LMFDB - Embedded newform 864.2.bn.a.683.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(35,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 9, 4]))

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

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

chi := DirichletCharacter("864.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bn (of order $24$, degree $8$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			683.2
Character	$\chi$	$=$	864.683
Dual form			864.2.bn.a.611.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39742 - 0.217290i) q^{2} +(1.90557 + 0.607292i) q^{4} +(-0.279615 - 2.12388i) q^{5} +(0.262694 + 0.980387i) q^{7} +(-2.53092 - 1.26270i) q^{8} +O(q^{10})$	\(q+(-1.39742 - 0.217290i) q^{2} +(1.90557 + 0.607292i) q^{4} +(-0.279615 - 2.12388i) q^{5} +(0.262694 + 0.980387i) q^{7} +(-2.53092 - 1.26270i) q^{8} +(-0.0707598 + 3.02872i) q^{10} +(-3.41279 + 2.61873i) q^{11} +(-0.912029 + 1.18858i) q^{13} +(-0.154065 - 1.42709i) q^{14} +(3.26239 + 2.31447i) q^{16} +5.39882 q^{17} +(6.75131 - 2.79649i) q^{19} +(0.756992 - 4.21702i) q^{20} +(5.33813 - 2.91790i) q^{22} +(2.26322 + 0.606428i) q^{23} +(0.396933 - 0.106358i) q^{25} +(1.53275 - 1.46277i) q^{26} +(-0.0947992 + 2.02773i) q^{28} +(4.40149 + 0.579467i) q^{29} +(-8.30037 + 4.79222i) q^{31} +(-4.05602 - 3.94318i) q^{32} +(-7.54443 - 1.17311i) q^{34} +(2.00877 - 0.832061i) q^{35} +(2.47820 - 5.98289i) q^{37} +(-10.0421 + 2.44087i) q^{38} +(-1.97415 + 5.72846i) q^{40} +(1.03703 - 3.87025i) q^{41} +(-5.15179 - 6.71394i) q^{43} +(-8.09365 + 2.91761i) q^{44} +(-3.03090 - 1.33921i) q^{46} +(7.46917 + 4.31233i) q^{47} +(5.17003 - 2.98492i) q^{49} +(-0.577793 + 0.0623770i) q^{50} +(-2.45975 + 1.71105i) q^{52} +(1.62188 - 3.91557i) q^{53} +(6.51614 + 6.51614i) q^{55} +(0.573080 - 2.81299i) q^{56} +(-6.02482 - 1.76616i) q^{58} +(2.91589 - 0.383885i) q^{59} +(0.0439705 - 0.333989i) q^{61} +(12.6404 - 4.89316i) q^{62} +(4.81116 + 6.39162i) q^{64} +(2.77942 + 1.60470i) q^{65} +(3.21736 - 4.19294i) q^{67} +(10.2878 + 3.27866i) q^{68} +(-2.98790 + 0.726253i) q^{70} +(2.98357 + 2.98357i) q^{71} +(-1.45130 + 1.45130i) q^{73} +(-4.76311 + 7.82213i) q^{74} +(14.5634 - 1.22888i) q^{76} +(-3.46389 - 2.65793i) q^{77} +(4.91023 - 8.50477i) q^{79} +(4.00346 - 7.57610i) q^{80} +(-2.29014 + 5.18303i) q^{82} +(-2.17172 - 0.285913i) q^{83} +(-1.50959 - 11.4665i) q^{85} +(5.74034 + 10.5016i) q^{86} +(11.9442 - 2.31846i) q^{88} +(-2.17841 + 2.17841i) q^{89} +(-1.40485 - 0.581909i) q^{91} +(3.94444 + 2.53002i) q^{92} +(-9.50055 - 7.64911i) q^{94} +(-7.82717 - 13.5571i) q^{95} +(4.24778 - 7.35737i) q^{97} +(-7.87330 + 3.04779i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34} - 16 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 24 q^{47} + 168 q^{50} - 4 q^{52} - 16 q^{55} + 12 q^{56} + 32 q^{58} + 12 q^{59} - 4 q^{61} - 16 q^{64} + 24 q^{65} - 4 q^{67} + 60 q^{68} - 4 q^{70} - 16 q^{73} + 12 q^{74} - 28 q^{76} + 12 q^{77} - 8 q^{79} - 16 q^{82} + 132 q^{83} - 24 q^{85} + 12 q^{86} - 4 q^{88} - 16 q^{91} - 216 q^{92} - 20 q^{94} - 8 q^{97}+O(q^{100}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.39742	−	0.217290i	−0.988126	−	0.153647i
$2$	−1.39742	−	0.217290i	−0.988126	−	0.153647i
$3$		0			0
$3$		0			0
$4$	1.90557	+	0.607292i	0.952785	+	0.303646i
$5$	−0.279615	−	2.12388i	−0.125047	−	0.949830i	−0.932822	−	0.360338i	$-0.882661\pi$
$5$	−0.279615	−	2.12388i	−0.125047	−	0.949830i	0.807774	−	0.589492i	$-0.200672\pi$
$6$		0			0
$7$	0.262694	+	0.980387i	0.0992889	+	0.370551i	0.997635	−	0.0687376i	$-0.0218971\pi$
$7$	0.262694	+	0.980387i	0.0992889	+	0.370551i	−0.898346	+	0.439289i	$0.855230\pi$
$8$	−2.53092	−	1.26270i	−0.894817	−	0.446433i
$9$		0			0
$10$	−0.0707598	+	3.02872i	−0.0223762	+	0.957764i
$11$	−3.41279	+	2.61873i	−1.02900	+	0.789576i	−0.977891	−	0.209117i	$-0.932941\pi$
$11$	−3.41279	+	2.61873i	−1.02900	+	0.789576i	−0.0511053	+	0.998693i	$0.516274\pi$
$12$		0			0
$13$	−0.912029	+	1.18858i	−0.252951	+	0.329653i	−0.902518	−	0.430652i	$-0.858284\pi$
$13$	−0.912029	+	1.18858i	−0.252951	+	0.329653i	0.649567	+	0.760305i	$0.274950\pi$
$14$	−0.154065	−	1.42709i	−0.0411757	−	0.381407i
$15$		0			0
$16$	3.26239	+	2.31447i	0.815598	+	0.578618i
$17$	5.39882			1.30941			0.654703	−	0.755886i	$-0.272794\pi$
$17$	5.39882			1.30941			0.654703	+	0.755886i	$0.272794\pi$
$18$		0			0
$19$	6.75131	−	2.79649i	1.54886	−	0.641558i	0.565748	−	0.824578i	$-0.308587\pi$
$19$	6.75131	−	2.79649i	1.54886	−	0.641558i	0.983109	+	0.183020i	$0.0585874\pi$
$20$	0.756992	−	4.21702i	0.169268	−	0.942953i
$21$		0			0
$22$	5.33813	−	2.91790i	1.13809	−	0.622098i
$23$	2.26322	+	0.606428i	0.471914	+	0.126449i	0.486935	−	0.873438i	$-0.338115\pi$
$23$	2.26322	+	0.606428i	0.471914	+	0.126449i	−0.0150211	+	0.999887i	$0.504782\pi$
$24$		0			0
$25$	0.396933	−	0.106358i	0.0793865	−	0.0212716i
$26$	1.53275	−	1.46277i	0.300598	−	0.286873i
$27$		0			0
$28$	−0.0947992	+	2.02773i	−0.0179154	+	0.383204i
$29$	4.40149	+	0.579467i	0.817337	+	0.107604i	0.527590	−	0.849499i	$-0.323096\pi$
$29$	4.40149	+	0.579467i	0.817337	+	0.107604i	0.289746	+	0.957103i	$0.406429\pi$
$30$		0			0
$31$	−8.30037	+	4.79222i	−1.49079	+	0.860708i	−0.999944	−	0.0105382i	$-0.996646\pi$
$31$	−8.30037	+	4.79222i	−1.49079	+	0.860708i	−0.490846	+	0.871246i	$0.663312\pi$
$32$	−4.05602	−	3.94318i	−0.717011	−	0.697062i
$33$		0			0
$34$	−7.54443	−	1.17311i	−1.29386	−	0.201187i
$35$	2.00877	−	0.832061i	0.339545	−	0.140644i
$36$		0			0
$37$	2.47820	−	5.98289i	0.407413	−	0.983582i	−0.578403	−	0.815751i	$-0.696324\pi$
$37$	2.47820	−	5.98289i	0.407413	−	0.983582i	0.985816	−	0.167831i	$-0.0536762\pi$
$38$	−10.0421	+	2.44087i	−1.62904	+	0.395962i
$39$		0			0
$40$	−1.97415	+	5.72846i	−0.312141	+	0.905749i
$41$	1.03703	−	3.87025i	0.161957	−	0.604432i	−0.836452	−	0.548040i	$-0.815374\pi$
$41$	1.03703	−	3.87025i	0.161957	−	0.604432i	0.998409	−	0.0563911i	$-0.0179594\pi$
$42$		0			0
$43$	−5.15179	−	6.71394i	−0.785640	−	1.02387i	−0.998901	−	0.0468706i	$-0.985075\pi$
$43$	−5.15179	−	6.71394i	−0.785640	−	1.02387i	0.213261	−	0.976995i	$-0.431592\pi$
$44$	−8.09365	+	2.91761i	−1.22016	+	0.439846i
$45$		0			0
$46$	−3.03090	−	1.33921i	−0.446882	−	0.197456i
$47$	7.46917	+	4.31233i	1.08949	+	0.629018i	0.933441	−	0.358732i	$-0.116791\pi$
$47$	7.46917	+	4.31233i	1.08949	+	0.629018i	0.156050	+	0.987749i	$0.450124\pi$
$48$		0			0
$49$	5.17003	−	2.98492i	0.738575	−	0.426417i
$50$	−0.577793	+	0.0623770i	−0.0817122	+	0.00882144i
$51$		0			0
$52$	−2.45975	+	1.71105i	−0.341106	+	0.237280i
$53$	1.62188	−	3.91557i	0.222783	−	0.537845i	−0.772483	−	0.635035i	$-0.780986\pi$
$53$	1.62188	−	3.91557i	0.222783	−	0.537845i	0.995266	+	0.0971903i	$0.0309856\pi$
$54$		0			0
$55$	6.51614	+	6.51614i	0.878636	+	0.878636i
$56$	0.573080	−	2.81299i	0.0765810	−	0.375901i
$57$		0			0
$58$	−6.02482	−	1.76616i	−0.791098	−	0.231908i
$59$	2.91589	−	0.383885i	0.379617	−	0.0499775i	0.0616966	−	0.998095i	$-0.480349\pi$
$59$	2.91589	−	0.383885i	0.379617	−	0.0499775i	0.317920	+	0.948117i	$0.397016\pi$
$60$		0			0
$61$	0.0439705	−	0.333989i	0.00562984	−	0.0427629i	−0.988399	−	0.151877i	$-0.951468\pi$
$61$	0.0439705	−	0.333989i	0.00562984	−	0.0427629i	0.994029	+	0.109114i	$0.0348015\pi$
$62$	12.6404	−	4.89316i	1.60533	−	0.621432i
$63$		0			0
$64$	4.81116	+	6.39162i	0.601395	+	0.798952i
$65$	2.77942	+	1.60470i	0.344745	+	0.199038i
$66$		0			0
$67$	3.21736	−	4.19294i	0.393063	−	0.512250i	−0.554341	−	0.832290i	$-0.687030\pi$
$67$	3.21736	−	4.19294i	0.393063	−	0.512250i	0.947404	+	0.320040i	$0.103696\pi$
$68$	10.2878	+	3.27866i	1.24758	+	0.397596i
$69$		0			0
$70$	−2.98790	+	0.726253i	−0.357123	+	0.0868038i
$71$	2.98357	+	2.98357i	0.354085	+	0.354085i	0.861627	−	0.507542i	$-0.169446\pi$
