LMFDB - Embedded newform 1.110.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,110,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, 110, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 110);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 110 $
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:	$75.2394221917$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2 x^{7} + \cdots + 46\!\cdots\!00 $ x^8 - 2x^7 - 105157544971824068037616107801x^6 - 720499541410571743705396073770132757852828x^5 + 3157824973101980775937296062188904495767314036215430711556x^4 + 37671158034607910359887282876456464717407719385407863123677334638658880x^3 - 26682190246404719175459095049828456574784707986590178877208641309384111166276615852400x^2 - 71955323358604442117150085274712244756758371417580977145751971458747375799621777969448934562232000*x + 4609371327848419314126692147678999375582532170698584812463847870719453732146321266257114251773496735082214200000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{118}\cdot 3^{40}\cdot 5^{14}\cdot 7^{6}\cdot 11^{3}\cdot 13 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.06740e14$ 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)

$f(q)$	$=$	$q-2.02081e16 q^{2} -7.88466e25 q^{3} -2.40671e32 q^{4} +1.60701e38 q^{5} +1.59334e42 q^{6} +1.73591e45 q^{7} +1.79793e49 q^{8} -3.92739e51 q^{9} +O(q^{10})$	\(q-2.02081e16 q^{2} -7.88466e25 q^{3} -2.40671e32 q^{4} +1.60701e38 q^{5} +1.59334e42 q^{6} +1.73591e45 q^{7} +1.79793e49 q^{8} -3.92739e51 q^{9} -3.24746e54 q^{10} -1.26288e56 q^{11} +1.89761e58 q^{12} -6.03445e60 q^{13} -3.50795e61 q^{14} -1.26707e64 q^{15} -2.07122e65 q^{16} -1.23439e67 q^{17} +7.93649e67 q^{18} +8.35349e69 q^{19} -3.86762e70 q^{20} -1.36871e71 q^{21} +2.55203e72 q^{22} +1.30595e74 q^{23} -1.41761e75 q^{24} +1.04174e76 q^{25} +1.21944e77 q^{26} +1.10950e78 q^{27} -4.17785e77 q^{28} -1.12636e79 q^{29} +2.56051e80 q^{30} -1.73636e81 q^{31} -7.48370e81 q^{32} +9.95736e81 q^{33} +2.49446e83 q^{34} +2.78963e83 q^{35} +9.45210e83 q^{36} +3.88192e85 q^{37} -1.68808e86 q^{38} +4.75796e86 q^{39} +2.88929e87 q^{40} +7.86296e87 q^{41} +2.76590e87 q^{42} +3.55561e88 q^{43} +3.03939e88 q^{44} -6.31135e89 q^{45} -2.63907e90 q^{46} -2.02854e90 q^{47} +1.63308e91 q^{48} -1.27509e92 q^{49} -2.10516e92 q^{50} +9.73273e92 q^{51} +1.45232e93 q^{52} +1.36263e94 q^{53} -2.24207e94 q^{54} -2.02946e94 q^{55} +3.12105e94 q^{56} -6.58645e95 q^{57} +2.27615e95 q^{58} +1.85357e96 q^{59} +3.04949e96 q^{60} -1.53133e97 q^{61} +3.50885e97 q^{62} -6.81761e96 q^{63} +2.85661e98 q^{64} -9.69743e98 q^{65} -2.01219e98 q^{66} -1.76671e99 q^{67} +2.97082e99 q^{68} -1.02970e100 q^{69} -5.63731e99 q^{70} +1.19527e101 q^{71} -7.06116e100 q^{72} -5.70675e101 q^{73} -7.84461e101 q^{74} -8.21378e101 q^{75} -2.01045e102 q^{76} -2.19225e101 q^{77} -9.61491e102 q^{78} -3.23840e103 q^{79} -3.32847e103 q^{80} -4.76398e103 q^{81} -1.58895e104 q^{82} -7.45225e104 q^{83} +3.29410e103 q^{84} -1.98367e105 q^{85} -7.18520e104 q^{86} +8.88096e104 q^{87} -2.27056e105 q^{88} +2.08758e106 q^{89} +1.27540e106 q^{90} -1.04753e106 q^{91} -3.14305e106 q^{92} +1.36906e107 q^{93} +4.09928e106 q^{94} +1.34242e108 q^{95} +5.90064e107 q^{96} -1.80786e107 q^{97} +2.57672e108 q^{98} +4.95981e107 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 22\!\cdots\!00 q^{2}+ \cdots + 24\!\cdots\!84 q^{9}+O(q^{10}) $ 8 * q + 2288392606915200 * q^2 - 79912254646281404120911200 * q^3 + 2561413209738240277879721565741056 * q^4 - 213255348687551833005583336469825970000 * q^5 + 6583361430969554396417990643904425772724736 * q^6 + 2340906693576137711090348032140051967265800000 * q^7 - 11615898303025646840479523942639805952956786278400 * q^8 + 2442167730177863701398288419313511486695316522756584 * q^9	$ 8 q + 22\!\cdots\!00 q^{2}+ \cdots + 71\!\cdots\!28 q^{99}+O(q^{100}) $ 8 * q + 2288392606915200 * q^2 - 79912254646281404120911200 * q^3 + 2561413209738240277879721565741056 * q^4 - 213255348687551833005583336469825970000 * q^5 + 6583361430969554396417990643904425772724736 * q^6 + 2340906693576137711090348032140051967265800000 * q^7 - 11615898303025646840479523942639805952956786278400 * q^8 + 2442167730177863701398288419313511486695316522756584 * q^9 + 1812920838217088357740086473089711591380968010637920000 * q^10 - 165947975430612920732153376325913672821997118332062700064 * q^11 - 91447218063548694114657346762586040488310132762945923481600 * q^12 - 7191403001708863672049265996058758403993505035337715331216400 * q^13 - 509718116120592395778374084857614778933075979029025208586042368 * q^14 + 23523118033136793898911835577576979866924828095398791554532760000 * q^15 + 1148530988697824742941824958565237185269878102817249769800092090368 * q^16 - 8656206993525090371911384042688075118245096778873514284447257516400 * q^17 - 594865916442544102448370621315341724156945499047441634064537134051200 * q^18 - 11207956347132239593501696340276604562903586944462900105290733089025760 * q^19 - 318028102788054771974342811943070552646655597179484587999192418007040000 * q^20 - 2767292515426156676853955740316424819275205191740879849349575383275847424 * q^21 + 14938820094709351316223859446246734647054202968288974693072213154286630400 * q^22 + 53936338606237446863185709770824957589455521350451701866403050553428350400 * q^23 + 5321978767822090266204570063167770260876413438542000203325176764538153861120 * q^24 + 18193458801058157698506203622645619662054791653093200756293219491399746875000 * q^25 - 435759349281531260141580744807392307738565554114182063684255943941959138178304 * q^26 - 272453442859186698036015029517519337343034663149290746308745684225146650622400 * q^27 + 31554975806041099413511213807244716611018915532477271262553604696632234310041600 * q^28 + 29771410364049527567872005799257248512262425259650062583814547510404351825013360 * q^29 - 751891125225161548033301007468436615543819263432942020592477930753653797722240000 * q^30 - 1466375047838170098337421957808047734223626673774209444573675519328499442335175424 * q^31 - 5937114879483988773905731140457152891870978542120977621282805115905850091556044800 * q^32 + 98313301892085553482704563970636693639651433404572558153235155127418907919206665600 * q^33 + 230323498000052302973276572671855085448946915340852153738007852434989492667839528192 * q^34 - 2881501566480835926866891176622148835419121956576388959555158972591401000555206480000 * q^35 + 1939555675122247234177033125266156026088405967647423925256129675441087219550987378688 * q^36 + 33117119032354918971772421960637107981416747079728699237422500438475360696577657658800 * q^37 + 11996231369252381781466269208385230328578753740510963392596214782634078981979819686400 * q^38 - 771921798225629223813541576850627931176100580853963300794965264851972743236296284337472 * q^39 - 1009702443147367270514989525871937316615498052888256181187241154243431845313822720000000 * q^40 + 2631322094324930918487353619268593963294779980083389672280377185771701226284660975010896 * q^41 + 65594383583093454058986149447123157383111717279272925654585914541457714878623959042969600 * q^42 - 31764236064988776927398716108299521712529891801740350383239284135241451092841492492916000 * q^43 - 1270138580535281866445275727176723968063639122939870285300305417276565925160179749765480448 * q^44 + 287550814354171023801469605323898278540973909702719042079897511272969200785142386583190000 * q^45 + 14731896191270382685679107493825145018801039145654619659863205374802348136428160980957203456 * q^46 + 1625966957623832725817330998098515479861611323645021162528642542135008566368994094752150400 * q^47 - 143515128231599226227412132210359595219087228680385094858911141289724103136282160567785881600 * q^48 + 157527210655459293654279435784054674911203740727991629561212852729050695391270938108305773256 * q^49 + 322389957080420808210330902387583711642761566269183034944052266108906361308513927567750000000 * q^50 + 489920249498412339580606438123981910239683109252240004744192036459028106019912596244615989056 * q^51 - 5418992932208438205367792844823104431376197758802798107419957407784673910371822411932948480000 * q^52 + 9079308927321999351839177242746605854068388719924761670955991989783550469317936688082585930800 * q^53 - 24658507391097864427096370814937103472102040716547930307285838917927527638460695296874932751360 * q^54 + 118053680695881329185791540339622577195944539453849780739010333239182345152398471707806930760000 * q^55 - 201389106942279308288684434910785164662432037404781190144927582600705075235687388648357243125760 * q^56 + 226496945243108169507552544266677467884770074749629615006273688546254129496817350185452963651200 * q^57 - 2256052219534551389222024892508180423211025192914838983567709038409124940298945339969797987462400 * q^58 + 4201127473917559295037000225082981757247285086029974371230017377519538448027563747794558119713120 * q^59 + 15216716099557435608186566564337243721720353898331991157134416546559198037722222436035882885120000 * q^60 - 30174048445162611506034669407223089181051188758336573543308996493766034896596718300335923046430864 * q^61 - 101544378414770749846552697740777177239249497144967223452446029336671969269242448735950839304089600 * q^62 + 14962713033462753217361258544731526063207174198501064720440567489611717321152011844939244550427200 * q^63 + 350038493426472551390597880934195636388642189179841132000343481745073872195685178531480362020765696 * q^64 + 476042359995918992070699407122502192834702528804977370861576537263180680689143678390528307394660000 * q^65 - 3275457019157048603844818296003073802975658177120439799661182596542152337047019411219264546535589888 * q^66 - 2436592395324825448922436507298035360575674608488356192165065318580447361065445345719842978744898400 * q^67 - 22959577515788229863200422300261772167503744576389306175032085019828406207819090307551668913740595200 * q^68 + 20962513668346194921311473125160506340730960425003577830665711051634607002491986052437616343941489408 * q^69 - 38525614227951931001890316995983503763039503305975313750394662544984531605107874814848981273114880000 * q^70 - 182573264747524893462812402066757238991600980622231780705554761994960061464852147866759574299425367744 * q^71 - 937013521429830591768584754113763645664639906707863675451385694160469158557397360724539243386123059200 * q^72 - 992896003296363120918893380101417451599330843653017480857467556556562812303212272149043323072822439600 * q^73 - 1316746856327833419755644274540778481224231099510738713247508136902506806815717963522494407938546706688 * q^74 - 5871153288989297422411624806238187142192319563981336377889812488967662534076652985829089331258062500000 * q^75 - 23122551287666805941113536895845604280282190834103625501792190953367813062086656110687054676514749317120 * q^76 - 44146648850167699533016381157041098991672229312739789979368878215748452932712438044537666517717336608000 * q^77 - 74892005734867915768666768757796138875218855701976264642428162201719215233844576875406596388579804800000 * q^78 - 90877532388837507952377455262957690392004628366214899622576763930269368002866396444184811504470015827840 * q^79 - 537781290078408386666779886550832547957426185756793627297710378503553917482370710673024120741030789120000 * q^80 - 646040908793719449537213596253179795437117284606067679926187088540718516170416551690117712718559479920952 * q^81 - 1848162147553486548774628152888041182300793513808419102386749930544002262019111364366904880902061490681600 * q^82 - 866870614432750569174068646397256005138067253779508313470225924424638854266524026533083951694014356632800 * q^83 - 5840321795963005263777537308314418455056100956933759881092476300148871178382910044395005678085199546810368 * q^84 - 4668598916513761978133063620912572637580033499314634770309162489375519884024385880981753435084614859780000 * q^85 - 11688849548141363142089712396810850759020238587238805174946214292159714105146960272302323952195024989223424 * q^86 - 14581012249541375875764697103578340512244662623918147927221635902236243713987632388375578563817763114939200 * q^87 + 1530700112628746576163110294213004687459510268085538799651168686191357904989458023327058330803008647987200 * q^88 + 5370705282028265416504724158890178832899726253313779513986675059327392734022379735004069389198976135292880 * q^89 + 161603588167186166620406432595952865977969553485604382571187217963936716570564141726485419061308378075360000 * q^90 + 194491542286867118776437353517384882722616087297518094870786488241189494865282342165823695439370137913188736 * q^91 + 396302396563700359070027419943848305453145578954245792583330941741389770954106976666840341236078014314905600 * q^92 + 568179503361190024971076757263143967044040944520818668848960482931727310093723555328260563778420711013401600 * q^93 + 2479261213469097720755806625234954860838342725140724073489565122893996978512713040202033247954948169489487872 * q^94 + 3756267234494004771512604096671502522809843506715611046331612224428460858882412872485716488615235385073400000 * q^95 + 6137029402133719259406354903032524770352961857248155285728041689493176172684541150438338362553846429716054016 * q^96 + 3101905862702772302621994244705111813594597058738421633214535517860020385681724882654741053598909419139696400 * q^97 + 1265481578258615993478779535911065302494358871538528748084590996688739571409881009859314203275359668334966400 * q^98 + 719245389651015996203722525987404961611392270203442708727501943323361320310359905092561649275451940844703328 * 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 $

$2$	−2.02081e16	−0.793213	−0.396606	−	0.917989i	$-0.629812\pi$
$2$	−2.02081e16	−0.793213	−0.396606	+	0.917989i	$0.629812\pi$
$3$	−7.88466e25	−0.782843	−0.391422	−	0.920212i	$-0.628017\pi$
$3$	−7.88466e25	−0.782843	−0.391422	+	0.920212i	$0.628017\pi$
$4$	−2.40671e32	−0.370813
$5$	1.60701e38	1.29465	0.647327	−	0.762212i	$-0.275887\pi$
$5$	1.60701e38	1.29465	0.647327	+	0.762212i	$0.275887\pi$
$6$	1.59334e42	0.620961
$7$	1.73591e45	0.151945	0.0759723	−	0.997110i	$-0.475794\pi$
$7$	1.73591e45	0.151945	0.0759723	+	0.997110i	$0.475794\pi$
$8$	1.79793e49	1.08735
$9$	−3.92739e51	−0.387157
$10$	−3.24746e54	−1.02694
$11$	−1.26288e56	−0.221544	−0.110772	−	0.993846i	$-0.535332\pi$
$11$	−1.26288e56	−0.221544	−0.110772	+	0.993846i	$0.535332\pi$
$12$	1.89761e58	0.290288
$13$	−6.03445e60	−1.17686	−0.588430	−	0.808548i	$-0.700254\pi$
$13$	−6.03445e60	−1.17686	−0.588430	+	0.808548i	$0.700254\pi$
$14$	−3.50795e61	−0.120524
$15$	−1.26707e64	−1.01351
$16$	−2.07122e65	−0.491684
$17$	−1.23439e67	−1.07643	−0.538214	−	0.842808i	$-0.680901\pi$
$17$	−1.23439e67	−1.07643	−0.538214	+	0.842808i	$0.680901\pi$
$18$	7.93649e67	0.307098
$19$	8.35349e69	1.69745	0.848725	−	0.528835i	$-0.177371\pi$
$19$	8.35349e69	1.69745	0.848725	+	0.528835i	$0.177371\pi$
$20$	−3.86762e70	−0.480075
$21$	−1.36871e71	−0.118949
$22$	2.55203e72	0.175731
$23$	1.30595e74	0.797552	0.398776	−	0.917048i	$-0.369435\pi$
$23$	1.30595e74	0.797552	0.398776	+	0.917048i	$0.369435\pi$
$24$	−1.41761e75	−0.851222
$25$	1.04174e76	0.676129
$26$	1.21944e77	0.933501
$27$	1.10950e78	1.08593
$28$	−4.17785e77	−0.0563431
$29$	−1.12636e79	−0.224381	−0.112191	−	0.993687i	$-0.535787\pi$
$29$	−1.12636e79	−0.224381	−0.112191	+	0.993687i	$0.535787\pi$
$30$	2.56051e80	0.803930
$31$	−1.73636e81	−0.912910	−0.456455	−	0.889747i	$-0.650881\pi$
$31$	−1.73636e81	−0.912910	−0.456455	+	0.889747i	$0.650881\pi$
$32$	−7.48370e81	−0.697336
$33$	9.95736e81	0.173434
$34$	2.49446e83	0.853837
$35$	2.78963e83	0.196716
$36$	9.45210e83	0.143563
$37$	3.88192e85	1.32450	0.662251	−	0.749282i	$-0.269601\pi$
$37$	3.88192e85	1.32450	0.662251	+	0.749282i	$0.269601\pi$
$38$	−1.68808e86	−1.34644
$39$	4.75796e86	0.921297
$40$	2.88929e87	1.40774
$41$	7.86296e87	0.997392	0.498696	−	0.866777i	$-0.333812\pi$
$41$	7.86296e87	0.997392	0.498696	+	0.866777i	$0.333812\pi$
$42$	2.76590e87	0.0943517
$43$	3.55561e88	0.336421	0.168211	−	0.985751i	$-0.446201\pi$
$43$	3.55561e88	0.336421	0.168211	+	0.985751i	$0.446201\pi$
$44$	3.03939e88	0.0821514
$45$	−6.31135e89	−0.501234
$46$	−2.63907e90	−0.632629
$47$	−2.02854e90	−0.150609	−0.0753044	−	0.997161i	$-0.523993\pi$
$47$	−2.02854e90	−0.150609	−0.0753044	+	0.997161i	$0.523993\pi$
$48$	1.63308e91	0.384912
$49$	−1.27509e92	−0.976913
$50$	−2.10516e92	−0.536314
$51$	9.73273e92	0.842675
$52$	1.45232e93	0.436395
$53$	1.36263e94	1.44992	0.724959	−	0.688792i	$-0.241858\pi$
$53$	1.36263e94	1.44992	0.724959	+	0.688792i	$0.241858\pi$
$54$	−2.24207e94	−0.861371
$55$	−2.02946e94	−0.286823
$56$	3.12105e94	0.165216
$57$	−6.58645e95	−1.32884
$58$	2.27615e95	0.177982
$59$	1.85357e96	0.570920	0.285460	−	0.958391i	$-0.407854\pi$
$59$	1.85357e96	0.570920	0.285460	+	0.958391i	$0.407854\pi$
$60$	3.04949e96	0.375823
$61$	−1.53133e97	−0.766640	−0.383320	−	0.923616i	$-0.625219\pi$
$61$	−1.53133e97	−0.766640	−0.383320	+	0.923616i	$0.625219\pi$
$62$	3.50885e97	0.724132
$63$	−6.81761e96	−0.0588264
$64$	2.85661e98	1.04482
$65$	−9.69743e98	−1.52363
$66$	−2.01219e98	−0.137570
$67$	−1.76671e99	−0.532216	−0.266108	−	0.963943i	$-0.585738\pi$
$67$	−1.76671e99	−0.532216	−0.266108	+	0.963943i	$0.585738\pi$
$68$	2.97082e99	0.399154
$69$	−1.02970e100	−0.624358
$70$	−5.63731e99	−0.156037
$71$	1.19527e101	1.52717	0.763583	−	0.645710i	$-0.223439\pi$
$71$	1.19527e101	1.52717	0.763583	+	0.645710i	$0.223439\pi$
$72$	−7.06116e100	−0.420974
$73$	−5.70675e101	−1.60433	−0.802164	−	0.597104i	$-0.796318\pi$
$73$	−5.70675e101	−1.60433	−0.802164	+	0.597104i	$0.796318\pi$
$74$	−7.84461e101	−1.05061
$75$	−8.21378e101	−0.529303
$76$	−2.01045e102	−0.629436
$77$	−2.19225e101	−0.0336624
$78$	−9.61491e102	−0.730785
$79$	−3.23840e103	−1.22929	−0.614644	−	0.788805i	$-0.710700\pi$
$79$	−3.23840e103	−1.22929	−0.614644	+	0.788805i	$0.710700\pi$
