LMFDB - Embedded newform 483.2.r.a.181.13

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			181.13
Character	$\chi$	$=$	483.181
Dual form			483.2.r.a.475.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.112500 - 0.782453i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(1.31941 - 0.387413i) q^{4} +(-1.72931 + 1.99573i) q^{5} +(-0.222709 + 0.758479i) q^{6} +(-1.86264 + 1.87898i) q^{7} +(-1.10834 - 2.42692i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(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} +(-1.86264 + 1.87898i) 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} +(1.67976 + 1.24604i) 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} +(2.47487 - 0.935413i) 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} +(-1.72964 + 3.20076i) 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} +(-0.528856 - 6.96665i) 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} +(-1.01034 - 1.83124i) 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} +(-0.0611428 - 6.99973i) 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} +(6.62457 + 2.43793i) 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} +(-2.63981 - 0.177218i) 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} +(-5.14832 + 3.88918i) 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} +(2.90298 - 2.19299i) 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} +(-5.47009 + 0.835310i) 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	−0.996612	−	0.0822473i	$-0.973790\pi$
$5$	−1.72931	+	1.99573i	−0.773369	+	0.892516i	0.223243	+	0.974763i	$0.428336\pi$
$6$	−0.222709	+	0.758479i	−0.0909208	+	0.309648i
$7$	−1.86264	+	1.87898i	−0.704012	+	0.710188i
$7$	−1.86264	+	1.87898i	−0.704012	+	0.710188i
$8$	−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	$-0.449530\pi$
$13$	3.57139	−	5.55718i	0.990524	−	1.54129i	0.832630	−	0.553830i	$-0.186834\pi$
$14$	1.67976	+	1.24604i	0.448935	+	0.333019i
$15$	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	0.788167	−	0.615462i	$-0.211030\pi$
$17$	4.61157	+	1.35408i	1.11847	+	0.328413i	0.330304	+	0.943874i	$0.392849\pi$
$18$	0.517667	−	0.597420i	0.122015	−	0.140813i
$19$	8.15115	−	2.39339i	1.87000	−	0.549082i	0.871752	−	0.489947i	$-0.162984\pi$
$19$	8.15115	−	2.39339i	1.87000	−	0.549082i	0.998250	−	0.0591349i	$-0.0188342\pi$
$20$	−1.50849	+	3.30313i	−0.337309	+	0.738603i
$21$	2.47487	−	0.935413i	0.540062	−	0.204124i
$22$		−	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
$28$	−1.72964	+	3.20076i	−0.326871	+	0.604886i
$29$	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	−0.446741	−	0.894663i	$-0.647416\pi$
$31$	−0.351622	+	0.160580i	−0.0631532	+	0.0288411i	0.383588	+	0.923504i	$0.374688\pi$
$32$	−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
$35$	−0.528856	−	6.96665i	−0.0893930	−	1.17758i
$36$	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	0.310111	−	0.950700i	$-0.399634\pi$
$41$	−3.75722	−	3.25565i	−0.586780	−	0.508448i	−0.896890	+	0.442253i	$0.854179\pi$
$42$	−1.01034	−	1.83124i	−0.155899	−	0.282566i
$43$	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	$0.269033\pi$
$47$			10.2574i			1.49620i	−0.663587	+	0.748099i	$0.730967\pi$
$48$	−0.634623	+	0.0912451i	−0.0916000	+	0.0131701i
$49$	−0.0611428	−	6.99973i	−0.00873469	−	0.999962i
$50$	−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
$56$	6.62457	+	2.43793i	0.885245	+	0.325783i
$57$	−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	−0.791831	−	0.610740i	$-0.790872\pi$
$59$	0.711705	−	1.10743i	0.0926561	−	0.144176i	0.884487	+	0.466564i	$0.154508\pi$
$60$	2.74434	−	2.37799i	0.354293	−	0.306997i
$61$	2.14833	+	4.70418i	0.275065	+	0.602309i	0.995866	−	0.0908333i	$-0.0289531\pi$
$61$	2.14833	+	4.70418i	0.275065	+	0.602309i	−0.720801	+	0.693142i	$0.756226\pi$
$62$	0.165204	+	0.257063i	0.0209809	+	0.0326470i
