LMFDB - Embedded newform 1.92.a.a.1.4

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			1.4
Root			$3.73440e11$ 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)

$f(q)$	$=$	$q+9.51137e12 q^{2} +5.28795e21 q^{3} -2.38541e27 q^{4} -1.05575e32 q^{5} +5.02957e34 q^{6} -1.59557e38 q^{7} -4.62376e40 q^{8} +1.77856e42 q^{9} +O(q^{10})$	\(q+9.51137e12 q^{2} +5.28795e21 q^{3} -2.38541e27 q^{4} -1.05575e32 q^{5} +5.02957e34 q^{6} -1.59557e38 q^{7} -4.62376e40 q^{8} +1.77856e42 q^{9} -1.00417e45 q^{10} -4.48983e47 q^{11} -1.26140e49 q^{12} +5.36517e49 q^{13} -1.51760e51 q^{14} -5.58277e53 q^{15} +5.46622e54 q^{16} +1.62103e56 q^{17} +1.69166e55 q^{18} +6.01996e57 q^{19} +2.51841e59 q^{20} -8.43728e59 q^{21} -4.27045e60 q^{22} -6.17236e61 q^{23} -2.44502e62 q^{24} +7.10717e63 q^{25} +5.10302e62 q^{26} -1.29054e65 q^{27} +3.80608e65 q^{28} +1.16770e66 q^{29} -5.30998e66 q^{30} +5.07732e67 q^{31} +1.66470e68 q^{32} -2.37420e69 q^{33} +1.54182e69 q^{34} +1.68452e70 q^{35} -4.24260e69 q^{36} -1.37511e71 q^{37} +5.72581e70 q^{38} +2.83708e71 q^{39} +4.88154e72 q^{40} -5.73229e72 q^{41} -8.02501e72 q^{42} -2.86408e74 q^{43} +1.07101e75 q^{44} -1.87772e74 q^{45} -5.87077e74 q^{46} -1.58900e75 q^{47} +2.89051e76 q^{48} -5.46951e76 q^{49} +6.75989e76 q^{50} +8.57194e77 q^{51} -1.27982e77 q^{52} +1.36032e78 q^{53} -1.22748e78 q^{54} +4.74015e79 q^{55} +7.37751e78 q^{56} +3.18333e79 q^{57} +1.11065e79 q^{58} +5.82820e80 q^{59} +1.33172e81 q^{60} -5.21921e80 q^{61} +4.82923e80 q^{62} -2.83781e80 q^{63} -1.19503e82 q^{64} -5.66430e81 q^{65} -2.25819e82 q^{66} -2.56121e82 q^{67} -3.86683e83 q^{68} -3.26392e83 q^{69} +1.60221e83 q^{70} -2.34247e83 q^{71} -8.22363e82 q^{72} +2.47038e84 q^{73} -1.30792e84 q^{74} +3.75824e85 q^{75} -1.43601e85 q^{76} +7.16382e85 q^{77} +2.69845e84 q^{78} +2.98446e86 q^{79} -5.77097e86 q^{80} -7.29002e86 q^{81} -5.45219e85 q^{82} +9.13354e86 q^{83} +2.01264e87 q^{84} -1.71141e88 q^{85} -2.72413e87 q^{86} +6.17476e87 q^{87} +2.07599e88 q^{88} +5.81468e88 q^{89} -1.78597e87 q^{90} -8.56049e87 q^{91} +1.47236e89 q^{92} +2.68486e89 q^{93} -1.51136e88 q^{94} -6.35559e89 q^{95} +8.80285e89 q^{96} -3.70488e90 q^{97} -5.20225e89 q^{98} -7.98544e89 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	9.51137e12	0.191152	0.0955759	−	0.995422i	$-0.469531\pi$
$2$	9.51137e12	0.191152	0.0955759	+	0.995422i	$0.469531\pi$
$3$	5.28795e21	1.03340	0.516702	−	0.856165i	$-0.327159\pi$
$3$	5.28795e21	1.03340	0.516702	+	0.856165i	$0.327159\pi$
$4$	−2.38541e27	−0.963461
$5$	−1.05575e32	−1.66122	−0.830610	−	0.556855i	$-0.812008\pi$
$5$	−1.05575e32	−1.66122	−0.830610	+	0.556855i	$0.812008\pi$
$6$	5.02957e34	0.197537
$7$	−1.59557e38	−0.563578	−0.281789	−	0.959476i	$-0.590928\pi$
$7$	−1.59557e38	−0.563578	−0.281789	+	0.959476i	$0.590928\pi$
$8$	−4.62376e40	−0.375319
$9$	1.77856e42	0.0679257
$10$	−1.00417e45	−0.317545
$11$	−4.48983e47	−1.85722	−0.928609	−	0.371059i	$-0.878995\pi$
$11$	−4.48983e47	−1.85722	−0.928609	+	0.371059i	$0.878995\pi$
$12$	−1.26140e49	−0.995645
$13$	5.36517e49	0.110959	0.0554793	−	0.998460i	$-0.482331\pi$
$13$	5.36517e49	0.110959	0.0554793	+	0.998460i	$0.482331\pi$
$14$	−1.51760e51	−0.107729
$15$	−5.58277e53	−1.71671
$16$	5.46622e54	0.891718
$17$	1.62103e56	1.67635	0.838177	−	0.545399i	$-0.183622\pi$
$17$	1.62103e56	1.67635	0.838177	+	0.545399i	$0.183622\pi$
$18$	1.69166e55	0.0129841
$19$	6.01996e57	0.394734	0.197367	−	0.980330i	$-0.436761\pi$
$19$	6.01996e57	0.394734	0.197367	+	0.980330i	$0.436761\pi$
$20$	2.51841e59	1.60052
$21$	−8.43728e59	−0.582404
$22$	−4.27045e60	−0.355011
$23$	−6.17236e61	−0.678946	−0.339473	−	0.940616i	$-0.610249\pi$
$23$	−6.17236e61	−0.678946	−0.339473	+	0.940616i	$0.610249\pi$
$24$	−2.44502e62	−0.387857
$25$	7.10717e63	1.75965
$26$	5.10302e62	0.0212100
$27$	−1.29054e65	−0.963210
$28$	3.80608e65	0.542985
$29$	1.16770e66	0.337461	0.168731	−	0.985662i	$-0.446033\pi$
$29$	1.16770e66	0.337461	0.168731	+	0.985662i	$0.446033\pi$
$30$	−5.30998e66	−0.328153
$31$	5.07732e67	0.705793	0.352897	−	0.935662i	$-0.385197\pi$
$31$	5.07732e67	0.705793	0.352897	+	0.935662i	$0.385197\pi$
$32$	1.66470e68	0.545773
$33$	−2.37420e69	−1.91926
$34$	1.54182e69	0.320438
$35$	1.68452e70	0.936226
$36$	−4.24260e69	−0.0654438
$37$	−1.37511e71	−0.609760	−0.304880	−	0.952391i	$-0.598616\pi$
$37$	−1.37511e71	−0.609760	−0.304880	+	0.952391i	$0.598616\pi$
$38$	5.72581e70	0.0754542
$39$	2.83708e71	0.114665
$40$	4.88154e72	0.623487
$41$	−5.73229e72	−0.238047	−0.119023	−	0.992891i	$-0.537976\pi$
$41$	−5.73229e72	−0.238047	−0.119023	+	0.992891i	$0.537976\pi$
$42$	−8.02501e72	−0.111328
$43$	−2.86408e74	−1.36198	−0.680989	−	0.732294i	$-0.738450\pi$
$43$	−2.86408e74	−1.36198	−0.680989	+	0.732294i	$0.738450\pi$
$44$	1.07101e75	1.78936
$45$	−1.87772e74	−0.112840
$46$	−5.87077e74	−0.129782
$47$	−1.58900e75	−0.132030	−0.0660148	−	0.997819i	$-0.521028\pi$
$47$	−1.58900e75	−0.132030	−0.0660148	+	0.997819i	$0.521028\pi$
$48$	2.89051e76	0.921506
$49$	−5.46951e76	−0.682380
$50$	6.75989e76	0.336360
$51$	8.57194e77	1.73235
$52$	−1.27982e77	−0.106904
$53$	1.36032e78	0.477626	0.238813	−	0.971066i	$-0.423242\pi$
$53$	1.36032e78	0.477626	0.238813	+	0.971066i	$0.423242\pi$
$54$	−1.22748e78	−0.184119
$55$	4.74015e79	3.08525
$56$	7.37751e78	0.211521
$57$	3.18333e79	0.407920
$58$	1.11065e79	0.0645063
$59$	5.82820e80	1.55513	0.777567	−	0.628800i	$-0.216453\pi$
$59$	5.82820e80	1.55513	0.777567	+	0.628800i	$0.216453\pi$
$60$	1.33172e81	1.65399
$61$	−5.21921e80	−0.305560	−0.152780	−	0.988260i	$-0.548823\pi$
$61$	−5.21921e80	−0.305560	−0.152780	+	0.988260i	$0.548823\pi$
$62$	4.82923e80	0.134914
$63$	−2.83781e80	−0.0382814
$64$	−1.19503e82	−0.787393
$65$	−5.66430e81	−0.184327
$66$	−2.25819e82	−0.366870
$67$	−2.56121e82	−0.209914	−0.104957	−	0.994477i	$-0.533470\pi$
$67$	−2.56121e82	−0.209914	−0.104957	+	0.994477i	$0.533470\pi$
$68$	−3.86683e83	−1.61510
$69$	−3.26392e83	−0.701626
$70$	1.60221e83	0.178961
$71$	−2.34247e83	−0.137221	−0.0686104	−	0.997644i	$-0.521857\pi$
$71$	−2.34247e83	−0.137221	−0.0686104	+	0.997644i	$0.521857\pi$
$72$	−8.22363e82	−0.0254938
$73$	2.47038e84	0.408859	0.204429	−	0.978881i	$-0.434466\pi$
$73$	2.47038e84	0.408859	0.204429	+	0.978881i	$0.434466\pi$
