LMFDB - Embedded newform 1.92.a.a.1.5

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			1.5
Root			$8.78141e11$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.16242e13 q^{2} -4.57928e21 q^{3} -2.00827e27 q^{4} +4.97855e31 q^{5} -9.90233e34 q^{6} -2.82571e38 q^{7} -9.69662e40 q^{8} -5.21406e42 q^{9} +O(q^{10})$	\(q+2.16242e13 q^{2} -4.57928e21 q^{3} -2.00827e27 q^{4} +4.97855e31 q^{5} -9.90233e34 q^{6} -2.82571e38 q^{7} -9.69662e40 q^{8} -5.21406e42 q^{9} +1.07657e45 q^{10} +1.15837e47 q^{11} +9.19646e48 q^{12} -6.90540e50 q^{13} -6.11037e51 q^{14} -2.27982e53 q^{15} +2.87543e54 q^{16} -5.85583e55 q^{17} -1.12750e56 q^{18} -2.50887e58 q^{19} -9.99829e58 q^{20} +1.29397e60 q^{21} +2.50489e60 q^{22} -1.24232e60 q^{23} +4.44036e62 q^{24} -1.56037e63 q^{25} -1.49324e64 q^{26} +1.43780e65 q^{27} +5.67481e65 q^{28} +1.70277e66 q^{29} -4.92992e66 q^{30} -3.90731e67 q^{31} +3.02256e68 q^{32} -5.30452e68 q^{33} -1.26628e69 q^{34} -1.40679e70 q^{35} +1.04713e70 q^{36} +2.18997e71 q^{37} -5.42524e71 q^{38} +3.16218e72 q^{39} -4.82751e72 q^{40} -2.33256e73 q^{41} +2.79811e73 q^{42} +1.45101e74 q^{43} -2.32633e74 q^{44} -2.59584e74 q^{45} -2.68642e73 q^{46} +1.72253e76 q^{47} -1.31674e76 q^{48} -3.06840e74 q^{49} -3.37418e76 q^{50} +2.68155e77 q^{51} +1.38679e78 q^{52} +3.47871e78 q^{53} +3.10913e78 q^{54} +5.76702e78 q^{55} +2.73999e79 q^{56} +1.14888e80 q^{57} +3.68210e79 q^{58} +5.44131e80 q^{59} +4.57850e80 q^{60} +9.48268e80 q^{61} -8.44924e80 q^{62} +1.47334e81 q^{63} -5.83187e80 q^{64} -3.43789e82 q^{65} -1.14706e82 q^{66} -2.20404e83 q^{67} +1.17601e83 q^{68} +5.68895e81 q^{69} -3.04208e83 q^{70} -3.41043e84 q^{71} +5.05588e83 q^{72} +1.00119e85 q^{73} +4.73563e84 q^{74} +7.14539e84 q^{75} +5.03851e85 q^{76} -3.27323e85 q^{77} +6.83795e85 q^{78} -7.90343e84 q^{79} +1.43155e86 q^{80} -5.21885e86 q^{81} -5.04397e86 q^{82} -8.82611e86 q^{83} -2.59865e87 q^{84} -2.91535e87 q^{85} +3.13768e87 q^{86} -7.79746e87 q^{87} -1.12323e88 q^{88} +6.33488e88 q^{89} -5.61330e87 q^{90} +1.95127e89 q^{91} +2.49492e87 q^{92} +1.78927e89 q^{93} +3.72484e89 q^{94} -1.24905e90 q^{95} -1.38411e90 q^{96} -2.81205e88 q^{97} -6.63517e87 q^{98} -6.03983e89 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.16242e13	0.434585	0.217293	−	0.976106i	$-0.430277\pi$
$2$	2.16242e13	0.434585	0.217293	+	0.976106i	$0.430277\pi$
$3$	−4.57928e21	−0.894912	−0.447456	−	0.894306i	$-0.647670\pi$
$3$	−4.57928e21	−0.894912	−0.447456	+	0.894306i	$0.647670\pi$
$4$	−2.00827e27	−0.811136
$5$	4.97855e31	0.783371	0.391686	−	0.920099i	$-0.371892\pi$
$5$	4.97855e31	0.783371	0.391686	+	0.920099i	$0.371892\pi$
$6$	−9.90233e34	−0.388916
$7$	−2.82571e38	−0.998084	−0.499042	−	0.866578i	$-0.666315\pi$
$7$	−2.82571e38	−0.998084	−0.499042	+	0.866578i	$0.666315\pi$
$8$	−9.69662e40	−0.787093
$9$	−5.21406e42	−0.199132
$10$	1.07657e45	0.340442
$11$	1.15837e47	0.479161	0.239580	−	0.970877i	$-0.422990\pi$
$11$	1.15837e47	0.479161	0.239580	+	0.970877i	$0.422990\pi$
$12$	9.19646e48	0.725895
$13$	−6.90540e50	−1.42812	−0.714062	−	0.700082i	$-0.753147\pi$
$13$	−6.90540e50	−1.42812	−0.714062	+	0.700082i	$0.753147\pi$
$14$	−6.11037e51	−0.433753
$15$	−2.27982e53	−0.701048
$16$	2.87543e54	0.469076
$17$	−5.85583e55	−0.605567	−0.302784	−	0.953059i	$-0.597916\pi$
$17$	−5.85583e55	−0.605567	−0.302784	+	0.953059i	$0.597916\pi$
$18$	−1.12750e56	−0.0865400
$19$	−2.50887e58	−1.64509	−0.822545	−	0.568699i	$-0.807447\pi$
$19$	−2.50887e58	−1.64509	−0.822545	+	0.568699i	$0.807447\pi$
$20$	−9.99829e58	−0.635420
$21$	1.29397e60	0.893198
$22$	2.50489e60	0.208236
$23$	−1.24232e60	−0.0136653	−0.00683263	−	0.999977i	$-0.502175\pi$
$23$	−1.24232e60	−0.0136653	−0.00683263	+	0.999977i	$0.502175\pi$
$24$	4.44036e62	0.704379
$25$	−1.56037e63	−0.386330
$26$	−1.49324e64	−0.620642
$27$	1.43780e65	1.07312
$28$	5.67481e65	0.809581
$29$	1.70277e66	0.492093	0.246046	−	0.969258i	$-0.420868\pi$
$29$	1.70277e66	0.492093	0.246046	+	0.969258i	$0.420868\pi$
$30$	−4.92992e66	−0.304665
$31$	−3.90731e67	−0.543151	−0.271576	−	0.962417i	$-0.587545\pi$
$31$	−3.90731e67	−0.543151	−0.271576	+	0.962417i	$0.587545\pi$
$32$	3.02256e68	0.990947
$33$	−5.30452e68	−0.428807
$34$	−1.26628e69	−0.263171
$35$	−1.40679e70	−0.781870
$36$	1.04713e70	0.161523
$37$	2.18997e71	0.971091	0.485545	−	0.874212i	$-0.338621\pi$
$37$	2.18997e71	0.971091	0.485545	+	0.874212i	$0.338621\pi$
$38$	−5.42524e71	−0.714932
$39$	3.16218e72	1.27805
$40$	−4.82751e72	−0.616586
$41$	−2.33256e73	−0.968650	−0.484325	−	0.874888i	$-0.660935\pi$
$41$	−2.33256e73	−0.968650	−0.484325	+	0.874888i	$0.660935\pi$
$42$	2.79811e73	0.388171
$43$	1.45101e74	0.690008	0.345004	−	0.938601i	$-0.387878\pi$
$43$	1.45101e74	0.690008	0.345004	+	0.938601i	$0.387878\pi$
$44$	−2.32633e74	−0.388665
$45$	−2.59584e74	−0.155994
$46$	−2.68642e73	−0.00593872
$47$	1.72253e76	1.43125	0.715625	−	0.698485i	$-0.246142\pi$
$47$	1.72253e76	1.43125	0.715625	+	0.698485i	$0.246142\pi$
$48$	−1.31674e76	−0.419782
$49$	−3.06840e74	−0.00382816
$50$	−3.37418e76	−0.167893
$51$	2.68155e77	0.541929
$52$	1.38679e78	1.15840
$53$	3.47871e78	1.22142	0.610711	−	0.791853i	$-0.290884\pi$
$53$	3.47871e78	1.22142	0.610711	+	0.791853i	$0.290884\pi$
$54$	3.10913e78	0.466361
$55$	5.76702e78	0.375361
$56$	2.73999e79	0.785585
$57$	1.14888e80	1.47221
$58$	3.68210e79	0.213856
$59$	5.44131e80	1.45190	0.725950	−	0.687747i	$-0.241400\pi$
$59$	5.44131e80	1.45190	0.725950	+	0.687747i	$0.241400\pi$
$60$	4.57850e80	0.568645
$61$	9.48268e80	0.555167	0.277583	−	0.960702i	$-0.410467\pi$
$61$	9.48268e80	0.555167	0.277583	+	0.960702i	$0.410467\pi$
$62$	−8.44924e80	−0.236046
$63$	1.47334e81	0.198751
$64$	−5.83187e80	−0.0384254
$65$	−3.43789e82	−1.11875
$66$	−1.14706e82	−0.186353
$67$	−2.20404e83	−1.80640	−0.903202	−	0.429215i	$-0.858790\pi$
$67$	−2.20404e83	−1.80640	−0.903202	+	0.429215i	$0.858790\pi$
$68$	1.17601e83	0.491197
$69$	5.68895e81	0.0122292
$70$	−3.04208e83	−0.339789
$71$	−3.41043e84	−1.99781	−0.998904	−	0.0468065i	$-0.985096\pi$
$71$	−3.41043e84	−1.99781	−0.998904	+	0.0468065i	$0.985096\pi$
$72$	5.05588e83	0.156736
$73$	1.00119e85	1.65702	0.828511	−	0.559972i	$-0.189188\pi$
$73$	1.00119e85	1.65702	0.828511	+	0.559972i	$0.189188\pi$
$74$	4.73563e84	0.422022
