LMFDB - Embedded newform 1.92.a.a.1.7

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			1.7
Root			$3.16475e12$ 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)

$f(q)$	$=$	$q+7.65028e13 q^{2} -2.65748e21 q^{3} +3.37680e27 q^{4} -4.45639e31 q^{5} -2.03305e35 q^{6} +2.84237e38 q^{7} +6.89228e40 q^{8} -1.91217e43 q^{9} +O(q^{10})$	\(q+7.65028e13 q^{2} -2.65748e21 q^{3} +3.37680e27 q^{4} -4.45639e31 q^{5} -2.03305e35 q^{6} +2.84237e38 q^{7} +6.89228e40 q^{8} -1.91217e43 q^{9} -3.40927e45 q^{10} +9.72727e46 q^{11} -8.97378e48 q^{12} +6.30388e50 q^{13} +2.17449e52 q^{14} +1.18428e53 q^{15} -3.08776e54 q^{16} -5.77591e55 q^{17} -1.46286e57 q^{18} +1.72189e58 q^{19} -1.50483e59 q^{20} -7.55354e59 q^{21} +7.44163e60 q^{22} +1.13922e62 q^{23} -1.83161e62 q^{24} -2.05302e63 q^{25} +4.82265e64 q^{26} +1.20399e65 q^{27} +9.59811e65 q^{28} +5.78948e66 q^{29} +9.06006e66 q^{30} +5.69673e67 q^{31} -4.06867e68 q^{32} -2.58500e68 q^{33} -4.41873e69 q^{34} -1.26667e70 q^{35} -6.45701e70 q^{36} +4.23882e71 q^{37} +1.31729e72 q^{38} -1.67525e72 q^{39} -3.07147e72 q^{40} -2.50923e72 q^{41} -5.77867e73 q^{42} -1.35809e74 q^{43} +3.28470e74 q^{44} +8.52138e74 q^{45} +8.71538e75 q^{46} -1.35732e76 q^{47} +8.20566e75 q^{48} +6.37215e74 q^{49} -1.57062e77 q^{50} +1.53494e77 q^{51} +2.12870e78 q^{52} +4.17132e78 q^{53} +9.21084e78 q^{54} -4.33485e78 q^{55} +1.95904e79 q^{56} -4.57588e79 q^{57} +4.42912e80 q^{58} +3.62948e80 q^{59} +3.99907e80 q^{60} +9.25617e80 q^{61} +4.35816e81 q^{62} -5.43509e81 q^{63} -2.34815e82 q^{64} -2.80926e82 q^{65} -1.97760e82 q^{66} +1.21510e83 q^{67} -1.95041e83 q^{68} -3.02746e83 q^{69} -9.69039e83 q^{70} -9.39434e82 q^{71} -1.31792e84 q^{72} -5.75947e84 q^{73} +3.24281e85 q^{74} +5.45587e84 q^{75} +5.81446e85 q^{76} +2.76485e85 q^{77} -1.28161e86 q^{78} -1.40597e86 q^{79} +1.37603e86 q^{80} +1.80723e86 q^{81} -1.91963e86 q^{82} -1.48810e87 q^{83} -2.55068e87 q^{84} +2.57397e87 q^{85} -1.03898e88 q^{86} -1.53854e88 q^{87} +6.70431e87 q^{88} +3.15928e88 q^{89} +6.51909e88 q^{90} +1.79180e89 q^{91} +3.84693e89 q^{92} -1.51390e89 q^{93} -1.03839e90 q^{94} -7.67340e89 q^{95} +1.08124e90 q^{96} -8.67008e89 q^{97} +4.87487e88 q^{98} -1.86002e90 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	7.65028e13	1.53749	0.768745	−	0.639555i	$-0.220881\pi$
$2$	7.65028e13	1.53749	0.768745	+	0.639555i	$0.220881\pi$
$3$	−2.65748e21	−0.519341	−0.259671	−	0.965697i	$-0.583614\pi$
$3$	−2.65748e21	−0.519341	−0.259671	+	0.965697i	$0.583614\pi$
$4$	3.37680e27	1.36388
$5$	−4.45639e31	−0.701210	−0.350605	−	0.936523i	$-0.614024\pi$
$5$	−4.45639e31	−0.701210	−0.350605	+	0.936523i	$0.614024\pi$
$6$	−2.03305e35	−0.798483
$7$	2.84237e38	1.00397	0.501984	−	0.864877i	$-0.332604\pi$
$7$	2.84237e38	1.00397	0.501984	+	0.864877i	$0.332604\pi$
$8$	6.89228e40	0.559459
$9$	−1.91217e43	−0.730284
$10$	−3.40927e45	−1.07810
$11$	9.72727e46	0.402368	0.201184	−	0.979553i	$-0.435521\pi$
$11$	9.72727e46	0.402368	0.201184	+	0.979553i	$0.435521\pi$
$12$	−8.97378e48	−0.708319
$13$	6.30388e50	1.30372	0.651862	−	0.758338i	$-0.273988\pi$
$13$	6.30388e50	1.30372	0.651862	+	0.758338i	$0.273988\pi$
$14$	2.17449e52	1.54359
$15$	1.18428e53	0.364168
$16$	−3.08776e54	−0.503714
$17$	−5.77591e55	−0.597302	−0.298651	−	0.954362i	$-0.596537\pi$
$17$	−5.77591e55	−0.597302	−0.298651	+	0.954362i	$0.596537\pi$
$18$	−1.46286e57	−1.12281
$19$	1.72189e58	1.12906	0.564528	−	0.825414i	$-0.309058\pi$
$19$	1.72189e58	1.12906	0.564528	+	0.825414i	$0.309058\pi$
$20$	−1.50483e59	−0.956365
$21$	−7.55354e59	−0.521402
$22$	7.44163e60	0.618638
$23$	1.13922e62	1.25312	0.626560	−	0.779374i	$-0.284463\pi$
$23$	1.13922e62	1.25312	0.626560	+	0.779374i	$0.284463\pi$
$24$	−1.83161e62	−0.290550
$25$	−2.05302e63	−0.508304
$26$	4.82265e64	2.00446
$27$	1.20399e65	0.898608
$28$	9.59811e65	1.36929
$29$	5.78948e66	1.67313	0.836567	−	0.547864i	$-0.184559\pi$
$29$	5.78948e66	1.67313	0.836567	+	0.547864i	$0.184559\pi$
$30$	9.06006e66	0.559904
$31$	5.69673e67	0.791897	0.395949	−	0.918273i	$-0.370416\pi$
$31$	5.69673e67	0.791897	0.395949	+	0.918273i	$0.370416\pi$
$32$	−4.06867e68	−1.33392
$33$	−2.58500e68	−0.208967
$34$	−4.41873e69	−0.918347
$35$	−1.26667e70	−0.703992
$36$	−6.45701e70	−0.996019
$37$	4.23882e71	1.87960	0.939802	−	0.341719i	$-0.111009\pi$
$37$	4.23882e71	1.87960	0.939802	+	0.341719i	$0.111009\pi$
$38$	1.31729e72	1.73591
$39$	−1.67525e72	−0.677078
$40$	−3.07147e72	−0.392299
$41$	−2.50923e72	−0.104202	−0.0521010	−	0.998642i	$-0.516592\pi$
$41$	−2.50923e72	−0.104202	−0.0521010	+	0.998642i	$0.516592\pi$
$42$	−5.77867e73	−0.801650
$43$	−1.35809e74	−0.645824	−0.322912	−	0.946429i	$-0.604662\pi$
$43$	−1.35809e74	−0.645824	−0.322912	+	0.946429i	$0.604662\pi$
$44$	3.28470e74	0.548781
$45$	8.52138e74	0.512083
$46$	8.71538e75	1.92666
$47$	−1.35732e76	−1.12780	−0.563898	−	0.825844i	$-0.690699\pi$
$47$	−1.35732e76	−1.12780	−0.563898	+	0.825844i	$0.690699\pi$
$48$	8.20566e75	0.261600
$49$	6.37215e74	0.00794995
$50$	−1.57062e77	−0.781513
$51$	1.53494e77	0.310204
$52$	2.12870e78	1.77812
$53$	4.17132e78	1.46461	0.732304	−	0.680978i	$-0.238445\pi$
$53$	4.17132e78	1.46461	0.732304	+	0.680978i	$0.238445\pi$
$54$	9.21084e78	1.38160
$55$	−4.33485e78	−0.282145
$56$	1.95904e79	0.561679
$57$	−4.57588e79	−0.586366
$58$	4.42912e80	2.57243
$59$	3.62948e80	0.968451	0.484226	−	0.874943i	$-0.339101\pi$
$59$	3.62948e80	0.968451	0.484226	+	0.874943i	$0.339101\pi$
$60$	3.99907e80	0.496680
$61$	9.25617e80	0.541906	0.270953	−	0.962593i	$-0.412661\pi$
$61$	9.25617e80	0.541906	0.270953	+	0.962593i	$0.412661\pi$
$62$	4.35816e81	1.21753
$63$	−5.43509e81	−0.733182
$64$	−2.34815e82	−1.54717
$65$	−2.80926e82	−0.914185
$66$	−1.97760e82	−0.321284
$67$	1.21510e83	0.995881	0.497940	−	0.867211i	$-0.334090\pi$
$67$	1.21510e83	0.995881	0.497940	+	0.867211i	$0.334090\pi$
$68$	−1.95041e83	−0.814648
$69$	−3.02746e83	−0.650797
$70$	−9.69039e83	−1.08238
$71$	−9.39434e82	−0.0550315	−0.0275158	−	0.999621i	$-0.508760\pi$
$71$	−9.39434e82	−0.0550315	−0.0275158	+	0.999621i	$0.508760\pi$
$72$	−1.31792e84	−0.408565
$73$	−5.75947e84	−0.953219	−0.476609	−	0.879115i	$-0.658134\pi$
$73$	−5.75947e84	−0.953219	−0.476609	+	0.879115i	$0.658134\pi$
