LMFDB - Embedded newform 441.2.w.a.188.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,2,Mod(62,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([7, 11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.62"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.w (of order $14$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			188.12
Character	$\chi$	$=$	441.188
Dual form			441.2.w.a.251.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.203165 - 0.162019i) q^{2} +(-0.430016 + 1.88402i) q^{4} +(2.46158 - 1.18543i) q^{5} +(-1.53249 - 2.15673i) q^{7} +(0.443379 + 0.920685i) q^{8} +(0.308044 - 0.639659i) q^{10} +(2.00878 - 1.60195i) q^{11} +(4.63632 - 3.69734i) q^{13} +(-0.660778 - 0.189879i) q^{14} +(-3.24295 - 1.56172i) q^{16} +(1.48891 + 6.52334i) q^{17} +0.418798i q^{19} +(1.17487 + 5.14742i) q^{20} +(0.148568 - 0.650919i) q^{22} +(5.32955 + 1.21643i) q^{23} +(1.53666 - 1.92691i) q^{25} +(0.342899 - 1.50234i) q^{26} +(4.72232 - 1.95982i) q^{28} +(-2.32890 + 0.531557i) q^{29} +5.40375i q^{31} +(-2.90441 + 0.662912i) q^{32} +(1.35940 + 1.08408i) q^{34} +(-6.32900 - 3.49228i) q^{35} +(-1.37636 - 6.03022i) q^{37} +(0.0678530 + 0.0850850i) q^{38} +(2.18282 + 1.74074i) q^{40} +(5.97322 - 2.87655i) q^{41} +(-7.06131 - 3.40055i) q^{43} +(2.15430 + 4.47345i) q^{44} +(1.27986 - 0.616349i) q^{46} +(-2.90399 - 3.64149i) q^{47} +(-2.30293 + 6.61033i) q^{49} -0.640448i q^{50} +(4.97219 + 10.3249i) q^{52} +(13.5007 + 3.08145i) q^{53} +(3.04576 - 6.32459i) q^{55} +(1.30619 - 2.36719i) q^{56} +(-0.387029 + 0.485319i) q^{58} +(-5.52357 - 2.66001i) q^{59} +(-9.77982 + 2.23218i) q^{61} +(0.875508 + 1.09785i) q^{62} +(4.00571 - 5.02301i) q^{64} +(7.02971 - 14.5973i) q^{65} -8.37721 q^{67} -12.9304 q^{68} +(-1.85164 + 0.315907i) q^{70} +(-6.34846 - 1.44900i) q^{71} +(-5.32281 - 4.24480i) q^{73} +(-1.25664 - 1.00213i) q^{74} +(-0.789025 - 0.180090i) q^{76} +(-6.53340 - 1.87741i) q^{77} +0.883489 q^{79} -9.83409 q^{80} +(0.747494 - 1.55219i) q^{82} +(-6.46744 + 8.10992i) q^{83} +(11.3980 + 14.2927i) q^{85} +(-1.98556 + 0.453192i) q^{86} +(2.36554 + 1.13918i) q^{88} +(1.58193 - 1.98368i) q^{89} +(-15.0793 - 4.33313i) q^{91} +(-4.58358 + 9.51791i) q^{92} +(-1.17998 - 0.269322i) q^{94} +(0.496457 + 1.03090i) q^{95} +3.88426i q^{97} +(0.603122 + 1.71611i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70}+ \cdots - 112 q^{94}+O(q^{100}) $ 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{14}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.203165	−	0.162019i	0.143659	−	0.114564i	−0.549023	−	0.835807i	$-0.685000\pi$
$2$	0.203165	−	0.162019i	0.143659	−	0.114564i	0.692682	+	0.721243i	$0.256429\pi$
$3$		0			0
$3$		0			0
$4$	−0.430016	+	1.88402i	−0.215008	+	0.942011i
$5$	2.46158	−	1.18543i	1.10085	−	0.530142i	0.206925	−	0.978357i	$-0.433654\pi$
$5$	2.46158	−	1.18543i	1.10085	−	0.530142i	0.893926	+	0.448215i	$0.147940\pi$
$6$		0			0
$7$	−1.53249	−	2.15673i	−0.579228	−	0.815166i
$7$	−1.53249	−	2.15673i	−0.579228	−	0.815166i
$8$	0.443379	+	0.920685i	0.156758	+	0.325511i
$9$		0			0
$10$	0.308044	−	0.639659i	0.0974120	−	0.202278i
$11$	2.00878	−	1.60195i	0.605670	−	0.483005i	−0.271983	−	0.962302i	$-0.587680\pi$
$11$	2.00878	−	1.60195i	0.605670	−	0.483005i	0.877653	+	0.479297i	$0.159108\pi$
$12$		0			0
$13$	4.63632	−	3.69734i	1.28588	−	1.02546i	0.288192	−	0.957573i	$-0.406946\pi$
$13$	4.63632	−	3.69734i	1.28588	−	1.02546i	0.997693	−	0.0678861i	$-0.0216255\pi$
$14$	−0.660778	−	0.189879i	−0.176600	−	0.0507472i
$15$		0			0
$16$	−3.24295	−	1.56172i	−0.810738	−	0.390431i
$17$	1.48891	+	6.52334i	0.361114	+	1.58214i	0.750373	+	0.661014i	$0.229874\pi$
$17$	1.48891	+	6.52334i	0.361114	+	1.58214i	−0.389260	+	0.921128i	$0.627269\pi$
$18$		0			0
$19$			0.418798i			0.0960788i	0.998845	+	0.0480394i	$0.0152973\pi$
$19$			0.418798i			0.0960788i	−0.998845	+	0.0480394i	$0.984703\pi$
$20$	1.17487	+	5.14742i	0.262708	+	1.15100i
$21$		0			0
$22$	0.148568	−	0.650919i	0.0316748	−	0.138776i
$23$	5.32955	+	1.21643i	1.11129	+	0.253644i	0.738487	−	0.674267i	$-0.235540\pi$
$23$	5.32955	+	1.21643i	1.11129	+	0.253644i	0.372800	+	0.927912i	$0.378398\pi$
$24$		0			0
$25$	1.53666	−	1.92691i	0.307332	−	0.385382i
$26$	0.342899	−	1.50234i	0.0672481	−	0.294633i
$27$		0			0
$28$	4.72232	−	1.95982i	0.892434	−	0.370372i
$29$	−2.32890	+	0.531557i	−0.432466	+	0.0987076i	−0.433212	−	0.901292i	$-0.642620\pi$
$29$	−2.32890	+	0.531557i	−0.432466	+	0.0987076i	0.000745584		1.00000i	$0.499763\pi$
$30$		0			0
$31$			5.40375i			0.970542i	0.874364	+	0.485271i	$0.161279\pi$
$31$			5.40375i			0.970542i	−0.874364	+	0.485271i	$0.838721\pi$
$32$	−2.90441	+	0.662912i	−0.513431	+	0.117187i
$33$		0			0
$34$	1.35940	+	1.08408i	0.233135	+	0.185919i
$35$	−6.32900	−	3.49228i	−1.06980	−	0.590303i
$36$		0			0
$37$	−1.37636	−	6.03022i	−0.226272	−	0.991362i	−0.952651	−	0.304067i	$-0.901655\pi$
$37$	−1.37636	−	6.03022i	−0.226272	−	0.991362i	0.726379	−	0.687295i	$-0.241202\pi$
$38$	0.0678530	+	0.0850850i	0.0110072	+	0.0138026i
$39$		0			0
$40$	2.18282	+	1.74074i	0.345134	+	0.275235i
$41$	5.97322	−	2.87655i	0.932861	−	0.449242i	0.0952155	−	0.995457i	$-0.469646\pi$
$41$	5.97322	−	2.87655i	0.932861	−	0.449242i	0.837645	+	0.546215i	$0.183932\pi$
$42$		0			0
$43$	−7.06131	−	3.40055i	−1.07684	−	0.518579i	−0.190535	−	0.981680i	$-0.561022\pi$
$43$	−7.06131	−	3.40055i	−1.07684	−	0.518579i	−0.886305	+	0.463102i	$0.846736\pi$
$44$	2.15430	+	4.47345i	0.324773	+	0.674398i
$45$		0			0
$46$	1.27986	−	0.616349i	0.188705	−	0.0908757i
$47$	−2.90399	−	3.64149i	−0.423590	−	0.531165i	0.523546	−	0.851997i	$-0.324609\pi$
$47$	−2.90399	−	3.64149i	−0.423590	−	0.531165i	−0.947136	+	0.320832i	$0.896037\pi$
$48$		0			0
$49$	−2.30293	+	6.61033i	−0.328990	+	0.944333i
$50$		−	0.640448i		−	0.0905730i
$51$		0			0
$52$	4.97219	+	10.3249i	0.689519	+	1.43180i
$53$	13.5007	+	3.08145i	1.85447	+	0.423270i	0.995981	−	0.0895695i	$-0.0285491\pi$
$53$	13.5007	+	3.08145i	1.85447	+	0.423270i	0.858485	+	0.512839i	$0.171406\pi$
$54$		0			0
$55$	3.04576	−	6.32459i	0.410690	−	0.852807i
$56$	1.30619	−	2.36719i	0.174547	−	0.316329i
$57$		0			0
$58$	−0.387029	+	0.485319i	−0.0508194	+	0.0637255i
$59$	−5.52357	−	2.66001i	−0.719107	−	0.346304i	0.0382823	−	0.999267i	$-0.487811\pi$
$59$	−5.52357	−	2.66001i	−0.719107	−	0.346304i	−0.757390	+	0.652963i	$0.773526\pi$
$60$		0			0
$61$	−9.77982	+	2.23218i	−1.25218	+	0.285801i	−0.796661	−	0.604426i	$-0.793403\pi$
$61$	−9.77982	+	2.23218i	−1.25218	+	0.285801i	−0.455517	+	0.890227i	$0.650545\pi$
$62$	0.875508	+	1.09785i	0.111190	+	0.139427i
$63$		0			0
$64$	4.00571	−	5.02301i	0.500714	−	0.627876i
$65$	7.02971	−	14.5973i	0.871928	−	1.81058i
$66$		0			0
$67$	−8.37721			−1.02344			−0.511719	−	0.859153i	$-0.670991\pi$
$67$	−8.37721			−1.02344			−0.511719	+	0.859153i	$0.670991\pi$
$68$	−12.9304			−1.56804
$69$		0			0
$70$	−1.85164	+	0.315907i	−0.221314	+	0.0377582i
$71$	−6.34846	−	1.44900i	−0.753424	−	0.171964i	−0.171474	−	0.985189i	$-0.554853\pi$
$71$	−6.34846	−	1.44900i	−0.753424	−	0.171964i	−0.581950	+	0.813225i	$0.697710\pi$
$72$		0			0
$73$	−5.32281	−	4.24480i	−0.622987	−	0.496816i	0.260374	−	0.965508i	$-0.416154\pi$
$73$	−5.32281	−	4.24480i	−0.622987	−	0.496816i	−0.883362	+	0.468692i	$0.844725\pi$
$74$	−1.25664	−	1.00213i	−0.146081	−	0.116496i
$75$		0			0
$76$	−0.789025	−	0.180090i	−0.0905074	−	0.0206577i
$77$	−6.53340	−	1.87741i	−0.744550	−	0.213951i
$78$		0			0
$79$	0.883489			0.0994002			0.0497001	−	0.998764i	$-0.484173\pi$
