LMFDB - Embedded newform 9.86.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,86,Mod(1,9)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 86, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 86);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 86 $
Character orbit:	$[\chi]$	$=$	9.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:	$411.794619216$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3 x^{5} + \cdots - 17\!\cdots\!50 $ x^6 - 3x^5 - 20125264230072359909772x^4 - 314483190102207151531480871396326x^3 + 90192008136736578291529572869233310390975625x^2 + 2091285328888251081155130451204419887619836339467659225*x - 17301527721628842869681120067092990846953613013306724567953408750
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	multiple of $ 2^{65}\cdot 3^{30}\cdot 5^{6}\cdot 7^{3}\cdot 11\cdot 17^{2} $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$8.03621e10$ 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)

$f(q)$	$=$	$q-7.11528e12 q^{2} +1.19416e25 q^{4} -1.39389e29 q^{5} -1.69824e35 q^{7} +1.90292e38 q^{8} +O(q^{10})$	\(q-7.11528e12 q^{2} +1.19416e25 q^{4} -1.39389e29 q^{5} -1.69824e35 q^{7} +1.90292e38 q^{8} +9.91791e41 q^{10} +1.22442e44 q^{11} -1.14869e47 q^{13} +1.20835e48 q^{14} -1.81594e51 q^{16} +7.63802e51 q^{17} +1.44057e54 q^{19} -1.66452e54 q^{20} -8.71207e56 q^{22} +9.42435e57 q^{23} -2.39065e59 q^{25} +8.17328e59 q^{26} -2.02796e60 q^{28} -2.61757e62 q^{29} +1.28619e63 q^{31} +5.55940e63 q^{32} -5.43466e64 q^{34} +2.36716e64 q^{35} +3.23546e66 q^{37} -1.02500e67 q^{38} -2.65245e67 q^{40} +5.86119e68 q^{41} +2.22405e69 q^{43} +1.46215e69 q^{44} -6.70569e70 q^{46} +1.28917e71 q^{47} -6.52452e71 q^{49} +1.70101e72 q^{50} -1.37172e72 q^{52} +1.71828e73 q^{53} -1.70670e73 q^{55} -3.23161e73 q^{56} +1.86247e75 q^{58} -1.15535e75 q^{59} -2.68706e75 q^{61} -9.15160e75 q^{62} +3.06943e76 q^{64} +1.60115e76 q^{65} -6.45785e77 q^{67} +9.12098e76 q^{68} -1.68430e77 q^{70} -1.20251e78 q^{71} +2.24741e79 q^{73} -2.30212e79 q^{74} +1.72026e79 q^{76} -2.07936e79 q^{77} +4.39089e80 q^{79} +2.53123e80 q^{80} -4.17040e81 q^{82} +1.12159e81 q^{83} -1.06466e81 q^{85} -1.58247e82 q^{86} +2.32996e82 q^{88} +1.84370e82 q^{89} +1.95076e82 q^{91} +1.12541e83 q^{92} -9.17279e83 q^{94} -2.00799e83 q^{95} +1.25383e84 q^{97} +4.64238e84 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3596910688800 q^{2} + 14\!\cdots\!32 q^{4}+ \cdots - 44\!\cdots\!00 q^{8}+O(q^{10}) $ 6 * q + 3596910688800 * q^2 + 140991407339885551387640832 * q^4 + 937371071374809475998758615100 * q^5 + 376764526445862177226143056468406000 * q^7 - 444573639427992844351424894916577689600 * q^8	$ 6 q + 3596910688800 q^{2} + 14\!\cdots\!32 q^{4}+ \cdots - 49\!\cdots\!00 q^{98}+O(q^{100}) $ 6 * q + 3596910688800 * q^2 + 140991407339885551387640832 * q^4 + 937371071374809475998758615100 * q^5 + 376764526445862177226143056468406000 * q^7 - 444573639427992844351424894916577689600 * q^8 + 94651165962435813693946284861726959764800 * q^10 + 56344805701335918998354740625397619012956888 * q^11 - 380409468466294979156527797290184755501373645900 * q^13 - 7432102291035232990382031969981134697595704847104 * q^14 + 2636948568634008151994191667083023793288011486068736 * q^16 + 51365945458144838311659694040021464865555671618554900 * q^17 + 2653138201866103222242250000135395331152453781661358360 * q^19 + 52474536419792695778976723338965188133980339812187187200 * q^20 + 3581897081140779531372538339240606543513118132263441718400 * q^22 + 2885510207115801266245992081450013398631817932489294263600 * q^23 + 669968020810517762245853029111649576216707129701526846916250 * q^25 + 145338677717367061512932551412743816475529536844287947743168 * q^26 + 26317831788111975278561322769557791839073407987295193709977600 * q^28 + 126005957659709196887223202461409590769523616790635653593969260 * q^29 - 5173343222869174361945421290475955243870433981978751385509914688 * q^31 - 18707915462589185913352646999729455863851090555123851448234803200 * q^32 - 261567067349813682388055634030637558284890219695677173368549801536 * q^34 + 54720272714504178732776803597096361295121671934223039039646799200 * q^35 - 5097772448818865838142977649516403030637492688710699135052039832700 * q^37 + 48700117286552805406633697613393636582143669921611431061746550761600 * q^38 - 142216395874814214555238931398128417040750190812408712268526706688000 * q^40 + 37443196175066827621993378286362463826782697218192853395514169611588 * q^41 - 1200203503033233321208433978807766368170132198490662545566874292959000 * q^43 + 18639061742892206758508411691062975986004422355135358223957061170139136 * q^44 - 191201172378193769791517179835271412887470991983918549920785652631609088 * q^46 + 239424902055614885318194585971856964272866563499240512979067317687189600 * q^47 - 3550036072199457619495079372134003262477445775089732177587676397325457258 * q^49 + 11494548593012586974824937998111766287236762210273483206149818153415980000 * q^50 - 58712069233310142887861446777253810318205781466445594810258784313124096000 * q^52 + 50490336878498884627542374457418517146058176491360508941999343448428076700 * q^53 + 39301939079139487846929886085782264562447760597309570618345636737530354800 * q^55 - 587681993552427976427603903951469305598093495610137163751240432058398146560 * q^56 + 1968773654564353990385431635289950834066592911242318428340655057560215041600 * q^58 - 6616590288827867291331513194467053420958403068835561414972249041164074836680 * q^59 + 14357623272339506273937696878826484910577784548921932472541795844444520630612 * q^61 - 6341655988756470271607502111666483932112595649902706601178034698608656870400 * q^62 - 15036793202050903912474653273096694719068286214625123977211579195245857865728 * q^64 + 207821434856417257245443053802293031083793273150318306362240037299645012878600 * q^65 - 676342476586532149280756429155984326543089556982073869153059292790609382659400 * q^67 + 3163312242521042817824168546059434229649323239544821535981619303392310998579200 * q^68 - 6084039126370540917643976340500810012180196811570702685650569892863510961958400 * q^70 + 6034633570006156478287618014555933721359683069405109018337202921275711590822288 * q^71 + 35801030708258502256835696755718519936386302900895514245440128302587327554955900 * q^73 - 107340388271157498582387358259935699803904453010588240913436902735784529206718784 * q^74 + 161366039234563681095121956921292746446621209914504282248055858395547636251627520 * q^76 - 251398792676383195671611646509617352303457127744134928661968949244057263571048000 * q^77 - 1371264739680910465180747804297591457073099822996075412863178473301594188074547360 * q^79 + 4133302113696354289363675864719400535772990320893278365909081697225137404615065600 * q^80 - 1521817925451755348555955193889971681134404529402094946034920762170082779676769600 * q^82 + 6003587143963376493630220870754035373224271946820478343977301287860006839810301800 * q^83 + 17517819416067376478784379475048913828437460883636030543204171384490930355142297800 * q^85 - 21492879965867203934779808388379416439833228958041181100627630027642419671434758272 * q^86 + 272530707230233729788642007241687387343090541246894873629875449706966387853783859200 * q^88 - 160168600498492831669414330089333488062247500152820008689246769174592053409073033820 * q^89 - 25835286532054033379869466839714977397623074555127707439218236615589791891497666528 * q^91 + 409168494351117176400001947891440713569740400895293133641599839567086438014810726400 * q^92 - 1363919087472816080652148503710266001883533236220476628035821611168261836377449504256 * q^94 + 5333227198671761899795642368410473530089556162431166206847226445312136951029790006000 * q^95 + 1982258923770441792809455137165411551481047984016852591852301644261535493014975149900 * q^97 - 4998389537167322966144480371748484731963375313000939154777788888434561052122410226400 * q^98

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 $

$2$	−7.11528e12	−1.14398	−0.571988	−	0.820262i	$-0.693828\pi$
$2$	−7.11528e12	−1.14398	−0.571988	+	0.820262i	$0.693828\pi$
$3$	0	0
$3$	0	0
$4$	1.19416e25	0.308682
$5$	−1.39389e29	−0.274159	−0.137080	−	0.990560i	$-0.543772\pi$
$5$	−1.39389e29	−0.274159	−0.137080	+	0.990560i	$0.543772\pi$
$6$	0	0
$7$	−1.69824e35	−0.205747	−0.102873	−	0.994694i	$-0.532804\pi$
$7$	−1.69824e35	−0.205747	−0.102873	+	0.994694i	$0.532804\pi$
$8$	1.90292e38	0.790852
$9$	0	0
$10$	9.91791e41	0.313632
$11$	1.22442e44	0.674125	0.337063	−	0.941482i	$-0.390567\pi$
$11$	1.22442e44	0.674125	0.337063	+	0.941482i	$0.390567\pi$
$12$	0	0
$13$	−1.14869e47	−0.521930	−0.260965	−	0.965348i	$-0.584041\pi$
$13$	−1.14869e47	−0.521930	−0.260965	+	0.965348i	$0.584041\pi$
$14$	1.20835e48	0.235369
$15$	0	0
$16$	−1.81594e51	−1.21340
$17$	7.63802e51	0.388062	0.194031	−	0.980995i	$-0.437844\pi$
$17$	7.63802e51	0.388062	0.194031	+	0.980995i	$0.437844\pi$
$18$	0	0
$19$	1.44057e54	0.647896	0.323948	−	0.946075i	$-0.394990\pi$
$19$	1.44057e54	0.647896	0.323948	+	0.946075i	$0.394990\pi$
$20$	−1.66452e54	−0.0846281
$21$	0	0
$22$	−8.71207e56	−0.771183
$23$	9.42435e57	1.26130	0.630650	−	0.776067i	$-0.282788\pi$
$23$	9.42435e57	1.26130	0.630650	+	0.776067i	$0.282788\pi$
$24$	0	0
$25$	−2.39065e59	−0.924837
$26$	8.17328e59	0.597075
$27$	0	0
$28$	−2.02796e60	−0.0635103
$29$	−2.61757e62	−1.84494	−0.922471	−	0.386067i	$-0.873833\pi$
$29$	−2.61757e62	−1.84494	−0.922471	+	0.386067i	$0.873833\pi$
$30$	0	0
$31$	1.28619e63	0.532639	0.266320	−	0.963885i	$-0.414192\pi$
$31$	1.28619e63	0.532639	0.266320	+	0.963885i	$0.414192\pi$
$32$	5.55940e63	0.597246
$33$	0	0
$34$	−5.43466e64	−0.443934
$35$	2.36716e64	0.0564074
$36$	0	0
$37$	3.23546e66	0.726713	0.363356	−	0.931650i	$-0.381631\pi$
$37$	3.23546e66	0.726713	0.363356	+	0.931650i	$0.381631\pi$
$38$	−1.02500e67	−0.741178
$39$	0	0
$40$	−2.65245e67	−0.216819
$41$	5.86119e68	1.67754	0.838768	−	0.544489i	$-0.183276\pi$
$41$	5.86119e68	1.67754	0.838768	+	0.544489i	$0.183276\pi$
$42$	0	0
$43$	2.22405e69	0.840883	0.420441	−	0.907320i	$-0.361875\pi$
$43$	2.22405e69	0.840883	0.420441	+	0.907320i	$0.361875\pi$
$44$	1.46215e69	0.208090
$45$	0	0
$46$	−6.70569e70	−1.44290
$47$	1.28917e71	1.11212	0.556059	−	0.831143i	$-0.312313\pi$
$47$	1.28917e71	1.11212	0.556059	+	0.831143i	$0.312313\pi$
$48$	0	0
$49$	−6.52452e71	−0.957668
$50$	1.70101e72	1.05799
$51$	0	0
$52$	−1.37172e72	−0.161110
$53$	1.71828e73	0.898195	0.449097	−	0.893483i	$-0.351746\pi$
$53$	1.71828e73	0.898195	0.449097	+	0.893483i	$0.351746\pi$
$54$	0	0
$55$	−1.70670e73	−0.184818
$56$	−3.23161e73	−0.162715
$57$	0	0
$58$	1.86247e75	2.11057
$59$	−1.15535e75	−0.633144	−0.316572	−	0.948568i	$-0.602532\pi$
$59$	−1.15535e75	−0.633144	−0.316572	+	0.948568i	$0.602532\pi$
$60$	0	0
$61$	−2.68706e75	−0.357075	−0.178538	−	0.983933i	$-0.557137\pi$
$61$	−2.68706e75	−0.357075	−0.178538	+	0.983933i	$0.557137\pi$
$62$	−9.15160e75	−0.609327
$63$	0	0
$64$	3.06943e76	0.530162
$65$	1.60115e76	0.143092
$66$	0	0
$67$	−6.45785e77	−1.59187	−0.795937	−	0.605380i	$-0.793021\pi$
$67$	−6.45785e77	−1.59187	−0.795937	+	0.605380i	$0.793021\pi$
$68$	9.12098e76	0.119788
$69$	0	0
$70$	−1.68430e77	−0.0645287
$71$	−1.20251e78	−0.252121	−0.126060	−	0.992023i	$-0.540233\pi$
$71$	−1.20251e78	−0.252121	−0.126060	+	0.992023i	$0.540233\pi$
$72$	0	0
$73$	2.24741e79	1.44697	0.723486	−	0.690339i	$-0.242538\pi$
$73$	2.24741e79	1.44697	0.723486	+	0.690339i	$0.242538\pi$
$74$	−2.30212e79	−0.831342
$75$	0	0
$76$	1.72026e79	0.199994
$77$	−2.07936e79	−0.138699
$78$	0	0
$79$	4.39089e80	0.984921	0.492461	−	0.870335i	$-0.336098\pi$
$79$	4.39089e80	0.984921	0.492461	+	0.870335i	$0.336098\pi$
$80$	2.53123e80	0.332664
$81$	0	0
$82$	−4.17040e81	−1.91906
$83$	1.12159e81	0.308331	0.154165	−	0.988045i	$-0.450731\pi$
$83$	1.12159e81	0.308331	0.154165	+	0.988045i	$0.450731\pi$
$84$	0	0
$85$	−1.06466e81	−0.106391
$86$	−1.58247e82	−0.961950
$87$	0	0
$88$	2.32996e82	0.533133
$89$	1.84370e82	0.260984	0.130492	−	0.991449i	$-0.458344\pi$
$89$	1.84370e82	0.260984	0.130492	+	0.991449i	$0.458344\pi$
$90$	0	0
$91$	1.95076e82	0.107385
$92$	1.12541e83	0.389340
$93$	0	0
$94$	−9.17279e83	−1.27224
$95$	−2.00799e83	−0.177627
$96$	0	0
$97$	1.25383e84	0.457551	0.228775	−	0.973479i	$-0.426528\pi$
$97$	1.25383e84	0.457551	0.228775	+	0.973479i	$0.426528\pi$
$98$	4.64238e84	1.09555
$99$	0	0
$100$	−2.85480e84	−0.285480
$101$	−2.18173e85	−1.42936	−0.714682	−	0.699450i	$-0.753429\pi$
$101$	−2.18173e85	−1.42936	−0.714682	+	0.699450i	$0.753429\pi$
$102$	0	0
$103$	6.05830e85	1.72492	0.862459	−	0.506127i	$-0.168923\pi$
$103$	6.05830e85	1.72492	0.862459	+	0.506127i	$0.168923\pi$
$104$	−2.18587e85	−0.412769
$105$	0	0
$106$	−1.22261e86	−1.02751
$107$	2.90227e86	1.63654	0.818272	−	0.574831i	$-0.194932\pi$
$107$	2.90227e86	1.63654	0.818272	+	0.574831i	$0.194932\pi$
$108$	0	0
$109$	1.20378e86	0.308973	0.154487	−	0.987995i	$-0.450628\pi$
$109$	1.20378e86	0.308973	0.154487	+	0.987995i	$0.450628\pi$
$110$	1.21437e86	0.211427
$111$	0	0
$112$	3.08391e86	0.249652
$113$	6.56433e86	0.364214	0.182107	−	0.983279i	$-0.441708\pi$
$113$	6.56433e86	0.364214	0.182107	+	0.983279i	$0.441708\pi$
$114$	0	0
$115$	−1.31365e87	−0.345797
$116$	−3.12578e87	−0.569500
$117$	0	0
$118$	8.22062e87	0.724302
$119$	−1.29712e87	−0.0798425
$120$	0	0
$121$	−1.79977e88	−0.545555
$122$	1.91192e88	0.408486
$123$	0	0
$124$	1.53591e88	0.164416
$125$	6.93542e88	0.527712
$126$	0	0
$127$	8.74949e88	0.339097	0.169549	−	0.985522i	$-0.445769\pi$
