LMFDB - Embedded newform 1.110.a.a.1.1

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			1.1
Root			$2.47185e14$ 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)

$f(q)$	$=$	$q-4.71735e16 q^{2} -1.38575e26 q^{3} +1.57631e33 q^{4} -1.39304e38 q^{5} +6.53705e42 q^{6} +1.59904e46 q^{7} -4.37425e49 q^{8} +9.05875e51 q^{9} +O(q^{10})$	\(q-4.71735e16 q^{2} -1.38575e26 q^{3} +1.57631e33 q^{4} -1.39304e38 q^{5} +6.53705e42 q^{6} +1.59904e46 q^{7} -4.37425e49 q^{8} +9.05875e51 q^{9} +6.57147e54 q^{10} -5.93232e56 q^{11} -2.18436e59 q^{12} +1.89568e60 q^{13} -7.54325e62 q^{14} +1.93040e64 q^{15} +1.04041e66 q^{16} -1.15719e67 q^{17} -4.27333e68 q^{18} -3.88309e69 q^{19} -2.19586e71 q^{20} -2.21587e72 q^{21} +2.79849e73 q^{22} -1.96493e74 q^{23} +6.06160e75 q^{24} +3.99823e75 q^{25} -8.94260e76 q^{26} +1.50412e77 q^{27} +2.52058e79 q^{28} +5.20249e79 q^{29} -9.10639e80 q^{30} +8.91312e80 q^{31} -2.06892e82 q^{32} +8.22069e82 q^{33} +5.45885e83 q^{34} -2.22753e84 q^{35} +1.42794e85 q^{36} +1.37849e85 q^{37} +1.83179e86 q^{38} -2.62693e86 q^{39} +6.09352e87 q^{40} +8.15104e87 q^{41} +1.04530e89 q^{42} +3.10377e88 q^{43} -9.35115e89 q^{44} -1.26192e90 q^{45} +9.26927e90 q^{46} -1.80658e91 q^{47} -1.44174e92 q^{48} +1.25171e92 q^{49} -1.88610e92 q^{50} +1.60356e93 q^{51} +2.98817e93 q^{52} +1.31683e94 q^{53} -7.09548e93 q^{54} +8.26397e94 q^{55} -6.99461e95 q^{56} +5.38098e95 q^{57} -2.45420e96 q^{58} -5.81637e95 q^{59} +3.04290e97 q^{60} -2.73879e97 q^{61} -4.20463e97 q^{62} +1.44853e98 q^{63} +3.00720e98 q^{64} -2.64076e98 q^{65} -3.87799e99 q^{66} +1.37350e99 q^{67} -1.82408e100 q^{68} +2.72289e100 q^{69} +1.05081e101 q^{70} -9.18618e99 q^{71} -3.96252e101 q^{72} -1.17575e101 q^{73} -6.50281e101 q^{74} -5.54053e101 q^{75} -6.12094e102 q^{76} -9.48603e102 q^{77} +1.23922e103 q^{78} +4.74076e103 q^{79} -1.44933e104 q^{80} -1.12737e104 q^{81} -3.84513e104 q^{82} +7.42464e104 q^{83} -3.49288e105 q^{84} +1.61201e105 q^{85} -1.46416e105 q^{86} -7.20933e105 q^{87} +2.59495e106 q^{88} -1.07483e106 q^{89} +5.95293e106 q^{90} +3.03128e106 q^{91} -3.09733e107 q^{92} -1.23513e107 q^{93} +8.52228e107 q^{94} +5.40931e107 q^{95} +2.86700e108 q^{96} +2.33996e108 q^{97} -5.90475e108 q^{98} -5.37394e108 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.71735e16	−1.85167	−0.925835	−	0.377928i	$-0.876637\pi$
$2$	−4.71735e16	−1.85167	−0.925835	+	0.377928i	$0.876637\pi$
$3$	−1.38575e26	−1.37586	−0.687932	−	0.725775i	$-0.741481\pi$
$3$	−1.38575e26	−1.37586	−0.687932	+	0.725775i	$0.741481\pi$
$4$	1.57631e33	2.42868
$5$	−1.39304e38	−1.12227	−0.561137	−	0.827723i	$-0.689636\pi$
$5$	−1.39304e38	−1.12227	−0.561137	+	0.827723i	$0.689636\pi$
$6$	6.53705e42	2.54765
$7$	1.59904e46	1.39964	0.699821	−	0.714318i	$-0.253263\pi$
$7$	1.59904e46	1.39964	0.699821	+	0.714318i	$0.253263\pi$
$8$	−4.37425e49	−2.64545
$9$	9.05875e51	0.893000
$10$	6.57147e54	2.07808
$11$	−5.93232e56	−1.04069	−0.520347	−	0.853955i	$-0.674198\pi$
$11$	−5.93232e56	−1.04069	−0.520347	+	0.853955i	$0.674198\pi$
$12$	−2.18436e59	−3.34154
$13$	1.89568e60	0.369703	0.184851	−	0.982766i	$-0.440820\pi$
$13$	1.89568e60	0.369703	0.184851	+	0.982766i	$0.440820\pi$
$14$	−7.54325e62	−2.59167
$15$	1.93040e64	1.54410
$16$	1.04041e66	2.46982
$17$	−1.15719e67	−1.00911	−0.504553	−	0.863381i	$-0.668343\pi$
$17$	−1.15719e67	−1.00911	−0.504553	+	0.863381i	$0.668343\pi$
$18$	−4.27333e68	−1.65354
$19$	−3.88309e69	−0.789053	−0.394527	−	0.918885i	$-0.629091\pi$
$19$	−3.88309e69	−0.789053	−0.394527	+	0.918885i	$0.629091\pi$
$20$	−2.19586e71	−2.72565
$21$	−2.21587e72	−1.92572
$22$	2.79849e73	1.92702
$23$	−1.96493e74	−1.20000	−0.599998	−	0.800001i	$-0.704832\pi$
$23$	−1.96493e74	−1.20000	−0.599998	+	0.800001i	$0.704832\pi$
$24$	6.06160e75	3.63978
$25$	3.99823e75	0.259500
$26$	−8.94260e76	−0.684567
$27$	1.50412e77	0.147217
$28$	2.52058e79	3.39929
$29$	5.20249e79	1.03638	0.518191	−	0.855265i	$-0.326605\pi$
$29$	5.20249e79	1.03638	0.518191	+	0.855265i	$0.326605\pi$
$30$	−9.10639e80	−2.85916
$31$	8.91312e80	0.468616	0.234308	−	0.972162i	$-0.424718\pi$
$31$	8.91312e80	0.468616	0.234308	+	0.972162i	$0.424718\pi$
$32$	−2.06892e82	−1.92784
$33$	8.22069e82	1.43185
$34$	5.45885e83	1.86853
$35$	−2.22753e84	−1.57078
$36$	1.42794e85	2.16881
$37$	1.37849e85	0.470336	0.235168	−	0.971955i	$-0.424436\pi$
$37$	1.37849e85	0.470336	0.235168	+	0.971955i	$0.424436\pi$
$38$	1.83179e86	1.46107
$39$	−2.62693e86	−0.508660
$40$	6.09352e87	2.96892
$41$	8.15104e87	1.03393	0.516967	−	0.856005i	$-0.327061\pi$
$41$	8.15104e87	1.03393	0.516967	+	0.856005i	$0.327061\pi$
$42$	1.04530e89	3.56579
$43$	3.10377e88	0.293670	0.146835	−	0.989161i	$-0.453091\pi$
$43$	3.10377e88	0.293670	0.146835	+	0.989161i	$0.453091\pi$
$44$	−9.35115e89	−2.52752
$45$	−1.26192e90	−1.00219
$46$	9.26927e90	2.22200
$47$	−1.80658e91	−1.34129	−0.670647	−	0.741776i	$-0.733984\pi$
$47$	−1.80658e91	−1.34129	−0.670647	+	0.741776i	$0.733984\pi$
$48$	−1.44174e92	−3.39813
$49$	1.25171e92	0.958997
$50$	−1.88610e92	−0.480508
$51$	1.60356e93	1.38839
$52$	2.98817e93	0.897890
$53$	1.31683e94	1.40118	0.700592	−	0.713562i	$-0.252919\pi$
$53$	1.31683e94	1.40118	0.700592	+	0.713562i	$0.252919\pi$
$54$	−7.09548e93	−0.272598
$55$	8.26397e94	1.16794
$56$	−6.99461e95	−3.70268
$57$	5.38098e95	1.08563
$58$	−2.45420e96	−1.91904
$59$	−5.81637e95	−0.179150	−0.0895751	−	0.995980i	$-0.528551\pi$
$59$	−5.81637e95	−0.179150	−0.0895751	+	0.995980i	$0.528551\pi$
$60$	3.04290e97	3.75012
$61$	−2.73879e97	−1.37114	−0.685572	−	0.728005i	$-0.740448\pi$
$61$	−2.73879e97	−1.37114	−0.685572	+	0.728005i	$0.740448\pi$
$62$	−4.20463e97	−0.867723
$63$	1.44853e98	1.24988
$64$	3.00720e98	1.09990
$65$	−2.64076e98	−0.414908
$66$	−3.87799e99	−2.65132
$67$	1.37350e99	0.413763	0.206881	−	0.978366i	$-0.433669\pi$
$67$	1.37350e99	0.413763	0.206881	+	0.978366i	$0.433669\pi$
$68$	−1.82408e100	−2.45080
$69$	2.72289e100	1.65103
$70$	1.05081e101	2.90857
$71$	−9.18618e99	−0.117369	−0.0586847	−	0.998277i	$-0.518691\pi$
$71$	−9.18618e99	−0.117369	−0.0586847	+	0.998277i	$0.518691\pi$
$72$	−3.96252e101	−2.36239
$73$	−1.17575e101	−0.330535	−0.165267	−	0.986249i	$-0.552849\pi$
