LMFDB - Embedded newform 1.110.a.a.1.8

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			1.8
Root			$-2.42126e14$ 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)

$f(q)$	$=$	$q+4.67743e16 q^{2} +3.08304e25 q^{3} +1.53880e33 q^{4} -1.66073e38 q^{5} +1.44207e42 q^{6} +8.52831e45 q^{7} +4.16178e49 q^{8} -9.19366e51 q^{9} +O(q^{10})$	\(q+4.67743e16 q^{2} +3.08304e25 q^{3} +1.53880e33 q^{4} -1.66073e38 q^{5} +1.44207e42 q^{6} +8.52831e45 q^{7} +4.16178e49 q^{8} -9.19366e51 q^{9} -7.76792e54 q^{10} -4.17646e56 q^{11} +4.74417e58 q^{12} -8.29806e60 q^{13} +3.98905e62 q^{14} -5.12008e63 q^{15} +9.47907e65 q^{16} -6.45752e65 q^{17} -4.30027e68 q^{18} -6.23924e69 q^{19} -2.55552e71 q^{20} +2.62931e71 q^{21} -1.95351e73 q^{22} +2.48258e74 q^{23} +1.28309e75 q^{24} +1.21727e76 q^{25} -3.88135e77 q^{26} -5.96193e77 q^{27} +1.31233e79 q^{28} +1.15567e79 q^{29} -2.39488e80 q^{30} -2.19372e81 q^{31} +1.73262e82 q^{32} -1.28762e82 q^{33} -3.02046e82 q^{34} -1.41632e84 q^{35} -1.41472e85 q^{36} +5.13467e85 q^{37} -2.91836e86 q^{38} -2.55832e86 q^{39} -6.91157e87 q^{40} -1.09454e88 q^{41} +1.22984e88 q^{42} -1.31384e89 q^{43} -6.42672e89 q^{44} +1.52682e90 q^{45} +1.16121e91 q^{46} +4.22488e89 q^{47} +2.92243e91 q^{48} -5.77907e91 q^{49} +5.69368e92 q^{50} -1.99088e91 q^{51} -1.27690e94 q^{52} +5.60887e93 q^{53} -2.78865e94 q^{54} +6.93596e94 q^{55} +3.54929e95 q^{56} -1.92358e95 q^{57} +5.40556e95 q^{58} +2.61491e96 q^{59} -7.87876e96 q^{60} +2.27336e96 q^{61} -1.02610e98 q^{62} -7.84064e97 q^{63} +1.95192e98 q^{64} +1.37808e99 q^{65} -6.02275e98 q^{66} -1.52450e98 q^{67} -9.93680e98 q^{68} +7.65389e99 q^{69} -6.62473e100 q^{70} -2.16290e100 q^{71} -3.82620e101 q^{72} -1.09055e101 q^{73} +2.40171e102 q^{74} +3.75288e101 q^{75} -9.60092e102 q^{76} -3.56181e102 q^{77} -1.19664e103 q^{78} -1.07406e103 q^{79} -1.57421e104 q^{80} +7.48812e103 q^{81} -5.11965e104 q^{82} +3.89026e104 q^{83} +4.04597e104 q^{84} +1.07242e104 q^{85} -6.14537e105 q^{86} +3.56298e104 q^{87} -1.73815e106 q^{88} -1.88126e105 q^{89} +7.14157e106 q^{90} -7.07684e106 q^{91} +3.82018e107 q^{92} -6.76332e106 q^{93} +1.97616e106 q^{94} +1.03617e108 q^{95} +5.34172e107 q^{96} -3.05793e108 q^{97} -2.70312e108 q^{98} +3.83970e108 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.67743e16	1.83600	0.917999	−	0.396582i	$-0.129804\pi$
$2$	4.67743e16	1.83600	0.917999	+	0.396582i	$0.129804\pi$
$3$	3.08304e25	0.306105	0.153053	−	0.988218i	$-0.451090\pi$
$3$	3.08304e25	0.306105	0.153053	+	0.988218i	$0.451090\pi$
$4$	1.53880e33	2.37089
$5$	−1.66073e38	−1.33793	−0.668964	−	0.743295i	$-0.733262\pi$
$5$	−1.66073e38	−1.33793	−0.668964	+	0.743295i	$0.733262\pi$
$6$	1.44207e42	0.562009
$7$	8.52831e45	0.746483	0.373241	−	0.927734i	$-0.378246\pi$
$7$	8.52831e45	0.746483	0.373241	+	0.927734i	$0.378246\pi$
$8$	4.16178e49	2.51695
$9$	−9.19366e51	−0.906300
$10$	−7.76792e54	−2.45643
$11$	−4.17646e56	−0.732668	−0.366334	−	0.930483i	$-0.619387\pi$
$11$	−4.17646e56	−0.732668	−0.366334	+	0.930483i	$0.619387\pi$
$12$	4.74417e58	0.725742
$13$	−8.29806e60	−1.61832	−0.809159	−	0.587590i	$-0.800077\pi$
$13$	−8.29806e60	−1.61832	−0.809159	+	0.587590i	$0.800077\pi$
$14$	3.98905e62	1.37054
$15$	−5.12008e63	−0.409547
$16$	9.47907e65	2.25023
$17$	−6.45752e65	−0.0563118	−0.0281559	−	0.999604i	$-0.508963\pi$
$17$	−6.45752e65	−0.0563118	−0.0281559	+	0.999604i	$0.508963\pi$
$18$	−4.30027e68	−1.66396
$19$	−6.23924e69	−1.26783	−0.633915	−	0.773403i	$-0.718553\pi$
$19$	−6.23924e69	−1.26783	−0.633915	+	0.773403i	$0.718553\pi$
$20$	−2.55552e71	−3.17208
$21$	2.62931e71	0.228502
$22$	−1.95351e73	−1.34518
$23$	2.48258e74	1.51613	0.758064	−	0.652180i	$-0.226145\pi$
$23$	2.48258e74	1.51613	0.758064	+	0.652180i	$0.226145\pi$
$24$	1.28309e75	0.770452
$25$	1.21727e76	0.790051
$26$	−3.88135e77	−2.97123
$27$	−5.96193e77	−0.583528
$28$	1.31233e79	1.76983
$29$	1.15567e79	0.230220	0.115110	−	0.993353i	$-0.463278\pi$
$29$	1.15567e79	0.230220	0.115110	+	0.993353i	$0.463278\pi$
$30$	−2.39488e80	−0.751927
$31$	−2.19372e81	−1.15337	−0.576685	−	0.816967i	$-0.695654\pi$
$31$	−2.19372e81	−1.15337	−0.576685	+	0.816967i	$0.695654\pi$
$32$	1.73262e82	1.61446
$33$	−1.28762e82	−0.224273
$34$	−3.02046e82	−0.103388
$35$	−1.41632e84	−0.998740
$36$	−1.41472e85	−2.14874
$37$	5.13467e85	1.75194	0.875969	−	0.482367i	$-0.160223\pi$
$37$	5.13467e85	1.75194	0.875969	+	0.482367i	$0.160223\pi$
$38$	−2.91836e86	−2.32773
$39$	−2.55832e86	−0.495375
$40$	−6.91157e87	−3.36750
$41$	−1.09454e88	−1.38839	−0.694197	−	0.719785i	$-0.744240\pi$
$41$	−1.09454e88	−1.38839	−0.694197	+	0.719785i	$0.744240\pi$
$42$	1.22984e88	0.419530
$43$	−1.31384e89	−1.24311	−0.621556	−	0.783370i	$-0.713499\pi$
$43$	−1.31384e89	−1.24311	−0.621556	+	0.783370i	$0.713499\pi$
$44$	−6.42672e89	−1.73707
$45$	1.52682e90	1.21256
$46$	1.16121e91	2.78361
$47$	4.22488e89	0.0313676	0.0156838	−	0.999877i	$-0.495007\pi$
$47$	4.22488e89	0.0313676	0.0156838	+	0.999877i	$0.495007\pi$
$48$	2.92243e91	0.688807
$49$	−5.77907e91	−0.442764
$50$	5.69368e92	1.45053
$51$	−1.99088e91	−0.0172373
$52$	−1.27690e94	−3.83685
$53$	5.60887e93	0.596816	0.298408	−	0.954438i	$-0.403544\pi$
$53$	5.60887e93	0.596816	0.298408	+	0.954438i	$0.403544\pi$
$54$	−2.78865e94	−1.07136
$55$	6.93596e94	0.980257
$56$	3.54929e95	1.87886
$57$	−1.92358e95	−0.388089
$58$	5.40556e95	0.422683
$59$	2.61491e96	0.805419	0.402709	−	0.915328i	$-0.368069\pi$
$59$	2.61491e96	0.805419	0.402709	+	0.915328i	$0.368069\pi$
$60$	−7.87876e96	−0.970990
$61$	2.27336e96	0.113813	0.0569066	−	0.998380i	$-0.481876\pi$
$61$	2.27336e96	0.113813	0.0569066	+	0.998380i	$0.481876\pi$
$62$	−1.02610e98	−2.11758
$63$	−7.84064e97	−0.676537
$64$	1.95192e98	0.713925
$65$	1.37808e99	2.16519
$66$	−6.02275e98	−0.411766
$67$	−1.52450e98	−0.0459253	−0.0229626	−	0.999736i	$-0.507310\pi$
$67$	−1.52450e98	−0.0459253	−0.0229626	+	0.999736i	$0.507310\pi$
$68$	−9.93680e98	−0.133509
$69$	7.65389e99	0.464095
$70$	−6.62473e100	−1.83369
$71$	−2.16290e100	−0.276349	−0.138174	−	0.990408i	$-0.544123\pi$
$71$	−2.16290e100	−0.276349	−0.138174	+	0.990408i	$0.544123\pi$
$72$	−3.82620e101	−2.28111
$73$	−1.09055e101	−0.306583	−0.153291	−	0.988181i	$-0.548987\pi$
