LMFDB - Embedded newform 1.96.a.a.1.3

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			1.3
Root			$-6.56924e12$ 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)

$f(q)$	$=$	$q-1.58391e14 q^{2} +9.80327e21 q^{3} -1.45263e28 q^{4} -7.31691e32 q^{5} -1.55275e36 q^{6} -1.37055e39 q^{7} +8.57536e42 q^{8} -2.02479e45 q^{9} +O(q^{10})$	\(q-1.58391e14 q^{2} +9.80327e21 q^{3} -1.45263e28 q^{4} -7.31691e32 q^{5} -1.55275e36 q^{6} -1.37055e39 q^{7} +8.57536e42 q^{8} -2.02479e45 q^{9} +1.15893e47 q^{10} -1.77564e49 q^{11} -1.42405e50 q^{12} -4.53188e52 q^{13} +2.17083e53 q^{14} -7.17297e54 q^{15} -7.82816e56 q^{16} -3.88116e57 q^{17} +3.20709e59 q^{18} -8.75641e59 q^{19} +1.06288e61 q^{20} -1.34359e61 q^{21} +2.81246e63 q^{22} -1.90280e64 q^{23} +8.40666e64 q^{24} -1.98898e66 q^{25} +7.17809e66 q^{26} -4.06413e67 q^{27} +1.99090e67 q^{28} -4.05377e69 q^{29} +1.13613e69 q^{30} -7.95372e70 q^{31} -2.15714e71 q^{32} -1.74071e71 q^{33} +6.14742e71 q^{34} +1.00282e72 q^{35} +2.94127e73 q^{36} +2.93459e74 q^{37} +1.38694e74 q^{38} -4.44272e74 q^{39} -6.27451e75 q^{40} -2.78348e76 q^{41} +2.12812e75 q^{42} +4.90861e76 q^{43} +2.57935e77 q^{44} +1.48152e78 q^{45} +3.01387e78 q^{46} -1.43188e78 q^{47} -7.67415e78 q^{48} -1.90570e80 q^{49} +3.15037e80 q^{50} -3.80481e79 q^{51} +6.58314e80 q^{52} +9.09844e81 q^{53} +6.43722e81 q^{54} +1.29922e82 q^{55} -1.17530e82 q^{56} -8.58415e81 q^{57} +6.42081e83 q^{58} +2.06207e84 q^{59} +1.04197e83 q^{60} +1.22605e85 q^{61} +1.25980e85 q^{62} +2.77508e84 q^{63} +6.51777e85 q^{64} +3.31593e85 q^{65} +2.75713e85 q^{66} +6.33834e86 q^{67} +5.63790e85 q^{68} -1.86537e86 q^{69} -1.58838e86 q^{70} -1.27499e88 q^{71} -1.73633e88 q^{72} -1.33744e88 q^{73} -4.64812e88 q^{74} -1.94985e88 q^{75} +1.27198e88 q^{76} +2.43360e88 q^{77} +7.03688e88 q^{78} -3.85669e89 q^{79} +5.72779e89 q^{80} +3.89595e90 q^{81} +4.40879e90 q^{82} +2.10785e91 q^{83} +1.95174e89 q^{84} +2.83981e90 q^{85} -7.77481e90 q^{86} -3.97402e91 q^{87} -1.52267e92 q^{88} -5.00386e92 q^{89} -2.34660e92 q^{90} +6.21116e91 q^{91} +2.76407e92 q^{92} -7.79725e92 q^{93} +2.26797e92 q^{94} +6.40699e92 q^{95} -2.11470e93 q^{96} +1.70309e94 q^{97} +3.01846e94 q^{98} +3.59530e94 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.58391e14	−0.795804	−0.397902	−	0.917428i	$-0.630262\pi$
$2$	−1.58391e14	−0.795804	−0.397902	+	0.917428i	$0.630262\pi$
$3$	9.80327e21	0.212869	0.106434	−	0.994320i	$-0.466057\pi$
$3$	9.80327e21	0.212869	0.106434	+	0.994320i	$0.466057\pi$
$4$	−1.45263e28	−0.366696
$5$	−7.31691e32	−0.460524	−0.230262	−	0.973129i	$-0.573958\pi$
$5$	−7.31691e32	−0.460524	−0.230262	+	0.973129i	$0.573958\pi$
$6$	−1.55275e36	−0.169402
$7$	−1.37055e39	−0.0987957	−0.0493978	−	0.998779i	$-0.515730\pi$
$7$	−1.37055e39	−0.0987957	−0.0493978	+	0.998779i	$0.515730\pi$
$8$	8.57536e42	1.08762
$9$	−2.02479e45	−0.954687
$10$	1.15893e47	0.366487
$11$	−1.77564e49	−0.607019	−0.303509	−	0.952828i	$-0.598158\pi$
$11$	−1.77564e49	−0.607019	−0.303509	+	0.952828i	$0.598158\pi$
$12$	−1.42405e50	−0.0780579
$13$	−4.53188e52	−0.554586	−0.277293	−	0.960785i	$-0.589437\pi$
$13$	−4.53188e52	−0.554586	−0.277293	+	0.960785i	$0.589437\pi$
$14$	2.17083e53	0.0786220
$15$	−7.17297e54	−0.0980311
$16$	−7.82816e56	−0.498839
$17$	−3.88116e57	−0.138880	−0.0694398	−	0.997586i	$-0.522121\pi$
$17$	−3.88116e57	−0.138880	−0.0694398	+	0.997586i	$0.522121\pi$
$18$	3.20709e59	0.759744
$19$	−8.75641e59	−0.159049	−0.0795243	−	0.996833i	$-0.525340\pi$
$19$	−8.75641e59	−0.159049	−0.0795243	+	0.996833i	$0.525340\pi$
$20$	1.06288e61	0.168872
$21$	−1.34359e61	−0.0210305
$22$	2.81246e63	0.483068
$23$	−1.90280e64	−0.395659	−0.197829	−	0.980236i	$-0.563389\pi$
$23$	−1.90280e64	−0.395659	−0.197829	+	0.980236i	$0.563389\pi$
$24$	8.40666e64	0.231521
$25$	−1.98898e66	−0.787917
$26$	7.17809e66	0.441342
$27$	−4.06413e67	−0.416091
$28$	1.99090e67	0.0362279
$29$	−4.05377e69	−1.39301	−0.696505	−	0.717552i	$-0.745263\pi$
$29$	−4.05377e69	−1.39301	−0.696505	+	0.717552i	$0.745263\pi$
$30$	1.13613e69	0.0780136
$31$	−7.95372e70	−1.15051	−0.575255	−	0.817974i	$-0.695097\pi$
$31$	−7.95372e70	−1.15051	−0.575255	+	0.817974i	$0.695097\pi$
$32$	−2.15714e71	−0.690644
$33$	−1.74071e71	−0.129215
$34$	6.14742e71	0.110521
$35$	1.00282e72	0.0454978
$36$	2.94127e73	0.350079
$37$	2.93459e74	0.950528	0.475264	−	0.879843i	$-0.342353\pi$
$37$	2.93459e74	0.950528	0.475264	+	0.879843i	$0.342353\pi$
$38$	1.38694e74	0.126572
$39$	−4.44272e74	−0.118054
$40$	−6.27451e75	−0.500876
$41$	−2.78348e76	−0.687631	−0.343815	−	0.939037i	$-0.611719\pi$
$41$	−2.78348e76	−0.687631	−0.343815	+	0.939037i	$0.611719\pi$
$42$	2.12812e75	0.0167362
$43$	4.90861e76	0.126243	0.0631215	−	0.998006i	$-0.479894\pi$
$43$	4.90861e76	0.126243	0.0631215	+	0.998006i	$0.479894\pi$
$44$	2.57935e77	0.222591
$45$	1.48152e78	0.439656
$46$	3.01387e78	0.314867
$47$	−1.43188e78	−0.0538589	−0.0269295	−	0.999637i	$-0.508573\pi$
$47$	−1.43188e78	−0.0538589	−0.0269295	+	0.999637i	$0.508573\pi$
$48$	−7.67415e78	−0.106187
$49$	−1.90570e80	−0.990239
$50$	3.15037e80	0.627028
$51$	−3.80481e79	−0.0295631
$52$	6.58314e80	0.203364
$53$	9.09844e81	1.13727	0.568634	−	0.822590i	$-0.307472\pi$
$53$	9.09844e81	1.13727	0.568634	+	0.822590i	$0.307472\pi$
$54$	6.43722e81	0.331127
$55$	1.29922e82	0.279547
$56$	−1.17530e82	−0.107452
$57$	−8.58415e81	−0.0338565
$58$	6.42081e83	1.10856
$59$	2.06207e84	1.58064	0.790318	−	0.612697i	$-0.209915\pi$
$59$	2.06207e84	1.58064	0.790318	+	0.612697i	$0.209915\pi$
$60$	1.04197e83	0.0359476
$61$	1.22605e85	1.92904	0.964521	−	0.264005i	$-0.0850437\pi$
$61$	1.22605e85	1.92904	0.964521	+	0.264005i	$0.0850437\pi$
$62$	1.25980e85	0.915580
$63$	2.77508e84	0.0943189
$64$	6.51777e85	1.04846
$65$	3.31593e85	0.255400
$66$	2.75713e85	0.102830
$67$	6.33834e86	1.15724	0.578618	−	0.815598i	$-0.303592\pi$
$67$	6.33834e86	1.15724	0.578618	+	0.815598i	$0.303592\pi$
$68$	5.63790e85	0.0509265
$69$	−1.86537e86	−0.0842233
$70$	−1.58838e86	−0.0362073
$71$	−1.27499e88	−1.48162	−0.740809	−	0.671715i	$-0.765558\pi$
$71$	−1.27499e88	−1.48162	−0.740809	+	0.671715i	$0.765558\pi$
$72$	−1.73633e88	−1.03834
$73$	−1.33744e88	−0.415374	−0.207687	−	0.978195i	$-0.566594\pi$
$73$	−1.33744e88	−0.415374	−0.207687	+	0.978195i	$0.566594\pi$
