LMFDB - Embedded newform 936.2.dg.f.901.12

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			901.12
Character	$\chi$	$=$	936.901
Dual form			936.2.dg.f.829.12

$q$-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 $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

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

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	−0.710117	−	0.704083i	$-0.751358\pi$
$7$	−1.20493	+	0.695669i	−0.455422	+	0.262938i	0.254695	+	0.967021i	$0.418025\pi$
$8$	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	−0.428178	−	0.903694i	$-0.640844\pi$
$11$	1.88561	−	3.26597i	0.568533	−	0.984729i	0.996711	−	0.0810341i	$-0.0258223\pi$
$12$		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	0.837895	−	0.545831i	$-0.183786\pi$
$17$	−0.221643	−	0.383897i	−0.0537563	−	0.0931087i	−0.891651	+	0.452723i	$0.850453\pi$
$18$		0			0
$19$	0.639519	+	1.10768i	0.146716	+	0.254119i	0.930012	−	0.367530i	$-0.119796\pi$
$19$	0.639519	+	1.10768i	0.146716	+	0.254119i	−0.783296	+	0.621649i	$0.786463\pi$
$20$	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	0.140594	+	0.990067i	$0.455099\pi$
$23$	−3.77493	+	6.53836i	−0.787126	+	1.36334i	−0.927721	+	0.373275i	$0.878235\pi$
$24$		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	0.994036	+	0.109051i	$0.0347812\pi$
$29$	8.53815	+	4.92951i	1.58550	+	0.915386i	0.591459	+	0.806335i	$0.298552\pi$
$30$		0			0
$31$			7.17868i			1.28933i	0.764466	+	0.644664i	$0.223003\pi$
$31$			7.17868i			1.28933i	−0.764466	+	0.644664i	$0.776997\pi$
$32$	−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	−0.985131	−	0.171806i	$-0.945040\pi$
$37$	−2.09112	+	3.62192i	−0.343777	+	0.595440i	0.641353	+	0.767246i	$0.278373\pi$
$38$	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	0.989734	−	0.142922i	$-0.0456498\pi$
$41$	8.71354	+	5.03077i	1.36083	+	0.785674i	0.371093	+	0.928596i	$0.378983\pi$
$42$		0			0
$43$	−6.12848	+	3.53828i	−0.934585	+	0.539583i	−0.888259	−	0.459343i	$-0.848085\pi$
$43$	−6.12848	+	3.53828i	−0.934585	+	0.539583i	−0.0463263	+	0.998926i	$0.514751\pi$
$44$	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	$-0.982716\pi$
$47$		−	0.744154i		−	0.108546i	0.998526	−	0.0542730i	$-0.0172841\pi$
$48$		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	$0.0272169\pi$
$53$			1.24345i			0.170801i	−0.996347	+	0.0854004i	$0.972783\pi$
$54$		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	0.770373	−	0.637593i	$-0.220070\pi$
$59$	−1.28264	−	2.22159i	−0.166985	−	0.289227i	−0.937358	+	0.348366i	$0.886737\pi$
$60$		0			0
$61$	8.48782	−	4.90045i	1.08675	−	0.627438i	0.154044	−	0.988064i	$-0.450770\pi$
$61$	8.48782	−	4.90045i	1.08675	−	0.627438i	0.932711	+	0.360626i	$0.117437\pi$
$62$	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	−0.370424	−	0.928863i	$-0.620788\pi$
$67$	5.06843	−	8.77877i	0.619207	−	1.07250i	0.989631	−	0.143635i	$-0.0458791\pi$
$68$	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	−0.870214	−	0.492675i	$-0.836019\pi$
$71$	−7.40365	+	4.27450i	−0.878652	+	0.507290i	−0.00843816	+	0.999964i	$0.502686\pi$
$72$		0			0
$73$			14.6006i			1.70887i	0.519556	+	0.854436i	$0.326097\pi$
