LMFDB - Embedded newform 1.92.a.a.1.6

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			1.6
Root			$2.95949e12$ 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)

$f(q)$	$=$	$q+7.15766e13 q^{2} +9.10839e21 q^{3} +2.64733e27 q^{4} +1.09575e32 q^{5} +6.51948e35 q^{6} -1.62560e38 q^{7} +1.22718e40 q^{8} +5.67789e43 q^{9} +O(q^{10})$	\(q+7.15766e13 q^{2} +9.10839e21 q^{3} +2.64733e27 q^{4} +1.09575e32 q^{5} +6.51948e35 q^{6} -1.62560e38 q^{7} +1.22718e40 q^{8} +5.67789e43 q^{9} +7.84298e45 q^{10} -9.18735e46 q^{11} +2.41129e49 q^{12} +1.76153e50 q^{13} -1.16355e52 q^{14} +9.98048e53 q^{15} -5.67610e54 q^{16} -5.68005e55 q^{17} +4.06404e57 q^{18} +1.30287e58 q^{19} +2.90080e59 q^{20} -1.48066e60 q^{21} -6.57599e60 q^{22} -6.51130e61 q^{23} +1.11777e62 q^{24} +7.96762e63 q^{25} +1.26084e64 q^{26} +2.78672e65 q^{27} -4.30351e65 q^{28} +7.19965e65 q^{29} +7.14369e67 q^{30} -6.19885e67 q^{31} -4.36659e68 q^{32} -8.36820e68 q^{33} -4.06559e69 q^{34} -1.78125e70 q^{35} +1.50313e71 q^{36} -3.48286e71 q^{37} +9.32553e71 q^{38} +1.60447e72 q^{39} +1.34468e72 q^{40} -4.92808e72 q^{41} -1.05981e74 q^{42} -1.54947e74 q^{43} -2.43220e74 q^{44} +6.22153e75 q^{45} -4.66057e75 q^{46} +9.93250e75 q^{47} -5.17001e76 q^{48} -5.37275e76 q^{49} +5.70295e77 q^{50} -5.17361e77 q^{51} +4.66335e77 q^{52} +3.16592e78 q^{53} +1.99464e79 q^{54} -1.00670e79 q^{55} -1.99491e78 q^{56} +1.18671e80 q^{57} +5.15326e79 q^{58} -1.69372e80 q^{59} +2.64216e81 q^{60} +2.96057e81 q^{61} -4.43692e81 q^{62} -9.23000e81 q^{63} -1.72013e82 q^{64} +1.93019e82 q^{65} -5.98967e82 q^{66} +8.96842e82 q^{67} -1.50370e83 q^{68} -5.93075e83 q^{69} -1.27496e84 q^{70} +1.16955e84 q^{71} +6.96781e83 q^{72} +4.43684e84 q^{73} -2.49291e85 q^{74} +7.25722e85 q^{75} +3.44914e85 q^{76} +1.49350e85 q^{77} +1.14842e86 q^{78} -3.89794e86 q^{79} -6.21956e86 q^{80} +1.05156e87 q^{81} -3.52735e86 q^{82} +1.58683e87 q^{83} -3.91981e87 q^{84} -6.22389e87 q^{85} -1.10906e88 q^{86} +6.55772e87 q^{87} -1.12746e87 q^{88} -7.73439e88 q^{89} +4.45316e89 q^{90} -2.86355e88 q^{91} -1.72376e89 q^{92} -5.64615e89 q^{93} +7.10935e89 q^{94} +1.42762e90 q^{95} -3.97726e90 q^{96} +1.03889e90 q^{97} -3.84563e90 q^{98} -5.21648e90 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	7.15766e13	1.43849	0.719244	−	0.694757i	$-0.244488\pi$
$2$	7.15766e13	1.43849	0.719244	+	0.694757i	$0.244488\pi$
$3$	9.10839e21	1.78002	0.890010	−	0.455942i	$-0.150698\pi$
$3$	9.10839e21	1.78002	0.890010	+	0.455942i	$0.150698\pi$
$4$	2.64733e27	1.06925
$5$	1.09575e32	1.72415	0.862074	−	0.506782i	$-0.169165\pi$
$5$	1.09575e32	1.72415	0.862074	+	0.506782i	$0.169165\pi$
$6$	6.51948e35	2.56054
$7$	−1.62560e38	−0.574188	−0.287094	−	0.957902i	$-0.592689\pi$
$7$	−1.62560e38	−0.574188	−0.287094	+	0.957902i	$0.592689\pi$
$8$	1.22718e40	0.0996126
$9$	5.67789e43	2.16847
$10$	7.84298e45	2.48017
$11$	−9.18735e46	−0.380035	−0.190017	−	0.981781i	$-0.560854\pi$
$11$	−9.18735e46	−0.380035	−0.190017	+	0.981781i	$0.560854\pi$
$12$	2.41129e49	1.90328
$13$	1.76153e50	0.364307	0.182153	−	0.983270i	$-0.441693\pi$
$13$	1.76153e50	0.364307	0.182153	+	0.983270i	$0.441693\pi$
$14$	−1.16355e52	−0.825962
$15$	9.98048e53	3.06902
$16$	−5.67610e54	−0.925957
$17$	−5.68005e55	−0.587390	−0.293695	−	0.955899i	$-0.594885\pi$
$17$	−5.68005e55	−0.587390	−0.293695	+	0.955899i	$0.594885\pi$
$18$	4.06404e57	3.11932
$19$	1.30287e58	0.854306	0.427153	−	0.904179i	$-0.359517\pi$
$19$	1.30287e58	0.854306	0.427153	+	0.904179i	$0.359517\pi$
$20$	2.90080e59	1.84354
$21$	−1.48066e60	−1.02207
$22$	−6.57599e60	−0.546675
$23$	−6.51130e61	−0.716228	−0.358114	−	0.933678i	$-0.616580\pi$
$23$	−6.51130e61	−0.716228	−0.358114	+	0.933678i	$0.616580\pi$
$24$	1.11777e62	0.177312
$25$	7.96762e63	1.97269
$26$	1.26084e64	0.524051
$27$	2.78672e65	2.07990
$28$	−4.30351e65	−0.613949
$29$	7.19965e65	0.208067	0.104033	−	0.994574i	$-0.466825\pi$
$29$	7.19965e65	0.208067	0.104033	+	0.994574i	$0.466825\pi$
$30$	7.14369e67	4.41474
$31$	−6.19885e67	−0.861696	−0.430848	−	0.902425i	$-0.641785\pi$
$31$	−6.19885e67	−0.861696	−0.430848	+	0.902425i	$0.641785\pi$
$32$	−4.36659e68	−1.43159
$33$	−8.36820e68	−0.676469
$34$	−4.06559e69	−0.844953
$35$	−1.78125e70	−0.989985
$36$	1.50313e71	2.31863
$37$	−3.48286e71	−1.54439	−0.772196	−	0.635385i	$-0.780842\pi$
$37$	−3.48286e71	−1.54439	−0.772196	+	0.635385i	$0.780842\pi$
$38$	9.32553e71	1.22891
$39$	1.60447e72	0.648473
$40$	1.34468e72	0.171747
$41$	−4.92808e72	−0.204650	−0.102325	−	0.994751i	$-0.532628\pi$
$41$	−4.92808e72	−0.204650	−0.102325	+	0.994751i	$0.532628\pi$
$42$	−1.05981e74	−1.47023
$43$	−1.54947e74	−0.736831	−0.368416	−	0.929661i	$-0.620100\pi$
$43$	−1.54947e74	−0.736831	−0.368416	+	0.929661i	$0.620100\pi$
$44$	−2.43220e74	−0.406351
$45$	6.22153e75	3.73876
$46$	−4.66057e75	−1.03029
$47$	9.93250e75	0.825289	0.412645	−	0.910892i	$-0.364605\pi$
$47$	9.93250e75	0.825289	0.412645	+	0.910892i	$0.364605\pi$
$48$	−5.17001e76	−1.64822
$49$	−5.37275e76	−0.670308
$50$	5.70295e77	2.83769
$51$	−5.17361e77	−1.04556
$52$	4.66335e77	0.389534
$53$	3.16592e78	1.11160	0.555799	−	0.831317i	$-0.312412\pi$
$53$	3.16592e78	1.11160	0.555799	+	0.831317i	$0.312412\pi$
$54$	1.99464e79	2.99191
$55$	−1.00670e79	−0.655236
$56$	−1.99491e78	−0.0571964
$57$	1.18671e80	1.52068
$58$	5.15326e79	0.299301
$59$	−1.69372e80	−0.451934	−0.225967	−	0.974135i	$-0.572554\pi$
$59$	−1.69372e80	−0.451934	−0.225967	+	0.974135i	$0.572554\pi$
$60$	2.64216e81	3.28154
$61$	2.96057e81	1.73327	0.866637	−	0.498939i	$-0.166277\pi$
$61$	2.96057e81	1.73327	0.866637	+	0.498939i	$0.166277\pi$
$62$	−4.43692e81	−1.23954
$63$	−9.23000e81	−1.24511
$64$	−1.72013e82	−1.13337
$65$	1.93019e82	0.628119
$66$	−5.98967e82	−0.973093
$67$	8.96842e82	0.735043	0.367521	−	0.930015i	$-0.380207\pi$
$67$	8.96842e82	0.735043	0.367521	+	0.930015i	$0.380207\pi$
$68$	−1.50370e83	−0.628065
$69$	−5.93075e83	−1.27490
$70$	−1.27496e84	−1.42408
$71$	1.16955e84	0.685115	0.342558	−	0.939497i	$-0.388707\pi$
$71$	1.16955e84	0.685115	0.342558	+	0.939497i	$0.388707\pi$
$72$	6.96781e83	0.216007
$73$	4.43684e84	0.734316	0.367158	−	0.930159i	$-0.380331\pi$
$73$	4.43684e84	0.734316	0.367158	+	0.930159i	$0.380331\pi$
