LMFDB - Embedded newform 1.108.a.a.1.6

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			1.6
Root			$-3.22655e14$ 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)

$f(q)$	$=$	$q+8.35103e15 q^{2} -1.73817e25 q^{3} -9.25196e31 q^{4} +3.17576e36 q^{5} -1.45155e41 q^{6} +2.61780e45 q^{7} -2.12767e48 q^{8} -8.25006e50 q^{9} +O(q^{10})$	\(q+8.35103e15 q^{2} -1.73817e25 q^{3} -9.25196e31 q^{4} +3.17576e36 q^{5} -1.45155e41 q^{6} +2.61780e45 q^{7} -2.12767e48 q^{8} -8.25006e50 q^{9} +2.65209e52 q^{10} +8.64945e55 q^{11} +1.60815e57 q^{12} -6.75605e59 q^{13} +2.18613e61 q^{14} -5.52002e61 q^{15} -2.75603e63 q^{16} +1.59475e64 q^{17} -6.88965e66 q^{18} -1.47885e68 q^{19} -2.93820e68 q^{20} -4.55018e70 q^{21} +7.22318e71 q^{22} -5.90239e72 q^{23} +3.69825e73 q^{24} -6.06212e74 q^{25} -5.64200e75 q^{26} +3.39315e76 q^{27} -2.42198e77 q^{28} +1.14316e78 q^{29} -4.60978e77 q^{30} +3.47876e78 q^{31} +3.22218e80 q^{32} -1.50342e81 q^{33} +1.33178e80 q^{34} +8.31350e81 q^{35} +7.63293e82 q^{36} +1.19248e84 q^{37} -1.23499e84 q^{38} +1.17432e85 q^{39} -6.75695e84 q^{40} +2.31907e86 q^{41} -3.79987e86 q^{42} +1.86399e87 q^{43} -8.00243e87 q^{44} -2.62002e87 q^{45} -4.92910e88 q^{46} -1.99006e89 q^{47} +4.79046e88 q^{48} +4.18914e90 q^{49} -5.06249e90 q^{50} -2.77196e89 q^{51} +6.25067e91 q^{52} -1.87760e92 q^{53} +2.83363e92 q^{54} +2.74686e92 q^{55} -5.56980e93 q^{56} +2.57049e93 q^{57} +9.54658e93 q^{58} +2.90733e94 q^{59} +5.10710e93 q^{60} +1.48641e95 q^{61} +2.90512e94 q^{62} -2.15970e96 q^{63} +3.13804e96 q^{64} -2.14556e96 q^{65} -1.25551e97 q^{66} +8.17363e97 q^{67} -1.47546e96 q^{68} +1.02594e98 q^{69} +6.94263e97 q^{70} +6.38103e98 q^{71} +1.75534e99 q^{72} -6.69192e98 q^{73} +9.95840e99 q^{74} +1.05370e100 q^{75} +1.36822e100 q^{76} +2.26425e101 q^{77} +9.80676e100 q^{78} +3.24637e101 q^{79} -8.75249e99 q^{80} +3.40102e101 q^{81} +1.93666e102 q^{82} +2.72752e102 q^{83} +4.20981e102 q^{84} +5.06455e100 q^{85} +1.55662e103 q^{86} -1.98701e103 q^{87} -1.84031e104 q^{88} +3.51653e103 q^{89} -2.18799e103 q^{90} -1.76860e105 q^{91} +5.46086e104 q^{92} -6.04668e103 q^{93} -1.66190e105 q^{94} -4.69646e104 q^{95} -5.60070e105 q^{96} +1.41014e106 q^{97} +3.49836e106 q^{98} -7.13585e106 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	8.35103e15	0.655594	0.327797	−	0.944748i	$-0.393694\pi$
$2$	8.35103e15	0.655594	0.327797	+	0.944748i	$0.393694\pi$
$3$	−1.73817e25	−0.517733	−0.258866	−	0.965913i	$-0.583349\pi$
$3$	−1.73817e25	−0.517733	−0.258866	+	0.965913i	$0.583349\pi$
$4$	−9.25196e31	−0.570196
$5$	3.17576e36	0.127924	0.0639621	−	0.997952i	$-0.479626\pi$
$5$	3.17576e36	0.127924	0.0639621	+	0.997952i	$0.479626\pi$
$6$	−1.45155e41	−0.339423
$7$	2.61780e45	1.60395	0.801975	−	0.597357i	$-0.203782\pi$
$7$	2.61780e45	1.60395	0.801975	+	0.597357i	$0.203782\pi$
$8$	−2.12767e48	−1.02941
$9$	−8.25006e50	−0.731953
$10$	2.65209e52	0.0838663
$11$	8.64945e55	1.66909	0.834545	−	0.550940i	$-0.185731\pi$
$11$	8.64945e55	1.66909	0.834545	+	0.550940i	$0.185731\pi$
$12$	1.60815e57	0.295209
$13$	−6.75605e59	−1.71287	−0.856433	−	0.516258i	$-0.827325\pi$
$13$	−6.75605e59	−1.71287	−0.856433	+	0.516258i	$0.827325\pi$
$14$	2.18613e61	1.05154
$15$	−5.52002e61	−0.0662305
$16$	−2.75603e63	−0.104680
$17$	1.59475e64	0.0236416	0.0118208	−	0.999930i	$-0.496237\pi$
$17$	1.59475e64	0.0236416	0.0118208	+	0.999930i	$0.496237\pi$
$18$	−6.88965e66	−0.479864
$19$	−1.47885e68	−0.570960	−0.285480	−	0.958385i	$-0.592153\pi$
$19$	−1.47885e68	−0.570960	−0.285480	+	0.958385i	$0.592153\pi$
$20$	−2.93820e68	−0.0729418
$21$	−4.55018e70	−0.830418
$22$	7.22318e71	1.09425
$23$	−5.90239e72	−0.829065	−0.414532	−	0.910035i	$-0.636055\pi$
$23$	−5.90239e72	−0.829065	−0.414532	+	0.910035i	$0.636055\pi$
$24$	3.69825e73	0.532960
$25$	−6.06212e74	−0.983635
$26$	−5.64200e75	−1.12295
$27$	3.39315e76	0.896689
$28$	−2.42198e77	−0.914567
$29$	1.14316e78	0.660412	0.330206	−	0.943909i	$-0.392882\pi$
$29$	1.14316e78	0.660412	0.330206	+	0.943909i	$0.392882\pi$
$30$	−4.60978e77	−0.0434203
$31$	3.47876e78	0.0566987	0.0283494	−	0.999598i	$-0.490975\pi$
$31$	3.47876e78	0.0566987	0.0283494	+	0.999598i	$0.490975\pi$
$32$	3.22218e80	0.960784
$33$	−1.50342e81	−0.864142
$34$	1.33178e80	0.0154993
$35$	8.31350e81	0.205184
$36$	7.63293e82	0.417357
$37$	1.19248e84	1.50542	0.752710	−	0.658352i	$-0.228746\pi$
$37$	1.19248e84	1.50542	0.752710	+	0.658352i	$0.228746\pi$
$38$	−1.23499e84	−0.374318
$39$	1.17432e85	0.886807
$40$	−6.75695e84	−0.131687
$41$	2.31907e86	1.20608	0.603042	−	0.797709i	$-0.293955\pi$
$41$	2.31907e86	1.20608	0.603042	+	0.797709i	$0.293955\pi$
$42$	−3.79987e86	−0.544417
$43$	1.86399e87	0.758369	0.379184	−	0.925321i	$-0.376205\pi$
$43$	1.86399e87	0.758369	0.379184	+	0.925321i	$0.376205\pi$
$44$	−8.00243e87	−0.951708
$45$	−2.62002e87	−0.0936344
$46$	−4.92910e88	−0.543530
$47$	−1.99006e89	−0.694433	−0.347217	−	0.937785i	$-0.612873\pi$
$47$	−1.99006e89	−0.694433	−0.347217	+	0.937785i	$0.612873\pi$
$48$	4.79046e88	0.0541964
$49$	4.18914e90	1.57266
$50$	−5.06249e90	−0.644866
$51$	−2.77196e89	−0.0122400
$52$	6.25067e91	0.976670
$53$	−1.87760e92	−1.05887	−0.529437	−	0.848349i	$-0.677597\pi$
$53$	−1.87760e92	−1.05887	−0.529437	+	0.848349i	$0.677597\pi$
$54$	2.83363e92	0.587864
$55$	2.74686e92	0.213517
$56$	−5.56980e93	−1.65113
$57$	2.57049e93	0.295605
$58$	9.54658e93	0.432963
$59$	2.90733e94	0.528338	0.264169	−	0.964476i	$-0.414902\pi$
$59$	2.90733e94	0.528338	0.264169	+	0.964476i	$0.414902\pi$
$60$	5.10710e93	0.0377644
$61$	1.48641e95	0.453935	0.226968	−	0.973902i	$-0.427119\pi$
$61$	1.48641e95	0.453935	0.226968	+	0.973902i	$0.427119\pi$
$62$	2.90512e94	0.0371714
$63$	−2.15970e96	−1.17402
$64$	3.13804e96	0.734565
$65$	−2.14556e96	−0.219117
$66$	−1.25551e97	−0.566527
$67$	8.17363e97	1.64973	0.824866	−	0.565329i	$-0.191251\pi$
$67$	8.17363e97	1.64973	0.824866	+	0.565329i	$0.191251\pi$
$68$	−1.47546e96	−0.0134803
$69$	1.02594e98	0.429234
$70$	6.94263e97	0.134517
$71$	6.38103e98	0.578854	0.289427	−	0.957200i	$-0.406535\pi$
$71$	6.38103e98	0.578854	0.289427	+	0.957200i	$0.406535\pi$
$72$	1.75534e99	0.753481
$73$	−6.69192e98	−0.137334	−0.0686669	−	0.997640i	$-0.521875\pi$
$73$	−6.69192e98	−0.137334	−0.0686669	+	0.997640i	$0.521875\pi$
