LMFDB - Embedded newform 220.2.l.c.23.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(23,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.23"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$220 = 2^{2} \cdot 5 \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	220.l (of order $4$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [28,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.9
Character	$\chi$	$=$	220.23
Dual form			220.2.l.c.67.9

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.493487 + 1.32532i) q^{2} +(0.130983 - 0.130983i) q^{3} +(-1.51294 + 1.30805i) q^{4} +(2.21938 + 0.272654i) q^{5} +(0.238233 + 0.108956i) q^{6} +(0.450097 + 0.450097i) q^{7} +(-2.48021 - 1.35962i) q^{8} +2.96569i q^{9} +(0.733881 + 3.07594i) q^{10} -1.00000i q^{11} +(-0.0268369 + 0.369503i) q^{12} +(1.30725 + 1.30725i) q^{13} +(-0.374406 + 0.818640i) q^{14} +(0.326415 - 0.254989i) q^{15} +(0.577988 - 3.95802i) q^{16} +(1.51127 - 1.51127i) q^{17} +(-3.93048 + 1.46353i) q^{18} -4.82820 q^{19} +(-3.71444 + 2.49056i) q^{20} +0.117910 q^{21} +(1.32532 - 0.493487i) q^{22} +(-1.60193 + 1.60193i) q^{23} +(-0.502954 + 0.146777i) q^{24} +(4.85132 + 1.21025i) q^{25} +(-1.08741 + 2.37763i) q^{26} +(0.781405 + 0.781405i) q^{27} +(-1.26972 - 0.0922195i) q^{28} -6.86674i q^{29} +(0.499023 + 0.306771i) q^{30} -8.23887i q^{31} +(5.53087 - 1.18721i) q^{32} +(-0.130983 - 0.130983i) q^{33} +(2.74870 + 1.25712i) q^{34} +(0.876217 + 1.12166i) q^{35} +(-3.87928 - 4.48691i) q^{36} +(-0.0879673 + 0.0879673i) q^{37} +(-2.38265 - 6.39890i) q^{38} +0.342456 q^{39} +(-5.13382 - 3.69377i) q^{40} -2.87414 q^{41} +(0.0581872 + 0.156269i) q^{42} +(7.00618 - 7.00618i) q^{43} +(1.30805 + 1.51294i) q^{44} +(-0.808607 + 6.58199i) q^{45} +(-2.91360 - 1.33254i) q^{46} +(5.17857 + 5.17857i) q^{47} +(-0.442728 - 0.594141i) q^{48} -6.59482i q^{49} +(0.790095 + 7.02679i) q^{50} -0.395902i q^{51} +(-3.68775 - 0.267840i) q^{52} +(0.125688 + 0.125688i) q^{53} +(-0.649998 + 1.42122i) q^{54} +(0.272654 - 2.21938i) q^{55} +(-0.504371 - 1.72830i) q^{56} +(-0.632413 + 0.632413i) q^{57} +(9.10062 - 3.38864i) q^{58} -1.18586 q^{59} +(-0.160308 + 0.812752i) q^{60} -7.84865 q^{61} +(10.9191 - 4.06577i) q^{62} +(-1.33485 + 1.33485i) q^{63} +(4.30284 + 6.74430i) q^{64} +(2.54486 + 3.25772i) q^{65} +(0.108956 - 0.238233i) q^{66} +(3.17032 + 3.17032i) q^{67} +(-0.309640 + 4.26328i) q^{68} +0.419652i q^{69} +(-1.05416 + 1.71479i) q^{70} +13.3181i q^{71} +(4.03222 - 7.35551i) q^{72} +(-6.57673 - 6.57673i) q^{73} +(-0.159995 - 0.0731741i) q^{74} +(0.793964 - 0.476919i) q^{75} +(7.30478 - 6.31555i) q^{76} +(0.450097 - 0.450097i) q^{77} +(0.168997 + 0.453863i) q^{78} -10.1866 q^{79} +(2.36195 - 8.62677i) q^{80} -8.69236 q^{81} +(-1.41835 - 3.80915i) q^{82} +(7.91935 - 7.91935i) q^{83} +(-0.178392 + 0.154233i) q^{84} +(3.76614 - 2.94203i) q^{85} +(12.7429 + 5.82797i) q^{86} +(-0.899428 - 0.899428i) q^{87} +(-1.35962 + 2.48021i) q^{88} -3.59942i q^{89} +(-9.12228 + 2.17646i) q^{90} +1.17678i q^{91} +(0.328215 - 4.51903i) q^{92} +(-1.07915 - 1.07915i) q^{93} +(-4.30771 + 9.41882i) q^{94} +(-10.7156 - 1.31643i) q^{95} +(0.568947 - 0.879956i) q^{96} +(-8.41221 + 8.41221i) q^{97} +(8.74025 - 3.25446i) q^{98} +2.96569 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$28 q - 2 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 12 q^{6} - 2 q^{7} - 14 q^{8} + 6 q^{10} - 8 q^{12} + 6 q^{13} - 20 q^{14} + 8 q^{15} + 8 q^{16} - 14 q^{17} + 34 q^{18} + 4 q^{19} + 8 q^{20} - 16 q^{21}+ \cdots - 20 q^{99}+O(q^{100})$ 28 * q - 2 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 12 * q^6 - 2 * q^7 - 14 * q^8 + 6 * q^10 - 8 * q^12 + 6 * q^13 - 20 * q^14 + 8 * q^15 + 8 * q^16 - 14 * q^17 + 34 * q^18 + 4 * q^19 + 8 * q^20 - 16 * q^21 - 2 * q^22 - 8 * q^23 + 28 * q^24 - 4 * q^25 + 4 * q^26 + 44 * q^27 - 28 * q^28 - 2 * q^32 + 4 * q^33 - 52 * q^34 - 10 * q^35 - 4 * q^36 + 20 * q^37 + 16 * q^38 + 32 * q^39 - 6 * q^40 + 12 * q^41 - 32 * q^42 + 2 * q^43 - 10 * q^45 + 4 * q^46 - 44 * q^47 - 36 * q^48 + 22 * q^50 + 24 * q^52 - 28 * q^53 - 40 * q^54 - 2 * q^55 + 4 * q^56 - 8 * q^57 + 28 * q^58 - 16 * q^59 - 48 * q^60 - 12 * q^61 - 24 * q^62 - 10 * q^63 + 28 * q^64 - 30 * q^65 + 16 * q^67 - 32 * q^68 + 72 * q^70 + 18 * q^72 + 22 * q^73 - 20 * q^74 - 56 * q^75 + 4 * q^76 - 2 * q^77 + 104 * q^78 - 20 * q^79 - 44 * q^80 + 12 * q^81 - 92 * q^82 + 2 * q^83 + 120 * q^84 - 14 * q^85 - 20 * q^86 - 48 * q^87 + 2 * q^88 + 70 * q^90 + 52 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^95 + 40 * q^96 + 16 * q^97 + 18 * q^98 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$ .

$n$	$101$	$111$	$177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	0.493487	+	1.32532i	0.348948	+	0.937142i
$2$	0.493487	+	1.32532i	0.348948	+	0.937142i
$3$	0.130983	−	0.130983i	0.0756232	−	0.0756232i	−0.668283	−	0.743907i	$-0.732971\pi$
$3$	0.130983	−	0.130983i	0.0756232	−	0.0756232i	0.743907	+	0.668283i	$0.232971\pi$
$4$	−1.51294	+	1.30805i	−0.756471	+	0.654027i
$5$	2.21938	+	0.272654i	0.992538	+	0.121935i
$5$	2.21938	+	0.272654i	0.992538	+	0.121935i
$6$	0.238233	+	0.108956i	0.0972583	+	0.0444812i
$7$	0.450097	+	0.450097i	0.170121	+	0.170121i	0.787032	−	0.616912i	$-0.211616\pi$
$7$	0.450097	+	0.450097i	0.170121	+	0.170121i	−0.616912	+	0.787032i	$0.711616\pi$
$8$	−2.48021	−	1.35962i	−0.876885	−	0.480700i
$9$			2.96569i			0.988562i
$10$	0.733881	+	3.07594i	0.232074	+	0.972698i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	−0.0268369	+	0.369503i	−0.00774714	+	0.106666i
$13$	1.30725	+	1.30725i	0.362566	+	0.362566i	0.864757	−	0.502191i	$-0.167473\pi$
$13$	1.30725	+	1.30725i	0.362566	+	0.362566i	−0.502191	+	0.864757i	$0.667473\pi$
$14$	−0.374406	+	0.818640i	−0.100064	+	0.218791i
$15$	0.326415	−	0.254989i	0.0842800	−	0.0658378i
$16$	0.577988	−	3.95802i	0.144497	−	0.989505i
$17$	1.51127	−	1.51127i	0.366536	−	0.366536i	−0.499676	−	0.866212i	$-0.666548\pi$
$17$	1.51127	−	1.51127i	0.366536	−	0.366536i	0.866212	+	0.499676i	$0.166548\pi$
$18$	−3.93048	+	1.46353i	−0.926423	+	0.344956i
$19$	−4.82820			−1.10766			−0.553832	−	0.832628i	$-0.686835\pi$
$19$	−4.82820			−1.10766			−0.553832	+	0.832628i	$0.686835\pi$
$20$	−3.71444	+	2.49056i	−0.830575	+	0.556907i
$21$	0.117910			0.0257302
$22$	1.32532	−	0.493487i	0.282559	−	0.105212i
$23$	−1.60193	+	1.60193i	−0.334025	+	0.334025i	−0.854113	−	0.520088i	$-0.825899\pi$
$23$	−1.60193	+	1.60193i	−0.334025	+	0.334025i	0.520088	+	0.854113i	$0.325899\pi$
$24$	−0.502954	+	0.146777i	−0.102665	+	0.0299608i
$25$	4.85132	+	1.21025i	0.970264	+	0.242050i
$26$	−1.08741	+	2.37763i	−0.213259	+	0.466292i
$27$	0.781405	+	0.781405i	0.150381	+	0.150381i
$28$	−1.26972	−	0.0922195i	−0.239955	−	0.0174278i
$29$		−	6.86674i		−	1.27512i	−0.770400	−	0.637561i	$-0.779943\pi$
$29$		−	6.86674i		−	1.27512i	0.770400	−	0.637561i	$-0.220057\pi$
$30$	0.499023	+	0.306771i	0.0911087	+	0.0560084i
$31$		−	8.23887i		−	1.47974i	−0.672747	−	0.739872i	$-0.734886\pi$
$31$		−	8.23887i		−	1.47974i	0.672747	−	0.739872i	$-0.265114\pi$
$32$	5.53087	−	1.18721i	0.977729	−	0.209871i
$33$	−0.130983	−	0.130983i	−0.0228013	−	0.0228013i
$34$	2.74870	+	1.25712i	0.471399	+	0.215595i
$35$	0.876217	+	1.12166i	0.148108	+	0.189595i
$36$	−3.87928	−	4.48691i	−0.646547	−	0.747819i
$37$	−0.0879673	+	0.0879673i	−0.0144617	+	0.0144617i	−0.714301	−	0.699839i	$-0.753255\pi$
$37$	−0.0879673	+	0.0879673i	−0.0144617	+	0.0144617i	0.699839	+	0.714301i	$0.253255\pi$
$38$	−2.38265	−	6.39890i	−0.386517	−	1.03804i
$39$	0.342456			0.0548368
$40$	−5.13382	−	3.69377i	−0.811728	−	0.584036i
$41$	−2.87414			−0.448865			−0.224433	−	0.974490i	$-0.572053\pi$
$41$	−2.87414			−0.448865			−0.224433	+	0.974490i	$0.572053\pi$
$42$	0.0581872	+	0.156269i	0.00897848	+	0.0241128i
$43$	7.00618	−	7.00618i	1.06843	−	1.06843i	0.0709524	−	0.997480i	$-0.477396\pi$
$43$	7.00618	−	7.00618i	1.06843	−	1.06843i	0.997480	−	0.0709524i	$-0.0226038\pi$
$44$	1.30805	+	1.51294i	0.197197	+	0.228085i
$45$	−0.808607	+	6.58199i	−0.120540	+	0.981186i
$46$	−2.91360	−	1.33254i	−0.429586	−	0.196472i
$47$	5.17857	+	5.17857i	0.755373	+	0.755373i	0.975476	−	0.220104i	$-0.0706396\pi$
$47$	5.17857	+	5.17857i	0.755373	+	0.755373i	−0.220104	+	0.975476i	$0.570640\pi$
$48$	−0.442728	−	0.594141i	−0.0639023	−	0.0857569i
$49$		−	6.59482i		−	0.942118i
$50$	0.790095	+	7.02679i	0.111736	+	0.993738i
$51$		−	0.395902i		−	0.0554373i
$52$	−3.68775	−	0.267840i	−0.511399	−	0.0371427i
$53$	0.125688	+	0.125688i	0.0172646	+	0.0172646i	0.715686	−	0.698422i	$-0.246114\pi$
$53$	0.125688	+	0.125688i	0.0172646	+	0.0172646i	−0.698422	+	0.715686i	$0.746114\pi$
