LMFDB - Embedded newform 441.2.w.a.188.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(62,441)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			188.9
Character	$\chi$	$=$	441.188
Dual form			441.2.w.a.251.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

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	−0.692682	−	0.721243i	$-0.743571\pi$
$2$	−0.203165	+	0.162019i	−0.143659	+	0.114564i	0.549023	+	0.835807i	$0.315000\pi$
$3$		0			0
$3$		0			0
$4$	−0.430016	+	1.88402i	−0.215008	+	0.942011i
$5$	−2.46158	+	1.18543i	−1.10085	+	0.530142i	−0.893926	−	0.448215i	$-0.852060\pi$
$5$	−2.46158	+	1.18543i	−1.10085	+	0.530142i	−0.206925	+	0.978357i	$0.566346\pi$
$6$		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	−0.877653	−	0.479297i	$-0.840892\pi$
$11$	−2.00878	+	1.60195i	−0.605670	+	0.483005i	0.271983	+	0.962302i	$0.412320\pi$
$12$		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	$-0.770126\pi$
$17$	−1.48891	−	6.52334i	−0.361114	−	1.58214i	0.389260	−	0.921128i	$-0.372731\pi$
$18$		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	−0.372800	−	0.927912i	$-0.621602\pi$
$23$	−5.32955	−	1.21643i	−1.11129	−	0.253644i	−0.738487	+	0.674267i	$0.764460\pi$
$24$		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	−0.000745584	−	1.00000i	$-0.500237\pi$
$29$	2.32890	−	0.531557i	0.432466	−	0.0987076i	0.433212	+	0.901292i	$0.357380\pi$
$30$		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	−0.837645	−	0.546215i	$-0.816068\pi$
$41$	−5.97322	+	2.87655i	−0.932861	+	0.449242i	−0.0952155	+	0.995457i	$0.530354\pi$
$42$		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	0.947136	−	0.320832i	$-0.103963\pi$
$47$	2.90399	+	3.64149i	0.423590	+	0.531165i	−0.523546	+	0.851997i	$0.675391\pi$
$48$		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	−0.858485	−	0.512839i	$-0.828594\pi$
$53$	−13.5007	−	3.08145i	−1.85447	−	0.423270i	−0.995981	+	0.0895695i	$0.971451\pi$
$54$		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	0.757390	−	0.652963i	$-0.226474\pi$
$59$	5.52357	+	2.66001i	0.719107	+	0.346304i	−0.0382823	+	0.999267i	$0.512189\pi$
$60$		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	0.581950	−	0.813225i	$-0.302290\pi$
$71$	6.34846	+	1.44900i	0.753424	+	0.171964i	0.171474	+	0.985189i	$0.445147\pi$
$72$		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	−0.287825	−	0.957683i	$-0.592932\pi$
$83$	6.46744	−	8.10992i	0.709894	−	0.890179i	0.997719	+	0.0675041i	$0.0215036\pi$
$84$		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	−0.858573	−	0.512692i	$-0.828648\pi$
$89$	−1.58193	+	1.98368i	−0.167685	+	0.210270i	0.690888	+	0.722962i	$0.257220\pi$
$90$		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	0.0979838	−	0.995188i	$-0.468761\pi$
$101$	9.41819	−	4.53556i	0.937145	−	0.451305i	0.839161	+	0.543883i	$0.183046\pi$
$102$		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	0.971075	−	0.238773i	$-0.0767451\pi$
$107$	9.87212	+	7.87275i	0.954374	+	0.761088i	−0.0167017	+	0.999861i	$0.505317\pi$
$108$		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	0.00438565	−	0.999990i	$-0.498604\pi$
$113$	−10.3065	−	8.21919i	−0.969557	−	0.773196i	−0.973943	+	0.226794i	$0.927175\pi$
$114$		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	0.857539	−	0.514418i	$-0.171992\pi$
$131$	11.3313	+	5.45685i	0.990018	+	0.476768i	0.132479	+	0.991186i	$0.457706\pi$
$132$		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	−0.778625	−	0.627489i	$-0.784083\pi$
$137$	2.31086	−	4.79856i	0.197430	−	0.409969i	0.976056	+	0.217521i	$0.0697969\pi$
$138$		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	−0.959733	−	0.280914i	$-0.909363\pi$
$149$	−10.9789	+	8.75535i	−0.899423	+	0.717266i	0.0603099	+	0.998180i	$0.480791\pi$
$150$		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	$-0.953446\pi$
$167$	−2.08323	−	9.12724i	−0.161205	−	0.706287i	0.828118	−	0.560553i	$-0.189411\pi$
$168$		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	$-0.504829\pi$
