LMFDB - Embedded newform 1.108.a.a.1.7

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			1.7
Root			$-5.32911e14$ 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)

$f(q)$	$=$	$q+1.33972e16 q^{2} +4.78035e25 q^{3} +1.72251e31 q^{4} -4.75138e37 q^{5} +6.40432e41 q^{6} -7.19244e44 q^{7} -1.94305e48 q^{8} +1.15805e51 q^{9} +O(q^{10})$	\(q+1.33972e16 q^{2} +4.78035e25 q^{3} +1.72251e31 q^{4} -4.75138e37 q^{5} +6.40432e41 q^{6} -7.19244e44 q^{7} -1.94305e48 q^{8} +1.15805e51 q^{9} -6.36552e53 q^{10} +5.31887e55 q^{11} +8.23422e56 q^{12} +6.03576e59 q^{13} -9.63584e60 q^{14} -2.27133e63 q^{15} -2.88263e64 q^{16} +1.95528e65 q^{17} +1.55145e67 q^{18} +1.51075e67 q^{19} -8.18432e68 q^{20} -3.43824e70 q^{21} +7.12579e71 q^{22} +7.78244e72 q^{23} -9.28845e73 q^{24} +1.64127e75 q^{25} +8.08622e75 q^{26} +1.47783e75 q^{27} -1.23891e76 q^{28} +2.54095e78 q^{29} -3.04294e79 q^{30} +1.31370e79 q^{31} -7.09135e79 q^{32} +2.54261e81 q^{33} +2.61953e81 q^{34} +3.41740e82 q^{35} +1.99475e82 q^{36} +5.58255e82 q^{37} +2.02399e83 q^{38} +2.88531e85 q^{39} +9.23217e85 q^{40} +1.85028e85 q^{41} -4.60627e86 q^{42} -2.08676e86 q^{43} +9.16183e86 q^{44} -5.50232e88 q^{45} +1.04263e89 q^{46} +2.95144e87 q^{47} -1.37800e90 q^{48} -2.14642e90 q^{49} +2.19884e91 q^{50} +9.34694e90 q^{51} +1.03967e91 q^{52} -9.11818e91 q^{53} +1.97988e91 q^{54} -2.52720e93 q^{55} +1.39753e93 q^{56} +7.22194e92 q^{57} +3.40415e94 q^{58} -4.40712e94 q^{59} -3.91239e94 q^{60} +3.11921e95 q^{61} +1.75999e95 q^{62} -8.32917e95 q^{63} +3.72729e96 q^{64} -2.86782e97 q^{65} +3.40638e97 q^{66} +3.76125e97 q^{67} +3.36800e96 q^{68} +3.72028e98 q^{69} +4.57836e98 q^{70} -3.36143e98 q^{71} -2.25014e99 q^{72} +2.58608e99 q^{73} +7.47904e98 q^{74} +7.84584e100 q^{75} +2.60229e98 q^{76} -3.82557e100 q^{77} +3.86550e101 q^{78} +3.43229e100 q^{79} +1.36965e102 q^{80} -1.23462e102 q^{81} +2.47886e101 q^{82} +7.77077e102 q^{83} -5.92241e101 q^{84} -9.29030e102 q^{85} -2.79567e102 q^{86} +1.21466e104 q^{87} -1.03348e104 q^{88} -3.50478e104 q^{89} -7.37156e104 q^{90} -4.34118e104 q^{91} +1.34054e104 q^{92} +6.27995e104 q^{93} +3.95410e103 q^{94} -7.17818e104 q^{95} -3.38992e105 q^{96} +1.80712e105 q^{97} -2.87560e106 q^{98} +6.15950e106 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.33972e16	1.05174	0.525870	−	0.850565i	$-0.323740\pi$
$2$	1.33972e16	1.05174	0.525870	+	0.850565i	$0.323740\pi$
$3$	4.78035e25	1.42388	0.711939	−	0.702241i	$-0.247817\pi$
$3$	4.78035e25	1.42388	0.711939	+	0.702241i	$0.247817\pi$
$4$	1.72251e31	0.106158
$5$	−4.75138e37	−1.91393	−0.956963	−	0.290211i	$-0.906274\pi$
$5$	−4.75138e37	−1.91393	−0.956963	+	0.290211i	$0.906274\pi$
$6$	6.40432e41	1.49755
$7$	−7.19244e44	−0.440688	−0.220344	−	0.975422i	$-0.570718\pi$
$7$	−7.19244e44	−0.440688	−0.220344	+	0.975422i	$0.570718\pi$
$8$	−1.94305e48	−0.940090
$9$	1.15805e51	1.02743
$10$	−6.36552e53	−2.01295
$11$	5.31887e55	1.02639	0.513193	−	0.858273i	$-0.328462\pi$
$11$	5.31887e55	1.02639	0.513193	+	0.858273i	$0.328462\pi$
$12$	8.23422e56	0.151156
$13$	6.03576e59	1.53025	0.765126	−	0.643881i	$-0.222677\pi$
$13$	6.03576e59	1.53025	0.765126	+	0.643881i	$0.222677\pi$
$14$	−9.63584e60	−0.463489
$15$	−2.27133e63	−2.72520
$16$	−2.88263e64	−1.09489
$17$	1.95528e65	0.289863	0.144931	−	0.989442i	$-0.453704\pi$
$17$	1.95528e65	0.289863	0.144931	+	0.989442i	$0.453704\pi$
$18$	1.55145e67	1.08059
$19$	1.51075e67	0.0583279	0.0291639	−	0.999575i	$-0.490716\pi$
$19$	1.51075e67	0.0583279	0.0291639	+	0.999575i	$0.490716\pi$
$20$	−8.18432e68	−0.203179
$21$	−3.43824e70	−0.627485
$22$	7.12579e71	1.07949
$23$	7.78244e72	1.09314	0.546571	−	0.837413i	$-0.315933\pi$
$23$	7.78244e72	1.09314	0.546571	+	0.837413i	$0.315933\pi$
$24$	−9.28845e73	−1.33857
$25$	1.64127e75	2.66311
$26$	8.08622e75	1.60943
$27$	1.47783e75	0.0390538
$28$	−1.23891e76	−0.0467825
$29$	2.54095e78	1.46792	0.733960	−	0.679192i	$-0.237670\pi$
$29$	2.54095e78	1.46792	0.733960	+	0.679192i	$0.237670\pi$
$30$	−3.04294e79	−2.86620
$31$	1.31370e79	0.214114	0.107057	−	0.994253i	$-0.465857\pi$
$31$	1.31370e79	0.214114	0.107057	+	0.994253i	$0.465857\pi$
$32$	−7.09135e79	−0.211449
$33$	2.54261e81	1.46145
$34$	2.61953e81	0.304860
$35$	3.41740e82	0.843443
$36$	1.99475e82	0.109070
$37$	5.58255e82	0.0704758	0.0352379	−	0.999379i	$-0.488781\pi$
$37$	5.58255e82	0.0704758	0.0352379	+	0.999379i	$0.488781\pi$
$38$	2.02399e83	0.0613458
$39$	2.88531e85	2.17889
$40$	9.23217e85	1.79926
$41$	1.85028e85	0.0962281	0.0481141	−	0.998842i	$-0.484679\pi$
$41$	1.85028e85	0.0962281	0.0481141	+	0.998842i	$0.484679\pi$
$42$	−4.60627e86	−0.659952
$43$	−2.08676e86	−0.0849004	−0.0424502	−	0.999099i	$-0.513516\pi$
$43$	−2.08676e86	−0.0849004	−0.0424502	+	0.999099i	$0.513516\pi$
$44$	9.16183e86	0.108959
$45$	−5.50232e88	−1.96642
$46$	1.04263e89	1.14970
$47$	2.95144e87	0.0102991	0.00514955	−	0.999987i	$-0.498361\pi$
$47$	2.95144e87	0.0102991	0.00514955	+	0.999987i	$0.498361\pi$
$48$	−1.37800e90	−1.55899
$49$	−2.14642e90	−0.805794
$50$	2.19884e91	2.80090
$51$	9.34694e90	0.412729
$52$	1.03967e91	0.162448
$53$	−9.11818e91	−0.514220	−0.257110	−	0.966382i	$-0.582770\pi$
$53$	−9.11818e91	−0.514220	−0.257110	+	0.966382i	$0.582770\pi$
$54$	1.97988e91	0.0410744
$55$	−2.52720e93	−1.96443
$56$	1.39753e93	0.414286
$57$	7.22194e92	0.0830518
$58$	3.40415e94	1.54387
$59$	−4.40712e94	−0.800888	−0.400444	−	0.916321i	$-0.631144\pi$
$59$	−4.40712e94	−0.800888	−0.400444	+	0.916321i	$0.631144\pi$
$60$	−3.91239e94	−0.289301
$61$	3.11921e95	0.952573	0.476286	−	0.879290i	$-0.341983\pi$
$61$	3.11921e95	0.952573	0.476286	+	0.879290i	$0.341983\pi$
$62$	1.75999e95	0.225193
$63$	−8.32917e95	−0.452775
$64$	3.72729e96	0.872499
$65$	−2.86782e97	−2.92879
$66$	3.40638e97	1.53707
$67$	3.76125e97	0.759154	0.379577	−	0.925160i	$-0.376069\pi$
$67$	3.76125e97	0.759154	0.379577	+	0.925160i	$0.376069\pi$
$68$	3.36800e96	0.0307713
$69$	3.72028e98	1.55650
$70$	4.57836e98	0.887083
$71$	−3.36143e98	−0.304932	−0.152466	−	0.988309i	$-0.548721\pi$
$71$	−3.36143e98	−0.304932	−0.152466	+	0.988309i	$0.548721\pi$
$72$	−2.25014e99	−0.965874
$73$	2.58608e99	0.530725	0.265363	−	0.964149i	$-0.414508\pi$
$73$	2.58608e99	0.530725	0.265363	+	0.964149i	$0.414508\pi$
