LMFDB - Embedded newform 405.2.r.a.8.11

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			8.11
Character	$\chi$	$=$	405.8
Dual form			405.2.r.a.152.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.08817 - 0.761943i) q^{2} +(-0.0804885 + 0.221140i) q^{4} +(-1.23426 - 1.86457i) q^{5} +(0.827388 - 1.77434i) q^{7} +(0.768546 + 2.86825i) q^{8} +(-2.76377 - 1.08853i) q^{10} +(2.76562 - 3.29594i) q^{11} +(2.90740 - 4.15220i) q^{13} +(-0.451609 - 2.56120i) q^{14} +(2.66120 + 2.23301i) q^{16} +(0.828434 - 3.09176i) q^{17} +(-0.776109 - 0.448087i) q^{19} +(0.511675 - 0.122868i) q^{20} +(0.498142 - 5.69379i) q^{22} +(-5.07230 + 2.36525i) q^{23} +(-1.95322 + 4.60271i) q^{25} -6.73356i q^{26} +(0.325783 + 0.325783i) q^{28} +(-1.14702 + 6.50507i) q^{29} +(2.27652 + 0.828586i) q^{31} +(-1.31900 - 0.115398i) q^{32} +(-1.45427 - 3.99557i) q^{34} +(-4.32959 + 0.647269i) q^{35} +(6.96604 + 1.86654i) q^{37} +(-1.18595 + 0.103757i) q^{38} +(4.39947 - 4.97316i) q^{40} +(-8.33680 + 1.47000i) q^{41} +(0.112459 + 1.28541i) q^{43} +(0.506265 + 0.876877i) q^{44} +(-3.71732 + 6.43859i) q^{46} +(7.46943 + 3.48305i) q^{47} +(2.03580 + 2.42617i) q^{49} +(1.38157 + 6.49676i) q^{50} +(0.684206 + 0.977148i) q^{52} +(0.947342 - 0.947342i) q^{53} +(-9.55899 - 1.08866i) q^{55} +(5.72514 + 1.00950i) q^{56} +(3.70835 + 7.95258i) q^{58} +(3.72879 - 3.12883i) q^{59} +(-7.90101 + 2.87573i) q^{61} +(3.10857 - 0.832940i) q^{62} +(-7.54029 + 4.35339i) q^{64} +(-11.3305 - 0.296169i) q^{65} +(-7.90560 - 5.53556i) q^{67} +(0.617033 + 0.432051i) q^{68} +(-4.21814 + 4.00324i) q^{70} +(-4.92123 + 2.84127i) q^{71} +(4.93694 - 1.32285i) q^{73} +(9.00242 - 3.27661i) q^{74} +(0.161558 - 0.135563i) q^{76} +(-3.55988 - 7.63418i) q^{77} +(-0.410612 - 0.0724019i) q^{79} +(0.879000 - 7.71810i) q^{80} +(-7.95178 + 7.95178i) q^{82} +(5.31732 + 7.59392i) q^{83} +(-6.78729 + 2.27135i) q^{85} +(1.10179 + 1.31306i) q^{86} +(11.5791 + 5.39942i) q^{88} +(0.974450 - 1.68780i) q^{89} +(-4.96186 - 8.59420i) q^{91} +(-0.114791 - 1.31207i) q^{92} +(10.7819 - 1.90114i) q^{94} +(0.122429 + 2.00016i) q^{95} +(13.4552 - 1.17718i) q^{97} +(4.06390 + 1.08892i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{18}\right)$

Coefficient data

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

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

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

$2$	1.08817	−	0.761943i	0.769451	−	0.538775i	−0.121654	−	0.992573i	$-0.538820\pi$
$2$	1.08817	−	0.761943i	0.769451	−	0.538775i	0.891105	+	0.453797i	$0.149931\pi$
$3$		0			0
$3$		0			0
$4$	−0.0804885	+	0.221140i	−0.0402443	+	0.110570i
$5$	−1.23426	−	1.86457i	−0.551976	−	0.833860i
$5$	−1.23426	−	1.86457i	−0.551976	−	0.833860i
$6$		0			0
$7$	0.827388	−	1.77434i	0.312723	−	0.670638i	−0.685633	−	0.727947i	$-0.740474\pi$
$7$	0.827388	−	1.77434i	0.312723	−	0.670638i	0.998356	+	0.0573098i	$0.0182523\pi$
$8$	0.768546	+	2.86825i	0.271722	+	1.01408i
$9$		0			0
$10$	−2.76377	−	1.08853i	−0.873982	−	0.344223i
$11$	2.76562	−	3.29594i	0.833867	−	0.993764i	−0.166104	−	0.986108i	$-0.553119\pi$
$11$	2.76562	−	3.29594i	0.833867	−	0.993764i	0.999971	−	0.00765542i	$-0.00243682\pi$
$12$		0			0
$13$	2.90740	−	4.15220i	0.806368	−	1.15161i	−0.179446	−	0.983768i	$-0.557431\pi$
$13$	2.90740	−	4.15220i	0.806368	−	1.15161i	0.985814	−	0.167844i	$-0.0536806\pi$
$14$	−0.451609	−	2.56120i	−0.120698	−	0.684510i
$15$		0			0
$16$	2.66120	+	2.23301i	0.665301	+	0.558253i
$17$	0.828434	−	3.09176i	0.200925	−	0.749861i	−0.789729	−	0.613456i	$-0.789779\pi$
$17$	0.828434	−	3.09176i	0.200925	−	0.749861i	0.990653	−	0.136405i	$-0.0435547\pi$
$18$		0			0
$19$	−0.776109	−	0.448087i	−0.178052	−	0.102798i	0.408325	−	0.912836i	$-0.366113\pi$
$19$	−0.776109	−	0.448087i	−0.178052	−	0.102798i	−0.586377	+	0.810038i	$0.699446\pi$
$20$	0.511675	−	0.122868i	0.114414	−	0.0274740i
$21$		0			0
$22$	0.498142	−	5.69379i	0.106204	−	1.21392i
$23$	−5.07230	+	2.36525i	−1.05765	+	0.493189i	−0.872040	−	0.489435i	$-0.837203\pi$
$23$	−5.07230	+	2.36525i	−1.05765	+	0.493189i	−0.185607	+	0.982624i	$0.559425\pi$
$24$		0			0
$25$	−1.95322	+	4.60271i	−0.390645	+	0.920541i
$26$		−	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	0.671354	+	0.741137i	$0.265713\pi$
$29$	−1.14702	+	6.50507i	−0.212996	+	1.20796i	−0.884350	+	0.466825i	$0.845398\pi$
$30$		0			0
$31$	2.27652	+	0.828586i	0.408875	+	0.148818i	0.538266	−	0.842775i	$-0.319080\pi$
$31$	2.27652	+	0.828586i	0.408875	+	0.148818i	−0.129390	+	0.991594i	$0.541302\pi$
$32$	−1.31900	−	0.115398i	−0.233169	−	0.0203996i
$33$		0			0
$34$	−1.45427	−	3.99557i	−0.249405	−	0.685235i
$35$	−4.32959	+	0.647269i	−0.731834	+	0.109408i
$36$		0			0
$37$	6.96604	+	1.86654i	1.14521	+	0.306858i	0.781044	−	0.624476i	$-0.214688\pi$
$37$	6.96604	+	1.86654i	1.14521	+	0.306858i	0.364166	+	0.931334i	$0.381354\pi$
$38$	−1.18595	+	0.103757i	−0.192387	+	0.0168317i
$39$		0			0
$40$	4.39947	−	4.97316i	0.695617	−	0.786326i
$41$	−8.33680	+	1.47000i	−1.30199	+	0.229576i	−0.781292	−	0.624166i	$-0.785439\pi$
$41$	−8.33680	+	1.47000i	−1.30199	+	0.229576i	−0.520697	+	0.853742i	$0.674328\pi$
$42$		0			0
$43$	0.112459	+	1.28541i	0.0171499	+	0.196024i	0.999936	+	0.0112790i	$0.00359030\pi$
$43$	0.112459	+	1.28541i	0.0171499	+	0.196024i	−0.982787	+	0.184745i	$0.940854\pi$
$44$	0.506265	+	0.876877i	0.0763223	+	0.132194i
$45$		0			0
$46$	−3.71732	+	6.43859i	−0.548090	+	0.949319i
$47$	7.46943	+	3.48305i	1.08953	+	0.508055i	0.882516	−	0.470283i	$-0.155848\pi$
$47$	7.46943	+	3.48305i	1.08953	+	0.508055i	0.207013	+	0.978338i	$0.433626\pi$
$48$		0			0
$49$	2.03580	+	2.42617i	0.290829	+	0.346596i
$50$	1.38157	+	6.49676i	0.195383	+	0.918781i
$51$		0			0
$52$	0.684206	+	0.977148i	0.0948823	+	0.135506i
$53$	0.947342	−	0.947342i	0.130127	−	0.130127i	−0.639043	−	0.769171i	$-0.720670\pi$
$53$	0.947342	−	0.947342i	0.130127	−	0.130127i	0.769171	+	0.639043i	$0.220670\pi$
$54$		0			0
$55$	−9.55899	−	1.08866i	−1.28893	−	0.146794i
$56$	5.72514	+	1.00950i	0.765054	+	0.134900i
$57$		0			0
$58$	3.70835	+	7.95258i	0.486930	+	1.04422i
$59$	3.72879	−	3.12883i	0.485447	−	0.407339i	−0.366944	−	0.930243i	$-0.619596\pi$
$59$	3.72879	−	3.12883i	0.485447	−	0.407339i	0.852391	+	0.522904i	$0.175151\pi$
$60$		0			0
$61$	−7.90101	+	2.87573i	−1.01162	+	0.368200i	−0.794055	−	0.607846i	$-0.792034\pi$
$61$	−7.90101	+	2.87573i	−1.01162	+	0.368200i	−0.217566	+	0.976046i	$0.569812\pi$
$62$	3.10857	−	0.832940i	0.394789	−	0.105783i
$63$		0			0
$64$	−7.54029	+	4.35339i	−0.942536	+	0.544173i
$65$	−11.3305	−	0.296169i	−1.40538	−	0.0367352i
$66$		0			0
$67$	−7.90560	−	5.53556i	−0.965822	−	0.676276i	−0.0196049	−	0.999808i	$-0.506241\pi$
$67$	−7.90560	−	5.53556i	−0.965822	−	0.676276i	−0.946217	+	0.323532i	$0.895130\pi$
$68$	0.617033	+	0.432051i	0.0748262	+	0.0523939i
$69$		0			0
$70$	−4.21814	+	4.00324i	−0.504164	+	0.478478i
$71$	−4.92123	+	2.84127i	−0.584043	+	0.337197i	−0.762738	−	0.646707i	$-0.776146\pi$
$71$	−4.92123	+	2.84127i	−0.584043	+	0.337197i	0.178696	+	0.983904i	$0.442812\pi$
$72$		0			0
$73$	4.93694	−	1.32285i	0.577825	−	0.154828i	0.0419419	−	0.999120i	$-0.486646\pi$
$73$	4.93694	−	1.32285i	0.577825	−	0.154828i	0.535883	+	0.844292i	$0.319979\pi$
$74$	9.00242	−	3.27661i	1.04651	−	0.380898i
$75$		0			0
