LMFDB - Embedded newform 405.2.r.a.368.6

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			368.6
Character	$\chi$	$=$	405.368
Dual form			405.2.r.a.197.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.03978 - 0.0909691i) q^{2} +(-0.896746 - 0.158121i) q^{4} +(-2.23373 + 0.102160i) q^{5} +(-0.567627 - 0.397456i) q^{7} +(2.93441 + 0.786273i) q^{8} +(2.33189 + 0.0969768i) q^{10} +(-0.597632 + 1.64198i) q^{11} +(-0.0630233 - 0.720360i) q^{13} +(0.554051 + 0.464904i) q^{14} +(-1.26829 - 0.461619i) q^{16} +(2.95614 - 0.792096i) q^{17} +(3.38781 - 1.95596i) q^{19} +(2.01925 + 0.261588i) q^{20} +(0.770776 - 1.65293i) q^{22} +(4.63055 + 6.61310i) q^{23} +(4.97913 - 0.456395i) q^{25} +0.754750i q^{26} +(0.446171 + 0.446171i) q^{28} +(5.68683 - 4.77181i) q^{29} +(0.764639 - 4.33648i) q^{31} +(-4.22984 - 1.97241i) q^{32} +(-3.14580 + 0.554689i) q^{34} +(1.30853 + 0.829823i) q^{35} +(2.86540 + 10.6938i) q^{37} +(-3.70052 + 1.72558i) q^{38} +(-6.63502 - 1.45655i) q^{40} +(-2.71443 + 3.23493i) q^{41} +(2.74095 + 5.87799i) q^{43} +(0.795555 - 1.37794i) q^{44} +(-4.21317 - 7.29742i) q^{46} +(2.32838 - 3.32527i) q^{47} +(-2.22991 - 6.12663i) q^{49} +(-5.21872 + 0.0216046i) q^{50} +(-0.0573878 + 0.655945i) q^{52} +(5.90884 - 5.90884i) q^{53} +(1.16721 - 3.72880i) q^{55} +(-1.35314 - 1.61261i) q^{56} +(-6.34714 + 4.44432i) q^{58} +(-2.63750 + 0.959971i) q^{59} +(1.13591 + 6.44205i) q^{61} +(-1.18954 + 4.43943i) q^{62} +(6.55640 + 3.78534i) q^{64} +(0.214369 + 1.60265i) q^{65} +(11.1831 - 0.978397i) q^{67} +(-2.77616 + 0.242882i) q^{68} +(-1.28510 - 0.981870i) q^{70} +(-5.58689 - 3.22559i) q^{71} +(-2.16667 + 8.08612i) q^{73} +(-2.00658 - 11.3799i) q^{74} +(-3.34729 + 1.21831i) q^{76} +(0.991847 - 0.694499i) q^{77} +(-1.04738 - 1.24822i) q^{79} +(2.88018 + 0.901566i) q^{80} +(3.11669 - 3.11669i) q^{82} +(-0.156261 + 1.78607i) q^{83} +(-6.52232 + 2.07133i) q^{85} +(-2.31528 - 6.36117i) q^{86} +(-3.04474 + 4.34834i) q^{88} +(-2.78132 - 4.81739i) q^{89} +(-0.250538 + 0.433944i) q^{91} +(-3.10676 - 6.66246i) q^{92} +(-2.72350 + 3.24574i) q^{94} +(-7.36765 + 4.71518i) q^{95} +(-4.20036 + 1.95866i) q^{97} +(1.76129 + 6.57321i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	−1.03978	−	0.0909691i	−0.735236	−	0.0643248i	−0.286614	−	0.958046i	$-0.592530\pi$
$2$	−1.03978	−	0.0909691i	−0.735236	−	0.0643248i	−0.448622	+	0.893721i	$0.648085\pi$
$3$		0			0
$3$		0			0
$4$	−0.896746	−	0.158121i	−0.448373	−	0.0790603i
$5$	−2.23373	+	0.102160i	−0.998956	+	0.0456872i
$5$	−2.23373	+	0.102160i	−0.998956	+	0.0456872i
$6$		0			0
$7$	−0.567627	−	0.397456i	−0.214543	−	0.150224i	0.461366	−	0.887210i	$-0.347360\pi$
$7$	−0.567627	−	0.397456i	−0.214543	−	0.150224i	−0.675908	+	0.736986i	$0.736249\pi$
$8$	2.93441	+	0.786273i	1.03747	+	0.277990i
$9$		0			0
$10$	2.33189	+	0.0969768i	0.737407	+	0.0306668i
$11$	−0.597632	+	1.64198i	−0.180193	+	0.495076i	−0.996599	−	0.0824022i	$-0.973741\pi$
$11$	−0.597632	+	1.64198i	−0.180193	+	0.495076i	0.816406	+	0.577478i	$0.195963\pi$
$12$		0			0
$13$	−0.0630233	−	0.720360i	−0.0174795	−	0.199792i	−0.999913	−	0.0131795i	$-0.995805\pi$
$13$	−0.0630233	−	0.720360i	−0.0174795	−	0.199792i	0.982434	−	0.186612i	$-0.0597508\pi$
$14$	0.554051	+	0.464904i	0.148076	+	0.124251i
$15$		0			0
$16$	−1.26829	−	0.461619i	−0.317072	−	0.115405i
$17$	2.95614	−	0.792096i	0.716970	−	0.192112i	0.118151	−	0.992996i	$-0.462303\pi$
$17$	2.95614	−	0.792096i	0.716970	−	0.192112i	0.598819	+	0.800884i	$0.295637\pi$
$18$		0			0
$19$	3.38781	−	1.95596i	0.777218	−	0.448727i	−0.0582254	−	0.998303i	$-0.518544\pi$
$19$	3.38781	−	1.95596i	0.777218	−	0.448727i	0.835443	+	0.549576i	$0.185211\pi$
$20$	2.01925	+	0.261588i	0.451517	+	0.0584928i
$21$		0			0
$22$	0.770776	−	1.65293i	0.164330	−	0.352407i
$23$	4.63055	+	6.61310i	0.965535	+	1.37893i	0.925091	+	0.379746i	$0.123989\pi$
$23$	4.63055	+	6.61310i	0.965535	+	1.37893i	0.0404446	+	0.999182i	$0.487123\pi$
$24$		0			0
$25$	4.97913	−	0.456395i	0.995825	−	0.0912790i
$26$			0.754750i			0.148019i
$27$		0			0
$28$	0.446171	+	0.446171i	0.0843184	+	0.0843184i
$29$	5.68683	−	4.77181i	1.05602	−	0.886103i	0.0623035	−	0.998057i	$-0.480155\pi$
$29$	5.68683	−	4.77181i	1.05602	−	0.886103i	0.993713	+	0.111954i	$0.0357109\pi$
$30$		0			0
$31$	0.764639	−	4.33648i	0.137333	−	0.778855i	−0.835873	−	0.548922i	$-0.815038\pi$
$31$	0.764639	−	4.33648i	0.137333	−	0.778855i	0.973207	−	0.229933i	$-0.0738506\pi$
$32$	−4.22984	−	1.97241i	−0.747738	−	0.348676i
$33$		0			0
$34$	−3.14580	+	0.554689i	−0.539500	+	0.0951284i
$35$	1.30853	+	0.829823i	0.221182	+	0.140266i
$36$		0			0
$37$	2.86540	+	10.6938i	0.471069	+	1.75805i	0.635939	+	0.771739i	$0.280613\pi$
$37$	2.86540	+	10.6938i	0.471069	+	1.75805i	−0.164870	+	0.986315i	$0.552720\pi$
$38$	−3.70052	+	1.72558i	−0.600303	+	0.279926i
$39$		0			0
$40$	−6.63502	−	1.45655i	−1.04909	−	0.230300i
$41$	−2.71443	+	3.23493i	−0.423923	+	0.505212i	−0.935159	−	0.354229i	$-0.884743\pi$
$41$	−2.71443	+	3.23493i	−0.423923	+	0.505212i	0.511236	+	0.859441i	$0.329188\pi$
$42$		0			0
$43$	2.74095	+	5.87799i	0.417991	+	0.896385i	0.996725	+	0.0808685i	$0.0257694\pi$
$43$	2.74095	+	5.87799i	0.417991	+	0.896385i	−0.578733	+	0.815517i	$0.696453\pi$
$44$	0.795555	−	1.37794i	0.119934	−	0.207733i
$45$		0			0
$46$	−4.21317	−	7.29742i	−0.621197	−	1.07595i
$47$	2.32838	−	3.32527i	0.339628	−	0.485040i	−0.612614	−	0.790382i	$-0.709882\pi$
$47$	2.32838	−	3.32527i	0.339628	−	0.485040i	0.952243	+	0.305342i	$0.0987709\pi$
$48$		0			0
$49$	−2.22991	−	6.12663i	−0.318559	−	0.875234i
$50$	−5.21872	+	0.0216046i	−0.738038	+	0.00305535i
$51$		0			0
$52$	−0.0573878	+	0.655945i	−0.00795825	+	0.0909632i
$53$	5.90884	−	5.90884i	0.811642	−	0.811642i	−0.173238	−	0.984880i	$-0.555423\pi$
$53$	5.90884	−	5.90884i	0.811642	−	0.811642i	0.984880	+	0.173238i	$0.0554230\pi$
$54$		0			0
$55$	1.16721	−	3.72880i	0.157386	−	0.502791i
$56$	−1.35314	−	1.61261i	−0.180821	−	0.215494i
$57$		0			0
$58$	−6.34714	+	4.44432i	−0.833420	+	0.583567i
$59$	−2.63750	+	0.959971i	−0.343373	+	0.124978i	−0.507950	−	0.861387i	$-0.669596\pi$
$59$	−2.63750	+	0.959971i	−0.343373	+	0.124978i	0.164577	+	0.986364i	$0.447374\pi$
$60$		0			0
$61$	1.13591	+	6.44205i	0.145438	+	0.824820i	0.967014	+	0.254722i	$0.0819838\pi$
$61$	1.13591	+	6.44205i	0.145438	+	0.824820i	−0.821576	+	0.570098i	$0.806905\pi$
$62$	−1.18954	+	4.43943i	−0.151072	+	0.563808i
$63$		0			0
$64$	6.55640	+	3.78534i	0.819551	+	0.473168i
$65$	0.214369	+	1.60265i	0.0265892	+	0.198785i
$66$		0			0
$67$	11.1831	−	0.978397i	1.36624	−	0.119530i	0.619682	−	0.784853i	$-0.287262\pi$
$67$	11.1831	−	0.978397i	1.36624	−	0.119530i	0.746556	+	0.665323i	$0.231706\pi$
$68$	−2.77616	+	0.242882i	−0.336659	+	0.0294538i
$69$		0			0
$70$	−1.28510	−	0.981870i	−0.153598	−	0.117356i
$71$	−5.58689	−	3.22559i	−0.663042	−	0.382807i	0.130393	−	0.991462i	$-0.458376\pi$
$71$	−5.58689	−	3.22559i	−0.663042	−	0.382807i	−0.793435	+	0.608655i	$0.791709\pi$
$72$		0			0
$73$	−2.16667	+	8.08612i	−0.253589	+	0.946409i	0.715280	+	0.698838i	$0.246299\pi$
$73$	−2.16667	+	8.08612i	−0.253589	+	0.946409i	−0.968870	+	0.247571i	$0.920368\pi$
$74$	−2.00658	−	11.3799i	−0.233261	−	1.32289i
$75$		0			0
$76$	−3.34729	+	1.21831i	−0.383960	+	0.139750i
$77$	0.991847	−	0.694499i	0.113032	−	0.0791455i
$78$		0			0
$79$	−1.04738	−	1.24822i	−0.117840	−	0.140436i	0.703899	−	0.710300i	$-0.251441\pi$
$79$	−1.04738	−	1.24822i	−0.117840	−	0.140436i	−0.821739	+	0.569863i	$0.806996\pi$
$80$	2.88018	+	0.901566i	0.322013	+	0.100798i
$81$		0			0
$82$	3.11669	−	3.11669i	0.344181	−	0.344181i
$83$	−0.156261	+	1.78607i	−0.0171518	+	0.196046i	0.982784	+	0.184756i	$0.0591494\pi$