$74$	7.47904e98	0.0741223
$75$	7.84584e100	3.79194
$76$	2.60229e98	0.00619198
$77$	−3.82557e100	−0.452316
$78$	3.86550e101	2.29163
$79$	3.43229e100	0.102928	0.0514641	−	0.998675i	$-0.483611\pi$
$79$	3.43229e100	0.102928	0.0514641	+	0.998675i	$0.483611\pi$
$80$	1.36965e102	2.09553
$81$	−1.23462e102	−0.971820
$82$	2.47886e101	0.101207
$83$	7.77077e102	1.65877	0.829385	−	0.558677i	$-0.188691\pi$
$83$	7.77077e102	1.65877	0.829385	+	0.558677i	$0.188691\pi$
$84$	−5.92241e101	−0.0666126
$85$	−9.29030e102	−0.554776
$86$	−2.79567e102	−0.0892932
$87$	1.21466e104	2.09014
$88$	−1.03348e104	−0.964896
$89$	−3.50478e104	−1.78770	−0.893852	−	0.448361i	$-0.852008\pi$
$89$	−3.50478e104	−1.78770	−0.893852	+	0.448361i	$0.852008\pi$
$90$	−7.37156e104	−2.06816
$91$	−4.34118e104	−0.674363
$92$	1.34054e104	0.116046
$93$	6.27995e104	0.304873
$94$	3.95410e103	0.0108320
$95$	−7.17818e104	−0.111635
$96$	−3.38992e105	−0.301077
$97$	1.80712e105	0.0921931	0.0460966	−	0.998937i	$-0.485322\pi$
$97$	1.80712e105	0.0921931	0.0460966	+	0.998937i	$0.485322\pi$
$98$	−2.87560e106	−0.847487
$99$	6.15950e106	1.05454
$100$	2.82711e106	0.282711
$101$	2.59306e107	1.52272	0.761358	−	0.648332i	$-0.224533\pi$
$101$	2.59306e107	1.52272	0.761358	+	0.648332i	$0.224533\pi$
$102$	1.25223e107	0.434084
$103$	6.59599e107	1.35672	0.678358	−	0.734732i	$-0.262692\pi$
$103$	6.59599e107	1.35672	0.678358	+	0.734732i	$0.262692\pi$
$104$	−1.17278e108	−1.43857
$105$	1.63364e108	1.20096
$106$	−1.22158e108	−0.540826
$107$	−7.74847e107	−0.207579	−0.103790	−	0.994599i	$-0.533097\pi$
$107$	−7.74847e107	−0.207579	−0.103790	+	0.994599i	$0.533097\pi$
$108$	2.54558e106	0.00414587
$109$	−1.12492e109	−1.11893	−0.559466	−	0.828853i	$-0.688994\pi$
$109$	−1.12492e109	−1.11893	−0.559466	+	0.828853i	$0.688994\pi$
$110$	−3.38574e109	−2.06607
$111$	2.66865e108	0.100349
$112$	2.07331e109	0.482504
$113$	8.51366e109	1.23146	0.615729	−	0.787958i	$-0.288862\pi$
$113$	8.51366e109	1.23146	0.615729	+	0.787958i	$0.288862\pi$
$114$	9.67536e108	0.0873489
$115$	−3.69774e110	−2.09219
$116$	4.37681e109	0.155832
$117$	6.98969e110	1.57222
$118$	−5.90429e110	−0.842327
$119$	−1.40632e110	−0.127739
$120$	4.41330e111	2.56193
$121$	1.43592e110	0.0534702
$122$	4.17886e111	1.00186
$123$	8.84501e110	0.137017
$124$	2.26287e110	0.0227300
$125$	−4.87003e112	−3.18307
$126$	−1.11587e112	−0.476201
$127$	1.59419e112	0.445698	0.222849	−	0.974853i	$-0.428464\pi$
$127$	1.59419e112	0.445698	0.222849	+	0.974853i	$0.428464\pi$
$128$	6.14416e112	1.12909
$129$	−9.97543e111	−0.120888
$130$	−3.84207e113	−3.08032
$131$	3.11144e113	1.65557	0.827784	−	0.561047i	$-0.189601\pi$
$131$	3.11144e113	1.65557	0.827784	+	0.561047i	$0.189601\pi$
$132$	4.37968e112	0.155145
$133$	−1.08660e112	−0.0257044
$134$	5.03901e113	0.798433
$135$	−7.02174e112	−0.0747460
$136$	−3.79921e113	−0.272497
$137$	1.02355e114	0.496089	0.248045	−	0.968749i	$-0.420212\pi$
$137$	1.02355e114	0.496089	0.248045	+	0.968749i	$0.420212\pi$
$138$	4.98413e114	1.63703
$139$	−3.01664e114	−0.673335	−0.336667	−	0.941624i	$-0.609300\pi$
$139$	−3.01664e114	−0.673335	−0.336667	+	0.941624i	$0.609300\pi$
$140$	5.88652e113	0.0895383
$141$	1.41089e113	0.0146647
$142$	−4.50337e114	−0.320709
$143$	3.21035e115	1.57063
$144$	−3.33822e115	−1.12492
$145$	−1.20730e116	−2.80949
$146$	3.46462e115	0.558185
$147$	−1.02606e116	−1.14735
$148$	9.61601e113	0.00748157
$149$	−1.24700e116	−0.676708	−0.338354	−	0.941019i	$-0.609870\pi$
$149$	−1.24700e116	−0.676708	−0.338354	+	0.941019i	$0.609870\pi$
$150$	1.05112e117	3.98814
$151$	−2.35502e116	−0.626222	−0.313111	−	0.949716i	$-0.601371\pi$
$151$	−2.35502e116	−0.626222	−0.313111	+	0.949716i	$0.601371\pi$
$152$	−2.93547e115	−0.0548335
$153$	2.26431e116	0.297813
$154$	−5.12518e116	−0.475719
$155$	−6.24190e116	−0.409799
$156$	4.96998e116	0.231307
$157$	3.76655e117	1.24541	0.622705	−	0.782457i	$-0.286034\pi$
$157$	3.76655e117	1.24541	0.622705	+	0.782457i	$0.286034\pi$
$158$	4.59830e116	0.108254
$159$	−4.35881e117	−0.732187
$160$	3.36937e117	0.404697
$161$	−5.59747e117	−0.481734
$162$	−1.65405e118	−1.02210
$163$	1.17707e117	0.0523319	0.0261660	−	0.999658i	$-0.491670\pi$
$163$	1.17707e117	0.0523319	0.0261660	+	0.999658i	$0.491670\pi$
$164$	3.18714e116	0.0102154
$165$	−1.20809e119	−2.79711
$166$	1.04106e119	1.74460
$167$	1.15375e118	0.140210	0.0701050	−	0.997540i	$-0.477667\pi$
$167$	1.15375e118	0.140210	0.0701050	+	0.997540i	$0.477667\pi$
$168$	6.68066e118	0.589892
$169$	2.08730e119	1.34167
$170$	−1.24464e119	−0.583480
$171$	1.74952e118	0.0599277
$172$	−3.59447e117	−0.00901286
$173$	4.57189e119	0.840677	0.420338	−	0.907367i	$-0.361911\pi$
$173$	4.57189e119	0.840677	0.420338	+	0.907367i	$0.361911\pi$
$174$	1.62730e120	2.19828
$175$	−1.18047e120	−1.17360
$176$	−1.53324e120	−1.12378
$177$	−2.10676e120	−1.14037
$178$	−4.69542e120	−1.88020
$179$	5.78693e120	1.71716	0.858581	−	0.512678i	$-0.171346\pi$
$179$	5.78693e120	1.71716	0.858581	+	0.512678i	$0.171346\pi$
$180$	−9.47781e119	−0.208751
$181$	1.65938e120	0.271733	0.135866	−	0.990727i	$-0.456618\pi$
$181$	1.65938e120	0.271733	0.135866	+	0.990727i	$0.456618\pi$
$182$	−5.81596e120	−0.709255
$183$	1.49109e121	1.35635
$184$	−1.51217e121	−1.02765
$185$	−2.65248e120	−0.134885
$186$	8.41337e120	0.320647
$187$	1.03999e121	0.297511
$188$	5.08390e118	0.00109333
$189$	−1.06292e120	−0.0172105
$190$	−9.61673e120	−0.117411
$191$	1.83081e122	1.68794	0.843970	−	0.536390i	$-0.180212\pi$
$191$	1.83081e122	1.68794	0.843970	+	0.536390i	$0.180212\pi$
$192$	1.78178e122	1.24233
$193$	5.97707e121	0.315626	0.157813	−	0.987469i	$-0.449556\pi$
$193$	5.97707e121	0.315626	0.157813	+	0.987469i	$0.449556\pi$
$194$	2.42103e121	0.0969632
$195$	−1.37092e123	−4.17023
$196$	−3.69723e121	−0.0855416
$197$	−3.71656e122	−0.654934	−0.327467	−	0.944863i	$-0.606195\pi$
$197$	−3.71656e122	−0.654934	−0.327467	+	0.944863i	$0.606195\pi$
$198$	8.25199e122	1.10910
$199$	9.25436e122	0.949963	0.474981	−	0.879996i	$-0.342455\pi$
$199$	9.25436e122	0.949963	0.474981	+	0.879996i	$0.342455\pi$
$200$	−3.18906e123	−2.50356
$201$	1.79801e123	1.08094
$202$	3.47397e123	1.60150
$203$	−1.82756e123	−0.646894
$204$	1.61002e122	0.0438145
$205$	−8.79141e122	−0.184173
$206$	8.83677e123	1.42691
