LMFDB - Embedded newform 441.2.w.a.62.9

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			62.9
Character	$\chi$	$=$	441.62
Dual form			441.2.w.a.377.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.514347 + 0.117396i) q^{2} +(-1.55117 + 0.747002i) q^{4} +(1.31830 + 1.65310i) q^{5} +(1.93236 + 1.80720i) q^{7} +(1.53509 - 1.22420i) q^{8} +O(q^{10})$	\(q+(-0.514347 + 0.117396i) q^{2} +(-1.55117 + 0.747002i) q^{4} +(1.31830 + 1.65310i) q^{5} +(1.93236 + 1.80720i) q^{7} +(1.53509 - 1.22420i) q^{8} +(-0.872134 - 0.695503i) q^{10} +(-5.51408 + 1.25855i) q^{11} +(2.35470 - 0.537446i) q^{13} +(-1.20607 - 0.702675i) q^{14} +(1.50103 - 1.88223i) q^{16} +(-3.71620 - 1.78963i) q^{17} +7.31415i q^{19} +(-3.27978 - 1.57946i) q^{20} +(2.68840 - 1.29467i) q^{22} +(-0.0740985 - 0.153867i) q^{23} +(0.117789 - 0.516067i) q^{25} +(-1.14804 + 0.552867i) q^{26} +(-4.34740 - 1.35979i) q^{28} +(-2.72613 + 5.66088i) q^{29} +7.05525i q^{31} +(-2.25491 + 4.68236i) q^{32} +(2.12151 + 0.484222i) q^{34} +(-0.440038 + 5.57683i) q^{35} +(-5.40367 - 2.60227i) q^{37} +(-0.858655 - 3.76201i) q^{38} +(4.04743 + 0.923800i) q^{40} +(3.35489 + 4.20690i) q^{41} +(-0.802644 + 1.00648i) q^{43} +(7.61311 - 6.07125i) q^{44} +(0.0561758 + 0.0704423i) q^{46} +(0.861746 + 3.77556i) q^{47} +(0.468065 + 6.98433i) q^{49} +0.279266i q^{50} +(-3.25106 + 2.59264i) q^{52} +(-3.82750 - 7.94789i) q^{53} +(-9.34974 - 7.45617i) q^{55} +(5.17872 + 0.408625i) q^{56} +(0.737613 - 3.23169i) q^{58} +(6.79983 - 8.52672i) q^{59} +(4.41256 - 9.16279i) q^{61} +(-0.828261 - 3.62885i) q^{62} +(-0.461308 + 2.02112i) q^{64} +(3.99266 + 3.18404i) q^{65} +16.0520 q^{67} +7.10130 q^{68} +(-0.428367 - 2.92008i) q^{70} +(4.49782 + 9.33982i) q^{71} +(-9.05018 - 2.06564i) q^{73} +(3.08486 + 0.704100i) q^{74} +(-5.46369 - 11.3455i) q^{76} +(-12.9297 - 7.53305i) q^{77} -4.06292 q^{79} +5.09032 q^{80} +(-2.21945 - 1.76996i) q^{82} +(1.61786 - 7.08830i) q^{83} +(-1.94064 - 8.50252i) q^{85} +(0.294680 - 0.611910i) q^{86} +(-6.92390 + 8.68230i) q^{88} +(-1.45687 + 6.38296i) q^{89} +(5.52142 + 3.21688i) q^{91} +(0.229878 + 0.183322i) q^{92} +(-0.886474 - 1.84078i) q^{94} +(-12.0910 + 9.64227i) q^{95} +5.92935i q^{97} +(-1.06068 - 3.53742i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{11}{14}\right)$	$-1$

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 $

$2$	−0.514347	+	0.117396i	−0.363698	+	0.0830118i	−0.400465	−	0.916312i	$-0.631151\pi$
$2$	−0.514347	+	0.117396i	−0.363698	+	0.0830118i	0.0367665	+	0.999324i	$0.488294\pi$
$3$		0			0
$3$		0			0
$4$	−1.55117	+	0.747002i	−0.775583	+	0.373501i
$5$	1.31830	+	1.65310i	0.589563	+	0.739289i	0.983711	−	0.179758i	$-0.0575316\pi$
$5$	1.31830	+	1.65310i	0.589563	+	0.739289i	−0.394148	+	0.919047i	$0.628960\pi$
$6$		0			0
$7$	1.93236	+	1.80720i	0.730365	+	0.683057i
$7$	1.93236	+	1.80720i	0.730365	+	0.683057i
$8$	1.53509	−	1.22420i	0.542737	−	0.432818i
$9$		0			0
$10$	−0.872134	−	0.695503i	−0.275793	−	0.219937i
$11$	−5.51408	+	1.25855i	−1.66256	+	0.379468i	−0.947540	−	0.319638i	$-0.896439\pi$
$11$	−5.51408	+	1.25855i	−1.66256	+	0.379468i	−0.715018	+	0.699106i	$0.753581\pi$
$12$		0			0
$13$	2.35470	−	0.537446i	0.653077	−	0.149061i	0.116870	−	0.993147i	$-0.462714\pi$
$13$	2.35470	−	0.537446i	0.653077	−	0.149061i	0.536207	+	0.844087i	$0.319857\pi$
$14$	−1.20607	−	0.702675i	−0.322334	−	0.187798i
$15$		0			0
$16$	1.50103	−	1.88223i	0.375257	−	0.470557i
$17$	−3.71620	−	1.78963i	−0.901311	−	0.434048i	−0.0749486	−	0.997187i	$-0.523879\pi$
$17$	−3.71620	−	1.78963i	−0.901311	−	0.434048i	−0.826362	+	0.563139i	$0.809594\pi$
$18$		0			0
$19$			7.31415i			1.67798i	0.544146	+	0.838991i	$0.316854\pi$
$19$			7.31415i			1.67798i	−0.544146	+	0.838991i	$0.683146\pi$
$20$	−3.27978	−	1.57946i	−0.733380	−	0.353177i
$21$		0			0
$22$	2.68840	−	1.29467i	0.573169	−	0.276024i
$23$	−0.0740985	−	0.153867i	−0.0154506	−	0.0320835i	0.893101	−	0.449857i	$-0.148525\pi$
$23$	−0.0740985	−	0.153867i	−0.0154506	−	0.0320835i	−0.908551	+	0.417773i	$0.862811\pi$
$24$		0			0
$25$	0.117789	−	0.516067i	0.0235578	−	0.103213i
$26$	−1.14804	+	0.552867i	−0.225149	+	0.108426i
$27$		0			0
$28$	−4.34740	−	1.35979i	−0.821582	−	0.256975i
$29$	−2.72613	+	5.66088i	−0.506230	+	1.05120i	0.478657	+	0.878002i	$0.341124\pi$
$29$	−2.72613	+	5.66088i	−0.506230	+	1.05120i	−0.984887	+	0.173196i	$0.944591\pi$
$30$		0			0
$31$			7.05525i			1.26716i	0.773677	+	0.633580i	$0.218415\pi$
$31$			7.05525i			1.26716i	−0.773677	+	0.633580i	$0.781585\pi$
$32$	−2.25491	+	4.68236i	−0.398615	+	0.827732i
$33$		0			0
$34$	2.12151	+	0.484222i	0.363837	+	0.0830433i
$35$	−0.440038	+	5.57683i	−0.0743800	+	0.942656i
$36$		0			0
$37$	−5.40367	−	2.60227i	−0.888358	−	0.427811i	−0.0666881	−	0.997774i	$-0.521243\pi$
$37$	−5.40367	−	2.60227i	−0.888358	−	0.427811i	−0.821670	+	0.569963i	$0.806958\pi$
$38$	−0.858655	−	3.76201i	−0.139292	−	0.610279i
$39$		0			0
$40$	4.04743	+	0.923800i	0.639955	+	0.146066i
$41$	3.35489	+	4.20690i	0.523946	+	0.657007i	0.971442	−	0.237279i	$-0.0762555\pi$
$41$	3.35489	+	4.20690i	0.523946	+	0.657007i	−0.447496	+	0.894286i	$0.647684\pi$
$42$		0			0
$43$	−0.802644	+	1.00648i	−0.122402	+	0.153487i	−0.839257	−	0.543735i	$-0.817010\pi$
$43$	−0.802644	+	1.00648i	−0.122402	+	0.153487i	0.716855	+	0.697223i	$0.245581\pi$
$44$	7.61311	−	6.07125i	1.14772	−	0.915276i
$45$		0			0
$46$	0.0561758	+	0.0704423i	0.00828267	+	0.0103861i
$47$	0.861746	+	3.77556i	0.125699	+	0.550721i	0.998082	+	0.0618999i	$0.0197159\pi$
$47$	0.861746	+	3.77556i	0.125699	+	0.550721i	−0.872384	+	0.488822i	$0.837427\pi$
$48$		0			0
$49$	0.468065	+	6.98433i	0.0668664	+	0.997762i
$50$			0.279266i			0.0394942i
$51$		0			0
$52$	−3.25106	+	2.59264i	−0.450841	+	0.359534i
$53$	−3.82750	−	7.94789i	−0.525748	−	1.09173i	−0.979657	−	0.200678i	$-0.935685\pi$
$53$	−3.82750	−	7.94789i	−0.525748	−	1.09173i	0.453910	−	0.891048i	$-0.350029\pi$
$54$		0			0
$55$	−9.34974	−	7.45617i	−1.26072	−	1.00539i
$56$	5.17872	+	0.408625i	0.692036	+	0.0546049i
$57$		0			0
$58$	0.737613	−	3.23169i	0.0968534	−	0.424342i
$59$	6.79983	−	8.52672i	0.885263	−	1.11008i	−0.107994	−	0.994152i	$-0.534443\pi$
$59$	6.79983	−	8.52672i	0.885263	−	1.11008i	0.993257	−	0.115933i	$-0.0369859\pi$
$60$		0			0
$61$	4.41256	−	9.16279i	0.564971	−	1.17317i	−0.401371	−	0.915915i	$-0.631466\pi$
$61$	4.41256	−	9.16279i	0.564971	−	1.17317i	0.966342	−	0.257259i	$-0.0828194\pi$
$62$	−0.828261	−	3.62885i	−0.105189	−	0.460864i
$63$		0			0
$64$	−0.461308	+	2.02112i	−0.0576635	+	0.252640i
$65$	3.99266	+	3.18404i	0.495229	+	0.394932i
$66$		0			0
$67$	16.0520			1.96106			0.980530	−	0.196370i	$-0.0629153\pi$
$67$	16.0520			1.96106			0.980530	+	0.196370i	$0.0629153\pi$
$68$	7.10130			0.861159
$69$		0			0
$70$	−0.428367	−	2.92008i	−0.0511997	−	0.349017i
$71$	4.49782	+	9.33982i	0.533793	+	1.10843i	0.977241	+	0.212132i	$0.0680408\pi$
$71$	4.49782	+	9.33982i	0.533793	+	1.10843i	−0.443448	+	0.896300i	$0.646245\pi$
$72$		0			0
$73$	−9.05018	−	2.06564i	−1.05924	−	0.241765i	−0.342798	−	0.939409i	$-0.611375\pi$
$73$	−9.05018	−	2.06564i	−1.05924	−	0.241765i	−0.716445	+	0.697644i	$0.754232\pi$
$74$	3.08486	+	0.704100i	0.358608	+	0.0818499i
$75$		0			0
$76$	−5.46369	−	11.3455i	−0.626728	−	1.30141i
$77$	−12.9297	−	7.53305i	−1.47347	−	0.858471i
$78$		0			0
$79$	−4.06292			−0.457114			−0.228557	−	0.973531i	$-0.573401\pi$
$79$	−4.06292			−0.457114			−0.228557	+	0.973531i	$0.573401\pi$
$80$	5.09032			0.569115