$54$	−0.649998	+	1.42122i	−0.0884536	+	0.193404i
$55$	0.272654	−	2.21938i	0.0367647	−	0.299262i
$56$	−0.504371	−	1.72830i	−0.0673994	−	0.230953i
$57$	−0.632413	+	0.632413i	−0.0837652	+	0.0837652i
$58$	9.10062	−	3.38864i	1.19497	−	0.444951i
$59$	−1.18586			−0.154386			−0.0771931	−	0.997016i	$-0.524596\pi$
$59$	−1.18586			−0.154386			−0.0771931	+	0.997016i	$0.524596\pi$
$60$	−0.160308	+	0.812752i	−0.0206957	+	0.104926i
$61$	−7.84865			−1.00492			−0.502459	−	0.864601i	$-0.667571\pi$
$61$	−7.84865			−1.00492			−0.502459	+	0.864601i	$0.667571\pi$
$62$	10.9191	−	4.06577i	1.38673	−	0.516354i
$63$	−1.33485	+	1.33485i	−0.168175	+	0.168175i
$64$	4.30284	+	6.74430i	0.537856	+	0.843037i
$65$	2.54486	+	3.25772i	0.315651	+	0.404070i
$66$	0.108956	−	0.238233i	0.0134116	−	0.0293245i
$67$	3.17032	+	3.17032i	0.387316	+	0.387316i	0.873729	−	0.486413i	$-0.161695\pi$
$67$	3.17032	+	3.17032i	0.387316	+	0.387316i	−0.486413	+	0.873729i	$0.661695\pi$
$68$	−0.309640	+	4.26328i	−0.0375494	+	0.516999i
$69$			0.419652i			0.0505201i
$70$	−1.05416	+	1.71479i	−0.125996	+	0.204957i
$71$			13.3181i			1.58056i	0.612744	+	0.790281i	$0.290066\pi$
$71$			13.3181i			1.58056i	−0.612744	+	0.790281i	$0.709934\pi$
$72$	4.03222	−	7.35551i	0.475202	−	0.866856i
$73$	−6.57673	−	6.57673i	−0.769749	−	0.769749i	0.208314	−	0.978062i	$-0.433203\pi$
$73$	−6.57673	−	6.57673i	−0.769749	−	0.769749i	−0.978062	+	0.208314i	$0.933203\pi$
$74$	−0.159995	−	0.0731741i	−0.0185991	−	0.00850631i
$75$	0.793964	−	0.476919i	0.0916791	−	0.0550699i
$76$	7.30478	−	6.31555i	0.837916	−	0.724443i
$77$	0.450097	−	0.450097i	0.0512934	−	0.0512934i
$78$	0.168997	+	0.453863i	0.0191352	+	0.0513899i
$79$	−10.1866			−1.14608			−0.573041	−	0.819527i	$-0.694236\pi$
$79$	−10.1866			−1.14608			−0.573041	+	0.819527i	$0.694236\pi$
$80$	2.36195	−	8.62677i	0.264074	−	0.964502i
$81$	−8.69236			−0.965818
$82$	−1.41835	−	3.80915i	−0.156631	−	0.420651i
$83$	7.91935	−	7.91935i	0.869261	−	0.869261i	−0.123129	−	0.992391i	$-0.539293\pi$
$83$	7.91935	−	7.91935i	0.869261	−	0.869261i	0.992391	+	0.123129i	$0.0392930\pi$
$84$	−0.178392	+	0.154233i	−0.0194641	+	0.0168282i
$85$	3.76614	−	2.94203i	0.408495	−	0.319108i
$86$	12.7429	+	5.82797i	1.37410	+	0.628446i
$87$	−0.899428	−	0.899428i	−0.0964288	−	0.0964288i
$88$	−1.35962	+	2.48021i	−0.144936	+	0.264391i
$89$		−	3.59942i		−	0.381538i	−0.981635	−	0.190769i	$-0.938902\pi$
$89$		−	3.59942i		−	0.381538i	0.981635	−	0.190769i	$-0.0610981\pi$
$90$	−9.12228	+	2.17646i	−0.961573	+	0.229419i
$91$			1.17678i			0.123360i
$92$	0.328215	−	4.51903i	0.0342188	−	0.471142i
$93$	−1.07915	−	1.07915i	−0.111903	−	0.111903i
$94$	−4.30771	+	9.41882i	−0.444306	+	0.971477i
$95$	−10.7156	−	1.31643i	−1.09940	−	0.135063i
$96$	0.568947	−	0.879956i	0.0580679	−	0.0898102i
$97$	−8.41221	+	8.41221i	−0.854130	+	0.854130i	−0.990639	−	0.136509i	$-0.956412\pi$
$97$	−8.41221	+	8.41221i	−0.854130	+	0.854130i	0.136509	+	0.990639i	$0.456412\pi$
$98$	8.74025	−	3.25446i	0.882898	−	0.328750i
$99$	2.96569			0.298063
$100$	−8.92284	+	4.51475i	−0.892284	+	0.451475i
$101$	−11.0128			−1.09582			−0.547909	−	0.836538i	$-0.684576\pi$
$101$	−11.0128			−1.09582			−0.547909	+	0.836538i	$0.684576\pi$
$102$	0.524696	−	0.195372i	0.0519527	−	0.0193447i
$103$	−13.3236	+	13.3236i	−1.31281	+	1.31281i	−0.393474	+	0.919336i	$0.628727\pi$
$103$	−13.3236	+	13.3236i	−1.31281	+	1.31281i	−0.919336	+	0.393474i	$0.871273\pi$
$104$	−1.46488	−	5.01962i	−0.143643	−	0.492214i
$105$	0.261688	+	0.0321488i	0.0255382	+	0.00313740i
$106$	−0.104551	+	0.228602i	−0.0101549	+	0.0222038i
$107$	7.63271	+	7.63271i	0.737882	+	0.737882i	0.972168	−	0.234285i	$-0.0752750\pi$
$107$	7.63271	+	7.63271i	0.737882	+	0.737882i	−0.234285	+	0.972168i	$0.575275\pi$
$108$	−2.20434	−	0.160100i	−0.212113	−	0.0154057i
$109$		−	2.71189i		−	0.259752i	−0.991530	−	0.129876i	$-0.958542\pi$
$109$		−	2.71189i		−	0.259752i	0.991530	−	0.129876i	$-0.0414580\pi$
$110$	3.07594	−	0.733881i	0.293280	−	0.0699728i
$111$			0.0230445i			0.00218729i
$112$	2.04165	−	1.52134i	0.192917	−	0.143753i
$113$	13.6991	+	13.6991i	1.28870	+	1.28870i	0.935578	+	0.353120i	$0.114879\pi$
$113$	13.6991	+	13.6991i	1.28870	+	1.28870i	0.353120	+	0.935578i	$0.385121\pi$
$114$	−1.15024	−	0.526062i	−0.107730	−	0.0492702i
$115$	−3.99206	+	3.11852i	−0.372262	+	0.290803i
$116$	8.98207	+	10.3890i	0.833964	+	0.964593i
$117$	−3.87689	+	3.87689i	−0.358419	+	0.358419i
$118$	−0.585207	−	1.57165i	−0.0538727	−	0.144682i
$119$	1.36044			0.124711
$120$	−1.15627	+	0.188623i	−0.105552	+	0.0172188i
$121$	−1.00000			−0.0909091
$122$	−3.87320	−	10.4020i	−0.350663	−	0.941750i
$123$	−0.376464	+	0.376464i	−0.0339446	+	0.0339446i
$124$	10.7769	+	12.4649i	0.967793	+	1.11938i
$125$	10.4370	+	4.00874i	0.933510	+	0.358552i
$126$	−2.42783	−	1.11037i	−0.216288	−	0.0989196i
$127$	−13.7862	−	13.7862i	−1.22333	−	1.22333i	−0.966442	−	0.256885i	$-0.917304\pi$
$127$	−13.7862	−	13.7862i	−1.22333	−	1.22333i	−0.256885	−	0.966442i	$-0.582696\pi$
$128$	−6.81495	+	9.03086i	−0.602362	+	0.798223i
$129$		−	1.83538i		−	0.161597i
$130$	−3.06166	+	4.98039i	−0.268525	+	0.436809i
$131$			3.94923i			0.345045i	0.985006	+	0.172523i	$0.0551918\pi$
$131$			3.94923i			0.345045i	−0.985006	+	0.172523i	$0.944808\pi$
$132$	0.369503	+	0.0268369i	0.0321611	+	0.00233585i
$133$	−2.17316	−	2.17316i	−0.188437	−	0.188437i
$134$	−2.63718	+	5.76620i	−0.227817	+	0.498123i
$135$	1.52118	+	1.94729i	0.130923	+	0.167596i
$136$	−5.80301	+	1.69350i	−0.497604	+	0.145216i
$137$	−2.55385	+	2.55385i	−0.218190	+	0.218190i	−0.807735	−	0.589545i	$-0.799307\pi$
$137$	−2.55385	+	2.55385i	−0.218190	+	0.218190i	0.589545	+	0.807735i	$0.299307\pi$
$138$	−0.556172	+	0.207092i	−0.0473445	+	0.0176289i
$139$	3.88791			0.329769			0.164884	−	0.986313i	$-0.447275\pi$
$139$	3.88791			0.329769			0.164884	+	0.986313i	$0.447275\pi$
$140$	−2.79286	−	0.550866i	−0.236040	−	0.0465567i
$141$	1.35661			0.114247
$142$	−17.6507	+	6.57228i	−1.48121	+	0.551534i
$143$	1.30725	−	1.30725i	0.109318	−	0.109318i
$144$	11.7383	+	1.71413i	0.978188	+	0.142844i
$145$	1.87225	−	15.2399i	0.155482	−	1.26561i
$146$	5.47074	−	11.9618i	0.452762	−	0.989966i
$147$	−0.863812	−	0.863812i	−0.0712460	−	0.0712460i
$148$	0.0180234	−	0.248155i	0.00148152	−	0.0203982i
$149$			5.06412i			0.414869i	0.978249	+	0.207434i	$0.0665114\pi$
$149$			5.06412i			0.414869i	−0.978249	+	0.207434i	$0.933489\pi$
$150$	1.02388	+	0.816902i	0.0835995	+	0.0666998i
$151$			22.1317i			1.80105i	0.434803	+	0.900526i	$0.356818\pi$
$151$			22.1317i			1.80105i	−0.434803	+	0.900526i	$0.643182\pi$
$152$	11.9749	+	6.56453i	0.971295	+	0.532454i
$153$	4.48195	+	4.48195i	0.362344	+	0.362344i
$154$	0.818640	+	0.374406i	0.0659679	+	0.0301705i
$155$	2.24636	−	18.2852i	0.180432	−	1.46870i
$156$	−0.518116	+	0.447951i	−0.0414825	+	0.0358648i
$157$	0.970860	−	0.970860i	0.0774831	−	0.0774831i	−0.667303	−	0.744786i	$-0.732551\pi$
$157$	0.970860	−	0.970860i	0.0774831	−	0.0774831i	0.744786	+	0.667303i	$0.232551\pi$
$158$	−5.02695	−	13.5005i	−0.399922	−	1.07404i
$159$	0.0329260			0.00261120
$160$	12.5988	−	1.12686i	0.996024	−	0.0890862i
$161$	−1.44205			−0.113649
$162$	−4.28956	−	11.5201i	−0.337020	−	0.905108i
$163$	13.1271	−	13.1271i	1.02819	−	1.02819i	0.0286012	−	0.999591i	$-0.490895\pi$
$163$	13.1271	−	13.1271i	1.02819	−	1.02819i	0.999591	−	0.0286012i	$-0.00910530\pi$
$164$	4.34841	−	3.75953i	0.339554	−	0.293570i
$165$	−0.254989	−	0.326415i	−0.0198509	−	0.0254114i
$166$	14.4038	+	6.58757i	1.11795	+	0.511295i
$167$	6.50750	+	6.50750i	0.503565	+	0.503565i	0.912544	−	0.408979i	$-0.134115\pi$
$167$	6.50750	+	6.50750i	0.503565	+	0.503565i	−0.408979	+	0.912544i	$0.634115\pi$
$168$	−0.292442	−	0.160314i	−0.0225624	−	0.0123685i
$169$		−	9.58219i		−	0.737092i
$170$	5.75766	+	3.53948i	0.441593	+	0.271466i
$171$		−	14.3189i		−	1.09500i
$172$	−1.43548	+	19.7644i	−0.109454	+	1.50702i
$173$	0.0577844	+	0.0577844i	0.00439327	+	0.00439327i	0.709300	−	0.704907i	$-0.249011\pi$
$173$	0.0577844	+	0.0577844i	0.00439327	+	0.00439327i	−0.704907	+	0.709300i	$0.749011\pi$
$174$	0.748174	−	1.63589i	0.0567189	−	0.124016i
$175$	1.63884	+	2.72830i	0.123884	+	0.206240i
$176$	−3.95802	−	0.577988i	−0.298347	−	0.0435675i
$177$	−0.155328	+	0.155328i	−0.0116752	+	0.0116752i
$178$	4.77038	−	1.77627i	0.357555	−	0.133137i
$179$	9.72886			0.727169			0.363584	−	0.931561i	$-0.381553\pi$
$179$	9.72886			0.727169			0.363584	+	0.931561i	$0.381553\pi$
$180$	−7.38623	−	11.0159i	−0.550537	−	0.821075i
$181$	13.1687			0.978822			0.489411	−	0.872053i	$-0.337212\pi$
$181$	13.1687			0.978822			0.489411	+	0.872053i	$0.337212\pi$
