LMFDB - Embedded newform 9.96.a.c.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9,96,Mod(1,9)] 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("9.1"); S:= CuspForms(chi, 96); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 96, names="a")

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 96 $
Character orbit:	$[\chi]$	$=$	9.a (trivial)

Newform invariants

comment:select newform

sage:traces = [8,5835659138280] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$514.382317934$
Analytic rank:	$1$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	multiple of $ 2^{104}\cdot 3^{57}\cdot 5^{12}\cdot 7^{7}\cdot 11\cdot 13\cdot 19^{3} $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$9.80521e12$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.34596e14 q^{2} +1.54210e28 q^{4} +2.52565e33 q^{5} +4.80687e39 q^{7} +5.67559e42 q^{8} -5.92506e47 q^{10} +3.16113e49 q^{11} -9.97774e52 q^{13} -1.12767e54 q^{14} -1.94236e57 q^{16} +3.48353e57 q^{17} -1.04863e61 q^{19} +3.89480e61 q^{20} -7.41586e63 q^{22} -1.70644e64 q^{23} +3.85455e66 q^{25} +2.34073e67 q^{26} +7.41266e67 q^{28} -1.55539e69 q^{29} +1.02679e71 q^{31} +2.30835e71 q^{32} -8.17221e71 q^{34} +1.21405e73 q^{35} -2.81257e74 q^{37} +2.46005e75 q^{38} +1.43346e76 q^{40} -3.26782e76 q^{41} +7.50961e75 q^{43} +4.87477e77 q^{44} +4.00322e78 q^{46} +2.42784e79 q^{47} -1.69342e80 q^{49} -9.04260e80 q^{50} -1.53867e81 q^{52} +1.40525e82 q^{53} +7.98389e82 q^{55} +2.72818e82 q^{56} +3.64887e83 q^{58} +1.17208e84 q^{59} +7.58248e84 q^{61} -2.40880e85 q^{62} +2.27918e85 q^{64} -2.52003e86 q^{65} -8.84858e86 q^{67} +5.37195e85 q^{68} -2.84810e87 q^{70} -6.46617e86 q^{71} +1.01177e88 q^{73} +6.59817e88 q^{74} -1.61710e89 q^{76} +1.51951e89 q^{77} +1.04527e89 q^{79} -4.90571e90 q^{80} +7.66617e90 q^{82} -1.05596e91 q^{83} +8.79818e90 q^{85} -1.76172e90 q^{86} +1.79413e92 q^{88} +3.90606e92 q^{89} -4.79617e92 q^{91} -2.63149e92 q^{92} -5.69559e93 q^{94} -2.64848e94 q^{95} +3.16941e94 q^{97} +3.97269e94 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5835659138280 q^{2} + 20\!\cdots\!84 q^{4} - 19\!\cdots\!60 q^{5} + 31\!\cdots\!00 q^{7} + 14\!\cdots\!60 q^{8} - 35\!\cdots\!40 q^{10} - 53\!\cdots\!16 q^{11} + 11\!\cdots\!40 q^{13} - 88\!\cdots\!08 q^{14}+ \cdots - 14\!\cdots\!60 q^{98}+O(q^{100}) $ 8 * q + 5835659138280 * q^2 + 208956598309707350371623569984 * q^4 - 1941568507475850402526904141070960 * q^5 + 31232311735415758067806325356531573912000 * q^7 + 14761127603920085098561309094124598702287360 * q^8 - 355384205613899841010372205704985147108657534640 * q^10 - 53080108095821756826858489331993621982645992125216 * q^11 + 117293508281179239843264964380833942161194396039342640 * q^13 - 8850886815767090581799564344683737269936151852930265408 * q^14 + 9517116971431211282501221161054789131283343644054948220928 * q^16 + 13655041265063090981829171372625119189425374473948274915440 * q^17 - 5232175975370167369536369873888207394303637759872553281713440 * q^19 - 136065209104116992530471413843386338746929879497239386344644480 * q^20 - 20365500099170357171519767897869972385636855003458825137197491360 * q^22 + 7129054072165937484825035531327773489156117409617881426435061440 * q^23 + 8177806376085721196783759852983887433280593317172609841487587996600 * q^25 + 69072273179717436642550386629266724895941590936463282023015399323504 * q^26 + 303354815522537415860404332264897505740906926923909508834765584637440 * q^28 - 7715272198415359380593902919630157934289467091855373333108685675435440 * q^29 + 48520677903801540370519073843711920597057994260920479636592334181199616 * q^31 - 911347110324473008775326747695560179887781374647708612161794209209221120 * q^32 - 16409772766982648656985219134942803587399227958333745923026675404562961232 * q^34 - 58800416933815614414155173269063056087887600285328689246425433374756677760 * q^35 - 181116344963557296256979160619337453378797091102974834966000994855965247120 * q^37 + 1676466315180766681626408275142200947978975839695306622930354052184199692640 * q^38 + 39028182173606372825635252450401491624189758401191157685601991729209269171200 * q^40 + 87541390126560450267544465567119030351560808726320656469732601708266148308784 * q^41 + 360093033489081253538156425248276463103949347025569853491672117723107522861600 * q^43 - 1942224484251042670482996667732829207493398934442399145050649033803969221005568 * q^44 - 19332434944442851407749457669991401004991143268030327859543986888040547882373184 * q^46 - 38672453335683563852366980570346257355794761888911368752480783496161211070336640 * q^47 + 265668043093542548841947390620517395072194945166225827717144824590425137465244744 * q^49 + 1423963459280866882678609595824694565889878038511273700600414891648711070234429400 * q^50 + 15678746704556392183126484026214298441253990030076674973212546269606119207477104000 * q^52 + 2922690482809426126710991861168746969788895886261814706776237561500358605037675280 * q^53 + 77963865832782922646862204005771036172886494149999882551809226033579503680996905920 * q^55 - 723822110434297992891221750986765045769194525611914833690699475848521019635777392640 * q^56 + 2398120500739528001867383787619453843290390222445601081527493426426916763954522209040 * q^58 - 2444569112045817337560949868287606200158569651761097862873350630901953709318185022880 * q^59 + 26252719580888049069066995575288184611473664654647035829209505915961690057602967485616 * q^61 - 109318411457586083204284032417457169492313955459811319765445849679642744506848521207040 * q^62 + 407545659960425058121678577897271227683793728749313452587765989597513138495845491277824 * q^64 - 711217468942010938456527729098183388378886665557115838437689631605619958224435834575520 * q^65 - 646475642994207391400653355260241732956721934256209274545597969100350739031184431188640 * q^67 - 91675839067201266020688320385568861573762045194469769590554263557238860857176520405120 * q^68 - 15589682350948763132524633727148211085350313303119537319661619119948806738470696493235840 * q^70 + 14595295080721751466823982356267079020901744922845645857244436108167397828048945561374784 * q^71 - 167722859263497180232486905674536831998056258335586734743256934373976249561602911979579440 * q^73 + 209312489678791718598684146630297797595302804804578868479635191055424978871400486510408112 * q^74 - 959273209575432254809587692424149415253949631691365417587931662952012091653615772375589120 * q^76 + 358973379150050060834656745211596557040941835816686113329022190288009228708654757892460800 * q^77 + 4672642903096907209502768293890247708239627672362847349478671278970829923925879535283527040 * q^79 - 18415268594255335517079731605762998550074832241200743044677945286622776635630921688252866560 * q^80 + 