LMFDB - Embedded newform 855.2.cj.g.217.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(217,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("855.217");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.cj (of order $12$, degree $4$, 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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 285)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			217.11
Character	$\chi$	$=$	855.217
Dual form			855.2.cj.g.658.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.124631 + 0.465131i) q^{2} +(1.53124 - 0.884060i) q^{4} +(0.780151 - 2.09556i) q^{5} +(2.89550 + 2.89550i) q^{7} +(1.28304 + 1.28304i) q^{8} +O(q^{10})$	\(q+(0.124631 + 0.465131i) q^{2} +(1.53124 - 0.884060i) q^{4} +(0.780151 - 2.09556i) q^{5} +(2.89550 + 2.89550i) q^{7} +(1.28304 + 1.28304i) q^{8} +(1.07194 + 0.101700i) q^{10} +3.71777 q^{11} +(-1.39607 + 5.21021i) q^{13} +(-0.985918 + 1.70766i) q^{14} +(1.33124 - 2.30578i) q^{16} +(-5.48905 + 1.47079i) q^{17} +(3.77513 + 2.17909i) q^{19} +(-0.658004 - 3.89850i) q^{20} +(0.463351 + 1.72925i) q^{22} +(-6.05233 - 1.62172i) q^{23} +(-3.78273 - 3.26970i) q^{25} -2.59743 q^{26} +(6.99350 + 1.87390i) q^{28} +(0.466565 + 0.808113i) q^{29} -4.61021i q^{31} +(4.74375 + 1.27108i) q^{32} +(-1.36822 - 2.36982i) q^{34} +(8.32663 - 3.80877i) q^{35} +(-2.90441 + 2.90441i) q^{37} +(-0.543062 + 2.02751i) q^{38} +(3.68966 - 1.68773i) q^{40} +(3.28171 + 1.89470i) q^{41} +(-2.29305 - 8.55777i) q^{43} +(5.69279 - 3.28673i) q^{44} -3.01724i q^{46} +(0.663204 - 2.47511i) q^{47} +9.76789i q^{49} +(1.04939 - 2.16697i) q^{50} +(2.46842 + 9.21228i) q^{52} +(1.59302 - 5.94524i) q^{53} +(2.90042 - 7.79081i) q^{55} +7.43011i q^{56} +(-0.317730 + 0.317730i) q^{58} +(-2.76120 + 4.78254i) q^{59} +(-2.38157 - 4.12500i) q^{61} +(2.14435 - 0.574577i) q^{62} -2.96010i q^{64} +(9.82915 + 6.99030i) q^{65} +(-7.13011 - 1.91051i) q^{67} +(-7.10477 + 7.10477i) q^{68} +(2.80934 + 3.39828i) q^{70} +(-1.82076 - 1.05122i) q^{71} +(-1.89717 - 7.08033i) q^{73} +(-1.71291 - 0.988950i) q^{74} +(7.70706 - 0.000738608i) q^{76} +(10.7648 + 10.7648i) q^{77} +(3.60177 - 6.23846i) q^{79} +(-3.79333 - 4.58856i) q^{80} +(-0.472278 + 1.76256i) q^{82} +(1.56735 - 1.56735i) q^{83} +(-1.20017 + 12.6501i) q^{85} +(3.69470 - 2.13314i) q^{86} +(4.77006 + 4.77006i) q^{88} +(-1.21167 - 2.09867i) q^{89} +(-19.1285 + 11.0439i) q^{91} +(-10.7012 + 2.86739i) q^{92} +1.23391 q^{94} +(7.51157 - 6.21098i) q^{95} +(-1.83851 - 6.86140i) q^{97} +(-4.54335 + 1.21739i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{5} + 8 q^{7}+O(q^{10}) $ 80 * q - 4 * q^5 + 8 * q^7	$ 80 q - 4 q^{5} + 8 q^{7} + 16 q^{11} + 28 q^{16} + 4 q^{17} + 80 q^{20} - 24 q^{22} - 8 q^{23} + 4 q^{25} + 32 q^{26} - 28 q^{28} - 12 q^{32} + 44 q^{35} + 96 q^{38} + 132 q^{40} - 72 q^{41} + 12 q^{47} + 36 q^{53} + 8 q^{55} + 40 q^{58} - 40 q^{61} + 4 q^{62} - 88 q^{68} - 24 q^{70} + 40 q^{73} + 24 q^{76} + 40 q^{77} - 24 q^{80} - 36 q^{82} + 8 q^{83} + 80 q^{85} - 48 q^{86} + 72 q^{91} - 12 q^{92} - 48 q^{95} + 12 q^{97} - 96 q^{98}+O(q^{100}) $ 80 * q - 4 * q^5 + 8 * q^7 + 16 * q^11 + 28 * q^16 + 4 * q^17 + 80 * q^20 - 24 * q^22 - 8 * q^23 + 4 * q^25 + 32 * q^26 - 28 * q^28 - 12 * q^32 + 44 * q^35 + 96 * q^38 + 132 * q^40 - 72 * q^41 + 12 * q^47 + 36 * q^53 + 8 * q^55 + 40 * q^58 - 40 * q^61 + 4 * q^62 - 88 * q^68 - 24 * q^70 + 40 * q^73 + 24 * q^76 + 40 * q^77 - 24 * q^80 - 36 * q^82 + 8 * q^83 + 80 * q^85 - 48 * q^86 + 72 * q^91 - 12 * q^92 - 48 * q^95 + 12 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.124631	+	0.465131i	0.0881278	+	0.328897i	0.995888	−	0.0905919i	$-0.0288759\pi$
$2$	0.124631	+	0.465131i	0.0881278	+	0.328897i	−0.907760	+	0.419489i	$0.862209\pi$
$3$		0			0
$3$		0			0
$4$	1.53124	−	0.884060i	0.765618	−	0.442030i
$5$	0.780151	−	2.09556i	0.348894	−	0.937162i
$5$	0.780151	−	2.09556i	0.348894	−	0.937162i
$6$		0			0
$7$	2.89550	+	2.89550i	1.09440	+	1.09440i	0.995053	+	0.0993447i	$0.0316747\pi$
$7$	2.89550	+	2.89550i	1.09440	+	1.09440i	0.0993447	+	0.995053i	$0.468325\pi$
$8$	1.28304	+	1.28304i	0.453624	+	0.453624i
$9$		0			0
$10$	1.07194	+	0.101700i	0.338977	+	0.0321603i
$11$	3.71777			1.12095			0.560475	−	0.828171i	$-0.310619\pi$
$11$	3.71777			1.12095			0.560475	+	0.828171i	$0.310619\pi$
$12$		0			0
$13$	−1.39607	+	5.21021i	−0.387201	+	1.44505i	0.447468	+	0.894300i	$0.352326\pi$
$13$	−1.39607	+	5.21021i	−0.387201	+	1.44505i	−0.834669	+	0.550752i	$0.814341\pi$
$14$	−0.985918	+	1.70766i	−0.263498	+	0.456391i
$15$		0			0
$16$	1.33124	−	2.30578i	0.332811	−	0.576446i
$17$	−5.48905	+	1.47079i	−1.33129	+	0.356718i	−0.853196	−	0.521591i	$-0.825339\pi$
$17$	−5.48905	+	1.47079i	−1.33129	+	0.356718i	−0.478094	+	0.878309i	$0.658672\pi$
$18$		0			0
$19$	3.77513	+	2.17909i	0.866073	+	0.499917i
$19$	3.77513	+	2.17909i	0.866073	+	0.499917i
$20$	−0.658004	−	3.89850i	−0.147134	−	0.871730i
$21$		0			0
$22$	0.463351	+	1.72925i	0.0987869	+	0.368678i
$23$	−6.05233	−	1.62172i	−1.26200	−	0.338151i	−0.435037	−	0.900412i	$-0.643265\pi$
$23$	−6.05233	−	1.62172i	−1.26200	−	0.338151i	−0.826960	+	0.562261i	$0.809932\pi$
$24$		0			0
$25$	−3.78273	−	3.26970i	−0.756546	−	0.653940i
$26$	−2.59743			−0.509397
$27$		0			0
$28$	6.99350	+	1.87390i	1.32165	+	0.354134i
$29$	0.466565	+	0.808113i	0.0866389	+	0.150063i	0.906088	−	0.423088i	$-0.139054\pi$
$29$	0.466565	+	0.808113i	0.0866389	+	0.150063i	−0.819450	+	0.573151i	$0.805721\pi$
$30$		0			0
$31$		−	4.61021i		−	0.828018i	−0.910273	−	0.414009i	$-0.864128\pi$
$31$		−	4.61021i		−	0.828018i	0.910273	−	0.414009i	$-0.135872\pi$
$32$	4.74375	+	1.27108i	0.838584	+	0.224698i
$33$		0			0
$34$	−1.36822	−	2.36982i	−0.234647	−	0.406421i
$35$	8.32663	−	3.80877i	1.40746	−	0.643799i
$36$		0			0
$37$	−2.90441	+	2.90441i	−0.477482	+	0.477482i	−0.904326	−	0.426844i	$-0.859626\pi$
$37$	−2.90441	+	2.90441i	−0.477482	+	0.477482i	0.426844	+	0.904326i	$0.359626\pi$
$38$	−0.543062	+	2.02751i	−0.0880963	+	0.328906i
$39$		0			0
$40$	3.68966	−	1.68773i	0.583386	−	0.266853i
$41$	3.28171	+	1.89470i	0.512517	+	0.295902i	0.733868	−	0.679292i	$-0.237713\pi$
$41$	3.28171	+	1.89470i	0.512517	+	0.295902i	−0.221351	+	0.975194i	$0.571047\pi$
$42$		0			0
$43$	−2.29305	−	8.55777i	−0.349687	−	1.30505i	−0.887041	−	0.461691i	$-0.847243\pi$
$43$	−2.29305	−	8.55777i	−0.349687	−	1.30505i	0.537354	−	0.843357i	$-0.319424\pi$
$44$	5.69279	−	3.28673i	0.858220	−	0.495494i
$45$		0			0
$46$		−	3.01724i		−	0.444868i
$47$	0.663204	−	2.47511i	0.0967383	−	0.361032i	−0.900539	−	0.434775i	$-0.856828\pi$
$47$	0.663204	−	2.47511i	0.0967383	−	0.361032i	0.997277	+	0.0737431i	$0.0234945\pi$
$48$		0			0
$49$			9.76789i			1.39541i
$50$	1.04939	−	2.16697i	0.148407	−	0.306456i
$51$		0			0
$52$	2.46842	+	9.21228i	0.342309	+	1.27751i
$53$	1.59302	−	5.94524i	0.218819	−	0.816642i	−0.765969	−	0.642878i	$-0.777740\pi$
$53$	1.59302	−	5.94524i	0.218819	−	0.816642i	0.984787	−	0.173764i	$-0.0555930\pi$
$54$		0			0
$55$	2.90042	−	7.79081i	0.391093	−	1.05051i
$56$			7.43011i			0.992891i
$57$		0			0
$58$	−0.317730	+	0.317730i	−0.0417200	+	0.0417200i
$59$	−2.76120	+	4.78254i	−0.359478	+	0.622633i	−0.987874	−	0.155260i	$-0.950378\pi$
$59$	−2.76120	+	4.78254i	−0.359478	+	0.622633i	0.628396	+	0.777894i	$0.283712\pi$
$60$		0			0
$61$	−2.38157	−	4.12500i	−0.304929	−	0.528152i	0.672317	−	0.740263i	$-0.265299\pi$
$61$	−2.38157	−	4.12500i	−0.304929	−	0.528152i	−0.977245	+	0.212112i	$0.931966\pi$
$62$	2.14435	−	0.574577i	0.272333	−	0.0729714i
$63$		0			0
$64$		−	2.96010i		−	0.370012i
$65$	9.82915	+	6.99030i	1.21916	+	0.867040i
$66$		0			0
$67$	−7.13011	−	1.91051i	−0.871081	−	0.233406i	−0.204526	−	0.978861i	$-0.565565\pi$
