LMFDB - Embedded newform 1.92.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,92,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, 92, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 92);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 92 $
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:	$52.4421558310$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2 x^{6} + \cdots + 37\!\cdots\!00 $ x^7 - 2x^6 - 19965898505076685758763041x^5 + 704885126882155619610489099544084432x^4 + 107067825809672902244360085998174063583690648295951x^3 + 2760974505633618159712492393750116169743299337348578140163910x^2 - 117290449585568076678331590341364312042793082454528443905095325102023447375x + 37970201148992037926462243830462339624462239310525820322458780504727338931040585255500
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{83}\cdot 3^{31}\cdot 5^{8}\cdot 7^{6}\cdot 11\cdot 13^{3}\cdot 23 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.52994e12$ 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)

$f(q)$	$=$	$q-8.41697e13 q^{2} +2.94143e21 q^{3} +4.60866e27 q^{4} +2.26211e30 q^{5} -2.47580e35 q^{6} -5.00335e38 q^{7} -1.79515e41 q^{8} -1.75319e43 q^{9} +O(q^{10})$	\(q-8.41697e13 q^{2} +2.94143e21 q^{3} +4.60866e27 q^{4} +2.26211e30 q^{5} -2.47580e35 q^{6} -5.00335e38 q^{7} -1.79515e41 q^{8} -1.75319e43 q^{9} -1.90401e44 q^{10} +2.78249e45 q^{11} +1.35561e49 q^{12} -1.56747e49 q^{13} +4.21131e52 q^{14} +6.65384e51 q^{15} +3.69926e54 q^{16} -1.72828e56 q^{17} +1.47565e57 q^{18} +2.32937e58 q^{19} +1.04253e58 q^{20} -1.47170e60 q^{21} -2.34201e59 q^{22} +2.66688e61 q^{23} -5.28033e62 q^{24} -4.03385e63 q^{25} +1.31933e63 q^{26} -1.28587e65 q^{27} -2.30588e66 q^{28} -3.58912e66 q^{29} -5.60052e65 q^{30} -5.81396e67 q^{31} +1.33092e68 q^{32} +8.18452e66 q^{33} +1.45469e70 q^{34} -1.13181e69 q^{35} -8.07983e70 q^{36} +2.30013e71 q^{37} -1.96063e72 q^{38} -4.61060e70 q^{39} -4.06083e71 q^{40} +3.01078e73 q^{41} +1.23873e74 q^{42} -2.62077e74 q^{43} +1.28236e73 q^{44} -3.96589e73 q^{45} -2.24471e75 q^{46} -1.02701e76 q^{47} +1.08811e76 q^{48} +1.70182e77 q^{49} +3.39528e77 q^{50} -5.08362e77 q^{51} -7.22392e76 q^{52} -5.84910e77 q^{53} +1.08231e79 q^{54} +6.29429e75 q^{55} +8.98179e79 q^{56} +6.85170e79 q^{57} +3.02095e80 q^{58} -1.61305e80 q^{59} +3.06653e79 q^{60} -1.04388e81 q^{61} +4.89359e81 q^{62} +8.77181e81 q^{63} -2.03613e82 q^{64} -3.54578e79 q^{65} -6.88888e80 q^{66} -9.78731e82 q^{67} -7.96504e83 q^{68} +7.84446e82 q^{69} +9.52643e82 q^{70} +1.35234e84 q^{71} +3.14724e84 q^{72} +4.09747e84 q^{73} -1.93602e85 q^{74} -1.18653e85 q^{75} +1.07353e86 q^{76} -1.39218e84 q^{77} +3.88073e84 q^{78} +2.41714e86 q^{79} +8.36813e84 q^{80} +8.08220e85 q^{81} -2.53416e87 q^{82} -5.94425e86 q^{83} -6.78258e87 q^{84} -3.90955e86 q^{85} +2.20589e88 q^{86} -1.05572e88 q^{87} -4.99500e86 q^{88} +2.81561e88 q^{89} +3.33808e87 q^{90} +7.84259e87 q^{91} +1.22908e89 q^{92} -1.71014e89 q^{93} +8.64432e89 q^{94} +5.26929e88 q^{95} +3.91483e89 q^{96} +1.10101e90 q^{97} -1.43242e91 q^{98} -4.87822e88 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 3841716838056 q^{2} + 62\!\cdots\!32 q^{3}+ \cdots + 38\!\cdots\!59 q^{9}+O(q^{10}) $ 7 * q + 3841716838056 * q^2 + 6226865993447967511332 * q^3 + 5671662926176418572725837376 * q^4 + 23504964778584408375486754830930 * q^5 + 451174906579592943363587112684473184 * q^6 - 171085178649369081126501604564827872344 * q^7 - 10385570201002723586914837423420014159360 * q^8 + 38080901154162874719072934775718033448005459 * q^9	$ 7 q + 3841716838056 q^{2} + 62\!\cdots\!32 q^{3}+ \cdots - 23\!\cdots\!92 q^{99}+O(q^{100}) $ 7 * q + 3841716838056 * q^2 + 6226865993447967511332 * q^3 + 5671662926176418572725837376 * q^4 + 23504964778584408375486754830930 * q^5 + 451174906579592943363587112684473184 * q^6 - 171085178649369081126501604564827872344 * q^7 - 10385570201002723586914837423420014159360 * q^8 + 38080901154162874719072934775718033448005459 * q^9 + 4697789292978379445837627874024155681811061680 * q^10 - 240582832892068760628122732280591830839146659316 * q^11 + 15234465137330235186821811325942149339051634358016 * q^12 + 712268684544237976989939315593627958143865337752122 * q^13 + 17766212926078897376844163559794320416860400218986432 * q^14 + 818092333276881407770547708857297926161740517153634360 * q^15 - 5543121629719415776419174196841312964977690510556459008 * q^16 - 116788563921119361626790446343979264424208809345044156194 * q^17 + 2532221674884609223972217344567154578664327889292374599112 * q^18 + 24914430965691713272160835064548829827762713320225549023860 * q^19 + 213622308691313951002559876190359340784045827397766986247040 * q^20 - 2997932825643989744485469587195205163128865044067155102498976 * q^21 + 2770354076929612113872013355190927517116944942304065995485472 * q^22 + 28060217473226028795108958325793316282935533444516172471797112 * q^23 - 676645515624503740032420639044230674317241134651601877083678720 * q^24 + 3263569264491109562693810546136813966434457662326151208223443025 * q^25 + 14647231349517882504358224484901087010163561052132416579801164144 * q^26 + 88534490857595263563477937784200716693877558838426769810977256360 * q^27 - 1267961512722154560010156489449223630509765593702989988702255606272 * q^28 - 1998207010601468906936357688217559269263973686319086789407593851510 * q^29 + 46684773092381185628041557878825569520483461165868165669687502423360 * q^30 - 59925208170796133190382607870079728441723654705660441096474565882976 * q^31 - 349236116256080438032682462092197690284580228848172295706337753268224 * q^32 + 48956964959741209887245659130472098420831296585540373363667238885584 * q^33 + 4422724362741906584267050702673869603971959112955389299199109971390672 * q^34 - 13368721150607890395306302586915792313883425318712829768566063087971920 * q^35 + 48271193532350417136817688340793844028122089698778111115225583548795712 * q^36 - 193385642725694230212647842547384176779300890377457537180445039472551694 * q^37 + 648885030040198126856514202904430175712235671732708835862375911231617760 * q^38 - 1888050736392299353100554804844814233146715239003942457135725287045138792 * q^39 + 612437306889339293021693643280174203404468934648721750255585003111910400 * q^40 + 27467963396808209903058935820529109024708043852794661490538346949004391894 * q^41 + 2490746600045939910899268282231591851463383036227202908840686832900714752 * q^42 - 305936680392367608196854535263961824203961856383604167638158912234512481108 * q^43 + 205463536657254300042685770932278214832998693823974867822888457185152941312 * q^44 + 4760687647415457141753353234910279174019798332678698076640623508070611166010 * q^45 - 1366266407223913965782607380535324534407310537728351887747959292074575330496 * q^46 + 6016385666666683617266527127107702489089132053603324831460234388201640236656 * q^47 + 34119609737617524136090987754275812795178080643639536100065326182318914650112 * q^48 + 147622366871958729066285529870014845360644877218444002326443275466876372382751 * q^49 + 987686706148773430200902630527966650567454297252982416951455545242325575637400 * q^50 + 742769239785716829162529676417470760468992847219971127251563531253033686474504 * q^51 + 4318717132385281312358095915519383012120671308396466785048290702799702098686336 * q^52 + 13308120064559469621843967381370895719631000840255977547855692839275328956239682 * q^53 + 49855304363851366001446865238806860151072717129384273575810932439561849626548160 * q^54 + 71294075726222567616681402637553088151526343199773263267028104308906720840973160 * q^55 + 221193813355805774602587289215941353561793271848452643887988504737893638457815040 * q^56 + 528504764627515846582196025944068103123296527378022647769732650016063847427593520 * q^57 + 1238229446269131105368662021237658933365297194812595452448484778585094416520960240 * q^58 + 1315161090691534242045211041321797641427216505845115765078938874240054573263728380 * q^59 + 4823153254365391976824193526392851616116082049689724166967862952927612944155374080 * q^60 + 5062201896875711919454365982321524134556244374094873318866473906778984033476168234 * q^61 + 5944009317613068040880423794674923373270855087786172352031955991395153732464744192 * q^62 - 3636043453736261219929075304472074905914693023981615502769720183430994506848383288 * q^63 - 51461933507510968227229909173673546488880558907251327588128558485838721977163710464 * q^64 - 77004978625744224526600511688707953799859895672813324064129546096894713766789516340 * q^65 - 308541964188130582740963794759741868505184177678097911786772179394411954828298046592 * q^66 - 375865111304983135837477510931607479316175718244865448118159181323617876690058988444 * q^67 - 1534213067668968494728693973596412463295117507399423353249302546218581933051381708672 * q^68 - 2173315533882618835358431426746324715455060324131802571545777868624263537306736200672 * q^69 - 2678915571128698388724922631831368101885281292954514535801987008907571514431164929920 * q^70 + 965663858399224787677892593054987300813257337626219343051035389437608903566853136104 * q^71 + 4759225550598725097796726774244526164682601876181738961172151381039656425240893268480 * q^72 + 9530120766269923537811918138494095655717782977571711295781136472585782479177982847862 * q^73 + 19110889051618327071497328002063508382221976511726809975089825510120232325728977189552 * q^74 + 125021668038726866132333086418803849235968631984043287433627055625310081344612351442300 * q^75 + 201417481997189328603388340686282158978023686930352491852420967420198850453092214874880 * q^76 + 203838117981454989170200594078013407199331583446926407393231313568448855161412400016672 * q^77 + 348422592585817152583346169273764440235290509078131053609004533439300203952600764751424 * q^78 - 5875385290546216656185911308903463222289330212802402962421344496345859662855253387760 * q^79 - 704730665751803958915921202265388401277484106681191434954636540435925847481999762923520 * q^80 - 645876221088024404019866830164659790161069128158743050337018784266949283332298558348353 * q^81 - 5377119810649520829232661929626958820402325732939303335851648698643252753720266284836848 * q^82 - 7188939673179725085045886441204184334512306517239973817301478804674514872311469770345548 * q^83 - 17037797188065238374634346038194001797920522141104843305926325070074414892172026480416768 * q^84 - 18949626274852488910142757348951127712395103983201418376580212098044613619651779587066620 * q^85 - 13930550649009692825744367374854352346751992408208092118301786049776748630048877827166176 * q^86 + 14997220283992832178383660427617039138145206474606482931148662045188858037160846958683480 * q^87 + 35205946317573638735966560050796709996519491901124319190557129002743085716478822258247680 * q^88 + 58910603928414585742462774445274283779895728554450265497847918725594089228346625287686470 * q^89 + 596817611113547745433166439395807555701671900247626319346669516201533941956589878026043760 * q^90 + 431556051755722691175733360455273666621786312136528121760420810812400911428233396155619184 * q^91 + 649582018326251344367774515135408104477035917640264872918599325106081734967368208117408256 * q^92 + 176140526645345381525949017432055243763067046580068760248910898954659817267839614775511424 * q^93 + 528728237301347142597743478920778358077668394817645608650770473672424789094546213047704192 * q^94 + 460150241832447303916160340674008161933312298406246509746195633852627501820464219531336600 * q^95 - 5308520687978816513495454896751155260796827272022533467944875093089923121365143311537012736 * q^96 - 7025964934206676021621272614488614108607978598995771668040441707563730547939229623877790994 * q^97 - 20729666350145773779493369529709111649648862211758783582357755821769845548186544170995584792 * q^98 - 23913014682919445875702212438204672119308558146529134638425833150071457007907375951005388292 * 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 $

$2$	−8.41697e13	−1.69157	−0.845787	−	0.533521i	$-0.820869\pi$
$2$	−8.41697e13	−1.69157	−0.845787	+	0.533521i	$0.820869\pi$
$3$	2.94143e21	0.574834	0.287417	−	0.957806i	$-0.407204\pi$
$3$	2.94143e21	0.574834	0.287417	+	0.957806i	$0.407204\pi$
$4$	4.60866e27	1.86142
$5$	2.26211e30	0.0355941	0.0177970	−	0.999842i	$-0.494335\pi$
$5$	2.26211e30	0.0355941	0.0177970	+	0.999842i	$0.494335\pi$
$6$	−2.47580e35	−0.972373
$7$	−5.00335e38	−1.76726	−0.883630	−	0.468186i	$-0.844908\pi$
$7$	−5.00335e38	−1.76726	−0.883630	+	0.468186i	$0.844908\pi$
$8$	−1.79515e41	−1.45716
$9$	−1.75319e43	−0.669566
$10$	−1.90401e44	−0.0602100
$11$	2.78249e45	0.0115098	0.00575489	−	0.999983i	$-0.498168\pi$
$11$	2.78249e45	0.0115098	0.00575489	+	0.999983i	$0.498168\pi$
$12$	1.35561e49	1.07001
$13$	−1.56747e49	−0.0324172	−0.0162086	−	0.999869i	$-0.505160\pi$
$13$	−1.56747e49	−0.0324172	−0.0162086	+	0.999869i	$0.505160\pi$
$14$	4.21131e52	2.98945
$15$	6.65384e51	0.0204607
$16$	3.69926e54	0.603471
$17$	−1.72828e56	−1.78726	−0.893630	−	0.448805i	$-0.851850\pi$
$17$	−1.72828e56	−1.78726	−0.893630	+	0.448805i	$0.851850\pi$
$18$	1.47565e57	1.13262
$19$	2.32937e58	1.52739	0.763695	−	0.645577i	$-0.223383\pi$
$19$	2.32937e58	1.52739	0.763695	+	0.645577i	$0.223383\pi$
$20$	1.04253e58	0.0662556
$21$	−1.47170e60	−1.01588
$22$	−2.34201e59	−0.0194696
$23$	2.66688e61	0.293351	0.146675	−	0.989185i	$-0.453143\pi$
$23$	2.66688e61	0.293351	0.146675	+	0.989185i	$0.453143\pi$
$24$	−5.28033e62	−0.837624
$25$	−4.03385e63	−0.998733
$26$	1.31933e63	0.0548361
$27$	−1.28587e65	−0.959723
$28$	−2.30588e66	−3.28962
$29$	−3.58912e66	−1.03724	−0.518619	−	0.855005i	$-0.673554\pi$
$29$	−3.58912e66	−1.03724	−0.518619	+	0.855005i	$0.673554\pi$
$30$	−5.60052e65	−0.0346107
$31$	−5.81396e67	−0.808193	−0.404096	−	0.914716i	$-0.632414\pi$
$31$	−5.81396e67	−0.808193	−0.404096	+	0.914716i	$0.632414\pi$
$32$	1.33092e68	0.436344
$33$	8.18452e66	0.00661620
$34$	1.45469e70	3.02328
$35$	−1.13181e69	−0.0629040
$36$	−8.07983e70	−1.24635
$37$	2.30013e71	1.01994	0.509970	−	0.860192i	$-0.329656\pi$
$37$	2.30013e71	1.01994	0.509970	+	0.860192i	$0.329656\pi$
$38$	−1.96063e72	−2.58369
$39$	−4.61060e70	−0.0186345
$40$	−4.06083e71	−0.0518663
$41$	3.01078e73	1.25030	0.625149	−	0.780506i	$-0.285038\pi$
$41$	3.01078e73	1.25030	0.625149	+	0.780506i	$0.285038\pi$
$42$	1.23873e74	1.71844
$43$	−2.62077e74	−1.24627	−0.623137	−	0.782113i	$-0.714142\pi$
$43$	−2.62077e74	−1.24627	−0.623137	+	0.782113i	$0.714142\pi$
$44$	1.28236e73	0.0214245
$45$	−3.96589e73	−0.0238326
$46$	−2.24471e75	−0.496225
$47$	−1.02701e76	−0.853340	−0.426670	−	0.904407i	$-0.640313\pi$
$47$	−1.02701e76	−0.853340	−0.426670	+	0.904407i	$0.640313\pi$
$48$	1.08811e76	0.346895
$49$	1.70182e77	2.12321
$50$	3.39528e77	1.68943
$51$	−5.08362e77	−1.02738
$52$	−7.22392e76	−0.0603421
$53$	−5.84910e77	−0.205370	−0.102685	−	0.994714i	$-0.532743\pi$
$53$	−5.84910e77	−0.205370	−0.102685	+	0.994714i	$0.532743\pi$
$54$	1.08231e79	1.62344
$55$	6.29429e75	0.000409680 0
$56$	8.98179e79	2.57518
$57$	6.85170e79	0.877995
$58$	3.02095e80	1.75457
$59$	−1.61305e80	−0.430409	−0.215204	−	0.976569i	$-0.569042\pi$
$59$	−1.61305e80	−0.430409	−0.215204	+	0.976569i	$0.569042\pi$
$60$	3.06653e79	0.0380860
$61$	−1.04388e81	−0.611141	−0.305571	−	0.952169i	$-0.598847\pi$
$61$	−1.04388e81	−0.611141	−0.305571	+	0.952169i	$0.598847\pi$
$62$	4.89359e81	1.36712
$63$	8.77181e81	1.18330
$64$	−2.03613e82	−1.34158
$65$	−3.54578e79	−0.00115386
$66$	−6.88888e80	−0.0111918
$67$	−9.78731e82	−0.802158	−0.401079	−	0.916043i	$-0.631365\pi$
$67$	−9.78731e82	−0.802158	−0.401079	+	0.916043i	$0.631365\pi$
$68$	−7.96504e83	−3.32685
$69$	7.84446e82	0.168628
$70$	9.52643e82	0.106407
$71$	1.35234e84	0.792192	0.396096	−	0.918209i	$-0.370365\pi$
$71$	1.35234e84	0.792192	0.396096	+	0.918209i	$0.370365\pi$
$72$	3.14724e84	0.975665
$73$	4.09747e84	0.678150	0.339075	−	0.940759i	$-0.389886\pi$
$73$	4.09747e84	0.678150	0.339075	+	0.940759i	$0.389886\pi$
$74$	−1.93602e85	−1.72530
$75$	−1.18653e85	−0.574105
$76$	1.07353e86	2.84312
$77$	−1.39218e84	−0.0203408
$78$	3.88073e84	0.0315216
$79$	2.41714e86	1.09969	0.549844	−	0.835268i	$-0.314687\pi$
$79$	2.41714e86	1.09969	0.549844	+	0.835268i	$0.314687\pi$
$80$	8.36813e84	0.0214800
$81$	8.08220e85	0.117886
$82$	−2.53416e87	−2.11497
$83$	−5.94425e86	−0.285788	−0.142894	−	0.989738i	$-0.545641\pi$
$83$	−5.94425e86	−0.285788	−0.142894	+	0.989738i	$0.545641\pi$
$84$	−6.78258e87	−1.89098
$85$	−3.90955e86	−0.0636159
$86$	2.20589e88	2.10817
$87$	−1.05572e88	−0.596240
$88$	−4.99500e86	−0.0167716
$89$	2.81561e88	0.565363	0.282681	−	0.959214i	$-0.408776\pi$
$89$	2.81561e88	0.565363	0.282681	+	0.959214i	$0.408776\pi$
$90$	3.33808e87	0.0403146
$91$	7.84259e87	0.0572896
$92$	1.22908e89	0.546050
$93$	−1.71014e89	−0.464576
$94$	8.64432e89	1.44349
$95$	5.26929e88	0.0543661
$96$	3.91483e89	0.250825
$97$	1.10101e90	0.440228	0.220114	−	0.975474i	$-0.429357\pi$
$97$	1.10101e90	0.440228	0.220114	+	0.975474i	$0.429357\pi$
$98$	−1.43242e91	−3.59156
$99$	−4.87822e88	−0.00770656
$100$	−1.85906e91	−1.85906