$71$	2.98357	+	2.98357i	0.354085	+	0.354085i	−0.507542	+	0.861627i	$0.669446\pi$
$72$		0			0
$73$	−1.45130	+	1.45130i	−0.169862	+	0.169862i	−0.786919	−	0.617057i	$-0.788325\pi$
$73$	−1.45130	+	1.45130i	−0.169862	+	0.169862i	0.617057	+	0.786919i	$0.288325\pi$
$74$	−4.76311	+	7.82213i	−0.553700	+	0.909305i
$75$		0			0
$76$	14.5634	−	1.22888i	1.67053	−	0.140962i
$77$	−3.46389	−	2.65793i	−0.394746	−	0.302900i
$78$		0			0
$79$	4.91023	−	8.50477i	0.552444	−	0.956861i	−0.445653	−	0.895206i	$-0.647029\pi$
$79$	4.91023	−	8.50477i	0.552444	−	0.956861i	0.998097	−	0.0616558i	$-0.0196381\pi$
$80$	4.00346	−	7.57610i	0.447600	−	0.847034i
$81$		0			0
$82$	−2.29014	+	5.18303i	−0.252903	+	0.572370i
$83$	−2.17172	−	0.285913i	−0.238378	−	0.0313830i	0.0103908	−	0.999946i	$-0.496692\pi$
$83$	−2.17172	−	0.285913i	−0.238378	−	0.0313830i	−0.248768	+	0.968563i	$0.580026\pi$
$84$		0			0
$85$	−1.50959	−	11.4665i	−0.163738	−	1.24371i
$86$	5.74034	+	10.5016i	0.618997	+	1.13242i
$87$		0			0
$88$	11.9442	−	2.31846i	1.27326	−	0.247148i
$89$	−2.17841	+	2.17841i	−0.230911	+	0.230911i	−0.813073	−	0.582162i	$-0.802207\pi$
$89$	−2.17841	+	2.17841i	−0.230911	+	0.230911i	0.582162	+	0.813073i	$0.302207\pi$
$90$		0			0
$91$	−1.40485	−	0.581909i	−0.147268	−	0.0610006i
$92$	3.94444	+	2.53002i	0.411237	+	0.263773i
$93$		0			0
$94$	−9.50055	−	7.64911i	−0.979907	−	0.788946i
$95$	−7.82717	−	13.5571i	−0.803051	−	1.39093i
$96$		0			0
$97$	4.24778	−	7.35737i	0.431297	−	0.747028i	−0.565689	−	0.824619i	$-0.691390\pi$
$97$	4.24778	−	7.35737i	0.431297	−	0.747028i	0.996985	+	0.0775912i	$0.0247229\pi$
$98$	−7.87330	+	3.04779i	−0.795323	+	0.307873i
$99$		0			0
$100$	0.820973	+	0.0383817i	0.0820973	+	0.00383817i
$101$	−7.98538	+	6.12739i	−0.794575	+	0.609698i	−0.924219	−	0.381862i	$-0.875283\pi$
$101$	−7.98538	+	6.12739i	−0.794575	+	0.609698i	0.129645	+	0.991560i	$0.458616\pi$
$102$		0			0
$103$	16.1860	+	4.33702i	1.59485	+	0.427339i	0.943482	−	0.331423i	$-0.107529\pi$
$103$	16.1860	+	4.33702i	1.59485	+	0.427339i	0.651368	+	0.758762i	$0.274195\pi$
$104$	3.80910	−	1.85658i	0.373513	−	0.182053i
$105$		0			0
$106$	−3.11727	+	5.11928i	−0.302776	+	0.497228i
$107$	8.79307	+	3.64221i	0.850058	+	0.352106i	0.764811	−	0.644254i	$-0.222832\pi$
$107$	8.79307	+	3.64221i	0.850058	+	0.352106i	0.0852469	+	0.996360i	$0.472832\pi$
$108$		0			0
$109$	2.67483	+	6.45762i	0.256203	+	0.618528i	0.998681	−	0.0513420i	$-0.0163499\pi$
$109$	2.67483	+	6.45762i	0.256203	+	0.618528i	−0.742479	+	0.669870i	$0.766350\pi$
$110$	−7.68990	−	10.5217i	−0.733203	−	1.00320i
$111$		0			0
$112$	−1.41207	+	3.80641i	−0.133428	+	0.359671i
$113$	−3.88868	−	6.73539i	−0.365816	−	0.633612i	0.623091	−	0.782150i	$-0.285877\pi$
$113$	−3.88868	−	6.73539i	−0.365816	−	0.633612i	−0.988907	+	0.148537i	$0.952543\pi$
$114$		0			0
$115$	0.655153	−	4.97638i	0.0610933	−	0.464050i
$116$	8.03545	+	3.77721i	0.746072	+	0.350705i
$117$		0			0
$118$	−4.15814	−	0.0971466i	−0.382788	−	0.00894307i
$119$	1.41824	+	5.29293i	0.130010	+	0.485202i
$120$		0			0
$121$	1.94241	−	7.24917i	0.176583	−	0.659016i
$122$	−0.134018	+	0.457169i	−0.0121334	+	0.0413901i
$123$		0			0
$124$	−18.7272	+	4.09117i	−1.68175	+	0.367398i
$125$	−4.43582	−	10.7090i	−0.396752	−	0.957844i
$126$		0			0
$127$			16.4140i			1.45650i	0.685309	+	0.728252i	$0.259667\pi$
$127$			16.4140i			1.45650i	−0.685309	+	0.728252i	$0.740333\pi$
$128$	−5.33438	−	9.97719i	−0.471497	−	0.881868i
$129$		0			0
$130$	−3.53533	−	2.84638i	−0.310069	−	0.249644i
$131$	13.9074	+	10.6715i	1.21509	+	0.932372i	0.999031	−	0.0440080i	$-0.0140127\pi$
$131$	13.9074	+	10.6715i	1.21509	+	0.932372i	0.216060	+	0.976380i	$0.430679\pi$
$132$		0			0
$133$	4.51517	+	5.88428i	0.391514	+	0.510232i
$134$	−5.40709	+	5.16021i	−0.467101	+	0.445774i
$135$		0			0
$136$	−13.6640	−	6.81711i	−1.17168	−	0.584562i
$137$	20.2591	−	5.42840i	1.73085	−	0.463780i	0.750470	−	0.660904i	$-0.229827\pi$
$137$	20.2591	−	5.42840i	1.73085	−	0.463780i	0.980378	+	0.197125i	$0.0631603\pi$
$138$		0			0
$139$	2.66709	−	0.351130i	0.226220	−	0.0297824i	−0.0165640	−	0.999863i	$-0.505273\pi$
$139$	2.66709	−	0.351130i	0.226220	−	0.0297824i	0.242784	+	0.970080i	$0.421939\pi$
$140$	4.33316	−	0.365640i	0.366219	−	0.0309022i
$141$		0			0
$142$	−3.52101	−	4.81761i	−0.295476	−	0.404285i
$143$		−	6.44473i		−	0.538935i
$144$		0			0
$145$		−	9.51028i		−	0.789786i
$146$	2.34343	−	1.71272i	0.193944	−	0.141746i
$147$		0			0
$148$	8.35574	−	9.89584i	0.686837	−	0.813433i
$149$	−16.7129	+	2.20030i	−1.36918	+	0.180256i	−0.779003	−	0.627020i	$-0.784274\pi$
$149$	−16.7129	+	2.20030i	−1.36918	+	0.180256i	−0.590174	+	0.807276i	$0.700941\pi$
$150$		0			0
$151$	−11.5109	+	3.08432i	−0.936740	+	0.250999i	−0.694726	−	0.719274i	$-0.744475\pi$
$151$	−11.5109	+	3.08432i	−0.936740	+	0.250999i	−0.242014	+	0.970273i	$0.577808\pi$
$152$	−20.6182	−	1.44721i	−1.67236	−	0.117385i
$153$		0			0
$154$	4.26296	+	4.46692i	0.343519	+	0.359955i
$155$	12.4990	+	16.2890i	1.00395	+	1.30837i
$156$		0			0
$157$	−11.7454	−	9.01257i	−0.937385	−	0.719281i	0.0224786	−	0.999747i	$-0.492844\pi$
$157$	−11.7454	−	9.01257i	−0.937385	−	0.719281i	−0.959864	+	0.280466i	$0.909511\pi$
$158$	−8.70966	+	10.8178i	−0.692904	+	0.860618i
$159$		0			0
$160$	−7.24073	+	9.71709i	−0.572430	+	0.768204i
$161$			2.37813i			0.187423i
$162$		0			0
$163$	1.16595	+	2.81484i	0.0913240	+	0.220476i	0.962941	−	0.269712i	$-0.0869284\pi$
$163$	1.16595	+	2.81484i	0.0913240	+	0.220476i	−0.871617	+	0.490187i	$0.836928\pi$
$164$	4.32650	−	6.74525i	0.337843	−	0.526716i
$165$		0			0
$166$	2.97268	+	0.871435i	0.230725	+	0.0676364i
$167$	−0.941472	+	3.51362i	−0.0728533	+	0.271892i	−0.992738	−	0.120297i	$-0.961615\pi$
$167$	−0.941472	+	3.51362i	−0.0728533	+	0.271892i	0.919885	+	0.392189i	$0.128282\pi$
$168$		0			0
$169$	2.78372	+	10.3890i	0.214133	+	0.799154i
$170$	−0.382020	+	16.3515i	−0.0292996	+	1.25410i
$171$		0			0
$172$	−5.73977	−	15.9225i	−0.437653	−	1.21408i
$173$	2.46882	−	18.7526i	0.187701	−	1.42573i	−0.595196	−	0.803581i	$-0.702925\pi$
$173$	2.46882	−	18.7526i	0.187701	−	1.42573i	0.782897	−	0.622152i	$-0.213741\pi$
$174$		0			0
$175$	0.208544	+	0.361208i	0.0157644	+	0.0273048i
$176$	−17.1949	+	0.644504i	−1.29611	+	0.0485813i
$177$		0			0
$178$	3.51750	−	2.57080i	0.263648	−	0.192690i
$179$	−2.08061	−	5.02303i	−0.155512	−	0.375439i	0.826852	−	0.562420i	$-0.190130\pi$
$179$	−2.08061	−	5.02303i	−0.155512	−	0.375439i	−0.982363	+	0.186981i	$0.940130\pi$
$180$		0			0
$181$	−1.19920	−	0.496727i	−0.0891362	−	0.0369214i	0.337670	−	0.941265i	$-0.390361\pi$
$181$	−1.19920	−	0.496727i	−0.0891362	−	0.0369214i	−0.426806	+	0.904343i	$0.640361\pi$
$182$	1.83673	+	1.11843i	0.136147	+	0.0829037i
$183$		0			0
$184$	−4.96230	−	4.39260i	−0.365825	−	0.323827i
$185$	−13.3999	−	3.59050i	−0.985181	−	0.263978i
$186$		0			0
$187$	−18.4251	+	14.1380i	−1.34737	+	1.03388i
$188$	11.6142	+	12.7534i	0.847052	+	0.930138i
$189$		0			0
$190$	7.99204	+	20.6457i	0.579804	+	1.49780i
$191$	−9.67208	+	16.7525i	−0.699847	+	1.21217i	0.268672	+	0.963232i	$0.413415\pi$
$191$	−9.67208	+	16.7525i	−0.699847	+	1.21217i	−0.968519	+	0.248939i	$0.919918\pi$
$192$		0			0
$193$	7.28617	+	12.6200i	0.524470	+	0.908408i	0.999594	+	0.0284897i	$0.00906978\pi$
$193$	7.28617	+	12.6200i	0.524470	+	0.908408i	−0.475124	+	0.879919i	$0.657597\pi$
$194$	−7.53462	+	9.35834i	−0.540954	+	0.671890i
$195$		0			0
$196$	11.6646	−	2.54825i	0.833183	−	0.182018i
$197$	−9.24225	−	3.82826i	−0.658483	−	0.272753i	0.0283171	−	0.999599i	$-0.490985\pi$
$197$	−9.24225	−	3.82826i	−0.658483	−	0.272753i	−0.686800	+	0.726846i	$0.740985\pi$
$198$		0			0
$199$	−18.4609	+	18.4609i	−1.30866	+	1.30866i	−0.386276	+	0.922383i	$0.626239\pi$
$199$	−18.4609	+	18.4609i	−1.30866	+	1.30866i	−0.922383	+	0.386276i	$0.873761\pi$
$200$	−1.13891	−	0.232025i	−0.0805328	−	0.0164066i
