LMFDB - Embedded newform 405.2.r.a.233.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,2,Mod(8,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([2, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.r (of order $36$, degree $12$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			233.11
Character	$\chi$	$=$	405.233
Dual form			405.2.r.a.332.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.761943 - 1.08817i) q^{2} +(0.0804885 + 0.221140i) q^{4} +(-1.62191 + 1.53928i) q^{5} +(1.77434 - 0.827388i) q^{7} +(2.86825 + 0.768546i) q^{8} +(0.439192 + 2.93776i) q^{10} +(2.76562 + 3.29594i) q^{11} +(-4.15220 + 2.90740i) q^{13} +(0.451609 - 2.56120i) q^{14} +(2.66120 - 2.23301i) q^{16} +(3.09176 - 0.828434i) q^{17} +(0.776109 - 0.448087i) q^{19} +(-0.470943 - 0.234776i) q^{20} +(5.69379 - 0.498142i) q^{22} +(2.36525 - 5.07230i) q^{23} +(0.261212 - 4.99317i) q^{25} +6.73356i q^{26} +(0.325783 + 0.325783i) q^{28} +(1.14702 + 6.50507i) q^{29} +(2.27652 - 0.828586i) q^{31} +(0.115398 + 1.31900i) q^{32} +(1.45427 - 3.99557i) q^{34} +(-1.60424 + 4.07317i) q^{35} +(-1.86654 - 6.96604i) q^{37} +(0.103757 - 1.18595i) q^{38} +(-5.83507 + 3.16854i) q^{40} +(-8.33680 - 1.47000i) q^{41} +(1.28541 + 0.112459i) q^{43} +(-0.506265 + 0.876877i) q^{44} +(-3.71732 - 6.43859i) q^{46} +(-3.48305 - 7.46943i) q^{47} +(-2.03580 + 2.42617i) q^{49} +(-5.23438 - 4.08876i) q^{50} +(-0.977148 - 0.684206i) q^{52} +(-0.947342 + 0.947342i) q^{53} +(-9.55899 - 1.08866i) q^{55} +(5.72514 - 1.00950i) q^{56} +(7.95258 + 3.70835i) q^{58} +(-3.72879 - 3.12883i) q^{59} +(-7.90101 - 2.87573i) q^{61} +(0.832940 - 3.10857i) q^{62} +(7.54029 + 4.35339i) q^{64} +(2.25919 - 11.1070i) q^{65} +(5.53556 + 7.90560i) q^{67} +(0.432051 + 0.617033i) q^{68} +(3.20995 + 4.84921i) q^{70} +(-4.92123 - 2.84127i) q^{71} +(-1.32285 + 4.93694i) q^{73} +(-9.00242 - 3.27661i) q^{74} +(0.161558 + 0.135563i) q^{76} +(7.63418 + 3.55988i) q^{77} +(0.410612 - 0.0724019i) q^{79} +(-0.879000 + 7.71810i) q^{80} +(-7.95178 + 7.95178i) q^{82} +(7.59392 + 5.31732i) q^{83} +(-3.73937 + 6.10274i) q^{85} +(1.10179 - 1.31306i) q^{86} +(5.39942 + 11.5791i) q^{88} +(-0.974450 - 1.68780i) q^{89} +(-4.96186 + 8.59420i) q^{91} +(1.31207 + 0.114791i) q^{92} +(-10.7819 - 1.90114i) q^{94} +(-0.569049 + 1.92141i) q^{95} +(1.17718 - 13.4552i) q^{97} +(1.08892 + 4.06390i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$	0.761943	−	1.08817i	0.538775	−	0.769451i	−0.453797	−	0.891105i	$-0.649931\pi$
$2$	0.761943	−	1.08817i	0.538775	−	0.769451i	0.992573	+	0.121654i	$0.0388198\pi$
$3$		0			0
$3$		0			0
$4$	0.0804885	+	0.221140i	0.0402443	+	0.110570i
$5$	−1.62191	+	1.53928i	−0.725342	+	0.688389i
$5$	−1.62191	+	1.53928i	−0.725342	+	0.688389i
$6$		0			0
$7$	1.77434	−	0.827388i	0.670638	−	0.312723i	−0.0573098	−	0.998356i	$-0.518252\pi$
$7$	1.77434	−	0.827388i	0.670638	−	0.312723i	0.727947	+	0.685633i	$0.240474\pi$
$8$	2.86825	+	0.768546i	1.01408	+	0.271722i
$9$		0			0
$10$	0.439192	+	2.93776i	0.138885	+	0.929002i
$11$	2.76562	+	3.29594i	0.833867	+	0.993764i	0.999971	+	0.00765542i	$0.00243682\pi$
$11$	2.76562	+	3.29594i	0.833867	+	0.993764i	−0.166104	+	0.986108i	$0.553119\pi$
$12$		0			0
$13$	−4.15220	+	2.90740i	−1.15161	+	0.806368i	−0.983768	−	0.179446i	$-0.942569\pi$
$13$	−4.15220	+	2.90740i	−1.15161	+	0.806368i	−0.167844	+	0.985814i	$0.553681\pi$
$14$	0.451609	−	2.56120i	0.120698	−	0.684510i
$15$		0			0
$16$	2.66120	−	2.23301i	0.665301	−	0.558253i
$17$	3.09176	−	0.828434i	0.749861	−	0.200925i	0.136405	−	0.990653i	$-0.456445\pi$
$17$	3.09176	−	0.828434i	0.749861	−	0.200925i	0.613456	+	0.789729i	$0.289779\pi$
$18$		0			0
$19$	0.776109	−	0.448087i	0.178052	−	0.102798i	−0.408325	−	0.912836i	$-0.633887\pi$
$19$	0.776109	−	0.448087i	0.178052	−	0.102798i	0.586377	+	0.810038i	$0.300554\pi$
$20$	−0.470943	−	0.234776i	−0.105306	−	0.0524975i
$21$		0			0
$22$	5.69379	−	0.498142i	1.21392	−	0.106204i
$23$	2.36525	−	5.07230i	0.493189	−	1.05765i	−0.489435	−	0.872040i	$-0.662797\pi$
$23$	2.36525	−	5.07230i	0.493189	−	1.05765i	0.982624	−	0.185607i	$-0.0594253\pi$
$24$		0			0
$25$	0.261212	−	4.99317i	0.0522423	−	0.998634i
$26$			6.73356i			1.32056i
$27$		0			0
$28$	0.325783	+	0.325783i	0.0615672	+	0.0615672i
$29$	1.14702	+	6.50507i	0.212996	+	1.20796i	0.884350	+	0.466825i	$0.154602\pi$
$29$	1.14702	+	6.50507i	0.212996	+	1.20796i	−0.671354	+	0.741137i	$0.734287\pi$
$30$		0			0
$31$	2.27652	−	0.828586i	0.408875	−	0.148818i	−0.129390	−	0.991594i	$-0.541302\pi$
$31$	2.27652	−	0.828586i	0.408875	−	0.148818i	0.538266	+	0.842775i	$0.319080\pi$
$32$	0.115398	+	1.31900i	0.0203996	+	0.233169i
$33$		0			0
$34$	1.45427	−	3.99557i	0.249405	−	0.685235i
$35$	−1.60424	+	4.07317i	−0.271166	+	0.688491i
$36$		0			0
$37$	−1.86654	−	6.96604i	−0.306858	−	1.14521i	−0.931334	−	0.364166i	$-0.881354\pi$
$37$	−1.86654	−	6.96604i	−0.306858	−	1.14521i	0.624476	−	0.781044i	$-0.285312\pi$
$38$	0.103757	−	1.18595i	0.0168317	−	0.192387i
$39$		0			0
$40$	−5.83507	+	3.16854i	−0.922606	+	0.500990i
$41$	−8.33680	−	1.47000i	−1.30199	−	0.229576i	−0.520697	−	0.853742i	$-0.674328\pi$
$41$	−8.33680	−	1.47000i	−1.30199	−	0.229576i	−0.781292	+	0.624166i	$0.785439\pi$
$42$		0			0
$43$	1.28541	+	0.112459i	0.196024	+	0.0171499i	0.184745	−	0.982787i	$-0.440854\pi$
$43$	1.28541	+	0.112459i	0.196024	+	0.0171499i	0.0112790	+	0.999936i	$0.496410\pi$
$44$	−0.506265	+	0.876877i	−0.0763223	+	0.132194i
$45$		0			0
$46$	−3.71732	−	6.43859i	−0.548090	−	0.949319i
$47$	−3.48305	−	7.46943i	−0.508055	−	1.08953i	−0.978338	−	0.207013i	$-0.933626\pi$
$47$	−3.48305	−	7.46943i	−0.508055	−	1.08953i	0.470283	−	0.882516i	$-0.344152\pi$
$48$		0			0
$49$	−2.03580	+	2.42617i	−0.290829	+	0.346596i
$50$	−5.23438	−	4.08876i	−0.740253	−	0.578238i
$51$		0			0
$52$	−0.977148	−	0.684206i	−0.135506	−	0.0948823i
$53$	−0.947342	+	0.947342i	−0.130127	+	0.130127i	−0.769171	−	0.639043i	$-0.779330\pi$
$53$	−0.947342	+	0.947342i	−0.130127	+	0.130127i	0.639043	+	0.769171i	$0.279330\pi$
$54$		0			0
$55$	−9.55899	−	1.08866i	−1.28893	−	0.146794i
$56$	5.72514	−	1.00950i	0.765054	−	0.134900i
$57$		0			0
$58$	7.95258	+	3.70835i	1.04422	+	0.486930i
$59$	−3.72879	−	3.12883i	−0.485447	−	0.407339i	0.366944	−	0.930243i	$-0.380404\pi$
$59$	−3.72879	−	3.12883i	−0.485447	−	0.407339i	−0.852391	+	0.522904i	$0.824849\pi$
$60$		0			0
$61$	−7.90101	−	2.87573i	−1.01162	−	0.368200i	−0.217566	−	0.976046i	$-0.569812\pi$
$61$	−7.90101	−	2.87573i	−1.01162	−	0.368200i	−0.794055	+	0.607846i	$0.792034\pi$
$62$	0.832940	−	3.10857i	0.105783	−	0.394789i
$63$		0			0
$64$	7.54029	+	4.35339i	0.942536	+	0.544173i
$65$	2.25919	−	11.1070i	0.280219	−	1.37765i
$66$		0			0
$67$	5.53556	+	7.90560i	0.676276	+	0.965822i	0.999808	+	0.0196049i	$0.00624085\pi$
$67$	5.53556	+	7.90560i	0.676276	+	0.965822i	−0.323532	+	0.946217i	$0.604870\pi$
$68$	0.432051	+	0.617033i	0.0523939	+	0.0748262i
$69$		0			0
$70$	3.20995	+	4.84921i	0.383662	+	0.579591i
$71$	−4.92123	−	2.84127i	−0.584043	−	0.337197i	0.178696	−	0.983904i	$-0.442812\pi$
$71$	−4.92123	−	2.84127i	−0.584043	−	0.337197i	−0.762738	+	0.646707i	$0.776146\pi$
$72$		0			0
$73$	−1.32285	+	4.93694i	−0.154828	+	0.577825i	0.844292	+	0.535883i	$0.180021\pi$
$73$	−1.32285	+	4.93694i	−0.154828	+	0.577825i	−0.999120	+	0.0419419i	$0.986646\pi$
$74$	−9.00242	−	3.27661i	−1.04651	−	0.380898i
$75$		0			0
$76$	0.161558	+	0.135563i	0.0185320	+	0.0155502i
$77$	7.63418	+	3.55988i	0.869996	+	0.405686i
$78$		0			0
$79$	0.410612	−	0.0724019i	0.0461974	−	0.00814585i	−0.150502	−	0.988610i	$-0.548089\pi$
$79$	0.410612	−	0.0724019i	0.0461974	−	0.00814585i	0.196699	+	0.980464i	$0.436978\pi$
$80$	−0.879000	+	7.71810i	−0.0982752	+	0.862910i
