LMFDB - Embedded newform 81.3.f.a.35.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,3,Mod(8,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("81.8");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	81.f (of order $18$, degree $6$, not minimal)

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:	no
Analytic conductor:	$2.20709014132$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			35.3
Character	$\chi$	$=$	81.35
Dual form			81.3.f.a.44.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.374063 - 0.445791i) q^{2} +(0.635786 + 3.60572i) q^{4} +(-2.62195 + 7.20376i) q^{5} +(0.231638 - 1.31369i) q^{7} +(3.86112 + 2.22922i) q^{8} +(2.23059 + 3.86350i) q^{10} +(-0.367624 - 1.01004i) q^{11} +(16.0318 - 13.4523i) q^{13} +(-0.498982 - 0.594664i) q^{14} +(-11.3241 + 4.12163i) q^{16} +(12.1867 - 7.03599i) q^{17} +(-9.79833 + 16.9712i) q^{19} +(-27.6418 - 4.87399i) q^{20} +(-0.587780 - 0.213935i) q^{22} +(1.76488 - 0.311197i) q^{23} +(-25.8684 - 21.7062i) q^{25} -12.1788i q^{26} +4.88406 q^{28} +(25.8129 - 30.7626i) q^{29} +(-2.95677 - 16.7687i) q^{31} +(-8.49804 + 23.3482i) q^{32} +(1.42201 - 8.06462i) q^{34} +(8.85613 + 5.11309i) q^{35} +(1.80012 + 3.11791i) q^{37} +(3.90042 + 10.7163i) q^{38} +(-26.1824 + 21.9697i) q^{40} +(3.09265 + 3.68568i) q^{41} +(16.1462 - 5.87675i) q^{43} +(3.40819 - 1.96772i) q^{44} +(0.521449 - 0.903176i) q^{46} +(-45.1184 - 7.95560i) q^{47} +(44.3728 + 16.1504i) q^{49} +(-19.3528 + 3.41242i) q^{50} +(58.6979 + 49.2534i) q^{52} +51.2852i q^{53} +8.23996 q^{55} +(3.82288 - 4.55593i) q^{56} +(-4.05804 - 23.0143i) q^{58} +(32.0502 - 88.0571i) q^{59} +(-3.88855 + 22.0530i) q^{61} +(-8.58136 - 4.95445i) q^{62} +(-16.8721 - 29.2233i) q^{64} +(54.8722 + 150.760i) q^{65} +(-14.9624 + 12.5549i) q^{67} +(33.1179 + 39.4684i) q^{68} +(5.59212 - 2.03537i) q^{70} +(-74.9736 + 43.2860i) q^{71} +(18.0755 - 31.3076i) q^{73} +(2.06330 + 0.363815i) q^{74} +(-67.4231 - 24.5400i) q^{76} +(-1.41203 + 0.248979i) q^{77} +(-22.3922 - 18.7892i) q^{79} -92.3828i q^{80} +2.79989 q^{82} +(76.1905 - 90.8003i) q^{83} +(18.7326 + 106.238i) q^{85} +(3.41991 - 9.39613i) q^{86} +(0.832156 - 4.71939i) q^{88} +(-104.884 - 60.5550i) q^{89} +(-13.9585 - 24.1768i) q^{91} +(2.24418 + 6.16583i) q^{92} +(-20.4237 + 17.1375i) q^{94} +(-96.5657 - 115.083i) q^{95} +(9.05396 - 3.29537i) q^{97} +(23.7979 - 13.7397i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 6 q^{2} - 6 q^{4} + 15 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 6 q^{11} - 6 q^{13} + 15 q^{14} - 18 q^{16} + 9 q^{17} - 3 q^{19} - 213 q^{20} - 42 q^{22} - 120 q^{23} - 15 q^{25} - 12 q^{28} + 168 q^{29}+ \cdots - 882 q^{98}+O(q^{100}) $ 30 * q + 6 * q^2 - 6 * q^4 + 15 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 + 6 * q^11 - 6 * q^13 + 15 * q^14 - 18 * q^16 + 9 * q^17 - 3 * q^19 - 213 * q^20 - 42 * q^22 - 120 * q^23 - 15 * q^25 - 12 * q^28 + 168 * q^29 + 39 * q^31 + 360 * q^32 + 54 * q^34 + 252 * q^35 - 3 * q^37 + 84 * q^38 - 33 * q^40 - 228 * q^41 - 96 * q^43 - 639 * q^44 - 3 * q^46 - 399 * q^47 - 78 * q^49 - 303 * q^50 - 9 * q^52 - 12 * q^55 + 393 * q^56 + 129 * q^58 + 474 * q^59 + 138 * q^61 + 900 * q^62 - 51 * q^64 + 411 * q^65 + 354 * q^67 - 99 * q^68 + 489 * q^70 - 315 * q^71 - 66 * q^73 - 321 * q^74 + 258 * q^76 - 201 * q^77 + 30 * q^79 - 12 * q^82 + 33 * q^83 - 261 * q^85 + 258 * q^86 - 642 * q^88 - 72 * q^89 + 96 * q^91 + 3 * q^92 - 861 * q^94 - 681 * q^95 - 582 * q^97 - 882 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	0.374063	−	0.445791i	0.187032	−	0.222895i	−0.664378	−	0.747396i	$-0.731304\pi$
$2$	0.374063	−	0.445791i	0.187032	−	0.222895i	0.851410	+	0.524501i	$0.175748\pi$
$3$		0			0
$3$		0			0
$4$	0.635786	+	3.60572i	0.158947	+	0.901431i
$5$	−2.62195	+	7.20376i	−0.524391	+	1.44075i	0.341196	+	0.939992i	$0.389168\pi$
$5$	−2.62195	+	7.20376i	−0.524391	+	1.44075i	−0.865586	+	0.500760i	$0.833054\pi$
$6$		0			0
$7$	0.231638	−	1.31369i	0.0330912	−	0.187669i	−0.963782	−	0.266693i	$-0.914069\pi$
$7$	0.231638	−	1.31369i	0.0330912	−	0.187669i	0.996873	+	0.0790234i	$0.0251802\pi$
$8$	3.86112	+	2.22922i	0.482640	+	0.278652i
$9$		0			0
$10$	2.23059	+	3.86350i	0.223059	+	0.386350i
$11$	−0.367624	−	1.01004i	−0.0334203	−	0.0918217i	0.921860	−	0.387523i	$-0.126669\pi$
$11$	−0.367624	−	1.01004i	−0.0334203	−	0.0918217i	−0.955281	+	0.295701i	$0.904447\pi$
$12$		0			0
$13$	16.0318	−	13.4523i	1.23321	−	1.03479i	0.235190	−	0.971949i	$-0.424429\pi$
$13$	16.0318	−	13.4523i	1.23321	−	1.03479i	0.998024	−	0.0628396i	$-0.0200156\pi$
$14$	−0.498982	−	0.594664i	−0.0356416	−	0.0424760i
$15$		0			0
$16$	−11.3241	+	4.12163i	−0.707756	+	0.257602i
$17$	12.1867	−	7.03599i	0.716864	−	0.413881i	−0.0967335	−	0.995310i	$-0.530839\pi$
$17$	12.1867	−	7.03599i	0.716864	−	0.413881i	0.813597	+	0.581429i	$0.197506\pi$
$18$		0			0
$19$	−9.79833	+	16.9712i	−0.515702	+	0.893221i	0.484132	+	0.874995i	$0.339135\pi$
$19$	−9.79833	+	16.9712i	−0.515702	+	0.893221i	−0.999834	+	0.0182265i	$0.994198\pi$
$20$	−27.6418	−	4.87399i	−1.38209	−	0.243699i
$21$		0			0
$22$	−0.587780	−	0.213935i	−0.0267173	−	0.00972430i
$23$	1.76488	−	0.311197i	0.0767341	−	0.0135303i	−0.135149	−	0.990825i	$-0.543151\pi$
$23$	1.76488	−	0.311197i	0.0767341	−	0.0135303i	0.211883	+	0.977295i	$0.432040\pi$
$24$		0			0
$25$	−25.8684	−	21.7062i	−1.03474	−	0.868246i
$26$		−	12.1788i		−	0.468416i
$27$		0			0
$28$	4.88406			0.174431
$29$	25.8129	−	30.7626i	0.890099	−	1.06078i	−0.107681	−	0.994185i	$-0.534343\pi$
$29$	25.8129	−	30.7626i	0.890099	−	1.06078i	0.997780	−	0.0665930i	$-0.0212129\pi$
$30$		0			0
$31$	−2.95677	−	16.7687i	−0.0953798	−	0.540926i	−0.994630	−	0.103492i	$-0.966998\pi$
$31$	−2.95677	−	16.7687i	−0.0953798	−	0.540926i	0.899250	−	0.437434i	$-0.144113\pi$
$32$	−8.49804	+	23.3482i	−0.265564	+	0.729630i
$33$		0			0
$34$	1.42201	−	8.06462i	0.0418238	−	0.237195i
$35$	8.85613	+	5.11309i	0.253032	+	0.146088i
$36$		0			0
$37$	1.80012	+	3.11791i	0.0486520	+	0.0842678i	0.889326	−	0.457274i	$-0.151174\pi$
$37$	1.80012	+	3.11791i	0.0486520	+	0.0842678i	−0.840674	+	0.541542i	$0.817841\pi$
$38$	3.90042	+	10.7163i	0.102643	+	0.282008i
$39$		0			0
$40$	−26.1824	+	21.9697i	−0.654561	+	0.549241i
$41$	3.09265	+	3.68568i	0.0754305	+	0.0898946i	0.802440	−	0.596733i	$-0.203535\pi$
$41$	3.09265	+	3.68568i	0.0754305	+	0.0898946i	−0.727009	+	0.686627i	$0.759090\pi$
$42$		0			0
$43$	16.1462	−	5.87675i	0.375494	−	0.136669i	−0.147377	−	0.989080i	$-0.547083\pi$
$43$	16.1462	−	5.87675i	0.375494	−	0.136669i	0.522871	+	0.852412i	$0.324861\pi$
$44$	3.40819	−	1.96772i	0.0774588	−	0.0447209i
$45$		0			0
$46$	0.521449	−	0.903176i	0.0113359	−	0.0196343i
$47$	−45.1184	−	7.95560i	−0.959966	−	0.169268i	−0.328356	−	0.944554i	$-0.606495\pi$
$47$	−45.1184	−	7.95560i	−0.959966	−	0.169268i	−0.631610	+	0.775286i	$0.717606\pi$
$48$		0			0
$49$	44.3728	+	16.1504i	0.905568	+	0.329600i
$50$	−19.3528	+	3.41242i	−0.387056	+	0.0682485i
$51$		0			0
$52$	58.6979	+	49.2534i	1.12881	+	0.947180i
$53$			51.2852i			0.967645i	0.875166	+	0.483822i	$0.160752\pi$
$53$			51.2852i			0.967645i	−0.875166	+	0.483822i	$0.839248\pi$
$54$		0			0
$55$	8.23996			0.149818
$56$	3.82288	−	4.55593i	0.0682656	−	0.0813558i
$57$		0			0
$58$	−4.05804	−	23.0143i	−0.0699662	−	0.396798i
$59$	32.0502	−	88.0571i	0.543223	−	1.49249i	−0.299473	−	0.954105i	$-0.596811\pi$
$59$	32.0502	−	88.0571i	0.543223	−	1.49249i	0.842697	−	0.538389i	$-0.180967\pi$
$60$		0			0
$61$	−3.88855	+	22.0530i	−0.0637467	+	0.361525i	0.936203	+	0.351461i	$0.114315\pi$
$61$	−3.88855	+	22.0530i	−0.0637467	+	0.361525i	−0.999949	+	0.0100647i	$0.996796\pi$
$62$	−8.58136	−	4.95445i	−0.138409	−	0.0799105i
$63$		0			0
$64$	−16.8721	−	29.2233i	−0.263627	−	0.456615i
$65$	54.8722	+	150.760i	0.844188	+	2.31939i
$66$		0			0
