LMFDB - Embedded newform 441.2.bg.a.26.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(17,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 25]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("441.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bg (of order $42$, degree $12$, 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:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			26.8
Character	$\chi$	$=$	441.26
Dual form			441.2.bg.a.17.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.601956 - 0.0451104i) q^{2} +(-1.61735 - 0.243776i) q^{4} +(-1.12371 - 1.04265i) q^{5} +(-0.186554 + 2.63917i) q^{7} +(2.13959 + 0.488348i) q^{8} +O(q^{10})$	\(q+(-0.601956 - 0.0451104i) q^{2} +(-1.61735 - 0.243776i) q^{4} +(-1.12371 - 1.04265i) q^{5} +(-0.186554 + 2.63917i) q^{7} +(2.13959 + 0.488348i) q^{8} +(0.629389 + 0.678320i) q^{10} +(0.794667 - 1.16556i) q^{11} +(0.574735 + 1.19345i) q^{13} +(0.231351 - 1.58025i) q^{14} +(1.85999 + 0.573730i) q^{16} +(2.32250 - 5.91762i) q^{17} +(3.74233 + 2.16064i) q^{19} +(1.56325 + 1.96026i) q^{20} +(-0.530933 + 0.665769i) q^{22} +(2.23055 - 0.875428i) q^{23} +(-0.198047 - 2.64275i) q^{25} +(-0.292128 - 0.744331i) q^{26} +(0.945087 - 4.22297i) q^{28} +(5.49332 - 4.38078i) q^{29} +(1.56080 - 0.901126i) q^{31} +(-5.17957 - 2.03283i) q^{32} +(-1.66499 + 3.45738i) q^{34} +(2.96136 - 2.77115i) q^{35} +(8.91545 - 1.34379i) q^{37} +(-2.15525 - 1.46942i) q^{38} +(-1.89510 - 2.77961i) q^{40} +(-1.88456 + 8.25681i) q^{41} +(1.93041 + 8.45767i) q^{43} +(-1.56939 + 1.69140i) q^{44} +(-1.38219 + 0.426348i) q^{46} +(-0.0438619 + 0.585297i) q^{47} +(-6.93040 - 0.984693i) q^{49} +1.59975i q^{50} +(-0.638612 - 2.07033i) q^{52} +(-0.517738 + 3.43497i) q^{53} +(-2.10825 + 0.481194i) q^{55} +(-1.68798 + 5.55564i) q^{56} +(-3.50435 + 2.38923i) q^{58} +(2.80416 - 2.60188i) q^{59} +(-0.728803 - 4.83529i) q^{61} +(-0.980180 + 0.472030i) q^{62} +(-0.481233 - 0.231750i) q^{64} +(0.598515 - 1.94034i) q^{65} +(-3.31539 - 5.74243i) q^{67} +(-5.19885 + 9.00467i) q^{68} +(-1.90761 + 1.53452i) q^{70} +(3.54100 + 2.82385i) q^{71} +(10.3796 - 0.777843i) q^{73} +(-5.42733 + 0.406722i) q^{74} +(-5.52593 - 4.40678i) q^{76} +(2.92786 + 2.31470i) q^{77} +(1.25290 - 2.17009i) q^{79} +(-1.49188 - 2.58402i) q^{80} +(1.50689 - 4.88522i) q^{82} +(10.1383 + 4.88235i) q^{83} +(-8.77982 + 4.22814i) q^{85} +(-0.780492 - 5.17822i) q^{86} +(2.26946 - 2.10575i) q^{88} +(-11.4610 + 7.81400i) q^{89} +(-3.25693 + 1.29418i) q^{91} +(-3.82099 + 0.872115i) q^{92} +(0.0528059 - 0.350344i) q^{94} +(-1.95251 - 6.32987i) q^{95} -15.6296i q^{97} +(4.12737 + 0.905375i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) $ 216 * q - 16 * q^4 + 2 * q^7	$ 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) $ 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{17}{42}\right)$	$-1$

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 $

$2$	−0.601956	−	0.0451104i	−0.425647	−	0.0318978i	−0.139815	−	0.990178i	$-0.544651\pi$
$2$	−0.601956	−	0.0451104i	−0.425647	−	0.0318978i	−0.285832	+	0.958280i	$0.592270\pi$
$3$		0			0
$3$		0			0
$4$	−1.61735	−	0.243776i	−0.808673	−	0.121888i
$5$	−1.12371	−	1.04265i	−0.502538	−	0.466287i	0.387698	−	0.921786i	$-0.373270\pi$
$5$	−1.12371	−	1.04265i	−0.502538	−	0.466287i	−0.890236	+	0.455499i	$0.849461\pi$
$6$		0			0
$7$	−0.186554	+	2.63917i	−0.0705107	+	0.997511i
$7$	−0.186554	+	2.63917i	−0.0705107	+	0.997511i
$8$	2.13959	+	0.488348i	0.756460	+	0.172657i
$9$		0			0
$10$	0.629389	+	0.678320i	0.199030	+	0.214504i
$11$	0.794667	−	1.16556i	0.239601	−	0.351430i	−0.687538	−	0.726149i	$-0.741308\pi$
$11$	0.794667	−	1.16556i	0.239601	−	0.351430i	0.927139	+	0.374719i	$0.122261\pi$
$12$		0			0
$13$	0.574735	+	1.19345i	0.159403	+	0.331003i	0.965339	−	0.260999i	$-0.0840519\pi$
$13$	0.574735	+	1.19345i	0.159403	+	0.331003i	−0.805936	+	0.592002i	$0.798338\pi$
$14$	0.231351	−	1.58025i	0.0618311	−	0.422339i
$15$		0			0
$16$	1.85999	+	0.573730i	0.464997	+	0.143432i
$17$	2.32250	−	5.91762i	0.563288	−	1.43523i	−0.311274	−	0.950320i	$-0.600756\pi$
$17$	2.32250	−	5.91762i	0.563288	−	1.43523i	0.874562	−	0.484914i	$-0.161149\pi$
$18$		0			0
$19$	3.74233	+	2.16064i	0.858549	+	0.495684i	0.863526	−	0.504304i	$-0.168251\pi$
$19$	3.74233	+	2.16064i	0.858549	+	0.495684i	−0.00497684	+	0.999988i	$0.501584\pi$
$20$	1.56325	+	1.96026i	0.349554	+	0.438327i
$21$		0			0
$22$	−0.530933	+	0.665769i	−0.113195	+	0.141942i
$23$	2.23055	−	0.875428i	0.465103	−	0.182539i	−0.121205	−	0.992627i	$-0.538676\pi$
$23$	2.23055	−	0.875428i	0.465103	−	0.182539i	0.586308	+	0.810088i	$0.300581\pi$
$24$		0			0
$25$	−0.198047	−	2.64275i	−0.0396093	−	0.528550i
$26$	−0.292128	−	0.744331i	−0.0572911	−	0.145975i
$27$		0			0
$28$	0.945087	−	4.22297i	0.178605	−	0.798066i
$29$	5.49332	−	4.38078i	1.02008	−	0.813490i	0.0374977	−	0.999297i	$-0.488061\pi$
$29$	5.49332	−	4.38078i	1.02008	−	0.813490i	0.982586	+	0.185807i	$0.0594899\pi$
$30$		0			0
$31$	1.56080	−	0.901126i	0.280327	−	0.161847i	−0.353244	−	0.935531i	$-0.614922\pi$
$31$	1.56080	−	0.901126i	0.280327	−	0.161847i	0.633571	+	0.773684i	$0.281588\pi$
$32$	−5.17957	−	2.03283i	−0.915627	−	0.359357i
$33$		0			0
$34$	−1.66499	+	3.45738i	−0.285543	+	0.592936i
$35$	2.96136	−	2.77115i	0.500561	−	0.468409i
$36$		0			0
$37$	8.91545	−	1.34379i	1.46569	−	0.220917i	0.632783	−	0.774329i	$-0.281912\pi$
$37$	8.91545	−	1.34379i	1.46569	−	0.220917i	0.832908	+	0.553412i	$0.186674\pi$
$38$	−2.15525	−	1.46942i	−0.349628	−	0.238372i
$39$		0			0
$40$	−1.89510	−	2.77961i	−0.299642	−	0.439494i
$41$	−1.88456	+	8.25681i	−0.294319	+	1.28950i	0.584129	+	0.811661i	$0.301436\pi$
$41$	−1.88456	+	8.25681i	−0.294319	+	1.28950i	−0.878449	+	0.477837i	$0.841421\pi$
$42$		0			0
$43$	1.93041	+	8.45767i	0.294384	+	1.28978i	0.878356	+	0.478008i	$0.158641\pi$
$43$	1.93041	+	8.45767i	0.294384	+	1.28978i	−0.583971	+	0.811774i	$0.698502\pi$
$44$	−1.56939	+	1.69140i	−0.236594	+	0.254988i
$45$		0			0
$46$	−1.38219	+	0.426348i	−0.203792	+	0.0628616i
$47$	−0.0438619	+	0.585297i	−0.00639792	+	0.0853743i	−0.999489	−	0.0319744i	$-0.989820\pi$
$47$	−0.0438619	+	0.585297i	−0.00639792	+	0.0853743i	0.993091	+	0.117349i	$0.0374395\pi$
$48$		0			0
$49$	−6.93040	−	0.984693i	−0.990056	−	0.140670i
$50$			1.59975i			0.226239i
$51$		0			0
$52$	−0.638612	−	2.07033i	−0.0885595	−	0.287103i
$53$	−0.517738	+	3.43497i	−0.0711168	+	0.471829i	0.924718	+	0.380653i	$0.124301\pi$
$53$	−0.517738	+	3.43497i	−0.0711168	+	0.471829i	−0.995835	+	0.0911763i	$0.970937\pi$
$54$		0			0
$55$	−2.10825	+	0.481194i	−0.284276	+	0.0648841i
$56$	−1.68798	+	5.55564i	−0.225566	+	0.742403i
$57$		0			0
$58$	−3.50435	+	2.38923i	−0.460144	+	0.313721i
$59$	2.80416	−	2.60188i	0.365071	−	0.338737i	−0.476213	−	0.879330i	$-0.657991\pi$
$59$	2.80416	−	2.60188i	0.365071	−	0.338737i	0.841284	+	0.540594i	$0.181800\pi$
$60$		0			0
$61$	−0.728803	−	4.83529i	−0.0933137	−	0.619096i	−0.985788	−	0.167997i	$-0.946270\pi$
$61$	−0.728803	−	4.83529i	−0.0933137	−	0.619096i	0.892474	−	0.451099i	$-0.148968\pi$
$62$	−0.980180	+	0.472030i	−0.124483	+	0.0599478i
$63$		0			0
$64$	−0.481233	−	0.231750i	−0.0601542	−	0.0289687i
$65$	0.598515	−	1.94034i	0.0742367	−	0.240669i
$66$		0			0
$67$	−3.31539	−	5.74243i	−0.405040	−	0.701549i	0.589286	−	0.807924i	$-0.299409\pi$
$67$	−3.31539	−	5.74243i	−0.405040	−	0.701549i	−0.994326	+	0.106375i	$0.966076\pi$
$68$	−5.19885	+	9.00467i	−0.630453	+	1.09198i
$69$		0			0
$70$	−1.90761	+	1.53452i	−0.228004	+	0.183410i
$71$	3.54100	+	2.82385i	0.420239	+	0.335130i	0.810671	−	0.585502i	$-0.199103\pi$
$71$	3.54100	+	2.82385i	0.420239	+	0.335130i	−0.390431	+	0.920632i	$0.627674\pi$
$72$		0			0
$73$	10.3796	−	0.777843i	1.21484	−	0.0910397i	0.548153	−	0.836378i	$-0.315331\pi$