32657845092209493410036294321958173121440540177602229019397776717126981442788576405027965040 * q^82 - 34387792212015780744754986808561666458900302762495709021597904850967930099747337487085254880 * q^83 + 58585978711733607272815047107060888289878133655773893600270763487144112403111490135244590560 * q^85 + 153511472921832187435283964804212642635464712353485304877046031498544471884447149897205104544 * q^86 - 1202425497404423912185881933157195269872332267934742515736241252480851349730675866727622174720 * q^88 + 342673661311688548077760584785109887358595471462214186557789870415877447806348084055852796080 * q^89 - 3490211360016960529246147249335483533013067701963330513611222538458526220206688421639066690944 * q^91 + 12008074146638359830472895966704879561255070000267734630900014099911412498586265442549753546240 * q^92 + 15433462798640093333378242254437202047220637579307237556798289796157532672617883642933732299648 * q^94 - 15321400721190643816477985005690604983976540891819618748501840926190750159388834713154020724800 * q^95 + 10072532354157458294768094296505188523874048354320514397914144859011793551098974691865811668240 * q^97 - 146363464831387371243245039459581022362075942196915081212239417921551560440470151788055390975960 * q^98

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 $

$2$	−2.34596e14	−1.17868	−0.589339	−	0.807886i	$-0.700612\pi$
$2$	−2.34596e14	−1.17868	−0.589339	+	0.807886i	$0.700612\pi$
$3$	0	0
$3$	0	0
$4$	1.54210e28	0.389280
$5$	2.52565e33	1.58964	0.794818	−	0.606847i	$-0.207566\pi$
$5$	2.52565e33	1.58964	0.794818	+	0.606847i	$0.207566\pi$
$6$	0	0
$7$	4.80687e39	0.346502	0.173251	−	0.984878i	$-0.444573\pi$
$7$	4.80687e39	0.346502	0.173251	+	0.984878i	$0.444573\pi$
$8$	5.67559e42	0.719841
$9$	0	0
$10$	−5.92506e47	−1.87367
$11$	3.16113e49	1.08066	0.540330	−	0.841453i	$-0.318299\pi$
$11$	3.16113e49	1.08066	0.540330	+	0.841453i	$0.318299\pi$
$12$	0	0
$13$	−9.97774e52	−1.22102	−0.610510	−	0.792008i	$-0.709036\pi$
$13$	−9.97774e52	−1.22102	−0.610510	+	0.792008i	$0.709036\pi$
$14$	−1.12767e54	−0.408414
$15$	0	0
$16$	−1.94236e57	−1.23774
$17$	3.48353e57	0.124651	0.0623256	−	0.998056i	$-0.480148\pi$
$17$	3.48353e57	0.124651	0.0623256	+	0.998056i	$0.480148\pi$
$18$	0	0
$19$	−1.04863e61	−1.90470	−0.952352	−	0.305002i	$-0.901343\pi$
$19$	−1.04863e61	−1.90470	−0.952352	+	0.305002i	$0.901343\pi$
$20$	3.89480e61	0.618814
$21$	0	0
$22$	−7.41586e63	−1.27375
$23$	−1.70644e64	−0.354828	−0.177414	−	0.984136i	$-0.556773\pi$
$23$	−1.70644e64	−0.354828	−0.177414	+	0.984136i	$0.556773\pi$
$24$	0	0
$25$	3.85455e66	1.52694
$26$	2.34073e67	1.43919
$27$	0	0
$28$	7.41266e67	0.134886
$29$	−1.55539e69	−0.534483	−0.267242	−	0.963630i	$-0.586112\pi$
$29$	−1.55539e69	−0.534483	−0.267242	+	0.963630i	$0.586112\pi$
$30$	0	0
$31$	1.02679e71	1.48525	0.742626	−	0.669706i	$-0.233580\pi$
$31$	1.02679e71	1.48525	0.742626	+	0.669706i	$0.233580\pi$
$32$	2.30835e71	0.739056
$33$	0	0
$34$	−8.17221e71	−0.146923
$35$	1.21405e73	0.550812
$36$	0	0
$37$	−2.81257e74	−0.911007	−0.455503	−	0.890234i	$-0.650541\pi$
$37$	−2.81257e74	−0.911007	−0.455503	+	0.890234i	$0.650541\pi$
$38$	2.46005e75	2.24503
$39$	0	0
$40$	1.43346e76	1.14429
$41$	−3.26782e76	−0.807282	−0.403641	−	0.914917i	$-0.632256\pi$
$41$	−3.26782e76	−0.807282	−0.403641	+	0.914917i	$0.632256\pi$
$42$	0	0
$43$	7.50961e75	0.0193137	0.00965686	−	0.999953i	$-0.496926\pi$
$43$	7.50961e75	0.0193137	0.00965686	+	0.999953i	$0.496926\pi$
$44$	4.87477e77	0.420680
$45$	0	0
$46$	4.00322e78	0.418227
$47$	2.42784e79	0.913211	0.456605	−	0.889669i	$-0.349065\pi$
$47$	2.42784e79	0.913211	0.456605	+	0.889669i	$0.349065\pi$
$48$	0	0
$49$	−1.69342e80	−0.879937
$50$	−9.04260e80	−1.79978
$51$	0	0
$52$	−1.53867e81	−0.475320
$53$	1.40525e82	1.75650	0.878252	−	0.478197i	$-0.158710\pi$
$53$	1.40525e82	1.75650	0.878252	+	0.478197i	$0.158710\pi$
$54$	0	0
$55$	7.98389e82	1.71786
$56$	2.72818e82	0.249426
$57$	0	0
$58$	3.64887e83	0.629983
$59$	1.17208e84	0.898437	0.449218	−	0.893422i	$-0.351703\pi$
$59$	1.17208e84	0.898437	0.449218	+	0.893422i	$0.351703\pi$
$60$	0	0
$61$	7.58248e84	1.19301	0.596505	−	0.802609i	$-0.296555\pi$
$61$	7.58248e84	1.19301	0.596505	+	0.802609i	$0.296555\pi$
$62$	−2.40880e85	−1.75063
$63$	0	0
$64$	2.27918e85	0.366632
$65$	−2.52003e86	−1.94098
$66$	0	0
$67$	−8.84858e86	−1.61555	−0.807775	−	0.589491i	$-0.799328\pi$
$67$	−8.84858e86	−1.61555	−0.807775	+	0.589491i	$0.799328\pi$
$68$	5.37195e85	0.0485242
$69$	0	0
$70$	−2.84810e87	−0.649229
$71$	−6.46617e86	−0.0751407	−0.0375704	−	0.999294i	$-0.511962\pi$
$71$	−6.46617e86	−0.0751407	−0.0375704	+	0.999294i	$0.511962\pi$
$72$	0	0
$73$	1.01177e88	0.314229	0.157115	−	0.987580i	$-0.449781\pi$
$73$	1.01177e88	0.314229	0.157115	+	0.987580i	$0.449781\pi$
$74$	6.59817e88	1.07378
$75$	0	0
$76$	−1.61710e89	−0.741464
$77$	1.51951e89	0.374450
$78$	0	0
$79$	1.04527e89	0.0761980	0.0380990	−	0.999274i	$-0.487870\pi$
$79$	1.04527e89	0.0761980	0.0380990	+	0.999274i	$0.487870\pi$
$80$	−4.90571e90	−1.96756
$81$	0	0
$82$	7.66617e90	0.951525
$83$	−1.05596e91	−0.736952	−0.368476	−	0.929637i	$-0.620120\pi$
$83$	−1.05596e91	−0.736952	−0.368476	+	0.929637i	$0.620120\pi$
$84$	0	0
$85$	8.79818e90	0.198150
$86$	−1.76172e90	−0.0227646
$87$	0	0
$88$	1.79413e92	0.777904
$89$	3.90606e92	0.990178	0.495089	−	0.868842i	$-0.335135\pi$
$89$	3.90606e92	0.990178	0.495089	+	0.868842i	$0.335135\pi$
$90$	0	0
$91$	−4.79617e92	−0.423086
$92$	−2.63149e92	−0.138128
$93$	0	0
$94$	−5.69559e93	−1.07638
$95$	−2.64848e94	−3.02779
$96$	0	0
$97$	3.16941e94	1.34685	0.673427	−	0.739253i	$-0.264821\pi$
$97$	3.16941e94	1.34685	0.673427	+	0.739253i	$0.264821\pi$
$98$	3.97269e94	1.03716
$99$	0	0
$100$	5.94410e94	0.594410
$101$	3.19125e93	0.0198928	0.00994639	−	0.999951i	$-0.496834\pi$
$101$	3.19125e93	0.0198928	0.00994639	+	0.999951i	$0.496834\pi$
$102$	0	0
$103$	−4.65433e95	−1.14311	−0.571557	−	0.820563i	$-0.693660\pi$
$103$	−4.65433e95	−1.14311	−0.571557	+	0.820563i	$0.693660\pi$
$104$	−5.66296e95	−0.878941
$105$	0	0
$106$	−3.29665e96	−2.07035
$107$	2.14933e96	0.864120	0.432060	−	0.901845i	$-0.357787\pi$
$107$	2.14933e96	0.864120	0.432060	+	0.901845i	$0.357787\pi$
$108$	0	0
$109$	−9.13418e96	−1.52374	−0.761870	−	0.647730i	$-0.775718\pi$
$109$	−9.13418e96	−1.52374	−0.761870	+	0.647730i	$0.775718\pi$
$110$	−1.87299e97	−2.02480
$111$	0	0
$112$	−9.33665e96	−0.428879
$113$	1.86534e97	0.561737	0.280869	−	0.959746i	$-0.409378\pi$
$113$	1.86534e97	0.561737	0.280869	+	0.959746i	$0.409378\pi$
$114$	0	0
$115$	−4.30986e97	−0.564047
$116$	−2.39856e97	−0.208064
$117$	0	0
$118$	−2.74965e98	−1.05897
$119$	1.67449e97	0.0431918
$120$	0	0
$121$	1.43604e98	0.167826
$122$	−1.77882e99	−1.40617
$123$	0	0
$124$	1.58341e99	0.578180
$125$	3.35961e99	0.837651
$126$	0	0
$127$	−4.70738e99	−0.552208	−0.276104	−	0.961128i	$-0.589043\pi$
