LMFDB - Embedded newform 936.2.dg.f.829.9

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			829.9
Character	$\chi$	$=$	936.829
Dual form			936.2.dg.f.901.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.869780 - 1.11512i) q^{2} +(-0.486965 + 1.93981i) q^{4} +0.189692 q^{5} +(-1.84703 - 1.06638i) q^{7} +(2.58667 - 1.14419i) q^{8} +(-0.164990 - 0.211528i) q^{10} +(0.681249 + 1.17996i) q^{11} +(-0.163331 + 3.60185i) q^{13} +(0.417370 + 2.98717i) q^{14} +(-3.52573 - 1.88924i) q^{16} +(2.82570 - 4.89426i) q^{17} +(-2.09665 + 3.63151i) q^{19} +(-0.0923733 + 0.367966i) q^{20} +(0.723252 - 1.78597i) q^{22} +(2.99588 + 5.18901i) q^{23} -4.96402 q^{25} +(4.15854 - 2.95069i) q^{26} +(2.96802 - 3.06360i) q^{28} +(0.0901081 - 0.0520240i) q^{29} +2.73867i q^{31} +(0.959891 + 5.57482i) q^{32} +(-7.91540 + 1.10595i) q^{34} +(-0.350366 - 0.202284i) q^{35} +(1.06198 + 1.83940i) q^{37} +(5.87318 - 0.820605i) q^{38} +(0.490669 - 0.217043i) q^{40} +(8.00410 - 4.62117i) q^{41} +(6.06888 + 3.50387i) q^{43} +(-2.62064 + 0.746896i) q^{44} +(3.18059 - 7.85405i) q^{46} +6.80383i q^{47} +(-1.22566 - 2.12290i) q^{49} +(4.31760 + 5.53545i) q^{50} +(-6.90737 - 2.07080i) q^{52} +9.28824i q^{53} +(0.129227 + 0.223828i) q^{55} +(-5.99779 - 0.645029i) q^{56} +(-0.136387 - 0.0552316i) q^{58} +(-1.76132 + 3.05070i) q^{59} +(10.2886 + 5.94011i) q^{61} +(3.05394 - 2.38204i) q^{62} +(5.38167 - 5.91926i) q^{64} +(-0.0309825 + 0.683242i) q^{65} +(6.02495 + 10.4355i) q^{67} +(8.11792 + 7.86466i) q^{68} +(0.0791716 + 0.566642i) q^{70} +(-1.24609 - 0.719429i) q^{71} +7.83052i q^{73} +(1.12745 - 2.78410i) q^{74} +(-6.02344 - 5.83553i) q^{76} -2.90589i q^{77} +5.68079 q^{79} +(-0.668802 - 0.358373i) q^{80} +(-12.1149 - 4.90609i) q^{82} -12.8862 q^{83} +(0.536013 - 0.928401i) q^{85} +(-1.37137 - 9.81510i) q^{86} +(3.11225 + 2.27268i) q^{88} +(4.22833 - 2.44123i) q^{89} +(4.14263 - 6.47855i) q^{91} +(-11.5246 + 3.28457i) q^{92} +(7.58705 - 5.91783i) q^{94} +(-0.397718 + 0.688868i) q^{95} +(6.22643 + 3.59483i) q^{97} +(-1.30122 + 3.21320i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.869780	−	1.11512i	−0.615027	−	0.788506i
$2$	−0.869780	−	1.11512i	−0.615027	−	0.788506i
$3$		0			0
$3$		0			0
$4$	−0.486965	+	1.93981i	−0.243482	+	0.969905i
$5$	0.189692			0.0848328			0.0424164	−	0.999100i	$-0.486494\pi$
$5$	0.189692			0.0848328			0.0424164	+	0.999100i	$0.486494\pi$
$6$		0			0
$7$	−1.84703	−	1.06638i	−0.698111	−	0.403055i	0.108532	−	0.994093i	$-0.465385\pi$
$7$	−1.84703	−	1.06638i	−0.698111	−	0.403055i	−0.806644	+	0.591038i	$0.798718\pi$
$8$	2.58667	−	1.14419i	0.914524	−	0.404531i
$9$		0			0
$10$	−0.164990	−	0.211528i	−0.0521745	−	0.0668911i
$11$	0.681249	+	1.17996i	0.205404	+	0.355770i	0.950261	−	0.311453i	$-0.100816\pi$
$11$	0.681249	+	1.17996i	0.205404	+	0.355770i	−0.744857	+	0.667224i	$0.767482\pi$
$12$		0			0
$13$	−0.163331	+	3.60185i	−0.0452998	+	0.998973i
$13$	−0.163331	+	3.60185i	−0.0452998	+	0.998973i
$14$	0.417370	+	2.98717i	0.111547	+	0.798355i
$15$		0			0
$16$	−3.52573	−	1.88924i	−0.881433	−	0.472310i
$17$	2.82570	−	4.89426i	0.685333	−	1.18703i	−0.287999	−	0.957631i	$-0.592990\pi$
$17$	2.82570	−	4.89426i	0.685333	−	1.18703i	0.973332	−	0.229401i	$-0.0736768\pi$
$18$		0			0
$19$	−2.09665	+	3.63151i	−0.481005	+	0.833125i	−0.999762	−	0.0217961i	$-0.993062\pi$
$19$	−2.09665	+	3.63151i	−0.481005	+	0.833125i	0.518757	+	0.854922i	$0.326395\pi$
$20$	−0.0923733	+	0.367966i	−0.0206553	+	0.0822798i
$21$		0			0
$22$	0.723252	−	1.78597i	0.154198	−	0.380771i
$23$	2.99588	+	5.18901i	0.624683	+	1.08198i	0.988602	+	0.150553i	$0.0481053\pi$
$23$	2.99588	+	5.18901i	0.624683	+	1.08198i	−0.363919	+	0.931431i	$0.618561\pi$
$24$		0			0
$25$	−4.96402			−0.992803
$26$	4.15854	−	2.95069i	0.815557	−	0.578677i
$27$		0			0
$28$	2.96802	−	3.06360i	0.560903	−	0.578965i
$29$	0.0901081	−	0.0520240i	0.0167327	−	0.00966061i	−0.491610	−	0.870815i	$-0.663592\pi$
$29$	0.0901081	−	0.0520240i	0.0167327	−	0.00966061i	0.508343	+	0.861155i	$0.330258\pi$
$30$		0			0
$31$			2.73867i			0.491880i	0.969285	+	0.245940i	$0.0790967\pi$
$31$			2.73867i			0.491880i	−0.969285	+	0.245940i	$0.920903\pi$
$32$	0.959891	+	5.57482i	0.169686	+	0.985498i
$33$		0			0
$34$	−7.91540	+	1.10595i	−1.35748	+	0.189668i
$35$	−0.350366	−	0.202284i	−0.0592227	−	0.0341923i
$36$		0			0
$37$	1.06198	+	1.83940i	0.174588	+	0.302395i	0.940019	−	0.341123i	$-0.110807\pi$
$37$	1.06198	+	1.83940i	0.174588	+	0.302395i	−0.765431	+	0.643518i	$0.777474\pi$
$38$	5.87318	−	0.820605i	0.952756	−	0.133120i
$39$		0			0
$40$	0.490669	−	0.217043i	0.0775816	−	0.0343175i
$41$	8.00410	−	4.62117i	1.25003	−	0.721705i	0.278914	−	0.960316i	$-0.410025\pi$
$41$	8.00410	−	4.62117i	1.25003	−	0.721705i	0.971115	+	0.238611i	$0.0766921\pi$
$42$		0			0
$43$	6.06888	+	3.50387i	0.925496	+	0.534335i	0.885384	−	0.464860i	$-0.153895\pi$
$43$	6.06888	+	3.50387i	0.925496	+	0.534335i	0.0401118	+	0.999195i	$0.487229\pi$
$44$	−2.62064	+	0.746896i	−0.395076	+	0.112599i
$45$		0			0
$46$	3.18059	−	7.85405i	0.468953	−	1.15802i
$47$			6.80383i			0.992440i	0.868197	+	0.496220i	$0.165279\pi$
$47$			6.80383i			0.992440i	−0.868197	+	0.496220i	$0.834721\pi$
$48$		0			0
$49$	−1.22566	−	2.12290i	−0.175094	−	0.303271i
$50$	4.31760	+	5.53545i	0.610601	+	0.782831i
$51$		0			0
$52$	−6.90737	−	2.07080i	−0.957880	−	0.287169i
$53$			9.28824i			1.27584i	0.770103	+	0.637919i	$0.220205\pi$
$53$			9.28824i			1.27584i	−0.770103	+	0.637919i	$0.779795\pi$
$54$		0			0
$55$	0.129227	+	0.223828i	0.0174250	+	0.0301810i
$56$	−5.99779	−	0.645029i	−0.801488	−	0.0861956i
$57$		0			0
$58$	−0.136387	−	0.0552316i	−0.0179085	−	0.00725226i
$59$	−1.76132	+	3.05070i	−0.229305	+	0.397168i	−0.957602	−	0.288093i	$-0.906979\pi$
$59$	−1.76132	+	3.05070i	−0.229305	+	0.397168i	0.728297	+	0.685261i	$0.240312\pi$
$60$		0			0
$61$	10.2886	+	5.94011i	1.31732	+	0.760554i	0.983296	−	0.182012i	$-0.0582610\pi$
$61$	10.2886	+	5.94011i	1.31732	+	0.760554i	0.334021	+	0.942566i	$0.391594\pi$
$62$	3.05394	−	2.38204i	0.387850	−	0.302520i
$63$		0			0
$64$	5.38167	−	5.91926i	0.672709	−	0.739907i
$65$	−0.0309825	+	0.683242i	−0.00384291	+	0.0847457i
$66$		0			0
$67$	6.02495	+	10.4355i	0.736065	+	1.27490i	0.954255	+	0.298995i	$0.0966514\pi$
$67$	6.02495	+	10.4355i	0.736065	+	1.27490i	−0.218190	+	0.975906i	$0.570015\pi$
$68$	8.11792	+	7.86466i	0.984442	+	0.953730i
$69$		0			0
$70$	0.0791716	+	0.566642i	0.00946282	+	0.0677266i
$71$	−1.24609	−	0.719429i	−0.147883	−	0.0853805i	0.424232	−	0.905553i	$-0.360544\pi$
$71$	−1.24609	−	0.719429i	−0.147883	−	0.0853805i	−0.572116	+	0.820173i	$0.693877\pi$
$72$		0			0
$73$			7.83052i			0.916493i	0.888825	+	0.458246i	$0.151522\pi$
$73$			7.83052i			0.916493i	−0.888825	+	0.458246i	$0.848478\pi$
$74$	1.12745	−	2.78410i	0.131064	−	0.323645i
$75$		0			0
$76$	−6.02344	−	5.83553i	−0.690937	−	0.669381i
$77$		−	2.90589i		−	0.331157i
$78$		0			0
$79$	5.68079			0.639138			0.319569	−	0.947563i	$-0.396462\pi$
$79$	5.68079			0.639138			0.319569	+	0.947563i	$0.396462\pi$
$80$	−0.668802	−	0.358373i	−0.0747744	−	0.0400673i
$81$		0			0
$82$	−12.1149	−	4.90609i	−1.33787	−	0.541787i
$83$	−12.8862			−1.41444			−0.707222	−	0.706992i	$-0.750052\pi$
$83$	−12.8862			−1.41444			−0.707222	+	0.706992i	$0.750052\pi$
$84$		0			0
$85$	0.536013	−	0.928401i	0.0581387	−	0.100699i