$73$	−1.09055e101	−0.306583	−0.153291	+	0.988181i	$0.548987\pi$
$74$	2.40171e102	3.21656
$75$	3.75288e101	0.241839
$76$	−9.60092e102	−3.00588
$77$	−3.56181e102	−0.546924
$78$	−1.19664e103	−0.909508
$79$	−1.07406e103	−0.407709	−0.203855	−	0.979001i	$-0.565347\pi$
$79$	−1.07406e103	−0.407709	−0.203855	+	0.979001i	$0.565347\pi$
$80$	−1.57421e104	−3.01064
$81$	7.48812e103	0.727678
$82$	−5.11965e104	−2.54909
$83$	3.89026e104	1.00051	0.500256	−	0.865878i	$-0.333239\pi$
$83$	3.89026e104	1.00051	0.500256	+	0.865878i	$0.333239\pi$
$84$	4.04597e104	0.541754
$85$	1.07242e104	0.0753412
$86$	−6.14537e105	−2.28235
$87$	3.56298e104	0.0704715
$88$	−1.73815e106	−1.84409
$89$	−1.88126e105	−0.107818	−0.0539092	−	0.998546i	$-0.517168\pi$
$89$	−1.88126e105	−0.107818	−0.0539092	+	0.998546i	$0.517168\pi$
$90$	7.14157e106	2.22626
$91$	−7.07684e106	−1.20805
$92$	3.82018e107	3.59457
$93$	−6.76332e106	−0.353052
$94$	1.97616e106	0.0575909
$95$	1.03617e108	1.69626
$96$	5.34172e107	0.494196
$97$	−3.05793e108	−1.60830	−0.804152	−	0.594424i	$-0.797380\pi$
$97$	−3.05793e108	−1.60830	−0.804152	+	0.594424i	$0.797380\pi$
$98$	−2.70312e108	−0.812913
$99$	3.83970e108	0.664016
$100$	1.87312e109	1.87312
$101$	−2.94022e108	−0.170949	−0.0854743	−	0.996340i	$-0.527241\pi$
$101$	−2.94022e108	−0.170949	−0.0854743	+	0.996340i	$0.527241\pi$
$102$	−9.31220e107	−0.0316477
$103$	1.50195e109	0.299935	0.149967	−	0.988691i	$-0.452083\pi$
$103$	1.50195e109	0.299935	0.149967	+	0.988691i	$0.452083\pi$
$104$	−3.45347e110	−4.07322
$105$	−4.36657e109	−0.305720
$106$	2.62351e110	1.09575
$107$	−2.81838e110	−0.705642	−0.352821	−	0.935691i	$-0.614777\pi$
$107$	−2.81838e110	−0.705642	−0.352821	+	0.935691i	$0.614777\pi$
$108$	−9.17419e110	−1.38348
$109$	−1.73813e110	−0.158613	−0.0793063	−	0.996850i	$-0.525271\pi$
$109$	−1.73813e110	−0.158613	−0.0793063	+	0.996850i	$0.525271\pi$
$110$	3.24424e111	1.79975
$111$	1.58304e111	0.536278
$112$	8.08404e111	1.67976
$113$	4.30162e111	0.550626	0.275313	−	0.961355i	$-0.411218\pi$
$113$	4.30162e111	0.550626	0.275313	+	0.961355i	$0.411218\pi$
$114$	−8.99743e111	−0.712531
$115$	−4.12288e112	−2.02847
$116$	1.77834e112	0.545826
$117$	7.62895e112	1.46668
$118$	1.22310e113	1.47875
$119$	−5.50717e111	−0.0420358
$120$	−2.13087e113	−1.03081
$121$	−1.50511e113	−0.463198
$122$	1.06335e113	0.208961
$123$	−3.37452e113	−0.424995
$124$	−3.37568e114	−2.73451
$125$	5.37207e113	0.280896
$126$	−3.66740e114	−1.24212
$127$	8.64009e114	1.90202	0.951011	−	0.309157i	$-0.100047\pi$
$127$	8.64009e114	1.90202	0.951011	+	0.309157i	$0.100047\pi$
$128$	−2.11537e114	−0.303699
$129$	−4.05061e114	−0.380523
$130$	6.44587e115	3.97529
$131$	−1.38263e115	−0.561591	−0.280796	−	0.959768i	$-0.590598\pi$
$131$	−1.38263e115	−0.561591	−0.280796	+	0.959768i	$0.590598\pi$
$132$	−1.98138e115	−0.531728
$133$	−5.32102e115	−0.946413
$134$	−7.13076e114	−0.0843188
$135$	9.90114e115	0.780719
$136$	−2.68748e115	−0.141734
$137$	3.52196e115	0.124599	0.0622994	−	0.998058i	$-0.480157\pi$
$137$	3.52196e115	0.124599	0.0622994	+	0.998058i	$0.480157\pi$
$138$	3.58005e116	0.852078
$139$	1.75361e116	0.281596	0.140798	−	0.990038i	$-0.455033\pi$
$139$	1.75361e116	0.281596	0.140798	+	0.990038i	$0.455033\pi$
$140$	−2.17942e117	−2.36790
$141$	1.30255e115	0.00960179
$142$	−1.01168e117	−0.507376
$143$	3.46565e117	1.18569
$144$	−8.71473e117	−2.03938
$145$	−1.91925e117	−0.308018
$146$	−5.10095e117	−0.562886
$147$	−1.78171e117	−0.135532
$148$	7.90121e118	4.15365
$149$	1.23479e118	0.449720	0.224860	−	0.974391i	$-0.427808\pi$
$149$	1.23479e118	0.449720	0.224860	+	0.974391i	$0.427808\pi$
$150$	1.75538e118	0.444016
$151$	6.97436e118	1.22818	0.614088	−	0.789238i	$-0.289524\pi$
$151$	6.97436e118	1.22818	0.614088	+	0.789238i	$0.289524\pi$
$152$	−2.59664e119	−3.19106
$153$	5.93683e117	0.0510354
$154$	−1.66601e119	−1.00415
$155$	3.64316e119	1.54312
$156$	−3.93674e119	−1.17448
$157$	4.92390e119	1.03700	0.518499	−	0.855078i	$-0.326491\pi$
$157$	4.92390e119	1.03700	0.518499	+	0.855078i	$0.326491\pi$
$158$	−5.02382e119	−0.748554
$159$	1.72924e119	0.182688
$160$	−2.87740e120	−2.16004
$161$	2.11722e120	1.13176
$162$	3.50252e120	1.33602
$163$	8.28398e119	0.225951	0.112976	−	0.993598i	$-0.463962\pi$
$163$	8.28398e119	0.225951	0.112976	+	0.993598i	$0.463962\pi$
$164$	−1.68428e121	−3.29173
$165$	2.13838e120	0.300062
$166$	1.81964e121	1.83694
$167$	8.40831e120	0.611873	0.305936	−	0.952052i	$-0.401031\pi$
$167$	8.40831e120	0.611873	0.305936	+	0.952052i	$0.401031\pi$
$168$	1.09426e121	0.575129
$169$	4.25656e121	1.61895
$170$	5.01615e120	0.138326
$171$	5.73615e121	1.14903
$172$	−2.02172e122	−2.94728
$173$	−1.26829e122	−1.34805	−0.674026	−	0.738708i	$-0.735436\pi$
$173$	−1.26829e122	−1.34805	−0.674026	+	0.738708i	$0.735436\pi$
$174$	1.66656e121	0.129386
$175$	1.03812e122	0.589760
$176$	−3.95889e122	−1.64867
$177$	8.06186e121	0.246543
$178$	−8.79944e121	−0.197954
$179$	−3.37812e122	−0.559996	−0.279998	−	0.960001i	$-0.590334\pi$
$179$	−3.37812e122	−0.559996	−0.279998	+	0.960001i	$0.590334\pi$
$180$	2.34946e123	2.87485
$181$	4.26762e122	0.386103	0.193051	−	0.981189i	$-0.438162\pi$
$181$	4.26762e122	0.386103	0.193051	+	0.981189i	$0.438162\pi$
$182$	−3.31014e123	−2.21797
$183$	7.00887e121	0.0348388
$184$	1.03319e124	3.81602
$185$	−8.52728e123	−2.34397
$186$	−3.16349e123	−0.648204
$187$	2.69696e122	0.0412579
$188$	6.50123e122	0.0743691
$189$	−5.08452e123	−0.435594
$190$	4.84660e124	3.11434
$191$	−8.64736e123	−0.417412	−0.208706	−	0.977978i	$-0.566925\pi$
$191$	−8.64736e123	−0.417412	−0.208706	+	0.977978i	$0.566925\pi$
$192$	6.01783e123	0.218536
$193$	−5.71799e124	−1.56448	−0.782240	−	0.622977i	$-0.785923\pi$
$193$	−5.71799e124	−1.56448	−0.782240	+	0.622977i	$0.785923\pi$
$194$	−1.43032e125	−2.95284
$195$	4.24867e124	0.662777
$196$	−8.89281e124	−1.04974
$197$	1.17702e124	0.105287	0.0526435	−	0.998613i	$-0.483235\pi$
$197$	1.17702e124	0.105287	0.0526435	+	0.998613i	$0.483235\pi$
$198$	1.79599e125	1.21913
$199$	8.00207e123	0.0412772	0.0206386	−	0.999787i	$-0.493430\pi$
$199$	8.00207e123	0.0412772	0.0206386	+	0.999787i	$0.493430\pi$
$200$	5.06600e125	1.98852
$201$	−4.70011e123	−0.0140580
$202$	−1.37527e125	−0.313861
$203$	9.85591e124	0.171855