$63$	−2.63981	−	0.177218i	−0.332585	−	0.0223274i
$64$	−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	$-0.931343\pi$
$73$	−2.31353	−	7.87917i	−0.270779	−	0.922188i	0.706049	−	0.708163i	$-0.250476\pi$
$74$	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
$77$	−5.14832	+	3.88918i	−0.586705	+	0.443213i
$78$	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	0.610359	−	0.792125i	$-0.291025\pi$
$83$	−2.37388	−	2.73960i	−0.260567	−	0.300710i	−0.870926	+	0.491415i	$0.836480\pi$
$84$	2.90298	−	2.19299i	0.316741	−	0.239275i
$85$	−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	−0.950038	−	0.312134i	$-0.898956\pi$
$89$	−0.867930	+	1.90050i	−0.0920004	+	0.201453i	0.858038	+	0.513587i	$0.171684\pi$
$90$	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	−0.909796	−	0.415056i	$-0.863762\pi$
$97$	−3.63902	+	4.19966i	−0.369487	+	0.426410i	0.540309	+	0.841467i	$0.318307\pi$
$98$	−5.47009	+	0.835310i	−0.552562	+	0.0843791i
$99$	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	−0.668822	−	0.743423i	$-0.733201\pi$
$101$	−0.282896	+	0.245131i	−0.0281492	+	0.0243914i	0.640673	+	0.767814i	$0.278656\pi$
$102$	−2.05408	+	3.19622i	−0.203384	+	0.316472i
$103$	−0.552136	+	3.84019i	−0.0544035	+	0.378385i	0.944371	+	0.328883i	$0.106672\pi$
$103$	−0.552136	+	3.84019i	−0.0544035	+	0.378385i	−0.998774	+	0.0495014i	$0.984237\pi$
$104$	−17.4451	−	2.50823i	−1.71064	−	0.245952i
$105$	−2.41299	+	6.55678i	−0.235483	+	0.639877i
$106$	−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
$112$	−0.353336	+	1.65911i	−0.0333872	+	0.156772i
$113$	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
$119$	−11.1340	+	6.14290i	−1.02065	+	0.563119i
$120$	−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
$126$	0.158313	+	2.08547i	0.0141036	+	0.185788i
$127$	−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	0.988678	−	0.150055i	$-0.0479452\pi$
$131$	5.05287	+	7.86241i	0.441471	+	0.686942i	−0.547207	+	0.836998i	$0.684309\pi$
$132$	−3.21765	−	0.944786i	−0.280060	−	0.0822331i
$133$	−10.6855	+	19.7739i	−0.926552	+	1.71461i
$134$	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	$-0.926013\pi$
$139$		−	5.43160i		−	0.460702i	0.973108	−	0.230351i	$-0.0739875\pi$
$140$	−3.39675	−	8.98698i	−0.287078	−	0.759538i
$141$	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
$147$	−2.85218	+	6.39258i	−0.235244	+	0.527251i
$148$	−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
$154$	3.62229	+	3.59079i	0.291892	+	0.289354i
$155$	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	−0.399393	−	0.916780i	$-0.630779\pi$
$157$	−3.00386	+	0.882013i	−0.239734	+	0.0703923i	0.159658	+	0.987172i	$0.448961\pi$
$158$	−4.49845	−	2.05437i	−0.357877	−	0.163437i
$159$	1.26852	+	8.82273i	0.100600	+	0.699688i
$160$	15.4294			1.21980
$161$	−0.675662	−	12.6706i	−0.0532496	−	0.998581i
$162$	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	$-0.780375\pi$
$167$	2.86487	−	9.75685i	0.221690	−	0.755008i	0.992955	−	0.118493i	$-0.0378064\pi$
$168$	−5.01317	−	4.96957i	−0.386774	−	0.383410i
$169$	−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	0.693350	−	0.720601i	$-0.256134\pi$
$173$	15.1995	+	2.18536i	1.15560	+	0.166150i	0.462247	+	0.886751i	$0.347043\pi$
$174$	−2.41226	+	3.75356i	−0.182873	+	0.284556i
$175$	4.19339	+	3.11065i	0.316991	+	0.235143i
$176$	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	$0.355032\pi$
$181$	−7.08882	+	15.5224i	−0.526908	+	1.15377i	−0.966757	+	0.255696i	$0.917695\pi$
$182$	12.9236	−	4.88464i	0.957959	−	0.362074i
$183$		−	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
$189$	2.32764	+	1.25782i	0.169311	+	0.0914929i
$190$	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
$196$	−2.79246	−	9.21182i	−0.199462	−	0.657987i
$197$	−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	$0.0993318\pi$
