LMFDB - Embedded newform 1.108.a.a.1.5

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			1.5
Root			$-2.01415e13$ 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)

$f(q)$	$=$	$q+1.09070e15 q^{2} +6.73736e23 q^{3} -1.61070e32 q^{4} +1.05761e37 q^{5} +7.34847e38 q^{6} -2.03867e45 q^{7} -3.52656e47 q^{8} -1.12668e51 q^{9} +O(q^{10})$	\(q+1.09070e15 q^{2} +6.73736e23 q^{3} -1.61070e32 q^{4} +1.05761e37 q^{5} +7.34847e38 q^{6} -2.03867e45 q^{7} -3.52656e47 q^{8} -1.12668e51 q^{9} +1.15354e52 q^{10} -7.45477e55 q^{11} -1.08518e56 q^{12} +2.59243e59 q^{13} -2.22359e60 q^{14} +7.12550e60 q^{15} +2.57504e64 q^{16} -7.34083e65 q^{17} -1.22887e66 q^{18} -3.57415e68 q^{19} -1.70349e69 q^{20} -1.37353e69 q^{21} -8.13095e70 q^{22} +7.52678e72 q^{23} -2.37597e71 q^{24} -5.04444e74 q^{25} +2.82758e74 q^{26} -1.51847e75 q^{27} +3.28368e77 q^{28} -2.05471e78 q^{29} +7.77182e75 q^{30} +1.28283e79 q^{31} +8.53078e79 q^{32} -5.02254e79 q^{33} -8.00668e80 q^{34} -2.15612e82 q^{35} +1.81473e83 q^{36} -1.78987e83 q^{37} -3.89834e83 q^{38} +1.74662e83 q^{39} -3.72973e84 q^{40} +1.47248e86 q^{41} -1.49811e84 q^{42} -3.56843e87 q^{43} +1.20074e88 q^{44} -1.19159e88 q^{45} +8.20950e87 q^{46} -1.50890e89 q^{47} +1.73490e88 q^{48} +1.49246e90 q^{49} -5.50199e89 q^{50} -4.94578e89 q^{51} -4.17562e91 q^{52} +1.54297e92 q^{53} -1.65620e90 q^{54} -7.88424e92 q^{55} +7.18951e92 q^{56} -2.40803e92 q^{57} -2.24108e93 q^{58} +2.89466e94 q^{59} -1.14770e93 q^{60} -1.93533e95 q^{61} +1.39918e94 q^{62} +2.29693e96 q^{63} -4.08520e96 q^{64} +2.74178e96 q^{65} -5.47811e94 q^{66} +5.07544e96 q^{67} +1.18239e98 q^{68} +5.07106e96 q^{69} -2.35169e97 q^{70} +6.83457e98 q^{71} +3.97330e98 q^{72} +9.17350e99 q^{73} -1.95222e98 q^{74} -3.39862e98 q^{75} +5.75687e100 q^{76} +1.51978e101 q^{77} +1.90504e98 q^{78} +4.03132e101 q^{79} +2.72339e101 q^{80} +1.26889e102 q^{81} +1.60604e101 q^{82} +6.14578e102 q^{83} +2.21234e101 q^{84} -7.76374e102 q^{85} -3.89211e102 q^{86} -1.38433e102 q^{87} +2.62897e103 q^{88} -3.67747e104 q^{89} -1.29967e103 q^{90} -5.28512e104 q^{91} -1.21234e105 q^{92} +8.64286e102 q^{93} -1.64576e104 q^{94} -3.78006e105 q^{95} +5.74750e103 q^{96} +1.35690e105 q^{97} +1.62783e105 q^{98} +8.39911e106 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.09070e15	0.0856254	0.0428127	−	0.999083i	$-0.486368\pi$
$2$	1.09070e15	0.0856254	0.0428127	+	0.999083i	$0.486368\pi$
$3$	6.73736e23	0.0200679	0.0100340	−	0.999950i	$-0.496806\pi$
$3$	6.73736e23	0.0200679	0.0100340	+	0.999950i	$0.496806\pi$
$4$	−1.61070e32	−0.992668
$5$	1.05761e37	0.426021	0.213010	−	0.977050i	$-0.431673\pi$
$5$	1.05761e37	0.426021	0.213010	+	0.977050i	$0.431673\pi$
$6$	7.34847e38	0.00171832
$7$	−2.03867e45	−1.24912	−0.624558	−	0.780979i	$-0.714721\pi$
$7$	−2.03867e45	−1.24912	−0.624558	+	0.780979i	$0.714721\pi$
$8$	−3.52656e47	−0.170623
$9$	−1.12668e51	−0.999597
$10$	1.15354e52	0.0364782
$11$	−7.45477e55	−1.43855	−0.719276	−	0.694725i	$-0.755526\pi$
$11$	−7.45477e55	−1.43855	−0.719276	+	0.694725i	$0.755526\pi$
$12$	−1.08518e56	−0.0199208
$13$	2.59243e59	0.657262	0.328631	−	0.944458i	$-0.393413\pi$
$13$	2.59243e59	0.657262	0.328631	+	0.944458i	$0.393413\pi$
$14$	−2.22359e60	−0.106956
$15$	7.12550e60	0.00854935
$16$	2.57504e64	0.978059
$17$	−7.34083e65	−1.08825	−0.544124	−	0.839005i	$-0.683138\pi$
$17$	−7.34083e65	−1.08825	−0.544124	+	0.839005i	$0.683138\pi$
$18$	−1.22887e66	−0.0855909
$19$	−3.57415e68	−1.37992	−0.689962	−	0.723846i	$-0.742373\pi$
$19$	−3.57415e68	−1.37992	−0.689962	+	0.723846i	$0.742373\pi$
$20$	−1.70349e69	−0.422897
$21$	−1.37353e69	−0.0250672
$22$	−8.13095e70	−0.123176
$23$	7.52678e72	1.05723	0.528616	−	0.848861i	$-0.322711\pi$
$23$	7.52678e72	1.05723	0.528616	+	0.848861i	$0.322711\pi$
$24$	−2.37597e71	−0.00342405
$25$	−5.04444e74	−0.818507
$26$	2.82758e74	0.0562783
$27$	−1.51847e75	−0.0401278
$28$	3.28368e77	1.23996
$29$	−2.05471e78	−1.18702	−0.593510	−	0.804827i	$-0.702258\pi$
$29$	−2.05471e78	−1.18702	−0.593510	+	0.804827i	$0.702258\pi$
$30$	7.77182e75	0.000732041 0
$31$	1.28283e79	0.209082	0.104541	−	0.994521i	$-0.466663\pi$
$31$	1.28283e79	0.209082	0.104541	+	0.994521i	$0.466663\pi$
$32$	8.53078e79	0.254370
$33$	−5.02254e79	−0.0288688
$34$	−8.00668e80	−0.0931817
$35$	−2.15612e82	−0.532149
$36$	1.81473e83	0.992269
$37$	−1.78987e83	−0.225959	−0.112979	−	0.993597i	$-0.536039\pi$
$37$	−1.78987e83	−0.225959	−0.112979	+	0.993597i	$0.536039\pi$
$38$	−3.89834e83	−0.118156
$39$	1.74662e83	0.0131899
$40$	−3.72973e84	−0.0726889
$41$	1.47248e86	0.765795	0.382897	−	0.923791i	$-0.374926\pi$
$41$	1.47248e86	0.765795	0.382897	+	0.923791i	$0.374926\pi$
$42$	−1.49811e84	−0.00214638
$43$	−3.56843e87	−1.45183	−0.725914	−	0.687786i	$-0.758583\pi$
$43$	−3.56843e87	−1.45183	−0.725914	+	0.687786i	$0.758583\pi$
$44$	1.20074e88	1.42800
$45$	−1.19159e88	−0.425849
$46$	8.20950e87	0.0905258
$47$	−1.50890e89	−0.526532	−0.263266	−	0.964723i	$-0.584800\pi$
$47$	−1.50890e89	−0.526532	−0.263266	+	0.964723i	$0.584800\pi$
$48$	1.73490e88	0.0196276
$49$	1.49246e90	0.560288
$50$	−5.50199e89	−0.0700849
$51$	−4.94578e89	−0.0218389
$52$	−4.17562e91	−0.652443
$53$	1.54297e92	0.870160	0.435080	−	0.900392i	$-0.356720\pi$
$53$	1.54297e92	0.870160	0.435080	+	0.900392i	$0.356720\pi$
$54$	−1.65620e90	−0.00343596
$55$	−7.88424e92	−0.612852
$56$	7.18951e92	0.213128
$57$	−2.40803e92	−0.0276922
$58$	−2.24108e93	−0.101639
$59$	2.89466e94	0.526036	0.263018	−	0.964791i	$-0.415282\pi$
$59$	2.89466e94	0.526036	0.263018	+	0.964791i	$0.415282\pi$
$60$	−1.14770e93	−0.00848667
$61$	−1.93533e95	−0.591030	−0.295515	−	0.955338i	$-0.595491\pi$
$61$	−1.93533e95	−0.591030	−0.295515	+	0.955338i	$0.595491\pi$
$62$	1.39918e94	0.0179027
$63$	2.29693e96	1.24861
$64$	−4.08520e96	−0.956278
$65$	2.74178e96	0.280007
$66$	−5.47811e94	−0.00247190
$67$	5.07544e96	0.102441	0.0512203	−	0.998687i	$-0.483689\pi$
$67$	5.07544e96	0.102441	0.0512203	+	0.998687i	$0.483689\pi$
$68$	1.18239e98	1.08027
$69$	5.07106e96	0.0212165
$70$	−2.35169e97	−0.0455654
$71$	6.83457e98	0.619997	0.309999	−	0.950737i	$-0.399671\pi$
$71$	6.83457e98	0.619997	0.309999	+	0.950737i	$0.399671\pi$
$72$	3.97330e98	0.170554
$73$	9.17350e99	1.88262	0.941308	−	0.337548i	$-0.109598\pi$
$73$	9.17350e99	1.88262	0.941308	+	0.337548i	$0.109598\pi$
