LMFDB - Embedded newform 936.2.dg.f.829.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(829,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.829"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.dg (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			829.12
Character	$\chi$	$=$	936.829
Dual form			936.2.dg.f.901.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.402157 + 1.35583i) q^{2} +(-1.67654 - 1.09051i) q^{4} -0.607438 q^{5} +(-1.20493 - 0.695669i) q^{7} +(2.15278 - 1.83454i) q^{8} +(0.244286 - 0.823582i) q^{10} +(1.88561 + 3.26597i) q^{11} +(-3.60551 - 0.0168667i) q^{13} +(1.42778 - 1.35392i) q^{14} +(1.62157 + 3.65657i) q^{16} +(-0.221643 + 0.383897i) q^{17} +(0.639519 - 1.10768i) q^{19} +(1.01839 + 0.662418i) q^{20} +(-5.18641 + 1.24313i) q^{22} +(-3.77493 - 6.53836i) q^{23} -4.63102 q^{25} +(1.47285 - 4.88167i) q^{26} +(1.26148 + 2.48031i) q^{28} +(8.53815 - 4.92951i) q^{29} -7.17868i q^{31} +(-5.60981 + 0.728052i) q^{32} +(-0.431363 - 0.454897i) q^{34} +(0.731923 + 0.422576i) q^{35} +(-2.09112 - 3.62192i) q^{37} +(1.24464 + 1.31254i) q^{38} +(-1.30768 + 1.11437i) q^{40} +(8.71354 - 5.03077i) q^{41} +(-6.12848 - 3.53828i) q^{43} +(0.400282 - 7.53182i) q^{44} +(10.3830 - 2.48870i) q^{46} +0.744154i q^{47} +(-2.53209 - 4.38571i) q^{49} +(1.86240 - 6.27887i) q^{50} +(6.02639 + 3.96013i) q^{52} -1.24345i q^{53} +(-1.14539 - 1.98388i) q^{55} +(-3.87019 + 0.712881i) q^{56} +(3.24988 + 13.5587i) q^{58} +(-1.28264 + 2.22159i) q^{59} +(8.48782 + 4.90045i) q^{61} +(9.73306 + 2.88696i) q^{62} +(1.26891 - 7.89873i) q^{64} +(2.19013 + 0.0102455i) q^{65} +(5.06843 + 8.77877i) q^{67} +(0.790237 - 0.401914i) q^{68} +(-0.867288 + 0.822420i) q^{70} +(-7.40365 - 4.27450i) q^{71} -14.6006i q^{73} +(5.75166 - 1.37861i) q^{74} +(-2.28012 + 1.15966i) q^{76} -5.24705i q^{77} -12.7982 q^{79} +(-0.985003 - 2.22114i) q^{80} +(3.31664 + 13.8372i) q^{82} -6.19029 q^{83} +(0.134634 - 0.233194i) q^{85} +(7.26192 - 6.88623i) q^{86} +(10.0509 + 3.57169i) q^{88} +(-0.530897 + 0.306513i) q^{89} +(4.33267 + 2.52857i) q^{91} +(-0.801349 + 15.0784i) q^{92} +(-1.00894 - 0.299267i) q^{94} +(-0.388468 + 0.672847i) q^{95} +(-5.74744 - 3.31829i) q^{97} +(6.96456 - 1.66933i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{10} - 4 q^{16} + 64 q^{25} - 48 q^{28} - 48 q^{40} + 20 q^{49} - 12 q^{52} + 16 q^{55} + 12 q^{58} - 72 q^{64} - 84 q^{76} + 80 q^{79} - 12 q^{82} - 12 q^{88} - 24 q^{94} + 24 q^{97}+O(q^{100}) $ 56 * q - 4 * q^10 - 4 * q^16 + 64 * q^25 - 48 * q^28 - 48 * q^40 + 20 * q^49 - 12 * q^52 + 16 * q^55 + 12 * q^58 - 72 * q^64 - 84 * q^76 + 80 * q^79 - 12 * q^82 - 12 * q^88 - 24 * q^94 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

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 $

$2$	−0.402157	+	1.35583i	−0.284368	+	0.958715i
$2$	−0.402157	+	1.35583i	−0.284368	+	0.958715i
$3$		0			0
$3$		0			0
$4$	−1.67654	−	1.09051i	−0.838270	−	0.545256i
$5$	−0.607438			−0.271655			−0.135827	−	0.990733i	$-0.543369\pi$
$5$	−0.607438			−0.271655			−0.135827	+	0.990733i	$0.543369\pi$
$6$		0			0
$7$	−1.20493	−	0.695669i	−0.455422	−	0.262938i	0.254695	−	0.967021i	$-0.418025\pi$
$7$	−1.20493	−	0.695669i	−0.455422	−	0.262938i	−0.710117	+	0.704083i	$0.751358\pi$
$8$	2.15278	−	1.83454i	0.761122	−	0.648609i
$9$		0			0
$10$	0.244286	−	0.823582i	0.0772499	−	0.260439i
$11$	1.88561	+	3.26597i	0.568533	+	0.984729i	0.996711	+	0.0810341i	$0.0258223\pi$
$11$	1.88561	+	3.26597i	0.568533	+	0.984729i	−0.428178	+	0.903694i	$0.640844\pi$
$12$		0			0
$13$	−3.60551	−	0.0168667i	−0.999989	−	0.00467797i
$13$	−3.60551	−	0.0168667i	−0.999989	−	0.00467797i
$14$	1.42778	−	1.35392i	0.381590	−	0.361849i
$15$		0			0
$16$	1.62157	+	3.65657i	0.405392	+	0.914143i
$17$	−0.221643	+	0.383897i	−0.0537563	+	0.0931087i	−0.891651	−	0.452723i	$-0.850453\pi$
$17$	−0.221643	+	0.383897i	−0.0537563	+	0.0931087i	0.837895	+	0.545831i	$0.183786\pi$
$18$		0			0
$19$	0.639519	−	1.10768i	0.146716	−	0.254119i	−0.783296	−	0.621649i	$-0.786463\pi$
$19$	0.639519	−	1.10768i	0.146716	−	0.254119i	0.930012	+	0.367530i	$0.119796\pi$
$20$	1.01839	+	0.662418i	0.227720	+	0.148121i
$21$		0			0
$22$	−5.18641	+	1.24313i	−1.10575	+	0.265036i
$23$	−3.77493	−	6.53836i	−0.787126	−	1.36334i	−0.927721	−	0.373275i	$-0.878235\pi$
$23$	−3.77493	−	6.53836i	−0.787126	−	1.36334i	0.140594	−	0.990067i	$-0.455099\pi$
$24$		0			0
$25$	−4.63102			−0.926204
$26$	1.47285	−	4.88167i	0.288850	−	0.957374i
$27$		0			0
$28$	1.26148	+	2.48031i	0.238398	+	0.468735i
$29$	8.53815	−	4.92951i	1.58550	−	0.915386i	0.591459	−	0.806335i	$-0.298552\pi$
$29$	8.53815	−	4.92951i	1.58550	−	0.915386i	0.994036	−	0.109051i	$-0.0347812\pi$
$30$		0			0
$31$		−	7.17868i		−	1.28933i	−0.764466	−	0.644664i	$-0.776997\pi$
$31$		−	7.17868i		−	1.28933i	0.764466	−	0.644664i	$-0.223003\pi$
$32$	−5.60981	+	0.728052i	−0.991683	+	0.128703i
$33$		0			0
$34$	−0.431363	−	0.454897i	−0.0739781	−	0.0780141i
$35$	0.731923	+	0.422576i	0.123718	+	0.0714284i
$36$		0			0
$37$	−2.09112	−	3.62192i	−0.343777	−	0.595440i	0.641353	−	0.767246i	$-0.278373\pi$
$37$	−2.09112	−	3.62192i	−0.343777	−	0.595440i	−0.985131	+	0.171806i	$0.945040\pi$
$38$	1.24464	+	1.31254i	0.201907	+	0.212922i
$39$		0			0
$40$	−1.30768	+	1.11437i	−0.206762	+	0.176197i
$41$	8.71354	−	5.03077i	1.36083	−	0.785674i	0.371093	−	0.928596i	$-0.378983\pi$
$41$	8.71354	−	5.03077i	1.36083	−	0.785674i	0.989734	+	0.142922i	$0.0456498\pi$
$42$		0			0
$43$	−6.12848	−	3.53828i	−0.934585	−	0.539583i	−0.0463263	−	0.998926i	$-0.514751\pi$
$43$	−6.12848	−	3.53828i	−0.934585	−	0.539583i	−0.888259	+	0.459343i	$0.848085\pi$
$44$	0.400282	−	7.53182i	0.0603447	−	1.13546i
$45$		0			0
$46$	10.3830	−	2.48870i	1.53089	−	0.366939i
$47$			0.744154i			0.108546i	0.998526	+	0.0542730i	$0.0172841\pi$
$47$			0.744154i			0.108546i	−0.998526	+	0.0542730i	$0.982716\pi$
$48$		0			0
$49$	−2.53209	−	4.38571i	−0.361727	−	0.626530i
$50$	1.86240	−	6.27887i	0.263383	−	0.887966i
$51$		0			0
$52$	6.02639	+	3.96013i	0.835710	+	0.549171i
$53$		−	1.24345i		−	0.170801i	−0.996347	−	0.0854004i	$-0.972783\pi$
$53$		−	1.24345i		−	0.170801i	0.996347	−	0.0854004i	$-0.0272169\pi$
$54$		0			0
$55$	−1.14539	−	1.98388i	−0.154445	−	0.267506i
$56$	−3.87019	+	0.712881i	−0.517176	+	0.0952627i
$57$		0			0
$58$	3.24988	+	13.5587i	0.426731	+	1.78034i
$59$	−1.28264	+	2.22159i	−0.166985	+	0.289227i	−0.937358	−	0.348366i	$-0.886737\pi$
$59$	−1.28264	+	2.22159i	−0.166985	+	0.289227i	0.770373	+	0.637593i	$0.220070\pi$
$60$		0			0
$61$	8.48782	+	4.90045i	1.08675	+	0.627438i	0.932711	−	0.360626i	$-0.117437\pi$
$61$	8.48782	+	4.90045i	1.08675	+	0.627438i	0.154044	+	0.988064i	$0.450770\pi$
$62$	9.73306	+	2.88696i	1.23610	+	0.366644i
$63$		0			0
$64$	1.26891	−	7.89873i	0.158614	−	0.987341i
$65$	2.19013	+	0.0102455i	0.271652	+	0.00127079i
$66$		0			0
$67$	5.06843	+	8.77877i	0.619207	+	1.07250i	0.989631	+	0.143635i	$0.0458791\pi$
$67$	5.06843	+	8.77877i	0.619207	+	1.07250i	−0.370424	+	0.928863i	$0.620788\pi$
$68$	0.790237	−	0.401914i	0.0958303	−	0.0487392i
$69$		0			0
$70$	−0.867288	+	0.822420i	−0.103661	+	0.0982980i
$71$	−7.40365	−	4.27450i	−0.878652	−	0.507290i	−0.00843816	−	0.999964i	$-0.502686\pi$
$71$	−7.40365	−	4.27450i	−0.878652	−	0.507290i	−0.870214	+	0.492675i	$0.836019\pi$
$72$		0			0
$73$		−	14.6006i		−	1.70887i	−0.519556	−	0.854436i	$-0.673903\pi$
$73$		−	14.6006i		−	1.70887i	0.519556	−	0.854436i	$-0.326097\pi$
