LMFDB - Embedded newform 162.3.f.a.17.5

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			17.5
Character	$\chi$	$=$	162.17
Dual form			162.3.f.a.143.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.483690 - 1.32893i) q^{2} +(-1.53209 - 1.28558i) q^{4} +(-3.98669 - 0.702961i) q^{5} +(-10.1193 + 8.49107i) q^{7} +(-2.44949 + 1.41421i) q^{8} +O(q^{10})$	\(q+(0.483690 - 1.32893i) q^{2} +(-1.53209 - 1.28558i) q^{4} +(-3.98669 - 0.702961i) q^{5} +(-10.1193 + 8.49107i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(-2.86250 + 4.95800i) q^{10} +(-13.3731 + 2.35805i) q^{11} +(17.4463 - 6.34995i) q^{13} +(6.38942 + 17.5548i) q^{14} +(0.694593 + 3.93923i) q^{16} +(-13.8790 - 8.01304i) q^{17} +(0.327006 + 0.566391i) q^{19} +(5.20426 + 6.20219i) q^{20} +(-3.33478 + 18.9125i) q^{22} +(-4.24411 + 5.05793i) q^{23} +(-8.09277 - 2.94553i) q^{25} -26.2563i q^{26} +26.4195 q^{28} +(-0.466584 + 1.28193i) q^{29} +(-14.3033 - 12.0019i) q^{31} +(5.57091 + 0.982302i) q^{32} +(-17.3619 + 14.5683i) q^{34} +(46.3112 - 26.7378i) q^{35} +(-8.43940 + 14.6175i) q^{37} +(0.910861 - 0.160609i) q^{38} +(10.7595 - 3.91614i) q^{40} +(14.6609 + 40.2805i) q^{41} +(0.0113866 + 0.0645766i) q^{43} +(23.5203 + 13.5794i) q^{44} +(4.66878 + 8.08657i) q^{46} +(-30.0861 - 35.8552i) q^{47} +(21.7924 - 123.591i) q^{49} +(-7.82877 + 9.32997i) q^{50} +(-34.8927 - 12.6999i) q^{52} -14.3109i q^{53} +54.9722 q^{55} +(12.7788 - 35.1096i) q^{56} +(1.47791 + 1.24011i) q^{58} +(4.79039 + 0.844675i) q^{59} +(-12.0703 + 10.1282i) q^{61} +(-22.8680 + 13.2029i) q^{62} +(4.00000 - 6.92820i) q^{64} +(-74.0169 + 13.0512i) q^{65} +(-37.1304 + 13.5143i) q^{67} +(10.9625 + 30.1192i) q^{68} +(-13.1323 - 74.4770i) q^{70} +(60.9106 + 35.1667i) q^{71} +(-34.1753 - 59.1934i) q^{73} +(15.3435 + 18.2857i) q^{74} +(0.227136 - 1.28815i) q^{76} +(115.304 - 137.414i) q^{77} +(47.4059 + 17.2543i) q^{79} -16.1928i q^{80} +60.6211 q^{82} +(-50.2457 + 138.049i) q^{83} +(49.6984 + 41.7019i) q^{85} +(0.0913252 + 0.0161031i) q^{86} +(29.4226 - 24.6885i) q^{88} +(17.2957 - 9.98568i) q^{89} +(-122.626 + 212.395i) q^{91} +(13.0047 - 2.29308i) q^{92} +(-62.2012 + 22.6394i) q^{94} +(-0.905521 - 2.48790i) q^{95} +(18.3596 + 104.122i) q^{97} +(-153.703 - 88.7402i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	0.483690	−	1.32893i	0.241845	−	0.664463i
$2$	0.483690	−	1.32893i	0.241845	−	0.664463i
$3$		0			0
$3$		0			0
$4$	−1.53209	−	1.28558i	−0.383022	−	0.321394i
$5$	−3.98669	−	0.702961i	−0.797338	−	0.140592i	−0.239886	−	0.970801i	$-0.577110\pi$
$5$	−3.98669	−	0.702961i	−0.797338	−	0.140592i	−0.557452	+	0.830209i	$0.688221\pi$
$6$		0			0
$7$	−10.1193	+	8.49107i	−1.44561	+	1.21301i	−0.509901	+	0.860233i	$0.670318\pi$
$7$	−10.1193	+	8.49107i	−1.44561	+	1.21301i	−0.935708	+	0.352776i	$0.885238\pi$
$8$	−2.44949	+	1.41421i	−0.306186	+	0.176777i
$9$		0			0
$10$	−2.86250	+	4.95800i	−0.286250	+	0.495800i
$11$	−13.3731	+	2.35805i	−1.21574	+	0.214368i	−0.744491	−	0.667632i	$-0.767308\pi$
$11$	−13.3731	+	2.35805i	−1.21574	+	0.214368i	−0.471249	+	0.882000i	$0.656197\pi$
$12$		0			0
$13$	17.4463	−	6.34995i	1.34203	−	0.488458i	0.431576	−	0.902077i	$-0.357958\pi$
$13$	17.4463	−	6.34995i	1.34203	−	0.488458i	0.910450	+	0.413619i	$0.135735\pi$
$14$	6.38942	+	17.5548i	0.456387	+	1.25391i
$15$		0			0
$16$	0.694593	+	3.93923i	0.0434120	+	0.246202i
$17$	−13.8790	−	8.01304i	−0.816411	−	0.471355i	0.0327659	−	0.999463i	$-0.489568\pi$
$17$	−13.8790	−	8.01304i	−0.816411	−	0.471355i	−0.849177	+	0.528108i	$0.822902\pi$
$18$		0			0
$19$	0.327006	+	0.566391i	0.0172108	+	0.0298100i	0.874503	−	0.485021i	$-0.161188\pi$
$19$	0.327006	+	0.566391i	0.0172108	+	0.0298100i	−0.857292	+	0.514831i	$0.827855\pi$
$20$	5.20426	+	6.20219i	0.260213	+	0.310109i
$21$		0			0
$22$	−3.33478	+	18.9125i	−0.151581	+	0.859658i
$23$	−4.24411	+	5.05793i	−0.184526	+	0.219910i	−0.850375	−	0.526177i	$-0.823625\pi$
$23$	−4.24411	+	5.05793i	−0.184526	+	0.219910i	0.665849	+	0.746087i	$0.268070\pi$
$24$		0			0
$25$	−8.09277	−	2.94553i	−0.323711	−	0.117821i
$26$		−	26.2563i		−	1.00986i
$27$		0			0
$28$	26.4195			0.943554
$29$	−0.466584	+	1.28193i	−0.0160891	+	0.0442044i	−0.947477	−	0.319823i	$-0.896376\pi$
$29$	−0.466584	+	1.28193i	−0.0160891	+	0.0442044i	0.931388	+	0.364028i	$0.118599\pi$
$30$		0			0
$31$	−14.3033	−	12.0019i	−0.461397	−	0.387158i	0.382247	−	0.924060i	$-0.375150\pi$
$31$	−14.3033	−	12.0019i	−0.461397	−	0.387158i	−0.843645	+	0.536902i	$0.819595\pi$
$32$	5.57091	+	0.982302i	0.174091	+	0.0306970i
$33$		0			0
$34$	−17.3619	+	14.5683i	−0.510643	+	0.428480i
$35$	46.3112	−	26.7378i	1.32318	−	0.763937i
$36$		0			0
$37$	−8.43940	+	14.6175i	−0.228092	+	0.395067i	−0.957243	−	0.289286i	$-0.906582\pi$
$37$	−8.43940	+	14.6175i	−0.228092	+	0.395067i	0.729151	+	0.684353i	$0.239915\pi$
$38$	0.910861	−	0.160609i	0.0239700	−	0.00422656i
$39$		0			0
$40$	10.7595	−	3.91614i	0.268987	−	0.0979034i
$41$	14.6609	+	40.2805i	0.357583	+	0.982450i	0.979866	+	0.199658i	$0.0639830\pi$
$41$	14.6609	+	40.2805i	0.357583	+	0.982450i	−0.622283	+	0.782792i	$0.713795\pi$
$42$		0			0
$43$	0.0113866	+	0.0645766i	0.000264805	+	0.00150178i	0.984940	−	0.172897i	$-0.0553129\pi$
$43$	0.0113866	+	0.0645766i	0.000264805	+	0.00150178i	−0.984675	+	0.174399i	$0.944202\pi$
$44$	23.5203	+	13.5794i	0.534552	+	0.308624i
$45$		0			0
$46$	4.66878	+	8.08657i	0.101495	+	0.175795i
$47$	−30.0861	−	35.8552i	−0.640129	−	0.762876i	0.344262	−	0.938874i	$-0.388129\pi$
$47$	−30.0861	−	35.8552i	−0.640129	−	0.762876i	−0.984391	+	0.175998i	$0.943685\pi$
$48$		0			0
$49$	21.7924	−	123.591i	0.444744	−	2.52227i
$50$	−7.82877	+	9.32997i	−0.156575	+	0.186599i
$51$		0			0
$52$	−34.8927	−	12.6999i	−0.671013	−	0.244229i
$53$		−	14.3109i		−	0.270017i	−0.990844	−	0.135008i	$-0.956894\pi$
$53$		−	14.3109i		−	0.270017i	0.990844	−	0.135008i	$-0.0431061\pi$
$54$		0			0
$55$	54.9722			0.999494
$56$	12.7788	−	35.1096i	0.228194	−	0.626957i
$57$		0			0
$58$	1.47791	+	1.24011i	0.0254811	+	0.0213812i
$59$	4.79039	+	0.844675i	0.0811930	+	0.0143165i	0.214097	−	0.976812i	$-0.431319\pi$
$59$	4.79039	+	0.844675i	0.0811930	+	0.0143165i	−0.132904	+	0.991129i	$0.542430\pi$
$60$		0			0
$61$	−12.0703	+	10.1282i	−0.197874	+	0.166036i	−0.736341	−	0.676611i	$-0.763448\pi$
$61$	−12.0703	+	10.1282i	−0.197874	+	0.166036i	0.538467	+	0.842646i	$0.319004\pi$
$62$	−22.8680	+	13.2029i	−0.368839	+	0.212949i
$63$		0			0
$64$	4.00000	−	6.92820i	0.0625000	−	0.108253i
$65$	−74.0169	+	13.0512i	−1.13872	+	0.200787i
$66$		0			0
$67$	−37.1304	+	13.5143i	−0.554185	+	0.201707i	−0.603905	−	0.797056i	$-0.706389\pi$
$67$	−37.1304	+	13.5143i	−0.554185	+	0.201707i	0.0497202	+	0.998763i	$0.484167\pi$
$68$	10.9625	+	30.1192i	0.161213	+	0.442929i
$69$		0			0
$70$	−13.1323	−	74.4770i	−0.187604	−	1.06396i
$71$	60.9106	+	35.1667i	0.857896	+	0.495306i	0.863307	−	0.504679i	$-0.168389\pi$
$71$	60.9106	+	35.1667i	0.857896	+	0.495306i	−0.00541136	+	0.999985i	$0.501722\pi$
$72$		0			0
$73$	−34.1753	−	59.1934i	−0.468155	−	0.810868i	0.531183	−	0.847257i	$-0.321748\pi$
$73$	−34.1753	−	59.1934i	−0.468155	−	0.810868i	−0.999338	+	0.0363890i	$0.988414\pi$
$74$	15.3435	+	18.2857i	0.207344	+	0.247103i
$75$		0			0
$76$	0.227136	−	1.28815i	0.00298863	−	0.0169494i
$77$	115.304	−	137.414i	1.49745	−	1.78460i
$78$		0			0
$79$	47.4059	+	17.2543i	0.600074	+	0.218409i	0.624155	−	0.781301i	$-0.285444\pi$
$79$	47.4059	+	17.2543i	0.600074	+	0.218409i	−0.0240804	+	0.999710i	$0.507666\pi$
$80$		−	16.1928i		−	0.202410i
$81$		0			0