$73$			14.6006i			1.70887i	−0.519556	+	0.854436i	$0.673903\pi$
$74$	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	0.471599	−	0.881813i	$-0.343677\pi$
$89$	−0.530897	−	0.306513i	−0.0562749	−	0.0324903i	−0.527873	+	0.849323i	$0.677010\pi$
$90$		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	−0.762548	−	0.646931i	$-0.776052\pi$
$97$	−5.74744	+	3.31829i	−0.583564	+	0.336921i	0.178985	+	0.983852i	$0.442719\pi$
$98$	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	0.596349	−	0.802725i	$-0.296617\pi$
$101$	2.00337	+	1.15665i	0.199343	+	0.115091i	−0.397006	+	0.917816i	$0.629951\pi$
$102$		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	0.244562	−	0.969634i	$-0.421356\pi$
$107$	−4.89156	−	2.82414i	−0.472885	−	0.273020i	−0.717447	+	0.696614i	$0.754689\pi$
$108$		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	−0.999988	−	0.00485717i	$-0.998454\pi$
$113$	−5.35973	−	9.28332i	−0.504201	−	0.873301i	0.495788	−	0.868444i	$-0.334879\pi$
$114$		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	0.449351	+	0.893355i	$0.351655\pi$
$127$	−6.18684	+	10.7159i	−0.548993	+	0.950884i	−0.998344	+	0.0575284i	$0.981678\pi$
$128$	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	$-0.750555\pi$
$131$		−	16.1582i		−	1.41175i	0.708338	−	0.705873i	$-0.249445\pi$
$132$		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	0.364520	−	0.931195i	$-0.381233\pi$
$137$	15.8390	−	9.14467i	1.35322	−	0.781282i	0.988699	+	0.149914i	$0.0478996\pi$
$138$		0			0
$139$	−9.71715	+	5.61020i	−0.824198	+	0.475851i	−0.851862	−	0.523766i	$-0.824526\pi$
$139$	−9.71715	+	5.61020i	−0.824198	+	0.475851i	0.0276641	+	0.999617i	$0.491193\pi$
$140$	−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	0.987511	−	0.157552i	$-0.0503601\pi$
$149$	4.36154	+	7.55442i	0.357312	+	0.618882i	−0.630199	+	0.776434i	$0.717027\pi$
$150$		0			0
$151$			6.78085i			0.551818i	0.961184	+	0.275909i	$0.0889788\pi$
$151$			6.78085i			0.551818i	−0.961184	+	0.275909i	$0.911021\pi$
$152$	−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	$0.0812392\pi$
$157$			6.32660i			0.504917i	−0.967608	+	0.252459i	$0.918761\pi$
$158$	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	0.988723	+	0.149757i	$0.0478491\pi$
$163$	7.96740	+	13.7999i	0.624055	+	1.08089i	−0.364668	+	0.931138i	$0.618818\pi$
$164$	−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	0.135904	−	0.990722i	$-0.456606\pi$
$167$	−8.45328	−	4.88050i	−0.654134	−	0.377665i	−0.790038	+	0.613057i	$0.789939\pi$
$168$		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	−0.859828	−	0.510583i	$-0.829429\pi$
$173$	−11.1480	+	6.43628i	−0.847564	+	0.489342i	0.0122640	+	0.999925i	$0.496096\pi$
$174$		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	0.695651	−	0.718380i	$-0.255116\pi$
$179$	5.63716	+	3.25461i	0.421341	+	0.243261i	−0.274310	+	0.961641i	$0.588449\pi$
$180$		0			0
$181$		−	16.7439i		−	1.24457i	−0.782793	−	0.622283i	$-0.786205\pi$
$181$		−	16.7439i		−	1.24457i	0.782793	−	0.622283i	$-0.213795\pi$
$182$	−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	−0.999184	−	0.0403942i	$-0.987139\pi$
$191$	−7.38796	−	12.7963i	−0.534574	−	0.925910i	0.464609	−	0.885516i	$-0.346195\pi$