$74$	3.24281e85	2.88987
$75$	5.45587e84	0.263983
$76$	5.81446e85	1.53990
$77$	2.76485e85	0.403965
$78$	−1.28161e86	−1.04100
$79$	−1.40597e86	−0.639650	−0.319825	−	0.947477i	$-0.603624\pi$
$79$	−1.40597e86	−0.639650	−0.319825	+	0.947477i	$0.603624\pi$
$80$	1.37603e86	0.353210
$81$	1.80723e86	0.263600
$82$	−1.91963e86	−0.160209
$83$	−1.48810e87	−0.715449	−0.357725	−	0.933827i	$-0.616447\pi$
$83$	−1.48810e87	−0.715449	−0.357725	+	0.933827i	$0.616447\pi$
$84$	−2.55068e87	−0.711128
$85$	2.57397e87	0.418835
$86$	−1.03898e88	−0.992949
$87$	−1.53854e88	−0.868928
$88$	6.70431e87	0.225109
$89$	3.15928e88	0.634371	0.317186	−	0.948363i	$-0.397262\pi$
$89$	3.15928e88	0.634371	0.317186	+	0.948363i	$0.397262\pi$
$90$	6.51909e88	0.787323
$91$	1.79180e89	1.30890
$92$	3.84693e89	1.70910
$93$	−1.51390e89	−0.411265
$94$	−1.03839e90	−1.73398
$95$	−7.67340e89	−0.791706
$96$	1.08124e90	0.692758
$97$	−8.67008e89	−0.346664	−0.173332	−	0.984863i	$-0.555453\pi$
$97$	−8.67008e89	−0.346664	−0.173332	+	0.984863i	$0.555453\pi$
$98$	4.87487e88	0.0122230
$99$	−1.86002e90	−0.293843
$100$	−6.93265e90	−0.693265
$101$	5.04616e90	0.320877	0.160439	−	0.987046i	$-0.448709\pi$
$101$	5.04616e90	0.320877	0.160439	+	0.987046i	$0.448709\pi$
$102$	1.17427e91	0.476936
$103$	−7.16410e91	−1.86667	−0.933336	−	0.359003i	$-0.883117\pi$
$103$	−7.16410e91	−1.86667	−0.933336	+	0.359003i	$0.883117\pi$
$104$	4.34482e91	0.729381
$105$	3.36615e91	0.365612
$106$	3.19117e92	2.25182
$107$	4.70443e90	0.0216544	0.0108272	−	0.999941i	$-0.496554\pi$
$107$	4.70443e90	0.0216544	0.0108272	+	0.999941i	$0.496554\pi$
$108$	4.06562e92	1.22559
$109$	−6.62183e92	−1.31242	−0.656210	−	0.754579i	$-0.727841\pi$
$109$	−6.62183e92	−1.31242	−0.656210	+	0.754579i	$0.727841\pi$
$110$	−3.31628e92	−0.433795
$111$	−1.12646e93	−0.976156
$112$	−8.77655e92	−0.505713
$113$	7.37318e92	0.283521	0.141761	−	0.989901i	$-0.454724\pi$
$113$	7.37318e92	0.283521	0.141761	+	0.989901i	$0.454724\pi$
$114$	−3.50068e93	−0.901532
$115$	−5.07683e93	−0.878700
$116$	1.95499e94	2.28195
$117$	−1.20541e94	−0.952090
$118$	2.77665e94	1.48899
$119$	−1.64173e94	−0.599672
$120$	8.16238e93	0.203737
$121$	−4.89813e94	−0.838100
$122$	7.08123e94	0.833176
$123$	6.66824e93	0.0541164
$124$	1.92367e95	1.08005
$125$	2.71483e95	1.05764
$126$	−4.15799e95	−1.12726
$127$	−9.00021e95	−1.70288	−0.851438	−	0.524455i	$-0.824269\pi$
$127$	−9.00021e95	−1.70288	−0.851438	+	0.524455i	$0.824269\pi$
$128$	−7.89050e95	−1.04484
$129$	3.60910e95	0.335403
$130$	−2.14916e96	−1.40555
$131$	3.29742e96	1.52171	0.760853	−	0.648924i	$-0.224781\pi$
$131$	3.29742e96	1.52171	0.760853	+	0.648924i	$0.224781\pi$
$132$	−8.72904e95	−0.285005
$133$	4.89424e96	1.13354
$134$	9.29583e96	1.53116
$135$	−5.36544e96	−0.630114
$136$	−3.98092e96	−0.334167
$137$	2.40720e97	1.44786	0.723931	−	0.689873i	$-0.242334\pi$
$137$	2.40720e97	1.44786	0.723931	+	0.689873i	$0.242334\pi$
$138$	−2.31609e97	−1.00059
$139$	−2.25749e97	−0.702188	−0.351094	−	0.936340i	$-0.614190\pi$
$139$	−2.25749e97	−0.702188	−0.351094	+	0.936340i	$0.614190\pi$
$140$	−4.27729e97	−0.960159
$141$	3.60706e97	0.585711
$142$	−7.18693e96	−0.0846104
$143$	6.13196e97	0.524577
$144$	5.90432e97	0.367855
$145$	−2.58002e98	−1.17322
$146$	−4.40616e98	−1.46557
$147$	−1.69339e96	−0.00412874
$148$	1.43136e99	2.56355
$149$	−7.91147e98	−1.04299	−0.521497	−	0.853253i	$-0.674626\pi$
$149$	−7.91147e98	−1.04299	−0.521497	+	0.853253i	$0.674626\pi$
$150$	4.17389e98	0.405872
$151$	6.97984e98	0.501643	0.250821	−	0.968033i	$-0.419299\pi$
$151$	6.97984e98	0.501643	0.250821	+	0.968033i	$0.419299\pi$
$152$	1.18677e99	0.631661
$153$	1.10445e99	0.436201
$154$	2.11519e99	0.621092
$155$	−2.53869e99	−0.555287
$156$	−5.65697e99	−0.923452
$157$	−1.17190e100	−1.43040	−0.715199	−	0.698920i	$-0.753664\pi$
$157$	−1.17190e100	−1.43040	−0.715199	+	0.698920i	$0.753664\pi$
$158$	−1.07560e100	−0.983457
$159$	−1.10852e100	−0.760631
$160$	1.81316e100	0.935355
$161$	3.23809e100	1.25809
$162$	1.38258e100	0.405282
$163$	3.05692e100	0.677249	0.338625	−	0.940922i	$-0.390038\pi$
$163$	3.05692e100	0.677249	0.338625	+	0.940922i	$0.390038\pi$
$164$	−8.47318e99	−0.142119
$165$	1.15198e100	0.146529
$166$	−1.13844e101	−1.10000
$167$	9.24706e100	0.679836	0.339918	−	0.940455i	$-0.389601\pi$
$167$	9.24706e100	0.679836	0.339918	+	0.940455i	$0.389601\pi$
$168$	−5.20611e100	−0.291703
$169$	1.63589e101	0.699697
$170$	1.96916e101	0.643954
$171$	−3.29254e101	−0.824532
$172$	−4.58600e101	−0.880826
$173$	8.94594e101	1.31986	0.659930	−	0.751327i	$-0.270586\pi$
$173$	8.94594e101	1.31986	0.659930	+	0.751327i	$0.270586\pi$
$174$	−1.17703e102	−1.33597
$175$	−5.83545e101	−0.510321
$176$	−3.00355e101	−0.202679
$177$	−9.64527e101	−0.502957
$178$	2.41694e102	0.975340
$179$	−3.16769e102	−0.990672	−0.495336	−	0.868702i	$-0.664955\pi$
$179$	−3.16769e102	−0.990672	−0.495336	+	0.868702i	$0.664955\pi$
$180$	2.87750e102	0.698419
$181$	4.61589e102	0.870724	0.435362	−	0.900256i	$-0.356620\pi$
$181$	4.61589e102	0.870724	0.435362	+	0.900256i	$0.356620\pi$
$182$	1.37077e103	2.01242
$183$	−2.45981e102	−0.281434
$184$	7.85185e102	0.701069
$185$	−1.88898e103	−1.31800
$186$	−1.15817e103	−0.632316
$187$	−5.61838e102	−0.240336
$188$	−4.58341e103	−1.53818
$189$	3.42217e103	0.902173
$190$	−5.87037e103	−1.21724
$191$	1.83652e103	0.299901	0.149951	−	0.988693i	$-0.452089\pi$
$191$	1.83652e103	0.299901	0.149951	+	0.988693i	$0.452089\pi$
$192$	6.24017e103	0.803509
$193$	5.73963e103	0.583481	0.291740	−	0.956498i	$-0.405766\pi$
$193$	5.73963e103	0.583481	0.291740	+	0.956498i	$0.405766\pi$
$194$	−6.63285e103	−0.532993
$195$	7.46555e103	0.474774
$196$	2.15175e102	0.0108428
$197$	2.37058e104	0.947636	0.473818	−	0.880623i	$-0.342875\pi$
$197$	2.37058e104	0.947636	0.473818	+	0.880623i	$0.342875\pi$
$198$	−1.42297e104	−0.451781
$199$	−9.26599e103	−0.233925	−0.116963	−	0.993136i	$-0.537316\pi$
$199$	−9.26599e103	−0.233925	−0.116963	+	0.993136i	$0.537316\pi$
$200$	−1.41500e104	−0.284376
$201$	−3.22910e104	−0.517202
$202$	3.86046e104	0.493346
$203$	1.64558e105	1.67977
$204$	5.18317e104	0.423080
$205$	1.11821e104	0.0730675
$206$	−5.48074e105	−2.86999
$207$	−2.17839e105	−0.915133