$101$	2.69264e91	1.71221	0.856103	−	0.516805i	$-0.172879\pi$
$101$	2.69264e91	1.71221	0.856103	+	0.516805i	$0.172879\pi$
$102$	4.27886e91	1.73788
$103$	−6.96324e90	−0.181433	−0.0907167	−	0.995877i	$-0.528916\pi$
$103$	−6.96324e90	−0.181433	−0.0907167	+	0.995877i	$0.528916\pi$
$104$	2.81384e90	0.0472371
$105$	−3.32915e90	−0.0361593
$106$	4.92317e91	0.347398
$107$	3.14916e92	1.44955	0.724774	−	0.688986i	$-0.241944\pi$
$107$	3.14916e92	1.44955	0.724774	+	0.688986i	$0.241944\pi$
$108$	−5.92614e92	−1.78645
$109$	1.94503e92	0.385497	0.192748	−	0.981248i	$-0.438260\pi$
$109$	1.94503e92	0.385497	0.192748	+	0.981248i	$0.438260\pi$
$110$	−5.29789e89	−0.000693004 0
$111$	6.76569e92	0.586296
$112$	−1.85087e93	−1.06649
$113$	2.58862e93	0.995405	0.497703	−	0.867348i	$-0.334177\pi$
$113$	2.58862e93	0.995405	0.497703	+	0.867348i	$0.334177\pi$
$114$	−5.76705e93	−1.48519
$115$	6.03277e91	0.0104416
$116$	−1.65410e94	−1.93074
$117$	2.74806e92	0.0217055
$118$	1.35770e94	0.728068
$119$	8.64719e94	3.15855
$120$	−1.19447e93	−0.0298145
$121$	−5.84355e94	−0.999868
$122$	8.78628e94	1.03379
$123$	8.85601e94	0.718713
$124$	−2.67945e95	−1.50439
$125$	−1.82616e94	−0.0711431
$126$	−7.38320e95	−2.00164
$127$	−9.28267e94	−0.175632	−0.0878160	−	0.996137i	$-0.527989\pi$
$127$	−9.28267e94	−0.175632	−0.0878160	+	0.996137i	$0.527989\pi$
$128$	1.38428e96	1.83304
$129$	−7.70881e95	−0.716400
$130$	2.98447e93	0.00195184
$131$	1.76841e96	0.816093	0.408046	−	0.912961i	$-0.366210\pi$
$131$	1.76841e96	0.816093	0.408046	+	0.912961i	$0.366210\pi$
$132$	3.77196e94	0.0123155
$133$	−1.16547e97	−2.69930
$134$	8.23795e96	1.35691
$135$	−2.90878e95	−0.0341605
$136$	3.10252e97	2.60432
$137$	4.28416e96	0.257679	0.128840	−	0.991665i	$-0.458875\pi$
$137$	4.28416e96	0.257679	0.128840	+	0.991665i	$0.458875\pi$
$138$	−6.60266e96	−0.285247
$139$	−1.42370e97	−0.442839	−0.221420	−	0.975179i	$-0.571069\pi$
$139$	−1.42370e97	−0.442839	−0.221420	+	0.975179i	$0.571069\pi$
$140$	−5.21614e96	−0.117091
$141$	−3.02088e97	−0.490529
$142$	−1.13826e98	−1.34005
$143$	−4.36146e94	−0.000373115 0
$144$	−6.48550e97	−0.404064
$145$	−8.11897e96	−0.0369196
$146$	−3.44883e98	−1.14714
$147$	5.00580e98	1.22049
$148$	1.06005e99	1.89854
$149$	4.11570e98	0.542586	0.271293	−	0.962497i	$-0.412549\pi$
$149$	4.11570e98	0.542586	0.271293	+	0.962497i	$0.412549\pi$
$150$	9.98699e98	0.971141
$151$	−1.37204e99	−0.986086	−0.493043	−	0.870005i	$-0.664116\pi$
$151$	−1.37204e99	−0.986086	−0.493043	+	0.870005i	$0.664116\pi$
$152$	−4.18158e99	−2.22565
$153$	3.02999e99	1.19669
$154$	1.17179e98	0.0344079
$155$	−1.31518e98	−0.0287669
$156$	−2.12487e98	−0.0346867
$157$	1.06729e100	1.30271	0.651356	−	0.758773i	$-0.274201\pi$
$157$	1.06729e100	1.30271	0.651356	+	0.758773i	$0.274201\pi$
$158$	−2.03450e100	−1.86020
$159$	−1.72047e99	−0.118053
$160$	3.01069e98	0.0155313
$161$	−1.33434e100	−0.518427
$162$	−6.80276e99	−0.199412
$163$	−5.22763e100	−1.15816	−0.579081	−	0.815270i	$-0.696588\pi$
$163$	−5.22763e100	−1.15816	−0.579081	+	0.815270i	$0.696588\pi$
$164$	1.38756e101	2.32733
$165$	1.85143e97	0.000235498 0
$166$	5.00326e100	0.483431
$167$	1.01118e101	0.743407	0.371704	−	0.928351i	$-0.378774\pi$
$167$	1.01118e101	0.743407	0.371704	+	0.928351i	$0.378774\pi$
$168$	2.64193e101	1.48030
$169$	−2.33555e101	−0.998949
$170$	3.29066e100	0.107611
$171$	−4.08382e101	−1.02269
$172$	−1.20782e102	−2.31984
$173$	−7.63026e101	−1.12575	−0.562874	−	0.826542i	$-0.690305\pi$
$173$	−7.63026e101	−1.12575	−0.562874	+	0.826542i	$0.690305\pi$
$174$	8.88592e101	1.00858
$175$	2.01828e102	1.76502
$176$	1.02932e100	0.00694581
$177$	−4.74468e101	−0.247413
$178$	−2.36989e102	−0.956353
$179$	3.29289e102	1.02983	0.514913	−	0.857242i	$-0.327824\pi$
$179$	3.29289e102	1.02983	0.514913	+	0.857242i	$0.327824\pi$
$180$	−1.82774e101	−0.0443626
$181$	5.70159e102	1.07553	0.537763	−	0.843096i	$-0.319270\pi$
$181$	5.70159e102	1.07553	0.537763	+	0.843096i	$0.319270\pi$
$182$	−6.60108e101	−0.0969097
$183$	−3.07049e102	−0.351304
$184$	−4.78746e102	−0.427459
$185$	5.20315e101	0.0363039
$186$	1.43942e103	0.785865
$187$	−4.80892e101	−0.0205710
$188$	−4.73314e103	−1.58843
$189$	6.43366e103	1.69608
$190$	−4.43515e102	−0.0919643
$191$	−6.97664e103	−1.13927	−0.569637	−	0.821897i	$-0.692916\pi$
$191$	−6.97664e103	−1.13927	−0.569637	+	0.821897i	$0.692916\pi$
$192$	−5.98914e103	−0.771185
$193$	−1.08693e104	−1.10495	−0.552477	−	0.833528i	$-0.686317\pi$
$193$	−1.08693e104	−1.10495	−0.552477	+	0.833528i	$0.686317\pi$
$194$	−9.26717e103	−0.744678
$195$	−1.04297e101	−0.000663278 0
$196$	7.84312e104	3.95219
$197$	1.48891e104	0.595190	0.297595	−	0.954692i	$-0.403815\pi$
$197$	1.48891e104	0.595190	0.297595	+	0.954692i	$0.403815\pi$
$198$	4.10599e102	0.0130362
$199$	−2.96119e104	−0.747568	−0.373784	−	0.927516i	$-0.621940\pi$
$199$	−2.96119e104	−0.747568	−0.373784	+	0.927516i	$0.621940\pi$
$200$	7.24138e104	1.45531
$201$	−2.87887e104	−0.461107
$202$	−2.26639e105	−2.89632
$203$	1.79576e105	1.83307
$204$	−2.34287e105	−1.91238
$205$	6.81070e103	0.0445032
$206$	5.86094e104	0.306908
$207$	−4.67554e104	−0.196418
$208$	−5.79847e103	−0.0195628
$209$	6.48146e103	0.0175799
$210$	2.80214e104	0.0611662
$211$	1.08480e106	1.90764	0.953820	−	0.300379i	$-0.0971133\pi$
$211$	1.08480e106	1.90764	0.953820	+	0.300379i	$0.0971133\pi$
$212$	−2.69565e105	−0.382280
$213$	3.97781e105	0.455378
$214$	−2.65064e106	−2.45202
$215$	−5.92845e104	−0.0443600
$216$	2.30833e106	1.39847
$217$	2.90893e106	1.42829
$218$	−1.63713e106	−0.652096
$219$	1.20524e106	0.389823
$220$	2.90082e103	0.000762587 0
$221$	2.70902e105	0.0579380
$222$	−5.69466e106	−0.991763
$223$	−6.94162e106	−0.985347	−0.492674	−	0.870214i	$-0.663980\pi$
$223$	−6.94162e106	−0.985347	−0.492674	+	0.870214i	$0.663980\pi$
$224$	−6.65908e106	−0.771134
$225$	7.07209e106	0.668718
$226$	−2.17884e107	−1.68380
$227$	1.23561e107	0.781096	0.390548	−	0.920582i	$-0.372285\pi$
$227$	1.23561e107	0.781096	0.390548	+	0.920582i	$0.372285\pi$
$228$	3.15771e107	1.63432
$229$	−3.80950e106	−0.161567	−0.0807836	−	0.996732i	$-0.525742\pi$
$229$	−3.80950e106	−0.161567	−0.0807836	+	0.996732i	$0.525742\pi$
$230$	−5.07777e105	−0.0176627
$231$	−4.09500e105	−0.0116925
$232$	6.44301e107	1.51142
$233$	4.02777e107	0.776910	0.388455	−	0.921468i	$-0.373009\pi$
$233$	4.02777e107	0.776910	0.388455	+	0.921468i	$0.373009\pi$
$234$	−2.31303e106	−0.0367164
$235$	−2.32321e106	−0.0303739
$236$	−7.43399e107	−0.801173
$237$	7.10986e107	0.632137
$238$	−7.27831e108	−5.34293
$239$	3.11736e108	1.89096	0.945481	−	0.325678i	$-0.105592\pi$
$239$	3.11736e108	1.89096	0.945481	+	0.325678i	$0.105592\pi$
$240$	2.46143e106	0.0123474
$241$	5.57175e107	0.231322	0.115661	−	0.993289i	$-0.463101\pi$
$241$	5.57175e107	0.231322	0.115661	+	0.993289i	$0.463101\pi$
$242$	4.91850e108	1.69135
$243$	3.60464e108	1.02749
$244$	−4.81087e108	−1.13759
$245$	3.84970e107	0.0755737
$246$	−7.45407e108	−1.21576
$247$	−3.65121e107	−0.0495138
$248$	1.04369e109	1.17767
$249$	−1.74846e108	−0.164280
$250$	1.53707e108	0.120344
$251$	−1.35263e109	−0.883128	−0.441564	−	0.897230i	$-0.645576\pi$
$251$	−1.35263e109	−0.883128	−0.441564	+	0.897230i	$0.645576\pi$
$252$	4.04263e109	2.20262
$253$	7.42058e106	0.00337640
$254$	7.81320e108	0.297095
$255$	−1.14997e108	−0.0365685
$256$	−6.61025e109	−1.75914
$257$	−2.69787e109	−0.601263	−0.300632	−	0.953740i	$-0.597197\pi$
$257$	−2.69787e109	−0.601263	−0.300632	+	0.953740i	$0.597197\pi$
$258$	6.48849e109	1.21184
$259$	−1.15084e110	−1.80250
$260$	−1.63413e107	−0.00214782
$261$	6.29239e109	0.694500
$262$	−1.48847e110	−1.38048
$263$	5.03297e108	0.0392499	0.0196249	−	0.999807i	$-0.493753\pi$
$263$	5.03297e108	0.0392499	0.0196249	+	0.999807i	$0.493753\pi$
$264$	−1.46925e108	−0.00964086
$265$	−1.32313e108	−0.00730995
$266$	9.80971e110	4.56606
$267$	8.28193e109	0.324989
$268$	−4.51064e110	−1.49316
$269$	−1.79811e109	−0.0502444	−0.0251222	−	0.999684i	$-0.507997\pi$
$269$	−1.79811e109	−0.0502444	−0.0251222	+	0.999684i	$0.507997\pi$
$270$	2.44831e109	0.0577849
$271$	−3.43434e110	−0.685080	−0.342540	−	0.939503i	$-0.611287\pi$
$271$	−3.43434e110	−0.685080	−0.342540	+	0.939503i	$0.611287\pi$
$272$	−6.39336e110	−1.07856
$273$	2.30685e109	0.0329320
$274$	−3.60596e110	−0.435884
$275$	−1.12242e109	−0.0114952
$276$	3.61524e110	0.313888
$277$	−1.45192e111	−1.06933	−0.534665	−	0.845064i	$-0.679562\pi$
$277$	−1.45192e111	−1.06933	−0.534665	+	0.845064i	$0.679562\pi$
$278$	1.19833e111	0.749095
$279$	1.01929e111	0.541139
$280$	2.03178e110	0.0916612
$281$	−2.24632e111	−0.861657	−0.430828	−	0.902434i	$-0.641779\pi$