$192$		0			0
$193$	8.52397	+	4.92132i	0.613569	+	0.354244i	0.774361	−	0.632744i	$-0.218072\pi$
$193$	8.52397	+	4.92132i	0.613569	+	0.354244i	−0.160792	+	0.986988i	$0.551405\pi$
$194$	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	−0.987047	−	0.160429i	$-0.948712\pi$
$197$	−4.97689	+	8.62022i	−0.354588	+	0.614165i	0.632459	+	0.774594i	$0.282046\pi$
$198$		0			0
$199$	−3.12577	−	5.41400i	−0.221580	−	0.383788i	0.733708	−	0.679465i	$-0.237788\pi$
$199$	−3.12577	−	5.41400i	−0.221580	−	0.383788i	−0.955288	+	0.295677i	$0.904455\pi$
$200$	−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	0.369800	−	0.929111i	$-0.379426\pi$
$211$	−3.63050	−	2.09607i	−0.249934	−	0.144299i	−0.619734	+	0.784812i	$0.712759\pi$
$212$	−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	0.0260950	−	0.999659i	$-0.491693\pi$
$223$	−12.3436	−	7.12658i	−0.826588	−	0.477231i	−0.852683	+	0.522429i	$0.825026\pi$
$224$	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	−0.842651	−	0.538459i	$-0.819006\pi$
$227$	−13.3737	−	23.1640i	−0.887645	−	1.53745i	−0.0449939	−	0.998987i	$-0.514327\pi$
$228$		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	$0.158921\pi$
$239$			14.8036i			0.957562i	−0.877934	+	0.478781i	$0.841079\pi$
$240$		0			0
$241$	−4.83757	+	2.79297i	−0.311615	+	0.179911i	−0.647649	−	0.761939i	$-0.724248\pi$
$241$	−4.83757	+	2.79297i	−0.311615	+	0.179911i	0.336034	+	0.941850i	$0.390914\pi$
$242$	−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	−0.956077	−	0.293116i	$-0.905308\pi$
$251$	−18.6990	+	10.7959i	−1.18027	+	0.681429i	−0.224193	+	0.974545i	$0.571974\pi$
$252$		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	−0.590917	−	0.806732i	$-0.701234\pi$
$257$	6.46366	−	11.1954i	0.403192	−	0.698349i	0.994109	+	0.108383i	$0.0345673\pi$
$258$		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	−0.472459	−	0.881353i	$-0.656633\pi$
$263$	8.54722	−	14.8042i	0.527044	−	0.912868i	0.999503	−	0.0315150i	$-0.0100332\pi$
$264$		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	−0.425355	−	0.905026i	$-0.639851\pi$
$269$	2.39036	−	1.38007i	0.145743	−	0.0841446i	0.571098	+	0.820882i	$0.306518\pi$
$270$		0			0
$271$	6.76352	+	3.90492i	0.410854	+	0.237207i	0.691157	−	0.722705i	$-0.257101\pi$
$271$	6.76352	+	3.90492i	0.410854	+	0.237207i	−0.280302	+	0.959912i	$0.590435\pi$
$272$	−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	−0.998059	−	0.0622790i	$-0.980163\pi$
$277$	−24.0189	+	13.8673i	−1.44315	+	0.833205i	−0.445094	+	0.895484i	$0.646830\pi$
$278$	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	$0.0232511\pi$
$281$			2.44676i			0.145961i	−0.997333	+	0.0729806i	$0.976749\pi$
$282$		0			0
$283$	−22.1821	−	12.8069i	−1.31859	−	0.761289i	−0.335090	−	0.942186i	$-0.608767\pi$
$283$	−22.1821	−	12.8069i	−1.31859	−	0.761289i	−0.983502	+	0.180897i	$0.942100\pi$
$284$	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	0.986472	+	0.163932i	$0.0524177\pi$
$293$	10.8730	+	18.8325i	0.635205	+	1.10021i	−0.351267	+	0.936275i	$0.614249\pi$
$294$		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	0.909336	+	0.416061i	$0.136590\pi$
