LMFDB - Embedded newform 162.3.f.a.89.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,3,Mod(17,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11]))

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

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

chi := DirichletCharacter("162.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	162.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:	$4.41418028264$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			89.1
Character	$\chi$	$=$	162.89
Dual form			162.3.f.a.71.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39273 - 0.245576i) q^{2} +(1.87939 + 0.684040i) q^{4} +(-1.85971 - 2.21631i) q^{5} +(2.17427 - 0.791369i) q^{7} +(-2.44949 - 1.41421i) q^{8} +O(q^{10})$	\(q+(-1.39273 - 0.245576i) q^{2} +(1.87939 + 0.684040i) q^{4} +(-1.85971 - 2.21631i) q^{5} +(2.17427 - 0.791369i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(2.04580 + 3.54342i) q^{10} +(0.401092 - 0.478003i) q^{11} +(-4.06850 - 23.0736i) q^{13} +(-3.22251 + 0.568215i) q^{14} +(3.06418 + 2.57115i) q^{16} +(-2.71755 + 1.56898i) q^{17} +(2.04119 - 3.53544i) q^{19} +(-1.97906 - 5.43742i) q^{20} +(-0.675999 + 0.567230i) q^{22} +(15.5068 - 42.6045i) q^{23} +(2.88767 - 16.3768i) q^{25} +33.1344i q^{26} +4.62762 q^{28} +(-19.6570 - 3.46606i) q^{29} +(-42.6238 - 15.5138i) q^{31} +(-3.63616 - 4.33340i) q^{32} +(4.17011 - 1.51780i) q^{34} +(-5.79743 - 3.34715i) q^{35} +(18.7730 + 32.5159i) q^{37} +(-3.71104 + 4.42264i) q^{38} +(1.42100 + 8.05886i) q^{40} +(45.6993 - 8.05802i) q^{41} +(46.3885 + 38.9246i) q^{43} +(1.08078 - 0.623989i) q^{44} +(-32.0594 + 55.5285i) q^{46} +(-1.06082 - 2.91457i) q^{47} +(-33.4350 + 28.0553i) q^{49} +(-8.04348 + 22.0993i) q^{50} +(8.13700 - 46.1472i) q^{52} +79.9023i q^{53} -1.80532 q^{55} +(-6.44501 - 1.13643i) q^{56} +(26.5257 + 9.65457i) q^{58} +(41.9763 + 50.0254i) q^{59} +(-33.1902 + 12.0803i) q^{61} +(55.5536 + 32.0739i) q^{62} +(4.00000 + 6.92820i) q^{64} +(-43.5721 + 51.9272i) q^{65} +(-4.92896 - 27.9535i) q^{67} +(-6.18056 + 1.08980i) q^{68} +(7.25227 + 6.08537i) q^{70} +(70.7261 - 40.8337i) q^{71} +(-12.6048 + 21.8321i) q^{73} +(-18.1606 - 49.8960i) q^{74} +(6.25456 - 5.24820i) q^{76} +(0.493805 - 1.35672i) q^{77} +(11.5555 - 65.5347i) q^{79} -11.5728i q^{80} -65.6256 q^{82} +(-49.1681 - 8.66967i) q^{83} +(8.53120 + 3.10510i) q^{85} +(-55.0476 - 65.6032i) q^{86} +(-1.65847 + 0.603634i) q^{88} +(-111.133 - 64.1626i) q^{89} +(-27.1057 - 46.9485i) q^{91} +(58.2864 - 69.4631i) q^{92} +(0.761683 + 4.31972i) q^{94} +(-11.6317 + 2.05097i) q^{95} +(107.970 + 90.5977i) q^{97} +(53.4556 - 30.8626i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 18 q^{5}+O(q^{10}) $ 36 * q - 18 * q^5	$ 36 q - 18 q^{5} + 18 q^{11} + 36 q^{14} + 72 q^{20} + 36 q^{22} + 180 q^{23} + 18 q^{25} - 144 q^{29} - 90 q^{31} - 72 q^{34} - 486 q^{35} - 180 q^{38} + 90 q^{41} + 90 q^{43} + 378 q^{47} + 72 q^{49} + 72 q^{56} - 252 q^{59} - 144 q^{61} + 144 q^{64} - 18 q^{65} - 594 q^{67} + 180 q^{68} - 360 q^{70} + 648 q^{71} + 126 q^{73} + 504 q^{74} - 72 q^{76} + 342 q^{77} - 72 q^{79} - 594 q^{83} + 360 q^{85} - 540 q^{86} + 144 q^{88} - 648 q^{89} - 198 q^{91} - 396 q^{92} + 504 q^{94} - 252 q^{95} + 702 q^{97} - 648 q^{98}+O(q^{100}) $ 36 * q - 18 * q^5 + 18 * q^11 + 36 * q^14 + 72 * q^20 + 36 * q^22 + 180 * q^23 + 18 * q^25 - 144 * q^29 - 90 * q^31 - 72 * q^34 - 486 * q^35 - 180 * q^38 + 90 * q^41 + 90 * q^43 + 378 * q^47 + 72 * q^49 + 72 * q^56 - 252 * q^59 - 144 * q^61 + 144 * q^64 - 18 * q^65 - 594 * q^67 + 180 * q^68 - 360 * q^70 + 648 * q^71 + 126 * q^73 + 504 * q^74 - 72 * q^76 + 342 * q^77 - 72 * q^79 - 594 * q^83 + 360 * q^85 - 540 * q^86 + 144 * q^88 - 648 * q^89 - 198 * q^91 - 396 * q^92 + 504 * q^94 - 252 * q^95 + 702 * q^97 - 648 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	−1.39273	−	0.245576i	−0.696364	−	0.122788i
$2$	−1.39273	−	0.245576i	−0.696364	−	0.122788i
$3$		0			0
$3$		0			0
$4$	1.87939	+	0.684040i	0.469846	+	0.171010i
$5$	−1.85971	−	2.21631i	−0.371942	−	0.443263i	0.547312	−	0.836929i	$-0.315651\pi$
$5$	−1.85971	−	2.21631i	−0.371942	−	0.443263i	−0.919254	+	0.393666i	$0.871207\pi$
$6$		0			0
$7$	2.17427	−	0.791369i	0.310610	−	0.113053i	−0.182012	−	0.983296i	$-0.558261\pi$
$7$	2.17427	−	0.791369i	0.310610	−	0.113053i	0.492622	+	0.870244i	$0.336039\pi$
$8$	−2.44949	−	1.41421i	−0.306186	−	0.176777i
$9$		0			0
$10$	2.04580	+	3.54342i	0.204580	+	0.354342i
$11$	0.401092	−	0.478003i	0.0364629	−	0.0434548i	−0.747505	−	0.664256i	$-0.768748\pi$
$11$	0.401092	−	0.478003i	0.0364629	−	0.0434548i	0.783968	+	0.620802i	$0.213193\pi$
$12$		0			0
$13$	−4.06850	−	23.0736i	−0.312961	−	1.77489i	−0.583430	−	0.812163i	$-0.698290\pi$
$13$	−4.06850	−	23.0736i	−0.312961	−	1.77489i	0.270469	−	0.962729i	$-0.412821\pi$
$14$	−3.22251	+	0.568215i	−0.230179	+	0.0405868i
$15$		0			0
$16$	3.06418	+	2.57115i	0.191511	+	0.160697i
$17$	−2.71755	+	1.56898i	−0.159856	+	0.0922928i	−0.577794	−	0.816183i	$-0.696086\pi$
$17$	−2.71755	+	1.56898i	−0.159856	+	0.0922928i	0.417938	+	0.908476i	$0.362753\pi$
$18$		0			0
$19$	2.04119	−	3.53544i	0.107431	−	0.186076i	−0.807298	−	0.590144i	$-0.799071\pi$
$19$	2.04119	−	3.53544i	0.107431	−	0.186076i	0.914729	+	0.404068i	$0.132404\pi$
$20$	−1.97906	−	5.43742i	−0.0989530	−	0.271871i
$21$		0			0
$22$	−0.675999	+	0.567230i	−0.0307272	+	0.0257832i
$23$	15.5068	−	42.6045i	0.674208	−	1.85237i	0.178351	−	0.983967i	$-0.442924\pi$
$23$	15.5068	−	42.6045i	0.674208	−	1.85237i	0.495857	−	0.868404i	$-0.334854\pi$
$24$		0			0
$25$	2.88767	−	16.3768i	0.115507	−	0.655072i
$26$			33.1344i			1.27440i
$27$		0			0
$28$	4.62762			0.165272
$29$	−19.6570	−	3.46606i	−0.677828	−	0.119519i	−0.175873	−	0.984413i	$-0.556275\pi$
$29$	−19.6570	−	3.46606i	−0.677828	−	0.119519i	−0.501955	+	0.864894i	$0.667386\pi$
$30$		0			0
$31$	−42.6238	−	15.5138i	−1.37496	−	0.500445i	−0.454315	−	0.890841i	$-0.650116\pi$
$31$	−42.6238	−	15.5138i	−1.37496	−	0.500445i	−0.920647	+	0.390395i	$0.872338\pi$
$32$	−3.63616	−	4.33340i	−0.113630	−	0.135419i
$33$		0			0
$34$	4.17011	−	1.51780i	0.122650	−	0.0446411i
$35$	−5.79743	−	3.34715i	−0.165641	−	0.0956328i
$36$		0			0
$37$	18.7730	+	32.5159i	0.507379	+	0.878807i	0.999964	+	0.00854213i	$0.00271908\pi$
$37$	18.7730	+	32.5159i	0.507379	+	0.878807i	−0.492584	+	0.870265i	$0.663948\pi$
$38$	−3.71104	+	4.42264i	−0.0976588	+	0.116385i
$39$		0			0
$40$	1.42100	+	8.05886i	0.0355249	+	0.201472i
$41$	45.6993	−	8.05802i	1.11462	−	0.196537i	0.414141	−	0.910213i	$-0.364082\pi$
$41$	45.6993	−	8.05802i	1.11462	−	0.196537i	0.700477	+	0.713675i	$0.252971\pi$
$42$		0			0
$43$	46.3885	+	38.9246i	1.07880	+	0.905222i	0.995821	−	0.0913289i	$-0.0291115\pi$
$43$	46.3885	+	38.9246i	1.07880	+	0.905222i	0.0829811	+	0.996551i	$0.473556\pi$
$44$	1.08078	−	0.623989i	0.0245632	−	0.0141816i
$45$		0			0
$46$	−32.0594	+	55.5285i	−0.696943	+	1.20714i
$47$	−1.06082	−	2.91457i	−0.0225706	−	0.0620122i	0.927896	−	0.372840i	$-0.121616\pi$
$47$	−1.06082	−	2.91457i	−0.0225706	−	0.0620122i	−0.950466	+	0.310828i	$0.899394\pi$
$48$		0			0
$49$	−33.4350	+	28.0553i	−0.682347	+	0.572557i
$50$	−8.04348	+	22.0993i	−0.160870	+	0.441986i
$51$		0			0
$52$	8.13700	−	46.1472i	0.156481	−	0.887446i
$53$			79.9023i			1.50759i	0.657109	+	0.753795i	$0.271779\pi$
$53$			79.9023i			1.50759i	−0.657109	+	0.753795i	$0.728221\pi$
$54$		0			0
$55$	−1.80532			−0.0328240
$56$	−6.44501	−	1.13643i	−0.115090	−	0.0202934i
$57$		0			0
$58$	26.5257	+	9.65457i	0.457340	+	0.166458i
$59$	41.9763	+	50.0254i	0.711463	+	0.847888i	0.993772	−	0.111435i	$-0.0355448\pi$
$59$	41.9763	+	50.0254i	0.711463	+	0.847888i	−0.282309	+	0.959323i	$0.591100\pi$
$60$		0			0
$61$	−33.1902	+	12.0803i	−0.544102	+	0.198037i	−0.599424	−	0.800432i	$-0.704604\pi$
$61$	−33.1902	+	12.0803i	−0.544102	+	0.198037i	0.0553219	+	0.998469i	$0.482382\pi$