$73$	−1.17575e101	−0.330535	−0.165267	+	0.986249i	$0.552849\pi$
$74$	−6.50281e101	−0.870908
$75$	−5.54053e101	−0.357036
$76$	−6.12094e102	−1.91636
$77$	−9.48603e102	−1.45660
$78$	1.23922e103	0.941871
$79$	4.74076e103	1.79958	0.899792	−	0.436320i	$-0.143718\pi$
$79$	4.74076e103	1.79958	0.899792	+	0.436320i	$0.143718\pi$
$80$	−1.44933e104	−2.77181
$81$	−1.12737e104	−1.09555
$82$	−3.84513e104	−1.91450
$83$	7.42464e104	1.90950	0.954749	−	0.297412i	$-0.0961235\pi$
$83$	7.42464e104	1.90950	0.954749	+	0.297412i	$0.0961235\pi$
$84$	−3.49288e105	−4.67695
$85$	1.61201e105	1.13249
$86$	−1.46416e105	−0.543780
$87$	−7.20933e105	−1.42592
$88$	2.59495e106	2.75310
$89$	−1.07483e106	−0.616004	−0.308002	−	0.951386i	$-0.599660\pi$
$89$	−1.07483e106	−0.616004	−0.308002	+	0.951386i	$0.599660\pi$
$90$	5.95293e106	1.85573
$91$	3.03128e106	0.517451
$92$	−3.09733e107	−2.91441
$93$	−1.23513e107	−0.644752
$94$	8.52228e107	2.48364
$95$	5.40931e107	0.885534
$96$	2.86700e108	2.65244
$97$	2.33996e108	1.23069	0.615344	−	0.788259i	$-0.289017\pi$
$97$	2.33996e108	1.23069	0.615344	+	0.788259i	$0.289017\pi$
$98$	−5.90475e108	−1.77575
$99$	−5.37394e108	−0.929340
$100$	6.30242e108	0.630242
$101$	9.45240e108	0.549575	0.274788	−	0.961505i	$-0.411392\pi$
$101$	9.45240e108	0.549575	0.274788	+	0.961505i	$0.411392\pi$
$102$	−7.56458e109	−2.57084
$103$	−1.41845e109	−0.283261	−0.141630	−	0.989920i	$-0.545234\pi$
$103$	−1.41845e109	−0.283261	−0.141630	+	0.989920i	$0.545234\pi$
$104$	−8.29218e109	−0.978030
$105$	3.08680e110	2.16118
$106$	−6.21195e110	−2.59453
$107$	5.22090e110	1.30716	0.653581	−	0.756856i	$-0.273266\pi$
$107$	5.22090e110	1.30716	0.653581	+	0.756856i	$0.273266\pi$
$108$	2.37096e110	0.357544
$109$	−5.92760e110	−0.540922	−0.270461	−	0.962731i	$-0.587176\pi$
$109$	−5.92760e110	−0.540922	−0.270461	+	0.962731i	$0.587176\pi$
$110$	−3.89841e111	−2.16265
$111$	−1.91023e111	−0.647118
$112$	1.66366e112	3.45686
$113$	7.64888e111	0.979090	0.489545	−	0.871978i	$-0.337163\pi$
$113$	7.64888e111	0.979090	0.489545	+	0.871978i	$0.337163\pi$
$114$	−2.53840e112	−2.01023
$115$	2.73723e112	1.34673
$116$	8.20071e112	2.51704
$117$	1.71725e112	0.330145
$118$	2.74379e112	0.331727
$119$	−1.85039e113	−1.41239
$120$	−8.44407e113	−4.08483
$121$	2.69847e112	0.0830453
$122$	1.29198e114	2.53891
$123$	−1.12953e114	−1.42255
$124$	1.40498e114	1.13812
$125$	1.58935e114	0.831044
$126$	−6.83324e114	−2.31437
$127$	−1.46989e114	−0.323580	−0.161790	−	0.986825i	$-0.551727\pi$
$127$	−1.46989e114	−0.323580	−0.161790	+	0.986825i	$0.551727\pi$
$128$	−7.57951e113	−0.108817
$129$	−4.30104e114	−0.404049
$130$	1.24574e115	0.768273
$131$	4.52763e114	0.183902	0.0919508	−	0.995764i	$-0.470690\pi$
$131$	4.52763e114	0.183902	0.0919508	+	0.995764i	$0.470690\pi$
$132$	1.29583e116	3.47752
$133$	−6.20923e115	−1.10439
$134$	−6.47927e115	−0.766152
$135$	−2.09531e115	−0.165218
$136$	5.06182e116	2.66954
$137$	9.68902e115	0.342775	0.171387	−	0.985204i	$-0.445175\pi$
$137$	9.68902e115	0.342775	0.171387	+	0.985204i	$0.445175\pi$
$138$	−1.28449e117	−3.05717
$139$	1.81881e116	0.292066	0.146033	−	0.989280i	$-0.453349\pi$
$139$	1.81881e116	0.292066	0.146033	+	0.989280i	$0.453349\pi$
$140$	−3.51127e117	−3.81493
$141$	2.50346e117	1.84544
$142$	4.33344e116	0.217329
$143$	−1.12458e117	−0.384748
$144$	9.42480e117	2.20555
$145$	−7.24729e117	−1.16311
$146$	5.54641e117	0.612042
$147$	−1.73455e118	−1.31945
$148$	2.17291e118	1.14230
$149$	−6.34226e117	−0.230990	−0.115495	−	0.993308i	$-0.536845\pi$
$149$	−6.34226e117	−0.230990	−0.115495	+	0.993308i	$0.536845\pi$
$150$	2.61366e118	0.661113
$151$	−6.83251e118	−1.20320	−0.601598	−	0.798799i	$-0.705469\pi$
$151$	−6.83251e118	−1.20320	−0.601598	+	0.798799i	$0.705469\pi$
$152$	1.69856e119	2.08740
$153$	−1.04827e119	−0.901132
$154$	4.47490e119	2.69714
$155$	−1.24163e119	−0.525916
$156$	−4.14085e119	−1.23537
$157$	1.79026e119	0.377037	0.188519	−	0.982070i	$-0.439631\pi$
$157$	1.79026e119	0.377037	0.188519	+	0.982070i	$0.439631\pi$
$158$	−2.23639e120	−3.33223
$159$	−1.82479e120	−1.92784
$160$	2.88209e120	2.16356
$161$	−3.14201e120	−1.67957
$162$	5.31820e120	2.02860
$163$	4.13047e120	1.12661	0.563306	−	0.826248i	$-0.309529\pi$
$163$	4.13047e120	1.12661	0.563306	+	0.826248i	$0.309529\pi$
$164$	1.28485e121	2.51110
$165$	−1.14518e121	−1.60693
$166$	−3.50246e121	−3.53576
$167$	1.26735e121	0.922250	0.461125	−	0.887335i	$-0.347446\pi$
$167$	1.26735e121	0.922250	0.461125	+	0.887335i	$0.347446\pi$
$168$	9.69276e121	5.09438
$169$	−2.26985e121	−0.863320
$170$	−7.60441e121	−2.09700
$171$	−3.51759e121	−0.704625
$172$	4.89249e121	0.713231
$173$	−1.71087e122	−1.81846	−0.909231	−	0.416292i	$-0.863330\pi$
$173$	−1.71087e122	−1.81846	−0.909231	+	0.416292i	$0.863330\pi$
$174$	3.40089e122	2.64034
$175$	6.39333e121	0.363207
$176$	−6.17203e122	−2.57032
$177$	8.06001e121	0.246486
$178$	5.07035e122	1.14064
$179$	−4.41932e122	−0.732598	−0.366299	−	0.930497i	$-0.619375\pi$
$179$	−4.41932e122	−0.732598	−0.366299	+	0.930497i	$0.619375\pi$
$180$	−1.98917e123	−2.43400
$181$	6.21437e122	0.562231	0.281115	−	0.959674i	$-0.409296\pi$
$181$	6.21437e122	0.562231	0.281115	+	0.959674i	$0.409296\pi$
$182$	−1.42996e123	−0.958149
$183$	3.79527e123	1.88651
$184$	8.59510e123	3.17453
$185$	−1.92029e123	−0.527846
$186$	5.82655e123	1.19387
$187$	6.86479e123	1.05017
$188$	−2.84772e124	−3.25758
$189$	2.40516e123	0.206051
$190$	−2.55176e124	−1.63972
$191$	3.71768e124	1.79454	0.897271	−	0.441481i	$-0.145547\pi$
$191$	3.71768e124	1.79454	0.897271	+	0.441481i	$0.145547\pi$
$192$	−4.16721e124	−1.51331
$193$	1.92715e124	0.527280	0.263640	−	0.964621i	$-0.415077\pi$
$193$	1.92715e124	0.527280	0.263640	+	0.964621i	$0.415077\pi$
$194$	−1.10384e125	−2.27883
$195$	3.65943e124	0.570857
$196$	1.97308e125	2.32910
$197$	−7.39002e124	−0.661053	−0.330526	−	0.943797i	$-0.607226\pi$
$197$	−7.39002e124	−0.661053	−0.330526	+	0.943797i	$0.607226\pi$
$198$	2.53508e125	1.72083
$199$	−2.88558e125	−1.48847	−0.744235	−	0.667918i	$-0.767186\pi$
$199$	−2.88558e125	−1.48847	−0.744235	+	0.667918i	$0.767186\pi$
$200$	−1.74892e125	−0.686493
$201$	−1.90332e125	−0.569281
$202$	−4.45903e125	−1.01763
$203$	8.31900e125	1.45056
