LMFDB - Embedded newform 952.2.z.c.781.102

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [952,2,Mod(373,952)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("952.373"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(952, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 952 = 2^{3} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	952.z (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [272,-6,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.60175827243$
Analytic rank:	$0$
Dimension:	$272$
Relative dimension:	$136$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			781.102
Character	$\chi$	$=$	952.781
Dual form			952.2.z.c.373.102

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.910352 - 1.08225i) q^{2} +(1.13482 - 1.96557i) q^{3} +(-0.342520 - 1.97045i) q^{4} +(0.297569 + 0.515405i) q^{5} +(-1.09414 - 3.01751i) q^{6} +(1.98085 - 1.75392i) q^{7} +(-2.44433 - 1.42311i) q^{8} +(-1.07563 - 1.86305i) q^{9} +(0.828689 + 0.147156i) q^{10} +(-1.45989 + 2.52861i) q^{11} +(-4.26175 - 1.56286i) q^{12} -0.637068i q^{13} +(-0.0949104 - 3.74045i) q^{14} +1.35075 q^{15} +(-3.76536 + 1.34984i) q^{16} +(-0.970435 - 4.00728i) q^{17} +(-2.99549 - 0.531930i) q^{18} +(3.15083 - 1.81913i) q^{19} +(0.913658 - 0.762883i) q^{20} +(-1.19954 - 5.88387i) q^{21} +(1.40757 + 3.88189i) q^{22} +(-6.02090 + 3.47617i) q^{23} +(-5.57110 + 3.18952i) q^{24} +(2.32290 - 4.02339i) q^{25} +(-0.689466 - 0.579956i) q^{26} +1.92632 q^{27} +(-4.13450 - 3.30241i) q^{28} +5.28378 q^{29} +(1.22966 - 1.46185i) q^{30} +(-8.87639 - 5.12478i) q^{31} +(-1.96694 + 5.30388i) q^{32} +(3.31343 + 5.73904i) q^{33} +(-5.22030 - 2.59778i) q^{34} +(1.49342 + 0.499026i) q^{35} +(-3.30263 + 2.75762i) q^{36} +(3.35036 + 5.80299i) q^{37} +(0.899610 - 5.06602i) q^{38} +(-1.25220 - 0.722958i) q^{39} +(0.00612179 - 1.68330i) q^{40} +9.63861i q^{41} +(-7.45981 - 4.05819i) q^{42} -3.51167i q^{43} +(5.48255 + 2.01055i) q^{44} +(0.640151 - 1.10877i) q^{45} +(-1.71906 + 9.68065i) q^{46} +(4.34318 + 7.52260i) q^{47} +(-1.61981 + 8.93289i) q^{48} +(0.847514 - 6.94850i) q^{49} +(-2.23964 - 6.17666i) q^{50} +(-8.97783 - 2.64008i) q^{51} +(-1.25531 + 0.218209i) q^{52} +(8.12280 + 4.68970i) q^{53} +(1.75363 - 2.08476i) q^{54} -1.73768 q^{55} +(-7.33787 + 1.46820i) q^{56} -8.25754i q^{57} +(4.81010 - 5.71836i) q^{58} +(10.3746 + 5.98976i) q^{59} +(-0.462659 - 2.66159i) q^{60} +(3.38243 + 5.85854i) q^{61} +(-13.6269 + 4.94109i) q^{62} +(-5.39831 - 1.80384i) q^{63} +(3.94950 + 