LMFDB - Embedded newform 1.96.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,96,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, 96, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 96);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 96 $
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:	$57.1535908815$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + \cdots + 12\!\cdots\!76 $ x^8 - x^7 - 456480027345544641394773612x^6 + 339329782338279955661332506368261395760x^5 + 59416097258977044989967193525017781867755241062538816x^4 - 123333481272707766511586825940129187946017943991568425334323966720x^3 - 2095214953359612636412863727366527579550578420280500659704186845017628059993088x^2 + 4629118030090922642937991592467690897026031030167011441378882798867864401974811543004909568x + 12580947281346973442685392853423155834893282648684156383693372843595042753411312943646281706520481611776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{104}\cdot 3^{38}\cdot 5^{12}\cdot 7^{7}\cdot 11\cdot 13\cdot 19^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.48943e13$ 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)

$f(q)$	$=$	$q-3.58194e14 q^{2} -7.12911e22 q^{3} +8.86885e28 q^{4} -1.64420e33 q^{5} +2.55360e37 q^{6} -1.35904e40 q^{7} -1.75781e43 q^{8} +2.96152e45 q^{9} +O(q^{10})$	\(q-3.58194e14 q^{2} -7.12911e22 q^{3} +8.86885e28 q^{4} -1.64420e33 q^{5} +2.55360e37 q^{6} -1.35904e40 q^{7} -1.75781e43 q^{8} +2.96152e45 q^{9} +5.88943e47 q^{10} +4.57322e49 q^{11} -6.32270e51 q^{12} +7.91094e52 q^{13} +4.86801e54 q^{14} +1.17217e56 q^{15} +2.78306e57 q^{16} -3.60982e57 q^{17} -1.06080e60 q^{18} -1.15920e60 q^{19} -1.45822e62 q^{20} +9.68877e62 q^{21} -1.63810e64 q^{22} -4.43116e64 q^{23} +1.25316e66 q^{24} +1.79050e65 q^{25} -2.83365e67 q^{26} -5.99290e67 q^{27} -1.20532e69 q^{28} +3.11912e69 q^{29} -4.19864e70 q^{30} -6.79915e70 q^{31} -3.00533e71 q^{32} -3.26030e72 q^{33} +1.29301e72 q^{34} +2.23455e73 q^{35} +2.62653e74 q^{36} -2.19553e74 q^{37} +4.15219e74 q^{38} -5.63979e75 q^{39} +2.89021e76 q^{40} -7.21825e76 q^{41} -3.47046e77 q^{42} +9.95921e76 q^{43} +4.05592e78 q^{44} -4.86934e78 q^{45} +1.58721e79 q^{46} +1.61545e79 q^{47} -1.98408e80 q^{48} -7.74788e78 q^{49} -6.41346e79 q^{50} +2.57348e80 q^{51} +7.01609e81 q^{52} -2.46146e81 q^{53} +2.14662e82 q^{54} -7.51930e82 q^{55} +2.38895e83 q^{56} +8.26407e82 q^{57} -1.11725e84 q^{58} +1.31371e84 q^{59} +1.03958e85 q^{60} +8.03762e84 q^{61} +2.43541e85 q^{62} -4.02484e85 q^{63} -2.59939e84 q^{64} -1.30072e86 q^{65} +1.16782e87 q^{66} -4.90861e86 q^{67} -3.20149e86 q^{68} +3.15902e87 q^{69} -8.00400e87 q^{70} +4.39734e87 q^{71} -5.20580e88 q^{72} -3.36142e88 q^{73} +7.86425e88 q^{74} -1.27647e88 q^{75} -1.02808e89 q^{76} -6.21521e89 q^{77} +2.02014e90 q^{78} +1.11166e89 q^{79} -4.57592e90 q^{80} -2.00867e90 q^{81} +2.58553e91 q^{82} -1.87032e91 q^{83} +8.59283e91 q^{84} +5.93527e90 q^{85} -3.56733e91 q^{86} -2.22365e92 q^{87} -8.03887e92 q^{88} +3.70282e92 q^{89} +1.74417e93 q^{90} -1.07513e93 q^{91} -3.92993e93 q^{92} +4.84719e93 q^{93} -5.78643e93 q^{94} +1.90596e93 q^{95} +2.14253e94 q^{96} -2.62608e94 q^{97} +2.77524e93 q^{98} +1.35437e95 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5835659138280 q^{2} - 95\!\cdots\!80 q^{3}+ \cdots + 92\!\cdots\!36 q^{9}+O(q^{10}) $ 8 * q - 5835659138280 * q^2 - 9565982513916703570080 * q^3 + 208956598309707350371623569984 * q^4 + 1941568507475850402526904141070960 * q^5 + 10651800775920653731297343298528492576 * q^6 + 31232311735415758067806325356531573912000 * q^7 - 14761127603920085098561309094124598702287360 * q^8 + 9274438133561954597944854467482391143953072936 * q^9	$ 8 q - 5835659138280 q^{2} - 95\!\cdots\!80 q^{3}+ \cdots + 30\!\cdots\!72 q^{99}+O(q^{100}) $ 8 * q - 5835659138280 * q^2 - 9565982513916703570080 * q^3 + 208956598309707350371623569984 * q^4 + 1941568507475850402526904141070960 * q^5 + 10651800775920653731297343298528492576 * q^6 + 31232311735415758067806325356531573912000 * q^7 - 14761127603920085098561309094124598702287360 * q^8 + 9274438133561954597944854467482391143953072936 * q^9 - 355384205613899841010372205704985147108657534640 * q^10 + 53080108095821756826858489331993621982645992125216 * q^11 + 1065031032961827853079380844579017283696993846403840 * q^12 + 117293508281179239843264964380833942161194396039342640 * q^13 + 8850886815767090581799564344683737269936151852930265408 * q^14 + 187812376414067333691564154745798290909917959215041625920 * q^15 + 9517116971431211282501221161054789131283343644054948220928 * q^16 - 13655041265063090981829171372625119189425374473948274915440 * q^17 - 1790266901749030205580776247252673430153004351197542602854280 * q^18 - 5232175975370167369536369873888207394303637759872553281713440 * q^19 + 136065209104116992530471413843386338746929879497239386344644480 * q^20 + 1346571177849118208545064341536207444072396945735327627682503936 * q^21 - 20365500099170357171519767897869972385636855003458825137197491360 * q^22 - 7129054072165937484825035531327773489156117409617881426435061440 * q^23 + 288860682603965362857322541557744811472884721216169744526242990080 * q^24 + 8177806376085721196783759852983887433280593317172609841487587996600 * q^25 - 69072273179717436642550386629266724895941590936463282023015399323504 * q^26 + 64049503386294800673569522679695786753122795388715525750679249767360 * q^27 + 303354815522537415860404332264897505740906926923909508834765584637440 * q^28 + 7715272198415359380593902919630157934289467091855373333108685675435440 * q^29 - 62913685170287068298704199843316213881225133796680396150164526710345280 * q^30 + 48520677903801540370519073843711920597057994260920479636592334181199616 * q^31 + 911347110324473008775326747695560179887781374647708612161794209209221120 * q^32 - 1535322742350198888271103254480947687741587903792512354063710702943493760 * q^33 - 16409772766982648656985219134942803587399227958333745923026675404562961232 * q^34 + 58800416933815614414155173269063056087887600285328689246425433374756677760 * q^35 + 51665208441213434468989869710710146210173003797753332160946711226240568128 * q^36 - 181116344963557296256979160619337453378797091102974834966000994855965247120 * q^37 - 1676466315180766681626408275142200947978975839695306622930354052184199692640 * q^38 + 465478714369259758144024065308323445042256641733578800363164365799686202432 * q^39 + 39028182173606372825635252450401491624189758401191157685601991729209269171200 * q^40 - 87541390126560450267544465567119030351560808726320656469732601708266148308784 * q^41 - 157435820560022140348706044721413472652300880194209574021901207450891596867840 * q^42 + 360093033489081253538156425248276463103949347025569853491672117723107522861600 * q^43 + 1942224484251042670482996667732829207493398934442399145050649033803969221005568 * q^44 - 1611554371538604569657837598986488298494511731253236200388961579880024486332880 * q^45 - 19332434944442851407749457669991401004991143268030327859543986888040547882373184 * q^46 + 38672453335683563852366980570346257355794761888911368752480783496161211070336640 * q^47 + 93863838769591236482712272126012963144755254935077324856132076191099747033333760 * q^48 + 265668043093542548841947390620517395072194945166225827717144824590425137465244744 * q^49 - 1423963459280866882678609595824694565889878038511273700600414891648711070234429400 * q^50 + 2434476695354895883532253554814552047229450451049452072207263289482820720406821056 * q^51 + 15678746704556392183126484026214298441253990030076674973212546269606119207477104000 * q^52 - 2922690482809426126710991861168746969788895886261814706776237561500358605037675280 * q^53 + 44393564079821957628952458152403809172972567715888333832276777433089826621820157760 * q^54 + 77963865832782922646862204005771036172886494149999882551809226033579503680996905920 * q^55 + 723822110434297992891221750986765045769194525611914833690699475848521019635777392640 * q^56 + 1459603943948321457517074656112276013643674313689343212415092604638087582879924782720 * q^57 + 2398120500739528001867383787619453843290390222445601081527493426426916763954522209040 * q^58 + 2444569112045817337560949868287606200158569651761097862873350630901953709318185022880 * q^59 + 41015921945833187827435663222575462810347191746192004435818365735996703011205515880960 * q^60 + 26252719580888049069066995575288184611473664654647035829209505915961690057602967485616 * q^61 + 109318411457586083204284032417457169492313955459811319765445849679642744506848521207040 * q^62 + 170984018880767416687602973051010439420211230624233991381305273834268390445660056281280 * q^63 + 407545659960425058121678577897271227683793728749313452587765989597513138495845491277824 * q^64 + 711217468942010938456527729098183388378886665557115838437689631605619958224435834575520 * q^65 + 1747938075646007071584137716302374690644541046339320226994976444199784352790302021223552 * q^66 - 646475642994207391400653355260241732956721934256209274545597969100350739031184431188640 * q^67 + 91675839067201266020688320385568861573762045194469769590554263557238860857176520405120 * q^68 - 1671348258106164448387617904756675195481964064504427142194954632911883632406377850960128 * q^69 - 15589682350948763132524633727148211085350313303119537319661619119948806738470696493235840 * q^70 - 14595295080721751466823982356267079020901744922845645857244436108167397828048945561374784 * q^71 - 168731956650076191328348463912100975176233311308158667034794509156143705616303905637470720 * q^72 - 167722859263497180232486905674536831998056258335586734743256934373976249561602911979579440 * q^73 - 209312489678791718598684146630297797595302804804578868479635191055424978871400486510408112 * q^74 - 319918492419260578418623942107150301135641877679303067145274604119881385565549842206216800 * q^75 - 959273209575432254809587692424149415253949631691365417587931662952012091653615772375589120 * q^76 - 358973379150050060834656745211596557040941835816686113329022190288009228708654757892460800 * q^77 + 590425535394410417923583601115147442109710886806797004396557673983317347484688655751672000 * q^78 + 4672642903096907209502768293890247708239627672362847349478671278970829923925879535283527040 * q^79 + 18415268594255335517079731605762998550074832241200743044677945286622776635630921688252866560 * q^80 + 12509737552066767544095911653095580991572013599361129872125476231341584536182121238921405768 * q^81 + 32657845092209493410036294321958173121440540177602229019397776717126981442788576405027965040 * q^82 + 34387792212015780744754986808561666458900302762495709021597904850967930099747337487085254880 * q^83 + 173836457542583880184373241725060178629119564679421678850358203433258194499103546320231344128 * q^84 + 58585978711733607272815047107060888289878133655773893600270763487144112403111490135244590560 * q^85 - 153511472921832187435283964804212642635464712353485304877046031498544471884447149897205104544 * q^86 - 544464219458114578116693663783217812912359092004929393234553696235186032730900539616052969920 * q^87 - 1202425497404423912185881933157195269872332267934742515736241252480851349730675866727622174720 * q^88 - 342673661311688548077760584785109887358595471462214186557789870415877447806348084055852796080 * q^89 - 3514062299884453064121468346218192535289244482618329972865712072788945397515179474700715316080 * q^90 - 3490211360016960529246147249335483533013067701963330513611222538458526220206688421639066690944 * q^91 - 12008074146638359830472895966704879561255070000267734630900014099911412498586265442549753546240 * q^92 + 197667690727810326296814984504358164807428856713575716952413727748092885643497784281407575040 * q^93 + 15433462798640093333378242254437202047220637579307237556798289796157532672617883642933732299648 * q^94 + 15321400721190643816477985005690604983976540891819618748501840926190750159388834713154020724800 * q^95 + 97555071644510782149318139986276901553221426854121546320985366392022081200430710682001871077376 * q^96 + 10072532354157458294768094296505188523874048354320514397914144859011793551098974691865811668240 * q^97 + 146363464831387371243245039459581022362075942196915081212239417921551560440470151788055390975960 * q^98 + 307096415144337525387251975813943414746365371627429389615225939474864146107991251707726185786272 * 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 $

$2$	−3.58194e14	−1.79967	−0.899835	−	0.436230i	$-0.856313\pi$
$2$	−3.58194e14	−1.79967	−0.899835	+	0.436230i	$0.856313\pi$
$3$	−7.12911e22	−1.54802	−0.774008	−	0.633176i	$-0.781751\pi$
$3$	−7.12911e22	−1.54802	−0.774008	+	0.633176i	$0.781751\pi$
$4$	8.86885e28	2.23881
$5$	−1.64420e33	−1.03486	−0.517429	−	0.855726i	$-0.673111\pi$
$5$	−1.64420e33	−1.03486	−0.517429	+	0.855726i	$0.673111\pi$
$6$	2.55360e37	2.78592
$7$	−1.35904e40	−0.979663	−0.489832	−	0.871817i	$-0.662942\pi$
$7$	−1.35904e40	−0.979663	−0.489832	+	0.871817i	$0.662942\pi$
$8$	−1.75781e43	−2.22946
$9$	2.96152e45	1.39635
$10$	5.88943e47	1.86240
$11$	4.57322e49	1.56340	0.781699	−	0.623656i	$-0.214354\pi$
$11$	4.57322e49	1.56340	0.781699	+	0.623656i	$0.214354\pi$
$12$	−6.32270e51	−3.46572
$13$	7.91094e52	0.968096	0.484048	−	0.875041i	$-0.339166\pi$
$13$	7.91094e52	0.968096	0.484048	+	0.875041i	$0.339166\pi$
$14$	4.86801e54	1.76307
$15$	1.17217e56	1.60198
$16$	2.78306e57	1.77347
$17$	−3.60982e57	−0.129170	−0.0645849	−	0.997912i	$-0.520572\pi$
$17$	−3.60982e57	−0.129170	−0.0645849	+	0.997912i	$0.520572\pi$
$18$	−1.06080e60	−2.51298
$19$	−1.15920e60	−0.210554	−0.105277	−	0.994443i	$-0.533573\pi$
$19$	−1.15920e60	−0.210554	−0.105277	+	0.994443i	$0.533573\pi$
$20$	−1.45822e62	−2.31685
$21$	9.68877e62	1.51653
$22$	−1.63810e64	−2.81360
$23$	−4.43116e64	−0.921393	−0.460697	−	0.887558i	$-0.652400\pi$
$23$	−4.43116e64	−0.921393	−0.460697	+	0.887558i	$0.652400\pi$
$24$	1.25316e66	3.45123
$25$	1.79050e65	0.0709291
$26$	−2.83365e67	−1.74225
$27$	−5.99290e67	−0.613562
$28$	−1.20532e69	−2.19328
$29$	3.11912e69	1.07183	0.535916	−	0.844271i	$-0.319966\pi$
$29$	3.11912e69	1.07183	0.535916	+	0.844271i	$0.319966\pi$
$30$	−4.19864e70	−2.88303
$31$	−6.79915e70	−0.983500	−0.491750	−	0.870737i	$-0.663643\pi$
$31$	−6.79915e70	−0.983500	−0.491750	+	0.870737i	$0.663643\pi$
$32$	−3.00533e71	−0.962208
$33$	−3.26030e72	−2.42016
$34$	1.29301e72	0.232463
$35$	2.23455e73	1.01381
$36$	2.62653e74	3.12617
$37$	−2.19553e74	−0.711144	−0.355572	−	0.934649i	$-0.615714\pi$
$37$	−2.19553e74	−0.711144	−0.355572	+	0.934649i	$0.615714\pi$
$38$	4.15219e74	0.378927
$39$	−5.63979e75	−1.49863
$40$	2.89021e76	2.30717
$41$	−7.21825e76	−1.78320	−0.891598	−	0.452828i	$-0.850415\pi$
$41$	−7.21825e76	−1.78320	−0.891598	+	0.452828i	$0.850415\pi$
$42$	−3.47046e77	−2.72926
$43$	9.95921e76	0.256138	0.128069	−	0.991765i	$-0.459122\pi$
$43$	9.95921e76	0.256138	0.128069	+	0.991765i	$0.459122\pi$
$44$	4.05592e78	3.50015
$45$	−4.86934e78	−1.44503
$46$	1.58721e79	1.65820
$47$	1.61545e79	0.607638	0.303819	−	0.952730i	$-0.401738\pi$
$47$	1.61545e79	0.607638	0.303819	+	0.952730i	$0.401738\pi$
$48$	−1.98408e80	−2.74536
$49$	−7.74788e78	−0.0402596
$50$	−6.41346e79	−0.127649
$51$	2.57348e80	0.199957
$52$	7.01609e81	2.16739
$53$	−2.46146e81	−0.307673	−0.153836	−	0.988096i	$-0.549163\pi$
$53$	−2.46146e81	−0.307673	−0.153836	+	0.988096i	$0.549163\pi$
$54$	2.14662e82	1.10421
$55$	−7.51930e82	−1.61789
$56$	2.38895e83	2.18412
$57$	8.26407e82	0.325941
$58$	−1.11725e84	−1.92895
$59$	1.31371e84	1.00700	0.503499	−	0.863996i	$-0.332046\pi$
$59$	1.31371e84	1.00700	0.503499	+	0.863996i	$0.332046\pi$
$60$	1.03958e85	3.58652
$61$	8.03762e84	1.26462	0.632310	−	0.774715i	$-0.282107\pi$
$61$	8.03762e84	1.26462	0.632310	+	0.774715i	$0.282107\pi$
$62$	2.43541e85	1.76997
$63$	−4.02484e85	−1.36796
$64$	−2.59939e84	−0.0418141
$65$	−1.30072e86	−1.00184
$66$	1.16782e87	4.35550
$67$	−4.90861e86	−0.896201	−0.448101	−	0.893983i	$-0.647899\pi$
$67$	−4.90861e86	−0.896201	−0.448101	+	0.893983i	$0.647899\pi$
$68$	−3.20149e86	−0.289187
$69$	3.15902e87	1.42633
$70$	−8.00400e87	−1.82453
$71$	4.39734e87	0.510997	0.255498	−	0.966809i	$-0.417760\pi$
$71$	4.39734e87	0.510997	0.255498	+	0.966809i	$0.417760\pi$
$72$	−5.20580e88	−3.11311
$73$	−3.36142e88	−1.04397	−0.521983	−	0.852956i	$-0.674808\pi$
$73$	−3.36142e88	−1.04397	−0.521983	+	0.852956i	$0.674808\pi$
$74$	7.86425e88	1.27983
$75$	−1.27647e88	−0.109799
$76$	−1.02808e89	−0.471390
$77$	−6.21521e89	−1.53160
$78$	2.02014e90	2.69704
$79$	1.11166e89	0.0810373	0.0405186	−	0.999179i	$-0.487099\pi$
$79$	1.11166e89	0.0810373	0.0405186	+	0.999179i	$0.487099\pi$
$80$	−4.57592e90	−1.83529
$81$	−2.00867e90	−0.446550
$82$	2.58553e91	3.20916
$83$	−1.87032e91	−1.30529	−0.652646	−	0.757663i	$-0.726341\pi$
$83$	−1.87032e91	−1.30529	−0.652646	+	0.757663i	$0.726341\pi$
$84$	8.59283e91	3.39524
$85$	5.93527e90	0.133672
$86$	−3.56733e91	−0.460963
$87$	−2.22365e92	−1.65921
$88$	−8.03887e92	−3.48552
$89$	3.70282e92	0.938657	0.469329	−	0.883024i	$-0.344496\pi$
$89$	3.70282e92	0.938657	0.469329	+	0.883024i	$0.344496\pi$
$90$	1.74417e93	2.60057
$91$	−1.07513e93	−0.948409
