LMFDB - Embedded newform 1.96.a.a.1.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1,96,Mod(1,1)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1, base_ring=CyclotomicField(1)) chi = DirichletCharacter(H, H._module([])) N = Newforms(chi, 96, names="a")

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 96 $
Character orbit:	$[\chi]$	$=$	1.a (trivial)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			1.8
Root			$1.62871e13$ 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)

$f(q)$	$=$	\(q+3.90162e14 q^{2} +2.16924e22 q^{3} +1.12612e29 q^{4} +1.39914e33 q^{5} +8.46353e36 q^{6} +1.75361e40 q^{7} +2.84812e43 q^{8} -1.65034e45 q^{9} +5.45891e47 q^{10} -5.41264e48 q^{11} +2.44283e51 q^{12} +1.04831e52 q^{13} +6.84194e54 q^{14} +3.03506e55 q^{15} +6.65124e57 q^{16} -2.56029e58 q^{17} -6.43899e59 q^{18} -4.34204e60 q^{19} +1.57560e62 q^{20} +3.80400e62 q^{21} -2.11181e63 q^{22} -7.48379e64 q^{23} +6.17824e65 q^{24} -5.66766e65 q^{25} +4.09009e66 q^{26} -8.18069e67 q^{27} +1.97479e69 q^{28} +2.03053e69 q^{29} +1.18417e70 q^{30} +3.72805e70 q^{31} +1.46681e72 q^{32} -1.17413e71 q^{33} -9.98929e72 q^{34} +2.45355e73 q^{35} -1.85848e74 q^{36} -1.43964e74 q^{37} -1.69410e75 q^{38} +2.27402e74 q^{39} +3.98491e76 q^{40} -4.16311e76 q^{41} +1.48418e77 q^{42} +4.94148e76 q^{43} -6.09530e77 q^{44} -2.30905e78 q^{45} -2.91989e79 q^{46} +4.71948e79 q^{47} +1.44281e80 q^{48} +1.15068e80 q^{49} -2.21131e80 q^{50} -5.55388e80 q^{51} +1.18052e81 q^{52} +9.21253e80 q^{53} -3.19180e82 q^{54} -7.57304e81 q^{55} +4.99450e83 q^{56} -9.41891e82 q^{57} +7.92238e83 q^{58} -1.44917e84 q^{59} +3.41785e84 q^{60} +2.68780e84 q^{61} +1.45454e85 q^{62} -2.89406e85 q^{63} +3.08809e86 q^{64} +1.46673e85 q^{65} -4.58101e85 q^{66} +3.24337e86 q^{67} -2.88321e87 q^{68} -1.62341e87 q^{69} +9.57282e87 q^{70} +2.78222e87 q^{71} -4.70035e88 q^{72} +2.94316e88 q^{73} -5.61691e88 q^{74} -1.22945e88 q^{75} -4.88967e89 q^{76} -9.49169e88 q^{77} +8.87238e88 q^{78} +9.20074e89 q^{79} +9.30600e90 q^{80} +1.72561e90 q^{81} -1.62429e91 q^{82} -2.26821e90 q^{83} +4.28378e91 q^{84} -3.58220e91 q^{85} +1.92798e91 q^{86} +4.40471e91 q^{87} -1.54158e92 q^{88} +3.95651e92 q^{89} -9.00904e92 q^{90} +1.83833e92 q^{91} -8.42767e93 q^{92} +8.08702e92 q^{93} +1.84136e94 q^{94} -6.07512e93 q^{95} +3.18185e94 q^{96} -3.21613e94 q^{97} +4.48953e94 q^{98} +8.93268e93 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5835659138280 q^{2} - 95\!\cdots\!80 q^{3} + 20\!\cdots\!84 q^{4} + 19\!\cdots\!60 q^{5} + 10\!\cdots\!76 q^{6} + 31\!\cdots\!00 q^{7} - 14\!\cdots\!60 q^{8} + 92\!\cdots\!36 q^{9} - 35\!\cdots\!40 q^{10}+ \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

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 $

$2$	3.90162e14	1.96029	0.980145	−	0.198283i	$-0.0635364\pi$
$2$	3.90162e14	1.96029	0.980145	+	0.198283i	$0.0635364\pi$
$3$	2.16924e22	0.471028	0.235514	−	0.971871i	$-0.424323\pi$
$3$	2.16924e22	0.471028	0.235514	+	0.971871i	$0.424323\pi$
$4$	1.12612e29	2.84274
$5$	1.39914e33	0.880614	0.440307	−	0.897847i	$-0.354870\pi$
$5$	1.39914e33	0.880614	0.440307	+	0.897847i	$0.354870\pi$
$6$	8.46353e36	0.923352
$7$	1.75361e40	1.26409	0.632044	−	0.774932i	$-0.282216\pi$
$7$	1.75361e40	1.26409	0.632044	+	0.774932i	$0.282216\pi$
$8$	2.84812e43	3.61230
$9$	−1.65034e45	−0.778132
$10$	5.45891e47	1.72626
$11$	−5.41264e48	−0.185036	−0.0925181	−	0.995711i	$-0.529492\pi$
$11$	−5.41264e48	−0.185036	−0.0925181	+	0.995711i	$0.529492\pi$
$12$	2.44283e51	1.33901
$13$	1.04831e52	0.128286	0.0641430	−	0.997941i	$-0.479569\pi$
$13$	1.04831e52	0.128286	0.0641430	+	0.997941i	$0.479569\pi$
$14$	6.84194e54	2.47798
$15$	3.03506e55	0.414794
$16$	6.65124e57	4.23841
$17$	−2.56029e58	−0.916148	−0.458074	−	0.888914i	$-0.651461\pi$
$17$	−2.56029e58	−0.916148	−0.458074	+	0.888914i	$0.651461\pi$
$18$	−6.43899e59	−1.52536
$19$	−4.34204e60	−0.788674	−0.394337	−	0.918966i	$-0.629026\pi$
$19$	−4.34204e60	−0.788674	−0.394337	+	0.918966i	$0.629026\pi$
$20$	1.57560e62	2.50335
$21$	3.80400e62	0.595421
$22$	−2.11181e63	−0.362725
$23$	−7.48379e64	−1.55614	−0.778071	−	0.628177i	$-0.783802\pi$
$23$	−7.48379e64	−1.55614	−0.778071	+	0.628177i	$0.783802\pi$
$24$	6.17824e65	1.70149
$25$	−5.66766e65	−0.224519
$26$	4.09009e66	0.251478
$27$	−8.18069e67	−0.837551
$28$	1.97479e69	3.59347
$29$	2.03053e69	0.697759	0.348880	−	0.937168i	$-0.386562\pi$
$29$	2.03053e69	0.697759	0.348880	+	0.937168i	$0.386562\pi$
$30$	1.18417e70	0.813117
$31$	3.72805e70	0.539264	0.269632	−	0.962963i	$-0.413098\pi$
$31$	3.72805e70	0.539264	0.269632	+	0.962963i	$0.413098\pi$
$32$	1.46681e72	4.69622
$33$	−1.17413e71	−0.0871573
$34$	−9.98929e72	−1.79592
$35$	2.45355e73	1.11317
$36$	−1.85848e74	−2.21202
$37$	−1.43964e74	−0.466305	−0.233153	−	0.972440i	$-0.574904\pi$
$37$	−1.43964e74	−0.466305	−0.233153	+	0.972440i	$0.574904\pi$
$38$	−1.69410e75	−1.54603
$39$	2.27402e74	0.0604263
$40$	3.98491e76	3.18104
$41$	−4.16311e76	−1.02845	−0.514227	−	0.857654i	$-0.671921\pi$
$41$	−4.16311e76	−1.02845	−0.514227	+	0.857654i	$0.671921\pi$
$42$	1.48418e77	1.16720
$43$	4.94148e76	0.127088	0.0635441	−	0.997979i	$-0.479760\pi$
$43$	4.94148e76	0.127088	0.0635441	+	0.997979i	$0.479760\pi$
$44$	−6.09530e77	−0.526009
$45$	−2.30905e78	−0.685234
$46$	−2.91989e79	−3.05049
$47$	4.71948e79	1.77519	0.887596	−	0.460622i	$-0.152374\pi$
$47$	4.71948e79	1.77519	0.887596	+	0.460622i	$0.152374\pi$
$48$	1.44281e80	1.99641
$49$	1.15068e80	0.597919
$50$	−2.21131e80	−0.440122
$51$	−5.55388e80	−0.431532
$52$	1.18052e81	0.364683
$53$	9.21253e80	0.115153	0.0575765	−	0.998341i	$-0.481663\pi$
$53$	9.21253e80	0.115153	0.0575765	+	0.998341i	$0.481663\pi$
$54$	−3.19180e82	−1.64184
$55$	−7.57304e81	−0.162945
$56$	4.99450e83	4.56626
$57$	−9.41891e82	−0.371488
$58$	7.92238e83	1.36781
$59$	−1.44917e84	−1.11083	−0.555417	−	0.831572i	$-0.687442\pi$
$59$	−1.44917e84	−1.11083	−0.555417	+	0.831572i	$0.687442\pi$
$60$	3.41785e84	1.17915
$61$	2.68780e84	0.422892	0.211446	−	0.977390i	$-0.432183\pi$
$61$	2.68780e84	0.422892	0.211446	+	0.977390i	$0.432183\pi$
$62$	1.45454e85	1.05711
$63$	−2.89406e85	−0.983628
$64$	3.08809e86	4.96754
$65$	1.46673e85	0.112970
$66$	−4.58101e85	−0.170854
$67$	3.24337e86	0.592165	0.296083	−	0.955162i	$-0.404320\pi$