$74$	−1.30792e84	−0.116557
$75$	3.75824e85	1.81843
$76$	−1.43601e85	−0.380311
$77$	7.16382e85	1.04669
$78$	2.69845e84	0.0219185
$79$	2.98446e86	1.35779	0.678895	−	0.734235i	$-0.262459\pi$
$79$	2.98446e86	1.35779	0.678895	+	0.734235i	$0.262459\pi$
$80$	−5.77097e86	−1.48134
$81$	−7.29002e86	−1.06331
$82$	−5.45219e85	−0.0455031
$83$	9.13354e86	0.439123	0.219561	−	0.975599i	$-0.429537\pi$
$83$	9.13354e86	0.439123	0.219561	+	0.975599i	$0.429537\pi$
$84$	2.01264e87	0.561123
$85$	−1.71141e88	−2.78479
$86$	−2.72413e87	−0.260345
$87$	6.17476e87	0.348734
$88$	2.07599e88	0.697050
$89$	5.81468e88	1.16756	0.583781	−	0.811911i	$-0.301573\pi$
$89$	5.81468e88	1.16756	0.583781	+	0.811911i	$0.301573\pi$
$90$	−1.78597e87	−0.0215695
$91$	−8.56049e87	−0.0625338
$92$	1.47236e89	0.654138
$93$	2.68486e89	0.729370
$94$	−1.51136e88	−0.0252377
$95$	−6.35559e89	−0.655740
$96$	8.80285e89	0.564004
$97$	−3.70488e90	−1.48136	−0.740680	−	0.671858i	$-0.765496\pi$
$97$	−3.70488e90	−1.48136	−0.740680	+	0.671858i	$0.765496\pi$
$98$	−5.20225e89	−0.130438
$99$	−7.98544e89	−0.126153
$100$	−1.69535e91	−1.69535
$101$	2.12341e91	1.35024	0.675119	−	0.737709i	$-0.264092\pi$
$101$	2.12341e91	1.35024	0.675119	+	0.737709i	$0.264092\pi$
$102$	8.15309e90	0.331142
$103$	−1.42659e91	−0.371710	−0.185855	−	0.982577i	$-0.559506\pi$
$103$	−1.42659e91	−0.371710	−0.185855	+	0.982577i	$0.559506\pi$
$104$	−2.48073e90	−0.0416449
$105$	8.90768e91	0.967501
$106$	1.29385e91	0.0912990
$107$	2.01851e92	0.929114	0.464557	−	0.885543i	$-0.346214\pi$
$107$	2.01851e92	0.929114	0.464557	+	0.885543i	$0.346214\pi$
$108$	3.07848e92	0.928015
$109$	−7.38378e92	−1.46343	−0.731717	−	0.681609i	$-0.761281\pi$
$109$	−7.38378e92	−1.46343	−0.731717	+	0.681609i	$0.761281\pi$
$110$	4.50854e92	0.589751
$111$	−7.27151e92	−0.630129
$112$	−8.72170e92	−0.502552
$113$	−4.08204e93	−1.56967	−0.784834	−	0.619706i	$-0.787252\pi$
$113$	−4.08204e93	−1.56967	−0.784834	+	0.619706i	$0.787252\pi$
$114$	3.02778e92	0.0779747
$115$	6.51649e93	1.12788
$116$	−2.78546e93	−0.325131
$117$	9.54229e91	0.00753695
$118$	5.54342e93	0.297267
$119$	−2.58646e94	−0.944755
$120$	2.58134e94	0.644315
$121$	1.43143e95	2.44926
$122$	−4.96418e93	−0.0584084
$123$	−3.03121e94	−0.245999
$124$	−1.21115e95	−0.680004
$125$	−3.23926e95	−1.26194
$126$	−2.69915e93	−0.00731757
$127$	6.67436e95	1.26282	0.631408	−	0.775451i	$-0.282477\pi$
$127$	6.67436e95	1.26282	0.631408	+	0.775451i	$0.282477\pi$
$128$	−5.25824e95	−0.696284
$129$	−1.51451e96	−1.40747
$130$	−5.38752e94	−0.0352344
$131$	−1.50938e96	−0.696552	−0.348276	−	0.937392i	$-0.613233\pi$
$131$	−1.50938e96	−0.696552	−0.348276	+	0.937392i	$0.613233\pi$
$132$	5.66346e96	1.84913
$133$	−9.60524e95	−0.222464
$134$	−2.43606e95	−0.0401254
$135$	1.36249e97	1.60010
$136$	−7.49526e96	−0.629167
$137$	1.46199e97	0.879345	0.439672	−	0.898158i	$-0.355095\pi$
$137$	1.46199e97	0.879345	0.439672	+	0.898158i	$0.355095\pi$
$138$	−3.10443e96	−0.134117
$139$	−1.46671e97	−0.456216	−0.228108	−	0.973636i	$-0.573254\pi$
$139$	−1.46671e97	−0.456216	−0.228108	+	0.973636i	$0.573254\pi$
$140$	−4.01828e97	−0.902017
$141$	−8.40256e96	−0.136440
$142$	−2.22801e96	−0.0262300
$143$	−2.40887e97	−0.206075
$144$	9.72199e96	0.0605706
$145$	−1.23281e98	−0.560597
$146$	2.34967e97	0.0781541
$147$	−2.89225e98	−0.705175
$148$	3.28020e98	0.587480
$149$	9.47367e98	1.24894	0.624472	−	0.781047i	$-0.285314\pi$
$149$	9.47367e98	1.24894	0.624472	+	0.781047i	$0.285314\pi$
$150$	3.57460e98	0.347596
$151$	7.76649e98	0.558179	0.279090	−	0.960265i	$-0.409967\pi$
$151$	7.76649e98	0.558179	0.279090	+	0.960265i	$0.409967\pi$
$152$	−2.78349e98	−0.148151
$153$	2.88310e98	0.113868
$154$	6.81378e98	0.200076
$155$	−5.36039e99	−1.17248
$156$	−6.76761e98	−0.110475
$157$	−7.56834e99	−0.923776	−0.461888	−	0.886938i	$-0.652828\pi$
$157$	−7.56834e99	−0.923776	−0.461888	+	0.886938i	$0.652828\pi$
$158$	2.83863e99	0.259544
$159$	7.19329e99	0.493581
$160$	−1.75751e100	−0.906648
$161$	9.84841e99	0.382639
$162$	−6.93382e99	−0.203254
$163$	−3.83231e100	−0.849033	−0.424517	−	0.905420i	$-0.639556\pi$
$163$	−3.83231e100	−0.849033	−0.424517	+	0.905420i	$0.639556\pi$
$164$	1.36739e100	0.229349
$165$	2.50657e101	3.18831
$166$	8.68725e99	0.0839391
$167$	−1.07085e101	−0.787283	−0.393641	−	0.919264i	$-0.628785\pi$
$167$	−1.07085e101	−0.787283	−0.393641	+	0.919264i	$0.628785\pi$
$168$	3.90119e100	0.218587
$169$	−2.30922e101	−0.987688
$170$	−1.62778e101	−0.532318
$171$	1.07069e100	0.0268126
$172$	6.83201e101	1.31221
$173$	−6.76650e101	−0.998313	−0.499156	−	0.866512i	$-0.666357\pi$
$173$	−6.76650e101	−0.998313	−0.499156	+	0.866512i	$0.666357\pi$
$174$	5.87305e100	0.0666611
$175$	−1.13400e102	−0.991699
$176$	−2.45424e102	−1.65612
$177$	3.08193e102	1.60708
$178$	5.53056e101	0.223182
$179$	8.18800e101	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$179$	8.18800e101	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$180$	4.47914e101	0.108717
$181$	6.50193e102	1.22650	0.613249	−	0.789889i	$-0.289862\pi$
$181$	6.50193e102	1.22650	0.613249	+	0.789889i	$0.289862\pi$
$182$	−8.14220e100	−0.0119535
$183$	−2.75989e102	−0.315768
$184$	2.85395e102	0.254821
$185$	1.45178e103	1.01294
$186$	2.55367e102	0.139420
$187$	−7.27816e103	−3.11335
$188$	3.79042e102	0.127205
$189$	2.05914e103	0.542844
$190$	−6.04504e102	−0.125346
$191$	3.02296e103	0.493645	0.246822	−	0.969061i	$-0.420614\pi$
$191$	3.02296e103	0.493645	0.246822	+	0.969061i	$0.420614\pi$
$192$	−6.31928e103	−0.813695
$193$	2.17835e103	0.221447	0.110724	−	0.993851i	$-0.464683\pi$
$193$	2.17835e103	0.221447	0.110724	+	0.993851i	$0.464683\pi$
$194$	−3.52385e103	−0.283165
$195$	−2.99525e103	−0.190484
$196$	1.30470e104	0.657447
$197$	2.79811e104	1.11854	0.559270	−	0.828985i	$-0.311081\pi$
$197$	2.79811e104	1.11854	0.559270	+	0.828985i	$0.311081\pi$
$198$	−7.59525e102	−0.0241144
$199$	4.16283e104	1.05093	0.525465	−	0.850815i	$-0.323891\pi$
$199$	4.16283e104	1.05093	0.525465	+	0.850815i	$0.323891\pi$
$200$	−3.28618e104	−0.660430
$201$	−1.35435e104	−0.216926
$202$	2.01965e104	0.258100
$203$	−1.86315e104	−0.190186
$204$	−2.04476e105	−1.66905
$205$	6.05188e104	0.395448
$206$	−1.35688e104	−0.0710531
$207$	−1.09779e104	−0.0461179