$201$		0			0
$202$	12.4904	−	6.82740i	0.878818	−	0.480374i
$203$	0.588143	+	4.46739i	0.0412795	+	0.313549i
$204$		0			0
$205$	−8.50993	−	1.12035i	−0.594359	−	0.0782489i
$206$	−21.6762	−	9.57769i	−1.51025	−	0.667309i
$207$		0			0
$208$	−5.72633	+	1.76675i	−0.397050	+	0.122502i
$209$	−15.7176	+	27.2237i	−1.08721	+	1.88310i
$210$		0			0
$211$	6.11216	+	4.69003i	0.420779	+	0.322875i	0.797355	−	0.603511i	$-0.206232\pi$
$211$	6.11216	+	4.69003i	0.420779	+	0.322875i	−0.376576	+	0.926386i	$0.622899\pi$
$212$	5.46850	−	6.47644i	0.375578	−	0.444804i
$213$		0			0
$214$	−11.4962	−	7.00035i	−0.785864	−	0.478534i
$215$	−12.8191	+	12.8191i	−0.874256	+	0.874256i
$216$		0			0
$217$	−6.87868	−	6.87868i	−0.466956	−	0.466956i
$218$	−2.33469	−	9.60523i	−0.158125	−	0.650548i
$219$		0			0
$220$	8.45976	+	16.3742i	0.570357	+	1.10395i
$221$	−4.92388	+	6.41693i	−0.331216	+	0.431649i
$222$		0			0
$223$	−15.0037	−	8.66241i	−1.00472	−	0.580078i	−0.0950816	−	0.995469i	$-0.530311\pi$
$223$	−15.0037	−	8.66241i	−1.00472	−	0.580078i	−0.909643	+	0.415392i	$0.863645\pi$
$224$	2.80035	−	5.01232i	0.187106	−	0.334900i
$225$		0			0
$226$	3.97059	+	10.2571i	0.264120	+	0.682295i
$227$	3.35498	−	25.4836i	0.222678	−	1.69140i	−0.406108	−	0.913825i	$-0.633114\pi$
$227$	3.35498	−	25.4836i	0.222678	−	1.69140i	0.628785	−	0.777579i	$-0.283552\pi$
$228$		0			0
$229$	3.10447	−	0.408711i	0.205149	−	0.0270084i	−0.0272513	−	0.999629i	$-0.508675\pi$
$229$	3.10447	−	0.408711i	0.205149	−	0.0270084i	0.232400	+	0.972620i	$0.425342\pi$
$230$	−1.99684	+	6.81174i	−0.131668	+	0.449153i
$231$		0			0
$232$	−10.4081	−	7.02437i	−0.683329	−	0.461172i
$233$	20.9855	+	20.9855i	1.37481	+	1.37481i	0.853163	+	0.521645i	$0.174681\pi$
$233$	20.9855	+	20.9855i	1.37481	+	1.37481i	0.521645	+	0.853163i	$0.325319\pi$
$234$		0			0
$235$	7.07039	−	17.0694i	0.461222	−	1.11349i
$236$	5.78957	+	1.03928i	0.376869	+	0.0676513i
$237$		0			0
$238$	−0.831772	−	7.70462i	−0.0539157	−	0.499417i
$239$	3.78438	−	2.18491i	0.244791	−	0.141330i	−0.372586	−	0.927998i	$-0.621529\pi$
$239$	3.78438	−	2.18491i	0.244791	−	0.141330i	0.617377	+	0.786667i	$0.288195\pi$
$240$		0			0
$241$	−6.71220	−	3.87529i	−0.432371	−	0.249629i	0.267985	−	0.963423i	$-0.413642\pi$
$241$	−6.71220	−	3.87529i	−0.432371	−	0.249629i	−0.700356	+	0.713794i	$0.746975\pi$
$242$	−4.28954	+	9.70808i	−0.275742	+	0.624059i
$243$		0			0
$244$	0.286617	−	0.609736i	0.0183488	−	0.0390344i
$245$	−7.78523	−	10.1459i	−0.497380	−	0.648198i
$246$		0			0
$247$	−2.83355	+	10.5749i	−0.180294	+	0.672868i
$248$	27.0588	−	1.64784i	1.71823	−	0.104638i
$249$		0			0
$250$	3.87174	+	15.9289i	0.244871	+	1.00743i
$251$	−2.35690	+	5.69006i	−0.148766	+	0.359153i	−0.980642	−	0.195808i	$-0.937267\pi$
$251$	−2.35690	+	5.69006i	−0.148766	+	0.359153i	0.831876	+	0.554961i	$0.187267\pi$
$252$		0			0
$253$	−9.31197	+	3.85714i	−0.585438	+	0.242497i
$254$	3.56660	−	22.9372i	0.223788	−	1.43921i
$255$		0			0
$256$	5.28643	+	15.1014i	0.330402	+	0.943840i
$257$	−13.5420	+	7.81847i	−0.844726	+	0.487703i	−0.858868	−	0.512197i	$-0.828832\pi$
$257$	−13.5420	+	7.81847i	−0.844726	+	0.487703i	0.0141420	+	0.999900i	$0.495498\pi$
$258$		0			0
$259$	6.51656	+	0.857921i	0.404919	+	0.0533086i
$260$	4.32186	+	4.74578i	0.268030	+	0.294321i
$261$		0			0
$262$	−17.1156	−	17.9345i	−1.05741	−	1.10800i
$263$	−4.92734	+	1.32028i	−0.303833	+	0.0814117i	−0.407514	−	0.913199i	$-0.633604\pi$
$263$	−4.92734	+	1.32028i	−0.303833	+	0.0814117i	0.103682	+	0.994611i	$0.466938\pi$
$264$		0			0
$265$	−8.76972	−	2.34984i	−0.538719	−	0.144349i
$266$	−5.03099	−	9.20391i	−0.308470	−	0.564328i
$267$		0			0
$268$	8.67724	−	6.03607i	0.530047	−	0.368712i
$269$	1.56831	−	0.649614i	0.0956214	−	0.0396077i	−0.334360	−	0.942445i	$-0.608520\pi$
$269$	1.56831	−	0.649614i	0.0956214	−	0.0396077i	0.429981	+	0.902838i	$0.358520\pi$
$270$		0			0
$271$	−1.58685			−0.0963942			−0.0481971	−	0.998838i	$-0.515348\pi$
$271$	−1.58685			−0.0963942			−0.0481971	+	0.998838i	$0.515348\pi$
$272$	17.6131	+	12.4954i	1.06795	+	0.757647i
$273$		0			0
$274$	−29.4900	+	3.18366i	−1.78155	+	0.192332i
$275$	−1.07613	+	1.40244i	−0.0648929	+	0.0845701i
$276$		0			0
$277$	10.3814	−	7.96596i	0.623760	−	0.478628i	−0.247869	−	0.968793i	$-0.579730\pi$
$277$	10.3814	−	7.96596i	0.623760	−	0.478628i	0.871629	+	0.490166i	$0.163064\pi$
$278$	−3.80335	−	0.0888576i	−0.228110	−	0.00532932i
$279$		0			0
$280$	−6.13470	−	0.430601i	−0.366619	−	0.0257334i
$281$	−0.699325	−	2.60992i	−0.0417182	−	0.155695i	0.941925	−	0.335824i	$-0.109015\pi$
$281$	−0.699325	−	2.60992i	−0.0417182	−	0.155695i	−0.983643	+	0.180130i	$0.942348\pi$
$282$		0			0
$283$	−0.786331	−	5.97277i	−0.0467425	−	0.355045i	−0.998794	−	0.0491055i	$-0.984363\pi$
$283$	−0.786331	−	5.97277i	−0.0467425	−	0.355045i	0.952051	−	0.305939i	$-0.0989704\pi$
$284$	3.87351	+	7.49731i	0.229850	+	0.444883i
$285$		0			0
$286$	−1.40038	+	9.00600i	−0.0828060	+	0.532536i
$287$	4.06676			0.240053
$288$		0			0
$289$	12.1473			0.714545
$290$	−2.06649	+	13.2899i	−0.121349	+	0.780408i
$291$		0			0
$292$	−3.64692	+	1.88419i	−0.213420	+	0.110264i
$293$	1.14284	+	8.68074i	0.0667655	+	0.507134i	0.991854	+	0.127382i	$0.0406574\pi$
$293$	1.14284	+	8.68074i	0.0667655	+	0.507134i	−0.925088	+	0.379752i	$0.876009\pi$
$294$		0			0
$295$	−1.63065	−	6.08568i	−0.0949403	−	0.354322i
$296$	−13.8268	+	12.0130i	−0.803664	+	0.698243i
$297$		0			0
$298$	23.8331	+	0.556812i	1.38062	+	0.0322553i
$299$	−2.78491	+	2.13694i	−0.161055	+	0.123582i
$300$		0			0
$301$	5.22891	−	6.81445i	0.301389	−	0.392778i
$302$	16.7557	−	1.80890i	0.964182	−	0.104091i
$303$		0			0
$304$	28.4978	+	6.50250i	1.63446	+	0.372944i
$305$	−0.721648			−0.0413214
$306$		0			0
$307$	−25.8866	+	10.7226i	−1.47742	+	0.611969i	−0.968538	−	0.248865i	$-0.919942\pi$
$307$	−25.8866	+	10.7226i	−1.47742	+	0.611969i	−0.508886	+	0.860834i	$0.669942\pi$
$308$	−4.98654	−	7.16847i	−0.284134	−	0.408461i
$309$		0			0
$310$	−13.9269	−	25.4786i	−0.790997	−	1.44709i
$311$	−0.827596	−	0.221754i	−0.0469287	−	0.0125745i	0.235278	−	0.971928i	$-0.424400\pi$
$311$	−0.827596	−	0.221754i	−0.0469287	−	0.0125745i	−0.282207	+	0.959354i	$0.591066\pi$
$312$		0			0
$313$	17.6037	−	4.71691i	0.995022	−	0.266615i	0.275663	−	0.961254i	$-0.411102\pi$
$313$	17.6037	−	4.71691i	0.995022	−	0.266615i	0.719359	+	0.694639i	$0.244436\pi$
$314$	14.4549	+	15.1465i	0.815739	+	0.854767i
$315$		0			0
$316$	14.5217	−	13.2245i	0.816908	−	0.743936i
$317$	11.9153	+	1.56867i	0.669227	+	0.0881055i	0.457481	−	0.889219i	$-0.348752\pi$
$317$	11.9153	+	1.56867i	0.669227	+	0.0881055i	0.211746	+	0.977325i	$0.432085\pi$
$318$		0			0
$319$	−16.5389	+	9.54871i	−0.925998	+	0.534625i
$320$	12.2298	−	12.0055i	0.683665	−	0.671129i
$321$		0			0
$322$	0.516745	−	3.32325i	0.0287971	−	0.185198i
$323$	36.4491	−	15.0977i	2.02808	−	0.840060i
$324$		0			0
$325$	−0.235599	+	0.568787i	−0.0130687	+	0.0315506i
$326$	−1.01768	−	4.18687i	−0.0563641	−	0.231889i
$327$		0			0
$328$	−7.51163	+	8.48585i	−0.414760	+	0.468553i
$329$	−2.26564	+	8.45550i	−0.124909	+	0.466167i
$330$		0			0
$331$	9.82898	+	12.8094i	0.540249	+	0.704067i	0.981097	−	0.193515i	$-0.0619888\pi$
$331$	9.82898	+	12.8094i	0.540249	+	0.704067i	−0.440848	+	0.897582i	$0.645322\pi$
$332$	−3.96474	−	1.86370i	−0.217593	−	0.102284i
$333$		0			0
$334$	2.07911	−	4.70544i	0.113764	−	0.257470i
$335$	−9.80494	−	5.66089i	−0.535701	−	0.309287i
$336$		0			0
$337$	−11.5406	+	6.66299i	−0.628658	+	0.362956i	−0.780232	−	0.625490i	$-0.784899\pi$
$337$	−11.5406	+	6.66299i	−0.628658	+	0.362956i	0.151574	+	0.988446i	$0.451566\pi$
$338$	−1.63261	−	15.1227i	−0.0888021	−	0.822565i
$339$		0			0
$340$	4.08686	−	22.7669i	0.221641	−	1.23471i
$341$	15.7779	−	38.0913i	0.854422	−	2.06276i
$342$		0			0
$343$	9.30836	+	9.30836i	0.502604	+	0.502604i