$75$	7.14539e84	0.345731
$76$	5.03851e85	1.33439
$77$	−3.27323e85	−0.478243
$78$	6.83795e85	0.555420
$79$	−7.90343e84	−0.0359569	−0.0179785	−	0.999838i	$-0.505723\pi$
$79$	−7.90343e84	−0.0359569	−0.0179785	+	0.999838i	$0.505723\pi$
$80$	1.43155e86	0.367461
$81$	−5.21885e86	−0.761214
$82$	−5.04397e86	−0.420961
$83$	−8.82611e86	−0.424342	−0.212171	−	0.977233i	$-0.568053\pi$
$83$	−8.82611e86	−0.424342	−0.212171	+	0.977233i	$0.568053\pi$
$84$	−2.59865e87	−0.724504
$85$	−2.91535e87	−0.474384
$86$	3.13768e87	0.299868
$87$	−7.79746e87	−0.440380
$88$	−1.12323e88	−0.377144
$89$	6.33488e88	1.27202	0.636008	−	0.771682i	$-0.280584\pi$
$89$	6.33488e88	1.27202	0.636008	+	0.771682i	$0.280584\pi$
$90$	−5.61330e87	−0.0677929
$91$	1.95127e89	1.42539
$92$	2.49492e87	0.0110844
$93$	1.78927e89	0.486073
$94$	3.72484e89	0.622000
$95$	−1.24905e90	−1.28872
$96$	−1.38411e90	−0.886810
$97$	−2.81205e88	−0.0112437	−0.00562185	−	0.999984i	$-0.501789\pi$
$97$	−2.81205e88	−0.0112437	−0.00562185	+	0.999984i	$0.501789\pi$
$98$	−6.63517e87	−0.00166366
$99$	−6.03983e89	−0.0954164
$100$	3.13366e90	0.313366
$101$	−2.97951e91	−1.89462	−0.947309	−	0.320321i	$-0.896209\pi$
$101$	−2.97951e91	−1.89462	−0.947309	+	0.320321i	$0.896209\pi$
$102$	5.79863e90	0.235515
$103$	9.41131e90	0.245220	0.122610	−	0.992455i	$-0.460874\pi$
$103$	9.41131e90	0.245220	0.122610	+	0.992455i	$0.460874\pi$
$104$	6.69590e91	1.12407
$105$	6.44211e91	0.699705
$106$	7.52242e91	0.530812
$107$	4.65373e91	0.214210	0.107105	−	0.994248i	$-0.465842\pi$
$107$	4.65373e91	0.214210	0.107105	+	0.994248i	$0.465842\pi$
$108$	−2.88750e92	−0.870444
$109$	4.60957e92	0.913597	0.456798	−	0.889570i	$-0.348996\pi$
$109$	4.60957e92	0.913597	0.456798	+	0.889570i	$0.348996\pi$
$110$	1.24707e92	0.163126
$111$	−1.00285e93	−0.869041
$112$	−8.12514e92	−0.468178
$113$	−4.05480e93	−1.55920	−0.779598	−	0.626280i	$-0.784577\pi$
$113$	−4.05480e93	−1.55920	−0.779598	+	0.626280i	$0.784577\pi$
$114$	2.48437e93	0.639802
$115$	−6.18496e91	−0.0107050
$116$	−3.41963e93	−0.399154
$117$	3.60051e93	0.284386
$118$	1.17664e94	0.630975
$119$	1.65469e94	0.604407
$120$	2.21065e94	0.551790
$121$	−4.50250e94	−0.770405
$122$	2.05055e94	0.241267
$123$	1.06814e95	0.866857
$124$	7.84695e94	0.440569
$125$	−2.78766e95	−1.08601
$126$	3.18599e94	0.0863742
$127$	−1.75044e95	−0.331190	−0.165595	−	0.986194i	$-0.552954\pi$
$127$	−1.75044e95	−0.331190	−0.165595	+	0.986194i	$0.552954\pi$
$128$	−7.60960e95	−1.00765
$129$	−6.64456e95	−0.617497
$130$	−7.43415e95	−0.486193
$131$	1.20554e96	0.556336	0.278168	−	0.960532i	$-0.410273\pi$
$131$	1.20554e96	0.556336	0.278168	+	0.960532i	$0.410273\pi$
$132$	1.06529e96	0.347821
$133$	7.08935e96	1.64194
$134$	−4.76605e96	−0.785037
$135$	7.15816e96	0.840650
$136$	5.67817e96	0.476638
$137$	−1.54818e97	−0.931184	−0.465592	−	0.884999i	$-0.654159\pi$
$137$	−1.54818e97	−0.931184	−0.465592	+	0.884999i	$0.654159\pi$
$138$	1.23019e95	0.00531463
$139$	2.10145e97	0.653649	0.326825	−	0.945085i	$-0.394021\pi$
$139$	2.10145e97	0.653649	0.326825	+	0.945085i	$0.394021\pi$
$140$	2.82523e97	0.634203
$141$	−7.88797e97	−1.28084
$142$	−7.37477e97	−0.868218
$143$	−7.99903e97	−0.684302
$144$	−1.49927e97	−0.0934083
$145$	8.47732e97	0.385491
$146$	2.16500e98	0.720118
$147$	1.40511e96	0.00342587
$148$	−4.39806e98	−0.787686
$149$	6.77426e98	0.893072	0.446536	−	0.894766i	$-0.352657\pi$
$149$	6.77426e98	0.893072	0.446536	+	0.894766i	$0.352657\pi$
$150$	1.54513e98	0.150250
$151$	1.84082e98	0.132300	0.0661501	−	0.997810i	$-0.478928\pi$
$151$	1.84082e98	0.132300	0.0661501	+	0.997810i	$0.478928\pi$
$152$	2.43276e99	1.29484
$153$	3.05326e98	0.120588
$154$	−7.07810e98	−0.207837
$155$	−1.94527e99	−0.425489
$156$	−6.35052e99	−1.03667
$157$	−3.91220e99	−0.477514	−0.238757	−	0.971079i	$-0.576740\pi$
$157$	−3.91220e99	−0.477514	−0.238757	+	0.971079i	$0.576740\pi$
$158$	−1.70905e98	−0.0156264
$159$	−1.59300e100	−1.09307
$160$	1.50479e100	0.776279
$161$	3.51045e98	0.0136391
$162$	−1.12854e100	−0.330812
$163$	5.39127e100	1.19442	0.597208	−	0.802087i	$-0.296277\pi$
$163$	5.39127e100	1.19442	0.597208	+	0.802087i	$0.296277\pi$
$164$	4.68441e100	0.785706
$165$	−2.64088e100	−0.335915
$166$	−1.90858e100	−0.184413
$167$	6.82450e100	0.501732	0.250866	−	0.968022i	$-0.419285\pi$
$167$	6.82450e100	0.501732	0.250866	+	0.968022i	$0.419285\pi$
$168$	−1.25472e101	−0.703030
$169$	2.43045e101	1.03954
$170$	−6.30421e100	−0.206160
$171$	1.30814e101	0.327591
$172$	−2.91402e101	−0.559690
$173$	−1.08270e102	−1.59739	−0.798695	−	0.601736i	$-0.794476\pi$
$173$	−1.08270e102	−1.59739	−0.798695	+	0.601736i	$0.794476\pi$
$174$	−1.68614e101	−0.191383
$175$	4.40917e101	0.385590
$176$	3.33082e101	0.224763
$177$	−2.49173e102	−1.29932
$178$	1.36987e102	0.552800
$179$	4.74613e102	1.48432	0.742159	−	0.670224i	$-0.233802\pi$
$179$	4.74613e102	1.48432	0.742159	+	0.670224i	$0.233802\pi$
$180$	5.21317e101	0.126533
$181$	7.60560e100	0.0143469	0.00717345	−	0.999974i	$-0.497717\pi$
$181$	7.60560e100	0.0143469	0.00717345	+	0.999974i	$0.497717\pi$
$182$	4.21946e102	0.619453
$183$	−4.34239e102	−0.496825
$184$	1.20463e101	0.0107558
$185$	1.09029e103	0.760724
$186$	3.86915e102	0.211240
$187$	−6.78324e102	−0.290164
$188$	−3.45932e103	−1.16094
$189$	−4.06281e103	−1.07106
$190$	−2.70098e103	−0.560057
$191$	2.05554e103	0.335667	0.167833	−	0.985815i	$-0.446323\pi$
$191$	2.05554e103	0.335667	0.167833	+	0.985815i	$0.446323\pi$
$192$	2.67058e102	0.0343874
$193$	7.77261e103	0.790150	0.395075	−	0.918649i	$-0.370719\pi$
$193$	7.77261e103	0.790150	0.395075	+	0.918649i	$0.370719\pi$
$194$	−6.08083e101	−0.00488635
$195$	1.57431e104	1.00118
$196$	6.16219e101	0.00310516
$197$	−1.51107e104	−0.604049	−0.302025	−	0.953300i	$-0.597663\pi$
$197$	−1.51107e104	−0.604049	−0.302025	+	0.953300i	$0.597663\pi$
$198$	−1.30606e103	−0.0414666
$199$	7.93413e103	0.200302	0.100151	−	0.994972i	$-0.468067\pi$
$199$	7.93413e103	0.200302	0.100151	+	0.994972i	$0.468067\pi$
$200$	1.51304e104	0.304078
$201$	1.00929e105	1.61657
$202$	−6.44294e104	−0.823373
$203$	−4.81154e104	−0.491150
$204$	−5.38529e104	−0.439578
$205$	−1.16127e105	−0.758812
$206$	2.03512e104	0.106569
$207$	6.47754e102	0.00272119
$208$	−1.98560e105	−0.669900
$209$	−2.90621e105	−0.788263