$86$	−1.37137	−	9.81510i	−0.147879	−	1.05839i
$87$		0			0
$88$	3.11225	+	2.27268i	0.331767	+	0.242268i
$89$	4.22833	−	2.44123i	0.448202	−	0.258770i	−0.258868	−	0.965913i	$-0.583350\pi$
$89$	4.22833	−	2.44123i	0.448202	−	0.258770i	0.707071	+	0.707143i	$0.250016\pi$
$90$		0			0
$91$	4.14263	−	6.47855i	0.434265	−	0.679136i
$92$	−11.5246	+	3.28457i	−1.20152	+	0.342440i
$93$		0			0
$94$	7.58705	−	5.91783i	0.782545	−	0.610378i
$95$	−0.397718	+	0.688868i	−0.0408050	+	0.0706763i
$96$		0			0
$97$	6.22643	+	3.59483i	0.632198	+	0.365000i	0.781603	−	0.623776i	$-0.214402\pi$
$97$	6.22643	+	3.59483i	0.632198	+	0.365000i	−0.149405	+	0.988776i	$0.547736\pi$
$98$	−1.30122	+	3.21320i	−0.131444	+	0.324582i
$99$		0			0
$100$	2.41730	−	9.62925i	0.241730	−	0.962925i
$101$	11.2612	−	6.50163i	1.12053	−	0.646937i	0.178992	−	0.983851i	$-0.442716\pi$
$101$	11.2612	−	6.50163i	1.12053	−	0.646937i	0.941535	+	0.336914i	$0.109383\pi$
$102$		0			0
$103$	−12.8045			−1.26167			−0.630834	−	0.775918i	$-0.717287\pi$
$103$	−12.8045			−1.26167			−0.630834	+	0.775918i	$0.717287\pi$
$104$	3.69871	+	9.50366i	0.362688	+	0.931911i
$105$		0			0
$106$	10.3575	−	8.07873i	1.00601	−	0.784676i
$107$	15.6901	−	9.05871i	1.51682	−	0.875738i	0.517018	−	0.855974i	$-0.327042\pi$
$107$	15.6901	−	9.05871i	1.51682	−	0.875738i	0.999805	−	0.0197640i	$-0.00629150\pi$
$108$		0			0
$109$	−5.50733			−0.527507			−0.263753	−	0.964590i	$-0.584961\pi$
$109$	−5.50733			−0.527507			−0.263753	+	0.964590i	$0.584961\pi$
$110$	0.137195	−	0.338785i	0.0130810	−	0.0323019i
$111$		0			0
$112$	4.49748	+	7.24926i	0.424971	+	0.684991i
$113$	5.96077	−	10.3244i	0.560742	−	0.971234i	−0.436690	−	0.899612i	$-0.643849\pi$
$113$	5.96077	−	10.3244i	0.560742	−	0.971234i	0.997432	−	0.0716216i	$-0.0228174\pi$
$114$		0			0
$115$	0.568293	+	0.984313i	0.0529936	+	0.0917876i
$116$	0.0570371	+	0.200127i	0.00529576	+	0.0185813i
$117$		0			0
$118$	4.93385	−	0.689361i	0.454198	−	0.0634609i
$119$	−10.4383	+	6.02656i	−0.956878	+	0.552454i
$120$		0			0
$121$	4.57180	−	7.91859i	0.415618	−	0.719872i
$122$	−2.32489	−	16.6395i	−0.210486	−	1.50647i
$123$		0			0
$124$	−5.31251	−	1.33364i	−0.477077	−	0.119764i
$125$	−1.89009			−0.169055
$126$		0			0
$127$	−1.00642	−	1.74317i	−0.0893055	−	0.154682i	0.817912	−	0.575343i	$-0.195131\pi$
$127$	−1.00642	−	1.74317i	−0.0893055	−	0.154682i	−0.907218	+	0.420661i	$0.861798\pi$
$128$	−11.2815	−	0.852734i	−0.997156	−	0.0753718i
$129$		0			0
$130$	0.788841	−	0.559721i	0.0691859	−	0.0490908i
$131$			2.68138i			0.234273i	0.993116	+	0.117137i	$0.0373715\pi$
$131$			2.68138i			0.234273i	−0.993116	+	0.117137i	$0.962628\pi$
$132$		0			0
$133$	7.74516	−	4.47167i	0.671590	−	0.387743i
$134$	6.39643	−	15.7951i	0.552567	−	1.36449i
$135$		0			0
$136$	1.70920	−	15.8929i	0.146562	−	1.36281i
$137$	−7.55372	−	4.36114i	−0.645358	−	0.372598i	0.141317	−	0.989964i	$-0.454866\pi$
$137$	−7.55372	−	4.36114i	−0.645358	−	0.372598i	−0.786676	+	0.617367i	$0.788200\pi$
$138$		0			0
$139$	−4.71129	−	2.72007i	−0.399607	−	0.230713i	0.286708	−	0.958018i	$-0.407439\pi$
$139$	−4.71129	−	2.72007i	−0.399607	−	0.230713i	−0.686314	+	0.727305i	$0.740773\pi$
$140$	0.563009	−	0.581139i	0.0475829	−	0.0491152i
$141$		0			0
$142$	0.281576	+	2.01528i	0.0236293	+	0.169118i
$143$	−4.36130	+	2.26103i	−0.364710	+	0.189077i
$144$		0			0
$145$	0.0170928	−	0.00986852i	0.00141948	−	0.000819536i
$146$	8.73193	−	6.81083i	0.722660	−	0.563668i
$147$		0			0
$148$	−4.08523	+	1.16431i	−0.335804	+	0.0957058i
$149$	−4.35351	+	7.54051i	−0.356654	+	0.617742i	−0.987400	−	0.158247i	$-0.949416\pi$
$149$	−4.35351	+	7.54051i	−0.356654	+	0.617742i	0.630746	+	0.775989i	$0.282749\pi$
$150$		0			0
$151$			11.5767i			0.942102i	0.882106	+	0.471051i	$0.156125\pi$
$151$			11.5767i			0.942102i	−0.882106	+	0.471051i	$0.843875\pi$
$152$	−1.26821	+	11.7925i	−0.102866	+	0.956495i
$153$		0			0
$154$	−3.24040	+	2.52748i	−0.261119	+	0.203670i
$155$			0.519504i			0.0417276i
$156$		0			0
$157$			17.8314i			1.42310i	0.702634	+	0.711552i	$0.252007\pi$
$157$			17.8314i			1.42310i	−0.702634	+	0.711552i	$0.747993\pi$
$158$	−4.94104	−	6.33473i	−0.393088	−	0.503964i
$159$		0			0
$160$	0.182083	+	1.05750i	0.0143950	+	0.0836025i
$161$		−	12.7790i		−	1.00713i
$162$		0			0
$163$	−1.93263	+	3.34741i	−0.151375	+	0.262189i	−0.931733	−	0.363143i	$-0.881703\pi$
$163$	−1.93263	+	3.34741i	−0.151375	+	0.262189i	0.780358	+	0.625333i	$0.215037\pi$
$164$	5.06648	+	17.7768i	0.395625	+	1.38813i
$165$		0			0
$166$	11.2082	+	14.3696i	0.869922	+	1.11530i
$167$	−17.2142	+	9.93865i	−1.33208	+	0.769076i	−0.985618	−	0.168989i	$-0.945950\pi$
$167$	−17.2142	+	9.93865i	−1.33208	+	0.769076i	−0.346461	+	0.938065i	$0.612617\pi$
$168$		0			0
$169$	−12.9466	−	1.17659i	−0.995896	−	0.0905066i
$170$	−1.50149	+	0.209789i	−0.115159	+	0.0160901i
$171$		0			0
$172$	−9.75218	+	10.0662i	−0.743597	+	0.767542i
$173$	−11.8468	−	6.83976i	−0.900696	−	0.520017i	−0.0232702	−	0.999729i	$-0.507408\pi$
$173$	−11.8468	−	6.83976i	−0.900696	−	0.520017i	−0.877426	+	0.479712i	$0.840741\pi$
$174$		0			0
$175$	9.16868	+	5.29354i	0.693087	+	0.400154i
$176$	−0.172678	−	5.44725i	−0.0130161	−	0.410602i
$177$		0			0
$178$	−6.39997	−	2.59175i	−0.479698	−	0.194260i
$179$	−3.06137	+	1.76748i	−0.228817	+	0.132108i	−0.610026	−	0.792381i	$-0.708841\pi$
$179$	−3.06137	+	1.76748i	−0.228817	+	0.132108i	0.381209	+	0.924489i	$0.375508\pi$
$180$		0			0
$181$		−	5.66016i		−	0.420717i	−0.977624	−	0.210358i	$-0.932537\pi$
$181$		−	5.66016i		−	0.420717i	0.977624	−	0.210358i	$-0.0674631\pi$
$182$	−10.8275	+	1.01541i	−0.802588	+	0.0752669i
$183$		0			0
$184$	13.6865	+	9.99439i	1.00898	+	0.736796i
$185$	0.201448	+	0.348919i	0.0148108	+	0.0256530i
$186$		0			0
$187$	7.70002			0.563081
$188$	−13.1981	−	3.31322i	−0.962573	−	0.241642i
$189$		0			0
$190$	1.11409	−	0.155662i	0.0808249	−	0.0112929i
$191$	−10.2536	+	17.7597i	−0.741923	+	1.28505i	0.209695	+	0.977767i	$0.432753\pi$
$191$	−10.2536	+	17.7597i	−0.741923	+	1.28505i	−0.951619	+	0.307282i	$0.900581\pi$
$192$		0			0
$193$	−9.93758	+	5.73747i	−0.715323	+	0.412992i	−0.813029	−	0.582224i	$-0.802183\pi$
$193$	−9.93758	+	5.73747i	−0.715323	+	0.412992i	0.0977060	+	0.995215i	$0.468850\pi$
$194$	−1.40697	−	10.0699i	−0.101015	−	0.722977i
$195$		0			0
$196$	4.71487	−	1.34376i	0.336776	−	0.0959831i
$197$	−8.30543	−	14.3854i	−0.591737	−	1.02492i	−0.993998	−	0.109394i	$-0.965109\pi$
$197$	−8.30543	−	14.3854i	−0.591737	−	1.02492i	0.402261	−	0.915525i	$-0.368224\pi$
$198$		0			0
$199$	11.7805	−	20.4043i	0.835094	−	1.44643i	−0.0588595	−	0.998266i	$-0.518746\pi$
$199$	11.7805	−	20.4043i	0.835094	−	1.44643i	0.893954	−	0.448159i	$-0.147920\pi$
$200$	−12.8402	+	5.67976i	−0.907943	+	0.401620i
$201$		0			0
$202$	−17.0448	−	6.90250i	−1.19927	−	0.485658i
$203$	−0.221910			−0.0155750
$204$		0			0
$205$	1.51831	−	0.876598i	0.106043	−	0.0612242i
$206$	11.1371	+	14.2785i	0.775961	+	0.994833i
$207$		0			0
$208$	7.38062	−	12.3906i	0.511754	−	0.859132i
$209$	−5.71337			−0.395202
$210$		0			0
$211$	−8.68952	+	5.01690i	−0.598212	+	0.345378i	−0.768338	−	0.640045i	$-0.778916\pi$
$211$	−8.68952	+	5.01690i	−0.598212	+	0.345378i	0.170126	+	0.985422i	$0.445582\pi$
$212$	−18.0174	−	4.52305i	−1.23744	−	0.310644i
$213$		0			0
$214$	−23.7485	−	9.61723i	−1.62341	−	0.657421i
$215$	1.15122	+	0.664656i	0.0785124	+	0.0453292i
$216$		0			0
