LMFDB - Embedded newform 1.96.a.a.1.6

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			1.6
Root			$6.86315e12$ 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)

$f(q)$	$=$	$q+1.63986e14 q^{2} +6.46739e21 q^{3} -1.27226e28 q^{4} +1.20020e33 q^{5} +1.06056e36 q^{6} -2.14893e40 q^{7} -8.58249e42 q^{8} -2.07907e45 q^{9} +O(q^{10})$	\(q+1.63986e14 q^{2} +6.46739e21 q^{3} -1.27226e28 q^{4} +1.20020e33 q^{5} +1.06056e36 q^{6} -2.14893e40 q^{7} -8.58249e42 q^{8} -2.07907e45 q^{9} +1.96817e47 q^{10} +1.70307e49 q^{11} -8.22823e49 q^{12} +1.01181e53 q^{13} -3.52395e54 q^{14} +7.76219e54 q^{15} -9.03414e56 q^{16} +2.27059e58 q^{17} -3.40938e59 q^{18} +5.33207e60 q^{19} -1.52698e61 q^{20} -1.38980e62 q^{21} +2.79280e63 q^{22} +5.74222e62 q^{23} -5.55064e64 q^{24} -1.08387e66 q^{25} +1.65923e67 q^{26} -2.71628e67 q^{27} +2.73401e68 q^{28} +2.72768e69 q^{29} +1.27289e69 q^{30} +8.24705e70 q^{31} +1.91840e71 q^{32} +1.10144e71 q^{33} +3.72345e72 q^{34} -2.57916e73 q^{35} +2.64512e73 q^{36} -5.13786e74 q^{37} +8.74385e74 q^{38} +6.54379e74 q^{39} -1.03007e76 q^{40} +7.35670e76 q^{41} -2.27908e76 q^{42} -6.17805e76 q^{43} -2.16676e77 q^{44} -2.49530e78 q^{45} +9.41643e76 q^{46} +3.75012e78 q^{47} -5.84273e78 q^{48} +2.69343e80 q^{49} -1.77739e80 q^{50} +1.46848e80 q^{51} -1.28729e81 q^{52} +2.90261e81 q^{53} -4.45432e81 q^{54} +2.04403e82 q^{55} +1.84432e83 q^{56} +3.44846e82 q^{57} +4.47301e83 q^{58} +1.68978e84 q^{59} -9.87556e82 q^{60} +2.77082e84 q^{61} +1.35240e85 q^{62} +4.46778e85 q^{63} +6.72471e85 q^{64} +1.21438e86 q^{65} +1.80621e85 q^{66} +3.14536e85 q^{67} -2.88879e86 q^{68} +3.71372e84 q^{69} -4.22946e87 q^{70} -4.28767e87 q^{71} +1.78436e88 q^{72} -4.92275e88 q^{73} -8.42538e88 q^{74} -7.00979e87 q^{75} -6.78380e88 q^{76} -3.65979e89 q^{77} +1.07309e89 q^{78} +2.67794e90 q^{79} -1.08428e90 q^{80} +4.23381e90 q^{81} +1.20640e91 q^{82} -1.35258e91 q^{83} +1.76819e90 q^{84} +2.72517e91 q^{85} -1.01311e91 q^{86} +1.76409e91 q^{87} -1.46166e92 q^{88} +3.19257e91 q^{89} -4.09195e92 q^{90} -2.17432e93 q^{91} -7.30562e90 q^{92} +5.33369e92 q^{93} +6.14967e92 q^{94} +6.39957e93 q^{95} +1.24071e93 q^{96} +2.36851e94 q^{97} +4.41685e94 q^{98} -3.54080e94 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.63986e14	0.823915	0.411957	−	0.911203i	$-0.364845\pi$
$2$	1.63986e14	0.823915	0.411957	+	0.911203i	$0.364845\pi$
$3$	6.46739e21	0.140433	0.0702166	−	0.997532i	$-0.477631\pi$
$3$	6.46739e21	0.140433	0.0702166	+	0.997532i	$0.477631\pi$
$4$	−1.27226e28	−0.321165
$5$	1.20020e33	0.755405	0.377702	−	0.925927i	$-0.376714\pi$
$5$	1.20020e33	0.755405	0.377702	+	0.925927i	$0.376714\pi$
$6$	1.06056e36	0.115705
$7$	−2.14893e40	−1.54905	−0.774526	−	0.632542i	$-0.782012\pi$
$7$	−2.14893e40	−1.54905	−0.774526	+	0.632542i	$0.782012\pi$
$8$	−8.58249e42	−1.08853
$9$	−2.07907e45	−0.980279
$10$	1.96817e47	0.622389
$11$	1.70307e49	0.582211	0.291106	−	0.956691i	$-0.405977\pi$
$11$	1.70307e49	0.582211	0.291106	+	0.956691i	$0.405977\pi$
$12$	−8.22823e49	−0.0451022
$13$	1.01181e53	1.23820	0.619101	−	0.785312i	$-0.287497\pi$
$13$	1.01181e53	1.23820	0.619101	+	0.785312i	$0.287497\pi$
$14$	−3.52395e54	−1.27629
$15$	7.76219e54	0.106084
$16$	−9.03414e56	−0.575688
$17$	2.27059e58	0.812484	0.406242	−	0.913765i	$-0.366839\pi$
$17$	2.27059e58	0.812484	0.406242	+	0.913765i	$0.366839\pi$
$18$	−3.40938e59	−0.807666
$19$	5.33207e60	0.968500	0.484250	−	0.874930i	$-0.339093\pi$
$19$	5.33207e60	0.968500	0.484250	+	0.874930i	$0.339093\pi$
$20$	−1.52698e61	−0.242609
$21$	−1.38980e62	−0.217538
$22$	2.79280e63	0.479692
$23$	5.74222e62	0.0119401	0.00597004	−	0.999982i	$-0.498100\pi$
$23$	5.74222e62	0.0119401	0.00597004	+	0.999982i	$0.498100\pi$
$24$	−5.55064e64	−0.152865
$25$	−1.08387e66	−0.429364
$26$	1.65923e67	1.02017
$27$	−2.71628e67	−0.278097
$28$	2.73401e68	0.497501
$29$	2.72768e69	0.937320	0.468660	−	0.883379i	$-0.344737\pi$
$29$	2.72768e69	0.937320	0.468660	+	0.883379i	$0.344737\pi$
$30$	1.27289e69	0.0874040
$31$	8.24705e70	1.19294	0.596469	−	0.802636i	$-0.296570\pi$
$31$	8.24705e70	1.19294	0.596469	+	0.802636i	$0.296570\pi$
$32$	1.91840e71	0.614209
$33$	1.10144e71	0.0817618
$34$	3.72345e72	0.669418
$35$	−2.57916e73	−1.17016
$36$	2.64512e73	0.314831
$37$	−5.13786e74	−1.66418	−0.832091	−	0.554639i	$-0.812856\pi$
$37$	−5.13786e74	−1.66418	−0.832091	+	0.554639i	$0.812856\pi$
$38$	8.74385e74	0.797961
$39$	6.54379e74	0.173884
$40$	−1.03007e76	−0.822278
$41$	7.35670e76	1.81740	0.908699	−	0.417452i	$-0.137077\pi$
$41$	7.35670e76	1.81740	0.908699	+	0.417452i	$0.137077\pi$
$42$	−2.27908e76	−0.179233
$43$	−6.17805e76	−0.158891	−0.0794456	−	0.996839i	$-0.525315\pi$
$43$	−6.17805e76	−0.158891	−0.0794456	+	0.996839i	$0.525315\pi$
$44$	−2.16676e77	−0.186986
$45$	−2.49530e78	−0.740507
$46$	9.41643e76	0.00983761
$47$	3.75012e78	0.141058	0.0705288	−	0.997510i	$-0.477531\pi$
$47$	3.75012e78	0.141058	0.0705288	+	0.997510i	$0.477531\pi$
$48$	−5.84273e78	−0.0808457
$49$	2.69343e80	1.39956
$50$	−1.77739e80	−0.353759
$51$	1.46848e80	0.114100
$52$	−1.28729e81	−0.397667
$53$	2.90261e81	0.362814	0.181407	−	0.983408i	$-0.441935\pi$
$53$	2.90261e81	0.362814	0.181407	+	0.983408i	$0.441935\pi$
$54$	−4.45432e81	−0.229128
$55$	2.04403e82	0.439805
$56$	1.84432e83	1.68618
$57$	3.44846e82	0.136009
$58$	4.47301e83	0.772272
$59$	1.68978e84	1.29527	0.647635	−	0.761950i	$-0.275758\pi$
$59$	1.68978e84	1.29527	0.647635	+	0.761950i	$0.275758\pi$
$60$	−9.87556e82	−0.0340704
$61$	2.77082e84	0.435954	0.217977	−	0.975954i	$-0.430054\pi$
$61$	2.77082e84	0.435954	0.217977	+	0.975954i	$0.430054\pi$
$62$	1.35240e85	0.982879
$63$	4.46778e85	1.51850
$64$	6.72471e85	1.08174
$65$	1.21438e86	0.935343
$66$	1.80621e85	0.0673647
$67$	3.14536e85	0.0574271	0.0287135	−	0.999588i	$-0.490859\pi$
$67$	3.14536e85	0.0574271	0.0287135	+	0.999588i	$0.490859\pi$
$68$	−2.88879e86	−0.260941
$69$	3.71372e84	0.00167678
$70$	−4.22946e87	−0.964113
$71$	−4.28767e87	−0.498252	−0.249126	−	0.968471i	$-0.580143\pi$
$71$	−4.28767e87	−0.498252	−0.249126	+	0.968471i	$0.580143\pi$
$72$	1.78436e88	1.06706
$73$	−4.92275e88	−1.52888	−0.764438	−	0.644697i	$-0.776983\pi$
$73$	−4.92275e88	−1.52888	−0.764438	+	0.644697i	$0.776983\pi$
