LMFDB - Embedded newform 1.110.a.a.1.7

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			1.7
Root			$-1.48210e14$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.87423e16 q^{2} -1.13913e26 q^{3} +1.77081e32 q^{4} +7.39260e37 q^{5} -3.27412e42 q^{6} +4.38791e45 q^{7} -1.35651e49 q^{8} +2.83200e51 q^{9} +O(q^{10})$	\(q+2.87423e16 q^{2} -1.13913e26 q^{3} +1.77081e32 q^{4} +7.39260e37 q^{5} -3.27412e42 q^{6} +4.38791e45 q^{7} -1.35651e49 q^{8} +2.83200e51 q^{9} +2.12480e54 q^{10} -7.83713e55 q^{11} -2.01719e58 q^{12} +8.60718e60 q^{13} +1.26119e62 q^{14} -8.42113e63 q^{15} -5.04824e65 q^{16} +2.34591e66 q^{17} +8.13980e67 q^{18} -2.47996e69 q^{19} +1.30909e70 q^{20} -4.99840e71 q^{21} -2.25257e72 q^{22} +1.12887e74 q^{23} +1.54524e75 q^{24} -9.94238e75 q^{25} +2.47390e77 q^{26} +8.32952e77 q^{27} +7.77018e77 q^{28} +6.35552e79 q^{29} -2.42043e80 q^{30} -1.95922e81 q^{31} -5.70554e81 q^{32} +8.92751e81 q^{33} +6.74269e82 q^{34} +3.24381e83 q^{35} +5.01494e83 q^{36} -4.05048e85 q^{37} -7.12798e85 q^{38} -9.80469e86 q^{39} -1.00281e87 q^{40} -4.51771e86 q^{41} -1.43665e88 q^{42} -1.62041e89 q^{43} -1.38781e88 q^{44} +2.09358e89 q^{45} +3.24464e90 q^{46} +1.71486e91 q^{47} +5.75060e91 q^{48} -1.11269e92 q^{49} -2.85767e92 q^{50} -2.67230e92 q^{51} +1.52417e93 q^{52} -1.69761e94 q^{53} +2.39409e94 q^{54} -5.79368e93 q^{55} -5.95224e94 q^{56} +2.82500e95 q^{57} +1.82672e96 q^{58} -3.70093e95 q^{59} -1.49123e96 q^{60} -2.20654e97 q^{61} -5.63124e97 q^{62} +1.24266e97 q^{63} +1.63659e98 q^{64} +6.36294e98 q^{65} +2.56597e98 q^{66} -1.91653e99 q^{67} +4.15418e98 q^{68} -1.28593e100 q^{69} +9.32344e99 q^{70} -1.02494e101 q^{71} -3.84163e100 q^{72} +8.76953e100 q^{73} -1.16420e102 q^{74} +1.13257e102 q^{75} -4.39155e101 q^{76} -3.43886e101 q^{77} -2.81809e103 q^{78} -4.80871e103 q^{79} -3.73196e103 q^{80} -1.23612e104 q^{81} -1.29849e103 q^{82} -1.49463e104 q^{83} -8.85124e103 q^{84} +1.73424e104 q^{85} -4.65743e105 q^{86} -7.23977e105 q^{87} +1.06311e105 q^{88} +1.76822e106 q^{89} +6.01743e105 q^{90} +3.77675e106 q^{91} +1.99903e106 q^{92} +2.23180e107 q^{93} +4.92891e107 q^{94} -1.83334e107 q^{95} +6.49936e107 q^{96} +1.33463e108 q^{97} -3.19813e108 q^{98} -2.21947e107 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 22\!\cdots\!00 q^{2}+ \cdots + 24\!\cdots\!84 q^{9}+O(q^{10}) $ 8 * q + 2288392606915200 * q^2 - 79912254646281404120911200 * q^3 + 2561413209738240277879721565741056 * q^4 - 213255348687551833005583336469825970000 * q^5 + 6583361430969554396417990643904425772724736 * q^6 + 2340906693576137711090348032140051967265800000 * q^7 - 11615898303025646840479523942639805952956786278400 * q^8 + 2442167730177863701398288419313511486695316522756584 * q^9	$ 8 q + 22\!\cdots\!00 q^{2}+ \cdots + 71\!\cdots\!28 q^{99}+O(q^{100}) $ 8 * q + 2288392606915200 * q^2 - 79912254646281404120911200 * q^3 + 2561413209738240277879721565741056 * q^4 - 213255348687551833005583336469825970000 * q^5 + 6583361430969554396417990643904425772724736 * q^6 + 2340906693576137711090348032140051967265800000 * q^7 - 11615898303025646840479523942639805952956786278400 * q^8 + 2442167730177863701398288419313511486695316522756584 * q^9 + 1812920838217088357740086473089711591380968010637920000 * q^10 - 165947975430612920732153376325913672821997118332062700064 * q^11 - 91447218063548694114657346762586040488310132762945923481600 * q^12 - 7191403001708863672049265996058758403993505035337715331216400 * q^13 - 509718116120592395778374084857614778933075979029025208586042368 * q^14 + 23523118033136793898911835577576979866924828095398791554532760000 * q^15 + 1148530988697824742941824958565237185269878102817249769800092090368 * q^16 - 8656206993525090371911384042688075118245096778873514284447257516400 * q^17 - 594865916442544102448370621315341724156945499047441634064537134051200 * q^18 - 11207956347132239593501696340276604562903586944462900105290733089025760 * q^19 - 318028102788054771974342811943070552646655597179484587999192418007040000 * q^20 - 2767292515426156676853955740316424819275205191740879849349575383275847424 * q^21 + 14938820094709351316223859446246734647054202968288974693072213154286630400 * q^22 + 53936338606237446863185709770824957589455521350451701866403050553428350400 * q^23 + 5321978767822090266204570063167770260876413438542000203325176764538153861120 * q^24 + 18193458801058157698506203622645619662054791653093200756293219491399746875000 * q^25 - 435759349281531260141580744807392307738565554114182063684255943941959138178304 * q^26 - 272453442859186698036015029517519337343034663149290746308745684225146650622400 * q^27 + 31554975806041099413511213807244716611018915532477271262553604696632234310041600 * q^28 + 29771410364049527567872005799257248512262425259650062583814547510404351825013360 * q^29 - 751891125225161548033301007468436615543819263432942020592477930753653797722240000 * q^30 - 1466375047838170098337421957808047734223626673774209444573675519328499442335175424 * q^31 - 5937114879483988773905731140457152891870978542120977621282805115905850091556044800 * q^32 + 98313301892085553482704563970636693639651433404572558153235155127418907919206665600 * q^33 + 230323498000052302973276572671855085448946915340852153738007852434989492667839528192 * q^34 - 2881501566480835926866891176622148835419121956576388959555158972591401000555206480000 * q^35 + 1939555675122247234177033125266156026088405967647423925256129675441087219550987378688 * q^36 + 33117119032354918971772421960637107981416747079728699237422500438475360696577657658800 * q^37 + 11996231369252381781466269208385230328578753740510963392596214782634078981979819686400 * q^38 - 771921798225629223813541576850627931176100580853963300794965264851972743236296284337472 * q^39 - 1009702443147367270514989525871937316615498052888256181187241154243431845313822720000000 * q^40 + 2631322094324930918487353619268593963294779980083389672280377185771701226284660975010896 * q^41 + 65594383583093454058986149447123157383111717279272925654585914541457714878623959042969600 * q^42 - 31764236064988776927398716108299521712529891801740350383239284135241451092841492492916000 * q^43 - 1270138580535281866445275727176723968063639122939870285300305417276565925160179749765480448 * q^44 + 287550814354171023801469605323898278540973909702719042079897511272969200785142386583190000 * q^45 + 14731896191270382685679107493825145018801039145654619659863205374802348136428160980957203456 * q^46 + 1625966957623832725817330998098515479861611323645021162528642542135008566368994094752150400 * q^47 - 143515128231599226227412132210359595219087228680385094858911141289724103136282160567785881600 * q^48 + 157527210655459293654279435784054674911203740727991629561212852729050695391270938108305773256 * q^49 + 322389957080420808210330902387583711642761566269183034944052266108906361308513927567750000000 * q^50 + 489920249498412339580606438123981910239683109252240004744192036459028106019912596244615989056 * q^51 - 5418992932208438205367792844823104431376197758802798107419957407784673910371822411932948480000 * q^52 + 9079308927321999351839177242746605854068388719924761670955991989783550469317936688082585930800 * q^53 - 24658507391097864427096370814937103472102040716547930307285838917927527638460695296874932751360 * q^54 + 118053680695881329185791540339622577195944539453849780739010333239182345152398471707806930760000 * q^55 - 201389106942279308288684434910785164662432037404781190144927582600705075235687388648357243125760 * q^56 + 226496945243108169507552544266677467884770074749629615006273688546254129496817350185452963651200 * q^57 - 2256052219534551389222024892508180423211025192914838983567709038409124940298945339969797987462400 * q^58 + 4201127473917559295037000225082981757247285086029974371230017377519538448027563747794558119713120 * q^59 + 15216716099557435608186566564337243721720353898331991157134416546559198037722222436035882885120000 * q^60 - 30174048445162611506034669407223089181051188758336573543308996493766034896596718300335923046430864 * q^61 - 101544378414770749846552697740777177239249497144967223452446029336671969269242448735950839304089600 * q^62 + 14962713033462753217361258544731526063207174198501064720440567489611717321152011844939244550427200 * q^63 + 350038493426472551390597880934195636388642189179841132000343481745073872195685178531480362020765696 * q^64 + 476042359995918992070699407122502192834702528804977370861576537263180680689143678390528307394660000 * q^65 - 3275457019157048603844818296003073802975658177120439799661182596542152337047019411219264546535589888 * q^66 - 2436592395324825448922436507298035360575674608488356192165065318580447361065445345719842978744898400 * q^67 - 22959577515788229863200422300261772167503744576389306175032085019828406207819090307551668913740595200 * q^68 + 20962513668346194921311473125160506340730960425003577830665711051634607002491986052437616343941489408 * q^69 - 38525614227951931001890316995983503763039503305975313750394662544984531605107874814848981273114880000 * q^70 - 182573264747524893462812402066757238991600980622231780705554761994960061464852147866759574299425367744 * q^71 - 937013521429830591768584754113763645664639906707863675451385694160469158557397360724539243386123059200 * q^72 - 992896003296363120918893380101417451599330843653017480857467556556562812303212272149043323072822439600 * q^73 - 1316746856327833419755644274540778481224231099510738713247508136902506806815717963522494407938546706688 * q^74 - 5871153288989297422411624806238187142192319563981336377889812488967662534076652985829089331258062500000 * q^75 - 23122551287666805941113536895845604280282190834103625501792190953367813062086656110687054676514749317120 * q^76 - 44146648850167699533016381157041098991672229312739789979368878215748452932712438044537666517717336608000 * q^77 - 74892005734867915768666768757796138875218855701976264642428162201719215233844576875406596388579804800000 * q^78 - 90877532388837507952377455262957690392004628366214899622576763930269368002866396444184811504470015827840 * q^79 - 537781290078408386666779886550832547957426185756793627297710378503553917482370710673024120741030789120000 * q^80 - 646040908793719449537213596253179795437117284606067679926187088540718516170416551690117712718559479920952 * q^81 - 1848162147553486548774628152888041182300793513808419102386749930544002262019111364366904880902061490681600 * q^82 - 866870614432750569174068646397256005138067253779508313470225924424638854266524026533083951694014356632800 * q^83 - 5840321795963005263777537308314418455056100956933759881092476300148871178382910044395005678085199546810368 * q^84 - 4668598916513761978133063620912572637580033499314634770309162489375519884024385880981753435084614859780000 * q^85 - 11688849548141363142089712396810850759020238587238805174946214292159714105146960272302323952195024989223424 * q^86 - 14581012249541375875764697103578340512244662623918147927221635902236243713987632388375578563817763114939200 * q^87 + 1530700112628746576163110294213004687459510268085538799651168686191357904989458023327058330803008647987200 * q^88 + 5370705282028265416504724158890178832899726253313779513986675059327392734022379735004069389198976135292880 * q^89 + 161603588167186166620406432595952865977969553485604382571187217963936716570564141726485419061308378075360000 * q^90 + 194491542286867118776437353517384882722616087297518094870786488241189494865282342165823695439370137913188736 * q^91 + 396302396563700359070027419943848305453145578954245792583330941741389770954106976666840341236078014314905600 * q^92 + 568179503361190024971076757263143967044040944520818668848960482931727310093723555328260563778420711013401600 * q^93 + 2479261213469097720755806625234954860838342725140724073489565122893996978512713040202033247954948169489487872 * q^94 + 3756267234494004771512604096671502522809843506715611046331612224428460858882412872485716488615235385073400000 * q^95 + 6137029402133719259406354903032524770352961857248155285728041689493176172684541150438338362553846429716054016 * q^96 + 3101905862702772302621994244705111813594597058738421633214535517860020385681724882654741053598909419139696400 * q^97 + 1265481578258615993478779535911065302494358871538528748084590996688739571409881009859314203275359668334966400 * q^98 + 719245389651015996203722525987404961611392270203442708727501943323361320310359905092561649275451940844703328 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.87423e16	1.12820	0.564100	−	0.825706i	$-0.309223\pi$
$2$	2.87423e16	1.12820	0.564100	+	0.825706i	$0.309223\pi$
$3$	−1.13913e26	−1.13101	−0.565503	−	0.824746i	$-0.691318\pi$
$3$	−1.13913e26	−1.13101	−0.565503	+	0.824746i	$0.691318\pi$
$4$	1.77081e32	0.272837
$5$	7.39260e37	0.595569	0.297784	−	0.954633i	$-0.403752\pi$
$5$	7.39260e37	0.595569	0.297784	+	0.954633i	$0.403752\pi$
$6$	−3.27412e42	−1.27600
$7$	4.38791e45	0.384074	0.192037	−	0.981388i	$-0.438491\pi$
$7$	4.38791e45	0.384074	0.192037	+	0.981388i	$0.438491\pi$
$8$	−1.35651e49	−0.820386
$9$	2.83200e51	0.279175
$10$	2.12480e54	0.671921
$11$	−7.83713e55	−0.137485	−0.0687425	−	0.997634i	$-0.521899\pi$
$11$	−7.83713e55	−0.137485	−0.0687425	+	0.997634i	$0.521899\pi$
$12$	−2.01719e58	−0.308581
$13$	8.60718e60	1.67860	0.839302	−	0.543666i	$-0.182964\pi$
$13$	8.60718e60	1.67860	0.839302	+	0.543666i	$0.182964\pi$
$14$	1.26119e62	0.433312
$15$	−8.42113e63	−0.673592
$16$	−5.04824e65	−1.19840
$17$	2.34591e66	0.204572	0.102286	−	0.994755i	$-0.467384\pi$
$17$	2.34591e66	0.204572	0.102286	+	0.994755i	$0.467384\pi$
$18$	8.13980e67	0.314965
$19$	−2.47996e69	−0.503934	−0.251967	−	0.967736i	$-0.581077\pi$
$19$	−2.47996e69	−0.503934	−0.251967	+	0.967736i	$0.581077\pi$
$20$	1.30909e70	0.162493
$21$	−4.99840e71	−0.434390
$22$	−2.25257e72	−0.155111
$23$	1.12887e74	0.689411	0.344706	−	0.938711i	$-0.387979\pi$
$23$	1.12887e74	0.689411	0.344706	+	0.938711i	$0.387979\pi$
$24$	1.54524e75	0.927861
$25$	−9.94238e75	−0.645298
$26$	2.47390e77	1.89380
$27$	8.32952e77	0.815258
$28$	7.77018e77	0.104790
$29$	6.35552e79	1.26608	0.633039	−	0.774120i	$-0.281807\pi$
$29$	6.35552e79	1.26608	0.633039	+	0.774120i	$0.281807\pi$
$30$	−2.42043e80	−0.759947
$31$	−1.95922e81	−1.03008	−0.515039	−	0.857167i	$-0.672223\pi$
$31$	−1.95922e81	−1.03008	−0.515039	+	0.857167i	$0.672223\pi$
$32$	−5.70554e81	−0.531647
$33$	8.92751e81	0.155496
$34$	6.74269e82	0.230798
$35$	3.24381e83	0.228742
$36$	5.01494e83	0.0761692
$37$	−4.05048e85	−1.38201	−0.691007	−	0.722848i	$-0.742833\pi$
$37$	−4.05048e85	−1.38201	−0.691007	+	0.722848i	$0.742833\pi$
$38$	−7.12798e85	−0.568539
$39$	−9.80469e86	−1.89851
$40$	−1.00281e87	−0.488596
$41$	−4.51771e86	−0.0573058	−0.0286529	−	0.999589i	$-0.509122\pi$
$41$	−4.51771e86	−0.0573058	−0.0286529	+	0.999589i	$0.509122\pi$
$42$	−1.43665e88	−0.490079
$43$	−1.62041e89	−1.53318	−0.766592	−	0.642134i	$-0.778049\pi$
$43$	−1.62041e89	−1.53318	−0.766592	+	0.642134i	$0.778049\pi$
$44$	−1.38781e88	−0.0375110