$207$	9.01242e123	1.12312
$208$	−1.73989e124	−1.67545
$209$	8.03552e122	0.0598670
$210$	2.18862e124	1.26310
$211$	−2.95610e124	−1.32315	−0.661573	−	0.749881i	$-0.730111\pi$
$211$	−2.95610e124	−1.32315	−0.661573	+	0.749881i	$0.730111\pi$
$212$	−1.57062e123	−0.0545886
$213$	−1.60688e124	−0.434185
$214$	−1.03808e124	−0.218319
$215$	9.91499e123	0.162493
$216$	−2.87149e123	−0.0367141
$217$	−9.44871e123	−0.0943576
$218$	−1.50708e125	−1.17683
$219$	1.23624e125	0.755688
$220$	−4.35314e124	−0.208540
$221$	1.18016e125	0.443563
$222$	3.57524e124	0.105541
$223$	−5.30353e125	−1.23099	−0.615496	−	0.788140i	$-0.711044\pi$
$223$	−5.30353e125	−1.23099	−0.615496	+	0.788140i	$0.711044\pi$
$224$	5.10041e124	0.0931829
$225$	1.90066e126	2.73615
$226$	1.14059e126	1.29517
$227$	−1.90928e125	−0.171193	−0.0855966	−	0.996330i	$-0.527280\pi$
$227$	−1.90928e125	−0.171193	−0.0855966	+	0.996330i	$0.527280\pi$
$228$	1.24399e124	0.00881662
$229$	8.65004e123	0.00485087	0.00242544	−	0.999997i	$-0.499228\pi$
$229$	8.65004e123	0.00485087	0.00242544	+	0.999997i	$0.499228\pi$
$230$	−4.95393e126	−2.20044
$231$	−1.82876e126	−0.644043
$232$	−4.93718e126	−1.37998
$233$	−1.29498e126	−0.287555	−0.143778	−	0.989610i	$-0.545925\pi$
$233$	−1.29498e126	−0.287555	−0.143778	+	0.989610i	$0.545925\pi$
$234$	9.36421e126	1.65357
$235$	−1.40234e125	−0.0197117
$236$	−7.59132e125	−0.0850207
$237$	1.64076e126	0.146557
$238$	−1.88408e126	−0.134348
$239$	−1.98881e127	−1.13320	−0.566599	−	0.823993i	$-0.691741\pi$
$239$	−1.98881e127	−1.13320	−0.566599	+	0.823993i	$0.691741\pi$
$240$	6.54740e127	2.98379
$241$	−1.68033e127	−0.613033	−0.306516	−	0.951865i	$-0.599163\pi$
$241$	−1.68033e127	−0.613033	−0.306516	+	0.951865i	$0.599163\pi$
$242$	1.92372e126	0.0562368
$243$	−6.06850e127	−1.42281
$244$	5.37288e126	0.101123
$245$	1.01985e128	1.54223
$246$	1.18498e127	0.144106
$247$	9.11856e126	0.0892563
$248$	−2.55258e127	−0.201287
$249$	3.71470e128	2.36189
$250$	−6.52447e128	−3.34776
$251$	−3.88893e128	−1.61171	−0.805854	−	0.592114i	$-0.798293\pi$
$251$	−3.88893e128	−1.61171	−0.805854	+	0.592114i	$0.798293\pi$
$252$	−1.43471e127	−0.0480657
$253$	4.13938e128	1.12199
$254$	2.13576e128	0.468758
$255$	−4.44109e128	−0.789933
$256$	2.18356e128	0.315012
$257$	−3.75653e128	−0.439911	−0.219955	−	0.975510i	$-0.570591\pi$
$257$	−3.75653e128	−0.439911	−0.219955	+	0.975510i	$0.570591\pi$
$258$	−1.33643e128	−0.127143
$259$	−4.01521e127	−0.0310578
$260$	−4.93986e128	−0.310914
$261$	2.94253e129	1.50818
$262$	4.16845e129	1.74123
$263$	2.35564e129	0.802557	0.401279	−	0.915956i	$-0.368566\pi$
$263$	2.35564e129	0.802557	0.401279	+	0.915956i	$0.368566\pi$
$264$	−4.94041e129	−1.37389
$265$	4.33240e129	0.984179
$266$	−1.45574e128	−0.0270343
$267$	−1.67541e130	−2.54547
$268$	6.47880e128	0.0805903
$269$	5.33998e128	0.0544243	0.0272122	−	0.999630i	$-0.491337\pi$
$269$	5.33998e128	0.0544243	0.0272122	+	0.999630i	$0.491337\pi$
$270$	−9.40715e128	−0.0786134
$271$	−1.01152e130	−0.693613	−0.346807	−	0.937937i	$-0.612734\pi$
$271$	−1.01152e130	−0.693613	−0.346807	+	0.937937i	$0.612734\pi$
$272$	−5.63636e129	−0.317367
$273$	−2.07524e130	−0.960210
$274$	1.37127e130	0.521757
$275$	8.72970e130	2.73338
$276$	6.40823e129	0.165235
$277$	−3.54701e130	−0.753693	−0.376846	−	0.926276i	$-0.622992\pi$
$277$	−3.54701e130	−0.753693	−0.376846	+	0.926276i	$0.622992\pi$
$278$	−4.04144e130	−0.708173
$279$	1.52133e130	0.219987
$280$	−6.64018e130	−0.792912
$281$	7.77476e130	0.767182	0.383591	−	0.923503i	$-0.374687\pi$
$281$	7.77476e130	0.767182	0.383591	+	0.923503i	$0.374687\pi$
$282$	1.89020e129	0.0154234
$283$	1.25408e131	0.846744	0.423372	−	0.905956i	$-0.360846\pi$
$283$	1.25408e131	0.846744	0.423372	+	0.905956i	$0.360846\pi$
$284$	−5.79011e129	−0.0323709
$285$	−3.43142e130	−0.158955
$286$	4.30096e131	1.65190
$287$	−1.33080e130	−0.0424065
$288$	−8.21211e130	−0.217248
$289$	−4.16793e131	−0.915980
$290$	−1.61744e132	−2.95485
$291$	8.63865e130	0.131272
$292$	4.45456e130	0.0563408
$293$	9.45026e131	0.995465	0.497733	−	0.867331i	$-0.334166\pi$
$293$	9.45026e131	0.995465	0.497733	+	0.867331i	$0.334166\pi$
$294$	−1.37464e132	−1.20672
$295$	2.09399e132	1.53284
$296$	−1.08472e131	−0.0662536
$297$	7.86039e130	0.0400843
$298$	−1.67063e132	−0.711722
$299$	4.69730e132	1.67278
$300$	1.35146e132	0.402545
$301$	1.50089e131	0.0374145
$302$	−3.15507e132	−0.658623
$303$	1.23957e133	2.16816
$304$	−4.35495e131	−0.0638625
$305$	−1.48206e133	−1.82315
$306$	3.03353e132	0.313222
$307$	−2.04751e133	−1.77551	−0.887755	−	0.460315i	$-0.847736\pi$
$307$	−2.04751e133	−1.77551	−0.887755	+	0.460315i	$0.847736\pi$
$308$	−6.58959e131	−0.0480170
$309$	3.15312e133	1.93180
$310$	−8.36238e132	−0.431002
$311$	−2.62476e133	−1.13870	−0.569349	−	0.822096i	$-0.692805\pi$
$311$	−2.62476e133	−1.13870	−0.569349	+	0.822096i	$0.692805\pi$
$312$	−5.60629e133	−2.04835
$313$	1.29454e133	0.398560	0.199280	−	0.979943i	$-0.436140\pi$
$313$	1.29454e133	0.398560	0.199280	+	0.979943i	$0.436140\pi$
$314$	5.04611e133	1.30985
$315$	3.95751e133	0.866577
$316$	5.91217e131	0.0109267
$317$	5.59072e133	0.872563	0.436282	−	0.899810i	$-0.356295\pi$
$317$	5.59072e133	0.872563	0.436282	+	0.899810i	$0.356295\pi$
$318$	−5.83958e133	−0.770071
$319$	1.35150e134	1.50665
$320$	−1.77098e134	−1.66990
$321$	−3.70404e133	−0.295567
$322$	−7.49903e133	−0.506659
$323$	2.95395e132	0.0169071
$324$	−2.12665e133	−0.103167
$325$	9.90630e134	4.07523
$326$	1.57695e133	0.0550396
$327$	−5.37751e134	−1.59322
$328$	−3.59519e133	−0.0904631
$329$	−2.12281e132	−0.00453868
$330$	−1.61850e135	−2.94183
$331$	1.07420e134	0.166069	0.0830346	−	0.996547i	$-0.473539\pi$
$331$	1.07420e134	0.166069	0.0830346	+	0.996547i	$0.473539\pi$
$332$	1.33853e134	0.176092
$333$	6.46484e133	0.0724088
$334$	1.54569e134	0.147465
$335$	−1.78711e135	−1.45296
$336$	9.91117e134	0.687026
$337$	−4.37411e134	−0.258637	−0.129318	−	0.991603i	$-0.541279\pi$
$337$	−4.37411e134	−0.258637	−0.129318	+	0.991603i	$0.541279\pi$
$338$	2.79639e135	1.41109
$339$	4.06983e135	1.75345
$340$	−1.60027e134	−0.0588939
$341$	6.98741e134	0.219764
$342$	2.34387e134	0.0630284
$343$	3.45967e135	0.795791
$344$	4.05467e134	0.0798140
$345$	−1.76765e136	−2.97903
$346$	6.12504e135	0.884174