$182$	−1.55961	+	0.580725i	−0.115606	+	0.0430462i
$183$	−1.02804	+	1.02804i	−0.0759951	+	0.0759951i
$184$	6.15113	−	1.79509i	0.453467	−	0.132336i
$185$	−0.219218	+	0.171248i	−0.0161172	+	0.0125904i
$186$	0.897676	−	1.96277i	0.0658208	−	0.143917i
$187$	−1.51127	−	1.51127i	−0.110515	−	0.110515i
$188$	−14.6087	−	1.06103i	−1.06545	−	0.0773833i
$189$			0.703417i			0.0511660i
$190$	−3.54332	−	14.8513i	−0.257060	−	1.07742i
$191$			12.9465i			0.936777i	0.883523	+	0.468388i	$0.155165\pi$
$191$			12.9465i			0.936777i	−0.883523	+	0.468388i	$0.844835\pi$
$192$	1.44699	+	0.319789i	0.104428	+	0.0230788i
$193$	−6.86229	−	6.86229i	−0.493958	−	0.493958i	0.415593	−	0.909551i	$-0.363574\pi$
$193$	−6.86229	−	6.86229i	−0.493958	−	0.493958i	−0.909551	+	0.415593i	$0.863574\pi$
$194$	−15.3002	−	6.99755i	−1.09849	−	0.502395i
$195$	0.760040	+	0.0933721i	0.0544276	+	0.00668651i
$196$	8.62639	+	9.97759i	0.616171	+	0.712685i
$197$	−9.23206	+	9.23206i	−0.657757	+	0.657757i	−0.954849	−	0.297092i	$-0.903983\pi$
$197$	−9.23206	+	9.23206i	−0.657757	+	0.657757i	0.297092	+	0.954849i	$0.403983\pi$
$198$	1.46353	+	3.93048i	0.104008	+	0.279327i
$199$	−0.0379759			−0.00269204			−0.00134602	−	0.999999i	$-0.500428\pi$
$199$	−0.0379759			−0.00269204			−0.00134602	+	0.999999i	$0.500428\pi$
$200$	−10.3868	−	9.59764i	−0.734457	−	0.678655i
$201$	0.830518			0.0585802
$202$	−5.43469	−	14.5955i	−0.382383	−	1.02694i
$203$	3.09070	−	3.09070i	0.216925	−	0.216925i
$204$	0.517861	+	0.598976i	0.0362575	+	0.0419367i
$205$	−6.37882	−	0.783647i	−0.445516	−	0.0547323i
$206$	−24.2330	−	11.0830i	−1.68839	−	0.772187i
$207$	−4.75082	−	4.75082i	−0.330205	−	0.330205i
$208$	5.92970	−	4.41855i	0.411151	−	0.306371i
$209$			4.82820i			0.333973i
$210$	0.0865323	+	0.362686i	0.00597130	+	0.0250277i
$211$		−	15.6859i		−	1.07986i	−0.841709	−	0.539931i	$-0.818450\pi$
$211$		−	15.6859i		−	1.07986i	0.841709	−	0.539931i	$-0.181550\pi$
$212$	−0.354565	−	0.0257519i	−0.0243516	−	0.00176865i
$213$	1.74444	+	1.74444i	0.119527	+	0.119527i
$214$	−6.34914	+	13.8824i	−0.434018	+	0.948983i
$215$	17.4597	−	13.6391i	1.19074	−	0.930181i
$216$	−0.875629	−	3.00046i	−0.0595790	−	0.204156i
$217$	3.70829	−	3.70829i	0.251735	−	0.251735i
$218$	3.59412	−	1.33828i	0.243425	−	0.0906399i
$219$	−1.72288			−0.116422
$220$	2.49056	+	3.71444i	0.167914	+	0.250428i
$221$	3.95121			0.265787
$222$	−0.0305413	+	0.0113721i	−0.00204980	+	0.000763248i
$223$	−11.5641	+	11.5641i	−0.774388	+	0.774388i	−0.978870	−	0.204483i	$-0.934449\pi$
$223$	−11.5641	+	11.5641i	−0.774388	+	0.774388i	0.204483	+	0.978870i	$0.434449\pi$
$224$	3.02379	+	1.95507i	0.202036	+	0.130629i
$225$	−3.58922	+	14.3875i	−0.239281	+	0.959166i
$226$	−11.3953	+	24.9159i	−0.758005	+	1.65738i
$227$	−4.37686	−	4.37686i	−0.290502	−	0.290502i	0.546776	−	0.837279i	$-0.315855\pi$
$227$	−4.37686	−	4.37686i	−0.290502	−	0.290502i	−0.837279	+	0.546776i	$0.815855\pi$
$228$	0.129574	−	1.78404i	0.00858123	−	0.118151i
$229$		−	29.7092i		−	1.96324i	−0.190842	−	0.981621i	$-0.561122\pi$
$229$		−	29.7092i		−	1.96324i	0.190842	−	0.981621i	$-0.438878\pi$
$230$	−6.10306	−	3.75181i	−0.402424	−	0.247387i
$231$		−	0.117910i		−	0.00775794i
$232$	−9.33619	+	17.0309i	−0.612951	+	1.11814i
$233$	9.07729	+	9.07729i	0.594673	+	0.594673i	0.938890	−	0.344217i	$-0.111856\pi$
$233$	9.07729	+	9.07729i	0.594673	+	0.594673i	−0.344217	+	0.938890i	$0.611856\pi$
$234$	−7.05132	−	3.22493i	−0.460959	−	0.210820i
$235$	10.0813	+	12.9052i	0.657630	+	0.841842i
$236$	1.79414	−	1.55117i	0.116789	−	0.100973i
$237$	−1.33427	+	1.33427i	−0.0866704	+	0.0866704i
$238$	0.671357	+	1.80301i	0.0435176	+	0.116872i
$239$	−21.1659			−1.36911			−0.684555	−	0.728961i	$-0.740004\pi$
$239$	−21.1659			−1.36911			−0.684555	+	0.728961i	$0.740004\pi$
$240$	−0.820587	−	1.43934i	−0.0529687	−	0.0929089i
$241$	28.4869			1.83501			0.917503	−	0.397730i	$-0.130202\pi$
$241$	28.4869			1.83501			0.917503	+	0.397730i	$0.130202\pi$
$242$	−0.493487	−	1.32532i	−0.0317225	−	0.0851947i
$243$	−3.48277	+	3.48277i	−0.223420	+	0.223420i
$244$	11.8746	−	10.2665i	0.760191	−	0.657243i
$245$	1.79811	−	14.6364i	0.114877	−	0.935088i
$246$	−0.684716	−	0.313155i	−0.0436559	−	0.0199661i
$247$	−6.31166	−	6.31166i	−0.401601	−	0.401601i
$248$	−11.2018	+	20.4341i	−0.711313	+	1.29757i
$249$		−	2.07460i		−	0.131473i
$250$	−0.162361	+	15.8106i	−0.0102686	+	0.999947i
$251$		−	22.1209i		−	1.39626i	−0.715973	−	0.698128i	$-0.754017\pi$
$251$		−	22.1209i		−	1.39626i	0.715973	−	0.698128i	$-0.245983\pi$
$252$	0.273494	−	3.76560i	0.0172285	−	0.237211i
$253$	1.60193	+	1.60193i	0.100712	+	0.100712i
$254$	11.4678	−	25.0744i	0.719554	−	1.57331i
$255$	0.107944	−	0.878657i	0.00675973	−	0.0550237i
$256$	−15.3319	−	4.57538i	−0.958241	−	0.285961i
$257$	12.7085	−	12.7085i	0.792734	−	0.792734i	−0.189204	−	0.981938i	$-0.560591\pi$
$257$	12.7085	−	12.7085i	0.792734	−	0.792734i	0.981938	+	0.189204i	$0.0605908\pi$
$258$	2.43247	−	0.905737i	0.151439	−	0.0563887i
$259$	−0.0791877			−0.00492048
$260$	−8.11150	−	1.59992i	−0.503054	−	0.0992228i
$261$	20.3646			1.26054
$262$	−5.23398	+	1.94889i	−0.323357	+	0.120403i
$263$	−5.54816	+	5.54816i	−0.342114	+	0.342114i	−0.857162	−	0.515048i	$-0.827774\pi$
$263$	−5.54816	+	5.54816i	−0.342114	+	0.342114i	0.515048	+	0.857162i	$0.327774\pi$
$264$	0.146777	+	0.502954i	0.00903353	+	0.0309546i
$265$	0.244680	+	0.313219i	0.0150306	+	0.0192409i
$266$	1.80771	−	3.95255i	0.110838	−	0.242347i
$267$	−0.471464	−	0.471464i	−0.0288531	−	0.0288531i
$268$	−8.94346	−	0.649560i	−0.546309	−	0.0396782i
$269$			5.57306i			0.339795i	0.985462	+	0.169898i	$0.0543437\pi$
$269$			5.57306i			0.339795i	−0.985462	+	0.169898i	$0.945656\pi$
$270$	−1.83010	+	2.97702i	−0.111376	+	0.181175i
$271$		−	12.9739i		−	0.788108i	−0.919087	−	0.394054i	$-0.871072\pi$
$271$		−	12.9739i		−	0.788108i	0.919087	−	0.394054i	$-0.128928\pi$
$272$	−5.10814	−	6.85513i	−0.309726	−	0.415653i
$273$	0.154138	+	0.154138i	0.00932888	+	0.00932888i
$274$	−4.64495	−	2.12437i	−0.280612	−	0.128338i
$275$	1.21025	−	4.85132i	0.0729807	−	0.292546i
$276$	−0.548927	−	0.634908i	−0.0330415	−	0.0382170i
$277$	0.719135	−	0.719135i	0.0432086	−	0.0432086i	−0.685172	−	0.728381i	$-0.740273\pi$
$277$	0.719135	−	0.719135i	0.0432086	−	0.0432086i	0.728381	+	0.685172i	$0.240273\pi$
$278$	1.91863	+	5.15273i	0.115072	+	0.309040i
$279$	24.4339			1.46282
$280$	−0.648164	−	3.97327i	−0.0387352	−	0.237448i
$281$	−21.2210			−1.26594			−0.632968	−	0.774178i	$-0.718164\pi$
$281$	−21.2210			−1.26594			−0.632968	+	0.774178i	$0.718164\pi$
$282$	0.669470	+	1.79795i	0.0398664	+	0.107066i
$283$	−3.04585	+	3.04585i	−0.181057	+	0.181057i	−0.791816	−	0.610759i	$-0.790864\pi$
$283$	−3.04585	+	3.04585i	−0.181057	+	0.181057i	0.610759	+	0.791816i	$0.290864\pi$
$284$	−17.4207	−	20.1495i	−1.03373	−	1.19565i
$285$	−1.57600	+	1.23114i	−0.0933540	+	0.0729262i
$286$	2.37763	+	1.08741i	0.140592	+	0.0643001i
$287$	−1.29364	−	1.29364i	−0.0763613	−	0.0763613i
$288$	3.52090	+	16.4028i	0.207471	+	0.966546i
$289$			12.4321i			0.731302i
$290$	21.1217	−	5.03937i	1.24031	−	0.295922i
$291$			2.20372i			0.129184i
$292$	18.5529	+	1.34749i	1.08573	+	0.0788560i
$293$	18.5778	+	18.5778i	1.08533	+	1.08533i	0.996002	+	0.0893270i	$0.0284716\pi$
$293$	18.5778	+	18.5778i	1.08533	+	1.08533i	0.0893270	+	0.996002i	$0.471528\pi$
$294$	0.718547	−	1.57111i	0.0419065	−	0.0916287i
$295$	−2.63188	−	0.323331i	−0.153234	−	0.0188250i
$296$	0.337779	−	0.0985745i	0.0196330	−	0.00572953i
$297$	0.781405	−	0.781405i	0.0453417	−	0.0453417i
$298$	−6.71157	+	2.49907i	−0.388791	+	0.144768i
$299$	−4.18824			−0.242212
$300$	−0.577385	+	1.76010i	−0.0333353	+	0.101619i
$301$	6.30692			0.363525
$302$	−29.3316	+	10.9217i	−1.68784	+	0.628473i
$303$	−1.44250	+	1.44250i	−0.0828694	+	0.0828694i
$304$	−2.79064	+	19.1101i	−0.160054	+	1.09604i
$305$	−17.4192	−	2.13997i	−0.997419	−	0.122534i
$306$	−3.72823	+	8.15179i	−0.213129	+	0.466007i
$307$	15.0794	+	15.0794i	0.860627	+	0.860627i	0.991411	−	0.130784i	$-0.0417493\pi$
$307$	15.0794	+	15.0794i	0.860627	+	0.860627i	−0.130784	+	0.991411i	$0.541749\pi$
$308$	−0.0922195	+	1.26972i	−0.00525469	+	0.0723492i
$309$			3.49033i			0.198558i
$310$	25.3423	−	6.04635i	1.43935	−	0.343410i
$311$			6.20650i			0.351938i	0.984396	+	0.175969i	$0.0563059\pi$
$311$			6.20650i			0.351938i	−0.984396	+	0.175969i	$0.943694\pi$
$312$	−0.849361	−	0.465611i	−0.0480856	−	0.0263600i
$313$	2.04714	+	2.04714i	0.115711	+	0.115711i	0.762592	−	0.646880i	$-0.223927\pi$
$313$	2.04714	+	2.04714i	0.115711	+	0.115711i	−0.646880	+	0.762592i	$0.723927\pi$
$314$	1.76581	+	0.807593i	0.0996502	+	0.0455751i