$199$	7.90683	+	17.3135i	0.560500	+	1.22732i	−0.391203	+	0.920304i	$0.627941\pi$
$200$	−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
$203$	−13.0755	+	7.21407i	−0.917720	+	0.506329i
$204$	−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
$210$	5.40184	+	1.15041i	0.372762	+	0.0793860i
$211$	−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
$217$	0.353218	−	0.959795i	0.0239780	−	0.0651551i
$218$	−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	0.596416	−	0.802676i	$-0.296591\pi$
$223$	−5.69677	−	8.86434i	−0.381484	−	0.593600i	−0.977900	+	0.209075i	$0.932955\pi$
$224$	15.4241	+	1.03546i	1.03056	+	0.0691849i
$225$	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	$-0.581644\pi$
$227$	9.69482	−	21.2287i	0.643468	−	1.40900i	0.897157	−	0.441712i	$-0.145629\pi$
$228$	−11.5630	+	1.66251i	−0.765780	+	0.110103i
$229$	−26.4321			−1.74668			−0.873342	−	0.487108i	$-0.838052\pi$
$229$	−26.4321			−1.74668			−0.873342	+	0.487108i	$0.838052\pi$
$230$	−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
$238$	6.05910	+	8.02076i	0.392753	+	0.519909i
$239$	−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	−0.964812	−	0.262939i	$-0.915308\pi$
$241$	0.543299	−	3.77872i	0.0349969	−	0.243409i	0.999809	+	0.0195305i	$0.00621713\pi$
$242$	−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
$245$	14.0753	+	11.9827i	0.899237	+	0.765544i
$246$	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	$0.0957832\pi$
$251$	1.93585	+	13.4642i	0.122190	+	0.849850i	−0.832877	+	0.553459i	$0.813308\pi$
$252$	−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	0.971583	−	0.236701i	$-0.0760661\pi$
$257$	0.421064	+	1.43401i	0.0262652	+	0.0894511i	−0.945317	+	0.326152i	$0.894248\pi$
$258$	−4.50650	+	5.20078i	−0.280563	+	0.323787i
$259$	0.741289	−	11.0421i	0.0460615	−	0.686123i
$260$	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
$266$	16.6743	+	6.13636i	1.02237	+	0.376244i
$267$	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	0.797096	−	0.603852i	$-0.206368\pi$
$269$	−1.36643	−	2.12621i	−0.0833130	−	0.129638i	−0.880409	+	0.474215i	$0.842732\pi$
$270$	0.588114	−	2.00293i	0.0357915	−	0.121895i
$271$	−14.9580	−	12.9612i	−0.908636	−	0.787337i	0.0690057	−	0.997616i	$-0.478017\pi$
$271$	−14.9580	−	12.9612i	−0.908636	−	0.787337i	−0.977641	+	0.210279i	$0.932563\pi$
$272$	2.95671	−	0.868168i	0.179277	−	0.0526404i
$273$	3.64047	−	17.0941i	0.220331	−	1.03458i
$274$	−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
$280$	−16.3214	+	9.00489i	−0.975387	+	0.538145i
$281$	−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	$0.649911\pi$
$283$	−24.4405	+	15.7070i	−1.45284	+	0.933682i	−0.999094	+	0.0425488i	$0.986452\pi$
$284$	−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
$287$	13.1157	−	0.995644i	0.774193	−	0.0587710i
$288$	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	0.537083	−	0.843529i	$-0.319526\pi$
$293$	9.12108	+	2.67819i	0.532859	+	0.156462i	−0.00422350	+	0.999991i	$0.501344\pi$
$294$	5.32277	+	1.51253i	0.310430	+	0.0882126i
$295$	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
$301$	−21.5448	+	8.14315i	−1.24182	+	0.469363i
$302$	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	−0.792096	−	0.610396i	$-0.791010\pi$
$307$	−14.8845	+	6.79752i	−0.849503	+	0.387955i	−0.0574063	+	0.998351i	$0.518283\pi$
$308$	−5.28601	+	7.12595i	−0.301198	+	0.406038i
$309$	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	−0.537944	−	0.842981i	$-0.680799\pi$
$311$	−22.7775	−	3.27491i	−1.29159	−	0.185703i	−0.753648	+	0.657278i	$0.771708\pi$
$312$	14.8267	+	9.52854i	0.839396	+	0.539447i
$313$	14.9797	+	17.2875i	0.846705	+	0.977149i	0.999939	−	0.0110407i	$-0.00351445\pi$
$313$	14.9797	+	17.2875i	0.846705	+	0.977149i	−0.153235	+	0.988190i	$0.548969\pi$
$314$	1.02807	+	2.25115i	0.0580172	+	0.127040i
$315$	4.91872	−	4.96187i	0.277138	−	0.279570i
