LMFDB - Embedded newform 441.2.w.a.62.13

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			62.13
Character	$\chi$	$=$	441.62
Dual form			441.2.w.a.377.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.843773 - 0.192586i) q^{2} +(-1.12707 + 0.542770i) q^{4} +(0.0384932 + 0.0482690i) q^{5} +(-2.43436 + 1.03628i) q^{7} +(-2.19977 + 1.75426i) q^{8} +O(q^{10})$	\(q+(0.843773 - 0.192586i) q^{2} +(-1.12707 + 0.542770i) q^{4} +(0.0384932 + 0.0482690i) q^{5} +(-2.43436 + 1.03628i) q^{7} +(-2.19977 + 1.75426i) q^{8} +(0.0417755 + 0.0333148i) q^{10} +(-3.40028 + 0.776091i) q^{11} +(-4.60676 + 1.05146i) q^{13} +(-1.85448 + 1.34321i) q^{14} +(0.0416542 - 0.0522327i) q^{16} +(2.52315 + 1.21509i) q^{17} -3.97727i q^{19} +(-0.0695837 - 0.0335097i) q^{20} +(-2.71960 + 1.30969i) q^{22} +(2.91013 + 6.04296i) q^{23} +(1.11176 - 4.87092i) q^{25} +(-3.68457 + 1.77439i) q^{26} +(2.18125 - 2.48926i) q^{28} +(-2.79271 + 5.79911i) q^{29} +5.72297i q^{31} +(2.46665 - 5.12205i) q^{32} +(2.36298 + 0.539334i) q^{34} +(-0.143727 - 0.0776146i) q^{35} +(-7.25379 - 3.49324i) q^{37} +(-0.765965 - 3.35591i) q^{38} +(-0.169353 - 0.0386537i) q^{40} +(0.544686 + 0.683014i) q^{41} +(-0.942514 + 1.18188i) q^{43} +(3.41112 - 2.72028i) q^{44} +(3.61928 + 4.53844i) q^{46} +(2.98681 + 13.0861i) q^{47} +(4.85225 - 5.04536i) q^{49} -4.32406i q^{50} +(4.62146 - 3.68549i) q^{52} +(-2.89428 - 6.01004i) q^{53} +(-0.168349 - 0.134254i) q^{55} +(3.53714 - 6.55008i) q^{56} +(-1.23958 + 5.43097i) q^{58} +(4.09325 - 5.13277i) q^{59} +(1.01825 - 2.11443i) q^{61} +(1.10216 + 4.82889i) q^{62} +(1.06513 - 4.66663i) q^{64} +(-0.228082 - 0.181890i) q^{65} -6.92744 q^{67} -3.50329 q^{68} +(-0.136220 - 0.0378094i) q^{70} +(1.87659 + 3.89678i) q^{71} +(12.7355 + 2.90680i) q^{73} +(-6.79330 - 1.55053i) q^{74} +(2.15874 + 4.48267i) q^{76} +(7.47327 - 5.41293i) q^{77} -6.76297 q^{79} +0.00412462 q^{80} +(0.591130 + 0.471411i) q^{82} +(0.469890 - 2.05872i) q^{83} +(0.0384733 + 0.168563i) q^{85} +(-0.567656 + 1.17875i) q^{86} +(6.11837 - 7.67220i) q^{88} +(2.55267 - 11.1840i) q^{89} +(10.1249 - 7.33353i) q^{91} +(-6.55987 - 5.23132i) q^{92} +(5.04038 + 10.4664i) q^{94} +(0.191979 - 0.153098i) q^{95} +19.0907i q^{97} +(3.12254 - 5.19161i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.843773	−	0.192586i	0.596638	−	0.136179i	0.0864713	−	0.996254i	$-0.472441\pi$
$2$	0.843773	−	0.192586i	0.596638	−	0.136179i	0.510167	+	0.860076i	$0.329584\pi$
$3$		0			0
$3$		0			0
$4$	−1.12707	+	0.542770i	−0.563537	+	0.271385i
$5$	0.0384932	+	0.0482690i	0.0172147	+	0.0215866i	0.790364	−	0.612637i	$-0.209891\pi$
$5$	0.0384932	+	0.0482690i	0.0172147	+	0.0215866i	−0.773150	+	0.634224i	$0.781320\pi$
$6$		0			0
$7$	−2.43436	+	1.03628i	−0.920103	+	0.391677i
$7$	−2.43436	+	1.03628i	−0.920103	+	0.391677i
$8$	−2.19977	+	1.75426i	−0.777737	+	0.620225i
$9$		0			0
$10$	0.0417755	+	0.0333148i	0.0132106	+	0.0105351i
$11$	−3.40028	+	0.776091i	−1.02522	+	0.234000i	−0.701890	−	0.712285i	$-0.747660\pi$
$11$	−3.40028	+	0.776091i	−1.02522	+	0.234000i	−0.323332	+	0.946285i	$0.604803\pi$
$12$		0			0
$13$	−4.60676	+	1.05146i	−1.27769	+	0.291623i	−0.806934	−	0.590642i	$-0.798875\pi$
$13$	−4.60676	+	1.05146i	−1.27769	+	0.291623i	−0.470752	+	0.882266i	$0.656017\pi$
$14$	−1.85448	+	1.34321i	−0.495630	+	0.358988i
$15$		0			0
$16$	0.0416542	−	0.0522327i	0.0104135	−	0.0130582i
$17$	2.52315	+	1.21509i	0.611955	+	0.294702i	0.714074	−	0.700070i	$-0.246848\pi$
$17$	2.52315	+	1.21509i	0.611955	+	0.294702i	−0.102119	+	0.994772i	$0.532562\pi$
$18$		0			0
$19$		−	3.97727i		−	0.912447i	−0.889865	−	0.456224i	$-0.849202\pi$
$19$		−	3.97727i		−	0.912447i	0.889865	−	0.456224i	$-0.150798\pi$
$20$	−0.0695837	−	0.0335097i	−0.0155594	−	0.00749300i
$21$		0			0
$22$	−2.71960	+	1.30969i	−0.579821	+	0.279227i
$23$	2.91013	+	6.04296i	0.606805	+	1.26004i	0.947466	+	0.319857i	$0.103635\pi$
$23$	2.91013	+	6.04296i	0.606805	+	1.26004i	−0.340661	+	0.940186i	$0.610651\pi$
$24$		0			0
$25$	1.11176	−	4.87092i	0.222351	−	0.974185i
$26$	−3.68457	+	1.77439i	−0.722603	+	0.347987i
$27$		0			0
$28$	2.18125	−	2.48926i	0.412217	−	0.470426i
$29$	−2.79271	+	5.79911i	−0.518592	+	1.07687i	0.463084	+	0.886314i	$0.346743\pi$
$29$	−2.79271	+	5.79911i	−0.518592	+	1.07687i	−0.981677	+	0.190554i	$0.938972\pi$
$30$		0			0
$31$			5.72297i			1.02787i	0.857828	+	0.513937i	$0.171814\pi$
$31$			5.72297i			1.02787i	−0.857828	+	0.513937i	$0.828186\pi$
$32$	2.46665	−	5.12205i	0.436046	−	0.905460i
$33$		0			0
$34$	2.36298	+	0.539334i	0.405248	+	0.0924951i
$35$	−0.143727	−	0.0776146i	−0.0242942	−	0.0131193i
$36$		0			0
$37$	−7.25379	−	3.49324i	−1.19251	−	0.574285i	−0.270982	−	0.962584i	$-0.587348\pi$
$37$	−7.25379	−	3.49324i	−1.19251	−	0.574285i	−0.921533	+	0.388300i	$0.873063\pi$
$38$	−0.765965	−	3.35591i	−0.124256	−	0.544401i
$39$		0			0
$40$	−0.169353	−	0.0386537i	−0.0267770	−	0.00611168i
$41$	0.544686	+	0.683014i	0.0850656	+	0.106669i	0.822543	−	0.568703i	$-0.192555\pi$
$41$	0.544686	+	0.683014i	0.0850656	+	0.106669i	−0.737477	+	0.675372i	$0.763983\pi$
$42$		0			0
$43$	−0.942514	+	1.18188i	−0.143732	+	0.180234i	−0.848487	−	0.529217i	$-0.822486\pi$
$43$	−0.942514	+	1.18188i	−0.143732	+	0.180234i	0.704754	+	0.709451i	$0.251057\pi$
$44$	3.41112	−	2.72028i	0.514246	−	0.410098i
$45$		0			0
$46$	3.61928	+	4.53844i	0.533634	+	0.669156i
$47$	2.98681	+	13.0861i	0.435671	+	1.90880i	0.416852	+	0.908974i	$0.363133\pi$
$47$	2.98681	+	13.0861i	0.435671	+	1.90880i	0.0188188	+	0.999823i	$0.494009\pi$
$48$		0			0
$49$	4.85225	−	5.04536i	0.693179	−	0.720766i
$50$		−	4.32406i		−	0.611515i
$51$		0			0
$52$	4.62146	−	3.68549i	0.640881	−	0.511085i
$53$	−2.89428	−	6.01004i	−0.397560	−	0.825542i	−0.999633	−	0.0271006i	$-0.991373\pi$
$53$	−2.89428	−	6.01004i	−0.397560	−	0.825542i	0.602073	−	0.798441i	$-0.294342\pi$
$54$		0			0
$55$	−0.168349	−	0.134254i	−0.0227002	−	0.0181028i
$56$	3.53714	−	6.55008i	0.472671	−	0.875292i
$57$		0			0
$58$	−1.23958	+	5.43097i	−0.162765	+	0.713122i
$59$	4.09325	−	5.13277i	0.532895	−	0.668230i	−0.440396	−	0.897804i	$-0.645162\pi$
$59$	4.09325	−	5.13277i	0.532895	−	0.668230i	0.973291	+	0.229574i	$0.0737333\pi$
$60$		0			0
$61$	1.01825	−	2.11443i	0.130374	−	0.270725i	−0.825555	−	0.564321i	$-0.809138\pi$
$61$	1.01825	−	2.11443i	0.130374	−	0.270725i	0.955929	+	0.293597i	$0.0948523\pi$
$62$	1.10216	+	4.82889i	0.139975	+	0.613269i
$63$		0			0
$64$	1.06513	−	4.66663i	0.133141	−	0.583328i
$65$	−0.228082	−	0.181890i	−0.0282901	−	0.0225606i
$66$		0			0
$67$	−6.92744			−0.846322			−0.423161	−	0.906055i	$-0.639079\pi$
$67$	−6.92744			−0.846322			−0.423161	+	0.906055i	$0.639079\pi$
$68$	−3.50329			−0.424837
$69$		0			0
$70$	−0.136220	−	0.0378094i	−0.0162814	−	0.00451909i
$71$	1.87659	+	3.89678i	0.222711	+	0.462463i	0.982146	−	0.188119i	$-0.0602391\pi$
$71$	1.87659	+	3.89678i	0.222711	+	0.462463i	−0.759436	+	0.650582i	$0.774525\pi$
$72$		0			0
$73$	12.7355	+	2.90680i	1.49058	+	0.340215i	0.888743	−	0.458406i	$-0.151579\pi$
$73$	12.7355	+	2.90680i	1.49058	+	0.340215i	0.601835	+	0.798620i	$0.294437\pi$
$74$	−6.79330	−	1.55053i	−0.789705	−	0.180245i
$75$		0			0
$76$	2.15874	+	4.48267i	0.247625	+	0.514198i
$77$	7.47327	−	5.41293i	0.851658	−	0.616860i
$78$		0			0
$79$	−6.76297			−0.760894			−0.380447	−	0.924803i	$-0.624230\pi$
$79$	−6.76297			−0.760894			−0.380447	+	0.924803i	$0.624230\pi$
$80$	0.00412462			0.000461147
$81$		0			0
$82$	0.591130	+	0.471411i	0.0652794	+	0.0520586i