$45$	2.09358e89	0.166268
$46$	3.24464e90	0.777794
$47$	1.71486e91	1.27320	0.636599	−	0.771195i	$-0.280341\pi$
$47$	1.71486e91	1.27320	0.636599	+	0.771195i	$0.280341\pi$
$48$	5.75060e91	1.35539
$49$	−1.11269e92	−0.852487
$50$	−2.85767e92	−0.728025
$51$	−2.67230e92	−0.231372
$52$	1.52417e93	0.457985
$53$	−1.69761e94	−1.80636	−0.903179	−	0.429264i	$-0.858773\pi$
$53$	−1.69761e94	−1.80636	−0.903179	+	0.429264i	$0.858773\pi$
$54$	2.39409e94	0.919775
$55$	−5.79368e93	−0.0818818
$56$	−5.95224e94	−0.315089
$57$	2.82500e95	0.569953
$58$	1.82672e96	1.42839
$59$	−3.70093e95	−0.113992	−0.0569962	−	0.998374i	$-0.518152\pi$
$59$	−3.70093e95	−0.113992	−0.0569962	+	0.998374i	$0.518152\pi$
$60$	−1.49123e96	−0.183781
$61$	−2.20654e97	−1.10468	−0.552338	−	0.833620i	$-0.686264\pi$
$61$	−2.20654e97	−1.10468	−0.552338	+	0.833620i	$0.686264\pi$
$62$	−5.63124e97	−1.16214
$63$	1.24266e97	0.107224
$64$	1.63659e98	0.598593
$65$	6.36294e98	0.999724
$66$	2.56597e98	0.175431
$67$	−1.91653e99	−0.577348	−0.288674	−	0.957427i	$-0.593214\pi$
$67$	−1.91653e99	−0.577348	−0.288674	+	0.957427i	$0.593214\pi$
$68$	4.15418e98	0.0558148
$69$	−1.28593e100	−0.779728
$70$	9.32344e99	0.258067
$71$	−1.02494e101	−1.30954	−0.654771	−	0.755828i	$-0.727235\pi$
$71$	−1.02494e101	−1.30954	−0.654771	+	0.755828i	$0.727235\pi$
$72$	−3.84163e100	−0.229031
$73$	8.76953e100	0.246536	0.123268	−	0.992373i	$-0.460663\pi$
$73$	8.76953e100	0.246536	0.123268	+	0.992373i	$0.460663\pi$
$74$	−1.16420e102	−1.55919
$75$	1.13257e102	0.729835
$76$	−4.39155e101	−0.137492
$77$	−3.43886e101	−0.0528044
$78$	−2.81809e103	−2.14190
$79$	−4.80871e103	−1.82537	−0.912687	−	0.408659i	$-0.865997\pi$
$79$	−4.80871e103	−1.82537	−0.912687	+	0.408659i	$0.865997\pi$
$80$	−3.73196e103	−0.713728
$81$	−1.23612e104	−1.20124
$82$	−1.29849e103	−0.0646524
$83$	−1.49463e104	−0.384394	−0.192197	−	0.981356i	$-0.561561\pi$
$83$	−1.49463e104	−0.384394	−0.192197	+	0.981356i	$0.561561\pi$
$84$	−8.85124e103	−0.118518
$85$	1.73424e104	0.121837
$86$	−4.65743e105	−1.72974
$87$	−7.23977e105	−1.43194
$88$	1.06311e105	0.112791
$89$	1.76822e106	1.01340	0.506699	−	0.862123i	$-0.330866\pi$
$89$	1.76822e106	1.01340	0.506699	+	0.862123i	$0.330866\pi$
$90$	6.01743e105	0.187583
$91$	3.77675e106	0.644708
$92$	1.99903e106	0.188097
$93$	2.23180e107	1.16502
$94$	4.92891e107	1.43642
$95$	−1.83334e107	−0.300128
$96$	6.49936e107	0.601296
$97$	1.33463e108	0.701941	0.350970	−	0.936387i	$-0.385852\pi$
$97$	1.33463e108	0.701941	0.350970	+	0.936387i	$0.385852\pi$
$98$	−3.19813e108	−0.961777
$99$	−2.21947e107	−0.0383823
$100$	−1.76061e108	−0.176061
$101$	2.22296e109	1.29246	0.646229	−	0.763144i	$-0.276345\pi$
$101$	2.22296e109	1.29246	0.646229	+	0.763144i	$0.276345\pi$
$102$	−7.68080e108	−0.261034
$103$	−2.88859e109	−0.576842	−0.288421	−	0.957504i	$-0.593130\pi$
$103$	−2.88859e109	−0.576842	−0.288421	+	0.957504i	$0.593130\pi$
$104$	−1.16757e110	−1.37710
$105$	−3.69512e109	−0.258709
$106$	−4.87933e110	−2.03793
$107$	−1.79463e110	−0.449324	−0.224662	−	0.974437i	$-0.572128\pi$
$107$	−1.79463e110	−0.449324	−0.224662	+	0.974437i	$0.572128\pi$
$108$	1.47500e110	0.222433
$109$	1.45003e111	1.32322	0.661611	−	0.749847i	$-0.269873\pi$
$109$	1.45003e111	1.32322	0.661611	+	0.749847i	$0.269873\pi$
$110$	−1.66523e110	−0.0923792
$111$	4.61402e111	1.56307
$112$	−2.21512e111	−0.460273
$113$	−2.10067e111	−0.268894	−0.134447	−	0.990921i	$-0.542926\pi$
$113$	−2.10067e111	−0.268894	−0.134447	+	0.990921i	$0.542926\pi$
$114$	8.11969e111	0.643021
$115$	8.34531e111	0.410592
$116$	1.12545e112	0.345433
$117$	2.43755e112	0.468623
$118$	−1.06373e112	−0.128606
$119$	1.02937e112	0.0785707
$120$	1.14233e113	0.552605
$121$	−3.18798e113	−0.981098
$122$	−6.34209e113	−1.24630
$123$	5.14626e112	0.0648132
$124$	−3.46941e113	−0.281044
$125$	−1.87401e114	−0.979888
$126$	3.57167e113	0.120970
$127$	−8.46443e114	−1.86335	−0.931677	−	0.363289i	$-0.881654\pi$
$127$	−8.46443e114	−1.86335	−0.931677	+	0.363289i	$0.881654\pi$
$128$	8.40704e114	1.20698
$129$	1.84586e115	1.73404
$130$	1.82886e115	1.12789
$131$	4.02860e114	0.163632	0.0818161	−	0.996647i	$-0.473928\pi$
$131$	4.02860e114	0.163632	0.0818161	+	0.996647i	$0.473928\pi$
$132$	1.58090e114	0.0424252
$133$	−1.08819e115	−0.193548
$134$	−5.50853e115	−0.651365
$135$	6.15768e115	0.485542
$136$	−3.18225e115	−0.167828
$137$	2.45297e116	0.867804	0.433902	−	0.900960i	$-0.357136\pi$
$137$	2.45297e116	0.867804	0.433902	+	0.900960i	$0.357136\pi$
$138$	−3.69607e116	−0.879690
$139$	4.52903e116	0.727275	0.363638	−	0.931541i	$-0.381535\pi$
$139$	4.52903e116	0.727275	0.363638	+	0.931541i	$0.381535\pi$
$140$	5.74418e115	0.0624095
$141$	−1.95345e117	−1.44000
$142$	−2.94592e117	−1.47743
$143$	−6.74555e116	−0.230783
$144$	−1.42966e117	−0.334562
$145$	4.69839e117	0.754037
$146$	2.52056e117	0.278142
$147$	1.26750e118	0.964168
$148$	−7.17265e117	−0.377065
$149$	4.13838e118	1.50723	0.753613	−	0.657318i	$-0.228309\pi$
$149$	4.13838e118	1.50723	0.753613	+	0.657318i	$0.228309\pi$
$150$	3.25526e118	0.823401
$151$	−5.49901e118	−0.968369	−0.484185	−	0.874966i	$-0.660884\pi$
$151$	−5.49901e118	−0.968369	−0.484185	+	0.874966i	$0.660884\pi$
$152$	3.36409e118	0.413420
$153$	6.64362e117	0.0571113
$154$	−9.88407e117	−0.0595740
$155$	−1.44837e119	−0.613483
$156$	−1.73623e119	−0.517984
$157$	−2.34779e118	−0.0494456	−0.0247228	−	0.999694i	$-0.507870\pi$
$157$	−2.34779e118	−0.0494456	−0.0247228	+	0.999694i	$0.507870\pi$
$158$	−1.38213e120	−2.05939
$159$	1.93380e120	2.04300
$160$	−4.21788e119	−0.316632
$161$	4.95340e119	0.264785
$162$	−3.55290e120	−1.35524
$163$	1.91256e120	0.521662	0.260831	−	0.965384i	$-0.416003\pi$
$163$	1.91256e120	0.521662	0.260831	+	0.965384i	$0.416003\pi$
$164$	−8.00003e118	−0.0156351
$165$	6.59975e119	0.0926089
$166$	−4.29589e120	−0.433673
$167$	1.77626e121	1.29259	0.646293	−	0.763089i	$-0.276318\pi$
$167$	1.77626e121	1.29259	0.646293	+	0.763089i	$0.276318\pi$
$168$	6.78037e120	0.356367
$169$	4.77914e121	1.81771
$170$	4.98460e120	0.137456
$171$	−7.02324e120	−0.140686
$172$	−2.86945e121	−0.418310
$173$	−1.32692e122	−1.41037	−0.705185	−	0.709024i	$-0.749136\pi$
$173$	−1.32692e122	−1.41037	−0.705185	+	0.709024i	$0.749136\pi$
$174$	−2.08087e122	−1.61552
$175$	−4.36263e121	−0.247842
$176$	3.95637e121	0.164762
$177$	4.21584e121	0.128926
$178$	5.08225e122	1.14332
$179$	−4.74082e122	−0.785892	−0.392946	−	0.919561i	$-0.628544\pi$
$179$	−4.74082e122	−0.785892	−0.392946	+	0.919561i	$0.628544\pi$
$180$	3.70735e121	0.0453640
$181$	−3.61432e122	−0.326997	−0.163499	−	0.986544i	$-0.552278\pi$
$181$	−3.61432e122	−0.326997	−0.163499	+	0.986544i	$0.552278\pi$
$182$	1.08553e123	0.727360
$183$	2.51353e123	1.24940
$184$	−1.53133e123	−0.565583
$185$	−2.99436e123	−0.823085
$186$	6.41471e123	1.31438
$187$	−1.83852e122	−0.0281256
$188$	3.03670e123	0.347376
$189$	3.65492e123	0.313119
$190$	−5.26943e123	−0.338604
$191$	−1.05767e124	−0.510542	−0.255271	−	0.966869i	$-0.582165\pi$
$191$	−1.05767e124	−0.510542	−0.255271	+	0.966869i	$0.582165\pi$
$192$	−1.86429e124	−0.677012
$193$	−1.39311e124	−0.381165	−0.190583	−	0.981671i	$-0.561038\pi$
$193$	−1.39311e124	−0.381165	−0.190583	+	0.981671i	$0.561038\pi$
$194$	3.83602e124	0.791930
$195$	−7.24822e124	−1.13069
$196$	−1.97037e124	−0.232590
$197$	−1.04161e125	−0.931740	−0.465870	−	0.884853i	$-0.654259\pi$
$197$	−1.04161e125	−0.931740	−0.465870	+	0.884853i	$0.654259\pi$
$198$	−6.37927e123	−0.0433030
$199$	1.35105e125	0.696915	0.348457	−	0.937325i	$-0.386706\pi$
$199$	1.35105e125	0.696915	0.348457	+	0.937325i	$0.386706\pi$