$62$	55.5536	+	32.0739i	0.896026	+	0.517321i
$63$		0			0
$64$	4.00000	+	6.92820i	0.0625000	+	0.108253i
$65$	−43.5721	+	51.9272i	−0.670340	+	0.798881i
$66$		0			0
$67$	−4.92896	−	27.9535i	−0.0735666	−	0.417217i	−0.999243	−	0.0389009i	$-0.987614\pi$
$67$	−4.92896	−	27.9535i	−0.0735666	−	0.417217i	0.925676	−	0.378316i	$-0.123497\pi$
$68$	−6.18056	+	1.08980i	−0.0908907	+	0.0160265i
$69$		0			0
$70$	7.25227	+	6.08537i	0.103604	+	0.0869339i
$71$	70.7261	−	40.8337i	0.996142	−	0.575123i	0.0890378	−	0.996028i	$-0.471621\pi$
$71$	70.7261	−	40.8337i	0.996142	−	0.575123i	0.907105	+	0.420905i	$0.138287\pi$
$72$		0			0
$73$	−12.6048	+	21.8321i	−0.172668	+	0.299070i	−0.939352	−	0.342955i	$-0.888572\pi$
$73$	−12.6048	+	21.8321i	−0.172668	+	0.299070i	0.766684	+	0.642025i	$0.221905\pi$
$74$	−18.1606	−	49.8960i	−0.245414	−	0.674270i
$75$		0			0
$76$	6.25456	−	5.24820i	0.0822968	−	0.0690552i
$77$	0.493805	−	1.35672i	0.00641306	−	0.0176197i
$78$		0			0
$79$	11.5555	−	65.5347i	0.146273	−	0.829553i	−0.820064	−	0.572272i	$-0.806062\pi$
$79$	11.5555	−	65.5347i	0.146273	−	0.829553i	0.966337	−	0.257281i	$-0.0828267\pi$
$80$		−	11.5728i		−	0.144660i
$81$		0			0
$82$	−65.6256			−0.800312
$83$	−49.1681	−	8.66967i	−0.592387	−	0.104454i	−0.130585	−	0.991437i	$-0.541686\pi$
$83$	−49.1681	−	8.66967i	−0.592387	−	0.104454i	−0.461802	+	0.886983i	$0.652797\pi$
$84$		0			0
$85$	8.53120	+	3.10510i	0.100367	+	0.0365306i
$86$	−55.0476	−	65.6032i	−0.640089	−	0.762828i
$87$		0			0
$88$	−1.65847	+	0.603634i	−0.0188463	+	0.00685947i
$89$	−111.133	−	64.1626i	−1.24868	−	0.720928i	−0.277838	−	0.960628i	$-0.589618\pi$
$89$	−111.133	−	64.1626i	−1.24868	−	0.720928i	−0.970847	+	0.239700i	$0.922951\pi$
$90$		0			0
$91$	−27.1057	−	46.9485i	−0.297865	−	0.515918i
$92$	58.2864	−	69.4631i	0.633548	−	0.755033i
$93$		0			0
$94$	0.761683	+	4.31972i	0.00810301	+	0.0459544i
$95$	−11.6317	+	2.05097i	−0.122438	+	0.0215892i
$96$		0			0
$97$	107.970	+	90.5977i	1.11309	+	0.933997i	0.998235	−	0.0593849i	$-0.0189139\pi$
$97$	107.970	+	90.5977i	1.11309	+	0.933997i	0.114859	+	0.993382i	$0.463358\pi$
$98$	53.4556	−	30.8626i	0.545465	−	0.314924i
$99$		0			0
$100$	16.6294	−	28.8030i	0.166294	−	0.288030i
$101$	13.5909	+	37.3408i	0.134564	+	0.369710i	0.988613	−	0.150482i	$-0.0480825\pi$
$101$	13.5909	+	37.3408i	0.134564	+	0.369710i	−0.854049	+	0.520192i	$0.825860\pi$
$102$		0			0
$103$	35.6457	−	29.9103i	0.346074	−	0.290391i	−0.453137	−	0.891441i	$-0.649695\pi$
$103$	35.6457	−	29.9103i	0.346074	−	0.290391i	0.799211	+	0.601050i	$0.205251\pi$
$104$	−22.6653	+	62.2723i	−0.217935	+	0.598772i
$105$		0			0
$106$	19.6221	−	111.282i	0.185114	−	1.04983i
$107$		−	107.937i		−	1.00876i	−0.863482	−	0.504379i	$-0.831721\pi$
$107$		−	107.937i		−	1.00876i	0.863482	−	0.504379i	$-0.168279\pi$
$108$		0			0
$109$	61.3938			0.563246			0.281623	−	0.959525i	$-0.409127\pi$
$109$	61.3938			0.563246			0.281623	+	0.959525i	$0.409127\pi$
$110$	2.51432	+	0.443343i	0.0228575	+	0.00403039i
$111$		0			0
$112$	8.69707	+	3.16548i	0.0776525	+	0.0282632i
$113$	−26.3026	−	31.3463i	−0.232767	−	0.277401i	0.637000	−	0.770864i	$-0.280175\pi$
$113$	−26.3026	−	31.3463i	−0.232767	−	0.277401i	−0.869767	+	0.493463i	$0.835731\pi$
$114$		0			0
$115$	−123.263	+	44.8641i	−1.07185	+	0.390123i
$116$	−34.5722	−	19.9603i	−0.298036	−	0.172071i
$117$		0			0
$118$	−46.1766	−	79.9801i	−0.391327	−	0.677798i
$119$	−4.66704	+	5.56196i	−0.0392188	+	0.0467392i
$120$		0			0
$121$	20.9438	+	118.778i	0.173089	+	0.981639i
$122$	49.1916	−	8.67381i	0.403210	−	0.0710968i
$123$		0			0
$124$	−69.4945	−	58.3128i	−0.560440	−	0.470265i
$125$	−104.306	+	60.2210i	−0.834447	+	0.481768i
$126$		0			0
$127$	106.842	−	185.055i	0.841272	−	1.45713i	−0.0475484	−	0.998869i	$-0.515141\pi$
$127$	106.842	−	185.055i	0.841272	−	1.45713i	0.888820	−	0.458256i	$-0.151526\pi$
$128$	−3.86952	−	10.6314i	−0.0302306	−	0.0830579i
$129$		0			0
$130$	73.4362	−	61.6203i	0.564894	−	0.474002i
$131$	5.01372	−	13.7751i	0.0382727	−	0.105153i	−0.919084	−	0.394061i	$-0.871070\pi$
$131$	5.01372	−	13.7751i	0.0382727	−	0.105153i	0.957357	+	0.288908i	$0.0932921\pi$
$132$		0			0
$133$	1.64025	−	9.30232i	0.0123327	−	0.0699423i
$134$			40.1421i			0.299568i
$135$		0			0
$136$	8.87548			0.0652609
$137$	133.156	+	23.4789i	0.971938	+	0.171379i	0.637002	−	0.770862i	$-0.280174\pi$
$137$	133.156	+	23.4789i	0.971938	+	0.171379i	0.334936	+	0.942241i	$0.391285\pi$
$138$		0			0
$139$	−70.1461	−	25.5311i	−0.504648	−	0.183677i	0.0771354	−	0.997021i	$-0.475423\pi$
$139$	−70.1461	−	25.5311i	−0.504648	−	0.183677i	−0.581783	+	0.813344i	$0.697645\pi$
$140$	−8.60602	−	10.2563i	−0.0614716	−	0.0732590i
$141$		0			0
$142$	−108.530	+	39.5017i	−0.764296	+	0.278181i
$143$	−12.6611	−	7.30989i	−0.0885391	−	0.0511181i
$144$		0			0
$145$	28.8744	+	50.0120i	0.199134	+	0.344910i
$146$	22.9164	−	27.3107i	0.156962	−	0.187060i
$147$		0			0
$148$	13.0396	+	73.9513i	0.0881055	+	0.499671i
$149$	−216.356	+	38.1494i	−1.45205	+	0.256036i	−0.843351	−	0.537363i	$-0.819420\pi$
$149$	−216.356	+	38.1494i	−1.45205	+	0.256036i	−0.608702	+	0.793399i	$0.708309\pi$
$150$		0			0
$151$	92.8259	+	77.8901i	0.614741	+	0.515829i	0.896145	−	0.443760i	$-0.146356\pi$
$151$	92.8259	+	77.8901i	0.614741	+	0.515829i	−0.281405	+	0.959589i	$0.590800\pi$
$152$	−9.99973	+	5.77335i	−0.0657877	+	0.0379825i
$153$		0			0
$154$	−1.02091	+	1.76828i	−0.00662931	+	0.0114823i
$155$	44.8844	+	123.319i	0.289577	+	0.795606i
$156$		0			0
$157$	53.3237	−	44.7439i	0.339641	−	0.284993i	−0.456973	−	0.889480i	$-0.651066\pi$
$157$	53.3237	−	44.7439i	0.339641	−	0.284993i	0.796615	+	0.604487i	$0.206622\pi$
$158$	−32.1874	+	88.4343i	−0.203718	+	0.559711i
$159$		0			0
$160$	−2.84199	+	16.1177i	−0.0177624	+	0.100736i
$161$		−	104.905i		−	0.651586i
$162$		0			0
$163$	67.8167			0.416054			0.208027	−	0.978123i	$-0.433296\pi$
$163$	67.8167			0.416054			0.208027	+	0.978123i	$0.433296\pi$
$164$	91.3987	+	16.1160i	0.557309	+	0.0982686i
$165$		0			0
$166$	66.3488	+	24.1490i	0.399692	+	0.145476i
$167$	150.446	+	179.295i	0.900875	+	1.07362i	0.996934	+	0.0782459i	$0.0249319\pi$
$167$	150.446	+	179.295i	0.900875	+	1.07362i	−0.0960587	+	0.995376i	$0.530624\pi$
$168$		0			0
$169$	−357.030	+	129.948i	−2.11260	+	0.768925i
$170$	−11.1191	−	6.41962i	−0.0654065	−	0.0377625i
$171$		0			0
$172$	60.5559	+	104.886i	0.352069	+	0.609801i
$173$	34.4431	−	41.0477i	0.199093	−	0.237270i	−0.657256	−	0.753667i	$-0.728283\pi$
$173$	34.4431	−	41.0477i	0.199093	−	0.237270i	0.856349	+	0.516398i	$0.172727\pi$
$174$		0			0
$175$	−6.68152	−	37.8928i	−0.0381801	−	0.216530i
$176$	2.45804	−	0.433418i	0.0139661	−	0.00246260i
$177$		0			0
$178$	139.021	+	116.653i	0.781018	+	0.655352i
$179$	8.59027	−	4.95959i	0.0479903	−	0.0277072i	−0.475813	−	0.879547i	$-0.657846\pi$
$179$	8.59027	−	4.95959i	0.0479903	−	0.0277072i	0.523803	+	0.851839i	$0.324513\pi$
$180$		0			0
$181$	−54.1558	+	93.8006i	−0.299203	+	0.518235i	−0.975954	−	0.217977i	$-0.930054\pi$
$181$	−54.1558	+	93.8006i	−0.299203	+	0.518235i	0.676751	+	0.736212i	$0.263388\pi$
$182$	26.2215	+	72.0430i	0.144074	+	0.395841i
$183$		0			0
$184$	−98.2356	+	82.4295i	−0.533889	+	0.447986i
$185$	37.1530	−	102.077i	0.200827	−	0.551767i
$186$		0			0
$187$	−0.340012	+	1.92830i	−0.00181824	+	0.0103118i
$188$		−	6.20324i		−	0.0329960i
$189$		0			0
$190$	16.7034			0.0879127
$191$	153.674	+	27.0970i	0.804578	+	0.141869i	0.560788	−	0.827959i	$-0.310498\pi$
$191$	153.674	+	27.0970i	0.804578	+	0.141869i	0.243790	+	0.969828i	$0.421609\pi$
$192$		0			0
$193$	247.481	+	90.0756i	1.28228	+	0.466713i	0.891187	−	0.453636i	$-0.149874\pi$
$193$	247.481	+	90.0756i	1.28228	+	0.466713i	0.391097	+	0.920350i	$0.372096\pi$
$194$	−128.124	−	152.693i	−0.660436	−	0.787076i
$195$		0			0
$196$	−82.0282	+	29.8558i	−0.418511	+	0.152326i