6.95711i) q^{64} +(0.328348 - 0.189572i) q^{65} +(9.22745 + 1.63858i) q^{66} +(-11.9866 - 6.92048i) q^{67} +(-7.56375 + 3.28477i) q^{68} +15.7793i q^{69} +(1.89961 - 1.16196i) q^{70} -6.09967i q^{71} +(-0.0221286 + 6.08466i) q^{72} +(3.83038 + 2.21147i) q^{73} +(9.33027 + 1.65684i) q^{74} +(-5.27216 - 9.13165i) q^{75} +(-4.66373 - 5.58546i) q^{76} +(1.54316 + 7.56933i) q^{77} +(-1.92236 + 0.697044i) q^{78} +(3.55913 - 2.05486i) q^{79} +(-1.81617 - 1.53902i) q^{80} +(5.41293 - 9.37546i) q^{81} +(10.4314 + 8.77452i) q^{82} -4.84610i q^{83} +(-11.1830 + 4.37899i) q^{84} +(1.77660 - 1.69261i) q^{85} +(-3.80050 - 3.19686i) q^{86} +(5.99614 - 10.3856i) q^{87} +(7.16696 - 4.10317i) q^{88} +(-8.18033 - 14.1687i) q^{89} +(-0.617206 - 1.70218i) q^{90} +(-1.11737 - 1.26193i) q^{91} +(8.91191 + 10.6732i) q^{92} +(-20.1462 + 11.6314i) q^{93} +(12.0951 + 2.14782i) q^{94} +(1.87518 + 1.08264i) q^{95} +(8.19300 + 9.88510i) q^{96} -3.56669i q^{97} +(-6.74847 - 7.24280i) q^{98} +6.28124 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 272 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 132 q^{9} - 40 q^{15} - 26 q^{16} - 6 q^{17} + 6 q^{18} - 112 q^{25} - 8 q^{26} - 2 q^{30} + 44 q^{32} - 28 q^{33} - 56 q^{34} + 40 q^{36} - 42 q^{38} + 12 q^{42}+ \cdots + 14 q^{98}+O(q^{100}) $ 272 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 132 * q^9 - 40 * q^15 - 26 * q^16 - 6 * q^17 + 6 * q^18 - 112 * q^25 - 8 * q^26 - 2 * q^30 + 44 * q^32 - 28 * q^33 - 56 * q^34 + 40 * q^36 - 42 * q^38 + 12 * q^42 + 28 * q^47 - 60 * q^49 + 72 * q^50 - 38 * q^52 + 232 * q^55 - 6 * q^60 + 40 * q^64 + 48 * q^66 + 32 * q^68 + 86 * q^70 - 36 * q^72 - 148 * q^76 - 168 * q^81 - 34 * q^84 + 22 * q^86 + 16 * q^87 - 72 * q^89 + 62 * q^94 + 14 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/952\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$477$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0.910352	−	1.08225i	0.643716	−	0.765265i
$2$	0.910352	−	1.08225i	0.643716	−	0.765265i
$3$	1.13482	−	1.96557i	0.655189	−	1.13482i	−0.326658	−	0.945143i	$-0.605922\pi$
$3$	1.13482	−	1.96557i	0.655189	−	1.13482i	0.981846	−	0.189677i	$-0.0607442\pi$
$4$	−0.342520	−	1.97045i	−0.171260	−	0.985226i
$5$	0.297569	+	0.515405i	0.133077	+	0.230496i	0.924861	−	0.380305i	$-0.124181\pi$
$5$	0.297569	+	0.515405i	0.133077	+	0.230496i	−0.791784	+	0.610801i	$0.790848\pi$
$6$	−1.09414	−	3.01751i	−0.446682	−	1.23189i
$7$	1.98085	−	1.75392i	0.748690	−	0.662920i
$7$	1.98085	−	1.75392i	0.748690	−	0.662920i