$80$	−3.32847e103	−0.636561
$81$	−4.76398e103	−0.462953
$82$	−1.58895e104	−0.791144
$83$	−7.45225e104	−1.91660	−0.958300	−	0.285763i	$-0.907753\pi$
$83$	−7.45225e104	−1.91660	−0.958300	+	0.285763i	$0.907753\pi$
$84$	3.29410e103	0.0441078
$85$	−1.98367e105	−1.39360
$86$	−7.18520e104	−0.266854
$87$	8.88096e104	0.175655
$88$	−2.27056e105	−0.240895
$89$	2.08758e106	1.19643	0.598215	−	0.801335i	$-0.295877\pi$
$89$	2.08758e106	1.19643	0.598215	+	0.801335i	$0.295877\pi$
$90$	1.27540e106	0.397585
$91$	−1.04753e106	−0.178818
$92$	−3.14305e106	−0.295743
$93$	1.36906e107	0.714665
$94$	4.09928e106	0.119465
$95$	1.34242e108	2.19761
$96$	5.90064e107	0.545905
$97$	−1.80786e107	−0.0950836	−0.0475418	−	0.998869i	$-0.515139\pi$
$97$	−1.80786e107	−0.0950836	−0.0475418	+	0.998869i	$0.515139\pi$
$98$	2.57672e108	0.774900
$99$	4.95981e107	0.0857722
$100$	−2.50717e108	−0.250717
$101$	−2.94530e109	−1.71244	−0.856218	−	0.516615i	$-0.827192\pi$
$101$	−2.94530e109	−1.71244	−0.856218	+	0.516615i	$0.827192\pi$
$102$	−1.96679e109	−0.668420
$103$	5.99033e109	1.19625	0.598125	−	0.801403i	$-0.295913\pi$
$103$	5.99033e109	1.19625	0.598125	+	0.801403i	$0.295913\pi$
$104$	−1.08495e110	−1.27966
$105$	−2.19953e109	−0.153997
$106$	−2.75361e110	−1.15009
$107$	−1.26731e108	−0.00317298	−0.00158649	−	0.999999i	$-0.500505\pi$
$107$	−1.26731e108	−0.00317298	−0.00158649	+	0.999999i	$0.500505\pi$
$108$	−2.67024e110	−0.402676
$109$	1.00300e111	0.915288	0.457644	−	0.889136i	$-0.348694\pi$
$109$	1.00300e111	0.915288	0.457644	+	0.889136i	$0.348694\pi$
$110$	4.10114e110	0.227511
$111$	−3.06076e111	−1.03688
$112$	−3.59546e110	−0.0747088
$113$	1.07443e112	1.37531	0.687657	−	0.726036i	$-0.258639\pi$
$113$	1.07443e112	1.37531	0.687657	+	0.726036i	$0.258639\pi$
$114$	1.33099e112	1.05405
$115$	2.09867e112	1.03255
$116$	2.71083e111	0.0832034
$117$	2.36996e112	0.455630
$118$	−3.74571e112	−0.452861
$119$	−2.14279e112	−0.163557
$120$	−2.27811e113	−1.10204
$121$	−3.08991e113	−0.950918
$122$	3.09451e113	0.608109
$123$	−6.19968e113	−0.780801
$124$	4.17893e113	0.338519
$125$	−8.01903e113	−0.419301
$126$	1.37771e113	0.0466619
$127$	−3.33395e114	−0.733932	−0.366966	−	0.930234i	$-0.619603\pi$
$127$	−3.33395e114	−0.733932	−0.366966	+	0.930234i	$0.619603\pi$
$128$	−9.15450e113	−0.131429
$129$	−2.80348e114	−0.263365
$130$	1.95966e115	1.20856
$131$	2.77122e115	1.12561	0.562803	−	0.826591i	$-0.309723\pi$
$131$	2.77122e115	1.12561	0.562803	+	0.826591i	$0.309723\pi$
$132$	−2.39645e114	−0.0643116
$133$	1.45010e115	0.257918
$134$	3.57017e115	0.422160
$135$	1.78297e116	1.40590
$136$	−2.21934e116	−1.17045
$137$	−1.12448e116	−0.397815	−0.198908	−	0.980018i	$-0.563739\pi$
$137$	−1.12448e116	−0.397815	−0.198908	+	0.980018i	$0.563739\pi$
$138$	2.08082e116	0.495249
$139$	−1.17016e117	−1.87905	−0.939527	−	0.342474i	$-0.888735\pi$
$139$	−1.17016e117	−1.87905	−0.939527	+	0.342474i	$0.888735\pi$
$140$	−6.71386e115	−0.0729447
$141$	1.59943e116	0.117903
$142$	−2.41541e117	−1.21137
$143$	7.62077e116	0.260726
$144$	8.13447e116	0.190359
$145$	−1.81007e117	−0.290496
$146$	1.15322e118	1.27257
$147$	1.00537e118	0.764769
$148$	−9.34268e117	−0.491143
$149$	−2.31830e118	−0.844340	−0.422170	−	0.906517i	$-0.638731\pi$
$149$	−2.31830e118	−0.844340	−0.422170	+	0.906517i	$0.638731\pi$
$150$	1.65984e118	0.419850
$151$	1.21179e118	0.213394	0.106697	−	0.994292i	$-0.465972\pi$
$151$	1.21179e118	0.213394	0.106697	+	0.994292i	$0.465972\pi$
$152$	1.50190e119	1.84572
$153$	4.84792e118	0.416747
$154$	4.43011e117	0.0267014
$155$	−2.79035e119	−1.18190
$156$	−1.14511e119	−0.341629
$157$	−7.17482e119	−1.51105	−0.755527	−	0.655118i	$-0.772619\pi$
$157$	−7.17482e119	−1.51105	−0.755527	+	0.655118i	$0.772619\pi$
$158$	6.54417e119	0.975087
$159$	−1.07439e120	−1.13506
$160$	−1.20264e120	−0.902809
$161$	2.26702e119	0.121184
$162$	9.62708e119	0.367220
$163$	4.55298e120	1.24186	0.620929	−	0.783867i	$-0.286756\pi$
$163$	4.55298e120	1.24186	0.620929	+	0.783867i	$0.286756\pi$
$164$	−1.89239e120	−0.369846
$165$	1.60016e120	0.224537
$166$	1.50596e121	1.52027
$167$	−1.07078e121	−0.779207	−0.389604	−	0.920983i	$-0.627388\pi$
$167$	−1.07078e121	−0.779207	−0.389604	+	0.920983i	$0.627388\pi$
$168$	−2.46084e120	−0.129339
$169$	1.01225e121	0.385000
$170$	4.00862e121	1.10542
$171$	−3.28074e121	−0.657179
$172$	−8.55734e120	−0.124749
$173$	−9.11584e121	−0.968912	−0.484456	−	0.874816i	$-0.660982\pi$
$173$	−9.11584e121	−0.968912	−0.484456	+	0.874816i	$0.660982\pi$
$174$	−1.79467e121	−0.139332
$175$	1.80837e121	0.102734
$176$	2.61569e121	0.108930
$177$	−1.46148e122	−0.446941
$178$	−4.21859e122	−0.949024
$179$	5.19538e121	0.0861245	0.0430623	−	0.999072i	$-0.486289\pi$
$179$	5.19538e121	0.0861245	0.0430623	+	0.999072i	$0.486289\pi$
$180$	1.51896e122	0.185864
$181$	−4.40963e122	−0.398951	−0.199476	−	0.979903i	$-0.563924\pi$
$181$	−4.40963e122	−0.398951	−0.199476	+	0.979903i	$0.563924\pi$
$182$	2.11685e122	0.141840
$183$	1.20740e123	0.600159
$184$	2.34800e123	0.867216
$185$	6.23829e123	1.71477
$186$	−2.76661e123	−0.566882
$187$	1.55888e123	0.238476
$188$	4.88212e122	0.0558477
$189$	1.92599e123	0.165001
$190$	−2.71276e124	−1.74317
$191$	1.51871e123	0.0733089	0.0366545	−	0.999328i	$-0.488330\pi$
$191$	1.51871e123	0.0733089	0.0366545	+	0.999328i	$0.488330\pi$
$192$	−2.25234e124	−0.817931
$193$	−2.55629e124	−0.699418	−0.349709	−	0.936858i	$-0.613720\pi$
$193$	−2.55629e124	−0.699418	−0.349709	+	0.936858i	$0.613720\pi$
$194$	3.65334e123	0.0754216
$195$	7.64609e124	1.19276
$196$	3.06879e124	0.362252
$197$	−8.87164e124	−0.793587	−0.396794	−	0.917908i	$-0.629877\pi$
$197$	−8.87164e124	−0.793587	−0.396794	+	0.917908i	$0.629877\pi$
$198$	−1.00228e124	−0.0680356
$199$	−1.96586e125	−1.01405	−0.507025	−	0.861931i	$-0.669255\pi$
$199$	−1.96586e125	−1.01405	−0.507025	+	0.861931i	$0.669255\pi$
$200$	1.87298e125	0.735186
$201$	1.39299e125	0.416641
$202$	5.95187e125	1.35833
$203$	−1.95526e124	−0.0340935
$204$	−2.34239e125	−0.312475
$205$	1.26359e126	1.29128
$206$	−1.21053e126	−0.948881
$207$	−5.12897e125	−0.308778
$208$	1.24987e126	0.578644
$209$	−1.05494e126	−0.376059
$210$	4.44483e125	0.122153
$211$	−5.05613e126	−1.07257	−0.536283	−	0.844038i	$-0.680172\pi$
$211$	−5.05613e126	−1.07257	−0.536283	+	0.844038i	$0.680172\pi$
$212$	−3.27947e126	−0.537649
$213$	−9.42430e126	−1.19553
$214$	2.56099e124	0.00251685
$215$	5.71390e126	0.435549
$216$	1.99479e127	1.18078
$217$	−3.01418e126	−0.138712
$218$	−2.02687e127	−0.726018
$219$	4.49958e127	1.25594
$220$	4.88433e126	0.106358
$221$	7.44885e127	1.26681
$222$	6.18521e127	0.822465
$223$	−1.04489e128	−1.08757	−0.543783	−	0.839226i	$-0.683009\pi$
$223$	−1.04489e128	−1.08757	−0.543783	+	0.839226i	$0.683009\pi$
$224$	−1.29911e127	−0.105956
$225$	−4.09132e127	−0.261768
$226$	−2.17121e128	−1.09092
$227$	−1.22626e128	−0.484365	−0.242182	−	0.970231i	$-0.577863\pi$
$227$	−1.22626e128	−0.484365	−0.242182	+	0.970231i	$0.577863\pi$
$228$	1.58517e128	0.492750
$229$	3.37596e128	0.826731	0.413365	−	0.910565i	$-0.364353\pi$
$229$	3.37596e128	0.826731	0.413365	+	0.910565i	$0.364353\pi$
$230$	−4.24101e128	−0.819035
$231$	1.72851e127	0.0263524
$232$	−2.02511e128	−0.243980
$233$	−2.38000e128	−0.226819	−0.113409	−	0.993548i	$-0.536177\pi$
$233$	−2.38000e128	−0.226819	−0.113409	+	0.993548i	$0.536177\pi$
$234$	−4.78923e128	−0.361411
$235$	−3.25989e128	−0.194986
$236$	−4.46102e128	−0.211705
$237$	2.55337e129	0.962339
$238$	4.33016e128	0.129736
$239$	3.09606e129	0.738114	0.369057	−	0.929407i	$-0.379681\pi$
$239$	3.09606e129	0.738114	0.369057	+	0.929407i	$0.379681\pi$
$240$	2.62438e129	0.498327
$241$	3.25402e129	0.492597	0.246299	−	0.969194i	$-0.420786\pi$
$241$	3.25402e129	0.492597	0.246299	+	0.969194i	$0.420786\pi$
$242$	6.24411e129	0.754281
$243$	−7.49867e129	−0.723507
$244$	3.68547e129	0.284280
$245$	−2.04909e130	−1.26476
$246$	1.25283e130	0.619342
$247$	−5.04087e130	−1.99766
$248$	−3.12185e130	−0.992650
$249$	5.87585e130	1.50040
$250$	1.62049e130	0.332595
$251$	−6.78846e130	−1.12086	−0.560432	−	0.828200i	$-0.689365\pi$
$251$	−6.78846e130	−1.12086	−0.560432	+	0.828200i	$0.689365\pi$
$252$	1.64080e129	0.0218136
$253$	−1.64925e130	−0.176693
$254$	6.73726e130	0.582164
$255$	1.56406e131	1.09097
$256$	−1.66905e131	−0.940569
$257$	2.82918e131	1.28915	0.644577	−	0.764539i	$-0.277033\pi$
$257$	2.82918e131	1.28915	0.644577	+	0.764539i	$0.277033\pi$
$258$	5.66528e130	0.208904
$259$	6.73869e130	0.201251
$260$	2.33389e131	0.564981
$261$	4.42365e130	0.0868707
$262$	−5.60011e131	−0.892845
$263$	−1.33349e132	−1.72743	−0.863717	−	0.503977i	$-0.831870\pi$
$263$	−1.33349e132	−1.72743	−0.863717	+	0.503977i	$0.831870\pi$
$264$	1.79026e131	0.188583
$265$	2.18977e132	1.87714
$266$	−2.93036e131	−0.204584
$267$	−1.64599e132	−0.936617
$268$	4.25196e131	0.197353
$269$	−1.26851e132	−0.480612	−0.240306	−	0.970697i	$-0.577248\pi$
$269$	−1.26851e132	−0.480612	−0.240306	+	0.970697i	$0.577248\pi$
