LMFDB - Embedded newform 1.108.a.a.1.8

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			1.8
Root			$-7.86617e14$ 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)

$f(q)$	$=$	$q+1.94861e16 q^{2} -5.50693e25 q^{3} +2.17450e32 q^{4} -2.12470e37 q^{5} -1.07309e42 q^{6} -2.04209e45 q^{7} +1.07545e48 q^{8} +1.90550e51 q^{9} +O(q^{10})$	\(q+1.94861e16 q^{2} -5.50693e25 q^{3} +2.17450e32 q^{4} -2.12470e37 q^{5} -1.07309e42 q^{6} -2.04209e45 q^{7} +1.07545e48 q^{8} +1.90550e51 q^{9} -4.14022e53 q^{10} -5.01029e55 q^{11} -1.19748e58 q^{12} -3.86543e59 q^{13} -3.97924e61 q^{14} +1.17006e63 q^{15} -1.43270e64 q^{16} -8.98743e65 q^{17} +3.71308e67 q^{18} +4.12313e68 q^{19} -4.62015e69 q^{20} +1.12457e71 q^{21} -9.76312e71 q^{22} -1.03501e73 q^{23} -5.92241e73 q^{24} -1.64862e74 q^{25} -7.53223e75 q^{26} -4.28643e76 q^{27} -4.44052e77 q^{28} +2.16738e78 q^{29} +2.27999e79 q^{30} +2.11872e79 q^{31} -4.53678e80 q^{32} +2.75914e81 q^{33} -1.75130e82 q^{34} +4.33883e82 q^{35} +4.14350e83 q^{36} +9.35592e82 q^{37} +8.03438e84 q^{38} +2.12867e85 q^{39} -2.28500e85 q^{40} -8.27578e85 q^{41} +2.19134e87 q^{42} -1.41772e86 q^{43} -1.08949e88 q^{44} -4.04862e88 q^{45} -2.01683e89 q^{46} +1.56371e89 q^{47} +7.88976e89 q^{48} +1.50640e90 q^{49} -3.21253e90 q^{50} +4.94932e91 q^{51} -8.40537e91 q^{52} +2.18993e92 q^{53} -8.35259e92 q^{54} +1.06454e93 q^{55} -2.19616e93 q^{56} -2.27058e94 q^{57} +4.22339e94 q^{58} +2.47163e94 q^{59} +2.54429e95 q^{60} -6.90882e94 q^{61} +4.12856e95 q^{62} -3.89120e96 q^{63} -6.51574e96 q^{64} +8.21288e96 q^{65} +5.37649e97 q^{66} -1.21967e97 q^{67} -1.95431e98 q^{68} +5.69972e98 q^{69} +8.45470e98 q^{70} -1.44219e99 q^{71} +2.04926e99 q^{72} -9.19427e98 q^{73} +1.82311e99 q^{74} +9.07886e99 q^{75} +8.96573e100 q^{76} +1.02315e101 q^{77} +4.14795e101 q^{78} -1.01291e101 q^{79} +3.04405e101 q^{80} +2.12762e101 q^{81} -1.61263e102 q^{82} -1.38994e102 q^{83} +2.44536e103 q^{84} +1.90956e103 q^{85} -2.76258e102 q^{86} -1.19356e104 q^{87} -5.38830e103 q^{88} -6.76249e102 q^{89} -7.88919e104 q^{90} +7.89356e104 q^{91} -2.25062e105 q^{92} -1.16676e105 q^{93} +3.04706e105 q^{94} -8.76041e105 q^{95} +2.49837e106 q^{96} -1.19441e106 q^{97} +2.93539e106 q^{98} -9.54712e106 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.94861e16	1.52975	0.764875	−	0.644178i	$-0.222801\pi$
$2$	1.94861e16	1.52975	0.764875	+	0.644178i	$0.222801\pi$
$3$	−5.50693e25	−1.64030	−0.820149	−	0.572150i	$-0.806109\pi$
$3$	−5.50693e25	−1.64030	−0.820149	+	0.572150i	$0.806109\pi$
$4$	2.17450e32	1.34014
$5$	−2.12470e37	−0.855859	−0.427930	−	0.903812i	$-0.640757\pi$
$5$	−2.12470e37	−0.855859	−0.427930	+	0.903812i	$0.640757\pi$
$6$	−1.07309e42	−2.50925
$7$	−2.04209e45	−1.25121	−0.625604	−	0.780140i	$-0.715148\pi$
$7$	−2.04209e45	−1.25121	−0.625604	+	0.780140i	$0.715148\pi$
$8$	1.07545e48	0.520324
$9$	1.90550e51	1.69058
$10$	−4.14022e53	−1.30925
$11$	−5.01029e55	−0.966840	−0.483420	−	0.875389i	$-0.660606\pi$
$11$	−5.01029e55	−0.966840	−0.483420	+	0.875389i	$0.660606\pi$
$12$	−1.19748e58	−2.19822
$13$	−3.86543e59	−0.980006	−0.490003	−	0.871721i	$-0.663004\pi$
$13$	−3.86543e59	−0.980006	−0.490003	+	0.871721i	$0.663004\pi$
$14$	−3.97924e61	−1.91404
$15$	1.17006e63	1.40386
$16$	−1.43270e64	−0.544170
$17$	−8.98743e65	−1.33235	−0.666175	−	0.745795i	$-0.732070\pi$
$17$	−8.98743e65	−1.33235	−0.666175	+	0.745795i	$0.732070\pi$
$18$	3.71308e67	2.58616
$19$	4.12313e68	1.59188	0.795938	−	0.605378i	$-0.206978\pi$
$19$	4.12313e68	1.59188	0.795938	+	0.605378i	$0.206978\pi$
$20$	−4.62015e69	−1.14697
$21$	1.12457e71	2.05235
$22$	−9.76312e71	−1.47902
$23$	−1.03501e73	−1.45380	−0.726900	−	0.686743i	$-0.759040\pi$
$23$	−1.03501e73	−1.45380	−0.726900	+	0.686743i	$0.759040\pi$
$24$	−5.92241e73	−0.853487
$25$	−1.64862e74	−0.267505
$26$	−7.53223e75	−1.49916
$27$	−4.28643e76	−1.13275
$28$	−4.44052e77	−1.67679
$29$	2.16738e78	1.25211	0.626055	−	0.779779i	$-0.284668\pi$
$29$	2.16738e78	1.25211	0.626055	+	0.779779i	$0.284668\pi$
$30$	2.27999e79	2.14756
$31$	2.11872e79	0.345321	0.172660	−	0.984981i	$-0.444764\pi$
$31$	2.11872e79	0.345321	0.172660	+	0.984981i	$0.444764\pi$
$32$	−4.53678e80	−1.35277
$33$	2.75914e81	1.58591
$34$	−1.75130e82	−2.03816
$35$	4.33883e82	1.07086
$36$	4.14350e83	2.26560
$37$	9.35592e82	0.118112	0.0590561	−	0.998255i	$-0.481191\pi$
$37$	9.35592e82	0.118112	0.0590561	+	0.998255i	$0.481191\pi$
$38$	8.03438e84	2.43517
$39$	2.12867e85	1.60750
$40$	−2.28500e85	−0.445324
$41$	−8.27578e85	−0.430400	−0.215200	−	0.976570i	$-0.569040\pi$
$41$	−8.27578e85	−0.430400	−0.215200	+	0.976570i	$0.569040\pi$
$42$	2.19134e87	3.13959
$43$	−1.41772e86	−0.0576802	−0.0288401	−	0.999584i	$-0.509181\pi$
$43$	−1.41772e86	−0.0576802	−0.0288401	+	0.999584i	$0.509181\pi$
$44$	−1.08949e88	−1.29570
$45$	−4.04862e88	−1.44690
$46$	−2.01683e89	−2.22395
$47$	1.56371e89	0.545657	0.272829	−	0.962063i	$-0.412041\pi$
$47$	1.56371e89	0.545657	0.272829	+	0.962063i	$0.412041\pi$
$48$	7.88976e89	0.892601
$49$	1.50640e90	0.565523
$50$	−3.21253e90	−0.409215
$51$	4.94932e91	2.18545
$52$	−8.40537e91	−1.31334
$53$	2.18993e92	1.23501	0.617506	−	0.786566i	$-0.288143\pi$
$53$	2.18993e92	1.23501	0.617506	+	0.786566i	$0.288143\pi$
$54$	−8.35259e92	−1.73283
$55$	1.06454e93	0.827479
$56$	−2.19616e93	−0.651034
$57$	−2.27058e94	−2.61115
$58$	4.22339e94	1.91542
$59$	2.47163e94	0.449161	0.224580	−	0.974456i	$-0.427899\pi$
$59$	2.47163e94	0.449161	0.224580	+	0.974456i	$0.427899\pi$
$60$	2.54429e95	1.88137
$61$	−6.90882e94	−0.210988	−0.105494	−	0.994420i	$-0.533642\pi$
$61$	−6.90882e94	−0.210988	−0.105494	+	0.994420i	$0.533642\pi$
$62$	4.12856e95	0.528254
$63$	−3.89120e96	−2.11526
$64$	−6.51574e96	−1.52523
$65$	8.21288e96	0.838747
$66$	5.37649e97	2.42604
$67$	−1.21967e97	−0.246172	−0.123086	−	0.992396i	$-0.539279\pi$
$67$	−1.21967e97	−0.246172	−0.123086	+	0.992396i	$0.539279\pi$
$68$	−1.95431e98	−1.78553
$69$	5.69972e98	2.38467
$70$	8.45470e98	1.63815
$71$	−1.44219e99	−1.30828	−0.654140	−	0.756374i	$-0.726969\pi$
$71$	−1.44219e99	−1.30828	−0.654140	+	0.756374i	$0.726969\pi$
$72$	2.04926e99	0.879648
$73$	−9.19427e98	−0.188688	−0.0943440	−	0.995540i	$-0.530075\pi$