$67$	3.24337e86	0.592165	0.296083	+	0.955162i	$0.404320\pi$
$68$	−2.88321e87	−2.60437
$69$	−1.62341e87	−0.732987
$70$	9.57282e87	2.18214
$71$	2.78222e87	0.323311	0.161656	−	0.986847i	$-0.448317\pi$
$71$	2.78222e87	0.323311	0.161656	+	0.986847i	$0.448317\pi$
$72$	−4.70035e88	−2.81084
$73$	2.94316e88	0.914067	0.457033	−	0.889450i	$-0.348912\pi$
$73$	2.94316e88	0.914067	0.457033	+	0.889450i	$0.348912\pi$
$74$	−5.61691e88	−0.914094
$75$	−1.22945e88	−0.105755
$76$	−4.88967e89	−2.24199
$77$	−9.49169e88	−0.233902
$78$	8.87238e88	0.118453
$79$	9.20074e89	0.670712	0.335356	−	0.942092i	$-0.391143\pi$
$79$	9.20074e89	0.670712	0.335356	+	0.942092i	$0.391143\pi$
$80$	9.30600e90	3.73241
$81$	1.72561e90	0.383622
$82$	−1.62429e91	−2.01607
$83$	−2.26821e90	−0.158298	−0.0791488	−	0.996863i	$-0.525220\pi$
$83$	−2.26821e90	−0.158298	−0.0791488	+	0.996863i	$0.525220\pi$
$84$	4.28378e91	1.69263
$85$	−3.58220e91	−0.806773
$86$	1.92798e91	0.249130
$87$	4.40471e91	0.328664
$88$	−1.54158e92	−0.668406
$89$	3.95651e92	1.00297	0.501484	−	0.865167i	$-0.332788\pi$
$89$	3.95651e92	1.00297	0.501484	+	0.865167i	$0.332788\pi$
$90$	−9.00904e92	−1.34326
$91$	1.83833e92	0.162165
$92$	−8.42767e93	−4.42370
$93$	8.08702e92	0.254009
$94$	1.84136e94	3.47989
$95$	−6.07512e93	−0.694518
$96$	3.18185e94	2.21205
$97$	−3.21613e94	−1.36671	−0.683354	−	0.730087i	$-0.739479\pi$
$97$	−3.21613e94	−1.36671	−0.683354	+	0.730087i	$0.739479\pi$
$98$	4.48953e94	1.17209
$99$	8.93268e93	0.143983
$100$	−6.38248e94	−0.638248
$101$	1.10577e95	0.689289	0.344645	−	0.938733i	$-0.387999\pi$
$101$	1.10577e95	0.689289	0.344645	+	0.938733i	$0.387999\pi$
$102$	−2.16691e95	−0.845927
$103$	−2.78781e95	−0.684691	−0.342345	−	0.939574i	$-0.611221\pi$
$103$	−2.78781e95	−0.684691	−0.342345	+	0.939574i	$0.611221\pi$
$104$	2.98570e95	0.463407
$105$	5.32233e95	0.524336
$106$	3.59438e95	0.225733
$107$	−2.08016e96	−0.836311	−0.418155	−	0.908376i	$-0.637323\pi$
$107$	−2.08016e96	−0.836311	−0.418155	+	0.908376i	$0.637323\pi$
$108$	−9.21247e96	−2.38094
$109$	4.86869e95	0.0812182	0.0406091	−	0.999175i	$-0.487070\pi$
$109$	4.86869e95	0.0812182	0.0406091	+	0.999175i	$0.487070\pi$
$110$	−2.95471e96	−0.319420
$111$	−3.12291e96	−0.219643
$112$	1.16637e98	5.35773
$113$	−1.92348e97	−0.579246	−0.289623	−	0.957141i	$-0.593530\pi$
$113$	−1.92348e97	−0.579246	−0.289623	+	0.957141i	$0.593530\pi$
$114$	−3.67490e97	−0.728224
$115$	−1.04709e98	−1.37036
$116$	2.28663e98	1.98354
$117$	−1.73006e97	−0.0998234
$118$	−5.65412e98	−2.17756
$119$	−4.48977e98	−1.15809
$120$	8.64421e98	1.49836
$121$	−8.26371e98	−0.965762
$122$	1.04868e99	0.828991
$123$	−9.03076e98	−0.484431
$124$	4.19825e99	1.53298
$125$	−4.32491e99	−1.07833
$126$	−1.12915e100	−1.92820
$127$	−1.37038e100	−1.60755	−0.803777	−	0.594930i	$-0.797180\pi$
$127$	−1.37038e100	−1.60755	−0.803777	+	0.594930i	$0.797180\pi$
$128$	6.23795e100	5.04160
$129$	1.07192e99	0.0598621
$130$	5.72261e99	0.221455
$131$	−3.14879e98	−0.00846754	−0.00423377	−	0.999991i	$-0.501348\pi$
$131$	−3.14879e98	−0.00846754	−0.00423377	+	0.999991i	$0.501348\pi$
$132$	−1.32222e100	−0.247765
$133$	−7.61427e100	−0.996954
$134$	1.26544e101	1.16082
$135$	−1.14459e101	−0.737559
$136$	−7.29201e101	−3.30940
$137$	5.08244e101	1.62872	0.814358	−	0.580363i	$-0.197089\pi$
$137$	5.08244e101	1.62872	0.814358	+	0.580363i	$0.197089\pi$
$138$	−6.33393e101	−1.43687
$139$	−3.57121e101	−0.574927	−0.287464	−	0.957792i	$-0.592812\pi$
$139$	−3.57121e101	−0.574927	−0.287464	+	0.957792i	$0.592812\pi$
$140$	2.76300e102	3.16446
$141$	1.02377e102	0.836166
$142$	1.08552e102	0.633783
$143$	−5.67411e100	−0.0237375
$144$	−1.09768e103	−3.29805
$145$	2.84100e102	0.614456
$146$	1.14831e103	1.79184
$147$	2.49610e102	0.281637
$148$	−1.62121e103	−1.32558
$149$	3.30116e103	1.96029	0.980143	−	0.198293i	$-0.0635398\pi$
$149$	3.30116e103	1.96029	0.980143	+	0.198293i	$0.0635398\pi$
$150$	−4.79684e102	−0.207310
$151$	−1.44275e103	−0.454763	−0.227381	−	0.973806i	$-0.573016\pi$
$151$	−1.44275e103	−0.454763	−0.227381	+	0.973806i	$0.573016\pi$
$152$	−1.23666e104	−2.84893
$153$	4.22534e103	0.712884
$154$	−3.70330e103	−0.458516
$155$	5.21606e103	0.474883
$156$	2.56083e103	0.171776
$157$	−2.05317e104	−1.01670	−0.508349	−	0.861151i	$-0.669744\pi$
$157$	−2.05317e104	−1.01670	−0.508349	+	0.861151i	$0.669744\pi$
$158$	3.58978e104	1.31479
$159$	1.99841e103	0.0542403
$160$	2.05226e105	4.13556
$161$	−1.31237e105	−1.96710
$162$	6.73266e104	0.752010
$163$	−6.60439e104	−0.550708	−0.275354	−	0.961343i	$-0.588795\pi$
$163$	−6.60439e104	−0.550708	−0.275354	+	0.961343i	$0.588795\pi$
$164$	−4.68818e105	−2.92362
$165$	−1.64277e104	−0.0767520
$166$	−8.84970e104	−0.310309
$167$	1.63767e105	0.431712	0.215856	−	0.976425i	$-0.430746\pi$
$167$	1.63767e105	0.431712	0.215856	+	0.976425i	$0.430746\pi$
$168$	1.08342e106	2.15084
$169$	−6.56768e105	−0.983543
$170$	−1.39764e106	−1.58151
$171$	7.16583e105	0.613693
$172$	5.56472e105	0.361278
$173$	7.86049e105	0.387489	0.193745	−	0.981052i	$-0.437937\pi$
$173$	7.86049e105	0.387489	0.193745	+	0.981052i	$0.437937\pi$
$174$	1.71855e106	0.644277
$175$	−9.93889e105	−0.283812
$176$	−3.60008e106	−0.784260
$177$	−3.14360e106	−0.523235
$178$	1.54368e107	1.96611
$179$	1.21900e107	1.18983	0.594916	−	0.803788i	$-0.297185\pi$
$179$	1.21900e107	1.18983	0.594916	+	0.803788i	$0.297185\pi$
$180$	−2.60028e107	−1.94794
$181$	3.05359e107	1.75824	0.879120	−	0.476600i	$-0.158131\pi$
$181$	3.05359e107	1.75824	0.879120	+	0.476600i	$0.158131\pi$
$182$	7.17245e106	0.317890
$183$	5.83047e106	0.199194
$184$	−2.13147e108	−5.62125
$185$	−2.01425e107	−0.410635
$186$	3.15525e107	0.497931
$187$	1.38579e107	0.169521
$188$	5.31471e108	5.04640
$189$	−1.43458e108	−1.05874
$190$	−2.37028e108	−1.36146
$191$	−3.48114e107	−0.155825	−0.0779124	−	0.996960i	$-0.524825\pi$
$191$	−3.48114e107	−0.155825	−0.0779124	+	0.996960i	$0.524825\pi$
$192$	6.69880e108	2.33985
$193$	2.23194e108	0.609130	0.304565	−	0.952492i	$-0.401489\pi$
$193$	2.23194e108	0.609130	0.304565	+	0.952492i	$0.401489\pi$
$194$	−1.25481e109	−2.67914
$195$	3.18167e107	0.0532123
$196$	1.29581e109	1.69973
$197$	−1.91029e109	−1.96767	−0.983837	−	0.179065i	$-0.942693\pi$
$197$	−1.91029e109	−1.96767	−0.983837	+	0.179065i	$0.942693\pi$