$344$	4.56107	+	23.4976i	0.245916	+	1.26691i
$345$		0			0
$346$	−7.52474	+	25.6688i	−0.404532	+	1.37996i
$347$	5.41397	−	0.712763i	0.290637	−	0.0382631i	0.0162021	−	0.999869i	$-0.494842\pi$
$347$	5.41397	−	0.712763i	0.290637	−	0.0382631i	0.274435	+	0.961606i	$0.411509\pi$
$348$		0			0
$349$	−4.32405	+	32.8444i	−0.231461	+	1.75812i	0.342763	+	0.939422i	$0.388637\pi$
$349$	−4.32405	+	32.8444i	−0.231461	+	1.75812i	−0.574224	+	0.818698i	$0.694696\pi$
$350$	−0.212936	−	0.550074i	−0.0113819	−	0.0294027i
$351$		0			0
$352$	24.1685	+	2.83563i	1.28818	+	0.151140i
$353$	−29.4504	−	17.0032i	−1.56748	−	0.904988i	−0.996461	−	0.0840537i	$-0.973213\pi$
$353$	−29.4504	−	17.0032i	−1.56748	−	0.904988i	−0.571023	−	0.820934i	$-0.693453\pi$
$354$		0			0
$355$	5.50251	−	7.17101i	0.292043	−	0.380598i
$356$	−5.47403	+	2.82818i	−0.290123	+	0.149893i
$357$		0			0
$358$	1.81603	+	7.47138i	0.0959801	+	0.394875i
$359$	−13.1660	−	13.1660i	−0.694877	−	0.694877i	0.268424	−	0.963301i	$-0.413497\pi$
$359$	−13.1660	−	13.1660i	−0.694877	−	0.694877i	−0.963301	+	0.268424i	$0.913497\pi$
$360$		0			0
$361$	24.3249	−	24.3249i	1.28026	−	1.28026i
$362$	1.56786	+	0.954712i	0.0824049	+	0.0501785i
$363$		0			0
$364$	−2.32365	−	1.96202i	−0.121793	−	0.102838i
$365$	3.48820	+	2.67659i	0.182581	+	0.140099i
$366$		0			0
$367$	−0.868465	+	1.50423i	−0.0453335	+	0.0785199i	−0.887802	−	0.460226i	$-0.847768\pi$
$367$	−0.868465	+	1.50423i	−0.0453335	+	0.0785199i	0.842468	+	0.538746i	$0.181102\pi$
$368$	5.97995	+	7.21657i	0.311726	+	0.376189i
$369$		0			0
$370$	17.9451	+	7.92910i	0.932923	+	0.412214i
$371$	4.26483	+	0.561476i	0.221419	+	0.0291504i
$372$		0			0
$373$	−4.10050	−	31.1464i	−0.212316	−	1.61270i	−0.683015	−	0.730404i	$-0.739332\pi$
$373$	−4.10050	−	31.1464i	−0.212316	−	1.61270i	0.470699	−	0.882294i	$-0.344002\pi$
$374$	28.8196	−	15.7532i	1.49023	−	0.814579i
$375$		0			0
$376$	−13.4587	−	20.3455i	−0.694080	−	1.04924i
$377$	−4.70303	+	4.70303i	−0.242218	+	0.242218i
$378$		0			0
$379$	−24.9141	−	10.3198i	−1.27975	−	0.530091i	−0.363837	−	0.931462i	$-0.618534\pi$
$379$	−24.9141	−	10.3198i	−1.27975	−	0.530091i	−0.915915	+	0.401372i	$0.868534\pi$
$380$	−6.68214	−	30.5873i	−0.342786	−	1.56910i
$381$		0			0
$382$	17.1561	−	21.3087i	0.877784	−	1.09025i
$383$	−5.45733	−	9.45238i	−0.278857	−	0.482994i	0.692244	−	0.721663i	$-0.256622\pi$
$383$	−5.45733	−	9.45238i	−0.278857	−	0.482994i	−0.971101	+	0.238669i	$0.923289\pi$
$384$		0			0
$385$	−4.67659	+	8.10009i	−0.238341	+	0.412819i
$386$	−7.43964	−	19.2187i	−0.378668	−	0.978205i
$387$		0			0
$388$	12.5625	−	11.4403i	0.637765	−	0.580795i
$389$	2.46155	−	1.88881i	0.124805	−	0.0957665i	−0.544473	−	0.838779i	$-0.683270\pi$
$389$	2.46155	−	1.88881i	0.124805	−	0.0957665i	0.669278	+	0.743012i	$0.266604\pi$
$390$		0			0
$391$	12.2187	+	3.27399i	0.617927	+	0.165573i
$392$	−16.8540	+	1.02639i	−0.851256	+	0.0518404i
$393$		0			0
$394$	12.0835	+	7.35795i	0.608756	+	0.370688i
$395$	−19.4361	−	8.05070i	−0.977937	−	0.405075i
$396$		0			0
$397$	−9.05217	−	21.8539i	−0.454316	−	1.09681i	−0.970665	−	0.240437i	$-0.922709\pi$
$397$	−9.05217	−	21.8539i	−0.454316	−	1.09681i	0.516349	−	0.856378i	$-0.327291\pi$
$398$	29.8090	−	21.7863i	1.49419	−	1.09205i
$399$		0			0
$400$	1.54111	+	0.571709i	0.0770557	+	0.0285855i
$401$	−7.88970	−	13.6654i	−0.393993	−	0.682416i	0.598979	−	0.800765i	$-0.295573\pi$
$401$	−7.88970	−	13.6654i	−0.393993	−	0.682416i	−0.992972	+	0.118349i	$0.962240\pi$
$402$		0			0
$403$	1.87424	−	14.2363i	0.0933627	−	0.709160i
$404$	−18.9378	+	6.82673i	−0.942191	+	0.339642i
$405$		0			0
$406$	0.148837	−	6.37062i	0.00738663	−	0.316168i
$407$	7.21001	+	26.9081i	0.357387	+	1.33379i
$408$		0			0
$409$	−6.88466	+	25.6939i	−0.340425	+	1.27048i	0.557443	+	0.830215i	$0.311783\pi$
$409$	−6.88466	+	25.6939i	−0.340425	+	1.27048i	−0.897867	+	0.440266i	$0.854884\pi$
$410$	11.6485	+	3.41473i	0.575279	+	0.168641i
$411$		0			0
$412$	28.2097	+	18.0941i	1.38979	+	0.891432i
$413$	1.14234	+	2.75786i	0.0562110	+	0.135705i
$414$		0			0
$415$			4.69243i			0.230342i
$416$	8.38599	−	1.22461i	0.411157	−	0.0600416i
$417$		0			0
$418$	27.8795	−	34.6277i	1.36363	−	1.69369i
$419$	−14.1183	−	10.8334i	−0.689725	−	0.529245i	0.203376	−	0.979101i	$-0.434809\pi$
$419$	−14.1183	−	10.8334i	−0.689725	−	0.529245i	−0.893101	+	0.449856i	$0.851475\pi$
$420$		0			0
$421$	−6.35570	−	8.28291i	−0.309758	−	0.403684i	0.612369	−	0.790572i	$-0.290217\pi$
$421$	−6.35570	−	8.28291i	−0.309758	−	0.403684i	−0.922127	+	0.386888i	$0.873550\pi$
$422$	−7.52217	−	7.88206i	−0.366173	−	0.383692i
$423$		0			0
$424$	−9.04907	+	7.86206i	−0.439462	+	0.381815i
$425$	2.14297	−	0.574207i	0.103949	−	0.0278531i
$426$		0			0
$427$	0.338989	−	0.0446287i	0.0164048	−	0.00215974i
$428$	14.5439	+	12.2804i	0.703007	+	0.593598i
$429$		0			0
$430$	20.6992	−	15.1282i	0.998202	−	0.729548i
$431$		−	33.1788i		−	1.59817i	−0.601220	−	0.799084i	$-0.705318\pi$
$431$		−	33.1788i		−	1.59817i	0.601220	−	0.799084i	$-0.294682\pi$
$432$		0			0
$433$		−	12.9633i		−	0.622976i	−0.950250	−	0.311488i	$-0.899173\pi$
$433$		−	12.9633i		−	0.622976i	0.950250	−	0.311488i	$-0.100827\pi$
$434$	8.11775	+	11.1071i	0.389664	+	0.533157i
$435$		0			0
$436$	1.17542	+	13.9299i	0.0562926	+	0.667119i
$437$	16.9756	−	2.23488i	0.812051	−	0.106909i
$438$		0			0
$439$	12.2184	−	3.27390i	0.583151	−	0.156255i	0.0448299	−	0.998995i	$-0.485725\pi$
$439$	12.2184	−	3.27390i	0.583151	−	0.156255i	0.538321	+	0.842740i	$0.319059\pi$
$440$	−8.26391	−	24.7198i	−0.393966	−	1.17847i
$441$		0			0
$442$	8.27507	−	7.89724i	0.393605	−	0.375633i
$443$	−5.21798	−	6.80020i	−0.247914	−	0.323087i	0.652776	−	0.757551i	$-0.273604\pi$
$443$	−5.21798	−	6.80020i	−0.247914	−	0.323087i	−0.900689	+	0.434464i	$0.856938\pi$
$444$		0			0
$445$	5.23580	+	4.01757i	0.248201	+	0.190451i
$446$	19.0843	+	15.3652i	0.903667	+	0.727563i
$447$		0			0
$448$	−5.00239	+	6.39583i	−0.236341	+	0.302175i
$449$			14.4515i			0.682010i	0.940061	+	0.341005i	$0.110767\pi$
$449$			14.4515i			0.682010i	−0.940061	+	0.341005i	$0.889233\pi$
$450$		0			0
$451$	6.59596	+	15.9241i	0.310592	+	0.749835i
$452$	−3.31981	−	15.1963i	−0.156150	−	0.714775i
$453$		0			0
$454$	−10.2256	+	34.8823i	−0.479913	+	1.63711i
$455$	−0.843089	+	3.14645i	−0.0395246	+	0.147508i
$456$		0			0
$457$	10.8555	+	40.5132i	0.507797	+	1.89513i	0.441349	+	0.897335i	$0.354500\pi$
$457$	10.8555	+	40.5132i	0.507797	+	1.89513i	0.0664480	+	0.997790i	$0.478833\pi$
$458$	−4.42706	−	0.103429i	−0.206863	−	0.00483293i
$459$		0			0
$460$	4.27055	−	9.08497i	0.199116	−	0.423589i
$461$	−4.86953	+	36.9877i	−0.226796	+	1.72269i	0.377568	+	0.925982i	$0.376761\pi$
$461$	−4.86953	+	36.9877i	−0.226796	+	1.72269i	−0.604364	+	0.796708i	$0.706573\pi$
$462$		0			0
$463$	−3.54843	−	6.14606i	−0.164910	−	0.285632i	0.771714	−	0.635970i	$-0.219400\pi$
$463$	−3.54843	−	6.14606i	−0.164910	−	0.285632i	−0.936623	+	0.350339i	$0.886067\pi$
$464$	13.0182	+	12.0776i	0.604357	+	0.560688i
$465$		0			0
$466$	−24.7657	−	33.8856i	−1.14725	−	1.56972i
$467$	−4.76497	−	11.5037i	−0.220497	−	0.532326i	0.774461	−	0.632622i	$-0.218021\pi$
$467$	−4.76497	−	11.5037i	−0.220497	−	0.532326i	−0.994958	+	0.100296i	$0.968021\pi$
$468$		0			0
$469$	4.95589	+	2.05280i	0.228842	+	0.0947893i
$470$	−13.5893	+	22.3169i	−0.626829	+	1.02940i
$471$		0			0
$472$	−7.86464	−	2.71033i	−0.361999	−	0.124753i
$473$	35.1640	+	9.42215i	1.61684	+	0.433231i
$474$		0			0
$475$	2.38239	−	1.82807i	0.109312	−	0.0838777i
$476$	−0.511804	+	10.9473i	−0.0234585	+	0.501770i
$477$		0			0
$478$	−5.76314	+	2.23094i	−0.263600	+	0.102041i
$479$	−17.9620	+	31.1111i	−0.820706	+	1.42150i	0.0844520	+	0.996428i	$0.473086\pi$
$479$	−17.9620	+	31.1111i	−0.820706	+	1.42150i	−0.905158	+	0.425076i	$0.860247\pi$
$480$		0			0
$481$	4.85096	+	8.40210i	0.221185	+	0.383103i