$127$	8.74949e88	0.339097	0.169549	+	0.985522i	$0.445769\pi$
$128$	−4.33467e89	−1.20374
$129$	0	0
$130$	−1.13927e89	−0.163694
$131$	−8.56820e89	−0.888913	−0.444457	−	0.895800i	$-0.646603\pi$
$131$	−8.56820e89	−0.888913	−0.444457	+	0.895800i	$0.646603\pi$
$132$	0	0
$133$	−2.44643e89	−0.133303
$134$	4.59494e90	1.82107
$135$	0	0
$136$	1.45345e90	0.306900
$137$	−7.75141e90	−1.19883	−0.599414	−	0.800439i	$-0.704600\pi$
$137$	−7.75141e90	−1.19883	−0.599414	+	0.800439i	$0.704600\pi$
$138$	0	0
$139$	7.88623e89	0.0658780	0.0329390	−	0.999457i	$-0.489513\pi$
$139$	7.88623e89	0.0658780	0.0329390	+	0.999457i	$0.489513\pi$
$140$	2.82676e89	0.0174119
$141$	0	0
$142$	8.55619e90	0.288420
$143$	−1.40648e91	−0.351846
$144$	0	0
$145$	3.64860e91	0.505808
$146$	−1.59909e92	−1.65530
$147$	0	0
$148$	3.86364e91	0.224323
$149$	2.75011e92	1.19932	0.599658	−	0.800256i	$-0.295303\pi$
$149$	2.75011e92	1.19932	0.599658	+	0.800256i	$0.295303\pi$
$150$	0	0
$151$	−1.77295e92	−0.438709	−0.219354	−	0.975645i	$-0.570395\pi$
$151$	−1.77295e92	−0.438709	−0.219354	+	0.975645i	$0.570395\pi$
$152$	2.74128e92	0.512390
$153$	0	0
$154$	1.47952e92	0.158668
$155$	−1.79281e92	−0.146028
$156$	0	0
$157$	2.44253e93	1.15373	0.576865	−	0.816839i	$-0.304276\pi$
$157$	2.44253e93	1.15373	0.576865	+	0.816839i	$0.304276\pi$
$158$	−3.12424e93	−1.12673
$159$	0	0
$160$	−7.74919e92	−0.163741
$161$	−1.60048e93	−0.259508
$162$	0	0
$163$	2.66045e93	0.255259	0.127630	−	0.991822i	$-0.459263\pi$
$163$	2.66045e93	0.255259	0.127630	+	0.991822i	$0.459263\pi$
$164$	6.99917e93	0.517825
$165$	0	0
$166$	−7.98045e93	−0.352723
$167$	−5.71794e93	−0.195789	−0.0978947	−	0.995197i	$-0.531211\pi$
$167$	−5.71794e93	−0.195789	−0.0978947	+	0.995197i	$0.531211\pi$
$168$	0	0
$169$	−3.52429e94	−0.727589
$170$	7.57532e93	0.121709
$171$	0	0
$172$	2.65586e94	0.259565
$173$	−9.58895e92	−0.00732507	−0.00366253	−	0.999993i	$-0.501166\pi$
$173$	−9.58895e92	−0.00732507	−0.00366253	+	0.999993i	$0.501166\pi$
$174$	0	0
$175$	4.05990e94	0.190282
$176$	−2.22347e95	−0.817982
$177$	0	0
$178$	−1.31184e95	−0.298560
$179$	8.97189e95	1.60927	0.804637	−	0.593766i	$-0.202360\pi$
$179$	8.97189e95	1.60927	0.804637	+	0.593766i	$0.202360\pi$
$180$	0	0
$181$	−1.50309e96	−1.68130	−0.840652	−	0.541575i	$-0.817828\pi$
$181$	−1.50309e96	−1.68130	−0.840652	+	0.541575i	$0.817828\pi$
$182$	−1.38802e95	−0.122846
$183$	0	0
$184$	1.79337e96	0.997501
$185$	−4.50988e95	−0.199235
$186$	0	0
$187$	9.35213e95	0.261603
$188$	1.53947e96	0.343291
$189$	0	0
$190$	1.42874e96	0.203201
$191$	−3.57988e96	−0.407334	−0.203667	−	0.979040i	$-0.565286\pi$
$191$	−3.57988e96	−0.407334	−0.203667	+	0.979040i	$0.565286\pi$
$192$	0	0
$193$	−1.43204e97	−1.04657	−0.523286	−	0.852157i	$-0.675294\pi$
$193$	−1.43204e97	−1.04657	−0.523286	+	0.852157i	$0.675294\pi$
$194$	−8.92133e96	−0.523427
$195$	0	0
$196$	−7.79129e96	−0.295615
$197$	4.64164e96	0.141859	0.0709295	−	0.997481i	$-0.477403\pi$
$197$	4.64164e96	0.141859	0.0709295	+	0.997481i	$0.477403\pi$
$198$	0	0
$199$	−9.05700e97	−1.80189	−0.900945	−	0.433932i	$-0.857126\pi$
$199$	−9.05700e97	−1.80189	−0.900945	+	0.433932i	$0.857126\pi$
$200$	−4.54920e97	−0.731408
$201$	0	0
$202$	1.55236e98	1.63516
$203$	4.44526e97	0.379591
$204$	0	0
$205$	−8.16985e97	−0.459912
$206$	−4.31065e98	−1.97327
$207$	0	0
$208$	2.08596e98	0.633308
$209$	1.76386e98	0.436763
$210$	0	0
$211$	−9.30008e98	−1.53632	−0.768161	−	0.640257i	$-0.778828\pi$
$211$	−9.30008e98	−1.53632	−0.768161	+	0.640257i	$0.778828\pi$
$212$	2.05190e98	0.277256
$213$	0	0
$214$	−2.06505e99	−1.87217
$215$	−3.10008e98	−0.230536
$216$	0	0
$217$	−2.18426e98	−0.109589
$218$	−8.56522e98	−0.353458
$219$	0	0
$220$	−2.03807e98	−0.0570499
$221$	−8.77375e98	−0.202541
$222$	0	0
$223$	−9.40091e99	−1.47984	−0.739918	−	0.672698i	$-0.765135\pi$
$223$	−9.40091e99	−1.47984	−0.739918	+	0.672698i	$0.765135\pi$
$224$	−9.44120e98	−0.122881
$225$	0	0
$226$	−4.67070e99	−0.416652
$227$	−1.83130e100	−1.35413	−0.677067	−	0.735921i	$-0.736749\pi$
$227$	−1.83130e100	−1.35413	−0.677067	+	0.735921i	$0.736749\pi$
$228$	0	0
$229$	−1.74672e100	−0.889640	−0.444820	−	0.895620i	$-0.646732\pi$
$229$	−1.74672e100	−0.889640	−0.444820	+	0.895620i	$0.646732\pi$
$230$	9.34699e99	0.395584
$231$	0	0
$232$	−4.98100e100	−1.45907
$233$	2.22863e99	0.0543764	0.0271882	−	0.999630i	$-0.491345\pi$
$233$	2.22863e99	0.0543764	0.0271882	+	0.999630i	$0.491345\pi$
$234$	0	0
$235$	−1.79696e100	−0.304898
$236$	−1.37967e100	−0.195440
$237$	0	0
$238$	9.22937e99	0.0913380
$239$	−2.06280e101	−1.70823	−0.854115	−	0.520084i	$-0.825900\pi$
$239$	−2.06280e101	−1.70823	−0.854115	+	0.520084i	$0.825900\pi$
$240$	0	0
$241$	1.83892e100	0.106866	0.0534330	−	0.998571i	$-0.482984\pi$
$241$	1.83892e100	0.106866	0.0534330	+	0.998571i	$0.482984\pi$
$242$	1.28059e101	0.624102
$243$	0	0
$244$	−3.20877e100	−0.110223
$245$	9.09446e100	0.262554
$246$	0	0
$247$	−1.65477e101	−0.338156
$248$	2.44751e101	0.421239
$249$	0	0
$250$	−4.93474e101	−0.603690
$251$	−1.14623e102	−1.18342	−0.591708	−	0.806153i	$-0.701546\pi$
$251$	−1.14623e102	−1.18342	−0.591708	+	0.806153i	$0.701546\pi$
$252$	0	0
$253$	1.15393e102	0.850274
$254$	−6.22550e101	−0.387919
$255$	0	0
$256$	1.89681e102	0.846887
$257$	3.42715e102	1.29651	0.648255	−	0.761424i	$-0.275499\pi$
$257$	3.42715e102	1.29651	0.648255	+	0.761424i	$0.275499\pi$
$258$	0	0
$259$	−5.49459e101	−0.149519
$260$	1.91203e101	0.0441699
$261$	0	0
$262$	6.09651e102	1.01690
$263$	3.14379e102	0.445999	0.222999	−	0.974819i	$-0.428415\pi$
$263$	3.14379e102	0.445999	0.222999	+	0.974819i	$0.428415\pi$
$264$	0	0
$265$	−2.39510e102	−0.246249
$266$	1.74070e102	0.152495
$267$	0	0
$268$	−7.71167e102	−0.491383
$269$	2.58659e103	1.40687	0.703437	−	0.710757i	$-0.251648\pi$
$269$	2.58659e103	1.40687	0.703437	+	0.710757i	$0.251648\pi$
$270$	0	0
$271$	2.55238e103	1.01333	0.506664	−	0.862143i	$-0.330878\pi$
$271$	2.55238e103	1.01333	0.506664	+	0.862143i	$0.330878\pi$
$272$	−1.38702e103	−0.470874
$273$	0	0
$274$	5.51535e103	1.37143
$275$	−2.92715e103	−0.623456
$276$	0	0
$277$	3.45051e103	0.540123	0.270062	−	0.962843i	$-0.412956\pi$
$277$	3.45051e103	0.540123	0.270062	+	0.962843i	$0.412956\pi$
$278$	−5.61127e102	−0.0753629
$279$	0	0
$280$	4.50451e102	0.0446099
$281$	1.83487e104	1.56166	0.780832	−	0.624741i	$-0.214796\pi$
$281$	1.83487e104	1.56166	0.780832	+	0.624741i	$0.214796\pi$
$282$	0	0
$283$	−5.24976e103	−0.330534	−0.165267	−	0.986249i	$-0.552849\pi$
$283$	−5.24976e103	−0.330534	−0.165267	+	0.986249i	$0.552849\pi$
$284$	−1.43598e103	−0.0778251
$285$	0	0
$286$	1.00075e104	0.402503
$287$	−9.95372e103	−0.345147
$288$	0	0
$289$	−3.29060e104	−0.849408
$290$	−2.59608e104	−0.578633
$291$	0	0
$292$	2.68375e104	0.446654
$293$	−8.07040e104	−1.16150	−0.580752	−	0.814080i	$-0.697242\pi$
