LMFDB - Embedded newform 441.2.w.a.62.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			62.14
Character	$\chi$	$=$	441.62
Dual form			441.2.w.a.377.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.880699 - 0.201014i) q^{2} +(-1.06671 + 0.513702i) q^{4} +(-2.70158 - 3.38767i) q^{5} +(2.62942 + 0.293490i) q^{7} +(-2.24872 + 1.79330i) q^{8} +(-3.06025 - 2.44047i) q^{10} +(-2.23309 + 0.509689i) q^{11} +(-5.63896 + 1.28706i) q^{13} +(2.37473 - 0.270074i) q^{14} +(-0.143595 + 0.180062i) q^{16} +(-4.20422 - 2.02465i) q^{17} -5.60936i q^{19} +(4.62207 + 2.22587i) q^{20} +(-1.86423 + 0.897765i) q^{22} +(-0.518590 - 1.07686i) q^{23} +(-3.06519 + 13.4295i) q^{25} +(-4.70751 + 2.26702i) q^{26} +(-2.95561 + 1.03767i) q^{28} +(1.47898 - 3.07113i) q^{29} -0.588888i q^{31} +(2.40563 - 4.99534i) q^{32} +(-4.10964 - 0.937998i) q^{34} +(-6.10934 - 9.70051i) q^{35} +(1.11676 + 0.537802i) q^{37} +(-1.12756 - 4.94016i) q^{38} +(12.1502 + 2.77321i) q^{40} +(0.526282 + 0.659937i) q^{41} +(1.25480 - 1.57347i) q^{43} +(2.12024 - 1.69084i) q^{44} +(-0.673187 - 0.844149i) q^{46} +(0.851950 + 3.73264i) q^{47} +(6.82773 + 1.54342i) q^{49} +12.4435i q^{50} +(5.35399 - 4.26967i) q^{52} +(1.27448 + 2.64649i) q^{53} +(7.75953 + 6.18802i) q^{55} +(-6.43916 + 4.05536i) q^{56} +(0.685196 - 3.00204i) q^{58} +(8.71710 - 10.9309i) q^{59} +(1.57855 - 3.27789i) q^{61} +(-0.118375 - 0.518633i) q^{62} +(1.21700 - 5.33202i) q^{64} +(19.5942 + 15.6259i) q^{65} -6.27020 q^{67} +5.52477 q^{68} +(-7.33043 - 7.31517i) q^{70} +(-1.87256 - 3.88841i) q^{71} +(-7.77931 - 1.77558i) q^{73} +(1.09163 + 0.249158i) q^{74} +(2.88154 + 5.98358i) q^{76} +(-6.02133 + 0.684797i) q^{77} -0.653795 q^{79} +0.997922 q^{80} +(0.596153 + 0.475416i) q^{82} +(-1.57947 + 6.92012i) q^{83} +(4.49920 + 19.7123i) q^{85} +(0.788810 - 1.63798i) q^{86} +(4.10759 - 5.15075i) q^{88} +(-2.56309 + 11.2296i) q^{89} +(-15.2050 + 1.72924i) q^{91} +(1.10637 + 0.882304i) q^{92} +(1.50062 + 3.11607i) q^{94} +(-19.0027 + 15.1541i) q^{95} -14.6184i q^{97} +(6.32342 - 0.0131793i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70}+ \cdots - 112 q^{94}+O(q^{100}) $ 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

Character values

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

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

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 $

$2$	0.880699	−	0.201014i	0.622748	−	0.142138i	0.100508	−	0.994936i	$-0.467953\pi$
$2$	0.880699	−	0.201014i	0.622748	−	0.142138i	0.522241	+	0.852798i	$0.325096\pi$
$3$		0			0
$3$		0			0
$4$	−1.06671	+	0.513702i	−0.533357	+	0.256851i
$5$	−2.70158	−	3.38767i	−1.20818	−	1.51501i	−0.797596	−	0.603192i	$-0.793895\pi$
$5$	−2.70158	−	3.38767i	−1.20818	−	1.51501i	−0.410587	−	0.911822i	$-0.634676\pi$
$6$		0			0
$7$	2.62942	+	0.293490i	0.993828	+	0.110929i
$7$	2.62942	+	0.293490i	0.993828	+	0.110929i
$8$	−2.24872	+	1.79330i	−0.795044	+	0.634026i
$9$		0			0
$10$	−3.06025	−	2.44047i	−0.967735	−	0.771743i
$11$	−2.23309	+	0.509689i	−0.673303	+	0.153677i	−0.545485	−	0.838121i	$-0.683654\pi$
$11$	−2.23309	+	0.509689i	−0.673303	+	0.153677i	−0.127818	+	0.991798i	$0.540797\pi$
$12$		0			0
$13$	−5.63896	+	1.28706i	−1.56397	+	0.356965i	−0.914873	−	0.403742i	$-0.867709\pi$
$13$	−5.63896	+	1.28706i	−1.56397	+	0.356965i	−0.649095	+	0.760708i	$0.724852\pi$
$14$	2.37473	−	0.270074i	0.634672	−	0.0721802i
$15$		0			0
$16$	−0.143595	+	0.180062i	−0.0358986	+	0.0450155i
$17$	−4.20422	−	2.02465i	−1.01967	−	0.491049i	−0.152104	−	0.988364i	$-0.548605\pi$
$17$	−4.20422	−	2.02465i	−1.01967	−	0.491049i	−0.867570	+	0.497315i	$0.834319\pi$
$18$		0			0
$19$		−	5.60936i		−	1.28687i	−0.765499	−	0.643437i	$-0.777508\pi$
$19$		−	5.60936i		−	1.28687i	0.765499	−	0.643437i	$-0.222492\pi$
$20$	4.62207	+	2.22587i	1.03353	+	0.497719i
$21$		0			0
$22$	−1.86423	+	0.897765i	−0.397455	+	0.191404i
$23$	−0.518590	−	1.07686i	−0.108134	−	0.224542i	0.839880	−	0.542773i	$-0.182625\pi$
$23$	−0.518590	−	1.07686i	−0.108134	−	0.224542i	−0.948013	+	0.318231i	$0.896911\pi$
$24$		0			0
$25$	−3.06519	+	13.4295i	−0.613039	+	2.68590i
$26$	−4.70751	+	2.26702i	−0.923220	+	0.444599i
$27$		0			0
$28$	−2.95561	+	1.03767i	−0.558557	+	0.196101i
$29$	1.47898	−	3.07113i	0.274640	−	0.570295i	−0.717335	−	0.696728i	$-0.754638\pi$
$29$	1.47898	−	3.07113i	0.274640	−	0.570295i	0.991975	+	0.126433i	$0.0403527\pi$
$30$		0			0
$31$		−	0.588888i		−	0.105767i	−0.998601	−	0.0528837i	$-0.983159\pi$
$31$		−	0.588888i		−	0.105767i	0.998601	−	0.0528837i	$-0.0168413\pi$
$32$	2.40563	−	4.99534i	0.425259	−	0.883059i
$33$		0			0
$34$	−4.10964	−	0.937998i	−0.704797	−	0.160865i
$35$	−6.10934	−	9.70051i	−1.03267	−	1.63969i
$36$		0			0
$37$	1.11676	+	0.537802i	0.183594	+	0.0884141i	0.523423	−	0.852073i	$-0.324655\pi$
$37$	1.11676	+	0.537802i	0.183594	+	0.0884141i	−0.339829	+	0.940487i	$0.610369\pi$
$38$	−1.12756	−	4.94016i	−0.182914	−	0.801399i
$39$		0			0
$40$	12.1502	+	2.77321i	1.92112	+	0.438482i
$41$	0.526282	+	0.659937i	0.0821914	+	0.103065i	0.821227	−	0.570602i	$-0.193290\pi$
$41$	0.526282	+	0.659937i	0.0821914	+	0.103065i	−0.739036	+	0.673666i	$0.764718\pi$
$42$		0			0
$43$	1.25480	−	1.57347i	0.191355	−	0.239951i	−0.676894	−	0.736081i	$-0.736674\pi$
$43$	1.25480	−	1.57347i	0.191355	−	0.239951i	0.868249	+	0.496129i	$0.165246\pi$
$44$	2.12024	−	1.69084i	0.319638	−	0.254903i
$45$		0			0
$46$	−0.673187	−	0.844149i	−0.0992559	−	0.124463i
$47$	0.851950	+	3.73264i	0.124270	+	0.544461i	0.998284	+	0.0585605i	$0.0186510\pi$
$47$	0.851950	+	3.73264i	0.124270	+	0.544461i	−0.874014	+	0.485900i	$0.838492\pi$
$48$		0			0
$49$	6.82773	+	1.54342i	0.975390	+	0.220489i
$50$			12.4435i			1.75978i
$51$		0			0
$52$	5.35399	−	4.26967i	0.742465	−	0.592096i
$53$	1.27448	+	2.64649i	0.175063	+	0.363523i	0.969976	−	0.243201i	$-0.0781975\pi$
$53$	1.27448	+	2.64649i	0.175063	+	0.363523i	−0.794912	+	0.606724i	$0.792483\pi$
$54$		0			0
$55$	7.75953	+	6.18802i	1.04630	+	0.834393i
$56$	−6.43916	+	4.05536i	−0.860469	+	0.541920i
$57$		0			0
$58$	0.685196	−	3.00204i	0.0899707	−	0.394187i
$59$	8.71710	−	10.9309i	1.13487	−	1.42308i	0.243444	−	0.969915i	$-0.421723\pi$
$59$	8.71710	−	10.9309i	1.13487	−	1.42308i	0.891426	−	0.453167i	$-0.149706\pi$
$60$		0			0
$61$	1.57855	−	3.27789i	0.202112	−	0.419690i	−0.775134	−	0.631796i	$-0.782318\pi$
$61$	1.57855	−	3.27789i	0.202112	−	0.419690i	0.977247	+	0.212106i	$0.0680322\pi$
$62$	−0.118375	−	0.518633i	−0.0150336	−	0.0658665i
$63$		0			0
$64$	1.21700	−	5.33202i	0.152125	−	0.666502i
$65$	19.5942	+	15.6259i	2.43037	+	1.93815i
$66$		0			0
$67$	−6.27020			−0.766027			−0.383014	−	0.923743i	$-0.625114\pi$
$67$	−6.27020			−0.766027			−0.383014	+	0.923743i	$0.625114\pi$
$68$	5.52477			0.669977
$69$		0			0
$70$	−7.33043	−	7.31517i	−0.876154	−	0.874330i
$71$	−1.87256	−	3.88841i	−0.222232	−	0.461469i	0.759807	−	0.650149i	$-0.225293\pi$
$71$	−1.87256	−	3.88841i	−0.222232	−	0.461469i	−0.982039	+	0.188680i	$0.939579\pi$
$72$		0			0
$73$	−7.77931	−	1.77558i	−0.910500	−	0.207816i	−0.258479	−	0.966017i	$-0.583221\pi$
$73$	−7.77931	−	1.77558i	−0.910500	−	0.207816i	−0.652021	+	0.758201i	$0.726078\pi$
$74$	1.09163	+	0.249158i	0.126900	+	0.0289640i
$75$		0			0
$76$	2.88154	+	5.98358i	0.330535	+	0.686363i
$77$	−6.02133	+	0.684797i	−0.686195	+	0.0780398i
$78$		0			0
$79$	−0.653795			−0.0735577			−0.0367789	−	0.999323i	$-0.511710\pi$