$198$	3.48519e108	0.282248
$199$	−5.55220e108	−0.353952	−0.176976	−	0.984215i	$-0.556631\pi$
$199$	−5.55220e108	−0.353952	−0.176976	+	0.984215i	$0.556631\pi$
$200$	−1.61422e109	−0.811029
$201$	7.03563e108	0.278927
$202$	4.31431e109	1.35121
$203$	3.56078e109	0.882029
$204$	−6.25435e109	−1.22673
$205$	−5.82477e109	−0.905670
$206$	−1.08770e110	−1.34219
$207$	1.23508e110	1.21088
$208$	6.97253e109	0.543729
$209$	2.35019e109	0.145933
$210$	2.07657e110	1.02785
$211$	3.40905e110	1.34653	0.673266	−	0.739401i	$-0.264891\pi$
$211$	3.40905e110	1.34653	0.673266	+	0.739401i	$0.264891\pi$
$212$	1.03744e110	0.327349
$213$	6.03530e109	0.152289
$214$	−8.11600e110	−1.63941
$215$	6.91381e109	0.111916
$216$	−2.32996e111	−3.02548
$217$	6.53757e110	0.681677
$218$	1.89958e110	0.159211
$219$	6.38441e110	0.430552
$220$	−8.52818e110	−0.463211
$221$	−2.68397e110	−0.117529
$222$	−1.21844e111	−0.430564
$223$	−3.82469e111	−1.09173	−0.545864	−	0.837874i	$-0.683799\pi$
$223$	−3.82469e111	−1.09173	−0.545864	+	0.837874i	$0.683799\pi$
$224$	2.57221e112	5.93644
$225$	9.35354e110	0.174705
$226$	−7.50471e111	−1.13549
$227$	−1.17158e112	−1.43729	−0.718645	−	0.695377i	$-0.755237\pi$
$227$	−1.17158e112	−1.43729	−0.718645	+	0.695377i	$0.755237\pi$
$228$	−1.06069e112	−1.05604
$229$	1.67490e112	1.35458	0.677288	−	0.735718i	$-0.263155\pi$
$229$	1.67490e112	1.35458	0.677288	+	0.735718i	$0.263155\pi$
$230$	−4.08533e112	−2.68630
$231$	−2.05897e111	−0.110175
$232$	5.78320e112	2.52051
$233$	6.96313e111	0.247399	0.123700	−	0.992320i	$-0.460524\pi$
$233$	6.96313e111	0.247399	0.123700	+	0.992320i	$0.460524\pi$
$234$	−6.75003e111	−0.195683
$235$	6.60320e112	1.56326
$236$	−1.63195e113	−3.15781
$237$	1.99586e112	0.315924
$238$	−1.75174e113	−2.27020
$239$	5.54701e112	0.589059	0.294530	−	0.955642i	$-0.404837\pi$
$239$	5.54701e112	0.589059	0.294530	+	0.955642i	$0.404837\pi$
$240$	2.01869e113	1.75807
$241$	1.57841e113	1.12827	0.564133	−	0.825684i	$-0.309211\pi$
$241$	1.57841e113	1.12827	0.564133	+	0.825684i	$0.309211\pi$
$242$	−3.22419e113	−1.89317
$243$	2.10936e113	1.01825
$244$	3.02679e113	1.20217
$245$	1.60997e113	0.526536
$246$	−3.52346e113	−0.949625
$247$	−4.55179e112	−0.101176
$248$	1.06179e114	1.94798
$249$	−4.92029e112	−0.0745627
$250$	−1.68741e114	−2.11384
$251$	1.09858e114	1.13849	0.569244	−	0.822168i	$-0.307236\pi$
$251$	1.09858e114	1.13849	0.569244	+	0.822168i	$0.307236\pi$
$252$	−3.25906e114	−2.79619
$253$	4.05070e113	0.287943
$254$	−5.34672e114	−3.15127
$255$	−7.77064e113	−0.380013
$256$	1.21049e115	4.91545
$257$	2.55612e114	0.862498	0.431249	−	0.902233i	$-0.358073\pi$
$257$	2.55612e114	0.862498	0.431249	+	0.902233i	$0.358073\pi$
$258$	4.18224e113	0.117347
$259$	−2.52457e114	−0.589451
$260$	1.65172e114	0.321145
$261$	−3.35107e114	−0.542949
$262$	−1.22854e113	−0.0165988
$263$	4.76486e114	0.537220	0.268610	−	0.963249i	$-0.413436\pi$
$263$	4.76486e114	0.537220	0.268610	+	0.963249i	$0.413436\pi$
$264$	−3.34406e114	−0.314838
$265$	1.28896e114	0.101405
$266$	−2.97080e115	−1.95432
$267$	8.58260e114	0.472426
$268$	3.65243e115	1.68337
$269$	7.95205e114	0.307076	0.153538	−	0.988143i	$-0.450933\pi$
$269$	7.95205e114	0.307076	0.153538	+	0.988143i	$0.450933\pi$
$270$	−4.46576e115	−1.44583
$271$	6.86155e115	1.86372	0.931861	−	0.362816i	$-0.118185\pi$
$271$	6.86155e115	1.86372	0.931861	+	0.362816i	$0.118185\pi$
$272$	−1.70291e116	−3.88301
$273$	3.98776e114	0.0763842
$274$	1.98297e116	3.19275
$275$	3.06770e114	0.0415442
$276$	−1.82816e116	−2.08369
$277$	−4.72757e115	−0.453783	−0.226892	−	0.973920i	$-0.572856\pi$
$277$	−4.72757e115	−0.453783	−0.226892	+	0.973920i	$0.572856\pi$
$278$	−1.39335e116	−1.12702
$279$	−6.15254e115	−0.419619
$280$	6.98800e116	4.02111
$281$	4.14167e115	0.201199	0.100599	−	0.994927i	$-0.467924\pi$
$281$	4.14167e115	0.201199	0.100599	+	0.994927i	$0.467924\pi$
$282$	3.99434e116	1.63913
$283$	−3.67313e116	−1.27403	−0.637016	−	0.770851i	$-0.719831\pi$
$283$	−3.67313e116	−1.27403	−0.637016	+	0.770851i	$0.719831\pi$
$284$	3.13313e116	0.919088
$285$	−1.31784e116	−0.327138
$286$	−2.21382e115	−0.0465325
$287$	−7.30049e116	−1.30006
$288$	−2.42072e117	−3.65428
$289$	−1.25484e116	−0.160673
$290$	1.10845e117	1.20451
$291$	−6.97653e116	−0.643758
$292$	3.31436e117	2.59845
$293$	1.78692e115	0.0119095	0.00595475	−	0.999982i	$-0.498105\pi$
$293$	1.78692e115	0.0119095	0.00595475	+	0.999982i	$0.498105\pi$
$294$	9.73885e116	0.552090
$295$	−2.02759e117	−0.978217
$296$	−4.10025e117	−1.68443
$297$	4.42791e116	0.154977
$298$	1.28799e118	3.84273
$299$	−7.84530e116	−0.199631
$300$	−1.38451e117	−0.300633
$301$	8.66545e116	0.160651
$302$	−5.62905e117	−0.891466
$303$	2.39869e117	0.324675
$304$	−2.88799e118	−3.34273
$305$	3.76060e117	0.372405
$306$	1.64857e118	1.39746
$307$	1.98631e118	1.44203	0.721016	−	0.692918i	$-0.243675\pi$
$307$	1.98631e118	1.44203	0.721016	+	0.692918i	$0.243675\pi$
$308$	−1.06888e118	−0.664922
$309$	−6.04741e117	−0.322509
$310$	2.03511e118	0.930909
$311$	−1.19899e118	−0.470648	−0.235324	−	0.971917i	$-0.575615\pi$
$311$	−1.19899e118	−0.470648	−0.235324	+	0.971917i	$0.575615\pi$
$312$	6.47669e117	0.218278
$313$	−4.85938e118	−1.40678	−0.703388	−	0.710806i	$-0.748330\pi$
$313$	−4.85938e118	−1.40678	−0.703388	+	0.710806i	$0.748330\pi$
$314$	−8.01070e118	−1.99302
$315$	−4.04919e118	−0.866196
$316$	1.03612e119	1.90666
$317$	8.42986e118	1.33507	0.667537	−	0.744577i	$-0.267349\pi$
$317$	8.42986e118	1.33507	0.667537	+	0.744577i	$0.267349\pi$
$318$	7.79705e117	0.106327
$319$	−1.09906e118	−0.129111
$320$	4.32067e119	4.37449
$321$	−4.51236e118	−0.393926
$322$	−5.12036e119	−3.85609
$323$	1.11169e119	0.722543
$324$	1.94325e119	1.09054
$325$	−5.94144e117	−0.0288026
$326$	−2.57678e119	−1.07955
$327$	1.05613e118	0.0382561
$328$	−1.18570e120	−3.71508
$329$	8.27614e119	2.24400
$330$	−6.40947e118	−0.150456
$331$	−3.58104e119	−0.728081	−0.364040	−	0.931383i	$-0.618603\pi$
$331$	−3.58104e119	−0.728081	−0.364040	+	0.931383i	$0.618603\pi$
$332$	−2.55429e119	−0.449998
$333$	2.37588e119	0.362847
$334$	6.38956e119	0.846280
$335$	4.53792e119	0.521469
$336$	2.53013e120	2.52364
$337$	1.94649e120	1.68590	0.842951	−	0.537990i	$-0.180816\pi$
$337$	1.94649e120	1.68590	0.842951	+	0.537990i	$0.180816\pi$
$338$	−2.56246e120	−1.92803