$217$	2.92048	−	5.05841i	0.198255	−	0.343387i
$218$	4.79017	+	6.14131i	0.324431	+	0.415942i
$219$		0			0
$220$	−0.497114	+	0.141680i	−0.0335154	+	0.00955206i
$221$	17.1669	+	10.9771i	1.15477	+	0.738402i
$222$		0			0
$223$	−5.39103	+	3.11251i	−0.361010	+	0.208429i	−0.669524	−	0.742791i	$-0.733502\pi$
$223$	−5.39103	+	3.11251i	−0.361010	+	0.208429i	0.308514	+	0.951220i	$0.400168\pi$
$224$	4.17194	−	11.3205i	0.278750	−	0.756380i
$225$		0			0
$226$	−16.6974	+	2.33297i	−1.11070	+	0.155187i
$227$	6.07319	−	10.5191i	0.403092	−	0.698175i	−0.591006	−	0.806667i	$-0.701269\pi$
$227$	6.07319	−	10.5191i	0.403092	−	0.698175i	0.994097	+	0.108492i	$0.0346022\pi$
$228$		0			0
$229$	−11.8639			−0.783987			−0.391994	−	0.919968i	$-0.628215\pi$
$229$	−11.8639			−0.783987			−0.391994	+	0.919968i	$0.628215\pi$
$230$	0.603332	−	1.48985i	0.0397825	−	0.0982377i
$231$		0			0
$232$	0.173554	−	0.237669i	0.0113944	−	0.0156037i
$233$	7.14863			0.468322			0.234161	−	0.972198i	$-0.424766\pi$
$233$	7.14863			0.468322			0.234161	+	0.972198i	$0.424766\pi$
$234$		0			0
$235$			1.29063i			0.0841914i
$236$	−5.06008	−	4.90222i	−0.329383	−	0.319107i
$237$		0			0
$238$	15.7993	+	6.39814i	1.02412	+	0.414729i
$239$			0.661526i			0.0427906i	0.999771	+	0.0213953i	$0.00681085\pi$
$239$			0.661526i			0.0427906i	−0.999771	+	0.0213953i	$0.993189\pi$
$240$		0			0
$241$	8.42049	+	4.86157i	0.542411	+	0.313161i	0.746056	−	0.665884i	$-0.231945\pi$
$241$	8.42049	+	4.86157i	0.542411	+	0.313161i	−0.203644	+	0.979045i	$0.565279\pi$
$242$	−12.8066	+	1.78935i	−0.823240	+	0.115024i
$243$		0			0
$244$	−16.5329	+	17.0653i	−1.05841	+	1.09249i
$245$	−0.232497	−	0.402696i	−0.0148537	−	0.0257273i
$246$		0			0
$247$	−12.7377	−	8.14497i	−0.810481	−	0.518252i
$248$	3.13356	+	7.08403i	0.198981	+	0.449837i
$249$		0			0
$250$	1.64397	+	2.10767i	0.103973	+	0.133301i
$251$	−16.7178	−	9.65204i	−1.05522	−	0.609232i	−0.131114	−	0.991367i	$-0.541855\pi$
$251$	−16.7178	−	9.65204i	−1.05522	−	0.609232i	−0.924106	+	0.382136i	$0.875189\pi$
$252$		0			0
$253$	−4.08187	+	7.07001i	−0.256625	+	0.444488i
$254$	−1.06847	+	2.63845i	−0.0670420	+	0.165551i
$255$		0			0
$256$	8.86155	+	13.3219i	0.553847	+	0.832618i
$257$	−5.38456	−	9.32633i	−0.335879	−	0.581760i	0.647774	−	0.761833i	$-0.275700\pi$
$257$	−5.38456	−	9.32633i	−0.335879	−	0.581760i	−0.983653	+	0.180072i	$0.942367\pi$
$258$		0			0
$259$		−	4.52990i		−	0.281474i
$260$	−1.31027	−	0.392815i	−0.0812596	−	0.0243613i
$261$		0			0
$262$	2.99005	−	2.33221i	0.184726	−	0.144084i
$263$	14.1235	+	24.4626i	0.870892	+	1.50843i	0.861075	+	0.508478i	$0.169792\pi$
$263$	14.1235	+	24.4626i	0.870892	+	1.50843i	0.00981755	+	0.999952i	$0.496875\pi$
$264$		0			0
$265$			1.76190i			0.108233i
$266$	−11.7230	−	4.74738i	−0.718784	−	0.291080i
$267$		0			0
$268$	−23.1769	+	6.60553i	−1.41575	+	0.403497i
$269$	18.6043	+	10.7412i	1.13432	+	0.654902i	0.945019	−	0.327017i	$-0.106043\pi$
$269$	18.6043	+	10.7412i	1.13432	+	0.654902i	0.189305	+	0.981918i	$0.439377\pi$
$270$		0			0
$271$	−3.77766	+	2.18103i	−0.229476	+	0.132488i	−0.610330	−	0.792147i	$-0.708963\pi$
$271$	−3.77766	+	2.18103i	−0.229476	+	0.132488i	0.380854	+	0.924635i	$0.375630\pi$
$272$	−19.2091	+	11.9174i	−1.16472	+	0.722599i
$273$		0			0
$274$	1.70690	+	12.2165i	0.103118	+	0.738026i
$275$	−3.38173	−	5.85733i	−0.203926	−	0.353210i
$276$		0			0
$277$	8.44257	+	4.87432i	0.507265	+	0.292870i	0.731709	−	0.681617i	$-0.238723\pi$
$277$	8.44257	+	4.87432i	0.507265	+	0.292870i	−0.224444	+	0.974487i	$0.572056\pi$
$278$	1.06460	+	7.61949i	0.0638505	+	0.456987i
$279$		0			0
$280$	−1.13773	−	0.122357i	−0.0679925	−	0.00731221i
$281$		−	22.3245i		−	1.33177i	−0.746055	−	0.665884i	$-0.768055\pi$
$281$		−	22.3245i		−	1.33177i	0.746055	−	0.665884i	$-0.231945\pi$
$282$		0			0
$283$	−3.69872	+	2.13546i	−0.219866	+	0.126940i	−0.605888	−	0.795550i	$-0.707182\pi$
$283$	−3.69872	+	2.13546i	−0.219866	+	0.126940i	0.386022	+	0.922489i	$0.373849\pi$
$284$	2.00236	−	2.06684i	0.118818	−	0.122644i
$285$		0			0
$286$	6.31468	+	2.89675i	0.373395	+	0.171288i
$287$	−19.7117			−1.16355
$288$		0			0
$289$	−7.46918	−	12.9370i	−0.439363	−	0.761000i
$290$	−0.0258715	−	0.0104770i	−0.00151923	−	0.000615229i
$291$		0			0
$292$	−15.1897	−	3.81319i	−0.888911	−	0.223150i
$293$	4.86107	−	8.41962i	0.283987	−	0.491880i	−0.688376	−	0.725354i	$-0.741676\pi$
$293$	4.86107	−	8.41962i	0.283987	−	0.491880i	0.972363	+	0.233474i	$0.0750095\pi$
$294$		0			0
$295$	−0.334109	+	0.578694i	−0.0194526	+	0.0336928i
$296$	4.85159	+	3.54281i	0.281993	+	0.205921i
$297$		0			0
$298$	12.1951	−	1.70391i	0.706445	−	0.0987050i
$299$	−19.1794	+	9.94317i	−1.10917	+	0.575028i
$300$		0			0
$301$	−7.47294	−	12.9435i	−0.430733	−	0.746051i
$302$	12.9094	−	10.0692i	0.742853	−	0.579419i
$303$		0			0
$304$	14.2530	−	8.84265i	0.817467	−	0.507161i
$305$	1.95166	+	1.12679i	0.111752	+	0.0645199i
$306$		0			0
$307$	−10.9126			−0.622813			−0.311407	−	0.950277i	$-0.600800\pi$
$307$	−10.9126			−0.622813			−0.311407	+	0.950277i	$0.600800\pi$
$308$	5.63687	+	1.41506i	0.321191	+	0.0806308i
$309$		0			0
$310$	0.579307	−	0.451854i	0.0329024	−	0.0256636i
$311$	−5.20379			−0.295080			−0.147540	−	0.989056i	$-0.547136\pi$
$311$	−5.20379			−0.295080			−0.147540	+	0.989056i	$0.547136\pi$
$312$		0			0
$313$	24.5947			1.39017			0.695086	−	0.718926i	$-0.255366\pi$
$313$	24.5947			1.39017			0.695086	+	0.718926i	$0.255366\pi$
$314$	19.8841	−	15.5094i	1.12213	−	0.875248i
$315$		0			0
$316$	−2.76634	+	11.0197i	−0.155619	+	0.619904i
$317$	−5.59568			−0.314285			−0.157142	−	0.987576i	$-0.550228\pi$
$317$	−5.59568			−0.314285			−0.157142	+	0.987576i	$0.550228\pi$
$318$		0			0
$319$	0.122772	+	0.0708825i	0.00687392	+	0.00396866i
$320$	1.02086	−	1.12283i	0.0570678	−	0.0627684i
$321$		0			0
$322$	−14.2501	+	11.1149i	−0.794125	+	0.619411i
$323$	11.8490	+	20.5231i	0.659298	+	1.14194i
$324$		0			0
$325$	0.810776	−	17.8796i	0.0449738	−	0.991784i
$326$	5.41371	−	0.756408i	0.299838	−	0.0418936i
$327$		0			0
$328$	15.4164	−	21.1116i	0.851230	−	1.16569i
$329$	7.25548	−	12.5669i	0.400008	−	0.692834i
$330$		0			0
$331$	8.64559	−	14.9746i	0.475205	−	0.823078i	−0.524392	−	0.851477i	$-0.675707\pi$
$331$	8.64559	−	14.9746i	0.475205	−	0.823078i	0.999597	+	0.0283984i	$0.00904072\pi$
$332$	6.27512	−	24.9968i	0.344392	−	1.37188i
$333$		0			0
$334$	26.0554	+	10.5514i	1.42569	+	0.577349i
$335$	1.14288	+	1.97953i	0.0624424	+	0.108153i
$336$		0			0
$337$	−13.5143			−0.736168			−0.368084	−	0.929792i	$-0.619986\pi$
$337$	−13.5143			−0.736168			−0.368084	+	0.929792i	$0.619986\pi$
$338$	9.94871	+	15.4604i	0.541138	+	0.840934i
$339$		0			0
$340$	1.53990	+	1.49186i	0.0835130	+	0.0809075i
$341$	−3.23152	+	1.86572i	−0.174997	+	0.101034i
$342$		0			0
$343$			20.1574i			1.08840i
$344$	19.7073	+	2.11941i	1.06254	+	0.114271i
$345$		0			0
$346$	2.67700	+	19.1596i	0.143916	+	1.03003i
$347$	−0.739226	−	0.426792i	−0.0396837	−	0.0229114i	0.480027	−	0.877254i	$-0.340627\pi$
$347$	−0.739226	−	0.426792i	−0.0396837	−	0.0229114i	−0.519711	+	0.854342i	$0.673960\pi$
$348$		0			0
$349$	−7.04582	−	12.2037i	−0.377154	−	0.653250i	0.613493	−	0.789700i	$-0.289764\pi$
$349$	−7.04582	−	12.2037i	−0.377154	−	0.653250i	−0.990647	+	0.136450i	$0.956431\pi$
$350$	−2.07183	−	14.8284i	−0.110744	−	0.792609i
$351$		0			0
$352$	−5.92412	+	4.93047i	−0.315757	+	0.262795i