$81$		0			0
$82$	−7.95178	+	7.95178i	−0.878127	+	0.878127i
$83$	7.59392	+	5.31732i	0.833541	+	0.583652i	0.910560	−	0.413378i	$-0.135651\pi$
$83$	7.59392	+	5.31732i	0.833541	+	0.583652i	−0.0770185	+	0.997030i	$0.524540\pi$
$84$		0			0
$85$	−3.73937	+	6.10274i	−0.405592	+	0.661935i
$86$	1.10179	−	1.31306i	0.118809	−	0.141591i
$87$		0			0
$88$	5.39942	+	11.5791i	0.575580	+	1.23434i
$89$	−0.974450	−	1.68780i	−0.103292	−	0.178906i	0.809747	−	0.586779i	$-0.199604\pi$
$89$	−0.974450	−	1.68780i	−0.103292	−	0.178906i	−0.913039	+	0.407872i	$0.866271\pi$
$90$		0			0
$91$	−4.96186	+	8.59420i	−0.520144	+	0.900917i
$92$	1.31207	+	0.114791i	0.136792	+	0.0119678i
$93$		0			0
$94$	−10.7819	−	1.90114i	−1.11207	−	0.196087i
$95$	−0.569049	+	1.92141i	−0.0583832	+	0.197132i
$96$		0			0
$97$	1.17718	−	13.4552i	0.119524	−	1.36617i	−0.665359	−	0.746524i	$-0.731721\pi$
$97$	1.17718	−	13.4552i	0.119524	−	1.36617i	0.784883	−	0.619644i	$-0.212723\pi$
$98$	1.08892	+	4.06390i	0.109997	+	0.410516i
$99$		0			0
$100$	1.12522	−	0.344129i	0.112522	−	0.0344129i
$101$	1.45521	−	3.99814i	0.144798	−	0.397830i	−0.845999	−	0.533185i	$-0.820995\pi$
$101$	1.45521	−	3.99814i	0.144798	−	0.397830i	0.990797	+	0.135354i	$0.0432173\pi$
$102$		0			0
$103$	−1.16385	−	13.3028i	−0.114677	−	1.31077i	−0.807589	−	0.589745i	$-0.799228\pi$
$103$	−1.16385	−	13.3028i	−0.114677	−	1.31077i	0.692912	−	0.721022i	$-0.256327\pi$
$104$	−14.1440	+	5.14800i	−1.38694	+	0.504803i
$105$		0			0
$106$	0.309046	+	1.75269i	0.0300172	+	0.170236i
$107$	−10.2616	−	10.2616i	−0.992026	−	0.992026i	0.00794276	−	0.999968i	$-0.497472\pi$
$107$	−10.2616	−	10.2616i	−0.992026	−	0.992026i	−0.999968	+	0.00794276i	$0.997472\pi$
$108$		0			0
$109$		−	14.3459i		−	1.37409i	−0.726615	−	0.687045i	$-0.758908\pi$
$109$		−	14.3459i		−	1.37409i	0.726615	−	0.687045i	$-0.241092\pi$
$110$	−8.46805	+	9.57229i	−0.807397	+	0.912682i
$111$		0			0
$112$	2.87431	−	6.16397i	0.271597	−	0.582441i
$113$	13.5865	−	1.18867i	1.27811	−	0.111821i	0.572198	−	0.820116i	$-0.306091\pi$
$113$	13.5865	−	1.18867i	1.27811	−	0.111821i	0.705916	+	0.708295i	$0.250535\pi$
$114$		0			0
$115$	3.97147	+	11.8676i	0.370341	+	1.10666i
$116$	−1.34621	+	0.777236i	−0.124993	+	0.0721646i
$117$		0			0
$118$	−6.24582	+	1.67356i	−0.574974	+	0.154064i
$119$	4.80039	−	4.02801i	0.440051	−	0.369247i
$120$		0			0
$121$	−1.30443	+	7.39778i	−0.118584	+	0.672525i
$122$	−9.14940	+	6.40648i	−0.828348	+	0.580016i
$123$		0			0
$124$	0.366468	+	0.436739i	0.0329098	+	0.0392204i
$125$	7.26225	+	8.50058i	0.649555	+	0.760315i
$126$		0			0
$127$	−3.47767	−	0.931838i	−0.308593	−	0.0826872i	0.101199	−	0.994866i	$-0.467732\pi$
$127$	−3.47767	−	0.931838i	−0.308593	−	0.0826872i	−0.409792	+	0.912179i	$0.634399\pi$
$128$	8.08251	−	3.76894i	0.714400	−	0.333130i
$129$		0			0
$130$	−10.3649	−	10.9213i	−0.909058	−	0.957858i
$131$	−0.189922	−	0.521807i	−0.0165936	−	0.0455905i	0.931119	−	0.364715i	$-0.118833\pi$
$131$	−0.189922	−	0.521807i	−0.0165936	−	0.0455905i	−0.947713	+	0.319124i	$0.896611\pi$
$132$		0			0
$133$	1.00634	−	1.43720i	0.0872607	−	0.124621i
$134$	12.8204			1.10751
$135$		0			0
$136$	9.50463			0.815015
$137$	3.46624	−	4.95031i	0.296141	−	0.422934i	−0.643315	−	0.765601i	$-0.722442\pi$
$137$	3.46624	−	4.95031i	0.296141	−	0.422934i	0.939457	+	0.342668i	$0.111330\pi$
$138$		0			0
$139$	6.33390	+	17.4022i	0.537234	+	1.47604i	0.850295	+	0.526306i	$0.176423\pi$
$139$	6.33390	+	17.4022i	0.537234	+	1.47604i	−0.313061	+	0.949733i	$0.601354\pi$
$140$	−1.02986	−	0.0269197i	−0.0870395	−	0.00227513i
$141$		0			0
$142$	−6.84148	+	3.19024i	−0.574125	+	0.267719i
$143$	−21.0660	−	5.64463i	−1.76163	−	0.472027i
$144$		0			0
$145$	−11.8735	−	8.78508i	−0.986042	−	0.729561i
$146$	4.36428	+	5.20115i	0.361190	+	0.430450i
$147$		0			0
$148$	1.39024	−	0.973455i	0.114277	−	0.0800175i
$149$	1.50609	−	8.54145i	0.123384	−	0.699743i	−0.858871	−	0.512192i	$-0.828834\pi$
$149$	1.50609	−	8.54145i	0.123384	−	0.699743i	0.982255	−	0.187551i	$-0.0600551\pi$
$150$		0			0
$151$	−12.2052	+	10.2414i	−0.993244	+	0.833431i	−0.986034	−	0.166543i	$-0.946740\pi$
$151$	−12.2052	+	10.2414i	−0.993244	+	0.833431i	−0.00721007	+	0.999974i	$0.502295\pi$
$152$	2.57045	−	0.688750i	0.208491	−	0.0558650i
$153$		0			0
$154$	9.69056	−	5.59485i	0.780887	−	0.450846i
$155$	−2.41689	+	4.84811i	−0.194130	+	0.389409i
$156$		0			0
$157$	13.2243	−	1.15698i	1.05541	−	0.0923367i	0.453784	−	0.891112i	$-0.350074\pi$
$157$	13.2243	−	1.15698i	1.05541	−	0.0923367i	0.601630	+	0.798775i	$0.294518\pi$
$158$	0.234077	−	0.501981i	0.0186222	−	0.0399354i
$159$		0			0
$160$	−2.21748	−	1.96168i	−0.175307	−	0.155084i
$161$		−	10.9570i		−	0.863530i
$162$		0			0
$163$	5.24760	+	5.24760i	0.411024	+	0.411024i	0.882095	−	0.471071i	$-0.156133\pi$
$163$	5.24760	+	5.24760i	0.411024	+	0.411024i	−0.471071	+	0.882095i	$0.656133\pi$
$164$	−0.345940	−	1.96192i	−0.0270133	−	0.153200i
$165$		0			0
$166$	11.5723	−	4.21196i	0.898183	−	0.326912i
$167$	0.717512	+	8.20120i	0.0555227	+	0.634628i	0.972068	+	0.234698i	$0.0754101\pi$
$167$	0.717512	+	8.20120i	0.0555227	+	0.634628i	−0.916546	+	0.399930i	$0.869034\pi$
$168$		0			0
$169$	4.34150	−	11.9282i	0.333962	−	0.917553i
$170$	3.79162	+	8.71900i	0.290804	+	0.668717i
$171$		0			0
$172$	0.0785918	+	0.293309i	0.00599257	+	0.0223646i
$173$	−0.677506	+	7.74393i	−0.0515098	+	0.588760i	0.925951	+	0.377643i	$0.123265\pi$
$173$	−0.677506	+	7.74393i	−0.0515098	+	0.588760i	−0.977461	+	0.211116i	$0.932290\pi$
$174$		0			0
$175$	−3.66781	−	9.07571i	−0.277261	−	0.686059i
$176$	14.7198	+	2.59549i	1.10954	+	0.195643i
$177$		0			0
$178$	−2.57908	−	0.225641i	−0.193310	−	0.0169125i
$179$	2.19929	−	3.80928i	0.164382	−	0.284719i	−0.772053	−	0.635558i	$-0.780770\pi$
$179$	2.19929	−	3.80928i	0.164382	−	0.284719i	0.936436	+	0.350839i	$0.114104\pi$
$180$		0			0
$181$	−2.85830	−	4.95072i	−0.212456	−	0.367984i	0.740027	−	0.672577i	$-0.234813\pi$
$181$	−2.85830	−	4.95072i	−0.212456	−	0.367984i	−0.952483	+	0.304593i	$0.901479\pi$
$182$	5.57127	+	11.9476i	0.412970	+	0.885617i
$183$		0			0
$184$	10.6824	−	12.7308i	0.787519	−	0.938529i
$185$	13.7501	+	8.42517i	1.01093	+	0.619431i
$186$		0			0
$187$	11.2811	+	7.89911i	0.824956	+	0.577640i
$188$	1.37145	−	1.37145i	0.100023	−	0.100023i
$189$		0			0
$190$	1.65723	+	2.08323i	0.120228	+	0.151133i
$191$	−14.2067	+	2.50503i	−1.02796	+	0.181258i	−0.662104	−	0.749412i	$-0.730336\pi$
$191$	−14.2067	+	2.50503i	−1.02796	+	0.181258i	−0.365860	+	0.930670i	$0.619225\pi$
$192$		0			0
$193$	15.7247	+	7.33254i	1.13189	+	0.527808i	0.896036	−	0.443981i	$-0.146434\pi$
$193$	15.7247	+	7.33254i	1.13189	+	0.527808i	0.235852	+	0.971789i	$0.424212\pi$
$194$	−13.7446	−	11.5331i	−0.986802	−	0.828025i
$195$		0			0
$196$	−0.700384	−	0.254919i	−0.0500274	−	0.0182085i
$197$	3.52289	−	13.1476i	0.250995	−	0.936727i	−0.719280	−	0.694721i	$-0.755528\pi$
$197$	3.52289	−	13.1476i	0.250995	−	0.936727i	0.970275	−	0.242006i	$-0.0778054\pi$
$198$		0			0
$199$	7.78555	+	4.49499i	0.551903	+	0.318641i	0.749889	−	0.661564i	$-0.230107\pi$
$199$	7.78555	+	4.49499i	0.551903	+	0.318641i	−0.197986	+	0.980205i	$0.563440\pi$
$200$	4.58670	−	14.1209i	0.324329	−	0.998500i
$201$		0			0
$202$	−3.24187	−	4.62987i	−0.228097	−	0.325756i
$203$	7.41743	+	10.5932i	0.520601	+	0.743496i
$204$		0			0
$205$	15.7843	−	10.4485i	1.10242	−	0.729753i
$206$	−15.3625	−	8.86955i	−1.07036	−	0.617971i
$207$		0			0
$208$	−4.55757	+	17.0091i	−0.316011	+	1.17937i
$209$	3.62329	+	1.31877i	0.250628	+	0.0912212i
$210$		0			0
$211$	−14.3607	−	12.0500i	−0.988631	−	0.829559i	−0.00326162	−	0.999995i	$-0.501038\pi$
$211$	−14.3607	−	12.0500i	−0.988631	−	0.829559i	−0.985369	+	0.170435i	$0.945483\pi$
