LMFDB - Embedded newform 882.2.bl.a.395.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [882,2,Mod(17,882)] 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("882.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(882, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([21, 25])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.bl (of order $42$, degree $12$, 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$20$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			395.13
Character	$\chi$	$=$	882.395
Dual form			882.2.bl.a.719.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.930874 + 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(-1.63709 - 1.11615i) q^{5} +(-2.45942 - 0.975316i) q^{7} +(0.433884 + 0.900969i) q^{8} +(-1.11615 - 1.63709i) q^{10} +(0.838558 + 5.56347i) q^{11} +(-2.27837 + 1.81694i) q^{13} +(-1.93309 - 1.80642i) q^{14} +(0.0747301 + 0.997204i) q^{16} +(-1.68804 - 0.520691i) q^{17} +(-6.29755 + 3.63589i) q^{19} +(-0.440897 - 1.93170i) q^{20} +(-1.25197 + 5.48525i) q^{22} +(1.94874 + 6.31765i) q^{23} +(-0.392435 - 0.999907i) q^{25} +(-2.78468 + 0.858960i) q^{26} +(-1.13950 - 2.38779i) q^{28} +(8.15398 - 1.86109i) q^{29} +(3.38676 + 1.95535i) q^{31} +(-0.294755 + 0.955573i) q^{32} +(-1.38112 - 1.10141i) q^{34} +(2.93769 + 4.34176i) q^{35} +(0.211701 - 0.196430i) q^{37} +(-7.19056 + 1.08380i) q^{38} +(0.295308 - 1.95924i) q^{40} +(-9.79045 + 4.71483i) q^{41} +(-8.98886 - 4.32881i) q^{43} +(-3.16941 + 4.64868i) q^{44} +(-0.494069 + 6.59289i) q^{46} +(-2.58457 + 6.58538i) q^{47} +(5.09752 + 4.79743i) q^{49} -1.07416i q^{50} +(-2.90600 - 0.217774i) q^{52} +(-2.38375 + 2.56907i) q^{53} +(4.83686 - 10.0438i) q^{55} +(-0.188374 - 2.63904i) q^{56} +(8.27026 + 1.24654i) q^{58} +(11.4492 - 7.80592i) q^{59} +(-3.85220 - 4.15169i) q^{61} +(2.43828 + 3.05750i) q^{62} +(-0.623490 + 0.781831i) q^{64} +(5.75787 - 0.431493i) q^{65} +(3.06901 - 5.31569i) q^{67} +(-0.883260 - 1.52985i) q^{68} +(1.14840 + 5.11489i) q^{70} +(-4.16730 - 0.951159i) q^{71} +(-8.67775 + 3.40576i) q^{73} +(0.268831 - 0.105508i) q^{74} +(-7.08947 - 1.61812i) q^{76} +(3.36378 - 14.5008i) q^{77} +(-5.42299 - 9.39290i) q^{79} +(0.990687 - 1.71592i) q^{80} +(-10.8362 + 0.812060i) q^{82} +(4.38954 - 5.50431i) q^{83} +(2.18230 + 2.73652i) q^{85} +(-6.78600 - 7.31357i) q^{86} +(-4.64868 + 3.16941i) q^{88} +(11.0890 + 1.67140i) q^{89} +(7.37557 - 2.24649i) q^{91} +(-2.86857 + 5.95665i) q^{92} +(-4.81182 + 5.18591i) q^{94} +(14.3678 + 1.07672i) q^{95} -9.55626i q^{97} +(2.99245 + 6.32813i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 20 q^{4} - 4 q^{7} - 12 q^{10} + 20 q^{16} + 24 q^{19} - 20 q^{22} + 24 q^{25} + 4 q^{28} + 12 q^{31} - 32 q^{37} + 44 q^{40} - 48 q^{43} + 204 q^{49} + 140 q^{55} + 136 q^{58} + 88 q^{61} + 40 q^{64}+ \cdots + 80 q^{94}+O(q^{100}) $ 240 * q - 20 * q^4 - 4 * q^7 - 12 * q^10 + 20 * q^16 + 24 * q^19 - 20 * q^22 + 24 * q^25 + 4 * q^28 + 12 * q^31 - 32 * q^37 + 44 * q^40 - 48 * q^43 + 204 * q^49 + 140 * q^55 + 136 * q^58 + 88 * q^61 + 40 * q^64 - 32 * q^67 - 16 * q^70 - 24 * q^73 - 28 * q^79 - 48 * q^82 - 112 * q^85 + 4 * q^88 + 80 * q^91 + 80 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{42}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.930874	+	0.365341i	0.658227	+	0.258335i
$2$	0.930874	+	0.365341i	0.658227	+	0.258335i
$3$		0			0
$3$		0			0
$4$	0.733052	+	0.680173i	0.366526	+	0.340086i
$5$	−1.63709	−	1.11615i	−0.732128	−	0.499156i	0.138951	−	0.990299i	$-0.455627\pi$
$5$	−1.63709	−	1.11615i	−0.732128	−	0.499156i	−0.871079	+	0.491143i	$0.836579\pi$
$6$		0			0
$7$	−2.45942	−	0.975316i	−0.929574	−	0.368635i
$7$	−2.45942	−	0.975316i	−0.929574	−	0.368635i
$8$	0.433884	+	0.900969i	0.153401	+	0.318541i
$9$		0			0
$10$	−1.11615	−	1.63709i	−0.352957	−	0.517693i
$11$	0.838558	+	5.56347i	0.252835	+	1.67745i	0.650180	+	0.759780i	$0.274694\pi$
$11$	0.838558	+	5.56347i	0.252835	+	1.67745i	−0.397345	+	0.917669i	$0.630068\pi$
$12$		0			0
$13$	−2.27837	+	1.81694i	−0.631907	+	0.503929i	−0.886263	−	0.463182i	$-0.846708\pi$
$13$	−2.27837	+	1.81694i	−0.631907	+	0.503929i	0.254357	+	0.967110i	$0.418136\pi$
$14$	−1.93309	−	1.80642i	−0.516640	−	0.482787i
$15$		0			0
$16$	0.0747301	+	0.997204i	0.0186825	+	0.249301i
$17$	−1.68804	−	0.520691i	−0.409409	−	0.126286i	0.0832078	−	0.996532i	$-0.473483\pi$
$17$	−1.68804	−	0.520691i	−0.409409	−	0.126286i	−0.492617	+	0.870246i	$0.663960\pi$
$18$		0			0
$19$	−6.29755	+	3.63589i	−1.44476	+	0.834131i	−0.998162	−	0.0606052i	$-0.980697\pi$
$19$	−6.29755	+	3.63589i	−1.44476	+	0.834131i	−0.446595	+	0.894736i	$0.647364\pi$
$20$	−0.440897	−	1.93170i	−0.0985876	−	0.431940i
$21$		0			0
$22$	−1.25197	+	5.48525i	−0.266921	+	1.16946i
$23$	1.94874	+	6.31765i	0.406340	+	1.31732i	0.895474	+	0.445113i	$0.146837\pi$
$23$	1.94874	+	6.31765i	0.406340	+	1.31732i	−0.489134	+	0.872209i	$0.662687\pi$
$24$		0			0
$25$	−0.392435	−	0.999907i	−0.0784869	−	0.199981i
$26$	−2.78468	+	0.858960i	−0.546121	+	0.168456i
$27$		0			0
$28$	−1.13950	−	2.38779i	−0.215345	−	0.451250i
$29$	8.15398	−	1.86109i	1.51416	−	0.345596i	0.616877	−	0.787060i	$-0.288398\pi$
$29$	8.15398	−	1.86109i	1.51416	−	0.345596i	0.897279	+	0.441464i	$0.145541\pi$
$30$		0			0
$31$	3.38676	+	1.95535i	0.608280	+	0.351190i	0.772292	−	0.635268i	$-0.219110\pi$
$31$	3.38676	+	1.95535i	0.608280	+	0.351190i	−0.164012	+	0.986458i	$0.552444\pi$
$32$	−0.294755	+	0.955573i	−0.0521058	+	0.168923i
$33$		0			0
$34$	−1.38112	−	1.10141i	−0.236860	−	0.188890i
$35$	2.93769	+	4.34176i	0.496561	+	0.733891i
$36$		0			0
$37$	0.211701	−	0.196430i	0.0348035	−	0.0322929i	−0.662579	−	0.748992i	$-0.730538\pi$
$37$	0.211701	−	0.196430i	0.0348035	−	0.0322929i	0.697383	+	0.716699i	$0.254348\pi$
$38$	−7.19056	+	1.08380i	−1.16646	+	0.175816i
$39$		0			0
$40$	0.295308	−	1.95924i	0.0466924	−	0.309784i
$41$	−9.79045	+	4.71483i	−1.52901	+	0.736333i	−0.994089	−	0.108569i	$-0.965373\pi$
$41$	−9.79045	+	4.71483i	−1.52901	+	0.736333i	−0.534922	+	0.844902i	$0.679659\pi$
$42$		0			0
$43$	−8.98886	−	4.32881i	−1.37079	−	0.660137i	−0.403774	−	0.914859i	$-0.632302\pi$
$43$	−8.98886	−	4.32881i	−1.37079	−	0.660137i	−0.967014	+	0.254722i	$0.918016\pi$
$44$	−3.16941	+	4.64868i	−0.477807	+	0.700814i
$45$		0			0
$46$	−0.494069	+	6.59289i	−0.0728465	+	0.972069i
$47$	−2.58457	+	6.58538i	−0.376999	+	0.960577i	0.608902	+	0.793245i	$0.291610\pi$
$47$	−2.58457	+	6.58538i	−0.376999	+	0.960577i	−0.985901	+	0.167331i	$0.946485\pi$
$48$		0			0
$49$	5.09752	+	4.79743i	0.728217	+	0.685347i
$50$		−	1.07416i		−	0.151909i
$51$		0			0
$52$	−2.90600	−	0.217774i	−0.402989	−	0.0301999i
$53$	−2.38375	+	2.56907i	−0.327433	+	0.352889i	−0.875217	−	0.483731i	$-0.839281\pi$
$53$	−2.38375	+	2.56907i	−0.327433	+	0.352889i	0.547784	+	0.836620i	$0.315472\pi$
$54$		0			0
$55$	4.83686	−	10.0438i	0.652202	−	1.35431i
$56$	−0.188374	−	2.63904i	−0.0251725	−	0.352656i
$57$		0			0
$58$	8.27026	+	1.24654i	1.08594	+	0.163679i
$59$	11.4492	−	7.80592i	1.49056	−	1.01624i	0.502087	−	0.864817i	$-0.332566\pi$
$59$	11.4492	−	7.80592i	1.49056	−	1.01624i	0.988468	−	0.151427i	$-0.0483868\pi$
$60$		0			0
$61$	−3.85220	−	4.15169i	−0.493224	−	0.531569i	0.436560	−	0.899675i	$-0.356197\pi$
$61$	−3.85220	−	4.15169i	−0.493224	−	0.531569i	−0.929784	+	0.368106i	$0.880006\pi$
$62$	2.43828	+	3.05750i	0.309661	+	0.388303i
$63$		0			0
$64$	−0.623490	+	0.781831i	−0.0779362	+	0.0977289i
$65$	5.75787	−	0.431493i	0.714176	−	0.0535201i
$66$		0			0
$67$	3.06901	−	5.31569i	0.374940	−	0.649415i	−0.615378	−	0.788232i	$-0.710997\pi$
$67$	3.06901	−	5.31569i	0.374940	−	0.649415i	0.990318	+	0.138817i	$0.0443301\pi$
$68$	−0.883260	−	1.52985i	−0.107111	−	0.185522i
$69$		0			0
$70$	1.14840	+	5.11489i	0.137260	+	0.611346i
$71$	−4.16730	−	0.951159i	−0.494567	−	0.112882i	−0.0320397	−	0.999487i	$-0.510200\pi$