$83$	−0.156261	+	1.78607i	−0.0171518	+	0.196046i	−0.999936	+	0.0112903i	$0.996406\pi$
$84$		0			0
$85$	−6.52232	+	2.07133i	−0.707444	+	0.224667i
$86$	−2.31528	−	6.36117i	−0.249663	−	0.685942i
$87$		0			0
$88$	−3.04474	+	4.34834i	−0.324571	+	0.463535i
$89$	−2.78132	−	4.81739i	−0.294820	−	0.510643i	0.680123	−	0.733098i	$-0.261926\pi$
$89$	−2.78132	−	4.81739i	−0.294820	−	0.510643i	−0.974943	+	0.222455i	$0.928593\pi$
$90$		0			0
$91$	−0.250538	+	0.433944i	−0.0262635	+	0.0454897i
$92$	−3.10676	−	6.66246i	−0.323902	−	0.694610i
$93$		0			0
$94$	−2.72350	+	3.24574i	−0.280907	+	0.334772i
$95$	−7.36765	+	4.71518i	−0.755905	+	0.483767i
$96$		0			0
$97$	−4.20036	+	1.95866i	−0.426482	+	0.198872i	−0.623995	−	0.781429i	$-0.714491\pi$
$97$	−4.20036	+	1.95866i	−0.426482	+	0.198872i	0.197513	+	0.980300i	$0.436714\pi$
$98$	1.76129	+	6.57321i	0.177917	+	0.663995i
$99$		0			0
$100$	−4.53718	−	0.378032i	−0.453718	−	0.0378032i
$101$	−11.1359	+	1.96356i	−1.10806	+	0.195381i	−0.697594	−	0.716493i	$-0.745746\pi$
$101$	−11.1359	+	1.96356i	−1.10806	+	0.195381i	−0.410469	+	0.911875i	$0.634635\pi$
$102$		0			0
$103$	−4.47475	−	2.08661i	−0.440911	−	0.205600i	0.189470	−	0.981887i	$-0.439323\pi$
$103$	−4.47475	−	2.08661i	−0.440911	−	0.205600i	−0.630380	+	0.776287i	$0.717101\pi$
$104$	0.381463	−	2.16339i	0.0374055	−	0.212137i
$105$		0			0
$106$	−6.68142	+	5.60638i	−0.648957	+	0.544540i
$107$	11.1511	+	11.1511i	1.07801	+	1.07801i	0.996688	+	0.0813251i	$0.0259152\pi$
$107$	11.1511	+	11.1511i	1.07801	+	1.07801i	0.0813251	+	0.996688i	$0.474085\pi$
$108$		0			0
$109$		−	20.3152i		−	1.94584i	−0.231133	−	0.972922i	$-0.574243\pi$
$109$		−	20.3152i		−	1.94584i	0.231133	−	0.972922i	$-0.425757\pi$
$110$	−1.55284	+	3.77096i	−0.148058	+	0.359546i
$111$		0			0
$112$	0.536441	+	0.766117i	0.0506889	+	0.0723912i
$113$	−0.0516106	+	0.110679i	−0.00485512	+	0.0104118i	−0.908720	−	0.417405i	$-0.862940\pi$
$113$	−0.0516106	+	0.110679i	−0.00485512	+	0.0104118i	0.903865	+	0.427817i	$0.140717\pi$
$114$		0			0
$115$	−11.0190	−	14.2989i	−1.02753	−	1.33338i
$116$	−5.85416	+	3.37990i	−0.543545	+	0.313816i
$117$		0			0
$118$	2.82975	−	0.758229i	0.260500	−	0.0698006i
$119$	−1.99281	−	0.725323i	−0.182681	−	0.0664903i
$120$		0			0
$121$	6.08755	+	5.10806i	0.553414	+	0.464369i
$122$	−0.595068	−	6.80165i	−0.0538749	−	0.615793i
$123$		0			0
$124$	−1.37137	+	3.76782i	−0.123153	+	0.338360i
$125$	−11.0754	+	1.52813i	−0.990615	+	0.136680i
$126$		0			0
$127$	−16.0361	−	4.29687i	−1.42298	−	0.381286i	−0.536439	−	0.843939i	$-0.680231\pi$
$127$	−16.0361	−	4.29687i	−1.42298	−	0.381286i	−0.886539	+	0.462654i	$0.846897\pi$
$128$	1.17328	+	0.821539i	0.103704	+	0.0726144i
$129$		0			0
$130$	−0.0771050	−	1.68591i	−0.00676256	−	0.147864i
$131$	22.1825	+	3.91138i	1.93810	+	0.341739i	0.999989	−	0.00460251i	$-0.00146503\pi$
$131$	22.1825	+	3.91138i	1.93810	+	0.341739i	0.938109	+	0.346341i	$0.112576\pi$
$132$		0			0
$133$	−2.70042	−	0.236256i	−0.234156	−	0.0204860i
$134$	−11.7170			−1.01220
$135$		0			0
$136$	9.29735			0.797241
$137$	−5.19392	−	0.454409i	−0.443747	−	0.0388228i	−0.136907	−	0.990584i	$-0.543716\pi$
$137$	−5.19392	−	0.454409i	−0.443747	−	0.0388228i	−0.306840	+	0.951761i	$0.599272\pi$
$138$		0			0
$139$	12.7974	+	2.25653i	1.08546	+	0.191396i	0.687630	−	0.726061i	$-0.258651\pi$
$139$	12.7974	+	2.25653i	1.08546	+	0.191396i	0.397833	+	0.917458i	$0.369762\pi$
$140$	−1.04221	−	0.951046i	−0.0880826	−	0.0803781i
$141$		0			0
$142$	5.51571	+	3.86214i	0.462868	+	0.324104i
$143$	1.22048	+	0.327027i	0.102062	+	0.0273474i
$144$		0			0
$145$	−12.2154	+	11.2399i	−1.01443	+	0.933425i
$146$	2.98845	−	8.21069i	0.247326	−	0.679522i
$147$		0			0
$148$	−0.878625	−	10.0427i	−0.0722225	−	0.825507i
$149$	8.70742	+	7.30639i	0.713340	+	0.598563i	0.925534	−	0.378664i	$-0.123617\pi$
$149$	8.70742	+	7.30639i	0.713340	+	0.598563i	−0.212194	+	0.977227i	$0.568061\pi$
$150$		0			0
$151$	−8.54652	−	3.11068i	−0.695506	−	0.253143i	−0.0300149	−	0.999549i	$-0.509555\pi$
$151$	−8.54652	−	3.11068i	−0.695506	−	0.253143i	−0.665491	+	0.746406i	$0.731778\pi$
$152$	11.4792	−	3.07583i	0.931083	−	0.249483i
$153$		0			0
$154$	−1.09448	+	0.631900i	−0.0881959	+	0.0509199i
$155$	−1.26498	+	9.76466i	−0.101606	+	0.784316i
$156$		0			0
$157$	1.41498	−	3.03444i	0.112928	−	0.242175i	−0.841718	−	0.539917i	$-0.818456\pi$
$157$	1.41498	−	3.03444i	0.112928	−	0.242175i	0.954646	+	0.297742i	$0.0962335\pi$
$158$	0.975501	+	1.39316i	0.0776067	+	0.110834i
$159$		0			0
$160$	9.64984	+	3.97371i	0.762887	+	0.314150i
$161$		−	5.59421i		−	0.440886i
$162$		0			0
$163$	9.97670	+	9.97670i	0.781435	+	0.781435i	0.980073	−	0.198638i	$-0.0636517\pi$
$163$	9.97670	+	9.97670i	0.781435	+	0.781435i	−0.198638	+	0.980073i	$0.563652\pi$
$164$	2.94567	−	2.47171i	0.230018	−	0.193008i
$165$		0			0
$166$	0.324953	−	1.84290i	0.0252213	−	0.143037i
$167$	12.6150	+	5.88249i	0.976182	+	0.455201i	0.844187	−	0.536049i	$-0.180084\pi$
$167$	12.6150	+	5.88249i	0.976182	+	0.455201i	0.131995	+	0.991250i	$0.457862\pi$
$168$		0			0
$169$	12.2876	−	2.16663i	0.945196	−	0.166664i
$170$	6.97021	−	1.56040i	0.534590	−	0.119677i
$171$		0			0
$172$	−1.52851	−	5.70447i	−0.116548	−	0.434962i
$173$	2.81939	−	1.31470i	0.214354	−	0.0999551i	−0.312476	−	0.949926i	$-0.601158\pi$
$173$	2.81939	−	1.31470i	0.214354	−	0.0999551i	0.526830	+	0.849971i	$0.323380\pi$
$174$		0			0
$175$	−3.00768	−	1.71992i	−0.227359	−	0.130014i
$176$	1.51594	−	1.80663i	0.114268	−	0.136180i
$177$		0			0
$178$	2.45373	+	5.26205i	0.183915	+	0.394407i
$179$	−2.53650	+	4.39334i	−0.189587	+	0.328374i	−0.945113	−	0.326745i	$-0.894048\pi$
$179$	−2.53650	+	4.39334i	−0.189587	+	0.328374i	0.755526	+	0.655119i	$0.227381\pi$
$180$		0			0
$181$	−4.66805	−	8.08530i	−0.346974	−	0.600976i	0.638737	−	0.769425i	$-0.279457\pi$
$181$	−4.66805	−	8.08530i	−0.346974	−	0.600976i	−0.985710	+	0.168449i	$0.946124\pi$
$182$	0.299980	−	0.428416i	0.0222360	−	0.0317563i
$183$		0			0
$184$	8.38822	+	23.0464i	0.618388	+	1.69901i
$185$	−7.49302	−	23.5944i	−0.550898	−	1.73470i
$186$		0			0
$187$	−0.466079	+	5.32731i	−0.0340831	+	0.389572i
$188$	−2.61375	+	2.61375i	−0.190628	+	0.190628i
$189$		0			0
$190$	8.08968	−	4.23253i	0.586887	−	0.307060i
$191$	−0.729528	−	0.869417i	−0.0527868	−	0.0629088i	0.739005	−	0.673700i	$-0.235296\pi$
$191$	−0.729528	−	0.869417i	−0.0527868	−	0.0629088i	−0.791792	+	0.610791i	$0.790852\pi$
$192$		0			0
$193$	11.2910	−	7.90607i	0.812746	−	0.569091i	−0.0916467	−	0.995792i	$-0.529213\pi$
$193$	11.2910	−	7.90607i	0.812746	−	0.569091i	0.904393	+	0.426701i	$0.140324\pi$
$194$	4.54563	−	1.65447i	0.326357	−	0.118784i
$195$		0			0
$196$	1.03092	+	5.84663i	0.0736371	+	0.417617i
$197$	−0.517983	+	1.93314i	−0.0369048	+	0.137730i	−0.981920	−	0.189295i	$-0.939380\pi$
$197$	−0.517983	+	1.93314i	−0.0369048	+	0.137730i	0.945015	+	0.327026i	$0.106046\pi$
$198$		0			0
$199$	16.0030	+	9.23931i	1.13442	+	0.654957i	0.945043	−	0.326947i	$-0.106020\pi$
$199$	16.0030	+	9.23931i	1.13442	+	0.654957i	0.189377	+	0.981905i	$0.439353\pi$
$200$	14.9697	+	2.57570i	1.05851	+	0.182130i
$201$		0			0
$202$	11.7575	−	1.02865i	0.827256	−	0.0723755i
$203$	−5.12458	+	0.448343i	−0.359675	+	0.0314675i
$204$		0			0
$205$	5.73284	−	7.50329i	0.400399	−	0.524052i
$206$	4.46295	+	2.57668i	0.310948	+	0.179526i
$207$		0			0
$208$	−0.252600	+	0.942717i	−0.0175147	+	0.0653656i
$209$	1.18697	+	6.73167i	0.0821047	+	0.465639i
$210$		0			0
$211$	15.7638	−	5.73754i	1.08522	−	0.394989i	0.263374	−	0.964694i	$-0.415165\pi$
$211$	15.7638	−	5.73754i	1.08522	−	0.394989i	0.821849	+	0.569705i	$0.192943\pi$
$212$	−6.23304	+	4.36442i	−0.428087	+	0.299750i
$213$		0			0