$81$		0			0
$82$	−2.21945	−	1.76996i	−0.245098	−	0.195459i
$83$	1.61786	−	7.08830i	0.177583	−	0.778042i	−0.805159	−	0.593060i	$-0.797920\pi$
$83$	1.61786	−	7.08830i	0.177583	−	0.778042i	0.982742	−	0.184983i	$-0.0592230\pi$
$84$		0			0
$85$	−1.94064	−	8.50252i	−0.210492	−	0.922228i
$86$	0.294680	−	0.611910i	0.0317762	−	0.0659840i
$87$		0			0
$88$	−6.92390	+	8.68230i	−0.738091	+	0.925536i
$89$	−1.45687	+	6.38296i	−0.154428	+	0.676592i	0.837138	+	0.546991i	$0.184227\pi$
$89$	−1.45687	+	6.38296i	−0.154428	+	0.676592i	−0.991566	+	0.129601i	$0.958630\pi$
$90$		0			0
$91$	5.52142	+	3.21688i	0.578802	+	0.337220i
$92$	0.229878	+	0.183322i	0.0239665	+	0.0191126i
$93$		0			0
$94$	−0.886474	−	1.84078i	−0.0914328	−	0.189862i
$95$	−12.0910	+	9.64227i	−1.24051	+	0.989276i
$96$		0			0
$97$			5.92935i			0.602034i	0.953619	+	0.301017i	$0.0973261\pi$
$97$			5.92935i			0.602034i	−0.953619	+	0.301017i	$0.902674\pi$
$98$	−1.06068	−	3.53742i	−0.107145	−	0.357334i
$99$		0			0
$100$	0.202793	+	0.888495i	0.0202793	+	0.0888495i
$101$	−2.62288	−	3.28899i	−0.260986	−	0.327266i	0.634023	−	0.773314i	$-0.281403\pi$
$101$	−2.62288	−	3.28899i	−0.260986	−	0.327266i	−0.895009	+	0.446048i	$0.852831\pi$
$102$		0			0
$103$	9.17579	−	7.31745i	0.904118	−	0.721010i	−0.0566411	−	0.998395i	$-0.518039\pi$
$103$	9.17579	−	7.31745i	0.904118	−	0.721010i	0.960759	+	0.277385i	$0.0894677\pi$
$104$	2.95675	−	3.70764i	0.289933	−	0.363564i
$105$		0			0
$106$	2.90172	+	3.63864i	0.281840	+	0.353416i
$107$	8.96045	+	2.04516i	0.866240	+	0.197714i	0.632476	−	0.774580i	$-0.282039\pi$
$107$	8.96045	+	2.04516i	0.866240	+	0.197714i	0.233764	+	0.972293i	$0.424896\pi$
$108$		0			0
$109$	−0.120265	−	0.526914i	−0.0115193	−	0.0504692i	0.968842	−	0.247681i	$-0.0796685\pi$
$109$	−0.120265	−	0.526914i	−0.0115193	−	0.0504692i	−0.980361	+	0.197212i	$0.936811\pi$
$110$	5.68434	+	2.73743i	0.541981	+	0.261004i
$111$		0			0
$112$	6.30209	−	0.924497i	0.595492	−	0.0873567i
$113$	6.08503	+	1.38887i	0.572432	+	0.130654i	0.498931	−	0.866641i	$-0.333726\pi$
$113$	6.08503	+	1.38887i	0.572432	+	0.130654i	0.0735001	+	0.997295i	$0.476583\pi$
$114$		0			0
$115$	0.156673	−	0.325336i	0.0146099	−	0.0303377i
$116$		−	10.8174i		−	1.00437i
$117$		0			0
$118$	−2.49647	+	5.18397i	−0.229819	+	0.477223i
$119$	−3.94684	−	10.1741i	−0.361806	−	0.932660i
$120$		0			0
$121$	18.9105	−	9.10679i	1.71913	−	0.827890i
$122$	−1.19391	+	5.23087i	−0.108092	+	0.473581i
$123$		0			0
$124$	−5.27029	−	10.9439i	−0.473286	−	0.982789i
$125$	10.5334	−	5.07262i	0.942137	−	0.453709i
$126$		0			0
$127$	4.20637	+	2.02568i	0.373255	+	0.179750i	0.611101	−	0.791553i	$-0.290727\pi$
$127$	4.20637	+	2.02568i	0.373255	+	0.179750i	−0.237846	+	0.971303i	$0.576441\pi$
$128$		−	11.4878i		−	1.01539i
$129$		0			0
$130$	−2.42741	−	1.16898i	−0.212898	−	0.102526i
$131$	9.65188	−	12.1031i	0.843289	−	1.05745i	−0.154299	−	0.988024i	$-0.549312\pi$
$131$	9.65188	−	12.1031i	0.843289	−	1.05745i	0.997587	−	0.0694261i	$-0.0221168\pi$
$132$		0			0
$133$	−13.2181	+	14.1336i	−1.14616	+	1.22554i
$134$	−8.25629	+	1.88444i	−0.713234	+	0.162791i
$135$		0			0
$136$	−7.89556	+	1.80211i	−0.677039	+	0.154530i
$137$	13.8306	+	11.0296i	1.18163	+	0.942319i	0.999164	−	0.0408932i	$-0.0130203\pi$
$137$	13.8306	+	11.0296i	1.18163	+	0.942319i	0.182467	+	0.983212i	$0.441592\pi$
$138$		0			0
$139$	−4.63505	+	3.69633i	−0.393140	+	0.313519i	−0.800032	−	0.599958i	$-0.795184\pi$
$139$	−4.63505	+	3.69633i	−0.393140	+	0.313519i	0.406892	+	0.913476i	$0.366613\pi$
$140$	−3.48333	−	8.97930i	−0.294395	−	0.758889i
$141$		0			0
$142$	−3.40990	−	4.27588i	−0.286153	−	0.358824i
$143$	−12.3076	+	5.92703i	−1.02921	+	0.495644i
$144$		0			0
$145$	−12.9519	+	2.95618i	−1.07559	+	0.245497i
$146$	4.89743			0.405315
$147$		0			0
$148$	10.3259			0.848784
$149$	5.96750	−	1.36204i	0.488877	−	0.111583i	0.0290252	−	0.999579i	$-0.490760\pi$
$149$	5.96750	−	1.36204i	0.488877	−	0.111583i	0.459852	+	0.887996i	$0.347903\pi$
$150$		0			0
$151$	1.83222	−	0.882352i	0.149104	−	0.0718048i	−0.357844	−	0.933781i	$-0.616488\pi$
$151$	1.83222	−	0.882352i	0.149104	−	0.0718048i	0.506948	+	0.861977i	$0.330774\pi$
$152$	8.95395	+	11.2279i	0.726261	+	0.910703i
$153$		0			0
$154$	7.53469	+	2.35671i	0.607163	+	0.189909i
$155$	−11.6630	+	9.30096i	−0.936797	+	0.747071i
$156$		0			0
$157$	−7.53284	−	6.00724i	−0.601186	−	0.479430i	0.274973	−	0.961452i	$-0.411331\pi$
$157$	−7.53284	−	6.00724i	−0.601186	−	0.479430i	−0.876159	+	0.482022i	$0.839903\pi$
$158$	2.08975	−	0.476972i	0.166252	−	0.0379459i
$159$		0			0
$160$	−10.7131	+	2.44519i	−0.846941	+	0.193309i
$161$	0.134883	−	0.431238i	0.0106303	−	0.0339863i
$162$		0			0
$163$	9.49489	−	11.9062i	0.743697	−	0.932567i	−0.255718	−	0.966751i	$-0.582312\pi$
$163$	9.49489	−	11.9062i	0.743697	−	0.932567i	0.999416	+	0.0341845i	$0.0108834\pi$
$164$	−8.34656	−	4.01949i	−0.651757	−	0.313869i
$165$		0			0
$166$			3.83578i			0.297714i
$167$	13.4231	+	6.46422i	1.03871	+	0.500216i	0.873898	−	0.486109i	$-0.161584\pi$
$167$	13.4231	+	6.46422i	1.03871	+	0.500216i	0.164811	+	0.986325i	$0.447299\pi$
$168$		0			0
$169$	−6.45682	+	3.10944i	−0.496678	+	0.239188i
$170$	1.99633	+	4.14542i	0.153112	+	0.317939i
$171$		0			0
$172$	0.493189	−	2.16080i	0.0376053	−	0.164760i
$173$	−3.12247	+	1.50370i	−0.237397	+	0.114324i	−0.548800	−	0.835954i	$-0.684915\pi$
$173$	−3.12247	+	1.50370i	−0.237397	+	0.114324i	0.311403	+	0.950278i	$0.399201\pi$
$174$		0			0
$175$	1.16025	−	0.784362i	0.0877065	−	0.0592922i
$176$	−5.90790	+	12.2679i	−0.445324	+	0.924726i
$177$		0			0
$178$		−	3.45409i		−	0.258895i
$179$	−8.50242	+	17.6555i	−0.635500	+	1.31963i	0.295755	+	0.955264i	$0.404429\pi$
$179$	−8.50242	+	17.6555i	−0.635500	+	1.31963i	−0.931256	+	0.364367i	$0.881286\pi$
$180$		0			0
$181$	1.95640	+	0.446536i	0.145418	+	0.0331908i	0.294610	−	0.955617i	$-0.404810\pi$
$181$	1.95640	+	0.446536i	0.145418	+	0.0331908i	−0.149192	+	0.988808i	$0.547667\pi$
$182$	−3.21757	−	1.00640i	−0.238503	−	0.0745991i
$183$		0			0
$184$	−0.302111	−	0.145489i	−0.0222720	−	0.0107256i
$185$	−2.82186	−	12.3634i	−0.207468	−	0.908975i
$186$		0			0
$187$	22.7438	+	5.19111i	1.66319	+	0.379612i
$188$	−4.15706	−	5.21279i	−0.303185	−	0.380182i
$189$		0			0
$190$	5.08702	−	6.37892i	0.369051	−	0.462775i
$191$	−13.3458	+	10.6429i	−0.965668	+	0.770095i	−0.973220	−	0.229877i	$-0.926168\pi$
$191$	−13.3458	+	10.6429i	−0.965668	+	0.770095i	0.00755144	+	0.999971i	$0.497596\pi$
$192$		0			0
$193$	12.3690	+	15.5102i	0.890340	+	1.11645i	0.992568	+	0.121690i	$0.0388313\pi$
$193$	12.3690	+	15.5102i	0.890340	+	1.11645i	−0.102228	+	0.994761i	$0.532597\pi$
$194$	−0.696084	−	3.04974i	−0.0499759	−	0.218959i
$195$		0			0
$196$	−5.94336	−	10.4842i	−0.424526	−	0.748873i
$197$			1.51469i			0.107917i	0.998543	+	0.0539587i	$0.0171839\pi$
$197$			1.51469i			0.107917i	−0.998543	+	0.0539587i	$0.982816\pi$
$198$		0			0
$199$	2.62048	−	2.08976i	0.185761	−	0.148139i	−0.526194	−	0.850365i	$-0.676381\pi$
$199$	2.62048	−	2.08976i	0.185761	−	0.148139i	0.711955	+	0.702225i	$0.247810\pi$
$200$	−0.450950	−	0.936408i	−0.0318870	−	0.0662140i
$201$		0			0
$202$	1.73519	+	1.38377i	0.122087	+	0.0973614i
$203$	−15.4982	+	6.01221i	−1.08776	+	0.421974i
$204$		0			0
$205$	−2.53166	+	11.0919i	−0.176819	+	0.774694i
$206$	−3.86050	+	4.84092i	−0.268974	+	0.337283i
$207$		0			0
$208$	2.52288	−	5.23881i	0.174930	−	0.363246i
$209$	−9.20524	−	40.3308i	−0.636740	−	2.78974i
$210$		0			0