$71$	−4.16730	−	0.951159i	−0.494567	−	0.112882i	−0.462528	+	0.886605i	$0.653057\pi$
$72$		0			0
$73$	−8.67775	+	3.40576i	−1.01565	+	0.398615i	−0.814014	−	0.580845i	$-0.802722\pi$
$73$	−8.67775	+	3.40576i	−1.01565	+	0.398615i	−0.201639	+	0.979460i	$0.564627\pi$
$74$	0.268831	−	0.105508i	0.0312510	−	0.0122651i
$75$		0			0
$76$	−7.08947	−	1.61812i	−0.813217	−	0.185612i
$77$	3.36378	−	14.5008i	0.383338	−	1.65252i
$78$		0			0
$79$	−5.42299	−	9.39290i	−0.610134	−	1.05678i	−0.991217	−	0.132243i	$-0.957782\pi$
$79$	−5.42299	−	9.39290i	−0.610134	−	1.05678i	0.381083	−	0.924541i	$-0.375551\pi$
$80$	0.990687	−	1.71592i	0.110762	−	0.191846i
$81$		0			0
$82$	−10.8362	+	0.812060i	−1.19666	+	0.0896770i
$83$	4.38954	−	5.50431i	0.481814	−	0.604176i	−0.480205	−	0.877156i	$-0.659438\pi$
$83$	4.38954	−	5.50431i	0.481814	−	0.604176i	0.962020	+	0.272980i	$0.0880093\pi$
$84$		0			0
$85$	2.18230	+	2.73652i	0.236703	+	0.296817i
$86$	−6.78600	−	7.31357i	−0.731754	−	0.788643i
$87$		0			0
$88$	−4.64868	+	3.16941i	−0.495551	+	0.337861i
$89$	11.0890	+	1.67140i	1.17543	+	0.177168i	0.707577	−	0.706636i	$-0.249788\pi$
$89$	11.0890	+	1.67140i	1.17543	+	0.177168i	0.467856	+	0.883805i	$0.345026\pi$
$90$		0			0
$91$	7.37557	−	2.24649i	0.773170	−	0.235496i
$92$	−2.86857	+	5.95665i	−0.299069	+	0.621023i
$93$		0			0
$94$	−4.81182	+	5.18591i	−0.496301	+	0.534886i
$95$	14.3678	+	1.07672i	1.47411	+	0.110469i
$96$		0			0
$97$		−	9.55626i		−	0.970291i	−0.874433	−	0.485145i	$-0.838767\pi$
$97$		−	9.55626i		−	0.970291i	0.874433	−	0.485145i	$-0.161233\pi$
$98$	2.99245	+	6.32813i	0.302283	+	0.639238i
$99$		0			0
$100$	0.392435	−	0.999907i	0.0392435	−	0.0999907i
$101$	0.546464	−	7.29205i	0.0543752	−	0.725586i	−0.901681	−	0.432402i	$-0.857666\pi$
$101$	0.546464	−	7.29205i	0.0543752	−	0.725586i	0.956056	−	0.293184i	$-0.0947148\pi$
$102$		0			0
$103$	−0.674705	+	0.989610i	−0.0664806	+	0.0975092i	−0.858039	−	0.513584i	$-0.828318\pi$
$103$	−0.674705	+	0.989610i	−0.0664806	+	0.0975092i	0.791559	+	0.611093i	$0.209270\pi$
$104$	−2.62556	−	1.26440i	−0.257457	−	0.123985i
$105$		0			0
$106$	−3.15755	+	1.52060i	−0.306689	+	0.147694i
$107$	−2.37255	+	15.7409i	−0.229363	+	1.52173i	0.516883	+	0.856056i	$0.327092\pi$
$107$	−2.37255	+	15.7409i	−0.229363	+	1.52173i	−0.746246	+	0.665670i	$0.768146\pi$
$108$		0			0
$109$	6.03223	−	0.909213i	0.577783	−	0.0870868i	0.146352	−	0.989233i	$-0.453247\pi$
$109$	6.03223	−	0.909213i	0.577783	−	0.0870868i	0.431431	+	0.902146i	$0.358009\pi$
$110$	8.17193	−	7.58245i	0.779163	−	0.722958i
$111$		0			0
$112$	0.788796	−	2.52543i	0.0745342	−	0.238631i
$113$	−5.93362	−	4.73190i	−0.558188	−	0.445140i	0.303317	−	0.952890i	$-0.401906\pi$
$113$	−5.93362	−	4.73190i	−0.558188	−	0.445140i	−0.861505	+	0.507750i	$0.830477\pi$
$114$		0			0
$115$	3.86118	−	12.5176i	0.360057	−	1.16728i
$116$	7.24315	+	4.18184i	0.672510	+	0.388274i
$117$		0			0
$118$	13.5096	−	3.08347i	1.24366	−	0.283856i
$119$	3.64376	+	2.92697i	0.334023	+	0.268315i
$120$		0			0
$121$	−19.7377	+	6.08828i	−1.79434	+	0.553480i
$122$	−2.06913	−	5.27207i	−0.187331	−	0.477310i
$123$		0			0
$124$	1.15270	+	3.73695i	0.103515	+	0.335588i
$125$	−2.67808	+	11.7334i	−0.239535	+	1.04947i
$126$		0			0
$127$	4.54324	+	19.9052i	0.403147	+	1.76630i	0.614524	+	0.788898i	$0.289348\pi$
$127$	4.54324	+	19.9052i	0.403147	+	1.76630i	−0.211376	+	0.977405i	$0.567795\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	5.51749	+	1.70192i	0.483916	+	0.149268i
$131$	0.0646252	+	0.862363i	0.00564633	+	0.0753450i	0.999315	−	0.0370042i	$-0.0117815\pi$
$131$	0.0646252	+	0.862363i	0.00564633	+	0.0753450i	−0.993669	+	0.112349i	$0.964162\pi$
$132$		0			0
$133$	19.0345	−	2.80009i	1.65050	−	0.242799i
$134$	4.79890	−	3.82700i	0.414562	−	0.330602i
$135$		0			0
$136$	−0.263286	−	1.74679i	−0.0225766	−	0.149786i
$137$	1.79241	+	2.62898i	0.153136	+	0.224609i	0.895139	−	0.445788i	$-0.147076\pi$
$137$	1.79241	+	2.62898i	0.153136	+	0.224609i	−0.742003	+	0.670397i	$0.766124\pi$
$138$		0			0
$139$	4.62497	+	9.60384i	0.392285	+	0.814587i	0.999794	+	0.0202752i	$0.00645425\pi$
$139$	4.62497	+	9.60384i	0.392285	+	0.814587i	−0.607510	+	0.794312i	$0.707831\pi$
$140$	−0.799663	+	5.18087i	−0.0675838	+	0.437863i
$141$		0			0
$142$	−3.53173	−	2.40789i	−0.296376	−	0.202066i
$143$	−12.0190	−	11.1520i	−1.00508	−	0.932581i
$144$		0			0
$145$	−15.4260	−	6.05427i	−1.28106	−	0.502780i
$146$	−9.32215			−0.771507
$147$		0			0
$148$	0.288794			0.0237387
$149$	1.71769	+	0.674143i	0.140719	+	0.0552280i	0.434655	−	0.900597i	$-0.356870\pi$
$149$	1.71769	+	0.674143i	0.140719	+	0.0552280i	−0.293937	+	0.955825i	$0.594965\pi$
$150$		0			0
$151$	17.1903	+	15.9503i	1.39893	+	1.29802i	0.902991	+	0.429658i	$0.141366\pi$
$151$	17.1903	+	15.9503i	1.39893	+	1.29802i	0.495938	+	0.868358i	$0.334824\pi$
$152$	−6.00823	−	4.09634i	−0.487332	−	0.332257i
$153$		0			0
$154$	8.42898	−	12.2695i	0.679227	−	0.988702i
$155$	−3.36196	−	6.98119i	−0.270039	−	0.560743i
$156$		0			0
$157$	−3.19585	−	4.68745i	−0.255056	−	0.374099i	0.677259	−	0.735744i	$-0.263168\pi$
$157$	−3.19585	−	4.68745i	−0.255056	−	0.374099i	−0.932316	+	0.361645i	$0.882215\pi$
$158$	−1.61651	−	10.7248i	−0.128603	−	0.853223i
$159$		0			0
$160$	1.54910	−	1.23537i	0.122467	−	0.0976643i
$161$	1.36894	−	17.4384i	0.107888	−	1.37434i
$162$		0			0
$163$	−1.45441	−	19.4077i	−0.113918	−	1.52013i	−0.702495	−	0.711689i	$-0.747930\pi$
$163$	−1.45441	−	19.4077i	−0.113918	−	1.52013i	0.588577	−	0.808442i	$-0.299689\pi$
$164$	−10.3838	−	3.20298i	−0.810839	−	0.250111i
$165$		0			0
$166$	6.09705	−	3.52014i	0.473223	−	0.273216i
$167$	4.13038	+	18.0964i	0.319619	+	1.40034i	0.838223	+	0.545327i	$0.183594\pi$
$167$	4.13038	+	18.0964i	0.319619	+	1.40034i	−0.518605	+	0.855014i	$0.673548\pi$
$168$		0			0
$169$	−1.00307	+	4.39473i	−0.0771591	+	0.338056i
$170$	1.03168	+	3.34463i	0.0791264	+	0.256522i
$171$		0			0
$172$	−3.64497	−	9.28722i	−0.277926	−	0.708144i
$173$	−0.144414	+	0.0445457i	−0.0109796	+	0.00338675i	−0.300240	−	0.953864i	$-0.597067\pi$
$173$	−0.144414	+	0.0445457i	−0.0109796	+	0.00338675i	0.289261	+	0.957250i	$0.406591\pi$
$174$		0			0
$175$	−0.0100633	+	2.84194i	−0.000760711	+	0.214831i
$176$	−5.48525	+	1.25197i	−0.413466	+	0.0943710i
$177$		0			0
$178$	9.71184	+	5.60713i	0.727933	+	0.420272i
$179$	1.60449	−	5.20164i	0.119925	−	0.388789i	−0.875628	−	0.482986i	$-0.839552\pi$
$179$	1.60449	−	5.20164i	0.119925	−	0.388789i	0.995554	+	0.0941971i	$0.0300284\pi$
$180$		0			0
$181$	6.81760	+	5.43686i	0.506748	+	0.404118i	0.843214	−	0.537577i	$-0.180660\pi$
$181$	6.81760	+	5.43686i	0.506748	+	0.404118i	−0.336466	+	0.941696i	$0.609232\pi$
$182$	7.68646	+	0.603398i	0.569758	+	0.0447269i
$183$		0			0
$184$	−4.84648	+	4.49688i	−0.357288	+	0.331514i
$185$	−0.565818	+	0.0852834i	−0.0415998	+	0.00627016i
$186$		0			0
$187$	1.48133	−	9.82798i	0.108326	−	0.718693i
$188$	−6.37382	+	3.06947i	−0.464859	+	0.223864i
$189$		0			0
$190$	12.9813	+	6.25145i	0.941760	+	0.453528i
$191$	5.48231	−	8.04107i	0.396686	−	0.581832i	−0.574986	−	0.818163i	$-0.694993\pi$
$191$	5.48231	−	8.04107i	0.396686	−	0.581832i	0.971673	+	0.236331i	$0.0759451\pi$
$192$		0			0
$193$	−1.52829	+	20.3936i	−0.110009	+	1.46797i	0.620039	+	0.784571i	$0.287117\pi$
$193$	−1.52829	+	20.3936i	−0.110009	+	1.46797i	−0.730048	+	0.683396i	$0.760502\pi$
$194$	3.49129	−	8.89567i	0.250660	−	0.638672i
$195$		0			0
$196$	0.473663	+	6.98396i	0.0338331	+	0.498854i
$197$			8.17589i			0.582508i	0.956646	+	0.291254i	$0.0940725\pi$
$197$			8.17589i			0.582508i	−0.956646	+	0.291254i	$0.905927\pi$
$198$		0			0
$199$	27.2666	+	2.04335i	1.93288	+	0.144849i	0.984858	−	0.173365i	$-0.0554640\pi$
$199$	27.2666	+	2.04335i	1.93288	+	0.144849i	0.948019	+	0.318214i	$0.103083\pi$
$200$	0.730614	−	0.787415i	0.0516622	−	0.0556786i