$74$	−8.42538e88	−1.37114
$75$	−7.00979e87	−0.0602969
$76$	−6.78380e88	−0.311048
$77$	−3.65979e89	−0.901876
$78$	1.07309e89	0.143266
$79$	2.67794e90	1.95216	0.976078	−	0.217419i	$-0.0697637\pi$
$79$	2.67794e90	1.95216	0.976078	+	0.217419i	$0.0697637\pi$
$80$	−1.08428e90	−0.434878
$81$	4.23381e90	0.941225
$82$	1.20640e91	1.49738
$83$	−1.35258e91	−0.943960	−0.471980	−	0.881609i	$-0.656461\pi$
$83$	−1.35258e91	−0.943960	−0.471980	+	0.881609i	$0.656461\pi$
$84$	1.76819e90	0.0698656
$85$	2.72517e91	0.613755
$86$	−1.01311e91	−0.130913
$87$	1.76409e91	0.131631
$88$	−1.46166e92	−0.633753
$89$	3.19257e91	0.0809310	0.0404655	−	0.999181i	$-0.487116\pi$
$89$	3.19257e91	0.0809310	0.0404655	+	0.999181i	$0.487116\pi$
$90$	−4.09195e92	−0.610115
$91$	−2.17432e93	−1.91804
$92$	−7.30562e90	−0.00383473
$93$	5.33369e92	0.167528
$94$	6.14967e92	0.116219
$95$	6.39957e93	0.731609
$96$	1.24071e93	0.0862553
$97$	2.36851e94	1.00651	0.503254	−	0.864139i	$-0.332136\pi$
$97$	2.36851e94	1.00651	0.503254	+	0.864139i	$0.332136\pi$
$98$	4.41685e94	1.15312
$99$	−3.54080e94	−0.570729
$100$	1.37896e94	0.137896
$101$	−8.86374e94	−0.552525	−0.276263	−	0.961082i	$-0.589096\pi$
$101$	−8.86374e94	−0.552525	−0.276263	+	0.961082i	$0.589096\pi$
$102$	2.40810e94	0.0940084
$103$	3.21722e95	0.790155	0.395078	−	0.918648i	$-0.370718\pi$
$103$	3.21722e95	0.790155	0.395078	+	0.918648i	$0.370718\pi$
$104$	−8.68388e95	−1.34782
$105$	−1.66804e95	−0.164329
$106$	4.75987e95	0.298928
$107$	−4.10230e96	−1.64929	−0.824647	−	0.565648i	$-0.808626\pi$
$107$	−4.10230e96	−1.64929	−0.824647	+	0.565648i	$0.808626\pi$
$108$	3.45583e95	0.0893149
$109$	−2.93013e95	−0.0488797	−0.0244399	−	0.999701i	$-0.507780\pi$
$109$	−2.93013e95	−0.0488797	−0.0244399	+	0.999701i	$0.507780\pi$
$110$	3.35193e96	0.362362
$111$	−3.32286e96	−0.233706
$112$	1.94138e97	0.891771
$113$	5.98774e97	1.80317	0.901585	−	0.432602i	$-0.142405\pi$
$113$	5.98774e97	1.80317	0.901585	+	0.432602i	$0.142405\pi$
$114$	5.65499e96	0.112060
$115$	6.89183e95	0.00901959
$116$	−3.47033e97	−0.301034
$117$	−2.10363e98	−1.21378
$118$	2.77101e98	1.06719
$119$	−4.87935e98	−1.25858
$120$	−6.66189e97	−0.115475
$121$	−5.65622e98	−0.661030
$122$	4.54376e98	0.359189
$123$	4.75787e98	0.255223
$124$	−1.04924e99	−0.383130
$125$	−4.33060e99	−1.07975
$126$	7.32653e99	1.25112
$127$	3.91647e99	0.459429	0.229715	−	0.973258i	$-0.426221\pi$
$127$	3.91647e99	0.459429	0.229715	+	0.973258i	$0.426221\pi$
$128$	3.42800e99	0.277056
$129$	−3.99559e98	−0.0223136
$130$	1.99142e100	0.770643
$131$	3.64051e100	0.978984	0.489492	−	0.872008i	$-0.337182\pi$
$131$	3.64051e100	0.978984	0.489492	+	0.872008i	$0.337182\pi$
$132$	−1.40133e99	−0.0262590
$133$	−1.14583e101	−1.50026
$134$	5.15795e99	0.0473150
$135$	−3.26009e100	−0.210076
$136$	−1.94873e101	−0.884411
$137$	−4.17919e101	−1.33926	−0.669630	−	0.742695i	$-0.733547\pi$
$137$	−4.17919e101	−1.33926	−0.669630	+	0.742695i	$0.733547\pi$
$138$	6.08998e98	0.00138153
$139$	9.19462e101	1.48024	0.740118	−	0.672477i	$-0.234770\pi$
$139$	9.19462e101	1.48024	0.740118	+	0.672477i	$0.234770\pi$
$140$	3.28137e101	0.375815
$141$	2.42535e100	0.0198092
$142$	−7.03118e101	−0.410517
$143$	1.72319e102	0.720895
$144$	1.87826e102	0.564335
$145$	3.27377e102	0.708056
$146$	−8.07263e102	−1.25966
$147$	1.74195e102	0.196545
$148$	6.53672e102	0.534476
$149$	−6.33085e102	−0.375936	−0.187968	−	0.982175i	$-0.560190\pi$
$149$	−6.33085e102	−0.375936	−0.187968	+	0.982175i	$0.560190\pi$
$150$	−1.14951e102	−0.0496795
$151$	4.05634e102	0.127858	0.0639291	−	0.997954i	$-0.479637\pi$
$151$	4.05634e102	0.127858	0.0639291	+	0.997954i	$0.479637\pi$
$152$	−4.57624e103	−1.05424
$153$	−4.72071e103	−0.796461
$154$	−6.00155e103	−0.743069
$155$	9.89814e103	0.901151
$156$	−8.32544e102	−0.0558456
$157$	7.12511e102	0.0352824	0.0176412	−	0.999844i	$-0.494384\pi$
$157$	7.12511e102	0.0352824	0.0176412	+	0.999844i	$0.494384\pi$
$158$	4.39146e104	1.60841
$159$	1.87723e103	0.0509511
$160$	2.30247e104	0.463976
$161$	−1.23396e103	−0.0184958
$162$	6.94286e104	0.775489
$163$	−1.01435e105	−0.845818	−0.422909	−	0.906172i	$-0.638991\pi$
$163$	−1.01435e105	−0.845818	−0.422909	+	0.906172i	$0.638991\pi$
$164$	−9.35967e104	−0.583684
$165$	1.32196e104	0.0617632
$166$	−2.21804e105	−0.777742
$167$	−3.58858e105	−0.945997	−0.472999	−	0.881063i	$-0.656828\pi$
$167$	−3.58858e105	−0.945997	−0.472999	+	0.881063i	$0.656828\pi$
$168$	1.19279e105	0.236796
$169$	3.56009e105	0.533142
$170$	4.46890e105	0.505681
$171$	−1.10857e106	−0.949400
$172$	7.86011e104	0.0510302
$173$	1.33621e106	0.658695	0.329347	−	0.944209i	$-0.393171\pi$
$173$	1.33621e106	0.658695	0.329347	+	0.944209i	$0.393171\pi$
$174$	2.89287e105	0.108453
$175$	2.32916e106	0.665107
$176$	−1.53858e106	−0.335172
$177$	1.09285e106	0.181899
$178$	5.23537e105	0.0666802
$179$	1.23426e107	1.20472	0.602360	−	0.798224i	$-0.294227\pi$
$179$	1.23426e107	1.20472	0.602360	+	0.798224i	$0.294227\pi$
$180$	3.17469e106	0.237825
$181$	−1.32796e107	−0.764630	−0.382315	−	0.924032i	$-0.624873\pi$
$181$	−1.32796e107	−0.764630	−0.382315	+	0.924032i	$0.624873\pi$
$182$	−3.56558e107	−1.58030
$183$	1.79200e106	0.0612224
$184$	−4.92825e105	−0.0129971
$185$	−6.16648e107	−1.25713
$186$	8.74651e106	0.138029
$187$	3.86698e107	0.473038
$188$	−4.77114e106	−0.0453027
$189$	5.83711e107	0.430786
$190$	1.04944e108	0.602784
$191$	3.17513e108	1.42127	0.710635	−	0.703560i	$-0.248408\pi$
$191$	3.17513e108	1.42127	0.710635	+	0.703560i	$0.248408\pi$
$192$	4.34913e107	0.151913
$193$	−4.45866e108	−1.21684	−0.608418	−	0.793617i	$-0.708195\pi$
$193$	−4.45866e108	−1.21684	−0.608418	+	0.793617i	$0.708195\pi$
$194$	3.88402e108	0.829276
$195$	7.85389e107	0.131353
$196$	−3.42676e108	−0.449490
$197$	−9.71943e108	−1.00114	−0.500570	−	0.865696i	$-0.666876\pi$
$197$	−9.71943e108	−1.00114	−0.500570	+	0.865696i	$0.666876\pi$
$198$	−5.80643e108	−0.470232
$199$	5.78285e108	0.368656	0.184328	−	0.982865i	$-0.440989\pi$
$199$	5.78285e108	0.368656	0.184328	+	0.982865i	$0.440989\pi$
$200$	9.30228e108	0.467374
$201$	2.03423e107	0.00806467
$202$	−1.45353e109	−0.455233
$203$	−5.86159e109	−1.45196
$204$	−1.86829e108	−0.0366448
$205$	8.82954e109	1.37287
$206$	5.27579e109	0.651020
$207$	−1.19385e108	−0.0117046