$92$	−3.92993e93	−2.06283
$93$	4.84719e93	1.52247
$94$	−5.78643e93	−1.09355
$95$	1.90596e93	0.217893
$96$	2.14253e94	1.48951
$97$	−2.62608e94	−1.11597	−0.557983	−	0.829852i	$-0.688425\pi$
$97$	−2.62608e94	−1.11597	−0.557983	+	0.829852i	$0.688425\pi$
$98$	2.77524e93	0.0724540
$99$	1.35437e95	2.18306
$100$	1.58797e94	0.158797
$101$	1.10372e95	0.688009	0.344005	−	0.938968i	$-0.388216\pi$
$101$	1.10372e95	0.688009	0.344005	+	0.938968i	$0.388216\pi$
$102$	−9.21802e94	−0.359857
$103$	−4.87066e94	−0.119624	−0.0598122	−	0.998210i	$-0.519050\pi$
$103$	−4.87066e94	−0.119624	−0.0598122	+	0.998210i	$0.519050\pi$
$104$	−1.39060e96	−2.15833
$105$	−1.59303e96	−1.56940
$106$	8.81679e95	0.553709
$107$	2.94696e96	1.18480	0.592399	−	0.805644i	$-0.298181\pi$
$107$	2.94696e96	1.18480	0.592399	+	0.805644i	$0.298181\pi$
$108$	−5.31502e96	−1.37365
$109$	−3.38805e96	−0.565185	−0.282593	−	0.959240i	$-0.591194\pi$
$109$	−3.38805e96	−0.565185	−0.282593	+	0.959240i	$0.591194\pi$
$110$	2.69336e97	2.91167
$111$	1.56522e97	1.10086
$112$	−3.78231e97	−1.73740
$113$	−2.97454e97	−0.895764	−0.447882	−	0.894093i	$-0.647821\pi$
$113$	−2.97454e97	−0.895764	−0.447882	+	0.894093i	$0.647821\pi$
$114$	−2.96014e97	−0.586586
$115$	7.28573e97	0.953510
$116$	2.76630e98	2.39963
$117$	2.34284e98	1.35181
$118$	−4.70562e98	−1.81227
$119$	4.90590e97	0.126543
$120$	−2.06046e99	−3.57153
$121$	1.23576e99	1.44421
$122$	−2.87902e99	−2.27590
$123$	5.14597e99	2.76041
$124$	−6.03007e99	−2.20187
$125$	3.85616e99	0.961456
$126$	1.44167e100	2.46187
$127$	−1.39487e100	−1.63628	−0.818142	−	0.575017i	$-0.804996\pi$
$127$	−1.39487e100	−1.63628	−0.818142	+	0.575017i	$0.804996\pi$
$128$	1.28364e100	1.03746
$129$	−7.10003e99	−0.396505
$130$	4.65909e100	1.80298
$131$	6.13269e100	1.64917	0.824583	−	0.565742i	$-0.191410\pi$
$131$	6.13269e100	1.64917	0.824583	+	0.565742i	$0.191410\pi$
$132$	−2.89151e101	−5.41830
$133$	1.57541e100	0.206272
$134$	1.75823e101	1.61287
$135$	9.85355e100	0.634949
$136$	6.34539e100	0.287978
$137$	4.22259e100	0.135317	0.0676585	−	0.997709i	$-0.478447\pi$
$137$	4.22259e100	0.135317	0.0676585	+	0.997709i	$0.478447\pi$
$138$	−1.13154e102	−2.56693
$139$	−6.55501e101	−1.05529	−0.527643	−	0.849466i	$-0.676924\pi$
$139$	−6.55501e101	−1.05529	−0.527643	+	0.849466i	$0.676924\pi$
$140$	1.98179e102	2.26973
$141$	−1.15167e102	−0.940633
$142$	−1.57510e102	−0.919626
$143$	3.61784e102	1.51352
$144$	8.24210e102	2.47639
$145$	−5.12847e102	−1.10919
$146$	1.20404e103	1.87879
$147$	5.52355e101	0.0623225
$148$	−1.94718e103	−1.59212
$149$	−3.04800e103	−1.80995	−0.904976	−	0.425464i	$-0.860111\pi$
$149$	−3.04800e103	−1.80995	−0.904976	+	0.425464i	$0.860111\pi$
$150$	4.57222e102	0.197603
$151$	−5.07378e103	−1.59929	−0.799643	−	0.600475i	$-0.794978\pi$
$151$	−5.07378e103	−1.59929	−0.799643	+	0.600475i	$0.794978\pi$
$152$	2.03766e103	0.469420
$153$	−1.06905e103	−0.180367
$154$	2.22625e104	2.75638
$155$	1.11792e104	1.01778
$156$	−5.00185e104	−3.35515
$157$	1.04876e104	0.519329	0.259664	−	0.965699i	$-0.416388\pi$
$157$	1.04876e104	0.519329	0.259664	+	0.965699i	$0.416388\pi$
$158$	−3.98189e103	−0.145840
$159$	1.75480e104	0.476282
$160$	4.94138e104	0.995748
$161$	6.02214e104	0.902655
$162$	7.19493e104	0.803643
$163$	−7.18400e104	−0.599039	−0.299520	−	0.954090i	$-0.596826\pi$
$163$	−7.18400e104	−0.599039	−0.299520	+	0.954090i	$0.596826\pi$
$164$	−6.40176e105	−3.99224
$165$	5.36059e105	2.50452
$166$	6.69938e105	2.34909
$167$	−1.96165e105	−0.517117	−0.258559	−	0.965996i	$-0.583248\pi$
$167$	−1.96165e105	−0.517117	−0.258559	+	0.965996i	$0.583248\pi$
$168$	−1.70311e106	−3.38105
$169$	−4.19280e104	−0.0627892
$170$	−2.12598e105	−0.240566
$171$	−3.43300e105	−0.294007
$172$	8.83268e105	0.573444
$173$	−1.11719e106	−0.550728	−0.275364	−	0.961340i	$-0.588798\pi$
$173$	−1.11719e106	−0.550728	−0.275364	+	0.961340i	$0.588798\pi$
$174$	7.96498e106	2.98604
$175$	−2.43337e105	−0.0694866
$176$	1.27276e107	2.77264
$177$	−9.36558e106	−1.55885
$178$	−1.32633e107	−1.68927
$179$	9.98989e106	0.975083	0.487542	−	0.873100i	$-0.337894\pi$
$179$	9.98989e106	0.975083	0.487542	+	0.873100i	$0.337894\pi$
$180$	−4.31855e107	−3.23514
$181$	1.13843e107	0.655499	0.327750	−	0.944765i	$-0.393710\pi$
$181$	1.13843e107	0.655499	0.327750	+	0.944765i	$0.393710\pi$
$182$	3.85105e107	1.70682
$183$	−5.73010e107	−1.95765
$184$	7.78916e107	2.05420
$185$	3.60990e107	0.735933
$186$	−1.73623e108	−2.73995
$187$	−1.65085e107	−0.201944
$188$	1.43272e108	1.36039
$189$	8.14462e107	0.601084
$190$	−6.82704e107	−0.392136
$191$	−3.11456e108	−1.39416	−0.697079	−	0.716994i	$-0.745517\pi$
$191$	−3.11456e108	−1.39416	−0.697079	+	0.716994i	$0.745517\pi$
$192$	1.85313e107	0.0647289
$193$	3.56393e108	0.972651	0.486326	−	0.873778i	$-0.338337\pi$
$193$	3.56393e108	0.972651	0.486326	+	0.873778i	$0.338337\pi$
$194$	9.40645e108	2.00837
$195$	9.27296e108	1.55087
$196$	−6.87148e107	−0.0901337
$197$	−1.01687e109	−1.04742	−0.523710	−	0.851897i	$-0.675452\pi$
$197$	−1.01687e109	−1.04742	−0.523710	+	0.851897i	$0.675452\pi$
$198$	−4.85126e109	−3.92878
$199$	1.24725e109	0.795118	0.397559	−	0.917577i	$-0.369857\pi$
$199$	1.24725e109	0.795118	0.397559	+	0.917577i	$0.369857\pi$
$200$	−3.14737e108	−0.158133
$201$	3.49940e109	1.38733
$202$	−3.95346e109	−1.23819
$203$	−4.23902e109	−1.05004
$204$	2.28238e109	0.447666
$205$	1.18683e110	1.84535
$206$	1.74464e109	0.215284
$207$	−1.31230e110	−1.28659
$208$	2.20166e110	1.71689
$209$	−5.30128e109	−0.329179
$210$	5.70614e110	2.82440
$211$	−3.92681e110	−1.55104	−0.775521	−	0.631322i	$-0.782513\pi$
$211$	−3.92681e110	−1.55104	−0.775521	+	0.631322i	$0.782513\pi$
$212$	−2.18303e110	−0.688821
$213$	−3.13491e110	−0.791031
$214$	−1.05558e111	−2.13225
$215$	−1.63750e110	−0.265066
$216$	1.05344e111	1.36791
$217$	9.24035e110	0.963498
$218$	1.21358e111	1.01715
$219$	2.39639e111	1.61608
$220$	−6.66876e111	−3.62216
$221$	−2.85570e110	−0.125049
$222$	−5.60651e111	−1.98119
$223$	3.85773e111	1.10116	0.550581	−	0.834782i	$-0.314406\pi$
$223$	3.85773e111	1.10116	0.550581	+	0.834782i	$0.314406\pi$
$224$	4.08438e111	0.942640
$225$	5.30260e110	0.0990420
$226$	1.06546e112	1.61208
$227$	3.19587e111	0.392067	0.196034	−	0.980597i	$-0.437194\pi$
$227$	3.19587e111	0.392067	0.196034	+	0.980597i	$0.437194\pi$
$228$	7.32928e111	0.729720
$229$	2.95707e111	0.239153	0.119576	−	0.992825i	$-0.461846\pi$
$229$	2.95707e111	0.239153	0.119576	+	0.992825i	$0.461846\pi$
$230$	−2.60970e112	−1.71600
$231$	4.43089e112	2.37095
$232$	−5.48283e112	−2.38960
$233$	−9.57245e111	−0.340108	−0.170054	−	0.985435i	$-0.554394\pi$
$233$	−9.57245e111	−0.340108	−0.170054	+	0.985435i	$0.554394\pi$
$234$	−8.39190e112	−2.43280
$235$	−2.65613e112	−0.628818
$236$	1.16511e113	2.25448
$237$	−7.92514e111	−0.125447
$238$	−1.75726e112	−0.227736
$239$	−8.40460e112	−0.892517	−0.446259	−	0.894904i	$-0.647244\pi$
$239$	−8.40460e112	−0.892517	−0.446259	+	0.894904i	$0.647244\pi$
$240$	3.26222e113	2.84106
$241$	8.08769e112	0.578116	0.289058	−	0.957312i	$-0.406658\pi$
$241$	8.08769e112	0.578116	0.289058	+	0.957312i	$0.406658\pi$
$242$	−4.42643e113	−2.59910
$243$	2.70303e113	1.30483
$244$	7.12845e113	2.83125
$245$	1.27391e112	0.0416629
$246$	−1.84325e114	−4.96784
$247$	−9.17037e112	−0.203836
$248$	1.19516e114	2.19267
$249$	1.33337e114	2.02061
$250$	−1.38125e114	−1.73030
$251$	1.49134e114	1.54553	0.772763	−	0.634695i	$-0.218874\pi$
$251$	1.49134e114	1.54553	0.772763	+	0.634695i	$0.218874\pi$
$252$	−3.56957e114	−3.06260
$253$	−2.02647e114	−1.44050
$254$	4.99635e114	2.94477
$255$	−4.23132e113	−0.206927
$256$	−4.49496e114	−1.82527
$257$	2.97216e114	1.00288	0.501440	−	0.865193i	$-0.332804\pi$
$257$	2.97216e114	1.00288	0.501440	+	0.865193i	$0.332804\pi$
$258$	2.54318e114	0.713579
$259$	2.98382e114	0.696682
$260$	−1.15359e115	−2.24294
$261$	9.23733e114	1.49666
$262$	−2.19669e115	−2.96795
$263$	1.12954e115	1.27351	0.636757	−	0.771064i	$-0.280275\pi$
$263$	1.12954e115	1.27351	0.636757	+	0.771064i	$0.280275\pi$
$264$	5.73100e115	5.39565
$265$	4.04714e114	0.318397
$266$	−5.64301e114	−0.371221
$267$	−2.63978e115	−1.45306
$268$	−4.35337e115	−2.00643
$269$	−3.11950e115	−1.20462	−0.602311	−	0.798261i	$-0.705753\pi$
$269$	−3.11950e115	−1.20462	−0.602311	+	0.798261i	$0.705753\pi$
$270$	−3.52948e115	−1.14270
$271$	−1.08254e115	−0.294037	−0.147019	−	0.989134i	$-0.546968\pi$
$271$	−1.08254e115	−0.294037	−0.147019	+	0.989134i	$0.546968\pi$
$272$	−1.00463e115	−0.229079
$273$	7.66473e115	1.46815
$274$	−1.51251e115	−0.243526
$275$	8.18835e114	0.110890
$276$	2.80169e116	3.19329
$277$	−1.22498e116	−1.17582	−0.587910	−	0.808926i	$-0.700049\pi$