$315$	−3.32649	+	2.59859i	−0.187426	+	0.146414i
$316$	15.4117	−	13.3246i	0.866977	−	0.749568i
$317$	−5.60378	+	5.60378i	−0.314739	+	0.314739i	−0.846742	−	0.532003i	$-0.821439\pi$
$317$	−5.60378	+	5.60378i	−0.314739	+	0.314739i	0.532003	+	0.846742i	$0.321439\pi$
$318$	0.0162485	+	0.0436375i	0.000911173	+	0.00244707i
$319$	−6.86674			−0.384464
$320$	7.71080	+	16.1414i	0.431047	+	0.902330i
$321$	1.99952			0.111602
$322$	−0.711631	−	1.91117i	−0.0396576	−	0.106505i
$323$	−7.29670	+	7.29670i	−0.405999	+	0.405999i
$324$	13.1510	−	11.3701i	0.730613	−	0.631671i
$325$	4.75979	+	7.92399i	0.264026	+	0.439544i
$326$	23.8756	+	10.9195i	1.32235	+	0.604777i
$327$	−0.355213	−	0.355213i	−0.0196433	−	0.0196433i
$328$	7.12846	+	3.90775i	0.393603	+	0.215769i
$329$			4.66172i			0.257009i
$330$	0.306771	−	0.499023i	0.0168872	−	0.0274703i
$331$			18.9458i			1.04136i	0.853753	+	0.520678i	$0.174321\pi$
$331$			18.9458i			1.04136i	−0.853753	+	0.520678i	$0.825679\pi$
$332$	−1.62258	+	22.3405i	−0.0890505	+	1.22609i
$333$	−0.260883	−	0.260883i	−0.0142963	−	0.0142963i
$334$	−5.41315	+	11.8359i	−0.296194	+	0.647630i
$335$	6.17175	+	7.90055i	0.337199	+	0.431653i
$336$	0.0681508	−	0.466692i	0.00371793	−	0.0254601i
$337$	−16.7152	+	16.7152i	−0.910536	+	0.910536i	−0.996314	−	0.0857784i	$-0.972662\pi$
$337$	−16.7152	+	16.7152i	−0.910536	+	0.910536i	0.0857784	+	0.996314i	$0.472662\pi$
$338$	12.6995	−	4.72868i	0.690760	−	0.257206i
$339$	3.58869			0.194911
$340$	−1.84961	+	9.37743i	−0.100309	+	0.508563i
$341$	−8.23887			−0.446160
$342$	18.9771	−	7.06620i	1.02617	−	0.382096i
$343$	6.11899	−	6.11899i	0.330395	−	0.330395i
$344$	−26.9025	+	7.85100i	−1.45049	+	0.423297i
$345$	−0.114420	+	0.931367i	−0.00616015	+	0.0501431i
$346$	−0.0480670	+	0.105099i	−0.00258410	+	0.00565014i
$347$	−9.86605	−	9.86605i	−0.529637	−	0.529637i	0.390827	−	0.920464i	$-0.372189\pi$
$347$	−9.86605	−	9.86605i	−0.529637	−	0.529637i	−0.920464	+	0.390827i	$0.872189\pi$
$348$	2.53728	+	0.184282i	0.136013	+	0.00987855i
$349$			20.0654i			1.07408i	0.843557	+	0.537039i	$0.180457\pi$
$349$			20.0654i			1.07408i	−0.843557	+	0.537039i	$0.819543\pi$
$350$	−2.80712	+	3.51836i	−0.150047	+	0.188064i
$351$			2.04298i			0.109046i
$352$	−1.18721	−	5.53087i	−0.0632786	−	0.294796i
$353$	−16.8986	−	16.8986i	−0.899420	−	0.899420i	0.0959650	−	0.995385i	$-0.469406\pi$
$353$	−16.8986	−	16.8986i	−0.899420	−	0.899420i	−0.995385	+	0.0959650i	$0.969406\pi$
$354$	−0.282512	−	0.129207i	−0.0150153	−	0.00686728i
$355$	−3.63123	+	29.5579i	−0.192725	+	1.56877i
$356$	4.70824	+	5.44571i	0.249536	+	0.288622i
$357$	0.178194	−	0.178194i	0.00943104	−	0.00943104i
$358$	4.80106	+	12.8938i	0.253744	+	0.681461i
$359$	12.8608			0.678765			0.339382	−	0.940649i	$-0.389782\pi$
$359$	12.8608			0.678765			0.339382	+	0.940649i	$0.389782\pi$
$360$	10.9546	−	15.2253i	0.577356	−	0.802444i
$361$	4.31150			0.226921
$362$	6.49858	+	17.4527i	0.341558	+	0.917296i
$363$	−0.130983	+	0.130983i	−0.00687484	+	0.00687484i
$364$	−1.53929	−	1.78040i	−0.0806808	−	0.0933183i
$365$	−12.8031	−	16.3895i	−0.670146	−	0.857864i
$366$	−1.86981	−	0.855159i	−0.0977365	−	0.0446999i
$367$	−24.0770	−	24.0770i	−1.25681	−	1.25681i	−0.952607	−	0.304205i	$-0.901609\pi$
$367$	−24.0770	−	24.0770i	−1.25681	−	1.25681i	−0.304205	−	0.952607i	$-0.598391\pi$
$368$	5.41457	+	7.26636i	0.282254	+	0.378785i
$369$		−	8.52380i		−	0.443731i
$370$	−0.335140	−	0.206025i	−0.0174231	−	0.0107107i
$371$			0.113144i			0.00587412i
$372$	3.04429	+	0.221106i	0.157839	+	0.0114638i
$373$	−22.7111	−	22.7111i	−1.17594	−	1.17594i	−0.980770	−	0.195169i	$-0.937475\pi$
$373$	−22.7111	−	22.7111i	−1.17594	−	1.17594i	−0.195169	−	0.980770i	$-0.562525\pi$
$374$	1.25712	−	2.74870i	0.0650042	−	0.142132i
$375$	1.89214	−	0.841989i	0.0977099	−	0.0434801i
$376$	−5.80302	−	19.8848i	−0.299268	−	1.02548i
$377$	8.97655	−	8.97655i	0.462316	−	0.462316i
$378$	−0.932252	+	0.347127i	−0.0479499	+	0.0178543i
$379$	−9.16837			−0.470947			−0.235474	−	0.971881i	$-0.575664\pi$
$379$	−9.16837			−0.470947			−0.235474	+	0.971881i	$0.575664\pi$
$380$	17.9341	−	12.0249i	0.919999	−	0.616866i
$381$	−3.61152			−0.185024
$382$	−17.1583	+	6.38893i	−0.877893	+	0.326886i
$383$	−0.844729	+	0.844729i	−0.0431636	+	0.0431636i	−0.728359	−	0.685196i	$-0.759717\pi$
$383$	−0.844729	+	0.844729i	−0.0431636	+	0.0431636i	0.685196	+	0.728359i	$0.259717\pi$
$384$	0.290247	+	2.07554i	0.0148116	+	0.105917i
$385$	1.12166	−	0.876217i	0.0571651	−	0.0446562i
$386$	5.70827	−	12.4812i	0.290544	−	0.635275i
$387$	20.7781	+	20.7781i	1.05621	+	1.05621i
$388$	1.72356	−	23.7308i	0.0875004	−	1.20475i
$389$			25.5793i			1.29692i	0.761249	+	0.648460i	$0.224587\pi$
$389$			25.5793i			1.29692i	−0.761249	+	0.648460i	$0.775413\pi$
$390$	0.251322	+	1.05337i	0.0127262	+	0.0533397i
$391$			4.84189i			0.244865i
$392$	−8.96648	+	16.3565i	−0.452876	+	0.826129i
$393$	0.517282	+	0.517282i	0.0260934	+	0.0260934i
$394$	−16.7913	−	7.67953i	−0.845935	−	0.386889i
$395$	−22.6079	−	2.77742i	−1.13753	−	0.139747i
$396$	−4.48691	+	3.87928i	−0.225476	+	0.194941i
$397$	13.8635	−	13.8635i	0.695788	−	0.695788i	−0.267711	−	0.963499i	$-0.586267\pi$
$397$	13.8635	−	13.8635i	0.695788	−	0.695788i	0.963499	+	0.267711i	$0.0862673\pi$
$398$	−0.0187406	−	0.0503302i	−0.000939381	−	0.00252282i
$399$	−0.569295			−0.0285004
$400$	7.59419	−	18.5021i	0.379710	−	0.925106i
$401$	−1.01381			−0.0506274			−0.0253137	−	0.999680i	$-0.508058\pi$
$401$	−1.01381			−0.0506274			−0.0253137	+	0.999680i	$0.508058\pi$
$402$	0.409849	+	1.10070i	0.0204414	+	0.0548980i
$403$	10.7703	−	10.7703i	0.536505	−	0.536505i
$404$	16.6618	−	14.4054i	0.828955	−	0.716695i
$405$	−19.2917	−	2.37001i	−0.958611	−	0.117767i
$406$	5.62139	+	2.57095i	0.278985	+	0.127594i
$407$	0.0879673	+	0.0879673i	0.00436038	+	0.00436038i
$408$	−0.538277	+	0.981918i	−0.0266487	+	0.0486122i
$409$			17.2743i			0.854160i	0.904214	+	0.427080i	$0.140458\pi$
$409$			17.2743i			0.854160i	−0.904214	+	0.427080i	$0.859542\pi$
$410$	−2.10928	−	8.84069i	−0.104170	−	0.436611i
$411$			0.669022i			0.0330004i
$412$	2.72984	−	37.5857i	0.134489	−	1.85172i
$413$	−0.533754	−	0.533754i	−0.0262643	−	0.0262643i
$414$	3.95188	−	8.64081i	0.194225	−	0.424673i
$415$	19.7353	−	15.4168i	0.968768	−	0.756782i
$416$	8.78221	+	5.67825i	0.430583	+	0.278399i
$417$	0.509252	−	0.509252i	0.0249382	−	0.0249382i
$418$	−6.39890	+	2.38265i	−0.312981	+	0.116539i
$419$	−8.43717			−0.412183			−0.206091	−	0.978533i	$-0.566074\pi$
$419$	−8.43717			−0.412183			−0.206091	+	0.978533i	$0.566074\pi$
$420$	−0.437972	+	0.293663i	−0.0213708	+	0.0143293i
$421$	−20.1417			−0.981648			−0.490824	−	0.871259i	$-0.663304\pi$
$421$	−20.1417			−0.981648			−0.490824	+	0.871259i	$0.663304\pi$
$422$	20.7888	−	7.74079i	1.01199	−	0.376816i
$423$	−15.3580	+	15.3580i	−0.746733	+	0.746733i
$424$	−0.140844	−	0.482620i	−0.00683997	−	0.0234381i
$425$	9.16065	−	5.50263i	0.444357	−	0.266917i
$426$	−1.45108	+	3.17280i	−0.0703053	+	0.153723i
$427$	−3.53266	−	3.53266i	−0.170957	−	0.170957i
$428$	−21.5319	−	1.56385i	−1.04078	−	0.0755915i
$429$		−	0.342456i		−	0.0165339i
$430$	26.6923	+	16.4089i	1.28722	+	0.791307i
$431$		−	0.347336i		−	0.0167306i	−0.999965	−	0.00836528i	$-0.997337\pi$
$431$		−	0.347336i		−	0.0167306i	0.999965	−	0.00836528i	$-0.00266278\pi$
$432$	3.54446	−	2.64118i	0.170533	−	0.127074i
$433$	−20.5748	−	20.5748i	−0.988760	−	0.988760i	0.0111777	−	0.999938i	$-0.496442\pi$
$433$	−20.5748	−	20.5748i	−0.988760	−	0.988760i	−0.999938	+	0.0111777i	$0.996442\pi$
$434$	6.74467	+	3.08468i	0.323754	+	0.148069i
$435$	−1.75094	−	2.24141i	−0.0839513	−	0.107467i
$436$	3.54730	+	4.10294i	0.169885	+	0.196495i
$437$	7.73443	−	7.73443i	0.369988	−	0.369988i
$438$	−0.850220	−	2.28337i	−0.0406251	−	0.109104i
$439$	−1.36529			−0.0651619			−0.0325809	−	0.999469i	$-0.510373\pi$
$439$	−1.36529			−0.0651619			−0.0325809	+	0.999469i	$0.510373\pi$
$440$	−3.69377	+	5.13382i	−0.176093	+	0.244745i
$441$	19.5582			0.931342
$442$	1.94987	+	5.23662i	0.0927458	+	0.249080i
$443$	−13.5779	+	13.5779i	−0.645104	+	0.645104i	−0.951806	−	0.306701i	$-0.900775\pi$
$443$	−13.5779	+	13.5779i	−0.645104	+	0.645104i	0.306701	+	0.951806i	$0.400775\pi$
$444$	−0.0301434	−	0.0348650i	−0.00143054	−	0.00165462i
$445$	0.981397	−	7.98849i	0.0465227	−	0.378691i
$446$	−21.0328	−	9.61937i	−0.995932	−	0.455491i
$447$	0.663315	+	0.663315i	0.0313737	+	0.0313737i
$448$	−1.09889	+	4.97229i	−0.0519177	+	0.234919i
$449$			11.4720i			0.541396i	0.962664	+	0.270698i	$0.0872545\pi$
$449$			11.4720i			0.541396i	−0.962664	+	0.270698i	$0.912746\pi$
$450$	−20.8393	+	2.34317i	−0.982372	+	0.110458i