$331$	14.8274	+	25.6818i	0.814988	+	1.41160i	−0.0943484	+	0.995539i	$0.530077\pi$
$332$	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	0.130106	−	0.991500i	$-0.458468\pi$
$347$	19.6305	−	11.3337i	1.05382	−	0.608425i	0.923717	+	0.383075i	$0.125135\pi$
$348$		0			0
$349$	5.28130	−	9.14748i	0.282702	−	0.489654i	−0.689348	−	0.724431i	$-0.742103\pi$
$349$	5.28130	−	9.14748i	0.282702	−	0.489654i	0.972049	+	0.234777i	$0.0754360\pi$
$350$	−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	0.856018	−	0.516946i	$-0.172931\pi$
$353$	15.7134	+	9.07213i	0.836339	+	0.482861i	−0.0196788	+	0.999806i	$0.506264\pi$
$354$		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	$0.0978059\pi$
$359$			11.4614i			0.604908i	−0.953164	+	0.302454i	$0.902194\pi$
$360$		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	−0.580954	−	0.813936i	$-0.697321\pi$
$367$	7.93899	−	13.7507i	0.414412	−	0.717783i	0.995367	+	0.0961533i	$0.0306539\pi$
$368$	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	−0.353430	−	0.935461i	$-0.614985\pi$
$373$	5.40748	−	3.12201i	0.279989	−	0.161652i	0.633418	+	0.773810i	$0.281651\pi$
$374$	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	−0.950596	−	0.310429i	$-0.899527\pi$
$379$	−4.01932	+	6.96166i	−0.206459	+	0.357597i	0.744138	+	0.668026i	$0.232861\pi$
$380$	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	0.212070	−	0.977254i	$-0.431979\pi$
$383$	22.7884	−	13.1569i	1.16443	−	0.672285i	0.952362	+	0.304969i	$0.0986461\pi$
$384$		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	$-0.778318\pi$
$389$		−	25.3042i		−	1.28297i	0.767135	−	0.641486i	$-0.221682\pi$
$390$		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	0.636168	−	0.771551i	$-0.280519\pi$
$397$	−6.97567	−	12.0822i	−0.350099	−	0.606389i	−0.986266	+	0.165162i	$0.947185\pi$
$398$	−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	0.848608	−	0.529023i	$-0.177441\pi$
$401$	16.3156	+	9.41984i	0.814764	+	0.470404i	−0.0338433	+	0.999427i	$0.510775\pi$
$402$		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	0.327143	−	0.944975i	$-0.393914\pi$
$409$	26.4746	−	15.2851i	1.30909	−	0.755802i	0.981944	+	0.189173i	$0.0605808\pi$
$410$	−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	0.830683	−	0.556745i	$-0.187950\pi$
$419$	15.6360	+	9.02746i	0.763870	+	0.441020i	−0.0668136	+	0.997765i	$0.521283\pi$
$420$		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	0.749181	−	0.662366i	$-0.230447\pi$
$431$	11.4213	+	6.59410i	0.550146	+	0.317627i	−0.199035	+	0.979992i	$0.563781\pi$
$432$		0			0
$433$	−1.91654	−	3.31955i	−0.0921032	−	0.159527i	0.816293	−	0.577638i	$-0.196026\pi$
$433$	−1.91654	−	3.31955i	−0.0921032	−	0.159527i	−0.908396	+	0.418111i	$0.862692\pi$
$434$	−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	−0.758897	−	0.651210i	$-0.774262\pi$
$439$	3.86604	−	6.69617i	0.184516	−	0.319591i	0.943413	+	0.331619i	$0.107595\pi$
$440$	−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	$0.113537\pi$
$443$			14.6984i			0.698341i	−0.937059	+	0.349171i	$0.886463\pi$
$444$		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	−0.955831	−	0.293918i	$-0.905041\pi$