$82$	60.6211			0.739281
$83$	−50.2457	+	138.049i	−0.605370	+	1.66324i	0.134841	+	0.990867i	$0.456948\pi$
$83$	−50.2457	+	138.049i	−0.605370	+	1.66324i	−0.740211	+	0.672374i	$0.765275\pi$
$84$		0			0
$85$	49.6984	+	41.7019i	0.584687	+	0.490611i
$86$	0.0913252	+	0.0161031i	0.00106192	+	0.000187245i
$87$		0			0
$88$	29.4226	−	24.6885i	0.334348	−	0.280551i
$89$	17.2957	−	9.98568i	0.194334	−	0.112199i	−0.399676	−	0.916656i	$-0.630877\pi$
$89$	17.2957	−	9.98568i	0.194334	−	0.112199i	0.594010	+	0.804458i	$0.297544\pi$
$90$		0			0
$91$	−122.626	+	212.395i	−1.34754	+	2.33401i
$92$	13.0047	−	2.29308i	0.141355	−	0.0249248i
$93$		0			0
$94$	−62.2012	+	22.6394i	−0.661715	+	0.240844i
$95$	−0.905521	−	2.48790i	−0.00953180	−	0.0261884i
$96$		0			0
$97$	18.3596	+	104.122i	0.189274	+	1.07343i	0.920340	+	0.391120i	$0.127912\pi$
$97$	18.3596	+	104.122i	0.189274	+	1.07343i	−0.731066	+	0.682307i	$0.760977\pi$
$98$	−153.703	−	88.7402i	−1.56839	−	0.905513i
$99$		0			0
$100$	8.61214	+	14.9167i	0.0861214	+	0.149167i
$101$	−38.7455	−	46.1751i	−0.383619	−	0.457179i	0.539334	−	0.842092i	$-0.318676\pi$
$101$	−38.7455	−	46.1751i	−0.383619	−	0.457179i	−0.922953	+	0.384913i	$0.874232\pi$
$102$		0			0
$103$	−16.6921	+	94.6657i	−0.162059	+	0.919085i	0.789985	+	0.613126i	$0.210088\pi$
$103$	−16.6921	+	94.6657i	−0.162059	+	0.919085i	−0.952045	+	0.305959i	$0.901023\pi$
$104$	−33.7544	+	40.2270i	−0.324562	+	0.386798i
$105$		0			0
$106$	−19.0181	−	6.92202i	−0.179416	−	0.0653021i
$107$			107.330i			1.00308i	0.865133	+	0.501542i	$0.167234\pi$
$107$			107.330i			1.00308i	−0.865133	+	0.501542i	$0.832766\pi$
$108$		0			0
$109$	85.1199			0.780917			0.390458	−	0.920621i	$-0.372317\pi$
$109$	85.1199			0.780917			0.390458	+	0.920621i	$0.372317\pi$
$110$	26.5895	−	73.0540i	0.241722	−	0.664127i
$111$		0			0
$112$	−40.4770	−	33.9643i	−0.361402	−	0.303252i
$113$	−165.620	−	29.2032i	−1.46566	−	0.258436i	−0.616828	−	0.787098i	$-0.711583\pi$
$113$	−165.620	−	29.2032i	−1.46566	−	0.258436i	−0.848832	+	0.528662i	$0.822694\pi$
$114$		0			0
$115$	20.4755	−	17.1810i	0.178047	−	0.149400i
$116$	2.36286	−	1.36420i	0.0203695	−	0.0117603i
$117$		0			0
$118$	3.43957	−	5.95751i	0.0291489	−	0.0504874i
$119$	208.484	−	36.7614i	1.75197	−	0.308920i
$120$		0			0
$121$	59.5777	−	21.6845i	0.492378	−	0.179211i
$122$	7.62133	+	20.9394i	0.0624699	+	0.171635i
$123$		0			0
$124$	6.48460	+	36.7760i	0.0522952	+	0.296581i
$125$	117.839	+	68.0342i	0.942710	+	0.544274i
$126$		0			0
$127$	−85.8323	−	148.666i	−0.675845	−	1.17060i	−0.976221	−	0.216777i	$-0.930446\pi$
$127$	−85.8323	−	148.666i	−0.675845	−	1.17060i	0.300377	−	0.953821i	$-0.402888\pi$
$128$	−7.27231	−	8.66680i	−0.0568149	−	0.0677094i
$129$		0			0
$130$	−18.4572	+	104.676i	−0.141978	+	0.805198i
$131$	−112.534	+	134.113i	−0.859038	+	1.02376i	0.140395	+	0.990096i	$0.455163\pi$
$131$	−112.534	+	134.113i	−0.859038	+	1.02376i	−0.999433	+	0.0336659i	$0.989282\pi$
$132$		0			0
$133$	−8.11832	−	2.95483i	−0.0610400	−	0.0222167i
$134$			55.8803i			0.417017i
$135$		0			0
$136$	45.3286			0.333299
$137$	−16.7909	+	46.1327i	−0.122561	+	0.336735i	−0.985767	−	0.168118i	$-0.946231\pi$
$137$	−16.7909	+	46.1327i	−0.122561	+	0.336735i	0.863205	+	0.504853i	$0.168453\pi$
$138$		0			0
$139$	−107.159	−	89.9168i	−0.770926	−	0.646884i	0.170020	−	0.985441i	$-0.445617\pi$
$139$	−107.159	−	89.9168i	−0.770926	−	0.646884i	−0.940946	+	0.338557i	$0.890061\pi$
$140$	−105.326	−	18.5719i	−0.752332	−	0.132656i
$141$		0			0
$142$	76.1958	−	63.9359i	0.536590	−	0.450253i
$143$	−218.339	+	126.058i	−1.52685	+	0.881525i
$144$		0			0
$145$	2.76127	−	4.78266i	0.0190432	−	0.0329839i
$146$	−95.1939	+	16.7853i	−0.652013	+	0.114967i
$147$		0			0
$148$	31.7218	−	11.5458i	0.214336	−	0.0780120i
$149$	−82.1753	−	225.775i	−0.551512	−	1.51527i	−0.831646	−	0.555306i	$-0.812601\pi$
$149$	−82.1753	−	225.775i	−0.551512	−	1.51527i	0.280134	−	0.959961i	$-0.409621\pi$
$150$		0			0
$151$	3.53844	+	20.0675i	0.0234334	+	0.132897i	0.994280	−	0.106804i	$-0.0340617\pi$
$151$	3.53844	+	20.0675i	0.0234334	+	0.132897i	−0.970847	+	0.239701i	$0.922951\pi$
$152$	−1.60200	−	0.924912i	−0.0105394	−	0.00608495i
$153$		0			0
$154$	−126.842	−	219.696i	−0.823647	−	1.42660i
$155$	48.5860	+	57.9026i	0.313458	+	0.373565i
$156$		0			0
$157$	−39.0295	+	221.347i	−0.248596	+	1.40986i	0.563396	+	0.826187i	$0.309495\pi$
$157$	−39.0295	+	221.347i	−0.248596	+	1.40986i	−0.811992	+	0.583669i	$0.801617\pi$
$158$	45.8594	−	54.6531i	0.290250	−	0.345906i
$159$		0			0
$160$	−21.5190	−	7.83227i	−0.134494	−	0.0489517i
$161$		−	87.2195i		−	0.541736i
$162$		0			0
$163$	−155.441			−0.953626			−0.476813	−	0.879005i	$-0.658208\pi$
$163$	−155.441			−0.953626			−0.476813	+	0.879005i	$0.658208\pi$
$164$	29.3218	−	80.5609i	0.178791	−	0.491225i
$165$		0			0
$166$	159.154	+	133.546i	0.958757	+	0.804493i
$167$	316.191	+	55.7529i	1.89336	+	0.333850i	0.994530	−	0.104454i	$-0.0333095\pi$
$167$	316.191	+	55.7529i	1.89336	+	0.333850i	0.898827	+	0.438304i	$0.144421\pi$
$168$		0			0
$169$	134.591	−	112.936i	0.796399	−	0.668258i
$170$	79.4574	−	45.8747i	0.467396	−	0.269851i
$171$		0			0
$172$	0.0655728	−	0.113575i	0.000381237	−	0.000660323i
$173$	140.320	−	24.7423i	0.811100	−	0.143019i	0.247309	−	0.968937i	$-0.420454\pi$
$173$	140.320	−	24.7423i	0.811100	−	0.143019i	0.563791	+	0.825918i	$0.309342\pi$
$174$		0			0
$175$	106.903	−	38.9097i	0.610877	−	0.222341i
$176$	−18.5778	−	51.0420i	−0.105556	−	0.290011i
$177$		0			0
$178$	−4.90448	−	27.8147i	−0.0275533	−	0.156262i
$179$	−186.101	−	107.445i	−1.03967	−	0.600253i	−0.119930	−	0.992782i	$-0.538267\pi$
$179$	−186.101	−	107.445i	−1.03967	−	0.600253i	−0.919740	+	0.392529i	$0.871600\pi$
$180$		0			0
$181$	−150.873	−	261.319i	−0.833550	−	1.44375i	−0.895205	−	0.445654i	$-0.852971\pi$
$181$	−150.873	−	261.319i	−0.833550	−	1.44375i	0.0616551	−	0.998098i	$-0.480362\pi$
$182$	222.944	+	265.694i	1.22497	+	1.45986i
$183$		0			0
$184$	3.24290	−	18.3914i	0.0176245	−	0.0999533i
$185$	43.9208	−	52.3427i	0.237410	−	0.282934i
$186$		0			0
$187$	204.501	+	74.4322i	1.09359	+	0.398033i
$188$			93.6112i			0.497932i
$189$		0			0
$190$	−3.74422			−0.0197064
$191$	101.886	−	279.928i	0.533433	−	1.46559i	−0.321527	−	0.946900i	$-0.604196\pi$
$191$	101.886	−	279.928i	0.533433	−	1.46559i	0.854960	−	0.518694i	$-0.173582\pi$
$192$		0			0
$193$	96.4229	+	80.9084i	0.499601	+	0.419215i	0.857452	−	0.514564i	$-0.172046\pi$
$193$	96.4229	+	80.9084i	0.499601	+	0.419215i	−0.357852	+	0.933778i	$0.616491\pi$
$194$	147.251	+	25.9644i	0.759027	+	0.133837i
$195$		0			0
$196$	−192.274	+	161.337i	−0.980987	+	0.823146i
$197$	37.5877	−	21.7013i	0.190801	−	0.110159i	−0.401557	−	0.915834i	$-0.631531\pi$
$197$	37.5877	−	21.7013i	0.190801	−	0.110159i	0.592357	+	0.805675i	$0.298197\pi$
$198$		0			0
$199$	37.8343	−	65.5310i	0.190122	−	0.329301i	−0.755168	−	0.655531i	$-0.772445\pi$
$199$	37.8343	−	65.5310i	0.190122	−	0.329301i	0.945291	+	0.326230i	$0.105778\pi$
$200$	23.9888	−	4.22986i	0.119944	−	0.0211493i
$201$		0			0
$202$	−80.1041	+	29.1555i	−0.396555	+	0.144334i
$203$	−6.16346	−	16.9340i	−0.0303619	−	0.0834185i
$204$		0			0
$205$	−30.1328	−	170.892i	−0.146989	−	0.833618i
$206$	117.730	+	67.9714i	0.571505	+	0.329958i
$207$		0			0
$208$	37.1320	+	64.3145i	0.178519	+	0.309205i
$209$	−5.70867	−	6.80333i	−0.0273142	−	0.0325518i
$210$		0			0
$211$	37.4085	−	212.154i	0.177291	−	1.00547i	−0.758174	−	0.652052i	$-0.773908\pi$
$211$	37.4085	−	212.154i	0.177291	−	1.00547i	0.935466	−	0.353418i	$-0.114981\pi$