$74$	9.95840e99	0.986945
$75$	1.05370e100	0.509260
$76$	1.36822e100	0.325559
$77$	2.26425e101	2.67714
$78$	9.80676e100	0.581386
$79$	3.24637e101	0.973527	0.486764	−	0.873534i	$-0.338177\pi$
$79$	3.24637e101	0.973527	0.486764	+	0.873534i	$0.338177\pi$
$80$	−8.75249e99	−0.0133911
$81$	3.40102e101	0.267708
$82$	1.93666e102	0.790702
$83$	2.72752e102	0.582223	0.291111	−	0.956689i	$-0.405975\pi$
$83$	2.72752e102	0.582223	0.291111	+	0.956689i	$0.405975\pi$
$84$	4.20981e102	0.473501
$85$	5.06455e100	0.00302433
$86$	1.55662e103	0.497182
$87$	−1.98701e103	−0.341917
$88$	−1.84031e104	−1.71818
$89$	3.51653e103	0.179370	0.0896848	−	0.995970i	$-0.471414\pi$
$89$	3.51653e103	0.179370	0.0896848	+	0.995970i	$0.471414\pi$
$90$	−2.18799e103	−0.0613862
$91$	−1.76860e105	−2.74735
$92$	5.46086e104	0.472729
$93$	−6.04668e103	−0.0293548
$94$	−1.66190e105	−0.455267
$95$	−4.69646e104	−0.0730395
$96$	−5.60070e105	−0.497429
$97$	1.41014e106	0.719406	0.359703	−	0.933067i	$-0.382878\pi$
$97$	1.41014e106	0.719406	0.359703	+	0.933067i	$0.382878\pi$
$98$	3.49836e106	1.03103
$99$	−7.13585e106	−1.22169
$100$	5.60865e106	0.560865
$101$	3.00087e107	1.76219	0.881097	−	0.472935i	$-0.156805\pi$
$101$	3.00087e107	1.76219	0.881097	+	0.472935i	$0.156805\pi$
$102$	−2.31487e105	−0.00802448
$103$	1.10514e107	0.227314	0.113657	−	0.993520i	$-0.463743\pi$
$103$	1.10514e107	0.227314	0.113657	+	0.993520i	$0.463743\pi$
$104$	1.43746e108	1.76324
$105$	−1.44503e107	−0.106230
$106$	−1.56799e108	−0.694192
$107$	−4.63701e108	−1.24224	−0.621120	−	0.783715i	$-0.713322\pi$
$107$	−4.63701e108	−1.24224	−0.621120	+	0.783715i	$0.713322\pi$
$108$	−3.13933e108	−0.511288
$109$	−1.96831e108	−0.195783	−0.0978917	−	0.995197i	$-0.531210\pi$
$109$	−1.96831e108	−0.195783	−0.0978917	+	0.995197i	$0.531210\pi$
$110$	2.29391e108	0.139980
$111$	−2.07273e109	−0.779405
$112$	−7.21473e108	−0.167902
$113$	−3.58803e109	−0.518991	−0.259495	−	0.965744i	$-0.583556\pi$
$113$	−3.58803e109	−0.518991	−0.259495	+	0.965744i	$0.583556\pi$
$114$	2.14662e109	0.193797
$115$	−1.87446e109	−0.106057
$116$	−1.05765e110	−0.376565
$117$	5.57378e110	1.25374
$118$	2.42792e110	0.346375
$119$	4.17474e109	0.0379199
$120$	1.17448e110	0.0681785
$121$	4.79584e111	1.78586
$122$	1.24131e111	0.297597
$123$	−4.03095e111	−0.624430
$124$	−3.21853e110	−0.0323294
$125$	−3.88240e111	−0.253755
$126$	−1.80357e112	−0.769678
$127$	−2.90725e112	−0.812801	−0.406400	−	0.913695i	$-0.633216\pi$
$127$	−2.90725e112	−0.812801	−0.406400	+	0.913695i	$0.633216\pi$
$128$	−2.60770e112	−0.479207
$129$	−3.23993e112	−0.392632
$130$	−1.79176e112	−0.143652
$131$	9.01555e112	0.479709	0.239854	−	0.970809i	$-0.422900\pi$
$131$	9.01555e112	0.479709	0.239854	+	0.970809i	$0.422900\pi$
$132$	1.39096e113	0.492731
$133$	−3.87132e113	−0.915792
$134$	6.82582e113	1.08155
$135$	1.07758e113	0.114708
$136$	−3.39310e112	−0.0243369
$137$	4.87758e113	0.236403	0.118202	−	0.992990i	$-0.462287\pi$
$137$	4.87758e113	0.236403	0.118202	+	0.992990i	$0.462287\pi$
$138$	8.56762e113	0.281403
$139$	5.93238e114	1.32415	0.662075	−	0.749438i	$-0.269676\pi$
$139$	5.93238e114	1.32415	0.662075	+	0.749438i	$0.269676\pi$
$140$	−7.69162e113	−0.116995
$141$	3.45907e114	0.359531
$142$	5.32881e114	0.379493
$143$	−5.84361e115	−2.85893
$144$	2.27374e114	0.0766210
$145$	3.63041e114	0.0844827
$146$	−5.58844e114	−0.0900353
$147$	−7.28144e115	−0.814217
$148$	−1.10327e116	−0.858384
$149$	2.51594e116	1.36532	0.682662	−	0.730734i	$-0.260822\pi$
$149$	2.51594e116	1.36532	0.682662	+	0.730734i	$0.260822\pi$
$150$	8.79949e115	0.333868
$151$	−1.14211e116	−0.303699	−0.151849	−	0.988404i	$-0.548523\pi$
$151$	−1.14211e116	−0.303699	−0.151849	+	0.988404i	$0.548523\pi$
$152$	3.14649e116	0.587753
$153$	−1.31568e115	−0.0173045
$154$	1.89088e117	1.75512
$155$	1.10477e115	0.00725313
$156$	−1.08647e117	−0.505654
$157$	−3.31075e117	−1.09470	−0.547350	−	0.836904i	$-0.684363\pi$
$157$	−3.31075e117	−1.09470	−0.547350	+	0.836904i	$0.684363\pi$
$158$	2.71105e117	0.638239
$159$	3.26360e117	0.548214
$160$	1.02329e117	0.122907
$161$	−1.54513e118	−1.32978
$162$	2.84020e117	0.175508
$163$	−1.27124e118	−0.565185	−0.282592	−	0.959240i	$-0.591194\pi$
$163$	−1.27124e118	−0.565185	−0.282592	+	0.959240i	$0.591194\pi$
$164$	−2.14560e118	−0.687705
$165$	−4.77451e117	−0.110545
$166$	2.27776e118	0.381702
$167$	−1.19678e119	−1.45440	−0.727200	−	0.686426i	$-0.759179\pi$
$167$	−1.19678e119	−1.45440	−0.727200	+	0.686426i	$0.759179\pi$
$168$	9.68127e118	0.854842
$169$	3.00868e119	1.93391
$170$	4.22942e116	0.00198273
$171$	1.22006e119	0.417916
$172$	−1.72455e119	−0.432419
$173$	9.87793e119	1.81635	0.908174	−	0.418592i	$-0.137476\pi$
$173$	9.87793e119	1.81635	0.908174	+	0.418592i	$0.137476\pi$
$174$	−1.65936e119	−0.224159
$175$	−1.58694e120	−1.57770
$176$	−2.38381e119	−0.174721
$177$	−5.05344e119	−0.273538
$178$	2.93666e119	0.117594
$179$	−2.72635e120	−0.808994	−0.404497	−	0.914539i	$-0.632553\pi$
$179$	−2.72635e120	−0.808994	−0.404497	+	0.914539i	$0.632553\pi$
$180$	2.42403e119	0.0533900
$181$	6.61539e120	1.08331	0.541654	−	0.840602i	$-0.317798\pi$
$181$	6.61539e120	1.08331	0.541654	+	0.840602i	$0.317798\pi$
$182$	−1.47696e121	−1.80115
$183$	−2.58365e120	−0.235017
$184$	1.25583e121	0.853449
$185$	3.78702e120	0.192579
$186$	−5.04960e119	−0.0192448
$187$	1.37937e120	0.0394599
$188$	1.84119e121	0.395963
$189$	8.88258e121	1.43824
$190$	−3.92203e120	−0.0478843
$191$	−1.44733e121	−0.133439	−0.0667193	−	0.997772i	$-0.521253\pi$
$191$	−1.44733e121	−0.133439	−0.0667193	+	0.997772i	$0.521253\pi$
$192$	−5.45446e121	−0.380308
$193$	−1.21351e121	−0.0640806	−0.0320403	−	0.999487i	$-0.510200\pi$
$193$	−1.21351e121	−0.0640806	−0.0320403	+	0.999487i	$0.510200\pi$
$194$	1.17761e122	0.471638
$195$	3.72935e121	0.113444
$196$	−3.87577e122	−0.896724
$197$	−4.93322e122	−0.869336	−0.434668	−	0.900591i	$-0.643134\pi$
$197$	−4.93322e122	−0.869336	−0.434668	+	0.900591i	$0.643134\pi$
$198$	−5.95917e122	−0.800936
$199$	−8.12508e122	−0.834042	−0.417021	−	0.908897i	$-0.636926\pi$
$199$	−8.12508e122	−0.834042	−0.417021	+	0.908897i	$0.636926\pi$
$200$	1.28982e123	1.01257
$201$	−1.42072e123	−0.854120
$202$	2.50604e123	1.15528
$203$	2.99257e123	1.05927
$204$	2.56460e121	0.00697921