$316$	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
$322$	−9.83812	+	1.95411i	−0.548257	+	0.108898i
$323$	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
$329$	−19.2735	−	19.1059i	−1.06258	−	1.05334i
$330$	−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
$336$	1.01063	−	1.36240i	0.0551342	−	0.0743251i
$337$	−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
$343$	13.2663	+	12.9231i	0.716310	+	0.697782i
$344$		−	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	$-0.775744\pi$
$349$	−8.80103	−	29.9735i	−0.471108	−	1.60445i	0.290815	−	0.956779i	$-0.406074\pi$
$350$	1.96218	−	3.63108i	0.104883	−	0.194089i
$351$	−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	0.473854	−	0.880603i	$-0.342862\pi$
$353$	27.2370	−	12.4387i	1.44968	−	0.662046i	0.975824	+	0.218558i	$0.0701352\pi$
$354$	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
$357$	12.6797	−	0.962548i	0.671080	−	0.0509434i
$358$	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
$364$	11.6100	+	21.0431i	0.608528	+	1.10296i
$365$	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	$-0.628642\pi$
$367$	−15.0664			−0.786460			−0.393230	+	0.919440i	$0.628642\pi$
$368$	−0.505936	+	3.03293i	−0.0263737	+	0.158103i
$369$		−	4.97152i		−	0.258807i
$370$	−8.64292	+	1.24266i	−0.449324	+	0.0646030i
$371$	23.0655	+	4.91219i	1.19750	+	0.255028i
$372$	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
$378$	0.722327	−	1.96277i	0.0371525	−	0.100954i
$379$	−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	$-0.896753\pi$
$383$	−11.1160	−	24.3407i	−0.568002	−	1.24375i	0.379853	−	0.925047i	$-0.375975\pi$
$384$	4.89186	+	7.61188i	0.249636	+	0.388442i
$385$	1.14128	−	17.0002i	0.0581648	−	0.866411i
$386$	−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	$0.276419\pi$
$397$	−6.17887	+	21.0433i	−0.310109	+	1.05613i	−0.956161	+	0.292841i	$0.905399\pi$
$398$	12.6575	−	8.13449i	0.634464	−	0.407745i
$399$	17.9343	−	13.5480i	0.897836	−	0.678250i
$400$	−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
$406$	7.11567	+	9.41939i	0.353145	+	0.467476i
$407$	−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	0.803390	−	0.595454i	$-0.203028\pi$
$409$	6.64009	+	5.75367i	0.328331	+	0.284501i	−0.475058	+	0.879954i	$0.657573\pi$
$410$	−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	−0.181392	−	0.983411i	$-0.558060\pi$
$419$	16.7404	−	19.3195i	0.817824	−	0.943819i	0.999216	+	0.0395917i	$0.0126057\pi$
$420$	−0.643531	+	9.58590i	−0.0314011	+	0.467744i
$421$	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
$427$	−12.8406	−	4.72553i	−0.621402	−	0.228684i
$428$	−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	−0.506699	−	0.862123i	$-0.669134\pi$
$433$	−9.71476	+	2.85251i	−0.466861	+	0.137083i	0.0398371	+	0.999206i	$0.487316\pi$
$434$	−0.790731	−	0.168400i	−0.0379563	−	0.00808344i
$435$	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	−0.0685150	−	0.997650i	$-0.521826\pi$
$439$	3.07613	−	0.442281i	0.146816	−	0.0211089i	0.215331	+	0.976541i	$0.430917\pi$
$440$	15.6292	+	7.13762i	0.745093	+	0.340273i
$441$	5.25001	−	4.63006i	0.250000	−	0.220479i
$442$	−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
$448$	−0.668198	−	8.80220i	−0.0315694	−	0.415865i
$449$	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
$455$	−40.6037	−	21.9416i	−1.90353	−	1.02864i
$456$	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	$0.0589120\pi$
$461$			7.90227i			0.368045i	−0.982922	+	0.184023i	$0.941088\pi$
$462$	−1.80328	−	4.77105i	−0.0838963	−	0.221969i
$463$	−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	−0.593837	−	0.804585i	$-0.702388\pi$
$467$	−2.34793	+	1.50892i	−0.108649	+	0.0698247i	0.485188	+	0.874410i	$0.338751\pi$
$468$	8.26288	−	3.77353i	0.381952	−	0.174431i
$469$	8.97580	−	12.1001i	0.414464	−	0.558729i
$470$	−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