$347$	−7.56957e135	−0.936363	−0.468182	−	0.883632i	$-0.655091\pi$
$347$	−7.56957e135	−0.936363	−0.468182	+	0.883632i	$0.655091\pi$
$348$	2.09227e135	0.221885
$349$	2.02443e136	1.84138	0.920688	−	0.390299i	$-0.127628\pi$
$349$	2.02443e136	1.84138	0.920688	+	0.390299i	$0.127628\pi$
$350$	−1.58150e136	−1.23432
$351$	8.91983e134	0.0597621
$352$	−3.77180e135	−0.217028
$353$	−9.36315e135	−0.462887	−0.231444	−	0.972848i	$-0.574345\pi$
$353$	−9.36315e135	−0.462887	−0.231444	+	0.972848i	$0.574345\pi$
$354$	−2.82246e136	−1.19937
$355$	1.59714e136	0.583616
$356$	−6.03703e135	−0.189779
$357$	−6.72273e135	−0.181885
$358$	7.75286e136	1.80601
$359$	−4.74719e136	−0.952541	−0.476271	−	0.879299i	$-0.658012\pi$
$359$	−4.74719e136	−0.952541	−0.476271	+	0.879299i	$0.658012\pi$
$360$	1.06913e137	1.84861
$361$	−6.68583e136	−0.996598
$362$	2.22310e136	0.285792
$363$	6.86418e135	0.0761350
$364$	−7.47774e135	−0.0715890
$365$	−1.22875e137	−1.01577
$366$	1.99764e137	1.42653
$367$	1.46853e137	0.906254	0.453127	−	0.891446i	$-0.350308\pi$
$367$	1.46853e137	0.906254	0.453127	+	0.891446i	$0.350308\pi$
$368$	−2.24339e137	−1.19687
$369$	2.14271e136	0.0988674
$370$	−3.55358e136	−0.141864
$371$	6.55819e136	0.226611
$372$	1.08173e136	0.0323647
$373$	−7.64528e135	−0.0198140	−0.00990698	−	0.999951i	$-0.503154\pi$
$373$	−7.64528e135	−0.0198140	−0.00990698	+	0.999951i	$0.503154\pi$
$374$	1.39329e137	0.312905
$375$	−2.32805e138	−4.53230
$376$	−5.73480e135	−0.00968207
$377$	1.53365e138	2.24629
$378$	−1.42401e136	−0.0181010
$379$	−7.10954e136	−0.0784592	−0.0392296	−	0.999230i	$-0.512490\pi$
$379$	−7.10954e136	−0.0784592	−0.0392296	+	0.999230i	$0.512490\pi$
$380$	−1.23645e136	−0.0118510
$381$	7.62078e137	0.634619
$382$	2.45276e138	1.77528
$383$	−2.19219e138	−1.37957	−0.689784	−	0.724015i	$-0.742295\pi$
$383$	−2.19219e138	−1.37957	−0.689784	+	0.724015i	$0.742295\pi$
$384$	2.93712e138	1.60769
$385$	1.81767e138	0.865699
$386$	8.00759e137	0.331956
$387$	−2.41656e137	−0.0872290
$388$	3.11278e136	0.00978704
$389$	−2.86727e138	−0.785535	−0.392768	−	0.919638i	$-0.628482\pi$
$389$	−2.86727e138	−0.785535	−0.392768	+	0.919638i	$0.628482\pi$
$390$	−1.83665e139	−4.38600
$391$	1.52169e138	0.316861
$392$	4.17060e138	0.757519
$393$	1.48738e139	2.35733
$394$	−4.97914e138	−0.688821
$395$	−1.63081e138	−0.196997
$396$	1.06098e138	0.111948
$397$	−3.47129e138	−0.320036	−0.160018	−	0.987114i	$-0.551155\pi$
$397$	−3.47129e138	−0.320036	−0.160018	+	0.987114i	$0.551155\pi$
$398$	1.23982e139	0.999115
$399$	−5.19433e137	−0.0365999
$400$	−4.73117e139	−2.91581
$401$	4.76156e138	0.256759	0.128380	−	0.991725i	$-0.459022\pi$
$401$	4.76156e138	0.256759	0.128380	+	0.991725i	$0.459022\pi$
$402$	2.40882e139	1.13687
$403$	7.92919e138	0.327649
$404$	4.46658e138	0.161648
$405$	5.86617e139	1.85999
$406$	−2.44841e139	−0.680365
$407$	2.96929e138	0.0723354
$408$	−1.81616e139	−0.388002
$409$	9.91633e138	0.185846	0.0929232	−	0.995673i	$-0.470379\pi$
$409$	9.91633e138	0.185846	0.0929232	+	0.995673i	$0.470379\pi$
$410$	−1.17780e139	−0.193703
$411$	4.89294e139	0.706370
$412$	1.13617e139	0.144026
$413$	3.16979e139	0.352942
$414$	1.20741e140	1.18124
$415$	−3.69219e140	−3.17476
$416$	−4.28017e139	−0.323570
$417$	−1.44206e140	−0.958746
$418$	1.07653e139	0.0629645
$419$	5.93563e139	0.305504	0.152752	−	0.988265i	$-0.451186\pi$
$419$	5.93563e139	0.305504	0.152752	+	0.988265i	$0.451186\pi$
$420$	2.81396e139	0.127492
$421$	3.15684e140	1.25939	0.629695	−	0.776843i	$-0.283180\pi$
$421$	3.15684e140	1.25939	0.629695	+	0.776843i	$0.283180\pi$
$422$	−3.96034e140	−1.39161
$423$	3.41791e138	0.0105816
$424$	1.77171e140	0.483413
$425$	3.20914e140	0.771936
$426$	−2.15277e140	−0.456650
$427$	−2.24347e140	−0.419787
$428$	−1.33468e139	−0.0220362
$429$	1.53466e141	2.23638
$430$	1.32833e140	0.170900
$431$	1.36370e141	1.54948	0.774739	−	0.632281i	$-0.217881\pi$
$431$	1.36370e141	1.54948	0.774739	+	0.632281i	$0.217881\pi$
$432$	−4.26004e139	−0.0427595
$433$	−3.04049e140	−0.269676	−0.134838	−	0.990868i	$-0.543051\pi$
$433$	−3.04049e140	−0.269676	−0.134838	+	0.990868i	$0.543051\pi$
$434$	−1.26586e140	−0.0992397
$435$	−5.77132e141	−4.00037
$436$	−1.93769e140	−0.118784
$437$	1.17574e140	0.0637607
$438$	1.65621e141	0.794787
$439$	−3.08196e141	−1.30911	−0.654555	−	0.756015i	$-0.727144\pi$
$439$	−3.08196e141	−1.30911	−0.654555	+	0.756015i	$0.727144\pi$
$440$	4.91048e141	1.84674
$441$	−2.48565e141	−0.827896
$442$	1.58108e141	0.466513
$443$	−3.25003e141	−0.849745	−0.424873	−	0.905253i	$-0.639681\pi$
$443$	−3.25003e141	−0.849745	−0.424873	+	0.905253i	$0.639681\pi$
$444$	4.59679e139	0.0106528
$445$	1.66526e142	3.42153
$446$	−7.10524e141	−1.29468
$447$	−5.96111e141	−0.963550
$448$	−2.68083e141	−0.384500
$449$	−1.53438e142	−1.95323	−0.976614	−	0.215002i	$-0.931024\pi$
$449$	−1.53438e142	−1.95323	−0.976614	+	0.215002i	$0.931024\pi$
$450$	2.54635e142	2.87772
$451$	9.84143e140	0.0987673
$452$	1.46649e141	0.130729
$453$	−1.12578e142	−0.891664
$454$	−2.55790e141	−0.180051
$455$	2.06266e142	1.29068
$456$	−1.40326e141	−0.0780761
$457$	2.28164e142	1.12909	0.564547	−	0.825401i	$-0.309051\pi$
$457$	2.28164e142	1.12909	0.564547	+	0.825401i	$0.309051\pi$
$458$	1.15886e140	0.00510186
$459$	2.88958e140	0.0113202
$460$	−6.36940e141	−0.222103
$461$	−4.16681e142	−1.29361	−0.646806	−	0.762655i	$-0.723896\pi$
$461$	−4.16681e142	−1.29361	−0.646806	+	0.762655i	$0.723896\pi$
$462$	−2.45002e142	−0.677366
$463$	7.39192e141	0.182043	0.0910216	−	0.995849i	$-0.470987\pi$
$463$	7.39192e141	0.182043	0.0910216	+	0.995849i	$0.470987\pi$
$464$	−7.32461e142	−1.60721
$465$	−2.98385e142	−0.583504
$466$	−1.73491e142	−0.302434
$467$	7.89821e142	1.22765	0.613826	−	0.789441i	$-0.289630\pi$
$467$	7.89821e142	1.22765	0.613826	+	0.789441i	$0.289630\pi$
$468$	1.20398e142	0.166904
$469$	−2.70525e142	−0.334550
$470$	−1.87875e141	−0.0207316
$471$	1.80054e143	1.77331
$472$	8.56324e142	0.752907
$473$	−1.10992e142	−0.0871406
$474$	2.19815e142	0.154140
$475$	2.47955e142	0.155334
$476$	−2.42241e141	−0.0135605
$477$	−1.05593e143	−0.528324
$478$	−2.66445e143	−1.19183
$479$	4.09015e143	1.63602	0.818012	−	0.575202i	$-0.195076\pi$
$479$	4.09015e143	1.63602	0.818012	+	0.575202i	$0.195076\pi$
$480$	1.61068e143	0.576239
$481$	3.36949e142	0.107846
