LMFDB - Embedded newform 9.52.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,52,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, 52, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 52);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 52 $
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:	$148.258218073$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 495735060514x^{2} - 23954614981416598x + 48979992255622025570313 $ x^4 - 2x^3 - 495735060514x^2 - 23954614981416598*x + 48979992255622025570313
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{23}\cdot 3^{14}\cdot 5^{3}\cdot 7^{2}\cdot 13\cdot 17 $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-457245.$ 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)

$f(q)$	$=$	$q+8.71140e7 q^{2} +5.33705e15 q^{4} -8.70295e17 q^{5} +3.14283e21 q^{7} +2.68769e23 q^{8} +O(q^{10})$	\(q+8.71140e7 q^{2} +5.33705e15 q^{4} -8.70295e17 q^{5} +3.14283e21 q^{7} +2.68769e23 q^{8} -7.58149e25 q^{10} -4.69985e26 q^{11} +9.04757e27 q^{13} +2.73785e29 q^{14} +1.13956e31 q^{16} +1.94276e30 q^{17} -2.88440e32 q^{19} -4.64481e33 q^{20} -4.09423e34 q^{22} -1.73996e34 q^{23} +3.13324e35 q^{25} +7.88170e35 q^{26} +1.67734e37 q^{28} -2.51798e37 q^{29} -3.39978e37 q^{31} +3.87499e38 q^{32} +1.69241e38 q^{34} -2.73519e39 q^{35} +1.41519e40 q^{37} -2.51271e40 q^{38} -2.33908e41 q^{40} -1.62359e41 q^{41} -1.06168e41 q^{43} -2.50834e42 q^{44} -1.51575e42 q^{46} +2.33100e42 q^{47} -2.71188e42 q^{49} +2.72949e43 q^{50} +4.82874e43 q^{52} +5.52737e43 q^{53} +4.09026e44 q^{55} +8.44695e44 q^{56} -2.19351e45 q^{58} -2.66580e45 q^{59} -3.00082e45 q^{61} -2.96168e45 q^{62} +8.09610e45 q^{64} -7.87405e45 q^{65} +1.24565e45 q^{67} +1.03686e46 q^{68} -2.38273e47 q^{70} -2.67507e47 q^{71} +4.01968e47 q^{73} +1.23283e48 q^{74} -1.53942e48 q^{76} -1.47708e48 q^{77} -3.09063e48 q^{79} -9.91749e48 q^{80} -1.41437e49 q^{82} -1.48588e48 q^{83} -1.69077e48 q^{85} -9.24873e48 q^{86} -1.26317e50 q^{88} +1.49141e49 q^{89} +2.84350e49 q^{91} -9.28627e49 q^{92} +2.03063e50 q^{94} +2.51028e50 q^{95} -5.46477e50 q^{97} -2.36242e50 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 32756040 q^{2} + 79\!\cdots\!12 q^{4}+ \cdots + 13\!\cdots\!20 q^{8}+O(q^{10}) $ 4 * q - 32756040 * q^2 + 7978103470875712 * q^4 - 1214113112967557880 * q^5 + 6566332044151252469600 * q^7 + 139242173294665691205120 * q^8	$ 4 q - 32756040 q^{2} + 79\!\cdots\!12 q^{4}+ \cdots + 31\!\cdots\!80 q^{98}+O(q^{100}) $ 4 * q - 32756040 * q^2 + 7978103470875712 * q^4 - 1214113112967557880 * q^5 + 6566332044151252469600 * q^7 + 139242173294665691205120 * q^8 - 26338767422633182993407120 * q^10 - 352319730227217761184247248 * q^11 + 30737495492092678036022901080 * q^13 - 116878411871248994844784530624 * q^14 + 13655541308212814904424583532544 * q^16 - 48152025926602119975132578130120 * q^17 + 817578654717102241686587953106480 * q^19 - 6688106698568613691058684703008640 * q^20 - 34873949046188270313389204382330720 * q^22 + 54442545328795748403982512519744480 * q^23 - 577962011134461749109509927876368100 * q^25 - 1509847347916659653711306190553689648 * q^26 + 34411298173690719862562837156054996480 * q^28 - 24524817706178324469842039147126378520 * q^29 - 74015080632891216448581759119415494272 * q^31 + 698885110517892283834830116511622594560 * q^32 + 599176354190711613816800945566309634064 * q^34 - 5459558934032100428649177266758776617280 * q^35 + 9223299799194559520674909690367653437560 * q^37 - 42209741287618122996397532876280940717920 * q^38 - 260218563144774091908833544090781982745600 * q^40 - 146626572441904135431040424870320811649768 * q^41 - 383253403750663564628750277915860311246000 * q^43 - 3919911265019437916289330658643948094246144 * q^44 - 687622182810100175391810298681828635813312 * q^46 - 703242125794576181922406089648904926204480 * q^47 - 21525353693695885888621049774661370126875228 * q^49 + 65550763083377103476240548536052846777230600 * q^50 + 205575224727950383449569813934278240424406400 * q^52 + 46053881458574871528873628680364599519093960 * q^53 + 288271437023082169121432211103105268991934560 * q^55 + 718413197664523425962520880364481249783828480 * q^56 - 3260382815057328392932619475690091710393763920 * q^58 - 1119164779584192618652811959209270069996506640 * q^59 + 3426848506305498355799302542081826532801316248 * q^61 - 9652948821672246376570757837225648817671719680 * q^62 - 3410402571656263891001355509990182780636233728 * q^64 - 10662663070585071183633914150857043524084084560 * q^65 + 30875136607724238160818607702139418169238276720 * q^67 + 92264980123003683860202361552579885626636888960 * q^68 - 127365497175284237875848441551548839150619662720 * q^70 - 396890633217178572952249989093970445513163336288 * q^71 + 1093181650202404127682760092563948835468903177320 * q^73 + 2446722614206037598896806276944107193380656941456 * q^74 - 1930298057964975808050160660816178333985982024960 * q^76 - 1379856740595107958858322062475643650952236464000 * q^77 + 4057123342028363124154537966955503984273281629120 * q^79 - 6556705282035289158041818706914507044939664711680 * q^80 + 2672741123252406904410297531162443665031405248080 * q^82 - 10514534101014085301175610601927458547806407366960 * q^83 - 2214700921000481207852358003497850667551075883920 * q^85 + 43819383990098235110217468422860464230535375092832 * q^86 - 25053936600673669378312978656608794916631597373440 * q^88 + 90777724780188979543741952283884054816841444724440 * q^89 + 100567720661332633308233017957549269313038849882688 * q^91 - 192025202572015319809189966047000799088692638097920 * q^92 + 639818007616166555781273040037466169910601363859584 * q^94 + 418719878951800677902105757696028542296429654882400 * q^95 - 1321788056943507607869460465290134726019322989433720 * q^97 + 317844097908560926995320900303041587618753340105080 * 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 $

$2$	8.71140e7	1.83579	0.917895	−	0.396823i	$-0.129887\pi$
$2$	8.71140e7	1.83579	0.917895	+	0.396823i	$0.129887\pi$
$3$	0	0
$3$	0	0
$4$	5.33705e15	2.37013
$5$	−8.70295e17	−1.30596	−0.652982	−	0.757373i	$-0.726482\pi$
