129	1.42052
$259$	−9.05130e128	−0.700122
$260$	6.65692e128	0.418985
$261$	−4.37385e129	−2.24180
$262$	4.42591e128	0.184877
$263$	2.58760e129	0.881584	0.440792	−	0.897609i	$-0.354698\pi$
$263$	2.58760e129	0.881584	0.440792	+	0.897609i	$0.354698\pi$
$264$	7.11547e129	1.97876
$265$	2.31199e129	0.525208
$266$	−2.82559e128	−0.0524738
$267$	−1.13825e129	−0.172936
$268$	−5.07796e129	−0.631652
$269$	−5.80557e129	−0.591694	−0.295847	−	0.955235i	$-0.595602\pi$
$269$	−5.80557e129	−0.591694	−0.295847	+	0.955235i	$0.595602\pi$
$270$	−3.60906e130	−3.01601
$271$	1.86511e130	1.27893	0.639467	−	0.768818i	$-0.279155\pi$
$271$	1.86511e130	1.27893	0.639467	+	0.768818i	$0.279155\pi$
$272$	1.62572e128	0.00915396
$273$	−1.14568e130	−0.530104
$274$	2.18953e130	0.833098
$275$	2.99055e130	0.936379
$276$	−5.17236e130	−1.33368
$277$	7.10429e130	1.50957	0.754785	−	0.655972i	$-0.227741\pi$
$277$	7.10429e130	1.50957	0.754785	+	0.655972i	$0.227741\pi$
$278$	−6.17450e130	−1.08195
$279$	−2.75724e130	−0.398703
$280$	6.49009e130	0.774990
$281$	1.27687e131	1.25997	0.629984	−	0.776608i	$-0.283061\pi$
$281$	1.27687e131	1.25997	0.629984	+	0.776608i	$0.283061\pi$
$282$	7.04586e130	0.574919
$283$	−1.64507e131	−1.11073	−0.555366	−	0.831606i	$-0.687422\pi$
$283$	−1.64507e131	−1.11073	−0.555366	+	0.831606i	$0.687422\pi$
$284$	2.01797e131	1.12820
$285$	8.95076e130	0.414629
$286$	7.73260e130	0.296991
$287$	−9.17205e130	−0.292271
$288$	−1.07984e132	−2.85667
$289$	−4.12026e131	−0.905504
$290$	3.64333e131	0.665588
$291$	1.34127e131	0.203817
$292$	−1.55073e131	−0.196135
$293$	3.61670e131	0.380974	0.190487	−	0.981690i	$-0.438993\pi$
$293$	3.61670e131	0.380974	0.190487	+	0.981690i	$0.438993\pi$
$294$	9.21881e131	0.809268
$295$	−1.36763e132	−1.00113
$296$	−2.00966e132	−1.22749
$297$	7.17726e132	3.66006
$298$	−2.22935e131	−0.0949749
$299$	−1.45251e132	−0.517264
$300$	−3.80707e132	−1.13398
$301$	−2.70840e132	−0.675157
$302$	−5.16488e132	−1.07817
$303$	1.95993e133	3.42815
$304$	3.10593e130	0.00455466
$305$	5.78488e132	0.711628
$306$	−5.12013e132	−0.528671
$307$	6.51322e131	0.0564798	0.0282399	−	0.999601i	$-0.491010\pi$
$307$	6.51322e131	0.0564798	0.0282399	+	0.999601i	$0.491010\pi$
$308$	−4.99466e132	−0.363951
$309$	−2.28851e133	−1.40208
$310$	2.29672e132	0.118375
$311$	−2.97318e133	−1.28985	−0.644926	−	0.764245i	$-0.723112\pi$
$311$	−2.97318e133	−1.28985	−0.644926	+	0.764245i	$0.723112\pi$
$312$	−2.54375e133	−0.929403
$313$	7.67685e132	0.236353	0.118177	−	0.992993i	$-0.462295\pi$
$313$	7.67685e132	0.236353	0.118177	+	0.992993i	$0.462295\pi$
$314$	−1.70498e133	−0.442571
$315$	1.01194e134	2.21586
$316$	−1.57717e133	−0.291487
$317$	6.55882e133	1.02366	0.511829	−	0.859087i	$-0.328968\pi$
$317$	6.55882e133	1.02366	0.511829	+	0.859087i	$0.328968\pi$
$318$	−3.41884e133	−0.450845
$319$	−7.24541e133	−0.807721
$320$	8.55750e133	0.806907
$321$	2.81748e134	2.24823
$322$	−5.48010e133	−0.370254
$323$	8.21479e132	0.0470177
$324$	−5.45137e134	−2.64452
$325$	−1.06911e134	−0.439808
$326$	3.04214e134	1.06179
$327$	6.88134e134	2.03877
$328$	−2.03648e134	−0.512423
$329$	−1.27804e134	−0.273253
$330$	−9.24152e134	−1.67976
$331$	−1.07624e134	−0.166384	−0.0831921	−	0.996534i	$-0.526512\pi$
$331$	−1.07624e134	−0.166384	−0.0831921	+	0.996534i	$0.526512\pi$
$332$	5.53968e134	0.728782
$333$	−3.13350e135	−3.50964
$334$	9.57604e134	0.913587
$335$	1.70427e135	1.38561
$336$	4.75131e133	0.0329353
$337$	2.43383e135	1.43910	0.719549	−	0.694441i	$-0.244348\pi$
$337$	2.43383e135	1.43910	0.719549	+	0.694441i	$0.244348\pi$
$338$	9.26923e134	0.467736
$339$	7.18666e134	0.309630
$340$	−7.30176e134	−0.268724
$341$	−4.56745e134	−0.143653
$342$	−9.78202e134	−0.263046
$343$	−4.12844e135	−0.949621
$344$	−6.01347e135	−1.18372
$345$	1.73596e136	2.92561
$346$	−5.00651e133	−0.00722710
$347$	−1.37149e135	−0.169655	−0.0848275	−	0.996396i	$-0.527034\pi$
$347$	−1.37149e135	−0.169655	−0.0848275	+	0.996396i	$0.527034\pi$
$348$	9.22366e135	0.978168
$349$	−5.96539e135	−0.542598	−0.271299	−	0.962495i	$-0.587453\pi$
$349$	−5.96539e135	−0.542598	−0.271299	+	0.962495i	$0.587453\pi$
$350$	−4.03358e135	−0.314811
$351$	−2.56585e136	−1.71909
$352$	−1.78878e136	−1.02926
$353$	1.45854e136	0.721062	0.360531	−	0.932747i	$-0.382596\pi$
$353$	1.45854e136	0.721062	0.360531	+	0.932747i	$0.382596\pi$
$354$	2.02238e136	0.859384
$355$	−6.77275e136	−2.47485
$356$	1.77400e135	0.0557672
$357$	1.25666e136	0.339991
$358$	1.70385e136	0.396908
$359$	1.51431e136	0.303852	0.151926	−	0.988392i	$-0.451452\pi$
$359$	1.51431e136	0.303852	0.151926	+	0.988392i	$0.451452\pi$
$360$	2.24682e137	3.88495
$361$	−6.55171e136	−0.976606
$362$	−4.17579e136	−0.536822
$363$	7.29057e135	0.0808644
$364$	1.78557e136	0.170944
$365$	5.20459e136	0.430247
$366$	−8.55435e136	−0.610870
$367$	−1.31474e137	−0.811346	−0.405673	−	0.914018i	$-0.632963\pi$
$367$	−1.31474e137	−0.811346	−0.405673	+	0.914018i	$0.632963\pi$
$368$	6.02381e135	0.0321376
$369$	−3.17530e137	−1.46512
$370$	2.61014e137	1.04201
$371$	6.20141e136	0.214282
$372$	5.81452e136	0.173967
$373$	−7.87355e136	−0.204055	−0.102028	−	0.994782i	$-0.532533\pi$
$373$	−7.87355e136	−0.204055	−0.102028	+	0.994782i	$0.532533\pi$
$374$	−8.48165e136	−0.190480
$375$	−1.14712e137	−0.223323
$376$	−2.83765e137	−0.479081
$377$	2.59021e137	0.379378
$378$	−9.68052e137	−1.23052
$379$	1.64949e136	0.0182034	0.00910171	−	0.999959i	$-0.497103\pi$
$379$	1.64949e136	0.0182034	0.00910171	+	0.999959i	$0.497103\pi$
$380$	−1.39500e137	−0.133706
$381$	1.79818e138	1.49743
$382$	5.24315e137	0.379492
$383$	2.83446e136	0.0178376	0.00891879	−	0.999960i	$-0.497161\pi$