$208$	2.93272e104	0.0989439
$209$	−2.70286e105	−0.733108
$210$	8.47242e104	0.184940
$211$	4.44287e105	0.781289	0.390645	−	0.920542i	$-0.372252\pi$
$211$	4.44287e105	0.781289	0.390645	+	0.920542i	$0.372252\pi$
$212$	−3.24492e105	−0.460174
$213$	−1.23869e105	−0.141805
$214$	1.91988e105	0.177602
$215$	3.02376e106	2.26254
$216$	5.96716e105	0.361511
$217$	−8.10120e105	−0.397769
$218$	−7.02299e105	−0.279738
$219$	1.30632e106	0.422517
$220$	−1.13072e107	−2.97252
$221$	8.69712e105	0.186006
$222$	−6.91621e105	−0.120450
$223$	8.71097e106	1.23650	0.618251	−	0.785980i	$-0.287841\pi$
$223$	8.71097e106	1.23650	0.618251	+	0.785980i	$0.287841\pi$
$224$	−2.65614e106	−0.307585
$225$	1.26405e106	0.119526
$226$	−3.88258e106	−0.300045
$227$	−1.43742e107	−0.908672	−0.454336	−	0.890830i	$-0.650123\pi$
$227$	−1.43742e107	−0.908672	−0.454336	+	0.890830i	$0.650123\pi$
$228$	−7.59356e106	−0.393015
$229$	3.29883e107	1.39909	0.699545	−	0.714588i	$-0.253386\pi$
$229$	3.29883e107	1.39909	0.699545	+	0.714588i	$0.253386\pi$
$230$	6.19808e106	0.215596
$231$	3.78820e107	1.08165
$232$	−5.39918e106	−0.126656
$233$	7.27050e106	0.140239	0.0701196	−	0.997539i	$-0.477662\pi$
$233$	7.27050e106	0.140239	0.0701196	+	0.997539i	$0.477662\pi$
$234$	9.07603e104	0.00144070
$235$	1.67759e107	0.219330
$236$	−1.39027e108	−1.49831
$237$	1.57817e108	1.40315
$238$	−2.46008e107	−0.180592
$239$	−8.01532e107	−0.486201	−0.243101	−	0.970001i	$-0.578165\pi$
$239$	−8.01532e107	−0.486201	−0.243101	+	0.970001i	$0.578165\pi$
$240$	−3.05166e108	−1.53082
$241$	−1.37954e108	−0.572742	−0.286371	−	0.958119i	$-0.592449\pi$
$241$	−1.37954e108	−0.572742	−0.286371	+	0.958119i	$0.592449\pi$
$242$	1.36148e108	0.468181
$243$	−4.75789e107	−0.135622
$244$	1.24500e108	0.294396
$245$	5.77444e108	1.13358
$246$	−2.88309e107	−0.0470231
$247$	3.22982e107	0.0437992
$248$	−2.34763e108	−0.264898
$249$	4.82977e108	0.453791
$250$	−3.08098e108	−0.241223
$251$	1.21352e109	0.792304	0.396152	−	0.918185i	$-0.370345\pi$
$251$	1.21352e109	0.792304	0.396152	+	0.918185i	$0.370345\pi$
$252$	6.76935e107	0.0368827
$253$	2.77129e109	1.26095
$254$	6.34823e108	0.241390
$255$	−9.04985e109	−2.87782
$256$	2.45863e109	0.654297
$257$	−5.62677e109	−1.25401	−0.627007	−	0.779014i	$-0.715720\pi$
$257$	−5.62677e109	−1.25401	−0.627007	+	0.779014i	$0.715720\pi$
$258$	−1.44051e109	−0.269041
$259$	2.19408e109	0.343647
$260$	1.35117e109	0.177592
$261$	2.07683e108	0.0229223
$262$	−1.43562e109	−0.133147
$263$	9.22254e109	0.719223	0.359612	−	0.933102i	$-0.382909\pi$
$263$	9.22254e109	0.719223	0.359612	+	0.933102i	$0.382909\pi$
$264$	1.09777e110	0.720335
$265$	−1.43616e110	−0.793441
$266$	−9.13591e108	−0.0425243
$267$	3.07477e110	1.20656
$268$	6.10953e109	0.202244
$269$	−3.66507e110	−1.02413	−0.512063	−	0.858948i	$-0.671118\pi$
$269$	−3.66507e110	−1.02413	−0.512063	+	0.858948i	$0.671118\pi$
$270$	1.29592e110	0.305863
$271$	−3.25808e109	−0.0649918	−0.0324959	−	0.999472i	$-0.510346\pi$
$271$	−3.25808e109	−0.0649918	−0.0324959	+	0.999472i	$0.510346\pi$
$272$	8.86091e110	1.49483
$273$	−4.52675e109	−0.0646228
$274$	1.39056e110	0.168088
$275$	−3.19100e111	−3.26805
$276$	7.78579e110	0.675989
$277$	−9.26757e110	−0.682553	−0.341276	−	0.939963i	$-0.610859\pi$
$277$	−9.26757e110	−0.682553	−0.341276	+	0.939963i	$0.610859\pi$
$278$	−1.39504e110	−0.0872065
$279$	9.03032e109	0.0479415
$280$	−7.78882e110	−0.351384
$281$	4.40559e111	1.68992	0.844961	−	0.534828i	$-0.179623\pi$
$281$	4.40559e111	1.68992	0.844961	+	0.534828i	$0.179623\pi$
$282$	−7.99199e109	−0.0260808
$283$	2.80637e111	0.779583	0.389791	−	0.920903i	$-0.372547\pi$
$283$	2.80637e111	0.779583	0.389791	+	0.920903i	$0.372547\pi$
$284$	5.58777e110	0.132207
$285$	−3.36081e111	−0.677645
$286$	−2.29117e110	−0.0393915
$287$	9.14624e110	0.134158
$288$	2.96077e110	0.0370720
$289$	1.69266e112	1.81016
$290$	−1.17257e111	−0.107159
$291$	−1.95912e112	−1.53084
$292$	−5.89287e111	−0.393919
$293$	8.27638e111	0.473548	0.236774	−	0.971565i	$-0.423910\pi$
$293$	8.27638e111	0.473548	0.236774	+	0.971565i	$0.423910\pi$
$294$	−2.75093e111	−0.134796
$295$	−6.15314e112	−2.58342
$296$	6.35817e111	0.228855
$297$	5.79432e112	1.78889
$298$	9.01076e111	0.238738
$299$	−3.31158e111	−0.0753349
$300$	−8.96495e112	−1.75199
$301$	4.56982e112	0.767580
$302$	7.38700e111	0.106697
$303$	1.12285e113	1.39534
$304$	3.29064e112	0.351992
$305$	5.51019e112	0.507603
$306$	2.74223e111	0.0217660
$307$	3.48052e112	0.238149	0.119074	−	0.992885i	$-0.462007\pi$
$307$	3.48052e112	0.238149	0.119074	+	0.992885i	$0.462007\pi$
$308$	−1.70887e113	−1.00844
$309$	−7.54373e112	−0.384127
$310$	−5.09847e112	−0.224121
$311$	−3.24712e112	−0.123282	−0.0616411	−	0.998098i	$-0.519633\pi$
$311$	−3.24712e112	−0.123282	−0.0616411	+	0.998098i	$0.519633\pi$
$312$	−1.31180e112	−0.0430361
$313$	2.87678e113	0.815904	0.407952	−	0.913003i	$-0.366243\pi$
$313$	2.87678e113	0.815904	0.407952	+	0.913003i	$0.366243\pi$
$314$	−7.19854e112	−0.176581
$315$	2.99602e112	0.0635939
$316$	−7.11916e113	−1.30818
$317$	−6.39563e113	−1.01786	−0.508929	−	0.860809i	$-0.669958\pi$
$317$	−6.39563e113	−1.01786	−0.508929	+	0.860809i	$0.669958\pi$
$318$	6.84180e112	0.0943489
$319$	−5.24279e113	−0.626739
$320$	1.26166e114	1.30803
$321$	1.06738e114	0.960151
$322$	9.36719e112	0.0731421
$323$	9.75855e113	0.661714
$324$	1.73897e114	1.02446
$325$	3.81312e113	0.195248
$326$	−3.64505e113	−0.162294
$327$	−3.90451e114	−1.51232
$328$	2.65047e113	0.0893436
$329$	2.53535e113	0.0744089
$330$	2.38409e114	0.609451
$331$	−4.49806e114	−1.00196	−0.500982	−	0.865458i	$-0.667028\pi$
$331$	−4.49806e114	−1.00196	−0.500982	+	0.865458i	$0.667028\pi$
$332$	−2.17873e114	−0.423077
$333$	−2.44571e113	−0.0414184
$334$	−1.01853e114	−0.150491
$335$	2.70400e114	0.348713
$336$	−4.61200e114	−0.519340
$337$	3.86408e114	0.380089	0.190044	−	0.981775i	$-0.439137\pi$
$337$	3.86408e114	0.380089	0.190044	+	0.981775i	$0.439137\pi$
$338$	−2.19638e114	−0.188798
$339$	−2.15856e115	−1.62210
$340$	4.08242e115	2.68304
$341$	−2.27963e115	−1.31081
$342$	1.01837e113	0.00512528
$343$	2.15159e115	0.948152
$344$	1.32428e115	0.511176
$345$	3.44589e115	1.16555
$346$	−6.43587e114	−0.190829
$347$	1.45516e115	0.378374	0.189187	−	0.981941i	$-0.439415\pi$