$211$	−3.87964	+	16.9978i	−0.267085	+	1.17018i	0.646301	+	0.763083i	$0.276315\pi$
$211$	−3.87964	+	16.9978i	−0.267085	+	1.17018i	−0.913386	+	0.407095i	$0.866542\pi$
$212$	11.8742	+	9.46934i	0.815522	+	0.650357i
$213$		0			0
$214$	−4.84888			−0.331463
$215$	−2.72195			−0.185635
$216$		0			0
$217$	−12.7502	+	13.6333i	−0.865543	+	0.925490i
$218$	0.123716	+	0.256898i	0.00837908	+	0.0173993i
$219$		0			0
$220$	20.0728	+	4.58148i	1.35331	+	0.308883i
$221$	−9.71237	−	2.21679i	−0.653325	−	0.149117i
$222$		0			0
$223$	−9.61037	−	19.9561i	−0.643558	−	1.33636i	−0.926162	−	0.377125i	$-0.876913\pi$
$223$	−9.61037	−	19.9561i	−0.643558	−	1.33636i	0.282604	−	0.959237i	$-0.408802\pi$
$224$	−12.8193	+	4.97296i	−0.856523	+	0.332270i
$225$		0			0
$226$	−3.29287			−0.219038
$227$	5.13967			0.341132			0.170566	−	0.985346i	$-0.445440\pi$
$227$	5.13967			0.341132			0.170566	+	0.985346i	$0.445440\pi$
$228$		0			0
$229$	−8.15119	−	6.50036i	−0.538646	−	0.429556i	0.316006	−	0.948757i	$-0.397658\pi$
$229$	−8.15119	−	6.50036i	−0.538646	−	0.429556i	−0.854652	+	0.519201i	$0.826229\pi$
$230$	−0.0423913	+	0.185728i	−0.00279520	+	0.0122466i
$231$		0			0
$232$	2.74515	+	12.0273i	0.180228	+	0.789630i
$233$	5.04832	−	10.4829i	0.330726	−	0.686760i	−0.667604	−	0.744516i	$-0.732680\pi$
$233$	5.04832	−	10.4829i	0.330726	−	0.686760i	0.998331	+	0.0577558i	$0.0183945\pi$
$234$		0			0
$235$	−5.10533	+	6.40188i	−0.333035	+	0.417613i
$236$	−4.17819	+	18.3059i	−0.271977	+	1.19161i
$237$		0			0
$238$	3.22445	+	4.76969i	0.209010	+	0.309173i
$239$	8.51936	+	6.79396i	0.551072	+	0.439465i	0.859023	−	0.511937i	$-0.171072\pi$
$239$	8.51936	+	6.79396i	0.551072	+	0.439465i	−0.307951	+	0.951402i	$0.599643\pi$
$240$		0			0
$241$	0.0921951	+	0.191445i	0.00593881	+	0.0123321i	0.903917	−	0.427708i	$-0.140679\pi$
$241$	0.0921951	+	0.191445i	0.00593881	+	0.0123321i	−0.897978	+	0.440040i	$0.854964\pi$
$242$	−8.65744	+	6.90407i	−0.556521	+	0.443811i
$243$		0			0
$244$			17.5092i			1.12091i
$245$	−10.9287	+	9.98123i	−0.698212	+	0.637677i
$246$		0			0
$247$	3.93096	+	17.2227i	0.250121	+	1.09585i
$248$	8.63700	+	10.8305i	0.548450	+	0.687735i
$249$		0			0
$250$	−4.82232	+	3.84567i	−0.304990	+	0.243222i
$251$	−10.7448	+	13.4736i	−0.678207	+	0.850445i	−0.995188	−	0.0979871i	$-0.968760\pi$
$251$	−10.7448	+	13.4736i	−0.678207	+	0.850445i	0.316980	+	0.948432i	$0.397331\pi$
$252$		0			0
$253$	0.602235	+	0.755179i	0.0378622	+	0.0474777i
$254$	−2.40134	−	0.548091i	−0.150674	−	0.0343903i
$255$		0			0
$256$	0.426007	+	1.86646i	0.0266254	+	0.116654i
$257$	3.78577	+	1.82313i	0.236150	+	0.113724i	0.548216	−	0.836337i	$-0.315307\pi$
$257$	3.78577	+	1.82313i	0.236150	+	0.113724i	−0.312067	+	0.950060i	$0.601021\pi$
$258$		0			0
$259$	−5.73904	−	14.7941i	−0.356607	−	0.919258i
$260$	−8.57177	−	1.95645i	−0.531599	−	0.121334i
$261$		0			0
$262$	−3.54356	+	7.35828i	−0.218922	+	0.454596i
$263$		−	0.457017i		−	0.0281808i	−0.999901	−	0.0140904i	$-0.995515\pi$
$263$		−	0.457017i		−	0.0281808i	0.999901	−	0.0140904i	$-0.00448527\pi$
$264$		0			0
$265$	8.09284	−	16.8050i	0.497139	−	1.03232i
$266$	5.13947	−	8.82134i	0.315121	−	0.540871i
$267$		0			0
$268$	−24.8993	+	11.9909i	−1.52097	+	0.732458i
$269$	6.12581	−	26.8389i	0.373497	−	1.63640i	−0.343379	−	0.939197i	$-0.611572\pi$
$269$	6.12581	−	26.8389i	0.373497	−	1.63640i	0.716876	−	0.697200i	$-0.245571\pi$
$270$		0			0
$271$	4.78694	+	9.94018i	0.290786	+	0.603823i	0.994271	−	0.106887i	$-0.0340882\pi$
$271$	4.78694	+	9.94018i	0.290786	+	0.603823i	−0.703485	+	0.710710i	$0.748374\pi$
$272$	−8.94660	+	4.30846i	−0.542467	+	0.261239i
$273$		0			0
$274$	−8.40858	−	4.04936i	−0.507981	−	0.244631i
$275$			2.99388i			0.180538i
$276$		0			0
$277$	9.25927	+	4.45903i	0.556335	+	0.267917i	0.690854	−	0.722994i	$-0.257235\pi$
$277$	9.25927	+	4.45903i	0.556335	+	0.267917i	−0.134519	+	0.990911i	$0.542949\pi$
$278$	1.95009	−	2.44534i	0.116959	−	0.146661i
$279$		0			0
$280$	6.15162	+	9.09963i	0.367630	+	0.543807i
$281$	3.31754	−	0.757208i	0.197908	−	0.0451712i	−0.122418	−	0.992479i	$-0.539065\pi$
$281$	3.31754	−	0.757208i	0.197908	−	0.0451712i	0.320326	+	0.947307i	$0.396208\pi$
$282$		0			0
$283$	−15.6998	+	3.58337i	−0.933254	+	0.213009i	−0.662005	−	0.749500i	$-0.730294\pi$
$283$	−15.6998	+	3.58337i	−0.933254	+	0.213009i	−0.271250	+	0.962509i	$0.587437\pi$
$284$	−13.9537	−	11.1277i	−0.828002	−	0.660309i
$285$		0			0
$286$	5.63458	−	4.49342i	0.333179	−	0.265702i
$287$	−1.11983	+	14.1922i	−0.0661016	+	0.837740i
$288$		0			0
$289$	0.00804766	+	0.0100914i	0.000473392	+	0.000593614i
$290$	6.31471	−	3.04100i	0.370813	−	0.178574i
$291$		0			0
$292$	15.5814	−	3.55635i	0.911831	−	0.208120i
$293$	−7.07043			−0.413059			−0.206530	−	0.978440i	$-0.566217\pi$
$293$	−7.07043			−0.413059			−0.206530	+	0.978440i	$0.566217\pi$
$294$		0			0
$295$	23.0598			1.34259
$296$	−11.4808	+	2.62042i	−0.667309	+	0.152309i
$297$		0			0
$298$	−2.90947	+	1.40113i	−0.168541	+	0.0811651i
$299$	−0.257175	−	0.322488i	−0.0148728	−	0.0186499i
$300$		0			0
$301$	−3.36992	+	0.494356i	−0.194239	+	0.0284942i
$302$	−0.838814	+	0.668932i	−0.0482683	+	0.0384927i
$303$		0			0
$304$	13.7669	+	10.9787i	0.789586	+	0.629674i
$305$	20.9641	−	4.78492i	1.20040	−	0.273984i
$306$		0			0
$307$	6.91108	−	1.57741i	0.394436	−	0.0900275i	−0.0207023	−	0.999786i	$-0.506590\pi$
$307$	6.91108	−	1.57741i	0.394436	−	0.0900275i	0.415139	+	0.909758i	$0.363733\pi$
$308$	25.6833	+	2.02653i	1.46344	+	0.115472i
$309$		0			0
$310$	4.90695	−	6.15312i	0.278696	−	0.349474i
$311$	−12.6509	−	6.09234i	−0.717365	−	0.345465i	0.0393360	−	0.999226i	$-0.487476\pi$
$311$	−12.6509	−	6.09234i	−0.717365	−	0.345465i	−0.756701	+	0.653761i	$0.773190\pi$
$312$		0			0
$313$		−	30.3649i		−	1.71633i	−0.513376	−	0.858164i	$-0.671605\pi$
$313$		−	30.3649i		−	1.71633i	0.513376	−	0.858164i	$-0.328395\pi$
$314$	4.57973	+	2.20548i	0.258449	+	0.124462i
$315$		0			0
$316$	6.30226	−	3.03501i	0.354530	−	0.170733i
$317$	4.58233	+	9.51530i	0.257369	+	0.534432i	0.989115	−	0.147145i	$-0.0470085\pi$
$317$	4.58233	+	9.51530i	0.257369	+	0.534432i	−0.731746	+	0.681578i	$0.761294\pi$
$318$		0			0
$319$	7.90761	−	34.6455i	0.442741	−	1.93978i
$320$	−3.94926	+	1.90186i	−0.220770	+	0.106317i
$321$		0			0
$322$	−0.0187510	+	0.237641i	−0.00104495	+	0.0132432i
$323$	13.0896	−	27.1808i	0.728325	−	1.51238i
$324$		0			0
$325$		−	1.27849i		−	0.0709179i
$326$	−3.48592	+	7.23860i	−0.193068	+	0.400909i
$327$		0			0
$328$	10.3001	+	2.35094i	0.568729	+	0.129809i
$329$	−5.15797	+	8.85310i	−0.284368	+	0.488087i
$330$		0			0
$331$	−20.3723	−	9.81076i	−1.11976	−	0.539248i	−0.219942	−	0.975513i	$-0.570587\pi$
$331$	−20.3723	−	9.81076i	−1.11976	−	0.539248i	−0.899818	+	0.436265i	$0.856301\pi$
$332$	2.78541	+	12.2037i	0.152869	+	0.669764i
$333$		0			0
$334$	−7.66300	−	1.74903i	−0.419301	−	0.0957027i
$335$	21.1614	+	26.5355i	1.15617	+	1.44979i
$336$		0			0
$337$	8.58540	−	10.7658i	0.467677	−	0.586448i	−0.490924	−	0.871203i	$-0.663341\pi$
$337$	8.58540	−	10.7658i	0.467677	−	0.586448i	0.958600	+	0.284754i	$0.0919121\pi$
$338$	2.95601	−	2.35734i	0.160786	−	0.128222i
$339$		0			0
$340$	9.36167	+	11.7392i	0.507708	+	0.636645i
$341$	−8.87940	−	38.9032i	−0.480847	−	2.10673i
$342$		0			0
$343$	−11.7176	+	14.3422i	−0.632691	+	0.774404i
$344$			2.52764i			0.136281i
$345$		0			0
$346$	1.42950	−	1.13999i	0.0768506	−	0.0612863i
$347$	0.423101	+	0.878579i	0.0227133	+	0.0471646i	0.912017	−	0.410153i	$-0.134525\pi$