$74$	5.75166	−	1.37861i	0.668617	−	0.160261i
$75$		0			0
$76$	−2.28012	+	1.15966i	−0.261547	+	0.133023i
$77$		−	5.24705i		−	0.597956i
$78$		0			0
$79$	−12.7982			−1.43991			−0.719957	−	0.694019i	$-0.755839\pi$
$79$	−12.7982			−1.43991			−0.719957	+	0.694019i	$0.755839\pi$
$80$	−0.985003	−	2.22114i	−0.110127	−	0.248331i
$81$		0			0
$82$	3.31664	+	13.8372i	0.366262	+	1.52807i
$83$	−6.19029			−0.679472			−0.339736	−	0.940521i	$-0.610338\pi$
$83$	−6.19029			−0.679472			−0.339736	+	0.940521i	$0.610338\pi$
$84$		0			0
$85$	0.134634	−	0.233194i	0.0146032	−	0.0252934i
$86$	7.26192	−	6.88623i	0.783072	−	0.742561i
$87$		0			0
$88$	10.0509	+	3.57169i	1.07143	+	0.380743i
$89$	−0.530897	+	0.306513i	−0.0562749	+	0.0324903i	−0.527873	−	0.849323i	$-0.677010\pi$
$89$	−0.530897	+	0.306513i	−0.0562749	+	0.0324903i	0.471599	+	0.881813i	$0.343677\pi$
$90$		0			0
$91$	4.33267	+	2.52857i	0.454187	+	0.265066i
$92$	−0.801349	+	15.0784i	−0.0835465	+	1.57203i
$93$		0			0
$94$	−1.00894	−	0.299267i	−0.104065	−	0.0308670i
$95$	−0.388468	+	0.672847i	−0.0398560	+	0.0690326i
$96$		0			0
$97$	−5.74744	−	3.31829i	−0.583564	−	0.336921i	0.178985	−	0.983852i	$-0.442719\pi$
$97$	−5.74744	−	3.31829i	−0.583564	−	0.336921i	−0.762548	+	0.646931i	$0.776052\pi$
$98$	6.96456	−	1.66933i	0.703527	−	0.168628i
$99$		0			0
$100$	7.76409	+	5.05018i	0.776409	+	0.505018i
$101$	2.00337	−	1.15665i	0.199343	−	0.115091i	−0.397006	−	0.917816i	$-0.629951\pi$
$101$	2.00337	−	1.15665i	0.199343	−	0.115091i	0.596349	+	0.802725i	$0.296617\pi$
$102$		0			0
$103$	10.1914			1.00419			0.502093	−	0.864813i	$-0.332563\pi$
$103$	10.1914			1.00419			0.502093	+	0.864813i	$0.332563\pi$
$104$	−7.79281	+	6.57815i	−0.764148	+	0.645041i
$105$		0			0
$106$	1.68590	+	0.500062i	0.163749	+	0.0485703i
$107$	−4.89156	+	2.82414i	−0.472885	+	0.273020i	−0.717447	−	0.696614i	$-0.754689\pi$
$107$	−4.89156	+	2.82414i	−0.472885	+	0.273020i	0.244562	+	0.969634i	$0.421356\pi$
$108$		0			0
$109$	2.83631			0.271670			0.135835	−	0.990731i	$-0.456628\pi$
$109$	2.83631			0.271670			0.135835	+	0.990731i	$0.456628\pi$
$110$	3.15042	−	0.755125i	0.300381	−	0.0719983i
$111$		0			0
$112$	0.589880	−	5.53400i	0.0557384	−	0.522914i
$113$	−5.35973	+	9.28332i	−0.504201	+	0.873301i	0.495788	+	0.868444i	$0.334879\pi$
$113$	−5.35973	+	9.28332i	−0.504201	+	0.873301i	−0.999988	+	0.00485717i	$0.998454\pi$
$114$		0			0
$115$	2.29303	+	3.97165i	0.213826	+	0.370358i
$116$	−19.6902	−	1.04645i	−1.82819	−	0.0971601i
$117$		0			0
$118$	−2.49628	−	2.63246i	−0.229801	−	0.242338i
$119$	0.534130	−	0.308380i	0.0489636	−	0.0282692i
$120$		0			0
$121$	−1.61106	+	2.79044i	−0.146460	+	0.253676i
$122$	−10.0576	+	9.53728i	−0.910573	+	0.863465i
$123$		0			0
$124$	−7.82843	+	12.0353i	−0.703014	+	1.08081i
$125$	5.85025			0.523262
$126$		0			0
$127$	−6.18684	−	10.7159i	−0.548993	−	0.950884i	−0.998344	−	0.0575284i	$-0.981678\pi$
$127$	−6.18684	−	10.7159i	−0.548993	−	0.950884i	0.449351	−	0.893355i	$-0.351655\pi$
$128$	10.1990	+	4.89695i	0.901474	+	0.432834i
$129$		0			0
$130$	−0.894665	+	2.96531i	−0.0784673	+	0.260075i
$131$			16.1582i			1.41175i	0.708338	+	0.705873i	$0.249445\pi$
$131$			16.1582i			1.41175i	−0.708338	+	0.705873i	$0.750555\pi$
$132$		0			0
$133$	−1.54116	+	0.889787i	−0.133635	+	0.0771543i
$134$	−13.9408	+	3.34147i	−1.20430	+	0.288659i
$135$		0			0
$136$	0.227127	+	1.23306i	0.0194760	+	0.105734i
$137$	15.8390	+	9.14467i	1.35322	+	0.781282i	0.988699	−	0.149914i	$-0.0478996\pi$
$137$	15.8390	+	9.14467i	1.35322	+	0.781282i	0.364520	+	0.931195i	$0.381233\pi$
$138$		0			0
$139$	−9.71715	−	5.61020i	−0.824198	−	0.475851i	0.0276641	−	0.999617i	$-0.491193\pi$
$139$	−9.71715	−	5.61020i	−0.824198	−	0.475851i	−0.851862	+	0.523766i	$0.824526\pi$
$140$	−0.766274	−	1.50664i	−0.0647619	−	0.127334i
$141$		0			0
$142$	8.77292	−	8.31906i	0.736207	−	0.698120i
$143$	−6.74351	−	11.8073i	−0.563921	−	0.987377i
$144$		0			0
$145$	−5.18640	+	2.99437i	−0.430707	+	0.248669i
$146$	19.7959	+	5.87174i	1.63832	+	0.485949i
$147$		0			0
$148$	−0.443907	+	8.35268i	−0.0364889	+	0.686586i
$149$	4.36154	−	7.55442i	0.357312	−	0.618882i	−0.630199	−	0.776434i	$-0.717027\pi$
$149$	4.36154	−	7.55442i	0.357312	−	0.618882i	0.987511	+	0.157552i	$0.0503601\pi$
$150$		0			0
$151$		−	6.78085i		−	0.551818i	−0.961184	−	0.275909i	$-0.911021\pi$
$151$		−	6.78085i		−	0.551818i	0.961184	−	0.275909i	$-0.0889788\pi$
$152$	−0.655342	−	3.55781i	−0.0531552	−	0.288577i
$153$		0			0
$154$	7.11409	+	2.11014i	0.573270	+	0.170040i
$155$			4.36060i			0.350252i
$156$		0			0
$157$		−	6.32660i		−	0.504917i	−0.967608	−	0.252459i	$-0.918761\pi$
$157$		−	6.32660i		−	0.504917i	0.967608	−	0.252459i	$-0.0812392\pi$
$158$	5.14690	−	17.3522i	0.409466	−	1.38047i
$159$		0			0
$160$	3.40761	−	0.442247i	0.269395	−	0.0349627i
$161$			10.5044i			0.827862i
$162$		0			0
$163$	7.96740	−	13.7999i	0.624055	−	1.08089i	−0.364668	−	0.931138i	$-0.618818\pi$
$163$	7.96740	−	13.7999i	0.624055	−	1.08089i	0.988723	−	0.149757i	$-0.0478491\pi$
$164$	−20.0947	−	1.06794i	−1.56913	−	0.0833923i
$165$		0			0
$166$	2.48947	−	8.39297i	0.193220	−	0.651421i
$167$	−8.45328	+	4.88050i	−0.654134	+	0.377665i	−0.790038	−	0.613057i	$-0.789939\pi$
$167$	−8.45328	+	4.88050i	−0.654134	+	0.377665i	0.135904	+	0.990722i	$0.456606\pi$
$168$		0			0
$169$	12.9994	+	0.121626i	0.999956	+	0.00935584i
$170$	0.262026	+	0.276322i	0.0200965	+	0.0211929i
$171$		0			0
$172$	6.41611	+	12.6153i	0.489224	+	0.961904i
$173$	−11.1480	−	6.43628i	−0.847564	−	0.489342i	0.0122640	−	0.999925i	$-0.496096\pi$
$173$	−11.1480	−	6.43628i	−0.847564	−	0.489342i	−0.859828	+	0.510583i	$0.829429\pi$
$174$		0			0
$175$	5.58007	+	3.22166i	0.421814	+	0.243534i
$176$	−8.88462	+	12.1909i	−0.669704	+	0.918922i
$177$		0			0
$178$	−0.202075	−	0.843071i	−0.0151462	−	0.0631908i
$179$	5.63716	−	3.25461i	0.421341	−	0.243261i	−0.274310	−	0.961641i	$-0.588449\pi$
$179$	5.63716	−	3.25461i	0.421341	−	0.243261i	0.695651	+	0.718380i	$0.255116\pi$
$180$		0			0
$181$			16.7439i			1.24457i	0.782793	+	0.622283i	$0.213795\pi$
$181$			16.7439i			1.24457i	−0.782793	+	0.622283i	$0.786205\pi$
$182$	−5.17071	+	4.85748i	−0.383279	+	0.360060i
$183$		0			0
$184$	−20.1215	−	7.15039i	−1.48338	−	0.527133i
$185$	1.27022	+	2.20009i	0.0933887	+	0.161754i
$186$		0			0
$187$	−1.67173			−0.122249
$188$	0.811508	−	1.24760i	0.0591853	−	0.0909908i
$189$		0			0
$190$	−0.756039	−	0.797286i	−0.0548488	−	0.0578412i
$191$	−7.38796	+	12.7963i	−0.534574	+	0.925910i	0.464609	+	0.885516i	$0.346195\pi$
$191$	−7.38796	+	12.7963i	−0.534574	+	0.925910i	−0.999184	+	0.0403942i	$0.987139\pi$
$192$		0			0
$193$	8.52397	−	4.92132i	0.613569	−	0.354244i	−0.160792	−	0.986988i	$-0.551405\pi$
$193$	8.52397	−	4.92132i	0.613569	−	0.354244i	0.774361	+	0.632744i	$0.218072\pi$
$194$	6.81040	−	6.45807i	0.488958	−	0.463662i
$195$		0			0
$196$	−0.537518	+	10.1141i	−0.0383941	+	0.722435i
$197$	−4.97689	−	8.62022i	−0.354588	−	0.614165i	0.632459	−	0.774594i	$-0.282046\pi$
$197$	−4.97689	−	8.62022i	−0.354588	−	0.614165i	−0.987047	+	0.160429i	$0.948712\pi$
$198$		0			0
$199$	−3.12577	+	5.41400i	−0.221580	+	0.383788i	−0.955288	−	0.295677i	$-0.904455\pi$
$199$	−3.12577	+	5.41400i	−0.221580	+	0.383788i	0.733708	+	0.679465i	$0.237788\pi$
$200$	−9.96956	+	8.49580i	−0.704954	+	0.600744i
$201$		0			0
$202$	0.762545	+	3.18138i	0.0536524	+	0.223841i
$203$	−13.7172			−0.962760
$204$		0			0
$205$	−5.29294	+	3.05588i	−0.369675	+	0.213432i
$206$	−4.09854	+	13.8178i	−0.285559	+	0.962729i
