LMFDB - Embedded newform 483.2.r.a.181.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(34,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 9]))

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

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

chi := DirichletCharacter("483.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.r (of order $22$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$32$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			181.14
Character	$\chi$	$=$	483.181
Dual form			483.2.r.a.475.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.112500 - 0.782453i) q^{2} +(0.909632 + 0.415415i) q^{3} +(1.31941 - 0.387413i) q^{4} +(1.72931 - 1.99573i) q^{5} +(0.222709 - 0.758479i) q^{6} +(2.48295 - 0.913760i) q^{7} +(-1.10834 - 2.42692i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.112500 - 0.782453i) q^{2} +(0.909632 + 0.415415i) q^{3} +(1.31941 - 0.387413i) q^{4} +(1.72931 - 1.99573i) q^{5} +(0.222709 - 0.758479i) q^{6} +(2.48295 - 0.913760i) q^{7} +(-1.10834 - 2.42692i) q^{8} +(0.654861 + 0.755750i) q^{9} +(-1.75611 - 1.12858i) q^{10} +(2.41388 + 0.347064i) q^{11} +(1.36111 + 0.195699i) q^{12} +(-3.57139 + 5.55718i) q^{13} +(-0.994306 - 1.84000i) q^{14} +(2.40209 - 1.09700i) q^{15} +(0.539369 - 0.346631i) q^{16} +(-4.61157 - 1.35408i) q^{17} +(0.517667 - 0.597420i) q^{18} +(-8.15115 + 2.39339i) q^{19} +(1.50849 - 3.30313i) q^{20} +(2.63816 + 0.200270i) q^{21} -1.92779i q^{22} +(-3.22132 + 3.55290i) q^{23} -2.66802i q^{24} +(-0.280847 - 1.95333i) q^{25} +(4.75002 + 2.16926i) q^{26} +(0.281733 + 0.959493i) q^{27} +(2.92202 - 2.16755i) q^{28} +(5.41572 + 1.59020i) q^{29} +(-1.12858 - 1.75611i) q^{30} +(0.351622 - 0.160580i) q^{31} +(-3.82627 - 4.41575i) q^{32} +(2.05157 + 1.31846i) q^{33} +(-0.540704 + 3.76068i) q^{34} +(2.47017 - 6.53546i) q^{35} +(1.15682 + 0.743441i) q^{36} +(-3.16124 + 2.73923i) q^{37} +(2.78972 + 6.10864i) q^{38} +(-5.55718 + 3.57139i) q^{39} +(-6.76012 - 1.98495i) q^{40} +(3.75722 + 3.25565i) q^{41} +(-0.140091 - 2.08677i) q^{42} +(7.91872 + 3.61636i) q^{43} +(3.31935 - 0.477251i) q^{44} +2.64072 q^{45} +(3.14237 + 2.12084i) q^{46} -10.2574i q^{47} +(0.634623 - 0.0912451i) q^{48} +(5.33009 - 4.53764i) q^{49} +(-1.49680 + 0.439499i) q^{50} +(-3.63233 - 3.14743i) q^{51} +(-2.55919 + 8.71580i) q^{52} +(-4.81898 - 7.49847i) q^{53} +(0.719064 - 0.328385i) q^{54} +(4.86698 - 4.21726i) q^{55} +(-4.96957 - 5.01317i) q^{56} +(-8.40880 - 1.20900i) q^{57} +(0.634989 - 4.41645i) q^{58} +(-0.711705 + 1.10743i) q^{59} +(2.74434 - 2.37799i) q^{60} +(-2.14833 - 4.70418i) q^{61} +(-0.165204 - 0.257063i) q^{62} +(2.31656 + 1.27810i) q^{63} +(-2.18494 + 2.52155i) q^{64} +(4.91460 + 16.7376i) q^{65} +(0.800834 - 1.75358i) q^{66} +(-5.63635 + 0.810385i) q^{67} -6.60914 q^{68} +(-4.40615 + 1.89364i) q^{69} +(-5.39158 - 1.19755i) q^{70} +(-0.314576 - 2.18793i) q^{71} +(1.10834 - 2.42692i) q^{72} +(2.31353 + 7.87917i) q^{73} +(2.49896 + 2.16536i) q^{74} +(0.555976 - 1.89348i) q^{75} +(-9.82747 + 6.31573i) q^{76} +(6.31068 - 1.34397i) q^{77} +(3.41963 + 3.94646i) q^{78} +(3.38224 - 5.26287i) q^{79} +(0.240953 - 1.67586i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(2.12471 - 3.30611i) q^{82} +(2.37388 + 2.73960i) q^{83} +(3.55840 - 0.757821i) q^{84} +(-10.6772 + 6.86182i) q^{85} +(1.93878 - 6.60287i) q^{86} +(4.26572 + 3.69627i) q^{87} +(-1.83310 - 6.24296i) q^{88} +(0.867930 - 1.90050i) q^{89} +(-0.297081 - 2.06624i) q^{90} +(-3.78964 + 17.0616i) q^{91} +(-2.87380 + 5.93571i) q^{92} +0.386554 q^{93} +(-8.02595 + 1.15396i) q^{94} +(-9.31928 + 20.4064i) q^{95} +(-1.64613 - 5.60620i) q^{96} +(3.63902 - 4.19966i) q^{97} +(-4.15013 - 3.66006i) q^{98} +(1.31846 + 2.05157i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{22}\right)$

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 $

$2$	−0.112500	−	0.782453i	−0.0795494	−	0.553278i	−0.990152	−	0.139995i	$-0.955291\pi$
$2$	−0.112500	−	0.782453i	−0.0795494	−	0.553278i	0.910603	−	0.413283i	$-0.135618\pi$
$3$	0.909632	+	0.415415i	0.525176	+	0.239840i
$3$	0.909632	+	0.415415i	0.525176	+	0.239840i
$4$	1.31941	−	0.387413i	0.659704	−	0.193707i
$5$	1.72931	−	1.99573i	0.773369	−	0.892516i	−0.223243	−	0.974763i	$-0.571664\pi$
$5$	1.72931	−	1.99573i	0.773369	−	0.892516i	0.996612	+	0.0822473i	$0.0262097\pi$
$6$	0.222709	−	0.758479i	0.0909208	−	0.309648i
$7$	2.48295	−	0.913760i	0.938467	−	0.345369i
$7$	2.48295	−	0.913760i	0.938467	−	0.345369i
$8$	−1.10834	−	2.42692i	−0.391856	−	0.858046i
$9$	0.654861	+	0.755750i	0.218287	+	0.251917i
$10$	−1.75611	−	1.12858i	−0.555330	−	0.356889i
$11$	2.41388	+	0.347064i	0.727812	+	0.104644i	0.496254	−	0.868177i	$-0.334709\pi$
$11$	2.41388	+	0.347064i	0.727812	+	0.104644i	0.231558	+	0.972821i	$0.425618\pi$
$12$	1.36111	+	0.195699i	0.392920	+	0.0564933i
$13$	−3.57139	+	5.55718i	−0.990524	+	1.54129i	−0.157894	+	0.987456i	$0.550470\pi$
$13$	−3.57139	+	5.55718i	−0.990524	+	1.54129i	−0.832630	+	0.553830i	$0.813166\pi$
$14$	−0.994306	−	1.84000i	−0.265740	−	0.491759i
$15$	2.40209	−	1.09700i	0.620216	−	0.283243i
$16$	0.539369	−	0.346631i	0.134842	−	0.0866579i
$17$	−4.61157	−	1.35408i	−1.11847	−	0.328413i	−0.330304	−	0.943874i	$-0.607151\pi$
$17$	−4.61157	−	1.35408i	−1.11847	−	0.328413i	−0.788167	+	0.615462i	$0.788970\pi$
$18$	0.517667	−	0.597420i	0.122015	−	0.140813i
$19$	−8.15115	+	2.39339i	−1.87000	+	0.549082i	−0.871752	+	0.489947i	$0.837016\pi$
$19$	−8.15115	+	2.39339i	−1.87000	+	0.549082i	−0.998250	+	0.0591349i	$0.981166\pi$
$20$	1.50849	−	3.30313i	0.337309	−	0.738603i
$21$	2.63816	+	0.200270i	0.575694	+	0.0437024i
$22$		−	1.92779i		−	0.411007i
$23$	−3.22132	+	3.55290i	−0.671692	+	0.740830i
$23$	−3.22132	+	3.55290i	−0.671692	+	0.740830i
$24$		−	2.66802i		−	0.544608i
$25$	−0.280847	−	1.95333i	−0.0561694	−	0.390666i
$26$	4.75002	+	2.16926i	0.931555	+	0.425427i
$27$	0.281733	+	0.959493i	0.0542195	+	0.184655i
$28$	2.92202	−	2.16755i	0.552211	−	0.409629i
$29$	5.41572	+	1.59020i	1.00567	+	0.295293i	0.742783	−	0.669533i	$-0.233506\pi$
$29$	5.41572	+	1.59020i	1.00567	+	0.295293i	0.262892	+	0.964825i	$0.415324\pi$
$30$	−1.12858	−	1.75611i	−0.206050	−	0.320620i
$31$	0.351622	−	0.160580i	0.0631532	−	0.0288411i	−0.383588	−	0.923504i	$-0.625312\pi$
$31$	0.351622	−	0.160580i	0.0631532	−	0.0288411i	0.446741	+	0.894663i	$0.352584\pi$
$32$	−3.82627	−	4.41575i	−0.676395	−	0.780602i
$33$	2.05157	+	1.31846i	0.357132	+	0.229515i
$34$	−0.540704	+	3.76068i	−0.0927299	+	0.644951i
$35$	2.47017	−	6.53546i	0.417534	−	1.10469i
$36$	1.15682	+	0.743441i	0.192803	+	0.123907i
$37$	−3.16124	+	2.73923i	−0.519704	+	0.450326i	−0.874786	−	0.484509i	$-0.838998\pi$
$37$	−3.16124	+	2.73923i	−0.519704	+	0.450326i	0.355082	+	0.934835i	$0.384453\pi$
$38$	2.78972	+	6.10864i	0.452553	+	0.990952i
$39$	−5.55718	+	3.57139i	−0.889862	+	0.571879i
$40$	−6.76012	−	1.98495i	−1.06887	−	0.313848i
$41$	3.75722	+	3.25565i	0.586780	+	0.508448i	0.896890	−	0.442253i	$-0.145821\pi$
$41$	3.75722	+	3.25565i	0.586780	+	0.508448i	−0.310111	+	0.950700i	$0.600366\pi$
$42$	−0.140091	−	2.08677i	−0.0216165	−	0.321995i
$43$	7.91872	+	3.61636i	1.20759	+	0.551489i	0.914497	−	0.404594i	$-0.132587\pi$
$43$	7.91872	+	3.61636i	1.20759	+	0.551489i	0.293096	+	0.956083i	$0.405314\pi$
$44$	3.31935	−	0.477251i	0.500411	−	0.0719482i
$45$	2.64072			0.393656
$46$	3.14237	+	2.12084i	0.463318	+	0.312700i
$47$		−	10.2574i		−	1.49620i	−0.663587	−	0.748099i	$-0.730967\pi$
$47$		−	10.2574i		−	1.49620i	0.663587	−	0.748099i	$-0.269033\pi$
$48$	0.634623	−	0.0912451i	0.0916000	−	0.0131701i
$49$	5.33009	−	4.53764i	0.761441	−	0.648235i
$50$	−1.49680	+	0.439499i	−0.211679	+	0.0621546i
$51$	−3.63233	−	3.14743i	−0.508628	−	0.440729i
$52$	−2.55919	+	8.71580i	−0.354896	+	1.20866i
$53$	−4.81898	−	7.49847i	−0.661937	−	1.02999i	−0.996164	−	0.0875018i	$-0.972112\pi$
$53$	−4.81898	−	7.49847i	−0.661937	−	1.02999i	0.334227	−	0.942493i	$-0.391525\pi$
$54$	0.719064	−	0.328385i	0.0978522	−	0.0446876i
$55$	4.86698	−	4.21726i	0.656263	−	0.568656i
$56$	−4.96957	−	5.01317i	−0.664086	−	0.669913i
$57$	−8.40880	−	1.20900i	−1.11377	−	0.160136i
$58$	0.634989	−	4.41645i	0.0833782	−	0.579908i
$59$	−0.711705	+	1.10743i	−0.0926561	+	0.144176i	−0.884487	−	0.466564i	$-0.845492\pi$
$59$	−0.711705	+	1.10743i	−0.0926561	+	0.144176i	0.791831	+	0.610740i	$0.209128\pi$
$60$	2.74434	−	2.37799i	0.354293	−	0.306997i
$61$	−2.14833	−	4.70418i	−0.275065	−	0.602309i	0.720801	−	0.693142i	$-0.243774\pi$
$61$	−2.14833	−	4.70418i	−0.275065	−	0.602309i	−0.995866	+	0.0908333i	$0.971047\pi$
$62$	−0.165204	−	0.257063i	−0.0209809	−	0.0326470i
$63$	2.31656	+	1.27810i	0.291859	+	0.161026i
$64$	−2.18494	+	2.52155i	−0.273117	+	0.315194i
$65$	4.91460	+	16.7376i	0.609581	+	2.07604i
$66$	0.800834	−	1.75358i	0.0985759	−	0.215851i
$67$	−5.63635	+	0.810385i	−0.688590	+	0.0990043i	−0.477723	−	0.878510i	$-0.658538\pi$
$67$	−5.63635	+	0.810385i	−0.688590	+	0.0990043i	−0.210867	+	0.977515i	$0.567629\pi$
$68$	−6.60914			−0.801476
$69$	−4.40615	+	1.89364i	−0.530438	+	0.227968i
$70$	−5.39158	−	1.19755i	−0.644418	−	0.143135i
$71$	−0.314576	−	2.18793i	−0.0373334	−	0.259659i	0.962603	−	0.270915i	$-0.0873262\pi$
$71$	−0.314576	−	2.18793i	−0.0373334	−	0.259659i	−0.999937	+	0.0112557i	$0.996417\pi$