$79$	0.883489			0.0994002			0.0497001	+	0.998764i	$0.484173\pi$
$80$	−9.83409			−1.09948
$81$		0			0
$82$	0.747494	−	1.55219i	0.0825469	−	0.171410i
$83$	−6.46744	+	8.10992i	−0.709894	+	0.890179i	−0.997719	−	0.0675041i	$-0.978496\pi$
$83$	−6.46744	+	8.10992i	−0.709894	+	0.890179i	0.287825	+	0.957683i	$0.407068\pi$
$84$		0			0
$85$	11.3980	+	14.2927i	1.23629	+	1.55026i
$86$	−1.98556	+	0.453192i	−0.214109	+	0.0488689i
$87$		0			0
$88$	2.36554	+	1.13918i	0.252167	+	0.121437i
$89$	1.58193	−	1.98368i	0.167685	−	0.210270i	−0.690888	−	0.722962i	$-0.742780\pi$
$89$	1.58193	−	1.98368i	0.167685	−	0.210270i	0.858573	+	0.512692i	$0.171352\pi$
$90$		0			0
$91$	−15.0793	−	4.33313i	−1.58074	−	0.454235i
$92$	−4.58358	+	9.51791i	−0.477871	+	0.992310i
$93$		0			0
$94$	−1.17998	−	0.269322i	−0.121705	−	0.0277784i
$95$	0.496457	+	1.03090i	0.0509354	+	0.105768i
$96$		0			0
$97$			3.88426i			0.394387i	0.980365	+	0.197193i	$0.0631827\pi$
$97$			3.88426i			0.394387i	−0.980365	+	0.197193i	$0.936817\pi$
$98$	0.603122	+	1.71611i	0.0609245	+	0.173353i
$99$		0			0
$100$	2.96955	+	3.72370i	0.296955	+	0.372370i
$101$	−9.41819	+	4.53556i	−0.937145	+	0.451305i	−0.839161	−	0.543883i	$-0.816954\pi$
$101$	−9.41819	+	4.53556i	−0.937145	+	0.451305i	−0.0979838	+	0.995188i	$0.531239\pi$
$102$		0			0
$103$	3.43174	+	7.12609i	0.338140	+	0.702154i	0.998823	−	0.0485107i	$-0.0154475\pi$
$103$	3.43174	+	7.12609i	0.338140	+	0.702154i	−0.660683	+	0.750665i	$0.729733\pi$
$104$	5.45974	+	2.62927i	0.535371	+	0.257821i
$105$		0			0
$106$	3.24212	−	1.56132i	0.314903	−	0.151649i
$107$	−9.87212	−	7.87275i	−0.954374	−	0.761088i	0.0167017	−	0.999861i	$-0.494683\pi$
$107$	−9.87212	−	7.87275i	−0.954374	−	0.761088i	−0.971075	+	0.238773i	$0.923255\pi$
$108$		0			0
$109$	−2.69069	−	3.37402i	−0.257721	−	0.323172i	0.636091	−	0.771614i	$-0.280550\pi$
$109$	−2.69069	−	3.37402i	−0.257721	−	0.323172i	−0.893812	+	0.448442i	$0.851979\pi$
$110$	−0.405909	−	1.77840i	−0.0387019	−	0.169564i
$111$		0			0
$112$	1.60159	+	9.38748i	0.151336	+	0.887034i
$113$	10.3065	+	8.21919i	0.969557	+	0.773196i	0.973943	−	0.226794i	$-0.0728246\pi$
$113$	10.3065	+	8.21919i	0.969557	+	0.773196i	−0.00438565	+	0.999990i	$0.501396\pi$
$114$		0			0
$115$	14.5611	−	3.32347i	1.35783	−	0.309916i
$116$		−	4.61628i		−	0.428611i
$117$		0			0
$118$	−1.55317	+	0.354500i	−0.142981	+	0.0326344i
$119$	11.7873	−	13.2081i	1.08054	−	1.21079i
$120$		0			0
$121$	−0.978775	+	4.28829i	−0.0889795	+	0.389845i
$122$	−1.62526	+	2.03801i	−0.147144	+	0.184513i
$123$		0			0
$124$	−10.1808	−	2.32370i	−0.914262	−	0.208674i
$125$	−1.54141	+	6.75337i	−0.137868	+	0.604040i
$126$		0			0
$127$	4.65209	+	20.3822i	0.412807	+	1.80862i	0.570690	+	0.821166i	$0.306676\pi$
$127$	4.65209	+	20.3822i	0.412807	+	1.80862i	−0.157883	+	0.987458i	$0.550467\pi$
$128$		−	7.62770i		−	0.674199i
$129$		0			0
$130$	−0.936851	−	4.10461i	−0.0821673	−	0.359998i
$131$	−11.3313	−	5.45685i	−0.990018	−	0.476768i	−0.132479	−	0.991186i	$-0.542294\pi$
$131$	−11.3313	−	5.45685i	−0.990018	−	0.476768i	−0.857539	+	0.514418i	$0.828008\pi$
$132$		0			0
$133$	0.903232	−	0.641805i	0.0783202	−	0.0556515i
$134$	−1.70195	+	1.35726i	−0.147026	+	0.117250i
$135$		0			0
$136$	−5.34579	+	4.26313i	−0.458398	+	0.365560i
$137$	−2.31086	+	4.79856i	−0.197430	+	0.409969i	−0.976056	−	0.217521i	$-0.930203\pi$
$137$	−2.31086	+	4.79856i	−0.197430	+	0.409969i	0.778625	+	0.627489i	$0.215917\pi$
$138$		0			0
$139$	−1.02034	−	2.11876i	−0.0865442	−	0.179711i	0.853205	−	0.521576i	$-0.174656\pi$
$139$	−1.02034	−	2.11876i	−0.0865442	−	0.179711i	−0.939749	+	0.341865i	$0.888941\pi$
$140$	9.30110	−	10.4222i	0.786087	−	0.880841i
$141$		0			0
$142$	−1.52455	+	0.734184i	−0.127937	+	0.0616113i
$143$	3.39040	−	14.8543i	0.283519	−	1.24218i
$144$		0			0
$145$	−5.10265	+	4.06922i	−0.423752	+	0.337931i
$146$	−1.76914			−0.146415
$147$		0			0
$148$	11.9529			0.982525
$149$	10.9789	−	8.75535i	0.899423	−	0.717266i	−0.0603099	−	0.998180i	$-0.519209\pi$
$149$	10.9789	−	8.75535i	0.899423	−	0.717266i	0.959733	+	0.280914i	$0.0906375\pi$
$150$		0			0
$151$	4.50982	−	19.7588i	0.367004	−	1.60795i	−0.367960	−	0.929842i	$-0.619944\pi$
$151$	4.50982	−	19.7588i	0.367004	−	1.60795i	0.734964	−	0.678107i	$-0.237199\pi$
$152$	−0.385581	+	0.185686i	−0.0312747	+	0.0150611i
$153$		0			0
$154$	−1.63153	+	0.677108i	−0.131473	+	0.0545629i
$155$	6.40578	+	13.3017i	0.514525	+	1.06842i
$156$		0			0
$157$	−1.46300	+	3.03795i	−0.116760	+	0.242455i	−0.951156	−	0.308711i	$-0.900102\pi$
$157$	−1.46300	+	3.03795i	−0.116760	+	0.242455i	0.834396	+	0.551166i	$0.185817\pi$
$158$	0.179494	−	0.143142i	0.0142798	−	0.0113877i
$159$		0			0
$160$	−6.36358	+	5.07479i	−0.503085	+	0.401197i
$161$	−5.54398	−	13.3586i	−0.436927	−	1.05280i
$162$		0			0
$163$	−16.2148	−	7.80862i	−1.27004	−	0.611618i	−0.327227	−	0.944946i	$-0.606114\pi$
$163$	−16.2148	−	7.80862i	−1.27004	−	0.611618i	−0.942811	+	0.333328i	$0.891828\pi$
$164$	2.85091	+	12.4907i	0.222619	+	0.975356i
$165$		0			0
$166$			2.69550i			0.209211i
$167$	2.08323	+	9.12724i	0.161205	+	0.706287i	0.989324	+	0.145734i	$0.0465543\pi$
$167$	2.08323	+	9.12724i	0.161205	+	0.706287i	−0.828118	+	0.560553i	$0.810589\pi$
$168$		0			0
$169$	4.93237	−	21.6101i	0.379413	−	1.66232i
$170$	4.63136	+	1.05708i	0.355209	+	0.0810742i
$171$		0			0
$172$	9.44319	−	11.8414i	0.720036	−	0.902897i
$173$	−5.68643	+	24.9139i	−0.432332	+	1.89417i	0.0151690	+	0.999885i	$0.495171\pi$
$173$	−5.68643	+	24.9139i	−0.432332	+	1.89417i	−0.447501	+	0.894284i	$0.647686\pi$
$174$		0			0
$175$	−6.51074	−	0.361178i	−0.492165	−	0.0273025i
$176$	−9.01617	+	2.05788i	−0.679619	+	0.155119i
$177$		0			0
$178$		−	0.659317i		−	0.0494179i
$179$	14.5634	−	3.32400i	1.08852	−	0.248447i	0.359640	−	0.933091i	$-0.382899\pi$
$179$	14.5634	−	3.32400i	1.08852	−	0.248447i	0.728878	+	0.684644i	$0.240042\pi$
$180$		0			0
$181$	−2.80247	−	2.23490i	−0.208306	−	0.166118i	0.513780	−	0.857922i	$-0.328245\pi$
$181$	−2.80247	−	2.23490i	−0.208306	−	0.166118i	−0.722086	+	0.691804i	$0.756816\pi$
$182$	−3.76563	+	1.56279i	−0.279127	+	0.115841i
$183$		0			0
$184$	1.24305	+	5.44618i	0.0916392	+	0.401497i
$185$	−10.5364	−	13.2123i	−0.774654	−	0.971385i
$186$		0			0
$187$	13.4409	+	10.7188i	0.982899	+	0.783836i
$188$	8.10940	−	3.90528i	0.591439	−	0.284822i
$189$		0			0
$190$	0.267888	+	0.129008i	0.0194346	+	0.00935923i
$191$	−2.17795	−	4.52256i	−0.157591	−	0.327241i	0.807192	−	0.590289i	$-0.200986\pi$
$191$	−2.17795	−	4.52256i	−0.157591	−	0.327241i	−0.964783	+	0.263049i	$0.915272\pi$
$192$		0			0
$193$	7.94264	−	3.82497i	0.571724	−	0.275328i	−0.125604	−	0.992081i	$-0.540087\pi$
$193$	7.94264	−	3.82497i	0.571724	−	0.275328i	0.697327	+	0.716753i	$0.254372\pi$
$194$	0.629322	+	0.789145i	0.0451827	+	0.0566573i
$195$		0			0
$196$	−11.4637	−	7.18133i	−0.818837	−	0.512952i
$197$		−	8.68699i		−	0.618922i	−0.950912	−	0.309461i	$-0.899851\pi$
$197$		−	8.68699i		−	0.618922i	0.950912	−	0.309461i	$-0.100149\pi$
$198$		0			0
$199$	−3.05048	−	6.33439i	−0.216243	−	0.449033i	0.764425	−	0.644713i	$-0.223023\pi$
$199$	−3.05048	−	6.33439i	−0.216243	−	0.449033i	−0.980668	+	0.195680i	$0.937309\pi$
$200$	2.45540	+	0.560429i	0.173623	+	0.0396283i
$201$		0			0
$202$	−1.17860	+	2.44739i	−0.0829260	+	0.172198i
$203$	4.71545	+	4.20820i	0.330960	+	0.295358i
$204$		0			0
$205$	11.2936	−	14.1617i	0.788778	−	0.989097i
$206$	1.85177	+	0.891764i	0.129019	+	0.0621322i
$207$		0			0