$205$	7.36481e122	0.154287
$206$	9.22908e122	0.149026
$207$	4.86951e123	0.606836
$208$	1.86199e123	0.179303
$209$	−1.27912e124	−0.952983
$210$	−1.20675e123	−0.0696441
$211$	1.71900e123	0.0769424	0.0384712	−	0.999260i	$-0.487751\pi$
$211$	1.71900e123	0.0769424	0.0384712	+	0.999260i	$0.487751\pi$
$212$	1.73715e124	0.603766
$213$	−1.10913e124	−0.299692
$214$	−3.87238e124	−0.814406
$215$	5.91957e123	0.0970137
$216$	−7.21949e124	−0.923062
$217$	9.10668e123	0.0909420
$218$	−1.64374e124	−0.128354
$219$	1.16317e124	0.0711022
$220$	−2.54138e124	−0.121746
$221$	−1.07742e124	−0.0404949
$222$	−1.73094e125	−0.510974
$223$	5.64488e125	1.31022	0.655111	−	0.755533i	$-0.272622\pi$
$223$	5.64488e125	1.31022	0.655111	+	0.755533i	$0.272622\pi$
$224$	8.43501e125	1.54105
$225$	5.00129e125	0.719975
$226$	−2.99637e125	−0.340247
$227$	−1.24898e126	−1.11988	−0.559941	−	0.828533i	$-0.689176\pi$
$227$	−1.24898e126	−1.11988	−0.559941	+	0.828533i	$0.689176\pi$
$228$	−2.37821e125	−0.168553
$229$	2.18374e126	1.22462	0.612311	−	0.790617i	$-0.290240\pi$
$229$	2.18374e126	1.22462	0.612311	+	0.790617i	$0.290240\pi$
$230$	−1.56536e125	−0.0695306
$231$	−3.93566e126	−1.38604
$232$	−2.43227e126	−0.679836
$233$	−3.90709e126	−0.867583	−0.433792	−	0.901013i	$-0.642825\pi$
$233$	−3.90709e126	−0.867583	−0.433792	+	0.901013i	$0.642825\pi$
$234$	4.65468e126	0.821943
$235$	−6.31995e125	−0.0888348
$236$	−2.68985e126	−0.301256
$237$	−5.64274e126	−0.504027
$238$	3.48634e125	0.0248601
$239$	2.19139e127	1.24863	0.624313	−	0.781175i	$-0.285379\pi$
$239$	2.19139e127	1.24863	0.624313	+	0.781175i	$0.285379\pi$
$240$	1.52133e125	0.00693303
$241$	1.73248e127	0.632057	0.316029	−	0.948750i	$-0.397650\pi$
$241$	1.73248e127	0.632057	0.316029	+	0.948750i	$0.397650\pi$
$242$	4.00502e127	1.17080
$243$	−4.41568e127	−1.03529
$244$	−1.37523e127	−0.258832
$245$	1.33037e127	0.201181
$246$	−3.36625e127	−0.409372
$247$	9.99117e127	0.977978
$248$	−7.40163e126	−0.0583663
$249$	−4.74089e127	−0.301436
$250$	−3.24220e127	−0.166360
$251$	−1.36421e128	−0.565375	−0.282687	−	0.959212i	$-0.591226\pi$
$251$	−1.36421e128	−0.565375	−0.282687	+	0.959212i	$0.591226\pi$
$252$	1.99815e128	0.669419
$253$	−5.10524e128	−1.38378
$254$	−2.42786e128	−0.532867
$255$	−8.80307e125	−0.00156579
$256$	−7.26946e128	−1.04873
$257$	7.83580e128	0.917617	0.458808	−	0.888535i	$-0.348276\pi$
$257$	7.83580e128	0.917617	0.458808	+	0.888535i	$0.348276\pi$
$258$	−2.70567e128	−0.257408
$259$	3.12166e129	2.41462
$260$	1.98506e128	0.124940
$261$	−9.43117e128	−0.483391
$262$	7.52891e128	0.314494
$263$	3.40413e128	0.115978	0.0579888	−	0.998317i	$-0.481531\pi$
$263$	3.40413e128	0.115978	0.0579888	+	0.998317i	$0.481531\pi$
$264$	3.19878e129	0.889558
$265$	−5.96281e128	−0.135456
$266$	−3.23295e129	−0.600388
$267$	−6.11233e128	−0.0928655
$268$	−7.56221e129	−0.940670
$269$	−1.78314e129	−0.181735	−0.0908673	−	0.995863i	$-0.528964\pi$
$269$	−1.78314e129	−0.181735	−0.0908673	+	0.995863i	$0.528964\pi$
$270$	8.99893e128	0.0752020
$271$	−1.87344e130	−1.28464	−0.642322	−	0.766435i	$-0.722029\pi$
$271$	−1.87344e130	−1.28464	−0.642322	+	0.766435i	$0.722029\pi$
$272$	−4.39519e127	−0.00247481
$273$	3.07413e130	1.42240
$274$	4.07328e129	0.154985
$275$	−5.24340e130	−1.64178
$276$	−9.49192e129	−0.244748
$277$	6.32114e130	1.34316	0.671580	−	0.740932i	$-0.265616\pi$
$277$	6.32114e130	1.34316	0.671580	+	0.740932i	$0.265616\pi$
$278$	4.95414e130	0.868105
$279$	−2.87000e129	−0.0415008
$280$	−1.76883e130	−0.211219
$281$	−4.10606e130	−0.405170	−0.202585	−	0.979265i	$-0.564934\pi$
$281$	−4.10606e130	−0.405170	−0.202585	+	0.979265i	$0.564934\pi$
$282$	2.88868e130	0.235706
$283$	2.45813e131	1.65971	0.829853	−	0.557982i	$-0.188424\pi$
$283$	2.45813e131	1.65971	0.829853	+	0.557982i	$0.188424\pi$
$284$	−5.90370e130	−0.330060
$285$	8.16326e129	0.0378150
$286$	−4.88001e131	−1.87430
$287$	6.07086e131	1.93450
$288$	−2.65832e131	−0.703248
$289$	−4.54770e131	−0.999441
$290$	3.03177e130	0.0553863
$291$	−2.45106e131	−0.372460
$292$	6.19133e130	0.0783072
$293$	−2.53145e131	−0.266656	−0.133328	−	0.991072i	$-0.542566\pi$
$293$	−2.53145e131	−0.266656	−0.133328	+	0.991072i	$0.542566\pi$
$294$	−6.08075e131	−0.533796
$295$	9.23298e130	0.0675871
$296$	−2.53719e132	−1.54970
$297$	2.93489e132	1.49665
$298$	2.10107e132	0.895098
$299$	3.98768e132	1.42008
$300$	−9.74880e131	−0.290378
$301$	4.87954e132	1.21639
$302$	−9.53782e131	−0.199103
$303$	−5.21603e132	−0.912346
$304$	4.07575e131	0.0597683
$305$	4.72050e131	0.0580693
$306$	−1.09873e131	−0.0113447
$307$	−4.64951e132	−0.403185	−0.201592	−	0.979470i	$-0.564612\pi$
$307$	−4.64951e132	−0.403185	−0.201592	+	0.979470i	$0.564612\pi$
$308$	−2.09488e133	−1.52649
$309$	−1.92093e132	−0.117688
$310$	9.22596e130	0.00475511
$311$	3.09033e133	1.34068	0.670338	−	0.742056i	$-0.266149\pi$
$311$	3.09033e133	1.34068	0.670338	+	0.742056i	$0.266149\pi$
$312$	−2.49856e133	−0.912890
$313$	2.05509e133	0.632716	0.316358	−	0.948640i	$-0.397540\pi$
$313$	2.05509e133	0.632716	0.316358	+	0.948640i	$0.397540\pi$
$314$	−2.76482e133	−0.717679
$315$	−6.85869e132	−0.150185
$316$	−3.00353e133	−0.555101
$317$	2.94758e133	0.460040	0.230020	−	0.973186i	$-0.426121\pi$
$317$	2.94758e133	0.460040	0.230020	+	0.973186i	$0.426121\pi$
$318$	2.72544e133	0.359406
$319$	9.88772e133	1.10229
$320$	9.96567e132	0.0939685
$321$	8.05991e133	0.643148
$322$	−1.29034e134	−0.871796
$323$	−2.35840e132	−0.0134984
$324$	−3.14661e133	−0.152646
$325$	4.09560e134	1.68484
$326$	−1.06162e134	−0.370532
$327$	3.42126e133	0.101363
$328$	−4.93421e134	−1.24156
$329$	−5.20957e134	−1.11384
$330$	−3.98721e133	−0.0724724
$331$	7.59680e134	1.17445	0.587223	−	0.809425i	$-0.300221\pi$
$331$	7.59680e134	1.17445	0.587223	+	0.809425i	$0.300221\pi$
$332$	−2.52349e134	−0.331981
$333$	−9.83801e134	−1.10190
$334$	−9.99435e134	−0.953496
$335$	2.59575e134	0.211040
$336$	1.25404e134	0.0869284
$337$	1.08762e135	0.643098	0.321549	−	0.946893i	$-0.395797\pi$
$337$	1.08762e135	0.643098	0.321549	+	0.946893i	$0.395797\pi$
$338$	2.51255e135	1.26786
$339$	6.23662e134	0.268698
$340$	−4.68571e132	−0.00172446
$341$	3.00893e134	0.0946353
$342$	1.01887e135	0.273983
$343$	3.99321e135	0.918516
$344$	−3.96594e135	−0.780674
$345$	3.25813e134	0.0549094
