LMFDB - Embedded newform 1.108.a.a.1.3

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			1.3
Root			$4.82720e14$ 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)

$f(q)$	$=$	$q-1.09780e16 q^{2} -5.69800e25 q^{3} -4.17435e31 q^{4} +2.81503e36 q^{5} +6.25524e41 q^{6} +3.42403e44 q^{7} +2.23954e48 q^{8} +2.11959e51 q^{9} +O(q^{10})$	\(q-1.09780e16 q^{2} -5.69800e25 q^{3} -4.17435e31 q^{4} +2.81503e36 q^{5} +6.25524e41 q^{6} +3.42403e44 q^{7} +2.23954e48 q^{8} +2.11959e51 q^{9} -3.09033e52 q^{10} +2.99607e55 q^{11} +2.37854e57 q^{12} +6.92627e59 q^{13} -3.75889e60 q^{14} -1.60400e62 q^{15} -1.78123e64 q^{16} +1.03294e66 q^{17} -2.32688e67 q^{18} +7.83862e67 q^{19} -1.17509e68 q^{20} -1.95101e70 q^{21} -3.28908e71 q^{22} +3.41145e72 q^{23} -1.27609e74 q^{24} -6.08373e74 q^{25} -7.60364e75 q^{26} -5.65502e76 q^{27} -1.42931e76 q^{28} +1.31728e78 q^{29} +1.76087e78 q^{30} +1.11826e80 q^{31} -1.67843e80 q^{32} -1.70716e81 q^{33} -1.13396e82 q^{34} +9.63873e80 q^{35} -8.84789e82 q^{36} +7.06400e83 q^{37} -8.60521e83 q^{38} -3.94659e85 q^{39} +6.30435e84 q^{40} -2.42080e86 q^{41} +2.14181e86 q^{42} +3.45013e87 q^{43} -1.25066e87 q^{44} +5.96669e87 q^{45} -3.74508e88 q^{46} +1.83633e89 q^{47} +1.01494e90 q^{48} -2.54649e90 q^{49} +6.67870e90 q^{50} -5.88568e91 q^{51} -2.89127e91 q^{52} +1.73504e92 q^{53} +6.20806e92 q^{54} +8.43402e91 q^{55} +7.66824e92 q^{56} -4.46644e93 q^{57} -1.44611e94 q^{58} +1.65099e94 q^{59} +6.69566e93 q^{60} +2.05126e95 q^{61} -1.22762e96 q^{62} +7.25753e95 q^{63} +4.73278e96 q^{64} +1.94976e96 q^{65} +1.87412e97 q^{66} -8.20998e96 q^{67} -4.31184e97 q^{68} -1.94385e98 q^{69} -1.05814e97 q^{70} +1.83246e99 q^{71} +4.74689e99 q^{72} +2.72339e99 q^{73} -7.75484e99 q^{74} +3.46651e100 q^{75} -3.27211e99 q^{76} +1.02586e100 q^{77} +4.33255e101 q^{78} +2.64195e101 q^{79} -5.01421e100 q^{80} +8.33175e101 q^{81} +2.65755e102 q^{82} +5.13406e102 q^{83} +8.14420e101 q^{84} +2.90775e102 q^{85} -3.78754e103 q^{86} -7.50587e103 q^{87} +6.70981e103 q^{88} -1.30053e104 q^{89} -6.55022e103 q^{90} +2.37158e104 q^{91} -1.42406e104 q^{92} -6.37183e105 q^{93} -2.01592e105 q^{94} +2.20659e104 q^{95} +9.56367e105 q^{96} +2.53729e105 q^{97} +2.79553e106 q^{98} +6.35044e106 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.09780e16	−0.861821	−0.430911	−	0.902395i	$-0.641808\pi$
$2$	−1.09780e16	−0.861821	−0.430911	+	0.902395i	$0.641808\pi$
$3$	−5.69800e25	−1.69721	−0.848604	−	0.529028i	$-0.822557\pi$
$3$	−5.69800e25	−1.69721	−0.848604	+	0.529028i	$0.822557\pi$
$4$	−4.17435e31	−0.257264
$5$	2.81503e36	0.113393	0.0566966	−	0.998391i	$-0.481943\pi$
$5$	2.81503e36	0.113393	0.0566966	+	0.998391i	$0.481943\pi$
$6$	6.25524e41	1.46269
$7$	3.42403e44	0.209794	0.104897	−	0.994483i	$-0.466549\pi$
$7$	3.42403e44	0.209794	0.104897	+	0.994483i	$0.466549\pi$
$8$	2.23954e48	1.08354
$9$	2.11959e51	1.88052
$10$	−3.09033e52	−0.0977247
$11$	2.99607e55	0.578154	0.289077	−	0.957306i	$-0.406652\pi$
$11$	2.99607e55	0.578154	0.289077	+	0.957306i	$0.406652\pi$
$12$	2.37854e57	0.436631
$13$	6.92627e59	1.75602	0.878011	−	0.478640i	$-0.158870\pi$
$13$	6.92627e59	1.75602	0.878011	+	0.478640i	$0.158870\pi$
$14$	−3.75889e60	−0.180805
$15$	−1.60400e62	−0.192452
$16$	−1.78123e64	−0.676551
$17$	1.03294e66	1.53129	0.765644	−	0.643265i	$-0.222420\pi$
$17$	1.03294e66	1.53129	0.765644	+	0.643265i	$0.222420\pi$
$18$	−2.32688e67	−1.62067
$19$	7.83862e67	0.302637	0.151318	−	0.988485i	$-0.451648\pi$
$19$	7.83862e67	0.302637	0.151318	+	0.988485i	$0.451648\pi$
$20$	−1.17509e68	−0.0291720
$21$	−1.95101e70	−0.356064
$22$	−3.28908e71	−0.498266
$23$	3.41145e72	0.479182	0.239591	−	0.970874i	$-0.422987\pi$
$23$	3.41145e72	0.479182	0.239591	+	0.970874i	$0.422987\pi$
$24$	−1.27609e74	−1.83899
$25$	−6.08373e74	−0.987142
$26$	−7.60364e75	−1.51338
$27$	−5.65502e76	−1.49442
$28$	−1.42931e76	−0.0539724
$29$	1.31728e78	0.761002	0.380501	−	0.924781i	$-0.375752\pi$
$29$	1.31728e78	0.761002	0.380501	+	0.924781i	$0.375752\pi$
$30$	1.76087e78	0.165859
$31$	1.11826e80	1.82260	0.911300	−	0.411744i	$-0.135080\pi$
$31$	1.11826e80	1.82260	0.911300	+	0.411744i	$0.135080\pi$
$32$	−1.67843e80	−0.500471
$33$	−1.70716e81	−0.981248
$34$	−1.13396e82	−1.31970
$35$	9.63873e80	0.0237892
$36$	−8.84789e82	−0.483789
$37$	7.06400e83	0.891782	0.445891	−	0.895087i	$-0.352887\pi$
$37$	7.06400e83	0.891782	0.445891	+	0.895087i	$0.352887\pi$
$38$	−8.60521e83	−0.260819
$39$	−3.94659e85	−2.98034
$40$	6.30435e84	0.122866
$41$	−2.42080e86	−1.25899	−0.629496	−	0.777004i	$-0.716739\pi$
$41$	−2.42080e86	−1.25899	−0.629496	+	0.777004i	$0.716739\pi$
$42$	2.14181e86	0.306863
$43$	3.45013e87	1.40370	0.701848	−	0.712326i	$-0.252358\pi$
$43$	3.45013e87	1.40370	0.701848	+	0.712326i	$0.252358\pi$
$44$	−1.25066e87	−0.148738
$45$	5.96669e87	0.213238
$46$	−3.74508e88	−0.412969
$47$	1.83633e89	0.640790	0.320395	−	0.947284i	$-0.396184\pi$
$47$	1.83633e89	0.640790	0.320395	+	0.947284i	$0.396184\pi$
$48$	1.01494e90	1.14825
$49$	−2.54649e90	−0.955987
$50$	6.67870e90	0.850740
$51$	−5.88568e91	−2.59891
$52$	−2.89127e91	−0.451761
$53$	1.73504e92	0.978475	0.489238	−	0.872150i	$-0.337275\pi$
$53$	1.73504e92	0.978475	0.489238	+	0.872150i	$0.337275\pi$
$54$	6.20806e92	1.28792
$55$	8.43402e91	0.0655588
$56$	7.66824e92	0.227319
$57$	−4.46644e93	−0.513638
$58$	−1.44611e94	−0.655848
$59$	1.65099e94	0.300027	0.150014	−	0.988684i	$-0.452068\pi$
$59$	1.65099e94	0.300027	0.150014	+	0.988684i	$0.452068\pi$
$60$	6.69566e93	0.0495109
$61$	2.05126e95	0.626433	0.313217	−	0.949682i	$-0.398593\pi$
$61$	2.05126e95	0.626433	0.313217	+	0.949682i	$0.398593\pi$
$62$	−1.22762e96	−1.57076
$63$	7.25753e95	0.394520
$64$	4.73278e96	1.10787
$65$	1.94976e96	0.199121
$66$	1.87412e97	0.845661
$67$	−8.20998e96	−0.165707	−0.0828534	−	0.996562i	$-0.526403\pi$
$67$	−8.20998e96	−0.165707	−0.0828534	+	0.996562i	$0.526403\pi$
$68$	−4.31184e97	−0.393945
$69$	−1.94385e98	−0.813272
$70$	−1.05814e97	−0.0205020
$71$	1.83246e99	1.66232	0.831159	−	0.556035i	$-0.187678\pi$
$71$	1.83246e99	1.66232	0.831159	+	0.556035i	$0.187678\pi$
$72$	4.74689e99	2.03761
$73$	2.72339e99	0.558903	0.279451	−	0.960160i	$-0.409847\pi$
$73$	2.72339e99	0.558903	0.279451	+	0.960160i	$0.409847\pi$
$74$	−7.75484e99	−0.768557