$76$	0.161558	−	0.135563i	0.0185320	−	0.0155502i
$77$	−3.55988	−	7.63418i	−0.405686	−	0.869996i
$78$		0			0
$79$	−0.410612	−	0.0724019i	−0.0461974	−	0.00814585i	0.150502	−	0.988610i	$-0.451911\pi$
$79$	−0.410612	−	0.0724019i	−0.0461974	−	0.00814585i	−0.196699	+	0.980464i	$0.563022\pi$
$80$	0.879000	−	7.71810i	0.0982752	−	0.862910i
$81$		0			0
$82$	−7.95178	+	7.95178i	−0.878127	+	0.878127i
$83$	5.31732	+	7.59392i	0.583652	+	0.833541i	0.997030	−	0.0770185i	$-0.0245401\pi$
$83$	5.31732	+	7.59392i	0.583652	+	0.833541i	−0.413378	+	0.910560i	$0.635651\pi$
$84$		0			0
$85$	−6.78729	+	2.27135i	−0.736185	+	0.246362i
$86$	1.10179	+	1.31306i	0.118809	+	0.141591i
$87$		0			0
$88$	11.5791	+	5.39942i	1.23434	+	0.575580i
$89$	0.974450	−	1.68780i	0.103292	−	0.178906i	−0.809747	−	0.586779i	$-0.800396\pi$
$89$	0.974450	−	1.68780i	0.103292	−	0.178906i	0.913039	+	0.407872i	$0.133729\pi$
$90$		0			0
$91$	−4.96186	−	8.59420i	−0.520144	−	0.900917i
$92$	−0.114791	−	1.31207i	−0.0119678	−	0.136792i
$93$		0			0
$94$	10.7819	−	1.90114i	1.11207	−	0.196087i
$95$	0.122429	+	2.00016i	0.0125610	+	0.205212i
$96$		0			0
$97$	13.4552	−	1.17718i	1.36617	−	0.119524i	0.619644	−	0.784883i	$-0.287277\pi$
$97$	13.4552	−	1.17718i	1.36617	−	0.119524i	0.746524	+	0.665359i	$0.231721\pi$
$98$	4.06390	+	1.08892i	0.410516	+	0.109997i
$99$		0			0
$100$	−0.860633	−	0.802402i	−0.0860633	−	0.0802402i
$101$	1.45521	+	3.99814i	0.144798	+	0.397830i	0.990797	−	0.135354i	$-0.0432173\pi$
$101$	1.45521	+	3.99814i	0.144798	+	0.397830i	−0.845999	+	0.533185i	$0.820995\pi$
$102$		0			0
$103$	−13.3028	−	1.16385i	−1.31077	−	0.114677i	−0.589745	−	0.807589i	$-0.700772\pi$
$103$	−13.3028	−	1.16385i	−1.31077	−	0.114677i	−0.721022	+	0.692912i	$0.756327\pi$
$104$	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	0.999968	−	0.00794276i	$-0.00252829\pi$
$107$	10.2616	+	10.2616i	0.992026	+	0.992026i	−0.00794276	+	0.999968i	$0.502528\pi$
$108$		0			0
$109$		−	14.3459i		−	1.37409i	−0.726615	−	0.687045i	$-0.758908\pi$
$109$		−	14.3459i		−	1.37409i	0.726615	−	0.687045i	$-0.241092\pi$
$110$	−11.2313	+	6.09877i	−1.07086	+	0.581495i
$111$		0			0
$112$	6.16397	−	2.87431i	0.582441	−	0.271597i
$113$	−1.18867	+	13.5865i	−0.111821	+	1.27811i	0.708295	+	0.705916i	$0.249465\pi$
$113$	−1.18867	+	13.5865i	−0.111821	+	1.27811i	−0.820116	+	0.572198i	$0.806091\pi$
$114$		0			0
$115$	10.6707	+	6.53832i	0.995046	+	0.609701i
$116$	−1.34621	−	0.777236i	−0.124993	−	0.0721646i
$117$		0			0
$118$	1.67356	−	6.24582i	0.154064	−	0.574974i
$119$	−4.80039	−	4.02801i	−0.440051	−	0.369247i
$120$		0			0
$121$	−1.30443	−	7.39778i	−0.118584	−	0.672525i
$122$	−6.40648	+	9.14940i	−0.580016	+	0.828348i
$123$		0			0
$124$	−0.366468	+	0.436739i	−0.0329098	+	0.0392204i
$125$	10.9928	−	2.03900i	0.983229	−	0.182374i
$126$		0			0
$127$	0.931838	+	3.47767i	0.0826872	+	0.308593i	0.994866	−	0.101199i	$-0.0322679\pi$
$127$	0.931838	+	3.47767i	0.0826872	+	0.308593i	−0.912179	+	0.409792i	$0.865601\pi$
$128$	−3.76894	+	8.08251i	−0.333130	+	0.714400i
$129$		0			0
$130$	−12.5552	+	8.31094i	−1.10116	+	0.728918i
$131$	−0.189922	+	0.521807i	−0.0165936	+	0.0455905i	−0.947713	−	0.319124i	$-0.896611\pi$
$131$	−0.189922	+	0.521807i	−0.0165936	+	0.0455905i	0.931119	+	0.364715i	$0.118833\pi$
$132$		0			0
$133$	−1.43720	+	1.00634i	−0.124621	+	0.0872607i
$134$	−12.8204			−1.10751
$135$		0			0
$136$	9.50463			0.815015
$137$	4.95031	−	3.46624i	0.422934	−	0.296141i	−0.342668	−	0.939457i	$-0.611330\pi$
$137$	4.95031	−	3.46624i	0.422934	−	0.296141i	0.765601	+	0.643315i	$0.222442\pi$
$138$		0			0
$139$	−6.33390	+	17.4022i	−0.537234	+	1.47604i	0.313061	+	0.949733i	$0.398646\pi$
$139$	−6.33390	+	17.4022i	−0.537234	+	1.47604i	−0.850295	+	0.526306i	$0.823577\pi$
$140$	0.205345	−	1.00954i	0.0173548	−	0.0853221i
$141$		0			0
$142$	−3.19024	+	6.84148i	−0.267719	+	0.574125i
$143$	−5.64463	−	21.0660i	−0.472027	−	1.76163i
$144$		0			0
$145$	13.5449	−	5.89023i	1.12484	−	0.489157i
$146$	4.36428	−	5.20115i	0.361190	−	0.430450i
$147$		0			0
$148$	−0.973455	+	1.39024i	−0.0800175	+	0.114277i
$149$	−1.50609	−	8.54145i	−0.123384	−	0.699743i	−0.982255	−	0.187551i	$-0.939945\pi$
$149$	−1.50609	−	8.54145i	−0.123384	−	0.699743i	0.858871	−	0.512192i	$-0.171166\pi$
$150$		0			0
$151$	−12.2052	−	10.2414i	−0.993244	−	0.833431i	−0.00721007	−	0.999974i	$-0.502295\pi$
$151$	−12.2052	−	10.2414i	−0.993244	−	0.833431i	−0.986034	+	0.166543i	$0.946740\pi$
$152$	0.688750	−	2.57045i	0.0558650	−	0.208491i
$153$		0			0
$154$	−9.69056	−	5.59485i	−0.780887	−	0.450846i
$155$	−1.26486	−	5.26742i	−0.101596	−	0.423089i
$156$		0			0
$157$	1.15698	−	13.2243i	0.0923367	−	1.05541i	−0.798775	−	0.601630i	$-0.794518\pi$
$157$	1.15698	−	13.2243i	0.0923367	−	1.05541i	0.891112	−	0.453784i	$-0.149926\pi$
$158$	−0.501981	+	0.234077i	−0.0399354	+	0.0186222i
$159$		0			0
$160$	1.41282	+	2.60180i	0.111693	+	0.205690i
$161$			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
$167$	−8.20120	−	0.717512i	−0.634628	−	0.0555227i	−0.234698	−	0.972068i	$-0.575410\pi$
$167$	−8.20120	−	0.717512i	−0.634628	−	0.0555227i	−0.399930	+	0.916546i	$0.630966\pi$
$168$		0			0
$169$	−4.34150	−	11.9282i	−0.333962	−	0.917553i
$170$	−5.65507	+	7.64314i	−0.433724	+	0.586202i
$171$		0			0
$172$	−0.293309	−	0.0785918i	−0.0223646	−	0.00599257i
$173$	7.74393	−	0.677506i	0.588760	−	0.0515098i	0.211116	−	0.977461i	$-0.432290\pi$
$173$	7.74393	−	0.677506i	0.588760	−	0.0515098i	0.377643	+	0.925951i	$0.376735\pi$
$174$		0			0
$175$	6.55069	+	7.27391i	0.495186	+	0.549856i
$176$	14.7198	−	2.59549i	1.10954	−	0.195643i
$177$		0			0
$178$	−0.225641	−	2.57908i	−0.0169125	−	0.193310i
$179$	−2.19929	−	3.80928i	−0.164382	−	0.284719i	0.772053	−	0.635558i	$-0.219230\pi$
$179$	−2.19929	−	3.80928i	−0.164382	−	0.284719i	−0.936436	+	0.350839i	$0.885896\pi$
$180$		0			0
$181$	−2.85830	+	4.95072i	−0.212456	+	0.367984i	−0.952483	−	0.304593i	$-0.901479\pi$
$181$	−2.85830	+	4.95072i	−0.212456	+	0.367984i	0.740027	+	0.672577i	$0.234813\pi$
$182$	−11.9476	−	5.57127i	−0.885617	−	0.412970i
$183$		0			0
$184$	−10.6824	−	12.7308i	−0.787519	−	0.938529i
$185$	−5.11758	−	15.2924i	−0.376252	−	1.12432i
$186$		0			0
$187$	−7.89911	−	11.2811i	−0.577640	−	0.824956i
$188$	−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	−0.365860	−	0.930670i	$-0.619225\pi$
$191$	−14.2067	−	2.50503i	−1.02796	−	0.181258i	−0.662104	+	0.749412i	$0.730336\pi$
$192$		0			0
$193$	7.33254	+	15.7247i	0.527808	+	1.13189i	0.971789	+	0.235852i	$0.0757879\pi$
$193$	7.33254	+	15.7247i	0.527808	+	1.13189i	−0.443981	+	0.896036i	$0.646434\pi$
$194$	13.7446	−	11.5331i	0.986802	−	0.828025i
$195$		0			0
$196$	−0.700384	+	0.254919i	−0.0500274	+	0.0182085i
$197$	13.1476	−	3.52289i	0.936727	−	0.250995i	0.242006	−	0.970275i	$-0.422195\pi$
$197$	13.1476	−	3.52289i	0.936727	−	0.250995i	0.694721	+	0.719280i	$0.255528\pi$
$198$		0			0
$199$	−7.78555	+	4.49499i	−0.551903	+	0.318641i	−0.749889	−	0.661564i	$-0.769893\pi$
$199$	−7.78555	+	4.49499i	−0.551903	+	0.318641i	0.197986	+	0.980205i	$0.436560\pi$
$200$	−14.7029	−	2.06495i	−1.03965	−	0.146014i
$201$		0			0
$202$	4.62987	+	3.24187i	0.325756	+	0.228097i
$203$	10.5932	+	7.41743i	0.743496	+	0.520601i
$204$		0			0
$205$	13.0307	+	13.7302i	0.910101	+	0.958956i