$74$	−2.49291e85	−2.22159
$75$	7.25722e85	3.51142
$76$	3.44914e85	0.913465
$77$	1.49350e85	0.218211
$78$	1.14842e86	0.932821
$79$	−3.89794e86	−1.77338	−0.886692	−	0.462361i	$-0.847002\pi$
$79$	−3.89794e86	−1.77338	−0.886692	+	0.462361i	$0.847002\pi$
$80$	−6.21956e86	−1.59649
$81$	1.05156e87	1.53379
$82$	−3.52735e86	−0.294387
$83$	1.58683e87	0.762916	0.381458	−	0.924386i	$-0.375422\pi$
$83$	1.58683e87	0.762916	0.381458	+	0.924386i	$0.375422\pi$
$84$	−3.91981e87	−1.09284
$85$	−6.22389e87	−1.01275
$86$	−1.10906e88	−1.05992
$87$	6.55772e87	0.370362
$88$	−1.12746e87	−0.0378563
$89$	−7.73439e88	−1.55303	−0.776517	−	0.630097i	$-0.783015\pi$
$89$	−7.73439e88	−1.55303	−0.776517	+	0.630097i	$0.783015\pi$
$90$	4.45316e89	5.37816
$91$	−2.86355e88	−0.209180
$92$	−1.72376e89	−0.765826
$93$	−5.64615e89	−1.53383
$94$	7.10935e89	1.18717
$95$	1.42762e90	1.47295
$96$	−3.97726e90	−2.54826
$97$	1.03889e90	0.415391	0.207695	−	0.978194i	$-0.433404\pi$
$97$	1.03889e90	0.415391	0.207695	+	0.978194i	$0.433404\pi$
$98$	−3.84563e90	−0.964231
$99$	−5.21648e90	−0.824093
$100$	2.10929e91	2.10929
$101$	−1.55804e91	−0.990735	−0.495367	−	0.868684i	$-0.664967\pi$
$101$	−1.55804e91	−0.990735	−0.495367	+	0.868684i	$0.664967\pi$
$102$	−3.70310e91	−1.50403
$103$	6.59719e91	1.71896	0.859479	−	0.511172i	$-0.170788\pi$
$103$	6.59719e91	1.71896	0.859479	+	0.511172i	$0.170788\pi$
$104$	2.16172e90	0.0362896
$105$	−1.62243e92	−1.76219
$106$	2.26606e92	1.59902
$107$	3.66570e92	1.68731	0.843656	−	0.536884i	$-0.180399\pi$
$107$	3.66570e92	1.68731	0.843656	+	0.536884i	$0.180399\pi$
$108$	7.37736e92	2.22392
$109$	−6.54355e92	−1.29690	−0.648452	−	0.761256i	$-0.724583\pi$
$109$	−6.54355e92	−1.29690	−0.648452	+	0.761256i	$0.724583\pi$
$110$	−7.20562e92	−0.942549
$111$	−3.17232e93	−2.74905
$112$	9.22708e92	0.531673
$113$	−2.60687e93	−1.00242	−0.501210	−	0.865326i	$-0.667111\pi$
$113$	−2.60687e93	−1.00242	−0.501210	+	0.865326i	$0.667111\pi$
$114$	8.49406e93	2.18748
$115$	−7.13473e93	−1.23488
$116$	1.90598e93	0.222475
$117$	1.00018e94	0.789988
$118$	−1.21231e94	−0.650102
$119$	9.23351e93	0.337272
$120$	1.22479e94	0.305713
$121$	−5.00025e94	−0.855574
$122$	2.11907e95	2.49329
$123$	−4.48868e94	−0.364281
$124$	−1.64104e95	−0.921366
$125$	4.30480e95	1.67706
$126$	−6.60652e95	−1.79107
$127$	−3.20231e95	−0.605890	−0.302945	−	0.953008i	$-0.597970\pi$
$127$	−3.20231e95	−0.605890	−0.302945	+	0.953008i	$0.597970\pi$
$128$	−1.50091e95	−0.198748
$129$	−1.41132e96	−1.31157
$130$	1.38156e96	0.903542
$131$	6.49991e95	0.299960	0.149980	−	0.988689i	$-0.452079\pi$
$131$	6.49991e95	0.299960	0.149980	+	0.988689i	$0.452079\pi$
$132$	−2.21534e96	−0.723313
$133$	−2.11796e96	−0.490532
$134$	6.41929e96	1.05735
$135$	3.05353e97	3.58605
$136$	−6.97045e95	−0.0585114
$137$	−1.76249e97	−1.06008	−0.530041	−	0.847972i	$-0.677824\pi$
$137$	−1.76249e97	−1.06008	−0.530041	+	0.847972i	$0.677824\pi$
$138$	−4.24503e97	−1.83393
$139$	−8.65589e96	−0.269239	−0.134620	−	0.990897i	$-0.542981\pi$
$139$	−8.65589e96	−0.269239	−0.134620	+	0.990897i	$0.542981\pi$
$140$	−4.71555e97	−1.05854
$141$	9.04691e97	1.46903
$142$	8.37124e97	0.985530
$143$	−1.61838e97	−0.138449
$144$	−3.22283e98	−2.00791
$145$	7.88898e97	0.358738
$146$	3.17574e98	1.05631
$147$	−4.89371e98	−1.19316
$148$	−9.22028e98	−1.65134
$149$	−1.68006e98	−0.221488	−0.110744	−	0.993849i	$-0.535323\pi$
$149$	−1.68006e98	−0.221488	−0.110744	+	0.993849i	$0.535323\pi$
$150$	5.19447e99	5.05114
$151$	−2.75801e98	−0.198219	−0.0991093	−	0.995077i	$-0.531599\pi$
$151$	−2.75801e98	−0.198219	−0.0991093	+	0.995077i	$0.531599\pi$
$152$	1.59886e98	0.0850997
$153$	−3.22507e99	−1.27374
$154$	1.06900e99	0.313894
$155$	−6.79236e99	−1.48569
$156$	4.24756e99	0.693379
$157$	1.85283e99	0.226153	0.113076	−	0.993586i	$-0.463930\pi$
$157$	1.85283e99	0.226153	0.113076	+	0.993586i	$0.463930\pi$
$158$	−2.79001e100	−2.55099
$159$	2.88364e100	1.97867
$160$	−4.78468e100	−2.46827
$161$	1.05848e100	0.411249
$162$	7.52669e100	2.20633
$163$	2.92402e100	0.647806	0.323903	−	0.946090i	$-0.395005\pi$
$163$	2.92402e100	0.647806	0.323903	+	0.946090i	$0.395005\pi$
$164$	−1.30462e100	−0.218822
$165$	−9.16942e100	−1.16633
$166$	1.13580e101	1.09745
$167$	1.12362e101	0.826078	0.413039	−	0.910713i	$-0.364467\pi$
$167$	1.12362e101	0.826078	0.413039	+	0.910713i	$0.364467\pi$
$168$	−1.81704e100	−0.101811
$169$	−2.02770e101	−0.867281
$170$	−4.45485e101	−1.45682
$171$	7.39758e101	1.85254
$172$	−4.10196e101	−0.787855
$173$	1.14452e101	0.168859	0.0844297	−	0.996429i	$-0.473093\pi$
$173$	1.14452e101	0.168859	0.0844297	+	0.996429i	$0.473093\pi$
$174$	4.69379e101	0.532762
$175$	−1.29522e102	−1.13269
$176$	5.21483e101	0.351896
$177$	−1.54271e102	−0.804452
$178$	−5.53601e102	−2.23402
$179$	−3.80655e101	−0.119047	−0.0595234	−	0.998227i	$-0.518958\pi$
$179$	−3.80655e101	−0.119047	−0.0595234	+	0.998227i	$0.518958\pi$
$180$	1.64704e103	3.99766
$181$	8.82203e100	0.0166415	0.00832076	−	0.999965i	$-0.497351\pi$
$181$	8.82203e100	0.0166415	0.00832076	+	0.999965i	$0.497351\pi$
$182$	−2.04963e102	−0.300904
$183$	2.69660e103	3.08526
$184$	−7.99055e101	−0.0713454
$185$	−3.81633e103	−2.66276
$186$	−4.04133e103	−2.20640
$187$	5.21846e102	0.223228
$188$	2.62946e103	0.882439
$189$	−4.53010e103	−1.19425
$190$	1.02184e104	2.11882
$191$	−3.08898e103	−0.504426	−0.252213	−	0.967672i	$-0.581158\pi$
$191$	−3.08898e103	−0.504426	−0.252213	+	0.967672i	$0.581158\pi$
$192$	−1.56676e104	−2.01742
$193$	7.94342e103	0.807513	0.403757	−	0.914866i	$-0.367704\pi$
$193$	7.94342e103	0.807513	0.403757	+	0.914866i	$0.367704\pi$
$194$	7.43604e103	0.597534
$195$	1.75809e104	1.11806
$196$	−1.42234e104	−0.716726
$197$	1.26766e104	0.506747	0.253373	−	0.967369i	$-0.418460\pi$
$197$	1.26766e104	0.506747	0.253373	+	0.967369i	$0.418460\pi$
$198$	−3.73378e104	−1.18545
$199$	5.11420e104	1.29111	0.645554	−	0.763715i	$-0.276627\pi$
$199$	5.11420e104	1.29111	0.645554	+	0.763715i	$0.276627\pi$
$200$	9.77772e103	0.196505
$201$	8.16879e104	1.30839
$202$	−1.11520e105	−1.42516
$203$	−1.17038e104	−0.119469
$204$	−1.36963e105	−1.11797
$205$	−5.39992e104	−0.352847
$206$	4.72204e105	2.47270
$207$	−3.69705e105	−1.55312