$67$	−14.9624	+	12.5549i	−0.223319	+	0.187387i	−0.747582	−	0.664169i	$-0.768785\pi$
$67$	−14.9624	+	12.5549i	−0.223319	+	0.187387i	0.524263	+	0.851556i	$0.324341\pi$
$68$	33.1179	+	39.4684i	0.487029	+	0.580418i
$69$		0			0
$70$	5.59212	−	2.03537i	0.0798875	−	0.0290767i
$71$	−74.9736	+	43.2860i	−1.05597	+	0.609663i	−0.924314	−	0.381633i	$-0.875362\pi$
$71$	−74.9736	+	43.2860i	−1.05597	+	0.609663i	−0.131653	+	0.991296i	$0.542028\pi$
$72$		0			0
$73$	18.0755	−	31.3076i	0.247609	−	0.428871i	−0.715253	−	0.698866i	$-0.753689\pi$
$73$	18.0755	−	31.3076i	0.247609	−	0.428871i	0.962862	+	0.269994i	$0.0870218\pi$
$74$	2.06330	+	0.363815i	0.0278824	+	0.00491641i
$75$		0			0
$76$	−67.4231	−	24.5400i	−0.887146	−	0.322895i
$77$	−1.41203	+	0.248979i	−0.0183380	+	0.00323349i
$78$		0			0
$79$	−22.3922	−	18.7892i	−0.283445	−	0.237839i	0.489969	−	0.871740i	$-0.337008\pi$
$79$	−22.3922	−	18.7892i	−0.283445	−	0.237839i	−0.773414	+	0.633901i	$0.781453\pi$
$80$		−	92.3828i		−	1.15479i
$81$		0			0
$82$	2.79989			0.0341450
$83$	76.1905	−	90.8003i	0.917957	−	1.09398i	−0.0773297	−	0.997006i	$-0.524639\pi$
$83$	76.1905	−	90.8003i	0.917957	−	1.09398i	0.995287	−	0.0969733i	$-0.0309162\pi$
$84$		0			0
$85$	18.7326	+	106.238i	0.220384	+	1.24986i
$86$	3.41991	−	9.39613i	0.0397664	−	0.109257i
$87$		0			0
$88$	0.832156	−	4.71939i	0.00945632	−	0.0536294i
$89$	−104.884	−	60.5550i	−1.17848	−	0.680394i	−0.222815	−	0.974861i	$-0.571524\pi$
$89$	−104.884	−	60.5550i	−1.17848	−	0.680394i	−0.955662	+	0.294467i	$0.904858\pi$
$90$		0			0
$91$	−13.9585	−	24.1768i	−0.153390	−	0.265679i
$92$	2.24418	+	6.16583i	0.0243932	+	0.0670199i
$93$		0			0
$94$	−20.4237	+	17.1375i	−0.217273	+	0.182314i
$95$	−96.5657	−	115.083i	−1.01648	−	1.21139i
$96$		0			0
$97$	9.05396	−	3.29537i	0.0933398	−	0.0339729i	−0.294928	−	0.955519i	$-0.595296\pi$
$97$	9.05396	−	3.29537i	0.0933398	−	0.0339729i	0.388268	+	0.921547i	$0.373074\pi$
$98$	23.7979	−	13.7397i	0.242836	−	0.140201i
$99$		0			0
$100$	61.8196	−	107.075i	0.618196	−	1.07075i
$101$	−3.79771	−	0.669639i	−0.0376011	−	0.00663009i	0.154816	−	0.987943i	$-0.450522\pi$
$101$	−3.79771	−	0.669639i	−0.0376011	−	0.00663009i	−0.192417	+	0.981313i	$0.561633\pi$
$102$		0			0
$103$	−115.073	−	41.8832i	−1.11722	−	0.406633i	−0.283580	−	0.958948i	$-0.591522\pi$
$103$	−115.073	−	41.8832i	−1.11722	−	0.406633i	−0.833635	+	0.552315i	$0.813744\pi$
$104$	91.8886	−	16.2024i	0.883544	−	0.155793i
$105$		0			0
$106$	22.8625	+	19.1839i	0.215684	+	0.180980i
$107$			80.0804i			0.748415i	0.927345	+	0.374207i	$0.122085\pi$
$107$			80.0804i			0.748415i	−0.927345	+	0.374207i	$0.877915\pi$
$108$		0			0
$109$	−96.8098			−0.888163			−0.444081	−	0.895986i	$-0.646470\pi$
$109$	−96.8098			−0.888163			−0.444081	+	0.895986i	$0.646470\pi$
$110$	3.08227	−	3.67330i	0.0280206	−	0.0333937i
$111$		0			0
$112$	2.79144	+	15.8310i	0.0249236	+	0.141349i
$113$	−22.1070	+	60.7386i	−0.195637	+	0.537509i	−0.998259	−	0.0589789i	$-0.981216\pi$
$113$	−22.1070	+	60.7386i	−0.195637	+	0.537509i	0.802622	+	0.596488i	$0.203438\pi$
$114$		0			0
$115$	−2.38566	+	13.5297i	−0.0207449	+	0.117650i
$116$	127.333	+	73.5156i	1.09770	+	0.633755i
$117$		0			0
$118$	−27.2663	−	47.2266i	−0.231070	−	0.400225i
$119$	−6.42017	−	17.6393i	−0.0539510	−	0.148229i
$120$		0			0
$121$	91.8063	−	77.0347i	0.758730	−	0.636650i
$122$	8.37648	+	9.98271i	0.0686597	+	0.0818255i
$123$		0			0
$124$	58.5834	−	21.3226i	0.472447	−	0.171957i
$125$	58.2161	−	33.6111i	0.465729	−	0.268889i
$126$		0			0
$127$	−82.7295	+	143.292i	−0.651414	+	1.12828i	0.331366	+	0.943502i	$0.392490\pi$
$127$	−82.7295	+	143.292i	−0.651414	+	1.12828i	−0.982780	+	0.184779i	$0.940843\pi$
$128$	−117.215	−	20.6682i	−0.915744	−	0.161470i
$129$		0			0
$130$	87.7332	+	31.9323i	0.674871	+	0.245633i
$131$	−36.1521	+	6.37458i	−0.275970	+	0.0486610i	−0.309920	−	0.950763i	$-0.600302\pi$
$131$	−36.1521	+	6.37458i	−0.275970	+	0.0486610i	0.0339502	+	0.999424i	$0.489191\pi$
$132$		0			0
$133$	20.0252	+	16.8031i	0.150565	+	0.126339i
$134$			11.3664i			0.0848241i
$135$		0			0
$136$	62.7390			0.461316
$137$	−74.9644	+	89.3391i	−0.547185	+	0.652110i	−0.966783	−	0.255600i	$-0.917727\pi$
$137$	−74.9644	+	89.3391i	−0.547185	+	0.652110i	0.419597	+	0.907710i	$0.362171\pi$
$138$		0			0
$139$	−17.1095	−	97.0328i	−0.123090	−	0.698078i	−0.982424	−	0.186663i	$-0.940233\pi$
$139$	−17.1095	−	97.0328i	−0.123090	−	0.698078i	0.859334	−	0.511415i	$-0.170878\pi$
$140$	−12.8058	+	35.1836i	−0.0914699	+	0.251311i
$141$		0			0
$142$	−8.74834	+	49.6143i	−0.0616080	+	0.349396i
$143$	−19.4810	−	11.2473i	−0.136230	−	0.0786527i
$144$		0			0
$145$	153.926	+	266.608i	1.06156	+	1.83867i
$146$	−7.19529	−	19.7689i	−0.0492828	−	0.135403i
$147$		0			0
$148$	−10.0978	+	8.47307i	−0.0682285	+	0.0572505i
$149$	89.3217	+	106.449i	0.599474	+	0.714426i	0.977397	−	0.211411i	$-0.0678060\pi$
$149$	89.3217	+	106.449i	0.599474	+	0.714426i	−0.377923	+	0.925837i	$0.623362\pi$
$150$		0			0
$151$	−122.547	+	44.6035i	−0.811571	+	0.295388i	−0.714272	−	0.699868i	$-0.753242\pi$
$151$	−122.547	+	44.6035i	−0.811571	+	0.295388i	−0.0972982	+	0.995255i	$0.531020\pi$
$152$	−75.6650	+	43.6852i	−0.497796	+	0.287403i
$153$		0			0
$154$	−0.417195	+	0.722604i	−0.00270906	+	0.00469223i
$155$	128.550	+	22.6669i	0.829356	+	0.146238i
$156$		0			0
$157$	219.522	+	79.8994i	1.39823	+	0.508913i	0.927652	−	0.373446i	$-0.121824\pi$
$157$	219.522	+	79.8994i	1.39823	+	0.508913i	0.470576	+	0.882359i	$0.344046\pi$
$158$	−16.7522	+	2.95386i	−0.106026	+	0.0186953i
$159$		0			0
$160$	−145.913	−	122.436i	−0.911957	−	0.765223i
$161$		−	2.39059i		−	0.0148484i
$162$		0			0
$163$	65.8701			0.404111			0.202056	−	0.979374i	$-0.435238\pi$
$163$	65.8701			0.404111			0.202056	+	0.979374i	$0.435238\pi$
$164$	−11.3233	+	13.4945i	−0.0690443	+	0.0822838i
$165$		0			0
$166$	−11.9779	−	67.9300i	−0.0721560	−	0.409217i
$167$	−57.3115	+	157.462i	−0.343182	+	0.942886i	0.641283	+	0.767305i	$0.278403\pi$
$167$	−57.3115	+	157.462i	−0.343182	+	0.942886i	−0.984465	+	0.175581i	$0.943820\pi$
$168$		0			0
$169$	46.7081	−	264.895i	0.276379	−	1.56742i
$170$	54.3671	+	31.3889i	0.319807	+	0.184640i
$171$		0			0
$172$	31.4555	+	54.4825i	0.182881	+	0.316759i
$173$	−90.8802	−	249.691i	−0.525319	−	1.44330i	−0.864525	−	0.502590i	$-0.832380\pi$
$173$	−90.8802	−	249.691i	−0.525319	−	1.44330i	0.339206	−	0.940712i	$-0.389842\pi$
$174$		0			0
$175$	−34.5072	+	28.9550i	−0.197184	+	0.165457i
$176$	8.32602	+	9.92256i	0.0473069	+	0.0563782i
$177$		0			0
$178$	−66.2283	+	24.1051i	−0.372069	+	0.135422i
$179$	213.546	−	123.291i	1.19299	−	0.688776i	0.234010	−	0.972234i	$-0.424815\pi$
$179$	213.546	−	123.291i	1.19299	−	0.688776i	0.958985	+	0.283458i	$0.0914818\pi$
$180$		0			0
$181$	0.670719	−	1.16172i	0.00370563	−	0.00641834i	−0.864167	−	0.503206i	$-0.832154\pi$
$181$	0.670719	−	1.16172i	0.00370563	−	0.00641834i	0.867872	+	0.496787i	$0.165487\pi$
$182$	−15.9991	−	2.82108i	−0.0879074	−	0.0155004i
$183$		0			0
$184$	7.50815	+	2.73274i	0.0408052	+	0.0148519i
$185$	−27.1805	+	4.79266i	−0.146922	+	0.0259062i
$186$		0			0
$187$	−11.5867	−	9.72242i	−0.0619611	−	0.0519916i
$188$		−	167.743i		−	0.892248i
$189$		0			0
$190$	−87.4244			−0.460128
$191$	−29.8515	+	35.5757i	−0.156291	+	0.186260i	−0.838508	−	0.544890i	$-0.816572\pi$
$191$	−29.8515	+	35.5757i	−0.156291	+	0.186260i	0.682217	+	0.731150i	$0.261016\pi$
$192$		0			0
$193$	−24.7371	−	140.291i	−0.128171	−	0.726896i	−0.979374	−	0.202058i	$-0.935237\pi$
$193$	−24.7371	−	140.291i	−0.128171	−	0.726896i	0.851202	−	0.524838i	$-0.175874\pi$
$194$	1.91770	−	5.26885i	0.00988508	−	0.0271590i
$195$		0			0
$196$	−30.0222	+	170.264i	−0.153174	+	0.868695i
$197$	46.8442	+	27.0455i	0.237788	+	0.137287i	0.614160	−	0.789182i	$-0.289495\pi$
$197$	46.8442	+	27.0455i	0.237788	+	0.137287i	−0.376372	+	0.926469i	$0.622828\pi$
$198$		0			0