$214$	−10.5803	−	12.6091i	−0.723251	−	0.861937i
$215$	−6.72305	−	12.8498i	−0.458508	−	0.876352i
$216$		0			0
$217$	−2.15759	+	2.15759i	−0.146467	+	0.146467i
$218$	−1.84806	+	21.1234i	−0.125166	+	1.43066i
$219$		0			0
$220$	−1.63629	+	3.15923i	−0.110318	+	0.212995i
$221$	−0.756900	−	2.07957i	−0.0509146	−	0.139887i
$222$		0			0
$223$	11.5264	−	16.4615i	0.771868	−	1.10234i	−0.220054	−	0.975488i	$-0.570623\pi$
$223$	11.5264	−	16.4615i	0.771868	−	1.10234i	0.991921	−	0.126854i	$-0.0404879\pi$
$224$	1.61703	+	2.80077i	0.108042	+	0.187134i
$225$		0			0
$226$	0.0637321	−	0.110387i	0.00423940	−	0.00734285i
$227$	−1.96975	−	4.22414i	−0.130737	−	0.280366i	0.830032	−	0.557715i	$-0.188322\pi$
$227$	−1.96975	−	4.22414i	−0.130737	−	0.280366i	−0.960769	+	0.277349i	$0.910544\pi$
$228$		0			0
$229$	−15.6103	+	18.6036i	−1.03156	+	1.22936i	−0.0586205	+	0.998280i	$0.518670\pi$
$229$	−15.6103	+	18.6036i	−1.03156	+	1.22936i	−0.972935	+	0.231080i	$0.925774\pi$
$230$	10.1566	+	15.8701i	0.669706	+	1.04644i
$231$		0			0
$232$	20.4394	−	9.53106i	1.34191	−	0.625745i
$233$	−1.83322	−	6.84167i	−0.120098	−	0.448213i	0.879519	−	0.475863i	$-0.157864\pi$
$233$	−1.83322	−	6.84167i	−0.120098	−	0.448213i	−0.999618	+	0.0276501i	$0.991198\pi$
$234$		0			0
$235$	−4.86126	+	7.66562i	−0.317114	+	0.500050i
$236$	2.51696	−	0.443808i	0.163840	−	0.0288894i
$237$		0			0
$238$	2.00610	+	0.935462i	0.130036	+	0.0606370i
$239$	−2.01666	+	11.4370i	−0.130447	+	0.739799i	0.847476	+	0.530833i	$0.178121\pi$
$239$	−2.01666	+	11.4370i	−0.130447	+	0.739799i	−0.977923	+	0.208966i	$0.932990\pi$
$240$		0			0
$241$	8.02324	−	6.73230i	0.516822	−	0.433665i	−0.346700	−	0.937976i	$-0.612698\pi$
$241$	8.02324	−	6.73230i	0.516822	−	0.433665i	0.863522	+	0.504311i	$0.168253\pi$
$242$	−5.86505	−	5.86505i	−0.377020	−	0.377020i
$243$		0			0
$244$		−	5.95649i		−	0.381325i
$245$	5.60692	+	13.4575i	0.358213	+	0.859766i
$246$		0			0
$247$	−1.62250	−	2.31717i	−0.103237	−	0.147438i
$248$	5.65342	−	12.1238i	0.358993	−	0.769862i
$249$		0			0
$250$	11.6550	−	0.581402i	0.737128	−	0.0367711i
$251$	9.75413	−	5.63155i	0.615675	−	0.355460i	−0.159508	−	0.987197i	$-0.550991\pi$
$251$	9.75413	−	5.63155i	0.615675	−	0.355460i	0.775183	+	0.631736i	$0.217657\pi$
$252$		0			0
$253$	−13.6259	+	3.65106i	−0.856656	+	0.229540i
$254$	16.2832	+	5.92660i	1.02170	+	0.371868i
$255$		0			0
$256$	−12.7442	−	10.6936i	−0.796511	−	0.668352i
$257$	−1.72895	−	19.7620i	−0.107849	−	1.23272i	−0.836551	−	0.547890i	$-0.815431\pi$
$257$	−1.72895	−	19.7620i	−0.107849	−	1.23272i	0.728701	−	0.684832i	$-0.240124\pi$
$258$		0			0
$259$	2.62385	−	7.20897i	0.163038	−	0.447944i
$260$	0.0611778	−	1.47107i	0.00379408	−	0.0912318i
$261$		0			0
$262$	−22.7092	−	6.08491i	−1.40298	−	0.375927i
$263$	13.8257	+	9.68085i	0.852529	+	0.596947i	0.916064	−	0.401033i	$-0.131349\pi$
$263$	13.8257	+	9.68085i	0.852529	+	0.596947i	−0.0635351	+	0.997980i	$0.520237\pi$
$264$		0			0
$265$	−12.5951	+	13.8024i	−0.773713	+	0.847876i
$266$	2.78635	+	0.491310i	0.170842	+	0.0301241i
$267$		0			0
$268$	−10.1831	−	0.890909i	−0.622034	−	0.0544209i
$269$	−30.5994			−1.86568			−0.932838	−	0.360296i	$-0.882676\pi$
$269$	−30.5994			−1.86568			−0.932838	+	0.360296i	$0.882676\pi$
$270$		0			0
$271$	−5.21670			−0.316892			−0.158446	−	0.987368i	$-0.550648\pi$
$271$	−5.21670			−0.316892			−0.158446	+	0.987368i	$0.550648\pi$
$272$	−4.11489	−	0.360006i	−0.249502	−	0.0218286i
$273$		0			0
$274$	5.35921	+	0.944973i	0.323761	+	0.0570879i
$275$	−2.22629	+	8.44838i	−0.134251	+	0.509457i
$276$		0			0
$277$	−9.56033	−	6.69422i	−0.574425	−	0.402216i	0.249952	−	0.968258i	$-0.419585\pi$
$277$	−9.56033	−	6.69422i	−0.574425	−	0.402216i	−0.824377	+	0.566042i	$0.808474\pi$
$278$	−13.1012	−	3.51047i	−0.785760	−	0.210544i
$279$		0			0
$280$	3.18730	+	3.46390i	0.190478	+	0.207008i
$281$	−4.68215	+	12.8641i	−0.279313	+	0.767407i	0.718127	+	0.695912i	$0.244999\pi$
$281$	−4.68215	+	12.8641i	−0.279313	+	0.767407i	−0.997441	+	0.0714958i	$0.977223\pi$
$282$		0			0
$283$	0.773481	+	8.84093i	0.0459787	+	0.525539i	0.983904	+	0.178700i	$0.0571892\pi$
$283$	0.773481	+	8.84093i	0.0459787	+	0.525539i	−0.937925	+	0.346838i	$0.887255\pi$
$284$	4.49999	+	3.77594i	0.267025	+	0.224061i
$285$		0			0
$286$	−1.23928	−	0.451062i	−0.0732804	−	0.0266719i
$287$	2.82653	−	0.757366i	0.166845	−	0.0447059i
$288$		0			0
$289$	−6.61106	+	3.81690i	−0.388886	+	0.224524i
$290$	13.7238	−	10.5758i	0.805889	−	0.621035i
$291$		0			0
$292$	3.22153	−	6.90860i	0.188526	−	0.404295i
$293$	−6.47833	−	9.25201i	−0.378468	−	0.540508i	0.584053	−	0.811716i	$-0.301466\pi$
$293$	−6.47833	−	9.25201i	−0.378468	−	0.540508i	−0.962521	+	0.271207i	$0.912577\pi$
$294$		0			0
$295$	5.79340	−	2.41377i	0.337305	−	0.140535i
$296$			33.6331i			1.95488i
$297$		0			0
$298$	−8.38915	−	8.38915i	−0.485971	−	0.485971i
$299$	4.47198	−	3.75244i	0.258621	−	0.217009i
$300$		0			0
$301$	0.780408	−	4.42591i	0.0449820	−	0.255105i
$302$	8.60353	+	4.01189i	0.495078	+	0.230858i
$303$		0			0
$304$	−5.19963	+	0.916835i	−0.298219	+	0.0525841i
$305$	−3.19543	−	14.2738i	−0.182970	−	0.817314i
$306$		0			0
$307$	2.20847	+	8.24213i	0.126044	+	0.470403i	0.999875	−	0.0158274i	$-0.00503823\pi$
$307$	2.20847	+	8.24213i	0.126044	+	0.470403i	−0.873831	+	0.486230i	$0.838372\pi$
$308$	−0.999250	+	0.465958i	−0.0569376	+	0.0265504i
$309$		0			0
$310$	2.20359	−	10.0380i	0.125155	−	0.570122i
$311$	9.40563	−	11.2092i	0.533344	−	0.635615i	−0.430338	−	0.902668i	$-0.641606\pi$
$311$	9.40563	−	11.2092i	0.533344	−	0.635615i	0.963682	+	0.267053i	$0.0860500\pi$
$312$		0			0
$313$	−3.94117	−	8.45186i	−0.222768	−	0.477727i	0.762880	−	0.646540i	$-0.223785\pi$
$313$	−3.94117	−	8.45186i	−0.222768	−	0.477727i	−0.985648	+	0.168812i	$0.946007\pi$
$314$	−1.74731	+	3.02644i	−0.0986067	+	0.170792i
$315$		0			0
$316$	0.741868	+	1.28495i	0.0417333	+	0.0722843i
$317$	−13.5519	+	19.3542i	−0.761152	+	1.08704i	0.232283	+	0.972648i	$0.425380\pi$
$317$	−13.5519	+	19.3542i	−0.761152	+	1.08704i	−0.993436	+	0.114390i	$0.963509\pi$
$318$		0			0
$319$	4.43659	+	12.1894i	0.248402	+	0.682478i
$320$	−15.0320	−	7.78564i	−0.840312	−	0.435231i
$321$		0			0
$322$	−0.508900	+	5.81676i	−0.0283599	+	0.324155i
$323$	8.46556	−	8.46556i	0.471036	−	0.471036i
$324$		0			0
$325$	−0.642570	−	3.55800i	−0.0356434	−	0.197362i
$326$	−9.46601	−	11.2812i	−0.524274	−	0.624805i
$327$		0			0
$328$	−10.5088	+	7.35834i	−0.580252	+	0.406297i
$329$	−2.64330	+	0.962081i	−0.145730	+	0.0530413i
$330$		0			0
$331$	4.01625	+	22.7773i	0.220753	+	1.25195i	0.870639	+	0.491922i	$0.163705\pi$
$331$	4.01625	+	22.7773i	0.220753	+	1.25195i	−0.649886	+	0.760032i	$0.725183\pi$
$332$	0.422540	−	1.57694i	0.0231899	−	0.0865458i
$333$		0			0
$334$	−12.5818	−	7.26408i	−0.688443	−	0.397473i
$335$	−24.8802	+	3.32794i	−1.35935	+	0.181825i
$336$		0			0
$337$	−12.4168	+	1.08633i	−0.676384	+	0.0591760i	−0.420172	−	0.907445i	$-0.638030\pi$
$337$	−12.4168	+	1.08633i	−0.676384	+	0.0591760i	−0.256212	+	0.966621i	$0.582475\pi$
$338$	−12.9735	+	1.13503i	−0.705663	+	0.0617375i
$339$		0			0
$340$	6.17638	−	0.826146i	0.334961	−	0.0448040i
$341$	6.66344	+	3.84714i	0.360846	+	0.208334i
$342$		0			0
$343$	−2.42474	+	9.04926i	−0.130924	+	0.488614i
$344$	3.42137	+	19.4036i	0.184468	+	1.04617i
$345$		0			0
$346$	−3.05115	+	1.11053i	−0.164031	+	0.0597023i
$347$	−9.36840	+	6.55983i	−0.502922	+	0.352150i	−0.797343	−	0.603526i	$-0.793762\pi$
$347$	−9.36840	+	6.55983i	−0.502922	+	0.352150i	0.294421	+	0.955676i	$0.404873\pi$
$348$		0			0
$349$	−15.6113	−	18.6048i	−0.835652	−	0.995891i	−0.999955	−	0.00948135i	$-0.996982\pi$
$349$	−15.6113	−	18.6048i	−0.835652	−	0.995891i	0.164303	−	0.986410i	$-0.447462\pi$