$201$		0			0
$202$	3.17277	−	6.58833i	0.223236	−	0.463553i
$203$	−21.8692	−	3.37550i	−1.53492	−	0.236913i
$204$		0			0
$205$	21.2903	+	3.20899i	1.48698	+	0.224126i
$206$	−0.989610	+	0.674705i	−0.0689494	+	0.0470089i
$207$		0			0
$208$	−1.98212	−	2.13622i	−0.137436	−	0.148120i
$209$	−25.5090	−	31.9873i	−1.76450	−	2.21261i
$210$		0			0
$211$	1.48202	−	1.85840i	0.102027	−	0.127937i	−0.728197	−	0.685368i	$-0.759641\pi$
$211$	1.48202	−	1.85840i	0.102027	−	0.127937i	0.830224	+	0.557431i	$0.188213\pi$
$212$	−3.49482	+	0.261901i	−0.240025	+	0.0179874i
$213$		0			0
$214$	−7.95933	+	13.7860i	−0.544089	+	0.942389i
$215$	9.88397	+	17.1195i	0.674081	+	1.16754i
$216$		0			0
$217$	−6.42239	−	8.11218i	−0.435980	−	0.550691i
$218$	5.94742	+	1.35746i	0.402810	+	0.0919387i
$219$		0			0
$220$	10.3772	−	4.07276i	0.699632	−	0.274585i
$221$	4.79204	−	1.88074i	0.322348	−	0.126512i
$222$		0			0
$223$	−1.19798	−	0.273431i	−0.0802225	−	0.0183103i	0.182221	−	0.983258i	$-0.441671\pi$
$223$	−1.19798	−	0.273431i	−0.0802225	−	0.0183103i	−0.262444	+	0.964947i	$0.584528\pi$
$224$	1.65691	−	2.06268i	0.110707	−	0.137818i
$225$		0			0
$226$	−3.79469	−	6.57260i	−0.252419	−	0.437203i
$227$	0.369513	−	0.640016i	0.0245255	−	0.0424793i	−0.853502	−	0.521089i	$-0.825526\pi$
$227$	0.369513	−	0.640016i	0.0245255	−	0.0424793i	0.878028	+	0.478610i	$0.158859\pi$
$228$		0			0
$229$	0.609539	−	0.0456786i	0.0402795	−	0.00301853i	−0.0545751	−	0.998510i	$-0.517380\pi$
$229$	0.609539	−	0.0456786i	0.0402795	−	0.00301853i	0.0948546	+	0.995491i	$0.469761\pi$
$230$	8.16747	−	10.2417i	0.538547	−	0.675317i
$231$		0			0
$232$	5.21466	+	6.53898i	0.342359	+	0.429305i
$233$	−2.32897	−	2.51003i	−0.152576	−	0.164437i	0.652139	−	0.758100i	$-0.273872\pi$
$233$	−2.32897	−	2.51003i	−0.152576	−	0.164437i	−0.804714	+	0.593662i	$0.797682\pi$
$234$		0			0
$235$	11.5814	−	7.89608i	0.755489	−	0.515084i
$236$	13.7022	+	2.06528i	0.891938	+	0.134438i
$237$		0			0
$238$	2.32254	+	4.05585i	0.150548	+	0.262902i
$239$	−3.01310	+	6.25677i	−0.194901	+	0.404717i	−0.975401	−	0.220440i	$-0.929251\pi$
$239$	−3.01310	+	6.25677i	−0.194901	+	0.404717i	0.780499	+	0.625157i	$0.214965\pi$
$240$		0			0
$241$	14.9791	−	16.1436i	0.964887	−	1.03990i	−0.0342928	−	0.999412i	$-0.510918\pi$
$241$	14.9791	−	16.1436i	0.964887	−	1.03990i	0.999180	−	0.0404893i	$-0.0128917\pi$
$242$	−20.5976	−	1.54358i	−1.32407	−	0.0992250i
$243$		0			0
$244$		−	5.66357i		−	0.362573i
$245$	−2.99044	−	13.5434i	−0.191052	−	0.865256i
$246$		0			0
$247$	7.74196	−	19.7262i	0.492609	−	1.25515i
$248$	−0.292246	+	3.89975i	−0.0185577	+	0.247635i
$249$		0			0
$250$	−6.77966	+	9.94393i	−0.428783	+	0.628909i
$251$	−10.5792	−	5.09466i	−0.667751	−	0.321572i	0.0691172	−	0.997609i	$-0.477982\pi$
$251$	−10.5792	−	5.09466i	−0.667751	−	0.321572i	−0.736868	+	0.676037i	$0.763696\pi$
$252$		0			0
$253$	−33.5140	+	16.1395i	−2.10700	+	1.01468i
$254$	−3.04301	+	20.1891i	−0.190936	+	1.26678i
$255$		0			0
$256$	−0.988831	+	0.149042i	−0.0618019	+	0.00931514i
$257$	−7.77023	+	7.20972i	−0.484694	+	0.449730i	−0.884274	−	0.466968i	$-0.845346\pi$
$257$	−7.77023	+	7.20972i	−0.484694	+	0.449730i	0.399581	+	0.916698i	$0.369156\pi$
$258$		0			0
$259$	−0.712244	+	0.276629i	−0.0442567	+	0.0171889i
$260$	4.51431	+	3.60004i	0.279965	+	0.223265i
$261$		0			0
$262$	−0.254899	+	0.826362i	−0.0157477	+	0.0510528i
$263$	0.771865	+	0.445636i	0.0475952	+	0.0274791i	0.523609	−	0.851959i	$-0.324585\pi$
$263$	0.771865	+	0.445636i	0.0475952	+	0.0274791i	−0.476014	+	0.879438i	$0.657919\pi$
$264$		0			0
$265$	6.76986	−	1.54518i	0.415869	−	0.0949194i
$266$	18.7417	+	4.34755i	1.14913	+	0.266565i
$267$		0			0
$268$	5.86533	−	1.80922i	0.358282	−	0.110515i
$269$	5.33362	+	13.5898i	0.325197	+	0.828588i	0.996197	+	0.0871305i	$0.0277697\pi$
$269$	5.33362	+	13.5898i	0.325197	+	0.828588i	−0.671000	+	0.741457i	$0.734135\pi$
$270$		0			0
$271$	4.62715	+	15.0009i	0.281080	+	0.911238i	0.980499	+	0.196526i	$0.0629660\pi$
$271$	4.62715	+	15.0009i	0.281080	+	0.911238i	−0.699419	+	0.714712i	$0.746558\pi$
$272$	0.393088	−	1.72223i	0.0238344	−	0.104425i
$273$		0			0
$274$	0.708032	+	3.10209i	0.0427738	+	0.187404i
$275$	5.23387	−	3.02178i	0.315614	−	0.182220i
$276$		0			0
$277$	−3.91052	−	1.20623i	−0.234960	−	0.0724756i	0.175039	−	0.984561i	$-0.443995\pi$
$277$	−3.91052	−	1.20623i	−0.234960	−	0.0724756i	−0.409999	+	0.912086i	$0.634471\pi$
$278$	0.796583	+	10.6297i	0.0477759	+	0.637524i
$279$		0			0
$280$	−2.63717	+	4.53059i	−0.157601	+	0.270754i
$281$	2.06520	−	1.64694i	0.123199	−	0.0982481i	−0.559952	−	0.828525i	$-0.689180\pi$
$281$	2.06520	−	1.64694i	0.123199	−	0.0982481i	0.683151	+	0.730277i	$0.260609\pi$
$282$		0			0
$283$	−1.60937	−	10.6775i	−0.0956673	−	0.634711i	−0.984355	−	0.176198i	$-0.943620\pi$
$283$	−1.60937	−	10.6775i	−0.0956673	−	0.634711i	0.888688	−	0.458513i	$-0.151618\pi$
$284$	−2.40789	−	3.53173i	−0.142882	−	0.209570i
$285$		0			0
$286$	−7.11391	−	14.7722i	−0.420655	−	0.873498i
$287$	28.6773	−	2.04698i	1.69277	−	0.120829i
$288$		0			0
$289$	−11.4677	−	7.81855i	−0.674571	−	0.459915i
$290$	−12.1478	−	11.2715i	−0.713344	−	0.661887i
$291$		0			0
$292$	−8.67775	−	3.40576i	−0.507827	−	0.199307i
$293$	−18.8598			−1.10180			−0.550901	−	0.834571i	$-0.685716\pi$
$293$	−18.8598			−1.10180			−0.550901	+	0.834571i	$0.685716\pi$
$294$		0			0
$295$	−27.4559			−1.59854
$296$	0.268831	+	0.105508i	0.0156255	+	0.00613255i
$297$		0			0
$298$	1.35266	+	1.25508i	0.0783575	+	0.0727051i
$299$	−15.9188	−	10.8532i	−0.920605	−	0.627658i
$300$		0			0
$301$	17.8855	+	19.4134i	1.03090	+	1.11897i
$302$	10.1747	+	21.1280i	0.585490	+	1.21578i
$303$		0			0
$304$	−4.09634	−	6.00823i	−0.234941	−	0.344596i
$305$	1.67250	+	11.0963i	0.0957670	+	0.635373i
$306$		0			0
$307$	−20.5527	+	16.3903i	−1.17301	+	0.935442i	−0.998786	−	0.0492650i	$-0.984312\pi$
$307$	−20.5527	+	16.3903i	−1.17301	+	0.935442i	−0.174221	+	0.984707i	$0.555741\pi$
$308$	12.3289	−	8.34188i	0.702502	−	0.475323i
$309$		0			0
$310$	−0.579049	−	7.72687i	−0.0328878	−	0.438857i
$311$	0.340692	+	0.105090i	0.0193189	+	0.00595908i	0.304400	−	0.952544i	$-0.401544\pi$
$311$	0.340692	+	0.105090i	0.0193189	+	0.00595908i	−0.285081	+	0.958504i	$0.592020\pi$
$312$		0			0
$313$	−9.04486	+	5.22205i	−0.511246	+	0.295168i	−0.733346	−	0.679856i	$-0.762042\pi$
$313$	−9.04486	+	5.22205i	−0.511246	+	0.295168i	0.222100	+	0.975024i	$0.428709\pi$
$314$	−1.26241	−	5.53100i	−0.0712421	−	0.312132i
$315$		0			0
$316$	2.41346	−	10.5741i	0.135768	−	0.594837i
$317$	−5.84383	−	18.9452i	−0.328222	−	1.06407i	−0.957873	−	0.287192i	$-0.907278\pi$
$317$	−5.84383	−	18.9452i	−0.328222	−	1.06407i	0.629651	−	0.776878i	$-0.283198\pi$
$318$		0			0
$319$	17.1917	+	43.8038i	0.962551	+	2.45254i
$320$	1.89335	−	0.584020i	0.105841	−	0.0326477i
$321$		0			0
$322$	7.64528	−	15.7328i	0.426055	−	0.876757i
$323$	12.5237	−	2.85845i	0.696836	−	0.159048i
$324$		0			0
$325$	2.71088	+	1.56513i	0.150373	+	0.0868178i
$326$	5.73657	−	18.5975i	0.317719	−	1.03002i
$327$		0			0
$328$	−8.49583	−	6.77520i	−0.469104	−	0.374098i
$329$	12.7794	−	13.6755i	0.704550	−	0.753953i
$330$		0			0
$331$	−16.4376	+	15.2519i	−0.903494	+	0.838320i	−0.987415	−	0.158152i	$-0.949446\pi$
$331$	−16.4376	+	15.2519i	−0.903494	+	0.838320i	0.0839203	+	0.996472i	$0.473256\pi$
$332$	6.96164	−	1.04930i	0.382070	−	0.0575877i
$333$		0			0
$334$	−2.76649	+	18.3545i	−0.151376	+	1.00431i
$335$	−10.9573	+	5.27677i	−0.598663	+	0.288301i
$336$		0			0
$337$	−2.10218	−	1.01236i	−0.114513	−	0.0551465i	0.375750	−	0.926721i	$-0.377385\pi$
$337$	−2.10218	−	1.01236i	−0.114513	−	0.0551465i	−0.490263	+	0.871574i	$0.663099\pi$
$338$	−2.53931	+	3.72448i	−0.138120	+	0.202585i
$339$		0			0
$340$	−0.261565	+	3.49035i	−0.0141854	+	0.189291i
$341$	−8.03851	+	20.4818i	−0.435310	+	1.10915i