$347$	1.45516e115	0.378374	0.189187	+	0.981941i	$0.439415\pi$
$348$	−1.47294e115	−0.335992
$349$	−7.71153e115	−1.54377	−0.771886	−	0.635760i	$-0.780687\pi$
$349$	−7.71153e115	−1.54377	−0.771886	+	0.635760i	$0.780687\pi$
$350$	−1.07859e115	−0.189565
$351$	−6.92399e114	−0.106877
$352$	−7.47422e115	−1.01362
$353$	9.91284e115	1.18154	0.590771	−	0.806839i	$-0.298824\pi$
$353$	9.91284e115	1.18154	0.590771	+	0.806839i	$0.298824\pi$
$354$	2.93133e115	0.307197
$355$	2.47307e115	0.227954
$356$	−1.38704e116	−1.12490
$357$	−1.36771e116	−0.976315
$358$	7.78791e114	0.0489489
$359$	1.74881e116	0.968157	0.484078	−	0.875025i	$-0.339155\pi$
$359$	1.74881e116	0.968157	0.484078	+	0.875025i	$0.339155\pi$
$360$	8.68212e114	0.0423508
$361$	−1.96343e116	−0.844185
$362$	6.18423e115	0.234447
$363$	7.56932e116	2.53108
$364$	2.04203e115	0.0602489
$365$	−2.60811e116	−0.679204
$366$	−2.62504e115	−0.0603596
$367$	3.92876e116	0.797902	0.398951	−	0.916972i	$-0.369374\pi$
$367$	3.92876e116	0.797902	0.398951	+	0.916972i	$0.369374\pi$
$368$	−3.37395e116	−0.605428
$369$	−1.01952e115	−0.0161695
$370$	1.38084e116	0.193626
$371$	−2.17047e116	−0.269179
$372$	−6.40451e116	−0.702720
$373$	2.47635e116	0.240470	0.120235	−	0.992745i	$-0.461635\pi$
$373$	2.47635e116	0.240470	0.120235	+	0.992745i	$0.461635\pi$
$374$	−6.92253e116	−0.595123
$375$	−1.71291e117	−1.30410
$376$	7.34715e115	0.0495532
$377$	6.26493e115	0.0374442
$378$	1.95853e116	0.103766
$379$	1.26419e116	0.0593920	0.0296960	−	0.999559i	$-0.490546\pi$
$379$	1.26419e116	0.0593920	0.0296960	+	0.999559i	$0.490546\pi$
$380$	1.51607e117	0.631780
$381$	3.52937e117	1.30500
$382$	2.87525e116	0.0943611
$383$	3.06510e117	0.893102	0.446551	−	0.894758i	$-0.352652\pi$
$383$	3.06510e117	0.893102	0.446551	+	0.894758i	$0.352652\pi$
$384$	−2.78053e117	−0.719544
$385$	−7.56322e117	−1.73878
$386$	2.07191e116	0.0423300
$387$	−5.09393e116	−0.0925134
$388$	8.83768e117	1.42723
$389$	1.20562e118	1.73183	0.865915	−	0.500191i	$-0.166737\pi$
$389$	1.20562e118	1.73183	0.865915	+	0.500191i	$0.166737\pi$
$390$	−2.84890e116	−0.0364114
$391$	−1.00056e118	−1.13815
$392$	2.52897e117	0.256110
$393$	−7.98151e117	−0.719820
$394$	2.66139e117	0.213811
$395$	−3.15085e118	−2.25559
$396$	1.90486e117	0.121543
$397$	−8.60634e117	−0.489610	−0.244805	−	0.969572i	$-0.578724\pi$
$397$	−8.60634e117	−0.489610	−0.244805	+	0.969572i	$0.578724\pi$
$398$	3.95942e117	0.200887
$399$	−5.07921e117	−0.229895
$400$	3.88493e118	1.56911
$401$	6.60235e117	0.238029	0.119014	−	0.992893i	$-0.462027\pi$
$401$	6.60235e117	0.238029	0.119014	+	0.992893i	$0.462027\pi$
$402$	−1.28818e117	−0.0414658
$403$	2.72407e117	0.0783139
$404$	−5.06520e118	−1.30090
$405$	7.69646e118	1.76639
$406$	−1.77211e117	−0.0363543
$407$	6.17401e118	1.13246
$408$	−3.96346e118	−0.650185
$409$	−4.62393e118	−0.678579	−0.339290	−	0.940682i	$-0.610187\pi$
$409$	−4.62393e118	−0.678579	−0.339290	+	0.940682i	$0.610187\pi$
$410$	5.75617e117	0.0755906
$411$	7.73095e118	0.908719
$412$	3.40300e118	0.358128
$413$	−9.29928e118	−0.876439
$414$	−1.04415e117	−0.00881552
$415$	−9.64275e118	−0.729479
$416$	8.93140e117	0.0605582
$417$	−7.75589e118	−0.471456
$418$	−2.57079e118	−0.140135
$419$	−4.82399e118	−0.235868	−0.117934	−	0.993021i	$-0.537627\pi$
$419$	−4.82399e118	−0.235868	−0.117934	+	0.993021i	$0.537627\pi$
$420$	−2.12485e119	−0.932149
$421$	2.52840e118	0.0995431	0.0497716	−	0.998761i	$-0.484151\pi$
$421$	2.52840e118	0.0995431	0.0497716	+	0.998761i	$0.484151\pi$
$422$	4.22578e118	0.149345
$423$	−2.82613e117	−0.00896821
$424$	−6.28977e118	−0.179262
$425$	1.15209e120	2.94979
$426$	−1.17816e118	−0.0271062
$427$	8.32759e118	0.172207
$428$	−4.81498e119	−0.895165
$429$	−1.27380e119	−0.212958
$430$	2.87601e119	0.432489
$431$	3.83546e119	0.518921	0.259460	−	0.965754i	$-0.416455\pi$
$431$	3.83546e119	0.518921	0.259460	+	0.965754i	$0.416455\pi$
$432$	−7.05438e119	−0.858912
$433$	6.70220e118	0.0734544	0.0367272	−	0.999325i	$-0.488307\pi$
$433$	6.70220e118	0.0734544	0.0367272	+	0.999325i	$0.488307\pi$
$434$	−7.70535e118	−0.0760343
$435$	−6.51902e119	−0.579324
$436$	1.76134e120	1.40996
$437$	−3.71574e119	−0.268003
$438$	1.24249e119	0.0807648
$439$	−2.48210e120	−1.45440	−0.727200	−	0.686426i	$-0.759179\pi$
$439$	−2.48210e120	−1.45440	−0.727200	+	0.686426i	$0.759179\pi$
$440$	−2.19173e120	−1.15795
$441$	−9.72785e118	−0.0463512
$442$	8.27215e118	0.0355554
$443$	3.24421e120	1.25817	0.629085	−	0.777336i	$-0.283430\pi$
$443$	3.24421e120	1.25817	0.629085	+	0.777336i	$0.283430\pi$
$444$	1.73456e120	0.607104
$445$	−6.13886e120	−1.93958
$446$	8.28533e119	0.236360
$447$	5.00963e120	1.29066
$448$	1.90675e120	0.443757
$449$	−3.98399e120	−0.837741	−0.418871	−	0.908046i	$-0.637574\pi$
$449$	−3.98399e120	−0.837741	−0.418871	+	0.908046i	$0.637574\pi$
$450$	1.20229e119	0.0228475
$451$	2.57370e120	0.442105
$452$	9.73735e120	1.51231
$453$	4.10688e120	0.576825
$454$	−1.36718e120	−0.173694
$455$	9.03776e119	0.103882
$456$	−1.47189e120	−0.153100
$457$	−1.23244e121	−1.16032	−0.580161	−	0.814502i	$-0.697010\pi$
$457$	−1.23244e121	−1.16032	−0.580161	+	0.814502i	$0.697010\pi$
$458$	3.13764e120	0.267439
$459$	−2.09201e121	−1.61468
$460$	−1.55445e121	−1.08667
$461$	2.01621e120	0.127686	0.0638430	−	0.997960i	$-0.479664\pi$
$461$	2.01621e120	0.127686	0.0638430	+	0.997960i	$0.479664\pi$
$462$	3.60309e120	0.206760
$463$	3.17864e121	1.65313	0.826564	−	0.562843i	$-0.190292\pi$
$463$	3.17864e121	1.65313	0.826564	+	0.562843i	$0.190292\pi$
$464$	6.38292e120	0.300920
$465$	−2.83455e121	−1.21164
$466$	6.91524e119	0.0268070
$467$	3.20921e120	0.112844	0.0564222	−	0.998407i	$-0.482031\pi$
$467$	3.20921e120	0.112844	0.0564222	+	0.998407i	$0.482031\pi$
$468$	−2.27623e119	−0.00726156
$469$	4.08657e120	0.118303
$470$	1.59562e120	0.0419254
$471$	−4.00211e121	−0.954635
$472$	−2.69482e121	−0.583672
$473$	1.28592e122	2.52949
$474$	1.50105e121	0.268214
$475$	4.27849e121	0.694594
$476$	6.16978e121	0.910235
$477$	2.41940e120	0.0324431
$478$	−7.62367e120	−0.0929383
$479$	−1.51938e122	−1.68423	−0.842113	−	0.539301i	$-0.818689\pi$
$479$	−1.51938e122	−1.68423	−0.842113	+	0.539301i	$0.818689\pi$
$480$	−9.29363e121	−0.936935
$481$	−7.37770e120	−0.0676581
$482$	−1.31213e121	−0.109481
$483$	5.20779e121	0.395421