$293$	−8.07040e104	−1.16150	−0.580752	+	0.814080i	$0.697242\pi$
$294$	0	0
$295$	1.61043e104	0.173582
$296$	6.15681e104	0.574722
$297$	0	0
$298$	−1.95678e105	−1.37199
$299$	−1.08257e105	−0.658310
$300$	0	0
$301$	−3.77698e104	−0.173009
$302$	1.26150e105	0.501872
$303$	0	0
$304$	−2.61599e105	−0.786156
$305$	3.74547e104	0.0978956
$306$	0	0
$307$	−8.52700e105	−1.68817	−0.844083	−	0.536212i	$-0.819855\pi$
$307$	−8.52700e105	−1.68817	−0.844083	+	0.536212i	$0.819855\pi$
$308$	−2.48308e104	−0.0428139
$309$	0	0
$310$	1.27563e105	0.167053
$311$	1.59550e105	0.182214	0.0911068	−	0.995841i	$-0.470960\pi$
$311$	1.59550e105	0.182214	0.0911068	+	0.995841i	$0.470960\pi$
$312$	0	0
$313$	1.11133e106	0.966520	0.483260	−	0.875477i	$-0.339453\pi$
$313$	1.11133e106	0.966520	0.483260	+	0.875477i	$0.339453\pi$
$314$	−1.73793e106	−1.31984
$315$	0	0
$316$	5.24341e105	0.304027
$317$	1.62917e106	0.825939	0.412969	−	0.910745i	$-0.364492\pi$
$317$	1.62917e106	0.825939	0.412969	+	0.910745i	$0.364492\pi$
$318$	0	0
$319$	−3.20499e106	−1.24372
$320$	−4.27844e105	−0.145349
$321$	0	0
$322$	1.13879e106	0.296871
$323$	1.10031e106	0.251424
$324$	0	0
$325$	2.74612e106	0.482700
$326$	−1.89298e106	−0.292011
$327$	0	0
$328$	1.11533e107	1.32668
$329$	−2.18932e106	−0.228815
$330$	0	0
$331$	−1.53912e106	−0.124332	−0.0621660	−	0.998066i	$-0.519801\pi$
$331$	−1.53912e106	−0.124332	−0.0621660	+	0.998066i	$0.519801\pi$
$332$	1.33936e106	0.0951761
$333$	0	0
$334$	4.06847e106	0.223978
$335$	9.00153e106	0.436427
$336$	0	0
$337$	2.65042e107	0.997800	0.498900	−	0.866660i	$-0.333738\pi$
$337$	2.65042e107	0.997800	0.498900	+	0.866660i	$0.333738\pi$
$338$	2.50763e107	0.832345
$339$	0	0
$340$	−1.27136e106	−0.0328410
$341$	1.57483e107	0.359066
$342$	0	0
$343$	2.26502e107	0.402784
$344$	4.23218e107	0.665014
$345$	0	0
$346$	6.82281e105	0.00837971
$347$	−2.48808e107	−0.270309	−0.135155	−	0.990825i	$-0.543153\pi$
$347$	−2.48808e107	−0.270309	−0.135155	+	0.990825i	$0.543153\pi$
$348$	0	0
$349$	−2.04544e107	−0.174062	−0.0870312	−	0.996206i	$-0.527738\pi$
$349$	−2.04544e107	−0.174062	−0.0870312	+	0.996206i	$0.527738\pi$
$350$	−2.88873e107	−0.217678
$351$	0	0
$352$	6.80702e107	0.402619
$353$	−6.16575e107	−0.323267	−0.161633	−	0.986851i	$-0.551676\pi$
$353$	−6.16575e107	−0.323267	−0.161633	+	0.986851i	$0.551676\pi$
$354$	0	0
$355$	1.67617e107	0.0691213
$356$	2.20166e107	0.0805611
$357$	0	0
$358$	−6.38375e108	−1.84097
$359$	−3.89780e108	−0.998402	−0.499201	−	0.866486i	$-0.666373\pi$
$359$	−3.89780e108	−0.998402	−0.499201	+	0.866486i	$0.666373\pi$
$360$	0	0
$361$	−2.86851e108	−0.580230
$362$	1.06949e109	1.92337
$363$	0	0
$364$	2.32951e107	0.0331479
$365$	−3.13264e108	−0.396701
$366$	0	0
$367$	9.42672e108	0.946352	0.473176	−	0.880968i	$-0.343107\pi$
$367$	9.42672e108	0.946352	0.473176	+	0.880968i	$0.343107\pi$
$368$	−1.71141e109	−1.53046
$369$	0	0
$370$	3.20890e108	0.227920
$371$	−2.91806e108	−0.184801
$372$	0	0
$373$	−3.21783e109	−1.62158	−0.810789	−	0.585339i	$-0.800961\pi$
$373$	−3.21783e109	−1.62158	−0.810789	+	0.585339i	$0.800961\pi$
$374$	−6.65430e108	−0.299267
$375$	0	0
$376$	2.45318e109	0.879520
$377$	3.00678e109	0.962930
$378$	0	0
$379$	−2.43214e109	−0.622046	−0.311023	−	0.950402i	$-0.600672\pi$
$379$	−2.43214e109	−0.622046	−0.311023	+	0.950402i	$0.600672\pi$
$380$	−2.39785e108	−0.0548302
$381$	0	0
$382$	2.54718e109	0.465980
$383$	6.35016e109	1.03953	0.519765	−	0.854309i	$-0.326019\pi$
$383$	6.35016e109	1.03953	0.519765	+	0.854309i	$0.326019\pi$
$384$	0	0
$385$	2.89840e108	0.0380257
$386$	1.01894e110	1.19725
$387$	0	0
$388$	1.49726e109	0.141238
$389$	−3.92520e109	−0.331897	−0.165949	−	0.986134i	$-0.553069\pi$
$389$	−3.92520e109	−0.331897	−0.165949	+	0.986134i	$0.553069\pi$
$390$	0	0
$391$	7.19833e109	0.489463
$392$	−1.24156e110	−0.757373
$393$	0	0
$394$	−3.30266e109	−0.162283
$395$	−6.12042e109	−0.270026
$396$	0	0
$397$	4.42602e110	1.57549	0.787746	−	0.616000i	$-0.211248\pi$
$397$	4.42602e110	1.57549	0.787746	+	0.616000i	$0.211248\pi$
$398$	6.44431e110	2.06132
$399$	0	0
$400$	4.34128e110	1.12219
$401$	5.98111e110	1.39042	0.695210	−	0.718806i	$-0.255311\pi$
$401$	5.98111e110	1.39042	0.695210	+	0.718806i	$0.255311\pi$
$402$	0	0
$403$	−1.47744e110	−0.278000
$404$	−2.60533e110	−0.441219
$405$	0	0
$406$	−3.16293e110	−0.434243
$407$	3.96156e110	0.489895
$408$	0	0
$409$	1.51723e111	1.52339	0.761694	−	0.647937i	$-0.224368\pi$
$409$	1.51723e111	1.52339	0.761694	+	0.647937i	$0.224368\pi$
$410$	5.81308e110	0.526129
$411$	0	0
$412$	7.23455e110	0.532451
$413$	1.96206e110	0.130267
$414$	0	0
$415$	−1.56338e110	−0.0845318
$416$	−6.38605e110	−0.311721
$417$	0	0
$418$	−1.25503e111	−0.499647
$419$	9.81295e109	0.0352942	0.0176471	−	0.999844i	$-0.494382\pi$
$419$	9.81295e109	0.0352942	0.0176471	+	0.999844i	$0.494382\pi$
$420$	0	0
$421$	−3.89451e111	−1.14410	−0.572050	−	0.820219i	$-0.693852\pi$
$421$	−3.89451e111	−1.14410	−0.572050	+	0.820219i	$0.693852\pi$
$422$	6.61726e111	1.75752
$423$	0	0
$424$	3.26975e111	0.710339
$425$	−1.82598e111	−0.358894
$426$	0	0
$427$	4.56328e110	0.0734670
$428$	3.46576e111	0.505171
$429$	0	0
$430$	2.20580e111	0.263728
$431$	6.94740e111	0.752556	0.376278	−	0.926507i	$-0.377204\pi$
$431$	6.94740e111	0.752556	0.376278	+	0.926507i	$0.377204\pi$
$432$	0	0
$433$	−1.04259e112	−0.927641	−0.463820	−	0.885929i	$-0.653522\pi$
$433$	−1.04259e112	−0.927641	−0.463820	+	0.885929i	$0.653522\pi$
$434$	1.55416e111	0.125367
$435$	0	0
$436$	1.43750e111	0.0953744
$437$	1.35764e112	0.817191
$438$	0	0
$439$	1.97852e112	0.980839	0.490419	−	0.871487i	$-0.336844\pi$
$439$	1.97852e112	0.980839	0.490419	+	0.871487i	$0.336844\pi$
$440$	−3.24771e111	−0.146163
$441$	0	0
$442$	6.24277e111	0.231702
$443$	3.30999e112	1.11601	0.558005	−	0.829837i	$-0.311567\pi$
$443$	3.30999e112	1.11601	0.558005	+	0.829837i	$0.311567\pi$
$444$	0	0
$445$	−2.56991e111	−0.0715513
$446$	6.68901e112	1.69290
$447$	0	0
$448$	−5.21263e111	−0.109079
$449$	5.05111e112	0.961429	0.480715	−	0.876877i	$-0.340377\pi$
$449$	5.05111e112	0.961429	0.480715	+	0.876877i	$0.340377\pi$
$450$	0	0
$451$	7.17655e112	1.13087
$452$	7.83882e111	0.112426
$453$	0	0
$454$	1.30302e113	1.54910
$455$	−2.71915e111	−0.0294407
$456$	0	0
$457$	2.17418e113	1.95370	0.976848	−	0.213935i	$-0.0686282\pi$
$457$	2.17418e113	1.95370	0.976848	+	0.213935i	$0.0686282\pi$
$458$	1.24284e113	1.01773
$459$	0	0
$460$	−1.56870e112	−0.106741
$461$	−7.45280e112	−0.462413	−0.231206	−	0.972905i	$-0.574267\pi$
$461$	−7.45280e112	−0.462413	−0.231206	+	0.972905i	$0.574267\pi$
$462$	0	0
$463$	6.80695e112	0.351367	0.175683	−	0.984447i	$-0.443787\pi$
$463$	6.80695e112	0.351367	0.175683	+	0.984447i	$0.443787\pi$
$464$	4.75335e113	2.23865
$465$	0	0
$466$	−1.58573e112	−0.0622054
$467$	2.22210e113	0.795785	0.397893	−	0.917432i	$-0.369742\pi$