$270$	−3.60304e132	−1.11518
$271$	−7.14727e131	−0.180848	−0.0904241	−	0.995903i	$-0.528822\pi$
$271$	−7.14727e131	−0.180848	−0.0904241	+	0.995903i	$0.528822\pi$
$272$	2.55668e132	0.529263
$273$	8.25941e131	0.139986
$274$	2.27236e132	0.315552
$275$	−1.31559e132	−0.149792
$276$	2.47819e132	0.231520
$277$	1.85259e132	0.142113	0.0710564	−	0.997472i	$-0.477363\pi$
$277$	1.85259e132	0.142113	0.0710564	+	0.997472i	$0.477363\pi$
$278$	2.36467e133	1.49049
$279$	6.81936e132	0.353439
$280$	5.01556e132	0.213898
$281$	1.61784e133	0.568120	0.284060	−	0.958806i	$-0.408318\pi$
$281$	1.61784e133	0.568120	0.284060	+	0.958806i	$0.408318\pi$
$282$	−3.23215e132	−0.0935222
$283$	−4.43645e133	−1.05846	−0.529231	−	0.848478i	$-0.677519\pi$
$283$	−4.43645e133	−1.05846	−0.529231	+	0.848478i	$0.677519\pi$
$284$	−2.87667e133	−0.566293
$285$	−1.05845e134	−1.72038
$286$	−1.54001e133	−0.206811
$287$	1.36494e133	0.151548
$288$	2.93914e133	0.269979
$289$	2.08692e133	0.158698
$290$	3.65780e133	0.230425
$291$	1.42544e133	0.0744356
$292$	1.37345e134	0.594906
$293$	−2.06993e134	−0.744167	−0.372084	−	0.928199i	$-0.621357\pi$
$293$	−2.06993e134	−0.744167	−0.372084	+	0.928199i	$0.621357\pi$
$294$	−2.03165e134	−0.606625
$295$	2.97871e134	0.739144
$296$	6.97942e134	1.44019
$297$	−1.40116e134	−0.240580
$298$	4.68483e134	0.669741
$299$	−7.88068e134	−0.938607
$300$	1.97682e134	0.196272
$301$	6.17224e133	0.0511174
$302$	−2.44879e134	−0.169267
$303$	2.32227e135	1.34057
$304$	−1.73019e135	−0.834609
$305$	−2.46086e135	−0.992534
$306$	−9.79670e134	−0.330569
$307$	−3.30633e134	−0.0933910	−0.0466955	−	0.998909i	$-0.514869\pi$
$307$	−3.30633e134	−0.0933910	−0.0466955	+	0.998909i	$0.514869\pi$
$308$	5.27611e133	0.0124825
$309$	−4.72317e135	−0.936476
$310$	5.63876e135	0.937500
$311$	−6.22659e135	−0.868578	−0.434289	−	0.900774i	$-0.643000\pi$
$311$	−6.22659e135	−0.868578	−0.434289	+	0.900774i	$0.643000\pi$
$312$	8.55447e135	1.00177
$313$	−1.59179e136	−1.56574	−0.782869	−	0.622187i	$-0.786244\pi$
$313$	−1.59179e136	−1.56574	−0.782869	+	0.622187i	$0.786244\pi$
$314$	1.44989e136	1.19859
$315$	−1.09560e135	−0.0761598
$316$	7.79390e135	0.455836
$317$	6.40670e135	0.315431	0.157716	−	0.987485i	$-0.449587\pi$
$317$	6.40670e135	0.315431	0.157716	+	0.987485i	$0.449587\pi$
$318$	2.17113e136	0.900343
$319$	1.42245e135	0.0497102
$320$	4.59060e136	1.35268
$321$	9.99232e133	0.00248394
$322$	−4.58120e135	−0.0961245
$323$	−1.03114e137	−1.82718
$324$	1.14655e136	0.171669
$325$	−6.28633e136	−0.795709
$326$	−9.20070e136	−0.985057
$327$	−7.90833e136	−0.716526
$328$	1.41370e137	1.08451
$329$	−3.52137e135	−0.0228842
$330$	−3.23361e136	−0.178106
$331$	5.52641e136	0.258117	0.129059	−	0.991637i	$-0.458804\pi$
$331$	5.52641e136	0.258117	0.129059	+	0.991637i	$0.458804\pi$
$332$	1.79354e137	0.710701
$333$	−1.52458e137	−0.512790
$334$	2.16384e137	0.618077
$335$	−2.83912e137	−0.689035
$336$	2.83490e136	0.0584853
$337$	1.02462e138	1.79777	0.898884	−	0.438188i	$-0.144379\pi$
$337$	1.02462e138	1.79777	0.898884	+	0.438188i	$0.144379\pi$
$338$	−2.04555e137	−0.305387
$339$	−8.47149e137	−1.07665
$340$	4.77414e137	0.516766
$341$	2.19281e137	0.202250
$342$	6.62974e137	0.521283
$343$	−4.47922e137	−0.300381
$344$	6.39273e137	0.365806
$345$	−1.65473e138	−0.808328
$346$	1.84213e138	0.768553
$347$	−8.54076e137	−0.304467	−0.152233	−	0.988345i	$-0.548647\pi$
$347$	−8.54076e137	−0.304467	−0.152233	+	0.988345i	$0.548647\pi$
$348$	−2.13739e137	−0.0651352
$349$	−6.35450e138	−1.65613	−0.828067	−	0.560629i	$-0.810559\pi$
$349$	−6.35450e138	−1.65613	−0.828067	+	0.560629i	$0.810559\pi$
$350$	−3.65437e137	−0.0814900
$351$	−6.69519e138	−1.27798
$352$	9.45099e137	0.154491
$353$	2.96243e138	0.414885	0.207442	−	0.978247i	$-0.433486\pi$
$353$	2.96243e138	0.414885	0.207442	+	0.978247i	$0.433486\pi$
$354$	2.95337e138	0.354519
$355$	1.92081e139	1.97715
$356$	−5.02421e138	−0.443652
$357$	1.68952e138	0.128040
$358$	−1.04988e138	−0.0683151
$359$	−4.06039e138	−0.226945	−0.113472	−	0.993541i	$-0.536197\pi$
$359$	−4.06039e138	−0.226945	−0.113472	+	0.993541i	$0.536197\pi$
$360$	−1.13474e139	−0.545015
$361$	4.55626e139	1.88133
$362$	8.91100e138	0.316453
$363$	2.43629e139	0.744420
$364$	2.52110e138	0.0663079
$365$	−9.17081e139	−2.07705
$366$	−2.43992e139	−0.476054
$367$	2.36100e139	0.397005	0.198503	−	0.980100i	$-0.436392\pi$
$367$	2.36100e139	0.397005	0.198503	+	0.980100i	$0.436392\pi$
$368$	−2.70490e139	−0.392144
$369$	−3.08809e139	−0.386147
$370$	−1.26064e140	−1.36018
$371$	2.36541e139	0.220307
$372$	−3.29494e139	−0.265007
$373$	2.09244e140	1.45386	0.726928	−	0.686714i	$-0.240947\pi$
$373$	2.09244e140	1.45386	0.726928	+	0.686714i	$0.240947\pi$
$374$	−3.15019e139	−0.189162
$375$	6.32274e139	0.328247
$376$	−3.64717e139	−0.163764
$377$	6.79696e139	0.264065
$378$	−3.89205e139	−0.130881
$379$	4.84264e140	1.41009	0.705043	−	0.709165i	$-0.250928\pi$
$379$	4.84264e140	1.41009	0.705043	+	0.709165i	$0.250928\pi$
$380$	−3.23081e140	−0.814902
$381$	2.62870e140	0.574554
$382$	−3.06902e139	−0.0581496
$383$	−4.28896e140	−0.704724	−0.352362	−	0.935864i	$-0.614621\pi$
$383$	−4.28896e140	−0.704724	−0.352362	+	0.935864i	$0.614621\pi$
$384$	7.21802e139	0.102888
$385$	−3.52297e139	−0.0435811
$386$	5.16577e140	0.554788
$387$	−1.39643e140	−0.130248
$388$	4.35101e139	0.0352583
$389$	2.25334e141	1.58699	0.793493	−	0.608579i	$-0.208260\pi$
$389$	2.25334e141	1.58699	0.793493	+	0.608579i	$0.208260\pi$
$390$	−1.54513e141	−0.946113
$391$	−1.61205e141	−0.858508
$392$	−2.29253e141	−1.06224
$393$	−2.18502e141	−0.881172
$394$	1.79279e141	0.629484
$395$	−5.20414e141	−1.59150
$396$	−1.19368e140	−0.0318055
$397$	6.38247e141	1.48220	0.741098	−	0.671396i	$-0.234305\pi$
$397$	6.38247e141	1.48220	0.741098	+	0.671396i	$0.234305\pi$
$398$	3.97262e141	0.804358
$399$	−1.14335e141	−0.201909
$400$	−2.15767e141	−0.332442
$401$	9.54626e141	1.28370	0.641852	−	0.766828i	$-0.278166\pi$
$401$	9.54626e141	1.28370	0.641852	+	0.766828i	$0.278166\pi$
$402$	−2.81496e141	−0.330485
$403$	1.04780e142	1.07437
$404$	7.08849e141	0.634994
$405$	−7.65577e141	−0.599364
$406$	3.95121e140	0.0270434
$407$	−4.90239e141	−0.293436
$408$	1.74987e142	0.916279
$409$	−2.63643e142	−1.20808	−0.604041	−	0.796954i	$-0.706443\pi$
$409$	−2.63643e142	−1.20808	−0.604041	+	0.796954i	$0.706443\pi$
$410$	−2.55346e142	−1.02426
$411$	8.86616e141	0.311427
$412$	−1.44170e142	−0.443585
$413$	3.21765e141	0.0867482
$414$	1.03646e142	0.244927
$415$	−1.19759e143	−2.48133
$416$	4.51600e142	0.820667
$417$	9.22633e142	1.47101
$418$	2.13184e142	0.298295
$419$	−2.84726e142	−0.349754	−0.174877	−	0.984590i	$-0.555953\pi$
$419$	−2.84726e142	−0.349754	−0.174877	+	0.984590i	$0.555953\pi$
$420$	5.29365e141	0.0571043
$421$	−1.19780e143	−1.13504	−0.567521	−	0.823359i	$-0.692097\pi$
$421$	−1.19780e143	−1.13504	−0.567521	+	0.823359i	$0.692097\pi$
$422$	1.02175e143	0.850774
$423$	7.96686e141	0.0583092
$424$	2.44991e143	1.57656
$425$	−1.28591e143	−0.727804
$426$	1.90447e143	0.948310
$427$	−2.65825e142	−0.116487
$428$	3.05006e140	0.00117658
$429$	−6.00872e142	−0.204108
$430$	−1.15467e143	−0.345483
$431$	−4.31757e142	−0.113822	−0.0569112	−	0.998379i	$-0.518125\pi$
$431$	−4.31757e142	−0.113822	−0.0569112	+	0.998379i	$0.518125\pi$
$432$	−2.29800e143	−0.533933
$433$	1.94599e141	0.00398612	0.00199306	−	0.999998i	$-0.499366\pi$
$433$	1.94599e141	0.00398612	0.00199306	+	0.999998i	$0.499366\pi$
$434$	6.09106e142	0.110028
$435$	1.42718e143	0.227413
$436$	−2.41394e143	−0.339401
$437$	1.09092e144	1.35380
$438$	−9.09278e143	−0.996225
$439$	−1.44499e144	−1.39813	−0.699064	−	0.715059i	$-0.746400\pi$
$439$	−1.44499e144	−1.39813	−0.699064	+	0.715059i	$0.746400\pi$
$440$	−3.64882e143	−0.311876
$441$	5.00779e143	0.378218
$442$	−1.50527e144	−1.00485
$443$	−9.98754e143	−0.589461	−0.294731	−	0.955580i	$-0.595230\pi$
$443$	−9.98754e143	−0.589461	−0.294731	+	0.955580i	$0.595230\pi$
$444$	7.36639e143	0.384488
$445$	3.35476e144	1.54896
$446$	2.11152e144	0.862672
$447$	1.82790e144	0.660986
$448$	4.95882e143	0.158755
$449$	2.46229e144	0.698095	0.349047	−	0.937105i	$-0.386505\pi$
$449$	2.46229e144	0.698095	0.349047	+	0.937105i	$0.386505\pi$
$450$	8.26776e143	0.207638
$451$	−9.92995e143	−0.220966
$452$	−2.58584e144	−0.509984
$453$	−9.55453e143	−0.167054
$454$	2.47803e144	0.384204
$455$	−1.68339e144	−0.231507
$456$	−1.18420e145	−1.44491
$457$	5.95340e144	0.644662	0.322331	−	0.946627i	$-0.395534\pi$
$457$	5.95340e144	0.644662	0.322331	+	0.946627i	$0.395534\pi$
$458$	−6.82217e144	−0.655774
$459$	−1.36955e145	−1.16892
$460$	−5.05091e144	−0.382885
$461$	3.03421e144	0.204336	0.102168	−	0.994767i	$-0.467422\pi$
$461$	3.03421e144	0.204336	0.102168	+	0.994767i	$0.467422\pi$
$462$	−3.49299e143	−0.0209030
$463$	2.05145e145	1.09118	0.545591	−	0.838052i	$-0.316305\pi$
$463$	2.05145e145	1.09118	0.545591	+	0.838052i	$0.316305\pi$
$464$	2.33293e144	0.110325
$465$	2.20010e145	0.925244
$466$	4.80951e144	0.179915