$347$	0.423101	+	0.878579i	0.0227133	+	0.0471646i	−0.889304	+	0.457317i	$0.848810\pi$
$348$		0			0
$349$	7.20567	+	5.74633i	0.385711	+	0.307594i	0.797079	−	0.603875i	$-0.206377\pi$
$349$	7.20567	+	5.74633i	0.385711	+	0.307594i	−0.411368	+	0.911469i	$0.634949\pi$
$350$	−0.504689	+	0.539644i	−0.0269768	+	0.0288452i
$351$		0			0
$352$	6.54073	−	28.6568i	0.348622	−	1.52741i
$353$	10.1658	−	12.7475i	0.541070	−	0.678481i	−0.433863	−	0.900979i	$-0.642850\pi$
$353$	10.1658	−	12.7475i	0.541070	−	0.678481i	0.974933	+	0.222498i	$0.0714212\pi$
$354$		0			0
$355$	−9.51016	+	19.7481i	−0.504747	+	1.04812i
$356$	−2.50824	−	10.9893i	−0.132936	−	0.582433i
$357$		0			0
$358$	2.30051	−	10.0792i	0.121586	−	0.532702i
$359$	11.2791	+	8.99474i	0.595286	+	0.474724i	0.874183	−	0.485596i	$-0.161398\pi$
$359$	11.2791	+	8.99474i	0.595286	+	0.474724i	−0.278898	+	0.960321i	$0.589969\pi$
$360$		0			0
$361$	−34.4968			−1.81562
$362$	−1.05869			−0.0556436
$363$		0			0
$364$	−10.9676	−	0.865399i	−0.574861	−	0.0453592i
$365$	−8.51616	−	17.6840i	−0.445756	−	0.925623i
$366$		0			0
$367$	13.7526	+	3.13895i	0.717881	+	0.163852i	0.565831	−	0.824521i	$-0.308555\pi$
$367$	13.7526	+	3.13895i	0.717881	+	0.163852i	0.152050	+	0.988373i	$0.451412\pi$
$368$	−0.400837	−	0.0914884i	−0.0208951	−	0.00476916i
$369$		0			0
$370$	2.90284	+	6.02780i	0.150911	+	0.313370i
$371$	6.96728	−	22.2753i	0.361723	−	1.15647i
$372$		0			0
$373$	−20.3315			−1.05272			−0.526362	−	0.850261i	$-0.676444\pi$
$373$	−20.3315			−1.05272			−0.526362	+	0.850261i	$0.676444\pi$
$374$	−12.3076			−0.636411
$375$		0			0
$376$	5.94488	+	4.74088i	0.306584	+	0.244492i
$377$	−3.37682	+	14.7948i	−0.173915	+	0.761972i
$378$		0			0
$379$	−4.98269	−	21.8306i	−0.255943	−	1.12136i	−0.925544	−	0.378640i	$-0.876392\pi$
$379$	−4.98269	−	21.8306i	−0.255943	−	1.12136i	0.669601	−	0.742721i	$-0.266465\pi$
$380$	11.5524	−	23.9888i	0.592625	−	1.23060i
$381$		0			0
$382$	5.61494	−	7.04091i	0.287285	−	0.360244i
$383$	−6.89177	+	30.1948i	−0.352153	+	1.54288i	0.420047	+	0.907502i	$0.362014\pi$
$383$	−6.89177	+	30.1948i	−0.352153	+	1.54288i	−0.772200	+	0.635380i	$0.780844\pi$
$384$		0			0
$385$	−4.59233	−	31.3049i	−0.234047	−	1.59544i
$386$	−8.18281	−	6.52557i	−0.416494	−	0.332143i
$387$		0			0
$388$	−4.42924	−	9.19740i	−0.224860	−	0.466927i
$389$	14.2832	−	11.3905i	0.724188	−	0.577521i	−0.190497	−	0.981688i	$-0.561010\pi$
$389$	14.2832	−	11.3905i	0.724188	−	0.577521i	0.914685	+	0.404167i	$0.132439\pi$
$390$		0			0
$391$			0.704410i			0.0356235i
$392$	9.26871	+	10.1486i	0.468141	+	0.512581i
$393$		0			0
$394$	−0.177819	−	0.779078i	−0.00895842	−	0.0392494i
$395$	−5.35616	−	6.71641i	−0.269498	−	0.337939i
$396$		0			0
$397$	−9.41587	+	7.50891i	−0.472569	+	0.376861i	−0.830619	−	0.556841i	$-0.812013\pi$
$397$	−9.41587	+	7.50891i	−0.472569	+	0.376861i	0.358050	+	0.933702i	$0.383442\pi$
$398$	−1.10251	+	1.38250i	−0.0552636	+	0.0692984i
$399$		0			0
$400$	−0.794552	−	0.996337i	−0.0397276	−	0.0498168i
$401$	−1.41550	−	0.323079i	−0.0706867	−	0.0161338i	0.187031	−	0.982354i	$-0.440113\pi$
$401$	−1.41550	−	0.323079i	−0.0706867	−	0.0161338i	−0.257718	+	0.966220i	$0.582971\pi$
$402$		0			0
$403$	3.79181	+	16.6130i	0.188884	+	0.827554i
$404$	6.52540	+	3.14247i	0.324651	+	0.156344i
$405$		0			0
$406$	7.26565	−	4.91180i	0.360588	−	0.243768i
$407$	33.0714	+	7.54833i	1.63929	+	0.374157i
$408$		0			0
$409$	−2.88286	+	5.98632i	−0.142548	+	0.296005i	−0.960004	−	0.279987i	$-0.909670\pi$
$409$	−2.88286	+	5.98632i	−0.142548	+	0.296005i	0.817455	+	0.575992i	$0.195384\pi$
$410$		−	6.00231i		−	0.296433i
$411$		0			0
$412$	−8.76703	+	18.2049i	−0.431921	+	0.896892i
$413$	28.5492	−	4.18808i	1.40482	−	0.206082i
$414$		0			0
$415$	13.8505	−	6.67005i	0.679894	−	0.327420i
$416$	−2.79312	+	12.2375i	−0.136944	+	0.599991i
$417$		0			0
$418$	9.46938	+	19.6634i	0.463163	+	0.961767i
$419$	30.4497	−	14.6638i	1.48756	−	0.716373i	0.498920	−	0.866648i	$-0.333730\pi$
$419$	30.4497	−	14.6638i	1.48756	−	0.716373i	0.988644	+	0.150275i	$0.0480159\pi$
$420$		0			0
$421$	−5.20192	−	2.50511i	−0.253526	−	0.122092i	0.302805	−	0.953053i	$-0.402077\pi$
$421$	−5.20192	−	2.50511i	−0.253526	−	0.122092i	−0.556331	+	0.830961i	$0.687791\pi$
$422$		−	9.19824i		−	0.447763i
$423$		0			0
$424$	−15.6053	−	7.51513i	−0.757862	−	0.364967i
$425$	−1.36130	+	1.70701i	−0.0660326	+	0.0828022i
$426$		0			0
$427$	25.0857	−	9.73146i	1.21398	−	0.470938i
$428$	−15.4269	+	3.52109i	−0.745687	+	0.170198i
$429$		0			0
$430$	1.40003	−	0.319547i	0.0675153	−	0.0154099i
$431$	−1.09648	−	0.874414i	−0.0528156	−	0.0421191i	0.596726	−	0.802445i	$-0.296468\pi$
$431$	−1.09648	−	0.874414i	−0.0528156	−	0.0421191i	−0.649542	+	0.760326i	$0.725039\pi$
$432$		0			0
$433$	0.260382	−	0.207647i	0.0125131	−	0.00997890i	−0.617213	−	0.786796i	$-0.711738\pi$
$433$	0.260382	−	0.207647i	0.0125131	−	0.00997890i	0.629726	+	0.776817i	$0.283167\pi$
$434$	4.95755	−	8.50909i	0.237970	−	0.408450i
$435$		0			0
$436$	0.580157	+	0.727494i	0.0277845	+	0.0348406i
$437$	1.12541	−	0.541968i	0.0538356	−	0.0259258i
$438$		0			0
$439$	−20.0868	+	4.58469i	−0.958693	+	0.218815i	−0.673113	−	0.739539i	$-0.735043\pi$
$439$	−20.0868	+	4.58469i	−0.958693	+	0.218815i	−0.285580	+	0.958355i	$0.592186\pi$
$440$	−23.4805			−1.11939
$441$		0			0
$442$	5.25578			0.249992
$443$	−38.7351	+	8.84102i	−1.84036	+	0.420050i	−0.993699	−	0.112086i	$-0.964247\pi$
$443$	−38.7351	+	8.84102i	−1.84036	+	0.420050i	−0.846659	+	0.532135i	$0.821390\pi$
$444$		0			0
$445$	−12.4723	+	6.00632i	−0.591242	+	0.284727i
$446$	7.28585	+	9.13616i	0.344995	+	0.432610i
$447$		0			0
$448$	−4.54399	+	3.07187i	−0.214683	+	0.145132i
$449$	19.7080	−	15.7166i	0.930080	−	0.741714i	−0.0361634	−	0.999346i	$-0.511514\pi$
$449$	19.7080	−	15.7166i	0.930080	−	0.741714i	0.966243	+	0.257632i	$0.0829423\pi$
$450$		0			0
$451$	−23.7937	−	18.9749i	−1.12040	−	0.893492i
$452$	−10.4764	+	2.39117i	−0.492768	+	0.112471i
$453$		0			0
$454$	−2.64357	+	0.603378i	−0.124069	+	0.0283180i
$455$	1.96108	+	13.3683i	0.0919370	+	0.626714i
$456$		0			0
$457$	1.29895	−	1.62884i	0.0607625	−	0.0761938i	−0.750521	−	0.660846i	$-0.770198\pi$
$457$	1.29895	−	1.62884i	0.0607625	−	0.0761938i	0.811284	+	0.584652i	$0.198769\pi$
$458$	4.95566	+	2.38652i	0.231563	+	0.111515i
$459$		0			0
$460$			0.621685i			0.0289862i
$461$	6.15668	+	2.96490i	0.286745	+	0.138089i	0.571728	−	0.820444i	$-0.306273\pi$
$461$	6.15668	+	2.96490i	0.286745	+	0.138089i	−0.284982	+	0.958533i	$0.591988\pi$
$462$		0			0
$463$	−4.56591	+	2.19882i	−0.212196	+	0.102188i	−0.536963	−	0.843606i	$-0.680428\pi$
$463$	−4.56591	+	2.19882i	−0.212196	+	0.102188i	0.324767	+	0.945794i	$0.394714\pi$
$464$	6.56306	+	13.6283i	0.304682	+	0.632679i
$465$		0			0
$466$	−1.36593	+	5.98453i	−0.0632755	+	0.277228i
$467$	5.73529	−	2.76197i	0.265398	−	0.127809i	−0.296453	−	0.955047i	$-0.595804\pi$
$467$	5.73529	−	2.76197i	0.265398	−	0.127809i	0.561851	+	0.827239i	$0.310090\pi$
$468$		0			0
$469$	31.0182	+	29.0091i	1.43229	+	1.33952i
$470$	1.87435	−	3.89214i	0.0864575	−	0.179531i
$471$		0			0
$472$		−	21.4136i		−	0.985642i
$473$	3.15913	−	6.56000i	0.145257	−	0.301629i
$474$		0			0
$475$	3.77460	+	0.861527i	0.173190	+	0.0395296i
$476$	13.7223	+	12.8335i	0.628961	+	0.588221i
$477$		0			0
$478$	−5.17950	−	2.49431i	−0.236905	−	0.114087i
$479$	0.895913	+	3.92525i	0.0409353	+	0.179349i	0.991263	−	0.131903i	$-0.0421087\pi$
$479$	0.895913	+	3.92525i	0.0409353	+	0.179349i	−0.950327	+	0.311252i	$0.899252\pi$
$480$		0			0