$208$	−9.14086e109	−0.712818
$209$	9.08090e109	0.563872
$210$	−2.73536e109	−0.135393
$211$	4.93731e110	1.95018	0.975088	−	0.221820i	$-0.0711999\pi$
$211$	4.93731e110	1.95018	0.975088	+	0.221820i	$0.0711999\pi$
$212$	−3.69288e109	−0.116523
$213$	−2.77300e109	−0.0699712
$214$	−6.72720e110	−1.35888
$215$	−7.41492e109	−0.120027
$216$	2.33125e110	0.302716
$217$	−1.77224e111	−1.84792
$218$	−4.80501e109	−0.0402727
$219$	−3.18374e110	−0.214705
$220$	−2.60055e110	−0.141250
$221$	2.29741e111	1.00602
$222$	−5.44902e110	−0.192554
$223$	5.89985e111	1.68407	0.842035	−	0.539424i	$-0.181358\pi$
$223$	5.89985e111	1.68407	0.842035	+	0.539424i	$0.181358\pi$
$224$	−4.12252e111	−0.951441
$225$	2.25343e111	0.420896
$226$	9.81905e111	1.48566
$227$	−7.91864e111	−0.971454	−0.485727	−	0.874111i	$-0.661445\pi$
$227$	−7.91864e111	−0.971454	−0.485727	+	0.874111i	$0.661445\pi$
$228$	−4.38735e110	−0.0436814
$229$	−2.02023e111	−0.163386	−0.0816932	−	0.996658i	$-0.526033\pi$
$229$	−2.02023e111	−0.163386	−0.0816932	+	0.996658i	$0.526033\pi$
$230$	1.13016e110	0.00743138
$231$	−2.36693e111	−0.126653
$232$	−2.34103e112	−1.02030
$233$	3.53266e112	1.25515	0.627575	−	0.778556i	$-0.284047\pi$
$233$	3.53266e112	1.25515	0.627575	+	0.778556i	$0.284047\pi$
$234$	−3.44966e112	−1.00005
$235$	4.50090e111	0.106556
$236$	−2.14985e112	−0.415995
$237$	1.73193e112	0.274148
$238$	−8.00145e112	−1.03696
$239$	1.84333e112	0.195750	0.0978752	−	0.995199i	$-0.468795\pi$
$239$	1.84333e112	0.195750	0.0978752	+	0.995199i	$0.468795\pi$
$240$	−7.01247e111	−0.0610713
$241$	2.13239e113	1.52426	0.762128	−	0.647426i	$-0.224155\pi$
$241$	2.13239e113	1.52426	0.762128	+	0.647426i	$0.224155\pi$
$242$	−9.27541e112	−0.544632
$243$	8.49912e112	0.410276
$244$	−3.52522e112	−0.140013
$245$	3.23267e113	1.05724
$246$	7.80224e112	0.210282
$247$	5.39506e113	1.19920
$248$	−7.07802e113	−1.29855
$249$	−8.74766e112	−0.132563
$250$	−7.10158e113	−0.889620
$251$	−8.05597e113	−0.834865	−0.417432	−	0.908708i	$-0.637070\pi$
$251$	−8.05597e113	−0.834865	−0.417432	+	0.908708i	$0.637070\pi$
$252$	−5.68420e113	−0.487689
$253$	9.77941e111	0.00695165
$254$	6.42247e113	0.378530
$255$	1.76247e113	0.0861915
$256$	−2.10179e114	−0.853474
$257$	9.51752e113	0.321144	0.160572	−	0.987024i	$-0.448666\pi$
$257$	9.51752e113	0.321144	0.160572	+	0.987024i	$0.448666\pi$
$258$	−6.55221e112	−0.0183845
$259$	1.10409e115	2.57790
$260$	−1.54502e114	−0.300399
$261$	−5.67102e114	−0.918835
$262$	5.96993e114	0.806600
$263$	6.81950e113	0.0768872	0.0384436	−	0.999261i	$-0.487760\pi$
$263$	6.81950e113	0.0768872	0.0384436	+	0.999261i	$0.487760\pi$
$264$	−9.45314e113	−0.0889999
$265$	3.48372e114	0.274071
$266$	−1.87899e115	−1.23608
$267$	2.06476e113	0.0113654
$268$	−4.00173e113	−0.0184436
$269$	5.65119e114	0.218226	0.109113	−	0.994029i	$-0.465199\pi$
$269$	5.65119e114	0.218226	0.109113	+	0.994029i	$0.465199\pi$
$270$	−5.34609e114	−0.173084
$271$	1.41994e115	0.385681	0.192840	−	0.981230i	$-0.438230\pi$
$271$	1.41994e115	0.385681	0.192840	+	0.981230i	$0.438230\pi$
$272$	−2.05128e115	−0.467738
$273$	−1.40622e115	−0.269356
$274$	−6.85329e115	−1.10344
$275$	−1.84590e115	−0.249980
$276$	−4.72483e112	−0.000538524 0
$277$	1.28234e116	1.23088	0.615439	−	0.788185i	$-0.288979\pi$
$277$	1.28234e116	1.23088	0.615439	+	0.788185i	$0.288979\pi$
$278$	1.50779e116	1.21959
$279$	−1.71462e116	−1.16941
$280$	2.21356e116	1.27375
$281$	−5.28058e115	−0.256526	−0.128263	−	0.991740i	$-0.540940\pi$
$281$	−5.28058e115	−0.256526	−0.128263	+	0.991740i	$0.540940\pi$
$282$	3.97723e114	0.0163211
$283$	2.38789e116	0.828245	0.414122	−	0.910221i	$-0.364089\pi$
$283$	2.38789e116	0.828245	0.414122	+	0.910221i	$0.364089\pi$
$284$	5.45505e115	0.160021
$285$	4.13885e115	0.102742
$286$	2.82580e116	0.593956
$287$	−1.58091e117	−2.81524
$288$	−3.98849e116	−0.602096
$289$	−2.65436e116	−0.339869
$290$	5.36852e116	0.583378
$291$	1.53181e116	0.141347
$292$	6.26304e116	0.491021
$293$	−2.50752e117	−1.67121	−0.835607	−	0.549328i	$-0.814884\pi$
$293$	−2.50752e117	−1.67121	−0.835607	+	0.549328i	$0.814884\pi$
$294$	2.85655e116	0.161936
$295$	2.02808e117	0.978454
$296$	4.40957e117	1.81151
$297$	−4.62602e116	−0.161911
$298$	−1.03817e117	−0.309739
$299$	5.81005e115	0.0147842
$300$	8.91831e115	0.0193652
$301$	1.32762e117	0.246131
$302$	6.65183e116	0.105344
$303$	−5.73253e116	−0.0775928
$304$	−4.81706e117	−0.557554
$305$	3.32555e117	0.329322
$306$	−7.74131e117	−0.656216
$307$	−5.88342e117	−0.427127	−0.213563	−	0.976929i	$-0.568507\pi$
$307$	−5.88342e117	−0.427127	−0.213563	+	0.976929i	$0.568507\pi$
$308$	4.65622e117	0.289651
$309$	2.08070e117	0.110964
$310$	1.62316e118	0.742472
$311$	−4.43683e118	−1.74162	−0.870812	−	0.491617i	$-0.836406\pi$
$311$	−4.43683e118	−1.74162	−0.870812	+	0.491617i	$0.836406\pi$
$312$	−5.61621e117	−0.189278
$313$	−2.96526e117	−0.0858434	−0.0429217	−	0.999078i	$-0.513667\pi$
$313$	−2.96526e117	−0.0858434	−0.0429217	+	0.999078i	$0.513667\pi$
$314$	1.16842e117	0.0290697
$315$	5.36224e118	1.14708
$316$	−3.40705e118	−0.626964
$317$	4.39328e118	0.695783	0.347892	−	0.937535i	$-0.386898\pi$
$317$	4.39328e118	0.695783	0.347892	+	0.937535i	$0.386898\pi$
$318$	3.07839e117	0.0419794
$319$	4.64543e118	0.545718
$320$	8.07102e118	0.817155
$321$	−2.65312e118	−0.231615
$322$	−2.02353e117	−0.0152390
$323$	1.21069e119	0.786891
$324$	−5.38653e118	−0.302288
$325$	−1.09667e119	−0.531639
$326$	−1.66339e119	−0.696882
$327$	−1.89503e117	−0.00686433
$328$	−6.31389e119	−1.97829
$329$	−8.05875e118	−0.218506
$330$	2.16783e118	0.0508876
$331$	1.56421e119	0.318029	0.159014	−	0.987276i	$-0.449168\pi$
$331$	1.56421e119	0.318029	0.159014	+	0.987276i	$0.449168\pi$
$332$	1.72084e119	0.303167
$333$	1.06820e120	1.63136
$334$	−5.88477e119	−0.779421
$335$	3.77507e118	0.0433807
$336$	1.25556e119	0.125234
$337$	5.85058e119	0.506732	0.253366	−	0.967370i	$-0.418462\pi$
$337$	5.85058e119	0.506732	0.253366	+	0.967370i	$0.418462\pi$
$338$	5.83806e119	0.439264
$339$	3.87250e119	0.253225
$340$	−3.46714e119	−0.197116
$341$	1.40453e120	0.694542
$342$	−1.81791e120	−0.782224
$343$	−1.65242e120	−0.618943
$344$	5.30231e119	0.172957
$345$	4.45722e117	0.00126665
$346$	2.19119e120	0.542708
$347$	−5.43681e120	−1.17407	−0.587035	−	0.809562i	$-0.699705\pi$