$83$	0.469890	−	2.05872i	0.0515772	−	0.225974i	−0.942570	−	0.334009i	$-0.891599\pi$
$83$	0.469890	−	2.05872i	0.0515772	−	0.225974i	0.994147	+	0.108034i	$0.0344557\pi$
$84$		0			0
$85$	0.0384733	+	0.168563i	0.00417302	+	0.0182832i
$86$	−0.567656	+	1.17875i	−0.0612119	+	0.127108i
$87$		0			0
$88$	6.11837	−	7.67220i	0.652221	−	0.817859i
$89$	2.55267	−	11.1840i	0.270582	−	1.18550i	−0.638746	−	0.769418i	$-0.720547\pi$
$89$	2.55267	−	11.1840i	0.270582	−	1.18550i	0.909328	−	0.416080i	$-0.136596\pi$
$90$		0			0
$91$	10.1249	−	7.33353i	1.06138	−	0.768763i
$92$	−6.55987	−	5.23132i	−0.683914	−	0.545403i
$93$		0			0
$94$	5.04038	+	10.4664i	0.519875	+	1.07953i
$95$	0.191979	−	0.153098i	0.0196966	−	0.0157075i
$96$		0			0
$97$			19.0907i			1.93837i	0.246336	+	0.969184i	$0.420773\pi$
$97$			19.0907i			1.93837i	−0.246336	+	0.969184i	$0.579227\pi$
$98$	3.12254	−	5.19161i	0.315424	−	0.524432i
$99$		0			0
$100$	1.39076	+	6.09332i	0.139076	+	0.609332i
$101$	2.82183	+	3.53847i	0.280783	+	0.352091i	0.902145	−	0.431433i	$-0.141992\pi$
$101$	2.82183	+	3.53847i	0.280783	+	0.352091i	−0.621362	+	0.783524i	$0.713420\pi$
$102$		0			0
$103$	−6.58862	+	5.25425i	−0.649196	+	0.517717i	−0.891812	−	0.452406i	$-0.850566\pi$
$103$	−6.58862	+	5.25425i	−0.649196	+	0.517717i	0.242616	+	0.970122i	$0.421995\pi$
$104$	8.28929	−	10.3944i	0.812831	−	1.01926i
$105$		0			0
$106$	−3.59956	−	4.51371i	−0.349621	−	0.438410i
$107$	8.65693	+	1.97589i	0.836897	+	0.191016i	0.619430	−	0.785052i	$-0.287364\pi$
$107$	8.65693	+	1.97589i	0.836897	+	0.191016i	0.217466	+	0.976068i	$0.430221\pi$
$108$		0			0
$109$	−1.66829	−	7.30926i	−0.159793	−	0.700101i	−0.989814	−	0.142368i	$-0.954528\pi$
$109$	−1.66829	−	7.30926i	−0.159793	−	0.700101i	0.830020	−	0.557733i	$-0.188329\pi$
$110$	−0.167904	−	0.0808582i	−0.0160090	−	0.00770952i
$111$		0			0
$112$	−0.0472738	+	0.170319i	−0.00446695	+	0.0160936i
$113$	−17.5749	−	4.01136i	−1.65331	−	0.377357i	−0.708689	−	0.705521i	$-0.750713\pi$
$113$	−17.5749	−	4.01136i	−1.65331	−	0.377357i	−0.944621	+	0.328163i	$0.893570\pi$
$114$		0			0
$115$	−0.179667	+	0.373082i	−0.0167540	+	0.0347901i
$116$		−	8.05182i		−	0.747593i
$117$		0			0
$118$	2.46527	−	5.11920i	0.226947	−	0.471260i
$119$	−7.40144	−	0.343272i	−0.678489	−	0.0314677i
$120$		0			0
$121$	1.04892	−	0.505133i	0.0953563	−	0.0459212i
$122$	0.451967	−	1.98020i	0.0409192	−	0.179279i
$123$		0			0
$124$	−3.10625	−	6.45020i	−0.278950	−	0.579245i
$125$	0.556031	−	0.267771i	0.0497330	−	0.0239501i
$126$		0			0
$127$	−3.85424	−	1.85611i	−0.342009	−	0.164703i	0.254992	−	0.966943i	$-0.417927\pi$
$127$	−3.85424	−	1.85611i	−0.342009	−	0.164703i	−0.597001	+	0.802240i	$0.703641\pi$
$128$			7.22739i			0.638817i
$129$		0			0
$130$	−0.227479	−	0.109548i	−0.0199512	−	0.00960801i
$131$	−11.7995	+	14.7962i	−1.03093	+	1.29275i	−0.0756218	+	0.997137i	$0.524094\pi$
$131$	−11.7995	+	14.7962i	−1.03093	+	1.29275i	−0.955309	+	0.295610i	$0.904477\pi$
$132$		0			0
$133$	4.12156	+	9.68211i	0.357384	+	0.839546i
$134$	−5.84519	+	1.33413i	−0.504948	+	0.115251i
$135$		0			0
$136$	−7.68194	+	1.75335i	−0.658721	+	0.150349i
$137$	−6.23671	−	4.97361i	−0.532838	−	0.424924i	0.319754	−	0.947500i	$-0.396400\pi$
$137$	−6.23671	−	4.97361i	−0.532838	−	0.424924i	−0.852593	+	0.522576i	$0.824971\pi$
$138$		0			0
$139$	−13.9245	+	11.1044i	−1.18106	+	0.941863i	−0.999141	−	0.0414500i	$-0.986802\pi$
$139$	−13.9245	+	11.1044i	−1.18106	+	0.941863i	−0.181919	+	0.983314i	$0.558231\pi$
$140$	0.204117	+	0.00946677i	0.0172511	+	0.000800088i
$141$		0			0
$142$	2.33388	+	2.92660i	0.195855	+	0.245595i
$143$	14.8482	−	7.15054i	1.24167	−	0.597958i
$144$		0			0
$145$	−0.387418	+	0.0884255i	−0.0321733	+	0.00734334i
$146$	11.3057			0.935665
$147$		0			0
$148$	10.0716			0.827878
$149$	−0.0255145	+	0.00582353i	−0.00209023	+	0.000477082i	−0.223566	−	0.974689i	$-0.571770\pi$
$149$	−0.0255145	+	0.00582353i	−0.00209023	+	0.000477082i	0.221476	+	0.975166i	$0.428913\pi$
$150$		0			0
$151$	0.0316754	−	0.0152541i	0.00257771	−	0.00124136i	−0.432594	−	0.901589i	$-0.642402\pi$
$151$	0.0316754	−	0.0152541i	0.00257771	−	0.00124136i	0.435172	+	0.900347i	$0.356688\pi$
$152$	6.97716	+	8.74908i	0.565922	+	0.709644i
$153$		0			0
$154$	5.26329	−	6.00653i	0.424128	−	0.484020i
$155$	−0.276242	+	0.220296i	−0.0221883	+	0.0176946i
$156$		0			0
$157$	1.04529	+	0.833592i	0.0834233	+	0.0665279i	0.664314	−	0.747454i	$-0.268724\pi$
$157$	1.04529	+	0.833592i	0.0834233	+	0.0665279i	−0.580890	+	0.813982i	$0.697295\pi$
$158$	−5.70642	+	1.30245i	−0.453978	+	0.103618i
$159$		0			0
$160$	0.342186	−	0.0781017i	0.0270522	−	0.00617448i
$161$	−13.3465	−	11.6950i	−1.05185	−	0.921699i
$162$		0			0
$163$	6.98615	−	8.76035i	0.547197	−	0.686164i	−0.428936	−	0.903335i	$-0.641112\pi$
$163$	6.98615	−	8.76035i	0.547197	−	0.686164i	0.976134	+	0.217171i	$0.0696830\pi$
$164$	−0.984621	−	0.474168i	−0.0768859	−	0.0370263i
$165$		0			0
$166$		−	1.82759i		−	0.141849i
$167$	21.3614	+	10.2871i	1.65300	+	0.796041i	0.999226	+	0.0393487i	$0.0125283\pi$
$167$	21.3614	+	10.2871i	1.65300	+	0.796041i	0.653771	+	0.756692i	$0.273186\pi$
$168$		0			0
$169$	8.40408	−	4.04719i	0.646468	−	0.311322i
$170$	0.0649256	+	0.134819i	0.00497956	+	0.0103402i
$171$		0			0
$172$	0.420796	−	1.84363i	0.0320854	−	0.140575i
$173$	4.41988	−	2.12850i	0.336037	−	0.161827i	−0.258254	−	0.966077i	$-0.583147\pi$
$173$	4.41988	−	2.12850i	0.336037	−	0.161827i	0.594291	+	0.804250i	$0.297433\pi$
$174$		0			0
$175$	2.34122	+	13.0097i	0.176979	+	0.983440i
$176$	−0.101098	+	0.209933i	−0.00762059	+	0.0158243i
$177$		0			0
$178$		−	9.92834i		−	0.744160i
$179$	−2.68278	+	5.57086i	−0.200521	+	0.416385i	−0.976845	−	0.213948i	$-0.931368\pi$
$179$	−2.68278	+	5.57086i	−0.200521	+	0.416385i	0.776324	+	0.630334i	$0.217082\pi$
$180$		0			0
$181$	7.23695	+	1.65179i	0.537918	+	0.122776i	0.482845	−	0.875706i	$-0.339604\pi$
$181$	7.23695	+	1.65179i	0.537918	+	0.122776i	0.0550736	+	0.998482i	$0.482461\pi$
$182$	7.13081	−	8.13776i	0.528571	−	0.603211i
$183$		0			0
$184$	−17.0026	−	8.18800i	−1.25344	−	0.603627i
$185$	−0.110607	−	0.484599i	−0.00813196	−	0.0356284i
$186$		0			0
$187$	−9.52245	−	2.17344i	−0.696350	−	0.158937i
$188$	−10.4691	−	13.1278i	−0.763535	−	0.957443i
$189$		0			0
$190$	0.132502	−	0.166152i	0.00961271	−	0.0120540i
$191$	−4.05359	+	3.23263i	−0.293308	+	0.233905i	−0.759077	−	0.651001i	$-0.774349\pi$
$191$	−4.05359	+	3.23263i	−0.293308	+	0.233905i	0.465769	+	0.884906i	$0.345778\pi$
$192$		0			0
$193$	−3.39005	−	4.25099i	−0.244021	−	0.305993i	0.644705	−	0.764432i	$-0.276980\pi$
$193$	−3.39005	−	4.25099i	−0.244021	−	0.305993i	−0.888726	+	0.458439i	$0.848409\pi$
$194$	3.67660	+	16.1082i	0.263965	+	1.15650i
$195$		0			0
$196$	−2.73037	+	8.32015i	−0.195027	+	0.594296i
$197$			22.6860i			1.61631i	0.588968	+	0.808156i	$0.299534\pi$
$197$			22.6860i			1.61631i	−0.588968	+	0.808156i	$0.700466\pi$
$198$		0			0
$199$	0.219576	−	0.175106i	0.0155653	−	0.0124129i	−0.615676	−	0.787999i	$-0.711117\pi$
$199$	0.219576	−	0.175106i	0.0155653	−	0.0124129i	0.631242	+	0.775586i	$0.282546\pi$
$200$	6.09925	+	12.6652i	0.431282	+	0.895567i
$201$		0			0
$202$	3.06245	+	2.44222i	0.215473	+	0.171834i
$203$	0.788962	−	17.0112i	0.0553743	−	1.19395i
$204$		0			0
$205$	−0.0120017	+	0.0525829i	−0.000838235	+	0.00367255i
$206$	−4.54741	+	5.70227i	−0.316833	+	0.397296i
$207$		0			0
$208$	−0.136970	+	0.284421i	−0.00949717	+	0.0197211i
$209$	3.08672	+	13.5238i	0.213513	+	0.935462i
$210$		0			0
$211$	−2.58864	+	11.3416i	−0.178209	+	0.780786i	0.804247	+	0.594295i	$0.202569\pi$