$74$	−1.95222e98	−0.0193478
$75$	−3.39862e98	−0.0164257
$76$	5.75687e100	1.36981
$77$	1.51978e101	1.79692
$78$	1.90504e98	0.00112939
$79$	4.03132e101	1.20892	0.604461	−	0.796635i	$-0.293389\pi$
$79$	4.03132e101	1.20892	0.604461	+	0.796635i	$0.293389\pi$
$80$	2.72339e101	0.416673
$81$	1.26889e102	0.998792
$82$	1.60604e101	0.0655714
$83$	6.14578e102	1.31190	0.655948	−	0.754806i	$-0.272269\pi$
$83$	6.14578e102	1.31190	0.655948	+	0.754806i	$0.272269\pi$
$84$	2.21234e101	0.0248834
$85$	−7.76374e102	−0.463616
$86$	−3.89211e102	−0.124313
$87$	−1.38433e102	−0.0238210
$88$	2.62897e103	0.245450
$89$	−3.67747e104	−1.87579	−0.937895	−	0.346920i	$-0.887228\pi$
$89$	−3.67747e104	−1.87579	−0.937895	+	0.346920i	$0.887228\pi$
$90$	−1.29967e103	−0.0364635
$91$	−5.28512e104	−0.820995
$92$	−1.21234e105	−1.04948
$93$	8.64286e102	0.00419585
$94$	−1.64576e104	−0.0450845
$95$	−3.78006e105	−0.587876
$96$	5.74750e103	0.00510467
$97$	1.35690e105	0.0692244	0.0346122	−	0.999401i	$-0.488980\pi$
$97$	1.35690e105	0.0692244	0.0346122	+	0.999401i	$0.488980\pi$
$98$	1.62783e105	0.0479749
$99$	8.39911e106	1.43797
$100$	8.12505e106	0.812505
$101$	−6.75825e106	−0.396863	−0.198432	−	0.980115i	$-0.563585\pi$
$101$	−6.75825e106	−0.396863	−0.198432	+	0.980115i	$0.563585\pi$
$102$	−5.39439e104	−0.00186996
$103$	9.36892e107	1.92707	0.963536	−	0.267578i	$-0.0862232\pi$
$103$	9.36892e107	1.92707	0.963536	+	0.267578i	$0.0862232\pi$
$104$	−9.14238e106	−0.112144
$105$	−1.45266e106	−0.0106791
$106$	1.68293e107	0.0745078
$107$	−3.90001e108	−1.04480	−0.522401	−	0.852700i	$-0.674963\pi$
$107$	−3.90001e108	−1.04480	−0.522401	+	0.852700i	$0.674963\pi$
$108$	2.44580e107	0.0398336
$109$	−9.65585e108	−0.960446	−0.480223	−	0.877147i	$-0.659444\pi$
$109$	−9.65585e108	−0.960446	−0.480223	+	0.877147i	$0.659444\pi$
$110$	−8.59938e107	−0.0524757
$111$	−1.20590e107	−0.00453452
$112$	−5.24966e109	−1.22171
$113$	−3.37960e109	−0.488843	−0.244421	−	0.969669i	$-0.578598\pi$
$113$	−3.37960e109	−0.488843	−0.244421	+	0.969669i	$0.578598\pi$
$114$	−2.62645e107	−0.00237116
$115$	7.96040e109	0.450402
$116$	3.30951e110	1.17832
$117$	−2.92083e110	−0.656997
$118$	3.15722e109	0.0450420
$119$	1.49656e111	1.35935
$120$	−2.51285e108	−0.00145872
$121$	2.87190e111	1.06943
$122$	−2.11088e110	−0.0506071
$123$	9.92061e109	0.0153679
$124$	−2.06624e111	−0.207549
$125$	−1.18531e112	−0.774721
$126$	2.50527e111	0.106913
$127$	−3.41218e112	−0.953967	−0.476983	−	0.878912i	$-0.658270\pi$
$127$	−3.41218e112	−0.953967	−0.476983	+	0.878912i	$0.658270\pi$
$128$	−1.82977e112	−0.336251
$129$	−2.40418e111	−0.0291352
$130$	2.99048e111	0.0239757
$131$	−2.79357e113	−1.48643	−0.743216	−	0.669052i	$-0.766700\pi$
$131$	−2.79357e113	−1.48643	−0.743216	+	0.669052i	$0.766700\pi$
$132$	8.08979e111	0.0286571
$133$	7.28652e113	1.72368
$134$	5.53581e111	0.00877151
$135$	−1.60595e112	−0.0170953
$136$	2.58879e113	0.185680
$137$	2.33263e114	1.13056	0.565281	−	0.824898i	$-0.308768\pi$
$137$	2.33263e114	1.13056	0.565281	+	0.824898i	$0.308768\pi$
$138$	5.53103e111	0.00181667
$139$	−3.00026e113	−0.0669680	−0.0334840	−	0.999439i	$-0.510660\pi$
$139$	−3.00026e113	−0.0669680	−0.0334840	+	0.999439i	$0.510660\pi$
$140$	3.47286e114	0.528247
$141$	−1.01660e113	−0.0105664
$142$	7.45450e113	0.0530875
$143$	−1.93260e115	−0.945505
$144$	−2.90124e115	−0.977665
$145$	−2.17308e115	−0.505694
$146$	1.00056e115	0.161200
$147$	1.00552e114	0.0112438
$148$	2.88294e115	0.224302
$149$	−2.07037e116	−1.12352	−0.561762	−	0.827299i	$-0.689876\pi$
$149$	−2.07037e116	−1.12352	−0.561762	+	0.827299i	$0.689876\pi$
$150$	−3.70689e113	−0.00140646
$151$	4.16636e116	1.10787	0.553936	−	0.832559i	$-0.313125\pi$
$151$	4.16636e116	1.10787	0.553936	+	0.832559i	$0.313125\pi$
$152$	1.26045e116	0.235447
$153$	8.27075e116	1.08781
$154$	1.65763e116	0.153862
$155$	1.35673e116	0.0890733
$156$	−2.81327e115	−0.0130932
$157$	−2.93062e116	−0.0969010	−0.0484505	−	0.998826i	$-0.515428\pi$
$157$	−2.93062e116	−0.0969010	−0.0484505	+	0.998826i	$0.515428\pi$
$158$	4.39698e116	0.103514
$159$	1.03956e116	0.0174623
$160$	9.02225e116	0.108367
$161$	−1.53446e118	−1.32060
$162$	1.38398e117	0.0855219
$163$	−1.42305e118	−0.632680	−0.316340	−	0.948646i	$-0.602454\pi$
$163$	−1.42305e118	−0.632680	−0.316340	+	0.948646i	$0.602454\pi$
$164$	−2.37171e118	−0.760180
$165$	−5.31190e116	−0.0122987
$166$	6.70323e117	0.112332
$167$	1.01128e119	1.22896	0.614481	−	0.788931i	$-0.289365\pi$
$167$	1.01128e119	1.22896	0.614481	+	0.788931i	$0.289365\pi$
$168$	4.84383e116	0.00427703
$169$	−8.83675e118	−0.568007
$170$	−8.46795e117	−0.0396973
$171$	4.02691e119	1.37937
$172$	5.74766e119	1.44118
$173$	−6.31701e119	−1.16157	−0.580784	−	0.814057i	$-0.697254\pi$
$173$	−6.31701e119	−1.16157	−0.580784	+	0.814057i	$0.697254\pi$
$174$	−1.50990e117	−0.00203968
$175$	1.02840e120	1.02241
$176$	−1.91963e120	−1.40699
$177$	1.95024e118	0.0105564
$178$	−4.01104e119	−0.160615
$179$	−4.34289e120	−1.28867	−0.644335	−	0.764743i	$-0.722866\pi$
$179$	−4.34289e120	−1.28867	−0.644335	+	0.764743i	$0.722866\pi$
$180$	1.91928e120	0.422727
$181$	−1.69536e120	−0.277625	−0.138813	−	0.990319i	$-0.544329\pi$
$181$	−1.69536e120	−0.277625	−0.138813	+	0.990319i	$0.544329\pi$
$182$	−5.76451e119	−0.0702980
$183$	−1.30390e119	−0.0118607
$184$	−2.65437e120	−0.180388
$185$	−1.89299e120	−0.0962631
$186$	9.42680e117	0.000359271 0
$187$	5.47242e121	1.56550
$188$	2.43038e121	0.522671
$189$	3.09567e120	0.0501242
$190$	−4.12293e120	−0.0503371
$191$	1.38215e121	0.127429	0.0637147	−	0.997968i	$-0.479705\pi$
$191$	1.38215e121	0.127429	0.0637147	+	0.997968i	$0.479705\pi$
$192$	−2.75234e120	−0.0191905
$193$	−4.86262e121	−0.256776	−0.128388	−	0.991724i	$-0.540980\pi$
$193$	−4.86262e121	−0.256776	−0.128388	+	0.991724i	$0.540980\pi$
$194$	1.47997e120	0.00592736
$195$	1.84724e120	0.00561916
$196$	−2.40390e122	−0.556180
$197$	−5.61699e122	−0.989829	−0.494915	−	0.868942i	$-0.664801\pi$
$197$	−5.61699e122	−0.989829	−0.494915	+	0.868942i	$0.664801\pi$
$198$	9.16095e121	0.123127
$199$	−7.96193e122	−0.817295	−0.408647	−	0.912692i	$-0.633999\pi$
$199$	−7.96193e122	−0.817295	−0.408647	+	0.912692i	$0.633999\pi$
$200$	1.77895e122	0.139656
$201$	3.41951e120	0.00205577
$202$	−7.37125e121	−0.0339815
$203$	4.18888e123	1.48272
$204$	7.96616e121	0.0216788
$205$	1.55731e123	0.326244