$72$	1.10834	−	2.42692i	0.130619	−	0.286015i
$73$	2.31353	+	7.87917i	0.270779	+	0.922188i	0.976828	+	0.214025i	$0.0686574\pi$
$73$	2.31353	+	7.87917i	0.270779	+	0.922188i	−0.706049	+	0.708163i	$0.749524\pi$
$74$	2.49896	+	2.16536i	0.290498	+	0.251718i
$75$	0.555976	−	1.89348i	0.0641986	−	0.218640i
$76$	−9.82747	+	6.31573i	−1.12729	+	0.724464i
$77$	6.31068	−	1.34397i	0.719168	−	0.153159i
$78$	3.41963	+	3.94646i	0.387196	+	0.446848i
$79$	3.38224	−	5.26287i	0.380532	−	0.592119i	−0.597171	−	0.802114i	$-0.703709\pi$
$79$	3.38224	−	5.26287i	0.380532	−	0.592119i	0.977702	+	0.209995i	$0.0673449\pi$
$80$	0.240953	−	1.67586i	0.0269394	−	0.187367i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	2.12471	−	3.30611i	0.234635	−	0.365099i
$83$	2.37388	+	2.73960i	0.260567	+	0.300710i	0.870926	−	0.491415i	$-0.163520\pi$
$83$	2.37388	+	2.73960i	0.260567	+	0.300710i	−0.610359	+	0.792125i	$0.708975\pi$
$84$	3.55840	−	0.757821i	0.388253	−	0.0826851i
$85$	−10.6772	+	6.86182i	−1.15810	+	0.744269i
$86$	1.93878	−	6.60287i	0.209064	−	0.712005i
$87$	4.26572	+	3.69627i	0.457333	+	0.396282i
$88$	−1.83310	−	6.24296i	−0.195409	−	0.665501i
$89$	0.867930	−	1.90050i	0.0920004	−	0.201453i	−0.858038	−	0.513587i	$-0.828316\pi$
$89$	0.867930	−	1.90050i	0.0920004	−	0.201453i	0.950038	+	0.312134i	$0.101044\pi$
$90$	−0.297081	−	2.06624i	−0.0313151	−	0.217801i
$91$	−3.78964	+	17.0616i	−0.397262	+	1.78854i
$92$	−2.87380	+	5.93571i	−0.299615	+	0.618840i
$93$	0.386554			0.0400838
$94$	−8.02595	+	1.15396i	−0.827813	+	0.119022i
$95$	−9.31928	+	20.4064i	−0.956138	+	2.09365i
$96$	−1.64613	−	5.60620i	−0.168007	−	0.572180i
$97$	3.63902	−	4.19966i	0.369487	−	0.426410i	−0.540309	−	0.841467i	$-0.681693\pi$
$97$	3.63902	−	4.19966i	0.369487	−	0.426410i	0.909796	+	0.415056i	$0.136238\pi$
$98$	−4.15013	−	3.66006i	−0.419226	−	0.369722i
$99$	1.31846	+	2.05157i	0.132510	+	0.206190i
$100$	−1.12730	−	2.46844i	−0.112730	−	0.246844i
$101$	0.282896	−	0.245131i	0.0281492	−	0.0243914i	−0.640673	−	0.767814i	$-0.721344\pi$
$101$	0.282896	−	0.245131i	0.0281492	−	0.0243914i	0.668822	+	0.743423i	$0.266799\pi$
$102$	−2.05408	+	3.19622i	−0.203384	+	0.316472i
$103$	0.552136	−	3.84019i	0.0544035	−	0.378385i	−0.944371	−	0.328883i	$-0.893328\pi$
$103$	0.552136	−	3.84019i	0.0544035	−	0.378385i	0.998774	−	0.0495014i	$-0.0157632\pi$
$104$	17.4451	+	2.50823i	1.71064	+	0.245952i
$105$	4.96187	−	4.91872i	0.484229	−	0.480018i
$106$	−5.32507	+	4.61420i	−0.517217	+	0.448171i
$107$	−4.81326	+	2.19814i	−0.465315	+	0.212502i	−0.634255	−	0.773124i	$-0.718693\pi$
$107$	−4.81326	+	2.19814i	−0.465315	+	0.212502i	0.168940	+	0.985626i	$0.445966\pi$
$108$	0.743441	+	1.15682i	0.0715376	+	0.111315i
$109$	1.54595	−	5.26504i	0.148076	−	0.504299i	−0.851731	−	0.523980i	$-0.824447\pi$
$109$	1.54595	−	5.26504i	0.148076	−	0.504299i	0.999806	+	0.0196806i	$0.00626493\pi$
$110$	−3.84735	−	3.33374i	−0.366830	−	0.317860i
$111$	−4.01348	+	1.17846i	−0.380943	+	0.111855i
$112$	1.02249	−	1.35352i	0.0966161	−	0.127896i
$113$	10.3051	−	1.48165i	0.969424	−	0.139382i	0.360628	−	0.932710i	$-0.382562\pi$
$113$	10.3051	−	1.48165i	0.969424	−	0.139382i	0.608795	+	0.793328i	$0.291653\pi$
$114$			6.71551i			0.628965i
$115$	1.51995	+	12.5729i	0.141736	+	1.17243i
$116$	7.76161			0.720648
$117$	−6.53860	+	0.940109i	−0.604494	+	0.0869131i
$118$	0.946582	+	0.432290i	0.0871400	+	0.0397955i
$119$	−12.6876	+	0.851758i	−1.16307	+	0.0780805i
$120$	−5.32464	−	4.61383i	−0.486071	−	0.421183i
$121$	−4.84806	−	1.42352i	−0.440733	−	0.129411i
$122$	−3.43912	+	2.21019i	−0.311363	+	0.200101i
$123$	2.06524	+	4.52225i	0.186217	+	0.407758i
$124$	0.401722	−	0.348094i	0.0360757	−	0.0312598i
$125$	6.72360	+	4.32100i	0.601377	+	0.386482i
$126$	0.739444	−	1.95639i	0.0658749	−	0.174289i
$127$	−1.38648	+	9.64321i	−0.123031	+	0.855697i	0.831061	+	0.556182i	$0.187734\pi$
$127$	−1.38648	+	9.64321i	−0.123031	+	0.855697i	−0.954091	+	0.299515i	$0.903175\pi$
$128$	−7.61188	−	4.89186i	−0.672801	−	0.432383i
$129$	5.70083	+	6.57911i	0.501930	+	0.579258i
$130$	12.5435	−	5.72842i	1.10014	−	0.502415i
$131$	−5.05287	−	7.86241i	−0.441471	−	0.686942i	0.547207	−	0.836998i	$-0.315691\pi$
$131$	−5.05287	−	7.86241i	−0.441471	−	0.686942i	−0.988678	+	0.150055i	$0.952055\pi$
$132$	3.21765	+	0.944786i	0.280060	+	0.0822331i
$133$	−18.0519	+	13.3909i	−1.56530	+	1.16114i
$134$	1.26818	+	4.31902i	0.109554	+	0.373106i
$135$	2.40209	+	1.09700i	0.206739	+	0.0944144i
$136$	1.82493	+	12.6927i	0.156487	+	1.08839i
$137$		−	15.8226i		−	1.35182i	−0.736985	−	0.675909i	$-0.763751\pi$
$137$		−	15.8226i		−	1.35182i	0.736985	−	0.675909i	$-0.236249\pi$
$138$	1.97738	+	3.23457i	0.168326	+	0.275345i
$139$			5.43160i			0.460702i	0.973108	+	0.230351i	$0.0739875\pi$
$139$			5.43160i			0.460702i	−0.973108	+	0.230351i	$0.926013\pi$
$140$	0.727236	−	9.57992i	0.0614626	−	0.809651i
$141$	4.26108	−	9.33047i	0.358848	−	0.785767i
$142$	−1.67656	+	0.492283i	−0.140694	+	0.0413115i
$143$	−10.5496	+	12.1749i	−0.882201	+	1.01811i
$144$	0.615178	+	0.180633i	0.0512648	+	0.0150527i
$145$	12.5390	−	8.05835i	1.04131	−	0.669210i
$146$	5.90482	−	2.69664i	0.488686	−	0.223175i
$147$	6.73342	−	1.91339i	0.555363	−	0.157813i
$148$	−3.10975	+	4.83887i	−0.255620	+	0.397752i
$149$	9.24992	+	1.32994i	0.757783	+	0.108953i	0.510367	−	0.859957i	$-0.329509\pi$
$149$	9.24992	+	1.32994i	0.757783	+	0.108953i	0.247416	+	0.968909i	$0.420419\pi$
$150$	−1.54411	−	0.222009i	−0.126076	−	0.0181270i
$151$	19.4166	+	12.4783i	1.58010	+	1.01547i	0.975786	+	0.218727i	$0.0701905\pi$
$151$	19.4166	+	12.4783i	1.58010	+	1.01547i	0.604317	+	0.796744i	$0.293446\pi$
$152$	14.8428	+	17.1295i	1.20391	+	1.38939i
$153$	−1.99659	−	4.37193i	−0.161415	−	0.353450i
$154$	−1.76154	−	4.78661i	−0.141949	−	0.385716i
$155$	0.287588	−	0.979433i	0.0230996	−	0.0786700i
$156$	−5.94860	+	6.86504i	−0.476269	+	0.549643i
$157$	3.00386	−	0.882013i	0.239734	−	0.0703923i	−0.159658	−	0.987172i	$-0.551039\pi$
$157$	3.00386	−	0.882013i	0.239734	−	0.0703923i	0.399393	+	0.916780i	$0.369221\pi$
$158$	−4.49845	−	2.05437i	−0.357877	−	0.163437i
$159$	−1.26852	−	8.82273i	−0.100600	−	0.699688i
$160$	−15.4294			−1.21980
$161$	−4.75189	+	11.7652i	−0.374501	+	0.927226i
$162$	0.790500			0.0621075
$163$	0.875174	+	6.08697i	0.0685489	+	0.476768i	0.994961	+	0.100258i	$0.0319669\pi$
$163$	0.875174	+	6.08697i	0.0685489	+	0.476768i	−0.926413	+	0.376510i	$0.877124\pi$
$164$	6.21860	+	2.83994i	0.485591	+	0.221762i
$165$	6.17907	−	1.81434i	0.481040	−	0.141246i
$166$	1.87655	−	2.16565i	0.145649	−	0.168087i
$167$	−2.86487	+	9.75685i	−0.221690	+	0.755008i	0.771264	+	0.636515i	$0.219625\pi$
$167$	−2.86487	+	9.75685i	−0.221690	+	0.755008i	−0.992955	+	0.118493i	$0.962194\pi$
$168$	−2.43793	−	6.62457i	−0.188091	−	0.511097i
$169$	−12.7271	−	27.8685i	−0.979008	−	2.14373i
$170$	6.57024	+	7.58246i	0.503914	+	0.581548i
$171$	−7.14667	−	4.59289i	−0.546520	−	0.351227i
$172$	11.8490	+	1.70364i	0.903482	+	0.129901i
$173$	−15.1995	−	2.18536i	−1.15560	−	0.166150i	−0.462247	−	0.886751i	$-0.652957\pi$
$173$	−15.1995	−	2.18536i	−1.15560	−	0.166150i	−0.693350	+	0.720601i	$0.743866\pi$
$174$	2.41226	−	3.75356i	0.182873	−	0.284556i
$175$	−2.48221	−	4.59340i	−0.187637	−	0.347228i
$176$	1.42228	−	0.649531i	0.107208	−	0.0489603i
$177$	−1.10743	+	0.711705i	−0.0832399	+	0.0534950i
$178$	−1.58470	−	0.465309i	−0.118778	−	0.0348764i
$179$	−14.1133	+	16.2876i	−1.05488	+	1.21740i	−0.0795058	+	0.996834i	$0.525334\pi$
$179$	−14.1133	+	16.2876i	−1.05488	+	1.21740i	−0.975373	+	0.220561i	$0.929211\pi$
$180$	3.48419	−	1.02305i	0.259696	−	0.0762538i
$181$	7.08882	−	15.5224i	0.526908	−	1.15377i	−0.439849	−	0.898072i	$-0.644968\pi$
$181$	7.08882	−	15.5224i	0.526908	−	1.15377i	0.966757	−	0.255696i	$-0.0823047\pi$
$182$	13.7762	+	1.04579i	1.02116	+	0.0775191i
$183$		−	5.17152i		−	0.382290i
$184$	12.1929	+	3.88008i	0.898873	+	0.286044i
$185$			11.0459i			0.812112i
$186$	−0.0434873	−	0.302461i	−0.00318864	−	0.0221775i
$187$	−10.6618	−	4.86910i	−0.779671	−	0.356064i
$188$	−3.97386	−	13.5337i	−0.289823	−	0.987048i
$189$	1.57627	+	2.12494i	0.114657	+	0.154566i
$190$	17.0154	+	4.99619i	1.23443	+	0.362461i
$191$	−6.90269	−	10.7408i	−0.499461	−	0.777177i	0.496397	−	0.868096i	$-0.334656\pi$
$191$	−6.90269	−	10.7408i	−0.499461	−	0.777177i	−0.995858	+	0.0909188i	$0.971020\pi$
$192$	−3.03498	+	1.38603i	−0.219031	+	0.100028i
$193$	−6.39369	−	7.37871i	−0.460228	−	0.531131i	0.477440	−	0.878664i	$-0.341565\pi$
$193$	−6.39369	−	7.37871i	−0.460228	−	0.531131i	−0.937668	+	0.347533i	$0.887019\pi$
$194$	−3.69542	−	2.37490i	−0.265316	−	0.170508i
$195$	−2.48257	+	17.2666i	−0.177780	+	1.23649i
$196$	5.27462	−	8.05195i	0.376758	−	0.575139i
$197$	−6.42419	−	4.12858i	−0.457705	−	0.294149i	0.291399	−	0.956602i	$-0.405879\pi$
$197$	−6.42419	−	4.12858i	−0.457705	−	0.294149i	−0.749104	+	0.662453i	$0.769516\pi$
$198$	1.45693	−	1.26244i	0.103539	−	0.0897174i
$199$	−7.90683	−	17.3135i	−0.560500	−	1.22732i	−0.951703	−	0.307020i	$-0.900668\pi$
$199$	−7.90683	−	17.3135i	−0.560500	−	1.22732i	0.391203	−	0.920304i	$-0.372059\pi$
$200$	−4.42931	+	2.84654i	−0.313199	+	0.201281i
$201$	−5.46365	−	1.60427i	−0.385376	−	0.113157i
$202$	−0.223629	−	0.193776i	−0.0157345	−	0.0136340i
$203$	14.9000	−	1.00028i	1.04578	−	0.0702062i