$5$	−8.70295e17	−1.30596	−0.652982	+	0.757373i	$0.726482\pi$
$6$	0	0
$7$	3.14283e21	0.885770	0.442885	−	0.896578i	$-0.353955\pi$
$7$	3.14283e21	0.885770	0.442885	+	0.896578i	$0.353955\pi$
$8$	2.68769e23	2.51527
$9$	0	0
$10$	−7.58149e25	−2.39748
$11$	−4.69985e26	−1.30789	−0.653944	−	0.756543i	$-0.726887\pi$
$11$	−4.69985e26	−1.30789	−0.653944	+	0.756543i	$0.726887\pi$
$12$	0	0
$13$	9.04757e27	0.355612	0.177806	−	0.984066i	$-0.443100\pi$
$13$	9.04757e27	0.355612	0.177806	+	0.984066i	$0.443100\pi$
$14$	2.73785e29	1.62609
$15$	0	0
$16$	1.13956e31	2.24738
$17$	1.94276e30	0.0816527	0.0408264	−	0.999166i	$-0.487001\pi$
$17$	1.94276e30	0.0816527	0.0408264	+	0.999166i	$0.487001\pi$
$18$	0	0
$19$	−2.88440e32	−0.710949	−0.355474	−	0.934686i	$-0.615681\pi$
$19$	−2.88440e32	−0.710949	−0.355474	+	0.934686i	$0.615681\pi$
$20$	−4.64481e33	−3.09530
$21$	0	0
$22$	−4.09423e34	−2.40101
$23$	−1.73996e34	−0.328458	−0.164229	−	0.986422i	$-0.552514\pi$
$23$	−1.73996e34	−0.328458	−0.164229	+	0.986422i	$0.552514\pi$
$24$	0	0
$25$	3.13324e35	0.705542
$26$	7.88170e35	0.652829
$27$	0	0
$28$	1.67734e37	2.09939
$29$	−2.51798e37	−1.28796	−0.643980	−	0.765042i	$-0.722718\pi$
$29$	−2.51798e37	−1.28796	−0.643980	+	0.765042i	$0.722718\pi$
$30$	0	0
$31$	−3.39978e37	−0.317488	−0.158744	−	0.987320i	$-0.550744\pi$
$31$	−3.39978e37	−0.317488	−0.158744	+	0.987320i	$0.550744\pi$
$32$	3.87499e38	1.61045
$33$	0	0
$34$	1.69241e38	0.149897
$35$	−2.73519e39	−1.15678
$36$	0	0
$37$	1.41519e40	1.45101	0.725506	−	0.688216i	$-0.241606\pi$
$37$	1.41519e40	1.45101	0.725506	+	0.688216i	$0.241606\pi$
$38$	−2.51271e40	−1.30515
$39$	0	0
$40$	−2.33908e41	−3.28485
$41$	−1.62359e41	−1.21475	−0.607375	−	0.794415i	$-0.707778\pi$
$41$	−1.62359e41	−1.21475	−0.607375	+	0.794415i	$0.707778\pi$
$42$	0	0
$43$	−1.06168e41	−0.235802	−0.117901	−	0.993025i	$-0.537617\pi$
$43$	−1.06168e41	−0.235802	−0.117901	+	0.993025i	$0.537617\pi$
$44$	−2.50834e42	−3.09986
$45$	0	0
$46$	−1.51575e42	−0.602980
$47$	2.33100e42	0.535854	0.267927	−	0.963439i	$-0.413661\pi$
$47$	2.33100e42	0.535854	0.267927	+	0.963439i	$0.413661\pi$
$48$	0	0
$49$	−2.71188e42	−0.215412
$50$	2.72949e43	1.29523
$51$	0	0
$52$	4.82874e43	0.842846
$53$	5.52737e43	0.593587	0.296793	−	0.954942i	$-0.404083\pi$
$53$	5.52737e43	0.593587	0.296793	+	0.954942i	$0.404083\pi$
$54$	0	0
$55$	4.09026e44	1.70805
$56$	8.44695e44	2.22795
$57$	0	0
$58$	−2.19351e45	−2.36443
$59$	−2.66580e45	−1.85824	−0.929119	−	0.369782i	$-0.879433\pi$
$59$	−2.66580e45	−1.85824	−0.929119	+	0.369782i	$0.879433\pi$
$60$	0	0
$61$	−3.00082e45	−0.893983	−0.446992	−	0.894538i	$-0.647505\pi$
$61$	−3.00082e45	−0.893983	−0.446992	+	0.894538i	$0.647505\pi$
$62$	−2.96168e45	−0.582842
$63$	0	0
$64$	8.09610e45	0.709066
$65$	−7.87405e45	−0.464417
$66$	0	0
$67$	1.24565e45	0.0339224	0.0169612	−	0.999856i	$-0.494601\pi$
$67$	1.24565e45	0.0339224	0.0169612	+	0.999856i	$0.494601\pi$
$68$	1.03686e46	0.193527
$69$	0	0
$70$	−2.38273e47	−2.12361
$71$	−2.67507e47	−1.66053	−0.830266	−	0.557368i	$-0.811811\pi$
$71$	−2.67507e47	−1.66053	−0.830266	+	0.557368i	$0.811811\pi$
$72$	0	0
$73$	4.01968e47	1.22874	0.614368	−	0.789020i	$-0.289411\pi$
$73$	4.01968e47	1.22874	0.614368	+	0.789020i	$0.289411\pi$
$74$	1.23283e48	2.66376
$75$	0	0
$76$	−1.53942e48	−1.68504
$77$	−1.47708e48	−1.15849
$78$	0	0
$79$	−3.09063e48	−1.26054	−0.630269	−	0.776377i	$-0.717056\pi$
$79$	−3.09063e48	−1.26054	−0.630269	+	0.776377i	$0.717056\pi$
$80$	−9.91749e48	−2.93499
$81$	0	0
$82$	−1.41437e49	−2.23003
$83$	−1.48588e48	−0.171986	−0.0859929	−	0.996296i	$-0.527406\pi$
$83$	−1.48588e48	−0.171986	−0.0859929	+	0.996296i	$0.527406\pi$
$84$	0	0
$85$	−1.69077e48	−0.106636
$86$	−9.24873e48	−0.432884
$87$	0	0
$88$	−1.26317e50	−3.28969
$89$	1.49141e49	0.291173	0.145587	−	0.989346i	$-0.453493\pi$
$89$	1.49141e49	0.291173	0.145587	+	0.989346i	$0.453493\pi$
$90$	0	0
$91$	2.84350e49	0.314990
$92$	−9.28627e49	−0.778487
$93$	0	0
$94$	2.03063e50	0.983716
$95$	2.51028e50	0.928473
$96$	0	0
$97$	−5.46477e50	−1.18821	−0.594105	−	0.804388i	$-0.702494\pi$
$97$	−5.46477e50	−1.18821	−0.594105	+	0.804388i	$0.702494\pi$
$98$	−2.36242e50	−0.395451
$99$	0	0
$100$	1.67223e51	1.67223
$101$	−1.57367e51	−1.22101	−0.610503	−	0.792014i	$-0.709032\pi$
$101$	−1.57367e51	−1.22101	−0.610503	+	0.792014i	$0.709032\pi$
$102$	0	0
$103$	−2.10363e51	−0.989966	−0.494983	−	0.868903i	$-0.664826\pi$
$103$	−2.10363e51	−0.989966	−0.494983	+	0.868903i	$0.664826\pi$
$104$	2.43170e51	0.894459
$105$	0	0
$106$	4.81512e51	1.08970
$107$	−2.77520e51	−0.494319	−0.247160	−	0.968975i	$-0.579497\pi$
$107$	−2.77520e51	−0.494319	−0.247160	+	0.968975i	$0.579497\pi$
$108$	0	0
$109$	1.47283e52	1.63597	0.817986	−	0.575238i	$-0.195091\pi$
$109$	1.47283e52	1.63597	0.817986	+	0.575238i	$0.195091\pi$
$110$	3.56319e52	3.13563
$111$	0	0
$112$	3.58143e52	1.99066
$113$	3.63164e52	1.60917	0.804586	−	0.593836i	$-0.202387\pi$
$113$	3.63164e52	1.60917	0.804586	+	0.593836i	$0.202387\pi$
$114$	0	0
$115$	1.51428e52	0.428954
$116$	−1.34386e53	−3.05263
$117$	0	0
$118$	−2.32229e53	−3.41134
$119$	6.10575e51	0.0723255
$120$	0	0
$121$	9.17560e52	0.710571
$122$	−2.61414e53	−1.64117
$123$	0	0
$124$	−1.81448e53	−0.752487
$125$	1.13805e53	0.384551
$126$	0	0
$127$	−2.33329e53	−0.525986	−0.262993	−	0.964798i	$-0.584710\pi$
$127$	−2.33329e53	−0.525986	−0.262993	+	0.964798i	$0.584710\pi$
$128$	−1.67287e53	−0.308750
$129$	0	0
$130$	−6.85940e53	−0.852572
$131$	3.64141e53	0.372264	0.186132	−	0.982525i	$-0.440405\pi$
$131$	3.64141e53	0.372264	0.186132	+	0.982525i	$0.440405\pi$
$132$	0	0
$133$	−9.06517e53	−0.629737
$134$	1.08513e53	0.0622745
$135$	0	0
$136$	5.22152e53	0.205378
$137$	4.42139e53	0.144273	0.0721364	−	0.997395i	$-0.477018\pi$
$137$	4.42139e53	0.144273	0.0721364	+	0.997395i	$0.477018\pi$
$138$	0	0
$139$	6.82260e54	1.53841	0.769205	−	0.639002i	$-0.220652\pi$
$139$	6.82260e54	1.53841	0.769205	+	0.639002i	$0.220652\pi$
$140$	−1.45978e55	−2.74172
$141$	0	0
$142$	−2.33036e55	−3.04839
$143$	−4.25222e54	−0.465101
$144$	0	0
$145$	2.19138e55	1.68203
$146$	3.50170e55	2.25570
$147$	0	0
$148$	7.55295e55	3.43908
$149$	1.19546e55	0.458441	0.229221	−	0.973374i	$-0.426382\pi$
$149$	1.19546e55	0.458441	0.229221	+	0.973374i	$0.426382\pi$