$173$	5.68643	−	24.9139i	0.432332	−	1.89417i	0.447501	−	0.894284i	$-0.352314\pi$
$174$		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	−0.728878	−	0.684644i	$-0.759958\pi$
$179$	−14.5634	+	3.32400i	−1.08852	+	0.248447i	−0.359640	+	0.933091i	$0.617101\pi$
$180$		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	0.964783	−	0.263049i	$-0.0847280\pi$
$191$	2.17795	+	4.52256i	0.157591	+	0.327241i	−0.807192	+	0.590289i	$0.799014\pi$
$192$		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	$0.100149\pi$
$197$			8.68699i			0.618922i	−0.950912	+	0.309461i	$0.899851\pi$
$198$		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	$-0.587236\pi$
$227$	−8.15525			−0.541283			−0.270641	+	0.962680i	$0.587236\pi$
$228$		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	−0.705510	−	0.708700i	$-0.749282\pi$
$233$	−15.7781	+	3.60125i	−1.03366	+	0.235926i	−0.328149	+	0.944626i	$0.606425\pi$
$234$		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	−0.942099	−	0.335335i	$-0.891150\pi$
$239$	−1.43054	+	2.97056i	−0.0925342	+	0.192149i	0.849565	+	0.527484i	$0.176865\pi$
$240$		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	−0.0177924	−	0.999842i	$-0.505664\pi$
$251$	−12.8422	−	6.18449i	−0.810594	−	0.390361i	−0.792801	+	0.609480i	$0.791378\pi$
$252$		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	$0.0331276\pi$
$257$	2.30160	+	10.0840i	0.143570	+	0.629020i	−0.851020	+	0.525134i	$0.824015\pi$
$258$		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	$0.184799\pi$
$263$			17.7902i			1.09699i	−0.836154	+	0.548495i	$0.815201\pi$
$264$		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	−0.419846	−	0.907595i	$-0.637916\pi$
$269$	9.15874	−	11.4847i	0.558418	−	0.700234i	0.978264	+	0.207361i	$0.0664875\pi$
$270$		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	0.211240	−	0.977434i	$-0.432250\pi$
$281$	20.3030	−	16.1911i	1.21117	−	0.965878i	0.999933	+	0.0115558i	$0.00367841\pi$
$282$		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	$-0.458293\pi$
$293$	4.47285			0.261307			0.130653	+	0.991428i	$0.458293\pi$
$294$		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	$-0.957215\pi$
$311$	−2.75607	−	12.0751i	−0.156282	−	0.684717i	0.834698	−	0.550708i	$-0.185642\pi$
$312$		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	0.504494	−	0.863415i	$-0.331679\pi$
$317$	10.4050	+	2.37488i	0.584406	+	0.133387i	0.0799117	+	0.996802i	$0.474536\pi$
$318$		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	0.113097	−	0.993584i	$-0.463923\pi$
$347$	−4.02560	−	0.918818i	−0.216106	−	0.0493247i	−0.329203	+	0.944259i	$0.606780\pi$
$348$		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	$-0.932622\pi$
$353$	−32.9080	−	15.8477i	−1.75152	−	0.843485i	−0.773835	−	0.633387i	$-0.781664\pi$
$354$		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	−0.653616	−	0.756826i	$-0.726749\pi$
$359$	6.54851	−	13.5981i	0.345617	−	0.717681i	0.999234	+	0.0391446i	$0.0124633\pi$
$360$		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	−0.713555	−	0.700599i	$-0.752916\pi$
$383$	2.51010	−	3.14756i	0.128260	−	0.160833i	0.841815	+	0.539766i	$0.181487\pi$
$384$		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	$0.220558\pi$
$389$	15.5635	+	32.3178i	0.789098	+	1.63858i	0.0197035	+	0.999806i	$0.493728\pi$
$390$		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	0.240487	−	0.970652i	$-0.422693\pi$
$401$	−13.0626	−	10.4171i	−0.652316	−	0.520205i	−0.892803	+	0.450448i	$0.851264\pi$
$402$		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	−0.996788	−	0.0800903i	$-0.974479\pi$
$419$	−1.30929	+	5.73638i	−0.0639631	+	0.280241i	0.932824	+	0.360331i	$0.117336\pi$
$420$		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	−0.868706	−	0.495328i	$-0.835048\pi$
$431$	1.24950	−	2.59462i	0.0601865	−	0.124978i	0.928892	+	0.370350i	$0.120762\pi$
$432$		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	−0.575426	−	0.817854i	$-0.695164\pi$
$443$	1.97589	−	1.57572i	0.0938774	−	0.0748647i	0.669304	+	0.742989i	$0.266592\pi$