$206$	−15.3625	+	8.86955i	−1.07036	+	0.617971i
$207$		0			0
$208$	17.0091	−	4.55757i	1.17937	−	0.316011i
$209$	−3.62329	+	1.31877i	−0.250628	+	0.0912212i
$210$		0			0
$211$	−14.3607	+	12.0500i	−0.988631	+	0.829559i	−0.985369	−	0.170435i	$-0.945483\pi$
$211$	−14.3607	+	12.0500i	−0.988631	+	0.829559i	−0.00326162	+	0.999995i	$0.501038\pi$
$212$	0.133245	+	0.285746i	0.00915134	+	0.0196251i
$213$		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
$218$	−10.9308	−	15.6108i	−0.740326	−	1.05729i
$219$		0			0
$220$	1.01014	−	2.02626i	0.0681033	−	0.136610i
$221$	−10.4290	−	12.4288i	−0.701530	−	0.836051i
$222$		0			0
$223$	−15.0323	−	7.00968i	−1.00664	−	0.469403i	−0.151862	−	0.988402i	$-0.548527\pi$
$223$	−15.0323	−	7.00968i	−1.00664	−	0.469403i	−0.854775	+	0.518999i	$0.826305\pi$
$224$	−1.29608	+	2.24488i	−0.0865981	+	0.149992i
$225$		0			0
$226$	9.05870	+	15.6901i	0.602576	+	1.04369i
$227$	1.57696	+	18.0248i	0.104667	+	1.19634i	0.848947	+	0.528478i	$0.177237\pi$
$227$	1.57696	+	18.0248i	0.104667	+	1.19634i	−0.744281	+	0.667867i	$0.767207\pi$
$228$		0			0
$229$	18.7074	−	3.29862i	1.23622	−	0.217979i	0.482924	−	0.875662i	$-0.339575\pi$
$229$	18.7074	−	3.29862i	1.23622	−	0.217979i	0.753294	+	0.657684i	$0.228464\pi$
$230$	16.5933	−	1.01567i	1.09413	−	0.0669714i
$231$		0			0
$232$	−19.5397	+	1.70951i	−1.28285	+	0.112235i
$233$	7.30551	+	1.95750i	0.478600	+	0.128240i	0.490050	−	0.871694i	$-0.336978\pi$
$233$	7.30551	+	1.95750i	0.478600	+	0.128240i	−0.0114509	+	0.999934i	$0.503645\pi$
$234$		0			0
$235$	−2.72480	−	18.2262i	−0.177747	−	1.18895i
$236$	0.391785	+	1.07642i	0.0255031	+	0.0700691i
$237$		0			0
$238$	−8.29275	−	0.725521i	−0.537539	−	0.0470286i
$239$	−11.7518	−	4.27731i	−0.760162	−	0.276676i	−0.0672867	−	0.997734i	$-0.521434\pi$
$239$	−11.7518	−	4.27731i	−0.760162	−	0.276676i	−0.692875	+	0.721057i	$0.743656\pi$
$240$		0			0
$241$	2.97320	−	16.8619i	0.191521	−	1.08617i	−0.725766	−	0.687942i	$-0.758514\pi$
$241$	2.97320	−	16.8619i	0.191521	−	1.08617i	0.917287	−	0.398227i	$-0.130374\pi$
$242$	−7.05612	−	7.05612i	−0.453585	−	0.453585i
$243$		0			0
$244$		−	1.97870i		−	0.126673i
$245$	2.01106	−	6.79041i	0.128482	−	0.433823i
$246$		0			0
$247$	−4.11700	+	1.91979i	−0.261958	+	0.122153i
$248$	−0.626983	+	7.16645i	−0.0398134	+	0.455070i
$249$		0			0
$250$	10.4085	−	10.5947i	0.658288	−	0.670067i
$251$	−4.66370	−	2.69259i	−0.294370	−	0.169955i	0.345541	−	0.938404i	$-0.387696\pi$
$251$	−4.66370	−	2.69259i	−0.294370	−	0.169955i	−0.639911	+	0.768449i	$0.721029\pi$
$252$		0			0
$253$	−6.23233	+	23.2594i	−0.391823	+	1.46231i
$254$	3.66378	+	3.07428i	0.229886	+	0.192897i
$255$		0			0
$256$	−0.966651	−	5.48215i	−0.0604157	−	0.342634i
$257$	7.03325	−	10.0445i	0.438722	−	0.626560i	−0.537518	−	0.843252i	$-0.680638\pi$
$257$	7.03325	−	10.0445i	0.438722	−	0.626560i	0.976240	+	0.216692i	$0.0695268\pi$
$258$		0			0
$259$	9.07550	−	10.8158i	0.563924	−	0.672059i
$260$	0.977472	−	2.48180i	0.0606203	−	0.153915i
$261$		0			0
$262$	0.190920	+	0.712524i	0.0117951	+	0.0440199i
$263$	5.75913	−	12.3505i	0.355123	−	0.761563i	−0.644873	−	0.764289i	$-0.723090\pi$
$263$	5.75913	−	12.3505i	0.355123	−	0.761563i	0.999996	+	0.00272594i	$0.000867694\pi$
$264$		0			0
$265$	−2.93565	−	0.597121i	−0.180335	−	0.0366808i
$266$	−0.797143	+	2.19013i	−0.0488760	+	0.134286i
$267$		0			0
$268$	1.86045	−	1.30270i	0.113645	−	0.0795749i
$269$	−12.3342			−0.752028			−0.376014	−	0.926614i	$-0.622706\pi$
$269$	−12.3342			−0.752028			−0.376014	+	0.926614i	$0.622706\pi$
$270$		0			0
$271$	19.7578			1.20020			0.600099	−	0.799926i	$-0.295128\pi$
$271$	19.7578			1.20020			0.600099	+	0.799926i	$0.295128\pi$
$272$	9.10856	−	6.37789i	0.552288	−	0.386716i
$273$		0			0
$274$	2.74569	−	7.54371i	0.165873	−	0.455732i
$275$	9.76837	+	19.1671i	0.589055	+	1.15582i
$276$		0			0
$277$	−0.856962	+	1.83776i	−0.0514898	+	0.110420i	−0.930370	−	0.366623i	$-0.880514\pi$
$277$	−0.856962	+	1.83776i	−0.0514898	+	0.110420i	0.878880	+	0.477044i	$0.158292\pi$
$278$	6.36718	+	23.7626i	0.381878	+	1.42519i
$279$		0			0
$280$	−5.18402	−	11.9209i	−0.309804	−	0.712410i
$281$	16.8041	−	20.0263i	1.00245	−	1.19467i	0.0216244	−	0.999766i	$-0.493116\pi$
$281$	16.8041	−	20.0263i	1.00245	−	1.19467i	0.980822	−	0.194903i	$-0.0624393\pi$
$282$		0			0
$283$	1.33019	−	1.89971i	0.0790717	−	0.112926i	−0.777668	−	0.628675i	$-0.783597\pi$
$283$	1.33019	−	1.89971i	0.0790717	−	0.112926i	0.856740	+	0.515749i	$0.172486\pi$
$284$	−0.232218	−	1.31697i	−0.0137796	−	0.0781480i
$285$		0			0
$286$	−22.1934	−	18.6225i	−1.31232	−	1.10117i
$287$	−4.28949	+	16.0086i	−0.253200	+	0.944956i
$288$		0			0
$289$	5.84978	+	3.37737i	0.344105	+	0.198669i
$290$	10.2511	−	16.7300i	0.601963	−	0.982418i
$291$		0			0
$292$	−0.104832	+	1.19823i	−0.00613480	+	0.0701211i
$293$	10.9251	−	5.09445i	0.638250	−	0.297621i	−0.0764274	−	0.997075i	$-0.524351\pi$
$293$	10.9251	−	5.09445i	0.638250	−	0.297621i	0.714677	+	0.699454i	$0.246574\pi$
$294$		0			0
$295$	−10.4362	−	3.09081i	−0.607619	−	0.179954i
$296$			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
$302$	−21.0846	−	1.84467i	−1.21328	−	0.106149i
$303$		0			0
$304$	−1.06480	−	2.92551i	−0.0610704	−	0.167790i
$305$	15.1139	+	11.1826i	0.865418	+	0.640313i
$306$		0			0
$307$	22.6984	+	6.08202i	1.29547	+	0.347119i	0.839734	−	0.542998i	$-0.182711\pi$
$307$	22.6984	+	6.08202i	1.29547	+	0.347119i	0.455732	+	0.890117i	$0.349378\pi$
$308$	1.97476	−	0.172769i	0.112522	−	0.00984441i
$309$		0			0
$310$	−5.38985	−	4.76809i	−0.306123	−	0.270809i
$311$	−3.91683	+	0.690642i	−0.222103	+	0.0391627i	−0.283592	−	0.958945i	$-0.591526\pi$
$311$	−3.91683	+	0.690642i	−0.222103	+	0.0391627i	0.0614891	+	0.998108i	$0.480415\pi$
$312$		0			0
$313$	−0.0797089	−	0.911077i	−0.00450541	−	0.0514971i	0.993609	−	0.112875i	$-0.0360060\pi$
$313$	−0.0797089	−	0.911077i	−0.00450541	−	0.0514971i	−0.998115	+	0.0613781i	$0.980450\pi$
$314$	−8.81718	−	15.2718i	−0.497582	−	0.861838i
$315$		0			0
$316$	0.0490605	−	0.0849753i	0.00275987	−	0.00478023i
$317$	−23.8990	−	11.1443i	−1.34230	−	0.625924i	−0.387141	−	0.922021i	$-0.626537\pi$
$317$	−23.8990	−	11.1443i	−1.34230	−	0.625924i	−0.955158	+	0.296096i	$0.904315\pi$
$318$		0			0
$319$	18.2681	+	21.7711i	1.02282	+	1.21895i
$320$	17.4238	+	8.68618i	0.974021	+	0.485572i
$321$		0			0
$322$	8.34859	+	11.9230i	0.465249	+	0.664444i
$323$	−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
$328$	−10.6235	−	22.7823i	−0.586587	−	1.25794i
$329$	12.3602	−	10.3715i	0.681442	−	0.571798i
$330$		0			0
$331$	−12.0746	+	4.39481i	−0.663682	+	0.241561i	−0.651825	−	0.758369i	$-0.725996\pi$
$331$	−12.0746	+	4.39481i	−0.663682	+	0.241561i	−0.0118569	+	0.999930i	$0.503774\pi$
$332$	−2.10731	+	0.564651i	−0.115653	+	0.0309893i
$333$		0			0
$334$	−9.47099	+	5.46808i	−0.518229	+	0.299200i
$335$	−0.563892	+	21.5728i	−0.0308087	+	1.17865i
$336$		0			0
$337$	−6.96283	−	4.87543i	−0.379290	−	0.265581i	0.368349	−	0.929688i	$-0.379923\pi$
$337$	−6.96283	−	4.87543i	−0.379290	−	0.265581i	−0.747638	+	0.664106i	$0.768812\pi$
$338$	−13.8129	−	9.67189i	−0.751322	−	0.526081i
$339$		0			0
$340$	0.0440119	−	1.68376i	0.00238688	−	0.0913148i
$341$	9.02697	−	5.21173i	0.488838	−	0.282231i
$342$		0			0
$343$	19.2267	−	5.15177i	1.03814	−	0.278169i
$344$	−3.60046	+	1.31046i	−0.194124	+	0.0706553i