$353$	2.37214	−	1.36955i	0.126256	−	0.0728940i	−0.435542	−	0.900169i	$-0.643443\pi$
$353$	2.37214	−	1.36955i	0.126256	−	0.0728940i	0.561798	+	0.827275i	$0.310110\pi$
$354$		0			0
$355$	−0.236373	−	0.136470i	−0.0125454	−	0.00724307i
$356$	2.67647	+	9.39096i	0.141853	+	0.497720i
$357$		0			0
$358$	4.63366	+	1.87646i	0.244897	+	0.0991739i
$359$		−	14.5013i		−	0.765350i	−0.923883	−	0.382675i	$-0.875003\pi$
$359$		−	14.5013i		−	0.765350i	0.923883	−	0.382675i	$-0.124997\pi$
$360$		0			0
$361$	0.708092	+	1.22645i	0.0372680	+	0.0645500i
$362$	−6.31174	+	4.92310i	−0.331738	+	0.258752i
$363$		0			0
$364$	10.5498	+	11.1907i	0.552962	+	0.586554i
$365$			1.48539i			0.0777486i
$366$		0			0
$367$	−7.28507	−	12.6181i	−0.380277	−	0.658660i	0.610824	−	0.791766i	$-0.290838\pi$
$367$	−7.28507	−	12.6181i	−0.380277	−	0.658660i	−0.991102	+	0.133106i	$0.957505\pi$
$368$	−0.759372	−	23.9550i	−0.0395850	−	1.24874i
$369$		0			0
$370$	0.213869	−	0.528121i	0.0111185	−	0.0274557i
$371$	9.90482	−	17.1557i	0.514233	−	0.890677i
$372$		0			0
$373$	−26.5637	−	15.3365i	−1.37541	−	0.794096i	−0.383811	−	0.923412i	$-0.625389\pi$
$373$	−26.5637	−	15.3365i	−1.37541	−	0.794096i	−0.991603	+	0.129316i	$0.958722\pi$
$374$	−6.69733	−	8.58641i	−0.346310	−	0.443993i
$375$		0			0
$376$	7.78485	+	17.5992i	0.401473	+	0.907610i
$377$	0.172665	+	0.333053i	0.00889270	+	0.0171531i
$378$		0			0
$379$	−14.8941	−	25.7974i	−0.765059	−	1.32512i	−0.940215	−	0.340581i	$-0.889376\pi$
$379$	−14.8941	−	25.7974i	−0.765059	−	1.32512i	0.175156	−	0.984541i	$-0.443957\pi$
$380$	−1.14260	−	1.10695i	−0.0586141	−	0.0567854i
$381$		0			0
$382$	28.7225	−	4.01313i	1.46957	−	0.205330i
$383$	5.15086	+	2.97385i	0.263197	+	0.151957i	0.625792	−	0.779990i	$-0.284776\pi$
$383$	5.15086	+	2.97385i	0.263197	+	0.151957i	−0.362595	+	0.931947i	$0.618109\pi$
$384$		0			0
$385$		−	0.551223i		−	0.0280929i
$386$	15.0414	+	6.09122i	0.765590	+	0.310035i
$387$		0			0
$388$	−10.0053	+	10.3275i	−0.507944	+	0.524301i
$389$		−	5.39933i		−	0.273757i	−0.990588	−	0.136878i	$-0.956293\pi$
$389$		−	5.39933i		−	0.273757i	0.990588	−	0.136878i	$-0.0437070\pi$
$390$		0			0
$391$	33.8618			1.71247
$392$	−5.59935	−	4.08885i	−0.282810	−	0.206518i
$393$		0			0
$394$	−8.81751	+	21.7737i	−0.444220	+	1.09694i
$395$	1.07760			0.0542199
$396$		0			0
$397$	5.09195	−	8.81952i	0.255558	−	0.442639i	−0.709489	−	0.704716i	$-0.751074\pi$
$397$	5.09195	−	8.81952i	0.255558	−	0.442639i	0.965047	+	0.262077i	$0.0844076\pi$
$398$	−32.9996	+	4.61073i	−1.65412	+	0.231115i
$399$		0			0
$400$	17.5018	+	9.37821i	0.875089	+	0.468911i
$401$	−2.13475	+	1.23250i	−0.106604	+	0.0615481i	−0.552354	−	0.833609i	$-0.686270\pi$
$401$	−2.13475	+	1.23250i	−0.106604	+	0.0615481i	0.445750	+	0.895158i	$0.352937\pi$
$402$		0			0
$403$	−9.86429	−	0.447310i	−0.491375	−	0.0222821i
$404$	7.12815	+	25.0106i	0.354639	+	1.24432i
$405$		0			0
$406$	0.193013	+	0.247455i	0.00957906	+	0.0122810i
$407$	−1.44694	+	2.50617i	−0.0717222	+	0.124226i
$408$		0			0
$409$	21.2131	+	12.2474i	1.04892	+	0.605595i	0.922347	−	0.386362i	$-0.126269\pi$
$409$	21.2131	+	12.2474i	1.04892	+	0.605595i	0.126574	+	0.991957i	$0.459602\pi$
$410$	−2.29810	−	0.930645i	−0.113495	−	0.0459613i
$411$		0			0
$412$	6.23536	−	24.8384i	0.307194	−	1.22370i
$413$	6.50644	−	3.75649i	0.320161	−	0.184845i
$414$		0			0
$415$	−2.44441			−0.119991
$416$	−20.2364	+	2.54684i	−0.992173	+	0.124869i
$417$		0			0
$418$	4.96937	+	6.37106i	0.243060	+	0.311619i
$419$	34.2729	−	19.7874i	1.67434	−	0.966680i	0.709175	−	0.705032i	$-0.249068\pi$
$419$	34.2729	−	19.7874i	1.67434	−	0.966680i	0.965164	−	0.261647i	$-0.0842658\pi$
$420$		0			0
$421$	5.17255			0.252095			0.126047	−	0.992024i	$-0.459771\pi$
$421$	5.17255			0.252095			0.126047	+	0.992024i	$0.459771\pi$
$422$	13.1524	+	5.32622i	0.640249	+	0.259276i
$423$		0			0
$424$	10.6275	+	24.0256i	0.516116	+	1.16679i
$425$	−14.0268	+	24.2952i	−0.680401	+	1.17849i
$426$		0			0
$427$	−12.6689	−	21.9431i	−0.613090	−	1.06190i
$428$	9.93163	+	34.8472i	0.480063	+	1.68440i
$429$		0			0
$430$	−0.260138	−	1.86185i	−0.0125450	−	0.0897862i
$431$	20.9732	−	12.1089i	1.01025	−	0.583265i	0.0989818	−	0.995089i	$-0.468441\pi$
$431$	20.9732	−	12.1089i	1.01025	−	0.583265i	0.911263	+	0.411824i	$0.135108\pi$
$432$		0			0
$433$	16.2179	−	28.0903i	0.779385	−	1.34993i	−0.152912	−	0.988240i	$-0.548865\pi$
$433$	16.2179	−	28.0903i	0.779385	−	1.34993i	0.932297	−	0.361694i	$-0.117802\pi$
$434$	−8.18088	+	1.14304i	−0.392695	+	0.0548676i
$435$		0			0
$436$	2.68188	−	10.6832i	0.128439	−	0.511632i
$437$	−25.1253			−1.20190
$438$		0			0
$439$	1.43286	+	2.48179i	0.0683868	+	0.118449i	0.898191	−	0.439605i	$-0.144881\pi$
$439$	1.43286	+	2.48179i	0.0683868	+	0.118449i	−0.829805	+	0.558054i	$0.811548\pi$
$440$	0.590369	+	0.431109i	0.0281447	+	0.0205523i
$441$		0			0
$442$	−2.69062	−	28.6907i	−0.127980	−	1.36468i
$443$			16.2626i			0.772659i	0.922361	+	0.386329i	$0.126257\pi$
$443$			16.2626i			0.772659i	−0.922361	+	0.386329i	$0.873743\pi$
$444$		0			0
$445$	0.802080	−	0.463081i	0.0380223	−	0.0219522i
$446$	8.15982	+	3.30442i	0.386379	+	0.156469i
$447$		0			0
$448$	−16.2523	+	5.19412i	−0.767849	+	0.245399i
$449$	33.7388	+	19.4791i	1.59223	+	0.919277i	0.992923	+	0.118760i	$0.0378919\pi$
$449$	33.7388	+	19.4791i	1.59223	+	0.919277i	0.599311	+	0.800516i	$0.295441\pi$
$450$		0			0
$451$	10.9056	+	6.29633i	0.513523	+	0.296482i
$452$	17.1246	+	16.5904i	0.805474	+	0.780345i
$453$		0			0
$454$	−17.0123	+	2.37697i	−0.798428	+	0.111557i
$455$	0.785823	−	1.22893i	0.0368399	−	0.0576130i
$456$		0			0
$457$	−11.6025	+	6.69870i	−0.542742	+	0.313352i	−0.746189	−	0.665734i	$-0.768119\pi$
$457$	−11.6025	+	6.69870i	−0.542742	+	0.313352i	0.203448	+	0.979086i	$0.434785\pi$
$458$	10.3190	+	13.2296i	0.482174	+	0.618179i
$459$		0			0
$460$	−2.18612	+	0.623056i	−0.101928	+	0.0290501i
$461$	−13.6463	+	23.6361i	−0.635571	+	1.10084i	0.350823	+	0.936442i	$0.385902\pi$
$461$	−13.6463	+	23.6361i	−0.635571	+	1.10084i	−0.986394	+	0.164399i	$0.947431\pi$
$462$		0			0
$463$		−	28.3889i		−	1.31934i	−0.751555	−	0.659671i	$-0.770696\pi$
$463$		−	28.3889i		−	1.31934i	0.751555	−	0.659671i	$-0.229304\pi$
$464$	−0.415983	+	0.0131866i	−0.0193115	+	0.000612174i
$465$		0			0
$466$	−6.21773	−	7.97154i	−0.288031	−	0.369275i
$467$			34.7603i			1.60852i	0.594280	+	0.804258i	$0.297437\pi$
$467$			34.7603i			1.60852i	−0.594280	+	0.804258i	$0.702563\pi$
$468$		0			0
$469$		−	25.6996i		−	1.18670i
$470$	1.43920	−	1.12256i	0.0663854	−	0.0517800i
$471$		0			0
$472$	−1.06538	+	9.90643i	−0.0490382	+	0.455981i
$473$			9.54803i			0.439019i
$474$		0			0
$475$	10.4078	−	18.0269i	0.477544	−	0.827130i
$476$	−6.60730	−	23.1831i	−0.302845	−	1.06259i
$477$		0			0
$478$	0.737678	−	0.575382i	0.0337406	−	0.0263174i
$479$	29.7344	−	17.1671i	1.35860	−	0.784387i	0.369163	−	0.929365i	$-0.379644\pi$
$479$	29.7344	−	17.1671i	1.35860	−	0.784387i	0.989435	+	0.144978i	$0.0463110\pi$
$480$		0			0
$481$	−6.79869	+	3.52465i	−0.309994	+	0.160710i
$482$	−1.90276	−	13.6183i	−0.0866684	−	0.620297i
$483$		0			0
$484$	13.1343	+	12.7245i	0.597012	+	0.578386i
$485$	1.18110	+	0.681910i	0.0536311	+	0.0309639i
$486$		0			0
$487$	19.0115	+	10.9763i	0.861494	+	0.497384i	0.864512	−	0.502612i	$-0.167627\pi$
$487$	19.0115	+	10.9763i	0.861494	+	0.497384i	−0.00301815	+	0.999995i	$0.500961\pi$
$488$	33.4097	+	3.59303i	1.51239	+	0.162649i