$208$	−9.99861e104	−0.337332
$209$	−1.19700e105	−0.324666
$210$	−1.16128e106	−2.53489
$211$	5.31720e105	0.935042	0.467521	−	0.883982i	$-0.345147\pi$
$211$	5.31720e105	0.935042	0.467521	+	0.883982i	$0.345147\pi$
$212$	8.38123e105	1.18857
$213$	1.06527e106	1.21952
$214$	2.62379e106	2.42718
$215$	−1.69782e106	−1.27041
$216$	3.41981e105	0.207184
$217$	1.00769e106	0.494775
$218$	−4.68365e106	−1.86558
$219$	4.04124e106	1.30710
$220$	−2.66507e106	−0.700610
$221$	−1.00056e106	−0.213990
$222$	−2.27064e107	−3.95447
$223$	4.93325e106	0.700263	0.350132	−	0.936700i	$-0.386137\pi$
$223$	4.93325e106	0.700263	0.350132	+	0.936700i	$0.386137\pi$
$224$	7.09835e106	0.822001
$225$	4.52393e107	4.27771
$226$	−1.86591e107	−1.44197
$227$	−2.82136e107	−1.78354	−0.891768	−	0.452494i	$-0.850535\pi$
$227$	−2.82136e107	−1.78354	−0.891768	+	0.452494i	$0.850535\pi$
$228$	3.14161e107	1.62599
$229$	−1.06109e107	−0.450026	−0.225013	−	0.974356i	$-0.572243\pi$
$229$	−1.06109e107	−0.450026	−0.225013	+	0.974356i	$0.572243\pi$
$230$	−5.10680e107	−1.77637
$231$	1.36034e107	0.388420
$232$	8.83528e105	0.0207261
$233$	7.49893e107	1.44646	0.723228	−	0.690610i	$-0.242658\pi$
$233$	7.49893e107	1.44646	0.723228	+	0.690610i	$0.242658\pi$
$234$	7.15893e107	1.13639
$235$	1.08835e108	1.42292
$236$	−4.48384e107	−0.483230
$237$	−3.55040e108	−3.15666
$238$	6.60903e107	0.485162
$239$	2.70670e108	1.64186	0.820929	−	0.571030i	$-0.193456\pi$
$239$	2.70670e108	1.64186	0.820929	+	0.571030i	$0.193456\pi$
$240$	−5.66502e108	−2.84178
$241$	1.49592e108	0.621057	0.310529	−	0.950564i	$-0.399494\pi$
$241$	1.49592e108	0.621057	0.310529	+	0.950564i	$0.399494\pi$
$242$	−3.57901e108	−1.23073
$243$	2.28129e108	0.650273
$244$	7.83759e108	1.85330
$245$	−5.88716e108	−1.15571
$246$	−3.21285e108	−0.524014
$247$	2.29505e108	0.311229
$248$	−7.60711e107	−0.0858358
$249$	1.44534e109	1.35800
$250$	3.08123e109	2.41243
$251$	−3.15835e108	−0.206208	−0.103104	−	0.994671i	$-0.532878\pi$
$251$	−3.15835e108	−0.206208	−0.103104	+	0.994671i	$0.532878\pi$
$252$	−2.44349e109	−1.33133
$253$	5.98216e108	0.272192
$254$	−2.29210e109	−0.871565
$255$	−5.66897e109	−1.80271
$256$	3.18452e109	0.847473
$257$	−1.76904e108	−0.0394259	−0.0197129	−	0.999806i	$-0.506275\pi$
$257$	−1.76904e108	−0.0394259	−0.0197129	+	0.999806i	$0.506275\pi$
$258$	−1.01017e110	−1.88668
$259$	5.66175e109	0.886771
$260$	5.10984e109	0.671615
$261$	4.08788e109	0.451186
$262$	4.65242e109	0.431489
$263$	−4.08887e109	−0.318873	−0.159436	−	0.987208i	$-0.550968\pi$
$263$	−4.08887e109	−0.318873	−0.159436	+	0.987208i	$0.550968\pi$
$264$	−1.02693e109	−0.0673849
$265$	3.46904e110	1.91656
$266$	−1.51596e110	−0.705625
$267$	−7.04479e110	−2.76443
$268$	2.37424e110	0.785943
$269$	−6.80035e110	−1.90022	−0.950108	−	0.311922i	$-0.899027\pi$
$269$	−6.80035e110	−1.90022	−0.950108	+	0.311922i	$0.899027\pi$
$270$	2.18562e111	5.15849
$271$	−2.01148e110	−0.401247	−0.200624	−	0.979668i	$-0.564297\pi$
$271$	−2.01148e110	−0.401247	−0.200624	+	0.979668i	$0.564297\pi$
$272$	3.22405e110	0.543897
$273$	−2.60823e110	−0.372345
$274$	−1.26153e111	−1.52492
$275$	−7.32013e110	−0.749689
$276$	−1.57007e111	−1.36318
$277$	2.15066e111	1.58395	0.791976	−	0.610552i	$-0.209052\pi$
$277$	2.15066e111	1.58395	0.791976	+	0.610552i	$0.209052\pi$
$278$	−6.19559e110	−0.387297
$279$	−3.51964e111	−1.86856
$280$	−2.18592e110	−0.0986150
$281$	−7.86710e110	−0.301771	−0.150885	−	0.988551i	$-0.548212\pi$
$281$	−7.86710e110	−0.301771	−0.150885	+	0.988551i	$0.548212\pi$
$282$	6.47547e111	2.11318
$283$	−2.63126e109	−0.00730939	−0.00365470	−	0.999993i	$-0.501163\pi$
$283$	−2.63126e109	−0.00730939	−0.00365470	+	0.999993i	$0.501163\pi$
$284$	3.09618e111	0.732558
$285$	1.30033e112	2.62188
$286$	−1.15838e111	−0.199158
$287$	8.01110e110	0.117508
$288$	−2.47930e112	−3.10436
$289$	−6.12457e111	−0.654973
$290$	5.64667e111	0.516040
$291$	9.46264e111	0.739403
$292$	1.17458e112	0.785166
$293$	9.19419e111	0.526062	0.263031	−	0.964787i	$-0.415278\pi$
$293$	9.19419e111	0.526062	0.263031	+	0.964787i	$0.415278\pi$
$294$	−3.50275e112	−1.71635
$295$	−1.85589e112	−0.779202
$296$	−4.27410e111	−0.153841
$297$	−2.56025e112	−0.790432
$298$	−1.20253e112	−0.318608
$299$	−1.14698e112	−0.260927
$300$	1.92123e113	3.75458
$301$	2.51882e112	0.423079
$302$	−1.97409e112	−0.285135
$303$	−1.41913e113	−1.76353
$304$	−7.39524e112	−0.791050
$305$	3.24403e113	2.98842
$306$	−2.30840e113	−1.83225
$307$	−1.59060e113	−1.08834	−0.544171	−	0.838974i	$-0.683156\pi$
$307$	−1.59060e113	−1.08834	−0.544171	+	0.838974i	$0.683156\pi$
$308$	3.95379e112	0.233322
$309$	6.00898e113	3.05978
$310$	−4.86174e113	−2.13715
$311$	2.29655e113	0.871922	0.435961	−	0.899966i	$-0.356409\pi$
$311$	2.29655e113	0.871922	0.435961	+	0.899966i	$0.356409\pi$
$312$	1.96898e112	0.0645961
$313$	1.65038e113	0.468076	0.234038	−	0.972228i	$-0.424806\pi$
$313$	1.65038e113	0.468076	0.234038	+	0.972228i	$0.424806\pi$
$314$	1.32619e113	0.325318
$315$	−1.01137e114	−2.14675
$316$	−1.03191e114	−1.89619
$317$	−1.04058e114	−1.65608	−0.828039	−	0.560670i	$-0.810544\pi$
$317$	−1.04058e114	−1.65608	−0.828039	+	0.560670i	$0.810544\pi$
$318$	2.06401e114	2.84629
$319$	−6.61457e112	−0.0790725
$320$	−1.88482e114	−1.95410
$321$	3.33887e114	3.00345
$322$	7.57624e113	0.591577
$323$	−7.40039e113	−0.501811
$324$	2.78382e114	1.64000
$325$	1.40352e114	0.718663
$326$	2.09292e114	0.931861
$327$	−5.96012e114	−2.30851
$328$	−6.04764e112	−0.0203857
$329$	−1.61463e114	−0.473871
$330$	−6.56316e114	−1.67776
$331$	3.18706e114	0.709931	0.354966	−	0.934879i	$-0.384493\pi$
$331$	3.18706e114	0.709931	0.354966	+	0.934879i	$0.384493\pi$
$332$	4.20086e114	0.815746
$333$	−1.97753e115	−3.34896
$334$	8.04251e114	1.18830
$335$	9.82711e114	1.26732
$336$	8.40439e114	0.946388
$337$	1.40180e115	1.37888	0.689439	−	0.724343i	$-0.257857\pi$
$337$	1.40180e115	1.37888	0.689439	+	0.724343i	$0.257857\pi$
$338$	−1.45136e115	−1.24757
$339$	−2.37444e115	−1.78433
$340$	−1.64767e115	−1.08288
$341$	5.69510e114	0.327474
$342$	5.29494e115	2.66485
$343$	2.17637e115	0.959071
$344$	−1.90148e114	−0.0733977
$345$	−6.49860e115	−2.19812
$346$	8.19207e114	0.242902
$347$	4.98340e115	1.29579	0.647895	−	0.761730i	$-0.275650\pi$