$67$	−7.13011	−	1.91051i	−0.871081	−	0.233406i	−0.666555	+	0.745456i	$0.732232\pi$
$68$	−7.10477	+	7.10477i	−0.861580	+	0.861580i
$69$		0			0
$70$	2.80934	+	3.39828i	0.335780	+	0.406172i
$71$	−1.82076	−	1.05122i	−0.216085	−	0.124757i	0.388051	−	0.921638i	$-0.373148\pi$
$71$	−1.82076	−	1.05122i	−0.216085	−	0.124757i	−0.604136	+	0.796881i	$0.706482\pi$
$72$		0			0
$73$	−1.89717	−	7.08033i	−0.222047	−	0.828689i	−0.983566	−	0.180548i	$-0.942213\pi$
$73$	−1.89717	−	7.08033i	−0.222047	−	0.828689i	0.761520	−	0.648142i	$-0.224454\pi$
$74$	−1.71291	−	0.988950i	−0.199122	−	0.114963i
$75$		0			0
$76$	7.70706		0.000738608i	0.884060		8.47241e-5i
$77$	10.7648	+	10.7648i	1.22677	+	1.22677i
$78$		0			0
$79$	3.60177	−	6.23846i	0.405231	−	0.701881i	−0.589117	−	0.808048i	$-0.700524\pi$
$79$	3.60177	−	6.23846i	0.405231	−	0.701881i	0.994348	+	0.106167i	$0.0338577\pi$
$80$	−3.79333	−	4.58856i	−0.424107	−	0.513016i
$81$		0			0
$82$	−0.472278	+	1.76256i	−0.0521544	+	0.194643i
$83$	1.56735	−	1.56735i	0.172039	−	0.172039i	−0.615835	−	0.787875i	$-0.711181\pi$
$83$	1.56735	−	1.56735i	0.172039	−	0.172039i	0.787875	+	0.615835i	$0.211181\pi$
$84$		0			0
$85$	−1.20017	+	12.6501i	−0.130176	+	1.37209i
$86$	3.69470	−	2.13314i	0.398410	−	0.230022i
$87$		0			0
$88$	4.77006	+	4.77006i	0.508490	+	0.508490i
$89$	−1.21167	−	2.09867i	−0.128436	−	0.222458i	0.794635	−	0.607088i	$-0.207662\pi$
$89$	−1.21167	−	2.09867i	−0.128436	−	0.222458i	−0.923071	+	0.384630i	$0.874329\pi$
$90$		0			0
$91$	−19.1285	+	11.0439i	−2.00521	+	1.15771i
$92$	−10.7012	+	2.86739i	−1.11568	+	0.298946i
$93$		0			0
$94$	1.23391			0.127268
$95$	7.51157	−	6.21098i	0.770671	−	0.637233i
$96$		0			0
$97$	−1.83851	−	6.86140i	−0.186672	−	0.696670i	−0.994266	−	0.106931i	$-0.965897\pi$
$97$	−1.83851	−	6.86140i	−0.186672	−	0.696670i	0.807594	−	0.589738i	$-0.200769\pi$
$98$	−4.54335	+	1.21739i	−0.458948	+	0.122975i
$99$		0			0
$100$	−8.68287	−	1.66253i	−0.868287	−	0.166253i
$101$	−3.88671	−	6.73198i	−0.386742	−	0.669857i	0.605267	−	0.796022i	$-0.293066\pi$
$101$	−3.88671	−	6.73198i	−0.386742	−	0.669857i	−0.992009	+	0.126165i	$0.959733\pi$
$102$		0			0
$103$	6.77888	+	6.77888i	0.667943	+	0.667943i	0.957240	−	0.289296i	$-0.0934213\pi$
$103$	6.77888	+	6.77888i	0.667943	+	0.667943i	−0.289296	+	0.957240i	$0.593421\pi$
$104$	−8.47615	+	4.89371i	−0.831154	+	0.479867i
$105$		0			0
$106$	2.96386			0.287875
$107$	−7.33831	+	7.33831i	−0.709421	+	0.709421i	−0.966413	−	0.256992i	$-0.917269\pi$
$107$	−7.33831	+	7.33831i	−0.709421	+	0.709421i	0.256992	+	0.966413i	$0.417269\pi$
$108$		0			0
$109$	0.945425	−	1.63752i	0.0905553	−	0.156846i	−0.817190	−	0.576369i	$-0.804469\pi$
$109$	0.945425	−	1.63752i	0.0905553	−	0.156846i	0.907745	+	0.419522i	$0.137802\pi$
$110$	3.98523	+	0.378096i	0.379977	+	0.0360501i
$111$		0			0
$112$	10.5310	−	2.82178i	0.995089	−	0.266633i
$113$	12.2144	+	12.2144i	1.14903	+	1.14903i	0.986744	+	0.162287i	$0.0518871\pi$
$113$	12.2144	+	12.2144i	1.14903	+	1.14903i	0.162287	+	0.986744i	$0.448113\pi$
$114$		0			0
$115$	−8.12013	+	11.4178i	−0.757206	+	1.06472i
$116$	1.42884	+	0.824942i	0.132665	+	0.0765940i
$117$		0			0
$118$	−2.56864	−	0.688265i	−0.236462	−	0.0633599i
$119$	−20.1522	−	11.6349i	−1.84735	−	1.06657i
$120$		0			0
$121$	2.82183			0.256530
$122$	1.62185	−	1.62185i	0.146835	−	0.146835i
$123$		0			0
$124$	−4.07570	−	7.05932i	−0.366009	−	0.633946i
$125$	−9.80295	+	5.37607i	−0.876803	+	0.480850i
$126$		0			0
$127$	8.86900	+	2.37644i	0.786997	+	0.210875i	0.629867	−	0.776703i	$-0.283109\pi$
$127$	8.86900	+	2.37644i	0.786997	+	0.210875i	0.157130	+	0.987578i	$0.449776\pi$
$128$	10.8643	−	2.91109i	0.960280	−	0.257306i
$129$		0			0
$130$	−2.02638	+	5.44306i	−0.177726	+	0.477388i
$131$	−6.67488	+	11.5612i	−0.583187	+	1.01011i	0.411912	+	0.911224i	$0.364861\pi$
$131$	−6.67488	+	11.5612i	−0.583187	+	1.01011i	−0.995099	+	0.0988859i	$0.968472\pi$
$132$		0			0
$133$	4.62134	+	17.2405i	0.400721	+	1.49494i
$134$		−	3.55454i		−	0.307066i
$135$		0			0
$136$	−8.92977	−	5.15560i	−0.765721	−	0.442089i
$137$	3.39547	−	12.6721i	0.290095	−	1.08265i	−0.654941	−	0.755680i	$-0.727306\pi$
$137$	3.39547	−	12.6721i	0.290095	−	1.08265i	0.945035	−	0.326968i	$-0.106027\pi$
$138$		0			0
$139$	10.0273	−	5.78926i	0.850504	−	0.491039i	−0.0103168	−	0.999947i	$-0.503284\pi$
$139$	10.0273	−	5.78926i	0.850504	−	0.491039i	0.860821	+	0.508908i	$0.169951\pi$
$140$	9.38286	−	13.1934i	0.792996	−	1.11504i
$141$		0			0
$142$	0.262030	−	0.977908i	0.0219890	−	0.0820642i
$143$	−5.19028	+	19.3704i	−0.434033	+	1.61983i
$144$		0			0
$145$	2.05744	−	0.347263i	0.170861	−	0.0288386i
$146$	3.05683	−	1.76486i	0.252985	−	0.146061i
$147$		0			0
$148$	−1.87967	+	7.01501i	−0.154508	+	0.576630i
$149$	−7.79701	−	4.50161i	−0.638756	−	0.368786i	0.145379	−	0.989376i	$-0.453560\pi$
$149$	−7.79701	−	4.50161i	−0.638756	−	0.368786i	−0.784135	+	0.620590i	$0.786893\pi$
$150$		0			0
$151$		−	11.2644i		−	0.916687i	−0.888775	−	0.458344i	$-0.848443\pi$
$151$		−	11.2644i		−	0.916687i	0.888775	−	0.458344i	$-0.151557\pi$
$152$	2.04779	+	7.63951i	0.166097	+	0.619646i
$153$		0			0
$154$	−3.66542	+	6.34869i	−0.295368	+	0.511592i
$155$	−9.66096	−	3.59666i	−0.775987	−	0.288890i
$156$		0			0
$157$	−17.1427	+	4.59336i	−1.36813	+	0.366590i	−0.866797	−	0.498662i	$-0.833825\pi$
$157$	−17.1427	+	4.59336i	−1.36813	+	0.366590i	−0.501337	+	0.865252i	$0.667158\pi$
$158$	3.35059	+	0.897789i	0.266559	+	0.0714243i
$159$		0			0
$160$	6.36446	−	8.94916i	0.503155	−	0.707493i
$161$	−12.8289	−	22.2202i	−1.01106	−	1.75120i
$162$		0			0
$163$	8.14240	−	8.14240i	0.637762	−	0.637762i	−0.312241	−	0.950003i	$-0.601080\pi$
$163$	8.14240	−	8.14240i	0.637762	−	0.637762i	0.950003	+	0.312241i	$0.101080\pi$
$164$	6.70010			0.523190
$165$		0			0
$166$	0.924366	+	0.533683i	0.0717447	+	0.0414218i
$167$	−16.7150	−	4.47877i	−1.29345	−	0.346578i	−0.454478	−	0.890758i	$-0.650174\pi$
$167$	−16.7150	−	4.47877i	−1.29345	−	0.346578i	−0.838968	+	0.544180i	$0.816841\pi$
$168$		0			0
$169$	−13.9389	−	8.04766i	−1.07223	−	0.619050i
$170$	−6.03351	+	1.01836i	−0.462749	+	0.0781047i
$171$		0			0
$172$	−11.0768	−	11.0768i	−0.844597	−	0.844597i
$173$	21.8115	−	5.84437i	1.65830	−	0.444339i	0.696377	−	0.717676i	$-0.254794\pi$
$173$	21.8115	−	5.84437i	1.65830	−	0.444339i	0.961918	+	0.273337i	$0.0881275\pi$
$174$		0			0
$175$	−1.48547	−	20.4203i	−0.112291	−	1.54363i
$176$	4.94926	−	8.57237i	0.373065	−	0.646167i
$177$		0			0
$178$	0.825144	−	0.825144i	0.0618472	−	0.0618472i
$179$	−23.9774			−1.79215			−0.896076	−	0.443901i	$-0.853594\pi$
$179$	−23.9774			−1.79215			−0.896076	+	0.443901i	$0.853594\pi$
$180$		0			0
$181$	18.8155	−	10.8631i	1.39855	−	0.807451i	0.404305	−	0.914624i	$-0.367513\pi$
$181$	18.8155	−	10.8631i	1.39855	−	0.807451i	0.994240	+	0.107174i	$0.0341801\pi$
$182$	−7.52086	−	7.52086i	−0.557483	−	0.557483i
$183$		0			0
$184$	−5.68466	−	9.84613i	−0.419079	−	0.725866i
$185$	3.82048	+	8.35224i	0.280888	+	0.614069i
$186$		0			0
$187$	−20.4070	+	5.46805i	−1.49231	+	0.399863i
$188$	−1.17262	−	4.37629i	−0.0855224	−	0.319174i
$189$		0			0
$190$	3.82510	+	2.71978i	0.277502	+	0.197314i
$191$	17.4548			1.26298			0.631491	−	0.775383i	$-0.282443\pi$
$191$	17.4548			1.26298			0.631491	+	0.775383i	$0.282443\pi$
$192$		0			0
$193$	−17.0952	+	4.58063i	−1.23054	+	0.329721i	−0.814788	−	0.579759i	$-0.803147\pi$
$193$	−17.0952	+	4.58063i	−1.23054	+	0.329721i	−0.415748	+	0.909480i	$0.636480\pi$
$194$	2.96232	−	1.71029i	0.212682	−	0.122792i
$195$		0			0
$196$	8.63540	+	14.9570i	0.616814	+	1.06835i
$197$	−5.50658	−	5.50658i	−0.392328	−	0.392328i	0.483189	−	0.875516i	$-0.339479\pi$
$197$	−5.50658	−	5.50658i	−0.392328	−	0.392328i	−0.875516	+	0.483189i	$0.839479\pi$
$198$		0			0