$207$		0			0
$208$	−5.78491	−	13.2112i	−0.401111	−	0.916029i
$209$	4.82354			0.333651
$210$		0			0
$211$	−3.63050	+	2.09607i	−0.249934	+	0.144299i	−0.619734	−	0.784812i	$-0.712759\pi$
$211$	−3.63050	+	2.09607i	−0.249934	+	0.144299i	0.369800	+	0.929111i	$0.379426\pi$
$212$	−1.35600	+	2.08469i	−0.0931301	+	0.143177i
$213$		0			0
$214$	−1.86188	−	7.76786i	−0.127275	−	0.531000i
$215$	3.72267	+	2.14929i	0.253884	+	0.146580i
$216$		0			0
$217$	−4.99398	+	8.64984i	−0.339014	+	0.587189i
$218$	−1.14064	+	3.84555i	−0.0772542	+	0.260454i
$219$		0			0
$220$	−0.243146	+	4.57511i	−0.0163929	+	0.308454i
$221$	0.805611	−	1.38041i	0.0541913	−	0.0928562i
$222$		0			0
$223$	−12.3436	+	7.12658i	−0.826588	+	0.477231i	−0.852683	−	0.522429i	$-0.825026\pi$
$223$	−12.3436	+	7.12658i	−0.826588	+	0.477231i	0.0260950	+	0.999659i	$0.491693\pi$
$224$	7.26593	+	3.02531i	0.485475	+	0.202137i
$225$		0			0
$226$	−10.4311	−	11.0002i	−0.693868	−	0.731724i
$227$	−13.3737	+	23.1640i	−0.887645	+	1.53745i	−0.0449939	+	0.998987i	$0.514327\pi$
$227$	−13.3737	+	23.1640i	−0.887645	+	1.53745i	−0.842651	+	0.538459i	$0.819006\pi$
$228$		0			0
$229$	−12.3227			−0.814307			−0.407153	−	0.913360i	$-0.633479\pi$
$229$	−12.3227			−0.814307			−0.407153	+	0.913360i	$0.633479\pi$
$230$	−6.30703	+	1.51173i	−0.415874	+	0.0996806i
$231$		0			0
$232$	9.33737	−	26.2757i	0.613028	−	1.72509i
$233$	15.9484			1.04482			0.522408	−	0.852696i	$-0.325034\pi$
$233$	15.9484			1.04482			0.522408	+	0.852696i	$0.325034\pi$
$234$		0			0
$235$		−	0.452027i		−	0.0294870i
$236$	4.57306	−	2.32586i	0.297681	−	0.151400i
$237$		0			0
$238$	0.203306	+	0.848206i	0.0131784	+	0.0549810i
$239$		−	14.8036i		−	0.957562i	−0.877934	−	0.478781i	$-0.841079\pi$
$239$		−	14.8036i		−	0.957562i	0.877934	−	0.478781i	$-0.158921\pi$
$240$		0			0
$241$	−4.83757	−	2.79297i	−0.311615	−	0.179911i	0.336034	−	0.941850i	$-0.390914\pi$
$241$	−4.83757	−	2.79297i	−0.311615	−	0.179911i	−0.647649	+	0.761939i	$0.724248\pi$
$242$	−3.13546	−	3.30652i	−0.201555	−	0.212551i
$243$		0			0
$244$	−8.88618	−	17.4719i	−0.568879	−	1.11852i
$245$	1.53809	+	2.66405i	0.0982648	+	0.170200i
$246$		0			0
$247$	−2.32448	+	3.98296i	−0.147903	+	0.253430i
$248$	−13.1696	−	15.4541i	−0.836270	−	0.981337i
$249$		0			0
$250$	−2.35272	+	7.93193i	−0.148799	+	0.501659i
$251$	−18.6990	−	10.7959i	−1.18027	−	0.681429i	−0.224193	−	0.974545i	$-0.571974\pi$
$251$	−18.6990	−	10.7959i	−1.18027	−	0.681429i	−0.956077	+	0.293116i	$0.905308\pi$
$252$		0			0
$253$	14.2361	−	24.6576i	0.895015	−	1.55021i
$254$	17.0170	−	4.07881i	1.06774	−	0.255927i
$255$		0			0
$256$	−10.7410	+	11.8588i	−0.671314	+	0.741173i
$257$	6.46366	+	11.1954i	0.403192	+	0.698349i	0.994109	−	0.108383i	$-0.0345673\pi$
$257$	6.46366	+	11.1954i	0.403192	+	0.698349i	−0.590917	+	0.806732i	$0.701234\pi$
$258$		0			0
$259$			5.81890i			0.361569i
$260$	−3.66066	−	2.40553i	−0.227024	−	0.149185i
$261$		0			0
$262$	−21.9077	−	6.49812i	−1.35346	−	0.401455i
$263$	8.54722	+	14.8042i	0.527044	+	0.912868i	0.999503	+	0.0315150i	$0.0100332\pi$
$263$	8.54722	+	14.8042i	0.527044	+	0.912868i	−0.472459	+	0.881353i	$0.656633\pi$
$264$		0			0
$265$			0.755318i			0.0463988i
$266$	−0.586611	−	2.44738i	−0.0359674	−	0.150058i
$267$		0			0
$268$	1.07594	−	20.2451i	0.0657233	−	1.23667i
$269$	2.39036	+	1.38007i	0.145743	+	0.0841446i	0.571098	−	0.820882i	$-0.306518\pi$
$269$	2.39036	+	1.38007i	0.145743	+	0.0841446i	−0.425355	+	0.905026i	$0.639851\pi$
$270$		0			0
$271$	6.76352	−	3.90492i	0.410854	−	0.237207i	−0.280302	−	0.959912i	$-0.590435\pi$
$271$	6.76352	−	3.90492i	0.410854	−	0.237207i	0.691157	+	0.722705i	$0.257101\pi$
$272$	−1.76316	−	0.187938i	−0.106907	−	0.0113954i
$273$		0			0
$274$	−18.7684	+	17.7974i	−1.13384	+	1.07518i
$275$	−8.73230	−	15.1248i	−0.526578	−	0.912059i
$276$		0			0
$277$	−24.0189	−	13.8673i	−1.44315	−	0.833205i	−0.445094	−	0.895484i	$-0.646830\pi$
$277$	−24.0189	−	13.8673i	−1.44315	−	0.833205i	−0.998059	+	0.0622790i	$0.980163\pi$
$278$	11.5143	−	10.9186i	0.690581	−	0.654854i
$279$		0			0
$280$	2.35090	−	0.433031i	0.140493	−	0.0258786i
$281$		−	2.44676i		−	0.145961i	−0.997333	−	0.0729806i	$-0.976749\pi$
$281$		−	2.44676i		−	0.145961i	0.997333	−	0.0729806i	$-0.0232511\pi$
$282$		0			0
$283$	−22.1821	+	12.8069i	−1.31859	+	0.761289i	−0.983502	−	0.180897i	$-0.942100\pi$
$283$	−22.1821	+	12.8069i	−1.31859	+	0.761289i	−0.335090	+	0.942186i	$0.608767\pi$
$284$	7.75112	+	15.2401i	0.459944	+	0.904336i
$285$		0			0
$286$	18.7206	−	4.39464i	1.10697	−	0.259861i
$287$	−13.9990			−0.826334
$288$		0			0
$289$	8.40175	+	14.5523i	0.494221	+	0.856015i
$290$	−1.97410	−	8.23607i	−0.115923	−	0.483639i
$291$		0			0
$292$	−15.9221	+	24.4785i	−0.931773	+	1.43250i
$293$	10.8730	−	18.8325i	0.635205	−	1.10021i	−0.351267	−	0.936275i	$-0.614249\pi$
$293$	10.8730	−	18.8325i	0.635205	−	1.10021i	0.986472	−	0.163932i	$-0.0524177\pi$
$294$		0			0
$295$	0.779123	−	1.34948i	0.0453623	−	0.0785698i
$296$	−11.1463	−	3.96095i	−0.647864	−	0.230226i
$297$		0			0
$298$	8.48846	+	8.95157i	0.491724	+	0.518550i
$299$	13.5003	+	23.6378i	0.780740	+	1.36701i
$300$		0			0
$301$	4.92295	+	8.52679i	0.283754	+	0.491476i
$302$	9.19366	+	2.72697i	0.529036	+	0.156919i
$303$		0			0
$304$	5.08733	+	0.542269i	0.291778	+	0.0311012i
$305$	−5.15583	−	2.97672i	−0.295222	−	0.170446i
$306$		0			0
$307$	0.632102			0.0360760			0.0180380	−	0.999837i	$-0.494258\pi$
$307$	0.632102			0.0360760			0.0180380	+	0.999837i	$0.494258\pi$
$308$	−5.72196	+	8.79688i	−0.326039	+	0.501249i
$309$		0			0
$310$	−5.91223	−	1.75365i	−0.335792	−	0.0996005i
$311$	−29.0266			−1.64595			−0.822975	−	0.568078i	$-0.807687\pi$
$311$	−29.0266			−1.64595			−0.822975	+	0.568078i	$0.807687\pi$
$312$		0			0
$313$	−22.4588			−1.26945			−0.634723	−	0.772740i	$-0.718886\pi$
$313$	−22.4588			−1.26945			−0.634723	+	0.772740i	$0.718886\pi$
$314$	8.57777	+	2.54428i	0.484072	+	0.143582i
$315$		0			0
$316$	21.4567	+	13.9566i	1.20704	+	0.785122i
$317$	−17.1312			−0.962182			−0.481091	−	0.876671i	$-0.659759\pi$
$317$	−17.1312			−0.962182			−0.481091	+	0.876671i	$0.659759\pi$
$318$		0			0
$319$	32.1993	+	18.5903i	1.80281	+	1.04085i
$320$	−0.770784	+	4.79799i	−0.0430882	+	0.268216i
$321$		0			0
$322$	−14.2422	−	4.22442i	−0.793684	−	0.235418i
$323$	0.283490	+	0.491019i	0.0157738	+	0.0273210i
$324$		0			0
$325$	16.6972	+	0.0781098i	0.926194	+	0.00433275i
$326$	15.5062	+	16.3522i	0.858809	+	0.905662i
$327$		0			0
$328$	9.52917	−	26.8155i	0.526161	−	1.48064i
$329$	0.517685	−	0.896656i	0.0285409	−	0.0494342i
$330$		0			0
$331$	14.8274	−	25.6818i	0.814988	−	1.41160i	−0.0943484	−	0.995539i	$-0.530077\pi$
$331$	14.8274	−	25.6818i	0.814988	−	1.41160i	0.909336	−	0.416061i	$-0.136590\pi$
$332$	10.3783	+	6.75058i	0.569581	+	0.370486i
$333$		0			0
$334$	−3.21758	−	13.4239i	−0.176058	−	0.734524i
$335$	−3.07876	−	5.33256i	−0.168210	−	0.291349i
$336$		0			0
$337$	15.9922			0.871151			0.435576	−	0.900152i	$-0.356545\pi$
$337$	15.9922			0.871151			0.435576	+	0.900152i	$0.356545\pi$
$338$	−5.39272	+	17.5761i	−0.293325	+	0.956013i
$339$		0			0
$340$	−0.480020	+	0.244138i	−0.0260328	+	0.0132402i
$341$	23.4454	−	13.5362i	1.26964	−	0.733026i
$342$		0			0
$343$			16.7854i			0.906324i
$344$	−19.6844	+	3.62583i	−1.06131	+	0.195491i
$345$		0			0
$346$	13.2097	−	12.5263i	0.710159	−	0.673420i
$347$	19.6305	+	11.3337i	1.05382	+	0.608425i	0.923717	−	0.383075i	$-0.125135\pi$