$281$	−2.24632e111	−0.861657	−0.430828	+	0.902434i	$0.641779\pi$
$282$	2.54267e111	0.829765
$283$	−1.40228e111	−0.389540	−0.194770	−	0.980849i	$-0.562396\pi$
$283$	−1.40228e111	−0.389540	−0.194770	+	0.980849i	$0.562396\pi$
$284$	6.23246e111	1.47460
$285$	1.54993e110	0.0312514
$286$	3.67103e108	0.000631151 0
$287$	−1.50640e112	−2.20960
$288$	−2.33336e111	−0.292161
$289$	2.05186e112	2.19430
$290$	6.83371e110	0.0624522
$291$	3.23855e111	0.253058
$292$	1.88838e112	1.26232
$293$	−1.04157e111	−0.0595954	−0.0297977	−	0.999556i	$-0.509486\pi$
$293$	−1.04157e111	−0.0595954	−0.0297977	+	0.999556i	$0.509486\pi$
$294$	−4.21336e112	−2.06455
$295$	−3.64889e110	−0.0153200
$296$	−4.12909e112	−1.48622
$297$	−3.57792e110	−0.0110462
$298$	−3.46417e112	−0.917825
$299$	−4.18025e110	−0.00950962
$300$	−5.46831e112	−1.06865
$301$	1.31126e113	2.20249
$302$	1.15484e113	1.66804
$303$	7.92023e112	0.984233
$304$	8.61697e112	0.921736
$305$	−2.36136e111	−0.0217530
$306$	−2.55034e113	−2.02429
$307$	5.22792e112	0.357712	0.178856	−	0.983875i	$-0.442760\pi$
$307$	5.22792e112	0.357712	0.178856	+	0.983875i	$0.442760\pi$
$308$	−6.41608e111	−0.0378627
$309$	−2.04819e112	−0.104294
$310$	1.10698e112	0.0486613
$311$	−7.65851e112	−0.290768	−0.145384	−	0.989375i	$-0.546442\pi$
$311$	−7.65851e112	−0.290768	−0.145384	+	0.989375i	$0.546442\pi$
$312$	8.27673e111	0.0271534
$313$	−2.47148e113	−0.700954	−0.350477	−	0.936571i	$-0.613981\pi$
$313$	−2.47148e113	−0.700954	−0.350477	+	0.936571i	$0.613981\pi$
$314$	−8.98335e113	−2.20363
$315$	1.98428e112	0.0421184
$316$	1.11398e114	2.04698
$317$	1.21961e113	0.194100	0.0970499	−	0.995280i	$-0.469059\pi$
$317$	1.21961e113	0.194100	0.0970499	+	0.995280i	$0.469059\pi$
$318$	1.44812e113	0.199696
$319$	−9.98669e111	−0.0119384
$320$	−4.60594e112	−0.0477523
$321$	9.26304e113	0.833249
$322$	1.12311e114	0.876958
$323$	−4.02580e114	−2.72984
$324$	3.72481e113	0.219435
$325$	6.32293e112	0.0323761
$326$	4.40008e114	1.95912
$327$	5.72118e113	0.221597
$328$	−5.40481e114	−1.82188
$329$	5.13850e114	1.50807
$330$	−1.55834e111	−0.000398362 0
$331$	3.56194e114	0.793438	0.396719	−	0.917940i	$-0.370149\pi$
$331$	3.56194e114	0.793438	0.396719	+	0.917940i	$0.370149\pi$
$332$	−2.73950e114	−0.531972
$333$	−4.03256e114	−0.682918
$334$	−8.51103e114	−1.25753
$335$	−2.21400e113	−0.0285521
$336$	−5.44422e114	−0.613054
$337$	−1.75943e115	−1.73066	−0.865331	−	0.501200i	$-0.832892\pi$
$337$	−1.75943e115	−1.73066	−0.865331	+	0.501200i	$0.832892\pi$
$338$	1.96582e115	1.68980
$339$	7.61427e114	0.572192
$340$	−1.80178e114	−0.118416
$341$	−1.61773e113	−0.00930211
$342$	3.43734e115	1.72996
$343$	−4.50446e115	−1.98500
$344$	4.70468e115	1.81602
$345$	1.77450e113	0.00600216
$346$	6.42236e115	1.90429
$347$	5.45237e115	1.41773	0.708867	−	0.705343i	$-0.249207\pi$
$347$	5.45237e115	1.41773	0.708867	+	0.705343i	$0.249207\pi$
$348$	−4.86543e115	−1.10985
$349$	−5.88565e115	−1.17825	−0.589125	−	0.808042i	$-0.700527\pi$
$349$	−5.88565e115	−1.17825	−0.589125	+	0.808042i	$0.700527\pi$
$350$	−1.69878e116	−2.98566
$351$	2.01556e114	0.0311115
$352$	3.70328e113	0.00502222
$353$	−7.08715e115	−0.844739	−0.422370	−	0.906424i	$-0.638802\pi$
$353$	−7.08715e115	−0.844739	−0.422370	+	0.906424i	$0.638802\pi$
$354$	3.99358e115	0.418518
$355$	3.05913e114	0.0281973
$356$	1.29762e116	1.05238
$357$	2.54351e116	1.81564
$358$	−2.77161e116	−1.74203
$359$	1.25840e116	0.696659	0.348330	−	0.937372i	$-0.386749\pi$
$359$	1.25840e116	0.696659	0.348330	+	0.937372i	$0.386749\pi$
$360$	7.11938e114	0.0347279
$361$	3.10015e116	1.33292
$362$	−4.79901e116	−1.81933
$363$	−1.71884e116	−0.574757
$364$	3.61438e115	0.106640
$365$	9.26892e114	0.0241381
$366$	2.58443e116	0.594257
$367$	8.24171e116	1.67383	0.836915	−	0.547333i	$-0.184357\pi$
$367$	8.24171e116	1.67383	0.836915	+	0.547333i	$0.184357\pi$
$368$	9.86551e115	0.177029
$369$	−5.27845e116	−0.837157
$370$	−4.37948e115	−0.0614106
$371$	2.92651e116	0.362942
$372$	−7.88144e116	−0.864772
$373$	−8.26164e116	−0.802259	−0.401130	−	0.916021i	$-0.631382\pi$
$373$	−8.26164e116	−0.802259	−0.401130	+	0.916021i	$0.631382\pi$
$374$	4.04765e115	0.0347973
$375$	−5.37152e115	−0.0408954
$376$	1.84364e117	1.24345
$377$	5.62582e115	0.0336244
$378$	−5.41519e117	−2.86904
$379$	3.03593e116	0.142629	0.0713146	−	0.997454i	$-0.477281\pi$
$379$	3.03593e116	0.142629	0.0713146	+	0.997454i	$0.477281\pi$
$380$	2.42844e116	0.101198
$381$	−2.73044e116	−0.100959
$382$	5.87221e117	1.92716
$383$	−4.44802e117	−1.29605	−0.648025	−	0.761619i	$-0.724405\pi$
$383$	−4.44802e117	−1.29605	−0.648025	+	0.761619i	$0.724405\pi$
$384$	4.07178e117	1.05369
$385$	−3.14926e114	−0.000724011 0
$386$	9.14866e117	1.86911
$387$	4.59469e117	0.834464
$388$	5.07418e117	0.819450
$389$	−7.02812e117	−1.00956	−0.504780	−	0.863248i	$-0.668426\pi$
$389$	−7.02812e117	−1.00956	−0.504780	+	0.863248i	$0.668426\pi$
$390$	8.77862e114	0.00112198
$391$	−4.60912e117	−0.524294
$392$	−3.05503e118	−3.09385
$393$	5.20167e117	0.469117
$394$	−1.25321e118	−1.00681
$395$	5.46783e116	0.0391424
$396$	−2.24821e116	−0.0143452
$397$	2.37950e118	1.35369	0.676843	−	0.736128i	$-0.263348\pi$
$397$	2.37950e118	1.35369	0.676843	+	0.736128i	$0.263348\pi$
$398$	2.49242e118	1.26457
$399$	−3.42815e118	−1.55165
$400$	−1.49223e118	−0.602706
$401$	2.00185e117	0.0721712	0.0360856	−	0.999349i	$-0.488511\pi$
$401$	2.00185e117	0.0721712	0.0360856	+	0.999349i	$0.488511\pi$
$402$	2.42314e118	0.779997
$403$	9.11318e116	0.0261994
$404$	1.24095e119	3.18714
$405$	1.82828e116	0.00419603
$406$	−1.51149e119	−3.10077
$407$	6.40010e116	0.0117393
$408$	9.12587e118	1.49705
$409$	−7.75233e118	−1.13768	−0.568842	−	0.822447i	$-0.692608\pi$
$409$	−7.75233e118	−1.13768	−0.568842	+	0.822447i	$0.692608\pi$
$410$	−5.73255e117	−0.0752804
$411$	1.26016e118	0.148123
$412$	−3.20912e118	−0.337724
$413$	8.07066e118	0.760644
$414$	3.93539e118	0.332255
$415$	−1.34465e117	−0.0101724
$416$	−2.08618e117	−0.0141451
$417$	−4.18773e118	−0.254559
$418$	−5.45543e117	−0.0297377
$419$	−2.99746e118	−0.146560	−0.0732800	−	0.997311i	$-0.523347\pi$
$419$	−2.99746e118	−0.146560	−0.0732800	+	0.997311i	$0.523347\pi$
$420$	−1.53429e118	−0.0673078
$421$	−1.12504e119	−0.442927	−0.221464	−	0.975169i	$-0.571083\pi$
$421$	−1.12504e119	−0.442927	−0.221464	+	0.975169i	$0.571083\pi$
$422$	−9.13069e119	−3.22691
$423$	1.80054e119	0.571368
$424$	1.05000e119	0.299257
$425$	6.97162e119	1.78500
$426$	−3.34811e119	−0.770306
$427$	5.22288e119	1.08005
$428$	1.45134e120	2.69822
$429$	−1.28290e116	−0.000214479 0
$430$	4.98996e118	0.0750382
$431$	−8.50900e118	−0.115123	−0.0575616	−	0.998342i	$-0.518333\pi$
$431$	−8.50900e118	−0.115123	−0.0575616	+	0.998342i	$0.518333\pi$
$432$	−4.75677e119	−0.579165
$433$	3.30468e119	0.362184	0.181092	−	0.983466i	$-0.442037\pi$
$433$	3.30468e119	0.362184	0.181092	+	0.983466i	$0.442037\pi$
$434$	−2.44844e120	−2.41605
$435$	−2.38814e118	−0.0212226
$436$	8.96398e119	0.717572
$437$	6.21217e119	0.448061
$438$	−1.01445e120	−0.659415
$439$	−1.01798e120	−0.596489	−0.298244	−	0.954490i	$-0.596401\pi$
$439$	−1.01798e120	−0.596489	−0.298244	+	0.954490i	$0.596401\pi$
$440$	−1.12992e117	−0.000596969 0
$441$	−2.98361e120	−1.42163
$442$	−2.28017e119	−0.0980064
$443$	−1.37128e120	−0.531810	−0.265905	−	0.963999i	$-0.585671\pi$
$443$	−1.37128e120	−0.531810	−0.265905	+	0.963999i	$0.585671\pi$
$444$	3.11808e120	1.09134
$445$	6.36921e118	0.0201236
$446$	5.84274e120	1.66679
$447$	1.21061e120	0.311897
$448$	1.01875e121	2.37092
$449$	−7.38886e120	−1.55371	−0.776854	−	0.629681i	$-0.783185\pi$
$449$	−7.38886e120	−1.55371	−0.776854	+	0.629681i	$0.783185\pi$
$450$	−5.95256e120	−1.13119
$451$	8.37747e118	0.0143906
$452$	1.19301e121	1.85287
$453$	−4.03576e120	−0.566835
$454$	−1.04001e121	−1.32128
$455$	1.77408e118	0.00203917
$456$	−1.22998e121	−1.27938
$457$	−1.81515e120	−0.170894	−0.0854468	−	0.996343i	$-0.527232\pi$
$457$	−1.81515e120	−0.170894	−0.0854468	+	0.996343i	$0.527232\pi$
$458$	3.20644e120	0.273303
$459$	2.22234e121	1.71527
$460$	2.78030e119	0.0194362
$461$	8.48095e120	0.537096	0.268548	−	0.963266i	$-0.413456\pi$
$461$	8.48095e120	0.537096	0.268548	+	0.963266i	$0.413456\pi$
$462$	3.44675e119	0.0197788
$463$	−1.31716e121	−0.685022	−0.342511	−	0.939514i	$-0.611277\pi$
$463$	−1.31716e121	−0.685022	−0.342511	+	0.939514i	$0.611277\pi$
$464$	−1.32771e121	−0.625943
$465$	−3.86851e119	−0.0165362
$466$	−3.39017e121	−1.31420
$467$	−3.07380e121	−1.08083	−0.540415	−	0.841399i	$-0.681733\pi$
$467$	−3.07380e121	−1.08083	−0.540415	+	0.841399i	$0.681733\pi$
$468$	1.26649e120	0.0404031