$489$		0			0
$490$	−0.246832	+	0.609518i	−0.0111507	+	0.0275352i
$491$	−16.3189	+	9.42172i	−0.736462	+	0.425196i	−0.820781	−	0.571242i	$-0.806462\pi$
$491$	−16.3189	+	9.42172i	−0.736462	+	0.425196i	0.0843196	+	0.996439i	$0.473128\pi$
$492$		0			0
$493$		−	0.588017i		−	0.0264829i
$494$	1.99643	+	21.2883i	0.0898234	+	0.957808i
$495$		0			0
$496$	5.17401	−	9.65583i	0.232320	−	0.433559i
$497$	1.53437	+	2.65761i	0.0688261	+	0.119210i
$498$		0			0
$499$	−39.7400			−1.77900			−0.889502	−	0.456931i	$-0.848949\pi$
$499$	−39.7400			−1.77900			−0.889502	+	0.456931i	$0.848949\pi$
$500$	0.920409	−	3.66642i	0.0411619	−	0.163967i
$501$		0			0
$502$	3.77769	+	27.0375i	0.168607	+	1.20674i
$503$	14.7001	−	25.4614i	0.655447	−	1.13527i	−0.326335	−	0.945254i	$-0.605814\pi$
$503$	14.7001	−	25.4614i	0.655447	−	1.13527i	0.981782	−	0.190013i	$-0.0608530\pi$
$504$		0			0
$505$	2.13615	−	1.23331i	0.0950574	−	0.0548814i
$506$	11.4342	−	1.59760i	0.508313	−	0.0710218i
$507$		0			0
$508$	3.87152	−	1.10340i	0.171771	−	0.0489556i
$509$	−19.7550	−	34.2167i	−0.875626	−	1.51663i	−0.856094	−	0.516820i	$-0.827116\pi$
$509$	−19.7550	−	34.2167i	−0.875626	−	1.51663i	−0.0195318	−	0.999809i	$-0.506218\pi$
$510$		0			0
$511$	8.35033	−	14.4632i	0.369397	−	0.639814i
$512$	7.14785	−	21.4688i	0.315893	−	0.948795i
$513$		0			0
$514$	−5.71655	+	14.1163i	−0.252146	+	0.622641i
$515$	−2.42892			−0.107031
$516$		0			0
$517$	−8.02822	+	4.63510i	−0.353081	+	0.203851i
$518$	−5.05136	+	3.94001i	−0.221944	+	0.173114i
$519$		0			0
$520$	0.701615	+	1.80277i	0.0307678	+	0.0790566i
$521$	9.39408			0.411562			0.205781	−	0.978598i	$-0.434027\pi$
$521$	9.39408			0.411562			0.205781	+	0.978598i	$0.434027\pi$
$522$		0			0
$523$	33.5910	−	19.3938i	1.46883	−	0.848031i	0.469443	−	0.882963i	$-0.344455\pi$
$523$	33.5910	−	19.3938i	1.46883	−	0.848031i	0.999390	+	0.0349315i	$0.0111213\pi$
$524$	−5.20137	−	1.30574i	−0.227223	−	0.0570414i
$525$		0			0
$526$	14.9943	−	37.0264i	0.653783	−	1.61443i
$527$	13.4038	+	7.73868i	0.583878	+	0.337102i
$528$		0			0
$529$	−6.45055	+	11.1727i	−0.280459	+	0.485769i
$530$	1.96473	−	1.53247i	0.0853423	−	0.0665662i
$531$		0			0
$532$	4.90257	+	17.2017i	0.212553	+	0.745788i
$533$	15.3374	+	29.5843i	0.664338	+	1.28144i
$534$		0			0
$535$	2.97629	−	1.71836i	0.128676	−	0.0742913i
$536$	27.5247	+	20.0995i	1.18889	+	0.868167i
$537$		0			0
$538$	−4.20397	−	30.0884i	−0.181246	−	1.29720i
$539$	1.66995	−	2.89244i	0.0719299	−	0.124586i
$540$		0			0
$541$	4.35170			0.187094			0.0935471	−	0.995615i	$-0.470179\pi$
$541$	4.35170			0.187094			0.0935471	+	0.995615i	$0.470179\pi$
$542$	5.71783	+	2.31551i	0.245602	+	0.0994595i
$543$		0			0
$544$	29.9970	+	11.0548i	1.28611	+	0.473972i
$545$	−1.04470			−0.0447499
$546$		0			0
$547$			37.5399i			1.60509i	0.596591	+	0.802546i	$0.296522\pi$
$547$			37.5399i			1.60509i	−0.596591	+	0.802546i	$0.703478\pi$
$548$	12.1382	−	12.5291i	0.518518	−	0.535215i
$549$		0			0
$550$	−3.59023	+	8.86561i	−0.153088	+	0.378031i
$551$			0.436305i			0.0185872i
$552$		0			0
$553$	−10.4926	−	6.05789i	−0.446190	−	0.257608i
$554$	−1.90775	−	13.6540i	−0.0810526	−	0.580104i
$555$		0			0
$556$	7.57065	−	7.81444i	0.321067	−	0.331406i
$557$	4.81938	+	8.34741i	0.204204	+	0.353691i	0.949879	−	0.312619i	$-0.101206\pi$
$557$	4.81938	+	8.34741i	0.204204	+	0.353691i	−0.745675	+	0.666310i	$0.767873\pi$
$558$		0			0
$559$	−13.6117	+	21.2869i	−0.575712	+	0.900341i
$560$	0.853134	+	1.37513i	0.0360515	+	0.0581096i
$561$		0			0
$562$	−24.8944	+	19.4174i	−1.05011	+	0.819074i
$563$	−10.7740	−	6.22039i	−0.454071	−	0.262158i	0.255477	−	0.966815i	$-0.417768\pi$
$563$	−10.7740	−	6.22039i	−0.454071	−	0.262158i	−0.709548	+	0.704657i	$0.751101\pi$
$564$		0			0
$565$	1.13071	−	1.95845i	0.0475693	−	0.0823925i
$566$	5.59835	+	2.26712i	0.235316	+	0.0952942i
$567$		0			0
$568$	−4.04637	−	0.435165i	−0.169782	−	0.0182591i
$569$	18.1774	+	31.4841i	0.762034	+	1.31988i	0.941800	+	0.336173i	$0.109133\pi$
$569$	18.1774	+	31.4841i	0.762034	+	1.31988i	−0.179766	+	0.983709i	$0.557534\pi$
$570$		0			0
$571$		−	28.0964i		−	1.17580i	−0.808934	−	0.587899i	$-0.799955\pi$
$571$		−	28.0964i		−	1.17580i	0.808934	−	0.587899i	$-0.200045\pi$
$572$	−2.26218	−	9.56113i	−0.0945863	−	0.399771i
$573$		0			0
$574$	17.1449	+	21.9809i	0.715613	+	0.917463i
$575$	−14.8716	−	25.7583i	−0.620188	−	1.07420i
$576$		0			0
$577$			30.9511i			1.28851i	0.764811	+	0.644255i	$0.222832\pi$
$577$			30.9511i			1.28851i	−0.764811	+	0.644255i	$0.777168\pi$
$578$	−7.92970	+	19.5813i	−0.329832	+	0.814476i
$579$		0			0
$580$	0.0108195	+	0.0379624i	0.000449254	+	0.00157630i
$581$	23.8012	+	13.7416i	0.987439	+	0.570098i
$582$		0			0
$583$	−10.9597	+	6.32760i	−0.453906	+	0.262063i
$584$	8.95958	+	20.2549i	0.370750	+	0.838155i
$585$		0			0
$586$	−13.6169	+	1.90257i	−0.562510	+	0.0785943i
$587$	−0.0914707	−	0.158432i	−0.00377540	−	0.00653919i	0.864132	−	0.503266i	$-0.167868\pi$
$587$	−0.0914707	−	0.158432i	−0.00377540	−	0.00653919i	−0.867907	+	0.496727i	$0.834535\pi$
$588$		0			0
$589$	−9.94552	−	5.74205i	−0.409798	−	0.236597i
$590$	0.935911	−	0.130766i	0.0385309	−	0.00538356i
$591$		0			0
$592$	−0.269182	−	8.49155i	−0.0110633	−	0.349001i
$593$			26.1358i			1.07327i	0.843815	+	0.536634i	$0.180305\pi$
$593$			26.1358i			1.07327i	−0.843815	+	0.536634i	$0.819695\pi$
$594$		0			0
$595$	−1.98006	+	1.14319i	−0.0811746	+	0.0468662i
$596$	−12.5071	−	12.1170i	−0.512313	−	0.496330i
$597$		0			0
$598$	27.7696	+	12.7388i	1.13558	+	0.520929i
$599$	29.3928			1.20096			0.600479	−	0.799641i	$-0.294977\pi$
$599$	29.3928			1.20096			0.600479	+	0.799641i	$0.294977\pi$
$600$		0			0
$601$	−6.85899	−	11.8801i	−0.279784	−	0.484600i	0.691547	−	0.722332i	$-0.256930\pi$
$601$	−6.85899	−	11.8801i	−0.279784	−	0.484600i	−0.971331	+	0.237731i	$0.923596\pi$
$602$	−7.93369	+	19.5912i	−0.323353	+	0.798478i
$603$		0			0
$604$	−22.4567	−	5.63747i	−0.913750	−	0.229385i
$605$	0.867233	−	1.50209i	0.0352580	−	0.0610687i
$606$		0			0
$607$	−11.6750	+	20.2216i	−0.473872	+	0.820771i	−0.999553	−	0.0299112i	$-0.990478\pi$
$607$	−11.6750	+	20.2216i	−0.473872	+	0.820771i	0.525680	+	0.850682i	$0.323811\pi$
$608$	−22.2576	−	8.20261i	−0.902664	−	0.332660i
$609$		0			0
$610$	−0.441013	−	3.15639i	−0.0178561	−	0.127798i
$611$	−24.5064	−	1.11127i	−0.991421	−	0.0449573i
$612$		0			0
$613$	22.6961	+	39.3108i	0.916688	+	1.58775i	0.804411	+	0.594073i	$0.202481\pi$
$613$	22.6961	+	39.3108i	0.916688	+	1.58775i	0.112277	+	0.993677i	$0.464186\pi$
$614$	9.49154	+	12.1688i	0.383047	+	0.491092i
$615$		0			0
$616$	−3.32488	−	7.51656i	−0.133963	−	0.302851i
$617$	−29.6144	−	17.0979i	−1.19223	−	0.688334i	−0.233417	−	0.972377i	$-0.574991\pi$
$617$	−29.6144	−	17.0979i	−1.19223	−	0.688334i	−0.958812	+	0.284043i	$0.908324\pi$
$618$		0			0
$619$	15.8251			0.636065			0.318033	−	0.948080i	$-0.396978\pi$
$619$	15.8251			0.636065			0.318033	+	0.948080i	$0.396978\pi$
$620$	−1.00774	−	0.252980i	−0.0404718	−	0.0101599i
$621$		0			0
$622$	4.52615	+	5.80283i	0.181482	+	0.232672i
$623$	−10.4131			−0.417194
$624$		0			0
$625$	24.4615			0.978462
$626$	−21.3920	−	27.4259i	−0.854994	−	1.09616i
$627$		0			0
$628$	−34.5896	−	8.68328i	−1.38028	−	0.346501i
$629$	12.0033			0.478604
$630$		0			0
$631$	−8.68918	−	5.01670i	−0.345911	−	0.199712i	0.316972	−	0.948435i	$-0.397334\pi$