$8$	−2.44433	−	1.42311i	−0.864201	−	0.503146i
$9$	−1.07563	−	1.86305i	−0.358544	−	0.621017i
$10$	0.828689	+	0.147156i	0.262054	+	0.0465349i
$11$	−1.45989	+	2.52861i	−0.440175	+	0.762405i	−0.997702	−	0.0677537i	$-0.978417\pi$
$11$	−1.45989	+	2.52861i	−0.440175	+	0.762405i	0.557528	+	0.830158i	$0.311750\pi$
$12$	−4.26175	−	1.56286i	−1.23026	−	0.451160i
$13$		−	0.637068i		−	0.176691i	−0.996090	−	0.0883455i	$-0.971842\pi$
$13$		−	0.637068i		−	0.176691i	0.996090	−	0.0883455i	$-0.0281579\pi$
$14$	−0.0949104	−	3.74045i	−0.0253659	−	0.999678i
$15$	1.35075			0.348762
$16$	−3.76536	+	1.34984i	−0.941340	+	0.337460i
$17$	−0.970435	−	4.00728i	−0.235365	−	0.971907i
$17$	−0.970435	−	4.00728i	−0.235365	−	0.971907i
$18$	−2.99549	−	0.531930i	−0.706043	−	0.125377i
$19$	3.15083	−	1.81913i	0.722849	−	0.417337i	−0.0929513	−	0.995671i	$-0.529630\pi$
$19$	3.15083	−	1.81913i	0.722849	−	0.417337i	0.815800	+	0.578334i	$0.196297\pi$
$20$	0.913658	−	0.762883i	0.204300	−	0.170586i
$21$	−1.19954	−	5.88387i	−0.261762	−	1.28397i
$22$	1.40757	+	3.88189i	0.300094	+	0.827622i
$23$	−6.02090	+	3.47617i	−1.25545	+	0.724832i	−0.972186	−	0.234212i	$-0.924749\pi$
$23$	−6.02090	+	3.47617i	−1.25545	+	0.724832i	−0.283260	+	0.959043i	$0.591416\pi$
$24$	−5.57110	+	3.18952i	−1.13720	+	0.651057i
$25$	2.32290	−	4.02339i	0.464581	−	0.804678i
$26$	−0.689466	−	0.579956i	−0.135215	−	0.113739i
$27$	1.92632			0.370720
$28$	−4.13450	−	3.30241i	−0.781347	−	0.624097i
$29$	5.28378			0.981174			0.490587	−	0.871392i	$-0.336782\pi$
$29$	5.28378			0.981174			0.490587	+	0.871392i	$0.336782\pi$
$30$	1.22966	−	1.46185i	0.224504	−	0.266896i
$31$	−8.87639	−	5.12478i	−1.59425	−	0.920438i	−0.992567	−	0.121701i	$-0.961165\pi$
$31$	−8.87639	−	5.12478i	−1.59425	−	0.920438i	−0.601679	−	0.798738i	$-0.705501\pi$
$32$	−1.96694	+	5.30388i	−0.347710	+	0.937602i
$33$	3.31343	+	5.73904i	0.576795	+	0.999038i
$34$	−5.22030	−	2.59778i	−0.895274	−	0.445515i
$35$	1.49342	+	0.499026i	0.252434	+	0.0843508i
$36$	−3.30263	+	2.75762i	−0.550438	+	0.459603i
$37$	3.35036	+	5.80299i	0.550795	+	0.954005i	0.998217	+	0.0596826i	$0.0190088\pi$
$37$	3.35036	+	5.80299i	0.550795	+	0.954005i	−0.447422	+	0.894323i	$0.647658\pi$
$38$	0.899610	−	5.06602i	0.145936	−	0.821817i
$39$	−1.25220	−	0.722958i	−0.200512	−	0.115766i
$40$	0.00612179	−	1.68330i	0.000967939	−	0.266152i
$41$			9.63861i			1.50530i	0.658422	+	0.752649i	$0.271224\pi$
$41$			9.63861i			1.50530i	−0.658422	+	0.752649i	$0.728776\pi$
$42$	−7.45981	−	4.05819i	−1.15107	−	0.626192i