$73$	10.3796	−	0.777843i	1.21484	−	0.0910397i	0.666687	+	0.745338i	$0.267712\pi$
$74$	−5.42733	+	0.406722i	−0.630914	+	0.0472805i
$75$		0			0
$76$	−5.52593	−	4.40678i	−0.633868	−	0.505493i
$77$	2.92786	+	2.31470i	0.333661	+	0.263784i
$78$		0			0
$79$	1.25290	−	2.17009i	0.140963	−	0.244154i	−0.786897	−	0.617085i	$-0.788314\pi$
$79$	1.25290	−	2.17009i	0.140963	−	0.244154i	0.927859	+	0.372930i	$0.121647\pi$
$80$	−1.49188	−	2.58402i	−0.166798	−	0.288902i
$81$		0			0
$82$	1.50689	−	4.88522i	0.166408	−	0.539483i
$83$	10.1383	+	4.88235i	1.11282	+	0.535908i	0.897668	−	0.440672i	$-0.145260\pi$
$83$	10.1383	+	4.88235i	1.11282	+	0.535908i	0.215156	+	0.976580i	$0.430974\pi$
$84$		0			0
$85$	−8.77982	+	4.22814i	−0.952305	+	0.458606i
$86$	−0.780492	−	5.17822i	−0.0841626	−	0.558382i
$87$		0			0
$88$	2.26946	−	2.10575i	0.241926	−	0.224474i
$89$	−11.4610	+	7.81400i	−1.21487	+	0.828282i	−0.989293	−	0.145944i	$-0.953378\pi$
$89$	−11.4610	+	7.81400i	−1.21487	+	0.828282i	−0.225574	+	0.974226i	$0.572426\pi$
$90$		0			0
$91$	−3.25693	+	1.29418i	−0.341419	+	0.135667i
$92$	−3.82099	+	0.872115i	−0.398365	+	0.0909243i
$93$		0			0
$94$	0.0528059	−	0.350344i	0.00544651	−	0.0361353i
$95$	−1.95251	−	6.32987i	−0.200323	−	0.649431i
$96$		0			0
$97$		−	15.6296i		−	1.58694i	−0.608607	−	0.793472i	$-0.708271\pi$
$97$		−	15.6296i		−	1.58694i	0.608607	−	0.793472i	$-0.291729\pi$
$98$	4.12737	+	0.905375i	0.416928	+	0.0914566i
$99$		0			0
$100$	−0.323928	+	4.32252i	−0.0323928	+	0.432252i
$101$	−11.4089	+	3.51918i	−1.13523	+	0.350172i	−0.804733	−	0.593636i	$-0.797692\pi$
$101$	−11.4089	+	3.51918i	−1.13523	+	0.350172i	−0.330495	+	0.943808i	$0.607216\pi$
$102$		0			0
$103$	−5.23533	+	5.64234i	−0.515852	+	0.555956i	−0.936228	−	0.351394i	$-0.885708\pi$
$103$	−5.23533	+	5.64234i	−0.515852	+	0.555956i	0.420376	+	0.907350i	$0.361898\pi$
$104$	0.646880	+	2.83417i	0.0634318	+	0.277913i
$105$		0			0
$106$	0.466608	−	2.04434i	0.0453210	−	0.198564i
$107$	−8.82674	−	12.9465i	−0.853313	−	1.25158i	−0.966154	−	0.257968i	$-0.916947\pi$
$107$	−8.82674	−	12.9465i	−0.853313	−	1.25158i	0.112840	−	0.993613i	$-0.464005\pi$
$108$		0			0
$109$	−0.526899	−	0.359234i	−0.0504678	−	0.0344084i	0.537823	−	0.843058i	$-0.319247\pi$
$109$	−0.526899	−	0.359234i	−0.0504678	−	0.0344084i	−0.588291	+	0.808649i	$0.700199\pi$
$110$	1.29078	−	0.194554i	0.123071	−	0.0185500i
$111$		0			0
$112$	−1.86116	+	4.80178i	−0.175863	+	0.453726i
$113$	4.60166	−	9.55545i	0.432888	−	0.898901i	−0.564414	−	0.825492i	$-0.690898\pi$
$113$	4.60166	−	9.55545i	0.432888	−	0.898901i	0.997302	−	0.0734093i	$-0.0233879\pi$
$114$		0			0
$115$	−3.41926	−	1.34196i	−0.318848	−	0.125139i
$116$	−9.95252	+	5.74609i	−0.924069	+	0.533511i
$117$		0			0
$118$	−1.80536	+	1.43972i	−0.166196	+	0.132537i
$119$	15.1843	+	7.23341i	1.39194	+	0.663085i
$120$		0			0
$121$	3.29171	+	8.38714i	0.299247	+	0.762468i
$122$	0.220586	+	2.94351i	0.0199709	+	0.266493i
$123$		0			0
$124$	−2.74402	+	1.07695i	−0.246420	+	0.0967128i
$125$	−7.31171	+	9.16860i	−0.653979	+	0.820064i
$126$		0			0
$127$	12.5450	+	15.7310i	1.11319	+	1.39590i	0.908912	+	0.416987i	$0.136914\pi$
$127$	12.5450	+	15.7310i	1.11319	+	1.39590i	0.204280	+	0.978912i	$0.434515\pi$
$128$	9.91671	+	5.72541i	0.876521	+	0.506060i
$129$		0			0
$130$	−0.447809	+	1.14100i	−0.0392755	+	0.100072i
$131$	−14.2714	−	4.40215i	−1.24690	−	0.384617i	−0.400071	−	0.916484i	$-0.631014\pi$
$131$	−14.2714	−	4.40215i	−1.24690	−	0.384617i	−0.846828	+	0.531867i	$0.821491\pi$
$132$		0			0
$133$	−6.40042	+	9.47356i	−0.554987	+	0.821461i
$134$	1.73668	+	3.60625i	0.150026	+	0.311532i
$135$		0			0
$136$	7.85905	−	11.5271i	0.673908	−	0.988442i
$137$	−7.23328	−	7.79562i	−0.617981	−	0.666025i	0.344054	−	0.938950i	$-0.388200\pi$
$137$	−7.23328	−	7.79562i	−0.617981	−	0.666025i	−0.962035	+	0.272925i	$0.912009\pi$
$138$		0			0
$139$	−6.94388	−	1.58489i	−0.588972	−	0.134429i	−0.0823592	−	0.996603i	$-0.526245\pi$
$139$	−6.94388	−	1.58489i	−0.588972	−	0.134429i	−0.506613	+	0.862174i	$0.669103\pi$
$140$	−5.46508	+	3.75999i	−0.461883	+	0.317777i
$141$		0			0
$142$	−2.00414	−	1.85957i	−0.168184	−	0.156052i
$143$	1.84776	+	0.278505i	0.154518	+	0.0232898i
$144$		0			0
$145$	−10.7405	−	0.804890i	−0.891951	−	0.0668425i
$146$	−6.28315			−0.519997
$147$		0			0
$148$	−14.7469			−1.21219
$149$	16.4812	+	1.23509i	1.35019	+	0.101183i	0.730096	−	0.683345i	$-0.239476\pi$
$149$	16.4812	+	1.23509i	1.35019	+	0.101183i	0.620094	+	0.784528i	$0.287095\pi$
$150$		0			0
$151$	17.8626	+	2.69236i	1.45364	+	0.219101i	0.827876	−	0.560911i	$-0.189549\pi$
$151$	17.8626	+	2.69236i	1.45364	+	0.219101i	0.625765	+	0.780012i	$0.284787\pi$
$152$	6.95192	+	6.45044i	0.563875	+	0.523200i
$153$		0			0
$154$	−1.65803	−	1.52542i	−0.133608	−	0.122922i
$155$	−2.69344	−	0.614760i	−0.216342	−	0.0493787i
$156$		0			0
$157$	−9.45839	−	10.1937i	−0.754862	−	0.813547i	0.232405	−	0.972619i	$-0.425340\pi$
$157$	−9.45839	−	10.1937i	−0.754862	−	0.813547i	−0.987267	+	0.159072i	$0.949150\pi$
$158$	−0.852086	+	1.24978i	−0.0677883	+	0.0994272i
$159$		0			0
$160$	3.70080	+	7.68479i	0.292574	+	0.607536i
$161$	1.89428	+	6.05012i	0.149290	+	0.476816i
$162$		0			0
$163$	6.72659	+	2.07488i	0.526867	+	0.162517i	0.546767	−	0.837285i	$-0.315858\pi$
$163$	6.72659	+	2.07488i	0.526867	+	0.162517i	−0.0198995	+	0.999802i	$0.506335\pi$
$164$	5.06080	−	12.8947i	0.395182	−	1.00691i
$165$		0			0
$166$	−5.88257	−	3.39630i	−0.456576	−	0.263604i
$167$	−0.809859	−	1.01553i	−0.0626688	−	0.0785842i	0.749509	−	0.661994i	$-0.230290\pi$
$167$	−0.809859	−	1.01553i	−0.0626688	−	0.0785842i	−0.812178	+	0.583410i	$0.801718\pi$
$168$		0			0
$169$	7.01137	−	8.79197i	0.539336	−	0.676306i
$170$	5.47580	−	2.14909i	0.419974	−	0.164828i
$171$		0			0
$172$	−1.06036	−	14.1496i	−0.0808519	−	1.07889i
$173$	0.761818	+	1.94108i	0.0579200	+	0.147578i	0.956905	−	0.290403i	$-0.0937892\pi$
$173$	0.761818	+	1.94108i	0.0579200	+	0.147578i	−0.898985	+	0.437980i	$0.855694\pi$
$174$		0			0
$175$	7.01160	−	0.0296629i	0.530027	−	0.00224230i
$176$	2.14679	−	1.71201i	0.161820	−	0.129047i
$177$		0			0
$178$	7.25152	−	4.18667i	0.543525	−	0.313804i
$179$	−4.95577	−	1.94500i	−0.370412	−	0.145376i	0.172831	−	0.984951i	$-0.444709\pi$
$179$	−4.95577	−	1.94500i	−0.370412	−	0.145376i	−0.543243	+	0.839575i	$0.682804\pi$
$180$		0			0
$181$	−3.34891	+	6.95407i	−0.248922	+	0.516892i	−0.987566	−	0.157203i	$-0.949752\pi$
$181$	−3.34891	+	6.95407i	−0.248922	+	0.516892i	0.738644	+	0.674096i	$0.235466\pi$
$182$	2.01891	−	0.632117i	0.149652	−	0.0468556i
$183$		0			0
$184$	5.19999	−	0.783773i	0.383348	−	0.0577805i
$185$	−11.4195	−	7.78567i	−0.839577	−	0.572414i
$186$		0			0
$187$	−5.05175	−	7.40955i	−0.369420	−	0.541840i
$188$	0.213621	−	0.935935i	0.0155799	−	0.0682601i
$189$		0			0
$190$	0.889779	+	3.89838i	0.0645514	+	0.282818i
$191$	8.01667	−	8.63992i	0.580066	−	0.625163i	−0.373034	−	0.927818i	$-0.621683\pi$
$191$	8.01667	−	8.63992i	0.580066	−	0.625163i	0.953100	+	0.302655i	$0.0978730\pi$
$192$		0			0
$193$	−3.44997	+	1.06417i	−0.248334	+	0.0766009i	−0.416423	−	0.909171i	$-0.636717\pi$
$193$	−3.44997	+	1.06417i	−0.248334	+	0.0766009i	0.168089	+	0.985772i	$0.446240\pi$
$194$	−0.705056	+	9.40832i	−0.0506201	+	0.675478i
$195$		0			0
$196$	10.9688	+	3.28205i	0.783486	+	0.234432i
$197$		−	3.33632i		−	0.237703i	−0.992912	−	0.118851i	$-0.962079\pi$
$197$		−	3.33632i		−	0.237703i	0.992912	−	0.118851i	$-0.0379212\pi$
$198$		0			0
$199$	1.40174	+	4.54433i	0.0993668	+	0.322139i	0.991584	−	0.129468i	$-0.0413270\pi$
$199$	1.40174	+	4.54433i	0.0993668	+	0.322139i	−0.892217	+	0.451607i	$0.850851\pi$
$200$	0.866842	−	5.75112i	0.0612950	−	0.406665i
$201$		0			0
$202$	7.02641	−	1.60373i	0.494376	−	0.112838i