$277$	−1.22498e116	−1.17582	−0.587910	+	0.808926i	$0.700049\pi$
$278$	2.34796e116	1.89917
$279$	−2.01358e116	−1.37331
$280$	−3.92792e116	−2.26025
$281$	−1.11820e116	−0.543213	−0.271606	−	0.962408i	$-0.587555\pi$
$281$	−1.11820e116	−0.543213	−0.271606	+	0.962408i	$0.587555\pi$
$282$	4.12521e116	1.69283
$283$	2.17495e116	0.754388	0.377194	−	0.926134i	$-0.376889\pi$
$283$	2.17495e116	0.754388	0.377194	+	0.926134i	$0.376889\pi$
$284$	3.89993e116	1.14403
$285$	−1.35878e116	−0.337302
$286$	−1.29589e117	−2.72384
$287$	9.80993e116	1.74693
$288$	−8.90036e116	−1.34358
$289$	−7.67963e116	−0.983315
$290$	1.83698e117	1.99618
$291$	1.87216e117	1.72753
$292$	−2.98119e117	−2.33725
$293$	−1.51971e117	−1.01286	−0.506430	−	0.862281i	$-0.669035\pi$
$293$	−1.51971e117	−1.01286	−0.506430	+	0.862281i	$0.669035\pi$
$294$	−1.97850e116	−0.112160
$295$	−2.16001e117	−1.04210
$296$	3.85934e117	1.58546
$297$	−2.74068e117	−0.959241
$298$	1.09177e118	3.25732
$299$	−3.50546e117	−0.891998
$300$	−1.13208e117	−0.245820
$301$	−1.35350e117	−0.250929
$302$	1.81739e118	2.87819
$303$	−7.86855e117	−1.06505
$304$	−3.22613e117	−0.373411
$305$	−1.32155e118	−1.30870
$306$	3.82928e117	0.324601
$307$	2.13565e118	1.55045	0.775223	−	0.631687i	$-0.217637\pi$
$307$	2.13565e118	1.55045	0.775223	+	0.631687i	$0.217637\pi$
$308$	−5.51218e118	−3.42897
$309$	3.47234e117	0.185180
$310$	−4.00431e118	−1.83167
$311$	−9.62267e117	−0.377726	−0.188863	−	0.982003i	$-0.560480\pi$
$311$	−9.62267e117	−0.377726	−0.188863	+	0.982003i	$0.560480\pi$
$312$	9.91371e118	3.34113
$313$	−1.77984e118	−0.515258	−0.257629	−	0.966244i	$-0.582941\pi$
$313$	−1.77984e118	−0.515258	−0.257629	+	0.966244i	$0.582941\pi$
$314$	−3.75659e118	−0.934621
$315$	6.61765e118	1.41564
$316$	9.85914e117	0.181427
$317$	1.02465e119	1.62279	0.811393	−	0.584501i	$-0.198710\pi$
$317$	1.02465e119	1.62279	0.811393	+	0.584501i	$0.198710\pi$
$318$	−6.28558e118	−0.857151
$319$	1.42644e119	1.67570
$320$	4.27393e117	0.0432716
$321$	−2.10092e119	−1.83409
$322$	−2.15709e119	−1.62448
$323$	4.18450e117	0.0271972
$324$	−1.78146e119	−0.999742
$325$	1.41645e118	0.0686662
$326$	2.57326e119	1.07807
$327$	2.41538e119	0.874916
$328$	1.26884e120	3.97555
$329$	−2.19547e119	−0.595281
$330$	−1.92013e120	−4.50732
$331$	5.85572e119	1.19056	0.595279	−	0.803519i	$-0.297042\pi$
$331$	5.85572e119	1.19056	0.595279	+	0.803519i	$0.297042\pi$
$332$	−1.65876e120	−2.92230
$333$	−6.50211e119	−0.993009
$334$	7.02650e119	0.930641
$335$	8.07075e119	0.927440
$336$	2.69645e120	2.68953
$337$	−8.46137e119	−0.732859	−0.366430	−	0.930446i	$-0.619420\pi$
$337$	−8.46137e119	−0.732859	−0.366430	+	0.930446i	$0.619420\pi$
$338$	1.50183e119	0.113000
$339$	2.12058e120	1.38666
$340$	5.26390e119	0.299267
$341$	−3.10940e120	−1.53760
$342$	1.22968e120	0.529116
$343$	2.72075e120	1.01910
$344$	−1.75065e120	−0.571047
$345$	−5.19407e120	−1.47605
$346$	4.00170e120	0.991129
$347$	2.91087e120	0.628597	0.314299	−	0.949324i	$-0.398231\pi$
$347$	2.91087e120	0.628597	0.314299	+	0.949324i	$0.398231\pi$
$348$	−1.97212e121	−3.71467
$349$	7.18026e120	1.18014	0.590069	−	0.807353i	$-0.299101\pi$
$349$	7.18026e120	1.18014	0.590069	+	0.807353i	$0.299101\pi$
$350$	8.71618e119	0.125053
$351$	−4.74095e120	−0.593987
$352$	−1.37441e121	−1.50431
$353$	2.46295e120	0.235590	0.117795	−	0.993038i	$-0.462417\pi$
$353$	2.46295e120	0.235590	0.117795	+	0.993038i	$0.462417\pi$
$354$	3.35469e121	2.80542
$355$	−7.23012e120	−0.528809
$356$	3.28397e121	2.10148
$357$	−3.49747e120	−0.195891
$358$	−3.57831e121	−1.75483
$359$	1.17808e121	0.506043	0.253021	−	0.967461i	$-0.418576\pi$
$359$	1.17808e121	0.506043	0.253021	+	0.967461i	$0.418576\pi$
$360$	8.55940e121	3.22162
$361$	−2.89667e121	−0.955667
$362$	−4.07777e121	−1.17968
$363$	−8.80990e121	−2.23566
$364$	−9.53518e121	−2.12331
$365$	5.52685e121	1.08036
$366$	2.05249e122	3.52313
$367$	9.29894e121	1.40215	0.701077	−	0.713086i	$-0.252703\pi$
$367$	9.29894e121	1.40215	0.701077	+	0.713086i	$0.252703\pi$
$368$	−1.23322e122	−1.63406
$369$	−2.13770e122	−2.48997
$370$	−1.29304e122	−1.32444
$371$	3.34523e121	0.301416
$372$	4.29890e122	3.40853
$373$	−4.86262e121	−0.339391	−0.169696	−	0.985497i	$-0.554278\pi$
$373$	−4.86262e121	−0.339391	−0.169696	+	0.985497i	$0.554278\pi$
$374$	5.91323e121	0.363432
$375$	−2.74910e122	−1.48835
$376$	−2.83966e122	−1.35470
$377$	2.46751e122	1.03764
$378$	−2.91735e122	−1.08175
$379$	−2.94369e122	−0.962785	−0.481393	−	0.876505i	$-0.659869\pi$
$379$	−2.94369e122	−0.962785	−0.481393	+	0.876505i	$0.659869\pi$
$380$	1.69037e122	0.487822
$381$	9.94421e122	2.53299
$382$	1.11562e123	2.50903
$383$	1.85689e122	0.368845	0.184423	−	0.982847i	$-0.440958\pi$
$383$	1.85689e122	0.368845	0.184423	+	0.982847i	$0.440958\pi$
$384$	−9.15124e122	−1.60600
$385$	1.02191e123	1.58499
$386$	−1.27658e123	−1.75045
$387$	2.94944e122	0.357659
$388$	−2.32903e123	−2.49844
$389$	1.47687e123	1.40197	0.700983	−	0.713178i	$-0.252745\pi$
$389$	1.47687e123	1.40197	0.700983	+	0.713178i	$0.252745\pi$
$390$	−3.32151e123	−2.79105
$391$	1.59957e122	0.119016
$392$	1.36193e122	0.0897569
$393$	−4.37206e123	−2.55293
$394$	3.64237e123	1.88501
$395$	−1.82779e122	−0.0838620
$396$	1.20117e124	4.88745
$397$	−9.98437e121	−0.0360389	−0.0180194	−	0.999838i	$-0.505736\pi$
$397$	−9.98437e121	−0.0360389	−0.0180194	+	0.999838i	$0.505736\pi$
$398$	−4.46756e123	−1.43095
$399$	−1.12312e123	−0.319312
$400$	4.98308e122	0.125791
$401$	6.05539e123	1.35764	0.678820	−	0.734305i	$-0.262492\pi$
$401$	6.05539e123	1.35764	0.678820	+	0.734305i	$0.262492\pi$
$402$	−1.25346e124	−2.49674
$403$	−5.37876e123	−0.952122
$404$	9.78874e123	1.54032
$405$	3.30266e123	0.462116
$406$	1.51839e124	1.88972
$407$	−1.00406e124	−1.11180
$408$	−4.52369e123	−0.445795
$409$	1.17885e124	1.03420	0.517098	−	0.855926i	$-0.327012\pi$
$409$	1.17885e124	1.03420	0.517098	+	0.855926i	$0.327012\pi$
$410$	−4.25114e124	−3.32103
$411$	−3.01033e123	−0.209473
$412$	−4.31972e123	−0.267817
$413$	−1.78539e124	−0.986520
$414$	4.70056e124	2.31544
$415$	3.07519e124	1.35079
$416$	−2.37750e124	−0.931510
$417$	4.67313e124	1.63360
$418$	1.89888e124	0.592414
$419$	−4.50330e124	−1.25419	−0.627097	−	0.778941i	$-0.715757\pi$
$419$	−4.50330e124	−1.25419	−0.627097	+	0.778941i	$0.715757\pi$
$420$	−1.41284e125	−3.51359
$421$	−5.43889e124	−1.20812	−0.604061	−	0.796938i	$-0.706452\pi$
$421$	−5.43889e124	−1.20812	−0.604061	+	0.796938i	$0.706452\pi$
$422$	1.40656e125	2.79136
$423$	4.78418e124	0.848477
$424$	4.32679e124	0.685942
$425$	−6.46338e122	−0.00916190
$426$	1.12290e125	1.42360
$427$	−1.09235e125	−1.23890
$428$	2.61361e125	2.65254
$429$	−2.57920e125	−2.34295
$430$	5.86541e124	0.477031
$431$	1.19807e125	0.872590	0.436295	−	0.899804i	$-0.356290\pi$
$431$	1.19807e125	0.872590	0.436295	+	0.899804i	$0.356290\pi$
$432$	−1.66786e125	−1.08813
$433$	−2.47491e125	−1.44672	−0.723359	−	0.690472i	$-0.757403\pi$
$433$	−2.47491e125	−1.44672	−0.723359	+	0.690472i	$0.757403\pi$
$434$	−3.30983e125	−1.73398
$435$	3.65614e125	1.71705
$436$	−3.00481e125	−1.26534
$437$	5.13661e124	0.194003
$438$	−8.58371e125	−2.90840
$439$	1.37659e125	0.418543	0.209271	−	0.977858i	$-0.432891\pi$
$439$	1.37659e125	0.418543	0.209271	+	0.977858i	$0.432891\pi$
$440$	1.32175e126	3.60702
$441$	−2.29455e124	−0.0562166
$442$	1.02289e125	0.225047
$443$	1.72244e125	0.340382	0.170191	−	0.985411i	$-0.445562\pi$
$443$	1.72244e125	0.340382	0.170191	+	0.985411i	$0.445562\pi$
$444$	1.38817e126	2.46463
$445$	−6.08818e125	−0.971376
$446$	−1.38182e126	−1.98173
$447$	2.17295e126	2.80183
$448$	3.53269e124	0.0409637
$449$	−7.14699e125	−0.745456	−0.372728	−	0.927941i	$-0.621578\pi$
$449$	−7.14699e125	−0.745456	−0.372728	+	0.927941i	$0.621578\pi$
$450$	−1.89936e125	−0.178243
$451$	−3.30106e126	−2.78784
$452$	−2.63807e126	−2.00545
$453$	3.61715e126	2.47572
$454$	−1.14474e126	−0.705592
$455$	1.76774e126	0.981467
$456$	−1.45267e126	−0.726670
$457$	3.36219e126	1.51566	0.757832	−	0.652449i	$-0.226258\pi$
$457$	3.36219e126	1.51566	0.757832	+	0.652449i	$0.226258\pi$
$458$	−1.05920e126	−0.430396
$459$	2.16333e125	0.0792537
$460$	6.46160e126	2.13473
$461$	−5.01596e125	−0.149472	−0.0747361	−	0.997203i	$-0.523811\pi$
$461$	−5.01596e125	−0.149472	−0.0747361	+	0.997203i	$0.523811\pi$
$462$	−1.58712e127	−4.26692
$463$	−1.34311e126	−0.325846	−0.162923	−	0.986639i	$-0.552092\pi$
$463$	−1.34311e126	−0.325846	−0.162923	+	0.986639i	$0.552092\pi$
$464$	8.68071e126	1.90086
$465$	−7.96976e126	−1.57554
$466$	3.42879e126	0.612082
$467$	−3.33841e126	−0.538255	−0.269127	−	0.963105i	$-0.586735\pi$