$150$	0	0
$151$	−1.21853e55	−0.332602	−0.166301	−	0.986075i	$-0.553182\pi$
$151$	−1.21853e55	−0.332602	−0.166301	+	0.986075i	$0.553182\pi$
$152$	−7.75236e55	−1.78823
$153$	0	0
$154$	−1.28675e56	−2.12674
$155$	2.95881e55	0.414628
$156$	0	0
$157$	−3.87399e55	−0.391487	−0.195743	−	0.980655i	$-0.562712\pi$
$157$	−3.87399e55	−0.391487	−0.195743	+	0.980655i	$0.562712\pi$
$158$	−2.69237e56	−2.31409
$159$	0	0
$160$	−3.37238e56	−2.10319
$161$	−5.46840e55	−0.290938
$162$	0	0
$163$	−1.93511e56	−0.751487	−0.375743	−	0.926724i	$-0.622613\pi$
$163$	−1.93511e56	−0.751487	−0.375743	+	0.926724i	$0.622613\pi$
$164$	−8.66517e56	−2.87911
$165$	0	0
$166$	−1.29441e56	−0.315730
$167$	−2.83095e56	−0.592463	−0.296232	−	0.955116i	$-0.595730\pi$
$167$	−2.83095e56	−0.592463	−0.296232	+	0.955116i	$0.595730\pi$
$168$	0	0
$169$	−5.65449e56	−0.873540
$170$	−1.47290e56	−0.195760
$171$	0	0
$172$	−5.66625e56	−0.558882
$173$	2.17979e57	1.85455	0.927275	−	0.374380i	$-0.122144\pi$
$173$	2.17979e57	1.85455	0.927275	+	0.374380i	$0.122144\pi$
$174$	0	0
$175$	9.84723e56	0.624948
$176$	−5.35574e57	−2.93932
$177$	0	0
$178$	1.29923e57	0.534533
$179$	−4.26922e56	−0.152264	−0.0761319	−	0.997098i	$-0.524257\pi$
$179$	−4.26922e56	−0.152264	−0.0761319	+	0.997098i	$0.524257\pi$
$180$	0	0
$181$	2.18558e57	0.587168	0.293584	−	0.955933i	$-0.405152\pi$
$181$	2.18558e57	0.587168	0.293584	+	0.955933i	$0.405152\pi$
$182$	2.47708e57	0.578256
$183$	0	0
$184$	−4.67647e57	−0.826160
$185$	−1.23163e58	−1.89497
$186$	0	0
$187$	−9.13066e56	−0.106793
$188$	1.24407e58	1.27004
$189$	0	0
$190$	2.18680e58	1.70448
$191$	1.12224e58	0.765130	0.382565	−	0.923929i	$-0.375041\pi$
$191$	1.12224e58	0.765130	0.382565	+	0.923929i	$0.375041\pi$
$192$	0	0
$193$	−1.46948e58	−0.768159	−0.384080	−	0.923300i	$-0.625481\pi$
$193$	−1.46948e58	−0.768159	−0.384080	+	0.923300i	$0.625481\pi$
$194$	−4.76058e58	−2.18130
$195$	0	0
$196$	−1.44734e58	−0.510554
$197$	3.80845e58	1.17994	0.589969	−	0.807426i	$-0.299140\pi$
$197$	3.80845e58	1.17994	0.589969	+	0.807426i	$0.299140\pi$
$198$	0	0
$199$	−2.34549e58	−0.561669	−0.280834	−	0.959756i	$-0.590611\pi$
$199$	−2.34549e58	−0.561669	−0.280834	+	0.959756i	$0.590611\pi$
$200$	8.42116e58	1.77463
$201$	0	0
$202$	−1.37088e59	−2.24151
$203$	−7.91357e58	−1.14084
$204$	0	0
$205$	1.41300e59	1.58642
$206$	−1.83256e59	−1.81737
$207$	0	0
$208$	1.03102e59	0.799194
$209$	1.35562e59	0.929841
$210$	0	0
$211$	6.94465e58	0.373635	0.186818	−	0.982395i	$-0.440183\pi$
$211$	6.94465e58	0.373635	0.186818	+	0.982395i	$0.440183\pi$
$212$	2.94999e59	1.40688
$213$	0	0
$214$	−2.41759e59	−0.907466
$215$	9.23975e58	0.307950
$216$	0	0
$217$	−1.06849e59	−0.281221
$218$	1.28304e60	3.00330
$219$	0	0
$220$	2.18299e60	4.04831
$221$	1.75772e58	0.0290367
$222$	0	0
$223$	−7.27716e59	−0.955406	−0.477703	−	0.878521i	$-0.658530\pi$
$223$	−7.27716e59	−0.955406	−0.477703	+	0.878521i	$0.658530\pi$
$224$	1.21784e60	1.42648
$225$	0	0
$226$	3.16367e60	2.95410
$227$	−1.77581e60	−1.48162	−0.740809	−	0.671716i	$-0.765558\pi$
$227$	−1.77581e60	−1.48162	−0.740809	+	0.671716i	$0.765558\pi$
$228$	0	0
$229$	−5.95206e59	−0.397066	−0.198533	−	0.980094i	$-0.563618\pi$
$229$	−5.95206e59	−0.397066	−0.198533	+	0.980094i	$0.563618\pi$
$230$	1.31915e60	0.787470
$231$	0	0
$232$	−6.76753e60	−3.23957
$233$	5.94034e59	0.254821	0.127410	−	0.991850i	$-0.459333\pi$
$233$	5.94034e59	0.254821	0.127410	+	0.991850i	$0.459333\pi$
$234$	0	0
$235$	−2.02866e60	−0.699806
$236$	−1.42275e61	−4.40426
$237$	0	0
$238$	5.31896e59	0.132774
$239$	6.11275e60	1.37117	0.685583	−	0.727995i	$-0.259547\pi$
$239$	6.11275e60	1.37117	0.685583	+	0.727995i	$0.259547\pi$
$240$	0	0
$241$	5.01746e60	0.910016	0.455008	−	0.890487i	$-0.349636\pi$
$241$	5.01746e60	0.910016	0.455008	+	0.890487i	$0.349636\pi$
$242$	7.99324e60	1.30446
$243$	0	0
$244$	−1.60155e61	−2.11885
$245$	2.36013e60	0.281320
$246$	0	0
$247$	−2.60968e60	−0.252822
$248$	−9.13754e60	−0.798567
$249$	0	0
$250$	9.91397e60	0.705956
$251$	−2.83094e61	−1.82075	−0.910376	−	0.413783i	$-0.864207\pi$
$251$	−2.83094e61	−1.82075	−0.910376	+	0.413783i	$0.864207\pi$
$252$	0	0
$253$	8.17756e60	0.429586
$254$	−2.03263e61	−0.965601
$255$	0	0
$256$	−3.28038e61	−1.27587
$257$	2.64892e61	0.932769	0.466384	−	0.884582i	$-0.345556\pi$
$257$	2.64892e61	0.932769	0.466384	+	0.884582i	$0.345556\pi$
$258$	0	0
$259$	4.44771e61	1.28526
$260$	−4.20242e61	−1.10073
$261$	0	0
$262$	3.17217e61	0.683399
$263$	3.49990e61	0.684201	0.342101	−	0.939663i	$-0.388862\pi$
$263$	3.49990e61	0.684201	0.342101	+	0.939663i	$0.388862\pi$
$264$	0	0
$265$	−4.81044e61	−0.775203
$266$	−7.89703e61	−1.15606
$267$	0	0
$268$	6.64808e60	0.0804005
$269$	1.25062e62	1.37544	0.687718	−	0.725978i	$-0.258612\pi$
$269$	1.25062e62	1.37544	0.687718	+	0.725978i	$0.258612\pi$
$270$	0	0
$271$	8.34364e61	0.759694	0.379847	−	0.925049i	$-0.375977\pi$
$271$	8.34364e61	0.759694	0.379847	+	0.925049i	$0.375977\pi$
$272$	2.21388e61	0.183504
$273$	0	0
$274$	3.85165e61	0.264855
$275$	−1.47257e62	−0.922770
$276$	0	0
$277$	7.61658e61	0.396758	0.198379	−	0.980125i	$-0.436432\pi$
$277$	7.61658e61	0.396758	0.198379	+	0.980125i	$0.436432\pi$
$278$	5.94344e62	2.82420
$279$	0	0
$280$	−7.35133e62	−2.90962
$281$	−1.57065e61	−0.0567634	−0.0283817	−	0.999597i	$-0.509035\pi$
$281$	−1.57065e61	−0.0567634	−0.0283817	+	0.999597i	$0.509035\pi$
$282$	0	0
$283$	−2.43727e61	−0.0735104	−0.0367552	−	0.999324i	$-0.511702\pi$
$283$	−2.43727e61	−0.0735104	−0.0367552	+	0.999324i	$0.511702\pi$
$284$	−1.42770e63	−3.93567
$285$	0	0
$286$	−3.70428e62	−0.853828
$287$	−5.10266e62	−1.07599
$288$	0	0
$289$	−5.62328e62	−0.993333
$290$	1.90900e63	3.08786
$291$	0	0
$292$	2.14532e63	2.91226
$293$	3.92051e62	0.487773	0.243887	−	0.969804i	$-0.421578\pi$
$293$	3.92051e62	0.487773	0.243887	+	0.969804i	$0.421578\pi$
$294$	0	0
$295$	2.32003e63	2.42679
$296$	3.80359e63	3.64968
$297$	0	0
$298$	1.04141e63	0.841602
$299$	−1.57424e62	−0.116804
$300$	0	0
$301$	−3.33668e62	−0.208867
$302$	−1.06151e63	−0.610588
$303$	0	0
$304$	−3.28693e63	−1.59777
$305$	2.61160e63	1.16751
$306$	0	0
$307$	3.00029e63	1.13536	0.567682	−	0.823248i	$-0.307840\pi$