$75$	3.46651e100	1.67539
$76$	−3.27211e99	−0.0778575
$77$	1.02586e100	0.121293
$78$	4.33255e101	2.56852
$79$	2.64195e101	0.792275	0.396137	−	0.918191i	$-0.370350\pi$
$79$	2.64195e101	0.792275	0.396137	+	0.918191i	$0.370350\pi$
$80$	−5.01421e100	−0.0767163
$81$	8.33175e101	0.655825
$82$	2.65755e102	1.08503
$83$	5.13406e102	1.09593	0.547966	−	0.836501i	$-0.315402\pi$
$83$	5.13406e102	1.09593	0.547966	+	0.836501i	$0.315402\pi$
$84$	8.14420e101	0.0916023
$85$	2.90775e102	0.173638
$86$	−3.78754e103	−1.20974
$87$	−7.50587e103	−1.29158
$88$	6.70981e103	0.626452
$89$	−1.30053e104	−0.663367	−0.331683	−	0.943391i	$-0.607617\pi$
$89$	−1.30053e104	−0.663367	−0.331683	+	0.943391i	$0.607617\pi$
$90$	−6.55022e103	−0.183773
$91$	2.37158e104	0.368403
$92$	−1.42406e104	−0.123276
$93$	−6.37183e105	−3.09333
$94$	−2.01592e105	−0.552246
$95$	2.20659e104	0.0343170
$96$	9.56367e105	0.849403
$97$	2.53729e105	0.129444	0.0647220	−	0.997903i	$-0.479384\pi$
$97$	2.53729e105	0.129444	0.0647220	+	0.997903i	$0.479384\pi$
$98$	2.79553e106	0.823890
$99$	6.35044e106	1.08723
$100$	2.53956e106	0.253956
$101$	−1.92532e107	−1.13060	−0.565300	−	0.824886i	$-0.691239\pi$
$101$	−1.92532e107	−1.13060	−0.565300	+	0.824886i	$0.691239\pi$
$102$	6.46128e107	2.23980
$103$	−5.50821e107	−1.13297	−0.566486	−	0.824071i	$-0.691697\pi$
$103$	−5.50821e107	−1.13297	−0.566486	+	0.824071i	$0.691697\pi$
$104$	1.55116e108	1.90272
$105$	−5.49215e106	−0.0403752
$106$	−1.90472e108	−0.843271
$107$	−3.89699e108	−1.04399	−0.521996	−	0.852948i	$-0.674813\pi$
$107$	−3.89699e108	−1.04399	−0.521996	+	0.852948i	$0.674813\pi$
$108$	2.36060e108	0.384460
$109$	2.06192e108	0.205094	0.102547	−	0.994728i	$-0.467301\pi$
$109$	2.06192e108	0.205094	0.102547	+	0.994728i	$0.467301\pi$
$110$	−9.25884e107	−0.0565000
$111$	−4.02507e109	−1.51354
$112$	−6.09898e108	−0.141936
$113$	−1.19230e110	−1.72460	−0.862298	−	0.506401i	$-0.830976\pi$
$113$	−1.19230e110	−1.72460	−0.862298	+	0.506401i	$0.830976\pi$
$114$	4.90325e109	0.442664
$115$	9.60333e108	0.0543360
$116$	−5.49879e109	−0.195778
$117$	1.46808e111	3.30223
$118$	−1.81245e110	−0.258570
$119$	3.53681e110	0.321255
$120$	−3.59222e110	−0.208529
$121$	−1.78781e111	−0.665738
$122$	−2.25187e111	−0.539874
$123$	1.37937e112	2.13677
$124$	−4.66799e111	−0.468889
$125$	−3.44748e111	−0.225328
$126$	−7.96730e111	−0.340006
$127$	−2.48285e110	−0.00694148	−0.00347074	−	0.999994i	$-0.501105\pi$
$127$	−2.48285e110	−0.00694148	−0.00347074	+	0.999994i	$0.501105\pi$
$128$	−2.47223e112	−0.454313
$129$	−1.96588e113	−2.38237
$130$	−2.14044e112	−0.171607
$131$	1.83329e113	0.975478	0.487739	−	0.872990i	$-0.337822\pi$
$131$	1.83329e113	0.975478	0.487739	+	0.872990i	$0.337822\pi$
$132$	7.12628e112	0.252440
$133$	2.68397e112	0.0634913
$134$	9.01289e112	0.142810
$135$	−1.59190e113	−0.169457
$136$	2.31330e114	1.65921
$137$	−5.34864e113	−0.259235	−0.129617	−	0.991564i	$-0.541375\pi$
$137$	−5.34864e113	−0.259235	−0.129617	+	0.991564i	$0.541375\pi$
$138$	2.13395e114	0.700895
$139$	4.09989e114	0.915125	0.457562	−	0.889178i	$-0.348723\pi$
$139$	4.09989e114	0.915125	0.457562	+	0.889178i	$0.348723\pi$
$140$	−4.02354e112	−0.00612010
$141$	−1.04634e115	−1.08755
$142$	−2.01167e115	−1.43262
$143$	2.07516e115	1.01525
$144$	−3.77547e115	−1.27227
$145$	3.70818e114	0.0862925
$146$	−2.98972e115	−0.481674
$147$	1.45099e116	1.62251
$148$	−2.94876e115	−0.229423
$149$	−2.16962e116	−1.17739	−0.588693	−	0.808357i	$-0.700357\pi$
$149$	−2.16962e116	−1.17739	−0.588693	+	0.808357i	$0.700357\pi$
$150$	−3.80552e116	−1.44388
$151$	9.53642e115	0.253582	0.126791	−	0.991929i	$-0.459532\pi$
$151$	9.53642e115	0.253582	0.126791	+	0.991929i	$0.459532\pi$
$152$	1.75549e116	0.327918
$153$	2.18940e117	2.87961
$154$	−1.12619e116	−0.104533
$155$	3.14792e116	0.206670
$156$	1.64744e117	0.766733
$157$	4.45332e116	0.147249	0.0736245	−	0.997286i	$-0.476543\pi$
$157$	4.45332e116	0.147249	0.0736245	+	0.997286i	$0.476543\pi$
$158$	−2.90033e117	−0.682799
$159$	−9.88624e117	−1.66068
$160$	−4.72481e116	−0.0567500
$161$	1.16809e117	0.100529
$162$	−9.14657e117	−0.565204
$163$	−8.85902e116	−0.0393866	−0.0196933	−	0.999806i	$-0.506269\pi$
$163$	−8.85902e116	−0.0393866	−0.0196933	+	0.999806i	$0.506269\pi$
$164$	1.01053e118	0.323893
$165$	−4.80570e117	−0.111267
$166$	−5.63616e118	−0.944497
$167$	2.76682e118	0.336240	0.168120	−	0.985767i	$-0.446230\pi$
$167$	2.76682e118	0.336240	0.168120	+	0.985767i	$0.446230\pi$
$168$	−4.36936e118	−0.385808
$169$	3.24158e119	2.08362
$170$	−3.19212e118	−0.149645
$171$	1.66146e119	0.569113
$172$	−1.44020e119	−0.361121
$173$	−2.15319e119	−0.395928	−0.197964	−	0.980209i	$-0.563433\pi$
$173$	−2.15319e119	−0.395928	−0.197964	+	0.980209i	$0.563433\pi$
$174$	8.23992e119	1.11311
$175$	−2.08309e119	−0.207096
$176$	−5.33669e119	−0.391151
$177$	−9.40731e119	−0.509209
$178$	1.42771e120	0.571704
$179$	−8.02574e119	−0.238149	−0.119074	−	0.992885i	$-0.537993\pi$
$179$	−8.02574e119	−0.238149	−0.119074	+	0.992885i	$0.537993\pi$
$180$	−2.49070e119	−0.0548584
$181$	−1.05652e121	−1.73011	−0.865056	−	0.501675i	$-0.832717\pi$
$181$	−1.05652e121	−1.73011	−0.865056	+	0.501675i	$0.832717\pi$
$182$	−2.60351e120	−0.317497
$183$	−1.16881e121	−1.06319
$184$	7.64008e120	0.519211
$185$	1.98854e120	0.101122
$186$	6.99497e121	2.66590
$187$	3.09476e121	0.885321
$188$	−7.66548e120	−0.164852
$189$	−1.93629e121	−0.313520
$190$	−2.42239e120	−0.0295751
$191$	4.81943e121	0.444335	0.222168	−	0.975008i	$-0.428687\pi$
$191$	4.81943e121	0.444335	0.222168	+	0.975008i	$0.428687\pi$
$192$	−2.69674e122	−1.88028
$193$	1.29032e122	0.681366	0.340683	−	0.940178i	$-0.389342\pi$
$193$	1.29032e122	0.681366	0.340683	+	0.940178i	$0.389342\pi$
$194$	−2.78543e121	−0.111558
$195$	−1.11097e122	−0.337950
$196$	1.06299e122	0.245941
$197$	7.01406e122	1.23602	0.618011	−	0.786169i	$-0.287939\pi$
$197$	7.01406e122	1.23602	0.618011	+	0.786169i	$0.287939\pi$
$198$	−6.97149e122	−0.936997
$199$	−1.43459e123	−1.47261	−0.736304	−	0.676650i	$-0.763431\pi$
$199$	−1.43459e123	−1.47261	−0.736304	+	0.676650i	$0.763431\pi$
$200$	−1.36247e123	−1.06960
$201$	4.67804e122	0.281239
$202$	2.11361e123	0.974375
$203$	4.51041e122	0.159653
$204$	2.45689e123	0.668607
$205$	−6.81462e122	−0.142761