$444$		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	$0.0207158\pi$
$449$	9.03863	+	18.7689i	0.426559	+	0.885759i	−0.571324	+	0.820725i	$0.693570\pi$
$450$		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	0.987395	−	0.158273i	$-0.0505926\pi$
$461$	0.625035	+	2.73846i	0.0291108	+	0.127543i	−0.958285	+	0.285816i	$0.907735\pi$
$462$		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	$-0.590111\pi$
$467$	8.40531	−	36.8261i	0.388951	−	1.70411i	0.668278	−	0.743911i	$-0.267031\pi$
$468$		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	$0.000476991\pi$
$479$	17.0479	+	21.3774i	0.778939	+	0.976759i	−0.221060	+	0.975260i	$0.570952\pi$
$480$		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	$0.179921\pi$
$491$			23.7370i			1.07124i	−0.844460	+	0.535618i	$0.820079\pi$
$492$		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	0.982454	−	0.186503i	$-0.0597153\pi$
$503$	13.0531	+	16.3681i	0.582011	+	0.729819i	−0.400443	+	0.916321i	$0.631144\pi$
$504$		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	$-0.440578\pi$
$509$	8.37447			0.371192			0.185596	+	0.982626i	$0.440578\pi$
$510$		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	$-0.603334\pi$
$521$	−14.5608			−0.637921			−0.318960	+	0.947768i	$0.603334\pi$
$522$		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	$0.206924\pi$
$557$			28.5685i			1.21048i	−0.796041	+	0.605242i	$0.793076\pi$
$558$		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	$0.481885\pi$
$563$	−22.0460	+	27.6448i	−0.929128	+	1.16509i	−0.986006	+	0.166709i	$0.946686\pi$
$564$		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	$-0.879277\pi$
$569$		−	17.6630i		−	0.740472i	0.928938	−	0.370236i	$-0.120723\pi$
$570$		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	$-0.429716\pi$
$587$	10.6126			0.438027			0.219014	+	0.975722i	$0.429716\pi$
$588$		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	−0.742869	−	0.669437i	$-0.766535\pi$
$593$	−16.6237	+	8.00554i	−0.682652	+	0.328748i	0.0602163	+	0.998185i	$0.480821\pi$
$594$		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	0.170024	−	0.985440i	$-0.445615\pi$
$599$	28.6007	−	22.8083i	1.16859	−	0.931920i	0.998567	+	0.0535196i	$0.0170440\pi$
$600$		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	−0.0488161	−	0.998808i	$-0.515545\pi$
$617$	8.45955	−	1.93084i	0.340569	−	0.0777326i	0.389385	+	0.921075i	$0.372688\pi$
$618$		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	−0.278143	−	0.960540i	$-0.589719\pi$
$641$	−23.9383	−	5.46375i	−0.945504	−	0.215805i	−0.667361	+	0.744734i	$0.732576\pi$
$642$		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	−0.347503	−	0.937679i	$-0.612970\pi$
$647$	−32.9977	−	15.8909i	−1.29727	−	0.624734i	−0.949771	+	0.312945i	$0.898685\pi$
$648$		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	$0.342326\pi$
$653$	−13.0041	+	27.0033i	−0.508889	+	1.05672i	−0.984226	+	0.176915i	$0.943388\pi$
$654$		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	−0.582823	−	0.812599i	$-0.698052\pi$
$659$	−37.4925	−	8.55743i	−1.46050	−	0.333350i	−0.877679	+	0.479249i	$0.840909\pi$
$660$		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	$-0.427360\pi$
$677$	29.2857	−	36.7231i	1.12554	−	1.41138i	0.899312	−	0.437308i	$-0.144068\pi$
$678$		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	0.691187	−	0.722676i	$-0.257088\pi$
$683$	−7.96499	−	16.5395i	−0.304772	−	0.632865i	−0.995959	+	0.0898106i	$0.971374\pi$
$684$		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	0.922383	−	0.386275i	$-0.126239\pi$
$701$	19.8849	+	15.8577i	0.751042	+	0.598936i	−0.171341	+	0.985212i	$0.554810\pi$
$702$		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	−0.545876	−	0.837866i	$-0.683803\pi$
$719$	−41.3285	−	19.9028i	−1.54129	−	0.742248i	−0.995418	+	0.0956182i	$0.969517\pi$
$720$		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	0.981111	−	0.193444i	$-0.0619658\pi$
$743$	5.94655	+	12.3481i	0.218158	+	0.453009i	−0.762954	+	0.646453i	$0.776251\pi$