$307$	3.00029e63	1.13536	0.567682	+	0.823248i	$0.307840\pi$
$308$	−7.88327e63	−2.74576
$309$	0	0
$310$	2.57754e63	0.761170
$311$	2.05385e63	0.558700	0.279350	−	0.960189i	$-0.409881\pi$
$311$	2.05385e63	0.558700	0.279350	+	0.960189i	$0.409881\pi$
$312$	0	0
$313$	−3.26529e63	−0.754295	−0.377147	−	0.926153i	$-0.623095\pi$
$313$	−3.26529e63	−0.754295	−0.377147	+	0.926153i	$0.623095\pi$
$314$	−3.37479e63	−0.718688
$315$	0	0
$316$	−1.64949e64	−2.98764
$317$	2.33370e63	0.389972	0.194986	−	0.980806i	$-0.437534\pi$
$317$	2.33370e63	0.389972	0.194986	+	0.980806i	$0.437534\pi$
$318$	0	0
$319$	1.18341e64	1.68451
$320$	−7.04599e63	−0.926014
$321$	0	0
$322$	−4.76375e63	−0.534101
$323$	−5.60368e62	−0.0580509
$324$	0	0
$325$	2.83482e63	0.250899
$326$	−1.68575e64	−1.37957
$327$	0	0
$328$	−4.36369e64	−3.05542
$329$	7.32593e63	0.474644
$330$	0	0
$331$	3.40604e64	1.89076	0.945378	−	0.325977i	$-0.105693\pi$
$331$	3.40604e64	1.89076	0.945378	+	0.325977i	$0.105693\pi$
$332$	−7.93023e63	−0.407628
$333$	0	0
$334$	−2.46615e64	−1.08764
$335$	−1.08408e63	−0.0443015
$336$	0	0
$337$	2.02190e64	0.709899	0.354949	−	0.934885i	$-0.384498\pi$
$337$	2.02190e64	0.709899	0.354949	+	0.934885i	$0.384498\pi$
$338$	−4.92586e64	−1.60364
$339$	0	0
$340$	−9.02373e63	−0.252740
$341$	1.59784e64	0.415239
$342$	0	0
$343$	−4.80889e64	−1.07658
$344$	−2.85347e64	−0.593106
$345$	0	0
$346$	1.89890e65	3.40457
$347$	9.66734e64	1.61029	0.805147	−	0.593075i	$-0.202086\pi$
$347$	9.66734e64	1.61029	0.805147	+	0.593075i	$0.202086\pi$
$348$	0	0
$349$	5.19371e64	0.747187	0.373594	−	0.927593i	$-0.378126\pi$
$349$	5.19371e64	0.747187	0.373594	+	0.927593i	$0.378126\pi$
$350$	8.57832e64	1.14727
$351$	0	0
$352$	−1.82119e65	−2.10628
$353$	3.23561e64	0.348097	0.174049	−	0.984737i	$-0.444315\pi$
$353$	3.23561e64	0.348097	0.174049	+	0.984737i	$0.444315\pi$
$354$	0	0
$355$	2.32810e65	2.16859
$356$	7.95972e64	0.690117
$357$	0	0
$358$	−3.71909e64	−0.279524
$359$	−2.12862e63	−0.0149001	−0.00745005	−	0.999972i	$-0.502371\pi$
$359$	−2.12862e63	−0.0149001	−0.00745005	+	0.999972i	$0.502371\pi$
$360$	0	0
$361$	−8.14040e64	−0.494552
$362$	1.90394e65	1.07792
$363$	0	0
$364$	1.51759e65	0.746567
$365$	−3.49831e65	−1.60468
$366$	0	0
$367$	−3.44041e65	−1.37286	−0.686429	−	0.727196i	$-0.740823\pi$
$367$	−3.44041e65	−1.37286	−0.686429	+	0.727196i	$0.740823\pi$
$368$	−1.98278e65	−0.738169
$369$	0	0
$370$	−1.07293e66	−3.47877
$371$	1.73716e65	0.525781
$372$	0	0
$373$	6.74887e65	1.78097	0.890484	−	0.455015i	$-0.150366\pi$
$373$	6.74887e65	1.78097	0.890484	+	0.455015i	$0.150366\pi$
$374$	−7.95408e64	−0.196049
$375$	0	0
$376$	6.26500e65	1.34782
$377$	−2.27816e65	−0.458014
$378$	0	0
$379$	−2.27327e65	−0.399348	−0.199674	−	0.979862i	$-0.563988\pi$
$379$	−2.27327e65	−0.399348	−0.199674	+	0.979862i	$0.563988\pi$
$380$	1.33975e66	2.20060
$381$	0	0
$382$	9.77629e65	1.40462
$383$	1.15048e66	1.54637	0.773183	−	0.634183i	$-0.218664\pi$
$383$	1.15048e66	1.54637	0.773183	+	0.634183i	$0.218664\pi$
$384$	0	0
$385$	1.28550e66	1.51294
$386$	−1.28012e66	−1.41018
$387$	0	0
$388$	−2.91658e66	−2.81621
$389$	−7.64966e65	−0.691715	−0.345857	−	0.938287i	$-0.612412\pi$
$389$	−7.64966e65	−0.691715	−0.345857	+	0.938287i	$0.612412\pi$
$390$	0	0
$391$	−3.38032e64	−0.0268195
$392$	−7.28868e65	−0.541819
$393$	0	0
$394$	3.31769e66	2.16612
$395$	2.68976e66	1.64622
$396$	0	0
$397$	−1.60215e66	−0.862074	−0.431037	−	0.902334i	$-0.641852\pi$
$397$	−1.60215e66	−0.862074	−0.431037	+	0.902334i	$0.641852\pi$
$398$	−2.04325e66	−1.03111
$399$	0	0
$400$	3.57050e66	1.58562
$401$	−1.99632e65	−0.0831857	−0.0415929	−	0.999135i	$-0.513243\pi$
$401$	−1.99632e65	−0.0831857	−0.0415929	+	0.999135i	$0.513243\pi$
$402$	0	0
$403$	−3.07597e65	−0.112903
$404$	−8.39874e66	−2.89394
$405$	0	0
$406$	−6.89383e66	−2.09434
$407$	−6.65119e66	−1.89776
$408$	0	0
$409$	−3.81426e66	−0.960430	−0.480215	−	0.877151i	$-0.659441\pi$
$409$	−3.81426e66	−0.960430	−0.480215	+	0.877151i	$0.659441\pi$
$410$	1.23092e67	2.91234
$411$	0	0
$412$	−1.12272e67	−2.34635
$413$	−8.37815e66	−1.64597
$414$	0	0
$415$	1.29315e66	0.224607
$416$	3.50593e66	0.572694
$417$	0	0
$418$	1.18094e67	1.70699
$419$	4.78644e66	0.650961	0.325480	−	0.945549i	$-0.394474\pi$
$419$	4.78644e66	0.650961	0.325480	+	0.945549i	$0.394474\pi$
$420$	0	0
$421$	−8.14181e66	−0.980681	−0.490340	−	0.871531i	$-0.663128\pi$
$421$	−8.14181e66	−0.980681	−0.490340	+	0.871531i	$0.663128\pi$
$422$	6.04977e66	0.685916
$423$	0	0
$424$	1.48559e67	1.49303
$425$	6.08711e65	0.0576094
$426$	0	0
$427$	−9.43107e66	−0.791863
$428$	−1.48114e67	−1.17160
$429$	0	0
$430$	8.04912e66	0.565331
$431$	5.75151e66	0.380725	0.190362	−	0.981714i	$-0.439034\pi$
$431$	5.75151e66	0.380725	0.190362	+	0.981714i	$0.439034\pi$
$432$	0	0
$433$	−3.28347e67	−1.93148	−0.965742	−	0.259505i	$-0.916441\pi$
$433$	−3.28347e67	−1.93148	−0.965742	+	0.259505i	$0.916441\pi$
$434$	−9.30807e66	−0.516263
$435$	0	0
$436$	7.86055e67	3.87746
$437$	5.01874e66	0.233517
$438$	0	0
$439$	1.32507e67	0.548775	0.274388	−	0.961619i	$-0.411525\pi$
$439$	1.32507e67	0.548775	0.274388	+	0.961619i	$0.411525\pi$
$440$	1.09933e68	4.29621
$441$	0	0
$442$	1.53122e66	0.0533053
$443$	−2.21195e67	−0.726909	−0.363454	−	0.931612i	$-0.618403\pi$
$443$	−2.21195e67	−0.726909	−0.363454	+	0.931612i	$0.618403\pi$
$444$	0	0
$445$	−1.29796e67	−0.380262
$446$	−6.33943e67	−1.75393
$447$	0	0
$448$	2.54447e67	0.628069
$449$	−2.50690e66	−0.0584596	−0.0292298	−	0.999573i	$-0.509305\pi$
$449$	−2.50690e66	−0.0584596	−0.0292298	+	0.999573i	$0.509305\pi$
$450$	0	0
$451$	7.63061e67	1.58876
$452$	1.93822e68	3.81394
$453$	0	0
$454$	−1.54698e68	−2.71994
$455$	−2.47468e67	−0.411366
$456$	0	0
$457$	−6.35904e67	−0.945211	−0.472605	−	0.881274i	$-0.656686\pi$
$457$	−6.35904e67	−0.945211	−0.472605	+	0.881274i	$0.656686\pi$
$458$	−5.18508e67	−0.728930
$459$	0	0
$460$	8.08179e67	1.01668
$461$	2.39534e67	0.285097	0.142549	−	0.989788i	$-0.454470\pi$
$461$	2.39534e67	0.285097	0.142549	+	0.989788i	$0.454470\pi$
$462$	0	0
$463$	−4.29264e67	−0.457519	−0.228759	−	0.973483i	$-0.573467\pi$
$463$	−4.29264e67	−0.457519	−0.228759	+	0.973483i	$0.573467\pi$
$464$	−2.86937e68	−2.89453
$465$	0	0
$466$	5.17487e67	0.467798