$342$		0			0
$343$	−7.85793	−	16.7706i	−0.424289	−	0.905527i
$344$		−	9.97688i		−	0.537918i
$345$		0			0
$346$	−0.150705	−	0.0112938i	−0.00810196	−	0.000607158i
$347$	2.68029	−	2.88866i	0.143885	−	0.155072i	−0.656997	−	0.753893i	$-0.728174\pi$
$347$	2.68029	−	2.88866i	0.143885	−	0.155072i	0.800882	+	0.598822i	$0.204364\pi$
$348$		0			0
$349$	0.427842	−	0.888422i	0.0229018	−	0.0475562i	−0.889204	−	0.457511i	$-0.848741\pi$
$349$	0.427842	−	0.888422i	0.0229018	−	0.0475562i	0.912106	+	0.409955i	$0.134455\pi$
$350$	−1.04765	+	2.64181i	−0.0559990	+	0.141211i
$351$		0			0
$352$	−5.56347	−	0.838558i	−0.296534	−	0.0446953i
$353$	−4.28346	+	2.92041i	−0.227985	+	0.155438i	−0.671926	−	0.740619i	$-0.734533\pi$
$353$	−4.28346	+	2.92041i	−0.227985	+	0.155438i	0.443940	+	0.896056i	$0.353580\pi$
$354$		0			0
$355$	5.76060	+	6.20845i	0.305741	+	0.329510i
$356$	6.99198	+	8.76767i	0.370574	+	0.464685i
$357$		0			0
$358$	3.39395	−	4.25588i	0.179376	−	0.224930i
$359$	−23.2193	+	1.74004i	−1.22547	+	0.0918360i	−0.671692	−	0.740831i	$-0.734432\pi$
$359$	−23.2193	+	1.74004i	−1.22547	+	0.0918360i	−0.553774	+	0.832667i	$0.686813\pi$
$360$		0			0
$361$	16.9394	−	29.3399i	0.891549	−	1.54421i
$362$	4.36002	+	7.55177i	0.229158	+	0.396912i
$363$		0			0
$364$	6.93468	+	3.36987i	0.363476	+	0.176629i
$365$	18.0076	+	4.11011i	0.942559	+	0.215133i
$366$		0			0
$367$	28.3620	−	11.1313i	1.48048	−	0.581048i	0.518725	−	0.854941i	$-0.326407\pi$
$367$	28.3620	−	11.1313i	1.48048	−	0.581048i	0.961760	+	0.273894i	$0.0883116\pi$
$368$	−6.15436	+	2.41541i	−0.320818	+	0.125912i
$369$		0			0
$370$	−0.557863	−	0.127329i	−0.0290019	−	0.00661950i
$371$	8.36829	−	3.99352i	0.434460	−	0.207333i
$372$		0			0
$373$	−12.0734	−	20.9118i	−0.625139	−	1.08277i	−0.988514	−	0.151130i	$-0.951709\pi$
$373$	−12.0734	−	20.9118i	−0.625139	−	1.08277i	0.363375	−	0.931643i	$-0.381624\pi$
$374$	4.96949	−	8.60742i	0.256966	−	0.445079i
$375$		0			0
$376$	−7.05463	+	0.528671i	−0.363815	+	0.0272641i
$377$	−15.1963	+	19.0556i	−0.782649	+	0.981411i
$378$		0			0
$379$	13.6961	+	17.1744i	0.703523	+	0.882190i	0.997281	−	0.0736898i	$-0.0234775\pi$
$379$	13.6961	+	17.1744i	0.703523	+	0.882190i	−0.293758	+	0.955880i	$0.594906\pi$
$380$	9.80001	+	10.5619i	0.502730	+	0.541814i
$381$		0			0
$382$	8.04107	−	5.48231i	0.411417	−	0.280499i
$383$	7.14212	+	1.07650i	0.364945	+	0.0550066i	0.328955	−	0.944346i	$-0.393303\pi$
$383$	7.14212	+	1.07650i	0.364945	+	0.0550066i	0.0359899	+	0.999352i	$0.488542\pi$
$384$		0			0
$385$	−21.6918	+	19.9846i	−1.10552	+	1.01851i
$386$	−8.87328	+	18.4256i	−0.451638	+	0.937836i
$387$		0			0
$388$	6.49991	−	7.00523i	0.329983	−	0.355637i
$389$	−11.0566	−	0.828575i	−0.560590	−	0.0420104i	−0.208578	−	0.978006i	$-0.566883\pi$
$389$	−11.0566	−	0.828575i	−0.560590	−	0.0420104i	−0.352012	+	0.935995i	$0.614502\pi$
$390$		0			0
$391$		−	11.6791i		−	0.590639i
$392$	−2.11061	+	6.67423i	−0.106602	+	0.337100i
$393$		0			0
$394$	−2.98699	+	7.61072i	−0.150482	+	0.383423i
$395$	−1.60595	+	21.4299i	−0.0808039	+	1.07825i
$396$		0			0
$397$	−5.89844	+	8.65142i	−0.296034	+	0.434202i	−0.945223	−	0.326425i	$-0.894156\pi$
$397$	−5.89844	+	8.65142i	−0.296034	+	0.434202i	0.649189	+	0.760627i	$0.275108\pi$
$398$	24.6352	+	11.8637i	1.23485	+	0.594673i
$399$		0			0
$400$	0.967784	−	0.466060i	0.0483892	−	0.0233030i
$401$	0.211014	−	1.39999i	0.0105375	−	0.0699120i	−0.982944	−	0.183905i	$-0.941126\pi$
$401$	0.211014	−	1.39999i	0.0105375	−	0.0699120i	0.993482	+	0.113993i	$0.0363642\pi$
$402$		0			0
$403$	−11.2690	+	1.69853i	−0.561351	+	0.0846100i
$404$	5.36044	−	4.97376i	0.266692	−	0.247454i
$405$		0			0
$406$	−19.1243	−	11.1319i	−0.949122	−	0.552466i
$407$	1.27036	+	1.01308i	0.0629692	+	0.0502163i
$408$		0			0
$409$	−10.8256	+	35.0956i	−0.535289	+	1.73537i	0.132662	+	0.991161i	$0.457647\pi$
$409$	−10.8256	+	35.0956i	−0.535289	+	1.73537i	−0.667952	+	0.744205i	$0.732829\pi$
$410$	18.6462	+	10.7654i	0.920869	+	0.531664i
$411$		0			0
$412$	−1.16770	+	0.266520i	−0.0575284	+	0.0131305i
$413$	−35.7716	+	8.03148i	−1.76021	+	0.395203i
$414$		0			0
$415$	−13.3297	+	4.11166i	−0.654328	+	0.201833i
$416$	−1.06466	−	2.71270i	−0.0521991	−	0.133001i
$417$		0			0
$418$	−12.0594	−	39.0957i	−0.589845	−	1.91223i
$419$	−1.65829	+	7.26544i	−0.0810128	+	0.354940i	−0.999145	−	0.0413330i	$-0.986840\pi$
$419$	−1.65829	+	7.26544i	−0.0810128	+	0.354940i	0.918133	+	0.396273i	$0.129697\pi$
$420$		0			0
$421$	0.407933	+	1.78727i	0.0198814	+	0.0871063i	0.983895	−	0.178746i	$-0.0572039\pi$
$421$	0.407933	+	1.78727i	0.0198814	+	0.0871063i	−0.964014	+	0.265852i	$0.914347\pi$
$422$	2.05853	−	1.18849i	0.100208	−	0.0578548i
$423$		0			0
$424$	−3.34892	−	1.03300i	−0.162638	−	0.0501672i
$425$	0.141802	+	1.89222i	0.00687841	+	0.0917860i
$426$		0			0
$427$	5.42499	+	13.9679i	0.262534	+	0.675953i
$428$	−12.4457	+	9.92512i	−0.601586	+	0.479749i
$429$		0			0
$430$	2.94626	+	19.5471i	0.142081	+	0.942647i
$431$	14.4572	+	21.2048i	0.696378	+	1.02140i	0.997694	+	0.0678744i	$0.0216217\pi$
$431$	14.4572	+	21.2048i	0.696378	+	1.02140i	−0.301316	+	0.953524i	$0.597426\pi$
$432$		0			0
$433$	−3.04088	−	6.31445i	−0.146135	−	0.303453i	0.815034	−	0.579414i	$-0.196718\pi$
$433$	−3.04088	−	6.31445i	−0.146135	−	0.303453i	−0.961169	+	0.275961i	$0.911004\pi$
$434$	−3.01472	−	9.89777i	−0.144711	−	0.475108i
$435$		0			0
$436$	5.04036	+	3.43646i	0.241389	+	0.164577i
$437$	−35.2426	−	32.7003i	−1.68588	−	1.56427i
$438$		0			0
$439$	−5.86680	−	2.30255i	−0.280007	−	0.109895i	0.221182	−	0.975233i	$-0.429009\pi$
$439$	−5.86680	−	2.30255i	−0.280007	−	0.109895i	−0.501189	+	0.865338i	$0.667104\pi$
$440$	11.1478			0.531452
$441$		0			0
$442$	5.14790			0.244860
$443$	25.3715	+	9.95758i	1.20544	+	0.473099i	0.881140	−	0.472856i	$-0.156777\pi$
$443$	25.3715	+	9.95758i	1.20544	+	0.473099i	0.324297	+	0.945955i	$0.394872\pi$
$444$		0			0
$445$	−16.2882	−	15.1132i	−0.772133	−	0.716434i
$446$	−1.01527	−	0.692200i	−0.0480745	−	0.0327766i
$447$		0			0
$448$	2.29596	−	1.31475i	0.108474	−	0.0621163i
$449$	−3.16053	−	6.56292i	−0.149155	−	0.309723i	0.812983	−	0.582288i	$-0.197842\pi$
$449$	−3.16053	−	6.56292i	−0.149155	−	0.309723i	−0.962137	+	0.272565i	$0.912128\pi$
$450$		0			0
$451$	−34.4407	−	50.5152i	−1.62175	−	2.37867i
$452$	−1.13114	−	7.50462i	−0.0532043	−	0.352988i
$453$		0			0
$454$	0.577794	−	0.460776i	0.0271172	−	0.0216253i
$455$	−14.5819	−	4.55452i	−0.683609	−	0.213519i
$456$		0			0
$457$	−0.754952	−	10.0741i	−0.0353152	−	0.471248i	−0.986624	−	0.163010i	$-0.947880\pi$
$457$	−0.754952	−	10.0741i	−0.0353152	−	0.471248i	0.951309	−	0.308238i	$-0.0997394\pi$
$458$	0.584092	+	0.180168i	0.0272928	+	0.00841872i
$459$		0			0
$460$	11.3446	−	6.54981i	0.528945	−	0.305386i
$461$	−5.23058	−	22.9167i	−0.243613	−	1.06734i	−0.937700	−	0.347446i	$-0.887049\pi$
$461$	−5.23058	−	22.9167i	−0.243613	−	1.06734i	0.694087	−	0.719891i	$-0.255808\pi$
$462$		0			0
$463$	0.164749	−	0.721811i	0.00765652	−	0.0335454i	−0.970955	−	0.239261i	$-0.923095\pi$
$463$	0.164749	−	0.721811i	0.00765652	−	0.0335454i	0.978612	+	0.205715i	$0.0659521\pi$
$464$	2.46524	+	7.99210i	0.114446	+	0.371024i
$465$		0			0
$466$	−1.25096	−	3.18739i	−0.0579495	−	0.147653i
$467$	10.5022	−	3.23950i	0.485984	−	0.149906i	−0.0420739	−	0.999115i	$-0.513396\pi$
$467$	10.5022	−	3.23950i	0.485984	−	0.149906i	0.528058	+	0.849208i	$0.322920\pi$
$468$		0			0
$469$	−12.7325	+	10.0803i	−0.587931	+	0.465463i
$470$	13.6656	−	3.11909i	0.630348	−	0.143873i
$471$		0			0
$472$	12.0005	+	6.92849i	0.552368	+	0.318910i
$473$	16.5455	−	53.6392i	0.760763	−	2.46633i
$474$		0			0
$475$	6.10693	+	4.87011i	0.280205	+	0.223456i
$476$	0.680220	+	4.62401i	0.0311778	+	0.211941i
$477$		0			0
$478$	−5.09068	+	4.72346i	−0.232842	+	0.216046i
$479$	21.6663	−	3.26567i	0.989957	−	0.149212i	0.365953	−	0.930633i	$-0.380743\pi$