$127$	−4.70738e99	−0.552208	−0.276104	+	0.961128i	$0.589043\pi$
$128$	−1.44912e100	−1.17120
$129$	0	0
$130$	5.91187e100	2.28779
$131$	1.31142e100	0.352660	0.176330	−	0.984331i	$-0.443577\pi$
$131$	1.31142e100	0.352660	0.176330	+	0.984331i	$0.443577\pi$
$132$	0	0
$133$	−5.04064e100	−0.659983
$134$	2.07584e101	1.90421
$135$	0	0
$136$	1.97711e100	0.0897290
$137$	−2.88473e101	−0.924440	−0.462220	−	0.886765i	$-0.652947\pi$
$137$	−2.88473e101	−0.924440	−0.462220	+	0.886765i	$0.652947\pi$
$138$	0	0
$139$	−9.04382e100	−0.145596	−0.0727979	−	0.997347i	$-0.523193\pi$
$139$	−9.04382e100	−0.145596	−0.0727979	+	0.997347i	$0.523193\pi$
$140$	1.87218e101	0.214420
$141$	0	0
$142$	1.51693e101	0.0885667
$143$	−3.15409e102	−1.31951
$144$	0	0
$145$	−3.92837e102	−0.849634
$146$	−2.37357e102	−0.370375
$147$	0	0
$148$	−4.33726e102	−0.354637
$149$	−1.04129e103	−0.618335	−0.309167	−	0.951008i	$-0.600050\pi$
$149$	−1.04129e103	−0.618335	−0.309167	+	0.951008i	$0.600050\pi$
$150$	0	0
$151$	−1.59249e103	−0.501964	−0.250982	−	0.967992i	$-0.580753\pi$
$151$	−1.59249e103	−0.501964	−0.250982	+	0.967992i	$0.580753\pi$
$152$	−5.95161e103	−1.37108
$153$	0	0
$154$	−3.56470e103	−0.441356
$155$	2.59331e104	2.36101
$156$	0	0
$157$	1.96027e104	0.970695	0.485348	−	0.874321i	$-0.338693\pi$
$157$	1.96027e104	0.970695	0.485348	+	0.874321i	$0.338693\pi$
$158$	−2.45217e103	−0.0898129
$159$	0	0
$160$	5.83008e104	1.17483
$161$	−8.20261e103	−0.122948
$162$	0	0
$163$	−5.17949e104	−0.431893	−0.215946	−	0.976405i	$-0.569284\pi$
$163$	−5.17949e104	−0.431893	−0.215946	+	0.976405i	$0.569284\pi$
$164$	−5.03931e104	−0.314259
$165$	0	0
$166$	2.47724e105	0.868629
$167$	2.44321e105	0.644064	0.322032	−	0.946729i	$-0.395634\pi$
$167$	2.44321e105	0.644064	0.322032	+	0.946729i	$0.395634\pi$
$168$	0	0
$169$	3.27797e105	0.490892
$170$	−2.06401e105	−0.233555
$171$	0	0
$172$	1.15806e104	0.00751845
$173$	−8.48274e105	−0.418164	−0.209082	−	0.977898i	$-0.567047\pi$
$173$	−8.48274e105	−0.418164	−0.209082	+	0.977898i	$0.567047\pi$
$174$	0	0
$175$	1.85283e106	0.529089
$176$	−6.14003e106	−1.33758
$177$	0	0
$178$	−9.16344e106	−1.16710
$179$	−4.09354e106	−0.399559	−0.199779	−	0.979841i	$-0.564023\pi$
$179$	−4.09354e106	−0.399559	−0.199779	+	0.979841i	$0.564023\pi$
$180$	0	0
$181$	3.39061e106	0.195229	0.0976147	−	0.995224i	$-0.468879\pi$
$181$	3.39061e106	0.195229	0.0976147	+	0.995224i	$0.468879\pi$
$182$	1.12516e107	0.498681
$183$	0	0
$184$	−9.68503e106	−0.255420
$185$	−7.10357e107	−1.44817
$186$	0	0
$187$	1.10119e107	0.134705
$188$	3.74396e107	0.355495
$189$	0	0
$190$	6.21321e108	3.56878
$191$	1.24535e108	0.557450	0.278725	−	0.960371i	$-0.410088\pi$
$191$	1.24535e108	0.557450	0.278725	+	0.960371i	$0.410088\pi$
$192$	0	0
$193$	1.34117e107	0.0366026	0.0183013	−	0.999833i	$-0.494174\pi$
$193$	1.34117e107	0.0366026	0.0183013	+	0.999833i	$0.494174\pi$
$194$	−7.43529e108	−1.58751
$195$	0	0
$196$	−2.61142e108	−0.342542
$197$	−7.02757e108	−0.723868	−0.361934	−	0.932204i	$-0.617883\pi$
$197$	−7.02757e108	−0.723868	−0.361934	+	0.932204i	$0.617883\pi$
$198$	0	0
$199$	−1.04024e109	−0.663149	−0.331575	−	0.943429i	$-0.607580\pi$
$199$	−1.04024e109	−0.663149	−0.331575	+	0.943429i	$0.607580\pi$
$200$	2.18769e109	1.09916
$201$	0	0
$202$	−7.48653e107	−0.0234472
$203$	−7.47655e108	−0.185199
$204$	0	0
$205$	−8.25338e109	−1.28329
$206$	1.09189e110	1.34736
$207$	0	0
$208$	1.93803e110	1.51131
$209$	−3.31486e110	−2.05834
$210$	0	0
$211$	−6.82443e109	−0.269556	−0.134778	−	0.990876i	$-0.543032\pi$
$211$	−6.82443e109	−0.269556	−0.134778	+	0.990876i	$0.543032\pi$
$212$	2.16703e110	0.683773
$213$	0	0
$214$	−5.04224e110	−1.01852
$215$	1.89667e109	0.0307018
$216$	0	0
$217$	4.93563e110	0.514642
$218$	2.14284e111	1.79600
$219$	0	0
$220$	1.23120e111	0.668728
$221$	−3.47578e110	−0.152202
$222$	0	0
$223$	5.51903e110	0.157537	0.0787683	−	0.996893i	$-0.474901\pi$
$223$	5.51903e110	0.157537	0.0787683	+	0.996893i	$0.474901\pi$
$224$	1.10959e111	0.256084
$225$	0	0
$226$	−4.37602e111	−0.662107
$227$	−1.13992e112	−1.39844	−0.699222	−	0.714905i	$-0.746470\pi$
$227$	−1.13992e112	−1.39844	−0.699222	+	0.714905i	$0.746470\pi$
$228$	0	0
$229$	−2.01230e112	−1.62745	−0.813724	−	0.581252i	$-0.802563\pi$
$229$	−2.01230e112	−1.62745	−0.813724	+	0.581252i	$0.802563\pi$
$230$	1.01107e112	0.664830
$231$	0	0
$232$	−8.82775e111	−0.384743
$233$	1.66461e112	0.591435	0.295718	−	0.955275i	$-0.404441\pi$
$233$	1.66461e112	0.591435	0.295718	+	0.955275i	$0.404441\pi$
$234$	0	0
$235$	6.13186e112	1.45167
$236$	1.80747e112	0.349744
$237$	0	0
$238$	−3.92827e111	−0.0509092
$239$	−1.78548e112	−0.189608	−0.0948038	−	0.995496i	$-0.530222\pi$
$239$	−1.78548e112	−0.189608	−0.0948038	+	0.995496i	$0.530222\pi$
$240$	0	0
$241$	1.84544e113	1.31914	0.659571	−	0.751643i	$-0.270738\pi$
$241$	1.84544e113	1.31914	0.659571	+	0.751643i	$0.270738\pi$
$242$	−3.36888e112	−0.197813
$243$	0	0
$244$	1.16929e113	0.464416
$245$	−4.27699e113	−1.39878
$246$	0	0
$247$	1.04630e114	2.32568
$248$	5.82763e113	1.06915
$249$	0	0
$250$	−7.88149e113	−0.987320
$251$	9.74969e113	1.01039	0.505195	−	0.863005i	$-0.331421\pi$
$251$	9.74969e113	1.01039	0.505195	+	0.863005i	$0.331421\pi$
$252$	0	0
$253$	−5.39426e113	−0.383448
$254$	1.10433e114	0.650875
$255$	0	0
$256$	2.49669e114	1.01383
$257$	−4.79912e114	−1.61934	−0.809671	−	0.586884i	$-0.800354\pi$
$257$	−4.79912e114	−1.61934	−0.809671	+	0.586884i	$0.800354\pi$
$258$	0	0
$259$	−1.35197e114	−0.315665
$260$	−3.88613e114	−0.755585
$261$	0	0
$262$	−3.07654e114	−0.415673
$263$	8.59726e114	0.969309	0.484654	−	0.874706i	$-0.338945\pi$
$263$	8.59726e114	0.969309	0.484654	+	0.874706i	$0.338945\pi$
$264$	0	0
$265$	3.54917e115	2.79220
$266$	1.18251e115	0.777907
$267$	0	0
$268$	−1.36454e115	−0.628902
$269$	4.76127e115	1.83861	0.919305	−	0.393546i	$-0.128752\pi$
$269$	4.76127e115	1.83861	0.919305	+	0.393546i	$0.128752\pi$
$270$	0	0
$271$	3.00132e115	0.815212	0.407606	−	0.913158i	$-0.366364\pi$
$271$	3.00132e115	0.815212	0.407606	+	0.913158i	$0.366364\pi$
$272$	−6.76626e114	−0.154286
$273$	0	0
$274$	6.76745e115	1.08962
$275$	1.21847e116	1.65011
$276$	0	0
$277$	1.42446e115	0.136729	0.0683647	−	0.997660i	$-0.478222\pi$
$277$	1.42446e115	0.136729	0.0683647	+	0.997660i	$0.478222\pi$
$278$	2.12164e115	0.171610
$279$	0	0
$280$	6.89043e115	0.396497
$281$	−5.39650e115	−0.262158	−0.131079	−	0.991372i	$-0.541844\pi$
$281$	−5.39650e115	−0.262158	−0.131079	+	0.991372i	$0.541844\pi$
$282$	0	0
$283$	3.65205e116	1.26672	0.633361	−	0.773857i	$-0.281675\pi$
$283$	3.65205e116	1.26672	0.633361	+	0.773857i	$0.281675\pi$
$284$	−9.97147e114	−0.0292508
$285$	0	0
$286$	7.39935e116	1.55528
$287$	−1.57080e116	−0.279725
$288$	0	0
$289$	−7.68859e116	−0.984462
$290$	9.21578e116	1.00144
$291$	0	0
$292$	1.56025e116	0.122323
$293$	−1.22883e117	−0.818990	−0.409495	−	0.912312i	$-0.634295\pi$