$208$	−1.94649e105	−0.656705
$209$	1.67493e105	0.454297
$210$	2.57520e105	0.562126
$211$	−1.24609e105	−0.219128	−0.109564	−	0.993980i	$-0.534946\pi$
$211$	−1.24609e105	−0.219128	−0.109564	+	0.993980i	$0.534946\pi$
$212$	1.40857e106	1.99755
$213$	2.49653e104	0.0285801
$214$	3.59902e104	0.0332934
$215$	6.05219e105	0.452859
$216$	8.29822e105	0.502735
$217$	1.61922e106	0.795039
$218$	−5.06589e106	−2.01783
$219$	1.53057e106	0.495046
$220$	−1.46379e106	−0.384811
$221$	−3.64107e106	−0.778718
$222$	−8.61772e106	−1.50083
$223$	1.18088e107	1.67623	0.838115	−	0.545494i	$-0.183658\pi$
$223$	1.18088e107	1.67623	0.838115	+	0.545494i	$0.183658\pi$
$224$	−1.15647e107	−1.33921
$225$	3.92573e106	0.371207
$226$	5.64069e106	0.435911
$227$	2.60172e107	1.64469	0.822345	−	0.568990i	$-0.192666\pi$
$227$	2.60172e107	1.64469	0.822345	+	0.568990i	$0.192666\pi$
$228$	−1.54518e107	−0.799732
$229$	1.52020e107	0.644741	0.322371	−	0.946614i	$-0.395520\pi$
$229$	1.52020e107	0.644741	0.322371	+	0.946614i	$0.395520\pi$
$230$	−3.88391e107	−1.35099
$231$	−7.34753e106	−0.209796
$232$	3.99027e107	0.936051
$233$	4.64822e107	0.896588	0.448294	−	0.893886i	$-0.352032\pi$
$233$	4.64822e107	0.896588	0.448294	+	0.893886i	$0.352032\pi$
$234$	−9.22172e107	−1.46383
$235$	6.04877e107	0.790823
$236$	1.22560e108	1.32085
$237$	3.73633e107	0.332197
$238$	−1.25597e108	−0.921990
$239$	−2.31048e108	−1.40151	−0.700756	−	0.713401i	$-0.747154\pi$
$239$	−2.31048e108	−1.40151	−0.700756	+	0.713401i	$0.747154\pi$
$240$	−3.65677e107	−0.183436
$241$	1.41996e108	0.589523	0.294761	−	0.955571i	$-0.404760\pi$
$241$	1.41996e108	0.589523	0.294761	+	0.955571i	$0.404760\pi$
$242$	−3.74720e108	−1.28857
$243$	−3.63277e108	−1.03551
$244$	3.12562e108	0.739094
$245$	−2.83968e106	−0.00557459
$246$	5.10139e107	0.0832034
$247$	1.08546e109	1.47198
$248$	3.92635e108	0.443034
$249$	3.95460e108	0.371562
$250$	2.07692e109	1.62611
$251$	−2.33394e108	−0.152383	−0.0761913	−	0.997093i	$-0.524276\pi$
$251$	−2.33394e108	−0.152383	−0.0761913	+	0.997093i	$0.524276\pi$
$252$	−1.83532e109	−0.999970
$253$	1.10815e109	0.504215
$254$	−6.88541e109	−2.61816
$255$	−6.84028e108	−0.217518
$256$	−2.22705e108	−0.0592667
$257$	−1.73355e109	−0.386348	−0.193174	−	0.981165i	$-0.561878\pi$
$257$	−1.73355e109	−0.386348	−0.193174	+	0.981165i	$0.561878\pi$
$258$	2.76106e109	0.515680
$259$	1.20483e110	1.88706
$260$	−9.48630e109	−1.24684
$261$	−1.10705e110	−1.22186
$262$	2.52262e110	2.33961
$263$	−1.55268e110	−1.21086	−0.605432	−	0.795897i	$-0.707000\pi$
$263$	−1.55268e110	−1.21086	−0.605432	+	0.795897i	$0.707000\pi$
$264$	−1.78166e109	−0.116908
$265$	−1.85890e110	−1.02700
$266$	3.74423e110	1.74280
$267$	−8.39574e109	−0.329455
$268$	4.10314e110	1.35826
$269$	1.15451e110	0.322603	0.161302	−	0.986905i	$-0.448431\pi$
$269$	1.15451e110	0.322603	0.161302	+	0.986905i	$0.448431\pi$
$270$	−4.10471e110	−0.968794
$271$	−3.16290e110	−0.630931	−0.315466	−	0.948937i	$-0.602161\pi$
$271$	−3.16290e110	−0.630931	−0.315466	+	0.948937i	$0.602161\pi$
$272$	1.78346e110	0.300870
$273$	−4.76166e110	−0.679764
$274$	1.84158e111	2.22607
$275$	−1.99703e110	−0.204525
$276$	−1.02231e111	−0.887607
$277$	−1.64461e111	−1.21125	−0.605626	−	0.795749i	$-0.707077\pi$
$277$	−1.64461e111	−1.21125	−0.605626	+	0.795749i	$0.707077\pi$
$278$	−1.72705e111	−1.07961
$279$	−1.08931e111	−0.578310
$280$	−8.73025e110	−0.393855
$281$	1.16351e111	0.446306	0.223153	−	0.974783i	$-0.428365\pi$
$281$	1.16351e111	0.446306	0.223153	+	0.974783i	$0.428365\pi$
$282$	2.75950e111	0.900526
$283$	5.98536e111	1.66268	0.831338	−	0.555767i	$-0.187575\pi$
$283$	5.98536e111	1.66268	0.831338	+	0.555767i	$0.187575\pi$
$284$	−3.17228e110	−0.0750563
$285$	2.03919e111	0.411166
$286$	4.69112e111	0.806533
$287$	−7.13217e110	−0.104615
$288$	7.77998e111	0.974138
$289$	−6.01476e111	−0.643230
$290$	−1.97379e112	−1.80381
$291$	2.30406e111	0.180037
$292$	−1.94486e112	−1.30007
$293$	5.82897e111	0.333515	0.166757	−	0.985998i	$-0.446670\pi$
$293$	5.82897e111	0.333515	0.166757	+	0.985998i	$0.446670\pi$
$294$	−1.29549e110	−0.00634790
$295$	−1.61744e112	−0.679088
$296$	2.92151e112	1.05156
$297$	1.17115e112	0.361572
$298$	−6.05249e112	−1.60359
$299$	7.18153e112	1.63372
$300$	1.84234e112	0.360041
$301$	−3.86020e112	−0.648386
$302$	5.33978e112	0.771271
$303$	−1.34101e112	−0.166645
$304$	−5.31677e112	−0.568722
$305$	−4.12491e112	−0.379990
$306$	8.44936e112	0.670655
$307$	−1.00898e112	−0.0690379	−0.0345189	−	0.999404i	$-0.510990\pi$
$307$	−1.00898e112	−0.0690379	−0.0345189	+	0.999404i	$0.510990\pi$
$308$	9.33634e112	0.550958
$309$	1.90385e113	0.969440
$310$	−1.94217e113	−0.853748
$311$	3.67767e113	1.39629	0.698145	−	0.715956i	$-0.254009\pi$
$311$	3.67767e113	1.39629	0.698145	+	0.715956i	$0.254009\pi$
$312$	−1.15463e113	−0.378798
$313$	−2.87467e113	−0.815305	−0.407653	−	0.913137i	$-0.633653\pi$
$313$	−2.87467e113	−0.815305	−0.407653	+	0.913137i	$0.633653\pi$
$314$	−8.96538e113	−2.19923
$315$	2.42209e113	0.514114
$316$	−4.74767e113	−0.872405
$317$	2.88231e113	0.458716	0.229358	−	0.973342i	$-0.426337\pi$
$317$	2.88231e113	0.458716	0.229358	+	0.973342i	$0.426337\pi$
$318$	−8.48048e113	−1.16946
$319$	5.63159e113	0.673216
$320$	1.04643e114	1.08489
$321$	−1.25019e112	−0.0112460
$322$	2.47723e114	1.93430
$323$	−9.94546e113	−0.674388
$324$	6.10265e113	0.359518
$325$	−1.29420e114	−0.662688
$326$	2.33863e114	1.04126
$327$	1.75974e114	0.681594
$328$	−1.72943e113	−0.0582967
$329$	−3.85801e114	−1.13227
$330$	8.81296e113	0.225288
$331$	−4.30338e114	−0.958596	−0.479298	−	0.877652i	$-0.659109\pi$
$331$	−4.30338e114	−0.958596	−0.479298	+	0.877652i	$0.659109\pi$
$332$	−5.02501e114	−0.975785
$333$	−8.10534e114	−1.37265
$334$	7.07426e114	1.04524
$335$	−5.41495e114	−0.698322
$336$	2.33235e114	0.262638
$337$	1.17499e115	1.15577	0.577886	−	0.816117i	$-0.303878\pi$
$337$	1.17499e115	1.15577	0.577886	+	0.816117i	$0.303878\pi$
$338$	1.25150e115	1.07578
$339$	−1.95941e114	−0.147244
$340$	8.69178e114	0.571239
$341$	5.54137e114	0.318634
$342$	−2.51888e115	−1.26771
$343$	−2.26014e115	−0.995986
$344$	−9.36035e114	−0.361313
$345$	1.34916e115	0.456345
$346$	6.84389e115	2.02927
$347$	−2.62689e114	−0.0683046	−0.0341523	−	0.999417i	$-0.510873\pi$