$204$	−3.06356e124	−0.0408678
$205$	1.81774e126	1.85757
$206$	7.02526e125	0.550680
$207$	−2.28240e126	−1.37407
$208$	−7.86578e126	−3.64158
$209$	2.60580e126	0.928898
$210$	−2.04243e126	−0.561301
$211$	3.87399e126	0.821797	0.410899	−	0.911681i	$-0.365215\pi$
$211$	3.87399e126	0.821797	0.410899	+	0.911681i	$0.365215\pi$
$212$	8.63090e126	1.41498
$213$	−6.66832e125	−0.0845918
$214$	−1.31828e127	−1.29556
$215$	2.18192e127	1.66319
$216$	−2.48123e127	−1.46871
$217$	−1.87087e127	−0.860970
$218$	−8.12997e126	−0.291212
$219$	−3.36220e126	−0.0938466
$220$	1.06730e128	2.32408
$221$	5.35849e126	0.0911304
$222$	7.40455e127	0.984605
$223$	−1.11748e128	−1.16312	−0.581562	−	0.813502i	$-0.697558\pi$
$223$	−1.11748e128	−1.16312	−0.581562	+	0.813502i	$0.697558\pi$
$224$	1.47763e128	1.20517
$225$	−1.11911e128	−0.716023
$226$	2.01205e128	1.01095
$227$	−6.90551e127	−0.272764	−0.136382	−	0.990656i	$-0.543547\pi$
$227$	−6.90551e127	−0.272764	−0.136382	+	0.990656i	$0.543547\pi$
$228$	−2.96000e128	−0.920117
$229$	2.75512e128	0.674695	0.337347	−	0.941380i	$-0.390470\pi$
$229$	2.75512e128	0.674695	0.337347	+	0.941380i	$0.390470\pi$
$230$	−1.92845e129	−3.72427
$231$	−1.09812e128	−0.167416
$232$	4.80964e128	0.579452
$233$	−1.59553e129	−1.52057	−0.760286	−	0.649588i	$-0.774941\pi$
$233$	−1.59553e129	−1.52057	−0.760286	+	0.649588i	$0.774941\pi$
$234$	3.56839e129	2.69282
$235$	−7.01637e127	−0.0419676
$236$	4.02381e129	1.90956
$237$	−3.31136e128	−0.124802
$238$	−2.57594e128	−0.0771777
$239$	5.26428e129	1.25503	0.627514	−	0.778605i	$-0.284072\pi$
$239$	5.26428e129	1.25503	0.627514	+	0.778605i	$0.284072\pi$
$240$	−4.85336e129	−0.921574
$241$	−8.15453e129	−1.23444	−0.617220	−	0.786791i	$-0.711741\pi$
$241$	−8.15453e129	−1.23444	−0.617220	+	0.786791i	$0.711741\pi$
$242$	−7.04006e129	−0.850431
$243$	8.35651e129	0.806275
$244$	3.49824e129	0.269838
$245$	9.59746e129	0.592386
$246$	−1.57841e130	−0.780289
$247$	5.17736e130	2.05175
$248$	−9.12977e130	−2.90297
$249$	1.19938e130	0.306262
$250$	2.51275e130	0.515725
$251$	−1.11197e130	−0.183601	−0.0918003	−	0.995777i	$-0.529262\pi$
$251$	−1.11197e130	−0.183601	−0.0918003	+	0.995777i	$0.529262\pi$
$252$	−1.20651e131	−1.60399
$253$	−1.03684e131	−1.11082
$254$	4.04134e131	3.49211
$255$	3.30631e129	0.0230623
$256$	−2.25632e131	−1.27152
$257$	−2.28561e131	−1.04147	−0.520736	−	0.853718i	$-0.674342\pi$
$257$	−2.28561e131	−1.04147	−0.520736	+	0.853718i	$0.674342\pi$
$258$	−1.89464e131	−0.698640
$259$	4.37901e131	1.30779
$260$	2.12058e132	5.13343
$261$	−1.06248e131	−0.208648
$262$	−6.46715e131	−1.03108
$263$	−1.00442e132	−1.30115	−0.650576	−	0.759441i	$-0.725472\pi$
$263$	−1.00442e132	−1.30115	−0.650576	+	0.759441i	$0.725472\pi$
$264$	−5.35879e131	−0.564485
$265$	−9.31479e131	−0.798496
$266$	−2.48887e132	−1.73761
$267$	−5.79999e130	−0.0330038
$268$	−2.34590e131	−0.108884
$269$	−2.10455e132	−0.797371	−0.398685	−	0.917088i	$-0.630533\pi$
$269$	−2.10455e132	−0.797371	−0.398685	+	0.917088i	$0.630533\pi$
$270$	4.63118e132	1.43340
$271$	4.86507e132	1.23101	0.615507	−	0.788131i	$-0.288951\pi$
$271$	4.86507e132	1.23101	0.615507	+	0.788131i	$0.288951\pi$
$272$	−6.12113e131	−0.126714
$273$	−2.18182e132	−0.369789
$274$	1.64737e132	0.228763
$275$	−5.08387e132	−0.578845
$276$	1.17778e133	1.10032
$277$	6.63632e132	0.509073	0.254536	−	0.967063i	$-0.418077\pi$
$277$	6.63632e132	0.509073	0.254536	+	0.967063i	$0.418077\pi$
$278$	8.20240e132	0.517011
$279$	2.01683e133	1.04530
$280$	−5.89441e133	−2.51378
$281$	−2.97492e133	−1.04468	−0.522338	−	0.852739i	$-0.674940\pi$
$281$	−2.97492e133	−1.04468	−0.522338	+	0.852739i	$0.674940\pi$
$282$	6.09257e131	0.0176289
$283$	6.85225e133	1.63483	0.817415	−	0.576050i	$-0.195407\pi$
$283$	6.85225e133	1.63483	0.817415	+	0.576050i	$0.195407\pi$
$284$	−3.32827e133	−0.655192
$285$	3.19455e133	0.519235
$286$	1.62103e134	2.17692
$287$	−9.33460e133	−1.03641
$288$	−1.59291e134	−1.46319
$289$	−1.31085e134	−0.996829
$290$	−8.97716e133	−0.565520
$291$	−9.42772e133	−0.492310
$292$	−1.67813e134	−0.726874
$293$	3.70158e134	1.33077	0.665383	−	0.746502i	$-0.268268\pi$
$293$	3.70158e134	1.33077	0.665383	+	0.746502i	$0.268268\pi$
$294$	−8.33383e133	−0.248837
$295$	−4.34264e134	−1.07759
$296$	2.13694e135	4.40954
$297$	2.48998e134	0.427532
$298$	5.77565e134	0.825685
$299$	−2.06006e135	−2.45358
$300$	5.77492e134	0.573373
$301$	−1.12048e135	−0.927961
$302$	3.26220e135	2.25493
$303$	−9.06483e133	−0.0523283
$304$	−5.91422e135	−2.85290
$305$	−3.77543e134	−0.152274
$306$	2.77691e134	0.0937009
$307$	−2.38576e135	−0.673885	−0.336942	−	0.941525i	$-0.609393\pi$
$307$	−2.38576e135	−0.673885	−0.336942	+	0.941525i	$0.609393\pi$
$308$	−5.48090e135	−1.29670
$309$	4.63057e134	0.0918116
$310$	1.70406e136	2.83317
$311$	−7.97308e135	−1.11221	−0.556103	−	0.831114i	$-0.687704\pi$
$311$	−7.97308e135	−1.11221	−0.556103	+	0.831114i	$0.687704\pi$
$312$	−1.06472e136	−1.24684
$313$	1.42971e136	1.40631	0.703157	−	0.711034i	$-0.251773\pi$
$313$	1.42971e136	1.40631	0.703157	+	0.711034i	$0.251773\pi$
$314$	2.30312e136	1.90393
$315$	1.30212e136	0.905158
$316$	−1.65275e136	−0.966634
$317$	−3.23507e136	−1.59277	−0.796386	−	0.604788i	$-0.793258\pi$
$317$	−3.23507e136	−1.59277	−0.796386	+	0.604788i	$0.793258\pi$
$318$	8.08838e135	0.335416
$319$	−4.82661e135	−0.168675
$320$	−3.24160e136	−0.955180
$321$	−8.68919e135	−0.216001
$322$	9.90315e136	2.07792
$323$	4.02901e135	0.0713938
$324$	1.15227e137	1.72525
$325$	−1.01009e137	−1.27855
$326$	3.87477e136	0.414846
$327$	−5.35872e135	−0.0485521
$328$	−4.55525e137	−3.49452
$329$	3.60311e135	0.0234154
$330$	1.00021e137	0.550913
$331$	−2.97402e137	−1.38905	−0.694525	−	0.719469i	$-0.744385\pi$
$331$	−2.97402e137	−1.38905	−0.694525	+	0.719469i	$0.744385\pi$
$332$	5.98631e137	2.37210
$333$	−4.72064e137	−1.58778
$334$	3.93293e137	1.12340
$335$	2.53178e136	0.0614447
$336$	2.49234e137	0.514182
$337$	−9.92582e137	−1.74155	−0.870777	−	0.491679i	$-0.836383\pi$
$337$	−9.92582e137	−1.74155	−0.870777	+	0.491679i	$0.836383\pi$
$338$	1.99098e138	2.97239
$339$	1.32621e137	0.168550
$340$	1.65023e137	0.178626
$341$	9.16197e137	0.845036
$342$	2.68304e138	2.10962
$343$	−1.60600e138	−1.07700
$344$	−5.46789e138	−3.12885