$346$	8.24908e135	1.19079
$347$	−1.46065e136	−1.80684	−0.903418	−	0.428760i	$-0.858951\pi$
$347$	−1.46065e136	−1.80684	−0.903418	+	0.428760i	$0.858951\pi$
$348$	1.83838e135	0.194960
$349$	−3.83173e135	−0.348525	−0.174263	−	0.984699i	$-0.555754\pi$
$349$	−3.83173e135	−0.348525	−0.174263	+	0.984699i	$0.555754\pi$
$350$	−1.32526e136	−1.03433
$351$	−2.29243e136	−1.53591
$352$	2.78701e136	1.60363
$353$	8.55363e135	0.422867	0.211433	−	0.977392i	$-0.432187\pi$
$353$	8.55363e135	0.422867	0.211433	+	0.977392i	$0.432187\pi$
$354$	−4.22014e135	−0.179330
$355$	2.02646e135	0.0740494
$356$	−3.25348e135	−0.102276
$357$	−7.25642e134	−0.0196324
$358$	−2.27679e136	−0.530372
$359$	5.90001e136	1.18386	0.591930	−	0.805990i	$-0.298366\pi$
$359$	5.90001e136	1.18386	0.591930	+	0.805990i	$0.298366\pi$
$360$	5.57453e135	0.0963883
$361$	−4.52166e136	−0.674005
$362$	5.52453e136	0.710210
$363$	−8.33600e136	−0.924598
$364$	1.63630e137	1.56653
$365$	−2.12519e135	−0.0175683
$366$	−2.15761e136	−0.154076
$367$	2.02132e137	1.24739	0.623693	−	0.781669i	$-0.285632\pi$
$367$	2.02132e137	1.24739	0.623693	+	0.781669i	$0.285632\pi$
$368$	1.62672e136	0.0867867
$369$	−1.91325e137	−0.882797
$370$	3.16255e136	0.126254
$371$	−4.91518e137	−1.69838
$372$	5.59436e135	0.0167380
$373$	−3.97885e137	−1.03118	−0.515590	−	0.856835i	$-0.672427\pi$
$373$	−3.97885e137	−1.03118	−0.515590	+	0.856835i	$0.672427\pi$
$374$	1.15192e136	0.0258697
$375$	6.74827e136	0.131377
$376$	4.23418e137	0.714858
$377$	−7.72326e137	−1.13120
$378$	7.41787e137	0.942905
$379$	−1.22393e137	−0.135069	−0.0675347	−	0.997717i	$-0.521513\pi$
$379$	−1.22393e137	−0.135069	−0.0675347	+	0.997717i	$0.521513\pi$
$380$	4.34515e136	0.0416469
$381$	5.05331e137	0.420814
$382$	−1.20867e137	−0.0874816
$383$	2.29715e138	1.44562	0.722811	−	0.691046i	$-0.242850\pi$
$383$	2.29715e138	1.44562	0.722811	+	0.691046i	$0.242850\pi$
$384$	4.53262e137	0.248101
$385$	7.19072e137	0.342470
$386$	−1.01340e137	−0.0420109
$387$	−1.53780e138	−0.555090
$388$	−1.30465e138	−0.410202
$389$	2.15032e138	0.589114	0.294557	−	0.955634i	$-0.404828\pi$
$389$	2.15032e138	0.589114	0.294557	+	0.955634i	$0.404828\pi$
$390$	3.11439e137	0.0743732
$391$	−9.41285e136	−0.0196004
$392$	−8.91308e138	−1.61891
$393$	−1.56706e138	−0.248361
$394$	−4.11975e138	−0.569932
$395$	1.03097e138	0.124538
$396$	6.60206e138	0.696606
$397$	−3.28089e138	−0.302482	−0.151241	−	0.988497i	$-0.548327\pi$
$397$	−3.28089e138	−0.302482	−0.151241	+	0.988497i	$0.548327\pi$
$398$	−6.78528e138	−0.546793
$399$	6.72903e138	0.474135
$400$	1.67074e138	0.102967
$401$	2.43399e139	1.31249	0.656243	−	0.754549i	$-0.272144\pi$
$401$	2.43399e139	1.31249	0.656243	+	0.754549i	$0.272144\pi$
$402$	−1.18645e139	−0.559956
$403$	−2.35027e138	−0.0971174
$404$	−2.77639e139	−1.00480
$405$	1.08008e138	0.0342463
$406$	2.49910e139	0.694451
$407$	1.03143e140	2.51268
$408$	5.89780e137	0.0126000
$409$	−9.46506e139	−1.77389	−0.886945	−	0.461876i	$-0.847177\pi$
$409$	−9.46506e139	−1.77389	−0.886945	+	0.461876i	$0.847177\pi$
$410$	6.15038e138	0.101150
$411$	−8.47807e138	−0.122394
$412$	−1.02247e139	−0.129614
$413$	7.61080e139	0.847428
$414$	4.06654e139	0.397838
$415$	8.66193e138	0.0744803
$416$	−2.17692e140	−1.64569
$417$	−1.03115e140	−0.685555
$418$	−1.06820e140	−0.624770
$419$	1.30546e139	0.0671911	0.0335956	−	0.999436i	$-0.489304\pi$
$419$	1.30546e139	0.0671911	0.0335956	+	0.999436i	$0.489304\pi$
$420$	1.33694e139	0.0605722
$421$	−1.74917e140	−0.697815	−0.348908	−	0.937157i	$-0.613447\pi$
$421$	−1.74917e140	−0.697815	−0.348908	+	0.937157i	$0.613447\pi$
$422$	1.43555e139	0.0504430
$423$	1.64181e140	0.508292
$424$	3.99491e140	1.09002
$425$	−9.66759e138	−0.0232547
$426$	−9.26240e139	−0.196476
$427$	3.89113e140	0.728090
$428$	4.29014e140	0.708320
$429$	1.01572e141	1.48016
$430$	4.94345e139	0.0636016
$431$	−9.99855e140	−1.13606	−0.568032	−	0.823006i	$-0.692295\pi$
$431$	−9.99855e140	−1.13606	−0.568032	+	0.823006i	$0.692295\pi$
$432$	−9.35163e139	−0.0938656
$433$	−1.48890e141	−1.32057	−0.660285	−	0.751015i	$-0.729565\pi$
$433$	−1.48890e141	−1.32057	−0.660285	+	0.751015i	$0.729565\pi$
$434$	7.60502e139	0.0596210
$435$	−6.31028e139	−0.0437394
$436$	1.82107e140	0.111635
$437$	8.72873e140	0.473363
$438$	9.71367e139	0.0466142
$439$	−1.62500e141	−0.690241	−0.345120	−	0.938558i	$-0.612162\pi$
$439$	−1.62500e141	−0.690241	−0.345120	+	0.938558i	$0.612162\pi$
$440$	−5.84439e140	−0.219797
$441$	−3.45607e141	−1.15111
$442$	−8.99759e139	−0.0265482
$443$	9.71239e140	0.253937	0.126969	−	0.991907i	$-0.459475\pi$
$443$	9.71239e140	0.253937	0.126969	+	0.991907i	$0.459475\pi$
$444$	1.91768e141	0.444414
$445$	1.11676e140	0.0229457
$446$	4.71406e141	0.858974
$447$	−4.37314e141	−0.706873
$448$	8.21476e141	1.17821
$449$	−1.45458e142	−1.85165	−0.925824	−	0.377954i	$-0.876628\pi$
$449$	−1.45458e142	−1.85165	−0.925824	+	0.377954i	$0.876628\pi$
$450$	4.17659e141	0.472011
$451$	2.00587e142	2.01306
$452$	3.31963e141	0.295926
$453$	1.98519e141	0.157235
$454$	−1.04303e142	−0.734188
$455$	−5.61664e141	−0.351453
$456$	−5.46915e141	−0.304299
$457$	−2.17490e141	−0.107627	−0.0538137	−	0.998551i	$-0.517138\pi$
$457$	−2.17490e141	−0.107627	−0.0538137	+	0.998551i	$0.517138\pi$
$458$	1.82365e142	0.802856
$459$	5.41124e140	0.0211991
$460$	1.73424e141	0.0604735
$461$	−3.30281e141	−0.102538	−0.0512689	−	0.998685i	$-0.516327\pi$
$461$	−3.30281e141	−0.102538	−0.0512689	+	0.998685i	$0.516327\pi$
$462$	−3.28668e142	−0.908681
$463$	−1.86484e142	−0.459259	−0.229630	−	0.973278i	$-0.573752\pi$
$463$	−1.86484e142	−0.459259	−0.229630	+	0.973278i	$0.573752\pi$
$464$	−3.15059e141	−0.0691322
$465$	−1.92028e140	−0.00375519
$466$	−3.26282e142	−0.568783
$467$	−9.01361e142	−1.40102	−0.700512	−	0.713640i	$-0.747045\pi$
$467$	−9.01361e142	−1.40102	−0.700512	+	0.713640i	$0.747045\pi$
$468$	−5.15684e142	−0.714876
$469$	2.13969e143	2.64609
$470$	−5.27781e141	−0.0582396
$471$	5.75466e142	0.566762
$472$	−6.18582e142	−0.543877
$473$	1.61225e143	1.26579
$474$	−4.71227e142	−0.330437
$475$	8.96495e142	0.561616
$476$	−3.86246e141	−0.0216218
$477$	1.54903e143	0.775046
$478$	1.83004e143	0.818592
$479$	−1.09479e143	−0.437907	−0.218954	−	0.975735i	$-0.570264\pi$
$479$	−1.09479e143	−0.437907	−0.218954	+	0.975735i	$0.570264\pi$