$484$	−3.41455e122	−2.35977
$485$	3.91144e122	2.46086
$486$	−4.52541e120	−0.0259243
$487$	−8.47472e121	−0.442138	−0.221069	−	0.975258i	$-0.570955\pi$
$487$	−8.47472e121	−0.442138	−0.221069	+	0.975258i	$0.570955\pi$
$488$	2.41324e121	0.114683
$489$	−2.02651e122	−0.877395
$490$	5.49229e121	0.216686
$491$	−5.14846e121	−0.185127	−0.0925634	−	0.995707i	$-0.529506\pi$
$491$	−5.14846e121	−0.185127	−0.0925634	+	0.995707i	$0.529506\pi$
$492$	7.23068e121	0.237010
$493$	1.89288e122	0.565704
$494$	3.07200e120	0.00837230
$495$	8.43065e121	0.209568
$496$	2.77537e122	0.629369
$497$	3.73757e121	0.0773345
$498$	4.59378e121	0.0867431
$499$	−3.01083e122	−0.518933	−0.259467	−	0.965752i	$-0.583547\pi$
$499$	−3.01083e122	−0.518933	−0.259467	+	0.965752i	$0.583547\pi$
$500$	7.72698e122	1.21583
$501$	−5.66262e122	−0.813582
$502$	1.15422e122	0.151450
$503$	1.47880e123	1.77242	0.886209	−	0.463285i	$-0.153329\pi$
$503$	1.47880e123	1.77242	0.886209	+	0.463285i	$0.153329\pi$
$504$	1.31213e121	0.0143678
$505$	−2.24179e123	−2.24304
$506$	2.63588e122	0.241033
$507$	−1.22110e123	−1.02068
$508$	−1.59211e123	−1.21667
$509$	1.13988e123	0.796527	0.398263	−	0.917271i	$-0.369613\pi$
$509$	1.13988e123	0.796527	0.398263	+	0.917271i	$0.369613\pi$
$510$	−8.60765e122	−0.550100
$511$	−3.94165e122	−0.230424
$512$	1.53573e123	0.821354
$513$	−7.76902e122	−0.380212
$514$	−5.35184e122	−0.239707
$515$	1.50612e123	0.617492
$516$	3.61274e123	1.35605
$517$	7.13434e122	0.245208
$518$	2.08687e122	0.0656887
$519$	−3.57810e123	−1.03166
$520$	2.61903e122	0.0691813
$521$	3.06073e123	0.740812	0.370406	−	0.928870i	$-0.379219\pi$
$521$	3.06073e123	0.740812	0.370406	+	0.928870i	$0.379219\pi$
$522$	1.97535e121	0.00438164
$523$	2.33893e123	0.475543	0.237772	−	0.971321i	$-0.423583\pi$
$523$	2.33893e123	0.475543	0.237772	+	0.971321i	$0.423583\pi$
$524$	3.60049e123	0.671101
$525$	−5.99651e123	−1.02483
$526$	8.77190e122	0.137481
$527$	8.23050e123	1.18316
$528$	−1.29779e124	−1.71144
$529$	−4.45501e123	−0.539033
$530$	−1.36598e123	−0.151668
$531$	1.03658e123	0.105634
$532$	2.29125e123	0.214335
$533$	−3.07547e122	−0.0264134
$534$	2.92453e123	0.230637
$535$	−2.13105e124	−1.54346
$536$	1.18424e123	0.0787846
$537$	4.32977e123	0.264628
$538$	−3.48598e123	−0.195763
$539$	2.45572e124	1.26733
$540$	−3.25011e124	−1.54164
$541$	1.61757e122	0.00705323	0.00352662	−	0.999994i	$-0.498877\pi$
$541$	1.61757e122	0.00705323	0.00352662	+	0.999994i	$0.498877\pi$
$542$	−3.09888e122	−0.0124233
$543$	3.43819e124	1.26747
$544$	2.69853e124	0.914908
$545$	7.79545e124	2.43108
$546$	−4.30556e122	−0.0123528
$547$	−5.93541e124	−1.56685	−0.783425	−	0.621486i	$-0.786529\pi$
$547$	−5.93541e124	−1.56685	−0.783425	+	0.621486i	$0.786529\pi$
$548$	−3.48746e124	−0.847214
$549$	−9.28268e122	−0.0207554
$550$	−3.03508e124	−0.624694
$551$	7.02953e123	0.133208
$552$	1.50916e124	0.263334
$553$	−4.76189e124	−0.765220
$554$	−8.81473e123	−0.130471
$555$	7.67692e124	1.04678
$556$	3.49871e124	0.439546
$557$	−7.22450e124	−0.836366	−0.418183	−	0.908363i	$-0.637333\pi$
$557$	−7.22450e124	−0.836366	−0.418183	+	0.908363i	$0.637333\pi$
$558$	8.58907e122	0.00916411
$559$	−1.53663e124	−0.151123
$560$	9.20796e124	0.834850
$561$	−3.84866e125	−3.21736
$562$	4.19032e124	0.323032
$563$	−1.56698e125	−1.11412	−0.557060	−	0.830472i	$-0.688071\pi$
$563$	−1.56698e125	−1.11412	−0.557060	+	0.830472i	$0.688071\pi$
$564$	2.00436e124	0.131455
$565$	4.30962e125	2.60756
$566$	2.66924e124	0.149019
$567$	1.16317e125	0.599259
$568$	1.08310e124	0.0515016
$569$	3.90892e125	1.71573	0.857865	−	0.513875i	$-0.171791\pi$
$569$	3.90892e125	1.71573	0.857865	+	0.513875i	$0.171791\pi$
$570$	−3.19659e124	−0.129533
$571$	−2.68089e125	−1.00308	−0.501541	−	0.865134i	$-0.667233\pi$
$571$	−2.68089e125	−1.00308	−0.501541	+	0.865134i	$0.667233\pi$
$572$	5.74616e124	0.198545
$573$	1.59853e125	0.510135
$574$	8.69933e123	0.0256445
$575$	−4.38680e125	−1.19471
$576$	−2.12544e124	−0.0534842
$577$	−4.49092e125	−1.04433	−0.522163	−	0.852846i	$-0.674875\pi$
$577$	−4.49092e125	−1.04433	−0.522163	+	0.852846i	$0.674875\pi$
$578$	1.60995e125	0.346015
$579$	1.15190e125	0.228845
$580$	2.94075e125	0.540113
$581$	−1.45732e125	−0.247480
$582$	−1.86340e125	−0.292624
$583$	−6.10759e125	−0.887055
$584$	−1.14224e125	−0.153452
$585$	−1.00743e124	−0.0125205
$586$	7.87198e124	0.0905195
$587$	−3.26160e125	−0.347054	−0.173527	−	0.984829i	$-0.555516\pi$
$587$	−3.26160e125	−0.347054	−0.173527	+	0.984829i	$0.555516\pi$
$588$	6.89921e125	0.679409
$589$	3.05653e125	0.278601
$590$	−5.85248e125	−0.493825
$591$	1.47963e126	1.15591
$592$	−7.51664e125	−0.543734
$593$	−6.68741e125	−0.447991	−0.223995	−	0.974590i	$-0.571910\pi$
$593$	−6.68741e125	−0.447991	−0.223995	+	0.974590i	$0.571910\pi$
$594$	5.51119e125	0.341950
$595$	2.73066e126	1.56945
$596$	−2.25986e126	−1.20331
$597$	2.20129e126	1.08604
$598$	−3.14977e124	−0.0144004
$599$	3.07750e125	0.130400	0.0652001	−	0.997872i	$-0.479231\pi$
$599$	3.07750e125	0.130400	0.0652001	+	0.997872i	$0.479231\pi$
$600$	−1.73772e126	−0.682492
$601$	4.39000e126	1.59837	0.799183	−	0.601088i	$-0.205266\pi$
$601$	4.39000e126	1.59837	0.799183	+	0.601088i	$0.205266\pi$
$602$	4.34653e125	0.146724
$603$	−4.55526e124	−0.0142585
$604$	−1.85263e126	−0.537784
$605$	−1.51123e127	−4.06876
$606$	1.06798e126	0.266722
$607$	5.52365e126	1.27980	0.639898	−	0.768460i	$-0.278977\pi$
$607$	5.52365e126	1.27980	0.639898	+	0.768460i	$0.278977\pi$
$608$	1.00214e126	0.215435
$609$	−9.85224e125	−0.196539
$610$	5.24095e125	0.0970292
$611$	−8.52526e124	−0.0146498
$612$	−6.87739e125	−0.109707
$613$	−1.51347e126	−0.224141	−0.112071	−	0.993700i	$-0.535748\pi$
$613$	−1.51347e126	−0.224141	−0.112071	+	0.993700i	$0.535748\pi$
$614$	3.31045e125	0.0455226
$615$	3.20021e126	0.408658
$616$	−3.31238e126	−0.392842
$617$	6.34646e126	0.699128	0.349564	−	0.936913i	$-0.386330\pi$
$617$	6.34646e126	0.699128	0.349564	+	0.936913i	$0.386330\pi$
$618$	−7.17512e125	−0.0734266
$619$	−4.99558e125	−0.0474965	−0.0237483	−	0.999718i	$-0.507560\pi$
$619$	−4.99558e125	−0.0474965	−0.0237483	+	0.999718i	$0.507560\pi$
$620$	1.27868e127	1.12964
$621$	7.96570e126	0.653967
$622$	−3.08845e125	−0.0235656
$623$	−9.27769e126	−0.658012
$624$	1.55081e126	0.102249