$208$	−20.8096	+	4.74965i	−1.44289	+	0.329329i
$209$	0.670892	+	0.841272i	0.0464066	+	0.0581920i
$210$		0			0
$211$	−6.31940	+	7.92428i	−0.435046	+	0.545530i	−0.950230	−	0.311549i	$-0.899152\pi$
$211$	−6.31940	+	7.92428i	−0.435046	+	0.545530i	0.515184	+	0.857079i	$0.327723\pi$
$212$	−11.6110	+	24.1106i	−0.797450	+	1.65592i
$213$		0			0
$214$	−3.28120			−0.224298
$215$	−21.4131			−1.46036
$216$		0			0
$217$	11.6544	−	8.28121i	0.791153	−	0.562165i
$218$	−1.09331	−	0.249540i	−0.0740481	−	0.0169010i
$219$		0			0
$220$	10.6059	+	8.45796i	0.715053	+	0.570235i
$221$	31.0221	+	24.7393i	2.08677	+	1.66415i
$222$		0			0
$223$	9.89847	+	2.25926i	0.662850	+	0.151291i	0.540694	−	0.841220i	$-0.318162\pi$
$223$	9.89847	+	2.25926i	0.662850	+	0.151291i	0.122157	+	0.992511i	$0.461019\pi$
$224$	5.88070	+	5.24810i	0.392921	+	0.350654i
$225$		0			0
$226$	3.42559			0.227867
$227$	8.15525			0.541283			0.270641	−	0.962680i	$-0.412764\pi$
$227$	8.15525			0.541283			0.270641	+	0.962680i	$0.412764\pi$
$228$		0			0
$229$	5.17943	−	10.7552i	0.342266	−	0.710723i	−0.656794	−	0.754070i	$-0.728088\pi$
$229$	5.17943	−	10.7552i	0.342266	−	0.710723i	0.999060	+	0.0433472i	$0.0138022\pi$
$230$	2.41984	−	3.03438i	0.159559	−	0.200081i
$231$		0			0
$232$	−1.52198	−	1.90850i	−0.0999230	−	0.125299i
$233$	15.7781	−	3.60125i	1.03366	−	0.235926i	0.328149	−	0.944626i	$-0.393575\pi$
$233$	15.7781	−	3.60125i	1.03366	−	0.235926i	0.705510	+	0.708700i	$0.250718\pi$
$234$		0			0
$235$	−11.4651	−	5.52131i	−0.747902	−	0.360171i
$236$	7.38674	−	9.26268i	0.480836	−	0.602949i
$237$		0			0
$238$	0.254804	−	4.59319i	0.0165165	−	0.297732i
$239$	1.43054	−	2.97056i	0.0925342	−	0.192149i	−0.849565	−	0.527484i	$-0.823135\pi$
$239$	1.43054	−	2.97056i	0.0925342	−	0.192149i	0.942099	+	0.335335i	$0.108850\pi$
$240$		0			0
$241$	−0.422284	−	0.0963835i	−0.0272017	−	0.00620861i	0.208898	−	0.977937i	$-0.433012\pi$
$241$	−0.422284	−	0.0963835i	−0.0272017	−	0.00620861i	−0.236100	+	0.971729i	$0.575869\pi$
$242$	0.495930	+	1.02981i	0.0318796	+	0.0661987i
$243$		0			0
$244$		−	19.3853i		−	1.24102i
$245$	2.16726	+	19.0018i	0.138461	+	1.21398i
$246$		0			0
$247$	1.54844	+	1.94168i	0.0985249	+	0.123546i
$248$	−4.97515	+	2.39591i	−0.315922	+	0.152140i
$249$		0			0
$250$	0.781011	+	1.62179i	0.0493955	+	0.102571i
$251$	12.8422	+	6.18449i	0.810594	+	0.390361i	0.792801	−	0.609480i	$-0.208622\pi$
$251$	12.8422	+	6.18449i	0.810594	+	0.390361i	0.0177924	+	0.999842i	$0.494336\pi$
$252$		0			0
$253$	12.6545	−	6.09411i	0.795585	−	0.383133i
$254$	4.24743	+	3.38721i	0.266507	+	0.212533i
$255$		0			0
$256$	6.77560	+	8.49633i	0.423475	+	0.531021i
$257$	−2.30160	−	10.0840i	−0.143570	−	0.629020i	−0.994589	−	0.103886i	$-0.966872\pi$
$257$	−2.30160	−	10.0840i	−0.143570	−	0.629020i	0.851020	−	0.525134i	$-0.175985\pi$
$258$		0			0
$259$	−10.8963	+	12.2097i	−0.677061	+	0.758674i
$260$	24.4788	+	19.5212i	1.51811	+	1.21066i
$261$		0			0
$262$	−3.18623	+	0.727236i	−0.196846	+	0.0449288i
$263$		−	17.7902i		−	1.09699i	−0.836154	−	0.548495i	$-0.815201\pi$
$263$		−	17.7902i		−	1.09699i	0.836154	−	0.548495i	$-0.184799\pi$
$264$		0			0
$265$	36.8859	−	8.41896i	2.26588	−	0.517173i
$266$	0.0795208	−	0.276733i	0.00487573	−	0.0169676i
$267$		0			0
$268$	3.60233	−	15.7829i	0.220048	−	0.964091i
$269$	−9.15874	+	11.4847i	−0.558418	+	0.700234i	−0.978264	−	0.207361i	$-0.933513\pi$
$269$	−9.15874	+	11.4847i	−0.558418	+	0.700234i	0.419846	+	0.907595i	$0.362084\pi$
$270$		0			0
$271$	22.7856	+	5.20067i	1.38413	+	0.315918i	0.848795	−	0.528722i	$-0.177329\pi$
$271$	22.7856	+	5.20067i	1.38413	+	0.315918i	0.535334	+	0.844641i	$0.320186\pi$
$272$	5.35919	−	23.4801i	0.324948	−	1.42369i
$273$		0			0
$274$	0.307969	+	1.34930i	0.0186051	+	0.0815143i
$275$		−	6.33238i		−	0.381857i
$276$		0			0
$277$	3.44499	+	15.0935i	0.206989	+	0.906880i	0.966557	+	0.256452i	$0.0825535\pi$
$277$	3.44499	+	15.0935i	0.206989	+	0.906880i	−0.759568	+	0.650428i	$0.774589\pi$
$278$	−0.550576	−	0.265143i	−0.0330214	−	0.0159022i
$279$		0			0
$280$	0.409145	−	7.37542i	0.0244511	−	0.440766i
$281$	−20.3030	+	16.1911i	−1.21117	+	0.965878i	−0.999933	−	0.0115558i	$-0.996322\pi$
$281$	−20.3030	+	16.1911i	−1.21117	+	0.965878i	−0.211240	+	0.977434i	$0.567750\pi$
$282$		0			0
$283$	−17.9985	+	14.3534i	−1.06990	+	0.853218i	−0.989642	−	0.143556i	$-0.954146\pi$
$283$	−17.9985	+	14.3534i	−1.06990	+	0.853218i	−0.0802597	+	0.996774i	$0.525575\pi$
$284$	5.45988	−	11.3376i	0.323984	−	0.672760i
$285$		0			0
$286$	−1.71786	−	3.56718i	−0.101579	−	0.210932i
$287$	−15.3579	−	8.47431i	−0.906546	−	0.500223i
$288$		0			0
$289$	−25.0206	+	12.0493i	−1.47180	+	0.708783i
$290$	−0.377388	+	1.65345i	−0.0221610	+	0.0970937i
$291$		0			0
$292$	10.2862	−	8.20296i	0.601954	−	0.480042i
$293$	−4.47285			−0.261307			−0.130653	−	0.991428i	$-0.541707\pi$
$293$	−4.47285			−0.261307			−0.130653	+	0.991428i	$0.541707\pi$
$294$		0			0
$295$	−16.7500			−0.975220
$296$	4.94169	−	3.94086i	0.287230	−	0.229058i
$297$		0			0
$298$	0.811989	−	3.55756i	0.0470373	−	0.206084i
$299$	29.2071	−	14.0654i	1.68909	−	0.813423i
$300$		0			0
$301$	3.48736	+	20.4406i	0.201008	+	1.17818i
$302$	−2.28506	−	4.74497i	−0.131490	−	0.273042i
$303$		0			0
$304$	0.654046	−	1.35814i	0.0375121	−	0.0778947i
$305$	−21.4277	+	17.0880i	−1.22695	+	0.978457i
$306$		0			0
$307$	−12.9156	+	10.2998i	−0.737131	+	0.587842i	−0.918429	−	0.395586i	$-0.870541\pi$
$307$	−12.9156	+	10.2998i	−0.737131	+	0.587842i	0.181298	+	0.983428i	$0.441970\pi$
$308$	6.34655	−	11.5018i	0.361628	−	0.655373i
$309$		0			0
$310$	3.45656	+	1.66459i	0.196319	+	0.0945424i
$311$	2.75607	+	12.0751i	0.156282	+	0.684717i	0.990980	+	0.134009i	$0.0427851\pi$
$311$	2.75607	+	12.0751i	0.156282	+	0.684717i	−0.834698	+	0.550708i	$0.814358\pi$
$312$		0			0
$313$		−	0.422739i		−	0.0238946i	−0.999929	−	0.0119473i	$-0.996197\pi$
$313$		−	0.422739i		−	0.0238946i	0.999929	−	0.0119473i	$-0.00380304\pi$
$314$	0.194974	+	0.854237i	0.0110030	+	0.0482074i
$315$		0			0
$316$	−0.379914	+	1.66451i	−0.0213718	+	0.0936361i
$317$	−10.4050	−	2.37488i	−0.584406	−	0.133387i	−0.0799117	−	0.996802i	$-0.525464\pi$
$317$	−10.4050	−	2.37488i	−0.584406	−	0.133387i	−0.504494	+	0.863415i	$0.668321\pi$
$318$		0			0
$319$	−3.82672	+	4.79856i	−0.214255	+	0.268668i
$320$	3.90594	−	17.1130i	0.218348	−	0.956647i
$321$		0			0
$322$	−3.29067	−	1.81576i	−0.183382	−	0.101188i
$323$	−2.73196	+	0.623552i	−0.152010	+	0.0346954i
$324$		0			0
$325$		−	14.6153i		−	0.810713i
$326$	−4.55941	+	1.04066i	−0.252522	+	0.0576366i
$327$		0			0
$328$	5.29680	+	4.22405i	0.292467	+	0.233234i
$329$	−3.40335	+	11.8437i	−0.187633	+	0.652962i
$330$		0			0
$331$	−3.67242	−	16.0899i	−0.201854	−	0.884382i	−0.969807	−	0.243875i	$-0.921581\pi$
$331$	−3.67242	−	16.0899i	−0.201854	−	0.884382i	0.767952	−	0.640507i	$-0.221276\pi$
$332$	−12.4982	−	15.6722i	−0.685926	−	0.860124i
$333$		0			0
$334$	1.90202	+	1.51681i	0.104074	+	0.0829963i
$335$	−20.6211	+	9.93062i	−1.12665	+	0.542568i
$336$		0			0
$337$	−21.9232	−	10.5577i	−1.19423	−	0.575113i	−0.272207	−	0.962239i	$-0.587754\pi$
$337$	−21.9232	−	10.5577i	−1.19423	−	0.575113i	−0.922027	+	0.387126i	$0.873468\pi$
$338$	−2.49916	−	5.18955i	−0.135936	−	0.282274i
$339$		0			0
$340$	−31.8291	+	15.3281i	−1.72618	+	0.831283i
$341$	8.65652	+	10.8549i	0.468777	+	0.587828i
$342$		0			0
$343$	17.7859	−	5.16349i	0.960348	−	0.278802i
$344$		−	8.00897i		−	0.431815i
$345$		0			0
$346$	2.88123	+	5.98294i	0.154896	+	0.321645i