$347$	−5.43681e120	−1.17407	−0.587035	+	0.809562i	$0.699705\pi$
$348$	−2.24440e119	−0.0422752
$349$	−2.60736e120	−0.428541	−0.214271	−	0.976774i	$-0.568737\pi$
$349$	−2.60736e120	−0.428541	−0.214271	+	0.976774i	$0.568737\pi$
$350$	3.81949e120	0.547991
$351$	−2.74837e120	−0.344340
$352$	3.26718e120	0.357599
$353$	−5.97113e120	−0.571160	−0.285580	−	0.958355i	$-0.592186\pi$
$353$	−5.97113e120	−0.571160	−0.285580	+	0.958355i	$0.592186\pi$
$354$	1.79212e120	0.149869
$355$	−5.14607e120	−0.376382
$356$	−4.06179e119	−0.0259922
$357$	−3.15566e120	−0.176746
$358$	2.02401e121	0.992587
$359$	2.73209e121	1.17357	0.586785	−	0.809743i	$-0.300393\pi$
$359$	2.73209e121	1.17357	0.586785	+	0.809743i	$0.300393\pi$
$360$	2.14159e121	0.806062
$361$	−1.87949e120	−0.0620079
$362$	−2.17766e121	−0.629990
$363$	−3.65810e120	−0.0928305
$364$	2.76631e121	0.616006
$365$	−5.90831e121	−1.15492
$366$	2.93863e120	0.0504421
$367$	3.72997e121	0.562428	0.281214	−	0.959645i	$-0.409263\pi$
$367$	3.72997e121	0.562428	0.281214	+	0.959645i	$0.409263\pi$
$368$	−5.18760e119	−0.00687377
$369$	−1.52951e122	−1.78156
$370$	−1.01122e122	−1.03577
$371$	−6.23750e121	−0.562018
$372$	−6.78586e120	−0.0538041
$373$	2.36498e122	1.65066	0.825331	−	0.564649i	$-0.190988\pi$
$373$	2.36498e122	1.65066	0.825331	+	0.564649i	$0.190988\pi$
$374$	6.34131e121	0.389743
$375$	−2.80077e121	−0.151632
$376$	−3.21854e121	−0.153545
$377$	2.75990e122	1.16059
$378$	9.57204e121	0.354931
$379$	−1.48042e121	−0.0484198	−0.0242099	−	0.999707i	$-0.507707\pi$
$379$	−1.48042e121	−0.0484198	−0.0242099	+	0.999707i	$0.507707\pi$
$380$	−8.14194e121	−0.234967
$381$	2.53294e121	0.0645191
$382$	5.20678e122	1.17101
$383$	−3.23333e122	−0.642256	−0.321128	−	0.947036i	$-0.604062\pi$
$383$	−3.23333e122	−0.642256	−0.321128	+	0.947036i	$0.604062\pi$
$384$	2.21702e121	0.0389078
$385$	−4.39249e122	−0.681281
$386$	−7.31157e122	−1.00257
$387$	1.28446e122	0.155758
$388$	−3.01337e122	−0.323255
$389$	1.11274e123	1.05630	0.528152	−	0.849150i	$-0.322885\pi$
$389$	1.11274e123	1.05630	0.528152	+	0.849150i	$0.322885\pi$
$390$	1.28793e122	0.108224
$391$	1.30382e121	0.00970113
$392$	−2.31164e123	−1.52346
$393$	2.35446e122	0.137482
$394$	−1.59385e123	−0.824855
$395$	3.21408e123	1.47467
$396$	4.50484e122	0.183298
$397$	−2.49367e123	−0.900098	−0.450049	−	0.893004i	$-0.648593\pi$
$397$	−2.49367e123	−0.900098	−0.450049	+	0.893004i	$0.648593\pi$
$398$	9.48307e122	0.303741
$399$	−7.41050e122	−0.210686
$400$	9.79180e122	0.247180
$401$	3.37714e123	0.757166	0.378583	−	0.925567i	$-0.376411\pi$
$401$	3.37714e123	0.757166	0.378583	+	0.925567i	$0.376411\pi$
$402$	3.33585e121	0.00664460
$403$	8.34447e123	1.47710
$404$	1.12770e123	0.177452
$405$	5.08144e123	0.711005
$406$	−9.61220e123	−1.19629
$407$	−8.75016e123	−0.968905
$408$	−1.26032e123	−0.124201
$409$	−5.89311e123	−0.516997	−0.258498	−	0.966012i	$-0.583228\pi$
$409$	−5.89311e123	−0.516997	−0.258498	+	0.966012i	$0.583228\pi$
$410$	1.44792e124	1.13113
$411$	−2.70284e123	−0.188076
$412$	−4.09315e123	−0.253770
$413$	−3.63123e124	−2.00644
$414$	−1.95774e122	−0.00964360
$415$	−1.62337e124	−0.713072
$416$	1.94107e124	0.760514
$417$	5.94652e123	0.207874
$418$	1.48914e124	0.464582
$419$	1.83713e124	0.511652	0.255826	−	0.966723i	$-0.417653\pi$
$419$	1.83713e124	0.511652	0.255826	+	0.966723i	$0.417653\pi$
$420$	2.12219e123	0.0527768
$421$	2.44174e124	0.542376	0.271188	−	0.962526i	$-0.412583\pi$
$421$	2.44174e124	0.542376	0.271188	+	0.962526i	$0.412583\pi$
$422$	8.09650e124	1.60678
$423$	−7.79675e123	−0.138276
$424$	−2.49116e124	−0.394933
$425$	−2.46102e124	−0.348851
$426$	−4.54734e123	−0.0576503
$427$	−5.95431e124	−0.675316
$428$	5.21921e124	0.529695
$429$	1.11446e124	0.101238
$430$	−1.21594e124	−0.0988921
$431$	−1.89871e125	−1.38289	−0.691445	−	0.722429i	$-0.743026\pi$
$431$	−1.89871e125	−1.38289	−0.691445	+	0.722429i	$0.743026\pi$
$432$	2.45393e124	0.160097
$433$	1.91296e125	1.11823	0.559114	−	0.829091i	$-0.311142\pi$
$433$	1.91296e125	1.11823	0.559114	+	0.829091i	$0.311142\pi$
$434$	−2.90622e125	−1.52253
$435$	2.11727e124	0.0994345
$436$	3.72791e123	0.0156984
$437$	3.06179e123	0.0115640
$438$	−5.22089e124	−0.176898
$439$	4.41012e125	1.34087	0.670434	−	0.741969i	$-0.266108\pi$
$439$	4.41012e125	1.34087	0.670434	+	0.741969i	$0.266108\pi$
$440$	−1.75429e125	−0.478740
$441$	−5.59983e125	−1.37196
$442$	3.76744e125	0.828874
$443$	1.39493e125	0.275661	0.137831	−	0.990456i	$-0.455987\pi$
$443$	1.39493e125	0.275661	0.137831	+	0.990456i	$0.455987\pi$
$444$	4.22755e124	0.0750582
$445$	3.83173e124	0.0611356
$446$	9.67493e125	1.38753
$447$	−4.09441e124	−0.0527939
$448$	−1.44509e126	−1.67568
$449$	1.35013e126	1.40823	0.704114	−	0.710087i	$-0.251345\pi$
$449$	1.35013e126	1.40823	0.704114	+	0.710087i	$0.251345\pi$
$450$	3.69531e125	0.346782
$451$	1.25290e126	1.05811
$452$	−7.61799e125	−0.579115
$453$	2.62339e124	0.0179555
$454$	−1.29855e126	−0.800395
$455$	−2.60963e126	−1.44890
$456$	−2.95964e125	−0.148050
$457$	−9.65799e125	−0.435379	−0.217689	−	0.976018i	$-0.569852\pi$
$457$	−9.65799e125	−0.435379	−0.217689	+	0.976018i	$0.569852\pi$
$458$	−3.31290e125	−0.134616
$459$	−6.16756e125	−0.225949
$460$	−8.76823e123	−0.00289678
$461$	2.06224e126	0.614532	0.307266	−	0.951624i	$-0.400586\pi$
$461$	2.06224e126	0.614532	0.307266	+	0.951624i	$0.400586\pi$
$462$	−3.88144e125	−0.104351
$463$	6.82135e125	0.165491	0.0827453	−	0.996571i	$-0.473631\pi$
$463$	6.82135e125	0.165491	0.0827453	+	0.996571i	$0.473631\pi$
$464$	−2.46422e126	−0.539604
$465$	6.40151e125	0.126552
$466$	5.79307e126	1.03414
$467$	9.82475e126	1.58405	0.792026	−	0.610487i	$-0.209026\pi$
$467$	9.82475e126	1.58405	0.792026	+	0.610487i	$0.209026\pi$
$468$	2.67637e126	0.389824
$469$	−6.75916e125	−0.0889575
$470$	7.38085e125	0.0877927
$471$	4.60809e124	0.00495482
$472$	−1.45026e127	−1.40994
$473$	−1.05217e126	−0.0925083
$474$	2.84013e126	0.225874
$475$	−5.77925e126	−0.415839
$476$	6.20782e126	0.404212
$477$	−6.03471e126	−0.355659
$478$	3.02281e126	0.161282
$479$	−1.26069e127	−0.609074	−0.304537	−	0.952501i	$-0.598502\pi$
$479$	−1.26069e127	−0.609074	−0.304537	+	0.952501i	$0.598502\pi$
$480$	1.48910e126	0.0651576
$481$	−5.19856e127	−2.06059
$482$	3.49683e127	1.25586