$467$	2.22210e113	0.795785	0.397893	+	0.917432i	$0.369742\pi$
$468$	0	0
$469$	1.09670e113	0.327523
$470$	1.27859e113	0.348796
$471$	0	0
$472$	−2.19853e113	−0.500723
$473$	2.72317e113	0.566860
$474$	0	0
$475$	−3.44389e113	−0.599198
$476$	−1.54896e112	−0.0246459
$477$	0	0
$478$	1.46774e114	1.95417
$479$	7.32431e113	0.892293	0.446146	−	0.894960i	$-0.352796\pi$
$479$	7.32431e113	0.892293	0.446146	+	0.894960i	$0.352796\pi$
$480$	0	0
$481$	−3.71656e113	−0.379293
$482$	−1.30845e113	−0.122252
$483$	0	0
$484$	−2.14920e113	−0.168403
$485$	−1.74770e113	−0.125442
$486$	0	0
$487$	−1.19786e114	−0.721814	−0.360907	−	0.932602i	$-0.617533\pi$
$487$	−1.19786e114	−0.721814	−0.360907	+	0.932602i	$0.617533\pi$
$488$	−5.11325e113	−0.282393
$489$	0	0
$490$	−6.47096e113	−0.300355
$491$	2.53284e113	0.107806	0.0539032	−	0.998546i	$-0.482834\pi$
$491$	2.53284e113	0.107806	0.0539032	+	0.998546i	$0.482834\pi$
$492$	0	0
$493$	−1.99930e114	−0.715952
$494$	1.17742e114	0.386843
$495$	0	0
$496$	−2.33565e114	−0.646303
$497$	2.04215e113	0.0518730
$498$	0	0
$499$	3.94124e113	0.0844033	0.0422017	−	0.999109i	$-0.486563\pi$
$499$	3.94124e113	0.0844033	0.0422017	+	0.999109i	$0.486563\pi$
$500$	8.28197e113	0.162895
$501$	0	0
$502$	8.15572e114	1.35380
$503$	−1.14379e115	−1.74464	−0.872319	−	0.488938i	$-0.837384\pi$
$503$	−1.14379e115	−1.74464	−0.872319	+	0.488938i	$0.837384\pi$
$504$	0	0
$505$	3.04109e114	0.391874
$506$	−8.21056e114	−0.972693
$507$	0	0
$508$	1.04482e114	0.104673
$509$	1.59810e115	1.47265	0.736324	−	0.676629i	$-0.236560\pi$
$509$	1.59810e115	1.47265	0.736324	+	0.676629i	$0.236560\pi$
$510$	0	0
$511$	−3.81664e114	−0.297710
$512$	3.27260e114	0.234920
$513$	0	0
$514$	−2.43851e115	−1.48318
$515$	−8.44460e114	−0.472903
$516$	0	0
$517$	1.57848e115	0.749707
$518$	3.90956e114	0.171046
$519$	0	0
$520$	3.04686e114	0.113165
$521$	−2.23432e115	−0.764789	−0.382395	−	0.923999i	$-0.624900\pi$
$521$	−2.23432e115	−0.764789	−0.382395	+	0.923999i	$0.624900\pi$
$522$	0	0
$523$	2.90809e115	0.845835	0.422917	−	0.906168i	$-0.361006\pi$
$523$	2.90809e115	0.845835	0.422917	+	0.906168i	$0.361006\pi$
$524$	−1.02318e115	−0.274391
$525$	0	0
$526$	−2.23689e115	−0.510212
$527$	9.82395e114	0.206697
$528$	0	0
$529$	3.29885e115	0.590877
$530$	1.70418e115	0.281703
$531$	0	0
$532$	−2.92142e114	−0.0411481
$533$	−6.73271e115	−0.875556
$534$	0	0
$535$	−4.04545e115	−0.448674
$536$	−1.22887e116	−1.25894
$537$	0	0
$538$	−1.84043e116	−1.60943
$539$	−7.98874e115	−0.645588
$540$	0	0
$541$	−5.34213e115	−0.368834	−0.184417	−	0.982848i	$-0.559040\pi$
$541$	−5.34213e115	−0.368834	−0.184417	+	0.982848i	$0.559040\pi$
$542$	−1.81609e116	−1.15922
$543$	0	0
$544$	4.24628e115	0.231769
$545$	−1.67794e115	−0.0847079
$546$	0	0
$547$	−3.54102e116	−1.52991	−0.764956	−	0.644082i	$-0.777239\pi$
$547$	−3.54102e116	−1.52991	−0.764956	+	0.644082i	$0.777239\pi$
$548$	−9.25639e115	−0.370057
$549$	0	0
$550$	2.08275e116	0.713219
$551$	−3.77078e116	−1.19533
$552$	0	0
$553$	−7.45680e115	−0.202644
$554$	−2.45513e116	−0.617888
$555$	0	0
$556$	9.41738e114	0.0203353
$557$	−3.05895e115	−0.0611965	−0.0305983	−	0.999532i	$-0.509741\pi$
$557$	−3.05895e115	−0.0611965	−0.0305983	+	0.999532i	$0.509741\pi$
$558$	0	0
$559$	−2.55476e116	−0.438882
$560$	−4.29863e115	−0.0684446
$561$	0	0
$562$	−1.30556e117	−1.78651
$563$	4.60778e116	0.584636	0.292318	−	0.956321i	$-0.405573\pi$
$563$	4.60778e116	0.584636	0.292318	+	0.956321i	$0.405573\pi$
$564$	0	0
$565$	−9.14995e115	−0.0998526
$566$	3.73535e116	0.378123
$567$	0	0
$568$	−2.28827e116	−0.199390
$569$	−1.23047e116	−0.0994944	−0.0497472	−	0.998762i	$-0.515842\pi$
$569$	−1.23047e116	−0.0994944	−0.0497472	+	0.998762i	$0.515842\pi$
$570$	0	0
$571$	2.42347e117	1.68812	0.844058	−	0.536252i	$-0.180160\pi$
$571$	2.42347e117	1.68812	0.844058	+	0.536252i	$0.180160\pi$
$572$	−1.67956e116	−0.108608
$573$	0	0
$574$	7.08235e116	0.394840
$575$	−2.25303e117	−1.16650
$576$	0	0
$577$	−6.46795e116	−0.288931	−0.144466	−	0.989510i	$-0.546146\pi$
$577$	−6.46795e116	−0.288931	−0.144466	+	0.989510i	$0.546146\pi$
$578$	2.34135e117	0.971702
$579$	0	0
$580$	4.35699e116	0.156134
$581$	−1.90474e116	−0.0634380
$582$	0	0
$583$	2.10390e117	0.605496
$584$	4.27663e117	1.14434
$585$	0	0
$586$	5.74231e117	1.32873
$587$	5.14572e117	1.10746	0.553728	−	0.832697i	$-0.313205\pi$
$587$	5.14572e117	1.10746	0.553728	+	0.832697i	$0.313205\pi$
$588$	0	0
$589$	1.85284e117	0.345095
$590$	−1.14586e117	−0.198574
$591$	0	0
$592$	−5.87541e117	−0.881791
$593$	6.08050e117	0.849406	0.424703	−	0.905333i	$-0.360379\pi$
$593$	6.08050e117	0.849406	0.424703	+	0.905333i	$0.360379\pi$
$594$	0	0
$595$	1.80804e116	0.0218896
$596$	3.28406e117	0.370207
$597$	0	0
$598$	7.70278e117	0.753091
$599$	−6.95061e116	−0.0632970	−0.0316485	−	0.999499i	$-0.510076\pi$
$599$	−6.95061e116	−0.0632970	−0.0316485	+	0.999499i	$0.510076\pi$
$600$	0	0
$601$	2.34715e118	1.85514	0.927568	−	0.373653i	$-0.121895\pi$
$601$	2.34715e118	1.85514	0.927568	+	0.373653i	$0.121895\pi$
$602$	2.68742e117	0.197918
$603$	0	0
$604$	−2.11718e117	−0.135421
$605$	2.50868e117	0.149569
$606$	0	0
$607$	−2.09245e118	−1.08426	−0.542132	−	0.840293i	$-0.682383\pi$
$607$	−2.09245e118	−1.08426	−0.542132	+	0.840293i	$0.682383\pi$
$608$	8.00868e117	0.386954
$609$	0	0
$610$	−2.66501e117	−0.111990
$611$	−1.48086e118	−0.580447
$612$	0	0
$613$	−5.75862e117	−0.196448	−0.0982241	−	0.995164i	$-0.531316\pi$
$613$	−5.75862e117	−0.196448	−0.0982241	+	0.995164i	$0.531316\pi$
$614$	6.06720e118	1.93122
$615$	0	0
$616$	−3.95684e117	−0.109690
$617$	1.99942e118	0.517350	0.258675	−	0.965964i	$-0.416714\pi$
$617$	1.99942e118	0.517350	0.258675	+	0.965964i	$0.416714\pi$
$618$	0	0
$619$	−7.65592e118	−1.72641	−0.863207	−	0.504850i	$-0.831548\pi$
$619$	−7.65592e118	−1.72641	−0.863207	+	0.504850i	$0.831548\pi$
$620$	−2.14089e117	−0.0450762
$621$	0	0
$622$	−1.13524e118	−0.208448
$623$	−3.13104e117	−0.0536966
$624$	0	0
$625$	5.21296e118	0.780159
$626$	−7.90746e118	−1.10568
$627$	0	0
$628$	2.91676e118	0.356136
$629$	2.47125e118	0.282010
$630$	0	0
$631$	1.51690e119	1.51255	0.756276	−	0.654253i	$-0.227017\pi$
$631$	1.51690e119	1.51255	0.756276	+	0.654253i	$0.227017\pi$
$632$	8.35550e118	0.778927
$633$	0	0
$634$	−1.15920e119	−0.944855
$635$	−1.21958e118	−0.0929668
$636$	0	0
$637$	7.49468e118	0.499836
$638$	2.28044e119	1.42279
$639$	0	0
$640$	6.04205e118	0.330016
$641$	−2.94751e119	−1.50657	−0.753284	−	0.657695i	$-0.771532\pi$
$641$	−2.94751e119	−1.50657	−0.753284	+	0.657695i	$0.771532\pi$
$642$	0	0
$643$	1.77154e119	0.793202	0.396601	−	0.917991i	$-0.370190\pi$
$643$	1.77154e119	0.793202	0.396601	+	0.917991i	$0.370190\pi$
$644$	−1.91122e118	−0.0801055
$645$	0	0
$646$	−7.82900e118	−0.287623
$647$	1.81550e119	0.624547	0.312274	−	0.949992i	$-0.398909\pi$