$480$	−1.77865e142	−0.0636332
$481$	−8.05643e143	−2.57858
$482$	1.44680e143	0.414373
$483$	2.68569e143	0.688470
$484$	−4.43709e143	−1.01829
$485$	4.47826e142	0.0920293
$486$	−3.68755e143	−0.678730
$487$	2.93991e143	0.484769	0.242384	−	0.970180i	$-0.422071\pi$
$487$	2.93991e143	0.484769	0.242384	+	0.970180i	$0.422071\pi$
$488$	−3.16259e143	−0.467286
$489$	2.20963e143	0.292615
$490$	1.11100e143	0.131893
$491$	−3.23674e143	−0.344547	−0.172273	−	0.985049i	$-0.555111\pi$
$491$	−3.23674e143	−0.344547	−0.172273	+	0.985049i	$0.555111\pi$
$492$	3.72942e143	0.356047
$493$	1.82306e142	0.0156132
$494$	8.34365e143	0.641157
$495$	−2.26617e143	−0.156284
$496$	−9.58756e141	−0.00593524
$497$	1.67042e144	0.928453
$498$	−3.95913e143	−0.197620
$499$	−1.90253e144	−0.853008	−0.426504	−	0.904486i	$-0.640255\pi$
$499$	−1.90253e144	−0.853008	−0.426504	+	0.904486i	$0.640255\pi$
$500$	3.59198e143	0.144690
$501$	2.08021e144	0.752990
$502$	−1.13925e144	−0.370656
$503$	2.04612e144	0.598473	0.299236	−	0.954179i	$-0.403268\pi$
$503$	2.04612e144	0.598473	0.299236	+	0.954179i	$0.403268\pi$
$504$	4.59512e144	1.20855
$505$	9.53005e143	0.225427
$506$	−4.26340e144	−0.907200
$507$	−5.22960e144	−1.00125
$508$	2.68978e144	0.463456
$509$	−9.00499e144	−1.39663	−0.698316	−	0.715790i	$-0.746067\pi$
$509$	−9.00499e144	−1.39663	−0.698316	+	0.715790i	$0.746067\pi$
$510$	−7.35147e141	−0.00102653
$511$	−1.75181e144	−0.220277
$512$	−1.83952e144	−0.208334
$513$	−5.01795e144	−0.511973
$514$	6.54370e144	0.601584
$515$	3.50967e143	0.0290790
$516$	2.99757e144	0.223877
$517$	−1.72129e145	−1.15907
$518$	2.60691e145	1.58301
$519$	−1.71695e145	−0.940383
$520$	4.56503e144	0.225562
$521$	3.10243e145	1.38320	0.691598	−	0.722283i	$-0.256907\pi$
$521$	3.10243e145	1.38320	0.691598	+	0.722283i	$0.256907\pi$
$522$	−7.87599e144	−0.316908
$523$	2.15734e145	0.783572	0.391786	−	0.920056i	$-0.371857\pi$
$523$	2.15734e145	0.783572	0.391786	+	0.920056i	$0.371857\pi$
$524$	−8.34115e144	−0.273528
$525$	2.75838e145	0.816828
$526$	2.84280e144	0.0760342
$527$	5.54776e142	0.00134045
$528$	4.14348e144	0.0904587
$529$	−1.58467e145	−0.312652
$530$	−4.97956e144	−0.0888039
$531$	−2.39856e145	−0.386718
$532$	3.58173e145	0.522181
$533$	−1.56678e146	−2.06586
$534$	−5.10442e144	−0.0608821
$535$	−1.47260e145	−0.158912
$536$	−1.73908e146	−1.69825
$537$	4.73887e145	0.418842
$538$	−1.48910e145	−0.119144
$539$	3.62337e146	2.62491
$540$	−9.96976e144	−0.0654061
$541$	5.53538e145	0.328923	0.164461	−	0.986384i	$-0.447411\pi$
$541$	5.53538e145	0.328923	0.164461	+	0.986384i	$0.447411\pi$
$542$	−1.56451e146	−0.842205
$543$	−1.14987e146	−0.560864
$544$	5.13858e144	0.0227144
$545$	−6.25088e144	−0.0250454
$546$	2.56721e146	0.932514
$547$	4.72787e146	1.55720	0.778598	−	0.627523i	$-0.215931\pi$
$547$	4.72787e146	1.55720	0.778598	+	0.627523i	$0.215931\pi$
$548$	−4.51272e145	−0.134796
$549$	−1.22630e146	−0.332259
$550$	−4.37878e146	−1.07634
$551$	−1.69056e146	−0.377069
$552$	−2.18285e146	−0.441858
$553$	8.49833e146	1.56149
$554$	5.27880e146	0.880568
$555$	−6.58249e145	−0.0997047
$556$	−5.48861e146	−0.755025
$557$	9.96724e145	0.124544	0.0622719	−	0.998059i	$-0.480165\pi$
$557$	9.96724e145	0.124544	0.0622719	+	0.998059i	$0.480165\pi$
$558$	−2.39674e145	−0.0272077
$559$	−1.25932e147	−1.29898
$560$	−2.29123e145	−0.0214787
$561$	−2.39759e145	−0.0204297
$562$	−3.42898e146	−0.265627
$563$	−1.06150e147	−0.747688	−0.373844	−	0.927492i	$-0.621960\pi$
$563$	−1.06150e147	−0.747688	−0.373844	+	0.927492i	$0.621960\pi$
$564$	−3.20031e146	−0.205003
$565$	−1.13947e146	−0.0663914
$566$	2.05279e147	1.08809
$567$	8.90319e146	0.429390
$568$	−1.35767e147	−0.595879
$569$	−2.86245e147	−1.14349	−0.571743	−	0.820433i	$-0.693733\pi$
$569$	−2.86245e147	−1.14349	−0.571743	+	0.820433i	$0.693733\pi$
$570$	6.81716e145	0.0247913
$571$	2.60005e147	0.860893	0.430447	−	0.902616i	$-0.358356\pi$
$571$	2.60005e147	0.860893	0.430447	+	0.902616i	$0.358356\pi$
$572$	5.40648e147	1.63015
$573$	2.51570e146	0.0690856
$574$	5.06979e147	1.26825
$575$	3.57810e147	0.815497
$576$	−2.58890e147	−0.537667
$577$	−5.53577e147	−1.04778	−0.523892	−	0.851785i	$-0.675521\pi$
$577$	−5.53577e147	−1.04778	−0.523892	+	0.851785i	$0.675521\pi$
$578$	−3.79780e147	−0.655228
$579$	2.10929e146	0.0331766
$580$	−3.35884e146	−0.0481717
$581$	7.14008e147	0.933857
$582$	−2.04689e147	−0.244183
$583$	−1.62402e148	−1.76736
$584$	1.42382e147	0.141373
$585$	1.77010e147	0.160383
$586$	−2.11402e147	−0.174818
$587$	−1.73457e148	−1.30935	−0.654673	−	0.755912i	$-0.727194\pi$
$587$	−1.73457e148	−1.30935	−0.654673	+	0.755912i	$0.727194\pi$
$588$	6.73676e147	0.464263
$589$	−5.14455e146	−0.0323727
$590$	7.71049e146	0.0443097
$591$	8.57479e147	0.450084
$592$	−3.28650e147	−0.157588
$593$	4.57315e146	0.0200350	0.0100175	−	0.999950i	$-0.496811\pi$
$593$	4.57315e146	0.0200350	0.0100175	+	0.999950i	$0.496811\pi$
$594$	2.45093e148	0.981198
$595$	1.32580e146	0.00485087
$596$	−2.32774e148	−0.778502
$597$	1.41228e148	0.431811
$598$	3.33012e148	0.930994
$599$	2.76207e148	0.706155	0.353077	−	0.935594i	$-0.385135\pi$
$599$	2.76207e148	0.706155	0.353077	+	0.935594i	$0.385135\pi$
$600$	−2.24192e148	−0.524238
$601$	1.62242e148	0.347039	0.173519	−	0.984830i	$-0.444486\pi$
$601$	1.62242e148	0.347039	0.173519	+	0.984830i	$0.444486\pi$
$602$	4.07492e148	0.797456
$603$	−6.74330e148	−1.20753
$604$	1.05668e148	0.173168
$605$	1.52304e148	0.228455
$606$	−4.35592e148	−0.598129
$607$	−2.58908e148	−0.325500	−0.162750	−	0.986667i	$-0.552036\pi$
$607$	−2.58908e148	−0.325500	−0.162750	+	0.986667i	$0.552036\pi$
$608$	−4.76511e148	−0.548569
$609$	−5.20160e148	−0.548418
$610$	3.94210e147	0.0380699
$611$	1.34449e149	1.18947
$612$	1.21726e147	0.00986697
$613$	7.88928e148	0.586006	0.293003	−	0.956112i	$-0.405345\pi$
$613$	7.88928e148	0.586006	0.293003	+	0.956112i	$0.405345\pi$
$614$	−3.88282e148	−0.264326
$615$	−1.28013e148	−0.0798796
$616$	−4.81757e149	−2.75588
$617$	3.54267e148	0.185812	0.0929060	−	0.995675i	$-0.470384\pi$
$617$	3.54267e148	0.185812	0.0929060	+	0.995675i	$0.470384\pi$
$618$	−1.60417e148	−0.0771556
$619$	2.67216e149	1.17873	0.589364	−	0.807868i	$-0.299379\pi$
$619$	2.67216e149	1.17873	0.589364	+	0.807868i	$0.299379\pi$