$200$	1.34869e125	0.529393
$201$	2.18317e125	0.652984
$202$	6.38928e125	1.45815
$203$	2.78875e125	0.486267
$204$	−4.73215e124	−0.0631269
$205$	−3.33976e124	−0.0341295
$206$	−8.30247e125	−0.650794
$207$	3.19697e125	0.192466
$208$	−4.34511e126	−2.01163
$209$	1.94358e125	0.0692834
$210$	−1.06206e126	−0.291876
$211$	3.35711e126	0.712151	0.356076	−	0.934457i	$-0.384115\pi$
$211$	3.35711e126	0.712151	0.356076	+	0.934457i	$0.384115\pi$
$212$	−3.00616e126	−0.492842
$213$	1.16754e127	1.48110
$214$	−5.15819e126	−0.506928
$215$	−1.19791e127	−0.913117
$216$	−1.12991e127	−0.668826
$217$	−8.59687e126	−0.395626
$218$	4.16772e127	1.49286
$219$	−9.98963e126	−0.278834
$220$	−1.02595e126	−0.0223404
$221$	2.01917e127	0.343395
$222$	1.32618e128	1.76345
$223$	4.21705e127	0.438928	0.219464	−	0.975621i	$-0.429569\pi$
$223$	4.21705e127	0.438928	0.219464	+	0.975621i	$0.429569\pi$
$224$	−2.50354e127	−0.204192
$225$	−2.81568e127	−0.180151
$226$	−6.03779e127	−0.303367
$227$	−3.57895e128	−1.41367	−0.706833	−	0.707380i	$-0.749877\pi$
$227$	−3.57895e128	−1.41367	−0.706833	+	0.707380i	$0.749877\pi$
$228$	5.00255e127	0.155504
$229$	−3.50202e128	−0.857599	−0.428800	−	0.903400i	$-0.641063\pi$
$229$	−3.50202e128	−0.857599	−0.428800	+	0.903400i	$0.641063\pi$
$230$	2.39863e128	0.463230
$231$	3.91731e127	0.0597221
$232$	−8.62132e128	−1.03867
$233$	−9.24813e128	−0.881366	−0.440683	−	0.897663i	$-0.645264\pi$
$233$	−9.24813e128	−0.881366	−0.440683	+	0.897663i	$0.645264\pi$
$234$	7.00607e128	0.528701
$235$	1.26773e129	0.758278
$236$	−6.55366e127	−0.0311014
$237$	5.47774e129	2.06451
$238$	2.95863e128	0.0886435
$239$	−2.52167e129	−0.601177	−0.300589	−	0.953754i	$-0.597183\pi$
$239$	−2.52167e129	−0.601177	−0.300589	+	0.953754i	$0.597183\pi$
$240$	4.25119e129	0.807231
$241$	−1.25256e128	−0.0189614	−0.00948069	−	0.999955i	$-0.503018\pi$
$241$	−1.25256e128	−0.0189614	−0.00948069	+	0.999955i	$0.503018\pi$
$242$	−9.16297e129	−1.10688
$243$	5.63144e129	0.543347
$244$	−3.90737e129	−0.301397
$245$	−8.22568e129	−0.507715
$246$	1.47915e129	0.0731223
$247$	−2.13455e130	−0.845906
$248$	2.65769e130	0.845061
$249$	1.70257e130	0.434752
$250$	−5.38634e130	−1.10551
$251$	2.51651e130	0.415509	0.207754	−	0.978181i	$-0.433385\pi$
$251$	2.51651e130	0.415509	0.207754	+	0.978181i	$0.433385\pi$
$252$	2.20051e129	0.0292546
$253$	−8.84713e129	−0.0947837
$254$	−2.43287e131	−2.10224
$255$	−1.97553e130	−0.137798
$256$	1.35417e131	0.763123
$257$	3.47768e131	1.58466	0.792328	−	0.610096i	$-0.208869\pi$
$257$	3.47768e131	1.58466	0.792328	+	0.610096i	$0.208869\pi$
$258$	5.30542e131	1.95635
$259$	−1.77732e131	−0.530796
$260$	1.12676e131	0.272762
$261$	1.79988e131	0.353457
$262$	1.15791e131	0.184610
$263$	−7.80780e131	−1.01144	−0.505721	−	0.862697i	$-0.668773\pi$
$263$	−7.80780e131	−1.01144	−0.505721	+	0.862697i	$0.668773\pi$
$264$	−1.21102e131	−0.127567
$265$	−1.25498e132	−1.07581
$266$	−3.12769e131	−0.218361
$267$	−2.01423e132	−1.14616
$268$	−3.39381e131	−0.157522
$269$	6.37919e131	0.241694	0.120847	−	0.992671i	$-0.461439\pi$
$269$	6.37919e131	0.241694	0.120847	+	0.992671i	$0.461439\pi$
$270$	1.76986e132	0.547789
$271$	2.82269e132	0.714227	0.357113	−	0.934061i	$-0.383761\pi$
$271$	2.82269e132	0.714227	0.357113	+	0.934061i	$0.383761\pi$
$272$	−1.18427e132	−0.245158
$273$	−4.30221e132	−0.729168
$274$	7.05040e132	0.979058
$275$	7.79197e131	0.0887188
$276$	−2.27715e132	−0.212739
$277$	8.94430e132	0.686118	0.343059	−	0.939314i	$-0.388537\pi$
$277$	8.94430e132	0.686118	0.343059	+	0.939314i	$0.388537\pi$
$278$	1.30175e133	0.820512
$279$	−5.54850e132	−0.287572
$280$	−4.40025e132	−0.187657
$281$	2.30782e133	0.810416	0.405208	−	0.914224i	$-0.367199\pi$
$281$	2.30782e133	0.810416	0.405208	+	0.914224i	$0.367199\pi$
$282$	−5.61467e133	−1.62460
$283$	1.82992e133	0.436589	0.218294	−	0.975883i	$-0.429951\pi$
$283$	1.82992e133	0.436589	0.218294	+	0.975883i	$0.429951\pi$
$284$	−1.81498e133	−0.357292
$285$	2.08841e133	0.339446
$286$	−1.93883e133	−0.260369
$287$	−1.98233e132	−0.0220096
$288$	−1.61581e133	−0.148422
$289$	−1.25999e134	−0.958150
$290$	1.35042e134	0.850705
$291$	−1.52031e134	−0.793899
$292$	1.55292e133	0.0672642
$293$	−3.87690e134	−1.39380	−0.696898	−	0.717170i	$-0.745437\pi$
$293$	−3.87690e134	−1.39380	−0.696898	+	0.717170i	$0.745437\pi$
$294$	3.64308e134	1.08778
$295$	−2.73595e133	−0.0678904
$296$	5.49451e134	1.13378
$297$	−6.52795e133	−0.112086
$298$	1.18946e135	1.70045
$299$	9.71642e134	1.15725
$300$	2.00557e134	0.199126
$301$	−7.11022e134	−0.588856
$302$	−1.58054e135	−1.09251
$303$	−2.53224e135	−1.46178
$304$	1.25194e135	0.603913
$305$	−1.63120e135	−0.657911
$306$	1.90953e134	0.0644330
$307$	−4.93886e135	−1.39504	−0.697518	−	0.716567i	$-0.745712\pi$
$307$	−4.93886e135	−1.39504	−0.697518	+	0.716567i	$0.745712\pi$
$308$	−6.08959e133	−0.0144070
$309$	3.29048e135	0.652412
$310$	−4.16295e135	−0.692132
$311$	7.02534e135	0.980000	0.490000	−	0.871722i	$-0.336997\pi$
$311$	7.02534e135	0.980000	0.490000	+	0.871722i	$0.336997\pi$
$312$	1.33001e136	1.55751
$313$	−3.34491e135	−0.329017	−0.164508	−	0.986376i	$-0.552604\pi$
$313$	−3.34491e135	−0.329017	−0.164508	+	0.986376i	$0.552604\pi$
$314$	−6.74807e134	−0.0557845
$315$	9.18645e134	0.0638591
$316$	−8.51533e135	−0.498030
$317$	−3.53839e136	−1.74211	−0.871056	−	0.491185i	$-0.836564\pi$
$317$	−3.53839e136	−1.74211	−0.871056	+	0.491185i	$0.836564\pi$
$318$	5.55819e136	2.30492
$319$	−4.98090e135	−0.174067
$320$	1.20987e136	0.356503
$321$	2.04432e136	0.508189
$322$	1.42372e136	0.298730
$323$	−5.81778e135	−0.103091
$324$	−2.18895e136	−0.327742
$325$	−8.55759e136	−1.08320
$326$	5.49712e136	0.588540
$327$	−1.65177e137	−1.49657
$328$	6.12831e135	0.0470128
$329$	7.52467e136	0.489002
$330$	1.89692e136	0.104481
$331$	−2.38134e137	−1.11223	−0.556117	−	0.831104i	$-0.687709\pi$
$331$	−2.38134e137	−1.11223	−0.556117	+	0.831104i	$0.687709\pi$
$332$	−2.64670e136	−0.104877
$333$	−1.14709e137	−0.385823
$334$	5.10538e137	1.45830
$335$	−1.41681e137	−0.343851
$336$	2.52331e137	0.520571
$337$	−3.62480e137	−0.635995	−0.317998	−	0.948091i	$-0.603010\pi$
$337$	−3.62480e137	−0.635995	−0.317998	+	0.948091i	$0.603010\pi$
$338$	1.37363e138	2.05074
$339$	2.39293e137	0.304121
$340$	3.07102e136	0.0332416
$341$	1.53546e137	0.141620
$342$	−2.01864e137	−0.158722
$343$	−1.06096e138	−0.711492
$344$	2.19810e138	1.25780
$345$	−9.50640e137	−0.464382
$346$	−3.81388e138	−1.59118
$347$	−4.15762e138	−1.48214	−0.741068	−	0.671430i	$-0.765680\pi$
$347$	−4.15762e138	−1.48214	−0.741068	+	0.671430i	$0.765680\pi$
$348$	−1.28203e138	−0.390687
$349$	−5.03016e137	−0.131098	−0.0655490	−	0.997849i	$-0.520880\pi$
$349$	−5.03016e137	−0.131098	−0.0655490	+	0.997849i	$0.520880\pi$
$350$	−1.25392e138	−0.279615
$351$	7.16937e138	1.36849
$352$	4.47151e137	0.0730935
$353$	1.04144e139	1.45852	0.729260	−	0.684237i	$-0.239865\pi$
$353$	1.04144e139	1.45852	0.729260	+	0.684237i	$0.239865\pi$
$354$	1.21173e138	0.145455
$355$	−7.57699e138	−0.779922
$356$	3.13118e138	0.276492
$357$	−1.17258e138	−0.0888639
$358$	−1.36262e139	−0.886644
$359$	2.66308e139	1.48846	0.744230	−	0.667924i	$-0.232817\pi$
$359$	2.66308e139	1.48846	0.744230	+	0.667924i	$0.232817\pi$
$360$	−2.83996e138	−0.136404
$361$	−1.80680e139	−0.746050
$362$	−1.03884e139	−0.368918
$363$	3.63152e139	1.10963
$364$	6.68793e138	0.175900
$365$	6.48296e138	0.146829
$366$	7.22446e139	1.40957
$367$	−6.34287e139	−1.06656	−0.533280	−	0.845939i	$-0.679041\pi$
$367$	−6.34287e139	−1.06656	−0.533280	+	0.845939i	$0.679041\pi$