$339$	−4.17249e119	−0.272841
$340$	−4.03400e120	−2.29344
$341$	−2.01786e119	−0.0997833
$342$	2.79583e120	1.20302
$343$	−1.35694e120	−0.508266
$344$	1.40739e120	0.459080
$345$	−2.27137e120	−0.645479
$346$	3.06686e120	0.759591
$347$	−2.05011e120	−0.442718	−0.221359	−	0.975192i	$-0.571049\pi$
$347$	−2.05011e120	−0.442718	−0.221359	+	0.975192i	$0.571049\pi$
$348$	4.96025e120	0.934306
$349$	−3.62930e119	−0.0596507	−0.0298254	−	0.999555i	$-0.509495\pi$
$349$	−3.62930e119	−0.0596507	−0.0298254	+	0.999555i	$0.509495\pi$
$350$	−3.87778e120	−0.556353
$351$	−8.57587e119	−0.107446
$352$	−7.93929e120	−0.868971
$353$	−1.01830e121	−0.974045	−0.487023	−	0.873389i	$-0.661917\pi$
$353$	−1.01830e121	−0.974045	−0.487023	+	0.873389i	$0.661917\pi$
$354$	−1.22651e121	−1.02569
$355$	3.89272e120	0.284712
$356$	4.45552e121	2.85117
$357$	−9.73936e120	−0.545494
$358$	4.75609e121	2.33242
$359$	−2.37747e121	−1.02124	−0.510621	−	0.859806i	$-0.670584\pi$
$359$	−2.37747e121	−1.02124	−0.510621	+	0.859806i	$0.670584\pi$
$360$	−6.57645e121	−2.47527
$361$	−1.14571e121	−0.377993
$362$	1.19139e122	3.44666
$363$	−1.79259e121	−0.454901
$364$	2.07018e121	0.460992
$365$	4.11789e121	0.804940
$366$	2.27483e121	0.390478
$367$	6.39719e121	0.964608	0.482304	−	0.876004i	$-0.339800\pi$
$367$	6.39719e121	0.964608	0.482304	+	0.876004i	$0.339800\pi$
$368$	−4.97764e122	−6.59557
$369$	6.87053e121	0.800273
$370$	−7.85884e121	−0.804964
$371$	1.61552e121	0.145563
$372$	9.10699e121	0.722079
$373$	−1.37493e122	−0.959649	−0.479825	−	0.877364i	$-0.659300\pi$
$373$	−1.37493e122	−0.959649	−0.479825	+	0.877364i	$0.659300\pi$
$374$	5.40684e121	0.332309
$375$	−9.38174e121	−0.507923
$376$	1.34416e123	6.41252
$377$	2.12862e121	0.0895127
$378$	−5.59718e122	−2.07543
$379$	2.70086e122	0.883363	0.441681	−	0.897172i	$-0.354382\pi$
$379$	2.70086e122	0.883363	0.441681	+	0.897172i	$0.354382\pi$
$380$	−6.84133e122	−1.97433
$381$	−2.97269e122	−0.757204
$382$	−1.35821e122	−0.305462
$383$	−3.51647e122	−0.698497	−0.349249	−	0.937030i	$-0.613563\pi$
$383$	−3.51647e122	−0.698497	−0.349249	+	0.937030i	$0.613563\pi$
$384$	1.35316e123	2.37474
$385$	−1.32802e122	−0.205977
$386$	8.70817e122	1.19407
$387$	−8.15510e121	−0.0988914
$388$	−3.62176e123	−3.88519
$389$	2.25584e122	0.214142	0.107071	−	0.994251i	$-0.465853\pi$
$389$	2.25584e122	0.214142	0.107071	+	0.994251i	$0.465853\pi$
$390$	1.24137e122	0.104311
$391$	1.91607e123	1.42566
$392$	3.27728e123	2.15986
$393$	−6.83047e120	−0.00398845
$394$	−7.45322e123	−3.85721
$395$	1.28731e123	0.590638
$396$	1.00593e123	0.409305
$397$	3.71554e123	1.34113	0.670567	−	0.741849i	$-0.266051\pi$
$397$	3.71554e123	1.34113	0.670567	+	0.741849i	$0.266051\pi$
$398$	−2.16626e123	−0.693848
$399$	−1.65171e123	−0.469594
$400$	−3.76969e123	−0.951604
$401$	2.99501e123	0.671492	0.335746	−	0.941953i	$-0.391012\pi$
$401$	2.99501e123	0.671492	0.335746	+	0.941953i	$0.391012\pi$
$402$	2.74503e123	0.546777
$403$	3.90814e122	0.0691800
$404$	1.24524e124	1.95947
$405$	2.41436e123	0.337823
$406$	1.38928e124	1.72903
$407$	7.79223e122	0.0862834
$408$	−1.58181e124	−1.55882
$409$	−1.54307e124	−1.35372	−0.676858	−	0.736114i	$-0.736659\pi$
$409$	−1.54307e124	−1.35372	−0.676858	+	0.736114i	$0.736659\pi$
$410$	−2.27260e124	−1.77538
$411$	1.10250e124	0.767171
$412$	−3.13941e124	−1.94639
$413$	−2.54129e124	−1.40419
$414$	4.81880e124	2.37368
$415$	−3.17354e123	−0.139399
$416$	1.53766e124	0.602459
$417$	−7.74681e123	−0.270807
$418$	9.16955e123	0.286072
$419$	−1.58097e124	−0.440308	−0.220154	−	0.975465i	$-0.570656\pi$
$419$	−1.58097e124	−0.440308	−0.220154	+	0.975465i	$0.570656\pi$
$420$	5.99360e124	1.49055
$421$	−3.10214e124	−0.689068	−0.344534	−	0.938774i	$-0.611963\pi$
$421$	−3.10214e124	−0.689068	−0.344534	+	0.938774i	$0.611963\pi$
$422$	1.33008e125	2.63959
$423$	−7.78872e124	−1.38133
$424$	2.62384e124	0.415966
$425$	1.45109e124	0.205693
$426$	2.35474e124	0.298530
$427$	4.71336e124	0.534573
$428$	−2.34252e125	−2.37741
$429$	−1.23085e123	−0.0111811
$430$	2.69751e124	0.219387
$431$	−2.08983e124	−0.152209	−0.0761045	−	0.997100i	$-0.524248\pi$
$431$	−2.08983e124	−0.152209	−0.0761045	+	0.997100i	$0.524248\pi$
$432$	−5.44117e125	−3.54989
$433$	2.84740e125	1.66446	0.832232	−	0.554428i	$-0.187063\pi$
$433$	2.84740e125	1.66446	0.832232	+	0.554428i	$0.187063\pi$
$434$	2.55071e125	1.33628
$435$	6.16280e124	0.289426
$436$	5.48275e124	0.230882
$437$	3.24949e125	1.22729
$438$	2.49095e125	0.844006
$439$	−5.91270e125	−1.79772	−0.898859	−	0.438238i	$-0.855603\pi$
$439$	−5.91270e125	−1.79772	−0.898859	+	0.438238i	$0.855603\pi$
$440$	−2.15689e125	−0.588607
$441$	−1.89902e125	−0.465260
$442$	−1.04718e125	−0.230391
$443$	−4.39519e124	−0.0868561	−0.0434281	−	0.999057i	$-0.513828\pi$
$443$	−4.39519e124	−0.0868561	−0.0434281	+	0.999057i	$0.513828\pi$
$444$	−3.51678e125	−0.624387
$445$	5.53570e125	0.883227
$446$	−1.49225e126	−2.14010
$447$	7.16100e125	0.923350
$448$	5.41532e126	6.27941
$449$	−1.31183e126	−1.36829	−0.684144	−	0.729347i	$-0.739824\pi$
$449$	−1.31183e126	−1.36829	−0.684144	+	0.729347i	$0.739824\pi$
$450$	3.64940e125	0.342473
$451$	2.25334e125	0.190301
$452$	−2.16608e126	−1.64664
$453$	−3.12965e125	−0.214206
$454$	−4.57107e126	−2.81750
$455$	2.57207e125	0.142805
$456$	−2.68261e126	−1.34193
$457$	2.56681e126	1.15711	0.578554	−	0.815644i	$-0.303617\pi$
$457$	2.56681e126	1.15711	0.578554	+	0.815644i	$0.303617\pi$
$458$	6.53483e126	2.65536
$459$	2.09450e126	0.767321
$460$	−1.17915e127	−3.89557
$461$	−4.70807e126	−1.40297	−0.701486	−	0.712683i	$-0.747480\pi$
$461$	−4.70807e126	−1.40297	−0.701486	+	0.712683i	$0.747480\pi$
$462$	−8.03332e125	−0.215974
$463$	1.07726e126	0.261350	0.130675	−	0.991425i	$-0.458286\pi$
$463$	1.07726e126	0.261350	0.130675	+	0.991425i	$0.458286\pi$
$464$	1.35056e127	2.95739
$465$	1.13149e126	0.223684
$466$	2.71675e126	0.484974
$467$	3.14969e126	0.507828	0.253914	−	0.967227i	$-0.418282\pi$
$467$	3.14969e126	0.507828	0.253914	+	0.967227i	$0.418282\pi$
$468$	−1.94826e126	−0.283772
$469$	5.68762e126	0.748549
$470$	2.57632e127	3.06444
$471$	−4.45382e126	−0.478894
$472$	−4.12741e127	−4.01267
$473$	−2.67464e125	−0.0235159
$474$	7.78708e126	0.619303
$475$	2.46092e126	0.177072
$476$	−5.05603e127	−3.29215
$477$	−1.52038e126	−0.0896042