$74$	−4.64812e88	−0.756434
$75$	−1.94985e88	−0.167723
$76$	1.27198e88	0.0583224
$77$	2.43360e88	0.0599708
$78$	7.03688e88	0.0939478
$79$	−3.85669e89	−0.281144	−0.140572	−	0.990070i	$-0.544894\pi$
$79$	−3.85669e89	−0.281144	−0.140572	+	0.990070i	$0.544894\pi$
$80$	5.72779e89	0.229727
$81$	3.89595e90	0.866114
$82$	4.40879e90	0.547219
$83$	2.10785e91	1.47106	0.735531	−	0.677491i	$-0.236933\pi$
$83$	2.10785e91	1.47106	0.735531	+	0.677491i	$0.236933\pi$
$84$	1.95174e89	0.00771179
$85$	2.83981e90	0.0639574
$86$	−7.77481e90	−0.100465
$87$	−3.97402e91	−0.296528
$88$	−1.52267e92	−0.660207
$89$	−5.00386e92	−1.26847	−0.634235	−	0.773140i	$-0.718685\pi$
$89$	−5.00386e92	−1.26847	−0.634235	+	0.773140i	$0.718685\pi$
$90$	−2.34660e92	−0.349880
$91$	6.21116e91	0.0547907
$92$	2.76407e92	0.145086
$93$	−7.79725e92	−0.244907
$94$	2.26797e92	0.0428612
$95$	6.40699e92	0.0732458
$96$	−2.11470e93	−0.147016
$97$	1.70309e94	0.723734	0.361867	−	0.932230i	$-0.382139\pi$
$97$	1.70309e94	0.723734	0.361867	+	0.932230i	$0.382139\pi$
$98$	3.01846e94	0.788037
$99$	3.59530e94	0.579513
$100$	2.88926e94	0.288926
$101$	9.35281e94	0.583011	0.291506	−	0.956569i	$-0.405844\pi$
$101$	9.35281e94	0.583011	0.291506	+	0.956569i	$0.405844\pi$
$102$	6.02649e93	0.0235264
$103$	−6.42771e95	−1.57866	−0.789329	−	0.613971i	$-0.789571\pi$
$103$	−6.42771e95	−1.57866	−0.789329	+	0.613971i	$0.789571\pi$
$104$	−3.88625e95	−0.603180
$105$	9.83090e93	0.00968505
$106$	−1.44111e96	−0.905043
$107$	−7.69767e95	−0.309478	−0.154739	−	0.987955i	$-0.549454\pi$
$107$	−7.69767e95	−0.309478	−0.154739	+	0.987955i	$0.549454\pi$
$108$	5.90368e95	0.152579
$109$	5.49317e96	0.916356	0.458178	−	0.888861i	$-0.348502\pi$
$109$	5.49317e96	0.916356	0.458178	+	0.888861i	$0.348502\pi$
$110$	−2.05785e96	−0.222465
$111$	2.87685e96	0.202337
$112$	1.07289e96	0.0492831
$113$	2.82929e97	0.852023	0.426011	−	0.904718i	$-0.359918\pi$
$113$	2.82929e97	0.852023	0.426011	+	0.904718i	$0.359918\pi$
$114$	1.35965e96	0.0269431
$115$	1.39226e97	0.182210
$116$	5.88863e97	0.510810
$117$	9.17610e97	0.529456
$118$	−3.26613e98	−1.25788
$119$	5.31933e96	0.0137207
$120$	−6.15108e97	−0.106621
$121$	−5.40378e98	−0.631528
$122$	−1.94196e99	−1.53514
$123$	−2.72872e98	−0.146375
$124$	1.15538e99	0.421887
$125$	3.30237e99	0.823379
$126$	−4.39548e98	−0.0750594
$127$	1.46221e100	1.71528	0.857638	−	0.514254i	$-0.171931\pi$
$127$	1.46221e100	1.71528	0.857638	+	0.514254i	$0.171931\pi$
$128$	−1.77827e99	−0.143722
$129$	4.81205e98	0.0268732
$130$	−5.25214e99	−0.203249
$131$	4.89204e99	0.131554	0.0657768	−	0.997834i	$-0.479047\pi$
$131$	4.89204e99	0.131554	0.0657768	+	0.997834i	$0.479047\pi$
$132$	2.52861e99	0.0473826
$133$	1.20011e99	0.0157133
$134$	−1.00394e101	−0.920934
$135$	2.97369e100	0.191620
$136$	−3.32824e100	−0.151048
$137$	−1.90845e101	−0.611581	−0.305790	−	0.952099i	$-0.598921\pi$
$137$	−1.90845e101	−0.611581	−0.305790	+	0.952099i	$0.598921\pi$
$138$	2.95458e100	0.0670253
$139$	−4.62520e101	−0.744607	−0.372304	−	0.928111i	$-0.621432\pi$
$139$	−4.62520e101	−0.744607	−0.372304	+	0.928111i	$0.621432\pi$
$140$	−1.45673e100	−0.0166838
$141$	−1.40371e100	−0.0114649
$142$	2.01948e102	1.17908
$143$	8.04698e101	0.336644
$144$	1.58504e102	0.476235
$145$	2.96611e102	0.641515
$146$	2.11839e102	0.330556
$147$	−1.86821e102	−0.210791
$148$	−4.26287e102	−0.348554
$149$	−1.63087e103	−0.968440	−0.484220	−	0.874946i	$-0.660897\pi$
$149$	−1.63087e103	−0.968440	−0.484220	+	0.874946i	$0.660897\pi$
$150$	3.08840e102	0.133475
$151$	−3.73881e103	−1.17850	−0.589248	−	0.807952i	$-0.700576\pi$
$151$	−3.73881e103	−1.17850	−0.589248	+	0.807952i	$0.700576\pi$
$152$	−7.50894e102	−0.172985
$153$	7.85855e102	0.132587
$154$	−3.85461e102	−0.0477250
$155$	5.81967e103	0.529837
$156$	6.45363e102	0.0432898
$157$	6.03866e103	0.299025	0.149512	−	0.988760i	$-0.452230\pi$
$157$	6.03866e103	0.299025	0.149512	+	0.988760i	$0.452230\pi$
$158$	6.10866e103	0.223735
$159$	8.91945e103	0.242089
$160$	1.57836e104	0.318058
$161$	2.60788e103	0.0390894
$162$	−6.17085e104	−0.689257
$163$	1.41991e105	1.18399	0.591997	−	0.805940i	$-0.298340\pi$
$163$	1.41991e105	1.18399	0.591997	+	0.805940i	$0.298340\pi$
$164$	4.04337e104	0.252151
$165$	1.27366e104	0.0595067
$166$	−3.33865e105	−1.17068
$167$	−3.70058e105	−0.975523	−0.487761	−	0.872977i	$-0.662186\pi$
$167$	−3.70058e105	−0.975523	−0.487761	+	0.872977i	$0.662186\pi$
$168$	−1.15217e104	−0.0228732
$169$	−4.62378e105	−0.692435
$170$	−4.49801e104	−0.0508976
$171$	1.77299e105	0.151842
$172$	−7.13040e104	−0.0462927
$173$	3.09162e106	1.52404	0.762019	−	0.647554i	$-0.224208\pi$
$173$	3.09162e106	1.52404	0.762019	+	0.647554i	$0.224208\pi$
$174$	6.29450e105	0.235978
$175$	2.72600e105	0.0778428
$176$	1.39000e106	0.302805
$177$	2.02150e106	0.336468
$178$	7.92568e106	1.00945
$179$	−1.56762e107	−1.53010	−0.765052	−	0.643968i	$-0.777287\pi$
$179$	−1.56762e107	−1.53010	−0.765052	+	0.643968i	$0.777287\pi$
$180$	−2.15210e106	−0.161220
$181$	−1.46036e107	−0.840865	−0.420433	−	0.907324i	$-0.638122\pi$
$181$	−1.46036e107	−0.840865	−0.420433	+	0.907324i	$0.638122\pi$
$182$	−9.83793e105	−0.0436026
$183$	1.20193e107	0.410632
$184$	−1.63172e107	−0.430327
$185$	−2.14721e107	−0.437741
$186$	1.23502e107	0.194898
$187$	6.89155e106	0.0843025
$188$	2.07999e106	0.0197498
$189$	5.57009e106	0.0411080
$190$	−1.01481e107	−0.0582893
$191$	1.34886e108	0.603784	0.301892	−	0.953342i	$-0.402382\pi$
$191$	1.34886e108	0.603784	0.301892	+	0.953342i	$0.402382\pi$
$192$	6.38955e107	0.223183
$193$	4.05040e108	1.10541	0.552707	−	0.833375i	$-0.313595\pi$
$193$	4.05040e108	1.10541	0.552707	+	0.833375i	$0.313595\pi$
$194$	−2.69754e108	−0.575951
$195$	3.25070e107	0.0543667
$196$	2.76827e108	0.363116
$197$	4.29277e108	0.442173	0.221086	−	0.975254i	$-0.429040\pi$
$197$	4.29277e108	0.442173	0.221086	+	0.975254i	$0.429040\pi$
$198$	−5.69464e108	−0.461179
$199$	−2.40376e109	−1.53239	−0.766195	−	0.642608i	$-0.777852\pi$
$199$	−2.40376e109	−1.53239	−0.766195	+	0.642608i	$0.777852\pi$
$200$	−1.70563e109	−0.856957
$201$	6.21364e108	0.246339
$202$	−1.48140e109	−0.463963
$203$	5.55589e108	0.137623
$204$	5.52699e107	0.0108407
$205$	2.03665e109	0.316670
$206$	1.01809e110	1.25630
$207$	3.85277e109	0.377730
$208$	3.54762e109	0.276649