$345$		0			0
$346$	7.91047	−	6.63767i	0.425270	−	0.356844i
$347$	2.22359	+	4.76851i	0.119369	+	0.255987i	0.956909	−	0.290389i	$-0.0937847\pi$
$347$	2.22359	+	4.76851i	0.119369	+	0.255987i	−0.837540	+	0.546376i	$0.816007\pi$
$348$		0			0
$349$	−20.3047	−	3.58026i	−1.08688	−	0.191647i	−0.398627	−	0.917113i	$-0.630513\pi$
$349$	−20.3047	−	3.58026i	−1.08688	−	0.191647i	−0.688258	+	0.725466i	$0.741624\pi$
$350$	12.6706	+	2.92398i	0.677270	+	0.156293i
$351$		0			0
$352$	−4.02821	+	4.02821i	−0.214704	+	0.214704i
$353$	−16.5268	−	23.6027i	−0.879631	−	1.25624i	−0.965623	−	0.259948i	$-0.916295\pi$
$353$	−16.5268	−	23.6027i	−0.879631	−	1.25624i	0.0859911	−	0.996296i	$-0.472594\pi$
$354$		0			0
$355$	11.3718	+	5.66911i	0.603553	+	0.300885i
$356$	0.294808	+	0.351339i	0.0156248	+	0.0186209i
$357$		0			0
$358$	−5.29565	−	2.46940i	−0.279884	−	0.130512i
$359$	−8.91393	+	15.4394i	−0.470459	+	0.814860i	−0.999429	−	0.0337810i	$-0.989245\pi$
$359$	−8.91393	+	15.4394i	−0.470459	+	0.814860i	0.528970	+	0.848641i	$0.322578\pi$
$360$		0			0
$361$	−9.09844	−	15.7590i	−0.478865	−	0.829419i
$362$	0.661859	+	7.56508i	0.0347865	+	0.397612i
$363$		0			0
$364$	2.29990	−	0.405534i	0.120547	−	0.0212558i
$365$	−8.55998	−	7.57252i	−0.448050	−	0.396364i
$366$		0			0
$367$	−21.8448	+	1.91117i	−1.14029	+	0.0997623i	−0.641614	−	0.767028i	$-0.721735\pi$
$367$	−21.8448	+	1.91117i	−1.14029	+	0.0997623i	−0.498674	+	0.866790i	$0.666179\pi$
$368$	−18.7800	−	5.03210i	−0.978978	−	0.262316i
$369$		0			0
$370$	−17.2208	−	12.7414i	−0.895264	−	0.662396i
$371$	−0.897087	−	2.46473i	−0.0465744	−	0.127962i
$372$		0			0
$373$	−17.1932	−	1.50421i	−0.890228	−	0.0778848i	−0.367142	−	0.930165i	$-0.619664\pi$
$373$	−17.1932	−	1.50421i	−0.890228	−	0.0778848i	−0.523086	+	0.852280i	$0.675219\pi$
$374$	−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	$0.754171\pi$
$380$	−0.452170	−	0.133916i	−0.0231959	−	0.00686974i
$381$		0			0
$382$	−17.3680	+	8.09883i	−0.888624	+	0.414372i
$383$	0.640436	−	7.32022i	0.0327248	−	0.374046i	−0.962119	−	0.272629i	$-0.912107\pi$
$383$	0.640436	−	7.32022i	0.0327248	−	0.374046i	0.994844	−	0.101417i	$-0.0323376\pi$
$384$		0			0
$385$	−9.84065	+	16.0602i	−0.501526	+	0.818502i
$386$	19.9604	+	11.5241i	1.01596	+	0.586562i
$387$		0			0
$388$	−0.822667	+	3.07024i	−0.0417646	+	0.155868i
$389$	23.9421	+	20.0898i	1.21391	+	1.01859i	0.999120	+	0.0419334i	$0.0133517\pi$
$389$	23.9421	+	20.0898i	1.21391	+	1.01859i	0.214792	+	0.976660i	$0.431093\pi$
$390$		0			0
$391$	3.11072	+	17.6418i	0.157316	+	0.892182i
$392$	−5.39427	+	7.70382i	−0.272452	+	0.389102i
$393$		0			0
$394$	11.6225	−	13.8512i	0.585535	−	0.697814i
$395$	0.371802	+	0.854976i	0.0187074	+	0.0430185i
$396$		0			0
$397$	4.26857	+	15.9305i	0.214234	+	0.799531i	0.986435	+	0.164153i	$0.0524890\pi$
$397$	4.26857	+	15.9305i	0.214234	+	0.799531i	−0.772201	+	0.635378i	$0.780844\pi$
$398$	−5.04706	+	10.8234i	−0.252986	+	0.542530i
$399$		0			0
$400$	−15.4758	+	7.88716i	−0.773792	+	0.394358i
$401$	0.517022	−	1.42051i	0.0258188	−	0.0709367i	−0.926114	−	0.377245i	$-0.876872\pi$
$401$	0.517022	−	1.42051i	0.0258188	−	0.0709367i	0.951932	+	0.306308i	$0.0990938\pi$
$402$		0			0
$403$	10.0592	−	7.04354i	0.501085	−	0.350864i
$404$	−1.00128			−0.0498155
$405$		0			0
$406$	17.1788			0.852571
$407$	25.4175	−	17.7975i	1.25990	−	0.882189i
$408$		0			0
$409$	−8.02778	+	22.0561i	−0.396948	+	1.09061i	0.566815	+	0.823845i	$0.308175\pi$
$409$	−8.02778	+	22.0561i	−0.396948	+	1.09061i	−0.963763	+	0.266760i	$0.914047\pi$
$410$	24.6412	+	5.01210i	1.21694	+	0.247530i
$411$		0			0
$412$	1.32810	−	2.84812i	0.0654308	−	0.140317i
$413$	−2.46645	−	9.20490i	−0.121366	−	0.452944i
$414$		0			0
$415$	7.59644	−	19.2873i	0.372895	−	0.946779i
$416$	−4.31402	+	5.14125i	−0.211512	+	0.252070i
$417$		0			0
$418$	−2.93792	+	4.19579i	−0.143698	+	0.205223i
$419$	2.76242	+	15.6665i	0.134953	+	0.765357i	0.974892	+	0.222677i	$0.0714794\pi$
$419$	2.76242	+	15.6665i	0.134953	+	0.765357i	−0.839939	+	0.542680i	$0.817409\pi$
$420$		0			0
$421$	27.8051	+	23.3312i	1.35514	+	1.13709i	0.977452	+	0.211160i	$0.0677241\pi$
$421$	27.8051	+	23.3312i	1.35514	+	1.13709i	0.377685	+	0.925934i	$0.376720\pi$
$422$	−6.44539	+	24.0545i	−0.313756	+	1.17096i
$423$		0			0
$424$	3.44529	+	1.98914i	0.167318	+	0.0966012i
$425$	12.6123	+	9.85193i	0.611788	+	0.477889i
$426$		0			0
$427$	−1.43468	+	16.3984i	−0.0694289	+	0.793576i
$428$	−3.09519	+	1.44331i	−0.149612	+	0.0697652i
$429$		0			0
$430$	1.08840	−	3.67501i	0.0524873	−	0.177225i
$431$		−	10.7570i		−	0.518146i	−0.965858	−	0.259073i	$-0.916583\pi$
$431$		−	10.7570i		−	0.518146i	0.965858	−	0.259073i	$-0.0834169\pi$
$432$		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
$437$	4.99649	+	0.437136i	0.239015	+	0.0209111i
$438$		0			0
$439$	4.76440	+	13.0901i	0.227393	+	0.624756i	0.999948	−	0.0101913i	$-0.00324405\pi$
$439$	4.76440	+	13.0901i	0.227393	+	0.624756i	−0.772556	+	0.634947i	$0.781022\pi$
$440$	−4.22398	−	28.2543i	−0.201371	−	1.34697i
$441$		0			0
$442$	−20.8185	−	5.57831i	−0.990237	−	0.265333i
$443$	11.3601	−	0.993879i	0.539734	−	0.0472206i	0.185970	−	0.982555i	$-0.440457\pi$
$443$	11.3601	−	0.993879i	0.539734	−	0.0472206i	0.353764	+	0.935335i	$0.384902\pi$
$444$		0			0
$445$	−4.34973	+	0.266246i	−0.206197	+	0.0126213i
$446$	−21.6986	+	3.82606i	−1.02746	+	0.181169i
$447$		0			0
$448$	1.48564	+	16.9810i	0.0701900	+	0.802276i
$449$	−0.807925	−	1.39937i	−0.0381283	−	0.0660402i	0.846332	−	0.532657i	$-0.178806\pi$
$449$	−0.807925	−	1.39937i	−0.0381283	−	0.0660402i	−0.884460	+	0.466616i	$0.845473\pi$
$450$		0			0
$451$	−18.2114	+	31.5431i	−0.857541	+	1.48530i
$452$	−2.90886	−	1.35642i	−0.136821	−	0.0638008i
$453$		0			0
$454$	15.4498	+	18.4124i	0.725097	+	0.864137i
$455$	−9.90025	+	19.8592i	−0.464131	+	0.931012i
$456$		0			0
$457$	−3.17737	−	4.53775i	−0.148631	−	0.212267i	0.737932	−	0.674875i	$-0.235803\pi$
$457$	−3.17737	−	4.53775i	−0.148631	−	0.212267i	−0.886563	+	0.462608i	$0.846914\pi$
$458$	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	−0.186123	−	0.982527i	$-0.559592\pi$
$461$	−14.9666	−	2.63902i	−0.697065	−	0.122911i	−0.510942	+	0.859615i	$0.670703\pi$
$462$		0			0
$463$	−13.9696	−	29.9580i	−0.649224	−	1.39226i	−0.904951	−	0.425516i	$-0.860093\pi$
$463$	−13.9696	−	29.9580i	−0.649224	−	1.39226i	0.255727	−	0.966749i	$-0.417685\pi$
$464$	−17.5784	+	14.7500i	−0.816056	+	0.684752i
$465$		0			0
$466$	9.44112	−	3.43629i	0.437352	−	0.159183i
$467$	−21.9378	+	5.87822i	−1.01516	+	0.272012i	−0.727784	−	0.685806i	$-0.759450\pi$
$467$	−21.9378	+	5.87822i	−1.01516	+	0.272012i	−0.287377	+	0.957818i	$0.592783\pi$
$468$		0			0
$469$	−16.3630	+	9.44716i	−0.755571	+	0.436229i
$470$	−16.8524	−	17.7571i	−0.777343	−	0.819072i
$471$		0			0
$472$	11.8400	+	8.29047i	0.544981	+	0.381600i
$473$	4.54767	+	3.18431i	0.209102	+	0.146415i
$474$		0			0
$475$	3.57833	−	2.69699i	0.164185	−	0.123746i
$476$	1.27713	−	0.737352i	0.0585372	−	0.0337965i
$477$		0			0
$478$	−16.0470	+	4.29979i	−0.733974	+	0.196668i
$479$	−21.4594	+	7.81060i	−0.980507	+	0.356875i	−0.782037	−	0.623232i	$-0.785819\pi$
$479$	−21.4594	+	7.81060i	−0.980507	+	0.356875i	−0.198470	+	0.980107i	$0.563597\pi$
$480$		0			0
$481$	28.0033	−	23.4976i	1.27684	−	1.07140i