$345$	−1.27110e138	−0.620926
$346$	−5.93234e138	−2.47502
$347$	2.45412e138	0.874863	0.437431	−	0.899252i	$-0.355888\pi$
$347$	2.45412e138	0.874863	0.437431	+	0.899252i	$0.355888\pi$
$348$	5.48269e137	0.167080
$349$	1.36925e138	0.356860	0.178430	−	0.983953i	$-0.442898\pi$
$349$	1.36925e138	0.356860	0.178430	+	0.983953i	$0.442898\pi$
$350$	4.85574e138	1.08280
$351$	4.94724e138	0.944334
$352$	−7.23620e138	−1.18287
$353$	2.45582e138	0.343934	0.171967	−	0.985103i	$-0.444988\pi$
$353$	2.45582e138	0.343934	0.171967	+	0.985103i	$0.444988\pi$
$354$	3.77088e138	0.452652
$355$	3.59199e138	0.369735
$356$	−2.89487e138	−0.255625
$357$	−1.69788e137	−0.0128674
$358$	−1.58009e139	−1.02815
$359$	−2.52971e139	−1.41392	−0.706958	−	0.707256i	$-0.749933\pi$
$359$	−2.52971e139	−1.41392	−0.706958	+	0.707256i	$0.749933\pi$
$360$	6.35427e139	3.05196
$361$	1.47099e139	0.607391
$362$	1.99615e139	0.708884
$363$	−4.64033e138	−0.141787
$364$	−1.08898e140	−2.86414
$365$	1.81110e139	0.410186
$366$	3.27835e138	0.0639640
$367$	−3.84161e139	−0.645970	−0.322985	−	0.946404i	$-0.604686\pi$
$367$	−3.84161e139	−0.645970	−0.322985	+	0.946404i	$0.604686\pi$
$368$	2.35325e140	3.41164
$369$	1.00629e140	1.25830
$370$	−3.98857e140	−4.30352
$371$	4.78342e139	0.445513
$372$	−1.04074e140	−0.837048
$373$	−1.16147e140	−0.807003	−0.403502	−	0.914979i	$-0.632207\pi$
$373$	−1.16147e140	−0.807003	−0.403502	+	0.914979i	$0.632207\pi$
$374$	1.26148e139	0.0757494
$375$	1.65623e139	0.0859838
$376$	1.75830e139	0.0789507
$377$	−9.58981e139	−0.372569
$378$	−2.37825e140	−0.799750
$379$	4.20001e140	1.22296	0.611481	−	0.791259i	$-0.290574\pi$
$379$	4.20001e140	1.22296	0.611481	+	0.791259i	$0.290574\pi$
$380$	1.59445e141	4.02166
$381$	2.66377e140	0.582219
$382$	−4.04474e140	−0.766368
$383$	4.92224e138	0.00808778	0.00404389	−	0.999992i	$-0.498713\pi$
$383$	4.92224e138	0.00808778	0.00404389	+	0.999992i	$0.498713\pi$
$384$	−6.52178e139	−0.0929640
$385$	5.91520e140	0.731745
$386$	−2.67455e141	−2.87238
$387$	1.20790e141	1.12663
$388$	−4.70553e141	−3.81311
$389$	1.77397e141	1.24937	0.624686	−	0.780876i	$-0.285227\pi$
$389$	1.77397e141	1.24937	0.624686	+	0.780876i	$0.285227\pi$
$390$	1.98729e141	1.21686
$391$	−1.60313e140	−0.0853760
$392$	−2.40512e141	−1.11441
$393$	−4.26270e140	−0.171906
$394$	5.50543e140	0.193307
$395$	1.78371e141	0.545486
$396$	5.90851e141	1.57431
$397$	−4.99793e141	−1.16067	−0.580334	−	0.814379i	$-0.697078\pi$
$397$	−4.99793e141	−1.16067	−0.580334	+	0.814379i	$0.697078\pi$
$398$	3.74291e140	0.0757848
$399$	−1.64049e141	−0.289702
$400$	1.15386e142	1.77780
$401$	−1.08238e142	−1.45549	−0.727745	−	0.685847i	$-0.759432\pi$
$401$	−1.08238e142	−1.45549	−0.727745	+	0.685847i	$0.759432\pi$
$402$	−2.19844e140	−0.0258104
$403$	1.82036e142	1.86652
$404$	−4.52440e141	−0.405300
$405$	−1.24357e142	−0.973581
$406$	4.61003e141	0.315526
$407$	−2.14448e142	−1.28359
$408$	−8.28560e140	−0.0433856
$409$	−1.56829e142	−0.718630	−0.359315	−	0.933216i	$-0.616990\pi$
$409$	−1.56829e142	−0.718630	−0.359315	+	0.933216i	$0.616990\pi$
$410$	8.50233e142	3.41050
$411$	1.08583e141	0.0381403
$412$	2.31119e142	0.711112
$413$	2.23007e142	0.601231
$414$	−1.06758e143	−2.52278
$415$	−6.46065e142	−1.33861
$416$	−1.43773e143	−2.61271
$417$	5.40646e141	0.0861982
$418$	1.21884e143	1.70545
$419$	−3.35220e142	−0.411781	−0.205890	−	0.978575i	$-0.566009\pi$
$419$	−3.35220e142	−0.411781	−0.205890	+	0.978575i	$0.566009\pi$
$420$	−6.71925e142	−0.724827
$421$	1.22649e143	1.16223	0.581113	−	0.813823i	$-0.302617\pi$
$421$	1.22649e143	1.16223	0.581113	+	0.813823i	$0.302617\pi$
$422$	1.81203e143	1.50882
$423$	−3.88421e141	−0.0284284
$424$	2.33429e143	1.50216
$425$	−7.86053e141	−0.0444892
$426$	−3.11906e142	−0.155310
$427$	1.93879e142	0.0849596
$428$	−4.33691e143	−1.67300
$429$	1.06847e143	0.362946
$430$	1.02058e144	3.05362
$431$	−9.65530e142	−0.254539	−0.127270	−	0.991868i	$-0.540621\pi$
$431$	−9.65530e142	−0.254539	−0.127270	+	0.991868i	$0.540621\pi$
$432$	−5.65136e143	−1.31307
$433$	−3.83027e143	−0.784582	−0.392291	−	0.919841i	$-0.628317\pi$
$433$	−3.83027e143	−0.784582	−0.392291	+	0.919841i	$0.628317\pi$
$434$	−8.75086e143	−1.58074
$435$	−5.91713e142	−0.0942858
$436$	−2.67462e143	−0.376053
$437$	−1.54894e144	−1.92219
$438$	−1.57264e143	−0.172302
$439$	6.91926e143	0.669489	0.334745	−	0.942309i	$-0.391350\pi$
$439$	6.91926e143	0.669489	0.334745	+	0.942309i	$0.391350\pi$
$440$	2.88659e144	2.46726
$441$	5.31308e143	0.401276
$442$	2.50639e143	0.167315
$443$	1.62442e143	0.0958727	0.0479364	−	0.998850i	$-0.484736\pi$
$443$	1.62442e143	0.0958727	0.0479364	+	0.998850i	$0.484736\pi$
$444$	2.43597e144	1.27145
$445$	3.12425e143	0.144253
$446$	−5.22695e144	−2.13549
$447$	3.80691e143	0.137662
$448$	1.66465e144	0.532932
$449$	−2.91783e144	−0.827245	−0.413623	−	0.910448i	$-0.635737\pi$
$449$	−2.91783e144	−0.827245	−0.413623	+	0.910448i	$0.635737\pi$
$450$	−5.23457e144	−1.31462
$451$	4.57132e144	1.01723
$452$	6.61932e144	1.30547
$453$	2.15022e144	0.375951
$454$	−3.23000e144	−0.500793
$455$	1.17527e145	1.61628
$456$	−8.00553e144	−0.976802
$457$	−2.54726e144	−0.275829	−0.137915	−	0.990444i	$-0.544040\pi$
$457$	−2.54726e144	−0.275829	−0.137915	+	0.990444i	$0.544040\pi$
$458$	1.28869e145	1.23874
$459$	3.84993e143	0.0328595
$460$	−6.34427e145	−4.80928
$461$	1.99590e145	1.34412	0.672060	−	0.740496i	$-0.265409\pi$
$461$	1.99590e145	1.34412	0.672060	+	0.740496i	$0.265409\pi$
$462$	−5.13638e144	−0.307376
$463$	1.76946e145	0.941186	0.470593	−	0.882350i	$-0.344040\pi$
$463$	1.76946e145	0.941186	0.470593	+	0.882350i	$0.344040\pi$
$464$	1.09547e145	0.518047
$465$	1.12320e145	0.472359
$466$	−7.46297e145	−2.79177
$467$	−4.46078e145	−1.48471	−0.742354	−	0.670007i	$-0.766291\pi$
$467$	−4.46078e145	−1.48471	−0.742354	+	0.670007i	$0.766291\pi$
$468$	1.17394e146	3.47734
$469$	−1.30014e144	−0.0342824
$470$	−3.28186e144	−0.0770524
$471$	1.51806e145	0.317430
$472$	1.08827e146	2.02720
$473$	5.48718e145	0.910788
$474$	−1.54886e145	−0.229136
$475$	−7.59482e145	−1.00165
$476$	−8.47441e144	−0.0996623
$477$	−5.15660e145	−0.540894
$478$	2.46233e146	2.30423
$479$	−6.72192e145	−0.561317	−0.280658	−	0.959808i	$-0.590553\pi$
$479$	−6.72192e145	−0.561317	−0.280658	+	0.959808i	$0.590553\pi$