$449$	−24.9869	+	14.4262i	−1.17921	+	0.680815i	−0.223375	+	0.974733i	$0.571707\pi$
$450$		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	0.536109	−	0.844148i	$-0.319893\pi$
$457$	1.56292	+	0.902350i	0.0731101	+	0.0422101i	−0.462999	+	0.886359i	$0.653227\pi$
$458$	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	0.958233	−	0.285990i	$-0.0923223\pi$
$461$	4.96927	+	8.60703i	0.231442	+	0.400869i	−0.726791	+	0.686859i	$0.758989\pi$
$462$		0			0
$463$			13.9156i			0.646713i	0.946277	+	0.323357i	$0.104811\pi$
$463$			13.9156i			0.646713i	−0.946277	+	0.323357i	$0.895189\pi$
$464$	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	$0.194702\pi$
$467$			24.8188i			1.14848i	−0.818688	+	0.574238i	$0.805298\pi$
$468$		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	0.564049	−	0.825742i	$-0.309243\pi$
$479$	2.86620	+	1.65480i	0.130960	+	0.0756098i	−0.433089	+	0.901351i	$0.642576\pi$
$480$		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	−0.803870	−	0.594806i	$-0.797229\pi$
$487$	−15.2421	+	8.80006i	−0.690688	+	0.398769i	0.113182	+	0.993574i	$0.463896\pi$
$488$	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	0.437530	−	0.899204i	$-0.355854\pi$
$491$	−2.71307	−	1.56639i	−0.122439	−	0.0706902i	−0.559969	+	0.828514i	$0.689187\pi$
$492$		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	0.984934	+	0.172930i	$0.0553233\pi$
$503$	14.4037	+	24.9479i	0.642229	+	1.11237i	−0.342706	+	0.939443i	$0.611343\pi$
$504$		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	−0.845953	−	0.533257i	$-0.820968\pi$
$509$	0.876217	−	1.51765i	0.0388376	−	0.0672688i	0.884791	+	0.465988i	$0.154301\pi$
$510$		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	0.104471	−	0.994528i	$-0.466685\pi$
$523$	−16.1132	−	9.30294i	−0.704580	−	0.406789i	−0.809051	+	0.587739i	$0.800018\pi$
$524$	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	$0.120537\pi$
$547$			17.2928i			0.739386i	−0.929154	+	0.369693i	$0.879463\pi$
$548$	−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	−0.389328	−	0.921099i	$-0.627293\pi$
$557$	14.2320	−	24.6506i	0.603031	−	1.04448i	0.992359	−	0.123382i	$-0.0393739\pi$
$558$		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	0.317269	−	0.948336i	$-0.397234\pi$
$563$	30.7791	−	17.7703i	1.29719	−	0.748931i	0.979917	+	0.199405i	$0.0639009\pi$
$564$		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	−0.646425	−	0.762978i	$-0.723737\pi$
$569$	8.05172	−	13.9460i	0.337546	−	0.584646i	0.983970	+	0.178332i	$0.0570700\pi$
$570$		0			0
$571$			12.5382i			0.524709i	0.964972	+	0.262354i	$0.0844989\pi$
$571$			12.5382i			0.524709i	−0.964972	+	0.262354i	$0.915501\pi$
$572$	−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	$0.151346\pi$
$577$			21.9913i			0.915508i	−0.889079	+	0.457754i	$0.848654\pi$
$578$	−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	−0.996070	−	0.0885691i	$-0.971771\pi$
$587$	−10.2081	+	17.6809i	−0.421332	+	0.729768i	0.574738	+	0.818337i	$0.305104\pi$
$588$		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	$0.444911\pi$
$593$			47.9756i			1.97012i	−0.172205	+	0.985061i	$0.555089\pi$
$594$		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	−0.993344	−	0.115188i	$-0.963253\pi$