$73$	−9.19427e98	−0.188688	−0.0943440	+	0.995540i	$0.530075\pi$
$74$	1.82311e99	0.180682
$75$	9.07886e99	0.438787
$76$	8.96573e100	2.13333
$77$	1.02315e101	1.20972
$78$	4.14795e101	2.45908
$79$	−1.01291e101	−0.303754	−0.151877	−	0.988399i	$-0.548532\pi$
$79$	−1.01291e101	−0.303754	−0.151877	+	0.988399i	$0.548532\pi$
$80$	3.04405e101	0.465733
$81$	2.12762e101	0.167473
$82$	−1.61263e102	−0.658405
$83$	−1.38994e102	−0.296701	−0.148351	−	0.988935i	$-0.547396\pi$
$83$	−1.38994e102	−0.296701	−0.148351	+	0.988935i	$0.547396\pi$
$84$	2.44536e103	2.75044
$85$	1.90956e103	1.14030
$86$	−2.76258e102	−0.0882364
$87$	−1.19356e104	−2.05383
$88$	−5.38830e103	−0.503070
$89$	−6.76249e102	−0.0344938	−0.0172469	−	0.999851i	$-0.505490\pi$
$89$	−6.76249e102	−0.0344938	−0.0172469	+	0.999851i	$0.505490\pi$
$90$	−7.88919e104	−2.21339
$91$	7.89356e104	1.22619
$92$	−2.25062e105	−1.94829
$93$	−1.16676e105	−0.566429
$94$	3.04706e105	0.834720
$95$	−8.76041e105	−1.36242
$96$	2.49837e106	2.21894
$97$	−1.19441e106	−0.609349	−0.304675	−	0.952456i	$-0.598548\pi$
$97$	−1.19441e106	−0.609349	−0.304675	+	0.952456i	$0.598548\pi$
$98$	2.93539e106	0.865110
$99$	−9.54712e106	−1.63452
$100$	−3.58493e106	−0.358493
$101$	8.79399e106	0.516407	0.258204	−	0.966091i	$-0.416869\pi$
$101$	8.79399e106	0.516407	0.258204	+	0.966091i	$0.416869\pi$
$102$	9.64430e107	3.34319
$103$	7.33534e107	1.50879	0.754395	−	0.656421i	$-0.227931\pi$
$103$	7.33534e107	1.50879	0.754395	+	0.656421i	$0.227931\pi$
$104$	−4.15706e107	−0.509921
$105$	−2.38936e108	−1.75653
$106$	4.26732e108	1.88926
$107$	−5.41024e108	−1.44939	−0.724694	−	0.689071i	$-0.758019\pi$
$107$	−5.41024e108	−1.44939	−0.724694	+	0.689071i	$0.758019\pi$
$108$	−9.32083e108	−1.51804
$109$	−1.63265e109	−1.62396	−0.811982	−	0.583682i	$-0.801611\pi$
$109$	−1.63265e109	−1.62396	−0.811982	+	0.583682i	$0.801611\pi$
$110$	2.07437e109	1.26584
$111$	−5.15225e108	−0.193739
$112$	2.92569e109	0.680871
$113$	6.47085e109	0.935976	0.467988	−	0.883735i	$-0.344979\pi$
$113$	6.47085e109	0.935976	0.467988	+	0.883735i	$0.344979\pi$
$114$	−4.42448e110	−3.99441
$115$	2.19908e110	1.24425
$116$	4.71297e110	1.67800
$117$	−7.36558e110	−1.65677
$118$	4.81626e110	0.687104
$119$	1.83531e111	1.66705
$120$	1.25833e111	0.730465
$121$	−1.75147e110	−0.0652205
$122$	−1.34626e111	−0.322759
$123$	4.55742e111	0.705985
$124$	4.60714e111	0.462777
$125$	1.65973e112	1.08481
$126$	−7.58245e112	−3.23583
$127$	−4.09479e112	−1.14481	−0.572404	−	0.819971i	$-0.693989\pi$
$127$	−4.09479e112	−1.14481	−0.572404	+	0.819971i	$0.693989\pi$
$128$	−5.33530e112	−0.980451
$129$	7.80727e111	0.0946128
$130$	1.60037e113	1.28307
$131$	3.86204e111	0.0205496	0.0102748	−	0.999947i	$-0.496729\pi$
$131$	3.86204e111	0.0205496	0.0102748	+	0.999947i	$0.496729\pi$
$132$	5.99973e113	2.12533
$133$	−8.41980e113	−1.99177
$134$	−2.37666e113	−0.376582
$135$	9.10739e113	0.969476
$136$	−9.66549e113	−0.693254
$137$	−2.88038e114	−1.39605	−0.698023	−	0.716075i	$-0.745937\pi$
$137$	−2.88038e114	−1.39605	−0.698023	+	0.716075i	$0.745937\pi$
$138$	1.11066e115	3.64794
$139$	5.49335e113	0.122615	0.0613077	−	0.998119i	$-0.480473\pi$
$139$	5.49335e113	0.122615	0.0613077	+	0.998119i	$0.480473\pi$
$140$	9.43477e114	1.43510
$141$	−8.61123e114	−0.895041
$142$	−2.81027e115	−2.00134
$143$	1.93669e115	0.947509
$144$	−2.73000e115	−0.919962
$145$	−4.60504e115	−1.07163
$146$	−1.79161e115	−0.288645
$147$	−8.29565e115	−0.927627
$148$	2.03444e115	0.158286
$149$	1.56378e116	0.848616	0.424308	−	0.905518i	$-0.360517\pi$
$149$	1.56378e116	0.848616	0.424308	+	0.905518i	$0.360517\pi$
$150$	1.76912e116	0.671235
$151$	2.68756e116	0.714647	0.357323	−	0.933981i	$-0.383689\pi$
$151$	2.68756e116	0.714647	0.357323	+	0.933981i	$0.383689\pi$
$152$	4.43420e116	0.828292
$153$	−1.71256e117	−2.25244
$154$	1.99372e117	1.85057
$155$	−4.50164e116	−0.295546
$156$	4.62878e117	2.15427
$157$	−4.53167e117	−1.49840	−0.749198	−	0.662346i	$-0.769561\pi$
$157$	−4.53167e117	−1.49840	−0.749198	+	0.662346i	$0.769561\pi$
$158$	−1.97377e117	−0.464667
$159$	−1.20598e118	−2.02579
$160$	9.63929e117	1.15778
$161$	2.11358e118	1.81901
$162$	4.14590e117	0.256192
$163$	−3.88415e118	−1.72687	−0.863433	−	0.504464i	$-0.831690\pi$
$163$	−3.88415e118	−1.72687	−0.863433	+	0.504464i	$0.831690\pi$
$164$	−1.79957e118	−0.576795
$165$	−5.86234e118	−1.35731
$166$	−2.70846e118	−0.453879
$167$	−1.38262e118	−0.168025	−0.0840123	−	0.996465i	$-0.526773\pi$
$167$	−1.38262e118	−0.168025	−0.0840123	+	0.996465i	$0.526773\pi$
$168$	1.20941e119	1.06789
$169$	−6.15900e117	−0.0395888
$170$	3.72099e119	1.74438
$171$	7.85663e119	2.69119
$172$	−3.08282e118	−0.0772994
$173$	−1.37303e119	−0.252473	−0.126236	−	0.992000i	$-0.540290\pi$
$173$	−1.37303e119	−0.252473	−0.126236	+	0.992000i	$0.540290\pi$
$174$	−2.32579e120	−3.14185
$175$	3.36664e119	0.334704
$176$	7.17823e119	0.526126
$177$	−1.36111e120	−0.736757
$178$	−1.31775e119	−0.0527670
$179$	5.90517e120	1.75225	0.876123	−	0.482088i	$-0.160122\pi$
$179$	5.90517e120	1.75225	0.876123	+	0.482088i	$0.160122\pi$
$180$	−8.80371e120	−1.93904
$181$	−9.45801e120	−1.54880	−0.774401	−	0.632695i	$-0.781949\pi$
$181$	−9.45801e120	−1.54880	−0.774401	+	0.632695i	$0.781949\pi$
$182$	1.53815e121	1.87577
$183$	3.80464e120	0.346083
$184$	−1.11310e121	−0.756448
$185$	−1.98785e120	−0.101087
$186$	−2.27357e121	−0.866495
$187$	4.50297e121	1.28817
$188$	3.40027e121	0.731255
$189$	8.75328e121	1.41731
$190$	−1.70706e122	−2.08417
$191$	−7.06309e120	−0.0651193	−0.0325597	−	0.999470i	$-0.510366\pi$
$191$	−7.06309e120	−0.0651193	−0.0325597	+	0.999470i	$0.510366\pi$
$192$	3.58817e122	2.50183
$193$	5.47689e121	0.289213	0.144607	−	0.989489i	$-0.453808\pi$
$193$	5.47689e121	0.289213	0.144607	+	0.989489i	$0.453808\pi$
$194$	−2.32745e122	−0.932153
$195$	−4.52278e122	−1.37580
$196$	3.27566e122	0.757879
$197$	−5.58894e122	−0.984887	−0.492443	−	0.870344i	$-0.663896\pi$
$197$	−5.58894e122	−0.984887	−0.492443	+	0.870344i	$0.663896\pi$
$198$	−1.86036e123	−2.50040
$199$	9.51673e122	0.976896	0.488448	−	0.872593i	$-0.337563\pi$
$199$	9.51673e122	0.976896	0.488448	+	0.872593i	$0.337563\pi$
$200$	−1.77301e122	−0.139189
$201$	6.71663e122	0.403796
$202$	1.71361e123	0.789974
$203$	−4.42599e123	−1.56665