$199$	−164.437	−	284.813i	−0.826317	−	1.43122i	−0.900909	−	0.434009i	$-0.857099\pi$
$199$	−164.437	−	284.813i	−0.826317	−	1.43122i	0.0745915	−	0.997214i	$-0.476235\pi$
$200$	−51.4932	−	141.476i	−0.257466	−	0.707382i
$201$		0			0
$202$	−1.71910	+	1.44250i	−0.00851041	+	0.00714108i
$203$	−34.4331	−	41.0358i	−0.169621	−	0.202147i
$204$		0			0
$205$	−34.6595	+	12.6150i	−0.169071	+	0.0615368i
$206$	−61.7158	+	35.6316i	−0.299591	+	0.172969i
$207$		0			0
$208$	−126.100	+	218.412i	−0.606250	+	1.05006i
$209$	20.7437	+	3.65767i	0.0992520	+	0.0175008i
$210$		0			0
$211$	−89.0532	−	32.4127i	−0.422053	−	0.153615i	0.122258	−	0.992498i	$-0.460987\pi$
$211$	−89.0532	−	32.4127i	−0.422053	−	0.153615i	−0.544311	+	0.838884i	$0.683209\pi$
$212$	−184.920	+	32.6064i	−0.872265	+	0.153804i
$213$		0			0
$214$	35.6991	+	29.9551i	0.166818	+	0.139977i
$215$			131.722i			0.612662i
$216$		0			0
$217$	−22.7137			−0.104671
$218$	−36.2130	+	43.1569i	−0.166114	+	0.197968i
$219$		0			0
$220$	5.23886	+	29.7110i	0.0238130	+	0.135050i
$221$	100.724	−	276.738i	0.455766	−	1.25221i
$222$		0			0
$223$	−14.1117	+	80.0312i	−0.0632810	+	0.358884i	0.936681	+	0.350183i	$0.113881\pi$
$223$	−14.1117	+	80.0312i	−0.0632810	+	0.358884i	−0.999962	+	0.00870098i	$0.997230\pi$
$224$	28.7037	+	16.5721i	0.128141	+	0.0739825i
$225$		0			0
$226$	18.8073	+	32.5752i	0.0832180	+	0.144138i
$227$	−57.3885	−	157.674i	−0.252813	−	0.694597i	−0.999565	−	0.0294950i	$-0.990610\pi$
$227$	−57.3885	−	157.674i	−0.252813	−	0.694597i	0.746752	−	0.665102i	$-0.231612\pi$
$228$		0			0
$229$	56.2458	−	47.1958i	0.245615	−	0.206095i	−0.511666	−	0.859184i	$-0.670972\pi$
$229$	56.2458	−	47.1958i	0.245615	−	0.206095i	0.757281	+	0.653089i	$0.226527\pi$
$230$	5.13905	+	6.12448i	0.0223437	+	0.0266282i
$231$		0			0
$232$	168.243	−	61.2354i	0.725185	−	0.263946i
$233$	159.041	−	91.8223i	0.682579	−	0.394087i	−0.118247	−	0.992984i	$-0.537728\pi$
$233$	159.041	−	91.8223i	0.682579	−	0.394087i	0.800826	+	0.598897i	$0.204394\pi$
$234$		0			0
$235$	175.609	−	304.163i	0.747271	−	1.29431i
$236$	337.887	+	59.5785i	1.43172	+	0.252451i
$237$		0			0
$238$	−10.2650	−	3.73615i	−0.0431302	−	0.0156981i
$239$	8.71524	−	1.53673i	0.0364655	−	0.00642984i	−0.155386	−	0.987854i	$-0.549662\pi$
$239$	8.71524	−	1.53673i	0.0364655	−	0.00642984i	0.191851	+	0.981424i	$0.438551\pi$
$240$		0			0
$241$	−12.1911	−	10.2295i	−0.0505853	−	0.0424461i	0.617145	−	0.786850i	$-0.288289\pi$
$241$	−12.1911	−	10.2295i	−0.0505853	−	0.0424461i	−0.667730	+	0.744404i	$0.732734\pi$
$242$		−	69.7423i		−	0.288191i
$243$		0			0
$244$	−81.9894			−0.336022
$245$	−232.687	+	277.306i	−0.949743	+	1.13186i
$246$		0			0
$247$	71.2164	+	403.888i	0.288325	+	1.63517i
$248$	25.9646	−	71.3372i	0.104696	−	0.287650i
$249$		0			0
$250$	6.79298	−	38.5249i	0.0271719	−	0.154100i
$251$	−228.852	−	132.128i	−0.911762	−	0.526406i	−0.0307645	−	0.999527i	$-0.509794\pi$
$251$	−228.852	−	132.128i	−0.911762	−	0.526406i	−0.880998	+	0.473121i	$0.843128\pi$
$252$		0			0
$253$	−0.963134	−	1.66820i	−0.00380685	−	0.00659366i
$254$	32.9321	+	90.4802i	0.129654	+	0.356221i
$255$		0			0
$256$	50.3387	−	42.2392i	0.196635	−	0.164997i
$257$	219.915	+	262.084i	0.855699	+	1.01978i	0.999544	+	0.0301818i	$0.00960864\pi$
$257$	219.915	+	262.084i	0.855699	+	1.01978i	−0.143846	+	0.989600i	$0.545947\pi$
$258$		0			0
$259$	4.51293	−	1.64257i	0.0174244	−	0.00634198i
$260$	−508.713	+	293.705i	−1.95659	+	1.12964i
$261$		0			0
$262$	−10.6814	+	18.5008i	−0.0407688	+	0.0706136i
$263$	374.609	+	66.0536i	1.42437	+	0.251154i	0.832117	−	0.554600i	$-0.187129\pi$
$263$	374.609	+	66.0536i	1.42437	+	0.251154i	0.592250	+	0.805754i	$0.298240\pi$
$264$		0			0
$265$	−369.446	−	134.467i	−1.39414	−	0.507424i
$266$	14.9813	−	2.64162i	0.0563209	−	0.00993089i
$267$		0			0
$268$	−54.7824	−	45.9679i	−0.204412	−	0.171522i
$269$			88.9301i			0.330595i	0.986244	+	0.165297i	$0.0528584\pi$
$269$			88.9301i			0.330595i	−0.986244	+	0.165297i	$0.947142\pi$
$270$		0			0
$271$	487.123			1.79750			0.898751	−	0.438460i	$-0.144476\pi$
$271$	487.123			1.79750			0.898751	+	0.438460i	$0.144476\pi$
$272$	−109.003	+	129.905i	−0.400748	+	0.477593i
$273$		0			0
$274$	11.7851	+	66.8369i	0.0430115	+	0.243930i
$275$	−12.4142	+	34.1078i	−0.0451426	+	0.124028i
$276$		0			0
$277$	−15.1883	+	86.1369i	−0.0548312	+	0.310963i	−0.999872	−	0.0159886i	$-0.994910\pi$
$277$	−15.1883	+	86.1369i	−0.0548312	+	0.310963i	0.945041	+	0.326952i	$0.106022\pi$
$278$	−49.6564	−	28.6691i	−0.178620	−	0.103126i
$279$		0			0
$280$	22.7964	+	39.4845i	0.0814157	+	0.141016i
$281$	55.1861	+	151.623i	0.196392	+	0.539582i	0.998326	−	0.0578296i	$-0.0184180\pi$
$281$	55.1861	+	151.623i	0.196392	+	0.539582i	−0.801935	+	0.597412i	$0.796196\pi$
$282$		0			0
$283$	−105.120	+	88.2058i	−0.371447	+	0.311681i	−0.809334	−	0.587349i	$-0.800172\pi$
$283$	−105.120	+	88.2058i	−0.371447	+	0.311681i	0.437886	+	0.899030i	$0.355727\pi$
$284$	−203.745	−	242.813i	−0.717411	−	0.854977i
$285$		0			0
$286$	−12.3011	+	4.47722i	−0.0430107	+	0.0156546i
$287$	5.55820	−	3.20903i	0.0193666	−	0.0111813i
$288$		0			0
$289$	−45.4898	+	78.7907i	−0.157404	+	0.272632i
$290$	176.429	+	31.1093i	0.608377	+	0.107273i
$291$		0			0
$292$	124.379	+	45.2701i	0.425954	+	0.155035i
$293$	382.393	−	67.4262i	1.30510	−	0.230124i	0.522492	−	0.852644i	$-0.325002\pi$
$293$	382.393	−	67.4262i	1.30510	−	0.230124i	0.782604	+	0.622520i	$0.213891\pi$
$294$		0			0
$295$	550.308	+	461.763i	1.86545	+	1.56530i
$296$			16.0515i			0.0542280i
$297$		0			0
$298$	80.8661			0.271363
$299$	24.1079	−	28.7307i	0.0806285	−	0.0960893i
$300$		0			0
$301$	−3.98012	−	22.5724i	−0.0132230	−	0.0749913i
$302$	−25.9565	+	71.3150i	−0.0859487	+	0.236142i
$303$		0			0
$304$	41.0081	−	232.569i	0.134895	−	0.765029i
$305$	−148.669	−	85.8342i	−0.487440	−	0.281424i
$306$		0			0
$307$	−207.323	−	359.093i	−0.675318	−	1.16969i	−0.976376	−	0.216080i	$-0.930673\pi$
$307$	−207.323	−	359.093i	−0.675318	−	1.16969i	0.301057	−	0.953606i	$-0.402660\pi$
$308$	−1.79550	−	4.93309i	−0.00582954	−	0.0160165i
$309$		0			0
$310$	58.1906	−	48.8277i	0.187712	−	0.157509i
$311$	−280.533	−	334.326i	−0.902036	−	1.07500i	−0.996834	−	0.0795082i	$-0.974665\pi$
$311$	−280.533	−	334.326i	−0.902036	−	1.07500i	0.0947982	−	0.995497i	$-0.469779\pi$
$312$		0			0
$313$	386.486	−	140.669i	1.23478	−	0.449423i	0.359548	−	0.933127i	$-0.382931\pi$
$313$	386.486	−	140.669i	1.23478	−	0.449423i	0.875232	+	0.483703i	$0.160709\pi$
$314$	117.733	−	67.9734i	0.374947	−	0.216476i
$315$		0			0
$316$	53.5122	−	92.6858i	0.169342	−	0.293310i
$317$	−402.773	−	71.0197i	−1.27058	−	0.224037i	−0.502602	−	0.864518i	$-0.667624\pi$
$317$	−402.773	−	71.0197i	−1.27058	−	0.224037i	−0.767974	+	0.640481i	$0.778735\pi$
$318$		0			0
$319$	−40.5608	−	14.7629i	−0.127150	−	0.0462788i
$320$	254.756	−	44.9203i	0.796112	−	0.140376i
$321$		0			0
$322$	−1.06570	−	0.894231i	−0.00330964	−	0.00277711i
$323$			275.764i			0.853757i
$324$		0			0
$325$	−706.713			−2.17450
$326$	24.6396	−	29.3643i	0.0755815	−	0.0900745i
$327$		0			0
$328$	3.72491	+	21.1250i	0.0113564	+	0.0644056i
$329$	−20.9023	+	57.4286i	−0.0635329	+	0.174555i
$330$		0			0
$331$	−56.8942	+	322.663i	−0.171886	+	0.974812i	0.769792	+	0.638295i	$0.220360\pi$
$331$	−56.8942	+	322.663i	−0.171886	+	0.974812i	−0.941677	+	0.336517i	$0.890751\pi$
$332$	375.841	+	216.992i	1.13205	+	0.653591i
$333$		0			0
$334$	48.7570	+	84.4496i	0.145979	+	0.252843i
$335$	−51.2120	−	140.704i	−0.152872	−	0.420011i
$336$		0			0
$337$	−430.977	+	361.633i	−1.27886	+	1.07309i	−0.285464	+	0.958389i	$0.592148\pi$
$337$	−430.977	+	361.633i	−1.27886	+	1.07309i	−0.993400	+	0.114705i	$0.963408\pi$
$338$	−100.616	−	119.909i	−0.297680	−	0.354761i
$339$		0			0
$340$	−371.155	+	135.089i	−1.09163	+	0.397321i
$341$	−15.8500	+	9.15103i	−0.0464811	+	0.0268359i
$342$		0			0
$343$	64.1768	−	111.157i	0.187104	−	0.324074i