$212$	−0.285746	−	0.133245i	−0.0196251	−	0.00915134i
$213$		0			0
$214$	−18.9851	+	3.34758i	−1.29779	+	0.228836i
$215$	−2.25794	+	1.79622i	−0.153990	+	0.122501i
$216$		0			0
$217$	3.35376	−	3.35376i	0.227668	−	0.227668i
$218$	−15.6108	−	10.9308i	−1.05729	−	0.740326i
$219$		0			0
$220$	−0.528643	−	2.20150i	−0.0356411	−	0.148425i
$221$	−10.4290	+	12.4288i	−0.701530	+	0.836051i
$222$		0			0
$223$	−7.00968	−	15.0323i	−0.469403	−	1.00664i	−0.988402	−	0.151862i	$-0.951473\pi$
$223$	−7.00968	−	15.0323i	−0.469403	−	1.00664i	0.518999	−	0.854775i	$-0.326305\pi$
$224$	1.29608	+	2.24488i	0.0865981	+	0.149992i
$225$		0			0
$226$	9.05870	−	15.6901i	0.602576	−	1.04369i
$227$	−18.0248	−	1.57696i	−1.19634	−	0.104667i	−0.528478	−	0.848947i	$-0.677237\pi$
$227$	−18.0248	−	1.57696i	−1.19634	−	0.104667i	−0.667867	+	0.744281i	$0.732793\pi$
$228$		0			0
$229$	−18.7074	−	3.29862i	−1.23622	−	0.217979i	−0.482924	−	0.875662i	$-0.660425\pi$
$229$	−18.7074	−	3.29862i	−1.23622	−	0.217979i	−0.753294	+	0.657684i	$0.771536\pi$
$230$	15.9400	+	4.72083i	1.05105	+	0.311282i
$231$		0			0
$232$	−1.70951	+	19.5397i	−0.112235	+	1.28285i
$233$	1.95750	+	7.30551i	0.128240	+	0.478600i	0.999934	−	0.0114509i	$-0.00364501\pi$
$233$	1.95750	+	7.30551i	0.128240	+	0.478600i	−0.871694	+	0.490050i	$0.836978\pi$
$234$		0			0
$235$	17.1468	+	6.75337i	1.11853	+	0.440541i
$236$	0.391785	−	1.07642i	0.0255031	−	0.0700691i
$237$		0			0
$238$	−0.725521	−	8.29275i	−0.0470286	−	0.537539i
$239$	11.7518	−	4.27731i	0.760162	−	0.276676i	0.0672867	−	0.997734i	$-0.478566\pi$
$239$	11.7518	−	4.27731i	0.760162	−	0.276676i	0.692875	+	0.721057i	$0.256344\pi$
$240$		0			0
$241$	2.97320	+	16.8619i	0.191521	+	1.08617i	0.917287	+	0.398227i	$0.130374\pi$
$241$	2.97320	+	16.8619i	0.191521	+	1.08617i	−0.725766	+	0.687942i	$0.758514\pi$
$242$	7.05612	+	7.05612i	0.453585	+	0.453585i
$243$		0			0
$244$		−	1.97870i		−	0.126673i
$245$	−0.432674	−	7.06872i	−0.0276425	−	0.451604i
$246$		0			0
$247$	−1.91979	+	4.11700i	−0.122153	+	0.261958i
$248$	7.16645	−	0.626983i	0.455070	−	0.0398134i
$249$		0			0
$250$	14.7835	−	1.42558i	0.934989	−	0.0901619i
$251$	−4.66370	+	2.69259i	−0.294370	+	0.169955i	−0.639911	−	0.768449i	$-0.721029\pi$
$251$	−4.66370	+	2.69259i	−0.294370	+	0.169955i	0.345541	+	0.938404i	$0.387696\pi$
$252$		0			0
$253$	23.2594	−	6.23233i	1.46231	−	0.391823i
$254$	−3.66378	+	3.07428i	−0.229886	+	0.192897i
$255$		0			0
$256$	−0.966651	+	5.48215i	−0.0604157	+	0.342634i
$257$	10.0445	−	7.03325i	0.626560	−	0.438722i	−0.216692	−	0.976240i	$-0.569527\pi$
$257$	10.0445	−	7.03325i	0.626560	−	0.438722i	0.843252	+	0.537518i	$0.180638\pi$
$258$		0			0
$259$	−9.07550	−	10.8158i	−0.563924	−	0.672059i
$260$	2.63804	−	0.394384i	0.163604	−	0.0244586i
$261$		0			0
$262$	−0.712524	−	0.190920i	−0.0440199	−	0.0117951i
$263$	−12.3505	+	5.75913i	−0.761563	+	0.355123i	−0.764289	−	0.644873i	$-0.776910\pi$
$263$	−12.3505	+	5.75913i	−0.761563	+	0.355123i	0.00272594	+	0.999996i	$0.499132\pi$
$264$		0			0
$265$	0.0782794	−	2.99474i	0.00480867	−	0.183965i
$266$	−0.797143	−	2.19013i	−0.0488760	−	0.134286i
$267$		0			0
$268$	−1.30270	+	1.86045i	−0.0795749	+	0.113645i
$269$	12.3342			0.752028			0.376014	−	0.926614i	$-0.377294\pi$
$269$	12.3342			0.752028			0.376014	+	0.926614i	$0.377294\pi$
$270$		0			0
$271$	19.7578			1.20020			0.600099	−	0.799926i	$-0.295128\pi$
$271$	19.7578			1.20020			0.600099	+	0.799926i	$0.295128\pi$
$272$	6.37789	−	9.10856i	0.386716	−	0.552288i
$273$		0			0
$274$	−2.74569	−	7.54371i	−0.165873	−	0.455732i
$275$	17.1796	−	12.9483i	1.03597	−	0.780811i
$276$		0			0
$277$	−1.83776	+	0.856962i	−0.110420	+	0.0514898i	−0.477044	−	0.878880i	$-0.658292\pi$
$277$	−1.83776	+	0.856962i	−0.110420	+	0.0514898i	0.366623	+	0.930370i	$0.380514\pi$
$278$	23.7626	+	6.36718i	1.42519	+	0.381878i
$279$		0			0
$280$	−7.73179	+	10.4499i	−0.462063	+	0.624503i
$281$	16.8041	+	20.0263i	1.00245	+	1.19467i	0.980822	+	0.194903i	$0.0624393\pi$
$281$	16.8041	+	20.0263i	1.00245	+	1.19467i	0.0216244	+	0.999766i	$0.493116\pi$
$282$		0			0
$283$	−1.89971	+	1.33019i	−0.112926	+	0.0790717i	−0.628675	−	0.777668i	$-0.716403\pi$
$283$	−1.89971	+	1.33019i	−0.112926	+	0.0790717i	0.515749	+	0.856740i	$0.327514\pi$
$284$	0.232218	−	1.31697i	0.0137796	−	0.0781480i
$285$		0			0
$286$	−22.1934	+	18.6225i	−1.31232	+	1.10117i
$287$	−16.0086	+	4.28949i	−0.944956	+	0.253200i
$288$		0			0
$289$	−5.84978	+	3.37737i	−0.344105	+	0.198669i
$290$	−18.6066	+	6.22665i	−1.09262	+	0.365642i
$291$		0			0
$292$	−1.19823	+	0.104832i	−0.0701211	+	0.00613480i
$293$	−5.09445	+	10.9251i	−0.297621	+	0.638250i	−0.997075	−	0.0764274i	$-0.975649\pi$
$293$	−5.09445	+	10.9251i	−0.297621	+	0.638250i	0.699454	+	0.714677i	$0.253426\pi$
$294$		0			0
$295$	10.8639	−	0.664978i	0.632523	−	0.0387165i
$296$		−	21.4149i		−	1.24471i
$297$		0			0
$298$	−8.14698	−	8.14698i	−0.471942	−	0.471942i
$299$	4.92621	+	27.9379i	0.284890	+	1.61569i
$300$		0			0
$301$	2.37381	−	0.863996i	0.136824	−	0.0497999i
$302$	1.84467	+	21.0846i	0.106149	+	1.21328i
$303$		0			0
$304$	1.06480	−	2.92551i	0.0610704	−	0.167790i
$305$	17.2413	−	7.49771i	0.987236	−	0.429317i
$306$		0			0
$307$	−6.08202	−	22.6984i	−0.347119	−	1.29547i	−0.890117	−	0.455732i	$-0.849378\pi$
$307$	−6.08202	−	22.6984i	−0.347119	−	1.29547i	0.542998	−	0.839734i	$-0.317289\pi$
$308$	−0.172769	+	1.97476i	−0.00984441	+	0.112522i
$309$		0			0
$310$	3.43402	+	6.32397i	0.195039	+	0.359177i
$311$	−3.91683	−	0.690642i	−0.222103	−	0.0391627i	0.0614891	−	0.998108i	$-0.480415\pi$
$311$	−3.91683	−	0.690642i	−0.222103	−	0.0391627i	−0.283592	+	0.958945i	$0.591526\pi$
$312$		0			0
$313$	−0.911077	−	0.0797089i	−0.0514971	−	0.00450541i	0.0613781	−	0.998115i	$-0.480450\pi$
$313$	−0.911077	−	0.0797089i	−0.0514971	−	0.00450541i	−0.112875	+	0.993609i	$0.536006\pi$
$314$	8.81718	−	15.2718i	0.497582	−	0.861838i
$315$		0			0
$316$	0.0490605	+	0.0849753i	0.00275987	+	0.00478023i
$317$	11.1443	+	23.8990i	0.625924	+	1.34230i	0.922021	+	0.387141i	$0.126537\pi$
$317$	11.1443	+	23.8990i	0.625924	+	1.34230i	−0.296096	+	0.955158i	$0.595685\pi$
$318$		0			0
$319$	−18.2681	+	21.7711i	−1.02282	+	1.21895i
$320$	−18.9308	+	4.54582i	−1.05826	+	0.254119i
$321$		0			0
$322$	−11.9230	−	8.34859i	−0.664444	−	0.465249i
$323$	2.02833	−	2.02833i	0.112859	−	0.112859i
$324$		0			0
$325$	13.4325	+	21.4921i	0.745103	+	1.19217i
$326$	9.70865	−	1.71190i	0.537712	−	0.0948132i
$327$		0			0
$328$	−22.7823	−	10.6235i	−1.25794	−	0.586587i
$329$	−12.3602	−	10.3715i	−0.681442	−	0.571798i
$330$		0			0
$331$	−12.0746	−	4.39481i	−0.663682	−	0.241561i	−0.0118569	−	0.999930i	$-0.503774\pi$
$331$	−12.0746	−	4.39481i	−0.663682	−	0.241561i	−0.651825	+	0.758369i	$0.725996\pi$
$332$	−0.564651	+	2.10731i	−0.0309893	+	0.115653i
$333$		0			0
$334$	9.47099	+	5.46808i	0.518229	+	0.299200i
$335$	−21.1472	−	4.30140i	−1.15539	−	0.235011i
$336$		0			0
$337$	4.87543	+	6.96283i	0.265581	+	0.379290i	0.929688	−	0.368349i	$-0.120077\pi$
$337$	4.87543	+	6.96283i	0.265581	+	0.379290i	−0.664106	+	0.747638i	$0.731188\pi$
$338$	−9.67189	−	13.8129i	−0.526081	−	0.751322i
$339$		0			0
$340$	−1.65054	−	0.335725i	−0.0895130	−	0.0182073i
$341$	9.02697	+	5.21173i	0.488838	+	0.282231i
$342$		0			0
$343$	−5.15177	+	19.2267i	−0.278169	+	1.03814i
$344$	3.60046	+	1.31046i	0.194124	+	0.0706553i
$345$		0			0
$346$	7.91047	+	6.63767i	0.425270	+	0.356844i
$347$	−4.76851	−	2.22359i	−0.255987	−	0.119369i	0.290389	−	0.956909i	$-0.406215\pi$
$347$	−4.76851	−	2.22359i	−0.255987	−	0.119369i	−0.546376	+	0.837540i	$0.683993\pi$
$348$		0			0
$349$	20.3047	−	3.58026i	1.08688	−	0.191647i	0.398627	−	0.917113i	$-0.369487\pi$