$212$	−18.3977	+	21.9255i	−0.0867817	+	0.103422i
$213$		0			0
$214$	142.634	+	51.9144i	0.666512	+	0.242591i
$215$		−	0.265451i		−	0.00123466i
$216$		0			0
$217$	246.648			1.13663
$218$	41.1716	−	113.118i	0.188861	−	0.518890i
$219$		0			0
$220$	−84.2223	−	70.6709i	−0.382829	−	0.321231i
$221$	−293.020	−	51.6673i	−1.32588	−	0.233789i
$222$		0			0
$223$	−63.7410	+	53.4851i	−0.285834	+	0.239843i	−0.774419	−	0.632673i	$-0.781958\pi$
$223$	−63.7410	+	53.4851i	−0.285834	+	0.239843i	0.488585	+	0.872516i	$0.337513\pi$
$224$	−64.7143	+	37.3628i	−0.288903	+	0.166798i
$225$		0			0
$226$	−118.917	+	205.971i	−0.526183	+	0.911376i
$227$	61.5724	−	10.8569i	0.271244	−	0.0478276i	−0.0363717	−	0.999338i	$-0.511580\pi$
$227$	61.5724	−	10.8569i	0.271244	−	0.0478276i	0.307616	+	0.951511i	$0.400469\pi$
$228$		0			0
$229$	−136.445	+	49.6621i	−0.595831	+	0.216865i	−0.622292	−	0.782785i	$-0.713798\pi$
$229$	−136.445	+	49.6621i	−0.595831	+	0.216865i	0.0264609	+	0.999650i	$0.491576\pi$
$230$	−12.9284	−	35.5206i	−0.0562106	−	0.154437i
$231$		0			0
$232$	−0.670028	−	3.79992i	−0.00288805	−	0.0163790i
$233$	117.176	+	67.6517i	0.502902	+	0.290351i	0.729911	−	0.683542i	$-0.239561\pi$
$233$	117.176	+	67.6517i	0.502902	+	0.290351i	−0.227009	+	0.973893i	$0.572895\pi$
$234$		0			0
$235$	94.7390	+	164.093i	0.403145	+	0.698267i
$236$	−6.25341	−	7.45252i	−0.0264975	−	0.0315785i
$237$		0			0
$238$	51.9885	−	294.842i	0.218439	−	1.23883i
$239$	−94.2026	+	112.266i	−0.394153	+	0.469733i	−0.926228	−	0.376964i	$-0.876968\pi$
$239$	−94.2026	+	112.266i	−0.394153	+	0.469733i	0.532075	+	0.846697i	$0.321412\pi$
$240$		0			0
$241$	−298.014	−	108.468i	−1.23657	−	0.450075i	−0.360728	−	0.932671i	$-0.617472\pi$
$241$	−298.014	−	108.468i	−1.23657	−	0.450075i	−0.875843	+	0.482596i	$0.839694\pi$
$242$		−	89.6629i		−	0.370508i
$243$		0			0
$244$	31.5133			0.129153
$245$	−173.759	+	477.400i	−0.709222	+	1.94857i
$246$		0			0
$247$	9.30161	+	7.80498i	0.0376583	+	0.0315991i
$248$	52.0091	+	9.17061i	0.209714	+	0.0369783i
$249$		0			0
$250$	147.410	−	123.691i	0.589639	−	0.494766i
$251$	137.930	−	79.6340i	0.549522	−	0.317267i	−0.199407	−	0.979917i	$-0.563902\pi$
$251$	137.930	−	79.6340i	0.549522	−	0.317267i	0.748929	+	0.662650i	$0.230568\pi$
$252$		0			0
$253$	44.8302	−	77.6482i	0.177194	−	0.306910i
$254$	−239.082	+	42.1566i	−0.941268	+	0.165971i
$255$		0			0
$256$	−15.0351	+	5.47232i	−0.0587308	+	0.0213763i
$257$	20.7153	+	56.9148i	0.0806043	+	0.221458i	0.973448	−	0.228908i	$-0.0735155\pi$
$257$	20.7153	+	56.9148i	0.0806043	+	0.221458i	−0.892844	+	0.450367i	$0.851293\pi$
$258$		0			0
$259$	−38.7174	−	219.577i	−0.149488	−	0.847789i
$260$	130.179	+	75.1588i	0.500688	+	0.289072i
$261$		0			0
$262$	123.794	+	214.418i	0.472498	+	0.818390i
$263$	−217.155	−	258.796i	−0.825686	−	0.984014i	0.174314	−	0.984690i	$-0.444229\pi$
$263$	−217.155	−	258.796i	−0.825686	−	0.984014i	−1.00000		0.000676331i	$0.999785\pi$
$264$		0			0
$265$	−10.0600	+	57.0530i	−0.0379622	+	0.215295i
$266$	−7.85349	+	9.35943i	−0.0295244	+	0.0351858i
$267$		0			0
$268$	74.2607	+	27.0287i	0.277092	+	0.100853i
$269$			39.0580i			0.145197i	0.997361	+	0.0725986i	$0.0231292\pi$
$269$			39.0580i			0.145197i	−0.997361	+	0.0725986i	$0.976871\pi$
$270$		0			0
$271$	247.005			0.911459			0.455730	−	0.890118i	$-0.349378\pi$
$271$	247.005			0.911459			0.455730	+	0.890118i	$0.349378\pi$
$272$	21.9250	−	60.2384i	0.0806065	−	0.221465i
$273$		0			0
$274$	53.1853	+	44.6278i	0.194107	+	0.162875i
$275$	115.171	+	20.3078i	0.418805	+	0.0738466i
$276$		0			0
$277$	−146.095	+	122.589i	−0.527420	+	0.442558i	−0.867209	−	0.497943i	$-0.834089\pi$
$277$	−146.095	+	122.589i	−0.527420	+	0.442558i	0.339789	+	0.940502i	$0.389644\pi$
$278$	−171.324	+	98.9142i	−0.616275	+	0.355806i
$279$		0			0
$280$	−75.6260	+	130.988i	−0.270093	+	0.467814i
$281$	−133.542	+	23.5471i	−0.475239	+	0.0837975i	−0.406137	−	0.913812i	$-0.633124\pi$
$281$	−133.542	+	23.5471i	−0.475239	+	0.0837975i	−0.0691020	+	0.997610i	$0.522013\pi$
$282$		0			0
$283$	−436.119	+	158.734i	−1.54106	+	0.560898i	−0.966298	−	0.257425i	$-0.917126\pi$
$283$	−436.119	+	158.734i	−1.54106	+	0.560898i	−0.574758	+	0.818324i	$0.694904\pi$
$284$	−48.1109	−	132.184i	−0.169405	−	0.465436i
$285$		0			0
$286$	61.9136	+	351.129i	0.216481	+	1.22772i
$287$	−490.381	−	283.122i	−1.70865	−	0.986487i
$288$		0			0
$289$	−16.0823	−	27.8554i	−0.0556482	−	0.0963855i
$290$	−5.02021	−	5.98285i	−0.0173111	−	0.0206305i
$291$		0			0
$292$	−23.7379	+	134.624i	−0.0812943	+	0.461043i
$293$	−86.9857	+	103.665i	−0.296879	+	0.353807i	−0.893778	−	0.448510i	$-0.851955\pi$
$293$	−86.9857	+	103.665i	−0.296879	+	0.353807i	0.596899	+	0.802317i	$0.296399\pi$
$294$		0			0
$295$	−18.5040	−	6.73492i	−0.0627255	−	0.0228302i
$296$		−	47.7404i		−	0.161285i
$297$		0			0
$298$	−339.785			−1.14022
$299$	−41.9265	+	115.192i	−0.140222	+	0.385258i
$300$		0			0
$301$	−0.663549	−	0.556783i	−0.00220448	−	0.00184978i
$302$	28.3797	+	5.00411i	0.0939726	+	0.0165699i
$303$		0			0
$304$	−2.00401	+	1.68156i	−0.00659213	+	0.00553146i
$305$	55.2403	−	31.8930i	0.181116	−	0.104567i
$306$		0			0
$307$	−174.308	+	301.910i	−0.567778	+	0.983421i	0.429007	+	0.903301i	$0.358864\pi$
$307$	−174.308	+	301.910i	−0.567778	+	0.983421i	−0.996785	+	0.0801195i	$0.974470\pi$
$308$	−353.312	+	62.2984i	−1.14712	+	0.202268i
$309$		0			0
$310$	100.449	−	36.5604i	0.324028	−	0.117937i
$311$	74.9120	+	205.819i	0.240875	+	0.661798i	0.999942	+	0.0107853i	$0.00343313\pi$
$311$	74.9120	+	205.819i	0.240875	+	0.661798i	−0.759067	+	0.651012i	$0.774345\pi$
$312$		0			0
$313$	47.2508	+	267.973i	0.150961	+	0.856143i	0.962386	+	0.271686i	$0.0875813\pi$
$313$	47.2508	+	267.973i	0.150961	+	0.856143i	−0.811425	+	0.584457i	$0.801308\pi$
$314$	275.276	+	158.931i	0.876676	+	0.506149i
$315$		0			0
$316$	−50.4483	−	87.3789i	−0.159646	−	0.276516i
$317$	−300.183	−	357.744i	−0.946949	−	1.12853i	−0.991576	−	0.129527i	$-0.958654\pi$
$317$	−300.183	−	357.744i	−0.946949	−	1.12853i	0.0446266	−	0.999004i	$-0.485790\pi$
$318$		0			0
$319$	3.21684	−	18.2436i	0.0100842	−	0.0571901i
$320$	−20.8170	+	24.8088i	−0.0650532	+	0.0775274i
$321$		0			0
$322$	−115.908	−	42.1871i	−0.359963	−	0.131016i
$323$		−	10.4812i		−	0.0324497i
$324$		0			0
$325$	−159.893			−0.491979
$326$	−75.1852	+	206.570i	−0.230630	+	0.633650i
$327$		0			0
$328$	−92.8768	−	77.9329i	−0.283161	−	0.237600i
$329$	608.897	+	107.365i	1.85075	+	0.326337i
$330$		0			0
$331$	79.5802	−	66.7757i	0.240423	−	0.201739i	−0.514612	−	0.857423i	$-0.672064\pi$
$331$	79.5802	−	66.7757i	0.240423	−	0.201739i	0.755036	+	0.655684i	$0.227620\pi$
$332$	254.453	−	146.909i	0.766426	−	0.442496i
$333$		0			0
$334$	227.030	−	393.227i	0.679729	−	1.17733i
$335$	157.527	−	27.7763i	0.470231	−	0.0829144i
$336$		0			0
$337$	529.219	−	192.620i	1.57038	−	0.571573i	0.597298	−	0.802020i	$-0.296241\pi$
$337$	529.219	−	192.620i	1.57038	−	0.571573i	0.973085	+	0.230447i	$0.0740189\pi$
$338$	−84.9826	−	233.488i	−0.251428	−	0.690792i
$339$		0			0
$340$	−22.5314	−	127.782i	−0.0662689	−	0.375830i
$341$	219.581	+	126.775i	0.643934	+	0.371775i
$342$		0			0
$343$	505.258	+	875.132i	1.47305	+	2.55140i
$344$	−0.119217	−	0.142077i	−0.000346560	−	0.000413014i
$345$		0			0
$346$	34.9908	−	198.443i	0.101130	−	0.573534i
$347$	−174.719	+	208.222i	−0.503512	+	0.600062i	−0.956600	−	0.291403i	$-0.905878\pi$
$347$	−174.719	+	208.222i	−0.503512	+	0.600062i	0.453088	+	0.891466i	$0.350322\pi$
$348$		0			0