$344$	75.4431	+	13.3027i	0.219311	+	0.0386705i
$345$		0			0
$346$	−145.305	−	52.8867i	−0.419957	−	0.152852i
$347$	−240.215	+	42.3563i	−0.692261	+	0.122064i	−0.508700	−	0.860944i	$-0.669874\pi$
$347$	−240.215	+	42.3563i	−0.692261	+	0.122064i	−0.183561	+	0.983008i	$0.558763\pi$
$348$		0			0
$349$	−282.886	−	237.369i	−0.810561	−	0.680141i	0.140181	−	0.990126i	$-0.455232\pi$
$349$	−282.886	−	237.369i	−0.810561	−	0.680141i	−0.950742	+	0.309985i	$0.899676\pi$
$350$			26.2140i			0.0748971i
$351$		0			0
$352$	26.7066			0.0758711
$353$	−60.3702	+	71.9464i	−0.171020	+	0.203814i	−0.844746	−	0.535167i	$-0.820249\pi$
$353$	−60.3702	+	71.9464i	−0.171020	+	0.203814i	0.673726	+	0.738982i	$0.264693\pi$
$354$		0			0
$355$	−115.245	−	653.586i	−0.324633	−	1.84109i
$356$	151.661	−	416.684i	0.426013	−	1.17046i
$357$		0			0
$358$	24.9177	−	141.315i	0.0696026	−	0.394736i
$359$	−89.5202	−	51.6845i	−0.249360	−	0.143968i	0.370111	−	0.928987i	$-0.379320\pi$
$359$	−89.5202	−	51.6845i	−0.249360	−	0.143968i	−0.619471	+	0.785019i	$0.712653\pi$
$360$		0			0
$361$	−11.5145	−	19.9437i	−0.0318962	−	0.0552458i
$362$	−0.266993	−	0.733557i	−0.000737550	−	0.00202640i
$363$		0			0
$364$	78.3002	−	65.7016i	0.215110	−	0.180499i
$365$	178.139	+	212.298i	0.488053	+	0.581639i
$366$		0			0
$367$	85.2083	−	31.0133i	0.232175	−	0.0845048i	−0.223313	−	0.974747i	$-0.571687\pi$
$367$	85.2083	−	31.0133i	0.232175	−	0.0845048i	0.455488	+	0.890242i	$0.349465\pi$
$368$	−18.7031	+	10.7982i	−0.0508236	+	0.0293430i
$369$		0			0
$370$	−8.03070	+	13.9096i	−0.0217046	+	0.0375935i
$371$	67.3726	+	11.8796i	0.181597	+	0.0320205i
$372$		0			0
$373$	406.838	+	148.077i	1.09072	+	0.396989i	0.823887	−	0.566754i	$-0.191801\pi$
$373$	406.838	+	148.077i	1.09072	+	0.396989i	0.266831	+	0.963743i	$0.414023\pi$
$374$	−8.66833	+	1.52846i	−0.0231774	+	0.00408679i
$375$		0			0
$376$	−156.473	−	131.296i	−0.416151	−	0.349192i
$377$		−	840.420i		−	2.22923i
$378$		0			0
$379$	333.700			0.880476			0.440238	−	0.897881i	$-0.354894\pi$
$379$	333.700			0.880476			0.440238	+	0.897881i	$0.354894\pi$
$380$	353.561	−	421.357i	0.930423	−	1.10883i
$381$		0			0
$382$	4.69296	+	26.6151i	0.0122852	+	0.0696730i
$383$	−203.470	+	559.030i	−0.531254	+	1.45961i	0.326325	+	0.945258i	$0.394190\pi$
$383$	−203.470	+	559.030i	−0.531254	+	1.45961i	−0.857579	+	0.514352i	$0.828033\pi$
$384$		0			0
$385$	1.90869	−	10.8247i	0.00495764	−	0.0281162i
$386$	−71.7937	−	41.4501i	−0.185994	−	0.107384i
$387$		0			0
$388$	17.6386	+	30.5509i	0.0454603	+	0.0787395i
$389$	−106.062	−	291.404i	−0.272654	−	0.749111i	−0.998145	−	0.0608795i	$-0.980609\pi$
$389$	−106.062	−	291.404i	−0.272654	−	0.749111i	0.725491	−	0.688232i	$-0.241613\pi$
$390$		0			0
$391$	19.3185	−	16.2102i	0.0494079	−	0.0414582i
$392$	135.326	+	161.275i	0.345219	+	0.411416i
$393$		0			0
$394$	29.5793	−	10.7660i	0.0750744	−	0.0273248i
$395$	194.064	−	112.043i	0.491302	−	0.283653i
$396$		0			0
$397$	−69.0323	+	119.567i	−0.173885	+	0.301177i	−0.939775	−	0.341794i	$-0.888965\pi$
$397$	−69.0323	+	119.567i	−0.173885	+	0.301177i	0.765890	+	0.642972i	$0.222299\pi$
$398$	−188.477	−	33.2336i	−0.473561	−	0.0835015i
$399$		0			0
$400$	382.401	+	139.183i	0.956003	+	0.347956i
$401$	−266.978	+	47.0754i	−0.665780	+	0.117395i	−0.496317	−	0.868142i	$-0.665314\pi$
$401$	−266.978	+	47.0754i	−0.665780	+	0.117395i	−0.169463	+	0.985537i	$0.554203\pi$
$402$		0			0
$403$	−272.979	−	229.057i	−0.677368	−	0.568379i
$404$		−	14.1192i		−	0.0349486i
$405$		0			0
$406$	−31.1735			−0.0767821
$407$	2.48744	−	2.96441i	0.00611164	−	0.00728357i
$408$		0			0
$409$	50.3565	+	285.586i	0.123121	+	0.698254i	0.982406	+	0.186757i	$0.0597976\pi$
$409$	50.3565	+	285.586i	0.123121	+	0.698254i	−0.859285	+	0.511497i	$0.829091\pi$
$410$	−7.34118	+	20.1697i	−0.0179053	+	0.0491944i
$411$		0			0
$412$	77.8573	−	441.551i	0.188974	−	1.07173i
$413$	−108.255	−	62.5013i	−0.262120	−	0.151335i
$414$		0			0
$415$	454.335	+	786.932i	1.09478	+	1.89622i
$416$	177.847	+	488.630i	0.427517	+	1.17459i
$417$		0			0
$418$	9.38999	−	7.87914i	0.0224641	−	0.0188496i
$419$	215.521	+	256.848i	0.514371	+	0.613003i	0.959240	−	0.282592i	$-0.0911944\pi$
$419$	215.521	+	256.848i	0.514371	+	0.613003i	−0.444870	+	0.895595i	$0.646750\pi$
$420$		0			0
$421$	−566.754	+	206.282i	−1.34621	+	0.489980i	−0.911763	−	0.410717i	$-0.865278\pi$
$421$	−566.754	+	206.282i	−1.34621	+	0.489980i	−0.434447	+	0.900697i	$0.643056\pi$
$422$	−47.7608	+	27.5747i	−0.113177	+	0.0653429i
$423$		0			0
$424$	−114.326	+	198.018i	−0.269636	+	0.467024i
$425$	−467.974	−	82.5165i	−1.10112	−	0.194156i
$426$		0			0
$427$	28.0700	+	10.2167i	0.0657378	+	0.0239266i
$428$	−288.748	+	50.9140i	−0.674644	+	0.118958i
$429$		0			0
$430$	58.7206	+	49.2724i	0.136560	+	0.114587i
$431$			773.546i			1.79477i	0.441247	+	0.897385i	$0.354536\pi$
$431$			773.546i			1.79477i	−0.441247	+	0.897385i	$0.645464\pi$
$432$		0			0
$433$	71.6603			0.165497			0.0827486	−	0.996570i	$-0.473630\pi$
$433$	71.6603			0.165497			0.0827486	+	0.996570i	$0.473630\pi$
$434$	−8.49636	+	10.1256i	−0.0195769	+	0.0233308i
$435$		0			0
$436$	−61.5503	−	349.069i	−0.141170	−	0.800617i
$437$	−12.0115	+	33.0014i	−0.0274863	+	0.0755181i
$438$		0			0
$439$	−118.933	+	674.503i	−0.270918	+	1.53645i	0.480717	+	0.876876i	$0.340376\pi$
$439$	−118.933	+	674.503i	−0.270918	+	1.53645i	−0.751636	+	0.659579i	$0.770735\pi$
$440$	31.8155	+	18.3687i	0.0723079	+	0.0417470i
$441$		0			0
$442$	−85.6900	−	148.419i	−0.193869	−	0.335790i
$443$	155.729	+	427.863i	0.351534	+	0.965831i	0.981878	+	0.189515i	$0.0606916\pi$
$443$	155.729	+	427.863i	0.351534	+	0.965831i	−0.630344	+	0.776316i	$0.717086\pi$
$444$		0			0
$445$	711.226	−	596.789i	1.59826	−	1.34110i
$446$	30.3985	+	36.2276i	0.0681582	+	0.0812278i
$447$		0			0
$448$	−42.2985	+	15.3954i	−0.0944163	+	0.0343647i
$449$	456.689	−	263.670i	1.01713	−	0.587238i	0.103856	−	0.994592i	$-0.466882\pi$
$449$	456.689	−	263.670i	1.01713	−	0.587238i	0.913270	+	0.407355i	$0.133549\pi$
$450$		0			0
$451$	2.58574	−	4.47864i	0.00573336	−	0.00993046i
$452$	−233.062	−	41.0951i	−0.515623	−	0.0909183i
$453$		0			0
$454$	−91.7564	−	33.3966i	−0.202107	−	0.0735608i
$455$	210.762	−	37.1631i	0.463214	−	0.0816770i
$456$		0			0
$457$	−112.672	−	94.5433i	−0.246548	−	0.206878i	0.511136	−	0.859500i	$-0.329225\pi$
$457$	−112.672	−	94.5433i	−0.246548	−	0.206878i	−0.757684	+	0.652622i	$0.773669\pi$
$458$		−	42.7281i		−	0.0932928i
$459$		0			0
$460$	−50.3013			−0.109351
$461$	230.109	−	274.233i	0.499152	−	0.594866i	−0.456368	−	0.889791i	$-0.650850\pi$
$461$	230.109	−	274.233i	0.499152	−	0.594866i	0.955521	+	0.294924i	$0.0952945\pi$
$462$		0			0
$463$	71.1591	+	403.563i	0.153691	+	0.871627i	0.959972	+	0.280095i	$0.0903659\pi$
$463$	71.1591	+	403.563i	0.153691	+	0.871627i	−0.806281	+	0.591533i	$0.798523\pi$
$464$	−165.515	+	454.750i	−0.356714	+	0.980064i
$465$		0			0
$466$	18.5578	−	105.246i	0.0398235	−	0.225850i
$467$	778.946	+	449.725i	1.66798	+	0.963008i	0.968726	+	0.248132i	$0.0798167\pi$
$467$	778.946	+	449.725i	1.66798	+	0.963008i	0.699252	+	0.714876i	$0.253517\pi$
$468$		0			0
$469$	13.0274	+	22.5641i	0.0277769	+	0.0481110i
$470$	−69.9044	−	192.061i	−0.148733	−	0.408640i
$471$		0			0
$472$	320.048	−	268.552i	0.678068	−	0.568966i
$473$	−11.8715	−	14.1479i	−0.0250983	−	0.0299110i
$474$		0			0
$475$	621.847	−	226.334i	1.30915	−	0.476492i
$476$	59.5205	−	34.3642i	0.125043	−	0.0721937i
$477$		0			0
$478$	2.57499	−	4.46001i	0.00538701	−	0.00933057i
$479$	−822.620	−	145.050i	−1.71737	−	0.302819i	−0.773662	−	0.633599i	$-0.781577\pi$
$479$	−822.620	−	145.050i	−1.71737	−	0.302819i	−0.943708	+	0.330780i	$0.892688\pi$
$480$		0			0
$481$	70.8021	+	25.7699i	0.147198	+	0.0535756i
$482$	−9.12045	+	1.60818i	−0.0189221	+	0.00333647i
$483$		0			0
$484$	336.135	+	282.051i	0.694494	+	0.582749i