$349$	20.3047	−	3.58026i	1.08688	−	0.191647i	0.688258	+	0.725466i	$0.258376\pi$
$350$	−12.6706	−	2.92398i	−0.677270	−	0.156293i
$351$		0			0
$352$	−4.02821	+	4.02821i	−0.214704	+	0.214704i
$353$	−23.6027	−	16.5268i	−1.25624	−	0.879631i	−0.259948	−	0.965623i	$-0.583705\pi$
$353$	−23.6027	−	16.5268i	−1.25624	−	0.879631i	−0.996296	+	0.0859911i	$0.972594\pi$
$354$		0			0
$355$	12.3553	−	2.96687i	0.655754	−	0.157465i
$356$	0.294808	−	0.351339i	0.0156248	−	0.0186209i
$357$		0			0
$358$	−2.46940	−	5.29565i	−0.130512	−	0.279884i
$359$	8.91393	+	15.4394i	0.470459	+	0.814860i	0.999429	−	0.0337810i	$-0.0107549\pi$
$359$	8.91393	+	15.4394i	0.470459	+	0.814860i	−0.528970	+	0.848641i	$0.677422\pi$
$360$		0			0
$361$	−9.09844	+	15.7590i	−0.478865	+	0.829419i
$362$	−7.56508	−	0.661859i	−0.397612	−	0.0347865i
$363$		0			0
$364$	−2.29990	−	0.405534i	−0.120547	−	0.0212558i
$365$	−5.45380	−	10.0435i	−0.285465	−	0.525702i
$366$		0			0
$367$	−1.91117	+	21.8448i	−0.0997623	+	1.14029i	0.767028	+	0.641614i	$0.221735\pi$
$367$	−1.91117	+	21.8448i	−0.0997623	+	1.14029i	−0.866790	+	0.498674i	$0.833821\pi$
$368$	−5.03210	−	18.7800i	−0.262316	−	0.978978i
$369$		0			0
$370$	19.6448	−	8.54289i	1.02128	−	0.444124i
$371$	−0.897087	+	2.46473i	−0.0465744	+	0.127962i
$372$		0			0
$373$	−1.50421	−	17.1932i	−0.0778848	−	0.890228i	−0.930165	−	0.367142i	$-0.880336\pi$
$373$	−1.50421	−	17.1932i	−0.0778848	−	0.890228i	0.852280	−	0.523086i	$-0.175219\pi$
$374$	17.1911	−	6.25706i	0.888932	−	0.323545i
$375$		0			0
$376$	−4.24967	−	24.1011i	−0.219160	−	1.24292i
$377$	−23.6755	−	23.6755i	−1.21935	−	1.21935i
$378$		0			0
$379$			27.1687i			1.39556i	0.716312	+	0.697780i	$0.245829\pi$
$379$			27.1687i			1.39556i	−0.716312	+	0.697780i	$0.754171\pi$
$380$	−0.470703	+	0.0288116i	−0.0241466	+	0.00147800i
$381$		0			0
$382$	−8.09883	+	17.3680i	−0.414372	+	0.888624i
$383$	−7.32022	+	0.640436i	−0.374046	+	0.0327248i	−0.272629	−	0.962119i	$-0.587893\pi$
$383$	−7.32022	+	0.640436i	−0.374046	+	0.0327248i	−0.101417	+	0.994844i	$0.532338\pi$
$384$		0			0
$385$	−17.8616	+	5.97735i	−0.910314	+	0.304634i
$386$	19.9604	−	11.5241i	1.01596	−	0.586562i
$387$		0			0
$388$	3.07024	−	0.822667i	0.155868	−	0.0417646i
$389$	−23.9421	+	20.0898i	−1.21391	+	1.01859i	−0.214792	+	0.976660i	$0.568907\pi$
$389$	−23.9421	+	20.0898i	−1.21391	+	1.01859i	−0.999120	+	0.0419334i	$0.986648\pi$
$390$		0			0
$391$	3.11072	−	17.6418i	0.157316	−	0.892182i
$392$	−7.70382	+	5.39427i	−0.389102	+	0.272452i
$393$		0			0
$394$	−11.6225	−	13.8512i	−0.585535	−	0.697814i
$395$	−0.554530	+	0.749477i	−0.0279014	+	0.0377103i
$396$		0			0
$397$	−15.9305	−	4.26857i	−0.799531	−	0.214234i	−0.164153	−	0.986435i	$-0.552489\pi$
$397$	−15.9305	−	4.26857i	−0.799531	−	0.214234i	−0.635378	+	0.772201i	$0.719156\pi$
$398$	10.8234	−	5.04706i	0.542530	−	0.252986i
$399$		0			0
$400$	−10.4547	−	13.8711i	−0.522734	−	0.693557i
$401$	0.517022	+	1.42051i	0.0258188	+	0.0709367i	0.951932	−	0.306308i	$-0.0990938\pi$
$401$	0.517022	+	1.42051i	0.0258188	+	0.0709367i	−0.926114	+	0.377245i	$0.876872\pi$
$402$		0			0
$403$	−7.04354	+	10.0592i	−0.350864	+	0.501085i
$404$	1.00128			0.0498155
$405$		0			0
$406$	17.1788			0.852571
$407$	17.7975	−	25.4175i	0.882189	−	1.25990i
$408$		0			0
$409$	8.02778	+	22.0561i	0.396948	+	1.09061i	0.963763	+	0.266760i	$0.0859532\pi$
$409$	8.02778	+	22.0561i	0.396948	+	1.09061i	−0.566815	+	0.823845i	$0.691825\pi$
$410$	0.657060	−	25.1371i	0.0324499	−	1.24143i
$411$		0			0
$412$	2.84812	−	1.32810i	0.140317	−	0.0654308i
$413$	−9.20490	−	2.46645i	−0.452944	−	0.121366i
$414$		0			0
$415$	−20.5016	+	3.06496i	−1.00638	+	0.150453i
$416$	−4.31402	−	5.14125i	−0.211512	−	0.252070i
$417$		0			0
$418$	4.19579	−	2.93792i	0.205223	−	0.143698i
$419$	−2.76242	+	15.6665i	−0.134953	+	0.765357i	0.839939	+	0.542680i	$0.182591\pi$
$419$	−2.76242	+	15.6665i	−0.134953	+	0.765357i	−0.974892	+	0.222677i	$0.928521\pi$
$420$		0			0
$421$	27.8051	−	23.3312i	1.35514	−	1.13709i	0.377685	−	0.925934i	$-0.376720\pi$
$421$	27.8051	−	23.3312i	1.35514	−	1.13709i	0.977452	−	0.211160i	$-0.0677241\pi$
$422$	−24.0545	+	6.44539i	−1.17096	+	0.313756i
$423$		0			0
$424$	−3.44529	+	1.98914i	−0.167318	+	0.0966012i
$425$	−3.32891	−	15.6541i	−0.161476	−	0.759334i
$426$		0			0
$427$	−16.3984	+	1.43468i	−0.793576	+	0.0694289i
$428$	1.44331	−	3.09519i	0.0697652	−	0.149612i
$429$		0			0
$430$	0.234166	+	3.82563i	0.0112925	+	0.184488i
$431$			10.7570i			0.518146i	0.965858	+	0.259073i	$0.0834169\pi$
$431$			10.7570i			0.518146i	−0.965858	+	0.259073i	$0.916583\pi$
$432$		0			0
$433$	−25.8369	−	25.8369i	−1.24164	−	1.24164i	−0.959320	−	0.282321i	$-0.908896\pi$
$433$	−25.8369	−	25.8369i	−1.24164	−	1.24164i	−0.282321	−	0.959320i	$-0.591104\pi$
$434$	−1.09408	−	6.20483i	−0.0525175	−	0.297842i
$435$		0			0
$436$	3.17246	−	1.15468i	0.151933	−	0.0552992i
$437$	−0.437136	−	4.99649i	−0.0209111	−	0.239015i
$438$		0			0
$439$	−4.76440	+	13.0901i	−0.227393	+	0.624756i	−0.999948	−	0.0101913i	$-0.996756\pi$
$439$	−4.76440	+	13.0901i	−0.227393	+	0.624756i	0.772556	+	0.634947i	$0.218978\pi$
$440$	−26.5809	−	10.4691i	−1.26720	−	0.499093i
$441$		0			0
$442$	5.57831	+	20.8185i	0.265333	+	0.990237i
$443$	−0.993879	+	11.3601i	−0.0472206	+	0.539734i	0.935335	+	0.353764i	$0.115098\pi$
$443$	−0.993879	+	11.3601i	−0.0472206	+	0.539734i	−0.982555	+	0.185970i	$0.940457\pi$
$444$		0			0
$445$	4.17847	+	1.23751i	0.198079	+	0.0586635i
$446$	−21.6986	−	3.82606i	−1.02746	−	0.181169i
$447$		0			0
$448$	16.9810	+	1.48564i	0.802276	+	0.0701900i
$449$	0.807925	−	1.39937i	0.0381283	−	0.0660402i	−0.846332	−	0.532657i	$-0.821194\pi$
$449$	0.807925	−	1.39937i	0.0381283	−	0.0660402i	0.884460	+	0.466616i	$0.154527\pi$
$450$		0			0
$451$	−18.2114	−	31.5431i	−0.857541	−	1.48530i
$452$	1.35642	+	2.90886i	0.0638008	+	0.136821i
$453$		0			0
$454$	−15.4498	+	18.4124i	−0.725097	+	0.864137i
$455$	−5.18119	−	21.5768i	−0.242898	−	1.01153i
$456$		0			0
$457$	4.53775	+	3.17737i	0.212267	+	0.148631i	0.674875	−	0.737932i	$-0.264197\pi$
$457$	4.53775	+	3.17737i	0.212267	+	0.148631i	−0.462608	+	0.886563i	$0.653086\pi$
$458$	−17.8434	+	17.8434i	−0.833768	+	0.833768i
$459$		0			0
$460$	−2.30475	+	1.83346i	−0.107460	+	0.0854855i
$461$	−14.9666	+	2.63902i	−0.697065	+	0.122911i	−0.510942	−	0.859615i	$-0.670703\pi$
$461$	−14.9666	+	2.63902i	−0.697065	+	0.122911i	−0.186123	+	0.982527i	$0.559592\pi$
$462$		0			0
$463$	−29.9580	−	13.9696i	−1.39226	−	0.649224i	−0.425516	−	0.904951i	$-0.639907\pi$
$463$	−29.9580	−	13.9696i	−1.39226	−	0.649224i	−0.966749	+	0.255727i	$0.917685\pi$
$464$	17.5784	+	14.7500i	0.816056	+	0.684752i
$465$		0			0
$466$	9.44112	+	3.43629i	0.437352	+	0.159183i
$467$	−5.87822	+	21.9378i	−0.272012	+	1.01516i	0.685806	+	0.727784i	$0.259450\pi$
$467$	−5.87822	+	21.9378i	−0.272012	+	1.01516i	−0.957818	+	0.287377i	$0.907217\pi$
$468$		0			0
$469$	16.3630	+	9.44716i	0.755571	+	0.436229i
$470$	20.4137	−	13.5129i	0.941613	−	0.623303i
$471$		0			0
$472$	−8.29047	−	11.8400i	−0.381600	−	0.544981i
$473$	3.18431	+	4.54767i	0.146415	+	0.209102i
$474$		0			0
$475$	−2.03464	−	3.99229i	−0.0933559	−	0.183179i
$476$	1.27713	+	0.737352i	0.0585372	+	0.0337965i
$477$		0			0
$478$	4.29979	−	16.0470i	0.196668	−	0.733974i
$479$	21.4594	+	7.81060i	0.980507	+	0.356875i	0.782037	−	0.623232i	$-0.214181\pi$
$479$	21.4594	+	7.81060i	0.980507	+	0.356875i	0.198470	+	0.980107i	$0.436403\pi$
$480$		0			0
$481$	28.0033	+	23.4976i	1.27684	+	1.07140i
$482$	20.6140	+	9.61245i	0.938941	+	0.437835i
$483$		0			0
$484$	−1.74094	+	0.306975i	−0.0791336	+	0.0139534i
$485$	18.8021	+	23.6352i	0.853758	+	1.07322i
$486$		0			0