$631$	−8.68918	−	5.01670i	−0.345911	−	0.199712i	−0.662883	+	0.748723i	$0.730667\pi$
$632$	14.6943	−	6.49988i	0.584508	−	0.258551i
$633$		0			0
$634$	4.86701	+	6.23983i	0.193294	+	0.247815i
$635$	−0.190910	−	0.330666i	−0.00757603	−	0.0131221i
$636$		0			0
$637$	7.84654	−	4.06789i	0.310891	−	0.161176i
$638$	−0.0277426	−	0.198557i	−0.00109834	−	0.00786096i
$639$		0			0
$640$	−2.14001	−	0.161757i	−0.0845915	−	0.00639400i
$641$	−10.9247	+	18.9221i	−0.431498	+	0.747376i	−0.997003	−	0.0773688i	$-0.975348\pi$
$641$	−10.9247	+	18.9221i	−0.431498	+	0.747376i	0.565505	+	0.824745i	$0.308681\pi$
$642$		0			0
$643$	−22.1023	+	38.2824i	−0.871631	+	1.50971i	−0.0113225	+	0.999936i	$0.503604\pi$
$643$	−22.1023	+	38.2824i	−0.871631	+	1.50971i	−0.860309	+	0.509774i	$0.829729\pi$
$644$	24.7888	+	6.22293i	0.976817	+	0.245218i
$645$		0			0
$646$	12.5796	−	31.0636i	0.494938	−	1.22218i
$647$	−20.6785	−	35.8163i	−0.812957	−	1.40808i	−0.910785	−	0.412880i	$-0.864523\pi$
$647$	−20.6785	−	35.8163i	−0.812957	−	1.40808i	0.0978282	−	0.995203i	$-0.468810\pi$
$648$		0			0
$649$	−4.79960			−0.188401
$650$	−20.6431	+	14.6473i	−0.809688	+	0.574512i
$651$		0			0
$652$	−5.55222	−	5.37901i	−0.217442	−	0.210658i
$653$	3.58215	−	2.06815i	0.140180	−	0.0809331i	−0.428270	−	0.903651i	$-0.640877\pi$
$653$	3.58215	−	2.06815i	0.140180	−	0.0809331i	0.568450	+	0.822718i	$0.307543\pi$
$654$		0			0
$655$			0.508636i			0.0198740i
$656$	−36.9508	+	1.17134i	−1.44269	+	0.0457331i
$657$		0			0
$658$	−20.3242	+	2.83971i	−0.792319	+	0.110703i
$659$	17.3575	+	10.0214i	0.676153	+	0.390377i	0.798404	−	0.602122i	$-0.205678\pi$
$659$	17.3575	+	10.0214i	0.676153	+	0.390377i	−0.122251	+	0.992499i	$0.539011\pi$
$660$		0			0
$661$	−0.306645	−	0.531125i	−0.0119271	−	0.0206584i	0.860000	−	0.510294i	$-0.170463\pi$
$661$	−0.306645	−	0.531125i	−0.0119271	−	0.0206584i	−0.871927	+	0.489635i	$0.837130\pi$
$662$	−24.2182	+	3.38378i	−0.941266	+	0.131514i
$663$		0			0
$664$	−33.3323	+	14.7442i	−1.29354	+	0.572187i
$665$	1.46919	−	0.848239i	0.0569729	−	0.0328933i
$666$		0			0
$667$	0.539906	+	0.311715i	0.0209052	+	0.0120696i
$668$	−10.8964	−	38.2322i	−0.421593	−	1.47925i
$669$		0			0
$670$	1.21335	−	2.99621i	0.0468758	−	0.115754i
$671$			16.1868i			0.624884i
$672$		0			0
$673$	−10.3246	−	17.8828i	−0.397985	−	0.689330i	0.595492	−	0.803361i	$-0.296957\pi$
$673$	−10.3246	−	17.8828i	−0.397985	−	0.689330i	−0.993477	+	0.114031i	$0.963624\pi$
$674$	11.7544	+	15.0700i	0.452764	+	0.580473i
$675$		0			0
$676$	8.58691	−	24.5411i	0.330266	−	0.943888i
$677$		−	14.9377i		−	0.574101i	−0.957915	−	0.287051i	$-0.907325\pi$
$677$		−	14.9377i		−	0.574101i	0.957915	−	0.287051i	$-0.0926748\pi$
$678$		0			0
$679$	−7.66693	−	13.2795i	−0.294230	−	0.509621i
$680$	0.324221	−	3.01476i	0.0124333	−	0.115611i
$681$		0			0
$682$	4.89120	+	1.98075i	0.187294	+	0.0758469i
$683$	22.2218	−	38.4892i	0.850292	−	1.47275i	−0.0306521	−	0.999530i	$-0.509758\pi$
$683$	22.2218	−	38.4892i	0.850292	−	1.47275i	0.880945	−	0.473220i	$-0.156908\pi$
$684$		0			0
$685$	−1.43288	−	0.827273i	−0.0547475	−	0.0316085i
$686$	22.4779	−	17.5325i	0.858209	−	0.669395i
$687$		0			0
$688$	−14.7776	−	23.8193i	−0.563391	−	0.908102i
$689$	−33.4549	−	1.51706i	−1.27453	−	0.0577952i
$690$		0			0
$691$	−0.557929	−	0.966361i	−0.0212246	−	0.0367621i	0.855218	−	0.518268i	$-0.173423\pi$
$691$	−0.557929	−	0.966361i	−0.0212246	−	0.0367621i	−0.876443	+	0.481506i	$0.840090\pi$
$692$	19.0368	−	19.6498i	0.723671	−	0.746975i
$693$		0			0
$694$	0.167041	+	1.19554i	0.00634080	+	0.0453820i
$695$	−0.893694	−	0.515974i	−0.0338997	−	0.0195720i
$696$		0			0
$697$		−	52.2322i		−	1.97843i
$698$	−7.48024	+	18.4714i	−0.283131	+	0.699154i
$699$		0			0
$700$	−14.7333	+	15.2077i	−0.556866	+	0.574799i
$701$		−	37.1382i		−	1.40269i	−0.712821	−	0.701346i	$-0.752583\pi$
$701$		−	37.1382i		−	1.40269i	0.712821	−	0.701346i	$-0.247417\pi$
$702$		0			0
$703$	−8.90639			−0.335911
$704$	10.6507	+	2.31766i	0.401414	+	0.0873500i
$705$		0			0
$706$	−3.59045	−	1.45400i	−0.135128	−	0.0547218i
$707$	−27.7329			−1.04300
$708$		0			0
$709$	−14.9752	+	25.9378i	−0.562404	+	0.974113i	0.434882	+	0.900488i	$0.356790\pi$
$709$	−14.9752	+	25.9378i	−0.562404	+	0.974113i	−0.997286	+	0.0736252i	$0.976543\pi$
$710$	0.0534127	+	0.382282i	0.00200454	+	0.0143468i
$711$		0			0
$712$	8.14406	−	11.1526i	0.305212	−	0.417963i
$713$	−14.2110	+	8.20473i	−0.532206	+	0.307270i
$714$		0			0
$715$	−0.827303	+	0.428899i	−0.0309394	+	0.0160399i
$716$	−1.93780	−	6.79918i	−0.0724190	−	0.254097i
$717$		0			0
$718$	−16.1706	+	12.6130i	−0.603483	+	0.470711i
$719$	17.4176	−	30.1682i	0.649568	−	1.12508i	−0.333658	−	0.942694i	$-0.608283\pi$
$719$	17.4176	−	30.1682i	0.649568	−	1.12508i	0.983226	−	0.182391i	$-0.0583835\pi$
$720$		0			0
$721$	23.6504	+	13.6545i	0.880785	+	0.508522i
$722$	0.751750	−	1.85635i	0.0279772	−	0.0690860i
$723$		0			0
$724$	10.9796	+	2.75630i	0.408055	+	0.102437i
$725$	−0.447298	+	0.258248i	−0.0166122	+	0.00959108i
$726$		0			0
$727$	10.7252			0.397776			0.198888	−	0.980022i	$-0.436267\pi$
$727$	10.7252			0.397776			0.198888	+	0.980022i	$0.436267\pi$
$728$	3.30292	−	21.4978i	0.122414	−	0.796761i
$729$		0			0
$730$	1.65638	−	1.29196i	0.0613052	−	0.0478175i
$731$	34.2977	−	19.8018i	1.26855	−	0.732396i
$732$		0			0
$733$	−5.20872			−0.192388			−0.0961942	−	0.995363i	$-0.530667\pi$
$733$	−5.20872			−0.192388			−0.0961942	+	0.995363i	$0.530667\pi$
$734$	−7.73424	+	19.0987i	−0.285476	+	0.704945i
$735$		0			0
$736$	−26.0521	+	21.6824i	−0.960292	+	0.799222i
$737$	−8.20898	+	14.2184i	−0.302382	+	0.523740i
$738$		0			0
$739$	14.2025	+	24.5995i	0.522448	+	0.904907i	0.999659	+	0.0261179i	$0.00831454\pi$
$739$	14.2025	+	24.5995i	0.522448	+	0.904907i	−0.477211	+	0.878789i	$0.658352\pi$
$740$	−0.774935	+	0.220860i	−0.0284872	+	0.00811899i
$741$		0			0
$742$	−27.7456	+	3.87663i	−1.01857	+	0.142316i
$743$	30.9116	−	17.8468i	1.13404	−	0.654737i	0.189090	−	0.981960i	$-0.439446\pi$
$743$	30.9116	−	17.8468i	1.13404	−	0.654737i	0.944947	+	0.327223i	$0.106113\pi$
$744$		0			0
$745$	−0.825826	+	1.43037i	−0.0302559	+	0.0524048i
$746$	6.00254	+	42.9610i	0.219769	+	1.57291i
$747$		0			0
$748$	−3.74964	+	14.9366i	−0.137100	+	0.546136i
$749$	−38.6402			−1.41188
$750$		0			0
$751$	−14.8764	−	25.7667i	−0.542849	−	0.940242i	−0.998739	−	0.0502058i	$-0.984012\pi$
$751$	−14.8764	−	25.7667i	−0.542849	−	0.940242i	0.455890	−	0.890036i	$-0.349321\pi$
$752$	12.8541	−	23.9885i	0.468739	−	0.874769i
$753$		0			0
$754$	0.221212	−	0.482224i	0.00805607	−	0.0175616i
$755$			2.19601i			0.0799211i
$756$		0			0
$757$	−31.1859	+	18.0052i	−1.13347	+	0.654409i	−0.944805	−	0.327633i	$-0.893749\pi$
$757$	−31.1859	+	18.0052i	−1.13347	+	0.654409i	−0.188664	+	0.982042i	$0.560416\pi$
$758$	−15.8124	+	39.0467i	−0.574333	+	1.41824i
$759$		0			0
$760$	−0.240570	+	2.23693i	−0.00872638	+	0.0811421i
$761$	−22.4482	−	12.9605i	−0.813747	−	0.469817i	0.0345084	−	0.999404i	$-0.489013\pi$
$761$	−22.4482	−	12.9605i	−0.813747	−	0.469817i	−0.848255	+	0.529587i	$0.822347\pi$
$762$		0			0
$763$	10.1722	+	5.87293i	0.368259	+	0.212614i
$764$	−29.4574	−	28.5384i	−1.06573	−	1.03248i
$765$		0			0
$766$	−1.16393	−	8.33040i	−0.0420545	−	0.300989i
$767$	−10.7005	−	6.84230i	−0.386373	−	0.247061i
$768$		0			0
$769$	6.38308	−	3.68527i	0.230180	−	0.132894i	−0.380475	−	0.924791i	$-0.624240\pi$