$199$	−10.6236	+	6.13351i	−0.753084	+	0.434793i	−0.826807	−	0.562486i	$-0.809845\pi$
$199$	−10.6236	+	6.13351i	−0.753084	+	0.434793i	0.0737233	+	0.997279i	$0.476512\pi$
$200$	−0.658237	−	9.04858i	−0.0465444	−	0.639831i
$201$		0			0
$202$	2.64685	−	2.64685i	0.186231	−	0.186231i
$203$	−0.988956	+	3.69084i	−0.0694111	+	0.259046i
$204$		0			0
$205$	6.53068	−	5.39887i	0.456122	−	0.377073i
$206$	−2.30821	+	3.99793i	−0.160820	+	0.278549i
$207$		0			0
$208$	10.1551	+	10.1551i	0.704130	+	0.704130i
$209$	14.0351	+	8.10135i	0.970825	+	0.560382i
$210$		0			0
$211$	4.81351	+	2.77908i	0.331375	+	0.191320i	0.656452	−	0.754368i	$-0.272057\pi$
$211$	4.81351	+	2.77908i	0.331375	+	0.191320i	−0.325076	+	0.945688i	$0.605390\pi$
$212$	−2.81666	−	10.5119i	−0.193449	−	0.721960i
$213$		0			0
$214$	−4.32786	−	2.49869i	−0.295846	−	0.170807i
$215$	−19.7222	−	1.87114i	−1.34505	−	0.127610i
$216$		0			0
$217$	13.3489	−	13.3489i	0.906181	−	0.906181i
$218$	0.879493	+	0.235660i	0.0595668	+	0.0159609i
$219$		0			0
$220$	−2.44631	−	14.4937i	−0.164930	−	0.977166i
$221$		−	30.6524i		−	2.06190i
$222$		0			0
$223$	8.94886	−	2.39784i	0.599260	−	0.160571i	0.0535782	−	0.998564i	$-0.482937\pi$
$223$	8.94886	−	2.39784i	0.599260	−	0.160571i	0.545682	+	0.837992i	$0.316271\pi$
$224$	10.0551	+	17.4160i	0.671835	+	1.16365i
$225$		0			0
$226$	−4.15899	+	7.20358i	−0.276652	+	0.479175i
$227$	−6.44800	+	6.44800i	−0.427969	+	0.427969i	−0.887936	−	0.459967i	$-0.847861\pi$
$227$	−6.44800	+	6.44800i	−0.427969	+	0.427969i	0.459967	+	0.887936i	$0.347861\pi$
$228$		0			0
$229$			21.8075i			1.44108i	0.693413	+	0.720540i	$0.256106\pi$
$229$			21.8075i			1.44108i	−0.693413	+	0.720540i	$0.743894\pi$
$230$	−6.32281	−	2.35390i	−0.416913	−	0.155212i
$231$		0			0
$232$	−0.438222	+	1.63547i	−0.0287707	+	0.107374i
$233$	0.677929	+	2.53007i	0.0444126	+	0.165750i	0.984570	−	0.174990i	$-0.0559892\pi$
$233$	0.677929	+	2.53007i	0.0444126	+	0.165750i	−0.940158	+	0.340740i	$0.889323\pi$
$234$		0			0
$235$	−4.66934	−	3.32074i	−0.304594	−	0.216621i
$236$			9.76426i			0.635599i
$237$		0			0
$238$	2.90015	−	10.8235i	0.187989	−	0.701583i
$239$		−	2.16933i		−	0.140322i	−0.997536	−	0.0701611i	$-0.977649\pi$
$239$		−	2.16933i		−	0.140322i	0.997536	−	0.0701611i	$-0.0223513\pi$
$240$		0			0
$241$	−18.8948	+	10.9089i	−1.21712	+	0.702707i	−0.964302	−	0.264806i	$-0.914692\pi$
$241$	−18.8948	+	10.9089i	−1.21712	+	0.702707i	−0.252822	+	0.967513i	$0.581359\pi$
$242$	0.351688	+	1.31252i	0.0226074	+	0.0843719i
$243$		0			0
$244$	−7.29349	−	4.21090i	−0.466918	−	0.269575i
$245$	20.4692	+	7.62043i	1.30773	+	0.486851i
$246$		0			0
$247$	−16.6239	+	16.6270i	−1.05775	+	1.05795i
$248$	5.91510	−	5.91510i	0.375609	−	0.375609i
$249$		0			0
$250$	−3.72233	−	3.88963i	−0.235421	−	0.246002i
$251$	12.9121	+	22.3645i	0.815007	+	1.41163i	0.909323	+	0.416091i	$0.136600\pi$
$251$	12.9121	+	22.3645i	0.815007	+	1.41163i	−0.0943157	+	0.995542i	$0.530066\pi$
$252$		0			0
$253$	−22.5012	−	6.02917i	−1.41464	−	0.379051i
$254$			4.42143i			0.277425i
$255$		0			0
$256$	−0.252023	−	0.436517i	−0.0157514	−	0.0272823i
$257$	−4.61816	−	1.23743i	−0.288073	−	0.0771889i	0.111889	−	0.993721i	$-0.464310\pi$
$257$	−4.61816	−	1.23743i	−0.288073	−	0.0771889i	−0.399962	+	0.916532i	$0.630977\pi$
$258$		0			0
$259$	−16.8195			−1.04511
$260$	21.2306	+	2.01424i	1.31667	+	0.124918i
$261$		0			0
$262$	−6.20939	−	1.66380i	−0.383617	−	0.102790i
$263$	1.14726	+	4.28163i	0.0707430	+	0.264016i	0.992234	−	0.124382i	$-0.0396950\pi$
$263$	1.14726	+	4.28163i	0.0707430	+	0.264016i	−0.921491	+	0.388399i	$0.873028\pi$
$264$		0			0
$265$	−11.2158	−	7.97646i	−0.688981	−	0.489990i
$266$	−7.44311	+	4.29823i	−0.456366	+	0.263541i
$267$		0			0
$268$	−12.6069	+	3.37801i	−0.770088	+	0.206344i
$269$	−11.4241	+	19.7872i	−0.696541	+	1.20644i	0.273118	+	0.961981i	$0.411945\pi$
$269$	−11.4241	+	19.7872i	−0.696541	+	1.20644i	−0.969658	+	0.244463i	$0.921388\pi$
$270$		0			0
$271$	−12.3950	+	21.4688i	−0.752944	+	1.30414i	0.193446	+	0.981111i	$0.438034\pi$
$271$	−12.3950	+	21.4688i	−0.752944	+	1.30414i	−0.946390	+	0.323027i	$0.895300\pi$
$272$	−3.91595	+	14.6145i	−0.237439	+	0.886136i
$273$		0			0
$274$	6.31736			0.381645
$275$	−14.0633	−	12.1560i	−0.848051	−	0.733035i
$276$		0			0
$277$	7.47470	+	7.47470i	0.449111	+	0.449111i	0.895059	−	0.445948i	$-0.147133\pi$
$277$	7.47470	+	7.47470i	0.449111	+	0.449111i	−0.445948	+	0.895059i	$0.647133\pi$
$278$	3.94248	+	3.94248i	0.236454	+	0.236454i
$279$		0			0
$280$	15.5702	+	5.79661i	0.930500	+	0.346414i
$281$	−4.64052	+	2.67921i	−0.276830	+	0.159828i	−0.631988	−	0.774979i	$-0.717761\pi$
$281$	−4.64052	+	2.67921i	−0.276830	+	0.159828i	0.355157	+	0.934807i	$0.384427\pi$
$282$		0			0
$283$	−3.39691	−	12.6774i	−0.201925	−	0.753595i	−0.990365	−	0.138483i	$-0.955777\pi$
$283$	−3.39691	−	12.6774i	−0.201925	−	0.753595i	0.788440	−	0.615112i	$-0.210889\pi$
$284$	−3.71736			−0.220585
$285$		0			0
$286$	−9.65663			−0.571009
$287$	4.01611	+	14.9883i	0.237063	+	0.884732i
$288$		0			0
$289$	13.2440	−	7.64642i	0.779058	−	0.449789i
$290$	0.417945	+	0.913699i	0.0245426	+	0.0536543i
$291$		0			0
$292$	−9.16445	−	9.16445i	−0.536309	−	0.536309i
$293$	20.8453	+	20.8453i	1.21779	+	1.21779i	0.968403	+	0.249389i	$0.0802299\pi$
$293$	20.8453	+	20.8453i	1.21779	+	1.21779i	0.249389	+	0.968403i	$0.419770\pi$
$294$		0			0
$295$	7.86793	+	9.51735i	0.458089	+	0.554122i
$296$	−7.45297			−0.433195
$297$		0			0
$298$	1.12208	−	4.18767i	0.0650006	−	0.242585i
$299$	16.8990	−	29.2699i	0.977292	−	1.69272i
$300$		0			0
$301$	18.1395	−	31.4186i	1.04555	−	1.81094i
$302$	5.23944	−	1.40390i	0.301496	−	0.0807856i
$303$		0			0
$304$	10.0501	−	5.80372i	0.576414	−	0.332866i
$305$	−10.5022	+	1.77260i	−0.601352	+	0.101499i
$306$		0			0
$307$	0.815039	+	3.04177i	0.0465167	+	0.173603i	0.985276	−	0.170970i	$-0.0546903\pi$
$307$	0.815039	+	3.04177i	0.0465167	+	0.173603i	−0.938759	+	0.344573i	$0.888024\pi$
$308$	26.0002	+	6.96675i	1.48150	+	0.396967i
$309$		0			0
$310$	0.468857	−	4.94187i	0.0266293	−	0.280679i
$311$	−18.8449			−1.06860			−0.534298	−	0.845296i	$-0.679424\pi$
$311$	−18.8449			−1.06860			−0.534298	+	0.845296i	$0.679424\pi$
$312$		0			0
$313$	21.0639	+	5.64405i	1.19060	+	0.319020i	0.799123	−	0.601167i	$-0.205297\pi$
$313$	21.0639	+	5.64405i	1.19060	+	0.319020i	0.391477	+	0.920188i	$0.371964\pi$
$314$	−4.27303	−	7.40111i	−0.241141	−	0.417669i
$315$		0			0
$316$		−	12.7367i		−	0.716497i
$317$	3.17508	+	0.850759i	0.178330	+	0.0477834i	0.346879	−	0.937910i	$-0.387241\pi$
$317$	3.17508	+	0.850759i	0.178330	+	0.0477834i	−0.168549	+	0.985693i	$0.553908\pi$
$318$		0			0
$319$	1.73458	+	3.00438i	0.0971179	+	0.168213i
$320$	−6.20306	−	2.30932i	−0.346761	−	0.129095i
$321$		0			0
$322$	8.73644	−	8.73644i	0.486863	−	0.486863i
$323$	−23.9268	−	6.40871i	−1.33132	−	0.356590i
$324$		0			0
$325$	22.3168	−	15.1441i	1.23791	−	0.840043i
$326$	4.80208	+	2.77248i	0.265963	+	0.153554i
$327$		0			0
$328$	1.77960	+	6.64155i	0.0982619	+	0.366719i
$329$	9.08701	−	5.24639i	0.500983	−	0.289243i
$330$		0			0
$331$			28.0361i			1.54100i	0.637438	+	0.770502i	$0.279994\pi$
$331$			28.0361i			1.54100i	−0.637438	+	0.770502i	$0.720006\pi$
$332$	1.01435	−	3.78562i	0.0556700	−	0.207763i
$333$		0			0
$334$		−	8.33286i		−	0.455954i
$335$	−9.56614	+	13.4511i	−0.522654	+	0.734911i
$336$		0			0
$337$	−3.78618	−	14.1302i	−0.206246	−	0.769721i	−0.989066	−	0.147473i	$-0.952886\pi$
$337$	−3.78618	−	14.1302i	−0.206246	−	0.769721i	0.782820	−	0.622248i	$-0.213781\pi$
$338$	2.00598	−	7.48643i	0.109111	−	0.407208i
$339$		0			0
$340$	9.34567	+	20.4312i	0.506840	+	1.10804i
$341$		−	17.1397i		−	0.928167i
$342$		0			0
$343$	−8.01444	+	8.01444i	−0.432739	+	0.432739i