$479$	21.6663	−	3.26567i	0.989957	−	0.149212i	0.624004	+	0.781421i	$0.285505\pi$
$480$		0			0
$481$	−0.125432	+	0.832189i	−0.00571922	+	0.0379446i
$482$	19.8416	−	9.55519i	0.903758	−	0.435227i
$483$		0			0
$484$	−18.6099	−	8.96204i	−0.845903	−	0.407365i
$485$	−10.6662	+	15.6444i	−0.484327	+	0.710377i
$486$		0			0
$487$	−0.806541	+	10.7625i	−0.0365479	+	0.487697i	0.948656	+	0.316310i	$0.102444\pi$
$487$	−0.806541	+	10.7625i	−0.0365479	+	0.487697i	−0.985204	+	0.171387i	$0.945175\pi$
$488$	2.06913	−	5.27207i	0.0936653	−	0.238655i
$489$		0			0
$490$	2.16423	−	13.6997i	0.0977701	−	0.618890i
$491$			11.4957i			0.518794i	0.965771	+	0.259397i	$0.0835239\pi$
$491$			11.4957i			0.518794i	−0.965771	+	0.259397i	$0.916476\pi$
$492$		0			0
$493$	−14.7333	−	1.10411i	−0.663553	−	0.0497264i
$494$	14.4136	−	15.5341i	0.648497	−	0.698914i
$495$		0			0
$496$	−1.69678	+	3.52341i	−0.0761879	+	0.158206i
$497$	9.32147	+	6.40374i	0.418125	+	0.287247i
$498$		0			0
$499$	−40.6067	−	6.12048i	−1.81781	−	0.273990i	−0.850202	−	0.526457i	$-0.823520\pi$
$499$	−40.6067	−	6.12048i	−1.81781	−	0.273990i	−0.967606	+	0.252467i	$0.918758\pi$
$500$	−9.94393	+	6.77966i	−0.444706	+	0.303195i
$501$		0			0
$502$	−7.98658	−	8.60748i	−0.356458	−	0.384171i
$503$	19.1535	+	24.0177i	0.854012	+	1.07090i	0.996704	+	0.0811302i	$0.0258530\pi$
$503$	19.1535	+	24.0177i	0.854012	+	1.07090i	−0.142691	+	0.989767i	$0.545576\pi$
$504$		0			0
$505$	−9.03361	+	11.3278i	−0.401990	+	0.504080i
$506$	−37.0937	+	2.77979i	−1.64901	+	0.123577i
$507$		0			0
$508$	−10.2086	+	17.6817i	−0.452932	+	0.784501i
$509$	14.2939	+	24.7578i	0.633567	+	1.09737i	0.986817	+	0.161842i	$0.0517433\pi$
$509$	14.2939	+	24.7578i	0.633567	+	1.09737i	−0.353249	+	0.935529i	$0.614923\pi$
$510$		0			0
$511$	24.6639	+	0.0873346i	1.09107	+	0.00386345i
$512$	−0.974928	−	0.222521i	−0.0430861	−	0.00983413i
$513$		0			0
$514$	−9.86711	+	3.87256i	−0.435220	+	0.170811i
$515$	2.20910	−	0.867008i	0.0973446	−	0.0382049i
$516$		0			0
$517$	−38.8049	−	8.85697i	−1.70664	−	0.389529i
$518$	−0.764073	−	0.00270557i	−0.0335714	−	0.000118876i
$519$		0			0
$520$	2.88701	+	5.00044i	0.126604	+	0.219284i
$521$	9.56740	−	16.5712i	0.419156	−	0.725999i	−0.576699	−	0.816957i	$-0.695660\pi$
$521$	9.56740	−	16.5712i	0.419156	−	0.725999i	0.995855	+	0.0909579i	$0.0289929\pi$
$522$		0			0
$523$	5.28333	−	0.395931i	0.231024	−	0.0173128i	0.0412849	−	0.999147i	$-0.486855\pi$
$523$	5.28333	−	0.395931i	0.231024	−	0.0173128i	0.189739	+	0.981835i	$0.439236\pi$
$524$	−0.539182	+	0.676113i	−0.0235543	+	0.0295362i
$525$		0			0
$526$	0.555699	+	0.696825i	0.0242296	+	0.0303830i
$527$	−4.69884	−	5.06415i	−0.204685	−	0.220598i
$528$		0			0
$529$	−17.1117	+	11.6665i	−0.743986	+	0.507241i
$530$	6.86640	+	1.03494i	0.298257	+	0.0449551i
$531$		0			0
$532$	15.8578	+	10.8941i	0.687523	+	0.472320i
$533$	13.7397	−	28.5308i	0.595133	−	1.23581i
$534$		0			0
$535$	21.4532	−	23.1210i	0.927503	−	0.999610i
$536$	6.12086	+	0.458695i	0.264381	+	0.0198126i
$537$		0			0
$538$			14.5990i			0.629409i
$539$	−22.4158	+	32.3828i	−0.965517	+	1.39483i
$540$		0			0
$541$	−5.20396	+	13.2595i	−0.223736	+	0.570069i	−0.998029	−	0.0627579i	$-0.980010\pi$
$541$	−5.20396	+	13.2595i	−0.223736	+	0.570069i	0.774293	+	0.632827i	$0.218106\pi$
$542$	−1.17314	+	15.6544i	−0.0503905	+	0.672414i
$543$		0			0
$544$	0.995116	−	1.45957i	0.0426652	−	0.0625784i
$545$	−10.8901	−	5.24440i	−0.466481	−	0.224645i
$546$		0			0
$547$	28.1280	−	13.5457i	1.20267	−	0.579173i	0.278231	−	0.960514i	$-0.410252\pi$
$547$	28.1280	−	13.5457i	1.20267	−	0.579173i	0.924434	+	0.381341i	$0.124538\pi$
$548$	−0.474232	+	3.14633i	−0.0202582	+	0.134404i
$549$		0			0
$550$	5.97606	−	0.900745i	0.254820	−	0.0384079i
$551$	−44.5834	+	41.3673i	−1.89931	+	1.76231i
$552$		0			0
$553$	4.17638	+	28.3902i	0.177598	+	1.20728i
$554$	−3.19951	−	2.55152i	−0.135934	−	0.108404i
$555$		0			0
$556$	−3.14193	+	10.1859i	−0.133248	+	0.431978i
$557$	33.6391	+	19.4216i	1.42534	+	0.822918i	0.996748	−	0.0805817i	$-0.0256778\pi$
$557$	33.6391	+	19.4216i	1.42534	+	0.822918i	0.428588	+	0.903500i	$0.359011\pi$
$558$		0			0
$559$	28.3452	−	6.46960i	1.19887	−	0.273635i
$560$	−4.11008	+	3.25394i	−0.173683	+	0.137504i
$561$		0			0
$562$	2.52413	−	0.778591i	0.106474	−	0.0328429i
$563$	4.10832	+	10.4678i	0.173145	+	0.441167i	0.990934	−	0.134352i	$-0.0428954\pi$
$563$	4.10832	+	10.4678i	0.173145	+	0.441167i	−0.817788	+	0.575519i	$0.804800\pi$
$564$		0			0
$565$	4.43235	+	14.3693i	0.186471	+	0.604523i
$566$	2.40280	−	10.5274i	0.100997	−	0.442498i
$567$		0			0
$568$	−0.951159	−	4.16730i	−0.0399097	−	0.174856i
$569$	−14.4407	+	8.33737i	−0.605388	+	0.349521i	−0.771158	−	0.636644i	$-0.780322\pi$
$569$	−14.4407	+	8.33737i	−0.605388	+	0.349521i	0.165770	+	0.986164i	$0.446989\pi$
$570$		0			0
$571$	−19.3279	−	5.96187i	−0.808848	−	0.249496i	−0.137369	−	0.990520i	$-0.543864\pi$
$571$	−19.3279	−	5.96187i	−0.808848	−	0.249496i	−0.671479	+	0.741024i	$0.734341\pi$
$572$	−1.22527	−	16.3501i	−0.0512310	−	0.683630i
$573$		0			0
$574$	27.4428	+	8.57151i	1.14544	+	0.357768i
$575$	5.55231	−	4.42782i	0.231548	−	0.184653i
$576$		0			0
$577$	0.633669	+	4.20412i	0.0263800	+	0.175020i	0.998141	−	0.0609475i	$-0.0194122\pi$
$577$	0.633669	+	4.20412i	0.0263800	+	0.175020i	−0.971761	+	0.235967i	$0.924174\pi$
$578$	−7.81855	−	11.4677i	−0.325209	−	0.476994i
$579$		0			0
$580$	−7.19013	−	14.9305i	−0.298554	−	0.619954i
$581$	−16.1642	+	9.25623i	−0.670603	+	0.384013i
$582$		0			0
$583$	−16.2918	−	11.1076i	−0.674739	−	0.460030i
$584$	−6.83362	−	6.34067i	−0.282777	−	0.262379i
$585$		0			0
$586$	−17.5561	−	6.89026i	−0.725236	−	0.284634i
$587$	7.73865			0.319408			0.159704	−	0.987165i	$-0.448946\pi$
$587$	7.73865			0.319408			0.159704	+	0.987165i	$0.448946\pi$
$588$		0			0
$589$	−28.4377			−1.17175
$590$	−25.5579	−	10.0308i	−1.05220	−	0.412959i
$591$		0			0
$592$	0.211701	+	0.196430i	0.00870087	+	0.00807322i
$593$	10.4169	+	7.10212i	0.427771	+	0.291649i	0.758004	−	0.652250i	$-0.226175\pi$
$593$	10.4169	+	7.10212i	0.427771	+	0.291649i	−0.330233	+	0.943900i	$0.607127\pi$
$594$		0			0
$595$	−2.69822	−	8.85868i	−0.110616	−	0.363170i
$596$	0.800621	+	1.66251i	0.0327947	+	0.0680989i
$597$		0			0
$598$	−10.8532	−	15.9188i	−0.443821	−	0.650966i
$599$	5.00581	+	33.2114i	0.204532	+	1.35698i	0.821598	+	0.570068i	$0.193083\pi$
$599$	5.00581	+	33.2114i	0.204532	+	1.35698i	−0.617066	+	0.786912i	$0.711679\pi$
$600$		0			0
$601$	23.8851	−	19.0477i	0.974293	−	0.776973i	−0.000518858	−	1.00000i	$-0.500165\pi$
$601$	23.8851	−	19.0477i	0.974293	−	0.776973i	0.974812	+	0.223027i	$0.0715937\pi$
$602$	9.55660	+	24.6057i	0.389498	+	1.00285i
$603$		0			0
$604$	1.75245	+	23.3848i	0.0713061	+	0.951513i
$605$	39.1078	+	12.0632i	1.58996	+	0.490437i
$606$		0			0
$607$	−6.91922	+	3.99481i	−0.280842	+	0.162144i	−0.633805	−	0.773493i	$-0.718508\pi$
$607$	−6.91922	+	3.99481i	−0.280842	+	0.162144i	0.352962	+	0.935638i	$0.385174\pi$
$608$	−1.61812	−	7.08947i	−0.0656236	−	0.287516i
$609$		0			0
$610$	−2.49705	+	10.9403i	−0.101103	+	0.442959i
$611$	−6.07663	−	19.7000i	−0.245834	−	0.796975i
$612$		0			0
$613$	6.20205	+	15.8026i	0.250499	+	0.638260i	0.999710	−	0.0240708i	$-0.00766270\pi$
$613$	6.20205	+	15.8026i	0.250499	+	0.638260i	−0.749212	+	0.662331i	$0.769567\pi$
$614$	−25.1200	+	7.74851i	−1.01376	+	0.312704i
$615$		0			0
$616$	14.5242	−	3.26100i	0.585198	−	0.131389i
$617$	10.6630	−	2.43375i	0.429275	−	0.0979792i	−0.00242379	−	0.999997i	$-0.500772\pi$
$617$	10.6630	−	2.43375i	0.429275	−	0.0979792i	0.431699	+	0.902018i	$0.357914\pi$
$618$		0			0
$619$	21.9193	+	12.6551i	0.881012	+	0.508653i	0.870992	−	0.491297i	$-0.163477\pi$
$619$	21.9193	+	12.6551i	0.881012	+	0.508653i	0.0100204	+	0.999950i	$0.496810\pi$