$347$	−2.62689e114	−0.0683046	−0.0341523	+	0.999417i	$0.510873\pi$
$348$	−5.19535e115	−1.18511
$349$	8.11277e115	1.62410	0.812049	−	0.583590i	$-0.198352\pi$
$349$	8.11277e115	1.62410	0.812049	+	0.583590i	$0.198352\pi$
$350$	−4.46428e115	−0.784613
$351$	7.58979e115	1.17154
$352$	−3.95770e115	−0.536725
$353$	−1.53892e116	−1.83428	−0.917142	−	0.398562i	$-0.869509\pi$
$353$	−1.53892e116	−1.83428	−0.917142	+	0.398562i	$0.869509\pi$
$354$	−7.37890e115	−0.773292
$355$	4.18649e114	0.0385887
$356$	1.06683e116	0.865205
$357$	4.36285e115	0.311435
$358$	−2.42337e116	−1.52315
$359$	−1.49511e116	−0.827707	−0.413854	−	0.910343i	$-0.635817\pi$
$359$	−1.49511e116	−0.827707	−0.413854	+	0.910343i	$0.635817\pi$
$360$	5.87317e115	0.286490
$361$	6.39065e115	0.274769
$362$	3.53129e116	1.33873
$363$	1.30167e116	0.435260
$364$	6.05053e116	1.78518
$365$	2.56665e116	0.668407
$366$	−1.88182e116	−0.432703
$367$	−4.00024e115	−0.0812419	−0.0406210	−	0.999175i	$-0.512934\pi$
$367$	−4.00024e115	−0.0812419	−0.0406210	+	0.999175i	$0.512934\pi$
$368$	−3.51765e116	−0.631214
$369$	4.79808e115	0.0760970
$370$	−1.44513e117	−2.02641
$371$	1.18564e117	1.47042
$372$	−5.11212e116	−0.560915
$373$	−1.38081e117	−1.34086	−0.670430	−	0.741973i	$-0.733890\pi$
$373$	−1.38081e117	−1.34086	−0.670430	+	0.741973i	$0.733890\pi$
$374$	−4.29822e116	−0.369514
$375$	−7.21461e116	−0.549275
$376$	−9.35505e116	−0.630956
$377$	3.64962e117	2.18131
$378$	2.61806e117	1.38708
$379$	−1.60656e117	−0.754765	−0.377382	−	0.926058i	$-0.623176\pi$
$379$	−1.60656e117	−0.754765	−0.377382	+	0.926058i	$0.623176\pi$
$380$	−2.59115e117	−1.07979
$381$	2.39179e117	0.884375
$382$	1.40499e117	0.461095
$383$	−2.75610e117	−0.803066	−0.401533	−	0.915845i	$-0.631522\pi$
$383$	−2.75610e117	−0.803066	−0.401533	+	0.915845i	$0.631522\pi$
$384$	2.09688e117	0.542630
$385$	−1.23212e117	−0.283264
$386$	4.39098e117	0.897096
$387$	2.59690e117	0.471635
$388$	−2.92771e117	−0.472808
$389$	−5.07882e117	−0.729552	−0.364776	−	0.931095i	$-0.618854\pi$
$389$	−5.07882e117	−0.729552	−0.364776	+	0.931095i	$0.618854\pi$
$390$	5.71136e117	0.729961
$391$	−6.58005e117	−0.748491
$392$	4.39186e115	0.00444767
$393$	−8.76284e117	−0.790285
$394$	1.81356e118	1.45698
$395$	6.26554e117	0.448529
$396$	−6.28091e117	−0.400767
$397$	−1.49532e118	−0.850681	−0.425341	−	0.905033i	$-0.639846\pi$
$397$	−1.49532e118	−0.850681	−0.425341	+	0.905033i	$0.639846\pi$
$398$	−7.08874e117	−0.359658
$399$	−1.30063e118	−0.588692
$400$	6.33925e117	0.256040
$401$	−3.22026e118	−1.16097	−0.580486	−	0.814270i	$-0.697137\pi$
$401$	−3.22026e118	−1.16097	−0.580486	+	0.814270i	$0.697137\pi$
$402$	−2.47035e118	−0.795194
$403$	3.59116e118	1.03242
$404$	1.70399e118	0.437637
$405$	−8.05373e117	−0.184839
$406$	1.25892e119	2.58263
$407$	4.12321e118	0.756293
$408$	1.05792e118	0.173547
$409$	5.55835e118	0.815709	0.407855	−	0.913047i	$-0.366277\pi$
$409$	5.55835e118	0.815709	0.407855	+	0.913047i	$0.366277\pi$
$410$	8.55465e117	0.112341
$411$	−6.39710e118	−0.751934
$412$	−2.41917e119	−2.54591
$413$	1.03163e119	0.972293
$414$	−1.66653e119	−1.40701
$415$	6.63156e118	0.501680
$416$	−2.56484e119	−1.73906
$417$	5.99925e118	0.364675
$418$	1.28136e119	0.698477
$419$	9.72650e117	0.0475575	0.0237787	−	0.999717i	$-0.492430\pi$
$419$	9.72650e117	0.0475575	0.0237787	+	0.999717i	$0.492430\pi$
$420$	1.13668e119	0.498651
$421$	−2.04688e119	−0.805856	−0.402928	−	0.915232i	$-0.632007\pi$
$421$	−2.04688e119	−0.805856	−0.402928	+	0.915232i	$0.632007\pi$
$422$	−9.53296e118	−0.336908
$423$	2.59543e119	0.823612
$424$	2.87499e119	0.819388
$425$	1.18581e119	0.303611
$426$	1.90991e118	0.0439417
$427$	2.63094e119	0.544056
$428$	1.58859e118	0.0295339
$429$	−1.62956e119	−0.272435
$430$	4.63010e119	0.696266
$431$	−1.07671e120	−1.45674	−0.728370	−	0.685184i	$-0.759722\pi$
$431$	−1.07671e120	−1.45674	−0.728370	+	0.685184i	$0.759722\pi$
$432$	−3.71762e119	−0.452642
$433$	−3.48113e119	−0.381523	−0.190761	−	0.981636i	$-0.561096\pi$
$433$	−3.48113e119	−0.381523	−0.190761	+	0.981636i	$0.561096\pi$
$434$	1.23875e120	1.22236
$435$	6.85636e119	0.609301
$436$	−2.23606e120	−1.78998
$437$	1.96161e120	1.41484
$438$	1.17093e120	0.761129
$439$	−1.61807e120	−0.948118	−0.474059	−	0.880493i	$-0.657212\pi$
$439$	−1.61807e120	−0.948118	−0.474059	+	0.880493i	$0.657212\pi$
$440$	−2.98770e119	−0.157849
$441$	−1.21846e118	−0.00580572
$442$	−2.78552e120	−1.19727
$443$	−4.95263e119	−0.192073	−0.0960366	−	0.995378i	$-0.530617\pi$
$443$	−4.95263e119	−0.192073	−0.0960366	+	0.995378i	$0.530617\pi$
$444$	−3.80382e120	−1.33136
$445$	−1.40790e120	−0.444828
$446$	9.03404e120	2.57719
$447$	2.10246e120	0.541670
$448$	−6.67432e120	−1.55331
$449$	5.00220e120	1.05185	0.525924	−	0.850532i	$-0.323720\pi$
$449$	5.00220e120	1.05185	0.525924	+	0.850532i	$0.323720\pi$
$450$	3.00329e120	0.570727
$451$	−2.44080e119	−0.0419275
$452$	2.48977e120	0.386688
$453$	−1.85488e120	−0.260524
$454$	1.99039e121	2.52870
$455$	−7.98495e120	−0.917812
$456$	−3.15383e120	−0.328048
$457$	−1.03532e121	−0.974733	−0.487366	−	0.873198i	$-0.662042\pi$
$457$	−1.03532e121	−0.974733	−0.487366	+	0.873198i	$0.662042\pi$
$458$	1.16299e121	0.991284
$459$	−6.95412e120	−0.536741
$460$	−1.71434e121	−1.19844
$461$	−1.87429e121	−1.18699	−0.593493	−	0.804839i	$-0.702252\pi$
$461$	−1.87429e121	−1.18699	−0.593493	+	0.804839i	$0.702252\pi$
$462$	−5.62107e120	−0.322559
$463$	−5.96169e120	−0.310052	−0.155026	−	0.987910i	$-0.549546\pi$
$463$	−5.96169e120	−0.310052	−0.155026	+	0.987910i	$0.549546\pi$
$464$	−1.78765e121	−0.842782
$465$	6.74651e120	0.288383
$466$	3.55602e121	1.37850
$467$	2.00783e121	0.706005	0.353003	−	0.935622i	$-0.385161\pi$
$467$	2.00783e121	0.706005	0.353003	+	0.935622i	$0.385161\pi$
$468$	−4.07042e121	−1.29853
$469$	3.45375e121	0.999832
$470$	4.62748e121	1.21588
$471$	3.11431e121	0.742865
$472$	2.50154e121	0.541809
$473$	−1.32105e121	−0.259859
$474$	2.85840e121	0.510750
$475$	−3.53507e121	−0.573904
$476$	−5.54378e121	−0.817880
$477$	−7.97626e121	−1.06958
$478$	−1.76758e122	−2.15481
$479$	1.49084e122	1.65259	0.826294	−	0.563239i	$-0.190445\pi$
$479$	1.49084e122	1.65259	0.826294	+	0.563239i	$0.190445\pi$
$480$	−4.81843e121	−0.485769
$481$	2.67210e122	2.45049