$211$	−2.58864	+	11.3416i	−0.178209	+	0.780786i	−0.982457	+	0.186491i	$0.940288\pi$
$212$	6.52413	+	5.20282i	0.448079	+	0.357331i
$213$		0			0
$214$	7.68501			0.525337
$215$	−0.0933284			−0.00636494
$216$		0			0
$217$	−5.93059	−	13.9318i	−0.402595	−	0.945751i
$218$	−2.81532	−	5.84607i	−0.190678	−	0.395946i
$219$		0			0
$220$	0.262610	+	0.0599391i	0.0177052	+	0.00404110i
$221$	−12.9012	−	2.94461i	−0.867828	−	0.198076i
$222$		0			0
$223$	−10.3037	−	21.3959i	−0.689987	−	1.43277i	−0.891377	−	0.453262i	$-0.850260\pi$
$223$	−10.3037	−	21.3959i	−0.689987	−	1.43277i	0.201390	−	0.979511i	$-0.435454\pi$
$224$	−0.696849	+	15.0251i	−0.0465602	+	1.00391i
$225$		0			0
$226$	−15.6018			−1.03782
$227$	−3.52272			−0.233811			−0.116906	−	0.993143i	$-0.537298\pi$
$227$	−3.52272			−0.233811			−0.116906	+	0.993143i	$0.537298\pi$
$228$		0			0
$229$	−7.53930	−	6.01239i	−0.498211	−	0.397310i	0.341890	−	0.939740i	$-0.388933\pi$
$229$	−7.53930	−	6.01239i	−0.498211	−	0.397310i	−0.840101	+	0.542430i	$0.817504\pi$
$230$	−0.0797479	+	0.349398i	−0.00525842	+	0.0230386i
$231$		0			0
$232$	−4.02983	−	17.6559i	−0.264572	−	1.15916i
$233$	−9.83501	+	20.4226i	−0.644313	+	1.33793i	0.281359	+	0.959603i	$0.409215\pi$
$233$	−9.83501	+	20.4226i	−0.644313	+	1.33793i	−0.925672	+	0.378327i	$0.876499\pi$
$234$		0			0
$235$	−0.516679	+	0.647895i	−0.0337044	+	0.0422640i
$236$	−1.82748	+	8.00670i	−0.118959	+	0.521192i
$237$		0			0
$238$	−6.31125	+	1.13577i	−0.409098	+	0.0736210i
$239$	−0.427038	−	0.340552i	−0.0276228	−	0.0220285i	0.609581	−	0.792724i	$-0.291338\pi$
$239$	−0.427038	−	0.340552i	−0.0276228	−	0.0220285i	−0.637204	+	0.770695i	$0.719909\pi$
$240$		0			0
$241$	−4.97519	−	10.3311i	−0.320480	−	0.665485i	0.677034	−	0.735952i	$-0.263265\pi$
$241$	−4.97519	−	10.3311i	−0.320480	−	0.665485i	−0.997514	+	0.0704676i	$0.977551\pi$
$242$	0.787769	−	0.628225i	0.0506397	−	0.0403838i
$243$		0			0
$244$			2.93579i			0.187945i
$245$	0.430313	+	0.0400011i	0.0274917	+	0.00255558i
$246$		0			0
$247$	4.18195	+	18.3223i	0.266091	+	1.16582i
$248$	−10.0396	−	12.5892i	−0.637513	−	0.799416i
$249$		0			0
$250$	0.417596	−	0.333021i	0.0264111	−	0.0210621i
$251$	−8.15760	+	10.2293i	−0.514903	+	0.645668i	−0.969518	−	0.245020i	$-0.921205\pi$
$251$	−8.15760	+	10.2293i	−0.514903	+	0.645668i	0.454615	+	0.890688i	$0.349777\pi$
$252$		0			0
$253$	−14.5852	−	18.2892i	−0.916961	−	1.14983i
$254$	−3.60957	−	0.823860i	−0.226484	−	0.0516936i
$255$		0			0
$256$	3.52215	+	15.4315i	0.220134	+	0.964471i
$257$	3.19417	+	1.53823i	0.199247	+	0.0959523i	0.530847	−	0.847468i	$-0.321874\pi$
$257$	3.19417	+	1.53823i	0.199247	+	0.0959523i	−0.331600	+	0.943420i	$0.607588\pi$
$258$		0			0
$259$	21.2783	+	0.986869i	1.32217	+	0.0613210i
$260$	0.355790	+	0.0812067i	0.0220651	+	0.00503622i
$261$		0			0
$262$	−7.10661	+	14.7570i	−0.439048	+	0.911692i
$263$			10.6792i			0.658506i	0.944242	+	0.329253i	$0.106797\pi$
$263$			10.6792i			0.658506i	−0.944242	+	0.329253i	$0.893203\pi$
$264$		0			0
$265$	0.178688	−	0.371050i	0.0109767	−	0.0227934i
$266$	5.34230	+	7.37576i	0.327557	+	0.452237i
$267$		0			0
$268$	7.80774	−	3.76001i	0.476933	−	0.229679i
$269$	3.32103	−	14.5504i	0.202487	−	0.887154i	−0.766929	−	0.641732i	$-0.778216\pi$
$269$	3.32103	−	14.5504i	0.202487	−	0.887154i	0.969416	−	0.245422i	$-0.0789265\pi$
$270$		0			0
$271$	3.17162	+	6.58594i	0.192662	+	0.400067i	0.974814	−	0.223021i	$-0.0715919\pi$
$271$	3.17162	+	6.58594i	0.192662	+	0.400067i	−0.782151	+	0.623088i	$0.785878\pi$
$272$	0.168567	−	0.0811777i	0.0102209	−	0.00492212i
$273$		0			0
$274$	−6.22022	−	2.99550i	−0.375777	−	0.180965i
$275$			17.4253i			1.05079i
$276$		0			0
$277$	8.65026	+	4.16575i	0.519744	+	0.250296i	0.675315	−	0.737529i	$-0.264008\pi$
$277$	8.65026	+	4.16575i	0.519744	+	0.250296i	−0.155571	+	0.987825i	$0.549722\pi$
$278$	−9.61056	+	12.0513i	−0.576403	+	0.722787i
$279$		0			0
$280$	0.452322	−	0.0813996i	0.0270314	−	0.00486456i
$281$	7.13655	−	1.62887i	0.425731	−	0.0971703i	−0.00428673	−	0.999991i	$-0.501365\pi$
$281$	7.13655	−	1.62887i	0.425731	−	0.0971703i	0.430018	+	0.902821i	$0.358507\pi$
$282$		0			0
$283$	−7.64831	+	1.74568i	−0.454645	+	0.103770i	−0.443710	−	0.896171i	$-0.646338\pi$
$283$	−7.64831	+	1.74568i	−0.454645	+	0.103770i	−0.0109349	+	0.999940i	$0.503481\pi$
$284$	−4.23012	−	3.37340i	−0.251011	−	0.200175i
$285$		0			0
$286$	11.1515	−	8.89299i	0.659400	−	0.525854i
$287$	−2.03376	−	1.09826i	−0.120049	−	0.0648282i
$288$		0			0
$289$	−5.70946	−	7.15943i	−0.335850	−	0.421143i
$290$	−0.309863	+	0.149222i	−0.0181958	+	0.00876263i
$291$		0			0
$292$	−15.9316	+	3.63628i	−0.932325	+	0.212797i
$293$	12.7206			0.743143			0.371572	−	0.928404i	$-0.378819\pi$
$293$	12.7206			0.743143			0.371572	+	0.928404i	$0.378819\pi$
$294$		0			0
$295$	0.405316			0.0235984
$296$	22.0847	−	5.04069i	1.28365	−	0.292984i
$297$		0			0
$298$	−0.0204070	+	0.00982747i	−0.00118214	+	0.000569290i
$299$	−19.7602	−	24.7786i	−1.14276	−	1.43298i
$300$		0			0
$301$	1.06967	−	3.85382i	0.0616547	−	0.222131i
$302$	0.0237892	−	0.0189712i	0.00136891	−	0.00109167i
$303$		0			0
$304$	−0.207743	−	0.165670i	−0.0119149	−	0.00950181i
$305$	0.141257	−	0.0322410i	0.00808836	−	0.00184612i
$306$		0			0
$307$	−3.00656	+	0.686228i	−0.171593	+	0.0391651i	−0.307454	−	0.951563i	$-0.599477\pi$
$307$	−3.00656	+	0.686228i	−0.171593	+	0.0391651i	0.135861	+	0.990728i	$0.456620\pi$
$308$	−5.48495	+	10.1570i	−0.312534	+	0.578750i
$309$		0			0
$310$	−0.190660	+	0.239080i	−0.0108287	+	0.0135788i
$311$	22.6761	+	10.9202i	1.28584	+	0.619229i	0.946885	−	0.321573i	$-0.104212\pi$
$311$	22.6761	+	10.9202i	1.28584	+	0.619229i	0.338957	+	0.940802i	$0.389926\pi$
$312$		0			0
$313$			20.6353i			1.16637i	0.812338	+	0.583187i	$0.198194\pi$
$313$			20.6353i			1.16637i	−0.812338	+	0.583187i	$0.801806\pi$
$314$	1.04253	+	0.502055i	0.0588332	+	0.0283326i
$315$		0			0
$316$	7.62237	−	3.67074i	0.428792	−	0.206495i
$317$	−8.49278	−	17.6354i	−0.477002	−	0.990505i	−0.991143	−	0.132799i	$-0.957603\pi$
$317$	−8.49278	−	17.6354i	−0.477002	−	0.990505i	0.514141	−	0.857706i	$-0.328111\pi$
$318$		0			0
$319$	4.99533	−	21.8860i	0.279685	−	1.22538i
$320$	0.266254	−	0.128221i	0.0148840	−	0.00716777i
$321$		0			0
$322$	−13.5137	−	7.29762i	−0.753091	−	0.406680i
$323$	4.83272	−	10.0353i	0.268900	−	0.558377i
$324$		0			0
$325$			23.6082i			1.30954i
$326$	4.20761	−	8.73718i	0.233038	−	0.483908i
$327$		0			0
$328$	−2.39637	−	0.546956i	−0.132317	−	0.0302006i
$329$	−20.8318	−	28.7611i	−1.14849	−	1.58565i
$330$		0			0
$331$	19.2323	+	9.26178i	1.05710	+	0.509074i	0.879929	−	0.475106i	$-0.157590\pi$
$331$	19.2323	+	9.26178i	1.05710	+	0.509074i	0.177174	+	0.984180i	$0.443305\pi$
$332$	0.587813	+	2.57538i	0.0322604	+	0.141342i
$333$		0			0
$334$	20.0054	+	4.56609i	1.09464	+	0.249845i
$335$	−0.266660	−	0.334381i	−0.0145692	−	0.0182692i
$336$		0			0
$337$	−9.72244	+	12.1916i	−0.529615	+	0.664117i	−0.972620	−	0.232403i	$-0.925341\pi$
$337$	−9.72244	+	12.1916i	−0.529615	+	0.664117i	0.443004	+	0.896519i	$0.353913\pi$
$338$	6.31171	−	5.03342i	0.343312	−	0.273782i
$339$		0			0
$340$	−0.134853	−	0.169100i	−0.00731344	−	0.00917076i
$341$	−4.44154	−	19.4597i	−0.240523	−	1.05380i
$342$		0			0
$343$	−6.58375	+	17.3105i	−0.355489	+	0.934681i
$344$		−	4.25327i		−	0.229321i
$345$		0			0
$346$	3.31946	−	2.64718i	0.178455	−	0.142313i
$347$	−0.0633374	−	0.131521i	−0.00340013	−	0.00706044i	0.899262	−	0.437411i	$-0.144104\pi$
$347$	−0.0633374	−	0.131521i	−0.00340013	−	0.00706044i	−0.902662	+	0.430350i	$0.858390\pi$