$210$	1.39305e105	0.304082
$211$	8.51011e105	1.49652	0.748262	−	0.663403i	$-0.230889\pi$
$211$	8.51011e105	1.49652	0.748262	+	0.663403i	$0.230889\pi$
$212$	−6.98620e105	−0.990739
$213$	1.56173e106	1.78786
$214$	1.00633e105	0.0930924
$215$	7.22390e105	0.540533
$216$	−1.39418e106	−0.844644
$217$	1.10409e106	0.542111
$218$	9.96782e105	0.397036
$219$	−4.58476e106	−1.48289
$220$	−1.15818e106	−0.304469
$221$	4.04368e106	0.864826
$222$	−2.16858e106	−0.377672
$223$	−3.12570e106	−0.443686	−0.221843	−	0.975082i	$-0.571207\pi$
$223$	−3.12570e106	−0.443686	−0.221843	+	0.975082i	$0.571207\pi$
$224$	−8.54087e106	−0.989048
$225$	8.13588e105	0.0769307
$226$	−8.76819e106	−0.677604
$227$	2.71471e107	1.71612	0.858060	−	0.513550i	$-0.171670\pi$
$227$	2.71471e107	1.71612	0.858060	+	0.513550i	$0.171670\pi$
$228$	−2.30727e107	−1.19416
$229$	4.35088e107	1.84528	0.922641	−	0.385661i	$-0.126027\pi$
$229$	4.35088e107	1.84528	0.922641	+	0.385661i	$0.126027\pi$
$230$	−1.33745e105	−0.00465222
$231$	1.49890e107	0.427985
$232$	−1.65111e107	−0.387323
$233$	−1.57898e107	−0.304566	−0.152283	−	0.988337i	$-0.548663\pi$
$233$	−1.57898e107	−0.304566	−0.152283	+	0.988337i	$0.548663\pi$
$234$	7.78582e106	0.123590
$235$	8.57572e107	1.12120
$236$	−1.09276e108	−1.17769
$237$	3.61920e106	0.0321783
$238$	3.57813e107	0.262666
$239$	−2.12426e107	−0.128856	−0.0644278	−	0.997922i	$-0.520522\pi$
$239$	−2.12426e107	−0.128856	−0.0644278	+	0.997922i	$0.520522\pi$
$240$	−6.55546e107	−0.328845
$241$	−1.92974e108	−0.801167	−0.400584	−	0.916260i	$-0.631193\pi$
$241$	−1.92974e108	−0.801167	−0.400584	+	0.916260i	$0.631193\pi$
$242$	−9.73628e107	−0.334807
$243$	−1.37486e108	−0.391898
$244$	−1.90438e108	−0.450315
$245$	−1.52762e106	−0.00299887
$246$	2.30978e108	0.376723
$247$	1.73248e109	2.34940
$248$	3.78877e108	0.427511
$249$	4.04173e108	0.379749
$250$	−6.02809e108	−0.471964
$251$	−9.11423e108	−0.595067	−0.297533	−	0.954711i	$-0.596164\pi$
$251$	−9.11423e108	−0.595067	−0.297533	+	0.954711i	$0.596164\pi$
$252$	−2.95888e108	−0.161214
$253$	−1.43907e107	−0.00654786
$254$	−3.78518e108	−0.143930
$255$	1.33502e109	0.424532
$256$	−1.50112e109	−0.399483
$257$	−2.93415e109	−0.653921	−0.326960	−	0.945038i	$-0.606024\pi$
$257$	−2.93415e109	−0.653921	−0.326960	+	0.945038i	$0.606024\pi$
$258$	−1.43683e109	−0.268355
$259$	−6.18823e109	−0.969230
$260$	6.90422e109	0.907459
$261$	−8.87834e108	−0.0979916
$262$	2.60688e109	0.241776
$263$	−7.95161e109	−0.620110	−0.310055	−	0.950719i	$-0.600347\pi$
$263$	−7.95161e109	−0.620110	−0.310055	+	0.950719i	$0.600347\pi$
$264$	5.14359e109	0.337511
$265$	1.73189e110	0.956827
$266$	1.53302e110	0.713563
$267$	−2.90092e110	−1.13834
$268$	4.42631e110	1.46524
$269$	−3.21549e110	−0.898502	−0.449251	−	0.893406i	$-0.648309\pi$
$269$	−3.21549e110	−0.898502	−0.449251	+	0.893406i	$0.648309\pi$
$270$	1.54789e110	0.365334
$271$	5.40371e110	1.07793	0.538963	−	0.842329i	$-0.318816\pi$
$271$	5.40371e110	1.07793	0.538963	+	0.842329i	$0.318816\pi$
$272$	−1.68380e110	−0.284057
$273$	−8.93540e110	−1.27560
$274$	−3.34782e110	−0.404679
$275$	−1.80750e110	−0.185114
$276$	−1.14250e109	−0.00991954
$277$	−9.21352e110	−0.678572	−0.339286	−	0.940683i	$-0.610186\pi$
$277$	−9.21352e110	−0.678572	−0.339286	+	0.940683i	$0.610186\pi$
$278$	4.54421e110	0.284066
$279$	2.03729e110	0.108159
$280$	1.36412e111	0.615405
$281$	−2.54324e111	−0.975552	−0.487776	−	0.872969i	$-0.662192\pi$
$281$	−2.54324e111	−0.975552	−0.487776	+	0.872969i	$0.662192\pi$
$282$	−1.70571e111	−0.556636
$283$	−3.76949e109	−0.0104713	−0.00523565	−	0.999986i	$-0.501667\pi$
$283$	−3.76949e109	−0.0104713	−0.00523565	+	0.999986i	$0.501667\pi$
$284$	6.84907e111	1.62049
$285$	5.71978e111	1.15329
$286$	−1.72973e111	−0.297388
$287$	6.59114e111	0.966794
$288$	−1.57598e111	−0.197330
$289$	−5.92179e111	−0.633288
$290$	1.83315e111	0.167529
$291$	1.28772e110	0.0100621
$292$	−2.01067e112	−1.34407
$293$	−2.17784e112	−1.24609	−0.623044	−	0.782187i	$-0.714104\pi$
$293$	−2.17784e112	−1.24609	−0.623044	+	0.782187i	$0.714104\pi$
$294$	3.03843e109	0.00148883
$295$	2.70898e112	1.13738
$296$	−2.12353e112	−0.764339
$297$	1.66551e112	0.514196
$298$	1.46488e112	0.388116
$299$	8.57873e110	0.0195157
$300$	−1.43499e112	−0.280435
$301$	−4.10012e112	−0.688686
$302$	3.98063e111	0.0574958
$303$	1.36440e113	1.69552
$304$	−7.21409e112	−0.771673
$305$	4.72100e112	0.434902
$306$	6.60243e111	0.0524058
$307$	1.13591e113	0.777229	0.388614	−	0.921400i	$-0.372954\pi$
$307$	1.13591e113	0.777229	0.388614	+	0.921400i	$0.372954\pi$
$308$	6.57354e112	0.387920
$309$	−4.30971e112	−0.219451
$310$	−4.20650e112	−0.184911
$311$	−2.90809e112	−0.110410	−0.0552052	−	0.998475i	$-0.517581\pi$
$311$	−2.90809e112	−0.110410	−0.0552052	+	0.998475i	$0.517581\pi$
$312$	−3.06624e113	−1.00594
$313$	−3.61753e113	−1.02599	−0.512997	−	0.858390i	$-0.671465\pi$
$313$	−3.61753e113	−1.02599	−0.512997	+	0.858390i	$0.671465\pi$
$314$	−8.45981e112	−0.207521
$315$	7.33511e112	0.155696
$316$	1.58723e112	0.0291660
$317$	4.06240e113	0.646526	0.323263	−	0.946309i	$-0.395220\pi$
$317$	4.06240e113	0.646526	0.323263	+	0.946309i	$0.395220\pi$
$318$	−3.44473e113	−0.475030
$319$	1.97244e113	0.235792
$320$	−2.90342e112	−0.0301014
$321$	−2.13107e113	−0.191699
$322$	7.59106e111	0.00592734
$323$	1.46915e114	0.996213
$324$	1.04809e114	0.617448
$325$	1.07750e114	0.551727
$326$	1.16582e114	0.519075
$327$	−2.11085e114	−0.817589
$328$	2.26179e114	0.762418
$329$	−4.86739e114	−1.42851
$330$	−5.71069e113	−0.145984
$331$	−2.77743e114	−0.618686	−0.309343	−	0.950951i	$-0.600109\pi$
$331$	−2.77743e114	−0.618686	−0.309343	+	0.950951i	$0.600109\pi$
$332$	1.77253e114	0.344199
$333$	−1.14186e114	−0.193376
$334$	1.47574e114	0.218045
$335$	−1.09729e115	−1.41509
$336$	3.72073e114	0.418978
$337$	−9.56251e114	−0.940614	−0.470307	−	0.882503i	$-0.655857\pi$
$337$	−9.56251e114	−0.940614	−0.470307	+	0.882503i	$0.655857\pi$
$338$	5.25565e114	0.451769
$339$	1.85681e115	1.39534
$340$	5.85483e114	0.384790
$341$	−4.52612e114	−0.260257
$342$	2.82875e114	0.142366
$343$	2.27357e115	1.00190
$344$	−1.40699e115	−0.543101
$345$	2.83227e113	0.00958000
$346$	−2.34125e115	−0.694203
$347$	7.81868e114	0.203302	0.101651	−	0.994820i	$-0.467587\pi$