$482$	−2.25117e143	−0.644751
$483$	−2.67579e143	−0.685931
$484$	2.47338e141	0.00567629
$485$	−8.58631e142	−0.176451
$486$	−8.13008e143	−1.49642
$487$	−4.13719e143	−0.682191	−0.341096	−	0.940029i	$-0.610798\pi$
$487$	−4.13719e143	−0.682191	−0.341096	+	0.940029i	$0.610798\pi$
$488$	−6.06077e143	−0.895504
$489$	5.62682e142	0.0745142
$490$	1.36631e144	1.62203
$491$	1.40836e144	1.49918	0.749590	−	0.661902i	$-0.230251\pi$
$491$	1.40836e144	1.49918	0.749590	+	0.661902i	$0.230251\pi$
$492$	1.52356e142	0.0145455
$493$	4.96827e143	0.425495
$494$	1.22163e143	0.0938745
$495$	−2.92661e144	−2.01831
$496$	−3.78691e143	−0.234431
$497$	2.41769e143	0.134380
$498$	4.97665e144	2.48409
$499$	4.46758e143	0.200306	0.100153	−	0.994972i	$-0.468067\pi$
$499$	4.46758e143	0.200306	0.100153	+	0.994972i	$0.468067\pi$
$500$	−8.38869e143	−0.337908
$501$	5.51531e143	0.199642
$502$	−5.21007e144	−1.69510
$503$	3.65229e144	1.06826	0.534131	−	0.845402i	$-0.320639\pi$
$503$	3.65229e144	1.06826	0.534131	+	0.845402i	$0.320639\pi$
$504$	1.61840e144	0.425649
$505$	−1.23206e145	−2.91436
$506$	5.54561e144	1.18004
$507$	9.97801e144	1.91037
$508$	2.74601e143	0.0473144
$509$	2.46259e144	0.381937	0.190968	−	0.981596i	$-0.438837\pi$
$509$	2.46259e144	0.381937	0.190968	+	0.981596i	$0.438837\pi$
$510$	−5.94981e144	−0.830804
$511$	−1.86002e144	−0.233884
$512$	−7.04411e144	−0.797781
$513$	2.23264e142	0.00227792
$514$	−5.03269e144	−0.462672
$515$	−3.13401e145	−2.59665
$516$	−1.71828e143	−0.0128332
$517$	1.56984e143	0.0105709
$518$	−5.37925e143	−0.0326648
$519$	2.18552e145	1.19702
$520$	5.57232e145	2.75332
$521$	5.19454e144	0.231595	0.115797	−	0.993273i	$-0.463058\pi$
$521$	5.19454e144	0.231595	0.115797	+	0.993273i	$0.463058\pi$
$522$	3.94216e145	1.58622
$523$	−9.90632e144	−0.359809	−0.179905	−	0.983684i	$-0.557579\pi$
$523$	−9.90632e144	−0.359809	−0.179905	+	0.983684i	$0.557579\pi$
$524$	5.35950e144	0.175752
$525$	−5.64307e145	−1.67106
$526$	3.15589e145	0.844082
$527$	2.56866e144	0.0620638
$528$	−7.32940e145	−1.60012
$529$	9.88152e144	0.194960
$530$	5.80419e145	1.03510
$531$	−5.10364e145	−0.822855
$532$	−1.87168e143	−0.00272873
$533$	1.11679e145	0.147253
$534$	−2.24458e146	−2.67718
$535$	3.68160e145	0.397291
$536$	−7.30829e145	−0.713673
$537$	2.76636e146	2.44503
$538$	7.15407e144	0.0572403
$539$	−1.14165e146	−0.827057
$540$	−1.20950e144	−0.00793489
$541$	8.27594e145	0.491772	0.245886	−	0.969299i	$-0.420921\pi$
$541$	8.27594e145	0.491772	0.245886	+	0.969299i	$0.420921\pi$
$542$	−1.35515e146	−0.729501
$543$	7.93242e145	0.386914
$544$	−1.38656e145	−0.0612911
$545$	5.34493e146	2.14155
$546$	−2.78023e146	−1.00989
$547$	−5.34801e146	−1.76145	−0.880725	−	0.473629i	$-0.842944\pi$
$547$	−5.34801e146	−1.76145	−0.880725	+	0.473629i	$0.842944\pi$
$548$	1.76308e145	0.0526638
$549$	3.61218e146	0.978700
$550$	1.16953e147	2.87481
$551$	3.83875e145	0.0856207
$552$	−7.22869e146	−1.46325
$553$	−2.46865e145	−0.0453592
$554$	−4.75199e146	−0.792689
$555$	−1.26798e146	−0.192060
$556$	−5.19619e145	−0.0714799
$557$	−1.76134e146	−0.220085	−0.110043	−	0.993927i	$-0.535099\pi$
$557$	−1.76134e146	−0.220085	−0.110043	+	0.993927i	$0.535099\pi$
$558$	2.03815e146	0.231369
$559$	−1.25952e146	−0.129919
$560$	−9.85111e146	−0.923476
$561$	4.97152e146	0.423620
$562$	1.04160e147	0.806877
$563$	−1.66870e146	−0.117539	−0.0587693	−	0.998272i	$-0.518718\pi$
$563$	−1.66870e146	−0.117539	−0.0587693	+	0.998272i	$0.518718\pi$
$564$	2.43028e144	0.00155677
$565$	−4.04517e147	−2.35692
$566$	1.68012e147	0.890555
$567$	8.87995e146	0.428269
$568$	6.53142e146	0.286663
$569$	−1.58744e147	−0.634147	−0.317074	−	0.948401i	$-0.602700\pi$
$569$	−1.58744e147	−0.634147	−0.317074	+	0.948401i	$0.602700\pi$
$570$	−4.59714e146	−0.167179
$571$	−2.67981e147	−0.887304	−0.443652	−	0.896199i	$-0.646317\pi$
$571$	−2.67981e147	−0.887304	−0.443652	+	0.896199i	$0.646317\pi$
$572$	5.52986e146	0.166735
$573$	8.75189e147	2.40342
$574$	−1.78290e146	−0.0446007
$575$	1.27731e148	2.91116
$576$	4.31638e147	0.896430
$577$	−9.60466e147	−1.81792	−0.908962	−	0.416878i	$-0.863124\pi$
$577$	−9.60466e147	−1.81792	−0.908962	+	0.416878i	$0.863124\pi$
$578$	−5.58385e147	−0.963373
$579$	2.85725e147	0.449412
$580$	−2.07959e147	−0.298250
$581$	−5.58908e147	−0.730999
$582$	1.15734e147	0.138064
$583$	−4.84985e147	−0.527789
$584$	−5.02489e147	−0.498929
$585$	−3.32107e148	−3.00912
$586$	1.26607e148	1.04697
$587$	7.40360e147	0.558862	0.279431	−	0.960166i	$-0.409854\pi$
$587$	7.40360e147	0.558862	0.279431	+	0.960166i	$0.409854\pi$
$588$	−1.76741e147	−0.121801
$589$	1.98468e146	0.0124888
$590$	2.80536e148	1.61215
$591$	−1.77665e148	−0.932546
$592$	−1.60924e147	−0.0771631
$593$	1.99738e148	0.875052	0.437526	−	0.899206i	$-0.355855\pi$
$593$	1.99738e148	0.875052	0.437526	+	0.899206i	$0.355855\pi$
$594$	1.05307e147	0.0421583
$595$	6.68199e147	0.244483
$596$	−2.14798e147	−0.0718381
$597$	4.42391e148	1.35263
$598$	6.29305e148	1.75933
$599$	−3.21030e148	−0.820751	−0.410375	−	0.911917i	$-0.634602\pi$
$599$	−3.21030e148	−0.820751	−0.410375	+	0.911917i	$0.634602\pi$
$600$	−1.52448e149	−3.56477
$601$	2.75210e147	0.0588681	0.0294340	−	0.999567i	$-0.490629\pi$
$601$	2.75210e147	0.0588681	0.0294340	+	0.999567i	$0.490629\pi$
$602$	2.01077e147	0.0393504
$603$	4.35570e148	0.779976
$604$	−4.05656e147	−0.0664785
$605$	−6.82259e147	−0.102338
$606$	1.66068e149	2.28034
$607$	8.77359e148	1.10302	0.551509	−	0.834169i	$-0.314052\pi$
$607$	8.77359e148	1.10302	0.551509	+	0.834169i	$0.314052\pi$
$608$	−1.07133e147	−0.0123334
$609$	−8.73638e148	−0.921099
$610$	−1.98554e149	−1.91748
$611$	1.78142e147	0.0157602
$612$	3.90030e147	0.0316153
$613$	−1.09165e149	−0.810861	−0.405431	−	0.914126i	$-0.632878\pi$
$613$	−1.09165e149	−0.810861	−0.405431	+	0.914126i	$0.632878\pi$
$614$	−2.74309e149	−1.86738
$615$	−4.20260e148	−0.262240
$616$	7.43326e148	0.425218
$617$	2.54993e149	1.33743	0.668716	−	0.743518i	$-0.266844\pi$
$617$	2.54993e149	1.33743	0.668716	+	0.743518i	$0.266844\pi$
$618$	4.22429e149	2.03175
$619$	−2.10777e149	−0.929765	−0.464882	−	0.885372i	$-0.653903\pi$
$619$	−2.10777e149	−0.929765	−0.464882	+	0.885372i	$0.653903\pi$
$620$	−1.07518e148	−0.0435035
$621$	1.15011e148	0.0426913
$622$	−3.51643e149	−1.19761