$206$	1.02187e123	0.165006
$207$	−8.48025e123	−1.05681
$208$	6.67562e123	0.642840
$209$	2.66444e124	1.98509
$210$	−1.58442e121	−0.000914404 0
$211$	−3.03790e124	−1.35976	−0.679879	−	0.733324i	$-0.737968\pi$
$211$	−3.03790e124	−1.35976	−0.679879	+	0.733324i	$0.737968\pi$
$212$	−2.48526e124	−0.863780
$213$	4.60470e122	0.0124421
$214$	−4.25376e123	−0.0894615
$215$	−3.77401e124	−0.618508
$216$	5.35498e122	0.00684672
$217$	−2.61526e124	−0.261168
$218$	−1.05317e124	−0.0822385
$219$	6.18051e123	0.0377802
$220$	1.26991e125	0.608359
$221$	−1.90306e125	−0.715264
$222$	−1.31528e122	−0.000388270 0
$223$	7.44382e125	1.72777	0.863885	−	0.503689i	$-0.168024\pi$
$223$	7.44382e125	1.72777	0.863885	+	0.503689i	$0.168024\pi$
$224$	−1.73915e125	−0.317737
$225$	5.68345e125	0.818177
$226$	−3.68615e124	−0.0418573
$227$	6.96469e125	0.624479	0.312240	−	0.950003i	$-0.398921\pi$
$227$	6.96469e125	0.624479	0.312240	+	0.950003i	$0.398921\pi$
$228$	3.87861e124	0.0274892
$229$	−2.83479e126	−1.58973	−0.794863	−	0.606789i	$-0.792457\pi$
$229$	−2.83479e126	−1.58973	−0.794863	+	0.606789i	$0.792457\pi$
$230$	8.68245e124	0.0385659
$231$	1.02393e125	0.0360604
$232$	7.24607e125	0.202533
$233$	−4.33603e126	−0.962833	−0.481416	−	0.876492i	$-0.659878\pi$
$233$	−4.33603e126	−0.962833	−0.481416	+	0.876492i	$0.659878\pi$
$234$	−3.18577e125	−0.0562556
$235$	−1.59583e126	−0.224313
$236$	−4.66242e126	−0.522179
$237$	2.71605e125	0.0242606
$238$	1.63230e126	0.116395
$239$	1.26316e127	0.719734	0.359867	−	0.933004i	$-0.382822\pi$
$239$	1.26316e127	0.719734	0.359867	+	0.933004i	$0.382822\pi$
$240$	1.83485e125	0.00836177
$241$	2.28722e127	0.834440	0.417220	−	0.908805i	$-0.363004\pi$
$241$	2.28722e127	0.834440	0.417220	+	0.908805i	$0.363004\pi$
$242$	3.13240e126	0.0915704
$243$	2.56641e126	0.0601715
$244$	3.11723e127	0.586696
$245$	1.57844e127	0.238694
$246$	1.08205e125	0.00131588
$247$	−9.26574e127	−0.906971
$248$	−4.52397e126	−0.0356742
$249$	4.14063e126	0.0263270
$250$	−1.29282e127	−0.0663358
$251$	1.80124e128	0.746498	0.373249	−	0.927731i	$-0.378244\pi$
$251$	1.80124e128	0.746498	0.373249	+	0.927731i	$0.378244\pi$
$252$	−3.69965e128	−1.23946
$253$	−5.61104e128	−1.52088
$254$	−3.72168e127	−0.0816838
$255$	−5.23071e126	−0.00930382
$256$	6.42903e128	0.927487
$257$	3.72418e128	0.436122	0.218061	−	0.975935i	$-0.430027\pi$
$257$	3.72418e128	0.436122	0.218061	+	0.975935i	$0.430027\pi$
$258$	−2.62225e126	−0.00249471
$259$	3.64896e128	0.282248
$260$	−4.41618e128	−0.277954
$261$	2.31499e129	1.18654
$262$	−3.04696e128	−0.127276
$263$	3.61162e128	0.123047	0.0615234	−	0.998106i	$-0.480404\pi$
$263$	3.61162e128	0.123047	0.0615234	+	0.998106i	$0.480404\pi$
$264$	1.77123e127	0.00492567
$265$	1.63186e129	0.370706
$266$	7.94744e128	0.147591
$267$	−2.47765e128	−0.0376432
$268$	−8.17500e128	−0.101690
$269$	−1.72522e130	−1.75832	−0.879159	−	0.476528i	$-0.841895\pi$
$269$	−1.72522e130	−1.75832	−0.879159	+	0.476528i	$0.841895\pi$
$270$	−1.75162e127	−0.00146379
$271$	3.53325e129	0.242280	0.121140	−	0.992635i	$-0.461345\pi$
$271$	3.53325e129	0.242280	0.121140	+	0.992635i	$0.461345\pi$
$272$	−1.89029e130	−1.06437
$273$	−3.56078e128	−0.0164757
$274$	2.54421e129	0.0968048
$275$	3.76051e130	1.17746
$276$	−8.16794e128	−0.0210609
$277$	−1.72957e130	−0.367510	−0.183755	−	0.982972i	$-0.558825\pi$
$277$	−1.72957e130	−0.367510	−0.183755	+	0.982972i	$0.558825\pi$
$278$	−3.27240e128	−0.00573416
$279$	−1.44533e130	−0.208998
$280$	7.60370e129	0.0907968
$281$	1.86652e131	1.84181	0.920903	−	0.389792i	$-0.127453\pi$
$281$	1.86652e131	1.84181	0.920903	+	0.389792i	$0.127453\pi$
$282$	−1.10881e128	−0.000904752 0
$283$	8.59338e130	0.580216	0.290108	−	0.956994i	$-0.406309\pi$
$283$	8.59338e130	0.580216	0.290108	+	0.956994i	$0.406309\pi$
$284$	−1.10084e131	−0.615451
$285$	−2.54676e129	−0.0117974
$286$	−2.10789e130	−0.0809592
$287$	−3.00190e131	−0.956566
$288$	−9.61144e130	−0.254267
$289$	8.38543e130	0.184285
$290$	−2.37019e130	−0.0433003
$291$	9.14190e128	0.00138919
$292$	−1.47757e132	−1.86881
$293$	8.23632e131	0.867592	0.433796	−	0.901011i	$-0.357174\pi$
$293$	8.23632e131	0.867592	0.433796	+	0.901011i	$0.357174\pi$
$294$	1.09673e129	0.000962757 0
$295$	3.06142e131	0.224102
$296$	6.31209e130	0.0385537
$297$	1.13198e131	0.0577259
$298$	−2.25816e131	−0.0962022
$299$	1.95127e132	0.694878
$300$	5.47414e130	0.0163053
$301$	7.27487e132	1.81350
$302$	4.54427e131	0.0948620
$303$	−4.55328e130	−0.00796422
$304$	−9.20358e132	−1.34965
$305$	−2.04683e132	−0.251791
$306$	9.02094e131	0.0931442
$307$	1.46494e133	1.27033	0.635163	−	0.772378i	$-0.280933\pi$
$307$	1.46494e133	1.27033	0.635163	+	0.772378i	$0.280933\pi$
$308$	−2.44791e133	−1.78374
$309$	6.31218e131	0.0386724
$310$	1.47979e131	0.00762693
$311$	−1.60107e133	−0.694591	−0.347295	−	0.937756i	$-0.612900\pi$
$311$	−1.60107e133	−0.694591	−0.347295	+	0.937756i	$0.612900\pi$
$312$	−6.15955e130	−0.00225050
$313$	−7.61033e132	−0.234305	−0.117153	−	0.993114i	$-0.537377\pi$
$313$	−7.61033e132	−0.234305	−0.117153	+	0.993114i	$0.537377\pi$
$314$	−3.19644e131	−0.00829719
$315$	2.42925e133	0.531934
$316$	−6.49324e133	−1.20006
$317$	7.05004e133	1.10033	0.550163	−	0.835058i	$-0.314566\pi$
$317$	7.05004e133	1.10033	0.550163	+	0.835058i	$0.314566\pi$
$318$	1.13385e131	0.00149522
$319$	1.53174e134	1.70759
$320$	−4.32055e133	−0.407394
$321$	−2.62758e132	−0.0209670
$322$	−1.67365e133	−0.113077
$323$	2.62372e134	1.50170
$324$	−2.04379e134	−0.991469
$325$	−1.30774e134	−0.537973
$326$	−1.55213e133	−0.0541735
$327$	−6.50549e132	−0.0192742
$328$	−5.19279e133	−0.130662
$329$	3.07615e134	0.657699
$330$	−5.79371e131	−0.00105308
$331$	−9.31406e134	−1.43993	−0.719965	−	0.694011i	$-0.755842\pi$
$331$	−9.31406e134	−1.43993	−0.719965	+	0.694011i	$0.755842\pi$
$332$	−9.89899e134	−1.30228
$333$	2.01660e134	0.225868
$334$	1.10300e134	0.105230
$335$	5.36784e133	0.0436418
$336$	−3.53689e133	−0.0245171
$337$	2.73301e135	1.61600	0.808000	−	0.589183i	$-0.200550\pi$
$337$	2.73301e135	1.61600	0.808000	+	0.589183i	$0.200550\pi$
$338$	−9.63828e133	−0.0486358
$339$	−2.27696e133	−0.00981006
$340$	1.25050e135	0.460217
$341$	−9.56316e134	−0.300775
$342$	4.39217e134	0.118109
$343$	2.38784e135	0.549250
$344$	1.25843e135	0.247715
$345$	5.36321e133	0.00903864
$346$	−6.88999e134	−0.0994597