$476$	−12.3105	+	12.4185i	−0.564249	+	0.569199i
$477$	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	−0.672939	−	0.739698i	$-0.734968\pi$
$479$	−18.3655	+	5.39259i	−0.839140	+	0.246394i	−0.166201	+	0.986092i	$0.553150\pi$
$480$	−14.0351	−	6.40961i	−0.640611	−	0.292557i
$481$	3.93240	+	27.3504i	0.179302	+	1.24707i
$482$	−3.01780			−0.137457
$483$	−4.64894	+	11.8062i	−0.211534	+	0.537203i
$484$	−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
$490$	7.79240	−	12.3613i	0.352025	−	0.558427i
$491$	−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
$497$	4.69702	+	3.48424i	0.210690	+	0.156289i
$498$	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	−0.953101	−	0.302653i	$-0.902128\pi$
$503$	−2.24776	+	4.92191i	−0.100223	+	0.219457i	0.852878	+	0.522110i	$0.174855\pi$
$504$	2.49570	+	6.60302i	0.111167	+	0.294122i
$505$		−	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	−0.429396	−	0.903116i	$-0.641273\pi$
$509$	−31.4302	−	14.3537i	−1.39312	−	0.636217i	−0.963724	+	0.266900i	$0.914001\pi$
$510$	−2.82663	−	9.62662i	−0.125165	−	0.426274i
$511$	19.1141	+	10.3290i	0.845558	+	0.456927i
$512$	−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
$518$	−8.72332	+	0.662210i	−0.383281	+	0.0290958i
$519$	−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	0.954376	−	0.298607i	$-0.0965219\pi$
$521$	2.36747	+	5.18404i	0.103721	+	0.227117i	−0.850655	+	0.525724i	$0.823795\pi$
$522$	3.75356	−	2.41226i	0.164289	−	0.105582i
$523$	−10.6790	−	3.13564i	−0.466961	−	0.137112i	0.0397838	−	0.999208i	$-0.487333\pi$
$523$	−10.6790	−	3.13564i	−0.466961	−	0.137112i	−0.506745	+	0.862096i	$0.669151\pi$
$524$	9.71280	+	8.41619i	0.424306	+	0.367663i
$525$	−2.52223	−	4.57154i	−0.110079	−	0.199519i
$526$	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
$532$	−6.43790	+	30.2296i	−0.279118	+	1.31062i
$533$	−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
$539$	2.28176	−	16.9177i	0.0982824	−	0.728698i
$540$	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
$546$	−13.7849	−	0.925419i	−0.589937	−	0.0396043i
$547$	−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
$560$	−2.70011	−	3.57428i	−0.114100	−	0.151041i
$561$	−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	$0.168957\pi$
$563$	−2.55510	+	17.7711i	−0.107685	+	0.748963i	−0.970090	+	0.242745i	$0.921952\pi$
$564$	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
$567$	−1.59477	−	2.11109i	−0.0669742	−	0.0886574i
$568$	−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	0.238522	−	0.971137i	$-0.423337\pi$
$577$	17.7990	−	2.55911i	0.740983	−	0.106537i	0.502461	+	0.864600i	$0.332428\pi$
$578$	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
$581$	9.56934	+	0.642419i	0.397003	+	0.0266520i
$582$	−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	−0.272272	−	0.962220i	$-0.587775\pi$
$587$	−19.4940	−	2.80282i	−0.804604	−	0.115685i	−0.532332	+	0.846536i	$0.678684\pi$
$588$	−1.28662	+	9.53940i	−0.0530591	+	0.393398i
$589$	−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	0.703445	−	0.710749i	$-0.251644\pi$
$593$	2.43616	+	2.11095i	0.100041	+	0.0866862i	−0.603404	+	0.797435i	$0.706189\pi$
$594$	−1.84970	+	0.543122i	−0.0758943	+	0.0222846i
$595$	6.99455	−	32.8433i	0.286748	−	1.34645i
$596$	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	0.376386	−	0.926463i	$-0.377167\pi$
$601$	−1.89522	−	0.865518i	−0.0773076	−	0.0353052i	−0.453694	+	0.891158i	$0.649894\pi$
$602$	8.79542	+	15.9417i	0.358475	+	0.649735i
$603$	−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	$-0.343470\pi$
$607$	34.7856	−	30.1419i	1.41190	−	1.22342i	0.939731	−	0.341915i	$-0.111075\pi$
$608$	−41.7571	−	26.8357i	−1.69348	−	1.08833i
$609$	14.8907	−	1.13039i	0.603403	−	0.0458058i
$610$	−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
$616$	15.1448	+	8.18402i	0.610201	+	0.329744i