$480$	−8.87114e145	−0.661198
$481$	−4.26078e146	−2.83519
$482$	−3.81422e146	−2.26643
$483$	6.52748e145	0.346439
$484$	−2.31606e146	−1.09819
$485$	5.07838e146	2.15179
$486$	3.90870e146	1.48032
$487$	9.21076e145	0.311865	0.155933	−	0.987768i	$-0.450162\pi$
$487$	9.21076e145	0.311865	0.155933	+	0.987768i	$0.450162\pi$
$488$	9.46123e145	0.286462
$489$	2.55398e145	0.0691648
$490$	4.48914e146	1.08762
$491$	−6.72259e146	−1.45745	−0.728727	−	0.684804i	$-0.759888\pi$
$491$	−6.72259e146	−1.45745	−0.728727	+	0.684804i	$0.759888\pi$
$492$	−5.19270e146	−1.00762
$493$	−7.46276e144	−0.0129641
$494$	2.42167e147	3.76701
$495$	−6.37668e146	−0.888406
$496$	−2.07944e147	−2.59534
$497$	−1.84459e146	−0.206289
$498$	5.61002e146	0.562297
$499$	1.28052e147	1.15055	0.575276	−	0.817960i	$-0.304895\pi$
$499$	1.28052e147	1.15055	0.575276	+	0.817960i	$0.304895\pi$
$500$	8.26652e146	0.665974
$501$	2.59232e146	0.187297
$502$	−5.20114e146	−0.337090
$503$	1.51237e146	0.0879434	0.0439717	−	0.999033i	$-0.485999\pi$
$503$	1.51237e146	0.0879434	0.0439717	+	0.999033i	$0.485999\pi$
$504$	−3.26310e147	−1.70281
$505$	4.88291e146	0.228717
$506$	−4.84974e147	−2.03946
$507$	1.31231e147	0.495569
$508$	1.32953e148	4.50948
$509$	−5.68917e147	−1.73352	−0.866762	−	0.498722i	$-0.833803\pi$
$509$	−5.68917e147	−1.73352	−0.866762	+	0.498722i	$0.833803\pi$
$510$	1.54650e146	0.0423424
$511$	−9.30051e146	−0.228859
$512$	−9.18080e147	−2.03080
$513$	3.71980e147	0.739814
$514$	−1.06908e148	−1.91214
$515$	−2.49433e147	−0.401291
$516$	−6.23306e147	−0.902178
$517$	−1.76450e146	−0.0229820
$518$	2.04825e148	2.40110
$519$	−3.91019e147	−0.412646
$520$	5.73526e148	5.44968
$521$	−7.37505e147	−0.631116	−0.315558	−	0.948906i	$-0.602192\pi$
$521$	−7.37505e147	−0.631116	−0.315558	+	0.948906i	$0.602192\pi$
$522$	−4.96969e147	−0.383078
$523$	1.34235e148	0.932228	0.466114	−	0.884725i	$-0.345654\pi$
$523$	1.34235e148	0.932228	0.466114	+	0.884725i	$0.345654\pi$
$524$	−2.12758e148	−1.33147
$525$	3.20057e147	0.180529
$526$	−4.69811e148	−2.38891
$527$	1.41660e147	0.0649483
$528$	−1.22054e148	−0.504666
$529$	3.48197e148	1.29865
$530$	−4.35693e148	−1.46604
$531$	−2.40406e148	−0.729951
$532$	−8.18796e148	−2.24384
$533$	9.08258e148	2.24686
$534$	−2.71290e147	−0.0605949
$535$	4.68056e148	0.944098
$536$	−6.34465e147	−0.115592
$537$	−1.04149e148	−0.171418
$538$	−9.84388e148	−1.46397
$539$	2.41361e148	0.324398
$540$	1.52358e149	1.85100
$541$	−7.73821e148	−0.849942	−0.424971	−	0.905207i	$-0.639716\pi$
$541$	−7.73821e148	−0.849942	−0.424971	+	0.905207i	$0.639716\pi$
$542$	2.27560e149	2.26014
$543$	1.31572e148	0.118188
$544$	−1.11884e148	−0.0909134
$545$	2.88655e148	0.212212
$546$	−1.02053e149	−0.678932
$547$	−1.47788e149	−0.889877	−0.444939	−	0.895561i	$-0.646775\pi$
$547$	−1.47788e149	−0.889877	−0.444939	+	0.895561i	$0.646775\pi$
$548$	5.41958e148	0.295410
$549$	−2.09005e148	−0.103149
$550$	−2.37794e149	−1.06276
$551$	−7.21051e148	−0.291880
$552$	3.18538e149	1.16810
$553$	−9.15989e148	−0.304348
$554$	3.10409e149	0.934657
$555$	−2.62900e149	−0.717501
$556$	2.69845e149	0.667634
$557$	−8.71713e149	−1.95553	−0.977767	−	0.209696i	$-0.932753\pi$
$557$	−8.71713e149	−1.95553	−0.977767	+	0.209696i	$0.932753\pi$
$558$	9.43357e149	1.91917
$559$	1.09023e150	2.01175
$560$	−1.34254e150	−2.24739
$561$	8.31483e147	0.0126292
$562$	−1.39150e150	−1.91802
$563$	−1.15897e150	−1.44999	−0.724997	−	0.688752i	$-0.758159\pi$
$563$	−1.15897e150	−1.44999	−0.724997	+	0.688752i	$0.758159\pi$
$564$	2.00435e148	0.0227648
$565$	−7.14381e149	−0.736698
$566$	3.20509e150	3.00154
$567$	6.38610e149	0.543199
$568$	−9.00153e149	−0.695556
$569$	−5.05714e149	−0.355048	−0.177524	−	0.984116i	$-0.556809\pi$
$569$	−5.05714e149	−0.355048	−0.177524	+	0.984116i	$0.556809\pi$
$570$	1.49423e150	0.953315
$571$	4.44981e149	0.258032	0.129016	−	0.991643i	$-0.458818\pi$
$571$	4.44981e149	0.258032	0.129016	+	0.991643i	$0.458818\pi$
$572$	5.33293e150	2.81114
$573$	−2.66602e149	−0.127772
$574$	−4.36619e150	−1.90285
$575$	3.02196e150	1.19782
$576$	−1.79452e150	−0.647030
$577$	4.06700e150	1.33411	0.667057	−	0.745007i	$-0.267554\pi$
$577$	4.06700e150	1.33411	0.667057	+	0.745007i	$0.267554\pi$
$578$	−6.13141e150	−1.83018
$579$	−1.76288e150	−0.478895
$580$	−2.95333e150	−0.730276
$581$	3.31773e150	0.746865
$582$	−4.40975e150	−0.903881
$583$	−2.34252e150	−0.437268
$584$	−4.53861e150	−0.771654
$585$	−1.26696e151	−1.96231
$586$	1.73139e151	2.44328
$587$	−5.98154e150	−0.769195	−0.384598	−	0.923084i	$-0.625660\pi$
$587$	−5.98154e150	−0.769195	−0.384598	+	0.923084i	$0.625660\pi$
$588$	−2.74169e150	−0.321332
$589$	1.36871e151	1.46228
$590$	−2.03124e151	−1.97846
$591$	3.62880e149	0.0322289
$592$	4.86719e151	3.94226
$593$	7.93269e150	0.586057	0.293028	−	0.956104i	$-0.405337\pi$
$593$	7.93269e150	0.586057	0.293028	+	0.956104i	$0.405337\pi$
$594$	1.16467e151	0.784949
$595$	9.14591e149	0.0562409
$596$	1.90009e151	1.06624
$597$	2.46707e149	0.0126352
$598$	−9.63577e151	−4.50476
$599$	−1.69552e151	−0.723671	−0.361836	−	0.932242i	$-0.617850\pi$
$599$	−1.69552e151	−0.723671	−0.361836	+	0.932242i	$0.617850\pi$
$600$	1.56187e151	0.608697
$601$	1.36331e151	0.485216	0.242608	−	0.970124i	$-0.421997\pi$
$601$	1.36331e151	0.485216	0.242608	+	0.970124i	$0.421997\pi$
$602$	−5.24096e151	−1.70374
$603$	1.40158e150	0.0416221
$604$	1.07321e152	2.91187
$605$	2.49958e151	0.619726
$606$	−4.24001e150	−0.0960746
$607$	3.55026e151	0.735321	0.367660	−	0.929960i	$-0.380159\pi$
$607$	3.55026e151	0.735321	0.367660	+	0.929960i	$0.380159\pi$
$608$	−1.08102e152	−2.04686
$609$	3.03862e150	0.0526058
$610$	−1.76593e151	−0.279575
$611$	−3.50583e150	−0.0507627
$612$	9.13556e150	0.120999
$613$	−2.55291e151	−0.309342	−0.154671	−	0.987966i	$-0.549432\pi$
$613$	−2.55291e151	−0.309342	−0.154671	+	0.987966i	$0.549432\pi$
$614$	−1.11592e152	−1.23725
$615$	5.60415e151	0.568612
$616$	−1.48235e152	−1.37658
$617$	1.61774e151	0.137520	0.0687601	−	0.997633i	$-0.478096\pi$
$617$	1.61774e151	0.137520	0.0687601	+	0.997633i	$0.478096\pi$
$618$	2.16592e151	0.168566
$619$	1.90686e152	1.35887	0.679434	−	0.733736i	$-0.262225\pi$
$619$	1.90686e152	1.35887	0.679434	+	0.733736i	$0.262225\pi$
$620$	5.60608e152	3.65858