$203$	10.5368	+	15.3150i	0.739538	+	1.07490i
$204$		0			0
$205$	10.7267	−	7.31332i	0.749183	−	0.510784i
$206$	3.40596	−	3.16027i	0.237305	−	0.220187i
$207$		0			0
$208$	0.384282	+	2.54954i	0.0266452	+	0.176779i
$209$	5.49226	−	2.64493i	0.379908	−	0.182954i
$210$		0			0
$211$	4.51692	+	2.17523i	0.310957	+	0.149749i	0.582853	−	0.812578i	$-0.301936\pi$
$211$	4.51692	+	2.17523i	0.310957	+	0.149749i	−0.271896	+	0.962327i	$0.587651\pi$
$212$	1.67472	−	5.42932i	0.115021	−	0.372887i
$213$		0			0
$214$	4.72929	+	8.19137i	0.323288	+	0.559951i
$215$	6.64917	−	11.5167i	0.453470	−	0.785432i
$216$		0			0
$217$	2.08705	+	4.28731i	0.141678	+	0.291041i
$218$	0.300965	+	0.240012i	0.0203839	+	0.0162556i
$219$		0			0
$220$	3.52707	−	0.264317i	0.237795	−	0.0178203i
$221$	8.39721	−	0.629284i	0.564857	−	0.0423302i
$222$		0			0
$223$	−6.85899	−	5.46987i	−0.459312	−	0.366289i	0.366328	−	0.930486i	$-0.380615\pi$
$223$	−6.85899	−	5.46987i	−0.459312	−	0.366289i	−0.825641	+	0.564196i	$0.809186\pi$
$224$	6.33125	−	13.2905i	0.423024	−	0.888010i
$225$		0			0
$226$	−3.20105	+	5.54438i	−0.212931	+	0.368806i
$227$	−8.47617	−	14.6812i	−0.562583	−	0.974423i	−0.997270	−	0.0738409i	$-0.976474\pi$
$227$	−8.47617	−	14.6812i	−0.562583	−	0.974423i	0.434687	−	0.900582i	$-0.356859\pi$
$228$		0			0
$229$	−2.58436	+	8.37830i	−0.170780	+	0.553654i	−0.999986	−	0.00528863i	$-0.998317\pi$
$229$	−2.58436	+	8.37830i	−0.170780	+	0.553654i	0.829206	+	0.558943i	$0.188793\pi$
$230$	1.99771	+	0.962045i	0.131725	+	0.0634354i
$231$		0			0
$232$	13.8928	−	6.69042i	0.912108	−	0.439248i
$233$	−2.06740	−	13.7163i	−0.135440	−	0.898585i	−0.948585	−	0.316523i	$-0.897484\pi$
$233$	−2.06740	−	13.7163i	−0.135440	−	0.898585i	0.813145	−	0.582061i	$-0.197754\pi$
$234$		0			0
$235$	0.659548	−	0.611971i	0.0430242	−	0.0399206i
$236$	−5.16958	+	3.52456i	−0.336511	+	0.229429i
$237$		0			0
$238$	−8.81399	−	5.03916i	−0.571326	−	0.326640i
$239$	21.5670	−	4.92253i	1.39505	−	0.318412i	0.542063	−	0.840338i	$-0.317643\pi$
$239$	21.5670	−	4.92253i	1.39505	−	0.318412i	0.852991	+	0.521925i	$0.174786\pi$
$240$		0			0
$241$	−3.06433	+	20.3305i	−0.197391	+	1.30960i	0.642264	+	0.766484i	$0.277995\pi$
$241$	−3.06433	+	20.3305i	−0.197391	+	1.30960i	−0.839655	+	0.543120i	$0.817243\pi$
$242$	−1.60312	−	5.19718i	−0.103052	−	0.334087i
$243$		0			0
$244$			7.99800i			0.512020i
$245$	6.76106	+	8.33249i	0.431948	+	0.532343i
$246$		0			0
$247$	−0.427761	+	5.70808i	−0.0272178	+	0.363196i
$248$	3.77953	−	1.16583i	0.240000	−	0.0740303i
$249$		0			0
$250$	4.81493	−	5.18926i	0.304523	−	0.328197i
$251$	0.638694	+	2.79830i	0.0403140	+	0.176627i	0.991077	−	0.133293i	$-0.0425550\pi$
$251$	0.638694	+	2.79830i	0.0403140	+	0.176627i	−0.950763	+	0.309920i	$0.899698\pi$
$252$		0			0
$253$	0.752182	−	3.29552i	0.0472893	−	0.207188i
$254$	−6.84193	−	10.0353i	−0.429301	−	0.629669i
$255$		0			0
$256$	−4.82851	−	3.29202i	−0.301782	−	0.205751i
$257$	−7.97753	+	1.20242i	−0.497625	+	0.0750049i	−0.393059	−	0.919513i	$-0.628583\pi$
$257$	−7.97753	+	1.20242i	−0.497625	+	0.0750049i	−0.104566	+	0.994518i	$0.533345\pi$
$258$		0			0
$259$	1.88327	+	23.7800i	0.117021	+	1.47762i
$260$	−1.44101	+	2.99230i	−0.0893679	+	0.185574i
$261$		0			0
$262$	8.39218	+	3.29369i	0.518470	+	0.203485i
$263$	13.1750	−	7.60659i	0.812406	−	0.469043i	−0.0353848	−	0.999374i	$-0.511266\pi$
$263$	13.1750	−	7.60659i	0.812406	−	0.469043i	0.847791	+	0.530331i	$0.177932\pi$
$264$		0			0
$265$	4.16326	−	3.32009i	0.255747	−	0.203951i
$266$	4.28013	−	5.41394i	0.262431	−	0.331950i
$267$		0			0
$268$	3.96227	+	10.0957i	0.242034	+	0.616693i
$269$	2.25171	+	30.0470i	0.137289	+	1.83200i	0.462802	+	0.886462i	$0.346844\pi$
$269$	2.25171	+	30.0470i	0.137289	+	1.83200i	−0.325513	+	0.945538i	$0.605537\pi$
$270$		0			0
$271$	28.4250	−	11.1560i	1.72669	−	0.677677i	0.726737	−	0.686916i	$-0.241036\pi$
$271$	28.4250	−	11.1560i	1.72669	−	0.677677i	0.999957	+	0.00923880i	$0.00294084\pi$
$272$	7.71493	−	9.67421i	0.467786	−	0.586585i
$273$		0			0
$274$	4.00245	+	5.01892i	0.241797	+	0.303204i
$275$	−3.23767	−	1.86927i	−0.195239	−	0.112721i
$276$		0			0
$277$	1.52270	−	3.87978i	0.0914903	−	0.233113i	−0.877803	−	0.479023i	$-0.840991\pi$
$277$	1.52270	−	3.87978i	0.0914903	−	0.233113i	0.969293	+	0.245909i	$0.0790865\pi$
$278$	4.10841	+	1.26728i	0.246406	+	0.0760062i
$279$		0			0
$280$	7.68938	−	4.48295i	0.459529	−	0.267907i
$281$	6.75670	+	14.0304i	0.403071	+	0.836985i	0.999413	+	0.0342550i	$0.0109058\pi$
$281$	6.75670	+	14.0304i	0.403071	+	0.836985i	−0.596342	+	0.802730i	$0.703380\pi$
$282$		0			0
$283$	2.00755	−	2.94454i	0.119337	−	0.175035i	−0.761922	−	0.647668i	$-0.775744\pi$
$283$	2.00755	−	2.94454i	0.119337	−	0.175035i	0.881259	+	0.472634i	$0.156697\pi$
$284$	−5.03864	−	5.43036i	−0.298988	−	0.322232i
$285$		0			0
$286$	−1.09971	−	0.251001i	−0.0650271	−	0.0148420i
$287$	−21.4395	−	6.51402i	−1.26554	−	0.384510i
$288$		0			0
$289$	−17.1624	−	15.9244i	−1.00955	−	0.936727i
$290$	6.42901	+	0.969017i	0.377524	+	0.0569026i
$291$		0			0
$292$	−16.9770	−	1.27225i	−0.993505	−	0.0744529i
$293$	−32.3680			−1.89096			−0.945480	−	0.325681i	$-0.894406\pi$
$293$	−32.3680			−1.89096			−0.945480	+	0.325681i	$0.894406\pi$
$294$		0			0
$295$	−5.86392			−0.341411
$296$	19.7317	+	1.47868i	1.14688	+	0.0859468i
$297$		0			0
$298$	−9.86522	−	1.48694i	−0.571477	−	0.0861362i
$299$	2.32676	+	2.15892i	0.134560	+	0.124853i
$300$		0			0
$301$	−22.6813	+	3.51686i	−1.30733	+	0.202708i
$302$	−10.6311	−	2.42647i	−0.611749	−	0.139628i
$303$		0			0
$304$	5.72106	+	6.16584i	0.328125	+	0.353635i
$305$	−4.22255	+	6.19335i	−0.241783	+	0.354630i
$306$		0			0
$307$	2.28300	+	4.74070i	0.130298	+	0.270566i	0.955903	−	0.293682i	$-0.0948805\pi$
$307$	2.28300	+	4.74070i	0.130298	+	0.270566i	−0.825605	+	0.564248i	$0.809166\pi$
$308$	−4.17110	−	4.45741i	−0.237670	−	0.253984i
$309$		0			0
$310$	1.59360	+	0.491560i	0.0905104	+	0.0279187i
$311$	7.91196	−	20.1594i	0.448646	−	1.14313i	−0.510414	−	0.859929i	$-0.670508\pi$
$311$	7.91196	−	20.1594i	0.448646	−	1.14313i	0.959060	−	0.283203i	$-0.0913970\pi$
$312$		0			0
$313$	2.20409	+	1.27253i	0.124583	+	0.0719279i	0.560996	−	0.827818i	$-0.310418\pi$
$313$	2.20409	+	1.27253i	0.124583	+	0.0719279i	−0.436414	+	0.899746i	$0.643752\pi$
$314$	5.23369	+	6.56284i	0.295354	+	0.370362i
$315$		0			0
$316$	−2.55539	+	3.20436i	−0.143752	+	0.180259i
$317$	−29.5211	+	11.5862i	−1.65807	+	0.650744i	−0.995188	−	0.0979816i	$-0.968761\pi$
$317$	−29.5211	+	11.5862i	−1.65807	+	0.650744i	−0.662880	+	0.748725i	$0.730666\pi$
$318$		0			0
$319$	−0.740708	−	9.88406i	−0.0414717	−	0.553401i
$320$	0.299133	+	0.762177i	0.0167220	+	0.0426070i
$321$		0			0
$322$	−0.867351	−	3.72736i	−0.0483356	−	0.207717i
$323$	21.4774	−	17.1276i	1.19503	−	0.953007i
$324$		0			0
$325$	3.04016	−	1.75524i	0.168638	−	0.0973631i
$326$	−3.95551	−	1.55242i	−0.219076	−	0.0859808i
$327$		0			0
$328$	−8.06440	+	16.7459i	−0.445282	+	0.924637i
$329$	−1.53651	−	0.224948i	−0.0847107	−	0.0124018i
$330$		0			0
$331$	3.80450	−	0.573436i	0.209114	−	0.0315189i	−0.0436495	−	0.999047i	$-0.513898\pi$
$331$	3.80450	−	0.573436i	0.209114	−	0.0315189i	0.252764	+	0.967528i	$0.418660\pi$
$332$	−15.2070	−	10.3679i	−0.834590	−	0.569014i
$333$		0			0
$334$	0.441689	+	0.647838i	0.0241681	+	0.0354481i
$335$	−2.26181	+	9.90962i	−0.123576	+	0.541420i
$336$		0			0
$337$	−3.83417	−	16.7986i	−0.208860	−	0.915077i	−0.965327	−	0.261044i	$-0.915933\pi$
$337$	−3.83417	−	16.7986i	−0.208860	−	0.915077i	0.756466	−	0.654033i	$-0.226924\pi$
$338$	−4.61714	+	4.97609i	−0.251139	+	0.270664i
$339$		0			0
$340$	15.2307	−	4.69805i	0.826002	−	0.254788i
$341$	0.189994	−	2.53530i	0.0102888	−	0.137294i
$342$		0			0