$79$	−0.653795			−0.0735577			−0.0367789	+	0.999323i	$0.511710\pi$
$80$	0.997922			0.111571
$81$		0			0
$82$	0.596153	+	0.475416i	0.0658340	+	0.0525009i
$83$	−1.57947	+	6.92012i	−0.173370	+	0.759582i	0.811226	+	0.584733i	$0.198801\pi$
$83$	−1.57947	+	6.92012i	−0.173370	+	0.759582i	−0.984595	+	0.174849i	$0.944056\pi$
$84$		0			0
$85$	4.49920	+	19.7123i	0.488007	+	2.13810i
$86$	0.788810	−	1.63798i	0.0850596	−	0.176628i
$87$		0			0
$88$	4.10759	−	5.15075i	0.437870	−	0.549072i
$89$	−2.56309	+	11.2296i	−0.271687	+	1.19034i	0.636333	+	0.771414i	$0.280450\pi$
$89$	−2.56309	+	11.2296i	−0.271687	+	1.19034i	−0.908020	+	0.418926i	$0.862407\pi$
$90$		0			0
$91$	−15.2050	+	1.72924i	−1.59391	+	0.181273i
$92$	1.10637	+	0.882304i	0.115348	+	0.0919866i
$93$		0			0
$94$	1.50062	+	3.11607i	0.154777	+	0.321399i
$95$	−19.0027	+	15.1541i	−1.94963	+	1.55478i
$96$		0			0
$97$		−	14.6184i		−	1.48427i	−0.670249	−	0.742136i	$-0.733813\pi$
$97$		−	14.6184i		−	1.48427i	0.670249	−	0.742136i	$-0.266187\pi$
$98$	6.32342	−	0.0131793i	0.638762	−	0.00133131i
$99$		0			0
$100$	−3.62907	−	15.9000i	−0.362907	−	1.59000i
$101$	2.17142	+	2.72287i	0.216064	+	0.270936i	0.878038	−	0.478591i	$-0.158852\pi$
$101$	2.17142	+	2.72287i	0.216064	+	0.270936i	−0.661974	+	0.749527i	$0.730281\pi$
$102$		0			0
$103$	1.97183	−	1.57248i	0.194290	−	0.154941i	−0.521513	−	0.853243i	$-0.674632\pi$
$103$	1.97183	−	1.57248i	0.194290	−	0.154941i	0.715803	+	0.698302i	$0.246061\pi$
$104$	10.3724	−	13.0066i	1.01710	−	1.27540i
$105$		0			0
$106$	1.65441	+	2.07457i	0.160691	+	0.201500i
$107$	−9.15970	−	2.09064i	−0.885502	−	0.202110i	−0.244500	−	0.969649i	$-0.578624\pi$
$107$	−9.15970	−	2.09064i	−0.885502	−	0.202110i	−0.641002	+	0.767539i	$0.721481\pi$
$108$		0			0
$109$	−2.54281	−	11.1408i	−0.243557	−	1.06709i	−0.937752	−	0.347306i	$-0.887097\pi$
$109$	−2.54281	−	11.1408i	−0.243557	−	1.06709i	0.694195	−	0.719787i	$-0.255760\pi$
$110$	8.07769	+	3.89001i	0.770178	+	0.370898i
$111$		0			0
$112$	−0.430417	+	0.431315i	−0.0406706	+	0.0407554i
$113$	−3.83148	−	0.874509i	−0.360435	−	0.0822669i	0.0384686	−	0.999260i	$-0.487752\pi$
$113$	−3.83148	−	0.874509i	−0.360435	−	0.0822669i	−0.398904	+	0.916993i	$0.630609\pi$
$114$		0			0
$115$	−2.24705	+	4.66605i	−0.209538	+	0.435111i
$116$			4.03578i			0.374712i
$117$		0			0
$118$	5.47988	−	11.3791i	0.504464	−	1.04753i
$119$	−10.4605	−	6.55755i	−0.958910	−	0.601130i
$120$		0			0
$121$	−5.18374	+	2.49636i	−0.471249	+	0.226942i
$122$	0.731324	−	3.20414i	0.0662110	−	0.290089i
$123$		0			0
$124$	0.302513	+	0.628175i	0.0271665	+	0.0564118i
$125$	34.2561	−	16.4969i	3.06396	−	1.47553i
$126$		0			0
$127$	19.9907	+	9.62702i	1.77389	+	0.854260i	0.963202	+	0.268779i	$0.0866200\pi$
$127$	19.9907	+	9.62702i	1.77389	+	0.854260i	0.810686	+	0.585481i	$0.199094\pi$
$128$			6.14827i			0.543435i
$129$		0			0
$130$	20.3976	+	9.82299i	1.78899	+	0.861533i
$131$	−7.87965	+	9.88077i	−0.688448	+	0.863287i	−0.996102	−	0.0882116i	$-0.971885\pi$
$131$	−7.87965	+	9.88077i	−0.688448	+	0.863287i	0.307653	+	0.951498i	$0.400456\pi$
$132$		0			0
$133$	1.64629	−	14.7494i	0.142752	−	1.27893i
$134$	−5.52216	+	1.26040i	−0.477042	+	0.108882i
$135$		0			0
$136$	13.0849	−	2.98655i	1.12202	−	0.256095i
$137$	−14.3556	−	11.4482i	−1.22648	−	0.978085i	−0.999992	−	0.00407088i	$-0.998704\pi$
$137$	−14.3556	−	11.4482i	−1.22648	−	0.978085i	−0.226488	−	0.974014i	$-0.572724\pi$
$138$		0			0
$139$	14.8002	−	11.8027i	1.25533	−	1.00110i	0.255926	−	0.966696i	$-0.417620\pi$
$139$	14.8002	−	11.8027i	1.25533	−	1.00110i	0.999408	−	0.0343994i	$-0.0109518\pi$
$140$	11.5001	+	7.20928i	0.971935	+	0.609296i
$141$		0			0
$142$	−2.43078	−	3.04811i	−0.203987	−	0.255792i
$143$	11.9363	−	5.74823i	0.998166	−	0.480691i
$144$		0			0
$145$	−14.3996	+	3.28661i	−1.19582	+	0.272938i
$146$	−7.20815			−0.596551
$147$		0			0
$148$	−1.46753			−0.120630
$149$	−13.2926	+	3.03394i	−1.08897	+	0.248550i	−0.729069	−	0.684441i	$-0.760046\pi$
$149$	−13.2926	+	3.03394i	−1.08897	+	0.248550i	−0.359900	+	0.932991i	$0.617189\pi$
$150$		0			0
$151$	−14.7372	+	7.09708i	−1.19930	+	0.577552i	−0.923476	−	0.383656i	$-0.874665\pi$
$151$	−14.7372	+	7.09708i	−1.19930	+	0.577552i	−0.275823	+	0.961208i	$0.588950\pi$
$152$	10.0592	+	12.6139i	0.815913	+	1.02312i
$153$		0			0
$154$	−5.16533	+	1.81347i	−0.416234	+	0.146134i
$155$	−1.99496	+	1.59093i	−0.160239	+	0.127786i
$156$		0			0
$157$	−2.20114	−	1.75535i	−0.175670	−	0.140092i	0.531708	−	0.846928i	$-0.321551\pi$
$157$	−2.20114	−	1.75535i	−0.175670	−	0.140092i	−0.707378	+	0.706836i	$0.750122\pi$
$158$	−0.575797	+	0.131422i	−0.0458079	+	0.0104554i
$159$		0			0
$160$	−23.4216	+	5.34582i	−1.85164	+	0.422624i
$161$	−1.04754	−	2.98373i	−0.0825580	−	0.235151i
$162$		0			0
$163$	13.1340	−	16.4695i	1.02874	−	1.28999i	0.0725088	−	0.997368i	$-0.476899\pi$
$163$	13.1340	−	16.4695i	1.02874	−	1.28999i	0.956227	−	0.292626i	$-0.0945291\pi$
$164$	−0.900403	−	0.433611i	−0.0703097	−	0.0338593i
$165$		0			0
$166$			6.41204i			0.497671i
$167$	−10.5862	−	5.09804i	−0.819184	−	0.394498i	−0.0231366	−	0.999732i	$-0.507365\pi$
$167$	−10.5862	−	5.09804i	−0.819184	−	0.394498i	−0.796048	+	0.605234i	$0.793080\pi$
$168$		0			0
$169$	18.4288	−	8.87485i	1.41760	−	0.682680i
$170$	7.92488	+	16.4562i	0.607811	+	1.26213i
$171$		0			0
$172$	−0.530216	+	2.32303i	−0.0404286	+	0.177129i
$173$	15.0494	−	7.24742i	1.14419	−	0.551011i	0.236905	−	0.971533i	$-0.423867\pi$
$173$	15.0494	−	7.24742i	1.14419	−	0.551011i	0.907283	+	0.420521i	$0.138153\pi$
$174$		0			0
$175$	−12.0011	+	34.4122i	−0.907199	+	2.60132i
$176$	0.228884	−	0.475283i	0.0172528	−	0.0358258i
$177$		0			0
$178$			10.4052i			0.779899i
$179$	−2.11939	+	4.40096i	−0.158411	+	0.328943i	−0.965035	−	0.262121i	$-0.915578\pi$
$179$	−2.11939	+	4.40096i	−0.158411	+	0.328943i	0.806624	+	0.591065i	$0.201292\pi$
$180$		0			0
$181$	−14.6014	−	3.33268i	−1.08532	−	0.247716i	−0.357794	−	0.933800i	$-0.616471\pi$
$181$	−14.6014	−	3.33268i	−1.08532	−	0.247716i	−0.727522	+	0.686084i	$0.759328\pi$
$182$	−13.0434	+	4.57934i	−0.966841	+	0.339444i
$183$		0			0
$184$	3.09730	+	1.49158i	0.228336	+	0.109961i
$185$	−1.19511	−	5.23612i	−0.0878663	−	0.384968i
$186$		0			0
$187$	10.4204	+	2.37838i	0.762012	+	0.173924i
$188$	−2.82625	−	3.54400i	−0.206125	−	0.258473i
$189$		0			0
$190$	−13.6894	+	17.1660i	−0.993137	+	1.24535i
$191$	−2.65384	+	2.11637i	−0.192025	+	0.153135i	−0.714783	−	0.699346i	$-0.753475\pi$
$191$	−2.65384	+	2.11637i	−0.192025	+	0.153135i	0.522758	+	0.852481i	$0.324903\pi$
$192$		0			0
$193$	1.38258	+	1.73370i	0.0995202	+	0.124794i	0.829098	−	0.559104i	$-0.188855\pi$
$193$	1.38258	+	1.73370i	0.0995202	+	0.124794i	−0.729577	+	0.683898i	$0.760283\pi$
$194$	−2.93850	−	12.8744i	−0.210972	−	0.924328i
$195$		0			0
$196$	−8.07609	+	1.86103i	−0.576863	+	0.132931i
$197$			10.1054i			0.719977i	0.932957	+	0.359989i	$0.117219\pi$
$197$			10.1054i			0.719977i	−0.932957	+	0.359989i	$0.882781\pi$
$198$		0			0
$199$	−17.9142	+	14.2861i	−1.26990	+	1.01271i	−0.271164	+	0.962533i	$0.587409\pi$
$199$	−17.9142	+	14.2861i	−1.26990	+	1.01271i	−0.998740	+	0.0501816i	$0.984020\pi$
$200$	−17.1903	−	35.6960i	−1.21554	−	2.52409i
$201$		0			0
$202$	2.45970	+	1.96155i	0.173064	+	0.138014i
$203$	4.79021	−	7.64125i	0.336207	−	0.536310i
$204$		0			0
$205$	0.813858	−	3.56574i	0.0568423	−	0.249042i
$206$	1.42050	−	1.78125i	0.0989707	−	0.124105i
$207$		0			0
$208$	0.577975	−	1.20018i	0.0400753	−	0.0832173i