$197$	124.915	+	72.1196i	0.634085	+	0.366089i	0.782332	−	0.622861i	$-0.214030\pi$
$197$	124.915	+	72.1196i	0.634085	+	0.366089i	−0.148247	+	0.988950i	$0.547363\pi$
$198$		0			0
$199$	−133.137	−	230.600i	−0.669030	−	1.15879i	−0.978176	−	0.207779i	$-0.933376\pi$
$199$	−133.137	−	230.600i	−0.669030	−	1.15879i	0.309146	−	0.951015i	$-0.399957\pi$
$200$	−30.2336	+	36.0310i	−0.151168	+	0.180155i
$201$		0			0
$202$	−9.75849	−	55.3431i	−0.0483093	−	0.273976i
$203$	−45.4826	+	8.01980i	−0.224052	+	0.0395064i
$204$		0			0
$205$	−102.847	−	86.2985i	−0.501690	−	0.420968i
$206$	−56.9900	+	32.9032i	−0.276650	+	0.159724i
$207$		0			0
$208$	46.8591	−	81.1623i	0.225284	−	0.390203i
$209$	−0.871247	−	2.39373i	−0.00416864	−	0.0114533i
$210$		0			0
$211$	−156.280	+	131.134i	−0.740663	+	0.621490i	−0.933016	−	0.359836i	$-0.882833\pi$
$211$	−156.280	+	131.134i	−0.740663	+	0.621490i	0.192352	+	0.981326i	$0.438388\pi$
$212$	−54.6564	+	150.167i	−0.257813	+	0.708336i
$213$		0			0
$214$	−26.5067	+	150.327i	−0.123863	+	0.702463i
$215$		−	175.200i		−	0.814883i
$216$		0			0
$217$	−104.953			−0.483654
$218$	−85.5049	−	15.0768i	−0.392224	−	0.0691597i
$219$		0			0
$220$	−3.39289	−	1.23491i	−0.0154222	−	0.00561323i
$221$	47.2583	+	56.3202i	0.213838	+	0.254843i
$222$		0			0
$223$	16.9442	−	6.16717i	0.0759828	−	0.0276555i	−0.303749	−	0.952752i	$-0.598238\pi$
$223$	16.9442	−	6.16717i	0.0759828	−	0.0276555i	0.379732	+	0.925097i	$0.376016\pi$
$224$	−11.3353	−	6.54444i	−0.0506040	−	0.0292162i
$225$		0			0
$226$	28.9346	+	50.1161i	0.128029	+	0.221753i
$227$	69.1464	−	82.4054i	0.304610	−	0.363020i	−0.591925	−	0.805993i	$-0.701632\pi$
$227$	69.1464	−	82.4054i	0.304610	−	0.363020i	0.896535	+	0.442973i	$0.146076\pi$
$228$		0			0
$229$	−24.1988	−	137.238i	−0.105672	−	0.599294i	−0.990950	−	0.134232i	$-0.957143\pi$
$229$	−24.1988	−	137.238i	−0.105672	−	0.599294i	0.885278	−	0.465062i	$-0.153968\pi$
$230$	182.690	−	32.2131i	0.794303	−	0.140057i
$231$		0			0
$232$	43.2479	+	36.2893i	0.186413	+	0.156419i
$233$	−56.5488	+	32.6485i	−0.242699	+	0.140122i	−0.616416	−	0.787420i	$-0.711416\pi$
$233$	−56.5488	+	32.6485i	−0.242699	+	0.140122i	0.373718	+	0.927542i	$0.378083\pi$
$234$		0			0
$235$	−4.48680	+	7.77136i	−0.0190927	+	0.0330696i
$236$	44.6702	+	122.730i	0.189281	+	0.520044i
$237$		0			0
$238$	7.86580	−	6.60019i	0.0330496	−	0.0277319i
$239$	27.3384	−	75.1116i	0.114387	−	0.314274i	−0.869268	−	0.494341i	$-0.835409\pi$
$239$	27.3384	−	75.1116i	0.114387	−	0.314274i	0.983654	+	0.180067i	$0.0576315\pi$
$240$		0			0
$241$	42.1583	−	239.092i	0.174931	−	0.992082i	−0.763293	−	0.646053i	$-0.776419\pi$
$241$	42.1583	−	239.092i	0.174931	−	0.992082i	0.938224	−	0.346029i	$-0.112470\pi$
$242$		−	170.569i		−	0.704831i
$243$		0			0
$244$	−70.6406			−0.289511
$245$	124.359	+	21.9278i	0.507587	+	0.0895012i
$246$		0			0
$247$	−89.8798	−	32.7136i	−0.363886	−	0.132444i
$248$	82.4668	+	98.2801i	0.332528	+	0.396291i
$249$		0			0
$250$	160.058	−	58.2565i	0.640234	−	0.233026i
$251$	110.677	+	63.8992i	0.440943	+	0.254579i	0.703998	−	0.710202i	$-0.251397\pi$
$251$	110.677	+	63.8992i	0.440943	+	0.254579i	−0.263055	+	0.964781i	$0.584730\pi$
$252$		0			0
$253$	−14.1455	−	24.5006i	−0.0559109	−	0.0968405i
$254$	−194.246	+	231.494i	−0.764749	+	0.911392i
$255$		0			0
$256$	2.77837	+	15.7569i	0.0108530	+	0.0615505i
$257$	−305.230	+	53.8203i	−1.18767	+	0.209418i	−0.732360	−	0.680918i	$-0.761581\pi$
$257$	−305.230	+	53.8203i	−1.18767	+	0.209418i	−0.455306	+	0.890335i	$0.650470\pi$
$258$		0			0
$259$	66.5497	+	55.8418i	0.256949	+	0.215605i
$260$	−117.409	+	67.7862i	−0.451574	+	0.260716i
$261$		0			0
$262$	−10.3656	+	17.9537i	−0.0395633	+	0.0685256i
$263$	−128.767	−	353.785i	−0.489609	−	1.34519i	−0.901035	−	0.433746i	$-0.857192\pi$
$263$	−128.767	−	353.785i	−0.489609	−	1.34519i	0.411427	−	0.911443i	$-0.365031\pi$
$264$		0			0
$265$	177.089	−	148.595i	0.668259	−	0.560736i
$266$	−4.56885	+	12.5528i	−0.0171761	+	0.0471910i
$267$		0			0
$268$	9.85793	−	55.9071i	0.0367833	−	0.208609i
$269$			265.016i			0.985188i	0.870259	+	0.492594i	$0.163951\pi$
$269$			265.016i			0.985188i	−0.870259	+	0.492594i	$0.836049\pi$
$270$		0			0
$271$	32.4939			0.119904			0.0599518	−	0.998201i	$-0.480905\pi$
$271$	32.4939			0.119904			0.0599518	+	0.998201i	$0.480905\pi$
$272$	−12.3611	−	2.17960i	−0.0454453	−	0.00801324i
$273$		0			0
$274$	−179.684	−	65.3995i	−0.655780	−	0.238684i
$275$	−6.66994	−	7.94892i	−0.0242543	−	0.0289052i
$276$		0			0
$277$	439.202	−	159.857i	1.58557	−	0.577099i	0.609162	−	0.793046i	$-0.291506\pi$
$277$	439.202	−	159.857i	1.58557	−	0.577099i	0.976405	+	0.215946i	$0.0692836\pi$
$278$	91.4246	+	52.7840i	0.328866	+	0.189871i
$279$		0			0
$280$	9.46716	+	16.3976i	0.0338113	+	0.0585629i
$281$	77.3744	−	92.2112i	0.275354	−	0.328154i	−0.610590	−	0.791947i	$-0.709068\pi$
$281$	77.3744	−	92.2112i	0.275354	−	0.328154i	0.885943	+	0.463793i	$0.153512\pi$
$282$		0			0
$283$	55.5870	+	315.249i	0.196420	+	1.11396i	0.910382	+	0.413770i	$0.135788\pi$
$283$	55.5870	+	315.249i	0.196420	+	1.11396i	−0.713961	+	0.700185i	$0.753101\pi$
$284$	160.854	−	28.3628i	0.566386	−	0.0998691i
$285$		0			0
$286$	15.8383	+	13.2899i	0.0553788	+	0.0464683i
$287$	92.9857	−	53.6853i	0.323992	−	0.187057i
$288$		0			0
$289$	−139.577	+	241.754i	−0.482964	+	0.836518i
$290$	−27.9325	−	76.7440i	−0.0963191	−	0.264634i
$291$		0			0
$292$	−38.6232	+	32.4087i	−0.132271	+	0.110989i
$293$	128.007	−	351.696i	0.436883	−	1.20033i	−0.504626	−	0.863338i	$-0.668370\pi$
$293$	128.007	−	351.696i	0.436883	−	1.20033i	0.941509	−	0.336988i	$-0.109408\pi$
$294$		0			0
$295$	32.8083	−	186.065i	0.111215	−	0.630730i
$296$		−	106.196i		−	0.358771i
$297$		0			0
$298$	310.693			1.04260
$299$	−1046.13	−	184.461i	−3.49876	−	0.616926i
$300$		0			0
$301$	131.665	+	47.9220i	0.437424	+	0.159209i
$302$	−110.153	−	131.276i	−0.364746	−	0.434687i
$303$		0			0
$304$	15.3447	−	5.58501i	0.0504760	−	0.0183718i
$305$	88.4978	+	51.0942i	0.290157	+	0.167522i
$306$		0			0
$307$	164.444	+	284.826i	0.535650	+	0.927773i	0.999132	+	0.0416662i	$0.0132666\pi$
$307$	164.444	+	284.826i	0.535650	+	0.927773i	−0.463482	+	0.886106i	$0.653400\pi$
$308$	1.85610	−	2.21202i	0.00602630	−	0.00718187i
$309$		0			0
$310$	−32.2277	−	182.772i	−0.103960	−	0.589588i
$311$	115.437	−	20.3546i	0.371180	−	0.0654490i	0.0150531	−	0.999887i	$-0.495208\pi$
$311$	115.437	−	20.3546i	0.371180	−	0.0654490i	0.356127	+	0.934438i	$0.384097\pi$
$312$		0			0
$313$	−286.451	−	240.361i	−0.915178	−	0.767926i	0.0579189	−	0.998321i	$-0.481554\pi$
$313$	−286.451	−	240.361i	−0.915178	−	0.767926i	−0.973097	+	0.230396i	$0.925998\pi$
$314$	−85.2535	+	49.2211i	−0.271508	+	0.156755i
$315$		0			0
$316$	66.5457	−	115.260i	0.210588	−	0.364748i
$317$	−63.7546	−	175.164i	−0.201118	−	0.552568i	0.797600	−	0.603187i	$-0.206103\pi$
$317$	−63.7546	−	175.164i	−0.201118	−	0.552568i	−0.998718	+	0.0506189i	$0.983881\pi$
$318$		0			0
$319$	−9.54107	+	8.00590i	−0.0299093	+	0.0250969i
$320$	7.91624	−	21.7497i	0.0247383	−	0.0679678i
$321$		0			0
$322$	−25.7622	+	146.105i	−0.0800068	+	0.453741i
$323$			12.8103i			0.0396604i
$324$		0			0
$325$	−389.620			−1.19883
$326$	−94.4503	−	16.6541i	−0.289725	−	0.0510863i
$327$		0			0
$328$	−123.336	−	44.8906i	−0.376024	−	0.136861i
$329$	−4.61300	−	5.49756i	−0.0140213	−	0.0167099i
$330$		0			0
$331$	437.065	−	159.079i	1.32044	−	0.480600i	0.416839	−	0.908980i	$-0.363138\pi$
$331$	437.065	−	159.079i	1.32044	−	0.480600i	0.903598	+	0.428381i	$0.140916\pi$
$332$	−86.4755	−	49.9266i	−0.260468	−	0.150381i
$333$		0			0
$334$	−165.500	−	286.655i	−0.495510	−	0.858248i
$335$	−52.7874	+	62.9096i	−0.157574	+	0.187790i
$336$		0			0
$337$	−77.3110	−	438.452i	−0.229409	−	1.30105i	−0.854074	−	0.520152i	$-0.825875\pi$
$337$	−77.3110	−	438.452i	−0.229409	−	1.30105i	0.624664	−	0.780893i	$-0.285236\pi$