$204$	2.52771e126	3.37196
$205$	−1.13547e126	−1.16036
$206$	6.69135e125	0.524506
$207$	−1.77998e126	−1.07160
$208$	1.97228e126	0.913098
$209$	2.30357e126	0.821163
$210$	−1.45615e127	−4.00180
$211$	−6.69610e126	−1.42046	−0.710229	−	0.703971i	$-0.751408\pi$
$211$	−6.69610e126	−1.42046	−0.710229	+	0.703971i	$0.751408\pi$
$212$	2.07573e127	3.40303
$213$	1.27297e126	0.161484
$214$	−2.46288e127	−2.42043
$215$	−4.32369e126	−0.329578
$216$	−6.57942e126	−0.389456
$217$	1.42525e127	0.655895
$218$	2.79626e127	1.00161
$219$	1.62928e127	0.454771
$220$	1.30265e128	2.83657
$221$	−2.19365e127	−0.373069
$222$	9.01124e127	1.19825
$223$	−1.21785e128	−1.26759	−0.633794	−	0.773502i	$-0.718503\pi$
$223$	−1.21785e128	−1.26759	−0.633794	+	0.773502i	$0.718503\pi$
$224$	−3.30829e128	−2.69828
$225$	3.62189e127	0.231733
$226$	−3.60825e128	−1.81295
$227$	1.34197e128	0.530071	0.265036	−	0.964239i	$-0.414616\pi$
$227$	1.34197e128	0.530071	0.265036	+	0.964239i	$0.414616\pi$
$228$	8.48206e128	2.63665
$229$	4.19421e128	1.02711	0.513555	−	0.858057i	$-0.328328\pi$
$229$	4.19421e128	1.02711	0.513555	+	0.858057i	$0.328328\pi$
$230$	−1.29125e129	−2.49369
$231$	1.31452e129	2.00408
$232$	−2.27570e129	−2.74170
$233$	2.65404e128	0.252935	0.126468	−	0.991971i	$-0.459636\pi$
$233$	2.65404e128	0.252935	0.126468	+	0.991971i	$0.459636\pi$
$234$	−8.10088e128	−0.611319
$235$	2.51664e129	1.50530
$236$	−9.16837e128	−0.435099
$237$	−6.56950e129	−2.47598
$238$	8.72894e129	2.61527
$239$	−5.27383e129	−1.25731	−0.628653	−	0.777686i	$-0.716393\pi$
$239$	−5.27383e129	−1.25731	−0.628653	+	0.777686i	$0.716393\pi$
$240$	2.00841e130	3.81363
$241$	3.26287e128	0.0493936	0.0246968	−	0.999695i	$-0.492138\pi$
$241$	3.26287e128	0.0493936	0.0246968	+	0.999695i	$0.492138\pi$
$242$	−1.27296e129	−0.153773
$243$	1.40967e130	1.36011
$244$	−4.31717e130	−3.33007
$245$	−1.74368e130	−1.07626
$246$	5.32838e130	2.63410
$247$	−7.36110e129	−0.291715
$248$	−3.89882e130	−1.23970
$249$	−1.02887e131	−2.62721
$250$	−7.49753e130	−1.53882
$251$	4.44276e130	0.733558	0.366779	−	0.930308i	$-0.380460\pi$
$251$	4.44276e130	0.733558	0.366779	+	0.930308i	$0.380460\pi$
$252$	2.28333e131	3.03556
$253$	1.16566e131	1.24883
$254$	6.93398e130	0.599163
$255$	−2.23383e131	−1.55816
$256$	−1.59423e131	−0.898407
$257$	1.62556e131	0.740709	0.370354	−	0.928891i	$-0.379236\pi$
$257$	1.62556e131	0.740709	0.370354	+	0.928891i	$0.379236\pi$
$258$	2.02895e131	0.748166
$259$	2.20426e131	0.658302
$260$	−4.16265e131	−1.00768
$261$	4.71280e131	0.925490
$262$	−2.13584e131	−0.340525
$263$	1.49206e132	1.93285	0.966425	−	0.256949i	$-0.0827171\pi$
$263$	1.49206e132	1.93285	0.966425	+	0.256949i	$0.0827171\pi$
$264$	−3.59594e132	−3.78790
$265$	−1.83440e132	−1.57251
$266$	2.92911e132	2.04497
$267$	1.48944e132	0.847538
$268$	2.16505e132	1.00490
$269$	−2.00465e132	−0.759520	−0.379760	−	0.925085i	$-0.623993\pi$
$269$	−2.00465e132	−0.759520	−0.379760	+	0.925085i	$0.623993\pi$
$270$	9.88431e131	0.305929
$271$	−8.97234e131	−0.227028	−0.113514	−	0.993536i	$-0.536211\pi$
$271$	−8.97234e131	−0.227028	−0.113514	+	0.993536i	$0.536211\pi$
$272$	−1.20394e133	−2.49231
$273$	−4.20058e132	−0.711942
$274$	−4.57065e132	−0.634706
$275$	−2.37188e132	−0.270060
$276$	4.29211e133	4.00983
$277$	7.68228e132	0.589309	0.294654	−	0.955604i	$-0.404795\pi$
$277$	7.68228e132	0.589309	0.294654	+	0.955604i	$0.404795\pi$
$278$	−8.57998e132	−0.540810
$279$	8.07417e132	0.418474
$280$	9.74379e133	4.15542
$281$	−2.42903e133	−0.852978	−0.426489	−	0.904493i	$-0.640250\pi$
$281$	−2.42903e133	−0.852978	−0.426489	+	0.904493i	$0.640250\pi$
$282$	−1.18097e134	−3.41714
$283$	−5.67399e133	−1.35372	−0.676859	−	0.736113i	$-0.736659\pi$
$283$	−5.67399e133	−1.35372	−0.676859	+	0.736113i	$0.736659\pi$
$284$	−1.44802e133	−0.285053
$285$	−7.49593e133	−1.21837
$286$	5.30504e133	0.712426
$287$	1.30339e134	1.44714
$288$	−1.87418e134	−1.72156
$289$	2.40573e132	0.0182943
$290$	3.41880e134	2.15369
$291$	−3.24258e134	−1.69326
$292$	−1.85333e134	−0.802764
$293$	2.19518e134	0.789195	0.394597	−	0.918854i	$-0.370884\pi$
$293$	2.19518e134	0.789195	0.394597	+	0.918854i	$0.370884\pi$
$294$	8.18249e134	2.44318
$295$	8.10245e133	0.201056
$296$	−6.02984e134	−1.24425
$297$	−8.92295e133	−0.153208
$298$	2.99187e134	0.427717
$299$	−3.72488e134	−0.443642
$300$	−8.73356e134	−0.867128
$301$	4.96307e134	0.411032
$302$	3.22314e135	2.22792
$303$	−1.30986e135	−0.756141
$304$	−4.04000e135	−1.94882
$305$	3.81525e135	1.53880
$306$	4.94504e135	1.66860
$307$	−3.90972e135	−1.10434	−0.552172	−	0.833730i	$-0.686201\pi$
$307$	−3.90972e135	−1.10434	−0.552172	+	0.833730i	$0.686201\pi$
$308$	−1.49529e136	−3.53762
$309$	1.96562e135	0.389728
$310$	5.85723e135	0.973823
$311$	−3.06682e135	−0.427806	−0.213903	−	0.976855i	$-0.568618\pi$
$311$	−3.06682e135	−0.427806	−0.213903	+	0.976855i	$0.568618\pi$
$312$	1.14909e136	1.34564
$313$	−1.43759e136	−1.41406	−0.707029	−	0.707184i	$-0.749965\pi$
$313$	−1.43759e136	−1.41406	−0.707029	+	0.707184i	$0.749965\pi$
$314$	−8.44527e135	−0.698149
$315$	−2.01787e136	−1.40271
$316$	7.47289e136	4.37062
$317$	−2.09847e136	−1.03317	−0.516585	−	0.856236i	$-0.672797\pi$
$317$	−2.09847e136	−1.03317	−0.516585	+	0.856236i	$0.672797\pi$
$318$	8.60819e136	3.56972
$319$	−3.08628e136	−1.07856
$320$	−4.18915e136	−1.23439
$321$	−7.23484e136	−1.79848
$322$	1.48220e137	3.11000
$323$	4.49345e136	0.796238
$324$	−1.77708e137	−2.66075
$325$	7.57936e135	0.0959377
$326$	−1.94849e137	−2.08612
$327$	8.21414e136	0.744234
$328$	−3.56547e137	−2.73522
$329$	−2.88880e137	−1.87733
$330$	5.40220e137	2.97551
$331$	1.86462e137	0.870895	0.435447	−	0.900214i	$-0.356590\pi$
$331$	1.86462e137	0.870895	0.435447	+	0.900214i	$0.356590\pi$
$332$	1.17035e138	4.63757
$333$	1.24874e137	0.420010
$334$	−5.97853e137	−1.70770
$335$	−1.91334e137	−0.464355
$336$	−2.30541e138	−4.75616
$337$	7.88367e137	1.38324	0.691622	−	0.722260i	$-0.256896\pi$
$337$	7.88367e137	1.38324	0.691622	+	0.722260i	$0.256896\pi$
$338$	1.07077e138	1.59858
$339$	−1.05994e138	−1.34709
$340$	2.54102e138	2.75047
$341$	−5.28755e137	−0.487686
$342$	1.65937e138	1.30473
$343$	−8.55787e136	−0.0573900
$344$	−1.35767e138	−0.776888