$293$	−1.22883e117	−0.818990	−0.409495	+	0.912312i	$0.634295\pi$
$294$	0	0
$295$	2.96027e117	1.42819
$296$	−1.59630e117	−0.655780
$297$	0	0
$298$	2.44282e117	0.728817
$299$	1.70264e117	0.433252
$300$	0	0
$301$	3.60977e115	0.00669223
$302$	3.73592e117	0.591653
$303$	0	0
$304$	2.03682e118	2.35753
$305$	1.91507e118	1.89645
$306$	0	0
$307$	1.46735e117	0.106527	0.0532635	−	0.998580i	$-0.483038\pi$
$307$	1.46735e117	0.106527	0.0532635	+	0.998580i	$0.483038\pi$
$308$	2.34324e117	0.145766
$309$	0	0
$310$	−6.08378e118	−2.78287
$311$	−3.27509e118	−1.28560	−0.642799	−	0.766035i	$-0.722227\pi$
$311$	−3.27509e118	−1.28560	−0.642799	+	0.766035i	$0.722227\pi$
$312$	0	0
$313$	−2.81510e118	−0.814964	−0.407482	−	0.913213i	$-0.633593\pi$
$313$	−2.81510e118	−0.814964	−0.407482	+	0.913213i	$0.633593\pi$
$314$	−4.59871e118	−1.14414
$315$	0	0
$316$	1.61192e117	0.0296624
$317$	−1.14868e118	−0.181921	−0.0909604	−	0.995855i	$-0.528994\pi$
$317$	−1.14868e118	−0.181921	−0.0909604	+	0.995855i	$0.528994\pi$
$318$	0	0
$319$	−4.91678e118	−0.577595
$320$	5.75642e118	0.582812
$321$	0	0
$322$	1.92429e118	0.144916
$323$	−3.65295e118	−0.237423
$324$	0	0
$325$	−3.84597e119	−1.86443
$326$	1.21509e119	0.509062
$327$	0	0
$328$	−1.85468e119	−0.581115
$329$	1.16703e119	0.316429
$330$	0	0
$331$	4.87830e119	0.991834	0.495917	−	0.868370i	$-0.334832\pi$
$331$	4.87830e119	0.991834	0.495917	+	0.868370i	$0.334832\pi$
$332$	−1.62840e119	−0.286881
$333$	0	0
$334$	−5.73167e119	−0.759143
$335$	−2.23484e120	−2.56814
$336$	0	0
$337$	2.24839e119	0.194738	0.0973691	−	0.995248i	$-0.468957\pi$
$337$	2.24839e119	0.194738	0.0973691	+	0.995248i	$0.468957\pi$
$338$	−7.68996e119	−0.578603
$339$	0	0
$340$	1.35677e119	0.0771359
$341$	3.24581e120	1.60505
$342$	0	0
$343$	−1.73908e120	−0.651401
$344$	4.26215e118	0.0139028
$345$	0	0
$346$	1.99001e120	0.492880
$347$	−5.72676e120	−1.23668	−0.618342	−	0.785909i	$-0.712195\pi$
$347$	−5.72676e120	−1.23668	−0.618342	+	0.785909i	$0.712195\pi$
$348$	0	0
$349$	−1.19478e121	−1.96372	−0.981860	−	0.189608i	$-0.939278\pi$
$349$	−1.19478e121	−1.96372	−0.981860	+	0.189608i	$0.939278\pi$
$350$	−4.34666e120	−0.623625
$351$	0	0
$352$	7.29698e120	0.798669
$353$	1.63379e121	1.56278	0.781391	−	0.624042i	$-0.214511\pi$
$353$	1.63379e121	1.56278	0.781391	+	0.624042i	$0.214511\pi$
$354$	0	0
$355$	−1.63313e120	−0.119446
$356$	6.02353e120	0.385457
$357$	0	0
$358$	9.60327e120	0.470951
$359$	4.74165e120	0.203677	0.101839	−	0.994801i	$-0.467527\pi$
$359$	4.74165e120	0.203677	0.101839	+	0.994801i	$0.467527\pi$
$360$	0	0
$361$	7.96526e121	2.62790
$362$	−7.95421e120	−0.230112
$363$	0	0
$364$	−7.39616e120	−0.164699
$365$	2.55538e121	0.499510
$366$	0	0
$367$	−1.06281e122	−1.60258	−0.801288	−	0.598278i	$-0.795852\pi$
$367$	−1.06281e122	−1.60258	−0.801288	+	0.598278i	$0.795852\pi$
$368$	3.31451e121	0.439185
$369$	0	0
$370$	1.66647e122	1.70692
$371$	6.75484e121	0.608632
$372$	0	0
$373$	−5.89096e121	−0.411165	−0.205583	−	0.978640i	$-0.565909\pi$
$373$	−5.89096e121	−0.411165	−0.205583	+	0.978640i	$0.565909\pi$
$374$	−2.58334e121	−0.158774
$375$	0	0
$376$	1.37794e122	0.657367
$377$	1.55193e122	0.652615
$378$	0	0
$379$	1.50810e122	0.493251	0.246625	−	0.969111i	$-0.420678\pi$
$379$	1.50810e122	0.493251	0.246625	+	0.969111i	$0.420678\pi$
$380$	−4.08422e122	−1.17866
$381$	0	0
$382$	−2.92153e122	−0.657054
$383$	2.95525e122	0.587019	0.293510	−	0.955956i	$-0.405177\pi$
$383$	2.95525e122	0.587019	0.293510	+	0.955956i	$0.405177\pi$
$384$	0	0
$385$	3.83775e122	0.595240
$386$	−3.14633e121	−0.0431426
$387$	0	0
$388$	4.88754e122	0.524304
$389$	−3.87600e122	−0.367940	−0.183970	−	0.982932i	$-0.558895\pi$
$389$	−3.87600e122	−0.367940	−0.183970	+	0.982932i	$0.558895\pi$
$390$	0	0
$391$	−5.94442e121	−0.0442297
$392$	−9.61117e122	−0.633415
$393$	0	0
$394$	1.64864e123	0.853207
$395$	2.64000e122	0.121127
$396$	0	0
$397$	−1.52456e122	−0.0550294	−0.0275147	−	0.999621i	$-0.508759\pi$
$397$	−1.52456e122	−0.0550294	−0.0275147	+	0.999621i	$0.508759\pi$
$398$	2.44035e123	0.781639
$399$	0	0
$400$	−7.48691e123	−1.88996
$401$	−5.92751e123	−1.32897	−0.664484	−	0.747303i	$-0.731349\pi$
$401$	−5.92751e123	−1.32897	−0.664484	+	0.747303i	$0.731349\pi$
$402$	0	0
$403$	−1.02450e124	−1.81352
$404$	4.92122e121	0.00774387
$405$	0	0
$406$	1.75396e123	0.218290
$407$	−8.89089e123	−0.984489
$408$	0	0
$409$	−1.54933e124	−1.35921	−0.679606	−	0.733577i	$-0.737849\pi$
$409$	−1.54933e124	−1.35921	−0.679606	+	0.733577i	$0.737849\pi$
$410$	1.93621e124	1.51258
$411$	0	0
$412$	−7.17744e123	−0.444992
$413$	5.63404e123	0.311310
$414$	0	0
$415$	−2.66699e124	−1.17149
$416$	−2.30321e124	−0.902403
$417$	0	0
$418$	7.77651e124	2.42612
$419$	−6.74054e123	−0.187728	−0.0938639	−	0.995585i	$-0.529922\pi$
$419$	−6.74054e123	−0.187728	−0.0938639	+	0.995585i	$0.529922\pi$
$420$	0	0
$421$	−1.49665e124	−0.332446	−0.166223	−	0.986088i	$-0.553157\pi$
$421$	−1.49665e124	−0.332446	−0.166223	+	0.986088i	$0.553157\pi$
$422$	1.60098e124	0.317720
$423$	0	0
$424$	7.97562e124	1.26440
$425$	1.34275e124	0.190335
$426$	0	0
$427$	3.64480e124	0.413380
$428$	3.31448e124	0.336385
$429$	0	0
$430$	−4.44949e123	−0.0361875
$431$	−1.57092e125	−1.14415	−0.572076	−	0.820201i	$-0.693862\pi$
$431$	−1.57092e125	−1.14415	−0.572076	+	0.820201i	$0.693862\pi$
$432$	0	0
$433$	−1.36231e125	−0.796344	−0.398172	−	0.917311i	$-0.630355\pi$
$433$	−1.36231e125	−0.796344	−0.398172	+	0.917311i	$0.630355\pi$
$434$	−1.15788e125	−0.606597
$435$	0	0
$436$	−1.40858e125	−0.593162
$437$	1.78942e125	0.675842
$438$	0	0
$439$	4.13575e125	1.25745	0.628723	−	0.777629i	$-0.283578\pi$
$439$	4.13575e125	1.25745	0.628723	+	0.777629i	$0.283578\pi$
$440$	4.53133e125	1.23658
$441$	0	0
$442$	8.15402e124	0.179397
$443$	−3.49485e125	−0.690639	−0.345319	−	0.938485i	$-0.612229\pi$
$443$	−3.49485e125	−0.690639	−0.345319	+	0.938485i	$0.612229\pi$
$444$	0	0
$445$	9.86534e125	1.57402
$446$	−1.29474e125	−0.185685
$447$	0	0
$448$	1.09557e125	0.127039
$449$	7.11658e125	0.742284	0.371142	−	0.928576i	$-0.378966\pi$
$449$	7.11658e125	0.742284	0.371142	+	0.928576i	$0.378966\pi$
$450$	0	0
$451$	−1.03300e126	−0.872398
$452$	2.87655e125	0.218673
$453$	0	0
$454$	2.67419e126	1.64831
$455$	−1.21134e126	−0.672552
$456$	0	0
$457$	−3.50368e126	−1.57945	−0.789724	−	0.613462i	$-0.789776\pi$
$457$	−3.50368e126	−1.57945	−0.789724	+	0.613462i	$0.789776\pi$
$458$	4.72076e126	1.91824
$459$	0	0
$460$	−6.64623e125	−0.219573
$461$	−3.10796e126	−0.926150	−0.463075	−	0.886319i	$-0.653254\pi$
$461$	−3.10796e126	−0.926150	−0.463075	+	0.886319i	$0.653254\pi$
$462$	0	0
$463$	−7.74133e125	−0.187810	−0.0939050	−	0.995581i	$-0.529935\pi$
$463$	−7.74133e125	−0.187810	−0.0939050	+	0.995581i	$0.529935\pi$
$464$	3.02112e126	0.661552
$465$	0	0
$466$	−3.90511e126	−0.697111
$467$	−8.79545e126	−1.41810	−0.709049	−	0.705159i	$-0.750875\pi$