$483$	−7.98053e124	−0.00259742
$484$	7.19621e126	0.212299
$485$	2.84269e127	0.760321
$486$	1.39374e127	0.338032
$487$	−9.89079e126	−0.217573	−0.108787	−	0.994065i	$-0.534697\pi$
$487$	−9.89079e126	−0.217573	−0.108787	+	0.994065i	$0.534697\pi$
$488$	−2.37805e127	−0.474548
$489$	−6.56020e126	−0.118781
$490$	5.30112e127	0.871072
$491$	−3.64184e127	−0.543188	−0.271594	−	0.962412i	$-0.587551\pi$
$491$	−3.64184e127	−0.543188	−0.271594	+	0.962412i	$0.587551\pi$
$492$	−6.05327e126	−0.0819686
$493$	6.19343e127	0.761558
$494$	8.84714e127	0.988037
$495$	−4.24969e127	−0.431132
$496$	−7.45050e127	−0.686761
$497$	9.21391e127	0.771819
$498$	−1.43450e127	−0.109221
$499$	5.28548e126	0.0365855	0.0182927	−	0.999833i	$-0.494177\pi$
$499$	5.28548e126	0.0365855	0.0182927	+	0.999833i	$0.494177\pi$
$500$	5.50967e127	0.346777
$501$	−2.32087e127	−0.132849
$502$	−1.32107e128	−0.687857
$503$	−3.95594e127	−0.187401	−0.0937003	−	0.995600i	$-0.529870\pi$
$503$	−3.95594e127	−0.187401	−0.0937003	+	0.995600i	$0.529870\pi$
$504$	−3.83447e128	−1.65293
$505$	−1.06383e128	−0.417380
$506$	1.60369e126	0.00572757
$507$	2.30245e127	0.0748708
$508$	−4.98279e127	−0.147552
$509$	8.10499e127	0.218604	0.109302	−	0.994009i	$-0.465138\pi$
$509$	8.10499e127	0.218604	0.109302	+	0.994009i	$0.465138\pi$
$510$	2.89021e127	0.0710144
$511$	1.05787e129	2.36831
$512$	−4.80461e128	−0.980245
$513$	−1.44834e128	−0.269337
$514$	1.56074e128	0.264596
$515$	3.86132e128	0.596887
$516$	5.08344e126	0.00716634
$517$	6.38672e127	0.0821253
$518$	1.81056e129	2.12397
$519$	8.64178e127	0.0925025
$520$	−1.04224e129	−1.01815
$521$	−1.43313e128	−0.127789	−0.0638947	−	0.997957i	$-0.520352\pi$
$521$	−1.43313e128	−0.127789	−0.0638947	+	0.997957i	$0.520352\pi$
$522$	−9.29969e128	−0.757041
$523$	−2.22337e129	−1.65265	−0.826325	−	0.563194i	$-0.809573\pi$
$523$	−2.22337e129	−1.65265	−0.826325	+	0.563194i	$0.809573\pi$
$524$	−4.63169e128	−0.314415
$525$	1.50636e128	0.0934030
$526$	1.11830e128	0.0633485
$527$	1.87257e129	0.969244
$528$	−9.95060e127	−0.0470693
$529$	−2.31250e129	−0.999857
$530$	5.71281e128	0.225812
$531$	−3.51317e129	−1.26973
$532$	1.45779e129	0.481830
$533$	7.44361e129	2.25030
$534$	3.38592e127	0.00936411
$535$	−4.92359e129	−1.24588
$536$	−2.69950e128	−0.0625109
$537$	7.98242e128	0.169183
$538$	9.26717e128	0.179800
$539$	4.58711e129	0.814841
$540$	4.14770e128	0.0674689
$541$	−1.27078e129	−0.189322	−0.0946611	−	0.995510i	$-0.530177\pi$
$541$	−1.27078e129	−0.189322	−0.0946611	+	0.995510i	$0.530177\pi$
$542$	2.32850e129	0.317768
$543$	−8.58841e128	−0.107379
$544$	4.35591e129	0.499035
$545$	−3.51676e128	−0.0369240
$546$	−2.30600e129	−0.221926
$547$	−5.92880e129	−0.523081	−0.261540	−	0.965193i	$-0.584230\pi$
$547$	−5.92880e129	−0.523081	−0.261540	+	0.965193i	$0.584230\pi$
$548$	5.31703e129	0.430123
$549$	−5.76072e129	−0.427357
$550$	−3.02702e129	−0.205963
$551$	1.45442e130	0.907794
$552$	−3.18729e127	−0.00182522
$553$	−5.75472e130	−3.02399
$554$	2.10286e130	1.01414
$555$	−3.98811e129	−0.176543
$556$	−1.16980e130	−0.475400
$557$	2.88397e130	1.07614	0.538071	−	0.842900i	$-0.319153\pi$
$557$	2.88397e130	1.07614	0.538071	+	0.842900i	$0.319153\pi$
$558$	−2.81173e130	−0.963496
$559$	−6.25103e129	−0.196739
$560$	2.33005e130	0.673648
$561$	2.50093e129	0.0664302
$562$	−8.65942e129	−0.211356
$563$	7.01490e130	1.57352	0.786761	−	0.617258i	$-0.211757\pi$
$563$	7.01490e130	1.57352	0.786761	+	0.617258i	$0.211757\pi$
$564$	−3.08568e128	−0.00636200
$565$	7.18650e130	1.36212
$566$	3.91581e130	0.682403
$567$	−9.09818e130	−1.45801
$568$	3.67989e130	0.542361
$569$	−5.72340e130	−0.775929	−0.387964	−	0.921674i	$-0.626822\pi$
$569$	−5.72340e130	−0.775929	−0.387964	+	0.921674i	$0.626822\pi$
$570$	6.78714e129	0.0846508
$571$	8.42125e130	0.966410	0.483205	−	0.875507i	$-0.339473\pi$
$571$	8.42125e130	0.966410	0.483205	+	0.875507i	$0.339473\pi$
$572$	−2.19236e130	−0.231526
$573$	2.05348e130	0.199594
$574$	−2.59247e131	−2.31952
$575$	−6.22379e128	−0.00512664
$576$	−1.39811e131	−1.06041
$577$	3.52841e130	0.246450	0.123225	−	0.992379i	$-0.460676\pi$
$577$	3.52841e130	0.246450	0.123225	+	0.992379i	$0.460676\pi$
$578$	−4.35278e130	−0.280023
$579$	−2.88359e130	−0.170884
$580$	−4.16510e130	−0.227403
$581$	2.90660e131	1.46224
$582$	2.51195e130	0.116458
$583$	4.94335e130	0.211235
$584$	4.22495e131	1.66422
$585$	−2.52478e131	−0.916897
$586$	−4.11198e131	−1.37694
$587$	8.25520e129	0.0254928	0.0127464	−	0.999919i	$-0.495943\pi$
$587$	8.25520e129	0.0254928	0.0127464	+	0.999919i	$0.495943\pi$
$588$	−2.21622e130	−0.0631233
$589$	4.39738e131	1.15536
$590$	3.32578e131	0.806162
$591$	−6.28594e130	−0.140593
$592$	4.64162e131	0.958050
$593$	−3.92820e131	−0.748335	−0.374168	−	0.927361i	$-0.622072\pi$
$593$	−3.92820e131	−0.748335	−0.374168	+	0.927361i	$0.622072\pi$
$594$	−7.58604e130	−0.133401
$595$	−5.85621e131	−0.950738
$596$	8.05451e130	0.120737
$597$	3.74000e130	0.0517715
$598$	9.52768e129	0.0121809
$599$	7.28826e131	0.860696	0.430348	−	0.902663i	$-0.358391\pi$
$599$	7.28826e131	0.860696	0.430348	+	0.902663i	$0.358391\pi$
$600$	6.01615e130	0.0656348
$601$	−1.38210e132	−1.39317	−0.696583	−	0.717476i	$-0.745297\pi$
$601$	−1.38210e132	−1.39317	−0.696583	+	0.717476i	$0.745297\pi$
$602$	2.17712e131	0.202791
$603$	−6.53941e130	−0.0562945
$604$	−5.16073e130	−0.0410636
$605$	−6.78861e131	−0.499345
$606$	−9.40055e130	−0.0639299
$607$	−1.67257e132	−1.05177	−0.525884	−	0.850556i	$-0.676266\pi$
$607$	−1.67257e132	−1.05177	−0.525884	+	0.850556i	$0.676266\pi$
$608$	1.02291e132	0.594861
$609$	−3.79092e131	−0.203903
$610$	5.45343e131	0.271333
$611$	3.79442e131	0.174658
$612$	6.00599e131	0.255795
$613$	3.79331e131	0.149501	0.0747507	−	0.997202i	$-0.476184\pi$
$613$	3.79331e131	0.149501	0.0747507	+	0.997202i	$0.476184\pi$
$614$	−9.64799e131	−0.351916
$615$	5.71041e131	0.192797
$616$	3.14101e132	0.981716
$617$	6.09726e132	1.76437	0.882185	−	0.470903i	$-0.156072\pi$
$617$	6.09726e132	1.76437	0.882185	+	0.470903i	$0.156072\pi$
$618$	3.41206e131	0.0914248
$619$	7.28990e131	0.180891	0.0904453	−	0.995901i	$-0.471171\pi$
$619$	7.28990e131	0.180891	0.0904453	+	0.995901i	$0.471171\pi$
$620$	−1.25930e132	−0.289418
$621$	−1.55975e130	−0.00332050
$622$	−7.27578e132	−1.43495