$769$	6.38308	−	3.68527i	0.230180	−	0.132894i	0.610655	+	0.791897i	$0.290906\pi$
$770$	−0.614677	+	0.479443i	−0.0221514	+	0.0172779i
$771$		0			0
$772$	−6.29034	−	22.0710i	−0.226394	−	0.794352i
$773$	−13.3741	+	23.1646i	−0.481032	+	0.833171i	−0.999763	−	0.0217661i	$-0.993071\pi$
$773$	−13.3741	+	23.1646i	−0.481032	+	0.833171i	0.518732	+	0.854937i	$0.326404\pi$
$774$		0			0
$775$		−	13.5948i		−	0.488341i
$776$	20.2188	+	2.17442i	0.725814	+	0.0780573i
$777$		0			0
$778$	−6.02087	+	4.69623i	−0.215859	+	0.168368i
$779$			38.7559i			1.38858i
$780$		0			0
$781$		−	1.96044i		−	0.0701501i
$782$	−29.4523	−	37.7598i	−1.05321	−	1.35029i
$783$		0			0
$784$	0.310670	+	9.80032i	0.0110954	+	0.350011i
$785$			3.38248i			0.120726i
$786$		0			0
$787$	−15.3334	+	26.5583i	−0.546578	+	0.946701i	0.451927	+	0.892055i	$0.350737\pi$
$787$	−15.3334	+	26.5583i	−0.546578	+	0.946701i	−0.998506	+	0.0546467i	$0.982597\pi$
$788$	31.9495	−	9.10576i	1.13815	−	0.324379i
$789$		0			0
$790$	−0.937274	−	1.20165i	−0.0333467	−	0.0427527i
$791$	−22.0194	+	12.7129i	−0.782921	+	0.452020i
$792$		0			0
$793$	−23.0758	+	36.0877i	−0.819447	+	1.28151i
$794$	−14.2637	+	1.99293i	−0.506198	+	0.0707264i
$795$		0			0
$796$	33.8439	+	32.7880i	1.19957	+	1.16214i
$797$	18.8596	+	10.8886i	0.668043	+	0.385695i	0.795335	−	0.606171i	$-0.207295\pi$
$797$	18.8596	+	10.8886i	0.668043	+	0.385695i	−0.127292	+	0.991865i	$0.540628\pi$
$798$		0			0
$799$	33.2997	+	19.2256i	1.17806	+	0.680152i
$800$	−4.76492	−	27.6735i	−0.168465	−	0.978406i
$801$		0			0
$802$	3.23114	+	1.30849i	0.114096	+	0.0462044i
$803$	−9.23968	+	5.33453i	−0.326061	+	0.188251i
$804$		0			0
$805$		−	2.42407i		−	0.0854373i
$806$	8.08097	+	11.3889i	0.284640	+	0.401156i
$807$		0			0
$808$	21.6898	−	29.7024i	0.763043	−	1.04493i
$809$	13.9705	+	24.1975i	0.491175	+	0.850740i	0.999948	−	0.0101606i	$-0.00323427\pi$
$809$	13.9705	+	24.1975i	0.491175	+	0.850740i	−0.508774	+	0.860900i	$0.669901\pi$
$810$		0			0
$811$	4.37189			0.153518			0.0767588	−	0.997050i	$-0.475543\pi$
$811$	4.37189			0.153518			0.0767588	+	0.997050i	$0.475543\pi$
$812$	0.108062	−	0.430463i	0.00379224	−	0.0151063i
$813$		0			0
$814$	4.05319	−	0.566315i	0.142064	−	0.0198493i
$815$	−0.366604	+	0.634977i	−0.0128416	+	0.0222423i
$816$		0			0
$817$	−25.4487	+	14.6928i	−0.890337	+	0.514036i
$818$	−4.79349	−	34.3076i	−0.167600	−	1.19954i
$819$		0			0
$820$	0.961069	+	3.37211i	0.0335620	+	0.117759i
$821$	−17.3163	−	29.9928i	−0.604344	−	1.04675i	−0.992155	−	0.125016i	$-0.960102\pi$
$821$	−17.3163	−	29.9928i	−0.604344	−	1.04675i	0.387811	−	0.921739i	$-0.373231\pi$
$822$		0			0
$823$	8.89278	−	15.4027i	0.309983	−	0.536906i	−0.668375	−	0.743824i	$-0.733010\pi$
$823$	8.89278	−	15.4027i	0.309983	−	0.536906i	0.978358	+	0.206918i	$0.0663434\pi$
$824$	−33.1211	+	14.6508i	−1.15383	+	0.510384i
$825$		0			0
$826$	−9.84809	−	3.98810i	−0.342659	−	0.138764i
$827$	36.6583			1.27473			0.637367	−	0.770560i	$-0.280023\pi$
$827$	36.6583			1.27473			0.637367	+	0.770560i	$0.280023\pi$
$828$		0			0
$829$	12.5682	−	7.25623i	0.436510	−	0.252019i	−0.265606	−	0.964082i	$-0.585572\pi$
$829$	12.5682	−	7.25623i	0.436510	−	0.252019i	0.702116	+	0.712062i	$0.252239\pi$
$830$	2.12610	+	2.72580i	0.0737979	+	0.0946137i
$831$		0			0
$832$	20.4413	+	20.3508i	0.708674	+	0.705536i
$833$	−13.8533			−0.479990
$834$		0			0
$835$	−3.26540	+	1.88528i	−0.113004	+	0.0652428i
$836$	2.78221	−	11.0829i	0.0962247	−	0.383308i
$837$		0			0
$838$	−51.8751	−	21.0075i	−1.79200	−	0.725691i
$839$	−11.5480	−	6.66727i	−0.398683	−	0.230180i	0.287233	−	0.957861i	$-0.407265\pi$
$839$	−11.5480	−	6.66727i	−0.398683	−	0.230180i	−0.685915	+	0.727681i	$0.740598\pi$
$840$		0			0
$841$	−14.4946	+	25.1054i	−0.499813	+	0.865702i
$842$	−4.49898	−	5.76799i	−0.155045	−	0.198778i
$843$		0			0
$844$	−5.50034	−	19.2991i	−0.189330	−	0.664302i
$845$	−2.45587	−	0.223189i	−0.0844846	−	0.00767792i
$846$		0			0
$847$	−16.8885	+	9.75058i	−0.580296	+	0.335034i
$848$	17.5477	−	32.7478i	0.602591	−	1.12457i
$849$		0			0
$850$	39.2922	−	5.48993i	1.34771	−	0.188303i
$851$	−6.36310	+	11.0212i	−0.218124	+	0.377802i
$852$		0			0
$853$	44.5742			1.52619			0.763095	−	0.646286i	$-0.223679\pi$
$853$	44.5742			1.52619			0.763095	+	0.646286i	$0.223679\pi$
$854$	−13.4500	+	33.2130i	−0.460249	+	1.13652i
$855$		0			0
$856$	30.2203	−	41.3843i	1.03291	−	1.41449i
$857$	−33.8713			−1.15702			−0.578510	−	0.815675i	$-0.696366\pi$
$857$	−33.8713			−1.15702			−0.578510	+	0.815675i	$0.696366\pi$
$858$		0			0
$859$		−	40.8552i		−	1.39396i	−0.717090	−	0.696981i	$-0.754526\pi$
$859$		−	40.8552i		−	1.39396i	0.717090	−	0.696981i	$-0.245474\pi$
$860$	−1.84991	+	1.90948i	−0.0630814	+	0.0651127i
$861$		0			0
$862$	−31.7449	−	12.8555i	−1.08124	−	0.437860i
$863$		−	28.3678i		−	0.965652i	−0.875716	−	0.482826i	$-0.839610\pi$
$863$		−	28.3678i		−	0.965652i	0.875716	−	0.482826i	$-0.160390\pi$
$864$		0			0
$865$	−2.24724	−	1.29745i	−0.0764086	−	0.0441145i
$866$	−45.4300	+	6.34751i	−1.54377	+	0.215697i
$867$		0			0
$868$	8.39019	+	8.12844i	0.284782	+	0.275897i
$869$	3.87003	+	6.70309i	0.131282	+	0.227387i
$870$		0			0
$871$	−38.5712	+	19.9965i	−1.30694	+	0.677556i
$872$	−14.2456	+	6.30142i	−0.482418	+	0.213393i
$873$		0			0
$874$	21.8534	+	28.0176i	0.739204	+	0.947708i
$875$	3.49106	+	2.01556i	0.118019	+	0.0681384i
$876$		0			0
$877$	−8.76923	+	15.1888i	−0.296116	+	0.512888i	−0.975244	−	0.221132i	$-0.929025\pi$
$877$	−8.76923	+	15.1888i	−0.296116	+	0.512888i	0.679128	+	0.734020i	$0.262358\pi$
$878$	1.52121	−	3.75642i	0.0513383	−	0.126773i
$879$		0			0
$880$	−0.0327556	−	1.03330i	−0.00110419	−	0.0348325i
$881$	5.35079	+	9.26785i	0.180273	+	0.312242i	0.941973	−	0.335688i	$-0.108969\pi$
$881$	5.35079	+	9.26785i	0.180273	+	0.312242i	−0.761701	+	0.647929i	$0.775635\pi$
$882$		0			0
$883$			57.4333i			1.93278i	0.257072	+	0.966392i	$0.417242\pi$
$883$			57.4333i			1.93278i	−0.257072	+	0.966392i	$0.582758\pi$
$884$	−29.6532	+	27.9550i	−0.997346	+	0.940228i
$885$		0			0
$886$	18.1347	−	14.1449i	0.609246	−	0.475206i
$887$	17.7688	+	30.7765i	0.596618	+	1.03337i	0.993316	+	0.115424i	$0.0368227\pi$
$887$	17.7688	+	30.7765i	0.596618	+	1.03337i	−0.396698	+	0.917949i	$0.629844\pi$
$888$		0			0
$889$			4.29292i			0.143980i
$890$	−1.21402	−	0.491633i	−0.0406941	−	0.0164796i
$891$		0			0
$892$	−3.41244	−	11.9733i	−0.114257	−	0.400894i
$893$	−24.7082	−	14.2653i	−0.826827	−	0.477369i
$894$		0			0
$895$	−0.580717	+	0.335277i	−0.0194112	+	0.0112071i
$896$	19.9280	+	13.6055i	0.665747	+	0.454526i
$897$		0			0
$898$	−7.62390	−	54.5652i	−0.254413	−	1.82087i
$899$	0.142477	+	0.246777i	0.00475186	+	0.00823047i
$900$		0			0
$901$	45.4591	+	26.2458i	1.51446	+	0.874374i
$902$	−2.46431	−	17.6374i	−0.0820525	−	0.587260i
$903$		0			0
$904$	3.60552	−	33.5259i	0.119918	−	1.11505i
$905$		−	1.07369i		−	0.0356906i
$906$		0			0
$907$	44.9702	−	25.9636i	1.49321	−	0.862106i	0.493241	−	0.869893i	$-0.335812\pi$
$907$	44.9702	−	25.9636i	1.49321	−	0.862106i	0.999970	+	0.00778704i	$0.00247872\pi$
$908$	17.4476	+	16.9033i	0.579018	+	0.560954i
$909$		0			0
$910$	−2.05389	+	0.192614i	−0.0680858	+	0.00638510i
$911$	−8.53527			−0.282786			−0.141393	−	0.989954i	$-0.545158\pi$
$911$	−8.53527			−0.282786			−0.141393	+	0.989954i	$0.545158\pi$
$912$		0			0
$913$	−8.77870	−	15.2052i	−0.290533	−	0.503217i
$914$	17.5614	+	7.11172i	0.580881	+	0.235235i