$601$	−9.73052	+	16.8538i	−0.396916	+	0.687479i	0.596427	+	0.802667i	$0.296586\pi$
$602$	−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	0.866834	−	0.498596i	$-0.166151\pi$
$607$	0.0399237	+	0.0691499i	0.00162045	+	0.00280671i	−0.865214	+	0.501403i	$0.832818\pi$
$608$	−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	−0.675334	−	0.737512i	$-0.736001\pi$
$613$	7.45333	−	12.9095i	0.301037	−	0.521411i	0.976371	+	0.216101i	$0.0693339\pi$
$614$	−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	−0.777761	−	0.628560i	$-0.783645\pi$
$617$	−15.4574	+	8.92435i	−0.622293	+	0.359281i	0.155468	+	0.987841i	$0.450311\pi$
$618$		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	−0.865115	−	0.501573i	$-0.832755\pi$
$631$	−21.6858	+	12.5203i	−0.863297	+	0.498425i	0.00181769	+	0.999998i	$0.499421\pi$
$632$	−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	0.999988	+	0.00491538i	$0.00156462\pi$
$641$	12.7666	+	22.1124i	0.504251	+	0.873388i	−0.495737	+	0.868473i	$0.665102\pi$
$642$		0			0
$643$	15.1058	+	26.1640i	0.595715	+	1.03181i	0.993446	+	0.114306i	$0.0364644\pi$
$643$	15.1058	+	26.1640i	0.595715	+	1.03181i	−0.397731	+	0.917502i	$0.630202\pi$
$644$	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	−0.394178	−	0.919034i	$-0.628971\pi$
$647$	15.2316	−	26.3820i	0.598818	−	1.03718i	0.992996	−	0.118149i	$-0.0376960\pi$
$648$		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	0.907684	−	0.419654i	$-0.137848\pi$
$653$	25.5052	+	14.7254i	0.998096	+	0.576251i	0.0904115	+	0.995904i	$0.471182\pi$
$654$		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	−0.602198	−	0.798347i	$-0.705708\pi$
$659$	−5.43988	+	3.14071i	−0.211907	+	0.122345i	0.390290	+	0.920692i	$0.372375\pi$
$660$		0			0
$661$	6.19056	−	10.7224i	0.240785	−	0.417052i	−0.720153	−	0.693815i	$-0.755928\pi$
$661$	6.19056	−	10.7224i	0.240785	−	0.417052i	0.960938	+	0.276763i	$0.0892618\pi$
$662$	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	0.443180	+	0.896432i	$0.353850\pi$
$673$	−14.3913	+	24.9264i	−0.554743	+	0.960843i	−0.997923	+	0.0644107i	$0.979483\pi$
$674$	−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	$-0.934455\pi$
$677$		−	10.6400i		−	0.408928i	0.978874	−	0.204464i	$-0.0655451\pi$
$678$		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	0.989295	+	0.145930i	$0.0466174\pi$
$683$	16.2301	+	28.1113i	0.621027	+	1.07565i	−0.368268	+	0.929720i	$0.620049\pi$
$684$		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	0.0479072	−	0.998852i	$-0.484745\pi$
$691$	23.3686	−	40.4757i	0.888985	−	1.53977i	0.841077	−	0.540915i	$-0.181922\pi$
$692$	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	$-0.781051\pi$
$701$		−	33.6184i		−	1.26975i	0.772615	−	0.634875i	$-0.218949\pi$
$702$		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	0.898439	+	0.439099i	$0.144702\pi$
$709$	22.0869	+	38.2556i	0.829490	+	1.43672i	−0.0689481	+	0.997620i	$0.521964\pi$
$710$	−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	0.999997	−	0.00223845i	$-0.000712522\pi$
$719$	13.3551	+	23.1317i	0.498060	+	0.862666i	−0.501937	+	0.864904i	$0.667379\pi$