$343$	3.89166	−	18.1068i	0.210130	−	0.977673i
$344$			19.0387i			1.02650i
$345$		0			0
$346$	−0.371018	−	1.20281i	−0.0199461	−	0.0646635i
$347$	−4.06039	+	26.9390i	−0.217973	+	1.44616i	0.565508	+	0.824743i	$0.308680\pi$
$347$	−4.06039	+	26.9390i	−0.217973	+	1.44616i	−0.783481	+	0.621416i	$0.786558\pi$
$348$		0			0
$349$	−28.4530	+	6.49422i	−1.52306	+	0.347627i	−0.900468	−	0.434923i	$-0.856776\pi$
$349$	−28.4530	+	6.49422i	−1.52306	+	0.347627i	−0.622587	+	0.782550i	$0.713918\pi$
$350$	−4.22201	−	0.298440i	−0.225676	−	0.0159523i
$351$		0			0
$352$	−6.48542	+	4.42169i	−0.345674	+	0.235677i
$353$	−22.4349	+	20.8166i	−1.19409	+	1.10796i	−0.202402	+	0.979302i	$0.564875\pi$
$353$	−22.4349	+	20.8166i	−1.19409	+	1.10796i	−0.991690	+	0.128653i	$0.958935\pi$
$354$		0			0
$355$	−1.03476	−	6.86521i	−0.0549196	−	0.364368i
$356$	20.4413	−	9.84401i	1.08339	−	0.521732i
$357$		0			0
$358$	2.89542	+	1.39436i	0.153028	+	0.0736942i
$359$	−4.87661	+	15.8096i	−0.257378	+	0.834398i	0.731000	+	0.682378i	$0.239054\pi$
$359$	−4.87661	+	15.8096i	−0.257378	+	0.834398i	−0.988377	+	0.152020i	$0.951422\pi$
$360$		0			0
$361$	−0.163310	−	0.282861i	−0.00859527	−	0.0148874i
$362$	2.32959	−	4.03498i	0.122441	−	0.212074i
$363$		0			0
$364$	5.58307	−	1.29917i	0.292633	−	0.0680952i
$365$	−12.4747	−	9.94822i	−0.652954	−	0.520714i
$366$		0			0
$367$	−30.6610	+	2.29773i	−1.60049	+	0.119940i	−0.844835	−	0.535027i	$-0.820301\pi$
$367$	−30.6610	+	2.29773i	−1.60049	+	0.119940i	−0.755657	+	0.654967i	$0.772682\pi$
$368$	4.65106	−	0.348549i	0.242453	−	0.0181694i
$369$		0			0
$370$	6.52281	+	5.20177i	0.339105	+	0.270427i
$371$	−8.96887	−	2.00720i	−0.465640	−	0.104209i
$372$		0			0
$373$	−0.568528	+	0.984719i	−0.0294373	+	0.0509868i	−0.880369	−	0.474290i	$-0.842705\pi$
$373$	−0.568528	+	0.984719i	−0.0294373	+	0.0509868i	0.850931	+	0.525277i	$0.176038\pi$
$374$	2.70668	+	4.68811i	0.139959	+	0.242416i
$375$		0			0
$376$	−0.379675	+	1.23088i	−0.0195803	+	0.0634776i
$377$	8.38544	+	4.03822i	0.431872	+	0.207979i
$378$		0			0
$379$	−18.4713	+	8.89530i	−0.948806	+	0.456921i	−0.843267	−	0.537494i	$-0.819371\pi$
$379$	−18.4713	+	8.89530i	−0.948806	+	0.456921i	−0.105538	+	0.994415i	$0.533657\pi$
$380$	1.61481	+	10.7136i	0.0828379	+	0.549594i
$381$		0			0
$382$	−5.21543	+	4.83922i	−0.266845	+	0.247596i
$383$	14.3448	−	9.78011i	0.732984	−	0.499740i	−0.138379	−	0.990379i	$-0.544189\pi$
$383$	14.3448	−	9.78011i	0.732984	−	0.499740i	0.871363	+	0.490639i	$0.163237\pi$
$384$		0			0
$385$	−0.876648	−	5.65378i	−0.0446781	−	0.288144i
$386$	2.12473	−	0.484956i	0.108146	−	0.0246836i
$387$		0			0
$388$	−3.81011	+	25.2784i	−0.193429	+	1.28332i
$389$	5.03975	+	16.3385i	0.255525	+	0.828393i	0.988902	+	0.148570i	$0.0474671\pi$
$389$	5.03975	+	16.3385i	0.255525	+	0.828393i	−0.733377	+	0.679823i	$0.762057\pi$
$390$		0			0
$391$		−	15.2328i		−	0.770354i
$392$	−14.3473	−	5.49129i	−0.724650	−	0.277352i
$393$		0			0
$394$	−0.150502	+	2.00832i	−0.00758220	+	0.101177i
$395$	−3.67055	+	1.13221i	−0.184685	+	0.0569678i
$396$		0			0
$397$	16.4764	−	17.7573i	0.826927	−	0.891215i	−0.168601	−	0.985684i	$-0.553925\pi$
$397$	16.4764	−	17.7573i	0.826927	−	0.891215i	0.995528	+	0.0944691i	$0.0301153\pi$
$398$	−0.638790	−	2.79872i	−0.0320196	−	0.140287i
$399$		0			0
$400$	1.14786	−	5.02910i	0.0573930	−	0.251455i
$401$	5.22178	+	7.65894i	0.260763	+	0.382469i	0.934185	−	0.356789i	$-0.116129\pi$
$401$	5.22178	+	7.65894i	0.260763	+	0.382469i	−0.673422	+	0.739258i	$0.735176\pi$
$402$		0			0
$403$	1.97249	+	1.34482i	0.0982568	+	0.0669904i
$404$	19.3100	−	2.91052i	0.960710	−	0.144804i
$405$		0			0
$406$	−5.65182	−	9.69429i	−0.280495	−	0.481120i
$407$	5.51854	−	11.4594i	0.273544	−	0.568020i
$408$		0			0
$409$	0.650608	+	0.255345i	0.0321705	+	0.0126260i	0.381372	−	0.924422i	$-0.375452\pi$
$409$	0.650608	+	0.255345i	0.0321705	+	0.0126260i	−0.349201	+	0.937048i	$0.613547\pi$
$410$	−6.78689	+	3.91841i	−0.335180	+	0.193517i
$411$		0			0
$412$	9.84280	−	7.84937i	0.484920	−	0.386711i
$413$	6.34368	+	7.88605i	0.312152	+	0.388047i
$414$		0			0
$415$	−6.30193	−	16.0571i	−0.309350	−	0.788210i
$416$	−0.550799	−	7.34990i	−0.0270051	−	0.360358i
$417$		0			0
$418$	−3.42541	+	1.34437i	−0.167542	+	0.0657555i
$419$	−14.4946	+	18.1756i	−0.708106	+	0.887937i	−0.997600	−	0.0692431i	$-0.977942\pi$
$419$	−14.4946	+	18.1756i	−0.708106	+	0.887937i	0.289494	+	0.957180i	$0.406513\pi$
$420$		0			0
$421$	−5.04168	−	6.32206i	−0.245716	−	0.308119i	0.643644	−	0.765325i	$-0.277422\pi$
$421$	−5.04168	−	6.32206i	−0.245716	−	0.308119i	−0.889361	+	0.457206i	$0.848850\pi$
$422$	−2.62086	−	1.51315i	−0.127581	−	0.0736592i
$423$		0			0
$424$	−2.78521	+	7.09660i	−0.135262	+	0.344641i
$425$	−16.0987	−	4.96581i	−0.780904	−	0.240877i
$426$		0			0
$427$	12.8971	−	1.02139i	0.624134	−	0.0494285i
$428$	11.1199	+	23.0906i	0.537499	+	1.11613i
$429$		0			0
$430$	−4.52203	+	6.63260i	−0.218072	+	0.319852i
$431$	11.4416	+	12.3311i	0.551121	+	0.593967i	0.945759	−	0.324870i	$-0.105321\pi$
$431$	11.4416	+	12.3311i	0.551121	+	0.593967i	−0.394638	+	0.918837i	$0.629130\pi$
$432$		0			0
$433$	5.30788	+	1.21149i	0.255081	+	0.0582205i	0.348149	−	0.937439i	$-0.386810\pi$
$433$	5.30788	+	1.21149i	0.255081	+	0.0582205i	−0.0930683	+	0.995660i	$0.529667\pi$
$434$	−1.06291	−	2.67492i	−0.0510212	−	0.128400i
$435$		0			0
$436$	0.764606	+	0.709451i	0.0366180	+	0.0339765i
$437$	10.2390	+	1.54327i	0.489796	+	0.0738248i
$438$		0			0
$439$	−4.88765	−	0.366278i	−0.233275	−	0.0174815i	−0.0424201	−	0.999100i	$-0.513507\pi$
$439$	−4.88765	−	0.366278i	−0.233275	−	0.0174815i	−0.190854	+	0.981618i	$0.561126\pi$
$440$	−4.74578			−0.226246
$441$		0			0
$442$	−5.08313			−0.241780
$443$	−31.7040	−	2.37588i	−1.50630	−	0.112882i	−0.704171	−	0.710030i	$-0.748681\pi$
$443$	−31.7040	−	2.37588i	−1.50630	−	0.112882i	−0.802131	+	0.597149i	$0.796300\pi$
$444$		0			0
$445$	21.0261	+	3.16918i	0.996734	+	0.150233i
$446$	3.88206	+	3.60203i	0.183821	+	0.170561i
$447$		0			0
$448$	0.701402	−	1.22682i	0.0331381	−	0.0579618i
$449$	−34.0327	−	7.76774i	−1.60610	−	0.366583i	−0.676877	−	0.736096i	$-0.736667\pi$
$449$	−34.0327	−	7.76774i	−1.60610	−	0.366583i	−0.929225	+	0.369513i	$0.879524\pi$
$450$		0			0
$451$	8.12623	+	8.75799i	0.382649	+	0.412398i
$452$	−9.77187	+	14.3327i	−0.459630	+	0.674153i
$453$		0			0
$454$	4.44001	+	9.21977i	0.208380	+	0.432705i
$455$	5.00922	+	1.94156i	0.234836	+	0.0910217i
$456$		0			0
$457$	−20.1938	−	6.22895i	−0.944624	−	0.291378i	−0.216079	−	0.976376i	$-0.569327\pi$
$457$	−20.1938	−	6.22895i	−0.944624	−	0.291378i	−0.728545	+	0.684998i	$0.759803\pi$
$458$	1.93362	−	4.92679i	0.0903522	−	0.230214i
$459$		0			0
$460$	5.20299	+	3.00395i	0.242591	+	0.140060i
$461$	−18.9768	−	23.7961i	−0.883837	−	1.10830i	−0.993444	−	0.114321i	$-0.963531\pi$
$461$	−18.9768	−	23.7961i	−0.883837	−	1.10830i	0.109607	−	0.993975i	$-0.465041\pi$
$462$		0			0
$463$	2.88928	−	3.62305i	0.134276	−	0.168377i	−0.710147	−	0.704053i	$-0.751372\pi$
$463$	2.88928	−	3.62305i	0.134276	−	0.168377i	0.844424	+	0.535676i	$0.179943\pi$
$464$	12.7309	−	4.99650i	0.591016	−	0.231957i
$465$		0			0
$466$	0.625736	+	8.34987i	0.0289867	+	0.386800i
$467$	−2.76621	−	7.04819i	−0.128005	−	0.326151i	0.852476	−	0.522767i	$-0.175100\pi$
$467$	−2.76621	−	7.04819i	−0.128005	−	0.326151i	−0.980481	+	0.196616i	$0.937005\pi$
$468$		0			0
$469$	15.7737	−	7.67860i	0.728363	−	0.354565i
$470$	−0.424625	+	0.338627i	−0.0195865	+	0.0156197i
$471$		0			0
$472$	7.27039	−	4.19756i	0.334647	−	0.193209i
$473$	11.3920	+	4.47102i	0.523803	+	0.205578i
$474$		0			0
$475$	4.96886	−	10.3179i	0.227987	−	0.473420i
$476$	−22.7950	−	15.4005i	−1.04481	−	0.705880i
$477$		0			0
$478$	−13.2045	+	1.99025i	−0.603958	+	0.0910320i