$467$	−3.81715e145	−1.27048	−0.635242	−	0.772313i	$-0.719100\pi$
$467$	−3.81715e145	−1.27048	−0.635242	+	0.772313i	$0.719100\pi$
$468$	−5.70382e144	−0.168953
$469$	−3.06685e144	−0.0808673
$470$	6.58760e144	0.154666
$471$	5.65710e145	1.18292
$472$	3.33259e145	0.620788
$473$	−4.49030e144	−0.0745320
$474$	−5.15986e145	−0.763340
$475$	8.70218e145	1.14769
$476$	5.15709e144	0.0606493
$477$	−5.35158e145	−0.561346
$478$	−6.25653e145	−0.585482
$479$	4.00424e145	0.334375	0.167188	−	0.985925i	$-0.446531\pi$
$479$	4.00424e145	0.334375	0.167188	+	0.985925i	$0.446531\pi$
$480$	9.48240e145	0.706758
$481$	−2.34253e146	−1.55875
$482$	−6.57575e145	−0.390734
$483$	−1.78747e145	−0.0948678
$484$	7.43653e145	0.352613
$485$	−2.90525e145	−0.123100
$486$	1.51534e146	0.573895
$487$	−1.68879e146	−0.571803	−0.285902	−	0.958259i	$-0.592293\pi$
$487$	−1.68879e146	−0.571803	−0.285902	+	0.958259i	$0.592293\pi$
$488$	−2.75321e146	−0.833604
$489$	−3.58987e146	−0.972179
$490$	4.14081e146	1.00323
$491$	−5.52881e145	−0.119864	−0.0599322	−	0.998202i	$-0.519088\pi$
$491$	−5.52881e145	−0.119864	−0.0599322	+	0.998202i	$0.519088\pi$
$492$	1.49209e146	0.289531
$493$	1.39036e146	0.241530
$494$	1.01866e147	1.58457
$495$	7.97047e145	0.111045
$496$	3.59638e146	0.448864
$497$	2.07489e146	0.232044
$498$	−1.18740e147	−1.19013
$499$	6.08024e146	0.546313	0.273156	−	0.961970i	$-0.411932\pi$
$499$	6.08024e146	0.546313	0.273156	+	0.961970i	$0.411932\pi$
$500$	1.92995e146	0.155482
$501$	8.44275e146	0.609997
$502$	1.37181e147	0.889084
$503$	−1.95917e147	−1.13925	−0.569623	−	0.821906i	$-0.692911\pi$
$503$	−1.95917e147	−1.13925	−0.569623	+	0.821906i	$0.692911\pi$
$504$	−1.22576e146	−0.0639647
$505$	−4.73313e147	−2.21701
$506$	3.33282e146	0.140155
$507$	−7.98122e146	−0.301395
$508$	8.02386e146	0.272152
$509$	−2.33539e147	−0.711608	−0.355804	−	0.934561i	$-0.615793\pi$
$509$	−2.33539e147	−0.711608	−0.355804	+	0.934561i	$0.615793\pi$
$510$	−3.16066e147	−0.865373
$511$	−9.90643e146	−0.243769
$512$	3.96698e147	0.877501
$513$	9.26816e147	1.84330
$514$	−5.71722e147	−1.02257
$515$	9.62652e147	1.54873
$516$	6.74717e146	0.0976592
$517$	2.56180e146	0.0333664
$518$	−1.36176e147	−0.159635
$519$	7.18753e147	0.758506
$520$	−1.74353e148	−1.65671
$521$	7.61822e147	0.651925	0.325963	−	0.945383i	$-0.394312\pi$
$521$	7.61822e147	0.651925	0.325963	+	0.945383i	$0.394312\pi$
$522$	−8.93934e146	−0.0689069
$523$	−2.77215e147	−0.192520	−0.0962599	−	0.995356i	$-0.530688\pi$
$523$	−2.77215e147	−0.192520	−0.0962599	+	0.995356i	$0.530688\pi$
$524$	−6.66955e147	−0.417389
$525$	−1.42584e147	−0.0804247
$526$	2.69472e148	1.37022
$527$	2.14334e148	0.982682
$528$	−2.06238e147	−0.0852748
$529$	−9.75728e147	−0.363911
$530$	−4.42509e148	−1.48897
$531$	−7.27970e147	−0.221036
$532$	−3.48997e147	−0.0956395
$533$	−4.74486e148	−1.17379
$534$	3.32622e148	0.742937
$535$	−2.03658e146	−0.00410791
$536$	−3.17641e148	−0.578703
$537$	−4.09638e147	−0.0674220
$538$	2.56341e148	0.381228
$539$	1.61029e148	0.216429
$540$	−4.29110e148	−0.521326
$541$	2.69350e148	0.295847	0.147923	−	0.988999i	$-0.452741\pi$
$541$	2.69350e148	0.295847	0.147923	+	0.988999i	$0.452741\pi$
$542$	1.44433e148	0.143451
$543$	3.47684e148	0.312316
$544$	9.23778e148	0.750633
$545$	1.61184e149	1.18498
$546$	−1.66907e148	−0.111039
$547$	−1.20412e148	−0.0725040	−0.0362520	−	0.999343i	$-0.511542\pi$
$547$	−1.20412e148	−0.0725040	−0.0362520	+	0.999343i	$0.511542\pi$
$548$	2.70631e148	0.147515
$549$	6.01411e148	0.296810
$550$	2.65855e148	0.118817
$551$	−9.40903e148	−0.380875
$552$	−1.85132e149	−0.678894
$553$	−5.62158e148	−0.186784
$554$	−3.74373e148	−0.112726
$555$	−4.91868e149	−1.34240
$556$	2.81625e149	0.696778
$557$	−2.42461e148	−0.0543918	−0.0271959	−	0.999630i	$-0.508658\pi$
$557$	−2.42461e148	−0.0543918	−0.0271959	+	0.999630i	$0.508658\pi$
$558$	−1.37806e149	−0.280353
$559$	−2.14561e149	−0.395921
$560$	−5.77794e148	−0.0967220
$561$	−1.22912e149	−0.186689
$562$	−3.26933e149	−0.450640
$563$	−5.48610e149	−0.686367	−0.343183	−	0.939268i	$-0.611505\pi$
$563$	−5.48610e149	−0.686367	−0.343183	+	0.939268i	$0.611505\pi$
$564$	−3.84938e148	−0.0437200
$565$	1.72662e150	1.78055
$566$	8.96521e149	0.839586
$567$	−8.26987e148	−0.0703432
$568$	2.14901e150	1.66056
$569$	−1.03965e150	−0.729909	−0.364955	−	0.931025i	$-0.618915\pi$
$569$	−1.03965e150	−0.729909	−0.364955	+	0.931025i	$0.618915\pi$
$570$	2.13892e150	1.36463
$571$	−3.12319e150	−1.81105	−0.905525	−	0.424293i	$-0.860523\pi$
$571$	−3.12319e150	−1.81105	−0.905525	+	0.424293i	$0.860523\pi$
$572$	−1.83410e149	−0.0966807
$573$	−1.19745e149	−0.0573894
$574$	−2.75828e149	−0.120210
$575$	1.36046e150	0.539248
$576$	−1.12190e150	−0.404509
$577$	−1.10348e150	−0.361980	−0.180990	−	0.983485i	$-0.557930\pi$
$577$	−1.10348e150	−0.361980	−0.180990	+	0.983485i	$0.557930\pi$
$578$	−4.21725e149	−0.125882
$579$	2.01555e150	0.547535
$580$	4.35633e149	0.107720
$581$	−1.29365e150	−0.291217
$582$	−2.88053e149	−0.0590433
$583$	−1.72084e150	−0.321221
$584$	−1.02603e151	−1.74446
$585$	3.80855e150	0.589883
$586$	4.18293e150	0.590283
$587$	9.68240e150	1.24511	0.622553	−	0.782578i	$-0.286095\pi$
$587$	9.68240e150	1.24511	0.622553	+	0.782578i	$0.286095\pi$
$588$	−2.41964e150	−0.283587
$589$	−1.45047e151	−1.54962
$590$	−6.01940e150	−0.586298
$591$	6.99499e150	0.621254
$592$	−8.04030e150	−0.651237
$593$	1.47148e151	1.08711	0.543556	−	0.839373i	$-0.317078\pi$
$593$	1.47148e151	1.08711	0.543556	+	0.839373i	$0.317078\pi$
$594$	2.83146e150	0.190831
$595$	−3.44349e150	−0.211750
$596$	5.57948e150	0.313092
$597$	1.55001e151	0.793842
$598$	1.59253e151	0.744516
$599$	4.12302e151	1.75976	0.879880	−	0.475197i	$-0.157623\pi$
$599$	4.12302e151	1.75976	0.879880	+	0.475197i	$0.157623\pi$
$600$	−1.47678e151	−0.575535
$601$	−1.38950e151	−0.494538	−0.247269	−	0.968947i	$-0.579533\pi$
$601$	−1.38950e151	−0.494538	−0.247269	+	0.968947i	$0.579533\pi$
$602$	−1.24729e150	−0.0405470
$603$	6.93854e150	0.206051
$604$	−2.91643e150	−0.0791294
$605$	−4.96552e151	−1.23111
$606$	−4.69285e151	−1.06336
$607$	−2.06428e151	−0.427547	−0.213774	−	0.976883i	$-0.568575\pi$
$607$	−2.06428e151	−0.427547	−0.213774	+	0.976883i	$0.568575\pi$
$608$	−6.25150e151	−1.18369
$609$	1.54166e150	0.0266898
$610$	4.97292e151	0.787291
$611$	1.22411e151	0.177245
$612$	−1.16676e151	−0.154535
$613$	8.42364e151	1.02071	0.510357	−	0.859963i	$-0.329513\pi$
$613$	8.42364e151	1.02071	0.510357	+	0.859963i	$0.329513\pi$
$614$	6.68145e150	0.0740789
$615$	−9.96295e151	−1.01087
$616$	−3.94150e150	−0.0366027
$617$	−4.60473e151	−0.391437	−0.195719	−	0.980660i	$-0.562704\pi$
$617$	−4.60473e151	−0.391437	−0.195719	+	0.980660i	$0.562704\pi$
$618$	9.54461e151	0.742825
$619$	3.04167e151	0.216756	0.108378	−	0.994110i	$-0.465434\pi$
$619$	3.04167e151	0.216756	0.108378	+	0.994110i	$0.465434\pi$
$620$	6.71558e151	0.438265
$621$	1.44894e152	0.866083
$622$	1.25827e152	0.688967
$623$	3.62386e151	0.181791
$624$	−9.85476e151	−0.452987
$625$	−2.89372e152	−1.21898
$626$	3.21670e152	1.24196
$627$	8.31787e151	0.294396
$628$	1.72677e152	0.560319
$629$	−4.79180e152	−1.42573
$630$	2.21399e151	0.0604110
$631$	−1.19759e152	−0.299714	−0.149857	−	0.988708i	$-0.547881\pi$
$631$	−1.19759e152	−0.299714	−0.149857	+	0.988708i	$0.547881\pi$
$632$	−5.82240e152	−1.33666
$633$	3.98659e152	0.839651
$634$	−1.29467e152	−0.250204
$635$	−5.35769e152	−0.950188
$636$	2.58575e152	0.420895
$637$	7.69449e152	1.14969
$638$	−2.87450e151	−0.0394308
$639$	−4.69429e152	−0.591252
$640$	−1.47114e152	−0.170155
$641$	−6.77928e152	−0.720147	−0.360073	−	0.932924i	$-0.617248\pi$
$641$	−6.77928e152	−0.720147	−0.360073	+	0.932924i	$0.617248\pi$
$642$	−2.01925e150	−0.00197030
$643$	3.86671e152	0.346612	0.173306	−	0.984868i	$-0.444555\pi$
$643$	3.86671e152	0.346612	0.173306	+	0.984868i	$0.444555\pi$
$644$	−5.45606e151	−0.0449365
$645$	−4.50522e152	−0.340966
$646$	2.08374e153	1.44935
$647$	5.87101e152	0.375344	0.187672	−	0.982232i	$-0.439906\pi$
$647$	5.87101e152	0.375344	0.187672	+	0.982232i	$0.439906\pi$
$648$	−8.56530e152	−0.503390
$649$	−2.34084e152	−0.126484
$650$	1.27035e153	0.631167
$651$	2.37658e152	0.108589
$652$	−1.09577e153	−0.460497
$653$	−2.80940e152	−0.108604	−0.0543020	−	0.998525i	$-0.517293\pi$
$653$	−2.80940e152	−0.108604	−0.0543020	+	0.998525i	$0.517293\pi$
$654$	1.59812e153	0.568358
$655$	4.45339e153	1.45727
$656$	−1.62859e153	−0.490402
$657$	2.24126e153	0.621126
$658$	7.11601e151	0.0181520
$659$	−4.92434e153	−1.15636	−0.578179	−	0.815910i	$-0.696237\pi$
$659$	−4.92434e153	−1.15636	−0.578179	+	0.815910i	$0.696237\pi$
$660$	−3.85113e152	−0.0832613
$661$	−2.80800e153	−0.559007	−0.279503	−	0.960145i	$-0.590170\pi$
$661$	−2.80800e153	−0.559007	−0.279503	+	0.960145i	$0.590170\pi$
$662$	−1.11678e153	−0.204742
$663$	−5.87316e153	−0.991710
$664$	−1.33986e154	−2.08401
$665$	2.33032e153	0.333915
$666$	3.08088e153	0.406752
$667$	−1.47097e153	−0.178956
$668$	2.57706e153	0.288940