$368$	−5.69882e139	−0.826188
$369$	−1.27941e138	−0.0159983
$370$	−8.60647e139	−0.928605
$371$	−7.44898e139	−0.693775
$372$	3.95211e139	0.317862
$373$	−1.85495e140	−1.28885	−0.644424	−	0.764668i	$-0.722903\pi$
$373$	−1.85495e140	−1.28885	−0.644424	+	0.764668i	$0.722903\pi$
$374$	−5.28433e138	−0.0317313
$375$	2.13474e140	1.10826
$376$	−2.32623e140	−1.04451
$377$	5.47031e140	2.12524
$378$	1.05051e140	0.353261
$379$	−1.77264e140	−0.516160	−0.258080	−	0.966124i	$-0.583090\pi$
$379$	−1.77264e140	−0.516160	−0.258080	+	0.966124i	$0.583090\pi$
$380$	−3.24650e139	−0.0818860
$381$	9.64209e140	2.10746
$382$	−3.03999e140	−0.575994
$383$	7.54232e140	1.23929	0.619643	−	0.784884i	$-0.287277\pi$
$383$	7.54232e140	1.23929	0.619643	+	0.784884i	$0.287277\pi$
$384$	−9.57671e140	−1.36510
$385$	−2.54221e139	−0.0314487
$386$	−4.00413e140	−0.430031
$387$	−4.58900e140	−0.428026
$388$	2.36338e140	0.191516
$389$	−2.28308e140	−0.160793	−0.0803967	−	0.996763i	$-0.525619\pi$
$389$	−2.28308e140	−0.160793	−0.0803967	+	0.996763i	$0.525619\pi$
$390$	−2.08330e141	−1.27565
$391$	2.64824e140	0.141034
$392$	1.50937e141	0.699368
$393$	−4.58910e140	−0.185069
$394$	−2.99382e141	−1.05119
$395$	−3.55489e141	−1.08714
$396$	−3.93027e139	−0.0104721
$397$	8.23623e141	1.91270	0.956348	−	0.292230i	$-0.0943972\pi$
$397$	8.23623e141	1.91270	0.956348	+	0.292230i	$0.0943972\pi$
$398$	3.88323e141	0.786260
$399$	1.23958e141	0.218904
$400$	5.01915e141	0.773323
$401$	−2.90316e141	−0.390394	−0.195197	−	0.980764i	$-0.562535\pi$
$401$	−2.90316e141	−0.390394	−0.195197	+	0.980764i	$0.562535\pi$
$402$	6.27493e141	0.736698
$403$	−1.68633e142	−1.72909
$404$	3.93644e141	0.352630
$405$	−9.13817e141	−0.715419
$406$	8.01550e141	0.548607
$407$	3.17441e141	0.190006
$408$	3.62500e141	0.189814
$409$	2.39609e142	1.09795	0.548974	−	0.835839i	$-0.315018\pi$
$409$	2.39609e142	1.09795	0.548974	+	0.835839i	$0.315018\pi$
$410$	−9.59924e140	−0.0385050
$411$	−2.79425e142	−0.981492
$412$	−5.11516e141	−0.157384
$413$	−1.62394e141	−0.0437815
$414$	9.18881e141	0.217140
$415$	−1.10492e142	−0.228933
$416$	−4.91086e142	−0.892424
$417$	−5.15916e142	−0.822552
$418$	5.58629e141	0.0781656
$419$	−1.06566e143	−1.30905	−0.654523	−	0.756042i	$-0.727131\pi$
$419$	−1.06566e143	−1.30905	−0.654523	+	0.756042i	$0.727131\pi$
$420$	−6.54337e141	−0.0705855
$421$	1.18964e143	1.12730	0.563652	−	0.826012i	$-0.309396\pi$
$421$	1.18964e143	1.12730	0.563652	+	0.826012i	$0.309396\pi$
$422$	9.64911e142	0.803450
$423$	4.85649e142	0.355445
$424$	2.30283e143	1.48191
$425$	−2.33240e142	−0.132010
$426$	3.35578e143	1.67098
$427$	−9.68209e142	−0.424277
$428$	−3.17796e142	−0.122592
$429$	7.68406e142	0.261017
$430$	−3.44305e143	−1.03018
$431$	−4.95283e143	−1.30570	−0.652848	−	0.757489i	$-0.726426\pi$
$431$	−4.95283e143	−1.30570	−0.652848	+	0.757489i	$0.726426\pi$
$432$	−4.20494e143	−0.977003
$433$	7.17055e143	1.46880	0.734399	−	0.678718i	$-0.237464\pi$
$433$	7.17055e143	1.46880	0.734399	+	0.678718i	$0.237464\pi$
$434$	−2.47094e143	−0.446346
$435$	−5.35207e143	−0.852820
$436$	2.56773e143	0.361024
$437$	−2.79956e143	−0.347418
$438$	−2.87125e143	−0.314580
$439$	2.59904e143	0.251476	0.125738	−	0.992063i	$-0.459870\pi$
$439$	2.59904e143	0.251476	0.125738	+	0.992063i	$0.459870\pi$
$440$	7.85917e142	0.0671747
$441$	−3.15113e143	−0.237993
$442$	5.80356e143	0.387419
$443$	2.63477e143	0.155503	0.0777516	−	0.996973i	$-0.475226\pi$
$443$	2.63477e143	0.155503	0.0777516	+	0.996973i	$0.475226\pi$
$444$	8.17058e143	0.426463
$445$	1.30717e144	0.603548
$446$	1.21207e144	0.495199
$447$	−4.71415e144	−1.70468
$448$	7.18121e143	0.229904
$449$	5.37943e144	1.52514	0.762572	−	0.646903i	$-0.223936\pi$
$449$	5.37943e144	1.52514	0.762572	+	0.646903i	$0.223936\pi$
$450$	−8.09290e143	−0.203246
$451$	3.54059e142	0.00787869
$452$	−3.71989e143	−0.0733644
$453$	6.26409e144	1.09523
$454$	−1.02867e145	−1.59490
$455$	2.79200e144	0.383968
$456$	−3.83213e144	−0.467581
$457$	3.21591e144	0.348234	0.174117	−	0.984725i	$-0.444293\pi$
$457$	3.21591e144	0.348234	0.174117	+	0.984725i	$0.444293\pi$
$458$	−1.00656e145	−0.967544
$459$	1.95403e144	0.166779
$460$	1.47780e144	0.112025
$461$	7.19117e144	0.484283	0.242142	−	0.970241i	$-0.422150\pi$
$461$	7.19117e144	0.484283	0.242142	+	0.970241i	$0.422150\pi$
$462$	1.12592e144	0.0673785
$463$	−1.73003e145	−0.920215	−0.460107	−	0.887863i	$-0.652189\pi$
$463$	−1.73003e145	−0.920215	−0.460107	+	0.887863i	$0.652189\pi$
$464$	−3.20842e145	−1.51726
$465$	1.64988e145	0.693853
$466$	−2.65812e145	−0.994358
$467$	4.39768e145	1.46371	0.731853	−	0.681463i	$-0.238656\pi$
$467$	4.39768e145	1.46371	0.731853	+	0.681463i	$0.238656\pi$
$468$	4.31645e144	0.127858
$469$	−8.40955e144	−0.221744
$470$	3.64374e145	0.855489
$471$	2.67443e144	0.0559232
$472$	5.02034e144	0.0935178
$473$	1.26994e145	0.210790
$474$	1.57443e146	2.32918
$475$	2.46567e145	0.325187
$476$	1.82282e144	0.0214370
$477$	−4.80763e145	−0.504289
$478$	−7.24785e145	−0.678249
$479$	−1.69583e146	−1.41611	−0.708055	−	0.706158i	$-0.750427\pi$
$479$	−1.69583e146	−1.41611	−0.708055	+	0.706158i	$0.750427\pi$
$480$	4.80472e145	0.358113
$481$	−3.48632e146	−2.31985
$482$	−3.60014e144	−0.0213922
$483$	−5.64256e145	−0.299473
$484$	−5.64531e145	−0.267680
$485$	9.86636e145	0.418054
$486$	1.61860e146	0.613005
$487$	2.62234e146	0.887892	0.443946	−	0.896053i	$-0.353578\pi$
$487$	2.62234e146	0.887892	0.443946	+	0.896053i	$0.353578\pi$
$488$	2.99318e146	0.906261
$489$	−2.17865e146	−0.590003
$490$	−2.36425e146	−0.572804
$491$	3.75103e146	0.813221	0.406611	−	0.913602i	$-0.366711\pi$
$491$	3.75103e146	0.813221	0.406611	+	0.913602i	$0.366711\pi$
$492$	9.11307e144	0.0176834
$493$	1.49095e146	0.259004
$494$	−6.13518e146	−0.954351
$495$	−1.64077e145	−0.0228593
$496$	9.89059e146	1.23444
$497$	−4.49736e146	−0.502961
$498$	4.89358e146	0.490487
$499$	5.00428e146	0.449637	0.224819	−	0.974401i	$-0.427821\pi$
$499$	5.00428e146	0.449637	0.224819	+	0.974401i	$0.427821\pi$
$500$	−3.31853e146	−0.267350
$501$	−2.02339e147	−1.46192
$502$	7.23301e146	0.468777
$503$	2.00763e147	1.16742	0.583711	−	0.811962i	$-0.301600\pi$
$503$	2.00763e147	1.16742	0.583711	+	0.811962i	$0.301600\pi$
$504$	−1.68567e146	−0.0879648
$505$	1.64334e147	0.769747
$506$	−2.54287e146	−0.106935
$507$	−5.44406e147	−2.05584
$508$	−1.49889e147	−0.508392
$509$	−1.21015e147	−0.368741	−0.184370	−	0.982857i	$-0.559025\pi$
$509$	−1.21015e147	−0.368741	−0.184370	+	0.982857i	$0.559025\pi$
$510$	−5.67811e146	−0.155464
$511$	3.84799e146	0.0946880
$512$	−1.56430e147	−0.346024
$513$	−2.06569e147	−0.410836
$514$	9.99566e147	1.78781
$515$	−2.13542e147	−0.343549
$516$	3.26867e147	0.473111
$517$	−1.34396e147	−0.175046
$518$	−5.10841e147	−0.598844
$519$	1.51154e148	1.59514
$520$	−8.63138e147	−0.820159
$521$	7.86957e146	0.0673434	0.0336717	−	0.999433i	$-0.489280\pi$
$521$	7.86957e146	0.0673434	0.0336717	+	0.999433i	$0.489280\pi$
$522$	5.17327e147	0.398770
$523$	2.78252e148	1.93240	0.966199	−	0.257798i	$-0.0829968\pi$
$523$	2.78252e148	1.93240	0.966199	+	0.257798i	$0.0829968\pi$
$524$	7.13390e146	0.0446449
$525$	4.96960e147	0.280311
$526$	−2.24414e148	−1.14111
$527$	−4.59615e147	−0.210725
$528$	−4.50682e147	−0.186346
$529$	−1.40687e148	−0.524712
$530$	−3.60709e148	−1.21373
$531$	−1.04810e147	−0.0318238
$532$	−1.92697e147	−0.0528071
$533$	−3.88847e147	−0.0961936
$534$	−5.78935e148	−1.29310
$535$	−1.32670e148	−0.267604
$536$	2.59978e148	0.473648
$537$	5.40041e148	0.888849
$538$	1.83352e148	0.272679
$539$	8.72029e147	0.117204