$348$		0			0
$349$	11.8509	+	9.45081i	0.634366	+	0.505890i	0.887059	−	0.461656i	$-0.152745\pi$
$349$	11.8509	+	9.45081i	0.634366	+	0.505890i	−0.252693	+	0.967547i	$0.581316\pi$
$350$	4.48094	+	10.5263i	0.239516	+	0.562657i
$351$		0			0
$352$	−4.41212	+	19.3308i	−0.235167	+	1.03033i
$353$	3.94296	−	4.94431i	0.209862	−	0.263159i	−0.665749	−	0.746176i	$-0.731888\pi$
$353$	3.94296	−	4.94431i	0.209862	−	0.263159i	0.875611	+	0.483017i	$0.160459\pi$
$354$		0			0
$355$	−0.115858	+	0.240581i	−0.00614909	+	0.0127687i
$356$	3.19328	+	13.9907i	0.169243	+	0.741503i
$357$		0			0
$358$	−1.19079	+	5.21721i	−0.0629354	+	0.275738i
$359$	−25.2928	−	20.1703i	−1.33490	−	1.06455i	−0.992141	−	0.125127i	$-0.960066\pi$
$359$	−25.2928	−	20.1703i	−1.33490	−	1.06455i	−0.342762	−	0.939422i	$-0.611362\pi$
$360$		0			0
$361$	3.18135			0.167440
$362$	6.42446			0.337662
$363$		0			0
$364$	−7.43111	+	13.7609i	−0.389496	+	0.721269i
$365$	0.349923	+	0.726622i	0.0183158	+	0.0380331i
$366$		0			0
$367$	9.33500	+	2.13065i	0.487283	+	0.111219i	0.459102	−	0.888384i	$-0.348171\pi$
$367$	9.33500	+	2.13065i	0.487283	+	0.111219i	0.0281812	+	0.999603i	$0.491028\pi$
$368$	0.436859	+	0.0997103i	0.0227729	+	0.00519776i
$369$		0			0
$370$	−0.186654	−	0.387591i	−0.00970367	−	0.0201499i
$371$	13.2738	+	11.6313i	0.689142	+	0.603869i
$372$		0			0
$373$	13.4756			0.697740			0.348870	−	0.937171i	$-0.386566\pi$
$373$	13.4756			0.697740			0.348870	+	0.937171i	$0.386566\pi$
$374$	−8.45336			−0.437113
$375$		0			0
$376$	−29.5266	−	23.5467i	−1.52272	−	1.21433i
$377$	6.76777	−	29.6516i	0.348558	−	1.52713i
$378$		0			0
$379$	−1.51751	−	6.64863i	−0.0779490	−	0.341517i	0.920883	−	0.389840i	$-0.127470\pi$
$379$	−1.51751	−	6.64863i	−0.0779490	−	0.341517i	−0.998832	+	0.0483226i	$0.984612\pi$
$380$	−0.133277	+	0.276753i	−0.00683697	+	0.0141971i
$381$		0			0
$382$	−2.79776	+	3.50827i	−0.143146	+	0.179499i
$383$	4.77281	−	20.9111i	0.243879	−	1.06851i	−0.693572	−	0.720388i	$-0.743964\pi$
$383$	4.77281	−	20.9111i	0.243879	−	1.06851i	0.937451	−	0.348118i	$-0.113179\pi$
$384$		0			0
$385$	0.548947	+	0.152366i	0.0279769	+	0.00776529i
$386$	−3.67911	−	2.93399i	−0.187262	−	0.149336i
$387$		0			0
$388$	−10.3619	−	21.5166i	−0.526044	−	1.09234i
$389$	8.78880	−	7.00883i	0.445610	−	0.355362i	−0.374831	−	0.927093i	$-0.622299\pi$
$389$	8.78880	−	7.00883i	0.445610	−	0.355362i	0.820441	+	0.571731i	$0.193728\pi$
$390$		0			0
$391$			18.7834i			0.949916i
$392$	−1.82298	+	19.6108i	−0.0920743	+	0.990493i
$393$		0			0
$394$	4.36901	+	19.1419i	0.220107	+	0.964354i
$395$	−0.260329	−	0.326442i	−0.0130986	−	0.0164251i
$396$		0			0
$397$	23.1518	−	18.4629i	1.16195	−	0.926627i	0.163748	−	0.986502i	$-0.447642\pi$
$397$	23.1518	−	18.4629i	1.16195	−	0.926627i	0.998206	+	0.0598748i	$0.0190701\pi$
$398$	0.151549	−	0.190037i	0.00759649	−	0.00952569i
$399$		0			0
$400$	−0.208112	−	0.260964i	−0.0104056	−	0.0130482i
$401$	−12.7588	−	2.91212i	−0.637145	−	0.145424i	−0.108267	−	0.994122i	$-0.534530\pi$
$401$	−12.7588	−	2.91212i	−0.637145	−	0.145424i	−0.528878	+	0.848698i	$0.677387\pi$
$402$		0			0
$403$	−6.01749	−	26.3643i	−0.299752	−	1.31330i
$404$	−5.10099	−	2.45651i	−0.253784	−	0.122216i
$405$		0			0
$406$	−2.61040	−	14.5055i	−0.129552	−	0.719897i
$407$	27.3760	+	6.24839i	1.35698	+	0.309721i
$408$		0			0
$409$	16.9849	−	35.2695i	0.839848	−	1.74396i	0.193224	−	0.981155i	$-0.438106\pi$
$409$	16.9849	−	35.2695i	0.839848	−	1.74396i	0.646624	−	0.762809i	$-0.276180\pi$
$410$			0.0466794i			0.00230533i
$411$		0			0
$412$	4.57401	−	9.49804i	0.225345	−	0.467935i
$413$	−4.64547	+	16.7368i	−0.228589	+	0.823563i
$414$		0			0
$415$	0.117460	−	0.0565658i	0.00576589	−	0.00277671i
$416$	−5.97762	+	26.1897i	−0.293077	+	1.28405i
$417$		0			0
$418$	5.20899	+	10.8166i	0.254780	+	0.529056i
$419$	−33.9245	+	16.3372i	−1.65732	+	0.798123i	−0.658351	+	0.752711i	$0.728746\pi$
$419$	−33.9245	+	16.3372i	−1.65732	+	0.798123i	−0.998968	+	0.0454117i	$0.985540\pi$
$420$		0			0
$421$	28.6493	+	13.7968i	1.39628	+	0.672414i	0.972403	−	0.233306i	$-0.0749543\pi$
$421$	28.6493	+	13.7968i	1.39628	+	0.672414i	0.423878	+	0.905719i	$0.360669\pi$
$422$			10.0683i			0.490115i
$423$		0			0
$424$	16.9099	+	8.14339i	0.821218	+	0.395478i
$425$	8.72373	−	10.9392i	0.423163	−	0.530630i
$426$		0			0
$427$	−0.287665	+	6.20248i	−0.0139211	+	0.300159i
$428$	−10.8294	+	2.47175i	−0.523461	+	0.119477i
$429$		0			0
$430$	−0.0787480	+	0.0179737i	−0.00379757	+	0.000866770i
$431$	9.63401	+	7.68286i	0.464054	+	0.370071i	0.827427	−	0.561573i	$-0.189804\pi$
$431$	9.63401	+	7.68286i	0.464054	+	0.370071i	−0.363373	+	0.931644i	$0.618375\pi$
$432$		0			0
$433$	29.2541	−	23.3294i	1.40586	−	1.12114i	0.429982	−	0.902838i	$-0.358520\pi$
$433$	29.2541	−	23.3294i	1.40586	−	1.12114i	0.975882	−	0.218301i	$-0.0700514\pi$
$434$	−7.68714	−	10.6131i	−0.368994	−	0.509446i
$435$		0			0
$436$	5.84754	+	7.33258i	0.280046	+	0.351167i
$437$	24.0344	−	11.5744i	1.14972	−	0.553678i
$438$		0			0
$439$	−27.8246	+	6.35079i	−1.32800	+	0.303107i	−0.826932	−	0.562302i	$-0.809916\pi$
$439$	−27.8246	+	6.35079i	−1.32800	+	0.303107i	−0.501066	+	0.865409i	$0.667059\pi$
$440$	0.605845			0.0288825
$441$		0			0
$442$	−11.4528			−0.544753
$443$	34.6668	−	7.91248i	1.64707	−	0.375933i	0.704439	−	0.709765i	$-0.251199\pi$
$443$	34.6668	−	7.91248i	1.64707	−	0.375933i	0.942633	+	0.333831i	$0.108342\pi$
$444$		0			0
$445$	0.638099	−	0.307292i	0.0302488	−	0.0145671i
$446$	−12.8145	−	16.0689i	−0.606786	−	0.760885i
$447$		0			0
$448$	2.24302	+	12.4640i	0.105973	+	0.588870i
$449$	29.2058	−	23.2908i	1.37831	−	1.09916i	0.394703	−	0.918809i	$-0.370847\pi$
$449$	29.2058	−	23.2908i	1.37831	−	1.09916i	0.983602	−	0.180353i	$-0.0577240\pi$
$450$		0			0
$451$	−2.38216	−	1.89971i	−0.112172	−	0.0894540i
$452$	21.9855	−	5.01804i	1.03411	−	0.236029i
$453$		0			0
$454$	−2.97238	+	0.678427i	−0.139501	+	0.0318401i
$455$	0.743723	+	0.206428i	0.0348663	+	0.00967751i
$456$		0			0
$457$	7.65086	−	9.59387i	0.357892	−	0.448782i	−0.569993	−	0.821650i	$-0.693054\pi$
$457$	7.65086	−	9.59387i	0.357892	−	0.448782i	0.927885	+	0.372867i	$0.121625\pi$
$458$	−7.51936	−	3.62113i	−0.351357	−	0.169204i
$459$		0			0
$460$		−	0.518009i		−	0.0241523i
$461$	−34.5881	−	16.6567i	−1.61093	−	0.775782i	−0.611052	−	0.791590i	$-0.709253\pi$
$461$	−34.5881	−	16.6567i	−1.61093	−	0.775782i	−0.999875	+	0.0158086i	$0.994968\pi$
$462$		0			0
$463$	−4.90057	+	2.35999i	−0.227749	+	0.109678i	−0.544279	−	0.838904i	$-0.683197\pi$
$463$	−4.90057	+	2.35999i	−0.227749	+	0.109678i	0.316530	+	0.948583i	$0.397482\pi$
$464$	0.186575	+	0.387428i	0.00866155	+	0.0179859i
$465$		0			0
$466$	−4.36542	+	19.1261i	−0.202224	+	0.886001i
$467$	26.4297	−	12.7279i	1.22302	−	0.588977i	0.292871	−	0.956152i	$-0.405389\pi$
$467$	26.4297	−	12.7279i	1.22302	−	0.588977i	0.930152	+	0.367176i	$0.119675\pi$
$468$		0			0
$469$	16.8639	−	7.17876i	0.778703	−	0.331484i
$470$	−0.311185	+	0.646181i	−0.0143539	+	0.0298061i
$471$		0			0
$472$			18.4715i			0.850222i
$473$	2.28757	−	4.75018i	0.105182	−	0.218414i
$474$		0			0
$475$	−19.3730	−	4.42175i	−0.888892	−	0.202884i
$476$	8.52829	−	3.63039i	0.390893	−	0.166399i
$477$		0			0
$478$	−0.425909	−	0.205107i	−0.0194806	−	0.00938137i
$479$	−6.74091	−	29.5338i	−0.308000	−	1.34944i	−0.857733	−	0.514096i	$-0.828128\pi$
$479$	−6.74091	−	29.5338i	−0.308000	−	1.34944i	0.549733	−	0.835340i	$-0.314729\pi$
$480$		0			0
$481$	37.0895	+	8.46543i	1.69113	+	0.385990i