$647$	1.81550e119	0.624547	0.312274	+	0.949992i	$0.398909\pi$
$648$	0	0
$649$	−1.41463e119	−0.426818
$650$	−1.95394e119	−0.552197
$651$	0	0
$652$	3.17699e118	0.0787939
$653$	2.82590e119	0.656669	0.328335	−	0.944562i	$-0.393513\pi$
$653$	2.82590e119	0.656669	0.328335	+	0.944562i	$0.393513\pi$
$654$	0	0
$655$	1.19431e119	0.243704
$656$	−1.06436e120	−2.03552
$657$	0	0
$658$	1.55776e119	0.261758
$659$	−1.13945e119	−0.179500	−0.0897500	−	0.995964i	$-0.528607\pi$
$659$	−1.13945e119	−0.179500	−0.0897500	+	0.995964i	$0.528607\pi$
$660$	0	0
$661$	8.81386e118	0.122069	0.0610343	−	0.998136i	$-0.480560\pi$
$661$	8.81386e118	0.122069	0.0610343	+	0.998136i	$0.480560\pi$
$662$	1.09513e119	0.142233
$663$	0	0
$664$	2.13430e119	0.243844
$665$	3.41006e118	0.0365461
$666$	0	0
$667$	−2.46688e120	−2.32702
$668$	−6.82810e118	−0.0604367
$669$	0	0
$670$	−6.40484e119	−0.499262
$671$	−3.29009e119	−0.240713
$672$	0	0
$673$	−1.45790e119	−0.0939910	−0.0469955	−	0.998895i	$-0.514965\pi$
$673$	−1.45790e119	−0.0939910	−0.0469955	+	0.998895i	$0.514965\pi$
$674$	−1.88585e120	−1.14146
$675$	0	0
$676$	−4.20855e119	−0.224594
$677$	−2.68461e120	−1.34544	−0.672718	−	0.739899i	$-0.734873\pi$
$677$	−2.68461e120	−1.34544	−0.672718	+	0.739899i	$0.734873\pi$
$678$	0	0
$679$	−2.12930e119	−0.0941395
$680$	−2.02595e119	−0.0841395
$681$	0	0
$682$	−1.12054e120	−0.410763
$683$	−7.62763e118	−0.0262730	−0.0131365	−	0.999914i	$-0.504182\pi$
$683$	−7.62763e118	−0.0262730	−0.0131365	+	0.999914i	$0.504182\pi$
$684$	0	0
$685$	1.08046e120	0.328670
$686$	−1.61162e120	−0.460775
$687$	0	0
$688$	−4.03875e120	−1.02033
$689$	−1.97378e120	−0.468795
$690$	0	0
$691$	−5.17922e120	−1.08755	−0.543773	−	0.839232i	$-0.683005\pi$
$691$	−5.17922e120	−1.08755	−0.543773	+	0.839232i	$0.683005\pi$
$692$	−1.14507e118	−0.00226112
$693$	0	0
$694$	1.77033e120	0.309227
$695$	−1.09925e119	−0.0180611
$696$	0	0
$697$	4.47679e120	0.650989
$698$	1.45538e120	0.199123
$699$	0	0
$700$	4.84815e119	0.0587366
$701$	−4.03989e120	−0.460631	−0.230316	−	0.973116i	$-0.573976\pi$
$701$	−4.03989e120	−0.460631	−0.230316	+	0.973116i	$0.573976\pi$
$702$	0	0
$703$	4.66090e120	0.470835
$704$	3.75826e120	0.357395
$705$	0	0
$706$	4.38710e120	0.369809
$707$	3.70511e120	0.294087
$708$	0	0
$709$	1.03782e121	0.730559	0.365279	−	0.930898i	$-0.380973\pi$
$709$	1.03782e121	0.730559	0.365279	+	0.930898i	$0.380973\pi$
$710$	−1.19264e120	−0.0790732
$711$	0	0
$712$	3.50840e120	0.206400
$713$	1.21215e121	0.671818
$714$	0	0
$715$	1.96048e120	0.0964619
$716$	1.07138e121	0.496754
$717$	0	0
$718$	2.77339e121	1.14215
$719$	2.67902e121	1.03992	0.519958	−	0.854192i	$-0.325948\pi$
$719$	2.67902e121	1.03992	0.519958	+	0.854192i	$0.325948\pi$
$720$	0	0
$721$	−1.02885e121	−0.354896
$722$	2.04103e121	0.663770
$723$	0	0
$724$	−1.79493e121	−0.518988
$725$	6.25767e121	1.70627
$726$	0	0
$727$	5.01652e120	0.121672	0.0608359	−	0.998148i	$-0.480623\pi$
$727$	5.01652e120	0.121672	0.0608359	+	0.998148i	$0.480623\pi$
$728$	3.71213e120	0.0849258
$729$	0	0
$730$	2.22896e121	0.453817
$731$	1.69873e121	0.326315
$732$	0	0
$733$	3.32847e121	0.569280	0.284640	−	0.958634i	$-0.408126\pi$
$733$	3.32847e121	0.569280	0.284640	+	0.958634i	$0.408126\pi$
$734$	−6.70737e121	−1.08260
$735$	0	0
$736$	5.23937e121	0.753307
$737$	−7.90710e121	−1.07312
$738$	0	0
$739$	−5.03362e121	−0.608824	−0.304412	−	0.952540i	$-0.598460\pi$
$739$	−5.03362e121	−0.608824	−0.304412	+	0.952540i	$0.598460\pi$
$740$	−5.38549e120	−0.0615003
$741$	0	0
$742$	2.07628e121	0.211408
$743$	1.10466e122	1.06219	0.531096	−	0.847312i	$-0.321780\pi$
$743$	1.10466e122	1.06219	0.531096	+	0.847312i	$0.321780\pi$
$744$	0	0
$745$	−3.83335e121	−0.328804
$746$	2.28958e122	1.85505
$747$	0	0
$748$	1.11679e121	0.0807520
$749$	−4.92876e121	−0.336713
$750$	0	0
$751$	−1.64280e122	−1.00205	−0.501023	−	0.865434i	$-0.667043\pi$
$751$	−1.64280e122	−1.00205	−0.501023	+	0.865434i	$0.667043\pi$
$752$	−2.34106e122	−1.34944
$753$	0	0
$754$	−2.13941e122	−1.10157
$755$	2.47130e121	0.120276
$756$	0	0
$757$	3.36710e122	1.46447	0.732237	−	0.681050i	$-0.238476\pi$
$757$	3.36710e122	1.46447	0.732237	+	0.681050i	$0.238476\pi$
$758$	1.73054e122	0.711606
$759$	0	0
$760$	−3.82104e121	−0.140477
$761$	−1.12323e122	−0.390498	−0.195249	−	0.980754i	$-0.562552\pi$
$761$	−1.12323e122	−0.390498	−0.195249	+	0.980754i	$0.562552\pi$
$762$	0	0
$763$	−2.04431e121	−0.0635702
$764$	−4.27493e121	−0.125737
$765$	0	0
$766$	−4.51832e122	−1.18920
$767$	1.32714e122	0.330457
$768$	0	0
$769$	6.90046e122	1.53819	0.769093	−	0.639137i	$-0.220708\pi$
$769$	6.90046e122	1.53819	0.769093	+	0.639137i	$0.220708\pi$
$770$	−2.06229e121	−0.0435004
$771$	0	0
$772$	−1.71008e122	−0.323058
$773$	−6.33678e122	−1.13303	−0.566513	−	0.824053i	$-0.691708\pi$
$773$	−6.33678e122	−1.13303	−0.566513	+	0.824053i	$0.691708\pi$
$774$	0	0
$775$	−3.07483e122	−0.492604
$776$	2.38593e122	0.361855
$777$	0	0
$778$	2.79289e122	0.379683
$779$	8.44344e122	1.08687
$780$	0	0
$781$	−1.47237e122	−0.169961
$782$	−5.12182e122	−0.559934
$783$	0	0
$784$	1.18482e123	1.16203
$785$	−3.40461e122	−0.316306
$786$	0	0
$787$	−5.78520e122	−0.482383	−0.241192	−	0.970477i	$-0.577538\pi$
$787$	−5.78520e122	−0.482383	−0.241192	+	0.970477i	$0.577538\pi$
$788$	5.54284e121	0.0437893
$789$	0	0
$790$	4.35485e122	0.308903
$791$	−1.11478e122	−0.0749358
$792$	0	0
$793$	3.08661e122	0.186368
$794$	−3.14923e123	−1.80233
$795$	0	0
$796$	−1.08155e123	−0.556211
$797$	−3.16392e123	−1.54258	−0.771290	−	0.636484i	$-0.780388\pi$
$797$	−3.16392e123	−1.54258	−0.771290	+	0.636484i	$0.780388\pi$
$798$	0	0
$799$	9.84670e122	0.431571
$800$	−1.32905e123	−0.552355
$801$	0	0
$802$	−4.25573e123	−1.59061
$803$	2.75177e123	0.975441
$804$	0	0
$805$	2.23090e122	0.0711466
$806$	1.05124e123	0.318026
$807$	0	0
$808$	−4.15165e123	−1.13041
$809$	−3.81973e122	−0.0986781	−0.0493390	−	0.998782i	$-0.515711\pi$
$809$	−3.81973e122	−0.0986781	−0.0493390	+	0.998782i	$0.515711\pi$
$810$	0	0
$811$	3.48486e123	0.810585	0.405292	−	0.914187i	$-0.367170\pi$
$811$	3.48486e123	0.810585	0.405292	+	0.914187i	$0.367170\pi$
$812$	5.30833e122	0.117173
$813$	0	0
$814$	−2.81876e123	−0.560429
$815$	−3.70837e122	−0.0699818
$816$	0	0
$817$	3.20390e123	0.544805
$818$	−1.07955e124	−1.74272
$819$	0	0
$820$	−9.75607e122	−0.141967
$821$	−7.55967e123	−1.04453	−0.522263	−	0.852785i	$-0.674912\pi$
$821$	−7.55967e123	−1.04453	−0.522263	+	0.852785i	$0.674912\pi$
$822$	0	0
$823$	−1.18964e124	−1.48225	−0.741127	−	0.671365i	$-0.765708\pi$
$823$	−1.18964e124	−1.48225	−0.741127	+	0.671365i	$0.765708\pi$
$824$	1.15284e124	1.36415
$825$	0	0
$826$	−1.39606e123	−0.149023
$827$	7.43241e123	0.753608	0.376804	−	0.926293i	$-0.377023\pi$
$827$	7.43241e123	0.753608	0.376804	+	0.926293i	$0.377023\pi$