$204$	1.07623e124	2.92880
$205$	1.75836e123	0.368362
$206$	1.42937e124	2.30807
$207$	−1.97221e124	−2.45776
$208$	5.53799e123	0.533290
$209$	−2.06581e124	−1.53909
$210$	−4.65594e124	−2.68705
$211$	3.90983e124	1.75004	0.875018	−	0.484090i	$-0.160849\pi$
$211$	3.90983e124	1.75004	0.875018	+	0.484090i	$0.160849\pi$
$212$	4.76200e124	1.65509
$213$	7.94204e124	2.14597
$214$	−1.05425e125	−2.21720
$215$	3.01222e123	0.0493662
$216$	−4.60982e124	−0.589398
$217$	−4.32661e124	−0.432068
$218$	−3.18141e125	−2.48426
$219$	5.06322e124	0.309504
$220$	2.31483e125	1.10894
$221$	3.47403e125	1.30571
$222$	−1.00397e125	−0.296372
$223$	−1.49345e125	−0.346642	−0.173321	−	0.984865i	$-0.555450\pi$
$223$	−1.49345e125	−0.346642	−0.173321	+	0.984865i	$0.555450\pi$
$224$	9.26451e125	1.69260
$225$	−3.14145e125	−0.452237
$226$	1.26092e126	1.43181
$227$	1.59595e126	1.43099	0.715493	−	0.698620i	$-0.246202\pi$
$227$	1.59595e126	1.43099	0.715493	+	0.698620i	$0.246202\pi$
$228$	−4.93737e126	−3.49930
$229$	1.45991e125	0.0818707	0.0409353	−	0.999162i	$-0.486966\pi$
$229$	1.45991e125	0.0818707	0.0409353	+	0.999162i	$0.486966\pi$
$230$	4.28516e126	1.90339
$231$	−5.63440e126	−1.98430
$232$	2.33090e126	0.651504
$233$	−1.04002e126	−0.230940	−0.115470	−	0.993311i	$-0.536837\pi$
$233$	−1.04002e126	−0.230940	−0.115470	+	0.993311i	$0.536837\pi$
$234$	−1.43527e127	−2.53445
$235$	−3.32241e126	−0.467006
$236$	5.37456e126	0.601937
$237$	5.57803e126	0.498247
$238$	3.57632e127	2.55017
$239$	2.92937e126	0.166912	0.0834559	−	0.996511i	$-0.473404\pi$
$239$	2.92937e126	0.166912	0.0834559	+	0.996511i	$0.473404\pi$
$240$	−1.67634e127	−0.763941
$241$	−7.43982e126	−0.271426	−0.135713	−	0.990748i	$-0.543332\pi$
$241$	−7.43982e126	−0.271426	−0.135713	+	0.990748i	$0.543332\pi$
$242$	−3.41293e126	−0.0997711
$243$	3.65971e127	0.858046
$244$	−1.50232e127	−0.282753
$245$	−3.20065e127	−0.484008
$246$	8.88064e127	1.07998
$247$	−1.59377e128	−1.56005
$248$	2.27857e127	0.179679
$249$	7.65433e127	0.486679
$250$	3.23417e128	1.65948
$251$	7.93679e127	0.328928	0.164464	−	0.986383i	$-0.447411\pi$
$251$	7.93679e127	0.328928	0.164464	+	0.986383i	$0.447411\pi$
$252$	−8.46141e128	−2.83474
$253$	5.18570e128	1.40559
$254$	−7.97916e128	−1.75127
$255$	−1.05158e129	−1.87044
$256$	1.75954e127	0.0253840
$257$	1.15848e129	1.35665	0.678323	−	0.734764i	$-0.262707\pi$
$257$	1.15848e129	1.35665	0.678323	+	0.734764i	$0.262707\pi$
$258$	1.52133e128	0.144734
$259$	−1.91056e128	−0.147783
$260$	1.78589e129	1.12404
$261$	4.12995e129	2.11679
$262$	7.52562e127	0.0314357
$263$	1.60323e129	0.546215	0.273107	−	0.961984i	$-0.411949\pi$
$263$	1.60323e129	0.546215	0.273107	+	0.961984i	$0.411949\pi$
$264$	2.96730e129	0.825185
$265$	−4.65295e129	−1.05700
$266$	−1.64069e130	−3.04691
$267$	3.72406e128	0.0565802
$268$	−2.65216e129	−0.329905
$269$	−1.79755e128	−0.0183203	−0.00916017	−	0.999958i	$-0.502916\pi$
$269$	−1.79755e128	−0.0183203	−0.00916017	+	0.999958i	$0.502916\pi$
$270$	1.77468e130	1.48306
$271$	3.52701e129	0.241852	0.120926	−	0.992662i	$-0.461414\pi$
$271$	3.52701e129	0.241852	0.120926	+	0.992662i	$0.461414\pi$
$272$	1.28763e130	0.725025
$273$	−4.34693e130	−2.01132
$274$	−5.61275e130	−2.13560
$275$	8.26009e129	0.258634
$276$	1.23940e131	3.19578
$277$	−4.08962e130	−0.868991	−0.434496	−	0.900674i	$-0.643073\pi$
$277$	−4.08962e130	−0.868991	−0.434496	+	0.900674i	$0.643073\pi$
$278$	1.07044e130	0.187571
$279$	4.03722e130	0.583791
$280$	4.66617e130	0.557194
$281$	3.95328e130	0.390094	0.195047	−	0.980794i	$-0.437514\pi$
$281$	3.95328e130	0.390094	0.195047	+	0.980794i	$0.437514\pi$
$282$	−1.67799e131	−1.36919
$283$	−3.16998e129	−0.0214034	−0.0107017	−	0.999943i	$-0.503407\pi$
$283$	−3.16998e129	−0.0214034	−0.0107017	+	0.999943i	$0.503407\pi$
$284$	−3.13603e131	−1.75327
$285$	4.82430e131	2.23478
$286$	3.77387e131	1.44945
$287$	1.68999e131	0.538521
$288$	−8.64483e131	−2.28696
$289$	3.52715e131	0.775156
$290$	−8.97344e131	−1.63933
$291$	6.57755e131	0.999515
$292$	−1.99929e131	−0.252868
$293$	−1.01052e132	−1.06446	−0.532228	−	0.846601i	$-0.678645\pi$
$293$	−1.01052e132	−1.06446	−0.532228	+	0.846601i	$0.678645\pi$
$294$	−1.61650e132	−1.41904
$295$	−5.25148e131	−0.384418
$296$	1.00618e131	0.0614566
$297$	2.14763e132	1.09519
$298$	3.04721e132	1.29817
$299$	4.00076e132	1.42473
$300$	1.97419e132	0.588035
$301$	2.89511e131	0.0721700
$302$	5.23701e132	1.09323
$303$	−4.84279e132	−0.847062
$304$	−5.90719e132	−0.866252
$305$	1.46792e132	0.180576
$306$	−3.33711e133	−3.44567
$307$	2.01077e133	1.74365	0.871823	−	0.489821i	$-0.162938\pi$
$307$	2.01077e133	1.74365	0.871823	+	0.489821i	$0.162938\pi$
$308$	2.22483e133	1.62119
$309$	−4.03952e133	−2.47486
$310$	−8.77195e132	−0.452112
$311$	3.45843e132	0.150037	0.0750185	−	0.997182i	$-0.476098\pi$
$311$	3.45843e132	0.150037	0.0750185	+	0.997182i	$0.476098\pi$
$312$	2.28927e133	0.836422
$313$	6.27524e133	1.93200	0.966002	−	0.258534i	$-0.0832395\pi$
$313$	6.27524e133	1.93200	0.966002	+	0.258534i	$0.0832395\pi$
$314$	−8.83047e133	−2.29217
$315$	8.26764e133	1.81037
$316$	−2.20257e133	−0.407072
$317$	5.17520e133	0.807712	0.403856	−	0.914823i	$-0.367670\pi$
$317$	5.17520e133	0.807712	0.403856	+	0.914823i	$0.367670\pi$
$318$	−2.34999e134	−3.09895
$319$	−1.08592e134	−1.21059
$320$	1.38440e134	1.30538
$321$	2.97938e134	2.37743
$322$	4.11855e134	2.78263
$323$	−3.70563e134	−2.12094
$324$	4.62649e133	0.224437
$325$	6.37264e133	0.262156
$326$	−7.56869e134	−2.64167
$327$	8.99092e134	2.66379
$328$	−8.90015e133	−0.223948
$329$	−3.19323e134	−0.682731
$330$	−1.14234e135	−2.07635
$331$	4.13620e134	0.639446	0.319723	−	0.947511i	$-0.396410\pi$
$331$	4.13620e134	0.639446	0.319723	+	0.947511i	$0.396410\pi$
$332$	−3.02243e134	−0.397620
$333$	1.78277e134	0.199678
$334$	−2.69420e134	−0.257036
$335$	2.59143e134	0.210689
$336$	−1.61116e135	−1.11683
$337$	2.55608e135	1.51138	0.755691	−	0.654929i	$-0.227301\pi$
$337$	2.55608e135	1.51138	0.755691	+	0.654929i	$0.227301\pi$
$338$	−1.20015e134	−0.0605609
$339$	−3.56346e135	−1.53528
$340$	4.15233e135	1.52816
$341$	−1.06154e135	−0.333870
$342$	1.53095e136	4.11685
$343$	2.36337e135	0.543621
$344$	−1.52468e134	−0.0300124
$345$	−1.21102e136	−2.04094