$209$	1.55482e109	0.0965455
$210$	−1.55713e108	−0.00770740
$211$	−2.86933e109	−0.113335	−0.0566676	−	0.998393i	$-0.518048\pi$
$211$	−2.86933e109	−0.113335	−0.0566676	+	0.998393i	$0.518048\pi$
$212$	−1.32167e110	−0.417031
$213$	−1.24991e110	−0.315390
$214$	1.21924e110	0.246284
$215$	−3.59159e109	−0.0581379
$216$	−3.48514e110	−0.452550
$217$	1.09010e110	0.113665
$218$	−8.70069e110	−0.729240
$219$	−1.31113e110	−0.0884200
$220$	−1.88729e110	−0.102509
$221$	1.75890e110	0.0770206
$222$	−4.55668e110	−0.161021
$223$	2.09181e111	0.597093	0.298547	−	0.954395i	$-0.403498\pi$
$223$	2.09181e111	0.597093	0.298547	+	0.954395i	$0.403498\pi$
$224$	2.95647e110	0.0682326
$225$	4.02728e111	0.752215
$226$	−4.48134e111	−0.678043
$227$	9.25938e111	1.13594	0.567968	−	0.823051i	$-0.307730\pi$
$227$	9.25938e111	1.13594	0.567968	+	0.823051i	$0.307730\pi$
$228$	1.24696e110	0.0124150
$229$	1.09157e112	0.882808	0.441404	−	0.897308i	$-0.354481\pi$
$229$	1.09157e112	0.882808	0.441404	+	0.897308i	$0.354481\pi$
$230$	−2.20522e111	−0.145004
$231$	2.38573e110	0.0127659
$232$	−3.47625e112	−1.51507
$233$	−1.51519e112	−0.538347	−0.269173	−	0.963092i	$-0.586750\pi$
$233$	−1.51519e112	−0.538347	−0.269173	+	0.963092i	$0.586750\pi$
$234$	−1.45341e112	−0.421343
$235$	1.04769e111	0.0248033
$236$	−2.99542e112	−0.579612
$237$	−3.78082e111	−0.0598466
$238$	−8.42535e110	−0.0109190
$239$	9.51210e112	1.01013	0.505064	−	0.863082i	$-0.331469\pi$
$239$	9.51210e112	1.01013	0.505064	+	0.863082i	$0.331469\pi$
$240$	5.61511e111	0.0489017
$241$	6.63734e112	0.474444	0.237222	−	0.971455i	$-0.423763\pi$
$241$	6.63734e112	0.474444	0.237222	+	0.971455i	$0.423763\pi$
$242$	8.55911e112	0.502573
$243$	1.24389e113	0.600460
$244$	−1.78100e113	−0.707371
$245$	1.39438e113	0.456029
$246$	4.32206e112	0.116486
$247$	3.96830e112	0.0882061
$248$	−6.82061e113	−1.25132
$249$	2.06639e113	0.313143
$250$	−5.23066e113	−0.655249
$251$	7.06257e113	0.731916	0.365958	−	0.930631i	$-0.380741\pi$
$251$	7.06257e113	0.731916	0.365958	+	0.930631i	$0.380741\pi$
$252$	−4.03116e112	−0.0345863
$253$	3.37869e113	0.240172
$254$	−2.31602e114	−1.36502
$255$	2.78395e112	0.0136145
$256$	−2.30029e114	−0.934082
$257$	3.55726e114	1.20031	0.600153	−	0.799886i	$-0.295107\pi$
$257$	3.55726e114	1.20031	0.600153	+	0.799886i	$0.295107\pi$
$258$	−7.62186e112	−0.0213858
$259$	−4.02199e113	−0.0939080
$260$	−4.81682e113	−0.0936541
$261$	8.20804e114	1.32989
$262$	−7.74855e113	−0.104691
$263$	1.23426e115	1.39158	0.695792	−	0.718243i	$-0.255053\pi$
$263$	1.23426e115	1.39158	0.695792	+	0.718243i	$0.255053\pi$
$264$	−1.49272e114	−0.140537
$265$	−6.65725e114	−0.523740
$266$	−1.90087e113	−0.0125047
$267$	−4.90542e114	−0.270017
$268$	−9.20726e114	−0.424354
$269$	−1.09917e115	−0.424456	−0.212228	−	0.977220i	$-0.568072\pi$
$269$	−1.09917e115	−0.424456	−0.212228	+	0.977220i	$0.568072\pi$
$270$	−4.71006e114	−0.152492
$271$	−5.13910e115	−1.39587	−0.697936	−	0.716160i	$-0.745898\pi$
$271$	−5.13910e115	−1.39587	−0.697936	+	0.716160i	$0.745898\pi$
$272$	3.03824e114	0.0692785
$273$	6.08897e113	0.0116632
$274$	3.02282e115	0.486699
$275$	3.53172e115	0.478281
$276$	2.70969e114	0.0308843
$277$	−2.11630e115	−0.203136	−0.101568	−	0.994829i	$-0.532386\pi$
$277$	−2.11630e115	−0.203136	−0.101568	+	0.994829i	$0.532386\pi$
$278$	7.32591e115	0.592562
$279$	1.61046e116	1.09838
$280$	8.59953e114	0.0494844
$281$	7.23403e115	0.351423	0.175711	−	0.984442i	$-0.443777\pi$
$281$	7.23403e115	0.351423	0.175711	+	0.984442i	$0.443777\pi$
$282$	2.22335e114	0.00912380
$283$	−4.66108e116	−1.61670	−0.808352	−	0.588700i	$-0.799640\pi$
$283$	−4.66108e116	−1.61670	−0.808352	+	0.588700i	$0.799640\pi$
$284$	1.85210e116	0.543303
$285$	6.28094e114	0.0155917
$286$	−1.27457e116	−0.267903
$287$	3.81490e115	0.0679349
$288$	4.36776e116	0.659349
$289$	−7.65930e116	−0.980712
$290$	−4.69805e116	−0.510520
$291$	1.66958e116	0.154060
$292$	1.94281e116	0.152316
$293$	−1.15589e117	−0.770376	−0.385188	−	0.922838i	$-0.625863\pi$
$293$	−1.15589e117	−0.770376	−0.385188	+	0.922838i	$0.625863\pi$
$294$	2.95908e116	0.167748
$295$	−1.50879e117	−0.727921
$296$	2.51651e117	1.03382
$297$	7.21643e116	0.252575
$298$	2.58316e117	0.770689
$299$	8.62325e116	0.219427
$300$	2.83242e116	0.0615032
$301$	−6.72750e115	−0.0124723
$302$	5.92194e117	0.937853
$303$	9.16882e116	0.124105
$304$	6.85465e116	0.0793397
$305$	−8.97091e117	−0.888371
$306$	−1.24472e117	−0.105513
$307$	−2.13540e118	−1.55027	−0.775135	−	0.631796i	$-0.782318\pi$
$307$	−2.13540e118	−1.55027	−0.775135	+	0.631796i	$0.782318\pi$
$308$	−3.53512e116	−0.0219910
$309$	−6.30126e117	−0.336046
$310$	−9.21784e117	−0.421647
$311$	−1.04083e117	−0.0408563	−0.0204282	−	0.999791i	$-0.506503\pi$
$311$	−1.04083e117	−0.0408563	−0.0204282	+	0.999791i	$0.506503\pi$
$312$	−3.80979e117	−0.128398
$313$	5.96092e118	1.72567	0.862834	−	0.505487i	$-0.168687\pi$
$313$	5.96092e118	1.72567	0.862834	+	0.505487i	$0.168687\pi$
$314$	−9.56471e117	−0.237965
$315$	−2.03050e117	−0.0434361
$316$	5.60235e117	0.103094
$317$	4.89731e118	0.775608	0.387804	−	0.921742i	$-0.373234\pi$
$317$	4.89731e118	0.775608	0.387804	+	0.921742i	$0.373234\pi$
$318$	−1.41276e118	−0.192655
$319$	7.19803e118	0.845583
$320$	−4.76899e118	−0.482840
$321$	−7.54624e117	−0.0658781
$322$	−4.13066e117	−0.0311075
$323$	3.39851e117	0.0220886
$324$	−5.65938e118	−0.317600
$325$	9.01382e118	0.436968
$326$	−2.24901e119	−0.942227
$327$	5.38510e118	0.195063
$328$	−2.38694e119	−0.747882
$329$	1.96246e117	0.00532103
$330$	−2.01737e118	−0.0473557
$331$	3.77600e119	0.767719	0.383860	−	0.923391i	$-0.374595\pi$
$331$	3.77600e119	0.767719	0.383860	+	0.923391i	$0.374595\pi$
$332$	−3.06193e119	−0.539432
$333$	−5.94192e119	−0.907457
$334$	5.86139e119	0.776325
$335$	−4.63770e119	−0.532935
$336$	1.05178e118	0.0104908
$337$	1.27092e120	1.10078	0.550389	−	0.834909i	$-0.314480\pi$
$337$	1.27092e120	1.10078	0.550389	+	0.834909i	$0.314480\pi$
$338$	7.32366e119	0.551042
$339$	2.77363e119	0.181369
$340$	−4.12520e118	−0.0234529
$341$	1.41229e120	0.698381
$342$	−2.80826e119	−0.120836
$343$	5.24945e119	0.196627
$344$	4.20931e119	0.137305
$345$	1.36487e119	0.0387869
$346$	−4.89685e120	−1.21284
$347$	−5.19900e120	−1.12272	−0.561358	−	0.827573i	$-0.689721\pi$