$345$	−3.79311e138	−1.85291
$346$	8.07078e138	3.36719
$347$	−2.10832e138	−0.751588	−0.375794	−	0.926703i	$-0.622630\pi$
$347$	−2.10832e138	−0.751588	−0.375794	+	0.926703i	$0.622630\pi$
$348$	−1.13641e139	−3.46311
$349$	2.35789e138	0.614522	0.307261	−	0.951625i	$-0.400588\pi$
$349$	2.35789e138	0.614522	0.307261	+	0.951625i	$0.400588\pi$
$350$	−3.01596e138	−0.672539
$351$	2.85134e137	0.0544266
$352$	1.22735e139	2.00629
$353$	−9.68777e138	−1.35676	−0.678379	−	0.734712i	$-0.737317\pi$
$353$	−9.68777e138	−1.35676	−0.678379	+	0.734712i	$0.737317\pi$
$354$	−3.80219e138	−0.456411
$355$	1.27967e138	0.131721
$356$	−1.69426e139	−1.49608
$357$	2.56417e139	1.94325
$358$	2.08475e139	1.35653
$359$	−6.41840e138	−0.358740	−0.179370	−	0.983782i	$-0.557406\pi$
$359$	−6.41840e138	−0.358740	−0.179370	+	0.983782i	$0.557406\pi$
$360$	5.51996e139	2.65125
$361$	−9.13984e138	−0.377395
$362$	−2.93154e139	−1.04107
$363$	−3.73940e138	−0.114259
$364$	4.77821e139	1.25672
$365$	1.63786e139	0.370951
$366$	−1.79036e140	−3.49319
$367$	1.74773e139	0.293883	0.146942	−	0.989145i	$-0.453057\pi$
$367$	1.74773e139	0.293883	0.146942	+	0.989145i	$0.453057\pi$
$368$	−2.04433e140	−2.96377
$369$	7.38382e139	0.923303
$370$	9.05868e139	0.977397
$371$	2.10567e140	1.96115
$372$	−1.94694e140	−1.56590
$373$	1.93532e140	1.34469	0.672344	−	0.740239i	$-0.265288\pi$
$373$	1.93532e140	1.34469	0.672344	+	0.740239i	$0.265288\pi$
$374$	−3.23837e140	−1.94457
$375$	−2.20244e140	−1.14340
$376$	7.90244e140	3.54833
$377$	9.86226e139	0.383154
$378$	−1.13460e140	−0.381539
$379$	−4.29785e140	−1.25145	−0.625727	−	0.780042i	$-0.715198\pi$
$379$	−4.29785e140	−1.25145	−0.625727	+	0.780042i	$0.715198\pi$
$380$	8.52672e140	2.15068
$381$	2.03689e140	0.445202
$382$	−1.75376e141	−3.32290
$383$	−2.42666e139	−0.0398727	−0.0199363	−	0.999801i	$-0.506346\pi$
$383$	−2.42666e139	−0.0398727	−0.0199363	+	0.999801i	$0.506346\pi$
$384$	1.05033e140	0.149718
$385$	1.32144e141	1.63470
$386$	−9.09103e140	−0.976349
$387$	2.81163e140	0.262247
$388$	3.68848e141	2.98895
$389$	−1.36551e141	−0.961704	−0.480852	−	0.876802i	$-0.659672\pi$
$389$	−1.36551e141	−0.961704	−0.480852	+	0.876802i	$0.659672\pi$
$390$	−1.72628e141	−1.05704
$391$	2.27379e141	1.21092
$392$	−5.47529e141	−2.53698
$393$	−6.27415e140	−0.253023
$394$	3.48613e141	1.22405
$395$	−6.60408e141	−2.01963
$396$	−8.47097e141	−2.25707
$397$	−5.30890e141	−1.23288	−0.616442	−	0.787400i	$-0.711426\pi$
$397$	−5.30890e141	−1.23288	−0.616442	+	0.787400i	$0.711426\pi$
$398$	1.36123e142	2.75616
$399$	8.60441e141	1.51949
$400$	4.15979e141	0.640917
$401$	4.22919e141	0.568708	0.284354	−	0.958719i	$-0.408221\pi$
$401$	4.22919e141	0.568708	0.284354	+	0.958719i	$0.408221\pi$
$402$	8.97863e141	1.05412
$403$	1.68964e141	0.173249
$404$	1.48999e142	1.33474
$405$	1.57047e142	1.22951
$406$	−3.92437e142	−2.68597
$407$	−8.17762e141	−0.489476
$408$	−7.01440e142	−3.67292
$409$	2.87320e142	1.31657	0.658286	−	0.752768i	$-0.271282\pi$
$409$	2.87320e142	1.31657	0.658286	+	0.752768i	$0.271282\pi$
$410$	5.35643e142	2.14860
$411$	−1.34265e142	−0.471611
$412$	−2.23592e142	−0.687950
$413$	−9.30062e141	−0.250746
$414$	8.39680e142	1.98424
$415$	−1.03428e143	−2.14298
$416$	−3.92202e142	−0.712726
$417$	−2.52041e142	−0.401843
$418$	−1.08668e143	−1.52052
$419$	−1.40826e143	−1.72990	−0.864948	−	0.501862i	$-0.832648\pi$
$419$	−1.40826e143	−1.72990	−0.864948	+	0.501862i	$0.832648\pi$
$420$	4.86573e143	5.24882
$421$	1.82884e143	1.73301	0.866505	−	0.499169i	$-0.166361\pi$
$421$	1.82884e143	1.73301	0.866505	+	0.499169i	$0.166361\pi$
$422$	3.15879e143	2.63022
$423$	−1.63654e143	−1.19778
$424$	−5.76015e143	−3.70676
$425$	−4.62669e142	−0.261863
$426$	−6.00505e142	−0.299016
$427$	−4.37944e143	−1.91911
$428$	8.22973e143	3.17468
$429$	1.55838e143	0.529360
$430$	2.03964e143	0.610270
$431$	−4.53523e143	−1.19561	−0.597803	−	0.801643i	$-0.703960\pi$
$431$	−4.53523e143	−1.19561	−0.597803	+	0.801643i	$0.703960\pi$
$432$	1.56490e143	0.363599
$433$	2.56699e143	0.525817	0.262908	−	0.964821i	$-0.415318\pi$
$433$	2.56699e143	0.525817	0.262908	+	0.964821i	$0.415318\pi$
$434$	−6.72339e143	−1.21450
$435$	1.00429e144	1.60027
$436$	−9.34370e143	−1.31373
$437$	7.63000e143	0.946861
$438$	−7.68591e143	−0.842086
$439$	−4.56420e143	−0.441620	−0.220810	−	0.975317i	$-0.570870\pi$
$439$	−4.56420e143	−0.441620	−0.220810	+	0.975317i	$0.570870\pi$
$440$	−3.61487e144	−3.08974
$441$	1.13389e144	0.856384
$442$	1.03482e144	0.690801
$443$	5.83986e143	0.344667	0.172333	−	0.985039i	$-0.444869\pi$
$443$	5.83986e143	0.344667	0.172333	+	0.985039i	$0.444869\pi$
$444$	−3.01111e144	−1.57165
$445$	1.49728e144	0.691326
$446$	5.74502e144	2.34716
$447$	8.78876e143	0.317810
$448$	4.80864e144	1.53947
$449$	−1.68497e144	−0.477713	−0.238857	−	0.971055i	$-0.576773\pi$
$449$	−1.68497e144	−0.477713	−0.238857	+	0.971055i	$0.576773\pi$
$450$	−1.70858e144	−0.429094
$451$	−4.83546e144	−1.07601
$452$	1.20570e145	2.37790
$453$	9.46812e144	1.65543
$454$	−6.33056e144	−0.981517
$455$	−4.22269e144	−0.580722
$456$	−2.35377e145	−2.87198
$457$	−1.39230e145	−1.50765	−0.753823	−	0.657078i	$-0.771792\pi$
$457$	−1.39230e145	−1.50765	−0.753823	+	0.657078i	$0.771792\pi$
$458$	−1.97856e145	−1.90187
$459$	−1.74055e144	−0.148558
$460$	4.31471e145	3.27077
$461$	1.55703e145	1.04857	0.524283	−	0.851544i	$-0.324333\pi$
$461$	1.55703e145	1.04857	0.524283	+	0.851544i	$0.324333\pi$
$462$	−6.20107e145	−3.71090
$463$	2.93745e145	1.56245	0.781226	−	0.624249i	$-0.214595\pi$
$463$	2.93745e145	1.56245	0.781226	+	0.624249i	$0.214595\pi$
$464$	5.41271e145	2.55968
$465$	1.72059e145	0.723589
$466$	−1.25200e145	−0.468352
$467$	−3.05255e145	−1.01600	−0.507999	−	0.861358i	$-0.669615\pi$
$467$	−3.05255e145	−1.01600	−0.507999	+	0.861358i	$0.669615\pi$
$468$	2.70691e145	0.801816
$469$	2.19628e145	0.579119
$470$	−1.18719e146	−2.78732
$471$	−2.48084e145	−0.518752
$472$	2.54423e145	0.473933
$473$	−1.84126e145	−0.305621
$474$	3.09906e146	4.58470
$475$	−1.55255e145	−0.204759
$476$	−2.91678e146	−3.43024
$477$	1.19288e146	1.25126
$478$	2.48785e146	2.32811
$479$	−1.12113e146	−0.936200	−0.468100	−	0.883675i	$-0.655061\pi$
$479$	−1.12113e146	−0.936200	−0.468100	+	0.883675i	$0.655061\pi$