$479$	22.4646	+	15.3161i	1.02644	+	0.699812i	0.954687	−	0.297611i	$-0.0961899\pi$
$479$	22.4646	+	15.3161i	1.02644	+	0.699812i	0.0717480	+	0.997423i	$0.477142\pi$
$480$		0			0
$481$	6.72777	+	9.86782i	0.306760	+	0.449934i
$482$	2.76171	−	12.0998i	0.125792	−	0.551133i
$483$		0			0
$484$	−3.27925	−	14.3674i	−0.149057	−	0.653061i
$485$	−16.2962	+	17.5631i	−0.739972	+	0.797500i
$486$		0			0
$487$	−29.5163	+	9.10457i	−1.33751	+	0.412567i	−0.879297	−	0.476274i	$-0.841987\pi$
$487$	−29.5163	+	9.10457i	−1.33751	+	0.412567i	−0.458214	+	0.888842i	$0.651511\pi$
$488$	0.801964	−	10.7015i	0.0363032	−	0.484433i
$489$		0			0
$490$	−3.69398	−	5.32078i	−0.166877	−	0.240368i
$491$			42.6971i			1.92689i	0.267901	+	0.963447i	$0.413670\pi$
$491$			42.6971i			1.92689i	−0.267901	+	0.963447i	$0.586330\pi$
$492$		0			0
$493$	−13.1656	−	42.6817i	−0.592947	−	1.92229i
$494$	0.514987	−	3.41671i	0.0231704	−	0.153725i
$495$		0			0
$496$	3.42006	−	0.780607i	0.153565	−	0.0350503i
$497$	−8.11321	+	8.81849i	−0.363927	+	0.395563i
$498$		0			0
$499$	2.47156	−	1.68508i	0.110642	−	0.0754346i	−0.506735	−	0.862102i	$-0.669148\pi$
$499$	2.47156	−	1.68508i	0.110642	−	0.0754346i	0.617377	+	0.786667i	$0.288195\pi$
$500$	14.0606	−	13.0464i	0.628811	−	0.583452i
$501$		0			0
$502$	−0.258233	−	1.71326i	−0.0115255	−	0.0764667i
$503$	20.3511	−	9.80056i	0.907410	−	0.436985i	0.0788501	−	0.996886i	$-0.474875\pi$
$503$	20.3511	−	9.80056i	0.907410	−	0.436985i	0.828559	+	0.559901i	$0.189161\pi$
$504$		0			0
$505$	16.4896	+	7.94096i	0.733776	+	0.353368i
$506$	−0.601442	+	1.94983i	−0.0267374	+	0.0866804i
$507$		0			0
$508$	−16.4548	−	28.5006i	−0.730066	−	1.26451i
$509$	−0.548485	+	0.950004i	−0.0243112	+	0.0421082i	−0.877925	−	0.478798i	$-0.841073\pi$
$509$	−0.548485	+	0.950004i	−0.0243112	+	0.0421082i	0.853614	+	0.520906i	$0.174406\pi$
$510$		0			0
$511$	0.116503	+	27.5386i	0.00515380	+	1.21824i
$512$	−15.1472	−	12.0795i	−0.669417	−	0.533843i
$513$		0			0
$514$	4.85636	−	0.363934i	0.214205	−	0.0160524i
$515$	11.7660	−	0.881737i	0.518471	−	0.0388540i
$516$		0			0
$517$	0.647344	+	0.516240i	0.0284702	+	0.0227042i
$518$	−0.0609177	−	14.3995i	−0.00267657	−	0.632677i
$519$		0			0
$520$	2.22814	−	3.85925i	0.0977104	−	0.169239i
$521$	9.80296	+	16.9792i	0.429475	+	0.743873i	0.996827	−	0.0796026i	$-0.0253651\pi$
$521$	9.80296	+	16.9792i	0.429475	+	0.743873i	−0.567351	+	0.823476i	$0.692032\pi$
$522$		0			0
$523$	−3.71962	+	12.0587i	−0.162648	+	0.527291i	−0.999807	−	0.0196687i	$-0.993739\pi$
$523$	−3.71962	+	12.0587i	−0.162648	+	0.527291i	0.837159	+	0.546960i	$0.184215\pi$
$524$	22.0087	+	10.5988i	0.961453	+	0.463011i
$525$		0			0
$526$	−8.27391	+	3.98451i	−0.360760	+	0.173733i
$527$	−1.70758	−	11.3291i	−0.0743834	−	0.493501i
$528$		0			0
$529$	−12.6512	+	11.7386i	−0.550052	+	0.510374i
$530$	−2.65587	+	1.81074i	−0.115364	+	0.0786535i
$531$		0			0
$532$	12.6611	−	13.7617i	0.548929	−	0.596647i
$533$	−10.9372	+	2.49635i	−0.473744	+	0.108129i
$534$		0			0
$535$	−3.57993	+	23.7513i	−0.154774	+	1.02686i
$536$	−4.28929	−	13.9055i	−0.185269	−	0.600627i
$537$		0			0
$538$		−	18.1886i		−	0.784164i
$539$	−6.65508	+	7.29530i	−0.286654	+	0.314231i
$540$		0			0
$541$	1.02645	−	13.6971i	0.0441307	−	0.588883i	−0.930678	−	0.365840i	$-0.880782\pi$
$541$	1.02645	−	13.6971i	0.0441307	−	0.588883i	0.974809	−	0.223043i	$-0.0715992\pi$
$542$	−17.6138	+	5.43315i	−0.756579	+	0.233374i
$543$		0			0
$544$	−24.0591	+	25.9295i	−1.03152	+	1.11172i
$545$	0.217527	+	0.953046i	0.00931781	+	0.0408240i
$546$		0			0
$547$	8.97747	−	39.3329i	0.383849	−	1.68175i	−0.301443	−	0.953484i	$-0.597468\pi$
$547$	8.97747	−	39.3329i	0.383849	−	1.68175i	0.685292	−	0.728268i	$-0.259675\pi$
$548$	9.79833	+	14.3715i	0.418564	+	0.613921i
$549$		0			0
$550$	1.86461	+	1.27127i	0.0795072	+	0.0542071i
$551$	30.0231	−	4.52525i	1.27903	−	0.192782i
$552$		0			0
$553$	5.49350	+	3.71146i	0.233607	+	0.157827i
$554$	−1.09162	+	2.26677i	−0.0463784	+	0.0963057i
$555$		0			0
$556$	10.8443	+	4.25607i	0.459900	+	0.180498i
$557$	21.1622	−	12.2180i	0.896670	−	0.517693i	0.0205518	−	0.999789i	$-0.493458\pi$
$557$	21.1622	−	12.2180i	0.896670	−	0.517693i	0.876118	+	0.482096i	$0.160124\pi$
$558$		0			0
$559$	−8.98433	+	7.16476i	−0.379997	+	0.303037i
$560$	7.09798	−	3.45527i	0.299944	−	0.146012i
$561$		0			0
$562$	−3.43432	−	8.75050i	−0.144868	−	0.369117i
$563$	3.13401	+	41.8204i	0.132083	+	1.76252i	0.532727	+	0.846287i	$0.321167\pi$
$563$	3.13401	+	41.8204i	0.132083	+	1.76252i	−0.400644	+	0.916234i	$0.631214\pi$
$564$		0			0
$565$	−15.1339	+	5.93963i	−0.636689	+	0.249882i
$566$	−1.34129	+	1.68192i	−0.0563786	+	0.0706965i
$567$		0			0
$568$	6.19727	+	7.77114i	0.260032	+	0.326070i
$569$	11.1379	+	6.43044i	0.466923	+	0.269578i	0.714951	−	0.699175i	$-0.246449\pi$
$569$	11.1379	+	6.43044i	0.466923	+	0.269578i	−0.248028	+	0.968753i	$0.579782\pi$
$570$		0			0
$571$	−8.53989	+	21.7593i	−0.357383	+	0.910598i	0.633237	+	0.773958i	$0.281726\pi$
$571$	−8.53989	+	21.7593i	−0.357383	+	0.910598i	−0.990621	+	0.136640i	$0.956370\pi$
$572$	−2.92058	−	0.900879i	−0.122116	−	0.0376676i
$573$		0			0
$574$	12.6118	+	4.88830i	0.526406	+	0.204034i
$575$	−2.75529	−	5.72142i	−0.114904	−	0.238600i
$576$		0			0
$577$	16.8833	−	24.7633i	0.702862	−	1.03091i	−0.294306	−	0.955711i	$-0.595089\pi$
$577$	16.8833	−	24.7633i	0.702862	−	1.03091i	0.997169	−	0.0751986i	$-0.0239591\pi$
$578$	9.61264	+	10.3600i	0.399833	+	0.430918i
$579$		0			0
$580$	17.1749	+	3.92006i	0.713149	+	0.162772i
$581$	−14.7767	+	25.8459i	−0.613040	+	1.07227i
$582$		0			0
$583$	3.59224	+	3.33311i	0.148775	+	0.138043i
$584$	22.5880	+	3.40459i	0.934697	+	0.140883i
$585$		0			0
$586$	19.4841	+	1.46013i	0.804881	+	0.0603175i
$587$	−10.1476			−0.418837			−0.209419	−	0.977826i	$-0.567157\pi$
$587$	−10.1476			−0.418837			−0.209419	+	0.977826i	$0.567157\pi$
$588$		0			0
$589$	7.78802			0.320900
$590$	3.52982	+	0.264524i	0.145320	+	0.0108903i
$591$		0			0
$592$	17.3536	+	2.61563i	0.713228	+	0.107502i
$593$	−12.4548	−	11.5563i	−0.511456	−	0.474562i	0.381714	−	0.924280i	$-0.375334\pi$
$593$	−12.4548	−	11.5563i	−0.511456	−	0.474562i	−0.893170	+	0.449718i	$0.851524\pi$
$594$		0			0
$595$	−9.52085	−	23.9602i	−0.390317	−	0.982271i
$596$	−26.3546	−	6.01528i	−1.07953	−	0.246395i
$597$		0			0
$598$	−1.30322	−	1.40453i	−0.0532925	−	0.0574356i
$599$	19.2342	−	28.2114i	0.785887	−	1.15268i	−0.199087	−	0.979982i	$-0.563798\pi$
$599$	19.2342	−	28.2114i	0.785887	−	1.15268i	0.984974	−	0.172703i	$-0.0552501\pi$
$600$		0			0
$601$	−5.26420	−	10.9312i	−0.214731	−	0.445894i	0.765583	−	0.643337i	$-0.222450\pi$
$601$	−5.26420	−	10.9312i	−0.214731	−	0.445894i	−0.980314	+	0.197443i	$0.936736\pi$
$602$	13.8118	−	1.09383i	0.562927	−	0.0445812i
$603$		0			0
$604$	−28.2337	−	8.70895i	−1.14881	−	0.354362i
$605$	5.04593	−	12.8568i	0.205146	−	0.522704i
$606$		0			0
$607$	33.0895	+	19.1042i	1.34306	+	0.775416i	0.987255	−	0.159144i	$-0.0508735\pi$
$607$	33.0895	+	19.1042i	1.34306	+	0.775416i	0.355805	+	0.934560i	$0.384207\pi$
$608$	−14.9915	−	18.7987i	−0.607984	−	0.762387i
$609$		0			0
$610$	2.82118	−	3.53764i	0.114226	−	0.143235i
$611$	−0.723732	+	0.284044i	−0.0292791	+	0.0114912i
$612$		0			0
$613$	2.06834	+	27.6001i	0.0835397	+	1.11476i	0.868658	+	0.495413i	$0.164983\pi$
$613$	2.06834	+	27.6001i	0.0835397	+	1.11476i	−0.785118	+	0.619346i	$0.787398\pi$
$614$	−1.16041	−	2.95668i	−0.0468304	−	0.119322i
$615$		0			0
$616$	5.13406	+	6.38232i	0.206857	+	0.257151i
$617$	25.4856	−	20.3241i	1.02601	−	0.818218i	0.0425073	−	0.999096i	$-0.486465\pi$
$617$	25.4856	−	20.3241i	1.02601	−	0.818218i	0.983505	+	0.180878i	$0.0578940\pi$
$618$		0			0
$619$	−38.1707	+	22.0379i	−1.53421	+	0.885777i	−0.535051	+	0.844820i	$0.679708\pi$