$621$	−1.48010e152	−0.884704
$622$	−3.72935e152	−2.04201
$623$	−1.60439e151	−0.0804845
$624$	−2.42505e152	−1.11471
$625$	−2.76765e152	−1.16587
$626$	6.68738e152	2.58199
$627$	8.03377e151	0.284340
$628$	7.57687e152	2.45861
$629$	−3.31573e151	−0.0986548
$630$	6.09055e152	1.66187
$631$	−5.64845e152	−1.41361	−0.706804	−	0.707410i	$-0.749864\pi$
$631$	−5.64845e152	−1.41361	−0.706804	+	0.707410i	$0.749864\pi$
$632$	−4.46999e152	−1.02618
$633$	1.19437e152	0.251556
$634$	−1.51318e153	−2.92433
$635$	−1.43488e153	−2.54477
$636$	2.66094e152	0.433134
$637$	4.79551e152	0.716532
$638$	−2.25761e152	−0.309686
$639$	1.98850e152	0.250455
$640$	3.51306e152	0.406328
$641$	−4.43476e152	−0.471094	−0.235547	−	0.971863i	$-0.575688\pi$
$641$	−4.43476e152	−0.471094	−0.235547	+	0.971863i	$0.575688\pi$
$642$	−4.06430e152	−0.396577
$643$	2.48936e152	0.223146	0.111573	−	0.993756i	$-0.464411\pi$
$643$	2.48936e152	0.223146	0.111573	+	0.993756i	$0.464411\pi$
$644$	3.25797e153	2.68329
$645$	6.72695e152	0.509112
$646$	1.88454e152	0.131079
$647$	5.34940e152	0.341997	0.170998	−	0.985271i	$-0.445301\pi$
$647$	5.34940e152	0.341997	0.170998	+	0.985271i	$0.445301\pi$
$648$	3.11639e153	1.83153
$649$	−1.09211e153	−0.590104
$650$	−4.72464e153	−2.34742
$651$	−5.76797e152	−0.263548
$652$	1.27474e153	0.535705
$653$	1.89403e153	0.732181	0.366090	−	0.930579i	$-0.380696\pi$
$653$	1.89403e153	0.732181	0.366090	+	0.930579i	$0.380696\pi$
$654$	−2.50650e152	−0.0891417
$655$	2.29617e153	0.751369
$656$	−1.03752e154	−3.12420
$657$	1.00261e153	0.277856
$658$	1.68533e152	0.0429906
$659$	6.39578e153	1.50189	0.750945	−	0.660364i	$-0.229598\pi$
$659$	6.39578e153	1.50189	0.750945	+	0.660364i	$0.229598\pi$
$660$	3.29053e153	0.711413
$661$	−5.33971e153	−1.06301	−0.531506	−	0.847055i	$-0.678374\pi$
$661$	−5.33971e153	−1.06301	−0.531506	+	0.847055i	$0.678374\pi$
$662$	−1.39107e154	−2.55029
$663$	1.65204e152	0.0278955
$664$	1.61904e154	2.51824
$665$	8.83676e153	1.26623
$666$	−2.20805e154	−2.91516
$667$	2.86904e153	0.349043
$668$	1.29387e154	1.45068
$669$	−3.44525e153	−0.356039
$670$	1.18422e153	0.112812
$671$	−9.49461e152	−0.0833872
$672$	4.55559e153	0.368909
$673$	−3.31144e153	−0.247284	−0.123642	−	0.992327i	$-0.539457\pi$
$673$	−3.31144e153	−0.247284	−0.123642	+	0.992327i	$0.539457\pi$
$674$	−4.64273e154	−3.19749
$675$	−7.25726e153	−0.461017
$676$	6.54998e154	3.83835
$677$	−1.62873e151	−0.000880578 0	−0.000440289	−	1.00000i	$-0.500140\pi$
$677$	−1.62873e151	−0.000880578 0	−0.000440289		1.00000i	$0.500140\pi$
$678$	6.20324e153	0.309457
$679$	−2.60790e154	−1.20057
$680$	4.46316e153	0.189630
$681$	−2.12900e153	−0.0834944
$682$	4.28545e154	1.55149
$683$	2.33523e154	0.780549	0.390275	−	0.920698i	$-0.372380\pi$
$683$	2.33523e154	0.780549	0.390275	+	0.920698i	$0.372380\pi$
$684$	8.82676e154	2.72423
$685$	−5.84901e153	−0.166704
$686$	−7.51193e154	−1.97737
$687$	8.49416e153	0.206528
$688$	−1.24539e155	−2.79728
$689$	−4.65427e154	−0.965837
$690$	−5.94549e154	−1.14002
$691$	9.64926e154	1.70978	0.854890	−	0.518809i	$-0.173624\pi$
$691$	9.64926e154	1.70978	0.854890	+	0.518809i	$0.173624\pi$
$692$	−1.95164e155	−3.19608
$693$	3.27461e154	0.495677
$694$	1.14790e155	1.60625
$695$	−2.91227e154	−0.376756
$696$	1.48283e154	0.177373
$697$	7.06803e153	0.0781830
$698$	6.40458e154	0.655195
$699$	−4.91908e154	−0.465455
$700$	1.59746e155	1.39825
$701$	1.63235e155	1.32184	0.660922	−	0.750455i	$-0.270165\pi$
$701$	1.63235e155	1.32184	0.660922	+	0.750455i	$0.270165\pi$
$702$	2.31404e155	1.73380
$703$	−3.20365e155	−2.22116
$704$	−8.15210e154	−0.523069
$705$	−2.16318e153	−0.0128465
$706$	1.14869e155	0.631461
$707$	−2.50751e154	−0.127610
$708$	1.24056e155	0.584526
$709$	6.64908e154	0.290096	0.145048	−	0.989425i	$-0.453666\pi$
$709$	6.64908e154	0.290096	0.145048	+	0.989425i	$0.453666\pi$
$710$	1.68013e155	0.678832
$711$	9.87451e154	0.369507
$712$	−7.82938e154	−0.271374
$713$	−5.44608e155	−1.74866
$714$	−7.94173e153	−0.0236245
$715$	−5.75549e155	−1.58637
$716$	−5.19824e155	−1.32769
$717$	1.62300e155	0.384171
$718$	−1.18325e156	−2.59595
$719$	6.77304e155	1.37740	0.688699	−	0.725048i	$-0.258182\pi$
$719$	6.77304e155	1.37740	0.688699	+	0.725048i	$0.258182\pi$
$720$	1.44728e156	2.72854
$721$	1.28091e155	0.223896
$722$	6.88047e155	1.11517
$723$	−2.51407e155	−0.377868
$724$	6.56699e155	0.915408
$725$	1.40676e155	0.181886
$726$	−2.17048e155	−0.260321
$727$	1.43056e155	0.159177	0.0795885	−	0.996828i	$-0.474639\pi$
$727$	1.43056e155	0.159177	0.0795885	+	0.996828i	$0.474639\pi$
$728$	−2.94522e156	−3.04059
$729$	−5.01974e155	−0.480874
$730$	8.47127e155	0.753100
$731$	8.48412e154	0.0700019
$732$	1.07852e155	0.0825990
$733$	9.45126e155	0.671929	0.335964	−	0.941875i	$-0.390938\pi$
$733$	9.45126e155	0.671929	0.335964	+	0.941875i	$0.390938\pi$
$734$	−1.79688e156	−1.18600
$735$	2.95893e155	0.181332
$736$	4.30135e156	2.44773
$737$	6.36703e154	0.0336480
$738$	4.70683e156	2.31024
$739$	3.62912e156	1.65455	0.827275	−	0.561798i	$-0.189890\pi$
$739$	3.62912e156	1.65455	0.827275	+	0.561798i	$0.189890\pi$
$740$	−1.31217e157	−5.55729
$741$	1.59620e156	0.628051
$742$	2.23741e156	0.817960
$743$	5.08282e156	1.72669	0.863345	−	0.504613i	$-0.168365\pi$
$743$	5.08282e156	1.72669	0.863345	+	0.504613i	$0.168365\pi$
$744$	−2.81474e156	−0.888616
$745$	−2.05065e156	−0.601693
$746$	−5.43267e156	−1.48166
$747$	−3.57657e156	−0.906764
$748$	4.15007e155	0.0978178
$749$	−2.40360e156	−0.526749
$750$	7.74690e155	0.157866
$751$	5.04119e156	0.955337	0.477668	−	0.878540i	$-0.341482\pi$
$751$	5.04119e156	0.955337	0.477668	+	0.878540i	$0.341482\pi$
$752$	4.00479e155	0.0705842
$753$	−3.42824e155	−0.0562011
$754$	−4.48556e156	−0.684036
$755$	−1.15825e157	−1.64321
$756$	−7.82404e156	−1.03274
$757$	1.21571e156	0.149316	0.0746579	−	0.997209i	$-0.476214\pi$
$757$	1.21571e156	0.149316	0.0746579	+	0.997209i	$0.476214\pi$
$758$	1.96452e157	2.24536
$759$	−3.19662e156	−0.340027
$760$	4.31230e157	4.26941
$761$	−1.51125e155	−0.0139275	−0.00696373	−	0.999976i	$-0.502217\pi$
$761$	−1.51125e155	−0.0139275	−0.00696373	+	0.999976i	$0.502217\pi$
$762$	1.24596e157	1.06895
$763$	−1.48233e156	−0.118402
$764$	−1.33065e157	−0.989638
$765$	−9.85944e155	−0.0682817