$623$	2.52079e149	0.787819
$624$	−8.31727e149	−2.38564
$625$	1.30243e150	3.42904
$626$	1.73432e149	0.419181
$627$	3.84126e148	0.0852433
$628$	6.48793e148	0.132210
$629$	1.09155e148	0.0204283
$630$	5.30194e149	0.911414
$631$	1.41628e148	0.0223656	0.0111828	−	0.999937i	$-0.496440\pi$
$631$	1.41628e148	0.0223656	0.0111828	+	0.999937i	$0.496440\pi$
$632$	−6.66911e148	−0.0967618
$633$	−1.41312e150	−1.88400
$634$	7.48998e149	0.917710
$635$	−7.57460e149	−0.853032
$636$	−7.50811e148	−0.0777275
$637$	−1.29553e150	−1.23307
$638$	1.81063e150	1.58461
$639$	−3.89269e149	−0.313295
$640$	−2.91933e150	−2.16100
$641$	−1.21030e149	−0.0824117	−0.0412058	−	0.999151i	$-0.513120\pi$
$641$	−1.21030e149	−0.0824117	−0.0412058	+	0.999151i	$0.513120\pi$
$642$	−4.96237e149	−0.310860
$643$	1.61974e150	0.933595	0.466798	−	0.884364i	$-0.345408\pi$
$643$	1.61974e150	0.933595	0.466798	+	0.884364i	$0.345408\pi$
$644$	−9.64172e148	−0.0511400
$645$	4.73971e149	0.231370
$646$	3.95746e148	0.0177819
$647$	−1.65829e150	−0.685933	−0.342967	−	0.939348i	$-0.611432\pi$
$647$	−1.65829e150	−0.685933	−0.342967	+	0.939348i	$0.611432\pi$
$648$	2.39893e150	0.913598
$649$	−2.34409e150	−0.822021
$650$	1.32717e151	4.28608
$651$	−4.51682e149	−0.134354
$652$	2.02752e148	0.00555545
$653$	7.49401e150	1.89173	0.945865	−	0.324559i	$-0.105216\pi$
$653$	7.49401e150	1.89173	0.945865	+	0.324559i	$0.105216\pi$
$654$	−7.20435e150	−1.67566
$655$	−1.47836e151	−3.16863
$656$	−5.33368e149	−0.105359
$657$	2.99480e150	0.545282
$658$	−2.84396e148	−0.00477352
$659$	−5.17052e150	−0.800138	−0.400069	−	0.916485i	$-0.631014\pi$
$659$	−5.17052e150	−0.800138	−0.400069	+	0.916485i	$0.631014\pi$
$660$	−2.08095e150	−0.296935
$661$	1.25848e151	1.65603	0.828016	−	0.560704i	$-0.189469\pi$
$661$	1.25848e151	1.65603	0.828016	+	0.560704i	$0.189469\pi$
$662$	1.43913e150	0.174662
$663$	5.64159e150	0.631579
$664$	−1.50990e151	−1.55939
$665$	5.16286e149	0.0491963
$666$	8.66106e149	0.0761553
$667$	1.97748e151	1.60465
$668$	1.98734e149	0.0148844
$669$	−2.53528e151	−1.75278
$670$	−2.39423e151	−1.52814
$671$	1.65907e151	0.977708
$672$	2.43818e150	0.132681
$673$	−1.82046e151	−0.914902	−0.457451	−	0.889235i	$-0.651237\pi$
$673$	−1.82046e151	−0.914902	−0.457451	+	0.889235i	$0.651237\pi$
$674$	−5.86008e150	−0.272019
$675$	2.42551e150	0.104004
$676$	3.59539e150	0.142429
$677$	8.39817e150	0.307391	0.153695	−	0.988118i	$-0.450883\pi$
$677$	8.39817e150	0.307391	0.153695	+	0.988118i	$0.450883\pi$
$678$	5.45242e151	1.84417
$679$	−1.29976e150	−0.0406284
$680$	1.80515e151	0.521539
$681$	−9.12703e150	−0.243758
$682$	9.36116e150	0.231135
$683$	5.46158e151	1.24684	0.623420	−	0.781887i	$-0.285743\pi$
$683$	5.46158e151	1.24684	0.623420	+	0.781887i	$0.285743\pi$
$684$	3.01357e149	0.00636181
$685$	−4.86329e151	−0.949477
$686$	4.63498e151	0.836966
$687$	4.13502e149	0.00690705
$688$	6.01535e150	0.0929565
$689$	−5.50352e151	−0.786886
$690$	−2.36815e152	−3.13316
$691$	1.07319e152	1.31402	0.657011	−	0.753881i	$-0.271820\pi$
$691$	1.07319e152	1.31402	0.657011	+	0.753881i	$0.271820\pi$
$692$	7.87513e150	0.0892446
$693$	−4.43018e151	−0.464722
$694$	−1.01411e152	−0.984811
$695$	1.43332e152	1.28871
$696$	−2.36015e152	−1.96492
$697$	3.61783e150	0.0278929
$698$	2.71217e152	1.93665
$699$	−6.19046e151	−0.409444
$700$	−2.03338e151	−0.124587
$701$	1.19135e152	0.676278	0.338139	−	0.941096i	$-0.390203\pi$
$701$	1.19135e152	0.676278	0.338139	+	0.941096i	$0.390203\pi$
$702$	1.19501e151	0.0628542
$703$	8.43386e149	0.00411071
$704$	1.98250e152	0.895522
$705$	−6.70370e150	−0.0280670
$706$	−1.25440e152	−0.486838
$707$	−1.86504e152	−0.671042
$708$	−3.62892e151	−0.121059
$709$	4.63294e152	1.43312	0.716562	−	0.697524i	$-0.245715\pi$
$709$	4.63294e152	1.43312	0.716562	+	0.697524i	$0.245715\pi$
$710$	2.13972e152	0.613813
$711$	3.97475e151	0.105751
$712$	6.80996e152	1.68060
$713$	1.02238e152	0.234058
$714$	−9.00656e151	−0.191295
$715$	−1.52536e153	−3.00607
$716$	9.96807e151	0.182291
$717$	−9.50722e152	−1.61354
$718$	−6.35990e152	−1.00183
$719$	2.51126e152	0.367194	0.183597	−	0.983002i	$-0.441226\pi$
$719$	2.51126e152	0.367194	0.183597	+	0.983002i	$0.441226\pi$
$720$	1.58612e153	2.15301
$721$	−4.74413e152	−0.597888
$722$	−8.95712e152	−1.04816
$723$	−8.03258e152	−0.872884
$724$	2.85830e151	0.0288466
$725$	4.17037e153	3.90923
$726$	9.19607e151	0.0800743
$727$	−1.84362e153	−1.49135	−0.745674	−	0.666310i	$-0.767873\pi$
$727$	−1.84362e153	−1.49135	−0.745674	+	0.666310i	$0.767873\pi$
$728$	8.43513e152	0.633962
$729$	−1.50938e153	−1.05408
$730$	−1.64618e153	−1.06832
$731$	−4.08020e151	−0.0246095
$732$	2.56842e152	0.143987
$733$	−2.61358e153	−1.36199	−0.680994	−	0.732289i	$-0.738452\pi$
$733$	−2.61358e153	−1.36199	−0.680994	+	0.732289i	$0.738452\pi$
$734$	1.96742e153	0.953144
$735$	4.87522e153	2.19595
$736$	−5.51880e152	−0.231144
$737$	2.00056e153	0.779186
$738$	2.87063e152	0.103983
$739$	−1.73520e153	−0.584619	−0.292310	−	0.956324i	$-0.594424\pi$
$739$	−1.73520e153	−0.584619	−0.292310	+	0.956324i	$0.594424\pi$
$740$	−4.56893e151	−0.0143192
$741$	4.35899e152	0.127090
$742$	8.78613e152	0.238336
$743$	−2.32473e153	−0.586775	−0.293388	−	0.955994i	$-0.594783\pi$
$743$	−2.32473e153	−0.586775	−0.293388	+	0.955994i	$0.594783\pi$
$744$	−1.22023e153	−0.286608
$745$	5.92498e153	1.29517
$746$	−1.02425e152	−0.0208391
$747$	8.99891e153	1.70427
$748$	1.79140e152	0.0315832
$749$	5.57304e152	0.0914776
$750$	−3.11892e154	−4.76680
$751$	−1.04954e154	−1.49369	−0.746846	−	0.664997i	$-0.768433\pi$
$751$	−1.04954e154	−1.49369	−0.746846	+	0.664997i	$0.768433\pi$
$752$	−8.50792e151	−0.0112764
$753$	−1.85905e154	−2.29488
$754$	2.05466e154	2.36251
$755$	1.11896e154	1.19854
$756$	−1.83089e151	−0.00182703
$757$	−5.03389e152	−0.0468030	−0.0234015	−	0.999726i	$-0.507450\pi$
$757$	−5.03389e152	−0.0468030	−0.0234015	+	0.999726i	$0.507450\pi$
$758$	−9.52478e152	−0.0825188
$759$	1.97877e154	1.59757
$760$	1.39475e153	0.104947
$761$	1.72649e154	1.21083	0.605416	−	0.795909i	$-0.293007\pi$
$761$	1.72649e154	1.21083	0.605416	+	0.795909i	$0.293007\pi$
$762$	1.02097e154	0.667454
$763$	8.09092e153	0.493100
$764$	3.15359e153	0.179188
$765$	−1.07586e154	−0.569992
$766$	−2.93691e154	−1.45095
$767$	−2.66003e154	−1.22556