$467$	−3.33841e126	−0.538255	−0.269127	+	0.963105i	$0.586735\pi$
$468$	2.07783e127	3.02644
$469$	6.67102e126	0.877975
$470$	9.51407e126	1.13167
$471$	−7.47672e126	−0.803930
$472$	−2.30926e127	−2.24506
$473$	4.55457e126	0.400445
$474$	2.83873e126	0.225763
$475$	−2.07555e125	−0.0149344
$476$	4.35097e126	0.283306
$477$	−7.28966e126	−0.429620
$478$	3.01047e127	1.60624
$479$	−1.67585e127	−0.809653	−0.404827	−	0.914393i	$-0.632668\pi$
$479$	−1.67585e127	−0.809653	−0.404827	+	0.914393i	$0.632668\pi$
$480$	−3.52276e127	−1.54143
$481$	−1.73687e127	−0.688456
$482$	−2.89696e127	−1.04042
$483$	−4.29325e127	−1.39732
$484$	1.09598e128	3.23332
$485$	4.31781e127	1.15486
$486$	−9.68209e127	−2.34826
$487$	4.16780e127	0.916815	0.458408	−	0.888742i	$-0.348420\pi$
$487$	4.16780e127	0.916815	0.458408	+	0.888742i	$0.348420\pi$
$488$	−1.41286e128	−2.81941
$489$	5.12155e127	0.927322
$490$	−4.56306e126	−0.0749795
$491$	9.93764e127	1.48222	0.741110	−	0.671384i	$-0.234300\pi$
$491$	9.93764e127	1.48222	0.741110	+	0.671384i	$0.234300\pi$
$492$	4.56388e128	6.18005
$493$	−1.12594e127	−0.138449
$494$	3.28477e127	0.366838
$495$	−2.22686e128	−2.25915
$496$	−1.89225e128	−1.74421
$497$	−5.97618e127	−0.500605
$498$	−4.77606e128	−3.63644
$499$	3.25262e126	0.0225143	0.0112571	−	0.999937i	$-0.496417\pi$
$499$	3.25262e126	0.0225143	0.0112571	+	0.999937i	$0.496417\pi$
$500$	3.41997e128	2.15252
$501$	1.39848e128	0.800506
$502$	−5.34190e128	−2.78144
$503$	−3.08967e127	−0.146364	−0.0731819	−	0.997319i	$-0.523315\pi$
$503$	−3.08967e127	−0.146364	−0.0731819	+	0.997319i	$0.523315\pi$
$504$	7.07492e128	3.04980
$505$	−1.81474e128	−0.711991
$506$	7.25867e128	2.59243
$507$	2.98909e127	0.0971987
$508$	−1.23709e129	−3.66333
$509$	−2.89553e128	−0.780969	−0.390484	−	0.920610i	$-0.627692\pi$
$509$	−2.89553e128	−0.780969	−0.390484	+	0.920610i	$0.627692\pi$
$510$	1.51563e128	0.372400
$511$	4.56832e128	1.02274
$512$	1.10156e129	2.24743
$513$	6.94698e127	0.129188
$514$	−1.06461e129	−1.80485
$515$	8.00835e127	0.123794
$516$	−6.29691e128	−0.887701
$517$	7.38780e128	0.949979
$518$	−1.06879e129	−1.25380
$519$	7.96457e128	0.852536
$520$	2.28642e129	2.23356
$521$	−2.20919e128	−0.196989	−0.0984945	−	0.995138i	$-0.531403\pi$
$521$	−2.20919e128	−0.196989	−0.0984945	+	0.995138i	$0.531403\pi$
$522$	−3.30875e129	−2.69349
$523$	1.61181e129	1.19807	0.599036	−	0.800722i	$-0.295550\pi$
$523$	1.61181e129	1.19807	0.599036	+	0.800722i	$0.295550\pi$
$524$	5.43899e129	3.69217
$525$	1.73478e128	0.107566
$526$	−4.04594e129	−2.29191
$527$	2.45437e128	0.127039
$528$	−9.07361e129	−4.29209
$529$	−3.49318e128	−0.151034
$530$	−1.44966e129	−0.573010
$531$	3.89058e129	1.40613
$532$	1.39721e129	0.461804
$533$	−5.71031e129	−1.72631
$534$	9.45551e129	2.61502
$535$	−4.84540e129	−1.22610
$536$	8.62843e129	1.99804
$537$	−7.12190e129	−1.50944
$538$	1.11738e130	2.16792
$539$	−3.54328e128	−0.0629417
$540$	8.73897e129	1.42153
$541$	−4.10453e129	−0.611496	−0.305748	−	0.952113i	$-0.598906\pi$
$541$	−4.10453e129	−0.611496	−0.305748	+	0.952113i	$0.598906\pi$
$542$	3.87759e129	0.529170
$543$	−8.11595e129	−1.01472
$544$	1.08487e129	0.124288
$545$	5.57064e129	0.584886
$546$	−2.74546e130	−2.64219
$547$	−5.62480e127	−0.00496259	−0.00248130	−	0.999997i	$-0.500790\pi$
$547$	−5.62480e127	−0.00496259	−0.00248130	+	0.999997i	$0.500790\pi$
$548$	3.74496e129	0.302949
$549$	2.38036e130	1.76586
$550$	−2.93301e129	−0.199566
$551$	−3.61569e129	−0.225678
$552$	−5.55297e130	−3.17994
$553$	−1.51080e129	−0.0793893
$554$	4.38781e130	2.11609
$555$	−2.57354e130	−1.13924
$556$	−5.81354e130	−2.36259
$557$	1.89115e130	0.705672	0.352836	−	0.935685i	$-0.385217\pi$
$557$	1.89115e130	0.705672	0.352836	+	0.935685i	$0.385217\pi$
$558$	7.21252e130	2.47151
$559$	7.87867e129	0.247966
$560$	6.21889e130	1.79797
$561$	1.17691e130	0.312612
$562$	4.00533e130	0.977604
$563$	−2.59348e130	−0.581747	−0.290874	−	0.956761i	$-0.593946\pi$
$563$	−2.59348e130	−0.581747	−0.290874	+	0.956761i	$0.593946\pi$
$564$	−1.02140e131	−2.10590
$565$	4.89075e130	0.926987
$566$	−7.79055e130	−1.35765
$567$	2.72987e130	0.437469
$568$	−7.72970e130	−1.13924
$569$	−9.69620e130	−1.31453	−0.657263	−	0.753661i	$-0.728286\pi$
$569$	−9.69620e130	−1.31453	−0.657263	+	0.753661i	$0.728286\pi$
$570$	4.86707e130	0.607032
$571$	3.14741e130	0.361192	0.180596	−	0.983557i	$-0.442197\pi$
$571$	3.14741e130	0.361192	0.180596	+	0.983557i	$0.442197\pi$
$572$	3.20861e131	3.38849
$573$	2.22040e131	2.15818
$574$	−3.51385e131	−3.14390
$575$	−7.93399e129	−0.0653536
$576$	−7.69814e129	−0.0583873
$577$	−6.67413e130	−0.466169	−0.233085	−	0.972456i	$-0.574882\pi$
$577$	−6.67413e130	−0.466169	−0.233085	+	0.972456i	$0.574882\pi$
$578$	2.75079e131	1.76964
$579$	−2.54076e131	−1.50568
$580$	−4.54836e131	−2.48328
$581$	2.54186e131	1.27875
$582$	−6.70596e131	−3.10899
$583$	−1.12568e131	−0.481015
$584$	5.90875e131	2.32748
$585$	−3.85210e131	−1.39892
$586$	5.44351e131	1.82281
$587$	3.41186e131	1.05361	0.526807	−	0.849985i	$-0.323389\pi$
$587$	3.41186e131	1.05361	0.526807	+	0.849985i	$0.323389\pi$
$588$	4.89875e130	0.139528
$589$	7.88159e130	0.207079
$590$	7.73700e131	1.87544
$591$	7.24939e131	1.62142
$592$	−6.11030e131	−1.26119
$593$	−3.62270e131	−0.690135	−0.345067	−	0.938578i	$-0.612144\pi$
$593$	−3.62270e131	−0.690135	−0.345067	+	0.938578i	$0.612144\pi$
$594$	9.81695e131	1.72632
$595$	−8.06630e130	−0.130954
$596$	−2.70322e132	−4.05214
$597$	−8.89176e131	−1.23086
$598$	1.25563e132	1.60530
$599$	1.25699e132	1.48443	0.742214	−	0.670163i	$-0.233776\pi$
$599$	1.25699e132	1.48443	0.742214	+	0.670163i	$0.233776\pi$
$600$	2.24379e131	0.244793
$601$	−6.15850e131	−0.620780	−0.310390	−	0.950609i	$-0.600460\pi$
$601$	−6.15850e131	−0.620780	−0.310390	+	0.950609i	$0.600460\pi$
$602$	4.84816e131	0.451589
$603$	−1.45369e132	−1.25141
$604$	−4.49986e132	−3.58050
$605$	−2.03185e132	−1.49455
$606$	2.81846e132	1.91674
$607$	2.50627e132	1.57604	0.788018	−	0.615653i	$-0.211108\pi$
$607$	2.50627e132	1.57604	0.788018	+	0.615653i	$0.211108\pi$
$608$	3.48379e131	0.202596
$609$	3.02204e132	1.62547
$610$	4.73370e132	2.35523
$611$	1.27797e132	0.588252
$612$	−9.48128e131	−0.403808
$613$	−1.10392e132	−0.435078	−0.217539	−	0.976052i	$-0.569803\pi$
$613$	−1.10392e132	−0.435078	−0.217539	+	0.976052i	$0.569803\pi$
$614$	−7.64975e132	−2.79029
$615$	−8.46102e132	−2.85663
$616$	1.09252e133	3.41464
$617$	2.97655e131	0.0861327	0.0430663	−	0.999072i	$-0.486287\pi$
$617$	2.97655e131	0.0861327	0.0430663	+	0.999072i	$0.486287\pi$
$618$	−1.24377e132	−0.333264
$619$	−1.37709e132	−0.341708	−0.170854	−	0.985296i	$-0.554653\pi$
$619$	−1.37709e132	−0.341708	−0.170854	+	0.985296i	$0.554653\pi$
$620$	9.91465e132	2.27862
$621$	2.65555e132	0.565332
$622$	3.44678e132	0.679783
$623$	−5.03229e132	−0.919568
$624$	−1.56959e133	−2.65777
$625$	−6.79229e132	−1.06590
$626$	6.37527e132	0.927294
$627$	3.77934e132	0.509575
$628$	9.30130e132	1.16268
$629$	7.92546e131	0.0918584
$630$	−2.37040e133	−2.54768
$631$	5.91102e132	0.589207	0.294603	−	0.955620i	$-0.404812\pi$
$631$	5.91102e132	0.589207	0.294603	+	0.955620i	$0.404812\pi$
$632$	−1.95409e132	−0.180669
$633$	2.79947e133	2.40104
$634$	−3.67024e133	−2.92048
$635$	2.29346e133	1.69332
$636$	1.55631e133	1.06631
$637$	−6.12930e131	−0.0389752
$638$	−5.10942e133	−3.01571
$639$	1.30228e133	0.713532
$640$	−2.11057e133	−1.07362
$641$	−3.24606e133	−1.53321	−0.766603	−	0.642121i	$-0.778055\pi$
$641$	−3.24606e133	−1.53321	−0.766603	+	0.642121i	$0.778055\pi$
$642$	7.52535e133	3.30075
$643$	1.37740e133	0.561096	0.280548	−	0.959840i	$-0.409484\pi$
$643$	1.37740e133	0.561096	0.280548	+	0.959840i	$0.409484\pi$
$644$	5.34095e133	2.02088
$645$	1.16739e133	0.410326
$646$	−1.49886e132	−0.0489460
$647$	−4.40655e133	−1.33704	−0.668522	−	0.743692i	$-0.733073\pi$
$647$	−4.40655e133	−1.33704	−0.668522	+	0.743692i	$0.733073\pi$
$648$	3.53087e133	0.995564
$649$	6.00788e133	1.57434
$650$	−5.07365e132	−0.123576
$651$	−6.58754e133	−1.49151
$652$	−6.37138e133	−1.34114
$653$	6.94599e133	1.35943	0.679717	−	0.733474i	$-0.262103\pi$
$653$	6.94599e133	1.35943	0.679717	+	0.733474i	$0.262103\pi$
$654$	−8.65172e133	−1.57456
$655$	−1.00834e134	−1.70665
$656$	−2.00889e134	−3.16245
$657$	−9.95490e133	−1.45775
$658$	7.86402e133	1.07131
$659$	1.19862e133	0.151924	0.0759619	−	0.997111i	$-0.475797\pi$
$659$	1.19862e133	0.151924	0.0759619	+	0.997111i	$0.475797\pi$
$660$	4.75423e134	5.60716
$661$	1.13466e133	0.124537	0.0622684	−	0.998059i	$-0.480167\pi$
$661$	1.13466e133	0.124537	0.0622684	+	0.998059i	$0.480167\pi$
$662$	−2.09748e134	−2.14261
$663$	2.03586e133	0.193578