$467$	−1.29125e68	−1.10518	−0.552588	−	0.833455i	$-0.686360\pi$
$467$	−1.29125e68	−1.10518	−0.552588	+	0.833455i	$0.686360\pi$
$468$	0	0
$469$	3.91485e66	0.0300475
$470$	−1.76724e68	−1.28470
$471$	0	0
$472$	−7.16484e68	−4.67396
$473$	4.98974e67	0.308403
$474$	0	0
$475$	−9.03750e67	−0.501604
$476$	3.25867e67	0.171421
$477$	0	0
$478$	5.32506e68	2.51717
$479$	−1.65481e67	−0.0741637	−0.0370819	−	0.999312i	$-0.511806\pi$
$479$	−1.65481e67	−0.0741637	−0.0370819	+	0.999312i	$0.511806\pi$
$480$	0	0
$481$	1.28040e68	0.515997
$482$	4.37091e68	1.67060
$483$	0	0
$484$	4.89707e68	1.68414
$485$	4.75596e68	1.55176
$486$	0	0
$487$	2.64354e68	0.776599	0.388300	−	0.921533i	$-0.373063\pi$
$487$	2.64354e68	0.776599	0.388300	+	0.921533i	$0.373063\pi$
$488$	−8.06527e68	−2.24861
$489$	0	0
$490$	2.05601e68	0.516445
$491$	2.78351e68	0.663766	0.331883	−	0.943320i	$-0.392316\pi$
$491$	2.78351e68	0.663766	0.331883	+	0.943320i	$0.392316\pi$
$492$	0	0
$493$	−4.89181e67	−0.105165
$494$	−2.27340e68	−0.464128
$495$	0	0
$496$	−3.87424e68	−0.713515
$497$	−8.40729e68	−1.47085
$498$	0	0
$499$	6.14422e67	0.0970293	0.0485147	−	0.998822i	$-0.484551\pi$
$499$	6.14422e67	0.0970293	0.0485147	+	0.998822i	$0.484551\pi$
$500$	6.07381e68	0.911436
$501$	0	0
$502$	−2.46614e69	−3.34252
$503$	2.46940e68	0.318133	0.159066	−	0.987268i	$-0.449152\pi$
$503$	2.46940e68	0.318133	0.159066	+	0.987268i	$0.449152\pi$
$504$	0	0
$505$	1.36955e69	1.59459
$506$	7.12380e68	0.788630
$507$	0	0
$508$	−1.24529e69	−1.24665
$509$	−1.09348e69	−1.04114	−0.520570	−	0.853819i	$-0.674281\pi$
$509$	−1.09348e69	−1.04114	−0.520570	+	0.853819i	$0.674281\pi$
$510$	0	0
$511$	1.26332e69	1.08838
$512$	−2.48098e69	−2.03347
$513$	0	0
$514$	2.30758e69	1.71237
$515$	1.83078e69	1.29286
$516$	0	0
$517$	−1.09553e69	−0.700837
$518$	3.87457e69	2.35947
$519$	0	0
$520$	−2.11630e69	−1.16813
$521$	1.75420e69	0.921972	0.460986	−	0.887407i	$-0.347496\pi$
$521$	1.75420e69	0.921972	0.460986	+	0.887407i	$0.347496\pi$
$522$	0	0
$523$	1.24675e69	0.594272	0.297136	−	0.954835i	$-0.403969\pi$
$523$	1.24675e69	0.594272	0.297136	+	0.954835i	$0.403969\pi$
$524$	1.94344e69	0.882313
$525$	0	0
$526$	3.04890e69	1.25605
$527$	−6.60494e67	−0.0259238
$528$	0	0
$529$	−2.50346e69	−0.892115
$530$	−4.19057e69	−1.42311
$531$	0	0
$532$	−4.83813e69	−1.49256
$533$	−1.46895e69	−0.431980
$534$	0	0
$535$	2.41524e69	0.645563
$536$	3.34791e68	0.0853240
$537$	0	0
$538$	1.08946e70	2.52501
$539$	1.27454e69	0.281735
$540$	0	0
$541$	1.90153e69	0.382449	0.191225	−	0.981546i	$-0.438754\pi$
$541$	1.90153e69	0.382449	0.191225	+	0.981546i	$0.438754\pi$
$542$	7.26848e69	1.39464
$543$	0	0
$544$	7.52816e68	0.131497
$545$	−1.28179e70	−2.13652
$546$	0	0
$547$	−1.93403e69	−0.293621	−0.146810	−	0.989165i	$-0.546901\pi$
$547$	−1.93403e69	−0.293621	−0.146810	+	0.989165i	$0.546901\pi$
$548$	2.35972e69	0.341945
$549$	0	0
$550$	−1.28282e70	−1.69401
$551$	7.26284e69	0.915674
$552$	0	0
$553$	−9.71332e69	−1.11655
$554$	6.63511e69	0.728365
$555$	0	0
$556$	3.64126e70	3.64623
$557$	3.13526e69	0.299893	0.149946	−	0.988694i	$-0.452090\pi$
$557$	3.13526e69	0.299893	0.149946	+	0.988694i	$0.452090\pi$
$558$	0	0
$559$	−9.60563e68	−0.0838542
$560$	−3.11690e70	−2.59973
$561$	0	0
$562$	−1.36826e69	−0.104206
$563$	−9.08297e69	−0.661095	−0.330547	−	0.943789i	$-0.607233\pi$
$563$	−9.08297e69	−0.661095	−0.330547	+	0.943789i	$0.607233\pi$
$564$	0	0
$565$	−3.16060e70	−2.10152
$566$	−2.12320e69	−0.134950
$567$	0	0
$568$	−7.18975e70	−4.17668
$569$	−7.13609e69	−0.396367	−0.198184	−	0.980165i	$-0.563504\pi$
$569$	−7.13609e69	−0.396367	−0.198184	+	0.980165i	$0.563504\pi$
$570$	0	0
$571$	3.32172e70	1.68710	0.843552	−	0.537048i	$-0.180460\pi$
$571$	3.32172e70	1.68710	0.843552	+	0.537048i	$0.180460\pi$
$572$	−2.26943e70	−1.10235
$573$	0	0
$574$	−4.44513e70	−1.97529
$575$	−5.45171e69	−0.231741
$576$	0	0
$577$	−2.70924e70	−1.05406	−0.527028	−	0.849848i	$-0.676694\pi$
$577$	−2.70924e70	−1.05406	−0.527028	+	0.849848i	$0.676694\pi$
$578$	−4.89867e70	−1.82355
$579$	0	0
$580$	1.16955e71	3.98663
$581$	−4.66987e69	−0.152340
$582$	0	0
$583$	−2.59778e70	−0.776345
$584$	1.08036e71	3.09060
$585$	0	0
$586$	3.41531e70	0.895450
$587$	−4.21203e70	−1.05735	−0.528676	−	0.848824i	$-0.677311\pi$
$587$	−4.21203e70	−1.05735	−0.528676	+	0.848824i	$0.677311\pi$
$588$	0	0
$589$	9.80631e69	0.225718
$590$	2.02107e71	4.45508
$591$	0	0
$592$	1.61269e71	3.26097
$593$	6.81213e68	0.0131944	0.00659718	−	0.999978i	$-0.497900\pi$
$593$	6.81213e68	0.0131944	0.00659718	+	0.999978i	$0.497900\pi$
$594$	0	0
$595$	−5.31380e69	−0.0944545
$596$	6.38021e70	1.08656
$597$	0	0
$598$	−1.37139e70	−0.214427
$599$	−6.95350e70	−1.04188	−0.520942	−	0.853592i	$-0.674419\pi$
$599$	−6.95350e70	−1.04188	−0.520942	+	0.853592i	$0.674419\pi$
$600$	0	0
$601$	−1.18115e71	−1.62557	−0.812786	−	0.582563i	$-0.802050\pi$
$601$	−1.18115e71	−1.62557	−0.812786	+	0.582563i	$0.802050\pi$
$602$	−2.90672e70	−0.383436
$603$	0	0
$604$	−6.50338e70	−0.788310
$605$	−7.98548e70	−0.927980
$606$	0	0
$607$	6.67421e70	0.712998	0.356499	−	0.934296i	$-0.383970\pi$
$607$	6.67421e70	0.712998	0.356499	+	0.934296i	$0.383970\pi$
$608$	−1.11770e71	−1.14494
$609$	0	0
$610$	2.27507e71	2.14330
$611$	2.10899e70	0.190556
$612$	0	0
$613$	1.23137e71	1.02364	0.511821	−	0.859092i	$-0.328971\pi$
$613$	1.23137e71	1.02364	0.511821	+	0.859092i	$0.328971\pi$
$614$	2.61367e71	2.08429
$615$	0	0
$616$	−3.96994e71	−2.91391
$617$	−5.54308e70	−0.390372	−0.195186	−	0.980766i	$-0.562531\pi$
$617$	−5.54308e70	−0.390372	−0.195186	+	0.980766i	$0.562531\pi$
$618$	0	0
$619$	−1.74222e71	−1.12978	−0.564888	−	0.825168i	$-0.691081\pi$
$619$	−1.74222e71	−1.12978	−0.564888	+	0.825168i	$0.691081\pi$
$620$	1.57913e71	0.982721
$621$	0	0
$622$	1.78919e71	1.02566
$623$	4.68724e70	0.257912
$624$	0	0
$625$	−2.38187e71	−1.20775
$626$	−2.84453e71	−1.38473
$627$	0	0
$628$	−2.06757e71	−0.927874
$629$	2.74937e70	0.118479
$630$	0	0
$631$	3.02907e70	0.120382	0.0601909	−	0.998187i	$-0.480829\pi$
$631$	3.02907e70	0.120382	0.0601909	+	0.998187i	$0.480829\pi$
$632$	−8.30665e71	−3.17059
$633$	0	0
$634$	2.03298e71	0.715906
$635$	2.03065e71	0.686919
$636$	0	0
$637$	−2.45359e70	−0.0766031