$347$	−5.19900e120	−1.12272	−0.561358	+	0.827573i	$0.689721\pi$
$348$	5.77278e119	0.108735
$349$	−6.40191e120	−1.05221	−0.526104	−	0.850420i	$-0.676348\pi$
$349$	−6.40191e120	−1.05221	−0.526104	+	0.850420i	$0.676348\pi$
$350$	−4.31774e119	−0.0619477
$351$	1.84181e120	0.230758
$352$	3.83030e120	0.419234
$353$	4.04177e120	0.386610	0.193305	−	0.981139i	$-0.438079\pi$
$353$	4.04177e120	0.386610	0.193305	+	0.981139i	$0.438079\pi$
$354$	−3.20188e120	−0.267762
$355$	9.32901e120	0.682321
$356$	7.26877e120	0.465142
$357$	5.21468e118	0.00292070
$358$	2.48297e121	1.21766
$359$	−1.66803e121	−0.716501	−0.358251	−	0.933625i	$-0.616627\pi$
$359$	−1.66803e121	−0.716501	−0.358251	+	0.933625i	$0.616627\pi$
$360$	1.27046e121	0.478180
$361$	−2.95437e121	−0.974704
$362$	2.31308e121	0.669164
$363$	−5.29747e120	−0.134432
$364$	−9.02252e119	−0.0200915
$365$	9.78594e120	0.191290
$366$	−1.90376e121	−0.326783
$367$	−1.09516e122	−1.65134	−0.825672	−	0.564150i	$-0.809204\pi$
$367$	−1.09516e122	−1.65134	−0.825672	+	0.564150i	$0.809204\pi$
$368$	1.48954e121	0.197370
$369$	5.63597e121	0.656472
$370$	3.40099e121	0.348356
$371$	−1.24699e121	−0.112357
$372$	1.13265e121	0.0898064
$373$	−1.99395e122	−1.39170	−0.695848	−	0.718189i	$-0.744971\pi$
$373$	−1.99395e122	−1.39170	−0.695848	+	0.718189i	$0.744971\pi$
$374$	−1.09156e121	−0.0670883
$375$	3.23740e121	0.175272
$376$	−1.22789e121	−0.0585782
$377$	1.83712e122	0.772543
$378$	−8.82253e120	−0.0327139
$379$	3.34987e122	1.09563	0.547816	−	0.836599i	$-0.315459\pi$
$379$	3.34987e122	1.09563	0.547816	+	0.836599i	$0.315459\pi$
$380$	−9.30698e120	−0.0268589
$381$	1.43345e122	0.365128
$382$	−2.13648e122	−0.480494
$383$	5.98903e122	1.18964	0.594818	−	0.803860i	$-0.297224\pi$
$383$	5.98903e122	1.18964	0.594818	+	0.803860i	$0.297224\pi$
$384$	−1.74328e121	−0.0305939
$385$	−1.78064e121	−0.0276180
$386$	−6.41547e122	−0.879694
$387$	−9.93892e121	−0.120523
$388$	−2.47395e122	−0.265390
$389$	−7.50248e122	−0.712195	−0.356097	−	0.934449i	$-0.615893\pi$
$389$	−7.50248e122	−0.712195	−0.356097	+	0.934449i	$0.615893\pi$
$390$	−5.14882e121	−0.0432652
$391$	7.38508e121	0.0549489
$392$	−1.63420e123	−1.07701
$393$	4.79580e121	0.0280036
$394$	−6.79937e122	−0.351883
$395$	2.82191e122	0.129473
$396$	−5.22264e122	−0.212505
$397$	3.70171e123	1.33614	0.668072	−	0.744096i	$-0.267120\pi$
$397$	3.70171e123	1.33614	0.668072	+	0.744096i	$0.267120\pi$
$398$	3.80734e123	1.21948
$399$	1.17650e121	0.00334487
$400$	1.55701e123	0.393044
$401$	−6.40769e122	−0.143663	−0.0718313	−	0.997417i	$-0.522884\pi$
$401$	−6.40769e122	−0.143663	−0.0718313	+	0.997417i	$0.522884\pi$
$402$	−9.84187e122	−0.196038
$403$	3.60453e123	0.638056
$404$	−1.35862e123	−0.213788
$405$	−2.85063e123	−0.398867
$406$	−8.80004e122	−0.109521
$407$	−5.21076e123	−0.576988
$408$	−3.26276e122	−0.0321535
$409$	−1.95811e123	−0.171783	−0.0858915	−	0.996304i	$-0.527374\pi$
$409$	−1.95811e123	−0.171783	−0.0858915	+	0.996304i	$0.527374\pi$
$410$	−3.22587e123	−0.252008
$411$	−1.87091e123	−0.130186
$412$	9.33708e123	0.578887
$413$	−2.82616e123	−0.156160
$414$	−6.10245e123	−0.300599
$415$	−1.54230e124	−0.677459
$416$	9.77589e123	0.383021
$417$	−4.53421e123	−0.158503
$418$	−2.46270e123	−0.0768314
$419$	1.05246e124	0.293116	0.146558	−	0.989202i	$-0.453181\pi$
$419$	1.05246e124	0.293116	0.146558	+	0.989202i	$0.453181\pi$
$420$	−1.42807e122	−0.00355146
$421$	9.96237e123	0.221291	0.110645	−	0.993860i	$-0.464708\pi$
$421$	9.96237e123	0.221291	0.110645	+	0.993860i	$0.464708\pi$
$422$	4.54477e123	0.0901926
$423$	2.89925e123	0.0514184
$424$	7.80224e124	1.23692
$425$	7.71957e123	0.109426
$426$	1.97975e124	0.250989
$427$	−1.68037e124	−0.190581
$428$	1.11819e124	0.113484
$429$	7.88867e123	0.0716609
$430$	5.68876e123	0.0462664
$431$	−1.18119e125	−0.860298	−0.430149	−	0.902758i	$-0.641539\pi$
$431$	−1.18119e125	−0.860298	−0.430149	+	0.902758i	$0.641539\pi$
$432$	3.18146e124	0.207563
$433$	−2.80100e125	−1.63734	−0.818670	−	0.574265i	$-0.805288\pi$
$433$	−2.80100e125	−1.63734	−0.818670	+	0.574265i	$0.805288\pi$
$434$	−1.72662e124	−0.0904553
$435$	2.90775e124	0.136558
$436$	−7.97954e124	−0.336024
$437$	1.66617e124	0.0629290
$438$	2.07672e124	0.0703650
$439$	−3.25145e125	−0.988583	−0.494291	−	0.869296i	$-0.664572\pi$
$439$	−3.25145e125	−0.988583	−0.494291	+	0.869296i	$0.664572\pi$
$440$	1.11413e125	0.304041
$441$	3.85864e125	0.945369
$442$	−2.78594e124	−0.0612933
$443$	9.92410e125	1.96117	0.980583	−	0.196106i	$-0.0628295\pi$
$443$	9.92410e125	1.96117	0.980583	+	0.196106i	$0.0628295\pi$
$444$	−4.17901e124	−0.0741962
$445$	3.66128e125	0.584161
$446$	−3.31325e125	−0.475169
$447$	−1.59879e125	−0.206151
$448$	−8.93293e124	−0.103583
$449$	2.95384e125	0.308095	0.154048	−	0.988063i	$-0.450769\pi$
$449$	2.95384e125	0.308095	0.154048	+	0.988063i	$0.450769\pi$
$450$	−6.37885e125	−0.598616
$451$	4.94246e125	0.417405
$452$	−4.10991e125	−0.312433
$453$	−3.66526e125	−0.250865
$454$	−1.46660e126	−0.903982
$455$	−4.54465e124	−0.0252324
$456$	−7.36122e124	−0.0368230
$457$	7.06615e125	0.318540	0.159270	−	0.987235i	$-0.449086\pi$
$457$	7.06615e125	0.318540	0.159270	+	0.987235i	$0.449086\pi$
$458$	−1.72895e126	−0.702543
$459$	1.57736e125	0.0577866
$460$	−2.02244e125	−0.0668158
$461$	1.62307e126	0.483662	0.241831	−	0.970318i	$-0.422252\pi$
$461$	1.62307e126	0.483662	0.241831	+	0.970318i	$0.422252\pi$
$462$	−3.77878e124	−0.0101592
$463$	−1.72484e126	−0.418457	−0.209228	−	0.977867i	$-0.567095\pi$
$463$	−1.72484e126	−0.418457	−0.209228	+	0.977867i	$0.567095\pi$
$464$	3.17335e126	0.694887
$465$	5.70518e125	0.112786
$466$	2.39993e126	0.428419
$467$	−1.02389e126	−0.165083	−0.0825413	−	0.996588i	$-0.526304\pi$
$467$	−1.02389e126	−0.165083	−0.0825413	+	0.996588i	$0.526304\pi$
$468$	−1.33295e126	−0.194149
$469$	−8.68701e125	−0.114330
$470$	−1.65945e125	−0.0197386
$471$	5.91987e125	0.0636530
$472$	1.76830e127	1.71914
$473$	−8.71593e125	−0.0766319
$474$	5.98849e125	0.0476262
$475$	1.74164e126	0.125317
$476$	−7.72702e124	−0.00503132
$477$	−1.84224e127	−1.08574
$478$	−1.50663e127	−0.803864
$479$	−9.17343e126	−0.443195	−0.221597	−	0.975138i	$-0.571127\pi$
$479$	−9.17343e126	−0.443195	−0.221597	+	0.975138i	$0.571127\pi$
$480$	1.54731e126	0.0677046
$481$	−1.32992e127	−0.527149
$482$	−1.05130e127	−0.377564