$338$	529.158	−	93.3049i	1.56556	−	0.276050i
$339$		0			0
$340$	13.9094	+	11.6714i	0.0409100	+	0.0343275i
$341$	−24.5117	+	14.1519i	−0.0718819	+	0.0415011i
$342$		0			0
$343$	−107.183	+	185.646i	−0.312487	+	0.541243i
$344$	−58.5805	−	160.949i	−0.170292	−	0.467874i
$345$		0			0
$346$	−58.0502	+	48.7099i	−0.167775	+	0.140780i
$347$	−165.942	+	455.923i	−0.478220	+	1.31390i	0.432782	+	0.901498i	$0.357532\pi$
$347$	−165.942	+	455.923i	−0.478220	+	1.31390i	−0.911003	+	0.412401i	$0.864690\pi$
$348$		0			0
$349$	41.3173	−	234.322i	0.118388	−	0.671409i	−0.866629	−	0.498952i	$-0.833718\pi$
$349$	41.3173	−	234.322i	0.118388	−	0.671409i	0.985017	−	0.172457i	$-0.0551706\pi$
$350$			54.4152i			0.155472i
$351$		0			0
$352$	−3.52981			−0.0100279
$353$	500.675	+	88.2825i	1.41834	+	0.250092i	0.829659	−	0.558271i	$-0.188535\pi$
$353$	500.675	+	88.2825i	1.41834	+	0.250092i	0.588684	+	0.808363i	$0.299646\pi$
$354$		0			0
$355$	−222.030	−	80.8124i	−0.625438	−	0.227641i
$356$	−164.972	−	196.606i	−0.463404	−	0.552263i
$357$		0			0
$358$	−13.1819	+	4.79781i	−0.0368209	+	0.0134017i
$359$	439.887	+	253.969i	1.22531	+	0.707435i	0.966046	−	0.258371i	$-0.0831857\pi$
$359$	439.887	+	253.969i	1.22531	+	0.707435i	0.259267	+	0.965806i	$0.416519\pi$
$360$		0			0
$361$	172.167	+	298.202i	0.476917	+	0.826045i
$362$	98.4595	−	117.339i	0.271987	−	0.324142i
$363$		0			0
$364$	−18.8274	−	106.776i	−0.0517238	−	0.293340i
$365$	71.8279	−	12.6652i	0.196789	−	0.0346992i
$366$		0			0
$367$	70.1493	+	58.8623i	0.191143	+	0.160388i	0.733337	−	0.679866i	$-0.237962\pi$
$367$	70.1493	+	58.8623i	0.191143	+	0.160388i	−0.542194	+	0.840253i	$0.682406\pi$
$368$	157.058	−	90.6776i	0.426789	−	0.246407i
$369$		0			0
$370$	−76.8116	+	133.042i	−0.207599	+	0.359572i
$371$	63.2322	+	173.729i	0.170437	+	0.468273i
$372$		0			0
$373$	−175.435	+	147.207i	−0.470335	+	0.394658i	−0.846917	−	0.531725i	$-0.821544\pi$
$373$	−175.435	+	147.207i	−0.470335	+	0.394658i	0.376582	+	0.926383i	$0.377099\pi$
$374$	0.947088	−	2.60210i	0.00253232	−	0.00695749i
$375$		0			0
$376$	−1.52337	+	8.63943i	−0.00405150	+	0.0229772i
$377$			467.660i			1.24048i
$378$		0			0
$379$	−143.466			−0.378539			−0.189269	−	0.981925i	$-0.560612\pi$
$379$	−143.466			−0.378539			−0.189269	+	0.981925i	$0.560612\pi$
$380$	−23.2633	−	4.10195i	−0.0612192	−	0.0107946i
$381$		0			0
$382$	−207.372	−	75.4774i	−0.542860	−	0.197585i
$383$	101.565	+	121.040i	0.265183	+	0.316032i	0.882161	−	0.470948i	$-0.156088\pi$
$383$	101.565	+	121.040i	0.265183	+	0.316032i	−0.616979	+	0.786980i	$0.711643\pi$
$384$		0			0
$385$	−3.92525	+	1.42867i	−0.0101955	+	0.00371084i
$386$	−322.553	−	186.226i	−0.835630	−	0.482451i
$387$		0			0
$388$	140.945	+	244.124i	0.363260	+	0.629185i
$389$	−141.000	+	168.037i	−0.362468	+	0.431972i	−0.916199	−	0.400723i	$-0.868759\pi$
$389$	−141.000	+	168.037i	−0.362468	+	0.431972i	0.553732	+	0.832695i	$0.313203\pi$
$390$		0			0
$391$	24.7051	+	140.110i	0.0631844	+	0.358337i
$392$	121.575	−	21.4369i	0.310140	−	0.0546860i
$393$		0			0
$394$	−156.262	−	131.119i	−0.396603	−	0.332789i
$395$	−166.735	+	96.2647i	−0.422115	+	0.243708i
$396$		0			0
$397$	−39.9845	+	69.2553i	−0.100717	+	0.174447i	−0.911980	−	0.410234i	$-0.865447\pi$
$397$	−39.9845	+	69.2553i	−0.100717	+	0.174447i	0.811263	+	0.584681i	$0.198780\pi$
$398$	128.794	+	353.858i	0.323603	+	0.889091i
$399$		0			0
$400$	50.9555	−	42.7568i	0.127389	−	0.106892i
$401$	204.847	−	562.811i	0.510839	−	1.40352i	−0.369525	−	0.929221i	$-0.620479\pi$
$401$	204.847	−	562.811i	0.510839	−	1.40352i	0.880364	−	0.474299i	$-0.157298\pi$
$402$		0			0
$403$	−184.544	+	1046.60i	−0.457927	+	2.59703i
$404$			79.4744i			0.196719i
$405$		0			0
$406$	65.3143			0.160873
$407$	23.0724	+	4.06829i	0.0566890	+	0.00999579i
$408$		0			0
$409$	88.1001	+	32.0658i	0.215404	+	0.0784005i	0.447468	−	0.894300i	$-0.352326\pi$
$409$	88.1001	+	32.0658i	0.215404	+	0.0784005i	−0.232064	+	0.972700i	$0.574548\pi$
$410$	122.045	+	145.447i	0.297670	+	0.354749i
$411$		0			0
$412$	87.4518	−	31.8298i	0.212262	−	0.0772569i
$413$	130.856	+	75.5499i	0.316843	+	0.182930i
$414$		0			0
$415$	72.2237	+	125.095i	0.174033	+	0.301434i
$416$	−85.1935	+	101.530i	−0.204792	+	0.244062i
$417$		0			0
$418$	0.625568	+	3.54777i	0.00149657	+	0.00848750i
$419$	−473.542	+	83.4983i	−1.13017	+	0.199280i	−0.707303	−	0.706911i	$-0.750088\pi$
$419$	−473.542	+	83.4983i	−1.13017	+	0.199280i	−0.422870	+	0.906191i	$0.638977\pi$
$420$		0			0
$421$	−160.713	−	134.854i	−0.381742	−	0.320319i	0.431644	−	0.902044i	$-0.357934\pi$
$421$	−160.713	−	134.854i	−0.381742	−	0.320319i	−0.813386	+	0.581725i	$0.802378\pi$
$422$	249.859	−	144.256i	0.592083	−	0.341839i
$423$		0			0
$424$	112.999	−	195.720i	0.266507	−	0.461604i
$425$	17.8474	+	49.0354i	0.0419940	+	0.115377i
$426$		0			0
$427$	−62.6046	+	52.5315i	−0.146615	+	0.123024i
$428$	73.8333	−	202.855i	0.172508	−	0.473961i
$429$		0			0
$430$	−43.0248	+	244.006i	−0.100058	+	0.567455i
$431$			323.120i			0.749698i	0.927086	+	0.374849i	$0.122305\pi$
$431$			323.120i			0.749698i	−0.927086	+	0.374849i	$0.877695\pi$
$432$		0			0
$433$	382.089			0.882422			0.441211	−	0.897403i	$-0.354549\pi$
$433$	382.089			0.882422			0.441211	+	0.897403i	$0.354549\pi$
$434$	146.171	+	25.7739i	0.336799	+	0.0593868i
$435$		0			0
$436$	115.383	+	41.9958i	0.264639	+	0.0963207i
$437$	−118.973	−	141.787i	−0.272250	−	0.324456i
$438$		0			0
$439$	263.667	−	95.9670i	0.600609	−	0.218604i	−0.0237804	−	0.999717i	$-0.507570\pi$
$439$	263.667	−	95.9670i	0.600609	−	0.218604i	0.624389	+	0.781114i	$0.285348\pi$
$440$	4.42211	+	2.55311i	0.0100503	+	0.00580252i
$441$		0			0
$442$	−51.9871	−	90.0443i	−0.117618	−	0.203720i
$443$	58.0355	−	69.1641i	0.131006	−	0.156127i	−0.696554	−	0.717505i	$-0.745284\pi$
$443$	58.0355	−	69.1641i	0.131006	−	0.156127i	0.827559	+	0.561378i	$0.189729\pi$
$444$		0			0
$445$	64.4703	+	365.629i	0.144877	+	0.821639i
$446$	−25.1131	+	4.42812i	−0.0563075	+	0.00992853i
$447$		0			0
$448$	14.1798	+	11.8983i	0.0316514	+	0.0265587i
$449$	−327.853	+	189.286i	−0.730186	+	0.421573i	−0.818490	−	0.574521i	$-0.805188\pi$
$449$	−327.853	+	189.286i	−0.730186	+	0.421573i	0.0883044	+	0.996094i	$0.471855\pi$
$450$		0			0
$451$	14.4779	−	25.0764i	0.0321017	−	0.0556019i
$452$	−27.9907	−	76.9038i	−0.0619263	−	0.170141i
$453$		0			0
$454$	−116.539	+	97.7877i	−0.256694	+	0.215391i
$455$	−53.6439	+	147.385i	−0.117899	+	0.323924i
$456$		0			0
$457$	−69.0721	+	391.727i	−0.151142	+	0.857171i	0.811086	+	0.584927i	$0.198877\pi$
$457$	−69.0721	+	391.727i	−0.151142	+	0.857171i	−0.962228	+	0.272244i	$0.912234\pi$
$458$			197.079i			0.430302i
$459$		0			0
$460$	−262.348			−0.570321
$461$	395.858	+	69.8004i	0.858694	+	0.151411i	0.585624	−	0.810583i	$-0.300850\pi$
$461$	395.858	+	69.8004i	0.858694	+	0.151411i	0.273070	+	0.961994i	$0.411961\pi$
$462$		0			0
$463$	−179.095	−	65.1851i	−0.386814	−	0.140789i	0.141291	−	0.989968i	$-0.454875\pi$
$463$	−179.095	−	65.1851i	−0.386814	−	0.140789i	−0.528104	+	0.849180i	$0.677097\pi$
$464$	−51.3208	−	61.1618i	−0.110605	−	0.131814i
$465$		0			0
$466$	86.7748	−	31.5834i	0.186212	−	0.0677756i
$467$	−746.239	−	430.841i	−1.59794	−	0.922572i	−0.991883	−	0.127151i	$-0.959417\pi$
$467$	−746.239	−	430.841i	−1.59794	−	0.922572i	−0.606058	−	0.795420i	$-0.707250\pi$
$468$		0			0
$469$	−32.8385	−	56.8779i	−0.0700180	−	0.121275i
$470$	8.15734	−	9.72154i	0.0173561	−	0.0206841i
$471$		0			0
$472$	−32.0739	−	181.900i	−0.0679532	−	0.385382i
$473$	37.2121	−	6.56150i	0.0786726	−	0.0138721i
$474$		0			0
$475$	−52.0049	−	43.6373i	−0.109484	−	0.0918679i
$476$	−12.5758	+	7.26063i	−0.0264197	+	0.0152534i
$477$		0			0
$478$	−56.5205	+	97.8964i	−0.118244	+	0.204804i
$479$	162.154	+	445.513i	0.338525	+	0.930090i	0.985813	+	0.167845i	$0.0536808\pi$
$479$	162.154	+	445.513i	0.338525	+	0.930090i	−0.647288	+	0.762245i	$0.724097\pi$