$487$	13.1004	−	13.1004i	0.593634	−	0.593634i	−0.344977	−	0.938611i	$-0.612113\pi$
$487$	13.1004	−	13.1004i	0.593634	−	0.593634i	0.938611	+	0.344977i	$0.112113\pi$
$488$	−20.4520	−	14.3206i	−0.925817	−	0.648264i
$489$		0			0
$490$	−8.02163	−	4.91514i	−0.362380	−	0.222044i
$491$	5.95862	−	7.10121i	0.268909	−	0.320473i	−0.614644	−	0.788805i	$-0.710700\pi$
$491$	5.95862	−	7.10121i	0.268909	−	0.320473i	0.883553	+	0.468332i	$0.155145\pi$
$492$		0			0
$493$	8.93533	+	19.1619i	0.402427	+	0.863007i
$494$	3.01722	+	5.22597i	0.135751	+	0.235128i
$495$		0			0
$496$	4.20804	−	7.28854i	0.188947	−	0.327265i
$497$	−11.0828	−	0.969617i	−0.497131	−	0.0434933i
$498$		0			0
$499$	20.3482	+	3.58794i	0.910911	+	0.160618i	0.609417	−	0.792850i	$-0.291404\pi$
$499$	20.3482	+	3.58794i	0.910911	+	0.160618i	0.301494	+	0.953468i	$0.402515\pi$
$500$	−1.29529	+	2.29018i	−0.0579273	+	0.102420i
$501$		0			0
$502$	−0.623488	+	7.12650i	−0.0278276	+	0.318071i
$503$	−1.21585	−	4.53760i	−0.0542119	−	0.202322i	0.933508	−	0.358557i	$-0.116731\pi$
$503$	−1.21585	−	4.53760i	−0.0542119	−	0.202322i	−0.987720	+	0.156235i	$0.950064\pi$
$504$		0			0
$505$	3.79406	+	8.72462i	0.168833	+	0.388241i
$506$	10.9405	−	30.0588i	0.486365	−	1.33628i
$507$		0			0
$508$	−0.0738452	−	0.844055i	−0.00327635	−	0.0374489i
$509$	−30.3526	+	11.0475i	−1.34536	+	0.489670i	−0.911496	−	0.411309i	$-0.865072\pi$
$509$	−30.3526	+	11.0475i	−1.34536	+	0.489670i	−0.433862	+	0.900979i	$0.642849\pi$
$510$		0			0
$511$	1.73758	+	9.85432i	0.0768661	+	0.435929i
$512$	17.8410	+	17.8410i	0.788469	+	0.788469i
$513$		0			0
$514$		−	16.2891i		−	0.718480i
$515$	22.3645	+	19.7846i	0.985497	+	0.871812i
$516$		0			0
$517$	14.9860	−	32.1376i	0.659083	−	1.41341i
$518$	−18.6844	+	1.63467i	−0.820945	+	0.0718234i
$519$		0			0
$520$	15.0162	−	30.1213i	0.658502	−	1.32091i
$521$	2.29310	−	1.32392i	0.100463	−	0.0580021i	−0.448927	−	0.893568i	$-0.648194\pi$
$521$	2.29310	−	1.32392i	0.100463	−	0.0580021i	0.549390	+	0.835566i	$0.314860\pi$
$522$		0			0
$523$	−12.5901	+	3.37351i	−0.550527	+	0.147513i	−0.523351	−	0.852117i	$-0.675318\pi$
$523$	−12.5901	+	3.37351i	−0.550527	+	0.147513i	−0.0271764	+	0.999631i	$0.508652\pi$
$524$	0.100106	−	0.0839990i	0.00437316	−	0.00366951i
$525$		0			0
$526$	−3.14347	+	17.8275i	−0.137062	+	0.777317i
$527$	6.35202	−	4.44773i	0.276698	−	0.193746i
$528$		0			0
$529$	−5.34967	−	6.37549i	−0.232594	−	0.277195i
$530$	−3.19913	−	2.36700i	−0.138961	−	0.102816i
$531$		0			0
$532$	0.398822	+	0.106864i	0.0172911	+	0.00463314i
$533$	38.8899	−	18.1347i	1.68451	−	0.785499i
$534$		0			0
$535$	32.4389	+	0.847922i	1.40246	+	0.0366589i
$536$	9.80156	+	26.9296i	0.423363	+	1.16318i
$537$		0			0
$538$	9.39794	−	13.4217i	0.405174	−	0.578649i
$539$	−13.6268			−0.586947
$540$		0			0
$541$	−42.0435			−1.80759			−0.903796	−	0.427963i	$-0.859231\pi$
$541$	−42.0435			−1.80759			−0.903796	+	0.427963i	$0.859231\pi$
$542$	15.0543	−	21.4998i	0.646637	−	0.923494i
$543$		0			0
$544$	1.44949	+	3.98243i	0.0621463	+	0.170745i
$545$	22.0824	+	23.2678i	0.945908	+	0.996685i
$546$		0			0
$547$	−20.8870	+	9.73975i	−0.893062	+	0.416442i	−0.814295	−	0.580451i	$-0.802876\pi$
$547$	−20.8870	+	9.73975i	−0.893062	+	0.416442i	−0.0787671	+	0.996893i	$0.525098\pi$
$548$	1.37371	+	0.368084i	0.0586818	+	0.0157238i
$549$		0			0
$550$	−1.00002	−	28.5602i	−0.0426412	−	1.21781i
$551$	3.80505	+	4.53468i	0.162101	+	0.193184i
$552$		0			0
$553$	0.668660	−	0.468201i	0.0284343	−	0.0199099i
$554$	−0.467751	+	2.65275i	−0.0198728	+	0.112704i
$555$		0			0
$556$	−3.33853	+	2.80136i	−0.141585	+	0.118804i
$557$	34.3132	−	9.19419i	1.45390	−	0.389570i	0.556519	−	0.830835i	$-0.312137\pi$
$557$	34.3132	−	9.19419i	1.45390	−	0.389570i	0.897377	+	0.441265i	$0.145470\pi$
$558$		0			0
$559$	−5.66426	+	3.27026i	−0.239572	+	0.138317i
$560$	4.82622	+	14.4218i	0.203945	+	0.609433i
$561$		0			0
$562$	34.5957	−	3.02674i	1.45933	−	0.127675i
$563$	−1.97748	+	4.24073i	−0.0833410	+	0.178725i	−0.943562	−	0.331196i	$-0.892548\pi$
$563$	−1.97748	+	4.24073i	−0.0833410	+	0.178725i	0.860221	+	0.509922i	$0.170326\pi$
$564$		0			0
$565$	−20.2065	+	22.8415i	−0.850094	+	0.960947i
$566$			3.08073i			0.129493i
$567$		0			0
$568$	−11.9317	−	11.9317i	−0.500642	−	0.500642i
$569$	1.37633	+	7.80556i	0.0576988	+	0.327226i	0.999971	−	0.00762185i	$-0.00242613\pi$
$569$	1.37633	+	7.80556i	0.0576988	+	0.327226i	−0.942272	+	0.334848i	$0.891315\pi$
$570$		0			0
$571$	4.65824	−	1.69546i	0.194941	−	0.0709528i	−0.242705	−	0.970100i	$-0.578035\pi$
$571$	4.65824	−	1.69546i	0.194941	−	0.0709528i	0.437646	+	0.899147i	$0.355812\pi$
$572$	−0.447319	−	5.11288i	−0.0187033	−	0.213780i
$573$		0			0
$574$	−7.52995	+	20.6884i	−0.314294	+	0.863516i
$575$	−24.7090	−	13.1350i	−1.03044	−	0.547769i
$576$		0			0
$577$	−5.90200	−	22.0266i	−0.245703	−	0.916977i	−0.973029	−	0.230684i	$-0.925904\pi$
$577$	−5.90200	−	22.0266i	−0.245703	−	0.916977i	0.727325	−	0.686293i	$-0.240763\pi$
$578$	−0.782053	+	8.93890i	−0.0325291	+	0.371809i
$579$		0			0
$580$	0.987055	−	3.33281i	0.0409852	−	0.138388i
$581$	17.8737	+	3.15161i	0.741526	+	0.130751i
$582$		0			0
$583$	−5.74237	−	0.502393i	−0.237825	−	0.0208070i
$584$	−7.58853	+	13.1437i	−0.314015	+	0.543891i
$585$		0			0
$586$	8.00664	+	13.8679i	0.330751	+	0.572878i
$587$	15.8151	+	33.9155i	0.652758	+	1.39984i	0.902142	+	0.431439i	$0.141994\pi$
$587$	15.8151	+	33.9155i	0.652758	+	1.39984i	−0.249384	+	0.968405i	$0.580228\pi$
$588$		0			0
$589$	1.39555	−	1.66315i	0.0575026	−	0.0685290i
$590$	7.55410	−	12.3285i	0.310997	−	0.507555i
$591$		0			0
$592$	−20.5225	−	14.3700i	−0.843470	−	0.590604i
$593$	−5.46266	+	5.46266i	−0.224324	+	0.224324i	−0.810317	−	0.585992i	$-0.800705\pi$
$593$	−5.46266	+	5.46266i	−0.224324	+	0.224324i	0.585992	+	0.810317i	$0.300705\pi$
$594$		0			0
$595$	−1.58558	+	13.9222i	−0.0650024	+	0.570756i
$596$	2.01008	−	0.354432i	0.0823362	−	0.0145181i
$597$		0			0
$598$	34.1546	+	15.9266i	1.39669	+	0.651286i
$599$	−1.79656	−	1.50749i	−0.0734055	−	0.0615946i	0.605347	−	0.795962i	$-0.293035\pi$
$599$	−1.79656	−	1.50749i	−0.0734055	−	0.0615946i	−0.678752	+	0.734367i	$0.737479\pi$
$600$		0			0
$601$	38.1639	+	13.8905i	1.55674	+	0.566607i	0.969987	−	0.243159i	$-0.0781836\pi$
$601$	38.1639	+	13.8905i	1.55674	+	0.566607i	0.586753	+	0.809766i	$0.300406\pi$
$602$	0.868536	−	3.24142i	0.0353989	−	0.132110i
$603$		0			0
$604$	−3.24716	−	1.87475i	−0.132125	−	0.0762824i
$605$	−9.27161	−	14.0064i	−0.376944	−	0.569443i
$606$		0			0
$607$	1.07501	+	1.53527i	0.0436332	+	0.0623147i	0.840376	−	0.542004i	$-0.182334\pi$
$607$	1.07501	+	1.53527i	0.0436332	+	0.0623147i	−0.796743	+	0.604319i	$0.793445\pi$
$608$	0.680588	+	0.971981i	0.0276015	+	0.0394190i
$609$		0			0
$610$	4.97816	−	24.4743i	0.201560	−	0.990935i
$611$	36.1789	+	20.8879i	1.46364	+	0.845035i
$612$		0			0
$613$	4.71349	−	17.5910i	0.190376	−	0.710494i	−0.803039	−	0.595926i	$-0.796785\pi$
$613$	4.71349	−	17.5910i	0.190376	−	0.710494i	0.993415	−	0.114568i	$-0.0365482\pi$
$614$	−29.3338	−	10.6766i	−1.18382	−	0.430874i
$615$		0			0
$616$	19.1608	+	16.0778i	0.772012	+	0.647795i
$617$	−16.8885	−	7.87526i	−0.679907	−	0.317046i	0.0518073	−	0.998657i	$-0.483502\pi$
$617$	−16.8885	−	7.87526i	−0.679907	−	0.317046i	−0.731715	+	0.681611i	$0.761280\pi$
$618$		0			0
$619$	28.0130	−	4.93945i	1.12594	−	0.198533i	0.420492	−	0.907296i	$-0.361858\pi$
$619$	28.0130	−	4.93945i	1.12594	−	0.198533i	0.705447	+	0.708763i	$0.250746\pi$
$620$	−1.26665	−	0.144256i	−0.0508697	−	0.00579345i
$621$		0			0
$622$	−3.73594	+	3.73594i	−0.149797	+	0.149797i
$623$	−3.12547	−	2.18848i	−0.125219	−	0.0876795i
$624$		0			0
$625$	−24.8635	−	2.60855i	−0.994541	−	0.104342i