$43$		−	3.51167i		−	0.535525i	−0.963485	−	0.267763i	$-0.913716\pi$
$43$		−	3.51167i		−	0.535525i	0.963485	−	0.267763i	$-0.0862843\pi$
$44$	5.48255	+	2.01055i	0.826525	+	0.303102i
$45$	0.640151	−	1.10877i	0.0954281	−	0.165286i
$46$	−1.71906	+	9.68065i	−0.253462	+	1.42733i
$47$	4.34318	+	7.52260i	0.633518	+	1.09728i	0.986827	+	0.161778i	$0.0517229\pi$
$47$	4.34318	+	7.52260i	0.633518	+	1.09728i	−0.353310	+	0.935506i	$0.614944\pi$
$48$	−1.61981	+	8.93289i	−0.233799	+	1.28935i
$49$	0.847514	−	6.94850i	0.121073	−	0.992644i
$50$	−2.23964	−	6.17666i	−0.316733	−	0.873511i
$51$	−8.97783	−	2.64008i	−1.25715	−	0.369685i
$52$	−1.25531	+	0.218209i	−0.174080	+	0.0302601i
$53$	8.12280	+	4.68970i	1.11575	+	0.644180i	0.940313	−	0.340310i	$-0.110532\pi$
$53$	8.12280	+	4.68970i	1.11575	+	0.644180i	0.175440	+	0.984490i	$0.443865\pi$
$54$	1.75363	−	2.08476i	0.238639	−	0.283699i
$55$	−1.73768			−0.234309
$56$	−7.33787	+	1.46820i	−0.980565	+	0.196196i
$57$		−	8.25754i		−	1.09374i
$58$	4.81010	−	5.71836i	0.631597	−	0.750858i
$59$	10.3746	+	5.98976i	1.35065	+	0.779800i	0.988341	−	0.152257i	$-0.0486542\pi$
$59$	10.3746	+	5.98976i	1.35065	+	0.779800i	0.362312	+	0.932057i	$0.381988\pi$
$60$	−0.462659	−	2.66159i	−0.0597290	−	0.343610i
$61$	3.38243	+	5.85854i	0.433076	+	0.750109i	0.997136	−	0.0756243i	$-0.0240950\pi$
$61$	3.38243	+	5.85854i	0.433076	+	0.750109i	−0.564061	+	0.825733i	$0.690762\pi$
$62$	−13.6269	+	4.94109i	−1.73062	+	0.627519i
$63$	−5.39831	−	1.80384i	−0.680123	−	0.227263i
$64$	3.94950	+	6.95711i	0.493688	+	0.869639i
$65$	0.328348	−	0.189572i	0.0407266	−	0.0235135i
$66$	9.22745	+	1.63858i	1.13582	+	0.201696i
$67$	−11.9866	−	6.92048i	−1.46440	−	0.845471i	−0.465189	−	0.885211i	$-0.654014\pi$
$67$	−11.9866	−	6.92048i	−1.46440	−	0.845471i	−0.999210	+	0.0397400i	$0.987347\pi$
$68$	−7.56375	+	3.28477i	−0.917239	+	0.398337i
$69$			15.7793i			1.89961i
$70$	1.89961	−	1.16196i	0.227047	−	0.138881i
$71$		−	6.09967i		−	0.723897i	−0.932198	−	0.361949i	$-0.882112\pi$
$71$		−	6.09967i		−	0.723897i	0.932198	−	0.361949i	$-0.117888\pi$
$72$	−0.0221286	+	6.08466i	−0.00260788	+	0.717084i
$73$	3.83038	+	2.21147i	0.448313	+	0.258833i	0.707117	−	0.707096i	$-0.249995\pi$
$73$	3.83038	+	2.21147i	0.448313	+	0.258833i	−0.258805	+	0.965930i	$0.583329\pi$
$74$	9.33027	+	1.65684i	1.08462	+	0.192604i
$75$	−5.27216	−	9.13165i	−0.608776	−	1.05443i
$76$	−4.66373	−	5.58546i	−0.534966	−	0.640697i
$77$	1.54316	+	7.56933i	0.175859	+	0.862605i
$78$	−1.92236	+	0.697044i	−0.217665	+	0.0789247i