$206$	6.04690e123	0.976419
$207$	7.23088e123	0.901109
$208$	−1.23373e124	−1.18804
$209$	2.34851e123	0.174971
$210$	6.02926e122	0.0347962
$211$	3.18108e124	1.42385	0.711923	−	0.702258i	$-0.247825\pi$
$211$	3.18108e124	1.42385	0.711923	+	0.702258i	$0.247825\pi$
$212$	−7.24265e123	−0.251726
$213$	−1.04414e125	−2.82130
$214$	4.27811e124	0.899735
$215$	9.71221e123	0.159170
$216$	−1.26646e125	−1.61926
$217$	3.82895e124	0.382370
$218$	−2.26357e124	−0.176755
$219$	−1.55178e125	−0.948574
$220$	−3.52065e123	−0.0168659
$221$	7.15441e125	2.68898
$222$	4.41871e125	1.30440
$223$	−1.39870e125	−0.324650	−0.162325	−	0.986737i	$-0.551899\pi$
$223$	−1.39870e125	−0.324650	−0.162325	+	0.986737i	$0.551899\pi$
$224$	−5.74698e124	−0.104996
$225$	−1.28950e126	−1.85634
$226$	1.30890e126	1.48629
$227$	−8.03823e125	−0.720738	−0.360369	−	0.932810i	$-0.617349\pi$
$227$	−8.03823e125	−0.720738	−0.360369	+	0.932810i	$0.617349\pi$
$228$	1.86445e125	0.132140
$229$	2.50586e125	0.140526	0.0702632	−	0.997528i	$-0.477616\pi$
$229$	2.50586e125	0.140526	0.0702632	+	0.997528i	$0.477616\pi$
$230$	−1.05425e125	−0.0468279
$231$	−5.84537e125	−0.205860
$232$	2.95010e126	0.824574
$233$	3.82433e126	0.849207	0.424603	−	0.905379i	$-0.360414\pi$
$233$	3.82433e126	0.849207	0.424603	+	0.905379i	$0.360414\pi$
$234$	−1.61166e127	−2.84593
$235$	5.16932e125	0.0726612
$236$	−6.89179e125	−0.0771862
$237$	−1.50538e127	−1.34466
$238$	−3.88270e126	−0.276864
$239$	2.52682e127	1.43975	0.719873	−	0.694105i	$-0.244200\pi$
$239$	2.52682e127	1.43975	0.719873	+	0.694105i	$0.244200\pi$
$240$	2.85709e126	0.130204
$241$	4.88308e127	1.78148	0.890742	−	0.454509i	$-0.150185\pi$
$241$	4.88308e127	1.78148	0.890742	+	0.454509i	$0.150185\pi$
$242$	1.96265e127	0.573747
$243$	1.62651e127	0.381348
$244$	−8.56268e126	−0.161159
$245$	−7.16844e126	−0.108402
$246$	−1.51427e128	−1.84152
$247$	5.42924e127	0.531437
$248$	2.50438e128	1.97485
$249$	−2.92539e128	−1.86002
$250$	3.78463e127	0.194193
$251$	−3.10114e128	−1.28522	−0.642609	−	0.766194i	$-0.722148\pi$
$251$	−3.10114e128	−1.28522	−0.642609	+	0.766194i	$0.722148\pi$
$252$	−3.02954e127	−0.101496
$253$	1.02210e128	0.277041
$254$	2.72567e126	0.00598232
$255$	−1.65683e128	−0.294699
$256$	−4.96537e128	−0.716331
$257$	−2.30918e128	−0.270418	−0.135209	−	0.990817i	$-0.543171\pi$
$257$	−2.30918e128	−0.270418	−0.135209	+	0.990817i	$0.543171\pi$
$258$	2.15814e129	2.05317
$259$	2.41874e128	0.187090
$260$	−8.13899e127	−0.0512267
$261$	2.79209e129	1.43108
$262$	−2.01258e129	−0.840688
$263$	2.54146e128	0.0865867	0.0432934	−	0.999062i	$-0.486215\pi$
$263$	2.54146e128	0.0865867	0.0432934	+	0.999062i	$0.486215\pi$
$264$	−3.82325e129	−1.06322
$265$	4.88418e128	0.110952
$266$	−2.94645e128	−0.0547182
$267$	7.41039e129	1.12587
$268$	3.42713e128	0.0426304
$269$	−1.84809e129	−0.188354	−0.0941771	−	0.995555i	$-0.530022\pi$
$269$	−1.84809e129	−0.188354	−0.0941771	+	0.995555i	$0.530022\pi$
$270$	1.74758e129	0.146042
$271$	−1.19009e130	−0.816059	−0.408029	−	0.912969i	$-0.633784\pi$
$271$	−1.19009e130	−0.816059	−0.408029	+	0.912969i	$0.633784\pi$
$272$	−1.83990e130	−1.03599
$273$	−1.35132e130	−0.625256
$274$	5.87172e129	0.223414
$275$	−1.82273e130	−0.570720
$276$	8.11429e129	0.209225
$277$	−3.82877e129	−0.0813563	−0.0406781	−	0.999172i	$-0.512952\pi$
$277$	−3.82877e129	−0.0813563	−0.0406781	+	0.999172i	$0.512952\pi$
$278$	−4.50084e130	−0.788674
$279$	2.37024e131	3.42743
$280$	2.15863e129	0.0257765
$281$	1.05073e131	1.03682	0.518408	−	0.855134i	$-0.326525\pi$
$281$	1.05073e131	1.03682	0.518408	+	0.855134i	$0.326525\pi$
$282$	1.14867e131	0.937277
$283$	−2.48240e131	−1.67609	−0.838047	−	0.545598i	$-0.816302\pi$
$283$	−2.48240e131	−1.67609	−0.838047	+	0.545598i	$0.816302\pi$
$284$	−7.64934e130	−0.427654
$285$	−1.25731e130	−0.0582430
$286$	−2.27811e131	−0.874966
$287$	−8.28890e130	−0.264129
$288$	−3.55757e131	−0.941143
$289$	6.11936e131	1.34484
$290$	−4.07083e130	−0.0743687
$291$	−1.44575e131	−0.219693
$292$	−1.13684e131	−0.143785
$293$	2.87768e131	0.303127	0.151563	−	0.988448i	$-0.451569\pi$
$293$	2.87768e131	0.303127	0.151563	+	0.988448i	$0.451569\pi$
$294$	−1.59289e132	−1.39831
$295$	4.64757e130	0.0340211
$296$	1.58201e132	0.966279
$297$	−1.69428e132	−0.864005
$298$	2.38181e132	1.01470
$299$	2.36287e132	0.841454
$300$	−1.44704e132	−0.431016
$301$	1.18134e132	0.294487
$302$	−1.04690e132	−0.218542
$303$	1.09705e133	1.91886
$304$	−1.39624e132	−0.204749
$305$	5.77436e131	0.0710333
$306$	−2.40352e133	−2.48171
$307$	−4.08483e132	−0.354218	−0.177109	−	0.984191i	$-0.556675\pi$
$307$	−4.08483e132	−0.354218	−0.177109	+	0.984191i	$0.556675\pi$
$308$	−4.28231e131	−0.0312044
$309$	3.13858e133	1.92289
$310$	−3.45578e132	−0.178113
$311$	1.60174e133	0.694881	0.347440	−	0.937702i	$-0.387051\pi$
$311$	1.60174e133	0.694881	0.347440	+	0.937702i	$0.387051\pi$
$312$	−8.83852e133	−3.22930
$313$	7.18513e132	0.221214	0.110607	−	0.993864i	$-0.464721\pi$
$313$	7.18513e132	0.221214	0.110607	+	0.993864i	$0.464721\pi$
$314$	−4.88884e132	−0.126902
$315$	2.04301e132	0.0447360
$316$	−1.10284e133	−0.203824
$317$	−1.64006e132	−0.0255970	−0.0127985	−	0.999918i	$-0.504074\pi$
$317$	−1.64006e132	−0.0255970	−0.0127985	+	0.999918i	$0.504074\pi$
$318$	1.08531e134	1.43121
$319$	3.94667e133	0.439977
$320$	1.33229e133	0.125625
$321$	2.22051e134	1.77187
$322$	−1.28233e133	−0.0866383
$323$	8.09680e133	0.463424
$324$	−3.47796e133	−0.168720
$325$	−4.21376e134	−1.73344
$326$	9.72540e132	0.0339442
$327$	−1.17488e134	−0.348088
$328$	−5.42147e134	−1.36416
$329$	6.28765e133	0.134434
$330$	5.27569e133	0.0958922
$331$	6.59401e133	0.101942	0.0509709	−	0.998700i	$-0.483768\pi$
$331$	6.59401e133	0.101942	0.0509709	+	0.998700i	$0.483768\pi$
$332$	−2.14314e134	−0.281944
$333$	1.49728e135	1.67701
$334$	−3.03740e134	−0.289779
$335$	−2.31113e133	−0.0187900
$336$	3.47520e134	0.240895
$337$	−2.92350e135	−1.72863	−0.864317	−	0.502947i	$-0.832249\pi$
$337$	−2.92350e135	−1.72863	−0.864317	+	0.502947i	$0.832249\pi$
$338$	−3.55859e135	−1.79570
$339$	6.79370e135	2.92700
$340$	−1.21379e134	−0.0446707
$341$	3.35038e135	1.05374
$342$	−1.82395e135	−0.490474
$343$	−1.78400e135	−0.410354
$344$	7.72669e135	1.52096
$345$	−5.47198e134	−0.0922195
$346$	2.36377e135	0.341219