$482$	−6.18756	−	7.75895i	−0.281836	−	0.353411i
$483$		0			0
$484$	−0.908038	+	1.13864i	−0.0412745	+	0.0517565i
$485$	−0.921490	+	0.734864i	−0.0418427	+	0.0333684i
$486$		0			0
$487$	9.46958	+	11.8745i	0.429108	+	0.538084i	0.948636	−	0.316369i	$-0.102464\pi$
$487$	9.46958	+	11.8745i	0.429108	+	0.538084i	−0.519528	+	0.854453i	$0.673892\pi$
$488$	1.46933	+	6.43754i	0.0665133	+	0.291414i
$489$		0			0
$490$	0.370791	−	0.0491204i	0.0167506	−	0.00221903i
$491$			22.0177i			0.993643i	0.867853	+	0.496821i	$0.165500\pi$
$491$			22.0177i			0.993643i	−0.867853	+	0.496821i	$0.834500\pi$
$492$		0			0
$493$	−14.0928	+	11.2387i	−0.634710	+	0.506164i
$494$	7.05723	+	14.6545i	0.317520	+	0.659337i
$495$		0			0
$496$	0.298926	+	0.238385i	0.0134222	+	0.0107038i
$497$	−8.60646	−	7.54152i	−0.386053	−	0.338283i
$498$		0			0
$499$	9.10921	−	39.9101i	0.407784	−	1.78662i	−0.186597	−	0.982437i	$-0.559746\pi$
$499$	9.10921	−	39.9101i	0.407784	−	1.78662i	0.594381	−	0.804183i	$-0.297397\pi$
$500$	−0.481350	+	0.603594i	−0.0215266	+	0.0269936i
$501$		0			0
$502$	−4.91315	+	10.2023i	−0.219284	+	0.455349i
$503$	6.99232	+	30.6353i	0.311772	+	1.36596i	0.851602	+	0.524188i	$0.175631\pi$
$503$	6.99232	+	30.6353i	0.311772	+	1.36596i	−0.539830	+	0.841774i	$0.681512\pi$
$504$		0			0
$505$	−0.0621768	+	0.272414i	−0.00276683	+	0.0121223i
$506$	−15.8288	−	12.6231i	−0.703676	−	0.561163i
$507$		0			0
$508$	5.35145			0.237432
$509$	−11.4957			−0.509537			−0.254768	−	0.967002i	$-0.581999\pi$
$509$	−11.4957			−0.509537			−0.254768	+	0.967002i	$0.581999\pi$
$510$		0			0
$511$	−34.0151	+	6.12134i	−1.50474	+	0.270792i
$512$	−0.327909	−	0.680909i	−0.0144916	−	0.0300922i
$513$		0			0
$514$	2.99140	+	0.682767i	0.131945	+	0.0301156i
$515$	−0.507235	−	0.115773i	−0.0223514	−	0.00510157i
$516$		0			0
$517$	−20.3120	−	42.1782i	−0.893319	−	1.85500i
$518$	18.1441	−	3.26521i	0.797208	−	0.143465i
$519$		0			0
$520$	0.820811			0.0359949
$521$	−22.1935			−0.972315			−0.486157	−	0.873871i	$-0.661602\pi$
$521$	−22.1935			−0.972315			−0.486157	+	0.873871i	$0.661602\pi$
$522$		0			0
$523$	17.6618	+	14.0848i	0.772295	+	0.615885i	0.928283	−	0.371874i	$-0.121285\pi$
$523$	17.6618	+	14.0848i	0.772295	+	0.615885i	−0.155988	+	0.987759i	$0.549856\pi$
$524$	5.26804	−	23.0808i	0.230135	−	1.00829i
$525$		0			0
$526$	2.05666	+	9.01080i	0.0896744	+	0.392889i
$527$	−6.95390	+	14.4399i	−0.302917	+	0.629013i
$528$		0			0
$529$	−13.7082	+	17.1895i	−0.596008	+	0.747370i
$530$	0.0793134	−	0.347495i	0.00344515	−	0.0150942i
$531$		0			0
$532$	−9.90046	−	8.67539i	−0.429239	−	0.376126i
$533$	−3.22740	−	2.57377i	−0.139794	−	0.111482i
$534$		0			0
$535$	0.237859	+	0.493920i	0.0102835	+	0.0213540i
$536$	15.2388	−	12.1525i	0.658216	−	0.524910i
$537$		0			0
$538$		−	12.9168i		−	0.556884i
$539$	−12.5833	+	20.9214i	−0.542003	+	0.901149i
$540$		0			0
$541$	−4.83952	−	21.2033i	−0.208067	−	0.911601i	−0.965852	−	0.259096i	$-0.916575\pi$
$541$	−4.83952	−	21.2033i	−0.208067	−	0.911601i	0.757784	−	0.652505i	$-0.226282\pi$
$542$	3.94449	+	4.94623i	0.169430	+	0.212459i
$543$		0			0
$544$	12.4475	−	9.92653i	0.533681	−	0.425597i
$545$	0.288593	−	0.361884i	0.0123620	−	0.0155014i
$546$		0			0
$547$	13.7085	+	17.1899i	0.586131	+	0.734985i	0.983145	−	0.182827i	$-0.0585249\pi$
$547$	13.7085	+	17.1899i	0.586131	+	0.734985i	−0.397014	+	0.917813i	$0.629953\pi$
$548$	9.72876	+	2.22053i	0.415592	+	0.0948562i
$549$		0			0
$550$	3.35587	+	14.7030i	0.143095	+	0.626939i
$551$	23.0646	+	11.1073i	0.982585	+	0.473188i
$552$		0			0
$553$	16.4635	−	7.00833i	0.700101	−	0.298024i
$554$	8.10113	+	1.84903i	0.344184	+	0.0785577i
$555$		0			0
$556$	9.66678	−	20.0733i	0.409963	−	0.851296i
$557$			31.9207i			1.35252i	0.736662	+	0.676262i	$0.236401\pi$
$557$			31.9207i			1.35252i	−0.736662	+	0.676262i	$0.763599\pi$
$558$		0			0
$559$	3.09924	−	6.43564i	0.131084	−	0.272198i
$560$	−0.0100408	+	0.00427426i	−0.000424303	+	0.000180621i
$561$		0			0
$562$	5.70793	−	2.74880i	0.240775	−	0.115951i
$563$	−2.67208	+	11.7071i	−0.112615	+	0.493398i	0.886892	+	0.461978i	$0.152860\pi$
$563$	−2.67208	+	11.7071i	−0.112615	+	0.493398i	−0.999506	+	0.0314198i	$0.989997\pi$
$564$		0			0
$565$	−0.482892	−	1.00273i	−0.0203154	−	0.0421854i
$566$	−6.11725	+	2.94591i	−0.257127	+	0.123826i
$567$		0			0
$568$	−10.9640	−	5.28001i	−0.460041	−	0.221544i
$569$			16.1597i			0.677450i	0.940886	+	0.338725i	$0.109996\pi$
$569$			16.1597i			0.677450i	−0.940886	+	0.338725i	$0.890004\pi$
$570$		0			0
$571$	−20.1418	−	9.69978i	−0.842908	−	0.405923i	−0.0379679	−	0.999279i	$-0.512088\pi$
$571$	−20.1418	−	9.69978i	−0.842908	−	0.405923i	−0.804940	+	0.593356i	$0.797803\pi$
$572$	−12.8540	+	16.1184i	−0.537451	+	0.673942i
$573$		0			0
$574$	−1.92754	−	0.535009i	−0.0804539	−	0.0223308i
$575$	32.6701	−	7.45675i	1.36244	−	0.310968i
$576$		0			0
$577$	−29.0434	+	6.62897i	−1.20909	+	0.275967i	−0.779120	−	0.626875i	$-0.784334\pi$
$577$	−29.0434	+	6.62897i	−1.20909	+	0.275967i	−0.429972	+	0.902842i	$0.641477\pi$
$578$	−6.19629	−	4.94138i	−0.257732	−	0.205534i
$579$		0			0
$580$	0.388653	−	0.309941i	0.0161380	−	0.0128696i
$581$	0.989529	+	5.49862i	0.0410526	+	0.228121i
$582$		0			0
$583$	14.5057	+	18.1896i	0.600765	+	0.753335i
$584$	−33.1145	+	15.9471i	−1.37029	+	0.659895i
$585$		0			0
$586$	10.7333	−	2.44980i	0.443387	−	0.101200i
$587$	21.0093			0.867148			0.433574	−	0.901118i	$-0.357252\pi$
$587$	21.0093			0.867148			0.433574	+	0.901118i	$0.357252\pi$
$588$		0			0
$589$	22.7618			0.937882
$590$	0.341995	−	0.0780581i	0.0140797	−	0.00321360i
$591$		0			0
$592$	−0.484612	+	0.233377i	−0.0199174	+	0.00959173i
$593$	5.16895	+	6.48165i	0.212263	+	0.266170i	0.876553	−	0.481306i	$-0.159837\pi$
$593$	5.16895	+	6.48165i	0.212263	+	0.266170i	−0.664290	+	0.747475i	$0.731266\pi$
$594$		0			0
$595$	−0.268336	−	0.370474i	−0.0110007	−	0.0151879i
$596$	0.0255959	−	0.0204121i	0.00104845	−	0.000836111i
$597$		0			0
$598$	−21.4452	−	17.1019i	−0.876958	−	0.699351i
$599$	−29.1262	+	6.64786i	−1.19006	+	0.271624i	−0.771300	−	0.636472i	$-0.780393\pi$
$599$	−29.1262	+	6.64786i	−1.19006	+	0.271624i	−0.418763	+	0.908096i	$0.637536\pi$
$600$		0			0
$601$	−32.3719	+	7.38868i	−1.32048	+	0.301390i	−0.823966	−	0.566640i	$-0.808243\pi$
$601$	−32.3719	+	7.38868i	−1.32048	+	0.301390i	−0.496512	+	0.868030i	$0.665386\pi$
$602$	0.160367	−	3.45776i	0.00653609	−	0.140928i
$603$		0			0
$604$	−0.0274211	+	0.0343849i	−0.00111575	+	0.00139910i
$605$	0.0647586	+	0.0311861i	0.00263281	+	0.00126789i
$606$		0			0
$607$		−	21.1596i		−	0.858840i	−0.903105	−	0.429420i	$-0.858718\pi$
$607$		−	21.1596i		−	0.858840i	0.903105	−	0.429420i	$-0.141282\pi$
$608$	−20.3718	−	9.81053i	−0.826184	−	0.397869i
$609$		0			0
$610$	0.112980	−	0.0544082i	0.00457442	−	0.00220292i
$611$	−27.5190	−	57.1438i	−1.11330	−	2.31179i
$612$		0			0
$613$	−8.60815	+	37.7148i	−0.347680	+	1.52329i	0.434752	+	0.900550i	$0.356836\pi$
$613$	−8.60815	+	37.7148i	−0.347680	+	1.52329i	−0.782432	+	0.622736i	$0.786021\pi$
$614$	−2.40470	+	1.15804i	−0.0970457	+	0.0467347i
$615$		0			0
$616$	−6.94381	+	25.0173i	−0.279774	+	1.00797i
$617$	−3.14453	+	6.52968i	−0.126594	+	0.262875i	−0.954627	−	0.297804i	$-0.903746\pi$
$617$	−3.14453	+	6.52968i	−0.126594	+	0.262875i	0.828033	+	0.560679i	$0.189460\pi$
$618$		0			0
$619$		−	2.50182i		−	0.100557i	−0.998735	−	0.0502784i	$-0.983989\pi$
$619$		−	2.50182i		−	0.100557i	0.998735	−	0.0502784i	$-0.0160109\pi$
$620$	0.191775	−	0.398225i	0.00770187	−	0.0159931i
$621$		0			0
$622$	21.2365	+	4.84710i	0.851508	+	0.194351i