$79$	3.55913	−	2.05486i	0.400433	−	0.231190i	−0.286238	−	0.958159i	$-0.592405\pi$
$79$	3.55913	−	2.05486i	0.400433	−	0.231190i	0.686671	+	0.726969i	$0.259071\pi$
$80$	−1.81617	−	1.53902i	−0.203054	−	0.172067i
$81$	5.41293	−	9.37546i	0.601436	−	1.04172i
$82$	10.4314	+	8.77452i	1.15195	+	0.968984i
$83$		−	4.84610i		−	0.531929i	−0.963983	−	0.265964i	$-0.914310\pi$
$83$		−	4.84610i		−	0.531929i	0.963983	−	0.265964i	$-0.0856903\pi$
$84$	−11.1830	+	4.37899i	−1.22017	+	0.477787i
$85$	1.77660	−	1.69261i	0.192699	−	0.183589i
$86$	−3.80050	−	3.19686i	−0.409819	−	0.344726i
$87$	5.99614	−	10.3856i	0.642854	−	1.11346i
$88$	7.16696	−	4.10317i	0.764000	−	0.437399i
$89$	−8.18033	−	14.1687i	−0.867113	−	1.50188i	−0.864934	−	0.501886i	$-0.832640\pi$
$89$	−8.18033	−	14.1687i	−0.867113	−	1.50188i	−0.00217959	−	0.999998i	$-0.500694\pi$
$90$	−0.617206	−	1.70218i	−0.0650592	−	0.179425i
$91$	−1.11737	−	1.26193i	−0.117132	−	0.132287i
$92$	8.91191	+	10.6732i	0.929130	+	1.11276i
$93$	−20.1462	+	11.6314i	−2.08906	+	1.20612i
$94$	12.0951	+	2.14782i	1.24752	+	0.221531i
$95$	1.87518	+	1.08264i	0.192389	+	0.111076i
$96$	8.19300	+	9.88510i	0.836195	+	1.00889i
$97$		−	3.56669i		−	0.362143i	−0.983470	−	0.181071i	$-0.942043\pi$
$97$		−	3.56669i		−	0.362143i	0.983470	−	0.181071i	$-0.0579565\pi$
$98$	−6.74847	−	7.24280i	−0.681698	−	0.731634i
$99$	6.28124			0.631288
$100$	−8.72354	−	3.19908i	−0.872354	−	0.319908i
$101$	0.606999	+	0.350451i	0.0603987	+	0.0348712i	0.529895	−	0.848063i	$-0.322231\pi$
$101$	0.606999	+	0.350451i	0.0603987	+	0.0348712i	−0.469497	+	0.882934i	$0.655565\pi$
$102$	−11.0302	+	7.31284i	−1.09215	+	0.724079i
$103$	9.51100	+	16.4735i	0.937147	+	1.62319i	0.770760	+	0.637125i	$0.219877\pi$
$103$	9.51100	+	16.4735i	0.937147	+	1.62319i	0.166386	+	0.986061i	$0.446790\pi$
$104$	−0.906620	+	1.55721i	−0.0889014	+	0.152697i
$105$	2.67563	−	2.36911i	0.261115	−	0.231202i
$106$	12.4700	−	4.52161i	1.21120	−	0.439177i
$107$	5.35570	+	9.27634i	0.517755	+	0.896777i	0.999787	+	0.0206241i	$0.00656531\pi$
$107$	5.35570	+	9.27634i	0.517755	+	0.896777i	−0.482033	+	0.876153i	$0.660101\pi$
$108$	−0.659803	−	3.79572i	−0.0634896	−	0.365243i
$109$	−6.83687	+	11.8418i	−0.654853	+	1.13424i	0.327077	+	0.944998i	$0.393936\pi$
$109$	−6.83687	+	11.8418i	−0.654853	+	1.13424i	−0.981931	+	0.189242i	$0.939397\pi$
$110$	−1.58190	+	1.88060i	−0.150828	+	0.179308i
$111$	15.2082			1.44350
$112$	−5.09109	+	9.27797i	−0.481063	+	0.876686i
$113$		−	6.04520i		−	0.568684i	−0.958723	−	0.284342i	$-0.908225\pi$