$478$	2.16423e127	1.15473
$479$	−5.24878e126	−0.253584	−0.126792	−	0.991929i	$-0.540468\pi$
$479$	−5.24878e126	−0.253584	−0.126792	+	0.991929i	$0.540468\pi$
$480$	4.45184e127	1.94796
$481$	−1.50918e126	−0.0598204
$482$	6.15837e127	2.21173
$483$	−2.84683e127	−0.926560
$484$	−9.30596e127	−2.74541
$485$	−4.49981e127	−1.20354
$486$	8.22994e127	1.99606
$487$	−4.92430e127	−1.08322	−0.541612	−	0.840628i	$-0.682186\pi$
$487$	−4.92430e127	−1.08322	−0.541612	+	0.840628i	$0.682186\pi$
$488$	7.65516e127	1.52761
$489$	−1.43265e127	−0.259399
$490$	6.28148e127	1.03216
$491$	3.83490e127	0.571983	0.285991	−	0.958232i	$-0.407677\pi$
$491$	3.83490e127	0.571983	0.285991	+	0.958232i	$0.407677\pi$
$492$	−1.01698e128	−1.37711
$493$	−5.19876e127	−0.639251
$494$	−1.77594e127	−0.198334
$495$	1.24981e127	0.126793
$496$	2.47961e128	2.28562
$497$	4.87895e127	0.408694
$498$	−1.91971e127	−0.146164
$499$	6.32043e127	0.437492	0.218746	−	0.975782i	$-0.429803\pi$
$499$	6.32043e127	0.437492	0.218746	+	0.975782i	$0.429803\pi$
$500$	−4.87038e128	−3.06540
$501$	3.55249e127	0.203348
$502$	4.28623e128	2.23177
$503$	2.36417e128	1.11995	0.559976	−	0.828509i	$-0.310810\pi$
$503$	2.36417e128	1.11995	0.559976	+	0.828509i	$0.310810\pi$
$504$	−8.24261e128	−3.55316
$505$	1.54713e128	0.606998
$506$	1.58043e128	0.564451
$507$	−1.42468e128	−0.463277
$508$	−1.54322e129	−4.56985
$509$	1.67765e128	0.452488	0.226244	−	0.974071i	$-0.427355\pi$
$509$	1.67765e128	0.452488	0.226244	+	0.974071i	$0.427355\pi$
$510$	−3.03181e128	−0.744935
$511$	5.16117e128	1.15546
$512$	2.25177e129	4.59411
$513$	3.55209e128	0.660555
$514$	9.97301e128	1.69075
$515$	−3.90053e128	−0.602948
$516$	1.20712e128	0.170172
$517$	−2.55448e128	−0.328475
$518$	−9.84990e128	−1.15550
$519$	1.70512e128	0.182518
$520$	4.17741e128	0.408083
$521$	−8.31621e128	−0.741539	−0.370769	−	0.928725i	$-0.620906\pi$
$521$	−8.31621e128	−0.741539	−0.370769	+	0.928725i	$0.620906\pi$
$522$	−1.30746e129	−1.06434
$523$	−1.77551e129	−1.31975	−0.659876	−	0.751375i	$-0.729391\pi$
$523$	−1.77551e129	−1.31975	−0.659876	+	0.751375i	$0.729391\pi$
$524$	−3.54593e127	−0.0240710
$525$	−2.15598e128	−0.133683
$526$	1.85907e129	1.05311
$527$	−9.54490e128	−0.494046
$528$	−7.80941e128	−0.369409
$529$	3.28787e129	1.42158
$530$	5.02903e128	0.198784
$531$	2.39162e129	0.864376
$532$	−8.57461e129	−2.83408
$533$	−4.36421e128	−0.131936
$534$	3.34860e129	0.926092
$535$	−2.91043e129	−0.736467
$536$	9.23749e129	2.13908
$537$	2.64431e129	0.560445
$538$	3.10259e129	0.601958
$539$	−6.22824e128	−0.110637
$540$	−1.28895e130	−2.09669
$541$	−8.69602e129	−1.29554	−0.647769	−	0.761836i	$-0.724298\pi$
$541$	−8.69602e129	−1.29554	−0.647769	+	0.761836i	$0.724298\pi$
$542$	2.67712e130	3.65343
$543$	6.62395e129	0.828181
$544$	−3.75545e130	−4.30243
$545$	6.81197e128	0.0715219
$546$	1.55587e129	0.149735
$547$	−1.69219e129	−0.149297	−0.0746486	−	0.997210i	$-0.523784\pi$
$547$	−1.69219e129	−0.149297	−0.0746486	+	0.997210i	$0.523784\pi$
$548$	5.72345e130	4.63001
$549$	−4.43577e129	−0.329066
$550$	1.19690e129	0.0814386
$551$	−8.81666e129	−0.550305
$552$	−4.62366e130	−2.64777
$553$	1.61346e130	0.847839
$554$	−1.84452e130	−0.889547
$555$	−4.36938e129	−0.193421
$556$	−4.02163e130	−1.63437
$557$	−3.92915e130	−1.46615	−0.733073	−	0.680150i	$-0.761915\pi$
$557$	−3.92915e130	−1.46615	−0.733073	+	0.680150i	$0.761915\pi$
$558$	−2.40049e130	−0.822574
$559$	5.18018e128	0.0163036
$560$	1.63191e131	4.71809
$561$	3.00611e129	0.0798490
$562$	1.61592e130	0.394408
$563$	−1.16339e130	−0.260961	−0.130480	−	0.991451i	$-0.541652\pi$
$563$	−1.16339e130	−0.260961	−0.130480	+	0.991451i	$0.541652\pi$
$564$	1.15289e131	2.37700
$565$	−2.69122e130	−0.510092
$566$	−1.43311e131	−2.49747
$567$	3.02605e130	0.484932
$568$	7.92410e130	1.16790
$569$	1.94656e130	0.263897	0.131949	−	0.991257i	$-0.457877\pi$
$569$	1.94656e130	0.263897	0.131949	+	0.991257i	$0.457877\pi$
$570$	−5.14170e130	−0.641284
$571$	1.14236e131	1.31095	0.655477	−	0.755215i	$-0.272468\pi$
$571$	1.14236e131	1.31095	0.655477	+	0.755215i	$0.272468\pi$
$572$	−6.38975e129	−0.0674796
$573$	−7.55142e129	−0.0733979
$574$	−2.84837e131	−2.54849
$575$	4.24155e130	0.349383
$576$	−5.09639e131	−3.86540
$577$	2.21067e131	1.54409	0.772046	−	0.635566i	$-0.219233\pi$
$577$	2.21067e131	1.54409	0.772046	+	0.635566i	$0.219233\pi$
$578$	−4.89592e130	−0.314965
$579$	4.84160e130	0.286917
$580$	3.19932e131	1.74674
$581$	−3.97757e130	−0.200102
$582$	−2.72198e131	−1.26195
$583$	−4.98641e129	−0.0213075
$584$	8.38246e131	3.30188
$585$	−2.42059e130	−0.0879059
$586$	6.97190e129	0.0233461
$587$	2.31134e131	0.713762	0.356881	−	0.934150i	$-0.383840\pi$
$587$	2.31134e131	0.713762	0.356881	+	0.934150i	$0.383840\pi$
$588$	2.81092e131	0.800619
$589$	−1.61873e131	−0.425304
$590$	−7.91090e131	−1.91759
$591$	−4.14387e131	−0.926831
$592$	−9.57535e131	−1.97640
$593$	3.62448e131	0.690475	0.345237	−	0.938515i	$-0.387798\pi$
$593$	3.62448e131	0.690475	0.345237	+	0.938515i	$0.387798\pi$
$594$	1.72760e131	0.303800
$595$	−6.28181e131	−1.01983
$596$	3.71752e132	5.57257
$597$	−1.20440e131	−0.166721
$598$	−3.06094e131	−0.391335
$599$	−1.56783e132	−1.85151	−0.925755	−	0.378123i	$-0.876570\pi$
$599$	−1.56783e132	−1.85151	−0.925755	+	0.378123i	$0.876570\pi$
$600$	−3.50161e131	−0.382018
$601$	5.86108e131	0.590800	0.295400	−	0.955374i	$-0.404547\pi$
$601$	5.86108e131	0.590800	0.295400	+	0.955374i	$0.404547\pi$
$602$	3.38093e131	0.314922
$603$	−5.35265e131	−0.460783
$604$	−1.62471e132	−1.29277
$605$	−1.15621e132	−0.850463
$606$	9.35876e131	0.636457
$607$	2.12158e132	1.33412	0.667062	−	0.745002i	$-0.267552\pi$
$607$	2.12158e132	1.33412	0.667062	+	0.745002i	$0.267552\pi$
$608$	−6.36893e132	−3.70379
$609$	7.72416e131	0.415461
$610$	1.46724e132	0.730021
$611$	4.94746e131	0.227732
$612$	4.75826e132	2.02654
$613$	−3.13561e132	−1.23580	−0.617902	−	0.786255i	$-0.712017\pi$
$613$	−3.13561e132	−1.23580	−0.617902	+	0.786255i	$0.712017\pi$
$614$	7.74984e132	2.82680
$615$	−1.26353e132	−0.426596
$616$	−2.70334e132	−0.844924
$617$	−1.81663e132	−0.525679	−0.262840	−	0.964840i	$-0.584659\pi$
$617$	−1.81663e132	−0.525679	−0.262840	+	0.964840i	$0.584659\pi$
$618$	−2.35947e132	−0.632211
$619$	3.22452e132	0.800127	0.400063	−	0.916487i	$-0.368988\pi$