$482$	8.53770	+	6.87391i	0.388882	+	0.313098i
$483$		0			0
$484$	8.10376	−	12.6342i	0.368353	−	0.574282i
$485$	−16.8139	−	6.96456i	−0.763482	−	0.316244i
$486$		0			0
$487$	1.72336	−	1.72336i	0.0780927	−	0.0780927i	−0.666982	−	0.745074i	$-0.732414\pi$
$487$	1.72336	−	1.72336i	0.0780927	−	0.0780927i	0.745074	+	0.666982i	$0.232414\pi$
$488$	−0.533015	+	0.789779i	−0.0241284	+	0.0357516i
$489$		0			0
$490$	8.67464	+	15.8698i	0.391880	+	0.716923i
$491$	0.937781	+	7.12316i	0.0423215	+	0.321464i	0.999490	+	0.0319323i	$0.0101661\pi$
$491$	0.937781	+	7.12316i	0.0423215	+	0.321464i	−0.957169	+	0.289531i	$0.906501\pi$
$492$		0			0
$493$	23.7629	+	3.12844i	1.07023	+	0.140898i
$494$	6.25749	−	14.1619i	0.281538	−	0.637176i
$495$		0			0
$496$	−38.1705	−	3.57687i	−1.71391	−	0.160606i
$497$	−2.14129	+	3.70882i	−0.0960499	+	0.166363i
$498$		0			0
$499$	28.0851	+	21.5504i	1.25726	+	0.964730i	0.999999	−	0.00161157i	$-0.000512980\pi$
$499$	28.0851	+	21.5504i	1.25726	+	0.964730i	0.257262	+	0.966342i	$0.417180\pi$
$500$	−1.94927	−	23.1006i	−0.0871740	−	1.03309i
$501$		0			0
$502$	4.52997	−	7.43927i	0.202183	−	0.332031i
$503$	14.0204	−	14.0204i	0.625137	−	0.625137i	−0.321704	−	0.946840i	$-0.604255\pi$
$503$	14.0204	−	14.0204i	0.625137	−	0.625137i	0.946840	+	0.321704i	$0.104255\pi$
$504$		0			0
$505$	15.2467	+	15.2467i	0.678469	+	0.678469i
$506$	13.8509	−	3.36665i	0.615746	−	0.149666i
$507$		0			0
$508$	−9.96807	+	31.2780i	−0.442262	+	1.38774i
$509$	18.9980	−	24.7587i	0.842072	−	1.09741i	−0.151967	−	0.988386i	$-0.548561\pi$
$509$	18.9980	−	24.7587i	0.842072	−	1.09741i	0.994039	−	0.109025i	$-0.0347727\pi$
$510$		0			0
$511$	−1.80408	−	1.04159i	−0.0798079	−	0.0460771i
$512$	−4.10596	−	22.2518i	−0.181460	−	0.983398i
$513$		0			0
$514$	20.6227	−	7.98315i	0.909629	−	0.352122i
$515$	4.68549	−	35.5898i	0.206467	−	1.56827i
$516$		0			0
$517$	−36.7836	+	4.84265i	−1.61774	+	0.212979i
$518$	−8.91995	−	2.61486i	−0.391920	−	0.114890i
$519$		0			0
$520$	−5.00824	−	7.57096i	−0.219626	−	0.332008i
$521$	6.89274	+	6.89274i	0.301977	+	0.301977i	0.841787	−	0.539810i	$-0.181504\pi$
$521$	6.89274	+	6.89274i	0.301977	+	0.301977i	−0.539810	+	0.841787i	$0.681504\pi$
$522$		0			0
$523$	−0.948159	+	2.28906i	−0.0414601	+	0.100094i	−0.943253	−	0.332075i	$-0.892251\pi$
$523$	−0.948159	+	2.28906i	−0.0414601	+	0.100094i	0.901793	+	0.432168i	$0.142251\pi$
$524$	20.0207	+	28.7811i	0.874610	+	1.25731i
$525$		0			0
$526$	7.17244	−	0.774319i	0.312733	−	0.0337619i
$527$	−44.8122	+	25.8723i	−1.95205	+	1.12702i
$528$		0			0
$529$	−15.1642	−	8.75504i	−0.659312	−	0.380654i
$530$	11.7444	+	5.18929i	0.510144	+	0.225408i
$531$		0			0
$532$	5.03049	+	13.9549i	0.218099	+	0.605023i
$533$	3.65430	+	4.76237i	0.158285	+	0.206281i
$534$		0			0
$535$	5.27696	−	19.6939i	0.228143	−	0.851440i
$536$	−13.4373	+	6.54945i	−0.580405	+	0.282893i
$537$		0			0
$538$	−2.33274	+	0.567006i	−0.100572	+	0.0244454i
$539$	−9.82755	+	23.7258i	−0.423303	+	1.02194i
$540$		0			0
$541$	−33.1384	+	13.7264i	−1.42473	+	0.590142i	−0.956044	−	0.293223i	$-0.905272\pi$
$541$	−33.1384	+	13.7264i	−1.42473	+	0.590142i	−0.468685	+	0.883365i	$0.655272\pi$
$542$	2.21749	+	0.344807i	0.0952496	+	0.0148107i
$543$		0			0
$544$	−21.8978	−	21.2885i	−0.938858	−	0.912738i
$545$	12.9673	−	7.48668i	0.555459	−	0.320694i
$546$		0			0
$547$	22.4101	+	2.95034i	0.958186	+	0.126148i	0.593368	−	0.804931i	$-0.297798\pi$
$547$	22.4101	+	2.95034i	0.958186	+	0.126148i	0.364818	+	0.931079i	$0.381131\pi$
$548$	41.9017	+	1.95897i	1.78995	+	0.0836828i
$549$		0			0
$550$	1.80854	−	1.72596i	0.0771163	−	0.0735953i
$551$	31.3363	−	8.39654i	1.33497	−	0.357705i
$552$		0			0
$553$	9.62785	+	2.57977i	0.409418	+	0.109703i
$554$	−16.2382	+	8.87601i	−0.689893	+	0.377106i
$555$		0			0
$556$	5.29557	+	0.950602i	0.224582	+	0.0403145i
$557$	−27.8912	+	11.5529i	−1.18179	+	0.489513i	−0.885073	−	0.465453i	$-0.845892\pi$
$557$	−27.8912	+	11.5529i	−1.18179	+	0.489513i	−0.296716	+	0.954966i	$0.595892\pi$
$558$		0			0
$559$	12.6786			0.536249
$560$	8.47920	+	1.93474i	0.358311	+	0.0817578i
$561$		0			0
$562$	0.410142	+	3.79911i	0.0173008	+	0.160256i
$563$	−14.0095	+	18.2575i	−0.590429	+	0.769462i	−0.989038	−	0.147659i	$-0.952826\pi$
$563$	−14.0095	+	18.2575i	−0.590429	+	0.769462i	0.398609	+	0.917121i	$0.369493\pi$
$564$		0			0
$565$	−13.2179	+	10.1424i	−0.556079	+	0.426695i
$566$	−0.198990	+	8.51734i	−0.00836419	+	0.358011i
$567$		0			0
$568$	−3.78383	−	11.3186i	−0.158766	−	0.474917i
$569$	−8.67494	−	32.3753i	−0.363673	−	1.35724i	−0.869211	−	0.494441i	$-0.835373\pi$
$569$	−8.67494	−	32.3753i	−0.363673	−	1.35724i	0.505539	−	0.862804i	$-0.331294\pi$
$570$		0			0
$571$	0.282974	+	2.14940i	0.0118421	+	0.0899495i	0.996345	−	0.0854171i	$-0.0272223\pi$
$571$	0.282974	+	2.14940i	0.0118421	+	0.0899495i	−0.984503	+	0.175367i	$0.943889\pi$
$572$	3.91383	−	12.2809i	0.163646	−	0.513490i
$573$		0			0
$574$	−5.68298	−	0.883668i	−0.237203	−	0.0368836i
$575$	0.962844			0.0401534
$576$		0			0
$577$	26.0027			1.08251			0.541254	−	0.840859i	$-0.317950\pi$
$577$	26.0027			1.08251			0.541254	+	0.840859i	$0.317950\pi$
$578$	−16.9748	−	2.63948i	−0.706061	−	0.109788i
$579$		0			0
$580$	5.77552	−	18.1225i	0.239815	−	0.752496i
$581$	−0.290193	−	2.20424i	−0.0120392	−	0.0914471i
$582$		0			0
$583$	4.71867	+	17.6103i	0.195427	+	0.729344i
$584$	5.50569	−	1.84057i	0.227827	−	0.0761633i
$585$		0			0
$586$	0.289210	−	12.3790i	0.0119471	−	0.511371i
$587$	2.40040	−	1.84189i	0.0990750	−	0.0760229i	−0.558036	−	0.829817i	$-0.688445\pi$
$587$	2.40040	−	1.84189i	0.0990750	−	0.0760229i	0.657111	+	0.753794i	$0.271778\pi$
$588$		0			0
$589$	−42.6370	+	55.5656i	−1.75683	+	2.28954i
$590$	0.956350	+	8.85858i	0.0393723	+	0.364702i
$591$		0			0
$592$	21.9321	−	13.7828i	0.901404	−	0.566471i
$593$	−11.5374			−0.473783			−0.236891	−	0.971536i	$-0.576129\pi$
$593$	−11.5374			−0.473783			−0.236891	+	0.971536i	$0.576129\pi$
$594$		0			0
$595$	10.8450	−	4.49215i	0.444602	−	0.184160i
$596$	−33.1839	−	5.95680i	−1.35927	−	0.244000i
$597$		0			0
$598$	4.35602	−	2.38106i	0.178131	−	0.0973690i
$599$	−41.6644	−	11.1639i	−1.70236	−	0.456146i	−0.728828	−	0.684697i	$-0.759935\pi$
$599$	−41.6644	−	11.1639i	−1.70236	−	0.456146i	−0.973532	+	0.228551i	$0.926601\pi$
$600$		0			0
$601$	31.8874	−	8.54420i	1.30071	−	0.348525i	0.458994	−	0.888440i	$-0.348210\pi$
$601$	31.8874	−	8.54420i	1.30071	−	0.348525i	0.841720	+	0.539914i	$0.181543\pi$
$602$	−8.78770	+	8.38646i	−0.358160	+	0.341807i
$603$		0			0
$604$	−23.8078	−	1.11305i	−0.968726	−	0.0452894i
$605$	−15.9395	−	2.09848i	−0.648034	−	0.0853153i
$606$		0			0
$607$	18.3285	−	10.5819i	0.743929	−	0.429508i	−0.0795670	−	0.996830i	$-0.525354\pi$
$607$	18.3285	−	10.5819i	0.743929	−	0.429508i	0.823496	+	0.567322i	$0.192020\pi$
$608$	−38.4105	−	15.2790i	−1.55775	−	0.619646i
$609$		0			0
$610$	1.00845	+	0.156807i	0.0408308	+	0.00634893i
$611$	−11.9376	+	4.94473i	−0.482945	+	0.200042i
$612$		0			0
$613$	−7.04864	+	17.0169i	−0.284692	+	0.687307i	−0.999933	−	0.0115710i	$-0.996317\pi$
$613$	−7.04864	+	17.0169i	−0.284692	+	0.687307i	0.715241	+	0.698878i	$0.246317\pi$
$614$	38.5043	−	9.35904i	1.55391	−	0.377700i
$615$		0			0
$616$	5.41065	+	11.1009i	0.218001	+	0.447268i
$617$	3.78551	−	14.1277i	0.152399	−	0.568760i	−0.846915	−	0.531728i	$-0.821543\pi$
$617$	3.78551	−	14.1277i	0.152399	−	0.568760i	0.999314	−	0.0370322i	$-0.0117904\pi$
$618$		0			0
$619$	−21.5005	−	28.0199i	−0.864176	−	1.12622i	−0.990943	−	0.134284i	$-0.957127\pi$
$619$	−21.5005	−	28.0199i	−0.864176	−	1.12622i	0.126767	−	0.991933i	$-0.459540\pi$
$620$	13.9256	+	38.6305i	0.559264	+	1.55144i
$621$		0			0
$622$	1.10831	+	0.489712i	0.0444394	+	0.0196356i
$623$	−2.70793	−	1.56343i	−0.108491	−	0.0626374i
$624$		0			0
$625$	−19.7250	+	11.3882i	−0.789000	+	0.455529i