$347$	−1.38921e135	−0.171847	−0.0859234	−	0.996302i	$-0.527384\pi$
$347$	−1.38921e135	−0.171847	−0.0859234	+	0.996302i	$0.527384\pi$
$348$	2.22974e134	0.0236464
$349$	−1.02077e136	−0.928471	−0.464235	−	0.885712i	$-0.653671\pi$
$349$	−1.02077e136	−0.928471	−0.464235	+	0.885712i	$0.653671\pi$
$350$	1.12168e135	0.0875441
$351$	−3.93653e134	−0.0263744
$352$	−6.35950e135	−0.365924
$353$	−3.54130e136	−1.75072	−0.875359	−	0.483474i	$-0.839375\pi$
$353$	−3.54130e136	−1.75072	−0.875359	+	0.483474i	$0.839375\pi$
$354$	2.12713e133	0.000903900 0
$355$	7.22831e135	0.264131
$356$	5.92329e136	1.86204
$357$	1.00828e135	0.0272793
$358$	−4.73681e135	−0.110343
$359$	−3.85619e136	−0.773758	−0.386879	−	0.922130i	$-0.626447\pi$
$359$	−3.85619e136	−0.773758	−0.386879	+	0.922130i	$0.626447\pi$
$360$	4.20220e135	0.0726596
$361$	6.06589e136	0.904189
$362$	−1.84914e135	−0.0237718
$363$	1.93490e135	0.0214613
$364$	8.51273e136	0.814976
$365$	9.70199e136	0.802033
$366$	−1.42217e134	−0.00101558
$367$	−2.30844e137	−1.42457	−0.712284	−	0.701891i	$-0.752339\pi$
$367$	−2.30844e137	−1.42457	−0.712284	+	0.701891i	$0.752339\pi$
$368$	1.93818e137	1.03403
$369$	−1.65901e137	−0.765486
$370$	−2.06469e135	−0.00824256
$371$	−3.14562e137	−1.08693
$372$	−1.39210e135	−0.00416508
$373$	−1.89123e137	−0.490142	−0.245071	−	0.969505i	$-0.578811\pi$
$373$	−1.89123e137	−0.490142	−0.245071	+	0.969505i	$0.578811\pi$
$374$	5.96879e136	0.134047
$375$	−7.98584e135	−0.0155470
$376$	5.32123e136	0.0898384
$377$	−5.32670e137	−0.780182
$378$	3.37646e135	0.00429190
$379$	8.04523e137	0.887852	0.443926	−	0.896063i	$-0.353585\pi$
$379$	8.04523e137	0.887852	0.443926	+	0.896063i	$0.353585\pi$
$380$	6.08853e137	0.583566
$381$	−2.29891e136	−0.0191441
$382$	1.50752e136	0.0109112
$383$	1.70319e137	0.107184	0.0535918	−	0.998563i	$-0.482933\pi$
$383$	1.70319e137	0.107184	0.0535918	+	0.998563i	$0.482933\pi$
$384$	−1.23278e136	−0.00674787
$385$	1.60734e138	0.765523
$386$	−5.30368e136	−0.0219865
$387$	4.02047e138	1.45124
$388$	−2.18555e137	−0.0687169
$389$	−4.71557e138	−1.29191	−0.645953	−	0.763377i	$-0.723540\pi$
$389$	−4.71557e138	−1.29191	−0.645953	+	0.763377i	$0.723540\pi$
$390$	2.01479e135	0.000481143 0
$391$	−5.52529e138	−1.15053
$392$	−5.26324e137	−0.0955980
$393$	−1.88213e137	−0.0298296
$394$	−6.12647e137	−0.0847545
$395$	4.26357e138	0.515025
$396$	−1.35284e139	−1.42743
$397$	7.37355e138	0.679805	0.339903	−	0.940461i	$-0.389606\pi$
$397$	7.37355e138	0.679805	0.339903	+	0.940461i	$0.389606\pi$
$398$	−8.68411e137	−0.0699811
$399$	4.90919e137	0.0345908
$400$	−1.29896e139	−0.800547
$401$	1.71963e139	0.927281	0.463641	−	0.886023i	$-0.346543\pi$
$401$	1.71963e139	0.927281	0.463641	+	0.886023i	$0.346543\pi$
$402$	3.72967e135	0.000176026 0
$403$	3.32564e138	0.137422
$404$	1.08855e139	0.393953
$405$	1.34199e139	0.425506
$406$	4.56883e138	0.126959
$407$	1.33431e139	0.325053
$408$	1.74416e137	0.00372622
$409$	6.16133e139	1.15472	0.577361	−	0.816489i	$-0.304083\pi$
$409$	6.16133e139	1.15472	0.577361	+	0.816489i	$0.304083\pi$
$410$	1.69856e138	0.0279348
$411$	1.57157e138	0.0226881
$412$	−1.50905e140	−1.91294
$413$	−5.90127e139	−0.657079
$414$	−9.24945e138	−0.0904894
$415$	6.49984e139	0.558894
$416$	2.21155e139	0.167187
$417$	−2.02138e137	−0.00134391
$418$	2.90612e139	0.169974
$419$	−2.71238e140	−1.39605	−0.698024	−	0.716074i	$-0.745937\pi$
$419$	−2.71238e140	−1.39605	−0.698024	+	0.716074i	$0.745937\pi$
$420$	2.33979e138	0.0106008
$421$	−8.50226e139	−0.339190	−0.169595	−	0.985514i	$-0.554246\pi$
$421$	−8.50226e139	−0.339190	−0.169595	+	0.985514i	$0.554246\pi$
$422$	−3.31345e139	−0.116430
$423$	1.70004e140	0.526320
$424$	−5.44139e139	−0.148469
$425$	3.70304e140	0.890739
$426$	5.02236e137	0.00106536
$427$	3.94551e140	0.738264
$428$	6.28173e140	1.03714
$429$	−1.30206e139	−0.0189743
$430$	−4.11633e139	−0.0529600
$431$	−3.37722e140	−0.383730	−0.191865	−	0.981421i	$-0.561454\pi$
$431$	−3.37722e140	−0.383730	−0.191865	+	0.981421i	$0.561454\pi$
$432$	−3.91012e139	−0.0392473
$433$	−5.01000e140	−0.444360	−0.222180	−	0.975006i	$-0.571317\pi$
$433$	−5.01000e140	−0.444360	−0.222180	+	0.975006i	$0.571317\pi$
$434$	−2.85248e139	−0.0223626
$435$	−1.46408e139	−0.0101482
$436$	1.55526e141	0.953404
$437$	−2.69018e141	−1.45890
$438$	6.74111e138	0.00323494
$439$	−1.20558e141	−0.512088	−0.256044	−	0.966665i	$-0.582419\pi$
$439$	−1.20558e141	−0.512088	−0.256044	+	0.966665i	$0.582419\pi$
$440$	2.78043e140	0.104567
$441$	−1.68152e141	−0.560063
$442$	−2.07568e140	−0.0612447
$443$	8.68329e140	0.227031	0.113516	−	0.993536i	$-0.463789\pi$
$443$	8.68329e140	0.227031	0.113516	+	0.993536i	$0.463789\pi$
$444$	1.94234e139	0.00450128
$445$	−3.88933e141	−0.799125
$446$	8.11901e140	0.147941
$447$	−1.39488e140	−0.0225468
$448$	8.32838e141	1.19450
$449$	1.26686e142	1.61268	0.806340	−	0.591453i	$-0.201445\pi$
$449$	1.26686e142	1.61268	0.806340	+	0.591453i	$0.201445\pi$
$450$	6.19896e140	0.0700567
$451$	−1.09770e142	−1.10164
$452$	5.44352e141	0.485259
$453$	2.80703e140	0.0222327
$454$	7.59642e140	0.0534713
$455$	−5.58960e141	−0.349761
$456$	8.49208e139	0.00472493
$457$	1.67590e142	0.829336	0.414668	−	0.909973i	$-0.363898\pi$
$457$	1.67590e142	0.829336	0.414668	+	0.909973i	$0.363898\pi$
$458$	−3.09192e141	−0.136121
$459$	1.11468e141	0.0436690
$460$	−1.28218e142	−0.447100
$461$	−4.34348e142	−1.34846	−0.674230	−	0.738521i	$-0.735524\pi$
$461$	−4.34348e142	−1.34846	−0.674230	+	0.738521i	$0.735524\pi$
$462$	1.11681e140	0.00308768
$463$	1.94165e142	0.478177	0.239089	−	0.970998i	$-0.423151\pi$
$463$	1.94165e142	0.478177	0.239089	+	0.970998i	$0.423151\pi$
$464$	−5.29096e142	−1.16097
$465$	9.14078e139	0.00178752
$466$	−4.72933e141	−0.0824429
$467$	−5.48383e141	−0.0852375	−0.0426187	−	0.999091i	$-0.513570\pi$
$467$	−5.48383e141	−0.0852375	−0.0426187	+	0.999091i	$0.513570\pi$
$468$	4.70458e142	0.652180
$469$	−1.03472e142	−0.127960
$470$	−1.74058e141	−0.0192069
$471$	−1.97447e140	−0.00194460
$472$	−1.02082e142	−0.0897537
$473$	2.66018e143	2.08853
$474$	2.96240e140	0.00207732
$475$	1.80296e143	1.12948
$476$	−2.41050e143	−1.34938
$477$	−1.73843e143	−0.869810
$478$	1.37774e142	0.0616275
$479$	2.74692e143	1.09874	0.549372	−	0.835578i	$-0.314867\pi$
$479$	2.74692e143	1.09874	0.549372	+	0.835578i	$0.314867\pi$
$480$	6.07861e140	0.00217469