$480$		0			0
$481$	673.880	−	565.452i	1.40100	−	1.17558i
$482$	−117.430	+	322.637i	−0.243631	+	0.669371i
$483$		0			0
$484$	−41.8876	+	237.557i	−0.0865447	+	0.490819i
$485$		−	407.781i		−	0.840786i
$486$		0			0
$487$	118.562			0.243454			0.121727	−	0.992564i	$-0.461157\pi$
$487$	118.562			0.243454			0.121727	+	0.992564i	$0.461157\pi$
$488$	98.3832	+	17.3476i	0.201605	+	0.0355484i
$489$		0			0
$490$	−167.813	−	61.0789i	−0.342475	−	0.124651i
$491$	251.435	+	299.648i	0.512087	+	0.610282i	0.958691	−	0.284450i	$-0.0918111\pi$
$491$	251.435	+	299.648i	0.512087	+	0.610282i	−0.446604	+	0.894732i	$0.647367\pi$
$492$		0			0
$493$	58.8571	−	21.4222i	0.119386	−	0.0434528i
$494$	117.145	+	67.6334i	0.237135	+	0.136910i
$495$		0			0
$496$	−90.7187	−	157.129i	−0.182901	−	0.316793i
$497$	121.463	−	144.754i	0.244392	−	0.291256i
$498$		0			0
$499$	32.0248	+	181.622i	0.0641779	+	0.363971i	0.999936	+	0.0113281i	$0.00360592\pi$
$499$	32.0248	+	181.622i	0.0641779	+	0.363971i	−0.935758	+	0.352643i	$0.885283\pi$
$500$	−237.224	+	41.8291i	−0.474449	+	0.0836581i
$501$		0			0
$502$	−138.451	−	116.174i	−0.275798	−	0.231422i
$503$	758.479	−	437.908i	1.50791	−	0.870593i	0.507953	−	0.861385i	$-0.330402\pi$
$503$	758.479	−	437.908i	1.50791	−	0.870593i	0.999958	−	0.00920825i	$-0.00293112\pi$
$504$		0			0
$505$	57.4837	−	99.5647i	0.113829	−	0.197158i
$506$	13.6840	+	37.5965i	0.0270435	+	0.0743014i
$507$		0			0
$508$	327.381	−	274.706i	0.644451	−	0.540759i
$509$	−21.7815	+	59.8443i	−0.0427928	+	0.117572i	−0.959248	−	0.282564i	$-0.908815\pi$
$509$	−21.7815	+	59.8443i	−0.0427928	+	0.117572i	0.916456	+	0.400136i	$0.131037\pi$
$510$		0			0
$511$	−10.1289	+	57.4438i	−0.0198217	+	0.112415i
$512$		−	22.6274i		−	0.0441942i
$513$		0			0
$514$	438.320			0.852762
$515$	−132.581	−	23.3776i	−0.257439	−	0.0453935i
$516$		0			0
$517$	−1.81866	−	0.661938i	−0.00351772	−	0.00128034i
$518$	−78.9722	−	94.1155i	−0.152456	−	0.181690i
$519$		0			0
$520$	180.166	−	65.5749i	0.346472	−	0.126106i
$521$	−418.613	−	241.686i	−0.803479	−	0.463889i	0.0412070	−	0.999151i	$-0.486880\pi$
$521$	−418.613	−	241.686i	−0.803479	−	0.463889i	−0.844686	+	0.535262i	$0.820213\pi$
$522$		0			0
$523$	−353.459	−	612.209i	−0.675830	−	1.17057i	−0.976226	−	0.216757i	$-0.930452\pi$
$523$	−353.459	−	612.209i	−0.675830	−	1.17057i	0.300396	−	0.953815i	$-0.402881\pi$
$524$	18.8454	−	22.4591i	0.0359646	−	0.0428609i
$525$		0			0
$526$	92.4567	+	524.348i	0.175773	+	0.996859i
$527$	140.173	−	24.7163i	0.265983	−	0.0469000i
$528$		0			0
$529$	−1169.45	−	981.284i	−2.21068	−	1.85498i
$530$	−283.128	+	163.464i	−0.534203	+	0.308422i
$531$		0			0
$532$	9.44583	−	16.3607i	0.0177553	−	0.0307531i
$533$	−371.855	−	1021.66i	−0.697665	−	1.91682i
$534$		0			0
$535$	−239.223	+	200.732i	−0.447145	+	0.375199i
$536$	−27.4588	+	75.4425i	−0.0512292	+	0.140751i
$537$		0			0
$538$	65.0814	−	369.095i	0.120969	−	0.686050i
$539$			27.2348i			0.0505284i
$540$		0			0
$541$	−64.3040			−0.118861			−0.0594307	−	0.998232i	$-0.518929\pi$
$541$	−64.3040			−0.118861			−0.0594307	+	0.998232i	$0.518929\pi$
$542$	−45.2552	−	7.97971i	−0.0834966	−	0.0147227i
$543$		0			0
$544$	16.6804	+	6.07118i	0.0306626	+	0.0111603i
$545$	−114.175	−	136.068i	−0.209495	−	0.249666i
$546$		0			0
$547$	−162.501	+	59.1454i	−0.297076	+	0.108127i	−0.486258	−	0.873815i	$-0.661639\pi$
$547$	−162.501	+	59.1454i	−0.297076	+	0.108127i	0.189182	+	0.981942i	$0.439416\pi$
$548$	234.190	+	135.210i	0.427354	+	0.246733i
$549$		0			0
$550$	7.33735	+	12.7087i	0.0133406	+	0.0231067i
$551$	−52.3777	+	62.4213i	−0.0950593	+	0.113287i
$552$		0			0
$553$	−26.7373	−	151.635i	−0.0483495	−	0.274204i
$554$	−650.946	+	114.779i	−1.17499	+	0.207183i
$555$		0			0
$556$	−114.367	−	95.9655i	−0.205696	−	0.172600i
$557$	575.226	−	332.107i	1.03272	−	0.596242i	0.114958	−	0.993370i	$-0.463327\pi$
$557$	575.226	−	332.107i	1.03272	−	0.596242i	0.917763	+	0.397128i	$0.129993\pi$
$558$		0			0
$559$	709.398	−	1228.71i	1.26905	−	2.19806i
$560$	−9.15833	−	25.1623i	−0.0163542	−	0.0449327i
$561$		0			0
$562$	−130.406	+	109.424i	−0.232040	+	0.194704i
$563$	106.367	−	292.240i	0.188929	−	0.519077i	−0.808676	−	0.588255i	$-0.799815\pi$
$563$	106.367	−	292.240i	0.188929	−	0.519077i	0.997604	+	0.0691777i	$0.0220376\pi$
$564$		0			0
$565$	−20.5579	+	116.590i	−0.0363857	+	0.206354i
$566$		−	452.707i		−	0.799837i
$567$		0			0
$568$	−230.991			−0.406673
$569$	322.708	+	56.9022i	0.567150	+	0.100004i	0.449869	−	0.893095i	$-0.351471\pi$
$569$	322.708	+	56.9022i	0.567150	+	0.100004i	0.117282	+	0.993099i	$0.462582\pi$
$570$		0			0
$571$	557.293	+	202.838i	0.975995	+	0.355233i	0.780282	−	0.625428i	$-0.215076\pi$
$571$	557.293	+	202.838i	0.975995	+	0.355233i	0.195713	+	0.980661i	$0.437298\pi$
$572$	−18.7948	−	22.3988i	−0.0328581	−	0.0391587i
$573$		0			0
$574$	−142.688	+	51.9341i	−0.248585	+	0.0904775i
$575$	−652.947	−	376.979i	−1.13556	−	0.655616i
$576$		0			0
$577$	−87.0488	−	150.773i	−0.150864	−	0.261305i	0.780681	−	0.624930i	$-0.214872\pi$
$577$	−87.0488	−	150.773i	−0.150864	−	0.261305i	−0.931546	+	0.363625i	$0.881539\pi$
$578$	253.761	−	302.421i	0.439033	−	0.523219i
$579$		0			0
$580$	20.0560	+	113.743i	0.0345793	+	0.196109i
$581$	−113.766	+	20.0599i	−0.195810	+	0.0345266i
$582$		0			0
$583$	38.1936	+	32.0482i	0.0655121	+	0.0549712i
$584$	61.7505	−	35.6516i	0.105737	−	0.0610473i
$585$		0			0
$586$	−264.647	+	458.381i	−0.451615	+	0.782220i
$587$	214.475	+	589.265i	0.365375	+	1.00386i	0.977099	+	0.212787i	$0.0682541\pi$
$587$	214.475	+	589.265i	0.365375	+	1.00386i	−0.611724	+	0.791071i	$0.709524\pi$
$588$		0			0
$589$	−141.851	+	119.027i	−0.240834	+	0.202084i
$590$	−91.3862	+	251.082i	−0.154892	+	0.425562i
$591$		0			0
$592$	−26.0792	+	147.903i	−0.0440528	+	0.249836i
$593$		−	495.118i		−	0.834938i	−0.908691	−	0.417469i	$-0.862917\pi$
$593$		−	495.118i		−	0.834938i	0.908691	−	0.417469i	$-0.137083\pi$
$594$		0			0
$595$	21.0064			0.0353049
$596$	−432.712	−	76.2987i	−0.726026	−	0.128018i
$597$		0			0
$598$	1411.67	+	513.808i	2.36066	+	0.859210i
$599$	109.105	+	130.026i	0.182145	+	0.217072i	0.849389	−	0.527767i	$-0.176971\pi$
$599$	109.105	+	130.026i	0.182145	+	0.217072i	−0.667244	+	0.744839i	$0.732526\pi$
$600$		0			0
$601$	317.677	−	115.625i	0.528581	−	0.192388i	−0.0639237	−	0.997955i	$-0.520361\pi$
$601$	317.677	−	115.625i	0.528581	−	0.192388i	0.592505	+	0.805567i	$0.298139\pi$
$602$	−171.605	−	99.0760i	−0.285058	−	0.164578i
$603$		0			0
$604$	121.176	+	209.882i	0.200622	+	0.347487i
$605$	224.301	−	267.311i	0.370745	−	0.441837i
$606$		0			0
$607$	−160.570	−	910.637i	−0.264530	−	1.50023i	−0.770369	−	0.637598i	$-0.779928\pi$
$607$	−160.570	−	910.637i	−0.264530	−	1.50023i	0.505839	−	0.862628i	$-0.331183\pi$
$608$	−22.7425	+	4.01012i	−0.0374055	+	0.00659560i
$609$		0			0
$610$	−110.706	−	92.8933i	−0.181485	−	0.152284i
$611$	−62.9337	+	36.3348i	−0.103001	+	0.0594677i
$612$		0			0
$613$	56.5416	−	97.9329i	0.0922375	−	0.159760i	−0.816215	−	0.577748i	$-0.803931\pi$
$613$	56.5416	−	97.9329i	0.0922375	−	0.159760i	0.908452	+	0.417989i	$0.137265\pi$
$614$	−159.080	−	437.069i	−0.259088	−	0.711839i
$615$		0			0
$616$	−3.12826	+	2.62492i	−0.00507835	+	0.00426124i
$617$	−309.177	+	849.458i	−0.501098	+	1.37675i	0.389106	+	0.921193i	$0.372784\pi$
$617$	−309.177	+	849.458i	−0.501098	+	1.37675i	−0.890204	+	0.455562i	$0.849438\pi$
$618$		0			0
$619$	−57.2390	+	324.618i	−0.0924700	+	0.524424i	0.903023	+	0.429592i	$0.141343\pi$
$619$	−57.2390	+	324.618i	−0.0924700	+	0.524424i	−0.995493	+	0.0948320i	$0.969769\pi$
$620$			262.467i			0.423333i
$621$		0			0
$622$	−165.771			−0.266513
$623$	−292.409	−	51.5596i	−0.469357	−	0.0827602i
$624$		0			0
$625$	−63.2168	−	23.0090i	−0.101147	−	0.0368145i
$626$	339.921	+	405.103i	0.543005	+	0.647129i
$627$		0			0
$628$	130.822	−	47.6155i	0.208316	−	0.0758208i