$349$	−75.3775	−	27.4352i	−0.215981	−	0.0786108i	0.231763	−	0.972772i	$-0.425550\pi$
$349$	−75.3775	−	27.4352i	−0.215981	−	0.0786108i	−0.447745	+	0.894161i	$0.647773\pi$
$350$		−	160.887i		−	0.459677i
$351$		0			0
$352$	−76.8169			−0.218230
$353$	40.8280	−	112.174i	0.115660	−	0.317773i	−0.868333	−	0.495982i	$-0.834808\pi$
$353$	40.8280	−	112.174i	0.115660	−	0.317773i	0.983993	+	0.178209i	$0.0570303\pi$
$354$		0			0
$355$	−218.111	−	183.017i	−0.614397	−	0.515540i
$356$	−39.3359	−	6.93598i	−0.110494	−	0.0194831i
$357$		0			0
$358$	−232.802	+	195.344i	−0.650285	+	0.545654i
$359$	225.320	−	130.089i	0.627633	−	0.362364i	−0.152202	−	0.988349i	$-0.548636\pi$
$359$	225.320	−	130.089i	0.627633	−	0.362364i	0.779835	+	0.625985i	$0.215303\pi$
$360$		0			0
$361$	180.286	−	312.265i	0.499408	−	0.864999i
$362$	−420.249	+	74.1013i	−1.16091	+	0.204700i
$363$		0			0
$364$	460.924	−	167.763i	1.26627	−	0.460886i
$365$	94.6358	+	260.010i	0.259276	+	0.712355i
$366$		0			0
$367$	−68.0453	−	385.904i	−0.185410	−	1.05151i	−0.925428	−	0.378924i	$-0.876294\pi$
$367$	−68.0453	−	385.904i	−0.185410	−	1.05151i	0.740018	−	0.672587i	$-0.234817\pi$
$368$	−22.8723	−	13.2053i	−0.0621529	−	0.0358840i
$369$		0			0
$370$	−48.3156	−	83.6851i	−0.130583	−	0.226176i
$371$	121.515	+	144.815i	0.327533	+	0.390338i
$372$		0			0
$373$	−19.2839	+	109.365i	−0.0516996	+	0.293203i	−0.999685	−	0.0251119i	$-0.992006\pi$
$373$	−19.2839	+	109.365i	−0.0516996	+	0.293203i	0.947985	+	0.318315i	$0.103117\pi$
$374$	197.830	−	235.764i	0.528957	−	0.630386i
$375$		0			0
$376$	124.402	+	45.2788i	0.330857	+	0.120422i
$377$			25.3277i			0.0671823i
$378$		0			0
$379$	396.757			1.04685			0.523427	−	0.852071i	$-0.324653\pi$
$379$	396.757			1.04685			0.523427	+	0.852071i	$0.324653\pi$
$380$	−1.81104	+	4.97579i	−0.00476590	+	0.0130942i
$381$		0			0
$382$	−322.723	−	270.797i	−0.844825	−	0.708893i
$383$	−222.640	−	39.2574i	−0.581305	−	0.102500i	−0.124739	−	0.992190i	$-0.539809\pi$
$383$	−222.640	−	39.2574i	−0.581305	−	0.102500i	−0.456566	+	0.889690i	$0.650921\pi$
$384$		0			0
$385$	−556.278	+	466.773i	−1.44488	+	1.21240i
$386$	154.160	−	89.0043i	0.399378	−	0.230581i
$387$		0			0
$388$	105.729	−	183.127i	0.272497	−	0.471978i
$389$	637.851	−	112.470i	1.63972	−	0.289127i	0.723657	−	0.690160i	$-0.242460\pi$
$389$	637.851	−	112.470i	1.63972	−	0.289127i	0.916063	+	0.401033i	$0.131349\pi$
$390$		0			0
$391$	99.4333	−	36.1908i	0.254305	−	0.0925595i
$392$	121.404	+	333.554i	0.309704	+	0.850904i
$393$		0			0
$394$	−10.6586	−	60.4480i	−0.0270523	−	0.153421i
$395$	−176.863	−	102.112i	−0.447755	−	0.258512i
$396$		0			0
$397$	180.080	+	311.908i	0.453602	+	0.785662i	0.998607	−	0.0527712i	$-0.0168054\pi$
$397$	180.080	+	311.908i	0.453602	+	0.785662i	−0.545005	+	0.838433i	$0.683472\pi$
$398$	−68.7858	−	81.9757i	−0.172829	−	0.205969i
$399$		0			0
$400$	5.98193	−	33.9252i	0.0149548	−	0.0848131i
$401$	−158.429	+	188.808i	−0.395084	+	0.470843i	−0.926514	−	0.376259i	$-0.877210\pi$
$401$	−158.429	+	188.808i	−0.395084	+	0.470843i	0.531431	+	0.847102i	$0.321655\pi$
$402$		0			0
$403$	−325.752	−	118.564i	−0.808318	−	0.294204i
$404$			120.555i			0.298402i
$405$		0			0
$406$	−25.4852			−0.0627714
$407$	78.3926	−	215.382i	0.192611	−	0.529194i
$408$		0			0
$409$	33.7067	+	28.2832i	0.0824124	+	0.0691522i	0.683063	−	0.730359i	$-0.260647\pi$
$409$	33.7067	+	28.2832i	0.0824124	+	0.0691522i	−0.600651	+	0.799511i	$0.705092\pi$
$410$	−241.677	−	42.6142i	−0.589457	−	0.103937i
$411$		0			0
$412$	147.274	−	123.577i	0.357460	−	0.299945i
$413$	−55.6474	+	32.1280i	−0.134739	+	0.0777918i
$414$		0			0
$415$	297.357	−	515.038i	0.716524	−	1.24106i
$416$	103.430	−	18.2374i	0.248629	−	0.0438400i
$417$		0			0
$418$	−11.8023	+	4.29570i	−0.0282353	+	0.0102768i
$419$	102.584	+	281.846i	0.244830	+	0.672664i	0.999856	+	0.0169693i	$0.00540175\pi$
$419$	102.584	+	281.846i	0.244830	+	0.672664i	−0.755027	+	0.655694i	$0.772376\pi$
$420$		0			0
$421$	65.6847	+	372.517i	0.156021	+	0.884837i	0.957847	+	0.287280i	$0.0927509\pi$
$421$	65.6847	+	372.517i	0.156021	+	0.884837i	−0.801826	+	0.597558i	$0.796138\pi$
$422$	−263.843	−	152.330i	−0.625220	−	0.360971i
$423$		0			0
$424$	20.2386	+	35.0543i	0.0477326	+	0.0826754i
$425$	88.7169	+	105.729i	0.208746	+	0.248773i
$426$		0			0
$427$	36.1434	−	204.979i	0.0846450	−	0.480046i
$428$	137.981	−	164.439i	0.322385	−	0.384203i
$429$		0			0
$430$	−0.352765	−	0.128396i	−0.000820385	−	0.000298596i
$431$		−	739.788i		−	1.71645i	−0.513278	−	0.858223i	$-0.671569\pi$
$431$		−	739.788i		−	1.71645i	0.513278	−	0.858223i	$-0.328431\pi$
$432$		0			0
$433$	−856.804			−1.97876			−0.989381	−	0.145344i	$-0.953571\pi$
$433$	−856.804			−1.97876			−0.989381	+	0.145344i	$0.953571\pi$
$434$	119.301	−	327.777i	0.274887	−	0.755247i
$435$		0			0
$436$	−130.411	−	109.428i	−0.299108	−	0.250982i
$437$	−4.25261	−	0.749850i	−0.00973138	−	0.00171590i
$438$		0			0
$439$	614.827	−	515.901i	1.40052	−	1.17517i	0.439648	−	0.898170i	$-0.355103\pi$
$439$	614.827	−	515.901i	1.40052	−	1.17517i	0.960869	−	0.277003i	$-0.0893413\pi$
$440$	−134.654	+	77.7424i	−0.306031	+	0.176687i
$441$		0			0
$442$	−210.393	+	364.411i	−0.476002	+	0.824459i
$443$	301.057	−	53.0845i	0.679587	−	0.119829i	0.176809	−	0.984245i	$-0.443423\pi$
$443$	301.057	−	53.0845i	0.679587	−	0.119829i	0.502778	+	0.864416i	$0.332311\pi$
$444$		0			0
$445$	−75.9722	+	27.6516i	−0.170724	+	0.0621385i
$446$	40.2468	+	110.577i	0.0902396	+	0.247931i
$447$		0			0
$448$	18.3508	+	104.073i	0.0409616	+	0.232305i
$449$	357.480	+	206.391i	0.796169	+	0.459668i	0.842130	−	0.539275i	$-0.181302\pi$
$449$	357.480	+	206.391i	0.796169	+	0.459668i	−0.0459609	+	0.998943i	$0.514635\pi$
$450$		0			0
$451$	−291.045	−	504.105i	−0.645333	−	1.11775i
$452$	216.201	+	257.658i	0.478321	+	0.570041i
$453$		0			0
$454$	15.3539	−	87.0765i	0.0338192	−	0.191798i
$455$	638.178	−	760.551i	1.40259	−	1.67154i
$456$		0			0
$457$	−465.412	−	169.396i	−1.01841	−	0.370670i	−0.221752	−	0.975103i	$-0.571177\pi$
$457$	−465.412	−	169.396i	−1.01841	−	0.370670i	−0.796656	+	0.604433i	$0.793400\pi$
$458$			205.347i			0.448356i
$459$		0			0
$460$	−53.4576			−0.116212
$461$	−278.892	+	766.250i	−0.604972	+	1.66215i	0.136079	+	0.990698i	$0.456550\pi$
$461$	−278.892	+	766.250i	−0.604972	+	1.66215i	−0.741051	+	0.671449i	$0.765672\pi$
$462$		0			0
$463$	318.881	+	267.573i	0.688727	+	0.577910i	0.918542	−	0.395324i	$-0.129368\pi$
$463$	318.881	+	267.573i	0.688727	+	0.577910i	−0.229815	+	0.973234i	$0.573812\pi$
$464$	−5.37390	−	0.947563i	−0.0115817	−	0.00204216i
$465$		0			0
$466$	146.581	−	122.996i	0.314552	−	0.263940i
$467$	−123.567	+	71.3412i	−0.264597	+	0.152765i	−0.626430	−	0.779478i	$-0.715484\pi$
$467$	−123.567	+	71.3412i	−0.264597	+	0.152765i	0.361833	+	0.932243i	$0.382151\pi$
$468$		0			0
$469$	260.981	−	452.032i	0.556462	−	0.963820i
$470$	263.891	−	46.5312i	0.561471	−	0.0990025i
$471$		0			0
$472$	−12.9286	+	4.70561i	−0.0273910	+	0.00996952i
$473$	−0.304549	−	0.836742i	−0.000643868	−	0.00176901i
$474$		0			0
$475$	−0.978063	−	5.54687i	−0.00205908	−	0.0116776i
$476$	−366.676	−	211.701i	−0.770328	−	0.444749i
$477$		0			0
$478$	103.629	+	179.490i	0.216797	+	0.375503i
$479$	−66.5425	−	79.3023i	−0.138920	−	0.165558i	0.692099	−	0.721803i	$-0.256686\pi$
$479$	−66.5425	−	79.3023i	−0.138920	−	0.165558i	−0.831019	+	0.556245i	$0.812242\pi$
$480$		0			0
$481$	−54.4165	+	308.611i	−0.113132	+	0.641603i
$482$	−288.292	+	343.573i	−0.598116	+	0.712807i
$483$		0			0
$484$	−119.155	−	43.3690i	−0.246189	−	0.0896054i
$485$		−	428.010i		−	0.882495i