$481$	−14.1226	−	3.22340i	−0.643936	−	0.146974i
$482$	−0.0698953	−	0.0876459i	−0.00318364	−	0.00399216i
$483$		0			0
$484$	−22.5305	+	28.2523i	−1.02411	+	1.28420i
$485$	−9.80180	+	7.81668i	−0.445077	+	0.354937i
$486$		0			0
$487$	−2.03233	−	2.54846i	−0.0920937	−	0.115482i	0.733650	−	0.679528i	$-0.237815\pi$
$487$	−2.03233	−	2.54846i	−0.0920937	−	0.115482i	−0.825743	+	0.564046i	$0.809244\pi$
$488$	−4.44334	−	19.4676i	−0.201141	−	0.881255i
$489$		0			0
$490$	4.44941	−	6.41681i	0.201004	−	0.289882i
$491$		−	42.0998i		−	1.89994i	−0.312345	−	0.949969i	$-0.601114\pi$
$491$		−	42.0998i		−	1.89994i	0.312345	−	0.949969i	$-0.398886\pi$
$492$		0			0
$493$	20.2617	−	16.1582i	0.912542	−	0.727728i
$494$	−4.04376	−	8.39695i	−0.181937	−	0.377796i
$495$		0			0
$496$	13.2796	+	10.5901i	0.596271	+	0.475510i
$497$	−8.18748	+	26.1764i	−0.367259	+	1.17417i
$498$		0			0
$499$	−8.22740	+	36.0466i	−0.368309	+	1.61367i	0.363115	+	0.931745i	$0.381713\pi$
$499$	−8.22740	+	36.0466i	−0.368309	+	1.61367i	−0.731424	+	0.681923i	$0.761144\pi$
$500$	−12.5498	+	15.7370i	−0.561244	+	0.703778i
$501$		0			0
$502$	3.94482	−	8.19150i	0.176066	−	0.365605i
$503$	2.90271	+	12.7176i	0.129426	+	0.567051i	0.997503	+	0.0706220i	$0.0224984\pi$
$503$	2.90271	+	12.7176i	0.129426	+	0.567051i	−0.868078	+	0.496429i	$0.834644\pi$
$504$		0			0
$505$	1.97927	−	8.67176i	0.0880765	−	0.385888i
$506$	−0.398413	−	0.317724i	−0.0177116	−	0.0141246i
$507$		0			0
$508$	−8.03797			−0.356627
$509$	−25.1907			−1.11656			−0.558280	−	0.829653i	$-0.688538\pi$
$509$	−25.1907			−1.11656			−0.558280	+	0.829653i	$0.688538\pi$
$510$		0			0
$511$	−13.7552	−	20.3471i	−0.608495	−	0.900101i
$512$	9.53048	+	19.7902i	0.421192	+	0.874614i
$513$		0			0
$514$	−2.16123	−	0.493286i	−0.0953276	−	0.0217579i
$515$	24.1930	+	5.52188i	1.06607	+	0.243323i
$516$		0			0
$517$	−9.50347	−	19.7342i	−0.417962	−	0.867907i
$518$	4.68863	+	6.93554i	0.206007	+	0.304730i
$519$		0			0
$520$	10.0270			0.439713
$521$	40.2957			1.76539			0.882694	−	0.469948i	$-0.155727\pi$
$521$	40.2957			1.76539			0.882694	+	0.469948i	$0.155727\pi$
$522$		0			0
$523$	−15.0358	−	11.9907i	−0.657471	−	0.524315i	0.236961	−	0.971519i	$-0.423848\pi$
$523$	−15.0358	−	11.9907i	−0.657471	−	0.524315i	−0.894432	+	0.447204i	$0.852420\pi$
$524$	−5.93065	+	25.9839i	−0.259081	+	1.13511i
$525$		0			0
$526$	0.0536521	+	0.235065i	0.00233934	+	0.0102493i
$527$	12.6263	−	26.2187i	0.550009	−	1.14211i
$528$		0			0
$529$	14.3221	−	17.9593i	0.622699	−	0.780840i
$530$	−2.18969	+	9.59366i	−0.0951140	+	0.416722i
$531$		0			0
$532$	9.94568	−	31.7975i	0.431200	−	1.37860i
$533$	10.1607	+	8.10293i	0.440111	+	0.350977i
$534$		0			0
$535$	8.43173	+	17.5087i	0.364535	+	0.756966i
$536$	24.6412	−	19.6507i	1.06434	−	0.848783i
$537$		0			0
$538$			14.5237i			0.626160i
$539$	−11.3711	−	37.9231i	−0.489788	−	1.63346i
$540$		0			0
$541$	3.91029	+	17.1321i	0.168116	+	0.736566i	0.986750	+	0.162250i	$0.0518750\pi$
$541$	3.91029	+	17.1321i	0.168116	+	0.736566i	−0.818633	+	0.574317i	$0.805268\pi$
$542$	−3.62909	−	4.55074i	−0.155883	−	0.195471i
$543$		0			0
$544$	16.7594	−	13.3651i	0.718552	−	0.573026i
$545$	0.712496	−	0.893442i	0.0305200	−	0.0382709i
$546$		0			0
$547$	−19.7200	−	24.7281i	−0.843165	−	1.05730i	−0.997596	−	0.0692922i	$-0.977926\pi$
$547$	−19.7200	−	24.7281i	−0.843165	−	1.05730i	0.154431	−	0.988004i	$-0.450645\pi$
$548$	−29.6927	−	6.77717i	−1.26841	−	0.289506i
$549$		0			0
$550$	−0.351471	−	1.53989i	−0.0149868	−	0.0656613i
$551$	−41.4045	−	19.9394i	−1.76389	−	0.849445i
$552$		0			0
$553$	−7.85104	−	7.34250i	−0.333860	−	0.312235i
$554$	−5.28595	−	1.20648i	−0.224579	−	0.0512586i
$555$		0			0
$556$	4.42857	−	9.19602i	0.187813	−	0.389998i
$557$			29.1713i			1.23603i	0.786167	+	0.618014i	$0.212063\pi$
$557$			29.1713i			1.23603i	−0.786167	+	0.618014i	$0.787937\pi$
$558$		0			0
$559$	−1.34906	+	2.80135i	−0.0570591	+	0.118484i
$560$	9.83635	+	9.19922i	0.415662	+	0.388738i
$561$		0			0
$562$	−1.61748	+	0.778936i	−0.0682291	+	0.0328574i
$563$	−4.74943	+	20.8086i	−0.200165	+	0.876978i	0.770671	+	0.637233i	$0.219921\pi$
$563$	−4.74943	+	20.8086i	−0.200165	+	0.876978i	−0.970836	+	0.239745i	$0.922936\pi$
$564$		0			0
$565$	5.72598	+	11.8901i	0.240894	+	0.500221i
$566$	7.65446	−	3.68619i	0.321741	−	0.154942i
$567$		0			0
$568$	18.3383	+	8.83127i	0.769459	+	0.370552i
$569$		−	16.7773i		−	0.703340i	−0.936124	−	0.351670i	$-0.885614\pi$
$569$		−	16.7773i		−	0.703340i	0.936124	−	0.351670i	$-0.114386\pi$
$570$		0			0
$571$	10.1446	+	4.88538i	0.424538	+	0.204447i	0.633939	−	0.773383i	$-0.281437\pi$
$571$	10.1446	+	4.88538i	0.424538	+	0.204447i	−0.209401	+	0.977830i	$0.567151\pi$
$572$	14.6636	−	18.3876i	0.613118	−	0.768826i
$573$		0			0
$574$	−1.09013	−	7.43119i	−0.0455012	−	0.310172i
$575$	−0.0881338	+	0.0201160i	−0.00367544	+	0.000838894i
$576$		0			0
$577$	−7.96484	+	1.81792i	−0.331581	+	0.0756812i	−0.385070	−	0.922887i	$-0.625823\pi$
$577$	−7.96484	+	1.81792i	−0.331581	+	0.0756812i	0.0534894	+	0.998568i	$0.482966\pi$
$578$	−0.00532399	−	0.00424574i	−0.000221449	−	0.000176600i
$579$		0			0
$580$	17.8822	−	14.2606i	0.742519	−	0.592139i
$581$	15.9363	−	10.7734i	0.661148	−	0.446956i
$582$		0			0
$583$	31.1080	+	39.0082i	1.28836	+	1.61555i
$584$	−16.4216	+	7.90823i	−0.679531	+	0.327245i
$585$		0			0
$586$	3.63666	−	0.830043i	0.150229	−	0.0342888i
$587$	−42.5611			−1.75668			−0.878342	−	0.478032i	$-0.841350\pi$
$587$	−42.5611			−1.75668			−0.878342	+	0.478032i	$0.841350\pi$
$588$		0			0
$589$	−51.6032			−2.12627
$590$	−11.8607	+	2.70713i	−0.488298	+	0.111451i
$591$		0			0
$592$	−13.0091	+	6.26487i	−0.534672	+	0.257484i
$593$	−26.0023	−	32.6059i	−1.06779	−	1.33896i	−0.937695	−	0.347461i	$-0.887044\pi$
$593$	−26.0023	−	32.6059i	−1.06779	−	1.33896i	−0.130092	−	0.991502i	$-0.541527\pi$
$594$		0			0
$595$	11.6157	−	19.9371i	0.476198	−	0.817341i
$596$	−8.23914	+	6.57050i	−0.337488	+	0.269138i
$597$		0			0
$598$	0.170136	+	0.135679i	0.00695739	+	0.00554833i
$599$	3.73278	−	0.851983i	0.152517	−	0.0348111i	−0.145581	−	0.989346i	$-0.546505\pi$
$599$	3.73278	−	0.851983i	0.152517	−	0.0348111i	0.298098	+	0.954535i	$0.403648\pi$
$600$		0			0
$601$	1.25869	−	0.287287i	0.0513428	−	0.0117187i	−0.196772	−	0.980449i	$-0.563046\pi$
$601$	1.25869	−	0.287287i	0.0513428	−	0.0117187i	0.248115	+	0.968731i	$0.420189\pi$
$602$	1.67527	−	0.649887i	0.0682790	−	0.0264874i
$603$		0			0
$604$	−2.18296	+	2.73735i	−0.0888235	+	0.111381i
$605$	39.9841	+	19.2553i	1.62559	+	0.782841i
$606$		0			0
$607$		−	9.81597i		−	0.398418i	−0.979957	−	0.199209i	$-0.936163\pi$
$607$		−	9.81597i		−	0.398418i	0.979957	−	0.199209i	$-0.0638372\pi$
$608$	−34.2475	−	16.4927i	−1.38892	−	0.668868i
$609$		0			0
$610$	−10.2211	+	4.92222i	−0.413840	+	0.199295i
$611$	4.05831	+	8.42717i	0.164182	+	0.340927i
$612$		0			0
$613$	1.60716	−	7.04143i	0.0649126	−	0.284401i	−0.932045	−	0.362342i	$-0.881977\pi$
$613$	1.60716	−	7.04143i	0.0649126	−	0.284401i	0.996958	+	0.0779409i	$0.0248345\pi$
$614$	−3.36951	+	1.62267i	−0.135983	+	0.0654857i
$615$		0			0
$616$	−29.0702	+	4.26450i	−1.17127	+	0.171822i
$617$	−16.3313	+	33.9123i	−0.657474	+	1.36526i	0.259278	+	0.965803i	$0.416515\pi$
$617$	−16.3313	+	33.9123i	−0.657474	+	1.36526i	−0.916752	+	0.399456i	$0.869199\pi$
$618$		0			0
$619$			37.3926i			1.50294i	0.659770	+	0.751468i	$0.270654\pi$
$619$			37.3926i			1.50294i	−0.659770	+	0.751468i	$0.729346\pi$
$620$	11.1435	−	23.1396i	0.447532	−	0.929311i