$204$	−6.01189	−	2.74554i	−0.420916	−	0.192226i
$205$	12.9948	−	1.86837i	0.907595	−	0.130492i
$206$	−3.06688			−0.213680
$207$	−4.79462	−	0.107861i	−0.333249	−	0.00749684i
$208$			4.23533i			0.293667i
$209$	−20.5066	+	2.94840i	−1.41847	+	0.203945i
$210$	−4.40688	−	3.32908i	−0.304103	−	0.229728i
$211$	−3.97264	+	1.16647i	−0.273488	+	0.0803033i	−0.415601	−	0.909547i	$-0.636429\pi$
$211$	−3.97264	+	1.16647i	−0.273488	+	0.0803033i	0.142113	+	0.989850i	$0.454610\pi$
$212$	−9.26321	−	8.02661i	−0.636200	−	0.551270i
$213$	0.622749	−	2.12089i	0.0426701	−	0.145321i
$214$	2.26143	+	3.51886i	0.154588	+	0.240544i
$215$	20.9111	−	9.54980i	1.42613	−	0.651291i
$216$	2.01636	−	1.74718i	0.137196	−	0.118881i
$217$	0.726328	−	0.720011i	0.0493063	−	0.0488775i
$218$	−4.29357	−	0.617322i	−0.290797	−	0.0418103i
$219$	−1.16866	+	8.12823i	−0.0789709	+	0.549255i
$220$	4.78771	−	7.44983i	0.322787	−	0.502267i
$221$	23.9946	−	20.7914i	1.61405	−	1.39858i
$222$	1.37361	+	3.00778i	0.0921906	+	0.201869i
$223$	5.69677	+	8.86434i	0.381484	+	0.593600i	0.977900	−	0.209075i	$-0.0670454\pi$
$223$	5.69677	+	8.86434i	0.381484	+	0.593600i	−0.596416	+	0.802676i	$0.703409\pi$
$224$	−13.5354	−	7.46780i	−0.904370	−	0.498963i
$225$	1.29231	−	1.49141i	0.0861543	−	0.0994274i
$226$	−2.31865	−	7.89659i	−0.154234	−	0.525273i
$227$	−9.69482	+	21.2287i	−0.643468	+	1.40900i	0.253689	+	0.967286i	$0.418356\pi$
$227$	−9.69482	+	21.2287i	−0.643468	+	1.40900i	−0.897157	+	0.441712i	$0.854371\pi$
$228$	−11.5630	+	1.66251i	−0.765780	+	0.110103i
$229$	26.4321			1.74668			0.873342	−	0.487108i	$-0.161948\pi$
$229$	26.4321			1.74668			0.873342	+	0.487108i	$0.161948\pi$
$230$	9.66673	−	2.60374i	0.637405	−	0.171686i
$231$	6.29870	+	1.39904i	0.414424	+	0.0920498i
$232$	−2.14316	−	14.9060i	−0.140705	−	0.978627i
$233$	6.22711	−	13.6355i	0.407951	−	0.893289i	−0.588450	−	0.808533i	$-0.700262\pi$
$233$	6.22711	−	13.6355i	0.407951	−	0.893289i	0.996402	−	0.0847555i	$-0.0270109\pi$
$234$	1.47118	+	5.01039i	0.0961742	+	0.327539i
$235$	−20.4710	−	17.7382i	−1.33538	−	1.15711i
$236$	−0.509995	+	1.73688i	−0.0331978	+	0.113061i
$237$	5.26287	−	3.38224i	0.341860	−	0.219700i
$238$	2.09382	+	9.83165i	0.135722	+	0.637291i
$239$	−0.785889	−	0.906965i	−0.0508350	−	0.0586667i	0.729763	−	0.683701i	$-0.239631\pi$
$239$	−0.785889	−	0.906965i	−0.0508350	−	0.0586667i	−0.780598	+	0.625034i	$0.785085\pi$
$240$	0.915358	−	1.42432i	0.0590861	−	0.0919397i
$241$	−0.543299	+	3.77872i	−0.0349969	+	0.243409i	−0.999809	−	0.0195305i	$-0.993783\pi$
$241$	−0.543299	+	3.77872i	−0.0349969	+	0.243409i	0.964812	+	0.262939i	$0.0846920\pi$
$242$	−0.568431	+	3.95353i	−0.0365402	+	0.254142i
$243$	−0.540641	+	0.841254i	−0.0346821	+	0.0539664i
$244$	−4.65699	−	5.37445i	−0.298133	−	0.344064i
$245$	0.161461	−	18.4844i	0.0103154	−	1.18092i
$246$	3.30611	−	2.12471i	0.210790	−	0.135467i
$247$	15.8104	−	53.8452i	1.00599	−	3.42609i
$248$	−0.779431	−	0.675381i	−0.0494939	−	0.0428867i
$249$	1.02128	+	3.47817i	0.0647213	+	0.220420i
$250$	2.62458	−	5.74702i	0.165993	−	0.363473i
$251$	−1.93585	−	13.4642i	−0.122190	−	0.849850i	−0.955067	−	0.296391i	$-0.904217\pi$
$251$	−1.93585	−	13.4642i	−0.122190	−	0.849850i	0.832877	−	0.553459i	$-0.186692\pi$
$252$	3.55164	+	0.788874i	0.223733	+	0.0496944i
$253$	−9.00897	+	7.45826i	−0.566389	+	0.468897i
$254$	7.70135			0.483225
$255$	−12.5628	+	1.80626i	−0.786714	+	0.113112i
$256$	−5.74337	+	12.5762i	−0.358961	+	0.786014i
$257$	−0.421064	−	1.43401i	−0.0262652	−	0.0894511i	0.945317	−	0.326152i	$-0.105752\pi$
$257$	−0.421064	−	1.43401i	−0.0262652	−	0.0894511i	−0.971583	+	0.236701i	$0.923934\pi$
$258$	4.50650	−	5.20078i	0.280563	−	0.323787i
$259$	−5.34620	+	9.68998i	−0.332197	+	0.602106i
$260$	12.9687	+	20.1797i	0.804286	+	1.25149i
$261$	2.34475	+	5.13429i	0.145136	+	0.317804i
$262$	−5.58353	+	4.83815i	−0.344951	+	0.298902i
$263$	−11.1638	+	17.3712i	−0.688388	+	1.07115i	0.304547	+	0.952497i	$0.401495\pi$
$263$	−11.1638	+	17.3712i	−0.688388	+	1.07115i	−0.992935	+	0.118656i	$0.962142\pi$
$264$	0.925974	−	6.44029i	0.0569897	−	0.396372i
$265$	−23.2984	−	3.34980i	−1.43121	−	0.205777i
$266$	12.5086	+	12.6183i	0.766950	+	0.773678i
$267$	1.57899	−	1.36821i	0.0966328	−	0.0837328i
$268$	−7.12270	+	3.25283i	−0.435088	+	0.198698i
$269$	1.36643	+	2.12621i	0.0833130	+	0.129638i	0.880409	−	0.474215i	$-0.157268\pi$
$269$	1.36643	+	2.12621i	0.0833130	+	0.129638i	−0.797096	+	0.603852i	$0.793632\pi$
$270$	0.588114	−	2.00293i	0.0357915	−	0.121895i
$271$	14.9580	+	12.9612i	0.908636	+	0.787337i	0.977641	−	0.210279i	$-0.0674372\pi$
$271$	14.9580	+	12.9612i	0.908636	+	0.787337i	−0.0690057	+	0.997616i	$0.521983\pi$
$272$	−2.95671	+	0.868168i	−0.179277	+	0.0526404i
$273$	−10.5348	+	13.9455i	−0.637597	+	0.844020i
$274$	−12.3805	+	1.78004i	−0.747932	+	0.107536i
$275$		−	4.81258i		−	0.290210i
$276$	−5.07988	+	4.20549i	−0.305773	+	0.253141i
$277$	−7.85706			−0.472085			−0.236043	−	0.971743i	$-0.575850\pi$
$277$	−7.85706			−0.472085			−0.236043	+	0.971743i	$0.575850\pi$
$278$	4.24997	−	0.611054i	0.254896	−	0.0366486i
$279$	0.351622	+	0.160580i	0.0210511	+	0.00961369i
$280$	−18.5988	+	1.24859i	−1.11149	+	0.0746178i
$281$	−1.84310	−	1.59706i	−0.109950	−	0.0952726i	0.598151	−	0.801384i	$-0.295902\pi$
$281$	−1.84310	−	1.59706i	−0.109950	−	0.0952726i	−0.708101	+	0.706111i	$0.750448\pi$
$282$	−7.78003	−	2.28442i	−0.463294	−	0.136035i
$283$	24.4405	−	15.7070i	1.45284	−	0.933682i	0.453743	−	0.891133i	$-0.350089\pi$
$283$	24.4405	−	15.7070i	1.45284	−	0.933682i	0.999094	−	0.0425488i	$-0.0135478\pi$
$284$	−1.26269	−	2.76490i	−0.0749267	−	0.164067i
$285$	−16.9542	+	14.6909i	−1.00428	+	0.870215i
$286$	10.7131	+	6.88489i	0.633479	+	0.407112i
$287$	12.3039	+	4.65042i	0.726275	+	0.274506i
$288$	0.831528	−	5.78340i	0.0489982	−	0.340790i
$289$	5.13178	+	3.29799i	0.301869	+	0.194000i
$290$	−7.71593	−	8.90465i	−0.453095	−	0.522899i
$291$	5.05477	−	2.30844i	0.296316	−	0.135323i
$292$	6.10500	+	9.49956i	0.357268	+	0.555920i
$293$	−9.12108	−	2.67819i	−0.532859	−	0.156462i	0.00422350	−	0.999991i	$-0.498656\pi$
$293$	−9.12108	−	2.67819i	−0.532859	−	0.156462i	−0.537083	+	0.843529i	$0.680474\pi$
$294$	−2.25464	−	5.05333i	−0.131494	−	0.294716i
$295$	0.979379	+	3.33546i	0.0570217	+	0.194198i
$296$	10.1516	+	4.63608i	0.590050	+	0.269467i
$297$	0.347064	+	2.41388i	0.0201387	+	0.140068i
$298$		−	7.38725i		−	0.427932i
$299$	−8.23952	−	30.5903i	−0.476504	−	1.76908i
$300$		−	2.71367i		−	0.156674i
$301$	22.9663	+	1.74343i	1.32375	+	0.100489i
$302$	7.57933	−	16.5964i	0.436142	−	0.955017i
$303$	0.359162	−	0.105459i	0.0206333	−	0.00605849i
$304$	−3.56685	+	4.11637i	−0.204573	+	0.236090i
$305$	−13.1034	−	3.84750i	−0.750297	−	0.220307i
$306$	−3.19622	+	2.05408i	−0.182715	+	0.117424i
$307$	14.8845	−	6.79752i	0.849503	−	0.387955i	0.0574063	−	0.998351i	$-0.481717\pi$
$307$	14.8845	−	6.79752i	0.849503	−	0.387955i	0.792096	+	0.610396i	$0.208990\pi$
$308$	7.80569	−	4.21808i	0.444771	−	0.240347i
$309$	2.09751	−	3.26379i	0.119323	−	0.185671i
$310$	−0.798715	−	0.114838i	−0.0453639	−	0.00652235i
$311$	22.7775	+	3.27491i	1.29159	+	0.185703i	0.753648	−	0.657278i	$-0.228292\pi$
$311$	22.7775	+	3.27491i	1.29159	+	0.185703i	0.537944	+	0.842981i	$0.319201\pi$
$312$	14.8267	+	9.52854i	0.839396	+	0.539447i
$313$	−14.9797	−	17.2875i	−0.846705	−	0.977149i	0.153235	−	0.988190i	$-0.451031\pi$
$313$	−14.9797	−	17.2875i	−0.846705	−	0.977149i	−0.999939	+	0.0110407i	$0.996486\pi$
$314$	−1.02807	−	2.25115i	−0.0580172	−	0.127040i
$315$	6.55678	−	2.41299i	0.369433	−	0.135956i
$316$	2.42365	−	8.25420i	0.136341	−	0.464335i
$317$	−6.90560	+	7.96948i	−0.387857	+	0.447611i	−0.915779	−	0.401682i	$-0.868426\pi$
$317$	−6.90560	+	7.96948i	−0.387857	+	0.447611i	0.527922	+	0.849293i	$0.322971\pi$
$318$	−6.76066	+	1.98511i	−0.379119	+	0.111319i
$319$	12.5210	+	5.71815i	0.701041	+	0.320155i
$320$	1.25390	+	8.72107i	0.0700952	+	0.487523i
$321$	−5.29143			−0.295339
$322$	9.74030	+	2.39455i	0.542805	+	0.133443i
$323$	40.8305			2.27187
$324$	0.195699	+	1.36111i	0.0108721	+	0.0756174i
$325$	11.8580	+	5.41539i	0.657766	+	0.300392i
$326$	4.66431	−	1.36957i	0.258332	−	0.0758532i
$327$	3.59343	−	4.14703i	0.198717	−	0.229332i
$328$	3.73694	−	12.7268i	0.206338	−	0.702722i
$329$	−9.37281	−	25.4686i	−0.516740	−	1.40413i
$330$	−2.11478	−	4.63073i	−0.116415	−	0.254913i
$331$	13.6871	+	15.7958i	0.752313	+	0.868215i	0.994790	−	0.101942i	$-0.0325056\pi$
$331$	13.6871	+	15.7958i	0.752313	+	0.868215i	−0.242478	+	0.970157i	$0.577960\pi$
$332$	4.19347	+	2.69498i	0.230147	+	0.147906i
$333$	−4.14034	−	0.595291i	−0.226889	−	0.0326217i
$334$	7.95658	+	1.14398i	0.435365	+	0.0625960i
$335$	−8.12967	+	12.6500i	−0.444172	+	0.691144i
$336$	1.49236	−	0.806450i	0.0814150	−	0.0439955i
$337$	−2.45595	+	1.12159i	−0.133784	+	0.0610971i	−0.481182	−	0.876621i	$-0.659792\pi$
$337$	−2.45595	+	1.12159i	−0.133784	+	0.0610971i	0.347398	+	0.937718i	$0.387065\pi$
$338$	−20.3740	+	13.0936i	−1.10820	+	0.712196i
$339$	9.98936	+	2.93314i	0.542548	+	0.159306i
$340$	−11.4292	+	13.1900i	−0.619837	+	0.715330i
$341$	0.904505	−	0.265587i	0.0489817	−	0.0143823i
$342$	−2.78972	+	6.10864i	−0.150851	+	0.330317i
$343$	9.08802	−	16.1372i	0.490707	−	0.871325i
$344$		−	23.2262i		−	1.25227i