$486$		0			0
$487$	−757.163			−1.55475			−0.777374	−	0.629038i	$-0.783449\pi$
$487$	−757.163			−1.55475			−0.777374	+	0.629038i	$0.783449\pi$
$488$	15.2427	−	41.8789i	0.0312350	−	0.0858173i
$489$		0			0
$490$	550.384	+	461.827i	1.12323	+	0.942504i
$491$	−559.039	−	98.5737i	−1.13857	−	0.200761i	−0.427592	−	0.903972i	$-0.640638\pi$
$491$	−559.039	−	98.5737i	−1.13857	−	0.200761i	−0.710981	+	0.703211i	$0.751749\pi$
$492$		0			0
$493$	16.7479	−	14.0531i	0.0339713	−	0.0285053i
$494$	14.8713	−	8.58596i	0.0301039	−	0.0173805i
$495$		0			0
$496$	37.3433	−	64.6805i	0.0752889	−	0.130404i
$497$	−914.973	+	161.334i	−1.84099	+	0.324617i
$498$		0			0
$499$	−436.182	+	158.757i	−0.874113	+	0.318151i	−0.739832	−	0.672792i	$-0.765095\pi$
$499$	−436.182	+	158.757i	−0.874113	+	0.318151i	−0.134282	+	0.990943i	$0.542873\pi$
$500$	−93.0763	−	255.725i	−0.186153	−	0.511450i
$501$		0			0
$502$	−39.1123	−	221.817i	−0.0779130	−	0.441866i
$503$	6.81535	+	3.93484i	0.0135494	+	0.00782275i	0.506759	−	0.862088i	$-0.330843\pi$
$503$	6.81535	+	3.93484i	0.0135494	+	0.00782275i	−0.493210	+	0.869910i	$0.664177\pi$
$504$		0			0
$505$	122.007	+	211.322i	0.241598	+	0.418460i
$506$	−81.5048	−	97.1336i	−0.161077	−	0.191964i
$507$		0			0
$508$	−59.6185	+	338.113i	−0.117359	+	0.665577i
$509$	−39.3894	+	46.9424i	−0.0773858	+	0.0922248i	−0.803348	−	0.595510i	$-0.796950\pi$
$509$	−39.3894	+	46.9424i	−0.0773858	+	0.0922248i	0.725962	+	0.687734i	$0.241395\pi$
$510$		0			0
$511$	848.444	+	308.808i	1.66036	+	0.604322i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	85.6553			0.166645
$515$	133.093	−	365.669i	0.258432	−	0.710037i
$516$		0			0
$517$	486.893	+	408.552i	0.941766	+	0.790236i
$518$	−310.529	−	54.7547i	−0.599478	−	0.105704i
$519$		0			0
$520$	162.847	−	136.644i	0.313166	−	0.262778i
$521$	−838.293	+	483.988i	−1.60901	+	0.928961i	−0.619414	+	0.785064i	$0.712630\pi$
$521$	−838.293	+	483.988i	−1.60901	+	0.928961i	−0.989593	+	0.143896i	$0.954037\pi$
$522$		0			0
$523$	182.559	−	316.201i	0.349061	−	0.604591i	−0.637022	−	0.770845i	$-0.719834\pi$
$523$	182.559	−	316.201i	0.349061	−	0.604591i	0.986083	+	0.166255i	$0.0531674\pi$
$524$	344.824	−	60.8018i	0.658061	−	0.116034i
$525$		0			0
$526$	−448.956	+	163.407i	−0.853528	+	0.310659i
$527$	102.344	+	281.188i	0.194201	+	0.533563i
$528$		0			0
$529$	84.2897	+	478.031i	0.159338	+	0.903649i
$530$	70.9534	+	40.9649i	0.133874	+	0.0772923i
$531$		0			0
$532$	8.63934	+	14.9638i	0.0162394	+	0.0281274i
$533$	511.558	+	609.651i	0.959770	+	1.14381i
$534$		0			0
$535$	75.4488	−	427.891i	0.141026	−	0.799797i
$536$	71.8383	−	85.6135i	0.134027	−	0.159727i
$537$		0			0
$538$	51.9052	+	18.8920i	0.0964781	+	0.0351152i
$539$			1704.19i			3.16176i
$540$		0			0
$541$	1.90773			0.00352630			0.00176315	−	0.999998i	$-0.499439\pi$
$541$	1.90773			0.00352630			0.00176315	+	0.999998i	$0.499439\pi$
$542$	119.474	−	328.252i	0.220432	−	0.605631i
$543$		0			0
$544$	−69.4475	−	58.2733i	−0.127661	−	0.107120i
$545$	−339.347	−	59.8360i	−0.622655	−	0.109791i
$546$		0			0
$547$	−0.552346	+	0.463474i	−0.00100977	+	0.000847301i	−0.643292	−	0.765621i	$-0.722432\pi$
$547$	−0.552346	+	0.463474i	−0.00100977	+	0.000847301i	0.642283	+	0.766468i	$0.277988\pi$
$548$	85.0322	−	49.0934i	0.155168	−	0.0895864i
$549$		0			0
$550$	82.6948	−	143.232i	0.150354	−	0.260421i
$551$	−0.878648	+	0.154929i	−0.00159464	+	0.000281179i
$552$		0			0
$553$	−626.220	+	227.925i	−1.13240	+	0.412162i
$554$	92.2464	+	253.445i	0.166510	+	0.457482i
$555$		0			0
$556$	48.5818	+	275.521i	0.0873774	+	0.495542i
$557$	550.670	+	317.930i	0.988636	+	0.570789i	0.904866	−	0.425696i	$-0.139971\pi$
$557$	550.670	+	317.930i	0.988636	+	0.570789i	0.0837699	+	0.996485i	$0.473304\pi$
$558$		0			0
$559$	0.608713	+	1.05432i	0.00108893	+	0.00188609i
$560$	137.494	+	163.859i	0.245525	+	0.292605i
$561$		0			0
$562$	−33.3006	+	188.857i	−0.0592538	+	0.336045i
$563$	−61.9267	+	73.8014i	−0.109994	+	0.131086i	−0.818232	−	0.574888i	$-0.805046\pi$
$563$	−61.9267	+	73.8014i	−0.109994	+	0.131086i	0.708238	+	0.705973i	$0.249490\pi$
$564$		0			0
$565$	639.746	+	232.848i	1.13229	+	0.412121i
$566$			656.348i			1.15962i
$567$		0			0
$568$	−198.933			−0.350234
$569$	356.298	−	978.920i	0.626182	−	1.72042i	−0.0651419	−	0.997876i	$-0.520750\pi$
$569$	356.298	−	978.920i	0.626182	−	1.72042i	0.691324	−	0.722545i	$-0.257028\pi$
$570$		0			0
$571$	−199.435	−	167.346i	−0.349274	−	0.293075i	0.451225	−	0.892410i	$-0.350987\pi$
$571$	−199.435	−	167.346i	−0.349274	−	0.293075i	−0.800498	+	0.599335i	$0.795432\pi$
$572$	496.572	+	87.5590i	0.868132	+	0.153075i
$573$		0			0
$574$	−613.440	+	514.737i	−1.06871	+	0.896755i
$575$	49.2448	−	28.4315i	0.0856432	−	0.0494461i
$576$		0			0
$577$	−192.470	+	333.369i	−0.333571	+	0.577762i	−0.983209	−	0.182482i	$-0.941587\pi$
$577$	−192.470	+	333.369i	−0.333571	+	0.577762i	0.649638	+	0.760243i	$0.274920\pi$
$578$	−44.7966	+	7.89885i	−0.0775028	+	0.0136658i
$579$		0			0
$580$	−10.3790	+	3.77764i	−0.0178948	+	0.00651317i
$581$	−663.734	−	1823.59i	−1.14240	−	3.13872i
$582$		0			0
$583$	33.7457	+	191.381i	0.0578828	+	0.328270i
$584$	167.424	+	96.6624i	0.286685	+	0.165518i
$585$		0			0
$586$	95.6897	+	165.739i	0.163293	+	0.282832i
$587$	−667.584	−	795.596i	−1.13728	−	1.35536i	−0.925816	−	0.377974i	$-0.876621\pi$
$587$	−667.584	−	795.596i	−1.13728	−	1.35536i	−0.211465	−	0.977385i	$-0.567824\pi$
$588$		0			0
$589$	2.12050	−	12.0260i	0.00360017	−	0.0204176i
$590$	−17.9004	+	21.3329i	−0.0303397	+	0.0361574i
$591$		0			0
$592$	−63.4435	−	23.0916i	−0.107168	−	0.0390060i
$593$		−	464.135i		−	0.782690i	−0.920244	−	0.391345i	$-0.872010\pi$
$593$		−	464.135i		−	0.782690i	0.920244	−	0.391345i	$-0.127990\pi$
$594$		0			0
$595$	−857.005			−1.44034
$596$	−164.351	+	451.549i	−0.275756	+	0.757633i
$597$		0			0
$598$	132.802	+	111.434i	0.222078	+	0.186345i
$599$	−804.360	−	141.830i	−1.34284	−	0.236778i	−0.544385	−	0.838836i	$-0.683237\pi$
$599$	−804.360	−	141.830i	−1.34284	−	0.236778i	−0.798453	+	0.602057i	$0.794348\pi$
$600$		0			0
$601$	184.846	−	155.104i	0.307563	−	0.258076i	−0.475921	−	0.879488i	$-0.657885\pi$
$601$	184.846	−	155.104i	0.307563	−	0.258076i	0.783484	+	0.621412i	$0.213441\pi$
$602$	−1.06088	+	0.612497i	−0.00176225	+	0.00101744i
$603$		0			0
$604$	20.3771	−	35.2941i	0.0337369	−	0.0584340i
$605$	−252.761	+	44.5686i	−0.417787	+	0.0736671i
$606$		0			0
$607$	492.438	−	179.233i	0.811266	−	0.295277i	0.0971191	−	0.995273i	$-0.469037\pi$
$607$	492.438	−	179.233i	0.811266	−	0.295277i	0.714147	+	0.699996i	$0.246815\pi$
$608$	1.26535	+	3.47653i	0.00208118	+	0.00571798i
$609$		0			0
$610$	−15.6643	−	88.8365i	−0.0256791	−	0.145634i
$611$	−752.570	−	434.497i	−1.23170	−	0.711124i
$612$		0			0
$613$	164.324	+	284.617i	0.268064	+	0.464301i	0.968362	−	0.249550i	$-0.0802826\pi$
$613$	164.324	+	284.617i	0.268064	+	0.464301i	−0.700297	+	0.713851i	$0.746949\pi$
$614$	316.905	+	377.673i	0.516132	+	0.615103i
$615$		0			0
$616$	−88.1033	+	499.658i	−0.143025	+	0.811134i
$617$	538.270	−	641.486i	0.872399	−	1.03968i	−0.126462	−	0.991971i	$-0.540362\pi$
$617$	538.270	−	641.486i	0.872399	−	1.03968i	0.998861	−	0.0477134i	$-0.0151934\pi$
$618$		0			0
$619$	193.537	+	70.4416i	0.312660	+	0.113799i	0.493584	−	0.869698i	$-0.335687\pi$
$619$	193.537	+	70.4416i	0.312660	+	0.113799i	−0.180924	+	0.983497i	$0.557909\pi$
$620$		−	151.173i		−	0.243827i
$621$		0			0
$622$	309.752			0.497994
$623$	−90.2307	+	247.907i	−0.144833	+	0.397924i
$624$		0			0