$347$	−3.00697e135	−0.371965	−0.185983	−	0.982553i	$-0.559547\pi$
$347$	−3.00697e135	−0.371965	−0.185983	+	0.982553i	$0.559547\pi$
$348$	3.13321e135	0.332277
$349$	−1.31485e136	−1.19596	−0.597981	−	0.801510i	$-0.704030\pi$
$349$	−1.31485e136	−1.19596	−0.597981	+	0.801510i	$0.704030\pi$
$350$	2.28681e135	0.178480
$351$	−3.91682e136	−2.62423
$352$	−5.02869e135	−0.289349
$353$	2.04546e136	1.01121	0.505607	−	0.862764i	$-0.331268\pi$
$353$	2.04546e136	1.01121	0.505607	+	0.862764i	$0.331268\pi$
$354$	1.03273e136	0.438847
$355$	5.15843e135	0.188496
$356$	5.42885e135	0.170660
$357$	−2.01527e136	−0.545236
$358$	8.81063e135	0.205242
$359$	1.33840e136	0.268555	0.134278	−	0.990944i	$-0.457129\pi$
$359$	1.33840e136	0.268555	0.134278	+	0.990944i	$0.457129\pi$
$360$	1.33626e136	0.231051
$361$	−6.09421e136	−0.908411
$362$	1.15985e137	1.49105
$363$	1.01869e137	1.12990
$364$	−9.89978e135	−0.0947767
$365$	7.66640e135	0.0633758
$366$	1.28311e137	0.916278
$367$	−5.74132e136	−0.354305	−0.177152	−	0.984183i	$-0.556689\pi$
$367$	−5.74132e136	−0.354305	−0.177152	+	0.984183i	$0.556689\pi$
$368$	−6.07658e136	−0.324191
$369$	−5.13110e137	−2.36755
$370$	−2.18301e136	−0.0871491
$371$	5.94082e136	0.205278
$372$	2.65982e137	0.795803
$373$	−5.93283e137	−1.53759	−0.768793	−	0.639498i	$-0.779142\pi$
$373$	−5.93283e137	−1.53759	−0.768793	+	0.639498i	$0.779142\pi$
$374$	−3.39742e137	−0.762988
$375$	1.96437e137	0.382429
$376$	4.11253e137	0.694319
$377$	9.12385e137	1.33634
$378$	2.12566e137	0.270198
$379$	−3.35450e137	−0.370195	−0.185097	−	0.982720i	$-0.559260\pi$
$379$	−3.35450e137	−0.370195	−0.185097	+	0.982720i	$0.559260\pi$
$380$	−9.21107e135	−0.00882852
$381$	1.41473e136	0.0117811
$382$	−5.29076e137	−0.382938
$383$	−1.56614e138	−0.985588	−0.492794	−	0.870146i	$-0.664024\pi$
$383$	−1.56614e138	−0.985588	−0.492794	+	0.870146i	$0.664024\pi$
$384$	1.40868e138	0.771064
$385$	2.88784e136	0.0137538
$386$	−1.41651e138	−0.587216
$387$	7.31286e138	2.63967
$388$	−1.05915e137	−0.0333013
$389$	−4.31255e137	−0.118149	−0.0590746	−	0.998254i	$-0.518815\pi$
$389$	−4.31255e137	−0.118149	−0.0590746	+	0.998254i	$0.518815\pi$
$390$	1.21962e138	0.291252
$391$	3.52382e138	0.733766
$392$	−5.70296e138	−1.03585
$393$	−1.04461e139	−1.65559
$394$	−7.70001e138	−1.06523
$395$	7.43717e137	0.0898386
$396$	−2.65089e138	−0.279705
$397$	−1.21177e139	−1.11719	−0.558595	−	0.829441i	$-0.688659\pi$
$397$	−1.21177e139	−1.11719	−0.558595	+	0.829441i	$0.688659\pi$
$398$	1.57489e139	1.26913
$399$	−1.52932e138	−0.107758
$400$	1.08365e139	0.667852
$401$	−2.02030e139	−1.08941	−0.544706	−	0.838627i	$-0.683359\pi$
$401$	−2.02030e139	−1.08941	−0.544706	+	0.838627i	$0.683359\pi$
$402$	−5.13554e138	−0.242378
$403$	7.74535e139	3.20053
$404$	8.03694e138	0.290862
$405$	2.34541e138	0.0743661
$406$	−4.95152e138	−0.137593
$407$	2.11643e139	0.515588
$408$	−1.31812e140	−2.81602
$409$	6.38008e139	1.19572	0.597860	−	0.801601i	$-0.296018\pi$
$409$	6.38008e139	1.19572	0.597860	+	0.801601i	$0.296018\pi$
$410$	7.48107e138	0.123035
$411$	3.04766e139	0.439975
$412$	2.29932e139	0.291473
$413$	5.65303e138	0.0629438
$414$	−7.93803e139	−0.776595
$415$	1.44525e139	0.124271
$416$	−1.16252e140	−0.878838
$417$	−2.33612e140	−1.55316
$418$	−2.57818e139	−0.150794
$419$	3.10649e140	1.59890	0.799448	−	0.600735i	$-0.205125\pi$
$419$	3.10649e140	1.59890	0.799448	+	0.600735i	$0.205125\pi$
$420$	2.29261e138	0.0103871
$421$	−1.04252e140	−0.415902	−0.207951	−	0.978139i	$-0.566680\pi$
$421$	−1.04252e140	−0.415902	−0.207951	+	0.978139i	$0.566680\pi$
$422$	−3.49218e140	−1.22710
$423$	3.89226e140	1.20502
$424$	3.88568e140	1.06021
$425$	−6.28412e140	−1.51160
$426$	1.14625e141	2.43146
$427$	7.02358e139	0.131422
$428$	1.62674e140	0.268582
$429$	−1.18243e141	−1.72309
$430$	−1.06620e140	−0.137176
$431$	3.81070e140	0.432983	0.216492	−	0.976284i	$-0.430539\pi$
$431$	3.81070e140	0.432983	0.216492	+	0.976284i	$0.430539\pi$
$432$	1.00729e141	1.01105
$433$	−3.61924e140	−0.321007	−0.160503	−	0.987035i	$-0.551312\pi$
$433$	−3.61924e140	−0.321007	−0.160503	+	0.987035i	$0.551312\pi$
$434$	−4.20341e140	−0.329535
$435$	−2.11292e140	−0.146456
$436$	−8.60715e139	−0.0527633
$437$	2.67411e140	0.145018
$438$	1.70354e141	0.817501
$439$	9.04823e140	0.384337	0.192168	−	0.981362i	$-0.438448\pi$
$439$	9.04823e140	0.384337	0.192168	+	0.981362i	$0.438448\pi$
$440$	1.88883e140	0.0710354
$441$	−5.39751e141	−1.79775
$442$	−7.85409e141	−2.31742
$443$	−2.21615e141	−0.579429	−0.289714	−	0.957113i	$-0.593560\pi$
$443$	−2.21615e141	−0.579429	−0.289714	+	0.957113i	$0.593560\pi$
$444$	1.68020e141	0.389379
$445$	−3.66101e140	−0.0752213
$446$	1.53549e141	0.279790
$447$	1.23625e142	1.99827
$448$	1.62052e141	0.232424
$449$	4.02998e141	0.513007	0.256504	−	0.966543i	$-0.417429\pi$
$449$	4.02998e141	0.513007	0.256504	+	0.966543i	$0.417429\pi$
$450$	1.41561e142	1.59983
$451$	−7.25290e141	−0.727892
$452$	4.97706e141	0.443676
$453$	−5.43385e141	−0.430382
$454$	8.82435e141	0.621147
$455$	6.67605e140	0.0417744
$456$	−1.00028e142	−0.556545
$457$	−1.47002e142	−0.727455	−0.363728	−	0.931505i	$-0.618496\pi$
$457$	−1.47002e142	−0.727455	−0.363728	+	0.931505i	$0.618496\pi$
$458$	−2.75092e141	−0.121109
$459$	−5.84128e142	−2.28839
$460$	−4.00876e140	−0.0139787
$461$	4.03613e142	1.25304	0.626521	−	0.779405i	$-0.284478\pi$
$461$	4.03613e142	1.25304	0.626521	+	0.779405i	$0.284478\pi$
$462$	6.41703e141	0.177414
$463$	4.09394e142	1.00823	0.504114	−	0.863637i	$-0.331819\pi$
$463$	4.09394e142	1.00823	0.504114	+	0.863637i	$0.331819\pi$
$464$	−2.34638e142	−0.514857
$465$	−1.79369e142	−0.350763
$466$	−4.19834e142	−0.731864
$467$	5.58998e142	0.868874	0.434437	−	0.900702i	$-0.356947\pi$
$467$	5.58998e142	0.868874	0.434437	+	0.900702i	$0.356947\pi$
$468$	−6.12829e142	−0.849544
$469$	−2.81112e141	−0.0347642
$470$	−5.67486e141	−0.0626210
$471$	−2.53750e142	−0.249912
$472$	3.69744e142	0.325091
$473$	1.03368e143	0.811553
$474$	1.65261e143	1.15885
$475$	−4.76880e142	−0.298745
$476$	−1.47639e142	−0.0826472
$477$	3.67756e143	1.84004
$478$	−2.77393e143	−1.24080
$479$	−2.49569e143	−0.998253	−0.499127	−	0.866529i	$-0.666346\pi$
$479$	−2.49569e143	−0.998253	−0.499127	+	0.866529i	$0.666346\pi$
$480$	2.69220e142	0.0963165
$481$	4.89272e143	1.56599