$467$	−8.79545e126	−1.41810	−0.709049	+	0.705159i	$0.750875\pi$
$468$	0	0
$469$	−4.25339e126	−0.559790
$470$	−1.43851e127	−1.71105
$471$	0	0
$472$	6.65226e126	0.646732
$473$	2.37388e125	0.0208716
$474$	0	0
$475$	−4.04201e127	−2.90838
$476$	2.58222e125	0.0168137
$477$	0	0
$478$	4.18867e126	0.223486
$479$	−2.97559e127	−1.43760	−0.718798	−	0.695219i	$-0.755307\pi$
$479$	−2.97559e127	−1.43760	−0.718798	+	0.695219i	$0.755307\pi$
$480$	0	0
$481$	2.80631e127	1.11236
$482$	−4.32933e127	−1.55484
$483$	0	0
$484$	2.21451e126	0.0653315
$485$	8.00481e127	2.14101
$486$	0	0
$487$	−3.69546e127	−0.812911	−0.406455	−	0.913671i	$-0.633235\pi$
$487$	−3.69546e127	−0.812911	−0.406455	+	0.913671i	$0.633235\pi$
$488$	4.30351e127	0.858779
$489$	0	0
$490$	1.00336e128	1.64871
$491$	2.26267e127	0.337481	0.168741	−	0.985660i	$-0.446030\pi$
$491$	2.26267e127	0.337481	0.168741	+	0.985660i	$0.446030\pi$
$492$	0	0
$493$	−5.41825e126	−0.0666239
$494$	−2.45457e128	−2.74123
$495$	0	0
$496$	−1.99439e128	−1.83836
$497$	−3.10820e126	−0.0260364
$498$	0	0
$499$	1.13378e128	0.784786	0.392393	−	0.919798i	$-0.371647\pi$
$499$	1.13378e128	0.784786	0.392393	+	0.919798i	$0.371647\pi$
$500$	5.18085e127	0.326081
$501$	0	0
$502$	−2.28723e128	−1.19092
$503$	1.72721e128	0.818214	0.409107	−	0.912486i	$-0.365840\pi$
$503$	1.72721e128	0.818214	0.409107	+	0.912486i	$0.365840\pi$
$504$	0	0
$505$	8.05997e126	0.0316223
$506$	1.26547e128	0.451962
$507$	0	0
$508$	−7.25925e127	−0.214964
$509$	−5.19969e128	−1.40243	−0.701217	−	0.712948i	$-0.747360\pi$
$509$	−5.19969e128	−1.40243	−0.701217	+	0.712948i	$0.747360\pi$
$510$	0	0
$511$	4.86345e127	0.108881
$512$	−1.16571e127	−0.0237830
$513$	0	0
$514$	1.12585e129	1.90868
$515$	−1.17552e129	−1.81713
$516$	0	0
$517$	7.67469e128	0.986871
$518$	3.17165e128	0.372067
$519$	0	0
$520$	−1.43027e129	−1.39720
$521$	2.82044e128	0.251492	0.125746	−	0.992062i	$-0.459867\pi$
$521$	2.82044e128	0.251492	0.125746	+	0.992062i	$0.459867\pi$
$522$	0	0
$523$	1.04986e129	0.780373	0.390186	−	0.920736i	$-0.372411\pi$
$523$	1.04986e129	0.780373	0.390186	+	0.920736i	$0.372411\pi$
$524$	2.02234e128	0.137284
$525$	0	0
$526$	−2.01688e129	−1.14250
$527$	3.57685e128	0.185138
$528$	0	0
$529$	−2.02164e129	−0.874097
$530$	−8.32618e129	−3.29111
$531$	0	0
$532$	−7.77316e128	−0.256918
$533$	3.26055e129	0.985708
$534$	0	0
$535$	5.42846e129	1.37364
$536$	−5.02209e129	−1.16294
$537$	0	0
$538$	−1.11697e130	−2.16713
$539$	−5.35312e129	−0.950913
$540$	0	0
$541$	−1.09474e130	−1.63095	−0.815475	−	0.578792i	$-0.803524\pi$
$541$	−1.09474e130	−1.63095	−0.815475	+	0.578792i	$0.803524\pi$
$542$	−7.04096e129	−0.960872
$543$	0	0
$544$	8.04121e128	0.0921242
$545$	−2.30697e130	−2.42219
$546$	0	0
$547$	−9.31044e129	−0.821433	−0.410717	−	0.911763i	$-0.634721\pi$
$547$	−9.31044e129	−0.821433	−0.410717	+	0.911763i	$0.634721\pi$
$548$	−4.44854e129	−0.359866
$549$	0	0
$550$	−2.85848e130	−1.94495
$551$	1.63103e130	1.01803
$552$	0	0
$553$	5.02450e128	0.0264027
$554$	−3.34173e129	−0.161160
$555$	0	0
$556$	−1.39465e129	−0.0566776
$557$	9.20667e129	0.343543	0.171771	−	0.985137i	$-0.445051\pi$
$557$	9.20667e129	0.343543	0.171771	+	0.985137i	$0.445051\pi$
$558$	0	0
$559$	−7.49290e128	−0.0235825
$560$	−2.35811e130	−0.681762
$561$	0	0
$562$	1.26600e130	0.308999
$563$	−3.58585e130	−0.804348	−0.402174	−	0.915563i	$-0.631745\pi$
$563$	−3.58585e130	−0.804348	−0.402174	+	0.915563i	$0.631745\pi$
$564$	0	0
$565$	4.71121e130	0.892958
$566$	−8.56755e130	−1.49306
$567$	0	0
$568$	−3.66993e129	−0.0540894
$569$	−1.14908e131	−1.55782	−0.778911	−	0.627134i	$-0.784228\pi$
$569$	−1.14908e131	−1.55782	−0.778911	+	0.627134i	$0.784228\pi$
$570$	0	0
$571$	−1.05014e131	−1.20513	−0.602564	−	0.798071i	$-0.705854\pi$
$571$	−1.05014e131	−1.20513	−0.602564	+	0.798071i	$0.705854\pi$
$572$	−4.86392e130	−0.513659
$573$	0	0
$574$	3.68502e130	0.329705
$575$	−6.57754e130	−0.541802
$576$	0	0
$577$	−8.12255e130	−0.567337	−0.283669	−	0.958922i	$-0.591552\pi$
$577$	−8.12255e130	−0.567337	−0.283669	+	0.958922i	$0.591552\pi$
$578$	1.80371e131	1.16036
$579$	0	0
$580$	−6.05793e130	−0.330746
$581$	−5.07587e130	−0.255355
$582$	0	0
$583$	4.44217e131	1.89818
$584$	5.74240e130	0.226195
$585$	0	0
$586$	2.88277e131	0.965325
$587$	−4.95615e131	−1.53051	−0.765253	−	0.643730i	$-0.777386\pi$
$587$	−4.95615e131	−1.53051	−0.765253	+	0.643730i	$0.777386\pi$
$588$	0	0
$589$	−1.07672e132	−2.82897
$590$	−6.94466e131	−1.68337
$591$	0	0
$592$	5.46302e131	1.12759
$593$	4.41739e131	0.841527	0.420763	−	0.907170i	$-0.361762\pi$
$593$	4.41739e131	0.841527	0.420763	+	0.907170i	$0.361762\pi$
$594$	0	0
$595$	4.22917e130	0.0686593
$596$	−1.60577e131	−0.240706
$597$	0	0
$598$	−3.99431e131	−0.510665
$599$	5.19239e131	0.613187	0.306594	−	0.951841i	$-0.400811\pi$
$599$	5.19239e131	0.613187	0.306594	+	0.951841i	$0.400811\pi$
$600$	0	0
$601$	−4.50468e131	−0.454074	−0.227037	−	0.973886i	$-0.572904\pi$
$601$	−4.50468e131	−0.454074	−0.227037	+	0.973886i	$0.572904\pi$
$602$	−8.46836e129	−0.00788798
$603$	0	0
$604$	−2.45578e131	−0.195405
$605$	3.62692e131	0.266783
$606$	0	0
$607$	−1.48875e132	−0.936178	−0.468089	−	0.883681i	$-0.655057\pi$
$607$	−1.48875e132	−0.936178	−0.468089	+	0.883681i	$0.655057\pi$
$608$	−2.42061e132	−1.40768
$609$	0	0
$610$	−4.49267e132	−2.23531
$611$	−2.42243e132	−1.11505
$612$	0	0
$613$	−1.17585e131	−0.0463423	−0.0231712	−	0.999732i	$-0.507376\pi$
$613$	−1.17585e131	−0.0463423	−0.0231712	+	0.999732i	$0.507376\pi$
$614$	−3.44233e131	−0.125561
$615$	0	0
$616$	8.62412e131	0.269545
$617$	−1.28747e132	−0.372556	−0.186278	−	0.982497i	$-0.559642\pi$
$617$	−1.28747e132	−0.372556	−0.186278	+	0.982497i	$0.559642\pi$
$618$	0	0
$619$	−3.57292e131	−0.0886578	−0.0443289	−	0.999017i	$-0.514115\pi$
$619$	−3.57292e131	−0.0886578	−0.0443289	+	0.999017i	$0.514115\pi$
$620$	3.99913e132	0.919096
$621$	0	0
$622$	7.68323e132	1.51531
$623$	1.87759e132	0.343098
$624$	0	0
$625$	−1.24506e132	−0.195384
$626$	6.60411e132	0.960580
$627$	0	0
$628$	3.02293e132	0.377873
$629$	−9.79768e131	−0.113558
$630$	0	0
$631$	8.05657e132	0.803074	0.401537	−	0.915843i	$-0.368476\pi$
$631$	8.05657e132	0.803074	0.401537	+	0.915843i	$0.368476\pi$
$632$	5.93255e131	0.0548505
$633$	0	0
$634$	2.69474e132	0.214426
$635$	−1.18892e133	−0.877810
$636$	0	0
$637$	1.68965e133	1.07442
$638$	1.15345e133	0.680798
$639$	0	0
$640$	−3.65996e133	−1.86178
$641$	1.70084e133	0.803354	0.401677	−	0.915781i	$-0.368428\pi$
$641$	1.70084e133	0.803354	0.401677	+	0.915781i	$0.368428\pi$
$642$	0	0
$643$	3.55754e133	1.44920	0.724600	−	0.689170i	$-0.242025\pi$
$643$	3.55754e133	1.44920	0.724600	+	0.689170i	$0.242025\pi$
$644$	−1.26492e132	−0.0478614
$645$	0	0
$646$	8.56965e132	0.279846
$647$	3.43446e133	1.04209	0.521044	−	0.853530i	$-0.325543\pi$
$647$	3.43446e133	1.04209	0.521044	+	0.853530i	$0.325543\pi$