$626$	−0.780926	+	0.930671i	−0.0312121	+	0.0371971i
$627$		0			0
$628$	1.32026	+	2.83130i	0.0526840	+	0.112981i
$629$	−11.5418	−	19.9910i	−0.460202	−	0.797093i
$630$		0			0
$631$	−16.2016	+	28.0619i	−0.644974	+	1.11713i	0.339333	+	0.940666i	$0.389799\pi$
$631$	−16.2016	+	28.0619i	−0.644974	+	1.11713i	−0.984307	+	0.176462i	$0.943535\pi$
$632$	1.23338	+	0.107907i	0.0490613	+	0.00429231i
$633$		0			0
$634$	34.4974	+	6.08282i	1.37007	+	0.241580i
$635$	7.07484	−	3.84175i	0.280756	−	0.152455i
$636$		0			0
$637$	1.39919	−	15.9928i	0.0554380	−	0.633659i
$638$	9.77134	+	36.4671i	0.386851	+	1.44375i
$639$		0			0
$640$	−7.30768	+	18.5542i	−0.288861	+	0.733418i
$641$	7.10695	−	19.5262i	0.280708	−	0.771238i	−0.716571	−	0.697514i	$-0.754289\pi$
$641$	7.10695	−	19.5262i	0.280708	−	0.771238i	0.997279	−	0.0737239i	$-0.0234884\pi$
$642$		0			0
$643$	3.44122	+	39.3334i	0.135709	+	1.55116i	0.693060	+	0.720880i	$0.256262\pi$
$643$	3.44122	+	39.3334i	0.135709	+	1.55116i	−0.557351	+	0.830277i	$0.688182\pi$
$644$	2.42303	−	0.881910i	0.0954807	−	0.0347521i
$645$		0			0
$646$	−0.661691	−	3.75263i	−0.0260339	−	0.147645i
$647$	27.7872	+	27.7872i	1.09243	+	1.09243i	0.995269	+	0.0971593i	$0.0309756\pi$
$647$	27.7872	+	27.7872i	1.09243	+	1.09243i	0.0971593	+	0.995269i	$0.469024\pi$
$648$		0			0
$649$		−	20.9430i		−	0.822086i
$650$	33.6218	+	1.75888i	1.31876	+	0.0689891i
$651$		0			0
$652$	−0.738085	+	1.58283i	−0.0289056	+	0.0619884i
$653$	−16.8852	+	1.47726i	−0.660770	+	0.0578098i	−0.412608	−	0.910909i	$-0.635382\pi$
$653$	−16.8852	+	1.47726i	−0.660770	+	0.0578098i	−0.248162	+	0.968719i	$0.579826\pi$
$654$		0			0
$655$	1.11125	+	0.553982i	0.0434200	+	0.0216459i
$656$	−25.4684	+	14.7042i	−0.994375	+	0.574103i
$657$		0			0
$658$	−20.7037	+	5.54754i	−0.807115	+	0.216266i
$659$	36.7210	−	30.8125i	1.43045	−	1.20029i	0.484997	−	0.874516i	$-0.338821\pi$
$659$	36.7210	−	30.8125i	1.43045	−	1.20029i	0.945449	−	0.325770i	$-0.105624\pi$
$660$		0			0
$661$	−0.726513	+	4.12026i	−0.0282581	+	0.160259i	−0.995671	−	0.0929427i	$-0.970373\pi$
$661$	−0.726513	+	4.12026i	−0.0282581	+	0.160259i	0.967413	+	0.253202i	$0.0814838\pi$
$662$	−13.9825	+	9.79064i	−0.543445	+	0.380524i
$663$		0			0
$664$	17.6947	+	21.0877i	0.686687	+	0.818361i
$665$	0.580065	+	3.88006i	0.0224939	+	0.150462i
$666$		0			0
$667$	35.7087	+	9.56811i	1.38264	+	0.370479i
$668$	−1.75587	+	0.818774i	−0.0679365	+	0.0316793i
$669$		0			0
$670$	−20.7936	+	19.7342i	−0.803326	+	0.762400i
$671$	−12.3730	−	33.9945i	−0.477653	−	1.31234i
$672$		0			0
$673$	13.6940	−	19.5570i	0.527863	−	0.753867i	−0.463345	−	0.886178i	$-0.653351\pi$
$673$	13.6940	−	19.5570i	0.527863	−	0.753867i	0.991208	+	0.132311i	$0.0422398\pi$
$674$	11.2915			0.434933
$675$		0			0
$676$	2.98725			0.114894
$677$	12.6903	−	18.1236i	0.487727	−	0.696547i	−0.497565	−	0.867427i	$-0.665772\pi$
$677$	12.6903	−	18.1236i	0.487727	−	0.696547i	0.985292	+	0.170880i	$0.0546611\pi$
$678$		0			0
$679$	−9.04396	−	24.8481i	−0.347075	−	0.953581i
$680$	−15.4157	+	14.6303i	−0.591165	+	0.561047i
$681$		0			0
$682$	12.5493	−	5.85182i	0.480537	−	0.224078i
$683$	−24.3829	−	6.53337i	−0.932985	−	0.249993i	−0.239858	−	0.970808i	$-0.577101\pi$
$683$	−24.3829	−	6.53337i	−0.932985	−	0.249993i	−0.693127	+	0.720815i	$0.743768\pi$
$684$		0			0
$685$	1.99798	+	13.3645i	0.0763389	+	0.510632i
$686$	16.9965	+	20.2556i	0.648929	+	0.773363i
$687$		0			0
$688$	3.67187	−	2.57107i	0.139989	−	0.0980212i
$689$	1.17925	−	6.68785i	0.0449258	−	0.254787i
$690$		0			0
$691$	25.5999	−	21.4808i	0.973865	−	0.817170i	−0.00928734	−	0.999957i	$-0.502956\pi$
$691$	25.5999	−	21.4808i	0.973865	−	0.817170i	0.983153	+	0.182787i	$0.0585118\pi$
$692$	−1.76703	+	0.473473i	−0.0671723	+	0.0179988i
$693$		0			0
$694$	−6.05298	+	3.49469i	−0.229768	+	0.132657i
$695$	−37.0600	−	18.4753i	−1.40577	−	0.700807i
$696$		0			0
$697$	−26.9931	+	2.36159i	−1.02244	+	0.0894517i
$698$	11.5751	−	24.8229i	0.438124	−	0.939559i
$699$		0			0
$700$	1.71179	−	1.54159i	0.0646996	−	0.0582667i
$701$		−	12.4042i		−	0.468499i	−0.972177	−	0.234249i	$-0.924737\pi$
$701$		−	12.4042i		−	0.468499i	0.972177	−	0.234249i	$-0.0752632\pi$
$702$		0			0
$703$	−4.57003	−	4.57003i	−0.172362	−	0.172362i
$704$	6.50508	+	36.8922i	0.245170	+	1.39043i
$705$		0			0
$706$	−35.9678	+	13.0912i	−1.35367	+	0.492694i
$707$	−0.725989	−	8.29809i	−0.0273036	−	0.312082i
$708$		0			0
$709$	4.29127	−	11.7902i	0.161162	−	0.442789i	−0.832659	−	0.553786i	$-0.813182\pi$
$709$	4.29127	−	11.7902i	0.161162	−	0.442789i	0.993821	+	0.110998i	$0.0354046\pi$
$710$	6.18562	−	15.7053i	0.232142	−	0.589408i
$711$		0			0
$712$	−1.49782	−	5.58994i	−0.0561332	−	0.209492i
$713$	1.18171	−	13.5070i	0.0442554	−	0.505842i
$714$		0			0
$715$	42.8560	−	23.2715i	1.60272	−	0.870305i
$716$	1.01940	+	0.179748i	0.0380969	+	0.00671750i
$717$		0			0
$718$	23.5926	+	2.06408i	0.880466	+	0.0770308i
$719$	9.10268	−	15.7663i	0.339473	−	0.587984i	−0.644861	−	0.764300i	$-0.723085\pi$
$719$	9.10268	−	15.7663i	0.339473	−	0.587984i	0.984334	+	0.176316i	$0.0564181\pi$
$720$		0			0
$721$	−13.0717	−	22.6408i	−0.486815	−	0.843188i
$722$	10.2159	+	21.9081i	0.380196	+	0.815334i
$723$		0			0
$724$	0.864744	−	1.03056i	0.0321380	−	0.0383005i
$725$	32.7806	−	4.02807i	1.21744	−	0.149599i
$726$		0			0
$727$	8.06014	+	5.64377i	0.298934	+	0.209316i	0.713414	−	0.700742i	$-0.247148\pi$
$727$	8.06014	+	5.64377i	0.298934	+	0.209316i	−0.414480	+	0.910058i	$0.636037\pi$
$728$	−20.8369	+	20.8369i	−0.772267	+	0.772267i
$729$		0			0
$730$	−15.0845	−	1.71795i	−0.558304	−	0.0635841i
$731$	4.06735	−	0.717184i	0.150436	−	0.0265260i
$732$		0			0
$733$	−33.5024	−	15.6224i	−1.23744	−	0.577027i	−0.309905	−	0.950767i	$-0.600297\pi$
$733$	−33.5024	−	15.6224i	−1.23744	−	0.577027i	−0.927533	+	0.373740i	$0.878075\pi$
$734$	22.3146	+	18.7242i	0.823646	+	0.691121i
$735$		0			0
$736$	6.96332	+	2.53444i	0.256671	+	0.0934207i
$737$	−10.7471	+	40.1088i	−0.395875	+	1.47743i
$738$		0			0
$739$	7.02338	+	4.05495i	0.258359	+	0.149164i	0.623586	−	0.781755i	$-0.285675\pi$
$739$	7.02338	+	4.05495i	0.258359	+	0.149164i	−0.365227	+	0.930919i	$0.619009\pi$
$740$	−0.756423	+	3.71883i	−0.0278067	+	0.136707i
$741$		0			0
$742$	1.99851	+	2.85416i	0.0733675	+	0.104780i
$743$	−17.8592	−	25.5056i	−0.655190	−	0.935709i	0.344805	−	0.938674i	$-0.387945\pi$
$743$	−17.8592	−	25.5056i	−0.655190	−	0.935709i	−0.999996	+	0.00296531i	$0.999056\pi$
$744$		0			0
$745$	10.7050	+	16.1718i	0.392200	+	0.592489i
$746$	−19.8552	−	11.4634i	−0.726949	−	0.419704i
$747$		0			0
$748$	−0.838814	+	3.13050i	−0.0306701	+	0.114462i
$749$	−26.6979	−	9.71724i	−0.975519	−	0.355060i
$750$		0			0
$751$	−13.4156	−	11.2570i	−0.489541	−	0.410774i	0.364321	−	0.931273i	$-0.381301\pi$
$751$	−13.4156	−	11.2570i	−0.489541	−	0.410774i	−0.853862	+	0.520500i	$0.825746\pi$
$752$	−25.9484	−	12.1000i	−0.946243	−	0.441240i
$753$		0			0
$754$	−43.8023	+	7.72353i	−1.59519	+	0.281274i
$755$	4.03140	−	35.3979i	0.146718	−	1.28826i
$756$		0			0
$757$	−20.1777	+	20.1777i	−0.733371	+	0.733371i	−0.971286	−	0.237915i	$-0.923536\pi$
$757$	−20.1777	+	20.1777i	−0.733371	+	0.733371i	0.237915	+	0.971286i	$0.423536\pi$
$758$	29.5641	+	20.7010i	1.07381	+	0.751893i
$759$		0			0
$760$	−3.10887	+	5.07375i	−0.112771	+	0.184044i
$761$	−23.7584	+	28.3141i	−0.861240	+	1.02639i	0.138113	+	0.990416i	$0.455896\pi$
$761$	−23.7584	+	28.3141i	−0.861240	+	1.02639i	−0.999353	+	0.0359689i	$0.988548\pi$
$762$		0			0
$763$	−11.8696	−	25.4545i	−0.429710	−	0.921516i
$764$	−1.69744	−	2.94006i	−0.0614113	−	0.106368i
$765$		0			0
$766$	−4.88069	+	8.45360i	−0.176346	+	0.305441i
$767$	24.5794	+	2.15042i	0.887512	+	0.0776472i
$768$		0			0