$623$	5.37559	+	29.8711i	0.215368	+	1.19676i
$624$		0			0
$625$	−22.4727	−	10.8223i	−0.898909	−	0.432892i
$626$	3.97406	+	17.4115i	0.158835	+	0.695903i
$627$		0			0
$628$	−1.63057	−	0.372167i	−0.0650668	−	0.0148511i
$629$	−14.0578	−	17.6280i	−0.560522	−	0.702873i
$630$		0			0
$631$	−10.5968	+	13.2880i	−0.421852	+	0.528986i	−0.946660	−	0.322235i	$-0.895566\pi$
$631$	−10.5968	+	13.2880i	−0.421852	+	0.528986i	0.524807	+	0.851221i	$0.324137\pi$
$632$	14.8770	−	11.8640i	0.591775	−	0.471925i
$633$		0			0
$634$	−10.5623	−	13.2447i	−0.419483	−	0.526015i
$635$	−0.0587700	−	0.257488i	−0.00233221	−	0.0102181i
$636$		0			0
$637$	−17.0482	+	28.3447i	−0.675473	+	1.12306i
$638$		−	19.4288i		−	0.769195i
$639$		0			0
$640$	−0.348859	+	0.278206i	−0.0137899	+	0.0109971i
$641$	3.78762	+	7.86507i	0.149602	+	0.310652i	0.962280	−	0.272062i	$-0.0877054\pi$
$641$	3.78762	+	7.86507i	0.149602	+	0.310652i	−0.812678	+	0.582713i	$0.801991\pi$
$642$		0			0
$643$	22.4798	+	17.9270i	0.886516	+	0.706973i	0.956860	−	0.290550i	$-0.0938383\pi$
$643$	22.4798	+	17.9270i	0.886516	+	0.706973i	−0.0703440	+	0.997523i	$0.522410\pi$
$644$	21.3902	+	5.93709i	0.842893	+	0.233954i
$645$		0			0
$646$	2.14508	−	9.39820i	0.0843969	−	0.369767i
$647$	−28.4335	+	35.6545i	−1.11784	+	1.40172i	−0.212432	+	0.977176i	$0.568138\pi$
$647$	−28.4335	+	35.6545i	−1.11784	+	1.40172i	−0.905405	+	0.424548i	$0.860433\pi$
$648$		0			0
$649$	−9.93468	+	20.6296i	−0.389970	+	0.809782i
$650$	4.54659	+	19.9199i	0.178332	+	0.781324i
$651$		0			0
$652$	−3.11905	+	13.6654i	−0.122151	+	0.535180i
$653$	−36.8526	−	29.3890i	−1.44215	−	1.15008i	−0.962052	−	0.272868i	$-0.912028\pi$
$653$	−36.8526	−	29.3890i	−1.44215	−	1.15008i	−0.480103	−	0.877212i	$-0.659401\pi$
$654$		0			0
$655$	−1.16840			−0.0456531
$656$	0.0583641			0.00227874
$657$		0			0
$658$	−23.1163	−	20.2559i	−0.901166	−	0.789657i
$659$	9.12325	+	18.9446i	0.355391	+	0.737978i	0.999640	−	0.0268386i	$-0.00854403\pi$
$659$	9.12325	+	18.9446i	0.355391	+	0.737978i	−0.644249	+	0.764816i	$0.722830\pi$
$660$		0			0
$661$	−2.69086	−	0.614172i	−0.104663	−	0.0238885i	0.169869	−	0.985467i	$-0.445666\pi$
$661$	−2.69086	−	0.614172i	−0.104663	−	0.0238885i	−0.274531	+	0.961578i	$0.588523\pi$
$662$	18.0114	+	4.11098i	0.700032	+	0.159778i
$663$		0			0
$664$	2.57789	+	5.35303i	0.100041	+	0.207738i
$665$	−0.308694	+	0.571639i	−0.0119706	+	0.0221672i
$666$		0			0
$667$	−43.1709			−1.67159
$668$	−29.6594			−1.14756
$669$		0			0
$670$	−0.289397	−	0.230787i	−0.0111804	−	0.00891607i
$671$	−1.82136	+	7.97990i	−0.0703128	+	0.308060i
$672$		0			0
$673$	0.0827287	+	0.362458i	0.00318896	+	0.0139717i	0.976497	−	0.215529i	$-0.0691477\pi$
$673$	0.0827287	+	0.362458i	0.00318896	+	0.0139717i	−0.973308	+	0.229501i	$0.926291\pi$
$674$	−5.85562	+	12.1593i	−0.225550	+	0.468359i
$675$		0			0
$676$	−7.27532	+	9.12296i	−0.279820	+	0.350883i
$677$	6.28042	−	27.5163i	0.241376	−	1.05754i	−0.698389	−	0.715718i	$-0.746100\pi$
$677$	6.28042	−	27.5163i	0.241376	−	1.05754i	0.939765	−	0.341820i	$-0.111043\pi$
$678$		0			0
$679$	−19.7833	−	46.4737i	−0.759214	−	1.78350i
$680$	−0.380335	−	0.303307i	−0.0145852	−	0.0116313i
$681$		0			0
$682$	−7.49531	−	15.5642i	−0.287010	−	0.595983i
$683$	−7.50909	+	5.98830i	−0.287327	+	0.229136i	−0.756537	−	0.653951i	$-0.773110\pi$
$683$	−7.50909	+	5.98830i	−0.287327	+	0.229136i	0.469210	+	0.883087i	$0.344539\pi$
$684$		0			0
$685$		−	0.492490i		−	0.0188171i
$686$	−2.22143	+	15.8741i	−0.0848145	+	0.606076i
$687$		0			0
$688$	0.0224729	+	0.0984601i	0.000856771	+	0.00375376i
$689$	19.6526	+	24.6436i	0.748704	+	0.938845i
$690$		0			0
$691$	18.8209	−	15.0092i	0.715980	−	0.570975i	−0.196299	−	0.980544i	$-0.562892\pi$
$691$	18.8209	−	15.0092i	0.715980	−	0.570975i	0.912279	+	0.409569i	$0.134321\pi$
$692$	−3.82624	+	4.79796i	−0.145452	+	0.182391i
$693$		0			0
$694$	−0.0787716	−	0.0987765i	−0.00299013	−	0.00374950i
$695$	−1.07200	−	0.244676i	−0.0406632	−	0.00928110i
$696$		0			0
$697$	0.544404	+	2.38519i	0.0206208	+	0.0903455i
$698$	11.8196	+	5.69202i	0.447378	+	0.215446i
$699$		0			0
$700$	−9.69999	−	13.3921i	−0.366625	−	0.506175i
$701$	−37.8776	−	8.64531i	−1.43062	−	0.326529i	−0.564112	−	0.825698i	$-0.690781\pi$
$701$	−37.8776	−	8.64531i	−1.43062	−	0.326529i	−0.866504	+	0.499169i	$0.833639\pi$
$702$		0			0
$703$	−13.8935	+	28.8502i	−0.524005	+	1.08811i
$704$			16.6945i			0.629196i
$705$		0			0
$706$	2.37476	−	4.93123i	0.0893752	−	0.185589i
$707$	−10.5362	−	5.68971i	−0.396255	−	0.213984i
$708$		0			0
$709$	28.1686	−	13.5653i	1.05789	−	0.509455i	0.177707	−	0.984083i	$-0.443132\pi$
$709$	28.1686	−	13.5653i	1.05789	−	0.509455i	0.880186	+	0.474629i	$0.157418\pi$
$710$	−0.0514252	+	0.225308i	−0.00192995	+	0.00845568i
$711$		0			0
$712$	14.0043	+	29.0802i	0.524833	+	1.08983i
$713$	−34.5836	+	16.6546i	−1.29517	+	0.623720i
$714$		0			0
$715$	0.916706	+	0.441462i	0.0342829	+	0.0165098i
$716$		−	7.73490i		−	0.289067i
$717$		0			0
$718$	−25.2259	−	12.1482i	−0.941423	−	0.453365i
$719$	10.0809	−	12.6411i	0.375955	−	0.471432i	−0.557474	−	0.830194i	$-0.688230\pi$
$719$	10.0809	−	12.6411i	0.375955	−	0.471432i	0.933429	+	0.358762i	$0.116801\pi$
$720$		0			0
$721$	10.5942	−	19.6184i	0.394550	−	0.730628i
$722$	2.68434	−	0.612684i	0.0999009	−	0.0228017i
$723$		0			0
$724$	−9.05312	+	2.06632i	−0.336456	+	0.0767940i
$725$	25.1422	+	20.0503i	0.933759	+	0.744648i
$726$		0			0
$727$	−22.6368	+	18.0523i	−0.839553	+	0.669521i	−0.945775	−	0.324821i	$-0.894696\pi$
$727$	−22.6368	+	18.0523i	−0.839553	+	0.669521i	0.106222	+	0.994342i	$0.466124\pi$
$728$	−9.40760	+	33.8938i	−0.348669	+	1.25619i
$729$		0			0
$730$	0.435193	+	0.545714i	0.0161072	+	0.0201978i
$731$	−3.81419	+	1.83682i	−0.141073	+	0.0679371i
$732$		0			0
$733$	3.00523	−	0.685925i	0.111001	−	0.0253352i	−0.166660	−	0.986014i	$-0.553298\pi$
$733$	3.00523	−	0.685925i	0.111001	−	0.0253352i	0.277661	+	0.960679i	$0.410441\pi$
$734$	8.28696			0.305877
$735$		0			0
$736$	38.1306			1.40551
$737$	23.5552	−	5.37633i	0.867668	−	0.198040i
$738$		0			0
$739$	−36.1985	+	17.4323i	−1.33159	+	0.641258i	−0.958115	−	0.286385i	$-0.907546\pi$
$739$	−36.1985	+	17.4323i	−1.33159	+	0.641258i	−0.373470	+	0.927642i	$0.621832\pi$
$740$	0.387688	+	0.486145i	0.0142517	+	0.0178710i
$741$		0			0
$742$	13.4401	+	7.25786i	0.493402	+	0.266444i
$743$	4.63509	−	3.69636i	0.170045	−	0.135606i	−0.534770	−	0.844998i	$-0.679602\pi$
$743$	4.63509	−	3.69636i	0.170045	−	0.135606i	0.704815	+	0.709392i	$0.251030\pi$
$744$		0			0
$745$	−0.00126323	−	0.00100739i	−4.62813e−5	−	3.69081e-5i
$746$	11.3703	−	2.59521i	0.416298	−	0.0950173i
$747$		0			0
$748$	11.9122	−	2.71888i	0.435552	−	0.0994119i
$749$	−23.1217	+	4.16096i	−0.844848	+	0.152038i
$750$		0			0
$751$	24.2461	−	30.4037i	0.884753	−	1.10945i	−0.108571	−	0.994089i	$-0.534627\pi$
$751$	24.2461	−	30.4037i	0.884753	−	1.10945i	0.993324	−	0.115357i	$-0.0368012\pi$
$752$	0.807933	+	0.389080i	0.0294623	+	0.0141883i
$753$		0			0
$754$		−	26.3226i		−	0.958611i
$755$	0.00195559		0.000941762i	7.11711e−5		3.42742e-5i
$756$		0			0
$757$	−28.5246	+	13.7367i	−1.03674	+	0.499269i	−0.873249	−	0.487275i	$-0.837991\pi$
$757$	−28.5246	+	13.7367i	−1.03674	+	0.499269i	−0.163495	+	0.986544i	$0.552277\pi$
$758$	−2.56086	−	5.31769i	−0.0930147	−	0.193147i
$759$		0			0
$760$	−0.153736	+	0.673561i	−0.00557659	+	0.0244326i
$761$	35.6689	−	17.1772i	1.29300	−	0.622674i	0.344299	−	0.938860i	$-0.388117\pi$
$761$	35.6689	−	17.1772i	1.29300	−	0.622674i	0.948697	+	0.316186i	$0.102402\pi$