$347$	19.6305	+	11.3337i	1.05382	+	0.608425i	0.130106	+	0.991500i	$0.458468\pi$
$348$		0			0
$349$	5.28130	+	9.14748i	0.282702	+	0.489654i	0.972049	−	0.234777i	$-0.0754360\pi$
$349$	5.28130	+	9.14748i	0.282702	+	0.489654i	−0.689348	+	0.724431i	$0.742103\pi$
$350$	−6.61208	+	6.27001i	−0.353430	+	0.335146i
$351$		0			0
$352$	−12.9557	−	16.9487i	−0.690542	−	0.903367i
$353$	15.7134	−	9.07213i	0.836339	−	0.482861i	−0.0196788	−	0.999806i	$-0.506264\pi$
$353$	15.7134	−	9.07213i	0.836339	−	0.482861i	0.856018	+	0.516946i	$0.172931\pi$
$354$		0			0
$355$	4.49726	+	2.59649i	0.238690	+	0.137808i
$356$	1.22433	+	0.0650673i	0.0648891	+	0.00344856i
$357$		0			0
$358$	2.14568	+	8.95188i	0.113402	+	0.473122i
$359$		−	11.4614i		−	0.604908i	−0.953164	−	0.302454i	$-0.902194\pi$
$359$		−	11.4614i		−	0.604908i	0.953164	−	0.302454i	$-0.0978059\pi$
$360$		0			0
$361$	8.68203	+	15.0377i	0.456949	+	0.791459i
$362$	−22.7019	−	6.73368i	−1.19318	−	0.353915i
$363$		0			0
$364$	−4.50646	−	8.96407i	−0.236203	−	0.469845i
$365$			8.86897i			0.464223i
$366$		0			0
$367$	7.93899	+	13.7507i	0.414412	+	0.717783i	0.995367	−	0.0961533i	$-0.0306539\pi$
$367$	7.93899	+	13.7507i	0.414412	+	0.717783i	−0.580954	+	0.813936i	$0.697321\pi$
$368$	17.7867	−	24.4057i	0.927195	−	1.27223i
$369$		0			0
$370$	−3.49378	+	0.837423i	−0.181633	+	0.0435355i
$371$	−0.865029	+	1.49827i	−0.0449100	+	0.0777865i
$372$		0			0
$373$	5.40748	+	3.12201i	0.279989	+	0.161652i	0.633418	−	0.773810i	$-0.281651\pi$
$373$	5.40748	+	3.12201i	0.279989	+	0.161652i	−0.353430	+	0.935461i	$0.614985\pi$
$374$	0.672298	−	2.26658i	0.0347637	−	0.117202i
$375$		0			0
$376$	1.36518	+	1.60200i	0.0704038	+	0.0826167i
$377$	−30.8676	+	17.6294i	−1.58976	+	0.907959i
$378$		0			0
$379$	−4.01932	−	6.96166i	−0.206459	−	0.357597i	0.744138	−	0.668026i	$-0.232861\pi$
$379$	−4.01932	−	6.96166i	−0.206459	−	0.357597i	−0.950596	+	0.310429i	$0.899527\pi$
$380$	1.38503	−	0.704425i	0.0710505	−	0.0361362i
$381$		0			0
$382$	−14.3785	−	15.1629i	−0.735668	−	0.775804i
$383$	22.7884	+	13.1569i	1.16443	+	0.672285i	0.952362	−	0.304969i	$-0.0986461\pi$
$383$	22.7884	+	13.1569i	1.16443	+	0.672285i	0.212070	+	0.977254i	$0.431979\pi$
$384$		0			0
$385$			3.18726i			0.162438i
$386$	3.24448	+	13.5362i	0.165140	+	0.688973i
$387$		0			0
$388$	6.01718	+	11.8309i	0.305476	+	0.600622i
$389$			25.3042i			1.28297i	0.767135	+	0.641486i	$0.221682\pi$
$389$			25.3042i			1.28297i	−0.767135	+	0.641486i	$0.778318\pi$
$390$		0			0
$391$	3.34674			0.169252
$392$	−13.4968	−	4.79623i	−0.681691	−	0.242246i
$393$		0			0
$394$	13.6890	−	3.28112i	0.689643	−	0.165300i
$395$	7.77414			0.391159
$396$		0			0
$397$	−6.97567	+	12.0822i	−0.350099	+	0.606389i	−0.986266	−	0.165162i	$-0.947185\pi$
$397$	−6.97567	+	12.0822i	−0.350099	+	0.606389i	0.636168	+	0.771551i	$0.280519\pi$
$398$	−6.08340	−	6.41529i	−0.304933	−	0.321569i
$399$		0			0
$400$	−7.50952	−	16.9337i	−0.375476	−	0.846683i
$401$	16.3156	−	9.41984i	0.814764	−	0.470404i	−0.0338433	−	0.999427i	$-0.510775\pi$
$401$	16.3156	−	9.41984i	0.814764	−	0.470404i	0.848608	+	0.529023i	$0.177441\pi$
$402$		0			0
$403$	−0.121080	+	25.8828i	−0.00603144	+	1.28931i
$404$	−4.62007	−	0.245536i	−0.229857	−	0.0122159i
$405$		0			0
$406$	5.51648	−	18.5982i	0.273778	−	0.923012i
$407$	7.88607	−	13.6591i	0.390898	−	0.677055i
$408$		0			0
$409$	26.4746	+	15.2851i	1.30909	+	0.755802i	0.981944	−	0.189173i	$-0.0605808\pi$
$409$	26.4746	+	15.2851i	1.30909	+	0.755802i	0.327143	+	0.944975i	$0.393914\pi$
$410$	−2.01465	−	8.40526i	−0.0994967	−	0.415106i
$411$		0			0
$412$	−17.0863	−	11.1138i	−0.841779	−	0.547539i
$413$	3.09099	−	1.78458i	0.152097	−	0.0878135i
$414$		0			0
$415$	3.76022			0.184582
$416$	20.2385	−	2.53038i	0.992274	−	0.124062i
$417$		0			0
$418$	−1.93982	+	6.53989i	−0.0948797	+	0.319876i
$419$	15.6360	−	9.02746i	0.763870	−	0.441020i	−0.0668136	−	0.997765i	$-0.521283\pi$
$419$	15.6360	−	9.02746i	0.763870	−	0.441020i	0.830683	+	0.556745i	$0.187950\pi$
$420$		0			0
$421$	14.1711			0.690659			0.345330	−	0.938481i	$-0.387767\pi$
$421$	14.1711			0.690659			0.345330	+	0.938481i	$0.387767\pi$
$422$	−1.38188	−	5.76528i	−0.0672688	−	0.280649i
$423$		0			0
$424$	−2.28116	−	2.67687i	−0.110783	−	0.130000i
$425$	1.02643	−	1.77783i	0.0497893	−	0.0862376i
$426$		0			0
$427$	−6.81818	−	11.8094i	−0.329955	−	0.571498i
$428$	11.2807	+	0.599515i	0.545271	+	0.0289787i
$429$		0			0
$430$	−4.41116	+	4.18296i	−0.212725	+	0.201720i
$431$	11.4213	−	6.59410i	0.550146	−	0.317627i	−0.199035	−	0.979992i	$-0.563781\pi$
$431$	11.4213	−	6.59410i	0.550146	−	0.317627i	0.749181	+	0.662366i	$0.230447\pi$
$432$		0			0
$433$	−1.91654	+	3.31955i	−0.0921032	+	0.159527i	−0.908396	−	0.418111i	$-0.862692\pi$
$433$	−1.91654	+	3.31955i	−0.0921032	+	0.159527i	0.816293	+	0.577638i	$0.196026\pi$
$434$	−9.71932	−	10.2496i	−0.466542	−	0.491995i
$435$		0			0
$436$	−4.75519	−	3.09303i	−0.227732	−	0.148129i
$437$	−9.65654			−0.461935
$438$		0			0
$439$	3.86604	+	6.69617i	0.184516	+	0.319591i	0.943413	−	0.331619i	$-0.107595\pi$
$439$	3.86604	+	6.69617i	0.184516	+	0.319591i	−0.758897	+	0.651210i	$0.774262\pi$
$440$	−6.10528	−	2.16958i	−0.291058	−	0.103431i
$441$		0			0
$442$	1.54761	+	1.64741i	0.0736124	+	0.0783593i
$443$		−	14.6984i		−	0.698341i	−0.937059	−	0.349171i	$-0.886463\pi$
$443$		−	14.6984i		−	0.698341i	0.937059	−	0.349171i	$-0.113537\pi$
$444$		0			0
$445$	0.322487	−	0.186188i	0.0152873	−	0.00882615i
$446$	−4.69835	−	19.6018i	−0.222473	−	0.928172i
$447$		0			0
$448$	−7.02385	+	8.63470i	−0.331846	+	0.407951i
$449$	−24.9869	−	14.4262i	−1.17921	−	0.680815i	−0.223375	−	0.974733i	$-0.571707\pi$
$449$	−24.9869	−	14.4262i	−1.17921	−	0.680815i	−0.955831	+	0.293918i	$0.905041\pi$
$450$		0			0
$451$	32.8607	+	18.9721i	1.54735	+	0.893363i
$452$	19.1094	−	9.71900i	0.898828	−	0.457143i
$453$		0			0
$454$	−26.0280	−	27.4480i	−1.22156	−	1.28820i
$455$	−2.63183	−	1.53595i	−0.123382	−	0.0720063i
$456$		0			0
$457$	1.56292	−	0.902350i	0.0731101	−	0.0422101i	−0.462999	−	0.886359i	$-0.653227\pi$
$457$	1.56292	−	0.902350i	0.0731101	−	0.0422101i	0.536109	+	0.844148i	$0.319893\pi$
$458$	4.95566	−	16.7075i	0.231563	−	0.780688i
$459$		0			0
$460$	0.486770	−	9.15921i	0.0226958	−	0.427050i
$461$	4.96927	−	8.60703i	0.231442	−	0.400869i	−0.726791	−	0.686859i	$-0.758989\pi$
$461$	4.96927	−	8.60703i	0.231442	−	0.400869i	0.958233	+	0.285990i	$0.0923223\pi$
$462$		0			0
$463$		−	13.9156i		−	0.646713i	−0.946277	−	0.323357i	$-0.895189\pi$
$463$		−	13.9156i		−	0.646713i	0.946277	−	0.323357i	$-0.104811\pi$
$464$	31.8703	+	23.2268i	1.47954	+	1.07828i
$465$		0			0
$466$	−6.41377	+	21.6233i	−0.297112	+	1.00168i
$467$		−	24.8188i		−	1.14848i	−0.818688	−	0.574238i	$-0.805298\pi$
$467$		−	24.8188i		−	1.14848i	0.818688	−	0.574238i	$-0.194702\pi$
$468$		0			0
$469$		−	14.1038i		−	0.651252i
$470$	0.612871	+	0.181786i	0.0282696	+	0.00838516i
$471$		0			0
$472$	1.31437	+	7.13565i	0.0604989	+	0.328445i
$473$		−	26.6873i		−	1.22708i
$474$		0			0
$475$	−2.96162	+	5.12968i	−0.135889	+	0.235366i
$476$	−1.23178	−	0.0654637i	−0.0564587	−	0.00300052i
$477$		0			0
$478$	20.0711	+	5.95335i	0.918029	+	0.272300i
$479$	2.86620	−	1.65480i	0.130960	−	0.0756098i	−0.433089	−	0.901351i	$-0.642576\pi$
$479$	2.86620	−	1.65480i	0.130960	−	0.0756098i	0.564049	+	0.825742i	$0.309243\pi$
$480$		0			0
$481$	7.47846	+	13.0941i	0.340988	+	0.597042i
$482$	5.73225	−	5.43570i	0.261097	−	0.247589i
$483$		0			0
$484$	5.74402	−	2.92140i	0.261092	−	0.132791i