$540$	1.09041e148	0.132474
$541$	6.54366e148	0.718736	0.359368	−	0.933196i	$-0.382992\pi$
$541$	6.54366e148	0.718736	0.359368	+	0.933196i	$0.382992\pi$
$542$	8.11304e148	0.805791
$543$	4.11718e148	0.369836
$544$	−1.33847e148	−0.108760
$545$	1.07195e149	0.788070
$546$	−1.23655e149	−0.822648
$547$	−1.88179e149	−1.13309	−0.566543	−	0.824032i	$-0.691720\pi$
$547$	−1.88179e149	−1.13309	−0.566543	+	0.824032i	$0.691720\pi$
$548$	4.34376e148	0.236769
$549$	−6.24890e148	−0.308398
$550$	2.23959e148	0.100093
$551$	−1.57615e149	−0.638020
$552$	1.74438e149	0.639678
$553$	−2.11002e149	−0.701078
$554$	2.57080e149	0.774079
$555$	3.41096e149	0.930914
$556$	8.02007e148	0.198428
$557$	1.82969e149	0.410458	0.205229	−	0.978714i	$-0.434206\pi$
$557$	1.82969e149	0.410458	0.205229	+	0.978714i	$0.434206\pi$
$558$	−1.59476e149	−0.324439
$559$	−1.39472e150	−2.57361
$560$	−1.63755e149	−0.274124
$561$	2.09432e148	0.0318102
$562$	6.63321e149	0.914312
$563$	−6.90101e149	−0.863387	−0.431693	−	0.902020i	$-0.642084\pi$
$563$	−6.90101e149	−0.863387	−0.431693	+	0.902020i	$0.642084\pi$
$564$	−3.45920e149	−0.392884
$565$	−1.55294e149	−0.160145
$566$	5.25962e149	0.492560
$567$	−5.42400e149	−0.461363
$568$	1.39034e150	1.07433
$569$	1.82837e150	1.28365	0.641824	−	0.766852i	$-0.278178\pi$
$569$	1.82837e150	1.28365	0.641824	+	0.766852i	$0.278178\pi$
$570$	6.00256e149	0.382963
$571$	1.41475e150	0.820374	0.410187	−	0.912001i	$-0.365463\pi$
$571$	1.41475e150	0.820374	0.410187	+	0.912001i	$0.365463\pi$
$572$	−1.19451e149	−0.0629662
$573$	1.20482e150	0.577427
$574$	−5.69767e148	−0.0248313
$575$	−1.12237e150	−0.444875
$576$	4.63482e149	0.167112
$577$	−3.45161e150	−1.13224	−0.566121	−	0.824322i	$-0.691557\pi$
$577$	−3.45161e150	−1.13224	−0.566121	+	0.824322i	$0.691557\pi$
$578$	−3.62149e150	−1.08099
$579$	1.58694e150	0.431100
$580$	8.31997e149	0.205729
$581$	−6.55828e149	−0.147636
$582$	−4.36973e150	−0.895678
$583$	1.33044e150	0.248347
$584$	−1.18959e150	−0.202255
$585$	1.80198e150	0.279098
$586$	−1.11431e151	−1.57248
$587$	−1.90467e150	−0.244931	−0.122465	−	0.992473i	$-0.539080\pi$
$587$	−1.90467e150	−0.244931	−0.122465	+	0.992473i	$0.539080\pi$
$588$	2.24451e150	0.263061
$589$	4.85878e150	0.519092
$590$	−7.86374e149	−0.0765940
$591$	1.18653e151	1.05380
$592$	2.04478e151	1.65620
$593$	−6.80678e150	−0.502876	−0.251438	−	0.967873i	$-0.580903\pi$
$593$	−6.80678e150	−0.502876	−0.251438	+	0.967873i	$0.580903\pi$
$594$	−1.87628e150	−0.126455
$595$	7.60970e149	0.0467943
$596$	7.32830e150	0.411227
$597$	−1.53903e151	−0.788215
$598$	2.79272e151	1.30561
$599$	−2.85482e150	−0.121847	−0.0609237	−	0.998142i	$-0.519405\pi$
$599$	−2.85482e150	−0.121847	−0.0609237	+	0.998142i	$0.519405\pi$
$600$	−1.53634e151	−0.598747
$601$	2.00690e151	0.714276	0.357138	−	0.934052i	$-0.383753\pi$
$601$	2.00690e151	0.714276	0.357138	+	0.934052i	$0.383753\pi$
$602$	−2.04364e151	−0.664348
$603$	−5.42759e150	−0.161181
$604$	−9.73773e150	−0.264207
$605$	−2.35674e151	−0.584311
$606$	−7.27823e151	−1.64918
$607$	6.64897e151	1.37712	0.688558	−	0.725181i	$-0.258244\pi$
$607$	6.64897e151	1.37712	0.688558	+	0.725181i	$0.258244\pi$
$608$	1.41495e151	0.267915
$609$	−3.17675e151	−0.549971
$610$	−4.68845e151	−0.742256
$611$	1.47601e152	2.13720
$612$	1.17646e150	0.0155821
$613$	8.61671e150	0.104411	0.0522054	−	0.998636i	$-0.483375\pi$
$613$	8.61671e150	0.104411	0.0522054	+	0.998636i	$0.483375\pi$
$614$	−1.41954e152	−1.57388
$615$	3.80443e150	0.0386007
$616$	4.66484e150	0.0433200
$617$	−2.93727e151	−0.249691	−0.124845	−	0.992176i	$-0.539843\pi$
$617$	−2.93727e151	−0.249691	−0.124845	+	0.992176i	$0.539843\pi$
$618$	9.45759e151	0.736052
$619$	−2.59604e152	−1.85000	−0.924999	−	0.379968i	$-0.875935\pi$
$619$	−2.59604e152	−1.85000	−0.924999	+	0.379968i	$0.875935\pi$
$620$	−2.56480e151	−0.167381
$621$	9.40298e151	0.562048
$622$	2.01924e152	1.10564
$623$	7.75877e151	0.389219
$624$	4.94964e152	2.27517
$625$	1.46485e151	0.0617066
$626$	−9.61404e151	−0.371197
$627$	−2.21399e151	−0.0783600
$628$	−4.15749e150	−0.0134906
$629$	−9.50208e151	−0.282721
$630$	2.64040e151	0.0720459
$631$	−2.45044e152	−0.613259	−0.306629	−	0.951829i	$-0.599201\pi$
$631$	−2.45044e152	−0.613259	−0.306629	+	0.951829i	$0.599201\pi$
$632$	6.52305e152	1.49751
$633$	−3.82419e152	−0.805447
$634$	−1.01701e153	−1.96545
$635$	−6.25742e152	−1.10976
$636$	3.42440e152	0.557407
$637$	−9.57712e152	−1.43099
$638$	−1.43163e152	−0.196382
$639$	−2.90263e152	−0.365591
$640$	6.21499e152	0.718840
$641$	1.84101e152	0.195566	0.0977830	−	0.995208i	$-0.468825\pi$
$641$	1.84101e152	0.195566	0.0977830	+	0.995208i	$0.468825\pi$
$642$	5.87585e152	0.573339
$643$	1.87520e153	1.68093	0.840466	−	0.541864i	$-0.182281\pi$
$643$	1.87520e153	1.68093	0.840466	+	0.541864i	$0.182281\pi$
$644$	8.77155e151	0.0722431
$645$	1.36457e153	1.03274
$646$	−1.67216e152	−0.116307
$647$	−1.73800e153	−1.11114	−0.555568	−	0.831471i	$-0.687499\pi$
$647$	−1.73800e153	−1.11114	−0.555568	+	0.831471i	$0.687499\pi$
$648$	1.67681e153	0.985477
$649$	2.90047e151	0.0156723
$650$	−2.45965e153	−1.22207
$651$	9.79295e152	0.447455
$652$	3.38678e152	0.142329
$653$	4.12205e153	1.59347	0.796737	−	0.604326i	$-0.206557\pi$
$653$	4.12205e153	1.59347	0.796737	+	0.604326i	$0.206557\pi$
$654$	−4.74757e153	−1.68843
$655$	2.97818e152	0.0974542
$656$	2.28065e152	0.0686751
$657$	2.48353e152	0.0688266
$658$	2.16276e153	0.551693
$659$	−4.33211e153	−1.01729	−0.508644	−	0.860977i	$-0.669853\pi$
$659$	−4.33211e153	−1.01729	−0.508644	+	0.860977i	$0.669853\pi$
$660$	1.16869e152	0.0252671
$661$	1.44519e153	0.287704	0.143852	−	0.989599i	$-0.454051\pi$
$661$	1.44519e153	0.287704	0.143852	+	0.989599i	$0.454051\pi$
$662$	−6.84452e153	−1.25482
$663$	−2.30010e153	−0.388382
$664$	2.02747e153	0.315351
$665$	−8.04452e152	−0.115271
$666$	−3.29701e153	−0.435286
$667$	7.17458e153	0.872848
$668$	3.14543e153	0.352666
$669$	−4.80376e153	−0.496430
$670$	−4.07224e153	−0.387933
$671$	1.72929e153	0.151877
$672$	2.85186e153	0.230942
$673$	2.09954e154	1.56784	0.783922	−	0.620860i	$-0.213216\pi$
$673$	2.09954e154	1.56784	0.783922	+	0.620860i	$0.213216\pi$
$674$	−1.04185e154	−0.717531
$675$	−8.28153e153	−0.526084
$676$	8.46297e153	0.495939
$677$	−1.03285e154	−0.558410	−0.279205	−	0.960232i	$-0.590071\pi$
$677$	−1.03285e154	−0.558410	−0.279205	+	0.960232i	$0.590071\pi$
$678$	6.87783e153	0.343110
$679$	5.85623e153	0.269597
$680$	−2.35251e153	−0.0999531
$681$	4.07689e154	1.59886
$682$	4.41327e153	0.159776
$683$	−2.79528e154	−0.934323	−0.467161	−	0.884172i	$-0.654723\pi$
$683$	−2.79528e154	−0.934323	−0.467161	+	0.884172i	$0.654723\pi$
$684$	−1.24369e153	−0.0383843
$685$	1.81338e154	0.516837
$686$	−3.04944e154	−0.802706
$687$	3.98925e154	0.969950
$688$	8.18022e154	1.83736
$689$	−1.46117e155	−3.03216
$690$	−2.73236e154	−0.523916
$691$	−5.69657e154	−1.00939	−0.504696	−	0.863297i	$-0.668395\pi$
$691$	−5.69657e154	−1.00939	−0.504696	+	0.863297i	$0.668395\pi$
$692$	−2.34973e154	−0.384801
$693$	−9.73885e152	−0.0147417
$694$	−1.19499e155	−1.67215
$695$	3.34813e154	0.433142
$696$	9.82080e154	1.17474
$697$	−1.05982e153	−0.0117231
$698$	−1.44578e154	−0.147905
$699$	1.05348e155	0.996830
$700$	−7.72541e153	−0.0676205
$701$	2.43030e154	0.196802	0.0984008	−	0.995147i	$-0.468627\pi$
$701$	2.43030e154	0.196802	0.0984008	+	0.995147i	$0.468627\pi$
$702$	2.06064e155	1.54394
$703$	1.00450e155	0.696444
$704$	−1.28262e154	−0.0822975
$705$	−1.44411e155	−0.857616
$706$	2.99333e155	1.64550
$707$	9.75414e154	0.496399
$708$	7.46547e153	0.0351759