$481$	−4.64012e142	−0.148514
$482$	2.49468e142	0.0714493
$483$	−1.03382e142	−0.0265018
$484$	−4.62576e143	−1.06159
$485$	1.43507e142	0.0294910
$486$	2.79920e141	0.00515220
$487$	−9.00443e143	−1.48476	−0.742381	−	0.669978i	$-0.766304\pi$
$487$	−9.00443e143	−1.48476	−0.742381	+	0.669978i	$0.766304\pi$
$488$	6.82507e142	0.100843
$489$	−9.58762e141	−0.0126966
$490$	1.72161e142	0.0204383
$491$	−1.10957e143	−0.118112	−0.0590562	−	0.998255i	$-0.518809\pi$
$491$	−1.10957e143	−0.118112	−0.0590562	+	0.998255i	$0.518809\pi$
$492$	−1.59791e142	−0.0152552
$493$	1.50833e144	1.29177
$494$	−1.01062e143	−0.0776597
$495$	8.88299e143	0.612606
$496$	3.30333e143	0.204495
$497$	−1.39335e144	−0.774448
$498$	4.51621e141	0.00225426
$499$	1.08381e144	0.485928	0.242964	−	0.970035i	$-0.421880\pi$
$499$	1.08381e144	0.485928	0.242964	+	0.970035i	$0.421880\pi$
$500$	1.90917e144	0.769041
$501$	6.81333e142	0.0246627
$502$	1.96463e143	0.0639191
$503$	1.77366e143	0.0518779	0.0259390	−	0.999664i	$-0.491742\pi$
$503$	1.77366e143	0.0518779	0.0259390	+	0.999664i	$0.491742\pi$
$504$	−8.10025e143	−0.213042
$505$	−7.14760e143	−0.169072
$506$	−6.11999e143	−0.130226
$507$	−5.95364e142	−0.0113987
$508$	5.49599e144	0.946973
$509$	−9.07312e144	−1.40720	−0.703599	−	0.710597i	$-0.748425\pi$
$509$	−9.07312e144	−1.40720	−0.703599	+	0.710597i	$0.748425\pi$
$510$	−5.70516e141	−0.000796643 0
$511$	−1.87018e145	−2.35160
$512$	3.67019e144	0.415668
$513$	5.42724e143	0.0553733
$514$	4.06197e143	0.0373431
$515$	9.90867e144	0.820973
$516$	3.87241e143	0.0289216
$517$	1.12485e145	0.757443
$518$	3.97994e143	0.0241676
$519$	−4.25599e143	−0.0233103
$520$	−9.66908e143	−0.0477756
$521$	−2.07774e145	−0.926346	−0.463173	−	0.886268i	$-0.653289\pi$
$521$	−2.07774e145	−0.926346	−0.463173	+	0.886268i	$0.653289\pi$
$522$	2.52497e144	0.101598
$523$	2.59401e145	0.942174	0.471087	−	0.882087i	$-0.343862\pi$
$523$	2.59401e145	0.942174	0.471087	+	0.882087i	$0.343862\pi$
$524$	4.49959e145	1.47553
$525$	6.92867e143	0.0205176
$526$	3.93922e143	0.0105359
$527$	−9.41701e144	−0.227533
$528$	−1.29333e144	−0.0282353
$529$	5.96758e144	0.117739
$530$	1.77988e144	0.0317418
$531$	−3.26135e145	−0.525824
$532$	−1.17364e146	−1.71105
$533$	3.81730e145	0.503327
$534$	−2.70238e143	−0.00322321
$535$	−4.12469e145	−0.445107
$536$	−1.78989e144	−0.0174787
$537$	−2.92596e144	−0.0258610
$538$	−1.88171e145	−0.150557
$539$	−1.11259e146	−0.806004
$540$	2.58670e144	0.0169699
$541$	2.65642e146	1.57850	0.789248	−	0.614075i	$-0.210471\pi$
$541$	2.65642e146	1.57850	0.789248	+	0.614075i	$0.210471\pi$
$542$	3.85373e144	0.0207453
$543$	−1.14223e144	−0.00557137
$544$	−6.26231e145	−0.276817
$545$	−1.02121e146	−0.409170
$546$	−3.88376e143	−0.00141074
$547$	5.82492e146	1.91853	0.959263	−	0.282515i	$-0.0911686\pi$
$547$	5.82492e146	1.91853	0.959263	+	0.282515i	$0.0911686\pi$
$548$	−3.75715e146	−1.12227
$549$	2.18049e146	0.590792
$550$	4.10160e145	0.100821
$551$	7.34384e146	1.63800
$552$	−1.78834e144	−0.00362001
$553$	−8.21855e146	−1.51008
$554$	−1.88645e145	−0.0314682
$555$	−1.27537e144	−0.00193180
$556$	4.83251e145	0.0664770
$557$	−3.87851e146	−0.484632	−0.242316	−	0.970197i	$-0.577907\pi$
$557$	−3.87851e146	−0.484632	−0.242316	+	0.970197i	$0.577907\pi$
$558$	−1.57643e145	−0.0178955
$559$	−9.25092e146	−0.954230
$560$	−5.55210e146	−0.520473
$561$	3.68697e145	0.0314164
$562$	2.03582e146	0.157705
$563$	7.22867e146	0.509166	0.254583	−	0.967051i	$-0.418062\pi$
$563$	7.22867e146	0.509166	0.254583	+	0.967051i	$0.418062\pi$
$564$	1.63743e145	0.0104889
$565$	−3.57431e146	−0.208257
$566$	9.37284e145	0.0496812
$567$	−2.58685e147	−1.24761
$568$	−2.41025e146	−0.105786
$569$	4.18022e147	1.66991	0.834956	−	0.550317i	$-0.185493\pi$
$569$	4.18022e147	1.66991	0.834956	+	0.550317i	$0.185493\pi$
$570$	−2.77776e144	−0.00101016
$571$	6.25416e146	0.207080	0.103540	−	0.994625i	$-0.466983\pi$
$571$	6.25416e146	0.207080	0.103540	+	0.994625i	$0.466983\pi$
$572$	3.11283e147	0.938572
$573$	9.31204e144	0.00255725
$574$	−3.27419e146	−0.0819063
$575$	−3.79684e147	−0.865351
$576$	4.60269e147	0.955893
$577$	4.47852e147	0.847673	0.423836	−	0.905739i	$-0.360683\pi$
$577$	4.47852e147	0.847673	0.423836	+	0.905739i	$0.360683\pi$
$578$	9.14602e145	0.0157795
$579$	−3.27612e145	−0.00515296
$580$	3.50018e147	0.501987
$581$	−1.25292e148	−1.63871
$582$	9.97112e143	0.000118950 0
$583$	−1.15025e148	−1.25177
$584$	−3.23509e147	−0.321218
$585$	−3.08911e147	−0.279894
$586$	8.98340e146	0.0742879
$587$	1.17847e148	0.889569	0.444784	−	0.895638i	$-0.353280\pi$
$587$	1.17847e148	0.889569	0.444784	+	0.895638i	$0.353280\pi$
$588$	−1.61959e146	−0.0111614
$589$	−4.58501e147	−0.288517
$590$	3.33911e146	0.0191888
$591$	−3.78437e146	−0.0198638
$592$	−4.60899e147	−0.221001
$593$	−1.88312e148	−0.824996	−0.412498	−	0.910959i	$-0.635344\pi$
$593$	−1.88312e148	−0.824996	−0.412498	+	0.910959i	$0.635344\pi$
$594$	1.23466e146	0.00494280
$595$	1.58277e148	0.579110
$596$	3.33474e148	1.11529
$597$	−5.36424e146	−0.0164014
$598$	2.12826e147	0.0594992
$599$	3.60066e148	0.920550	0.460275	−	0.887776i	$-0.347751\pi$
$599$	3.60066e148	0.920550	0.460275	+	0.887776i	$0.347751\pi$
$600$	1.19854e146	0.00280261
$601$	2.56861e148	0.549433	0.274716	−	0.961525i	$-0.411416\pi$
$601$	2.56861e148	0.549433	0.274716	+	0.961525i	$0.411416\pi$
$602$	7.93473e147	0.155282
$603$	−5.71838e147	−0.102399
$604$	−6.71074e148	−1.09975
$605$	3.03736e148	0.455599
$606$	−4.96628e145	−0.000681939 0
$607$	−3.99396e148	−0.502121	−0.251061	−	0.967971i	$-0.580779\pi$
$607$	−3.99396e148	−0.502121	−0.251061	+	0.967971i	$0.580779\pi$
$608$	−3.04903e148	−0.351011
$609$	2.82220e147	0.0297552
$610$	−2.23248e147	−0.0215597
$611$	−3.91172e148	−0.346069
$612$	−1.33217e149	−1.07983
$613$	1.02810e149	0.763658	0.381829	−	0.924233i	$-0.375294\pi$
$613$	1.02810e149	0.763658	0.381829	+	0.924233i	$0.375294\pi$
$614$	1.59781e148	0.108772
$615$	1.04921e147	0.00654705
$616$	−5.35961e148	−0.306595
$617$	−5.36508e148	−0.281397	−0.140699	−	0.990052i	$-0.544935\pi$
$617$	−5.36508e148	−0.281397	−0.140699	+	0.990052i	$0.544935\pi$
$618$	6.88472e146	0.00331133
$619$	−9.80775e148	−0.432633	−0.216316	−	0.976323i	$-0.569404\pi$
$619$	−9.80775e148	−0.432633	−0.216316	+	0.976323i	$0.569404\pi$
$620$	−2.18528e148	−0.0884202
$621$	−1.14292e148	−0.0424244