$209$	2.85903	+	12.5262i	0.197763	+	0.866456i
$210$		0			0
$211$	4.15135	−	18.1882i	0.285791	−	1.25213i	−0.604451	−	0.796642i	$-0.706608\pi$
$211$	4.15135	−	18.1882i	0.285791	−	1.25213i	0.890242	−	0.455488i	$-0.150535\pi$
$212$	−2.71901	−	2.16834i	−0.186742	−	0.148922i
$213$		0			0
$214$	−8.48719			−0.580172
$215$	−8.72032			−0.594721
$216$		0			0
$217$	0.172833	−	1.54844i	0.0117327	−	0.105115i
$218$	−4.47890	−	9.30053i	−0.303349	−	0.629911i
$219$		0			0
$220$	−11.4560	−	2.61476i	−0.772363	−	0.176287i
$221$	26.3133	+	6.00584i	1.77002	+	0.403997i
$222$		0			0
$223$	2.19793	+	4.56404i	0.147184	+	0.305631i	0.961507	−	0.274782i	$-0.0886056\pi$
$223$	2.19793	+	4.56404i	0.147184	+	0.305631i	−0.814323	+	0.580413i	$0.802891\pi$
$224$	7.79149	−	12.4288i	0.520591	−	0.830435i
$225$		0			0
$226$	−3.55017			−0.236154
$227$	−17.2441			−1.14453			−0.572266	−	0.820068i	$-0.693935\pi$
$227$	−17.2441			−1.14453			−0.572266	+	0.820068i	$0.693935\pi$
$228$		0			0
$229$	−8.18030	−	6.52357i	−0.540569	−	0.431090i	0.314762	−	0.949171i	$-0.398075\pi$
$229$	−8.18030	−	6.52357i	−0.540569	−	0.431090i	−0.855332	+	0.518081i	$0.826647\pi$
$230$	−1.04103	+	4.56107i	−0.0686438	+	0.300748i
$231$		0			0
$232$	2.18164	+	9.55839i	0.143232	+	0.627539i
$233$	5.28618	−	10.9769i	0.346309	−	0.719119i	−0.652958	−	0.757394i	$-0.726472\pi$
$233$	5.28618	−	10.9769i	0.346309	−	0.719119i	0.999267	+	0.0382756i	$0.0121865\pi$
$234$		0			0
$235$	10.3433	−	12.9701i	0.674725	−	0.846078i
$236$	−3.68342	+	16.1381i	−0.239770	+	1.05050i
$237$		0			0
$238$	−10.5307	−	3.67253i	−0.682603	−	0.238055i
$239$	−0.370472	−	0.295442i	−0.0239638	−	0.0191105i	0.611435	−	0.791295i	$-0.290593\pi$
$239$	−0.370472	−	0.295442i	−0.0239638	−	0.0191105i	−0.635399	+	0.772184i	$0.719164\pi$
$240$		0			0
$241$	−3.43409	−	7.13095i	−0.221209	−	0.459345i	0.760599	−	0.649222i	$-0.224905\pi$
$241$	−3.43409	−	7.13095i	−0.221209	−	0.459345i	−0.981808	+	0.189877i	$0.939191\pi$
$242$	−4.06351	+	3.24054i	−0.261212	+	0.208310i
$243$		0			0
$244$			4.30747i			0.275757i
$245$	−13.2170	−	27.2998i	−0.844406	−	1.74412i
$246$		0			0
$247$	7.21956	+	31.6310i	0.459370	+	2.01263i
$248$	1.05605	+	1.32425i	0.0670594	+	0.0840898i
$249$		0			0
$250$	26.8532	−	21.4147i	1.69835	−	1.35439i
$251$	3.76595	−	4.72236i	0.237705	−	0.298073i	−0.648643	−	0.761093i	$-0.724663\pi$
$251$	3.76595	−	4.72236i	0.237705	−	0.298073i	0.886348	+	0.463021i	$0.153234\pi$
$252$		0			0
$253$	1.70693	+	2.14042i	0.107313	+	0.134567i
$254$	19.5410	+	4.46010i	1.22611	+	0.279851i
$255$		0			0
$256$	3.66988	+	16.0788i	0.229368	+	1.00493i
$257$	−4.63028	−	2.22982i	−0.288829	−	0.139093i	0.283859	−	0.958866i	$-0.408385\pi$
$257$	−4.63028	−	2.22982i	−0.288829	−	0.139093i	−0.572688	+	0.819773i	$0.694099\pi$
$258$		0			0
$259$	2.77859	+	1.74187i	0.172653	+	0.108234i
$260$	−28.9285	−	6.60274i	−1.79407	−	0.409484i
$261$		0			0
$262$	−4.95343	+	10.2859i	−0.306024	+	0.635465i
$263$			12.7789i			0.787979i	0.919115	+	0.393990i	$0.128905\pi$
$263$			12.7789i			0.787979i	−0.919115	+	0.393990i	$0.871095\pi$
$264$		0			0
$265$	5.52232	−	11.4672i	0.339233	−	0.704426i
$266$	−1.51494	−	13.3207i	−0.0928869	−	0.816744i
$267$		0			0
$268$	6.68851	−	3.22102i	0.408566	−	0.196755i
$269$	0.218109	−	0.955599i	0.0132984	−	0.0582639i	−0.967843	−	0.251554i	$-0.919059\pi$
$269$	0.218109	−	0.955599i	0.0132984	−	0.0582639i	0.981142	+	0.193290i	$0.0619157\pi$
$270$		0			0
$271$	4.44545	+	9.23108i	0.270042	+	0.560748i	0.991254	−	0.131966i	$-0.0421290\pi$
$271$	4.44545	+	9.23108i	0.270042	+	0.560748i	−0.721212	+	0.692714i	$0.756415\pi$
$272$	0.968265	−	0.466292i	0.0587097	−	0.0282731i
$273$		0			0
$274$	−14.9442	−	7.19674i	−0.902811	−	0.434771i
$275$		−	31.5516i		−	1.90263i
$276$		0			0
$277$	23.6016	+	11.3659i	1.41808	+	0.682913i	0.976740	−	0.214425i	$-0.0687878\pi$
$277$	23.6016	+	11.3659i	1.41808	+	0.682913i	0.441343	+	0.897338i	$0.354502\pi$
$278$	10.6620	−	13.3697i	0.639463	−	0.801862i
$279$		0			0
$280$	31.1341	+	10.8579i	1.86062	+	0.648884i
$281$	19.5942	−	4.47224i	1.16889	−	0.266792i	0.406341	−	0.913722i	$-0.366805\pi$
$281$	19.5942	−	4.47224i	1.16889	−	0.266792i	0.762549	+	0.646930i	$0.223947\pi$
$282$		0			0
$283$	−15.5784	+	3.55567i	−0.926041	+	0.211363i	−0.658844	−	0.752279i	$-0.728954\pi$
$283$	−15.5784	+	3.55567i	−0.926041	+	0.211363i	−0.267197	+	0.963642i	$0.586097\pi$
$284$	3.99497	+	3.18588i	0.237058	+	0.189047i
$285$		0			0
$286$	9.35684	−	7.46183i	0.553282	−	0.441227i
$287$	1.19013	+	1.88971i	0.0702513	+	0.111546i
$288$		0			0
$289$	2.97698	+	3.73302i	0.175116	+	0.219589i
$290$	−12.0210	+	5.78903i	−0.705900	+	0.339944i
$291$		0			0
$292$	9.21041	−	2.10222i	0.538999	−	0.123023i
$293$	−23.8502			−1.39335			−0.696673	−	0.717389i	$-0.745337\pi$
$293$	−23.8502			−1.39335			−0.696673	+	0.717389i	$0.745337\pi$
$294$		0			0
$295$	−60.5802			−3.52712
$296$	−3.47572	+	0.793310i	−0.202022	+	0.0461102i
$297$		0			0
$298$	−11.0969	+	5.34398i	−0.642825	+	0.309568i
$299$	4.31030	+	5.40494i	0.249271	+	0.312576i
$300$		0			0
$301$	3.76119	−	3.76903i	0.216791	−	0.217244i
$302$	−11.5525	+	9.21278i	−0.664769	+	0.530136i
$303$		0			0
$304$	1.01003	+	0.805473i	0.0579292	+	0.0461970i
$305$	−15.3690	+	3.50787i	−0.880025	+	0.200860i
$306$		0			0
$307$	−23.2393	+	5.30422i	−1.32634	+	0.302728i	−0.826278	−	0.563263i	$-0.809546\pi$
$307$	−23.2393	+	5.30422i	−1.32634	+	0.302728i	−0.500060	+	0.865991i	$0.666689\pi$
$308$	6.07125	−	3.82365i	0.345942	−	0.217873i
$309$		0			0
$310$	−1.43716	+	1.80214i	−0.0816253	+	0.102355i
$311$	14.4864	+	6.97629i	0.821449	+	0.395589i	0.796901	−	0.604110i	$-0.206471\pi$
$311$	14.4864	+	6.97629i	0.821449	+	0.395589i	0.0245480	+	0.999699i	$0.492185\pi$
$312$		0			0
$313$			7.93963i			0.448774i	0.974500	+	0.224387i	$0.0720380\pi$
$313$			7.93963i			0.448774i	−0.974500	+	0.224387i	$0.927962\pi$
$314$	−2.29139	−	1.10348i	−0.129311	−	0.0622728i
$315$		0			0
$316$	0.697412	−	0.335856i	0.0392325	−	0.0188934i
$317$	7.66940	+	15.9257i	0.430756	+	0.894475i	0.997506	+	0.0705846i	$0.0224865\pi$
$317$	7.66940	+	15.9257i	0.430756	+	0.894475i	−0.566749	+	0.823890i	$0.691799\pi$
$318$		0			0
$319$	−1.73738	+	7.61195i	−0.0972745	+	0.426187i
$320$	−21.3510	+	10.2821i	−1.19355	+	0.574786i
$321$		0			0
$322$	−1.52234	−	2.41720i	−0.0848368	−	0.134705i
$323$	−11.3570	+	23.5830i	−0.631919	+	1.31219i
$324$		0			0
$325$		−	79.6735i		−	4.41949i
$326$	8.25651	−	17.1448i	0.457286	−	0.949564i
$327$		0			0
$328$	−2.36693	−	0.540235i	−0.130692	−	0.0298295i
$329$	1.14464	+	10.0647i	0.0631063	+	0.554886i
$330$		0			0
$331$	−10.3891	−	5.00311i	−0.571034	−	0.274996i	0.126004	−	0.992030i	$-0.459785\pi$
$331$	−10.3891	−	5.00311i	−0.571034	−	0.274996i	−0.697038	+	0.717034i	$0.745499\pi$
$332$	−1.87004	−	8.19317i	−0.102632	−	0.449659i
$333$		0			0
$334$	−10.3480	−	2.36187i	−0.566219	−	0.129236i
$335$	16.9394	+	21.2414i	0.925501	+	1.16054i
$336$		0			0
$337$	16.3395	−	20.4891i	0.890072	−	1.11611i	−0.102534	−	0.994730i	$-0.532695\pi$
$337$	16.3395	−	20.4891i	0.890072	−	1.11611i	0.992605	−	0.121385i	$-0.0387336\pi$
$338$	14.4463	−	11.5205i	0.785773	−	0.626633i
$339$		0			0
$340$	−14.9256	−	18.7161i	−0.809454	−	1.01502i
$341$	0.300150	+	1.31504i	0.0162540	+	0.0712135i
$342$		0			0
$343$	17.5000	+	6.06217i	0.944911	+	0.327327i
$344$			5.78851i			0.312096i
$345$		0			0
$346$	11.7972	−	9.40794i	0.634221	−	0.505774i
$347$	10.5180	+	21.8408i	0.564635	+	1.17248i	0.966474	+	0.256766i	$0.0826570\pi$