$383$	2.83446e136	0.0178376	0.00891879	+	0.999960i	$0.497161\pi$
$384$	2.34185e138	1.28185
$385$	1.67631e138	0.798374
$386$	2.18505e138	0.905818
$387$	−9.37628e138	−3.38450
$388$	−2.09040e137	−0.0657254
$389$	1.84621e138	0.505798	0.252899	−	0.967493i	$-0.418616\pi$
$389$	1.84621e138	0.505798	0.252899	+	0.967493i	$0.418616\pi$
$390$	3.30381e138	0.788967
$391$	1.59322e138	0.331756
$392$	−3.71278e138	−0.674365
$393$	−3.76060e138	−0.596013
$394$	−3.78729e138	−0.523938
$395$	5.29331e138	0.639415
$396$	−1.72912e139	−1.82445
$397$	8.78582e138	0.810010	0.405005	−	0.914314i	$-0.367270\pi$
$397$	8.78582e138	0.810010	0.405005	+	0.914314i	$0.367270\pi$
$398$	5.53059e138	0.445684
$399$	2.40085e138	0.169166
$400$	4.43377e137	0.0273252
$401$	−1.50050e139	−0.809117	−0.404559	−	0.914512i	$-0.632575\pi$
$401$	−1.50050e139	−0.809117	−0.404559	+	0.914512i	$0.632575\pi$
$402$	−2.52018e139	−1.18943
$403$	1.63285e138	0.0674723
$404$	−3.05461e139	−1.10548
$405$	1.82960e140	5.80111
$406$	9.77244e138	0.271556
$407$	−5.19073e139	−1.26453
$408$	2.79016e139	0.596089
$409$	2.00330e139	0.375446	0.187723	−	0.982222i	$-0.439889\pi$
$409$	2.00330e139	0.375446	0.187723	+	0.982222i	$0.439889\pi$
$410$	2.64496e139	0.434994
$411$	−1.86040e140	−2.68577
$412$	3.56670e139	0.452133
$413$	−3.66837e139	−0.408457
$414$	−1.89717e140	−1.85605
$415$	−1.85924e140	−1.59868
$416$	6.39484e139	0.483433
$417$	5.24634e140	3.48801
$418$	−1.62042e139	−0.0947755
$419$	7.34776e139	0.378185	0.189093	−	0.981959i	$-0.439445\pi$
$419$	7.34776e139	0.378185	0.189093	+	0.981959i	$0.439445\pi$
$420$	−2.13401e140	−0.966849
$421$	3.42476e139	0.136627	0.0683137	−	0.997664i	$-0.478238\pi$
$421$	3.42476e139	0.136627	0.0683137	+	0.997664i	$0.478238\pi$
$422$	−2.77219e140	−0.974107
$423$	−4.42450e140	−1.36979
$424$	1.37690e140	0.375690
$425$	1.17267e140	0.282078
$426$	1.00152e141	2.12444
$427$	1.55167e140	0.290341
$428$	−4.39112e140	−0.724993
$429$	−6.57022e140	−0.957447
$430$	7.81025e140	1.00485
$431$	4.84233e140	0.550199	0.275100	−	0.961416i	$-0.411289\pi$
$431$	4.84233e140	0.550199	0.275100	+	0.961416i	$0.411289\pi$
$432$	1.06410e140	0.106807
$433$	2.15343e141	1.90998	0.954990	−	0.296638i	$-0.0958656\pi$
$433$	2.15343e141	1.90998	0.954990	+	0.296638i	$0.0958656\pi$
$434$	6.16046e139	0.0482962
$435$	−3.09566e141	−2.14574
$436$	−1.07248e141	−0.657447
$437$	3.04384e140	0.165069
$438$	−7.69625e140	−0.369330
$439$	−2.75926e141	−1.17204	−0.586018	−	0.810298i	$-0.699305\pi$
$439$	−2.75926e141	−1.17204	−0.586018	+	0.810298i	$0.699305\pi$
$440$	3.72193e141	1.39975
$441$	−5.78902e141	−1.92815
$442$	3.03216e140	0.0894665
$443$	−1.83176e141	−0.478927	−0.239464	−	0.970905i	$-0.576972\pi$
$443$	−1.83176e141	−0.478927	−0.239464	+	0.970905i	$0.576972\pi$
$444$	6.60798e141	1.53137
$445$	−5.95392e140	−0.122333
$446$	2.95606e141	0.538639
$447$	1.89423e141	0.306183
$448$	2.29536e141	0.329214
$449$	4.09229e141	0.520939	0.260469	−	0.965482i	$-0.416123\pi$
$449$	4.09229e141	0.520939	0.260469	+	0.965482i	$0.416123\pi$
$450$	−1.39640e142	−1.57812
$451$	−5.25998e141	−0.527885
$452$	−1.12006e141	−0.0998471
$453$	4.38848e142	3.47585
$454$	−3.55795e140	−0.0250445
$455$	−5.99276e141	−0.374988
$456$	5.33061e141	0.296591
$457$	−3.39802e142	−1.68155	−0.840774	−	0.541386i	$-0.817900\pi$
$457$	−3.39802e142	−1.68155	−0.840774	+	0.541386i	$0.817900\pi$
$458$	6.90725e141	0.304090
$459$	2.81440e142	1.10257
$460$	−2.70554e142	−0.943430
$461$	−3.95104e142	−1.22662	−0.613312	−	0.789841i	$-0.710163\pi$
$461$	−3.95104e142	−1.22662	−0.613312	+	0.789841i	$0.710163\pi$
$462$	−2.47884e142	−0.685334
$463$	−3.09482e142	−0.762171	−0.381086	−	0.924540i	$-0.624450\pi$
$463$	−3.09482e142	−0.762171	−0.381086	+	0.924540i	$0.624450\pi$
$464$	−1.07420e141	−0.0235707
$465$	−1.95148e142	−0.381619
$466$	6.03553e142	1.05213
$467$	−1.63171e142	−0.253623	−0.126812	−	0.991927i	$-0.540474\pi$
$467$	−1.63171e142	−0.253623	−0.126812	+	0.991927i	$0.540474\pi$
$468$	6.18153e142	0.856925
$469$	4.57134e142	0.565323
$470$	3.68552e142	0.406690
$471$	1.44868e143	1.42677
$472$	−8.14491e142	−0.716126
$473$	−1.55321e143	−1.21943
$474$	−7.82745e142	−0.548882
$475$	2.24039e142	0.140351
$476$	−1.95854e142	−0.109638
$477$	2.14689e143	1.07418
$478$	9.37768e142	0.419472
$479$	3.24819e143	1.29925	0.649623	−	0.760256i	$-0.274927\pi$
$479$	3.24819e143	1.29925	0.649623	+	0.760256i	$0.274927\pi$
$480$	−7.64271e143	−2.73427
$481$	1.85567e143	0.593934
$482$	2.90243e143	0.831275
$483$	4.65632e143	1.19364
$484$	−1.13626e142	−0.0260765
$485$	7.01585e142	0.144177
$486$	−1.52221e144	−2.80178
$487$	1.36544e143	0.225150	0.112575	−	0.993643i	$-0.464090\pi$
$487$	1.36544e143	0.225150	0.112575	+	0.993643i	$0.464090\pi$
$488$	3.44518e143	0.509039
$489$	−2.58484e144	−3.42302
$490$	4.82214e143	0.572465
$491$	1.51119e143	0.160864	0.0804321	−	0.996760i	$-0.474370\pi$
$491$	1.51119e143	0.160864	0.0804321	+	0.996760i	$0.474370\pi$
$492$	6.69613e143	0.639280
$493$	−2.84112e143	−0.243321
$494$	5.79294e142	0.0445151
$495$	5.80329e144	4.00217
$496$	−6.77167e141	−0.00419205
$497$	−1.81664e144	−1.00972
$498$	2.74933e144	1.37233
$499$	−6.57004e143	−0.294570	−0.147285	−	0.989094i	$-0.547053\pi$
$499$	−6.57004e143	−0.294570	−0.147285	+	0.989094i	$0.547053\pi$
$500$	1.78781e143	0.0720157
$501$	−8.13655e144	−2.94525
$502$	5.18021e143	0.168538
$503$	−1.07087e144	−0.313219	−0.156609	−	0.987661i	$-0.550056\pi$
$503$	−1.07087e144	−0.313219	−0.156609	+	0.987661i	$0.550056\pi$
$504$	6.02662e144	1.58504
$505$	1.02519e145	2.42502
$506$	−3.14272e144	−0.668734
$507$	−7.87586e144	−1.50790
$508$	−2.80252e144	−0.482882