$617$	−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	$0.0937136\pi$
$619$	2.99840	+	20.8543i	0.120516	+	0.838207i	−0.836458	+	0.548032i	$0.815377\pi$
$620$		−	1.40369i		−	0.0563735i
$621$	4.31653	+	2.08987i	0.173216	+	0.0838636i
$622$			18.1907i			0.729382i
$623$	−1.95437	−	5.17077i	−0.0783000	−	0.207163i
$624$	−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
$630$	−4.43579	−	3.29046i	−0.176726	−	0.131095i
$631$	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
$637$	−39.1172	−	24.6590i	−1.54988	−	0.977024i
$638$	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	$-0.174220\pi$
$643$	43.3063			1.70783			0.853917	+	0.520409i	$0.174220\pi$
$644$	−5.80022	−	16.4559i	−0.228561	−	0.648454i
$645$	22.9886			0.905174
$646$	−4.59342	−	31.9480i	−0.180726	−	1.25698i
$647$	38.7370	+	17.6906i	1.52291	+	0.695489i	0.988706	−	0.149869i	$-0.0478851\pi$
$647$	38.7370	+	17.6906i	1.52291	+	0.695489i	0.534202	+	0.845357i	$0.320612\pi$
$648$	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
$651$	−0.720011	+	0.726328i	−0.0282195	+	0.0284670i
$652$	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
$658$	−12.7812	+	17.2300i	−0.498263	+	0.671696i
$659$	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	0.242220	−	0.970221i	$-0.422124\pi$
$661$	−2.01959	−	0.593006i	−0.0785531	−	0.0230653i	−0.320773	+	0.947156i	$0.603943\pi$
$662$	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
$665$	−20.9847	−	55.5205i	−0.813753	−	2.15299i
$666$			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
$672$	−13.6001	−	7.34928i	−0.524635	−	0.283505i
$673$	−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	0.564270	−	0.825590i	$-0.309158\pi$
$677$	1.24094	+	0.797505i	0.0476933	+	0.0306506i	−0.516577	+	0.856241i	$0.672794\pi$
$678$	−1.17125	+	8.14619i	−0.0449814	+	0.312852i
$679$	−1.11289	−	14.6601i	−0.0427086	−	0.562603i
$680$	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
$686$	8.61927	−	11.8341i	0.329085	−	0.451827i
$687$	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	$-0.866781\pi$
$691$		−	21.3664i		−	0.812815i	0.913692	−	0.406408i	$-0.133219\pi$
$692$	20.9010	−	3.00511i	0.794536	−	0.114237i
$693$	−6.31068	−	1.34397i	−0.239723	−	0.0510530i
$694$	−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
$700$	6.73791	+	2.47964i	0.254669	+	0.0937217i
$701$	−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
$707$	0.0663372	−	0.988146i	0.00249487	−	0.0371631i
$708$	−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	−0.952457	−	0.304673i	$-0.901453\pi$
$719$	0.362506	−	1.23458i	0.0135192	−	0.0460421i	0.965976	+	0.258630i	$0.0832712\pi$
$720$	−1.42432	+	0.915358i	−0.0530814	+	0.0341134i
$721$	−6.18721	−	8.19034i	−0.230424	−	0.305024i
$722$	−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	0.441379	−	0.897321i	$-0.354489\pi$
$727$	−13.7409	−	15.8579i	−0.509623	−	0.588136i	−0.951002	+	0.309185i	$0.899944\pi$
$728$	37.2069	−	28.1072i	1.37898	−	1.04172i
$729$	−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	−0.995626	−	0.0934291i	$-0.970217\pi$
$733$	−7.39175	+	16.1857i	−0.273021	+	0.597832i	0.722605	+	0.691261i	$0.242944\pi$
$734$	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
$742$	1.24869	−	18.6003i	0.0458410	−	0.682839i
$743$	−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
$749$	4.83510	−	13.1384i	0.176671	−	0.480065i
$750$	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
$756$	3.55840	+	0.757821i	0.129418	+	0.0275617i
$757$	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	−0.654694	−	0.755894i	$-0.727202\pi$
$761$	−29.5147	+	4.24358i	−1.06991	+	0.153830i	−0.415214	+	0.909724i	$0.636293\pi$
$762$	−7.00539	−	3.19925i	−0.253779	−	0.115897i
$763$	7.01335	+	12.7117i	0.253900	+	0.460194i
$764$	−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	0.566857	−	0.823816i	$-0.308159\pi$