$347$	10.5180	+	21.8408i	0.564635	+	1.17248i	−0.401839	+	0.915710i	$0.631629\pi$
$348$		0			0
$349$	−1.25766	−	1.00295i	−0.0673209	−	0.0536866i	0.589251	−	0.807950i	$-0.299423\pi$
$349$	−1.25766	−	1.00295i	−0.0673209	−	0.0536866i	−0.656572	+	0.754263i	$0.727994\pi$
$350$	−3.65204	+	32.7192i	−0.195210	+	1.74891i
$351$		0			0
$352$	−2.82592	+	12.3812i	−0.150622	+	0.659918i
$353$	2.22612	−	2.79147i	0.118485	−	0.148575i	−0.719052	−	0.694956i	$-0.755424\pi$
$353$	2.22612	−	2.79147i	0.118485	−	0.148575i	0.837537	+	0.546381i	$0.183995\pi$
$354$		0			0
$355$	−8.11379	+	16.8485i	−0.430635	+	0.894223i
$356$	−3.03461	−	13.2955i	−0.160834	−	0.704659i
$357$		0			0
$358$	−0.981892	+	4.30195i	−0.0518946	+	0.227365i
$359$	1.41736	+	1.13031i	0.0748056	+	0.0596555i	0.660179	−	0.751109i	$-0.270481\pi$
$359$	1.41736	+	1.13031i	0.0748056	+	0.0596555i	−0.585373	+	0.810764i	$0.699052\pi$
$360$		0			0
$361$	−12.4649			−0.656047
$362$	−13.5294			−0.711089
$363$		0			0
$364$	15.3310	−	9.65542i	0.803564	−	0.506081i
$365$	15.0013	+	31.1506i	0.785207	+	1.63050i
$366$		0			0
$367$	14.9617	+	3.41491i	0.780994	+	0.178257i	0.594388	−	0.804178i	$-0.297394\pi$
$367$	14.9617	+	3.41491i	0.780994	+	0.178257i	0.186606	+	0.982435i	$0.440251\pi$
$368$	0.268369	+	0.0612534i	0.0139897	+	0.00319306i
$369$		0			0
$370$	−2.10507	−	4.37122i	−0.109437	−	0.227249i
$371$	2.57443	+	7.33278i	0.133658	+	0.380699i
$372$		0			0
$373$	19.1260			0.990306			0.495153	−	0.868806i	$-0.335112\pi$
$373$	19.1260			0.990306			0.495153	+	0.868806i	$0.335112\pi$
$374$	9.65529			0.499263
$375$		0			0
$376$	−8.60952	−	6.86587i	−0.444002	−	0.354080i
$377$	−4.38719	+	19.2216i	−0.225952	+	0.989960i
$378$		0			0
$379$	−6.62972	−	29.0467i	−0.340546	−	1.49203i	−0.797925	−	0.602757i	$-0.794069\pi$
$379$	−6.62972	−	29.0467i	−0.340546	−	1.49203i	0.457379	−	0.889272i	$-0.348788\pi$
$380$	12.4857	−	25.9268i	0.640503	−	1.33002i
$381$		0			0
$382$	−1.91182	+	2.39734i	−0.0978170	+	0.122659i
$383$	−0.965199	+	4.22881i	−0.0493194	+	0.216082i	−0.993583	−	0.113109i	$-0.963919\pi$
$383$	−0.965199	+	4.22881i	−0.0493194	+	0.216082i	0.944263	+	0.329191i	$0.106776\pi$
$384$		0			0
$385$	18.5870	+	18.5483i	0.947280	+	0.945308i
$386$	1.56613	+	1.24895i	0.0797141	+	0.0635699i
$387$		0			0
$388$	7.50950	+	15.5936i	0.381237	+	0.791647i
$389$	11.5074	−	9.17687i	0.583450	−	0.465286i	−0.286736	−	0.958010i	$-0.592570\pi$
$389$	11.5074	−	9.17687i	0.583450	−	0.465286i	0.870186	+	0.492724i	$0.163999\pi$
$390$		0			0
$391$			5.57734i			0.282058i
$392$	−18.1215	+	8.77342i	−0.915273	+	0.443125i
$393$		0			0
$394$	2.03132	+	8.89979i	0.102336	+	0.448365i
$395$	1.76628	+	2.21484i	0.0888712	+	0.111441i
$396$		0			0
$397$	−20.1552	+	16.0732i	−1.01156	+	0.806691i	−0.981228	−	0.192849i	$-0.938227\pi$
$397$	−20.1552	+	16.0732i	−1.01156	+	0.806691i	−0.0303298	+	0.999540i	$0.509656\pi$
$398$	−12.9053	+	16.1828i	−0.646885	+	0.811168i
$399$		0			0
$400$	−1.97799	−	2.48033i	−0.0988997	−	0.124016i
$401$	0.424547	+	0.0969002i	0.0212009	+	0.00483896i	0.233108	−	0.972451i	$-0.425110\pi$
$401$	0.424547	+	0.0969002i	0.0212009	+	0.00483896i	−0.211907	+	0.977290i	$0.567968\pi$
$402$		0			0
$403$	0.757933	+	3.32072i	0.0377553	+	0.165417i
$404$	−3.71503	−	1.78906i	−0.184830	−	0.0890092i
$405$		0			0
$406$	2.68274	−	7.69254i	0.133142	−	0.381774i
$407$	−2.76793	−	0.631763i	−0.137201	−	0.0313153i
$408$		0			0
$409$	0.726290	−	1.50816i	0.0359127	−	0.0745735i	−0.882241	−	0.470799i	$-0.843966\pi$
$409$	0.726290	−	1.50816i	0.0359127	−	0.0745735i	0.918153	+	0.396225i	$0.129680\pi$
$410$		−	3.30394i		−	0.163170i
$411$		0			0
$412$	−1.29559	+	2.69032i	−0.0638291	+	0.132542i
$413$	26.1291	−	26.1836i	1.28573	−	1.28841i
$414$		0			0
$415$	27.7102	−	13.3445i	1.36024	−	0.655057i
$416$	−7.13596	+	31.2647i	−0.349869	+	1.53288i
$417$		0			0
$418$	5.03588	+	10.4571i	0.246313	+	0.511474i
$419$	29.1182	−	14.0226i	1.42252	−	0.685047i	0.444926	−	0.895567i	$-0.353230\pi$
$419$	29.1182	−	14.0226i	1.42252	−	0.685047i	0.977589	+	0.210520i	$0.0675158\pi$
$420$		0			0
$421$	6.34125	+	3.05379i	0.309054	+	0.148832i	0.581981	−	0.813202i	$-0.302278\pi$
$421$	6.34125	+	3.05379i	0.309054	+	0.148832i	−0.272928	+	0.962035i	$0.587992\pi$
$422$		−	16.8528i		−	0.820384i
$423$		0			0
$424$	−7.61189	−	3.66569i	−0.369666	−	0.178022i
$425$	40.0768	−	50.2547i	1.94401	−	2.43771i
$426$		0			0
$427$	5.11270	−	8.15566i	0.247421	−	0.394680i
$428$	10.8447	−	2.47524i	0.524200	−	0.119645i
$429$		0			0
$430$	−7.67998	+	1.75290i	−0.370361	+	0.0845326i
$431$	−15.6426	−	12.4745i	−0.753477	−	0.600877i	0.169591	−	0.985514i	$-0.445755\pi$
$431$	−15.6426	−	12.4745i	−0.753477	−	0.600877i	−0.923068	+	0.384637i	$0.874327\pi$
$432$		0			0
$433$	−2.32509	+	1.85420i	−0.111737	+	0.0891071i	−0.677764	−	0.735279i	$-0.737051\pi$
$433$	−2.32509	+	1.85420i	−0.111737	+	0.0891071i	0.566028	+	0.824386i	$0.308480\pi$
$434$	−0.159043	−	1.39845i	−0.00763432	−	0.0671277i
$435$		0			0
$436$	8.43549	+	10.5778i	0.403987	+	0.506583i
$437$	−6.04051	+	2.90896i	−0.288957	+	0.139154i
$438$		0			0
$439$	7.56298	−	1.72620i	0.360961	−	0.0823871i	−0.0381941	−	0.999270i	$-0.512161\pi$
$439$	7.56298	−	1.72620i	0.360961	−	0.0823871i	0.399155	+	0.916883i	$0.369303\pi$
$440$	−28.5460			−1.36088
$441$		0			0
$442$	24.3814			1.15970
$443$	−12.7104	+	2.90106i	−0.603889	+	0.137834i	−0.513524	−	0.858075i	$-0.671660\pi$
$443$	−12.7104	+	2.90106i	−0.603889	+	0.137834i	−0.0903645	+	0.995909i	$0.528803\pi$
$444$		0			0
$445$	44.9668	−	21.6549i	2.13163	−	1.02654i
$446$	2.85315	+	3.57773i	0.135100	+	0.169411i
$447$		0			0
$448$	4.76490	−	13.6630i	0.225120	−	0.645514i
$449$	23.3381	−	18.6115i	1.10139	−	0.878332i	0.108121	−	0.994138i	$-0.465516\pi$
$449$	23.3381	−	18.6115i	1.10139	−	0.878332i	0.993272	+	0.115806i	$0.0369450\pi$
$450$		0			0
$451$	−1.51160	−	1.20546i	−0.0711784	−	0.0567629i
$452$	4.53632	−	1.03539i	0.213371	−	0.0487005i
$453$		0			0
$454$	−15.1869	+	3.46630i	−0.712755	+	0.162682i
$455$	46.9355	+	46.8378i	2.20037	+	2.19579i
$456$		0			0
$457$	−1.26926	+	1.59161i	−0.0593737	+	0.0744523i	−0.810632	−	0.585557i	$-0.800876\pi$
$457$	−1.26926	+	1.59161i	−0.0593737	+	0.0744523i	0.751258	+	0.660009i	$0.229447\pi$
$458$	−8.51571	−	4.10095i	−0.397913	−	0.191625i
$459$		0			0
$460$		−	6.13165i		−	0.285890i
$461$	12.4446	+	5.99301i	0.579603	+	0.279122i	0.700627	−	0.713527i	$-0.252904\pi$
$461$	12.4446	+	5.99301i	0.579603	+	0.279122i	−0.121024	+	0.992650i	$0.538618\pi$
$462$		0			0
$463$	−13.2412	+	6.37663i	−0.615371	+	0.296347i	−0.715484	−	0.698629i	$-0.753794\pi$
$463$	−13.2412	+	6.37663i	−0.615371	+	0.296347i	0.100113	+	0.994976i	$0.468079\pi$
$464$	0.340621	+	0.707306i	0.0158129	+	0.0328359i
$465$		0			0
$466$	2.44903	−	10.7299i	0.113449	−	0.497054i
$467$	−20.4064	+	9.82721i	−0.944296	+	0.454749i	−0.841683	−	0.539972i	$-0.818435\pi$
$467$	−20.4064	+	9.82721i	−0.944296	+	0.454749i	−0.102613	+	0.994721i	$0.532720\pi$
$468$		0			0
$469$	−16.4870	−	1.84024i	−0.761299	−	0.0849745i
$470$	6.50219	−	13.5019i	0.299924	−	0.622798i
$471$		0			0
$472$			40.2129i			1.85095i
$473$	−2.00010	+	4.15325i	−0.0919647	+	0.190967i
$474$		0			0
$475$	75.3308	+	17.1938i	3.45641	+	0.788904i
$476$	14.5270	+	1.62147i	0.665842	+	0.0743197i
$477$		0			0
$478$	−0.385662	−	0.185725i	−0.0176398	−	0.00849487i
$479$	−5.90077	−	25.8529i	−0.269613	−	1.18125i	−0.910465	−	0.413587i	$-0.864276\pi$