$350$	2.97087	+	2.06195i	0.158800	+	0.110216i
$351$		0			0
$352$	5.76654	−	5.76654i	0.307358	−	0.307358i
$353$	2.92059	−	33.3825i	0.155447	−	1.77677i	−0.373024	−	0.927822i	$-0.621679\pi$
$353$	2.92059	−	33.3825i	0.155447	−	1.77677i	0.528472	−	0.848951i	$-0.322765\pi$
$354$		0			0
$355$	12.8091	+	6.63436i	0.679839	+	0.352115i
$356$	1.73241	+	4.75976i	0.0918177	+	0.252267i
$357$		0			0
$358$	3.03706	−	4.33737i	0.160514	−	0.229237i
$359$	−9.34241	−	16.1815i	−0.493073	−	0.854028i	0.506895	−	0.862008i	$-0.330793\pi$
$359$	−9.34241	−	16.1815i	−0.493073	−	0.854028i	−0.999968	+	0.00797981i	$0.997460\pi$
$360$		0			0
$361$	−1.84847	+	3.20165i	−0.0972881	+	0.168508i
$362$	4.11824	+	8.83159i	0.216450	+	0.464178i
$363$		0			0
$364$	0.293285	−	0.349523i	0.0153723	−	0.0183200i
$365$	4.01368	−	18.2836i	0.210086	−	0.957006i
$366$		0			0
$367$	−6.45312	+	3.00914i	−0.336850	+	0.157076i	−0.583682	−	0.811983i	$-0.698388\pi$
$367$	−6.45312	+	3.00914i	−0.336850	+	0.157076i	0.246831	+	0.969058i	$0.420611\pi$
$368$	−2.82013	−	10.5249i	−0.147009	−	0.548647i
$369$		0			0
$370$	5.64474	+	25.2147i	0.293456	+	1.31085i
$371$	−5.70252	+	1.00551i	−0.296060	+	0.0522034i
$372$		0			0
$373$	−9.36399	−	4.36650i	−0.484849	−	0.226089i	0.164794	−	0.986328i	$-0.447304\pi$
$373$	−9.36399	−	4.36650i	−0.484849	−	0.226089i	−0.649643	+	0.760239i	$0.725082\pi$
$374$	0.969241	−	5.49684i	0.0501183	−	0.284235i
$375$		0			0
$376$	9.44698	−	7.92696i	0.487191	−	0.408802i
$377$	−3.79582	−	3.79582i	−0.195495	−	0.195495i
$378$		0			0
$379$			5.45309i			0.280106i	0.990144	+	0.140053i	$0.0447273\pi$
$379$			5.45309i			0.280106i	−0.990144	+	0.140053i	$0.955273\pi$
$380$	7.35248	−	3.06334i	0.377174	−	0.157146i
$381$		0			0
$382$	0.679459	+	0.970368i	0.0347641	+	0.0496483i
$383$	1.88914	−	4.05128i	0.0965307	−	0.207011i	−0.852113	−	0.523359i	$-0.824679\pi$
$383$	1.88914	−	4.05128i	0.0965307	−	0.207011i	0.948643	+	0.316348i	$0.102457\pi$
$384$		0			0
$385$	−2.14457	+	1.65265i	−0.109298	+	0.0842270i
$386$	−12.4594	+	7.19344i	−0.634167	+	0.366137i
$387$		0			0
$388$	4.07636	−	1.09226i	0.206946	−	0.0554510i
$389$	9.10172	+	3.31276i	0.461476	+	0.167963i	0.562287	−	0.826942i	$-0.309922\pi$
$389$	9.10172	+	3.31276i	0.461476	+	0.167963i	−0.100811	+	0.994906i	$0.532144\pi$
$390$		0			0
$391$	18.9268	+	15.8814i	0.957168	+	0.803159i
$392$	−1.72627	−	19.7314i	−0.0871899	−	0.996586i
$393$		0			0
$394$	0.714445	−	1.96292i	0.0359932	−	0.0988906i
$395$	2.46710	+	2.68120i	0.124133	+	0.134906i
$396$		0			0
$397$	−0.981728	−	0.263053i	−0.0492715	−	0.0132023i	0.234099	−	0.972213i	$-0.424786\pi$
$397$	−0.981728	−	0.263053i	−0.0492715	−	0.0132023i	−0.283371	+	0.959010i	$0.591453\pi$
$398$	−15.7991	−	11.0626i	−0.791936	−	0.554520i
$399$		0			0
$400$	−6.52565	−	1.71962i	−0.326282	−	0.0859810i
$401$	−8.07342	−	1.42356i	−0.403168	−	0.0710893i	−0.0316124	−	0.999500i	$-0.510064\pi$
$401$	−8.07342	−	1.42356i	−0.403168	−	0.0710893i	−0.371555	+	0.928411i	$0.621175\pi$
$402$		0			0
$403$	−3.17202	−	0.277515i	−0.158009	−	0.0138240i
$404$	10.2965			0.512272
$405$		0			0
$406$	5.36923			0.266470
$407$	−19.2715	−	1.68604i	−0.955253	−	0.0835738i
$408$		0			0
$409$	−28.0740	−	4.95021i	−1.38817	−	0.244772i	−0.570897	−	0.821021i	$-0.693405\pi$
$409$	−28.0740	−	4.95021i	−1.38817	−	0.244772i	−0.817274	+	0.576249i	$0.804516\pi$
$410$	−6.64346	+	7.28026i	−0.328097	+	0.359547i
$411$		0			0
$412$	3.68278	+	2.57871i	0.181438	+	0.127044i
$413$	1.87866	+	0.503386i	0.0924429	+	0.0247700i
$414$		0			0
$415$	0.166580	−	4.00556i	0.00817710	−	0.196625i
$416$	−1.15426	+	3.17132i	−0.0565925	+	0.155487i
$417$		0			0
$418$	−0.621820	−	7.10744i	−0.0304142	−	0.347636i
$419$	19.6956	+	16.5265i	0.962192	+	0.807375i	0.981308	−	0.192443i	$-0.0616409\pi$
$419$	19.6956	+	16.5265i	0.962192	+	0.807375i	−0.0191165	+	0.999817i	$0.506085\pi$
$420$		0			0
$421$	−12.0396	−	4.38206i	−0.586775	−	0.213569i	0.0315356	−	0.999503i	$-0.489960\pi$
$421$	−12.0396	−	4.38206i	−0.586775	−	0.213569i	−0.618310	+	0.785934i	$0.712182\pi$
$422$	−16.9128	+	4.53177i	−0.823303	+	0.220603i
$423$		0			0
$424$	21.9849	−	12.6930i	1.06768	−	0.616427i
$425$	14.3575	−	5.29312i	0.696441	−	0.256754i
$426$		0			0
$427$	1.91566	−	4.10815i	0.0927054	−	0.198807i
$428$	−8.23645	−	11.7629i	−0.398124	−	0.568580i
$429$		0			0
$430$	5.82156	+	13.9726i	0.280741	+	0.673819i
$431$		−	5.16823i		−	0.248945i	−0.992223	−	0.124473i	$-0.960276\pi$
$431$		−	5.16823i		−	0.248945i	0.992223	−	0.124473i	$-0.0397239\pi$
$432$		0			0
$433$	−2.74947	−	2.74947i	−0.132131	−	0.132131i	0.637948	−	0.770079i	$-0.279783\pi$
$433$	−2.74947	−	2.74947i	−0.132131	−	0.132131i	−0.770079	+	0.637948i	$0.779783\pi$
$434$	2.43970	−	2.04715i	0.117109	−	0.0982663i
$435$		0			0
$436$	−3.21225	+	18.2176i	−0.153839	+	0.872464i
$437$	28.6224	+	13.3468i	1.36919	+	0.638465i
$438$		0			0
$439$	−31.6512	+	5.58095i	−1.51063	+	0.266364i	−0.866742	−	0.498757i	$-0.833790\pi$
$439$	−31.6512	+	5.58095i	−1.51063	+	0.266364i	−0.643886	+	0.765122i	$0.722679\pi$
$440$	6.35692	−	10.0241i	0.303054	−	0.477880i
$441$		0			0
$442$	0.597834	+	2.23115i	0.0284361	+	0.106125i
$443$	−13.9035	+	6.48333i	−0.660577	+	0.308032i	−0.723843	−	0.689965i	$-0.757626\pi$
$443$	−13.9035	+	6.48333i	−0.660577	+	0.308032i	0.0632661	+	0.997997i	$0.479848\pi$
$444$		0			0
$445$	6.70488	+	10.4766i	0.317842	+	0.496640i
$446$	−13.4825	+	16.0678i	−0.638413	+	0.760831i
$447$		0			0
$448$	−2.21708	−	4.75455i	−0.104747	−	0.224631i
$449$	1.37821	−	2.38713i	0.0650416	−	0.112655i	−0.831671	−	0.555269i	$-0.812615\pi$
$449$	1.37821	−	2.38713i	0.0650416	−	0.112655i	0.896712	+	0.442614i	$0.145949\pi$
$450$		0			0
$451$	−3.68947	−	6.39034i	−0.173730	−	0.300910i
$452$	0.0637823	−	0.0910905i	0.00300007	−	0.00428454i
$453$		0			0
$454$	1.66384	+	4.57137i	0.0780879	+	0.214545i
$455$	0.515303	−	0.994911i	0.0241578	−	0.0466421i
$456$		0			0
$457$	−2.98806	+	34.1536i	−0.139775	+	1.59764i	0.525335	+	0.850895i	$0.323940\pi$
$457$	−2.98806	+	34.1536i	−0.139775	+	1.59764i	−0.665111	+	0.746745i	$0.731616\pi$
$458$	17.9236	−	17.9236i	0.837515	−	0.837515i
$459$		0			0
$460$	7.62030	+	14.5648i	0.355298	+	0.679086i
$461$	1.95614	+	2.33124i	0.0911067	+	0.108577i	0.809672	−	0.586883i	$-0.199645\pi$
$461$	1.95614	+	2.33124i	0.0911067	+	0.108577i	−0.718565	+	0.695460i	$0.755201\pi$
$462$		0			0
$463$	22.0633	−	15.4489i	1.02537	−	0.717970i	0.0653361	−	0.997863i	$-0.479188\pi$
$463$	22.0633	−	15.4489i	1.02537	−	0.717970i	0.960031	+	0.279894i	$0.0902992\pi$
$464$	−9.41529	+	3.42689i	−0.437094	+	0.159089i
$465$		0			0
$466$	1.28377	+	7.28061i	0.0594694	+	0.337268i
$467$	−4.45355	+	16.6209i	−0.206086	+	0.769122i	0.783030	+	0.621983i	$0.213673\pi$
$467$	−4.45355	+	16.6209i	−0.206086	+	0.769122i	−0.989116	+	0.147138i	$0.952994\pi$
$468$		0			0
$469$	−6.73671	−	3.88944i	−0.311073	−	0.179598i
$470$	5.75198	−	7.52834i	0.265319	−	0.347257i
$471$		0			0
$472$	−8.49431	+	0.743156i	−0.390982	+	0.0342065i
$473$	−11.2896	+	0.987714i	−0.519098	+	0.0454152i
$474$		0			0
$475$	15.9757	−	11.2851i	0.733014	−	0.517797i
$476$	1.67236	+	0.965535i	0.0766523	+	0.0442552i
$477$		0			0
$478$	3.13729	−	11.7085i	0.143497	−	0.535536i
$479$	−6.03903	−	34.2490i	−0.275930	−	1.56488i	−0.735991	−	0.676991i	$-0.763283\pi$
$479$	−6.03903	−	34.2490i	−0.275930	−	1.56488i	0.460061	−	0.887888i	$-0.347828\pi$
$480$		0			0
$481$	7.52282	−	2.73808i	0.343011	−	0.124846i
$482$	−8.95484	+	6.27025i	−0.407882	+	0.285602i
$483$		0			0
$484$	−4.65130	−	5.54320i	−0.211423	−	0.251964i
$485$	9.18238	−	4.80423i	0.416951	−	0.218149i
$486$		0			0
$487$	−10.1713	+	10.1713i	−0.460908	+	0.460908i	−0.898953	−	0.438045i	$-0.855671\pi$