$469$	4.89694e121	1.41762
$470$	1.95544e120	0.0513797
$471$	3.13936e121	0.748842
$472$	2.89567e121	0.627174
$473$	−7.29226e119	−0.0143443
$474$	−5.98435e121	−1.06931
$475$	−9.39634e121	−1.52546
$476$	3.98519e122	5.87940
$477$	1.02546e121	0.137509
$478$	−2.62387e122	−3.19870
$479$	8.05730e121	0.893149	0.446574	−	0.894747i	$-0.352644\pi$
$479$	8.05730e121	0.893149	0.446574	+	0.894747i	$0.352644\pi$
$480$	8.85575e119	0.00892790
$481$	−3.60538e120	−0.0330636
$482$	−4.68973e121	−0.391298
$483$	−3.92486e121	−0.298009
$484$	−2.69309e122	−1.86118
$485$	2.49060e120	0.0156695
$486$	−3.03401e122	−1.73807
$487$	2.13639e121	0.111458	0.0557291	−	0.998446i	$-0.482252\pi$
$487$	2.13639e121	0.111458	0.0557291	+	0.998446i	$0.482252\pi$
$488$	1.87392e122	0.890530
$489$	−1.53767e122	−0.665750
$490$	−3.24028e121	−0.127838
$491$	3.87160e122	1.39214	0.696070	−	0.717974i	$-0.254930\pi$
$491$	3.87160e122	1.39214	0.696070	+	0.717974i	$0.254930\pi$
$492$	4.08143e122	1.33783
$493$	6.20299e122	1.85382
$494$	3.07322e121	0.0837562
$495$	−1.10351e119	−0.000274308 0
$496$	−2.15074e122	−0.487721
$497$	−6.76623e122	−1.40001
$498$	1.47168e122	0.277893
$499$	−5.00525e122	−0.862683	−0.431341	−	0.902189i	$-0.641960\pi$
$499$	−5.00525e122	−0.862683	−0.431341	+	0.902189i	$0.641960\pi$
$500$	−8.41614e121	−0.132427
$501$	2.97430e122	0.427335
$502$	1.13850e123	1.49388
$503$	1.67615e122	0.200895	0.100447	−	0.994942i	$-0.467973\pi$
$503$	1.67615e122	0.200895	0.100447	+	0.994942i	$0.467973\pi$
$504$	−1.57467e123	−1.72425
$505$	6.09104e121	0.0609444
$506$	−6.24588e120	−0.00571143
$507$	−6.86986e122	−0.574229
$508$	−4.27807e122	−0.326925
$509$	1.57422e123	1.10004	0.550018	−	0.835153i	$-0.314621\pi$
$509$	1.57422e123	1.10004	0.550018	+	0.835153i	$0.314621\pi$
$510$	9.67925e121	0.0618584
$511$	−2.05011e123	−1.19847
$512$	2.13651e123	1.14267
$513$	−2.99527e123	−1.46587
$514$	2.27079e123	1.01708
$515$	−1.57516e121	−0.00645796
$516$	−3.55273e123	−1.33352
$517$	−2.85765e121	−0.00982175
$518$	9.68658e123	3.04906
$519$	−2.24439e123	−0.647118
$520$	6.36521e120	0.00168136
$521$	−6.86902e123	−1.66256	−0.831281	−	0.555852i	$-0.812392\pi$
$521$	−6.86902e123	−1.66256	−0.831281	+	0.555852i	$0.812392\pi$
$522$	−5.29628e123	−1.17480
$523$	5.83786e123	1.18693	0.593467	−	0.804858i	$-0.297759\pi$
$523$	5.83786e123	1.18693	0.593467	+	0.804858i	$0.297759\pi$
$524$	8.15001e123	1.51909
$525$	5.93663e123	1.01459
$526$	−4.23624e122	−0.0663940
$527$	1.00481e124	1.44445
$528$	3.02767e121	0.00399268
$529$	−7.55359e123	−0.913945
$530$	1.11367e122	0.0123653
$531$	2.82797e123	0.288187
$532$	−5.37124e124	−5.02453
$533$	−4.71929e122	−0.0405312
$534$	−6.97088e123	−0.549744
$535$	7.12373e122	0.0515954
$536$	1.75697e124	1.16887
$537$	9.68581e123	0.591979
$538$	1.51346e123	0.0849921
$539$	4.73531e122	0.0244376
$540$	−1.34056e123	−0.0635870
$541$	3.56440e124	1.55421	0.777107	−	0.629369i	$-0.216687\pi$
$541$	3.56440e124	1.55421	0.777107	+	0.629369i	$0.216687\pi$
$542$	2.89068e124	1.15886
$543$	1.67708e124	0.618248
$544$	−2.30021e124	−0.779860
$545$	4.39987e122	0.0137214
$546$	−1.94167e123	−0.0557069
$547$	−1.42805e124	−0.376982	−0.188491	−	0.982075i	$-0.560360\pi$
$547$	−1.42805e124	−0.376982	−0.188491	+	0.982075i	$0.560360\pi$
$548$	1.97442e124	0.479650
$549$	1.83011e124	0.409200
$550$	9.44734e122	0.0194450
$551$	−8.36039e124	−1.58427
$552$	−1.40820e124	−0.245718
$553$	−1.20938e125	−1.94343
$554$	1.22207e125	1.80885
$555$	1.53047e123	0.0208687
$556$	−6.56136e124	−0.824311
$557$	1.00291e125	1.16105	0.580525	−	0.814243i	$-0.302847\pi$
$557$	1.00291e125	1.16105	0.580525	+	0.814243i	$0.302847\pi$
$558$	−8.57937e124	−0.915376
$559$	4.10796e123	0.0404007
$560$	−4.18687e123	−0.0379607
$561$	−1.41451e123	−0.0118249
$562$	1.89072e125	1.45756
$563$	−1.25013e123	−0.00888838	−0.00444419	−	0.999990i	$-0.501415\pi$
$563$	−1.25013e123	−0.00888838	−0.00444419	+	0.999990i	$0.501415\pi$
$564$	−1.39222e125	−0.913081
$565$	5.85574e123	0.0354305
$566$	1.18030e125	0.658936
$567$	−4.04381e124	−0.208335
$568$	−2.42765e125	−1.15435
$569$	−8.84831e124	−0.388376	−0.194188	−	0.980964i	$-0.562207\pi$
$569$	−8.84831e124	−0.388376	−0.194188	+	0.980964i	$0.562207\pi$
$570$	−1.30457e124	−0.0528641
$571$	2.86259e125	1.07107	0.535533	−	0.844514i	$-0.320111\pi$
$571$	2.86259e125	1.07107	0.535533	+	0.844514i	$0.320111\pi$
$572$	−2.01005e122	−0.000694524 0
$573$	−2.05213e125	−0.654892
$574$	1.26793e126	3.73770
$575$	−1.07578e125	−0.292979
$576$	3.56971e125	0.898276
$577$	2.42057e125	0.562883	0.281441	−	0.959578i	$-0.409188\pi$
$577$	2.42057e125	0.562883	0.281441	+	0.959578i	$0.409188\pi$
$578$	−1.72704e126	−3.71182
$579$	−3.19714e125	−0.635165
$580$	−3.74175e124	−0.0687229
$581$	2.97412e125	0.505061
$582$	−2.72588e125	−0.428066
$583$	−1.62751e123	−0.00236376
$584$	−7.35559e125	−0.988173
$585$	6.21640e122	0.000772587 0
$586$	8.76688e124	0.100810
$587$	−1.26935e126	−1.35067	−0.675333	−	0.737513i	$-0.736000\pi$
$587$	−1.26935e126	−1.35067	−0.675333	+	0.737513i	$0.736000\pi$
$588$	2.30700e126	2.27185
$589$	−1.35429e126	−1.23443
$590$	3.07126e124	0.0259149
$591$	4.37954e125	0.342135
$592$	8.50881e125	0.615504
$593$	1.84327e126	1.23481	0.617405	−	0.786646i	$-0.288184\pi$
$593$	1.84327e126	1.23481	0.617405	+	0.786646i	$0.288184\pi$
$594$	3.01153e124	0.0186854
$595$	1.95609e125	0.112426
$596$	1.89679e126	1.00998
$597$	−8.71014e125	−0.429727
$598$	3.51850e124	0.0160862
$599$	3.47948e126	1.47433	0.737163	−	0.675715i	$-0.236165\pi$
$599$	3.47948e126	1.47433	0.737163	+	0.675715i	$0.236165\pi$
$600$	2.13000e126	0.836563
$601$	−1.57950e125	−0.0575083	−0.0287541	−	0.999587i	$-0.509154\pi$
$601$	−1.57950e125	−0.0575083	−0.0287541	+	0.999587i	$0.509154\pi$
$602$	−1.10369e127	−3.72568
$603$	1.71590e126	0.537098
$604$	−6.32325e126	−1.83552
$605$	−1.32187e125	−0.0355894
$606$	−6.66643e126	−1.66490
$607$	2.42424e126	0.561683	0.280841	−	0.959754i	$-0.409387\pi$
$607$	2.42424e126	0.561683	0.280841	+	0.959754i	$0.409387\pi$
$608$	3.10022e126	0.666468
$609$	5.28212e126	1.05371
$610$	1.98755e125	0.0367968
$611$	1.60980e125	0.0276629
$612$	1.39642e127	2.22754
$613$	−3.04188e126	−0.450495	−0.225248	−	0.974302i	$-0.572319\pi$
$613$	−3.04188e126	−0.450495	−0.225248	+	0.974302i	$0.572319\pi$
$614$	−4.40033e126	−0.605096
$615$	2.00332e125	0.0255819
$616$	2.49917e125	0.0296397
$617$	−8.41285e126	−0.926762	−0.463381	−	0.886159i	$-0.653364\pi$
$617$	−8.41285e126	−0.926762	−0.463381	+	0.886159i	$0.653364\pi$
$618$	1.72396e126	0.176421
$619$	2.65742e126	0.252660	0.126330	−	0.991988i	$-0.459680\pi$
$619$	2.65742e126	0.252660	0.126330	+	0.991988i	$0.459680\pi$
$620$	−6.06121e125	−0.0535473
$621$	−3.42926e126	−0.281536
$622$	6.44614e126	0.491855
$623$	−1.40875e127	−0.999143
$624$	−1.70558e125	−0.0112454
$625$	1.62513e127	0.996201
$626$	2.08024e127	1.18572
$627$	1.90648e125	0.0101055
$628$	4.91877e127	2.42490
$629$	−3.97527e127	−1.82290
$630$	−1.67016e126	−0.0712464
$631$	−3.69424e127	−1.46619	−0.733093	−	0.680128i	$-0.761924\pi$
$631$	−3.69424e127	−1.46619	−0.733093	+	0.680128i	$0.761924\pi$
$632$	−4.33914e127	−1.60242
$633$	3.19086e127	1.09658
$634$	−1.02654e127	−0.328334
$635$	−2.09984e125	−0.00625146
$636$	−7.92907e126	−0.219747
$637$	−2.66755e126	−0.0688285
$638$	8.40577e125	0.0201947
$639$	−2.37090e127	−0.530425
$640$	3.13139e126	0.0652453
$641$	4.52562e127	0.878289	0.439144	−	0.898416i	$-0.355282\pi$
$641$	4.52562e127	0.878289	0.439144	+	0.898416i	$0.355282\pi$
$642$	−7.79668e127	−1.40950
$643$	−3.43786e127	−0.579014	−0.289507	−	0.957176i	$-0.593491\pi$
$643$	−3.43786e127	−0.579014	−0.289507	+	0.957176i	$0.593491\pi$
$644$	−6.14950e127	−0.965012
$645$	−1.74382e126	−0.0254996
$646$	3.38851e128	4.61773
$647$	1.29564e128	1.64566	0.822829	−	0.568289i	$-0.192394\pi$
$647$	1.29564e128	1.64566	0.822829	+	0.568289i	$0.192394\pi$
$648$	−1.45088e127	−0.171778
$649$	−4.48830e125	−0.00495391
$650$	−5.32199e126	−0.0547666
$651$	8.55643e127	0.821027
$652$	−2.40924e128	−2.15583
$653$	−7.55874e127	−0.630811	−0.315406	−	0.948957i	$-0.602141\pi$
$653$	−7.55874e127	−0.630811	−0.315406	+	0.948957i	$0.602141\pi$
$654$	−4.81550e127	−0.374847
$655$	4.00034e126	0.0290481
$656$	1.11377e128	0.754518
$657$	−7.18363e127	−0.454066
$658$	−4.32506e128	−2.55102
$659$	−6.73860e127	−0.370922	−0.185461	−	0.982652i	$-0.559378\pi$
$659$	−6.73860e127	−0.370922	−0.185461	+	0.982652i	$0.559378\pi$
$660$	8.53259e124	0.000438361 0
$661$	4.01662e128	1.92617	0.963084	−	0.269203i	$-0.0867602\pi$
$661$	4.01662e128	1.92617	0.963084	+	0.269203i	$0.0867602\pi$