$482$	1.08631e122	0.906386
$483$	−8.60517e121	−0.653378
$484$	−1.65400e122	−1.14307
$485$	3.86373e121	0.243085
$486$	−2.77917e122	−1.59208
$487$	6.76405e121	0.352890	0.176445	−	0.984311i	$-0.443540\pi$
$487$	6.76405e121	0.352890	0.176445	+	0.984311i	$0.443540\pi$
$488$	6.37962e121	0.303174
$489$	−8.12372e121	−0.351724
$490$	−2.17243e120	−0.00857087
$491$	−1.17686e122	−0.423174	−0.211587	−	0.977359i	$-0.567863\pi$
$491$	−1.17686e122	−0.423174	−0.211587	+	0.977359i	$0.567863\pi$
$492$	2.25173e121	0.0738081
$493$	−3.34395e122	−0.999367
$494$	8.30405e122	2.26315
$495$	8.28897e121	0.206046
$496$	−1.75901e122	−0.398890
$497$	−2.67022e121	−0.0552498
$498$	3.02538e122	0.571274
$499$	2.34304e121	0.0403835	0.0201918	−	0.999796i	$-0.493572\pi$
$499$	2.34304e121	0.0403835	0.0201918	+	0.999796i	$0.493572\pi$
$500$	9.16744e122	1.44249
$501$	−2.45739e122	−0.353067
$502$	−1.78553e122	−0.234287
$503$	2.37983e122	0.285235	0.142618	−	0.989778i	$-0.454448\pi$
$503$	2.37983e122	0.285235	0.142618	+	0.989778i	$0.454448\pi$
$504$	−3.74602e122	−0.410185
$505$	−2.24877e122	−0.225002
$506$	8.47768e122	0.775227
$507$	−4.34735e122	−0.363382
$508$	−3.03919e123	−2.32252
$509$	−1.46725e123	−1.02528	−0.512642	−	0.858602i	$-0.671333\pi$
$509$	−1.46725e123	−1.02528	−0.512642	+	0.858602i	$0.671333\pi$
$510$	−5.23300e122	−0.334432
$511$	−1.63705e123	−0.957000
$512$	1.78322e123	0.953720
$513$	2.07313e123	1.01458
$514$	−1.32621e123	−0.594006
$515$	3.19261e123	1.30893
$516$	1.21872e123	0.457449
$517$	−1.32030e123	−0.453790
$518$	9.21727e123	2.90134
$519$	−2.37737e123	−0.685459
$520$	−1.93622e123	−0.511449
$521$	2.19177e123	0.530491	0.265245	−	0.964181i	$-0.414547\pi$
$521$	2.19177e123	0.530491	0.265245	+	0.964181i	$0.414547\pi$
$522$	−8.46922e123	−1.87860
$523$	2.26855e122	0.0461235	0.0230617	−	0.999734i	$-0.492659\pi$
$523$	2.26855e122	0.0461235	0.0230617	+	0.999734i	$0.492659\pi$
$524$	1.11347e124	2.07542
$525$	1.55076e123	0.265031
$526$	−1.18784e124	−1.86169
$527$	−3.29038e123	−0.473002
$528$	7.98187e122	0.105259
$529$	4.71348e123	0.570307
$530$	−1.42211e124	−1.57900
$531$	−6.94018e123	−0.707245
$532$	1.65268e124	1.54600
$533$	−1.58179e123	−0.135851
$534$	−6.42298e123	−0.506535
$535$	−2.09648e122	−0.0151843
$536$	8.37479e123	0.557155
$537$	8.41807e123	0.514497
$538$	8.83232e123	0.495999
$539$	6.19836e121	0.00319881
$540$	−1.81180e124	−0.859398
$541$	−4.45614e123	−0.194305	−0.0971523	−	0.995270i	$-0.530973\pi$
$541$	−4.45614e123	−0.194305	−0.0971523	+	0.995270i	$0.530973\pi$
$542$	−2.41970e124	−0.970051
$543$	−1.22666e124	−0.452203
$544$	2.35003e124	0.796751
$545$	2.95095e124	0.920282
$546$	−3.64281e124	−1.04513
$547$	3.74310e124	0.988117	0.494058	−	0.869429i	$-0.335513\pi$
$547$	3.74310e124	0.988117	0.494058	+	0.869429i	$0.335513\pi$
$548$	8.12864e124	1.97471
$549$	−1.76994e124	−0.395746
$550$	−1.52779e124	−0.314456
$551$	9.96883e124	1.88906
$552$	−2.08661e124	−0.364094
$553$	−3.99628e124	−0.642188
$554$	−1.25818e125	−1.86229
$555$	5.01994e124	0.684491
$556$	−7.62310e124	−0.957699
$557$	−5.44949e124	−0.630876	−0.315438	−	0.948946i	$-0.602152\pi$
$557$	−5.44949e124	−0.630876	−0.315438	+	0.948946i	$0.602152\pi$
$558$	−8.33354e124	−0.889147
$559$	−8.56125e124	−0.841977
$560$	3.91118e124	0.354611
$561$	1.49307e124	0.124816
$562$	8.90118e124	0.686191
$563$	−1.19709e125	−0.851130	−0.425565	−	0.904928i	$-0.639925\pi$
$563$	−1.19709e125	−0.851130	−0.425565	+	0.904928i	$0.639925\pi$
$564$	1.21803e125	0.798839
$565$	−3.28578e124	−0.198808
$566$	4.57897e125	2.55635
$567$	5.13681e124	0.264646
$568$	−6.47484e123	−0.0307879
$569$	−6.68469e124	−0.293409	−0.146704	−	0.989180i	$-0.546867\pi$
$569$	−6.68469e124	−0.293409	−0.146704	+	0.989180i	$0.546867\pi$
$570$	1.56004e125	0.632164
$571$	−2.52153e125	−0.943454	−0.471727	−	0.881745i	$-0.656369\pi$
$571$	−2.52153e125	−0.943454	−0.471727	+	0.881745i	$0.656369\pi$
$572$	2.07064e125	0.715460
$573$	−4.88053e124	−0.155751
$574$	−5.45631e124	−0.160845
$575$	−2.33885e125	−0.636966
$576$	4.49007e125	1.12987
$577$	1.51499e123	0.00352298	0.00176149	−	0.999998i	$-0.499439\pi$
$577$	1.51499e123	0.00352298	0.00176149	+	0.999998i	$0.499439\pi$
$578$	−4.60146e125	−0.988960
$579$	−1.52530e125	−0.303026
$580$	−8.71221e125	−1.60013
$581$	−4.22973e125	−0.718287
$582$	1.76267e125	0.276806
$583$	4.05755e125	0.589312
$584$	−3.96959e125	−0.533287
$585$	5.37178e125	0.667615
$586$	4.45932e125	0.512776
$587$	1.12840e126	1.20068	0.600341	−	0.799744i	$-0.295032\pi$
$587$	1.12840e126	1.20068	0.600341	+	0.799744i	$0.295032\pi$
$588$	−5.71822e123	−0.00563110
$589$	9.80913e125	0.894097
$590$	−1.23739e126	−1.04409
$591$	−6.29977e125	−0.492147
$592$	−1.30885e126	−0.946784
$593$	1.04945e125	0.0703027	0.0351513	−	0.999382i	$-0.488809\pi$
$593$	1.04945e125	0.0703027	0.0351513	+	0.999382i	$0.488809\pi$
$594$	8.95963e125	0.555913
$595$	7.31617e125	0.420496
$596$	−2.67154e126	−1.42252
$597$	2.46242e125	0.121487
$598$	5.49407e126	2.51183
$599$	1.10494e126	0.468184	0.234092	−	0.972214i	$-0.424788\pi$
$599$	1.10494e126	0.468184	0.234092	+	0.972214i	$0.424788\pi$
$600$	3.76034e125	0.147688
$601$	−5.49638e125	−0.200119	−0.100060	−	0.994981i	$-0.531903\pi$
$601$	−5.49638e125	−0.200119	−0.100060	+	0.994981i	$0.531903\pi$
$602$	−2.95316e126	−0.996888
$603$	−2.32347e126	−0.727276
$604$	2.35695e126	0.684180
$605$	2.18280e126	0.587684
$606$	−1.02591e126	−0.256215
$607$	2.48198e126	0.575059	0.287529	−	0.957772i	$-0.407166\pi$
$607$	2.48198e126	0.575059	0.287529	+	0.957772i	$0.407166\pi$
$608$	−7.00579e126	−1.50607
$609$	−4.37311e126	−0.872375
$610$	−3.15568e126	−0.584231
$611$	−8.55641e126	−1.47034
$612$	3.72951e126	0.594925
$613$	7.69081e126	1.13899	0.569496	−	0.821994i	$-0.307138\pi$
$613$	7.69081e126	1.13899	0.569496	+	0.821994i	$0.307138\pi$
$614$	−7.71900e125	−0.106145
$615$	−2.97163e125	−0.0379470
$616$	1.90561e126	0.226002
$617$	−8.77551e126	−0.966713	−0.483357	−	0.875424i	$-0.660583\pi$
$617$	−8.77551e126	−0.966713	−0.483357	+	0.875424i	$0.660583\pi$
$618$	1.45650e127	1.49051
$619$	5.94866e126	0.565581	0.282791	−	0.959182i	$-0.408740\pi$
$619$	5.94866e126	0.565581	0.282791	+	0.959182i	$0.408740\pi$
$620$	−8.57264e126	−0.757343