$669$	8.23861e153	0.851394
$670$	5.73730e153	0.546551
$671$	1.93388e153	0.169844
$672$	1.02430e153	0.0829473
$673$	2.09723e154	1.56612	0.783059	−	0.621947i	$-0.213658\pi$
$673$	2.09723e154	1.56612	0.783059	+	0.621947i	$0.213658\pi$
$674$	−2.07056e154	−1.42601
$675$	1.15581e154	0.734226
$676$	−2.43619e153	−0.142763
$677$	1.54611e154	0.835909	0.417955	−	0.908468i	$-0.362747\pi$
$677$	1.54611e154	0.835909	0.417955	+	0.908468i	$0.362747\pi$
$678$	1.71192e154	0.854016
$679$	−3.13829e152	−0.0144474
$680$	−3.56650e154	−1.51533
$681$	9.66863e153	0.379182
$682$	−4.43125e153	−0.160427
$683$	−6.91785e153	−0.231229	−0.115615	−	0.993294i	$-0.536884\pi$
$683$	−6.91785e153	−0.231229	−0.115615	+	0.993294i	$0.536884\pi$
$684$	7.89580e153	0.243691
$685$	−1.80706e154	−0.515033
$686$	9.05163e153	0.238266
$687$	−2.66183e154	−0.647200
$688$	−7.36444e153	−0.165413
$689$	−8.22273e154	−1.70635
$690$	3.34390e154	0.641176
$691$	9.31506e154	1.65056	0.825281	−	0.564722i	$-0.191017\pi$
$691$	9.31506e154	1.65056	0.825281	+	0.564722i	$0.191017\pi$
$692$	2.19392e154	0.359285
$693$	8.60980e152	0.0130326
$694$	1.72592e154	0.241507
$695$	−1.88046e155	−2.43273
$696$	1.59673e154	0.190998
$697$	−9.70593e154	−1.07362
$698$	1.28412e155	1.31367
$699$	1.87655e154	0.177563
$700$	−4.35224e153	−0.0380951
$701$	−9.35937e154	−0.757905	−0.378952	−	0.925416i	$-0.623716\pi$
$701$	−9.35937e154	−0.757905	−0.378952	+	0.925416i	$0.623716\pi$
$702$	1.35297e155	1.01371
$703$	3.24276e155	2.24828
$704$	−3.60754e154	−0.231474
$705$	2.57031e154	0.152644
$706$	−5.98650e154	−0.329092
$707$	−5.11278e154	−0.260195
$708$	3.51737e154	0.165732
$709$	5.44968e154	0.237767	0.118883	−	0.992908i	$-0.462069\pi$
$709$	5.44968e154	0.237767	0.118883	+	0.992908i	$0.462069\pi$
$710$	−3.88159e155	−1.56830
$711$	1.27184e155	0.475927
$712$	3.75332e155	1.30093
$713$	−2.26760e155	−0.728093
$714$	−3.41419e154	−0.101563
$715$	1.22467e155	0.337550
$716$	−1.25038e154	−0.0319361
$717$	−2.44114e155	−0.577828
$718$	8.20526e154	0.180016
$719$	−6.08067e155	−1.23659	−0.618296	−	0.785945i	$-0.712177\pi$
$719$	−6.08067e155	−1.23659	−0.618296	+	0.785945i	$0.712177\pi$
$720$	1.30722e155	0.246449
$721$	1.03987e155	0.181764
$722$	−9.20731e155	−1.49230
$723$	−2.56569e155	−0.385626
$724$	1.06127e155	0.147936
$725$	−1.17337e155	−0.151710
$726$	−4.92327e155	−0.590483
$727$	1.28804e156	1.43319	0.716595	−	0.697490i	$-0.245700\pi$
$727$	1.28804e156	1.43319	0.716595	+	0.697490i	$0.245700\pi$
$728$	−1.88338e155	−0.194437
$729$	1.07451e156	1.02934
$730$	1.85324e156	1.64754
$731$	−4.38900e155	−0.362133
$732$	−2.90586e155	−0.222547
$733$	1.37466e156	0.977302	0.488651	−	0.872479i	$-0.337489\pi$
$733$	1.37466e156	0.977302	0.488651	+	0.872479i	$0.337489\pi$
$734$	−4.77113e155	−0.314910
$735$	1.61564e156	0.990112
$736$	−9.77332e155	−0.556162
$737$	2.23113e155	0.117909
$738$	6.24043e155	0.306297
$739$	−4.06035e156	−1.85115	−0.925576	−	0.378563i	$-0.876418\pi$
$739$	−4.06035e156	−1.85115	−0.925576	+	0.378563i	$0.876418\pi$
$740$	−1.50138e156	−0.635860
$741$	3.97456e156	1.56385
$742$	−4.78004e155	−0.174751
$743$	−4.21117e156	−1.43058	−0.715290	−	0.698828i	$-0.753705\pi$
$743$	−4.21117e156	−1.43058	−0.715290	+	0.698828i	$0.753705\pi$
$744$	2.46148e156	0.777089
$745$	−3.72553e156	−1.09313
$746$	−4.22841e156	−1.15322
$747$	2.92679e156	0.742025
$748$	−3.75178e155	−0.0884301
$749$	−2.19994e153	−0.000482117 0
$750$	−1.27770e156	−0.260370
$751$	4.45990e156	0.845178	0.422589	−	0.906321i	$-0.361121\pi$
$751$	4.45990e156	0.845178	0.422589	+	0.906321i	$0.361121\pi$
$752$	4.20155e155	0.0740520
$753$	5.35247e156	0.877461
$754$	−1.37353e156	−0.209460
$755$	1.94735e156	0.276272
$756$	−4.63531e155	−0.0611844
$757$	−6.80456e156	−0.835746	−0.417873	−	0.908505i	$-0.637224\pi$
$757$	−6.80456e156	−0.835746	−0.417873	+	0.908505i	$0.637224\pi$
$758$	−9.78604e156	−1.11850
$759$	1.30038e156	0.138323
$760$	2.41357e157	2.38956
$761$	−5.56021e156	−0.512422	−0.256211	−	0.966621i	$-0.582474\pi$
$761$	−5.56021e156	−0.512422	−0.256211	+	0.966621i	$0.582474\pi$
$762$	−5.31210e156	−0.455743
$763$	1.74113e156	0.139073
$764$	−3.65511e155	−0.0271839
$765$	7.79066e156	0.539543
$766$	8.66716e156	0.558996
$767$	−1.11853e157	−0.671893
$768$	1.31599e157	0.736318
$769$	2.44625e157	1.27501	0.637507	−	0.770444i	$-0.279966\pi$
$769$	2.44625e157	1.27501	0.637507	+	0.770444i	$0.279966\pi$
$770$	7.11923e155	0.0345691
$771$	−2.23071e157	−1.00921
$772$	6.15226e156	0.259353
$773$	−5.02179e157	−1.97277	−0.986384	−	0.164459i	$-0.947412\pi$
$773$	−5.02179e157	−1.97277	−0.986384	+	0.164459i	$0.947412\pi$
$774$	2.82190e156	0.103314
$775$	−1.80884e157	−0.617244
$776$	−3.25041e156	−0.103389
$777$	−5.31323e156	−0.157548
$778$	−4.55356e157	−1.25882
$779$	6.56831e157	1.69302
$780$	−1.84020e157	−0.442291
$781$	−1.50948e157	−0.338334
$782$	3.25763e157	0.680980
$783$	−1.24969e157	−0.243661
$784$	2.64100e157	0.480333
$785$	−1.15300e158	−1.95629
$786$	4.41549e157	0.698957
$787$	1.65806e157	0.244894	0.122447	−	0.992475i	$-0.460926\pi$
$787$	1.65806e157	0.244894	0.122447	+	0.992475i	$0.460926\pi$
$788$	2.13515e157	0.294273
$789$	1.05141e158	1.35231
$790$	1.05166e158	1.26240
$791$	1.86511e157	0.208971
$792$	8.91738e156	0.0932642
$793$	9.24071e157	0.902229
$794$	−1.28977e158	−1.17570
$795$	−1.72656e158	−1.46951
$796$	4.73126e157	0.376023
$797$	1.17946e158	0.875398	0.437699	−	0.899122i	$-0.355794\pi$
$797$	1.17946e158	0.875398	0.437699	+	0.899122i	$0.355794\pi$
$798$	2.31049e157	0.160157
$799$	2.50400e157	0.162120
$800$	−7.79607e157	−0.471489
$801$	−8.19873e157	−0.463206
$802$	−1.92911e158	−1.01825
$803$	7.20692e157	0.355429
$804$	−3.35252e157	−0.154496
$805$	3.64312e157	0.156891
$806$	−2.11740e158	−0.852202
$807$	1.00018e158	0.376244
$808$	−5.29543e158	−1.86201
$809$	−1.56148e158	−0.513266	−0.256633	−	0.966509i	$-0.582613\pi$
$809$	−1.56148e158	−0.513266	−0.256633	+	0.966509i	$0.582613\pi$
$810$	1.54708e158	0.475423
$811$	3.59356e158	1.03250	0.516248	−	0.856439i	$-0.327328\pi$
$811$	3.59356e158	1.03250	0.516248	+	0.856439i	$0.327328\pi$
$812$	4.70576e156	0.0126423
$813$	5.63538e157	0.141576
$814$	9.90678e157	0.232757
$815$	7.31670e158	1.60778
$816$	−2.01586e158	−0.414330
$817$	2.97018e158	0.571058
$818$	5.32771e158	0.958266
$819$	4.11405e157	0.0692304
$820$	−3.04109e158	−0.478822
$821$	−7.23662e158	−1.06619	−0.533094	−	0.846056i	$-0.678971\pi$
$821$	−7.23662e158	−1.06619	−0.533094	+	0.846056i	$0.678971\pi$
$822$	−1.79168e158	−0.247028
$823$	−9.73203e158	−1.25578	−0.627889	−	0.778303i	$-0.716081\pi$
$823$	−9.73203e158	−1.25578	−0.627889	+	0.778303i	$0.716081\pi$
$824$	1.07702e159	1.30074
$825$	1.03730e158	0.117264
$826$	−6.50224e157	−0.0688098
$827$	9.51553e157	0.0942720	0.0471360	−	0.998888i	$-0.484991\pi$
$827$	9.51553e157	0.0942720	0.0471360	+	0.998888i	$0.484991\pi$
$828$	1.23440e158	0.114499
$829$	−2.43775e158	−0.211722	−0.105861	−	0.994381i	$-0.533760\pi$
$829$	−2.43775e158	−0.211722	−0.105861	+	0.994381i	$0.533760\pi$
$830$	2.42009e159	1.96823
$831$	−1.46071e158	−0.111252
$832$	−1.72380e159	−1.22961
$833$	1.57396e159	1.05158
$834$	−1.86446e159	−1.16682
$835$	−1.72076e159	−1.00880
$836$	2.53895e158	0.139448
$837$	−1.92648e159	−0.991353
$838$	5.75375e158	0.277429
$839$	−1.44453e158	−0.0652680	−0.0326340	−	0.999467i	$-0.510390\pi$
$839$	−1.44453e158	−0.0652680	−0.0326340	+	0.999467i	$0.510390\pi$
$840$	−3.95460e158	−0.167449
$841$	−2.39302e159	−0.949653
$842$	2.42053e159	0.900329
$843$	−1.27561e159	−0.444749
$844$	1.21687e159	0.397722
$845$	1.62669e159	0.498442
$846$	−1.60995e158	−0.0462516
$847$	−5.36382e158	−0.144487
$848$	−2.82231e159	−0.712903
$849$	3.49799e159	0.828609
$850$	2.59858e159	0.577304
$851$	5.06959e159	1.05636
$852$	2.26816e159	0.443318
$853$	6.74706e159	1.23707	0.618533	−	0.785759i	$-0.287727\pi$
$853$	6.74706e159	1.23707	0.618533	+	0.785759i	$0.287727\pi$
$854$	5.37181e158	0.0923989
$855$	−5.27218e159	−0.850819
$856$	−2.27853e157	−0.00345013
$857$	1.99228e159	0.283072	0.141536	−	0.989933i	$-0.454796\pi$
$857$	1.99228e159	0.283072	0.141536	+	0.989933i	$0.454796\pi$
$858$	1.21425e159	0.161901
$859$	−1.20799e160	−1.51160	−0.755798	−	0.654805i	$-0.772751\pi$
$859$	−1.20799e160	−1.51160	−0.755798	+	0.654805i	$0.772751\pi$
$860$	−1.37517e159	−0.161507
$861$	−1.07621e159	−0.118639
$862$	8.72496e158	0.0902854
$863$	3.63464e158	0.0353080	0.0176540	−	0.999844i	$-0.494380\pi$
$863$	3.63464e158	0.0353080	0.0176540	+	0.999844i	$0.494380\pi$
$864$	−8.30312e159	−0.757256
$865$	−1.46493e160	−1.25441
$866$	−3.93247e157	−0.00316185
$867$	−1.64546e159	−0.124236
$868$	7.25426e158	0.0514361
$869$	4.08970e159	0.272341
$870$	−2.88406e159	−0.180387
$871$	1.06611e160	0.626343
$872$	1.80333e160	0.995235
$873$	7.10017e158	0.0368123
$874$	−2.20454e160	−1.07385
$875$	−1.39204e159	−0.0637106
$876$	−1.08292e160	−0.465718
$877$	−2.60739e158	−0.0105373	−0.00526864	−	0.999986i	$-0.501677\pi$
$877$	−2.60739e158	−0.0105373	−0.00526864	+	0.999986i	$0.501677\pi$