$451$			2.87414i			0.135338i
$452$	−38.6450	−	2.80677i	−1.81771	−	0.132019i
$453$	2.89888	+	2.89888i	0.136201	+	0.136201i
$454$	3.64081	−	7.96066i	0.170872	−	0.373612i
$455$	−0.320854	+	2.61172i	−0.0150419	+	0.122440i
$456$	2.42836	−	0.708671i	0.113718	−	0.0331866i
$457$	6.66780	−	6.66780i	0.311907	−	0.311907i	−0.533741	−	0.845648i	$-0.679214\pi$
$457$	6.66780	−	6.66780i	0.311907	−	0.311907i	0.845648	+	0.533741i	$0.179214\pi$
$458$	39.3742	−	14.6611i	1.83984	−	0.685069i
$459$	2.36183			0.110241
$460$	1.96057	−	9.93997i	0.0914120	−	0.463454i
$461$	−15.1883			−0.707389			−0.353694	−	0.935361i	$-0.615075\pi$
$461$	−15.1883			−0.707389			−0.353694	+	0.935361i	$0.615075\pi$
$462$	0.156269	−	0.0581872i	0.00727029	−	0.00270711i
$463$	18.1074	−	18.1074i	0.841524	−	0.841524i	−0.147533	−	0.989057i	$-0.547133\pi$
$463$	18.1074	−	18.1074i	0.841524	−	0.841524i	0.989057	+	0.147533i	$0.0471333\pi$
$464$	−27.1787	−	3.96889i	−1.26174	−	0.184251i
$465$	−2.10082	−	2.68929i	−0.0974232	−	0.124713i
$466$	−7.55078	+	16.5098i	−0.349783	+	0.764803i
$467$	16.9943	+	16.9943i	0.786401	+	0.786401i	0.980902	−	0.194501i	$-0.0623087\pi$
$467$	16.9943	+	16.9943i	0.786401	+	0.786401i	−0.194501	+	0.980902i	$0.562309\pi$
$468$	0.794328	−	10.9367i	0.0367178	−	0.505549i
$469$			2.85390i			0.131781i
$470$	−12.1285	+	19.7295i	−0.559447	+	0.910052i
$471$		−	0.254333i		−	0.0117190i
$472$	2.94118	+	1.61233i	0.135379	+	0.0742134i
$473$	−7.00618	−	7.00618i	−0.322144	−	0.322144i
$474$	−2.42678	−	1.10989i	−0.111466	−	0.0509790i
$475$	−23.4231	−	5.84332i	−1.07473	−	0.268110i
$476$	−2.05826	+	1.77952i	−0.0943402	+	0.0815643i
$477$	−0.372751	+	0.372751i	−0.0170671	+	0.0170671i
$478$	−10.4451	−	28.0516i	−0.477748	−	1.28305i
$479$	19.6200			0.896463			0.448231	−	0.893918i	$-0.352054\pi$
$479$	19.6200			0.896463			0.448231	+	0.893918i	$0.352054\pi$
$480$	1.50263	−	1.79783i	0.0685856	−	0.0820595i
$481$	−0.229990			−0.0104867
$482$	14.0579	+	37.7543i	0.640321	+	1.71966i
$483$	−0.188884	+	0.188884i	−0.00859452	+	0.00859452i
$484$	1.51294	−	1.30805i	0.0687701	−	0.0594570i
$485$	−20.9635	+	16.3763i	−0.951905	+	0.743609i
$486$	−6.33448	−	2.89708i	−0.287338	−	0.131414i
$487$	−5.76934	−	5.76934i	−0.261434	−	0.261434i	0.564203	−	0.825636i	$-0.309184\pi$
$487$	−5.76934	−	5.76934i	−0.261434	−	0.261434i	−0.825636	+	0.564203i	$0.809184\pi$
$488$	19.4663	+	10.6712i	0.881197	+	0.483063i
$489$		−	3.43886i		−	0.155510i
$490$	20.2853	−	4.83982i	0.916396	−	0.218641i
$491$		−	30.7490i		−	1.38768i	−0.720129	−	0.693841i	$-0.755917\pi$
$491$		−	30.7490i		−	1.38768i	0.720129	−	0.693841i	$-0.244083\pi$
$492$	0.0771330	−	1.06200i	0.00347742	−	0.0478789i
$493$	−10.3775	−	10.3775i	−0.467379	−	0.467379i
$494$	5.25025	−	11.4797i	0.236220	−	0.516496i
$495$	6.58199	+	0.808607i	0.295839	+	0.0363442i
$496$	−32.6096	−	4.76197i	−1.46422	−	0.213819i
$497$	−5.99442	+	5.99442i	−0.268887	+	0.268887i
$498$	2.74951	−	1.02379i	0.123209	−	0.0458771i
$499$	31.2497			1.39893			0.699465	−	0.714667i	$-0.253422\pi$
$499$	31.2497			1.39893			0.699465	+	0.714667i	$0.253422\pi$
$500$	−21.0342	+	7.58712i	−0.940676	+	0.339306i
$501$	1.70475			0.0761625
$502$	29.3172	−	10.9163i	1.30849	−	0.487220i
$503$	18.7349	−	18.7349i	0.835346	−	0.835346i	−0.152896	−	0.988242i	$-0.548860\pi$
$503$	18.7349	−	18.7349i	0.835346	−	0.835346i	0.988242	+	0.152896i	$0.0488599\pi$
$504$	5.12559	−	1.49581i	0.228312	−	0.0666285i
$505$	−24.4417	−	3.00270i	−1.08764	−	0.133618i
$506$	−1.33254	+	2.91360i	−0.0592385	+	0.129525i
$507$	−1.25511	−	1.25511i	−0.0557413	−	0.0557413i
$508$	38.8908	+	2.82462i	1.72550	+	0.125322i
$509$		−	14.4389i		−	0.639993i	−0.947419	−	0.319996i	$-0.896318\pi$
$509$		−	14.4389i		−	0.639993i	0.947419	−	0.319996i	$-0.103682\pi$
$510$	1.21777	−	0.290545i	0.0539238	−	0.0128655i
$511$		−	5.92034i		−	0.261900i
$512$	−1.50223	−	22.5775i	−0.0663900	−	0.997794i
$513$	−3.77278	−	3.77278i	−0.166572	−	0.166572i
$514$	23.1143	+	10.5713i	1.01953	+	0.466282i
$515$	−33.2028	+	25.9374i	−1.46309	+	1.14294i
$516$	2.40078	+	2.77683i	0.105689	+	0.122243i
$517$	5.17857	−	5.17857i	0.227753	−	0.227753i
$518$	−0.0390780	−	0.104949i	−0.00171699	−	0.00461119i
$519$	0.0151376			0.000664466
$520$	−1.88251	−	11.5399i	−0.0825536	−	0.506056i
$521$	−20.4978			−0.898025			−0.449013	−	0.893525i	$-0.648224\pi$
$521$	−20.4978			−0.898025			−0.449013	+	0.893525i	$0.648224\pi$
$522$	10.0497	+	26.9896i	0.439862	+	1.18130i
$523$	−8.78829	+	8.78829i	−0.384285	+	0.384285i	−0.872643	−	0.488358i	$-0.837596\pi$
$523$	−8.78829	+	8.78829i	−0.384285	+	0.384285i	0.488358	+	0.872643i	$0.337596\pi$
$524$	−5.16580	−	5.97495i	−0.225669	−	0.261017i
$525$	0.572021	+	0.142701i	0.0249651	+	0.00622798i
$526$	−10.0910	−	4.61514i	−0.439989	−	0.201230i
$527$	−12.4511	−	12.4511i	−0.542380	−	0.542380i
$528$	−0.594141	+	0.442728i	−0.0258567	+	0.0192673i
$529$			17.8677i			0.776855i
$530$	−0.294369	+	0.478849i	−0.0127866	+	0.0207999i
$531$		−	3.51690i		−	0.152620i
$532$	6.13047	+	0.445254i	0.265790	+	0.0193042i
$533$	−3.75722	−	3.75722i	−0.162743	−	0.162743i
$534$	0.392179	−	0.857501i	0.0169712	−	0.0371077i
$535$	14.8588	+	19.0210i	0.642403	+	0.822350i
$536$	−3.55260	−	12.1735i	−0.153449	−	0.525815i
$537$	1.27432	−	1.27432i	0.0549908	−	0.0549908i
$538$	−7.38608	+	2.75023i	−0.318437	+	0.118571i
$539$	−6.59482			−0.284059
$540$	−4.84862	−	0.956347i	−0.208652	−	0.0411546i
$541$	19.5937			0.842400			0.421200	−	0.906968i	$-0.361609\pi$
$541$	19.5937			0.842400			0.421200	+	0.906968i	$0.361609\pi$
$542$	17.1946	−	6.40244i	0.738569	−	0.275008i
$543$	1.72488	−	1.72488i	0.0740217	−	0.0740217i
$544$	6.56443	−	10.1528i	0.281448	−	0.435299i
$545$	0.739409	−	6.01873i	0.0316728	−	0.257814i
$546$	−0.128217	+	0.280348i	−0.00548720	+	0.0119978i
$547$	28.6394	+	28.6394i	1.22453	+	1.22453i	0.966003	+	0.258531i	$0.0832383\pi$
$547$	28.6394	+	28.6394i	1.22453	+	1.22453i	0.258531	+	0.966003i	$0.416762\pi$
$548$	0.523252	−	7.20439i	0.0223522	−	0.307756i
$549$		−	23.2766i		−	0.993423i
$550$	7.02679	−	0.790095i	0.299623	−	0.0336898i
$551$			33.1540i			1.41241i
$552$	0.570568	−	1.04082i	0.0242850	−	0.0443003i
$553$	−4.58496	−	4.58496i	−0.194972	−	0.194972i
$554$	1.30797	+	0.598200i	0.0555702	+	0.0254151i
$555$	−0.00628318	+	0.0511445i	−0.000266706	+	0.00217096i
$556$	−5.88219	+	5.08560i	−0.249460	+	0.215678i
$557$	12.3215	−	12.3215i	0.522080	−	0.522080i	−0.396119	−	0.918199i	$-0.629643\pi$
$557$	12.3215	−	12.3215i	0.522080	−	0.522080i	0.918199	+	0.396119i	$0.129643\pi$
$558$	12.0578	+	32.3827i	0.510448	+	1.37087i
$559$	18.3177			0.774754
$560$	4.94599	−	2.81978i	0.209006	−	0.119158i
$561$	−0.395902			−0.0167150
$562$	−10.4723	−	28.1245i	−0.441745	−	1.18636i
$563$	21.8674	−	21.8674i	0.921603	−	0.921603i	−0.0755402	−	0.997143i	$-0.524068\pi$
$563$	21.8674	−	21.8674i	0.921603	−	0.921603i	0.997143	+	0.0755402i	$0.0240681\pi$
$564$	−2.05248	+	1.77452i	−0.0864249	+	0.0747209i
$565$	26.6683	+	34.1385i	1.12195	+	1.43622i
$566$	−5.53980	−	2.53363i	−0.232855	−	0.106497i
$567$	−3.91241	−	3.91241i	−0.164306	−	0.164306i
$568$	18.1076	−	33.0315i	0.759776	−	1.38597i
$569$			23.0589i			0.966678i	0.875433	+	0.483339i	$0.160576\pi$
$569$			23.0589i			0.966678i	−0.875433	+	0.483339i	$0.839424\pi$
$570$	−2.40938	−	1.48115i	−0.100918	−	0.0620385i
$571$		−	26.4366i		−	1.10634i	−0.833070	−	0.553168i	$-0.813419\pi$
$571$		−	26.4366i		−	1.10634i	0.833070	−	0.553168i	$-0.186581\pi$
$572$	−0.267840	+	3.68775i	−0.0111989	+	0.154192i
$573$	1.69578	+	1.69578i	0.0708421	+	0.0708421i
$574$	1.07609	−	2.35289i	0.0449153	−	0.0982075i
$575$	−9.71019	+	5.83273i	−0.404943	+	0.243242i
$576$	−20.0015	+	12.7609i	−0.833395	+	0.531704i
$577$	25.1370	−	25.1370i	1.04647	−	1.04647i	0.0475994	−	0.998867i	$-0.484843\pi$
$577$	25.1370	−	25.1370i	1.04647	−	1.04647i	0.998867	−	0.0475994i	$-0.0151571\pi$
$578$	−16.4766	+	6.13509i	−0.685334	+	0.255186i
$579$	−1.79769			−0.0747094
$580$	17.1021	+	25.5061i	0.710124	+	1.05908i
$581$	7.12896			0.295759
$582$	−2.92063	+	1.08750i	−0.121064	+	0.0450785i
$583$	0.125688	−	0.125688i	0.00520546	−	0.00520546i
$584$	7.36977	+	25.2535i	0.304963	+	1.04500i
$585$	−9.66136	+	7.54726i	−0.399448	+	0.312041i
$586$	−15.4537	+	33.7895i	−0.638385	+	1.39583i
$587$	−30.8833	−	30.8833i	−1.27469	−	1.27469i	−0.943600	−	0.331089i	$-0.892584\pi$
$587$	−30.8833	−	30.8833i	−1.27469	−	1.27469i	−0.331089	−	0.943600i	$-0.607416\pi$
$588$	2.43681	+	0.176984i	0.100492	+	0.00729872i
$589$			39.7789i			1.63906i
$590$	−0.870283	−	3.64765i	−0.0358290	−	0.150171i
$591$			2.41849i			0.0994834i
$592$	0.297332	+	0.399020i	0.0122203	+	0.0163996i