$487$	−10.1713	+	10.1713i	−0.460908	+	0.460908i	0.438045	+	0.898953i	$0.355671\pi$
$488$	−1.73199	+	19.7968i	−0.0784036	+	0.896157i
$489$		0			0
$490$	−4.60576	−	14.5029i	−0.208067	−	0.655173i
$491$	−10.0702	−	27.6677i	−0.454462	−	1.24863i	−0.929553	−	0.368688i	$-0.879807\pi$
$491$	−10.0702	−	27.6677i	−0.454462	−	1.24863i	0.475091	−	0.879937i	$-0.342415\pi$
$492$		0			0
$493$	13.0313	−	18.6107i	0.586902	−	0.838183i
$494$	1.47626	+	2.55695i	0.0664199	+	0.115043i
$495$		0			0
$496$	−2.97158	+	5.14694i	−0.133428	+	0.231104i
$497$	1.88923	+	4.05148i	0.0847438	+	0.181734i
$498$		0			0
$499$	11.3613	−	13.5399i	0.508604	−	0.606130i	−0.449243	−	0.893410i	$-0.648306\pi$
$499$	11.3613	−	13.5399i	0.508604	−	0.606130i	0.957847	+	0.287279i	$0.0927507\pi$
$500$	10.1735	+	0.380905i	0.454971	+	0.0170346i
$501$		0			0
$502$	−10.6545	+	4.96826i	−0.475532	+	0.221744i
$503$	3.36375	+	12.5537i	0.149982	+	0.559742i	0.999483	+	0.0321541i	$0.0102367\pi$
$503$	3.36375	+	12.5537i	0.149982	+	0.559742i	−0.849501	+	0.527588i	$0.823097\pi$
$504$		0			0
$505$	24.6740	−	5.52370i	1.09798	−	0.245802i
$506$	14.5001	−	2.55677i	0.644610	−	0.113662i
$507$		0			0
$508$	13.7009	+	6.38885i	0.607880	+	0.283459i
$509$	0.0644329	−	0.365417i	0.00285594	−	0.0161968i	−0.983346	−	0.181741i	$-0.941827\pi$
$509$	0.0644329	−	0.365417i	0.00285594	−	0.0161968i	0.986202	+	0.165544i	$0.0529380\pi$
$510$		0			0
$511$	4.44374	−	3.72874i	0.196579	−	0.164950i
$512$	10.2528	+	10.2528i	0.453113	+	0.453113i
$513$		0			0
$514$			20.7055i			0.913279i
$515$	10.2086	+	4.20379i	0.449843	+	0.185241i
$516$		0			0
$517$	4.06851	+	5.81043i	0.178933	+	0.255542i
$518$	−3.38403	+	7.25707i	−0.148686	+	0.318857i
$519$		0			0
$520$	−0.631076	+	4.87140i	−0.0276745	+	0.213625i
$521$	2.40696	−	1.38966i	0.105451	−	0.0608820i	−0.446347	−	0.894860i	$-0.647275\pi$
$521$	2.40696	−	1.38966i	0.105451	−	0.0608820i	0.551798	+	0.833978i	$0.313942\pi$
$522$		0			0
$523$	14.6842	−	3.93462i	0.642096	−	0.172049i	0.0769434	−	0.997035i	$-0.475484\pi$
$523$	14.6842	−	3.93462i	0.642096	−	0.172049i	0.565153	+	0.824986i	$0.308817\pi$
$524$	−19.2736	−	7.01503i	−0.841973	−	0.306453i
$525$		0			0
$526$	−13.4950	−	11.3237i	−0.588411	−	0.493736i
$527$	−1.17453	−	13.4249i	−0.0511633	−	0.584799i
$528$		0			0
$529$	−14.4247	+	39.6316i	−0.627162	+	1.72311i
$530$	14.3518	−	13.2057i	0.623401	−	0.573620i
$531$		0			0
$532$	2.38424	+	0.638854i	0.103370	+	0.0276978i
$533$	2.50139	+	1.75149i	0.108347	+	0.0758655i
$534$		0			0
$535$	−26.0477	−	23.7693i	−1.12614	−	1.02764i
$536$	33.5852	+	5.92198i	1.45066	+	0.255790i
$537$		0			0
$538$	31.8166	+	2.78359i	1.37171	+	0.120009i
$539$	11.3925			0.490709
$540$		0			0
$541$	−16.6575			−0.716163			−0.358081	−	0.933690i	$-0.616569\pi$
$541$	−16.6575			−0.716163			−0.358081	+	0.933690i	$0.616569\pi$
$542$	5.42423	+	0.474558i	0.232990	+	0.0203840i
$543$		0			0
$544$	−14.0664	−	2.48028i	−0.603090	−	0.106341i
$545$	2.07540	+	45.3788i	0.0889002	+	1.94381i
$546$		0			0
$547$	0.317541	+	0.222344i	0.0135771	+	0.00950676i	0.580345	−	0.814371i	$-0.302918\pi$
$547$	0.317541	+	0.222344i	0.0135771	+	0.00950676i	−0.566768	+	0.823877i	$0.691806\pi$
$548$	4.58578	+	1.22876i	0.195895	+	0.0524899i
$549$		0			0
$550$	3.08340	−	8.58195i	0.131477	−	0.365935i
$551$	9.93246	−	27.2892i	0.423137	−	1.16256i
$552$		0			0
$553$	0.0984086	+	1.12482i	0.00418476	+	0.0478320i
$554$	9.33168	+	7.83021i	0.396465	+	0.332674i
$555$		0			0
$556$	−11.1192	−	4.04707i	−0.471561	−	0.171634i
$557$	−12.2853	+	3.29185i	−0.520546	+	0.139480i	−0.509519	−	0.860459i	$-0.670177\pi$
$557$	−12.2853	+	3.29185i	−0.520546	+	0.139480i	−0.0110271	+	0.999939i	$0.503510\pi$
$558$		0			0
$559$	4.06152	−	2.34492i	0.171784	−	0.0991797i
$560$	−1.27653	−	1.65650i	−0.0539433	−	0.0699998i
$561$		0			0
$562$	6.03864	−	12.9499i	0.254725	−	0.546259i
$563$	16.7779	+	23.9613i	0.707102	+	1.00985i	0.998580	+	0.0532691i	$0.0169641\pi$
$563$	16.7779	+	23.9613i	0.707102	+	1.00985i	−0.291478	+	0.956578i	$0.594147\pi$
$564$		0			0
$565$	0.103977	−	0.252500i	0.00437436	−	0.0106228i
$566$		−	9.26299i		−	0.389353i
$567$		0			0
$568$	−13.8580	−	13.8580i	−0.581470	−	0.581470i
$569$	3.92124	−	3.29031i	0.164387	−	0.137937i	−0.556884	−	0.830591i	$-0.688003\pi$
$569$	3.92124	−	3.29031i	0.164387	−	0.137937i	0.721270	+	0.692654i	$0.243559\pi$
$570$		0			0
$571$	1.16063	−	6.58228i	0.0485710	−	0.275460i	−0.950844	−	0.309671i	$-0.899781\pi$
$571$	1.16063	−	6.58228i	0.0485710	−	0.275460i	0.999415	+	0.0342116i	$0.0108920\pi$
$572$	−1.04275	−	0.486243i	−0.0435997	−	0.0203309i
$573$		0			0
$574$	−3.00787	+	0.530368i	−0.125546	+	0.0221372i
$575$	26.0743	+	30.8141i	1.08737	+	1.28504i
$576$		0			0
$577$	−11.9622	−	44.6435i	−0.497992	−	1.85853i	−0.512580	−	0.858640i	$-0.671310\pi$
$577$	−11.9622	−	44.6435i	−0.497992	−	1.85853i	0.0145873	−	0.999894i	$-0.495357\pi$
$578$	7.22128	−	3.36734i	0.300366	−	0.140063i
$579$		0			0
$580$	12.7313	−	8.14786i	0.528640	−	0.338321i
$581$	0.798581	−	0.951712i	0.0331307	−	0.0394837i
$582$		0			0
$583$	6.17089	+	13.2335i	0.255572	+	0.548076i
$584$	−12.7158	+	22.0244i	−0.526183	+	0.911376i
$585$		0			0
$586$	5.89440	+	10.2094i	0.243495	+	0.421746i
$587$	−1.01832	+	1.45431i	−0.0420306	+	0.0600260i	−0.839617	−	0.543178i	$-0.817221\pi$
$587$	−1.01832	+	1.45431i	−0.0420306	+	0.0600260i	0.797587	+	0.603204i	$0.206110\pi$
$588$		0			0
$589$	−5.89151	−	16.1868i	−0.242755	−	0.666965i
$590$	−6.24344	+	1.98277i	−0.257039	+	0.0816293i
$591$		0			0
$592$	1.30232	−	14.8856i	0.0535250	−	0.611794i
$593$	−27.8118	+	27.8118i	−1.14209	+	1.14209i	−0.154028	+	0.988066i	$0.549225\pi$
$593$	−27.8118	+	27.8118i	−1.14209	+	1.14209i	−0.988066	+	0.154028i	$0.950775\pi$
$594$		0			0
$595$	4.52550	+	1.41659i	0.185528	+	0.0580747i
$596$	−6.65306	−	7.92880i	−0.272520	−	0.324776i
$597$		0			0
$598$	−4.99124	+	3.49490i	−0.204107	+	0.142917i
$599$	−37.7245	+	13.7306i	−1.54138	+	0.561017i	−0.966376	−	0.257133i	$-0.917222\pi$
$599$	−37.7245	+	13.7306i	−1.54138	+	0.561017i	−0.575005	+	0.818150i	$0.695000\pi$
$600$		0			0
$601$	3.13840	+	17.7988i	0.128018	+	0.726027i	0.979469	+	0.201593i	$0.0646119\pi$
$601$	3.13840	+	17.7988i	0.128018	+	0.726027i	−0.851451	+	0.524434i	$0.824277\pi$
$602$	−1.21407	+	4.53099i	−0.0494820	+	0.184669i
$603$		0			0
$604$	7.17219	+	4.14087i	0.291832	+	0.168490i
$605$	−14.1198	−	10.7881i	−0.574052	−	0.438601i
$606$		0			0
$607$	−14.2779	+	1.24916i	−0.579522	+	0.0507016i	−0.373149	−	0.927772i	$-0.621722\pi$
$607$	−14.2779	+	1.24916i	−0.579522	+	0.0507016i	−0.206374	+	0.978473i	$0.566166\pi$
$608$	−18.1879	+	1.59123i	−0.737616	+	0.0645330i
$609$		0			0
$610$	2.02408	+	15.1323i	0.0819525	+	0.612688i
$611$	−2.54213	−	1.46770i	−0.102844	−	0.0593767i
$612$		0			0
$613$	7.34062	−	27.3956i	0.296485	−	1.10650i	−0.643546	−	0.765408i	$-0.722537\pi$
$613$	7.34062	−	27.3956i	0.296485	−	1.10650i	0.940031	−	0.341090i	$-0.110796\pi$
$614$	−1.54655	−	8.77091i	−0.0624136	−	0.353965i
$615$		0			0
$616$	3.45655	−	1.25808i	0.139269	−	0.0506896i
$617$	−19.2569	+	13.4838i	−0.775255	+	0.542839i	−0.892921	−	0.450214i	$-0.851348\pi$
$617$	−19.2569	+	13.4838i	−0.775255	+	0.542839i	0.117666	+	0.993053i	$0.462459\pi$
$618$		0			0
$619$	5.35313	+	6.37961i	0.215160	+	0.256418i	0.862820	−	0.505512i	$-0.168696\pi$
$619$	5.35313	+	6.37961i	0.215160	+	0.256418i	−0.647659	+	0.761930i	$0.724252\pi$
$620$	2.67836	−	8.55640i	0.107566	−	0.343633i
$621$		0			0
$622$	−10.7995	+	10.7995i	−0.433020	+	0.433020i
$623$	−0.335951	+	3.83994i	−0.0134596	+	0.153844i
$624$		0			0
$625$	24.5834	−	4.54490i	0.983336	−	0.181796i
$626$	3.32909	+	9.14661i	0.133057	+	0.365572i
$627$		0			0
$628$	−1.74869	+	2.49739i	−0.0697803	+	0.0996566i