$347$	7.81868e114	0.203302	0.101651	+	0.994820i	$0.467587\pi$
$348$	1.56594e115	0.357208
$349$	3.60513e115	0.721712	0.360856	−	0.932621i	$-0.382485\pi$
$349$	3.60513e115	0.721712	0.360856	+	0.932621i	$0.382485\pi$
$350$	9.53447e114	0.167572
$351$	−9.92859e115	−1.53255
$352$	3.50125e115	0.474823
$353$	7.47493e115	0.890960	0.445480	−	0.895292i	$-0.353033\pi$
$353$	7.47493e115	0.890960	0.445480	+	0.895292i	$0.353033\pi$
$354$	−5.38817e115	−0.564667
$355$	−1.69790e116	−1.56502
$356$	−1.27222e116	−1.03178
$357$	−7.57729e115	−0.540891
$358$	1.02631e116	0.645063
$359$	9.63578e115	0.533445	0.266722	−	0.963773i	$-0.414059\pi$
$359$	9.63578e115	0.533445	0.266722	+	0.963773i	$0.414059\pi$
$360$	2.51709e115	0.122782
$361$	3.96862e116	1.70632
$362$	1.64465e114	0.00623495
$363$	2.06182e116	0.689445
$364$	−3.91868e116	−1.15618
$365$	4.98450e116	1.29806
$366$	−9.39006e115	−0.215913
$367$	−1.93268e116	−0.392513	−0.196256	−	0.980553i	$-0.562878\pi$
$367$	−1.93268e116	−0.392513	−0.196256	+	0.980553i	$0.562878\pi$
$368$	−3.57221e114	−0.00641005
$369$	1.21621e116	0.192889
$370$	2.35766e116	0.330600
$371$	−9.82983e116	−1.21908
$372$	−3.59334e116	−0.394271
$373$	−2.13248e115	−0.0207078	−0.0103539	−	0.999946i	$-0.503296\pi$
$373$	−2.13248e115	−0.0207078	−0.0103539	+	0.999946i	$0.503296\pi$
$374$	−1.46682e116	−0.126101
$375$	1.27655e117	0.971884
$376$	−1.67028e117	−1.12653
$377$	−1.17583e117	−0.702770
$378$	−8.78550e116	−0.465468
$379$	1.88843e116	0.0887192	0.0443596	−	0.999016i	$-0.485875\pi$
$379$	1.88843e116	0.0887192	0.0443596	+	0.999016i	$0.485875\pi$
$380$	2.50844e117	1.04532
$381$	8.01574e116	0.296386
$382$	4.44495e116	0.145876
$383$	1.52422e117	0.444123	0.222062	−	0.975033i	$-0.428721\pi$
$383$	1.52422e117	0.444123	0.222062	+	0.975033i	$0.428721\pi$
$384$	3.48465e117	0.901755
$385$	−1.62959e117	−0.374642
$386$	1.68076e117	0.343387
$387$	−7.56563e116	−0.137403
$388$	5.64737e115	0.00912016
$389$	−5.47038e117	−0.785797	−0.392899	−	0.919582i	$-0.628528\pi$
$389$	−5.47038e117	−0.785797	−0.392899	+	0.919582i	$0.628528\pi$
$390$	3.40431e117	0.435100
$391$	7.27483e115	0.00827523
$392$	2.97531e115	0.00301312
$393$	−5.52050e117	−0.497872
$394$	−3.26758e117	−0.262511
$395$	−3.93476e116	−0.0281676
$396$	1.21296e117	0.0773957
$397$	−3.48482e116	−0.0198250	−0.00991249	−	0.999951i	$-0.503155\pi$
$397$	−3.48482e116	−0.0198250	−0.00991249	+	0.999951i	$0.503155\pi$
$398$	1.71569e117	0.0870482
$399$	−3.24642e118	−1.46939
$400$	−4.48675e117	−0.181218
$401$	−1.03962e118	−0.374804	−0.187402	−	0.982283i	$-0.560007\pi$
$401$	−1.03962e118	−0.374804	−0.187402	+	0.982283i	$0.560007\pi$
$402$	2.18251e118	0.702539
$403$	2.69815e118	0.775688
$404$	5.98366e118	1.53679
$405$	−2.59823e118	−0.596313
$406$	−1.04046e118	−0.213447
$407$	2.53680e118	0.465309
$408$	−2.60020e118	−0.426549
$409$	9.91702e118	1.45536	0.727680	−	0.685917i	$-0.240599\pi$
$409$	9.91702e118	1.45536	0.727680	+	0.685917i	$0.240599\pi$
$410$	−2.51116e118	−0.329769
$411$	7.08956e118	0.833328
$412$	−1.89005e118	−0.198907
$413$	−1.53756e119	−1.44912
$414$	1.40072e116	0.00118259
$415$	−4.39412e118	−0.332418
$416$	−2.08720e119	−1.41520
$417$	−9.62311e118	−0.584958
$418$	−6.28445e118	−0.342568
$419$	2.58897e119	1.26587	0.632935	−	0.774205i	$-0.281850\pi$
$419$	2.58897e119	1.26587	0.632935	+	0.774205i	$0.281850\pi$
$420$	−1.29375e119	−0.567556
$421$	3.43527e119	1.35246	0.676231	−	0.736690i	$-0.263612\pi$
$421$	3.43527e119	1.35246	0.676231	+	0.736690i	$0.263612\pi$
$422$	1.84024e119	0.650367
$423$	−8.98140e118	−0.285008
$424$	−3.37317e119	−0.961373
$425$	9.13728e118	0.233949
$426$	3.37712e119	0.776979
$427$	−2.67953e119	−0.554103
$428$	−9.34596e118	−0.173753
$429$	3.66298e119	0.612390
$430$	1.56211e119	0.234908
$431$	8.40427e119	1.13706	0.568531	−	0.822662i	$-0.307512\pi$
$431$	8.40427e119	1.13706	0.568531	+	0.822662i	$0.307512\pi$
$432$	4.13430e119	0.503374
$433$	−9.47708e119	−1.03866	−0.519332	−	0.854572i	$-0.673819\pi$
$433$	−9.47708e119	−1.03866	−0.519332	+	0.854572i	$0.673819\pi$
$434$	2.38751e119	0.235593
$435$	−3.88200e119	−0.344981
$436$	−9.25728e119	−0.741051
$437$	3.11683e118	0.0224806
$438$	−9.91416e119	−0.644442
$439$	−6.08301e119	−0.356437	−0.178218	−	0.983991i	$-0.557033\pi$
$439$	−6.08301e119	−0.356437	−0.178218	+	0.983991i	$0.557033\pi$
$440$	−5.59206e119	−0.295444
$441$	1.59988e117	0.000762311 0
$442$	8.74414e119	0.375841
$443$	−1.98484e120	−0.769761	−0.384880	−	0.922966i	$-0.625757\pi$
$443$	−1.98484e120	−0.769761	−0.384880	+	0.922966i	$0.625757\pi$
$444$	2.01400e120	0.704910
$445$	3.15385e120	0.996461
$446$	−6.75907e119	−0.192820
$447$	−3.10212e120	−0.799221
$448$	1.64792e119	0.0383518
$449$	3.86980e120	0.813729	0.406865	−	0.913488i	$-0.366622\pi$
$449$	3.86980e120	0.813729	0.406865	+	0.913488i	$0.366622\pi$
$450$	1.75932e119	0.0334330
$451$	−2.70197e120	−0.464139
$452$	8.14316e120	1.26472
$453$	−8.42964e119	−0.118397
$454$	5.87035e120	0.745801
$455$	9.71448e120	1.11661
$456$	−1.11403e121	−1.15877
$457$	−1.35462e121	−1.27536	−0.637678	−	0.770303i	$-0.720105\pi$
$457$	−1.35462e121	−1.27536	−0.637678	+	0.770303i	$0.720105\pi$
$458$	9.40842e120	0.801932
$459$	−8.41951e120	−0.649845
$460$	1.24211e119	0.00868318
$461$	−1.36082e121	−0.861806	−0.430903	−	0.902398i	$-0.641805\pi$
$461$	−1.36082e121	−0.861806	−0.430903	+	0.902398i	$0.641805\pi$
$462$	3.24126e120	0.185996
$463$	−3.33812e121	−1.73607	−0.868035	−	0.496503i	$-0.834617\pi$
$463$	−3.33812e121	−1.73607	−0.868035	+	0.496503i	$0.834617\pi$
$464$	4.89619e120	0.230829
$465$	8.90796e120	0.380775
$466$	−3.41441e120	−0.132360
$467$	1.02057e121	0.358860	0.179430	−	0.983771i	$-0.442575\pi$
$467$	1.02057e121	0.358860	0.179430	+	0.983771i	$0.442575\pi$
$468$	−7.23082e120	−0.230675
$469$	6.22797e121	1.80294
$470$	1.85443e121	0.487257
$471$	1.79151e121	0.427333
$472$	−5.27623e121	−1.14278
$473$	1.68081e121	0.330625
$474$	7.82623e119	0.0139842
$475$	3.91478e121	0.635548
$476$	−3.32307e121	−0.490256
$477$	−1.81382e121	−0.243225
$478$	−4.59354e120	−0.0559988
$479$	1.44119e122	1.59755	0.798776	−	0.601629i	$-0.205481\pi$
$479$	1.44119e122	1.59755	0.798776	+	0.601629i	$0.205481\pi$
$480$	−6.89088e121	−0.694701
$481$	−1.51226e122	−1.38684
$482$	−4.17291e121	−0.348176
$483$	−1.60753e120	−0.0122058