$762$		0			0
$763$	11.6357	+	16.0646i	0.421239	+	0.581577i
$764$	2.81412	−	5.84358i	0.101811	−	0.211413i
$765$		0			0
$766$		−	18.5634i		−	0.670722i
$767$	−13.4597	+	27.9493i	−0.486001	+	1.00919i
$768$		0			0
$769$	−12.5680	−	2.86855i	−0.453212	−	0.103443i	−0.0101794	−	0.999948i	$-0.503240\pi$
$769$	−12.5680	−	2.86855i	−0.453212	−	0.103443i	−0.443033	+	0.896505i	$0.646097\pi$
$770$	0.492530	+	0.0228431i	0.0177496	+	0.000823208i
$771$		0			0
$772$	6.12814	+	2.95116i	0.220557	+	0.106214i
$773$	7.48695	+	32.8025i	0.269287	+	1.17982i	0.910845	+	0.412749i	$0.135431\pi$
$773$	7.48695	+	32.8025i	0.269287	+	1.17982i	−0.641558	+	0.767075i	$0.721712\pi$
$774$		0			0
$775$	27.8761	+	6.36254i	1.00134	+	0.228549i
$776$	−33.4901	−	41.9952i	−1.20222	−	1.50754i
$777$		0			0
$778$	6.06595	−	7.60646i	0.217475	−	0.272705i
$779$	2.71653	−	2.16636i	0.0973298	−	0.0776179i
$780$		0			0
$781$	−9.40520	−	11.7937i	−0.336544	−	0.422013i
$782$	3.61741	+	15.8489i	0.129358	+	0.566756i
$783$		0			0
$784$	−0.0614161	−	0.463607i	−0.00219343	−	0.0165574i
$785$			0.0825428i			0.00294608i
$786$		0			0
$787$	39.1022	−	31.1830i	1.39384	−	1.11155i	0.414341	−	0.910122i	$-0.364012\pi$
$787$	39.1022	−	31.1830i	1.39384	−	1.11155i	0.979503	−	0.201431i	$-0.0645593\pi$
$788$	−12.3133	−	25.5688i	−0.438643	−	0.910852i
$789$		0			0
$790$	−0.282527	−	0.225307i	−0.0100518	−	0.00801608i
$791$	46.9407	−	8.44741i	1.66902	−	0.300355i
$792$		0			0
$793$	−2.46761	+	10.8113i	−0.0876275	+	0.383921i
$794$	15.9792	−	20.0372i	0.567079	−	0.711094i
$795$		0			0
$796$	−0.152436	+	0.316537i	−0.00540295	+	0.0112193i
$797$	5.89005	+	25.8060i	0.208636	+	0.914095i	0.965475	+	0.260494i	$0.0838855\pi$
$797$	5.89005	+	25.8060i	0.208636	+	0.914095i	−0.756839	+	0.653601i	$0.773257\pi$
$798$		0			0
$799$	−8.36452	+	36.6474i	−0.295916	+	1.29649i
$800$	−22.2068	−	17.7093i	−0.785129	−	0.626120i
$801$		0			0
$802$	−11.3264			−0.399948
$803$	−45.5602			−1.60778
$804$		0			0
$805$	0.0507574	−	1.09440i	0.00178896	−	0.0385726i
$806$	−10.1548	−	21.0866i	−0.357687	−	0.742745i
$807$		0			0
$808$	−12.4148	−	2.83359i	−0.436751	−	0.0996855i
$809$	37.8226	+	8.63276i	1.32977	+	0.303512i	0.827630	−	0.561274i	$-0.189689\pi$
$809$	37.8226	+	8.63276i	1.32977	+	0.303512i	0.502141	+	0.864786i	$0.332546\pi$
$810$		0			0
$811$	−13.6624	−	28.3702i	−0.479751	−	0.996213i	−0.990632	−	0.136561i	$-0.956395\pi$
$811$	−13.6624	−	28.3702i	−0.479751	−	0.996213i	0.510881	−	0.859652i	$-0.329319\pi$
$812$	8.34393	+	19.6011i	0.292815	+	0.687862i
$813$		0			0
$814$	24.3025			0.851801
$815$	0.691773			0.0242317
$816$		0			0
$817$	4.70063	+	3.74863i	0.164454	+	0.131148i
$818$	7.53899	−	33.0305i	0.263595	−	1.15488i
$819$		0			0
$820$	−0.0150136	−	0.0657789i	−0.000524298	−	0.00229710i
$821$	−19.9376	+	41.4008i	−0.695826	+	1.44490i	0.190430	+	0.981701i	$0.439012\pi$
$821$	−19.9376	+	41.4008i	−0.695826	+	1.44490i	−0.886256	+	0.463196i	$0.846703\pi$
$822$		0			0
$823$	12.9117	−	16.1908i	0.450074	−	0.564376i	−0.504093	−	0.863650i	$-0.668173\pi$
$823$	12.9117	−	16.1908i	0.450074	−	0.564376i	0.954167	+	0.299274i	$0.0967445\pi$
$824$	5.27615	−	23.1163i	0.183803	−	0.805295i
$825$		0			0
$826$	−0.696460	+	15.0167i	−0.0242330	+	0.522498i
$827$	4.31401	+	3.44030i	0.150013	+	0.119631i	0.695620	−	0.718410i	$-0.255130\pi$
$827$	4.31401	+	3.44030i	0.150013	+	0.119631i	−0.545608	+	0.838041i	$0.683701\pi$
$828$		0			0
$829$	7.80709	+	16.2116i	0.271152	+	0.563052i	0.991431	−	0.130632i	$-0.0417007\pi$
$829$	7.80709	+	16.2116i	0.271152	+	0.563052i	−0.720279	+	0.693684i	$0.755986\pi$
$830$	0.0882160	−	0.0703499i	0.00306202	−	0.00244188i
$831$		0			0
$832$			22.6180i			0.784137i
$833$	18.3735	−	6.83431i	0.636605	−	0.236795i
$834$		0			0
$835$	0.325721	+	1.42708i	0.0112721	+	0.0493861i
$836$	−10.8193	−	13.5670i	−0.374193	−	0.469223i
$837$		0			0
$838$	−25.4783	+	20.3182i	−0.880132	+	0.701882i
$839$	3.36402	−	4.21834i	0.116139	−	0.145633i	−0.720364	−	0.693596i	$-0.756025\pi$
$839$	3.36402	−	4.21834i	0.116139	−	0.145633i	0.836503	+	0.547963i	$0.184597\pi$
$840$		0			0
$841$	−7.74929	−	9.71731i	−0.267217	−	0.335079i
$842$	26.8306	+	6.12390i	0.924643	+	0.211044i
$843$		0			0
$844$	−3.23828	−	14.1878i	−0.111466	−	0.488365i
$845$	0.518854	+	0.249867i	0.0178491	+	0.00859569i
$846$		0			0
$847$	−2.02999	+	2.31665i	−0.0697514	+	0.0796010i
$848$	−0.434479	−	0.0991671i	−0.0149201	−	0.00340541i
$849$		0			0
$850$	5.25411	−	10.9103i	0.180215	−	0.374220i
$851$		−	54.0001i		−	1.85110i
$852$		0			0
$853$	−7.13459	+	14.8151i	−0.244284	+	0.507260i	−0.986674	−	0.162707i	$-0.947978\pi$
$853$	−7.13459	+	14.8151i	−0.244284	+	0.507260i	0.742391	+	0.669967i	$0.233692\pi$
$854$	0.951785	+	5.28889i	0.0325694	+	0.180982i
$855$		0			0
$856$	−22.5095	+	10.8400i	−0.769359	+	0.370504i
$857$	−8.82414	+	38.6611i	−0.301427	+	1.32064i	0.566548	+	0.824029i	$0.308279\pi$
$857$	−8.82414	+	38.6611i	−0.301427	+	1.32064i	−0.867975	+	0.496609i	$0.834578\pi$
$858$		0			0
$859$	3.27523	+	6.80109i	0.111749	+	0.232050i	0.949342	−	0.314246i	$-0.101752\pi$
$859$	3.27523	+	6.80109i	0.111749	+	0.232050i	−0.837592	+	0.546296i	$0.816037\pi$
$860$	0.105188	−	0.0506558i	0.00358688	−	0.00172735i
$861$		0			0
$862$	9.60853	+	4.62722i	0.327268	+	0.157604i
$863$		−	14.9631i		−	0.509351i	−0.967027	−	0.254675i	$-0.918031\pi$
$863$		−	14.9631i		−	0.509351i	0.967027	−	0.254675i	$-0.0819686\pi$
$864$		0			0
$865$	0.272876	+	0.131410i	0.00927807	+	0.00446808i
$866$	20.1909	−	25.3186i	0.686116	−	0.860362i
$867$		0			0
$868$	14.2460	+	12.4832i	0.483539	+	0.423707i
$869$	22.9960	−	5.24868i	0.780086	−	0.178049i
$870$		0			0
$871$	31.9131	−	7.28395i	1.08133	−	0.246807i
$872$	16.4922	+	13.1521i	0.558497	+	0.445386i
$873$		0			0
$874$	18.0506	−	14.3948i	0.610570	−	0.486913i
$875$	−1.07610	+	1.22805i	−0.0363787	+	0.0415158i
$876$		0			0
$877$	11.8428	+	14.8503i	0.399901	+	0.501460i	0.940488	−	0.339828i	$-0.110369\pi$
$877$	11.8428	+	14.8503i	0.399901	+	0.501460i	−0.540586	+	0.841289i	$0.681798\pi$
$878$	−22.2546	+	10.7173i	−0.751057	+	0.361690i
$879$		0			0
$880$	−0.0140249	+	0.00320109i	−0.000472778	+	0.000107909i
$881$	−7.79930			−0.262765			−0.131382	−	0.991332i	$-0.541942\pi$
$881$	−7.79930			−0.262765			−0.131382	+	0.991332i	$0.541942\pi$
$882$		0			0
$883$	14.9421			0.502842			0.251421	−	0.967878i	$-0.419102\pi$
$883$	14.9421			0.502842			0.251421	+	0.967878i	$0.419102\pi$
$884$	16.1388	−	3.68358i	0.542808	−	0.123892i
$885$		0			0
$886$	27.7271	−	13.3527i	0.931511	−	0.448592i
$887$	12.3392	+	15.4728i	0.414308	+	0.519526i	0.944571	−	0.328307i	$-0.106478\pi$
$887$	12.3392	+	15.4728i	0.414308	+	0.519526i	−0.530263	+	0.847833i	$0.677907\pi$
$888$		0			0
$889$	11.3061	+	0.524365i	0.379194	+	0.0175866i
$890$	0.479231	−	0.382174i	0.0160639	−	0.0128105i
$891$		0			0
$892$	23.2261	+	18.5222i	0.777666	+	0.620168i
$893$	52.0467	−	11.8793i	1.74168	−	0.397526i
$894$		0			0
$895$	−0.372169	+	0.0849451i	−0.0124402	+	0.00283940i
$896$	−7.48960	−	17.5941i	−0.250210	−	0.587778i
$897$		0			0
$898$	20.1576	−	25.2768i	0.672667	−	0.843497i
$899$	−33.1881	−	15.9826i	−1.10689	−	0.533048i
$900$		0			0
$901$		−	18.6810i		−	0.622356i
$902$	−2.37587	−	1.14416i	−0.0791077	−	0.0380962i
$903$		0			0
$904$	45.6978	−	22.0069i	1.51989	−	0.731939i
$905$	0.198844	+	0.412903i	0.00660979	+	0.0137254i
$906$		0			0
$907$	3.74119	−	16.3912i	0.124224	−	0.544262i	−0.874066	−	0.485808i	$-0.838526\pi$
$907$	3.74119	−	16.3912i	0.124224	−	0.544262i	0.998290	−	0.0584547i	$-0.0186173\pi$