$345$	−3.84038	+	12.0681i	−0.206759	+	0.649727i
$346$			12.1388i			0.652583i
$347$	−0.802793	−	5.58355i	−0.0430962	−	0.299741i	−0.999958	−	0.00919622i	$-0.997073\pi$
$347$	−0.802793	−	5.58355i	−0.0430962	−	0.299741i	0.956862	−	0.290544i	$-0.0938364\pi$
$348$	7.06021	+	3.22429i	0.378467	+	0.172840i
$349$	8.80103	+	29.9735i	0.471108	+	1.60445i	0.761923	+	0.647668i	$0.224256\pi$
$349$	8.80103	+	29.9735i	0.471108	+	1.60445i	−0.290815	+	0.956779i	$0.593926\pi$
$350$	−3.31487	+	2.45897i	−0.177188	+	0.131437i
$351$	−6.33825	−	1.86108i	−0.338311	−	0.0993371i
$352$	−7.70361	−	11.9870i	−0.410604	−	0.638912i
$353$	−27.2370	+	12.4387i	−1.44968	+	0.662046i	−0.975824	−	0.218558i	$-0.929865\pi$
$353$	−27.2370	+	12.4387i	−1.44968	+	0.662046i	−0.473854	+	0.880603i	$0.657138\pi$
$354$	0.681462	+	0.786449i	0.0362193	+	0.0417993i
$355$	−4.91050	−	3.15579i	−0.260622	−	0.167492i
$356$	0.408875	−	2.84379i	0.0216703	−	0.150720i
$357$	−11.8949	−	4.49584i	−0.629545	−	0.237945i
$358$	14.3321	+	9.21066i	0.757473	+	0.486798i
$359$	−23.9199	+	20.7267i	−1.26244	+	1.09391i	−0.271108	+	0.962549i	$0.587390\pi$
$359$	−23.9199	+	20.7267i	−1.26244	+	1.09391i	−0.991334	+	0.131364i	$0.958064\pi$
$360$	−2.92681	−	6.40882i	−0.154256	−	0.337775i
$361$	44.7291	−	28.7456i	2.35416	−	1.51293i
$362$	−12.9430	−	3.80041i	−0.680270	−	0.199745i
$363$	−3.81860	−	3.30884i	−0.200424	−	0.173669i
$364$	1.60981	+	23.9794i	0.0843769	+	1.25686i
$365$	19.7255	+	9.00832i	1.03248	+	0.471517i
$366$	−4.04648	+	0.581795i	−0.211513	+	0.0304109i
$367$	15.0664			0.786460			0.393230	−	0.919440i	$-0.371358\pi$
$367$	15.0664			0.786460			0.393230	+	0.919440i	$0.371358\pi$
$368$	−0.505936	+	3.03293i	−0.0263737	+	0.158103i
$369$			4.97152i			0.258807i
$370$	8.64292	−	1.24266i	0.449324	−	0.0646030i
$371$	−18.8171	−	14.2149i	−0.976934	−	0.738003i
$372$	0.510023	−	0.149756i	0.0264434	−	0.00776450i
$373$	−17.2952	−	14.9864i	−0.895511	−	0.775964i	0.0797979	−	0.996811i	$-0.474573\pi$
$373$	−17.2952	−	14.9864i	−0.895511	−	0.775964i	−0.975309	+	0.220847i	$0.929118\pi$
$374$	−2.61039	+	8.89016i	−0.134980	+	0.459699i
$375$	4.32100	+	6.72360i	0.223135	+	0.347205i
$376$	−24.8939	+	11.3687i	−1.28381	+	0.586294i
$377$	−28.1787	+	24.4169i	−1.45127	+	1.25754i
$378$	1.48533	−	1.47242i	0.0763973	−	0.0757329i
$379$	−22.3083	−	3.20745i	−1.14590	−	0.164755i	−0.456900	−	0.889518i	$-0.651040\pi$
$379$	−22.3083	−	3.20745i	−1.14590	−	0.164755i	−0.688999	+	0.724763i	$0.741949\pi$
$380$	−4.39023	+	30.5348i	−0.225214	+	1.56640i
$381$	−5.26713	+	8.19581i	−0.269843	+	0.419884i
$382$	−7.62762	+	6.60937i	−0.390263	+	0.338165i
$383$	11.1160	+	24.3407i	0.568002	+	1.24375i	0.947854	+	0.318703i	$0.103247\pi$
$383$	11.1160	+	24.3407i	0.568002	+	1.24375i	−0.379853	+	0.925047i	$0.624025\pi$
$384$	−4.89186	−	7.61188i	−0.249636	−	0.388442i
$385$	8.23090	−	14.9185i	0.419486	−	0.760317i
$386$	−5.05421	+	5.83286i	−0.257252	+	0.296885i
$387$	2.45260	+	8.35278i	0.124672	+	0.424596i
$388$	3.17435	−	6.95087i	0.161153	−	0.352877i
$389$	2.19854	−	0.316102i	0.111470	−	0.0160270i	−0.0863539	−	0.996265i	$-0.527522\pi$
$389$	2.19854	−	0.316102i	0.111470	−	0.0160270i	0.197824	+	0.980238i	$0.436612\pi$
$390$	13.7896			0.698265
$391$	19.6663	−	12.0225i	0.994567	−	0.608005i
$392$	−16.9200	−	7.90645i	−0.854590	−	0.399336i
$393$	−1.33008	−	9.25094i	−0.0670939	−	0.466648i
$394$	−2.50770	+	5.49110i	−0.126336	+	0.276637i
$395$	−4.65431	−	15.8511i	−0.234184	−	0.797557i
$396$	2.53439	+	2.19607i	0.127358	+	0.110356i
$397$	6.17887	−	21.0433i	0.310109	−	1.05613i	−0.646053	−	0.763293i	$-0.723581\pi$
$397$	6.17887	−	21.0433i	0.310109	−	1.05613i	0.956161	−	0.292841i	$-0.0946005\pi$
$398$	−12.6575	+	8.13449i	−0.634464	+	0.407745i
$399$	−21.9834	+	4.68173i	−1.10054	+	0.234380i
$400$	−0.828567	−	0.956217i	−0.0414283	−	0.0478108i
$401$	−12.7335	+	19.8138i	−0.635882	+	0.989452i	0.362466	+	0.931997i	$0.381935\pi$
$401$	−12.7335	+	19.8138i	−0.635882	+	0.989452i	−0.998348	+	0.0574553i	$0.981701\pi$
$402$	−0.640609	+	4.45554i	−0.0319507	+	0.222222i
$403$	−0.363403	+	2.52752i	−0.0181024	+	0.125905i
$404$	0.278288	−	0.433025i	0.0138454	−	0.0215438i
$405$	1.72931	+	1.99573i	0.0859299	+	0.0991684i
$406$	−2.45893	−	11.5460i	−0.122034	−	0.573021i
$407$	−8.58153	+	5.51502i	−0.425371	+	0.273369i
$408$	−3.61272	+	12.3038i	−0.178856	+	0.609128i
$409$	−6.64009	−	5.75367i	−0.328331	−	0.284501i	0.475058	−	0.879954i	$-0.342427\pi$
$409$	−6.64009	−	5.75367i	−0.328331	−	0.284501i	−0.803390	+	0.595454i	$0.796972\pi$
$410$	−2.92382	−	9.95762i	−0.144397	−	0.491772i
$411$	6.57296	−	14.3928i	0.324220	−	0.709943i
$412$	−0.759247	−	5.28068i	−0.0374054	−	0.260160i
$413$	−0.755199	+	3.40003i	−0.0371609	+	0.167305i
$414$	0.454998	+	3.76370i	0.0223619	+	0.184976i
$415$	9.57266			0.469903
$416$	38.2042	−	5.49294i	1.87312	−	0.269313i
$417$	−2.25637	+	4.94076i	−0.110495	+	0.241950i
$418$	4.61397	+	15.7137i	0.225677	+	0.768584i
$419$	−16.7404	+	19.3195i	−0.817824	+	0.943819i	−0.999216	−	0.0395917i	$-0.987394\pi$
$419$	−16.7404	+	19.3195i	−0.817824	+	0.943819i	0.181392	+	0.983411i	$0.441940\pi$
$420$	4.64116	−	8.41209i	0.226465	−	0.410468i
$421$	21.2219	+	33.0219i	1.03429	+	1.60939i	0.762449	+	0.647048i	$0.223997\pi$
$421$	21.2219	+	33.0219i	1.03429	+	1.60939i	0.271843	+	0.962342i	$0.412367\pi$
$422$	1.35963	+	2.97718i	0.0661859	+	0.144927i
$423$	7.75204	−	6.71718i	0.376917	−	0.326600i
$424$	−12.8571	+	20.0061i	−0.624398	+	0.971582i
$425$	−1.34982	+	9.38823i	−0.0654760	+	0.455396i
$426$	−1.72956	−	0.248673i	−0.0837972	−	0.0120482i
$427$	−9.63269	−	9.71720i	−0.466158	−	0.470248i
$428$	−5.49906	+	4.76496i	−0.265807	+	0.230323i
$429$	−14.6539	+	6.69220i	−0.707496	+	0.323102i
$430$	−9.82477	−	15.2876i	−0.473793	−	0.737236i
$431$	−1.37712	+	4.69003i	−0.0663334	+	0.225911i	−0.985988	−	0.166818i	$-0.946651\pi$
$431$	−1.37712	+	4.69003i	−0.0663334	+	0.225911i	0.919654	+	0.392729i	$0.128469\pi$
$432$	0.484548	+	0.419863i	0.0233128	+	0.0202007i
$433$	9.71476	−	2.85251i	0.466861	−	0.137083i	−0.0398371	−	0.999206i	$-0.512684\pi$
$433$	9.71476	−	2.85251i	0.466861	−	0.137083i	0.506699	+	0.862123i	$0.330866\pi$
$434$	−0.645087	−	0.487317i	−0.0309652	−	0.0233919i
$435$	14.7535	−	2.12123i	0.707375	−	0.101705i
$436$		−	7.54566i		−	0.361372i
$437$	17.7540	−	36.6701i	0.849289	−	1.75417i
$438$	6.49143			0.310173
$439$	−3.07613	+	0.442281i	−0.146816	+	0.0211089i	−0.215331	−	0.976541i	$-0.569083\pi$
$439$	−3.07613	+	0.442281i	−0.146816	+	0.0211089i	0.0685150	+	0.997650i	$0.478174\pi$
$440$	−15.6292	−	7.13762i	−0.745093	−	0.340273i
$441$	6.91978	+	1.05669i	0.329514	+	0.0503184i
$442$	−18.9677	−	16.4356i	−0.902202	−	0.781762i
$443$	−15.4850	−	4.54680i	−0.735714	−	0.216025i	−0.107652	−	0.994189i	$-0.534333\pi$
$443$	−15.4850	−	4.54680i	−0.735714	−	0.216025i	−0.628062	+	0.778164i	$0.716151\pi$
$444$	−4.83887	+	3.10975i	−0.229642	+	0.147582i
$445$	−2.29196	−	5.01870i	−0.108649	−	0.237909i
$446$	6.29505	−	5.45469i	0.298079	−	0.258287i
$447$	7.86155	+	5.05231i	0.371839	+	0.238966i
$448$	−3.12100	+	8.25740i	−0.147453	+	0.390125i
$449$	3.51907	−	24.4757i	0.166075	−	1.15508i	−0.720825	−	0.693117i	$-0.756237\pi$
$449$	3.51907	−	24.4757i	0.166075	−	1.15508i	0.886900	−	0.461961i	$-0.152854\pi$
$450$	−1.31234	−	0.843393i	−0.0618645	−	0.0397579i
$451$	7.93957	+	9.16275i	0.373860	+	0.431457i
$452$	13.0226	−	5.94724i	0.612534	−	0.279735i
$453$	12.4783	+	19.4166i	0.586282	+	0.912273i
$454$	17.7011	+	5.19752i	0.830755	+	0.243932i
$455$	27.4968	+	37.0678i	1.28907	+	1.73777i
$456$	6.38563	+	21.7475i	0.299035	+	1.01842i
$457$	11.3921	+	5.20262i	0.532902	+	0.243368i	0.663644	−	0.748048i	$-0.269009\pi$
$457$	11.3921	+	5.20262i	0.532902	+	0.243368i	−0.130742	+	0.991416i	$0.541736\pi$
$458$	−2.97361	−	20.6819i	−0.138948	−	0.966402i
$459$		−	4.80626i		−	0.224337i
$460$	6.87636	+	16.0000i	0.320612	+	0.746003i
$461$		−	7.90227i		−	0.368045i	−0.982922	−	0.184023i	$-0.941088\pi$
$461$		−	7.90227i		−	0.368045i	0.982922	−	0.184023i	$-0.0589120\pi$
$462$	0.386078	−	5.08583i	0.0179620	−	0.236614i
$463$	−16.9498	+	37.1149i	−0.787723	+	1.72487i	−0.104668	+	0.994507i	$0.533378\pi$
$463$	−16.9498	+	37.1149i	−0.787723	+	1.72487i	−0.683055	+	0.730367i	$0.739349\pi$
$464$	3.47229	−	1.01956i	0.161197	−	0.0473317i
$465$	0.668470	−	0.771456i	0.0309996	−	0.0357754i
$466$	−11.3697	−	3.33843i	−0.526689	−	0.154650i
$467$	2.34793	−	1.50892i	0.108649	−	0.0698247i	−0.485188	−	0.874410i	$-0.661249\pi$
$467$	2.34793	−	1.50892i	0.108649	−	0.0698247i	0.593837	+	0.804585i	$0.297612\pi$
$468$	−8.26288	+	3.77353i	−0.381952	+	0.174431i
$469$	−13.2543	+	7.16242i	−0.612026	+	0.330730i
$470$	−11.5763	+	18.0131i	−0.533977	+	0.830884i
$471$	3.09881	+	0.445541i	0.142786	+	0.0205295i
$472$	3.47646	+	0.499840i	0.160017	+	0.0230070i
$473$	17.8597	+	11.4777i	0.821191	+	0.527747i
$474$	−3.23852	−	3.73745i	−0.148750	−	0.171667i
$475$	6.96432	+	15.2497i	0.319545	+	0.699706i
$476$	−16.4102	+	6.03917i	−0.752159	+	0.276805i
$477$	2.51121	−	8.55239i	0.114980	−	0.391587i
$478$	−0.621245	+	0.716955i	−0.0284151	+	0.0327928i
$479$	18.3655	−	5.39259i	0.839140	−	0.246394i	0.166201	−	0.986092i	$-0.446850\pi$
$479$	18.3655	−	5.39259i	0.839140	−	0.246394i	0.672939	+	0.739698i	$0.265032\pi$
$480$	−14.0351	−	6.40961i	−0.640611	−	0.292557i