$483$	2.55658e125	0.00832090
$484$	7.84970e126	0.231579
$485$	−1.24613e127	−0.333297
$486$	−1.97021e127	−0.477849
$487$	1.98568e127	0.436801	0.218401	−	0.975859i	$-0.429916\pi$
$487$	1.98568e127	0.436801	0.218401	+	0.975859i	$0.429916\pi$
$488$	1.05138e128	2.09807
$489$	1.39198e127	0.252035
$490$	−2.20858e127	−0.362910
$491$	4.00151e127	0.596833	0.298416	−	0.954436i	$-0.403542\pi$
$491$	4.00151e127	0.596833	0.298416	+	0.954436i	$0.403542\pi$
$492$	3.96383e126	0.0536750
$493$	1.57333e127	0.193461
$494$	−6.28543e126	−0.0701948
$495$	−2.63065e127	−0.266880
$496$	6.22630e127	0.573919
$497$	1.74744e127	0.146378
$498$	−3.27297e127	−0.249200
$499$	−2.21605e128	−1.53393	−0.766963	−	0.641692i	$-0.778233\pi$
$499$	−2.21605e128	−1.53393	−0.766963	+	0.641692i	$0.778233\pi$
$500$	−4.79712e127	−0.301929
$501$	−3.62778e127	−0.207658
$502$	−1.11865e128	−0.582462
$503$	1.80630e128	0.855679	0.427839	−	0.903855i	$-0.359275\pi$
$503$	1.80630e128	0.855679	0.427839	+	0.903855i	$0.359275\pi$
$504$	2.37973e127	0.102583
$505$	−6.84337e127	−0.268491
$506$	−5.35154e127	−0.191130
$507$	−4.53282e127	−0.147398
$508$	−2.12406e128	−0.628984
$509$	3.95836e128	1.06763	0.533815	−	0.845601i	$-0.320758\pi$
$509$	3.95836e128	1.06763	0.533815	+	0.845601i	$0.320758\pi$
$510$	−4.40953e126	−0.0108345
$511$	1.83303e127	0.0410371
$512$	4.34791e128	0.887068
$513$	3.55872e127	0.0661788
$514$	−5.63438e128	−0.955208
$515$	4.70309e128	0.727010
$516$	−6.99013e126	−0.00985427
$517$	2.54250e127	0.0326934
$518$	6.37049e127	0.0747324
$519$	3.03080e128	0.324420
$520$	2.84353e128	0.277779
$521$	8.99352e128	0.801932	0.400966	−	0.916093i	$-0.368675\pi$
$521$	8.99352e128	0.801932	0.400966	+	0.916093i	$0.368675\pi$
$522$	−1.30008e129	−1.05833
$523$	1.86877e128	0.138907	0.0694537	−	0.997585i	$-0.477874\pi$
$523$	1.86877e128	0.138907	0.0694537	+	0.997585i	$0.477874\pi$
$524$	−7.10632e127	−0.0482401
$525$	2.67237e127	0.0165703
$526$	−1.95496e129	−1.10743
$527$	3.08697e128	0.159782
$528$	1.36265e128	0.0644576
$529$	−1.95077e129	−0.843454
$530$	1.05445e129	0.416794
$531$	−4.17525e129	−1.50901
$532$	−1.74332e127	−0.00576200
$533$	1.26144e129	0.381350
$534$	7.76976e128	0.214881
$535$	5.63231e128	0.142522
$536$	5.43535e129	1.25864
$537$	−1.53678e129	−0.325711
$538$	1.74099e129	0.337784
$539$	3.38383e129	0.601094
$540$	−4.31967e128	−0.0702662
$541$	2.32075e129	0.345746	0.172873	−	0.984944i	$-0.444695\pi$
$541$	2.32075e129	0.345746	0.172873	+	0.984944i	$0.444695\pi$
$542$	8.13988e129	1.11084
$543$	−1.43163e129	−0.178994
$544$	8.37221e128	0.0959163
$545$	−4.01930e129	−0.422004
$546$	−9.64439e127	−0.00928163
$547$	−9.55184e129	−0.842731	−0.421366	−	0.906891i	$-0.638449\pi$
$547$	−9.55184e129	−0.842731	−0.421366	+	0.906891i	$0.638449\pi$
$548$	2.77227e129	0.224264
$549$	−2.48250e130	−1.84163
$550$	−5.59393e129	−0.380618
$551$	3.54965e129	0.221556
$552$	−1.59962e129	−0.0916032
$553$	5.28579e128	0.0277758
$554$	3.35203e129	0.161657
$555$	−2.10497e129	−0.0931813
$556$	6.71870e129	0.273044
$557$	3.74460e130	1.39728	0.698640	−	0.715474i	$-0.253789\pi$
$557$	3.74460e130	1.39728	0.698640	+	0.715474i	$0.253789\pi$
$558$	−2.55083e130	−0.874092
$559$	−2.22452e129	−0.0700126
$560$	−7.85022e128	−0.0226961
$561$	6.75597e128	0.0179454
$562$	−1.14581e130	−0.279664
$563$	4.96247e130	1.11314	0.556570	−	0.830801i	$-0.312117\pi$
$563$	4.96247e130	1.11314	0.556570	+	0.830801i	$0.312117\pi$
$564$	2.03907e128	0.00420412
$565$	−2.07016e130	−0.392377
$566$	7.38273e130	1.28658
$567$	−5.33960e129	−0.0855683
$568$	−1.09335e131	−1.61144
$569$	1.20184e131	1.62935	0.814674	−	0.579919i	$-0.196916\pi$
$569$	1.20184e131	1.62935	0.814674	+	0.579919i	$0.196916\pi$
$570$	−9.94846e128	−0.0124080
$571$	−5.24644e130	−0.602074	−0.301037	−	0.953613i	$-0.597333\pi$
$571$	−5.24644e130	−0.602074	−0.301037	+	0.953613i	$0.597333\pi$
$572$	−1.16893e130	−0.123446
$573$	1.32232e130	0.128527
$574$	−6.04247e129	−0.0540629
$575$	3.78464e130	0.311747
$576$	−1.31971e131	−1.00095
$577$	−1.74253e131	−1.21711	−0.608554	−	0.793512i	$-0.708250\pi$
$577$	−1.74253e131	−1.21711	−0.608554	+	0.793512i	$0.708250\pi$
$578$	1.21317e131	0.780455
$579$	3.97071e130	0.235308
$580$	−4.30866e130	−0.235241
$581$	−2.88892e130	−0.145334
$582$	−2.64447e130	−0.122602
$583$	−1.61555e131	−0.690344
$584$	−1.14690e131	−0.451770
$585$	−6.71407e130	−0.243827
$586$	1.83082e131	0.613069
$587$	5.88766e131	1.81816	0.909082	−	0.416616i	$-0.136784\pi$
$587$	5.88766e131	1.81816	0.909082	+	0.416616i	$0.136784\pi$
$588$	2.71382e130	0.0772961
$589$	6.96461e130	0.182987
$590$	2.38980e131	0.579283
$591$	4.20832e130	0.0941247
$592$	−2.29724e131	−0.474160
$593$	5.02581e131	0.957433	0.478717	−	0.877970i	$-0.341102\pi$
$593$	5.02581e131	0.957433	0.478717	+	0.877970i	$0.341102\pi$
$594$	−1.14302e131	−0.201001
$595$	−3.89210e129	−0.00631871
$596$	2.36906e131	0.355123
$597$	−2.35647e131	−0.326198
$598$	−1.36585e131	−0.174621
$599$	−1.09973e132	−1.29870	−0.649352	−	0.760488i	$-0.724960\pi$
$599$	−1.09973e132	−1.29870	−0.649352	+	0.760488i	$0.724960\pi$
$600$	−1.67207e131	−0.182419
$601$	−6.55632e131	−0.660881	−0.330440	−	0.943827i	$-0.607197\pi$
$601$	−6.55632e131	−0.660881	−0.330440	+	0.943827i	$0.607197\pi$
$602$	1.06558e130	0.00992548
$603$	−1.28338e132	−1.10480
$604$	5.43111e131	0.432149
$605$	3.95390e131	0.290834
$606$	−1.45226e131	−0.0987631
$607$	3.53897e131	0.222543	0.111272	−	0.993790i	$-0.464508\pi$
$607$	3.53897e131	0.222543	0.111272	+	0.993790i	$0.464508\pi$
$608$	1.88888e131	0.109846
$609$	5.44659e130	0.0292957
$610$	1.42091e132	0.706969
$611$	6.48909e130	0.0298694
$612$	−1.14156e131	−0.0486189
$613$	5.61589e131	0.221333	0.110666	−	0.993858i	$-0.464701\pi$
$613$	5.61589e131	0.221333	0.110666	+	0.993858i	$0.464701\pi$
$614$	3.38229e132	1.23371
$615$	1.99658e131	0.0674092
$616$	2.08690e131	0.0652256
$617$	−3.41314e132	−0.987664	−0.493832	−	0.869557i	$-0.664404\pi$
$617$	−3.41314e132	−0.987664	−0.493832	+	0.869557i	$0.664404\pi$
$618$	9.98064e131	0.267427
$619$	−3.46105e131	−0.0858820	−0.0429410	−	0.999078i	$-0.513673\pi$
$619$	−3.46105e131	−0.0858820	−0.0429410	+	0.999078i	$0.513673\pi$
$620$	−8.45383e131	−0.194289
$621$	7.73322e131	0.164630
$622$	1.64858e131	0.0325137
$623$	6.85804e131	0.125319
$624$	3.47783e131	0.0588899