$908$	3.97037	−	1.91203i	0.131761	−	0.0634529i
$909$		0			0
$910$	0.667289	+	0.0309482i	0.0221204	+	0.00102592i
$911$	7.06895	−	14.6788i	0.234205	−	0.486331i	−0.750432	−	0.660948i	$-0.770154\pi$
$911$	7.06895	−	14.6788i	0.234205	−	0.486331i	0.984636	+	0.174617i	$0.0558687\pi$
$912$		0			0
$913$			7.36491i			0.243743i
$914$	4.60795	−	9.56850i	0.152417	−	0.316498i
$915$		0			0
$916$	11.7607	+	2.68430i	0.388584	+	0.0886918i
$917$	13.3914	−	48.2468i	0.442224	−	1.59325i
$918$		0			0
$919$	−32.3318	−	15.5702i	−1.06653	−	0.513612i	−0.183541	−	0.983012i	$-0.558756\pi$
$919$	−32.3318	−	15.5702i	−1.06653	−	0.513612i	−0.882985	+	0.469400i	$0.844470\pi$
$920$	−0.259257	−	1.13588i	−0.00854745	−	0.0374488i
$921$		0			0
$922$	−32.3923	−	7.39334i	−1.06679	−	0.243487i
$923$	−12.7423	−	15.9784i	−0.419419	−	0.525935i
$924$		0			0
$925$	−25.0797	+	31.4490i	−0.824617	+	1.03404i
$926$	−3.68047	+	2.93508i	−0.120948	+	0.0964527i
$927$		0			0
$928$	22.8147	+	28.6088i	0.748930	+	0.939129i
$929$	−0.313570	−	1.37384i	−0.0102879	−	0.0450743i	0.969523	−	0.244999i	$-0.0787875\pi$
$929$	−0.313570	−	1.37384i	−0.0102879	−	0.0450743i	−0.979811	+	0.199924i	$0.935930\pi$
$930$		0			0
$931$	−20.0667	−	19.2987i	−0.657661	−	0.632489i
$932$		−	28.3559i		−	0.928829i
$933$		0			0
$934$	19.8495	−	15.8294i	0.649495	−	0.517955i
$935$	−0.261640	−	0.543301i	−0.00855655	−	0.0177679i
$936$		0			0
$937$	8.85736	+	7.06351i	0.289357	+	0.230755i	0.757400	−	0.652951i	$-0.226469\pi$
$937$	8.85736	+	7.06351i	0.289357	+	0.230755i	−0.468043	+	0.883706i	$0.655041\pi$
$938$	12.8468	−	9.30500i	0.419463	−	0.303819i
$939$		0			0
$940$	0.230677	−	1.01066i	0.00752386	−	0.0329642i
$941$	−1.36612	+	1.71307i	−0.0445344	+	0.0558443i	−0.803600	−	0.595170i	$-0.797085\pi$
$941$	−1.36612	+	1.71307i	−0.0445344	+	0.0558443i	0.759066	+	0.651014i	$0.225656\pi$
$942$		0			0
$943$	−2.54232	+	5.27918i	−0.0827893	+	0.171914i
$944$	−0.0975975	−	0.427603i	−0.00317653	−	0.0139173i
$945$		0			0
$946$	1.01537	−	4.44863i	0.0330126	−	0.144637i
$947$	−41.5779	−	33.1573i	−1.35110	−	1.07747i	−0.989407	−	0.145170i	$-0.953627\pi$
$947$	−41.5779	−	33.1573i	−1.35110	−	1.07747i	−0.361694	−	0.932297i	$-0.617802\pi$
$948$		0			0
$949$	−61.7258			−2.00370
$950$	−17.1980			−0.557975
$951$		0			0
$952$	16.8837	−	12.2289i	0.547203	−	0.396342i
$953$	22.5658	+	46.8584i	0.730979	+	1.51789i	0.851025	+	0.525124i	$0.175981\pi$
$953$	22.5658	+	46.8584i	0.730979	+	1.51789i	−0.120047	+	0.992768i	$0.538305\pi$
$954$		0			0
$955$	−0.312072	−	0.0712284i	−0.0100984	−	0.00230490i
$956$	0.666145	+	0.152043i	0.0215447	+	0.00491743i
$957$		0			0
$958$	−11.3756	−	23.6217i	−0.367529	−	0.763182i
$959$	20.3365	+	5.64461i	0.656699	+	0.182274i
$960$		0			0
$961$	−1.75234			−0.0565270
$962$	32.9254			1.06156
$963$		0			0
$964$	11.2148	+	8.94352i	0.361205	+	0.288051i
$965$	0.0746969	−	0.327269i	0.00240458	−	0.0105351i
$966$		0			0
$967$	11.2247	+	49.1785i	0.360961	+	1.58147i	0.750761	+	0.660573i	$0.229687\pi$
$967$	11.2247	+	49.1785i	0.360961	+	1.58147i	−0.389801	+	0.920899i	$0.627456\pi$
$968$	−1.42125	+	2.95125i	−0.0456807	+	0.0948569i
$969$		0			0
$970$	−0.636004	+	0.797524i	−0.0204209	+	0.0256070i
$971$	−0.427755	+	1.87412i	−0.0137273	+	0.0601432i	−0.981328	−	0.192343i	$-0.938391\pi$
$971$	−0.427755	+	1.87412i	−0.0137273	+	0.0601432i	0.967600	+	0.252487i	$0.0812484\pi$
$972$		0			0
$973$	22.3900	−	41.4618i	0.717790	−	1.32920i
$974$	10.2770	+	8.19567i	0.329298	+	0.262606i
$975$		0			0
$976$	−0.0680276	−	0.141261i	−0.00217751	−	0.00452165i
$977$	−43.4478	+	34.6484i	−1.39002	+	1.10850i	−0.409447	+	0.912334i	$0.634278\pi$
$977$	−43.4478	+	34.6484i	−1.39002	+	1.10850i	−0.980570	+	0.196167i	$0.937150\pi$
$978$		0			0
$979$			40.0097i			1.27872i
$980$	−0.506706	+	0.188477i	−0.0161861	+	0.00602068i
$981$		0			0
$982$	4.24029	+	18.5779i	0.135313	+	0.592845i
$983$	2.18098	+	2.73487i	0.0695625	+	0.0872287i	0.815395	−	0.578905i	$-0.196520\pi$
$983$	2.18098	+	2.73487i	0.0695625	+	0.0872287i	−0.745833	+	0.666133i	$0.767948\pi$
$984$		0			0
$985$	−1.09503	+	0.873259i	−0.0348906	+	0.0278243i
$986$	−9.72676	+	12.1970i	−0.309763	+	0.388431i
$987$		0			0
$988$	−14.6582	−	18.3808i	−0.466338	−	0.584770i
$989$	−9.88487	−	2.25616i	−0.314320	−	0.0717416i
$990$		0			0
$991$	10.8346	+	47.4696i	0.344173	+	1.50792i	0.790170	+	0.612887i	$0.209992\pi$
$991$	10.8346	+	47.4696i	0.344173	+	1.50792i	−0.445997	+	0.895034i	$0.647151\pi$
$992$	29.3133	+	14.1166i	0.930699	+	0.448201i
$993$		0			0
$994$	−8.71429	−	4.70585i	−0.276401	−	0.149260i
$995$	0.0169044	+	0.00385831i	0.000535905	+	0.000122317i
$996$		0			0
$997$	2.50166	−	5.19474i	0.0792282	−	0.164519i	−0.857592	−	0.514331i	$-0.828040\pi$
$997$	2.50166	−	5.19474i	0.0792282	−	0.164519i	0.936820	+	0.349812i	$0.113755\pi$
$998$		−	35.4294i		−	1.12150i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.w.a.62.13	yes	120
3.2	odd	2	inner	441.2.w.a.62.8	✓	120
49.34	odd	14	inner	441.2.w.a.377.8	yes	120
147.83	even	14	inner	441.2.w.a.377.13	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.w.a.62.8	✓	120	3.2	odd	2	inner
441.2.w.a.62.13	yes	120	1.1	even	1	trivial
441.2.w.a.377.8	yes	120	49.34	odd	14	inner
441.2.w.a.377.13	yes	120	147.83	even	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.843773 - 0.192586i) q^{2} +(-1.12707 + 0.542770i) q^{4} +(0.0384932 + 0.0482690i) q^{5} +(-2.43436 + 1.03628i) q^{7} +(-2.19977 + 1.75426i) q^{8} +O(q^{10})\)	\(q+(0.843773 - 0.192586i) q^{2} +(-1.12707 + 0.542770i) q^{4} +(0.0384932 + 0.0482690i) q^{5} +(-2.43436 + 1.03628i) q^{7} +(-2.19977 + 1.75426i) q^{8} +(0.0417755 + 0.0333148i) q^{10} +(-3.40028 + 0.776091i) q^{11} +(-4.60676 + 1.05146i) q^{13} +(-1.85448 + 1.34321i) q^{14} +(0.0416542 - 0.0522327i) q^{16} +(2.52315 + 1.21509i) q^{17} -3.97727i q^{19} +(-0.0695837 - 0.0335097i) q^{20} +(-2.71960 + 1.30969i) q^{22} +(2.91013 + 6.04296i) q^{23} +(1.11176 - 4.87092i) q^{25} +(-3.68457 + 1.77439i) q^{26} +(2.18125 - 2.48926i) q^{28} +(-2.79271 + 5.79911i) q^{29} +5.72297i q^{31} +(2.46665 - 5.12205i) q^{32} +(2.36298 + 0.539334i) q^{34} +(-0.143727 - 0.0776146i) q^{35} +(-7.25379 - 3.49324i) q^{37} +(-0.765965 - 3.35591i) q^{38} +(-0.169353 - 0.0386537i) q^{40} +(0.544686 + 0.683014i) q^{41} +(-0.942514 + 1.18188i) q^{43} +(3.41112 - 2.72028i) q^{44} +(3.61928 + 4.53844i) q^{46} +(2.98681 + 13.0861i) q^{47} +(4.85225 - 5.04536i) q^{49} -4.32406i q^{50} +(4.62146 - 3.68549i) q^{52} +(-2.89428 - 6.01004i) q^{53} +(-0.168349 - 0.134254i) q^{55} +(3.53714 - 6.55008i) q^{56} +(-1.23958 + 5.43097i) q^{58} +(4.09325 - 5.13277i) q^{59} +(1.01825 - 2.11443i) q^{61} +(1.10216 + 4.82889i) q^{62} +(1.06513 - 4.66663i) q^{64} +(-0.228082 - 0.181890i) q^{65} -6.92744 q^{67} -3.50329 q^{68} +(-0.136220 - 0.0378094i) q^{70} +(1.87659 + 3.89678i) q^{71} +(12.7355 + 2.90680i) q^{73} +(-6.79330 - 1.55053i) q^{74} +(2.15874 + 4.48267i) q^{76} +(7.47327 - 5.41293i) q^{77} -6.76297 q^{79} +0.00412462 q^{80} +(0.591130 + 0.471411i) q^{82} +(0.469890 - 2.05872i) q^{83} +(0.0384733 + 0.168563i) q^{85} +(-0.567656 + 1.17875i) q^{86} +(6.11837 - 7.67220i) q^{88} +(2.55267 - 11.1840i) q^{89} +(10.1249 - 7.33353i) q^{91} +(-6.55987 - 5.23132i) q^{92} +(5.04038 + 10.4664i) q^{94} +(0.191979 - 0.153098i) q^{95} +19.0907i q^{97} +(3.12254 - 5.19161i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 24 q^{4}+O(q^{10}) \) 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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