$638$	1.03092e72	3.09240
$639$	0	0
$640$	1.45589e71	0.403217
$641$	−4.16260e71	−1.10786	−0.553929	−	0.832564i	$-0.686872\pi$
$641$	−4.16260e71	−1.10786	−0.553929	+	0.832564i	$0.686872\pi$
$642$	0	0
$643$	−1.46280e71	−0.359587	−0.179794	−	0.983704i	$-0.557543\pi$
$643$	−1.46280e71	−0.359587	−0.179794	+	0.983704i	$0.557543\pi$
$644$	−2.91852e71	−0.689560
$645$	0	0
$646$	−4.88159e70	−0.106569
$647$	−4.77442e71	−1.00199	−0.500993	−	0.865451i	$-0.667032\pi$
$647$	−4.77442e71	−1.00199	−0.500993	+	0.865451i	$0.667032\pi$
$648$	0	0
$649$	1.25289e72	2.43037
$650$	2.46952e71	0.460599
$651$	0	0
$652$	−1.03278e72	−1.78112
$653$	−2.35120e71	−0.389946	−0.194973	−	0.980809i	$-0.562462\pi$
$653$	−2.35120e71	−0.389946	−0.194973	+	0.980809i	$0.562462\pi$
$654$	0	0
$655$	−3.16910e71	−0.486163
$656$	−1.85017e72	−2.73000
$657$	0	0
$658$	6.38192e71	0.871346
$659$	−3.04611e71	−0.400099	−0.200050	−	0.979786i	$-0.564110\pi$
$659$	−3.04611e71	−0.400099	−0.200050	+	0.979786i	$0.564110\pi$
$660$	0	0
$661$	5.21186e71	0.633659	0.316830	−	0.948482i	$-0.397382\pi$
$661$	5.21186e71	0.633659	0.316830	+	0.948482i	$0.397382\pi$
$662$	2.96713e72	3.47103
$663$	0	0
$664$	−3.99358e71	−0.432590
$665$	7.88937e71	0.822414
$666$	0	0
$667$	4.38118e71	0.423041
$668$	−1.51089e72	−1.40421
$669$	0	0
$670$	−9.44385e70	−0.0813283
$671$	1.41034e72	1.16923
$672$	0	0
$673$	6.60671e71	0.507693	0.253846	−	0.967245i	$-0.418304\pi$
$673$	6.60671e71	0.507693	0.253846	+	0.967245i	$0.418304\pi$
$674$	1.76136e72	1.30323
$675$	0	0
$676$	−3.01783e72	−2.07040
$677$	−6.23542e71	−0.411959	−0.205980	−	0.978556i	$-0.566038\pi$
$677$	−6.23542e71	−0.411959	−0.205980	+	0.978556i	$0.566038\pi$
$678$	0	0
$679$	−1.71749e72	−1.05248
$680$	−4.54426e71	−0.268217
$681$	0	0
$682$	1.39195e72	0.762292
$683$	−3.27198e72	−1.72617	−0.863083	−	0.505062i	$-0.831470\pi$
$683$	−3.27198e72	−1.72617	−0.863083	+	0.505062i	$0.831470\pi$
$684$	0	0
$685$	−3.84792e71	−0.188415
$686$	−4.18921e72	−1.97637
$687$	0	0
$688$	−1.20984e72	−0.529937
$689$	5.00093e71	0.211087
$690$	0	0
$691$	−2.74210e72	−1.07496	−0.537481	−	0.843276i	$-0.680624\pi$
$691$	−2.74210e72	−1.07496	−0.537481	+	0.843276i	$0.680624\pi$
$692$	1.16336e73	4.39552
$693$	0	0
$694$	8.42161e72	2.95616
$695$	−5.93767e72	−2.00911
$696$	0	0
$697$	−3.15423e71	−0.0991877
$698$	4.52445e72	1.37168
$699$	0	0
$700$	5.25552e72	1.48121
$701$	2.11073e72	0.573619	0.286810	−	0.957988i	$-0.407405\pi$
$701$	2.11073e72	0.573619	0.286810	+	0.957988i	$0.407405\pi$
$702$	0	0
$703$	−4.08197e72	−1.03160
$704$	−3.80505e72	−0.927379
$705$	0	0
$706$	2.81867e72	0.639034
$707$	−4.94576e72	−1.08153
$708$	0	0
$709$	−1.26460e72	−0.257321	−0.128661	−	0.991689i	$-0.541068\pi$
$709$	−1.26460e72	−0.257321	−0.128661	+	0.991689i	$0.541068\pi$
$710$	2.02810e73	3.98108
$711$	0	0
$712$	4.00844e72	0.732378
$713$	5.91548e71	0.104281
$714$	0	0
$715$	3.70069e72	0.607405
$716$	−2.27851e72	−0.360884
$717$	0	0
$718$	−1.85432e71	−0.0273535
$719$	−5.81095e72	−0.827296	−0.413648	−	0.910437i	$-0.635746\pi$
$719$	−5.81095e72	−0.827296	−0.413648	+	0.910437i	$0.635746\pi$
$720$	0	0
$721$	−6.61135e72	−0.876882
$722$	−7.09143e72	−0.907894
$723$	0	0
$724$	1.16645e73	1.39166
$725$	−7.88941e72	−0.908711
$726$	0	0
$727$	3.02801e72	0.325110	0.162555	−	0.986700i	$-0.448027\pi$
$727$	3.02801e72	0.325110	0.162555	+	0.986700i	$0.448027\pi$
$728$	7.64243e72	0.792285
$729$	0	0
$730$	−3.04751e73	−2.94587
$731$	−2.06259e71	−0.0192539
$732$	0	0
$733$	−1.84067e72	−0.160259	−0.0801297	−	0.996784i	$-0.525533\pi$
$733$	−1.84067e72	−0.160259	−0.0801297	+	0.996784i	$0.525533\pi$
$734$	−2.99708e73	−2.52028
$735$	0	0
$736$	−6.74234e72	−0.528964
$737$	−5.85435e71	−0.0443668
$738$	0	0
$739$	−2.72537e73	−1.92749	−0.963746	−	0.266820i	$-0.914027\pi$
$739$	−2.72537e73	−1.92749	−0.963746	+	0.266820i	$0.914027\pi$
$740$	−6.57329e73	−4.49132
$741$	0	0
$742$	1.51331e73	0.965224
$743$	1.44844e73	0.892662	0.446331	−	0.894868i	$-0.352730\pi$
$743$	1.44844e73	0.892662	0.446331	+	0.894868i	$0.352730\pi$
$744$	0	0
$745$	−1.04040e73	−0.598708
$746$	5.87922e73	3.26948
$747$	0	0
$748$	−4.87308e72	−0.253112
$749$	−8.72197e72	−0.437853
$750$	0	0
$751$	1.83054e73	0.858539	0.429270	−	0.903176i	$-0.358771\pi$
$751$	1.83054e73	0.858539	0.429270	+	0.903176i	$0.358771\pi$
$752$	2.65630e73	1.20427
$753$	0	0
$754$	−1.98459e73	−0.840818
$755$	1.06048e73	0.434367
$756$	0	0
$757$	−3.21435e73	−1.23069	−0.615344	−	0.788259i	$-0.710983\pi$
$757$	−3.21435e73	−1.23069	−0.615344	+	0.788259i	$0.710983\pi$
$758$	−1.98034e73	−0.733120
$759$	0	0
$760$	6.74684e73	2.33536
$761$	−2.98468e73	−0.999055	−0.499527	−	0.866298i	$-0.666493\pi$
$761$	−2.98468e73	−0.999055	−0.499527	+	0.866298i	$0.666493\pi$
$762$	0	0
$763$	4.62884e73	1.44909
$764$	5.98946e73	1.81346
$765$	0	0
$766$	1.00223e74	2.83880
$767$	−2.41190e73	−0.660812
$768$	0	0
$769$	−2.25014e73	−0.576883	−0.288442	−	0.957498i	$-0.593137\pi$
$769$	−2.25014e73	−0.576883	−0.288442	+	0.957498i	$0.593137\pi$
$770$	1.11985e74	2.77745
$771$	0	0
$772$	−7.84267e73	−1.82064
$773$	−1.94895e73	−0.437746	−0.218873	−	0.975753i	$-0.570238\pi$
$773$	−1.94895e73	−0.437746	−0.218873	+	0.975753i	$0.570238\pi$
$774$	0	0
$775$	−1.06523e73	−0.224001
$776$	−1.46876e74	−2.98866
$777$	0	0
$778$	−6.66392e73	−1.26984
$779$	4.68307e73	0.863625
$780$	0	0
$781$	1.25724e74	2.17179
$782$	−2.94473e72	−0.0492350
$783$	0	0
$784$	−3.09033e73	−0.484112
$785$	3.37151e73	0.511268
$786$	0	0
$787$	−5.33534e73	−0.758240	−0.379120	−	0.925348i	$-0.623773\pi$
$787$	−5.33534e73	−0.758240	−0.379120	+	0.925348i	$0.623773\pi$
$788$	2.03259e74	2.79660
$789$	0	0
$790$	2.34316e74	3.02211
$791$	1.14136e74	1.42536
$792$	0	0
$793$	−2.71501e73	−0.317911
$794$	−1.39569e74	−1.58259
$795$	0	0
$796$	−1.25180e74	−1.33123
$797$	−6.56993e73	−0.676664	−0.338332	−	0.941027i	$-0.609863\pi$
$797$	−6.56993e73	−0.676664	−0.338332	+	0.941027i	$0.609863\pi$
$798$	0	0
$799$	4.52856e72	0.0437540
$800$	1.21413e74	1.13624
$801$	0	0
$802$	−1.73908e73	−0.152712
$803$	−1.88919e74	−1.60705
$804$	0	0
$805$	4.75912e73	0.379955
$806$	−2.67960e73	−0.207265
$807$	0	0
$808$	−4.22952e74	−3.07115
$809$	1.11962e74	0.787738	0.393869	−	0.919167i	$-0.371136\pi$