$482$	−9.61245	−	20.6140i	−0.437835	−	0.938941i
$483$		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	$0.112113\pi$
$488$	−14.3206	−	20.4520i	−0.648264	−	0.925817i
$489$		0			0
$490$	−2.98553	−	8.92142i	−0.134873	−	0.403029i
$491$	5.95862	+	7.10121i	0.268909	+	0.320473i	0.883553	−	0.468332i	$-0.155145\pi$
$491$	5.95862	+	7.10121i	0.268909	+	0.320473i	−0.614644	+	0.788805i	$0.710700\pi$
$492$		0			0
$493$	19.1619	+	8.93533i	0.863007	+	0.402427i
$494$	−3.01722	+	5.22597i	−0.135751	+	0.235128i
$495$		0			0
$496$	4.20804	+	7.28854i	0.188947	+	0.327265i
$497$	0.969617	+	11.0828i	0.0434933	+	0.497131i
$498$		0			0
$499$	−20.3482	+	3.58794i	−0.910911	+	0.160618i	−0.609417	−	0.792850i	$-0.708596\pi$
$499$	−20.3482	+	3.58794i	−0.910911	+	0.160618i	−0.301494	+	0.953468i	$0.597485\pi$
$500$	−0.433892	+	2.59508i	−0.0194042	+	0.116055i
$501$		0			0
$502$	−7.12650	+	0.623488i	−0.318071	+	0.0278276i
$503$	−4.53760	−	1.21585i	−0.202322	−	0.0542119i	0.156235	−	0.987720i	$-0.450064\pi$
$503$	−4.53760	−	1.21585i	−0.202322	−	0.0542119i	−0.358557	+	0.933508i	$0.616731\pi$
$504$		0			0
$505$	5.65871	−	7.64806i	0.251809	−	0.340334i
$506$	10.9405	+	30.0588i	0.486365	+	1.33628i
$507$		0			0
$508$	−0.844055	−	0.0738452i	−0.0374489	−	0.00327635i
$509$	30.3526	+	11.0475i	1.34536	+	0.489670i	0.911496	−	0.411309i	$-0.134928\pi$
$509$	30.3526	+	11.0475i	1.34536	+	0.489670i	0.433862	+	0.900979i	$0.357151\pi$
$510$		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
$515$	14.2490	+	26.2405i	0.627887	+	1.15630i
$516$		0			0
$517$	32.1376	−	14.9860i	1.41341	−	0.659083i
$518$	1.63467	−	18.6844i	0.0718234	−	0.820945i
$519$		0			0
$520$	−7.85854	−	32.7264i	−0.344620	−	1.43515i
$521$	2.29310	+	1.32392i	0.100463	+	0.0580021i	0.549390	−	0.835566i	$-0.314860\pi$
$521$	2.29310	+	1.32392i	0.100463	+	0.0580021i	−0.448927	+	0.893568i	$0.648194\pi$
$522$		0			0
$523$	3.37351	−	12.5901i	0.147513	−	0.550527i	−0.852117	−	0.523351i	$-0.824682\pi$
$523$	3.37351	−	12.5901i	0.147513	−	0.550527i	0.999631	−	0.0271764i	$-0.00865159\pi$
$524$	−0.100106	−	0.0839990i	−0.00437316	−	0.00366951i
$525$		0			0
$526$	−3.14347	−	17.8275i	−0.137062	−	0.777317i
$527$	4.44773	−	6.35202i	0.193746	−	0.276698i
$528$		0			0
$529$	5.34967	−	6.37549i	0.232594	−	0.277195i
$530$	−3.64945	+	1.58703i	−0.158522	+	0.0689361i
$531$		0			0
$532$	−0.106864	−	0.398822i	−0.00463314	−	0.0172911i
$533$	−18.1347	+	38.8899i	−0.785499	+	1.68451i
$534$		0			0
$535$	6.46800	−	31.7989i	0.279636	−	1.37478i
$536$	9.80156	−	26.9296i	0.423363	−	1.16318i
$537$		0			0
$538$	−13.4217	+	9.39794i	−0.578649	+	0.405174i
$539$	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	$0.859231\pi$
$542$	21.4998	−	15.0543i	0.923494	−	0.646637i
$543$		0			0
$544$	−1.44949	+	3.98243i	−0.0621463	+	0.170745i
$545$	−26.7489	+	17.7065i	−1.14580	+	0.758465i
$546$		0			0
$547$	−9.73975	+	20.8870i	−0.416442	+	0.893062i	0.580451	+	0.814295i	$0.302876\pi$
$547$	−9.73975	+	20.8870i	−0.416442	+	0.893062i	−0.996893	+	0.0787671i	$0.974902\pi$
$548$	0.368084	+	1.37371i	0.0157238	+	0.0586818i
$549$		0			0
$550$	25.2338	+	13.4140i	1.07597	+	0.571977i
$551$	3.80505	−	4.53468i	0.162101	−	0.193184i
$552$		0			0
$553$	−0.468201	+	0.668660i	−0.0199099	+	0.0284343i
$554$	0.467751	+	2.65275i	0.0198728	+	0.112704i
$555$		0			0
$556$	−3.33853	−	2.80136i	−0.141585	−	0.118804i
$557$	9.19419	−	34.3132i	0.389570	−	1.45390i	−0.441265	−	0.897377i	$-0.645470\pi$
$557$	9.19419	−	34.3132i	0.389570	−	1.45390i	0.830835	−	0.556519i	$-0.187863\pi$
$558$		0			0
$559$	5.66426	+	3.27026i	0.239572	+	0.138317i
$560$	−12.9673	−	7.94551i	−0.547967	−	0.335759i
$561$		0			0
$562$	3.02674	−	34.5957i	0.127675	−	1.45933i
$563$	4.24073	−	1.97748i	0.178725	−	0.0833410i	−0.331196	−	0.943562i	$-0.607452\pi$
$563$	4.24073	−	1.97748i	0.178725	−	0.0833410i	0.509922	+	0.860221i	$0.329674\pi$
$564$		0			0
$565$	26.8001	−	14.5529i	1.12749	−	0.612246i
$566$		−	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	$-0.997574\pi$
$569$	−1.37633	+	7.80556i	−0.0576988	+	0.327226i	0.942272	+	0.334848i	$0.108685\pi$
$570$		0			0
$571$	4.65824	+	1.69546i	0.194941	+	0.0709528i	0.437646	−	0.899147i	$-0.355812\pi$
$571$	4.65824	+	1.69546i	0.194941	+	0.0709528i	−0.242705	+	0.970100i	$0.578035\pi$
$572$	5.11288	+	0.447319i	0.213780	+	0.0187033i
$573$		0			0
$574$	7.52995	+	20.6884i	0.314294	+	0.863516i
$575$	−0.979225	−	27.9662i	−0.0408365	−	1.16627i
$576$		0			0
$577$	22.0266	+	5.90200i	0.916977	+	0.245703i	0.686293	−	0.727325i	$-0.259237\pi$
$577$	22.0266	+	5.90200i	0.916977	+	0.245703i	0.230684	+	0.973029i	$0.425904\pi$
$578$	8.93890	−	0.782053i	0.371809	−	0.0325291i
$579$		0			0
$580$	0.212362	+	3.46941i	0.00881784	+	0.144060i
$581$	17.8737	−	3.15161i	0.741526	−	0.130751i
$582$		0			0
$583$	−0.502393	−	5.74237i	−0.0208070	−	0.237825i
$584$	7.58853	+	13.1437i	0.314015	+	0.543891i
$585$		0			0
$586$	8.00664	−	13.8679i	0.330751	−	0.572878i
$587$	−33.9155	−	15.8151i	−1.39984	−	0.652758i	−0.431439	−	0.902142i	$-0.641994\pi$
$587$	−33.9155	−	15.8151i	−1.39984	−	0.652758i	−0.968405	+	0.249384i	$0.919772\pi$
$588$		0			0
$589$	−1.39555	−	1.66315i	−0.0575026	−	0.0685290i
$590$	−13.7114	+	4.58847i	−0.564488	+	0.188904i
$591$		0			0
$592$	14.3700	+	20.5225i	0.590604	+	0.843470i
$593$	5.46266	−	5.46266i	0.224324	−	0.224324i	−0.585992	−	0.810317i	$-0.699295\pi$
$593$	5.46266	−	5.46266i	0.224324	−	0.224324i	0.810317	+	0.585992i	$0.199295\pi$
$594$		0			0
$595$	−1.58558	+	13.9222i	−0.0650024	+	0.570756i
$596$	2.01008	+	0.354432i	0.0823362	+	0.0145181i
$597$		0			0
$598$	15.9266	+	34.1546i	0.651286	+	1.39669i
$599$	1.79656	−	1.50749i	0.0734055	−	0.0615946i	−0.605347	−	0.795962i	$-0.706965\pi$
$599$	1.79656	−	1.50749i	0.0734055	−	0.0615946i	0.678752	+	0.734367i	$0.262521\pi$
$600$		0			0
$601$	38.1639	−	13.8905i	1.55674	−	0.566607i	0.586753	−	0.809766i	$-0.300406\pi$
$601$	38.1639	−	13.8905i	1.55674	−	0.566607i	0.969987	+	0.243159i	$0.0781836\pi$
$602$	3.24142	−	0.868536i	0.132110	−	0.0353989i
$603$		0			0
$604$	3.24716	−	1.87475i	0.132125	−	0.0762824i
$605$	−12.1837	+	11.5629i	−0.495336	+	0.470101i
$606$		0			0
$607$	−1.53527	−	1.07501i	−0.0623147	−	0.0436332i	0.542004	−	0.840376i	$-0.317666\pi$
$607$	−1.53527	−	1.07501i	−0.0623147	−	0.0436332i	−0.604319	+	0.796743i	$0.706555\pi$
$608$	0.971981	+	0.680588i	0.0394190	+	0.0276015i
$609$		0			0
$610$	24.9669	+	0.652611i	1.01088	+	0.0264234i
$611$	36.1789	−	20.8879i	1.46364	−	0.845035i
$612$		0			0
$613$	−17.5910	+	4.71349i	−0.710494	+	0.190376i	−0.595926	−	0.803039i	$-0.703215\pi$
$613$	−17.5910	+	4.71349i	−0.710494	+	0.190376i	−0.114568	+	0.993415i	$0.536548\pi$
$614$	29.3338	−	10.6766i	1.18382	−	0.430874i
$615$		0			0
$616$	19.1608	−	16.0778i	0.772012	−	0.647795i
$617$	7.87526	+	16.8885i	0.317046	+	0.679907i	0.998657	−	0.0518073i	$-0.0164982\pi$
$617$	7.87526	+	16.8885i	0.317046	+	0.679907i	−0.681611	+	0.731715i	$0.738720\pi$
$618$		0			0
$619$	−28.0130	−	4.93945i	−1.12594	−	0.198533i	−0.420492	−	0.907296i	$-0.638142\pi$
$619$	−28.0130	−	4.93945i	−1.12594	−	0.198533i	−0.705447	+	0.708763i	$0.749254\pi$
$620$	1.26665	+	0.144256i	0.0508697	+	0.00579345i
$621$		0			0
$622$	−3.73594	+	3.73594i	−0.149797	+	0.149797i
$623$	−2.18848	−	3.12547i	−0.0876795	−	0.125219i
$624$		0			0