$625$	2.60459e132	0.408731
$626$	−9.44158e132	−1.37329
$627$	1.52424e131	0.0205515
$628$	−8.77195e131	−0.109651
$629$	−1.13896e132	−0.132009
$630$	3.21613e131	0.0345667
$631$	4.47005e132	0.445572	0.222786	−	0.974867i	$-0.428485\pi$
$631$	4.47005e132	0.445572	0.222786	+	0.974867i	$0.428485\pi$
$632$	−3.30725e132	−0.305778
$633$	−2.81289e131	−0.0241255
$634$	−7.75691e132	−0.617233
$635$	−1.06989e133	−0.789926
$636$	−1.29567e132	−0.0887729
$637$	8.63638e132	0.549173
$638$	−1.14011e133	−0.672919
$639$	2.58160e133	1.41448
$640$	1.30114e132	0.0661875
$641$	2.46258e133	1.16315	0.581573	−	0.813494i	$-0.302438\pi$
$641$	2.46258e133	1.16315	0.581573	+	0.813494i	$0.302438\pi$
$642$	1.19526e132	0.0524261
$643$	1.35600e133	0.552379	0.276190	−	0.961103i	$-0.410928\pi$
$643$	1.35600e133	0.552379	0.276190	+	0.961103i	$0.410928\pi$
$644$	−3.78829e131	−0.0143339
$645$	−3.52093e131	−0.0123757
$646$	−5.38294e131	−0.0175782
$647$	2.27740e132	0.0691013	0.0345507	−	0.999403i	$-0.489000\pi$
$647$	2.27740e132	0.0691013	0.0345507	+	0.999403i	$0.489000\pi$
$648$	3.34092e133	0.942005
$649$	−3.66148e133	−0.959476
$650$	−1.42771e133	−0.347741
$651$	1.06865e132	0.0241958
$652$	−2.06260e133	−0.434165
$653$	−7.91804e133	−1.54968	−0.774839	−	0.632159i	$-0.782169\pi$
$653$	−7.91804e133	−1.54968	−0.774839	+	0.632159i	$0.782169\pi$
$654$	−8.52953e132	−0.155232
$655$	−3.57946e132	−0.0605837
$656$	2.17895e133	0.343017
$657$	2.70804e133	0.396552
$658$	−3.10836e131	−0.00423450
$659$	−1.02698e134	−1.30169	−0.650843	−	0.759212i	$-0.725584\pi$
$659$	−1.02698e134	−1.30169	−0.650843	+	0.759212i	$0.725584\pi$
$660$	−1.85016e132	−0.0218209
$661$	5.36310e133	0.588636	0.294318	−	0.955708i	$-0.404908\pi$
$661$	5.36310e133	0.588636	0.294318	+	0.955708i	$0.404908\pi$
$662$	−5.98085e133	−0.610954
$663$	1.72429e132	0.0163953
$664$	1.80756e134	1.59996
$665$	−8.78109e131	−0.00723636
$666$	9.41148e133	0.722158
$667$	7.71351e133	0.551157
$668$	5.37558e133	0.357720
$669$	2.05066e133	0.127102
$670$	7.34571e133	0.424112
$671$	−2.17703e134	−1.17097
$672$	2.89831e132	0.0145246
$673$	3.27600e133	0.152978	0.0764888	−	0.997070i	$-0.475629\pi$
$673$	3.27600e133	0.152978	0.0764888	+	0.997070i	$0.475629\pi$
$674$	−2.01303e134	−0.876003
$675$	8.08349e133	0.327846
$676$	6.71665e133	0.253913
$677$	−1.54260e134	−0.543617	−0.271808	−	0.962351i	$-0.587622\pi$
$677$	−1.54260e134	−0.543617	−0.271808	+	0.962351i	$0.587622\pi$
$678$	−4.39318e133	−0.144334
$679$	−2.33416e133	−0.0715018
$680$	2.43524e133	0.0695615
$681$	9.07722e133	0.241805
$682$	−2.23695e134	−0.555774
$683$	−1.72948e134	−0.400804	−0.200402	−	0.979714i	$-0.564225\pi$
$683$	−1.72948e134	−0.400804	−0.200402	+	0.979714i	$0.564225\pi$
$684$	−2.57550e133	−0.0556797
$685$	1.39640e134	0.281648
$686$	−8.31467e133	−0.156477
$687$	1.07010e134	0.187922
$688$	−3.84254e133	−0.0629749
$689$	−4.12330e134	−0.630713
$690$	−2.16184e133	−0.0308668
$691$	6.35279e134	0.846754	0.423377	−	0.905954i	$-0.360845\pi$
$691$	6.35279e134	0.846754	0.423377	+	0.905954i	$0.360845\pi$
$692$	−4.49098e134	−0.558858
$693$	−4.92753e133	−0.0572534
$694$	8.23476e134	0.893462
$695$	3.38422e134	0.342910
$696$	−3.40787e134	−0.322510
$697$	1.08032e134	0.0954978
$698$	1.01401e135	0.837351
$699$	−1.48539e134	−0.114597
$700$	−3.95987e133	−0.0285446
$701$	1.97594e135	1.33097	0.665485	−	0.746411i	$-0.268225\pi$
$701$	1.97594e135	1.33097	0.665485	+	0.746411i	$0.268225\pi$
$702$	−2.91727e134	−0.183638
$703$	−2.56964e134	−0.151180
$704$	−1.15732e135	−0.636433
$705$	1.02708e133	0.00527985
$706$	−6.40181e134	−0.307666
$707$	−1.28185e134	−0.0575990
$708$	−2.93649e134	−0.123381
$709$	−3.08810e135	−1.21338	−0.606688	−	0.794940i	$-0.707502\pi$
$709$	−3.08810e135	−1.21338	−0.606688	+	0.794940i	$0.707502\pi$
$710$	−1.47763e135	−0.542994
$711$	7.80900e134	0.268404
$712$	−4.29099e135	−1.37962
$713$	1.51343e135	0.455209
$714$	−8.25960e132	−0.00232431
$715$	−5.88790e134	−0.155033
$716$	2.27717e135	0.561082
$717$	9.32497e134	0.215024
$718$	2.64201e135	0.570195
$719$	2.37153e135	0.479078	0.239539	−	0.970887i	$-0.423004\pi$
$719$	2.37153e135	0.479078	0.239539	+	0.970887i	$0.423004\pi$
$720$	−1.15976e135	−0.219318
$721$	8.80949e134	0.155964
$722$	4.67946e135	0.775673
$723$	6.50677e134	0.100994
$724$	2.12136e135	0.308342
$725$	8.06288e135	1.09758
$726$	8.39073e134	0.106982
$727$	−6.85344e135	−0.818511	−0.409255	−	0.912420i	$-0.634211\pi$
$727$	−6.85344e135	−0.818511	−0.409255	+	0.912420i	$0.634211\pi$
$728$	5.32629e134	0.0595915
$729$	−7.04349e135	−0.738295
$730$	−1.55001e135	−0.152229
$731$	−1.90511e134	−0.0175326
$732$	−1.74596e135	−0.150577
$733$	−1.88469e136	−1.52335	−0.761676	−	0.647958i	$-0.775623\pi$
$733$	−1.88469e136	−1.52335	−0.761676	+	0.647958i	$0.775623\pi$
$734$	1.73463e136	1.31415
$735$	1.36695e135	0.0970743
$736$	4.10460e135	0.273259
$737$	−1.12546e136	−0.702465
$738$	−8.92688e135	−0.522423
$739$	−1.16392e136	−0.638725	−0.319363	−	0.947633i	$-0.603469\pi$
$739$	−1.16392e136	−0.638725	−0.319363	+	0.947633i	$0.603469\pi$
$740$	3.11910e135	0.160518
$741$	3.89023e134	0.0187763
$742$	1.97512e135	0.0894144
$743$	9.78146e135	0.415370	0.207685	−	0.978196i	$-0.433407\pi$
$743$	9.78146e135	0.415370	0.207685	+	0.978196i	$0.433407\pi$
$744$	−6.68643e135	−0.266367
$745$	1.19330e136	0.445990
$746$	3.15824e136	1.10752
$747$	−4.26796e136	−1.40440
$748$	−1.00109e135	−0.0309134
$749$	1.05500e135	0.0305751
$750$	−5.12776e135	−0.139482
$751$	6.59301e136	1.68340	0.841699	−	0.539947i	$-0.181556\pi$
$751$	6.59301e136	1.68340	0.841699	+	0.539947i	$0.181556\pi$
$752$	1.12090e135	0.0268669
$753$	6.92363e135	0.155802
$754$	−2.90983e136	−0.614793
$755$	2.73565e136	0.542726
$756$	−8.09128e134	−0.0150741
$757$	1.24814e136	0.218377	0.109189	−	0.994021i	$-0.465175\pi$
$757$	1.24814e136	0.218377	0.109189	+	0.994021i	$0.465175\pi$
$758$	−5.30589e136	−0.871909
$759$	3.31222e135	0.0511252
$760$	5.49422e135	0.0796637
$761$	9.60694e136	1.30862	0.654310	−	0.756226i	$-0.272959\pi$
$761$	9.60694e136	1.30862	0.654310	+	0.756226i	$0.272959\pi$
$762$	−2.27045e136	−0.290571
$763$	−7.52866e135	−0.0905320
$764$	−1.95939e136	−0.221405
$765$	−5.75003e135	−0.0610593
$766$	−9.48609e136	−0.946718
$767$	−9.34502e136	−0.876598
$768$	−2.25504e136	−0.198837