$485$			73.8629i			0.152295i
$486$		0			0
$487$	−601.667			−1.23546			−0.617728	−	0.786392i	$-0.711947\pi$
$487$	−601.667			−1.23546			−0.617728	+	0.786392i	$0.711947\pi$
$488$	−64.1752	+	76.4810i	−0.131506	+	0.156723i
$489$		0			0
$490$	36.5807	+	207.460i	0.0746545	+	0.423387i
$491$	146.639	−	402.888i	0.298655	−	0.820547i	−0.696071	−	0.717973i	$-0.745070\pi$
$491$	146.639	−	402.888i	0.298655	−	0.820547i	0.994725	−	0.102574i	$-0.0327077\pi$
$492$		0			0
$493$	98.1282	−	556.513i	0.199043	−	1.12883i
$494$	206.689	+	119.332i	0.418399	+	0.241563i
$495$		0			0
$496$	102.597	+	177.704i	0.206849	+	0.358274i
$497$	39.4975	+	108.519i	0.0794719	+	0.218347i
$498$		0			0
$499$	−435.651	+	365.554i	−0.873048	+	0.732574i	−0.964738	−	0.263214i	$-0.915218\pi$
$499$	−435.651	+	365.554i	−0.873048	+	0.732574i	0.0916899	+	0.995788i	$0.470773\pi$
$500$	158.205	+	188.542i	0.316411	+	0.377084i
$501$		0			0
$502$	−144.507	+	52.5961i	−0.287862	+	0.104773i
$503$	−178.281	+	102.930i	−0.354435	+	0.204633i	−0.666637	−	0.745383i	$-0.732267\pi$
$503$	−178.281	+	102.930i	−0.354435	+	0.204633i	0.312202	+	0.950016i	$0.398933\pi$
$504$		0			0
$505$	14.7813	−	25.6020i	0.0292700	−	0.0506971i
$506$	−1.10394	−	0.194654i	−0.00218170	−	0.000384692i
$507$		0			0
$508$	−569.269	−	207.197i	−1.12061	−	0.407868i
$509$	−663.268	+	116.952i	−1.30308	+	0.229768i	−0.781753	−	0.623589i	$-0.785674\pi$
$509$	−663.268	+	116.952i	−1.30308	+	0.229768i	−0.521327	+	0.853357i	$0.674563\pi$
$510$		0			0
$511$	−36.9414	−	30.9975i	−0.0722924	−	0.0606605i
$512$		−	514.334i		−	1.00456i
$513$		0			0
$514$	199.097			0.387347
$515$	603.433	−	719.144i	1.17172	−	1.39640i
$516$		0			0
$517$	8.55115	+	48.4960i	0.0165399	+	0.0938027i
$518$	0.955876	−	2.62625i	0.00184532	−	0.00506998i
$519$		0			0
$520$	−124.209	+	704.425i	−0.238864	+	1.35466i
$521$	−678.655	−	391.821i	−1.30260	−	0.752056i	−0.321751	−	0.946824i	$-0.604271\pi$
$521$	−678.655	−	391.821i	−1.30260	−	0.752056i	−0.980849	+	0.194768i	$0.937605\pi$
$522$		0			0
$523$	−231.463	−	400.906i	−0.442569	−	0.766551i	0.555311	−	0.831643i	$-0.312599\pi$
$523$	−231.463	−	400.906i	−0.442569	−	0.766551i	−0.997879	+	0.0650916i	$0.979266\pi$
$524$	−45.9700	−	126.301i	−0.0877290	−	0.241033i
$525$		0			0
$526$	169.573	−	142.289i	0.322383	−	0.270511i
$527$	−154.018	−	183.551i	−0.292254	−	0.348294i
$528$		0			0
$529$	−494.079	+	179.830i	−0.933988	+	0.339944i
$530$	−198.140	+	114.396i	−0.373850	+	0.215842i
$531$		0			0
$532$	−47.8556	+	82.8884i	−0.0899542	+	0.155805i
$533$	99.1614	+	17.4848i	0.186044	+	0.0328046i
$534$		0			0
$535$	−576.880	−	209.967i	−1.07828	−	0.392462i
$536$	−85.7591	+	15.1217i	−0.159998	+	0.0282120i
$537$		0			0
$538$	39.6442	+	33.2654i	0.0736881	+	0.0618317i
$539$		−	50.7555i		−	0.0941661i
$540$		0			0
$541$	595.277			1.10033			0.550164	−	0.835057i	$-0.314565\pi$
$541$	595.277			1.10033			0.550164	+	0.835057i	$0.314565\pi$
$542$	182.215	−	217.155i	0.336190	−	0.400655i
$543$		0			0
$544$	60.7145	+	344.329i	0.111607	+	0.632957i
$545$	253.831	−	697.394i	0.465744	−	1.27962i
$546$		0			0
$547$	175.350	−	994.459i	0.320567	−	1.81802i	−0.218588	−	0.975817i	$-0.570145\pi$
$547$	175.350	−	994.459i	0.320567	−	1.81802i	0.539154	−	0.842207i	$-0.318744\pi$
$548$	−369.793	−	213.500i	−0.674805	−	0.389599i
$549$		0			0
$550$	10.5612	+	18.2926i	0.0192022	+	0.0332593i
$551$	269.155	+	739.497i	0.488485	+	1.34210i
$552$		0			0
$553$	−29.8701	+	25.0639i	−0.0540146	+	0.0453236i
$554$	32.7177	+	38.9914i	0.0590572	+	0.0703816i
$555$		0			0
$556$	338.995	−	123.384i	0.609704	−	0.221914i
$557$	−53.4658	+	30.8685i	−0.0959889	+	0.0554192i	−0.547226	−	0.836985i	$-0.684316\pi$
$557$	−53.4658	+	30.8685i	−0.0959889	+	0.0554192i	0.451237	+	0.892404i	$0.350983\pi$
$558$		0			0
$559$	179.797	−	311.418i	0.321641	−	0.557099i
$560$	−121.362	−	21.3994i	−0.216718	−	0.0382132i
$561$		0			0
$562$	88.2351	+	32.1149i	0.157002	+	0.0571440i
$563$	955.335	−	168.451i	1.69686	−	0.299203i	0.760267	−	0.649611i	$-0.225068\pi$
$563$	955.335	−	168.451i	1.69686	−	0.299203i	0.936597	+	0.350408i	$0.113957\pi$
$564$		0			0
$565$	−379.582	−	318.507i	−0.671827	−	0.563730i
$566$			79.8559i			0.141088i
$567$		0			0
$568$	−385.976			−0.679535
$569$	61.7612	−	73.6041i	0.108543	−	0.129357i	−0.709037	−	0.705171i	$-0.750870\pi$
$569$	61.7612	−	73.6041i	0.108543	−	0.129357i	0.817581	+	0.575814i	$0.195315\pi$
$570$		0			0
$571$	−112.283	−	636.787i	−0.196642	−	1.11521i	−0.910061	−	0.414475i	$-0.863965\pi$
$571$	−112.283	−	636.787i	−0.196642	−	1.11521i	0.713419	−	0.700738i	$-0.247146\pi$
$572$	28.1691	−	77.3938i	0.0492466	−	0.135304i
$573$		0			0
$574$	0.648561	−	3.67817i	0.00112990	−	0.00640797i
$575$	−52.4096	−	30.2587i	−0.0911471	−	0.0526238i
$576$		0			0
$577$	−126.992	−	219.957i	−0.220091	−	0.381208i	0.734745	−	0.678344i	$-0.237302\pi$
$577$	−126.992	−	219.957i	−0.220091	−	0.381208i	−0.954835	+	0.297136i	$0.903969\pi$
$578$	18.1081	+	49.7516i	0.0313289	+	0.0860755i
$579$		0			0
$580$	−863.450	+	724.520i	−1.48871	+	1.24917i
$581$	−101.634	−	121.123i	−0.174930	−	0.208474i
$582$		0			0
$583$	51.8000	−	18.8537i	0.0888507	−	0.0323390i
$584$	139.583	−	80.5883i	0.239012	−	0.137994i
$585$		0			0
$586$	112.981	−	195.689i	0.192801	−	0.333940i
$587$	220.174	+	38.8225i	0.375083	+	0.0661372i	0.358012	−	0.933717i	$-0.383455\pi$
$587$	220.174	+	38.8225i	0.375083	+	0.0661372i	0.0170710	+	0.999854i	$0.494566\pi$
$588$		0			0
$589$	313.557	+	114.125i	0.532354	+	0.193761i
$590$	411.700	−	72.5938i	0.697796	−	0.123040i
$591$		0			0
$592$	−33.2357	−	27.8880i	−0.0561413	−	0.0471082i
$593$			69.9992i			0.118042i	0.998257	+	0.0590212i	$0.0187980\pi$
$593$			69.9992i			0.118042i	−0.998257	+	0.0590212i	$0.981202\pi$
$594$		0			0
$595$	143.903			0.241853
$596$	−327.038	+	389.748i	−0.548721	+	0.653940i
$597$		0			0
$598$	−3.79001	−	21.4942i	−0.00633780	−	0.0359435i
$599$	−143.261	+	393.606i	−0.239167	+	0.657105i	0.760800	+	0.648986i	$0.224807\pi$
$599$	−143.261	+	393.606i	−0.239167	+	0.657105i	−0.999967	+	0.00811910i	$0.997416\pi$
$600$		0			0
$601$	−137.993	+	782.595i	−0.229605	+	1.30216i	0.624078	+	0.781362i	$0.285475\pi$
$601$	−137.993	+	782.595i	−0.229605	+	1.30216i	−0.853683	+	0.520793i	$0.825636\pi$
$602$	−11.5514	−	6.66919i	−0.0191883	−	0.0110784i
$603$		0			0
$604$	−238.742	−	413.513i	−0.395268	−	0.684624i
$605$	314.227	+	863.332i	0.519384	+	1.42700i
$606$		0			0
$607$	251.711	−	211.211i	0.414681	−	0.347959i	−0.411454	−	0.911430i	$-0.634979\pi$
$607$	251.711	−	211.211i	0.414681	−	0.347959i	0.826135	+	0.563472i	$0.190535\pi$
$608$	−312.980	−	372.995i	−0.514770	−	0.613479i
$609$		0			0
$610$	−93.8758	+	34.1680i	−0.153895	+	0.0560131i
$611$	−830.349	+	479.402i	−1.35900	+	0.784619i
$612$		0			0
$613$	−367.664	+	636.812i	−0.599778	+	1.03885i	0.393076	+	0.919506i	$0.371411\pi$
$613$	−367.664	+	636.812i	−0.599778	+	1.03885i	−0.992853	+	0.119340i	$0.961922\pi$
$614$	−237.632	−	41.9010i	−0.387023	−	0.0682427i
$615$		0			0
$616$	−6.00704	−	2.18638i	−0.00975169	−	0.00354932i
$617$	331.915	−	58.5257i	0.537951	−	0.0948552i	0.101929	−	0.994792i	$-0.467498\pi$
$617$	331.915	−	58.5257i	0.537951	−	0.0948552i	0.436021	+	0.899936i	$0.356387\pi$
$618$		0			0
$619$	900.806	+	755.866i	1.45526	+	1.22111i	0.928627	+	0.371015i	$0.120990\pi$
$619$	900.806	+	755.866i	1.45526	+	1.22111i	0.526633	+	0.850093i	$0.323454\pi$
$620$			477.928i			0.770851i
$621$		0			0
$622$	−253.977			−0.408323
$623$	−103.846	+	123.758i	−0.166686	+	0.198649i
$624$		0			0
$625$	−57.1109	−	323.892i	−0.0913775	−	0.518227i
$626$	81.8610	−	224.911i	0.130768	−	0.359283i
$627$		0			0
$628$	−148.526	+	842.334i	−0.236507	+	1.34130i
$629$	43.8751	+	25.3313i	0.0697537	+	0.0402723i
$630$		0			0
$631$	107.380	+	185.988i	0.170175	+	0.294751i	0.938481	−	0.345332i	$-0.112234\pi$
$631$	107.380	+	185.988i	0.170175	+	0.294751i	−0.768306	+	0.640082i	$0.778900\pi$