$620$	2.28392	−	7.40429i	0.0917245	−	0.297363i
$621$		0			0
$622$	0.278748	+	0.222294i	0.0111768	+	0.00891317i
$623$	−25.6424	−	14.9260i	−1.02734	−	0.597997i
$624$		0			0
$625$	13.5434	−	12.5665i	0.541737	−	0.502658i
$626$	−10.3275	+	1.55661i	−0.412768	+	0.0622148i
$627$		0			0
$628$	0.845552	−	5.60987i	0.0337412	−	0.223858i
$629$	−0.459639	+	0.221350i	−0.0183270	+	0.00882582i
$630$		0			0
$631$	−3.70871	−	1.78602i	−0.147641	−	0.0711003i	0.358604	−	0.933490i	$-0.383253\pi$
$631$	−3.70871	−	1.78602i	−0.147641	−	0.0711003i	−0.506246	+	0.862389i	$0.668967\pi$
$632$	6.10976	−	8.96137i	0.243033	−	0.356464i
$633$		0			0
$634$	1.48160	−	19.7706i	0.0588420	−	0.785192i
$635$	14.7795	−	37.6575i	0.586506	−	1.49439i
$636$		0			0
$637$	−20.3307	−	1.66844i	−0.805531	−	0.0661061i
$638$			47.0566i			1.86299i
$639$		0			0
$640$	1.97583	+	0.148068i	0.0781017	+	0.00585291i
$641$	−8.77051	+	9.45237i	−0.346414	+	0.373346i	−0.882092	−	0.471076i	$-0.843866\pi$
$641$	−8.77051	+	9.45237i	−0.346414	+	0.373346i	0.535678	+	0.844422i	$0.320056\pi$
$642$		0			0
$643$	14.4593	−	30.0251i	0.570219	−	1.18407i	−0.394035	−	0.919095i	$-0.628921\pi$
$643$	14.4593	−	30.0251i	0.570219	−	1.18407i	0.964255	−	0.264977i	$-0.0853644\pi$
$644$	12.8646	−	11.8521i	0.506938	−	0.467040i
$645$		0			0
$646$	12.7023	+	1.91456i	0.499764	+	0.0753273i
$647$	20.7937	−	14.1769i	0.817484	−	0.557351i	−0.0808181	−	0.996729i	$-0.525753\pi$
$647$	20.7937	−	14.1769i	0.817484	−	0.557351i	0.898303	+	0.439377i	$0.144801\pi$
$648$		0			0
$649$	53.0288	+	57.1514i	2.08156	+	2.24339i
$650$	1.95168	+	2.44733i	0.0765514	+	0.0959924i
$651$		0			0
$652$	12.1345	−	15.2161i	0.475222	−	0.595909i
$653$	−27.9643	+	2.09564i	−1.09433	+	0.0820085i	−0.609640	−	0.792678i	$-0.708686\pi$
$653$	−27.9643	+	2.09564i	−1.09433	+	0.0820085i	−0.484688	+	0.874687i	$0.661067\pi$
$654$		0			0
$655$	0.856727	−	1.48390i	0.0334751	−	0.0579806i
$656$	−5.43329	−	9.41073i	−0.212134	−	0.367427i
$657$		0			0
$658$	16.8922	−	8.06129i	0.658527	−	0.314262i
$659$	−13.9774	−	3.19024i	−0.544481	−	0.124274i	−0.0585713	−	0.998283i	$-0.518654\pi$
$659$	−13.9774	−	3.19024i	−0.544481	−	0.124274i	−0.485910	+	0.874009i	$0.661512\pi$
$660$		0			0
$661$	−19.0215	+	7.46539i	−0.739851	+	0.290370i	−0.705180	−	0.709029i	$-0.749134\pi$
$661$	−19.0215	+	7.46539i	−0.739851	+	0.290370i	−0.0346715	+	0.999399i	$0.511038\pi$
$662$	−20.8735	+	8.19225i	−0.811272	+	0.318401i
$663$		0			0
$664$	6.86376	+	1.56661i	0.266365	+	0.0607962i
$665$	−34.2864	−	16.6613i	−1.32957	−	0.646097i
$666$		0			0
$667$	27.6477	+	47.8872i	1.07052	+	1.85420i
$668$	−9.28089	+	16.0750i	−0.359088	+	0.621959i
$669$		0			0
$670$	−12.1277	+	0.908847i	−0.468535	+	0.0351118i
$671$	19.8675	−	24.9131i	0.766976	−	0.961758i
$672$		0			0
$673$	−10.3675	−	13.0004i	−0.399638	−	0.501130i	0.540774	−	0.841168i	$-0.318132\pi$
$673$	−10.3675	−	13.0004i	−0.399638	−	0.501130i	−0.940412	+	0.340038i	$0.889560\pi$
$674$	−1.58701	−	1.71039i	−0.0611292	−	0.0658816i
$675$		0			0
$676$	−3.72448	+	2.53931i	−0.143249	+	0.0976656i
$677$	−16.0518	−	2.41941i	−0.616919	−	0.0929856i	−0.166855	−	0.985982i	$-0.553361\pi$
$677$	−16.0518	−	2.41941i	−0.616919	−	0.0929856i	−0.450065	+	0.892996i	$0.648599\pi$
$678$		0			0
$679$	−9.32037	+	23.5029i	−0.357683	+	0.901957i
$680$	−1.51865	+	3.15351i	−0.0582376	+	0.120932i
$681$		0			0
$682$	−14.9657	+	16.1292i	−0.573066	+	0.617618i
$683$	−29.6324	−	2.22064i	−1.13385	−	0.0849704i	−0.505447	−	0.862857i	$-0.668672\pi$
$683$	−29.6324	−	2.22064i	−1.13385	−	0.0849704i	−0.628404	+	0.777887i	$0.716292\pi$
$684$		0			0
$685$		−	6.30446i		−	0.240881i
$686$	−1.18776	−	18.4821i	−0.0453488	−	0.705651i
$687$		0			0
$688$	3.64497	−	9.28722i	0.138963	−	0.354072i
$689$	0.763217	−	10.1844i	0.0290762	−	0.387995i
$690$		0			0
$691$	−0.902761	+	1.32411i	−0.0343426	+	0.0503714i	−0.843026	−	0.537873i	$-0.819228\pi$
$691$	−0.902761	+	1.32411i	−0.0343426	+	0.0503714i	0.808684	+	0.588244i	$0.200181\pi$
$692$	−0.136161	−	0.0655719i	−0.00517608	−	0.00249267i
$693$		0			0
$694$	3.55036	−	1.70976i	0.134770	−	0.0649016i
$695$	3.14783	−	20.8845i	0.119404	−	0.792193i
$696$		0			0
$697$	18.9816	−	2.86102i	0.718980	−	0.108369i
$698$	0.722844	−	0.670701i	0.0273600	−	0.0253864i
$699$		0			0
$700$	−1.94039	+	2.07645i	−0.0733398	+	0.0784823i
$701$	−11.9122	−	9.49964i	−0.449917	−	0.358796i	0.372165	−	0.928167i	$-0.378616\pi$
$701$	−11.9122	−	9.49964i	−0.449917	−	0.358796i	−0.822081	+	0.569370i	$0.807187\pi$
$702$		0			0
$703$	−0.619001	+	2.00675i	−0.0233460	+	0.0756860i
$704$	−4.87253	−	2.81316i	−0.183640	−	0.106025i
$705$		0			0
$706$	−5.05430	+	1.15361i	−0.190221	+	0.0434167i
$707$	−8.45604	+	17.4013i	−0.318022	+	0.654441i
$708$		0			0
$709$	31.8469	−	9.82347i	1.19604	−	0.368928i	0.368119	−	0.929779i	$-0.380002\pi$
$709$	31.8469	−	9.82347i	1.19604	−	0.368928i	0.827917	+	0.560850i	$0.189526\pi$
$710$	3.09419	+	7.88387i	0.116123	+	0.295876i
$711$		0			0
$712$	3.30546	+	10.7160i	0.123877	+	0.401601i
$713$	−5.75329	+	25.2068i	−0.215462	+	0.944003i
$714$		0			0
$715$	7.22890	+	31.6719i	0.270346	+	1.18446i
$716$	4.71419	−	2.72174i	0.176178	−	0.101716i
$717$		0			0
$718$	−22.2499	−	6.86319i	−0.830359	−	0.256132i
$719$	2.90974	+	38.8278i	0.108515	+	1.44803i	0.739981	+	0.672628i	$0.234835\pi$
$719$	2.90974	+	38.8278i	0.108515	+	1.44803i	−0.631466	+	0.775404i	$0.717546\pi$
$720$		0			0
$721$	2.62457	−	1.77582i	0.0977439	−	0.0661349i
$722$	26.4875	−	21.1231i	0.985765	−	0.786121i
$723$		0			0
$724$	1.29965	+	8.62264i	0.0483013	+	0.320458i
$725$	−5.06082	−	7.42286i	−0.187954	−	0.275678i
$726$		0			0
$727$	−2.88592	−	5.99266i	−0.107033	−	0.222256i	0.840573	−	0.541698i	$-0.182219\pi$
$727$	−2.88592	−	5.99266i	−0.107033	−	0.222256i	−0.947606	+	0.319443i	$0.896504\pi$
$728$	5.22416	+	5.67044i	0.193620	+	0.210161i
$729$		0			0
$730$	15.2612	+	10.4049i	0.564841	+	0.385102i
$731$	12.9196	+	11.9876i	0.477848	+	0.443378i
$732$		0			0
$733$	−17.5582	−	6.89110i	−0.648528	−	0.254529i	0.0181945	−	0.999834i	$-0.494208\pi$
$733$	−17.5582	−	6.89110i	−0.648528	−	0.254529i	−0.666723	+	0.745306i	$0.732303\pi$
$734$	30.4682			1.12460
$735$		0			0
$736$	−6.61138			−0.243699
$737$	32.1472	+	12.6169i	1.18416	+	0.464748i
$738$		0			0
$739$	−5.78907	−	5.37147i	−0.212954	−	0.197593i	0.566482	−	0.824074i	$-0.308304\pi$
$739$	−5.78907	−	5.37147i	−0.212954	−	0.197593i	−0.779436	+	0.626481i	$0.784494\pi$
$740$	−0.472781	−	0.322337i	−0.0173798	−	0.0118493i
$741$		0			0
$742$	9.24882	−	0.660178i	0.339535	−	0.0242359i
$743$	0.829980	+	1.72347i	0.0304490	+	0.0632280i	0.915639	−	0.402003i	$-0.131686\pi$
$743$	0.829980	+	1.72347i	0.0304490	+	0.0632280i	−0.885190	+	0.465231i	$0.845971\pi$
$744$		0			0
$745$	−2.05956	−	3.02083i	−0.0754566	−	0.110674i
$746$	−3.59891	−	23.8772i	−0.131765	−	0.874206i
$747$		0			0
$748$	7.77061	−	6.19686i	0.284122	−	0.226580i
$749$	21.1874	−	36.3994i	0.774172	−	1.33001i
$750$		0			0
$751$	0.210852	+	2.81363i	0.00769412	+	0.102671i	0.999729	−	0.0232956i	$-0.00741588\pi$
$751$	0.210852	+	2.81363i	0.00769412	+	0.102671i	−0.992035	+	0.125966i	$0.959797\pi$
$752$	−6.76011	−	2.08522i	−0.246516	−	0.0760401i
$753$		0			0
$754$	−21.1076	+	12.1865i	−0.768694	+	0.443806i
$755$	−10.3392	−	45.2990i	−0.376282	−	1.64860i
$756$		0			0
$757$	12.1166	−	53.0861i	0.440384	−	1.92945i	0.0795103	−	0.996834i	$-0.474664\pi$
$757$	12.1166	−	53.0861i	0.440384	−	1.92945i	0.360874	−	0.932615i	$-0.382479\pi$
$758$	6.47485	+	20.9910i	0.235177	+	0.762426i
$759$		0			0
$760$	5.26388	+	13.4121i	0.190941	+	0.486509i
$761$	−21.4005	+	6.60119i	−0.775769	+	0.239293i	−0.657264	−	0.753661i	$-0.728286\pi$
$761$	−21.4005	+	6.60119i	−0.775769	+	0.239293i	−0.118505	+	0.992953i	$0.537810\pi$
$762$		0			0
$763$	−15.7226	−	3.64720i	−0.569195	−	0.132037i
$764$	9.48814	−	2.16561i	0.343269	−	0.0783488i