$621$		0			0
$622$	7.22216	+	1.64841i	0.289582	+	0.0660952i
$623$	−14.3505	+	9.70135i	−0.574940	+	0.388676i
$624$		0			0
$625$	19.8872	+	9.57716i	0.795487	+	0.383086i
$626$	3.56474	+	15.6181i	0.142475	+	0.624226i
$627$		0			0
$628$	16.1721	+	3.69118i	0.645338	+	0.147294i
$629$	15.4240	+	19.3411i	0.614996	+	0.771181i
$630$		0			0
$631$	−16.1239	+	20.2187i	−0.641883	+	0.804895i	−0.991237	−	0.132095i	$-0.957830\pi$
$631$	−16.1239	+	20.2187i	−0.641883	+	0.804895i	0.349354	+	0.936991i	$0.386401\pi$
$632$	−6.23696	+	4.97381i	−0.248093	+	0.197847i
$633$		0			0
$634$	−3.47397	−	4.35622i	−0.137969	−	0.173008i
$635$	2.19662	+	9.62401i	0.0871701	+	0.381917i
$636$		0			0
$637$	4.85585	+	16.1945i	0.192396	+	0.641648i
$638$			18.7481i			0.742246i
$639$		0			0
$640$	18.9904	−	15.1444i	0.750663	−	0.598633i
$641$	−0.970482	−	2.01523i	−0.0383317	−	0.0795967i	0.880924	−	0.473259i	$-0.156922\pi$
$641$	−0.970482	−	2.01523i	−0.0383317	−	0.0795967i	−0.919255	+	0.393662i	$0.871208\pi$
$642$		0			0
$643$	22.4581	+	17.9097i	0.885661	+	0.706291i	0.956667	−	0.291185i	$-0.0940494\pi$
$643$	22.4581	+	17.9097i	0.885661	+	0.706291i	−0.0710055	+	0.997476i	$0.522621\pi$
$644$	0.112910	+	0.769680i	0.00444926	+	0.0303297i
$645$		0			0
$646$	−3.54167	+	15.5171i	−0.139345	+	0.610511i
$647$	−26.1068	+	32.7369i	−1.02637	+	1.28702i	−0.0691618	+	0.997605i	$0.522032\pi$
$647$	−26.1068	+	32.7369i	−1.02637	+	1.28702i	−0.957203	+	0.289416i	$0.906539\pi$
$648$		0			0
$649$	−26.7635	+	55.5750i	−1.05056	+	2.18151i
$650$	0.150090	+	0.657588i	0.00588702	+	0.0257927i
$651$		0			0
$652$	−5.83418	+	25.5612i	−0.228484	+	1.00106i
$653$	26.4934	+	21.1278i	1.03677	+	0.826793i	0.985119	−	0.171873i	$-0.0549817\pi$
$653$	26.4934	+	21.1278i	1.03677	+	0.826793i	0.0516463	+	0.998665i	$0.483553\pi$
$654$		0			0
$655$	32.7317			1.27893
$656$	12.9541			0.505773
$657$		0			0
$658$	1.61367	−	5.15909i	0.0629073	−	0.201122i
$659$	−17.8450	−	37.0556i	−0.695144	−	1.44348i	−0.886863	−	0.462032i	$-0.847121\pi$
$659$	−17.8450	−	37.0556i	−0.695144	−	1.44348i	0.191719	−	0.981450i	$-0.438594\pi$
$660$		0			0
$661$	24.6014	+	5.61512i	0.956885	+	0.218403i	0.672325	−	0.740256i	$-0.265296\pi$
$661$	24.6014	+	5.61512i	0.956885	+	0.218403i	0.284559	+	0.958658i	$0.408153\pi$
$662$	11.6302	+	2.65451i	0.452019	+	0.103170i
$663$		0			0
$664$	−6.19390	−	12.8618i	−0.240370	−	0.499134i
$665$	−40.7898	−	3.21850i	−1.58176	−	0.124808i
$666$		0			0
$667$	1.07303			0.0415477
$668$	−25.6502			−0.992437
$669$		0			0
$670$	−13.9995	−	11.1642i	−0.540846	−	0.431310i
$671$	−12.7994	+	56.0778i	−0.494115	+	2.16486i
$672$		0			0
$673$	4.18747	+	18.3465i	0.161415	+	0.707205i	0.989250	+	0.146234i	$0.0467151\pi$
$673$	4.18747	+	18.3465i	0.161415	+	0.707205i	−0.827835	+	0.560971i	$0.810428\pi$
$674$	−3.15202	+	6.54523i	−0.121411	+	0.252113i
$675$		0			0
$676$	7.69284	−	9.64652i	0.295878	−	0.371020i
$677$	6.17303	−	27.0458i	0.237249	−	1.03945i	−0.706220	−	0.707993i	$-0.749601\pi$
$677$	6.17303	−	27.0458i	0.237249	−	1.03945i	0.943469	−	0.331462i	$-0.107542\pi$
$678$		0			0
$679$	−10.7155	+	11.4577i	−0.411223	+	0.439705i
$680$	−13.3878	−	10.6764i	−0.513399	−	0.409422i
$681$		0			0
$682$	9.13420	+	18.9674i	0.349766	+	0.726297i
$683$	4.47224	−	3.56649i	0.171125	−	0.136468i	−0.534182	−	0.845369i	$-0.679380\pi$
$683$	4.47224	−	3.56649i	0.171125	−	0.136468i	0.705308	+	0.708901i	$0.250809\pi$
$684$		0			0
$685$			37.4037i			1.42912i
$686$	4.34320	−	8.75246i	0.165824	−	0.334170i
$687$		0			0
$688$	0.689642	+	3.02152i	0.0262924	+	0.115194i
$689$	−13.2842	−	16.6578i	−0.506087	−	0.634613i
$690$		0			0
$691$	20.3200	−	16.2046i	0.773008	−	0.616453i	−0.155470	−	0.987841i	$-0.549689\pi$
$691$	20.3200	−	16.2046i	0.773008	−	0.616453i	0.928478	+	0.371387i	$0.121118\pi$
$692$	3.72020	−	4.66498i	0.141421	−	0.177336i
$693$		0			0
$694$	−0.320763	−	0.402224i	−0.0121760	−	0.0152682i
$695$	−12.2208	−	2.78932i	−0.463561	−	0.105805i
$696$		0			0
$697$	−4.93866	−	21.6377i	−0.187065	−	0.819586i
$698$	−4.38082	−	2.10969i	−0.165816	−	0.0798530i
$699$		0			0
$700$	−1.21382	+	2.08338i	−0.0458780	+	0.0787445i
$701$	−23.4971	−	5.36307i	−0.887475	−	0.202560i	−0.245601	−	0.969371i	$-0.578985\pi$
$701$	−23.4971	−	5.36307i	−0.887475	−	0.202560i	−0.641873	+	0.766811i	$0.721843\pi$
$702$		0			0
$703$	19.0334	−	39.5233i	0.717859	−	1.49065i
$704$		−	11.7252i		−	0.441910i
$705$		0			0
$706$	−3.73224	+	7.75007i	−0.140465	+	0.291678i
$707$	0.875494	−	11.0956i	0.0329263	−	0.417292i
$708$		0			0
$709$	31.7477	−	15.2889i	1.19231	−	0.574186i	0.270836	−	0.962626i	$-0.412700\pi$
$709$	31.7477	−	15.2889i	1.19231	−	0.574186i	0.921474	+	0.388439i	$0.126986\pi$
$710$	2.57318	−	11.2738i	0.0965695	−	0.423099i
$711$		0			0
$712$	5.57756	+	11.5819i	0.209028	+	0.434051i
$713$	1.08557	−	0.522784i	0.0406550	−	0.0195784i
$714$		0			0
$715$	−26.0231	−	12.5321i	−0.973210	−	0.468673i
$716$		−	33.7379i		−	1.26084i
$717$		0			0
$718$	−6.85730	−	3.30230i	−0.255912	−	0.123241i
$719$	2.56392	−	3.21506i	0.0956182	−	0.119901i	−0.731720	−	0.681605i	$-0.761282\pi$
$719$	2.56392	−	3.21506i	0.0956182	−	0.119901i	0.827339	+	0.561703i	$0.189854\pi$
$720$		0			0
$721$	30.9551	+	2.44250i	1.15283	+	0.0909635i
$722$	17.7433	−	4.04980i	0.660339	−	0.150718i
$723$		0			0
$724$	−3.36827	+	0.768785i	−0.125181	+	0.0285717i
$725$	2.60029	+	2.07366i	0.0965722	+	0.0770137i
$726$		0			0
$727$	26.8352	−	21.4003i	0.995261	−	0.793694i	0.0167442	−	0.999860i	$-0.494670\pi$
$727$	26.8352	−	21.4003i	0.995261	−	0.793694i	0.978517	+	0.206165i	$0.0660985\pi$
$728$	12.4140	−	1.82109i	0.460092	−	0.0674941i
$729$		0			0
$730$	6.45630	+	8.09595i	0.238958	+	0.299644i
$731$	4.78402	−	2.30386i	0.176943	−	0.0852114i
$732$		0			0
$733$	−28.9517	+	6.60804i	−1.06936	+	0.244073i	−0.720749	−	0.693196i	$-0.756202\pi$
$733$	−28.9517	+	6.60804i	−1.06936	+	0.244073i	−0.348606	+	0.937269i	$0.613345\pi$
$734$	−7.44213			−0.274694
$735$		0			0
$736$	0.887547			0.0327154
$737$	−88.5118	+	20.2022i	−3.26037	+	0.744159i
$738$		0			0
$739$	8.45006	−	4.06933i	0.310840	−	0.149693i	−0.271959	−	0.962309i	$-0.587672\pi$
$739$	8.45006	−	4.06933i	0.310840	−	0.149693i	0.582800	+	0.812616i	$0.301957\pi$
$740$	13.6127	+	17.0697i	0.500412	+	0.627496i
$741$		0			0
$742$	−0.968568	+	12.2752i	−0.0355572	+	0.450635i
$743$	−2.68756	+	2.14325i	−0.0985969	+	0.0786284i	−0.671548	−	0.740961i	$-0.734370\pi$
$743$	−2.68756	+	2.14325i	−0.0985969	+	0.0786284i	0.572951	+	0.819590i	$0.305799\pi$
$744$		0			0
$745$	10.1186	+	8.06929i	0.370716	+	0.295636i
$746$	10.4574	−	2.38684i	0.382874	−	0.0873885i
$747$		0			0
$748$	−39.1571	+	8.93736i	−1.43173	+	0.326782i
$749$	13.6188	+	20.1453i	0.497622	+	0.736094i
$750$		0			0
$751$	0.520561	−	0.652762i	0.0189955	−	0.0238196i	−0.772243	−	0.635327i	$-0.780865\pi$
$751$	0.520561	−	0.652762i	0.0189955	−	0.0238196i	0.791239	+	0.611508i	$0.209437\pi$
$752$	8.39996	+	4.04521i	0.306315	+	0.147514i
$753$		0			0
$754$		−	8.00611i		−	0.291565i
$755$	3.87404	+	1.86564i	0.140991	+	0.0678976i
$756$		0			0
$757$	29.9525	−	14.4244i	1.08864	−	0.524263i	0.198573	−	0.980086i	$-0.436369\pi$
$757$	29.9525	−	14.4244i	1.08864	−	0.524263i	0.890070	+	0.455823i	$0.150655\pi$
$758$	5.12566	+	10.6435i	0.186172	+	0.386591i
$759$		0			0
$760$	−6.75681	+	29.6035i	−0.245095	+	1.07383i
$761$	−37.6199	+	18.1168i	−1.36372	+	0.656733i	−0.965463	−	0.260541i	$-0.916099\pi$
$761$	−37.6199	+	18.1168i	−1.36372	+	0.656733i	−0.398257	+	0.917274i	$0.630385\pi$