$625$	−257.029	−	215.673i	−0.411246	−	0.345077i
$626$	378.971	+	66.8228i	0.605384	+	0.106746i
$627$		0			0
$628$	344.355	−	288.948i	0.548337	−	0.460109i
$629$	234.261	−	135.251i	0.372434	−	0.215025i
$630$		0			0
$631$	−189.681	+	328.538i	−0.300604	+	0.520662i	−0.976273	−	0.216544i	$-0.930522\pi$
$631$	−189.681	+	328.538i	−0.300604	+	0.520662i	0.675669	+	0.737205i	$0.263855\pi$
$632$	−140.521	+	24.7777i	−0.222344	+	0.0392053i
$633$		0			0
$634$	−620.611	+	225.884i	−0.978881	+	0.356284i
$635$	237.680	+	653.022i	0.374300	+	1.02838i
$636$		0			0
$637$	−404.599	−	2294.59i	−0.635163	−	3.60219i
$638$	−22.6885	−	13.0992i	−0.0355619	−	0.0205317i
$639$		0			0
$640$	22.9000	+	39.6640i	0.0357813	+	0.0619750i
$641$	567.812	+	676.691i	0.885821	+	1.05568i	0.998076	+	0.0620014i	$0.0197483\pi$
$641$	567.812	+	676.691i	0.885821	+	1.05568i	−0.112255	+	0.993679i	$0.535807\pi$
$642$		0			0
$643$	−167.973	+	952.623i	−0.261233	+	1.48153i	0.518317	+	0.855189i	$0.326559\pi$
$643$	−167.973	+	952.623i	−0.261233	+	1.48153i	−0.779550	+	0.626340i	$0.784552\pi$
$644$	−112.127	+	133.628i	−0.174111	+	0.207497i
$645$		0			0
$646$	−13.9288	−	5.06967i	−0.0215616	−	0.00784779i
$647$			199.904i			0.308971i	0.987995	+	0.154485i	$0.0493719\pi$
$647$			199.904i			0.308971i	−0.987995	+	0.154485i	$0.950628\pi$
$648$		0			0
$649$	−66.0543			−0.101779
$650$	−77.3386	+	212.486i	−0.118983	+	0.326902i
$651$		0			0
$652$	238.150	+	199.831i	0.365260	+	0.306490i
$653$	164.505	+	29.0068i	0.251923	+	0.0444208i	0.298183	−	0.954509i	$-0.403619\pi$
$653$	164.505	+	29.0068i	0.251923	+	0.0444208i	−0.0462606	+	0.998929i	$0.514730\pi$
$654$		0			0
$655$	542.914	−	455.559i	0.828877	−	0.695510i
$656$	−148.491	+	85.7311i	−0.226358	+	0.130688i
$657$		0			0
$658$	437.197	−	757.248i	0.664434	−	1.15083i
$659$	126.902	−	22.3762i	0.192567	−	0.0339548i	−0.0765325	−	0.997067i	$-0.524385\pi$
$659$	126.902	−	22.3762i	0.192567	−	0.0339548i	0.269100	+	0.963112i	$0.413274\pi$
$660$		0			0
$661$	273.433	−	99.5215i	0.413666	−	0.150562i	−0.126799	−	0.991928i	$-0.540470\pi$
$661$	273.433	−	99.5215i	0.413666	−	0.150562i	0.540465	+	0.841366i	$0.318248\pi$
$662$	−50.2479	−	138.055i	−0.0759031	−	0.208542i
$663$		0			0
$664$	−72.1544	−	409.208i	−0.108666	−	0.616277i
$665$	30.2881	+	17.4868i	0.0455460	+	0.0262960i
$666$		0			0
$667$	−4.50367	−	7.80058i	−0.00675213	−	0.0116950i
$668$	−412.757	−	491.905i	−0.617900	−	0.736385i
$669$		0			0
$670$	39.2817	−	222.777i	0.0586293	−	0.332503i
$671$	137.535	−	163.908i	0.204970	−	0.244274i
$672$		0			0
$673$	422.325	+	153.714i	0.627525	+	0.228401i	0.636154	−	0.771562i	$-0.280524\pi$
$673$	422.325	+	153.714i	0.627525	+	0.228401i	−0.00862844	+	0.999963i	$0.502747\pi$
$674$		−	796.461i		−	1.18169i
$675$		0			0
$676$	−351.393			−0.519813
$677$	−389.411	+	1069.90i	−0.575202	+	1.58035i	0.220969	+	0.975281i	$0.429078\pi$
$677$	−389.411	+	1069.90i	−0.575202	+	1.58035i	−0.796170	+	0.605073i	$0.793144\pi$
$678$		0			0
$679$	−1069.90	−	897.749i	−1.57569	−	1.32216i
$680$	−180.711	−	31.8642i	−0.265752	−	0.0468592i
$681$		0			0
$682$	274.684	−	230.487i	0.402763	−	0.337958i
$683$	−93.9542	+	54.2445i	−0.137561	+	0.0794209i	−0.567201	−	0.823579i	$-0.691974\pi$
$683$	−93.9542	+	54.2445i	−0.137561	+	0.0794209i	0.429640	+	0.903000i	$0.358640\pi$
$684$		0			0
$685$	99.3697	−	172.113i	0.145065	−	0.251260i
$686$	1407.37	−	248.158i	2.05156	−	0.361746i
$687$		0			0
$688$	−0.246473	+	0.0897089i	−0.000358246	+	0.000130391i
$689$	−90.8733	−	249.672i	−0.131892	−	0.362369i
$690$		0			0
$691$	195.940	+	1111.23i	0.283560	+	1.60815i	0.710385	+	0.703813i	$0.248521\pi$
$691$	195.940	+	1111.23i	0.283560	+	1.60815i	−0.426825	+	0.904334i	$0.640368\pi$
$692$	−246.791	−	142.485i	−0.356635	−	0.205903i
$693$		0			0
$694$	192.202	+	332.903i	0.276947	+	0.479687i
$695$	364.001	+	433.799i	0.523742	+	0.624171i
$696$		0			0
$697$	119.291	−	676.530i	0.171149	−	0.970632i
$698$	−72.9187	+	86.9011i	−0.104468	+	0.124500i
$699$		0			0
$700$	−213.807	−	77.8194i	−0.305439	−	0.111171i
$701$			778.410i			1.11043i	0.831707	+	0.555214i	$0.187364\pi$
$701$			778.410i			1.11043i	−0.831707	+	0.555214i	$0.812636\pi$
$702$		0			0
$703$	−11.0389			−0.0157026
$704$	−37.1555	+	102.084i	−0.0527778	+	0.145006i
$705$		0			0
$706$	−129.323	−	108.515i	−0.183177	−	0.153704i
$707$	784.152	+	138.267i	1.10913	+	0.195569i
$708$		0			0
$709$	−263.186	+	220.839i	−0.371207	+	0.311480i	−0.809239	−	0.587480i	$-0.800120\pi$
$709$	−263.186	+	220.839i	−0.371207	+	0.311480i	0.438032	+	0.898959i	$0.355676\pi$
$710$	−348.714	+	201.330i	−0.491146	+	0.283563i
$711$		0			0
$712$	−28.2438	+	48.9197i	−0.0396682	+	0.0687074i
$713$	121.410	−	21.4078i	0.170280	−	0.0300249i
$714$		0			0
$715$	959.064	−	349.071i	1.34135	−	0.488211i
$716$	146.994	+	403.862i	0.205299	+	0.564054i
$717$		0			0
$718$	−63.8933	−	362.357i	−0.0889878	−	0.504675i
$719$	528.455	+	305.104i	0.734986	+	0.424344i	0.820243	−	0.572015i	$-0.193838\pi$
$719$	528.455	+	305.104i	0.734986	+	0.424344i	−0.0852574	+	0.996359i	$0.527171\pi$
$720$		0			0
$721$	−634.901	−	1099.68i	−0.880584	−	1.52522i
$722$	−327.774	−	390.626i	−0.453981	−	0.541033i
$723$		0			0
$724$	−104.795	+	594.322i	−0.144744	+	0.820887i
$725$	7.55191	−	9.00001i	0.0104164	−	0.0124138i
$726$		0			0
$727$	−195.866	−	71.2895i	−0.269417	−	0.0980599i	0.203779	−	0.979017i	$-0.434678\pi$
$727$	−195.866	−	71.2895i	−0.269417	−	0.0980599i	−0.473196	+	0.880957i	$0.656900\pi$
$728$		−	693.679i		−	0.952855i
$729$		0			0
$730$	391.308			0.536038
$731$	0.359421	−	0.987500i	0.000491684	−	0.00135089i
$732$		0			0
$733$	−191.068	−	160.325i	−0.260665	−	0.218724i	0.503083	−	0.864238i	$-0.332199\pi$
$733$	−191.068	−	160.325i	−0.260665	−	0.218724i	−0.763749	+	0.645514i	$0.776643\pi$
$734$	−545.751	−	96.2306i	−0.743530	−	0.131104i
$735$		0			0
$736$	−28.6120	+	24.0083i	−0.0388749	+	0.0326200i
$737$	464.682	−	268.284i	0.630505	−	0.364022i
$738$		0			0
$739$	−87.7232	+	151.941i	−0.118705	+	0.205604i	−0.919255	−	0.393663i	$-0.871208\pi$
$739$	−87.7232	+	151.941i	−0.118705	+	0.205604i	0.800550	+	0.599267i	$0.204541\pi$
$740$	−134.581	+	23.7303i	−0.181866	+	0.0320679i
$741$		0			0
$742$	251.224	−	91.4382i	0.338577	−	0.123232i
$743$	−228.605	−	628.087i	−0.307678	−	0.845340i	−0.993108	−	0.117201i	$-0.962608\pi$
$743$	−228.605	−	628.087i	−0.307678	−	0.845340i	0.685430	−	0.728139i	$-0.259614\pi$
$744$		0			0
$745$	168.897	+	957.860i	0.226707	+	1.28572i
$746$	136.010	+	78.5255i	0.182319	+	0.105262i
$747$		0			0
$748$	−217.625	−	376.938i	−0.290943	−	0.503928i
$749$	−911.346	−	1086.10i	−1.21675	−	1.45007i
$750$		0			0
$751$	73.4096	−	416.327i	0.0977491	−	0.554363i	−0.896121	−	0.443810i	$-0.853627\pi$
$751$	73.4096	−	416.327i	0.0977491	−	0.554363i	0.993870	−	0.110553i	$-0.0352623\pi$
$752$	120.344	−	143.421i	0.160032	−	0.190719i
$753$		0			0
$754$	33.6587	+	12.2508i	0.0446402	+	0.0162477i
$755$		−	82.4903i		−	0.109259i
$756$		0			0
$757$	938.792			1.24015			0.620074	−	0.784543i	$-0.287103\pi$
$757$	938.792			1.24015			0.620074	+	0.784543i	$0.287103\pi$
$758$	191.907	−	527.261i	0.253176	−	0.695595i
$759$		0			0
$760$	5.73648	+	4.81348i	0.00754800	+	0.00633353i
$761$	708.743	+	124.971i	0.931331	+	0.164219i	0.618675	−	0.785647i	$-0.287670\pi$
$761$	708.743	+	124.971i	0.931331	+	0.164219i	0.312657	+	0.949866i	$0.398781\pi$
$762$		0			0
$763$	−861.351	+	722.759i	−1.12890	+	0.947259i
$764$	−515.967	+	297.894i	−0.675349	+	0.389913i
$765$		0			0
$766$	−159.859	+	276.883i	−0.208693	+	0.361467i
$767$	88.9384	−	15.6822i	0.115956	−	0.0204462i