$766$	2.30234e155	0.0148492
$767$	−2.16986e157	−1.30342
$768$	−6.95631e156	−0.389218
$769$	−2.41564e156	−0.125906	−0.0629529	−	0.998016i	$-0.520052\pi$
$769$	−2.41564e156	−0.125906	−0.0629529	+	0.998016i	$0.520052\pi$
$770$	2.76679e157	1.34348
$771$	−7.04664e156	−0.318800
$772$	−8.79881e157	−3.70921
$773$	1.09751e157	0.431148	0.215574	−	0.976487i	$-0.430838\pi$
$773$	1.09751e157	0.431148	0.215574	+	0.976487i	$0.430838\pi$
$774$	5.64985e157	2.06849
$775$	−2.67034e157	−0.911221
$776$	−1.27264e158	−4.04802
$777$	1.35007e157	0.400322
$778$	8.29760e157	2.29385
$779$	6.82912e157	1.76025
$780$	6.53784e157	1.57137
$781$	9.03328e156	0.202472
$782$	−7.49853e156	−0.156750
$783$	−6.89003e156	−0.134340
$784$	−5.47802e157	−0.996319
$785$	−8.17724e157	−1.38743
$786$	−1.99385e157	−0.315619
$787$	3.36137e157	0.496470	0.248235	−	0.968700i	$-0.420150\pi$
$787$	3.36137e157	0.496470	0.248235	+	0.968700i	$0.420150\pi$
$788$	1.81119e157	0.249624
$789$	−3.09667e157	−0.398290
$790$	8.34319e157	1.00151
$791$	3.66856e157	0.411033
$792$	1.59800e158	1.67130
$793$	−1.88645e157	−0.184186
$794$	−2.33775e158	−2.13098
$795$	−2.87179e157	−0.244424
$796$	1.23135e157	0.0978636
$797$	2.38250e158	1.76829	0.884145	−	0.467212i	$-0.154742\pi$
$797$	2.38250e158	1.76829	0.884145	+	0.467212i	$0.154742\pi$
$798$	−7.67328e157	−0.531892
$799$	−2.72823e155	−0.00176637
$800$	2.10905e158	1.27551
$801$	1.72956e157	0.0977157
$802$	−5.06273e158	−2.67228
$803$	4.55462e157	0.224623
$804$	−7.23250e156	−0.0333299
$805$	−3.51612e158	−1.51422
$806$	8.51460e158	3.42692
$807$	−6.48842e157	−0.244079
$808$	−1.22366e158	−0.430269
$809$	−7.61845e157	−0.250422	−0.125211	−	0.992130i	$-0.539961\pi$
$809$	−7.61845e157	−0.250422	−0.125211	+	0.992130i	$0.539961\pi$
$810$	−5.81672e158	−1.78749
$811$	−1.53803e158	−0.441903	−0.220952	−	0.975285i	$-0.570916\pi$
$811$	−1.53803e158	−0.441903	−0.220952	+	0.975285i	$0.570916\pi$
$812$	1.51662e158	0.407450
$813$	1.49992e158	0.376820
$814$	−1.00306e159	−2.35667
$815$	−1.37574e158	−0.302306
$816$	−1.88717e157	−0.0387880
$817$	8.19734e158	1.57605
$818$	−7.33555e158	−1.31940
$819$	6.50621e158	1.09485
$820$	2.79712e159	4.40410
$821$	−1.76748e157	−0.0260407	−0.0130203	−	0.999915i	$-0.504145\pi$
$821$	−1.76748e157	−0.0260407	−0.0130203	+	0.999915i	$0.504145\pi$
$822$	5.07891e157	0.0700256
$823$	4.09162e158	0.527964	0.263982	−	0.964528i	$-0.414964\pi$
$823$	4.09162e158	0.527964	0.263982	+	0.964528i	$0.414964\pi$
$824$	6.25079e158	0.754921
$825$	−1.56738e158	−0.177187
$826$	1.04310e159	1.10386
$827$	−7.97799e158	−0.790393	−0.395197	−	0.918597i	$-0.629324\pi$
$827$	−7.97799e158	−0.790393	−0.395197	+	0.918597i	$0.629324\pi$
$828$	−3.51215e159	−3.25776
$829$	1.11401e159	0.967538	0.483769	−	0.875196i	$-0.339268\pi$
$829$	1.11401e159	0.967538	0.483769	+	0.875196i	$0.339268\pi$
$830$	−3.02192e159	−2.45769
$831$	2.04600e158	0.155830
$832$	−1.61971e159	−1.15536
$833$	3.73185e157	0.0249328
$834$	2.52883e158	0.158260
$835$	−1.39639e159	−0.818642
$836$	4.00979e159	2.20231
$837$	1.30788e159	0.673024
$838$	−1.56797e159	−0.756029
$839$	−4.56509e158	−0.206264	−0.103132	−	0.994668i	$-0.532886\pi$
$839$	−4.56509e158	−0.206264	−0.103132	+	0.994668i	$0.532886\pi$
$840$	−1.81727e159	−0.769481
$841$	−2.38633e159	−0.946999
$842$	5.73683e159	2.13385
$843$	−9.17181e158	−0.319781
$844$	5.96128e159	1.94839
$845$	−7.06898e159	−2.16604
$846$	−1.81681e158	−0.0521946
$847$	−1.28361e159	−0.345769
$848$	5.31668e159	1.34297
$849$	2.11258e159	0.500430
$850$	−3.67670e158	−0.0816822
$851$	1.27472e160	2.65616
$852$	−1.02612e159	−0.200558
$853$	−5.02688e159	−0.921672	−0.460836	−	0.887485i	$-0.652450\pi$
$853$	−5.02688e159	−0.921672	−0.460836	+	0.887485i	$0.652450\pi$
$854$	9.06856e158	0.155986
$855$	−9.52617e159	−1.53732
$856$	−1.17295e160	−1.77607
$857$	−1.02689e160	−1.45904	−0.729521	−	0.683958i	$-0.760257\pi$
$857$	−1.02689e160	−1.45904	−0.729521	+	0.683958i	$0.760257\pi$
$858$	4.99771e159	0.666367
$859$	−8.31230e159	−1.04015	−0.520073	−	0.854122i	$-0.674095\pi$
$859$	−8.31230e159	−1.04015	−0.520073	+	0.854122i	$0.674095\pi$
$860$	3.35753e160	3.94325
$861$	−2.87790e159	−0.317251
$862$	−4.51620e159	−0.467334
$863$	1.87873e160	1.82506	0.912528	−	0.409013i	$-0.134127\pi$
$863$	1.87873e160	1.82506	0.912528	+	0.409013i	$0.134127\pi$
$864$	−1.03297e160	−0.942085
$865$	2.10629e160	1.80360
$866$	−1.79158e160	−1.44049
$867$	−4.04140e159	−0.305135
$868$	−2.87889e160	−2.04127
$869$	4.48575e159	0.298715
$870$	−2.76769e159	−0.173109
$871$	1.26504e159	0.0743217
$872$	−7.23371e159	−0.399220
$873$	2.81136e160	1.45760
$874$	−7.24506e160	−3.52914
$875$	4.58147e159	0.209684
$876$	−5.17373e159	−0.222500
$877$	4.79045e159	0.193597	0.0967986	−	0.995304i	$-0.469140\pi$
$877$	4.79045e159	0.193597	0.0967986	+	0.995304i	$0.469140\pi$
$878$	3.23643e160	1.22918
$879$	1.14121e160	0.407354
$880$	6.57464e160	2.20580
$881$	−6.08119e159	−0.191779	−0.0958895	−	0.995392i	$-0.530570\pi$
$881$	−6.08119e159	−0.191779	−0.0958895	+	0.995392i	$0.530570\pi$
$882$	2.48516e160	0.736743
$883$	1.48178e160	0.412976	0.206488	−	0.978449i	$-0.433797\pi$
$883$	1.48178e160	0.412976	0.206488	+	0.978449i	$0.433797\pi$
$884$	8.24561e159	0.216060
$885$	−1.33885e160	−0.329857
$886$	7.59810e159	0.176022
$887$	−8.37924e160	−1.82544	−0.912720	−	0.408586i	$-0.866022\pi$
$887$	−8.37924e160	−1.82544	−0.912720	+	0.408586i	$0.866022\pi$
$888$	6.58826e160	1.34978
$889$	7.36854e160	1.41983
$890$	1.46135e160	0.264849
$891$	−3.12739e160	−0.533146
$892$	−1.71958e161	−2.75764
$893$	−2.63601e159	−0.0397688
$894$	1.78065e160	0.252746
$895$	5.61013e160	0.749234
$896$	−1.80406e160	−0.226706
$897$	−6.35124e160	−0.751053
$898$	−1.36479e161	−1.51882
$899$	−2.53521e160	−0.265529
$900$	−1.72209e161	−1.69761
$901$	−3.62194e159	−0.0336078
$902$	2.13820e161	1.86763
$903$	−3.45448e160	−0.284054
$904$	1.79024e161	1.38590
$905$	−7.08734e160	−0.516578
$906$	1.00575e161	0.690245
$907$	−1.36362e160	−0.0881247	−0.0440624	−	0.999029i	$-0.514030\pi$
$907$	−1.36362e160	−0.0881247	−0.0440624	+	0.999029i	$0.514030\pi$
$908$	−1.06262e161	−0.646692
$909$	2.70314e160	0.154931
$910$	5.49723e161	2.96748
$911$	3.18163e161	1.61770	0.808851	−	0.588014i	$-0.200090\pi$