$769$	1.46887	+	0.943988i	0.0529689	+	0.0340411i	−0.513888	+	0.857857i	$0.671795\pi$
$770$	−13.4303	+	1.01953i	−0.483993	+	0.0367412i
$771$	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	0.891895	−	0.452243i	$-0.149376\pi$
$773$	8.82254	+	10.1818i	0.317325	+	0.366212i	−0.574570	+	0.818456i	$0.694831\pi$
$774$	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
$777$	−5.26135	+	9.73631i	−0.188750	+	0.349288i
$778$	−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
$784$	−2.45931	−	3.75425i	−0.0878324	−	0.134080i
$785$	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	−0.426776	−	0.904357i	$-0.640351\pi$
$787$	14.8435	−	17.1303i	0.529112	−	0.610628i	0.955889	+	0.293729i	$0.0948964\pi$
$788$	−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
$791$	−16.4107	+	22.1229i	−0.583498	+	0.786600i
$792$	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	$-0.849689\pi$
$797$	−18.3821	−	40.2513i	−0.651129	−	1.42577i	0.239433	−	0.970913i	$-0.423038\pi$
$798$	−12.6183	−	12.5086i	−0.446683	−	0.442799i
$799$	−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
$805$	26.4554	+	20.5629i	0.932431	+	0.724746i
$806$	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	$-0.802275\pi$
$811$	5.28421	−	17.9964i	0.185554	−	0.631938i	0.998752	−	0.0499510i	$-0.0159065\pi$
$812$	−14.4571	+	14.5839i	−0.507345	+	0.511796i
$813$	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
$819$	−10.4126	+	14.0370i	−0.363846	+	0.490492i
$820$	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
$826$	2.57541	−	0.973411i	0.0896099	−	0.0338693i
$827$			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	$0.120890\pi$
$829$			21.3480i			0.741448i	−0.928743	+	0.370724i	$0.879110\pi$
$830$	−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
$833$	9.19624	−	32.3626i	0.318631	−	1.12130i
$834$	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	$0.240794\pi$
$839$	−4.74778	+	33.0215i	−0.163911	+	1.14003i	−0.891171	+	0.453667i	$0.850116\pi$
$840$	18.5872	−	1.41100i	0.641319	−	0.0486842i
$841$	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
$847$	11.7050	−	6.45791i	0.402187	−	0.221896i
$848$	−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	−0.0472357	−	0.998884i	$-0.515041\pi$
$853$	5.51588	−	0.793064i	0.188860	−	0.0271540i	0.236096	+	0.971730i	$0.424132\pi$
$854$	−2.25294	+	10.5788i	−0.0770940	+	0.362000i
$855$	−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	−0.963112	−	0.269101i	$-0.913273\pi$
$857$	−0.216738	+	0.738142i	−0.00740364	+	0.0252145i	0.955708	+	0.294315i	$0.0950916\pi$
$858$	6.88489	+	10.7131i	0.235046	+	0.365739i
$859$	15.5140	−	7.08500i	0.529330	−	0.241737i	−0.132777	−	0.991146i	$-0.542389\pi$
$859$	15.5140	−	7.08500i	0.529330	−	0.241737i	0.662108	+	0.749409i	$0.269662\pi$
$860$	−23.8906	+	20.7013i	−0.814663	+	0.705910i
$861$	−12.3440	−	4.54278i	−0.420684	−	0.154817i
$862$	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
$868$	0.0942012	−	1.40320i	0.00319740	−	0.0476278i
$869$	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	−0.827592	−	0.561330i	$-0.810290\pi$
$881$	−19.6131	+	12.6046i	−0.660783	+	0.424659i	0.166809	+	0.985989i	$0.446654\pi$
$882$	−4.21343	−	3.58700i	−0.141874	−	0.120781i
$883$	−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	−0.818907	−	0.573926i	$-0.805420\pi$
$887$	1.29078	−	2.00850i	0.0433403	−	0.0674388i	0.862248	+	0.506487i	$0.169056\pi$
$888$	−7.30832	−	8.43425i	−0.245251	−	0.283035i
$889$	−15.5369	−	20.5670i	−0.521091	−	0.689796i
$890$	−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
$903$	22.9806	+	1.54276i	0.764747	+	0.0513398i
$904$	−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
$910$	−12.6004	+	34.2390i	−0.417699	+	1.13501i
$911$	−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
$917$	−24.1850	−	5.15060i	−0.798659	−	0.170088i
$918$	−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