$632$	−44.5734	−	122.464i	−0.0705276	−	0.193773i
$633$		0			0
$634$	−182.322	+	152.987i	−0.287575	+	0.241304i
$635$	−815.326	−	971.668i	−1.28398	−	1.53019i
$636$		0			0
$637$	928.634	−	337.995i	1.45782	−	0.530605i
$638$	−21.7535	+	12.5594i	−0.0340964	+	0.0196855i
$639$		0			0
$640$	456.222	−	790.199i	0.712846	−	1.23469i
$641$	979.635	+	172.736i	1.52829	+	0.269479i	0.873685	−	0.486491i	$-0.161724\pi$
$641$	979.635	+	172.736i	1.52829	+	0.269479i	0.654606	+	0.755970i	$0.272835\pi$
$642$		0			0
$643$	797.989	+	290.444i	1.24104	+	0.451702i	0.877365	−	0.479824i	$-0.159300\pi$
$643$	797.989	+	290.444i	1.24104	+	0.451702i	0.363675	+	0.931526i	$0.381522\pi$
$644$	8.61980	−	1.51990i	0.0133848	−	0.00236010i
$645$		0			0
$646$	122.933	+	103.153i	0.190299	+	0.159680i
$647$		−	350.755i		−	0.542125i	−0.962562	−	0.271063i	$-0.912625\pi$
$647$		−	350.755i		−	0.542125i	0.962562	−	0.271063i	$-0.0873751\pi$
$648$		0			0
$649$	−100.723			−0.155198
$650$	−264.355	+	315.046i	−0.406700	+	0.484687i
$651$		0			0
$652$	41.8793	+	237.509i	0.0642321	+	0.364278i
$653$	−96.2871	+	264.547i	−0.147453	+	0.405125i	−0.991327	−	0.131417i	$-0.958047\pi$
$653$	−96.2871	+	264.547i	−0.147453	+	0.405125i	0.843874	+	0.536542i	$0.180270\pi$
$654$		0			0
$655$	48.8681	−	277.145i	0.0746078	−	0.423122i
$656$	−50.2125	−	28.9902i	−0.0765434	−	0.0441924i
$657$		0			0
$658$	17.7824	+	30.8000i	0.0270249	+	0.0468085i
$659$	−34.4733	−	94.7146i	−0.0523115	−	0.143725i	0.910785	−	0.412881i	$-0.135477\pi$
$659$	−34.4733	−	94.7146i	−0.0523115	−	0.143725i	−0.963097	+	0.269156i	$0.913255\pi$
$660$		0			0
$661$	−555.119	+	465.801i	−0.839818	+	0.704691i	−0.957523	−	0.288358i	$-0.906891\pi$
$661$	−555.119	+	465.801i	−0.839818	+	0.704691i	0.117705	+	0.993049i	$0.462446\pi$
$662$	122.558	+	146.059i	0.185133	+	0.220633i
$663$		0			0
$664$	496.594	−	180.745i	0.747882	−	0.272207i
$665$	−173.551	+	100.199i	−0.260978	+	0.150676i
$666$		0			0
$667$	35.9835	−	62.3252i	0.0539483	−	0.0934412i
$668$	−604.202	−	106.537i	−0.904494	−	0.159487i
$669$		0			0
$670$	−81.8810	−	29.8022i	−0.122210	−	0.0444810i
$671$	23.7039	−	4.17964i	0.0353263	−	0.00622898i
$672$		0			0
$673$	313.428	+	262.997i	0.465717	+	0.390783i	0.845229	−	0.534404i	$-0.179464\pi$
$673$	313.428	+	262.997i	0.465717	+	0.390783i	−0.379512	+	0.925187i	$0.623908\pi$
$674$			327.399i			0.485755i
$675$		0			0
$676$	984.833			1.45685
$677$	217.703	−	259.448i	0.321570	−	0.383232i	−0.580907	−	0.813970i	$-0.697302\pi$
$677$	217.703	−	259.448i	0.321570	−	0.383232i	0.902477	+	0.430738i	$0.141747\pi$
$678$		0			0
$679$	−2.23184	−	12.6574i	−0.00328695	−	0.0186412i
$680$	−164.499	+	451.956i	−0.241910	+	0.664642i
$681$		0			0
$682$	−1.84947	+	10.4889i	−0.00271183	+	0.0153796i
$683$	269.651	+	155.683i	0.394804	+	0.227940i	0.684239	−	0.729257i	$-0.260134\pi$
$683$	269.651	+	155.683i	0.394804	+	0.227940i	−0.289436	+	0.957197i	$0.593468\pi$
$684$		0			0
$685$	−447.024	−	774.268i	−0.652590	−	1.13032i
$686$	−25.5468	−	70.1893i	−0.0372403	−	0.102317i
$687$		0			0
$688$	−158.620	+	133.098i	−0.230552	+	0.193456i
$689$	689.901	+	822.192i	1.00131	+	1.19331i
$690$		0			0
$691$	−777.773	+	283.086i	−1.12558	+	0.409676i	−0.836684	−	0.547686i	$-0.815509\pi$
$691$	−777.773	+	283.086i	−1.12558	+	0.409676i	−0.288891	+	0.957362i	$0.593287\pi$
$692$	842.537	−	486.439i	1.21754	−	0.702947i
$693$		0			0
$694$	−70.9733	+	122.929i	−0.102267	+	0.177132i
$695$	743.861	+	131.163i	1.07030	+	0.188723i
$696$		0			0
$697$	63.6215	+	23.1563i	0.0912791	+	0.0332229i
$698$	−211.634	+	37.3168i	−0.303201	+	0.0534625i
$699$		0			0
$700$	−126.343	−	106.014i	−0.180490	−	0.151449i
$701$			215.718i			0.307729i	0.988092	+	0.153864i	$0.0491718\pi$
$701$			215.718i			0.307729i	−0.988092	+	0.153864i	$0.950828\pi$
$702$		0			0
$703$	−70.5529			−0.100360
$704$	−23.3141	+	27.7847i	−0.0331166	+	0.0394669i
$705$		0			0
$706$	9.49079	+	53.8250i	0.0134430	+	0.0762393i
$707$	−1.75939	+	4.83389i	−0.00248853	+	0.00683718i
$708$		0			0
$709$	179.173	−	1016.14i	0.252712	−	1.43320i	−0.549167	−	0.835713i	$-0.685055\pi$
$709$	179.173	−	1016.14i	0.252712	−	1.43320i	0.801878	−	0.597487i	$-0.203834\pi$
$710$	−334.472	−	193.107i	−0.471087	−	0.271982i
$711$		0			0
$712$	−269.981	−	467.620i	−0.379186	−	0.656770i
$713$	−10.4367	−	28.6747i	−0.0146378	−	0.0402169i
$714$		0			0
$715$	132.101	−	110.846i	0.184757	−	0.155030i
$716$	580.322	+	691.601i	0.810506	+	0.965924i
$717$		0			0
$718$	−56.5267	+	20.5740i	−0.0787280	+	0.0286546i
$719$	−539.953	+	311.742i	−0.750978	+	0.433578i	−0.826047	−	0.563601i	$-0.809416\pi$
$719$	−539.953	+	311.742i	−0.750978	+	0.433578i	0.0750689	+	0.997178i	$0.476082\pi$
$720$		0			0
$721$	−81.6768	+	141.468i	−0.113283	+	0.196211i
$722$	−13.1979	−	2.32714i	−0.0182796	−	0.00322319i
$723$		0			0
$724$	4.61527	+	1.67982i	0.00637469	+	0.00232020i
$725$	−1335.47	+	235.480i	−1.84203	+	0.324800i
$726$		0			0
$727$	−575.569	−	482.959i	−0.791704	−	0.664318i	0.154463	−	0.987999i	$-0.450635\pi$
$727$	−575.569	−	482.959i	−0.791704	−	0.664318i	−0.946167	+	0.323680i	$0.895080\pi$
$728$		−	124.466i		−	0.170970i
$729$		0			0
$730$	161.276			0.220926
$731$	155.420	−	185.223i	0.212614	−	0.253383i
$732$		0			0
$733$	130.291	+	738.919i	0.177751	+	1.00807i	0.934921	+	0.354857i	$0.115470\pi$
$733$	130.291	+	738.919i	0.177751	+	1.00807i	−0.757170	+	0.653218i	$0.773419\pi$
$734$	18.0478	−	49.5860i	0.0245883	−	0.0675558i
$735$		0			0
$736$	−7.73218	+	43.8514i	−0.0105057	+	0.0595807i
$737$	18.1815	+	10.4971i	0.0246696	+	0.0142430i
$738$		0			0
$739$	676.597	+	1171.90i	0.915557	+	1.58579i	0.806083	+	0.591802i	$0.201583\pi$
$739$	676.597	+	1171.90i	0.915557	+	1.58579i	0.109474	+	0.993990i	$0.465083\pi$
$740$	−34.5620	−	94.9583i	−0.0467054	−	0.128322i
$741$		0			0
$742$	30.4974	−	25.5904i	0.0411017	−	0.0344884i
$743$	−545.577	−	650.194i	−0.734290	−	0.875092i	0.261646	−	0.965164i	$-0.415735\pi$
$743$	−545.577	−	650.194i	−0.734290	−	0.875092i	−0.995935	+	0.0900717i	$0.971290\pi$
$744$		0			0
$745$	−1001.03	+	364.346i	−1.34367	+	0.489056i
$746$	218.194	−	125.975i	0.292486	−	0.168867i
$747$		0			0
$748$	27.6897	−	47.9599i	0.0370183	−	0.0641175i
$749$	105.200	+	18.5497i	0.140455	+	0.0247659i
$750$		0			0
$751$	−757.303	−	275.636i	−1.00839	−	0.367025i	−0.215577	−	0.976487i	$-0.569163\pi$
$751$	−757.303	−	275.636i	−1.00839	−	0.367025i	−0.792816	+	0.609462i	$0.791386\pi$
$752$	543.715	−	95.8717i	0.723026	−	0.127489i
$753$		0			0
$754$	−374.652	−	314.370i	−0.496886	−	0.416936i
$755$		−	999.749i		−	1.32417i
$756$		0			0
$757$	−171.631			−0.226725			−0.113363	−	0.993554i	$-0.536162\pi$
$757$	−171.631			−0.226725			−0.113363	+	0.993554i	$0.536162\pi$
$758$	124.825	−	148.761i	0.164677	−	0.196254i
$759$		0			0
$760$	−116.308	−	659.613i	−0.153036	−	0.867912i
$761$	462.136	−	1269.71i	0.607275	−	1.66847i	−0.128880	−	0.991660i	$-0.541138\pi$
$761$	462.136	−	1269.71i	0.607275	−	1.66847i	0.736154	−	0.676814i	$-0.236640\pi$
$762$		0			0
$763$	−22.4248	+	127.178i	−0.0293904	+	0.166681i
$764$	−147.255	−	85.0178i	−0.192742	−	0.111280i
$765$		0			0
$766$	173.100	+	299.818i	0.225979	+	0.391407i
$767$	−670.746	−	1842.86i	−0.874506	−	2.40268i
$768$		0			0
$769$	770.979	−	646.928i	1.00257	−	0.841259i	0.0152349	−	0.999884i	$-0.495150\pi$
$769$	770.979	−	646.928i	1.00257	−	0.841259i	0.987339	+	0.158625i	$0.0507060\pi$
$770$	−4.11159	−	4.90001i	−0.00533973	−	0.00636365i
$771$		0			0
$772$	490.123	−	178.390i	0.634874	−	0.231075i
$773$	−24.6722	+	14.2445i	−0.0319175	+	0.0184276i	−0.515874	−	0.856665i	$-0.672533\pi$
$773$	−24.6722	+	14.2445i	−0.0319175	+	0.0184276i	0.483956	+	0.875092i	$0.339199\pi$
$774$		0			0
$775$	−287.497	+	497.960i	−0.370964	+	0.642528i
$776$	42.3045	+	7.45943i	0.0545161	+	0.00961266i
$777$		0			0
$778$	−169.579	−	61.7219i	−0.217968	−	0.0793340i