$809$	1.11962e74	0.787738	0.393869	+	0.919167i	$0.371136\pi$
$810$	0	0
$811$	1.56076e74	1.03111	0.515553	−	0.856858i	$-0.327587\pi$
$811$	1.56076e74	1.03111	0.515553	+	0.856858i	$0.327587\pi$
$812$	−4.22351e74	−2.70393
$813$	0	0
$814$	−5.79412e74	−3.48389
$815$	1.68411e74	0.981414
$816$	0	0
$817$	3.06231e73	0.167643
$818$	−3.32275e74	−1.76315
$819$	0	0
$820$	7.54125e74	3.76002
$821$	2.63166e74	1.27198	0.635989	−	0.771698i	$-0.280592\pi$
$821$	2.63166e74	1.27198	0.635989	+	0.771698i	$0.280592\pi$
$822$	0	0
$823$	3.49608e74	1.58813	0.794063	−	0.607835i	$-0.207962\pi$
$823$	3.49608e74	1.58813	0.794063	+	0.607835i	$0.207962\pi$
$824$	−5.65390e74	−2.49003
$825$	0	0
$826$	−7.29855e74	−3.02166
$827$	3.08226e74	1.23731	0.618656	−	0.785662i	$-0.287678\pi$
$827$	3.08226e74	1.23731	0.618656	+	0.785662i	$0.287678\pi$
$828$	0	0
$829$	−3.63825e73	−0.137326	−0.0686629	−	0.997640i	$-0.521873\pi$
$829$	−3.63825e73	−0.137326	−0.0686629	+	0.997640i	$0.521873\pi$
$830$	1.12652e74	0.412332
$831$	0	0
$832$	7.32500e73	0.252152
$833$	−5.26851e72	−0.0175890
$834$	0	0
$835$	2.46376e74	0.773736
$836$	7.23503e74	2.20384
$837$	0	0
$838$	4.16966e74	1.19503
$839$	−1.84060e74	−0.511717	−0.255859	−	0.966714i	$-0.582358\pi$
$839$	−1.84060e74	−0.511717	−0.255859	+	0.966714i	$0.582358\pi$
$840$	0	0
$841$	2.51814e74	0.658842
$842$	−7.09266e74	−1.80032
$843$	0	0
$844$	3.70640e74	0.885564
$845$	4.92108e74	1.14081
$846$	0	0
$847$	2.88374e74	0.629402
$848$	6.29875e74	1.33401
$849$	0	0
$850$	5.30273e73	0.105759
$851$	−2.46238e74	−0.476597
$852$	0	0
$853$	−8.40007e74	−1.53138	−0.765689	−	0.643211i	$-0.777602\pi$
$853$	−8.40007e74	−1.53138	−0.765689	+	0.643211i	$0.777602\pi$
$854$	−8.21578e74	−1.45370
$855$	0	0
$856$	−7.45886e74	−1.24334
$857$	−2.87444e74	−0.465095	−0.232548	−	0.972585i	$-0.574706\pi$
$857$	−2.87444e74	−0.465095	−0.232548	+	0.972585i	$0.574706\pi$
$858$	0	0
$859$	−9.96707e74	−1.51964	−0.759822	−	0.650131i	$-0.774714\pi$
$859$	−9.96707e74	−1.51964	−0.759822	+	0.650131i	$0.774714\pi$
$860$	4.93130e74	0.729880
$861$	0	0
$862$	5.01037e74	0.698931
$863$	−9.87545e74	−1.33746	−0.668732	−	0.743504i	$-0.733162\pi$
$863$	−9.87545e74	−1.33746	−0.668732	+	0.743504i	$0.733162\pi$
$864$	0	0
$865$	−1.89706e75	−2.42198
$866$	−2.86036e75	−3.54580
$867$	0	0
$868$	−5.70260e74	−0.666530
$869$	1.45255e75	1.64864
$870$	0	0
$871$	1.12701e73	0.0120632
$872$	3.95850e75	4.11491
$873$	0	0
$874$	4.37202e74	0.428688
$875$	3.57668e74	0.340624
$876$	0	0
$877$	1.76322e75	1.58422	0.792112	−	0.610375i	$-0.208981\pi$
$877$	1.76322e75	1.58422	0.792112	+	0.610375i	$0.208981\pi$
$878$	1.15432e75	1.00744
$879$	0	0
$880$	4.66107e75	3.83864
$881$	−3.09062e74	−0.247263	−0.123632	−	0.992328i	$-0.539454\pi$
$881$	−3.09062e74	−0.247263	−0.123632	+	0.992328i	$0.539454\pi$
$882$	0	0
$883$	1.81758e75	1.37245	0.686223	−	0.727392i	$-0.259268\pi$
$883$	1.81758e75	1.37245	0.686223	+	0.727392i	$0.259268\pi$
$884$	9.38105e73	0.0688206
$885$	0	0
$886$	−1.92692e75	−1.33445
$887$	1.25497e75	0.844461	0.422230	−	0.906489i	$-0.361247\pi$
$887$	1.25497e75	0.844461	0.422230	+	0.906489i	$0.361247\pi$
$888$	0	0
$889$	−7.33315e74	−0.465903
$890$	−1.13071e75	−0.698081
$891$	0	0
$892$	−3.88386e75	−2.26443
$893$	−6.72353e74	−0.380965
$894$	0	0
$895$	3.71548e74	0.198851
$896$	−5.25754e74	−0.273482
$897$	0	0
$898$	−2.18386e74	−0.107320
$899$	8.56056e74	0.408912
$900$	0	0
$901$	1.07383e74	0.0484680
$902$	6.64733e75	2.91663
$903$	0	0
$904$	9.76071e75	4.04750
$905$	−1.90209e75	−0.766820
$906$	0	0
$907$	−1.93095e75	−0.735845	−0.367922	−	0.929857i	$-0.619931\pi$
$907$	−1.93095e75	−0.735845	−0.367922	+	0.929857i	$0.619931\pi$
$908$	−9.47757e75	−3.51162
$909$	0	0
$910$	−2.15579e75	−0.755182
$911$	9.00047e74	0.306582	0.153291	−	0.988181i	$-0.451013\pi$
$911$	9.00047e74	0.306582	0.153291	+	0.988181i	$0.451013\pi$
$912$	0	0
$913$	6.98342e74	0.224938
$914$	−5.53962e75	−1.73521
$915$	0	0
$916$	−3.17665e75	−0.941097
$917$	1.14443e75	0.329740
$918$	0	0
$919$	−6.41329e75	−1.74798	−0.873988	−	0.485948i	$-0.838475\pi$
$919$	−6.41329e75	−1.74798	−0.873988	+	0.485948i	$0.838475\pi$
$920$	4.06991e75	1.07893
$921$	0	0
$922$	2.08667e75	0.523379
$923$	−2.42029e75	−0.590505
$924$	0	0
$925$	4.43413e75	1.02375
$926$	−3.73949e75	−0.839909
$927$	0	0
$928$	−9.75713e75	−2.07419
$929$	6.16892e75	1.27588	0.637938	−	0.770088i	$-0.279788\pi$
$929$	6.16892e75	1.27588	0.637938	+	0.770088i	$0.279788\pi$
$930$	0	0
$931$	7.82212e74	0.153147
$932$	3.17039e75	0.603958
$933$	0	0
$934$	−1.12486e76	−2.02887
$935$	7.94636e74	0.139467
$936$	0	0
$937$	1.06049e76	1.76258	0.881290	−	0.472575i	$-0.156675\pi$
$937$	1.06049e76	1.76258	0.881290	+	0.472575i	$0.156675\pi$
$938$	3.41039e74	0.0551609
$939$	0	0
$940$	−1.08270e76	−1.65863
$941$	−3.41799e75	−0.509608	−0.254804	−	0.966993i	$-0.582011\pi$
$941$	−3.41799e75	−0.509608	−0.254804	+	0.966993i	$0.582011\pi$
$942$	0	0
$943$	2.82498e75	0.398994
$944$	−3.03783e76	−4.17616
$945$	0	0
$946$	4.34676e75	0.566164
$947$	6.63593e75	0.841351	0.420675	−	0.907211i	$-0.361793\pi$
$947$	6.63593e75	0.841351	0.420675	+	0.907211i	$0.361793\pi$
$948$	0	0
$949$	3.63683e75	0.436953
$950$	−7.87293e75	−0.920840
$951$	0	0
$952$	1.64103e75	0.181918
$953$	−1.31580e76	−1.42010	−0.710052	−	0.704149i	$-0.751329\pi$
$953$	−1.31580e76	−1.42010	−0.710052	+	0.704149i	$0.751329\pi$
$954$	0	0
$955$	−9.76680e75	−0.999232
$956$	3.26241e76	3.24984
$957$	0	0
$958$	−1.44157e75	−0.136149
$959$	1.38957e75	0.127793
$960$	0	0
$961$	−1.03111e76	−0.899201
$962$	1.11541e76	0.947263
$963$	0	0
$964$	2.67784e76	2.15685
$965$	1.27888e76	1.00319
$966$	0	0
$967$	1.67049e76	1.24299	0.621496	−	0.783417i	$-0.286525\pi$
$967$	1.67049e76	1.24299	0.621496	+	0.783417i	$0.286525\pi$
$968$	2.46612e76	1.78728
$969$	0	0
$970$	4.14311e76	2.84870
$971$	−1.63388e76	−1.09428	−0.547142	−	0.837040i	$-0.684284\pi$
$971$	−1.63388e76	−1.09428	−0.547142	+	0.837040i	$0.684284\pi$
$972$	0	0
$973$	2.14423e76	1.36268
$974$	2.30289e76	1.42567
$975$	0	0
$976$	−3.41960e76	−2.00912
$977$	2.38186e76	1.36334	0.681672	−	0.731658i	$-0.261253\pi$
$977$	2.38186e76	1.36334	0.681672	+	0.731658i	$0.261253\pi$
$978$	0	0
$979$	−7.00939e75	−0.380822