$344$	8.03791	−	13.9221i	0.433375	−	0.750628i
$345$		0			0
$346$	5.43679	+	9.41680i	0.292284	+	0.506250i
$347$	12.3779	−	3.31664i	0.664480	−	0.178047i	0.0892128	−	0.996013i	$-0.471565\pi$
$347$	12.3779	−	3.31664i	0.664480	−	0.178047i	0.575267	+	0.817966i	$0.304898\pi$
$348$		0			0
$349$			7.15359i			0.382923i	0.981500	+	0.191461i	$0.0613227\pi$
$349$			7.15359i			0.382923i	−0.981500	+	0.191461i	$0.938677\pi$
$350$	9.31300	−	3.23596i	0.497801	−	0.172969i
$351$		0			0
$352$	17.6362	+	4.72560i	0.940011	+	0.251875i
$353$	17.4674	−	17.4674i	0.929696	−	0.929696i	−0.0679902	−	0.997686i	$-0.521659\pi$
$353$	17.4674	−	17.4674i	0.929696	−	0.929696i	0.997686	+	0.0679902i	$0.0216587\pi$
$354$		0			0
$355$	−3.62336	+	2.99541i	−0.192308	+	0.158980i
$356$	−3.71070	−	2.14237i	−0.196667	−	0.113546i
$357$		0			0
$358$	−2.98833	−	11.1526i	−0.157938	−	0.589434i
$359$	19.1674	+	11.0663i	1.01162	+	0.584058i	0.911665	−	0.410934i	$-0.134797\pi$
$359$	19.1674	+	11.0663i	1.01162	+	0.584058i	0.0999529	+	0.994992i	$0.468131\pi$
$360$		0			0
$361$	9.50315	+	16.4527i	0.500166	+	0.865930i
$362$	7.39779	+	7.39779i	0.388819	+	0.388819i
$363$		0			0
$364$	−19.5269	+	33.8215i	−1.02349	+	1.77273i
$365$	−16.3173	−	1.54809i	−0.854087	−	0.0810310i
$366$		0			0
$367$	−0.263733	+	0.984264i	−0.0137667	+	0.0513782i	−0.972468	−	0.233038i	$-0.925133\pi$
$367$	−0.263733	+	0.984264i	−0.0137667	+	0.0513782i	0.958701	+	0.284417i	$0.0917999\pi$
$368$	−11.7964	+	11.7964i	−0.614932	+	0.614932i
$369$		0			0
$370$	−3.40873	+	2.81798i	−0.177212	+	0.146500i
$371$	21.8271	−	12.6019i	1.13321	−	0.654256i
$372$		0			0
$373$	−9.79894	−	9.79894i	−0.507370	−	0.507370i	0.406348	−	0.913718i	$-0.366802\pi$
$373$	−9.79894	−	9.79894i	−0.507370	−	0.507370i	−0.913718	+	0.406348i	$0.866802\pi$
$374$	−5.08672	−	8.81045i	−0.263028	−	0.455577i
$375$		0			0
$376$	4.02660	−	2.32476i	0.207656	−	0.119890i
$377$	−4.86180	+	1.30272i	−0.250395	+	0.0670932i
$378$		0			0
$379$	−1.00845			−0.0518004			−0.0259002	−	0.999665i	$-0.508245\pi$
$379$	−1.00845			−0.0518004			−0.0259002	+	0.999665i	$0.508245\pi$
$380$	6.01112	−	16.1512i	0.308364	−	0.828537i
$381$		0			0
$382$	2.17541	+	8.11875i	0.111304	+	0.415391i
$383$	−20.0380	+	5.36916i	−1.02389	+	0.274351i	−0.731424	−	0.681923i	$-0.761144\pi$
$383$	−20.0380	+	5.36916i	−1.02389	+	0.274351i	−0.292470	+	0.956275i	$0.594477\pi$
$384$		0			0
$385$	30.9565	−	14.1601i	1.57769	−	0.721667i
$386$	−4.26119	−	7.38060i	−0.216889	−	0.375663i
$387$		0			0
$388$	−8.88108	−	8.88108i	−0.450869	−	0.450869i
$389$	3.83301	−	2.21299i	0.194342	−	0.112203i	−0.399672	−	0.916658i	$-0.630876\pi$
$389$	3.83301	−	2.21299i	0.194342	−	0.112203i	0.594013	+	0.804455i	$0.297543\pi$
$390$		0			0
$391$	35.6067			1.80071
$392$	−12.5326	+	12.5326i	−0.632993	+	0.632993i
$393$		0			0
$394$	1.87499	−	3.24758i	0.0944606	−	0.163611i
$395$	−10.2631	−	12.4147i	−0.516394	−	0.624649i
$396$		0			0
$397$	19.7655	−	5.29614i	0.992000	−	0.265806i	0.273910	−	0.961755i	$-0.411683\pi$
$397$	19.7655	−	5.29614i	0.992000	−	0.265806i	0.718091	+	0.695950i	$0.245016\pi$
$398$	−4.17692	−	4.17692i	−0.209370	−	0.209370i
$399$		0			0
$400$	−12.5750	+	4.36938i	−0.628748	+	0.218469i
$401$	5.16995	+	2.98487i	0.258175	+	0.149057i	0.623502	−	0.781822i	$-0.285709\pi$
$401$	5.16995	+	2.98487i	0.258175	+	0.149057i	−0.365327	+	0.930879i	$0.619043\pi$
$402$		0			0
$403$	24.0201	+	6.43618i	1.19653	+	0.320609i
$404$	−11.9030	−	6.87217i	−0.592194	−	0.341903i
$405$		0			0
$406$	−1.83998			−0.0913166
$407$	−10.7979	+	10.7979i	−0.535234	+	0.535234i
$408$		0			0
$409$	14.4073	+	24.9541i	0.712393	+	1.23390i	0.963957	+	0.266060i	$0.0857218\pi$
$409$	14.4073	+	24.9541i	0.712393	+	1.23390i	−0.251564	+	0.967841i	$0.580945\pi$
$410$	3.32511	+	2.36475i	0.164215	+	0.116787i
$411$		0			0
$412$	16.3730	+	4.38714i	0.806641	+	0.216139i
$413$	−21.8429	+	5.85279i	−1.07482	+	0.287997i
$414$		0			0
$415$	−2.06171	−	4.50725i	−0.101205	−	0.221252i
$416$	−13.2452	+	22.9414i	−0.649400	+	1.12479i
$417$		0			0
$418$	−2.01898	+	7.53782i	−0.0987515	+	0.368687i
$419$			2.62471i			0.128226i	0.997943	+	0.0641128i	$0.0204217\pi$
$419$			2.62471i			0.128226i	−0.997943	+	0.0641128i	$0.979578\pi$
$420$		0			0
$421$	−17.8807	−	10.3234i	−0.871450	−	0.503132i	−0.00361991	−	0.999993i	$-0.501152\pi$
$421$	−17.8807	−	10.3234i	−0.871450	−	0.503132i	−0.867830	+	0.496862i	$0.834486\pi$
$422$	−0.692722	+	2.58527i	−0.0337212	+	0.125849i
$423$		0			0
$424$	9.67192	−	5.58409i	0.469710	−	0.271187i
$425$	25.5726	+	12.3840i	1.24045	+	0.600710i
$426$		0			0
$427$	5.04811	−	18.8398i	0.244295	−	0.911721i
$428$	−4.74918	+	17.7242i	−0.229560	+	0.856731i
$429$		0			0
$430$	−1.58769	−	9.40663i	−0.0765652	−	0.453628i
$431$	27.8030	−	16.0521i	1.33922	−	0.773201i	0.352531	−	0.935800i	$-0.385321\pi$
$431$	27.8030	−	16.0521i	1.33922	−	0.773201i	0.986692	+	0.162600i	$0.0519879\pi$
$432$		0			0
$433$	−5.55708	+	20.7393i	−0.267056	+	0.996668i	0.693923	+	0.720049i	$0.255881\pi$
$433$	−5.55708	+	20.7393i	−0.267056	+	0.996668i	−0.960980	+	0.276619i	$0.910786\pi$
$434$	7.87267	+	4.54529i	0.377900	+	0.218181i
$435$		0			0
$436$		−	3.34325i		−	0.160113i
$437$	−19.3144	−	19.3107i	−0.923935	−	0.923757i
$438$		0			0
$439$	−18.1902	+	31.5063i	−0.868170	+	1.50371i	−0.00430435	+	0.999991i	$0.501370\pi$
$439$	−18.1902	+	31.5063i	−0.868170	+	1.50371i	−0.863865	+	0.503723i	$0.831963\pi$
$440$	13.7173	−	6.27458i	0.653947	−	0.299129i
$441$		0			0
$442$	14.2574	−	3.82026i	0.678155	−	0.181711i
$443$	5.76798	+	1.54552i	0.274045	+	0.0734301i	0.393224	−	0.919443i	$-0.371360\pi$
$443$	5.76798	+	1.54552i	0.274045	+	0.0734301i	−0.119179	+	0.992873i	$0.538026\pi$
$444$		0			0
$445$	−5.34317	+	0.901841i	−0.253290	+	0.0427514i
$446$	2.23062	+	3.86355i	0.105623	+	0.182944i
$447$		0			0
$448$	8.57097	−	8.57097i	0.404940	−	0.404940i
$449$	−20.3019			−0.958105			−0.479052	−	0.877786i	$-0.659020\pi$
$449$	−20.3019			−0.958105			−0.479052	+	0.877786i	$0.659020\pi$
$450$		0			0
$451$	12.2007	+	7.04405i	0.574506	+	0.331691i
$452$	29.5013	+	7.90485i	1.38763	+	0.371813i
$453$		0			0
$454$	−3.80279	−	2.19554i	−0.178474	−	0.103042i
$455$	8.21992	+	48.7008i	0.385356	+	2.28313i
$456$		0			0
$457$	2.24726	+	2.24726i	0.105123	+	0.105123i	0.757712	−	0.652589i	$-0.226317\pi$
$457$	2.24726	+	2.24726i	0.105123	+	0.105123i	−0.652589	+	0.757712i	$0.726317\pi$
$458$	−10.1433	+	2.71790i	−0.473967	+	0.126999i
$459$		0			0
$460$	−2.33980	+	24.6621i	−0.109094	+	1.14987i
$461$	0.147735	−	0.255884i	0.00688069	−	0.0119177i	−0.862565	−	0.505947i	$-0.831143\pi$
$461$	0.147735	−	0.255884i	0.00688069	−	0.0119177i	0.869445	+	0.494029i	$0.164476\pi$
$462$		0			0
$463$	0.524606	−	0.524606i	0.0243805	−	0.0243805i	−0.694811	−	0.719192i	$-0.744512\pi$
$463$	0.524606	−	0.524606i	0.0243805	−	0.0243805i	0.719192	+	0.694811i	$0.244512\pi$
$464$	2.48445			0.115337
$465$		0			0
$466$	−1.09232	+	0.630652i	−0.0506008	+	0.0292144i
$467$	−0.823794	−	0.823794i	−0.0381206	−	0.0381206i	0.687790	−	0.725910i	$-0.258581\pi$
$467$	−0.823794	−	0.823794i	−0.0381206	−	0.0381206i	−0.725910	+	0.687790i	$0.758581\pi$
$468$		0			0
$469$	−15.1134	−	26.1771i	−0.697871	−	1.20875i
$470$	0.962634	−	2.58573i	0.0444030	−	0.119271i
$471$		0			0
$472$	−9.67894	+	2.59346i	−0.445509	+	0.119374i
$473$	−8.52503	−	31.8159i	−0.391981	−	1.46289i
$474$		0			0
$475$	−7.15532	−	20.5864i	−0.328308	−	0.944571i
$476$	−41.1438			−1.88582
$477$		0			0
$478$	1.00902	−	0.270366i	0.0461516	−	0.0123663i
$479$	1.45293	−	0.838847i	0.0663859	−	0.0383279i	−0.466440	−	0.884553i	$-0.654464\pi$
$479$	1.45293	−	0.838847i	0.0663859	−	0.0383279i	0.532826	+	0.846225i	$0.321130\pi$
$480$		0			0
$481$	−11.0778	−	19.1873i	−0.505105	−	0.874868i