$347$	4.02560	+	0.918818i	0.216106	+	0.0493247i	0.329203	−	0.944259i	$-0.393220\pi$
$347$	4.02560	+	0.918818i	0.216106	+	0.0493247i	−0.113097	+	0.993584i	$0.536077\pi$
$348$		0			0
$349$	4.37881	−	9.09270i	0.234393	−	0.486721i	−0.750283	−	0.661117i	$-0.770083\pi$
$349$	4.37881	−	9.09270i	0.234393	−	0.486721i	0.984676	+	0.174396i	$0.0557971\pi$
$350$	−1.38127	+	0.981482i	−0.0738320	+	0.0524624i
$351$		0			0
$352$	−4.77236	+	5.98435i	−0.254368	+	0.318967i
$353$	32.9080	+	15.8477i	1.75152	+	0.843485i	0.977680	+	0.210098i	$0.0673785\pi$
$353$	32.9080	+	15.8477i	1.75152	+	0.843485i	0.773835	+	0.633387i	$0.218336\pi$
$354$		0			0
$355$	−17.3449	+	3.95886i	−0.920572	+	0.210115i
$356$	3.05705	+	3.83341i	0.162023	+	0.203171i
$357$		0			0
$358$	2.42022	−	3.03486i	0.127912	−	0.160397i
$359$	−6.54851	+	13.5981i	−0.345617	+	0.717681i	−0.999234	−	0.0391446i	$-0.987537\pi$
$359$	−6.54851	+	13.5981i	−0.345617	+	0.717681i	0.653616	+	0.756826i	$0.273251\pi$
$360$		0			0
$361$	18.8246			0.990769
$362$	−0.931458			−0.0489563
$363$		0			0
$364$	14.6480	−	26.5464i	0.767766	−	1.39141i
$365$	−18.1344	−	4.13906i	−0.949199	−	0.216648i
$366$		0			0
$367$	13.1447	+	10.4825i	0.686147	+	0.547184i	0.903330	−	0.428947i	$-0.141115\pi$
$367$	13.1447	+	10.4825i	0.686147	+	0.547184i	−0.217183	+	0.976131i	$0.569687\pi$
$368$	−15.3837	−	12.2681i	−0.801932	−	0.639520i
$369$		0			0
$370$	−4.28127	−	0.977171i	−0.222572	−	0.0508007i
$371$	−14.0439	−	33.8396i	−0.729123	−	1.75687i
$372$		0			0
$373$	−14.6161			−0.756794			−0.378397	−	0.925643i	$-0.623525\pi$
$373$	−14.6161			−0.756794			−0.378397	+	0.925643i	$0.623525\pi$
$374$	4.46737			0.231002
$375$		0			0
$376$	2.06510	−	4.28821i	0.106499	−	0.221148i
$377$	−8.83220	+	11.0752i	−0.454881	+	0.570403i
$378$		0			0
$379$	−4.94967	−	6.20670i	−0.254248	−	0.318817i	0.638284	−	0.769801i	$-0.279644\pi$
$379$	−4.94967	−	6.20670i	−0.254248	−	0.318817i	−0.892532	+	0.450984i	$0.851073\pi$
$380$	−2.15573	+	0.492031i	−0.110587	+	0.0252407i
$381$		0			0
$382$	−1.17522	−	0.565956i	−0.0601295	−	0.0289568i
$383$	−2.51010	+	3.14756i	−0.128260	+	0.160833i	−0.841815	−	0.539766i	$-0.818513\pi$
$383$	−2.51010	+	3.14756i	−0.128260	+	0.160833i	0.713555	+	0.700599i	$0.247084\pi$
$384$		0			0
$385$	−18.3080	+	3.12351i	−0.933063	+	0.159189i
$386$	0.993948	−	2.06395i	0.0505906	−	0.105053i
$387$		0			0
$388$	−7.31803	−	1.67029i	−0.371517	−	0.0847963i
$389$	−15.5635	−	32.3178i	−0.789098	−	1.63858i	−0.769395	−	0.638774i	$-0.779442\pi$
$389$	−15.5635	−	32.3178i	−0.789098	−	1.63858i	−0.0197035	−	0.999806i	$-0.506272\pi$
$390$		0			0
$391$			36.5776i			1.84981i
$392$	−7.10710	+	0.810604i	−0.358963	+	0.0409417i
$393$		0			0
$394$	−1.40745	−	1.76489i	−0.0709064	−	0.0889139i
$395$	2.17477	−	1.04732i	0.109425	−	0.0526962i
$396$		0			0
$397$	−1.78352	−	3.70352i	−0.0895125	−	0.185875i	0.851406	−	0.524506i	$-0.175750\pi$
$397$	−1.78352	−	3.70352i	−0.0895125	−	0.185875i	−0.940919	+	0.338632i	$0.890036\pi$
$398$	−1.64604	−	0.792691i	−0.0825085	−	0.0397340i
$399$		0			0
$400$	−7.99261	+	3.84904i	−0.399631	+	0.192452i
$401$	13.0626	+	10.4171i	0.652316	+	0.520205i	0.892803	−	0.450448i	$-0.148736\pi$
$401$	13.0626	+	10.4171i	0.652316	+	0.520205i	−0.240487	+	0.970652i	$0.577307\pi$
$402$		0			0
$403$	19.9795	+	25.0535i	0.995251	+	1.24801i
$404$	−4.49513	−	19.6945i	−0.223641	−	0.979836i
$405$		0			0
$406$	1.63982	+	0.0909676i	0.0813829	+	0.00451465i
$407$	−12.4249	−	9.90852i	−0.615879	−	0.491147i
$408$		0			0
$409$	14.1052	−	3.21943i	0.697459	−	0.159191i	0.140931	−	0.990019i	$-0.454990\pi$
$409$	14.1052	−	3.21943i	0.697459	−	0.159191i	0.556528	+	0.830829i	$0.312133\pi$
$410$		−	4.70693i		−	0.232459i
$411$		0			0
$412$	−14.9014	+	3.40115i	−0.734140	+	0.167563i
$413$	2.72792	+	15.9893i	0.134232	+	0.786781i
$414$		0			0
$415$	−6.30634	+	27.6299i	−0.309566	+	1.35630i
$416$	−11.0148	+	13.8121i	−0.540043	+	0.677192i
$417$		0			0
$418$	0.272603	+	0.0622200i	0.0133335	+	0.00304328i
$419$	1.30929	−	5.73638i	0.0639631	−	0.280241i	−0.932824	−	0.360331i	$-0.882664\pi$
$419$	1.30929	−	5.73638i	0.0639631	−	0.280241i	0.996788	+	0.0800903i	$0.0255209\pi$
$420$		0			0
$421$	−0.158030	−	0.692373i	−0.00770190	−	0.0337442i	0.970931	−	0.239360i	$-0.0769375\pi$
$421$	−0.158030	−	0.692373i	−0.00770190	−	0.0337442i	−0.978633	+	0.205616i	$0.934080\pi$
$422$			2.63380i			0.128211i
$423$		0			0
$424$	3.14888	+	13.7962i	0.152923	+	0.670000i
$425$	14.8578	+	7.15516i	0.720711	+	0.347076i
$426$		0			0
$427$	19.8017	+	17.6716i	0.958272	+	0.855189i
$428$	19.0776	−	15.2139i	0.922151	−	0.735391i
$429$		0			0
$430$	−4.35039	+	3.46932i	−0.209794	+	0.167305i
$431$	−1.24950	+	2.59462i	−0.0601865	+	0.124978i	−0.928892	−	0.370350i	$-0.879238\pi$
$431$	−1.24950	+	2.59462i	−0.0601865	+	0.124978i	0.868706	+	0.495328i	$0.164952\pi$
$432$		0			0
$433$	−0.989981	−	2.05572i	−0.0475755	−	0.0987915i	0.875826	−	0.482627i	$-0.160317\pi$
$433$	−0.989981	−	2.05572i	−0.0475755	−	0.0987915i	−0.923402	+	0.383835i	$0.874603\pi$
$434$	1.02606	−	3.57068i	0.0492523	−	0.171398i
$435$		0			0
$436$	7.51377	−	3.61844i	0.359844	−	0.173292i
$437$	−0.509440	+	2.23200i	−0.0243698	+	0.106771i
$438$		0			0
$439$	9.52617	−	7.59686i	0.454659	−	0.362579i	−0.369222	−	0.929341i	$-0.620376\pi$
$439$	9.52617	−	7.59686i	0.454659	−	0.362579i	0.823881	+	0.566763i	$0.191804\pi$
$440$	7.17338			0.341977
$441$		0			0
$442$	10.3108			0.490436
$443$	−1.97589	+	1.57572i	−0.0938774	+	0.0748647i	−0.669304	−	0.742989i	$-0.733408\pi$
$443$	−1.97589	+	1.57572i	−0.0938774	+	0.0748647i	0.575426	+	0.817854i	$0.304836\pi$
$444$		0			0
$445$	1.54253	−	6.75826i	0.0731229	−	0.320372i
$446$	2.37706	−	1.14473i	0.112557	−	0.0542047i
$447$		0			0
$448$	−16.9720	−	0.941506i	−0.801850	−	0.0444820i
$449$	−9.03863	−	18.7689i	−0.426559	−	0.885759i	−0.997883	−	0.0650347i	$-0.979284\pi$
$449$	−9.03863	−	18.7689i	−0.426559	−	0.885759i	0.571324	−	0.820725i	$-0.306430\pi$
$450$		0			0
$451$	7.39080	−	15.3471i	0.348019	−	0.722669i
$452$	−19.9171	+	15.8834i	−0.936822	+	0.747090i
$453$		0			0
$454$	1.65686	−	1.32130i	0.0777603	−	0.0620118i
$455$	−42.2555	+	7.20917i	−1.98097	+	0.337971i
$456$		0			0
$457$	19.1035	+	9.19977i	0.893625	+	0.430347i	0.823582	−	0.567197i	$-0.191972\pi$
$457$	19.1035	+	9.19977i	0.893625	+	0.430347i	0.0700428	+	0.997544i	$0.477686\pi$
$458$	−0.690263	−	3.02424i	−0.0322539	−	0.141313i
$459$		0			0
$460$			28.8626i			1.34572i
$461$	−0.625035	−	2.73846i	−0.0291108	−	0.127543i	0.958285	−	0.285816i	$-0.0922645\pi$
$461$	−0.625035	−	2.73846i	−0.0291108	−	0.127543i	−0.987395	+	0.158273i	$0.949407\pi$
$462$		0			0
$463$	−2.91933	+	12.7904i	−0.135673	+	0.594422i	0.860684	+	0.509140i	$0.170036\pi$
$463$	−2.91933	+	12.7904i	−0.135673	+	0.594422i	−0.996357	+	0.0852824i	$0.972821\pi$
$464$	8.38266	+	1.91329i	0.389155	+	0.0888221i
$465$		0			0
$466$	2.62209	−	3.28800i	0.121466	−	0.152314i
$467$	−8.40531	+	36.8261i	−0.388951	+	1.70411i	0.279327	+	0.960196i	$0.409889\pi$
$467$	−8.40531	+	36.8261i	−0.388951	+	1.70411i	−0.668278	+	0.743911i	$0.732969\pi$
$468$		0			0
$469$	12.8380	+	18.0673i	0.592804	+	0.834272i
$470$	−3.22387	+	0.735826i	−0.148706	+	0.0339411i
$471$		0			0
$472$		−	6.26486i		−	0.288363i
$473$	−19.6321	+	4.48090i	−0.902685	+	0.206032i
$474$		0			0
$475$	0.806986	+	0.643550i	0.0370271	+	0.0295281i
$476$	19.8157	+	27.8873i	0.908251	+	1.27821i
$477$		0			0
$478$	−0.190649	−	0.835287i	−0.00872008	−	0.0382052i
$479$	−17.0479	−	21.3774i	−0.778939	−	0.976759i	−0.999999	−	0.00149851i	$-0.999523\pi$