$347$	4.98340e115	1.29579	0.647895	+	0.761730i	$0.275650\pi$
$348$	1.73605e115	0.396009
$349$	1.13226e115	0.226667	0.113334	−	0.993557i	$-0.463847\pi$
$349$	1.13226e115	0.226667	0.113334	+	0.993557i	$0.463847\pi$
$350$	−9.27074e115	−1.62937
$351$	4.90888e115	0.757720
$352$	4.01174e115	0.544054
$353$	−1.04855e116	−1.24980	−0.624899	−	0.780706i	$-0.714860\pi$
$353$	−1.04855e116	−1.24980	−0.624899	+	0.780706i	$0.714860\pi$
$354$	−1.10422e116	−1.15719
$355$	1.28153e116	1.18124
$356$	−2.04755e116	−1.66058
$357$	8.41025e115	0.600350
$358$	−2.72460e115	−0.171248
$359$	1.33655e116	0.739924	0.369962	−	0.929047i	$-0.379371\pi$
$359$	1.33655e116	0.739924	0.369962	+	0.929047i	$0.379371\pi$
$360$	7.63494e115	0.372428
$361$	−6.28348e115	−0.270161
$362$	6.31451e114	0.0239386
$363$	−4.55442e116	−1.52294
$364$	−7.58076e115	−0.223666
$365$	4.86164e116	1.26607
$366$	1.93013e117	4.43811
$367$	7.89484e115	0.160338	0.0801692	−	0.996781i	$-0.474454\pi$
$367$	7.89484e115	0.160338	0.0801692	+	0.996781i	$0.474454\pi$
$368$	3.69588e116	0.663196
$369$	−2.79811e116	−0.443777
$370$	−2.73160e117	−3.83035
$371$	−5.14653e116	−0.638266
$372$	−1.49472e117	−1.64005
$373$	−1.32652e117	−1.28813	−0.644067	−	0.764969i	$-0.722754\pi$
$373$	−1.32652e117	−1.28813	−0.644067	+	0.764969i	$0.722754\pi$
$374$	3.73520e116	0.321111
$375$	3.92098e117	2.98519
$376$	1.21890e116	0.0822092
$377$	1.26824e116	0.0758001
$378$	−3.24249e117	−1.71792
$379$	3.46717e117	1.62889	0.814443	−	0.580244i	$-0.197043\pi$
$379$	3.46717e117	1.62889	0.814443	+	0.580244i	$0.197043\pi$
$380$	3.77938e117	1.57495
$381$	−2.91679e117	−1.07850
$382$	−2.21099e117	−0.725610
$383$	1.13925e117	0.331952	0.165976	−	0.986130i	$-0.446923\pi$
$383$	1.13925e117	0.331952	0.165976	+	0.986130i	$0.446923\pi$
$384$	−1.36709e117	−0.353775
$385$	1.63650e117	0.376228
$386$	5.68563e117	1.16160
$387$	−8.79772e117	−1.59780
$388$	2.75029e117	0.444156
$389$	−5.89178e117	−0.846330	−0.423165	−	0.906053i	$-0.639081\pi$
$389$	−5.89178e117	−0.846330	−0.423165	+	0.906053i	$0.639081\pi$
$390$	1.25838e118	1.60832
$391$	3.69845e117	0.420705
$392$	−6.59334e116	−0.0667712
$393$	5.92037e117	0.533935
$394$	9.07351e117	0.728949
$395$	−4.27115e118	−3.05758
$396$	−1.38097e118	−0.881160
$397$	−5.05809e117	−0.287752	−0.143876	−	0.989596i	$-0.545957\pi$
$397$	−5.05809e117	−0.287752	−0.143876	+	0.989596i	$0.545957\pi$
$398$	3.66057e118	1.85724
$399$	−1.92912e118	−0.873156
$400$	−4.52250e118	−1.82662
$401$	1.31846e118	0.475333	0.237666	−	0.971347i	$-0.423617\pi$
$401$	1.31846e118	0.475333	0.237666	+	0.971347i	$0.423617\pi$
$402$	5.84694e118	1.88210
$403$	−1.09194e118	−0.313922
$404$	−4.12466e118	−1.05934
$405$	1.15224e119	2.64447
$406$	−8.37716e117	−0.171855
$407$	3.19982e118	0.586922
$408$	−6.34896e117	−0.104151
$409$	4.32149e118	0.634195	0.317097	−	0.948393i	$-0.397292\pi$
$409$	4.32149e118	0.634195	0.317097	+	0.948393i	$0.397292\pi$
$410$	−3.86508e118	−0.507566
$411$	−1.60534e119	−1.88697
$412$	1.74649e119	1.83799
$413$	2.75332e118	0.259495
$414$	−2.64622e119	−2.23414
$415$	1.73876e119	1.31538
$416$	−7.69188e118	−0.521538
$417$	−7.88412e118	−0.479251
$418$	−8.56769e118	−0.467028
$419$	−2.72300e119	−1.33140	−0.665701	−	0.746218i	$-0.731868\pi$
$419$	−2.72300e119	−1.33140	−0.665701	+	0.746218i	$0.731868\pi$
$420$	−4.29511e119	−1.88422
$421$	3.87386e119	1.52514	0.762568	−	0.646908i	$-0.223938\pi$
$421$	3.87386e119	1.52514	0.762568	+	0.646908i	$0.223938\pi$
$422$	3.80587e119	1.34505
$423$	5.63957e119	1.78961
$424$	3.88516e118	0.110729
$425$	−4.52565e119	−1.15874
$426$	7.62485e119	1.75426
$427$	−4.81271e119	−0.995225
$428$	9.70433e119	1.80416
$429$	−1.47408e119	−0.246442
$430$	−1.21524e120	−1.82746
$431$	3.27048e119	0.442482	0.221241	−	0.975219i	$-0.428989\pi$
$431$	3.27048e119	0.442482	0.221241	+	0.975219i	$0.428989\pi$
$432$	−1.58177e120	−1.92589
$433$	7.16612e119	0.785390	0.392695	−	0.919669i	$-0.371543\pi$
$433$	7.16612e119	0.785390	0.392695	+	0.919669i	$0.371543\pi$
$434$	7.21268e119	0.711728
$435$	7.18560e119	0.638560
$436$	−1.73229e120	−1.38671
$437$	−8.48341e119	−0.611878
$438$	2.89259e120	1.88024
$439$	1.66331e120	0.974628	0.487314	−	0.873227i	$-0.337977\pi$
$439$	1.66331e120	0.974628	0.487314	+	0.873227i	$0.337977\pi$
$440$	−1.23540e119	−0.0652698
$441$	−3.05059e120	−1.45354
$442$	−7.16165e119	−0.307822
$443$	4.59392e120	1.78162	0.890808	−	0.454379i	$-0.150139\pi$
$443$	4.59392e120	1.78162	0.890808	+	0.454379i	$0.150139\pi$
$444$	−8.39819e120	−2.93941
$445$	−8.47493e120	−2.67766
$446$	3.53105e120	1.00732
$447$	−1.53027e120	−0.394252
$448$	2.79624e120	0.650766
$449$	2.91487e120	0.612930	0.306465	−	0.951882i	$-0.400854\pi$
$449$	2.91487e120	0.612930	0.306465	+	0.951882i	$0.400854\pi$
$450$	3.23808e121	6.15343
$451$	4.52760e119	0.0777741
$452$	−6.90123e120	−1.07184
$453$	−2.51210e120	−0.352833
$454$	−2.01943e121	−2.56559
$455$	−3.13772e120	−0.360658
$456$	1.45631e120	0.151479
$457$	2.11004e121	1.98657	0.993284	−	0.115701i	$-0.0369115\pi$
$457$	2.11004e121	1.98657	0.993284	+	0.115701i	$0.0369115\pi$
$458$	−7.59492e120	−0.647357
$459$	−1.58287e121	−1.22171
$460$	−1.88880e121	−1.32040
$461$	1.38274e121	0.875688	0.437844	−	0.899051i	$-0.355742\pi$
$461$	1.38274e121	0.875688	0.437844	+	0.899051i	$0.355742\pi$
$462$	9.73684e120	0.558738
$463$	−2.01599e121	−1.04846	−0.524232	−	0.851575i	$-0.675648\pi$
$463$	−2.01599e121	−1.04846	−0.524232	+	0.851575i	$0.675648\pi$
$464$	−4.08659e120	−0.192661
$465$	−6.18675e121	−2.64456
$466$	5.36748e121	2.08071
$467$	1.54017e121	0.541564	0.270782	−	0.962641i	$-0.412718\pi$
$467$	1.54017e121	0.541564	0.270782	+	0.962641i	$0.412718\pi$
$468$	2.64780e121	0.844693
$469$	−1.45791e121	−0.422052
$470$	7.79004e121	2.04685
$471$	1.68763e121	0.402556
$472$	−2.07850e120	−0.0450184
$473$	1.42355e121	0.280021
$474$	−2.54125e122	−4.54081
$475$	1.03808e122	1.68528
$476$	2.44442e121	0.360627
$477$	1.79757e122	2.41046
$478$	1.93736e122	2.36179
$479$	−1.01649e122	−1.12678	−0.563388	−	0.826192i	$-0.690503\pi$
$479$	−1.01649e122	−1.12678	−0.563388	+	0.826192i	$0.690503\pi$
$480$	−4.35807e122	−4.39357
$481$	−6.13516e121	−0.562632
$482$	1.07073e122	0.893384
$483$	9.64105e121	0.732032
$484$	−1.32373e122	−0.914821