$619$	3.22452e132	0.800127	0.400063	+	0.916487i	$0.368988\pi$
$620$	5.87393e132	1.34997
$621$	6.12225e132	1.30335
$622$	−4.67799e132	−0.922606
$623$	6.93819e132	1.26784
$624$	1.51251e132	0.256112
$625$	−4.62043e132	−0.725072
$626$	−1.89595e133	−2.75769
$627$	5.09812e131	0.0687387
$628$	−2.31213e133	−2.89021
$629$	3.68589e132	0.427205
$630$	−1.57984e133	−1.69800
$631$	−3.95456e132	−0.394188	−0.197094	−	0.980385i	$-0.563150\pi$
$631$	−3.95456e132	−0.394188	−0.197094	+	0.980385i	$0.563150\pi$
$632$	2.62048e133	2.42281
$633$	7.39503e132	0.634255
$634$	3.28901e133	2.61713
$635$	−1.91736e133	−1.41563
$636$	2.25046e132	0.154191
$637$	1.20627e132	0.0767046
$638$	−4.28810e132	−0.253094
$639$	−4.59161e132	−0.251579
$640$	8.72776e133	4.43970
$641$	−6.24712e132	−0.295069	−0.147534	−	0.989057i	$-0.547134\pi$
$641$	−6.24712e132	−0.295069	−0.147534	+	0.989057i	$0.547134\pi$
$642$	−1.76055e133	−0.772209
$643$	−5.89855e131	−0.0240283	−0.0120142	−	0.999928i	$-0.503824\pi$
$643$	−5.89855e131	−0.0240283	−0.0120142	+	0.999928i	$0.503824\pi$
$644$	−1.47789e134	−5.59195
$645$	1.49977e132	0.0527154
$646$	4.33739e133	1.41639
$647$	3.09467e133	0.938989	0.469494	−	0.882935i	$-0.344436\pi$
$647$	3.09467e133	0.938989	0.469494	+	0.882935i	$0.344436\pi$
$648$	4.91473e133	1.38576
$649$	7.84385e132	0.205545
$650$	−2.31813e132	−0.0564615
$651$	1.41815e133	0.321089
$652$	−7.43736e133	−1.56552
$653$	4.75857e133	0.931322	0.465661	−	0.884963i	$-0.345817\pi$
$653$	4.75857e133	0.931322	0.465661	+	0.884963i	$0.345817\pi$
$654$	4.12063e132	0.0749930
$655$	−4.40560e131	−0.00745664
$656$	−2.76898e134	−4.35901
$657$	−4.85721e133	−0.711265
$658$	3.22904e134	4.39889
$659$	1.16586e134	1.47770	0.738852	−	0.673867i	$-0.235368\pi$
$659$	1.16586e134	1.47770	0.738852	+	0.673867i	$0.235368\pi$
$660$	−1.84996e133	−0.218186
$661$	−4.41100e133	−0.484136	−0.242068	−	0.970259i	$-0.577826\pi$
$661$	−4.41100e133	−0.484136	−0.242068	+	0.970259i	$0.577826\pi$
$662$	−1.39719e134	−1.42725
$663$	−5.82216e132	−0.0553595
$664$	−6.46013e133	−0.571818
$665$	−1.06534e134	−0.877932
$666$	9.26979e133	0.711286
$667$	−1.51961e134	−1.08581
$668$	1.84422e134	1.22724
$669$	−8.29664e133	−0.514235
$670$	1.77052e134	1.02223
$671$	−1.45481e133	−0.0782503
$672$	5.57973e134	2.79623
$673$	−1.51508e134	−0.707488	−0.353744	−	0.935342i	$-0.615092\pi$
$673$	−1.51508e134	−0.707488	−0.353744	+	0.935342i	$0.615092\pi$
$674$	7.59448e134	3.30486
$675$	4.63654e133	0.188046
$676$	−7.39602e134	−2.79595
$677$	3.47460e134	1.22446	0.612229	−	0.790681i	$-0.290273\pi$
$677$	3.47460e134	1.22446	0.612229	+	0.790681i	$0.290273\pi$
$678$	−1.62795e134	−0.534848
$679$	−5.63985e134	−1.72764
$680$	−1.02025e135	−2.91430
$681$	−2.54144e134	−0.677004
$682$	−7.87293e133	−0.195604
$683$	−5.39257e134	−1.24972	−0.624860	−	0.780737i	$-0.714844\pi$
$683$	−5.39257e134	−1.24972	−0.624860	+	0.780737i	$0.714844\pi$
$684$	8.06961e134	1.74457
$685$	7.11104e134	1.43427
$686$	−5.29428e134	−0.996349
$687$	3.63325e134	0.638044
$688$	3.28669e134	0.538652
$689$	9.65755e132	0.0147725
$690$	−8.86204e134	−1.26532
$691$	1.29214e135	1.72228	0.861139	−	0.508370i	$-0.169752\pi$
$691$	1.29214e135	1.72228	0.861139	+	0.508370i	$0.169752\pi$
$692$	8.85188e134	1.10153
$693$	1.56645e134	0.182007
$694$	−7.99875e134	−0.867855
$695$	−4.99662e134	−0.506289
$696$	1.25451e135	1.18723
$697$	1.06588e135	0.942215
$698$	−1.41602e134	−0.116933
$699$	1.51047e134	0.116532
$700$	−1.11924e135	−0.806802
$701$	−3.40450e134	−0.229323	−0.114661	−	0.993405i	$-0.536578\pi$
$701$	−3.40450e134	−0.229323	−0.114661	+	0.993405i	$0.536578\pi$
$702$	−3.34598e134	−0.210625
$703$	6.25095e134	0.367763
$704$	−1.67147e135	−0.919175
$705$	1.43239e135	0.736340
$706$	−3.97304e135	−1.90941
$707$	1.93910e135	0.871322
$708$	−3.54008e135	−1.48742
$709$	−1.83195e135	−0.719808	−0.359904	−	0.932989i	$-0.617190\pi$
$709$	−1.83195e135	−0.719808	−0.359904	+	0.932989i	$0.617190\pi$
$710$	1.51879e135	0.558118
$711$	−1.51843e135	−0.521902
$712$	1.12686e136	3.62302
$713$	−2.78999e135	−0.839171
$714$	−3.79993e135	−1.06933
$715$	−7.93886e133	−0.0209036
$716$	1.37275e136	3.38238
$717$	1.20328e135	0.277464
$718$	−9.27598e135	−2.00193
$719$	−2.23041e135	−0.450571	−0.225285	−	0.974293i	$-0.572331\pi$
$719$	−2.23041e135	−0.450571	−0.225285	+	0.974293i	$0.572331\pi$
$720$	−1.53580e136	−2.90430
$721$	−4.88874e135	−0.865509
$722$	−4.47013e135	−0.740975
$723$	3.42395e135	0.531445
$724$	3.43872e136	4.99821
$725$	−1.15084e135	−0.156660
$726$	−6.99402e135	−0.891738
$727$	−3.98658e135	−0.476119	−0.238060	−	0.971251i	$-0.576511\pi$
$727$	−3.98658e135	−0.476119	−0.238060	+	0.971251i	$0.576511\pi$
$728$	5.23577e135	0.585787
$729$	9.15875e134	0.0960016
$730$	1.60664e136	1.57792
$731$	−1.26516e135	−0.116432
$732$	6.56583e135	0.566256
$733$	−5.71056e135	−0.461572	−0.230786	−	0.973004i	$-0.574130\pi$
$733$	−5.71056e135	−0.461572	−0.230786	+	0.973004i	$0.574130\pi$
$734$	2.49594e136	1.89091
$735$	3.49240e135	0.248013
$736$	−1.09773e137	−7.30798
$737$	−1.75552e135	−0.109572
$738$	2.68062e136	1.56877
$739$	5.69069e135	0.312287	0.156143	−	0.987734i	$-0.450094\pi$
$739$	5.69069e135	0.312287	0.156143	+	0.987734i	$0.450094\pi$
$740$	−2.26829e136	−1.16733
$741$	−9.87390e134	−0.0476567
$742$	6.30316e135	0.285346
$743$	1.72036e135	0.0730549	0.0365275	−	0.999333i	$-0.488370\pi$
$743$	1.72036e135	0.0730549	0.0365275	+	0.999333i	$0.488370\pi$
$744$	2.30328e136	0.917555
$745$	4.61879e136	1.72625
$746$	−5.36447e136	−1.88119
$747$	3.74331e135	0.123176
$748$	1.56058e136	0.481902
$749$	−3.64780e136	−1.05717
$750$	−3.66040e136	−0.995677
$751$	−2.76595e136	−0.706231	−0.353116	−	0.935580i	$-0.614878\pi$
$751$	−2.76595e136	−0.706231	−0.353116	+	0.935580i	$0.614878\pi$
$752$	3.13903e137	7.52400
$753$	2.38307e136	0.536260
$754$	8.30508e135	0.175471
$755$	−2.01860e136	−0.400470
$756$	−1.61551e137	−3.00971
$757$	−8.70498e136	−1.52305	−0.761524	−	0.648137i	$-0.775549\pi$
$757$	−8.70498e136	−1.52305	−0.761524	+	0.648137i	$0.775549\pi$
$758$	1.05377e137	1.73165
$759$	8.78693e135	0.135629
$760$	−1.73026e137	−2.50880
$761$	5.14381e136	0.700670	0.350335	−	0.936624i	$-0.386068\pi$
$761$	5.14381e136	0.700670	0.350335	+	0.936624i	$0.386068\pi$
$762$	−1.15983e137	−1.48434
$763$	8.53781e135	0.102667
$764$	−3.92020e136	−0.442969