$620$	−1.02213e147	−0.00413571
$621$	−2.00277e149	−0.743413
$622$	2.58074e149	0.878939
$623$	9.20556e148	0.287700
$624$	−3.23646e148	−0.0928312
$625$	3.61278e149	0.951174
$626$	1.71621e149	0.414805
$627$	2.22333e149	0.493391
$628$	3.06310e149	0.624194
$629$	1.90171e148	0.0355905
$630$	−5.72771e148	−0.0984604
$631$	3.91073e147	0.00617571	0.00308786	−	0.999995i	$-0.499017\pi$
$631$	3.91073e147	0.00617571	0.00308786	+	0.999995i	$0.499017\pi$
$632$	−6.90718e149	−1.00216
$633$	−2.98793e148	−0.0398356
$634$	2.46153e149	0.301599
$635$	−9.23274e148	−0.103977
$636$	−3.01947e149	−0.312590
$637$	−2.83020e150	−2.69375
$638$	8.25727e149	0.722653
$639$	−5.26439e149	−0.423694
$640$	−8.28141e148	−0.0613022
$641$	1.92120e150	1.30818	0.654091	−	0.756416i	$-0.273051\pi$
$641$	1.92120e150	1.30818	0.654091	+	0.756416i	$0.273051\pi$
$642$	6.73086e149	0.421644
$643$	−3.16434e150	−1.82388	−0.911939	−	0.410325i	$-0.865415\pi$
$643$	−3.16434e150	−1.82388	−0.911939	+	0.410325i	$0.865415\pi$
$644$	1.42954e150	0.758235
$645$	−1.02892e149	−0.0502271
$646$	−1.96950e148	−0.00884947
$647$	1.24125e150	0.513431	0.256715	−	0.966487i	$-0.417360\pi$
$647$	1.24125e150	0.513431	0.256715	+	0.966487i	$0.417360\pi$
$648$	−7.23623e149	−0.275581
$649$	2.51468e150	0.881843
$650$	3.42025e150	1.10457
$651$	−1.58290e149	−0.0470836
$652$	1.17615e150	0.322266
$653$	−2.50959e150	−0.633500	−0.316750	−	0.948509i	$-0.602592\pi$
$653$	−2.50959e150	−0.633500	−0.316750	+	0.948509i	$0.602592\pi$
$654$	2.85710e149	0.0664533
$655$	2.86312e149	0.0613663
$656$	−6.39143e149	−0.126253
$657$	5.52087e149	0.100522
$658$	−4.35053e150	−0.730225
$659$	6.74911e150	1.04442	0.522212	−	0.852816i	$-0.325107\pi$
$659$	6.74911e150	1.04442	0.522212	+	0.852816i	$0.325107\pi$
$660$	4.41736e149	0.0630321
$661$	−1.03391e151	−1.36052	−0.680258	−	0.732973i	$-0.738132\pi$
$661$	−1.03391e151	−1.36052	−0.680258	+	0.732973i	$0.738132\pi$
$662$	6.34411e150	0.769960
$663$	1.87275e149	0.0209655
$664$	−5.80324e150	−0.599347
$665$	−1.22944e150	−0.117152
$666$	−8.21575e150	−0.722397
$667$	−6.74739e150	−0.547525
$668$	1.10726e151	0.829293
$669$	−9.81178e150	−0.678345
$670$	2.16772e150	0.138357
$671$	1.28567e151	0.757659
$672$	−1.46615e151	−0.797852
$673$	9.52987e150	0.478940	0.239470	−	0.970904i	$-0.423026\pi$
$673$	9.52987e150	0.478940	0.239470	+	0.970904i	$0.423026\pi$
$674$	9.08274e150	0.421611
$675$	−2.05697e151	−0.882015
$676$	−2.78361e151	−1.10271
$677$	4.82205e151	1.76497	0.882486	−	0.470339i	$-0.155868\pi$
$677$	4.82205e151	1.76497	0.882486	+	0.470339i	$0.155868\pi$
$678$	5.20822e150	0.176157
$679$	3.69146e151	1.15389
$680$	−1.07757e149	−0.00311328
$681$	2.17094e151	0.579799
$682$	2.51277e150	0.0620423
$683$	−3.34860e151	−0.764462	−0.382231	−	0.924067i	$-0.624844\pi$
$683$	−3.34860e151	−0.764462	−0.382231	+	0.924067i	$0.624844\pi$
$684$	−1.12879e151	−0.238294
$685$	1.54900e150	0.0302417
$686$	3.33474e151	0.602174
$687$	−3.79571e151	−0.634027
$688$	−5.13720e150	−0.0793863
$689$	1.26852e152	1.81371
$690$	2.72087e150	0.0359983
$691$	−4.91822e151	−0.602189	−0.301094	−	0.953594i	$-0.597352\pi$
$691$	−4.91822e151	−0.602189	−0.301094	+	0.953594i	$0.597352\pi$
$692$	−9.13902e151	−1.03568
$693$	−1.86802e152	−1.95954
$694$	−1.21979e152	−1.18455
$695$	1.88398e151	0.169391
$696$	4.22770e151	0.351973
$697$	3.69835e150	0.0285137
$698$	−3.19989e151	−0.228491
$699$	6.79119e151	0.449176
$700$	1.46823e152	0.899600
$701$	2.15863e152	1.22536	0.612681	−	0.790330i	$-0.290091\pi$
$701$	2.15863e152	1.22536	0.612681	+	0.790330i	$0.290091\pi$
$702$	−1.91441e152	−1.00693
$703$	−1.76349e152	−0.859534
$704$	2.71423e152	1.22605
$705$	1.09852e151	0.0459927
$706$	7.14316e151	0.277229
$707$	7.85568e152	2.82647
$708$	4.67542e151	0.155970
$709$	−6.11726e152	−1.89227	−0.946136	−	0.323770i	$-0.895049\pi$
$709$	−6.11726e152	−1.89227	−0.946136	+	0.323770i	$0.895049\pi$
$710$	1.69230e151	0.0485464
$711$	−2.67827e152	−0.712576
$712$	−7.48199e151	−0.184645
$713$	−2.05330e151	−0.0470069
$714$	−6.05986e150	−0.0128709
$715$	−1.85579e152	−0.365726
$716$	2.52241e152	0.461285
$717$	−3.80901e152	−0.646454
$718$	4.92712e152	0.776131
$719$	−2.24422e152	−0.328148	−0.164074	−	0.986448i	$-0.552464\pi$
$719$	−2.24422e152	−0.328148	−0.164074	+	0.986448i	$0.552464\pi$
$720$	7.22086e150	0.00980168
$721$	2.89304e152	0.364601
$722$	−3.77605e152	−0.441874
$723$	−3.01135e152	−0.327237
$724$	−6.12053e152	−0.617697
$725$	−6.92999e152	−0.649605
$726$	−6.96141e152	−0.606161
$727$	−1.30367e153	−1.05457	−0.527285	−	0.849689i	$-0.676790\pi$
$727$	−1.30367e153	−1.05457	−0.527285	+	0.849689i	$0.676790\pi$
$728$	3.76298e153	2.82816
$729$	3.84182e152	0.268296
$730$	−1.77475e151	−0.0115177
$731$	2.97260e151	0.0179290
$732$	2.39038e152	0.134006
$733$	−2.16423e153	−1.12782	−0.563912	−	0.825835i	$-0.690704\pi$
$733$	−2.16423e153	−1.12782	−0.563912	+	0.825835i	$0.690704\pi$
$734$	1.68801e153	0.817779
$735$	−2.31241e152	−0.104158
$736$	−1.90185e153	−0.796552
$737$	7.06974e153	2.75355
$738$	−1.59776e153	−0.578757
$739$	1.96865e153	0.663272	0.331636	−	0.943407i	$-0.392399\pi$
$739$	1.96865e153	0.663272	0.331636	+	0.943407i	$0.392399\pi$
$740$	−3.50373e152	−0.109808
$741$	−1.73664e153	−0.506331
$742$	−4.10468e153	−1.11345
$743$	5.81023e153	1.46653	0.733267	−	0.679941i	$-0.237995\pi$
$743$	5.81023e153	1.46653	0.733267	+	0.679941i	$0.237995\pi$
$744$	1.28653e152	0.0302182
$745$	7.99003e152	0.174658
$746$	−3.32275e153	−0.676036
$747$	−2.25022e153	−0.426160
$748$	−1.27619e152	−0.0224999
$749$	−1.21387e154	−1.99249
$750$	5.63550e152	0.0861301
$751$	3.67837e153	0.523502	0.261751	−	0.965135i	$-0.415700\pi$
$751$	3.67837e153	0.523502	0.261751	+	0.965135i	$0.415700\pi$
$752$	5.48466e152	0.0726935
$753$	2.37123e153	0.292713
$754$	−6.44972e153	−0.741607
$755$	−3.62708e152	−0.0388504
$756$	−8.21813e153	−0.820081
$757$	1.59692e153	0.148476	0.0742378	−	0.997241i	$-0.476348\pi$
$757$	1.59692e153	0.148476	0.0742378	+	0.997241i	$0.476348\pi$
$758$	−1.02210e153	−0.0885508
$759$	8.87378e153	0.716430
$760$	9.99250e152	0.0751878
$761$	2.78267e154	1.95156	0.975781	−	0.218751i	$-0.0701984\pi$
$761$	2.78267e154	1.95156	0.975781	+	0.218751i	$0.0701984\pi$
$762$	4.22003e153	0.275883
$763$	−5.15264e153	−0.314027
$764$	1.33906e153	0.0760862