$480$	−3.99385e146	−2.97676
$481$	2.61317e145	0.173885
$482$	−1.53921e145	−0.0914607
$483$	4.35402e146	2.31085
$484$	4.25362e145	0.201691
$485$	−3.25966e146	−1.38117
$486$	−6.64989e146	−2.51848
$487$	−3.19882e146	−1.08308	−0.541541	−	0.840674i	$-0.682159\pi$
$487$	−3.19882e146	−1.08308	−0.541541	+	0.840674i	$0.682159\pi$
$488$	1.19802e147	3.62729
$489$	−5.72378e146	−1.55007
$490$	8.22557e146	1.99287
$491$	4.41373e146	0.956895	0.478448	−	0.878116i	$-0.341200\pi$
$491$	4.41373e146	0.956895	0.478448	+	0.878116i	$0.341200\pi$
$492$	−1.78048e147	−3.45493
$493$	−6.02024e146	−1.04582
$494$	3.47249e146	0.540160
$495$	7.48613e146	1.04297
$496$	9.27328e146	1.15740
$497$	−1.46891e146	−0.164275
$498$	4.85353e147	4.86472
$499$	−2.11151e147	−1.89720	−0.948598	−	0.316482i	$-0.897498\pi$
$499$	−2.11151e147	−1.89720	−0.948598	+	0.316482i	$0.897498\pi$
$500$	2.50530e147	2.01834
$501$	−1.75622e147	−1.26889
$502$	−2.09580e147	−1.35831
$503$	1.05113e147	0.611227	0.305613	−	0.952156i	$-0.401139\pi$
$503$	1.05113e147	0.611227	0.305613	+	0.952156i	$0.401139\pi$
$504$	−6.33625e147	−3.30649
$505$	−1.31676e147	−0.616774
$506$	−5.49883e147	−2.31242
$507$	3.14544e147	1.18781
$508$	−2.31699e147	−0.785873
$509$	3.24831e146	0.0989780	0.0494890	−	0.998775i	$-0.484241\pi$
$509$	3.24831e146	0.0989780	0.0494890	+	0.998775i	$0.484241\pi$
$510$	1.05378e148	2.88519
$511$	−1.88007e147	−0.462630
$512$	8.01249e147	1.77237
$513$	−5.84065e146	−0.116162
$514$	−7.66834e147	−1.37155
$515$	1.97597e147	0.317896
$516$	−6.77976e147	−0.981308
$517$	1.07172e148	1.39588
$518$	−1.03983e148	−1.21896
$519$	2.37083e148	2.50196
$520$	1.15514e148	1.09762
$521$	−1.91111e148	−1.63542	−0.817709	−	0.575632i	$-0.804756\pi$
$521$	−1.91111e148	−1.63542	−0.817709	+	0.575632i	$0.804756\pi$
$522$	−2.22320e148	−1.71370
$523$	2.11342e148	1.46772	0.733862	−	0.679299i	$-0.237716\pi$
$523$	2.11342e148	1.46772	0.733862	+	0.679299i	$0.237716\pi$
$524$	7.13693e147	0.446638
$525$	−8.85954e147	−0.499723
$526$	−7.03858e148	−3.57900
$527$	−1.03141e148	−0.472883
$528$	8.55287e148	3.53642
$529$	1.17972e148	0.439992
$530$	8.65351e148	2.91177
$531$	−5.26890e147	−0.159981
$532$	−9.78764e148	−2.68222
$533$	1.54518e148	0.382248
$534$	−7.02621e148	−1.56936
$535$	−7.27294e148	−1.46699
$536$	−6.00802e148	−1.09459
$537$	6.12406e148	1.00795
$538$	9.45664e148	1.40638
$539$	−7.42554e148	−0.998023
$540$	−3.30285e148	−0.401262
$541$	4.73993e148	0.520620	0.260310	−	0.965525i	$-0.416175\pi$
$541$	4.73993e148	0.520620	0.260310	+	0.965525i	$0.416175\pi$
$542$	4.23257e148	0.420381
$543$	−8.61154e148	−0.773553
$544$	2.39413e149	1.94539
$545$	8.25739e148	0.607063
$546$	1.98156e149	1.31828
$547$	8.52224e148	0.513150	0.256575	−	0.966524i	$-0.417406\pi$
$547$	8.52224e148	0.513150	0.256575	+	0.966524i	$0.417406\pi$
$548$	1.52729e149	0.832491
$549$	−2.48100e149	−1.22443
$550$	1.11890e149	0.500062
$551$	−2.02017e149	−0.817761
$552$	−1.19106e150	−4.36772
$553$	7.58068e149	2.51877
$554$	−3.62400e149	−1.09121
$555$	2.66103e149	0.726244
$556$	2.86700e149	0.709336
$557$	4.63517e149	1.03982	0.519910	−	0.854221i	$-0.325966\pi$
$557$	4.63517e149	1.03982	0.519910	+	0.854221i	$0.325966\pi$
$558$	−3.80887e149	−0.774877
$559$	5.88377e148	0.108570
$560$	−2.31754e150	−3.87954
$561$	−9.51286e149	−1.44489
$562$	1.14586e150	1.57943
$563$	−8.04877e149	−1.00698	−0.503492	−	0.864000i	$-0.667952\pi$
$563$	−8.04877e149	−1.00698	−0.503492	+	0.864000i	$0.667952\pi$
$564$	3.94622e150	4.48198
$565$	−1.06552e150	−1.09881
$566$	2.67662e150	2.50664
$567$	−1.80271e150	−1.53338
$568$	4.01826e149	0.310495
$569$	−2.27486e149	−0.159712	−0.0798558	−	0.996806i	$-0.525446\pi$
$569$	−2.27486e149	−0.159712	−0.0798558	+	0.996806i	$0.525446\pi$
$570$	3.53609e150	2.25603
$571$	2.35542e150	1.36584	0.682920	−	0.730493i	$-0.260710\pi$
$571$	2.35542e150	1.36584	0.682920	+	0.730493i	$0.260710\pi$
$572$	−1.77268e150	−0.934430
$573$	−5.15176e150	−2.46904
$574$	−6.14853e150	−2.67962
$575$	−7.85623e149	−0.311399
$576$	2.72415e150	0.982212
$577$	5.43843e150	1.78399	0.891994	−	0.452048i	$-0.149306\pi$
$577$	5.43843e150	1.78399	0.891994	+	0.452048i	$0.149306\pi$
$578$	−1.13487e149	−0.0338749
$579$	−2.67054e150	−0.725466
$580$	−1.14239e151	−2.82481
$581$	1.18723e151	2.67261
$582$	1.52964e151	3.13536
$583$	−7.81186e150	−1.45820
$584$	5.14300e150	0.874413
$585$	−2.39220e150	−0.370513
$586$	−1.03554e151	−1.46133
$587$	3.72559e150	0.479092	0.239546	−	0.970885i	$-0.423001\pi$
$587$	3.72559e150	0.479092	0.239546	+	0.970885i	$0.423001\pi$
$588$	−2.73418e151	−3.20452
$589$	−3.46104e150	−0.369763
$590$	−3.82221e150	−0.372289
$591$	1.02407e151	0.909519
$592$	1.43419e151	1.16164
$593$	−8.99967e150	−0.664884	−0.332442	−	0.943124i	$-0.607873\pi$
$593$	−8.99967e150	−0.664884	−0.332442	+	0.943124i	$0.607873\pi$
$594$	4.20927e150	0.283691
$595$	2.57767e151	1.58508
$596$	−9.99734e150	−0.561000
$597$	3.99868e151	2.04793
$598$	1.75716e151	0.821479
$599$	−1.00935e151	−0.430806	−0.215403	−	0.976525i	$-0.569106\pi$
$599$	−1.00935e151	−0.430806	−0.215403	+	0.976525i	$0.569106\pi$
$600$	2.42357e151	0.944521
$601$	−1.51618e151	−0.539624	−0.269812	−	0.962913i	$-0.586962\pi$
$601$	−1.51618e151	−0.539624	−0.269812	+	0.962913i	$0.586962\pi$
$602$	−2.34125e151	−0.761096
$603$	1.24422e151	0.369490
$604$	−1.07701e152	−2.92218
$605$	−3.75909e150	−0.0931997
$606$	6.17909e151	1.40012
$607$	4.50398e151	0.932851	0.466426	−	0.884560i	$-0.345541\pi$
$607$	4.50398e151	0.932851	0.466426	+	0.884560i	$0.345541\pi$
$608$	8.03381e151	1.52117
$609$	−1.15280e152	−1.99578
$610$	−1.79979e152	−2.84935
$611$	−3.42470e151	−0.495880
$612$	−1.65239e152	−2.18856
$613$	−7.27362e151	−0.881362	−0.440681	−	0.897664i	$-0.645263\pi$
$613$	−7.27362e151	−0.881362	−0.440681	+	0.897664i	$0.645263\pi$
$614$	1.84435e152	2.04488
$615$	1.57348e152	1.59649
$616$	4.14943e152	3.85336
$617$	−4.88189e151	−0.414999	−0.207499	−	0.978235i	$-0.566533\pi$
$617$	−4.88189e151	−0.414999	−0.207499	+	0.978235i	$0.566533\pi$
$618$	−9.27251e151	−0.721648
$619$	2.26844e152	1.61654	0.808270	−	0.588812i	$-0.200404\pi$
$619$	2.26844e152	1.61654	0.808270	+	0.588812i	$0.200404\pi$