$664$	3.28768e134	2.91009
$665$	−2.59029e133	−0.213462
$666$	2.32901e134	1.78709
$667$	−1.38213e134	−0.987579
$668$	−1.73976e134	−1.15773
$669$	−2.75022e134	−1.70462
$670$	−2.89089e134	−1.66909
$671$	3.67578e134	1.97710
$672$	−2.91180e134	−1.45922
$673$	4.05940e134	1.89560	0.947800	−	0.318867i	$-0.103302\pi$
$673$	4.05940e134	1.89560	0.947800	+	0.318867i	$0.103302\pi$
$674$	3.03081e134	1.31891
$675$	−1.07303e133	−0.0435194
$676$	−3.71853e133	−0.140573
$677$	−2.02902e134	−0.715031	−0.357516	−	0.933907i	$-0.616376\pi$
$677$	−2.02902e134	−0.715031	−0.357516	+	0.933907i	$0.616376\pi$
$678$	−7.59578e134	−2.49552
$679$	3.56896e134	1.09327
$680$	−1.04331e134	−0.298017
$681$	−2.27837e134	−0.606927
$682$	1.11377e135	2.76717
$683$	−9.37400e133	−0.217241	−0.108620	−	0.994083i	$-0.534643\pi$
$683$	−9.37400e133	−0.217241	−0.108620	+	0.994083i	$0.534643\pi$
$684$	−3.04468e134	−0.658228
$685$	−6.94280e133	−0.140034
$686$	−9.74557e134	−1.83405
$687$	−2.10812e134	−0.370212
$688$	2.77171e134	0.454253
$689$	−1.94724e134	−0.297857
$690$	1.86048e135	2.65640
$691$	3.66093e134	0.487959	0.243980	−	0.969780i	$-0.421547\pi$
$691$	3.66093e134	0.487959	0.243980	+	0.969780i	$0.421547\pi$
$692$	−9.90819e134	−1.23298
$693$	−1.84065e135	−2.13866
$694$	−1.04265e135	−1.13127
$695$	1.07778e135	1.09207
$696$	3.90877e135	3.69914
$697$	2.60566e134	0.230335
$698$	−2.57192e135	−2.12386
$699$	6.82430e134	0.526493
$700$	−2.15812e134	−0.155568
$701$	1.07741e135	0.725733	0.362866	−	0.931841i	$-0.381798\pi$
$701$	1.07741e135	0.725733	0.362866	+	0.931841i	$0.381798\pi$
$702$	1.69818e135	1.06898
$703$	2.54506e134	0.149734
$704$	−1.18876e134	−0.0653720
$705$	1.89358e135	0.973421
$706$	−8.82213e134	−0.423985
$707$	−1.50001e135	−0.674017
$708$	−8.30619e135	−3.48997
$709$	−7.87850e134	−0.309562	−0.154781	−	0.987949i	$-0.549467\pi$
$709$	−7.87850e134	−0.309562	−0.154781	+	0.987949i	$0.549467\pi$
$710$	2.58978e135	0.951681
$711$	3.29220e134	0.113157
$712$	−6.50887e135	−2.09269
$713$	3.01281e135	0.906190
$714$	1.25277e135	0.352538
$715$	−5.94847e135	−1.56628
$716$	8.85988e135	2.18303
$717$	5.99173e135	1.38163
$718$	−4.21979e135	−0.910710
$719$	6.55550e135	1.32429	0.662146	−	0.749375i	$-0.269646\pi$
$719$	6.55550e135	1.32429	0.662146	+	0.749375i	$0.269646\pi$
$720$	−1.35517e136	−2.56271
$721$	6.61944e134	0.117192
$722$	1.03757e136	1.71989
$723$	−5.76580e135	−0.894933
$724$	1.00965e136	1.46754
$725$	5.58479e134	0.0760241
$726$	3.15565e136	4.02345
$727$	−1.29759e136	−1.54972	−0.774860	−	0.632133i	$-0.782179\pi$
$727$	−1.29759e136	−1.54972	−0.774860	+	0.632133i	$0.782179\pi$
$728$	1.88988e136	2.11443
$729$	−1.50100e136	−1.57335
$730$	−1.97968e136	−1.94428
$731$	−3.59509e134	−0.0330853
$732$	−5.08194e136	−4.38282
$733$	1.72350e136	1.39307	0.696534	−	0.717523i	$-0.254724\pi$
$733$	1.72350e136	1.39307	0.696534	+	0.717523i	$0.254724\pi$
$734$	−3.33082e136	−2.52341
$735$	−9.08184e134	−0.0644949
$736$	1.33171e136	0.886572
$737$	−2.24481e136	−1.40112
$738$	7.65710e136	4.48113
$739$	1.31516e136	0.721717	0.360859	−	0.932621i	$-0.382484\pi$
$739$	1.31516e136	0.721717	0.360859	+	0.932621i	$0.382484\pi$
$740$	3.20157e136	1.64762
$741$	6.53765e135	0.315542
$742$	−1.19824e136	−0.542449
$743$	−2.20041e136	−0.934406	−0.467203	−	0.884150i	$-0.654738\pi$
$743$	−2.20041e136	−0.934406	−0.467203	+	0.884150i	$0.654738\pi$
$744$	−8.52045e136	−3.39429
$745$	5.01153e136	1.87304
$746$	1.74176e136	0.610793
$747$	−5.53900e136	−1.82265
$748$	−1.46411e136	−0.452115
$749$	−4.00505e136	−1.16070
$750$	9.84708e136	2.67854
$751$	3.24494e136	0.828534	0.414267	−	0.910155i	$-0.364038\pi$
$751$	3.24494e136	0.828534	0.414267	+	0.910155i	$0.364038\pi$
$752$	4.49590e136	1.07763
$753$	−1.06320e137	−2.39250
$754$	−8.83848e136	−1.86741
$755$	8.34232e136	1.65503
$756$	7.22334e136	1.34571
$757$	1.48164e136	0.259232	0.129616	−	0.991564i	$-0.458626\pi$
$757$	1.48164e136	0.259232	0.129616	+	0.991564i	$0.458626\pi$
$758$	1.05441e137	1.73270
$759$	1.44469e137	2.22992
$760$	−3.35033e136	−0.485783
$761$	7.35976e136	1.00252	0.501260	−	0.865297i	$-0.332870\pi$
$761$	7.35976e136	1.00252	0.501260	+	0.865297i	$0.332870\pi$
$762$	−3.56195e137	−4.55855
$763$	4.60451e136	0.553692
$764$	−2.76226e137	−3.12126
$765$	1.75774e136	0.186654
$766$	−6.65126e136	−0.663800
$767$	1.03927e137	0.974872
$768$	3.20450e137	2.82555
$769$	−6.20169e136	−0.514054	−0.257027	−	0.966404i	$-0.582743\pi$
$769$	−6.20169e136	−0.514054	−0.257027	+	0.966404i	$0.582743\pi$
$770$	−3.66040e137	−2.85246
$771$	−2.11888e137	−1.55247
$772$	3.16080e137	2.17758
$773$	1.11173e137	0.720237	0.360118	−	0.932907i	$-0.382736\pi$
$773$	1.11173e137	0.720237	0.360118	+	0.932907i	$0.382736\pi$
$774$	−1.05647e137	−0.643668
$775$	−1.21739e136	−0.0697587
$776$	4.61616e137	2.48800
$777$	−2.12720e137	−1.07847
$778$	−5.29006e137	−2.52307
$779$	8.36741e136	0.375458
$780$	8.22405e137	3.47210
$781$	2.01100e137	0.798891
$782$	−5.72954e136	−0.214190
$783$	−1.86926e137	−0.657636
$784$	−2.15629e136	−0.0713992
$785$	−1.72437e137	−0.537431
$786$	1.56604e138	4.59444
$787$	−2.37365e137	−0.655567	−0.327783	−	0.944753i	$-0.606302\pi$
$787$	−2.37365e137	−0.655567	−0.327783	+	0.944753i	$0.606302\pi$
$788$	−9.01850e137	−2.34498
$789$	−8.05262e137	−1.97142
$790$	6.54704e136	0.150924
$791$	4.04253e137	0.877547
$792$	−2.38073e138	−4.86702
$793$	6.35851e137	1.22427
$794$	3.57634e136	0.0648581
$795$	−2.88525e137	−0.492884
$796$	1.10617e138	1.78012
$797$	2.71486e137	0.411601	0.205801	−	0.978594i	$-0.434020\pi$
$797$	2.71486e137	0.411601	0.205801	+	0.978594i	$0.434020\pi$
$798$	4.02296e137	0.574656
$799$	−5.83147e136	−0.0784885
$800$	−5.38106e136	−0.0682485
$801$	1.09660e138	1.31070
$802$	−2.16900e138	−2.44330
$803$	−1.53725e138	−1.63213
$804$	3.10357e138	3.10598
$805$	−9.90163e137	−0.934119
$806$	1.92664e138	1.71351
$807$	2.22392e138	1.86478
$808$	−1.94014e138	−1.53389
$809$	7.54984e137	0.562838	0.281419	−	0.959585i	$-0.409195\pi$
$809$	7.54984e137	0.562838	0.281419	+	0.959585i	$0.409195\pi$
$810$	−1.18299e138	−0.831656
$811$	−1.14937e138	−0.762024	−0.381012	−	0.924570i	$-0.624424\pi$
$811$	−1.14937e138	−0.762024	−0.381012	+	0.924570i	$0.624424\pi$
$812$	−3.75953e138	−2.35083
$813$	7.71754e137	0.455175
$814$	3.59649e138	2.00087
$815$	1.18120e138	0.619920
$816$	7.16215e137	0.354618
$817$	−1.15447e137	−0.0539307
$818$	−4.22258e138	−1.86121
$819$	−3.18402e138	−1.32431
$820$	1.05258e139	4.13140
$821$	−3.82935e138	−1.41849	−0.709243	−	0.704964i	$-0.750963\pi$
$821$	−3.82935e138	−1.41849	−0.709243	+	0.704964i	$0.750963\pi$
$822$	1.07828e138	0.376982
$823$	−1.59423e138	−0.526087	−0.263044	−	0.964784i	$-0.584726\pi$
$823$	−1.59423e138	−0.526087	−0.263044	+	0.964784i	$0.584726\pi$
$824$	8.56172e137	0.266697
$825$	−5.83756e137	−0.171660
$826$	6.39515e138	1.77541
$827$	−2.47556e138	−0.648876	−0.324438	−	0.945907i	$-0.605175\pi$
$827$	−2.47556e138	−0.648876	−0.324438	+	0.945907i	$0.605175\pi$
$828$	−1.16386e139	−2.88044
$829$	2.20584e138	0.515507	0.257754	−	0.966211i	$-0.417018\pi$
$829$	2.20584e138	0.515507	0.257754	+	0.966211i	$0.417018\pi$
$830$	−1.10151e139	−2.43098
$831$	8.73303e138	1.82019
$832$	−2.05636e137	−0.0404801
$833$	2.79684e136	0.00520033
$834$	−1.67389e139	−2.93994
$835$	3.22535e138	0.535142
$836$	−4.70163e138	−0.736971
$837$	4.07466e138	0.603438
$838$	1.61305e139	2.25714
$839$	1.04066e139	1.37599	0.687994	−	0.725716i	$-0.258491\pi$
$839$	1.04066e139	1.37599	0.687994	+	0.725716i	$0.258491\pi$
$840$	2.80025e139	3.49890
$841$	1.26034e138	0.148825
$842$	1.94818e139	2.17422
$843$	7.97178e138	0.840902
$844$	−3.48263e139	−3.47249
$845$	6.89381e137	0.0649779
$846$	−1.71366e139	−1.52698
$847$	−1.67946e139	−1.41484
$848$	−6.85040e138	−0.545648
$849$	−1.55055e139	−1.16780
$850$	2.31514e137	0.0164884
$851$	9.72874e138	0.655243
$852$	−2.78030e139	−1.77097
$853$	1.38575e139	0.834843	0.417421	−	0.908713i	$-0.362934\pi$
$853$	1.38575e139	0.834843	0.417421	+	0.908713i	$0.362934\pi$
$854$	3.91272e139	2.22962
$855$	5.64455e138	0.304256
$856$	−5.18021e139	−2.64146
$857$	−1.99070e139	−0.960324	−0.480162	−	0.877180i	$-0.659422\pi$
$857$	−1.99070e139	−0.960324	−0.480162	+	0.877180i	$0.659422\pi$
$858$	9.23852e139	4.21654
$859$	7.39417e138	0.319311	0.159656	−	0.987173i	$-0.448962\pi$
$859$	7.39417e138	0.319311	0.159656	+	0.987173i	$0.448962\pi$
$860$	−1.45227e139	−0.593433
$861$	−6.99360e139	−2.70428
$862$	−4.29139e139	−1.57037
$863$	−8.66310e138	−0.300027	−0.150014	−	0.988684i	$-0.547932\pi$
$863$	−8.66310e138	−0.300027	−0.150014	+	0.988684i	$0.547932\pi$
$864$	1.80107e139	0.590374
$865$	1.83689e139	0.569925