$720$		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	−0.460717	−	0.887547i	$-0.652408\pi$
$739$	14.6329	−	25.3449i	0.538279	−	0.932327i	0.998997	−	0.0447805i	$-0.0142589\pi$
$740$	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	−0.000934125	−	1.00000i	$-0.500297\pi$
$743$	−23.6443	−	13.6511i	−0.867426	−	0.500809i	−0.866492	+	0.499191i	$0.833631\pi$
$744$		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	−0.810288	−	0.586033i	$-0.800689\pi$
$751$	2.80553	−	4.85932i	0.102375	−	0.177319i	0.912663	+	0.408713i	$0.134022\pi$
$752$	−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	−0.168565	−	0.985690i	$-0.553913\pi$
$757$	−30.4433	−	17.5765i	−1.10648	−	0.638827i	−0.937916	+	0.346863i	$0.887247\pi$
$758$	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	−0.436806	−	0.899556i	$-0.643890\pi$
$761$	3.41599	−	1.97222i	0.123830	−	0.0714931i	0.560635	+	0.828063i	$0.310557\pi$
$762$		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	0.631409	−	0.775450i	$-0.282477\pi$
$769$	7.64135	+	4.41174i	0.275554	+	0.159091i	−0.355855	+	0.934541i	$0.615810\pi$
$770$	−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	−0.886753	−	0.462243i	$-0.847045\pi$
$773$	−23.4570	−	40.6288i	−0.843691	−	1.46132i	0.0430627	−	0.999072i	$-0.486288\pi$
$774$		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	0.754057	−	0.656809i	$-0.228094\pi$
$787$	−5.38025	−	9.31886i	−0.191785	−	0.332182i	−0.945842	+	0.324628i	$0.894761\pi$
$788$	−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	−0.676058	+	0.736848i	$0.736313\pi$
$797$	−46.6440	+	26.9299i	−1.65222	+	0.953908i	−0.976158	+	0.217060i	$0.930353\pi$
$798$		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	0.313694	+	0.949524i	$0.398433\pi$
$809$	−18.9278	+	32.7838i	−0.665465	+	1.15262i	−0.979159	+	0.203095i	$0.934900\pi$
$810$		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	−0.859819	−	0.510600i	$-0.829423\pi$
$821$	0.351948	−	0.609591i	0.0122831	−	0.0212749i	0.872102	+	0.489325i	$0.162757\pi$
$822$		0			0
$823$	24.5405	+	42.5054i	0.855429	+	1.48165i	0.876247	+	0.481863i	$0.160040\pi$
$823$	24.5405	+	42.5054i	0.855429	+	1.48165i	−0.0208180	+	0.999783i	$0.506627\pi$
$824$	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	0.0694293	−	0.997587i	$-0.477882\pi$
$829$	−21.8762	−	12.6302i	−0.759792	−	0.438666i	−0.829221	+	0.558921i	$0.811216\pi$
$830$	−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	0.355301	−	0.934752i	$-0.384378\pi$
$839$	38.8853	−	22.4504i	1.34247	−	0.775075i	0.987169	+	0.159677i	$0.0510451\pi$
$840$		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	$0.224044\pi$
$859$			37.9349i			1.29432i	−0.762353	+	0.647162i	$0.775956\pi$
$860$	−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	$0.0353735\pi$
$863$			6.51581i			0.221801i	−0.993832	+	0.110900i	$0.964627\pi$
$864$		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	0.996806	+	0.0798554i	$0.0254459\pi$
$877$	16.8078	+	29.1120i	0.567560	+	0.983043i	−0.429246	+	0.903187i	$0.641221\pi$
$878$	−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	−0.458938	−	0.888468i	$-0.651770\pi$
$881$	16.0271	−	27.7598i	0.539967	−	0.935250i	0.998905	−	0.0467821i	$-0.0148966\pi$