$662$	−2.99808e128	−1.34216
$663$	7.96840e126	0.0333047
$664$	1.06708e128	0.416439
$665$	−2.63641e127	−0.0960790
$666$	3.39420e128	1.15521
$667$	−9.57176e127	−0.304275
$668$	4.66016e128	1.38380
$669$	−2.04183e128	−0.566411
$670$	1.86351e127	0.0482980
$671$	−2.90458e126	−0.00703410
$672$	−1.95873e128	−0.443273
$673$	−6.62194e128	−1.40055	−0.700277	−	0.713871i	$-0.746940\pi$
$673$	−6.62194e128	−1.40055	−0.700277	+	0.713871i	$0.746940\pi$
$674$	1.48091e129	2.92754
$675$	5.18701e128	0.958507
$676$	−1.07637e129	−1.85947
$677$	5.72881e128	0.925294	0.462647	−	0.886543i	$-0.346900\pi$
$677$	5.72881e128	0.925294	0.462647	+	0.886543i	$0.346900\pi$
$678$	−6.40891e128	−0.967905
$679$	−5.50875e128	−0.777997
$680$	7.01824e127	0.0926985
$681$	3.63446e128	0.449000
$682$	1.36164e127	0.0157352
$683$	−1.94302e128	−0.210056	−0.105028	−	0.994469i	$-0.533493\pi$
$683$	−1.94302e128	−0.210056	−0.105028	+	0.994469i	$0.533493\pi$
$684$	−1.88209e129	−1.90366
$685$	9.69122e126	0.00917186
$686$	3.79139e129	3.35777
$687$	−1.12054e128	−0.0928743
$688$	−9.69491e128	−0.752090
$689$	9.16826e126	0.00665752
$690$	−1.49359e127	−0.0101531
$691$	1.36253e129	0.867153	0.433576	−	0.901117i	$-0.357251\pi$
$691$	1.36253e129	0.867153	0.433576	+	0.901117i	$0.357251\pi$
$692$	−3.51652e129	−2.09549
$693$	2.44075e127	0.0136195
$694$	−4.58925e129	−2.39820
$695$	−3.22057e127	−0.0157625
$696$	1.89517e129	0.868816
$697$	−5.20346e129	−2.23461
$698$	4.95393e129	1.99310
$699$	1.18474e129	0.446594
$700$	9.30156e129	3.28545
$701$	−1.08176e129	−0.358064	−0.179032	−	0.983843i	$-0.557297\pi$
$701$	−1.08176e129	−0.358064	−0.179032	+	0.983843i	$0.557297\pi$
$702$	−1.69649e128	−0.0526275
$703$	5.35787e129	1.55785
$704$	−5.66551e127	−0.0154413
$705$	−6.83356e127	−0.0174599
$706$	5.96523e129	1.42894
$707$	−1.34722e130	−3.02591
$708$	−2.18666e129	−0.460541
$709$	5.13204e129	1.01365	0.506823	−	0.862050i	$-0.330820\pi$
$709$	5.13204e129	1.01365	0.506823	+	0.862050i	$0.330820\pi$
$710$	−2.57486e128	−0.0476979
$711$	−4.23770e129	−0.736314
$712$	−5.05445e129	−0.823824
$713$	−1.55051e129	−0.237084
$714$	−2.14087e130	−3.07129
$715$	−9.86609e124	−1.32807e−5 0
$716$	1.51758e130	1.91694
$717$	9.16952e129	1.08699
$718$	−1.05919e130	−1.17845
$719$	1.01308e130	1.05798	0.528992	−	0.848627i	$-0.322570\pi$
$719$	1.01308e130	1.05798	0.528992	+	0.848627i	$0.322570\pi$
$720$	−1.46709e128	−0.0143823
$721$	3.48395e129	0.320640
$722$	−2.60939e130	−2.25474
$723$	1.63889e129	0.132972
$724$	2.62767e130	2.00201
$725$	1.44780e130	1.03592
$726$	1.44674e130	0.972245
$727$	−1.45321e130	−0.917300	−0.458650	−	0.888617i	$-0.651667\pi$
$727$	−1.45321e130	−0.917300	−0.458650	+	0.888617i	$0.651667\pi$
$728$	−1.40786e129	−0.0834802
$729$	8.48658e129	0.472749
$730$	−7.80162e128	−0.0408314
$731$	4.52941e130	2.22742
$732$	−1.41509e130	−0.653926
$733$	−2.54211e130	−1.10399	−0.551994	−	0.833848i	$-0.686133\pi$
$733$	−2.54211e130	−1.10399	−0.551994	+	0.833848i	$0.686133\pi$
$734$	−6.93702e130	−2.83141
$735$	1.13236e129	0.0434423
$736$	3.54942e129	0.128002
$737$	−2.72331e128	−0.00923266
$738$	4.44286e130	1.41611
$739$	−3.19554e129	−0.0957683	−0.0478841	−	0.998853i	$-0.515248\pi$
$739$	−3.19554e129	−0.0957683	−0.0478841	+	0.998853i	$0.515248\pi$
$740$	2.39795e129	0.0675768
$741$	−1.07398e129	−0.0284622
$742$	−2.46324e130	−0.613943
$743$	−2.97175e130	−0.696661	−0.348330	−	0.937372i	$-0.613251\pi$
$743$	−2.97175e130	−0.696661	−0.348330	+	0.937372i	$0.613251\pi$
$744$	3.06996e130	0.676962
$745$	9.31016e128	0.0193129
$746$	6.95380e130	1.35708
$747$	1.04214e130	0.191354
$748$	−2.21627e129	−0.0382912
$749$	−1.57564e131	−2.56173
$750$	4.52120e129	0.0691776
$751$	9.73214e129	0.140149	0.0700747	−	0.997542i	$-0.477676\pi$
$751$	9.73214e129	0.140149	0.0700747	+	0.997542i	$0.477676\pi$
$752$	−3.79918e130	−0.514966
$753$	−3.97866e130	−0.507652
$754$	−4.73524e129	−0.0568781
$755$	−3.10370e129	−0.0350988
$756$	2.96506e131	3.15712
$757$	2.53167e130	0.253831	0.126916	−	0.991914i	$-0.459492\pi$
$757$	2.53167e130	0.253831	0.126916	+	0.991914i	$0.459492\pi$
$758$	−2.55534e130	−0.241268
$759$	2.18271e128	0.00194087
$760$	−9.45918e129	−0.0792201
$761$	1.78963e131	1.41176	0.705880	−	0.708332i	$-0.250552\pi$
$761$	1.78963e131	1.41176	0.705880	+	0.708332i	$0.250552\pi$
$762$	2.29820e130	0.170780
$763$	−9.73168e130	−0.681273
$764$	−3.21529e131	−2.12067
$765$	6.85417e129	0.0425951
$766$	3.74388e131	2.19237
$767$	2.52840e129	0.0139527
$768$	−1.94436e131	−1.01121
$769$	1.99994e131	0.980319	0.490160	−	0.871633i	$-0.336938\pi$
$769$	1.99994e131	0.980319	0.490160	+	0.871633i	$0.336938\pi$
$770$	2.65072e128	0.00122472
$771$	−7.93562e130	−0.345626
$772$	−5.00929e131	−2.05679
$773$	−3.80240e131	−1.47194	−0.735971	−	0.677013i	$-0.763274\pi$
$773$	−3.80240e131	−1.47194	−0.735971	+	0.677013i	$0.763274\pi$
$774$	−3.86734e131	−1.41156
$775$	2.34526e131	0.807169
$776$	−1.97648e131	−0.641482
$777$	−3.38512e131	−1.03614
$778$	5.91555e131	1.70775
$779$	7.01323e131	1.90969
$780$	−4.80668e128	−0.00123464
$781$	3.76287e129	0.00911795
$782$	3.87948e131	0.886883
$783$	4.61514e131	0.995462
$784$	6.29549e131	1.28129
$785$	2.41432e130	0.0463688
$786$	−4.37823e131	−0.793547
$787$	−2.17196e131	−0.371536	−0.185768	−	0.982594i	$-0.559477\pi$
$787$	−2.17196e131	−0.371536	−0.185768	+	0.982594i	$0.559477\pi$
$788$	6.86189e131	1.10790
$789$	1.48042e130	0.0225621
$790$	−4.60226e130	−0.0662122
$791$	−1.29518e132	−1.75914
$792$	8.75716e129	0.0112297
$793$	1.63624e130	0.0198115
$794$	−2.00282e132	−2.28986
$795$	−3.89189e129	−0.00420201
$796$	−1.36471e132	−1.39154
$797$	3.04476e131	0.293224	0.146612	−	0.989194i	$-0.453163\pi$
$797$	3.04476e131	0.293224	0.146612	+	0.989194i	$0.453163\pi$
$798$	2.88546e132	2.62472
$799$	1.77496e132	1.52514
$800$	−5.36875e131	−0.435791
$801$	−4.93629e131	−0.378548
$802$	−1.68496e131	−0.122083
$803$	1.14012e130	0.00780535
$804$	−1.32677e132	−0.858316
$805$	−3.01841e130	−0.0184529
$806$	−7.67054e130	−0.0443181
$807$	−5.28903e130	−0.0288822
$808$	−4.83370e132	−2.49496
$809$	3.42473e132	1.67097	0.835486	−	0.549512i	$-0.185186\pi$
$809$	3.42473e132	1.67097	0.835486	+	0.549512i	$0.185186\pi$
$810$	−1.53886e130	−0.00709790
$811$	−1.49751e132	−0.653013	−0.326506	−	0.945195i	$-0.605871\pi$
$811$	−1.49751e132	−0.653013	−0.326506	+	0.945195i	$0.605871\pi$
$812$	8.27606e132	3.41212
$813$	−1.01019e132	−0.393807
$814$	−5.38695e130	−0.0198579
$815$	−1.18255e131	−0.0412237
$816$	−1.88056e132	−0.619992
$817$	−6.10474e132	−1.90355
$818$	6.52511e132	1.92448
$819$	−1.37495e131	−0.0383592
$820$	3.13882e131	0.0828392
$821$	1.48426e132	0.370593	0.185296	−	0.982683i	$-0.440675\pi$
$821$	1.48426e132	0.370593	0.185296	+	0.982683i	$0.440675\pi$
$822$	−1.06067e132	−0.250561
$823$	2.98745e132	0.667741	0.333870	−	0.942619i	$-0.391645\pi$
$823$	2.98745e132	0.667741	0.333870	+	0.942619i	$0.391645\pi$
$824$	1.25001e132	0.264378
$825$	−3.30151e130	−0.00660782
$826$	−6.79305e132	−1.28669
$827$	9.37271e132	1.68021	0.840107	−	0.542421i	$-0.182492\pi$
$827$	9.37271e132	1.68021	0.840107	+	0.542421i	$0.182492\pi$
$828$	−2.15480e132	−0.365617
$829$	−3.66010e132	−0.587843	−0.293921	−	0.955830i	$-0.594960\pi$
$829$	−3.66010e132	−0.587843	−0.293921	+	0.955830i	$0.594960\pi$
$830$	1.13179e131	0.0172073
$831$	−4.27071e132	−0.614687
$832$	3.19156e131	0.0434903
$833$	−2.94122e133	−3.79472
$834$	3.52480e132	0.430605
$835$	2.28739e131	0.0264609
$836$	2.98708e131	0.0327237
$837$	7.47599e132	0.775641
$838$	2.52295e132	0.247917
$839$	6.51720e132	0.606585	0.303293	−	0.952897i	$-0.401914\pi$
$839$	6.51720e132	0.606585	0.303293	+	0.952897i	$0.401914\pi$
$840$	5.97634e131	0.0526899
$841$	9.08353e131	0.0758642
$842$	9.46943e132	0.749244
$843$	−6.60741e132	−0.495309
$844$	4.99945e133	3.55092
$845$	−5.28325e131	−0.0355567
$846$	−1.51551e133	−0.966511
$847$	2.92374e133	1.76703
$848$	−2.16374e132	−0.123935
$849$	−4.12472e132	−0.223921
$850$	−5.86799e133	−3.01945
$851$	6.13419e132	0.299200
$852$	1.83324e133	0.847652
$853$	1.62781e133	0.713547	0.356773	−	0.934191i	$-0.383877\pi$
$853$	1.62781e133	0.713547	0.356773	+	0.934191i	$0.383877\pi$
$854$	−4.39608e133	−1.82698
$855$	−9.23804e131	−0.0364017
$856$	−5.65322e133	−2.11222
$857$	1.67475e133	0.593365	0.296682	−	0.954976i	$-0.404120\pi$
$857$	1.67475e133	0.593365	0.296682	+	0.954976i	$0.404120\pi$
$858$	1.07981e130	0.000362807 0
$859$	4.83461e133	1.54054	0.770270	−	0.637718i	$-0.220122\pi$
$859$	4.83461e133	1.54054	0.770270	+	0.637718i	$0.220122\pi$
$860$	−2.73222e132	−0.0825727
$861$	−4.43097e133	−1.27015
$862$	7.16200e132	0.194739