$482$	−7.42898	−	7.42898i	−0.338381	−	0.338381i
$483$		0			0
$484$	4.32088	−	2.49466i	0.196404	−	0.113394i
$485$	−15.8128	−	1.50023i	−0.718021	−	0.0681218i
$486$		0			0
$487$	−12.9320	+	12.9320i	−0.586007	+	0.586007i	−0.936547	−	0.350541i	$-0.885998\pi$
$487$	−12.9320	+	12.9320i	−0.586007	+	0.586007i	0.350541	+	0.936547i	$0.385998\pi$
$488$	2.23689	−	8.34820i	0.101259	−	0.377905i
$489$		0			0
$490$	−0.993392	+	10.4706i	−0.0448769	+	0.473013i
$491$	9.71899	−	16.8338i	0.438612	−	0.759698i	−0.558971	−	0.829187i	$-0.688804\pi$
$491$	9.71899	−	16.8338i	0.438612	−	0.759698i	0.997583	+	0.0694893i	$0.0221370\pi$
$492$		0			0
$493$	−3.74956	−	3.74956i	−0.168872	−	0.168872i
$494$	−9.80561	−	5.66002i	−0.441175	−	0.254656i
$495$		0			0
$496$	−10.6301	−	6.13731i	−0.477307	−	0.275573i
$497$	−2.22822	−	8.31583i	−0.0999494	−	0.373016i
$498$		0			0
$499$	−2.53922	−	1.46602i	−0.113671	−	0.0656281i	0.442086	−	0.896972i	$-0.354238\pi$
$499$	−2.53922	−	1.46602i	−0.113671	−	0.0656281i	−0.555758	+	0.831344i	$0.687572\pi$
$500$	−10.2579	+	16.8984i	−0.458746	+	0.755721i
$501$		0			0
$502$	−8.79316	+	8.79316i	−0.392458	+	0.392458i
$503$	37.4561	+	10.0363i	1.67009	+	0.447498i	0.965134	−	0.261756i	$-0.0843017\pi$
$503$	37.4561	+	10.0363i	1.67009	+	0.447498i	0.704952	+	0.709255i	$0.250968\pi$
$504$		0			0
$505$	−17.1395	+	2.89287i	−0.762697	+	0.128731i
$506$		−	11.2174i		−	0.498675i
$507$		0			0
$508$	15.6815	−	4.20183i	0.695752	−	0.186426i
$509$	0.142777	+	0.247298i	0.00632849	+	0.0109613i	0.869172	−	0.494509i	$-0.164652\pi$
$509$	0.142777	+	0.247298i	0.00632849	+	0.0109613i	−0.862844	+	0.505471i	$0.831319\pi$
$510$		0			0
$511$	15.0079	−	25.9944i	0.663909	−	1.14992i
$512$	16.0781	−	16.0781i	0.710558	−	0.710558i
$513$		0			0
$514$		−	2.30227i		−	0.101549i
$515$	19.4941	−	8.91700i	0.859012	−	0.392930i
$516$		0			0
$517$	2.46564	−	9.20190i	0.108439	−	0.404699i
$518$	−2.09623	−	7.82325i	−0.0921033	−	0.343734i
$519$		0			0
$520$	3.64237	+	21.5801i	0.159729	+	0.946349i
$521$		−	1.42374i		−	0.0623753i	−0.999514	−	0.0311876i	$-0.990071\pi$
$521$		−	1.42374i		−	0.0623753i	0.999514	−	0.0311876i	$-0.00992894\pi$
$522$		0			0
$523$	−10.1944	+	38.0462i	−0.445772	+	1.66364i	0.268120	+	0.963386i	$0.413598\pi$
$523$	−10.1944	+	38.0462i	−0.445772	+	1.66364i	−0.713891	+	0.700256i	$0.753069\pi$
$524$			23.6040i			1.03114i
$525$		0			0
$526$	−1.84853	+	1.06725i	−0.0805999	+	0.0465344i
$527$	6.78063	+	25.3056i	0.295369	+	1.10233i
$528$		0			0
$529$	14.0821	+	8.13030i	0.612265	+	0.353491i
$530$	2.31226	−	6.21094i	0.100438	−	0.269786i
$531$		0			0
$532$	22.3180	+	22.3137i	0.967606	+	0.967421i
$533$	−14.4533	+	14.4533i	−0.626041	+	0.626041i
$534$		0			0
$535$	9.65287	+	21.1028i	0.417330	+	0.912355i
$536$	−6.69697	−	11.5995i	−0.289265	−	0.501022i
$537$		0			0
$538$	−10.6274	−	2.84761i	−0.458181	−	0.122769i
$539$			36.3148i			1.56419i
$540$		0			0
$541$	−4.68601	−	8.11640i	−0.201467	−	0.348951i	0.747534	−	0.664223i	$-0.231238\pi$
$541$	−4.68601	−	8.11640i	−0.201467	−	0.348951i	−0.949001	+	0.315272i	$0.897904\pi$
$542$	−11.5306	−	3.08962i	−0.495283	−	0.132711i
$543$		0			0
$544$	−27.9081			−1.19655
$545$	−2.69395	−	3.25871i	−0.115396	−	0.139588i
$546$		0			0
$547$	−2.88281	−	0.772447i	−0.123260	−	0.0330274i	0.196662	−	0.980471i	$-0.436990\pi$
$547$	−2.88281	−	0.772447i	−0.123260	−	0.0330274i	−0.319922	+	0.947444i	$0.603657\pi$
$548$	−6.00360	−	22.4057i	−0.256461	−	0.957126i
$549$		0			0
$550$	3.90140	−	8.05631i	0.166356	−	0.343522i
$551$	0.000389802		4.06742i	1.66061e−5		0.173278i
$552$		0			0
$553$	28.4924	−	7.63452i	1.21162	−	0.324653i
$554$	−2.54513	+	4.40830i	−0.108132	+	0.187291i
$555$		0			0
$556$	10.2361	−	17.7295i	0.434108	−	0.751897i
$557$	3.00555	−	11.2169i	0.127349	−	0.475274i	−0.872563	−	0.488501i	$-0.837544\pi$
$557$	3.00555	−	11.2169i	0.127349	−	0.475274i	0.999913	+	0.0132274i	$0.00421054\pi$
$558$		0			0
$559$	47.7891			2.02126
$560$	2.30258	−	24.2698i	0.0973018	−	1.02559i
$561$		0			0
$562$	−1.82454	−	1.82454i	−0.0769634	−	0.0769634i
$563$	3.25198	+	3.25198i	0.137055	+	0.137055i	0.772306	−	0.635251i	$-0.219103\pi$
$563$	3.25198	+	3.25198i	0.137055	+	0.137055i	−0.635251	+	0.772306i	$0.719103\pi$
$564$		0			0
$565$	35.1250	−	16.0669i	1.47772	−	0.675938i
$566$	5.47330	−	3.16001i	0.230060	−	0.132825i
$567$		0			0
$568$	−0.987360	−	3.68488i	−0.0414287	−	0.154614i
$569$	−8.53546			−0.357825			−0.178913	−	0.983865i	$-0.557258\pi$
$569$	−8.53546			−0.357825			−0.178913	+	0.983865i	$0.557258\pi$
$570$		0			0
$571$	−17.0408			−0.713137			−0.356569	−	0.934269i	$-0.616053\pi$
$571$	−17.0408			−0.713137			−0.356569	+	0.934269i	$0.616053\pi$
$572$	9.17703	+	34.2491i	0.383711	+	1.43203i
$573$		0			0
$574$	−6.47100	+	3.73603i	−0.270094	+	0.155939i
$575$	17.5918	+	25.9238i	0.733628	+	1.08110i
$576$		0			0
$577$	24.5178	+	24.5178i	1.02069	+	1.02069i	0.999781	+	0.0209059i	$0.00665505\pi$
$577$	24.5178	+	24.5178i	1.02069	+	1.02069i	0.0209059	+	0.999781i	$0.493345\pi$
$578$	5.20721	+	5.20721i	0.216591	+	0.216591i
$579$		0			0
$580$	2.84343	−	2.35064i	0.118067	−	0.0976051i
$581$	9.07656			0.376559
$582$		0			0
$583$	5.92250	−	22.1031i	0.245285	−	0.915415i
$584$	6.65022	−	11.5185i	0.275188	−	0.476639i
$585$		0			0
$586$	−7.09780	+	12.2937i	−0.293207	+	0.507850i
$587$	28.7283	−	7.69772i	1.18574	−	0.317719i	0.388541	−	0.921431i	$-0.372979\pi$
$587$	28.7283	−	7.69772i	1.18574	−	0.317719i	0.797202	+	0.603712i	$0.206312\pi$
$588$		0			0
$589$	10.0460	−	17.4041i	0.413940	−	0.717124i
$590$	−3.44622	+	4.84578i	−0.141879	+	0.199498i
$591$		0			0
$592$	2.83046	+	10.5634i	0.116331	+	0.434154i
$593$	11.3636	+	3.04486i	0.466646	+	0.125037i	0.484478	−	0.874804i	$-0.339010\pi$
$593$	11.3636	+	3.04486i	0.466646	+	0.125037i	−0.0178317	+	0.999841i	$0.505676\pi$
$594$		0			0
$595$	−40.1034	+	33.1532i	−1.64408	+	1.35915i
$596$	−15.9188			−0.652058
$597$		0			0
$598$	15.7205	+	4.21229i	0.642858	+	0.172253i
$599$	20.2364	+	35.0504i	0.826835	+	1.43212i	0.900508	+	0.434839i	$0.143195\pi$
$599$	20.2364	+	35.0504i	0.826835	+	1.43212i	−0.0736729	+	0.997282i	$0.523472\pi$
$600$		0			0
$601$		−	9.60323i		−	0.391724i	−0.980631	−	0.195862i	$-0.937250\pi$
$601$		−	9.60323i		−	0.391724i	0.980631	−	0.195862i	$-0.0627505\pi$
$602$	16.8745	+	4.52152i	0.687754	+	0.184283i
$603$		0			0
$604$	−9.95844	−	17.2485i	−0.405203	−	0.701833i
$605$	2.20145	−	5.91330i	0.0895017	−	0.240410i
$606$		0			0
$607$	5.26120	−	5.26120i	0.213545	−	0.213545i	−0.592226	−	0.805772i	$-0.701751\pi$
$607$	5.26120	−	5.26120i	0.213545	−	0.213545i	0.805772	+	0.592226i	$0.201751\pi$
$608$	15.1384	+	15.1355i	0.613945	+	0.613827i
$609$		0			0
$610$	−2.13339	−	4.66396i	−0.0863784	−	0.188838i
$611$	11.9700	+	6.91087i	0.484253	+	0.279584i
$612$		0			0
$613$	−11.2627	−	42.0331i	−0.454898	−	1.69770i	−0.688388	−	0.725342i	$-0.741682\pi$
$613$	−11.2627	−	42.0331i	−0.454898	−	1.69770i	0.233491	−	0.972359i	$-0.424985\pi$
$614$	−1.31324	+	0.758200i	−0.0529981	+	0.0305985i
$615$		0			0
$616$			27.6235i			1.11298i
$617$	−4.58463	+	17.1101i	−0.184570	+	0.688826i	0.810152	+	0.586220i	$0.199385\pi$
$617$	−4.58463	+	17.1101i	−0.184570	+	0.688826i	−0.994722	+	0.102606i	$0.967282\pi$
$618$		0			0
$619$		−	28.8877i		−	1.16110i	−0.814226	−	0.580548i	$-0.802839\pi$
$619$		−	28.8877i		−	1.16110i	0.814226	−	0.580548i	$-0.197161\pi$
$620$	−17.9729	+	3.03354i	−0.721808	+	0.121830i
$621$		0			0
$622$	−2.34867	−	8.76534i	−0.0941729	−	0.351458i
$623$	2.56832	−	9.58509i	0.102897	−	0.384019i
$624$		0			0
$625$	3.61809	+	24.7368i	0.144724	+	0.989472i
$626$			10.5009i			0.419700i
$627$		0			0
$628$	−22.1887	+	22.1887i	−0.885424	+	0.885424i
$629$	11.6707	−	20.2142i	0.465340	−	0.805993i
$630$		0			0