$619$	−38.1707	+	22.0379i	−1.53421	+	0.885777i	−0.999161	+	0.0409576i	$0.986959\pi$
$620$	4.20636	+	1.65087i	0.168931	+	0.0663007i
$621$		0			0
$622$	−5.67205	+	11.7781i	−0.227428	+	0.472260i
$623$	−18.4843	−	31.7053i	−0.740559	−	1.27025i
$624$		0			0
$625$	4.67309	−	0.704355i	0.186924	−	0.0281742i
$626$	−1.26936	−	0.865437i	−0.0507339	−	0.0345898i
$627$		0			0
$628$	12.8125	+	18.7925i	0.511275	+	0.749902i
$629$	12.7541	−	55.8792i	0.508538	−	2.22805i
$630$		0			0
$631$	8.23478	+	36.0789i	0.327821	+	1.43628i	0.823274	+	0.567644i	$0.192145\pi$
$631$	8.23478	+	36.0789i	0.327821	+	1.43628i	−0.495453	+	0.868635i	$0.664998\pi$
$632$	3.74046	−	4.03126i	0.148788	−	0.160355i
$633$		0			0
$634$	18.2930	−	5.64265i	0.726509	−	0.224098i
$635$	2.30493	−	30.7572i	0.0914684	−	1.22056i
$636$		0			0
$637$	−2.80796	−	8.83702i	−0.111255	−	0.350135i
$638$			5.98318i			0.236876i
$639$		0			0
$640$	−5.17389	−	16.7734i	−0.204516	−	0.663025i
$641$	2.67765	−	17.7651i	0.105761	−	0.701678i	−0.871618	−	0.490185i	$-0.836929\pi$
$641$	2.67765	−	17.7651i	0.105761	−	0.701678i	0.977379	−	0.211493i	$-0.0678326\pi$
$642$		0			0
$643$	35.0503	−	8.00000i	1.38225	−	0.315489i	0.534177	−	0.845372i	$-0.320621\pi$
$643$	35.0503	−	8.00000i	1.38225	−	0.315489i	0.848071	+	0.529883i	$0.177764\pi$
$644$	−1.58884	−	10.2469i	−0.0626089	−	0.403785i
$645$		0			0
$646$	−13.7011	+	9.34123i	−0.539061	+	0.367526i
$647$	−18.8212	+	17.4635i	−0.739937	+	0.686561i	−0.957160	−	0.289561i	$-0.906491\pi$
$647$	−18.8212	+	17.4635i	−0.739937	+	0.686561i	0.217222	+	0.976122i	$0.430300\pi$
$648$		0			0
$649$	−0.804281	−	5.33606i	−0.0315708	−	0.209459i
$650$	−1.90922	+	0.919433i	−0.0748859	+	0.0360631i
$651$		0			0
$652$	−10.3734	−	4.99557i	−0.406254	−	0.195642i
$653$	2.47019	−	8.00815i	0.0966658	−	0.313383i	−0.894305	−	0.447457i	$-0.852330\pi$
$653$	2.47019	−	8.00815i	0.0966658	−	0.313383i	0.990971	+	0.134074i	$0.0428060\pi$
$654$		0			0
$655$	11.4470	+	19.8268i	0.447272	+	0.774698i
$656$	−8.24244	+	14.2763i	−0.321813	+	0.557397i
$657$		0			0
$658$	0.914766	+	0.204722i	0.0356613	+	0.00798088i
$659$	−32.2298	−	25.7024i	−1.25549	−	1.00122i	−0.999402	−	0.0345714i	$-0.988993\pi$
$659$	−32.2298	−	25.7024i	−1.25549	−	1.00122i	−0.256093	−	0.966652i	$-0.582435\pi$
$660$		0			0
$661$	−44.5580	+	3.33916i	−1.73311	+	0.129878i	−0.903533	−	0.428519i	$-0.859035\pi$
$661$	−44.5580	+	3.33916i	−1.73311	+	0.129878i	−0.829573	+	0.558398i	$0.811416\pi$
$662$	−2.31601	+	0.173561i	−0.0900143	+	0.00674564i
$663$		0			0
$664$	19.3076	+	15.3973i	0.749279	+	0.597530i
$665$	17.0698	−	3.97212i	0.661939	−	0.154032i
$666$		0			0
$667$	8.41810	−	14.5806i	0.325950	−	0.564562i
$668$	1.06226	+	1.83989i	0.0411001	+	0.0711875i
$669$		0			0
$670$	1.80853	−	5.86312i	0.0698697	−	0.226512i
$671$	−6.21499	−	2.99298i	−0.239927	−	0.115543i
$672$		0			0
$673$	−22.8586	+	11.0081i	−0.881135	+	0.424332i	−0.819039	−	0.573738i	$-0.805493\pi$
$673$	−22.8586	+	11.0081i	−0.881135	+	0.424332i	−0.0620958	+	0.998070i	$0.519778\pi$
$674$	1.55021	+	10.2850i	0.0597118	+	0.396162i
$675$		0			0
$676$	−13.4831	+	12.5105i	−0.518580	+	0.481172i
$677$	18.8263	−	12.8355i	0.723552	−	0.493309i	−0.144673	−	0.989479i	$-0.546213\pi$
$677$	18.8263	−	12.8355i	0.723552	−	0.493309i	0.868225	+	0.496170i	$0.165261\pi$
$678$		0			0
$679$	41.2491	+	2.91576i	1.58299	+	0.111897i
$680$	−20.8500	+	4.75888i	−0.799562	+	0.182495i
$681$		0			0
$682$	−0.228736	+	1.51757i	−0.00875877	+	0.0581106i
$683$	3.63755	+	11.7926i	0.139187	+	0.451233i	0.998150	−	0.0608051i	$-0.0193668\pi$
$683$	3.63755	+	11.7926i	0.139187	+	0.451233i	−0.858963	+	0.512038i	$0.828891\pi$
$684$		0			0
$685$			16.3018i			0.622860i
$686$	−3.15941	+	10.7239i	−0.120627	+	0.409441i
$687$		0			0
$688$	−1.26188	+	16.8387i	−0.0481089	+	0.641969i
$689$	−4.39703	+	1.35630i	−0.167513	+	0.0516710i
$690$		0			0
$691$	0.597222	−	0.643652i	0.0227194	−	0.0244857i	−0.721590	−	0.692321i	$-0.756588\pi$
$691$	0.597222	−	0.643652i	0.0227194	−	0.0244857i	0.744309	+	0.667835i	$0.232779\pi$
$692$	−0.758935	−	3.32511i	−0.0288504	−	0.126402i
$693$		0			0
$694$	3.65940	−	16.0329i	0.138909	−	0.608600i
$695$	6.15041	+	9.02099i	0.233298	+	0.342186i
$696$		0			0
$697$	44.4838	+	30.3285i	1.68494	+	1.14878i
$698$	17.4204	−	2.62571i	0.659372	−	0.0993844i
$699$		0			0
$700$	−11.3474	−	1.66128i	−0.428892	−	0.0627905i
$701$	−2.37466	+	4.93103i	−0.0896897	+	0.186242i	−0.940988	−	0.338439i	$-0.890101\pi$
$701$	−2.37466	+	4.93103i	−0.0896897	+	0.186242i	0.851299	+	0.524681i	$0.175815\pi$
$702$		0			0
$703$	36.2680	+	14.2341i	1.36787	+	0.536851i
$704$	−0.652539	+	0.376743i	−0.0245935	+	0.0141991i
$705$		0			0
$706$	14.4439	−	11.5186i	0.543603	−	0.433509i
$707$	−7.15933	−	30.7665i	−0.269254	−	1.15709i
$708$		0			0
$709$	6.18660	+	15.7632i	0.232343	+	0.592000i	0.998730	−	0.0503791i	$-0.0160429\pi$
$709$	6.18660	+	15.7632i	0.232343	+	0.592000i	−0.766387	+	0.642379i	$0.777948\pi$
$710$	0.313190	+	4.17923i	0.0117538	+	0.156844i
$711$		0			0
$712$	−28.3379	+	11.1218i	−1.06201	+	0.416807i
$713$	2.69257	−	3.37637i	0.100837	−	0.126446i
$714$		0			0
$715$	−1.78596	−	2.23953i	−0.0667913	−	0.0837536i
$716$	7.54106	+	4.35383i	0.281823	+	0.162710i
$717$		0			0
$718$	3.64868	−	9.29669i	0.136168	−	0.346949i
$719$	24.7405	+	7.63145i	0.922666	+	0.284605i	0.719462	−	0.694532i	$-0.244388\pi$
$719$	24.7405	+	7.63145i	0.922666	+	0.284605i	0.203204	+	0.979136i	$0.434865\pi$
$720$		0			0
$721$	−13.9144	−	14.8695i	−0.518199	−	0.553769i
$722$	0.0855455	+	0.177637i	0.00318367	+	0.00661097i
$723$		0			0
$724$	7.11157	−	10.4308i	0.264299	−	0.387656i
$725$	−12.6652	−	13.6499i	−0.470374	−	0.506943i
$726$		0			0
$727$	23.2231	+	5.30051i	0.861295	+	0.196585i	0.630283	−	0.776366i	$-0.282939\pi$
$727$	23.2231	+	5.30051i	0.861295	+	0.196585i	0.231013	+	0.972951i	$0.425796\pi$
$728$	−7.60052	+	1.17850i	−0.281694	+	0.0436781i
$729$		0			0
$730$	7.06043	+	6.55112i	0.261318	+	0.242468i
$731$	54.5326	+	8.21947i	2.01696	+	0.304008i
$732$		0			0
$733$	4.18509	+	0.313629i	0.154580	+	0.0115842i	0.151795	−	0.988412i	$-0.451495\pi$
$733$	4.18509	+	0.313629i	0.154580	+	0.0115842i	0.00278459	+	0.999996i	$0.499114\pi$
$734$	18.5602			0.685071
$735$		0			0
$736$	−13.3329			−0.491458
$737$	−9.32779	−	0.699021i	−0.343594	−	0.0257488i
$738$		0			0
$739$	−49.9115	−	7.52294i	−1.83602	−	0.276736i	−0.862623	−	0.505847i	$-0.831180\pi$
$739$	−49.9115	−	7.52294i	−1.83602	−	0.276736i	−0.973400	+	0.229111i	$0.926418\pi$
$740$	16.5713	+	15.3759i	0.609173	+	0.565230i
$741$		0			0
$742$	5.30832	+	1.61284i	0.194874	+	0.0592091i
$743$	−19.4034	−	4.42870i	−0.711841	−	0.162473i	−0.148758	−	0.988874i	$-0.547528\pi$
$743$	−19.4034	−	4.42870i	−0.711841	−	0.162473i	−0.563083	+	0.826400i	$0.690385\pi$
$744$		0			0
$745$	−17.2323	−	18.5720i	−0.631341	−	0.680424i
$746$	0.386650	−	0.567111i	0.0141563	−	0.0207634i
$747$		0			0
$748$	6.36415	+	13.2153i	0.232696	+	0.483199i
$749$	35.8145	−	20.8800i	1.30863	−	0.762940i
$750$		0			0
$751$	17.2360	+	5.31660i	0.628951	+	0.194006i	0.592812	−	0.805341i	$-0.298018\pi$
$751$	17.2360	+	5.31660i	0.628951	+	0.194006i	0.0361392	+	0.999347i	$0.488494\pi$
$752$	−0.417385	+	1.06348i	−0.0152205	+	0.0387811i
$753$		0			0
$754$	−4.86550	−	2.80910i	−0.177191	−	0.102301i
$755$	−17.2652	−	21.6499i	−0.628346	−	0.787921i
$756$		0			0
$757$	12.1304	−	15.2110i	0.440887	−	0.552855i	−0.510890	−	0.859646i	$-0.670684\pi$
$757$	12.1304	−	15.2110i	0.440887	−	0.552855i	0.951777	+	0.306792i	$0.0992555\pi$
$758$	11.5202	−	4.52133i	0.418431	−	0.164222i
$759$		0			0
$760$	−1.08639	−	14.4968i	−0.0394074	−	0.525856i
$761$	1.81635	+	4.62798i	0.0658426	+	0.167764i	0.960008	−	0.279973i	$-0.0903254\pi$
$761$	1.81635	+	4.62798i	0.0658426	+	0.167764i	−0.894165	+	0.447737i	$0.852230\pi$