$769$	−1.03509e137	−0.857982	−0.428991	−	0.903309i	$-0.641131\pi$
$769$	−1.03509e137	−0.857982	−0.428991	+	0.903309i	$0.641131\pi$
$770$	2.82038e135	0.0219785
$771$	3.48727e136	0.255507
$772$	−5.88373e136	−0.405351
$773$	−1.55146e136	−0.100511	−0.0502556	−	0.998736i	$-0.516004\pi$
$773$	−1.55146e136	−0.100511	−0.0502556	+	0.998736i	$0.516004\pi$
$774$	1.57424e136	0.0959124
$775$	1.58198e137	0.906506
$776$	1.46046e137	0.787149
$777$	−3.94287e135	−0.0199901
$778$	1.18833e137	0.566768
$779$	2.43733e136	0.109367
$780$	−4.72206e135	−0.0199360
$781$	2.26393e137	0.899371
$782$	−1.16973e136	−0.0437286
$783$	1.64750e137	0.579619
$784$	1.49181e137	0.493970
$785$	−4.41844e136	−0.137708
$786$	−7.59612e135	−0.0222854
$787$	−6.19569e137	−1.71116	−0.855579	−	0.517673i	$-0.826799\pi$
$787$	−6.19569e137	−1.71116	−0.855579	+	0.517673i	$0.826799\pi$
$788$	−6.23581e136	−0.162143
$789$	1.20998e137	0.296225
$790$	−4.46965e136	−0.103036
$791$	−3.87768e136	−0.0841761
$792$	3.08310e137	0.630291
$793$	−5.55632e137	−1.06982
$794$	−5.86319e137	−1.06331
$795$	−6.52628e136	−0.111488
$796$	3.49177e137	0.561921
$797$	−7.49113e137	−1.13573	−0.567867	−	0.823120i	$-0.692231\pi$
$797$	−7.49113e137	−1.13573	−0.567867	+	0.823120i	$0.692231\pi$
$798$	−1.86347e135	−0.00266186
$799$	5.55736e135	0.00747991
$800$	4.29051e137	0.544171
$801$	1.01318e138	1.21099
$802$	1.01492e137	0.114327
$803$	2.37481e137	0.252140
$804$	−9.02613e136	−0.0903315
$805$	−1.90816e136	−0.0180016
$806$	−5.70926e137	−0.507768
$807$	−1.07755e137	−0.0903533
$808$	8.02037e137	0.634096
$809$	−1.35628e138	−1.01110	−0.505549	−	0.862798i	$-0.668710\pi$
$809$	−1.35628e138	−1.01110	−0.505549	+	0.862798i	$0.668710\pi$
$810$	4.51515e137	0.317420
$811$	2.47817e138	1.64301	0.821505	−	0.570202i	$-0.193135\pi$
$811$	2.47817e138	1.64301	0.821505	+	0.570202i	$0.193135\pi$
$812$	−8.07066e136	−0.0504659
$813$	−5.03800e137	−0.297137
$814$	8.25339e137	0.459170
$815$	−1.03893e138	−0.545258
$816$	2.97847e136	0.0147472
$817$	−4.29818e136	−0.0200788
$818$	3.10148e137	0.136706
$819$	−1.25763e137	−0.0523079
$820$	−2.95850e137	−0.116122
$821$	−3.32339e137	−0.123107	−0.0615533	−	0.998104i	$-0.519605\pi$
$821$	−3.32339e137	−0.123107	−0.0615533	+	0.998104i	$0.519605\pi$
$822$	2.96335e137	0.103603
$823$	2.25748e138	0.744956	0.372478	−	0.928041i	$-0.378508\pi$
$823$	2.25748e138	0.744956	0.372478	+	0.928041i	$0.378508\pi$
$824$	−5.51199e138	−1.71698
$825$	3.46224e137	0.101811
$826$	4.47639e137	0.124273
$827$	−5.10022e138	−1.33683	−0.668416	−	0.743788i	$-0.733027\pi$
$827$	−5.10022e138	−1.33683	−0.668416	+	0.743788i	$0.733027\pi$
$828$	−5.59665e137	−0.138512
$829$	3.23772e137	0.0756657	0.0378329	−	0.999284i	$-0.487955\pi$
$829$	3.23772e137	0.0756657	0.0378329	+	0.999284i	$0.487955\pi$
$830$	2.44286e138	0.539125
$831$	−2.07466e137	−0.0432413
$832$	−2.95377e138	−0.581459
$833$	7.39633e137	0.137524
$834$	7.18179e137	0.126138
$835$	2.70768e138	0.449252
$836$	−2.25858e137	−0.0354028
$837$	3.23250e138	0.478717
$838$	−1.66700e138	−0.233263
$839$	9.45136e138	1.24969	0.624843	−	0.780750i	$-0.285163\pi$
$839$	9.45136e138	1.24969	0.624843	+	0.780750i	$0.285163\pi$
$840$	8.43036e136	0.0105337
$841$	7.96448e138	0.940476
$842$	−1.57795e138	−0.176104
$843$	7.09172e137	0.0748069
$844$	4.16808e137	0.0415595
$845$	3.38318e138	0.318883
$846$	−4.59216e137	−0.0409190
$847$	7.40615e137	0.0623922
$848$	−7.12240e138	−0.567314
$849$	−4.56938e138	−0.344145
$850$	−1.22271e138	−0.0870814
$851$	−5.58393e138	−0.376085
$852$	1.81566e138	0.115652
$853$	−2.86391e139	−1.72536	−0.862682	−	0.505747i	$-0.831217\pi$
$853$	−2.86391e139	−1.72536	−0.862682	+	0.505747i	$0.831217\pi$
$854$	2.66155e138	0.151665
$855$	−1.29728e138	−0.0699268
$856$	−6.60103e138	−0.336595
$857$	−3.38329e138	−0.163211	−0.0816057	−	0.996665i	$-0.526005\pi$
$857$	−3.38329e138	−0.163211	−0.0816057	+	0.996665i	$0.526005\pi$
$858$	−1.24950e138	−0.0570281
$859$	−7.40194e138	−0.319647	−0.159823	−	0.987146i	$-0.551092\pi$
$859$	−7.40194e138	−0.319647	−0.159823	+	0.987146i	$0.551092\pi$
$860$	5.21725e137	0.0213189
$861$	3.73985e137	0.0144612
$862$	1.87090e139	0.684629
$863$	3.81615e139	1.32164	0.660818	−	0.750546i	$-0.270209\pi$
$863$	3.81615e139	1.32164	0.660818	+	0.750546i	$0.270209\pi$
$864$	8.76689e138	0.287371
$865$	−2.26211e139	−0.701857
$866$	4.43654e139	1.30300
$867$	−7.50862e138	−0.208763
$868$	−1.58351e138	−0.0416806
$869$	6.84810e138	0.170660
$870$	−4.60563e138	−0.108674
$871$	−2.87246e139	−0.641787
$872$	4.71059e139	0.996649
$873$	−3.44839e139	−0.690939
$874$	−2.63907e138	−0.0500792
$875$	−4.52606e138	−0.0813463
$876$	1.90459e138	0.0324232
$877$	3.02430e138	0.0487691	0.0243846	−	0.999703i	$-0.492237\pi$
$877$	3.02430e138	0.0487691	0.0243846	+	0.999703i	$0.492237\pi$
$878$	5.15002e139	0.786718
$879$	−1.13315e139	−0.163989
$880$	−1.01705e139	−0.139449
$881$	−2.95780e139	−0.384249	−0.192125	−	0.981371i	$-0.561538\pi$
$881$	−2.95780e139	−0.384249	−0.192125	+	0.981371i	$0.561538\pi$
$882$	−6.11175e139	−0.752328
$883$	5.73715e139	0.669211	0.334605	−	0.942358i	$-0.391397\pi$
$883$	5.73715e139	0.669211	0.334605	+	0.942358i	$0.391397\pi$
$884$	−2.55503e138	−0.0282431
$885$	−1.47911e139	−0.154952
$886$	−1.57189e140	−1.56070
$887$	9.34047e139	0.879016	0.439508	−	0.898239i	$-0.355153\pi$
$887$	9.34047e139	0.879016	0.439508	+	0.898239i	$0.355153\pi$
$888$	2.46701e139	0.220067
$889$	−2.00404e139	−0.169462
$890$	−5.79915e139	−0.464878
$891$	−6.91780e139	−0.525748
$892$	−3.03863e139	−0.218951
$893$	1.25381e138	0.00856619
$894$	2.53234e139	0.164055
$895$	1.14701e140	0.704650
$896$	2.43720e138	0.0141991
$897$	8.45361e138	0.0467091
$898$	−4.67862e139	−0.245184
$899$	3.22426e140	1.60267
$900$	−5.85014e139	−0.275834
$901$	−3.53125e139	−0.157943
$902$	−7.82842e139	−0.332172
$903$	−6.59515e137	−0.00265495
$904$	2.42622e140	0.926679
$905$	1.06853e140	0.387239
$906$	5.80544e139	0.199639
$907$	5.17088e140	1.68740	0.843701	−	0.536813i	$-0.180372\pi$
$907$	5.17088e140	1.68740	0.843701	+	0.536813i	$0.180372\pi$
$908$	−1.34505e140	−0.416542
$909$	−1.89375e140	−0.556593
$910$	7.19832e138	0.0200801
$911$	−6.21237e140	−1.64488	−0.822441	−	0.568851i	$-0.807388\pi$
$911$	−6.21237e140	−1.64488	−0.822441	+	0.568851i	$0.807388\pi$
$912$	6.71980e138	0.0168889