$779$	−92.8532	+	16.3725i	−0.119195	+	0.0210174i
$780$		0			0
$781$	71.2827	+	59.8133i	0.0912710	+	0.0765855i
$782$		−	14.6756i		−	0.0187668i
$783$		0			0
$784$	−569.048			−0.725827
$785$	−1151.15	+	1371.89i	−1.46644	+	1.74763i
$786$		0			0
$787$	34.7237	+	196.928i	0.0441216	+	0.250226i	0.998889	−	0.0471280i	$-0.0150069\pi$
$787$	34.7237	+	196.928i	0.0441216	+	0.250226i	−0.954767	+	0.297354i	$0.903896\pi$
$788$	−67.7357	+	186.102i	−0.0859590	+	0.236170i
$789$		0			0
$790$	22.6445	−	128.423i	0.0286639	−	0.162561i
$791$	74.6706	+	43.1111i	0.0944002	+	0.0545020i
$792$		0			0
$793$	234.323	+	405.859i	0.295489	+	0.511802i
$794$	27.4797	+	75.4997i	0.0346091	+	0.0950878i
$795$		0			0
$796$	922.411	−	773.995i	1.15881	−	0.972356i
$797$	675.871	+	805.471i	0.848018	+	1.01063i	0.999753	+	0.0222076i	$0.00706948\pi$
$797$	675.871	+	805.471i	0.848018	+	1.01063i	−0.151735	+	0.988421i	$0.548486\pi$
$798$		0			0
$799$	−605.819	+	220.500i	−0.758222	+	0.275970i
$800$	726.630	−	419.520i	0.908287	−	0.524400i
$801$		0			0
$802$	−78.8807	+	136.625i	−0.0983550	+	0.170356i
$803$	−38.2669	−	6.74748i	−0.0476549	−	0.00840284i
$804$		0			0
$805$	17.2212	+	6.26801i	0.0213928	+	0.00778635i
$806$	−204.223	+	36.0100i	−0.253378	+	0.0446774i
$807$		0			0
$808$	−13.1706	−	11.0515i	−0.0163003	−	0.0136776i
$809$			482.349i			0.596229i	0.954530	+	0.298114i	$0.0963577\pi$
$809$			482.349i			0.596229i	−0.954530	+	0.298114i	$0.903642\pi$
$810$		0			0
$811$	−1202.48			−1.48272			−0.741358	−	0.671110i	$-0.765818\pi$
$811$	−1202.48			−1.48272			−0.741358	+	0.671110i	$0.765818\pi$
$812$	126.072	−	150.246i	0.155261	−	0.185032i
$813$		0			0
$814$	−0.391050	−	2.21775i	−0.000480405	−	0.00272451i
$815$	−172.708	+	474.512i	−0.211912	+	0.582224i
$816$		0			0
$817$	−58.4707	+	331.604i	−0.0715675	+	0.405880i
$818$	146.148	+	84.3786i	0.178665	+	0.103152i
$819$		0			0
$820$	−67.5224	−	116.952i	−0.0823444	−	0.142625i
$821$	−443.863	−	1219.50i	−0.540637	−	1.48539i	−0.846016	−	0.533157i	$-0.821006\pi$
$821$	−443.863	−	1219.50i	−0.540637	−	1.48539i	0.305380	−	0.952231i	$-0.401217\pi$
$822$		0			0
$823$	810.125	−	679.776i	0.984356	−	0.825973i	−0.000384609	−	1.00000i	$-0.500122\pi$
$823$	810.125	−	679.776i	0.984356	−	0.825973i	0.984741	+	0.174027i	$0.0556780\pi$
$824$	−350.944	−	418.239i	−0.425903	−	0.507572i
$825$		0			0
$826$	−68.3568	+	24.8799i	−0.0827565	+	0.0301209i
$827$	767.759	−	443.266i	0.928367	−	0.535993i	0.0420722	−	0.999115i	$-0.486604\pi$
$827$	767.759	−	443.266i	0.928367	−	0.535993i	0.886295	+	0.463122i	$0.153271\pi$
$828$		0			0
$829$	−406.625	+	704.295i	−0.490500	+	0.849572i	−0.999940	−	0.0109347i	$-0.996519\pi$
$829$	−406.625	+	704.295i	−0.490500	+	0.849572i	0.509440	+	0.860506i	$0.329853\pi$
$830$	520.757	+	91.8235i	0.627418	+	0.110631i
$831$		0			0
$832$	−663.610	−	241.534i	−0.797608	−	0.290306i
$833$	654.391	−	115.387i	0.785584	−	0.138520i
$834$		0			0
$835$	−984.050	−	825.716i	−1.17850	−	0.988881i
$836$			77.1214i			0.0922505i
$837$		0			0
$838$	195.119			0.232839
$839$	−960.723	+	1144.94i	−1.14508	+	1.36465i	−0.224325	+	0.974514i	$0.572018\pi$
$839$	−960.723	+	1144.94i	−1.14508	+	1.36465i	−0.920756	+	0.390140i	$0.872427\pi$
$840$		0			0
$841$	−133.994	−	759.917i	−0.159327	−	0.903588i
$842$	−120.043	+	329.816i	−0.142569	+	0.391706i
$843$		0			0
$844$	60.2525	−	341.709i	0.0713892	−	0.404868i
$845$	1785.77	+	1031.02i	2.11334	+	1.22014i
$846$		0			0
$847$	−79.9335	−	138.449i	−0.0943725	−	0.163458i
$848$	−211.379	−	580.758i	−0.249267	−	0.684856i
$849$		0			0
$850$	−211.837	+	177.752i	−0.249220	+	0.209120i
$851$	4.14729	+	4.94255i	0.00487344	+	0.00580793i
$852$		0			0
$853$	786.440	−	286.241i	0.921969	−	0.335569i	0.162947	−	0.986635i	$-0.447900\pi$
$853$	786.440	−	286.241i	0.921969	−	0.335569i	0.759022	+	0.651065i	$0.225678\pi$
$854$	15.0545	−	8.69169i	0.0176282	−	0.0101776i
$855$		0			0
$856$	−178.517	+	309.200i	−0.208547	+	0.361215i
$857$	−781.650	−	137.826i	−0.912077	−	0.160824i	−0.302131	−	0.953266i	$-0.597698\pi$
$857$	−781.650	−	137.826i	−0.912077	−	0.160824i	−0.609947	+	0.792443i	$0.708809\pi$
$858$		0			0
$859$	925.160	+	336.731i	1.07702	+	0.392003i	0.818798	−	0.574082i	$-0.194641\pi$
$859$	925.160	+	336.731i	1.07702	+	0.392003i	0.258222	+	0.966086i	$0.416863\pi$
$860$	−474.954	+	83.7472i	−0.552272	+	0.0973805i
$861$		0			0
$862$	344.840	+	289.355i	0.400046	+	0.335679i
$863$			217.563i			0.252101i	0.992024	+	0.126050i	$0.0402301\pi$
$863$			217.563i			0.252101i	−0.992024	+	0.126050i	$0.959770\pi$
$864$		0			0
$865$	2037.00			2.35491
$866$	26.8055	−	31.9455i	0.0309532	−	0.0368886i
$867$		0			0
$868$	−14.4411	−	81.8994i	−0.0166372	−	0.0943541i
$869$	−10.7460	+	29.5243i	−0.0123659	+	0.0339750i
$870$		0			0
$871$	−70.9814	+	402.555i	−0.0814941	+	0.462176i
$872$	−373.794	−	215.810i	−0.428663	−	0.247489i
$873$		0			0
$874$	10.2187	+	17.6992i	0.0116918	+	0.0202508i
$875$	−30.6694	−	84.2634i	−0.0350507	−	0.0963010i
$876$		0			0
$877$	−237.821	+	199.556i	−0.271176	+	0.227544i	−0.768227	−	0.640178i	$-0.778861\pi$
$877$	−237.821	+	199.556i	−0.271176	+	0.227544i	0.497051	+	0.867721i	$0.334416\pi$
$878$	256.199	+	305.326i	0.291798	+	0.347752i
$879$		0			0
$880$	−93.3102	+	33.9621i	−0.106034	+	0.0385933i
$881$	−1349.01	+	778.850i	−1.53122	+	0.884053i	−0.531918	+	0.846796i	$0.678529\pi$
$881$	−1349.01	+	778.850i	−1.53122	+	0.884053i	−0.999306	+	0.0372567i	$0.988138\pi$
$882$		0			0
$883$	412.908	−	715.177i	0.467619	−	0.809940i	−0.531696	−	0.846935i	$-0.678445\pi$
$883$	412.908	−	715.177i	0.467619	−	0.809940i	0.999315	+	0.0369949i	$0.0117785\pi$
$884$	1061.88	+	187.238i	1.20122	+	0.211808i
$885$		0			0
$886$	248.990	+	90.6250i	0.281027	+	0.102286i
$887$	−402.913	+	71.0445i	−0.454243	+	0.0800953i	−0.396089	−	0.918212i	$-0.629633\pi$
$887$	−402.913	+	71.0445i	−0.454243	+	0.0800953i	−0.0581543	+	0.998308i	$0.518522\pi$
$888$		0			0
$889$	169.077	+	141.872i	0.190188	+	0.159587i
$890$		−	540.295i		−	0.607073i
$891$		0			0
$892$	−297.542			−0.333568
$893$	577.101	−	687.762i	0.646250	−	0.770171i
$894$		0			0
$895$	328.250	+	1861.60i	0.366760	+	2.08000i
$896$	−54.3031	+	149.196i	−0.0606061	+	0.166514i
$897$		0			0
$898$	53.2890	−	302.217i	0.0593419	−	0.336545i
$899$	−592.171	−	341.890i	−0.658700	−	0.380301i
$900$		0			0
$901$	360.842	+	624.996i	0.400490	+	0.693669i
$902$	−1.02931	−	2.82799i	−0.00114114	−	0.00313525i
$903$		0			0
$904$	−220.757	+	185.237i	−0.244201	+	0.204909i
$905$	6.61015	+	7.87768i	0.00730404	+	0.00870461i
$906$		0			0
$907$	−370.613	+	134.892i	−0.408614	+	0.148723i	−0.538145	−	0.842852i	$-0.680875\pi$
$907$	−370.613	+	134.892i	−0.408614	+	0.148723i	0.129532	+	0.991575i	$0.458653\pi$
$908$	532.041	−	307.174i	0.585948	−	0.338297i
$909$		0			0
$910$	62.2714	−	107.857i	0.0684301	−	0.118524i
$911$	217.128	+	38.2855i	0.238340	+	0.0420258i	0.291542	−	0.956558i	$-0.405832\pi$
$911$	217.128	+	38.2855i	0.238340	+	0.0420258i	−0.0532022	+	0.998584i	$0.516943\pi$
$912$		0			0
$913$	−119.721	−	43.5749i	−0.131129	−	0.0477272i
$914$	−84.2931	+	14.8631i	−0.0922244	+	0.0162617i
$915$		0			0
$916$	205.935	+	172.800i	0.224820	+	0.188647i
$917$			48.9691i			0.0534014i
$918$		0			0
$919$	−873.180			−0.950142			−0.475071	−	0.879948i	$-0.657578\pi$
$919$	−873.180			−0.950142			−0.475071	+	0.879948i	$0.657578\pi$
$920$	−39.3720	+	46.9218i	−0.0427957	+	0.0510019i
$921$		0			0
$922$	−36.1755	−	205.161i	−0.0392359	−	0.222518i
$923$	−619.665	+	1702.52i	−0.671360	+	1.84455i
$924$		0			0
$925$	21.1115	−	119.729i	0.0228232	−	0.129437i
$926$	206.523	+	119.236i	0.223027	+	0.128765i
$927$		0			0
$928$	498.891	+	864.105i	0.537598	+	0.931147i
$929$	−13.2277	−	36.3427i	−0.0142386	−	0.0391202i	0.932370	−	0.361506i	$-0.117737\pi$
$929$	−13.2277	−	36.3427i	−0.0142386	−	0.0391202i	−0.946608	+	0.322386i	$0.895515\pi$
$930$		0			0
$931$	−708.871	+	594.813i	−0.761408	+	0.638897i