$620$	−1.95720e152	−1.27728
$621$	−2.95550e151	−0.176660
$622$	1.44673e152	0.792155
$623$	−1.71870e152	−0.862185
$624$	−2.73308e152	−1.25630
$625$	−2.83006e152	−1.19216
$626$	6.78160e152	2.61837
$627$	−3.19217e152	−1.12981
$628$	2.82199e152	0.915704
$629$	−1.59516e152	−0.474619
$630$	9.51899e152	2.59735
$631$	−3.38724e152	−0.847706	−0.423853	−	0.905731i	$-0.639323\pi$
$631$	−3.38724e152	−0.847706	−0.423853	+	0.905731i	$0.639323\pi$
$632$	−2.07373e153	−4.76070
$633$	9.27909e152	1.95435
$634$	9.89920e152	1.91309
$635$	2.04762e152	0.363145
$636$	−2.87643e153	−4.68210
$637$	2.37284e152	0.354544
$638$	1.45591e153	1.99713
$639$	−8.32153e151	−0.104811
$640$	1.05586e152	0.122123
$641$	1.73006e152	0.183780	0.0918900	−	0.995769i	$-0.470709\pi$
$641$	1.73006e152	0.183780	0.0918900	+	0.995769i	$0.470709\pi$
$642$	3.41293e153	3.33019
$643$	6.90756e151	0.0619194	0.0309597	−	0.999521i	$-0.490144\pi$
$643$	6.90756e151	0.0619194	0.0309597	+	0.999521i	$0.490144\pi$
$644$	−4.95276e153	−4.07913
$645$	5.99153e152	0.453454
$646$	−2.11972e153	−1.47437
$647$	−1.40129e153	−0.895867	−0.447933	−	0.894067i	$-0.647840\pi$
$647$	−1.40129e153	−0.895867	−0.447933	+	0.894067i	$0.647840\pi$
$648$	4.93139e153	2.89822
$649$	3.45046e152	0.186441
$650$	−3.57545e152	−0.177645
$651$	−1.97503e153	−0.902422
$652$	6.51088e153	2.73619
$653$	−8.18554e152	−0.316431	−0.158215	−	0.987405i	$-0.550574\pi$
$653$	−8.18554e152	−0.316431	−0.158215	+	0.987405i	$0.550574\pi$
$654$	−3.87490e153	−1.37808
$655$	−6.30718e152	−0.206388
$656$	8.48040e153	2.55363
$657$	−1.06508e153	−0.295168
$658$	1.36275e154	3.47620
$659$	−2.28669e153	−0.536972	−0.268486	−	0.963284i	$-0.586523\pi$
$659$	−2.28669e153	−0.536972	−0.268486	+	0.963284i	$0.586523\pi$
$660$	−1.80515e154	−3.90273
$661$	1.69864e153	0.338159	0.169079	−	0.985602i	$-0.445921\pi$
$661$	1.69864e153	0.338159	0.169079	+	0.985602i	$0.445921\pi$
$662$	−8.79609e153	−1.61261
$663$	3.03985e153	0.513292
$664$	−3.24772e154	−5.05148
$665$	8.64972e153	1.23943
$666$	−5.89073e153	−0.777721
$667$	−1.02225e154	−1.24366
$668$	1.99773e154	2.23985
$669$	1.68763e154	1.74403
$670$	9.02590e153	0.859833
$671$	1.62474e154	1.42694
$672$	4.58446e154	3.71246
$673$	−1.56625e154	−1.16960	−0.584802	−	0.811176i	$-0.698828\pi$
$673$	−1.56625e154	−1.16960	−0.584802	+	0.811176i	$0.698828\pi$
$674$	−3.71900e154	−2.56131
$675$	6.01383e152	0.0382028
$676$	−3.57798e154	−2.09673
$677$	1.72855e154	0.934541	0.467270	−	0.884114i	$-0.345237\pi$
$677$	1.72855e154	0.934541	0.467270	+	0.884114i	$0.345237\pi$
$678$	5.00012e154	2.49437
$679$	3.74169e154	1.72252
$680$	−7.05133e154	−2.99595
$681$	−1.85963e154	−0.729306
$682$	2.49432e154	0.903034
$683$	1.75638e154	0.587070	0.293535	−	0.955948i	$-0.405168\pi$
$683$	1.75638e154	0.587070	0.293535	+	0.955948i	$0.405168\pi$
$684$	−5.54480e154	−1.71131
$685$	−1.34972e154	−0.384687
$686$	4.03705e153	0.106267
$687$	−5.81212e154	−1.41316
$688$	3.22919e154	0.725310
$689$	2.49629e154	0.518021
$690$	1.78934e155	3.43098
$691$	−1.02056e154	−0.180836	−0.0904179	−	0.995904i	$-0.528820\pi$
$691$	−1.02056e154	−0.180836	−0.0904179	+	0.995904i	$0.528820\pi$
$692$	−2.69685e155	−4.41647
$693$	−8.59316e154	−1.30074
$694$	9.94568e154	1.39169
$695$	−2.53368e154	−0.327778
$696$	3.15354e155	3.77220
$697$	−9.43226e154	−1.04335
$698$	−1.11230e155	−1.13789
$699$	−3.67782e154	−0.348004
$700$	1.00778e155	0.882114
$701$	5.12780e154	0.415240	0.207620	−	0.978210i	$-0.433428\pi$
$701$	5.12780e154	0.415240	0.207620	+	0.978210i	$0.433428\pi$
$702$	−1.34508e154	−0.100780
$703$	−5.35279e154	−0.371120
$704$	−1.78397e155	−1.14466
$705$	−3.48743e155	−2.07109
$706$	4.57006e155	2.51227
$707$	1.51148e155	0.769208
$708$	1.27050e155	0.598637
$709$	1.33999e155	0.584631	0.292315	−	0.956322i	$-0.405574\pi$
$709$	1.33999e155	0.584631	0.292315	+	0.956322i	$0.405574\pi$
$710$	−6.03667e154	−0.243903
$711$	4.29454e155	1.60703
$712$	4.70157e155	1.62961
$713$	−1.75137e155	−0.562338
$714$	−1.20961e156	−3.59826
$715$	1.56659e155	0.431792
$716$	−6.96620e155	−1.77925
$717$	7.30819e155	1.72988
$718$	3.02779e155	0.664268
$719$	−5.33416e155	−1.08478	−0.542390	−	0.840127i	$-0.682481\pi$
$719$	−5.33416e155	−1.08478	−0.542390	+	0.840127i	$0.682481\pi$
$720$	−1.31291e156	−2.47523
$721$	−2.26817e155	−0.396464
$722$	4.31159e155	0.698811
$723$	−4.52151e154	−0.0679589
$724$	9.79574e155	1.36548
$725$	2.08007e155	0.268941
$726$	1.76401e155	0.211570
$727$	2.56000e155	0.284849	0.142424	−	0.989806i	$-0.454510\pi$
$727$	2.56000e155	0.284849	0.142424	+	0.989806i	$0.454510\pi$
$728$	−1.32596e156	−1.36889
$729$	−8.09817e155	−0.775776
$730$	−7.72638e155	−0.686879
$731$	−3.59164e155	−0.296344
$732$	5.98250e156	4.58173
$733$	9.76773e155	0.694428	0.347214	−	0.937786i	$-0.387128\pi$
$733$	9.76773e155	0.694428	0.347214	+	0.937786i	$0.387128\pi$
$734$	−8.24467e155	−0.544174
$735$	2.41630e156	1.48078
$736$	4.06529e156	2.31340
$737$	−8.14803e155	−0.430601
$738$	−3.48321e156	−1.70965
$739$	−2.09989e156	−0.957360	−0.478680	−	0.877989i	$-0.658885\pi$
$739$	−2.09989e156	−0.957360	−0.478680	+	0.877989i	$0.658885\pi$
$740$	−3.02696e156	−1.28197
$741$	1.02006e156	0.401360
$742$	−9.93318e156	−3.63141
$743$	−5.65572e156	−1.92131	−0.960655	−	0.277744i	$-0.910413\pi$
$743$	−5.65572e156	−1.92131	−0.960655	+	0.277744i	$0.910413\pi$
$744$	5.40278e156	1.70566
$745$	8.83504e155	0.259234
$746$	−9.12959e156	−2.48992
$747$	6.72579e156	1.70518
$748$	1.08210e157	2.55053
$749$	8.34844e156	1.82956
$750$	1.03897e157	2.11721
$751$	−1.67403e156	−0.317239	−0.158619	−	0.987340i	$-0.550704\pi$
$751$	−1.67403e156	−0.317239	−0.158619	+	0.987340i	$0.550704\pi$
$752$	−1.87958e157	−3.31275
$753$	−6.15653e156	−1.00928
$754$	−4.65238e156	−0.709474
$755$	9.51797e156	1.35032
$756$	3.79126e156	0.500433
$757$	1.10892e156	0.136200	0.0680998	−	0.997679i	$-0.478306\pi$
$757$	1.10892e156	0.136200	0.0680998	+	0.997679i	$0.478306\pi$
$758$	2.02745e157	2.31728
$759$	−1.61531e157	−1.71822
$760$	−2.36617e157	−2.34264
$761$	−4.72490e156	−0.435441	−0.217720	−	0.976011i	$-0.569862\pi$
$761$	−4.72490e156	−0.435441	−0.217720	+	0.976011i	$0.569862\pi$
$762$	−9.60874e156	−0.824367
$763$	−9.47848e156	−0.757097
$764$	5.86020e157	4.35837