$623$	−6.86061e131	−0.125366
$624$	−5.91175e131	−0.100103
$625$	−2.46154e132	−0.386283
$626$	−4.86261e131	−0.0707276
$627$	5.87297e131	0.0791863
$628$	−9.06503e130	−0.0113315
$629$	−1.16660e133	−1.35212
$630$	8.79333e132	0.945099
$631$	−8.10964e131	−0.0808365	−0.0404182	−	0.999183i	$-0.512869\pi$
$631$	−8.10964e131	−0.0808365	−0.0404182	+	0.999183i	$0.512869\pi$
$632$	−2.29834e133	−2.12498
$633$	3.19315e132	0.273869
$634$	7.20437e132	0.573266
$635$	4.70057e132	0.347055
$636$	−2.38833e131	−0.0163637
$637$	2.72525e133	1.73294
$638$	7.61786e132	0.449625
$639$	8.91435e132	0.488426
$640$	4.11430e132	0.209289
$641$	−1.51150e133	−0.713925	−0.356963	−	0.934119i	$-0.616188\pi$
$641$	−1.51150e133	−0.713925	−0.356963	+	0.934119i	$0.616188\pi$
$642$	−4.35074e132	−0.190831
$643$	1.18653e132	0.0483347	0.0241674	−	0.999708i	$-0.492307\pi$
$643$	1.18653e132	0.0483347	0.0241674	+	0.999708i	$0.492307\pi$
$644$	1.56993e131	0.00594020
$645$	−4.79552e131	−0.0168558
$646$	1.98537e133	0.648331
$647$	−3.47654e132	−0.105486	−0.0527429	−	0.998608i	$-0.516796\pi$
$647$	−3.47654e132	−0.105486	−0.0527429	+	0.998608i	$0.516796\pi$
$648$	−3.63367e133	−1.02455
$649$	2.87782e133	0.754121
$650$	−1.79839e133	−0.438025
$651$	−1.14617e133	−0.259510
$652$	1.29052e133	0.271647
$653$	−5.37137e133	−1.05126	−0.525629	−	0.850714i	$-0.676170\pi$
$653$	−5.37137e133	−1.05126	−0.525629	+	0.850714i	$0.676170\pi$
$654$	−3.10759e131	−0.00565563
$655$	4.36935e133	0.739529
$656$	−6.64615e133	−1.04626
$657$	1.02347e134	1.49872
$658$	−1.32152e133	−0.180030
$659$	−7.94649e133	−1.00721	−0.503603	−	0.863935i	$-0.667993\pi$
$659$	−7.94649e133	−1.00721	−0.503603	+	0.863935i	$0.667993\pi$
$660$	−1.68188e132	−0.0198362
$661$	−1.03268e134	−1.13344	−0.566720	−	0.823911i	$-0.691788\pi$
$661$	−1.03268e134	−1.13344	−0.566720	+	0.823911i	$0.691788\pi$
$662$	2.56509e133	0.262029
$663$	1.48583e133	0.141278
$664$	1.16085e134	1.02753
$665$	−1.37522e134	−1.13330
$666$	1.75169e134	1.34410
$667$	1.56629e132	0.0111917
$668$	4.56562e133	0.303821
$669$	3.81566e133	0.236499
$670$	6.19059e132	0.0357420
$671$	4.71891e133	0.253818
$672$	−2.66620e133	−0.133614
$673$	2.68484e134	1.25373	0.626863	−	0.779129i	$-0.284338\pi$
$673$	2.68484e134	1.25373	0.626863	+	0.779129i	$0.284338\pi$
$674$	9.59414e133	0.417504
$675$	2.94409e133	0.119405
$676$	−4.52938e133	−0.171226
$677$	−3.22789e134	−1.13751	−0.568757	−	0.822505i	$-0.692576\pi$
$677$	−3.22789e134	−1.13751	−0.568757	+	0.822505i	$0.692576\pi$
$678$	6.35037e133	0.208636
$679$	−5.08976e134	−1.55913
$680$	−2.33888e134	−0.668088
$681$	−5.12129e133	−0.136424
$682$	2.30324e134	0.572244
$683$	−4.86102e133	−0.112653	−0.0563266	−	0.998412i	$-0.517939\pi$
$683$	−4.86102e133	−0.112653	−0.0563266	+	0.998412i	$0.517939\pi$
$684$	1.41040e134	0.304914
$685$	−5.01588e134	−1.01168
$686$	−2.70974e134	−0.509956
$687$	−1.30656e133	−0.0229449
$688$	5.58134e133	0.0914718
$689$	2.93690e134	0.449237
$690$	7.30921e131	0.00104361
$691$	1.00823e135	1.34386	0.671929	−	0.740616i	$-0.265466\pi$
$691$	1.00823e135	1.34386	0.671929	+	0.740616i	$0.265466\pi$
$692$	−1.70001e134	−0.211549
$693$	7.60895e134	0.884089
$694$	−8.91561e134	−0.967333
$695$	1.10354e135	1.11818
$696$	−1.51403e134	−0.143284
$697$	1.67041e135	1.47661
$698$	−4.27570e134	−0.353081
$699$	2.28471e134	0.176265
$700$	−2.96330e134	−0.213609
$701$	−1.11097e135	−0.748337	−0.374168	−	0.927361i	$-0.622072\pi$
$701$	−1.11097e135	−0.748337	−0.374168	+	0.927361i	$0.622072\pi$
$702$	−4.50694e134	−0.283707
$703$	−2.73954e135	−1.61176
$704$	1.14527e135	0.629804
$705$	2.91091e133	0.0149639
$706$	−9.79182e134	−0.470587
$707$	1.90476e135	0.855890
$708$	−1.39039e134	−0.0584195
$709$	2.50962e135	0.986079	0.493040	−	0.870007i	$-0.335886\pi$
$709$	2.50962e135	0.986079	0.493040	+	0.870007i	$0.335886\pi$
$710$	−8.43884e134	−0.310107
$711$	−5.56763e135	−1.91366
$712$	−2.74002e134	−0.0880955
$713$	4.73563e133	0.0142438
$714$	−5.17485e134	−0.145624
$715$	2.06818e135	0.544567
$716$	−1.57030e135	−0.386914
$717$	1.19215e134	0.0274899
$718$	4.48025e135	0.966922
$719$	2.88632e135	0.583071	0.291536	−	0.956560i	$-0.405834\pi$
$719$	2.88632e135	0.583071	0.291536	+	0.956560i	$0.405834\pi$
$720$	2.25429e135	0.426301
$721$	−6.91359e135	−1.22399
$722$	−3.08209e134	−0.0510892
$723$	1.37910e135	0.214056
$724$	1.68951e135	0.245572
$725$	−2.95644e135	−0.402451
$726$	−5.99877e134	−0.0764844
$727$	1.10048e136	1.31431	0.657154	−	0.753757i	$-0.271760\pi$
$727$	1.10048e136	1.31431	0.657154	+	0.753757i	$0.271760\pi$
$728$	1.86611e136	2.08784
$729$	−8.42980e135	−0.883608
$730$	−9.68880e135	−0.951555
$731$	−1.40278e135	−0.129097
$732$	−2.27989e134	−0.0196625
$733$	−6.00074e135	−0.485027	−0.242513	−	0.970148i	$-0.577972\pi$
$733$	−6.00074e135	−0.485027	−0.242513	+	0.970148i	$0.577972\pi$
$734$	6.11662e135	0.463392
$735$	2.09069e135	0.148471
$736$	1.10159e134	0.00733370
$737$	5.35677e134	0.0334347
$738$	−2.50818e136	−1.46785
$739$	−2.91120e136	−1.59757	−0.798787	−	0.601614i	$-0.794525\pi$
$739$	−2.91120e136	−1.59757	−0.798787	+	0.601614i	$0.794525\pi$
$740$	7.84540e135	0.403746
$741$	3.48920e135	0.168407
$742$	−1.02286e136	−0.463055
$743$	−6.64979e135	−0.282383	−0.141192	−	0.989982i	$-0.545093\pi$
$743$	−6.64979e135	−0.282383	−0.141192	+	0.989982i	$0.545093\pi$
$744$	−4.57764e135	−0.182359
$745$	−7.59831e135	−0.283984
$746$	3.87824e136	1.36000
$747$	2.81211e136	0.925344
$748$	−4.91982e135	−0.151923
$749$	8.81557e136	2.55484
$750$	−4.59287e135	−0.124932
$751$	−6.02614e136	−1.53866	−0.769330	−	0.638852i	$-0.779410\pi$
$751$	−6.02614e136	−1.53866	−0.769330	+	0.638852i	$0.779410\pi$
$752$	−3.38791e135	−0.0812052
$753$	−5.21011e135	−0.117243
$754$	4.52585e136	0.956228
$755$	4.86843e135	0.0965848
$756$	−7.42634e135	−0.138353
$757$	5.05045e136	0.883641	0.441820	−	0.897104i	$-0.354333\pi$
$757$	5.05045e136	0.883641	0.441820	+	0.897104i	$0.354333\pi$
$758$	−2.42769e135	−0.0398938
$759$	6.32473e133	0.000976242 0
$760$	−5.49242e136	−0.796377
$761$	−1.17563e137	−1.60139	−0.800697	−	0.599070i	$-0.795537\pi$
$761$	−1.17563e137	−1.60139	−0.800697	+	0.599070i	$0.795537\pi$
$762$	4.15367e135	0.0531582
$763$	6.29666e135	0.0757173
$764$	−4.03961e136	−0.456462
$765$	−5.66581e136	−0.601650