$346$	−2.67551e135	−0.386220
$347$	−7.72558e135	−0.955662	−0.477831	−	0.878452i	$-0.658577\pi$
$347$	−7.72558e135	−0.955662	−0.477831	+	0.878452i	$0.658577\pi$
$348$	−2.59540e136	−2.75242
$349$	5.82689e132	0.000530000 0	0.000265000	−	1.00000i	$-0.499916\pi$
$349$	5.82689e132	0.000530000 0	0.000265000		1.00000i	$0.499916\pi$
$350$	6.56027e135	0.512014
$351$	1.65689e136	1.11010
$352$	2.27306e136	1.30791
$353$	−1.11468e135	−0.0551068	−0.0275534	−	0.999620i	$-0.508772\pi$
$353$	−1.11468e135	−0.0551068	−0.0275534	+	0.999620i	$0.508772\pi$
$354$	−2.65228e136	−1.12705
$355$	3.06422e136	1.11970
$356$	−1.47050e135	−0.0462265
$357$	−1.01070e137	−2.73445
$358$	1.15069e137	2.68050
$359$	−1.27183e136	−0.255196	−0.127598	−	0.991826i	$-0.540727\pi$
$359$	−1.27183e136	−0.255196	−0.127598	+	0.991826i	$0.540727\pi$
$360$	−4.35407e136	−0.752855
$361$	1.02915e137	1.53407
$362$	−1.84300e137	−2.36928
$363$	9.64520e135	0.106981
$364$	1.71645e137	1.64326
$365$	1.95351e136	0.161490
$366$	7.41377e136	0.529421
$367$	1.60651e137	0.991397	0.495699	−	0.868495i	$-0.334912\pi$
$367$	1.60651e137	0.991397	0.495699	+	0.868495i	$0.334912\pi$
$368$	1.48285e137	0.791115
$369$	−1.57695e137	−0.727625
$370$	−3.87356e136	−0.154638
$371$	−4.47204e137	−1.54526
$372$	−2.53712e137	−0.759092
$373$	−6.95356e137	−1.80212	−0.901062	−	0.433690i	$-0.857211\pi$
$373$	−6.95356e137	−1.80212	−0.901062	+	0.433690i	$0.857211\pi$
$374$	8.77454e137	1.97058
$375$	−9.14003e137	−1.77940
$376$	1.68168e137	0.283919
$377$	−8.37787e137	−1.22708
$378$	1.70568e138	2.16813
$379$	9.53444e137	1.05220	0.526099	−	0.850423i	$-0.323654\pi$
$379$	9.53444e137	1.05220	0.526099	+	0.850423i	$0.323654\pi$
$380$	−1.90495e138	−1.82583
$381$	2.25498e138	1.87783
$382$	−1.37632e137	−0.0996163
$383$	6.79628e137	0.427698	0.213849	−	0.976867i	$-0.431400\pi$
$383$	6.79628e137	0.427698	0.213849	+	0.976867i	$0.431400\pi$
$384$	2.93812e138	1.60823
$385$	−2.17388e138	−1.03535
$386$	1.06723e138	0.442424
$387$	−2.70146e137	−0.0975129
$388$	−2.59724e138	−0.816612
$389$	2.76588e137	0.0757758	0.0378879	−	0.999282i	$-0.487937\pi$
$389$	2.76588e137	0.0757758	0.0378879	+	0.999282i	$0.487937\pi$
$390$	−8.81314e138	−2.10462
$391$	9.30207e138	1.93697
$392$	1.62005e138	0.294255
$393$	−2.12680e137	−0.0337074
$394$	−1.08907e139	−1.50663
$395$	2.15213e138	0.259971
$396$	−2.07602e139	−2.19048
$397$	−1.14667e139	−1.05717	−0.528586	−	0.848880i	$-0.677278\pi$
$397$	−1.14667e139	−1.05717	−0.528586	+	0.848880i	$0.677278\pi$
$398$	1.85444e139	1.49441
$399$	4.63673e139	3.26709
$400$	2.36198e138	0.145568
$401$	−2.34752e139	−1.26586	−0.632929	−	0.774210i	$-0.718147\pi$
$401$	−2.34752e139	−1.26586	−0.632929	+	0.774210i	$0.718147\pi$
$402$	1.30881e139	0.617707
$403$	−8.18976e138	−0.338416
$404$	1.91225e139	0.692056
$405$	−4.52055e138	−0.143333
$406$	−8.62454e139	−2.39659
$407$	−4.68759e138	−0.114196
$408$	5.32272e139	1.13714
$409$	−1.60156e139	−0.300156	−0.150078	−	0.988674i	$-0.547952\pi$
$409$	−1.60156e139	−0.300156	−0.150078	+	0.988674i	$0.547952\pi$
$410$	3.42635e139	0.563502
$411$	1.58621e140	2.28993
$412$	1.59507e140	2.02198
$413$	−5.04730e139	−0.561994
$414$	−3.84307e140	−3.75976
$415$	2.95322e139	0.253935
$416$	1.75366e140	1.32572
$417$	−3.02515e139	−0.201126
$418$	−4.02546e140	−2.35442
$419$	2.21867e139	0.114194	0.0570968	−	0.998369i	$-0.481816\pi$
$419$	2.21867e139	0.114194	0.0570968	+	0.998369i	$0.481816\pi$
$420$	−5.19566e140	−2.35399
$421$	−3.68940e140	−1.47185	−0.735924	−	0.677064i	$-0.763252\pi$
$421$	−3.68940e140	−1.47185	−0.735924	+	0.677064i	$0.763252\pi$
$422$	7.61875e140	2.67712
$423$	2.97965e140	0.922476
$424$	2.35515e140	0.642607
$425$	1.48169e140	0.356410
$426$	1.54759e141	3.28279
$427$	1.41084e140	0.263990
$428$	−1.17646e141	−1.94238
$429$	−1.06652e141	−1.55420
$430$	5.86966e139	0.0755180
$431$	1.31363e141	1.49258	0.746291	−	0.665620i	$-0.231833\pi$
$431$	1.31363e141	1.49258	0.746291	+	0.665620i	$0.231833\pi$
$432$	6.14115e140	0.616410
$433$	−7.03482e140	−0.623952	−0.311976	−	0.950090i	$-0.600991\pi$
$433$	−7.03482e140	−0.623952	−0.311976	+	0.950090i	$0.600991\pi$
$434$	−8.43089e140	−0.660957
$435$	2.53596e141	1.75779
$436$	−3.55020e141	−2.17633
$437$	−4.26747e141	−2.31427
$438$	9.86625e140	0.473464
$439$	−2.60603e140	−0.110695	−0.0553474	−	0.998467i	$-0.517627\pi$
$439$	−2.60603e140	−0.110695	−0.0553474	+	0.998467i	$0.517627\pi$
$440$	1.14485e141	0.430557
$441$	2.87045e141	0.956061
$442$	6.76954e141	1.99741
$443$	−6.48650e141	−1.69594	−0.847971	−	0.530042i	$-0.822176\pi$
$443$	−6.48650e141	−1.69594	−0.847971	+	0.530042i	$0.822176\pi$
$444$	−1.12035e141	−0.259637
$445$	1.43683e140	0.0295219
$446$	−2.91016e141	−0.530276
$447$	−8.61165e141	−1.39198
$448$	1.33057e142	1.90838
$449$	5.50060e141	0.700214	0.350107	−	0.936710i	$-0.386145\pi$
$449$	5.50060e141	0.700214	0.350107	+	0.936710i	$0.386145\pi$
$450$	−6.12148e141	−0.691810
$451$	4.14641e141	0.416128
$452$	1.40708e142	1.25434
$453$	−1.48002e142	−1.17223
$454$	3.10988e142	2.18905
$455$	−1.67714e142	−1.04945
$456$	−2.44188e142	−1.35865
$457$	−1.66869e142	−0.825770	−0.412885	−	0.910783i	$-0.635479\pi$
$457$	−1.66869e142	−0.825770	−0.412885	+	0.910783i	$0.635479\pi$
$458$	2.84480e141	0.125242
$459$	3.85240e142	1.50922
$460$	4.78190e142	1.66746
$461$	1.27806e142	0.396783	0.198391	−	0.980123i	$-0.436428\pi$
$461$	1.27806e142	0.396783	0.198391	+	0.980123i	$0.436428\pi$
$462$	−1.09793e143	−3.03548
$463$	−9.35656e141	−0.230427	−0.115213	−	0.993341i	$-0.536755\pi$
$463$	−9.35656e141	−0.230427	−0.115213	+	0.993341i	$0.536755\pi$
$464$	−3.10520e142	−0.681362
$465$	2.47902e142	0.484783
$466$	−2.02659e142	−0.353280
$467$	3.43832e142	0.534432	0.267216	−	0.963637i	$-0.413896\pi$
$467$	3.43832e142	0.534432	0.267216	+	0.963637i	$0.413896\pi$
$468$	−1.60164e143	−2.22030
$469$	2.49067e142	0.308013
$470$	−6.47409e142	−0.714403
$471$	2.49556e143	2.45782
$472$	2.65811e142	0.233709
$473$	7.10318e141	0.0557676
$474$	1.08694e143	0.762193
$475$	−6.79749e142	−0.425834
$476$	3.99088e143	2.23407
$477$	4.17291e143	2.08788
$478$	5.70821e142	0.255333
$479$	−4.82089e143	−1.92831	−0.964156	−	0.265335i	$-0.914518\pi$
$479$	−4.82089e143	−1.92831	−0.964156	+	0.265335i	$0.914518\pi$