$648$	0	0
$649$	3.70510e133	0.970905
$650$	9.02248e133	2.19756
$651$	0	0
$652$	−7.98729e132	−0.168127
$653$	4.55143e133	0.890783	0.445391	−	0.895336i	$-0.353065\pi$
$653$	4.55143e133	0.890783	0.445391	+	0.895336i	$0.353065\pi$
$654$	0	0
$655$	3.31220e133	0.560602
$656$	6.34728e133	0.999206
$657$	0	0
$658$	−2.73780e133	−0.372968
$659$	1.09030e134	1.38194	0.690969	−	0.722884i	$-0.257184\pi$
$659$	1.09030e134	1.38194	0.690969	+	0.722884i	$0.257184\pi$
$660$	0	0
$661$	7.88900e133	0.865870	0.432935	−	0.901425i	$-0.357478\pi$
$661$	7.88900e133	0.865870	0.432935	+	0.901425i	$0.357478\pi$
$662$	−1.14443e134	−1.16905
$663$	0	0
$664$	−5.99321e133	−0.530489
$665$	−1.27309e134	−1.04913
$666$	0	0
$667$	2.65417e133	0.189650
$668$	3.76767e133	0.250721
$669$	0	0
$670$	5.24284e134	3.02700
$671$	2.39692e134	1.28924
$672$	0	0
$673$	−3.42957e134	−1.60149	−0.800745	−	0.599006i	$-0.795563\pi$
$673$	−3.42957e134	−1.60149	−0.800745	+	0.599006i	$0.795563\pi$
$674$	−5.27462e133	−0.229534
$675$	0	0
$676$	5.05495e133	0.191095
$677$	−4.77519e133	−0.168278	−0.0841392	−	0.996454i	$-0.526814\pi$
$677$	−4.77519e133	−0.168278	−0.0841392	+	0.996454i	$0.526814\pi$
$678$	0	0
$679$	1.52349e134	0.466687
$680$	4.99349e133	0.142637
$681$	0	0
$682$	−7.61451e134	−1.89184
$683$	3.47812e134	0.806048	0.403024	−	0.915189i	$-0.367959\pi$
$683$	3.47812e134	0.806048	0.403024	+	0.915189i	$0.367959\pi$
$684$	0	0
$685$	−7.28582e134	−1.46952
$686$	4.07980e134	0.767792
$687$	0	0
$688$	−1.45863e133	−0.0239054
$689$	−1.40212e135	−2.14473
$690$	0	0
$691$	−3.20714e134	−0.427475	−0.213738	−	0.976891i	$-0.568564\pi$
$691$	−3.20714e134	−0.427475	−0.213738	+	0.976891i	$0.568564\pi$
$692$	−1.30812e134	−0.162783
$693$	0	0
$694$	1.34347e135	1.45765
$695$	−2.28415e134	−0.231444
$696$	0	0
$697$	−1.13836e134	−0.100629
$698$	2.80290e135	2.31459
$699$	0	0
$700$	2.85725e134	0.205964
$701$	−7.30037e134	−0.491744	−0.245872	−	0.969302i	$-0.579074\pi$
$701$	−7.30037e134	−0.491744	−0.245872	+	0.969302i	$0.579074\pi$
$702$	0	0
$703$	2.94935e135	1.73520
$704$	7.20479e134	0.396205
$705$	0	0
$706$	−3.83280e135	−1.84202
$707$	1.53399e133	0.00689288
$708$	0	0
$709$	4.15680e135	1.63329	0.816644	−	0.577142i	$-0.195832\pi$
$709$	4.15680e135	1.63329	0.816644	+	0.577142i	$0.195832\pi$
$710$	3.83124e134	0.140789
$711$	0	0
$712$	2.21692e135	0.712771
$713$	−1.75215e135	−0.527009
$714$	0	0
$715$	−7.96612e135	−2.09754
$716$	−6.31265e134	−0.155540
$717$	0	0
$718$	−1.11237e135	−0.240070
$719$	5.33664e135	1.07807	0.539033	−	0.842285i	$-0.318790\pi$
$719$	5.33664e135	1.07807	0.539033	+	0.842285i	$0.318790\pi$
$720$	0	0
$721$	−2.23728e135	−0.396090
$722$	−1.86862e136	−3.09744
$723$	0	0
$724$	5.22865e134	0.0759990
$725$	−5.99533e135	−0.816127
$726$	0	0
$727$	1.15888e136	1.38406	0.692031	−	0.721868i	$-0.256716\pi$
$727$	1.15888e136	1.38406	0.692031	+	0.721868i	$0.256716\pi$
$728$	−2.72211e135	−0.304555
$729$	0	0
$730$	−5.99481e135	−0.588761
$731$	2.61600e133	0.00240748
$732$	0	0
$733$	1.10067e136	0.889645	0.444822	−	0.895619i	$-0.353267\pi$
$733$	1.10067e136	0.889645	0.444822	+	0.895619i	$0.353267\pi$
$734$	2.49331e136	1.88892
$735$	0	0
$736$	−3.93905e135	−0.262238
$737$	−2.79715e136	−1.74586
$738$	0	0
$739$	−7.30942e135	−0.401118	−0.200559	−	0.979682i	$-0.564276\pi$
$739$	−7.30942e135	−0.401118	−0.200559	+	0.979682i	$0.564276\pi$
$740$	−1.09544e136	−0.563744
$741$	0	0
$742$	−1.58466e136	−0.717380
$743$	−3.66143e136	−1.55483	−0.777414	−	0.628989i	$-0.783469\pi$
$743$	−3.66143e136	−1.55483	−0.777414	+	0.628989i	$0.783469\pi$
$744$	0	0
$745$	−2.62993e136	−0.982928
$746$	1.38199e136	0.484631
$747$	0	0
$748$	1.69814e135	0.0524382
$749$	1.03316e136	0.299419
$750$	0	0
$751$	2.09910e136	0.535964	0.267982	−	0.963424i	$-0.413643\pi$
$751$	2.09910e136	0.535964	0.267982	+	0.963424i	$0.413643\pi$
$752$	−4.71572e136	−1.13032
$753$	0	0
$754$	−3.64075e136	−0.769223
$755$	−4.02208e136	−0.797940
$756$	0	0
$757$	−7.34784e136	−1.28560	−0.642799	−	0.766035i	$-0.722227\pi$
$757$	−7.34784e136	−1.28560	−0.642799	+	0.766035i	$0.722227\pi$
$758$	−3.53793e136	−0.581383
$759$	0	0
$760$	−1.50317e137	−2.17953
$761$	9.58660e136	1.30585	0.652925	−	0.757422i	$-0.273541\pi$
$761$	9.58660e136	1.30585	0.652925	+	0.757422i	$0.273541\pi$
$762$	0	0
$763$	−4.39068e136	−0.527978
$764$	1.92045e136	0.217005
$765$	0	0
$766$	−6.93288e136	−0.691906
$767$	−1.16947e137	−1.09701
$768$	0	0
$769$	1.57789e137	1.30790	0.653950	−	0.756538i	$-0.273111\pi$
$769$	1.57789e137	1.30790	0.653950	+	0.756538i	$0.273111\pi$
$770$	−9.00319e136	−0.701596
$771$	0	0
$772$	2.06822e135	0.0142487
$773$	−1.75047e137	−1.13404	−0.567021	−	0.823703i	$-0.691904\pi$
$773$	−1.75047e137	−1.13404	−0.567021	+	0.823703i	$0.691904\pi$
$774$	0	0
$775$	3.95781e137	2.26790
$776$	1.79883e137	0.969522
$777$	0	0
$778$	9.09291e136	0.433683
$779$	3.42675e137	1.53763
$780$	0	0
$781$	−2.04404e136	−0.0812016
$782$	1.39454e136	0.0521325
$783$	0	0
$784$	3.28923e137	1.08913
$785$	4.95096e137	1.54305
$786$	0	0
$787$	6.72817e137	1.85822	0.929110	−	0.369804i	$-0.120575\pi$
$787$	6.72817e137	1.85822	0.929110	+	0.369804i	$0.120575\pi$
$788$	−1.08372e137	−0.281788
$789$	0	0
$790$	−6.19332e136	−0.142770
$791$	8.96646e136	0.194643
$792$	0	0
$793$	−7.56561e137	−1.45669
$794$	3.57655e136	0.0648620
$795$	0	0
$796$	−1.60415e137	−0.258151
$797$	−3.20907e137	−0.486530	−0.243265	−	0.969960i	$-0.578218\pi$
$797$	−3.20907e137	−0.486530	−0.243265	+	0.969960i	$0.578218\pi$
$798$	0	0
$799$	8.45745e136	0.113833
$800$	8.89765e137	1.12850
$801$	0	0
$802$	1.39057e138	1.56642
$803$	3.19834e137	0.339575
$804$	0	0
$805$	−2.07169e137	−0.195443
$806$	2.40344e138	2.13756
$807$	0	0
$808$	1.81122e136	0.0143196
$809$	−1.47751e138	−1.10147	−0.550737	−	0.834679i	$-0.685653\pi$
$809$	−1.47751e138	−1.10147	−0.550737	+	0.834679i	$0.685653\pi$
$810$	0	0
$811$	−1.90707e138	−1.26438	−0.632189	−	0.774814i	$-0.717844\pi$
$811$	−1.90707e138	−1.26438	−0.632189	+	0.774814i	$0.717844\pi$
$812$	−1.15296e137	−0.0720945
$813$	0	0
$814$	2.08576e138	1.16039
$815$	−1.30816e138	−0.686553
$816$	0	0
$817$	−7.87483e136	−0.0367869
$818$	3.63466e138	1.60207
$819$	0	0
$820$	−1.27275e138	−0.499558
$821$	2.39011e138	0.885358	0.442679	−	0.896680i	$-0.354028\pi$
$821$	2.39011e138	0.885358	0.442679	+	0.896680i	$0.354028\pi$
$822$	0	0
$823$	−9.95240e136	−0.0328424	−0.0164212	−	0.999865i	$-0.505227\pi$
$823$	−9.95240e136	−0.0328424	−0.0164212	+	0.999865i	$0.505227\pi$
$824$	−2.64161e138	−0.822860
$825$	0	0
$826$	−1.32172e138	−0.366934
$827$	2.03165e138	0.532521	0.266261	−	0.963901i	$-0.414212\pi$
$827$	2.03165e138	0.532521	0.266261	+	0.963901i	$0.414212\pi$
$828$	0	0
$829$	5.35269e137	0.125093	0.0625463	−	0.998042i	$-0.480078\pi$
$829$	5.35269e137	0.125093	0.0625463	+	0.998042i	$0.480078\pi$
$830$	6.25664e138	1.38080
$831$	0	0
$832$	−2.27411e138	−0.447666