$482$	−5.36063e143	−1.53532
$483$	−6.65579e142	−0.170619
$484$	7.46292e142	0.171270
$485$	7.14253e141	0.0146781
$486$	−1.78558e143	−0.328654
$487$	−9.02207e143	−1.48767	−0.743835	−	0.668363i	$-0.766995\pi$
$487$	−9.02207e143	−1.48767	−0.743835	+	0.668363i	$0.766995\pi$
$488$	4.59387e143	0.678764
$489$	5.04787e142	0.0668473
$490$	7.86949e142	0.0934235
$491$	−3.48350e143	−0.370814	−0.185407	−	0.982662i	$-0.559360\pi$
$491$	−3.48350e143	−0.370814	−0.185407	+	0.982662i	$0.559360\pi$
$492$	−5.75798e143	−0.549714
$493$	1.36067e144	1.16531
$494$	−5.96020e143	−0.458004
$495$	1.78766e143	0.123284
$496$	−1.99187e144	−1.23308
$497$	6.27441e143	0.348744
$498$	3.21148e144	1.60301
$499$	4.08979e144	1.83367	0.916835	−	0.399266i	$-0.130735\pi$
$499$	4.08979e144	1.83367	0.916835	+	0.399266i	$0.130735\pi$
$500$	1.43910e143	0.0579689
$501$	−1.57653e144	−0.570669
$502$	3.40442e144	1.10763
$503$	−1.73342e144	−0.507011	−0.253506	−	0.967334i	$-0.581584\pi$
$503$	−1.73342e144	−0.507011	−0.253506	+	0.967334i	$0.581584\pi$
$504$	1.62535e144	0.427477
$505$	−5.41982e143	−0.128202
$506$	−1.12205e144	−0.238760
$507$	−1.84705e145	−3.53633
$508$	1.03643e142	0.00178579
$509$	−2.74973e144	−0.426470	−0.213235	−	0.977001i	$-0.568400\pi$
$509$	−2.74973e144	−0.426470	−0.213235	+	0.977001i	$0.568400\pi$
$510$	1.81887e144	0.253978
$511$	9.32496e143	0.117254
$512$	9.46239e144	1.07166
$513$	−4.43275e144	−0.452266
$514$	2.53501e144	0.233052
$515$	−1.55058e144	−0.128471
$516$	8.20628e144	0.612897
$517$	5.50178e144	0.370475
$518$	−2.65528e144	−0.161238
$519$	1.22689e145	0.671972
$520$	4.36656e144	0.215755
$521$	6.69516e144	0.298499	0.149250	−	0.988800i	$-0.452314\pi$
$521$	6.69516e144	0.298499	0.149250	+	0.988800i	$0.452314\pi$
$522$	−3.06515e145	−1.23333
$523$	−2.52137e145	−0.915790	−0.457895	−	0.889006i	$-0.651396\pi$
$523$	−2.52137e145	−0.915790	−0.457895	+	0.889006i	$0.651396\pi$
$524$	−7.65280e144	−0.250955
$525$	1.18694e145	0.351485
$526$	−2.79001e144	−0.0746223
$527$	1.15509e146	2.79092
$528$	3.04085e145	0.663865
$529$	−3.90469e145	−0.770385
$530$	−5.36183e144	−0.0956212
$531$	3.49941e145	0.564206
$532$	−1.12038e144	−0.0163340
$533$	−1.67671e146	−2.21082
$534$	−8.13511e145	−0.970300
$535$	−1.09701e145	−0.118382
$536$	−1.83865e145	−0.179549
$537$	4.57307e145	0.404188
$538$	2.02882e145	0.162328
$539$	−7.62947e145	−0.552708
$540$	6.64515e144	0.0435952
$541$	−2.54242e146	−1.51075	−0.755376	−	0.655292i	$-0.772546\pi$
$541$	−2.54242e146	−1.51075	−0.755376	+	0.655292i	$0.772546\pi$
$542$	1.30647e146	0.703297
$543$	6.02005e146	2.93636
$544$	−1.73371e146	−0.766365
$545$	5.80435e144	0.0232563
$546$	1.48348e146	0.538859
$547$	−2.55908e146	−0.842873	−0.421436	−	0.906858i	$-0.638474\pi$
$547$	−2.55908e146	−0.842873	−0.421436	+	0.906858i	$0.638474\pi$
$548$	2.23271e145	0.0666918
$549$	4.34783e146	1.17802
$550$	2.00099e146	0.491859
$551$	1.03257e146	0.230307
$552$	−4.35331e146	−0.881210
$553$	9.04613e145	0.166214
$554$	4.20321e145	0.0701146
$555$	−1.13307e146	−0.171625
$556$	−1.71144e146	−0.235429
$557$	5.10969e146	0.638471	0.319236	−	0.947675i	$-0.396574\pi$
$557$	5.10969e146	0.638471	0.319236	+	0.947675i	$0.396574\pi$
$558$	−2.60205e147	−2.95383
$559$	2.38965e147	2.46492
$560$	−1.71688e145	−0.0160946
$561$	−1.76339e147	−1.50257
$562$	−1.15348e147	−0.893550
$563$	−1.91685e147	−1.35017	−0.675087	−	0.737738i	$-0.735894\pi$
$563$	−1.91685e147	−1.35017	−0.675087	+	0.737738i	$0.735894\pi$
$564$	4.36779e146	0.279788
$565$	−3.35634e146	−0.195558
$566$	2.72518e147	1.44449
$567$	2.85282e146	0.137588
$568$	4.10387e147	1.80118
$569$	2.66276e147	1.06372	0.531859	−	0.846833i	$-0.321494\pi$
$569$	2.66276e147	1.06372	0.531859	+	0.846833i	$0.321494\pi$
$570$	1.38028e146	0.0501951
$571$	−2.25855e147	−0.747822	−0.373911	−	0.927465i	$-0.621983\pi$
$571$	−2.25855e147	−0.747822	−0.373911	+	0.927465i	$0.621983\pi$
$572$	−8.66244e146	−0.261188
$573$	−2.74611e147	−0.754130
$574$	9.09953e146	0.227632
$575$	−2.07544e147	−0.473021
$576$	1.00315e148	2.08336
$577$	1.60640e146	0.0304051	0.0152026	−	0.999884i	$-0.495161\pi$
$577$	1.60640e146	0.0304051	0.0152026	+	0.999884i	$0.495161\pi$
$578$	−6.71782e147	−1.15901
$579$	−7.35222e147	−1.15642
$580$	−1.54792e146	−0.0221999
$581$	1.75792e147	0.229919
$582$	1.58714e147	0.189337
$583$	5.19830e147	0.565710
$584$	6.09912e147	0.605592
$585$	4.13269e147	0.374450
$586$	−3.15910e147	−0.261241
$587$	−1.68866e148	−1.27469	−0.637346	−	0.770578i	$-0.719968\pi$
$587$	−1.68866e148	−1.27469	−0.637346	+	0.770578i	$0.719968\pi$
$588$	−6.05693e147	−0.417413
$589$	8.76559e147	0.551586
$590$	−5.10209e146	−0.0293201
$591$	−3.99661e148	−2.09779
$592$	−1.25826e148	−0.603336
$593$	−1.08714e147	−0.0476276	−0.0238138	−	0.999716i	$-0.507581\pi$
$593$	−1.08714e147	−0.0476276	−0.0238138	+	0.999716i	$0.507581\pi$
$594$	1.85998e148	0.744618
$595$	9.95621e146	0.0364281
$596$	9.05676e147	0.302899
$597$	8.17428e148	2.49932
$598$	−2.59395e148	−0.725183
$599$	3.60523e148	0.921718	0.460859	−	0.887473i	$-0.347541\pi$
$599$	3.60523e148	0.921718	0.460859	+	0.887473i	$0.347541\pi$
$600$	7.76337e148	1.81534
$601$	−1.97208e148	−0.421832	−0.210916	−	0.977504i	$-0.567645\pi$
$601$	−1.97208e148	−0.421832	−0.210916	+	0.977504i	$0.567645\pi$
$602$	−1.29687e148	−0.253795
$603$	−1.74018e148	−0.311614
$604$	−3.98083e147	−0.0652375
$605$	−5.03272e147	−0.0754901
$606$	−1.20433e149	−1.65372
$607$	−1.88567e148	−0.237067	−0.118533	−	0.992950i	$-0.537819\pi$
$607$	−1.88567e148	−0.237067	−0.118533	+	0.992950i	$0.537819\pi$
$608$	−1.31565e148	−0.151461
$609$	−2.57003e148	−0.270965
$610$	−6.33907e147	−0.0612180
$611$	1.27189e149	1.12524
$612$	−9.13932e148	−0.740820
$613$	−2.08585e149	−1.54934	−0.774672	−	0.632363i	$-0.782085\pi$
$613$	−2.08585e149	−1.54934	−0.774672	+	0.632363i	$0.782085\pi$
$614$	4.48432e148	0.305273
$615$	3.88297e148	0.242295
$616$	2.29746e148	0.131426
$617$	3.14487e149	1.64948	0.824739	−	0.565514i	$-0.191322\pi$
$617$	3.14487e149	1.64948	0.824739	+	0.565514i	$0.191322\pi$
$618$	−3.44552e149	−1.65719
$619$	2.43613e149	1.07461	0.537306	−	0.843388i	$-0.319442\pi$
$619$	2.43613e149	1.07461	0.537306	+	0.843388i	$0.319442\pi$
$620$	−1.31405e148	−0.0531689
$621$	−1.92918e149	−0.716099
$622$	−1.75838e149	−0.598863