$484$	9.04225e121	0.624903
$485$	−1.39999e120	−0.00880799
$486$	−2.97303e121	−0.170313
$487$	−3.30598e121	−0.172478	−0.0862388	−	0.996274i	$-0.527485\pi$
$487$	−3.30598e121	−0.172478	−0.0862388	+	0.996274i	$0.527485\pi$
$488$	−9.19499e121	−0.436968
$489$	−2.46882e122	−1.06890
$490$	−3.30335e119	−0.00130327
$491$	4.12494e122	1.48323	0.741617	−	0.670824i	$-0.234059\pi$
$491$	4.12494e122	1.48323	0.741617	+	0.670824i	$0.234059\pi$
$492$	−2.14513e122	−0.703138
$493$	−9.97112e121	−0.297995
$494$	3.74634e122	1.02101
$495$	−3.00696e121	−0.0747465
$496$	−1.12352e122	−0.254779
$497$	9.63688e122	1.99398
$498$	8.73991e121	0.165033
$499$	−2.58908e122	−0.446241	−0.223121	−	0.974791i	$-0.571624\pi$
$499$	−2.58908e122	−0.446241	−0.223121	+	0.974791i	$0.571624\pi$
$500$	5.59838e122	0.880902
$501$	−3.12513e122	−0.449006
$502$	−1.97088e122	−0.258607
$503$	−2.14460e122	−0.257041	−0.128520	−	0.991707i	$-0.541023\pi$
$503$	−2.14460e122	−0.257041	−0.128520	+	0.991707i	$0.541023\pi$
$504$	−1.42864e122	−0.156435
$505$	−1.48336e123	−1.48419
$506$	−3.11188e120	−0.00284560
$507$	−1.11297e123	−0.930298
$508$	3.51536e122	0.268640
$509$	2.75512e123	1.92522	0.962612	−	0.270884i	$-0.0873161\pi$
$509$	2.75512e123	1.92522	0.962612	+	0.270884i	$0.0873161\pi$
$510$	2.88688e122	0.184495
$511$	−2.82909e123	−1.65385
$512$	1.55944e123	0.834037
$513$	−3.60726e123	−1.76538
$514$	−6.34486e122	−0.284184
$515$	4.68547e122	0.192099
$516$	1.33441e123	0.500874
$517$	1.99534e123	0.685799
$518$	−1.33815e123	−0.421213
$519$	4.95800e123	1.42952
$520$	3.33359e123	0.880562
$521$	4.77425e123	1.15555	0.577775	−	0.816196i	$-0.303921\pi$
$521$	4.77425e123	1.15555	0.577775	+	0.816196i	$0.303921\pi$
$522$	−1.91987e122	−0.0425857
$523$	−4.44042e123	−0.902811	−0.451405	−	0.892319i	$-0.649077\pi$
$523$	−4.44042e123	−0.902811	−0.451405	+	0.892319i	$0.649077\pi$
$524$	−2.42105e123	−0.451264
$525$	−2.01908e123	−0.345069
$526$	−1.71947e123	−0.269491
$527$	2.28805e123	0.328915
$528$	−1.52528e123	−0.201143
$529$	−8.26327e123	−0.999813
$530$	3.74508e123	0.415823
$531$	−2.83713e123	−0.289120
$532$	−1.42374e124	−1.33184
$533$	1.61072e124	1.38335
$534$	−6.27300e123	−0.494707
$535$	2.31688e123	0.167806
$536$	2.13717e124	1.42181
$537$	−2.17339e124	−1.32833
$538$	−6.95325e123	−0.390476
$539$	−3.55435e121	−0.00183431
$540$	−1.43756e124	−0.681881
$541$	2.72954e124	1.19018	0.595091	−	0.803658i	$-0.297116\pi$
$541$	2.72954e124	1.19018	0.595091	+	0.803658i	$0.297116\pi$
$542$	1.16851e124	0.468451
$543$	−3.48282e122	−0.0128392
$544$	−1.76996e124	−0.600085
$545$	2.29490e124	0.715685
$546$	−1.93221e124	−0.554356
$547$	5.98890e124	1.58097	0.790485	−	0.612481i	$-0.209828\pi$
$547$	5.98890e124	1.58097	0.790485	+	0.612481i	$0.209828\pi$
$548$	3.10917e124	0.755317
$549$	−4.94432e123	−0.110552
$550$	−3.90856e123	−0.0804479
$551$	−4.27203e124	−0.809537
$552$	−5.51636e122	−0.00962552
$553$	2.23328e123	0.0358881
$554$	−1.99235e124	−0.294898
$555$	−4.99273e124	−0.680781
$556$	−4.22028e124	−0.530198
$557$	−5.91728e123	−0.0685032	−0.0342516	−	0.999413i	$-0.510905\pi$
$557$	−5.91728e123	−0.0685032	−0.0342516	+	0.999413i	$0.510905\pi$
$558$	4.40548e123	0.0470043
$559$	−1.00198e125	−0.985418
$560$	−4.04514e124	−0.366757
$561$	3.10624e124	0.259671
$562$	−5.49956e124	−0.423960
$563$	2.06382e125	1.46737	0.733687	−	0.679488i	$-0.237798\pi$
$563$	2.06382e125	1.46737	0.733687	+	0.679488i	$0.237798\pi$
$564$	1.58412e125	1.03894
$565$	−2.01870e125	−1.22143
$566$	−8.15123e122	−0.00455067
$567$	1.47470e125	0.759756
$568$	3.30696e125	1.57246
$569$	−2.71831e125	−1.19314	−0.596570	−	0.802561i	$-0.703470\pi$
$569$	−2.71831e125	−1.19314	−0.596570	+	0.802561i	$0.703470\pi$
$570$	1.23686e125	0.501202
$571$	−6.44815e124	−0.241264	−0.120632	−	0.992697i	$-0.538492\pi$
$571$	−6.44815e124	−0.241264	−0.120632	+	0.992697i	$0.538492\pi$
$572$	1.60642e125	0.555061
$573$	−9.41292e124	−0.300392
$574$	1.42528e125	0.420155
$575$	1.93849e123	0.00527930
$576$	3.04077e123	0.00765175
$577$	−2.84233e125	−0.660959	−0.330479	−	0.943813i	$-0.607210\pi$
$577$	−2.84233e125	−0.660959	−0.330479	+	0.943813i	$0.607210\pi$
$578$	−1.28054e125	−0.275218
$579$	−3.55930e125	−0.707114
$580$	−1.70248e125	−0.312686
$581$	2.49401e125	0.423529
$582$	2.78458e123	0.00437285
$583$	4.02964e125	0.585258
$584$	−9.70821e125	−1.30423
$585$	1.79253e125	0.222780
$586$	−4.70940e125	−0.541532
$587$	−6.90173e125	−0.734386	−0.367193	−	0.930145i	$-0.619681\pi$
$587$	−6.90173e125	−0.734386	−0.367193	+	0.930145i	$0.619681\pi$
$588$	−2.82184e123	−0.00277884
$589$	9.80295e125	0.893533
$590$	5.85796e125	0.494287
$591$	6.91964e125	0.540571
$592$	6.29711e125	0.455516
$593$	7.77384e125	0.520772	0.260386	−	0.965505i	$-0.416150\pi$
$593$	7.77384e125	0.520772	0.260386	+	0.965505i	$0.416150\pi$
$594$	3.60153e125	0.223462
$595$	8.23795e125	0.473475
$596$	−1.36046e126	−0.724403
$597$	−3.63326e125	−0.179252
$598$	1.85508e124	0.00848123
$599$	−2.03130e126	−0.860705	−0.430352	−	0.902661i	$-0.641611\pi$
$599$	−2.03130e126	−0.860705	−0.430352	+	0.902661i	$0.641611\pi$
$600$	−6.92862e125	−0.272123
$601$	3.71080e126	1.35107	0.675537	−	0.737326i	$-0.263912\pi$
$601$	3.71080e126	1.35107	0.675537	+	0.737326i	$0.263912\pi$
$602$	−8.86619e125	−0.299293
$603$	1.14920e126	0.359714
$604$	−3.69688e125	−0.107313
$605$	−2.24159e126	−0.603513
$606$	2.95040e126	0.736847
$607$	3.92642e125	0.0909727	0.0454864	−	0.998965i	$-0.485516\pi$
$607$	3.92642e125	0.0909727	0.0454864	+	0.998965i	$0.485516\pi$
$608$	−7.58321e126	−1.63020
$609$	2.20334e126	0.439536
$610$	1.02088e126	0.189002
$611$	−1.18948e127	−2.04400
$612$	−6.13179e125	−0.0978132
$613$	−4.45057e126	−0.659119	−0.329560	−	0.944135i	$-0.606900\pi$
$613$	−4.45057e126	−0.659119	−0.329560	+	0.944135i	$0.606900\pi$
$614$	2.45632e126	0.337772
$615$	5.31781e126	0.679070
$616$	3.17393e126	0.376422
$617$	1.05675e127	1.16412	0.582062	−	0.813144i	$-0.302246\pi$
$617$	1.05675e127	1.16412	0.582062	+	0.813144i	$0.302246\pi$
$618$	−9.31939e125	−0.0953701
$619$	1.87782e127	1.78538	0.892689	−	0.450673i	$-0.148816\pi$
$619$	1.87782e127	1.78538	0.892689	+	0.450673i	$0.148816\pi$
$620$	3.90664e126	0.345129
$621$	−1.78621e125	−0.0146644
$622$	−6.28850e125	−0.0479827
$623$	−1.79005e127	−1.26958