$863$	−1.13799e133	−0.293526	−0.146763	−	0.989172i	$-0.546885\pi$
$863$	−1.13799e133	−0.293526	−0.146763	+	0.989172i	$0.546885\pi$
$864$	−1.71140e133	−0.418769
$865$	−1.72605e132	−0.0400700
$866$	−2.78154e133	−0.612662
$867$	6.03541e133	1.26136
$868$	1.34063e134	2.65864
$869$	6.72567e131	0.0126572
$870$	2.01009e132	0.0358996
$871$	1.53413e132	0.0260037
$872$	−3.49163e133	−0.561730
$873$	−1.93028e133	−0.294762
$874$	−5.22876e133	−0.757929
$875$	9.13691e132	0.125728
$876$	5.55456e133	0.725626
$877$	−1.60225e134	−1.98724	−0.993618	−	0.112802i	$-0.964018\pi$
$877$	−1.60225e134	−1.98724	−0.993618	+	0.112802i	$0.964018\pi$
$878$	8.56828e133	1.00900
$879$	−3.06372e132	−0.0342574
$880$	2.32843e130	0.000247230 0
$881$	−1.20880e134	−1.21885	−0.609427	−	0.792842i	$-0.708601\pi$
$881$	−1.20880e134	−1.21885	−0.609427	+	0.792842i	$0.708601\pi$
$882$	2.51130e134	2.40479
$883$	−5.14322e133	−0.467760	−0.233880	−	0.972265i	$-0.575142\pi$
$883$	−5.14322e133	−0.467760	−0.233880	+	0.972265i	$0.575142\pi$
$884$	1.24849e133	0.107847
$885$	−1.07330e132	−0.00880646
$886$	1.15420e134	0.899595
$887$	1.29882e134	0.961662	0.480831	−	0.876813i	$-0.340335\pi$
$887$	1.29882e134	0.961662	0.480831	+	0.876813i	$0.340335\pi$
$888$	−1.21455e134	−0.854327
$889$	4.64445e133	0.310387
$890$	−5.36095e132	−0.0340405
$891$	2.24886e131	0.00135684
$892$	−3.19915e134	−1.83415
$893$	−2.39229e134	−1.30338
$894$	−1.01896e134	−0.527596
$895$	7.44886e132	0.0366557
$896$	−6.92605e134	−3.23945
$897$	−1.22959e132	−0.00546645
$898$	6.21918e134	2.62821
$899$	2.08670e134	0.838289
$900$	3.25928e134	1.24477
$901$	1.01089e134	0.367049
$902$	−7.05129e132	−0.0243428
$903$	3.85699e134	1.26607
$904$	−4.64698e134	−1.45046
$905$	1.28976e133	0.0382823
$906$	3.39689e134	0.958844
$907$	−5.87110e133	−0.157612	−0.0788058	−	0.996890i	$-0.525111\pi$
$907$	−5.87110e133	−0.157612	−0.0788058	+	0.996890i	$0.525111\pi$
$908$	5.69450e134	1.45395
$909$	−4.72070e134	−1.14644
$910$	−1.49324e132	−0.00344941
$911$	2.50756e134	0.551018	0.275509	−	0.961298i	$-0.411154\pi$
$911$	2.50756e134	0.551018	0.275509	+	0.961298i	$0.411154\pi$
$912$	2.53462e134	0.529845
$913$	−1.65398e132	−0.00328935
$914$	1.52781e134	0.289079
$915$	−6.94578e132	−0.0125044
$916$	−1.75567e134	−0.300745
$917$	−8.84799e134	−1.44225
$918$	−1.87054e135	−2.90151
$919$	1.00069e135	1.47722	0.738611	−	0.674132i	$-0.235482\pi$
$919$	1.00069e135	1.47722	0.738611	+	0.674132i	$0.235482\pi$
$920$	−1.08298e133	−0.0152150
$921$	1.53776e134	0.205625
$922$	−7.13839e134	−0.908538
$923$	−2.11974e133	−0.0256807
$924$	−1.88725e133	−0.0217648
$925$	−9.27840e134	−1.01865
$926$	1.10865e135	1.15877
$927$	1.22078e134	0.121482
$928$	−4.77684e134	−0.452593
$929$	−1.58586e135	−1.43071	−0.715353	−	0.698763i	$-0.753734\pi$
$929$	−1.58586e135	−1.43071	−0.715353	+	0.698763i	$0.753734\pi$
$930$	3.25612e133	0.0279721
$931$	3.96418e135	3.24297
$932$	1.85626e135	1.44616
$933$	−2.25270e134	−0.167143
$934$	2.58721e135	1.82830
$935$	−1.08783e132	−0.000732204 0
$936$	−4.93319e133	−0.0316283
$937$	−9.96079e134	−0.608335	−0.304167	−	0.952619i	$-0.598378\pi$
$937$	−9.96079e134	−0.608335	−0.304167	+	0.952619i	$0.598378\pi$
$938$	−4.12174e135	−2.39801
$939$	−7.26969e134	−0.402932
$940$	−1.07069e134	−0.0565386
$941$	1.11748e135	0.562226	0.281113	−	0.959675i	$-0.409296\pi$
$941$	1.11748e135	0.562226	0.281113	+	0.959675i	$0.409296\pi$
$942$	−2.64239e135	−1.26672
$943$	8.02939e134	0.366776
$944$	−5.96710e134	−0.259739
$945$	1.45536e134	0.0603704
$946$	6.13788e133	0.0242645
$947$	2.14523e135	0.808258	0.404129	−	0.914702i	$-0.367575\pi$
$947$	2.14523e135	0.808258	0.404129	+	0.914702i	$0.367575\pi$
$948$	3.27669e135	1.17667
$949$	−6.42265e133	−0.0219837
$950$	7.90887e135	2.58042
$951$	3.58741e134	0.111575
$952$	−1.55230e136	−4.60252
$953$	−4.40353e135	−1.24473	−0.622363	−	0.782728i	$-0.713827\pi$
$953$	−4.40353e135	−1.24473	−0.622363	+	0.782728i	$0.713827\pi$
$954$	−8.63123e134	−0.232606
$955$	−1.57819e134	−0.0405514
$956$	1.43669e136	3.51988
$957$	−2.93752e133	−0.00686258
$958$	−6.78181e135	−1.51083
$959$	−2.14352e135	−0.455386
$960$	−1.35481e134	−0.0274496
$961$	−1.79483e135	−0.346825
$962$	3.03464e134	0.0559296
$963$	−5.52106e135	−0.970569
$964$	2.56783e135	0.430587
$965$	−2.45875e134	−0.0393298
$966$	3.30354e135	0.504105
$967$	2.66371e135	0.387777	0.193888	−	0.981024i	$-0.437890\pi$
$967$	2.66371e135	0.387777	0.193888	+	0.981024i	$0.437890\pi$
$968$	1.04901e136	1.45697
$969$	−1.18416e136	−1.56921
$970$	−2.09633e134	−0.0265061
$971$	6.62805e135	0.799670	0.399835	−	0.916587i	$-0.369067\pi$
$971$	6.62805e135	0.799670	0.399835	+	0.916587i	$0.369067\pi$
$972$	1.66126e136	1.91259
$973$	7.12329e135	0.782612
$974$	−1.79819e135	−0.188540
$975$	1.85985e134	0.0186109
$976$	−3.86157e135	−0.368806
$977$	−9.52916e135	−0.868664	−0.434332	−	0.900753i	$-0.643016\pi$
$977$	−9.52916e135	−0.868664	−0.434332	+	0.900753i	$0.643016\pi$
$978$	1.29426e136	1.12617
$979$	7.83441e133	0.00650720
$980$	1.77420e135	0.140674
$981$	−3.41000e135	−0.258116
$982$	−3.25872e136	−2.35491
$983$	7.15543e135	0.493686	0.246843	−	0.969056i	$-0.420607\pi$
$983$	7.15543e135	0.493686	0.246843	+	0.969056i	$0.420607\pi$
$984$	−1.58979e136	−1.04728
$985$	3.36808e134	0.0211853
$986$	−5.22104e136	−3.13587
$987$	1.51146e136	0.866892
$988$	−1.68272e135	−0.0921660
$989$	−6.98928e135	−0.365596
$990$	9.28818e132	0.000464012 0
$991$	3.38314e136	1.61424	0.807120	−	0.590387i	$-0.201025\pi$
$991$	3.38314e136	1.61424	0.807120	+	0.590387i	$0.201025\pi$
$992$	−7.73794e135	−0.352650
$993$	1.04772e136	0.456095
$994$	5.69511e136	2.36822
$995$	−6.69852e134	−0.0266090
$996$	−8.05806e135	−0.305795
$997$	2.09070e136	0.757987	0.378993	−	0.925399i	$-0.376270\pi$
$997$	2.09070e136	0.757987	0.378993	+	0.925399i	$0.376270\pi$
$998$	4.21291e136	1.45929
$999$	−2.95767e136	−0.978860

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.92.a.a.1.1	✓	7
3.2	odd	2		9.92.a.b.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.92.a.a.1.1	✓	7	1.1	even	1	trivial
9.92.a.b.1.7		7	3.2	odd	2

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:	\( k \)	\(=\)	\( 92 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-8.41697e13 q^{2} +2.94143e21 q^{3} +4.60866e27 q^{4} +2.26211e30 q^{5} -2.47580e35 q^{6} -5.00335e38 q^{7} -1.79515e41 q^{8} -1.75319e43 q^{9} +O(q^{10})\)	\(q-8.41697e13 q^{2} +2.94143e21 q^{3} +4.60866e27 q^{4} +2.26211e30 q^{5} -2.47580e35 q^{6} -5.00335e38 q^{7} -1.79515e41 q^{8} -1.75319e43 q^{9} -1.90401e44 q^{10} +2.78249e45 q^{11} +1.35561e49 q^{12} -1.56747e49 q^{13} +4.21131e52 q^{14} +6.65384e51 q^{15} +3.69926e54 q^{16} -1.72828e56 q^{17} +1.47565e57 q^{18} +2.32937e58 q^{19} +1.04253e58 q^{20} -1.47170e60 q^{21} -2.34201e59 q^{22} +2.66688e61 q^{23} -5.28033e62 q^{24} -4.03385e63 q^{25} +1.31933e63 q^{26} -1.28587e65 q^{27} -2.30588e66 q^{28} -3.58912e66 q^{29} -5.60052e65 q^{30} -5.81396e67 q^{31} +1.33092e68 q^{32} +8.18452e66 q^{33} +1.45469e70 q^{34} -1.13181e69 q^{35} -8.07983e70 q^{36} +2.30013e71 q^{37} -1.96063e72 q^{38} -4.61060e70 q^{39} -4.06083e71 q^{40} +3.01078e73 q^{41} +1.23873e74 q^{42} -2.62077e74 q^{43} +1.28236e73 q^{44} -3.96589e73 q^{45} -2.24471e75 q^{46} -1.02701e76 q^{47} +1.08811e76 q^{48} +1.70182e77 q^{49} +3.39528e77 q^{50} -5.08362e77 q^{51} -7.22392e76 q^{52} -5.84910e77 q^{53} +1.08231e79 q^{54} +6.29429e75 q^{55} +8.98179e79 q^{56} +6.85170e79 q^{57} +3.02095e80 q^{58} -1.61305e80 q^{59} +3.06653e79 q^{60} -1.04388e81 q^{61} +4.89359e81 q^{62} +8.77181e81 q^{63} -2.03613e82 q^{64} -3.54578e79 q^{65} -6.88888e80 q^{66} -9.78731e82 q^{67} -7.96504e83 q^{68} +7.84446e82 q^{69} +9.52643e82 q^{70} +1.35234e84 q^{71} +3.14724e84 q^{72} +4.09747e84 q^{73} -1.93602e85 q^{74} -1.18653e85 q^{75} +1.07353e86 q^{76} -1.39218e84 q^{77} +3.88073e84 q^{78} +2.41714e86 q^{79} +8.36813e84 q^{80} +8.08220e85 q^{81} -2.53416e87 q^{82} -5.94425e86 q^{83} -6.78258e87 q^{84} -3.90955e86 q^{85} +2.20589e88 q^{86} -1.05572e88 q^{87} -4.99500e86 q^{88} +2.81561e88 q^{89} +3.33808e87 q^{90} +7.84259e87 q^{91} +1.22908e89 q^{92} -1.71014e89 q^{93} +8.64432e89 q^{94} +5.26929e88 q^{95} +3.91483e89 q^{96} +1.10101e90 q^{97} -1.43242e91 q^{98} -4.87822e88 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 3841716838056 q^{2} + 62\!\cdots\!32 q^{3}+ \cdots + 38\!\cdots\!59 q^{9}+O(q^{10}) \) 7 * q + 3841716838056 * q^2 + 6226865993447967511332 * q^3 + 5671662926176418572725837376 * q^4 + 23504964778584408375486754830930 * q^5 + 451174906579592943363587112684473184 * q^6 - 171085178649369081126501604564827872344 * q^7 - 10385570201002723586914837423420014159360 * q^8 + 38080901154162874719072934775718033448005459 * q^9	\( 7 q + 3841716838056 q^{2} + 62\!