$765$		0			0
$766$	6.25512	+	3.61140i	0.226007	+	0.130485i
$767$	−11.9026	+	38.5873i	−0.429778	+	1.39331i
$768$		0			0
$769$	19.3456	+	15.4276i	0.697619	+	0.556333i	0.906809	−	0.421542i	$-0.138511\pi$
$769$	19.3456	+	15.4276i	0.697619	+	0.556333i	−0.209190	+	0.977875i	$0.567083\pi$
$770$	−27.4935	+	10.6782i	−0.990798	+	0.384816i
$771$		0			0
$772$	−14.9915	+	13.9101i	−0.539556	+	0.500635i
$773$	−34.9311	+	5.26502i	−1.25639	+	0.189370i	−0.743294	−	0.668964i	$-0.766738\pi$
$773$	−34.9311	+	5.26502i	−1.25639	+	0.189370i	−0.513091	+	0.858334i	$0.671500\pi$
$774$		0			0
$775$	0.626083	−	4.15379i	0.0224896	−	0.149208i
$776$	8.60989	−	4.14630i	0.309077	−	0.148844i
$777$		0			0
$778$	−9.98955	−	4.81071i	−0.358143	−	0.172472i
$779$	44.5132	−	65.2889i	1.59485	−	2.33922i
$780$		0			0
$781$	1.79722	−	23.9822i	0.0643096	−	0.858152i
$782$	4.26686	−	10.8718i	0.152583	−	0.388775i
$783$		0			0
$784$	−4.40308	+	5.44177i	−0.157253	+	0.194349i
$785$			11.2408i			0.401201i
$786$		0			0
$787$	3.76163	+	0.281895i	0.134088	+	0.0100485i	0.141605	−	0.989923i	$-0.454774\pi$
$787$	3.76163	+	0.281895i	0.134088	+	0.0100485i	−0.00751722	+	0.999972i	$0.502393\pi$
$788$	−5.56102	+	5.99335i	−0.198103	+	0.213504i
$789$		0			0
$790$	−9.32414	+	19.3618i	−0.331738	+	0.688861i
$791$	9.97818	+	17.4249i	0.354783	+	0.619558i
$792$		0			0
$793$	16.3201	+	2.45986i	0.579545	+	0.0873523i
$794$	−8.65142	+	5.89844i	−0.307028	+	0.209328i
$795$		0			0
$796$	18.5980	+	20.0439i	0.659188	+	0.710436i
$797$	20.0207	+	25.1051i	0.709169	+	0.889270i	0.997671	−	0.0682095i	$-0.0217286\pi$
$797$	20.0207	+	25.1051i	0.709169	+	0.889270i	−0.288502	+	0.957479i	$0.593157\pi$
$798$		0			0
$799$	7.79180	−	9.77061i	0.275654	−	0.345659i
$800$	1.07116	−	0.0802720i	0.0378711	−	0.00283805i
$801$		0			0
$802$	0.707900	−	1.22612i	0.0249968	−	0.0432958i
$803$	−26.2247	−	45.4225i	−0.925448	−	1.60292i
$804$		0			0
$805$	−21.7049	+	27.0203i	−0.764998	+	0.952339i
$806$	−11.1106	−	2.53592i	−0.391354	−	0.0893240i
$807$		0			0
$808$	6.80701	−	2.67155i	0.239470	−	0.0939850i
$809$	16.0827	−	6.31201i	0.565439	−	0.221919i	−0.0653638	−	0.997862i	$-0.520821\pi$
$809$	16.0827	−	6.31201i	0.565439	−	0.221919i	0.630803	+	0.775943i	$0.282726\pi$
$810$		0			0
$811$	−35.1930	−	8.03258i	−1.23579	−	0.282062i	−0.445775	−	0.895145i	$-0.647072\pi$
$811$	−35.1930	−	8.03258i	−1.23579	−	0.282062i	−0.790019	+	0.613083i	$0.789929\pi$
$812$	−13.7354	−	17.3493i	−0.482017	−	0.608840i
$813$		0			0
$814$	0.812423	+	1.40716i	0.0284754	+	0.0493209i
$815$	−19.2809	+	33.3955i	−0.675380	+	1.16979i
$816$		0			0
$817$	72.3469	−	5.42165i	2.53110	−	0.189680i
$818$	−22.8991	+	28.7146i	−0.800648	+	1.00398i
$819$		0			0
$820$	13.4242	+	16.8334i	0.468793	+	0.587848i
$821$	38.7720	+	41.7863i	1.35315	+	1.45835i	0.751862	+	0.659320i	$0.229156\pi$
$821$	38.7720	+	41.7863i	1.35315	+	1.45835i	0.601290	+	0.799031i	$0.294654\pi$
$822$		0			0
$823$	27.0529	−	18.4443i	0.943004	−	0.642929i	0.00891113	−	0.999960i	$-0.497163\pi$
$823$	27.0529	−	18.4443i	0.943004	−	0.642929i	0.934092	+	0.357031i	$0.116211\pi$
$824$	−1.18435	−	0.178512i	−0.0412588	−	0.00621877i
$825$		0			0
$826$	−36.2331	−	5.59254i	−1.26071	−	0.194589i
$827$	13.7215	−	28.4931i	0.477144	−	0.990801i	−0.513972	−	0.857807i	$-0.671827\pi$
$827$	13.7215	−	28.4931i	0.477144	−	0.990801i	0.991117	−	0.132994i	$-0.0424591\pi$
$828$		0			0
$829$	20.0032	−	21.5583i	0.694739	−	0.748751i	−0.282875	−	0.959157i	$-0.591288\pi$
$829$	20.0032	−	21.5583i	0.694739	−	0.748751i	0.977614	+	0.210406i	$0.0674786\pi$
$830$	−13.9104	−	1.04244i	−0.482837	−	0.0361836i
$831$		0			0
$832$		−	2.91415i		−	0.101030i
$833$	−6.10682	−	10.7525i	−0.211589	−	0.372551i
$834$		0			0
$835$	13.4364	−	34.2355i	0.464987	−	1.18477i
$836$	3.05746	−	40.7989i	0.105744	−	1.41106i
$837$		0			0
$838$	−4.19802	+	6.15737i	−0.145018	+	0.212703i
$839$	−31.7433	−	15.2868i	−1.09590	−	0.527758i	−0.203534	−	0.979068i	$-0.565243\pi$
$839$	−31.7433	−	15.2868i	−1.09590	−	0.527758i	−0.892368	+	0.451309i	$0.850957\pi$
$840$		0			0
$841$	36.8956	−	17.7680i	1.27226	−	0.612689i
$842$	−0.273229	+	1.81276i	−0.00941611	+	0.0624718i
$843$		0			0
$844$	2.35043	−	0.354271i	0.0809052	−	0.0121945i
$845$	6.54728	−	6.07498i	0.225233	−	0.208986i
$846$		0			0
$847$	54.4814	+	4.27687i	1.87200	+	0.146955i
$848$	−2.74002	−	2.18509i	−0.0940928	−	0.0750365i
$849$		0			0
$850$	−0.559305	+	1.81322i	−0.0191840	+	0.0621930i
$851$	1.65353	+	0.954664i	0.0566822	+	0.0327255i
$852$		0			0
$853$	19.6655	−	4.48853i	0.673335	−	0.153684i	0.127835	−	0.991795i	$-0.459197\pi$
$853$	19.6655	−	4.48853i	0.673335	−	0.153684i	0.545500	+	0.838111i	$0.316340\pi$
$854$	−0.0530591	+	14.9843i	−0.00181565	+	0.512752i
$855$		0			0
$856$	−15.2114	+	4.69211i	−0.519916	+	0.160373i
$857$	18.1445	+	46.2313i	0.619803	+	1.57923i	0.802885	+	0.596134i	$0.203297\pi$
$857$	18.1445	+	46.2313i	0.619803	+	1.57923i	−0.183082	+	0.983098i	$0.558607\pi$
$858$		0			0
$859$	−10.0383	−	32.5433i	−0.342502	−	1.11036i	−0.948999	−	0.315278i	$-0.897902\pi$
$859$	−10.0383	−	32.5433i	−0.342502	−	1.11036i	0.606498	−	0.795085i	$-0.292574\pi$
$860$	−4.39878	+	19.2723i	−0.149997	+	0.657180i
$861$		0			0
$862$	5.71083	+	25.0208i	0.194512	+	0.852211i
$863$	−16.5561	+	9.55865i	−0.563575	+	0.325380i	−0.754579	−	0.656209i	$-0.772159\pi$
$863$	−16.5561	+	9.55865i	−0.563575	+	0.325380i	0.191004	+	0.981589i	$0.438826\pi$
$864$		0			0
$865$	0.286137	+	0.0882617i	0.00972896	+	0.00300099i
$866$	−0.523747	−	6.98891i	−0.0177976	−	0.237493i
$867$		0			0
$868$	0.809741	−	10.3150i	0.0274844	−	0.350113i
$869$	47.7096	−	38.0472i	1.61844	−	1.29066i
$870$		0			0
$871$	2.66594	+	17.6873i	0.0903318	+	0.599312i
$872$	3.43646	+	5.04036i	0.116373	+	0.170688i
$873$		0			0
$874$	−20.8596	−	43.3155i	−0.705587	−	1.46517i
$875$	18.0303	−	26.2455i	0.609537	−	0.887259i
$876$		0			0
$877$	19.4384	+	13.2529i	0.656387	+	0.447517i	0.845167	−	0.534502i	$-0.179501\pi$
$877$	19.4384	+	13.2529i	0.656387	+	0.447517i	−0.188780	+	0.982019i	$0.560453\pi$
$878$	−4.62003	−	4.28676i	−0.155919	−	0.144671i
$879$		0			0
$880$	10.3772	+	4.07276i	0.349816	+	0.137293i
$881$	14.1123			0.475456			0.237728	−	0.971332i	$-0.423597\pi$
$881$	14.1123			0.475456			0.237728	+	0.971332i	$0.423597\pi$
$882$		0			0
$883$	−8.10242			−0.272668			−0.136334	−	0.990663i	$-0.543532\pi$
$883$	−8.10242			−0.272668			−0.136334	+	0.990663i	$0.543532\pi$
$884$	4.79204	+	1.88074i	0.161174	+	0.0632561i
$885$		0			0
$886$	19.9798	+	18.5385i	0.671233	+	0.622813i
$887$	−3.20876	−	2.18770i	−0.107740	−	0.0734557i	0.508252	−	0.861209i	$-0.330292\pi$
$887$	−3.20876	−	2.18770i	−0.107740	−	0.0734557i	−0.615991	+	0.787753i	$0.711244\pi$
$888$		0			0
$889$	8.24015	−	53.3864i	0.276366	−	1.79052i
$890$	−9.64075	−	20.0192i	−0.323159	−	0.671046i
$891$		0			0
$892$	−0.692200	−	1.01527i	−0.0231766	−	0.0339938i
$893$	−7.66727	−	50.8690i	−0.256575	−	1.70227i
$894$		0			0
$895$	−8.43249	+	6.72469i	−0.281867	+	0.224782i
$896$	2.61758	−	0.385062i	0.0874472	−	0.0128640i
$897$		0			0
$898$	−0.544355	−	7.26392i	−0.0181654	−	0.242400i
$899$	31.2546	+	9.64077i	1.04240	+	0.321538i
$900$		0			0
$901$	5.36154	−	3.09549i	0.178619	−	0.103126i
$902$	−13.6046	−	59.6059i	−0.452985	−	1.98466i
$903$		0			0
$904$	1.68880	−	7.39910i	0.0561686	−	0.246091i
$905$	−5.09268	−	16.5101i	−0.169286	−	0.548813i
$906$		0			0
$907$	−13.0050	−	33.1361i	−0.431823	−	1.10027i	−0.966830	−	0.255420i	$-0.917786\pi$
$907$	−13.0050	−	33.1361i	−0.431823	−	1.10027i	0.535007	−	0.844848i	$-0.320309\pi$
$908$	0.706194	−	0.217832i	0.0234359	−	0.00722901i
$909$		0			0
$910$	−11.9099	−	9.56704i	−0.394810	−	0.317144i
$911$	39.7485	−	9.07235i	1.31693	−	0.300580i	0.494365	−	0.869254i	$-0.335401\pi$
$911$	39.7485	−	9.07235i	1.31693	−	0.300580i	0.822563	+	0.568674i	$0.192543\pi$
$912$		0			0