$766$	−5.30221e136	−0.529164
$767$	1.70975e137	1.60381
$768$	−1.35931e136	−0.119856
$769$	8.27255e135	0.0685706	0.0342853	−	0.999412i	$-0.489085\pi$
$769$	8.27255e135	0.0685706	0.0342853	+	0.999412i	$0.489085\pi$
$770$	−7.20308e136	−0.561318
$771$	6.15535e135	0.0450993
$772$	5.67259e136	0.390805
$773$	3.56497e136	0.230956	0.115478	−	0.993310i	$-0.463160\pi$
$773$	3.56497e136	0.230956	0.115478	+	0.993310i	$0.463160\pi$
$774$	2.10633e136	0.128331
$775$	−8.93870e136	−0.512204
$776$	−2.03277e137	−1.09561
$777$	7.14060e136	0.362023
$778$	1.82474e137	0.870304
$779$	3.92264e137	1.76015
$780$	−9.99222e135	−0.0421860
$781$	−7.30221e136	−0.290088
$782$	2.13809e135	0.00799290
$783$	−7.40913e136	−0.260666
$784$	−2.43328e137	−0.805712
$785$	8.55159e135	0.0266525
$786$	3.86099e136	0.113273
$787$	3.55364e137	0.981462	0.490731	−	0.871311i	$-0.336730\pi$
$787$	3.55364e137	0.981462	0.490731	+	0.871311i	$0.336730\pi$
$788$	1.23657e137	0.321531
$789$	4.41043e135	0.0107975
$790$	5.27064e137	1.21500
$791$	−1.28672e138	−2.79320
$792$	3.03889e137	0.621254
$793$	2.80355e137	0.539799
$794$	−4.08927e137	−0.741604
$795$	2.25306e136	0.0384887
$796$	−7.35732e136	−0.118399
$797$	−8.44993e137	−1.28110	−0.640550	−	0.767916i	$-0.721294\pi$
$797$	−8.44993e137	−1.28110	−0.640550	+	0.767916i	$0.721294\pi$
$798$	−1.21522e137	−0.173587
$799$	8.51498e136	0.114607
$800$	−2.07929e137	−0.263719
$801$	−6.63756e136	−0.0793349
$802$	5.53804e137	0.623840
$803$	−8.38381e137	−0.890129
$804$	−2.58807e135	−0.00259009
$805$	−1.48101e136	−0.0139718
$806$	1.36838e138	1.21700
$807$	3.65485e136	0.0306462
$808$	7.60730e137	0.601438
$809$	7.81827e137	0.582849	0.291424	−	0.956594i	$-0.405871\pi$
$809$	7.81827e137	0.582849	0.291424	+	0.956594i	$0.405871\pi$
$810$	8.33285e137	0.585808
$811$	9.96498e137	0.660672	0.330336	−	0.943863i	$-0.392838\pi$
$811$	9.96498e137	0.660672	0.330336	+	0.943863i	$0.392838\pi$
$812$	7.45750e137	0.466318
$813$	9.18330e136	0.0541624
$814$	−1.43490e138	−0.798295
$815$	−1.21743e138	−0.638935
$816$	−1.32664e137	−0.0656859
$817$	−3.29418e137	−0.153886
$818$	−9.66389e137	−0.425961
$819$	4.52056e138	1.88021
$820$	−1.12335e138	−0.440918
$821$	−4.63886e138	−1.71835	−0.859174	−	0.511683i	$-0.829022\pi$
$821$	−4.63886e138	−1.71835	−0.859174	+	0.511683i	$0.829022\pi$
$822$	−4.43229e137	−0.154959
$823$	3.92738e137	0.129602	0.0648009	−	0.997898i	$-0.479359\pi$
$823$	3.92738e137	0.129602	0.0648009	+	0.997898i	$0.479359\pi$
$824$	−2.76118e138	−0.860105
$825$	−1.19382e137	−0.0351055
$826$	−5.95472e138	−1.65314
$827$	2.50088e138	0.655513	0.327756	−	0.944762i	$-0.393707\pi$
$827$	2.50088e138	0.655513	0.327756	+	0.944762i	$0.393707\pi$
$828$	1.51889e136	0.00375911
$829$	3.30504e138	0.772390	0.386195	−	0.922417i	$-0.373789\pi$
$829$	3.30504e138	0.772390	0.386195	+	0.922417i	$0.373789\pi$
$830$	−2.66210e138	−0.587510
$831$	8.29341e137	0.172856
$832$	6.80415e138	1.33942
$833$	6.11568e138	1.13712
$834$	9.75147e137	0.171271
$835$	−4.30702e138	−0.714611
$836$	−1.15533e138	−0.181096
$837$	−2.24013e138	−0.331752
$838$	3.01264e138	0.421558
$839$	−2.40686e137	−0.0318242	−0.0159121	−	0.999873i	$-0.505065\pi$
$839$	−2.40686e137	−0.0318242	−0.0159121	+	0.999873i	$0.505065\pi$
$840$	1.43160e138	0.178877
$841$	−1.02835e138	−0.121431
$842$	4.00412e138	0.446872
$843$	−3.41516e137	−0.0360248
$844$	−6.28156e138	−0.626327
$845$	4.27284e138	0.402738
$846$	−1.27856e138	−0.113927
$847$	1.21548e139	1.02397
$848$	−2.62225e138	−0.208868
$849$	1.54434e138	0.116313
$850$	−4.03572e138	−0.287424
$851$	−2.95027e137	−0.0198705
$852$	3.52799e137	0.0224723
$853$	−2.26924e139	−1.36711	−0.683553	−	0.729901i	$-0.739566\pi$
$853$	−2.26924e139	−1.36711	−0.683553	+	0.729901i	$0.739566\pi$
$854$	−9.76423e138	−0.556403
$855$	−1.33051e139	−0.717181
$856$	3.52080e139	1.79530
$857$	−1.55036e139	−0.747899	−0.373949	−	0.927449i	$-0.621997\pi$
$857$	−1.55036e139	−0.747899	−0.373949	+	0.927449i	$0.621997\pi$
$858$	1.82755e138	0.0834111
$859$	2.86183e138	0.123586	0.0617929	−	0.998089i	$-0.480318\pi$
$859$	2.86183e138	0.123586	0.0617929	+	0.998089i	$0.480318\pi$
$860$	9.43374e137	0.0385485
$861$	−1.02243e139	−0.395354
$862$	−3.11362e139	−1.13938
$863$	−1.59903e138	−0.0553787	−0.0276893	−	0.999617i	$-0.508815\pi$
$863$	−1.59903e138	−0.0553787	−0.0276893	+	0.999617i	$0.508815\pi$
$864$	−5.21092e138	−0.170809
$865$	1.60372e139	0.497581
$866$	3.13698e139	0.921324
$867$	−1.71668e138	−0.0477289
$868$	2.25475e139	0.593488
$869$	4.56073e139	1.13657
$870$	3.47203e138	0.0819255
$871$	3.18251e138	0.0711063
$872$	2.51479e138	0.0532069
$873$	−4.92428e139	−0.986658
$874$	5.02091e137	0.00952772
$875$	9.30617e139	1.67259
$876$	4.05056e138	0.0689556
$877$	−3.23089e139	−0.521005	−0.260502	−	0.965473i	$-0.583888\pi$
$877$	−3.23089e139	−0.521005	−0.260502	+	0.965473i	$0.583888\pi$
$878$	7.23199e139	1.10476
$879$	−1.62171e139	−0.234694
$880$	−1.84661e139	−0.253191
$881$	−6.77669e139	−0.880363	−0.440182	−	0.897909i	$-0.645086\pi$
$881$	−6.77669e139	−0.880363	−0.440182	+	0.897909i	$0.645086\pi$
$882$	−9.18294e139	−1.13038
$883$	−1.39606e140	−1.62843	−0.814216	−	0.580561i	$-0.802833\pi$
$883$	−1.39606e140	−1.62843	−0.814216	+	0.580561i	$0.802833\pi$
$884$	−2.92292e139	−0.323098
$885$	1.31164e139	0.137407
$886$	2.28749e139	0.227121
$887$	5.79716e139	0.545561	0.272780	−	0.962076i	$-0.412057\pi$
$887$	5.79716e139	0.545561	0.272780	+	0.962076i	$0.412057\pi$
$888$	2.85184e139	0.254396
$889$	−8.41624e139	−0.711680
$890$	6.28350e138	0.0503705
$891$	7.21049e139	0.547992
$892$	−7.50617e139	−0.540864
$893$	1.99959e139	0.136614
$894$	−6.71426e138	−0.0434977
$895$	1.48136e140	0.910052
$896$	−7.36655e139	−0.429174
$897$	3.75759e137	0.00207619
$898$	2.21402e140	1.16026
$899$	2.24953e140	1.11817
$900$	−2.86696e139	−0.135177
$901$	6.59063e139	0.294781
$902$	2.05458e140	0.871792
$903$	8.58625e138	0.0345649
$904$	−5.13897e140	−1.96280
$905$	−1.59382e140	−0.577605
$906$	4.30200e138	0.0147938
$907$	−7.39451e139	−0.241303	−0.120652	−	0.992695i	$-0.538498\pi$
$907$	−7.39451e139	−0.241303	−0.120652	+	0.992695i	$0.538498\pi$
$908$	1.00746e140	0.311997
$909$	1.84283e140	0.541628
$910$	−4.27942e140	−1.19377
$911$	6.73751e140	1.78392	0.891962	−	0.452110i	$-0.149329\pi$