$709$	−2.20265e155	−0.961006	−0.480503	−	0.876993i	$-0.659546\pi$
$709$	−2.20265e155	−0.961006	−0.480503	+	0.876993i	$0.659546\pi$
$710$	−2.17780e155	−0.879909
$711$	−1.36182e155	−0.509598
$712$	−2.39860e155	−0.831377
$713$	−2.21171e155	−0.710147
$714$	−3.37027e154	−0.100256
$715$	−4.98672e154	−0.137447
$716$	−8.39511e154	−0.214421
$717$	2.87251e155	0.679935
$718$	7.65430e155	1.67928
$719$	−1.27708e155	−0.259714	−0.129857	−	0.991533i	$-0.541452\pi$
$719$	−1.27708e155	−0.259714	−0.129857	+	0.991533i	$0.541452\pi$
$720$	−1.05689e155	−0.199255
$721$	−1.26749e155	−0.221550
$722$	−5.19316e155	−0.841695
$723$	1.42683e154	0.0214454
$724$	−6.40029e154	−0.0892170
$725$	−6.31891e155	−0.816997
$726$	1.04378e156	1.25188
$727$	−2.15408e155	−0.239683	−0.119841	−	0.992793i	$-0.538239\pi$
$727$	−2.15408e155	−0.239683	−0.119841	+	0.992793i	$0.538239\pi$
$728$	−5.12320e155	−0.528909
$729$	6.12451e155	0.586707
$730$	1.86335e155	0.165653
$731$	−3.80134e155	−0.313646
$732$	4.45100e155	0.340882
$733$	2.33274e156	1.65844	0.829221	−	0.558921i	$-0.188785\pi$
$733$	2.33274e156	1.65844	0.829221	+	0.558921i	$0.188785\pi$
$734$	−1.82308e156	−1.20329
$735$	9.37011e155	0.574229
$736$	−6.44084e155	−0.366523
$737$	1.50201e155	0.0793768
$738$	−3.67733e154	−0.0180493
$739$	3.67028e156	1.67331	0.836656	−	0.547728i	$-0.184507\pi$
$739$	3.67028e156	1.67331	0.836656	+	0.547728i	$0.184507\pi$
$740$	−5.30245e155	−0.224568
$741$	2.43153e156	0.956724
$742$	−2.14101e156	−0.782717
$743$	−4.43062e156	−1.50513	−0.752565	−	0.658518i	$-0.771184\pi$
$743$	−4.43062e156	−1.50513	−0.752565	+	0.658518i	$0.771184\pi$
$744$	−3.02746e156	−0.955770
$745$	3.05934e156	0.897657
$746$	−5.33156e156	−1.45408
$747$	−4.23277e155	−0.107313
$748$	−3.25568e154	−0.00767370
$749$	−7.87470e155	−0.172574
$750$	6.13574e156	1.25034
$751$	−2.90141e156	−0.549834	−0.274917	−	0.961468i	$-0.588650\pi$
$751$	−2.90141e156	−0.549834	−0.274917	+	0.961468i	$0.588650\pi$
$752$	−8.65703e156	−1.52580
$753$	−2.86663e156	−0.469943
$754$	1.57229e157	2.39770
$755$	−4.06520e156	−0.576731
$756$	6.47219e155	0.0854306
$757$	−1.14031e156	−0.140055	−0.0700275	−	0.997545i	$-0.522309\pi$
$757$	−1.14031e156	−0.140055	−0.0700275	+	0.997545i	$0.522309\pi$
$758$	−5.09498e156	−0.582332
$759$	1.00780e156	0.107201
$760$	2.48694e156	0.246220
$761$	2.44138e156	0.224994	0.112497	−	0.993652i	$-0.464115\pi$
$761$	2.44138e156	0.224994	0.112497	+	0.993652i	$0.464115\pi$
$762$	2.77136e157	2.37764
$763$	6.36260e156	0.508215
$764$	−1.87294e156	−0.139295
$765$	4.91136e155	0.0340137
$766$	2.16783e157	1.39816
$767$	−3.18546e156	−0.191348
$768$	−1.54257e157	−0.863097
$769$	−2.18809e157	−1.14046	−0.570230	−	0.821485i	$-0.693146\pi$
$769$	−2.18809e157	−1.14046	−0.570230	+	0.821485i	$0.693146\pi$
$770$	−7.30690e155	−0.0354804
$771$	−3.96153e157	−1.79226
$772$	−2.46695e156	−0.103996
$773$	−1.11499e157	−0.438016	−0.219008	−	0.975723i	$-0.570282\pi$
$773$	−1.11499e157	−0.438016	−0.219008	+	0.975723i	$0.570282\pi$
$774$	−1.31898e157	−0.482899
$775$	1.94793e157	0.664707
$776$	−1.81043e157	−0.575862
$777$	2.02459e157	0.600333
$778$	−6.56209e156	−0.181407
$779$	1.12038e156	0.0288783
$780$	−1.28353e157	−0.308495
$781$	8.03260e156	0.180042
$782$	7.61165e156	0.159115
$783$	5.29385e157	1.03218
$784$	5.61712e157	1.02162
$785$	−1.73562e156	−0.0294482
$786$	−1.31901e157	−0.208795
$787$	−3.70296e157	−0.546923	−0.273462	−	0.961883i	$-0.588169\pi$
$787$	−3.70296e157	−0.546923	−0.273462	+	0.961883i	$0.588169\pi$
$788$	−1.84449e157	−0.254213
$789$	8.89411e157	1.14395
$790$	−1.02176e158	−1.22651
$791$	−9.21754e156	−0.103275
$792$	3.01073e156	0.0314883
$793$	−1.89921e158	−1.85431
$794$	2.36728e158	2.15791
$795$	1.42958e158	1.21675
$796$	2.39246e157	0.190144
$797$	−1.35844e158	−1.00824	−0.504118	−	0.863635i	$-0.668182\pi$
$797$	−1.35844e158	−1.00824	−0.504118	+	0.863635i	$0.668182\pi$
$798$	3.56285e157	0.246968
$799$	4.02292e157	0.260461
$800$	5.67267e157	0.343070
$801$	5.00758e157	0.282915
$802$	−8.34435e157	−0.440443
$803$	−6.87279e156	−0.0338950
$804$	3.86599e157	0.178158
$805$	3.66185e157	0.157698
$806$	−4.84690e158	−1.95076
$807$	−7.26672e157	−0.273357
$808$	−3.01546e158	−1.06031
$809$	1.27073e158	0.417694	0.208847	−	0.977948i	$-0.433029\pi$
$809$	1.27073e158	0.417694	0.208847	+	0.977948i	$0.433029\pi$
$810$	−2.62652e158	−0.807136
$811$	2.25895e158	0.649039	0.324520	−	0.945879i	$-0.394797\pi$
$811$	2.25895e158	0.649039	0.324520	+	0.945879i	$0.394797\pi$
$812$	4.93836e157	0.132672
$813$	−3.21541e158	−0.807795
$814$	9.12399e157	0.214365
$815$	1.41388e158	0.310686
$816$	1.34904e158	0.277276
$817$	4.01856e158	0.772624
$818$	6.88690e158	1.23871
$819$	1.06958e158	0.179986
$820$	−5.91410e156	−0.00931181
$821$	1.02538e159	1.51072	0.755361	−	0.655309i	$-0.227462\pi$
$821$	1.02538e159	1.51072	0.755361	+	0.655309i	$0.227462\pi$
$822$	−8.03132e158	−1.10732
$823$	1.70564e158	0.220088	0.110044	−	0.993927i	$-0.464901\pi$
$823$	1.70564e158	0.220088	0.110044	+	0.993927i	$0.464901\pi$
$824$	3.91840e158	0.473233
$825$	−8.87607e157	−0.100341
$826$	−4.66756e157	−0.0493944
$827$	−2.88291e158	−0.285615	−0.142807	−	0.989750i	$-0.545613\pi$
$827$	−2.88291e158	−0.285615	−0.142807	+	0.989750i	$0.545613\pi$
$828$	5.66123e157	0.0525119
$829$	−1.06776e159	−0.927369	−0.463685	−	0.886000i	$-0.653473\pi$
$829$	−1.06776e159	−0.927369	−0.463685	+	0.886000i	$0.653473\pi$
$830$	−3.17578e158	−0.258282
$831$	−1.01887e159	−0.776004
$832$	1.40864e159	1.00480
$833$	−2.61028e158	−0.174395
$834$	−1.48286e159	−0.928004
$835$	1.31312e159	0.769824
$836$	3.44172e157	0.0189031
$837$	−1.63193e159	−0.839779
$838$	−3.06296e159	−1.47687
$839$	−1.13834e159	−0.514333	−0.257167	−	0.966367i	$-0.582789\pi$
$839$	−1.13834e159	−0.514333	−0.257167	+	0.966367i	$0.582789\pi$
$840$	5.01246e158	0.212241
$841$	1.51938e159	0.602953
$842$	3.41930e159	1.27183
$843$	−2.62891e159	−0.916586
$844$	5.94483e158	0.194301
$845$	3.53303e159	1.08257
$846$	1.39586e159	0.401013
$847$	−1.39886e159	−0.376814
$848$	8.56995e159	2.16473
$849$	−2.08452e159	−0.493784
$850$	−6.70384e158	−0.148934
$851$	−4.57248e159	−0.952776
$852$	2.06750e159	0.404099
$853$	−3.66307e158	−0.0671619	−0.0335809	−	0.999436i	$-0.510691\pi$
$853$	−3.66307e158	−0.0671619	−0.0335809	+	0.999436i	$0.510691\pi$
$854$	−2.78285e159	−0.478670
$855$	−5.19200e158	−0.0837880
$856$	2.43444e159	0.368619
$857$	6.59030e159	0.936376	0.468188	−	0.883629i	$-0.344907\pi$
$857$	6.59030e159	0.936376	0.468188	+	0.883629i	$0.344907\pi$
$858$	2.20858e159	0.294479
$859$	−1.13385e160	−1.41882	−0.709409	−	0.704797i	$-0.751038\pi$
$859$	−1.13385e160	−1.41882	−0.709409	+	0.704797i	$0.751038\pi$
$860$	−2.12127e159	−0.249132
$861$	2.25813e158	0.0248930
$862$	−1.42356e160	−1.47309
$863$	1.31099e160	1.27354	0.636768	−	0.771055i	$-0.280271\pi$
$863$	1.31099e160	1.27354	0.636768	+	0.771055i	$0.280271\pi$
$864$	−4.75245e159	−0.433429
$865$	−9.80941e159	−0.839972
$866$	2.06098e160	1.65710
$867$	1.43529e160	1.08367
$868$	−1.52235e159	−0.107942
$869$	3.76865e159	0.250962
$870$	−1.53831e160	−0.962152
$871$	−1.64959e160	−0.969139
$872$	−1.96698e160	−1.08555
$873$	3.77966e159	0.195964
$874$	−8.04658e159	−0.391957
$875$	−8.22300e159	−0.376349
$876$	−1.76898e159	−0.0760762
$877$	−2.34442e160	−0.947454	−0.473727	−	0.880672i	$-0.657092\pi$
$877$	−2.34442e160	−0.947454	−0.473727	+	0.880672i	$0.657092\pi$
$878$	7.47023e159	0.283715
$879$	4.41629e160	1.57639
$880$	2.92479e159	0.0981270
$881$	5.77096e160	1.81996	0.909978	−	0.414656i	$-0.136098\pi$
$881$	5.77096e160	1.81996	0.909978	+	0.414656i	$0.136098\pi$