$479$	−5.90077	−	25.8529i	−0.269613	−	1.18125i	0.640852	−	0.767665i	$-0.278581\pi$
$480$		0			0
$481$	−6.98954	−	1.59532i	−0.318696	−	0.0727402i
$482$	−4.45782	−	5.58993i	−0.203048	−	0.254614i
$483$		0			0
$484$	4.24718	−	5.32579i	0.193054	−	0.242082i
$485$	−49.5223	+	39.4927i	−2.24869	+	1.79327i
$486$		0			0
$487$	10.7003	+	13.4177i	0.484875	+	0.608015i	0.962743	−	0.270417i	$-0.0871616\pi$
$487$	10.7003	+	13.4177i	0.484875	+	0.608015i	−0.477868	+	0.878432i	$0.658590\pi$
$488$	2.32851	+	10.2019i	0.105407	+	0.461817i
$489$		0			0
$490$	−17.1279	−	21.3861i	−0.773758	−	0.966125i
$491$		−	26.1049i		−	1.17810i	−0.808097	−	0.589049i	$-0.799502\pi$
$491$		−	26.1049i		−	1.17810i	0.808097	−	0.589049i	$-0.200498\pi$
$492$		0			0
$493$	−12.4359	+	9.91733i	−0.560086	+	0.446654i
$494$	12.7165	+	26.4061i	0.572143	+	1.18807i
$495$		0			0
$496$	0.106036	+	0.0845611i	0.00476117	+	0.00379691i
$497$	−3.78254	−	10.7738i	−0.169670	−	0.483273i
$498$		0			0
$499$	4.80784	−	21.0645i	0.215228	−	0.942977i	−0.745722	−	0.666257i	$-0.767895\pi$
$499$	4.80784	−	21.0645i	0.215228	−	0.942977i	0.960951	−	0.276720i	$-0.0892474\pi$
$500$	−28.0670	+	35.1949i	−1.25519	+	1.57396i
$501$		0			0
$502$	2.36741	−	4.91598i	0.105663	−	0.219411i
$503$	−2.00226	−	8.77249i	−0.0892766	−	0.391146i	0.910472	−	0.413571i	$-0.135719\pi$
$503$	−2.00226	−	8.77249i	−0.0892766	−	0.391146i	−0.999749	+	0.0224246i	$0.992861\pi$
$504$		0			0
$505$	3.35795	−	14.7121i	0.149427	−	0.654681i
$506$	1.93354	+	1.54195i	0.0859564	+	0.0685479i
$507$		0			0
$508$	−26.2698			−1.16553
$509$	33.4567			1.48294			0.741471	−	0.670985i	$-0.234128\pi$
$509$	33.4567			1.48294			0.741471	+	0.670985i	$0.234128\pi$
$510$		0			0
$511$	−19.9340	−	6.95189i	−0.881827	−	0.307534i
$512$	1.12886	+	2.34410i	0.0498890	+	0.103595i
$513$		0			0
$514$	−4.52611	−	1.03305i	−0.199638	−	0.0455661i
$515$	−10.6541	−	2.43173i	−0.469476	−	0.107155i
$516$		0			0
$517$	−3.80496	−	7.90109i	−0.167342	−	0.347490i
$518$	2.79724	+	0.975526i	0.122904	+	0.0428621i
$519$		0			0
$520$	−72.0839			−3.16109
$521$	17.1409			0.750958			0.375479	−	0.926831i	$-0.377478\pi$
$521$	17.1409			0.750958			0.375479	+	0.926831i	$0.377478\pi$
$522$		0			0
$523$	−15.5833	−	12.4272i	−0.681408	−	0.543405i	0.220471	−	0.975394i	$-0.429241\pi$
$523$	−15.5833	−	12.4272i	−0.681408	−	0.543405i	−0.901879	+	0.431989i	$0.857812\pi$
$524$	3.32956	−	14.5877i	0.145452	−	0.637268i
$525$		0			0
$526$	2.56873	+	11.2543i	0.112002	+	0.490713i
$527$	−1.19229	+	2.47582i	−0.0519370	+	0.107848i
$528$		0			0
$529$	13.4496	−	16.8652i	0.584764	−	0.733271i
$530$	2.55843	−	11.2092i	0.111131	−	0.486898i
$531$		0			0
$532$	5.82066	+	16.5791i	0.252358	+	0.718793i
$533$	−3.81706	−	3.04401i	−0.165335	−	0.131851i
$534$		0			0
$535$	17.6632	+	36.6781i	0.763649	+	1.58573i
$536$	14.1000	−	11.2443i	0.609025	−	0.485681i
$537$		0			0
$538$		−	0.885438i		−	0.0381739i
$539$	−16.0336	+	0.0334173i	−0.690616	+	0.00143939i
$540$		0			0
$541$	7.59738	+	33.2863i	0.326637	+	1.43109i	0.825496	+	0.564407i	$0.190895\pi$
$541$	7.59738	+	33.2863i	0.326637	+	1.43109i	−0.498859	+	0.866683i	$0.666248\pi$
$542$	5.77068	+	7.23621i	0.247872	+	0.310822i
$543$		0			0
$544$	−20.2276	+	16.1310i	−0.867251	+	0.691609i
$545$	−30.8717	+	38.7119i	−1.32240	+	1.65823i
$546$		0			0
$547$	6.88277	+	8.63072i	0.294286	+	0.369023i	0.906890	−	0.421367i	$-0.138450\pi$
$547$	6.88277	+	8.63072i	0.294286	+	0.369023i	−0.612604	+	0.790390i	$0.709878\pi$
$548$	21.1942	+	4.83745i	0.905373	+	0.206646i
$549$		0			0
$550$	−6.34231	−	27.7875i	−0.270437	−	1.18486i
$551$	−17.2271	−	8.29613i	−0.733899	−	0.353427i
$552$		0			0
$553$	−1.71910	−	0.191883i	−0.0731038	−	0.00815968i
$554$	23.0706	+	5.26572i	0.980177	+	0.223719i
$555$		0			0
$556$	−9.72445	+	20.1930i	−0.412408	+	0.856375i
$557$		−	38.9619i		−	1.65087i	−0.564499	−	0.825434i	$-0.690931\pi$
$557$		−	38.9619i		−	1.65087i	0.564499	−	0.825434i	$-0.309069\pi$
$558$		0			0
$559$	−5.05061	+	10.4877i	−0.213618	+	0.443583i
$560$	2.62396	+	0.292880i	0.110883	+	0.0123765i
$561$		0			0
$562$	16.3576	−	7.87740i	0.690003	−	0.332288i
$563$	−4.15659	+	18.2112i	−0.175179	+	0.767511i	0.808634	+	0.588313i	$0.200208\pi$
$563$	−4.15659	+	18.2112i	−0.175179	+	0.767511i	−0.983813	+	0.179198i	$0.942650\pi$
$564$		0			0
$565$	7.38848	+	15.3423i	0.310836	+	0.645457i
$566$	−13.0052	+	6.26296i	−0.546648	+	0.263252i
$567$		0			0
$568$	11.1839	+	5.38590i	0.469268	+	0.225987i
$569$			10.8214i			0.453657i	0.973935	+	0.226828i	$0.0728356\pi$
$569$			10.8214i			0.453657i	−0.973935	+	0.226828i	$0.927164\pi$
$570$		0			0
$571$	−31.8497	−	15.3380i	−1.33287	−	0.641876i	−0.374452	−	0.927246i	$-0.622169\pi$
$571$	−31.8497	−	15.3380i	−1.33287	−	0.641876i	−0.958417	+	0.285370i	$0.907884\pi$
$572$	−9.77976	+	12.2634i	−0.408912	+	0.512760i
$573$		0			0
$574$	1.42801	+	1.42503i	0.0596039	+	0.0594798i
$575$	16.0513	−	3.66361i	0.669386	−	0.152783i
$576$		0			0
$577$	31.3847	−	7.16336i	1.30656	−	0.298214i	0.488107	−	0.872784i	$-0.337688\pi$
$577$	31.3847	−	7.16336i	1.30656	−	0.298214i	0.818456	+	0.574569i	$0.194830\pi$
$578$	3.37221	+	2.68925i	0.140266	+	0.111858i
$579$		0			0
$580$	13.6719	−	10.9030i	0.567694	−	0.452721i
$581$	−6.18409	+	17.7324i	−0.256559	+	0.735663i
$582$		0			0
$583$	−4.19492	−	5.26026i	−0.173736	−	0.217858i
$584$	20.6777	−	9.95784i	0.855648	−	0.412058i
$585$		0			0
$586$	−21.0049	+	4.79423i	−0.867704	+	0.198048i
$587$	−16.4455			−0.678778			−0.339389	−	0.940646i	$-0.610220\pi$
$587$	−16.4455			−0.678778			−0.339389	+	0.940646i	$0.610220\pi$
$588$		0			0
$589$	−3.30328			−0.136109
$590$	−53.3530	+	12.1775i	−2.19651	+	0.501338i
$591$		0			0
$592$	−0.257198	+	0.123860i	−0.0105708	+	0.00509061i
$593$	10.9015	+	13.6701i	0.447672	+	0.561363i	0.953547	−	0.301244i	$-0.0974019\pi$
$593$	10.9015	+	13.6701i	0.447672	+	0.561363i	−0.505875	+	0.862607i	$0.668830\pi$
$594$		0			0
$595$	6.04494	+	53.1524i	0.247818	+	2.17904i
$596$	12.6208	−	10.0648i	0.516968	−	0.412269i
$597$		0			0
$598$	4.88254	+	3.89370i	0.199662	+	0.159225i
$599$	25.4090	−	5.79943i	1.03818	−	0.236958i	0.330735	−	0.943724i	$-0.392704\pi$
$599$	25.4090	−	5.79943i	1.03818	−	0.236958i	0.707448	+	0.706765i	$0.249846\pi$
$600$		0			0
$601$	−0.620588	+	0.141645i	−0.0253143	+	0.00577782i	−0.235159	−	0.971957i	$-0.575561\pi$
$601$	−0.620588	+	0.141645i	−0.0253143	+	0.00577782i	0.209845	+	0.977735i	$0.432704\pi$
$602$	2.55485	−	4.07544i	0.104128	−	0.166102i
$603$		0			0
$604$	12.0746	−	15.1411i	0.491309	−	0.616082i
$605$	22.4611	+	10.8167i	0.913174	+	0.439762i
$606$		0			0
$607$		−	36.7437i		−	1.49138i	−0.666293	−	0.745690i	$-0.732120\pi$
$607$		−	36.7437i		−	1.49138i	0.666293	−	0.745690i	$-0.267880\pi$
$608$	−28.0206	−	13.4940i	−1.13639	−	0.547255i
$609$		0			0
$610$	−12.8303	+	6.17875i	−0.519484	+	0.250170i
$611$	−9.60823	−	19.9517i	−0.388707	−	0.807159i
$612$		0			0
$613$	4.26392	−	18.6815i	0.172218	−	0.754538i	−0.812864	−	0.582454i	$-0.802093\pi$
$613$	4.26392	−	18.6815i	0.172218	−	0.754538i	0.985082	−	0.172084i	$-0.0550501\pi$
$614$	−19.4006	+	9.34284i	−0.782945	+	0.377046i
$615$		0			0
$616$	12.3123	−	12.3380i	0.496076	−	0.497111i
$617$	18.7842	−	39.0058i	0.756223	−	1.57031i	−0.0637875	−	0.997964i	$-0.520318\pi$
$617$	18.7842	−	39.0058i	0.756223	−	1.57031i	0.820010	−	0.572349i	$-0.193968\pi$
$618$		0			0
$619$		−	3.16461i		−	0.127196i	−0.997976	−	0.0635982i	$-0.979742\pi$