$623$	−4.45304e148	−0.139170
$624$	7.02978e149	2.01635
$625$	3.65234e149	0.961591
$626$	−7.88782e148	−0.190647
$627$	−1.33818e149	−0.296962
$628$	−1.85897e148	−0.0378818
$629$	7.29668e149	1.36557
$630$	−2.24281e148	−0.0385544
$631$	−7.10005e149	−1.12122	−0.560610	−	0.828080i	$-0.689433\pi$
$631$	−7.10005e149	−1.12122	−0.560610	+	0.828080i	$0.689433\pi$
$632$	5.91675e149	0.858459
$633$	−1.81258e150	−2.41656
$634$	1.80045e148	0.0220600
$635$	−6.98930e146	−0.000787117 0
$636$	4.12686e149	0.427232
$637$	−1.76377e150	−1.67873
$638$	−4.33265e149	−0.379181
$639$	3.88407e150	3.12601
$640$	−6.95939e148	−0.0515161
$641$	−1.14924e150	−0.782541	−0.391270	−	0.920276i	$-0.627964\pi$
$641$	−1.14924e150	−0.782541	−0.391270	+	0.920276i	$0.627964\pi$
$642$	−2.43766e150	−1.52704
$643$	1.89471e150	1.09208	0.546042	−	0.837758i	$-0.316134\pi$
$643$	1.89471e150	1.09208	0.546042	+	0.837758i	$0.316134\pi$
$644$	−4.87602e148	−0.0258626
$645$	−5.53401e149	−0.270144
$646$	−8.88864e149	−0.399389
$647$	−2.37002e150	−0.980331	−0.490165	−	0.871630i	$-0.663064\pi$
$647$	−2.37002e150	−0.980331	−0.490165	+	0.871630i	$0.663064\pi$
$648$	1.86593e150	0.710610
$649$	4.94648e149	0.173462
$650$	4.62585e150	1.49392
$651$	−2.18173e150	−0.648961
$652$	3.69806e148	0.0101328
$653$	−5.39680e149	−0.136233	−0.0681164	−	0.997677i	$-0.521699\pi$
$653$	−5.39680e149	−0.136233	−0.0681164	+	0.997677i	$0.521699\pi$
$654$	1.28978e150	0.299989
$655$	5.16077e149	0.110613
$656$	4.31200e150	0.851773
$657$	5.77245e150	1.05103
$658$	−6.90256e149	−0.115858
$659$	1.12446e151	1.74010	0.870051	−	0.492962i	$-0.164086\pi$
$659$	1.12446e151	1.74010	0.870051	+	0.492962i	$0.164086\pi$
$660$	2.00607e149	0.0286250
$661$	−9.48474e150	−1.24809	−0.624047	−	0.781387i	$-0.714513\pi$
$661$	−9.48474e150	−1.24809	−0.624047	+	0.781387i	$0.714513\pi$
$662$	−7.23888e149	−0.0878555
$663$	−4.07658e151	−4.56375
$664$	1.14979e151	1.18748
$665$	7.55543e148	0.00719948
$666$	−1.64371e151	−1.44528
$667$	4.49385e150	0.364658
$668$	−1.15497e150	−0.0865024
$669$	7.96981e150	0.550999
$670$	2.53715e149	0.0161936
$671$	6.14573e150	0.362175
$672$	3.27463e150	0.178199
$673$	−8.35304e150	−0.419796	−0.209898	−	0.977723i	$-0.567313\pi$
$673$	−8.35304e150	−0.419796	−0.209898	+	0.977723i	$0.567313\pi$
$674$	3.20941e151	1.48977
$675$	3.44036e151	1.47520
$676$	−1.35315e151	−0.536039
$677$	4.42954e151	1.62131	0.810653	−	0.585527i	$-0.199113\pi$
$677$	4.42954e151	1.62131	0.810653	+	0.585527i	$0.199113\pi$
$678$	−7.45810e151	−2.52255
$679$	8.68775e149	0.0271565
$680$	6.51200e150	0.188143
$681$	4.58018e151	1.22324
$682$	−3.67804e151	−0.908139
$683$	−8.21307e149	−0.0187498	−0.00937492	−	0.999956i	$-0.502984\pi$
$683$	−8.21307e149	−0.0187498	−0.00937492	+	0.999956i	$0.502984\pi$
$684$	−6.93552e150	−0.146412
$685$	−1.50566e150	−0.0293955
$686$	1.95846e151	0.353652
$687$	−1.42784e151	−0.238503
$688$	−6.14548e151	−0.949673
$689$	1.20173e152	1.71823
$690$	6.00712e150	0.0794767
$691$	−1.09478e152	−1.34046	−0.670229	−	0.742155i	$-0.733804\pi$
$691$	−1.09478e152	−1.34046	−0.670229	+	0.742155i	$0.733804\pi$
$692$	8.98816e150	0.101858
$693$	2.17441e151	0.228094
$694$	3.30104e151	0.320567
$695$	1.15413e151	0.103769
$696$	−1.68097e152	−1.39947
$697$	−2.50054e152	−1.92788
$698$	1.44344e152	1.03071
$699$	−2.17910e152	−1.44128
$700$	8.69553e150	0.0532784
$701$	2.03366e152	1.15442	0.577211	−	0.816595i	$-0.304141\pi$
$701$	2.03366e152	1.15442	0.577211	+	0.816595i	$0.304141\pi$
$702$	4.29987e152	2.26162
$703$	5.53720e151	0.269886
$704$	1.41798e152	0.640518
$705$	−2.94548e151	−0.123321
$706$	−2.24550e152	−0.871486
$707$	−6.59234e151	−0.237193
$708$	3.92694e151	0.131001
$709$	−1.37085e152	−0.424049	−0.212024	−	0.977264i	$-0.568006\pi$
$709$	−1.37085e152	−0.424049	−0.212024	+	0.977264i	$0.568006\pi$
$710$	−5.66291e151	−0.162449
$711$	5.59985e152	1.48989
$712$	−2.91257e152	−0.718782
$713$	3.81489e152	0.873357
$714$	2.21236e152	0.469896
$715$	5.84163e151	0.115123
$716$	3.35022e151	0.0612670
$717$	−1.43978e153	−2.44355
$718$	−1.46930e152	−0.231447
$719$	1.18124e153	1.72719	0.863597	−	0.504182i	$-0.168206\pi$
$719$	1.18124e153	1.72719	0.863597	+	0.504182i	$0.168206\pi$
$720$	−1.06280e152	−0.144266
$721$	−1.88603e152	−0.237690
$722$	6.69021e152	0.782888
$723$	−2.78238e153	−3.02355
$724$	4.41028e152	0.445095
$725$	−8.01399e152	−0.751217
$726$	−1.11832e153	−0.973768
$727$	1.23522e153	0.999202	0.499601	−	0.866256i	$-0.333480\pi$
$727$	1.23522e153	0.999202	0.499601	+	0.866256i	$0.333480\pi$
$728$	5.31123e152	0.399178
$729$	−1.86588e153	−1.30305
$730$	−8.41615e151	−0.0546186
$731$	3.56377e153	2.14946
$732$	4.87901e152	0.273520
$733$	3.07915e153	1.60461	0.802304	−	0.596916i	$-0.203607\pi$
$733$	3.07915e153	1.60461	0.802304	+	0.596916i	$0.203607\pi$
$734$	6.30280e152	0.305347
$735$	4.08457e152	0.183981
$736$	−5.72588e152	−0.239816
$737$	−2.45977e152	−0.0958041
$738$	5.63291e153	2.04041
$739$	−3.64845e153	−1.22922	−0.614612	−	0.788829i	$-0.710687\pi$
$739$	−3.64845e153	−1.22922	−0.614612	+	0.788829i	$0.710687\pi$
$740$	−8.30083e151	−0.0260151
$741$	−3.09358e153	−0.901959
$742$	−6.52182e152	−0.176913
$743$	−7.74326e152	−0.195444	−0.0977219	−	0.995214i	$-0.531156\pi$
$743$	−7.74326e152	−0.195444	−0.0977219	+	0.995214i	$0.531156\pi$
$744$	−1.42699e154	−3.35174
$745$	−6.10754e152	−0.133508
$746$	6.51304e153	1.32512
$747$	1.08821e154	2.06092
$748$	−1.29186e153	−0.227761
$749$	−1.33434e153	−0.219023
$750$	−2.15648e153	−0.329586
$751$	−6.51822e153	−0.927667	−0.463834	−	0.885922i	$-0.653526\pi$
$751$	−6.51822e153	−0.927667	−0.463834	+	0.885922i	$0.653526\pi$
$752$	−3.27093e153	−0.433527
$753$	1.76703e154	2.18128
$754$	−1.00161e154	−1.15168
$755$	2.68453e152	0.0287545
$756$	8.08276e152	0.0806573
$757$	−4.37857e153	−0.407101	−0.203551	−	0.979064i	$-0.565248\pi$
$757$	−4.37857e153	−0.407101	−0.203551	+	0.979064i	$0.565248\pi$
$758$	3.68256e153	0.319042
$759$	−5.82391e153	−0.470196
$760$	4.94174e152	0.0371837
$761$	−1.86661e153	−0.130911	−0.0654554	−	0.997855i	$-0.520850\pi$
$761$	−1.86661e153	−0.130911	−0.0654554	+	0.997855i	$0.520850\pi$
$762$	−1.55309e152	−0.0101532
$763$	7.06006e152	0.0430275
$764$	−2.01180e153	−0.114311
$765$	6.16322e153	0.326528
$766$	1.71930e154	0.849401
$767$	1.14352e154	0.526855