$480$	−5.30830e143	−1.89910
$481$	−3.61647e142	−0.115751
$482$	−1.44973e143	−0.415213
$483$	−1.16394e144	−2.98371
$484$	−3.80855e142	−0.0874044
$485$	2.53777e143	0.521518
$486$	7.13135e143	1.31260
$487$	−7.17127e142	−0.118249	−0.0591244	−	0.998251i	$-0.518831\pi$
$487$	−7.17127e142	−0.118249	−0.0591244	+	0.998251i	$0.518831\pi$
$488$	−7.43006e142	−0.109782
$489$	2.13897e144	2.83257
$490$	−6.23683e143	−0.740412
$491$	−3.25441e143	−0.346428	−0.173214	−	0.984884i	$-0.555415\pi$
$491$	−3.25441e143	−0.346428	−0.173214	+	0.984884i	$0.555415\pi$
$492$	9.91009e143	0.946116
$493$	−1.94792e144	−1.66825
$494$	−3.10563e144	−2.38648
$495$	2.02848e144	1.39892
$496$	−3.03548e143	−0.187913
$497$	2.94508e144	1.63693
$498$	1.49153e144	0.744497
$499$	−4.01482e144	−1.80006	−0.900030	−	0.435827i	$-0.856456\pi$
$499$	−4.01482e144	−1.80006	−0.900030	+	0.435827i	$0.856456\pi$
$500$	3.60908e144	1.45379
$501$	7.61401e143	0.275610
$502$	1.54657e144	0.503178
$503$	−3.10958e143	−0.0909526	−0.0454763	−	0.998965i	$-0.514481\pi$
$503$	−3.10958e143	−0.0909526	−0.0454763	+	0.998965i	$0.514481\pi$
$504$	−4.18478e144	−1.10062
$505$	−1.86846e144	−0.441972
$506$	1.01049e145	2.15021
$507$	3.39172e143	0.0649373
$508$	−8.90411e144	−1.53420
$509$	6.29448e144	0.976245	0.488123	−	0.872775i	$-0.337682\pi$
$509$	6.29448e144	0.976245	0.488123	+	0.872775i	$0.337682\pi$
$510$	−2.04913e145	−2.86130
$511$	1.87755e144	0.236088
$512$	8.99989e144	1.01928
$513$	−1.76735e145	−1.80320
$514$	2.25743e145	2.07533
$515$	−1.55854e145	−1.29131
$516$	1.69769e144	0.126794
$517$	−7.83463e144	−0.527563
$518$	−3.72295e144	−0.226071
$519$	7.56120e144	0.414130
$520$	8.83251e144	0.436421
$521$	−2.97464e145	−1.32622	−0.663112	−	0.748520i	$-0.730765\pi$
$521$	−2.97464e145	−1.32622	−0.663112	+	0.748520i	$0.730765\pi$
$522$	8.04767e145	3.23816
$523$	2.98722e145	1.08499	0.542496	−	0.840058i	$-0.317479\pi$
$523$	2.98722e145	1.08499	0.542496	+	0.840058i	$0.317479\pi$
$524$	8.39799e143	0.0275392
$525$	−1.85399e145	−0.549014
$526$	3.12408e145	0.835573
$527$	−1.90418e145	−0.460088
$528$	−3.95300e145	−0.863003
$529$	5.64394e145	1.11354
$530$	−9.06679e145	−1.61694
$531$	4.70970e145	0.759340
$532$	−1.83088e146	−2.66924
$533$	3.19895e145	0.421795
$534$	7.25675e144	0.0865535
$535$	1.14951e146	1.24047
$536$	−1.31169e145	−0.128089
$537$	−3.25194e146	−2.87420
$538$	−3.50272e144	−0.0280256
$539$	−7.54752e145	−0.546771
$540$	1.98040e146	1.29923
$541$	1.00307e146	0.596046	0.298023	−	0.954559i	$-0.403673\pi$
$541$	1.00307e146	0.596046	0.298023	+	0.954559i	$0.403673\pi$
$542$	6.87278e145	0.369974
$543$	5.20846e146	2.54050
$544$	4.07740e146	1.80236
$545$	3.46890e146	1.38989
$546$	−8.47048e146	−3.07682
$547$	−5.73547e146	−1.88906	−0.944532	−	0.328418i	$-0.893484\pi$
$547$	−5.73547e146	−1.88906	−0.944532	+	0.328418i	$0.893484\pi$
$548$	−6.26338e146	−1.87089
$549$	−1.31648e146	−0.356691
$550$	1.60957e146	0.395646
$551$	8.93640e146	1.99321
$552$	6.12974e146	1.24080
$553$	2.06845e146	0.380059
$554$	−7.96909e146	−1.32934
$555$	1.09470e146	0.165813
$556$	1.19453e146	0.164321
$557$	3.46459e146	0.432912	0.216456	−	0.976292i	$-0.430550\pi$
$557$	3.46459e146	0.432912	0.216456	+	0.976292i	$0.430550\pi$
$558$	7.86697e146	0.893055
$559$	5.48009e145	0.0565270
$560$	−6.21622e146	−0.582730
$561$	−2.47975e147	−2.11298
$562$	7.70341e146	0.596747
$563$	−5.37422e146	−0.378544	−0.189272	−	0.981925i	$-0.560613\pi$
$563$	−5.37422e146	−0.378544	−0.189272	+	0.981925i	$0.560613\pi$
$564$	−1.87251e147	−1.19948
$565$	−1.37486e147	−0.801064
$566$	−6.17706e145	−0.0327418
$567$	−4.34478e146	−0.209544
$568$	−1.55100e147	−0.680729
$569$	2.18498e147	0.872851	0.436426	−	0.899740i	$-0.356244\pi$
$569$	2.18498e147	0.872851	0.436426	+	0.899740i	$0.356244\pi$
$570$	9.40069e147	3.41865
$571$	−1.43567e147	−0.475359	−0.237679	−	0.971344i	$-0.576387\pi$
$571$	−1.43567e147	−0.475359	−0.237679	+	0.971344i	$0.576387\pi$
$572$	4.21134e147	1.26979
$573$	3.88960e146	0.106815
$574$	3.29313e147	0.823802
$575$	1.70634e147	0.388898
$576$	−1.24157e148	−2.57852
$577$	−5.30051e146	−0.100326	−0.0501628	−	0.998741i	$-0.515974\pi$
$577$	−5.30051e146	−0.100326	−0.0501628	+	0.998741i	$0.515974\pi$
$578$	6.87305e147	1.18580
$579$	−3.01609e147	−0.474395
$580$	−1.00136e148	−1.43613
$581$	2.83839e147	0.371235
$582$	1.28171e148	1.52901
$583$	−1.09722e148	−1.19406
$584$	−9.88793e146	−0.0981789
$585$	1.56497e148	1.41797
$586$	−1.96911e148	−1.62835
$587$	−2.37496e148	−1.79274	−0.896370	−	0.443306i	$-0.853806\pi$
$587$	−2.37496e148	−1.79274	−0.896370	+	0.443306i	$0.853806\pi$
$588$	−1.80389e148	−1.24315
$589$	8.73575e147	0.549708
$590$	−1.02331e148	−0.588064
$591$	3.07779e148	1.61551
$592$	−1.34042e147	−0.0642731
$593$	3.35825e148	1.47125	0.735627	−	0.677387i	$-0.236888\pi$
$593$	3.35825e148	1.47125	0.735627	+	0.677387i	$0.236888\pi$
$594$	4.18490e148	1.67537
$595$	−3.89949e148	−1.42676
$596$	3.40044e148	1.13726
$597$	−5.24080e148	−1.60240
$598$	7.79592e148	2.17949
$599$	−2.37425e148	−0.607003	−0.303501	−	0.952831i	$-0.598156\pi$
$599$	−2.37425e148	−0.607003	−0.303501	+	0.952831i	$0.598156\pi$
$600$	9.76382e147	0.228312
$601$	−6.98751e148	−1.49464	−0.747322	−	0.664462i	$-0.768661\pi$
$601$	−6.98751e148	−1.49464	−0.747322	+	0.664462i	$0.768661\pi$
$602$	5.64144e147	0.110402
$603$	−2.32408e148	−0.416173
$604$	5.84409e148	0.957724
$605$	3.72134e147	0.0558196
$606$	−9.43672e148	−1.29579
$607$	1.01867e149	1.28068	0.640338	−	0.768093i	$-0.278794\pi$
$607$	1.01867e149	1.28068	0.640338	+	0.768093i	$0.278794\pi$
$608$	−1.87057e149	−2.15344
$609$	2.43736e149	2.56978
$610$	2.86040e148	0.276236
$611$	−6.04440e148	−0.534747
$612$	−3.72395e149	−3.01858
$613$	1.36658e149	1.01508	0.507540	−	0.861628i	$-0.330555\pi$
$613$	1.36658e149	1.01508	0.507540	+	0.861628i	$0.330555\pi$
$614$	3.91820e149	2.66734
$615$	−9.68315e148	−0.604224
$616$	1.10034e149	0.629446
$617$	−2.37291e149	−1.24459	−0.622294	−	0.782784i	$-0.713799\pi$
$617$	−2.37291e149	−1.24459	−0.622294	+	0.782784i	$0.713799\pi$
$618$	−7.87146e149	−3.78592
$619$	2.71735e149	1.19866	0.599329	−	0.800503i	$-0.295434\pi$
$619$	2.71735e149	1.19866	0.599329	+	0.800503i	$0.295434\pi$
$620$	−9.78880e148	−0.396072