$882$		0			0
$883$		−	29.4544i		−	0.991220i	−0.868545	−	0.495610i	$-0.834945\pi$
$883$		−	29.4544i		−	0.991220i	0.868545	−	0.495610i	$-0.165055\pi$
$884$	−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	0.192447	−	0.981307i	$-0.438358\pi$
$887$	28.1761	−	48.8024i	0.946061	−	1.63863i	0.753613	−	0.657318i	$-0.228309\pi$
$888$		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	0.674393	−	0.738372i	$-0.264405\pi$
$907$	11.2076	+	6.47069i	0.372141	+	0.214856i	−0.302252	+	0.953228i	$0.597739\pi$
$908$	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	0.898858	−	0.438240i	$-0.144398\pi$
$919$	2.11908	+	3.67036i	0.0699021	+	0.121074i	−0.828956	+	0.559314i	$0.811065\pi$
$920$	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	−0.979135	−	0.203211i	$-0.934862\pi$
$929$	−39.4013	+	22.7484i	−1.29272	+	0.746350i	−0.313581	+	0.949561i	$0.601529\pi$
$930$		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	−0.760381	−	0.649477i	$-0.774988\pi$
$947$	5.60915	−	9.71533i	0.182273	−	0.315706i	0.942654	+	0.333771i	$0.108321\pi$
$948$		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	−0.987535	−	0.157397i	$-0.949690\pi$
$953$	−19.4509	−	33.6900i	−0.630077	−	1.09133i	0.357458	−	0.933929i	$-0.383643\pi$
$954$		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	$-0.990484\pi$
$967$		−	1.85906i		−	0.0597833i	0.999553	−	0.0298916i	$-0.00951622\pi$
$968$	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	−0.244564	−	0.969633i	$-0.578645\pi$
$971$	14.7354	−	8.50748i	0.472881	−	0.273018i	0.717445	+	0.696615i	$0.245311\pi$
$972$		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	0.841199	−	0.540725i	$-0.181850\pi$
$977$	24.8030	+	14.3200i	0.793518	+	0.458138i	−0.0476817	+	0.998863i	$0.515183\pi$
$978$		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	$-0.746932\pi$
$983$		−	44.7649i		−	1.42778i	0.700259	−	0.713889i	$-0.253068\pi$
$984$		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	0.292958	+	0.956125i	$0.405360\pi$
$991$	−21.4553	+	37.1617i	−0.681550	+	1.18048i	−0.974508	+	0.224354i	$0.927973\pi$
$992$	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	0.304288	−	0.952580i	$-0.401582\pi$
$997$	40.4603	−	23.3598i	1.28139	−	0.739811i	0.977102	+	0.212769i	$0.0682483\pi$
$998$	−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.901.12	yes	56
3.2	odd	2	inner	936.2.dg.f.901.17	yes	56
8.5	even	2	inner	936.2.dg.f.901.2	yes	56
13.10	even	6	inner	936.2.dg.f.829.2	✓	56
24.5	odd	2	inner	936.2.dg.f.901.27	yes	56
39.23	odd	6	inner	936.2.dg.f.829.27	yes	56
104.101	even	6	inner	936.2.dg.f.829.12	yes	56
312.101	odd	6	inner	936.2.dg.f.829.17	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.dg.f.829.2	✓	56	13.10	even	6	inner
936.2.dg.f.829.12	yes	56	104.101	even	6	inner
936.2.dg.f.829.17	yes	56	312.101	odd	6	inner
936.2.dg.f.829.27	yes	56	39.23	odd	6	inner
936.2.dg.f.901.2	yes	56	8.5	even	2	inner
936.2.dg.f.901.12	yes	56	1.1	even	1	trivial
936.2.dg.f.901.17	yes	56	3.2	odd	2	inner
936.2.dg.f.901.27	yes	56	24.5	odd	2	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

L-functions

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