$768$	2.82927e154	1.21576
$769$	2.91618e153	0.116884	0.0584419	−	0.998291i	$-0.481387\pi$
$769$	2.91618e153	0.116884	0.0584419	+	0.998291i	$0.481387\pi$
$770$	−3.17026e152	−0.0118533
$771$	1.31577e154	0.458955
$772$	−5.38623e153	−0.175291
$773$	3.16283e154	0.960445	0.480223	−	0.877147i	$-0.340556\pi$
$773$	3.16283e154	0.960445	0.480223	+	0.877147i	$0.340556\pi$
$774$	−8.02803e154	−2.27493
$775$	−6.80318e154	−1.79916
$776$	5.68235e153	0.140257
$777$	−1.37820e154	−0.317531
$778$	4.73431e153	0.101823
$779$	−1.89757e154	−0.381017
$780$	4.63759e153	0.0869423
$781$	5.49020e154	0.961076
$782$	−3.86844e154	−0.632375
$783$	−7.44925e154	−1.13726
$784$	4.53588e154	0.646774
$785$	1.25362e153	0.0166970
$786$	1.14677e155	1.42682
$787$	−5.78202e154	−0.672097	−0.336048	−	0.941845i	$-0.609091\pi$
$787$	−5.78202e154	−0.672097	−0.336048	+	0.941845i	$0.609091\pi$
$788$	−2.92791e154	−0.317984
$789$	−1.44813e154	−0.146956
$790$	−8.16450e153	−0.0774248
$791$	−4.08246e154	−0.361809
$792$	1.42220e155	1.17805
$793$	1.42076e155	1.10003
$794$	1.33027e155	0.962818
$795$	−2.78300e154	−0.188310
$796$	5.98846e154	0.378849
$797$	−2.72336e155	−1.61096	−0.805480	−	0.592623i	$-0.798092\pi$
$797$	−2.72336e155	−1.61096	−0.805480	+	0.592623i	$0.798092\pi$
$798$	1.67889e154	0.0928681
$799$	1.89682e155	0.981233
$800$	1.02111e155	0.494035
$801$	−2.75658e155	−1.24747
$802$	2.21788e155	0.938878
$803$	8.15946e154	0.323132
$804$	−1.95278e154	−0.0723526
$805$	3.28821e153	0.0113993
$806$	−8.50283e155	−2.75828
$807$	1.05304e155	0.319676
$808$	−4.31182e155	−1.22505
$809$	−5.47531e155	−1.45600	−0.728002	−	0.685575i	$-0.759551\pi$
$809$	−5.47531e155	−1.45600	−0.728002	+	0.685575i	$0.759551\pi$
$810$	−2.57478e154	−0.0640903
$811$	6.11514e155	1.42492	0.712461	−	0.701712i	$-0.247581\pi$
$811$	6.11514e155	1.42492	0.712461	+	0.701712i	$0.247581\pi$
$812$	−1.88280e154	−0.0410731
$813$	6.78111e155	1.38502
$814$	−2.32341e155	−0.444344
$815$	−2.49384e153	−0.00446618
$816$	1.04837e156	1.75830
$817$	2.70443e155	0.424810
$818$	−7.00404e155	−1.03050
$819$	5.02676e155	0.692787
$820$	2.84466e154	0.0367273
$821$	−2.19137e155	−0.265067	−0.132534	−	0.991179i	$-0.542311\pi$
$821$	−2.19137e155	−0.265067	−0.132534	+	0.991179i	$0.542311\pi$
$822$	−3.34571e155	−0.379180
$823$	−8.83784e154	−0.0938545	−0.0469273	−	0.998898i	$-0.514943\pi$
$823$	−8.83784e154	−0.0938545	−0.0469273	+	0.998898i	$0.514943\pi$
$824$	−1.23358e156	−1.22762
$825$	1.03859e156	0.968631
$826$	−6.20588e154	−0.0542463
$827$	4.74157e154	0.0388488	0.0194244	−	0.999811i	$-0.493817\pi$
$827$	4.74157e154	0.0388488	0.0194244	+	0.999811i	$0.493817\pi$
$828$	−3.01842e155	−0.231823
$829$	1.13497e156	0.817176	0.408588	−	0.912719i	$-0.366021\pi$
$829$	1.13497e156	0.817176	0.408588	+	0.912719i	$0.366021\pi$
$830$	−1.58659e155	−0.107100
$831$	2.18163e155	0.138079
$832$	3.27805e156	1.94544
$833$	−2.63037e156	−1.46389
$834$	2.56458e156	1.33854
$835$	7.78866e154	0.0381273
$836$	−9.80348e154	−0.0450137
$837$	−6.32376e156	−2.72373
$838$	−3.41030e156	−1.37796
$839$	4.68325e156	1.77534	0.887672	−	0.460477i	$-0.152322\pi$
$839$	4.68325e156	1.77534	0.887672	+	0.460477i	$0.152322\pi$
$840$	−1.22999e155	−0.0437480
$841$	−1.26107e156	−0.420876
$842$	1.14447e156	0.358433
$843$	−5.98704e156	−1.75969
$844$	−1.32789e156	−0.366304
$845$	9.12512e155	0.236268
$846$	−4.27291e156	−1.03851
$847$	−6.12150e155	−0.139668
$848$	−3.09050e156	−0.661989
$849$	1.41447e157	2.84468
$850$	6.89868e156	1.30273
$851$	2.40985e156	0.427326
$852$	4.35859e156	0.725818
$853$	7.32957e156	1.14632	0.573159	−	0.819444i	$-0.305718\pi$
$853$	7.32957e156	1.14632	0.573159	+	0.819444i	$0.305718\pi$
$854$	−7.71047e155	−0.113262
$855$	4.67706e155	0.0645336
$856$	−8.72745e156	−1.13120
$857$	−1.29385e157	−1.57547	−0.787737	−	0.616012i	$-0.788747\pi$
$857$	−1.29385e157	−1.57547	−0.787737	+	0.616012i	$0.788747\pi$
$858$	1.29806e157	1.48500
$859$	−4.35330e156	−0.467934	−0.233967	−	0.972245i	$-0.575171\pi$
$859$	−4.35330e156	−0.467934	−0.233967	+	0.972245i	$0.575171\pi$
$860$	−4.05421e155	−0.0409486
$861$	4.72301e156	0.448281
$862$	−4.18338e156	−0.373154
$863$	−1.03783e157	−0.870057	−0.435028	−	0.900417i	$-0.643262\pi$
$863$	−1.03783e157	−0.870057	−0.435028	+	0.900417i	$0.643262\pi$
$864$	9.49153e156	0.747913
$865$	−6.06129e155	−0.0448955
$866$	3.97319e156	0.276651
$867$	−3.48681e157	−2.28248
$868$	−1.59834e156	−0.0983700
$869$	7.91549e156	0.458057
$870$	2.31956e156	0.126219
$871$	−5.68645e156	−0.290985
$872$	4.61774e156	0.222227
$873$	5.37800e156	0.243422
$874$	−2.93563e156	−0.124980
$875$	−1.18043e156	−0.0472725
$876$	6.47769e156	0.244034
$877$	−1.06910e157	−0.378914	−0.189457	−	0.981889i	$-0.560673\pi$
$877$	−1.06910e157	−0.378914	−0.189457	+	0.981889i	$0.560673\pi$
$878$	−9.93312e156	−0.331230
$879$	−1.63970e157	−0.514469
$880$	−1.50229e156	−0.0443539
$881$	3.04938e157	0.847228	0.423614	−	0.905843i	$-0.360761\pi$
$881$	3.04938e157	0.847228	0.423614	+	0.905843i	$0.360761\pi$
$882$	5.92537e157	1.54934
$883$	4.02527e157	0.990597	0.495298	−	0.868723i	$-0.335059\pi$
$883$	4.02527e157	0.990597	0.495298	+	0.868723i	$0.335059\pi$
$884$	−2.98650e157	−0.691777
$885$	−2.64818e156	−0.0577408
$886$	2.43288e157	0.499364
$887$	6.01736e157	1.16277	0.581383	−	0.813630i	$-0.302512\pi$
$887$	6.01736e157	1.16277	0.581383	+	0.813630i	$0.302512\pi$
$888$	−9.01428e157	−1.63998
$889$	−8.50137e154	−0.00145628
$890$	4.01905e156	0.0648273
$891$	2.49625e157	0.379168
$892$	5.83867e156	0.0835208
$893$	1.43943e157	0.193926
$894$	−1.35715e158	−1.72215
$895$	−2.25927e156	−0.0270044
$896$	−8.46499e156	−0.0953121
$897$	−1.34636e158	−1.42812
$898$	−4.42410e157	−0.442121
$899$	1.47306e158	1.38700
$900$	5.38282e157	0.477568
$901$	1.79219e158	1.49833
$902$	7.96221e157	0.627313
$903$	−6.73125e157	−0.499805
$904$	−2.67019e158	−1.86866
$905$	−2.97413e157	−0.196183
$906$	5.96526e157	0.370912
$907$	−8.47774e157	−0.496925	−0.248462	−	0.968642i	$-0.579925\pi$
$907$	−8.47774e157	−0.496925	−0.248462	+	0.968642i	$0.579925\pi$
$908$	3.35544e157	0.185420
$909$	−4.08088e158	−2.12611
$910$	−7.32895e156	−0.0360020
$911$	2.29182e158	1.06157	0.530783	−	0.847508i	$-0.321898\pi$
$911$	2.29182e158	1.06157	0.530783	+	0.847508i	$0.321898\pi$
$912$	7.95576e157	0.347502