$625$	−17.3698	−	17.9802i	−0.694793	−	0.719210i
$626$	−0.780926	−	0.930671i	−0.0312121	−	0.0371971i
$627$		0			0
$628$	2.83130	+	1.32026i	0.112981	+	0.0526840i
$629$	11.5418	−	19.9910i	0.460202	−	0.797093i
$630$		0			0
$631$	−16.2016	−	28.0619i	−0.644974	−	1.11713i	−0.984307	−	0.176462i	$-0.943535\pi$
$631$	−16.2016	−	28.0619i	−0.644974	−	1.11713i	0.339333	−	0.940666i	$-0.389799\pi$
$632$	−0.107907	−	1.23338i	−0.00429231	−	0.0490613i
$633$		0			0
$634$	−34.4974	+	6.08282i	−1.37007	+	0.241580i
$635$	5.33422	−	6.02981i	0.211682	−	0.239286i
$636$		0			0
$637$	15.9928	−	1.39919i	0.633659	−	0.0554380i
$638$	36.4671	+	9.77134i	1.44375	+	0.386851i
$639$		0			0
$640$	19.7222	−	2.94845i	0.779589	−	0.116548i
$641$	7.10695	+	19.5262i	0.280708	+	0.771238i	0.997279	+	0.0737239i	$0.0234884\pi$
$641$	7.10695	+	19.5262i	0.280708	+	0.771238i	−0.716571	+	0.697514i	$0.754289\pi$
$642$		0			0
$643$	39.3334	+	3.44122i	1.55116	+	0.135709i	0.830277	−	0.557351i	$-0.188182\pi$
$643$	39.3334	+	3.44122i	1.55116	+	0.135709i	0.720880	+	0.693060i	$0.243738\pi$
$644$	−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	$-0.969024\pi$
$647$	−27.7872	−	27.7872i	−1.09243	−	1.09243i	−0.0971593	−	0.995269i	$-0.530976\pi$
$648$		0			0
$649$		−	20.9430i		−	0.822086i
$650$	30.9926	+	13.1522i	1.21563	+	0.515870i
$651$		0			0
$652$	−1.58283	+	0.738085i	−0.0619884	+	0.0289056i
$653$	1.47726	−	16.8852i	0.0578098	−	0.660770i	−0.910909	−	0.412608i	$-0.864618\pi$
$653$	1.47726	−	16.8852i	0.0578098	−	0.660770i	0.968719	−	0.248162i	$-0.0798264\pi$
$654$		0			0
$655$	1.20736	−	0.289921i	0.0471754	−	0.0113281i
$656$	−25.4684	−	14.7042i	−0.994375	−	0.574103i
$657$		0			0
$658$	5.54754	−	20.7037i	0.216266	−	0.807115i
$659$	−36.7210	−	30.8125i	−1.43045	−	1.20029i	−0.945449	−	0.325770i	$-0.894376\pi$
$659$	−36.7210	−	30.8125i	−1.43045	−	1.20029i	−0.484997	−	0.874516i	$-0.661179\pi$
$660$		0			0
$661$	−0.726513	−	4.12026i	−0.0282581	−	0.160259i	0.967413	−	0.253202i	$-0.0814838\pi$
$661$	−0.726513	−	4.12026i	−0.0282581	−	0.160259i	−0.995671	+	0.0929427i	$0.970373\pi$
$662$	−9.79064	+	13.9825i	−0.380524	+	0.543445i
$663$		0			0
$664$	−17.6947	+	21.0877i	−0.686687	+	0.818361i
$665$	3.65026	+	1.43768i	0.141551	+	0.0557508i
$666$		0			0
$667$	−9.56811	−	35.7087i	−0.370479	−	1.38264i
$668$	0.818774	−	1.75587i	0.0316793	−	0.0679365i
$669$		0			0
$670$	15.8237	+	23.9045i	0.611321	+	0.923511i
$671$	−12.3730	+	33.9945i	−0.477653	+	1.31234i
$672$		0			0
$673$	−19.5570	+	13.6940i	−0.753867	+	0.527863i	−0.886178	−	0.463345i	$-0.846649\pi$
$673$	−19.5570	+	13.6940i	−0.753867	+	0.527863i	0.132311	+	0.991208i	$0.457760\pi$
$674$	−11.2915			−0.434933
$675$		0			0
$676$	2.98725			0.114894
$677$	18.1236	−	12.6903i	0.696547	−	0.487727i	−0.170880	−	0.985292i	$-0.554661\pi$
$677$	18.1236	−	12.6903i	0.696547	−	0.487727i	0.867427	+	0.497565i	$0.165772\pi$
$678$		0			0
$679$	9.04396	−	24.8481i	0.347075	−	0.953581i
$680$	−11.7311	−	17.7220i	−0.449869	−	0.679608i
$681$		0			0
$682$	5.85182	−	12.5493i	0.224078	−	0.480537i
$683$	−6.53337	−	24.3829i	−0.249993	−	0.932985i	−0.970808	−	0.239858i	$-0.922899\pi$
$683$	−6.53337	−	24.3829i	−0.249993	−	0.932985i	0.720815	−	0.693127i	$-0.243768\pi$
$684$		0			0
$685$	−12.5730	−	4.95195i	−0.480389	−	0.189204i
$686$	16.9965	−	20.2556i	0.648929	−	0.773363i
$687$		0			0
$688$	−2.57107	+	3.67187i	−0.0980212	+	0.139989i
$689$	−1.17925	−	6.68785i	−0.0449258	−	0.254787i
$690$		0			0
$691$	25.5999	+	21.4808i	0.973865	+	0.817170i	0.983153	−	0.182787i	$-0.0585118\pi$
$691$	25.5999	+	21.4808i	0.973865	+	0.817170i	−0.00928734	+	0.999957i	$0.502956\pi$
$692$	−0.473473	+	1.76703i	−0.0179988	+	0.0671723i
$693$		0			0
$694$	6.05298	+	3.49469i	0.229768	+	0.132657i
$695$	40.2653	−	9.66884i	1.52735	−	0.366760i
$696$		0			0
$697$	−2.36159	+	26.9931i	−0.0894517	+	1.02244i
$698$	−24.8229	+	11.5751i	−0.939559	+	0.438124i
$699$		0			0
$700$	−2.13581	+	0.863157i	−0.0807261	+	0.0326243i
$701$			12.4042i			0.468499i	0.972177	+	0.234249i	$0.0752632\pi$
$701$			12.4042i			0.468499i	−0.972177	+	0.234249i	$0.924737\pi$
$702$		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
$707$	8.29809	+	0.725989i	0.312082	+	0.0273036i
$708$		0			0
$709$	−4.29127	−	11.7902i	−0.161162	−	0.442789i	0.832659	−	0.553786i	$-0.186818\pi$
$709$	−4.29127	−	11.7902i	−0.161162	−	0.442789i	−0.993821	+	0.110998i	$0.964595\pi$
$710$	16.6940	−	2.49573i	0.626514	−	0.0936631i
$711$		0			0
$712$	5.58994	+	1.49782i	0.209492	+	0.0561332i
$713$	−13.5070	+	1.18171i	−0.505842	+	0.0442554i
$714$		0			0
$715$	−32.3121	+	36.5257i	−1.20840	+	1.36598i
$716$	1.01940	−	0.179748i	0.0380969	−	0.00671750i
$717$		0			0
$718$	2.06408	+	23.5926i	0.0770308	+	0.880466i
$719$	−9.10268	−	15.7663i	−0.339473	−	0.587984i	0.644861	−	0.764300i	$-0.276915\pi$
$719$	−9.10268	−	15.7663i	−0.339473	−	0.587984i	−0.984334	+	0.176316i	$0.943582\pi$
$720$		0			0
$721$	−13.0717	+	22.6408i	−0.486815	+	0.843188i
$722$	−21.9081	−	10.2159i	−0.815334	−	0.380196i
$723$		0			0
$724$	−0.864744	−	1.03056i	−0.0321380	−	0.0383005i
$725$	−27.7006	−	17.9853i	−1.02877	−	0.667956i
$726$		0			0
$727$	−5.64377	−	8.06014i	−0.209316	−	0.298934i	0.700742	−	0.713414i	$-0.252852\pi$
$727$	−5.64377	−	8.06014i	−0.209316	−	0.298934i	−0.910058	+	0.414480i	$0.863963\pi$
$728$	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
$733$	−15.6224	−	33.5024i	−0.577027	−	1.23744i	−0.950767	−	0.309905i	$-0.899703\pi$
$733$	−15.6224	−	33.5024i	−0.577027	−	1.23744i	0.373740	−	0.927533i	$-0.378075\pi$
$734$	−22.3146	+	18.7242i	−0.823646	+	0.691121i
$735$		0			0
$736$	6.96332	−	2.53444i	0.256671	−	0.0934207i
$737$	−40.1088	+	10.7471i	−1.47743	+	0.395875i
$738$		0			0
$739$	−7.02338	+	4.05495i	−0.258359	+	0.149164i	−0.623586	−	0.781755i	$-0.714325\pi$
$739$	−7.02338	+	4.05495i	−0.258359	+	0.149164i	0.365227	+	0.930919i	$0.380991\pi$
$740$	3.79368	+	0.0991631i	0.139459	+	0.00364531i
$741$		0			0
$742$	−2.85416	−	1.99851i	−0.104780	−	0.0733675i
$743$	−25.5056	−	17.8592i	−0.935709	−	0.655190i	0.00296531	−	0.999996i	$-0.499056\pi$
$743$	−25.5056	−	17.8592i	−0.935709	−	0.655190i	−0.938674	+	0.344805i	$0.887945\pi$
$744$		0			0
$745$	−14.0672	+	13.3505i	−0.515383	+	0.489126i
$746$	−19.8552	+	11.4634i	−0.726949	+	0.419704i
$747$		0			0
$748$	3.13050	−	0.838814i	0.114462	−	0.0306701i
$749$	26.6979	−	9.71724i	0.975519	−	0.355060i
$750$		0			0
$751$	−13.4156	+	11.2570i	−0.489541	+	0.410774i	−0.853862	−	0.520500i	$-0.825746\pi$
$751$	−13.4156	+	11.2570i	−0.489541	+	0.410774i	0.364321	+	0.931273i	$0.381301\pi$
$752$	12.1000	+	25.9484i	0.441240	+	0.946243i
$753$		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	$0.423536\pi$
$758$	20.7010	+	29.5641i	0.751893	+	1.07381i
$759$		0			0
$760$	−5.64287	+	1.88837i	−0.204688	+	0.0684985i
$761$	−23.7584	−	28.3141i	−0.861240	−	1.02639i	−0.999353	−	0.0359689i	$-0.988548\pi$
$761$	−23.7584	−	28.3141i	−0.861240	−	1.02639i	0.138113	−	0.990416i	$-0.455896\pi$
$762$		0			0
$763$	−25.4545	−	11.8696i	−0.921516	−	0.429710i
$764$	1.69744	−	2.94006i	0.0614113	−	0.106368i
$765$		0			0
$766$	−4.88069	−	8.45360i	−0.176346	−	0.305441i
$767$	−2.15042	−	24.5794i	−0.0776472	−	0.887512i
$768$		0			0
$769$	8.53754	−	1.50540i	0.307872	−	0.0542861i	−0.0175779	−	0.999845i	$-0.505595\pi$