$624$	9.09262e126	0.599501
$625$	−7.57620e126	−0.464419
$626$	−7.82262e126	−0.445882
$627$	1.33084e127	0.705426
$628$	7.85676e126	0.387329
$629$	−1.28241e127	−0.588061
$630$	1.58616e126	0.0676630
$631$	−2.58592e127	−1.02631	−0.513156	−	0.858296i	$-0.671524\pi$
$631$	−2.58592e127	−1.02631	−0.513156	+	0.858296i	$0.671524\pi$
$632$	7.66365e125	0.0283015
$633$	−3.89702e127	−1.33926
$634$	8.78461e126	0.280971
$635$	−8.71463e126	−0.259444
$636$	3.19918e127	0.886624
$637$	2.11885e125	0.00546710
$638$	4.26525e126	0.102472
$639$	1.77822e127	0.397828
$640$	−3.78847e127	−0.789361
$641$	−4.55285e126	−0.0883574	−0.0441787	−	0.999024i	$-0.514067\pi$
$641$	−4.55285e126	−0.0883574	−0.0441787	+	0.999024i	$0.514067\pi$
$642$	−4.60828e126	−0.0833095
$643$	6.15204e127	1.03614	0.518072	−	0.855337i	$-0.326650\pi$
$643$	6.15204e127	1.03614	0.518072	+	0.855337i	$0.326650\pi$
$644$	−7.04994e125	−0.0110631
$645$	−3.30803e127	−0.483729
$646$	3.17692e127	0.432940
$647$	3.13105e127	0.397690	0.198845	−	0.980031i	$-0.436281\pi$
$647$	3.13105e127	0.397690	0.198845	+	0.980031i	$0.436281\pi$
$648$	5.06053e127	0.599146
$649$	6.30307e127	0.695694
$650$	2.33001e127	0.239773
$651$	−5.05596e127	−0.485141
$652$	−1.08272e128	−0.968833
$653$	7.30279e127	0.609452	0.304726	−	0.952440i	$-0.401435\pi$
$653$	7.30279e127	0.609452	0.304726	+	0.952440i	$0.401435\pi$
$654$	−4.56455e127	−0.355312
$655$	6.00183e127	0.435818
$656$	−6.70711e127	−0.454371
$657$	−5.22029e127	−0.329967
$658$	−1.05253e128	−0.620809
$659$	8.50597e127	0.468207	0.234103	−	0.972212i	$-0.424785\pi$
$659$	8.50597e127	0.468207	0.234103	+	0.972212i	$0.424785\pi$
$660$	5.30361e127	0.272473
$661$	−2.84619e128	−1.36489	−0.682445	−	0.730937i	$-0.739083\pi$
$661$	−2.84619e128	−1.36489	−0.682445	+	0.730937i	$0.739083\pi$
$662$	−6.00598e127	−0.268872
$663$	−1.85172e128	−0.773943
$664$	8.55835e127	0.333997
$665$	3.52947e128	1.28625
$666$	−2.46919e127	−0.0840382
$667$	−2.11539e126	−0.00672457
$668$	−1.37055e128	−0.406972
$669$	1.43135e128	0.397060
$670$	−2.37280e128	−0.614975
$671$	1.09845e128	0.266014
$672$	3.91111e128	0.885111
$673$	5.18808e128	1.09729	0.548645	−	0.836055i	$-0.315144\pi$
$673$	5.18808e128	1.09729	0.548645	+	0.836055i	$0.315144\pi$
$674$	−2.06782e128	−0.408777
$675$	−2.24351e128	−0.414577
$676$	−4.88101e128	−0.843208
$677$	1.15352e129	1.86313	0.931564	−	0.363578i	$-0.118445\pi$
$677$	1.15352e129	1.86313	0.931564	+	0.363578i	$0.118445\pi$
$678$	4.01520e128	0.606396
$679$	7.94604e126	0.0112222
$680$	2.82691e128	0.373384
$681$	−1.24314e129	−1.53578
$682$	−9.78738e127	−0.113104
$683$	3.20897e128	0.346916	0.173458	−	0.984841i	$-0.444506\pi$
$683$	3.20897e128	0.346916	0.173458	+	0.984841i	$0.444506\pi$
$684$	−2.62711e128	−0.265721
$685$	−7.70769e128	−0.729463
$686$	4.91642e128	0.435413
$687$	−1.99239e129	−1.65136
$688$	4.17226e128	0.323667
$689$	−2.40219e129	−1.74434
$690$	6.12455e126	0.00416333
$691$	3.49320e128	0.222317	0.111158	−	0.993803i	$-0.464544\pi$
$691$	3.49320e128	0.222317	0.111158	+	0.993803i	$0.464544\pi$
$692$	2.17436e129	1.29570
$693$	1.70668e128	0.0952336
$694$	1.69073e128	0.0883523
$695$	1.04621e129	0.512050
$696$	7.56090e128	0.346620
$697$	1.36591e129	0.586583
$698$	7.79581e128	0.313646
$699$	7.23059e128	0.272560
$700$	−8.85482e128	−0.312765
$701$	3.46599e129	1.14725	0.573625	−	0.819118i	$-0.305537\pi$
$701$	3.46599e129	1.14725	0.573625	+	0.819118i	$0.305537\pi$
$702$	−2.14698e129	−0.666022
$703$	−5.49436e129	−1.59753
$704$	−6.75548e127	−0.0184120
$705$	−3.92707e129	−1.00338
$706$	1.61639e129	0.387198
$707$	8.41923e129	1.89099
$708$	5.00408e129	1.05393
$709$	1.04854e127	0.00207100	0.00103550	−	0.999999i	$-0.499670\pi$
$709$	1.04854e127	0.00207100	0.00103550	+	0.999999i	$0.499670\pi$
$710$	−3.67157e129	−0.680137
$711$	4.12089e127	0.00716019
$712$	−6.14269e129	−1.00120
$713$	4.85414e127	0.00742230
$714$	−1.63853e129	−0.235063
$715$	−3.98236e129	−0.536062
$716$	−9.53154e129	−1.20398
$717$	9.72759e128	0.115314
$718$	2.08366e129	0.231827
$719$	−1.06415e129	−0.111132	−0.0555658	−	0.998455i	$-0.517696\pi$
$719$	−1.06415e129	−0.111132	−0.0555658	+	0.998455i	$0.517696\pi$
$720$	−7.46417e128	−0.0731733
$721$	−2.65937e129	−0.244751
$722$	8.58182e129	0.741544
$723$	8.83682e129	0.716975
$724$	−1.52741e128	−0.0116373
$725$	−2.65696e129	−0.190110
$726$	4.45852e129	0.299623
$727$	1.29079e130	0.814782	0.407391	−	0.913254i	$-0.366439\pi$
$727$	1.29079e130	0.814782	0.407391	+	0.913254i	$0.366439\pi$
$728$	−1.89207e130	−1.12191
$729$	1.99609e130	1.11193
$730$	1.07786e130	0.564120
$731$	−8.49684e129	−0.417846
$732$	8.72070e129	0.402993
$733$	4.04787e129	0.175791	0.0878953	−	0.996130i	$-0.471986\pi$
$733$	4.04787e129	0.175791	0.0878953	+	0.996130i	$0.471986\pi$
$734$	−4.17926e129	−0.170580
$735$	6.99540e127	0.00268373
$736$	−3.75499e128	−0.0135415
$737$	−2.55310e130	−0.865559
$738$	2.62995e129	0.0838269
$739$	5.40187e130	1.61891	0.809454	−	0.587183i	$-0.199763\pi$
$739$	5.40187e130	1.61891	0.809454	+	0.587183i	$0.199763\pi$
$740$	−2.18960e130	−0.617050
$741$	−7.93350e130	−2.10250
$742$	−2.12562e130	−0.529795
$743$	−6.63516e129	−0.155547	−0.0777733	−	0.996971i	$-0.524781\pi$
$743$	−6.63516e129	−0.155547	−0.0777733	+	0.996971i	$0.524781\pi$
$744$	−1.73499e130	−0.382584
$745$	3.37260e130	0.699607
$746$	−4.61132e128	−0.00899929
$747$	4.60199e129	0.0845003
$748$	1.36226e130	0.235362
$749$	−1.31501e130	−0.213799
$750$	2.76043e130	0.422367
$751$	−7.80135e130	−1.12345	−0.561724	−	0.827325i	$-0.689862\pi$
$751$	−7.80135e130	−1.12345	−0.561724	+	0.827325i	$0.689862\pi$
$752$	4.95303e130	0.671366
$753$	4.17366e130	0.532532
$754$	−2.54264e130	−0.305413
$755$	9.16462e129	0.103640
$756$	8.15924e130	0.868776
$757$	1.36410e131	1.36767	0.683837	−	0.729634i	$-0.260310\pi$
$757$	1.36410e131	1.36767	0.683837	+	0.729634i	$0.260310\pi$
$758$	4.08359e129	0.0385561
$759$	6.58992e128	0.00585976
$760$	1.21116e131	1.01434
$761$	−1.42868e131	−1.12702	−0.563512	−	0.826108i	$-0.690550\pi$
$761$	−1.42868e131	−1.12702	−0.563512	+	0.826108i	$0.690550\pi$
$762$	1.73334e130	0.128805
$763$	−1.30253e131	−0.911846
$764$	−4.12810e130	−0.272271
$765$	1.52008e130	0.0944651
$766$	3.29600e130	0.193010
$767$	−3.75744e131	−2.07350
$768$	6.87407e130	0.357502