$932$	432.202	+	515.078i	0.463736	+	0.552659i
$933$		0			0
$934$	491.858	−	179.022i	0.526614	−	0.191672i
$935$	100.418	−	57.9763i	0.107399	−	0.0620067i
$936$		0			0
$937$	402.676	−	697.456i	0.429750	−	0.744350i	−0.567100	−	0.823649i	$-0.691935\pi$
$937$	402.676	−	697.456i	0.429750	−	0.744350i	0.996851	+	0.0792991i	$0.0252682\pi$
$938$	14.9319	+	2.63290i	0.0159189	+	0.00280693i
$939$		0			0
$940$	1208.38	+	439.813i	1.28551	+	0.467887i
$941$	−1320.90	+	232.910i	−1.40372	+	0.247513i	−0.823670	−	0.567070i	$-0.808077\pi$
$941$	−1320.90	+	232.910i	−1.40372	+	0.247513i	−0.580047	+	0.814583i	$0.696966\pi$
$942$		0			0
$943$	6.60514	+	5.54237i	0.00700439	+	0.00587738i
$944$			1129.27i			1.19626i
$945$		0			0
$946$	−10.7477			−0.0113612
$947$	−379.824	+	452.656i	−0.401081	+	0.477990i	−0.928349	−	0.371709i	$-0.878772\pi$
$947$	−379.824	+	452.656i	−0.401081	+	0.477990i	0.527268	+	0.849699i	$0.323216\pi$
$948$		0			0
$949$	−131.376	−	745.072i	−0.138437	−	0.785113i
$950$	131.712	−	361.877i	0.138645	−	0.380923i
$951$		0			0
$952$	14.5327	−	82.4193i	0.0152655	−	0.0865749i
$953$	314.082	+	181.335i	0.329572	+	0.190278i	0.655651	−	0.755064i	$-0.272394\pi$
$953$	314.082	+	181.335i	0.329572	+	0.190278i	−0.326079	+	0.945342i	$0.605728\pi$
$954$		0			0
$955$	−178.009	−	308.321i	−0.186397	−	0.322849i
$956$	11.0821	+	30.4477i	0.0115921	+	0.0318491i
$957$		0			0
$958$	−372.374	+	312.459i	−0.388699	+	0.326157i
$959$	99.9989	+	119.174i	0.104274	+	0.124269i
$960$		0			0
$961$	630.598	−	229.519i	0.656189	−	0.238833i
$962$	37.9724	−	21.9234i	0.0394724	−	0.0227894i
$963$		0			0
$964$	29.1339	−	50.4614i	0.0302219	−	0.0523458i
$965$	1075.48	+	189.636i	1.11449	+	0.196514i
$966$		0			0
$967$	−27.9723	−	10.1811i	−0.0289269	−	0.0105285i	0.327516	−	0.944846i	$-0.393788\pi$
$967$	−27.9723	−	10.1811i	−0.0289269	−	0.0105285i	−0.356443	+	0.934317i	$0.616011\pi$
$968$	526.202	−	92.7836i	0.543597	−	0.0958509i
$969$		0			0
$970$	32.9274	+	27.6294i	0.0339458	+	0.0284839i
$971$		−	1095.66i		−	1.12839i	−0.825643	−	0.564193i	$-0.809188\pi$
$971$		−	1095.66i		−	1.12839i	0.825643	−	0.564193i	$-0.190812\pi$
$972$		0			0
$973$	−131.434			−0.135081
$974$	−225.061	+	268.218i	−0.231069	+	0.275377i
$975$		0			0
$976$	−46.8603	−	265.758i	−0.0480126	−	0.272293i
$977$	212.328	−	583.365i	0.217326	−	0.597099i	−0.782342	−	0.622849i	$-0.785975\pi$
$977$	212.328	−	583.365i	0.217326	−	0.597099i	0.999668	+	0.0257502i	$0.00819743\pi$
$978$		0			0
$979$	−22.6049	+	128.199i	−0.0230898	+	0.130949i
$980$	−1147.83	−	662.698i	−1.17125	−	0.676222i
$981$		0			0
$982$	−124.752	−	216.076i	−0.127038	−	0.220037i
$983$	207.764	+	570.827i	0.211357	+	0.580699i	0.999390	−	0.0349345i	$-0.0111223\pi$
$983$	207.764	+	570.827i	0.211357	+	0.580699i	−0.788032	+	0.615634i	$0.788900\pi$
$984$		0			0
$985$	−317.653	+	266.542i	−0.322490	+	0.270601i
$986$	−211.382	−	251.916i	−0.214384	−	0.255492i
$987$		0			0
$988$	−1411.03	+	513.573i	−1.42817	+	0.519811i
$989$	26.6674	−	15.3964i	0.0269640	−	0.0155677i
$990$		0			0
$991$	269.816	−	467.335i	0.272266	−	0.471579i	−0.697176	−	0.716900i	$-0.745560\pi$
$991$	269.816	−	467.335i	0.272266	−	0.471579i	0.969442	+	0.245322i	$0.0788935\pi$
$992$	416.645	+	73.4658i	0.420005	+	0.0740583i
$993$		0			0
$994$	63.1511	+	22.9851i	0.0635323	+	0.0231239i
$995$	2482.87	−	437.798i	2.49535	−	0.439998i
$996$		0			0
$997$	508.600	+	426.766i	0.510130	+	0.428050i	0.861175	−	0.508309i	$-0.169729\pi$
$997$	508.600	+	426.766i	0.510130	+	0.428050i	−0.351045	+	0.936359i	$0.614174\pi$
$998$			330.950i			0.331613i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.3.f.a.35.3		30
3.2	odd	2		27.3.f.a.11.3	yes	30
9.2	odd	6		243.3.f.c.26.3		30
9.4	even	3		243.3.f.a.188.3		30
9.5	odd	6		243.3.f.d.188.3		30
9.7	even	3		243.3.f.b.26.3		30
12.11	even	2		432.3.bc.a.65.2		30
27.4	even	9		243.3.f.c.215.3		30
27.5	odd	18	inner	81.3.f.a.44.3		30
27.7	even	9		729.3.b.a.728.13		30
27.13	even	9		243.3.f.d.53.3		30
27.14	odd	18		243.3.f.a.53.3		30
27.20	odd	18		729.3.b.a.728.18		30
27.22	even	9		27.3.f.a.5.3	✓	30
27.23	odd	18		243.3.f.b.215.3		30
108.103	odd	18		432.3.bc.a.113.2		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.5.3	✓	30	27.22	even	9
27.3.f.a.11.3	yes	30	3.2	odd	2
81.3.f.a.35.3		30	1.1	even	1	trivial
81.3.f.a.44.3		30	27.5	odd	18	inner
243.3.f.a.53.3		30	27.14	odd	18
243.3.f.a.188.3		30	9.4	even	3
243.3.f.b.26.3		30	9.7	even	3
243.3.f.b.215.3		30	27.23	odd	18
243.3.f.c.26.3		30	9.2	odd	6
243.3.f.c.215.3		30	27.4	even	9
243.3.f.d.53.3		30	27.13	even	9
243.3.f.d.188.3		30	9.5	odd	6
432.3.bc.a.65.2		30	12.11	even	2
432.3.bc.a.113.2		30	108.103	odd	18
729.3.b.a.728.13		30	27.7	even	9
729.3.b.a.728.18		30	27.20	odd	18

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	81.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.374063 - 0.445791i) q^{2} +(0.635786 + 3.60572i) q^{4} +(-2.62195 + 7.20376i) q^{5} +(0.231638 - 1.31369i) q^{7} +(3.86112 + 2.22922i) q^{8} +(2.23059 + 3.86350i) q^{10} +(-0.367624 - 1.01004i) q^{11} +(16.0318 - 13.4523i) q^{13} +(-0.498982 - 0.594664i) q^{14} +(-11.3241 + 4.12163i) q^{16} +(12.1867 - 7.03599i) q^{17} +(-9.79833 + 16.9712i) q^{19} +(-27.6418 - 4.87399i) q^{20} +(-0.587780 - 0.213935i) q^{22} +(1.76488 - 0.311197i) q^{23} +(-25.8684 - 21.7062i) q^{25} -12.1788i q^{26} +4.88406 q^{28} +(25.8129 - 30.7626i) q^{29} +(-2.95677 - 16.7687i) q^{31} +(-8.49804 + 23.3482i) q^{32} +(1.42201 - 8.06462i) q^{34} +(8.85613 + 5.11309i) q^{35} +(1.80012 + 3.11791i) q^{37} +(3.90042 + 10.7163i) q^{38} +(-26.1824 + 21.9697i) q^{40} +(3.09265 + 3.68568i) q^{41} +(16.1462 - 5.87675i) q^{43} +(3.40819 - 1.96772i) q^{44} +(0.521449 - 0.903176i) q^{46} +(-45.1184 - 7.95560i) q^{47} +(44.3728 + 16.1504i) q^{49} +(-19.3528 + 3.41242i) q^{50} +(58.6979 + 49.2534i) q^{52} +51.2852i q^{53} +8.23996 q^{55} +(3.82288 - 4.55593i) q^{56} +(-4.05804 - 23.0143i) q^{58} +(32.0502 - 88.0571i) q^{59} +(-3.88855 + 22.0530i) q^{61} +(-8.58136 - 4.95445i) q^{62} +(-16.8721 - 29.2233i) q^{64} +(54.8722 + 150.760i) q^{65} +(-14.9624 + 12.5549i) q^{67} +(33.1179 + 39.4684i) q^{68} +(5.59212 - 2.03537i) q^{70} +(-74.9736 + 43.2860i) q^{71} +(18.0755 - 31.3076i) q^{73} +(2.06330 + 0.363815i) q^{74} +(-67.4231 - 24.5400i) q^{76} +(-1.41203 + 0.248979i) q^{77} +(-22.3922 - 18.7892i) q^{79} -92.3828i q^{80} +2.79989 q^{82} +(76.1905 - 90.8003i) q^{83} +(18.7326 + 106.238i) q^{85} +(3.41991 - 9.39613i) q^{86} +(0.832156 - 4.71939i) q^{88} +(-104.884 - 60.5550i) q^{89} +(-13.9585 - 24.1768i) q^{91} +(2.24418 + 6.16583i) q^{92} +(-20.4237 + 17.1375i) q^{94} +(-96.5657 - 115.083i) q^{95} +(9.05396 - 3.29537i) q^{97} +(23.7979 - 13.7397i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{2} - 6 q^{4} + 15 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 6 q^{11} - 6 q^{13} + 15 q^{14} - 18 q^{16} + 9 q^{17} - 3 q^{19} - 213 q^{20} - 42 q^{22} - 120 q^{23} - 15 q^{25} - 12 q^{28} + 168 q^{29}+ \cdots - 882 q^{98}+O(q^{100}) \) 30 * q + 6 * q^2 - 6 * q^4 + 15 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 + 6 * q^11 - 6 * q^13 + 15 * q^14 - 18 * q^16 + 9 * q^17 - 3 * q^19 - 213 * q^20 - 42 * q^22 - 120 * q^23 - 15 * q^25 - 12 * q^28 + 168 * q^29 + 39 * q^31 + 360 * q^32 + 54 * q^34 + 252 * q^35 - 3 * q^37 + 84 * q^38 - 33 * q^40 - 228 * q^41 - 96 * q^43 - 639 * q^44 - 3 * q^46 - 399 * q^47 - 78 * q^49 - 303 * q^50 - 9 * q^52 - 12 * q^55 + 393 * q^56 + 129 * q^58 + 474 * q^59 + 138 * q^61 + 900 * q^62 - 51 * q^64 + 411 * q^65 + 354 * q^67 - 99 * q^68 + 489 * q^70 - 315 * q^71 - 66 * q^73 - 321 * q^74 + 258 * q^76 - 201 * q^77 + 30 * q^79 - 12 * q^82 + 33 * q^83 - 261 * q^85 + 258 * q^86 - 642 * q^88 - 72 * q^89 + 96 * q^91 + 3 * q^92 - 861 * q^94 - 681 * q^95 - 582 * q^97 - 882 * q^98

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