$625$	5.49295e126	0.336717
$626$	2.73621e126	0.155961
$627$	−1.42926e127	−0.757597
$628$	1.80536e127	0.890022
$629$	−2.22910e127	−1.02217
$630$	2.84963e125	0.0121561
$631$	8.10954e125	0.0321855	0.0160927	−	0.999871i	$-0.494877\pi$
$631$	8.10954e125	0.0321855	0.0160927	+	0.999871i	$0.494877\pi$
$632$	−1.37994e127	−0.509605
$633$	2.34937e127	0.807388
$634$	−6.08312e126	−0.194565
$635$	−7.04647e127	−2.09781
$636$	−1.71590e127	−0.475546
$637$	−2.93449e126	−0.0757160
$638$	−4.98662e126	−0.119802
$639$	−4.16623e125	−0.00932082
$640$	5.55140e127	1.15668
$641$	4.15945e127	0.807227	0.403613	−	0.914930i	$-0.367754\pi$
$641$	4.15945e127	0.807227	0.403613	+	0.914930i	$0.367754\pi$
$642$	1.01522e127	0.183535
$643$	−5.46914e126	−0.0921127	−0.0460564	−	0.998939i	$-0.514665\pi$
$643$	−5.46914e126	−0.0921127	−0.0460564	+	0.998939i	$0.514665\pi$
$644$	−2.34925e127	−0.368657
$645$	1.59895e128	2.33812
$646$	9.28172e126	0.126488
$647$	−9.19516e125	−0.0116792	−0.00583962	−	0.999983i	$-0.501859\pi$
$647$	−9.19516e125	−0.0116792	−0.00583962	+	0.999983i	$0.501859\pi$
$648$	3.37073e127	0.399081
$649$	−2.61677e128	−2.88823
$650$	3.62680e126	0.0373221
$651$	−4.28387e127	−0.411057
$652$	9.14164e127	0.818010
$653$	8.26345e127	0.689623	0.344812	−	0.938672i	$-0.387943\pi$
$653$	8.26345e127	0.689623	0.344812	+	0.938672i	$0.387943\pi$
$654$	−3.71372e127	−0.289083
$655$	1.59353e128	1.15713
$656$	−3.13339e127	−0.212271
$657$	4.39372e126	0.0277720
$658$	2.41147e126	0.0142234
$659$	3.22196e128	1.77351	0.886754	−	0.462242i	$-0.152955\pi$
$659$	3.22196e128	1.77351	0.886754	+	0.462242i	$0.152955\pi$
$660$	−5.97921e128	−3.07181
$661$	−3.81358e128	−1.82880	−0.914400	−	0.404813i	$-0.867337\pi$
$661$	−3.81358e128	−1.82880	−0.914400	+	0.404813i	$0.867337\pi$
$662$	−4.27828e127	−0.191527
$663$	4.59899e127	0.192219
$664$	−4.22313e127	−0.164811
$665$	1.01408e128	0.369561
$666$	−2.32621e126	−0.00791720
$667$	−7.20749e127	−0.229118
$668$	2.55443e128	0.758516
$669$	4.60632e128	1.27781
$670$	2.57187e127	0.0666571
$671$	2.34334e128	0.567492
$672$	−1.40455e128	−0.317860
$673$	4.52763e128	0.957603	0.478801	−	0.877923i	$-0.341071\pi$
$673$	4.52763e128	0.957603	0.478801	+	0.877923i	$0.341071\pi$
$674$	3.67527e127	0.0726547
$675$	−9.17210e128	−1.69491
$676$	5.50844e128	0.951599
$677$	−6.79511e126	−0.0109752	−0.00548759	−	0.999985i	$-0.501747\pi$
$677$	−6.79511e126	−0.0109752	−0.00548759	+	0.999985i	$0.501747\pi$
$678$	−2.05309e128	−0.310068
$679$	5.91138e128	0.834861
$680$	7.91314e128	1.04519
$681$	−7.60101e128	−0.939026
$682$	−2.16824e128	−0.250564
$683$	−7.81257e128	−0.844602	−0.422301	−	0.906456i	$-0.638777\pi$
$683$	−7.81257e128	−0.844602	−0.422301	+	0.906456i	$0.638777\pi$
$684$	−2.55403e127	−0.0258329
$685$	−1.54350e129	−1.46078
$686$	2.04646e128	0.181241
$687$	1.74441e129	1.44583
$688$	−1.56557e129	−1.21450
$689$	7.29833e127	0.0529967
$690$	3.27751e128	0.222798
$691$	−2.28997e129	−1.45740	−0.728701	−	0.684832i	$-0.759876\pi$
$691$	−2.28997e129	−1.45740	−0.728701	+	0.684832i	$0.759876\pi$
$692$	1.61409e129	0.961835
$693$	1.27413e128	0.0710970
$694$	1.38406e128	0.0723268
$695$	1.54848e129	0.757875
$696$	−2.85506e128	−0.130887
$697$	−9.29222e128	−0.399051
$698$	−7.33472e128	−0.295095
$699$	3.84460e128	0.144924
$700$	2.70505e129	0.955463
$701$	2.11498e129	0.700061	0.350030	−	0.936738i	$-0.386171\pi$
$701$	2.11498e129	0.700061	0.350030	+	0.936738i	$0.386171\pi$
$702$	−6.58566e127	−0.0204296
$703$	−8.27811e128	−0.240693
$704$	5.36550e129	1.46236
$705$	8.87102e128	0.226657
$706$	9.42848e128	0.225854
$707$	−3.38803e129	−0.760964
$708$	−7.35167e129	−1.54836
$709$	−4.27170e128	−0.0843718	−0.0421859	−	0.999110i	$-0.513432\pi$
$709$	−4.27170e128	−0.0843718	−0.0421859	+	0.999110i	$0.513432\pi$
$710$	2.35223e128	0.0435738
$711$	5.30804e128	0.0922289
$712$	−2.68857e129	−0.438209
$713$	−3.13391e129	−0.479195
$714$	−1.30088e129	−0.186624
$715$	2.54317e129	0.342335
$716$	−1.95318e129	−0.246717
$717$	−4.23846e129	−0.502443
$718$	1.66336e129	0.185065
$719$	8.13624e129	0.849687	0.424844	−	0.905267i	$-0.360329\pi$
$719$	8.13624e129	0.849687	0.424844	+	0.905267i	$0.360329\pi$
$720$	−1.02640e129	−0.100621
$721$	2.27621e129	0.209488
$722$	−1.86749e129	−0.161367
$723$	−7.29495e129	−0.591874
$724$	−1.55098e130	−1.18168
$725$	8.29907e129	0.593813
$726$	7.19946e129	0.483820
$727$	2.88715e130	1.82244	0.911221	−	0.411918i	$-0.135141\pi$
$727$	2.88715e130	1.82244	0.911221	+	0.411918i	$0.135141\pi$
$728$	3.95816e128	0.0234701
$729$	1.65722e130	0.923160
$730$	−2.48067e129	−0.129831
$731$	−4.64276e130	−2.28316
$732$	6.58349e129	0.304230
$733$	2.43296e130	1.05658	0.528291	−	0.849063i	$-0.322833\pi$
$733$	2.43296e130	1.05658	0.528291	+	0.849063i	$0.322833\pi$
$734$	3.73679e129	0.152520
$735$	3.05350e130	1.17145
$736$	−1.02751e130	−0.370550
$737$	1.14994e130	0.389856
$738$	−9.69706e127	−0.00309083
$739$	−3.69098e130	−1.10616	−0.553082	−	0.833127i	$-0.686549\pi$
$739$	−3.69098e130	−1.10616	−0.553082	+	0.833127i	$0.686549\pi$
$740$	−3.46308e130	−0.975933
$741$	1.70791e129	0.0452623
$742$	−2.06442e129	−0.0514541
$743$	−3.94946e130	−0.925863	−0.462931	−	0.886394i	$-0.653202\pi$
$743$	−3.94946e130	−0.925863	−0.462931	+	0.886394i	$0.653202\pi$
$744$	−1.24142e130	−0.273747
$745$	−1.00019e131	−2.07477
$746$	2.35535e129	0.0459663
$747$	1.62445e129	0.0298277
$748$	1.73614e131	2.99959
$749$	−3.22066e130	−0.523628
$750$	−1.62921e130	−0.249281
$751$	1.21487e131	1.74949	0.874746	−	0.484582i	$-0.161028\pi$
$751$	1.21487e131	1.74949	0.874746	+	0.484582i	$0.161028\pi$
$752$	−8.68582e129	−0.117733
$753$	6.41703e130	0.818771
$754$	5.95881e128	0.00715754
$755$	−8.19949e130	−0.927258
$756$	−4.91191e130	−0.523009
$757$	−9.68304e130	−0.970843	−0.485422	−	0.874280i	$-0.661334\pi$
$757$	−9.68304e130	−0.970843	−0.485422	+	0.874280i	$0.661334\pi$
$758$	1.20242e129	0.0113529
$759$	1.46544e131	1.30307
$760$	2.93867e130	0.246112
$761$	8.08211e129	0.0637562	0.0318781	−	0.999492i	$-0.489851\pi$
$761$	8.08211e129	0.0637562	0.0318781	+	0.999492i	$0.489851\pi$
$762$	3.35692e130	0.249453
$763$	1.17813e131	0.824759
$764$	−7.21101e130	−0.475607
$765$	−3.04384e130	−0.189159
$766$	2.91534e130	0.170718
$767$	3.12693e130	0.172556
$768$	1.30011e131	0.676153