$509$	−5.54511e144	−0.860020	−0.430010	−	0.902824i	$-0.641490\pi$
$509$	−5.54511e144	−0.860020	−0.430010	+	0.902824i	$0.641490\pi$
$510$	−3.62385e144	−0.506018
$511$	1.39602e144	0.175539
$512$	−5.25653e143	−0.0595328
$513$	5.37690e144	0.548597
$514$	−6.35628e144	−0.584355
$515$	−1.19706e145	−0.991814
$516$	1.97729e145	1.47676
$517$	−7.32932e144	−0.493537
$518$	7.00113e144	0.425134
$519$	4.25392e143	0.0232989
$520$	−1.33058e145	−0.657447
$521$	3.95129e145	1.76165	0.880827	−	0.473438i	$-0.156987\pi$
$521$	3.95129e145	1.76165	0.880827	+	0.473438i	$0.156987\pi$
$522$	3.38315e145	1.36129
$523$	−3.98929e145	−1.44896	−0.724478	−	0.689298i	$-0.757919\pi$
$523$	−3.98929e145	−1.44896	−0.724478	+	0.689298i	$0.757919\pi$
$524$	5.86100e144	0.192198
$525$	3.42725e145	1.01490
$526$	−2.00149e145	−0.535324
$527$	−1.79102e144	−0.0432745
$528$	2.72477e144	0.0594861
$529$	8.34898e144	0.164723
$530$	−1.78831e145	−0.318922
$531$	−1.26997e146	−2.04755
$532$	−3.74179e144	−0.0545515
$533$	1.88042e145	0.247942
$534$	8.80432e144	0.105012
$535$	1.47375e146	1.59037
$536$	1.01498e146	0.991151
$537$	−1.44773e146	−1.27956
$538$	4.49057e145	0.359294
$539$	−9.58968e145	−0.694713
$540$	−4.77929e146	−3.13543
$541$	1.09502e146	0.650679	0.325340	−	0.945597i	$-0.394521\pi$
$541$	1.09502e146	0.650679	0.325340	+	0.945597i	$0.394521\pi$
$542$	−1.44266e146	−0.776606
$543$	3.54808e146	1.73062
$544$	−7.01430e145	−0.310058
$545$	3.59946e146	1.44220
$546$	8.86176e145	0.321894
$547$	−1.03149e146	−0.339738	−0.169869	−	0.985467i	$-0.554335\pi$
$547$	−1.03149e146	−0.339738	−0.169869	+	0.985467i	$0.554335\pi$
$548$	2.89948e146	0.866085
$549$	5.37177e146	1.45545
$550$	−2.31317e146	−0.568597
$551$	−5.42796e145	−0.121067
$552$	1.03385e147	2.09274
$553$	1.41982e146	0.260878
$554$	−5.49513e146	−0.916655
$555$	−2.21778e147	−3.35926
$556$	−8.17658e146	−1.12479
$557$	5.26440e145	0.0657803	0.0328901	−	0.999459i	$-0.489529\pi$
$557$	5.26440e145	0.0657803	0.0328901	+	0.999459i	$0.489529\pi$
$558$	2.13271e146	0.242104
$559$	5.55266e146	0.572756
$560$	2.48529e145	0.0232980
$561$	7.20667e146	0.614075
$562$	−9.87655e146	−0.765090
$563$	−1.09572e147	−0.771796	−0.385898	−	0.922541i	$-0.626108\pi$
$563$	−1.09572e147	−0.771796	−0.385898	+	0.922541i	$0.626108\pi$
$564$	9.33047e146	0.597684
$565$	3.75917e146	0.219028
$566$	1.27245e147	0.674469
$567$	4.90749e147	2.36682
$568$	−4.03350e147	−1.77030
$569$	−4.17342e147	−1.66719	−0.833596	−	0.552375i	$-0.813722\pi$
$569$	−4.17342e147	−1.66719	−0.833596	+	0.552375i	$0.813722\pi$
$570$	−6.92336e146	−0.251775
$571$	4.01522e147	1.32947	0.664734	−	0.747080i	$-0.268545\pi$
$571$	4.01522e147	1.32947	0.664734	+	0.747080i	$0.268545\pi$
$572$	1.02399e147	0.308750
$573$	−4.45499e147	−1.22342
$574$	7.09453e146	0.177475
$575$	4.34514e147	0.990316
$576$	7.94639e147	1.65032
$577$	5.67656e147	1.07443	0.537217	−	0.843444i	$-0.319476\pi$
$577$	5.67656e147	1.07443	0.537217	+	0.843444i	$0.319476\pi$
$578$	3.18700e147	0.549848
$579$	−1.85659e148	−2.92020
$580$	4.82467e147	0.691943
$581$	−4.98700e147	−0.652253
$582$	−1.03746e147	−0.123764
$583$	3.55638e147	0.387026
$584$	3.09958e147	0.307763
$585$	−2.07465e148	−1.87978
$586$	−2.79750e147	−0.231338
$587$	−2.12060e148	−1.60074	−0.800370	−	0.599506i	$-0.795364\pi$
$587$	−2.12060e148	−1.60074	−0.800370	+	0.599506i	$0.795364\pi$
$588$	1.22080e148	0.841312
$589$	−3.42174e146	−0.0215317
$590$	1.05786e148	0.607916
$591$	3.21797e148	1.68909
$592$	−7.69574e146	−0.0369011
$593$	2.49619e148	1.09358	0.546791	−	0.837269i	$-0.315849\pi$
$593$	2.49619e148	1.09358	0.546791	+	0.837269i	$0.315849\pi$
$594$	−5.55157e148	−2.22250
$595$	6.57328e147	0.240505
$596$	−2.95222e147	−0.0987355
$597$	−4.69922e148	−1.43681
$598$	1.12351e148	0.314098
$599$	4.74144e148	1.21220	0.606101	−	0.795387i	$-0.292733\pi$
$599$	4.74144e148	1.21220	0.606101	+	0.795387i	$0.292733\pi$
$600$	7.60953e148	1.77937
$601$	−4.47824e148	−0.957906	−0.478953	−	0.877841i	$-0.658984\pi$
$601$	−4.47824e148	−0.957906	−0.478953	+	0.877841i	$0.658984\pi$
$602$	2.09493e148	0.409975
$603$	1.58257e149	2.83391
$604$	−6.83958e148	−1.12086
$605$	3.81352e147	0.0572023
$606$	−1.51599e149	−2.08167
$607$	4.86092e148	0.611116	0.305558	−	0.952173i	$-0.401157\pi$
$607$	4.86092e148	0.611116	0.305558	+	0.952173i	$0.401157\pi$
$608$	−1.34008e148	−0.154273
$609$	−8.30342e148	−0.875451
$610$	−4.47457e148	−0.432121
$611$	2.62020e148	0.231809
$612$	−6.78033e148	−0.549604
$613$	−3.37939e148	−0.251017	−0.125508	−	0.992093i	$-0.540056\pi$
$613$	−3.37939e148	−0.251017	−0.125508	+	0.992093i	$0.540056\pi$
$614$	−5.03794e147	−0.0342961
$615$	−2.24737e149	−1.40235
$616$	9.98326e148	0.571090
$617$	2.23961e147	0.0117467	0.00587334	−	0.999983i	$-0.498130\pi$
$617$	2.23961e147	0.0117467	0.00587334	+	0.999983i	$0.498130\pi$
$618$	1.77015e149	0.851385
$619$	−3.75019e149	−1.65426	−0.827129	−	0.562012i	$-0.810027\pi$
$619$	−3.75019e149	−1.65426	−0.827129	+	0.562012i	$0.810027\pi$
$620$	3.04143e148	0.123062
$621$	1.04282e150	3.87089
$622$	2.29973e149	0.783235
$623$	−1.59701e148	−0.0499111
$624$	−9.74097e147	−0.0279400
$625$	−4.08535e149	−1.07559
$626$	−5.93801e148	−0.143520
$627$	1.37683e149	0.305540
$628$	−2.25782e149	−0.460095
$629$	−2.03542e149	−0.380930
$630$	−7.82733e149	−1.34553
$631$	−5.73667e149	−0.905919	−0.452959	−	0.891531i	$-0.649632\pi$
$631$	−5.73667e149	−0.905919	−0.452959	+	0.891531i	$0.649632\pi$
$632$	3.15242e149	0.457384
$633$	2.35547e150	3.14036
$634$	−5.07321e149	−0.621595
$635$	9.40587e149	1.05926
$636$	−4.52739e149	−0.468697
$637$	3.42828e149	0.326299
$638$	5.60429e149	0.490472