$765$	5.91184e136	0.627776
$766$	−1.37199e137	−1.36926
$767$	−1.51918e136	−0.142504
$768$	2.62584e137	2.31532
$769$	3.53433e136	0.292959	0.146479	−	0.989214i	$-0.453206\pi$
$769$	3.53433e136	0.292959	0.146479	+	0.989214i	$0.453206\pi$
$770$	−5.18143e136	−0.403775
$771$	5.54483e136	0.406261
$772$	2.51344e137	1.73159
$773$	1.53305e137	0.993184	0.496592	−	0.867984i	$-0.334585\pi$
$773$	1.53305e137	0.993184	0.496592	+	0.867984i	$0.334585\pi$
$774$	−3.18181e136	−0.193856
$775$	−2.11293e136	−0.121075
$776$	−9.15990e137	−4.93695
$777$	−5.47638e136	−0.277648
$778$	8.80143e136	0.419780
$779$	1.80764e137	0.811115
$780$	3.58296e136	0.151268
$781$	−1.50592e136	−0.0598242
$782$	7.47577e137	2.79470
$783$	−1.66112e137	−0.584409
$784$	7.65347e137	2.53423
$785$	−2.87267e137	−0.895319
$786$	−2.66499e135	−0.00781853
$787$	6.40179e137	1.76808	0.884040	−	0.467412i	$-0.154813\pi$
$787$	6.40179e137	1.76808	0.884040	+	0.467412i	$0.154813\pi$
$788$	−2.15122e138	−5.59358
$789$	1.03361e137	0.253046
$790$	5.02260e137	1.15782
$791$	−3.37305e137	−0.732217
$792$	2.54413e137	0.520108
$793$	2.81764e136	0.0542511
$794$	1.44966e138	2.62901
$795$	2.79606e136	0.0477648
$796$	−6.25247e137	−1.00619
$797$	−8.24222e136	−0.124961	−0.0624804	−	0.998046i	$-0.519901\pi$
$797$	−8.24222e136	−0.124961	−0.0624804	+	0.998046i	$0.519901\pi$
$798$	−6.44436e137	−0.920540
$799$	−1.20832e138	−1.62634
$800$	−8.31335e137	−1.05439
$801$	−6.52957e137	−0.780441
$802$	1.16854e138	1.31632
$803$	−1.59303e137	−0.169135
$804$	7.92299e137	0.792915
$805$	−1.83618e138	−1.73226
$806$	1.52481e137	0.135613
$807$	1.72499e137	0.144641
$808$	3.14938e138	2.48992
$809$	−1.90271e137	−0.141846	−0.0709231	−	0.997482i	$-0.522594\pi$
$809$	−1.90271e137	−0.141846	−0.0709231	+	0.997482i	$0.522594\pi$
$810$	9.41993e137	0.662231
$811$	1.34401e138	0.891071	0.445535	−	0.895264i	$-0.353013\pi$
$811$	1.34401e138	0.891071	0.445535	+	0.895264i	$0.353013\pi$
$812$	4.00987e138	2.50738
$813$	1.48843e138	0.877866
$814$	3.04023e137	0.169140
$815$	−9.24046e137	−0.484961
$816$	−3.69401e138	−1.82901
$817$	−2.14561e137	−0.100231
$818$	−6.02046e138	−2.65368
$819$	−3.03386e137	−0.126186
$820$	−6.55941e138	−2.57458
$821$	3.82835e138	1.41811	0.709057	−	0.705151i	$-0.249121\pi$
$821$	3.82835e138	1.41811	0.709057	+	0.705151i	$0.249121\pi$
$822$	4.30154e138	1.50388
$823$	1.99636e138	0.658790	0.329395	−	0.944192i	$-0.393155\pi$
$823$	1.99636e138	0.658790	0.329395	+	0.944192i	$0.393155\pi$
$824$	−7.94000e138	−2.47331
$825$	6.65456e136	0.0195685
$826$	−9.91515e138	−2.75263
$827$	4.51785e138	1.18419	0.592093	−	0.805869i	$-0.298302\pi$
$827$	4.51785e138	1.18419	0.592093	+	0.805869i	$0.298302\pi$
$828$	1.39085e139	3.44222
$829$	2.58042e138	0.603046	0.301523	−	0.953459i	$-0.402505\pi$
$829$	2.58042e138	0.603046	0.301523	+	0.953459i	$0.402505\pi$
$830$	−1.23820e138	−0.273263
$831$	−1.02552e138	−0.213745
$832$	3.23727e138	0.637266
$833$	−2.94609e138	−0.547782
$834$	−3.02251e138	−0.530860
$835$	2.29133e138	0.380171
$836$	2.64661e138	0.414850
$837$	−3.04980e138	−0.451661
$838$	−6.16833e138	−0.863131
$839$	2.88363e138	0.381282	0.190641	−	0.981660i	$-0.438943\pi$
$839$	2.88363e138	0.381282	0.190641	+	0.981660i	$0.438943\pi$
$840$	1.51586e139	1.89406
$841$	−4.34549e138	−0.513132
$842$	−1.21034e139	−1.35077
$843$	8.98426e137	0.0947704
$844$	3.83901e139	3.82783
$845$	−9.18909e138	−0.866121
$846$	−3.03886e139	−2.70782
$847$	−1.44914e139	−1.22081
$848$	6.12747e138	0.488066
$849$	−7.96787e138	−0.600105
$850$	5.66159e138	0.403217
$851$	1.07739e139	0.725637
$852$	6.79649e138	0.432917
$853$	2.15831e139	1.30027	0.650136	−	0.759818i	$-0.274712\pi$
$853$	2.15831e139	1.30027	0.650136	+	0.759818i	$0.274712\pi$
$854$	1.83898e139	1.04792
$855$	1.00260e139	0.540427
$856$	−5.92454e139	−3.02100
$857$	−2.64220e138	−0.127461	−0.0637303	−	0.997967i	$-0.520300\pi$
$857$	−2.64220e138	−0.127461	−0.0637303	+	0.997967i	$0.520300\pi$
$858$	−4.80230e137	−0.0219181
$859$	−1.09312e139	−0.472055	−0.236028	−	0.971746i	$-0.575846\pi$
$859$	−1.09312e139	−0.472055	−0.236028	+	0.971746i	$0.575846\pi$
$860$	7.78581e138	0.318147
$861$	−1.58365e139	−0.612363
$862$	−8.15372e138	−0.298374
$863$	−2.73262e138	−0.0946384	−0.0473192	−	0.998880i	$-0.515068\pi$
$863$	−2.73262e138	−0.0946384	−0.0473192	+	0.998880i	$0.515068\pi$
$864$	−1.19995e140	−3.93332
$865$	1.09979e139	0.341228
$866$	1.11095e140	3.26283
$867$	−2.72205e138	−0.0756814
$868$	7.36211e139	1.93783
$869$	−4.98003e138	−0.124106
$870$	2.40449e139	0.567360
$871$	3.40004e138	0.0759665
$872$	1.38666e139	0.293384
$873$	5.30769e139	1.06348
$874$	1.26783e140	2.40584
$875$	−7.58422e139	−1.36310
$876$	7.18963e139	1.22394
$877$	−5.68771e139	−0.917184	−0.458592	−	0.888647i	$-0.651646\pi$
$877$	−5.68771e139	−0.917184	−0.458592	+	0.888647i	$0.651646\pi$
$878$	−2.30691e140	−3.52405
$879$	3.87626e137	0.00560972
$880$	−5.03701e139	−0.690630
$881$	6.46811e138	0.0840276	0.0420138	−	0.999117i	$-0.486623\pi$
$881$	6.46811e138	0.0840276	0.0420138	+	0.999117i	$0.486623\pi$
$882$	−7.40924e139	−0.912044
$883$	1.39161e140	1.62324	0.811621	−	0.584184i	$-0.198585\pi$
$883$	1.39161e140	1.62324	0.811621	+	0.584184i	$0.198585\pi$
$884$	−3.02248e139	−0.334104
$885$	−4.39833e139	−0.460768
$886$	−1.71484e139	−0.170263
$887$	1.27807e140	1.20277	0.601387	−	0.798958i	$-0.294615\pi$
$887$	1.27807e140	1.20277	0.601387	+	0.798958i	$0.294615\pi$
$888$	−8.89441e139	−0.793416
$889$	−2.40313e140	−2.03209
$890$	2.15982e140	1.73138
$891$	−9.34009e138	−0.0709840
$892$	−4.30707e140	−3.10350
$893$	−2.04921e140	−1.40005
$894$	2.79395e140	1.81003
$895$	1.70555e140	1.04778
$896$	1.09390e141	6.37302
$897$	−1.70183e139	−0.0940319
$898$	−5.11827e140	−2.68224
$899$	7.56993e139	0.376276
$900$	1.05332e140	0.496642
$901$	−2.35868e139	−0.105497
$902$	8.79168e139	0.373045
$903$	1.87974e139	0.0756710
$904$	−5.47831e140	−2.09241
$905$	4.27240e140	1.54833
$906$	−1.22107e140	−0.419906
$907$	2.75948e140	0.900496	0.450248	−	0.892904i	$-0.351336\pi$
$907$	2.75948e140	0.900496	0.450248	+	0.892904i	$0.351336\pi$
$908$	−1.31935e141	−4.08584
$909$	−1.82490e140	−0.536358
$910$	1.00353e140	0.279938
$911$	3.02990e140	0.802243	0.401121	−	0.916025i	$-0.368621\pi$
$911$	3.02990e140	0.802243	0.401121	+	0.916025i	$0.368621\pi$