$769$	8.53754	−	1.50540i	0.307872	−	0.0542861i	0.325450	+	0.945559i	$0.394484\pi$
$770$	1.52866	+	24.9742i	0.0550891	+	0.900007i
$771$		0			0
$772$	−4.06755	+	0.355865i	−0.146394	+	0.0128078i
$773$	−11.3983	−	3.05417i	−0.409969	−	0.109851i	0.0479396	−	0.998850i	$-0.484734\pi$
$773$	−11.3983	−	3.05417i	−0.409969	−	0.109851i	−0.457908	+	0.889000i	$0.651401\pi$
$774$		0			0
$775$	−8.26030	+	8.85975i	−0.296719	+	0.318252i
$776$	13.7174	+	37.6882i	0.492425	+	1.35293i
$777$		0			0
$778$	41.3603	+	3.61856i	1.48284	+	0.129732i
$779$	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
$785$	−26.0856	+	14.1649i	−0.931035	+	0.505567i
$786$		0			0
$787$	17.0214	−	7.93722i	0.606748	−	0.282931i	−0.0948643	−	0.995490i	$-0.530242\pi$
$787$	17.0214	−	7.93722i	0.606748	−	0.282931i	0.701612	+	0.712559i	$0.252464\pi$
$788$	−0.279178	+	3.19101i	−0.00994529	+	0.113675i
$789$		0			0
$790$	1.05603	+	0.647065i	0.0375717	+	0.0230215i
$791$	23.1237	+	13.3505i	0.822183	+	0.474687i
$792$		0			0
$793$	−11.0308	+	41.1675i	−0.391715	+	1.46190i
$794$	16.7831	+	14.0827i	0.595610	+	0.499776i
$795$		0			0
$796$	−0.367376	−	2.08349i	−0.0130213	−	0.0738475i
$797$	−12.3706	+	17.6670i	−0.438188	+	0.625797i	−0.976131	−	0.217184i	$-0.930313\pi$
$797$	−12.3706	+	17.6670i	−0.438188	+	0.625797i	0.537943	+	0.842981i	$0.319202\pi$
$798$		0			0
$799$	16.9567	−	20.2082i	0.599884	−	0.714914i
$800$	3.10745	−	5.84558i	0.109865	−	0.206673i
$801$		0			0
$802$	−0.519739	−	1.93969i	−0.0183526	−	0.0684929i
$803$	9.29368	−	19.9304i	0.327967	−	0.703327i
$804$		0			0
$805$	20.4300	−	13.5237i	0.720063	−	0.476648i
$806$	5.57934	−	15.3291i	0.196524	−	0.539945i
$807$		0			0
$808$	−10.3493	+	7.24665i	−0.364087	+	0.254936i
$809$	4.46938			0.157135			0.0785676	−	0.996909i	$-0.474965\pi$
$809$	4.46938			0.157135			0.0785676	+	0.996909i	$0.474965\pi$
$810$		0			0
$811$	37.9099			1.33120			0.665598	−	0.746311i	$-0.268177\pi$
$811$	37.9099			1.33120			0.665598	+	0.746311i	$0.268177\pi$
$812$	−2.49292	+	1.74556i	−0.0874845	+	0.0612573i
$813$		0			0
$814$	14.0978	−	38.7333i	0.494127	−	1.35760i
$815$	3.30762	−	16.2614i	0.115861	−	0.569612i
$816$		0			0
$817$	0.488696	−	1.04801i	0.0170973	−	0.0366653i
$818$	8.06996	+	30.1175i	0.282159	+	1.05303i
$819$		0			0
$820$	−4.08511	+	1.77649i	−0.142658	+	0.0620376i
$821$	−23.1674	+	27.6099i	−0.808549	+	0.963591i	−0.999839	−	0.0179428i	$-0.994288\pi$
$821$	−23.1674	+	27.6099i	−0.808549	+	0.963591i	0.191290	+	0.981533i	$0.438733\pi$
$822$		0			0
$823$	1.52711	−	2.18095i	0.0532319	−	0.0760230i	−0.791654	−	0.610970i	$-0.790780\pi$
$823$	1.52711	−	2.18095i	0.0532319	−	0.0760230i	0.844886	+	0.534947i	$0.179668\pi$
$824$	−6.88563	−	39.0504i	−0.239872	−	1.36038i
$825$		0			0
$826$	−9.69752	−	8.13719i	−0.337420	−	0.283129i
$827$	−10.6874	+	39.8859i	−0.371637	+	1.38697i	0.486560	+	0.873647i	$0.338252\pi$
$827$	−10.6874	+	39.8859i	−0.371637	+	1.38697i	−0.858197	+	0.513321i	$0.828415\pi$
$828$		0			0
$829$	19.6326	+	11.3349i	0.681869	+	0.393677i	0.800559	−	0.599254i	$-0.204536\pi$
$829$	19.6326	+	11.3349i	0.681869	+	0.393677i	−0.118690	+	0.992931i	$0.537869\pi$
$830$	−6.42966	−	26.7759i	−0.223177	−	0.929406i
$831$		0			0
$832$	−3.84651	+	43.9658i	−0.133354	+	1.52424i
$833$	9.18766	−	4.28428i	0.318334	−	0.148441i
$834$		0			0
$835$	8.78453	+	16.1773i	0.304001	+	0.559838i
$836$		−	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	$-0.898649\pi$
$839$	1.44230	−	8.17971i	0.0497938	−	0.282395i	0.999530	+	0.0306567i	$0.00975985\pi$
$840$		0			0
$841$	−13.7493	−	5.00432i	−0.474112	−	0.172563i
$842$	48.0337	+	4.20240i	1.65535	+	0.144824i
$843$		0			0
$844$	−1.50888	−	4.14562i	−0.0519379	−	0.142698i
$845$	−16.8824	+	22.8175i	−0.580771	+	0.784945i
$846$		0			0
$847$	−14.2054	−	3.80634i	−0.488105	−	0.130787i
$848$	4.63650	−	0.405641i	0.159218	−	0.0139298i
$849$		0			0
$850$	21.2310	+	1.11067i	0.728216	+	0.0380957i
$851$	−39.7487	+	7.00876i	−1.36257	+	0.240257i
$852$		0			0
$853$	−0.534954	−	6.11455i	−0.0183165	−	0.209358i	−0.999838	−	0.0180058i	$-0.994268\pi$
$853$	−0.534954	−	6.11455i	−0.0183165	−	0.209358i	0.981521	−	0.191352i	$-0.0612873\pi$
$854$	10.9335	+	18.9374i	0.374137	+	0.648024i
$855$		0			0
$856$	−21.5463	+	37.3193i	−0.736439	+	1.27555i
$857$	31.3187	+	14.6042i	1.06983	+	0.498869i	0.876072	−	0.482181i	$-0.160155\pi$
$857$	31.3187	+	14.6042i	1.06983	+	0.498869i	0.193756	+	0.981050i	$0.437933\pi$
$858$		0			0
$859$	−14.4078	−	17.1705i	−0.491587	−	0.585850i	0.462034	−	0.886862i	$-0.347120\pi$
$859$	−14.4078	−	17.1705i	−0.491587	−	0.585850i	−0.953620	+	0.301012i	$0.902676\pi$
$860$	0.215478	+	0.643896i	0.00734775	+	0.0219567i
$861$		0			0
$862$	−8.19621	−	11.7054i	−0.279164	−	0.398688i
$863$	−34.4337	+	34.4337i	−1.17214	+	1.17214i	−0.190436	+	0.981700i	$0.560990\pi$
$863$	−34.4337	+	34.4337i	−1.17214	+	1.17214i	−0.981700	+	0.190436i	$0.939010\pi$
$864$		0			0
$865$	−10.8212	−	13.6029i	−0.367933	−	0.462511i
$866$	−47.8011	−	8.42862i	−1.62435	−	0.286416i
$867$		0			0
$868$	0.471713	+	1.01159i	0.0160110	+	0.0343357i
$869$	−1.37423	+	1.15312i	−0.0466175	+	0.0391168i
$870$		0			0
$871$	−45.9694	+	16.7315i	−1.55762	+	0.566926i
$872$	41.1477	−	11.0255i	1.39344	−	0.373370i
$873$		0			0
$874$	5.77009	−	3.33137i	0.195176	−	0.112685i
$875$	5.47747	−	21.1921i	0.185172	−	0.716423i
$876$		0			0
$877$	11.3525	+	7.94910i	0.383347	+	0.268422i	0.749327	−	0.662201i	$-0.230377\pi$
$877$	11.3525	+	7.94910i	0.383347	+	0.268422i	−0.365980	+	0.930623i	$0.619266\pi$
$878$	15.1584	+	10.6140i	0.511571	+	0.358206i
$879$		0			0
$880$	−23.0074	−	24.2425i	−0.775580	−	0.817214i
$881$	20.3929	−	11.7738i	0.687054	−	0.396671i	−0.115453	−	0.993313i	$-0.536832\pi$
$881$	20.3929	−	11.7738i	0.687054	−	0.396671i	0.802507	+	0.596642i	$0.203499\pi$
$882$		0			0
$883$	−15.8795	+	4.25489i	−0.534386	+	0.143188i	−0.515913	−	0.856641i	$-0.672547\pi$
$883$	−15.8795	+	4.25489i	−0.534386	+	0.143188i	−0.0184733	+	0.999829i	$0.505881\pi$
$884$	3.58792	−	1.30590i	0.120675	−	0.0439221i
$885$		0			0
$886$	11.6044	−	9.73725i	0.389857	−	0.327129i
$887$	4.33234	+	9.29073i	0.145466	+	0.311952i	0.965518	−	0.260336i	$-0.0838335\pi$
$887$	4.33234	+	9.29073i	0.145466	+	0.311952i	−0.820052	+	0.572289i	$0.806056\pi$
$888$		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
$893$	−4.23638	−	6.05018i	−0.141765	−	0.202461i
$894$		0			0
$895$	−4.38817	+	8.80234i	−0.146680	+	0.294230i
$896$	11.2227	+	13.3748i	0.374926	+	0.446819i
$897$		0			0
$898$	−1.94540	−	0.907153i	−0.0649187	−	0.0302721i
$899$	−8.00123	+	13.8585i	−0.266856	+	0.462208i
$900$		0			0
$901$	−2.14414	−	3.71376i	−0.0714317	−	0.123723i
$902$	4.21697	+	48.2002i	0.140410	+	1.60489i
$903$		0			0
$904$	−39.8832	+	7.03248i	−1.32649	+	0.233897i
$905$	12.7588	−	0.780964i	0.424118	−	0.0259601i
$906$		0			0
$907$	−13.4551	+	1.17717i	−0.446769	+	0.0390872i	−0.308321	−	0.951283i	$-0.599767\pi$
$907$	−13.4551	+	1.17717i	−0.446769	+	0.0390872i	−0.138448	+	0.990370i	$0.544211\pi$
$908$	−4.11293	−	1.10206i	−0.136492	−	0.0365730i
$909$		0			0
$910$	4.35842	+	29.1535i	0.144480	+	0.966430i
$911$	−4.95701	−	13.6193i	−0.164233	−	0.451227i	0.830090	−	0.557629i	$-0.188289\pi$
$911$	−4.95701	−	13.6193i	−0.164233	−	0.451227i	−0.994323	+	0.106403i	$0.966067\pi$
$912$		0			0
$913$	39.7348	+	3.47635i	1.31503	+	0.115050i