$485$	3.49121	+	2.01565i	0.158528	+	0.0915261i
$486$		0			0
$487$	−15.2421	−	8.80006i	−0.690688	−	0.398769i	0.113182	−	0.993574i	$-0.463896\pi$
$487$	−15.2421	−	8.80006i	−0.690688	−	0.398769i	−0.803870	+	0.594806i	$0.797229\pi$
$488$	27.2625	−	5.02169i	1.23411	−	0.227321i
$489$		0			0
$490$	−4.23054	+	1.01402i	−0.191116	+	0.0458086i
$491$	−2.71307	+	1.56639i	−0.122439	+	0.0706902i	−0.559969	−	0.828514i	$-0.689187\pi$
$491$	−2.71307	+	1.56639i	−0.122439	+	0.0706902i	0.437530	+	0.899204i	$0.355854\pi$
$492$		0			0
$493$			4.37036i			0.196831i
$494$	−4.46541	−	4.75337i	−0.200908	−	0.213864i
$495$		0			0
$496$	26.2494	−	11.6407i	1.17863	−	0.522684i
$497$	5.94727	+	10.3010i	0.266772	+	0.462062i
$498$		0			0
$499$	41.9672			1.87871			0.939354	−	0.342948i	$-0.111425\pi$
$499$	41.9672			1.87871			0.939354	+	0.342948i	$0.111425\pi$
$500$	−9.80817	−	6.37976i	−0.438635	−	0.285312i
$501$		0			0
$502$	22.1573	−	21.0110i	0.988927	−	0.937766i
$503$	14.4037	−	24.9479i	0.642229	−	1.11237i	−0.342706	−	0.939443i	$-0.611343\pi$
$503$	14.4037	−	24.9479i	0.642229	−	1.11237i	0.984934	−	0.172930i	$-0.0553233\pi$
$504$		0			0
$505$	−1.21692	+	0.702591i	−0.0541524	+	0.0312649i
$506$	27.7064	+	29.2179i	1.23170	+	1.29890i
$507$		0			0
$508$	−1.31336	+	24.7125i	−0.0582707	+	1.09644i
$509$	0.876217	+	1.51765i	0.0388376	+	0.0672688i	0.884791	−	0.465988i	$-0.154301\pi$
$509$	0.876217	+	1.51765i	0.0388376	+	0.0672688i	−0.845953	+	0.533257i	$0.820968\pi$
$510$		0			0
$511$	−10.1572	+	17.5928i	−0.449328	+	0.778258i
$512$	−11.7589	−	19.3321i	−0.519673	−	0.854365i
$513$		0			0
$514$	−17.7784	+	4.26131i	−0.784173	+	0.187958i
$515$	−6.19063			−0.272792
$516$		0			0
$517$	−2.43039	+	1.40318i	−0.106888	+	0.0617120i
$518$	−7.88943	−	2.34011i	−0.346642	−	0.102819i
$519$		0			0
$520$	4.73365	−	3.99582i	0.207584	−	0.175228i
$521$	−26.8545			−1.17652			−0.588259	−	0.808673i	$-0.700186\pi$
$521$	−26.8545			−1.17652			−0.588259	+	0.808673i	$0.700186\pi$
$522$		0			0
$523$	−16.1132	+	9.30294i	−0.704580	+	0.406789i	−0.809051	−	0.587739i	$-0.800018\pi$
$523$	−16.1132	+	9.30294i	−0.704580	+	0.406789i	0.104471	+	0.994528i	$0.466685\pi$
$524$	17.6207	−	27.0898i	0.769763	−	1.18342i
$525$		0			0
$526$	−23.5093	+	5.63494i	−1.02505	+	0.245695i
$527$	2.75587	+	1.59110i	0.120048	+	0.0693096i
$528$		0			0
$529$	−17.0001	+	29.4451i	−0.739136	+	1.28022i
$530$	−1.02408	−	0.303756i	−0.0444832	−	0.0131943i
$531$		0			0
$532$	3.55413	+	0.188886i	0.154091	+	0.00818924i
$533$	−31.5016	+	17.9915i	−1.36449	+	0.779299i
$534$		0			0
$535$	2.97132	−	1.71549i	0.128461	−	0.0741672i
$536$	27.0162	+	9.60051i	1.16692	+	0.414679i
$537$		0			0
$538$	−2.83244	+	2.68591i	−0.122115	+	0.115798i
$539$	9.54907	−	16.5395i	0.411308	−	0.712406i
$540$		0			0
$541$	−27.0675			−1.16372			−0.581862	−	0.813287i	$-0.697676\pi$
$541$	−27.0675			−1.16372			−0.581862	+	0.813287i	$0.697676\pi$
$542$	2.57440	+	10.7406i	0.110580	+	0.461346i
$543$		0			0
$544$	0.963877	−	2.31496i	0.0413259	−	0.0992529i
$545$	−1.72289			−0.0738003
$546$		0			0
$547$		−	17.2928i		−	0.739386i	−0.929154	−	0.369693i	$-0.879463\pi$
$547$		−	17.2928i		−	0.739386i	0.929154	−	0.369693i	$-0.120537\pi$
$548$	−16.5824	−	32.6040i	−0.708365	−	1.39278i
$549$		0			0
$550$	24.0184	−	5.75696i	1.02415	−	0.245478i
$551$		−	12.6100i		−	0.537206i
$552$		0			0
$553$	15.4210	+	8.90334i	0.655769	+	0.378608i
$554$	28.4610	−	26.9886i	1.20919	−	1.14664i
$555$		0			0
$556$	10.1732	+	20.0024i	0.431440	+	0.848290i
$557$	14.2320	+	24.6506i	0.603031	+	1.04448i	0.992359	+	0.123382i	$0.0393739\pi$
$557$	14.2320	+	24.6506i	0.603031	+	1.04448i	−0.389328	+	0.921099i	$0.627293\pi$
$558$		0			0
$559$	22.0366	+	12.8607i	0.932051	+	0.543949i
$560$	−0.358316	+	3.36156i	−0.0151416	+	0.142052i
$561$		0			0
$562$	3.31738	+	0.983981i	0.139935	+	0.0415067i
$563$	30.7791	+	17.7703i	1.29719	+	0.748931i	0.979917	−	0.199405i	$-0.0639009\pi$
$563$	30.7791	+	17.7703i	1.29719	+	0.748931i	0.317269	+	0.948336i	$0.397234\pi$
$564$		0			0
$565$	3.25570	−	5.63904i	0.136968	−	0.237236i
$566$	−8.44320	−	35.2256i	−0.354894	−	1.48064i
$567$		0			0
$568$	−23.7802	+	4.38026i	−0.997794	+	0.183792i
$569$	8.05172	+	13.9460i	0.337546	+	0.584646i	0.983970	−	0.178332i	$-0.0570700\pi$
$569$	8.05172	+	13.9460i	0.337546	+	0.584646i	−0.646425	+	0.762978i	$0.723737\pi$
$570$		0			0
$571$		−	12.5382i		−	0.524709i	−0.964972	−	0.262354i	$-0.915501\pi$
$571$		−	12.5382i		−	0.524709i	0.964972	−	0.262354i	$-0.0844989\pi$
$572$	−1.57026	+	27.1493i	−0.0656558	+	1.13517i
$573$		0			0
$574$	5.62979	−	18.9802i	0.234983	−	0.792219i
$575$	17.4818	+	30.2793i	0.729039	+	1.26273i
$576$		0			0
$577$		−	21.9913i		−	0.915508i	−0.889079	−	0.457754i	$-0.848654\pi$
$577$		−	21.9913i		−	0.915508i	0.889079	−	0.457754i	$-0.151346\pi$
$578$	−23.1092	+	5.53903i	−0.961215	+	0.230393i
$579$		0			0
$580$	11.9606	+	0.635651i	0.496637	+	0.0263940i
$581$	7.45889	+	4.30639i	0.309447	+	0.178659i
$582$		0			0
$583$	4.06107	−	2.34466i	0.168192	−	0.0971059i
$584$	−26.7854	−	31.4319i	−1.10839	−	1.30066i
$585$		0			0
$586$	21.1610	+	22.3155i	0.874153	+	0.921844i
$587$	−10.2081	−	17.6809i	−0.421332	−	0.729768i	0.574738	−	0.818337i	$-0.305104\pi$
$587$	−10.2081	−	17.6809i	−0.421332	−	0.729768i	−0.996070	+	0.0885691i	$0.971771\pi$
$588$		0			0
$589$	−7.95167	−	4.59090i	−0.327643	−	0.189165i
$590$	1.51633	+	1.59906i	0.0624264	+	0.0658322i
$591$		0			0
$592$	9.85292	−	13.5195i	0.404953	−	0.555648i
$593$		−	47.9756i		−	1.97012i	−0.172205	−	0.985061i	$-0.555089\pi$
$593$		−	47.9756i		−	1.97012i	0.172205	−	0.985061i	$-0.444911\pi$
$594$		0			0
$595$	−0.324451	+	0.187322i	−0.0133012	+	0.00767945i
$596$	−15.5505	+	7.90896i	−0.636973	+	0.323964i
$597$		0			0
$598$	−37.4780	+	8.79791i	−1.53259	+	0.359773i
$599$	−8.54606			−0.349182			−0.174591	−	0.984641i	$-0.555860\pi$
$599$	−8.54606			−0.349182			−0.174591	+	0.984641i	$0.555860\pi$
$600$		0			0
$601$	−9.73052	−	16.8538i	−0.396916	−	0.687479i	0.596427	−	0.802667i	$-0.296586\pi$
$601$	−9.73052	−	16.8538i	−0.396916	−	0.687479i	−0.993344	+	0.115188i	$0.963253\pi$
$602$	−13.5407	+	3.24556i	−0.551876	+	0.132279i
$603$		0			0
$604$	−7.39459	+	11.3684i	−0.300882	+	0.462572i
$605$	0.978620	−	1.69502i	0.0397866	−	0.0689124i
$606$		0			0
$607$	0.0399237	−	0.0691499i	0.00162045	−	0.00280671i	−0.865214	−	0.501403i	$-0.832818\pi$
$607$	0.0399237	−	0.0691499i	0.00162045	−	0.00280671i	0.866834	+	0.498596i	$0.166151\pi$
$608$	−2.78113	+	6.67947i	−0.112790	+	0.270888i
$609$		0			0
$610$	6.10937	−	5.79331i	0.247361	−	0.234564i
$611$	0.0125514	−	2.68305i	0.000507775	−	0.108545i
$612$		0			0
$613$	7.45333	+	12.9095i	0.301037	+	0.521411i	0.976371	−	0.216101i	$-0.0693339\pi$
$613$	7.45333	+	12.9095i	0.301037	+	0.521411i	−0.675334	+	0.737512i	$0.736001\pi$
$614$	−0.254204	+	0.857022i	−0.0102589	+	0.0345866i
$615$		0			0
$616$	−9.62593	−	11.2957i	−0.387840	−	0.455118i
$617$	−15.4574	−	8.92435i	−0.622293	−	0.359281i	0.155468	−	0.987841i	$-0.450311\pi$
$617$	−15.4574	−	8.92435i	−0.622293	−	0.359281i	−0.777761	+	0.628560i	$0.783645\pi$
$618$		0			0
$619$	−49.5023			−1.98967			−0.994834	−	0.101519i	$-0.967630\pi$
$619$	−49.5023			−1.98967			−0.994834	+	0.101519i	$0.967630\pi$
$620$	4.75529	−	7.31072i	0.190977	−	0.293606i
$621$		0			0
$622$	11.6733	−	39.3551i	0.468055	−	1.57800i
$623$	0.852927			0.0341718
$624$		0			0
$625$	19.6014			0.784057
$626$	9.03196	−	30.4502i	0.360990	−	1.21704i
$627$		0			0