$481$	−3.93240	−	27.3504i	−0.179302	−	1.24707i
$482$	3.01780			0.137457
$483$	−9.20991	+	8.72798i	−0.419065	+	0.397137i
$484$	−6.94806			−0.315821
$485$	−2.08838	−	14.5250i	−0.0948283	−	0.659545i
$486$	0.719064	+	0.328385i	0.0326174	+	0.0148959i
$487$	−21.4796	+	6.30698i	−0.973333	+	0.285796i	−0.729470	−	0.684013i	$-0.760233\pi$
$487$	−21.4796	+	6.30698i	−0.973333	+	0.285796i	−0.243863	+	0.969810i	$0.578415\pi$
$488$	−9.03560	+	10.4276i	−0.409022	+	0.472037i
$489$	−1.73253	+	5.90046i	−0.0783478	+	0.266828i
$490$	−14.4813	+	1.95315i	−0.654199	+	0.0882344i
$491$	−4.02200	−	8.80695i	−0.181510	−	0.397452i	0.796904	−	0.604106i	$-0.206470\pi$
$491$	−4.02200	−	8.80695i	−0.181510	−	0.397452i	−0.978414	+	0.206654i	$0.933742\pi$
$492$	4.47688	+	5.16660i	0.201833	+	0.232928i
$493$	−22.8217	−	14.6666i	−1.02784	−	0.660552i
$494$	−43.9100	−	6.31331i	−1.97560	−	0.284049i
$495$	6.37439	+	0.916499i	0.286507	+	0.0411936i
$496$	0.133992	−	0.208495i	0.00601641	−	0.00936172i
$497$	−2.78032	−	5.14507i	−0.124714	−	0.230788i
$498$	2.60662	−	1.19040i	0.116805	−	0.0533432i
$499$	−6.87255	+	4.41672i	−0.307658	+	0.197719i	−0.685354	−	0.728210i	$-0.740353\pi$
$499$	−6.87255	+	4.41672i	−0.307658	+	0.197719i	0.377697	+	0.925929i	$0.376716\pi$
$500$	10.5452	+	3.09635i	0.471595	+	0.138473i
$501$	−6.65912	+	7.68504i	−0.297508	+	0.343342i
$502$	−10.3173	+	3.02943i	−0.460483	+	0.135210i
$503$	2.24776	−	4.92191i	0.100223	−	0.219457i	−0.852878	−	0.522110i	$-0.825145\pi$
$503$	2.24776	−	4.92191i	0.100223	−	0.219457i	0.953101	+	0.302653i	$0.0978723\pi$
$504$	0.534324	−	7.03867i	0.0238007	−	0.313527i
$505$		−	0.988488i		−	0.0439872i
$506$	6.84925	+	6.21004i	0.304486	+	0.276070i
$507$		−	30.6371i		−	1.36064i
$508$	1.90657	+	13.2605i	0.0845904	+	0.588339i
$509$	31.4302	+	14.3537i	1.39312	+	0.636217i	0.963724	−	0.266900i	$-0.0859993\pi$
$509$	31.4302	+	14.3537i	1.39312	+	0.636217i	0.429396	+	0.903116i	$0.358727\pi$
$510$	2.82663	+	9.62662i	0.125165	+	0.426274i
$511$	12.9441	+	17.4496i	0.572612	+	0.771924i
$512$	−6.87703	−	2.01928i	−0.303925	−	0.0892403i
$513$	−4.59289	−	7.14667i	−0.202781	−	0.315533i
$514$	−1.07468	+	0.490789i	−0.0474020	+	0.0216478i
$515$	−6.70915	−	7.74277i	−0.295640	−	0.341187i
$516$	10.0706	+	6.47195i	0.443332	+	0.284912i
$517$	3.55997	−	24.7602i	0.156567	−	1.08895i
$518$	8.18340	+	3.09303i	0.359558	+	0.135900i
$519$	−12.9181	−	8.30197i	−0.567043	−	0.364416i
$520$	35.1737	−	30.4782i	1.54247	−	1.33656i
$521$	−2.36747	−	5.18404i	−0.103721	−	0.227117i	0.850655	−	0.525724i	$-0.176205\pi$
$521$	−2.36747	−	5.18404i	−0.103721	−	0.227117i	−0.954376	+	0.298607i	$0.903478\pi$
$522$	3.75356	−	2.41226i	0.164289	−	0.105582i
$523$	10.6790	+	3.13564i	0.466961	+	0.137112i	0.506745	−	0.862096i	$-0.330849\pi$
$523$	10.6790	+	3.13564i	0.466961	+	0.137112i	−0.0397838	+	0.999208i	$0.512667\pi$
$524$	−9.71280	−	8.41619i	−0.424306	−	0.367663i
$525$	−0.349726	−	5.20945i	−0.0152633	−	0.227359i
$526$	14.8481	+	6.78088i	0.647406	+	0.295661i
$527$	−1.83897	+	0.264404i	−0.0801068	+	0.0115176i
$528$	1.56357			0.0680457
$529$	−2.24616	−	22.8901i	−0.0976589	−	0.995220i
$530$			18.6067i			0.808225i
$531$	−1.30301	+	0.187345i	−0.0565458	+	0.00813006i
$532$	−18.6301	+	24.6616i	−0.807715	+	1.06922i
$533$	−31.5108	+	9.25239i	−1.36488	+	0.400766i
$534$	−1.24819	−	1.08157i	−0.0540146	−	0.0468039i
$535$	−3.93671	+	13.4072i	−0.170199	+	0.579643i
$536$	8.21372	+	12.7808i	0.354779	+	0.552046i
$537$	−19.6041	+	8.95287i	−0.845977	+	0.386345i
$538$	1.50994	−	1.30837i	0.0650981	−	0.0564078i
$539$	14.4410	−	9.10344i	0.622019	−	0.392113i
$540$	3.59432	+	0.516786i	0.154675	+	0.0222389i
$541$	4.26830	−	29.6867i	0.183509	−	1.27633i	−0.664877	−	0.746953i	$-0.731516\pi$
$541$	4.26830	−	29.6867i	0.183509	−	1.27633i	0.848386	−	0.529378i	$-0.177575\pi$
$542$	8.45877	−	13.1621i	0.363335	−	0.565361i
$543$	12.8964	−	11.1748i	0.553439	−	0.479558i
$544$	11.6658	+	25.5446i	0.500169	+	1.09522i
$545$	−7.83414	−	12.1902i	−0.335578	−	0.522169i
$546$	12.0969	+	6.67414i	0.517698	+	0.285627i
$547$	−13.1051	+	15.1241i	−0.560334	+	0.646660i	−0.963259	−	0.268573i	$-0.913448\pi$
$547$	−13.1051	+	15.1241i	−0.560334	+	0.646660i	0.402926	+	0.915233i	$0.367993\pi$
$548$	−6.12990	−	20.8765i	−0.261856	−	0.891801i
$549$	2.14833	−	4.70418i	0.0916884	−	0.200770i
$550$	−3.76562	+	0.541415i	−0.160567	+	0.0230860i
$551$	−47.9503			−2.04275
$552$	9.47921	+	8.59457i	0.403462	+	0.365809i
$553$	3.58893	−	16.1580i	0.152617	−	0.687108i
$554$	0.883918	+	6.14778i	0.0375541	+	0.261194i
$555$	−4.58864	+	10.0477i	−0.194777	+	0.426502i
$556$	2.10427	+	7.16650i	0.0892411	+	0.303927i
$557$	−12.0147	−	10.4108i	−0.509080	−	0.441121i	0.362060	−	0.932155i	$-0.382074\pi$
$557$	−12.0147	−	10.4108i	−0.509080	−	0.441121i	−0.871140	+	0.491034i	$0.836619\pi$
$558$	0.0860892	−	0.293193i	0.00364445	−	0.0124119i
$559$	−48.3776	+	31.0904i	−2.04615	+	1.31498i
$560$	−0.933064	−	4.38126i	−0.0394291	−	0.185142i
$561$	−7.67565	−	8.85817i	−0.324066	−	0.373992i
$562$	−1.04228	+	1.62181i	−0.0439657	+	0.0684120i
$563$	2.55510	−	17.7711i	0.107685	−	0.748963i	−0.862406	−	0.506218i	$-0.831043\pi$
$563$	2.55510	−	17.7711i	0.107685	−	0.748963i	0.970090	−	0.242745i	$-0.0780477\pi$
$564$	2.00736	−	13.9615i	0.0845252	−	0.587885i
$565$	14.8637	−	23.1284i	0.625322	−	0.973019i
$566$	−15.0395	−	17.3565i	−0.632158	−	0.729549i
$567$	0.551099	+	2.58772i	0.0231440	+	0.108674i
$568$	−4.96127	+	3.18841i	−0.208170	+	0.133783i
$569$	6.70808	−	22.8456i	0.281217	−	0.957738i	−0.690843	−	0.723005i	$-0.742760\pi$
$569$	6.70808	−	22.8456i	0.281217	−	0.957738i	0.972060	−	0.234733i	$-0.0754215\pi$
$570$	13.4023	+	11.6132i	0.561361	+	0.486422i
$571$	8.45624	+	28.7993i	0.353883	+	1.20521i	0.923595	+	0.383370i	$0.125237\pi$
$571$	8.45624	+	28.7993i	0.353883	+	1.20521i	−0.569712	+	0.821844i	$0.692945\pi$
$572$	−9.20251	+	20.1507i	−0.384776	+	0.842543i
$573$	−1.81702	−	12.6377i	−0.0759071	−	0.527946i
$574$	2.25456	−	10.1504i	0.0941033	−	0.423669i
$575$	7.84469	+	5.29449i	0.327146	+	0.220796i
$576$	−3.33649			−0.139020
$577$	−17.7990	+	2.55911i	−0.740983	+	0.106537i	−0.502461	−	0.864600i	$-0.667572\pi$
$577$	−17.7990	+	2.55911i	−0.740983	+	0.106537i	−0.238522	+	0.971137i	$0.576663\pi$
$578$	2.00320	−	4.38640i	0.0833222	−	0.182450i
$579$	−2.75068	−	9.36794i	−0.114314	−	0.389318i
$580$	13.4222	−	15.4901i	0.557327	−	0.643189i
$581$	8.39756	+	4.63314i	0.348390	+	0.192215i
$582$	−2.37490	−	3.69542i	−0.0984430	−	0.153180i
$583$	−9.02998	−	19.7729i	−0.373984	−	0.818910i
$584$	16.5579	−	14.3475i	0.685173	−	0.593706i
$585$	−9.43104	+	14.6750i	−0.389926	+	0.606736i
$586$	−1.06944	+	7.43812i	−0.0441782	+	0.307266i
$587$	19.4940	+	2.80282i	0.804604	+	0.115685i	0.532332	−	0.846536i	$-0.321316\pi$
$587$	19.4940	+	2.80282i	0.804604	+	0.115685i	0.272272	+	0.962220i	$0.412225\pi$
$588$	8.14286	−	5.13316i	0.335806	−	0.211688i
$589$	−2.48179	+	2.15048i	−0.102260	+	0.0886092i
$590$	2.49966	−	1.14156i	0.102909	−	0.0469972i
$591$	−4.12858	−	6.42419i	−0.169827	−	0.264256i
$592$	−0.755571	+	2.57324i	−0.0310538	+	0.105759i
$593$	−2.43616	−	2.11095i	−0.100041	−	0.0866862i	0.603404	−	0.797435i	$-0.293811\pi$
$593$	−2.43616	−	2.11095i	−0.100041	−	0.0866862i	−0.703445	+	0.710749i	$0.748356\pi$
$594$	1.84970	−	0.543122i	0.0758943	−	0.0222846i
$595$	−20.2409	+	26.7939i	−0.829796	+	1.09844i
$596$	12.7197	−	1.82881i	0.521018	−	0.0749111i
$597$		−	19.0336i		−	0.778992i
$598$	−23.0085	+	9.88844i	−0.940888	+	0.404368i
$599$	24.4125			0.997470			0.498735	−	0.866755i	$-0.333798\pi$
$599$	24.4125			0.997470			0.498735	+	0.866755i	$0.333798\pi$
$600$	−5.21154	+	0.749306i	−0.212760	+	0.0305903i
$601$	1.89522	+	0.865518i	0.0773076	+	0.0353052i	0.453694	−	0.891158i	$-0.350106\pi$
$601$	1.89522	+	0.865518i	0.0773076	+	0.0353052i	−0.376386	+	0.926463i	$0.622833\pi$
$602$	−1.21955	−	18.1662i	−0.0497051	−	0.740398i
$603$	−4.30348	−	3.72898i	−0.175251	−	0.151856i
$604$	30.4527	+	8.94173i	1.23910	+	0.363834i
$605$	−11.2247	+	7.21370i	−0.456350	+	0.293278i
$606$	−0.122923	−	0.269163i	−0.00499340	−	0.0109340i
$607$	−34.7856	+	30.1419i	−1.41190	+	1.22342i	−0.472172	+	0.881506i	$0.656530\pi$
$607$	−34.7856	+	30.1419i	−1.41190	+	1.22342i	−0.939731	+	0.341915i	$0.888925\pi$
$608$	41.7571	+	26.8357i	1.69348	+	1.08833i
$609$	13.9691	+	5.27981i	0.566055	+	0.213949i
$610$	−1.53636	+	10.6856i	−0.0622054	+	0.432648i
$611$	57.0023	+	36.6332i	2.30607	+	1.48202i
$612$	−4.32807	−	4.99486i	−0.174952	−	0.201905i
$613$	8.43175	−	3.85065i	0.340555	−	0.155526i	−0.237794	−	0.971316i	$-0.576424\pi$
$613$	8.43175	−	3.85065i	0.340555	−	0.155526i	0.578349	+	0.815789i	$0.303697\pi$
$614$	−6.99324	−	10.8817i	−0.282224	−	0.439150i
$615$	12.5966	+	3.69870i	0.507945	+	0.149146i
$616$	−10.2561	−	13.8259i	−0.413228	−	0.557063i
$617$	−0.103415	−	0.352200i	−0.00416335	−	0.0141791i	0.957385	−	0.288814i	$-0.0932610\pi$
$617$	−0.103415	−	0.352200i	−0.00416335	−	0.0141791i	−0.961548	+	0.274635i	$0.911443\pi$
$618$	−2.78973	−	1.27403i	−0.112220	−	0.0512490i
$619$	−2.99840	−	20.8543i	−0.120516	−	0.838207i	−0.956974	−	0.290175i	$-0.906286\pi$
$619$	−2.99840	−	20.8543i	−0.120516	−	0.838207i	0.836458	−	0.548032i	$-0.184623\pi$
$620$		−	1.40369i		−	0.0563735i
$621$	−4.31653	−	2.08987i	−0.173216	−	0.0838636i