$769$	−3.51993e131	−1.72538	−0.862691	−	0.505731i	$-0.831223\pi$
$769$	−3.51993e131	−1.72538	−0.862691	+	0.505731i	$0.831223\pi$
$770$	−7.19366e130	−0.332370
$771$	−2.97541e131	−1.29590
$772$	−5.19626e130	−0.213356
$773$	−3.20933e131	−1.24236	−0.621179	−	0.783668i	$-0.713346\pi$
$773$	−3.20933e131	−1.24236	−0.621179	+	0.783668i	$0.713346\pi$
$774$	−4.84503e129	−0.0176841
$775$	3.60854e131	1.24195
$776$	1.71305e131	0.555983
$777$	1.16022e131	0.355126
$778$	1.14671e131	0.331043
$779$	−3.45082e130	−0.0939653
$780$	7.14492e130	0.183524
$781$	1.05173e131	0.254849
$782$	−9.51670e130	−0.217560
$783$	−1.50697e131	−0.325046
$784$	−2.98975e131	−0.608491
$785$	7.99030e131	1.53459
$786$	−7.59152e130	−0.137595
$787$	6.87924e131	1.17677	0.588383	−	0.808582i	$-0.299765\pi$
$787$	6.87924e131	1.17677	0.588383	+	0.808582i	$0.299765\pi$
$788$	−6.67465e131	−1.07767
$789$	4.87683e131	0.743249
$790$	−2.99689e131	−0.431160
$791$	6.51316e131	0.884630
$792$	3.69227e130	0.0473476
$793$	−2.80020e130	−0.0339046
$794$	−8.18581e130	−0.0935898
$795$	−7.59433e131	−0.819946
$796$	−9.93007e131	−1.01253
$797$	−4.27624e131	−0.411821	−0.205910	−	0.978571i	$-0.566016\pi$
$797$	−4.27624e131	−0.411821	−0.205910	+	0.978571i	$0.566016\pi$
$798$	−4.83103e130	−0.0439448
$799$	−2.57582e131	−0.221328
$800$	1.18313e132	0.960369
$801$	1.03418e131	0.0793076
$802$	6.27974e130	0.0454997
$803$	−1.10916e132	−0.759340
$804$	3.23069e131	0.209000
$805$	−1.03975e132	−0.635647
$806$	2.59097e130	0.0149698
$807$	−1.93807e132	−1.05834
$808$	−9.81811e131	−0.506770
$809$	3.05423e132	1.49020	0.745100	−	0.666953i	$-0.232402\pi$
$809$	3.05423e132	1.49020	0.745100	+	0.666953i	$0.232402\pi$
$810$	7.32039e131	0.337649
$811$	2.34102e131	0.102084	0.0510418	−	0.998697i	$-0.483746\pi$
$811$	2.34102e131	0.102084	0.0510418	+	0.998697i	$0.483746\pi$
$812$	4.44438e131	0.183236
$813$	−1.72286e131	−0.0671628
$814$	5.87233e131	0.216471
$815$	4.04597e132	1.41043
$816$	4.68561e132	1.54477
$817$	−1.72416e132	−0.537620
$818$	−4.39799e131	−0.129712
$819$	−1.52253e130	−0.00424766
$820$	−1.44362e132	−0.380999
$821$	−2.61542e132	−0.653021	−0.326511	−	0.945194i	$-0.605873\pi$
$821$	−2.61542e132	−0.653021	−0.326511	+	0.945194i	$0.605873\pi$
$822$	7.35319e131	0.173703
$823$	1.56769e132	0.350403	0.175201	−	0.984533i	$-0.443942\pi$
$823$	1.56769e132	0.350403	0.175201	+	0.984533i	$0.443942\pi$
$824$	6.59619e131	0.139510
$825$	−1.68739e133	−3.37722
$826$	−8.84489e131	−0.167533
$827$	8.77714e132	1.57345	0.786724	−	0.617305i	$-0.211775\pi$
$827$	8.77714e132	1.57345	0.786724	+	0.617305i	$0.211775\pi$
$828$	2.61869e131	0.0444328
$829$	4.15577e132	0.667452	0.333726	−	0.942670i	$-0.391694\pi$
$829$	4.15577e132	0.667452	0.333726	+	0.942670i	$0.391694\pi$
$830$	−9.17158e131	−0.139441
$831$	−4.90065e132	−0.705353
$832$	−6.41156e131	−0.0873680
$833$	−8.86624e132	−1.14391
$834$	−7.37691e131	−0.0901196
$835$	1.13056e133	1.30785
$836$	6.44745e132	0.706321
$837$	−6.55250e132	−0.679827
$838$	−4.58828e131	−0.0450866
$839$	4.26717e132	0.397164	0.198582	−	0.980084i	$-0.436366\pi$
$839$	4.26717e132	0.397164	0.198582	+	0.980084i	$0.436366\pi$
$840$	−4.11869e132	−0.363122
$841$	−1.06099e133	−0.886120
$842$	2.40486e131	0.0190278
$843$	2.32966e133	1.74637
$844$	−1.05981e133	−0.752742
$845$	2.43796e133	1.64077
$846$	−2.68804e130	−0.00171429
$847$	−2.28394e133	−1.38035
$848$	7.43578e132	0.425907
$849$	1.48400e133	0.805625
$850$	1.09580e133	0.563858
$851$	8.48767e132	0.413994
$852$	2.95479e132	0.136623
$853$	−1.67324e133	−0.733461	−0.366731	−	0.930327i	$-0.619523\pi$
$853$	−1.67324e133	−0.733461	−0.366731	+	0.930327i	$0.619523\pi$
$854$	7.92068e131	0.0329177
$855$	−1.13038e132	−0.0445417
$856$	−9.33310e132	−0.348714
$857$	−3.89139e133	−1.37872	−0.689362	−	0.724417i	$-0.742109\pi$
$857$	−3.89139e133	−1.37872	−0.689362	+	0.724417i	$0.742109\pi$
$858$	−1.21156e132	−0.0407074
$859$	−2.30483e132	−0.0734429	−0.0367215	−	0.999326i	$-0.511691\pi$
$859$	−2.30483e132	−0.0734429	−0.0367215	+	0.999326i	$0.511691\pi$
$860$	−7.21291e133	−2.17987
$861$	4.83649e132	0.138639
$862$	3.64805e132	0.0991927
$863$	2.67996e133	0.691252	0.345626	−	0.938372i	$-0.387667\pi$
$863$	2.67996e133	0.691252	0.345626	+	0.938372i	$0.387667\pi$
$864$	−2.14837e133	−0.525694
$865$	7.14375e133	1.65842
$866$	6.37471e131	0.0140409
$867$	8.95069e133	1.87063
$868$	1.93247e133	0.383235
$869$	−1.33997e134	−2.52171
$870$	−6.20049e132	−0.110739
$871$	−1.37413e132	−0.0232918
$872$	3.41408e133	0.549255
$873$	−6.58936e132	−0.100622
$874$	−3.53418e132	−0.0512293
$875$	5.16845e133	0.711204
$876$	−3.11612e133	−0.407078
$877$	1.10074e133	0.136522	0.0682610	−	0.997668i	$-0.478255\pi$
$877$	1.10074e133	0.136522	0.0682610	+	0.997668i	$0.478255\pi$
$878$	−2.36082e133	−0.278011
$879$	4.37651e133	0.489367
$880$	2.59107e134	2.75117
$881$	3.65169e133	0.368205	0.184103	−	0.982907i	$-0.441062\pi$
$881$	3.65169e133	0.368205	0.184103	+	0.982907i	$0.441062\pi$
$882$	−9.25252e131	−0.00886011
$883$	−7.26655e133	−0.660871	−0.330435	−	0.943829i	$-0.607196\pi$
$883$	−7.26655e133	−0.660871	−0.330435	+	0.943829i	$0.607196\pi$
$884$	−2.07462e133	−0.179209
$885$	−3.25375e134	−2.66972
$886$	3.08569e133	0.240502
$887$	−1.36712e134	−1.01223	−0.506117	−	0.862465i	$-0.668920\pi$
$887$	−1.36712e134	−1.01223	−0.506117	+	0.862465i	$0.668920\pi$
$888$	3.36217e133	0.236499
$889$	−1.06494e134	−0.711695
$890$	−5.83890e133	−0.370754
$891$	3.27310e134	1.97480
$892$	−2.07793e134	−1.19132
$893$	−9.56572e132	−0.0521166
$894$	4.76485e133	0.246713
$895$	−8.64450e133	−0.425394
$896$	8.38986e133	0.392410
$897$	−1.75115e133	−0.0778515
$898$	−3.78932e133	−0.160136
$899$	5.92881e133	0.238178
$900$	−3.01529e133	−0.115158
$901$	2.20511e134	0.800669
$902$	2.44794e133	0.0845092
$903$	2.41650e134	0.793221
$904$	1.88744e134	0.589126
$905$	−6.86443e134	−2.03748
$906$	3.90621e133	0.110261
$907$	6.85950e134	1.84145	0.920727	−	0.390207i	$-0.127596\pi$
$907$	6.85950e134	1.84145	0.920727	+	0.390207i	$0.127596\pi$
$908$	3.42884e134	0.875470
$909$	3.77660e133	0.0917159
$910$	8.59615e132	0.0198573
$911$	−5.93398e134	−1.30395	−0.651973	−	0.758242i	$-0.726059\pi$
$911$	−5.93398e134	−1.30395	−0.651973	+	0.758242i	$0.726059\pi$
$912$	1.74008e134	0.363750