$833$	−5.89909e137	−0.109685
$834$	0	0
$835$	6.17070e138	1.02383
$836$	−5.11184e138	−0.801270
$837$	0	0
$838$	1.58130e138	0.221271
$839$	−9.72921e138	−1.28642	−0.643212	−	0.765688i	$-0.722399\pi$
$839$	−9.72921e138	−1.28642	−0.643212	+	0.765688i	$0.722399\pi$
$840$	0	0
$841$	−6.04933e138	−0.714328
$842$	3.51108e138	0.391847
$843$	0	0
$844$	−1.05239e138	−0.104933
$845$	8.27900e138	0.780340
$846$	0	0
$847$	6.90283e137	0.0581521
$848$	−2.72949e139	−2.17410
$849$	0	0
$850$	−3.15002e138	−0.224344
$851$	4.79947e138	0.323250
$852$	0	0
$853$	8.37087e138	0.504303	0.252152	−	0.967688i	$-0.418862\pi$
$853$	8.37087e138	0.504303	0.252152	+	0.967688i	$0.418862\pi$
$854$	−8.55054e138	−0.487242
$855$	0	0
$856$	1.21987e139	0.622029
$857$	2.70903e139	1.30685	0.653424	−	0.756992i	$-0.273332\pi$
$857$	2.70903e139	1.30685	0.653424	+	0.756992i	$0.273332\pi$
$858$	0	0
$859$	−2.18967e139	−0.945589	−0.472795	−	0.881173i	$-0.656755\pi$
$859$	−2.18967e139	−0.945589	−0.472795	+	0.881173i	$0.656755\pi$
$860$	2.92484e137	0.0119516
$861$	0	0
$862$	3.68531e139	1.34859
$863$	−2.16635e138	−0.0750267	−0.0375133	−	0.999296i	$-0.511944\pi$
$863$	−2.16635e138	−0.0750267	−0.0375133	+	0.999296i	$0.511944\pi$
$864$	0	0
$865$	−2.14244e139	−0.664728
$866$	3.19592e139	0.938633
$867$	0	0
$868$	7.61123e138	0.200340
$869$	3.30424e138	0.0823442
$870$	0	0
$871$	8.82888e139	1.97262
$872$	−5.18419e139	−1.09685
$873$	0	0
$874$	−4.19791e139	−0.796599
$875$	1.61492e139	0.290247
$876$	0	0
$877$	−5.83625e139	−0.941137	−0.470569	−	0.882363i	$-0.655951\pi$
$877$	−5.83625e139	−0.941137	−0.470569	+	0.882363i	$0.655951\pi$
$878$	−9.70228e139	−1.48212
$879$	0	0
$880$	−1.55076e140	−2.12626
$881$	−9.21046e139	−1.19654	−0.598268	−	0.801296i	$-0.704144\pi$
$881$	−9.21046e139	−1.19654	−0.598268	+	0.801296i	$0.704144\pi$
$882$	0	0
$883$	−4.51820e139	−0.527026	−0.263513	−	0.964656i	$-0.584881\pi$
$883$	−4.51820e139	−0.527026	−0.263513	+	0.964656i	$0.584881\pi$
$884$	−5.36000e138	−0.0592491
$885$	0	0
$886$	8.19875e139	0.814040
$887$	1.77330e140	1.66883	0.834414	−	0.551139i	$-0.185807\pi$
$887$	1.77330e140	1.66883	0.834414	+	0.551139i	$0.185807\pi$
$888$	0	0
$889$	−2.26278e139	−0.191341
$890$	−2.31436e140	−1.85527
$891$	0	0
$892$	8.51089e138	0.0613259
$893$	−2.54591e140	−1.73940
$894$	0	0
$895$	−1.03389e140	−0.635153
$896$	−6.96572e139	−0.405822
$897$	0	0
$898$	−1.66952e140	−0.874914
$899$	−1.59705e140	−0.793843
$900$	0	0
$901$	4.89523e139	0.218950
$902$	2.42337e140	1.02828
$903$	0	0
$904$	1.05869e140	0.404362
$905$	8.56348e139	0.310344
$906$	0	0
$907$	−1.25161e140	−0.408435	−0.204217	−	0.978926i	$-0.565465\pi$
$907$	−1.25161e140	−0.408435	−0.204217	+	0.978926i	$0.565465\pi$
$908$	−1.75786e140	−0.544387
$909$	0	0
$910$	2.84176e140	0.792722
$911$	−4.72772e140	−1.25178	−0.625892	−	0.779910i	$-0.715265\pi$
$911$	−4.72772e140	−1.25178	−0.625892	+	0.779910i	$0.715265\pi$
$912$	0	0
$913$	−3.33803e140	−0.796395
$914$	8.21949e140	1.86166
$915$	0	0
$916$	−3.10316e140	−0.633533
$917$	6.30384e139	0.122197
$918$	0	0
$919$	4.73889e139	0.0828305	0.0414152	−	0.999142i	$-0.486813\pi$
$919$	4.73889e139	0.0828305	0.0414152	+	0.999142i	$0.486813\pi$
$920$	−2.44610e140	−0.406025
$921$	0	0
$922$	7.29113e140	1.09163
$923$	6.45178e139	0.0917484
$924$	0	0
$925$	−1.08412e141	−1.39106
$926$	1.81608e140	0.221367
$927$	0	0
$928$	−3.59038e140	−0.395013
$929$	1.52587e141	1.59504	0.797520	−	0.603293i	$-0.206145\pi$
$929$	1.52587e141	1.59504	0.797520	+	0.603293i	$0.206145\pi$
$930$	0	0
$931$	1.77578e141	1.67602
$932$	2.56700e140	0.230234
$933$	0	0
$934$	2.06337e141	1.67148
$935$	2.78122e140	0.214133
$936$	0	0
$937$	−4.18019e140	−0.290780	−0.145390	−	0.989374i	$-0.546444\pi$
$937$	−4.18019e140	−0.290780	−0.145390	+	0.989374i	$0.546444\pi$
$938$	9.97827e140	0.659812
$939$	0	0
$940$	9.45594e140	0.565108
$941$	1.40551e141	0.798593	0.399297	−	0.916822i	$-0.369254\pi$
$941$	1.40551e141	0.798593	0.399297	+	0.916822i	$0.369254\pi$
$942$	0	0
$943$	5.57633e140	0.286446
$944$	−2.27660e141	−1.11203
$945$	0	0
$946$	−5.56902e139	−0.0246008
$947$	−1.37847e141	−0.579127	−0.289564	−	0.957159i	$-0.593510\pi$
$947$	−1.37847e141	−0.579127	−0.289564	+	0.957159i	$0.593510\pi$
$948$	0	0
$949$	−1.00952e141	−0.383680
$950$	9.48237e141	3.42804
$951$	0	0
$952$	9.50371e139	0.0310912
$953$	1.95030e141	0.607000	0.303500	−	0.952831i	$-0.401845\pi$
$953$	1.95030e141	0.607000	0.303500	+	0.952831i	$0.401845\pi$
$954$	0	0
$955$	3.14532e141	0.886144
$956$	−2.75339e140	−0.0738105
$957$	0	0
$958$	6.98061e141	1.69446
$959$	−1.38665e141	−0.320320
$960$	0	0
$961$	5.76367e141	1.20598
$962$	−6.58348e141	−1.31111
$963$	0	0
$964$	2.84586e141	0.513516
$965$	3.38733e140	0.0581848
$966$	0	0
$967$	−1.09243e142	−1.70073	−0.850365	−	0.526193i	$-0.823619\pi$
$967$	−1.09243e142	−1.70073	−0.850365	+	0.526193i	$0.823619\pi$
$968$	8.15035e140	0.120808
$969$	0	0
$970$	−1.87789e142	−2.52356
$971$	−1.31822e142	−1.68685	−0.843423	−	0.537251i	$-0.819463\pi$
$971$	−1.31822e142	−1.68685	−0.843423	+	0.537251i	$0.819463\pi$
$972$	0	0
$973$	−4.34724e140	−0.0504492
$974$	8.66938e141	0.958160
$975$	0	0
$976$	−1.47279e142	−1.47664
$977$	1.47379e142	1.40748	0.703742	−	0.710456i	$-0.251511\pi$
$977$	1.47379e142	1.40748	0.703742	+	0.710456i	$0.251511\pi$
$978$	0	0
$979$	1.23475e142	1.07005
$980$	−6.59554e141	−0.544518
$981$	0	0
$982$	−5.30812e141	−0.397782
$983$	7.00451e141	0.500133	0.250067	−	0.968229i	$-0.419547\pi$
$983$	7.00451e141	0.500133	0.250067	+	0.968229i	$0.419547\pi$
$984$	0	0
$985$	−1.77492e142	−1.15069
$986$	1.27110e141	0.0785281
$987$	0	0
$988$	1.61350e142	0.905343
$989$	−1.28147e140	−0.00685304
$990$	0	0
$991$	−9.23865e141	−0.448859	−0.224430	−	0.974490i	$-0.572052\pi$
$991$	−9.23865e141	−0.448859	−0.224430	+	0.974490i	$0.572052\pi$
$992$	2.37018e142	1.09769
$993$	0	0
$994$	7.29170e140	0.0306885
$995$	−2.62728e142	−1.05417
$996$	0	0
$997$	4.50334e142	1.64254	0.821268	−	0.570543i	$-0.193267\pi$
$997$	4.50334e142	1.64254	0.821268	+	0.570543i	$0.193267\pi$
$998$	−2.65979e142	−0.925009
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.96.a.c.1.2		8
3.2	odd	2		1.96.a.a.1.7	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.96.a.a.1.7	✓	8	3.2	odd	2