$629$	16.9411	+	29.3428i	0.675485	+	1.16997i
$630$		0			0
$631$	10.7788	−	18.6694i	0.429097	−	0.743218i	−0.567696	−	0.823238i	$-0.692165\pi$
$631$	10.7788	−	18.6694i	0.429097	−	0.743218i	0.996793	+	0.0800204i	$0.0254985\pi$
$632$	−2.09201	−	4.48633i	−0.0832158	−	0.178457i
$633$		0			0
$634$	15.8517	−	18.8913i	0.629550	−	0.750269i
$635$	36.2594	+	7.95982i	1.43891	+	0.315876i
$636$		0			0
$637$	−4.27285	+	1.99246i	−0.169296	+	0.0789442i
$638$	−3.50422	−	13.0779i	−0.138734	−	0.517761i
$639$		0			0
$640$	−2.70472	−	1.71524i	−0.106913	−	0.0678007i
$641$	4.89330	−	0.862821i	0.193274	−	0.0340794i	−0.0761733	−	0.997095i	$-0.524270\pi$
$641$	4.89330	−	0.862821i	0.193274	−	0.0340794i	0.269447	+	0.963015i	$0.413159\pi$
$642$		0			0
$643$	−20.7326	−	9.66776i	−0.817613	−	0.381259i	−0.0316243	−	0.999500i	$-0.510068\pi$
$643$	−20.7326	−	9.66776i	−0.817613	−	0.381259i	−0.785989	+	0.618241i	$0.787846\pi$
$644$	−0.884560	+	5.01659i	−0.0348566	+	0.197681i
$645$		0			0
$646$	−9.57243	+	8.03223i	−0.376622	+	0.316024i
$647$	8.15287	+	8.15287i	0.320522	+	0.320522i	0.848967	−	0.528445i	$-0.177225\pi$
$647$	8.15287	+	8.15287i	0.320522	+	0.320522i	−0.528445	+	0.848967i	$0.677225\pi$
$648$		0			0
$649$		−	4.90443i		−	0.192516i
$650$	0.344464	+	3.75799i	0.0135110	+	0.147401i
$651$		0			0
$652$	−7.36905	−	10.5241i	−0.288594	−	0.412155i
$653$	15.6937	−	33.6553i	0.614142	−	1.31703i	−0.315625	−	0.948884i	$-0.602214\pi$
$653$	15.6937	−	33.6553i	0.614142	−	1.31703i	0.929767	−	0.368148i	$-0.120008\pi$
$654$		0			0
$655$	−49.9495	−	6.47082i	−1.95169	−	0.252836i
$656$	4.93599	−	2.84980i	0.192718	−	0.111266i
$657$		0			0
$658$	2.83597	−	0.759896i	0.110558	−	0.0296238i
$659$	−17.4051	−	6.33493i	−0.678005	−	0.246774i	−0.0200144	−	0.999800i	$-0.506371\pi$
$659$	−17.4051	−	6.33493i	−0.678005	−	0.246774i	−0.657991	+	0.753026i	$0.728593\pi$
$660$		0			0
$661$	32.6452	+	27.3925i	1.26975	+	1.06545i	0.994572	+	0.104053i	$0.0331813\pi$
$661$	32.6452	+	27.3925i	1.26975	+	1.06545i	0.275178	+	0.961393i	$0.411263\pi$
$662$	−2.10399	−	24.0488i	−0.0817740	−	0.934682i
$663$		0			0
$664$	−1.86287	+	5.11819i	−0.0722933	+	0.198624i
$665$	6.05616	+	0.251859i	0.234848	+	0.00976668i
$666$		0			0
$667$	57.8896	+	15.5115i	2.24149	+	0.600607i
$668$	−10.3824	−	7.26980i	−0.401705	−	0.281277i
$669$		0			0
$670$	26.1727	−	1.19701i	1.01114	−	0.0462444i
$671$	−11.2566	−	1.98484i	−0.434555	−	0.0766238i
$672$		0			0
$673$	9.45392	+	0.827111i	0.364422	+	0.0318828i	0.267896	−	0.963448i	$-0.413672\pi$
$673$	9.45392	+	0.827111i	0.364422	+	0.0318828i	0.0965254	+	0.995331i	$0.469227\pi$
$674$	13.0095			0.501109
$675$		0			0
$676$	−11.3614			−0.436977
$677$	10.7923	+	0.944208i	0.414783	+	0.0362888i	0.292638	−	0.956223i	$-0.405467\pi$
$677$	10.7923	+	0.944208i	0.414783	+	0.0362888i	0.122146	+	0.992512i	$0.461023\pi$
$678$		0			0
$679$	3.16272	+	0.557672i	0.121374	+	0.0214015i
$680$	−20.7678	+	0.949814i	−0.796408	+	0.0364237i
$681$		0			0
$682$	−6.57855	−	4.60635i	−0.251906	−	0.176386i
$683$	2.18859	+	0.586431i	0.0837441	+	0.0224392i	0.300448	−	0.953798i	$-0.402864\pi$
$683$	2.18859	+	0.586431i	0.0837441	+	0.0224392i	−0.216704	+	0.976237i	$0.569531\pi$
$684$		0			0
$685$	11.6483	+	0.484420i	0.445057	+	0.0185087i
$686$	3.34440	−	9.18868i	0.127690	−	0.350825i
$687$		0			0
$688$	−0.762924	−	8.72026i	−0.0290862	−	0.332457i
$689$	−4.62889	−	3.88410i	−0.176347	−	0.147972i
$690$		0			0
$691$	7.28698	+	2.65224i	0.277210	+	0.100896i	0.476884	−	0.878966i	$-0.341766\pi$
$691$	7.28698	+	2.65224i	0.277210	+	0.100896i	−0.199674	+	0.979862i	$0.563988\pi$
$692$	−2.73616	+	0.733152i	−0.104013	+	0.0278703i
$693$		0			0
$694$	10.3378	−	5.96855i	0.392419	−	0.226563i
$695$	−28.8165	−	3.73311i	−1.09307	−	0.141605i
$696$		0			0
$697$	−5.46187	+	11.7130i	−0.206883	+	0.443662i
$698$	14.5398	+	20.7650i	0.550341	+	0.785969i
$699$		0			0
$700$	2.42517	+	2.01791i	0.0916629	+	0.0762699i
$701$			3.06270i			0.115677i	0.998326	+	0.0578383i	$0.0184208\pi$
$701$			3.06270i			0.115677i	−0.998326	+	0.0578383i	$0.981579\pi$
$702$		0			0
$703$	30.6241	+	30.6241i	1.15501	+	1.15501i
$704$	−10.1338	+	8.50324i	−0.381931	+	0.320478i
$705$		0			0
$706$	−6.07355	+	34.4448i	−0.228581	+	1.29635i
$707$	7.10146	+	3.31146i	0.267078	+	0.124540i
$708$		0			0
$709$	45.6222	−	8.04442i	1.71338	−	0.302114i	0.771041	−	0.636785i	$-0.219736\pi$
$709$	45.6222	−	8.04442i	1.71338	−	0.302114i	0.942335	+	0.334671i	$0.108625\pi$
$710$	−12.7152	−	8.06351i	−0.477192	−	0.302618i
$711$		0			0
$712$	−4.37376	−	16.3231i	−0.163914	−	0.611734i
$713$	32.2183	−	15.0236i	1.20658	−	0.562640i
$714$		0			0
$715$	−2.75964	−	0.605807i	−0.103205	−	0.0226559i
$716$	2.96927	−	3.53864i	0.110967	−	0.132245i
$717$		0			0
$718$	8.24204	+	17.6751i	0.307590	+	0.659629i
$719$	25.2485	−	43.7317i	0.941610	−	1.63092i	0.179211	−	0.983811i	$-0.442646\pi$
$719$	25.2485	−	43.7317i	0.941610	−	1.63092i	0.762400	−	0.647106i	$-0.224021\pi$
$720$		0			0
$721$	1.71065	+	2.96294i	0.0637080	+	0.110346i
$722$	2.21326	−	3.16086i	0.0823690	−	0.117635i
$723$		0			0
$724$	2.90761	+	7.98858i	0.108060	+	0.296893i
$725$	26.1376	−	26.3549i	0.970726	−	0.978796i
$726$		0			0
$727$	−0.922993	+	10.5499i	−0.0342319	+	0.391273i	0.959680	+	0.281095i	$0.0906976\pi$
$727$	−0.922993	+	10.5499i	−0.0342319	+	0.391273i	−0.993912	+	0.110178i	$0.964858\pi$
$728$	−1.07638	+	1.07638i	−0.0398933	+	0.0398933i
$729$		0			0
$730$	−5.83659	+	18.6458i	−0.216022	+	0.690112i
$731$	12.7586	+	15.2051i	0.471893	+	0.562380i
$732$		0			0
$733$	−23.8946	+	16.7312i	−0.882569	+	0.617981i	−0.924518	−	0.381139i	$-0.875532\pi$
$733$	−23.8946	+	16.7312i	−0.882569	+	0.617981i	0.0419494	+	0.999120i	$0.486643\pi$
$734$	6.98357	−	2.54181i	0.257768	−	0.0938200i
$735$		0			0
$736$	−6.54274	−	37.1057i	−0.241169	−	1.36774i
$737$	−5.07689	+	18.9472i	−0.187010	+	0.697929i
$738$		0			0
$739$	5.54415	+	3.20092i	0.203945	+	0.117748i	0.598494	−	0.801127i	$-0.295766\pi$
$739$	5.54415	+	3.20092i	0.203945	+	0.117748i	−0.394549	+	0.918875i	$0.629099\pi$
$740$	2.98858	+	22.3430i	0.109862	+	0.821346i
$741$		0			0
$742$	6.02085	−	0.526756i	0.221032	−	0.0193378i
$743$	−29.7334	+	2.60134i	−1.09081	+	0.0954338i	−0.618339	−	0.785911i	$-0.712194\pi$
$743$	−29.7334	+	2.60134i	−1.09081	+	0.0954338i	−0.472473	+	0.881345i	$0.656639\pi$
$744$		0			0
$745$	−20.1965	−	15.4310i	−0.739941	−	0.565347i
$746$	9.33928	+	5.39204i	0.341935	+	0.197416i
$747$		0			0
$748$	1.26031	−	4.70355i	0.0460816	−	0.171979i
$749$	−1.89758	−	10.7617i	−0.0693359	−	0.393224i
$750$		0			0
$751$	−9.53000	+	3.46864i	−0.347755	+	0.126572i	−0.509991	−	0.860180i	$-0.670351\pi$
$751$	−9.53000	+	3.46864i	−0.347755	+	0.126572i	0.162237	+	0.986752i	$0.448129\pi$
$752$	−4.48806	+	3.14257i	−0.163663	+	0.114598i
$753$		0			0
$754$	3.60152	+	4.29213i	0.131160	+	0.156310i
$755$	19.4084	+	6.07531i	0.706345	+	0.221103i
$756$		0			0
$757$	6.39851	−	6.39851i	0.232558	−	0.232558i	−0.581202	−	0.813760i	$-0.697417\pi$
$757$	6.39851	−	6.39851i	0.232558	−	0.232558i	0.813760	+	0.581202i	$0.197417\pi$
$758$	0.496062	−	5.67002i	0.0180178	−	0.205944i
$759$		0			0
$760$	−25.3271	+	8.04329i	−0.918712	+	0.291761i
$761$	−9.16585	−	25.1830i	−0.332262	−	0.912882i	−0.987522	−	0.157479i	$-0.949663\pi$
$761$	−9.16585	−	25.1830i	−0.332262	−	0.912882i	0.655260	−	0.755403i	$-0.272559\pi$
$762$		0			0
$763$	−8.07441	+	11.5315i	−0.292313	+	0.417467i
$764$	0.516728	+	0.895000i	0.0186946	+	0.0323800i
$765$		0			0
$766$	−2.33284	+	4.04059i	−0.0842888	+	0.145993i
$767$	0.857749	+	1.83945i	0.0309715	+	0.0664186i
$768$		0			0
$769$	−8.41448	+	10.0280i	−0.303434	+	0.361619i	−0.896117	−	0.443817i	$-0.853624\pi$