$769$	2.02382e131	0.992025	0.496012	−	0.868315i	$-0.334797\pi$
$769$	2.02382e131	0.992025	0.496012	+	0.868315i	$0.334797\pi$
$770$	−3.52386e130	−0.162814
$771$	1.34363e131	0.585202
$772$	−1.56095e131	−0.640918
$773$	−3.05210e131	−1.18150	−0.590748	−	0.806856i	$-0.701167\pi$
$773$	−3.05210e131	−1.18150	−0.590748	+	0.806856i	$0.701167\pi$
$774$	−1.63601e130	−0.0597133
$775$	6.09686e130	0.209836
$776$	2.72674e129	0.00884984
$777$	2.83376e131	0.867376
$778$	−1.18293e131	−0.341496
$779$	5.85209e131	1.59352
$780$	−3.16164e131	−0.812096
$781$	−3.95055e131	−0.957272
$782$	1.57312e129	0.00359629
$783$	2.44824e131	0.528074
$784$	−8.82297e128	−0.00179570
$785$	−1.94771e131	−0.374071
$786$	−1.19376e131	−0.216368
$787$	5.46958e131	0.935629	0.467815	−	0.883827i	$-0.345041\pi$
$787$	5.46958e131	0.935629	0.467815	+	0.883827i	$0.345041\pi$
$788$	3.03465e131	0.489966
$789$	3.64127e131	0.554944
$790$	−8.50860e129	−0.0122412
$791$	1.14577e132	1.55621
$792$	5.85659e130	0.0751016
$793$	−6.54816e131	−0.792847
$794$	−7.53565e129	−0.00861565
$795$	−7.93082e131	−0.856276
$796$	−1.59339e131	−0.162472
$797$	−2.13422e131	−0.205535	−0.102768	−	0.994705i	$-0.532770\pi$
$797$	−2.13422e131	−0.205535	−0.102768	+	0.994705i	$0.532770\pi$
$798$	−7.02011e131	−0.638576
$799$	−1.00869e132	−0.866718
$800$	−4.71632e131	−0.382832
$801$	−3.30304e131	−0.253300
$802$	−2.24809e131	−0.162884
$803$	1.15976e132	0.793981
$804$	−2.02693e132	−1.31126
$805$	1.74769e130	0.0106845
$806$	5.83454e131	0.337103
$807$	1.47247e132	0.804080
$808$	2.88911e132	1.49124
$809$	−9.43123e131	−0.460162	−0.230081	−	0.973171i	$-0.573899\pi$
$809$	−9.43123e131	−0.460162	−0.230081	+	0.973171i	$0.573899\pi$
$810$	−5.61847e131	−0.259149
$811$	1.12387e132	0.490081	0.245041	−	0.969513i	$-0.421199\pi$
$811$	1.12387e132	0.490081	0.245041	+	0.969513i	$0.421199\pi$
$812$	9.66289e131	0.398389
$813$	−2.47451e132	−0.964649
$814$	5.48563e131	0.202216
$815$	2.68407e132	0.935670
$816$	7.71061e131	0.254206
$817$	−3.64039e132	−1.13513
$818$	2.14447e132	0.632478
$819$	−1.01740e132	−0.283841
$820$	2.33216e132	0.615500
$821$	4.66904e132	1.16577	0.582887	−	0.812554i	$-0.301923\pi$
$821$	4.66904e132	1.16577	0.582887	+	0.812554i	$0.301923\pi$
$822$	1.53306e132	0.362152
$823$	−3.91967e132	−0.876107	−0.438054	−	0.898949i	$-0.644332\pi$
$823$	−3.91967e132	−0.876107	−0.438054	+	0.898949i	$0.644332\pi$
$824$	−9.12580e131	−0.193011
$825$	8.27703e131	0.165661
$826$	−3.32484e132	−0.629766
$827$	−8.82729e132	−1.58244	−0.791219	−	0.611533i	$-0.790553\pi$
$827$	−8.82729e132	−1.58244	−0.791219	+	0.611533i	$0.790553\pi$
$828$	−1.30087e130	−0.00220726
$829$	−6.06846e132	−0.974646	−0.487323	−	0.873222i	$-0.662027\pi$
$829$	−6.06846e132	−0.974646	−0.487323	+	0.873222i	$0.662027\pi$
$830$	−9.50194e131	−0.144464
$831$	4.21913e132	0.607263
$832$	4.02714e131	0.0548763
$833$	1.79680e130	0.00231821
$834$	−2.08092e132	−0.254214
$835$	3.39761e132	0.393042
$836$	5.83647e132	0.639388
$837$	−5.61793e132	−0.582865
$838$	5.59844e132	0.550129
$839$	1.00406e133	0.934524	0.467262	−	0.884119i	$-0.345241\pi$
$839$	1.00406e133	0.934524	0.467262	+	0.884119i	$0.345241\pi$
$840$	−6.24667e132	−0.550733
$841$	−9.07399e132	−0.757845
$842$	7.42849e132	0.587760
$843$	1.16462e133	0.873033
$844$	−1.70906e133	−1.21388
$845$	1.21001e133	0.814346
$846$	−1.94215e132	−0.123860
$847$	1.27228e133	0.768929
$848$	1.00028e133	0.572940
$849$	1.72616e131	0.00937089
$850$	1.97586e132	0.101671
$851$	−2.72065e131	−0.0132702
$852$	−3.13638e133	−1.45020
$853$	8.05612e132	0.353139	0.176569	−	0.984288i	$-0.443500\pi$
$853$	8.05612e132	0.353139	0.176569	+	0.984288i	$0.443500\pi$
$854$	−5.79427e132	−0.240805
$855$	6.51264e132	0.256625
$856$	−4.51255e132	−0.168603
$857$	−1.01640e133	−0.360113	−0.180057	−	0.983656i	$-0.557628\pi$
$857$	−1.01640e133	−0.360113	−0.180057	+	0.983656i	$0.557628\pi$
$858$	7.92090e132	0.266136
$859$	1.42723e133	0.454785	0.227392	−	0.973803i	$-0.426980\pi$
$859$	1.42723e133	0.454785	0.227392	+	0.973803i	$0.426980\pi$
$860$	−1.45076e133	−0.438445
$861$	−3.01827e133	−0.865196
$862$	1.81735e133	0.494150
$863$	−5.12898e133	−1.32294	−0.661469	−	0.749972i	$-0.730067\pi$
$863$	−5.12898e133	−1.32294	−0.661469	+	0.749972i	$0.730067\pi$
$864$	4.34583e133	1.06340
$865$	−5.39028e133	−1.25135
$866$	−2.04934e133	−0.451388
$867$	2.71176e133	0.566737
$868$	−2.21732e133	−0.439725
$869$	−9.15512e131	−0.0172292
$870$	−8.39452e132	−0.149924
$871$	1.52197e134	2.57977
$872$	−4.46972e133	−0.719086
$873$	1.46622e131	0.00223898
$874$	6.73989e131	0.00976973
$875$	7.87712e133	1.08393
$876$	9.20745e133	1.20282
$877$	−3.06949e133	−0.380702	−0.190351	−	0.981716i	$-0.560963\pi$
$877$	−3.06949e133	−0.380702	−0.190351	+	0.981716i	$0.560963\pi$
$878$	−1.31540e133	−0.154902
$879$	9.97293e133	1.11514
$880$	1.65827e133	0.176073
$881$	−1.14919e134	−1.15875	−0.579375	−	0.815061i	$-0.696703\pi$
$881$	−1.14919e134	−1.15875	−0.579375	+	0.815061i	$0.696703\pi$
$882$	3.45962e130	0.000331289 0
$883$	−7.47296e133	−0.679642	−0.339821	−	0.940490i	$-0.610367\pi$
$883$	−7.47296e133	−0.679642	−0.339821	+	0.940490i	$0.610367\pi$
$884$	−8.12082e133	−0.701491
$885$	−1.24052e134	−1.01785
$886$	−4.29205e133	−0.334527
$887$	−1.93517e133	−0.143283	−0.0716413	−	0.997430i	$-0.522824\pi$
$887$	−1.93517e133	−0.143283	−0.0716413	+	0.997430i	$0.522824\pi$
$888$	9.72425e133	0.684016
$889$	4.94623e133	0.330555
$890$	6.81994e133	0.433047
$891$	−6.04538e133	−0.364744
$892$	6.27726e133	0.359890
$893$	−4.32162e134	−2.35454
$894$	−6.70809e133	−0.347330
$895$	2.36289e134	1.16277
$896$	2.15025e134	1.00572
$897$	−3.92844e132	−0.0174648
$898$	8.36813e133	0.353635
$899$	−6.65325e133	−0.267281
$900$	−1.63391e133	−0.0624013
$901$	−2.03707e134	−0.739653
$902$	−5.84280e133	−0.201708
$903$	1.87756e134	0.616314
$904$	3.93179e134	1.22723
$905$	3.78648e132	0.0112389
$906$	−1.82284e133	−0.0514536
$907$	1.61412e134	0.433315	0.216657	−	0.976248i	$-0.430485\pi$
$907$	1.61412e134	0.433315	0.216657	+	0.976248i	$0.430485\pi$
$908$	−5.45189e134	−1.39201
$909$	1.55353e134	0.377280
$910$	2.10068e134	0.485262
$911$	7.78212e134	1.71006	0.855031	−	0.518577i	$-0.173538\pi$
$911$	7.78212e134	1.71006	0.855031	+	0.518577i	$0.173538\pi$
$912$	3.30354e134	0.690580
$913$	−1.02239e134	−0.203328