9.96.a.c.1.2		8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 96 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q-2.34596e14 q^{2} +1.54210e28 q^{4} +2.52565e33 q^{5} +4.80687e39 q^{7} +5.67559e42 q^{8} -5.92506e47 q^{10} +3.16113e49 q^{11} -9.97774e52 q^{13} -1.12767e54 q^{14} -1.94236e57 q^{16} +3.48353e57 q^{17} -1.04863e61 q^{19} +3.89480e61 q^{20} -7.41586e63 q^{22} -1.70644e64 q^{23} +3.85455e66 q^{25} +2.34073e67 q^{26} +7.41266e67 q^{28} -1.55539e69 q^{29} +1.02679e71 q^{31} +2.30835e71 q^{32} -8.17221e71 q^{34} +1.21405e73 q^{35} -2.81257e74 q^{37} +2.46005e75 q^{38} +1.43346e76 q^{40} -3.26782e76 q^{41} +7.50961e75 q^{43} +4.87477e77 q^{44} +4.00322e78 q^{46} +2.42784e79 q^{47} -1.69342e80 q^{49} -9.04260e80 q^{50} -1.53867e81 q^{52} +1.40525e82 q^{53} +7.98389e82 q^{55} +2.72818e82 q^{56} +3.64887e83 q^{58} +1.17208e84 q^{59} +7.58248e84 q^{61} -2.40880e85 q^{62} +2.27918e85 q^{64} -2.52003e86 q^{65} -8.84858e86 q^{67} +5.37195e85 q^{68} -2.84810e87 q^{70} -6.46617e86 q^{71} +1.01177e88 q^{73} +6.59817e88 q^{74} -1.61710e89 q^{76} +1.51951e89 q^{77} +1.04527e89 q^{79} -4.90571e90 q^{80} +7.66617e90 q^{82} -1.05596e91 q^{83} +8.79818e90 q^{85} -1.76172e90 q^{86} +1.79413e92 q^{88} +3.90606e92 q^{89} -4.79617e92 q^{91} -2.63149e92 q^{92} -5.69559e93 q^{94} -2.64848e94 q^{95} +3.16941e94 q^{97} +3.97269e94 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5835659138280 q^{2} + 20\!\cdots\!84 q^{4} - 19\!\cdots\!60 q^{5} + 31\!\cdots\!00 q^{7} + 14\!\cdots\!60 q^{8} - 35\!\cdots\!40 q^{10} - 53\!\cdots\!16 q^{11} + 11\!\cdots\!40 q^{13} - 88\!\cdots\!08 q^{14}+ \cdots - 14\!\cdots\!60 q^{98}+O(q^{100}) \) 8 * q + 5835659138280 * q^2 + 208956598309707350371623569984 * q^4 - 1941568507475850402526904141070960 * q^5 + 31232311735415758067806325356531573912000 * q^7 + 14761127603920085098561309094124598702287360 * q^8 - 355384205613899841010372205704985147108657534640 * q^10 - 53080108095821756826858489331993621982645992125216 * q^11 + 117293508281179239843264964380833942161194396039342640 * q^13 - 8850886815767090581799564344683737269936151852930265408 * q^14 + 9517116971431211282501221161054789131283343644054948220928 * q^16 + 13655041265063090981829171372625119189425374473948274915440 * q^17 - 5232175975370167369536369873888207394303637759872553281713440 * q^19 - 136065209104116992530471413843386338746929879497239386344644480 * q^20 - 20365500099170357171519767897869972385636855003458825137197491360 * q^22 + 7129054072165937484825035531327773489156117409617881426435061440 * q^23 + 8177806376085721196783759852983887433280593317172609841487587996600 * q^25 + 69072273179717436642550386629266724895941590936463282023015399323504 * q^26 + 303354815522537415860404332264897505740906926923909508834765584637440 * q^28 - 7715272198415359380593902919630157934289467091855373333108685675435440 * q^29 + 48520677903801540370519073843711920597057994260920479636592334181199616 * q^31 - 911347110324473008775326747695560179887781374647708612161794209209221120 * q^32 - 16409772766982648656985219134942803587399227958333745923026675404562961232 * q^34 - 58800416933815614414155173269063056087887600285328689246425433374756677760 * q^35 - 181116344963557296256979160619337453378797091102974834966000994855965247120 * q^37 + 1676466315180766681626408275142200947978975839695306622930354052184199692640 * q^38 + 39028182173606372825635252450401491624189758401191157685601991729209269171200 * q^40 + 87541390126560450267544465567119030351560808726320656469732601708266148308784 * q^41 + 360093033489081253538156425248276463103949347025569853491672117723107522861600 * q^43 - 1942224484251042670482996667732829207493398934442399145050649033803969221005568 * q^44 - 19332434944442851407749457669991401004991143268030327859543986888040547882373184 * q^46 - 38672453335683563852366980570346257355794761888911368752480783496161211070336640 * q^47 + 265668043093542548841947390620517395072194945166225827717144824590425137465244744 * q^49 + 1423963459280866882678609595824694565889878038511273700600414891648711070234429400 * q^50 + 15678746704556392183126484026214298441253990030076674973212546269606119207477104000 * q^52 + 2922690482809426126710991861168746969788895886261814706776237561500358605037675280 * q^53 + 77963865832782922646862204005771036172886494149999882551809226033579503680996905920 * q^55 - 723822110434297992891221750986765045769194525611914833690699475848521019635777392640 * q^56 + 2398120500739528001867383787619453843290390222445601081527493426426916763954522209040 * q^58 - 2444569112045817337560949868287606200158569651761097862873350630901953709318185022880 * q^59 + 26252719580888049069066995575288184611473664654647035829209505915961690057602967485616 * q^61 - 109318411457586083204284032417457169492313955459811319765445849679642744506848521207040 * q^62 + 407545659960425058121678577897271227683793728749313452587765989597513138495845491277824 * q^64 - 711217468942010938456527729098183388378886665557115838437689631605619958224435834575520 * q^65 - 646475642994207391400653355260241732956721934256209274545597969100350739031184431188640 * q^67 - 91675839067201266020688320385568861573762045194469769590554263557238860857176520405120 * q^68 - 15589682350948763132524633727148211085350313303119537319661619119948806738470696493235840 * q^70 + 14595295080721751466823982356267079020901744922845645857244436108167397828048945561374784 * q^71 - 167722859263497180232486905674536831998056258335586734743256934373976249561602911979579440 * q^73 + 209312489678791718598684146630297797595302804804578868479635191055424978871400486510408112 * q^74 - 959273209575432254809587692424149415253949631691365417587931662952012091653615772375589120 * q^76 + 358973379150050060834656745211596557040941835816686113329022190288009228708654757892460800 * q^77 + 4672642903096907209502768293890247708239627672362847349478671278970829923925879535283527040 * q^79 - 18415268594255335517079731605762998550074832241200743044677945286622776635630921688252866560 * q^80 + 32657845092209493410036294321958173121440540177602229019397776717126981442788576405027965040 * q^82 - 34387792212015780744754986808561666458900302762495709021597904850967930099747337487085254880 * q^83 + 58585978711733607272815047107060888289878133655773893600270763487144112403111490135244590560 * q^85 + 153511472921832187435283964804212642635464712353485304877046031498544471884447149897205104544 * q^86 - 1202425497404423912185881933157195269872332267934742515736241252480851349730675866727622174720 * q^88 + 342673661311688548077760584785109887358595471462214186557789870415877447806348084055852796080 * q^89 - 3490211360016960529246147249335483533013067701963330513611222538458526220206688421639066690944 * q^91 + 12008074146638359830472895966704879561255070000267734630900014099911412498586265442549753546240 * q^92 + 15433462798640093333378242254437202047220637579307237556798289796157532672617883642933732299648 * q^94 - 15321400721190643816477985005690604983976540891819618748501840926190750159388834713154020724800 * q^95 + 10072532354157458294768094296505188523874048354320514397914144859011793551098974691865811668240 * q^97 - 146363464831387371243245039459581022362075942196915081212239417921551560440470151788055390975960 * q^98

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