$639$	−6.28909e150	−5.06165
$640$	1.22497e150	0.906766
$641$	2.20409e150	1.50081	0.750403	−	0.660981i	$-0.229860\pi$
$641$	2.20409e150	1.50081	0.750403	+	0.660981i	$0.229860\pi$
$642$	−2.17930e150	−1.36519
$643$	2.71161e150	1.56293	0.781465	−	0.623949i	$-0.214473\pi$
$643$	2.71161e150	1.56293	0.781465	+	0.623949i	$0.214473\pi$
$644$	−7.25702e149	−0.384914
$645$	−6.63620e150	−3.23947
$646$	−6.35410e148	−0.0285505
$647$	1.57949e150	0.653338	0.326669	−	0.945139i	$-0.394074\pi$
$647$	1.57949e150	0.653338	0.326669	+	0.945139i	$0.394074\pi$
$648$	1.08961e151	4.14963
$649$	−2.10374e150	−0.737734
$650$	8.26951e149	0.267064
$651$	−5.23441e149	−0.155699
$652$	4.02855e150	1.10383
$653$	2.39592e150	0.604807	0.302404	−	0.953180i	$-0.402211\pi$
$653$	2.39592e150	0.604807	0.302404	+	0.953180i	$0.402211\pi$
$654$	−5.32268e150	−1.23800
$655$	−1.96708e150	−0.421611
$656$	−7.79841e148	−0.0154046
$657$	4.83292e150	0.879958
$658$	9.88561e149	0.165927
$659$	1.99206e150	0.308271	0.154136	−	0.988050i	$-0.450741\pi$
$659$	1.99206e150	0.308271	0.154136	+	0.988050i	$0.450741\pi$
$660$	−1.22381e151	−1.74627
$661$	−8.22883e149	−0.108283	−0.0541415	−	0.998533i	$-0.517242\pi$
$661$	−8.22883e149	−0.108283	−0.0541415	+	0.998533i	$0.517242\pi$
$662$	8.32467e149	0.101033
$663$	−2.57636e150	−0.288425
$664$	−1.10727e151	−1.14356
$665$	1.25582e150	0.119666
$666$	2.42374e151	2.13116
$667$	−1.05273e151	−0.854247
$668$	1.26811e151	0.949762
$669$	−2.51170e151	−1.73648
$670$	−1.31825e151	−0.841384
$671$	8.89849e150	0.524399
$672$	−2.04999e151	−1.11557
$673$	−1.64181e151	−0.825119	−0.412559	−	0.910931i	$-0.635365\pi$
$673$	−1.64181e151	−0.825119	−0.412559	+	0.910931i	$0.635365\pi$
$674$	−1.88255e151	−0.873862
$675$	7.67562e151	3.29125
$676$	1.22748e151	0.486256
$677$	3.13789e151	1.14854	0.574268	−	0.818667i	$-0.305287\pi$
$677$	3.13789e151	1.14854	0.574268	+	0.818667i	$0.305287\pi$
$678$	−5.55884e150	−0.188016
$679$	1.88185e150	0.0588236
$680$	1.45947e151	0.421665
$681$	3.02311e150	0.0807391
$682$	3.53290e150	0.0872302
$683$	4.95808e151	1.13190	0.565948	−	0.824441i	$-0.308510\pi$
$683$	4.95808e151	1.13190	0.565948	+	0.824441i	$0.308510\pi$
$684$	−1.29538e151	−0.273462
$685$	−9.73129e151	−1.89987
$686$	3.19332e151	0.576637
$687$	−5.86894e151	−0.980334
$688$	−2.30278e150	−0.0355853
$689$	−1.27139e151	−0.181782
$690$	−1.34275e152	−1.77652
$691$	−5.32381e150	−0.0651849	−0.0325924	−	0.999469i	$-0.510376\pi$
$691$	−5.32381e150	−0.0651849	−0.0325924	+	0.999469i	$0.510376\pi$
$692$	−6.62986e149	−0.00751326
$693$	1.55660e152	1.63287
$694$	1.06084e151	0.103019
$695$	2.74423e152	2.46737
$696$	−1.84361e152	−1.53488
$697$	−2.06258e151	−0.159022
$698$	4.61420e151	0.329481
$699$	−5.12825e152	−3.39188
$700$	−5.34146e151	−0.327277
$701$	2.73158e152	1.55060	0.775300	−	0.631593i	$-0.217599\pi$
$701$	2.73158e152	1.55060	0.775300	+	0.631593i	$0.217599\pi$
$702$	1.98467e152	1.04388
$703$	−3.88868e151	−0.189536
$704$	1.31634e152	0.594609
$705$	−3.13151e152	−1.31110
$706$	−1.12818e152	−0.437850
$707$	2.74985e152	0.989397
$708$	2.67813e152	0.893412
$709$	−2.06990e152	−0.640290	−0.320145	−	0.947369i	$-0.603732\pi$
$709$	−2.06990e152	−0.640290	−0.320145	+	0.947369i	$0.603732\pi$
$710$	5.23869e152	1.50280
$711$	4.91531e152	1.30776
$712$	−3.54585e151	−0.0875066
$713$	−6.63630e151	−0.151927
$714$	−9.72019e151	−0.206453
$715$	−3.43672e152	−0.677285
$716$	2.25632e152	0.412624
$717$	−7.96801e152	−1.35231
$718$	−1.17131e152	−0.184508
$719$	−1.33685e152	−0.195473	−0.0977363	−	0.995212i	$-0.531160\pi$
$719$	−1.33685e152	−0.195473	−0.0977363	+	0.995212i	$0.531160\pi$
$720$	8.60392e151	0.116791
$721$	−3.21086e152	−0.404655
$722$	5.06771e152	0.593023
$723$	−2.46613e153	−2.67989
$724$	−5.52978e152	−0.558078
$725$	−7.74850e152	−0.726330
$726$	−5.63922e151	−0.0491032
$727$	1.91224e153	1.54686	0.773429	−	0.633882i	$-0.218540\pi$
$727$	1.91224e153	1.54686	0.773429	+	0.633882i	$0.218540\pi$
$728$	−3.56898e152	−0.268235
$729$	6.93523e153	4.84326
$730$	−4.02572e152	−0.261259
$731$	−6.09054e152	−0.367347
$732$	−1.13281e153	−0.635058
$733$	−1.42216e153	−0.741114	−0.370557	−	0.928810i	$-0.620833\pi$
$733$	−1.42216e153	−0.741114	−0.370557	+	0.928810i	$0.620833\pi$
$734$	1.01695e153	0.492673
$735$	−4.09726e153	−1.84553
$736$	−2.59902e153	−1.08855
$737$	2.62157e153	1.02106
$738$	2.45608e153	0.889666
$739$	2.44310e153	0.823120	0.411560	−	0.911383i	$-0.364984\pi$
$739$	2.44310e153	0.823120	0.411560	+	0.911383i	$0.364984\pi$
$740$	3.45647e153	1.08327
$741$	−4.92213e152	−0.143509
$742$	−4.79676e152	−0.130118
$743$	2.01693e153	0.509084	0.254542	−	0.967062i	$-0.418075\pi$
$743$	2.01693e153	0.509084	0.254542	+	0.967062i	$0.418075\pi$
$744$	−1.16220e153	−0.272978
$745$	9.90827e152	0.216589
$746$	6.09015e152	0.123908
$747$	−1.72646e154	−3.26968
$748$	−1.12318e153	−0.198022
$749$	3.95302e153	0.648862
$750$	8.87288e152	0.135609
$751$	−7.19595e153	−1.02412	−0.512061	−	0.858949i	$-0.671118\pi$
$751$	−7.19595e153	−1.02412	−0.512061	+	0.858949i	$0.671118\pi$
$752$	−1.08664e152	−0.0144023
$753$	−4.40151e153	−0.543338
$754$	−2.00351e153	−0.230370
$755$	2.29551e154	2.45877
$756$	−1.28194e154	−1.27924
$757$	1.70051e153	0.158106	0.0790531	−	0.996870i	$-0.474810\pi$
$757$	1.70051e153	0.158106	0.0790531	+	0.996870i	$0.474810\pi$
$758$	−1.27587e152	−0.0110536
$759$	2.67030e154	2.15588
$760$	2.78831e153	0.209804
$761$	−1.71700e154	−1.20418	−0.602091	−	0.798427i	$-0.705666\pi$
$761$	−1.71700e154	−1.20418	−0.602091	+	0.798427i	$0.705666\pi$
$762$	−1.39089e154	−0.909286
$763$	9.65478e153	0.588409
$764$	6.94324e153	0.394518
$765$	2.27562e154	1.20563