$593$	18.0920	+	18.0920i	0.742949	+	0.742949i	0.973144	−	0.230195i	$-0.0739365\pi$
$593$	18.0920	+	18.0920i	0.742949	+	0.742949i	−0.230195	+	0.973144i	$0.573937\pi$
$594$	1.42122	+	0.649998i	0.0583135	+	0.0266698i
$595$	3.01933	+	0.370929i	0.123780	+	0.0152066i
$596$	−6.62414	−	7.66172i	−0.271335	−	0.313836i
$597$	−0.00497421	+	0.00497421i	−0.000203581	+	0.000203581i
$598$	−2.06684	−	5.55076i	−0.0845194	−	0.226987i
$599$	26.8839			1.09845			0.549224	−	0.835675i	$-0.314923\pi$
$599$	26.8839			1.09845			0.549224	+	0.835675i	$0.314923\pi$
$600$	−2.61763	+	0.103366i	−0.106864	+	0.00421989i
$601$	34.0025			1.38699			0.693495	−	0.720462i	$-0.256070\pi$
$601$	34.0025			1.38699			0.693495	+	0.720462i	$0.256070\pi$
$602$	3.11238	+	8.35869i	0.126851	+	0.340675i
$603$	−9.40217	+	9.40217i	−0.382886	+	0.382886i
$604$	−28.9495	−	33.4840i	−1.17794	−	1.36244i
$605$	−2.21938	−	0.272654i	−0.0902307	−	0.0110850i
$606$	−2.62362	−	1.19992i	−0.106577	−	0.0487433i
$607$	−2.06127	−	2.06127i	−0.0836645	−	0.0836645i	0.664036	−	0.747701i	$-0.268842\pi$
$607$	−2.06127	−	2.06127i	−0.0836645	−	0.0836645i	−0.747701	+	0.664036i	$0.768842\pi$
$608$	−26.7041	+	5.73209i	−1.08300	+	0.232467i
$609$		−	0.809661i		−	0.0328091i
$610$	−5.75998	−	24.1420i	−0.233215	−	0.977481i
$611$			13.5394i			0.547745i
$612$	−12.6436	−	0.918296i	−0.511086	−	0.0371199i
$613$	−2.15187	−	2.15187i	−0.0869132	−	0.0869132i	0.662314	−	0.749227i	$-0.269575\pi$
$613$	−2.15187	−	2.15187i	−0.0869132	−	0.0869132i	−0.749227	+	0.662314i	$0.769575\pi$
$614$	−12.5435	+	27.4265i	−0.506216	+	1.10684i
$615$	−0.938163	+	0.732874i	−0.0378304	+	0.0295523i
$616$	−1.72830	+	0.504371i	−0.0696351	+	0.0203217i
$617$	−0.287637	+	0.287637i	−0.0115798	+	0.0115798i	−0.712873	−	0.701293i	$-0.752606\pi$
$617$	−0.287637	+	0.287637i	−0.0115798	+	0.0115798i	0.701293	+	0.712873i	$0.252606\pi$
$618$	−4.62580	+	1.72243i	−0.186077	+	0.0692863i
$619$	−17.3535			−0.697495			−0.348748	−	0.937217i	$-0.613393\pi$
$619$	−17.3535			−0.697495			−0.348748	+	0.937217i	$0.613393\pi$
$620$	20.5194	+	30.6028i	0.824080	+	1.22904i
$621$	−2.50351			−0.100462
$622$	−8.22559	+	3.06282i	−0.329816	+	0.122808i
$623$	1.62009	−	1.62009i	0.0649075	−	0.0649075i
$624$	0.197935	−	1.35545i	0.00792375	−	0.0542613i
$625$	22.0706	+	11.7426i	0.882824	+	0.469704i
$626$	−1.70288	+	3.72335i	−0.0680607	+	0.148815i
$627$	0.632413	+	0.632413i	0.0252562	+	0.0252562i
$628$	−0.198917	+	2.73879i	−0.00793767	+	0.109290i
$629$			0.265884i			0.0106015i
$630$	−5.08553	−	3.12629i	−0.202613	−	0.124555i
$631$		−	22.0436i		−	0.877540i	−0.898599	−	0.438770i	$-0.855414\pi$
$631$		−	22.0436i		−	0.877540i	0.898599	−	0.438770i	$-0.144586\pi$
$632$	25.2649	+	13.8499i	1.00498	+	0.550921i
$633$	−2.05459	−	2.05459i	−0.0816627	−	0.0816627i
$634$	−10.1922	−	4.66140i	−0.404783	−	0.185128i
$635$	−26.8380	−	34.3557i	−1.06503	−	1.36336i
$636$	−0.0498152	+	0.0430690i	−0.00197530	+	0.00170780i
$637$	8.62109	−	8.62109i	0.341580	−	0.341580i
$638$	−3.38864	−	9.10062i	−0.134158	−	0.360297i
$639$	−39.4972			−1.56248
$640$	−17.5873	+	18.1848i	−0.695198	+	0.718818i
$641$	1.96076			0.0774455			0.0387227	−	0.999250i	$-0.487671\pi$
$641$	1.96076			0.0774455			0.0387227	+	0.999250i	$0.487671\pi$
$642$	0.986734	+	2.65000i	0.0389433	+	0.104587i
$643$	−3.94673	+	3.94673i	−0.155644	+	0.155644i	−0.780633	−	0.624989i	$-0.785103\pi$
$643$	−3.94673	+	3.94673i	−0.155644	+	0.155644i	0.624989	+	0.780633i	$0.285103\pi$
$644$	2.18173	−	1.88628i	0.0859724	−	0.0743297i
$645$	0.500425	−	4.07342i	0.0197042	−	0.160391i
$646$	−13.2713	−	6.06964i	−0.522152	−	0.238807i
$647$	6.51354	+	6.51354i	0.256074	+	0.256074i	0.823455	−	0.567381i	$-0.192044\pi$
$647$	6.51354	+	6.51354i	0.256074	+	0.256074i	−0.567381	+	0.823455i	$0.692044\pi$
$648$	21.5588	+	11.8183i	0.846911	+	0.464268i
$649$			1.18586i			0.0465492i
$650$	−8.15292	+	10.2186i	−0.319784	+	0.400807i
$651$		−	0.971449i		−	0.0380741i
$652$	−2.68958	+	37.0314i	−0.105332	+	1.45026i
$653$	27.0181	+	27.0181i	1.05730	+	1.05730i	0.998255	+	0.0590447i	$0.0188054\pi$
$653$	27.0181	+	27.0181i	1.05730	+	1.05730i	0.0590447	+	0.998255i	$0.481195\pi$
$654$	0.295477	−	0.646063i	0.0115541	−	0.0252631i
$655$	−1.07677	+	8.76484i	−0.0420730	+	0.342471i
$656$	−1.66122	+	11.3759i	−0.0648597	+	0.444155i
$657$	19.5045	−	19.5045i	0.760944	−	0.760944i
$658$	−6.17827	+	2.30050i	−0.240854	+	0.0896828i
$659$	−23.8995			−0.930993			−0.465496	−	0.885050i	$-0.654124\pi$
$659$	−23.8995			−0.930993			−0.465496	+	0.885050i	$0.654124\pi$
$660$	0.812752	+	0.160308i	0.0316363	+	0.00623998i
$661$	6.91871			0.269107			0.134553	−	0.990906i	$-0.457040\pi$
$661$	6.91871			0.269107			0.134553	+	0.990906i	$0.457040\pi$
$662$	−25.1093	+	9.34951i	−0.975899	+	0.363379i
$663$	0.517543	−	0.517543i	0.0200997	−	0.0200997i
$664$	−30.4090	+	8.87428i	−1.18010	+	0.344389i
$665$	−4.23055	−	5.41559i	−0.164054	−	0.210008i
$666$	0.217011	−	0.474496i	0.00840902	−	0.0183864i
$667$	11.0000	+	11.0000i	0.425923	+	0.425923i
$668$	−18.3576	−	1.33331i	−0.710278	−	0.0515872i
$669$			3.02940i			0.117123i
$670$	−7.42508	+	12.0784i	−0.286856	+	0.466628i
$671$			7.84865i			0.302994i
$672$	0.652147	−	0.139985i	0.0251571	−	0.00540003i
$673$	19.6672	+	19.6672i	0.758113	+	0.758113i	0.975979	−	0.217865i	$-0.0699094\pi$
$673$	19.6672	+	19.6672i	0.758113	+	0.758113i	−0.217865	+	0.975979i	$0.569909\pi$
$674$	−30.4017	−	13.9043i	−1.17103	−	0.535572i
$675$	2.84515	+	4.73654i	0.109510	+	0.182310i
$676$	12.5340	+	14.4973i	0.482078	+	0.557589i
$677$	31.6934	−	31.6934i	1.21808	−	1.21808i	0.249771	−	0.968305i	$-0.419645\pi$
$677$	31.6934	−	31.6934i	1.21808	−	1.21808i	0.968305	−	0.249771i	$-0.0803552\pi$
$678$	1.77097	+	4.75616i	0.0680137	+	0.182659i
$679$	−7.57262			−0.290611
$680$	−13.3408	+	2.17631i	−0.511598	+	0.0834576i
$681$	−1.14659			−0.0439375
$682$	−4.06577	−	10.9191i	−0.155686	−	0.418115i
$683$	10.2702	−	10.2702i	0.392979	−	0.392979i	−0.482769	−	0.875748i	$-0.660369\pi$
$683$	10.2702	−	10.2702i	0.392979	−	0.392979i	0.875748	+	0.482769i	$0.160369\pi$
$684$	18.7299	+	21.6637i	0.716157	+	0.828332i
$685$	−6.36428	+	4.97165i	−0.243167	+	0.189957i
$686$	11.1293	+	5.08998i	0.424917	+	0.194336i
$687$	−3.89141	−	3.89141i	−0.148467	−	0.148467i
$688$	−23.6811	−	31.7801i	−0.902834	−	1.21160i
$689$			0.328611i			0.0125191i
$690$	−1.29082	+	0.307974i	−0.0491408	+	0.0117244i
$691$			14.7312i			0.560401i	0.959941	+	0.280201i	$0.0904010\pi$
$691$			14.7312i			0.560401i	−0.959941	+	0.280201i	$0.909599\pi$
$692$	−0.163010	−	0.0118393i	−0.00619669	−	0.000450063i
$693$	1.33485	+	1.33485i	0.0507067	+	0.0507067i
$694$	8.20690	−	17.9444i	0.311530	−	0.681161i
$695$	8.62877	+	1.06006i	0.327308	+	0.0402102i
$696$	1.00788	+	3.45365i	0.0382037	+	0.130910i
$697$	−4.34360	+	4.34360i	−0.164525	+	0.164525i
$698$	−26.5931	+	9.90202i	−1.00656	+	0.374797i
$699$	2.37795			0.0899421
$700$	−6.04822	−	1.98407i	−0.228601	−	0.0749907i
$701$	−7.48146			−0.282571			−0.141285	−	0.989969i	$-0.545124\pi$
$701$	−7.48146			−0.282571			−0.141285	+	0.989969i	$0.545124\pi$
$702$	−2.70761	+	1.00819i	−0.102192	+	0.0380515i
$703$	0.424723	−	0.424723i	0.0160187	−	0.0160187i
$704$	6.74430	−	4.30284i	0.254185	−	0.162170i
$705$	3.01084	+	0.369886i	0.113395	+	0.0139307i
$706$	14.0568	−	30.7352i	0.529034	−	1.15673i
$707$	−4.95685	−	4.95685i	−0.186422	−	0.186422i
$708$	0.0318249	−	0.438180i	0.00119605	−	0.0164678i
$709$			24.1185i			0.905789i	0.891564	+	0.452894i	$0.149609\pi$
$709$			24.1185i			0.905789i	−0.891564	+	0.452894i	$0.850391\pi$
$710$	−40.9656	+	9.77388i	−1.53741	+	0.366807i
$711$		−	30.2102i		−	1.13297i
$712$	−4.89386	+	8.92730i	−0.183405	+	0.334565i
$713$	13.1981	+	13.1981i	0.494272	+	0.494272i
$714$	0.324101	+	0.148228i	0.0121292	+	0.00554729i
$715$	3.25772	−	2.54486i	0.121832	−	0.0951724i
$716$	−14.7192	+	12.7259i	−0.550082	+	0.475588i
$717$	−2.77238	+	2.77238i	−0.103537	+	0.103537i
$718$	6.34661	+	17.0446i	0.236853	+	0.636099i
$719$	28.8200			1.07480			0.537402	−	0.843326i	$-0.319406\pi$
$719$	28.8200			1.07480			0.537402	+	0.843326i	$0.319406\pi$
$720$	25.5843	+	7.00480i	0.953471	+	0.261053i
$721$	−11.9938			−0.446672
$722$	2.12767	+	5.71411i	0.0791835	+	0.212657i
$723$	3.73131	−	3.73131i	0.138769	−	0.138769i
$724$	−19.9235	+	17.2254i	−0.740451	+	0.640176i
$725$	8.31046	−	33.3128i	0.308643	−	1.23720i
$726$	−0.238233	−	0.108956i	−0.00884166	−	0.00404374i
$727$	−4.65092	−	4.65092i	−0.172493	−	0.172493i	0.615581	−	0.788074i	$-0.288922\pi$
$727$	−4.65092	−	4.65092i	−0.172493	−	0.172493i	−0.788074	+	0.615581i	$0.788922\pi$
$728$	1.59998	−	2.91866i	0.0592991	−	0.108173i
$729$		−	25.1647i		−	0.932026i