$628$	−6.89923	+	10.6068i	−0.275309	+	0.423257i
$629$	1.85393			0.0739209
$630$		0			0
$631$	−21.6858	−	12.5203i	−0.863297	−	0.498425i	0.00181769	−	0.999998i	$-0.499421\pi$
$631$	−21.6858	−	12.5203i	−0.863297	−	0.498425i	−0.865115	+	0.501573i	$0.832755\pi$
$632$	−27.5518	+	23.4789i	−1.09595	+	0.933941i
$633$		0			0
$634$	6.88942	−	23.2269i	0.273614	−	0.922458i
$635$	3.75812	+	6.50926i	0.149136	+	0.258312i
$636$		0			0
$637$	9.05551	+	15.8554i	0.358792	+	0.628215i
$638$	−38.1544	+	36.1805i	−1.51055	+	1.43240i
$639$		0			0
$640$	−6.19527	−	2.97460i	−0.244890	−	0.117581i
$641$	12.7666	−	22.1124i	0.504251	−	0.873388i	−0.495737	−	0.868473i	$-0.665102\pi$
$641$	12.7666	−	22.1124i	0.504251	−	0.873388i	0.999988	−	0.00491538i	$-0.00156462\pi$
$642$		0			0
$643$	15.1058	−	26.1640i	0.595715	−	1.03181i	−0.397731	−	0.917502i	$-0.630202\pi$
$643$	15.1058	−	26.1640i	0.595715	−	1.03181i	0.993446	−	0.114306i	$-0.0364644\pi$
$644$	11.4552	−	17.6110i	0.451397	−	0.693972i
$645$		0			0
$646$	−0.779744	+	0.186897i	−0.0306786	+	0.00735335i
$647$	15.2316	+	26.3820i	0.598818	+	1.03718i	0.992996	+	0.118149i	$0.0376960\pi$
$647$	15.2316	+	26.3820i	0.598818	+	1.03718i	−0.394178	+	0.919034i	$0.628971\pi$
$648$		0			0
$649$	−9.67422			−0.379746
$650$	−6.82080	+	22.6071i	−0.267534	+	0.886724i
$651$		0			0
$652$	−28.4066	+	14.4476i	−1.11249	+	0.565812i
$653$	25.5052	−	14.7254i	0.998096	−	0.576251i	0.0904115	−	0.995904i	$-0.471182\pi$
$653$	25.5052	−	14.7254i	0.998096	−	0.576251i	0.907684	+	0.419654i	$0.137848\pi$
$654$		0			0
$655$		−	9.81509i		−	0.383507i
$656$	32.5250	+	23.7040i	1.26989	+	0.925484i
$657$		0			0
$658$	1.00752	+	1.06249i	0.0392772	+	0.0414201i
$659$	−5.43988	−	3.14071i	−0.211907	−	0.122345i	0.390290	−	0.920692i	$-0.372375\pi$
$659$	−5.43988	−	3.14071i	−0.211907	−	0.122345i	−0.602198	+	0.798347i	$0.705708\pi$
$660$		0			0
$661$	6.19056	+	10.7224i	0.240785	+	0.417052i	0.960938	−	0.276763i	$-0.0892618\pi$
$661$	6.19056	+	10.7224i	0.240785	+	0.417052i	−0.720153	+	0.693815i	$0.755928\pi$
$662$	28.8572	+	30.4315i	1.12157	+	1.18276i
$663$		0			0
$664$	−13.3263	+	11.3563i	−0.517162	+	0.440712i
$665$	0.936157	−	0.540490i	0.0363026	−	0.0209593i
$666$		0			0
$667$	−64.4618	−	37.2170i	−2.49597	−	1.44105i
$668$	19.4945	+	1.03604i	0.754265	+	0.0400857i
$669$		0			0
$670$	8.46818	−	2.02974i	0.327154	−	0.0784155i
$671$			36.9614i			1.42688i
$672$		0			0
$673$	−14.3913	−	24.9264i	−0.554743	−	0.960843i	−0.997923	−	0.0644107i	$-0.979483\pi$
$673$	−14.3913	−	24.9264i	−0.554743	−	0.960843i	0.443180	−	0.896432i	$-0.353850\pi$
$674$	−6.43138	+	21.6827i	−0.247728	+	0.835186i
$675$		0			0
$676$	−21.6614	−	14.3799i	−0.833132	−	0.553075i
$677$			10.6400i			0.408928i	0.978874	+	0.204464i	$0.0655451\pi$
$677$			10.6400i			0.408928i	−0.978874	+	0.204464i	$0.934455\pi$
$678$		0			0
$679$	4.61686	+	7.99663i	0.177179	+	0.306882i
$680$	−0.137965	−	0.749007i	−0.00529073	−	0.0287231i
$681$		0			0
$682$	8.92403	+	37.2316i	0.341719	+	1.42567i
$683$	16.2301	−	28.1113i	0.621027	−	1.07565i	−0.368268	−	0.929720i	$-0.620049\pi$
$683$	16.2301	−	28.1113i	0.621027	−	1.07565i	0.989295	−	0.145930i	$-0.0466174\pi$
$684$		0			0
$685$	−9.62123	−	5.55482i	−0.367608	−	0.212239i
$686$	−22.7580	−	6.75035i	−0.868906	−	0.257729i
$687$		0			0
$688$	3.00022	−	28.1468i	0.114382	−	1.07309i
$689$	−0.0209728	+	4.48327i	−0.000799001	+	0.170799i
$690$		0			0
$691$	23.3686	+	40.4757i	0.888985	+	1.53977i	0.841077	+	0.540915i	$0.181922\pi$
$691$	23.3686	+	40.4757i	0.888985	+	1.53977i	0.0479072	+	0.998852i	$0.484745\pi$
$692$	11.6712	+	22.9477i	0.443671	+	0.872340i
$693$		0			0
$694$	−23.2611	+	22.0577i	−0.882980	+	0.837299i
$695$	5.90257	+	3.40785i	0.223897	+	0.129267i
$696$		0			0
$697$			4.46014i			0.168940i
$698$	−14.5263	+	3.48181i	−0.549830	+	0.131789i
$699$		0			0
$700$	−5.84196	−	11.4864i	−0.220805	−	0.434144i
$701$			33.6184i			1.26975i	0.772615	+	0.634875i	$0.218949\pi$
$701$			33.6184i			1.26975i	−0.772615	+	0.634875i	$0.781051\pi$
$702$		0			0
$703$	−5.34923			−0.201750
$704$	28.1897	−	10.7497i	1.06244	−	0.405145i
$705$		0			0
$706$	5.98100	+	24.9531i	0.225098	+	0.939122i
$707$	−3.21857			−0.121047
$708$		0			0
$709$	22.0869	−	38.2556i	0.829490	−	1.43672i	−0.0689481	−	0.997620i	$-0.521964\pi$
$709$	22.0869	−	38.2556i	0.829490	−	1.43672i	0.898439	−	0.439099i	$-0.144702\pi$
$710$	−5.32900	+	5.05331i	−0.199994	+	0.189647i
$711$		0			0
$712$	−0.580591	+	1.63381i	−0.0217586	+	0.0612295i
$713$	−46.9368	+	27.0990i	−1.75780	+	1.01486i
$714$		0			0
$715$	4.09626	+	7.17221i	0.153192	+	0.268226i
$716$	−13.0001	−	0.690897i	−0.485837	−	0.0258200i
$717$		0			0
$718$	15.5397	+	4.60927i	0.579935	+	0.172017i
$719$	13.3551	−	23.1317i	0.498060	−	0.862666i	−0.501937	−	0.864904i	$-0.667379\pi$
$719$	13.3551	−	23.1317i	0.498060	−	0.862666i	0.999997	+	0.00223845i	$0.000712522\pi$
$720$		0			0
$721$	−12.2799	−	7.08983i	−0.457329	−	0.264039i
$722$	−23.8801	+	5.72382i	−0.888725	+	0.213018i
$723$		0			0
$724$	18.2594	−	28.0718i	0.678607	−	1.04328i
$725$	−39.5404	+	22.8286i	−1.46849	+	0.847834i
$726$		0			0
$727$	−14.4767			−0.536913			−0.268456	−	0.963292i	$-0.586514\pi$
$727$	−14.4767			−0.536913			−0.268456	+	0.963292i	$0.586514\pi$
$728$	13.9660	−	2.50502i	0.517616	−	0.0928424i
$729$		0			0
$730$	−12.0248	−	3.56672i	−0.445058	−	0.132010i
$731$	2.71667	−	1.56847i	0.100480	−	0.0580120i
$732$		0			0
$733$	11.4614			0.423335			0.211668	−	0.977342i	$-0.432111\pi$
$733$	11.4614			0.423335			0.211668	+	0.977342i	$0.432111\pi$
$734$	−21.8364	+	5.23395i	−0.805995	+	0.193189i
$735$		0			0
$736$	25.9369	+	33.9306i	0.956046	+	1.25070i
$737$	−19.1142	+	33.1067i	−0.704079	+	1.21950i
$738$		0			0
$739$	14.6329	+	25.3449i	0.538279	+	0.932327i	0.998997	+	0.0447805i	$0.0142589\pi$
$739$	14.6329	+	25.3449i	0.538279	+	0.932327i	−0.460717	+	0.887547i	$0.652408\pi$
$740$	0.269646	−	5.07374i	0.00991238	−	0.186514i
$741$		0			0
$742$	−1.68352	−	1.77537i	−0.0618041	−	0.0651759i
$743$	−23.6443	+	13.6511i	−0.867426	+	0.500809i	−0.866492	−	0.499191i	$-0.833631\pi$
$743$	−23.6443	+	13.6511i	−0.867426	+	0.500809i	−0.000934125		1.00000i	$0.500297\pi$
$744$		0			0
$745$	−2.64937	+	4.58884i	−0.0970654	+	0.168122i
$746$	−6.40757	+	6.07608i	−0.234598	+	0.222461i
$747$		0			0
$748$	2.80272	+	1.82304i	0.102478	+	0.0666570i
$749$	7.85868			0.287150
$750$		0			0
$751$	2.80553	+	4.85932i	0.102375	+	0.177319i	0.912663	−	0.408713i	$-0.134022\pi$
$751$	2.80553	+	4.85932i	0.102375	+	0.177319i	−0.810288	+	0.586033i	$0.800689\pi$
$752$	−2.72105	+	1.20670i	−0.0992265	+	0.0440037i
$753$		0			0
$754$	−11.4888	−	48.9409i	−0.418397	−	1.78232i
$755$			4.11895i			0.149904i
$756$		0			0
$757$	−30.4433	+	17.5765i	−1.10648	+	0.638827i	−0.937916	−	0.346863i	$-0.887247\pi$
$757$	−30.4433	+	17.5765i	−1.10648	+	0.638827i	−0.168565	+	0.985690i	$0.553913\pi$
$758$	11.0552	−	2.64982i	0.401544	−	0.0962459i
$759$		0			0
$760$	0.398080	+	2.16115i	0.0144399	+	0.0783932i
$761$	3.41599	+	1.97222i	0.123830	+	0.0714931i	0.560635	−	0.828063i	$-0.310557\pi$
$761$	3.41599	+	1.97222i	0.123830	+	0.0714931i	−0.436806	+	0.899556i	$0.643890\pi$
$762$		0			0
$763$	−3.41757	−	1.97314i	−0.123724	−	0.0714323i
$764$	26.3408	−	13.3969i	0.952975	−	0.484682i
$765$		0			0
$766$	−27.0030	+	25.6060i	−0.975658	+	0.925183i
$767$	4.66203	−	7.98834i	0.168336	−	0.288442i
$768$		0			0
$769$	7.64135	−	4.41174i	0.275554	−	0.159091i	−0.355855	−	0.934541i	$-0.615810\pi$