$622$	−1.74629e148	−0.0594746
$623$	7.49716e149	2.34308
$624$	4.49760e147	0.0129005
$625$	1.85528e149	0.488459
$626$	−8.30063e147	−0.0200625
$627$	1.79513e148	0.0398367
$628$	4.72034e148	0.0961906
$629$	1.31391e149	0.245899
$630$	2.64960e148	0.0455471
$631$	−6.50270e149	−1.02689	−0.513444	−	0.858123i	$-0.671630\pi$
$631$	−6.50270e149	−1.02689	−0.513444	+	0.858123i	$0.671630\pi$
$632$	−1.42167e149	−0.206270
$633$	−2.04674e148	−0.0272875
$634$	7.68951e148	0.0942157
$635$	−3.60876e149	−0.406409
$636$	−1.67441e148	−0.0173343
$637$	3.86910e149	0.368256
$638$	1.67067e149	0.146213
$639$	−7.70035e149	−0.619747
$640$	−1.93519e149	−0.143250
$641$	−2.17696e150	−1.48233	−0.741166	−	0.671322i	$-0.765727\pi$
$641$	−2.17696e150	−1.48233	−0.741166	+	0.671322i	$0.765727\pi$
$642$	−2.86591e147	−0.00179531
$643$	−1.48242e150	−0.854446	−0.427223	−	0.904146i	$-0.640508\pi$
$643$	−1.48242e150	−0.854446	−0.427223	+	0.904146i	$0.640508\pi$
$644$	2.47156e150	1.31092
$645$	−2.54269e148	−0.0124122
$646$	2.86171e149	0.128584
$647$	3.74915e150	1.55079	0.775397	−	0.631474i	$-0.217550\pi$
$647$	3.74915e150	1.55079	0.775397	+	0.631474i	$0.217550\pi$
$648$	−4.47482e149	−0.170417
$649$	−2.15790e150	−0.756729
$650$	−1.42635e149	−0.0460641
$651$	−1.76200e148	−0.00524109
$652$	2.29211e150	0.628042
$653$	7.80304e150	1.96974	0.984870	−	0.173295i	$-0.0554415\pi$
$653$	7.80304e150	1.96974	0.984870	+	0.173295i	$0.0554415\pi$
$654$	−7.09557e147	−0.00165036
$655$	−2.95451e150	−0.633250
$656$	3.79169e150	0.748992
$657$	−1.03356e151	−1.88186
$658$	3.35517e149	0.0563157
$659$	1.96756e150	0.304480	0.152240	−	0.988344i	$-0.451351\pi$
$659$	1.96756e150	0.304480	0.152240	+	0.988344i	$0.451351\pi$
$660$	8.55585e148	0.0122085
$661$	−2.76923e150	−0.364402	−0.182201	−	0.983261i	$-0.558322\pi$
$661$	−2.76923e150	−0.364402	−0.182201	+	0.983261i	$0.558322\pi$
$662$	−1.01589e150	−0.123294
$663$	−1.28216e149	−0.0143539
$664$	−2.16735e150	−0.223839
$665$	7.70630e150	0.734324
$666$	2.19952e149	0.0193400
$667$	−1.54654e151	−1.25495
$668$	−1.62886e151	−1.21995
$669$	5.01517e149	0.0346728
$670$	5.85473e148	0.00373684
$671$	1.44274e151	0.850227
$672$	−1.17173e149	−0.00637632
$673$	−7.04574e150	−0.354096	−0.177048	−	0.984202i	$-0.556655\pi$
$673$	−7.04574e150	−0.354096	−0.177048	+	0.984202i	$0.556655\pi$
$674$	2.98090e150	0.138370
$675$	7.65983e149	0.0328448
$676$	1.42333e151	0.563843
$677$	3.48582e151	1.27588	0.637941	−	0.770085i	$-0.279786\pi$
$677$	3.48582e151	1.27588	0.637941	+	0.770085i	$0.279786\pi$
$678$	−2.48349e148	−0.000839990 0
$679$	−2.76627e150	−0.0864692
$680$	2.73793e150	0.0791036
$681$	4.69236e149	0.0125320
$682$	−1.04306e150	−0.0257540
$683$	5.99023e151	1.36753	0.683763	−	0.729704i	$-0.260342\pi$
$683$	5.99023e151	1.36753	0.683763	+	0.729704i	$0.260342\pi$
$684$	−6.48613e151	−1.36925
$685$	2.46701e151	0.481643
$686$	2.60443e150	0.0470298
$687$	−1.90990e150	−0.0319025
$688$	−9.18885e151	−1.41997
$689$	4.00005e151	0.571923
$690$	5.84968e148	0.000773937 0
$691$	−3.15849e151	−0.386727	−0.193363	−	0.981127i	$-0.561940\pi$
$691$	−3.15849e151	−0.386727	−0.193363	+	0.981127i	$0.561940\pi$
$692$	1.01748e152	1.15305
$693$	−1.71230e152	−1.79619
$694$	−1.51522e150	−0.0147144
$695$	−3.17311e150	−0.0285297
$696$	4.88193e149	0.00406441
$697$	−1.08092e152	−0.833375
$698$	−1.11336e151	−0.0795006
$699$	−2.92134e150	−0.0193221
$700$	−1.65643e152	−1.01491
$701$	3.03901e152	1.72512	0.862558	−	0.505958i	$-0.168861\pi$
$701$	3.03901e152	1.72512	0.862558	+	0.505958i	$0.168861\pi$
$702$	−4.29360e149	−0.00225832
$703$	6.39726e151	0.311806
$704$	3.04542e152	1.37566
$705$	−1.07517e150	−0.00450150
$706$	−3.86251e151	−0.149906
$707$	1.37779e152	0.495728
$708$	−3.14124e150	−0.0104791
$709$	5.87102e151	0.181610	0.0908051	−	0.995869i	$-0.471056\pi$
$709$	5.87102e151	0.181610	0.0908051	+	0.995869i	$0.471056\pi$
$710$	7.88396e150	0.0226164
$711$	−4.54200e152	−1.20843
$712$	1.29688e152	0.320053
$713$	9.65555e151	0.221048
$714$	1.09974e150	0.00233580
$715$	−2.04394e152	−0.402804
$716$	6.99508e152	1.27922
$717$	8.51039e150	0.0144436
$718$	−4.20596e151	−0.0662533
$719$	−3.46365e152	−0.506452	−0.253226	−	0.967407i	$-0.581492\pi$
$719$	−3.46365e152	−0.506452	−0.253226	+	0.967407i	$0.581492\pi$
$720$	−3.06838e152	−0.416505
$721$	−1.91002e153	−2.40714
$722$	6.61609e151	0.0774215
$723$	1.54098e151	0.0167455
$724$	2.73072e152	0.275590
$725$	1.03649e153	0.971583
$726$	2.11041e150	0.00183763
$727$	−5.71687e152	−0.462452	−0.231226	−	0.972900i	$-0.574274\pi$
$727$	−5.71687e152	−0.462452	−0.231226	+	0.972900i	$0.574274\pi$
$728$	1.86383e152	0.140081
$729$	−1.42847e153	−0.997584
$730$	1.05820e152	0.0686744
$731$	2.61953e153	1.57995
$732$	2.10019e151	0.0117738
$733$	1.95444e153	1.01849	0.509247	−	0.860620i	$-0.329924\pi$
$733$	1.95444e153	1.01849	0.509247	+	0.860620i	$0.329924\pi$
$734$	−2.51782e152	−0.121979
$735$	1.06345e151	0.00479010
$736$	6.42094e152	0.268928
$737$	−3.78362e152	−0.147366
$738$	−1.80949e152	−0.0655450
$739$	−1.24615e153	−0.419849	−0.209924	−	0.977718i	$-0.567322\pi$
$739$	−1.24615e153	−0.419849	−0.209924	+	0.977718i	$0.567322\pi$
$740$	3.04902e152	0.0955573
$741$	−6.24266e151	−0.0182010
$742$	−3.43094e152	−0.0930688
$743$	6.87806e153	1.73606	0.868030	−	0.496512i	$-0.165386\pi$
$743$	6.87806e153	1.73606	0.868030	+	0.496512i	$0.165386\pi$
$744$	−3.04796e150	−0.000715908 0
$745$	−2.18964e153	−0.478644
$746$	−2.06277e152	−0.0419686
$747$	−6.92431e153	−1.31137
$748$	−8.81441e153	−1.55402
$749$	7.95085e153	1.30508
$750$	−8.71020e150	−0.00133122
$751$	−9.11976e153	−1.29792	−0.648958	−	0.760824i	$-0.724795\pi$
$751$	−9.11976e153	−1.29792	−0.648958	+	0.760824i	$0.724795\pi$
$752$	−3.88547e153	−0.514979
$753$	1.21356e152	0.0149807
$754$	−5.80986e152	−0.0668034
$755$	4.40638e153	0.471977
$756$	−4.98618e152	−0.0497567
$757$	1.27576e154	1.18615	0.593077	−	0.805146i	$-0.297913\pi$
$757$	1.27576e154	1.18615	0.593077	+	0.805146i	$0.297913\pi$
$758$	8.77497e152	0.0760227
$759$	−3.78036e152	−0.0305210
$760$	1.33306e153	0.100305
$761$	−7.99489e153	−0.560704	−0.280352	−	0.959897i	$-0.590451\pi$
$761$	−7.99489e153	−0.560704	−0.280352	+	0.959897i	$0.590451\pi$
$762$	−2.50743e151	−0.00163922
$763$	1.96851e154	1.19971
$764$	−2.22622e153	−0.126495
$765$	8.74723e153	0.463430
$766$	1.85768e152	0.00917763