$730$	15.4031	−	25.0562i	0.570095	−	0.927371i
$731$		−	21.1764i		−	0.783238i
$732$	0.210633	−	2.90010i	0.00778523	−	0.107191i
$733$	−9.08504	−	9.08504i	−0.335564	−	0.335564i	0.519131	−	0.854695i	$-0.326256\pi$
$733$	−9.08504	−	9.08504i	−0.335564	−	0.335564i	−0.854695	+	0.519131i	$0.826256\pi$
$734$	20.0281	−	43.7915i	0.739250	−	1.61637i
$735$	−1.68161	−	2.15265i	−0.0620270	−	0.0794017i
$736$	−6.95823	+	10.7619i	−0.256484	+	0.396688i
$737$	3.17032	−	3.17032i	0.116780	−	0.116780i
$738$	11.2968	−	4.20638i	0.415839	−	0.154839i
$739$	−34.8883			−1.28339			−0.641694	−	0.766961i	$-0.721768\pi$
$739$	−34.8883			−1.28339			−0.641694	+	0.766961i	$0.721768\pi$
$740$	0.107661	−	0.545838i	0.00395772	−	0.0200654i
$741$	−1.65344			−0.0607408
$742$	−0.149951	+	0.0558348i	−0.00550489	+	0.00204976i
$743$	−30.1347	+	30.1347i	−1.10554	+	1.10554i	−0.111805	+	0.993730i	$0.535663\pi$
$743$	−30.1347	+	30.1347i	−1.10554	+	1.10554i	−0.993730	+	0.111805i	$0.964337\pi$
$744$	1.20928	+	4.14377i	0.0443344	+	0.151918i
$745$	−1.38075	+	11.2392i	−0.0505869	+	0.411773i
$746$	18.8919	−	41.3072i	0.691680	−	1.51236i
$747$	23.4863	+	23.4863i	0.859319	+	0.859319i
$748$	4.26328	+	0.309640i	0.155881	+	0.0113216i
$749$			6.87093i			0.251058i
$750$	2.04965	+	2.09218i	0.0748427	+	0.0763958i
$751$		−	23.2064i		−	0.846814i	−0.905940	−	0.423407i	$-0.860834\pi$
$751$		−	23.2064i		−	0.846814i	0.905940	−	0.423407i	$-0.139166\pi$
$752$	23.4901	−	17.5038i	0.856594	−	0.638296i
$753$	−2.89746	−	2.89746i	−0.105589	−	0.105589i
$754$	16.3266	+	7.46699i	0.594580	+	0.271932i
$755$	−6.03430	+	49.1187i	−0.219611	+	1.78761i
$756$	−0.920107	−	1.06423i	−0.0334640	−	0.0387056i
$757$	−27.4533	+	27.4533i	−0.997807	+	0.997807i	−0.999998	−	0.00219104i	$-0.999303\pi$
$757$	−27.4533	+	27.4533i	−0.997807	+	0.997807i	0.00219104	+	0.999998i	$0.499303\pi$
$758$	−4.52446	−	12.1510i	−0.164336	−	0.441345i
$759$	0.419652			0.0152324
$760$	24.7871	+	17.8342i	0.899122	+	0.646916i
$761$	18.3814			0.666324			0.333162	−	0.942870i	$-0.391884\pi$
$761$	18.3814			0.666324			0.333162	+	0.942870i	$0.391884\pi$
$762$	−1.78224	−	4.78642i	−0.0645637	−	0.173394i
$763$	1.22062	−	1.22062i	0.0441893	−	0.0441893i
$764$	−16.9347	−	19.5873i	−0.612677	−	0.708644i
$765$	8.72513	+	11.1692i	0.315458	+	0.403823i
$766$	−1.53640	−	0.702673i	−0.0555123	−	0.0253886i
$767$	−1.55022	−	1.55022i	−0.0559752	−	0.0559752i
$768$	−2.60751	+	1.40892i	−0.0940906	+	0.0508400i
$769$			8.12363i			0.292945i	0.989215	+	0.146473i	$0.0467921\pi$
$769$			8.12363i			0.292945i	−0.989215	+	0.146473i	$0.953208\pi$
$770$	1.71479	+	1.05416i	0.0617968	+	0.0379891i
$771$		−	3.32920i		−	0.119898i
$772$	19.3585	+	1.40600i	0.696727	+	0.0506030i
$773$	−17.4899	−	17.4899i	−0.629068	−	0.629068i	0.318766	−	0.947834i	$-0.396732\pi$
$773$	−17.4899	−	17.4899i	−0.629068	−	0.629068i	−0.947834	+	0.318766i	$0.896732\pi$
$774$	−17.2839	+	37.7914i	−0.621258	+	1.35838i
$775$	9.97108	−	39.9694i	0.358172	−	1.43574i
$776$	32.3014	−	9.42657i	1.15955	−	0.338394i
$777$	−0.0103723	+	0.0103723i	−0.000372103	+	0.000372103i
$778$	−33.9007	+	12.6230i	−1.21540	+	0.452557i
$779$	13.8769			0.497192
$780$	−1.27203	+	0.852908i	−0.0455461	+	0.0305390i
$781$	13.3181			0.476558
$782$	−6.41704	+	2.38940i	−0.229473	+	0.0854449i
$783$	5.36571	−	5.36571i	0.191755	−	0.191755i
$784$	−26.1025	−	3.81173i	−0.932231	−	0.136133i
$785$	2.41942	−	1.89000i	0.0863528	−	0.0674570i
$786$	−0.430292	+	0.940836i	−0.0153480	+	0.0335585i
$787$	13.9998	+	13.9998i	0.499040	+	0.499040i	0.911139	−	0.412099i	$-0.135204\pi$
$787$	13.9998	+	13.9998i	0.499040	+	0.499040i	−0.412099	+	0.911139i	$0.635204\pi$
$788$	1.89154	−	26.0436i	0.0673832	−	0.927765i
$789$			1.45343i			0.0517435i
$790$	−7.47575	−	31.3334i	−0.265975	−	1.11479i
$791$			12.3318i			0.438469i
$792$	−7.35551	−	4.03222i	−0.261367	−	0.143279i
$793$	−10.2602	−	10.2602i	−0.364349	−	0.364349i
$794$	25.2150	+	11.5321i	0.894846	+	0.409259i
$795$	0.0730754	+	0.00897742i	0.00259172	+	0.000318396i
$796$	0.0574553	−	0.0496745i	0.00203645	−	0.00176067i
$797$	−6.43229	+	6.43229i	−0.227844	+	0.227844i	−0.811791	−	0.583948i	$-0.801507\pi$
$797$	−6.43229	+	6.43229i	−0.227844	+	0.227844i	0.583948	+	0.811791i	$0.301507\pi$
$798$	−0.280939	−	0.754498i	−0.00994515	−	0.0267089i
$799$	15.6524			0.553743
$800$	28.2688	+	0.934185i	0.999454	+	0.0330284i
$801$	10.6748			0.377174
$802$	−0.500303	−	1.34362i	−0.0176663	−	0.0474450i
$803$	−6.57673	+	6.57673i	−0.232088	+	0.232088i
$804$	−1.25653	+	1.08636i	−0.0443142	+	0.0383130i
$805$	−3.20045	−	0.393180i	−0.112801	−	0.0138578i
$806$	19.5890	+	8.95906i	0.689994	+	0.315569i
$807$	0.729977	+	0.729977i	0.0256964	+	0.0256964i
$808$	27.3141	+	14.9733i	0.960907	+	0.526760i
$809$		−	25.5252i		−	0.897418i	−0.893678	−	0.448709i	$-0.851884\pi$
$809$		−	25.5252i		−	0.897418i	0.893678	−	0.448709i	$-0.148116\pi$
$810$	−6.37916	−	26.7372i	−0.224141	−	0.939449i
$811$			9.92206i			0.348411i	0.984709	+	0.174205i	$0.0557356\pi$
$811$			9.92206i			0.348411i	−0.984709	+	0.174205i	$0.944264\pi$
$812$	−0.633247	+	8.71886i	−0.0222226	+	0.305972i
$813$	−1.69936	−	1.69936i	−0.0595993	−	0.0595993i
$814$	−0.0731741	+	0.159995i	−0.00256475	+	0.00560783i
$815$	32.7132	−	25.5549i	1.14589	−	0.895148i
$816$	−1.56699	−	0.228826i	−0.0548555	−	0.00801052i
$817$	−33.8272	+	33.8272i	−1.18346	+	1.18346i
$818$	−22.8940	+	8.52464i	−0.800469	+	0.298057i
$819$	−3.48996			−0.121949
$820$	10.6758	−	7.15823i	0.372816	−	0.249976i
$821$	−23.1074			−0.806453			−0.403227	−	0.915100i	$-0.632111\pi$
$821$	−23.1074			−0.806453			−0.403227	+	0.915100i	$0.632111\pi$
$822$	−0.886668	+	0.330154i	−0.0309261	+	0.0115154i
$823$	−17.1363	+	17.1363i	−0.597334	+	0.597334i	−0.939602	−	0.342268i	$-0.888805\pi$
$823$	−17.1363	+	17.1363i	−0.597334	+	0.597334i	0.342268	+	0.939602i	$0.388805\pi$
$824$	51.1602	−	14.9301i	1.78225	−	0.520116i
$825$	−0.476919	−	0.793964i	−0.0166042	−	0.0276423i
$826$	0.443994	−	0.970794i	0.0154485	−	0.0337783i
$827$	16.3747	+	16.3747i	0.569405	+	0.569405i	0.931962	−	0.362557i	$-0.118096\pi$
$827$	16.3747	+	16.3747i	0.569405	+	0.569405i	−0.362557	+	0.931962i	$0.618096\pi$
$828$	13.4020	+	0.973384i	0.465753	+	0.0338274i
$829$		−	29.1504i		−	1.01243i	−0.862406	−	0.506217i	$-0.831043\pi$
$829$		−	29.1504i		−	1.01243i	0.862406	−	0.506217i	$-0.168957\pi$
$830$	30.1713	+	18.5476i	1.04726	+	0.643796i
$831$		−	0.188389i		−	0.00653515i
$832$	−3.19159	+	14.4414i	−0.110648	+	0.500665i
$833$	−9.96655	−	9.96655i	−0.345320	−	0.345320i
$834$	0.926230	+	0.423612i	0.0320727	+	0.0146685i
$835$	12.6683	+	16.2169i	0.438406	+	0.561210i
$836$	−6.31555	−	7.30478i	−0.218428	−	0.252641i
$837$	6.43790	−	6.43790i	0.222526	−	0.222526i
$838$	−4.16363	−	11.1819i	−0.143830	−	0.386274i
$839$	51.5484			1.77965			0.889824	−	0.456303i	$-0.150827\pi$
$839$	51.5484			1.77965			0.889824	+	0.456303i	$0.150827\pi$
$840$	−0.605331	−	0.435534i	−0.0208859	−	0.0150273i
$841$	−18.1521			−0.625936
$842$	−9.93968	−	26.6942i	−0.342544	−	0.919944i
$843$	−2.77959	+	2.77959i	−0.0957342	+	0.0957342i
$844$	20.5180	+	23.7319i	0.706260	+	0.816885i
$845$	2.61263	−	21.2666i	0.0898771	−	0.731592i
$846$	−27.9333	−	12.7753i	−0.960366	−	0.439224i
$847$	−0.450097	−	0.450097i	−0.0154655	−	0.0154655i
$848$	0.570121	−	0.424829i	0.0195780	−	0.0145887i
$849$			0.797910i			0.0273842i
$850$	11.8134	+	9.42532i	0.405196	+	0.323286i
$851$		−	0.281834i		−	0.00966116i
$852$	−4.92107	−	0.357415i	−0.168593	−	0.0122448i
$853$	9.51241	+	9.51241i	0.325699	+	0.325699i	0.850948	−	0.525250i	$-0.176028\pi$
$853$	9.51241	+	9.51241i	0.325699	+	0.325699i	−0.525250	+	0.850948i	$0.676028\pi$
$854$	2.93858	−	6.42522i	0.100556	−	0.219866i
$855$	3.90412	−	31.7792i	0.133518	−	1.08682i
$856$	−8.55308	−	29.3083i	−0.292338	−	1.00174i
$857$	−17.0489	+	17.0489i	−0.582379	+	0.582379i	−0.935556	−	0.353177i	$-0.885101\pi$
$857$	−17.0489	+	17.0489i	−0.582379	+	0.582379i	0.353177	+	0.935556i	$0.385101\pi$
$858$	0.453863	−	0.168997i	0.0154946	−	0.00576947i
$859$	−34.1365			−1.16472			−0.582361	−	0.812930i	$-0.697871\pi$
$859$	−34.1365			−1.16472			−0.582361	+	0.812930i	$0.697871\pi$
$860$	−8.57473	+	43.4734i	−0.292396	+	1.48243i
$861$	−0.338891			−0.0115494
$862$	0.460331	−	0.171405i	0.0156789	−	0.00583809i
$863$	21.3626	−	21.3626i	0.727190	−	0.727190i	−0.242869	−	0.970059i	$-0.578089\pi$
$863$	21.3626	−	21.3626i	0.727190	−	0.727190i	0.970059	+	0.242869i	$0.0780886\pi$
$864$	5.24954	+	3.39416i	0.178593	+	0.115472i
$865$	0.112491	+	0.144001i	0.00382479	+	0.00489618i
$866$	17.1148	−	37.4215i	0.581583	−	1.27163i
$867$	1.62840	+	1.62840i	0.0553034	+	0.0553034i