$621$	4.43650e149	1.64679
$622$	6.73914e148	0.229519
$623$	1.38096e148	0.0431590
$624$	−3.04973e149	−0.874755
$625$	−2.51039e149	−0.660937
$626$	1.22280e150	2.95548
$627$	1.13763e150	2.52456
$628$	−9.85410e149	−2.00806
$629$	−8.40857e148	−0.157367
$630$	1.61104e150	2.76941
$631$	−2.69906e149	−0.426228	−0.213114	−	0.977027i	$-0.568361\pi$
$631$	−2.69906e149	−0.426228	−0.213114	+	0.977027i	$0.568361\pi$
$632$	−1.08933e149	−0.158050
$633$	−2.15312e150	−2.87058
$634$	1.00845e150	1.23560
$635$	8.70021e149	0.979796
$636$	−2.62240e150	−2.71483
$637$	−5.82289e149	−0.554216
$638$	−2.11604e150	−1.85190
$639$	−2.74809e150	−2.21175
$640$	1.13359e150	0.839128
$641$	−7.95942e149	−0.541972	−0.270986	−	0.962583i	$-0.587350\pi$
$641$	−7.95942e149	−0.541972	−0.270986	+	0.962583i	$0.587350\pi$
$642$	5.80566e150	3.63687
$643$	1.07476e150	0.619478	0.309739	−	0.950822i	$-0.399758\pi$
$643$	1.07476e150	0.619478	0.309739	+	0.950822i	$0.399758\pi$
$644$	4.59597e150	2.43772
$645$	−1.65881e149	−0.0809752
$646$	−7.22084e150	−3.24450
$647$	3.18242e150	1.31637	0.658186	−	0.752856i	$-0.271324\pi$
$647$	3.18242e150	1.31637	0.658186	+	0.752856i	$0.271324\pi$
$648$	2.28814e149	0.0871403
$649$	−1.23836e150	−0.434266
$650$	1.24178e150	0.401033
$651$	2.38264e150	0.708721
$652$	−8.44606e150	−2.31424
$653$	−3.23160e150	−0.815760	−0.407880	−	0.913036i	$-0.633732\pi$
$653$	−3.23160e150	−0.815760	−0.407880	+	0.913036i	$0.633732\pi$
$654$	1.75198e151	4.07493
$655$	−8.20568e148	−0.0175875
$656$	1.18567e150	0.234211
$657$	−1.75197e150	−0.318991
$658$	−6.22237e150	−1.04441
$659$	3.22008e149	0.0498307	0.0249153	−	0.999690i	$-0.492068\pi$
$659$	3.22008e149	0.0498307	0.0249153	+	0.999690i	$0.492068\pi$
$660$	−1.27476e151	−1.81898
$661$	9.01356e150	1.18609	0.593046	−	0.805169i	$-0.297925\pi$
$661$	9.01356e150	1.18609	0.593046	+	0.805169i	$0.297925\pi$
$662$	8.05984e150	0.978192
$663$	−1.91313e151	−2.14175
$664$	−1.49481e150	−0.154381
$665$	1.78896e151	1.70467
$666$	3.47393e150	0.305457
$667$	−2.24326e151	−1.82032
$668$	−3.00651e150	−0.225176
$669$	8.22434e150	0.568596
$670$	5.04969e150	0.322302
$671$	3.46152e150	0.203992
$672$	−5.10190e151	−2.77636
$673$	1.88054e151	0.945097	0.472548	−	0.881305i	$-0.343334\pi$
$673$	1.88054e151	0.945097	0.472548	+	0.881305i	$0.343334\pi$
$674$	4.98080e151	2.31204
$675$	7.06672e150	0.303016
$676$	−1.33927e150	−0.0530543
$677$	1.10658e151	0.405030	0.202515	−	0.979279i	$-0.435088\pi$
$677$	1.10658e151	0.405030	0.202515	+	0.979279i	$0.435088\pi$
$678$	−6.94379e151	−2.34860
$679$	2.43910e151	0.762423
$680$	2.05363e151	0.593328
$681$	−8.78877e151	−2.34724
$682$	−2.06853e151	−0.510738
$683$	6.26506e151	1.43027	0.715134	−	0.698988i	$-0.246366\pi$
$683$	6.26506e151	1.43027	0.715134	+	0.698988i	$0.246366\pi$
$684$	1.70842e152	3.60656
$685$	6.11995e151	1.19482
$686$	4.60529e151	0.831605
$687$	−8.03964e150	−0.134292
$688$	2.03116e150	0.0313879
$689$	−8.46503e151	−1.21032
$690$	−2.35981e152	−3.12213
$691$	−1.38107e152	−1.69098	−0.845491	−	0.533989i	$-0.820692\pi$
$691$	−1.38107e152	−1.69098	−0.845491	+	0.533989i	$0.820692\pi$
$692$	−2.98565e151	−0.338348
$693$	1.94961e152	2.04512
$694$	−1.50542e152	−1.46192
$695$	−1.16717e151	−0.104942
$696$	−1.28361e152	−1.06866
$697$	7.43780e151	0.573444
$698$	1.13543e149	0.000810768 0
$699$	5.72730e151	0.378810
$700$	7.32074e151	0.448549
$701$	−1.34305e152	−0.762391	−0.381195	−	0.924494i	$-0.624488\pi$
$701$	−1.34305e152	−0.762391	−0.381195	+	0.924494i	$0.624488\pi$
$702$	3.22864e152	1.69818
$703$	3.85757e151	0.188020
$704$	3.26458e152	1.47465
$705$	1.82963e152	0.766029
$706$	−2.17209e151	−0.0842996
$707$	−1.79581e152	−0.646133
$708$	−2.95973e152	−0.987355
$709$	3.01497e152	0.932629	0.466314	−	0.884619i	$-0.345582\pi$
$709$	3.01497e152	0.932629	0.466314	+	0.884619i	$0.345582\pi$
$710$	5.97097e152	1.71287
$711$	−1.93010e152	−0.513519
$712$	−7.27269e150	−0.0179480
$713$	−2.19289e152	−0.502027
$714$	−1.96945e153	−4.18303
$715$	−4.11490e152	−0.810934
$716$	1.28408e153	2.34825
$717$	−1.61319e152	−0.273785
$718$	−2.47829e152	−0.390387
$719$	1.14232e153	1.67030	0.835148	−	0.550025i	$-0.185382\pi$
$719$	1.14232e153	1.67030	0.835148	+	0.550025i	$0.185382\pi$
$720$	5.80044e152	0.787358
$721$	−1.49794e153	−1.88781
$722$	2.00542e153	2.34674
$723$	4.09706e152	0.445219
$724$	−2.05664e153	−2.07561
$725$	−3.57320e152	−0.334945
$726$	1.87948e152	0.163654
$727$	−6.46235e152	−0.522756	−0.261378	−	0.965236i	$-0.584177\pi$
$727$	−6.46235e152	−0.522756	−0.261378	+	0.965236i	$0.584177\pi$
$728$	8.48909e152	0.638017
$729$	−2.25519e153	−1.57492
$730$	3.80663e152	0.247040
$731$	1.27416e152	0.0768503
$732$	8.27317e152	0.463798
$733$	−3.15167e153	−1.64240	−0.821198	−	0.570644i	$-0.806694\pi$
$733$	−3.15167e153	−1.64240	−0.821198	+	0.570644i	$0.806694\pi$
$734$	3.13046e153	1.51659
$735$	1.76258e153	0.793918
$736$	4.69560e153	1.96666
$737$	6.11089e152	0.238009
$738$	−3.07287e153	−1.11308
$739$	5.15385e152	0.173642	0.0868209	−	0.996224i	$-0.472329\pi$
$739$	5.15385e152	0.173642	0.0868209	+	0.996224i	$0.472329\pi$
$740$	−4.32258e152	−0.135471
$741$	8.77677e153	2.55894
$742$	−8.71426e153	−2.36386
$743$	5.07005e153	1.27971	0.639854	−	0.768496i	$-0.278995\pi$
$743$	5.07005e153	1.27971	0.639854	+	0.768496i	$0.278995\pi$
$744$	−1.25479e153	−0.294727
$745$	−3.32257e153	−0.726296
$746$	−1.35498e154	−2.75680
$747$	−2.64854e153	−0.501596
$748$	9.79169e153	1.72632
$749$	1.10482e154	1.81349
$750$	−1.78104e154	−2.72204
$751$	1.28494e154	1.82872	0.914359	−	0.404904i	$-0.132695\pi$
$751$	1.28494e154	1.82872	0.914359	+	0.404904i	$0.132695\pi$
$752$	−2.24032e153	−0.296931
$753$	−4.37074e153	−0.539540
$754$	−1.63252e154	−1.87712
$755$	−5.71026e153	−0.611637
$756$	1.90340e154	1.89939
$757$	−1.25248e154	−1.16450	−0.582251	−	0.813009i	$-0.697828\pi$
$757$	−1.25248e154	−1.16450	−0.582251	+	0.813009i	$0.697828\pi$
$758$	1.85789e154	1.60960
$759$	−2.85573e154	−2.30559
$760$	−9.42135e153	−0.708901
$761$	−2.40168e153	−0.168437	−0.0842183	−	0.996447i	$-0.526839\pi$
$761$	−2.40168e153	−0.168437	−0.0842183	+	0.996447i	$0.526839\pi$
$762$	4.39407e154	2.87261
$763$	3.33403e154	2.03192
$764$	−1.53587e153	−0.0872688
$765$	3.63867e154	1.92777
$766$	1.32433e154	0.654271