$913$	34.3039	+	19.8054i	1.13529	+	0.655463i
$914$	2.97773	−	9.65357i	0.0984946	−	0.319312i
$915$		0			0
$916$	0.477893	+	0.381107i	0.0157900	+	0.0125921i
$917$	0.682136	−	2.18395i	0.0225261	−	0.0721202i
$918$		0			0
$919$	−9.32442	+	8.65180i	−0.307584	+	0.285397i	−0.818828	−	0.574040i	$-0.805376\pi$
$919$	−9.32442	+	8.65180i	−0.307584	+	0.285397i	0.511243	+	0.859436i	$0.329185\pi$
$920$	12.9533	−	1.95240i	0.427058	−	0.0643686i
$921$		0			0
$922$	3.50339	−	23.2435i	0.115378	−	0.765484i
$923$	11.2229	−	5.40464i	0.369405	−	0.177896i
$924$		0			0
$925$	−0.279491	−	0.134596i	−0.00918959	−	0.00442548i
$926$	0.417067	−	0.611725i	0.0137057	−	0.0201025i
$927$		0			0
$928$	−0.625018	+	8.34029i	−0.0205172	+	0.273783i
$929$	14.5832	−	37.1574i	0.478460	−	1.21910i	−0.464316	−	0.885669i	$-0.653700\pi$
$929$	14.5832	−	37.1574i	0.478460	−	1.21910i	0.942776	−	0.333426i	$-0.108205\pi$
$930$		0			0
$931$	−49.5448	−	11.6780i	−1.62377	−	0.382732i
$932$		−	3.42408i		−	0.112160i
$933$		0			0
$934$	10.9598	+	0.821320i	0.358614	+	0.0268744i
$935$	−13.3945	+	14.4359i	−0.438048	+	0.472104i
$936$		0			0
$937$	−24.0486	+	49.9374i	−0.785633	+	1.63138i	−0.0102039	+	0.999948i	$0.503248\pi$
$937$	−24.0486	+	49.9374i	−0.785633	+	1.63138i	−0.775429	+	0.631435i	$0.782466\pi$
$938$	−15.5351	+	4.73175i	−0.507238	+	0.154497i
$939$		0			0
$940$	13.8605	+	2.08913i	0.452079	+	0.0681400i
$941$	−4.13694	+	2.82052i	−0.134861	+	0.0919464i	−0.628871	−	0.777509i	$-0.716483\pi$
$941$	−4.13694	+	2.82052i	−0.134861	+	0.0919464i	0.494011	+	0.869456i	$0.335530\pi$
$942$		0			0
$943$	−48.8657	−	52.6647i	−1.59129	−	1.71500i
$944$	8.63969	+	10.8338i	0.281198	+	0.352611i
$945$		0			0
$946$	34.9984	−	43.8866i	1.13790	−	1.42688i
$947$	22.0818	−	1.65480i	0.717561	−	0.0537738i	0.289055	−	0.957313i	$-0.406659\pi$
$947$	22.0818	−	1.65480i	0.717561	−	0.0537738i	0.428506	+	0.903539i	$0.359040\pi$
$948$		0			0
$949$	13.5831	−	23.5265i	0.440925	−	0.763704i
$950$	3.90553	+	6.76457i	0.126712	+	0.219472i
$951$		0			0
$952$	−1.05614	+	4.55288i	−0.0342297	+	0.147560i
$953$	−10.5072	−	2.39819i	−0.340360	−	0.0776851i	0.0489244	−	0.998802i	$-0.484421\pi$
$953$	−10.5072	−	2.39819i	−0.340360	−	0.0776851i	−0.389285	+	0.921117i	$0.627278\pi$
$954$		0			0
$955$	−17.9500	+	7.04487i	−0.580850	+	0.227967i
$956$	−6.46445	+	2.53711i	−0.209075	+	0.0820560i
$957$		0			0
$958$	21.3616	+	4.87566i	0.690164	+	0.157525i
$959$	−1.84420	−	8.21394i	−0.0595524	−	0.265242i
$960$		0			0
$961$	−7.85325	−	13.6022i	−0.253331	−	0.438782i
$962$	−0.420794	+	0.728837i	−0.0135670	+	0.0234987i
$963$		0			0
$964$	21.9609	−	1.64574i	0.707312	−	0.0530057i
$965$	25.2643	−	31.6804i	0.813285	−	1.01983i
$966$		0			0
$967$	0.554989	+	0.695934i	0.0178472	+	0.0223797i	0.790675	−	0.612236i	$-0.209730\pi$
$967$	0.554989	+	0.695934i	0.0178472	+	0.0223797i	−0.772828	+	0.634616i	$0.781158\pi$
$968$	−14.0492	−	15.1415i	−0.451559	−	0.486665i
$969$		0			0
$970$	−15.6444	+	10.6662i	−0.502312	+	0.342471i
$971$	−19.1361	−	2.88431i	−0.614107	−	0.0925618i	−0.165379	−	0.986230i	$-0.552885\pi$
$971$	−19.1361	−	2.88431i	−0.614107	−	0.0925618i	−0.448728	+	0.893668i	$0.648123\pi$
$972$		0			0
$973$	−2.00796	−	28.1307i	−0.0643723	−	0.901829i
$974$	−4.68279	+	9.72390i	−0.150046	+	0.311574i
$975$		0			0
$976$	3.85220	−	4.15169i	0.123306	−	0.132892i
$977$	16.9361	+	1.26918i	0.541832	+	0.0406047i	0.342836	−	0.939395i	$-0.388613\pi$
$977$	16.9361	+	1.26918i	0.541832	+	0.0406047i	0.198997	+	0.980000i	$0.436232\pi$
$978$		0			0
$979$			63.0950i			2.01652i
$980$	7.01970	−	11.9620i	0.224236	−	0.382113i
$981$		0			0
$982$	−4.19986	+	10.7011i	−0.134023	+	0.341484i
$983$	−0.810211	+	10.8115i	−0.0258417	+	0.344834i	0.969264	+	0.246021i	$0.0791234\pi$
$983$	−0.810211	+	10.8115i	−0.0258417	+	0.344834i	−0.995106	+	0.0988123i	$0.968496\pi$
$984$		0			0
$985$	9.12550	−	13.3847i	0.290763	−	0.426470i
$986$	−13.3114	−	6.41045i	−0.423923	−	0.204150i
$987$		0			0
$988$	19.0925	−	9.19445i	0.607413	−	0.292514i
$989$	9.83097	−	65.2242i	0.312607	−	2.07401i
$990$		0			0
$991$	−43.7668	+	6.59678i	−1.39030	+	0.209554i	−0.801146	−	0.598469i	$-0.795776\pi$
$991$	−43.7668	+	6.59678i	−1.39030	+	0.209554i	−0.589151	+	0.808023i	$0.700538\pi$
$992$	−2.86674	+	2.65994i	−0.0910190	+	0.0844533i
$993$		0			0
$994$	6.33756	+	9.36658i	0.201015	+	0.297090i
$995$	−42.3571	−	33.7787i	−1.34281	−	1.07086i
$996$		0			0
$997$	13.9535	−	45.2361i	0.441911	−	1.43264i	−0.411503	−	0.911408i	$-0.634996\pi$
$997$	13.9535	−	45.2361i	0.441911	−	1.43264i	0.853414	−	0.521233i	$-0.174528\pi$
$998$	−35.5637	−	20.5327i	−1.12575	−	0.649951i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.bl.a.395.13	yes	240
3.2	odd	2	inner	882.2.bl.a.395.8	✓	240
49.33	odd	42	inner	882.2.bl.a.719.8	yes	240
147.131	even	42	inner	882.2.bl.a.719.13	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.bl.a.395.8	✓	240	3.2	odd	2	inner
882.2.bl.a.395.13	yes	240	1.1	even	1	trivial
882.2.bl.a.719.8	yes	240	49.33	odd	42	inner
882.2.bl.a.719.13	yes	240	147.131	even	42	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.bl (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.930874 + 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(-1.63709 - 1.11615i) q^{5} +(-2.45942 - 0.975316i) q^{7} +(0.433884 + 0.900969i) q^{8} +(-1.11615 - 1.63709i) q^{10} +(0.838558 + 5.56347i) q^{11} +(-2.27837 + 1.81694i) q^{13} +(-1.93309 - 1.80642i) q^{14} +(0.0747301 + 0.997204i) q^{16} +(-1.68804 - 0.520691i) q^{17} +(-6.29755 + 3.63589i) q^{19} +(-0.440897 - 1.93170i) q^{20} +(-1.25197 + 5.48525i) q^{22} +(1.94874 + 6.31765i) q^{23} +(-0.392435 - 0.999907i) q^{25} +(-2.78468 + 0.858960i) q^{26} +(-1.13950 - 2.38779i) q^{28} +(8.15398 - 1.86109i) q^{29} +(3.38676 + 1.95535i) q^{31} +(-0.294755 + 0.955573i) q^{32} +(-1.38112 - 1.10141i) q^{34} +(2.93769 + 4.34176i) q^{35} +(0.211701 - 0.196430i) q^{37} +(-7.19056 + 1.08380i) q^{38} +(0.295308 - 1.95924i) q^{40} +(-9.79045 + 4.71483i) q^{41} +(-8.98886 - 4.32881i) q^{43} +(-3.16941 + 4.64868i) q^{44} +(-0.494069 + 6.59289i) q^{46} +(-2.58457 + 6.58538i) q^{47} +(5.09752 + 4.79743i) q^{49} -1.07416i q^{50} +(-2.90600 - 0.217774i) q^{52} +(-2.38375 + 2.56907i) q^{53} +(4.83686 - 10.0438i) q^{55} +(-0.188374 - 2.63904i) q^{56} +(8.27026 + 1.24654i) q^{58} +(11.4492 - 7.80592i) q^{59} +(-3.85220 - 4.15169i) q^{61} +(2.43828 + 3.05750i) q^{62} +(-0.623490 + 0.781831i) q^{64} +(5.75787 - 0.431493i) q^{65} +(3.06901 - 5.31569i) q^{67} +(-0.883260 - 1.52985i) q^{68} +(1.14840 + 5.11489i) q^{70} +(-4.16730 - 0.951159i) q^{71} +(-8.67775 + 3.40576i) q^{73} +(0.268831 - 0.105508i) q^{74} +(-7.08947 - 1.61812i) q^{76} +(3.36378 - 14.5008i) q^{77} +(-5.42299 - 9.39290i) q^{79} +(0.990687 - 1.71592i) q^{80} +(-10.8362 + 0.812060i) q^{82} +(4.38954 - 5.50431i) q^{83} +(2.18230 + 2.73652i) q^{85} +(-6.78600 - 7.31357i) q^{86} +(-4.64868 + 3.16941i) q^{88} +(11.0890 + 1.67140i) q^{89} +(7.37557 - 2.24649i) q^{91} +(-2.86857 + 5.95665i) q^{92} +(-4.81182 + 5.18591i) q^{94} +(14.3678 + 1.07672i) q^{95} -9.55626i q^{97} +(2.99245 + 6.32813i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 20 q^{4} - 4 q^{7} - 12 q^{10} + 20 q^{16} + 24 q^{19} - 20 q^{22} + 24 q^{25} + 4 q^{28} + 12 q^{31} - 32 q^{37} + 44 q^{40} - 48 q^{43} + 204 q^{49} + 140 q^{55} + 136 q^{58} + 88 q^{61} + 40 q^{64}+ \cdots + 80 q^{94}+O(q^{100}) \) 240 * q - 20 * q^4 - 4 * q^7 - 12 * q^10 + 20 * q^16 + 24 * q^19 - 20 * q^22 + 24 * q^25 + 4 * q^28 + 12 * q^31 - 32 * q^37 + 44 * q^40 - 48 * q^43 + 204 * q^49 + 140 * q^55 + 136 * q^58 + 88 * q^61 + 40 * q^64 - 32 * q^67 - 16 * q^70 - 24 * q^73 - 28 * q^79 - 48 * q^82 - 112 * q^85 + 4 * q^88 + 80 * q^91 + 80 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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