$768$		0			0
$769$	1188.57	−	432.606i	1.54561	−	0.562556i	0.578228	−	0.815875i	$-0.303745\pi$
$769$	1188.57	−	432.606i	1.54561	−	0.562556i	0.967383	+	0.253319i	$0.0815223\pi$
$770$	351.240	+	965.025i	0.456156	+	1.25328i
$771$		0			0
$772$	−43.7146	−	247.918i	−0.0566251	−	0.321137i
$773$	820.153	+	473.515i	1.06100	+	0.612568i	0.925709	−	0.378237i	$-0.123470\pi$
$773$	820.153	+	473.515i	1.06100	+	0.612568i	0.135291	+	0.990806i	$0.456803\pi$
$774$		0			0
$775$	80.4015	+	139.259i	0.103744	+	0.179690i
$776$	−192.223	−	229.082i	−0.247710	−	0.295209i
$777$		0			0
$778$	159.057	−	902.058i	0.204444	−	1.15946i
$779$	−18.0203	+	21.4757i	−0.0231326	+	0.0275683i
$780$		0			0
$781$	−897.491	−	326.660i	−1.14916	−	0.418259i
$782$		−	149.645i		−	0.191361i
$783$		0			0
$784$	501.991			0.640294
$785$	311.197	−	855.007i	0.396430	−	1.08918i
$786$		0			0
$787$	601.980	+	505.121i	0.764905	+	0.641832i	0.939399	−	0.342827i	$-0.111384\pi$
$787$	601.980	+	505.121i	0.764905	+	0.641832i	−0.174494	+	0.984658i	$0.555829\pi$
$788$	−85.4863	−	15.0735i	−0.108485	−	0.0191289i
$789$		0			0
$790$	−221.246	+	185.648i	−0.280059	+	0.234997i
$791$	1923.91	−	1110.77i	2.43226	−	1.40426i
$792$		0			0
$793$	−146.269	+	253.346i	−0.184450	+	0.319477i
$794$	501.605	−	88.4465i	0.631745	−	0.111394i
$795$		0			0
$796$	−142.211	+	51.7604i	−0.178656	+	0.0650256i
$797$	241.656	+	663.944i	0.303207	+	0.833054i	0.993938	+	0.109942i	$0.0350666\pi$
$797$	241.656	+	663.944i	0.303207	+	0.833054i	−0.690731	+	0.723112i	$0.742711\pi$
$798$		0			0
$799$	130.255	+	738.714i	0.163023	+	0.924549i
$800$	−42.1907	−	24.3588i	−0.0527384	−	0.0304485i
$801$		0			0
$802$	174.281	+	301.864i	0.217309	+	0.376389i
$803$	596.612	+	711.015i	0.742979	+	0.885448i
$804$		0			0
$805$	−61.3119	+	347.717i	−0.0761638	+	0.431947i
$806$	−315.126	+	375.552i	−0.390975	+	0.465946i
$807$		0			0
$808$	160.208	+	58.3110i	0.198277	+	0.0721671i
$809$		−	604.777i		−	0.747562i	−0.927517	−	0.373781i	$-0.878061\pi$
$809$		−	604.777i		−	0.747562i	0.927517	−	0.373781i	$-0.121939\pi$
$810$		0			0
$811$	679.911			0.838362			0.419181	−	0.907903i	$-0.362317\pi$
$811$	679.911			0.838362			0.419181	+	0.907903i	$0.362317\pi$
$812$	−12.3269	+	33.8679i	−0.0151809	+	0.0417093i
$813$		0			0
$814$	−248.309	−	208.356i	−0.305048	−	0.255966i
$815$	619.696	+	109.269i	0.760363	+	0.134072i
$816$		0			0
$817$	−0.0328521	+	0.0275662i	−4.02107e−5	+	3.37408e-5i
$818$	53.8899	−	31.1133i	0.0658801	−	0.0380359i
$819$		0			0
$820$	−173.528	+	300.559i	−0.211620	+	0.366536i
$821$	−1237.08	+	218.131i	−1.50680	+	0.265689i	−0.865229	−	0.501376i	$-0.832827\pi$
$821$	−1237.08	+	218.131i	−1.50680	+	0.265689i	−0.641569	+	0.767066i	$0.721716\pi$
$822$		0			0
$823$	−604.842	+	220.144i	−0.734923	+	0.267490i	−0.682247	−	0.731122i	$-0.738997\pi$
$823$	−604.842	+	220.144i	−0.734923	+	0.267490i	−0.0526757	+	0.998612i	$0.516775\pi$
$824$	−92.9904	−	255.489i	−0.112852	−	0.310059i
$825$		0			0
$826$	15.7797	+	89.4913i	0.0191038	+	0.108343i
$827$	−915.813	−	528.745i	−1.10739	−	0.639353i	−0.169239	−	0.985575i	$-0.554131\pi$
$827$	−915.813	−	528.745i	−1.10739	−	0.639353i	−0.938152	+	0.346222i	$0.887464\pi$
$828$		0			0
$829$	49.5336	+	85.7947i	0.0597510	+	0.103492i	0.894354	−	0.447361i	$-0.147636\pi$
$829$	49.5336	+	85.7947i	0.0597510	+	0.103492i	−0.834603	+	0.550853i	$0.814303\pi$
$830$	−540.619	−	644.284i	−0.651348	−	0.776246i
$831$		0			0
$832$	25.7916	−	146.272i	0.0309996	−	0.175807i
$833$	−1292.80	+	1540.70i	−1.55198	+	1.84957i
$834$		0			0
$835$	−1221.36	−	444.539i	−1.46271	−	0.532382i
$836$			17.7622i			0.0212467i
$837$		0			0
$838$	424.171			0.506171
$839$	98.7318	−	271.263i	0.117678	−	0.323318i	−0.866844	−	0.498580i	$-0.833855\pi$
$839$	98.7318	−	271.263i	0.117678	−	0.323318i	0.984522	+	0.175262i	$0.0560773\pi$
$840$		0			0
$841$	642.818	+	539.388i	0.764349	+	0.641365i
$842$	526.818	+	92.8922i	0.625674	+	0.110323i
$843$		0			0
$844$	−330.053	+	276.947i	−0.391058	+	0.328137i
$845$	−615.964	+	355.627i	−0.728951	+	0.420860i
$846$		0			0
$847$	−418.758	+	725.309i	−0.494401	+	0.856328i
$848$	56.3739	−	9.94023i	0.0664786	−	0.0117220i
$849$		0			0
$850$	183.417	−	66.7583i	0.215785	−	0.0785392i
$851$	−38.1164	−	104.724i	−0.0447901	−	0.123060i
$852$		0			0
$853$	125.336	+	710.818i	0.146936	+	0.833315i	0.965792	+	0.259317i	$0.0834973\pi$
$853$	125.336	+	710.818i	0.146936	+	0.833315i	−0.818856	+	0.573998i	$0.805392\pi$
$854$	−254.920	−	147.178i	−0.298502	−	0.172340i
$855$		0			0
$856$	−151.788	−	262.904i	−0.177322	−	0.307130i
$857$	147.291	+	175.534i	0.171868	+	0.204824i	0.845102	−	0.534605i	$-0.179540\pi$
$857$	147.291	+	175.534i	0.171868	+	0.204824i	−0.673234	+	0.739430i	$0.735095\pi$
$858$		0			0
$859$	−110.309	+	625.592i	−0.128415	+	0.728279i	0.850805	+	0.525481i	$0.176115\pi$
$859$	−110.309	+	625.592i	−0.128415	+	0.728279i	−0.979221	+	0.202798i	$0.934996\pi$
$860$	−0.341258	+	0.406695i	−0.000396811	+	0.000472901i
$861$		0			0
$862$	−983.123	−	357.828i	−1.14051	−	0.415113i
$863$			644.463i			0.746771i	0.927676	+	0.373385i	$0.121803\pi$
$863$			644.463i			0.746771i	−0.927676	+	0.373385i	$0.878197\pi$
$864$		0			0
$865$	−576.807			−0.666828
$866$	−414.427	+	1138.63i	−0.478553	+	1.31481i
$867$		0			0
$868$	−377.887	−	317.085i	−0.435353	−	0.365305i
$869$	−674.652	−	118.959i	−0.776354	−	0.136892i
$870$		0			0
$871$	−561.974	+	471.552i	−0.645205	+	0.541391i
$872$	−208.500	+	120.378i	−0.239106	+	0.138048i
$873$		0			0
$874$	−3.05344	+	5.28871i	−0.00349364	+	0.00605116i
$875$	−1770.12	+	312.121i	−2.02300	+	0.356709i
$876$		0			0
$877$	−1564.76	+	569.527i	−1.78422	+	0.649404i	−0.784657	+	0.619931i	$0.787161\pi$
$877$	−1564.76	+	569.527i	−1.78422	+	0.649404i	−0.999566	+	0.0294732i	$0.990617\pi$
$878$	−388.209	−	1066.60i	−0.442152	−	1.21480i
$879$		0			0
$880$	38.1833	+	216.548i	0.0433901	+	0.246077i
$881$	−345.543	−	199.499i	−0.392217	−	0.226447i	0.290903	−	0.956752i	$-0.406044\pi$
$881$	−345.543	−	199.499i	−0.392217	−	0.226447i	−0.683120	+	0.730306i	$0.739378\pi$
$882$		0			0
$883$	−6.95099	−	12.0395i	−0.00787202	−	0.0136347i	0.862063	−	0.506802i	$-0.169172\pi$
$883$	−6.95099	−	12.0395i	−0.00787202	−	0.0136347i	−0.869935	+	0.493167i	$0.835839\pi$
$884$	382.511	+	455.858i	0.432704	+	0.515677i
$885$		0			0
$886$	75.0728	−	425.759i	0.0847322	−	0.480540i
$887$	−540.728	+	644.415i	−0.609615	+	0.726510i	−0.979248	−	0.202667i	$-0.935039\pi$
$887$	−540.728	+	644.415i	−0.609615	+	0.726510i	0.369633	+	0.929178i	$0.379483\pi$
$888$		0			0
$889$	2130.89	+	775.581i	2.39695	+	0.872419i
$890$			114.336i			0.128468i
$891$		0			0
$892$	166.416			0.186565
$893$	10.4697	−	28.7653i	0.0117242	−	0.0322120i
$894$		0			0
$895$	666.396	+	559.173i	0.744577	+	0.624774i
$896$	147.181	+	25.9520i	0.164264	+	0.0289642i
$897$		0			0
$898$	447.188	−	375.235i	0.497982	−	0.417856i
$899$	22.0593	−	12.7359i	0.0245376	−	0.0141668i
$900$		0			0
$901$	−114.674	+	198.621i	−0.127274	+	0.220445i
$902$	−810.694	+	142.947i	−0.898774	+	0.158478i
$903$		0			0
$904$	446.983	−	162.689i	0.494450	−	0.179965i
$905$	417.785	+	1147.86i	0.461641	+	1.26835i
$906$		0			0
$907$	−186.538	−	1057.91i	−0.205664	−	1.16638i	−0.896391	−	0.443265i	$-0.853820\pi$
$907$	−186.538	−	1057.91i	−0.205664	−	1.16638i	0.690726	−	0.723116i	$-0.257291\pi$
$908$	−108.292	−	62.5222i	−0.119264	−	0.0688571i
$909$		0			0
$910$	−702.036	−	1215.96i	−0.771468	−	1.33622i
$911$	437.583	+	521.491i	0.480333	+	0.572438i	0.950731	−	0.310016i	$-0.100334\pi$