$744$		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	−0.914668	−	0.404205i	$-0.867548\pi$
$761$	2.33924	−	10.2489i	0.0847974	−	0.371522i	0.999466	+	0.0326835i	$0.0104053\pi$
$762$		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	$-0.940353\pi$
$773$	−26.2873	−	32.9633i	−0.945490	−	1.18561i	0.0370050	−	0.999315i	$-0.488218\pi$
$774$		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	0.878642	−	0.477481i	$-0.158450\pi$
$797$	6.14356	+	7.70378i	0.217616	+	0.272882i	−0.661026	+	0.750363i	$0.729879\pi$
$798$		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	0.470827	−	0.882225i	$-0.343956\pi$
$809$	−8.09230	−	6.45339i	−0.284510	−	0.226889i	−0.755337	+	0.655336i	$0.772527\pi$
$810$		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	−0.766653	−	0.642062i	$-0.778079\pi$
$821$	−33.7764	+	7.70923i	−1.17880	+	0.269054i	−0.412150	+	0.911116i	$0.635222\pi$
$822$		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	−0.961543	−	0.274656i	$-0.911436\pi$
$827$	−4.23589	+	8.79591i	−0.147296	+	0.305864i	0.814246	+	0.580519i	$0.197150\pi$
$828$		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	0.508902	−	0.860824i	$-0.330051\pi$
$839$	4.43688	+	2.13669i	0.153178	+	0.0737667i	−0.355724	+	0.934591i	$0.615766\pi$
$840$		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	−0.784298	−	0.620385i	$-0.786977\pi$
$857$	−0.144754	+	0.181516i	−0.00494472	+	0.00620048i	0.779353	+	0.626585i	$0.215548\pi$
$858$		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	$-0.945871\pi$
$863$		−	9.94315i		−	0.338469i	0.985576	−	0.169234i	$-0.0541295\pi$
$864$		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	$-0.417119\pi$
$881$	15.2829			0.514893			0.257447	+	0.966293i	$0.417119\pi$
$882$		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	−0.406782	−	0.913525i	$-0.633349\pi$
$887$	1.60281	−	0.771874i	0.0538172	−	0.0259170i	0.460599	+	0.887608i	$0.347635\pi$
$888$		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	−0.905100	−	0.425199i	$-0.860204\pi$
$911$	−46.3632	+	10.5821i	−1.53608	+	0.350600i	−0.630980	+	0.775799i	$0.717347\pi$
$912$		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	0.906447	−	0.422319i	$-0.138784\pi$
$929$	8.93091	+	11.1990i	0.293014	+	0.367428i	−0.613434	+	0.789746i	$0.710212\pi$
$930$		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	0.669420	−	0.742884i	$-0.266543\pi$
$941$	15.5215	+	7.47476i	0.505987	+	0.243670i	−0.163434	+	0.986554i	$0.552257\pi$
$942$		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	−0.867528	−	0.497388i	$-0.834293\pi$
$947$	1.91534	−	3.97725i	0.0622403	−	0.129243i	0.929769	+	0.368145i	$0.120007\pi$
$948$		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	0.837847	−	0.545906i	$-0.183814\pi$
$953$	41.8564	+	9.55344i	1.35586	+	0.309466i	0.518014	+	0.855372i	$0.326671\pi$
$954$		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	−0.975419	−	0.220359i	$-0.929277\pi$
$971$	−16.9370	+	21.2383i	−0.543534	+	0.681570i	0.431885	+	0.901929i	$0.357849\pi$
$972$		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	$0.133143\pi$
$977$	20.6804	+	42.9432i	0.661624	+	1.37388i	−0.252164	+	0.967684i	$0.581142\pi$
$978$		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	−0.768633	−	0.639690i	$-0.779063\pi$
$983$	−23.4437	+	11.2899i	−0.747739	+	0.360092i	0.0208947	+	0.999782i	$0.493349\pi$
$984$		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.188.9	✓	120
3.2	odd	2	inner	441.2.w.a.188.12	yes	120
49.6	odd	14	inner	441.2.w.a.251.12	yes	120
147.104	even	14	inner	441.2.w.a.251.9	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.w.a.188.9	✓	120	1.1	even	1	trivial
441.2.w.a.188.12	yes	120	3.2	odd	2	inner
441.2.w.a.251.9	yes	120	147.104	even	14	inner
441.2.w.a.251.12	yes	120	49.6	odd	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 $\F_{q}$

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

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

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