$980$	1.25961e76	0.666765
$981$	0	0
$982$	2.42483e76	1.21854
$983$	−3.78819e76	−1.85488	−0.927442	−	0.373966i	$-0.877998\pi$
$983$	−3.78819e76	−1.85488	−0.927442	+	0.373966i	$0.877998\pi$
$984$	0	0
$985$	−3.31447e76	−1.54096
$986$	−4.26145e75	−0.193062
$987$	0	0
$988$	−1.39280e76	−0.599220
$989$	1.84728e75	0.0774512
$990$	0	0
$991$	2.49197e76	0.992349	0.496175	−	0.868223i	$-0.334738\pi$
$991$	2.49197e76	0.992349	0.496175	+	0.868223i	$0.334738\pi$
$992$	−1.31741e76	−0.511298
$993$	0	0
$994$	−7.32392e76	−2.70017
$995$	2.04127e76	0.733519
$996$	0	0
$997$	−2.96256e76	−1.01144	−0.505721	−	0.862697i	$-0.668773\pi$
$997$	−2.96256e76	−1.01144	−0.505721	+	0.862697i	$0.668773\pi$
$998$	5.35248e75	0.178126
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.52.a.b.1.4		4
3.2	odd	2		1.52.a.a.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.52.a.a.1.1	✓	4	3.2	odd	2
9.52.a.b.1.4		4	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:	\( k \)	\(=\)	\( 52 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q+8.71140e7 q^{2} +5.33705e15 q^{4} -8.70295e17 q^{5} +3.14283e21 q^{7} +2.68769e23 q^{8} +O(q^{10})\)	\(q+8.71140e7 q^{2} +5.33705e15 q^{4} -8.70295e17 q^{5} +3.14283e21 q^{7} +2.68769e23 q^{8} -7.58149e25 q^{10} -4.69985e26 q^{11} +9.04757e27 q^{13} +2.73785e29 q^{14} +1.13956e31 q^{16} +1.94276e30 q^{17} -2.88440e32 q^{19} -4.64481e33 q^{20} -4.09423e34 q^{22} -1.73996e34 q^{23} +3.13324e35 q^{25} +7.88170e35 q^{26} +1.67734e37 q^{28} -2.51798e37 q^{29} -3.39978e37 q^{31} +3.87499e38 q^{32} +1.69241e38 q^{34} -2.73519e39 q^{35} +1.41519e40 q^{37} -2.51271e40 q^{38} -2.33908e41 q^{40} -1.62359e41 q^{41} -1.06168e41 q^{43} -2.50834e42 q^{44} -1.51575e42 q^{46} +2.33100e42 q^{47} -2.71188e42 q^{49} +2.72949e43 q^{50} +4.82874e43 q^{52} +5.52737e43 q^{53} +4.09026e44 q^{55} +8.44695e44 q^{56} -2.19351e45 q^{58} -2.66580e45 q^{59} -3.00082e45 q^{61} -2.96168e45 q^{62} +8.09610e45 q^{64} -7.87405e45 q^{65} +1.24565e45 q^{67} +1.03686e46 q^{68} -2.38273e47 q^{70} -2.67507e47 q^{71} +4.01968e47 q^{73} +1.23283e48 q^{74} -1.53942e48 q^{76} -1.47708e48 q^{77} -3.09063e48 q^{79} -9.91749e48 q^{80} -1.41437e49 q^{82} -1.48588e48 q^{83} -1.69077e48 q^{85} -9.24873e48 q^{86} -1.26317e50 q^{88} +1.49141e49 q^{89} +2.84350e49 q^{91} -9.28627e49 q^{92} +2.03063e50 q^{94} +2.51028e50 q^{95} -5.46477e50 q^{97} -2.36242e50 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 32756040 q^{2} + 79\!\cdots\!12 q^{4}+ \cdots + 13\!\cdots\!20 q^{8}+O(q^{10}) \) 4 * q - 32756040 * q^2 + 7978103470875712 * q^4 - 1214113112967557880 * q^5 + 6566332044151252469600 * q^7 + 139242173294665691205120 * q^8	\( 4 q - 32756040 q^{2} + 79\!\cdots\!12 q^{4}+ \cdots + 31\!\cdots\!80 q^{98}+O(q^{100}) \) 4 * q - 32756040 * q^2 + 7978103470875712 * q^4 - 1214113112967557880 * q^5 + 6566332044151252469600 * q^7 + 139242173294665691205120 * q^8 - 26338767422633182993407120 * q^10 - 352319730227217761184247248 * q^11 + 30737495492092678036022901080 * q^13 - 116878411871248994844784530624 * q^14 + 13655541308212814904424583532544 * q^16 - 48152025926602119975132578130120 * q^17 + 817578654717102241686587953106480 * q^19 - 6688106698568613691058684703008640 * q^20 - 34873949046188270313389204382330720 * q^22 + 54442545328795748403982512519744480 * q^23 - 577962011134461749109509927876368100 * q^25 - 1509847347916659653711306190553689648 * q^26 + 34411298173690719862562837156054996480 * q^28 - 24524817706178324469842039147126378520 * q^29 - 74015080632891216448581759119415494272 * q^31 + 698885110517892283834830116511622594560 * q^32 + 599176354190711613816800945566309634064 * q^34 - 5459558934032100428649177266758776617280 * q^35 + 9223299799194559520674909690367653437560 * q^37 - 42209741287618122996397532876280940717920 * q^38 - 260218563144774091908833544090781982745600 * q^40 - 146626572441904135431040424870320811649768 * q^41 - 383253403750663564628750277915860311246000 * q^43 - 3919911265019437916289330658643948094246144 * q^44 - 687622182810100175391810298681828635813312 * q^46 - 703242125794576181922406089648904926204480 * q^47 - 21525353693695885888621049774661370126875228 * q^49 + 65550763083377103476240548536052846777230600 * q^50 + 205575224727950383449569813934278240424406400 * q^52 + 46053881458574871528873628680364599519093960 * q^53 + 288271437023082169121432211103105268991934560 * q^55 + 718413197664523425962520880364481249783828480 * q^56 - 3260382815057328392932619475690091710393763920 * q^58 - 1119164779584192618652811959209270069996506640 * q^59 + 3426848506305498355799302542081826532801316248 * q^61 - 9652948821672246376570757837225648817671719680 * q^62 - 3410402571656263891001355509990182780636233728 * q^64 - 10662663070585071183633914150857043524084084560 * q^65 + 30875136607724238160818607702139418169238276720 * q^67 + 92264980123003683860202361552579885626636888960 * q^68 - 127365497175284237875848441551548839150619662720 * q^70 - 396890633217178572952249989093970445513163336288 * q^71 + 1093181650202404127682760092563948835468903177320 * q^73 + 2446722614206037598896806276944107193380656941456 * q^74 - 1930298057964975808050160660816178333985982024960 * q^76 - 1379856740595107958858322062475643650952236464000 * q^77 + 4057123342028363124154537966955503984273281629120 * q^79 - 6556705282035289158041818706914507044939664711680 * q^80 + 2672741123252406904410297531162443665031405248080 * q^82 - 10514534101014085301175610601927458547806407366960 * q^83 - 2214700921000481207852358003497850667551075883920 * q^85 + 43819383990098235110217468422860464230535375092832 * q^86 - 25053936600673669378312978656608794916631597373440 * q^88 + 90777724780188979543741952283884054816841444724440 * q^89 + 100567720661332633308233017957549269313038849882688 * q^91 - 192025202572015319809189966047000799088692638097920 * q^92 + 639818007616166555781273040037466169910601363859584 * q^94 + 418719878951800677902105757696028542296429654882400 * q^95 - 1321788056943507607869460465290134726019322989433720 * q^97 + 317844097908560926995320900303041587618753340105080 * q^98

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