$767$	7.50422e153	0.345743
$768$	4.33147e152	0.0186127
$769$	−1.51969e153	−0.0609111	−0.0304556	−	0.999536i	$-0.509696\pi$
$769$	−1.51969e153	−0.0609111	−0.0304556	+	0.999536i	$0.509696\pi$
$770$	1.75313e153	0.0655482
$771$	2.50911e152	0.00875207
$772$	7.83220e153	0.254893
$773$	−3.46967e154	−1.05362	−0.526812	−	0.849982i	$-0.676613\pi$
$773$	−3.46967e154	−1.05362	−0.526812	+	0.849982i	$0.676613\pi$
$774$	4.38514e153	0.124263
$775$	−6.47113e153	−0.171135
$776$	−4.78518e152	−0.0118113
$777$	2.45843e152	0.00566414
$778$	−5.14330e153	−0.110620
$779$	−5.26285e154	−1.05674
$780$	−2.97534e152	−0.00557796
$781$	−5.09501e154	−0.891898
$782$	−6.02646e153	−0.0985146
$783$	3.12002e153	0.0476324
$784$	3.84314e154	0.547995
$785$	−3.09946e153	−0.0412818
$786$	−2.05284e152	−0.00255417
$787$	1.90451e154	0.221379	0.110689	−	0.993855i	$-0.464694\pi$
$787$	1.90451e154	0.221379	0.110689	+	0.993855i	$0.464694\pi$
$788$	9.04726e154	0.982572
$789$	2.43328e152	0.00246929
$790$	4.65029e153	0.0440992
$791$	6.88991e154	0.610621
$792$	−2.96200e154	−0.245351
$793$	−5.01722e154	−0.388461
$794$	8.04236e153	0.0582086
$795$	1.09945e153	0.00743930
$796$	1.28242e155	0.811302
$797$	−3.86423e154	−0.228583	−0.114291	−	0.993447i	$-0.536460\pi$
$797$	−3.86423e154	−0.228583	−0.114291	+	0.993447i	$0.536460\pi$
$798$	5.35448e152	0.00296185
$799$	1.10766e155	0.572998
$800$	−4.30330e154	−0.208203
$801$	4.14332e155	1.87503
$802$	1.87561e154	0.0793988
$803$	−6.83863e155	−2.70824
$804$	−5.50779e152	−0.00204070
$805$	−1.62287e155	−0.562604
$806$	3.62729e153	0.0117668
$807$	−1.16234e154	−0.0352858
$808$	2.38334e154	0.0677140
$809$	−1.93291e155	−0.514002	−0.257001	−	0.966411i	$-0.582734\pi$
$809$	−1.93291e155	−0.514002	−0.257001	+	0.966411i	$0.582734\pi$
$810$	1.46371e154	0.0364341
$811$	1.93197e155	0.450179	0.225090	−	0.974338i	$-0.427733\pi$
$811$	1.93197e155	0.450179	0.225090	+	0.974338i	$0.427733\pi$
$812$	−6.74702e155	−1.47185
$813$	2.38048e153	0.00486205
$814$	1.45533e154	0.0278328
$815$	−1.50504e155	−0.269535
$816$	−1.27356e154	−0.0213597
$817$	1.27541e156	2.00341
$818$	6.72019e154	0.0988734
$819$	5.95463e155	0.820665
$820$	−2.50835e155	−0.323852
$821$	−7.23516e155	−0.875163	−0.437582	−	0.899179i	$-0.644165\pi$
$821$	−7.23516e155	−0.875163	−0.437582	+	0.899179i	$0.644165\pi$
$822$	1.71412e153	0.00194267
$823$	5.24262e155	0.556746	0.278373	−	0.960473i	$-0.410205\pi$
$823$	5.24262e155	0.556746	0.278373	+	0.960473i	$0.410205\pi$
$824$	−3.30401e155	−0.328803
$825$	2.53359e154	0.0236293
$826$	−6.43654e154	−0.0562626
$827$	1.58616e156	1.29958	0.649791	−	0.760113i	$-0.274857\pi$
$827$	1.58616e156	1.29958	0.649791	+	0.760113i	$0.274857\pi$
$828$	1.36591e156	1.04906
$829$	−5.29528e155	−0.381260	−0.190630	−	0.981662i	$-0.561053\pi$
$829$	−5.29528e155	−0.381260	−0.190630	+	0.981662i	$0.561053\pi$
$830$	7.08941e154	0.0478555
$831$	−1.16527e154	−0.00737517
$832$	−1.05906e156	−0.628525
$833$	−1.09559e156	−0.609733
$834$	−2.20473e152	−0.000115073 0
$835$	1.06954e156	0.523563
$836$	−4.29161e156	−1.97054
$837$	−1.94793e154	−0.00839000
$838$	−2.95841e155	−0.119537
$839$	−2.09491e156	−0.794147	−0.397074	−	0.917787i	$-0.629974\pi$
$839$	−2.09491e156	−0.794147	−0.397074	+	0.917787i	$0.629974\pi$
$840$	5.12289e153	0.00182210
$841$	1.22553e156	0.409014
$842$	−9.27346e154	−0.0290432
$843$	1.25754e155	0.0369612
$844$	4.89313e156	1.34979
$845$	−9.34584e155	−0.241983
$846$	1.85424e155	0.0450663
$847$	−5.85487e156	−1.33584
$848$	3.97322e156	0.851067
$849$	5.78967e154	0.0116437
$850$	4.03892e155	0.0762698
$851$	−1.34720e156	−0.238891
$852$	−7.41677e154	−0.0123508
$853$	7.72047e156	1.20745	0.603727	−	0.797191i	$-0.293682\pi$
$853$	7.72047e156	1.20745	0.603727	+	0.797191i	$0.293682\pi$
$854$	4.30338e155	0.0632141
$855$	4.25890e156	0.587639
$856$	1.37536e156	0.178267
$857$	−8.97001e155	−0.109224	−0.0546121	−	0.998508i	$-0.517392\pi$
$857$	−8.97001e155	−0.109224	−0.0546121	+	0.998508i	$0.517392\pi$
$858$	−1.42016e154	−0.00162468
$859$	−3.30033e155	−0.0354750	−0.0177375	−	0.999843i	$-0.505646\pi$
$859$	−3.30033e155	−0.0354750	−0.0177375	+	0.999843i	$0.505646\pi$
$860$	6.07879e156	0.613974
$861$	−2.02249e155	−0.0191963
$862$	−3.68355e155	−0.0328570
$863$	−1.27368e157	−1.06778	−0.533892	−	0.845553i	$-0.679271\pi$
$863$	−1.27368e157	−1.06778	−0.533892	+	0.845553i	$0.679271\pi$
$864$	−1.29537e155	−0.0102073
$865$	−6.68093e156	−0.494852
$866$	−5.46443e155	−0.0380485
$867$	5.64956e154	0.00369822
$868$	4.21239e156	0.259253
$869$	−3.00526e157	−1.73910
$870$	−1.59688e154	−0.000868947 0
$871$	1.31577e156	0.0673303
$872$	3.40520e156	0.163874
$873$	−1.52878e156	−0.0691965
$874$	−2.93420e156	−0.124919
$875$	2.41645e157	0.967716
$876$	−9.95493e155	−0.0375032
$877$	−5.58705e156	−0.198018	−0.0990089	−	0.995087i	$-0.531567\pi$
$877$	−5.58705e156	−0.198018	−0.0990089	+	0.995087i	$0.531567\pi$
$878$	−1.31493e156	−0.0438477
$879$	5.54911e155	0.0174108
$880$	−2.03022e157	−0.599406
$881$	3.19791e157	0.888494	0.444247	−	0.895904i	$-0.353471\pi$
$881$	3.19791e157	0.888494	0.444247	+	0.895904i	$0.353471\pi$
$882$	−1.83404e156	−0.0479556
$883$	−8.33833e156	−0.205202	−0.102601	−	0.994723i	$-0.532716\pi$
$883$	−8.33833e156	−0.205202	−0.102601	+	0.994723i	$0.532716\pi$
$884$	3.06526e157	0.710020
$885$	2.06259e155	0.00449726
$886$	9.47091e155	0.0194396
$887$	8.91329e157	1.72236	0.861180	−	0.508299i	$-0.169726\pi$
$887$	8.91329e157	1.72236	0.861180	+	0.508299i	$0.169726\pi$
$888$	4.25268e154	0.000773694 0
$889$	6.95633e157	1.19161
$890$	−4.24211e156	−0.0684253
$891$	−9.45927e157	−1.43681
$892$	−1.19897e158	−1.71510
$893$	5.39303e157	0.726574
$894$	−1.52140e155	−0.00193058
$895$	−4.59309e157	−0.549000
$896$	3.73031e157	0.420016
$897$	1.31464e156	0.0139448
$898$	1.38177e157	0.138086
$899$	−2.63583e157	−0.248184
$900$	−9.15431e157	−0.812178
$901$	−1.13267e158	−0.946950
$902$	−1.19726e157	−0.0943279
$903$	4.90134e156	0.0363932
$904$	1.19184e157	0.0834078
$905$	−1.79303e157	−0.118274
$906$	3.06164e155	0.00190368
$907$	2.21271e158	1.29698	0.648491	−	0.761223i	$-0.275401\pi$
$907$	2.21271e158	1.29698	0.648491	+	0.761223i	$0.275401\pi$
$908$	−1.12180e158	−0.619901
$909$	7.61436e157	0.396703
$910$	−6.09661e156	−0.0299484
$911$	2.24546e158	1.04009	0.520047	−	0.854138i	$-0.325915\pi$
$911$	2.24546e158	1.04009	0.520047	+	0.854138i	$0.325915\pi$