$622$		−	18.1907i		−	0.729382i
$623$	0.418425	−	5.51193i	0.0167638	−	0.220831i
$624$	−1.75942	+	3.85259i	−0.0704331	+	0.154227i
$625$	29.7181	−	8.72602i	1.18872	−	0.349041i
$626$	−11.8415	+	13.6658i	−0.473280	+	0.546195i
$627$	−19.8782	−	5.83677i	−0.793860	−	0.233098i
$628$	3.62162	−	2.32747i	0.144518	−	0.0928762i
$629$	18.2874	−	8.35158i	0.729167	−	0.332999i
$630$	−2.62569	−	4.85892i	−0.104610	−	0.193584i
$631$	3.52841	−	5.49031i	0.140464	−	0.218566i	−0.763893	−	0.645343i	$-0.776715\pi$
$631$	3.52841	−	5.49031i	0.140464	−	0.218566i	0.904357	+	0.426777i	$0.140351\pi$
$632$	−16.5212	−	2.37539i	−0.657179	−	0.0944880i
$633$	−4.09821	−	0.589234i	−0.162889	−	0.0234199i
$634$	7.01263	+	4.50674i	0.278507	+	0.178986i
$635$	16.8476	+	19.4431i	0.668575	+	0.771576i
$636$	−5.09173	−	11.1493i	−0.201900	−	0.442100i
$637$	6.18072	+	45.8259i	0.244889	+	1.81569i
$638$	3.06558	−	10.4404i	0.121367	−	0.413339i
$639$	1.44752	−	1.67053i	0.0572631	−	0.0660851i
$640$	−22.9261	+	6.73170i	−0.906232	+	0.266094i
$641$	34.4434	+	15.7298i	1.36043	+	0.621288i	0.956023	−	0.293290i	$-0.0947502\pi$
$641$	34.4434	+	15.7298i	1.36043	+	0.621288i	0.404408	+	0.914579i	$0.367477\pi$
$642$	0.595285	+	4.14030i	0.0234940	+	0.163405i
$643$	−43.3063			−1.70783			−0.853917	−	0.520409i	$-0.825780\pi$
$643$	−43.3063			−1.70783			−0.853917	+	0.520409i	$0.825780\pi$
$644$	−1.71170	+	17.3640i	−0.0674503	+	0.684239i
$645$	22.9886			0.905174
$646$	−4.59342	−	31.9480i	−0.180726	−	1.25698i
$647$	−38.7370	−	17.6906i	−1.52291	−	0.695489i	−0.534202	−	0.845357i	$-0.679388\pi$
$647$	−38.7370	−	17.6906i	−1.52291	−	0.695489i	−0.988706	+	0.149869i	$0.952115\pi$
$648$	2.55995	−	0.751669i	0.100564	−	0.0295283i
$649$	−2.10232	+	2.42621i	−0.0825233	+	0.0952369i
$650$	2.90326	−	9.88759i	0.113875	−	0.387823i
$651$	0.959795	−	0.353218i	0.0376173	−	0.0138437i
$652$	3.51288	+	7.69214i	0.137575	+	0.301248i
$653$	26.3961	+	30.4627i	1.03296	+	1.19210i	0.981112	+	0.193442i	$0.0619650\pi$
$653$	26.3961	+	30.4627i	1.03296	+	1.19210i	0.0518458	+	0.998655i	$0.483490\pi$
$654$	−3.64912	−	2.34515i	−0.142692	−	0.0917025i
$655$	−24.4292	−	3.51238i	−0.954526	−	0.137240i
$656$	3.15504	+	0.453627i	0.123184	+	0.0177111i
$657$	−4.43964	+	6.90821i	−0.173207	+	0.269515i
$658$	−18.8736	+	10.1990i	−0.735769	+	0.397599i
$659$	30.8066	−	14.0689i	1.20005	−	0.548047i	0.287808	−	0.957688i	$-0.407073\pi$
$659$	30.8066	−	14.0689i	1.20005	−	0.548047i	0.912247	+	0.409641i	$0.134346\pi$
$660$	7.44983	−	4.78771i	0.289984	−	0.186361i
$661$	2.01959	+	0.593006i	0.0785531	+	0.0230653i	0.320773	−	0.947156i	$-0.396057\pi$
$661$	2.01959	+	0.593006i	0.0785531	+	0.0230653i	−0.242220	+	0.970221i	$0.577876\pi$
$662$	10.8197	−	12.4866i	0.420518	−	0.485304i
$663$	30.4633	−	8.94484i	1.18310	−	0.347389i
$664$	4.01774	−	8.79761i	0.155918	−	0.341414i
$665$	−4.49278	+	59.1836i	−0.174222	+	2.29504i
$666$			3.30659i			0.128128i
$667$	−23.0956	+	14.1190i	−0.894265	+	0.546688i
$668$			13.9832i			0.541025i
$669$	1.49958	+	10.4298i	0.0579771	+	0.403240i
$670$	10.8126	+	4.93797i	0.417729	+	0.190770i
$671$	−3.55316	−	12.1009i	−0.137168	−	0.467152i
$672$	−9.20997	−	12.4157i	−0.355282	−	0.478948i
$673$	−33.5832	−	9.86091i	−1.29454	−	0.380110i	−0.439297	−	0.898342i	$-0.644772\pi$
$673$	−33.5832	−	9.86091i	−1.29454	−	0.380110i	−0.855240	+	0.518232i	$0.826590\pi$
$674$	1.15389	+	1.79549i	0.0444461	+	0.0691595i
$675$	1.79509	−	0.819788i	0.0690929	−	0.0315536i
$676$	−27.5889	−	31.8393i	−1.06111	−	1.22459i
$677$	−1.24094	−	0.797505i	−0.0476933	−	0.0306506i	0.516577	−	0.856241i	$-0.327206\pi$
$677$	−1.24094	−	0.797505i	−0.0476933	−	0.0306506i	−0.564270	+	0.825590i	$0.690842\pi$
$678$	1.17125	−	8.14619i	0.0449814	−	0.312852i
$679$	5.19803	−	13.7527i	0.199482	−	0.527781i
$680$	28.4870	+	18.3075i	1.09243	+	0.702060i
$681$	−17.6374	+	15.2829i	−0.675868	+	0.585643i
$682$	−0.309566	−	0.677854i	−0.0118539	−	0.0259564i
$683$	38.0520	−	24.4545i	1.45602	−	0.935726i	0.457091	−	0.889420i	$-0.348892\pi$
$683$	38.0520	−	24.4545i	1.45602	−	0.935726i	0.998927	−	0.0463057i	$-0.0147448\pi$
$684$	−11.2087	−	3.29118i	−0.428577	−	0.125841i
$685$	−31.5776	−	27.3622i	−1.20652	−	1.04545i
$686$	−13.6490	−	5.29553i	−0.521120	−	0.202184i
$687$	24.0435	+	10.9803i	0.917317	+	0.418925i
$688$	5.52465	−	0.794325i	0.210625	−	0.0302834i
$689$	58.8808			2.24318
$690$	9.87480	+	1.64726i	0.375927	+	0.0627100i
$691$			21.3664i			0.812815i	0.913692	+	0.406408i	$0.133219\pi$
$691$			21.3664i			0.812815i	−0.913692	+	0.406408i	$0.866781\pi$
$692$	−20.9010	+	3.00511i	−0.794536	+	0.114237i
$693$	5.14832	+	3.88918i	0.195568	+	0.147738i
$694$	−4.27855	+	1.25630i	−0.162412	+	0.0476884i
$695$	10.8400	+	9.39290i	0.411184	+	0.356293i
$696$	4.24269	−	14.4493i	0.160819	−	0.547698i
$697$	−12.9183	−	20.1013i	−0.489316	−	0.761390i
$698$	22.4628	−	10.2584i	0.850229	−	0.388287i
$699$	11.3288	−	9.81642i	0.428493	−	0.371291i
$700$	−5.05459	−	5.09893i	−0.191045	−	0.192722i
$701$	−20.6740	−	2.97248i	−0.780847	−	0.112269i	−0.259647	−	0.965703i	$-0.583606\pi$
$701$	−20.6740	−	2.97248i	−0.780847	−	0.112269i	−0.521200	+	0.853435i	$0.674515\pi$
$702$	−0.743156	+	5.16876i	−0.0280486	+	0.195082i
$703$	19.2117	−	29.8939i	0.724582	−	1.12747i
$704$	−6.14932	+	5.32841i	−0.231761	+	0.200822i
$705$	−11.2523	−	24.6392i	−0.423788	−	0.927966i
$706$	12.7969	+	19.9123i	0.481616	+	0.749410i
$707$	0.478426	−	0.867146i	0.0179931	−	0.0326124i
$708$	−1.18543	+	1.36806i	−0.0445514	+	0.0514150i
$709$	−4.32143	−	14.7174i	−0.162295	−	0.552725i	−0.999978	−	0.00656924i	$-0.997909\pi$
$709$	−4.32143	−	14.7174i	−0.162295	−	0.552725i	0.837684	−	0.546156i	$-0.183909\pi$
$710$	−1.91683	+	4.19726i	−0.0719372	+	0.157521i
$711$	6.19230	−	0.890319i	0.232230	−	0.0333896i
$712$	−5.57432			−0.208907
$713$	−0.562162	+	1.76656i	−0.0210531	+	0.0661581i
$714$	−2.17961	+	9.81298i	−0.0815699	+	0.367242i
$715$	6.05424	+	42.1082i	0.226416	+	1.57476i
$716$	−12.3112	+	26.9577i	−0.460091	+	1.00746i
$717$	−0.338103	−	1.15147i	−0.0126267	−	0.0430026i
$718$	18.9086	+	16.3844i	0.705664	+	0.611462i
$719$	−0.362506	+	1.23458i	−0.0135192	+	0.0460421i	−0.965976	−	0.258630i	$-0.916729\pi$
$719$	−0.362506	+	1.23458i	−0.0135192	+	0.0460421i	0.952457	+	0.304673i	$0.0985470\pi$
$720$	1.42432	−	0.915358i	0.0530814	−	0.0341134i
$721$	−2.13808	−	10.0395i	−0.0796264	−	0.373891i
$722$	−27.5241	−	31.7646i	−1.02434	−	1.18215i
$723$	−2.06394	+	3.21155i	−0.0767588	+	0.119439i
$724$	3.33949	−	23.2266i	0.124111	−	0.863211i
$725$	1.58520	−	11.0253i	0.0588728	−	0.409470i
$726$	−2.15942	+	3.36012i	−0.0801435	+	0.124706i
$727$	13.7409	+	15.8579i	0.509623	+	0.588136i	0.951002	−	0.309185i	$-0.100056\pi$
$727$	13.7409	+	15.8579i	0.509623	+	0.588136i	−0.441379	+	0.897321i	$0.645511\pi$
$728$	45.6073	−	9.71285i	1.69032	−	0.359982i
$729$	−0.841254	+	0.540641i	−0.0311575	+	0.0200237i
$730$	4.82948	−	16.4477i	0.178747	−	0.608757i
$731$	−31.6209	−	27.3997i	−1.16954	−	1.01341i
$732$	−2.00352	−	6.82335i	−0.0740521	−	0.252198i
$733$	7.39175	−	16.1857i	0.273021	−	0.597832i	−0.722605	−	0.691261i	$-0.757056\pi$
$733$	7.39175	−	16.1857i	0.273021	−	0.597832i	0.995626	+	0.0934291i	$0.0297828\pi$
$734$	−1.69497	−	11.7888i	−0.0625624	−	0.435131i
$735$	7.82555	−	16.7469i	0.288650	−	0.617718i
$736$	28.0144	+	0.630217i	1.03262	+	0.0232301i
$737$	−13.8867			−0.511525
$738$	3.88998	−	0.559295i	0.143192	−	0.0205879i
$739$	13.3510	−	29.2347i	0.491126	−	1.07542i	−0.488127	−	0.872773i	$-0.662320\pi$
$739$	13.3510	−	29.2347i	0.491126	−	1.07542i	0.979253	−	0.202643i	$-0.0649531\pi$
$740$	4.27934	+	14.5741i	0.157312	+	0.535754i
$741$	36.7497	−	42.4114i	1.35003	−	1.55802i
$742$	−9.00562	+	16.3227i	−0.330607	+	0.599224i
$743$	−20.8474	−	32.4392i	−0.764816	−	1.19008i	−0.977082	−	0.212865i	$-0.931721\pi$
$743$	−20.8474	−	32.4392i	−0.764816	−	1.19008i	0.212266	−	0.977212i	$-0.431916\pi$
$744$	−0.428432	−	0.938136i	−0.0157071	−	0.0343937i
$745$	18.6501	−	16.1604i	0.683288	−	0.592073i
$746$	−9.78043	+	15.2186i	−0.358087	+	0.557194i
$747$	−0.515893	+	3.58812i	−0.0188755	+	0.131282i
$748$	−15.9537	−	2.29379i	−0.583324	−	0.0838693i
$749$	−9.94250	+	9.85603i	−0.363291	+	0.360132i
$750$	4.77480	−	4.13738i	0.174351	−	0.151076i
$751$	17.5163	−	7.99941i	0.639178	−	0.291903i	−0.0693429	−	0.997593i	$-0.522090\pi$
$751$	17.5163	−	7.99941i	0.639178	−	0.291903i	0.708520	+	0.705690i	$0.249363\pi$
$752$	−3.55554	−	5.53253i	−0.129657	−	0.201751i
$753$	3.83230	−	13.0516i	0.139657	−	0.475627i
$754$	22.2752	+	19.3016i	0.811216	+	0.702922i
$755$	58.4806	−	17.1715i	2.12833	−	0.624933i
$756$	2.90298	+	2.19299i	0.105580	+	0.0797583i
$757$	32.2824	−	4.64151i	1.17332	−	0.168698i	0.472037	−	0.881579i	$-0.343519\pi$
$757$	32.2824	−	4.64151i	1.17332	−	0.168698i	0.701286	+	0.712880i	$0.252610\pi$
$758$			17.8160i			0.647107i
$759$	−11.2931	+	3.04181i	−0.409914	+	0.110411i
$760$	59.8535			2.17111
$761$	29.5147	−	4.24358i	1.06991	−	0.153830i	0.415214	−	0.909724i	$-0.363707\pi$
$761$	29.5147	−	4.24358i	1.06991	−	0.153830i	0.654694	+	0.755894i	$0.272798\pi$
$762$	7.00539	+	3.19925i	0.253779	+	0.115897i
$763$	−0.972453	−	14.4855i	−0.0352051	−	0.524409i
$764$	−13.2686	−	11.4973i	−0.480041	−	0.415958i
$765$	−12.1779	−	3.57575i	−0.440293	−	0.129282i
$766$	17.7949	−	11.4361i	0.642956	−	0.413203i