$765$	−4.17829e151	−0.00221366
$766$	1.91836e154	0.947742
$767$	−1.96421e154	−0.904972
$768$	1.26356e154	0.542962
$769$	1.75880e153	0.0704950	0.0352475	−	0.999379i	$-0.488778\pi$
$769$	1.75880e153	0.0704950	0.0352475	+	0.999379i	$0.488778\pi$
$770$	6.00499e153	0.224522
$771$	−1.36200e154	−0.475080
$772$	1.12273e153	0.0365385
$773$	−7.37345e153	−0.223907	−0.111953	−	0.993713i	$-0.535711\pi$
$773$	−7.37345e153	−0.223907	−0.111953	+	0.993713i	$0.535711\pi$
$774$	−1.28422e154	−0.363914
$775$	−2.10886e153	−0.0557709
$776$	−3.00030e154	−0.740564
$777$	−5.42599e154	−1.25013
$778$	1.79574e154	0.386220
$779$	−3.42955e154	−0.688626
$780$	−3.45038e153	−0.0646853
$781$	5.51924e154	0.966159
$782$	−7.86070e152	−0.0128499
$783$	3.87892e154	0.592184
$784$	−1.15454e154	−0.164626
$785$	−1.05142e154	−0.140039
$786$	−1.30865e154	−0.162824
$787$	1.96968e154	0.228953	0.114477	−	0.993426i	$-0.463481\pi$
$787$	1.96968e154	0.228953	0.114477	+	0.993426i	$0.463481\pi$
$788$	4.56420e154	0.495692
$789$	−5.91697e153	−0.0600454
$790$	8.60964e153	0.0816461
$791$	−9.39274e154	−0.832435
$792$	1.51827e155	1.25763
$793$	−1.00423e155	−0.777530
$794$	−2.73988e154	−0.198306
$795$	1.03644e154	0.0701298
$796$	7.51729e154	0.475568
$797$	2.16810e155	1.28250	0.641252	−	0.767330i	$-0.278415\pi$
$797$	2.16810e155	1.28250	0.641252	+	0.767330i	$0.278415\pi$
$798$	5.61943e154	0.310840
$799$	−3.17365e153	−0.0164175
$800$	−1.95332e155	−0.945061
$801$	−2.90116e154	−0.131290
$802$	2.03263e155	0.860459
$803$	−5.78814e154	−0.229222
$804$	1.31444e155	0.487016
$805$	−4.90695e154	−0.170111
$806$	−1.96271e154	−0.0636696
$807$	3.09940e154	0.0940900
$808$	−6.38485e155	−1.81402
$809$	−6.75324e155	−1.79584	−0.897918	−	0.440163i	$-0.854921\pi$
$809$	−6.75324e155	−1.79584	−0.897918	+	0.440163i	$0.854921\pi$
$810$	9.01980e153	0.0224517
$811$	−1.25431e154	−0.0292273	−0.0146136	−	0.999893i	$-0.504652\pi$
$811$	−1.25431e154	−0.0292273	−0.0146136	+	0.999893i	$0.504652\pi$
$812$	−2.76871e155	−0.603991
$813$	3.25636e155	0.665102
$814$	8.61347e155	1.64730
$815$	−4.03715e154	−0.0723008
$816$	7.63960e152	0.00128129
$817$	−2.75655e155	−0.432998
$818$	−7.90430e155	−1.16295
$819$	1.45910e156	2.01093
$820$	−6.81390e154	−0.0879740
$821$	−1.23395e155	−0.149259	−0.0746294	−	0.997211i	$-0.523777\pi$
$821$	−1.23395e155	−0.149259	−0.0746294	+	0.997211i	$0.523777\pi$
$822$	−7.08006e154	−0.0802407
$823$	1.09516e156	1.16301	0.581506	−	0.813542i	$-0.302464\pi$
$823$	1.09516e156	1.16301	0.581506	+	0.813542i	$0.302464\pi$
$824$	−2.35137e155	−0.234000
$825$	9.11393e155	0.850001
$826$	6.35580e155	0.555569
$827$	−9.33658e155	−0.764968	−0.382484	−	0.923962i	$-0.624931\pi$
$827$	−9.33658e155	−0.764968	−0.382484	+	0.923962i	$0.624931\pi$
$828$	−4.50525e155	−0.346016
$829$	1.86072e156	1.33972	0.669860	−	0.742487i	$-0.266354\pi$
$829$	1.86072e156	1.33972	0.669860	+	0.742487i	$0.266354\pi$
$830$	7.23360e154	0.0488289
$831$	−1.09872e156	−0.695398
$832$	−2.12008e156	−1.25821
$833$	6.68064e154	0.0371801
$834$	−8.61116e155	−0.449446
$835$	−3.80069e155	−0.186053
$836$	1.18344e156	0.543387
$837$	1.18039e155	0.0508411
$838$	1.09019e155	0.0440501
$839$	−4.19022e156	−1.58845	−0.794223	−	0.607626i	$-0.792122\pi$
$839$	−4.19022e156	−1.58845	−0.794223	+	0.607626i	$0.792122\pi$
$840$	3.07454e155	0.109355
$841$	−1.68948e156	−0.563856
$842$	−1.46074e156	−0.457484
$843$	7.13704e155	0.209770
$844$	−1.59042e155	−0.0438723
$845$	9.55483e155	0.247394
$846$	1.37108e156	0.333234
$847$	1.25545e157	2.86443
$848$	5.17473e155	0.110843
$849$	−4.27266e156	−0.859284
$850$	−8.07343e154	−0.0152456
$851$	−7.03846e156	−1.24809
$852$	1.02617e156	0.170883
$853$	−1.98706e156	−0.310769	−0.155384	−	0.987854i	$-0.549662\pi$
$853$	−1.98706e156	−0.310769	−0.155384	+	0.987854i	$0.549662\pi$
$854$	3.24950e156	0.477332
$855$	3.87461e155	0.0534615
$856$	9.86600e156	1.27878
$857$	−2.68221e156	−0.326602	−0.163301	−	0.986576i	$-0.552214\pi$
$857$	−2.68221e156	−0.326602	−0.163301	+	0.986576i	$0.552214\pi$
$858$	8.48231e156	0.970385
$859$	3.02876e156	0.325560	0.162780	−	0.986662i	$-0.447954\pi$
$859$	3.02876e156	0.325560	0.162780	+	0.986662i	$0.447954\pi$
$860$	−5.47677e155	−0.0553168
$861$	−1.05522e157	−1.00155
$862$	−8.34982e156	−0.744798
$863$	−1.09643e157	−0.919189	−0.459595	−	0.888129i	$-0.652005\pi$
$863$	−1.09643e157	−0.919189	−0.459595	+	0.888129i	$0.652005\pi$
$864$	1.09333e157	0.861524
$865$	3.13699e156	0.232355
$866$	−1.24338e157	−0.865759
$867$	7.90469e156	0.517443
$868$	−8.42547e155	−0.0518548
$869$	2.80793e157	1.62490
$870$	−5.26973e155	−0.0286753
$871$	−5.52215e157	−2.82577
$872$	4.18790e156	0.201542
$873$	−1.16337e157	−0.526571
$874$	7.28939e156	0.310334
$875$	−1.01633e157	−0.407010
$876$	−1.07616e156	−0.0405422
$877$	8.25533e156	0.292588	0.146294	−	0.989241i	$-0.453266\pi$
$877$	8.25533e156	0.292588	0.146294	+	0.989241i	$0.453266\pi$
$878$	−1.35704e157	−0.452518
$879$	4.40009e156	0.138056
$880$	−7.57042e155	−0.0223510
$881$	6.61449e157	1.83775	0.918873	−	0.394554i	$-0.129101\pi$
$881$	6.61449e157	1.83775	0.918873	+	0.394554i	$0.129101\pi$
$882$	−2.88617e157	−0.754662
$883$	3.74621e157	0.921923	0.460961	−	0.887420i	$-0.347505\pi$
$883$	3.74621e157	0.921923	0.460961	+	0.887420i	$0.347505\pi$
$884$	9.96828e155	0.0230900
$885$	−1.60485e156	−0.0349921
$886$	8.11084e156	0.166480
$887$	8.53403e157	1.64907	0.824537	−	0.565807i	$-0.191435\pi$
$887$	8.53403e157	1.64907	0.824537	+	0.565807i	$0.191435\pi$
$888$	4.41008e157	0.802329
$889$	−7.61061e157	−1.30369
$890$	9.32613e155	0.0150431
$891$	2.94169e157	0.446828
$892$	−5.22262e157	−0.747083
$893$	2.94299e157	0.396494
$894$	−3.65202e157	−0.463422
$895$	−8.65824e156	−0.103490
$896$	−6.82642e157	−0.768625
$897$	−6.93128e157	−0.735220
$898$	−1.21472e158	−1.21393
$899$	3.97678e156	0.0374445
$900$	−4.62717e157	−0.410527
$901$	−2.99431e156	−0.0250335
$902$	1.67511e158	1.31975
$903$	−8.48148e157	−0.629763
$904$	7.63413e157	0.534255
$905$	2.10089e157	0.138581
$906$	1.65784e157	0.103082
$907$	−3.01147e157	−0.176518	−0.0882589	−	0.996098i	$-0.528130\pi$
$907$	−3.01147e157	−0.176518	−0.0882589	+	0.996098i	$0.528130\pi$
$908$	1.15555e158	0.638552
$909$	−2.47574e158	−1.28984
$910$	−4.69047e157	−0.230410
$911$	2.60272e158	1.20558	0.602788	−	0.797901i	$-0.294056\pi$