\cdots\!32 q^{3}+ \cdots - 23\!\cdots\!92 q^{99}+O(q^{100}) \) 7 * q + 3841716838056 * q^2 + 6226865993447967511332 * q^3 + 5671662926176418572725837376 * q^4 + 23504964778584408375486754830930 * q^5 + 451174906579592943363587112684473184 * q^6 - 171085178649369081126501604564827872344 * q^7 - 10385570201002723586914837423420014159360 * q^8 + 38080901154162874719072934775718033448005459 * q^9 + 4697789292978379445837627874024155681811061680 * q^10 - 240582832892068760628122732280591830839146659316 * q^11 + 15234465137330235186821811325942149339051634358016 * q^12 + 712268684544237976989939315593627958143865337752122 * q^13 + 17766212926078897376844163559794320416860400218986432 * q^14 + 818092333276881407770547708857297926161740517153634360 * q^15 - 5543121629719415776419174196841312964977690510556459008 * q^16 - 116788563921119361626790446343979264424208809345044156194 * q^17 + 2532221674884609223972217344567154578664327889292374599112 * q^18 + 24914430965691713272160835064548829827762713320225549023860 * q^19 + 213622308691313951002559876190359340784045827397766986247040 * q^20 - 2997932825643989744485469587195205163128865044067155102498976 * q^21 + 2770354076929612113872013355190927517116944942304065995485472 * q^22 + 28060217473226028795108958325793316282935533444516172471797112 * q^23 - 676645515624503740032420639044230674317241134651601877083678720 * q^24 + 3263569264491109562693810546136813966434457662326151208223443025 * q^25 + 14647231349517882504358224484901087010163561052132416579801164144 * q^26 + 88534490857595263563477937784200716693877558838426769810977256360 * q^27 - 1267961512722154560010156489449223630509765593702989988702255606272 * q^28 - 1998207010601468906936357688217559269263973686319086789407593851510 * q^29 + 46684773092381185628041557878825569520483461165868165669687502423360 * q^30 - 59925208170796133190382607870079728441723654705660441096474565882976 * q^31 - 349236116256080438032682462092197690284580228848172295706337753268224 * q^32 + 48956964959741209887245659130472098420831296585540373363667238885584 * q^33 + 4422724362741906584267050702673869603971959112955389299199109971390672 * q^34 - 13368721150607890395306302586915792313883425318712829768566063087971920 * q^35 + 48271193532350417136817688340793844028122089698778111115225583548795712 * q^36 - 193385642725694230212647842547384176779300890377457537180445039472551694 * q^37 + 648885030040198126856514202904430175712235671732708835862375911231617760 * q^38 - 1888050736392299353100554804844814233146715239003942457135725287045138792 * q^39 + 612437306889339293021693643280174203404468934648721750255585003111910400 * q^40 + 27467963396808209903058935820529109024708043852794661490538346949004391894 * q^41 + 2490746600045939910899268282231591851463383036227202908840686832900714752 * q^42 - 305936680392367608196854535263961824203961856383604167638158912234512481108 * q^43 + 205463536657254300042685770932278214832998693823974867822888457185152941312 * q^44 + 4760687647415457141753353234910279174019798332678698076640623508070611166010 * q^45 - 1366266407223913965782607380535324534407310537728351887747959292074575330496 * q^46 + 6016385666666683617266527127107702489089132053603324831460234388201640236656 * q^47 + 34119609737617524136090987754275812795178080643639536100065326182318914650112 * q^48 + 147622366871958729066285529870014845360644877218444002326443275466876372382751 * q^49 + 987686706148773430200902630527966650567454297252982416951455545242325575637400 * q^50 + 742769239785716829162529676417470760468992847219971127251563531253033686474504 * q^51 + 4318717132385281312358095915519383012120671308396466785048290702799702098686336 * q^52 + 13308120064559469621843967381370895719631000840255977547855692839275328956239682 * q^53 + 49855304363851366001446865238806860151072717129384273575810932439561849626548160 * q^54 + 71294075726222567616681402637553088151526343199773263267028104308906720840973160 * q^55 + 221193813355805774602587289215941353561793271848452643887988504737893638457815040 * q^56 + 528504764627515846582196025944068103123296527378022647769732650016063847427593520 * q^57 + 1238229446269131105368662021237658933365297194812595452448484778585094416520960240 * q^58 + 1315161090691534242045211041321797641427216505845115765078938874240054573263728380 * q^59 + 4823153254365391976824193526392851616116082049689724166967862952927612944155374080 * q^60 + 5062201896875711919454365982321524134556244374094873318866473906778984033476168234 * q^61 + 5944009317613068040880423794674923373270855087786172352031955991395153732464744192 * q^62 - 3636043453736261219929075304472074905914693023981615502769720183430994506848383288 * q^63 - 51461933507510968227229909173673546488880558907251327588128558485838721977163710464 * q^64 - 77004978625744224526600511688707953799859895672813324064129546096894713766789516340 * q^65 - 308541964188130582740963794759741868505184177678097911786772179394411954828298046592 * q^66 - 375865111304983135837477510931607479316175718244865448118159181323617876690058988444 * q^67 - 1534213067668968494728693973596412463295117507399423353249302546218581933051381708672 * q^68 - 2173315533882618835358431426746324715455060324131802571545777868624263537306736200672 * q^69 - 2678915571128698388724922631831368101885281292954514535801987008907571514431164929920 * q^70 + 965663858399224787677892593054987300813257337626219343051035389437608903566853136104 * q^71 + 4759225550598725097796726774244526164682601876181738961172151381039656425240893268480 * q^72 + 9530120766269923537811918138494095655717782977571711295781136472585782479177982847862 * q^73 + 19110889051618327071497328002063508382221976511726809975089825510120232325728977189552 * q^74 + 125021668038726866132333086418803849235968631984043287433627055625310081344612351442300 * q^75 + 201417481997189328603388340686282158978023686930352491852420967420198850453092214874880 * q^76 + 203838117981454989170200594078013407199331583446926407393231313568448855161412400016672 * q^77 + 348422592585817152583346169273764440235290509078131053609004533439300203952600764751424 * q^78 - 5875385290546216656185911308903463222289330212802402962421344496345859662855253387760 * q^79 - 704730665751803958915921202265388401277484106681191434954636540435925847481999762923520 * q^80 - 645876221088024404019866830164659790161069128158743050337018784266949283332298558348353 * q^81 - 5377119810649520829232661929626958820402325732939303335851648698643252753720266284836848 * q^82 - 7188939673179725085045886441204184334512306517239973817301478804674514872311469770345548 * q^83 - 17037797188065238374634346038194001797920522141104843305926325070074414892172026480416768 * q^84 - 18949626274852488910142757348951127712395103983201418376580212098044613619651779587066620 * q^85 - 13930550649009692825744367374854352346751992408208092118301786049776748630048877827166176 * q^86 + 14997220283992832178383660427617039138145206474606482931148662045188858037160846958683480 * q^87 + 35205946317573638735966560050796709996519491901124319190557129002743085716478822258247680 * q^88 + 58910603928414585742462774445274283779895728554450265497847918725594089228346625287686470 * q^89 + 596817611113547745433166439395807555701671900247626319346669516201533941956589878026043760 * q^90 + 431556051755722691175733360455273666621786312136528121760420810812400911428233396155619184 * q^91 + 649582018326251344367774515135408104477035917640264872918599325106081734967368208117408256 * q^92 + 176140526645345381525949017432055243763067046580068760248910898954659817267839614775511424 * q^93 + 528728237301347142597743478920778358077668394817645608650770473672424789094546213047704192 * q^94 + 460150241832447303916160340674008161933312298406246509746195633852627501820464219531336600 * q^95 - 5308520687978816513495454896751155260796827272022533467944875093089923121365143311537012736 * q^96 - 7025964934206676021621272614488614108607978598995771668040441707563730547939229623877790994 * q^97 - 20729666350145773779493369529709111649648862211758783582357755821769845548186544170995584792 * q^98 - 23913014682919445875702212438204672119308558146529134638425833150071457007907375951005388292 * q^99

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