$765$	1.46028e157	1.01132
$766$	1.14474e156	0.0738311
$767$	−1.10260e156	−0.0662323
$768$	2.20920e157	1.23609
$769$	1.40771e157	0.733715	0.366857	−	0.930277i	$-0.380434\pi$
$769$	1.40771e157	0.733715	0.366857	+	0.930277i	$0.380434\pi$
$770$	−6.23372e157	−3.02693
$771$	−2.25261e157	−1.01911
$772$	3.03777e157	1.28060
$773$	2.08791e157	0.820218	0.410109	−	0.912037i	$-0.365491\pi$
$773$	2.08791e157	0.820218	0.410109	+	0.912037i	$0.365491\pi$
$774$	−1.32635e157	−0.485595
$775$	3.56367e156	0.121606
$776$	−1.02355e158	−3.25572
$777$	−3.05454e157	−0.905734
$778$	6.44159e157	1.78076
$779$	−3.16512e157	−0.815829
$780$	5.76838e157	1.38643
$781$	5.44954e156	0.122146
$782$	−1.07263e158	−2.24223
$783$	7.82519e156	0.152573
$784$	1.30229e158	2.36855
$785$	−2.49390e157	−0.423139
$786$	2.95974e157	0.468516
$787$	−4.20264e157	−0.620725	−0.310363	−	0.950618i	$-0.600450\pi$
$787$	−4.20264e157	−0.620725	−0.310363	+	0.950618i	$0.600450\pi$
$788$	−1.16489e158	−1.60549
$789$	−2.06762e158	−2.65934
$790$	3.11538e158	3.73968
$791$	1.22309e158	1.37038
$792$	2.35070e158	2.45852
$793$	−5.19188e157	−0.506916
$794$	2.50440e158	2.28289
$795$	2.54201e158	2.16356
$796$	−4.54855e158	−3.61502
$797$	−1.23123e158	−0.913819	−0.456910	−	0.889513i	$-0.651044\pi$
$797$	−1.23123e158	−0.913819	−0.456910	+	0.889513i	$0.651044\pi$
$798$	−4.05901e158	−2.81360
$799$	2.09055e158	1.35351
$800$	−8.27202e157	−0.500273
$801$	−9.73660e157	−0.550092
$802$	−1.99506e158	−1.05306
$803$	6.97490e157	0.343986
$804$	−3.00021e158	−1.38260
$805$	4.37695e158	1.88493
$806$	−7.97064e157	−0.320799
$807$	2.77794e158	1.04500
$808$	−4.13472e158	−1.45387
$809$	1.65763e158	0.544870	0.272435	−	0.962174i	$-0.412171\pi$
$809$	1.65763e158	0.544870	0.272435	+	0.962174i	$0.412171\pi$
$810$	−7.40847e158	−2.27664
$811$	−2.95648e158	−0.849450	−0.424725	−	0.905322i	$-0.639629\pi$
$811$	−2.95648e158	−0.849450	−0.424725	+	0.905322i	$0.639629\pi$
$812$	1.31133e159	3.52296
$813$	1.24334e158	0.312360
$814$	3.85767e158	0.906349
$815$	−5.75391e158	−1.26437
$816$	1.66836e159	3.42907
$817$	−1.20522e158	−0.231721
$818$	−1.35539e159	−2.43786
$819$	2.74596e158	0.462084
$820$	−1.78985e159	−2.81814
$821$	1.08754e159	1.60230	0.801149	−	0.598464i	$-0.204222\pi$
$821$	1.08754e159	1.60230	0.801149	+	0.598464i	$0.204222\pi$
$822$	6.33377e158	0.873269
$823$	−2.47121e158	−0.318874	−0.159437	−	0.987208i	$-0.550968\pi$
$823$	−2.47121e158	−0.318874	−0.159437	+	0.987208i	$0.550968\pi$
$824$	6.20467e158	0.749352
$825$	3.28682e158	0.371566
$826$	4.38743e158	0.464299
$827$	−7.41827e158	−0.734941	−0.367470	−	0.930035i	$-0.619776\pi$
$827$	−7.41827e158	−0.734941	−0.367470	+	0.930035i	$0.619776\pi$
$828$	−2.80579e159	−2.60257
$829$	−1.38484e159	−1.20276	−0.601378	−	0.798964i	$-0.705382\pi$
$829$	−1.38484e159	−1.20276	−0.601378	+	0.798964i	$0.705382\pi$
$830$	4.87908e159	3.96809
$831$	−1.06457e159	−0.810808
$832$	5.70069e158	0.406636
$833$	−1.44846e159	−0.967729
$834$	1.18897e159	0.744081
$835$	−1.76547e159	−1.03502
$836$	3.63114e159	1.99435
$837$	1.34064e158	0.0689884
$838$	6.64328e159	3.20320
$839$	−5.53168e158	−0.249937	−0.124968	−	0.992161i	$-0.539883\pi$
$839$	−5.53168e158	−0.249937	−0.124968	+	0.992161i	$0.539883\pi$
$840$	−1.35024e160	−5.71729
$841$	1.86697e158	0.0740893
$842$	−8.62727e159	−3.20896
$843$	3.36602e159	1.17358
$844$	−1.05551e160	−3.44984
$845$	3.16200e159	0.968882
$846$	7.72012e159	2.21789
$847$	4.31497e158	0.116234
$848$	1.37004e160	3.46067
$849$	7.86272e159	1.86253
$850$	2.18257e159	0.484883
$851$	−2.70863e159	−0.564402
$852$	2.00659e159	0.392194
$853$	−7.81502e159	−1.43287	−0.716437	−	0.697652i	$-0.754228\pi$
$853$	−7.81502e159	−1.43287	−0.716437	+	0.697652i	$0.754228\pi$
$854$	2.06594e160	3.55356
$855$	4.90016e159	0.790782
$856$	−2.28375e160	−3.45803
$857$	2.15979e159	0.306872	0.153436	−	0.988159i	$-0.450966\pi$
$857$	2.15979e159	0.306872	0.153436	+	0.988159i	$0.450966\pi$
$858$	−7.35143e159	−0.980200
$859$	−5.21993e159	−0.653187	−0.326593	−	0.945165i	$-0.605901\pi$
$859$	−5.21993e159	−0.653187	−0.326593	+	0.945165i	$0.605901\pi$
$860$	−6.81545e159	−0.800440
$861$	−1.80616e160	−1.99106
$862$	2.13943e160	2.21387
$863$	−9.18916e159	−0.892663	−0.446331	−	0.894868i	$-0.647270\pi$
$863$	−9.18916e159	−0.892663	−0.446331	+	0.894868i	$0.647270\pi$
$864$	−3.11191e159	−0.283811
$865$	2.38331e160	2.04081
$866$	−1.21094e160	−0.973639
$867$	−3.33373e158	−0.0251704
$868$	2.24662e160	1.59296
$869$	−2.81237e160	−1.87282
$870$	−4.73759e160	−2.96318
$871$	2.60371e159	0.152969
$872$	2.59288e160	1.43098
$873$	2.11971e160	1.09900
$874$	−3.59934e160	−1.75327
$875$	2.54144e160	1.16316
$876$	2.56825e160	1.10449
$877$	2.00367e160	0.809744	0.404872	−	0.914373i	$-0.367316\pi$
$877$	2.00367e160	0.809744	0.404872	+	0.914373i	$0.367316\pi$
$878$	2.15310e160	0.817735
$879$	−3.04196e160	−1.08582
$880$	8.59790e160	2.88461
$881$	−2.34895e160	−0.740775	−0.370387	−	0.928877i	$-0.620775\pi$
$881$	−2.34895e160	−0.740775	−0.370387	+	0.928877i	$0.620775\pi$
$882$	−5.34897e160	−1.58574
$883$	2.56121e160	0.713817	0.356909	−	0.934139i	$-0.383831\pi$
$883$	2.56121e160	0.713817	0.356909	+	0.934139i	$0.383831\pi$
$884$	−3.45787e160	−0.906066
$885$	−1.12279e160	−0.276625
$886$	−2.75487e160	−0.638209
$887$	1.55464e160	0.338682	0.169341	−	0.985558i	$-0.445836\pi$
$887$	1.55464e160	0.338682	0.169341	+	0.985558i	$0.445836\pi$
$888$	8.35583e160	1.71192
$889$	−2.35041e160	−0.452896
$890$	−7.06321e160	−1.28011
$891$	6.68791e160	1.14013
$892$	−1.91970e161	−3.07857
$893$	7.01512e160	1.05835
$894$	−4.14597e160	−0.588480
$895$	6.15630e160	0.822175
$896$	−1.21200e160	−0.152305
$897$	5.16174e160	0.610391
$898$	7.94861e160	0.884567
$899$	4.63704e160	0.485666
$900$	5.70921e160	0.562807
$901$	−1.52382e161	−1.41394
$902$	2.28106e161	1.99241
$903$	−6.87755e160	−0.565524
$904$	−3.34581e161	−2.59013
$905$	−8.65688e160	−0.630977
$906$	−4.46645e161	−3.06532
$907$	1.22079e161	0.788937	0.394469	−	0.918909i	$-0.370929\pi$
$907$	1.22079e161	0.788937	0.394469	+	0.918909i	$0.370929\pi$
$908$	2.11536e161	1.28738
$909$	8.56269e160	0.490771
$910$	1.99199e161	1.07531
$911$	−1.61893e161	−0.823145	−0.411572	−	0.911377i	$-0.635020\pi$