$767$	−3.61244	−	7.91015i	−0.130438	−	0.285619i
$768$	−10.4487	+	9.05386i	−0.377035	+	0.326703i
$769$	−1.46887	−	0.943988i	−0.0529689	−	0.0340411i	0.513888	−	0.857857i	$-0.328205\pi$
$769$	−1.46887	−	0.943988i	−0.0529689	−	0.0340411i	−0.566857	+	0.823816i	$0.691841\pi$
$770$	−12.5990	−	4.76197i	−0.454037	−	0.171610i
$771$	0.212697	−	1.47934i	0.00766009	−	0.0532771i
$772$	−11.2945	−	7.25853i	−0.406498	−	0.261240i
$773$	−8.82254	−	10.1818i	−0.317325	−	0.366212i	0.574570	−	0.818456i	$-0.305169\pi$
$773$	−8.82254	−	10.1818i	−0.317325	−	0.366212i	−0.891895	+	0.452243i	$0.850624\pi$
$774$	6.25974	−	2.85873i	0.225002	−	0.102755i
$775$	−0.412419	−	0.641736i	−0.0148145	−	0.0230518i
$776$	−14.2255	−	4.17698i	−0.510665	−	0.149945i
$777$	−8.88843	+	6.59342i	−0.318871	+	0.236538i
$778$	−0.494670	−	1.68469i	−0.0177348	−	0.0603991i
$779$	−38.4178	−	17.5448i	−1.37646	−	0.628608i
$780$	3.41380	+	23.7435i	0.122234	+	0.850155i
$781$		−	5.39057i		−	0.192890i
$782$	−11.6195	−	14.0354i	−0.415513	−	0.501906i
$783$			5.64436i			0.201713i
$784$	1.30199	−	4.29504i	0.0464998	−	0.153394i
$785$	3.43434	−	7.52015i	0.122577	−	0.268406i
$786$	−7.08879	+	2.08146i	−0.252849	+	0.0742431i
$787$	−14.8435	+	17.1303i	−0.529112	+	0.610628i	−0.955889	−	0.293729i	$-0.905104\pi$
$787$	−14.8435	+	17.1303i	−0.529112	+	0.610628i	0.426776	+	0.904357i	$0.359649\pi$
$788$	−10.0756	−	2.95846i	−0.358929	−	0.105391i
$789$	−17.3712	+	11.1638i	−0.618430	+	0.397441i
$790$	−11.8792	+	5.42503i	−0.422642	+	0.193014i
$791$	24.2332	−	13.0953i	0.861634	−	0.465614i
$792$	3.51769	−	5.47363i	0.124996	−	0.194497i
$793$	33.8145	+	4.86179i	1.20079	+	0.172647i
$794$	−17.1605	−	2.46731i	−0.609005	−	0.0875616i
$795$	−19.8014	−	12.7256i	−0.702283	−	0.451330i
$796$	−17.1398	−	19.7804i	−0.607505	−	0.701098i
$797$	18.3821	+	40.2513i	0.651129	+	1.42577i	0.890562	+	0.454861i	$0.150311\pi$
$797$	18.3821	+	40.2513i	0.651129	+	1.42577i	−0.239433	+	0.970913i	$0.576962\pi$
$798$	6.13636	+	16.6743i	0.217225	+	0.590263i
$799$	−13.8894	+	47.3028i	−0.491370	+	1.67345i
$800$	−7.55083	+	8.71413i	−0.266962	+	0.308091i
$801$	2.00468	−	0.588626i	0.0708318	−	0.0207981i
$802$	16.9359	+	7.73435i	0.598026	+	0.273110i
$803$	2.85002	+	19.8223i	0.100575	+	0.699515i
$804$	−7.83031			−0.276154
$805$	15.2626	+	29.8291i	0.537936	+	1.05134i
$806$	2.01855			0.0711004
$807$	0.359691	+	2.50171i	0.0126617	+	0.0880643i
$808$	−0.908456	−	0.414878i	−0.0319594	−	0.0145954i
$809$	−29.4872	+	8.65823i	−1.03672	+	0.304407i	−0.755438	−	0.655220i	$-0.772576\pi$
$809$	−29.4872	+	8.65823i	−1.03672	+	0.304407i	−0.281277	+	0.959627i	$0.590758\pi$
$810$	1.36702	−	1.57762i	0.0480320	−	0.0554319i
$811$	−5.28421	+	17.9964i	−0.185554	+	0.631938i	0.813198	+	0.581987i	$0.197725\pi$
$811$	−5.28421	+	17.9964i	−0.185554	+	0.631938i	−0.998752	+	0.0499510i	$0.984093\pi$
$812$	19.2717	−	7.09225i	0.676304	−	0.248889i
$813$	8.22202	+	18.0037i	0.288359	+	0.631418i
$814$	5.28066	+	6.09421i	0.185087	+	0.213602i
$815$	13.6614	+	8.77962i	0.478537	+	0.307537i
$816$	−3.05017	−	0.438548i	−0.106777	−	0.0153522i
$817$	−73.2020	−	10.5249i	−2.56101	−	0.368218i
$818$	−3.75497	+	5.84285i	−0.131289	+	0.204290i
$819$	−15.3760	+	8.30895i	−0.537280	+	0.290338i
$820$	16.4216	−	7.49949i	0.573467	−	0.261894i
$821$	−6.75065	+	4.33838i	−0.235599	+	0.151411i	−0.653114	−	0.757260i	$-0.726538\pi$
$821$	−6.75065	+	4.33838i	−0.235599	+	0.151411i	0.417514	+	0.908670i	$0.362901\pi$
$822$	−12.0011	−	3.52385i	−0.418588	−	0.122908i
$823$	11.8186	−	13.6394i	0.411970	−	0.475438i	−0.511404	−	0.859340i	$-0.670874\pi$
$823$	11.8186	−	13.6394i	0.411970	−	0.475438i	0.923374	+	0.383902i	$0.125420\pi$
$824$	−9.93178	+	2.91623i	−0.345990	+	0.101592i
$825$	1.99922	−	4.37768i	0.0696039	−	0.152411i
$826$	2.74533	+	0.208405i	0.0955221	+	0.00725133i
$827$			36.8948i			1.28296i	0.767140	+	0.641479i	$0.221679\pi$
$827$			36.8948i			1.28296i	−0.767140	+	0.641479i	$0.778321\pi$
$828$	−6.36785	+	1.71519i	−0.221298	+	0.0596069i
$829$		−	21.3480i		−	0.741448i	−0.928743	−	0.370724i	$-0.879110\pi$
$829$		−	21.3480i		−	0.741448i	0.928743	−	0.370724i	$-0.120890\pi$
$830$	−1.07692	−	7.49016i	−0.0373805	−	0.259987i
$831$	−7.14703	−	3.26394i	−0.247928	−	0.113225i
$832$	−6.20948	−	21.1475i	−0.215275	−	0.733159i
$833$	−30.7244	+	13.7083i	−1.06454	+	0.474965i
$834$	4.11975	+	1.20967i	0.142655	+	0.0418874i
$835$	14.5178	+	22.5901i	0.502408	+	0.781762i
$836$	−25.9143	+	11.8347i	−0.896264	+	0.409310i
$837$	0.253139	+	0.292138i	0.00874977	+	0.0100978i
$838$	16.9999	+	10.9252i	0.587252	+	0.377404i
$839$	4.74778	−	33.0215i	0.163911	−	1.14003i	−0.727260	−	0.686362i	$-0.759206\pi$
$839$	4.74778	−	33.0215i	0.163911	−	1.14003i	0.891171	−	0.453667i	$-0.149884\pi$
$840$	−17.4368	−	6.59046i	−0.601625	−	0.227393i
$841$	2.40495	+	1.54557i	0.0829294	+	0.0532955i
$842$	23.4507	−	20.3201i	0.808163	−	0.700277i
$843$	−1.01310	−	2.21839i	−0.0348932	−	0.0764054i
$844$	−4.78963	+	3.07811i	−0.164866	+	0.105953i
$845$	−77.6269	−	22.7933i	−2.67045	−	0.784114i
$846$	−6.12798	−	5.30993i	−0.210684	−	0.182559i
$847$	−13.3382	+	0.895437i	−0.458308	+	0.0307676i
$848$	−5.19841	−	2.37404i	−0.178514	−	0.0815247i
$849$	28.7568	−	4.13460i	0.986930	−	0.141899i
$850$	7.49771			0.257169
$851$	0.451173	−	20.0555i	0.0154660	−	0.687493i
$852$		−	3.03958i		−	0.104134i
$853$	−5.51588	+	0.793064i	−0.188860	+	0.0271540i	−0.236096	−	0.971730i	$-0.575868\pi$
$853$	−5.51588	+	0.793064i	−0.188860	+	0.0271540i	0.0472357	+	0.998884i	$0.484959\pi$
$854$	−6.51958	+	8.63031i	−0.223095	+	0.295323i
$855$	−21.5249	+	6.32029i	−0.736137	+	0.216149i
$856$	10.6694	+	9.24510i	0.364673	+	0.315991i
$857$	0.216738	−	0.738142i	0.00740364	−	0.0252145i	−0.955708	−	0.294315i	$-0.904908\pi$
$857$	0.216738	−	0.738142i	0.00740364	−	0.0252145i	0.963112	+	0.269101i	$0.0867265\pi$
$858$	6.88489	+	10.7131i	0.235046	+	0.365739i
$859$	−15.5140	+	7.08500i	−0.529330	+	0.241737i	−0.662108	−	0.749409i	$-0.730338\pi$
$859$	−15.5140	+	7.08500i	−0.529330	+	0.241737i	0.132777	+	0.991146i	$0.457611\pi$
$860$	23.8906	−	20.7013i	0.814663	−	0.705910i
$861$	9.26015	+	9.34139i	0.315585	+	0.318354i
$862$	3.82466	+	0.549902i	0.130268	+	0.0187298i
$863$	4.29685	−	29.8853i	0.146267	−	1.01731i	−0.775995	−	0.630740i	$-0.782752\pi$
$863$	4.29685	−	29.8853i	0.146267	−	1.01731i	0.922261	−	0.386567i	$-0.126339\pi$
$864$	3.15890	−	4.91534i	0.107468	−	0.167223i
$865$	−30.6460	+	26.5549i	−1.04199	+	0.902893i
$866$	−3.32486	−	7.28044i	−0.112984	−	0.247399i
$867$	3.29799	+	5.13178i	0.112006	+	0.174284i
$868$	0.679381	−	1.23138i	0.0230597	−	0.0417957i
$869$	9.99087	−	11.5301i	0.338917	−	0.391131i
$870$	−3.31953	−	11.3053i	−0.112542	−	0.383284i
$871$	15.6261	−	34.2165i	0.529471	−	1.15938i
$872$	−14.4913	+	2.08353i	−0.490736	+	0.0705572i
$873$	5.55694			0.188074
$874$	−30.6900	−	9.76631i	−1.03810	−	0.330350i
$875$	20.6427	+	4.58506i	0.697852	+	0.155003i
$876$	1.60704	+	11.1772i	0.0542968	+	0.377643i
$877$	−6.17065	+	13.5118i	−0.208368	+	0.456262i	−0.984744	−	0.174007i	$-0.944328\pi$
$877$	−6.17065	+	13.5118i	−0.208368	+	0.456262i	0.776376	+	0.630270i	$0.217056\pi$
$878$	0.692129	+	2.35717i	0.0233582	+	0.0795508i
$879$	−7.18427	−	6.22520i	−0.242319	−	0.209971i
$880$	1.16326	−	3.96171i	0.0392136	−	0.133549i
$881$	19.6131	−	12.6046i	0.660783	−	0.424659i	−0.166809	−	0.985989i	$-0.553346\pi$
$881$	19.6131	−	12.6046i	0.660783	−	0.424659i	0.827592	+	0.561330i	$0.189710\pi$
$882$	0.0483334	−	5.53329i	0.00162747	−	0.186315i
$883$	−0.344046	−	0.397050i	−0.0115781	−	0.0133618i	0.749931	−	0.661516i	$-0.230087\pi$
$883$	−0.344046	−	0.397050i	−0.0115781	−	0.0133618i	−0.761509	+	0.648154i	$0.775541\pi$
$884$	23.6038	−	36.7282i	0.793881	−	1.23530i
$885$	−0.494725	+	3.44089i	−0.0166300	+	0.115664i
$886$	−1.81560	+	12.6278i	−0.0609964	+	0.424239i
$887$	−1.29078	+	2.00850i	−0.0433403	+	0.0674388i	−0.862248	−	0.506487i	$-0.830944\pi$
$887$	−1.29078	+	2.00850i	−0.0433403	+	0.0674388i	0.818907	+	0.573926i	$0.194580\pi$
$888$	7.30832	+	8.43425i	0.245251	+	0.283035i
$889$	5.36901	+	25.2105i	0.180071	+	0.845534i
$890$	−3.66905	+	2.35796i	−0.122987	+	0.0790389i
$891$	−0.687062	+	2.33992i	−0.0230174	+	0.0783902i
$892$	10.9505	+	9.48868i	0.366651	+	0.317705i
$893$	24.5500	+	83.6097i	0.821535	+	2.79789i
$894$	3.06878	−	6.71968i	0.102635	−	0.224740i
$895$	8.09941	+	56.3326i	0.270733	+	1.88299i
$896$	−23.3699	−	5.19081i	−0.780733	−	0.173413i
$897$	5.21272	−	31.2487i	0.174048	−	1.04336i
$898$	−19.5470			−0.652291
$899$	2.15964	−	0.310510i	0.0720281	−	0.0103561i
$900$	1.12730	−	2.46844i	0.0375766	−	0.0822813i
$901$	12.0695	+	41.1050i	0.402094	+	1.36941i
$902$	6.27623	−	7.24315i	0.208975	−	0.241171i
$903$	20.1666	+	11.1264i	0.671102	+	0.370264i
$904$	−15.0174	−	23.3675i	−0.499471	−	0.777192i
$905$	−18.7196	−	40.9903i	−0.622261	−	1.36256i
$906$	13.7888	−	11.9481i	0.458102	−	0.396948i
$907$	−3.23712	+	5.03706i	−0.107487	+	0.167253i	−0.890830	−	0.454337i	$-0.849876\pi$
$907$	−3.23712	+	5.03706i	−0.107487	+	0.167253i	0.783343	+	0.621589i	$0.213513\pi$
$908$	−4.56715	+	31.7652i	−0.151566	+	1.05417i
$909$	0.370515	+	0.0532720i	0.0122892	+	0.00176692i
$910$	25.9104	−	25.6851i	0.858923	−	0.851453i
$911$	−8.96076	+	7.76454i	−0.296883	+	0.257251i	−0.790546	−	0.612403i	$-0.790203\pi$