$762$		0			0
$763$	0.719843	−	1.23553i	0.0260601	−	0.0447293i
$764$	12.7513	−	26.4783i	0.461325	−	0.957951i
$765$		0			0
$766$		−	16.3397i		−	0.590377i
$767$	11.4289	−	23.7324i	0.412675	−	0.856929i
$768$		0			0
$769$	−34.1678	−	7.79858i	−1.23212	−	0.281224i	−0.443597	−	0.896226i	$-0.646298\pi$
$769$	−34.1678	−	7.79858i	−1.23212	−	0.281224i	−0.788525	+	0.615002i	$0.789155\pi$
$770$	6.03713	+	15.5625i	0.217563	+	0.560832i
$771$		0			0
$772$	−30.7726	−	14.8193i	−1.10753	−	0.533358i
$773$	8.38913	+	36.7552i	0.301736	+	1.32199i	0.867505	+	0.497428i	$0.165722\pi$
$773$	8.38913	+	36.7552i	0.301736	+	1.32199i	−0.565769	+	0.824564i	$0.691421\pi$
$774$		0			0
$775$	3.64099	+	0.831031i	0.130788	+	0.0298515i
$776$	7.25868	+	9.10209i	0.260571	+	0.326746i
$777$		0			0
$778$	−6.00933	+	7.53547i	−0.215445	+	0.270160i
$779$	−30.7699	+	24.5382i	−1.10245	+	0.879171i
$780$		0			0
$781$	−36.5560	−	45.8397i	−1.30808	−	1.64028i
$782$	−0.0826952	−	0.362311i	−0.00295717	−	0.0129562i
$783$		0			0
$784$	13.8487	+	9.60267i	0.494596	+	0.342952i
$785$		−	20.3719i		−	0.727104i
$786$		0			0
$787$	−33.7504	+	26.9150i	−1.20307	+	0.959417i	−0.999806	−	0.0197069i	$-0.993727\pi$
$787$	−33.7504	+	26.9150i	−1.20307	+	0.959417i	−0.203265	+	0.979124i	$0.565155\pi$
$788$	−1.13148	−	2.34954i	−0.0403073	−	0.0836989i
$789$		0			0
$790$	3.54341	+	2.82577i	0.126069	+	0.100537i
$791$	9.24854	+	13.6807i	0.328840	+	0.486428i
$792$		0			0
$793$	5.46578	−	23.9472i	0.194096	−	0.850388i
$794$	3.96151	−	4.96758i	0.140589	−	0.176293i
$795$		0			0
$796$	−2.50374	+	5.19908i	−0.0887428	+	0.184276i
$797$	−9.00901	−	39.4710i	−0.319115	−	1.39814i	−0.839108	−	0.543965i	$-0.816922\pi$
$797$	−9.00901	−	39.4710i	−0.319115	−	1.39814i	0.519992	−	0.854171i	$-0.325935\pi$
$798$		0			0
$799$	3.55442	−	15.5729i	0.125746	−	0.550930i
$800$	2.15081	+	1.71521i	0.0760426	+	0.0606420i
$801$		0			0
$802$	0.765987			0.0270479
$803$	52.5031			1.85280
$804$		0			0
$805$	0.890697	−	0.345527i	0.0313929	−	0.0121782i
$806$	−3.90062	−	8.09972i	−0.137393	−	0.285300i
$807$		0			0
$808$	−8.05272	−	1.83798i	−0.283294	−	0.0646600i
$809$	17.3104	+	3.95099i	0.608602	+	0.138909i	0.515705	−	0.856766i	$-0.327530\pi$
$809$	17.3104	+	3.95099i	0.608602	+	0.138909i	0.0928970	+	0.995676i	$0.470387\pi$
$810$		0			0
$811$	6.03064	+	12.5228i	0.211764	+	0.439733i	0.979612	−	0.200899i	$-0.0643864\pi$
$811$	6.03064	+	12.5228i	0.211764	+	0.439733i	−0.767848	+	0.640633i	$0.778672\pi$
$812$	19.5492	−	20.9031i	0.686041	−	0.733556i
$813$		0			0
$814$	−17.8963			−0.627266
$815$	32.1993			1.12789
$816$		0			0
$817$	−7.36158	−	5.87066i	−0.257549	−	0.205388i
$818$	0.780019	−	3.41749i	0.0272727	−	0.119490i
$819$		0			0
$820$	−4.35867	−	19.0966i	−0.152211	−	0.666882i
$821$	−9.01646	+	18.7229i	−0.314676	+	0.653432i	−0.996982	−	0.0776348i	$-0.975263\pi$
$821$	−9.01646	+	18.7229i	−0.314676	+	0.653432i	0.682305	+	0.731067i	$0.260977\pi$
$822$		0			0
$823$	3.05830	−	3.83499i	0.106606	−	0.133679i	−0.725666	−	0.688047i	$-0.758468\pi$
$823$	3.05830	−	3.83499i	0.106606	−	0.133679i	0.832272	+	0.554368i	$0.187040\pi$
$824$	5.12770	−	22.4659i	0.178632	−	0.782637i
$825$		0			0
$826$	−14.1926	+	5.50571i	−0.493822	+	0.191568i
$827$	−7.96281	−	6.35013i	−0.276894	−	0.220815i	0.475189	−	0.879883i	$-0.342380\pi$
$827$	−7.96281	−	6.35013i	−0.276894	−	0.220815i	−0.752083	+	0.659068i	$0.770951\pi$
$828$		0			0
$829$	−17.0066	−	35.3147i	−0.590665	−	1.22653i	−0.955372	−	0.295406i	$-0.904545\pi$
$829$	−17.0066	−	35.3147i	−0.590665	−	1.22653i	0.364707	−	0.931122i	$-0.381169\pi$
$830$	−6.34093	+	5.05672i	−0.220097	+	0.175521i
$831$		0			0
$832$			5.00707i			0.173589i
$833$	10.7599	−	26.7928i	0.372810	−	0.928317i
$834$		0			0
$835$	7.00970	+	30.7115i	0.242581	+	1.06281i
$836$	44.4061	+	55.6835i	1.53582	+	1.92585i
$837$		0			0
$838$	−13.9402	+	11.1170i	−0.481557	+	0.384029i
$839$	3.80423	−	4.77035i	0.131337	−	0.164691i	−0.711815	−	0.702367i	$-0.752126\pi$
$839$	3.80423	−	4.77035i	0.131337	−	0.164691i	0.843151	+	0.537677i	$0.180698\pi$
$840$		0			0
$841$	−6.53250	−	8.19150i	−0.225259	−	0.282465i
$842$	2.96969	+	0.677812i	0.102342	+	0.0233589i
$843$		0			0
$844$	−6.67944	−	29.2645i	−0.229916	−	1.00733i
$845$	−13.6523	−	6.57458i	−0.469652	−	0.226172i
$846$		0			0
$847$	52.9997	+	16.5773i	1.82109	+	0.569603i
$848$	−20.7049	−	4.72576i	−0.711010	−	0.162283i
$849$		0			0
$850$	0.499782	−	1.03781i	0.0171424	−	0.0355965i
$851$			1.02427i			0.0351116i
$852$		0			0
$853$	22.8974	−	47.5468i	0.783990	−	1.62797i	0.00576842	−	0.999983i	$-0.498164\pi$
$853$	22.8974	−	47.5468i	0.783990	−	1.62797i	0.778222	−	0.627989i	$-0.216122\pi$
$854$	−11.7603	+	7.95032i	−0.402429	+	0.272054i
$855$		0			0
$856$	16.2588	−	7.82982i	0.555714	−	0.267618i
$857$	−8.55918	+	37.5002i	−0.292376	+	1.28098i	0.588832	+	0.808255i	$0.299588\pi$
$857$	−8.55918	+	37.5002i	−0.292376	+	1.28098i	−0.881208	+	0.472728i	$0.843269\pi$
$858$		0			0
$859$	2.38678	+	4.95621i	0.0814360	+	0.169104i	0.937711	−	0.347417i	$-0.112941\pi$
$859$	2.38678	+	4.95621i	0.0814360	+	0.169104i	−0.856275	+	0.516521i	$0.827227\pi$
$860$	4.22219	−	2.03330i	0.143976	−	0.0693350i
$861$		0			0
$862$	0.666625	+	0.321030i	0.0227053	+	0.0109343i
$863$		−	22.0591i		−	0.750900i	−0.926843	−	0.375450i	$-0.877488\pi$
$863$		−	22.0591i		−	0.750900i	0.926843	−	0.375450i	$-0.122512\pi$
$864$		0			0
$865$	−6.60213	−	3.17942i	−0.224479	−	0.108103i
$866$	−0.109550	+	0.137371i	−0.00372265	+	0.00466805i
$867$		0			0
$868$	9.59363	−	30.6720i	0.325629	−	1.04108i
$869$	22.4033	−	5.11340i	0.759978	−	0.173460i
$870$		0			0
$871$	37.7976	−	8.62706i	1.28072	−	0.292317i
$872$	−0.829663	−	0.661634i	−0.0280959	−	0.0224058i
$873$		0			0
$874$	−0.515225	+	0.410879i	−0.0174278	+	0.0138982i
$875$	29.5216	+	9.23381i	0.998013	+	0.312160i
$876$		0			0
$877$	−9.59101	−	12.0267i	−0.323865	−	0.406114i	0.593070	−	0.805151i	$-0.297916\pi$
$877$	−9.59101	−	12.0267i	−0.323865	−	0.406114i	−0.916935	+	0.399037i	$0.869344\pi$
$878$	9.79339	−	4.71625i	0.330511	−	0.159166i
$879$		0			0
$880$	−28.0684	+	6.40643i	−0.946186	+	0.215961i
$881$	−39.7601			−1.33955			−0.669775	−	0.742564i	$-0.733610\pi$
$881$	−39.7601			−1.33955			−0.669775	+	0.742564i	$0.733610\pi$
$882$		0			0
$883$	30.7265			1.03403			0.517014	−	0.855977i	$-0.327044\pi$
$883$	30.7265			1.03403			0.517014	+	0.855977i	$0.327044\pi$
$884$	16.7215	−	3.81656i	0.562403	−	0.128365i
$885$		0			0
$886$	18.8854	−	9.09471i	0.634466	−	0.305543i
$887$	22.9419	+	28.7682i	0.770314	+	0.965943i	0.999973	−	0.00732797i	$-0.00233259\pi$
$887$	22.9419	+	28.7682i	0.770314	+	0.965943i	−0.229659	+	0.973271i	$0.573761\pi$
$888$		0			0
$889$	4.46743	+	11.5161i	0.149833	+	0.386238i
$890$	5.70995	−	4.55353i	0.191398	−	0.152635i
$891$		0			0
$892$	29.8146	+	23.7763i	0.998266	+	0.796090i
$893$	−27.6150	+	6.30294i	−0.924100	+	0.210920i
$894$		0			0
$895$	−40.3950	+	9.21989i	−1.35026	+	0.308187i
$896$	20.7607	−	22.1986i	0.693566	−	0.741602i
$897$		0			0
$898$	−8.29170	+	10.3975i	−0.276698	+	0.346968i
$899$	−39.9389	−	19.2336i	−1.33204	−	0.641475i
$900$		0			0
$901$			36.3857i			1.21218i
$902$	14.4658	+	6.96637i	0.481659	+	0.231955i
$903$		0			0
$904$	11.0413	−	5.31722i	0.367229	−	0.176848i
$905$	1.84096	+	3.82280i	0.0611956	+	0.127074i
$906$		0			0
$907$	−6.23061	+	27.2981i	−0.206884	+	0.906418i	0.759742	+	0.650225i	$0.225325\pi$
$907$	−6.23061	+	27.2981i	−0.206884	+	0.906418i	−0.966626	+	0.256193i	$0.917532\pi$