$912$	−6.20078e156	−0.0270846
$913$	−4.58154e158	−1.88723
$914$	1.82791e157	0.0710122
$915$	−1.37902e156	−0.00505292
$916$	4.56598e158	1.57807
$917$	5.69517e158	1.85672
$918$	1.21579e156	0.00373917
$919$	−2.86135e158	−0.830216	−0.415108	−	0.909772i	$-0.636256\pi$
$919$	−2.86135e158	−0.830216	−0.415108	+	0.909772i	$0.636256\pi$
$920$	−2.80729e157	−0.0768490
$921$	9.86980e156	0.0254928
$922$	−4.73745e157	−0.115462
$923$	1.77182e158	0.407500
$924$	−1.64924e157	−0.0357960
$925$	9.02888e157	0.184949
$926$	2.11777e157	0.0409441
$927$	−1.05557e159	−1.92630
$928$	−1.75283e158	−0.301941
$929$	−1.76828e158	−0.287548	−0.143774	−	0.989611i	$-0.545924\pi$
$929$	−1.76828e158	−0.287548	−0.143774	+	0.989611i	$0.545924\pi$
$930$	9.96989e154	0.000153057 0
$931$	−5.33426e158	−0.773155
$932$	6.98404e158	0.955774
$933$	−1.07870e157	−0.0139390
$934$	−5.98123e156	−0.00729849
$935$	5.78769e158	0.666936
$936$	1.03005e158	0.112099
$937$	−1.39516e159	−1.43402	−0.717012	−	0.697061i	$-0.754491\pi$
$937$	−1.39516e159	−1.43402	−0.717012	+	0.697061i	$0.754491\pi$
$938$	−1.12857e157	−0.0109566
$939$	−5.12736e156	−0.00470202
$940$	2.57039e158	0.222669
$941$	−5.43210e158	−0.444553	−0.222276	−	0.974984i	$-0.571349\pi$
$941$	−5.43210e158	−0.444553	−0.222276	+	0.974984i	$0.571349\pi$
$942$	−2.15356e155	−0.000166507 0
$943$	1.10830e159	0.809622
$944$	7.45387e158	0.514494
$945$	3.27401e157	0.0213539
$946$	2.90147e158	0.178831
$947$	2.22909e158	0.129838	0.0649192	−	0.997891i	$-0.479321\pi$
$947$	2.22909e158	0.129838	0.0649192	+	0.997891i	$0.479321\pi$
$948$	−4.37473e157	−0.0240827
$949$	2.37817e159	1.23737
$950$	1.96649e158	0.0967118
$951$	4.74986e157	0.0220812
$952$	−5.27770e158	−0.231936
$953$	1.54656e159	0.642534	0.321267	−	0.946989i	$-0.395891\pi$
$953$	1.54656e159	0.642534	0.321267	+	0.946989i	$0.395891\pi$
$954$	−1.89611e158	−0.0744777
$955$	1.46178e158	0.0542876
$956$	−2.03457e159	−0.714457
$957$	1.03199e158	0.0342678
$958$	2.99608e158	0.0940803
$959$	−4.75546e159	−1.41220
$960$	−2.91091e157	−0.00817556
$961$	−3.59988e159	−0.956285
$962$	−5.06100e157	−0.0127166
$963$	4.39405e159	1.04438
$964$	−3.68401e159	−0.828323
$965$	−5.14276e158	−0.109392
$966$	−1.12760e157	−0.00226923
$967$	3.57589e159	0.680875	0.340438	−	0.940267i	$-0.389425\pi$
$967$	3.57589e159	0.680875	0.340438	+	0.940267i	$0.389425\pi$
$968$	−1.01279e159	−0.182469
$969$	1.76770e158	0.0301360
$970$	1.56524e157	0.00252518
$971$	−5.14704e159	−0.785831	−0.392915	−	0.919575i	$-0.628533\pi$
$971$	−5.14704e159	−0.785831	−0.392915	+	0.919575i	$0.628533\pi$
$972$	−4.13371e158	−0.0597303
$973$	6.11655e158	0.0836507
$974$	−9.82118e158	−0.127133
$975$	−8.81069e157	−0.0107960
$976$	−4.98356e159	−0.578062
$977$	9.88361e159	1.08532	0.542658	−	0.839954i	$-0.317418\pi$
$977$	9.88361e159	1.08532	0.542658	+	0.839954i	$0.317418\pi$
$978$	−1.04573e157	−0.00108715
$979$	2.74147e160	2.69842
$980$	−2.54239e159	−0.236944
$981$	1.08790e160	0.960059
$982$	−1.21022e158	−0.0101134
$983$	−1.74116e160	−1.37793	−0.688963	−	0.724797i	$-0.741934\pi$
$983$	−1.74116e160	−1.37793	−0.688963	+	0.724797i	$0.741934\pi$
$984$	−3.49857e157	−0.00262212
$985$	−5.94058e159	−0.421688
$986$	1.64514e159	0.110608
$987$	2.07251e158	0.0131987
$988$	1.49243e160	0.900321
$989$	−2.68588e160	−1.53492
$990$	9.68872e158	0.0524546
$991$	1.29070e159	0.0662038	0.0331019	−	0.999452i	$-0.489461\pi$
$991$	1.29070e159	0.0662038	0.0331019	+	0.999452i	$0.489461\pi$
$992$	1.09435e159	0.0531841
$993$	−6.27521e158	−0.0288964
$994$	−1.51973e159	−0.0663123
$995$	−8.42062e159	−0.348184
$996$	−6.66930e158	−0.0261340
$997$	−3.68333e160	−1.36789	−0.683943	−	0.729535i	$-0.739736\pi$
$997$	−3.68333e160	−1.36789	−0.683943	+	0.729535i	$0.739736\pi$
$998$	1.18211e159	0.0416078
$999$	2.71787e158	0.00906722

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.108.a.a.1.5	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.108.a.a.1.5	✓	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)

\(f(q)\)	\(=\)	\(q+1.09070e15 q^{2} +6.73736e23 q^{3} -1.61070e32 q^{4} +1.05761e37 q^{5} +7.34847e38 q^{6} -2.03867e45 q^{7} -3.52656e47 q^{8} -1.12668e51 q^{9} +O(q^{10})\)	\(q+1.09070e15 q^{2} +6.73736e23 q^{3} -1.61070e32 q^{4} +1.05761e37 q^{5} +7.34847e38 q^{6} -2.03867e45 q^{7} -3.52656e47 q^{8} -1.12668e51 q^{9} +1.15354e52 q^{10} -7.45477e55 q^{11} -1.08518e56 q^{12} +2.59243e59 q^{13} -2.22359e60 q^{14} +7.12550e60 q^{15} +2.57504e64 q^{16} -7.34083e65 q^{17} -1.22887e66 q^{18} -3.57415e68 q^{19} -1.70349e69 q^{20} -1.37353e69 q^{21} -8.13095e70 q^{22} +7.52678e72 q^{23} -2.37597e71 q^{24} -5.04444e74 q^{25} +2.82758e74 q^{26} -1.51847e75 q^{27} +3.28368e77 q^{28} -2.05471e78 q^{29} +7.77182e75 q^{30} +1.28283e79 q^{31} +8.53078e79 q^{32} -5.02254e79 q^{33} -8.00668e80 q^{34} -2.15612e82 q^{35} +1.81473e83 q^{36} -1.78987e83 q^{37} -3.89834e83 q^{38} +1.74662e83 q^{39} -3.72973e84 q^{40} +1.47248e86 q^{41} -1.49811e84 q^{42} -3.56843e87 q^{43} +1.20074e88 q^{44} -1.19159e88 q^{45} +8.20950e87 q^{46} -1.50890e89 q^{47} +1.73490e88 q^{48} +1.49246e90 q^{49} -5.50199e89 q^{50} -4.94578e89 q^{51} -4.17562e91 q^{52} +1.54297e92 q^{53} -1.65620e90 q^{54} -7.88424e92 q^{55} +7.18951e92 q^{56} -2.40803e92 q^{57} -2.24108e93 q^{58} +2.89466e94 q^{59} -1.14770e93 q^{60} -1.93533e95 q^{61} +1.39918e94 q^{62} +2.29693e96 q^{63} -4.08520e96 q^{64} +2.74178e96 q^{65} -5.47811e94 q^{66} +5.07544e96 q^{67} +1.18239e98 q^{68} +5.07106e96 q^{69} -2.35169e97 q^{70} +6.83457e98 q^{71} +3.97330e98 q^{72} +9.17350e99 q^{73} -1.95222e98 q^{74} -3.39862e98 q^{75} +5.75687e100 q^{76} +1.51978e101 q^{77} +1.90504e98 q^{78} +4.03132e101 q^{79} +2.72339e101 q^{80} +1.26889e102 q^{81} +1.60604e101 q^{82} +6.14578e102 q^{83} +2.21234e101 q^{84} -7.76374e102 q^{85} -3.89211e102 q^{86} -1.38433e102 q^{87} +2.62897e103 q^{88} -3.67747e104 q^{89} -1.29967e103 q^{90} -5.28512e104 q^{91} -1.21234e105 q^{92} +8.64286e102 q^{93} -1.64576e104 q^{94} -3.78006e105 q^{95} +5.74750e103 q^{96} +1.35690e105 q^{97} +1.62783e105 q^{98} +8.39911e106 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 54\!\cdots\!96 q^{2}+ \cdots + 36\!\cdots\!13 q^{9}+O(q^{10}) \) 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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