$913$	1.53820e158	0.633617
$914$	1.61378e158	0.626937
$915$	−3.29023e157	−0.120558
$916$	−1.04603e157	−0.0361524
$917$	6.27725e157	0.204649
$918$	6.41254e158	1.97218
$919$	−1.45500e158	−0.422167	−0.211083	−	0.977468i	$-0.567699\pi$
$919$	−1.45500e158	−0.422167	−0.211083	+	0.977468i	$0.567699\pi$
$920$	2.15070e157	0.0588750
$921$	2.32754e158	0.601183
$922$	−4.43085e158	−1.07990
$923$	1.26921e159	2.91907
$924$	2.44006e157	0.0529603
$925$	−4.29755e158	−0.880315
$926$	−4.49432e158	−0.868912
$927$	−1.16751e159	−2.13057
$928$	−2.21096e158	−0.380859
$929$	−8.07146e158	−1.31254	−0.656268	−	0.754527i	$-0.727866\pi$
$929$	−8.07146e158	−1.31254	−0.656268	+	0.754527i	$0.727866\pi$
$930$	1.96910e158	0.302295
$931$	−1.99610e158	−0.289317
$932$	−1.59641e158	−0.218470
$933$	−9.12669e158	−1.17936
$934$	−6.13666e158	−0.748815
$935$	8.71182e157	0.100389
$936$	3.28783e159	3.57809
$937$	−1.37268e158	−0.141091	−0.0705457	−	0.997509i	$-0.522474\pi$
$937$	−1.37268e158	−0.141091	−0.0705457	+	0.997509i	$0.522474\pi$
$938$	3.08604e157	0.0299606
$939$	−4.09409e158	−0.375446
$940$	−2.15785e157	−0.0186931
$941$	1.76667e159	1.44580	0.722902	−	0.690950i	$-0.242808\pi$
$941$	1.76667e159	1.44580	0.722902	+	0.690950i	$0.242808\pi$
$942$	2.78566e158	0.215380
$943$	−8.25846e158	−0.603286
$944$	−2.94078e158	−0.202984
$945$	−5.45072e157	−0.0355510
$946$	−1.13478e159	−0.699414
$947$	−5.37518e158	−0.313090	−0.156545	−	0.987671i	$-0.550036\pi$
$947$	−5.37518e158	−0.313090	−0.156545	+	0.987671i	$0.550036\pi$
$948$	6.28400e158	0.345931
$949$	1.88629e159	0.981446
$950$	5.23518e158	0.257465
$951$	9.34505e157	0.0434434
$952$	7.92081e158	0.348091
$953$	2.58848e159	1.07541	0.537706	−	0.843132i	$-0.319291\pi$
$953$	2.58848e159	1.07541	0.537706	+	0.843132i	$0.319291\pi$
$954$	−4.03722e159	−1.58578
$955$	1.35668e158	0.0503846
$956$	−1.05478e159	−0.370395
$957$	−2.24881e159	−0.746732
$958$	2.73976e159	0.860316
$959$	−1.83139e158	−0.0543858
$960$	−7.59139e158	−0.213211
$961$	8.74055e159	2.32187
$962$	−5.37121e159	−1.34960
$963$	−8.26002e159	−1.96325
$964$	−2.03837e159	−0.458312
$965$	3.63228e158	0.0772623
$966$	7.30670e158	0.147043
$967$	3.91953e159	0.746308	0.373154	−	0.927769i	$-0.378276\pi$
$967$	3.91953e159	0.746308	0.373154	+	0.927769i	$0.378276\pi$
$968$	−4.00386e159	−0.721351
$969$	−4.61356e159	−0.786527
$970$	−7.84105e157	−0.0126499
$971$	−3.03936e159	−0.464038	−0.232019	−	0.972711i	$-0.574533\pi$
$971$	−3.03936e159	−0.464038	−0.232019	+	0.972711i	$0.574533\pi$
$972$	−6.78962e158	−0.0981071
$973$	1.40381e159	0.191987
$974$	9.90440e159	1.28211
$975$	2.40100e160	2.94202
$976$	−3.65377e159	−0.423814
$977$	−1.32527e160	−1.45528	−0.727639	−	0.685960i	$-0.759382\pi$
$977$	−1.32527e160	−1.45528	−0.727639	+	0.685960i	$0.759382\pi$
$978$	−5.54153e158	−0.0576104
$979$	−3.89647e159	−0.383528
$980$	2.99235e158	0.0278880
$981$	4.37041e159	0.385683
$982$	3.82418e159	0.319575
$983$	−1.46384e160	−1.15846	−0.579228	−	0.815165i	$-0.696646\pi$
$983$	−1.46384e160	−1.15846	−0.579228	+	0.815165i	$0.696646\pi$
$984$	3.08915e160	2.31527
$985$	1.97448e159	0.140157
$986$	−1.49374e160	−1.00429
$987$	−3.58270e159	−0.228162
$988$	−2.26635e159	−0.136720
$989$	1.17700e160	0.672626
$990$	−1.96249e159	−0.106249
$991$	2.45067e160	1.25703	0.628514	−	0.777798i	$-0.283664\pi$
$991$	2.45067e160	1.25703	0.628514	+	0.777798i	$0.283664\pi$
$992$	−1.87691e160	−0.912157
$993$	−3.75727e159	−0.173016
$994$	−6.88803e159	−0.300555
$995$	−4.03840e159	−0.166984
$996$	1.22116e160	0.478517
$997$	−2.93118e160	−1.08856	−0.544278	−	0.838905i	$-0.683196\pi$
$997$	−2.93118e160	−1.08856	−0.544278	+	0.838905i	$0.683196\pi$
$998$	−4.48975e160	−1.58030
$999$	−3.99471e160	−1.33270

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.108.a.a.1.3	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.108.a.a.1.3	✓	9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 108 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-1.09780e16 q^{2} -5.69800e25 q^{3} -4.17435e31 q^{4} +2.81503e36 q^{5} +6.25524e41 q^{6} +3.42403e44 q^{7} +2.23954e48 q^{8} +2.11959e51 q^{9} +O(q^{10})\)	\(q-1.09780e16 q^{2} -5.69800e25 q^{3} -4.17435e31 q^{4} +2.81503e36 q^{5} +6.25524e41 q^{6} +3.42403e44 q^{7} +2.23954e48 q^{8} +2.11959e51 q^{9} -3.09033e52 q^{10} +2.99607e55 q^{11} +2.37854e57 q^{12} +6.92627e59 q^{13} -3.75889e60 q^{14} -1.60400e62 q^{15} -1.78123e64 q^{16} +1.03294e66 q^{17} -2.32688e67 q^{18} +7.83862e67 q^{19} -1.17509e68 q^{20} -1.95101e70 q^{21} -3.28908e71 q^{22} +3.41145e72 q^{23} -1.27609e74 q^{24} -6.08373e74 q^{25} -7.60364e75 q^{26} -5.65502e76 q^{27} -1.42931e76 q^{28} +1.31728e78 q^{29} +1.76087e78 q^{30} +1.11826e80 q^{31} -1.67843e80 q^{32} -1.70716e81 q^{33} -1.13396e82 q^{34} +9.63873e80 q^{35} -8.84789e82 q^{36} +7.06400e83 q^{37} -8.60521e83 q^{38} -3.94659e85 q^{39} +6.30435e84 q^{40} -2.42080e86 q^{41} +2.14181e86 q^{42} +3.45013e87 q^{43} -1.25066e87 q^{44} +5.96669e87 q^{45} -3.74508e88 q^{46} +1.83633e89 q^{47} +1.01494e90 q^{48} -2.54649e90 q^{49} +6.67870e90 q^{50} -5.88568e91 q^{51} -2.89127e91 q^{52} +1.73504e92 q^{53} +6.20806e92 q^{54} +8.43402e91 q^{55} +7.66824e92 q^{56} -4.46644e93 q^{57} -1.44611e94 q^{58} +1.65099e94 q^{59} +6.69566e93 q^{60} +2.05126e95 q^{61} -1.22762e96 q^{62} +7.25753e95 q^{63} +4.73278e96 q^{64} +1.94976e96 q^{65} +1.87412e97 q^{66} -8.20998e96 q^{67} -4.31184e97 q^{68} -1.94385e98 q^{69} -1.05814e97 q^{70} +1.83246e99 q^{71} +4.74689e99 q^{72} +2.72339e99 q^{73} -7.75484e99 q^{74} +3.46651e100 q^{75} -3.27211e99 q^{76} +1.02586e100 q^{77} +4.33255e101 q^{78} +2.64195e101 q^{79} -5.01421e100 q^{80} +8.33175e101 q^{81} +2.65755e102 q^{82} +5.13406e102 q^{83} +8.14420e101 q^{84} +2.90775e102 q^{85} -3.78754e103 q^{86} -7.50587e103 q^{87} +6.70981e103 q^{88} -1.30053e104 q^{89} -6.55022e103 q^{90} +2.37158e104 q^{91} -1.42406e104 q^{92} -6.37183e105 q^{93} -2.01592e105 q^{94} +2.20659e104 q^{95} +9.56367e105 q^{96} +2.53729e105 q^{97} +2.79553e106 q^{98} +6.35044e106 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 54\!\cdots\!96 q^{2}+ \cdots + 36\!\cdots\!13 q^{9}+O(q^{10}) \) 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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