$908$	−7.97248	+	3.83934i	−0.264576	+	0.127413i
$909$		0			0
$910$	−2.57806	−	6.64571i	−0.0854620	−	0.220303i
$911$	18.2268	−	37.8483i	0.603880	−	1.25397i	−0.345079	−	0.938574i	$-0.612148\pi$
$911$	18.2268	−	37.8483i	0.603880	−	1.25397i	0.948960	−	0.315397i	$-0.102138\pi$
$912$		0			0
$913$			41.1216i			1.36093i
$914$	−0.476894	+	0.990280i	−0.0157742	+	0.0327556i
$915$		0			0
$916$	17.4996	+	3.99418i	0.578205	+	0.131971i
$917$	40.5236	−	5.94469i	1.33821	−	0.196311i
$918$		0			0
$919$	−2.92329	−	1.40778i	−0.0964305	−	0.0464385i	0.385047	−	0.922897i	$-0.374185\pi$
$919$	−2.92329	−	1.40778i	−0.0964305	−	0.0464385i	−0.481477	+	0.876459i	$0.659900\pi$
$920$	−0.157766	−	0.691219i	−0.00520140	−	0.0227888i
$921$		0			0
$922$	−3.51474	−	0.802217i	−0.115752	−	0.0264196i
$923$	15.6107	+	19.5752i	0.513832	+	0.644324i
$924$		0			0
$925$	−1.97944	+	2.48214i	−0.0650836	+	0.0816123i
$926$	2.09033	−	1.66698i	0.0686924	−	0.0547804i
$927$		0			0
$928$	−20.3591	−	25.5295i	−0.668320	−	0.838046i
$929$	−8.75379	−	38.3529i	−0.287202	−	1.25832i	−0.888346	−	0.459175i	$-0.848145\pi$
$929$	−8.75379	−	38.3529i	−0.287202	−	1.25832i	0.601143	−	0.799141i	$-0.294712\pi$
$930$		0			0
$931$	−51.0845	+	3.42350i	−1.67423	+	0.112201i
$932$			20.0319i			0.656167i
$933$		0			0
$934$	−2.62569	+	2.09391i	−0.0859151	+	0.0685150i
$935$	21.4017	+	44.4412i	0.699912	+	1.45338i
$936$		0			0
$937$	27.7830	+	22.1562i	0.907630	+	0.723811i	0.961520	−	0.274736i	$-0.0885905\pi$
$937$	27.7830	+	22.1562i	0.907630	+	0.723811i	−0.0538896	+	0.998547i	$0.517162\pi$
$938$	−19.3597	−	11.2793i	−0.632117	−	0.368283i
$939$		0			0
$940$	3.13699	−	13.7441i	0.102317	−	0.448282i
$941$	31.8596	−	39.9507i	1.03859	−	1.30235i	0.0865967	−	0.996243i	$-0.472401\pi$
$941$	31.8596	−	39.9507i	1.03859	−	1.30235i	0.951996	−	0.306111i	$-0.0990277\pi$
$942$		0			0
$943$	0.398711	−	0.827932i	0.0129838	−	0.0269612i
$944$	−5.84250	−	25.5977i	−0.190157	−	0.833133i
$945$		0			0
$946$	−0.854770	+	3.74499i	−0.0277910	+	0.121760i
$947$	16.0563	+	12.8045i	0.521761	+	0.416090i	0.848636	−	0.528977i	$-0.177424\pi$
$947$	16.0563	+	12.8045i	0.521761	+	0.416090i	−0.326875	+	0.945068i	$0.605996\pi$
$948$		0			0
$949$	−22.4207			−0.727805
$950$	−2.04259			−0.0662705
$951$		0			0
$952$	−18.5139	−	10.7865i	−0.600038	−	0.349593i
$953$	9.73136	+	20.2074i	0.315230	+	0.654581i	0.997035	−	0.0769527i	$-0.0245190\pi$
$953$	9.73136	+	20.2074i	0.315230	+	0.654581i	−0.681805	+	0.731534i	$0.738805\pi$
$954$		0			0
$955$	−35.1876	−	8.03134i	−1.13864	−	0.259888i
$956$	−18.2900	−	4.17458i	−0.591542	−	0.135016i
$957$		0			0
$958$	−0.921620	−	1.91376i	−0.0297762	−	0.0618309i
$959$	6.79321	+	46.3078i	0.219364	+	1.49536i
$960$		0			0
$961$	−18.7766			−0.605696
$962$	7.64235			0.246399
$963$		0			0
$964$	−0.286020	−	0.228093i	−0.00921208	−	0.00734639i
$965$	−9.33387	+	40.8944i	−0.300468	+	1.31644i
$966$		0			0
$967$	1.80444	+	7.90578i	0.0580270	+	0.254233i	0.995619	−	0.0935049i	$-0.0298071\pi$
$967$	1.80444	+	7.90578i	0.0580270	+	0.254233i	−0.937592	+	0.347738i	$0.886950\pi$
$968$	17.8808	−	37.1298i	0.574710	−	1.19340i
$969$		0			0
$970$	4.12388	−	5.17118i	0.132410	−	0.166037i
$971$	2.14524	−	9.39893i	0.0688441	−	0.301626i	−0.928770	−	0.370655i	$-0.879133\pi$
$971$	2.14524	−	9.39893i	0.0688441	−	0.301626i	0.997615	+	0.0690295i	$0.0219903\pi$
$972$		0			0
$973$	−15.6366	−	1.23380i	−0.501287	−	0.0395539i
$974$	1.34450	+	1.07221i	0.0430807	+	0.0343557i
$975$		0			0
$976$	−10.6231	−	22.0590i	−0.340036	−	0.706093i
$977$	−11.3360	+	9.04016i	−0.362671	+	0.289220i	−0.787823	−	0.615902i	$-0.788792\pi$
$977$	−11.3360	+	9.04016i	−0.362671	+	0.289220i	0.425152	+	0.905122i	$0.360220\pi$
$978$		0			0
$979$		−	37.0297i		−	1.18347i
$980$	9.49631	−	23.6463i	0.303348	−	0.755355i
$981$		0			0
$982$	4.94237	+	21.6539i	0.157717	+	0.691004i
$983$	−9.03295	−	11.3270i	−0.288106	−	0.361274i	0.616625	−	0.787257i	$-0.288500\pi$
$983$	−9.03295	−	11.3270i	−0.288106	−	0.361274i	−0.904731	+	0.425983i	$0.859928\pi$
$984$		0			0
$985$	−2.50394	+	1.99682i	−0.0797821	+	0.0636241i
$986$	−8.52465	+	10.6896i	−0.271480	+	0.340425i
$987$		0			0
$988$	−18.9629	−	23.7788i	−0.603291	−	0.756503i
$989$	0.214340	+	0.0489216i	0.00681560	+	0.00155562i
$990$		0			0
$991$	−3.71363	−	16.2705i	−0.117967	−	0.516849i	−0.999038	−	0.0438632i	$-0.986033\pi$
$991$	−3.71363	−	16.2705i	−0.117967	−	0.516849i	0.881070	−	0.472986i	$-0.156824\pi$
$992$	−33.0352	−	15.9089i	−1.04887	−	0.505109i
$993$		0			0
$994$	1.13820	−	14.4249i	0.0361014	−	0.457531i
$995$	6.90917	+	1.57697i	0.219036	+	0.0499934i
$996$		0			0
$997$	−3.70165	+	7.68656i	−0.117232	+	0.243436i	−0.951325	−	0.308188i	$-0.900277\pi$
$997$	−3.70165	+	7.68656i	−0.117232	+	0.243436i	0.834093	+	0.551624i	$0.185992\pi$
$998$		−	19.5063i		−	0.617463i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.w.a.62.9	✓	120
3.2	odd	2	inner	441.2.w.a.62.12	yes	120
49.34	odd	14	inner	441.2.w.a.377.12	yes	120
147.83	even	14	inner	441.2.w.a.377.9	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.w.a.62.9	✓	120	1.1	even	1	trivial
441.2.w.a.62.12	yes	120	3.2	odd	2	inner
441.2.w.a.377.9	yes	120	147.83	even	14	inner
441.2.w.a.377.12	yes	120	49.34	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)

\(f(q)\)	\(=\)	\(q+(-0.514347 + 0.117396i) q^{2} +(-1.55117 + 0.747002i) q^{4} +(1.31830 + 1.65310i) q^{5} +(1.93236 + 1.80720i) q^{7} +(1.53509 - 1.22420i) q^{8} +O(q^{10})\)	\(q+(-0.514347 + 0.117396i) q^{2} +(-1.55117 + 0.747002i) q^{4} +(1.31830 + 1.65310i) q^{5} +(1.93236 + 1.80720i) q^{7} +(1.53509 - 1.22420i) q^{8} +(-0.872134 - 0.695503i) q^{10} +(-5.51408 + 1.25855i) q^{11} +(2.35470 - 0.537446i) q^{13} +(-1.20607 - 0.702675i) q^{14} +(1.50103 - 1.88223i) q^{16} +(-3.71620 - 1.78963i) q^{17} +7.31415i q^{19} +(-3.27978 - 1.57946i) q^{20} +(2.68840 - 1.29467i) q^{22} +(-0.0740985 - 0.153867i) q^{23} +(0.117789 - 0.516067i) q^{25} +(-1.14804 + 0.552867i) q^{26} +(-4.34740 - 1.35979i) q^{28} +(-2.72613 + 5.66088i) q^{29} +7.05525i q^{31} +(-2.25491 + 4.68236i) q^{32} +(2.12151 + 0.484222i) q^{34} +(-0.440038 + 5.57683i) q^{35} +(-5.40367 - 2.60227i) q^{37} +(-0.858655 - 3.76201i) q^{38} +(4.04743 + 0.923800i) q^{40} +(3.35489 + 4.20690i) q^{41} +(-0.802644 + 1.00648i) q^{43} +(7.61311 - 6.07125i) q^{44} +(0.0561758 + 0.0704423i) q^{46} +(0.861746 + 3.77556i) q^{47} +(0.468065 + 6.98433i) q^{49} +0.279266i q^{50} +(-3.25106 + 2.59264i) q^{52} +(-3.82750 - 7.94789i) q^{53} +(-9.34974 - 7.45617i) q^{55} +(5.17872 + 0.408625i) q^{56} +(0.737613 - 3.23169i) q^{58} +(6.79983 - 8.52672i) q^{59} +(4.41256 - 9.16279i) q^{61} +(-0.828261 - 3.62885i) q^{62} +(-0.461308 + 2.02112i) q^{64} +(3.99266 + 3.18404i) q^{65} +16.0520 q^{67} +7.10130 q^{68} +(-0.428367 - 2.92008i) q^{70} +(4.49782 + 9.33982i) q^{71} +(-9.05018 - 2.06564i) q^{73} +(3.08486 + 0.704100i) q^{74} +(-5.46369 - 11.3455i) q^{76} +(-12.9297 - 7.53305i) q^{77} -4.06292 q^{79} +5.09032 q^{80} +(-2.21945 - 1.76996i) q^{82} +(1.61786 - 7.08830i) q^{83} +(-1.94064 - 8.50252i) q^{85} +(0.294680 - 0.611910i) q^{86} +(-6.92390 + 8.68230i) q^{88} +(-1.45687 + 6.38296i) q^{89} +(5.52142 + 3.21688i) q^{91} +(0.229878 + 0.183322i) q^{92} +(-0.886474 - 1.84078i) q^{94} +(-12.0910 + 9.64227i) q^{95} +5.92935i q^{97} +(-1.06068 - 3.53742i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 24 q^{4}+O(q^{10}) \) 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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