$485$	1.13836e122	0.716195
$486$	1.63287e122	0.935409
$487$	−2.24946e122	−1.17358	−0.586788	−	0.809741i	$-0.699608\pi$
$487$	−2.24946e122	−1.17358	−0.586788	+	0.809741i	$0.699608\pi$
$488$	3.63315e121	0.172656
$489$	2.66332e122	1.15311
$490$	−4.21383e122	−1.66248
$491$	2.31127e122	0.831080	0.415540	−	0.909575i	$-0.363593\pi$
$491$	2.31127e122	0.831080	0.415540	+	0.909575i	$0.363593\pi$
$492$	−1.18830e122	−0.389507
$493$	−4.08944e121	−0.122216
$494$	1.64272e122	0.447700
$495$	−5.71594e122	−1.42086
$496$	3.51853e122	0.797893
$497$	−1.90122e122	−0.393385
$498$	1.03453e123	1.95347
$499$	−8.32524e122	−1.43490	−0.717451	−	0.696609i	$-0.754691\pi$
$499$	−8.32524e122	−1.43490	−0.717451	+	0.696609i	$0.754691\pi$
$500$	1.13962e123	1.79319
$501$	1.02344e123	1.47043
$502$	−2.26064e122	−0.296628
$503$	5.53264e122	0.663116	0.331558	−	0.943435i	$-0.392426\pi$
$503$	5.53264e122	0.663116	0.331558	+	0.943435i	$0.392426\pi$
$504$	−1.13269e122	−0.124028
$505$	−1.70722e123	−1.70817
$506$	4.28183e122	0.391544
$507$	−1.84691e123	−1.54378
$508$	−8.47756e122	−0.647846
$509$	−1.00029e123	−0.698982	−0.349491	−	0.936940i	$-0.613646\pi$
$509$	−1.00029e123	−0.698982	−0.349491	+	0.936940i	$0.613646\pi$
$510$	−4.05765e123	−2.59318
$511$	−7.21254e122	−0.421635
$512$	2.65098e123	1.41783
$513$	3.63074e123	1.77687
$514$	−1.26622e122	−0.0567137
$515$	7.22884e123	2.96374
$516$	−3.73622e123	−1.40240
$517$	−9.12534e122	−0.313638
$518$	4.05249e123	1.27561
$519$	1.04247e123	0.300573
$520$	2.36869e122	0.0625686
$521$	−3.83388e123	−0.927946	−0.463973	−	0.885849i	$-0.653577\pi$
$521$	−3.83388e123	−0.927946	−0.463973	+	0.885849i	$0.653577\pi$
$522$	2.92597e123	0.649025
$523$	−1.64684e123	−0.334831	−0.167415	−	0.985886i	$-0.553542\pi$
$523$	−1.64684e123	−0.334831	−0.167415	+	0.985886i	$0.553542\pi$
$524$	1.72074e123	0.320732
$525$	−1.17974e124	−2.01621
$526$	−2.92668e123	−0.458694
$527$	3.52098e123	0.506151
$528$	4.74987e123	0.626381
$529$	−4.02511e123	−0.487017
$530$	2.48302e124	2.75695
$531$	−9.61677e123	−0.980005
$532$	−5.60693e123	−0.524500
$533$	−8.68095e122	−0.0745554
$534$	−5.04242e124	−3.97660
$535$	4.01668e124	2.90918
$536$	1.10059e123	0.0732195
$537$	−3.46715e123	−0.211906
$538$	−4.86746e124	−2.73344
$539$	4.93613e123	0.254740
$540$	8.08371e124	3.83438
$541$	1.19784e124	0.522302	0.261151	−	0.965298i	$-0.415898\pi$
$541$	1.19784e124	0.522302	0.261151	+	0.965298i	$0.415898\pi$
$542$	−1.43975e124	−0.577190
$543$	8.03545e122	0.0296222
$544$	2.48025e124	0.840901
$545$	−7.17006e124	−2.23605
$546$	−1.86688e124	−0.535614
$547$	2.59396e124	0.684762	0.342381	−	0.939561i	$-0.388767\pi$
$547$	2.59396e124	0.684762	0.342381	+	0.939561i	$0.388767\pi$
$548$	−4.66588e124	−1.13349
$549$	1.68098e125	3.75855
$550$	−5.23950e124	−1.07842
$551$	9.38023e123	0.177753
$552$	−7.27811e123	−0.126996
$553$	6.33651e124	1.01825
$554$	1.53937e125	2.27850
$555$	−3.47606e125	−4.73976
$556$	−2.29150e124	−0.287883
$557$	7.72041e124	0.893776	0.446888	−	0.894590i	$-0.352532\pi$
$557$	7.72041e124	0.893776	0.446888	+	0.894590i	$0.352532\pi$
$558$	−2.51924e125	−2.68790
$559$	−2.72943e124	−0.268433
$560$	1.01105e125	0.916683
$561$	4.75318e124	0.397351
$562$	−5.63101e124	−0.434094
$563$	1.10953e125	0.788871	0.394435	−	0.918924i	$-0.370940\pi$
$563$	1.10953e125	0.788871	0.394435	+	0.918924i	$0.370940\pi$
$564$	2.39502e125	1.57076
$565$	−2.85646e125	−1.72832
$566$	−1.88337e123	−0.0105145
$567$	−1.70942e125	−0.880681
$568$	1.43525e124	0.0682461
$569$	3.12180e125	1.37024	0.685119	−	0.728431i	$-0.259750\pi$
$569$	3.12180e125	1.37024	0.685119	+	0.728431i	$0.259750\pi$
$570$	9.30733e125	3.77154
$571$	2.35666e125	0.881766	0.440883	−	0.897565i	$-0.354665\pi$
$571$	2.35666e125	0.881766	0.440883	+	0.897565i	$0.354665\pi$
$572$	−4.28438e124	−0.148037
$573$	−2.81357e125	−0.897887
$574$	5.73407e124	0.169033
$575$	−5.18796e125	−1.41289
$576$	−9.76669e125	−2.45767
$577$	−5.26391e125	−1.22408	−0.612038	−	0.790828i	$-0.709650\pi$
$577$	−5.26391e125	−1.22408	−0.612038	+	0.790828i	$0.709650\pi$
$578$	−4.38376e125	−0.942171
$579$	7.23518e125	1.43739
$580$	2.08847e125	0.383580
$581$	−2.57955e125	−0.438057
$582$	6.77304e125	1.06362
$583$	−2.90864e125	−0.422446
$584$	5.44480e124	0.0731472
$585$	1.09594e126	1.36206
$586$	6.58089e125	0.756733
$587$	−1.77215e124	−0.0188567	−0.00942836	−	0.999956i	$-0.503001\pi$
$587$	−1.77215e124	−0.0188567	−0.00942836	+	0.999956i	$0.503001\pi$
$588$	−1.29553e126	−1.27579
$589$	−8.07632e125	−0.736152
$590$	−1.32838e126	−1.12087
$591$	1.15464e126	0.902019
$592$	1.97690e126	1.43004
$593$	−1.26063e126	−0.844496	−0.422248	−	0.906480i	$-0.638759\pi$
$593$	−1.26063e126	−0.844496	−0.422248	+	0.906480i	$0.638759\pi$
$594$	−1.83254e126	−1.13703
$595$	1.01176e126	0.581507
$596$	−4.44768e125	−0.236825
$597$	4.65821e126	2.29820
$598$	−8.20973e125	−0.375340
$599$	3.00967e125	0.127526	0.0637629	−	0.997965i	$-0.479690\pi$
$599$	3.00967e125	0.127526	0.0637629	+	0.997965i	$0.479690\pi$
$600$	8.90593e125	0.349782
$601$	−5.45560e125	−0.198634	−0.0993170	−	0.995056i	$-0.531666\pi$
$601$	−5.45560e125	−0.198634	−0.0993170	+	0.995056i	$0.531666\pi$
$602$	1.80289e126	0.608595
$603$	5.09217e126	1.59392
$604$	−7.30136e125	−0.211945
$605$	−5.47900e126	−1.47514
$606$	−1.01576e127	−2.53681
$607$	−5.83500e126	−1.35193	−0.675967	−	0.736932i	$-0.736274\pi$
$607$	−5.83500e126	−1.35193	−0.675967	+	0.736932i	$0.736274\pi$
$608$	−5.68912e126	−1.22302
$609$	−1.06603e126	−0.212658
$610$	2.32196e127	4.29881
$611$	1.74964e126	0.300658
$612$	−8.53783e126	−1.36194
$613$	3.71315e126	0.549909	0.274954	−	0.961457i	$-0.411337\pi$
$613$	3.71315e126	0.549909	0.274954	+	0.961457i	$0.411337\pi$
$614$	−1.13850e127	−1.56557
$615$	−4.91846e126	−0.628074
$616$	1.83280e125	0.0217366
$617$	−9.37755e126	−1.03303	−0.516517	−	0.856277i	$-0.672772\pi$
$617$	−9.37755e126	−1.03303	−0.516517	+	0.856277i	$0.672772\pi$
$618$	4.30102e127	4.40145
$619$	1.15946e127	1.10238	0.551190	−	0.834380i	$-0.314174\pi$
$619$	1.15946e127	1.10238	0.551190	+	0.834380i	$0.314174\pi$
$620$	−1.79816e127	−1.58857
$621$	−1.81452e127	−1.48968
$622$	1.64379e127	1.25425
$623$	1.25731e127	0.891733
$624$	−9.10713e126	−0.600458