$911$	437.583	+	521.491i	0.480333	+	0.572438i	−0.470399	+	0.882454i	$0.655890\pi$
$912$		0			0
$913$	346.417	−	1964.63i	0.379428	−	2.15184i
$914$	−450.230	+	536.563i	−0.492593	+	0.587050i
$915$		0			0
$916$	272.891	+	99.3241i	0.297916	+	0.108432i
$917$		−	2312.66i		−	2.52198i
$918$		0			0
$919$	643.866			0.700616			0.350308	−	0.936635i	$-0.386077\pi$
$919$	643.866			0.700616			0.350308	+	0.936635i	$0.386077\pi$
$920$	−25.8569	+	71.0412i	−0.0281053	+	0.0772187i
$921$		0			0
$922$	883.392	+	741.254i	0.958126	+	0.803963i
$923$	1285.97	+	226.752i	1.39325	+	0.245668i
$924$		0			0
$925$	111.354	−	93.4373i	0.120383	−	0.101013i
$926$	509.823	−	294.347i	0.550565	−	0.317869i
$927$		0			0
$928$	−3.85854	+	6.68319i	−0.00415791	+	0.00720171i
$929$	810.344	−	142.885i	0.872275	−	0.153806i	0.280447	−	0.959870i	$-0.409517\pi$
$929$	810.344	−	142.885i	0.872275	−	0.153806i	0.591828	+	0.806064i	$0.298406\pi$
$930$		0			0
$931$	77.1271	−	28.0720i	0.0828433	−	0.0301525i
$932$	−92.5530	−	254.287i	−0.0993058	−	0.272841i
$933$		0			0
$934$	35.0393	+	198.718i	0.0375154	+	0.212760i
$935$	−762.959	−	440.494i	−0.815999	−	0.471117i
$936$		0			0
$937$	160.172	+	277.427i	0.170942	+	0.296080i	0.938749	−	0.344601i	$-0.111986\pi$
$937$	160.172	+	277.427i	0.170942	+	0.296080i	−0.767808	+	0.640681i	$0.778652\pi$
$938$	−474.483	−	565.467i	−0.505845	−	0.602843i
$939$		0			0
$940$	65.8050	−	373.199i	0.0700053	−	0.397020i
$941$	220.965	−	263.336i	0.234820	−	0.279847i	−0.635747	−	0.771897i	$-0.719308\pi$
$941$	220.965	−	263.336i	0.234820	−	0.279847i	0.870567	+	0.492050i	$0.163752\pi$
$942$		0			0
$943$	−265.958	−	96.8008i	−0.282034	−	0.102652i
$944$			19.4572i			0.0206114i
$945$		0			0
$946$	−1.25928			−0.00133116
$947$	−350.583	+	963.219i	−0.370204	+	1.01713i	0.605079	+	0.796166i	$0.293142\pi$
$947$	−350.583	+	963.219i	−0.370204	+	1.01713i	−0.975283	+	0.220961i	$0.929081\pi$
$948$		0			0
$949$	−972.109	−	815.697i	−1.02435	−	0.859533i
$950$	−7.84446	−	1.38319i	−0.00825733	−	0.00145599i
$951$		0			0
$952$	−458.692	+	384.888i	−0.481819	+	0.404294i
$953$	−1591.27	+	918.721i	−1.66975	+	0.964030i	−0.701978	+	0.712199i	$0.747699\pi$
$953$	−1591.27	+	918.721i	−1.66975	+	0.964030i	−0.967771	+	0.251831i	$0.918967\pi$
$954$		0			0
$955$	−602.965	+	1044.37i	−0.631377	+	1.09358i
$956$	288.653	−	50.8974i	0.301939	−	0.0532399i
$957$		0			0
$958$	−137.573	+	50.0724i	−0.143604	+	0.0522677i
$959$	−221.804	−	609.401i	−0.231287	−	0.635455i
$960$		0			0
$961$	−106.337	−	603.066i	−0.110652	−	0.627540i
$962$	383.801	+	221.587i	0.398961	+	0.230340i
$963$		0			0
$964$	317.139	+	549.302i	0.328983	+	0.569815i
$965$	−327.533	−	390.338i	−0.339412	−	0.404496i
$966$		0			0
$967$	92.1926	−	522.850i	0.0953387	−	0.540693i	−0.899304	−	0.437323i	$-0.855926\pi$
$967$	92.1926	−	522.850i	0.0953387	−	0.540693i	0.994643	−	0.103369i	$-0.0329624\pi$
$968$	−115.268	+	137.372i	−0.119079	+	0.141913i
$969$		0			0
$970$	−568.793	−	207.024i	−0.586385	−	0.213427i
$971$		−	53.7560i		−	0.0553615i	−0.999617	−	0.0276807i	$-0.991188\pi$
$971$		−	53.7560i		−	0.0553615i	0.999617	−	0.0276807i	$-0.00881218\pi$
$972$		0			0
$973$	1847.86			1.89913
$974$	−366.232	+	1006.21i	−0.376008	+	1.03307i
$975$		0			0
$976$	−48.2812	−	40.5127i	−0.0494684	−	0.0415089i
$977$	796.139	+	140.381i	0.814881	+	0.143686i	0.565530	−	0.824728i	$-0.308672\pi$
$977$	796.139	+	140.381i	0.814881	+	0.143686i	0.249351	+	0.968413i	$0.419783\pi$
$978$		0			0
$979$	−207.751	+	174.324i	−0.212208	+	0.178063i
$980$	879.949	−	508.039i	0.897907	−	0.518407i
$981$		0			0
$982$	−401.399	+	695.243i	−0.408756	+	0.707987i
$983$	−846.485	+	149.258i	−0.861124	+	0.151839i	−0.586735	−	0.809779i	$-0.699587\pi$
$983$	−846.485	+	149.258i	−0.861124	+	0.151839i	−0.274389	+	0.961619i	$0.588476\pi$
$984$		0			0
$985$	−165.106	+	60.0936i	−0.167620	+	0.0610087i
$986$	−10.5748	−	29.0540i	−0.0107249	−	0.0294665i
$987$		0			0
$988$	−4.21701	−	23.9158i	−0.00426823	−	0.0242063i
$989$	−0.374950	−	0.216477i	−0.000379120	−	0.000218885i
$990$		0			0
$991$	303.299	+	525.330i	0.306054	+	0.530101i	0.977495	−	0.210957i	$-0.0676579\pi$
$991$	303.299	+	525.330i	0.306054	+	0.530101i	−0.671442	+	0.741057i	$0.734325\pi$
$992$	−67.8931	−	80.9118i	−0.0684406	−	0.0815643i
$993$		0			0
$994$	−228.161	+	1293.97i	−0.229539	+	1.30178i
$995$	−196.899	+	234.656i	−0.197889	+	0.235835i
$996$		0			0
$997$	−1169.32	−	425.597i	−1.17284	−	0.426878i	−0.319171	−	0.947697i	$-0.603404\pi$
$997$	−1169.32	−	425.597i	−1.17284	−	0.426878i	−0.853667	+	0.520819i	$0.825627\pi$
$998$			656.444i			0.657759i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.3.f.a.17.5		36
3.2	odd	2		54.3.f.a.23.2	✓	36
12.11	even	2		432.3.bc.c.401.4		36
27.7	even	9		54.3.f.a.47.2	yes	36
27.13	even	9		1458.3.b.c.1457.24		36
27.14	odd	18		1458.3.b.c.1457.13		36
27.20	odd	18	inner	162.3.f.a.143.5		36
108.7	odd	18		432.3.bc.c.209.4		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.3.f.a.23.2	✓	36	3.2	odd	2
54.3.f.a.47.2	yes	36	27.7	even	9
162.3.f.a.17.5		36	1.1	even	1	trivial
162.3.f.a.143.5		36	27.20	odd	18	inner
432.3.bc.c.209.4		36	108.7	odd	18
432.3.bc.c.401.4		36	12.11	even	2
1458.3.b.c.1457.13		36	27.14	odd	18
1458.3.b.c.1457.24		36	27.13	even	9

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)

\(f(q)\)	\(=\)	\(q+(0.483690 - 1.32893i) q^{2} +(-1.53209 - 1.28558i) q^{4} +(-3.98669 - 0.702961i) q^{5} +(-10.1193 + 8.49107i) q^{7} +(-2.44949 + 1.41421i) q^{8} +O(q^{10})\)	\(q+(0.483690 - 1.32893i) q^{2} +(-1.53209 - 1.28558i) q^{4} +(-3.98669 - 0.702961i) q^{5} +(-10.1193 + 8.49107i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(-2.86250 + 4.95800i) q^{10} +(-13.3731 + 2.35805i) q^{11} +(17.4463 - 6.34995i) q^{13} +(6.38942 + 17.5548i) q^{14} +(0.694593 + 3.93923i) q^{16} +(-13.8790 - 8.01304i) q^{17} +(0.327006 + 0.566391i) q^{19} +(5.20426 + 6.20219i) q^{20} +(-3.33478 + 18.9125i) q^{22} +(-4.24411 + 5.05793i) q^{23} +(-8.09277 - 2.94553i) q^{25} -26.2563i q^{26} +26.4195 q^{28} +(-0.466584 + 1.28193i) q^{29} +(-14.3033 - 12.0019i) q^{31} +(5.57091 + 0.982302i) q^{32} +(-17.3619 + 14.5683i) q^{34} +(46.3112 - 26.7378i) q^{35} +(-8.43940 + 14.6175i) q^{37} +(0.910861 - 0.160609i) q^{38} +(10.7595 - 3.91614i) q^{40} +(14.6609 + 40.2805i) q^{41} +(0.0113866 + 0.0645766i) q^{43} +(23.5203 + 13.5794i) q^{44} +(4.66878 + 8.08657i) q^{46} +(-30.0861 - 35.8552i) q^{47} +(21.7924 - 123.591i) q^{49} +(-7.82877 + 9.32997i) q^{50} +(-34.8927 - 12.6999i) q^{52} -14.3109i q^{53} +54.9722 q^{55} +(12.7788 - 35.1096i) q^{56} +(1.47791 + 1.24011i) q^{58} +(4.79039 + 0.844675i) q^{59} +(-12.0703 + 10.1282i) q^{61} +(-22.8680 + 13.2029i) q^{62} +(4.00000 - 6.92820i) q^{64} +(-74.0169 + 13.0512i) q^{65} +(-37.1304 + 13.5143i) q^{67} +(10.9625 + 30.1192i) q^{68} +(-13.1323 - 74.4770i) q^{70} +(60.9106 + 35.1667i) q^{71} +(-34.1753 - 59.1934i) q^{73} +(15.3435 + 18.2857i) q^{74} +(0.227136 - 1.28815i) q^{76} +(115.304 - 137.414i) q^{77} +(47.4059 + 17.2543i) q^{79} -16.1928i q^{80} +60.6211 q^{82} +(-50.2457 + 138.049i) q^{83} +(49.6984 + 41.7019i) q^{85} +(0.0913252 + 0.0161031i) q^{86} +(29.4226 - 24.6885i) q^{88} +(17.2957 - 9.98568i) q^{89} +(-122.626 + 212.395i) q^{91} +(13.0047 - 2.29308i) q^{92} +(-62.2012 + 22.6394i) q^{94} +(-0.905521 - 2.48790i) q^{95} +(18.3596 + 104.122i) q^{97} +(-153.703 - 88.7402i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{5}+O(q^{10}) \) 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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