$626$	−25.6248	+	2.76639i	−1.02417	+	0.110567i
$627$		0			0
$628$	−16.9084	−	24.3070i	−0.674720	−	0.969953i
$629$	13.3793	−	32.3006i	0.533469	−	1.28791i
$630$		0			0
$631$	−18.2865	−	18.2865i	−0.727975	−	0.727975i	0.242241	−	0.970216i	$-0.422117\pi$
$631$	−18.2865	−	18.2865i	−0.727975	−	0.727975i	−0.970216	+	0.242241i	$0.922117\pi$
$632$	−23.1664	+	15.3248i	−0.921511	+	0.609586i
$633$		0			0
$634$	−16.3098	−	4.78116i	−0.647744	−	0.189884i
$635$	34.8614	−	4.58959i	1.38343	−	0.182132i
$636$		0			0
$637$	−1.16740	+	8.86732i	−0.0462543	+	0.351336i
$638$	25.1866	−	9.74984i	0.997146	−	0.386000i
$639$		0			0
$640$	−19.6988	+	14.1194i	−0.778665	+	0.558117i
$641$	26.6775	+	15.4023i	1.05370	+	0.608352i	0.923682	−	0.383160i	$-0.125164\pi$
$641$	26.6775	+	15.4023i	1.05370	+	0.608352i	0.130015	+	0.991512i	$0.458497\pi$
$642$		0			0
$643$	8.78636	−	11.4506i	0.346500	−	0.451568i	−0.587296	−	0.809372i	$-0.699808\pi$
$643$	8.78636	−	11.4506i	0.346500	−	0.451568i	0.933797	+	0.357804i	$0.116474\pi$
$644$	−1.44422	+	4.53170i	−0.0569103	+	0.178574i
$645$		0			0
$646$	−54.2154	+	13.1778i	−2.13308	+	0.518475i
$647$	24.9147	+	24.9147i	0.979498	+	0.979498i	0.999794	−	0.0202960i	$-0.00646087\pi$
$647$	24.9147	+	24.9147i	0.979498	+	0.979498i	−0.0202960	+	0.999794i	$0.506461\pi$
$648$		0			0
$649$	−8.94605	+	8.94605i	−0.351163	+	0.351163i
$650$	0.452823	−	0.743642i	0.0177612	−	0.0291680i
$651$		0			0
$652$	0.512362	+	6.07195i	0.0200656	+	0.237796i
$653$	0.207119	+	0.158928i	0.00810520	+	0.00621934i	0.612806	−	0.790233i	$-0.290041\pi$
$653$	0.207119	+	0.158928i	0.00810520	+	0.00621934i	−0.604701	+	0.796453i	$0.706707\pi$
$654$		0			0
$655$	18.7763	−	32.5215i	0.733651	−	1.27072i
$656$	12.3408	−	10.2261i	0.481827	−	0.399262i
$657$		0			0
$658$	5.00335	−	11.3236i	0.195051	−	0.441439i
$659$	−9.44652	−	1.24366i	−0.367984	−	0.0484460i	−0.0557332	−	0.998446i	$-0.517750\pi$
$659$	−9.44652	−	1.24366i	−0.367984	−	0.0484460i	−0.312251	+	0.950000i	$0.601083\pi$
$660$		0			0
$661$	−0.965154	−	7.33107i	−0.0375402	−	0.285146i	−0.999910	−	0.0134033i	$-0.995733\pi$
$661$	−0.965154	−	7.33107i	−0.0375402	−	0.285146i	0.962370	−	0.271742i	$-0.0875999\pi$
$662$	−10.9519	−	20.0358i	−0.425656	−	0.778714i
$663$		0			0
$664$	5.13544	+	3.46587i	0.199294	+	0.134502i
$665$	11.2350	−	11.2350i	0.435675	−	0.435675i
$666$		0			0
$667$	9.61014	+	3.98065i	0.372106	+	0.154131i
$668$	−3.92783	+	6.12370i	−0.151972	+	0.236933i
$669$		0			0
$670$	12.4716	+	10.0412i	0.481819	+	0.387924i
$671$	0.724564	+	1.25498i	0.0279715	+	0.0484480i
$672$		0			0
$673$	−2.66322	+	4.61284i	−0.102660	+	0.177812i	−0.912780	−	0.408452i	$-0.866069\pi$
$673$	−2.66322	+	4.61284i	−0.102660	+	0.177812i	0.810120	+	0.586264i	$0.199402\pi$
$674$	17.5749	−	6.80333i	0.676961	−	0.262054i
$675$		0			0
$676$	−1.00457	+	21.4875i	−0.0386374	+	0.826442i
$677$	15.5474	−	11.9299i	0.597534	−	0.458504i	−0.265178	−	0.964199i	$-0.585431\pi$
$677$	15.5474	−	11.9299i	0.597534	−	0.458504i	0.862712	+	0.505696i	$0.168764\pi$
$678$		0			0
$679$	8.32893	+	2.23173i	0.319635	+	0.0856460i
$680$	−10.6581	+	30.9269i	−0.408719	+	1.18599i
$681$		0			0
$682$	−30.3253	+	49.8012i	−1.16121	+	1.90698i
$683$	19.9067	+	8.24564i	0.761710	+	0.315510i	0.729509	−	0.683971i	$-0.239749\pi$
$683$	19.9067	+	8.24564i	0.761710	+	0.315510i	0.0322004	+	0.999481i	$0.489749\pi$
$684$		0			0
$685$	−17.1940	−	41.5100i	−0.656950	−	1.58602i
$686$	−10.9851	−	15.0303i	−0.419412	−	0.573860i
$687$		0			0
$688$	−1.26792	−	33.8272i	−0.0483391	−	1.28965i
$689$	3.17476	+	5.49885i	0.120949	+	0.209489i
$690$		0			0
$691$	3.76739	−	28.6162i	0.143318	−	1.08861i	−0.757011	−	0.653402i	$-0.773341\pi$
$691$	3.76739	−	28.6162i	0.143318	−	1.08861i	0.900329	−	0.435209i	$-0.143326\pi$
$692$	16.0928	−	34.2351i	0.611757	−	1.30142i
$693$		0			0
$694$	−7.72047	−	0.180373i	−0.293065	−	0.00684687i
$695$	−1.49152	−	5.56642i	−0.0565765	−	0.211146i
$696$		0			0
$697$	5.59874	−	20.8948i	0.212067	−	0.791447i
$698$	13.1793	−	44.9579i	0.498843	−	1.70168i
$699$		0			0
$700$	0.178036	+	0.814954i	0.00672912	+	0.0308024i
$701$	17.0186	+	41.0865i	0.642784	+	1.55182i	0.822909	+	0.568174i	$0.192350\pi$
$701$	17.0186	+	41.0865i	0.642784	+	1.55182i	−0.180125	+	0.983644i	$0.557650\pi$
$702$		0			0
$703$		−	47.3226i		−	1.78481i
$704$	−33.1574	−	9.21414i	−1.24967	−	0.347271i
$705$		0			0
$706$	37.4599	+	30.1599i	1.40982	+	1.13508i
$707$	−8.10492	−	6.21913i	−0.304817	−	0.233894i
$708$		0			0
$709$	7.89339	+	10.2869i	0.296443	+	0.386331i	0.917699	−	0.397276i	$-0.130044\pi$
$709$	7.89339	+	10.2869i	0.296443	+	0.386331i	−0.621257	+	0.783607i	$0.713378\pi$
$710$	−9.24751	+	8.82528i	−0.347053	+	0.331207i
$711$		0			0
$712$	8.26406	−	2.76270i	0.309709	−	0.103537i
$713$	−21.6917	+	5.81227i	−0.812360	+	0.217671i
$714$		0			0
$715$	−13.6879	+	1.80204i	−0.511897	+	0.0673925i
$716$	−0.914298	−	10.8353i	−0.0341689	−	0.404933i
$717$		0			0
$718$	15.5377	+	21.2594i	0.579860	+	0.793392i
$719$			18.1643i			0.677416i	0.940892	+	0.338708i	$0.109990\pi$
$719$			18.1643i			0.677416i	−0.940892	+	0.338708i	$0.890010\pi$
$720$		0			0
$721$			17.0078i			0.633404i
$722$	−39.2776	+	28.7065i	−1.46176	+	1.06835i
$723$		0			0
$724$	−1.98351	−	1.67481i	−0.0737166	−	0.0622440i
$725$	1.80873	−	0.238123i	0.0671744	−	0.00884368i
$726$		0			0
$727$	−39.7845	+	10.6602i	−1.47552	+	0.395366i	−0.904822	−	0.425791i	$-0.859996\pi$
$727$	−39.7845	+	10.6602i	−1.47552	+	0.395366i	−0.570703	+	0.821157i	$0.693329\pi$
$728$	2.82080	+	3.24668i	0.104546	+	0.120330i
$729$		0			0
$730$	−4.29288	−	4.49827i	−0.158887	−	0.166488i
$731$	−27.8136	−	36.2473i	−1.02872	−	1.34066i
$732$		0			0
$733$	22.1966	+	17.0320i	0.819849	+	0.629092i	0.931126	−	0.364697i	$-0.118827\pi$
$733$	22.1966	+	17.0320i	0.819849	+	0.629092i	−0.111277	+	0.993789i	$0.535494\pi$
$734$	1.54046	−	1.91333i	0.0568596	−	0.0706222i
$735$		0			0
$736$	−6.78842	−	11.3840i	−0.250224	−	0.419618i
$737$			22.7350i			0.837456i
$738$		0			0
$739$	−10.8083	−	26.0935i	−0.397590	−	0.959866i	−0.988236	−	0.152936i	$-0.951127\pi$
$739$	−10.8083	−	26.0935i	−0.397590	−	0.959866i	0.590646	−	0.806931i	$-0.298873\pi$
$740$	−23.3540	−	14.9796i	−0.858510	−	0.550661i
$741$		0			0
$742$	−5.83776	−	1.71132i	−0.214311	−	0.0628247i
$743$	5.41476	−	20.2082i	0.198648	−	0.741366i	−0.792644	−	0.609685i	$-0.791296\pi$
$743$	5.41476	−	20.2082i	0.198648	−	0.741366i	0.991292	−	0.131681i	$-0.0420374\pi$
$744$		0			0
$745$	9.34636	+	34.8811i	0.342424	+	1.27794i
$746$	−1.03768	+	44.4156i	−0.0379922	+	1.62617i
$747$		0			0
$748$	−43.6962	+	15.7517i	−1.59769	+	0.575937i
$749$	−1.26089	+	9.57740i	−0.0460719	+	0.349950i
$750$		0			0
$751$	−5.34187	−	9.25238i	−0.194927	−	0.337624i	0.751949	−	0.659221i	$-0.229114\pi$
$751$	−5.34187	−	9.25238i	−0.194927	−	0.337624i	−0.946877	+	0.321597i	$0.895780\pi$
$752$	14.3866	+	31.3557i	0.524626	+	1.14343i
$753$		0			0
$754$	7.59404	−	5.55019i	0.276558	−	0.202126i
$755$	9.76935	+	23.5853i	0.355543	+	0.858356i
$756$		0			0
$757$	8.88251	+	3.67926i	0.322840	+	0.133725i	0.538217	−	0.842806i	$-0.319098\pi$
$757$	8.88251	+	3.67926i	0.322840	+	0.133725i	−0.215377	+	0.976531i	$0.569098\pi$
$758$	32.5731	+	19.8347i	1.18311	+	0.720427i
$759$		0			0
$760$	2.69143	+	44.1953i	0.0976286	+	1.60313i
$761$	−12.6843	−	3.39875i	−0.459805	−	0.123204i	0.0214785	−	0.999769i	$-0.493163\pi$
$761$	−12.6843	−	3.39875i	−0.459805	−	0.123204i	−0.481284	+	0.876565i	$0.659829\pi$
$762$		0			0
$763$	−5.62830	+	4.31875i	−0.203758	+	0.156349i
$764$	−28.6045	+	26.0494i	−1.03487	+	0.942433i
$765$		0			0
$766$	5.57228	+	14.3948i	0.201335	+	0.520104i
$767$	−2.20310	+	3.81588i	−0.0795494	+	0.137784i
$768$		0			0
$769$	−10.0871	−	17.4713i	−0.363750	−	0.630033i	0.624825	−	0.780765i	$-0.285170\pi$
$769$	−10.0871	−	17.4713i	−0.363750	−	0.630033i	−0.988575	+	0.150732i	$0.951837\pi$