$914$	−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	$0.937866\pi$
$920$	−10.5526	+	35.6312i	−0.347910	+	1.17473i
$921$		0			0
$922$	−18.2970	+	8.53202i	−0.602579	+	0.280987i
$923$	−2.51046	+	28.6946i	−0.0826327	+	0.944496i
$924$		0			0
$925$	−22.1974	+	28.4169i	−0.729846	+	0.934340i
$926$	−38.0276	−	21.9552i	−1.24966	−	0.721494i
$927$		0			0
$928$	2.26359	−	8.44784i	0.0743061	−	0.277314i
$929$	−36.0388	−	30.2401i	−1.18239	−	0.992146i	−0.999960	−	0.00892776i	$-0.997158\pi$
$929$	−36.0388	−	30.2401i	−1.18239	−	0.992146i	−0.182433	−	0.983218i	$-0.558397\pi$
$930$		0			0
$931$	−0.492867	−	2.79519i	−0.0161531	−	0.0916086i
$932$	−1.02089	+	1.45799i	−0.0334405	+	0.0477579i
$933$		0			0
$934$	−19.3932	+	23.1119i	−0.634563	+	0.756243i
$935$	−11.2848	+	28.6522i	−0.369054	+	0.937027i
$936$		0			0
$937$	−9.80740	−	36.6017i	−0.320394	−	1.19573i	−0.918862	−	0.394580i	$-0.870890\pi$
$937$	−9.80740	−	36.6017i	−0.320394	−	1.19573i	0.598468	−	0.801147i	$-0.295776\pi$
$938$	−10.6074	+	22.7477i	−0.346346	+	0.742740i
$939$		0			0
$940$	4.24987	+	0.864439i	0.138616	+	0.0281949i
$941$	3.79401	−	10.4240i	0.123681	−	0.339811i	−0.862364	−	0.506289i	$-0.831017\pi$
$941$	3.79401	−	10.4240i	0.123681	−	0.339811i	0.986045	+	0.166477i	$0.0532392\pi$
$942$		0			0
$943$	38.8098	−	27.1749i	1.26382	−	0.884937i
$944$	16.9098			0.550367
$945$		0			0
$946$	7.37489			0.239778
$947$	13.0294	−	9.12331i	0.423400	−	0.296468i	−0.342391	−	0.939558i	$-0.611237\pi$
$947$	13.0294	−	9.12331i	0.423400	−	0.296468i	0.765791	+	0.643090i	$0.222348\pi$
$948$		0			0
$949$	8.86092	−	24.3452i	0.287638	−	0.790278i
$950$	1.83887	−	5.66126i	0.0596607	−	0.183675i
$951$		0			0
$952$	7.86402	−	16.8644i	0.254874	−	0.546580i
$953$	9.45180	+	35.2746i	0.306174	+	1.14266i	0.931930	+	0.362638i	$0.118124\pi$
$953$	9.45180	+	35.2746i	0.306174	+	1.14266i	−0.625756	+	0.780019i	$0.715210\pi$
$954$		0			0
$955$	12.8639	+	29.5813i	0.416268	+	0.957227i
$956$	1.89177	−	2.25453i	0.0611843	−	0.0729167i
$957$		0			0
$958$	−17.4002	+	24.8501i	−0.562176	+	0.802871i
$959$	−2.05447	−	11.6515i	−0.0663422	−	0.376245i
$960$		0			0
$961$	−19.2514	−	16.1538i	−0.621012	−	0.521091i
$962$	12.5685	−	46.9062i	0.405224	−	1.51232i
$963$		0			0
$964$	3.48953	+	2.01468i	0.112390	+	0.0648886i
$965$	20.2695	−	33.0803i	0.652499	−	1.06489i
$966$		0			0
$967$	−0.170714	+	1.95128i	−0.00548981	+	0.0627488i	−0.998445	−	0.0557381i	$-0.982249\pi$
$967$	−0.170714	+	1.95128i	−0.00548981	+	0.0627488i	0.992956	+	0.118487i	$0.0378044\pi$
$968$	20.2162	−	9.42696i	0.649773	−	0.302994i
$969$		0			0
$970$	−38.4685	−	11.3929i	−1.23515	−	0.365805i
$971$		−	27.5442i		−	0.883934i	−0.897031	−	0.441967i	$-0.854281\pi$
$971$		−	27.5442i		−	0.883934i	0.897031	−	0.441967i	$-0.145719\pi$
$972$		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
$977$	32.5167	+	2.84484i	1.04030	+	0.0910146i	0.594483	−	0.804108i	$-0.297357\pi$
$977$	32.5167	+	2.84484i	1.04030	+	0.0910146i	0.445819	+	0.895123i	$0.352912\pi$
$978$		0			0
$979$	−2.86792	−	7.87954i	−0.0916591	−	0.251831i
$980$	1.33977	+	0.991278i	0.0427973	+	0.0316652i
$981$		0			0
$982$	11.8947	+	3.18718i	0.379575	+	0.101707i
$983$	31.9076	−	2.79155i	1.01769	−	0.0890367i	0.433919	−	0.900952i	$-0.357130\pi$
$983$	31.9076	−	2.79155i	1.01769	−	0.0890367i	0.583775	+	0.811915i	$0.301575\pi$
$984$		0			0
$985$	−22.7961	−	20.1664i	−0.726346	−	0.642556i
$986$	27.6596	−	4.87713i	0.880860	−	0.155319i
$987$		0			0
$988$	−0.0931716	−	1.06496i	−0.00296418	−	0.0338808i
$989$	−3.61075	−	6.25401i	−0.114815	−	0.198866i
$990$		0			0
$991$	24.5859	−	42.5840i	0.780995	−	1.35272i	−0.150367	−	0.988630i	$-0.548046\pi$
$991$	24.5859	−	42.5840i	0.780995	−	1.35272i	0.931362	−	0.364094i	$-0.118621\pi$
$992$	−2.90712	−	1.35561i	−0.0923012	−	0.0430407i
$993$		0			0
$994$	9.49956	+	11.3211i	0.301308	+	0.359084i
$995$	17.9906	+	8.96871i	0.570339	+	0.284327i
$996$		0			0
$997$	−18.0163	−	25.7299i	−0.570581	−	0.814874i	0.425347	−	0.905031i	$-0.360152\pi$
$997$	−18.0163	−	25.7299i	−0.570581	−	0.814874i	−0.995928	+	0.0901563i	$0.971263\pi$
$998$	−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.8.11		192
3.2	odd	2		135.2.q.a.83.6	yes	192
5.2	odd	4	inner	405.2.r.a.332.11		192
15.2	even	4		135.2.q.a.2.6	✓	192
15.8	even	4		675.2.ba.b.407.11		192
15.14	odd	2		675.2.ba.b.218.11		192
27.13	even	9		135.2.q.a.68.6	yes	192
27.14	odd	18	inner	405.2.r.a.233.11		192
135.13	odd	36		675.2.ba.b.257.11		192
135.67	odd	36		135.2.q.a.122.6	yes	192
135.94	even	18		675.2.ba.b.68.11		192
135.122	even	36	inner	405.2.r.a.152.11		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.6	✓	192	15.2	even	4
135.2.q.a.68.6	yes	192	27.13	even	9
135.2.q.a.83.6	yes	192	3.2	odd	2
135.2.q.a.122.6	yes	192	135.67	odd	36
405.2.r.a.8.11		192	1.1	even	1	trivial
405.2.r.a.152.11		192	135.122	even	36	inner
405.2.r.a.233.11		192	27.14	odd	18	inner
405.2.r.a.332.11		192	5.2	odd	4	inner
675.2.ba.b.68.11		192	135.94	even	18
675.2.ba.b.218.11		192	15.14	odd	2
675.2.ba.b.257.11		192	135.13	odd	36
675.2.ba.b.407.11		192	15.8	even	4

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)

\(f(q)\)	\(=\)	\(q+(1.08817 - 0.761943i) q^{2} +(-0.0804885 + 0.221140i) q^{4} +(-1.23426 - 1.86457i) q^{5} +(0.827388 - 1.77434i) q^{7} +(0.768546 + 2.86825i) q^{8} +(-2.76377 - 1.08853i) q^{10} +(2.76562 - 3.29594i) q^{11} +(2.90740 - 4.15220i) q^{13} +(-0.451609 - 2.56120i) q^{14} +(2.66120 + 2.23301i) q^{16} +(0.828434 - 3.09176i) q^{17} +(-0.776109 - 0.448087i) q^{19} +(0.511675 - 0.122868i) q^{20} +(0.498142 - 5.69379i) q^{22} +(-5.07230 + 2.36525i) q^{23} +(-1.95322 + 4.60271i) q^{25} -6.73356i q^{26} +(0.325783 + 0.325783i) q^{28} +(-1.14702 + 6.50507i) q^{29} +(2.27652 + 0.828586i) q^{31} +(-1.31900 - 0.115398i) q^{32} +(-1.45427 - 3.99557i) q^{34} +(-4.32959 + 0.647269i) q^{35} +(6.96604 + 1.86654i) q^{37} +(-1.18595 + 0.103757i) q^{38} +(4.39947 - 4.97316i) q^{40} +(-8.33680 + 1.47000i) q^{41} +(0.112459 + 1.28541i) q^{43} +(0.506265 + 0.876877i) q^{44} +(-3.71732 + 6.43859i) q^{46} +(7.46943 + 3.48305i) q^{47} +(2.03580 + 2.42617i) q^{49} +(1.38157 + 6.49676i) q^{50} +(0.684206 + 0.977148i) q^{52} +(0.947342 - 0.947342i) q^{53} +(-9.55899 - 1.08866i) q^{55} +(5.72514 + 1.00950i) q^{56} +(3.70835 + 7.95258i) q^{58} +(3.72879 - 3.12883i) q^{59} +(-7.90101 + 2.87573i) q^{61} +(3.10857 - 0.832940i) q^{62} +(-7.54029 + 4.35339i) q^{64} +(-11.3305 - 0.296169i) q^{65} +(-7.90560 - 5.53556i) q^{67} +(0.617033 + 0.432051i) q^{68} +(-4.21814 + 4.00324i) q^{70} +(-4.92123 + 2.84127i) q^{71} +(4.93694 - 1.32285i) q^{73} +(9.00242 - 3.27661i) q^{74} +(0.161558 - 0.135563i) q^{76} +(-3.55988 - 7.63418i) q^{77} +(-0.410612 - 0.0724019i) q^{79} +(0.879000 - 7.71810i) q^{80} +(-7.95178 + 7.95178i) q^{82} +(5.31732 + 7.59392i) q^{83} +(-6.78729 + 2.27135i) q^{85} +(1.10179 + 1.31306i) q^{86} +(11.5791 + 5.39942i) q^{88} +(0.974450 - 1.68780i) q^{89} +(-4.96186 - 8.59420i) q^{91} +(-0.114791 - 1.31207i) q^{92} +(10.7819 - 1.90114i) q^{94} +(0.122429 + 2.00016i) q^{95} +(13.4552 - 1.17718i) q^{97} +(4.06390 + 1.08892i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) \) 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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