$828$	0	0
$829$	2.81405e122	0.0257492	0.0128746	−	0.999917i	$-0.495902\pi$
$829$	2.81405e122	0.0257492	0.0128746	+	0.999917i	$0.495902\pi$
$830$	1.11239e123	0.0967023
$831$	0	0
$832$	−3.52583e123	−0.276707
$833$	−4.98344e123	−0.371635
$834$	0	0
$835$	7.97017e122	0.0536775
$836$	2.10632e123	0.134821
$837$	0	0
$838$	−6.98219e122	−0.0403758
$839$	1.60603e124	0.882818	0.441409	−	0.897306i	$-0.354479\pi$
$839$	1.60603e124	0.882818	0.441409	+	0.897306i	$0.354479\pi$
$840$	0	0
$841$	4.83871e124	2.40381
$842$	2.77105e124	1.30882
$843$	0	0
$844$	−1.11057e124	−0.474235
$845$	4.91247e123	0.199476
$846$	0	0
$847$	3.05644e123	0.112246
$848$	−3.12031e124	−1.08987
$849$	0	0
$850$	1.29924e124	0.410567
$851$	3.04921e124	0.916603
$852$	0	0
$853$	5.85095e124	1.59182	0.795908	−	0.605418i	$-0.206994\pi$
$853$	5.85095e124	1.59182	0.795908	+	0.605418i	$0.206994\pi$
$854$	−3.24690e123	−0.0840446
$855$	0	0
$856$	5.52278e124	1.29426
$857$	2.43950e124	0.544022	0.272011	−	0.962294i	$-0.412311\pi$
$857$	2.43950e124	0.544022	0.272011	+	0.962294i	$0.412311\pi$
$858$	0	0
$859$	−1.00229e124	−0.202433	−0.101217	−	0.994864i	$-0.532274\pi$
$859$	−1.00229e124	−0.202433	−0.101217	+	0.994864i	$0.532274\pi$
$860$	−3.70198e123	−0.0711623
$861$	0	0
$862$	−4.94327e124	−0.860906
$863$	8.20747e124	1.36066	0.680331	−	0.732905i	$-0.261836\pi$
$863$	8.20747e124	1.36066	0.680331	+	0.732905i	$0.261836\pi$
$864$	0	0
$865$	1.33659e122	0.00200824
$866$	7.41835e124	1.06120
$867$	0	0
$868$	−2.60835e123	−0.0338281
$869$	5.37629e124	0.663960
$870$	0	0
$871$	7.41809e124	0.830846
$872$	2.29069e124	0.244352
$873$	0	0
$874$	−9.65999e124	−0.934848
$875$	−1.17780e124	−0.108575
$876$	0	0
$877$	1.18022e124	0.0987368	0.0493684	−	0.998781i	$-0.484279\pi$
$877$	1.18022e124	0.0987368	0.0493684	+	0.998781i	$0.484279\pi$
$878$	−1.40777e125	−1.12206
$879$	0	0
$880$	3.09928e124	0.224257
$881$	−9.93103e124	−0.684728	−0.342364	−	0.939567i	$-0.611228\pi$
$881$	−9.93103e124	−0.684728	−0.342364	+	0.939567i	$0.611228\pi$
$882$	0	0
$883$	−4.38150e123	−0.0274342	−0.0137171	−	0.999906i	$-0.504366\pi$
$883$	−4.38150e123	−0.0274342	−0.0137171	+	0.999906i	$0.504366\pi$
$884$	−1.04772e124	−0.0625208
$885$	0	0
$886$	−2.35515e125	−1.27669
$887$	−1.62296e125	−0.838597	−0.419298	−	0.907849i	$-0.637724\pi$
$887$	−1.62296e125	−0.838597	−0.419298	+	0.907849i	$0.637724\pi$
$888$	0	0
$889$	−1.48587e124	−0.0697682
$890$	1.82856e124	0.0818530
$891$	0	0
$892$	−1.12261e125	−0.456798
$893$	1.85713e125	0.720537
$894$	0	0
$895$	−1.25058e125	−0.441198
$896$	7.36132e124	0.247665
$897$	0	0
$898$	−3.59401e125	−1.09985
$899$	−3.36669e125	−0.982689
$900$	0	0
$901$	1.31243e125	0.348556
$902$	−5.10631e125	−1.29369
$903$	0	0
$904$	1.24914e125	0.288039
$905$	2.09515e125	0.460946
$906$	0	0
$907$	1.62229e125	0.324951	0.162476	−	0.986713i	$-0.448052\pi$
$907$	1.62229e125	0.324951	0.162476	+	0.986713i	$0.448052\pi$
$908$	−2.18686e125	−0.417997
$909$	0	0
$910$	1.93475e124	0.0336795
$911$	6.69682e125	1.11260	0.556298	−	0.830983i	$-0.312221\pi$
$911$	6.69682e125	1.11260	0.556298	+	0.830983i	$0.312221\pi$
$912$	0	0
$913$	1.37330e125	0.207853
$914$	−1.54699e126	−2.23498
$915$	0	0
$916$	−2.08585e125	−0.274616
$917$	1.45509e125	0.182891
$918$	0	0
$919$	1.25762e126	1.44092	0.720458	−	0.693498i	$-0.243931\pi$
$919$	1.25762e126	1.44092	0.720458	+	0.693498i	$0.243931\pi$
$920$	−2.49977e125	−0.273474
$921$	0	0
$922$	5.30287e125	0.528989
$923$	1.38132e125	0.131589
$924$	0	0
$925$	−7.73484e125	−0.672091
$926$	−4.84334e125	−0.401955
$927$	0	0
$928$	−1.45521e126	−1.10188
$929$	3.95718e125	0.286232	0.143116	−	0.989706i	$-0.454288\pi$
$929$	3.95718e125	0.286232	0.143116	+	0.989706i	$0.454288\pi$
$930$	0	0
$931$	−9.39901e125	−0.620470
$932$	2.66133e124	0.0167850
$933$	0	0
$934$	−1.58108e126	−0.910359
$935$	−1.30358e125	−0.0717208
$936$	0	0
$937$	2.28071e126	1.14588	0.572938	−	0.819599i	$-0.305804\pi$
$937$	2.28071e126	1.14588	0.572938	+	0.819599i	$0.305804\pi$
$938$	−7.80331e125	−0.374678
$939$	0	0
$940$	−2.14585e125	−0.0941164
$941$	1.01451e126	0.425303	0.212652	−	0.977128i	$-0.431790\pi$
$941$	1.01451e126	0.425303	0.212652	+	0.977128i	$0.431790\pi$
$942$	0	0
$943$	5.52379e126	2.11588
$944$	2.09805e126	0.768255
$945$	0	0
$946$	−1.93761e126	−0.648475
$947$	−4.90614e126	−1.56988	−0.784940	−	0.619572i	$-0.787306\pi$
$947$	−4.90614e126	−1.56988	−0.784940	+	0.619572i	$0.787306\pi$
$948$	0	0
$949$	−2.58158e126	−0.755218
$950$	2.45042e126	0.685469
$951$	0	0
$952$	−2.46831e125	−0.0631436
$953$	2.22780e126	0.545040	0.272520	−	0.962150i	$-0.412143\pi$
$953$	2.22780e126	0.545040	0.272520	+	0.962150i	$0.412143\pi$
$954$	0	0
$955$	4.98996e125	0.111674
$956$	−2.46330e126	−0.527300
$957$	0	0
$958$	−5.21145e126	−1.02076
$959$	1.31638e126	0.246655
$960$	0	0
$961$	−4.17673e126	−0.716295
$962$	2.64443e126	0.433902
$963$	0	0
$964$	2.19596e125	0.0329876
$965$	1.99610e126	0.286928
$966$	0	0
$967$	7.99613e126	1.05258	0.526290	−	0.850305i	$-0.323583\pi$
$967$	7.99613e126	1.05258	0.526290	+	0.850305i	$0.323583\pi$
$968$	−3.42481e126	−0.431453
$969$	0	0
$970$	1.24354e126	0.143503
$971$	−3.94162e126	−0.435369	−0.217685	−	0.976019i	$-0.569850\pi$
$971$	−3.94162e126	−0.435369	−0.217685	+	0.976019i	$0.569850\pi$
$972$	0	0
$973$	−1.33927e125	−0.0135542
$974$	8.52311e126	0.825738
$975$	0	0
$976$	4.87955e126	0.433274
$977$	1.42908e126	0.121489	0.0607444	−	0.998153i	$-0.480653\pi$
$977$	1.42908e126	0.121489	0.0607444	+	0.998153i	$0.480653\pi$
$978$	0	0
$979$	2.25746e126	0.175936
$980$	1.08602e126	0.0810456
$981$	0	0
$982$	−1.80219e126	−0.123328
$983$	8.05184e126	0.527680	0.263840	−	0.964566i	$-0.415011\pi$
$983$	8.05184e126	0.527680	0.263840	+	0.964566i	$0.415011\pi$
$984$	0	0
$985$	−6.46994e125	−0.0388920
$986$	1.42256e127	0.819033
$987$	0	0
$988$	−1.97605e126	−0.104383
$989$	2.09602e127	1.06061
$990$	0	0
$991$	3.77893e127	1.75484	0.877421	−	0.479720i	$-0.159262\pi$
$991$	3.77893e127	1.75484	0.877421	+	0.479720i	$0.159262\pi$
$992$	7.15044e126	0.318117
$993$	0	0
$994$	−1.45305e126	−0.0593415
$995$	1.26245e127	0.494005
$996$	0	0
$997$	−3.94225e127	−1.41645	−0.708223	−	0.705989i	$-0.750503\pi$
$997$	−3.94225e127	−1.41645	−0.708223	+	0.705989i	$0.750503\pi$
$998$	−2.80430e126	−0.0965554
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.86.a.a.1.2		6
3.2	odd	2		1.86.a.a.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.86.a.a.1.5	✓	6	3.2	odd	2