$766$	−2.19244e152	−0.0108315
$767$	7.52078e153	0.346506
$768$	−4.46597e154	−1.91907
$769$	−1.58434e154	−0.635023	−0.317512	−	0.948254i	$-0.602847\pi$
$769$	−1.58434e154	−0.635023	−0.317512	+	0.948254i	$0.602847\pi$
$770$	−1.29662e154	−0.484796
$771$	5.40079e154	1.88386
$772$	2.89355e154	0.941685
$773$	−4.85906e154	−1.47553	−0.737767	−	0.675056i	$-0.764120\pi$
$773$	−4.85906e154	−1.47553	−0.737767	+	0.675056i	$0.764120\pi$
$774$	7.25250e154	2.05516
$775$	−4.88459e153	−0.129178
$776$	4.17828e153	0.103132
$777$	−5.94871e154	−1.37056
$778$	−1.42803e154	−0.307135
$779$	−3.94056e153	−0.0791231
$780$	4.37507e154	0.820207
$781$	−1.04181e155	−1.82371
$782$	−1.23235e154	−0.201452
$783$	−1.85962e155	−2.83904
$784$	−1.42176e153	−0.0202730
$785$	7.57771e154	1.00928
$786$	2.90880e154	0.361916
$787$	8.21955e154	0.955432	0.477716	−	0.878514i	$-0.341465\pi$
$787$	8.21955e154	0.955432	0.477716	+	0.878514i	$0.341465\pi$
$788$	−5.01531e154	−0.544684
$789$	1.70062e155	1.72579
$790$	−4.09435e154	−0.388272
$791$	1.00831e154	0.0893623
$792$	3.45614e155	2.86282
$793$	−3.18118e154	−0.246305
$794$	−6.79579e154	−0.491862
$795$	1.51949e155	1.02815
$796$	7.32387e154	0.463331
$797$	−3.24875e155	−1.92175	−0.960874	−	0.276986i	$-0.910664\pi$
$797$	−3.24875e155	−1.92175	−0.960874	+	0.276986i	$0.910664\pi$
$798$	−1.85704e154	−0.102723
$799$	−2.87402e154	−0.148675
$800$	−1.91299e155	−0.925546
$801$	−5.52874e154	−0.250200
$802$	1.16063e155	0.491320
$803$	8.00587e154	0.317049
$804$	−3.33734e155	−1.23652
$805$	2.43561e155	0.844361
$806$	−1.26300e154	−0.0409711
$807$	−3.81554e155	−1.15830
$808$	6.10551e155	1.73466
$809$	1.47329e155	0.391779	0.195890	−	0.980626i	$-0.437241\pi$
$809$	1.47329e155	0.391779	0.195890	+	0.980626i	$0.437241\pi$
$810$	−1.41518e156	−3.52260
$811$	2.02874e155	0.472728	0.236364	−	0.971665i	$-0.424044\pi$
$811$	2.02874e155	0.472728	0.236364	+	0.971665i	$0.424044\pi$
$812$	1.29411e155	0.282309
$813$	1.22579e156	2.50364
$814$	4.01500e155	0.767856
$815$	−1.35207e156	−2.42140
$816$	1.06846e154	0.0179198
$817$	−1.16360e155	−0.182778
$818$	−1.54954e155	−0.227982
$819$	−5.56481e155	−0.766940
$820$	3.50259e155	0.452218
$821$	5.33435e154	0.0645242	0.0322621	−	0.999479i	$-0.489729\pi$
$821$	5.33435e154	0.0645242	0.0322621	+	0.999479i	$0.489729\pi$
$822$	1.43901e156	1.63087
$823$	1.04411e156	1.10880	0.554401	−	0.832250i	$-0.312947\pi$
$823$	1.04411e156	1.10880	0.554401	+	0.832250i	$0.312947\pi$
$824$	−7.12909e155	−0.709460
$825$	1.96545e156	1.83306
$826$	2.83747e155	0.248027
$827$	−2.00348e156	−1.64150	−0.820749	−	0.571290i	$-0.806443\pi$
$827$	−2.00348e156	−1.64150	−0.820749	+	0.571290i	$0.806443\pi$
$828$	−2.51233e156	−1.92954
$829$	7.68441e155	0.553278	0.276639	−	0.960974i	$-0.410779\pi$
$829$	7.68441e155	0.553278	0.276639	+	0.960974i	$0.410779\pi$
$830$	1.43811e156	0.970765
$831$	4.66909e156	2.95514
$832$	−4.70588e155	−0.279282
$833$	−3.76037e155	−0.209278
$834$	−4.05802e156	−2.11802
$835$	−4.25603e156	−2.08343
$836$	−2.14584e155	−0.0985283
$837$	−1.17229e156	−0.504922
$838$	−5.68345e155	−0.229645
$839$	−3.90372e155	−0.147984	−0.0739919	−	0.997259i	$-0.523574\pi$
$839$	−3.90372e155	−0.147984	−0.0739919	+	0.997259i	$0.523574\pi$
$840$	4.26542e156	1.51712
$841$	−1.11902e156	−0.373467
$842$	−2.64903e155	−0.0829641
$843$	8.39189e156	2.46652
$844$	−3.67107e156	−1.01268
$845$	−4.11967e156	−1.06667
$846$	3.42233e156	0.831778
$847$	1.02289e155	0.0233382
$848$	5.27266e154	0.0112941
$849$	−1.08117e157	−2.17437
$850$	−9.07057e155	−0.171286
$851$	−7.54190e156	−1.33736
$852$	1.32626e157	2.20856
$853$	8.74338e156	1.36743	0.683717	−	0.729747i	$-0.260362\pi$
$853$	8.74338e156	1.36743	0.683717	+	0.729747i	$0.260362\pi$
$854$	−1.20021e156	−0.176303
$855$	4.34758e156	0.599874
$856$	8.77692e156	1.13762
$857$	−3.47500e156	−0.423137	−0.211569	−	0.977363i	$-0.567857\pi$
$857$	−3.47500e156	−0.423137	−0.211569	+	0.977363i	$0.567857\pi$
$858$	5.08203e156	0.581390
$859$	8.05448e156	0.865771	0.432886	−	0.901449i	$-0.357495\pi$
$859$	8.05448e156	0.865771	0.432886	+	0.901449i	$0.357495\pi$
$860$	1.03427e157	1.04464
$861$	−6.02807e156	−0.572150
$862$	−3.74551e156	−0.334097
$863$	9.27409e156	0.777488	0.388744	−	0.921346i	$-0.372909\pi$
$863$	9.27409e156	0.777488	0.388744	+	0.921346i	$0.372909\pi$
$864$	−4.59113e157	−3.61772
$865$	2.22512e155	0.0164813
$866$	−1.66567e157	−1.15980
$867$	−2.70792e157	−1.77262
$868$	8.15798e155	0.0502085
$869$	8.14235e156	0.471185
$870$	2.39447e157	1.30296
$871$	−9.37201e156	−0.479580
$872$	2.14366e157	1.03163
$873$	6.51483e156	0.294877
$874$	−2.35440e156	−0.100235
$875$	−1.60945e156	−0.0644534
$876$	−1.01917e157	−0.383954
$877$	−2.53961e157	−0.900095	−0.450048	−	0.893005i	$-0.648593\pi$
$877$	−2.53961e157	−0.900095	−0.450048	+	0.893005i	$0.648593\pi$
$878$	2.13427e157	0.711694
$879$	2.37697e157	0.745795
$880$	1.42526e156	0.0420797
$881$	3.46084e157	0.961547	0.480774	−	0.876845i	$-0.340356\pi$
$881$	3.46084e157	0.961547	0.480774	+	0.876845i	$0.340356\pi$
$882$	4.47778e157	1.17083
$883$	1.08345e157	0.266632	0.133316	−	0.991074i	$-0.457437\pi$
$883$	1.08345e157	0.266632	0.133316	+	0.991074i	$0.457437\pi$
$884$	4.01533e156	0.0930091
$885$	−8.98837e157	−1.95982
$886$	1.41686e157	0.290819
$887$	−4.42865e157	−0.855771	−0.427886	−	0.903833i	$-0.640741\pi$
$887$	−4.42865e157	−0.855771	−0.427886	+	0.903833i	$0.640741\pi$
$888$	−1.32079e158	−2.40293
$889$	2.52292e157	0.432174
$890$	4.60533e156	0.0742840
$891$	2.81434e158	4.27484
$892$	3.91455e157	0.559967
$893$	−5.49082e156	−0.0739748
$894$	−1.46518e157	−0.185923
$895$	−7.57271e157	−0.905146