$770$	8.29523	−	10.3031i	0.298939	−	0.371296i
$771$		0			0
$772$	6.22027	+	28.4731i	0.223873	+	1.02477i
$773$	−29.7330	−	12.3158i	−1.06942	−	0.442969i	−0.222635	−	0.974902i	$-0.571466\pi$
$773$	−29.7330	−	12.3158i	−1.06942	−	0.442969i	−0.846786	+	0.531933i	$0.821466\pi$
$774$		0			0
$775$	−2.78500	+	2.78500i	−0.100040	+	0.100040i
$776$	−20.0410	+	13.2573i	−0.719430	+	0.475908i
$777$		0			0
$778$	−3.85024	+	2.10459i	−0.138038	+	0.0754533i
$779$	−3.82178	−	29.0293i	−0.136930	−	1.04008i
$780$		0			0
$781$	−17.9955	−	2.36915i	−0.643929	−	0.0847749i
$782$	−16.3633	−	7.23015i	−0.585150	−	0.258550i
$783$		0			0
$784$	23.7752	+	2.22792i	0.849113	+	0.0795685i
$785$	−15.8575	+	27.4659i	−0.565977	+	0.980300i
$786$		0			0
$787$	−16.4390	−	12.6141i	−0.585988	−	0.449644i	0.272732	−	0.962090i	$-0.412073\pi$
$787$	−16.4390	−	12.6141i	−0.585988	−	0.449644i	−0.858720	+	0.512446i	$0.828740\pi$
$788$	−15.2869	−	12.9078i	−0.544572	−	0.459820i
$789$		0			0
$790$	25.4111	+	15.4735i	0.904086	+	0.550522i
$791$	5.58176	−	5.58176i	0.198464	−	0.198464i
$792$		0			0
$793$	0.356870	+	0.356870i	0.0126728	+	0.0126728i
$794$	7.90106	+	32.5060i	0.280398	+	1.15360i
$795$		0			0
$796$	−46.3897	+	23.9674i	−1.64424	+	0.849502i
$797$	−15.5862	+	20.3123i	−0.552090	+	0.719497i	−0.983145	−	0.182828i	$-0.941475\pi$
$797$	−15.5862	+	20.3123i	−0.552090	+	0.719497i	0.431055	+	0.902326i	$0.358141\pi$
$798$		0			0
$799$	40.3247	+	23.2815i	1.42659	+	0.823640i
$800$	−2.02936	−	1.13379i	−0.0717486	−	0.0400854i
$801$		0			0
$802$	8.05588	+	20.8106i	0.284463	+	0.734849i
$803$	1.15243	−	8.75355i	0.0406682	−	0.308906i
$804$		0			0
$805$	5.05088	−	0.664961i	0.178020	−	0.0234368i
$806$	−5.71251	+	19.4868i	−0.201215	+	0.686394i
$807$		0			0
$808$	27.9475	−	5.42481i	0.983188	−	0.190844i
$809$	10.6460	+	10.6460i	0.374293	+	0.374293i	0.869038	−	0.494745i	$-0.164739\pi$
$809$	10.6460	+	10.6460i	0.374293	+	0.374293i	−0.494745	+	0.869038i	$0.664739\pi$
$810$		0			0
$811$	−4.07895	+	9.84747i	−0.143231	+	0.345791i	−0.979173	−	0.203027i	$-0.934922\pi$
$811$	−4.07895	+	9.84747i	−0.143231	+	0.345791i	0.835942	+	0.548818i	$0.184922\pi$
$812$	−1.59226	+	8.87009i	−0.0558774	+	0.311279i
$813$		0			0
$814$	−4.22854	−	39.1686i	−0.148210	−	1.37286i
$815$	5.65239	−	3.26341i	0.197994	−	0.114312i
$816$		0			0
$817$	−53.5567	−	30.9210i	−1.87371	−	1.08179i
$818$	15.2038	−	34.4092i	0.531588	−	1.20309i
$819$		0			0
$820$	−15.5359	−	7.30292i	−0.542537	−	0.255029i
$821$	19.0390	+	24.8121i	0.664466	+	0.865948i	0.997021	−	0.0771355i	$-0.0245774\pi$
$821$	19.0390	+	24.8121i	0.664466	+	0.865948i	−0.332555	+	0.943084i	$0.607911\pi$
$822$		0			0
$823$	−1.34997	+	5.03815i	−0.0470569	+	0.175619i	−0.985455	−	0.169938i	$-0.945643\pi$
$823$	−1.34997	+	5.03815i	−0.0470569	+	0.175619i	0.938398	+	0.345557i	$0.112310\pi$
$824$	−35.4891	−	31.4147i	−1.23632	−	1.09438i
$825$		0			0
$826$	−0.997078	−	4.10211i	−0.0346928	−	0.142731i
$827$	−7.61758	+	18.3905i	−0.264889	+	0.639499i	−0.999228	−	0.0392837i	$-0.987492\pi$
$827$	−7.61758	+	18.3905i	−0.264889	+	0.639499i	0.734339	+	0.678783i	$0.237492\pi$
$828$		0			0
$829$	39.0063	−	16.1569i	1.35475	−	0.561154i	0.417136	−	0.908844i	$-0.363034\pi$
$829$	39.0063	−	16.1569i	1.35475	−	0.561154i	0.937609	+	0.347690i	$0.113034\pi$
$830$	1.01962	−	6.55730i	0.0353915	−	0.227607i
$831$		0			0
$832$	−11.9849	−	0.110895i	−0.415500	−	0.00384458i
$833$	27.9121	−	16.1150i	0.967095	−	0.558353i
$834$		0			0
$835$	7.72577	+	1.01712i	0.267361	+	0.0351988i
$836$	−46.4837	+	42.3315i	−1.60767	+	1.46406i
$837$		0			0
$838$	17.3752	+	18.2065i	0.600218	+	0.628935i
$839$	19.1062	−	5.11950i	0.659620	−	0.176745i	0.0865457	−	0.996248i	$-0.472417\pi$
$839$	19.1062	−	5.11950i	0.659620	−	0.176745i	0.573075	+	0.819503i	$0.305750\pi$
$840$		0			0
$841$	−8.97450	−	2.40471i	−0.309465	−	0.0829210i
$842$	7.08179	+	12.9557i	0.244055	+	0.446484i
$843$		0			0
$844$	8.79894	+	12.6490i	0.302872	+	0.435398i
$845$	21.2867	−	8.81722i	0.732283	−	0.303322i
$846$		0			0
$847$	7.61725			0.261732
$848$	14.3537	−	9.02033i	0.492908	−	0.309759i
$849$		0			0
$850$	−3.11940	+	0.336762i	−0.106994	+	0.0115509i
$851$	9.23689	−	12.0378i	0.316637	−	0.412649i
$852$		0			0
$853$	30.0905	−	23.0892i	1.03028	−	0.790560i	0.0521653	−	0.998638i	$-0.483388\pi$
$853$	30.0905	−	23.0892i	1.03028	−	0.790560i	0.978112	+	0.208079i	$0.0667210\pi$
$854$	−0.483408	−	0.0112938i	−0.0165419	−	0.000386467i
$855$		0			0
$856$	−17.6556	−	20.3212i	−0.603455	−	0.694564i
$857$	7.25866	+	27.0897i	0.247951	+	0.925366i	0.971877	+	0.235488i	$0.0756690\pi$
$857$	7.25866	+	27.0897i	0.247951	+	0.925366i	−0.723926	+	0.689878i	$0.757664\pi$
$858$		0			0
$859$	−4.33846	−	32.9539i	−0.148027	−	1.12437i	−0.890658	−	0.454673i	$-0.849756\pi$
$859$	−4.33846	−	32.9539i	−0.148027	−	1.12437i	0.742632	−	0.669700i	$-0.233577\pi$
$860$	−32.2126	+	16.6428i	−1.09844	+	0.567514i
$861$		0			0
$862$	−7.20943	+	46.3648i	−0.245554	+	1.57919i
$863$	−33.6814			−1.14653			−0.573264	−	0.819371i	$-0.694323\pi$
$863$	−33.6814			−1.14653			−0.573264	+	0.819371i	$0.694323\pi$
$864$		0			0
$865$	−40.5186			−1.37767
$866$	−2.81679	+	18.1152i	−0.0957186	+	0.615578i
$867$		0			0
$868$	−8.93045	−	17.2852i	−0.303119	−	0.586697i
$869$	5.51408	+	41.8836i	0.187052	+	1.42080i
$870$		0			0
$871$	2.04932	+	7.64817i	0.0694386	+	0.259148i
$872$	1.38426	−	19.7213i	0.0468769	−	0.667847i
$873$		0			0
$874$	−24.2076	−	0.565562i	−0.818835	−	0.0191304i
$875$	9.33372	−	7.16201i	0.315537	−	0.242120i
$876$		0			0
$877$	−19.4658	+	25.3684i	−0.657314	+	0.856628i	−0.996457	−	0.0841066i	$-0.973196\pi$
$877$	−19.4658	+	25.3684i	−0.657314	+	0.856628i	0.339143	+	0.940735i	$0.389863\pi$
$878$	−17.7856	+	1.92009i	−0.600235	+	0.0647998i
$879$		0			0
$880$	6.17678	+	36.3397i	0.208219	+	1.22501i
$881$	−1.81478			−0.0611416			−0.0305708	−	0.999533i	$-0.509733\pi$
$881$	−1.81478			−0.0611416			−0.0305708	+	0.999533i	$0.509733\pi$
$882$		0			0
$883$	−40.2761	+	16.6829i	−1.35540	+	0.561425i	−0.937791	−	0.347201i	$-0.887132\pi$
$883$	−40.2761	+	16.6829i	−1.35540	+	0.561425i	−0.417610	+	0.908627i	$0.637132\pi$
$884$	−13.2797	+	9.23767i	−0.446646	+	0.310696i
$885$		0			0
$886$	5.81409	+	10.6366i	0.195328	+	0.357342i
$887$	11.4271	+	3.06187i	0.383683	+	0.102808i	0.445505	−	0.895280i	$-0.353024\pi$
$887$	11.4271	+	3.06187i	0.383683	+	0.102808i	−0.0618215	+	0.998087i	$0.519691\pi$
$888$		0			0
$889$	−16.0920	+	4.31185i	−0.539710	+	0.144615i
$890$	−6.44363	−	6.75192i	−0.215991	−	0.226325i
$891$		0			0
$892$	−23.3301	−	25.6185i	−0.781148	−	0.857770i
$893$	62.4861	+	8.22645i	2.09102	+	0.275288i
$894$		0			0
$895$	−10.0866	+	5.82348i	−0.337156	+	0.194657i
$896$	8.38020	−	7.85070i	0.279963	−	0.262273i
$897$		0			0
$898$	3.14018	−	20.1949i	0.104789	−	0.673912i
$899$	−39.3109	+	16.2831i	−1.31109	+	0.543073i
$900$		0			0
$901$	8.75625	−	21.1395i	0.291713	−	0.704258i
$902$	−5.75719	−	23.6859i	−0.191694	−	0.788653i
$903$		0			0
$904$	1.33715	+	21.9570i	0.0444730	+	0.730280i
$905$	−0.719675	+	2.68586i	−0.0239228	+	0.0892811i
$906$		0			0
$907$	−4.23830	−	5.52346i	−0.140730	−	0.183403i	0.717671	−	0.696383i	$-0.245208\pi$
$907$	−4.23830	−	5.52346i	−0.140730	−	0.183403i	−0.858401	+	0.512979i	$0.828542\pi$
$908$	21.8691	−	46.5233i	0.725752	−	1.54393i
$909$		0			0
$910$	1.86184	−	4.21372i	0.0617195	−	0.139683i
$911$	−4.22132	−	2.43718i	−0.139859	−	0.0807474i	0.428438	−	0.903571i	$-0.359064\pi$
$911$	−4.22132	−	2.43718i	−0.139859	−	0.0807474i	−0.568297	+	0.822824i	$0.692397\pi$
$912$		0			0
$913$	8.16037	−	4.71139i	0.270069	−	0.155924i
$914$	−6.36654	−	58.9727i	−0.210587	−	1.95064i
$915$		0			0
$916$	6.16399	+	1.10649i	0.203664	+	0.0365594i
$917$	−6.80881	+	16.4379i	−0.224847	+	0.542828i
$918$		0			0