$769$	−8.41448	+	10.0280i	−0.303434	+	0.361619i	0.592684	+	0.805435i	$0.298068\pi$
$770$	2.38023	−	1.52331i	0.0857774	−	0.0548962i
$771$		0			0
$772$	−11.3753	+	5.30439i	−0.409406	+	0.190909i
$773$	3.35520	+	12.5218i	0.120678	+	0.450377i	0.999649	−	0.0264987i	$-0.00843577\pi$
$773$	3.35520	+	12.5218i	0.120678	+	0.450377i	−0.878971	+	0.476876i	$0.841769\pi$
$774$		0			0
$775$	1.82808	−	21.9409i	0.0656667	−	0.788139i
$776$	−13.8656	+	2.44488i	−0.497747	+	0.0877662i
$777$		0			0
$778$	−9.16244	−	4.27252i	−0.328489	−	0.153177i
$779$	−2.86861	+	16.2687i	−0.102778	+	0.582886i
$780$		0			0
$781$	8.63526	−	7.24584i	0.308994	−	0.259277i
$782$	−18.2350	−	18.2350i	−0.652082	−	0.652082i
$783$		0			0
$784$			8.79971i			0.314275i
$785$	−2.85070	+	6.92269i	−0.101746	+	0.247081i
$786$		0			0
$787$	−7.17412	−	10.2457i	−0.255730	−	0.365220i	0.670673	−	0.741753i	$-0.266005\pi$
$787$	−7.17412	−	10.2457i	−0.255730	−	0.365220i	−0.926403	+	0.376533i	$0.877116\pi$
$788$	0.770169	−	1.65163i	0.0274361	−	0.0588370i
$789$		0			0
$790$	−2.32133	−	3.01229i	−0.0825893	−	0.107172i
$791$	0.0732857	−	0.0423115i	0.00260574	−	0.00150443i
$792$		0			0
$793$	4.56900	−	1.22426i	0.162250	−	0.0434748i
$794$	0.996853	+	0.362825i	0.0353770	+	0.0128762i
$795$		0			0
$796$	−12.8897	−	10.8157i	−0.456862	−	0.383353i
$797$	−0.571540	−	6.53273i	−0.0202450	−	0.231401i	−0.999575	−	0.0291347i	$-0.990725\pi$
$797$	−0.571540	−	6.53273i	−0.0202450	−	0.231401i	0.979331	−	0.202267i	$-0.0648307\pi$
$798$		0			0
$799$	4.24908	−	11.6743i	0.150322	−	0.413006i
$800$	−21.9611	−	7.89039i	−0.776443	−	0.278967i
$801$		0			0
$802$	8.26509	+	2.21462i	0.291851	+	0.0782011i
$803$	−11.9824	−	8.39015i	−0.422849	−	0.296082i
$804$		0			0
$805$	0.571503	+	12.4960i	0.0201429	+	0.440425i
$806$	3.27296	+	0.577111i	0.115285	+	0.0203279i
$807$		0			0
$808$	−34.2212	−	2.99397i	−1.20390	−	0.105327i
$809$	21.1375			0.743156			0.371578	−	0.928402i	$-0.378817\pi$
$809$	21.1375			0.743156			0.371578	+	0.928402i	$0.378817\pi$
$810$		0			0
$811$	−48.6371			−1.70788			−0.853940	−	0.520371i	$-0.825794\pi$
$811$	−48.6371			−1.70788			−0.853940	+	0.520371i	$0.825794\pi$
$812$	4.66634	+	0.408252i	0.163756	+	0.0143268i
$813$		0			0
$814$	19.8848	+	3.50622i	0.696961	+	0.122893i
$815$	−23.3045	−	21.2661i	−0.816321	−	0.744918i
$816$		0			0
$817$	20.7829	+	14.5524i	0.727103	+	0.509123i
$818$	28.7405	+	7.70100i	1.00489	+	0.269259i
$819$		0			0
$820$	−6.32732	+	5.82206i	−0.220960	+	0.203315i
$821$	−8.00089	+	21.9823i	−0.279233	+	0.767186i	0.718217	+	0.695819i	$0.244958\pi$
$821$	−8.00089	+	21.9823i	−0.279233	+	0.767186i	−0.997450	+	0.0713672i	$0.977264\pi$
$822$		0			0
$823$	−0.292711	−	3.34570i	−0.0102033	−	0.116624i	0.989385	−	0.145318i	$-0.0464206\pi$
$823$	−0.292711	−	3.34570i	−0.0102033	−	0.116624i	−0.999588	+	0.0286943i	$0.990865\pi$
$824$	−11.4901	−	9.64136i	−0.400277	−	0.335873i
$825$		0			0
$826$	−1.90760	−	0.694311i	−0.0663740	−	0.0241582i
$827$	20.9358	−	5.60974i	0.728010	−	0.195070i	0.124267	−	0.992249i	$-0.460342\pi$
$827$	20.9358	−	5.60974i	0.728010	−	0.195070i	0.603743	+	0.797179i	$0.293675\pi$
$828$		0			0
$829$	−4.62453	+	2.66997i	−0.160617	+	0.0927320i	−0.578154	−	0.815928i	$-0.696227\pi$
$829$	−4.62453	+	2.66997i	−0.160617	+	0.0927320i	0.417537	+	0.908660i	$0.362893\pi$
$830$	−0.537589	+	4.14975i	−0.0186600	+	0.144040i
$831$		0			0
$832$	2.31360	−	4.96154i	0.0802097	−	0.172010i
$833$	−11.4448	−	16.3449i	−0.396540	−	0.566317i
$834$		0			0
$835$	−28.7796	−	11.8512i	−0.995959	−	0.410127i
$836$		−	6.22428i		−	0.215271i
$837$		0			0
$838$	−18.9757	−	18.9757i	−0.655504	−	0.655504i
$839$	−0.256169	+	0.214952i	−0.00884395	+	0.00742095i	−0.647199	−	0.762321i	$-0.724060\pi$
$839$	−0.256169	+	0.214952i	−0.00884395	+	0.00742095i	0.638355	+	0.769742i	$0.279615\pi$
$840$		0			0
$841$	4.53398	−	25.7135i	0.156344	−	0.886673i
$842$	12.1199	+	5.65161i	0.417680	+	0.194767i
$843$		0			0
$844$	−15.0433	+	2.65254i	−0.517813	+	0.0913043i
$845$	−27.2258	+	6.09496i	−0.936595	+	0.209673i
$846$		0			0
$847$	−1.42522	−	5.31901i	−0.0489713	−	0.182763i
$848$	−10.2217	+	4.76648i	−0.351016	+	0.163682i
$849$		0			0
$850$	−15.4102	+	4.19759i	−0.528565	+	0.143976i
$851$	−57.4510	+	68.4675i	−1.96940	+	2.34703i
$852$		0			0
$853$	7.30797	+	15.6720i	0.250220	+	0.536598i	0.990794	−	0.135376i	$-0.0432242\pi$
$853$	7.30797	+	15.6720i	0.250220	+	0.536598i	−0.740574	+	0.671974i	$0.765446\pi$
$854$	−2.36558	+	4.09731i	−0.0809486	+	0.140207i
$855$		0			0
$856$	23.9540	+	41.4895i	0.818731	+	1.41808i
$857$	6.28056	−	8.96957i	0.214540	−	0.306395i	−0.697429	−	0.716654i	$-0.745673\pi$
$857$	6.28056	−	8.96957i	0.214540	−	0.306395i	0.911969	+	0.410259i	$0.134562\pi$
$858$		0			0
$859$	−9.19021	−	25.2499i	−0.313566	−	0.861515i	−0.991930	−	0.126789i	$-0.959533\pi$
$859$	−9.19021	−	25.2499i	−0.313566	−	0.861515i	0.678364	−	0.734726i	$-0.262689\pi$
$860$	3.99704	+	12.5861i	0.136298	+	0.429183i
$861$		0			0
$862$	−0.470149	+	5.37383i	−0.0160133	+	0.183033i
$863$	−14.0569	+	14.0569i	−0.478502	+	0.478502i	−0.904652	−	0.426150i	$-0.859869\pi$
$863$	−14.0569	+	14.0569i	−0.478502	+	0.478502i	0.426150	+	0.904652i	$0.359869\pi$
$864$		0			0
$865$	−6.16346	+	3.22473i	−0.209564	+	0.109644i
$866$	2.60873	+	3.10897i	0.0886484	+	0.105647i
$867$		0			0
$868$	2.27597	−	1.59365i	0.0772515	−	0.0540921i
$869$	2.67551	−	0.973806i	0.0907605	−	0.0330341i
$870$		0			0
$871$	−1.40960	−	7.99422i	−0.0477623	−	0.270874i
$872$	15.9733	−	59.6132i	0.540924	−	2.01876i
$873$		0			0
$874$	−28.5469	−	16.4815i	−0.965612	−	0.557496i
$875$	6.89407	+	3.53459i	0.233062	+	0.119491i
$876$		0			0
$877$	−31.0262	+	2.71444i	−1.04768	+	0.0916602i	−0.597974	−	0.801516i	$-0.704027\pi$
$877$	−31.0262	+	2.71444i	−1.04768	+	0.0916602i	−0.449708	+	0.893176i	$0.648472\pi$
$878$	33.4180	−	2.92369i	1.12780	−	0.0986699i
$879$		0			0
$880$	−3.20164	+	4.19039i	−0.107927	+	0.141258i
$881$	10.7039	+	6.17988i	0.360623	+	0.208206i	0.669354	−	0.742944i	$-0.266571\pi$
$881$	10.7039	+	6.17988i	0.360623	+	0.208206i	−0.308731	+	0.951149i	$0.599904\pi$
$882$		0			0
$883$	−9.26338	+	34.5714i	−0.311738	+	1.16342i	0.615251	+	0.788331i	$0.289055\pi$
$883$	−9.26338	+	34.5714i	−0.311738	+	1.16342i	−0.926989	+	0.375089i	$0.877612\pi$
$884$	0.349925	+	1.98452i	0.0117693	+	0.0667468i
$885$		0			0
$886$	15.0464	−	5.47645i	0.505494	−	0.183985i
$887$	−1.91991	+	1.34433i	−0.0644642	+	0.0451383i	−0.605364	−	0.795949i	$-0.706973\pi$
$887$	−1.91991	+	1.34433i	−0.0644642	+	0.0451383i	0.540900	+	0.841087i	$0.318084\pi$
$888$		0			0
$889$	7.39472	+	8.81269i	0.248011	+	0.295568i
$890$	−6.01856	−	11.5033i	−0.201742	−	0.385593i
$891$		0			0
$892$	−12.9392	+	12.9392i	−0.433236	+	0.433236i
$893$	1.38403	−	15.8196i	0.0463149	−	0.529382i
$894$		0			0
$895$	5.21703	−	10.0727i	0.174386	−	0.336693i
$896$	−0.339458	−	0.932655i	−0.0113405	−	0.0311578i
$897$		0			0
$898$	−1.65019	+	2.35671i	−0.0550675	+	0.0786446i
$899$	−16.3445	−	28.3095i	−0.545120	−	0.944175i
$900$		0			0
$901$	12.7870	−	22.1478i	0.425997	−	0.737849i
$902$	3.25491	+	6.98019i	0.108377	+	0.232415i
$903$		0			0
$904$	−0.238471	+	0.284198i	−0.00793142	+	0.00945230i
$905$	11.2532	+	17.5835i	0.374068	+	0.584496i
$906$		0			0
$907$	50.7113	−	23.6471i	1.68384	−	0.785188i	0.685472	−	0.728099i	$-0.259596\pi$
$907$	50.7113	−	23.6471i	1.68384	−	0.785188i	0.998369	−	0.0570890i	$-0.0181819\pi$
$908$	1.09844	+	4.09944i	0.0364530	+	0.136045i
$909$		0			0
$910$	−0.626309	+	0.987613i	−0.0207619	+	0.0327391i
$911$	26.4465	−	4.66323i	0.876211	−	0.154500i	0.282587	−	0.959242i	$-0.408808\pi$
$911$	26.4465	−	4.66323i	0.876211	−	0.154500i	0.593625	+	0.804742i	$0.297696\pi$
$912$		0			0