$479$	−17.0479	−	21.3774i	−0.778939	−	0.976759i	0.221060	−	0.975260i	$-0.429048\pi$
$480$		0			0
$481$	−28.6770	−	22.8692i	−1.30756	−	1.04274i
$482$	−0.101409	+	0.0488361i	−0.00461906	+	0.00222442i
$483$		0			0
$484$	−7.65835	−	3.68807i	−0.348107	−	0.167639i
$485$	4.60453	+	9.56140i	0.209081	+	0.434161i
$486$		0			0
$487$	3.64611	−	1.75587i	0.165221	−	0.0795662i	−0.349446	−	0.936957i	$-0.613630\pi$
$487$	3.64611	−	1.75587i	0.165221	−	0.0795662i	0.514666	+	0.857390i	$0.327916\pi$
$488$	−6.39130	−	8.01444i	−0.289321	−	0.362796i
$489$		0			0
$490$	3.51896	+	3.50936i	0.158970	+	0.158537i
$491$		−	23.7370i		−	1.07124i	−0.844460	−	0.535618i	$-0.820079\pi$
$491$		−	23.7370i		−	1.07124i	0.844460	−	0.535618i	$-0.179921\pi$
$492$		0			0
$493$	−6.93505	−	14.4008i	−0.312339	−	0.648579i
$494$	0.629177	+	0.143606i	0.0283080	+	0.00646112i
$495$		0			0
$496$	8.43916	−	17.5241i	0.378929	−	0.786855i
$497$	6.60389	+	15.9125i	0.296225	+	0.713772i
$498$		0			0
$499$	13.3191	−	16.7017i	0.596247	−	0.747670i	−0.388541	−	0.921432i	$-0.627021\pi$
$499$	13.3191	−	16.7017i	0.596247	−	0.747670i	0.984788	+	0.173761i	$0.0555922\pi$
$500$	−12.0607	−	5.80812i	−0.539370	−	0.259747i
$501$		0			0
$502$	3.61109	−	0.824207i	0.161171	−	0.0367862i
$503$	−13.0531	−	16.3681i	−0.582011	−	0.729819i	0.400443	−	0.916321i	$-0.368856\pi$
$503$	−13.0531	−	16.3681i	−0.582011	−	0.729819i	−0.982454	+	0.186503i	$0.940285\pi$
$504$		0			0
$505$	−17.8070	+	22.3293i	−0.792401	+	0.993639i
$506$	1.58360	−	3.28838i	0.0703996	−	0.146186i
$507$		0			0
$508$	−40.4009			−1.79250
$509$	−8.37447			−0.371192			−0.185596	−	0.982626i	$-0.559422\pi$
$509$	−8.37447			−0.371192			−0.185596	+	0.982626i	$0.559422\pi$
$510$		0			0
$511$	−0.997701	+	17.9850i	−0.0441357	+	0.795608i
$512$	17.6260	+	4.02303i	0.778968	+	0.177794i
$513$		0			0
$514$	−2.10139	−	1.67580i	−0.0926884	−	0.0739165i
$515$	16.8950	+	13.4733i	0.744483	+	0.593705i
$516$		0			0
$517$	−11.6669	−	2.66290i	−0.513111	−	0.117114i
$518$	−0.235542	+	4.24598i	−0.0103491	+	0.186558i
$519$		0			0
$520$	16.5564			0.726045
$521$	14.5608			0.637921			0.318960	−	0.947768i	$-0.396666\pi$
$521$	14.5608			0.637921			0.318960	+	0.947768i	$0.396666\pi$
$522$		0			0
$523$	7.41416	−	15.3957i	0.324198	−	0.673205i	−0.673630	−	0.739069i	$-0.735266\pi$
$523$	7.41416	−	15.3957i	0.324198	−	0.673205i	0.997829	+	0.0658635i	$0.0209802\pi$
$524$	15.1535	−	19.0018i	0.661982	−	0.830099i
$525$		0			0
$526$	−2.88234	−	3.61434i	−0.125676	−	0.157593i
$527$	−35.2505	+	8.04569i	−1.53554	+	0.350476i
$528$		0			0
$529$	6.20209	+	2.98677i	0.269656	+	0.129860i
$530$	6.12989	−	7.68664i	0.266265	−	0.333886i
$531$		0			0
$532$	0.820771	+	1.97770i	0.0355849	+	0.0857440i
$533$	17.0582	−	35.4217i	0.738872	−	1.53428i
$534$		0			0
$535$	−33.6336	−	7.67665i	−1.45411	−	0.331890i
$536$	−3.71427	−	7.71277i	−0.160432	−	0.333141i
$537$		0			0
$538$			3.81717i			0.164570i
$539$	5.96332	+	16.9679i	0.256859	+	0.730858i
$540$		0			0
$541$	−7.15055	−	8.96651i	−0.307426	−	0.385500i	0.603986	−	0.796995i	$-0.293578\pi$
$541$	−7.15055	−	8.96651i	−0.307426	−	0.385500i	−0.911412	+	0.411495i	$0.865007\pi$
$542$	5.47185	−	2.63510i	0.235036	−	0.113187i
$543$		0			0
$544$	−8.64880	−	17.9594i	−0.370814	−	0.770004i
$545$	−10.6230	−	5.11577i	−0.455040	−	0.219136i
$546$		0			0
$547$	−10.3901	+	5.00362i	−0.444250	+	0.213939i	−0.642616	−	0.766189i	$-0.722151\pi$
$547$	−10.3901	+	5.00362i	−0.444250	+	0.213939i	0.198366	+	0.980128i	$0.436437\pi$
$548$	−8.04689	−	6.41718i	−0.343746	−	0.274128i
$549$		0			0
$550$	−1.02596	−	1.28652i	−0.0437472	−	0.0548573i
$551$	−0.222615	−	0.975339i	−0.00948371	−	0.0415509i
$552$		0			0
$553$	−1.35394	−	1.90544i	−0.0575754	−	0.0810277i
$554$	3.14533	+	2.50831i	0.133632	+	0.106568i
$555$		0			0
$556$	4.43056	−	1.01125i	0.187897	−	0.0428864i
$557$		−	28.5685i		−	1.21048i	−0.796041	−	0.605242i	$-0.793076\pi$
$557$		−	28.5685i		−	1.21048i	0.796041	−	0.605242i	$-0.206924\pi$
$558$		0			0
$559$	−45.3115	+	10.3421i	−1.91647	+	0.437423i
$560$	15.0707	+	21.2094i	0.636852	+	0.896262i
$561$		0			0
$562$	−1.50159	+	6.57891i	−0.0633409	+	0.277515i
$563$	22.0460	−	27.6448i	0.929128	−	1.16509i	−0.0568781	−	0.998381i	$-0.518115\pi$
$563$	22.0460	−	27.6448i	0.929128	−	1.16509i	0.986006	−	0.166709i	$-0.0533139\pi$
$564$		0			0
$565$	35.1136	+	8.01445i	1.47724	+	0.337171i
$566$	−1.33116	+	5.83219i	−0.0559528	+	0.245145i
$567$		0			0
$568$	−1.48070	−	6.48739i	−0.0621290	−	0.272205i
$569$			17.6630i			0.740472i	0.928938	+	0.370236i	$0.120723\pi$
$569$			17.6630i			0.740472i	−0.928938	+	0.370236i	$0.879277\pi$
$570$		0			0
$571$	−9.74752	−	42.7067i	−0.407921	−	1.78722i	−0.593765	−	0.804639i	$-0.702359\pi$
$571$	−9.74752	−	42.7067i	−0.407921	−	1.78722i	0.185844	−	0.982579i	$-0.440498\pi$
$572$	26.5279	+	12.7752i	1.10919	+	0.534156i
$573$		0			0
$574$	−4.49317	+	0.766576i	−0.187541	+	0.0319963i
$575$	10.5337	−	8.40032i	0.439284	−	0.350317i
$576$		0			0
$577$	19.5509	−	15.5913i	0.813913	−	0.649074i	−0.125411	−	0.992105i	$-0.540025\pi$
$577$	19.5509	−	15.5913i	0.813913	−	0.649074i	0.939324	+	0.343031i	$0.111454\pi$
$578$	−3.13110	+	6.50180i	−0.130237	+	0.270439i
$579$		0			0
$580$	−5.47229	−	11.3633i	−0.227225	−	0.471837i
$581$	27.4022	+	1.52011i	1.13683	+	0.0630649i
$582$		0			0
$583$	32.0563	−	15.4375i	1.32763	−	0.639355i
$584$	1.54810	−	6.78268i	0.0640609	−	0.280669i
$585$		0			0
$586$	−0.908725	+	0.724684i	−0.0375391	+	0.0299364i
$587$	−10.6126			−0.438027			−0.219014	−	0.975722i	$-0.570284\pi$
$587$	−10.6126			−0.438027			−0.219014	+	0.975722i	$0.570284\pi$
$588$		0			0
$589$	−2.26308			−0.0932485
$590$	−3.40300	+	2.71380i	−0.140099	+	0.111725i
$591$		0			0
$592$	−4.95407	+	21.7052i	−0.203611	+	0.892078i
$593$	16.6237	−	8.00554i	0.682652	−	0.328748i	−0.0602163	−	0.998185i	$-0.519179\pi$
$593$	16.6237	−	8.00554i	0.682652	−	0.328748i	0.742869	+	0.669437i	$0.233465\pi$
$594$		0			0
$595$	13.3580	−	46.4859i	0.547625	−	1.90574i
$596$	11.7742	+	24.4494i	0.482290	+	1.00148i
$597$		0			0
$598$	3.65500	−	7.58968i	0.149464	−	0.310365i
$599$	−28.6007	+	22.8083i	−1.16859	+	0.931920i	−0.998567	−	0.0535196i	$-0.982956\pi$
$599$	−28.6007	+	22.8083i	−1.16859	+	0.931920i	−0.170024	+	0.985440i	$0.554385\pi$
$600$		0			0
$601$	7.34653	−	5.85866i	0.299671	−	0.238980i	−0.462097	−	0.886829i	$-0.652903\pi$
$601$	7.34653	−	5.85866i	0.299671	−	0.238980i	0.761768	+	0.647850i	$0.224331\pi$
$602$	4.02027	+	3.58780i	0.163854	+	0.146228i
$603$		0			0
$604$	35.2867	+	16.9932i	1.43580	+	0.691443i
$605$	2.67415	+	11.7162i	0.108720	+	0.476333i
$606$		0			0
$607$		−	9.77984i		−	0.396951i	−0.980106	−	0.198476i	$-0.936401\pi$
$607$		−	9.77984i		−	0.396951i	0.980106	−	0.198476i	$-0.0635991\pi$
$608$	−0.277626	−	1.21636i	−0.0112592	−	0.0493299i
$609$		0			0
$610$	−1.58478	+	6.94336i	−0.0641658	+	0.281129i
$611$	−26.9277	−	6.14606i	−1.08938	−	0.248643i
$612$		0			0
$613$	16.9488	−	21.2532i	0.684557	−	0.858407i	−0.311208	−	0.950342i	$-0.600734\pi$
$613$	16.9488	−	21.2532i	0.684557	−	0.858407i	0.995765	+	0.0919348i	$0.0293051\pi$
$614$	−0.955227	+	4.18512i	−0.0385498	+	0.168898i
$615$		0			0
$616$	−1.16826	−	6.84761i	−0.0470707	−	0.275898i
$617$	−8.45955	+	1.93084i	−0.340569	+	0.0777326i	−0.389385	−	0.921075i	$-0.627312\pi$
$617$	−8.45955	+	1.93084i	−0.340569	+	0.0777326i	0.0488161	+	0.998808i	$0.484455\pi$
$618$		0			0
$619$			27.4830i			1.10463i	0.833634	+	0.552317i	$0.186256\pi$