$911$	2.60272e158	1.20558	0.602788	+	0.797901i	$0.294056\pi$
$912$	−7.08435e156	−0.0309440
$913$	2.35915e158	0.971782
$914$	−1.81626e157	−0.0705599
$915$	−8.20504e156	−0.0300644
$916$	−2.02039e158	−0.698275
$917$	2.36009e158	0.769429
$918$	4.51894e156	0.0138980
$919$	3.09871e158	0.899085	0.449543	−	0.893259i	$-0.351587\pi$
$919$	3.09871e158	0.899085	0.449543	+	0.893259i	$0.351587\pi$
$920$	3.98822e157	0.109177
$921$	8.08165e157	0.208742
$922$	−2.75819e157	−0.0672233
$923$	−4.31105e158	−0.991500
$924$	3.64125e158	0.790316
$925$	−7.22894e158	−1.48078
$926$	−1.55733e158	−0.301088
$927$	−9.11750e157	−0.166383
$928$	3.68347e158	0.634513
$929$	2.02078e158	0.328608	0.164304	−	0.986410i	$-0.447462\pi$
$929$	2.02078e158	0.328608	0.164304	+	0.986410i	$0.447462\pi$
$930$	−1.60363e156	−0.00246188
$931$	−6.19509e158	−0.897925
$932$	3.61482e158	0.494693
$933$	−5.37152e158	−0.694111
$934$	−7.52729e158	−0.918504
$935$	4.38056e156	0.00504787
$936$	−1.18591e159	−1.29061
$937$	1.72932e159	1.77749	0.888744	−	0.458405i	$-0.151579\pi$
$937$	1.72932e159	1.77749	0.888744	+	0.458405i	$0.151579\pi$
$938$	1.78686e159	1.73476
$939$	−3.57210e158	−0.327578
$940$	5.84719e157	0.0506532
$941$	−2.03689e159	−1.66695	−0.833474	−	0.552559i	$-0.813651\pi$
$941$	−2.03689e159	−1.66695	−0.833474	+	0.552559i	$0.813651\pi$
$942$	4.80573e158	0.371566
$943$	−1.36881e159	−0.999922
$944$	−8.01269e157	−0.0553065
$945$	2.82089e158	0.183986
$946$	1.34639e159	0.829842
$947$	2.25304e159	1.31234	0.656168	−	0.754615i	$-0.272176\pi$
$947$	2.25304e159	1.31234	0.656168	+	0.754615i	$0.272176\pi$
$948$	5.22064e158	0.287394
$949$	4.52109e158	0.235234
$950$	7.48666e158	0.368193
$951$	−5.12340e158	−0.238178
$952$	−8.88246e157	−0.0390352
$953$	1.92765e159	0.800864	0.400432	−	0.916326i	$-0.368860\pi$
$953$	1.92765e159	0.800864	0.400432	+	0.916326i	$0.368860\pi$
$954$	1.29360e159	0.508116
$955$	−4.59636e157	−0.0170700
$956$	−2.02747e159	−0.711961
$957$	−1.71866e159	−0.570690
$958$	−9.14265e158	−0.287089
$959$	1.27685e159	0.379179
$960$	−1.73220e158	−0.0486506
$961$	−3.75235e159	−0.996785
$962$	−6.72795e159	−1.69050
$963$	3.82556e159	0.909261
$964$	−1.60288e159	−0.360397
$965$	−3.85381e157	−0.00819746
$966$	2.24283e159	0.451357
$967$	−5.73352e158	−0.109170	−0.0545852	−	0.998509i	$-0.517384\pi$
$967$	−5.73352e158	−0.109170	−0.0545852	+	0.998509i	$0.517384\pi$
$968$	−1.02039e160	−1.83839
$969$	4.09930e157	0.00698856
$970$	3.73981e158	0.0603339
$971$	3.94014e158	0.0601565	0.0300782	−	0.999548i	$-0.490424\pi$
$971$	3.94014e158	0.0601565	0.0300782	+	0.999548i	$0.490424\pi$
$972$	4.08537e159	0.590318
$973$	1.55298e160	2.12387
$974$	2.45513e159	0.317812
$975$	−7.11886e159	−0.872295
$976$	−4.09661e158	−0.0475181
$977$	8.75433e159	0.961311	0.480655	−	0.876910i	$-0.340399\pi$
$977$	8.75433e159	0.961311	0.480655	+	0.876910i	$0.340399\pi$
$978$	1.84527e159	0.191837
$979$	3.04160e159	0.299384
$980$	−1.23085e159	−0.114713
$981$	1.62387e159	0.143304
$982$	−2.70301e159	−0.225883
$983$	−4.54882e159	−0.359986	−0.179993	−	0.983668i	$-0.557608\pi$
$983$	−4.54882e159	−0.359986	−0.179993	+	0.983668i	$0.557608\pi$
$984$	8.57650e159	0.642795
$985$	−1.56667e159	−0.111209
$986$	1.52244e158	0.0102359
$987$	9.05514e159	0.576670
$988$	−9.24379e159	−0.557639
$989$	−1.10020e160	−0.628737
$990$	−1.89249e159	−0.102459
$991$	−2.07831e160	−1.06603	−0.533015	−	0.846106i	$-0.678941\pi$
$991$	−2.07831e160	−1.06603	−0.533015	+	0.846106i	$0.678941\pi$
$992$	1.12092e159	0.0544752
$993$	−1.32045e160	−0.608049
$994$	1.39498e160	0.608689
$995$	−2.58033e159	−0.106694
$996$	4.38625e159	0.171878
$997$	3.74026e160	1.38903	0.694515	−	0.719479i	$-0.255619\pi$
$997$	3.74026e160	1.38903	0.694515	+	0.719479i	$0.255619\pi$
$998$	−1.58881e160	−0.559227
$999$	4.04625e160	1.34989

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.108.a.a.1.6	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.108.a.a.1.6	✓	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)

\(f(q)\)	\(=\)	\(q+8.35103e15 q^{2} -1.73817e25 q^{3} -9.25196e31 q^{4} +3.17576e36 q^{5} -1.45155e41 q^{6} +2.61780e45 q^{7} -2.12767e48 q^{8} -8.25006e50 q^{9} +O(q^{10})\)	\(q+8.35103e15 q^{2} -1.73817e25 q^{3} -9.25196e31 q^{4} +3.17576e36 q^{5} -1.45155e41 q^{6} +2.61780e45 q^{7} -2.12767e48 q^{8} -8.25006e50 q^{9} +2.65209e52 q^{10} +8.64945e55 q^{11} +1.60815e57 q^{12} -6.75605e59 q^{13} +2.18613e61 q^{14} -5.52002e61 q^{15} -2.75603e63 q^{16} +1.59475e64 q^{17} -6.88965e66 q^{18} -1.47885e68 q^{19} -2.93820e68 q^{20} -4.55018e70 q^{21} +7.22318e71 q^{22} -5.90239e72 q^{23} +3.69825e73 q^{24} -6.06212e74 q^{25} -5.64200e75 q^{26} +3.39315e76 q^{27} -2.42198e77 q^{28} +1.14316e78 q^{29} -4.60978e77 q^{30} +3.47876e78 q^{31} +3.22218e80 q^{32} -1.50342e81 q^{33} +1.33178e80 q^{34} +8.31350e81 q^{35} +7.63293e82 q^{36} +1.19248e84 q^{37} -1.23499e84 q^{38} +1.17432e85 q^{39} -6.75695e84 q^{40} +2.31907e86 q^{41} -3.79987e86 q^{42} +1.86399e87 q^{43} -8.00243e87 q^{44} -2.62002e87 q^{45} -4.92910e88 q^{46} -1.99006e89 q^{47} +4.79046e88 q^{48} +4.18914e90 q^{49} -5.06249e90 q^{50} -2.77196e89 q^{51} +6.25067e91 q^{52} -1.87760e92 q^{53} +2.83363e92 q^{54} +2.74686e92 q^{55} -5.56980e93 q^{56} +2.57049e93 q^{57} +9.54658e93 q^{58} +2.90733e94 q^{59} +5.10710e93 q^{60} +1.48641e95 q^{61} +2.90512e94 q^{62} -2.15970e96 q^{63} +3.13804e96 q^{64} -2.14556e96 q^{65} -1.25551e97 q^{66} +8.17363e97 q^{67} -1.47546e96 q^{68} +1.02594e98 q^{69} +6.94263e97 q^{70} +6.38103e98 q^{71} +1.75534e99 q^{72} -6.69192e98 q^{73} +9.95840e99 q^{74} +1.05370e100 q^{75} +1.36822e100 q^{76} +2.26425e101 q^{77} +9.80676e100 q^{78} +3.24637e101 q^{79} -8.75249e99 q^{80} +3.40102e101 q^{81} +1.93666e102 q^{82} +2.72752e102 q^{83} +4.20981e102 q^{84} +5.06455e100 q^{85} +1.55662e103 q^{86} -1.98701e103 q^{87} -1.84031e104 q^{88} +3.51653e103 q^{89} -2.18799e103 q^{90} -1.76860e105 q^{91} +5.46086e104 q^{92} -6.04668e103 q^{93} -1.66190e105 q^{94} -4.69646e104 q^{95} -5.60070e105 q^{96} +1.41014e106 q^{97} +3.49836e106 q^{98} -7.13585e106 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 54\!\cdots\!96 q^{2}+ \cdots + 36\!\cdots\!13 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more