$625$	1.49887e127	0.918808
$626$	1.18128e127	0.673321
$627$	−1.09027e127	−0.577912
$628$	4.90506e126	0.241813
$629$	1.97828e127	0.907160
$630$	−7.23907e127	−3.08807
$631$	−3.86513e127	−1.53401	−0.767005	−	0.641641i	$-0.778254\pi$
$631$	−3.86513e127	−1.53401	−0.767005	+	0.641641i	$0.778254\pi$
$632$	−4.78348e126	−0.176651
$633$	4.84311e127	1.66439
$634$	−7.44815e127	−2.38225
$635$	−3.50891e127	−1.04464
$636$	7.63395e127	2.11568
$637$	−9.46425e126	−0.244198
$638$	−4.73448e126	−0.113745
$639$	6.64057e127	1.48565
$640$	−1.64462e127	−0.342670
$641$	−1.01609e127	−0.197193	−0.0985965	−	0.995127i	$-0.531435\pi$
$641$	−1.01609e127	−0.197193	−0.0985965	+	0.995127i	$0.531435\pi$
$642$	2.38985e128	4.32043
$643$	−8.19898e127	−1.38089	−0.690447	−	0.723383i	$-0.742586\pi$
$643$	−8.19898e127	−1.38089	−0.690447	+	0.723383i	$0.742586\pi$
$644$	2.80215e127	0.439728
$645$	−1.54644e128	−2.26135
$646$	−5.29695e127	−0.721849
$647$	−7.36573e127	−0.935558	−0.467779	−	0.883845i	$-0.654946\pi$
$647$	−7.36573e127	−0.935558	−0.467779	+	0.883845i	$0.654946\pi$
$648$	1.29045e127	0.152784
$649$	1.55608e127	0.171751
$650$	1.00459e128	1.03379
$651$	9.17841e127	0.880709
$652$	7.74086e127	0.692665
$653$	1.29252e128	1.07867	0.539333	−	0.842092i	$-0.318676\pi$
$653$	1.29252e128	1.07867	0.539333	+	0.842092i	$0.318676\pi$
$654$	−4.26605e128	−3.32077
$655$	7.12225e127	0.517176
$656$	2.79722e127	0.189497
$657$	2.51919e128	1.59234
$658$	−1.15570e128	−0.681658
$659$	−1.49669e128	−0.823843	−0.411922	−	0.911219i	$-0.635142\pi$
$659$	−1.49669e128	−0.823843	−0.411922	+	0.911219i	$0.635142\pi$
$660$	−2.42745e128	−1.24710
$661$	3.33888e128	1.60116	0.800580	−	0.599226i	$-0.204525\pi$
$661$	3.33888e128	1.60116	0.800580	+	0.599226i	$0.204525\pi$
$662$	2.28119e128	1.02123
$663$	−9.11347e127	−0.380906
$664$	1.94733e127	0.0759960
$665$	−2.32074e128	−0.845750
$666$	−1.41545e129	−4.81744
$667$	−4.68791e127	−0.149023
$668$	2.97460e128	0.883282
$669$	4.49339e128	1.24648
$670$	7.03391e128	1.82303
$671$	−2.71998e128	−0.658704
$672$	6.46546e128	1.46318
$673$	−4.34193e128	−0.918326	−0.459163	−	0.888352i	$-0.651851\pi$
$673$	−4.34193e128	−0.918326	−0.459163	+	0.888352i	$0.651851\pi$
$674$	1.00336e129	1.98350
$675$	2.22035e129	4.10298
$676$	−5.36800e128	−0.927338
$677$	−1.67986e128	−0.271325	−0.135662	−	0.990755i	$-0.543316\pi$
$677$	−1.67986e128	−0.271325	−0.135662	+	0.990755i	$0.543316\pi$
$678$	−1.69954e129	−2.56673
$679$	−1.68883e128	−0.238512
$680$	−7.63785e127	−0.100882
$681$	−2.56980e129	−3.17473
$682$	4.07636e128	0.471068
$683$	4.42641e128	0.478530	0.239265	−	0.970954i	$-0.423093\pi$
$683$	4.42641e128	0.478530	0.239265	+	0.970954i	$0.423093\pi$
$684$	1.95838e129	1.98082
$685$	−1.93124e129	−1.82774
$686$	1.55777e129	1.37961
$687$	−9.66483e128	−0.801055
$688$	8.79493e128	0.682274
$689$	5.57686e128	0.404963
$690$	−4.65147e129	−3.16196
$691$	−3.13666e128	−0.199626	−0.0998128	−	0.995006i	$-0.531824\pi$
$691$	−3.13666e128	−0.199626	−0.0998128	+	0.995006i	$0.531824\pi$
$692$	3.02992e128	0.180553
$693$	8.47993e128	0.473184
$694$	3.56695e129	1.86398
$695$	−9.48465e128	−0.464208
$696$	8.04752e127	0.0368928
$697$	2.79917e128	0.120209
$698$	8.10433e128	0.326058
$699$	6.83032e129	2.57472
$700$	−3.42887e129	−1.21113
$701$	−3.83702e129	−1.27006	−0.635030	−	0.772488i	$-0.719012\pi$
$701$	−3.83702e129	−1.27006	−0.635030	+	0.772488i	$0.719012\pi$
$702$	3.51361e129	1.08997
$703$	−4.53773e129	−1.31938
$704$	1.58034e129	0.430719
$705$	9.91312e129	2.53283
$706$	−7.50516e129	−1.79782
$707$	2.53276e129	0.568868
$708$	−4.08406e129	−0.860159
$709$	−3.04795e129	−0.602011	−0.301005	−	0.953622i	$-0.597322\pi$
$709$	−3.04795e129	−0.602011	−0.301005	+	0.953622i	$0.597322\pi$
$710$	9.17275e129	1.69920
$711$	−2.21321e130	−3.84553
$712$	−9.49150e128	−0.154702
$713$	4.03626e129	0.617171
$714$	6.01977e129	0.863597
$715$	−1.77333e129	−0.238707
$716$	−1.00772e129	−0.127291
$717$	2.46537e130	2.92254
$718$	9.56656e129	1.06437
$719$	−2.04901e129	−0.213983	−0.106991	−	0.994260i	$-0.534122\pi$
$719$	−2.04901e129	−0.213983	−0.106991	+	0.994260i	$0.534122\pi$
$720$	−3.53140e130	−3.46193
$721$	−1.07244e130	−0.987004
$722$	−4.49750e129	−0.388623
$723$	1.36254e130	1.10549
$724$	2.33548e128	0.0177939
$725$	5.73641e129	0.410450
$726$	−3.25990e130	−2.19073
$727$	2.35602e130	1.48718	0.743588	−	0.668638i	$-0.233122\pi$
$727$	2.35602e130	1.48718	0.743588	+	0.668638i	$0.233122\pi$
$728$	−3.51409e128	−0.0208370
$729$	−6.75497e129	−0.376288
$730$	3.47980e130	1.82123
$731$	8.80106e129	0.432807
$732$	7.13879e130	3.29891
$733$	−1.57134e130	−0.682399	−0.341199	−	0.939991i	$-0.610833\pi$
$733$	−1.57134e130	−0.682399	−0.341199	+	0.939991i	$0.610833\pi$
$734$	5.65086e129	0.230645
$735$	−5.36226e130	−2.05719
$736$	2.84322e130	1.02535
$737$	−8.23960e129	−0.279342
$738$	−2.00279e130	−0.638368
$739$	2.27033e130	0.680405	0.340202	−	0.940352i	$-0.389504\pi$
$739$	2.27033e130	0.680405	0.340202	+	0.940352i	$0.389504\pi$
$740$	−1.01031e131	−2.84715
$741$	2.09042e130	0.553994
$742$	−3.68371e130	−0.918138
$743$	−2.68414e130	−0.629236	−0.314618	−	0.949218i	$-0.601876\pi$
$743$	−2.68414e130	−0.629236	−0.314618	+	0.949218i	$0.601876\pi$
$744$	−6.92886e129	−0.152789
$745$	−1.84092e130	−0.381878
$746$	−9.49475e130	−1.85296
$747$	9.00984e130	1.65436
$748$	1.38150e130	0.238687
$749$	−5.95898e130	−0.968834
$750$	2.80651e131	4.29417
$751$	5.64442e130	0.812835	0.406417	−	0.913687i	$-0.366778\pi$
$751$	5.64442e130	0.812835	0.406417	+	0.913687i	$0.366778\pi$
$752$	−5.63778e130	−0.764182
$753$	−2.87675e130	−0.367055
$754$	9.07762e129	0.109037
$755$	−3.02207e130	−0.341758
$756$	−1.19927e131	−1.27695
$757$	2.91891e130	0.292657	0.146328	−	0.989236i	$-0.453254\pi$
$757$	2.91891e130	0.292657	0.146328	+	0.989236i	$0.453254\pi$
$758$	2.48168e131	2.34313
$759$	5.44879e130	0.484506
$760$	1.75195e130	0.146724
$761$	−1.12162e131	−0.884798	−0.442399	−	0.896818i	$-0.645872\pi$
$761$	−1.12162e131	−0.884798	−0.442399	+	0.896818i	$0.645872\pi$
$762$	−2.08774e131	−1.55140
$763$	1.06372e131	0.744666
$764$	−8.17755e130	−0.539356
$765$	−3.53386e131	−2.19611
$766$	8.15438e130	0.477509
$767$	−2.98354e130	−0.164643
$768$	2.90059e131	1.50852