$896$	3.28570e157	0.369956
$897$	−9.54624e157	−1.01260
$898$	−3.16536e157	−0.316329
$899$	1.18342e157	0.111429
$900$	−1.84918e158	−1.64061
$901$	1.39455e157	0.116589
$902$	4.06856e157	0.320547
$903$	−1.78002e158	−1.32169
$904$	2.23877e157	0.156674
$905$	1.85591e158	1.22422
$906$	−3.39447e158	−2.11063
$907$	−2.41628e158	−1.41631	−0.708155	−	0.706057i	$-0.750472\pi$
$907$	−2.41628e158	−1.41631	−0.708155	+	0.706057i	$0.750472\pi$
$908$	−4.71161e156	−0.0260361
$909$	9.51980e158	4.95975
$910$	4.63537e157	0.227704
$911$	−2.12762e158	−0.985511	−0.492756	−	0.870168i	$-0.664010\pi$
$911$	−2.12762e158	−0.985511	−0.492756	+	0.870168i	$0.664010\pi$
$912$	2.04129e156	0.00891621
$913$	−2.85994e158	−1.17807
$914$	2.62835e158	1.02109
$915$	3.80195e158	1.39308
$916$	9.14691e157	0.316131
$917$	−5.27626e157	−0.172015
$918$	−2.17692e158	−0.669513
$919$	−5.51741e158	−1.60087	−0.800434	−	0.599421i	$-0.795397\pi$
$919$	−5.51741e158	−1.60087	−0.800434	+	0.599421i	$0.795397\pi$
$920$	5.40780e158	1.48037
$921$	4.28063e157	0.110565
$922$	3.05611e158	0.744842
$923$	3.72442e158	0.856580
$924$	−3.28260e158	−0.712471
$925$	−5.55115e158	−1.13710
$926$	2.39383e158	0.462813
$927$	−1.11158e159	−2.02850
$928$	4.63473e158	0.798376
$929$	1.26401e158	0.205546	0.102773	−	0.994705i	$-0.467229\pi$
$929$	1.26401e158	0.205546	0.102773	+	0.994705i	$0.467229\pi$
$930$	1.50946e158	0.231730
$931$	−7.18419e157	−0.104129
$932$	7.99253e158	1.09379
$933$	−1.95403e159	−2.52502
$934$	1.26212e158	0.154007
$935$	3.76964e158	0.434388
$936$	−1.23556e159	−1.34464
$937$	2.01667e158	0.207285	0.103642	−	0.994615i	$-0.466950\pi$
$937$	2.01667e158	0.207285	0.103642	+	0.994615i	$0.466950\pi$
$938$	−3.53591e158	−0.343280
$939$	5.04539e158	0.462685
$940$	4.88054e158	0.422793
$941$	8.44053e158	0.690756	0.345378	−	0.938464i	$-0.387751\pi$
$941$	8.44053e158	0.690756	0.345378	+	0.938464i	$0.387751\pi$
$942$	−1.12055e159	−0.866378
$943$	−7.64251e158	−0.558291
$944$	−3.11899e157	−0.0215284
$945$	4.30247e159	2.80618
$946$	1.20140e159	0.740476
$947$	7.01986e158	0.408888	0.204444	−	0.978878i	$-0.434461\pi$
$947$	7.01986e158	0.408888	0.204444	+	0.978878i	$0.434461\pi$
$948$	−1.03655e159	−0.570616
$949$	−2.86207e158	−0.148915
$950$	−1.73293e158	−0.0852254
$951$	4.31060e159	2.00392
$952$	3.91471e158	0.172037
$953$	−3.28637e159	−1.36536	−0.682678	−	0.730719i	$-0.739185\pi$
$953$	−3.28637e159	−1.36536	−0.682678	+	0.730719i	$0.739185\pi$
$954$	−1.66060e159	−0.652271
$955$	−2.33030e159	−0.865429
$956$	1.24184e159	0.436082
$957$	−4.76184e159	−1.58120
$958$	−2.51246e159	−0.788940
$959$	−2.61021e159	−0.775138
$960$	5.62417e159	1.57960
$961$	−3.68985e159	−0.980182
$962$	−1.43535e159	−0.360654
$963$	1.36851e160	3.25268
$964$	3.84353e159	0.864190
$965$	−9.71138e159	−2.06571
$966$	−3.60164e159	−0.724810
$967$	6.41144e159	1.22079	0.610393	−	0.792099i	$-0.291012\pi$
$967$	6.41144e159	1.22079	0.610393	+	0.792099i	$0.291012\pi$
$968$	2.27114e158	0.0409178
$969$	5.39894e158	0.0920420
$970$	−5.42672e158	−0.0875487
$971$	−4.34052e158	−0.0662694	−0.0331347	−	0.999451i	$-0.510549\pi$
$971$	−4.34052e158	−0.0662694	−0.0331347	+	0.999451i	$0.510549\pi$
$972$	−2.01578e160	−2.91272
$973$	7.36081e159	1.00667
$974$	−1.05616e159	−0.136718
$975$	−7.02642e159	−0.860969
$976$	1.31929e158	0.0153029
$977$	−7.87582e159	−0.864842	−0.432421	−	0.901672i	$-0.642341\pi$
$977$	−7.87582e159	−0.864842	−0.432421	+	0.901672i	$0.642341\pi$
$978$	1.99936e160	2.07856
$979$	−9.15851e158	−0.0901469
$980$	6.38571e159	0.595133
$981$	3.34242e160	2.94964
$982$	−1.16890e159	−0.0976814
$983$	9.28748e159	0.734996	0.367498	−	0.930024i	$-0.380215\pi$
$983$	9.28748e159	0.734996	0.367498	+	0.930024i	$0.380215\pi$
$984$	−1.33841e160	−1.00312
$985$	1.68324e160	1.19484
$986$	2.19759e159	0.147751
$987$	−8.39958e159	−0.534921
$988$	7.67129e158	0.0462777
$989$	−2.25674e160	−1.28968
$990$	−4.48881e160	−2.43024
$991$	5.09778e159	0.261481	0.130741	−	0.991417i	$-0.458265\pi$
$991$	5.09778e159	0.261481	0.130741	+	0.991417i	$0.458265\pi$
$992$	2.92169e159	0.141991
$993$	−7.07329e159	−0.325714
$994$	1.40516e160	0.613134
$995$	−2.45805e160	−1.01638
$996$	3.64080e160	1.42667
$997$	2.67375e160	0.992954	0.496477	−	0.868050i	$-0.334627\pi$
$997$	2.67375e160	0.992954	0.496477	+	0.868050i	$0.334627\pi$
$998$	5.08189e159	0.178872
$999$	−1.33227e161	−4.44464

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.108.a.a.1.4	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.108.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:	\( k \)	\(=\)	\( 108 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-7.73495e15 q^{2} +6.57221e25 q^{3} -1.02430e32 q^{4} +3.43777e37 q^{5} -5.08357e41 q^{6} +9.22106e44 q^{7} +2.04736e48 q^{8} +3.19227e51 q^{9} +O(q^{10})\)	\(q-7.73495e15 q^{2} +6.57221e25 q^{3} -1.02430e32 q^{4} +3.43777e37 q^{5} -5.08357e41 q^{6} +9.22106e44 q^{7} +2.04736e48 q^{8} +3.19227e51 q^{9} -2.65909e53 q^{10} +5.28808e55 q^{11} -6.73191e57 q^{12} -1.89047e59 q^{13} -7.13244e60 q^{14} +2.25937e63 q^{15} +7.84008e62 q^{16} +2.07360e65 q^{17} -2.46920e67 q^{18} +3.96161e67 q^{19} -3.52130e69 q^{20} +6.06028e70 q^{21} -4.09030e71 q^{22} +7.68335e72 q^{23} +1.34557e74 q^{24} +5.65526e74 q^{25} +1.46227e75 q^{26} +1.35725e77 q^{27} -9.44512e76 q^{28} -1.37014e78 q^{29} -1.74761e79 q^{30} -8.63725e78 q^{31} -3.38267e80 q^{32} +3.47544e81 q^{33} -1.60392e81 q^{34} +3.16998e82 q^{35} -3.26984e83 q^{36} -9.81590e83 q^{37} -3.06428e83 q^{38} -1.24246e85 q^{39} +7.03833e85 q^{40} -9.94685e85 q^{41} -4.68759e86 q^{42} -2.93719e87 q^{43} -5.41658e87 q^{44} +1.09743e89 q^{45} -5.94303e88 