$629$	−102.033	−	58.9090i	−0.162215	−	0.0936549i
$630$		0			0
$631$	−291.993	−	505.746i	−0.462746	−	0.801500i	0.536350	−	0.843995i	$-0.319803\pi$
$631$	−291.993	−	505.746i	−0.462746	−	0.801500i	−0.999097	+	0.0424954i	$0.986469\pi$
$632$	−120.985	+	144.185i	−0.191432	+	0.228140i
$633$		0			0
$634$	45.7767	+	259.613i	0.0722030	+	0.409484i
$635$	−608.834	+	107.354i	−0.958794	+	0.169061i
$636$		0			0
$637$	783.367	+	657.323i	1.22978	+	1.03190i
$638$	15.2542	−	8.80700i	0.0239094	−	0.0138041i
$639$		0			0
$640$	−16.3664	+	28.3474i	−0.0255725	+	0.0442928i
$641$	302.004	+	829.750i	0.471146	+	1.29446i	0.916832	+	0.399273i	$0.130737\pi$
$641$	302.004	+	829.750i	0.471146	+	1.29446i	−0.445687	+	0.895189i	$0.647040\pi$
$642$		0			0
$643$	−488.473	+	409.878i	−0.759679	+	0.637446i	−0.938043	−	0.346518i	$-0.887364\pi$
$643$	−488.473	+	409.878i	−0.759679	+	0.637446i	0.178365	+	0.983964i	$0.442919\pi$
$644$	71.7594	−	197.157i	0.111428	−	0.306145i
$645$		0			0
$646$	3.14590	−	17.8413i	0.00486981	−	0.0276181i
$647$		−	950.774i		−	1.46951i	−0.678332	−	0.734756i	$-0.737297\pi$
$647$		−	950.774i		−	1.46951i	0.678332	−	0.734756i	$-0.262703\pi$
$648$		0			0
$649$	40.7487			0.0627868
$650$	542.635	+	95.6812i	0.834823	+	0.147202i
$651$		0			0
$652$	127.454	+	46.3894i	0.195481	+	0.0711493i
$653$	−86.4460	−	103.022i	−0.132383	−	0.157768i	0.695781	−	0.718254i	$-0.255059\pi$
$653$	−86.4460	−	103.022i	−0.132383	−	0.157768i	−0.828163	+	0.560487i	$0.810614\pi$
$654$		0			0
$655$	−39.8540	+	14.5057i	−0.0608458	+	0.0221461i
$656$	160.749	+	92.8086i	0.245045	+	0.141477i
$657$		0			0
$658$	5.07459	+	8.78945i	0.00771215	+	0.0133578i
$659$	46.3613	−	55.2513i	0.0703510	−	0.0838411i	−0.729721	−	0.683745i	$-0.760350\pi$
$659$	46.3613	−	55.2513i	0.0703510	−	0.0838411i	0.800072	+	0.599904i	$0.204795\pi$
$660$		0			0
$661$	118.446	+	671.739i	0.179192	+	1.01625i	0.933194	+	0.359374i	$0.117010\pi$
$661$	118.446	+	671.739i	0.179192	+	1.01625i	−0.754002	+	0.656872i	$0.771879\pi$
$662$	−647.778	+	114.221i	−0.978517	+	0.172539i
$663$		0			0
$664$	108.176	+	90.7705i	0.162916	+	0.136703i
$665$	−23.6673	+	13.6643i	−0.0355899	+	0.0205478i
$666$		0			0
$667$	−452.487	+	783.731i	−0.678391	+	1.17501i
$668$	160.101	+	439.875i	0.239673	+	0.658496i
$669$		0			0
$670$	88.9676	−	74.6527i	0.132787	−	0.111422i
$671$	−7.53795	+	20.7103i	−0.0112339	+	0.0308649i
$672$		0			0
$673$	−57.0789	+	323.710i	−0.0848126	+	0.480996i	0.912584	+	0.408889i	$0.134084\pi$
$673$	−57.0789	+	323.710i	−0.0848126	+	0.480996i	−0.997397	+	0.0721075i	$0.977028\pi$
$674$			629.631i			0.934170i
$675$		0			0
$676$	−759.887			−1.12409
$677$	485.025	+	85.5230i	0.716433	+	0.126326i	0.519970	−	0.854185i	$-0.325943\pi$
$677$	485.025	+	85.5230i	0.716433	+	0.126326i	0.196463	+	0.980511i	$0.437054\pi$
$678$		0			0
$679$	306.452	+	111.540i	0.451329	+	0.164270i
$680$	−16.5058	−	19.6708i	−0.0242732	−	0.0289277i
$681$		0			0
$682$	37.6136	−	13.6902i	0.0551518	−	0.0200736i
$683$	725.236	+	418.715i	1.06184	+	0.613053i	0.925940	−	0.377669i	$-0.123274\pi$
$683$	725.236	+	418.715i	1.06184	+	0.613053i	0.135899	+	0.990723i	$0.456608\pi$
$684$		0			0
$685$	−195.594	−	338.778i	−0.285538	−	0.494567i
$686$	194.867	−	232.233i	0.284062	−	0.338532i
$687$		0			0
$688$	42.0617	+	238.544i	0.0611361	+	0.346720i
$689$	1843.63	−	325.082i	2.67581	−	0.471818i
$690$		0			0
$691$	−125.334	−	105.168i	−0.181381	−	0.152197i	0.547577	−	0.836756i	$-0.315551\pi$
$691$	−125.334	−	105.168i	−0.181381	−	0.152197i	−0.728958	+	0.684559i	$0.759995\pi$
$692$	92.8101	−	53.5839i	0.134119	−	0.0774334i
$693$		0			0
$694$	343.076	−	594.226i	0.494346	−	0.856233i
$695$	73.8663	+	202.946i	0.106283	+	0.292009i
$696$		0			0
$697$	−111.547	+	93.5993i	−0.160039	+	0.134289i
$698$	−115.087	+	316.200i	−0.164882	+	0.453009i
$699$		0			0
$700$	13.3630	−	75.7855i	0.0190900	−	0.108265i
$701$			730.990i			1.04278i	0.853318	+	0.521391i	$0.174587\pi$
$701$			730.990i			1.04278i	−0.853318	+	0.521391i	$0.825413\pi$
$702$		0			0
$703$	153.277			0.218033
$704$	4.91607	+	0.866836i	0.00698306	+	0.00123130i
$705$		0			0
$706$	−675.624	−	245.907i	−0.956975	−	0.348310i
$707$	59.1006	+	70.4334i	0.0835935	+	0.0996229i
$708$		0			0
$709$	−752.159	+	273.764i	−1.06087	+	0.386126i	−0.812756	−	0.582604i	$-0.802034\pi$
$709$	−752.159	+	273.764i	−1.06087	+	0.386126i	−0.248117	+	0.968730i	$0.579812\pi$
$710$	289.382	+	167.075i	0.407581	+	0.235317i
$711$		0			0
$712$	181.479	+	314.331i	0.254887	+	0.441477i
$713$	−1321.92	+	1575.40i	−1.85402	+	2.20954i
$714$		0			0
$715$	7.34494	+	41.6552i	0.0102726	+	0.0582591i
$716$	19.5370	−	3.44490i	0.0272863	−	0.00481131i
$717$		0			0
$718$	−550.275	−	461.735i	−0.766400	−	0.643086i
$719$	−103.412	+	59.7052i	−0.143828	+	0.0830392i	−0.570187	−	0.821515i	$-0.693129\pi$
$719$	−103.412	+	59.7052i	−0.143828	+	0.0830392i	0.426359	+	0.904554i	$0.359796\pi$
$720$		0			0
$721$	53.8332	−	93.2418i	0.0746646	−	0.129323i
$722$	−166.551	−	457.595i	−0.230680	−	0.633788i
$723$		0			0
$724$	−165.943	+	139.243i	−0.229203	+	0.192324i
$725$	−113.526	+	311.910i	−0.156588	+	0.430221i
$726$		0			0
$727$	−23.5632	+	133.634i	−0.0324116	+	0.183815i	−0.996716	−	0.0809827i	$-0.974194\pi$
$727$	−23.5632	+	133.634i	−0.0324116	+	0.183815i	0.964304	+	0.264798i	$0.0853052\pi$
$728$			153.333i			0.210623i
$729$		0			0
$730$	−103.147			−0.141297
$731$	−187.135	−	32.9969i	−0.255998	−	0.0451394i
$732$		0			0
$733$	−706.692	−	257.215i	−0.964110	−	0.350907i	−0.188467	−	0.982080i	$-0.560352\pi$
$733$	−706.692	−	257.215i	−0.964110	−	0.350907i	−0.775643	+	0.631172i	$0.782574\pi$
$734$	−83.2438	−	99.2061i	−0.113411	−	0.135158i
$735$		0			0
$736$	−241.008	+	87.7196i	−0.327456	+	0.119184i
$737$	−15.3389	−	8.85589i	−0.0208126	−	0.0120161i
$738$		0			0
$739$	568.765	+	985.130i	0.769642	+	1.33306i	0.937757	+	0.347291i	$0.112898\pi$
$739$	568.765	+	985.130i	0.769642	+	1.33306i	−0.168116	+	0.985767i	$0.553768\pi$
$740$	139.650	−	166.428i	0.188716	−	0.224902i
$741$		0			0
$742$	−45.4017	−	257.486i	−0.0611883	−	0.347016i
$743$	707.445	−	124.742i	0.952147	−	0.167889i	0.324064	−	0.946035i	$-0.394951\pi$
$743$	707.445	−	124.742i	0.952147	−	0.167889i	0.628083	+	0.778146i	$0.283840\pi$
$744$		0			0
$745$	486.910	+	408.566i	0.653570	+	0.548411i
$746$	280.484	−	161.937i	0.375984	−	0.217074i
$747$		0			0
$748$	−1.95805	+	3.39144i	−0.00261771	+	0.00453401i
$749$	−85.4181	−	234.684i	−0.114043	−	0.313330i
$750$		0			0
$751$	481.188	−	403.765i	0.640730	−	0.537636i	−0.263512	−	0.964656i	$-0.584881\pi$
$751$	481.188	−	403.765i	0.640730	−	0.537636i	0.904242	+	0.427020i	$0.140436\pi$
$752$	4.24327	−	11.6583i	0.00564264	−	0.0155030i
$753$		0			0
$754$	114.846	−	651.323i	0.152315	−	0.863824i
$755$		−	350.584i		−	0.464350i
$756$		0			0
$757$	393.374			0.519648			0.259824	−	0.965656i	$-0.416335\pi$
$757$	393.374			0.519648			0.259824	+	0.965656i	$0.416335\pi$
$758$	199.809	+	35.2318i	0.263601	+	0.0464799i
$759$		0			0
$760$	31.3921	+	11.4258i	0.0413054	+	0.0150339i
$761$	−519.995	−	619.706i	−0.683305	−	0.814331i	0.307224	−	0.951637i	$-0.400600\pi$
$761$	−519.995	−	619.706i	−0.683305	−	0.814331i	−0.990529	+	0.137306i	$0.956155\pi$
$762$		0			0
$763$	133.487	−	48.5852i	0.174950	−	0.0636765i
$764$	270.278	+	156.045i	0.353767	+	0.204248i
$765$		0			0
$766$	−111.728	−	193.518i	−0.145859	−	0.252635i
$767$	983.485	−	1172.07i	1.28225	−	1.52813i
$768$		0			0
$769$	15.5452	+	88.1614i	0.0202149	+	0.114644i	0.993246	−	0.116032i	$-0.0370174\pi$
$769$	15.5452	+	88.1614i	0.0202149	+	0.114644i	−0.973031	+	0.230676i	$0.925906\pi$
$770$	5.81766	−	1.02581i	0.00755540	−	0.00133222i
$771$		0			0
$772$	403.496	+	338.574i	0.522664	+	0.438567i
$773$	−1053.61	+	608.304i	−1.36302	+	0.786939i	−0.990025	−	0.140894i	$-0.955002\pi$
$773$	−1053.61	+	608.304i	−1.36302	+	0.786939i	−0.372994	+	0.927834i	$0.621669\pi$
$774$		0			0