$768$	1.04382e154	0.448539
$769$	3.32940e154	1.33447	0.667233	−	0.744849i	$-0.267479\pi$
$769$	3.32940e154	1.33447	0.667233	+	0.744849i	$0.267479\pi$
$770$	2.43517e154	0.910491
$771$	−1.79575e154	−0.626379
$772$	1.02956e153	0.0335062
$773$	−4.57798e154	−1.39018	−0.695089	−	0.718923i	$-0.744635\pi$
$773$	−4.57798e154	−1.39018	−0.695089	+	0.718923i	$0.744635\pi$
$774$	−3.23751e153	−0.0917423
$775$	2.15614e154	0.570210
$776$	−3.51132e153	−0.0866698
$777$	−1.91941e153	−0.0442225
$778$	−3.84134e154	−0.826179
$779$	2.79532e152	0.00561278
$780$	−2.36143e154	−0.442704
$781$	−1.78790e154	−0.312978
$782$	2.03863e154	0.333256
$783$	3.75509e153	0.0573278
$784$	6.18733e154	0.882255
$785$	−1.78963e155	−2.38362
$786$	1.99267e155	2.47930
$787$	−6.09923e154	−0.708968	−0.354484	−	0.935062i	$-0.615344\pi$
$787$	−6.09923e154	−0.708968	−0.354484	+	0.935062i	$0.615344\pi$
$788$	−6.40182e153	−0.0695266
$789$	1.12608e155	1.14274
$790$	−2.18483e154	−0.207190
$791$	−6.12340e154	−0.542688
$792$	−1.19682e155	−0.991361
$793$	1.88268e155	1.45768
$794$	−4.65055e154	−0.336595
$795$	2.07104e155	1.40135
$796$	1.59407e154	0.100846
$797$	7.05357e154	0.417243	0.208622	−	0.977996i	$-0.433102\pi$
$797$	7.05357e154	0.417243	0.208622	+	0.977996i	$0.433102\pi$
$798$	−6.95894e153	−0.0384936
$799$	5.77091e152	0.00298532
$800$	−1.16388e155	−0.563111
$801$	−4.05870e155	−1.83674
$802$	6.37915e154	0.270044
$803$	1.37551e155	0.544729
$804$	3.09709e154	0.114751
$805$	2.65957e155	0.922003
$806$	1.06229e155	0.344602
$807$	2.55270e154	0.0774936
$808$	−5.03844e155	−1.43149
$809$	−4.84938e155	−1.28956	−0.644778	−	0.764369i	$-0.723050\pi$
$809$	−4.84938e155	−1.28956	−0.644778	+	0.764369i	$0.723050\pi$
$810$	7.85901e155	1.95623
$811$	−5.22979e155	−1.21862	−0.609311	−	0.792931i	$-0.708554\pi$
$811$	−5.22979e155	−1.21862	−0.609311	+	0.792931i	$0.708554\pi$
$812$	−3.14799e154	−0.0686731
$813$	−4.83542e155	−0.987621
$814$	3.97801e154	0.0760781
$815$	−5.59273e154	−0.100159
$816$	−2.69438e155	−0.451892
$817$	−3.15258e153	−0.00495206
$818$	1.32851e155	0.195462
$819$	−5.02729e155	−0.692859
$820$	−1.51433e154	−0.0195515
$821$	1.18000e156	1.42733	0.713666	−	0.700487i	$-0.247034\pi$
$821$	1.18000e156	1.42733	0.713666	+	0.700487i	$0.247034\pi$
$822$	6.55516e155	0.742918
$823$	1.46510e156	1.55588	0.777938	−	0.628341i	$-0.216266\pi$
$823$	1.46510e156	1.55588	0.777938	+	0.628341i	$0.216266\pi$
$824$	−1.28163e156	−1.27543
$825$	4.17310e156	3.89200
$826$	4.24663e155	0.371203
$827$	−8.15119e155	−0.667846	−0.333923	−	0.942600i	$-0.608373\pi$
$827$	−8.15119e155	−0.667846	−0.333923	+	0.942600i	$0.608373\pi$
$828$	1.55240e155	0.119229
$829$	−2.30416e155	−0.165900	−0.0829498	−	0.996554i	$-0.526434\pi$
$829$	−2.30416e155	−0.165900	−0.0829498	+	0.996554i	$0.526434\pi$
$830$	−4.94650e156	−3.33903
$831$	−1.69559e156	−1.07317
$832$	2.24971e156	1.33514
$833$	−4.19686e155	−0.233570
$834$	−1.93195e156	−1.00835
$835$	−5.48189e155	−0.268351
$836$	1.38413e154	0.00635536
$837$	1.94143e154	0.00836198
$838$	7.95207e155	0.321311
$839$	−1.43941e156	−0.545656	−0.272828	−	0.962063i	$-0.587959\pi$
$839$	−1.43941e156	−0.545656	−0.272828	+	0.962063i	$0.587959\pi$
$840$	−3.17424e156	−1.12901
$841$	3.46010e156	1.15479
$842$	4.22927e156	1.32455
$843$	3.71661e156	1.09237
$844$	−5.09192e155	−0.140463
$845$	−9.91755e156	−2.56785
$846$	4.57903e154	0.0111291
$847$	−1.03277e155	−0.0235636
$848$	2.62844e156	0.563014
$849$	5.99496e156	1.20566
$850$	4.29935e156	0.811877
$851$	4.34458e155	0.0770401
$852$	−2.76787e155	−0.0460923
$853$	−4.18908e156	−0.655157	−0.327578	−	0.944824i	$-0.606233\pi$
$853$	−4.18908e156	−0.655157	−0.327578	+	0.944824i	$0.606233\pi$
$854$	−3.00562e156	−0.441507
$855$	−8.31265e155	−0.114697
$856$	1.50557e156	0.195143
$857$	−1.14373e157	−1.39267	−0.696335	−	0.717717i	$-0.745187\pi$
$857$	−1.14373e157	−1.39267	−0.696335	+	0.717717i	$0.745187\pi$
$858$	2.05601e157	2.35210
$859$	−8.95276e156	−0.962327	−0.481163	−	0.876631i	$-0.659786\pi$
$859$	−8.95276e156	−0.962327	−0.481163	+	0.876631i	$0.659786\pi$
$860$	1.70787e155	0.0172499
$861$	−6.36171e155	−0.0603817
$862$	1.82698e157	1.62965
$863$	2.10960e157	1.76857	0.884285	−	0.466947i	$-0.154646\pi$
$863$	2.10960e157	1.76857	0.884285	+	0.466947i	$0.154646\pi$
$864$	−1.04798e155	−0.00825787
$865$	−2.17228e157	−1.60899
$866$	−4.07340e156	−0.283629
$867$	−1.99242e157	−1.30424
$868$	−1.62755e155	−0.0100168
$869$	1.82559e156	0.105644
$870$	−7.73195e157	−4.20735
$871$	2.27020e157	1.16170
$872$	2.18577e157	1.05190
$873$	2.09272e156	0.0947218
$874$	1.57515e156	0.0670597
$875$	3.50274e157	1.40274
$876$	2.12944e156	0.0802223
$877$	−1.03381e157	−0.366406	−0.183203	−	0.983075i	$-0.558647\pi$
$877$	−1.03381e157	−0.366406	−0.183203	+	0.983075i	$0.558647\pi$
$878$	−4.12896e157	−1.37684
$879$	4.51756e157	1.41742
$880$	7.28499e157	2.15083
$881$	−6.11495e157	−1.69895	−0.849477	−	0.527626i	$-0.823082\pi$
$881$	−6.11495e157	−1.69895	−0.849477	+	0.527626i	$0.823082\pi$
$882$	−3.33007e157	−0.870731
$883$	−3.95685e157	−0.973761	−0.486880	−	0.873469i	$-0.661865\pi$
$883$	−3.95685e157	−0.973761	−0.486880	+	0.873469i	$0.661865\pi$
$884$	2.03284e156	0.0470878
$885$	1.00100e158	2.18258
$886$	−4.35413e157	−0.893711
$887$	7.49842e157	1.44896	0.724480	−	0.689296i	$-0.242080\pi$
$887$	7.49842e157	1.44896	0.724480	+	0.689296i	$0.242080\pi$
$888$	−5.18532e156	−0.0943370
$889$	−1.14661e157	−0.196413
$890$	2.23098e158	3.59857
$891$	−6.56680e157	−0.997463
$892$	−9.13541e156	−0.130680
$893$	4.45891e154	0.000600725 0
$894$	−7.98620e157	−1.01340
$895$	−2.74959e158	−3.28652
$896$	−4.41915e157	−0.497577
$897$	2.24547e158	2.38184
$898$	−2.05563e158	−2.05429
$899$	3.33804e157	0.314303
$900$	3.27392e157	0.290465
$901$	−1.78286e157	−0.149053
$902$	1.31847e157	0.103878
$903$	7.17477e156	0.0532737
$904$	−1.65425e158	−1.15768
$905$	−7.88436e157	−0.520076
$906$	−1.50823e158	−0.937799
$907$	1.73315e158	1.01589	0.507945	−	0.861390i	$-0.330405\pi$
$907$	1.73315e158	1.01589	0.507945	+	0.861390i	$0.330405\pi$
$908$	−3.28876e156	−0.0181735
$909$	3.00288e158	1.56448
$910$	2.76339e158	1.35746
$911$	−8.96077e155	−0.00415061	−0.00207531	−	0.999998i	$-0.500661\pi$
$911$	−8.96077e155	−0.00415061	−0.00207531	+	0.999998i	$0.500661\pi$