$868$	−0.759784	+	10.4611i	−0.0257888	+	0.355072i
$869$			10.1866i			0.345557i
$870$	2.10652	−	3.42666i	0.0714176	−	0.116175i
$871$			8.28880i			0.280855i
$872$	−3.68715	+	6.72605i	−0.124863	+	0.227773i
$873$	−24.9480	−	24.9480i	−0.844361	−	0.844361i
$874$	14.0674	+	6.43375i	0.475838	+	0.217625i
$875$	2.89332	+	6.50197i	0.0978122	+	0.219807i
$876$	2.60662	−	2.25363i	0.0880697	−	0.0761430i
$877$	−32.3501	+	32.3501i	−1.09239	+	1.09239i	−0.0971130	+	0.995273i	$0.530961\pi$
$877$	−32.3501	+	32.3501i	−1.09239	+	1.09239i	−0.995273	+	0.0971130i	$0.969039\pi$
$878$	−0.673754	−	1.80945i	−0.0227381	−	0.0610659i
$879$	4.86677			0.164152
$880$	−8.62677	−	2.36195i	−0.290808	−	0.0796212i
$881$	−30.2490			−1.01911			−0.509557	−	0.860437i	$-0.670191\pi$
$881$	−30.2490			−1.01911			−0.509557	+	0.860437i	$0.670191\pi$
$882$	9.65170	+	25.9208i	0.324990	+	0.872800i
$883$	27.7381	−	27.7381i	0.933462	−	0.933462i	−0.0644584	−	0.997920i	$-0.520532\pi$
$883$	27.7381	−	27.7381i	0.933462	−	0.933462i	0.997920	+	0.0644584i	$0.0205320\pi$
$884$	−5.97795	+	5.16840i	−0.201060	+	0.173832i
$885$	−0.387084	+	0.302382i	−0.0130117	+	0.0101645i
$886$	−24.6955	−	11.2945i	−0.829662	−	0.379447i
$887$	−14.2637	−	14.2637i	−0.478929	−	0.478929i	0.425860	−	0.904789i	$-0.359971\pi$
$887$	−14.2637	−	14.2637i	−0.478929	−	0.478929i	−0.904789	+	0.425860i	$0.859971\pi$
$888$	0.0313318	−	0.0571551i	0.00105143	−	0.00191800i
$889$		−	12.4103i		−	0.416227i
$890$	11.0716	−	2.64155i	0.371121	−	0.0885449i
$891$			8.69236i			0.291205i
$892$	2.36934	−	32.6222i	0.0793313	−	1.09227i
$893$	−25.0032	−	25.0032i	−0.836700	−	0.836700i
$894$	−0.551767	+	1.20644i	−0.0184539	+	0.0403494i
$895$	21.5921	+	2.65261i	0.721743	+	0.0886671i
$896$	−7.13216	+	0.997376i	−0.238269	+	0.0333200i
$897$	−0.548590	+	0.548590i	−0.0183169	+	0.0183169i
$898$	−15.2040	+	5.66126i	−0.507365	+	0.188919i
$899$	−56.5742			−1.88686
$900$	−13.3893	−	26.4623i	−0.446311	−	0.882078i
$901$	0.379896			0.0126562
$902$	−3.80915	+	1.41835i	−0.126831	+	0.0472259i
$903$	0.826102	−	0.826102i	0.0274909	−	0.0274909i
$904$	−15.3509	−	52.6020i	−0.510564	−	1.74952i
$905$	29.2264	+	3.59050i	0.971518	+	0.119352i
$906$	−2.41138	+	5.27250i	−0.0801129	+	0.175167i
$907$	−27.5037	−	27.5037i	−0.913247	−	0.913247i	0.0832794	−	0.996526i	$-0.473461\pi$
$907$	−27.5037	−	27.5037i	−0.913247	−	0.913247i	−0.996526	+	0.0832794i	$0.973461\pi$
$908$	12.3471	+	0.896765i	0.409753	+	0.0297602i
$909$		−	32.6606i		−	1.08329i
$910$	−3.61971	+	0.863617i	−0.119992	+	0.0286286i
$911$			4.13810i			0.137101i	0.997648	+	0.0685506i	$0.0218375\pi$
$911$			4.13810i			0.137101i	−0.997648	+	0.0685506i	$0.978163\pi$
$912$	2.13758	+	2.86863i	0.0707823	+	0.0949899i
$913$	−7.91935	−	7.91935i	−0.262092	−	0.262092i
$914$	12.1274	+	5.54650i	0.401140	+	0.183462i
$915$	−2.56192	+	2.00132i	−0.0846944	+	0.0661616i
$916$	38.8613	+	44.9484i	1.28401	+	1.48514i
$917$	−1.77754	+	1.77754i	−0.0586994	+	0.0586994i
$918$	1.16553	+	3.13017i	0.0384682	+	0.103311i
$919$	24.2614			0.800310			0.400155	−	0.916447i	$-0.368956\pi$
$919$	24.2614			0.800310			0.400155	+	0.916447i	$0.368956\pi$
$920$	14.1412	−	2.30686i	0.466220	−	0.0760550i
$921$	3.95030			0.130167
$922$	−7.49521	−	20.1293i	−0.246842	−	0.662924i
$923$	−17.4100	+	17.4100i	−0.573058	+	0.573058i
$924$	0.154233	+	0.178392i	0.00507390	+	0.00586866i
$925$	−0.533220	+	0.320295i	−0.0175322	+	0.0105312i
$926$	32.9339	+	15.0624i	1.08228	+	0.494980i
$927$	−39.5135	−	39.5135i	−1.29779	−	1.29779i
$928$	−8.15228	−	37.9791i	−0.267612	−	1.24672i
$929$		−	32.7417i		−	1.07422i	−0.843512	−	0.537110i	$-0.819516\pi$
$929$		−	32.7417i		−	1.07422i	0.843512	−	0.537110i	$-0.180484\pi$
$930$	2.52744	−	4.11139i	0.0828782	−	0.134818i
$931$			31.8411i			1.04355i
$932$	−25.6070	−	1.85983i	−0.838785	−	0.0609206i
$933$	0.812947	+	0.812947i	0.0266147	+	0.0266147i
$934$	−14.1364	+	30.9093i	−0.462557	+	1.01138i
$935$	−2.94203	−	3.76614i	−0.0962146	−	0.123166i
$936$	14.8866	−	4.34438i	0.486584	−	0.142000i
$937$	−14.2317	+	14.2317i	−0.464931	+	0.464931i	−0.900268	−	0.435337i	$-0.856629\pi$
$937$	−14.2317	+	14.2317i	−0.464931	+	0.464931i	0.435337	+	0.900268i	$0.356629\pi$
$938$	−3.78233	+	1.40836i	−0.123498	+	0.0459847i
$939$	0.536282			0.0175009
$940$	−32.1331	−	6.33796i	−1.04807	−	0.206721i
$941$	32.9526			1.07422			0.537112	−	0.843511i	$-0.319515\pi$
$941$	32.9526			1.07422			0.537112	+	0.843511i	$0.319515\pi$
$942$	0.337072	−	0.125510i	0.0109824	−	0.00408933i
$943$	4.60417	−	4.60417i	0.149932	−	0.149932i
$944$	−0.685414	+	4.69367i	−0.0223083	+	0.152766i
$945$	−0.191790	+	1.56115i	−0.00623892	+	0.0507842i
$946$	5.82797	−	12.7429i	0.189484	−	0.414307i
$947$	24.0437	+	24.0437i	0.781315	+	0.781315i	0.980053	−	0.198738i	$-0.0636842\pi$
$947$	24.0437	+	24.0437i	0.781315	+	0.781315i	−0.198738	+	0.980053i	$0.563684\pi$
$948$	0.273376	−	3.76398i	0.00887885	−	0.122248i
$949$		−	17.1949i		−	0.558169i
$950$	−3.81473	−	33.9267i	−0.123766	−	1.10073i
$951$			1.46800i			0.0476032i
$952$	−3.37416	−	1.84968i	−0.109357	−	0.0599485i
$953$	33.9941	+	33.9941i	1.10118	+	1.10118i	0.994269	+	0.106910i	$0.0340955\pi$
$953$	33.9941	+	33.9941i	1.10118	+	1.10118i	0.106910	+	0.994269i	$0.465904\pi$
$954$	−0.677961	−	0.310066i	−0.0219498	−	0.0100388i
$955$	−3.52992	+	28.7333i	−0.114226	+	0.929787i
$956$	32.0228	−	27.6862i	1.03569	−	0.895435i
$957$	−0.899428	+	0.899428i	−0.0290744	+	0.0290744i
$958$	9.68223	+	26.0028i	0.312819	+	0.840113i
$959$	−2.29896			−0.0742373
$960$	3.12423	+	1.10426i	0.100834	+	0.0356399i
$961$	−36.8790			−1.18964
$962$	−0.113497	−	0.304811i	−0.00365930	−	0.00982749i
$963$	−22.6362	+	22.6362i	−0.729443	+	0.729443i
$964$	−43.0991	+	37.2625i	−1.38813	+	1.20014i
$965$	−13.3590	−	17.1011i	−0.430042	−	0.550503i
$966$	−0.343543	−	0.157120i	−0.0110533	−	0.00505525i
$967$	28.5443	+	28.5443i	0.917924	+	0.917924i	0.996878	−	0.0789545i	$-0.0251582\pi$
$967$	28.5443	+	28.5443i	0.917924	+	0.917924i	−0.0789545	+	0.996878i	$0.525158\pi$
$968$	2.48021	+	1.35962i	0.0797168	+	0.0437000i
$969$			1.91149i			0.0614060i
$970$	−32.0490	−	19.7019i	−1.02903	−	0.632590i
$971$		−	53.5921i		−	1.71985i	−0.510419	−	0.859926i	$-0.670510\pi$
$971$		−	53.5921i		−	1.71985i	0.510419	−	0.859926i	$-0.329490\pi$
$972$	0.713577	−	9.82488i	0.0228880	−	0.315133i
$973$	1.74994	+	1.74994i	0.0561005	+	0.0561005i
$974$	4.79912	−	10.4933i	0.153774	−	0.336227i
$975$	1.66136	+	0.414457i	0.0532062	+	0.0132732i
$976$	−4.53643	+	31.0651i	−0.145207	+	0.994371i
$977$	30.6296	−	30.6296i	0.979926	−	0.979926i	−0.0198763	−	0.999802i	$-0.506327\pi$
$977$	30.6296	−	30.6296i	0.979926	−	0.979926i	0.999802	+	0.0198763i	$0.00632724\pi$
$978$	4.55758	−	1.69703i	0.145735	−	0.0542650i
$979$	−3.59942			−0.115038
$980$	16.4248	+	24.4961i	0.524672	+	0.782499i
$981$	8.04262			0.256781
$982$	40.7522	−	15.1742i	1.30045	−	0.484228i
$983$	−31.2572	+	31.2572i	−0.996950	+	0.996950i	−0.999995	−	0.00304578i	$-0.999030\pi$
$983$	−31.2572	+	31.2572i	−0.996950	+	0.996950i	0.00304578	+	0.999995i	$0.499030\pi$
$984$	1.44556	−	0.421859i	0.0460827	−	0.0134484i
$985$	−23.0066	+	17.9723i	−0.733052	+	0.572645i
$986$	8.63233	−	18.8746i	0.274909	−	0.601091i
$987$	0.610608	+	0.610608i	0.0194359	+	0.0194359i
$988$	17.8052	+	1.29318i	0.566458	+	0.0411416i
$989$			22.4468i			0.713766i
$990$	2.17646	+	9.12228i	0.0691725	+	0.289925i
$991$			20.5908i			0.654089i	0.945009	+	0.327045i	$0.106053\pi$
$991$			20.5908i			0.654089i	−0.945009	+	0.327045i	$0.893947\pi$
$992$	−9.78128	−	45.5681i	−0.310556	−	1.44679i
$993$	2.48159	+	2.48159i	0.0787508	+	0.0787508i
$994$	−10.9027	−	4.98636i	−0.345812	−	0.158158i
$995$	−0.0842831	−	0.0103543i	−0.00267195	−	0.000328253i
$996$	2.71369	+	3.13876i	0.0859867	+	0.0994553i
$997$	−17.6089	+	17.6089i	−0.557681	+	0.557681i	−0.928647	−	0.370966i	$-0.879027\pi$
$997$	−17.6089	+	17.6089i	−0.557681	+	0.557681i	0.370966	+	0.928647i	$0.379027\pi$
$998$	15.4213	+	41.4159i	0.488153	+	1.31100i
$999$	−0.137476			−0.00434955

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a_n

instead) (See

a_n

instead) Display

a_n

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.l.c.23.9	✓	28
4.3	odd	2		220.2.l.d.23.2	yes	28
5.2	odd	4		220.2.l.d.67.2	yes	28
20.7	even	4	inner	220.2.l.c.67.9	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.l.c.23.9	✓	28	1.1	even	1	trivial
220.2.l.c.67.9	yes	28	20.7	even	4	inner
220.2.l.d.23.2	yes	28	4.3	odd	2
220.2.l.d.67.2	yes	28	5.2	odd	4

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	220.2.l.c.23.9

Level	$220$
Weight	$2$
Character	220.23
Analytic conductor	$1.757$
Analytic rank	$0$
Dimension	$28$
Inner twists	$2$