9.86.a.a.1.2		6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 86 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q-7.11528e12 q^{2} +1.19416e25 q^{4} -1.39389e29 q^{5} -1.69824e35 q^{7} +1.90292e38 q^{8} +O(q^{10})\)	\(q-7.11528e12 q^{2} +1.19416e25 q^{4} -1.39389e29 q^{5} -1.69824e35 q^{7} +1.90292e38 q^{8} +9.91791e41 q^{10} +1.22442e44 q^{11} -1.14869e47 q^{13} +1.20835e48 q^{14} -1.81594e51 q^{16} +7.63802e51 q^{17} +1.44057e54 q^{19} -1.66452e54 q^{20} -8.71207e56 q^{22} +9.42435e57 q^{23} -2.39065e59 q^{25} +8.17328e59 q^{26} -2.02796e60 q^{28} -2.61757e62 q^{29} +1.28619e63 q^{31} +5.55940e63 q^{32} -5.43466e64 q^{34} +2.36716e64 q^{35} +3.23546e66 q^{37} -1.02500e67 q^{38} -2.65245e67 q^{40} +5.86119e68 q^{41} +2.22405e69 q^{43} +1.46215e69 q^{44} -6.70569e70 q^{46} +1.28917e71 q^{47} -6.52452e71 q^{49} +1.70101e72 q^{50} -1.37172e72 q^{52} +1.71828e73 q^{53} -1.70670e73 q^{55} -3.23161e73 q^{56} +1.86247e75 q^{58} -1.15535e75 q^{59} -2.68706e75 q^{61} -9.15160e75 q^{62} +3.06943e76 q^{64} +1.60115e76 q^{65} -6.45785e77 q^{67} +9.12098e76 q^{68} -1.68430e77 q^{70} -1.20251e78 q^{71} +2.24741e79 q^{73} -2.30212e79 q^{74} +1.72026e79 q^{76} -2.07936e79 q^{77} +4.39089e80 q^{79} +2.53123e80 q^{80} -4.17040e81 q^{82} +1.12159e81 q^{83} -1.06466e81 q^{85} -1.58247e82 q^{86} +2.32996e82 q^{88} +1.84370e82 q^{89} +1.95076e82 q^{91} +1.12541e83 q^{92} -9.17279e83 q^{94} -2.00799e83 q^{95} +1.25383e84 q^{97} +4.64238e84 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3596910688800 q^{2} + 14\!\cdots\!32 q^{4}+ \cdots - 44\!\cdots\!00 q^{8}+O(q^{10}) \) 6 * q + 3596910688800 * q^2 + 140991407339885551387640832 * q^4 + 937371071374809475998758615100 * q^5 + 376764526445862177226143056468406000 * q^7 - 444573639427992844351424894916577689600 * q^8	\( 6 q + 3596910688800 q^{2} + 14\!\cdots\!32 q^{4}+ \cdots - 49\!\cdots\!00 q^{98}+O(q^{100}) \) 6 * q + 3596910688800 * q^2 + 140991407339885551387640832 * q^4 + 937371071374809475998758615100 * q^5 + 376764526445862177226143056468406000 * q^7 - 444573639427992844351424894916577689600 * q^8 + 94651165962435813693946284861726959764800 * q^10 + 56344805701335918998354740625397619012956888 * q^11 - 380409468466294979156527797290184755501373645900 * q^13 - 7432102291035232990382031969981134697595704847104 * q^14 + 2636948568634008151994191667083023793288011486068736 * q^16 + 51365945458144838311659694040021464865555671618554900 * q^17 + 2653138201866103222242250000135395331152453781661358360 * q^19 + 52474536419792695778976723338965188133980339812187187200 * q^20 + 3581897081140779531372538339240606543513118132263441718400 * q^22 + 2885510207115801266245992081450013398631817932489294263600 * q^23 + 669968020810517762245853029111649576216707129701526846916250 * q^25 + 145338677717367061512932551412743816475529536844287947743168 * q^26 + 26317831788111975278561322769557791839073407987295193709977600 * q^28 + 126005957659709196887223202461409590769523616790635653593969260 * q^29 - 5173343222869174361945421290475955243870433981978751385509914688 * q^31 - 18707915462589185913352646999729455863851090555123851448234803200 * q^32 - 261567067349813682388055634030637558284890219695677173368549801536 * q^34 + 54720272714504178732776803597096361295121671934223039039646799200 * q^35 - 5097772448818865838142977649516403030637492688710699135052039832700 * q^37 + 48700117286552805406633697613393636582143669921611431061746550761600 * q^38 - 142216395874814214555238931398128417040750190812408712268526706688000 * q^40 + 37443196175066827621993378286362463826782697218192853395514169611588 * q^41 - 1200203503033233321208433978807766368170132198490662545566874292959000 * q^43 + 18639061742892206758508411691062975986004422355135358223957061170139136 * q^44 - 191201172378193769791517179835271412887470991983918549920785652631609088 * q^46 + 239424902055614885318194585971856964272866563499240512979067317687189600 * q^47 - 3550036072199457619495079372134003262477445775089732177587676397325457258 * q^49 + 11494548593012586974824937998111766287236762210273483206149818153415980000 * q^50 - 58712069233310142887861446777253810318205781466445594810258784313124096000 * q^52 + 50490336878498884627542374457418517146058176491360508941999343448428076700 * q^53 + 39301939079139487846929886085782264562447760597309570618345636737530354800 * q^55 - 587681993552427976427603903951469305598093495610137163751240432058398146560 * q^56 + 1968773654564353990385431635289950834066592911242318428340655057560215041600 * q^58 - 6616590288827867291331513194467053420958403068835561414972249041164074836680 * q^59 + 14357623272339506273937696878826484910577784548921932472541795844444520630612 * q^61 - 6341655988756470271607502111666483932112595649902706601178034698608656870400 * q^62 - 15036793202050903912474653273096694719068286214625123977211579195245857865728 * q^64 + 207821434856417257245443053802293031083793273150318306362240037299645012878600 * q^65 - 676342476586532149280756429155984326543089556982073869153059292790609382659400 * q^67 + 3163312242521042817824168546059434229649323239544821535981619303392310998579200 * q^68 - 6084039126370540917643976340500810012180196811570702685650569892863510961958400 * q^70 + 6034633570006156478287618014555933721359683069405109018337202921275711590822288 * q^71 + 35801030708258502256835696755718519936386302900895514245440128302587327554955900 * q^73 - 107340388271157498582387358259935699803904453010588240913436902735784529206718784 * q^74 + 161366039234563681095121956921292746446621209914504282248055858395547636251627520 * q^76 - 251398792676383195671611646509617352303457127744134928661968949244057263571048000 * q^77 - 1371264739680910465180747804297591457073099822996075412863178473301594188074547360 * q^79 + 4133302113696354289363675864719400535772990320893278365909081697225137404615065600 * q^80 - 1521817925451755348555955193889971681134404529402094946034920762170082779676769600 * q^82 + 6003587143963376493630220870754035373224271946820478343977301287860006839810301800 * q^83 + 17517819416067376478784379475048913828437460883636030543204171384490930355142297800 * q^85 - 21492879965867203934779808388379416439833228958041181100627630027642419671434758272 * q^86 + 272530707230233729788642007241687387343090541246894873629875449706966387853783859200 * q^88 - 160168600498492831669414330089333488062247500152820008689246769174592053409073033820 * q^89 - 25835286532054033379869466839714977397623074555127707439218236615589791891497666528 * q^91 + 409168494351117176400001947891440713569740400895293133641599839567086438014810726400 * q^92 - 1363919087472816080652148503710266001883533236220476628035821611168261836377449504256 * q^94 + 5333227198671761899795642368410473530089556162431166206847226445312136951029790006000 * q^95 + 1982258923770441792809455137165411551481047984016852591852301644261535493014975149900 * q^97 - 4998389537167322966144480371748484731963375313000939154777788888434561052122410226400 * q^98

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