$621$	1.37161e127	1.12606
$622$	2.81352e127	2.14678
$623$	8.97985e126	0.636888
$624$	5.17276e126	0.341054
$625$	−3.80626e126	−0.233323
$626$	−2.19920e127	−1.25352
$627$	−4.45108e126	−0.235935
$628$	−3.95728e127	−1.95089
$629$	−2.44830e127	−1.12269
$630$	1.85297e127	0.790446
$631$	−3.12255e127	−1.23929	−0.619646	−	0.784881i	$-0.712724\pi$
$631$	−3.12255e127	−1.23929	−0.619646	+	0.784881i	$0.712724\pi$
$632$	−9.69033e126	−0.357858
$633$	3.31147e126	0.113802
$634$	2.20505e127	0.705272
$635$	4.01085e127	1.19407
$636$	−3.74325e127	−1.03741
$637$	4.01693e125	0.0103645
$638$	4.30832e127	1.03506
$639$	1.79636e126	0.0401886
$640$	3.51632e127	0.732654
$641$	−3.54352e127	−0.687693	−0.343847	−	0.939026i	$-0.611730\pi$
$641$	−3.54352e127	−0.687693	−0.343847	+	0.939026i	$0.611730\pi$
$642$	−9.56433e125	−0.0172906
$643$	−8.42328e127	−1.41867	−0.709336	−	0.704870i	$-0.751005\pi$
$643$	−8.42328e127	−1.41867	−0.709336	+	0.704870i	$0.751005\pi$
$644$	1.09344e128	1.71588
$645$	−1.60836e127	−0.235188
$646$	−7.60855e127	−1.03687
$647$	1.35622e128	1.72261	0.861304	−	0.508089i	$-0.169648\pi$
$647$	1.35622e128	1.72261	0.861304	+	0.508089i	$0.169648\pi$
$648$	1.24559e127	0.147473
$649$	3.53049e127	0.389674
$650$	−9.90101e127	−1.01888
$651$	−4.30305e127	−0.412897
$652$	1.03226e128	0.923686
$653$	−4.71557e127	−0.393536	−0.196768	−	0.980450i	$-0.563045\pi$
$653$	−4.71557e127	−0.393536	−0.196768	+	0.980450i	$0.563045\pi$
$654$	1.34625e128	1.04794
$655$	−1.46946e128	−1.06704
$656$	7.74791e126	0.0524880
$657$	1.10131e128	0.696121
$658$	−2.95149e128	−1.74086
$659$	6.90957e127	0.380334	0.190167	−	0.981752i	$-0.439097\pi$
$659$	6.90957e127	0.380334	0.190167	+	0.981752i	$0.439097\pi$
$660$	3.89000e127	0.199848
$661$	2.41857e128	1.15983	0.579913	−	0.814679i	$-0.303087\pi$
$661$	2.41857e128	1.15983	0.579913	+	0.814679i	$0.303087\pi$
$662$	−3.29220e128	−1.47383
$663$	9.67606e127	0.404420
$664$	−1.02564e128	−0.400265
$665$	−2.18106e128	−0.794847
$666$	−6.20081e128	−2.11043
$667$	6.59551e128	2.09664
$668$	3.12255e128	0.927214
$669$	−3.13816e128	−0.870535
$670$	−4.14259e128	−1.07366
$671$	9.00373e127	0.218046
$672$	3.07328e128	0.695506
$673$	3.61944e128	0.765520	0.382760	−	0.923848i	$-0.374974\pi$
$673$	3.61944e128	0.765520	0.382760	+	0.923848i	$0.374974\pi$
$674$	8.98897e128	1.77699
$675$	−2.47181e128	−0.456766
$676$	5.52408e128	0.954301
$677$	6.71330e128	1.08431	0.542153	−	0.840280i	$-0.317609\pi$
$677$	6.71330e128	1.08431	0.542153	+	0.840280i	$0.317609\pi$
$678$	−1.49900e128	−0.226387
$679$	−2.46436e128	−0.348040
$680$	1.77405e128	0.234321
$681$	−6.91402e128	−0.854155
$682$	4.23930e128	0.489897
$683$	−1.16110e129	−1.25525	−0.627624	−	0.778517i	$-0.715972\pi$
$683$	−1.16110e129	−1.25525	−0.627624	+	0.778517i	$0.715972\pi$
$684$	−1.11182e129	−1.12456
$685$	−1.07274e129	−1.01526
$686$	−1.72907e129	−1.53132
$687$	−4.03989e128	−0.334841
$688$	4.19346e128	0.325311
$689$	2.62955e129	1.90944
$690$	1.03214e129	0.701627
$691$	−3.04763e129	−1.93959	−0.969796	−	0.243916i	$-0.921568\pi$
$691$	−3.04763e129	−1.93959	−0.969796	+	0.243916i	$0.921568\pi$
$692$	3.02086e129	1.80013
$693$	−5.28686e128	−0.295009
$694$	−2.00964e128	−0.105018
$695$	1.00603e129	0.492381
$696$	−1.06041e129	−0.486130
$697$	1.44931e128	0.0622401
$698$	6.20649e129	2.49704
$699$	−1.23526e129	−0.465635
$700$	−1.97051e129	−0.696015
$701$	−5.23191e129	−1.73177	−0.865885	−	0.500244i	$-0.833244\pi$
$701$	−5.23191e129	−1.73177	−0.865885	+	0.500244i	$0.833244\pi$
$702$	5.80641e129	1.80123
$703$	7.29876e129	2.12218
$704$	−2.28411e129	−0.622532
$705$	−1.60745e129	−0.410707
$706$	−1.17732e130	−2.82019
$707$	1.43431e129	0.322150
$708$	−3.25701e129	−0.685972
$709$	2.83247e129	0.559450	0.279725	−	0.960080i	$-0.409757\pi$
$709$	2.83247e129	0.559450	0.279725	+	0.960080i	$0.409757\pi$
$710$	3.20278e128	0.0593297
$711$	2.68845e129	0.467127
$712$	2.17747e129	0.354905
$713$	6.48985e129	0.992342
$714$	3.33771e129	0.478828
$715$	−2.73264e129	−0.367839
$716$	−1.06967e130	−1.35116
$717$	6.14005e129	0.727864
$718$	−1.14380e130	−1.27259
$719$	4.54468e129	0.474612	0.237306	−	0.971435i	$-0.423736\pi$
$719$	4.54468e129	0.474612	0.237306	+	0.971435i	$0.423736\pi$
$720$	−2.63120e129	−0.257944
$721$	−2.03630e130	−1.87408
$722$	4.88903e129	0.422454
$723$	−3.77351e129	−0.306164
$724$	1.55869e130	1.18756
$725$	−1.18859e130	−0.850461
$726$	9.95812e129	0.669208
$727$	8.47219e129	0.534786	0.267393	−	0.963588i	$-0.413838\pi$
$727$	8.47219e129	0.534786	0.267393	+	0.963588i	$0.413838\pi$
$728$	1.23496e130	0.732274
$729$	4.92199e129	0.274182
$730$	1.96356e130	1.02767
$731$	7.84421e129	0.385752
$732$	−8.30628e129	−0.383842
$733$	2.38609e130	1.03623	0.518114	−	0.855312i	$-0.326634\pi$
$733$	2.38609e130	1.03623	0.518114	+	0.855312i	$0.326634\pi$
$734$	−3.06030e129	−0.124909
$735$	7.54639e127	0.00289511
$736$	−4.63512e130	−1.67156
$737$	1.18196e130	0.400711
$738$	3.67066e129	0.116998
$739$	−2.04680e129	−0.0613413	−0.0306707	−	0.999530i	$-0.509764\pi$
$739$	−2.04680e129	−0.0613413	−0.0306707	+	0.999530i	$0.509764\pi$
$740$	−6.37872e130	−1.79759
$741$	−2.88458e130	−0.764459
$742$	9.07049e130	2.26075
$743$	−6.30926e130	−1.47907	−0.739533	−	0.673120i	$-0.764954\pi$
$743$	−6.30926e130	−1.47907	−0.739533	+	0.673120i	$0.764954\pi$
$744$	−1.04342e130	−0.230086
$745$	3.52566e130	0.731358
$746$	−1.05636e131	−2.06156
$747$	2.84550e130	0.522481
$748$	−1.89721e130	−0.327788
$749$	1.33717e129	0.0217403
$750$	−5.51938e130	−0.844506
$751$	6.56817e130	0.945860	0.472930	−	0.881100i	$-0.343196\pi$
$751$	6.56817e130	0.945860	0.472930	+	0.881100i	$0.343196\pi$
$752$	4.19109e130	0.568087
$753$	6.20240e129	0.0791386
$754$	2.79206e131	3.35374
$755$	−3.11049e130	−0.351757
$756$	1.15560e131	1.23045
$757$	1.89876e130	0.190374	0.0951871	−	0.995459i	$-0.469655\pi$
$757$	1.89876e130	0.190374	0.0951871	+	0.995459i	$0.469655\pi$
$758$	−1.22906e131	−1.16044
$759$	−2.94490e130	−0.261860
$760$	−5.28873e130	−0.442927
$761$	−1.78991e131	−1.41198	−0.705991	−	0.708221i	$-0.749498\pi$
$761$	−1.78991e131	−1.41198	−0.705991	+	0.708221i	$0.749498\pi$
$762$	1.82978e131	1.35972
$763$	−1.88217e131	−1.31763
$764$	6.20157e130	0.409029
$765$	−4.92187e130	−0.305868
$766$	−2.10850e131	−1.23471