$767$	−9.55393e153	−0.440180
$768$	−9.68966e152	−0.0416374
$769$	−8.92143e153	−0.357582	−0.178791	−	0.983887i	$-0.557219\pi$
$769$	−8.92143e153	−0.357582	−0.178791	+	0.983887i	$0.557219\pi$
$770$	−4.23605e154	−1.58383
$771$	−6.37967e154	−2.22530
$772$	1.19095e154	0.387585
$773$	−2.79161e153	−0.0847718	−0.0423859	−	0.999101i	$-0.513496\pi$
$773$	−2.79161e153	−0.0847718	−0.0423859	+	0.999101i	$0.513496\pi$
$774$	−5.26410e153	−0.149170
$775$	−3.49297e153	−0.0923748
$776$	−1.28453e154	−0.317059
$777$	1.05213e154	0.242408
$778$	5.38964e153	0.115918
$779$	−3.41221e154	−0.685144
$780$	−9.83477e154	−1.84375
$781$	7.22579e154	1.26490
$782$	1.81261e155	2.96308
$783$	−9.29034e154	−1.41833
$784$	−2.15822e154	−0.307741
$785$	9.62844e154	1.28242
$786$	−4.14431e153	−0.0515639
$787$	1.41664e155	1.64669	0.823346	−	0.567540i	$-0.192105\pi$
$787$	1.41664e155	1.64669	0.823346	+	0.567540i	$0.192105\pi$
$788$	−1.21531e155	−1.31988
$789$	−8.82889e154	−0.895955
$790$	4.19367e154	0.397690
$791$	−1.32141e155	−1.17110
$792$	−1.02674e155	−0.850479
$793$	2.67056e154	0.206769
$794$	−2.23441e155	−1.61721
$795$	2.56235e155	1.73379
$796$	2.06941e155	1.30917
$797$	−2.82379e155	−1.67037	−0.835185	−	0.549969i	$-0.814640\pi$
$797$	−2.82379e155	−1.67037	−0.835185	+	0.549969i	$0.814640\pi$
$798$	9.03518e155	4.99784
$799$	−1.40537e155	−0.727007
$800$	7.47944e154	0.361872
$801$	−1.28859e154	−0.0583145
$802$	−4.57440e155	−1.93645
$803$	4.60660e154	0.182431
$804$	1.46053e155	0.541142
$805$	−4.49073e155	−1.55682
$806$	−1.59587e155	−0.517692
$807$	9.89898e153	0.0300508
$808$	9.45745e154	0.268699
$809$	4.94650e155	1.31538	0.657691	−	0.753288i	$-0.271533\pi$
$809$	4.94650e155	1.31538	0.657691	+	0.753288i	$0.271533\pi$
$810$	−8.80879e154	−0.219264
$811$	−5.24246e155	−1.22157	−0.610786	−	0.791796i	$-0.709147\pi$
$811$	−5.24246e155	−1.22157	−0.610786	+	0.791796i	$0.709147\pi$
$812$	−9.62430e155	−2.09953
$813$	−1.94230e155	−0.396710
$814$	−9.13430e154	−0.174691
$815$	8.25264e155	1.47795
$816$	−7.09087e155	−1.18926
$817$	−5.84543e154	−0.0918198
$818$	−3.12082e155	−0.459164
$819$	1.50412e156	2.07297
$820$	3.82354e155	0.493656
$821$	−4.51760e155	−0.546448	−0.273224	−	0.961950i	$-0.588090\pi$
$821$	−4.51760e155	−0.546448	−0.273224	+	0.961950i	$0.588090\pi$
$822$	3.09090e156	3.50303
$823$	9.25750e155	0.983111	0.491555	−	0.870846i	$-0.336428\pi$
$823$	9.25750e155	0.983111	0.491555	+	0.870846i	$0.336428\pi$
$824$	7.88875e155	0.785060
$825$	−4.54878e155	−0.424237
$826$	−9.83523e155	−0.859710
$827$	−2.27169e156	−1.86125	−0.930625	−	0.365973i	$-0.880736\pi$
$827$	−2.27169e156	−1.86125	−0.930625	+	0.365973i	$0.880736\pi$
$828$	−4.28856e156	−3.29374
$829$	1.85803e156	1.33778	0.668892	−	0.743360i	$-0.266769\pi$
$829$	1.85803e156	1.33778	0.668892	+	0.743360i	$0.266769\pi$
$830$	5.75467e155	0.388457
$831$	2.25213e156	1.42540
$832$	2.51861e156	1.49473
$833$	−1.35387e156	−0.753475
$834$	−5.89484e155	−0.307672
$835$	2.93766e155	0.143805
$836$	−4.49209e156	−2.06259
$837$	−9.08174e155	−0.391163
$838$	4.32332e155	0.174688
$839$	1.14973e156	0.435842	0.217921	−	0.975966i	$-0.430072\pi$
$839$	1.14973e156	0.435842	0.217921	+	0.975966i	$0.430072\pi$
$840$	−2.56963e156	−0.913964
$841$	1.70125e156	0.567781
$842$	−7.18920e156	−2.25156
$843$	−2.17705e156	−0.639871
$844$	8.50192e156	2.34529
$845$	1.30860e155	0.0338824
$846$	5.80617e156	1.41116
$847$	3.57665e155	0.0816045
$848$	−3.13750e156	−0.672057
$849$	1.74569e155	0.0351079
$850$	2.88724e156	0.545218
$851$	−9.68346e155	−0.171711
$852$	1.72699e157	2.87589
$853$	−2.74435e156	−0.429206	−0.214603	−	0.976701i	$-0.568846\pi$
$853$	−2.74435e156	−0.429206	−0.214603	+	0.976701i	$0.568846\pi$
$854$	2.74919e156	0.403839
$855$	−1.66930e157	−2.30328
$856$	−5.81842e156	−0.754152
$857$	1.51608e157	1.84607	0.923035	−	0.384717i	$-0.125701\pi$
$857$	1.51608e157	1.84607	0.923035	+	0.384717i	$0.125701\pi$
$858$	−2.07824e157	−2.37753
$859$	−7.06499e156	−0.759412	−0.379706	−	0.925107i	$-0.623975\pi$
$859$	−7.06499e156	−0.759412	−0.379706	+	0.925107i	$0.623975\pi$
$860$	6.55007e155	0.0661574
$861$	−9.30666e156	−0.883334
$862$	2.55975e157	2.28328
$863$	8.37604e156	0.702200	0.351100	−	0.936338i	$-0.385808\pi$
$863$	8.37604e156	0.702200	0.351100	+	0.936338i	$0.385808\pi$
$864$	1.94466e157	1.53235
$865$	2.91728e156	0.216081
$866$	−1.37081e157	−0.954490
$867$	−1.94238e157	−1.27149
$868$	−9.40820e156	−0.579031
$869$	5.07498e156	0.293681
$870$	4.94161e157	2.68899
$871$	4.71454e156	0.241250
$872$	−1.75583e157	−0.844988
$873$	−2.27595e157	−1.03015
$874$	−8.31565e157	−3.54026
$875$	−3.38932e157	−1.35732
$876$	1.10100e157	0.414778
$877$	−4.33658e156	−0.153698	−0.0768492	−	0.997043i	$-0.524486\pi$
$877$	−4.33658e156	−0.153698	−0.0768492	+	0.997043i	$0.524486\pi$
$878$	−5.07814e156	−0.169335
$879$	5.56487e157	1.74603
$880$	−1.52516e157	−0.450290
$881$	2.21561e157	0.615577	0.307789	−	0.951455i	$-0.400411\pi$
$881$	2.21561e157	0.615577	0.307789	+	0.951455i	$0.400411\pi$
$882$	5.59339e157	1.46253
$883$	6.97440e157	1.71636	0.858181	−	0.513347i	$-0.171595\pi$
$883$	6.97440e157	1.71636	0.858181	+	0.513347i	$0.171595\pi$
$884$	7.55426e157	1.74983
$885$	2.89196e157	0.630560
$886$	−1.26397e158	−2.59437
$887$	1.04197e157	0.201345	0.100673	−	0.994920i	$-0.467901\pi$
$887$	1.04197e157	0.201345	0.100673	+	0.994920i	$0.467901\pi$
$888$	−5.54096e156	−0.100807
$889$	8.36194e157	1.43239
$890$	2.79982e156	0.0451611
$891$	−1.06600e157	−0.161920
$892$	−3.24751e157	−0.464548
$893$	6.44737e157	0.868619
$894$	−1.67808e158	−2.12939
$895$	−1.25467e158	−1.49968
$896$	1.08952e158	1.22675
$897$	−2.20319e158	−2.33699
$898$	1.07185e158	1.07115
$899$	4.59207e157	0.432380
$900$	−6.83108e157	−0.606059
$901$	−1.96818e158	−1.64547
$902$	8.07975e157	0.636573
$903$	−1.59432e157	−0.118380
$904$	6.95905e157	0.487011
$905$	2.00954e158	1.32556
$906$	−2.88399e158	−1.79322
$907$	1.94402e158	1.13949	0.569746	−	0.821821i	$-0.307042\pi$
$907$	1.94402e158	1.13949	0.569746	+	0.821821i	$0.307042\pi$
$908$	3.47038e158	1.91772
$909$	1.67569e158	0.873026
$910$	−3.26810e158	−1.60539
$911$	−2.13835e158	−0.990480	−0.495240	−	0.868756i	$-0.664920\pi$
$911$	−2.13835e158	−0.990480	−0.495240	+	0.868756i	$0.664920\pi$