$619$			27.4830i			1.10463i	−0.833634	+	0.552317i	$0.813744\pi$
$620$	−27.8154	+	6.34868i	−1.11709	+	0.254969i
$621$		0			0
$622$	2.51633	+	2.00670i	0.100896	+	0.0804615i
$623$	−6.70256	−	0.371819i	−0.268532	−	0.0148966i
$624$		0			0
$625$	6.95350	+	30.4653i	0.278140	+	1.21861i
$626$	−0.0684916	−	0.0858858i	−0.00273748	−	0.00343269i
$627$		0			0
$628$	−5.09445	−	4.06269i	−0.203291	−	0.162119i
$629$	37.2879	−	17.9569i	1.48677	−	0.715989i
$630$		0			0
$631$	44.8832	+	21.6146i	1.78677	+	0.860464i	0.949560	+	0.313585i	$0.101530\pi$
$631$	44.8832	+	21.6146i	1.78677	+	0.860464i	0.837212	+	0.546879i	$0.184184\pi$
$632$	0.391720	+	0.813415i	0.0155818	+	0.0323559i
$633$		0			0
$634$	−2.49872	+	1.20332i	−0.0992367	+	0.0477899i
$635$	35.6132	+	44.6575i	1.41327	+	1.77218i
$636$		0			0
$637$	13.7635	+	39.1624i	0.545331	+	1.55167i
$638$			1.59490i			0.0631426i
$639$		0			0
$640$	−9.04212	−	18.7762i	−0.357421	−	0.742193i
$641$	23.9383	+	5.46375i	0.945504	+	0.215805i	0.667361	−	0.744734i	$-0.267424\pi$
$641$	23.9383	+	5.46375i	0.945504	+	0.215805i	0.278143	+	0.960540i	$0.410281\pi$
$642$		0			0
$643$	−11.9790	+	24.8747i	−0.472407	+	0.980964i	0.519556	+	0.854436i	$0.326097\pi$
$643$	−11.9790	+	24.8747i	−0.472407	+	0.980964i	−0.991963	+	0.126527i	$0.959617\pi$
$644$	27.5518	−	4.70059i	1.08569	−	0.185229i
$645$		0			0
$646$	−0.454011	+	0.569312i	−0.0178628	+	0.0223993i
$647$	32.9977	+	15.8909i	1.29727	+	0.624734i	0.949771	−	0.312945i	$-0.101315\pi$
$647$	32.9977	+	15.8909i	1.29727	+	0.624734i	0.347503	+	0.937679i	$0.387030\pi$
$648$		0			0
$649$	−15.3568	+	3.50509i	−0.602808	+	0.137587i
$650$	−2.36796	−	2.96932i	−0.0928789	−	0.116466i
$651$		0			0
$652$	21.6842	−	27.1912i	0.849220	−	1.06489i
$653$	13.0041	−	27.0033i	0.508889	−	1.05672i	−0.475337	−	0.879804i	$-0.657674\pi$
$653$	13.0041	−	27.0033i	0.508889	−	1.05672i	0.984226	−	0.176915i	$-0.0566119\pi$
$654$		0			0
$655$	−34.3615			−1.34262
$656$	−23.8632			−0.931703
$657$		0			0
$658$	1.22745	+	2.95762i	0.0478510	+	0.115300i
$659$	37.4925	+	8.55743i	1.46050	+	0.333350i	0.877679	−	0.479249i	$-0.159091\pi$
$659$	37.4925	+	8.55743i	1.46050	+	0.333350i	0.582823	+	0.812599i	$0.301948\pi$
$660$		0			0
$661$	5.88490	+	4.69305i	0.228896	+	0.182539i	0.731221	−	0.682140i	$-0.238951\pi$
$661$	5.88490	+	4.69305i	0.228896	+	0.182539i	−0.502325	+	0.864679i	$0.667522\pi$
$662$	−3.35297	−	2.67391i	−0.130317	−	0.103924i
$663$		0			0
$664$	−10.3342	−	2.35871i	−0.401045	−	0.0915359i
$665$	1.46256	−	2.65057i	0.0567156	−	0.102785i
$666$		0			0
$667$	−13.0586			−0.505631
$668$	−18.0918			−0.699991
$669$		0			0
$670$	−2.58055	+	5.35856i	−0.0996952	+	0.207019i
$671$	−16.0697	+	20.1507i	−0.620362	+	0.777910i
$672$		0			0
$673$	−13.2415	−	16.6043i	−0.510422	−	0.640048i	0.458123	−	0.888889i	$-0.348522\pi$
$673$	−13.2415	−	16.6043i	−0.510422	−	0.640048i	−0.968544	+	0.248840i	$0.919951\pi$
$674$	−6.16457	+	1.40702i	−0.237450	+	0.0541965i
$675$		0			0
$676$	38.5929	+	18.5854i	1.48434	+	0.714822i
$677$	−29.2857	+	36.7231i	−1.12554	+	1.41138i	−0.226228	+	0.974074i	$0.572640\pi$
$677$	−29.2857	+	36.7231i	−1.12554	+	1.41138i	−0.899312	+	0.437308i	$0.855932\pi$
$678$		0			0
$679$	8.37728	−	5.95260i	0.321491	−	0.228440i
$680$	−8.10542	+	16.8311i	−0.310829	+	0.645443i
$681$		0			0
$682$	3.51740	+	0.802824i	0.134688	+	0.0307417i
$683$	7.96499	+	16.5395i	0.304772	+	0.632865i	0.995959	−	0.0898106i	$-0.0286262\pi$
$683$	7.96499	+	16.5395i	0.304772	+	0.632865i	−0.691187	+	0.722676i	$0.742912\pi$
$684$		0			0
$685$			14.5514i			0.555980i
$686$	2.77689	−	3.93069i	0.106022	−	0.150074i
$687$		0			0
$688$	17.5888	+	22.0556i	0.670566	+	0.840863i
$689$	73.9868	−	35.6302i	2.81867	−	1.35740i
$690$		0			0
$691$	−21.2272	−	44.0788i	−0.807521	−	1.67684i	−0.733610	−	0.679571i	$-0.762166\pi$
$691$	−21.2272	−	44.0788i	−0.807521	−	1.67684i	−0.0739115	−	0.997265i	$-0.523548\pi$
$692$	−44.4931	−	21.4267i	−1.69137	−	0.814523i
$693$		0			0
$694$	0.966726	−	0.465551i	0.0366964	−	0.0176721i
$695$	−5.02330	−	4.00595i	−0.190544	−	0.151954i
$696$		0			0
$697$	27.6583	+	34.6824i	1.04763	+	1.31369i
$698$	−0.583565	−	2.55677i	−0.0220883	−	0.0967750i
$699$		0			0
$700$	3.48019	−	12.1111i	0.131539	−	0.457755i
$701$	−19.8849	−	15.8577i	−0.751042	−	0.598936i	0.171341	−	0.985212i	$-0.445190\pi$
$701$	−19.8849	−	15.8577i	−0.751042	−	0.598936i	−0.922383	+	0.386275i	$0.873761\pi$
$702$		0			0
$703$	2.52544	−	0.576416i	0.0952489	−	0.0217399i
$704$		−	16.5071i		−	0.622133i
$705$		0			0
$706$	9.25336	−	2.11202i	0.348255	−	0.0794869i
$707$	24.2153	+	13.3617i	0.910709	+	0.502520i
$708$		0			0
$709$	3.82546	−	16.7604i	0.143668	−	0.629452i	−0.850897	−	0.525333i	$-0.823941\pi$
$709$	3.82546	−	16.7604i	0.143668	−	0.629452i	0.994565	−	0.104119i	$-0.0332022\pi$
$710$	−2.88247	+	3.61450i	−0.108177	+	0.135650i
$711$		0			0
$712$	2.52774	+	0.576941i	0.0947311	+	0.0216218i
$713$	−6.57331	+	28.7995i	−0.246172	+	1.07855i
$714$		0			0
$715$	−9.26305	−	40.5841i	−0.346418	−	1.51776i
$716$			28.8671i			1.07881i
$717$		0			0
$718$	0.872721	+	3.82364i	0.0325697	+	0.142697i
$719$	41.3285	+	19.9028i	1.54129	+	0.742248i	0.995418	−	0.0956182i	$-0.0304828\pi$
$719$	41.3285	+	19.9028i	1.54129	+	0.742248i	0.545876	+	0.837866i	$0.316197\pi$
$720$		0			0
$721$	10.1099	−	18.3220i	0.376512	−	0.682347i
$722$	3.82450	−	3.04994i	0.142333	−	0.113507i
$723$		0			0
$724$	5.41570	−	4.31888i	0.201273	−	0.160510i
$725$	−2.55447	+	5.30441i	−0.0948706	+	0.197001i
$726$		0			0
$727$	20.1261	+	41.7923i	0.746435	+	1.54999i	0.832705	+	0.553717i	$0.186791\pi$
$727$	20.1261	+	41.7923i	0.746435	+	1.54999i	−0.0862692	+	0.996272i	$0.527495\pi$
$728$	−2.69639	−	15.8045i	−0.0999349	−	0.585753i
$729$		0			0
$730$	−4.35488	+	2.09720i	−0.161181	+	0.0776209i
$731$	11.6693	−	51.1264i	0.431604	−	1.89098i
$732$		0			0
$733$	32.6020	−	25.9992i	1.20418	−	0.960303i	0.204355	−	0.978897i	$-0.434490\pi$
$733$	32.6020	−	25.9992i	1.20418	−	0.960303i	0.999827	+	0.0185935i	$0.00591884\pi$
$734$	4.36890			0.161259
$735$		0			0
$736$	−16.2856			−0.600294
$737$	−16.8280	+	13.4198i	−0.619866	+	0.494326i
$738$		0			0
$739$	4.98595	−	21.8449i	0.183411	−	0.803577i	−0.796579	−	0.604534i	$-0.793359\pi$
$739$	4.98595	−	21.8449i	0.183411	−	0.803577i	0.979991	−	0.199043i	$-0.0637835\pi$
$740$	29.4231	−	14.1694i	1.08161	−	0.520877i
$741$		0			0
$742$	−8.33587	−	4.59965i	−0.306020	−	0.168858i
$743$	−5.94655	−	12.3481i	−0.218158	−	0.453009i	0.762954	−	0.646453i	$-0.223749\pi$
$743$	−5.94655	−	12.3481i	−0.218158	−	0.453009i	−0.981111	+	0.193444i	$0.938034\pi$
$744$		0			0
$745$	16.6464	−	34.5667i	0.609878	−	1.26642i
$746$	−2.96948	+	2.36808i	−0.108720	+	0.0867017i
$747$		0			0
$748$	−25.9743	+	20.7138i	−0.949713	+	0.757371i
$749$	−1.85042	+	33.3564i	−0.0676128	+	1.21882i
$750$		0			0
$751$	−43.7822	−	21.0844i	−1.59764	−	0.769381i	−0.598148	−	0.801386i	$-0.704097\pi$
$751$	−43.7822	−	21.0844i	−1.59764	−	0.769381i	−0.999488	+	0.0320048i	$0.989811\pi$
$752$	3.73050	+	16.3444i	0.136037	+	0.596018i
$753$		0			0
$754$			3.68108i			0.134057i
$755$	−12.3215	−	53.9839i	−0.448424	−	1.96467i
$756$		0			0
$757$	−3.71116	+	16.2597i	−0.134884	+	0.590967i	0.861629	+	0.507538i	$0.169444\pi$
$757$	−3.71116	+	16.2597i	−0.134884	+	0.590967i	−0.996514	+	0.0834290i	$0.973413\pi$
$758$	−2.01120	−	0.459043i	−0.0730501	−	0.0166732i
$759$		0			0
$760$	−0.729019	+	0.914161i	−0.0264443	+	0.0331601i
$761$	−2.33924	+	10.2489i	−0.0847974	+	0.371522i	−0.999466	−	0.0326835i	$-0.989595\pi$