$882$	−9.05708e159	−0.268504
$883$	6.84698e160	1.90827	0.954137	−	0.299371i	$-0.0967767\pi$
$883$	6.84698e160	1.90827	0.954137	+	0.299371i	$0.0967767\pi$
$884$	3.57558e159	0.0936909
$885$	3.11660e159	0.0767844
$886$	7.57293e159	0.175439
$887$	4.20457e159	0.0915977	0.0457989	−	0.998951i	$-0.485417\pi$
$887$	4.20457e159	0.0915977	0.0457989	+	0.998951i	$0.485417\pi$
$888$	−6.25896e160	−1.28232
$889$	−3.71412e160	−0.715665
$890$	3.75711e160	0.680923
$891$	9.68766e159	0.165152
$892$	7.46761e159	0.119756
$893$	−4.25279e160	−0.641608
$894$	−1.35495e161	−1.92322
$895$	−3.50470e160	−0.468053
$896$	3.68894e160	0.463569
$897$	−1.10683e161	−1.30885
$898$	1.54617e161	1.72067
$899$	−1.24518e161	−1.30416
$900$	−4.98605e159	−0.0491518
$901$	−3.98245e160	−0.369530
$902$	1.01765e159	0.00888874
$903$	8.09947e160	0.666000
$904$	2.84957e160	0.220597
$905$	−2.67192e160	−0.194749
$906$	1.80044e161	1.23564
$907$	1.56599e161	1.01203	0.506013	−	0.862526i	$-0.331119\pi$
$907$	1.56599e161	1.01203	0.506013	+	0.862526i	$0.331119\pi$
$908$	−6.33766e160	−0.385701
$909$	6.29541e160	0.360821
$910$	8.02485e160	0.433193
$911$	−1.16358e161	−0.591623	−0.295812	−	0.955246i	$-0.595590\pi$
$911$	−1.16358e161	−0.591623	−0.295812	+	0.955246i	$0.595590\pi$
$912$	−1.42613e161	−0.683029
$913$	1.17136e160	0.0528484
$914$	9.24325e160	0.392878
$915$	1.85815e161	0.744101
$916$	−6.20142e160	−0.233985
$917$	1.76771e160	0.0628468
$918$	5.61634e160	0.188160
$919$	−2.39365e161	−0.755727	−0.377864	−	0.925861i	$-0.623341\pi$
$919$	−2.39365e161	−0.755727	−0.377864	+	0.925861i	$0.623341\pi$
$920$	−1.13205e161	−0.336844
$921$	5.62601e161	1.57779
$922$	2.06691e161	0.546369
$923$	−8.82186e161	−2.19820
$924$	6.93683e159	0.0162944
$925$	4.02714e161	0.891811
$926$	−4.97250e161	−1.03819
$927$	−8.18048e160	−0.161040
$928$	−3.62617e161	−0.673106
$929$	−2.66229e161	−0.466014	−0.233007	−	0.972475i	$-0.574857\pi$
$929$	−2.66229e161	−0.466014	−0.233007	+	0.972475i	$0.574857\pi$
$930$	4.74214e161	0.782805
$931$	2.75943e161	0.429597
$932$	−1.63767e161	−0.240469
$933$	−8.00278e161	−1.10839
$934$	1.26399e162	1.65135
$935$	−1.35915e160	−0.0167507
$936$	−3.30656e161	−0.384452
$937$	−9.41367e161	−1.03265	−0.516323	−	0.856394i	$-0.672699\pi$
$937$	−9.41367e161	−1.03265	−0.516323	+	0.856394i	$0.672699\pi$
$938$	−2.41709e161	−0.250172
$939$	3.81029e161	0.372120
$940$	2.24491e161	0.206886
$941$	1.31571e162	1.14427	0.572133	−	0.820161i	$-0.306116\pi$
$941$	1.31571e162	1.14427	0.572133	+	0.820161i	$0.306116\pi$
$942$	7.68693e160	0.0630926
$943$	−5.09993e160	−0.0395072
$944$	1.86832e161	0.136608
$945$	2.70194e161	0.186484
$946$	3.65009e161	0.237813
$947$	−2.92557e162	−1.79944	−0.899720	−	0.436468i	$-0.856229\pi$
$947$	−2.92557e162	−1.79944	−0.899720	+	0.436468i	$0.856229\pi$
$948$	9.70007e161	0.563275
$949$	7.54809e161	0.413836
$950$	7.08691e161	0.366877
$951$	4.03069e162	1.97034
$952$	−1.39634e161	−0.0644583
$953$	1.48435e162	0.647101	0.323550	−	0.946211i	$-0.395124\pi$
$953$	1.48435e162	0.647101	0.323550	+	0.946211i	$0.395124\pi$
$954$	−1.38182e162	−0.568940
$955$	−7.81894e161	−0.304063
$956$	−4.46541e161	−0.164024
$957$	5.67390e161	0.196871
$958$	−4.87420e162	−1.59766
$959$	1.07634e162	0.333301
$960$	−1.37819e162	−0.403207
$961$	2.20896e161	0.0610610
$962$	−1.00205e163	−2.61726
$963$	−5.08240e161	−0.125440
$964$	−2.21805e160	−0.00517337
$965$	−1.02987e162	−0.227010
$966$	−1.62180e162	−0.337866
$967$	7.71239e161	0.151861	0.0759305	−	0.997113i	$-0.475807\pi$
$967$	7.71239e161	0.151861	0.0759305	+	0.997113i	$0.475807\pi$
$968$	4.32451e162	0.804879
$969$	6.62721e161	0.116596
$970$	2.83582e162	0.471649
$971$	4.95027e162	0.778360	0.389180	−	0.921162i	$-0.372758\pi$
$971$	4.95027e162	0.778360	0.389180	+	0.921162i	$0.372758\pi$
$972$	9.97224e161	0.148245
$973$	1.98730e162	0.279327
$974$	7.53720e162	1.00172
$975$	9.74820e162	1.22510
$976$	1.11391e163	1.32384
$977$	−1.17842e163	−1.32448	−0.662240	−	0.749292i	$-0.730394\pi$
$977$	−1.17842e163	−1.32448	−0.662240	+	0.749292i	$0.730394\pi$
$978$	−6.26193e162	−0.665642
$979$	−1.38577e162	−0.139327
$980$	−1.45661e162	−0.138524
$981$	4.10648e162	0.369410
$982$	1.07813e163	0.917477
$983$	−2.13003e163	−1.71482	−0.857410	−	0.514635i	$-0.827928\pi$
$983$	−2.13003e163	−1.71482	−0.857410	+	0.514635i	$0.827928\pi$
$984$	−6.98094e161	−0.0531718
$985$	−7.70019e162	−0.554915
$986$	4.28533e162	0.292208
$987$	−8.57157e162	−0.553064
$988$	−3.77989e162	−0.230795
$989$	−1.82924e163	−1.05699
$990$	−4.71594e161	−0.0257899
$991$	1.23779e163	0.640666	0.320333	−	0.947305i	$-0.396205\pi$
$991$	1.23779e163	0.640666	0.320333	+	0.947305i	$0.396205\pi$
$992$	1.11784e163	0.547638
$993$	2.71266e163	1.25794
$994$	−1.29264e163	−0.567441
$995$	9.98780e162	0.415061
$996$	3.01494e162	0.118616
$997$	−3.91048e163	−1.45661	−0.728306	−	0.685252i	$-0.759692\pi$
$997$	−3.91048e163	−1.45661	−0.728306	+	0.685252i	$0.759692\pi$
$998$	1.43835e163	0.507281
$999$	−3.37386e163	−1.12670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.110.a.a.1.7	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.110.a.a.1.7	✓	8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 110 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+2.87423e16 q^{2} -1.13913e26 q^{3} +1.77081e32 q^{4} +7.39260e37 q^{5} -3.27412e42 q^{6} +4.38791e45 q^{7} -1.35651e49 q^{8} +2.83200e51 q^{9} +O(q^{10})\)	\(q+2.87423e16 q^{2} -1.13913e26 q^{3} +1.77081e32 q^{4} +7.39260e37 q^{5} -3.27412e42 q^{6} +4.38791e45 q^{7} -1.35651e49 q^{8} +2.83200e51 q^{9} +2.12480e54 q^{10} -7.83713e55 q^{11} -2.01719e58 q^{12} +8.60718e60 q^{13} +1.26119e62 q^{14} -8.42113e63 q^{15} -5.04824e65 q^{16} +2.34591e66 q^{17} +8.13980e67 q^{18} -2.47996e69 q^{19} +1.30909e70 q^{20} -4.99840e71 q^{21} -2.25257e72 q^{22} +1.12887e74 q^{23} +1.54524e75 q^{24} -9.94238e75 q^{25} +2.47390e77 q^{26} +8.32952e77 q^{27} +7.77018e77 q^{28} +6.35552e79 q^{29} -2.42043e80 q^{30} -1.95922e81 q^{31} -5.70554e81 q^{32} +8.92751e81 q^{33} +6.74269e82 q^{34} +3.24381e83 q^{35} +5.01494e83 q^{36} -4.05048e85 q^{37} -7.12798e85 q^{38} -9.80469e86 q^{39} -1.00281e87 q^{40} -4.51771e86 q^{41} -1.43665e88 q^{42} -1.62041e89 q^{43} -1.38781e88 q^{44} +2.09358e89 q^{45} +3.24464e90 q^{46} +1.71486e91 q^{47} +5.75060e91 q^{48} -1.11269e92 q^{49} -2.85767e92 q^{50} -2.67230e92 q^{51} +1.52417e93 q^{52} -1.69761e94 q^{53} +2.39409e94 q^{54} -5.79368e93 q^{55} -5.95224e94 q^{56} +2.82500e95 q^{57} +1.82672e96 q^{58} -3.70093e95 q^{59} -1.49123e96 q^{60} -2.20654e97 q^{61} -5.63124e97 q^{62} +1.24266e97 q^{63} +1.63659e98 q^{64} +6.36294e98 q^{65} +2.56597e98 q^{66} -1.91653e99 q^{67} +4.15418e98 q^{68} -1.28593e100 q^{69} +9.32344e99 q^{70} -1.02494e101 q^{71} -3.84163e100 q^{72} +8.76953e100 q^{73} -1.16420e102 q^{74} +1.13257e102 q^{75} -4.39155e101 q^{76} -3.43886e101 q^{77} -2.81809e103 q^{78} -4.80871e103 q^{79} -3.73196e103 q^{80} -1.23612e104 q^{81} -1.29849e103 q^{82} -1.49463e104 q^{83} -8.85124e103 q^{84} +1.73424e104 q^{85} -4.65743e105 q^{86} -7.23977e105 q^{87} +1.06311e105 q^{88} +1.76822e106 q^{89} +6.01743e105 q^{90} +3.77675e106 q^{91} +1.99903e106 q^{92} +2.23180e107 q^{93} +4.92891e107 q^{94} -1.83334e107 q^{95} +6.49936e107 q^{96} +1.33463e108 q^{97} -3.19813e108 q^{98} -2.21947e107 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 22\!\cdots\!00 q^{2}+ \cdots + 24\!\cdots\!84 q^{9}+O(q^{10}) \) 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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