$769$	−8.53754	−	1.50540i	−0.307872	−	0.0542861i	0.0175779	−	0.999845i	$-0.494405\pi$
$769$	−8.53754	−	1.50540i	−0.307872	−	0.0542861i	−0.325450	+	0.945559i	$0.605516\pi$
$770$	−7.10520	+	23.9909i	−0.256054	+	0.864571i
$771$		0			0
$772$	−0.355865	+	4.06755i	−0.0128078	+	0.146394i
$773$	−3.05417	−	11.3983i	−0.109851	−	0.409969i	0.889000	−	0.457908i	$-0.151401\pi$
$773$	−3.05417	−	11.3983i	−0.109851	−	0.409969i	−0.998850	+	0.0479396i	$0.984734\pi$
$774$		0			0
$775$	−3.54262	−	11.5835i	−0.127255	−	0.416092i
$776$	13.7174	−	37.6882i	0.492425	−	1.35293i
$777$		0			0
$778$	3.61856	+	41.3603i	0.129732	+	1.48284i
$779$	−7.12895	+	2.59472i	−0.255421	+	0.0929657i
$780$		0			0
$781$	−4.24560	−	24.0780i	−0.151919	−	0.861578i
$782$	−16.8270	−	16.8270i	−0.601733	−	0.601733i
$783$		0			0
$784$			11.0025i			0.392947i
$785$	−19.6678	+	22.2325i	−0.701972	+	0.793510i
$786$		0			0
$787$	7.93722	−	17.0214i	0.282931	−	0.606748i	−0.712559	−	0.701612i	$-0.752464\pi$
$787$	7.93722	−	17.0214i	0.282931	−	0.606748i	0.995490	+	0.0948643i	$0.0302417\pi$
$788$	3.19101	−	0.279178i	0.113675	−	0.00994529i
$789$		0			0
$790$	0.393037	+	1.17448i	0.0139836	+	0.0417862i
$791$	23.1237	−	13.3505i	0.822183	−	0.474687i
$792$		0			0
$793$	41.1675	−	11.0308i	1.46190	−	0.391715i
$794$	−16.7831	+	14.0827i	−0.595610	+	0.499776i
$795$		0			0
$796$	−0.367376	+	2.08349i	−0.0130213	+	0.0738475i
$797$	−17.6670	+	12.3706i	−0.625797	+	0.438188i	−0.842981	−	0.537943i	$-0.819202\pi$
$797$	−17.6670	+	12.3706i	−0.625797	+	0.438188i	0.217184	+	0.976131i	$0.430313\pi$
$798$		0			0
$799$	−16.9567	−	20.2082i	−0.599884	−	0.714914i
$800$	6.61615	−	0.231662i	0.233916	−	0.00819049i
$801$		0			0
$802$	1.93969	+	0.519739i	0.0684929	+	0.0183526i
$803$	−19.9304	+	9.29368i	−0.703327	+	0.327967i
$804$		0			0
$805$	16.8659	+	17.7713i	0.594444	+	0.626354i
$806$	5.57934	+	15.3291i	0.196524	+	0.539945i
$807$		0			0
$808$	7.24665	−	10.3493i	0.254936	−	0.364087i
$809$	−4.46938			−0.157135			−0.0785676	−	0.996909i	$-0.525035\pi$
$809$	−4.46938			−0.157135			−0.0785676	+	0.996909i	$0.525035\pi$
$810$		0			0
$811$	37.9099			1.33120			0.665598	−	0.746311i	$-0.268177\pi$
$811$	37.9099			1.33120			0.665598	+	0.746311i	$0.268177\pi$
$812$	−1.74556	+	2.49292i	−0.0612573	+	0.0874845i
$813$		0			0
$814$	−14.0978	−	38.7333i	−0.494127	−	1.35760i
$815$	−16.5887	−	0.433612i	−0.581077	−	0.0151888i
$816$		0			0
$817$	1.04801	−	0.488696i	0.0366653	−	0.0170973i
$818$	30.1175	+	8.06996i	1.05303	+	0.282159i
$819$		0			0
$820$	3.58104	+	2.64957i	0.125055	+	0.0925269i
$821$	−23.1674	−	27.6099i	−0.808549	−	0.963591i	0.191290	−	0.981533i	$-0.438733\pi$
$821$	−23.1674	−	27.6099i	−0.808549	−	0.963591i	−0.999839	+	0.0179428i	$0.994288\pi$
$822$		0			0
$823$	−2.18095	+	1.52711i	−0.0760230	+	0.0532319i	−0.610970	−	0.791654i	$-0.709220\pi$
$823$	−2.18095	+	1.52711i	−0.0760230	+	0.0532319i	0.534947	+	0.844886i	$0.320332\pi$
$824$	6.88563	−	39.0504i	0.239872	−	1.36038i
$825$		0			0
$826$	−9.69752	+	8.13719i	−0.337420	+	0.283129i
$827$	−39.8859	+	10.6874i	−1.38697	+	0.371637i	−0.873647	−	0.486560i	$-0.838252\pi$
$827$	−39.8859	+	10.6874i	−1.38697	+	0.371637i	−0.513321	+	0.858197i	$0.671585\pi$
$828$		0			0
$829$	−19.6326	+	11.3349i	−0.681869	+	0.393677i	−0.800559	−	0.599254i	$-0.795464\pi$
$829$	−19.6326	+	11.3349i	−0.681869	+	0.393677i	0.118690	+	0.992931i	$0.462131\pi$
$830$	−12.2858	+	24.6445i	−0.426447	+	0.855422i
$831$		0			0
$832$	−43.9658	+	3.84651i	−1.52424	+	0.133354i
$833$	−4.28428	+	9.18766i	−0.148441	+	0.318334i
$834$		0			0
$835$	−13.7877	−	12.1972i	−0.477144	−	0.422101i
$836$			0.907402i			0.0313832i
$837$		0			0
$838$	14.9429	+	14.9429i	0.516195	+	0.516195i
$839$	−1.44230	−	8.17971i	−0.0497938	−	0.282395i	0.949736	−	0.313052i	$-0.101351\pi$
$839$	−1.44230	−	8.17971i	−0.0497938	−	0.282395i	−0.999530	+	0.0306567i	$0.990240\pi$
$840$		0			0
$841$	−13.7493	+	5.00432i	−0.474112	+	0.172563i
$842$	−4.20240	−	48.0337i	−0.144824	−	1.65535i
$843$		0			0
$844$	1.50888	−	4.14562i	0.0519379	−	0.142698i
$845$	11.3193	+	26.0293i	0.389396	+	0.895435i
$846$		0			0
$847$	3.80634	+	14.2054i	0.130787	+	0.488105i
$848$	−0.405641	+	4.63650i	−0.0139298	+	0.159218i
$849$		0			0
$850$	−19.5707	−	8.30510i	−0.671269	−	0.284863i
$851$	−39.7487	−	7.00876i	−1.36257	−	0.240257i
$852$		0			0
$853$	−6.11455	−	0.534954i	−0.209358	−	0.0183165i	−0.0180058	−	0.999838i	$-0.505732\pi$
$853$	−6.11455	−	0.534954i	−0.209358	−	0.0183165i	−0.191352	+	0.981521i	$0.561287\pi$
$854$	−10.9335	+	18.9374i	−0.374137	+	0.648024i
$855$		0			0
$856$	−21.5463	−	37.3193i	−0.736439	−	1.27555i
$857$	−14.6042	−	31.3187i	−0.498869	−	1.06983i	−0.981050	−	0.193756i	$-0.937933\pi$
$857$	−14.6042	−	31.3187i	−0.498869	−	1.06983i	0.482181	−	0.876072i	$-0.339845\pi$
$858$		0			0
$859$	14.4078	−	17.1705i	0.491587	−	0.585850i	−0.462034	−	0.886862i	$-0.652880\pi$
$859$	14.4078	−	17.1705i	0.491587	−	0.585850i	0.953620	+	0.301012i	$0.0973245\pi$
$860$	−0.578954	−	0.354746i	−0.0197422	−	0.0120968i
$861$		0			0
$862$	11.7054	+	8.19621i	0.398688	+	0.279164i
$863$	34.4337	−	34.4337i	1.17214	−	1.17214i	0.190436	−	0.981700i	$-0.439010\pi$
$863$	34.4337	−	34.4337i	1.17214	−	1.17214i	0.981700	−	0.190436i	$-0.0609900\pi$
$864$		0			0
$865$	−10.8212	−	13.6029i	−0.367933	−	0.462511i
$866$	−47.8011	+	8.42862i	−1.62435	+	0.286416i
$867$		0			0
$868$	1.01159	+	0.471713i	0.0343357	+	0.0160110i
$869$	1.37423	+	1.15312i	0.0466175	+	0.0391168i
$870$		0			0
$871$	−45.9694	−	16.7315i	−1.55762	−	0.566926i
$872$	11.0255	−	41.1477i	0.373370	−	1.39344i
$873$		0			0
$874$	−5.77009	−	3.33137i	−0.195176	−	0.112685i
$875$	19.9190	+	9.07422i	0.673384	+	0.306765i
$876$		0			0
$877$	−7.94910	−	11.3525i	−0.268422	−	0.383347i	0.662201	−	0.749327i	$-0.269623\pi$
$877$	−7.94910	−	11.3525i	−0.268422	−	0.383347i	−0.930623	+	0.365980i	$0.880734\pi$
$878$	10.6140	+	15.1584i	0.358206	+	0.511571i
$879$		0			0
$880$	−27.8694	+	18.4482i	−0.939477	+	0.621890i
$881$	20.3929	+	11.7738i	0.687054	+	0.396671i	0.802507	−	0.596642i	$-0.203499\pi$
$881$	20.3929	+	11.7738i	0.687054	+	0.396671i	−0.115453	+	0.993313i	$0.536832\pi$
$882$		0			0
$883$	4.25489	−	15.8795i	0.143188	−	0.534386i	−0.856641	−	0.515913i	$-0.827453\pi$
$883$	4.25489	−	15.8795i	0.143188	−	0.534386i	0.999829	−	0.0184733i	$-0.00588057\pi$
$884$	−3.58792	−	1.30590i	−0.120675	−	0.0439221i
$885$		0			0
$886$	11.6044	+	9.73725i	0.389857	+	0.327129i
$887$	−9.29073	−	4.33234i	−0.311952	−	0.145466i	0.260336	−	0.965518i	$-0.416167\pi$
$887$	−9.29073	−	4.33234i	−0.311952	−	0.145466i	−0.572289	+	0.820052i	$0.693944\pi$
$888$		0			0
$889$	−6.94156	+	1.22398i	−0.232812	+	0.0410511i
$890$	4.53038	−	3.60397i	0.151859	−	0.120805i
$891$		0			0
$892$	2.76005	−	2.76005i	0.0924133	−	0.0924133i
$893$	−6.05018	−	4.23638i	−0.202461	−	0.141765i
$894$		0			0
$895$	2.29650	+	9.56364i	0.0767636	+	0.319677i
$896$	11.2227	−	13.3748i	0.374926	−	0.446819i
$897$		0			0
$898$	−0.907153	−	1.94540i	−0.0302721	−	0.0649187i
$899$	8.00123	+	13.8585i	0.266856	+	0.462208i
$900$		0			0
$901$	−2.14414	+	3.71376i	−0.0714317	+	0.123723i
$902$	−48.2002	−	4.21697i	−1.60489	−	0.140410i
$903$		0			0
$904$	39.8832	+	7.03248i	1.32649	+	0.233897i
$905$	12.2565	+	3.62991i	0.407419	+	0.120662i
$906$		0			0
$907$	−1.17717	+	13.4551i	−0.0390872	+	0.446769i	0.951283	+	0.308321i	$0.0997669\pi$
$907$	−1.17717	+	13.4551i	−0.0390872	+	0.446769i	−0.990370	+	0.138448i	$0.955789\pi$
$908$	−1.10206	−	4.11293i	−0.0365730	−	0.136492i
$909$		0			0
$910$	−27.4269	−	10.8023i	−0.909193	−	0.358092i
$911$	−4.95701	+	13.6193i	−0.164233	+	0.451227i	−0.994323	−	0.106403i	$-0.966067\pi$
$911$	−4.95701	+	13.6193i	−0.164233	+	0.451227i	0.830090	+	0.557629i	$0.188289\pi$