$913$	−4.10080e134	−0.815546
$914$	−1.17222e134	−0.221798
$915$	2.91376e134	0.524559
$916$	−7.86908e134	−1.34797
$917$	2.40831e134	0.392561
$918$	−1.98979e134	−0.308649
$919$	8.75591e134	1.29255	0.646273	−	0.763107i	$-0.276327\pi$
$919$	8.75591e134	1.29255	0.646273	+	0.763107i	$0.276327\pi$
$920$	−3.01307e134	−0.423314
$921$	1.84048e134	0.246104
$922$	1.91769e133	0.0244074
$923$	−1.25678e133	−0.0152258
$924$	−9.03641e134	−1.04213
$925$	−9.77313e134	−1.07296
$926$	3.02332e134	0.315998
$927$	−2.53727e133	−0.0252487
$928$	1.94388e134	0.184177
$929$	−5.77870e134	−0.521333	−0.260667	−	0.965429i	$-0.583942\pi$
$929$	−5.77870e134	−0.521333	−0.260667	+	0.965429i	$0.583942\pi$
$930$	−2.69605e134	−0.231608
$931$	−3.29262e134	−0.269359
$932$	−1.73431e134	−0.135115
$933$	−1.71706e134	−0.127400
$934$	3.05240e133	0.0215704
$935$	7.68394e135	5.17196
$936$	−4.41212e132	−0.00282876
$937$	−2.04151e135	−1.24681	−0.623404	−	0.781900i	$-0.714251\pi$
$937$	−2.04151e135	−1.24681	−0.623404	+	0.781900i	$0.714251\pi$
$938$	3.88689e133	0.0226138
$939$	1.52123e135	0.843159
$940$	−4.00175e134	−0.211316
$941$	−3.54798e135	−1.78506	−0.892531	−	0.450986i	$-0.851072\pi$
$941$	−3.54798e135	−1.78506	−0.892531	+	0.450986i	$0.851072\pi$
$942$	−3.80655e134	−0.182480
$943$	3.53818e134	0.161621
$944$	3.18582e135	1.38674
$945$	−2.17395e135	−0.901782
$946$	1.22309e135	0.483517
$947$	−1.03583e135	−0.390269	−0.195134	−	0.980777i	$-0.562514\pi$
$947$	−1.03583e135	−0.390269	−0.195134	+	0.980777i	$0.562514\pi$
$948$	−3.76458e135	−1.35188
$949$	1.32540e134	0.0453664
$950$	4.06943e134	0.132773
$951$	−3.38198e135	−1.05186
$952$	1.19592e135	0.354585
$953$	3.08692e135	0.872568	0.436284	−	0.899809i	$-0.356294\pi$
$953$	3.08692e135	0.872568	0.436284	+	0.899809i	$0.356294\pi$
$954$	2.30119e133	0.00620155
$955$	−3.19150e135	−0.820052
$956$	1.91198e135	0.468436
$957$	−2.77237e135	−0.647675
$958$	−1.44514e135	−0.321943
$959$	−2.33270e135	−0.495579
$960$	6.67160e135	1.35173
$961$	−2.59713e135	−0.501856
$962$	−7.01721e133	−0.0129330
$963$	3.59004e134	0.0631107
$964$	3.29078e135	0.551815
$965$	−2.29980e135	−0.367872
$966$	4.95333e134	0.0755854
$967$	6.63121e135	0.965357	0.482679	−	0.875798i	$-0.339664\pi$
$967$	6.63121e135	0.965357	0.482679	+	0.875798i	$0.339664\pi$
$968$	−6.61857e135	−0.919254
$969$	5.16028e135	0.683819
$970$	3.72032e135	0.470398
$971$	8.37663e135	1.01064	0.505318	−	0.862933i	$-0.331375\pi$
$971$	8.37663e135	1.01064	0.505318	+	0.862933i	$0.331375\pi$
$972$	1.13495e135	0.130666
$973$	2.34023e135	0.257113
$974$	−8.06062e134	−0.0845154
$975$	2.01636e135	0.201771
$976$	−2.85293e135	−0.272474
$977$	7.05154e135	0.642808	0.321404	−	0.946942i	$-0.395845\pi$
$977$	7.05154e135	0.642808	0.321404	+	0.946942i	$0.395845\pi$
$978$	−1.92749e135	−0.167716
$979$	−2.61069e136	−2.16842
$980$	−1.37744e136	−1.09216
$981$	−1.31325e135	−0.0994048
$982$	−4.89689e134	−0.0353873
$983$	1.51416e136	1.04469	0.522344	−	0.852735i	$-0.325058\pi$
$983$	1.51416e136	1.04469	0.522344	+	0.852735i	$0.325058\pi$
$984$	1.40156e135	0.0923281
$985$	−2.95411e136	−1.85814
$986$	1.80039e135	0.108135
$987$	1.34068e135	0.0768946
$988$	−7.70445e134	−0.0421988
$989$	1.76781e136	0.924709
$990$	8.01870e134	0.0400592
$991$	3.62646e136	1.73034	0.865170	−	0.501478i	$-0.167210\pi$
$991$	3.62646e136	1.73034	0.865170	+	0.501478i	$0.167210\pi$
$992$	8.45221e135	0.385203
$993$	−2.37855e136	−1.03543
$994$	3.55494e134	0.0147826
$995$	−4.39492e136	−1.74582
$996$	−1.15210e136	−0.437210
$997$	1.18377e136	0.429178	0.214589	−	0.976704i	$-0.431159\pi$
$997$	1.18377e136	0.429178	0.214589	+	0.976704i	$0.431159\pi$
$998$	−2.86371e135	−0.0991951
$999$	1.77464e136	0.587327

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.92.a.a.1.4	✓	7
3.2	odd	2		9.92.a.b.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.92.a.a.1.4	✓	7	1.1	even	1	trivial
9.92.a.b.1.4		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)

\(f(q)\)	\(=\)	\(q+9.51137e12 q^{2} +5.28795e21 q^{3} -2.38541e27 q^{4} -1.05575e32 q^{5} +5.02957e34 q^{6} -1.59557e38 q^{7} -4.62376e40 q^{8} +1.77856e42 q^{9} +O(q^{10})\)	\(q+9.51137e12 q^{2} +5.28795e21 q^{3} -2.38541e27 q^{4} -1.05575e32 q^{5} +5.02957e34 q^{6} -1.59557e38 q^{7} -4.62376e40 q^{8} +1.77856e42 q^{9} -1.00417e45 q^{10} -4.48983e47 q^{11} -1.26140e49 q^{12} +5.36517e49 q^{13} -1.51760e51 q^{14} -5.58277e53 q^{15} +5.46622e54 q^{16} +1.62103e56 q^{17} +1.69166e55 q^{18} +6.01996e57 q^{19} +2.51841e59 q^{20} -8.43728e59 q^{21} -4.27045e60 q^{22} -6.17236e61 q^{23} -2.44502e62 q^{24} +7.10717e63 q^{25} +5.10302e62 q^{26} -1.29054e65 q^{27} +3.80608e65 q^{28} +1.16770e66 q^{29} -5.30998e66 q^{30} +5.07732e67 q^{31} +1.66470e68 q^{32} -2.37420e69 q^{33} +1.54182e69 q^{34} +1.68452e70 q^{35} -4.24260e69 q^{36} -1.37511e71 q^{37} +5.72581e70 q^{38} +2.83708e71 q^{39} +4.88154e72 q^{40} -5.73229e72 q^{41} -8.02501e72 q^{42} -2.86408e74 q^{43} +1.07101e75 q^{44} -1.87772e74 q^{45} -5.87077e74 q^{46} -1.58900e75 q^{47} +2.89051e76 q^{48} -5.46951e76 q^{49} +6.75989e76 q^{50} +8.57194e77 q^{51} -1.27982e77 q^{52} +1.36032e78 q^{53} -1.22748e78 q^{54} +4.74015e79 q^{55} +7.37751e78 q^{56} +3.18333e79 q^{57} +1.11065e79 q^{58} +5.82820e80 q^{59} +1.33172e81 q^{60} -5.21921e80 q^{61} +4.82923e80 q^{62} -2.83781e80 q^{63} -1.19503e82 q^{64} -5.66430e81 q^{65} -2.25819e82 q^{66} -2.56121e82 q^{67} -3.86683e83 q^{68} -3.26392e83 q^{69} +1.60221e83 q^{70} -2.34247e83 q^{71} -8.22363e82 q^{72} +2.47038e84 q^{73} -1.30792e84 q^{74} +3.75824e85 q^{75} -1.43601e85 q^{76} +7.16382e85 q^{77} +2.69845e84 q^{78} +2.98446e86 q^{79} -5.77097e86 q^{80} -7.29002e86 q^{81} -5.45219e85 q^{82} +9.13354e86 q^{83} +2.01264e87 q^{84} -1.71141e88 q^{85} -2.72413e87 q^{86} +6.17476e87 q^{87} +2.07599e88 q^{88} +5.81468e88 q^{89} -1.78597e87 q^{90} -8.56049e87 q^{91} +1.47236e89 q^{92} +2.68486e89 q^{93} -1.51136e88 q^{94} -6.35559e89 q^{95} +8.80285e89 q^{96} -3.70488e90 q^{97} -5.20225e89 q^{98} -7.98544e89 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 3841716838056 q^{2} + 62\!\cdots\!32 q^{3}+ \cdots + 38\!\cdots\!59 q^{9}+O(q^{10}) \) 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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