$769$	7.64135	−	4.41174i	0.275554	−	0.159091i	0.631409	+	0.775450i	$0.282477\pi$
$770$	−4.32137	−	1.28178i	−0.155731	−	0.0461920i
$771$		0			0
$772$	−19.6575	−	1.04471i	−0.707490	−	0.0375999i
$773$	−23.4570	+	40.6288i	−0.843691	+	1.46132i	0.0430627	+	0.999072i	$0.486288\pi$
$773$	−23.4570	+	40.6288i	−0.843691	+	1.46132i	−0.886753	+	0.462243i	$0.847045\pi$
$774$		0			0
$775$			33.2446i			1.19418i
$776$	−18.4605	+	3.40039i	−0.662693	+	0.122067i
$777$		0			0
$778$	−34.3081	−	10.1762i	−1.23000	−	0.364836i
$779$		−	12.8691i		−	0.461083i
$780$		0			0
$781$		−	32.2402i		−	1.15364i
$782$	−1.34592	+	4.53761i	−0.0481299	+	0.162265i
$783$		0			0
$784$	11.9307	−	16.3705i	0.426096	−	0.584660i
$785$			3.84301i			0.137163i
$786$		0			0
$787$	−5.38025	+	9.31886i	−0.191785	+	0.332182i	−0.945842	−	0.324628i	$-0.894761\pi$
$787$	−5.38025	+	9.31886i	−0.191785	+	0.332182i	0.754057	+	0.656809i	$0.228094\pi$
$788$	−1.05650	+	19.8795i	−0.0376364	+	0.708177i
$789$		0			0
$790$	−3.12642	+	10.5404i	−0.111233	+	0.375010i
$791$	12.9162	−	7.45719i	0.459248	−	0.265147i
$792$		0			0
$793$	−30.5203	−	17.8118i	−1.08381	−	0.632515i
$794$	−13.5761	−	14.3167i	−0.481797	−	0.508082i
$795$		0			0
$796$	11.1445	−	5.66809i	0.395007	−	0.200900i
$797$	−46.6440	−	26.9299i	−1.65222	−	0.953908i	−0.976158	−	0.217060i	$-0.930353\pi$
$797$	−46.6440	−	26.9299i	−1.65222	−	0.953908i	−0.676058	−	0.736848i	$-0.736313\pi$
$798$		0			0
$799$	−0.285678	−	0.164936i	−0.0101066	−	0.00583503i
$800$	25.9791	−	3.37162i	0.918501	−	0.119205i
$801$		0			0
$802$	6.21023	+	25.9095i	0.219291	+	0.914895i
$803$	47.6852	−	27.5311i	1.68278	−	0.971551i
$804$		0			0
$805$		−	6.38077i		−	0.224893i
$806$	−35.0440	−	10.5731i	−1.23437	−	0.372422i
$807$		0			0
$808$	2.19090	−	6.16527i	0.0770755	−	0.216894i
$809$	−18.9278	−	32.7838i	−0.665465	−	1.15262i	−0.979159	−	0.203095i	$-0.934900\pi$
$809$	−18.9278	−	32.7838i	−0.665465	−	1.15262i	0.313694	−	0.949524i	$-0.398433\pi$
$810$		0			0
$811$	−8.84124			−0.310458			−0.155229	−	0.987879i	$-0.549612\pi$
$811$	−8.84124			−0.310458			−0.155229	+	0.987879i	$0.549612\pi$
$812$	22.9975	+	14.9588i	0.807052	+	0.524950i
$813$		0			0
$814$	15.3479	+	16.1852i	0.537944	+	0.567293i
$815$	−4.83970	+	8.38261i	−0.169527	+	0.293630i
$816$		0			0
$817$	−7.83856	+	4.52560i	−0.274237	+	0.158331i
$818$	−31.3710	+	29.7480i	−1.09686	+	1.04012i
$819$		0			0
$820$	12.2063	+	0.648709i	0.426262	+	0.0226539i
$821$	0.351948	+	0.609591i	0.0122831	+	0.0212749i	0.872102	−	0.489325i	$-0.162757\pi$
$821$	0.351948	+	0.609591i	0.0122831	+	0.0212749i	−0.859819	+	0.510600i	$0.829423\pi$
$822$		0			0
$823$	24.5405	−	42.5054i	0.855429	−	1.48165i	−0.0208180	−	0.999783i	$-0.506627\pi$
$823$	24.5405	−	42.5054i	0.855429	−	1.48165i	0.876247	−	0.481863i	$-0.160040\pi$
$824$	21.9398	−	18.6965i	0.764309	−	0.651324i
$825$		0			0
$826$	1.17652	+	4.90853i	0.0409365	+	0.170790i
$827$	−46.7086			−1.62422			−0.812109	−	0.583506i	$-0.801681\pi$
$827$	−46.7086			−1.62422			−0.812109	+	0.583506i	$0.801681\pi$
$828$		0			0
$829$	−21.8762	+	12.6302i	−0.759792	+	0.438666i	−0.829221	−	0.558921i	$-0.811216\pi$
$829$	−21.8762	+	12.6302i	−0.759792	+	0.438666i	0.0694293	+	0.997587i	$0.477882\pi$
$830$	−1.51220	+	5.09821i	−0.0524892	+	0.176961i
$831$		0			0
$832$	−4.70830	+	28.4575i	−0.163231	+	0.986588i
$833$	2.24488			0.0777805
$834$		0			0
$835$	5.13484	−	2.96460i	0.177699	−	0.102594i
$836$	−8.08685	−	5.26012i	−0.279690	−	0.181925i
$837$		0			0
$838$	5.95155	+	24.8302i	0.205593	+	0.857746i
$839$	38.8853	+	22.4504i	1.34247	+	0.775075i	0.987169	−	0.159677i	$-0.0510451\pi$
$839$	38.8853	+	22.4504i	1.34247	+	0.775075i	0.355301	+	0.934752i	$0.384378\pi$
$840$		0			0
$841$	34.1000	−	59.0630i	1.17586	−	2.03666i
$842$	−5.69903	+	19.2136i	−0.196401	+	0.662146i
$843$		0			0
$844$	8.37246	+	0.444958i	0.288192	+	0.0153161i
$845$	−7.89635	−	0.0738802i	−0.271643	−	0.00254156i
$846$		0			0
$847$	3.88245	−	2.24153i	0.133402	−	0.0770199i
$848$	4.54676	−	2.01634i	0.156136	−	0.0692413i
$849$		0			0
$850$	1.99765	+	2.10663i	0.0685188	+	0.0722570i
$851$	−15.7876	+	27.3450i	−0.541193	+	0.937373i
$852$		0			0
$853$	−11.4426			−0.391786			−0.195893	−	0.980625i	$-0.562761\pi$
$853$	−11.4426			−0.391786			−0.195893	+	0.980625i	$0.562761\pi$
$854$	18.7535	−	4.49503i	0.641733	−	0.153817i
$855$		0			0
$856$	−5.34943	+	15.0535i	−0.182840	+	0.514519i
$857$	26.9979			0.922229			0.461115	−	0.887341i	$-0.347450\pi$
$857$	26.9979			0.922229			0.461115	+	0.887341i	$0.347450\pi$
$858$		0			0
$859$		−	37.9349i		−	1.29432i	−0.762353	−	0.647162i	$-0.775956\pi$
$859$		−	37.9349i		−	1.29432i	0.762353	−	0.647162i	$-0.224044\pi$
$860$	−3.89739	−	7.66299i	−0.132900	−	0.261306i
$861$		0			0
$862$	4.34731	+	18.1372i	0.148070	+	0.617756i
$863$		−	6.51581i		−	0.221801i	−0.993832	−	0.110900i	$-0.964627\pi$
$863$		−	6.51581i		−	0.221801i	0.993832	−	0.110900i	$-0.0353735\pi$
$864$		0			0
$865$	6.77170	+	3.90964i	0.230245	+	0.132932i
$866$	−3.72999	−	3.93348i	−0.126750	−	0.133665i
$867$		0			0
$868$	17.8054	−	9.05579i	0.604353	−	0.307374i
$869$	−24.1325	−	41.7987i	−0.818639	−	1.41792i
$870$		0			0
$871$	−18.1262	−	31.7375i	−0.614183	−	1.07538i
$872$	6.10596	−	5.20334i	0.206774	−	0.176207i
$873$		0			0
$874$	3.88345	−	13.0926i	0.131360	−	0.442864i
$875$	−7.04916	−	4.06984i	−0.238305	−	0.137586i
$876$		0			0
$877$	16.8078	−	29.1120i	0.567560	−	0.983043i	−0.429246	−	0.903187i	$-0.641221\pi$
$877$	16.8078	−	29.1120i	0.567560	−	0.983043i	0.996806	−	0.0798554i	$-0.0254459\pi$
$878$	−10.6336	+	2.54877i	−0.358867	+	0.0860167i
$879$		0			0
$880$	5.39686	−	7.40520i	0.181928	−	0.249629i
$881$	16.0271	+	27.7598i	0.539967	+	0.935250i	0.998905	+	0.0467821i	$0.0148966\pi$
$881$	16.0271	+	27.7598i	0.539967	+	0.935250i	−0.458938	+	0.888468i	$0.651770\pi$
$882$		0			0
$883$			29.4544i			0.991220i	0.868545	+	0.495610i	$0.165055\pi$
$883$			29.4544i			0.991220i	−0.868545	+	0.495610i	$0.834945\pi$
$884$	−2.85599	+	1.43578i	−0.0960573	+	0.0482904i
$885$		0			0
$886$	19.9285	+	5.91106i	0.669511	+	0.198586i
$887$	28.1761	+	48.8024i	0.946061	+	1.63863i	0.753613	+	0.657318i	$0.228309\pi$
$887$	28.1761	+	48.8024i	0.946061	+	1.63863i	0.192447	+	0.981307i	$0.438358\pi$
$888$		0			0
$889$			17.2160i			0.577405i
$890$	0.122748	+	0.512113i	0.00411453	+	0.0171661i
$891$		0			0
$892$	28.4661	+	1.51285i	0.953116	+	0.0506538i
$893$	0.824283	+	0.475900i	0.0275836	+	0.0159254i
$894$		0			0
$895$	−3.42422	+	1.97698i	−0.114459	+	0.0660831i
$896$	−8.88248	−	12.9956i	−0.296743	−	0.434154i
$897$		0			0
$898$	29.6081	−	28.0764i	0.988036	−	0.936921i
$899$	−35.3873	−	61.2927i	−1.18023	−	2.04423i
$900$		0			0
$901$	0.477356	+	0.275602i	0.0159030	+	0.00918162i
$902$	−38.9381	+	36.9237i	−1.29650	+	1.22942i
$903$		0			0
$904$	5.49233	+	29.8176i	0.182672	+	0.991717i
$905$		−	10.1709i		−	0.338092i
$906$		0			0
$907$	11.2076	−	6.47069i	0.372141	−	0.214856i	−0.302252	−	0.953228i	$-0.597739\pi$
$907$	11.2076	−	6.47069i	0.372141	−	0.214856i	0.674393	+	0.738372i	$0.264405\pi$
$908$	47.6822	−	24.2511i	1.58239	−	0.804801i
$909$		0			0
$910$	3.14089	−	2.95062i	0.104119	−	0.0978120i
$911$	−3.09546			−0.102557			−0.0512785	−	0.998684i	$-0.516330\pi$
$911$	−3.09546			−0.102557			−0.0512785	+	0.998684i	$0.516330\pi$
$912$		0			0
$913$	−11.6725	−	20.2173i	−0.386303	−	0.669096i
$914$	0.594893	+	2.48193i	0.0196773	+	0.0820950i
$915$		0			0
$916$	20.6595	+	13.4380i	0.682609	+	0.444006i
$917$	11.2407	−	19.4695i	0.371202	−	0.642941i