$762$		0			0
$763$	1.04637	−	1.32356i	0.0378812	−	0.0479160i
$764$	−15.0719	+	12.0195i	−0.545284	+	0.434849i
$765$		0			0
$766$	−9.07611	+	5.24010i	−0.327933	+	0.189332i
$767$	4.71687	+	1.85124i	0.170316	+	0.0668442i
$768$		0			0
$769$	12.5604	−	26.0820i	0.452941	−	0.940541i	−0.542029	−	0.840360i	$-0.682344\pi$
$769$	12.5604	−	26.0820i	0.452941	−	0.940541i	0.994969	−	0.100181i	$-0.0319421\pi$
$770$	0.272659	+	3.44287i	0.00982596	+	0.124073i
$771$		0			0
$772$	5.83921	−	0.880119i	0.210158	−	0.0316762i
$773$	−14.5501	−	9.92007i	−0.523330	−	0.356800i	0.272660	−	0.962110i	$-0.412097\pi$
$773$	−14.5501	−	9.92007i	−0.523330	−	0.356800i	−0.795990	+	0.605310i	$0.793049\pi$
$774$		0			0
$775$	−2.69056	−	3.94632i	−0.0966477	−	0.141756i
$776$	7.63267	−	33.4409i	0.273997	−	1.20046i
$777$		0			0
$778$	−2.29667	−	10.0624i	−0.0823397	−	0.360754i
$779$	−24.8926	+	26.8279i	−0.891871	+	0.961208i
$780$		0			0
$781$	6.10529	−	1.88323i	0.218464	−	0.0673874i
$782$	−0.687155	+	9.16945i	−0.0245726	+	0.327899i
$783$		0			0
$784$	−12.3255	−	5.80769i	−0.440196	−	0.207418i
$785$			21.3166i			0.760821i
$786$		0			0
$787$	−4.96064	−	16.0820i	−0.176828	−	0.573262i	−0.999985	−	0.00544840i	$-0.998266\pi$
$787$	−4.96064	−	16.0820i	−0.176828	−	0.573262i	0.823157	−	0.567813i	$-0.192210\pi$
$788$	−0.813313	+	5.39598i	−0.0289731	+	0.192224i
$789$		0			0
$790$	2.26058	−	0.515963i	0.0804279	−	0.0183571i
$791$	24.3600	+	13.9272i	0.866141	+	0.495193i
$792$		0			0
$793$	5.35181	−	3.64880i	0.190048	−	0.129573i
$794$	−10.7191	+	9.94588i	−0.380407	+	0.352966i
$795$		0			0
$796$	−1.15930	−	7.69147i	−0.0410904	−	0.272617i
$797$	17.4494	−	8.40320i	0.618090	−	0.297656i	−0.0985151	−	0.995136i	$-0.531409\pi$
$797$	17.4494	−	8.40320i	0.618090	−	0.297656i	0.716605	+	0.697479i	$0.245695\pi$
$798$		0			0
$799$	3.36170	+	1.61891i	0.118928	+	0.0572729i
$800$	−4.34646	+	14.0909i	−0.153671	+	0.498188i
$801$		0			0
$802$	−2.79778	−	4.84590i	−0.0987931	−	0.171115i
$803$	7.34170	−	12.7162i	0.259083	−	0.448745i
$804$		0			0
$805$	4.17953	−	8.77365i	0.147309	−	0.309231i
$806$	−1.12669	−	0.898504i	−0.0396859	−	0.0316484i
$807$		0			0
$808$	−26.1290	+	1.95810i	−0.919214	+	0.0688856i
$809$	48.7288	−	3.65172i	1.71321	−	0.128387i	0.818347	−	0.574724i	$-0.194891\pi$
$809$	48.7288	−	3.65172i	1.71321	−	0.128387i	0.894865	+	0.446337i	$0.147272\pi$
$810$		0			0
$811$	−31.1868	−	24.8707i	−1.09512	−	0.873328i	−0.102515	−	0.994731i	$-0.532689\pi$
$811$	−31.1868	−	24.8707i	−1.09512	−	0.873328i	−0.992603	+	0.121404i	$0.961260\pi$
$812$	−13.3082	−	27.3383i	−0.467027	−	0.959387i
$813$		0			0
$814$	−3.83886	+	6.64909i	−0.134552	+	0.233051i
$815$	−5.39536	−	9.34504i	−0.188991	−	0.327342i
$816$		0			0
$817$	−11.0497	+	35.8223i	−0.386581	+	1.25326i
$818$	−0.380119	−	0.183055i	−0.0132905	−	0.00640038i
$819$		0			0
$820$	−19.1315	+	9.21326i	−0.668102	+	0.321741i
$821$	4.10640	+	27.2442i	0.143314	+	0.950829i	0.938703	+	0.344728i	$0.112029\pi$
$821$	4.10640	+	27.2442i	0.143314	+	0.950829i	−0.795388	+	0.606100i	$0.792733\pi$
$822$		0			0
$823$	−12.2220	+	11.3404i	−0.426033	+	0.395301i	−0.863838	−	0.503769i	$-0.831946\pi$
$823$	−12.2220	+	11.3404i	−0.426033	+	0.395301i	0.437806	+	0.899070i	$0.355756\pi$
$824$	−13.9569	+	9.51564i	−0.486211	+	0.331493i
$825$		0			0
$826$	−3.46287	−	5.03322i	−0.120489	−	0.175128i
$827$	−23.6729	+	5.40319i	−0.823188	+	0.187887i	−0.613312	−	0.789841i	$-0.710163\pi$
$827$	−23.6729	+	5.40319i	−0.823188	+	0.187887i	−0.209876	+	0.977728i	$0.567306\pi$
$828$		0			0
$829$	−4.47431	+	29.6851i	−0.155399	+	1.03101i	0.766127	+	0.642690i	$0.222181\pi$
$829$	−4.47431	+	29.6851i	−0.155399	+	1.03101i	−0.921526	+	0.388317i	$0.873057\pi$
$830$	3.06914	+	9.94992i	0.106532	+	0.345367i
$831$		0			0
$832$		−	0.707523i		−	0.0245289i
$833$	−21.9229	+	38.7245i	−0.759582	+	1.34172i
$834$		0			0
$835$	−0.148797	+	1.98556i	−0.00514934	+	0.0687132i
$836$	−9.52765	+	2.93889i	−0.329521	+	0.101644i
$837$		0			0
$838$	9.54500	−	10.2871i	0.329726	−	0.355361i
$839$	8.85827	+	38.8106i	0.305822	+	1.33989i	0.861188	+	0.508286i	$0.169721\pi$
$839$	8.85827	+	38.8106i	0.305822	+	1.33989i	−0.555367	+	0.831606i	$0.687422\pi$
$840$		0			0
$841$	4.53226	−	19.8571i	0.156285	−	0.684728i
$842$	2.74968	+	4.03304i	0.0947601	+	0.138988i
$843$		0			0
$844$	−6.77515	−	4.61922i	−0.233210	−	0.159000i
$845$	−17.0457	+	2.56922i	−0.586390	+	0.0883840i
$846$		0			0
$847$	−22.7492	+	7.12272i	−0.781670	+	0.244740i
$848$	−2.93373	+	6.09195i	−0.100745	+	0.209199i
$849$		0			0
$850$	9.46672	+	3.71542i	0.324706	+	0.127438i
$851$	18.7100	−	10.8022i	0.641371	−	0.370296i
$852$		0			0
$853$	38.6246	−	30.8021i	1.32248	−	1.05464i	0.328566	−	0.944481i	$-0.393435\pi$
$853$	38.6246	−	30.8021i	1.32248	−	1.05464i	0.993914	−	0.110161i	$-0.0351368\pi$
$854$	−7.80956	+	0.0330387i	−0.267238	+	0.00113056i
$855$		0			0
$856$	−12.5633	−	32.0107i	−0.429403	−	1.09410i
$857$	4.31439	+	57.5716i	0.147377	+	1.96661i	0.239605	+	0.970870i	$0.422982\pi$
$857$	4.31439	+	57.5716i	0.147377	+	1.96661i	−0.0922283	+	0.995738i	$0.529399\pi$
$858$		0			0
$859$	50.0498	−	19.6431i	1.70768	−	0.670214i	0.708314	−	0.705897i	$-0.249456\pi$
$859$	50.0498	−	19.6431i	1.70768	−	0.670214i	0.999363	+	0.0356833i	$0.0113608\pi$
$860$	−13.5615	+	17.0056i	−0.462443	+	0.579886i
$861$		0			0
$862$	−6.33106	−	7.93889i	−0.215637	−	0.270400i
$863$	−33.0032	−	19.0544i	−1.12344	−	0.648620i	−0.181165	−	0.983453i	$-0.557987\pi$
$863$	−33.0032	−	19.0544i	−1.12344	−	0.648620i	−0.942277	+	0.334833i	$0.891320\pi$
$864$		0			0
$865$	1.16781	−	2.97552i	0.0397066	−	0.101171i
$866$	−3.14046	−	0.968704i	−0.106717	−	0.0329179i
$867$		0			0
$868$	−2.33034	−	7.44283i	−0.0790968	−	0.252626i
$869$	−1.53374	−	3.18484i	−0.0520284	−	0.108038i
$870$		0			0
$871$	4.94783	−	7.25713i	0.167651	−	0.245899i
$872$	−0.951918	−	1.02592i	−0.0322360	−	0.0347422i
$873$		0			0
$874$	−6.09378	−	1.39087i	−0.206125	−	0.0470467i
$875$	−22.8334	−	21.0073i	−0.771911	−	0.710175i
$876$		0			0
$877$	19.4471	+	18.0443i	0.656682	+	0.609311i	0.936469	−	0.350751i	$-0.114073\pi$
$877$	19.4471	+	18.0443i	0.656682	+	0.609311i	−0.279787	+	0.960062i	$0.590264\pi$
$878$	2.92562	+	0.440967i	0.0987350	+	0.0148819i
$879$		0			0
$880$	−4.19739	−	0.314551i	−0.141494	−	0.0106035i
$881$	−24.5263			−0.826314			−0.413157	−	0.910660i	$-0.635574\pi$
$881$	−24.5263			−0.826314			−0.413157	+	0.910660i	$0.635574\pi$
$882$		0			0
$883$	−25.1652			−0.846876			−0.423438	−	0.905925i	$-0.639177\pi$
$883$	−25.1652			−0.846876			−0.423438	+	0.905925i	$0.639177\pi$
$884$	−13.7346	−	1.02927i	−0.461944	−	0.0346179i
$885$		0			0
$886$	18.9772	+	2.86036i	0.637552	+	0.0960955i
$887$	−22.1988	−	20.5975i	−0.745364	−	0.691597i	0.213030	−	0.977046i	$-0.431667\pi$
$887$	−22.1988	−	20.5975i	−0.745364	−	0.691597i	−0.958394	+	0.285449i	$0.907857\pi$
$888$		0			0
$889$	−43.8570	+	30.1738i	−1.47092	+	1.01200i
$890$	−12.5138	−	2.85620i	−0.419465	−	0.0957401i
$891$		0			0
$892$	9.75995	+	10.5187i	0.326787	+	0.352193i
$893$	−1.42876	+	2.09561i	−0.0478116	+	0.0701267i
$894$		0			0
$895$	3.54090	+	7.35275i	0.118359	+	0.245775i
$896$	−16.9603	+	25.1037i	−0.566604	+	0.838657i
$897$		0			0
$898$	20.1358	+	6.21107i	0.671940	+	0.207266i
$899$	4.62632	−	11.7877i	0.154296	−	0.393141i
$900$		0			0
$901$	19.1244	+	11.0415i	0.637126	+	0.367845i
$902$	−4.49655	−	5.63850i	−0.149719	−	0.187742i
$903$		0			0
$904$	14.5121	−	18.1976i	0.482664	−	0.605242i
$905$	11.0139	−	4.32262i	0.366113	−	0.143689i
$906$		0			0
$907$	−1.01935	−	13.6023i	−0.0338471	−	0.451659i	−0.988220	−	0.153041i	$-0.951093\pi$
$907$	−1.01935	−	13.6023i	−0.0338471	−	0.451659i	0.954373	−	0.298618i	$-0.0965256\pi$
$908$	10.1300	+	25.8108i	0.336175	+	0.856561i
$909$		0			0