$619$		−	3.16461i		−	0.127196i	0.997976	−	0.0635982i	$-0.0202576\pi$
$620$	1.31079	−	2.72188i	0.0526425	−	0.109313i
$621$		0			0
$622$	14.1605	+	3.23204i	0.567784	+	0.129593i
$623$	−10.0352	+	28.7752i	−0.402054	+	1.15286i
$624$		0			0
$625$	−86.3781	−	41.5975i	−3.45512	−	1.66390i
$626$	1.59598	+	6.99242i	0.0637880	+	0.279473i
$627$		0			0
$628$	3.24971	+	0.741726i	0.129678	+	0.0295981i
$629$	−3.60624	−	4.52208i	−0.143790	−	0.180307i
$630$		0			0
$631$	21.2880	−	26.6943i	0.847462	−	1.06268i	−0.149799	−	0.988717i	$-0.547863\pi$
$631$	21.2880	−	26.6943i	0.847462	−	1.06268i	0.997261	−	0.0739671i	$-0.0235660\pi$
$632$	1.47021	−	1.17245i	0.0584816	−	0.0466375i
$633$		0			0
$634$	9.95571	+	12.4841i	0.395392	+	0.495806i
$635$	−21.3933	−	93.7301i	−0.848967	−	3.71957i
$636$		0			0
$637$	−40.4878	+	0.0843848i	−1.60418	+	0.00334345i
$638$			7.05307i			0.279234i
$639$		0			0
$640$	20.8283	−	16.6100i	0.823312	−	0.656569i
$641$	6.40154	+	13.2929i	0.252845	+	0.525039i	0.988298	−	0.152538i	$-0.0487445\pi$
$641$	6.40154	+	13.2929i	0.252845	+	0.525039i	−0.735452	+	0.677577i	$0.763030\pi$
$642$		0			0
$643$	−17.3801	−	13.8602i	−0.685405	−	0.546592i	0.217698	−	0.976016i	$-0.430145\pi$
$643$	−17.3801	−	13.8602i	−0.685405	−	0.546592i	−0.903103	+	0.429424i	$0.858717\pi$
$644$	2.65018	+	2.64466i	0.104432	+	0.104214i
$645$		0			0
$646$	−5.26157	+	23.0524i	−0.207014	+	0.906986i
$647$	8.91706	−	11.1816i	0.350566	−	0.439596i	−0.575017	−	0.818142i	$-0.695004\pi$
$647$	8.91706	−	11.1816i	0.350566	−	0.439596i	0.925582	+	0.378546i	$0.123576\pi$
$648$		0			0
$649$	−13.8947	+	28.8527i	−0.545416	+	1.13257i
$650$	−16.0155	−	70.1684i	−0.628179	−	2.75223i
$651$		0			0
$652$	−5.54980	+	24.3153i	−0.217347	+	0.952259i
$653$	−22.6942	−	18.0981i	−0.888094	−	0.708232i	0.0691209	−	0.997608i	$-0.477981\pi$
$653$	−22.6942	−	18.0981i	−0.888094	−	0.708232i	−0.957215	+	0.289377i	$0.906552\pi$
$654$		0			0
$655$	54.7603			2.13966
$656$	−0.194401			−0.00759007
$657$		0			0
$658$	3.03123	+	8.63390i	0.118170	+	0.336584i
$659$	−18.2270	−	37.8488i	−0.710024	−	1.47438i	−0.872985	−	0.487747i	$-0.837819\pi$
$659$	−18.2270	−	37.8488i	−0.710024	−	1.47438i	0.162961	−	0.986632i	$-0.447895\pi$
$660$		0			0
$661$	−11.3129	−	2.58211i	−0.440023	−	0.100432i	−0.00323055	−	0.999995i	$-0.501028\pi$
$661$	−11.3129	−	2.58211i	−0.440023	−	0.100432i	−0.436792	+	0.899562i	$0.643885\pi$
$662$	−10.1553	−	2.31789i	−0.394698	−	0.0900872i
$663$		0			0
$664$	−8.85804	−	18.3939i	−0.343759	−	0.713822i
$665$	−54.4136	+	34.2695i	−2.11007	+	1.32891i
$666$		0			0
$667$	−4.07418			−0.157753
$668$	13.9113			0.538245
$669$		0			0
$670$	19.1884	+	15.3022i	0.741311	+	0.591176i
$671$	−1.85434	+	8.12439i	−0.0715860	+	0.313639i
$672$		0			0
$673$	3.40478	+	14.9173i	0.131245	+	0.575020i	0.997192	+	0.0748854i	$0.0238591\pi$
$673$	3.40478	+	14.9173i	0.131245	+	0.575020i	−0.865948	+	0.500135i	$0.833284\pi$
$674$	10.2716	−	21.3292i	0.395648	−	0.821572i
$675$		0			0
$676$	−15.0992	+	18.9338i	−0.580740	+	0.728224i
$677$	−3.63335	+	15.9187i	−0.139641	+	0.611807i	0.855873	+	0.517187i	$0.173021\pi$
$677$	−3.63335	+	15.9187i	−0.139641	+	0.611807i	−0.995513	+	0.0946200i	$0.969836\pi$
$678$		0			0
$679$	4.29035	−	38.4379i	0.164649	−	1.47511i
$680$	−45.4675	−	36.2591i	−1.74360	−	1.39047i
$681$		0			0
$682$	0.528683	+	1.09782i	0.0202443	+	0.0420378i
$683$	3.40737	−	2.71729i	0.130379	−	0.103974i	−0.556129	−	0.831096i	$-0.687714\pi$
$683$	3.40737	−	2.71729i	0.130379	−	0.103974i	0.686508	+	0.727122i	$0.259143\pi$
$684$		0			0
$685$			79.5602i			3.03984i
$686$	16.6308	+	1.82121i	0.634968	+	0.0695341i
$687$		0			0
$688$	0.103139	+	0.451882i	0.00393214	+	0.0172278i
$689$	−10.5929	−	13.2831i	−0.403558	−	0.506046i
$690$		0			0
$691$	0.537751	−	0.428842i	0.0204570	−	0.0163139i	−0.613208	−	0.789922i	$-0.710121\pi$
$691$	0.537751	−	0.428842i	0.0204570	−	0.0163139i	0.633665	+	0.773608i	$0.281550\pi$
$692$	−12.3304	+	15.4618i	−0.468732	+	0.587771i
$693$		0			0
$694$	13.6535	+	17.1209i	0.518279	+	0.649902i
$695$	−79.9677	−	18.2521i	−3.03335	−	0.692342i
$696$		0			0
$697$	−0.876468	−	3.84006i	−0.0331986	−	0.145453i
$698$	−1.30922	−	0.630490i	−0.0495549	−	0.0238644i
$699$		0			0
$700$	−4.87587	−	42.8730i	−0.184291	−	1.62045i
$701$	−3.24163	−	0.739880i	−0.122435	−	0.0279449i	0.160865	−	0.986976i	$-0.448572\pi$
$701$	−3.24163	−	0.739880i	−0.122435	−	0.0279449i	−0.283299	+	0.959032i	$0.591429\pi$
$702$		0			0
$703$	3.01672	−	6.26429i	0.113778	−	0.236262i
$704$			12.5272i			0.472136i
$705$		0			0
$706$	1.39942	−	2.90593i	0.0526679	−	0.109366i
$707$	4.91044	+	7.79688i	0.184676	+	0.293232i
$708$		0			0
$709$	−14.0022	+	6.74311i	−0.525864	+	0.253243i	−0.677929	−	0.735128i	$-0.737122\pi$
$709$	−14.0022	+	6.74311i	−0.525864	+	0.253243i	0.152064	+	0.988371i	$0.451408\pi$
$710$	−3.75904	+	16.4694i	−0.141074	+	0.618086i
$711$		0			0
$712$	−14.3744	−	29.8488i	−0.538704	−	1.11863i
$713$	−0.634152	+	0.305392i	−0.0237492	+	0.0114370i
$714$		0			0
$715$	−51.7201	−	24.9071i	−1.93422	−	0.931472i
$716$		−	5.78330i		−	0.216132i
$717$		0			0
$718$	1.47548	+	0.710554i	0.0550644	+	0.0265176i
$719$	3.97981	−	4.99052i	0.148422	−	0.186115i	−0.702063	−	0.712115i	$-0.747737\pi$
$719$	3.97981	−	4.99052i	0.148422	−	0.186115i	0.850485	+	0.526000i	$0.176309\pi$
$720$		0			0
$721$	5.64628	−	3.55600i	0.210278	−	0.132433i
$722$	−10.9778	+	2.50561i	−0.408552	+	0.0932493i
$723$		0			0
$724$	17.2876	−	3.94577i	0.642487	−	0.146643i
$725$	36.7104	+	29.2756i	1.36339	+	1.08727i
$726$		0			0
$727$	−5.40462	+	4.31004i	−0.200446	+	0.159851i	−0.718569	−	0.695456i	$-0.755202\pi$
$727$	−5.40462	+	4.31004i	−0.200446	+	0.159851i	0.518123	+	0.855306i	$0.326631\pi$
$728$	31.0907	−	31.1556i	1.15230	−	1.15470i
$729$		0			0
$730$	19.4734	+	24.4188i	0.720742	+	0.903782i
$731$	−8.46116	+	4.07468i	−0.312947	+	0.150707i
$732$		0			0
$733$	−29.5914	+	6.75405i	−1.09298	+	0.249466i	−0.730767	−	0.682627i	$-0.760837\pi$
$733$	−29.5914	+	6.75405i	−1.09298	+	0.249466i	−0.362217	+	0.932094i	$0.617980\pi$
$734$	13.8632			0.511700
$735$		0			0
$736$	−6.62683			−0.244268
$737$	14.0019	−	3.19585i	0.515768	−	0.117721i
$738$		0			0
$739$	−24.3072	+	11.7057i	−0.894156	+	0.430603i	−0.823775	−	0.566917i	$-0.808136\pi$
$739$	−24.3072	+	11.7057i	−0.894156	+	0.430603i	−0.0703813	+	0.997520i	$0.522422\pi$
$740$	3.96465	+	4.97151i	0.145743	+	0.182756i
$741$		0			0
$742$	3.74129	+	5.94048i	0.137347	+	0.218082i
$743$	12.2610	−	9.77781i	0.449812	−	0.358713i	−0.372229	−	0.928141i	$-0.621407\pi$
$743$	12.2610	−	9.77781i	0.449812	−	0.358713i	0.822041	+	0.569428i	$0.192835\pi$
$744$		0			0
$745$	46.1889	+	36.8344i	1.69223	+	1.34951i
$746$	16.8442	−	3.84459i	0.616712	−	0.140760i
$747$		0			0
$748$	−12.3373	+	2.81591i	−0.451097	+	0.102960i
$749$	−23.4711	−	8.18546i	−0.857617	−	0.299090i
$750$		0			0
$751$	−8.69392	+	10.9018i	−0.317246	+	0.397814i	−0.914729	−	0.404068i	$-0.867596\pi$
$751$	−8.69392	+	10.9018i	−0.317246	+	0.397814i	0.597483	+	0.801881i	$0.296167\pi$
$752$	−0.794440	−	0.382582i	−0.0289703	−	0.0139513i
$753$		0			0
$754$			17.8103i			0.648613i
$755$	63.8564	+	30.7516i	2.32397	+	1.11917i
$756$		0			0
$757$	−40.0279	+	19.2764i	−1.45484	+	0.700614i	−0.983428	−	0.181299i	$-0.941970\pi$
$757$	−40.0279	+	19.2764i	−1.45484	+	0.700614i	−0.471412	+	0.881913i	$0.656256\pi$
$758$	−11.6776	−	24.2487i	−0.424149	−	0.880754i
$759$		0			0
$760$	15.5559	−	68.1549i	0.564272	−	2.47224i