$769$	1.18446e131	0.580595	0.290297	−	0.956937i	$-0.406246\pi$
$769$	1.18446e131	0.580595	0.290297	+	0.956937i	$0.406246\pi$
$770$	1.17135e131	0.541200
$771$	−1.61131e130	−0.0701788
$772$	2.10288e131	0.863432
$773$	−4.68569e130	−0.181387	−0.0906936	−	0.995879i	$-0.528908\pi$
$773$	−4.68569e130	−0.181387	−0.0906936	+	0.995879i	$0.528908\pi$
$774$	−6.29711e131	−2.29841
$775$	−4.93901e131	−1.69986
$776$	1.27491e130	0.0413782
$777$	5.15694e131	1.57847
$778$	−4.21714e131	−1.21744
$779$	−6.42066e130	−0.174834
$780$	4.65425e131	1.19549
$781$	−1.07451e131	−0.260367
$782$	2.64723e131	0.605179
$783$	2.00634e131	0.432757
$784$	3.04962e131	0.620677
$785$	2.03023e131	0.389921
$786$	4.23760e131	0.768059
$787$	3.88301e131	0.664229	0.332115	−	0.943239i	$-0.392238\pi$
$787$	3.88301e131	0.664229	0.332115	+	0.943239i	$0.392238\pi$
$788$	3.35593e131	0.541838
$789$	−3.72431e131	−0.567599
$790$	−3.05715e132	−4.39829
$791$	4.23773e131	0.575577
$792$	−6.40157e130	−0.0820901
$793$	5.21512e131	0.631443
$794$	−3.62041e131	−0.413928
$795$	3.15974e132	3.41151
$796$	1.35390e132	1.38051
$797$	1.41668e132	1.36433	0.682165	−	0.731198i	$-0.261039\pi$
$797$	1.41668e132	1.36433	0.682165	+	0.731198i	$0.261039\pi$
$798$	−1.38080e132	−1.25603
$799$	−5.64171e131	−0.484766
$800$	−3.47914e132	−2.82408
$801$	−4.39150e132	−3.36770
$802$	9.43708e131	0.683761
$803$	−4.07628e131	−0.279066
$804$	2.16255e132	1.39899
$805$	1.15982e132	0.709055
$806$	−7.81577e131	−0.451572
$807$	−6.19403e132	−3.38242
$808$	−1.91200e131	−0.0986897
$809$	3.28891e132	1.60470	0.802350	−	0.596853i	$-0.203583\pi$
$809$	3.28891e132	1.60470	0.802350	+	0.596853i	$0.203583\pi$
$810$	8.24734e132	3.80404
$811$	−2.95398e131	−0.128813	−0.0644064	−	0.997924i	$-0.520515\pi$
$811$	−2.95398e131	−0.128813	−0.0644064	+	0.997924i	$0.520515\pi$
$812$	−3.09838e131	−0.127742
$813$	−1.83213e132	−0.714228
$814$	2.29033e132	0.844281
$815$	3.20399e132	1.11691
$816$	2.93659e132	0.968148
$817$	−2.01876e132	−0.629479
$818$	3.09317e132	0.912282
$819$	−1.62589e132	−0.453601
$820$	−1.42954e132	−0.377281
$821$	2.22430e132	0.555366	0.277683	−	0.960673i	$-0.410434\pi$
$821$	2.22430e132	0.555366	0.277683	+	0.960673i	$0.410434\pi$
$822$	−1.14905e133	−2.71438
$823$	−8.23681e130	−0.0184105	−0.00920527	−	0.999958i	$-0.502930\pi$
$823$	−8.23681e130	−0.0184105	−0.00920527	+	0.999958i	$0.502930\pi$
$824$	8.09595e131	0.171230
$825$	−6.66746e132	−1.33446
$826$	1.97073e132	0.373281
$827$	−8.02439e132	−1.43851	−0.719253	−	0.694749i	$-0.755516\pi$
$827$	−8.02439e132	−1.43851	−0.719253	+	0.694749i	$0.755516\pi$
$828$	−9.78731e132	−1.66067
$829$	1.99037e132	0.319670	0.159835	−	0.987144i	$-0.448904\pi$
$829$	1.99037e132	0.319670	0.159835	+	0.987144i	$0.448904\pi$
$830$	1.24455e133	1.89216
$831$	1.95890e133	2.81946
$832$	−3.03005e132	−0.412894
$833$	3.05175e132	0.393732
$834$	−5.64319e132	−0.689396
$835$	1.23120e133	1.42428
$836$	−3.16884e132	−0.347148
$837$	−1.72744e133	−1.79224
$838$	−1.94903e133	−1.91521
$839$	1.07671e133	1.00214	0.501070	−	0.865407i	$-0.332940\pi$
$839$	1.07671e133	1.00214	0.501070	+	0.865407i	$0.332940\pi$
$840$	−1.99102e132	−0.175537
$841$	−1.14551e133	−0.956708
$842$	2.77278e133	2.19389
$843$	−7.16567e132	−0.537158
$844$	1.40764e133	0.999792
$845$	−2.22185e133	−1.49532
$846$	4.03661e133	2.57434
$847$	8.12843e132	0.491260
$848$	−1.79701e133	−1.02929
$849$	−2.39666e131	−0.0130109
$850$	−3.23931e133	−1.66683
$851$	2.26780e133	1.10614
$852$	2.82012e133	1.30397
$853$	−1.19545e133	−0.524023	−0.262012	−	0.965065i	$-0.584386\pi$
$853$	−1.19545e133	−0.524023	−0.262012	+	0.965065i	$0.584386\pi$
$854$	−3.44477e133	−1.43162
$855$	8.10587e133	3.19405
$856$	4.49849e132	0.168078
$857$	−4.06069e133	−1.43871	−0.719353	−	0.694644i	$-0.755562\pi$
$857$	−4.06069e133	−1.43871	−0.719353	+	0.694644i	$0.755562\pi$
$858$	−1.05510e133	−0.354504
$859$	−5.99534e133	−1.91040	−0.955201	−	0.295958i	$-0.904361\pi$
$859$	−5.99534e133	−1.91040	−0.955201	+	0.295958i	$0.904361\pi$
$860$	−4.49470e133	−1.35838
$861$	7.29682e132	0.209166
$862$	2.34090e133	0.636506
$863$	6.13452e133	1.58230	0.791151	−	0.611620i	$-0.209482\pi$
$863$	6.13452e133	1.58230	0.791151	+	0.611620i	$0.209482\pi$
$864$	−1.21685e134	−2.97756
$865$	1.25410e133	0.291139
$866$	5.12927e133	1.12977
$867$	−5.57850e133	−1.16587
$868$	2.66768e133	0.529037
$869$	3.58118e133	0.673947
$870$	5.14321e133	0.918561
$871$	1.57981e133	0.267781
$872$	−8.03012e132	−0.129188
$873$	5.89872e133	0.900761
$874$	−6.07213e133	−0.880179
$875$	−6.99791e133	−0.962945
$876$	1.06985e134	1.39761
$877$	2.54524e133	0.315680	0.157840	−	0.987465i	$-0.449547\pi$
$877$	2.54524e133	0.315680	0.157840	+	0.987465i	$0.449547\pi$
$878$	1.19054e134	1.40199
$879$	8.37443e133	0.936400
$880$	5.71413e133	0.606720
$881$	−1.85836e134	−1.87381	−0.936904	−	0.349587i	$-0.886322\pi$
$881$	−1.85836e134	−1.87381	−0.936904	+	0.349587i	$0.886322\pi$
$882$	−2.18351e134	−2.09090
$883$	1.42578e134	1.29670	0.648351	−	0.761342i	$-0.275459\pi$
$883$	1.42578e134	1.29670	0.648351	+	0.761342i	$0.275459\pi$
$884$	−2.64881e133	−0.228808
$885$	−1.69042e134	−1.38699
$886$	3.28817e134	2.56283
$887$	−8.90015e133	−0.658981	−0.329490	−	0.944159i	$-0.606877\pi$
$887$	−8.90015e133	−0.658981	−0.329490	+	0.944159i	$0.606877\pi$
$888$	−3.89302e133	−0.273840
$889$	5.20568e133	0.347894
$890$	−6.06606e134	−3.85178
$891$	−9.66103e133	−0.582892
$892$	1.30599e134	0.748755
$893$	1.29408e134	0.705050
$894$	−1.09531e134	−0.567127
$895$	−4.17101e133	−0.205255
$896$	2.43989e133	0.114118
$897$	−1.04472e134	−0.464455
$898$	2.08637e134	0.881693
$899$	−4.46295e133	−0.179290
$900$	1.19763e135	4.57393
$901$	−1.79826e134	−0.652941
$902$	3.24070e133	0.111877
$903$	2.29424e134	0.753090
$904$	−3.19910e133	−0.0998536
$905$	9.66670e132	0.0286925
$906$	−1.79808e134	−0.507546
$907$	−1.05880e134	−0.284237	−0.142119	−	0.989850i	$-0.545391\pi$
$907$	−1.05880e134	−0.284237	−0.142119	+	0.989850i	$0.545391\pi$
$908$	−7.46907e134	−1.90704
$909$	−8.84641e134	−2.14838
$910$	−2.24587e134	−0.518802
$911$	3.55862e134	0.781979	0.390989	−	0.920395i	$-0.372133\pi$
$911$	3.55862e134	0.781979	0.390989	+	0.920395i	$0.372133\pi$
$912$	−6.73587e134	−1.40808
$913$	−1.45787e134	−0.289934