$911$	−8.96076	+	7.76454i	−0.296883	+	0.257251i	0.493663	+	0.869653i	$0.335658\pi$
$912$	−4.95452	+	2.26266i	−0.164061	+	0.0749240i
$913$	4.77944	+	7.43696i	0.158176	+	0.246127i
$914$	2.78919	−	9.49911i	0.0922583	−	0.314203i
$915$	−10.3209	−	8.94315i	−0.341200	−	0.295651i
$916$	34.8748	−	10.2402i	1.15229	−	0.338344i
$917$	−19.7304	−	14.9049i	−0.651554	−	0.492202i
$918$	−3.76068	+	0.540704i	−0.124121	+	0.0178459i
$919$		−	17.4896i		−	0.576929i	−0.957491	−	0.288465i	$-0.906855\pi$
$919$		−	17.4896i		−	0.576929i	0.957491	−	0.288465i	$-0.0931447\pi$
$920$	28.8288	−	17.6238i	0.950459	−	0.581041i
$921$	16.3632			0.539186
$922$	−6.18316	+	0.889003i	−0.203631	+	0.0292778i
$923$	13.2822	+	6.06577i	0.437189	+	0.199657i
$924$	8.85256	−	0.594299i	0.291228	−	0.0195510i
$925$	6.23844	+	5.40564i	0.205119	+	0.177736i
$926$	30.9475	+	9.08701i	1.01700	+	0.298618i
$927$	3.26379	−	2.09751i	0.107197	−	0.0688913i
$928$	−13.7001	−	29.9990i	−0.449727	−	0.984766i
$929$	43.5530	−	37.7389i	1.42893	−	1.23817i	0.500984	−	0.865457i	$-0.332972\pi$
$929$	43.5530	−	37.7389i	1.42893	−	1.23817i	0.927945	−	0.372717i	$-0.121574\pi$
$930$	−0.678831	−	0.436258i	−0.0222597	−	0.0143055i
$931$	−32.5860	+	49.7440i	−1.06796	+	1.63029i
$932$	2.93354	−	20.4032i	0.0960913	−	0.668329i
$933$	19.3587	+	12.4411i	0.633774	+	0.407302i
$934$	−1.44480	−	1.66739i	−0.0472754	−	0.0545588i
$935$	−28.1550	+	12.8579i	−0.920765	+	0.420499i
$936$	9.52854	+	14.8267i	0.311450	+	0.484626i
$937$	21.7658	+	6.39102i	0.711059	+	0.208786i	0.617207	−	0.786801i	$-0.288264\pi$
$937$	21.7658	+	6.39102i	0.711059	+	0.208786i	0.0938514	+	0.995586i	$0.470082\pi$
$938$	7.09537	+	9.56509i	0.231672	+	0.312311i
$939$	−6.44454	−	21.9481i	−0.210310	−	0.716249i
$940$	−33.8816	−	15.4732i	−1.10510	−	0.504681i
$941$	4.85042	+	33.7354i	0.158119	+	1.09974i	0.902095	+	0.431537i	$0.142028\pi$
$941$	4.85042	+	33.7354i	0.158119	+	1.09974i	−0.743976	+	0.668206i	$0.767062\pi$
$942$		−	2.47480i		−	0.0806332i
$943$	−23.6702	+	2.86152i	−0.770809	+	0.0931839i
$944$			0.844015i			0.0274704i
$945$	6.96665	+	0.528856i	0.226625	+	0.0172037i
$946$	6.97159	−	15.2656i	0.226666	−	0.496329i
$947$	−43.4646	+	12.7624i	−1.41241	+	0.414721i	−0.896927	−	0.442179i	$-0.854206\pi$
$947$	−43.4646	+	12.7624i	−1.41241	+	0.414721i	−0.515483	+	0.856900i	$0.672387\pi$
$948$	5.63355	−	6.50146i	0.182969	−	0.211158i
$949$	−52.0486	−	15.2828i	−1.68957	−	0.496102i
$950$	11.1487	−	7.16485i	0.361712	−	0.232458i
$951$	−9.59219	+	4.38061i	−0.311048	+	0.142051i
$952$	16.1293	+	29.8478i	0.522754	+	0.967372i
$953$	15.4780	−	24.0843i	0.501382	−	0.780166i	−0.494656	−	0.869089i	$-0.664706\pi$
$953$	15.4780	−	24.0843i	0.501382	−	0.780166i	0.996039	+	0.0889226i	$0.0283424\pi$
$954$	−6.97436	−	1.00276i	−0.225803	−	0.0324656i
$955$	−33.3725	−	4.79825i	−1.07991	−	0.155268i
$956$	−1.38828	−	0.892193i	−0.0449002	−	0.0288556i
$957$	9.01410	+	10.4028i	0.291384	+	0.336276i
$958$	−6.28557	−	13.7635i	−0.203077	−	0.444677i
$959$	−14.4581	−	39.2868i	−0.466876	−	1.26864i
$960$	−2.48228	+	8.45385i	−0.0801151	+	0.272847i
$961$	−20.2028	+	23.3153i	−0.651704	+	0.752107i
$962$	−20.9580	+	6.15383i	−0.675714	+	0.198408i
$963$	−4.81326	−	2.19814i	−0.155105	−	0.0708341i
$964$	0.747095	+	5.19616i	0.0240623	+	0.167357i
$965$	−25.7825			−0.829968
$966$	7.86535	+	6.22443i	0.253064	+	0.200268i
$967$	−14.5596			−0.468205			−0.234103	−	0.972212i	$-0.575215\pi$
$967$	−14.5596			−0.468205			−0.234103	+	0.972212i	$0.575215\pi$
$968$	1.91852	+	13.3436i	0.0616635	+	0.428879i
$969$	37.1407	+	16.9616i	1.19313	+	0.544885i
$970$	−11.1302	+	3.26811i	−0.357368	+	0.104933i
$971$	−0.125960	+	0.145366i	−0.00404226	+	0.00466501i	−0.757767	−	0.652525i	$-0.773710\pi$
$971$	−0.125960	+	0.145366i	−0.00404226	+	0.00466501i	0.753725	+	0.657190i	$0.228255\pi$
$972$	−0.387413	+	1.31941i	−0.0124263	+	0.0423201i
$973$	4.96318	+	13.4864i	0.159112	+	0.432354i
$974$	7.35136	+	16.0972i	0.235553	+	0.515789i
$975$	8.53682	+	9.85202i	0.273397	+	0.315517i
$976$	−2.78936	−	1.79261i	−0.0892852	−	0.0573801i
$977$	−16.2964	−	2.34306i	−0.521367	−	0.0749612i	−0.123393	−	0.992358i	$-0.539377\pi$
$977$	−16.2964	−	2.34306i	−0.521367	−	0.0749612i	−0.397974	+	0.917397i	$0.630287\pi$
$978$	4.81175	+	0.691825i	0.153863	+	0.0221221i
$979$	2.75467	−	4.28636i	0.0880397	−	0.136993i
$980$	−6.94805	−	24.4510i	−0.221947	−	0.781058i
$981$	4.99144	−	2.27951i	0.159364	−	0.0727792i
$982$	−6.43855	+	4.13781i	−0.205462	+	0.132043i
$983$	−2.07985	−	0.610699i	−0.0663369	−	0.0194783i	0.248396	−	0.968659i	$-0.420097\pi$
$983$	−2.07985	−	0.610699i	−0.0663369	−	0.0194783i	−0.314733	+	0.949180i	$0.601915\pi$
$984$	8.68616	−	10.0244i	0.276905	−	0.319565i
$985$	−19.3489	+	5.68135i	−0.616507	+	0.181023i
$986$	−8.90852	+	19.5069i	−0.283705	+	0.621228i
$987$	2.05425	−	27.0607i	0.0653874	−	0.861352i
$988$		−	77.1689i		−	2.45507i
$989$	−38.3573	+	16.4849i	−1.21969	+	0.524190i
$990$		−	5.09077i		−	0.161795i
$991$	4.49634	+	31.2728i	0.142831	+	0.993412i	0.927587	+	0.373607i	$0.121879\pi$
$991$	4.49634	+	31.2728i	0.142831	+	0.993412i	−0.784756	+	0.619805i	$0.787212\pi$
$992$	−2.05448	−	0.938251i	−0.0652299	−	0.0297895i
$993$	5.88844	+	20.0542i	0.186864	+	0.636400i
$994$	−3.71299	+	2.75429i	−0.117769	+	0.0873607i
$995$	−48.2264	−	14.1605i	−1.52888	−	0.448919i
$996$	2.69498	+	4.19347i	0.0853938	+	0.132875i
$997$	13.7583	−	6.28323i	0.435731	−	0.198992i	−0.185458	−	0.982652i	$-0.559377\pi$
$997$	13.7583	−	6.28323i	0.435731	−	0.198992i	0.621190	+	0.783660i	$0.286650\pi$
$998$	4.22904	+	4.88057i	0.133868	+	0.154492i
$999$	−3.51889	−	2.26146i	−0.111333	−	0.0715493i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.r.a.181.14	yes	320
7.6	odd	2	inner	483.2.r.a.181.13	✓	320
23.15	odd	22	inner	483.2.r.a.475.13	yes	320
161.153	even	22	inner	483.2.r.a.475.14	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.r.a.181.13	✓	320	7.6	odd	2	inner
483.2.r.a.181.14	yes	320	1.1	even	1	trivial
483.2.r.a.475.13	yes	320	23.15	odd	22	inner
483.2.r.a.475.14	yes	320	161.153	even	22	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.112500 - 0.782453i) q^{2} +(0.909632 + 0.415415i) q^{3} +(1.31941 - 0.387413i) q^{4} +(1.72931 - 1.99573i) q^{5} +(0.222709 - 0.758479i) q^{6} +(2.48295 - 0.913760i) q^{7} +(-1.10834 - 2.42692i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.112500 - 0.782453i) q^{2} +(0.909632 + 0.415415i) q^{3} +(1.31941 - 0.387413i) q^{4} +(1.72931 - 1.99573i) q^{5} +(0.222709 - 0.758479i) q^{6} +(2.48295 - 0.913760i) q^{7} +(-1.10834 - 2.42692i) q^{8} +(0.654861 + 0.755750i) q^{9} +(-1.75611 - 1.12858i) q^{10} +(2.41388 + 0.347064i) q^{11} +(1.36111 + 0.195699i) q^{12} +(-3.57139 + 5.55718i) q^{13} +(-0.994306 - 1.84000i) q^{14} +(2.40209 - 1.09700i) q^{15} +(0.539369 - 0.346631i) q^{16} +(-4.61157 - 1.35408i) q^{17} +(0.517667 - 0.597420i) q^{18} +(-8.15115 + 2.39339i) q^{19} +(1.50849 - 3.30313i) q^{20} +(2.63816 + 0.200270i) q^{21} -1.92779i q^{22} +(-3.22132 + 3.55290i) q^{23} -2.66802i q^{24} +(-0.280847 - 1.95333i) q^{25} +(4.75002 + 2.16926i) q^{26} +(0.281733 + 0.959493i) q^{27} +(2.92202 - 2.16755i) q^{28} +(5.41572 + 1.59020i) q^{29} +(-1.12858 - 1.75611i) q^{30} +(0.351622 - 0.160580i) q^{31} +(-3.82627 - 4.41575i) q^{32} +(2.05157 + 1.31846i) q^{33} +(-0.540704 + 3.76068i) q^{34} +(2.47017 - 6.53546i) q^{35} +(1.15682 + 0.743441i) q^{36} +(-3.16124 + 2.73923i) q^{37} +(2.78972 + 6.10864i) q^{38} +(-5.55718 + 3.57139i) q^{39} +(-6.76012 - 1.98495i) q^{40} +(3.75722 + 3.25565i) q^{41} +(-0.140091 - 2.08677i) q^{42} +(7.91872 + 3.61636i) q^{43} +(3.31935 - 0.477251i) q^{44} +2.64072 q^{45} +(3.14237 + 2.12084i) q^{46} -10.2574i q^{47} +(0.634623 - 0.0912451i) q^{48} +(5.33009 - 4.53764i) q^{49} +(-1.49680 + 0.439499i) q^{50} +(-3.63233 - 3.14743i) q^{51} +(-2.55919 + 8.71580i) q^{52} +(-4.81898 - 7.49847i) q^{53} +(0.719064 - 0.328385i) q^{54} +(4.86698 - 4.21726i) q^{55} +(-4.96957 - 5.01317i) q^{56} +(-8.40880 - 1.20900i) q^{57} +(0.634989 - 4.41645i) q^{58} +(-0.711705 + 1.10743i) q^{59} +(2.74434 - 2.37799i) q^{60} +(-2.14833 - 4.70418i) q^{61} +(-0.165204 - 0.257063i) q^{62} +(2.31656 + 1.27810i) q^{63} +(-2.18494 + 2.52155i) q^{64} +(4.91460 + 16.7376i) q^{65} +(0.800834 - 1.75358i) q^{66} +(-5.63635 + 0.810385i) q^{67} -6.60914 q^{68} +(-4.40615 + 1.89364i) q^{69} +(-5.39158 - 1.19755i) q^{70} +(-0.314576 - 2.18793i) q^{71} +(1.10834 - 2.42692i) q^{72} +(2.31353 + 7.87917i) q^{73} +(2.49896 + 2.16536i) q^{74} +(0.555976 - 1.89348i) q^{75} +(-9.82747 + 6.31573i) q^{76} +(6.31068 - 1.34397i) q^{77} +(3.41963 + 3.94646i) q^{78} +(3.38224 - 5.26287i) q^{79} +(0.240953 - 1.67586i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(2.12471 - 3.30611i) q^{82} +(2.37388 + 2.73960i) q^{83} +(3.55840 - 0.757821i) q^{84} +(-10.6772 + 6.86182i) q^{85} +(1.93878 - 6.60287i) q^{86} +(4.26572 + 3.69627i) q^{87} +(-1.83310 - 6.24296i) q^{88} +(0.867930 - 1.90050i) q^{89} +(-0.297081 - 2.06624i) q^{90} +(-3.78964 + 17.0616i) q^{91} +(-2.87380 + 5.93571i) q^{92} +0.386554 q^{93} +(-8.02595 + 1.15396i) q^{94} +(-9.31928 + 20.4064i) q^{95} +(-1.64613 - 5.60620i) q^{96} +(3.63902 - 4.19966i) q^{97} +(-4.15013 - 3.66006i) q^{98} +(1.31846 + 2.05157i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more