$911$	6.73751e140	1.78392	0.891962	+	0.452110i	$0.149329\pi$
$912$	−3.11538e139	−0.0782991
$913$	−2.30354e140	−0.549584
$914$	−1.58378e140	−0.358715
$915$	2.15076e139	0.0462477
$916$	2.57027e139	0.0524740
$917$	−7.82321e140	−1.51650
$918$	−1.01139e140	−0.186163
$919$	3.00639e140	0.525482	0.262741	−	0.964866i	$-0.415373\pi$
$919$	3.00639e140	0.525482	0.262741	+	0.964866i	$0.415373\pi$
$920$	−5.91491e138	−0.00981807
$921$	−3.80504e139	−0.0599828
$922$	3.38178e140	0.506322
$923$	−4.33832e140	−0.616937
$924$	3.01136e139	0.0406766
$925$	5.56876e140	0.714539
$926$	1.11861e140	0.136350
$927$	−6.68881e140	−0.774572
$928$	5.23278e140	0.575710
$929$	−9.92259e140	−1.03724	−0.518619	−	0.855005i	$-0.673554\pi$
$929$	−9.92259e140	−1.03724	−0.518619	+	0.855005i	$0.673554\pi$
$930$	1.04976e140	0.104268
$931$	1.43616e141	1.35548
$932$	−4.49448e140	−0.403110
$933$	−2.86947e140	−0.244582
$934$	1.61112e141	1.30512
$935$	4.64116e140	0.357335
$936$	1.80544e141	1.32123
$937$	−8.91256e140	−0.619972	−0.309986	−	0.950741i	$-0.600324\pi$
$937$	−8.91256e140	−0.619972	−0.309986	+	0.950741i	$0.600324\pi$
$938$	−1.10841e140	−0.0732934
$939$	−1.91775e139	−0.0120553
$940$	−5.72634e139	−0.0342219
$941$	−7.44078e140	−0.422777	−0.211388	−	0.977402i	$-0.567798\pi$
$941$	−7.44078e140	−0.422777	−0.211388	+	0.977402i	$0.567798\pi$
$942$	7.55663e138	0.00408235
$943$	4.22438e139	0.0216999
$944$	−1.52657e141	−0.745672
$945$	7.00572e140	0.325418
$946$	−1.72541e140	−0.0762189
$947$	−2.72982e141	−1.14686	−0.573429	−	0.819255i	$-0.694387\pi$
$947$	−2.72982e141	−1.14686	−0.573429	+	0.819255i	$0.694387\pi$
$948$	−2.20348e140	−0.0880465
$949$	−4.98091e141	−1.89306
$950$	−9.47716e140	−0.342616
$951$	2.84131e140	0.0977110
$952$	4.18770e141	1.37000
$953$	−1.54338e141	−0.480353	−0.240177	−	0.970729i	$-0.577205\pi$
$953$	−1.54338e141	−0.480353	−0.240177	+	0.970729i	$0.577205\pi$
$954$	−9.89609e140	−0.293033
$955$	3.81081e141	1.07363
$956$	−2.34520e140	−0.0628682
$957$	3.00438e140	0.0766369
$958$	−2.06735e141	−0.501825
$959$	8.98080e141	2.07458
$960$	5.21984e140	0.114756
$961$	2.02212e141	0.423102
$962$	−8.52491e141	−1.69775
$963$	8.52896e141	1.61677
$964$	−2.71297e141	−0.489537
$965$	−5.35129e141	−0.919203
$966$	−1.30870e139	−0.00214006
$967$	1.25094e142	1.94751	0.973757	−	0.227590i	$-0.0730846\pi$
$967$	1.25094e142	1.94751	0.973757	+	0.227590i	$0.0730846\pi$
$968$	4.85445e141	0.719549
$969$	7.83003e140	0.110506
$970$	4.66161e141	0.626439
$971$	−9.74143e141	−1.24655	−0.623275	−	0.782003i	$-0.714198\pi$
$971$	−9.74143e141	−1.24655	−0.623275	+	0.782003i	$0.714198\pi$
$972$	−1.08131e141	−0.131766
$973$	−1.97586e142	−2.29296
$974$	−1.62195e141	−0.179262
$975$	−7.09260e140	−0.0746597
$976$	−2.50320e141	−0.250974
$977$	6.36472e141	0.607838	0.303919	−	0.952698i	$-0.401705\pi$
$977$	6.36472e141	0.607838	0.303919	+	0.952698i	$0.401705\pi$
$978$	−1.07578e141	−0.0978653
$979$	5.43717e140	0.0471189
$980$	−4.11281e141	−0.339547
$981$	6.09195e140	0.0479158
$982$	−5.97212e141	−0.447541
$983$	1.89651e142	1.35414	0.677070	−	0.735919i	$-0.263249\pi$
$983$	1.89651e142	1.35414	0.677070	+	0.735919i	$0.263249\pi$
$984$	−4.08344e141	−0.277817
$985$	−1.16653e142	−0.756267
$986$	1.01564e142	0.627459
$987$	−5.21191e140	−0.0306854
$988$	−6.86394e141	−0.385140
$989$	−3.54757e139	−0.00189717
$990$	−6.96889e141	−0.355216
$991$	−2.23395e141	−0.108536	−0.0542681	−	0.998526i	$-0.517283\pi$
$991$	−2.23395e141	−0.108536	−0.0542681	+	0.998526i	$0.517283\pi$
$992$	1.58212e142	0.732713
$993$	1.01164e141	0.0446618
$994$	1.51095e142	0.635913
$995$	6.94060e141	0.278484
$996$	1.11293e141	0.0425746
$997$	−1.77016e142	−0.645644	−0.322822	−	0.946460i	$-0.604631\pi$
$997$	−1.77016e142	−0.645644	−0.322822	+	0.946460i	$0.604631\pi$
$998$	8.66746e140	0.0301433
$999$	1.39559e142	0.462803

Twists

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

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

\(f(q)\)	\(=\)	\(q+1.63986e14 q^{2} +6.46739e21 q^{3} -1.27226e28 q^{4} +1.20020e33 q^{5} +1.06056e36 q^{6} -2.14893e40 q^{7} -8.58249e42 q^{8} -2.07907e45 q^{9} +O(q^{10})\)	\(q+1.63986e14 q^{2} +6.46739e21 q^{3} -1.27226e28 q^{4} +1.20020e33 q^{5} +1.06056e36 q^{6} -2.14893e40 q^{7} -8.58249e42 q^{8} -2.07907e45 q^{9} +1.96817e47 q^{10} +1.70307e49 q^{11} -8.22823e49 q^{12} +1.01181e53 q^{13} -3.52395e54 q^{14} +7.76219e54 q^{15} -9.03414e56 q^{16} +2.27059e58 q^{17} -3.40938e59 q^{18} +5.33207e60 q^{19} -1.52698e61 q^{20} -1.38980e62 q^{21} +2.79280e63 q^{22} +5.74222e62 q^{23} -5.55064e64 q^{24} -1.08387e66 q^{25} +1.65923e67 q^{26} -2.71628e67 q^{27} +2.73401e68 q^{28} +2.72768e69 q^{29} +1.27289e69 q^{30} +8.24705e70 q^{31} +1.91840e71 q^{32} +1.10144e71 q^{33} +3.72345e72 q^{34} -2.57916e73 q^{35} +2.64512e73 q^{36} -5.13786e74 q^{37} +8.74385e74 q^{38} +6.54379e74 q^{39} -1.03007e76 q^{40} +7.35670e76 q^{41} -2.27908e76 q^{42} -6.17805e76 q^{43} -2.16676e77 q^{44} -2.49530e78 q^{45} +9.41643e76 q^{46} +3.75012e78 q^{47} -5.84273e78 q^{48} +2.69343e80 q^{49} -1.77739e80 q^{50} +1.46848e80 q^{51} -1.28729e81 q^{52} +2.90261e81 q^{53} -4.45432e81 q^{54} +2.04403e82 q^{55} +1.84432e83 q^{56} +3.44846e82 q^{57} +4.47301e83 q^{58} +1.68978e84 q^{59} -9.87556e82 q^{60} +2.77082e84 q^{61} +1.35240e85 q^{62} +4.46778e85 q^{63} +6.72471e85 q^{64} +1.21438e86 q^{65} +1.80621e85 q^{66} +3.14536e85 q^{67} -2.88879e86 q^{68} +3.71372e84 q^{69} -4.22946e87 q^{70} -4.28767e87 q^{71} +1.78436e88 q^{72} -4.92275e88 q^{73} -8.42538e88 q^{74} -7.00979e87 q^{75} -6.78380e88 q^{76} -3.65979e89 q^{77} +1.07309e89 q^{78} +2.67794e90 q^{79} -1.08428e90 q^{80} +4.23381e90 q^{81} +1.20640e91 q^{82} -1.35258e91 q^{83} +1.76819e90 q^{84} +2.72517e91 q^{85} -1.01311e91 q^{86} +1.76409e91 q^{87} -1.46166e92 q^{88} +3.19257e91 q^{89} -4.09195e92 q^{90} -2.17432e93 q^{91} -7.30562e90 q^{92} +5.33369e92 q^{93} +6.14967e92 q^{94} +6.39957e93 q^{95} +1.24071e93 q^{96} +2.36851e94 q^{97} +4.41685e94 q^{98} -3.54080e94 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5835659138280 q^{2} - 95\!\cdots\!80 q^{3}+ \cdots + 92\!\cdots\!36 q^{9}+O(q^{10}) \) 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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