$919$	23.9876	+	23.9876i	0.791278	+	0.791278i	0.981702	−	0.190424i	$-0.0609862\pi$
$919$	23.9876	+	23.9876i	0.791278	+	0.791278i	−0.190424	+	0.981702i	$0.560986\pi$
$920$	−7.94183	+	11.7676i	−0.261835	+	0.387965i
$921$		0			0
$922$	14.8418	−	50.6293i	0.488790	−	1.66739i
$923$	−6.26732	+	0.825108i	−0.206291	+	0.0271588i
$924$		0			0
$925$	0.347350	−	2.63838i	0.0114208	−	0.0867495i
$926$	3.62317	+	9.35967i	0.119065	+	0.307578i
$927$		0			0
$928$	−15.5676	−	19.7062i	−0.511032	−	0.646888i
$929$	−0.758151	−	0.437718i	−0.0248741	−	0.0143611i	0.487511	−	0.873117i	$-0.337905\pi$
$929$	−0.758151	−	0.437718i	−0.0248741	−	0.0143611i	−0.512385	+	0.858756i	$0.671238\pi$
$930$		0			0
$931$	26.5572	−	34.6100i	0.870377	−	1.13430i
$932$	27.2451	+	52.7337i	0.892441	+	1.72735i
$933$		0			0
$934$	4.15904	+	17.1108i	0.136088	+	0.559884i
$935$	35.1795	+	35.1795i	1.15049	+	1.15049i
$936$		0			0
$937$	24.9448	−	24.9448i	0.814909	−	0.814909i	−0.170456	−	0.985365i	$-0.554524\pi$
$937$	24.9448	−	24.9448i	0.814909	−	0.814909i	0.985365	+	0.170456i	$0.0545240\pi$
$938$	−6.47941	−	3.94548i	−0.211560	−	0.128825i
$939$		0			0
$940$	23.8393	−	28.2332i	0.777551	−	0.920866i
$941$	38.1406	+	29.2663i	1.24335	+	0.954055i	0.999874	−	0.0158517i	$-0.00504598\pi$
$941$	38.1406	+	29.2663i	1.24335	+	0.954055i	0.243475	+	0.969907i	$0.421713\pi$
$942$		0			0
$943$	4.69405	−	8.13034i	0.152859	−	0.264760i
$944$	10.4013	+	5.49638i	0.338533	+	0.178892i
$945$		0			0
$946$	−47.0915	−	20.8075i	−1.53108	−	0.676510i
$947$	7.34384	+	0.966835i	0.238643	+	0.0314179i	0.248899	−	0.968529i	$-0.419931\pi$
$947$	7.34384	+	0.966835i	0.238643	+	0.0314179i	−0.0102560	+	0.999947i	$0.503265\pi$
$948$		0			0
$949$	−0.401357	−	3.04861i	−0.0130286	−	0.0989621i
$950$	−3.72642	+	2.03692i	−0.120901	+	0.0660863i
$951$		0			0
$952$	3.09395	−	15.1868i	0.100276	−	0.492208i
$953$	20.7163	−	20.7163i	0.671065	−	0.671065i	−0.286896	−	0.957962i	$-0.592623\pi$
$953$	20.7163	−	20.7163i	0.671065	−	0.671065i	0.957962	+	0.286896i	$0.0926235\pi$
$954$		0			0
$955$	38.2849	+	15.8581i	1.23887	+	0.513157i
$956$	8.53829	−	1.86528i	0.276148	−	0.0603276i
$957$		0			0
$958$	31.8606	−	39.5724i	1.02937	−	1.27853i
$959$	10.6439	+	18.4357i	0.343708	+	0.595320i
$960$		0			0
$961$	30.4308	−	52.7076i	0.981637	−	1.70025i
$962$	−4.95313	−	12.7953i	−0.159695	−	0.412538i
$963$		0			0
$964$	−10.4371	−	11.4609i	−0.336157	−	0.369131i
$965$	24.7661	−	19.0037i	0.797250	−	0.611751i
$966$		0			0
$967$	−16.9520	−	4.54228i	−0.545140	−	0.146070i	−0.0242696	−	0.999705i	$-0.507726\pi$
$967$	−16.9520	−	4.54228i	−0.545140	−	0.146070i	−0.520871	+	0.853635i	$0.674393\pi$
$968$	−14.0697	+	15.8944i	−0.452216	+	0.510866i
$969$		0			0
$970$	21.9828	+	13.3859i	0.705826	+	0.429796i
$971$	−28.6212	−	11.8553i	−0.918497	−	0.380454i	−0.127194	−	0.991878i	$-0.540597\pi$
$971$	−28.6212	−	11.8553i	−0.918497	−	0.380454i	−0.791303	+	0.611424i	$0.790597\pi$
$972$		0			0
$973$	1.04487	+	2.52254i	0.0334971	+	0.0808691i
$974$	−2.78272	+	2.03379i	−0.0891642	+	0.0651667i
$975$		0			0
$976$	0.916457	−	0.987835i	0.0293351	−	0.0316198i
$977$	2.69148	+	4.66178i	0.0861081	+	0.149144i	0.905863	−	0.423571i	$-0.139224\pi$
$977$	2.69148	+	4.66178i	0.0861081	+	0.149144i	−0.819755	+	0.572715i	$0.805890\pi$
$978$		0			0
$979$	1.72980	−	13.1391i	0.0552845	−	0.419928i
$980$	−8.67378	−	24.0616i	−0.277074	−	0.768621i
$981$		0			0
$982$	0.237317	−	10.1578i	0.00757308	−	0.324149i
$983$	−9.25791	−	34.5510i	−0.295281	−	1.10200i	−0.940994	−	0.338424i	$-0.890106\pi$
$983$	−9.25791	−	34.5510i	−0.295281	−	1.10200i	0.645712	−	0.763581i	$-0.276561\pi$
$984$		0			0
$985$	−5.54652	+	20.6999i	−0.176727	+	0.659554i
$986$	−32.5270	−	9.53519i	−1.03587	−	0.303662i
$987$		0			0
$988$	−11.8216	+	18.4305i	−0.376095	+	0.586353i
$989$	−7.58810	−	18.3193i	−0.241288	−	0.582520i
$990$		0			0
$991$		−	24.3967i		−	0.774986i	−0.921873	−	0.387493i	$-0.873341\pi$
$991$		−	24.3967i		−	0.774986i	0.921873	−	0.387493i	$-0.126659\pi$
$992$	52.5631	+	13.2925i	1.66888	+	0.422037i
$993$		0			0
$994$	3.79817	−	4.71750i	0.120471	−	0.149630i
$995$	44.3708	+	34.0469i	1.40665	+	1.07936i
$996$		0			0
$997$	−23.5073	−	30.6353i	−0.744484	−	0.970230i	−0.999994	−	0.00342389i	$-0.998910\pi$
$997$	−23.5073	−	30.6353i	−0.744484	−	0.970230i	0.255510	−	0.966806i	$-0.417757\pi$
$998$	−34.5640	−	36.2176i	−1.09410	−	1.14645i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bn.a.683.2		368
3.2	odd	2		288.2.bf.a.11.45	✓	368
9.4	even	3		288.2.bf.a.203.34	yes	368
9.5	odd	6	inner	864.2.bn.a.395.13		368
32.3	odd	8	inner	864.2.bn.a.35.13		368
96.35	even	8		288.2.bf.a.227.34	yes	368
288.67	odd	24		288.2.bf.a.131.45	yes	368
288.131	even	24	inner	864.2.bn.a.611.2		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.45	✓	368	3.2	odd	2
288.2.bf.a.131.45	yes	368	288.67	odd	24
288.2.bf.a.203.34	yes	368	9.4	even	3
288.2.bf.a.227.34	yes	368	96.35	even	8
864.2.bn.a.35.13		368	32.3	odd	8	inner
864.2.bn.a.395.13		368	9.5	odd	6	inner
864.2.bn.a.611.2		368	288.131	even	24	inner
864.2.bn.a.683.2		368	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bn (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.39742 - 0.217290i) q^{2} +(1.90557 + 0.607292i) q^{4} +(-0.279615 - 2.12388i) q^{5} +(0.262694 + 0.980387i) q^{7} +(-2.53092 - 1.26270i) q^{8} +O(q^{10})\)	\(q+(-1.39742 - 0.217290i) q^{2} +(1.90557 + 0.607292i) q^{4} +(-0.279615 - 2.12388i) q^{5} +(0.262694 + 0.980387i) q^{7} +(-2.53092 - 1.26270i) q^{8} +(-0.0707598 + 3.02872i) q^{10} +(-3.41279 + 2.61873i) q^{11} +(-0.912029 + 1.18858i) q^{13} +(-0.154065 - 1.42709i) q^{14} +(3.26239 + 2.31447i) q^{16} +5.39882 q^{17} +(6.75131 - 2.79649i) q^{19} +(0.756992 - 4.21702i) q^{20} +(5.33813 - 2.91790i) q^{22} +(2.26322 + 0.606428i) q^{23} +(0.396933 - 0.106358i) q^{25} +(1.53275 - 1.46277i) q^{26} +(-0.0947992 + 2.02773i) q^{28} +(4.40149 + 0.579467i) q^{29} +(-8.30037 + 4.79222i) q^{31} +(-4.05602 - 3.94318i) q^{32} +(-7.54443 - 1.17311i) q^{34} +(2.00877 - 0.832061i) q^{35} +(2.47820 - 5.98289i) q^{37} +(-10.0421 + 2.44087i) q^{38} +(-1.97415 + 5.72846i) q^{40} +(1.03703 - 3.87025i) q^{41} +(-5.15179 - 6.71394i) q^{43} +(-8.09365 + 2.91761i) q^{44} +(-3.03090 - 1.33921i) q^{46} +(7.46917 + 4.31233i) q^{47} +(5.17003 - 2.98492i) q^{49} +(-0.577793 + 0.0623770i) q^{50} +(-2.45975 + 1.71105i) q^{52} +(1.62188 - 3.91557i) q^{53} +(6.51614 + 6.51614i) q^{55} +(0.573080 - 2.81299i) q^{56} +(-6.02482 - 1.76616i) q^{58} +(2.91589 - 0.383885i) q^{59} +(0.0439705 - 0.333989i) q^{61} +(12.6404 - 4.89316i) q^{62} +(4.81116 + 6.39162i) q^{64} +(2.77942 + 1.60470i) q^{65} +(3.21736 - 4.19294i) q^{67} +(10.2878 + 3.27866i) q^{68} +(-2.98790 + 0.726253i) q^{70} +(2.98357 + 2.98357i) q^{71} +(-1.45130 + 1.45130i) q^{73} +(-4.76311 + 7.82213i) q^{74} +(14.5634 - 1.22888i) q^{76} +(-3.46389 - 2.65793i) q^{77} +(4.91023 - 8.50477i) q^{79} +(4.00346 - 7.57610i) q^{80} +(-2.29014 + 5.18303i) q^{82} +(-2.17172 - 0.285913i) q^{83} +(-1.50959 - 11.4665i) q^{85} +(5.74034 + 10.5016i) q^{86} +(11.9442 - 2.31846i) q^{88} +(-2.17841 + 2.17841i) q^{89} +(-1.40485 - 0.581909i) q^{91} +(3.94444 + 2.53002i) q^{92} +(-9.50055 - 7.64911i) q^{94} +(-7.82717 - 13.5571i) q^{95} +(4.24778 - 7.35737i) q^{97} +(-7.87330 + 3.04779i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34} - 16 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 24 q^{47} + 168 q^{50} - 4 q^{52} - 16 q^{55} + 12 q^{56} + 32 q^{58} + 12 q^{59} - 4 q^{61} - 16 q^{64} + 24 q^{65} - 4 q^{67} + 60 q^{68} - 4 q^{70} - 16 q^{73} + 12 q^{74} - 28 q^{76} + 12 q^{77} - 8 q^{79} - 16 q^{82} + 132 q^{83} - 24 q^{85} + 12 q^{86} - 4 q^{88} - 16 q^{91} - 216 q^{92} - 20 q^{94} - 8 q^{97}+O(q^{100}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Introduction

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