$912$	3.25305e158	1.42091
$913$	6.96403e157	0.286863
$914$	−3.25163e158	−1.26322
$915$	−8.08372e157	−0.296198
$916$	3.17457e157	0.109718
$917$	−7.88663e156	−0.0257118
$918$	7.50684e158	2.30873
$919$	1.99446e158	0.578689	0.289345	−	0.957225i	$-0.406563\pi$
$919$	1.99446e158	0.578689	0.289345	+	0.957225i	$0.406563\pi$
$920$	2.36499e158	0.647413
$921$	−1.10732e159	−2.86010
$922$	2.49045e158	0.606979
$923$	5.57468e158	1.28212
$924$	−1.22520e159	−2.65923
$925$	−1.54244e157	−0.0315955
$926$	−1.82323e158	−0.352496
$927$	1.39775e159	2.55072
$928$	−9.83294e158	−1.69382
$929$	−3.92137e158	−0.637672	−0.318836	−	0.947810i	$-0.603292\pi$
$929$	−3.92137e158	−0.637672	−0.318836	+	0.947810i	$0.603292\pi$
$930$	4.83066e158	0.741598
$931$	6.21109e158	0.900243
$932$	−2.26151e158	−0.309491
$933$	−1.90454e158	−0.246105
$934$	6.69994e158	0.817548
$935$	−9.56746e158	−1.10249
$936$	−7.92128e158	−0.862060
$937$	−6.35866e157	−0.0653578	−0.0326789	−	0.999466i	$-0.510404\pi$
$937$	−6.35866e157	−0.0653578	−0.0326789	+	0.999466i	$0.510404\pi$
$938$	4.85335e158	0.471183
$939$	−3.45573e159	−3.16906
$940$	−7.22457e158	−0.625852
$941$	1.96729e159	1.60999	0.804997	−	0.593279i	$-0.202167\pi$
$941$	1.96729e159	1.60999	0.804997	+	0.593279i	$0.202167\pi$
$942$	4.86288e159	3.75985
$943$	8.56551e158	0.625716
$944$	−3.54110e158	−0.244420
$945$	−1.85981e159	−1.21302
$946$	1.38413e158	0.0853105
$947$	−2.28957e159	−1.33362	−0.666808	−	0.745230i	$-0.732340\pi$
$947$	−2.28957e159	−1.33362	−0.666808	+	0.745230i	$0.732340\pi$
$948$	1.21294e159	0.667719
$949$	3.55398e158	0.184915
$950$	−1.32457e159	−0.651420
$951$	−2.84995e159	−1.32489
$952$	1.97378e159	0.867405
$953$	2.67967e159	1.11330	0.556648	−	0.830748i	$-0.312087\pi$
$953$	2.67967e159	1.11330	0.556648	+	0.830748i	$0.312087\pi$
$954$	8.13139e159	3.19394
$955$	1.50070e158	0.0557330
$956$	6.36991e158	0.223685
$957$	5.98010e159	1.98573
$958$	−9.39405e159	−2.94984
$959$	5.88200e159	1.74675
$960$	−7.62379e159	−2.14121
$961$	−3.31555e159	−0.880754
$962$	−7.04709e158	−0.177069
$963$	−1.03092e160	−2.45030
$964$	−1.61779e159	−0.363747
$965$	−1.16367e159	−0.247526
$966$	−2.26806e160	−4.56434
$967$	6.50935e159	1.23943	0.619714	−	0.784827i	$-0.287248\pi$
$967$	6.50935e159	1.23943	0.619714	+	0.784827i	$0.287248\pi$
$968$	−1.88361e158	−0.0339358
$969$	2.04067e160	3.47897
$970$	4.94513e159	0.797792
$971$	5.88663e159	0.898748	0.449374	−	0.893344i	$-0.351647\pi$
$971$	5.88663e159	0.898748	0.449374	+	0.893344i	$0.351647\pi$
$972$	7.95802e159	1.14990
$973$	−1.12179e159	−0.153418
$974$	−1.39740e159	−0.180891
$975$	−3.50937e159	−0.430014
$976$	9.89823e158	0.114813
$977$	−7.47866e159	−0.821230	−0.410615	−	0.911809i	$-0.634686\pi$
$977$	−7.47866e159	−0.821230	−0.410615	+	0.911809i	$0.634686\pi$
$978$	4.16803e160	4.33313
$979$	3.38821e158	0.0333500
$980$	−6.95981e159	−0.648638
$981$	−3.11102e160	−2.74544
$982$	−6.34159e159	−0.529948
$983$	8.63845e159	0.683633	0.341816	−	0.939767i	$-0.388958\pi$
$983$	8.63845e159	0.683633	0.341816	+	0.939767i	$0.388958\pi$
$984$	4.90125e159	0.367341
$985$	1.18748e160	0.842925
$986$	−3.79574e160	−2.55201
$987$	1.75849e160	1.11988
$988$	−3.46564e160	−2.09068
$989$	1.46735e159	0.0838556
$990$	3.95271e160	2.13999
$991$	5.74045e159	0.294446	0.147223	−	0.989103i	$-0.452967\pi$
$991$	5.74045e159	0.294446	0.147223	+	0.989103i	$0.452967\pi$
$992$	−9.61215e159	−0.467139
$993$	−2.27778e160	−1.04888
$994$	5.73882e160	2.50409
$995$	−2.02202e160	−0.836085
$996$	1.66443e160	0.652216
$997$	9.28001e159	0.344634	0.172317	−	0.985042i	$-0.444875\pi$
$997$	9.28001e159	0.344634	0.172317	+	0.985042i	$0.444875\pi$
$998$	−7.82333e160	−2.75364
$999$	−4.01035e159	−0.133792

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.108.a.a.1.8	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.108.a.a.1.8	✓	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)

\(f(q)\)	\(=\)	\(q+1.94861e16 q^{2} -5.50693e25 q^{3} +2.17450e32 q^{4} -2.12470e37 q^{5} -1.07309e42 q^{6} -2.04209e45 q^{7} +1.07545e48 q^{8} +1.90550e51 q^{9} +O(q^{10})\)	\(q+1.94861e16 q^{2} -5.50693e25 q^{3} +2.17450e32 q^{4} -2.12470e37 q^{5} -1.07309e42 q^{6} -2.04209e45 q^{7} +1.07545e48 q^{8} +1.90550e51 q^{9} -4.14022e53 q^{10} -5.01029e55 q^{11} -1.19748e58 q^{12} -3.86543e59 q^{13} -3.97924e61 q^{14} +1.17006e63 q^{15} -1.43270e64 q^{16} -8.98743e65 q^{17} +3.71308e67 q^{18} +4.12313e68 q^{19} -4.62015e69 q^{20} +1.12457e71 q^{21} -9.76312e71 q^{22} -1.03501e73 q^{23} -5.92241e73 q^{24} -1.64862e74 q^{25} -7.53223e75 q^{26} -4.28643e76 q^{27} -4.44052e77 q^{28} +2.16738e78 q^{29} +2.27999e79 q^{30} +2.11872e79 q^{31} -4.53678e80 q^{32} +2.75914e81 q^{33} -1.75130e82 q^{34} +4.33883e82 q^{35} +4.14350e83 q^{36} +9.35592e82 q^{37} +8.03438e84 q^{38} +2.12867e85 q^{39} -2.28500e85 q^{40} -8.27578e85 q^{41} +2.19134e87 q^{42} -1.41772e86 q^{43} -1.08949e88 q^{44} -4.04862e88 q^{45} -2.01683e89 q^{46} +1.56371e89 q^{47} +7.88976e89 q^{48} +1.50640e90 q^{49} -3.21253e90 q^{50} +4.94932e91 q^{51} -8.40537e91 q^{52} +2.18993e92 q^{53} -8.35259e92 q^{54} +1.06454e93 q^{55} -2.19616e93 q^{56} -2.27058e94 q^{57} +4.22339e94 q^{58} +2.47163e94 q^{59} +2.54429e95 q^{60} -6.90882e94 q^{61} +4.12856e95 q^{62} -3.89120e96 q^{63} -6.51574e96 q^{64} +8.21288e96 q^{65} +5.37649e97 q^{66} -1.21967e97 q^{67} -1.95431e98 q^{68} +5.69972e98 q^{69} +8.45470e98 q^{70} -1.44219e99 q^{71} +2.04926e99 q^{72} -9.19427e98 q^{73} +1.82311e99 q^{74} +9.07886e99 q^{75} +8.96573e100 q^{76} +1.02315e101 q^{77} +4.14795e101 q^{78} -1.01291e101 q^{79} +3.04405e101 q^{80} +2.12762e101 q^{81} -1.61263e102 q^{82} -1.38994e102 q^{83} +2.44536e103 q^{84} +1.90956e103 q^{85} -2.76258e102 q^{86} -1.19356e104 q^{87} -5.38830e103 q^{88} -6.76249e102 q^{89} -7.88919e104 q^{90} +7.89356e104 q^{91} -2.25062e105 q^{92} -1.16676e105 q^{93} +3.04706e105 q^{94} -8.76041e105 q^{95} +2.49837e106 q^{96} -1.19441e106 q^{97} +2.93539e106 q^{98} -9.54712e106 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 54\!\cdots\!96 q^{2}+ \cdots + 36\!\cdots\!13 q^{9}+O(q^{10}) \) 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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