$866$	8.86496e139	2.60362
$867$	5.47489e139	1.52219
$868$	8.19513e139	2.15709
$869$	5.08386e138	0.126693
$870$	−1.30960e140	−3.09012
$871$	−3.88317e139	−0.867609
$872$	5.95556e139	1.26006
$873$	−7.77719e139	−1.55828
$874$	−1.83990e139	−0.349141
$875$	−5.24069e139	−0.941903
$876$	2.12532e140	3.61809
$877$	−6.89191e139	−1.11137	−0.555685	−	0.831393i	$-0.687544\pi$
$877$	−6.89191e139	−1.11137	−0.555685	+	0.831393i	$0.687544\pi$
$878$	−4.93085e139	−0.753239
$879$	1.08342e140	1.56792
$880$	−2.09267e140	−2.86929
$881$	6.56071e138	0.0852306	0.0426153	−	0.999092i	$-0.486431\pi$
$881$	6.56071e138	0.0852306	0.0426153	+	0.999092i	$0.486431\pi$
$882$	8.21893e138	0.101171
$883$	3.87183e139	0.451630	0.225815	−	0.974170i	$-0.427496\pi$
$883$	3.87183e139	0.451630	0.225815	+	0.974170i	$0.427496\pi$
$884$	−2.53268e139	−0.279961
$885$	1.53989e140	1.61319
$886$	−6.16966e139	−0.612576
$887$	−1.44476e139	−0.135964	−0.0679822	−	0.997687i	$-0.521656\pi$
$887$	−1.44476e139	−0.135964	−0.0679822	+	0.997687i	$0.521656\pi$
$888$	−2.75136e140	−2.45432
$889$	1.89570e140	1.60301
$890$	2.18075e140	1.74816
$891$	−9.18609e139	−0.698135
$892$	3.42137e140	2.46530
$893$	−1.87263e139	−0.127940
$894$	−7.78336e140	−5.04238
$895$	−1.64254e140	−1.00907
$896$	−1.74453e140	−1.01636
$897$	2.49908e140	1.38083
$898$	2.56000e140	1.34157
$899$	−2.12074e140	−1.05415
$900$	4.70280e139	0.221737
$901$	8.88541e138	0.0397420
$902$	1.18242e141	5.01720
$903$	9.64926e139	0.388442
$904$	5.22869e140	1.99706
$905$	−1.87180e140	−0.678348
$906$	−1.29564e141	−4.45548
$907$	2.54824e140	0.831561	0.415780	−	0.909465i	$-0.363509\pi$
$907$	2.54824e140	0.831561	0.415780	+	0.909465i	$0.363509\pi$
$908$	2.83437e140	0.877766
$909$	3.26869e140	0.960704
$910$	−6.33191e140	−1.76632
$911$	5.21440e140	1.38064	0.690322	−	0.723503i	$-0.257469\pi$
$911$	5.21440e140	1.38064	0.690322	+	0.723503i	$0.257469\pi$
$912$	2.29994e140	0.578046
$913$	−8.55340e140	−2.04069
$914$	−1.20432e141	−2.72770
$915$	9.42146e140	2.02589
$916$	2.62258e140	0.535418
$917$	−8.33459e140	−1.61563
$918$	−7.74890e139	−0.142631
$919$	1.14479e140	0.200097	0.100048	−	0.994983i	$-0.468100\pi$
$919$	1.14479e140	0.200097	0.100048	+	0.994983i	$0.468100\pi$
$920$	−1.28070e141	−2.12581
$921$	−1.52253e141	−2.40012
$922$	1.79669e140	0.269001
$923$	3.47871e140	0.494694
$924$	3.92969e141	5.30811
$925$	−3.93110e139	−0.0504408
$926$	4.81092e140	0.586416
$927$	−1.44246e140	−0.167038
$928$	−9.37400e140	−1.03133
$929$	−5.27794e139	−0.0551719	−0.0275859	−	0.999619i	$-0.508782\pi$
$929$	−5.27794e139	−0.0551719	−0.0275859	+	0.999619i	$0.508782\pi$
$930$	2.85472e141	2.83546
$931$	8.98136e138	0.00847681
$932$	−8.48967e140	−0.761438
$933$	6.86010e140	0.584726
$934$	1.19580e141	0.968681
$935$	2.71433e140	0.208983
$936$	−4.11828e141	−3.01379
$937$	−1.41143e141	−0.981811	−0.490906	−	0.871213i	$-0.663334\pi$
$937$	−1.41143e141	−0.981811	−0.490906	+	0.871213i	$0.663334\pi$
$938$	−2.38952e141	−1.58007
$939$	1.26887e141	0.797627
$940$	−2.35568e141	−1.40781
$941$	−6.89103e140	−0.391541	−0.195770	−	0.980650i	$-0.562721\pi$
$941$	−6.89103e140	−0.391541	−0.195770	+	0.980650i	$0.562721\pi$
$942$	2.67811e141	1.44681
$943$	3.19852e141	1.64302
$944$	3.65614e141	1.78588
$945$	−1.33914e141	−0.622036
$946$	−1.63142e141	−0.720669
$947$	2.74686e141	1.15402	0.577010	−	0.816737i	$-0.304220\pi$
$947$	2.74686e141	1.15402	0.577010	+	0.816737i	$0.304220\pi$
$948$	−7.02869e140	−0.280852
$949$	−2.65919e141	−1.01066
$950$	7.43449e139	0.0268770
$951$	−7.30485e141	−2.51210
$952$	−8.62367e140	−0.282122
$953$	4.62984e141	1.44096	0.720482	−	0.693473i	$-0.243921\pi$
$953$	4.62984e141	1.44096	0.720482	+	0.693473i	$0.243921\pi$
$954$	2.61111e141	0.773174
$955$	5.12097e141	1.44275
$956$	−7.45391e141	−1.99818
$957$	−1.01692e142	−2.59401
$958$	6.00280e141	1.45711
$959$	−5.73869e140	−0.132565
$960$	−3.04693e140	−0.0669851
$961$	−1.56419e140	−0.0327287
$962$	6.22136e141	1.23899
$963$	8.72748e141	1.65440
$964$	7.17285e141	1.29429
$965$	−5.85983e141	−1.00656
$966$	1.53781e142	2.51472
$967$	9.71788e140	0.151291	0.0756457	−	0.997135i	$-0.475898\pi$
$967$	9.71788e140	0.151291	0.0756457	+	0.997135i	$0.475898\pi$
$968$	−2.17225e142	−3.21980
$969$	−2.98318e140	−0.0421017
$970$	−1.54661e142	−2.07838
$971$	−8.05051e141	−1.03017	−0.515086	−	0.857138i	$-0.672240\pi$
$971$	−8.05051e141	−1.03017	−0.515086	+	0.857138i	$0.672240\pi$
$972$	2.39728e142	2.92127
$973$	8.90855e141	1.03383
$974$	−1.49288e142	−1.64996
$975$	−1.00980e141	−0.106296
$976$	2.23692e142	2.24277
$977$	1.12179e142	1.07133	0.535663	−	0.844432i	$-0.320062\pi$
$977$	1.12179e142	1.07133	0.535663	+	0.844432i	$0.320062\pi$
$978$	−1.83451e142	−1.66887
$979$	1.69338e142	1.46749
$980$	1.12981e141	0.0932755
$981$	−1.00338e142	−0.789199
$982$	−3.55960e142	−2.66751
$983$	1.15756e142	0.826518	0.413259	−	0.910613i	$-0.364390\pi$
$983$	1.15756e142	0.826518	0.413259	+	0.910613i	$0.364390\pi$
$984$	−9.04566e142	−6.15422
$985$	1.67195e142	1.08393
$986$	4.03306e141	0.249162
$987$	1.56517e142	0.921504
$988$	−8.13307e141	−0.456351
$989$	−4.41309e141	−0.236004
$990$	7.97645e142	4.06573
$991$	1.69568e142	0.823846	0.411923	−	0.911219i	$-0.364857\pi$
$991$	1.69568e142	0.823846	0.411923	+	0.911219i	$0.364857\pi$
$992$	2.04337e142	0.946331
$993$	−4.17460e142	−1.84300
$994$	2.14063e142	0.900924
$995$	−2.05073e142	−0.822833
$996$	1.18255e143	4.52377
$997$	−1.38557e142	−0.505370	−0.252685	−	0.967549i	$-0.581314\pi$
$997$	−1.38557e142	−0.505370	−0.252685	+	0.967549i	$0.581314\pi$
$998$	−1.16507e141	−0.0405183
$999$	1.31576e142	0.436331

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.96.a.a.1.1	✓	8
3.2	odd	2		9.96.a.c.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.96.a.a.1.1	✓	8	1.1	even	1	trivial
9.96.a.c.1.8		8	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:	\( k \)	\(=\)	\( 96 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-3.58194e14 q^{2} -7.12911e22 q^{3} +8.86885e28 q^{4} -1.64420e33 q^{5} +2.55360e37 q^{6} -1.35904e40 q^{7} -1.75781e43 q^{8} +2.96152e45 q^{9} +O(q^{10})\)	\(q-3.58194e14 q^{2} -7.12911e22 q^{3} +8.86885e28 q^{4} -1.64420e33 q^{5} +2.55360e37 q^{6} -1.35904e40 q^{7} -1.75781e43 q^{8} +2.96152e45 q^{9} +5.88943e47 q^{10} +4.57322e49 q^{11} -6.32270e51 q^{12} +7.91094e52 q^{13} +4.86801e54 q^{14} +1.17217e56 q^{15} +2.78306e57 q^{16} -3.60982e57 q^{17} -1.06080e60 q^{18} -1.15920e60 q^{19} -1.45822e62 q^{20} +9.68877e62 q^{21} -1.63810e64 q^{22} -4.43116e64 q^{23} +1.25316e66 q^{24} +1.79050e65 q^{25} -2.83365e67 q^{26} -5.99290e67 q^{27} -1.20532e69 q^{28} +3.11912e69 q^{29} -4.19864e70 q^{30} -6.79915e70 q^{31} -3.00533e71 q^{32} -3.26030e72 q^{33} +1.29301e72 q^{34} +2.23455e73 q^{35} +2.62653e74 q^{36} -2.19553e74 q^{37} +4.15219e74 q^{38} -5.63979e75 q^{39} +2.89021e76 q^{40} -7.21825e76 q^{41} -3.47046e77 q^{42} +9.95921e76 q^{43} +4.05592e78 q^{44} -4.86934e78 q^{45} +1.58721e79 q^{46} +1.61545e79 q^{47} -1.98408e80 q^{48} -7.74788e78 q^{49} -6.41346e79 q^{50} +2.57348e80 q^{51} +7.01609e81 q^{52} -2.46146e81 q^{53} +2.14662e82 q^{54} -7.51930e82 q^{55} +2.38895e83 q^{56} +8.26407e82 q^{57} -1.11725e84 q^{58} +1.31371e84 q^{59} +1.03958e85 q^{60} +8.03762e84 q^{61} +2.43541e85 q^{62} -4.02484e85 q^{63} -2.59939e84 q^{64} -1.30072e86 q^{65} +1.16782e87 q^{66} -4.90861e86 q^{67} -3.20149e86 q^{68} +3.15902e87 q^{69} -8.00400e87 q^{70} +4.39734e87 q^{71} -5.20580e88 q^{72} -3.36142e88 q^{73} +7.86425e88 q^{74} -1.27647e88 q^{75} -1.02808e89 q^{76} -6.21521e89 q^{77} +2.02014e90 q^{78} +1.11166e89 q^{79} -4.57592e90 q^{80} -2.00867e90 q^{81} +2.58553e91 q^{82} -1.87032e91 q^{83} +8.59283e91 q^{84} +5.93527e90 q^{85} -3.56733e91 q^{86} -2.22365e92 q^{87} -8.03887e92 q^{88} +3.70282e92 q^{89} +1.74417e93 q^{90} -1.07513e93 q^{91} -3.92993e93 q^{92} +4.84719e93 q^{93} -5.78643e93 q^{94} +1.90596e93 q^{95} +2.14253e94 q^{96} -2.62608e94 q^{97} +2.77524e93 q^{98} +1.35437e95 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5835659138280 q^{2} - 95\!\cdots\!80 q^{3}+ \cdots + 92\!\cdots\!36 q^{9}+O(q^{10}) \) 8 * q - 5835659138280 * q^2 - 9565982513916703570080 * q^3 + 208956598309707350371623569984 * q^4 + 1941568507475850402526904141070960 * q^5 + 10651800775920653731297343298528492576 * q^6 + 31232311735415758067806325356531573912000 * q^7 - 14761127603920085098561309094124598702287360 * q^8 + 9274438133561954597944854467482391143953072936 * q^9	\( 8 q - 5835659138280 q^{2} - 95\!\cdots\!80 q^{3}+ \cdots + 30\!