$918$		0			0
$919$	2.11908	−	3.67036i	0.0699021	−	0.121074i	−0.828956	−	0.559314i	$-0.811065\pi$
$919$	2.11908	−	3.67036i	0.0699021	−	0.121074i	0.898858	+	0.438240i	$0.144398\pi$
$920$	12.2226	+	4.34342i	0.402966	+	0.143198i
$921$		0			0
$922$	9.67122	+	10.1989i	0.318505	+	0.335881i
$923$	26.6219	+	15.5366i	0.876269	+	0.511395i
$924$		0			0
$925$	9.68400	+	16.7732i	0.318408	+	0.551499i
$926$	18.8672	+	5.59626i	0.620014	+	0.183905i
$927$		0			0
$928$	−44.3085	+	33.8698i	−1.45450	+	1.11183i
$929$	−39.4013	−	22.7484i	−1.29272	−	0.746350i	−0.313581	−	0.949561i	$-0.601529\pi$
$929$	−39.4013	−	22.7484i	−1.29272	−	0.746350i	−0.979135	+	0.203211i	$0.934862\pi$
$930$		0			0
$931$	−6.47728			−0.212284
$932$	−26.7382	−	17.3919i	−0.875838	−	0.569692i
$933$		0			0
$934$	33.6500	+	9.98105i	1.10106	+	0.326590i
$935$	1.01547			0.0332095
$936$		0			0
$937$	−4.22328			−0.137968			−0.0689842	−	0.997618i	$-0.521976\pi$
$937$	−4.22328			−0.137968			−0.0689842	+	0.997618i	$0.521976\pi$
$938$	19.1223	+	5.67194i	0.624366	+	0.185195i
$939$		0			0
$940$	−0.492941	+	0.757841i	−0.0160780	+	0.0247181i
$941$	−41.6566			−1.35797			−0.678984	−	0.734153i	$-0.737579\pi$
$941$	−41.6566			−1.35797			−0.678984	+	0.734153i	$0.737579\pi$
$942$		0			0
$943$	−65.7859	−	37.9815i	−2.14229	−	1.23685i
$944$	−10.2033	−	1.08759i	−0.332089	−	0.0353980i
$945$		0			0
$946$	36.1834	+	10.7325i	1.17642	+	0.348943i
$947$	5.60915	+	9.71533i	0.182273	+	0.315706i	0.942654	−	0.333771i	$-0.108321\pi$
$947$	5.60915	+	9.71533i	0.182273	+	0.315706i	−0.760381	+	0.649477i	$0.774988\pi$
$948$		0			0
$949$	−0.246264	+	52.6427i	−0.00799406	+	1.70885i
$950$	−5.76393	−	6.07839i	−0.187007	−	0.197209i
$951$		0			0
$952$	0.584128	−	1.64376i	0.0189317	−	0.0532745i
$953$	−19.4509	+	33.6900i	−0.630077	+	1.09133i	0.357458	+	0.933929i	$0.383643\pi$
$953$	−19.4509	+	33.6900i	−0.630077	+	1.09133i	−0.987535	+	0.157397i	$0.949690\pi$
$954$		0			0
$955$	4.48773	−	7.77298i	0.145220	−	0.251528i
$956$	−16.1434	+	24.8187i	−0.522116	+	0.802695i
$957$		0			0
$958$	1.09096	+	4.55156i	0.0352474	+	0.147054i
$959$	−12.7233	−	22.0374i	−0.410858	−	0.711626i
$960$		0			0
$961$	−20.5334			−0.662369
$962$	−20.7609	+	4.87360i	−0.669359	+	0.157131i
$963$		0			0
$964$	5.06461	+	9.95796i	0.163120	+	0.320724i
$965$	−5.17778	+	2.98940i	−0.166679	+	0.0962320i
$966$		0			0
$967$			1.85906i			0.0597833i	0.999553	+	0.0298916i	$0.00951622\pi$
$967$			1.85906i			0.0597833i	−0.999553	+	0.0298916i	$0.990484\pi$
$968$	1.65092	+	8.96276i	0.0530627	+	0.288074i
$969$		0			0
$970$	−4.13689	+	3.92288i	−0.132828	+	0.125956i
$971$	14.7354	+	8.50748i	0.472881	+	0.273018i	0.717445	−	0.696615i	$-0.245311\pi$
$971$	14.7354	+	8.50748i	0.472881	+	0.273018i	−0.244564	+	0.969633i	$0.578645\pi$
$972$		0			0
$973$	7.80568	+	13.5198i	0.250239	+	0.433426i
$974$	18.0611	−	17.1267i	0.578715	−	0.548776i
$975$		0			0
$976$	−4.15525	+	38.9827i	−0.133006	+	1.24781i
$977$	24.8030	−	14.3200i	0.793518	−	0.458138i	−0.0476817	−	0.998863i	$-0.515183\pi$
$977$	24.8030	−	14.3200i	0.793518	−	0.458138i	0.841199	+	0.540725i	$0.181850\pi$
$978$		0			0
$979$	−2.00213	−	1.15593i	−0.0639883	−	0.0369437i
$980$	0.326509	−	6.14368i	0.0104299	−	0.196253i
$981$		0			0
$982$	−1.03268	−	4.30839i	−0.0329541	−	0.137486i
$983$			44.7649i			1.42778i	0.700259	+	0.713889i	$0.253068\pi$
$983$			44.7649i			1.42778i	−0.700259	+	0.713889i	$0.746932\pi$
$984$		0			0
$985$	3.02315	+	5.23625i	0.0963256	+	0.166841i
$986$	−5.92546	−	1.75757i	−0.188705	−	0.0559725i
$987$		0			0
$988$	8.24054	−	4.14273i	0.262167	−	0.131798i
$989$			53.4270i			1.69888i
$990$		0			0
$991$	−21.4553	−	37.1617i	−0.681550	−	1.18048i	−0.974508	−	0.224354i	$-0.927973\pi$
$991$	−21.4553	−	37.1617i	−0.681550	−	1.18048i	0.292958	−	0.956125i	$-0.405360\pi$
$992$	5.22645	+	40.2710i	0.165940	+	1.27861i
$993$		0			0
$994$	−16.3581	+	3.92087i	−0.518847	+	0.124362i
$995$	1.89871	−	3.28867i	0.0601933	−	0.104258i
$996$		0			0
$997$	40.4603	+	23.3598i	1.28139	+	0.739811i	0.977102	−	0.212769i	$-0.0682483\pi$
$997$	40.4603	+	23.3598i	1.28139	+	0.739811i	0.304288	+	0.952580i	$0.401582\pi$
$998$	−16.8774	+	56.9003i	−0.534245	+	1.80115i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.dg.f.829.12	yes	56
3.2	odd	2	inner	936.2.dg.f.829.17	yes	56
8.5	even	2	inner	936.2.dg.f.829.2	✓	56
13.4	even	6	inner	936.2.dg.f.901.2	yes	56
24.5	odd	2	inner	936.2.dg.f.829.27	yes	56
39.17	odd	6	inner	936.2.dg.f.901.27	yes	56
104.69	even	6	inner	936.2.dg.f.901.12	yes	56
312.173	odd	6	inner	936.2.dg.f.901.17	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.dg.f.829.2	✓	56	8.5	even	2	inner
936.2.dg.f.829.12	yes	56	1.1	even	1	trivial
936.2.dg.f.829.17	yes	56	3.2	odd	2	inner
936.2.dg.f.829.27	yes	56	24.5	odd	2	inner
936.2.dg.f.901.2	yes	56	13.4	even	6	inner
936.2.dg.f.901.12	yes	56	104.69	even	6	inner
936.2.dg.f.901.17	yes	56	312.173	odd	6	inner
936.2.dg.f.901.27	yes	56	39.17	odd	6	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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.dg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.402157 + 1.35583i) q^{2} +(-1.67654 - 1.09051i) q^{4} -0.607438 q^{5} +(-1.20493 - 0.695669i) q^{7} +(2.15278 - 1.83454i) q^{8} +(0.244286 - 0.823582i) q^{10} +(1.88561 + 3.26597i) q^{11} +(-3.60551 - 0.0168667i) q^{13} +(1.42778 - 1.35392i) q^{14} +(1.62157 + 3.65657i) q^{16} +(-0.221643 + 0.383897i) q^{17} +(0.639519 - 1.10768i) q^{19} +(1.01839 + 0.662418i) q^{20} +(-5.18641 + 1.24313i) q^{22} +(-3.77493 - 6.53836i) q^{23} -4.63102 q^{25} +(1.47285 - 4.88167i) q^{26} +(1.26148 + 2.48031i) q^{28} +(8.53815 - 4.92951i) q^{29} -7.17868i q^{31} +(-5.60981 + 0.728052i) q^{32} +(-0.431363 - 0.454897i) q^{34} +(0.731923 + 0.422576i) q^{35} +(-2.09112 - 3.62192i) q^{37} +(1.24464 + 1.31254i) q^{38} +(-1.30768 + 1.11437i) q^{40} +(8.71354 - 5.03077i) q^{41} +(-6.12848 - 3.53828i) q^{43} +(0.400282 - 7.53182i) q^{44} +(10.3830 - 2.48870i) q^{46} +0.744154i q^{47} +(-2.53209 - 4.38571i) q^{49} +(1.86240 - 6.27887i) q^{50} +(6.02639 + 3.96013i) q^{52} -1.24345i q^{53} +(-1.14539 - 1.98388i) q^{55} +(-3.87019 + 0.712881i) q^{56} +(3.24988 + 13.5587i) q^{58} +(-1.28264 + 2.22159i) q^{59} +(8.48782 + 4.90045i) q^{61} +(9.73306 + 2.88696i) q^{62} +(1.26891 - 7.89873i) q^{64} +(2.19013 + 0.0102455i) q^{65} +(5.06843 + 8.77877i) q^{67} +(0.790237 - 0.401914i) q^{68} +(-0.867288 + 0.822420i) q^{70} +(-7.40365 - 4.27450i) q^{71} -14.6006i q^{73} +(5.75166 - 1.37861i) q^{74} +(-2.28012 + 1.15966i) q^{76} -5.24705i q^{77} -12.7982 q^{79} +(-0.985003 - 2.22114i) q^{80} +(3.31664 + 13.8372i) q^{82} -6.19029 q^{83} +(0.134634 - 0.233194i) q^{85} +(7.26192 - 6.88623i) q^{86} +(10.0509 + 3.57169i) q^{88} +(-0.530897 + 0.306513i) q^{89} +(4.33267 + 2.52857i) q^{91} +(-0.801349 + 15.0784i) q^{92} +(-1.00894 - 0.299267i) q^{94} +(-0.388468 + 0.672847i) q^{95} +(-5.74744 - 3.31829i) q^{97} +(6.96456 - 1.66933i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{10} - 4 q^{16} + 64 q^{25} - 48 q^{28} - 48 q^{40} + 20 q^{49} - 12 q^{52} + 16 q^{55} + 12 q^{58} - 72 q^{64} - 84 q^{76} + 80 q^{79} - 12 q^{82} - 12 q^{88} - 24 q^{94} + 24 q^{97}+O(q^{100}) \) 56 * q - 4 * q^10 - 4 * q^16 + 64 * q^25 - 48 * q^28 - 48 * q^40 + 20 * q^49 - 12 * q^52 + 16 * q^55 + 12 * q^58 - 72 * q^64 - 84 * q^76 + 80 * q^79 - 12 * q^82 - 12 * q^88 - 24 * q^94 + 24 * q^97

Introduction

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