$878$	2.92004e160	1.10901
$879$	1.63207e160	0.582566
$880$	4.20345e159	0.141026
$881$	1.40915e160	0.444398	0.222199	−	0.975001i	$-0.428677\pi$
$881$	1.40915e160	0.444398	0.222199	+	0.975001i	$0.428677\pi$
$882$	−1.01198e160	−0.300008
$883$	4.79701e160	1.33694	0.668471	−	0.743739i	$-0.266949\pi$
$883$	4.79701e160	1.33694	0.668471	+	0.743739i	$0.266949\pi$
$884$	−1.79273e160	−0.469748
$885$	−2.34862e160	−0.578634
$886$	2.01829e160	0.467568
$887$	4.44142e160	0.967576	0.483788	−	0.875185i	$-0.339261\pi$
$887$	4.44142e160	0.967576	0.483788	+	0.875185i	$0.339261\pi$
$888$	−5.50304e160	−1.12745
$889$	−5.78745e159	−0.111517
$890$	−6.77932e160	−1.22866
$891$	6.01633e159	0.102564
$892$	2.51475e160	0.403284
$893$	−1.69454e160	−0.255651
$894$	−3.69383e160	−0.524302
$895$	8.34903e159	0.111501
$896$	−1.58914e159	−0.0199699
$897$	6.21365e160	0.734782
$898$	−4.97582e160	−0.553738
$899$	1.95577e160	0.204840
$900$	9.84664e159	0.0970669
$901$	−1.68202e161	−1.56073
$902$	2.00665e160	0.175273
$903$	−4.86660e159	−0.0400169
$904$	1.93174e161	1.49544
$905$	−7.08632e160	−0.516504
$906$	1.93078e160	0.132510
$907$	−2.58297e161	−1.66925	−0.834625	−	0.550818i	$-0.814316\pi$
$907$	−2.58297e161	−1.66925	−0.834625	+	0.550818i	$0.814316\pi$
$908$	2.95125e160	0.179609
$909$	1.15673e161	0.662981
$910$	3.40181e160	0.183634
$911$	6.60482e160	0.335822	0.167911	−	0.985802i	$-0.446298\pi$
$911$	6.60482e160	0.335822	0.167911	+	0.985802i	$0.446298\pi$
$912$	1.36420e161	0.653368
$913$	9.41128e160	0.424611
$914$	−1.20307e161	−0.511354
$915$	1.94030e161	0.776998
$916$	−8.12498e160	−0.306563
$917$	4.81061e160	0.171030
$918$	2.76759e161	0.927204
$919$	−3.41052e160	−0.107678	−0.0538388	−	0.998550i	$-0.517146\pi$
$919$	−3.41052e160	−0.107678	−0.0538388	+	0.998550i	$0.517146\pi$
$920$	3.77327e161	1.12274
$921$	2.60693e160	0.0731105
$922$	−6.13156e160	−0.162082
$923$	−7.21280e161	−1.79726
$924$	−4.16004e159	−0.00977181
$925$	4.04396e161	0.895534
$926$	−4.14558e161	−0.865539
$927$	−2.35263e161	−0.463136
$928$	8.42933e160	0.156469
$929$	−1.04735e162	−1.83332	−0.916658	−	0.399673i	$-0.869124\pi$
$929$	−1.04735e162	−1.83332	−0.916658	+	0.399673i	$0.869124\pi$
$930$	−4.44597e161	−0.733915
$931$	−1.06515e162	−1.65826
$932$	5.72797e160	0.0841073
$933$	4.90945e161	0.679960
$934$	7.71372e161	1.00776
$935$	2.50514e161	0.308744
$936$	4.26102e161	0.495427
$937$	1.39582e162	1.53116	0.765581	−	0.643339i	$-0.222451\pi$
$937$	1.39582e162	1.53116	0.765581	+	0.643339i	$0.222451\pi$
$938$	6.19751e160	0.0641450
$939$	1.25507e162	1.22573
$940$	7.84562e160	0.0723034
$941$	−1.63454e162	−1.42155	−0.710774	−	0.703421i	$-0.751655\pi$
$941$	−1.63454e162	−1.42155	−0.710774	+	0.703421i	$0.751655\pi$
$942$	−1.14319e162	−0.938306
$943$	1.02686e162	0.795472
$944$	−3.83915e161	−0.280713
$945$	3.09509e161	0.213619
$946$	9.07402e160	0.0591198
$947$	1.53796e162	0.945958	0.472979	−	0.881074i	$-0.343179\pi$
$947$	1.53796e162	0.945958	0.472979	+	0.881074i	$0.343179\pi$
$948$	−6.14522e161	−0.356848
$949$	3.44371e162	1.88807
$950$	−1.75854e162	−0.910366
$951$	−5.05146e161	−0.246933
$952$	−3.85258e161	−0.177844
$953$	−2.92621e162	−1.27568	−0.637842	−	0.770167i	$-0.720173\pi$
$953$	−2.92621e162	−1.27568	−0.637842	+	0.770167i	$0.720173\pi$
$954$	1.08145e162	0.445267
$955$	2.44059e161	0.0949097
$956$	−7.45133e161	−0.273702
$957$	−1.12156e161	−0.0389153
$958$	−8.09179e161	−0.265231
$959$	−1.95201e161	−0.0604459
$960$	−3.61953e162	−1.05894
$961$	−6.02682e161	−0.166596
$962$	4.73379e162	1.23642
$963$	4.97722e159	0.00122844
$964$	−7.83151e161	−0.182661
$965$	−4.10799e162	−0.905505
$966$	3.61212e161	0.0752504
$967$	3.66355e162	0.721372	0.360686	−	0.932687i	$-0.382543\pi$
$967$	3.66355e162	0.721372	0.360686	+	0.932687i	$0.382543\pi$
$968$	−5.55544e162	−1.03398
$969$	8.13022e162	1.43040
$970$	5.87096e161	0.0976448
$971$	−1.05387e163	−1.65706	−0.828530	−	0.559945i	$-0.810822\pi$
$971$	−1.05387e163	−1.65706	−0.828530	+	0.559945i	$0.810822\pi$
$972$	1.80472e162	0.268286
$973$	−2.03130e162	−0.285512
$974$	3.41271e162	0.453562
$975$	4.95656e162	0.622915
$976$	3.17171e162	0.376945
$977$	6.61905e162	0.743947	0.371974	−	0.928243i	$-0.378681\pi$
$977$	6.61905e162	0.743947	0.371974	+	0.928243i	$0.378681\pi$
$978$	7.25444e162	0.771145
$979$	−2.63636e162	−0.265062
$980$	4.93158e162	0.468991
$981$	−3.93918e162	−0.354360
$982$	1.11727e162	0.0950780
$983$	1.03150e163	0.830428	0.415214	−	0.909724i	$-0.363707\pi$
$983$	1.03150e163	0.830428	0.415214	+	0.909724i	$0.363707\pi$
$984$	−1.11466e163	−0.849002
$985$	−1.42568e163	−1.02742
$986$	−2.80966e162	−0.191585
$987$	2.77648e161	0.0179147
$988$	1.21319e163	0.740759
$989$	4.64344e162	0.268313
$990$	−1.61068e162	−0.0880826
$991$	−1.54990e163	−0.802211	−0.401105	−	0.916032i	$-0.631374\pi$
$991$	−1.54990e163	−0.802211	−0.401105	+	0.916032i	$0.631374\pi$
$992$	1.29944e163	0.636605
$993$	−4.35739e162	−0.202065
$994$	−4.19294e162	−0.184061
$995$	−3.15916e163	−1.31284
$996$	−1.41415e163	−0.556367
$997$	−2.05067e163	−0.763851	−0.381926	−	0.924193i	$-0.624739\pi$
$997$	−2.05067e163	−0.763851	−0.381926	+	0.924193i	$0.624739\pi$
$998$	−1.22870e163	−0.433342
$999$	4.30697e163	1.43831

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.110.a.a.1.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.110.a.a.1.3	✓	8	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:	\( k \)	\(=\)	\( 110 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-2.02081e16 q^{2} -7.88466e25 q^{3} -2.40671e32 q^{4} +1.60701e38 q^{5} +1.59334e42 q^{6} +1.73591e45 q^{7} +1.79793e49 q^{8} -3.92739e51 q^{9} +O(q^{10})\)	\(q-2.02081e16 q^{2} -7.88466e25 q^{3} -2.40671e32 q^{4} +1.60701e38 q^{5} +1.59334e42 q^{6} +1.73591e45 q^{7} +1.79793e49 q^{8} -3.92739e51 q^{9} -3.24746e54 q^{10} -1.26288e56 q^{11} +1.89761e58 q^{12} -6.03445e60 q^{13} -3.50795e61 q^{14} -1.26707e64 q^{15} -2.07122e65 q^{16} -1.23439e67 q^{17} +7.93649e67 q^{18} +8.35349e69 q^{19} -3.86762e70 q^{20} -1.36871e71 q^{21} +2.55203e72 q^{22} +1.30595e74 q^{23} -1.41761e75 q^{24} +1.04174e76 q^{25} +1.21944e77 q^{26} +1.10950e78 q^{27} -4.17785e77 q^{28} -1.12636e79 q^{29} +2.56051e80 q^{30} -1.73636e81 q^{31} -7.48370e81 q^{32} +9.95736e81 q^{33} +2.49446e83 q^{34} +2.78963e83 q^{35} +9.45210e83 q^{36} +3.88192e85 q^{37} -1.68808e86 q^{38} +4.75796e86 q^{39} +2.88929e87 q^{40} +7.86296e87 q^{41} +2.76590e87 q^{42} +3.55561e88 q^{43} +3.03939e88 q^{44} -6.31135e89 q^{45} -2.63907e90 q^{46} -2.02854e90 q^{47} +1.63308e91 q^{48} -1.27509e92 q^{49} -2.10516e92 q^{50} +9.73273e92 q^{51} +1.45232e93 q^{52} +1.36263e94 q^{53} -2.24207e94 q^{54} -2.02946e94 q^{55} +3.12105e94 q^{56} -6.58645e95 q^{57} +2.27615e95 q^{58} +1.85357e96 q^{59} +3.04949e96 q^{60} -1.53133e97 q^{61} +3.50885e97 q^{62} -6.81761e96 q^{63} +2.85661e98 q^{64} -9.69743e98 q^{65} -2.01219e98 q^{66} -1.76671e99 q^{67} +2.97082e99 q^{68} -1.02970e100 q^{69} -5.63731e99 q^{70} +1.19527e101 q^{71} -7.06116e100 q^{72} -5.70675e101 q^{73} -7.84461e101 q^{74} -8.21378e101 q^{75} -2.01045e102 q^{76} -2.19225e101 q^{77} -9.61491e102 q^{78} -3.23840e103 q^{79} -3.32847e103 q^{80} -4.76398e103 q^{81} -1.58895e104 q^{82} -7.45225e104 q^{83} +3.29410e103 q^{84} -1.98367e105 q^{85} -7.18520e104 q^{86} +8.88096e104 q^{87} -2.27056e105 q^{88} +2.08758e106 q^{89} +1.27540e106 q^{90} -1.04753e106 q^{91} -3.14305e106 q^{92} +1.36906e107 q^{93} +4.09928e106 q^{94} +1.34242e108 q^{95} +5.90064e107 q^{96} -1.80786e107 q^{97} +2.57672e108 q^{98} +4.95981e107 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 22\!\cdots\!00 q^{2}+ \cdots + 24\!\cdots\!84 q^{9}+O(q^{10}) \) 8 * q + 2288392606915200 * q^2 - 79912254646281404120911200 * q^3 + 2561413209738240277879721565741056 * q^4 - 213255348687551833005583336469825970000 * q^5 + 6583361430969554396417990643904425772724736 * q^6 + 2340906693576137711090348032140051967265800000 * q^7 - 11615898303025646840479523942639805952956786278400 * q^8 + 2442167730177863701398288419313511486695316522756584 * q^9	\( 8 q + 22\!\cdots\!00 q^{2}+ \cdots + 71\!