$911$	−1.61893e161	−0.823145	−0.411572	+	0.911377i	$0.635020\pi$
$912$	5.59841e161	2.68131
$913$	−4.40453e161	−1.98720
$914$	6.56796e161	2.79166
$915$	−5.28697e161	−2.11718
$916$	6.61136e161	2.49452
$917$	7.23987e160	0.257396
$918$	8.21079e160	0.275080
$919$	2.86737e161	0.905292	0.452646	−	0.891690i	$-0.350480\pi$
$919$	2.86737e161	0.905292	0.452646	+	0.891690i	$0.350480\pi$
$920$	−1.19733e162	−3.56269
$921$	5.41788e161	1.51943
$922$	−7.34505e161	−1.94160
$923$	−1.74141e160	−0.0433918
$924$	2.07209e162	4.86728
$925$	5.51150e160	0.122052
$926$	−1.38570e162	−2.89314
$927$	−1.28494e161	−0.252952
$928$	−1.07635e162	−1.99798
$929$	−8.62702e161	−1.51009	−0.755047	−	0.655670i	$-0.772386\pi$
$929$	−8.62702e161	−1.51009	−0.755047	+	0.655670i	$0.772386\pi$
$930$	−8.11664e161	−1.33985
$931$	−4.86050e161	−0.756699
$932$	4.18357e161	0.614299
$933$	4.24983e161	0.588602
$934$	1.44000e162	1.88129
$935$	−9.56295e161	−1.17858
$936$	−7.51168e161	−0.873381
$937$	8.30813e161	0.911371	0.455686	−	0.890141i	$-0.349394\pi$
$937$	8.30813e161	0.911371	0.455686	+	0.890141i	$0.349394\pi$
$938$	−1.03606e162	−1.07234
$939$	1.99213e162	1.94555
$940$	3.96700e162	3.65590
$941$	1.18361e162	1.02937	0.514687	−	0.857378i	$-0.327908\pi$
$941$	1.18361e162	1.02937	0.514687	+	0.857378i	$0.327908\pi$
$942$	1.17030e162	0.960557
$943$	−1.60162e162	−1.24072
$944$	−6.05140e161	−0.442468
$945$	−3.35049e161	−0.231246
$946$	8.68587e161	0.565908
$947$	2.65712e161	0.163432	0.0817160	−	0.996656i	$-0.473960\pi$
$947$	2.65712e161	0.163432	0.0817160	+	0.996656i	$0.473960\pi$
$948$	−1.03555e163	−6.01337
$949$	−2.22884e161	−0.122200
$950$	7.32392e161	0.379146
$951$	2.90794e162	1.42150
$952$	8.09406e162	3.73640
$953$	3.16901e162	1.38153	0.690766	−	0.723078i	$-0.257273\pi$
$953$	3.16901e162	1.38153	0.690766	+	0.723078i	$0.257273\pi$
$954$	−5.62725e162	−2.31692
$955$	−5.17889e162	−2.01397
$956$	−8.31317e162	−3.05360
$957$	4.27680e162	1.48395
$958$	5.28875e162	1.73353
$959$	1.54932e162	0.479762
$960$	5.80511e162	1.69835
$961$	−2.82320e162	−0.780399
$962$	−1.23272e162	−0.321977
$963$	4.72948e162	1.16730
$964$	5.14328e161	0.119961
$965$	−2.68460e162	−0.591753
$966$	−2.05395e163	−4.27894
$967$	−3.42547e162	−0.674492	−0.337246	−	0.941417i	$-0.609495\pi$
$967$	−3.42547e162	−0.674492	−0.337246	+	0.941417i	$0.609495\pi$
$968$	−1.18038e162	−0.219692
$969$	−6.22679e162	−1.09551
$970$	1.53769e163	2.55747
$971$	−4.29278e161	−0.0674980	−0.0337490	−	0.999430i	$-0.510745\pi$
$971$	−4.29278e161	−0.0674980	−0.0337490	+	0.999430i	$0.510745\pi$
$972$	2.22206e163	3.30328
$973$	2.90836e162	0.408788
$974$	1.50900e163	2.00551
$975$	−1.05031e162	−0.131997
$976$	−2.84946e163	−3.38647
$977$	−1.19615e163	−1.34441	−0.672205	−	0.740365i	$-0.734653\pi$
$977$	−1.19615e163	−1.34441	−0.672205	+	0.740365i	$0.734653\pi$
$978$	2.70011e163	2.87021
$979$	6.37623e162	0.641072
$980$	−2.74858e163	−2.61389
$981$	−5.36966e162	−0.483043
$982$	−2.08211e163	−1.77185
$983$	−1.25172e163	−1.00772	−0.503860	−	0.863785i	$-0.668087\pi$
$983$	−1.25172e163	−1.00772	−0.503860	+	0.863785i	$0.668087\pi$
$984$	4.94083e163	3.76329
$985$	1.02946e163	0.741883
$986$	2.83996e163	1.93651
$987$	4.00314e163	2.58295
$988$	−1.16033e163	−0.708483
$989$	−6.09870e162	−0.352403
$990$	−3.53147e163	−1.93125
$991$	−1.45616e163	−0.753691	−0.376846	−	0.926276i	$-0.622991\pi$
$991$	−1.45616e163	−0.753691	−0.376846	+	0.926276i	$0.622991\pi$
$992$	−1.84405e163	−0.903415
$993$	−2.58390e163	−1.19823
$994$	6.92936e162	0.304183
$995$	4.01973e163	1.67047
$996$	−1.62181e164	−6.38066
$997$	−4.04544e162	−0.150688	−0.0753441	−	0.997158i	$-0.524006\pi$
$997$	−4.04544e162	−0.150688	−0.0753441	+	0.997158i	$0.524006\pi$
$998$	9.96072e163	3.51298
$999$	2.07341e162	0.0692416

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.110.a.a.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-4.71735e16 q^{2} -1.38575e26 q^{3} +1.57631e33 q^{4} -1.39304e38 q^{5} +6.53705e42 q^{6} +1.59904e46 q^{7} -4.37425e49 q^{8} +9.05875e51 q^{9} +O(q^{10})\)	\(q-4.71735e16 q^{2} -1.38575e26 q^{3} +1.57631e33 q^{4} -1.39304e38 q^{5} +6.53705e42 q^{6} +1.59904e46 q^{7} -4.37425e49 q^{8} +9.05875e51 q^{9} +6.57147e54 q^{10} -5.93232e56 q^{11} -2.18436e59 q^{12} +1.89568e60 q^{13} -7.54325e62 q^{14} +1.93040e64 q^{15} +1.04041e66 q^{16} -1.15719e67 q^{17} -4.27333e68 q^{18} -3.88309e69 q^{19} -2.19586e71 q^{20} -2.21587e72 q^{21} +2.79849e73 q^{22} -1.96493e74 q^{23} +6.06160e75 q^{24} +3.99823e75 q^{25} -8.94260e76 q^{26} +1.50412e77 q^{27} +2.52058e79 q^{28} +5.20249e79 q^{29} -9.10639e80 q^{30} +8.91312e80 q^{31} -2.06892e82 q^{32} +8.22069e82 q^{33} +5.45885e83 q^{34} -2.22753e84 q^{35} +1.42794e85 q^{36} +1.37849e85 q^{37} +1.83179e86 q^{38} -2.62693e86 q^{39} +6.09352e87 q^{40} +8.15104e87 q^{41} +1.04530e89 q^{42} +3.10377e88 q^{43} -9.35115e89 q^{44} -1.26192e90 q^{45} +9.26927e90 q^{46} -1.80658e91 q^{47} -1.44174e92 q^{48} +1.25171e92 q^{49} -1.88610e92 q^{50} +1.60356e93 q^{51} +2.98817e93 q^{52} +1.31683e94 q^{53} -7.09548e93 q^{54} +8.26397e94 q^{55} -6.99461e95 q^{56} +5.38098e95 q^{57} -2.45420e96 q^{58} -5.81637e95 q^{59} +3.04290e97 q^{60} -2.73879e97 q^{61} -4.20463e97 q^{62} +1.44853e98 q^{63} +3.00720e98 q^{64} -2.64076e98 q^{65} -3.87799e99 q^{66} +1.37350e99 q^{67} -1.82408e100 q^{68} +2.72289e100 q^{69} +1.05081e101 q^{70} -9.18618e99 q^{71} -3.96252e101 q^{72} -1.17575e101 q^{73} -6.50281e101 q^{74} -5.54053e101 q^{75} -6.12094e102 q^{76} -9.48603e102 q^{77} +1.23922e103 q^{78} +4.74076e103 q^{79} -1.44933e104 q^{80} -1.12737e104 q^{81} -3.84513e104 q^{82} +7.42464e104 q^{83} -3.49288e105 q^{84} +1.61201e105 q^{85} -1.46416e105 q^{86} -7.20933e105 q^{87} +2.59495e106 q^{88} -1.07483e106 q^{89} +5.95293e106 q^{90} +3.03128e106 q^{91} -3.09733e107 q^{92} -1.23513e107 q^{93} +8.52228e107 q^{94} +5.40931e107 q^{95} +2.86700e108 q^{96} +2.33996e108 q^{97} -5.90475e108 q^{98} -5.37394e108 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 22\!\cdots\!00 q^{2}+ \cdots + 24\!\cdots\!84 q^{9}+O(q^{10}) \) 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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