$761$	34.1086	−	16.4258i	1.23643	−	0.595435i	0.302592	−	0.953120i	$-0.402148\pi$
$761$	34.1086	−	16.4258i	1.23643	−	0.595435i	0.933842	+	0.357685i	$0.116434\pi$
$762$		0			0
$763$	−3.41641	−	30.0401i	−0.123682	−	1.08752i
$764$	1.74371	−	3.62084i	0.0630851	−	0.130997i
$765$		0			0
$766$			3.91833i			0.141575i
$767$	−35.0867	+	72.8584i	−1.26691	+	2.63076i
$768$		0			0
$769$	10.2500	+	2.33950i	0.369625	+	0.0843645i	0.403299	−	0.915068i	$-0.367864\pi$
$769$	10.2500	+	2.33950i	0.369625	+	0.0843645i	−0.0336737	+	0.999433i	$0.510721\pi$
$770$	20.0980	+	12.5992i	0.724281	+	0.454044i
$771$		0			0
$772$	−2.36542	−	1.13913i	−0.0851333	−	0.0409981i
$773$	9.39000	+	41.1403i	0.337735	+	1.47971i	0.803766	+	0.594945i	$0.202826\pi$
$773$	9.39000	+	41.1403i	0.337735	+	1.47971i	−0.466031	+	0.884768i	$0.654317\pi$
$774$		0			0
$775$	7.90847	+	1.80506i	0.284081	+	0.0648396i
$776$	26.2151	+	32.8727i	0.941068	+	1.18006i
$777$		0			0
$778$	8.28990	−	10.3952i	0.297207	−	0.372686i
$779$	3.70182	−	2.95210i	0.132632	−	0.105770i
$780$		0			0
$781$	6.16348	+	7.72875i	0.220547	+	0.276557i
$782$	1.12112	+	4.91196i	0.0400913	+	0.175651i
$783$		0			0
$784$	−1.25834	+	1.00779i	−0.0449405	+	0.0359924i
$785$			12.1990i			0.435400i
$786$		0			0
$787$	0.711713	−	0.567572i	0.0253698	−	0.0202318i	−0.610723	−	0.791844i	$-0.709121\pi$
$787$	0.711713	−	0.567572i	0.0253698	−	0.0202318i	0.636093	+	0.771613i	$0.280550\pi$
$788$	−5.19115	−	10.7795i	−0.184927	−	0.384005i
$789$		0			0
$790$	2.00078	+	1.59557i	0.0711844	+	0.0567677i
$791$	−9.81791	−	3.42396i	−0.349085	−	0.121742i
$792$		0			0
$793$	−4.68254	+	20.5156i	−0.166282	+	0.728529i
$794$	−14.5197	+	18.2071i	−0.515285	+	0.646146i
$795$		0			0
$796$	11.7705	−	24.4417i	0.417195	−	0.866314i
$797$	−5.79511	−	25.3901i	−0.205273	−	0.899362i	−0.967664	−	0.252244i	$-0.918831\pi$
$797$	−5.79511	−	25.3901i	−0.205273	−	0.899362i	0.762390	−	0.647118i	$-0.224026\pi$
$798$		0			0
$799$	3.97548	−	17.4177i	0.140643	−	0.616195i
$800$	59.7111	+	47.6180i	2.11111	+	1.68355i
$801$		0			0
$802$	0.393377			0.0138906
$803$	18.2769			0.644978
$804$		0			0
$805$	−7.27788	+	11.6095i	−0.256512	+	0.409182i
$806$	1.33502	+	2.77220i	0.0470241	+	0.0976466i
$807$		0			0
$808$	−9.76585	−	2.22899i	−0.343561	−	0.0784156i
$809$	25.1809	+	5.74737i	0.885313	+	0.202067i	0.640918	−	0.767609i	$-0.278554\pi$
$809$	25.1809	+	5.74737i	0.885313	+	0.202067i	0.244394	+	0.969676i	$0.421411\pi$
$810$		0			0
$811$	3.47238	+	7.21046i	0.121932	+	0.253194i	0.952996	−	0.302982i	$-0.0979823\pi$
$811$	3.47238	+	7.21046i	0.121932	+	0.253194i	−0.831065	+	0.556176i	$0.812268\pi$
$812$	−1.18446	+	10.6118i	−0.0415664	+	0.372400i
$813$		0			0
$814$	−2.56471			−0.0898931
$815$	−91.2760			−3.19726
$816$		0			0
$817$	−8.82613	−	7.03860i	−0.308787	−	0.246250i
$818$	0.336482	−	1.47423i	0.0117648	−	0.0515451i
$819$		0			0
$820$	0.963577	+	4.22171i	0.0336496	+	0.147428i
$821$	2.82253	−	5.86104i	0.0985069	−	0.204552i	−0.845892	−	0.533355i	$-0.820931\pi$
$821$	2.82253	−	5.86104i	0.0985069	−	0.204552i	0.944398	+	0.328803i	$0.106645\pi$
$822$		0			0
$823$	−24.7618	+	31.0503i	−0.863140	+	1.08234i	0.132693	+	0.991157i	$0.457637\pi$
$823$	−24.7618	+	31.0503i	−0.863140	+	1.08234i	−0.995834	+	0.0911868i	$0.970934\pi$
$824$	−1.61417	+	7.07215i	−0.0562323	+	0.246370i
$825$		0			0
$826$	17.7486	−	28.3121i	0.617552	−	0.985106i
$827$	34.5160	+	27.5256i	1.20024	+	0.957158i	0.999746	−	0.0225377i	$-0.00717458\pi$
$827$	34.5160	+	27.5256i	1.20024	+	0.957158i	0.200492	+	0.979695i	$0.435746\pi$
$828$		0			0
$829$	−11.7069	−	24.3097i	−0.406599	−	0.844312i	−0.999245	−	0.0388486i	$-0.987631\pi$
$829$	−11.7069	−	24.3097i	−0.406599	−	0.844312i	0.592646	−	0.805463i	$-0.298083\pi$
$830$	21.7219	−	17.3226i	0.753978	−	0.601278i
$831$		0			0
$832$			31.6334i			1.09669i
$833$	−25.5804	−	20.3126i	−0.886309	−	0.703791i
$834$		0			0
$835$	11.3289	+	49.6353i	0.392054	+	1.71770i
$836$	−9.48450	−	11.8932i	−0.328028	−	0.411335i
$837$		0			0
$838$	22.8256	−	18.2028i	0.788498	−	0.628806i
$839$	−16.6578	+	20.8883i	−0.575093	+	0.721144i	−0.981267	−	0.192652i	$-0.938291\pi$
$839$	−16.6578	+	20.8883i	−0.575093	+	0.721144i	0.406174	+	0.913796i	$0.366863\pi$
$840$		0			0
$841$	10.8367	+	13.5888i	0.373680	+	0.468580i
$842$	6.19859	+	1.41479i	0.213617	+	0.0487568i
$843$		0			0
$844$	4.91504	+	21.5342i	0.169183	+	0.741238i
$845$	−79.8520	−	38.4547i	−2.74699	−	1.32288i
$846$		0			0
$847$	−14.3629	+	5.04260i	−0.493515	+	0.173266i
$848$	−0.659540	−	0.150536i	−0.0226487	−	0.00516941i
$849$		0			0
$850$	25.1937	−	52.3152i	0.864136	−	1.79440i
$851$		−	1.48149i		−	0.0507850i
$852$		0			0
$853$	−11.5683	+	24.0219i	−0.396092	+	0.822494i	0.603590	+	0.797295i	$0.293736\pi$
$853$	−11.5683	+	24.0219i	−0.396092	+	0.822494i	−0.999682	+	0.0251995i	$0.991978\pi$
$854$	2.86335	−	8.21041i	0.0979817	−	0.280954i
$855$		0			0
$856$	24.3468	−	11.7248i	0.832156	−	0.400745i
$857$	6.43802	−	28.2068i	0.219919	−	0.963527i	−0.737619	−	0.675217i	$-0.764050\pi$
$857$	6.43802	−	28.2068i	0.219919	−	0.963527i	0.957537	−	0.288309i	$-0.0930931\pi$
$858$		0			0
$859$	−9.42345	−	19.5680i	−0.321524	−	0.667651i	0.676081	−	0.736828i	$-0.263677\pi$
$859$	−9.42345	−	19.5680i	−0.321524	−	0.667651i	−0.997604	+	0.0691766i	$0.977963\pi$
$860$	9.30208	−	4.47965i	0.317198	−	0.152755i
$861$		0			0
$862$	−16.2840	−	7.84194i	−0.554634	−	0.267098i
$863$		−	27.5878i		−	0.939101i	−0.882906	−	0.469551i	$-0.844416\pi$
$863$		−	27.5878i		−	0.939101i	0.882906	−	0.469551i	$-0.155584\pi$
$864$		0			0
$865$	−65.2091	−	31.4031i	−2.21718	−	1.06774i
$866$	−1.67499	+	2.10037i	−0.0569183	+	0.0713733i
$867$		0			0
$868$	0.611072	+	1.74052i	0.0207411	+	0.0590772i
$869$	1.45999	−	0.333232i	0.0495266	−	0.0113041i
$870$		0			0
$871$	35.3574	−	8.07011i	1.19804	−	0.273445i
$872$	25.6968	+	20.4925i	0.870203	+	0.693964i
$873$		0			0
$874$	−4.73513	+	3.77614i	−0.160168	+	0.127730i
$875$	94.9155	−	33.3234i	3.20873	−	1.12654i
$876$		0			0
$877$	19.4777	+	24.4242i	0.657714	+	0.824747i	0.993092	−	0.117336i	$-0.0374356\pi$
$877$	19.4777	+	24.4242i	0.657714	+	0.824747i	−0.335378	+	0.942084i	$0.608864\pi$
$878$	6.31372	−	3.04053i	0.213078	−	0.102613i
$879$		0			0
$880$	−2.22845	+	0.508630i	−0.0751211	+	0.0171459i
$881$	−47.1716			−1.58925			−0.794625	−	0.607101i	$-0.792333\pi$
$881$	−47.1716			−1.58925			−0.794625	+	0.607101i	$0.792333\pi$
$882$		0			0
$883$	42.3029			1.42361			0.711803	−	0.702379i	$-0.247879\pi$
$883$	42.3029			1.42361			0.711803	+	0.702379i	$0.247879\pi$
$884$	−31.1540	+	7.11069i	−1.04782	+	0.239158i
$885$		0			0
$886$	−10.6109	+	5.10993i	−0.356479	+	0.171671i
$887$	−12.8105	−	16.0638i	−0.430133	−	0.539370i	0.518780	−	0.854908i	$-0.326386\pi$
$887$	−12.8105	−	16.0638i	−0.430133	−	0.539370i	−0.948913	+	0.315538i	$0.897815\pi$
$888$		0			0
$889$	49.7386	+	31.1806i	1.66818	+	1.04576i
$890$	35.2493	−	28.1104i	1.18156	−	0.942261i
$891$		0			0
$892$	−4.68911	−	3.73944i	−0.157003	−	0.125206i
$893$	20.9377	−	4.77889i	0.700653	−	0.159919i
$894$		0			0
$895$	20.6347	−	4.70974i	0.689743	−	0.157429i
$896$	−1.80446	+	16.1664i	−0.0602827	+	0.540082i
$897$		0			0
$898$	16.8127	−	21.0824i	0.561046	−	0.703530i
$899$	−1.80856	−	0.870954i	−0.0603187	−	0.0290480i
$900$		0			0
$901$		−	13.7068i		−	0.456640i
$902$	−1.57358	−	0.757795i	−0.0523944	−	0.0252318i
$903$		0			0
$904$	10.1842	−	4.90445i	0.338721	−	0.163119i
$905$	28.1569	+	58.4684i	0.935967	+	1.94356i
$906$		0			0