$912$	−6.26474e140	−1.57452
$913$	1.22770e139	0.0292908
$914$	1.00147e141	2.26827
$915$	8.15763e139	0.175413
$916$	1.88615e141	3.85070
$917$	−5.52177e138	−0.0107037
$918$	8.17193e140	1.50417
$919$	−5.12257e140	−0.895366	−0.447683	−	0.894192i	$-0.647751\pi$
$919$	−5.12257e140	−0.895366	−0.447683	+	0.894192i	$0.647751\pi$
$920$	−2.98222e141	−4.95015
$921$	4.30878e140	0.679238
$922$	−1.83691e141	−2.75023
$923$	2.91662e139	0.0414763
$924$	−2.31866e140	−0.313197
$925$	8.15936e139	0.104694
$926$	4.20305e140	0.512321
$927$	4.60082e140	0.532780
$928$	2.97840e141	3.27683
$929$	−1.51285e141	−1.58142	−0.790712	−	0.612188i	$-0.790289\pi$
$929$	−1.51285e141	−1.58142	−0.790712	+	0.612188i	$0.790289\pi$
$930$	4.41463e140	0.438485
$931$	−4.99631e140	−0.471563
$932$	7.84135e140	0.703291
$933$	−2.60088e140	−0.221688
$934$	1.22889e141	0.995490
$935$	1.93892e140	0.149282
$936$	−4.92741e140	−0.360592
$937$	−1.80808e141	−1.25773	−0.628864	−	0.777515i	$-0.716480\pi$
$937$	−1.80808e141	−1.25773	−0.628864	+	0.777515i	$0.716480\pi$
$938$	2.21909e141	1.46737
$939$	−1.05411e141	−0.662632
$940$	7.43602e141	4.44393
$941$	−2.33281e141	−1.32548	−0.662738	−	0.748851i	$-0.730606\pi$
$941$	−2.33281e141	−1.32548	−0.662738	+	0.748851i	$0.730606\pi$
$942$	−1.73771e141	−0.938771
$943$	3.11558e141	1.60042
$944$	−9.63879e141	−4.70818
$945$	−2.00717e141	−0.932340
$946$	−1.04354e140	−0.0460980
$947$	6.08703e140	0.255730	0.127865	−	0.991792i	$-0.459188\pi$
$947$	6.08703e140	0.255730	0.127865	+	0.991792i	$0.459188\pi$
$948$	2.24758e141	0.898090
$949$	3.08533e140	0.117262
$950$	9.60157e140	0.347113
$951$	1.82863e141	0.628858
$952$	−1.27874e142	−4.18337
$953$	3.26685e140	0.101675	0.0508377	−	0.998707i	$-0.483811\pi$
$953$	3.26685e140	0.101675	0.0508377	+	0.998707i	$0.483811\pi$
$954$	−5.93193e140	−0.175650
$955$	−4.87060e140	−0.137222
$956$	6.24662e141	1.67454
$957$	−2.38411e140	−0.0608148
$958$	−2.04788e141	−0.497098
$959$	8.91264e141	2.05884
$960$	9.37255e141	2.06051
$961$	−3.38943e141	−0.709194
$962$	−5.88824e140	−0.117265
$963$	3.43297e141	0.650760
$964$	1.77749e142	3.20736
$965$	3.12279e141	0.536408
$966$	−1.11073e142	−1.81633
$967$	3.77302e140	0.0587397	0.0293698	−	0.999569i	$-0.490650\pi$
$967$	3.77302e140	0.0587397	0.0293698	+	0.999569i	$0.490650\pi$
$968$	−2.35360e142	−3.48862
$969$	2.41152e141	0.340338
$970$	−1.75565e142	−2.35929
$971$	5.65420e141	0.723532	0.361766	−	0.932269i	$-0.382174\pi$
$971$	5.65420e141	0.723532	0.361766	+	0.932269i	$0.382174\pi$
$972$	2.37540e142	2.89461
$973$	−6.26254e141	−0.726759
$974$	−1.92127e142	−2.12343
$975$	−1.28884e140	−0.0135669
$976$	1.78772e142	1.79239
$977$	−1.49169e142	−1.42458	−0.712288	−	0.701887i	$-0.752341\pi$
$977$	−1.49169e142	−1.42458	−0.712288	+	0.701887i	$0.752341\pi$
$978$	−5.58965e141	−0.508498
$979$	−2.14152e141	−0.185585
$980$	1.81302e142	1.49680
$981$	−8.03498e140	−0.0631985
$982$	1.49623e142	1.12125
$983$	2.48585e142	1.77494	0.887469	−	0.460868i	$-0.152462\pi$
$983$	2.48585e142	1.77494	0.887469	+	0.460868i	$0.152462\pi$
$984$	−2.57207e142	−1.74991
$985$	−2.67276e142	−1.73276
$986$	−2.02836e142	−1.25312
$987$	1.79529e142	1.05699
$988$	−5.12588e141	−0.287616
$989$	−3.69810e141	−0.197767
$990$	4.87627e141	0.248551
$991$	−6.94710e141	−0.337524	−0.168762	−	0.985657i	$-0.553977\pi$
$991$	−6.94710e141	−0.337524	−0.168762	+	0.985657i	$0.553977\pi$
$992$	5.46832e142	2.53250
$993$	−7.76812e141	−0.342947
$994$	1.90358e142	0.801158
$995$	−7.76830e141	−0.311695
$996$	−5.54085e141	−0.211962
$997$	−2.05676e142	−0.750175	−0.375088	−	0.926989i	$-0.622387\pi$
$997$	−2.05676e142	−0.750175	−0.375088	+	0.926989i	$0.622387\pi$
$998$	2.46599e142	0.857612
$999$	1.17772e142	0.390555

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.96.a.a.1.8	✓	8	1.1	even	1	trivial
9.96.a.c.1.1		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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 96 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+3.90162e14 q^{2} +2.16924e22 q^{3} +1.12612e29 q^{4} +1.39914e33 q^{5} +8.46353e36 q^{6} +1.75361e40 q^{7} +2.84812e43 q^{8} -1.65034e45 q^{9} +5.45891e47 q^{10} -5.41264e48 q^{11} +2.44283e51 q^{12} +1.04831e52 q^{13} +6.84194e54 q^{14} +3.03506e55 q^{15} +6.65124e57 q^{16} -2.56029e58 q^{17} -6.43899e59 q^{18} -4.34204e60 q^{19} +1.57560e62 q^{20} +3.80400e62 q^{21} -2.11181e63 q^{22} -7.48379e64 q^{23} +6.17824e65 q^{24} -5.66766e65 q^{25} +4.09009e66 q^{26} -8.18069e67 q^{27} +1.97479e69 q^{28} +2.03053e69 q^{29} +1.18417e70 q^{30} +3.72805e70 q^{31} +1.46681e72 q^{32} -1.17413e71 q^{33} -9.98929e72 q^{34} +2.45355e73 q^{35} -1.85848e74 q^{36} -1.43964e74 q^{37} -1.69410e75 q^{38} +2.27402e74 q^{39} +3.98491e76 q^{40} -4.16311e76 q^{41} +1.48418e77 q^{42} +4.94148e76 q^{43} -6.09530e77 q^{44} -2.30905e78 q^{45} -2.91989e79 q^{46} +4.71948e79 q^{47} +1.44281e80 q^{48} +1.15068e80 q^{49} -2.21131e80 q^{50} -5.55388e80 q^{51} +1.18052e81 q^{52} +9.21253e80 q^{53} -3.19180e82 q^{54} -7.57304e81 q^{55} +4.99450e83 q^{56} -9.41891e82 q^{57} +7.92238e83 q^{58} -1.44917e84 q^{59} +3.41785e84 q^{60} +2.68780e84 q^{61} +1.45454e85 q^{62} -2.89406e85 q^{63} +3.08809e86 q^{64} +1.46673e85 q^{65} -4.58101e85 q^{66} +3.24337e86 q^{67} -2.88321e87 q^{68} -1.62341e87 q^{69} +9.57282e87 q^{70} +2.78222e87 q^{71} -4.70035e88 q^{72} +2.94316e88 q^{73} -5.61691e88 q^{74} -1.22945e88 q^{75} -4.88967e89 q^{76} -9.49169e88 q^{77} +8.87238e88 q^{78} +9.20074e89 q^{79} +9.30600e90 q^{80} +1.72561e90 q^{81} -1.62429e91 q^{82} -2.26821e90 q^{83} +4.28378e91 q^{84} -3.58220e91 q^{85} +1.92798e91 q^{86} +4.40471e91 q^{87} -1.54158e92 q^{88} +3.95651e92 q^{89} -9.00904e92 q^{90} +1.83833e92 q^{91} -8.42767e93 q^{92} +8.08702e92 q^{93} +1.84136e94 q^{94} -6.07512e93 q^{95} +3.18185e94 q^{96} -3.21613e94 q^{97} +4.48953e94 q^{98} +8.93268e93 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5835659138280 q^{2} - 95\!\cdots\!80 q^{3} + 20\!\cdots\!84 q^{4} + 19\!\cdots\!60 q^{5} + 10\!\cdots\!76 q^{6} + 31\!\cdots\!00 q^{7} - 14\!\cdots\!60 q^{8} + 92\!\cdots\!36 q^{9} - 35\!\cdots\!40 q^{10}+ \cdots + 30\!\cdots\!72 q^{99}+O(q^{100}) \) 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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