$631$	−6.73777	−	11.6702i	−0.268226	−	0.464582i	0.700177	−	0.713969i	$-0.253104\pi$
$631$	−6.73777	−	11.6702i	−0.268226	−	0.464582i	−0.968404	+	0.249387i	$0.919771\pi$
$632$	12.6254	−	3.38298i	0.502213	−	0.134568i
$633$		0			0
$634$			1.58286i			0.0628633i
$635$	11.8991	−	16.7315i	0.472203	−	0.663971i
$636$		0			0
$637$	−50.8928	−	13.6367i	−2.01644	−	0.540305i
$638$	−1.18125	+	1.18125i	−0.0467660	+	0.0467660i
$639$		0			0
$640$	2.37546	−	25.0379i	0.0938982	−	0.989710i
$641$	−2.84529	−	1.64273i	−0.112382	−	0.0648839i	0.442755	−	0.896642i	$-0.354001\pi$
$641$	−2.84529	−	1.64273i	−0.112382	−	0.0648839i	−0.555138	+	0.831759i	$0.687334\pi$
$642$		0			0
$643$	−1.09411	−	4.08326i	−0.0431473	−	0.161028i	0.940991	−	0.338432i	$-0.109897\pi$
$643$	−1.09411	−	4.08326i	−0.0431473	−	0.161028i	−0.984138	+	0.177404i	$0.943230\pi$
$644$	−39.2880	−	22.6829i	−1.54816	−	0.893833i
$645$		0			0
$646$	−0.00114311	−	11.9278i	−4.49749e−5	−	0.469294i
$647$	−7.66422	−	7.66422i	−0.301311	−	0.301311i	0.540215	−	0.841527i	$-0.318343\pi$
$647$	−7.66422	−	7.66422i	−0.301311	−	0.301311i	−0.841527	+	0.540215i	$0.818343\pi$
$648$		0			0
$649$	−10.2655	+	17.7804i	−0.402956	+	0.697941i
$650$	9.82536	+	8.49281i	0.385382	+	0.333115i
$651$		0			0
$652$	5.26957	−	19.6663i	0.206372	−	0.770192i
$653$	16.2246	−	16.2246i	0.634918	−	0.634918i	−0.314379	−	0.949298i	$-0.601796\pi$
$653$	16.2246	−	16.2246i	0.634918	−	0.634918i	0.949298	+	0.314379i	$0.101796\pi$
$654$		0			0
$655$	19.0198	+	23.0071i	0.743166	+	0.898962i
$656$	8.73752	−	5.04461i	0.341143	−	0.196959i
$657$		0			0
$658$	3.57278	+	3.57278i	0.139282	+	0.139282i
$659$	−15.1241	−	26.1957i	−0.589151	−	1.02044i	−0.994344	−	0.106209i	$-0.966129\pi$
$659$	−15.1241	−	26.1957i	−0.589151	−	1.02044i	0.405192	−	0.914231i	$-0.367205\pi$
$660$		0			0
$661$	24.0329	−	13.8754i	0.934771	−	0.539691i	0.0464540	−	0.998920i	$-0.485208\pi$
$661$	24.0329	−	13.8754i	0.934771	−	0.539691i	0.888317	+	0.459230i	$0.151875\pi$
$662$	−13.0405	+	3.49418i	−0.506832	+	0.135805i
$663$		0			0
$664$	4.02196			0.156082
$665$	39.7337	+	3.76587i	1.54081	+	0.146034i
$666$		0			0
$667$	−1.51327	−	5.64760i	−0.0585941	−	0.218676i
$668$	−29.5541	+	7.91901i	−1.14348	+	0.306396i
$669$		0			0
$670$	−7.44875	−	2.77308i	−0.287770	−	0.107133i
$671$	−8.85413	−	15.3358i	−0.341810	−	0.592032i
$672$		0			0
$673$	12.1922	+	12.1922i	0.469974	+	0.469974i	0.901906	−	0.431932i	$-0.142168\pi$
$673$	12.1922	+	12.1922i	0.469974	+	0.469974i	−0.431932	+	0.901906i	$0.642168\pi$
$674$	6.10052	−	3.52214i	0.234983	−	0.135668i
$675$		0			0
$676$	−28.4584			−1.09456
$677$	25.1777	−	25.1777i	0.967657	−	0.967657i	−0.0318362	−	0.999493i	$-0.510135\pi$
$677$	25.1777	−	25.1777i	0.967657	−	0.967657i	0.999493	+	0.0318362i	$0.0101355\pi$
$678$		0			0
$679$	14.5438	−	25.1906i	0.558140	−	0.966727i
$680$	−17.7704	+	14.6907i	−0.681465	+	0.563363i
$681$		0			0
$682$	7.97221	−	2.13615i	0.305272	−	0.0817973i
$683$	−25.0637	−	25.0637i	−0.959035	−	0.959035i	0.0401584	−	0.999193i	$-0.487214\pi$
$683$	−25.0637	−	25.0637i	−0.959035	−	0.959035i	−0.999193	+	0.0401584i	$0.987214\pi$
$684$		0			0
$685$	−23.9061	−	17.0015i	−0.913405	−	0.649595i
$686$	−4.72662	−	2.72891i	−0.180463	−	0.104190i
$687$		0			0
$688$	−22.7850	−	6.10522i	−0.868669	−	0.232759i
$689$	28.7520	+	16.6000i	1.09536	+	0.632408i
$690$		0			0
$691$	−20.4892			−0.779446			−0.389723	−	0.920932i	$-0.627429\pi$
$691$	−20.4892			−0.779446			−0.389723	+	0.920932i	$0.627429\pi$
$692$	28.2318	−	28.2318i	1.07321	−	1.07321i
$693$		0			0
$694$	3.08535	+	5.34398i	0.117118	+	0.202855i
$695$	−4.30894	−	25.5293i	−0.163447	−	0.968381i
$696$		0			0
$697$	−20.8002	−	5.57339i	−0.787862	−	0.211107i
$698$	−3.32736	+	0.891562i	−0.125942	+	0.0337461i
$699$		0			0
$700$	−20.3274	−	29.9551i	−0.768305	−	1.13220i
$701$	−20.1658	+	34.9281i	−0.761650	+	1.31922i	0.180349	+	0.983603i	$0.442277\pi$
$701$	−20.1658	+	34.9281i	−0.761650	+	1.31922i	−0.941999	+	0.335614i	$0.891056\pi$
$702$		0			0
$703$	−17.2935	+	4.63555i	−0.652236	+	0.174833i
$704$		−	11.0050i		−	0.414765i
$705$		0			0
$706$	10.3016	+	5.94764i	0.387706	+	0.223842i
$707$	8.23849	−	30.7465i	0.309840	−	1.15634i
$708$		0			0
$709$	−32.0044	+	18.4777i	−1.20195	+	0.693946i	−0.960989	−	0.276588i	$-0.910796\pi$
$709$	−32.0044	+	18.4777i	−1.20195	+	0.693946i	−0.240962	+	0.970535i	$0.577463\pi$
$710$	−1.84484	−	1.31201i	−0.0692357	−	0.0492390i
$711$		0			0
$712$	1.13806	−	4.24730i	0.0426507	−	0.159174i
$713$	−7.47645	+	27.9025i	−0.279995	+	1.04496i
$714$		0			0
$715$	36.5426	+	25.9883i	1.36661	+	0.971909i
$716$	−36.7150	+	21.1974i	−1.37210	+	0.792185i
$717$		0			0
$718$	−2.75842	+	10.2946i	−0.102943	+	0.384190i
$719$	−10.2019	−	5.89004i	−0.380465	−	0.219662i	0.297556	−	0.954705i	$-0.403829\pi$
$719$	−10.2019	−	5.89004i	−0.380465	−	0.219662i	−0.678021	+	0.735043i	$0.737162\pi$
$720$		0			0
$721$			39.2566i			1.46199i
$722$	−6.46825	+	6.47073i	−0.240723	+	0.240816i
$723$		0			0
$724$	19.2073	−	33.2681i	0.713835	−	1.23640i
$725$	0.877403	−	4.58240i	0.0325859	−	0.170186i
$726$		0			0
$727$	−24.5041	+	6.56584i	−0.908805	+	0.243514i	−0.682794	−	0.730611i	$-0.739235\pi$
$727$	−24.5041	+	6.56584i	−0.908805	+	0.243514i	−0.226011	+	0.974125i	$0.572569\pi$
$728$	−38.7125	−	10.3730i	−1.43478	−	0.384448i
$729$		0			0
$730$	−1.31358	−	7.78263i	−0.0486179	−	0.288048i
$731$	25.1733	+	43.6014i	0.931068	+	1.61266i
$732$		0			0
$733$	9.37879	−	9.37879i	0.346413	−	0.346413i	−0.512358	−	0.858772i	$-0.671228\pi$
$733$	9.37879	−	9.37879i	0.346413	−	0.346413i	0.858772	+	0.512358i	$0.171228\pi$
$734$	−0.490681			−0.0181114
$735$		0			0
$736$	−26.6494	−	15.3860i	−0.982308	−	0.567136i
$737$	−26.5081	−	7.10283i	−0.976439	−	0.261636i
$738$		0			0
$739$	−11.9669	−	6.90912i	−0.440211	−	0.254156i	0.263476	−	0.964666i	$-0.415131\pi$
$739$	−11.9669	−	6.90912i	−0.440211	−	0.254156i	−0.703687	+	0.710510i	$0.748464\pi$
$740$	13.2339	+	9.41172i	0.486489	+	0.345982i
$741$		0			0
$742$	8.58186	+	8.58186i	0.315050	+	0.315050i
$743$	−34.4761	+	9.23785i	−1.26481	+	0.338904i	−0.828039	−	0.560671i	$-0.810543\pi$
$743$	−34.4761	+	9.23785i	−1.26481	+	0.338904i	−0.436767	+	0.899575i	$0.643877\pi$
$744$		0			0
$745$	−15.5162	+	12.8272i	−0.568470	+	0.469951i
$746$	3.33653	−	5.77905i	0.122159	−	0.211586i
$747$		0			0
$748$	−26.4139	+	26.4139i	−0.965788	+	0.965788i
$749$	−42.4962			−1.55278
$750$		0			0
$751$	−13.1689	+	7.60307i	−0.480540	+	0.277440i	−0.720641	−	0.693308i	$-0.756153\pi$
$751$	−13.1689	+	7.60307i	−0.480540	+	0.277440i	0.240102	+	0.970748i	$0.422819\pi$
$752$	−4.82418	−	4.82418i	−0.175920	−	0.175920i
$753$		0			0
$754$	−1.21187	−	2.09901i	−0.0441336	−	0.0764416i
$755$	−23.6053	−	8.78796i	−0.859084	−	0.319827i
$756$		0			0
$757$	30.1275	−	8.07263i	1.09500	−	0.293405i	0.334274	−	0.942476i	$-0.391509\pi$
$757$	30.1275	−	8.07263i	1.09500	−	0.293405i	0.760728	+	0.649071i	$0.224842\pi$
$758$	−0.125684	−	0.469060i	−0.00456506	−	0.0170370i
$759$		0			0
$760$	17.6066	+	1.66872i	0.638660	+	0.0605307i
$761$	31.9231			1.15721			0.578606	−	0.815607i	$-0.303597\pi$
$761$	31.9231			1.15721			0.578606	+	0.815607i	$0.303597\pi$
$762$		0			0
$763$	7.47894	−	2.00398i	0.270756	−	0.0725488i
$764$	26.7274	−	15.4311i	0.966962	−	0.558276i
$765$		0			0
$766$	−4.99473	−	8.65113i	−0.180467	−	0.312578i
$767$	−21.0632	−	21.0632i	−0.760548	−	0.760548i
$768$		0			0
$769$	2.24465	−	1.29595i	0.0809443	−	0.0467332i	−0.458982	−	0.888446i	$-0.651786\pi$
$769$	2.24465	−	1.29595i	0.0809443	−	0.0467332i	0.539926	+	0.841713i	$0.318452\pi$
$770$	10.4445	+	12.6340i	0.376393	+	0.455299i
$771$		0			0
$772$	−22.1272	+	22.1272i	−0.796375	+	0.796375i
$773$	13.0883	−	48.8461i	0.470753	−	1.75687i	−0.166322	−	0.986072i	$-0.553189\pi$