\cdots\!72 q^{99}+O(q^{100}) \) 8 * q - 5835659138280 * q^2 - 9565982513916703570080 * q^3 + 208956598309707350371623569984 * q^4 + 1941568507475850402526904141070960 * q^5 + 10651800775920653731297343298528492576 * q^6 + 31232311735415758067806325356531573912000 * q^7 - 14761127603920085098561309094124598702287360 * q^8 + 9274438133561954597944854467482391143953072936 * q^9 - 355384205613899841010372205704985147108657534640 * q^10 + 53080108095821756826858489331993621982645992125216 * q^11 + 1065031032961827853079380844579017283696993846403840 * q^12 + 117293508281179239843264964380833942161194396039342640 * q^13 + 8850886815767090581799564344683737269936151852930265408 * q^14 + 187812376414067333691564154745798290909917959215041625920 * q^15 + 9517116971431211282501221161054789131283343644054948220928 * q^16 - 13655041265063090981829171372625119189425374473948274915440 * q^17 - 1790266901749030205580776247252673430153004351197542602854280 * q^18 - 5232175975370167369536369873888207394303637759872553281713440 * q^19 + 136065209104116992530471413843386338746929879497239386344644480 * q^20 + 1346571177849118208545064341536207444072396945735327627682503936 * q^21 - 20365500099170357171519767897869972385636855003458825137197491360 * q^22 - 7129054072165937484825035531327773489156117409617881426435061440 * q^23 + 288860682603965362857322541557744811472884721216169744526242990080 * q^24 + 8177806376085721196783759852983887433280593317172609841487587996600 * q^25 - 69072273179717436642550386629266724895941590936463282023015399323504 * q^26 + 64049503386294800673569522679695786753122795388715525750679249767360 * q^27 + 303354815522537415860404332264897505740906926923909508834765584637440 * q^28 + 7715272198415359380593902919630157934289467091855373333108685675435440 * q^29 - 62913685170287068298704199843316213881225133796680396150164526710345280 * q^30 + 48520677903801540370519073843711920597057994260920479636592334181199616 * q^31 + 911347110324473008775326747695560179887781374647708612161794209209221120 * q^32 - 1535322742350198888271103254480947687741587903792512354063710702943493760 * q^33 - 16409772766982648656985219134942803587399227958333745923026675404562961232 * q^34 + 58800416933815614414155173269063056087887600285328689246425433374756677760 * q^35 + 51665208441213434468989869710710146210173003797753332160946711226240568128 * q^36 - 181116344963557296256979160619337453378797091102974834966000994855965247120 * q^37 - 1676466315180766681626408275142200947978975839695306622930354052184199692640 * q^38 + 465478714369259758144024065308323445042256641733578800363164365799686202432 * q^39 + 39028182173606372825635252450401491624189758401191157685601991729209269171200 * q^40 - 87541390126560450267544465567119030351560808726320656469732601708266148308784 * q^41 - 157435820560022140348706044721413472652300880194209574021901207450891596867840 * q^42 + 360093033489081253538156425248276463103949347025569853491672117723107522861600 * q^43 + 1942224484251042670482996667732829207493398934442399145050649033803969221005568 * q^44 - 1611554371538604569657837598986488298494511731253236200388961579880024486332880 * q^45 - 19332434944442851407749457669991401004991143268030327859543986888040547882373184 * q^46 + 38672453335683563852366980570346257355794761888911368752480783496161211070336640 * q^47 + 93863838769591236482712272126012963144755254935077324856132076191099747033333760 * q^48 + 265668043093542548841947390620517395072194945166225827717144824590425137465244744 * q^49 - 1423963459280866882678609595824694565889878038511273700600414891648711070234429400 * q^50 + 2434476695354895883532253554814552047229450451049452072207263289482820720406821056 * q^51 + 15678746704556392183126484026214298441253990030076674973212546269606119207477104000 * q^52 - 2922690482809426126710991861168746969788895886261814706776237561500358605037675280 * q^53 + 44393564079821957628952458152403809172972567715888333832276777433089826621820157760 * q^54 + 77963865832782922646862204005771036172886494149999882551809226033579503680996905920 * q^55 + 723822110434297992891221750986765045769194525611914833690699475848521019635777392640 * q^56 + 1459603943948321457517074656112276013643674313689343212415092604638087582879924782720 * q^57 + 2398120500739528001867383787619453843290390222445601081527493426426916763954522209040 * q^58 + 2444569112045817337560949868287606200158569651761097862873350630901953709318185022880 * q^59 + 41015921945833187827435663222575462810347191746192004435818365735996703011205515880960 * q^60 + 26252719580888049069066995575288184611473664654647035829209505915961690057602967485616 * q^61 + 109318411457586083204284032417457169492313955459811319765445849679642744506848521207040 * q^62 + 170984018880767416687602973051010439420211230624233991381305273834268390445660056281280 * q^63 + 407545659960425058121678577897271227683793728749313452587765989597513138495845491277824 * q^64 + 711217468942010938456527729098183388378886665557115838437689631605619958224435834575520 * q^65 + 1747938075646007071584137716302374690644541046339320226994976444199784352790302021223552 * q^66 - 646475642994207391400653355260241732956721934256209274545597969100350739031184431188640 * q^67 + 91675839067201266020688320385568861573762045194469769590554263557238860857176520405120 * q^68 - 1671348258106164448387617904756675195481964064504427142194954632911883632406377850960128 * q^69 - 15589682350948763132524633727148211085350313303119537319661619119948806738470696493235840 * q^70 - 14595295080721751466823982356267079020901744922845645857244436108167397828048945561374784 * q^71 - 168731956650076191328348463912100975176233311308158667034794509156143705616303905637470720 * q^72 - 167722859263497180232486905674536831998056258335586734743256934373976249561602911979579440 * q^73 - 209312489678791718598684146630297797595302804804578868479635191055424978871400486510408112 * q^74 - 319918492419260578418623942107150301135641877679303067145274604119881385565549842206216800 * q^75 - 959273209575432254809587692424149415253949631691365417587931662952012091653615772375589120 * q^76 - 358973379150050060834656745211596557040941835816686113329022190288009228708654757892460800 * q^77 + 590425535394410417923583601115147442109710886806797004396557673983317347484688655751672000 * q^78 + 4672642903096907209502768293890247708239627672362847349478671278970829923925879535283527040 * q^79 + 18415268594255335517079731605762998550074832241200743044677945286622776635630921688252866560 * q^80 + 12509737552066767544095911653095580991572013599361129872125476231341584536182121238921405768 * q^81 + 32657845092209493410036294321958173121440540177602229019397776717126981442788576405027965040 * q^82 + 34387792212015780744754986808561666458900302762495709021597904850967930099747337487085254880 * q^83 + 173836457542583880184373241725060178629119564679421678850358203433258194499103546320231344128 * q^84 + 58585978711733607272815047107060888289878133655773893600270763487144112403111490135244590560 * q^85 - 153511472921832187435283964804212642635464712353485304877046031498544471884447149897205104544 * q^86 - 544464219458114578116693663783217812912359092004929393234553696235186032730900539616052969920 * q^87 - 1202425497404423912185881933157195269872332267934742515736241252480851349730675866727622174720 * q^88 - 342673661311688548077760584785109887358595471462214186557789870415877447806348084055852796080 * q^89 - 3514062299884453064121468346218192535289244482618329972865712072788945397515179474700715316080 * q^90 - 3490211360016960529246147249335483533013067701963330513611222538458526220206688421639066690944 * q^91 - 12008074146638359830472895966704879561255070000267734630900014099911412498586265442549753546240 * q^92 + 197667690727810326296814984504358164807428856713575716952413727748092885643497784281407575040 * q^93 + 15433462798640093333378242254437202047220637579307237556798289796157532672617883642933732299648 * q^94 + 15321400721190643816477985005690604983976540891819618748501840926190750159388834713154020724800 * q^95 + 97555071644510782149318139986276901553221426854121546320985366392022081200430710682001871077376 * q^96 + 10072532354157458294768094296505188523874048354320514397914144859011793551098974691865811668240 * q^97 + 146363464831387371243245039459581022362075942196915081212239417921551560440470151788055390975960 * q^98 + 307096415144337525387251975813943414746365371627429389615225939474864146107991251707726185786272 * q^99

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