$911$	3.18163e161	1.61770	0.808851	+	0.588014i	$0.200090\pi$
$912$	−1.82338e161	−0.873289
$913$	−1.62475e161	−0.733043
$914$	−1.19146e161	−0.506422
$915$	−1.16398e160	−0.0466118
$916$	4.23957e161	1.59963
$917$	−1.17915e161	−0.419218
$918$	1.80078e160	0.0603301
$919$	−4.14517e161	−1.30872	−0.654360	−	0.756183i	$-0.727062\pi$
$919$	−4.14517e161	−1.30872	−0.654360	+	0.756183i	$0.727062\pi$
$920$	−1.71585e162	−5.10556
$921$	−7.35540e160	−0.206280
$922$	9.33568e161	2.46780
$923$	1.79479e161	0.447220
$924$	−1.68978e161	−0.396925
$925$	6.25027e161	1.38412
$926$	8.27650e161	1.72802
$927$	−1.38084e161	−0.271831
$928$	2.00233e161	0.371682
$929$	−3.95959e160	−0.0693096	−0.0346548	−	0.999399i	$-0.511033\pi$
$929$	−3.95959e160	−0.0693096	−0.0346548	+	0.999399i	$0.511033\pi$
$930$	5.25369e161	0.867250
$931$	3.60571e161	0.561349
$932$	−2.45519e162	−3.60511
$933$	−2.45813e161	−0.340452
$934$	−2.08650e162	−2.72592
$935$	−4.47891e160	−0.0552000
$936$	3.17500e162	3.69156
$937$	−6.80252e161	−0.746212	−0.373106	−	0.927789i	$-0.621707\pi$
$937$	−6.80252e161	−0.746212	−0.373106	+	0.927789i	$0.621707\pi$
$938$	−6.08133e160	−0.0629425
$939$	4.40786e161	0.430480
$940$	−1.07968e161	−0.0995005
$941$	−1.04634e162	−0.909994	−0.454997	−	0.890493i	$-0.650360\pi$
$941$	−1.04634e162	−0.909994	−0.454997	+	0.890493i	$0.650360\pi$
$942$	7.10060e161	0.582802
$943$	−2.71729e162	−2.10498
$944$	2.47869e162	1.81238
$945$	8.44400e161	0.582793
$946$	2.56659e162	1.67220
$947$	2.71740e162	1.67139	0.835697	−	0.549191i	$-0.185064\pi$
$947$	2.71740e162	1.67139	0.835697	+	0.549191i	$0.185064\pi$
$948$	−5.09550e161	−0.295892
$949$	9.04941e161	0.496148
$950$	−3.55242e162	−1.83903
$951$	−9.97385e161	−0.487556
$952$	−2.29196e161	−0.105802
$953$	1.88375e160	0.00821220	0.00410610	−	0.999992i	$-0.498693\pi$
$953$	1.88375e160	0.00821220	0.00410610	+	0.999992i	$0.498693\pi$
$954$	−2.41196e162	−0.993080
$955$	1.43609e162	0.558467
$956$	8.10065e162	2.97553
$957$	−1.48806e161	−0.0516322
$958$	−3.14413e162	−1.03058
$959$	3.00364e161	0.0930108
$960$	−9.99397e161	−0.292386
$961$	1.19476e162	0.330261
$962$	−1.99295e163	−5.20541
$963$	2.59113e162	0.639523
$964$	−1.25481e163	−2.92672
$965$	9.49601e162	2.09316
$966$	3.05318e162	0.636061
$967$	−3.29644e162	−0.649087	−0.324543	−	0.945871i	$-0.605211\pi$
$967$	−3.29644e162	−0.649087	−0.324543	+	0.945871i	$0.605211\pi$
$968$	−6.26395e162	−1.16585
$969$	1.24216e161	0.0218540
$970$	2.37538e163	3.95069
$971$	1.24152e162	0.195211	0.0976054	−	0.995225i	$-0.468882\pi$
$971$	1.24152e162	0.195211	0.0976054	+	0.995225i	$0.468882\pi$
$972$	1.28590e163	1.91159
$973$	1.49554e162	0.210207
$974$	4.30827e162	0.572584
$975$	−3.11416e162	−0.391372
$976$	2.15493e162	0.256106
$977$	−9.88178e162	−1.11066	−0.555330	−	0.831630i	$-0.687408\pi$
$977$	−9.88178e162	−1.11066	−0.555330	+	0.831630i	$0.687408\pi$
$978$	1.19461e162	0.126987
$979$	7.85699e161	0.0789950
$980$	1.47685e163	1.40448
$981$	1.59798e162	0.143751
$982$	−3.14444e163	−2.67588
$983$	−4.55541e162	−0.366742	−0.183371	−	0.983044i	$-0.558701\pi$
$983$	−4.55541e162	−0.366742	−0.183371	+	0.983044i	$0.558701\pi$
$984$	−1.40440e163	−1.06969
$985$	−1.95471e162	−0.140866
$986$	−3.49065e161	−0.0238021
$987$	1.11085e161	0.00716757
$988$	7.96690e163	4.86447
$989$	−3.26170e163	−1.88472
$990$	−2.98265e163	−1.63111
$991$	1.87254e163	0.969207	0.484603	−	0.874734i	$-0.338964\pi$
$991$	1.87254e163	0.969207	0.484603	+	0.874734i	$0.338964\pi$
$992$	−3.80087e163	−1.86207
$993$	−9.16901e162	−0.425195
$994$	−8.62794e162	−0.378747
$995$	−1.32892e162	−0.0552259
$996$	1.84560e163	0.726114
$997$	−3.16611e163	−1.17934	−0.589672	−	0.807643i	$-0.700743\pi$
$997$	−3.16611e163	−1.17934	−0.589672	+	0.807643i	$0.700743\pi$
$998$	5.98953e163	2.11241
$999$	−3.06126e163	−1.02231

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.110.a.a.1.8	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.110.a.a.1.8	✓	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)

\(f(q)\)	\(=\)	\(q+4.67743e16 q^{2} +3.08304e25 q^{3} +1.53880e33 q^{4} -1.66073e38 q^{5} +1.44207e42 q^{6} +8.52831e45 q^{7} +4.16178e49 q^{8} -9.19366e51 q^{9} +O(q^{10})\)	\(q+4.67743e16 q^{2} +3.08304e25 q^{3} +1.53880e33 q^{4} -1.66073e38 q^{5} +1.44207e42 q^{6} +8.52831e45 q^{7} +4.16178e49 q^{8} -9.19366e51 q^{9} -7.76792e54 q^{10} -4.17646e56 q^{11} +4.74417e58 q^{12} -8.29806e60 q^{13} +3.98905e62 q^{14} -5.12008e63 q^{15} +9.47907e65 q^{16} -6.45752e65 q^{17} -4.30027e68 q^{18} -6.23924e69 q^{19} -2.55552e71 q^{20} +2.62931e71 q^{21} -1.95351e73 q^{22} +2.48258e74 q^{23} +1.28309e75 q^{24} +1.21727e76 q^{25} -3.88135e77 q^{26} -5.96193e77 q^{27} +1.31233e79 q^{28} +1.15567e79 q^{29} -2.39488e80 q^{30} -2.19372e81 q^{31} +1.73262e82 q^{32} -1.28762e82 q^{33} -3.02046e82 q^{34} -1.41632e84 q^{35} -1.41472e85 q^{36} +5.13467e85 q^{37} -2.91836e86 q^{38} -2.55832e86 q^{39} -6.91157e87 q^{40} -1.09454e88 q^{41} +1.22984e88 q^{42} -1.31384e89 q^{43} -6.42672e89 q^{44} +1.52682e90 q^{45} +1.16121e91 q^{46} +4.22488e89 q^{47} +2.92243e91 q^{48} -5.77907e91 q^{49} +5.69368e92 q^{50} -1.99088e91 q^{51} -1.27690e94 q^{52} +5.60887e93 q^{53} -2.78865e94 q^{54} +6.93596e94 q^{55} +3.54929e95 q^{56} -1.92358e95 q^{57} +5.40556e95 q^{58} +2.61491e96 q^{59} -7.87876e96 q^{60} +2.27336e96 q^{61} -1.02610e98 q^{62} -7.84064e97 q^{63} +1.95192e98 q^{64} +1.37808e99 q^{65} -6.02275e98 q^{66} -1.52450e98 q^{67} -9.93680e98 q^{68} +7.65389e99 q^{69} -6.62473e100 q^{70} -2.16290e100 q^{71} -3.82620e101 q^{72} -1.09055e101 q^{73} +2.40171e102 q^{74} +3.75288e101 q^{75} -9.60092e102 q^{76} -3.56181e102 q^{77} -1.19664e103 q^{78} -1.07406e103 q^{79} -1.57421e104 q^{80} +7.48812e103 q^{81} -5.11965e104 q^{82} +3.89026e104 q^{83} +4.04597e104 q^{84} +1.07242e104 q^{85} -6.14537e105 q^{86} +3.56298e104 q^{87} -1.73815e106 q^{88} -1.88126e105 q^{89} +7.14157e106 q^{90} -7.07684e106 q^{91} +3.82018e107 q^{92} -6.76332e106 q^{93} +1.97616e106 q^{94} +1.03617e108 q^{95} +5.34172e107 q^{96} -3.05793e108 q^{97} -2.70312e108 q^{98} +3.83970e108 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 22\!\cdots\!00 q^{2}+ \cdots + 24\!\cdots\!84 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more