$761$	−2.33924	+	10.2489i	−0.0847974	+	0.371522i	0.914668	+	0.404205i	$0.132452\pi$
$762$		0			0
$763$	−3.15337	+	10.9737i	−0.114160	+	0.397276i
$764$	9.45715	−	2.15853i	0.342148	−	0.0780930i
$765$		0			0
$766$			1.04616i			0.0377992i
$767$	−35.4440	+	8.08987i	−1.27981	+	0.292108i
$768$		0			0
$769$	−26.3184	−	20.9882i	−0.949066	−	0.756855i	0.0209789	−	0.999780i	$-0.493322\pi$
$769$	−26.3184	−	20.9882i	−0.949066	−	0.756855i	−0.970045	+	0.242925i	$0.921893\pi$
$770$	−3.21348	+	3.60083i	−0.115806	+	0.129765i
$771$		0			0
$772$	3.79088	+	16.6089i	0.136437	+	0.597768i
$773$	26.2873	+	32.9633i	0.945490	+	1.18561i	0.982495	+	0.186291i	$0.0596468\pi$
$773$	26.2873	+	32.9633i	0.945490	+	1.18561i	−0.0370050	+	0.999315i	$0.511782\pi$
$774$		0			0
$775$	10.4125	+	8.30372i	0.374029	+	0.298279i
$776$	−3.57618	+	1.72220i	−0.128377	+	0.0618233i
$777$		0			0
$778$	−8.39804	−	4.04428i	−0.301084	−	0.144994i
$779$	1.20469	+	2.50157i	0.0431626	+	0.0896282i
$780$		0			0
$781$	−15.0739	+	7.25919i	−0.539385	+	0.259754i
$782$	5.92625	+	7.43129i	0.211922	+	0.265742i
$783$		0			0
$784$	17.7918	−	17.8404i	0.635422	−	0.637159i
$785$			9.21243i			0.328806i
$786$		0			0
$787$	−14.2218	−	29.5319i	−0.506952	−	1.05270i	−0.984709	−	0.174205i	$-0.944264\pi$
$787$	−14.2218	−	29.5319i	−0.506952	−	1.05270i	0.477757	−	0.878492i	$-0.341450\pi$
$788$	16.3665	+	3.73554i	0.583032	+	0.133073i
$789$		0			0
$790$	0.272153	−	0.565132i	0.00968277	−	0.0201065i
$791$	1.93184	−	34.8242i	0.0686885	−	1.23821i
$792$		0			0
$793$	−37.0893	+	46.5085i	−1.31708	+	1.65156i
$794$	−0.962389	−	0.463462i	−0.0341539	−	0.0164477i
$795$		0			0
$796$	13.2459	−	3.02329i	0.469488	−	0.107158i
$797$	−6.14356	−	7.70378i	−0.217616	−	0.272882i	0.661026	−	0.750363i	$-0.270121\pi$
$797$	−6.14356	−	7.70378i	−0.217616	−	0.272882i	−0.878642	+	0.477481i	$0.841550\pi$
$798$		0			0
$799$	19.4309	−	24.3655i	0.687415	−	0.861991i
$800$	−3.18571	+	6.61520i	−0.112632	+	0.233883i
$801$		0			0
$802$	4.34163			0.153308
$803$	−17.4923			−0.617289
$804$		0			0
$805$	−29.4826	−	26.3111i	−1.03912	−	0.927344i
$806$	8.11827	+	1.85294i	0.285954	+	0.0652671i
$807$		0			0
$808$	−8.35165	−	6.66022i	−0.293810	−	0.234306i
$809$	8.09230	+	6.45339i	0.284510	+	0.226889i	0.755337	−	0.655336i	$-0.227473\pi$
$809$	8.09230	+	6.45339i	0.284510	+	0.226889i	−0.470827	+	0.882225i	$0.656044\pi$
$810$		0			0
$811$	−13.1978	−	3.01231i	−0.463437	−	0.105776i	−0.0155740	−	0.999879i	$-0.504958\pi$
$811$	−13.1978	−	3.01231i	−0.463437	−	0.105776i	−0.447863	+	0.894102i	$0.647815\pi$
$812$	−9.95606	+	7.07442i	−0.349389	+	0.248263i
$813$		0			0
$814$	−4.12967			−0.144745
$815$	−49.1705			−1.72237
$816$		0			0
$817$	1.42414	−	2.95726i	0.0498244	−	0.103462i
$818$	2.34408	−	2.93939i	0.0819589	−	0.102773i
$819$		0			0
$820$	21.8246	+	27.3671i	0.762147	+	0.955702i
$821$	33.7764	−	7.70923i	1.17880	−	0.269054i	0.412150	−	0.911116i	$-0.364778\pi$
$821$	33.7764	−	7.70923i	1.17880	−	0.269054i	0.766653	+	0.642062i	$0.221921\pi$
$822$		0			0
$823$	−11.2473	−	5.41641i	−0.392056	−	0.188804i	0.227462	−	0.973787i	$-0.426957\pi$
$823$	−11.2473	−	5.41641i	−0.392056	−	0.188804i	−0.619517	+	0.784983i	$0.712672\pi$
$824$	−5.03932	+	6.31911i	−0.175553	+	0.220137i
$825$		0			0
$826$	3.14477	+	2.80648i	0.109421	+	0.0976501i
$827$	4.23589	−	8.79591i	0.147296	−	0.305864i	−0.814246	−	0.580519i	$-0.802850\pi$
$827$	4.23589	−	8.79591i	0.147296	−	0.305864i	0.961543	+	0.274656i	$0.0885638\pi$
$828$		0			0
$829$	−49.7946	−	11.3653i	−1.72944	−	0.394733i	−0.761948	−	0.647638i	$-0.775757\pi$
$829$	−49.7946	−	11.3653i	−1.72944	−	0.394733i	−0.967491	+	0.252905i	$0.918614\pi$
$830$	3.19533	+	6.63517i	0.110911	+	0.230310i
$831$		0			0
$832$		−	38.0988i		−	1.32084i
$833$	−46.5503	−	5.18062i	−1.61287	−	0.179498i
$834$		0			0
$835$	15.9478	+	19.9979i	0.551895	+	0.692055i
$836$	−1.87347	+	0.902216i	−0.0647953	+	0.0312038i
$837$		0			0
$838$	−0.663399	−	1.37756i	−0.0229167	−	0.0475871i
$839$	−4.43688	−	2.13669i	−0.153178	−	0.0737667i	0.355724	−	0.934591i	$-0.384234\pi$
$839$	−4.43688	−	2.13669i	−0.153178	−	0.0737667i	−0.508902	+	0.860824i	$0.669949\pi$
$840$		0			0
$841$	−20.9869	+	10.1067i	−0.723685	+	0.348508i
$842$	−0.144283	−	0.115062i	−0.00497233	−	0.00396530i
$843$		0			0
$844$	−12.2121	−	15.3135i	−0.420357	−	0.527111i
$845$	−13.4759	−	59.0419i	−0.463586	−	2.03110i
$846$		0			0
$847$	10.7486	−	4.46083i	0.369327	−	0.153276i
$848$	−38.9698	−	31.0774i	−1.33823	−	1.06720i
$849$		0			0
$850$	4.17786	−	0.953569i	0.143299	−	0.0327071i
$851$		−	33.8126i		−	1.15908i
$852$		0			0
$853$	−7.17110	+	1.63676i	−0.245534	+	0.0560415i	−0.343517	−	0.939147i	$-0.611618\pi$
$853$	−7.17110	+	1.63676i	−0.245534	+	0.0560415i	0.0979827	+	0.995188i	$0.468761\pi$
$854$	6.88614	+	0.382003i	0.235639	+	0.0130719i
$855$		0			0
$856$	2.87124	−	12.5797i	0.0981369	−	0.429966i
$857$	0.144754	−	0.181516i	0.00494472	−	0.00620048i	−0.779353	−	0.626585i	$-0.784452\pi$
$857$	0.144754	−	0.181516i	0.00494472	−	0.00620048i	0.784298	+	0.620385i	$0.213023\pi$
$858$		0			0
$859$	37.0982	+	8.46741i	1.26577	+	0.288904i	0.802147	−	0.597127i	$-0.203691\pi$
$859$	37.0982	+	8.46741i	1.26577	+	0.288904i	0.463626	+	0.886031i	$0.346548\pi$
$860$	9.20797	−	40.3427i	0.313989	−	1.37568i
$861$		0			0
$862$	0.166522	+	0.729578i	0.00567175	+	0.0248495i
$863$			9.94315i			0.338469i	0.985576	+	0.169234i	$0.0541295\pi$
$863$			9.94315i			0.338469i	−0.985576	+	0.169234i	$0.945871\pi$
$864$		0			0
$865$	15.5362	+	68.0684i	0.528245	+	2.31439i
$866$	−0.534194	−	0.257254i	−0.0181526	−	0.00874185i
$867$		0			0
$868$	10.5904	+	25.5182i	0.359462	+	0.866145i
$869$	1.77473	−	1.41530i	0.0602037	−	0.0480108i
$870$		0			0
$871$	−38.8395	+	30.9734i	−1.31602	+	1.04949i
$872$	1.91341	−	3.97324i	0.0647964	−	0.134551i
$873$		0			0
$874$	0.258126	+	0.536004i	0.00873123	+	0.0181306i
$875$	16.9274	−	7.02509i	0.572250	−	0.237491i
$876$		0			0
$877$	29.8213	−	14.3612i	1.00699	−	0.484943i	0.143688	−	0.989623i	$-0.454104\pi$
$877$	29.8213	−	14.3612i	1.00699	−	0.484943i	0.863306	+	0.504680i	$0.168390\pi$
$878$	0.704549	−	3.08683i	0.0237774	−	0.104176i
$879$		0			0
$880$	−19.7545	+	15.7537i	−0.665924	+	0.531057i
$881$	−15.2829			−0.514893			−0.257447	−	0.966293i	$-0.582881\pi$
$881$	−15.2829			−0.514893			−0.257447	+	0.966293i	$0.582881\pi$
$882$		0			0
$883$	−26.6582			−0.897121			−0.448560	−	0.893753i	$-0.648063\pi$
$883$	−26.6582			−0.897121			−0.448560	+	0.893753i	$0.648063\pi$
$884$	−59.9494	+	47.8081i	−2.01632	+	1.60796i
$885$		0			0
$886$	−0.146136	+	0.640262i	−0.00490952	+	0.0215100i
$887$	−1.60281	+	0.771874i	−0.0538172	+	0.0259170i	−0.460599	−	0.887608i	$-0.652365\pi$
$887$	−1.60281	+	0.771874i	−0.0538172	+	0.0259170i	0.406782	+	0.913525i	$0.366651\pi$
$888$		0			0
$889$	36.8294	−	41.2688i	1.23522	−	1.38411i
$890$	−0.781576	−	1.62296i	−0.0261985	−	0.0544017i
$891$		0			0
$892$	−8.51300	+	17.6774i	−0.285036	+	0.591884i
$893$	1.52505	−	1.21618i	0.0510337	−	0.0406980i
$894$		0			0
$895$	31.9085	−	25.4462i	1.06658	−	0.850572i
$896$	−16.4508	+	11.6894i	−0.549584	+	0.390515i
$897$		0			0
$898$	−4.87724	−	2.34876i	−0.162756	−	0.0783790i
$899$	−2.87240	−	12.5848i	−0.0957999	−	0.419727i
$900$		0			0
$901$			92.6577i			3.08688i
$902$	−0.984973	−	4.31545i	−0.0327960	−	0.143689i
$903$		0			0
$904$	−2.99759	+	13.1333i	−0.0996982	+	0.436806i
$905$	−9.54781	−	2.17923i	−0.317380	−	0.0724399i
$906$		0			0