$775$	−377.150	+	653.243i	−0.486645	+	0.842894i
$776$	−136.347	−	374.611i	−0.175705	−	0.482746i
$777$		0			0
$778$	237.640	−	199.404i	0.305450	−	0.256303i
$779$	64.7922	−	178.015i	0.0831735	−	0.228517i
$780$		0			0
$781$	8.84904	−	50.1854i	0.0113304	−	0.0642579i
$782$		−	201.202i		−	0.257291i
$783$		0			0
$784$	−174.585			−0.222685
$785$	−198.333	−	34.9715i	−0.252654	−	0.0445497i
$786$		0			0
$787$	−771.120	−	280.665i	−0.979822	−	0.356626i	−0.198051	−	0.980192i	$-0.563461\pi$
$787$	−771.120	−	280.665i	−0.979822	−	0.356626i	−0.781771	+	0.623566i	$0.785683\pi$
$788$	185.430	+	220.987i	0.235318	+	0.280441i
$789$		0			0
$790$	255.857	−	93.1245i	0.323870	−	0.117879i
$791$	−81.9955	−	47.3401i	−0.103661	−	0.0598484i
$792$		0			0
$793$	413.769	+	716.670i	0.521777	+	0.903745i
$794$	72.6950	−	86.6346i	0.0915554	−	0.109112i
$795$		0			0
$796$	−92.4760	−	524.457i	−0.116176	−	0.658866i
$797$	−942.932	+	166.264i	−1.18310	+	0.208613i	−0.730381	−	0.683040i	$-0.760658\pi$
$797$	−942.932	+	166.264i	−1.18310	+	0.208613i	−0.452720	+	0.891653i	$0.649546\pi$
$798$		0			0
$799$	7.45572	+	6.25609i	0.00933131	+	0.00782990i
$800$	−81.4673	+	47.0351i	−0.101834	+	0.0587939i
$801$		0			0
$802$	−423.508	+	733.538i	−0.528065	+	0.914636i
$803$	5.38013	+	14.7818i	0.00670004	+	0.0184082i
$804$		0			0
$805$	−232.503	+	195.093i	−0.288824	+	0.242352i
$806$	514.040	−	1412.31i	0.637767	−	1.75225i
$807$		0			0
$808$	19.5170	−	110.686i	0.0241547	−	0.136988i
$809$		−	180.576i		−	0.223209i	−0.993753	−	0.111605i	$-0.964401\pi$
$809$		−	180.576i		−	0.223209i	0.993753	−	0.111605i	$-0.0355990\pi$
$810$		0			0
$811$	518.424			0.639240			0.319620	−	0.947546i	$-0.396445\pi$
$811$	518.424			0.639240			0.319620	+	0.947546i	$0.396445\pi$
$812$	−90.9651	−	16.0396i	−0.112026	−	0.0197532i
$813$		0			0
$814$	−31.1345	−	11.3320i	−0.0382488	−	0.0139214i
$815$	−126.119	−	150.303i	−0.154748	−	0.184421i
$816$		0			0
$817$	232.303	−	84.5513i	0.284336	−	0.103490i
$818$	−114.825	−	66.2942i	−0.140373	−	0.0810443i
$819$		0			0
$820$	−134.257	−	232.539i	−0.163728	−	0.283585i
$821$	−176.439	+	210.271i	−0.214907	+	0.256116i	−0.862718	−	0.505685i	$-0.831240\pi$
$821$	−176.439	+	210.271i	−0.214907	+	0.256116i	0.647812	+	0.761801i	$0.275684\pi$
$822$		0			0
$823$	−107.367	−	608.911i	−0.130459	−	0.739867i	−0.977915	−	0.209002i	$-0.932978\pi$
$823$	−107.367	−	608.911i	−0.130459	−	0.739867i	0.847457	−	0.530865i	$-0.178133\pi$
$824$	−129.613	+	22.8543i	−0.157298	+	0.0277358i
$825$		0			0
$826$	−163.694	−	137.356i	−0.198177	−	0.166290i
$827$	−672.492	+	388.263i	−0.813170	+	0.469484i	−0.848056	−	0.529907i	$-0.822227\pi$
$827$	−672.492	+	388.263i	−0.813170	+	0.469484i	0.0348852	+	0.999391i	$0.488893\pi$
$828$		0			0
$829$	265.258	−	459.440i	0.319973	−	0.554209i	−0.660509	−	0.750818i	$-0.729660\pi$
$829$	265.258	−	459.440i	0.319973	−	0.554209i	0.980482	+	0.196609i	$0.0629928\pi$
$830$	−69.8677	−	191.960i	−0.0841779	−	0.231277i
$831$		0			0
$832$	143.585	−	120.482i	0.172578	−	0.144810i
$833$	46.8431	−	128.700i	0.0562342	−	0.154502i
$834$		0			0
$835$	117.588	−	666.872i	0.140823	−	0.798649i
$836$		−	5.09471i		−	0.00609415i
$837$		0			0
$838$	680.021			0.811481
$839$	−992.570	−	175.017i	−1.18304	−	0.208602i	−0.452685	−	0.891670i	$-0.649534\pi$
$839$	−992.570	−	175.017i	−1.18304	−	0.208602i	−0.730354	+	0.683069i	$0.760645\pi$
$840$		0			0
$841$	−415.897	−	151.374i	−0.494527	−	0.179993i
$842$	190.713	+	227.283i	0.226500	+	0.269932i
$843$		0			0
$844$	−383.411	+	139.550i	−0.454279	+	0.165344i
$845$	951.978	+	549.625i	1.12660	+	0.650444i
$846$		0			0
$847$	139.535	+	241.682i	0.164740	+	0.285338i
$848$	−205.441	+	244.835i	−0.242265	+	0.288720i
$849$		0			0
$850$	−12.8147	−	72.6759i	−0.0150762	−	0.0855011i
$851$	1676.43	−	295.600i	1.96996	−	0.347356i
$852$		0			0
$853$	668.076	+	560.582i	0.783207	+	0.657189i	0.944054	−	0.329791i	$-0.106978\pi$
$853$	668.076	+	560.582i	0.783207	+	0.657189i	−0.160847	+	0.986979i	$0.551423\pi$
$854$	100.092	−	57.7879i	0.117203	−	0.0676673i
$855$		0			0
$856$	−152.646	+	264.391i	−0.178325	+	0.308868i
$857$	−285.540	−	784.514i	−0.333185	−	0.915419i	−0.987278	−	0.159004i	$-0.949172\pi$
$857$	−285.540	−	784.514i	−0.333185	−	0.915419i	0.654093	−	0.756414i	$-0.273051\pi$
$858$		0			0
$859$	−51.8826	+	43.5347i	−0.0603989	+	0.0506807i	−0.672487	−	0.740109i	$-0.734774\pi$
$859$	−51.8826	+	43.5347i	−0.0603989	+	0.0506807i	0.612088	+	0.790789i	$0.290330\pi$
$860$	119.844	−	329.268i	0.139353	−	0.382870i
$861$		0			0
$862$	79.3504	−	450.018i	0.0920538	−	0.522063i
$863$			1191.58i			1.38074i	0.723456	+	0.690370i	$0.242552\pi$
$863$			1191.58i			1.38074i	−0.723456	+	0.690370i	$0.757448\pi$
$864$		0			0
$865$	−155.029			−0.179224
$866$	−532.146	−	93.8317i	−0.614487	−	0.108351i
$867$		0			0
$868$	−197.247	−	71.7920i	−0.227243	−	0.0827096i
$869$	−26.6910	−	31.8090i	−0.0307146	−	0.0366042i
$870$		0			0
$871$	−624.935	+	227.458i	−0.717492	+	0.261146i
$872$	−150.384	−	86.8240i	−0.172458	−	0.0995688i
$873$		0			0
$874$	130.878	+	226.688i	0.149746	+	0.259368i
$875$	−179.132	+	213.481i	−0.204722	+	0.243978i
$876$		0			0
$877$	−127.873	−	725.202i	−0.145807	−	0.826912i	−0.966716	−	0.255853i	$-0.917644\pi$
$877$	−127.873	−	725.202i	−0.145807	−	0.826912i	0.820909	−	0.571059i	$-0.193467\pi$
$878$	−390.784	+	68.9058i	−0.445084	+	0.0784804i
$879$		0			0
$880$	−5.53182	−	4.64175i	−0.00628616	−	0.00527472i
$881$	−1028.88	+	594.025i	−1.16786	+	0.674263i	−0.953174	−	0.302421i	$-0.902205\pi$
$881$	−1028.88	+	594.025i	−1.16786	+	0.674263i	−0.214683	+	0.976684i	$0.568872\pi$
$882$		0			0
$883$	509.485	−	882.454i	0.576993	−	0.999382i	−0.418829	−	0.908065i	$-0.637559\pi$
$883$	509.485	−	882.454i	0.576993	−	0.999382i	0.995822	−	0.0913164i	$-0.0291075\pi$
$884$	50.2912	+	138.174i	0.0568905	+	0.156305i
$885$		0			0
$886$	−97.8128	+	82.0747i	−0.110398	+	0.0926351i
$887$	267.381	−	734.624i	0.301445	−	0.828212i	−0.692805	−	0.721125i	$-0.743625\pi$
$887$	267.381	−	734.624i	0.301445	−	0.828212i	0.994250	−	0.107087i	$-0.0341524\pi$
$888$		0			0
$889$	85.8554	−	486.910i	0.0965752	−	0.547705i
$890$		−	525.055i		−	0.589949i
$891$		0			0
$892$	36.0632			0.0404296
$893$	−12.4696	−	2.19873i	−0.0139637	−	0.00246218i
$894$		0			0
$895$	−26.9674	−	9.81534i	−0.0301312	−	0.0109669i
$896$	−16.8267	−	20.0533i	−0.0187798	−	0.0223809i
$897$		0			0
$898$	503.095	−	183.112i	0.560239	−	0.203910i
$899$	784.086	+	452.692i	0.872175	+	0.503551i
$900$		0			0
$901$	−125.365	−	217.138i	−0.139140	−	0.240997i
$902$	−26.3219	+	31.3692i	−0.0291817	+	0.0347774i
$903$		0			0
$904$	20.0977	+	113.980i	0.0222320	+	0.126084i
$905$	308.606	−	54.4155i	0.341001	−	0.0601276i
$906$		0			0
$907$	367.436	+	308.315i	0.405111	+	0.339929i	0.822465	−	0.568815i	$-0.192598\pi$
$907$	367.436	+	308.315i	0.405111	+	0.339929i	−0.417354	+	0.908744i	$0.637042\pi$
$908$	186.321	−	107.573i	0.205200	−	0.118472i
$909$		0			0
$910$	110.906	−	192.094i	0.121874	−	0.211093i
$911$	218.659	+	600.761i	0.240021	+	0.659452i	0.999955	+	0.00945235i	$0.00300882\pi$
$911$	218.659	+	600.761i	0.240021	+	0.659452i	−0.759934	+	0.650000i	$0.774769\pi$
$912$		0			0
$913$	−23.8651	+	20.0252i	−0.0261392	+	0.0219334i
$914$	192.397	−	528.607i	0.210500	−	0.578345i
$915$		0			0
$916$	48.3977	−	274.477i	0.0528359	−	0.299647i
$917$		−	33.9184i		−	0.0369885i
$918$		0			0
$919$	−14.7768			−0.0160792			−0.00803959	−	0.999968i	$-0.502559\pi$
$919$	−14.7768			−0.0160792			−0.00803959	+	0.999968i	$0.502559\pi$
$920$	365.379	+	64.4262i	0.397151	+	0.0700285i
$921$		0			0
$922$	−534.181	−	194.426i	−0.579372	−	0.210874i
$923$	−1229.93	−	1465.77i	−1.33254	−	1.58805i
$924$		0			0
$925$	586.716	−	213.547i	0.634288	−	0.230862i
$926$	233.422	+	134.766i	0.252076	+	0.145536i
$927$		0			0
$928$	56.4561	+	97.7849i	0.0608363	+	0.105372i