$767$	2.28798e131	1.26259
$768$	5.91833e129	0.0307796
$769$	−2.31630e131	−1.13539	−0.567697	−	0.823237i	$-0.692166\pi$
$769$	−2.31630e131	−1.13539	−0.567697	+	0.823237i	$0.692166\pi$
$770$	−9.42610e130	−0.435516
$771$	4.60687e130	0.200646
$772$	1.93816e131	0.795797
$773$	2.95985e131	1.14579	0.572893	−	0.819630i	$-0.305821\pi$
$773$	2.95985e131	1.14579	0.572893	+	0.819630i	$0.305821\pi$
$774$	1.98670e131	0.725135
$775$	−1.16955e131	−0.402525
$776$	−5.97566e130	−0.193945
$777$	−3.20181e131	−0.980029
$778$	−3.88544e131	−1.12168
$779$	−4.32062e130	−0.117650
$780$	2.52097e131	0.647534
$781$	−9.13813e129	−0.0221429
$782$	−5.03392e131	−1.15080
$783$	6.97046e131	1.50349
$784$	−1.96757e129	−0.00400450
$785$	5.22246e131	1.00301
$786$	−6.70382e131	−1.21506
$787$	−1.56252e131	−0.267286	−0.133643	−	0.991030i	$-0.542667\pi$
$787$	−1.56252e131	−0.267286	−0.133643	+	0.991030i	$0.542667\pi$
$788$	8.00497e131	1.29246
$789$	4.12622e131	0.628852
$790$	4.79332e131	0.689610
$791$	2.09573e131	0.284646
$792$	−1.28198e131	−0.164393
$793$	5.83498e131	0.706496
$794$	−1.14396e132	−1.30791
$795$	4.94000e131	0.533362
$796$	−3.12894e131	−0.319045
$797$	−9.39961e131	−0.905225	−0.452612	−	0.891707i	$-0.649508\pi$
$797$	−9.39961e131	−0.905225	−0.452612	+	0.891707i	$0.649508\pi$
$798$	−9.95021e131	−0.905109
$799$	7.83977e131	0.673636
$800$	8.35308e131	0.678035
$801$	−6.04109e131	−0.463271
$802$	−2.46359e132	−1.78498
$803$	−5.60240e131	−0.383545
$804$	−1.09040e132	−0.705401
$805$	−1.44302e132	−0.882186
$806$	2.74733e132	1.58733
$807$	−3.06808e131	−0.167541
$808$	3.47796e131	0.179518
$809$	−1.48232e132	−0.723242	−0.361621	−	0.932325i	$-0.617777\pi$
$809$	−1.48232e132	−0.723242	−0.361621	+	0.932325i	$0.617777\pi$
$810$	−6.16133e131	−0.284188
$811$	3.90636e132	1.70343	0.851714	−	0.524007i	$-0.175564\pi$
$811$	3.90636e132	1.70343	0.851714	+	0.524007i	$0.175564\pi$
$812$	5.55681e132	2.29100
$813$	8.40533e131	0.327669
$814$	3.15437e132	1.16279
$815$	−1.36229e132	−0.474894
$816$	−4.73951e131	−0.156254
$817$	−2.33848e132	−0.729172
$818$	4.25229e132	1.25415
$819$	−3.42622e132	−0.955867
$820$	3.77598e131	0.0996551
$821$	−4.09469e132	−1.02237	−0.511184	−	0.859471i	$-0.670793\pi$
$821$	−4.09469e132	−1.02237	−0.511184	+	0.859471i	$0.670793\pi$
$822$	−4.89396e132	−1.15609
$823$	−1.69414e131	−0.0378667	−0.0189334	−	0.999821i	$-0.506027\pi$
$823$	−1.69414e131	−0.0378667	−0.0189334	+	0.999821i	$0.506027\pi$
$824$	−4.93770e132	−1.04433
$825$	5.30707e131	0.106219
$826$	7.89227e132	1.49489
$827$	7.96817e132	1.42843	0.714213	−	0.699928i	$-0.246785\pi$
$827$	7.96817e132	1.42843	0.714213	+	0.699928i	$0.246785\pi$
$828$	−7.35598e132	−1.24813
$829$	−9.27628e132	−1.48985	−0.744925	−	0.667148i	$-0.767515\pi$
$829$	−9.27628e132	−1.48985	−0.744925	+	0.667148i	$0.767515\pi$
$830$	5.07333e132	0.771329
$831$	4.37053e132	0.629054
$832$	−1.48025e133	−2.01708
$833$	−3.68049e130	−0.00474852
$834$	4.58959e132	0.560685
$835$	−4.12086e132	−0.476708
$836$	5.65589e132	0.619605
$837$	6.85879e132	0.711606
$838$	7.44105e131	0.0731192
$839$	2.74761e132	0.255733	0.127866	−	0.991791i	$-0.459187\pi$
$839$	2.74761e132	0.255733	0.127866	+	0.991791i	$0.459187\pi$
$840$	2.32005e132	0.204545
$841$	2.15447e133	1.79938
$842$	−1.56592e133	−1.23900
$843$	−3.09201e132	−0.231785
$844$	−4.20780e132	−0.298864
$845$	−7.29018e132	−0.490635
$846$	1.98558e133	1.26630
$847$	−1.39223e133	−0.841425
$848$	−1.28800e133	−0.737744
$849$	−1.59060e133	−0.863497
$850$	9.07176e132	0.466800
$851$	4.82896e133	2.35537
$852$	8.43027e131	0.0389798
$853$	−2.41435e133	−1.05833	−0.529163	−	0.848520i	$-0.677494\pi$
$853$	−2.41435e133	−1.05833	−0.529163	+	0.848520i	$0.677494\pi$
$854$	2.01275e133	0.836481
$855$	1.46728e133	0.578171
$856$	3.24243e131	0.0121147
$857$	−1.48144e133	−0.524875	−0.262437	−	0.964949i	$-0.584526\pi$
$857$	−1.48144e133	−0.524875	−0.262437	+	0.964949i	$0.584526\pi$
$858$	−1.24666e133	−0.418866
$859$	−8.95957e131	−0.0285495	−0.0142747	−	0.999898i	$-0.504544\pi$
$859$	−8.95957e131	−0.0285495	−0.0142747	+	0.999898i	$0.504544\pi$
$860$	2.04370e133	0.617644
$861$	1.89536e132	0.0543311
$862$	−8.23712e133	−2.23973
$863$	−3.08457e132	−0.0795616	−0.0397808	−	0.999208i	$-0.512666\pi$
$863$	−3.08457e132	−0.0795616	−0.0397808	+	0.999208i	$0.512666\pi$
$864$	−4.89862e133	−1.19867
$865$	−3.98666e133	−0.925500
$866$	−2.66316e133	−0.586588
$867$	1.59841e133	0.334056
$868$	5.46778e133	1.08434
$869$	−1.36762e133	−0.257375
$870$	5.24530e133	0.936795
$871$	7.65983e133	1.29835
$872$	−4.56395e133	−0.734245
$873$	1.65787e133	0.253164
$874$	1.50069e134	2.17531
$875$	7.71655e133	1.06183
$876$	5.16842e133	0.675183
$877$	−1.74936e133	−0.216970	−0.108485	−	0.994098i	$-0.534600\pi$
$877$	−1.74936e133	−0.216970	−0.108485	+	0.994098i	$0.534600\pi$
$878$	−1.23787e134	−1.45772
$879$	−1.54904e133	−0.173208
$880$	1.33850e133	0.142120
$881$	−9.21015e133	−0.928674	−0.464337	−	0.885659i	$-0.653707\pi$
$881$	−9.21015e133	−0.928674	−0.464337	+	0.885659i	$0.653707\pi$
$882$	−9.32158e131	−0.00892625
$883$	1.45349e134	1.32190	0.660952	−	0.750429i	$-0.270153\pi$
$883$	1.45349e134	1.32190	0.660952	+	0.750429i	$0.270153\pi$
$884$	−1.22951e134	−1.06208
$885$	4.29831e133	0.352679
$886$	−3.78890e133	−0.295311
$887$	−1.18830e134	−0.879835	−0.439917	−	0.898038i	$-0.644992\pi$
$887$	−1.18830e134	−0.879835	−0.439917	+	0.898038i	$0.644992\pi$
$888$	−7.76386e133	−0.546120
$889$	−2.55819e134	−1.70963
$890$	−1.07708e134	−0.683918
$891$	1.75794e133	0.106064
$892$	3.98758e134	2.28617
$893$	−2.33716e134	−1.27335
$894$	1.60844e134	0.832813
$895$	1.41165e134	0.694669
$896$	−2.24277e134	−1.04899
$897$	−1.90848e134	−0.848459
$898$	3.82683e134	1.61721
$899$	3.29811e134	1.32495
$900$	1.32564e134	0.506281
$901$	−2.40931e134	−0.874813
$902$	−1.86728e133	−0.0644632
$903$	1.02584e134	0.336734
$904$	5.08180e133	0.158619
$905$	−2.05702e134	−0.610561
$906$	−1.41904e134	−0.400553
$907$	−1.23100e134	−0.330466	−0.165233	−	0.986255i	$-0.552838\pi$
$907$	−1.23100e134	−0.330466	−0.165233	+	0.986255i	$0.552838\pi$
$908$	8.78548e134	2.24316
$909$	−9.64912e133	−0.234332
$910$	−6.10871e134	−1.41113
$911$	8.93954e133	0.196440	0.0982198	−	0.995165i	$-0.468685\pi$