$924$	7.76855	−	4.28610i	0.255567	−	0.141002i
$925$	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	$0.667028\pi$
$929$	−43.5530	+	37.7389i	−1.42893	+	1.23817i	−0.927945	+	0.372717i	$0.878426\pi$
$930$	0.678831	+	0.436258i	0.0222597	+	0.0143055i
$931$	−17.2515	−	56.9095i	−0.565395	−	1.86513i
$932$	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	−0.0938514	−	0.995586i	$-0.529918\pi$
$937$	−21.7658	−	6.39102i	−0.711059	−	0.208786i	−0.617207	+	0.786801i	$0.711736\pi$
$938$	−10.4775	−	5.66189i	−0.342103	−	0.184867i
$939$	−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	$-0.857972\pi$
$941$	−4.85042	−	33.7354i	−0.158119	−	1.09974i	0.743976	−	0.668206i	$-0.232938\pi$
$942$		−	2.47480i		−	0.0806332i
$943$	23.6702	−	2.86152i	0.770809	−	0.0931839i
$944$		−	0.844015i		−	0.0274704i
$945$	−6.53546	+	2.47017i	−0.212598	+	0.0803545i
$946$	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
$952$	27.2485	+	20.2129i	0.883130	+	0.655104i
$953$	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
$959$	29.7304	+	29.4719i	0.960046	+	0.951696i
$960$	−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
$966$	9.76084	+	2.30938i	0.314050	+	0.0743031i
$967$	−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	−0.753725	−	0.657190i	$-0.771745\pi$
$971$	0.125960	−	0.145366i	0.00404226	−	0.00466501i	0.757767	+	0.652525i	$0.226290\pi$
$972$	0.387413	−	1.31941i	0.0124263	−	0.0423201i
$973$	10.2059	+	10.1171i	0.327185	+	0.324340i
$974$	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
$980$	23.2133	+	10.3571i	0.741521	+	0.330844i
$981$	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	0.314733	−	0.949180i	$-0.398085\pi$
$983$	2.07985	+	0.610699i	0.0663369	+	0.0194783i	−0.248396	+	0.968659i	$0.579903\pi$
$984$	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
$987$	9.59492	+	25.3858i	0.305410	+	0.808039i
$988$		−	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
$994$	2.19784	−	4.06717i	0.0697113	−	0.129003i
$995$	−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	−0.621190	−	0.783660i	$-0.713350\pi$
$997$	−13.7583	+	6.28323i	−0.435731	+	0.198992i	0.185458	+	0.982652i	$0.440623\pi$
$998$	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.181.13	✓	320
7.6	odd	2	inner	483.2.r.a.181.14	yes	320
23.15	odd	22	inner	483.2.r.a.475.14	yes	320
161.153	even	22	inner	483.2.r.a.475.13	yes	320

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

\(f(q)\)	\(=\)	\(q+(-0.112500 - 0.782453i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(1.31941 - 0.387413i) q^{4} +(-1.72931 + 1.99573i) q^{5} +(-0.222709 + 0.758479i) q^{6} +(-1.86264 + 1.87898i) q^{7} +(-1.10834 - 2.42692i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(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} +(-1.86264 + 1.87898i) 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} +(1.67976 + 1.24604i) 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} +(2.47487 - 0.935413i) 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} +(-1.72964 + 3.20076i) 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} +(-0.528856 - 6.96665i) 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} +(-1.01034 - 1.83124i) 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} +(-0.0611428 - 6.99973i) 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} +(6.62457 + 2.43793i) 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} +(-2.63981 - 0.177218i) 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} +(-5.14832 + 3.88918i) 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} +(2.90298 - 2.19299i) 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} +(-5.47009 + 0.835310i) 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

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Representations

Groups

Database

Properties

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