$912$	−2.08182e157	−0.0909324
$913$	4.13318e158	1.70254
$914$	3.05675e158	1.18751
$915$	−7.08475e158	−2.59595
$916$	1.48998e155	0.000514959 0
$917$	−2.23788e158	−0.729589
$918$	3.87122e156	0.0119059
$919$	3.84005e158	1.11419	0.557093	−	0.830450i	$-0.311917\pi$
$919$	3.84005e158	1.11419	0.557093	+	0.830450i	$0.311917\pi$
$920$	7.18488e158	1.96685
$921$	−9.78783e158	−2.52811
$922$	−5.58235e158	−1.36054
$923$	−2.02888e158	−0.466622
$924$	−3.15005e157	−0.0683703
$925$	9.16245e157	0.187685
$926$	9.90309e157	0.191462
$927$	7.63846e158	1.39393
$928$	−1.80187e158	−0.310390
$929$	1.15114e159	1.87192	0.935961	−	0.352104i	$-0.114534\pi$
$929$	1.15114e159	1.87192	0.935961	+	0.352104i	$0.114534\pi$
$930$	−3.99751e158	−0.613694
$931$	−3.24271e157	−0.0470003
$932$	−2.23062e157	−0.0305263
$933$	−1.25473e159	−1.62137
$934$	1.05814e159	1.29117
$935$	−4.94140e158	−0.569414
$936$	−1.35813e159	−1.47803
$937$	−1.25699e159	−1.29200	−0.646002	−	0.763335i	$-0.723560\pi$
$937$	−1.25699e159	−1.29200	−0.646002	+	0.763335i	$0.723560\pi$
$938$	−3.62428e158	−0.351860
$939$	6.18836e158	0.567500
$940$	−2.41556e156	−0.00209256
$941$	−1.37242e159	−1.12316	−0.561581	−	0.827422i	$-0.689807\pi$
$941$	−1.37242e159	−1.12316	−0.561581	+	0.827422i	$0.689807\pi$
$942$	2.41222e159	1.86506
$943$	1.43997e158	0.105191
$944$	1.27041e159	0.876883
$945$	5.05034e157	0.0329396
$946$	−1.48698e158	−0.0916493
$947$	1.48647e159	0.865829	0.432915	−	0.901435i	$-0.357485\pi$
$947$	1.48647e159	0.865829	0.432915	+	0.901435i	$0.357485\pi$
$948$	2.82622e157	0.0155582
$949$	1.56090e159	0.812143
$950$	3.32190e158	0.163371
$951$	2.67256e159	1.24242
$952$	2.73256e158	0.120086
$953$	6.33742e155	0.000263295 0	0.000131647	−	1.00000i	$-0.499958\pi$
$953$	6.33742e155	0.000263295 0	0.000131647		1.00000i	$0.499958\pi$
$954$	−1.41464e159	−0.555660
$955$	−8.69886e159	−3.23059
$956$	−3.42575e158	−0.120298
$957$	6.46063e159	2.14529
$958$	5.47965e159	1.72067
$959$	−7.36183e158	−0.218620
$960$	−8.46591e159	−2.37773
$961$	−3.59187e159	−0.954155
$962$	4.51417e158	0.113426
$963$	−8.97308e158	−0.213273
$964$	−2.89440e158	−0.0650784
$965$	−2.83994e159	−0.604084
$966$	−3.58480e159	−0.721421
$967$	7.63251e159	1.45329	0.726643	−	0.687015i	$-0.241080\pi$
$967$	7.63251e159	1.45329	0.726643	+	0.687015i	$0.241080\pi$
$968$	−2.79005e158	−0.0502668
$969$	1.41209e158	0.0240736
$970$	−1.15032e159	−0.185580
$971$	−8.87243e159	−1.35461	−0.677304	−	0.735703i	$-0.736852\pi$
$971$	−8.87243e159	−1.35461	−0.677304	+	0.735703i	$0.736852\pi$
$972$	−1.04531e159	−0.151042
$973$	2.16970e159	0.296730
$974$	−5.54267e159	−0.717488
$975$	4.73556e160	5.80263
$976$	−8.99152e159	−1.04296
$977$	−2.38981e159	−0.262425	−0.131212	−	0.991354i	$-0.541887\pi$
$977$	−2.38981e159	−0.262425	−0.131212	+	0.991354i	$0.541887\pi$
$978$	7.53836e158	0.0783697
$979$	−1.86415e160	−1.83488
$980$	1.75670e159	0.163720
$981$	−1.30271e160	−1.14962
$982$	1.88681e160	1.57675
$983$	7.82734e159	0.619442	0.309721	−	0.950827i	$-0.399764\pi$
$983$	7.82734e159	0.619442	0.309721	+	0.950827i	$0.399764\pi$
$984$	−1.71863e159	−0.128808
$985$	1.76588e160	1.25350
$986$	6.65608e159	0.447511
$987$	−1.01478e158	−0.00646253
$988$	1.57068e158	0.00947528
$989$	−1.62401e159	−0.0928082
$990$	−3.92084e160	−2.12274
$991$	−2.86958e160	−1.47190	−0.735949	−	0.677037i	$-0.763264\pi$
$991$	−2.86958e160	−1.47190	−0.735949	+	0.677037i	$0.763264\pi$
$992$	−9.31592e158	−0.0452742
$993$	5.13508e159	0.236462
$994$	3.23902e159	0.141332
$995$	−4.39710e160	−1.81816
$996$	6.39862e159	0.250733
$997$	1.91871e160	0.712554	0.356277	−	0.934380i	$-0.384046\pi$
$997$	1.91871e160	0.712554	0.356277	+	0.934380i	$0.384046\pi$
$998$	5.98529e159	0.210669
$999$	8.25005e157	0.00275235

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.108.a.a.1.7	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.108.a.a.1.7	✓	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)

\(f(q)\)	\(=\)	\(q+1.33972e16 q^{2} +4.78035e25 q^{3} +1.72251e31 q^{4} -4.75138e37 q^{5} +6.40432e41 q^{6} -7.19244e44 q^{7} -1.94305e48 q^{8} +1.15805e51 q^{9} +O(q^{10})\)	\(q+1.33972e16 q^{2} +4.78035e25 q^{3} +1.72251e31 q^{4} -4.75138e37 q^{5} +6.40432e41 q^{6} -7.19244e44 q^{7} -1.94305e48 q^{8} +1.15805e51 q^{9} -6.36552e53 q^{10} +5.31887e55 q^{11} +8.23422e56 q^{12} +6.03576e59 q^{13} -9.63584e60 q^{14} -2.27133e63 q^{15} -2.88263e64 q^{16} +1.95528e65 q^{17} +1.55145e67 q^{18} +1.51075e67 q^{19} -8.18432e68 q^{20} -3.43824e70 q^{21} +7.12579e71 q^{22} +7.78244e72 q^{23} -9.28845e73 q^{24} +1.64127e75 q^{25} +8.08622e75 q^{26} +1.47783e75 q^{27} -1.23891e76 q^{28} +2.54095e78 q^{29} -3.04294e79 q^{30} +1.31370e79 q^{31} -7.09135e79 q^{32} +2.54261e81 q^{33} +2.61953e81 q^{34} +3.41740e82 q^{35} +1.99475e82 q^{36} +5.58255e82 q^{37} +2.02399e83 q^{38} +2.88531e85 q^{39} +9.23217e85 q^{40} +1.85028e85 q^{41} -4.60627e86 q^{42} -2.08676e86 q^{43} +9.16183e86 q^{44} -5.50232e88 q^{45} +1.04263e89 q^{46} +2.95144e87 q^{47} -1.37800e90 q^{48} -2.14642e90 q^{49} +2.19884e91 q^{50} +9.34694e90 q^{51} +1.03967e91 q^{52} -9.11818e91 q^{53} +1.97988e91 q^{54} -2.52720e93 q^{55} +1.39753e93 q^{56} +7.22194e92 q^{57} +3.40415e94 q^{58} -4.40712e94 q^{59} -3.91239e94 q^{60} +3.11921e95 q^{61} +1.75999e95 q^{62} -8.32917e95 q^{63} +3.72729e96 q^{64} -2.86782e97 q^{65} +3.40638e97 q^{66} +3.76125e97 q^{67} +3.36800e96 q^{68} +3.72028e98 q^{69} +4.57836e98 q^{70} -3.36143e98 q^{71} -2.25014e99 q^{72} +2.58608e99 q^{73} +7.47904e98 q^{74} +7.84584e100 q^{75} +2.60229e98 q^{76} -3.82557e100 q^{77} +3.86550e101 q^{78} +3.43229e100 q^{79} +1.36965e102 q^{80} -1.23462e102 q^{81} +2.47886e101 q^{82} +7.77077e102 q^{83} -5.92241e101 q^{84} -9.29030e102 q^{85} -2.79567e102 q^{86} +1.21466e104 q^{87} -1.03348e104 q^{88} -3.50478e104 q^{89} -7.37156e104 q^{90} -4.34118e104 q^{91} +1.34054e104 q^{92} +6.27995e104 q^{93} +3.95410e103 q^{94} -7.17818e104 q^{95} -3.38992e105 q^{96} +1.80712e105 q^{97} -2.87560e106 q^{98} +6.15950e106 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 54\!\cdots\!96 q^{2}+ \cdots + 36\!\cdots\!13 q^{9}+O(q^{10}) \) 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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