$914$	−2.92926e134	−0.554251
$915$	−2.16188e134	−0.389199
$916$	−8.73776e134	−1.49677
$917$	−3.40651e134	−0.555270
$918$	−1.82065e134	−0.282413
$919$	−3.53568e134	−0.521936	−0.260968	−	0.965348i	$-0.584042\pi$
$919$	−3.53568e134	−0.521936	−0.260968	+	0.965348i	$0.584042\pi$
$920$	5.99732e132	0.00842580
$921$	−5.20167e134	−0.695552
$922$	−2.94267e134	−0.374528
$923$	2.35503e135	2.85312
$924$	−3.01021e134	−0.347154
$925$	−3.41717e134	−0.375161
$926$	−7.21842e134	−0.754470
$927$	−4.90711e133	−0.0488313
$928$	5.14672e134	0.487638
$929$	−8.34216e134	−0.752598	−0.376299	−	0.926498i	$-0.622804\pi$
$929$	−8.34216e134	−0.752598	−0.376299	+	0.926498i	$0.622804\pi$
$930$	1.92627e134	0.165479
$931$	7.69823e132	0.00629768
$932$	3.17102e134	0.247045
$933$	1.33170e134	0.0988076
$934$	2.20690e134	0.155956
$935$	−3.37707e134	−0.227306
$936$	−3.49128e134	−0.223838
$937$	1.32445e135	0.808879	0.404440	−	0.914565i	$-0.367467\pi$
$937$	1.32445e135	0.808879	0.404440	+	0.914565i	$0.367467\pi$
$938$	1.34675e135	0.783533
$939$	1.65657e135	0.918175
$940$	−1.72224e135	−0.909445
$941$	1.55640e135	0.783055	0.391527	−	0.920166i	$-0.371947\pi$
$941$	1.55640e135	0.783055	0.391527	+	0.920166i	$0.371947\pi$
$942$	3.87399e134	0.185713
$943$	2.89779e133	0.0132368
$944$	1.56461e135	0.681052
$945$	−2.02269e135	−0.839039
$946$	3.63461e134	0.143685
$947$	9.44560e134	0.355882	0.177941	−	0.984041i	$-0.443056\pi$
$947$	9.44560e134	0.355882	0.177941	+	0.984041i	$0.443056\pi$
$948$	−7.26835e133	−0.0261010
$949$	−6.91365e135	−2.36644
$950$	8.46540e134	0.276200
$951$	−1.86029e135	−0.578584
$952$	−1.60449e135	−0.475725
$953$	−2.31734e135	−0.655034	−0.327517	−	0.944845i	$-0.606212\pi$
$953$	−2.31734e135	−0.655034	−0.327517	+	0.944845i	$0.606212\pi$
$954$	−3.92224e134	−0.105702
$955$	1.02336e135	0.262952
$956$	4.26610e134	0.104519
$957$	−9.03237e134	−0.211013
$958$	3.11645e135	0.694273
$959$	4.37471e135	0.929400
$960$	1.32956e134	0.0269381
$961$	−3.64834e135	−0.704987
$962$	−3.27014e135	−0.602700
$963$	−2.42648e134	−0.0426561
$964$	3.87545e135	0.649855
$965$	3.86963e135	0.618980
$966$	−3.47616e133	−0.00530445
$967$	1.00807e136	1.46752	0.733761	−	0.679408i	$-0.237763\pi$
$967$	1.00807e136	1.46752	0.733761	+	0.679408i	$0.237763\pi$
$968$	4.36590e135	0.606380
$969$	−6.72767e135	−0.891523
$970$	−3.02737e133	−0.00382782
$971$	4.71062e135	0.568333	0.284167	−	0.958775i	$-0.408283\pi$
$971$	4.71062e135	0.568333	0.284167	+	0.958775i	$0.408283\pi$
$972$	2.76110e135	0.317883
$973$	−5.93808e135	−0.652397
$974$	−7.14892e134	−0.0749563
$975$	−4.93418e135	−0.493747
$976$	2.72668e135	0.260416
$977$	−1.18195e136	−1.07745	−0.538725	−	0.842482i	$-0.681094\pi$
$977$	−1.18195e136	−1.07745	−0.538725	+	0.842482i	$0.681094\pi$
$978$	−5.33862e135	−0.464527
$979$	7.33815e135	0.609501
$980$	3.06788e133	0.00243249
$981$	−2.40346e135	−0.181927
$982$	8.91985e135	0.644592
$983$	8.99384e135	0.620526	0.310263	−	0.950651i	$-0.399583\pi$
$983$	8.99384e135	0.620526	0.310263	+	0.950651i	$0.399583\pi$
$984$	−1.03574e136	−0.682297
$985$	−7.52295e135	−0.473195
$986$	−2.15618e135	−0.129504
$987$	2.22891e136	1.27839
$988$	−3.47929e136	−1.90568
$989$	−1.80262e134	−0.00942914
$990$	−6.50230e134	−0.0324837
$991$	−2.37259e136	−1.13207	−0.566033	−	0.824383i	$-0.691523\pi$
$991$	−2.37259e136	−1.13207	−0.566033	+	0.824383i	$0.691523\pi$
$992$	−1.18101e136	−0.538234
$993$	1.27187e136	0.553669
$994$	2.08390e136	0.866555
$995$	3.95005e135	0.156911
$996$	−8.11690e135	−0.308028
$997$	1.76376e136	0.639453	0.319727	−	0.947510i	$-0.396409\pi$
$997$	1.76376e136	0.639453	0.319727	+	0.947510i	$0.396409\pi$
$998$	−5.59867e135	−0.193930
$999$	3.14874e136	1.04209

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.92.a.a.1.5	✓	7
3.2	odd	2		9.92.a.b.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.92.a.a.1.5	✓	7	1.1	even	1	trivial
9.92.a.b.1.3		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)

\(f(q)\)	\(=\)	\(q+2.16242e13 q^{2} -4.57928e21 q^{3} -2.00827e27 q^{4} +4.97855e31 q^{5} -9.90233e34 q^{6} -2.82571e38 q^{7} -9.69662e40 q^{8} -5.21406e42 q^{9} +O(q^{10})\)	\(q+2.16242e13 q^{2} -4.57928e21 q^{3} -2.00827e27 q^{4} +4.97855e31 q^{5} -9.90233e34 q^{6} -2.82571e38 q^{7} -9.69662e40 q^{8} -5.21406e42 q^{9} +1.07657e45 q^{10} +1.15837e47 q^{11} +9.19646e48 q^{12} -6.90540e50 q^{13} -6.11037e51 q^{14} -2.27982e53 q^{15} +2.87543e54 q^{16} -5.85583e55 q^{17} -1.12750e56 q^{18} -2.50887e58 q^{19} -9.99829e58 q^{20} +1.29397e60 q^{21} +2.50489e60 q^{22} -1.24232e60 q^{23} +4.44036e62 q^{24} -1.56037e63 q^{25} -1.49324e64 q^{26} +1.43780e65 q^{27} +5.67481e65 q^{28} +1.70277e66 q^{29} -4.92992e66 q^{30} -3.90731e67 q^{31} +3.02256e68 q^{32} -5.30452e68 q^{33} -1.26628e69 q^{34} -1.40679e70 q^{35} +1.04713e70 q^{36} +2.18997e71 q^{37} -5.42524e71 q^{38} +3.16218e72 q^{39} -4.82751e72 q^{40} -2.33256e73 q^{41} +2.79811e73 q^{42} +1.45101e74 q^{43} -2.32633e74 q^{44} -2.59584e74 q^{45} -2.68642e73 q^{46} +1.72253e76 q^{47} -1.31674e76 q^{48} -3.06840e74 q^{49} -3.37418e76 q^{50} +2.68155e77 q^{51} +1.38679e78 q^{52} +3.47871e78 q^{53} +3.10913e78 q^{54} +5.76702e78 q^{55} +2.73999e79 q^{56} +1.14888e80 q^{57} +3.68210e79 q^{58} +5.44131e80 q^{59} +4.57850e80 q^{60} +9.48268e80 q^{61} -8.44924e80 q^{62} +1.47334e81 q^{63} -5.83187e80 q^{64} -3.43789e82 q^{65} -1.14706e82 q^{66} -2.20404e83 q^{67} +1.17601e83 q^{68} +5.68895e81 q^{69} -3.04208e83 q^{70} -3.41043e84 q^{71} +5.05588e83 q^{72} +1.00119e85 q^{73} +4.73563e84 q^{74} +7.14539e84 q^{75} +5.03851e85 q^{76} -3.27323e85 q^{77} +6.83795e85 q^{78} -7.90343e84 q^{79} +1.43155e86 q^{80} -5.21885e86 q^{81} -5.04397e86 q^{82} -8.82611e86 q^{83} -2.59865e87 q^{84} -2.91535e87 q^{85} +3.13768e87 q^{86} -7.79746e87 q^{87} -1.12323e88 q^{88} +6.33488e88 q^{89} -5.61330e87 q^{90} +1.95127e89 q^{91} +2.49492e87 q^{92} +1.78927e89 q^{93} +3.72484e89 q^{94} -1.24905e90 q^{95} -1.38411e90 q^{96} -2.81205e88 q^{97} -6.63517e87 q^{98} -6.03983e89 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 3841716838056 q^{2} + 62\!\cdots\!32 q^{3}+ \cdots + 38\!\cdots\!59 q^{9}+O(q^{10}) \) 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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