$907$	−8.36281	+	10.4866i	−0.277683	+	0.348203i	−0.901041	−	0.433733i	$-0.857196\pi$
$907$	−8.36281	+	10.4866i	−0.277683	+	0.348203i	0.623359	+	0.781936i	$0.285768\pi$
$908$	−3.50689	+	15.3647i	−0.116380	+	0.509895i
$909$		0			0
$910$	−7.41680	+	8.31082i	−0.245865	+	0.275501i
$911$	46.3632	−	10.5821i	1.53608	−	0.350600i	0.630980	−	0.775799i	$-0.282653\pi$
$911$	46.3632	−	10.5821i	1.53608	−	0.350600i	0.905100	+	0.425199i	$0.139796\pi$
$912$		0			0
$913$			26.6515i			0.882037i
$914$	5.37170	−	1.22605i	0.177680	−	0.0405543i
$915$		0			0
$916$	18.0358	+	14.3831i	0.595919	+	0.475230i
$917$	5.59616	+	32.8010i	0.184801	+	1.08319i
$918$		0			0
$919$	9.70410	+	42.5164i	0.320109	+	1.40249i	0.837359	+	0.546654i	$0.184099\pi$
$919$	9.70410	+	42.5164i	0.320109	+	1.40249i	−0.517250	+	0.855834i	$0.673044\pi$
$920$	9.51595	+	11.9326i	0.313732	+	0.393407i
$921$		0			0
$922$	−0.570666	−	0.455091i	−0.0187939	−	0.0149876i
$923$	−34.7910	+	16.7544i	−1.14516	+	0.551479i
$924$		0			0
$925$	−13.7347	−	6.61428i	−0.451594	−	0.217476i
$926$	1.47918	+	3.07155i	0.0486090	+	0.100938i
$927$		0			0
$928$	6.41170	−	3.08771i	0.210474	−	0.101359i
$929$	−8.93091	−	11.1990i	−0.293014	−	0.367428i	0.613434	−	0.789746i	$-0.289788\pi$
$929$	−8.93091	−	11.1990i	−0.293014	−	0.367428i	−0.906447	+	0.422319i	$0.861216\pi$
$930$		0			0
$931$	−2.76839	−	0.964463i	−0.0907304	−	0.0316090i
$932$			31.2749i			1.02444i
$933$		0			0
$934$	4.25884	+	8.84358i	0.139354	+	0.289371i
$935$	45.7923	+	10.4518i	1.49757	+	0.341810i
$936$		0			0
$937$	0.951794	−	1.97642i	0.0310938	−	0.0645669i	−0.884843	−	0.465889i	$-0.845735\pi$
$937$	0.951794	−	1.97642i	0.0310938	−	0.0645669i	0.915937	+	0.401322i	$0.131449\pi$
$938$	5.53548	+	1.59065i	0.180740	+	0.0519367i
$939$		0			0
$940$	15.3325	−	19.2263i	0.500090	−	0.627093i
$941$	−15.5215	−	7.47476i	−0.505987	−	0.243670i	0.163434	−	0.986554i	$-0.447743\pi$
$941$	−15.5215	−	7.47476i	−0.505987	−	0.243670i	−0.669420	+	0.742884i	$0.733457\pi$
$942$		0			0
$943$	35.3337	−	8.06469i	1.15062	−	0.262622i
$944$	13.7585	+	17.2526i	0.447800	+	0.561523i
$945$		0			0
$946$	−3.26257	+	4.09113i	−0.106075	+	0.133014i
$947$	−1.91534	+	3.97725i	−0.0622403	+	0.129243i	−0.929769	−	0.368145i	$-0.879993\pi$
$947$	−1.91534	+	3.97725i	−0.0622403	+	0.129243i	0.867528	+	0.497388i	$0.165707\pi$
$948$		0			0
$949$	−40.3727			−1.31055
$950$	0.268218			0.00870215
$951$		0			0
$952$	17.3868	+	4.99620i	0.563509	+	0.161928i
$953$	−41.8564	−	9.55344i	−1.35586	−	0.309466i	−0.518014	−	0.855372i	$-0.673329\pi$
$953$	−41.8564	−	9.55344i	−1.35586	−	0.309466i	−0.837847	+	0.545906i	$0.816186\pi$
$954$		0			0
$955$	−10.7224	−	8.55081i	−0.346968	−	0.276698i
$956$	4.98144	+	3.97256i	0.161111	+	0.128482i
$957$		0			0
$958$	−6.92707	−	1.58106i	−0.223804	−	0.0510817i
$959$	13.8906	−	2.36986i	0.448550	−	0.0765267i
$960$		0			0
$961$	1.79950			0.0580484
$962$	−9.53140			−0.307305
$963$		0			0
$964$	0.363178	−	0.754146i	0.0116972	−	0.0242894i
$965$	15.0172	−	18.8309i	0.483420	−	0.606189i
$966$		0			0
$967$	−36.1786	−	45.3665i	−1.16343	−	1.45889i	−0.863086	−	0.505057i	$-0.831471\pi$
$967$	−36.1786	−	45.3665i	−1.16343	−	1.45889i	−0.300339	−	0.953832i	$-0.597100\pi$
$968$	−4.38213	+	1.00019i	−0.140847	+	0.0321474i
$969$		0			0
$970$	2.48460	+	1.19652i	0.0797758	+	0.0384180i
$971$	16.9370	−	21.2383i	0.543534	−	0.681570i	−0.431885	−	0.901929i	$-0.642151\pi$
$971$	16.9370	−	21.2383i	0.543534	−	0.681570i	0.975419	+	0.220359i	$0.0707228\pi$
$972$		0			0
$973$	−3.00592	+	5.44758i	−0.0963654	+	0.174641i
$974$	0.456277	−	0.947469i	0.0146201	−	0.0303589i
$975$		0			0
$976$	35.2015	+	8.03452i	1.12677	+	0.257179i
$977$	−20.6804	−	42.9432i	−0.661624	−	1.37388i	−0.913788	−	0.406191i	$-0.866857\pi$
$977$	−20.6804	−	42.9432i	−0.661624	−	1.37388i	0.252164	−	0.967684i	$-0.418858\pi$
$978$		0			0
$979$		−	6.51895i		−	0.208347i
$980$	−36.7318	−	4.08791i	−1.17335	−	0.130584i
$981$		0			0
$982$	−3.84584	−	4.82253i	−0.122726	−	0.153893i
$983$	23.4437	−	11.2899i	0.747739	−	0.360092i	−0.0208947	−	0.999782i	$-0.506651\pi$
$983$	23.4437	−	11.2899i	0.747739	−	0.360092i	0.768633	+	0.639690i	$0.220937\pi$
$984$		0			0
$985$	−10.2978	−	21.3837i	−0.328116	−	0.681341i
$986$	−3.74215	−	1.80213i	−0.119174	−	0.0573914i
$987$		0			0
$988$	−4.32403	+	2.08234i	−0.137566	+	0.0662481i
$989$	−33.4971	−	26.7130i	−1.06514	−	0.849424i
$990$		0			0
$991$	20.8926	+	26.1985i	0.663676	+	0.832223i	0.993738	−	0.111736i	$-0.0356412\pi$
$991$	20.8926	+	26.1985i	0.663676	+	0.832223i	−0.330062	+	0.943959i	$0.607070\pi$
$992$	−3.58221	−	15.6947i	−0.113735	−	0.498307i
$993$		0			0
$994$	3.91979	+	2.16290i	0.124328	+	0.0686031i
$995$	−15.0180	−	11.9764i	−0.476102	−	0.379679i
$996$		0			0
$997$	0.991215	−	0.226238i	0.0313921	−	0.00716504i	−0.206796	−	0.978384i	$-0.566304\pi$
$997$	0.991215	−	0.226238i	0.0313921	−	0.00716504i	0.238188	+	0.971219i	$0.423447\pi$
$998$		−	5.55114i		−	0.175718i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.w.a.188.12	yes	120
3.2	odd	2	inner	441.2.w.a.188.9	✓	120
49.6	odd	14	inner	441.2.w.a.251.9	yes	120
147.104	even	14	inner	441.2.w.a.251.12	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.w.a.188.9	✓	120	3.2	odd	2	inner
441.2.w.a.188.12	yes	120	1.1	even	1	trivial
441.2.w.a.251.9	yes	120	49.6	odd	14	inner
441.2.w.a.251.12	yes	120	147.104	even	14	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.w (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.203165 - 0.162019i) q^{2} +(-0.430016 + 1.88402i) q^{4} +(2.46158 - 1.18543i) q^{5} +(-1.53249 - 2.15673i) q^{7} +(0.443379 + 0.920685i) q^{8} +(0.308044 - 0.639659i) q^{10} +(2.00878 - 1.60195i) q^{11} +(4.63632 - 3.69734i) q^{13} +(-0.660778 - 0.189879i) q^{14} +(-3.24295 - 1.56172i) q^{16} +(1.48891 + 6.52334i) q^{17} +0.418798i q^{19} +(1.17487 + 5.14742i) q^{20} +(0.148568 - 0.650919i) q^{22} +(5.32955 + 1.21643i) q^{23} +(1.53666 - 1.92691i) q^{25} +(0.342899 - 1.50234i) q^{26} +(4.72232 - 1.95982i) q^{28} +(-2.32890 + 0.531557i) q^{29} +5.40375i q^{31} +(-2.90441 + 0.662912i) q^{32} +(1.35940 + 1.08408i) q^{34} +(-6.32900 - 3.49228i) q^{35} +(-1.37636 - 6.03022i) q^{37} +(0.0678530 + 0.0850850i) q^{38} +(2.18282 + 1.74074i) q^{40} +(5.97322 - 2.87655i) q^{41} +(-7.06131 - 3.40055i) q^{43} +(2.15430 + 4.47345i) q^{44} +(1.27986 - 0.616349i) q^{46} +(-2.90399 - 3.64149i) q^{47} +(-2.30293 + 6.61033i) q^{49} -0.640448i q^{50} +(4.97219 + 10.3249i) q^{52} +(13.5007 + 3.08145i) q^{53} +(3.04576 - 6.32459i) q^{55} +(1.30619 - 2.36719i) q^{56} +(-0.387029 + 0.485319i) q^{58} +(-5.52357 - 2.66001i) q^{59} +(-9.77982 + 2.23218i) q^{61} +(0.875508 + 1.09785i) q^{62} +(4.00571 - 5.02301i) q^{64} +(7.02971 - 14.5973i) q^{65} -8.37721 q^{67} -12.9304 q^{68} +(-1.85164 + 0.315907i) q^{70} +(-6.34846 - 1.44900i) q^{71} +(-5.32281 - 4.24480i) q^{73} +(-1.25664 - 1.00213i) q^{74} +(-0.789025 - 0.180090i) q^{76} +(-6.53340 - 1.87741i) q^{77} +0.883489 q^{79} -9.83409 q^{80} +(0.747494 - 1.55219i) q^{82} +(-6.46744 + 8.10992i) q^{83} +(11.3980 + 14.2927i) q^{85} +(-1.98556 + 0.453192i) q^{86} +(2.36554 + 1.13918i) q^{88} +(1.58193 - 1.98368i) q^{89} +(-15.0793 - 4.33313i) q^{91} +(-4.58358 + 9.51791i) q^{92} +(-1.17998 - 0.269322i) q^{94} +(0.496457 + 1.03090i) q^{95} +3.88426i q^{97} +(0.603122 + 1.71611i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70}+ \cdots - 112 q^{94}+O(q^{100}) \) 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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