$912$		0			0
$913$	3.47635	+	39.7348i	0.115050	+	1.31503i
$914$	6.91502	−	2.51686i	0.228729	−	0.0832504i
$915$		0			0
$916$	−0.776272	−	4.40246i	−0.0256488	−	0.145461i
$917$	−0.768724	−	0.768724i	−0.0253855	−	0.0253855i
$918$		0			0
$919$			11.7599i			0.387925i	0.981009	+	0.193962i	$0.0621340\pi$
$919$			11.7599i			0.387925i	−0.981009	+	0.193962i	$0.937866\pi$
$920$	2.27036	+	37.0916i	0.0748517	+	1.22287i
$921$		0			0
$922$	−8.53202	+	18.2970i	−0.280987	+	0.602579i
$923$	28.6946	−	2.51046i	0.944496	−	0.0826327i
$924$		0			0
$925$	−35.2702	+	7.50037i	−1.15968	+	0.246610i
$926$	−38.0276	+	21.9552i	−1.24966	+	0.721494i
$927$		0			0
$928$	−8.44784	+	2.26359i	−0.277314	+	0.0743061i
$929$	36.0388	−	30.2401i	1.18239	−	0.992146i	0.182433	−	0.983218i	$-0.441603\pi$
$929$	36.0388	−	30.2401i	1.18239	−	0.992146i	0.999960	−	0.00892776i	$-0.00284183\pi$
$930$		0			0
$931$	−0.492867	+	2.79519i	−0.0161531	+	0.0916086i
$932$	−1.45799	+	1.02089i	−0.0477579	+	0.0334405i
$933$		0			0
$934$	19.3932	+	23.1119i	0.634563	+	0.756243i
$935$	−30.4560	+	4.55313i	−0.996016	+	0.148903i
$936$		0			0
$937$	36.6017	+	9.80740i	1.19573	+	0.320394i	0.801147	−	0.598468i	$-0.204224\pi$
$937$	36.6017	+	9.80740i	1.19573	+	0.320394i	0.394580	+	0.918862i	$0.370890\pi$
$938$	22.7477	−	10.6074i	0.742740	−	0.346346i
$939$		0			0
$940$	−0.113324	+	4.33542i	−0.00369621	+	0.141406i
$941$	3.79401	+	10.4240i	0.123681	+	0.339811i	0.986045	−	0.166477i	$-0.0532392\pi$
$941$	3.79401	+	10.4240i	0.123681	+	0.339811i	−0.862364	+	0.506289i	$0.831017\pi$
$942$		0			0
$943$	−27.1749	+	38.8098i	−0.884937	+	1.26382i
$944$	−16.9098			−0.550367
$945$		0			0
$946$	7.37489			0.239778
$947$	9.12331	−	13.0294i	0.296468	−	0.423400i	−0.643090	−	0.765791i	$-0.722348\pi$
$947$	9.12331	−	13.0294i	0.296468	−	0.423400i	0.939558	+	0.342391i	$0.111237\pi$
$948$		0			0
$949$	−8.86092	−	24.3452i	−0.287638	−	0.790278i
$950$	−5.89457	−	0.827864i	−0.191245	−	0.0268594i
$951$		0			0
$952$	16.8644	−	7.86402i	0.546580	−	0.254874i
$953$	35.2746	+	9.45180i	1.14266	+	0.306174i	0.780019	−	0.625756i	$-0.215210\pi$
$953$	35.2746	+	9.45180i	1.14266	+	0.306174i	0.362638	+	0.931930i	$0.381876\pi$
$954$		0			0
$955$	19.1862	−	25.9311i	0.620849	−	0.839112i
$956$	1.89177	+	2.25453i	0.0611843	+	0.0729167i
$957$		0			0
$958$	24.8501	−	17.4002i	0.802871	−	0.562176i
$959$	2.05447	−	11.6515i	0.0663422	−	0.376245i
$960$		0			0
$961$	−19.2514	+	16.1538i	−0.621012	+	0.521091i
$962$	46.9062	−	12.5685i	1.51232	−	0.405224i
$963$		0			0
$964$	−3.48953	+	2.01468i	−0.112390	+	0.0648886i
$965$	−36.7910	+	12.3120i	−1.18434	+	0.396337i
$966$		0			0
$967$	−1.95128	+	0.170714i	−0.0627488	+	0.00548981i	−0.118487	−	0.992956i	$-0.537804\pi$
$967$	−1.95128	+	0.170714i	−0.0627488	+	0.00548981i	0.0557381	+	0.998445i	$0.482249\pi$
$968$	−9.42696	+	20.2162i	−0.302994	+	0.649773i
$969$		0			0
$970$	40.0452	−	2.45115i	1.28577	−	0.0787017i
$971$			27.5442i			0.883934i	0.897031	+	0.441967i	$0.145719\pi$
$971$			27.5442i			0.883934i	−0.897031	+	0.441967i	$0.854281\pi$
$972$		0			0
$973$	25.6369	+	25.6369i	0.821881	+	0.821881i
$974$	−4.27366	−	24.2371i	−0.136937	−	0.776607i
$975$		0			0
$976$	−27.4477	+	9.99016i	−0.878581	+	0.319777i
$977$	−2.84484	−	32.5167i	−0.0910146	−	1.04030i	−0.895123	−	0.445819i	$-0.852912\pi$
$977$	−2.84484	−	32.5167i	−0.0910146	−	1.04030i	0.804108	−	0.594483i	$-0.202643\pi$
$978$		0			0
$979$	2.86792	−	7.87954i	0.0916591	−	0.251831i
$980$	1.52835	−	0.664633i	0.0488215	−	0.0212309i
$981$		0			0
$982$	−3.18718	−	11.8947i	−0.101707	−	0.379575i
$983$	−2.79155	+	31.9076i	−0.0890367	+	1.01769i	0.811915	+	0.583775i	$0.198425\pi$
$983$	−2.79155	+	31.9076i	−0.0890367	+	1.01769i	−0.900952	+	0.433919i	$0.857130\pi$
$984$		0			0
$985$	14.5240	+	26.7470i	0.462775	+	0.852230i
$986$	27.6596	+	4.87713i	0.880860	+	0.155319i
$987$		0			0
$988$	−1.06496	−	0.0931716i	−0.0338808	−	0.00296418i
$989$	3.61075	−	6.25401i	0.114815	−	0.198866i
$990$		0			0
$991$	24.5859	+	42.5840i	0.780995	+	1.35272i	0.931362	+	0.364094i	$0.118621\pi$
$991$	24.5859	+	42.5840i	0.780995	+	1.35272i	−0.150367	+	0.988630i	$0.548046\pi$
$992$	1.35561	+	2.90712i	0.0430407	+	0.0923012i
$993$		0			0
$994$	−9.49956	+	11.3211i	−0.301308	+	0.359084i
$995$	−19.5466	+	4.69368i	−0.619667	+	0.148800i
$996$		0			0
$997$	25.7299	+	18.0163i	0.814874	+	0.570581i	0.905031	−	0.425347i	$-0.139848\pi$
$997$	25.7299	+	18.0163i	0.814874	+	0.570581i	−0.0901563	+	0.995928i	$0.528737\pi$
$998$	19.4085	−	19.4085i	0.614364	−	0.614364i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.233.11		192
3.2	odd	2		135.2.q.a.68.6	yes	192
5.2	odd	4	inner	405.2.r.a.152.11		192
15.2	even	4		135.2.q.a.122.6	yes	192
15.8	even	4		675.2.ba.b.257.11		192
15.14	odd	2		675.2.ba.b.68.11		192
27.2	odd	18	inner	405.2.r.a.8.11		192
27.25	even	9		135.2.q.a.83.6	yes	192
135.2	even	36	inner	405.2.r.a.332.11		192
135.52	odd	36		135.2.q.a.2.6	✓	192
135.79	even	18		675.2.ba.b.218.11		192
135.133	odd	36		675.2.ba.b.407.11		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.6	✓	192	135.52	odd	36
135.2.q.a.68.6	yes	192	3.2	odd	2
135.2.q.a.83.6	yes	192	27.25	even	9
135.2.q.a.122.6	yes	192	15.2	even	4
405.2.r.a.8.11		192	27.2	odd	18	inner
405.2.r.a.152.11		192	5.2	odd	4	inner
405.2.r.a.233.11		192	1.1	even	1	trivial
405.2.r.a.332.11		192	135.2	even	36	inner
675.2.ba.b.68.11		192	15.14	odd	2
675.2.ba.b.218.11		192	135.79	even	18
675.2.ba.b.257.11		192	15.8	even	4
675.2.ba.b.407.11		192	135.133	odd	36

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.r (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.761943 - 1.08817i) q^{2} +(0.0804885 + 0.221140i) q^{4} +(-1.62191 + 1.53928i) q^{5} +(1.77434 - 0.827388i) q^{7} +(2.86825 + 0.768546i) q^{8} +(0.439192 + 2.93776i) q^{10} +(2.76562 + 3.29594i) q^{11} +(-4.15220 + 2.90740i) q^{13} +(0.451609 - 2.56120i) q^{14} +(2.66120 - 2.23301i) q^{16} +(3.09176 - 0.828434i) q^{17} +(0.776109 - 0.448087i) q^{19} +(-0.470943 - 0.234776i) q^{20} +(5.69379 - 0.498142i) q^{22} +(2.36525 - 5.07230i) q^{23} +(0.261212 - 4.99317i) q^{25} +6.73356i q^{26} +(0.325783 + 0.325783i) q^{28} +(1.14702 + 6.50507i) q^{29} +(2.27652 - 0.828586i) q^{31} +(0.115398 + 1.31900i) q^{32} +(1.45427 - 3.99557i) q^{34} +(-1.60424 + 4.07317i) q^{35} +(-1.86654 - 6.96604i) q^{37} +(0.103757 - 1.18595i) q^{38} +(-5.83507 + 3.16854i) q^{40} +(-8.33680 - 1.47000i) q^{41} +(1.28541 + 0.112459i) q^{43} +(-0.506265 + 0.876877i) q^{44} +(-3.71732 - 6.43859i) q^{46} +(-3.48305 - 7.46943i) q^{47} +(-2.03580 + 2.42617i) q^{49} +(-5.23438 - 4.08876i) q^{50} +(-0.977148 - 0.684206i) q^{52} +(-0.947342 + 0.947342i) q^{53} +(-9.55899 - 1.08866i) q^{55} +(5.72514 - 1.00950i) q^{56} +(7.95258 + 3.70835i) q^{58} +(-3.72879 - 3.12883i) q^{59} +(-7.90101 - 2.87573i) q^{61} +(0.832940 - 3.10857i) q^{62} +(7.54029 + 4.35339i) q^{64} +(2.25919 - 11.1070i) q^{65} +(5.53556 + 7.90560i) q^{67} +(0.432051 + 0.617033i) q^{68} +(3.20995 + 4.84921i) q^{70} +(-4.92123 - 2.84127i) q^{71} +(-1.32285 + 4.93694i) q^{73} +(-9.00242 - 3.27661i) q^{74} +(0.161558 + 0.135563i) q^{76} +(7.63418 + 3.55988i) q^{77} +(0.410612 - 0.0724019i) q^{79} +(-0.879000 + 7.71810i) q^{80} +(-7.95178 + 7.95178i) q^{82} +(7.59392 + 5.31732i) q^{83} +(-3.73937 + 6.10274i) q^{85} +(1.10179 - 1.31306i) q^{86} +(5.39942 + 11.5791i) q^{88} +(-0.974450 - 1.68780i) q^{89} +(-4.96186 + 8.59420i) q^{91} +(1.31207 + 0.114791i) q^{92} +(-10.7819 - 1.90114i) q^{94} +(-0.569049 + 1.92141i) q^{95} +(1.17718 - 13.4552i) q^{97} +(1.08892 + 4.06390i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

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