$913$	−3.74279e140	−0.892962
$914$	−1.11922e140	−0.253495
$915$	−8.79443e139	−0.189106
$916$	−1.58565e140	−0.323722
$917$	−6.70478e138	−0.0129969
$918$	−2.49839e139	−0.0459868
$919$	−1.39988e140	−0.244682	−0.122341	−	0.992488i	$-0.539040\pi$
$919$	−1.39988e140	−0.244682	−0.122341	+	0.992488i	$0.539040\pi$
$920$	1.19391e140	0.198176
$921$	−2.09339e140	−0.330004
$922$	−2.57079e140	−0.384901
$923$	5.77811e140	0.821685
$924$	−3.46558e138	−0.00468120
$925$	−5.83684e140	−0.748937
$926$	2.73199e140	0.333010
$927$	1.30148e141	1.50712
$928$	8.74455e140	0.962074
$929$	−2.63829e140	−0.275788	−0.137894	−	0.990447i	$-0.544033\pi$
$929$	−2.63829e140	−0.275788	−0.137894	+	0.990447i	$0.544033\pi$
$930$	−9.03650e139	−0.0897553
$931$	1.66871e140	0.157496
$932$	2.20102e140	0.197409
$933$	−1.02035e139	−0.00869703
$934$	1.62175e140	0.131373
$935$	−5.04248e139	−0.0388233
$936$	7.86884e140	0.575848
$937$	−4.59872e140	−0.319894	−0.159947	−	0.987126i	$-0.551132\pi$
$937$	−4.59872e140	−0.319894	−0.159947	+	0.987126i	$0.551132\pi$
$938$	1.37595e140	0.0909843
$939$	5.84365e140	0.367341
$940$	−1.52191e139	−0.00909528
$941$	−3.38422e141	−1.92287	−0.961437	−	0.275025i	$-0.911314\pi$
$941$	−3.38422e141	−1.92287	−0.961437	+	0.275025i	$0.911314\pi$
$942$	−9.37655e139	−0.0506553
$943$	5.29641e140	0.272067
$944$	−1.61422e141	−0.788483
$945$	−4.07558e139	−0.0189312
$946$	1.38053e140	0.0609840
$947$	6.52645e140	0.274191	0.137095	−	0.990558i	$-0.456223\pi$
$947$	6.52645e140	0.274191	0.137095	+	0.990558i	$0.456223\pi$
$948$	5.49214e139	0.0219455
$949$	6.06112e140	0.230360
$950$	−2.75860e140	−0.0997280
$951$	4.80097e140	0.165103
$952$	4.56152e139	0.0149229
$953$	−4.03088e141	−1.25455	−0.627274	−	0.778799i	$-0.715829\pi$
$953$	−4.03088e141	−1.25455	−0.627274	+	0.778799i	$0.715829\pi$
$954$	2.91795e141	0.864033
$955$	−9.86948e140	−0.278057
$956$	−1.38176e141	−0.370409
$957$	7.05643e140	0.179998
$958$	1.45299e141	0.352696
$959$	2.61563e140	0.0604215
$960$	−4.67517e140	−0.102781
$961$	1.54691e141	0.323671
$962$	2.10647e141	0.419508
$963$	1.55862e141	0.295455
$964$	−9.64161e140	−0.173976
$965$	−2.96364e141	−0.509070
$966$	−4.04939e139	−0.00662181
$967$	1.00904e142	1.57091	0.785453	−	0.618921i	$-0.212430\pi$
$967$	1.00904e142	1.57091	0.785453	+	0.618921i	$0.212430\pi$
$968$	−4.63394e141	−0.686864
$969$	3.33165e139	0.00470197
$970$	1.97376e141	0.265239
$971$	1.30014e142	1.66370	0.831851	−	0.554999i	$-0.187281\pi$
$971$	1.30014e142	1.66370	0.831851	+	0.554999i	$0.187281\pi$
$972$	−1.80691e141	−0.220186
$973$	6.33906e140	0.0735640
$974$	−3.14514e141	−0.347608
$975$	8.83650e140	0.0930167
$976$	−9.59773e141	−0.962281
$977$	−2.02609e142	−1.93494	−0.967468	−	0.252994i	$-0.918585\pi$
$977$	−2.02609e142	−1.93494	−0.967468	+	0.252994i	$0.918585\pi$
$978$	−2.20477e141	−0.200571
$979$	8.88506e141	0.769985
$980$	−2.02552e141	−0.167224
$981$	−1.11225e142	−0.874833
$982$	−6.33803e141	−0.474962
$983$	6.66811e141	0.476113	0.238057	−	0.971251i	$-0.423490\pi$
$983$	6.66811e141	0.476113	0.238057	+	0.971251i	$0.423490\pi$
$984$	−2.33998e141	−0.159201
$985$	−3.14098e141	−0.203631
$986$	−2.49202e141	−0.153957
$987$	1.92385e139	0.00113268
$988$	−5.76447e140	−0.0323448
$989$	−9.34011e140	−0.0499492
$990$	4.16671e141	0.212384
$991$	3.05345e142	1.48352	0.741758	−	0.670668i	$-0.233992\pi$
$991$	3.05345e142	1.48352	0.741758	+	0.670668i	$0.233992\pi$
$992$	1.71573e142	0.794592
$993$	3.70172e141	0.163423
$994$	−2.76780e141	−0.116488
$995$	1.75881e142	0.705703
$996$	−3.00169e141	−0.114828
$997$	−3.48409e142	−1.27078	−0.635388	−	0.772193i	$-0.719160\pi$
$997$	−3.48409e142	−1.27078	−0.635388	+	0.772193i	$0.719160\pi$
$998$	3.51003e142	1.22070
$999$	−1.19265e142	−0.395506

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.96.a.a.1.3	✓	8
3.2	odd	2		9.96.a.c.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.96.a.a.1.3	✓	8	1.1	even	1	trivial
9.96.a.c.1.6		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)

\(f(q)\)	\(=\)	\(q-1.58391e14 q^{2} +9.80327e21 q^{3} -1.45263e28 q^{4} -7.31691e32 q^{5} -1.55275e36 q^{6} -1.37055e39 q^{7} +8.57536e42 q^{8} -2.02479e45 q^{9} +O(q^{10})\)	\(q-1.58391e14 q^{2} +9.80327e21 q^{3} -1.45263e28 q^{4} -7.31691e32 q^{5} -1.55275e36 q^{6} -1.37055e39 q^{7} +8.57536e42 q^{8} -2.02479e45 q^{9} +1.15893e47 q^{10} -1.77564e49 q^{11} -1.42405e50 q^{12} -4.53188e52 q^{13} +2.17083e53 q^{14} -7.17297e54 q^{15} -7.82816e56 q^{16} -3.88116e57 q^{17} +3.20709e59 q^{18} -8.75641e59 q^{19} +1.06288e61 q^{20} -1.34359e61 q^{21} +2.81246e63 q^{22} -1.90280e64 q^{23} +8.40666e64 q^{24} -1.98898e66 q^{25} +7.17809e66 q^{26} -4.06413e67 q^{27} +1.99090e67 q^{28} -4.05377e69 q^{29} +1.13613e69 q^{30} -7.95372e70 q^{31} -2.15714e71 q^{32} -1.74071e71 q^{33} +6.14742e71 q^{34} +1.00282e72 q^{35} +2.94127e73 q^{36} +2.93459e74 q^{37} +1.38694e74 q^{38} -4.44272e74 q^{39} -6.27451e75 q^{40} -2.78348e76 q^{41} +2.12812e75 q^{42} +4.90861e76 q^{43} +2.57935e77 q^{44} +1.48152e78 q^{45} +3.01387e78 q^{46} -1.43188e78 q^{47} -7.67415e78 q^{48} -1.90570e80 q^{49} +3.15037e80 q^{50} -3.80481e79 q^{51} +6.58314e80 q^{52} +9.09844e81 q^{53} +6.43722e81 q^{54} +1.29922e82 q^{55} -1.17530e82 q^{56} -8.58415e81 q^{57} +6.42081e83 q^{58} +2.06207e84 q^{59} +1.04197e83 q^{60} +1.22605e85 q^{61} +1.25980e85 q^{62} +2.77508e84 q^{63} +6.51777e85 q^{64} +3.31593e85 q^{65} +2.75713e85 q^{66} +6.33834e86 q^{67} +5.63790e85 q^{68} -1.86537e86 q^{69} -1.58838e86 q^{70} -1.27499e88 q^{71} -1.73633e88 q^{72} -1.33744e88 q^{73} -4.64812e88 q^{74} -1.94985e88 q^{75} +1.27198e88 q^{76} +2.43360e88 q^{77} +7.03688e88 q^{78} -3.85669e89 q^{79} +5.72779e89 q^{80} +3.89595e90 q^{81} +4.40879e90 q^{82} +2.10785e91 q^{83} +1.95174e89 q^{84} +2.83981e90 q^{85} -7.77481e90 q^{86} -3.97402e91 q^{87} -1.52267e92 q^{88} -5.00386e92 q^{89} -2.34660e92 q^{90} +6.21116e91 q^{91} +2.76407e92 q^{92} -7.79725e92 q^{93} +2.26797e92 q^{94} +6.40699e92 q^{95} -2.11470e93 q^{96} +1.70309e94 q^{97} +3.01846e94 q^{98} +3.59530e94 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5835659138280 q^{2} - 95\!\cdots\!80 q^{3}+ \cdots + 92\!\cdots\!36 q^{9}+O(q^{10}) \) 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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