$929$	−795.223	+	947.710i	−0.855999	+	1.02014i	0.143536	+	0.989645i	$0.454153\pi$
$929$	−795.223	+	947.710i	−0.855999	+	1.02014i	−0.999535	+	0.0304949i	$0.990292\pi$
$930$		0			0
$931$	30.9407	+	175.473i	0.0332338	+	0.188478i
$932$	−128.610	+	22.6774i	−0.137993	+	0.0243320i
$933$		0			0
$934$	933.504	+	783.303i	0.999469	+	0.838654i
$935$	4.90605	−	2.83251i	0.00524711	−	0.00302942i
$936$		0			0
$937$	−764.046	+	1323.37i	−0.815418	+	1.41234i	0.0936099	+	0.995609i	$0.470159\pi$
$937$	−764.046	+	1323.37i	−0.815418	+	1.41234i	−0.909028	+	0.416736i	$0.863174\pi$
$938$	31.7672	+	87.2798i	0.0338670	+	0.0930488i
$939$		0			0
$940$	−13.7483	+	11.5362i	−0.0146259	+	0.0122726i
$941$	−352.183	+	967.616i	−0.374265	+	1.02828i	0.599430	+	0.800427i	$0.295394\pi$
$941$	−352.183	+	967.616i	−0.374265	+	1.02828i	−0.973695	+	0.227857i	$0.926828\pi$
$942$		0			0
$943$	365.341	−	2071.95i	0.387424	−	2.19719i
$944$			261.214i			0.276710i
$945$		0			0
$946$	−53.4377			−0.0564881
$947$	−129.208	−	22.7828i	−0.136439	−	0.0240579i	0.105011	−	0.994471i	$-0.466512\pi$
$947$	−129.208	−	22.7828i	−0.136439	−	0.0240579i	−0.241451	+	0.970413i	$0.577623\pi$
$948$		0			0
$949$	555.027	+	202.013i	0.584855	+	0.212870i
$950$	61.7124	+	73.5460i	0.0649604	+	0.0774168i
$951$		0			0
$952$	19.2977	−	7.02378i	0.0202707	−	0.00737792i
$953$	−1223.02	−	706.112i	−1.28334	−	0.740936i	−0.305882	−	0.952069i	$-0.598951\pi$
$953$	−1223.02	−	706.112i	−1.28334	−	0.740936i	−0.977457	+	0.211133i	$0.932285\pi$
$954$		0			0
$955$	−225.734	−	390.983i	−0.236371	−	0.409407i
$956$	102.759	−	122.463i	0.107488	−	0.128099i
$957$		0			0
$958$	−116.429	−	660.300i	−0.121533	−	0.689249i
$959$	308.096	−	54.3257i	0.321268	−	0.0566483i
$960$		0			0
$961$	839.945	+	704.797i	0.874032	+	0.733400i
$962$	−1077.39	+	622.033i	−1.11995	+	0.646604i
$963$		0			0
$964$	242.780	−	420.508i	0.251847	−	0.436211i
$965$	−260.606	−	716.010i	−0.270058	−	0.741979i
$966$		0			0
$967$	445.513	−	373.830i	0.460717	−	0.386587i	−0.382678	−	0.923882i	$-0.624998\pi$
$967$	445.513	−	373.830i	0.460717	−	0.386587i	0.843395	+	0.537295i	$0.180554\pi$
$968$	116.676	−	320.565i	0.120533	−	0.331162i
$969$		0			0
$970$	−100.141	+	567.928i	−0.103238	+	0.585493i
$971$		−	208.668i		−	0.214900i	−0.994210	−	0.107450i	$-0.965731\pi$
$971$		−	208.668i		−	0.214900i	0.994210	−	0.107450i	$-0.0342686\pi$
$972$		0			0
$973$	−172.721			−0.177514
$974$	−165.125	−	29.1159i	−0.169533	−	0.0298932i
$975$		0			0
$976$	−132.761	−	48.3210i	−0.136026	−	0.0495093i
$977$	1130.45	+	1347.21i	1.15706	+	1.37893i	0.912391	+	0.409320i	$0.134234\pi$
$977$	1130.45	+	1347.21i	1.15706	+	1.37893i	0.244667	+	0.969607i	$0.421321\pi$
$978$		0			0
$979$	−75.2445	+	27.3868i	−0.0768585	+	0.0279742i
$980$	218.718	+	126.277i	0.223182	+	0.128854i
$981$		0			0
$982$	−276.594	−	479.075i	−0.281664	−	0.487856i
$983$	795.222	−	947.708i	0.808974	−	0.964098i	−0.190872	−	0.981615i	$-0.561132\pi$
$983$	795.222	−	947.708i	0.808974	−	0.964098i	0.999847	+	0.0175168i	$0.00557606\pi$
$984$		0			0
$985$	−72.4654	−	410.972i	−0.0735690	−	0.417230i
$986$	−87.2327	+	15.3815i	−0.0884713	+	0.0155999i
$987$		0			0
$988$	−146.541	−	122.963i	−0.148321	−	0.124456i
$989$	2377.70	−	1372.76i	2.40414	−	1.38803i
$990$		0			0
$991$	−384.670	+	666.268i	−0.388163	+	0.672319i	−0.992203	−	0.124636i	$-0.960224\pi$
$991$	−384.670	+	666.268i	−0.388163	+	0.672319i	0.604039	+	0.796955i	$0.293557\pi$
$992$	87.7594	+	241.117i	0.0884671	+	0.243061i
$993$		0			0
$994$	−204.713	+	171.775i	−0.205949	+	0.172812i
$995$	−263.486	+	723.922i	−0.264810	+	0.727560i
$996$		0			0
$997$	−15.4474	+	87.6066i	−0.0154939	+	0.0878702i	−0.991574	−	0.129540i	$-0.958650\pi$
$997$	−15.4474	+	87.6066i	−0.0154939	+	0.0878702i	0.976080	+	0.217410i	$0.0697610\pi$
$998$		−	260.814i		−	0.261337i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.3.f.a.89.1		36
3.2	odd	2		54.3.f.a.29.4	✓	36
12.11	even	2		432.3.bc.c.353.4		36
27.11	odd	18		1458.3.b.c.1457.31		36
27.13	even	9		54.3.f.a.41.4	yes	36
27.14	odd	18	inner	162.3.f.a.71.1		36
27.16	even	9		1458.3.b.c.1457.6		36
108.67	odd	18		432.3.bc.c.257.4		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.3.f.a.29.4	✓	36	3.2	odd	2
54.3.f.a.41.4	yes	36	27.13	even	9
162.3.f.a.71.1		36	27.14	odd	18	inner
162.3.f.a.89.1		36	1.1	even	1	trivial
432.3.bc.c.257.4		36	108.67	odd	18
432.3.bc.c.353.4		36	12.11	even	2
1458.3.b.c.1457.6		36	27.16	even	9
1458.3.b.c.1457.31		36	27.11	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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	162.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.39273 - 0.245576i) q^{2} +(1.87939 + 0.684040i) q^{4} +(-1.85971 - 2.21631i) q^{5} +(2.17427 - 0.791369i) q^{7} +(-2.44949 - 1.41421i) q^{8} +O(q^{10})\)	\(q+(-1.39273 - 0.245576i) q^{2} +(1.87939 + 0.684040i) q^{4} +(-1.85971 - 2.21631i) q^{5} +(2.17427 - 0.791369i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(2.04580 + 3.54342i) q^{10} +(0.401092 - 0.478003i) q^{11} +(-4.06850 - 23.0736i) q^{13} +(-3.22251 + 0.568215i) q^{14} +(3.06418 + 2.57115i) q^{16} +(-2.71755 + 1.56898i) q^{17} +(2.04119 - 3.53544i) q^{19} +(-1.97906 - 5.43742i) q^{20} +(-0.675999 + 0.567230i) q^{22} +(15.5068 - 42.6045i) q^{23} +(2.88767 - 16.3768i) q^{25} +33.1344i q^{26} +4.62762 q^{28} +(-19.6570 - 3.46606i) q^{29} +(-42.6238 - 15.5138i) q^{31} +(-3.63616 - 4.33340i) q^{32} +(4.17011 - 1.51780i) q^{34} +(-5.79743 - 3.34715i) q^{35} +(18.7730 + 32.5159i) q^{37} +(-3.71104 + 4.42264i) q^{38} +(1.42100 + 8.05886i) q^{40} +(45.6993 - 8.05802i) q^{41} +(46.3885 + 38.9246i) q^{43} +(1.08078 - 0.623989i) q^{44} +(-32.0594 + 55.5285i) q^{46} +(-1.06082 - 2.91457i) q^{47} +(-33.4350 + 28.0553i) q^{49} +(-8.04348 + 22.0993i) q^{50} +(8.13700 - 46.1472i) q^{52} +79.9023i q^{53} -1.80532 q^{55} +(-6.44501 - 1.13643i) q^{56} +(26.5257 + 9.65457i) q^{58} +(41.9763 + 50.0254i) q^{59} +(-33.1902 + 12.0803i) q^{61} +(55.5536 + 32.0739i) q^{62} +(4.00000 + 6.92820i) q^{64} +(-43.5721 + 51.9272i) q^{65} +(-4.92896 - 27.9535i) q^{67} +(-6.18056 + 1.08980i) q^{68} +(7.25227 + 6.08537i) q^{70} +(70.7261 - 40.8337i) q^{71} +(-12.6048 + 21.8321i) q^{73} +(-18.1606 - 49.8960i) q^{74} +(6.25456 - 5.24820i) q^{76} +(0.493805 - 1.35672i) q^{77} +(11.5555 - 65.5347i) q^{79} -11.5728i q^{80} -65.6256 q^{82} +(-49.1681 - 8.66967i) q^{83} +(8.53120 + 3.10510i) q^{85} +(-55.0476 - 65.6032i) q^{86} +(-1.65847 + 0.603634i) q^{88} +(-111.133 - 64.1626i) q^{89} +(-27.1057 - 46.9485i) q^{91} +(58.2864 - 69.4631i) q^{92} +(0.761683 + 4.31972i) q^{94} +(-11.6317 + 2.05097i) q^{95} +(107.970 + 90.5977i) q^{97} +(53.4556 - 30.8626i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{5}+O(q^{10}) \) 36 * q - 18 * q^5	\( 36 q - 18 q^{5} + 18 q^{11} + 36 q^{14} + 72 q^{20} + 36 q^{22} + 180 q^{23} + 18 q^{25} - 144 q^{29} - 90 q^{31} - 72 q^{34} - 486 q^{35} - 180 q^{38} + 90 q^{41} + 90 q^{43} + 378 q^{47} + 72 q^{49} + 72 q^{56} - 252 q^{59} - 144 q^{61} + 144 q^{64} - 18 q^{65} - 594 q^{67} + 180 q^{68} - 360 q^{70} + 648 q^{71} + 126 q^{73} + 504 q^{74} - 72 q^{76} + 342 q^{77} - 72 q^{79} - 594 q^{83} + 360 q^{85} - 540 q^{86} + 144 q^{88} - 648 q^{89} - 198 q^{91} - 396 q^{92} + 504 q^{94} - 252 q^{95} + 702 q^{97} - 648 q^{98}+O(q^{100}) \) 36 * q - 18 * q^5 + 18 * q^11 + 36 * q^14 + 72 * q^20 + 36 * q^22 + 180 * q^23 + 18 * q^25 - 144 * q^29 - 90 * q^31 - 72 * q^34 - 486 * q^35 - 180 * q^38 + 90 * q^41 + 90 * q^43 + 378 * q^47 + 72 * q^49 + 72 * q^56 - 252 * q^59 - 144 * q^61 + 144 * q^64 - 18 * q^65 - 594 * q^67 + 180 * q^68 - 360 * q^70 + 648 * q^71 + 126 * q^73 + 504 * q^74 - 72 * q^76 + 342 * q^77 - 72 * q^79 - 594 * q^83 + 360 * q^85 - 540 * q^86 + 144 * q^88 - 648 * q^89 - 198 * q^91 - 396 * q^92 + 504 * q^94 - 252 * q^95 + 702 * q^97 - 648 * q^98

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