$910$	−2.92775	−	1.39470i	−0.0970538	−	0.0462339i
$911$	42.2045	−	33.6570i	1.39830	−	1.11510i	0.420088	−	0.907484i	$-0.361999\pi$
$911$	42.2045	−	33.6570i	1.39830	−	1.11510i	0.978209	−	0.207621i	$-0.0665721\pi$
$912$		0			0
$913$	13.7473	−	7.93699i	0.454968	−	0.262676i
$914$	11.8748	+	4.66050i	0.392782	+	0.154156i
$915$		0			0
$916$	6.22224	−	12.9206i	0.205588	−	0.426909i
$917$	14.2804	−	36.8434i	0.471580	−	1.21668i
$918$		0			0
$919$	−53.6090	+	8.08026i	−1.76840	+	0.266543i	−0.950925	−	0.309423i	$-0.899864\pi$
$919$	−53.6090	+	8.08026i	−1.76840	+	0.266543i	−0.817474	+	0.575966i	$0.804626\pi$
$920$	−6.66048	−	4.54104i	−0.219590	−	0.149714i
$921$		0			0
$922$	10.3497	+	15.1803i	0.340850	+	0.499936i
$923$	−1.33499	+	5.84897i	−0.0439417	+	0.192521i
$924$		0			0
$925$	−5.31697	−	23.2952i	−0.174821	−	0.765940i
$926$	−1.90266	+	2.05058i	−0.0625252	+	0.0673862i
$927$		0			0
$928$	−37.3584	+	11.5235i	−1.22635	+	0.378279i
$929$	−1.96806	+	26.2619i	−0.0645699	+	0.861625i	0.867057	+	0.498209i	$0.166009\pi$
$929$	−1.96806	+	26.2619i	−0.0645699	+	0.861625i	−0.931627	+	0.363416i	$0.881610\pi$
$930$		0			0
$931$	−23.8083	−	18.6591i	−0.780284	−	0.611527i
$932$			22.6880i			0.743170i
$933$		0			0
$934$	1.34719	+	4.36748i	0.0440814	+	0.142908i
$935$	−2.04887	+	13.5934i	−0.0670053	+	0.444551i
$936$		0			0
$937$	−23.7453	+	5.41971i	−0.775724	+	0.177054i	−0.592015	−	0.805927i	$-0.701668\pi$
$937$	−23.7453	+	5.41971i	−0.775724	+	0.177054i	−0.183709	+	0.982981i	$0.558810\pi$
$938$	−9.84147	+	3.91062i	−0.321335	+	0.127686i
$939$		0			0
$940$	−1.21590	+	0.828987i	−0.0396583	+	0.0270386i
$941$	−13.8256	+	12.8283i	−0.450703	+	0.418191i	−0.872587	−	0.488458i	$-0.837559\pi$
$941$	−13.8256	+	12.8283i	−0.450703	+	0.418191i	0.421884	+	0.906650i	$0.361369\pi$
$942$		0			0
$943$	3.02462	+	20.0671i	0.0984953	+	0.653474i
$944$	6.70849	−	3.23064i	0.218343	−	0.105148i
$945$		0			0
$946$	−6.65577	−	3.20525i	−0.216398	−	0.104212i
$947$	−4.05076	+	13.1323i	−0.131632	+	0.426741i	−0.997262	−	0.0739427i	$-0.976442\pi$
$947$	−4.05076	+	13.1323i	−0.131632	+	0.426741i	0.865630	+	0.500684i	$0.166918\pi$
$948$		0			0
$949$	6.89384	+	11.9405i	0.223783	+	0.387604i
$950$	−3.45648	+	5.98680i	−0.112143	+	0.194237i
$951$		0			0
$952$	28.9558	+	22.8918i	0.938464	+	0.741927i
$953$	−20.7009	−	16.5084i	−0.670567	−	0.534759i	0.227964	−	0.973670i	$-0.426793\pi$
$953$	−20.7009	−	16.5084i	−0.670567	−	0.534759i	−0.898531	+	0.438910i	$0.855365\pi$
$954$		0			0
$955$	−18.0168	+	1.35017i	−0.583011	+	0.0436906i
$956$	−36.0813	+	2.70392i	−1.16695	+	0.0874511i
$957$		0			0
$958$	−12.8318	−	10.2330i	−0.414577	−	0.330614i
$959$	21.9233	−	17.6355i	0.707942	−	0.569481i
$960$		0			0
$961$	−13.8759	+	24.0338i	−0.447611	+	0.775285i
$962$	−3.60468	−	6.24349i	−0.116219	−	0.201298i
$963$		0			0
$964$	9.91217	−	32.1345i	0.319250	−	1.03498i
$965$	4.98632	+	2.40128i	0.160515	+	0.0773001i
$966$		0			0
$967$	12.0224	−	5.78967i	0.386613	−	0.186183i	−0.230473	−	0.973079i	$-0.574027\pi$
$967$	12.0224	−	5.78967i	0.386613	−	0.186183i	0.617086	+	0.786896i	$0.288313\pi$
$968$	2.94708	+	19.5526i	0.0947226	+	0.628443i
$969$		0			0
$970$	10.6019	−	9.83709i	0.340405	−	0.315850i
$971$	12.1606	−	8.29099i	0.390254	−	0.266070i	−0.352259	−	0.935903i	$-0.614586\pi$
$971$	12.1606	−	8.29099i	0.390254	−	0.266070i	0.742513	+	0.669832i	$0.233634\pi$
$972$		0			0
$973$	5.47821	−	18.0304i	0.175623	−	0.578027i
$974$	18.1782	−	4.14906i	0.582468	−	0.132944i
$975$		0			0
$976$	1.41859	−	9.41171i	0.0454079	−	0.301262i
$977$	4.97249	+	16.1204i	0.159084	+	0.515738i	0.999663	−	0.0259511i	$-0.00826140\pi$
$977$	4.97249	+	16.1204i	0.159084	+	0.515738i	−0.840579	+	0.541689i	$0.817785\pi$
$978$		0			0
$979$			19.5681i			0.625398i
$980$	−8.90371	−	15.1247i	−0.284419	−	0.483141i
$981$		0			0
$982$	1.92608	−	25.7018i	0.0614637	−	0.820176i
$983$	2.19330	−	0.676542i	0.0699553	−	0.0215783i	−0.259580	−	0.965722i	$-0.583584\pi$
$983$	2.19330	−	0.676542i	0.0699553	−	0.0215783i	0.329535	+	0.944143i	$0.393108\pi$
$984$		0			0
$985$	−3.47861	+	3.74905i	−0.110838	+	0.119455i
$986$	5.99970	+	26.2864i	0.191069	+	0.837130i
$987$		0			0
$988$	2.08333	−	9.12766i	0.0662795	−	0.290389i
$989$	11.7100	+	17.1754i	0.372355	+	0.546145i
$990$		0			0
$991$	−23.0212	−	15.6956i	−0.731293	−	0.498587i	0.139509	−	0.990221i	$-0.455448\pi$
$991$	−23.0212	−	15.6956i	−0.731293	−	0.498587i	−0.870802	+	0.491633i	$0.836400\pi$
$992$	−9.91608	+	1.49461i	−0.314836	+	0.0474539i
$993$		0			0
$994$	5.28160	−	4.94235i	0.167522	−	0.156762i
$995$	3.16300	−	6.56804i	0.100274	−	0.208221i
$996$		0			0
$997$	−10.4555	−	4.10348i	−0.331129	−	0.129958i	0.193952	−	0.981011i	$-0.437869\pi$
$997$	−10.4555	−	4.10348i	−0.331129	−	0.129958i	−0.525080	+	0.851053i	$0.675965\pi$
$998$	−1.56378	+	0.902851i	−0.0495007	+	0.0285793i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bg.a.26.8	yes	216
3.2	odd	2	inner	441.2.bg.a.26.11	yes	216
49.17	odd	42	inner	441.2.bg.a.17.11	yes	216
147.17	even	42	inner	441.2.bg.a.17.8	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bg.a.17.8	✓	216	147.17	even	42	inner
441.2.bg.a.17.11	yes	216	49.17	odd	42	inner
441.2.bg.a.26.8	yes	216	1.1	even	1	trivial
441.2.bg.a.26.11	yes	216	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bg (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.601956 - 0.0451104i) q^{2} +(-1.61735 - 0.243776i) q^{4} +(-1.12371 - 1.04265i) q^{5} +(-0.186554 + 2.63917i) q^{7} +(2.13959 + 0.488348i) q^{8} +O(q^{10})\)	\(q+(-0.601956 - 0.0451104i) q^{2} +(-1.61735 - 0.243776i) q^{4} +(-1.12371 - 1.04265i) q^{5} +(-0.186554 + 2.63917i) q^{7} +(2.13959 + 0.488348i) q^{8} +(0.629389 + 0.678320i) q^{10} +(0.794667 - 1.16556i) q^{11} +(0.574735 + 1.19345i) q^{13} +(0.231351 - 1.58025i) q^{14} +(1.85999 + 0.573730i) q^{16} +(2.32250 - 5.91762i) q^{17} +(3.74233 + 2.16064i) q^{19} +(1.56325 + 1.96026i) q^{20} +(-0.530933 + 0.665769i) q^{22} +(2.23055 - 0.875428i) q^{23} +(-0.198047 - 2.64275i) q^{25} +(-0.292128 - 0.744331i) q^{26} +(0.945087 - 4.22297i) q^{28} +(5.49332 - 4.38078i) q^{29} +(1.56080 - 0.901126i) q^{31} +(-5.17957 - 2.03283i) q^{32} +(-1.66499 + 3.45738i) q^{34} +(2.96136 - 2.77115i) q^{35} +(8.91545 - 1.34379i) q^{37} +(-2.15525 - 1.46942i) q^{38} +(-1.89510 - 2.77961i) q^{40} +(-1.88456 + 8.25681i) q^{41} +(1.93041 + 8.45767i) q^{43} +(-1.56939 + 1.69140i) q^{44} +(-1.38219 + 0.426348i) q^{46} +(-0.0438619 + 0.585297i) q^{47} +(-6.93040 - 0.984693i) q^{49} +1.59975i q^{50} +(-0.638612 - 2.07033i) q^{52} +(-0.517738 + 3.43497i) q^{53} +(-2.10825 + 0.481194i) q^{55} +(-1.68798 + 5.55564i) q^{56} +(-3.50435 + 2.38923i) q^{58} +(2.80416 - 2.60188i) q^{59} +(-0.728803 - 4.83529i) q^{61} +(-0.980180 + 0.472030i) q^{62} +(-0.481233 - 0.231750i) q^{64} +(0.598515 - 1.94034i) q^{65} +(-3.31539 - 5.74243i) q^{67} +(-5.19885 + 9.00467i) q^{68} +(-1.90761 + 1.53452i) q^{70} +(3.54100 + 2.82385i) q^{71} +(10.3796 - 0.777843i) q^{73} +(-5.42733 + 0.406722i) q^{74} +(-5.52593 - 4.40678i) q^{76} +(2.92786 + 2.31470i) q^{77} +(1.25290 - 2.17009i) q^{79} +(-1.49188 - 2.58402i) q^{80} +(1.50689 - 4.88522i) q^{82} +(10.1383 + 4.88235i) q^{83} +(-8.77982 + 4.22814i) q^{85} +(-0.780492 - 5.17822i) q^{86} +(2.26946 - 2.10575i) q^{88} +(-11.4610 + 7.81400i) q^{89} +(-3.25693 + 1.29418i) q^{91} +(-3.82099 + 0.872115i) q^{92} +(0.0528059 - 0.350344i) q^{94} +(-1.95251 - 6.32987i) q^{95} -15.6296i q^{97} +(4.12737 + 0.905375i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) 216 * q - 16 * q^4 + 2 * q^7	\( 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) \) 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Introduction

L-functions

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