$913$	−2.83930	−	1.32399i	−0.0939671	−	0.0438176i
$914$	6.21385	−	35.2405i	0.205536	−	1.16565i
$915$		0			0
$916$	16.9401	−	14.2144i	0.559715	−	0.469657i
$917$	−11.0368	−	11.0368i	−0.364467	−	0.364467i
$918$		0			0
$919$			30.8687i			1.01826i	0.860688	+	0.509132i	$0.170033\pi$
$919$			30.8687i			1.01826i	−0.860688	+	0.509132i	$0.829967\pi$
$920$	−21.0915	−	50.6227i	−0.695365	−	1.66898i
$921$		0			0
$922$	−1.82189	−	2.60193i	−0.0600008	−	0.0856900i
$923$	−1.97148	+	4.22786i	−0.0648921	+	0.139162i
$924$		0			0
$925$	19.1478	+	51.9382i	0.629576	+	1.70772i
$926$	−24.3463	+	14.0564i	−0.800070	+	0.461921i
$927$		0			0
$928$	−33.4663	+	8.96728i	−1.09859	+	0.294365i
$929$	14.1178	+	5.13847i	0.463191	+	0.168588i	0.563065	−	0.826412i	$-0.309622\pi$
$929$	14.1178	+	5.13847i	0.463191	+	0.168588i	−0.0998747	+	0.995000i	$0.531844\pi$
$930$		0			0
$931$	−19.5380	−	16.3943i	−0.640331	−	0.537301i
$932$	0.562125	+	6.42512i	0.0184130	+	0.210462i
$933$		0			0
$934$	6.14270	−	16.8769i	0.200995	−	0.552230i
$935$	0.496860	−	11.9474i	0.0162491	−	0.390722i
$936$		0			0
$937$	44.9601	+	12.0470i	1.46878	+	0.393559i	0.902514	−	0.430660i	$-0.141719\pi$
$937$	44.9601	+	12.0470i	1.46878	+	0.393559i	0.566270	+	0.824220i	$0.308386\pi$
$938$	6.65089	+	4.65700i	0.217159	+	0.152057i
$939$		0			0
$940$	5.57141	−	6.10545i	0.181719	−	0.199138i
$941$	13.0261	+	2.29686i	0.424640	+	0.0748755i	0.381884	−	0.924210i	$-0.375275\pi$
$941$	13.0261	+	2.29686i	0.424640	+	0.0748755i	0.0427555	+	0.999086i	$0.486386\pi$
$942$		0			0
$943$	−33.9623	−	2.97131i	−1.10596	−	0.0967593i
$944$	3.78825			0.123297
$945$		0			0
$946$	11.8286			0.384581
$947$	33.5777	+	2.93767i	1.09113	+	0.0954614i	0.618488	−	0.785794i	$-0.287745\pi$
$947$	33.5777	+	2.93767i	1.09113	+	0.0954614i	0.472640	+	0.881255i	$0.343301\pi$
$948$		0			0
$949$	5.96147	+	1.05117i	0.193517	+	0.0341223i
$950$	−17.6378	+	10.2808i	−0.572246	+	0.333552i
$951$		0			0
$952$	−5.27742	−	3.69529i	−0.171042	−	0.119765i
$953$	−37.8969	−	10.1544i	−1.22760	−	0.328935i	−0.413956	−	0.910297i	$-0.635853\pi$
$953$	−37.8969	−	10.1544i	−1.22760	−	0.328935i	−0.813645	+	0.581362i	$0.802520\pi$
$954$		0			0
$955$	1.71839	+	1.86752i	0.0556058	+	0.0604314i
$956$	3.61686	−	9.93723i	0.116977	−	0.321393i
$957$		0			0
$958$	3.16367	+	36.1609i	0.102213	+	1.16830i
$959$	2.76760	+	2.32229i	0.0893705	+	0.0749908i
$960$		0			0
$961$	10.9101	+	3.97094i	0.351938	+	0.128095i
$962$	−8.07116	+	2.16266i	−0.260225	+	0.0697270i
$963$		0			0
$964$	−8.25932	+	4.76852i	−0.266015	+	0.153584i
$965$	−24.4135	+	18.8135i	−0.785897	+	0.605629i
$966$		0			0
$967$	−10.7806	+	23.1190i	−0.346680	+	0.743457i	−0.999906	−	0.0137056i	$-0.995637\pi$
$967$	−10.7806	+	23.1190i	−0.346680	+	0.743457i	0.653226	+	0.757163i	$0.273415\pi$
$968$	13.8471	+	19.7756i	0.445061	+	0.635613i
$969$		0			0
$970$	−9.98470	+	4.16003i	−0.320590	+	0.133571i
$971$		−	23.0327i		−	0.739156i	−0.929200	−	0.369578i	$-0.879502\pi$
$971$		−	23.0327i		−	0.739156i	0.929200	−	0.369578i	$-0.120498\pi$
$972$		0			0
$973$	−6.36728	−	6.36728i	−0.204126	−	0.204126i
$974$	11.5013	−	9.65070i	0.368524	−	0.309228i
$975$		0			0
$976$	1.53312	−	8.69473i	0.0490738	−	0.278312i
$977$	0.251362	+	0.117212i	0.00804177	+	0.00374994i	0.426635	−	0.904424i	$-0.359699\pi$
$977$	0.251362	+	0.117212i	0.00804177	+	0.00374994i	−0.418593	+	0.908174i	$0.637477\pi$
$978$		0			0
$979$	9.57227	−	1.68785i	0.305931	−	0.0539439i
$980$	−2.90009	−	12.9545i	−0.0926399	−	0.413816i
$981$		0			0
$982$	7.95391	+	29.6844i	0.253820	+	0.947268i
$983$	−7.55984	+	3.52521i	−0.241122	+	0.112437i	−0.539423	−	0.842035i	$-0.681358\pi$
$983$	−7.55984	+	3.52521i	−0.241122	+	0.112437i	0.298302	+	0.954472i	$0.403580\pi$
$984$		0			0
$985$	0.959547	−	4.37104i	0.0305737	−	0.139273i
$986$	−15.2427	+	18.1656i	−0.485427	+	0.578510i
$987$		0			0
$988$	1.08858	+	2.33447i	0.0346324	+	0.0742694i
$989$	−26.1797	+	45.3445i	−0.832465	+	1.44187i
$990$		0			0
$991$	−3.48806	−	6.04150i	−0.110802	−	0.191914i	0.805292	−	0.592878i	$-0.202009\pi$
$991$	−3.48806	−	6.04150i	−0.110802	−	0.191914i	−0.916094	+	0.400964i	$0.868675\pi$
$992$	−11.7876	+	16.8345i	−0.374257	+	0.534494i
$993$		0			0
$994$	−1.59583	−	4.38451i	−0.0506167	−	0.139068i
$995$	−36.6902	−	19.0033i	−1.16316	−	0.602445i
$996$		0			0
$997$	4.81022	−	54.9810i	0.152341	−	1.74127i	−0.407980	−	0.912991i	$-0.633767\pi$
$997$	4.81022	−	54.9810i	0.152341	−	1.74127i	0.560321	−	0.828276i	$-0.310678\pi$
$998$	−13.0450	+	13.0450i	−0.412933	+	0.412933i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.368.6		192
3.2	odd	2		135.2.q.a.113.11	yes	192
5.2	odd	4	inner	405.2.r.a.287.11		192
15.2	even	4		135.2.q.a.32.6	✓	192
15.8	even	4		675.2.ba.b.32.11		192
15.14	odd	2		675.2.ba.b.518.6		192
27.11	odd	18	inner	405.2.r.a.278.11		192
27.16	even	9		135.2.q.a.38.6	yes	192
135.43	odd	36		675.2.ba.b.632.6		192
135.92	even	36	inner	405.2.r.a.197.6		192
135.97	odd	36		135.2.q.a.92.11	yes	192
135.124	even	18		675.2.ba.b.443.11		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.6	✓	192	15.2	even	4
135.2.q.a.38.6	yes	192	27.16	even	9
135.2.q.a.92.11	yes	192	135.97	odd	36
135.2.q.a.113.11	yes	192	3.2	odd	2
405.2.r.a.197.6		192	135.92	even	36	inner
405.2.r.a.278.11		192	27.11	odd	18	inner
405.2.r.a.287.11		192	5.2	odd	4	inner
405.2.r.a.368.6		192	1.1	even	1	trivial
675.2.ba.b.32.11		192	15.8	even	4
675.2.ba.b.443.11		192	135.124	even	18
675.2.ba.b.518.6		192	15.14	odd	2
675.2.ba.b.632.6		192	135.43	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)

\(f(q)\)	\(=\)	\(q+(-1.03978 - 0.0909691i) q^{2} +(-0.896746 - 0.158121i) q^{4} +(-2.23373 + 0.102160i) q^{5} +(-0.567627 - 0.397456i) q^{7} +(2.93441 + 0.786273i) q^{8} +(2.33189 + 0.0969768i) q^{10} +(-0.597632 + 1.64198i) q^{11} +(-0.0630233 - 0.720360i) q^{13} +(0.554051 + 0.464904i) q^{14} +(-1.26829 - 0.461619i) q^{16} +(2.95614 - 0.792096i) q^{17} +(3.38781 - 1.95596i) q^{19} +(2.01925 + 0.261588i) q^{20} +(0.770776 - 1.65293i) q^{22} +(4.63055 + 6.61310i) q^{23} +(4.97913 - 0.456395i) q^{25} +0.754750i q^{26} +(0.446171 + 0.446171i) q^{28} +(5.68683 - 4.77181i) q^{29} +(0.764639 - 4.33648i) q^{31} +(-4.22984 - 1.97241i) q^{32} +(-3.14580 + 0.554689i) q^{34} +(1.30853 + 0.829823i) q^{35} +(2.86540 + 10.6938i) q^{37} +(-3.70052 + 1.72558i) q^{38} +(-6.63502 - 1.45655i) q^{40} +(-2.71443 + 3.23493i) q^{41} +(2.74095 + 5.87799i) q^{43} +(0.795555 - 1.37794i) q^{44} +(-4.21317 - 7.29742i) q^{46} +(2.32838 - 3.32527i) q^{47} +(-2.22991 - 6.12663i) q^{49} +(-5.21872 + 0.0216046i) q^{50} +(-0.0573878 + 0.655945i) q^{52} +(5.90884 - 5.90884i) q^{53} +(1.16721 - 3.72880i) q^{55} +(-1.35314 - 1.61261i) q^{56} +(-6.34714 + 4.44432i) q^{58} +(-2.63750 + 0.959971i) q^{59} +(1.13591 + 6.44205i) q^{61} +(-1.18954 + 4.43943i) q^{62} +(6.55640 + 3.78534i) q^{64} +(0.214369 + 1.60265i) q^{65} +(11.1831 - 0.978397i) q^{67} +(-2.77616 + 0.242882i) q^{68} +(-1.28510 - 0.981870i) q^{70} +(-5.58689 - 3.22559i) q^{71} +(-2.16667 + 8.08612i) q^{73} +(-2.00658 - 11.3799i) q^{74} +(-3.34729 + 1.21831i) q^{76} +(0.991847 - 0.694499i) q^{77} +(-1.04738 - 1.24822i) q^{79} +(2.88018 + 0.901566i) q^{80} +(3.11669 - 3.11669i) q^{82} +(-0.156261 + 1.78607i) q^{83} +(-6.52232 + 2.07133i) q^{85} +(-2.31528 - 6.36117i) q^{86} +(-3.04474 + 4.34834i) q^{88} +(-2.78132 - 4.81739i) q^{89} +(-0.250538 + 0.433944i) q^{91} +(-3.10676 - 6.66246i) q^{92} +(-2.72350 + 3.24574i) q^{94} +(-7.36765 + 4.71518i) q^{95} +(-4.20036 + 1.95866i) q^{97} +(1.76129 + 6.57321i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) \) 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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