\cdots\!28 q^{99}+O(q^{100}) \) 8 * q + 2288392606915200 * q^2 - 79912254646281404120911200 * q^3 + 2561413209738240277879721565741056 * q^4 - 213255348687551833005583336469825970000 * q^5 + 6583361430969554396417990643904425772724736 * q^6 + 2340906693576137711090348032140051967265800000 * q^7 - 11615898303025646840479523942639805952956786278400 * q^8 + 2442167730177863701398288419313511486695316522756584 * q^9 + 1812920838217088357740086473089711591380968010637920000 * q^10 - 165947975430612920732153376325913672821997118332062700064 * q^11 - 91447218063548694114657346762586040488310132762945923481600 * q^12 - 7191403001708863672049265996058758403993505035337715331216400 * q^13 - 509718116120592395778374084857614778933075979029025208586042368 * q^14 + 23523118033136793898911835577576979866924828095398791554532760000 * q^15 + 1148530988697824742941824958565237185269878102817249769800092090368 * q^16 - 8656206993525090371911384042688075118245096778873514284447257516400 * q^17 - 594865916442544102448370621315341724156945499047441634064537134051200 * q^18 - 11207956347132239593501696340276604562903586944462900105290733089025760 * q^19 - 318028102788054771974342811943070552646655597179484587999192418007040000 * q^20 - 2767292515426156676853955740316424819275205191740879849349575383275847424 * q^21 + 14938820094709351316223859446246734647054202968288974693072213154286630400 * q^22 + 53936338606237446863185709770824957589455521350451701866403050553428350400 * q^23 + 5321978767822090266204570063167770260876413438542000203325176764538153861120 * q^24 + 18193458801058157698506203622645619662054791653093200756293219491399746875000 * q^25 - 435759349281531260141580744807392307738565554114182063684255943941959138178304 * q^26 - 272453442859186698036015029517519337343034663149290746308745684225146650622400 * q^27 + 31554975806041099413511213807244716611018915532477271262553604696632234310041600 * q^28 + 29771410364049527567872005799257248512262425259650062583814547510404351825013360 * q^29 - 751891125225161548033301007468436615543819263432942020592477930753653797722240000 * q^30 - 1466375047838170098337421957808047734223626673774209444573675519328499442335175424 * q^31 - 5937114879483988773905731140457152891870978542120977621282805115905850091556044800 * q^32 + 98313301892085553482704563970636693639651433404572558153235155127418907919206665600 * q^33 + 230323498000052302973276572671855085448946915340852153738007852434989492667839528192 * q^34 - 2881501566480835926866891176622148835419121956576388959555158972591401000555206480000 * q^35 + 1939555675122247234177033125266156026088405967647423925256129675441087219550987378688 * q^36 + 33117119032354918971772421960637107981416747079728699237422500438475360696577657658800 * q^37 + 11996231369252381781466269208385230328578753740510963392596214782634078981979819686400 * q^38 - 771921798225629223813541576850627931176100580853963300794965264851972743236296284337472 * q^39 - 1009702443147367270514989525871937316615498052888256181187241154243431845313822720000000 * q^40 + 2631322094324930918487353619268593963294779980083389672280377185771701226284660975010896 * q^41 + 65594383583093454058986149447123157383111717279272925654585914541457714878623959042969600 * q^42 - 31764236064988776927398716108299521712529891801740350383239284135241451092841492492916000 * q^43 - 1270138580535281866445275727176723968063639122939870285300305417276565925160179749765480448 * q^44 + 287550814354171023801469605323898278540973909702719042079897511272969200785142386583190000 * q^45 + 14731896191270382685679107493825145018801039145654619659863205374802348136428160980957203456 * q^46 + 1625966957623832725817330998098515479861611323645021162528642542135008566368994094752150400 * q^47 - 143515128231599226227412132210359595219087228680385094858911141289724103136282160567785881600 * q^48 + 157527210655459293654279435784054674911203740727991629561212852729050695391270938108305773256 * q^49 + 322389957080420808210330902387583711642761566269183034944052266108906361308513927567750000000 * q^50 + 489920249498412339580606438123981910239683109252240004744192036459028106019912596244615989056 * q^51 - 5418992932208438205367792844823104431376197758802798107419957407784673910371822411932948480000 * q^52 + 9079308927321999351839177242746605854068388719924761670955991989783550469317936688082585930800 * q^53 - 24658507391097864427096370814937103472102040716547930307285838917927527638460695296874932751360 * q^54 + 118053680695881329185791540339622577195944539453849780739010333239182345152398471707806930760000 * q^55 - 201389106942279308288684434910785164662432037404781190144927582600705075235687388648357243125760 * q^56 + 226496945243108169507552544266677467884770074749629615006273688546254129496817350185452963651200 * q^57 - 2256052219534551389222024892508180423211025192914838983567709038409124940298945339969797987462400 * q^58 + 4201127473917559295037000225082981757247285086029974371230017377519538448027563747794558119713120 * q^59 + 15216716099557435608186566564337243721720353898331991157134416546559198037722222436035882885120000 * q^60 - 30174048445162611506034669407223089181051188758336573543308996493766034896596718300335923046430864 * q^61 - 101544378414770749846552697740777177239249497144967223452446029336671969269242448735950839304089600 * q^62 + 14962713033462753217361258544731526063207174198501064720440567489611717321152011844939244550427200 * q^63 + 350038493426472551390597880934195636388642189179841132000343481745073872195685178531480362020765696 * q^64 + 476042359995918992070699407122502192834702528804977370861576537263180680689143678390528307394660000 * q^65 - 3275457019157048603844818296003073802975658177120439799661182596542152337047019411219264546535589888 * q^66 - 2436592395324825448922436507298035360575674608488356192165065318580447361065445345719842978744898400 * q^67 - 22959577515788229863200422300261772167503744576389306175032085019828406207819090307551668913740595200 * q^68 + 20962513668346194921311473125160506340730960425003577830665711051634607002491986052437616343941489408 * q^69 - 38525614227951931001890316995983503763039503305975313750394662544984531605107874814848981273114880000 * q^70 - 182573264747524893462812402066757238991600980622231780705554761994960061464852147866759574299425367744 * q^71 - 937013521429830591768584754113763645664639906707863675451385694160469158557397360724539243386123059200 * q^72 - 992896003296363120918893380101417451599330843653017480857467556556562812303212272149043323072822439600 * q^73 - 1316746856327833419755644274540778481224231099510738713247508136902506806815717963522494407938546706688 * q^74 - 5871153288989297422411624806238187142192319563981336377889812488967662534076652985829089331258062500000 * q^75 - 23122551287666805941113536895845604280282190834103625501792190953367813062086656110687054676514749317120 * q^76 - 44146648850167699533016381157041098991672229312739789979368878215748452932712438044537666517717336608000 * q^77 - 74892005734867915768666768757796138875218855701976264642428162201719215233844576875406596388579804800000 * q^78 - 90877532388837507952377455262957690392004628366214899622576763930269368002866396444184811504470015827840 * q^79 - 537781290078408386666779886550832547957426185756793627297710378503553917482370710673024120741030789120000 * q^80 - 646040908793719449537213596253179795437117284606067679926187088540718516170416551690117712718559479920952 * q^81 - 1848162147553486548774628152888041182300793513808419102386749930544002262019111364366904880902061490681600 * q^82 - 866870614432750569174068646397256005138067253779508313470225924424638854266524026533083951694014356632800 * q^83 - 5840321795963005263777537308314418455056100956933759881092476300148871178382910044395005678085199546810368 * q^84 - 4668598916513761978133063620912572637580033499314634770309162489375519884024385880981753435084614859780000 * q^85 - 11688849548141363142089712396810850759020238587238805174946214292159714105146960272302323952195024989223424 * q^86 - 14581012249541375875764697103578340512244662623918147927221635902236243713987632388375578563817763114939200 * q^87 + 1530700112628746576163110294213004687459510268085538799651168686191357904989458023327058330803008647987200 * q^88 + 5370705282028265416504724158890178832899726253313779513986675059327392734022379735004069389198976135292880 * q^89 + 161603588167186166620406432595952865977969553485604382571187217963936716570564141726485419061308378075360000 * q^90 + 194491542286867118776437353517384882722616087297518094870786488241189494865282342165823695439370137913188736 * q^91 + 396302396563700359070027419943848305453145578954245792583330941741389770954106976666840341236078014314905600 * q^92 + 568179503361190024971076757263143967044040944520818668848960482931727310093723555328260563778420711013401600 * q^93 + 2479261213469097720755806625234954860838342725140724073489565122893996978512713040202033247954948169489487872 * q^94 + 3756267234494004771512604096671502522809843506715611046331612224428460858882412872485716488615235385073400000 * q^95 + 6137029402133719259406354903032524770352961857248155285728041689493176172684541150438338362553846429716054016 * q^96 + 3101905862702772302621994244705111813594597058738421633214535517860020385681724882654741053598909419139696400 * q^97 + 1265481578258615993478779535911065302494358871538528748084590996688739571409881009859314203275359668334966400 * q^98 + 719245389651015996203722525987404961611392270203442708727501943323361320310359905092561649275451940844703328 * q^99

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