$773$	13.0883	−	48.8461i	0.470753	−	1.75687i	0.637075	−	0.770802i	$-0.280144\pi$
$774$		0			0
$775$	−15.0740	+	17.4392i	−0.541474	+	0.626433i
$776$	6.44459	−	11.1624i	0.231347	−	0.400705i
$777$		0			0
$778$	1.50705	+	1.50705i	0.0540302	+	0.0540302i
$779$	8.26016	+	14.3039i	0.295951	+	0.512489i
$780$		0			0
$781$	−6.76918	−	3.90819i	−0.242220	−	0.139846i
$782$	4.43772	+	16.5618i	0.158692	+	0.592248i
$783$		0			0
$784$	22.5226	+	13.0035i	0.804380	+	0.464409i
$785$	−3.74820	+	39.5070i	−0.133779	+	1.41006i
$786$		0			0
$787$	−30.9297	+	30.9297i	−1.10252	+	1.10252i	−0.108418	+	0.994105i	$0.534578\pi$
$787$	−30.9297	+	30.9297i	−1.10252	+	1.10252i	−0.994105	+	0.108418i	$0.965422\pi$
$788$	−13.3000	−	3.56373i	−0.473794	−	0.126953i
$789$		0			0
$790$	4.49534	−	6.32095i	0.159937	−	0.224889i
$791$			70.7335i			2.51499i
$792$		0			0
$793$	24.8169	−	6.64968i	0.881275	−	0.236137i
$794$	4.92680	+	8.53347i	0.174846	+	0.302841i
$795$		0			0
$796$	−10.8448	+	18.7837i	−0.384383	+	0.665771i
$797$	21.5095	−	21.5095i	0.761904	−	0.761904i	−0.214762	−	0.976666i	$-0.568898\pi$
$797$	21.5095	−	21.5095i	0.761904	−	0.761904i	0.976666	+	0.214762i	$0.0688976\pi$
$798$		0			0
$799$			14.5614i			0.515147i
$800$	−13.7882	−	20.3188i	−0.487488	−	0.718378i
$801$		0			0
$802$	−0.744018	+	2.77671i	−0.0262722	+	0.0980492i
$803$	−7.05324	−	26.3230i	−0.248903	−	0.928920i
$804$		0			0
$805$	−56.5722	+	9.54849i	−1.99391	+	0.336540i
$806$			11.9747i			0.421790i
$807$		0			0
$808$	3.65060	−	13.6242i	0.128428	−	0.479299i
$809$			15.4858i			0.544453i	0.962233	+	0.272226i	$0.0877600\pi$
$809$			15.4858i			0.544453i	−0.962233	+	0.272226i	$0.912240\pi$
$810$		0			0
$811$	21.4439	−	12.3806i	0.752997	−	0.434743i	−0.0737786	−	0.997275i	$-0.523506\pi$
$811$	21.4439	−	12.3806i	0.752997	−	0.434743i	0.826776	+	0.562531i	$0.190172\pi$
$812$	1.74859	+	6.52584i	0.0613636	+	0.229012i
$813$		0			0
$814$	−6.36822	−	3.67669i	−0.223206	−	0.128868i
$815$	−10.7106	−	23.4152i	−0.375175	−	0.820198i
$816$		0			0
$817$	9.99159	−	37.3034i	0.349562	−	1.30508i
$818$	−9.81133	+	9.81133i	−0.343045	+	0.343045i
$819$		0			0
$820$	5.22709	−	14.0405i	0.182538	−	0.490314i
$821$	18.3339	+	31.7553i	0.639859	+	1.10827i	0.985463	+	0.169888i	$0.0543406\pi$
$821$	18.3339	+	31.7553i	0.639859	+	1.10827i	−0.345604	+	0.938380i	$0.612326\pi$
$822$		0			0
$823$	5.21363	+	1.39699i	0.181736	+	0.0486960i	0.348539	−	0.937294i	$-0.386678\pi$
$823$	5.21363	+	1.39699i	0.181736	+	0.0486960i	−0.166803	+	0.985990i	$0.553344\pi$
$824$			17.3952i			0.605991i
$825$		0			0
$826$	−5.44463	−	9.43038i	−0.189443	−	0.328125i
$827$	7.98326	+	2.13911i	0.277605	+	0.0743841i	0.394935	−	0.918709i	$-0.370767\pi$
$827$	7.98326	+	2.13911i	0.277605	+	0.0743841i	−0.117330	+	0.993093i	$0.537434\pi$
$828$		0			0
$829$	23.2969			0.809136			0.404568	−	0.914508i	$-0.367422\pi$
$829$	23.2969			0.809136			0.404568	+	0.914508i	$0.367422\pi$
$830$	1.83951	−	1.52071i	0.0638503	−	0.0527846i
$831$		0			0
$832$	15.4227	+	4.13251i	0.534687	+	0.143269i
$833$	−14.3665	−	53.6164i	−0.497769	−	1.85770i
$834$		0			0
$835$	−22.4257	+	31.5332i	−0.776075	+	1.09125i
$836$	28.6531	−	0.00274597i	0.990987	−	9.49715e-5i
$837$		0			0
$838$	−1.22084	+	0.327122i	−0.0421731	+	0.0113002i
$839$	−0.212316	+	0.367743i	−0.00732998	+	0.0126959i	−0.869667	−	0.493639i	$-0.835667\pi$
$839$	−0.212316	+	0.367743i	−0.00732998	+	0.0126959i	0.862337	+	0.506335i	$0.169000\pi$
$840$		0			0
$841$	14.0646	−	24.3607i	0.484987	−	0.840023i
$842$	2.57324	−	9.60347i	0.0886797	−	0.330957i
$843$		0			0
$844$	9.82749			0.338276
$845$	−27.7388	+	22.9315i	−0.954244	+	0.788867i
$846$		0			0
$847$	8.17061	+	8.17061i	0.280746	+	0.280746i
$848$	−11.5877	−	11.5877i	−0.397924	−	0.397924i
$849$		0			0
$850$	−2.57301	+	13.4380i	−0.0882536	+	0.460921i
$851$	22.2886	−	12.8683i	0.764042	−	0.441120i
$852$		0			0
$853$	4.01714	+	14.9922i	0.137544	+	0.513322i	0.999974	+	0.00714604i	$0.00227467\pi$
$853$	4.01714	+	14.9922i	0.137544	+	0.513322i	−0.862430	+	0.506176i	$0.831059\pi$
$854$	9.39212			0.321392
$855$		0			0
$856$	−18.8307			−0.643621
$857$	4.86595	+	18.1600i	0.166218	+	0.620332i	0.997882	+	0.0650536i	$0.0207218\pi$
$857$	4.86595	+	18.1600i	0.166218	+	0.620332i	−0.831664	+	0.555279i	$0.812612\pi$
$858$		0			0
$859$	26.9114	−	15.5373i	0.918205	−	0.530126i	0.0351429	−	0.999382i	$-0.488811\pi$
$859$	26.9114	−	15.5373i	0.918205	−	0.530126i	0.883062	+	0.469256i	$0.155478\pi$
$860$	−31.8536	+	14.5705i	−1.08620	+	0.496850i
$861$		0			0
$862$	10.9314	+	10.9314i	0.372326	+	0.372326i
$863$	10.1773	+	10.1773i	0.346439	+	0.346439i	0.858781	−	0.512342i	$-0.171222\pi$
$863$	10.1773	+	10.1773i	0.346439	+	0.346439i	−0.512342	+	0.858781i	$0.671222\pi$
$864$		0			0
$865$	4.76902	−	50.2667i	0.162152	−	1.70912i
$866$	−10.3391			−0.351337
$867$		0			0
$868$	8.63908	−	32.2415i	0.293230	−	1.09435i
$869$	13.3906	−	23.1932i	0.454244	−	0.786774i
$870$		0			0
$871$	19.9083	−	34.4822i	0.674566	−	1.16838i
$872$	3.31404	−	0.887993i	0.112227	−	0.0300713i
$873$		0			0
$874$	6.57483	−	11.3905i	0.222397	−	0.385288i
$875$	−43.9509	−	12.8180i	−1.48581	−	0.433329i
$876$		0			0
$877$	−11.7387	−	43.8095i	−0.396389	−	1.47934i	−0.819402	−	0.573219i	$-0.805694\pi$
$877$	−11.7387	−	43.8095i	−0.396389	−	1.47934i	0.423013	−	0.906124i	$-0.360972\pi$
$878$	−16.9216	−	4.53414i	−0.571077	−	0.153020i
$879$		0			0
$880$	−14.1027	−	17.0592i	−0.475403	−	0.575066i
$881$	−47.3977			−1.59687			−0.798435	−	0.602081i	$-0.794338\pi$
$881$	−47.3977			−1.59687			−0.798435	+	0.602081i	$0.794338\pi$
$882$		0			0
$883$	−41.6677	−	11.1648i	−1.40223	−	0.375727i	−0.523086	−	0.852280i	$-0.675219\pi$
$883$	−41.6677	−	11.1648i	−1.40223	−	0.375727i	−0.879146	+	0.476553i	$0.841886\pi$
$884$	−27.0986	−	46.9361i	−0.911424	−	1.57863i
$885$		0			0
$886$			2.87549i			0.0966038i
$887$	−52.2533	−	14.0012i	−1.75449	−	0.470115i	−0.768918	−	0.639347i	$-0.779205\pi$
$887$	−52.2533	−	14.0012i	−1.75449	−	0.470115i	−0.985576	+	0.169232i	$0.945871\pi$
$888$		0			0
$889$	18.7992	+	32.5612i	0.630506	+	1.09207i
$890$	−1.08540	−	2.37287i	−0.0363827	−	0.0795389i
$891$		0			0
$892$	11.5830	−	11.5830i	0.387827	−	0.387827i
$893$	7.89717	−	7.89868i	0.264269	−	0.264319i
$894$		0			0
$895$	−18.7059	+	50.2460i	−0.625271	+	1.67954i
$896$	39.8868	+	23.0286i	1.33252	+	0.769333i
$897$		0			0
$898$	−2.53025	−	9.44303i	−0.0844356	−	0.315118i
$899$	3.72557	−	2.15096i	0.124255	−	0.0717385i
$900$		0			0
$901$			34.9767i			1.16524i
$902$	−1.75582	+	6.55281i	−0.0584624	+	0.218185i
$903$		0			0
$904$			31.3431i			1.04246i
$905$	−8.08541	−	47.9039i	−0.268768	−	1.59238i
$906$		0			0
$907$	−6.59019	−	24.5949i	−0.218824	−	0.816661i	−0.984785	−	0.173775i	$-0.944404\pi$
$907$	−6.59019	−	24.5949i	−0.218824	−	0.816661i	0.765962	−	0.642886i	$-0.222263\pi$
$908$	−4.17299	+	15.5738i	−0.138486	+	0.516836i
$909$		0			0
$910$	−21.6278	+	9.89299i	−0.716954	+	0.327950i
$911$		−	11.7431i		−	0.389065i	−0.980896	−	0.194533i	$-0.937681\pi$
$911$		−	11.7431i		−	0.389065i	0.980896	−	0.194533i	$-0.0623190\pi$
$912$		0			0
$913$	5.82706	−	5.82706i	0.192848	−	0.192848i
$914$	−0.765193	+	1.32535i	−0.0253103	+	0.0438388i
$915$		0			0
$916$	19.2791	+	33.3925i	0.637001	+	1.10332i
$917$	−52.8027	+	14.1485i	−1.74370	+	0.467223i
$918$		0			0
$919$		−	18.9337i		−	0.624565i	−0.949989	−	0.312283i	$-0.898906\pi$
$919$		−	18.9337i		−	0.624565i	0.949989	−	0.312283i	$-0.101094\pi$
$920$	−25.0680	+	4.23108i	−0.826468	+	0.139495i
$921$		0			0
$922$	0.137432	+	0.0368248i	0.00452608	+	0.00121276i
$923$	8.01898	−	8.01898i	0.263948	−	0.263948i
$924$		0			0
$925$	20.4832	−	1.49004i	0.673482	−	0.0489923i
$926$	0.309393	+	0.178628i	0.0101673	+	0.00587008i
$927$		0			0
$928$	1.18608	+	4.42653i	0.0389351	+	0.145308i