$914$	1.51029e135	2.85765
$915$	2.95479e135	5.31945
$916$	−2.80906e134	−0.481190
$917$	−1.05663e134	−0.172233
$918$	−1.13296e135	−1.75741
$919$	−8.75774e134	−1.29281	−0.646407	−	0.762993i	$-0.723729\pi$
$919$	−8.75774e134	−1.29281	−0.646407	+	0.762993i	$0.723729\pi$
$920$	−8.75561e133	−0.123010
$921$	−1.44878e135	−1.93727
$922$	9.89721e134	1.25967
$923$	2.06019e134	0.249592
$924$	3.60126e134	0.415318
$925$	−2.77501e135	−3.04660
$926$	−1.44298e135	−1.50820
$927$	3.74581e135	3.72750
$928$	−3.14379e134	−0.297866
$929$	8.15544e134	0.735754	0.367877	−	0.929874i	$-0.380085\pi$
$929$	8.15544e134	0.735754	0.367877	+	0.929874i	$0.380085\pi$
$930$	−4.42826e135	−3.80417
$931$	−7.00001e134	−0.572649
$932$	1.98522e135	1.54662
$933$	2.09178e135	1.55204
$934$	1.10240e135	0.779033
$935$	5.71811e134	0.384879
$936$	1.22740e134	0.0786928
$937$	5.77244e134	0.352540	0.176270	−	0.984342i	$-0.443597\pi$
$937$	5.77244e134	0.352540	0.176270	+	0.984342i	$0.443597\pi$
$938$	−1.04352e135	−0.607117
$939$	1.50323e135	0.833183
$940$	2.88122e135	1.52146
$941$	4.63487e133	0.0233190	0.0116595	−	0.999932i	$-0.496289\pi$
$941$	4.63487e133	0.0233190	0.0116595	+	0.999932i	$0.496289\pi$
$942$	1.20795e135	0.579072
$943$	3.20882e134	0.146576
$944$	9.61373e134	0.418472
$945$	−4.96383e135	−2.05906
$946$	1.01893e135	0.402807
$947$	−1.53770e135	−0.579358	−0.289679	−	0.957124i	$-0.593548\pi$
$947$	−1.53770e135	−0.579358	−0.289679	+	0.957124i	$0.593548\pi$
$948$	−9.39908e135	−3.37525
$949$	7.81561e134	0.267516
$950$	7.43023e135	2.42425
$951$	−9.47805e135	−2.94785
$952$	1.13312e134	0.0335965
$953$	−3.28765e135	−0.929305	−0.464653	−	0.885493i	$-0.653821\pi$
$953$	−3.28765e135	−0.929305	−0.464653	+	0.885493i	$0.653821\pi$
$954$	1.28664e136	3.46742
$955$	−3.38474e135	−0.869704
$956$	7.16553e135	1.75555
$957$	−6.02481e134	−0.140751
$958$	−7.27570e135	−1.62085
$959$	2.86510e135	0.608686
$960$	−1.71677e136	−3.47833
$961$	−1.33247e135	−0.257481
$962$	−4.39134e135	−0.809340
$963$	2.08135e136	3.65888
$964$	3.96018e135	0.664064
$965$	8.70396e135	1.39227
$966$	6.90074e135	1.05302
$967$	−1.80848e135	−0.263275	−0.131637	−	0.991298i	$-0.542023\pi$
$967$	−1.80848e135	−0.263275	−0.131637	+	0.991298i	$0.542023\pi$
$968$	−6.13622e134	−0.0852260
$969$	−6.74057e135	−0.893232
$970$	8.14801e135	1.03024
$971$	−1.04343e136	−1.25889	−0.629443	−	0.777046i	$-0.716717\pi$
$971$	−1.04343e136	−1.25889	−0.629443	+	0.777046i	$0.716717\pi$
$972$	6.03933e135	0.695303
$973$	1.40710e135	0.154594
$974$	−1.61009e136	−1.68817
$975$	1.27838e136	1.27923
$976$	−1.68045e136	−1.60494
$977$	−1.14734e135	−0.104590	−0.0522949	−	0.998632i	$-0.516654\pi$
$977$	−1.14734e135	−0.104590	−0.0522949	+	0.998632i	$0.516654\pi$
$978$	1.90631e136	1.65873
$979$	7.10586e135	0.590207
$980$	−1.55853e136	−1.23574
$981$	−3.71536e136	−2.81229
$982$	1.65433e136	1.19550
$983$	9.08811e135	0.627030	0.313515	−	0.949583i	$-0.398493\pi$
$983$	9.08811e135	0.627030	0.313515	+	0.949583i	$0.398493\pi$
$984$	−5.50843e134	−0.0362870
$985$	1.38904e136	0.873707
$986$	−2.92708e135	−0.175806
$987$	−1.47067e136	−0.843499
$988$	6.07575e135	0.332782
$989$	1.00891e136	0.527739
$990$	−4.09127e136	−2.04389
$991$	−1.06752e136	−0.509361	−0.254681	−	0.967025i	$-0.581970\pi$
$991$	−1.06752e136	−0.509361	−0.254681	+	0.967025i	$0.581970\pi$
$992$	2.70678e136	1.23359
$993$	2.90290e136	1.26369
$994$	−1.36083e136	−0.565879
$995$	5.60386e136	2.22606
$996$	3.82631e136	1.45204
$997$	−4.19352e136	−1.52037	−0.760184	−	0.649708i	$-0.774891\pi$
$997$	−4.19352e136	−1.52037	−0.760184	+	0.649708i	$0.774891\pi$
$998$	−5.95893e136	−2.06409
$999$	−9.70574e136	−3.21217

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.92.a.a.1.6	✓	7
3.2	odd	2		9.92.a.b.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.92.a.a.1.6	✓	7	1.1	even	1	trivial
9.92.a.b.1.2		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)

\(f(q)\)	\(=\)	\(q+7.15766e13 q^{2} +9.10839e21 q^{3} +2.64733e27 q^{4} +1.09575e32 q^{5} +6.51948e35 q^{6} -1.62560e38 q^{7} +1.22718e40 q^{8} +5.67789e43 q^{9} +O(q^{10})\)	\(q+7.15766e13 q^{2} +9.10839e21 q^{3} +2.64733e27 q^{4} +1.09575e32 q^{5} +6.51948e35 q^{6} -1.62560e38 q^{7} +1.22718e40 q^{8} +5.67789e43 q^{9} +7.84298e45 q^{10} -9.18735e46 q^{11} +2.41129e49 q^{12} +1.76153e50 q^{13} -1.16355e52 q^{14} +9.98048e53 q^{15} -5.67610e54 q^{16} -5.68005e55 q^{17} +4.06404e57 q^{18} +1.30287e58 q^{19} +2.90080e59 q^{20} -1.48066e60 q^{21} -6.57599e60 q^{22} -6.51130e61 q^{23} +1.11777e62 q^{24} +7.96762e63 q^{25} +1.26084e64 q^{26} +2.78672e65 q^{27} -4.30351e65 q^{28} +7.19965e65 q^{29} +7.14369e67 q^{30} -6.19885e67 q^{31} -4.36659e68 q^{32} -8.36820e68 q^{33} -4.06559e69 q^{34} -1.78125e70 q^{35} +1.50313e71 q^{36} -3.48286e71 q^{37} +9.32553e71 q^{38} +1.60447e72 q^{39} +1.34468e72 q^{40} -4.92808e72 q^{41} -1.05981e74 q^{42} -1.54947e74 q^{43} -2.43220e74 q^{44} +6.22153e75 q^{45} -4.66057e75 q^{46} +9.93250e75 q^{47} -5.17001e76 q^{48} -5.37275e76 q^{49} +5.70295e77 q^{50} -5.17361e77 q^{51} +4.66335e77 q^{52} +3.16592e78 q^{53} +1.99464e79 q^{54} -1.00670e79 q^{55} -1.99491e78 q^{56} +1.18671e80 q^{57} +5.15326e79 q^{58} -1.69372e80 q^{59} +2.64216e81 q^{60} +2.96057e81 q^{61} -4.43692e81 q^{62} -9.23000e81 q^{63} -1.72013e82 q^{64} +1.93019e82 q^{65} -5.98967e82 q^{66} +8.96842e82 q^{67} -1.50370e83 q^{68} -5.93075e83 q^{69} -1.27496e84 q^{70} +1.16955e84 q^{71} +6.96781e83 q^{72} +4.43684e84 q^{73} -2.49291e85 q^{74} +7.25722e85 q^{75} +3.44914e85 q^{76} +1.49350e85 q^{77} +1.14842e86 q^{78} -3.89794e86 q^{79} -6.21956e86 q^{80} +1.05156e87 q^{81} -3.52735e86 q^{82} +1.58683e87 q^{83} -3.91981e87 q^{84} -6.22389e87 q^{85} -1.10906e88 q^{86} +6.55772e87 q^{87} -1.12746e87 q^{88} -7.73439e88 q^{89} +4.45316e89 q^{90} -2.86355e88 q^{91} -1.72376e89 q^{92} -5.64615e89 q^{93} +7.10935e89 q^{94} +1.42762e90 q^{95} -3.97726e90 q^{96} +1.03889e90 q^{97} -3.84563e90 q^{98} -5.21648e90 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 3841716838056 q^{2} + 62\!\cdots\!32 q^{3}+ \cdots + 38\!\cdots\!59 q^{9}+O(q^{10}) \) 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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