$915$		0			0
$916$	5.77729	−	23.0137i	0.190887	−	0.760394i
$917$	2.85938	−	4.95259i	0.0944249	−	0.163549i
$918$		0			0
$919$	5.95251	−	10.3101i	0.196355	−	0.340097i	−0.750989	−	0.660315i	$-0.770423\pi$
$919$	5.95251	−	10.3101i	0.196355	−	0.340097i	0.947344	+	0.320218i	$0.103756\pi$
$920$	2.59622	+	1.89585i	0.0855949	+	0.0625045i
$921$		0			0
$922$	38.2262	−	5.34099i	1.25891	−	0.175896i
$923$	2.79480	−	4.37072i	0.0919920	−	0.143864i
$924$		0			0
$925$	−5.27167	−	9.13080i	−0.173331	−	0.300219i
$926$	−31.6568	+	24.6921i	−1.04031	+	0.811432i
$927$		0			0
$928$	0.376518	+	0.452399i	0.0123598	+	0.0148507i
$929$	7.68193	+	4.43517i	0.252036	+	0.145513i	0.620696	−	0.784051i	$-0.286850\pi$
$929$	7.68193	+	4.43517i	0.252036	+	0.145513i	−0.368660	+	0.929564i	$0.620183\pi$
$930$		0			0
$931$	10.2791			0.336884
$932$	−3.48113	+	13.8670i	−0.114028	+	0.454228i
$933$		0			0
$934$	38.7618	−	30.2338i	1.26832	−	0.989282i
$935$	1.46063			0.0477677
$936$		0			0
$937$	−10.6970			−0.349455			−0.174728	−	0.984617i	$-0.555905\pi$
$937$	−10.6970			−0.349455			−0.174728	+	0.984617i	$0.555905\pi$
$938$	−28.6580	+	22.3530i	−0.935718	+	0.729852i
$939$		0			0
$940$	−2.50358	−	0.628492i	−0.0816577	−	0.0204991i
$941$	15.6042			0.508683			0.254341	−	0.967115i	$-0.418141\pi$
$941$	15.6042			0.508683			0.254341	+	0.967115i	$0.418141\pi$
$942$		0			0
$943$	47.9586	+	27.6889i	1.56175	+	0.901674i
$944$	11.9735	−	7.42840i	0.389703	−	0.241774i
$945$		0			0
$946$	10.6472	−	8.30469i	0.346169	−	0.270009i
$947$	−27.2869	−	47.2622i	−0.886704	−	1.53582i	−0.843749	−	0.536739i	$-0.819656\pi$
$947$	−27.2869	−	47.2622i	−0.886704	−	1.53582i	−0.0429551	−	0.999077i	$-0.513677\pi$
$948$		0			0
$949$	−28.2044	−	1.27896i	−0.915552	−	0.0415169i
$950$	−29.1546	+	4.07350i	−0.945899	+	0.132162i
$951$		0			0
$952$	−20.1049	+	27.5321i	−0.651603	+	0.892319i
$953$	−16.3520	+	28.3224i	−0.529692	+	0.917454i	0.469708	+	0.882822i	$0.344359\pi$
$953$	−16.3520	+	28.3224i	−0.529692	+	0.917454i	−0.999400	+	0.0346321i	$0.988974\pi$
$954$		0			0
$955$	−1.94502	+	3.36888i	−0.0629394	+	0.109014i
$956$	−1.28324	−	0.322140i	−0.0415028	−	0.0104187i
$957$		0			0
$958$	−45.0057	−	18.2256i	−1.45407	−	0.588843i
$959$	9.30130	+	16.1103i	0.300355	+	0.520229i
$960$		0			0
$961$	23.4997			0.758054
$962$	9.84376	+	4.51565i	0.317375	+	0.145590i
$963$		0			0
$964$	−13.5310	+	13.9667i	−0.435804	+	0.449838i
$965$	−1.88508	+	1.08835i	−0.0606828	+	0.0350352i
$966$		0			0
$967$			39.1298i			1.25833i	0.777272	+	0.629165i	$0.216603\pi$
$967$			39.1298i			1.25833i	−0.777272	+	0.629165i	$0.783397\pi$
$968$	2.76537	−	25.7137i	0.0888823	−	0.826471i
$969$		0			0
$970$	−0.266891	−	1.91018i	−0.00856937	−	0.0613321i
$971$	−3.02789	−	1.74815i	−0.0971697	−	0.0561009i	0.450628	−	0.892712i	$-0.351200\pi$
$971$	−3.02789	−	1.74815i	−0.0971697	−	0.0561009i	−0.547797	+	0.836611i	$0.684534\pi$
$972$		0			0
$973$	5.80126	+	10.0481i	0.185980	+	0.322127i
$974$	−4.29600	−	30.7470i	−0.137653	−	0.985198i
$975$		0			0
$976$	−25.0525	−	40.3808i	−0.801910	−	1.29256i
$977$	−14.9605	+	8.63745i	−0.478629	+	0.276337i	−0.719845	−	0.694135i	$-0.755787\pi$
$977$	−14.9605	+	8.63745i	−0.478629	+	0.276337i	0.241216	+	0.970471i	$0.422454\pi$
$978$		0			0
$979$	5.76109	+	3.32617i	0.184125	+	0.106305i
$980$	0.894372	−	0.254901i	0.0285697	−	0.00814251i
$981$		0			0
$982$	24.7002	+	10.0026i	0.788214	+	0.319197i
$983$		−	39.4265i		−	1.25751i	−0.777604	−	0.628755i	$-0.783565\pi$
$983$		−	39.4265i		−	1.25751i	0.777604	−	0.628755i	$-0.216435\pi$
$984$		0			0
$985$	−1.57547	−	2.72880i	−0.0501987	−	0.0869467i
$986$	−0.655706	+	0.511445i	−0.0208819	+	0.0162877i
$987$		0			0
$988$	22.0025	−	20.7424i	0.699993	−	0.659904i
$989$			41.9887i			1.33516i
$990$		0			0
$991$	−0.265640	−	0.460102i	−0.00843833	−	0.0146156i	0.861775	−	0.507290i	$-0.169353\pi$
$991$	−0.265640	−	0.460102i	−0.00843833	−	0.0146156i	−0.870214	+	0.492674i	$0.836019\pi$
$992$	−15.2676	+	2.62883i	−0.484747	+	0.0834654i
$993$		0			0
$994$	1.62898	−	4.02254i	0.0516680	−	0.127587i
$995$	2.23466	−	3.87054i	0.0708434	−	0.122704i
$996$		0			0
$997$	32.7700	+	18.9198i	1.03784	+	0.599195i	0.919220	−	0.393745i	$-0.128821\pi$
$997$	32.7700	+	18.9198i	1.03784	+	0.599195i	0.118617	+	0.992940i	$0.462154\pi$
$998$	34.5650	+	44.3146i	1.09414	+	1.40276i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.dg.f.829.9	✓	56
3.2	odd	2	inner	936.2.dg.f.829.20	yes	56
8.5	even	2	inner	936.2.dg.f.829.18	yes	56
13.4	even	6	inner	936.2.dg.f.901.18	yes	56
24.5	odd	2	inner	936.2.dg.f.829.11	yes	56
39.17	odd	6	inner	936.2.dg.f.901.11	yes	56
104.69	even	6	inner	936.2.dg.f.901.9	yes	56
312.173	odd	6	inner	936.2.dg.f.901.20	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.dg.f.829.9	✓	56	1.1	even	1	trivial
936.2.dg.f.829.11	yes	56	24.5	odd	2	inner
936.2.dg.f.829.18	yes	56	8.5	even	2	inner
936.2.dg.f.829.20	yes	56	3.2	odd	2	inner
936.2.dg.f.901.9	yes	56	104.69	even	6	inner
936.2.dg.f.901.11	yes	56	39.17	odd	6	inner
936.2.dg.f.901.18	yes	56	13.4	even	6	inner
936.2.dg.f.901.20	yes	56	312.173	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)

\(f(q)\)	\(=\)	\(q+(-0.869780 - 1.11512i) q^{2} +(-0.486965 + 1.93981i) q^{4} +0.189692 q^{5} +(-1.84703 - 1.06638i) q^{7} +(2.58667 - 1.14419i) q^{8} +(-0.164990 - 0.211528i) q^{10} +(0.681249 + 1.17996i) q^{11} +(-0.163331 + 3.60185i) q^{13} +(0.417370 + 2.98717i) q^{14} +(-3.52573 - 1.88924i) q^{16} +(2.82570 - 4.89426i) q^{17} +(-2.09665 + 3.63151i) q^{19} +(-0.0923733 + 0.367966i) q^{20} +(0.723252 - 1.78597i) q^{22} +(2.99588 + 5.18901i) q^{23} -4.96402 q^{25} +(4.15854 - 2.95069i) q^{26} +(2.96802 - 3.06360i) q^{28} +(0.0901081 - 0.0520240i) q^{29} +2.73867i q^{31} +(0.959891 + 5.57482i) q^{32} +(-7.91540 + 1.10595i) q^{34} +(-0.350366 - 0.202284i) q^{35} +(1.06198 + 1.83940i) q^{37} +(5.87318 - 0.820605i) q^{38} +(0.490669 - 0.217043i) q^{40} +(8.00410 - 4.62117i) q^{41} +(6.06888 + 3.50387i) q^{43} +(-2.62064 + 0.746896i) q^{44} +(3.18059 - 7.85405i) q^{46} +6.80383i q^{47} +(-1.22566 - 2.12290i) q^{49} +(4.31760 + 5.53545i) q^{50} +(-6.90737 - 2.07080i) q^{52} +9.28824i q^{53} +(0.129227 + 0.223828i) q^{55} +(-5.99779 - 0.645029i) q^{56} +(-0.136387 - 0.0552316i) q^{58} +(-1.76132 + 3.05070i) q^{59} +(10.2886 + 5.94011i) q^{61} +(3.05394 - 2.38204i) q^{62} +(5.38167 - 5.91926i) q^{64} +(-0.0309825 + 0.683242i) q^{65} +(6.02495 + 10.4355i) q^{67} +(8.11792 + 7.86466i) q^{68} +(0.0791716 + 0.566642i) q^{70} +(-1.24609 - 0.719429i) q^{71} +7.83052i q^{73} +(1.12745 - 2.78410i) q^{74} +(-6.02344 - 5.83553i) q^{76} -2.90589i q^{77} +5.68079 q^{79} +(-0.668802 - 0.358373i) q^{80} +(-12.1149 - 4.90609i) q^{82} -12.8862 q^{83} +(0.536013 - 0.928401i) q^{85} +(-1.37137 - 9.81510i) q^{86} +(3.11225 + 2.27268i) q^{88} +(4.22833 - 2.44123i) q^{89} +(4.14263 - 6.47855i) q^{91} +(-11.5246 + 3.28457i) q^{92} +(7.58705 - 5.91783i) q^{94} +(-0.397718 + 0.688868i) q^{95} +(6.22643 + 3.59483i) q^{97} +(-1.30122 + 3.21320i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{10} - 4 q^{16} + 64 q^{25} - 48 q^{28} - 48 q^{40} + 20 q^{49} - 12 q^{52} + 16 q^{55} + 12 q^{58} - 72 q^{64} - 84 q^{76} + 80 q^{79} - 12 q^{82} - 12 q^{88} - 24 q^{94} + 24 q^{97}+O(q^{100}) \) 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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