$911$	8.93954e133	0.196440	0.0982198	+	0.995165i	$0.468685\pi$
$912$	1.41292e134	0.295361
$913$	−1.44751e134	−0.287874
$914$	−7.92045e134	−1.49864
$915$	1.09619e134	0.197345
$916$	5.13340e134	0.879348
$917$	9.37249e134	1.52774
$918$	−5.32009e134	−0.825234
$919$	1.04000e135	1.53524	0.767621	−	0.640904i	$-0.221440\pi$
$919$	1.04000e135	1.53524	0.767621	+	0.640904i	$0.221440\pi$
$920$	−3.49909e134	−0.491597
$921$	2.68135e133	0.0358542
$922$	−1.43389e135	−1.82498
$923$	−5.92208e133	−0.0717459
$924$	−2.48111e134	−0.286136
$925$	−8.70240e134	−0.955410
$926$	−4.56086e134	−0.476702
$927$	1.36990e135	1.36320
$928$	−2.35555e135	−2.23182
$929$	9.04260e134	0.815790	0.407895	−	0.913029i	$-0.366263\pi$
$929$	9.04260e134	0.815790	0.407895	+	0.913029i	$0.366263\pi$
$930$	5.16127e134	0.443387
$931$	1.09721e133	0.00897594
$932$	1.56961e135	1.22284
$933$	−9.77335e134	−0.725151
$934$	1.53604e135	1.08548
$935$	2.50377e134	0.168526
$936$	−8.30802e134	−0.532655
$937$	−1.40351e135	−0.857164	−0.428582	−	0.903503i	$-0.640987\pi$
$937$	−1.40351e135	−0.857164	−0.428582	+	0.903503i	$0.640987\pi$
$938$	2.64222e135	1.53723
$939$	7.63937e134	0.423422
$940$	2.04255e135	1.07859
$941$	−1.20392e135	−0.605719	−0.302859	−	0.953035i	$-0.597941\pi$
$941$	−1.20392e135	−0.605719	−0.302859	+	0.953035i	$0.597941\pi$
$942$	2.38253e135	1.14215
$943$	−2.85858e134	−0.130577
$944$	−1.12070e135	−0.487823
$945$	−1.52506e135	−0.632613
$946$	−1.01064e135	−0.399531
$947$	4.08595e135	1.53946	0.769732	−	0.638367i	$-0.220390\pi$
$947$	4.08595e135	1.53946	0.769732	+	0.638367i	$0.220390\pi$
$948$	1.26168e135	0.453076
$949$	−3.63071e135	−1.24273
$950$	−2.70443e135	−0.882372
$951$	−7.65968e134	−0.238230
$952$	−1.13152e135	−0.335492
$953$	−3.86981e135	−1.09386	−0.546932	−	0.837177i	$-0.684204\pi$
$953$	−3.86981e135	−1.09386	−0.546932	+	0.837177i	$0.684204\pi$
$954$	−6.10206e135	−1.64447
$955$	−8.18427e134	−0.210294
$956$	−7.80201e135	−1.91149
$957$	−1.49658e135	−0.349629
$958$	1.14053e136	2.54084
$959$	6.84216e135	1.45361
$960$	−2.78087e135	−0.563429
$961$	−1.92977e135	−0.372899
$962$	2.04423e136	3.76760
$963$	−8.99567e133	−0.0158138
$964$	4.79492e135	0.804037
$965$	−2.55781e135	−0.409143
$966$	−6.58319e135	−1.00456
$967$	1.61913e135	0.235709	0.117855	−	0.993031i	$-0.462398\pi$
$967$	1.61913e135	0.235709	0.117855	+	0.993031i	$0.462398\pi$
$968$	−3.37593e135	−0.468883
$969$	2.64299e135	0.350238
$970$	2.95586e135	0.373740
$971$	−1.26649e135	−0.152801	−0.0764004	−	0.997077i	$-0.524343\pi$
$971$	−1.26649e135	−0.152801	−0.0764004	+	0.997077i	$0.524343\pi$
$972$	−1.22671e136	−1.41231
$973$	−6.41663e135	−0.704973
$974$	5.17469e135	0.542565
$975$	3.43932e135	0.344162
$976$	−2.85808e135	−0.272966
$977$	6.89024e135	0.628104	0.314052	−	0.949406i	$-0.398313\pi$
$977$	6.89024e135	0.628104	0.314052	+	0.949406i	$0.398313\pi$
$978$	−6.21487e135	−0.540772
$979$	3.07312e135	0.255251
$980$	−9.58903e133	−0.00760306
$981$	1.26621e136	0.958439
$982$	−9.00334e135	−0.650625
$983$	−2.44578e135	−0.168746	−0.0843729	−	0.996434i	$-0.526889\pi$
$983$	−2.44578e135	−0.168746	−0.0843729	+	0.996434i	$0.526889\pi$
$984$	4.59594e134	0.0302759
$985$	−1.05642e136	−0.664492
$986$	−2.55822e136	−1.53652
$987$	1.02526e136	0.588035
$988$	3.66537e136	2.00760
$989$	−1.54717e136	−0.809295
$990$	6.34130e135	0.316794
$991$	−1.59975e136	−0.763310	−0.381655	−	0.924305i	$-0.624646\pi$
$991$	−1.59975e136	−0.763310	−0.381655	+	0.924305i	$0.624646\pi$
$992$	−2.31781e136	−1.05632
$993$	1.14361e136	0.497839
$994$	−2.04279e135	−0.0849461
$995$	4.12929e135	0.164031
$996$	1.33539e136	0.506766
$997$	−3.88729e136	−1.40934	−0.704672	−	0.709534i	$-0.748906\pi$
$997$	−3.88729e136	−1.40934	−0.704672	+	0.709534i	$0.748906\pi$
$998$	1.79249e135	0.0620893
$999$	5.10348e136	1.68903

Twists

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

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

\(f(q)\)	\(=\)	\(q+7.65028e13 q^{2} -2.65748e21 q^{3} +3.37680e27 q^{4} -4.45639e31 q^{5} -2.03305e35 q^{6} +2.84237e38 q^{7} +6.89228e40 q^{8} -1.91217e43 q^{9} +O(q^{10})\)	\(q+7.65028e13 q^{2} -2.65748e21 q^{3} +3.37680e27 q^{4} -4.45639e31 q^{5} -2.03305e35 q^{6} +2.84237e38 q^{7} +6.89228e40 q^{8} -1.91217e43 q^{9} -3.40927e45 q^{10} +9.72727e46 q^{11} -8.97378e48 q^{12} +6.30388e50 q^{13} +2.17449e52 q^{14} +1.18428e53 q^{15} -3.08776e54 q^{16} -5.77591e55 q^{17} -1.46286e57 q^{18} +1.72189e58 q^{19} -1.50483e59 q^{20} -7.55354e59 q^{21} +7.44163e60 q^{22} +1.13922e62 q^{23} -1.83161e62 q^{24} -2.05302e63 q^{25} +4.82265e64 q^{26} +1.20399e65 q^{27} +9.59811e65 q^{28} +5.78948e66 q^{29} +9.06006e66 q^{30} +5.69673e67 q^{31} -4.06867e68 q^{32} -2.58500e68 q^{33} -4.41873e69 q^{34} -1.26667e70 q^{35} -6.45701e70 q^{36} +4.23882e71 q^{37} +1.31729e72 q^{38} -1.67525e72 q^{39} -3.07147e72 q^{40} -2.50923e72 q^{41} -5.77867e73 q^{42} -1.35809e74 q^{43} +3.28470e74 q^{44} +8.52138e74 q^{45} +8.71538e75 q^{46} -1.35732e76 q^{47} +8.20566e75 q^{48} +6.37215e74 q^{49} -1.57062e77 q^{50} +1.53494e77 q^{51} +2.12870e78 q^{52} +4.17132e78 q^{53} +9.21084e78 q^{54} -4.33485e78 q^{55} +1.95904e79 q^{56} -4.57588e79 q^{57} +4.42912e80 q^{58} +3.62948e80 q^{59} +3.99907e80 q^{60} +9.25617e80 q^{61} +4.35816e81 q^{62} -5.43509e81 q^{63} -2.34815e82 q^{64} -2.80926e82 q^{65} -1.97760e82 q^{66} +1.21510e83 q^{67} -1.95041e83 q^{68} -3.02746e83 q^{69} -9.69039e83 q^{70} -9.39434e82 q^{71} -1.31792e84 q^{72} -5.75947e84 q^{73} +3.24281e85 q^{74} +5.45587e84 q^{75} +5.81446e85 q^{76} +2.76485e85 q^{77} -1.28161e86 q^{78} -1.40597e86 q^{79} +1.37603e86 q^{80} +1.80723e86 q^{81} -1.91963e86 q^{82} -1.48810e87 q^{83} -2.55068e87 q^{84} +2.57397e87 q^{85} -1.03898e88 q^{86} -1.53854e88 q^{87} +6.70431e87 q^{88} +3.15928e88 q^{89} +6.51909e88 q^{90} +1.79180e89 q^{91} +3.84693e89 q^{92} -1.51390e89 q^{93} -1.03839e90 q^{94} -7.67340e89 q^{95} +1.08124e90 q^{96} -8.67008e89 q^{97} +4.87487e88 q^{98} -1.86002e90 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 3841716838056 q^{2} + 62\!\cdots\!32 q^{3}+ \cdots + 38\!\cdots\!59 q^{9}+O(q^{10}) \) 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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