q^{46} -1.38601e89 q^{47} +5.15267e88 q^{48} -1.81345e90 q^{49} -4.37431e90 q^{50} +1.36281e91 q^{51} +1.93641e91 q^{52} +6.72527e91 q^{53} -1.04983e93 q^{54} +1.81792e93 q^{55} +1.88788e93 q^{56} +2.60365e93 q^{57} +1.05980e94 q^{58} -3.97826e94 q^{59} -2.31427e95 q^{60} +1.68274e95 q^{61} +6.68086e94 q^{62} +2.94361e96 q^{63} +2.48926e96 q^{64} -6.49900e96 q^{65} -2.68823e97 q^{66} +4.95750e97 q^{67} -2.12399e97 q^{68} +5.04966e98 q^{69} -2.45197e98 q^{70} -1.97010e99 q^{71} +6.53571e99 q^{72} +1.51394e99 q^{73} +7.59255e99 q^{74} +3.71676e100 q^{75} -4.05787e99 q^{76} +4.87617e100 q^{77} +9.61034e100 q^{78} +1.53975e101 q^{79} +2.69524e100 q^{80} +5.32205e102 q^{81} +7.69384e101 q^{82} -5.40827e102 q^{83} -6.20753e102 q^{84} +7.12855e102 q^{85} +2.27190e103 q^{86} -9.00485e103 q^{87} +1.08266e104 q^{88} -1.73192e103 q^{89} -8.48854e104 q^{90} -1.74321e104 q^{91} -7.87005e104 q^{92} -5.67658e104 q^{93} +1.07207e105 q^{94} +1.36191e105 q^{95} -2.22316e106 q^{96} +2.04081e105 q^{97} +1.40269e106 q^{98} +1.68810e107 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 54\!\cdots\!96 q^{2}+ \cdots + 36\!\cdots\!13 q^{9}+O(q^{10}) \) 9 * q + 5465779613435496 * q^2 + 15983866788128062714366812 * q^3 + 641838178072986908923140040636992 * q^4 + 24730262360170403173006735448079708750 * q^5 - 120659696701040014765473752948751733206432 * q^6 - 935936272579440558945885185297012359442693544 * q^7 - 1000549071290096181876510601182828415482105239040 * q^8 + 3695400441386851970702053152997489358579707799946813 * q^9	\( 9 q + 54\!\cdots\!96 q^{2}+ \cdots + 21\!\cdots\!36 q^{99}+O(q^{100}) \) 9 * q + 5465779613435496 * q^2 + 15983866788128062714366812 * q^3 + 641838178072986908923140040636992 * q^4 + 24730262360170403173006735448079708750 * q^5 - 120659696701040014765473752948751733206432 * q^6 - 935936272579440558945885185297012359442693544 * q^7 - 1000549071290096181876510601182828415482105239040 * q^8 + 3695400441386851970702053152997489358579707799946813 * q^9 - 1051865624814321749095840304599907252969934693398466000 * q^10 + 75371386674400378520973626363253224857093312063724664948 * q^11 - 7994600333787230851514661173029738426135745580020653426944 * q^12 + 386688410581830829569835770029121092890073212075170355706982 * q^13 - 7425120169660057221925189838061614099801999208262592119204416 * q^14 + 1114849595057357604173216029035423209082636701646415622289453000 * q^15 + 29408614076374287218252370499930154042728180304312580290885259264 * q^16 + 557190110555184717584150469172018747011155217501263013200292053826 * q^17 + 23686310065847344603267400477778156225688961326793890396260803764872 * q^18 + 858726527367010511176780653766124295103204700130810063275302960078860 * q^19 + 13293825016749054587175558577837356326662860013460552585283415249200000 * q^20 + 98208620574357072907810930779441373553105765539483211558155794396236448 * q^21 - 2120482037145318757833662337561674615184814159100624269907546121294686688 * q^22 - 10034721240753129475726648205629192527604953514063764213610508652545603448 * q^23 - 2941281585435310612767332425157841570788095859273373502643916660565125120 * q^24 + 2090668146509277585662418878235593338432069837730236508072952837108480609375 * q^25 + 297618678938898468541825094241452097503242676900281081118135240117081112048 * q^26 + 12010637132277372007849219431146961646841705965134800444369356096651346807640 * q^27 - 772836919356016231875276488741314175452898152873144799220188421863529684675072 * q^28 + 3591314969861592690040264647853795847194812597017039069680951706167032656423190 * q^29 + 1723952423459255307102435810928767115448833503290363214135969710252703496200000 * q^30 + 80089747856260124585510286878769275145759211608657844798932602922226546761434208 * q^31 - 1446206593191149472500309116447393072011146060673364310104554905463216959190564864 * q^32 + 3945091609919542459300423121384432970721444207912781947382890849249898482566767664 * q^33 + 11119656315304296004606294411853238631199272487238804497227126821893639468830096464 * q^34 + 49067962462953733482940013097788952961901858200557588372758479947688558453676754000 * q^35 - 471823079431745456450508655131148234440317478341437039102283657625130709182178187456 * q^36 - 211704323021230989692835910298149365559694037564054725936839839132550744753936919634 * q^37 + 8222885444046313840674570479741432975521521666418514540085950022601909450574547779040 * q^38 + 12361178896398609619161562511793017908827480821637222996756699411815138902405469354856 * q^39 - 46215645594071398383759344185895857310354869228136299740138569713991972194487637120000 * q^40 - 152723040798290839871602016171161581257438821965138798374317736485575056512069694567862 * q^41 + 1126972287891090202493176150041627427283154361091115578522922093800965746370272835782912 * q^42 + 588069515895858848125340008029591292900452115124091837264351724714905019444084944743892 * q^43 - 6139643207231705808426527030461811499402203060055049552369302116418471883341886274962176 * q^44 - 31911427383192526363701563735501578120849438309590564668521639113629216238459194946116250 * q^45 - 18263182784420532146882371818610257236316553965008962373113458516888555657572617999188672 * q^46 + 411127412634686500562199358253262979305374320422388983156864942033640143172424484152539536 * q^47 + 143930370214090114738516122425367964462847873560413052946256979092891611198246163544522752 * q^48 - 4997644842464582200845249613678276624838382931152181846690817178995051025280570789312693263 * q^49 - 327953810706856692980141167207241667907351028782006717494410015078645777795786692667625000 * q^50 + 42691516908125956684809245526355840553570893389914391645941980034335859681366662250925257208 * q^51 + 59364881289634100249284358230824565528876555321811374467351490113119501371198417490401094016 * q^52 - 53335374129204409504769785775612138052491162110126476217063770562215392060493506708504818338 * q^53 - 1554605781923117836337527850943594545571965959146902578434980467357667330247224121116945547840 * q^54 + 1474216898342963983363455770095216024051493885851745466905891181181387017915931645476666255000 * q^55 + 7453692229427932770491342947786818133880887558034867118652861854414844393630476278780284170240 * q^56 - 9382173343921294589567308072318971089362548602163794938031557584052656917238640814769133635120 * q^57 - 14675317362256339836240584983997175224307357531571668080947702647986363061369632064127758276240 * q^58 - 17201443369933521380448054479438020840215748691907958949057650623559478137031846309102734186620 * q^59 + 119942427235571024011403351926139340364016919293031353278124824892037701815579444998816654144000 * q^60 + 996825825169496808828278558344476432289838610202339535134269176536499940712988317319113083438198 * q^61 - 1806664642208894952880819938644089164868010113998872083788864908221482430118942433714202980872448 * q^62 - 525131716387364530569619107989883435883820178537003544594931993029001820968120281192738395294408 * q^63 + 8859800242100397923173345055025991374254635563298611761326132852774863587391298255452246238298112 * q^64 + 3354685369129755322181059460881157417967535549386685974710181837734684369198862379954288278640500 * q^65 + 57953332747637118130796913061247956114095776689582635716826448321044474448975464944502438440474496 * q^66 + 67272594646508937763531278535250984988721264552212406692490519409868542593541008988303512955099676 * q^67 - 5271355091203561642375555737902479878900668615857946963901492781607485228195805621489749763440512 * q^68 + 1211310643069343900708768635208063407543461033111793008132153244460934861341593025873966799465486816 * q^69 + 3012778566653438568685732696962102874663629250451589330912197198332559170935750394136926553795280000 * q^70 + 557606230265736297562017362716168472788611890356025926095319973789617215901574196175404049892853528 * q^71 + 16960010475120540092713267652235654327415255109531175122804202418279614126703951005828887393908830720 * q^72 + 13389828619022747318968894782762272535480348540089259518080823938522165418472525950139881426529375402 * q^73 + 72532783100036668116960948230568216484424073462645933664305672446671831241015488437308573521198008624 * q^74 + 181746227987304022931719943233189267636401541776890365701313509214346868335764760358972397994607562500 * q^75 + 369203366658532984115827909838760339113448992029578983924004973867253851696995490992782273693567066880 * q^76 + 388491114360440288787870394325327319503105866790556270795138762844335429572119358188629406545039198432 * q^77 + 1684225666426130585491319943814839912966891568955799622030995821490516792520001316121300784238905446464 * q^78 + 1767099872706468468805139692411742252367926917059947532799767578463589430448822266501638541217663494640 * q^79 + 6734051899360870505834986379536968461908477509814468240268598557190207937484585956747946194493844480000 * q^80 + 8587274871353378729934471647154494323432295856816917259751843692725713832863430007711361770205995287889 * q^81 + 8604324829509629266993327118230721908083540408244010940656031675054140623869235247377840945490064899472 * q^82 + 10573584024255166860785482858544789933175527426032260694531283318949407366175819470225352840720947271372 * q^83 + 29398865778509538549966771421066766907861809604721299372151512034272864117018289488710440505099182516224 * q^84 + 28217101873426464307527276596170727373321741101882319418731811087750656251683841267824081156479505981500 * q^85 - 5660340715902714082316421136856625160042953949488572010019823412763437338500312808862231168781884748512 * q^86 - 238801934255165782785740400186129085029676437910074769136670805304976544209174607407124977464878965608280 * q^87 - 649669481755409892912473717222108679378769149016402953512733477402495574055782427323588758822348679034880 * q^88 - 887044331989597087426634052611019082958734414422732136340380168408138968025139915003605988823387508725030 * q^89 - 2358060024132454293950038004387227695091155243819311445899211024200212376406755931436993187026324923882000 * q^90 - 2028610692814038362284016228595385975371756633777610476239575578728190535138139517202725484712408010671472 * q^91 - 9605953523619230804079170889956757296920712871591046684448269611692869761363895640295324681873778639117824 * q^92 - 10277229372847627124269654885108201819576328825280371977906378287406641199658335902623697673880879481373056 * q^93 - 13250229074063549042347396359745980974584115253516850536254551366146505318484654226001161612613989202932096 * q^94 + 1932498314000384011251898358613786886453409028619258552182745516014729315280931175089689966876445460945000 * q^95 + 8188689385662642160607934226103033776391463701323345460407294147322816918802843383187307295905239187980288 * q^96 + 18319527847032942156630290559559475585838161401404427251154943474039162663641018432069269659324962153774386 * q^97 + 91489091329550984599525415507771543780042234198589939082127267861983786873859650920519076378970080872245928 * q^98 + 211118154688143874137117803870035099572707397285369760168480766428388700807018832202269547436760962791157636 * q^99

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