$907$	−6.39116	+	28.0015i	−0.212215	+	0.929775i	0.750843	+	0.660481i	$0.229648\pi$
$907$	−6.39116	+	28.0015i	−0.212215	+	0.929775i	−0.963058	+	0.269294i	$0.913210\pi$
$908$	18.3945	−	8.85834i	0.610444	−	0.293974i
$909$		0			0
$910$	50.7511	+	31.8153i	1.68238	+	1.05467i
$911$	−20.5909	+	42.7574i	−0.682207	+	1.41662i	0.215712	+	0.976457i	$0.430793\pi$
$911$	−20.5909	+	42.7574i	−0.682207	+	1.41662i	−0.897919	+	0.440160i	$0.854922\pi$
$912$		0			0
$913$		−	16.2583i		−	0.538072i
$914$	−0.797905	+	1.65687i	−0.0263924	+	0.0548043i
$915$		0			0
$916$	12.0772	+	2.75654i	0.399042	+	0.0910788i
$917$	−23.6188	+	23.6681i	−0.779963	+	0.781590i
$918$		0			0
$919$	25.6226	+	12.3392i	0.845212	+	0.407032i	0.805798	−	0.592190i	$-0.201737\pi$
$919$	25.6226	+	12.3392i	0.845212	+	0.407032i	0.0394137	+	0.999223i	$0.487451\pi$
$920$	−3.31462	−	14.5223i	−0.109280	−	0.478785i
$921$		0			0
$922$	12.1646	+	2.77650i	0.400621	+	0.0914391i
$923$	15.5639	+	19.5165i	0.512292	+	0.642394i
$924$		0			0
$925$	−10.6455	+	13.3490i	−0.350022	+	0.438913i
$926$	−10.3797	+	8.27755i	−0.341099	+	0.272017i
$927$		0			0
$928$	−11.7835	−	14.7760i	−0.386811	−	0.485046i
$929$	−4.74560	−	20.7918i	−0.155698	−	0.682158i	−0.991167	−	0.132620i	$-0.957661\pi$
$929$	−4.74560	−	20.7918i	−0.155698	−	0.682158i	0.835469	−	0.549538i	$-0.185196\pi$
$930$		0			0
$931$	8.65759	−	38.2992i	0.283741	−	1.25520i
$932$			14.4247i			0.472497i
$933$		0			0
$934$	−15.9965	+	12.7568i	−0.523422	+	0.417415i
$935$	−20.0943	−	41.7262i	−0.657153	−	1.36459i
$936$		0			0
$937$	−25.0903	−	20.0088i	−0.819663	−	0.653659i	0.121132	−	0.992636i	$-0.461348\pi$
$937$	−25.0903	−	20.0088i	−0.819663	−	0.653659i	−0.940795	+	0.338977i	$0.889919\pi$
$938$	−14.8900	+	1.69342i	−0.486176	+	0.0552920i
$939$		0			0
$940$	−4.37059	+	19.1488i	−0.142553	+	0.624565i
$941$	3.74022	−	4.69009i	0.121928	−	0.152893i	−0.717121	−	0.696948i	$-0.754541\pi$
$941$	3.74022	−	4.69009i	0.121928	−	0.152893i	0.839049	+	0.544056i	$0.183112\pi$
$942$		0			0
$943$	0.437737	−	0.908971i	0.0142547	−	0.0296002i
$944$	0.716510	+	3.13923i	0.0233204	+	0.102173i
$945$		0			0
$946$	−0.926625	+	4.05981i	−0.0301272	+	0.131996i
$947$	33.1443	+	26.4317i	1.07704	+	0.858915i	0.990525	−	0.137335i	$-0.0438538\pi$
$947$	33.1443	+	26.4317i	1.07704	+	0.858915i	0.0865203	+	0.996250i	$0.472425\pi$
$948$		0			0
$949$	46.1525			1.49817
$950$	69.8000			2.26461
$951$		0			0
$952$	35.2824	−	4.01261i	1.14351	−	0.130049i
$953$	7.66592	+	15.9184i	0.248323	+	0.515649i	0.987453	−	0.157915i	$-0.0504771\pi$
$953$	7.66592	+	15.9184i	0.248323	+	0.515649i	−0.739129	+	0.673564i	$0.764763\pi$
$954$		0			0
$955$	14.3391	+	3.27281i	0.464003	+	0.105906i
$956$	0.546957	+	0.124839i	0.0176898	+	0.00403759i
$957$		0			0
$958$	−10.3936	−	21.5825i	−0.335802	−	0.697300i
$959$	−34.3869	−	34.3154i	−1.11041	−	1.10810i
$960$		0			0
$961$	30.6532			0.988813
$962$	−6.47636			−0.208806
$963$		0			0
$964$	7.32637	+	5.84259i	0.235967	+	0.188177i
$965$	2.13806	−	9.36745i	0.0688266	−	0.301549i
$966$		0			0
$967$	−11.9865	−	52.5164i	−0.385460	−	1.68881i	−0.680032	−	0.733183i	$-0.738034\pi$
$967$	−11.9865	−	52.5164i	−0.385460	−	1.68881i	0.294571	−	0.955630i	$-0.404823\pi$
$968$	7.18009	−	14.9096i	0.230777	−	0.479213i
$969$		0			0
$970$	−35.6757	+	44.7359i	−1.14548	+	1.43638i
$971$	−0.0674744	+	0.295625i	−0.00216536	+	0.00948704i	−0.975999	−	0.217775i	$-0.930120\pi$
$971$	−0.0674744	+	0.295625i	−0.00216536	+	0.00948704i	0.973834	+	0.227262i	$0.0729773\pi$
$972$		0			0
$973$	42.3799	−	26.6907i	1.35864	−	0.855664i
$974$	12.1209	+	9.66606i	0.388377	+	0.309721i
$975$		0			0
$976$	0.363552	+	0.754923i	0.0116370	+	0.0241645i
$977$	14.3702	−	11.4598i	0.459743	−	0.366633i	−0.366060	−	0.930591i	$-0.619294\pi$
$977$	14.3702	−	11.4598i	0.459743	−	0.366633i	0.825803	+	0.563958i	$0.190722\pi$
$978$		0			0
$979$		−	26.3832i		−	0.843211i
$980$	28.1227	+	22.3314i	0.898348	+	0.713351i
$981$		0			0
$982$	−5.24745	−	22.9906i	−0.167453	−	0.733659i
$983$	18.1203	+	22.7221i	0.577948	+	0.724724i	0.981761	−	0.190117i	$-0.0608869\pi$
$983$	18.1203	+	22.7221i	0.577948	+	0.724724i	−0.403813	+	0.914841i	$0.632315\pi$
$984$		0			0
$985$	34.2337	−	27.3004i	1.09078	−	0.869864i
$986$	−8.95880	+	11.2340i	−0.285306	+	0.357763i
$987$		0			0
$988$	−23.9501	−	30.0325i	−0.761954	−	0.955460i
$989$	−2.34513	−	0.535261i	−0.0745709	−	0.0170203i
$990$		0			0
$991$	1.03384	+	4.52955i	0.0328410	+	0.143886i	0.988690	−	0.149971i	$-0.0479181\pi$
$991$	1.03384	+	4.52955i	0.0328410	+	0.143886i	−0.955849	+	0.293857i	$0.905061\pi$
$992$	−2.94169	−	1.41665i	−0.0933989	−	0.0449785i
$993$		0			0
$994$	−5.49697	−	8.72818i	−0.174353	−	0.276841i
$995$	96.7933	+	22.0924i	3.06855	+	0.700377i
$996$		0			0
$997$	−6.67258	+	13.8558i	−0.211323	+	0.438816i	−0.979506	−	0.201413i	$-0.935447\pi$
$997$	−6.67258	+	13.8558i	−0.211323	+	0.438816i	0.768184	+	0.640230i	$0.221161\pi$
$998$		−	19.5179i		−	0.617829i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.w.a.62.14	yes	120
3.2	odd	2	inner	441.2.w.a.62.7	✓	120
49.34	odd	14	inner	441.2.w.a.377.7	yes	120
147.83	even	14	inner	441.2.w.a.377.14	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.w.a.62.7	✓	120	3.2	odd	2	inner
441.2.w.a.62.14	yes	120	1.1	even	1	trivial
441.2.w.a.377.7	yes	120	49.34	odd	14	inner
441.2.w.a.377.14	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.880699 - 0.201014i) q^{2} +(-1.06671 + 0.513702i) q^{4} +(-2.70158 - 3.38767i) q^{5} +(2.62942 + 0.293490i) q^{7} +(-2.24872 + 1.79330i) q^{8} +(-3.06025 - 2.44047i) q^{10} +(-2.23309 + 0.509689i) q^{11} +(-5.63896 + 1.28706i) q^{13} +(2.37473 - 0.270074i) q^{14} +(-0.143595 + 0.180062i) q^{16} +(-4.20422 - 2.02465i) q^{17} -5.60936i q^{19} +(4.62207 + 2.22587i) q^{20} +(-1.86423 + 0.897765i) q^{22} +(-0.518590 - 1.07686i) q^{23} +(-3.06519 + 13.4295i) q^{25} +(-4.70751 + 2.26702i) q^{26} +(-2.95561 + 1.03767i) q^{28} +(1.47898 - 3.07113i) q^{29} -0.588888i q^{31} +(2.40563 - 4.99534i) q^{32} +(-4.10964 - 0.937998i) q^{34} +(-6.10934 - 9.70051i) q^{35} +(1.11676 + 0.537802i) q^{37} +(-1.12756 - 4.94016i) q^{38} +(12.1502 + 2.77321i) q^{40} +(0.526282 + 0.659937i) q^{41} +(1.25480 - 1.57347i) q^{43} +(2.12024 - 1.69084i) q^{44} +(-0.673187 - 0.844149i) q^{46} +(0.851950 + 3.73264i) q^{47} +(6.82773 + 1.54342i) q^{49} +12.4435i q^{50} +(5.35399 - 4.26967i) q^{52} +(1.27448 + 2.64649i) q^{53} +(7.75953 + 6.18802i) q^{55} +(-6.43916 + 4.05536i) q^{56} +(0.685196 - 3.00204i) q^{58} +(8.71710 - 10.9309i) q^{59} +(1.57855 - 3.27789i) q^{61} +(-0.118375 - 0.518633i) q^{62} +(1.21700 - 5.33202i) q^{64} +(19.5942 + 15.6259i) q^{65} -6.27020 q^{67} +5.52477 q^{68} +(-7.33043 - 7.31517i) q^{70} +(-1.87256 - 3.88841i) q^{71} +(-7.77931 - 1.77558i) q^{73} +(1.09163 + 0.249158i) q^{74} +(2.88154 + 5.98358i) q^{76} +(-6.02133 + 0.684797i) q^{77} -0.653795 q^{79} +0.997922 q^{80} +(0.596153 + 0.475416i) q^{82} +(-1.57947 + 6.92012i) q^{83} +(4.49920 + 19.7123i) q^{85} +(0.788810 - 1.63798i) q^{86} +(4.10759 - 5.15075i) q^{88} +(-2.56309 + 11.2296i) q^{89} +(-15.2050 + 1.72924i) q^{91} +(1.10637 + 0.882304i) q^{92} +(1.50062 + 3.11607i) q^{94} +(-19.0027 + 15.1541i) q^{95} -14.6184i q^{97} +(6.32342 - 0.0131793i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70}+ \cdots - 112 q^{94}+O(q^{100}) \) 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

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