$929$	37.1721	+	21.4613i	1.21958	+	0.704123i	0.964827	−	0.262884i	$-0.0846736\pi$
$929$	37.1721	+	21.4613i	1.21958	+	0.704123i	0.254750	+	0.967007i	$0.418007\pi$
$930$		0			0
$931$	−21.2851	+	36.8750i	−0.697591	+	1.20853i
$932$	3.27480	+	3.27480i	0.107270	+	0.107270i
$933$		0			0
$934$	0.280502	−	0.485843i	0.00917829	−	0.0158973i
$935$	−4.46194	+	47.0300i	−0.145921	+	1.53805i
$936$		0			0
$937$	−6.59148	+	24.5997i	−0.215334	+	0.803638i	0.770714	+	0.637181i	$0.219900\pi$
$937$	−6.59148	+	24.5997i	−0.215334	+	0.803638i	−0.986049	+	0.166458i	$0.946767\pi$
$938$	10.2922	−	10.2922i	0.336052	−	0.336052i
$939$		0			0
$940$	−10.0856	−	0.956865i	−0.328956	−	0.0312095i
$941$	12.8301	−	7.40743i	0.418248	−	0.241475i	−0.276080	−	0.961135i	$-0.589035\pi$
$941$	12.8301	−	7.40743i	0.418248	−	0.241475i	0.694327	+	0.719659i	$0.255702\pi$
$942$		0			0
$943$	−16.7893	−	16.7893i	−0.546736	−	0.546736i
$944$	7.35166	+	12.7335i	0.239276	+	0.414439i
$945$		0			0
$946$	13.7361	−	7.93051i	0.446598	−	0.257843i
$947$	−47.4124	+	12.7041i	−1.54070	+	0.412828i	−0.926490	−	0.376319i	$-0.877190\pi$
$947$	−47.4124	+	12.7041i	−1.54070	+	0.412828i	−0.614205	+	0.789147i	$0.710523\pi$
$948$		0			0
$949$	39.5386			1.28348
$950$	8.68361	−	5.89388i	0.281734	−	0.191223i
$951$		0			0
$952$	−10.9281	−	40.7842i	−0.354182	−	1.32183i
$953$	6.69819	−	1.79478i	0.216976	−	0.0581385i	−0.148694	−	0.988883i	$-0.547507\pi$
$953$	6.69819	−	1.79478i	0.216976	−	0.0581385i	0.365669	+	0.930745i	$0.380840\pi$
$954$		0			0
$955$	13.6173	−	36.5775i	0.440647	−	1.18362i
$956$	−1.91782	−	3.32175i	−0.0620266	−	0.107433i
$957$		0			0
$958$	0.571254	+	0.571254i	0.0184564	+	0.0184564i
$959$	46.5236	−	26.8604i	1.50233	−	0.867369i
$960$		0			0
$961$	9.74599			0.314387
$962$	7.54399	−	7.54399i	0.243228	−	0.243228i
$963$		0			0
$964$	−19.2883	+	33.4083i	−0.621235	+	1.07601i
$965$	−3.73781	+	39.3975i	−0.120324	+	1.26825i
$966$		0			0
$967$	−39.0189	+	10.4551i	−1.25476	+	0.336212i	−0.824174	−	0.566336i	$-0.808360\pi$
$967$	−39.0189	+	10.4551i	−1.25476	+	0.336212i	−0.430588	+	0.902549i	$0.641694\pi$
$968$	3.62053	+	3.62053i	0.116368	+	0.116368i
$969$		0			0
$970$	−1.27297	−	7.54199i	−0.0408725	−	0.242159i
$971$	−39.8993	−	23.0359i	−1.28043	−	0.739257i	−0.303504	−	0.952830i	$-0.598157\pi$
$971$	−39.8993	−	23.0359i	−1.28043	−	0.739257i	−0.976927	+	0.213573i	$0.931490\pi$
$972$		0			0
$973$	45.7969	+	12.2712i	1.46818	+	0.393398i
$974$	−7.62683	−	4.40335i	−0.244379	−	0.141093i
$975$		0			0
$976$	−12.6818			−0.405934
$977$	7.99703	−	7.99703i	0.255848	−	0.255848i	−0.567515	−	0.823363i	$-0.692095\pi$
$977$	7.99703	−	7.99703i	0.255848	−	0.255848i	0.823363	+	0.567515i	$0.192095\pi$
$978$		0			0
$979$	−4.50470	−	7.80237i	−0.143971	−	0.249365i
$980$	38.0801	−	6.42731i	1.21642	−	0.205313i
$981$		0			0
$982$	9.04121	+	2.42258i	0.288517	+	0.0773078i
$983$	−2.54035	+	0.680684i	−0.0810245	+	0.0217104i	−0.299104	−	0.954221i	$-0.596688\pi$
$983$	−2.54035	+	0.680684i	−0.0810245	+	0.0217104i	0.218079	+	0.975931i	$0.430021\pi$
$984$		0			0
$985$	−15.8353	+	7.24340i	−0.504556	+	0.230794i
$986$	1.27672	−	2.21135i	0.0406591	−	0.0704237i
$987$		0			0
$988$	−10.7558	+	40.1564i	−0.342186	+	1.27755i
$989$			55.5131i			1.76521i
$990$		0			0
$991$	−9.62277	−	5.55571i	−0.305677	−	0.176483i	0.339313	−	0.940673i	$-0.389805\pi$
$991$	−9.62277	−	5.55571i	−0.305677	−	0.176483i	−0.644990	+	0.764191i	$0.723139\pi$
$992$	5.85996	−	21.8696i	0.186054	−	0.694362i
$993$		0			0
$994$	3.59025	−	2.07283i	0.113876	−	0.0657462i
$995$	4.56516	+	27.0473i	0.144725	+	0.857458i
$996$		0			0
$997$	−1.02133	+	3.81166i	−0.0323459	+	0.120716i	−0.980211	−	0.197955i	$-0.936570\pi$
$997$	−1.02133	+	3.81166i	−0.0323459	+	0.120716i	0.947865	+	0.318671i	$0.103237\pi$
$998$	0.365425	−	1.36378i	0.0115673	−	0.0431698i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.cj.g.217.11		80
3.2	odd	2		285.2.x.a.217.10	yes	80
5.3	odd	4	inner	855.2.cj.g.388.11		80
15.8	even	4		285.2.x.a.103.10	yes	80
19.12	odd	6	inner	855.2.cj.g.487.11		80
57.50	even	6		285.2.x.a.202.10	yes	80
95.88	even	12	inner	855.2.cj.g.658.11		80
285.278	odd	12		285.2.x.a.88.10	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.x.a.88.10	✓	80	285.278	odd	12
285.2.x.a.103.10	yes	80	15.8	even	4
285.2.x.a.202.10	yes	80	57.50	even	6
285.2.x.a.217.10	yes	80	3.2	odd	2
855.2.cj.g.217.11		80	1.1	even	1	trivial
855.2.cj.g.388.11		80	5.3	odd	4	inner
855.2.cj.g.487.11		80	19.12	odd	6	inner
855.2.cj.g.658.11		80	95.88	even	12	inner

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.cj (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.124631 + 0.465131i) q^{2} +(1.53124 - 0.884060i) q^{4} +(0.780151 - 2.09556i) q^{5} +(2.89550 + 2.89550i) q^{7} +(1.28304 + 1.28304i) q^{8} +O(q^{10})\)	\(q+(0.124631 + 0.465131i) q^{2} +(1.53124 - 0.884060i) q^{4} +(0.780151 - 2.09556i) q^{5} +(2.89550 + 2.89550i) q^{7} +(1.28304 + 1.28304i) q^{8} +(1.07194 + 0.101700i) q^{10} +3.71777 q^{11} +(-1.39607 + 5.21021i) q^{13} +(-0.985918 + 1.70766i) q^{14} +(1.33124 - 2.30578i) q^{16} +(-5.48905 + 1.47079i) q^{17} +(3.77513 + 2.17909i) q^{19} +(-0.658004 - 3.89850i) q^{20} +(0.463351 + 1.72925i) q^{22} +(-6.05233 - 1.62172i) q^{23} +(-3.78273 - 3.26970i) q^{25} -2.59743 q^{26} +(6.99350 + 1.87390i) q^{28} +(0.466565 + 0.808113i) q^{29} -4.61021i q^{31} +(4.74375 + 1.27108i) q^{32} +(-1.36822 - 2.36982i) q^{34} +(8.32663 - 3.80877i) q^{35} +(-2.90441 + 2.90441i) q^{37} +(-0.543062 + 2.02751i) q^{38} +(3.68966 - 1.68773i) q^{40} +(3.28171 + 1.89470i) q^{41} +(-2.29305 - 8.55777i) q^{43} +(5.69279 - 3.28673i) q^{44} -3.01724i q^{46} +(0.663204 - 2.47511i) q^{47} +9.76789i q^{49} +(1.04939 - 2.16697i) q^{50} +(2.46842 + 9.21228i) q^{52} +(1.59302 - 5.94524i) q^{53} +(2.90042 - 7.79081i) q^{55} +7.43011i q^{56} +(-0.317730 + 0.317730i) q^{58} +(-2.76120 + 4.78254i) q^{59} +(-2.38157 - 4.12500i) q^{61} +(2.14435 - 0.574577i) q^{62} -2.96010i q^{64} +(9.82915 + 6.99030i) q^{65} +(-7.13011 - 1.91051i) q^{67} +(-7.10477 + 7.10477i) q^{68} +(2.80934 + 3.39828i) q^{70} +(-1.82076 - 1.05122i) q^{71} +(-1.89717 - 7.08033i) q^{73} +(-1.71291 - 0.988950i) q^{74} +(7.70706 - 0.000738608i) q^{76} +(10.7648 + 10.7648i) q^{77} +(3.60177 - 6.23846i) q^{79} +(-3.79333 - 4.58856i) q^{80} +(-0.472278 + 1.76256i) q^{82} +(1.56735 - 1.56735i) q^{83} +(-1.20017 + 12.6501i) q^{85} +(3.69470 - 2.13314i) q^{86} +(4.77006 + 4.77006i) q^{88} +(-1.21167 - 2.09867i) q^{89} +(-19.1285 + 11.0439i) q^{91} +(-10.7012 + 2.86739i) q^{92} +1.23391 q^{94} +(7.51157 - 6.21098i) q^{95} +(-1.83851 - 6.86140i) q^{97} +(-4.54335 + 1.21739i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{5} + 8 q^{7}+O(q^{10}) \) 80 * q - 4 * q^5 + 8 * q^7	\( 80 q - 4 q^{5} + 8 q^{7} + 16 q^{11} + 28 q^{16} + 4 q^{17} + 80 q^{20} - 24 q^{22} - 8 q^{23} + 4 q^{25} + 32 q^{26} - 28 q^{28} - 12 q^{32} + 44 q^{35} + 96 q^{38} + 132 q^{40} - 72 q^{41} + 12 q^{47} + 36 q^{53} + 8 q^{55} + 40 q^{58} - 40 q^{61} + 4 q^{62} - 88 q^{68} - 24 q^{70} + 40 q^{73} + 24 q^{76} + 40 q^{77} - 24 q^{80} - 36 q^{82} + 8 q^{83} + 80 q^{85} - 48 q^{86} + 72 q^{91} - 12 q^{92} - 48 q^{95} + 12 q^{97} - 96 q^{98}+O(q^{100}) \) 80 * q - 4 * q^5 + 8 * q^7 + 16 * q^11 + 28 * q^16 + 4 * q^17 + 80 * q^20 - 24 * q^22 - 8 * q^23 + 4 * q^25 + 32 * q^26 - 28 * q^28 - 12 * q^32 + 44 * q^35 + 96 * q^38 + 132 * q^40 - 72 * q^41 + 12 * q^47 + 36 * q^53 + 8 * q^55 + 40 * q^58 - 40 * q^61 + 4 * q^62 - 88 * q^68 - 24 * q^70 + 40 * q^73 + 24 * q^76 + 40 * q^77 - 24 * q^80 - 36 * q^82 + 8 * q^83 + 80 * q^85 - 48 * q^86 + 72 * q^91 - 12 * q^92 - 48 * q^95 + 12 * q^97 - 96 * q^98

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