$113$		−	6.04520i		−	0.568684i	0.958723	−	0.284342i	$-0.0917752\pi$
$114$	−8.93671	−	7.51727i	−0.836999	−	0.704057i
$115$	−3.58327	−	2.06880i	−0.334142	−	0.192917i
$116$	−1.80980	−	10.4114i	−0.168036	−	0.966678i
$117$	−1.18689	+	0.685252i	−0.109728	+	0.0633515i
$118$	15.9269	−	5.77506i	1.46619	−	0.531637i
$119$	−8.95073	−	6.23573i	−0.820512	−	0.571629i
$120$	−3.30168	−	1.92227i	−0.301401	−	0.175478i
$121$	1.23742	+	2.14327i	0.112493	+	0.194843i
$122$	9.41959	+	1.67270i	0.852809	+	0.151440i
$123$	18.9453	+	10.9381i	1.70824	+	0.986254i
$124$	−7.05780	+	19.2458i	−0.633809	+	1.72833i
$125$	5.74060			0.513455
$126$	−6.86657	+	4.20018i	−0.611722	+	0.374182i
$127$	−19.3585			−1.71779			−0.858897	−	0.512149i	$-0.828850\pi$
$127$	−19.3585			−1.71779			−0.858897	+	0.512149i	$0.828850\pi$
$128$	11.1248	+	2.05908i	0.983299	+	0.181999i
$129$	−6.90243	−	3.98512i	−0.607725	−	0.350870i
$130$	0.0937486	−	0.527931i	0.00822229	−	0.0463026i
$131$	0.150996	+	0.261533i	0.0131926	+	0.0228502i	0.872546	−	0.488531i	$-0.162467\pi$
$131$	0.150996	+	0.261533i	0.0131926	+	0.0228502i	−0.859354	+	0.511382i	$0.829134\pi$
$132$	10.1736	−	8.49470i	0.885496	−	0.739368i
$133$	3.05069	−	9.12972i	0.264529	−	0.791647i
$134$	−18.4017	+	6.67243i	−1.58967	+	0.576410i
$135$	0.573214	+	0.992836i	0.0493344	+	0.0854497i
$136$	−3.33074	+	11.1761i	−0.285608	+	0.958346i
$137$	−1.97062	+	3.41322i	−0.168362	+	0.291611i	−0.937844	−	0.347057i	$-0.887181\pi$
$137$	−1.97062	+	3.41322i	−0.168362	+	0.291611i	0.769482	+	0.638668i	$0.220514\pi$
$138$	17.0771	+	14.3647i	1.45370	+	1.22281i
$139$	1.64953			0.139911			0.0699555	−	0.997550i	$-0.477714\pi$
$139$	1.64953			0.139911			0.0699555	+	0.997550i	$0.477714\pi$
$140$	0.471780	−	3.11364i	0.0398727	−	0.263151i
$141$	19.7149			1.66029
$142$	−6.60135	−	5.55284i	−0.553973	−	0.465984i
$143$	1.61090	+	0.930052i	0.134710	+	0.0777749i
$144$	6.56496	+	5.56313i	0.547080	+	0.463594i
$145$	1.57229	+	2.72329i	0.130572	+	0.226157i
$146$	5.88036	−	2.13221i	0.486662	−	0.176463i
$147$	−12.6960	−	9.55115i	−1.04715	−	0.787765i
$148$	10.2869	−	8.58936i	0.845582	−	0.706041i
$149$	−9.45513	+	5.45892i	−0.774595	+	0.447212i	−0.834511	−	0.550991i	$-0.814250\pi$
$149$	−9.45513	+	5.45892i	−0.774595	+	0.447212i	0.0599165	+	0.998203i	$0.480917\pi$
$150$	−14.6822	−	2.60723i	−1.19880	−	0.212879i
$151$	6.46910	−	11.2048i	0.526448	−	0.911835i	−0.473077	−	0.881021i	$-0.656857\pi$
$151$	6.46910	−	11.2048i	0.526448	−	0.911835i	0.999525	−	0.0308137i	$-0.00980985\pi$
$152$	−10.2905	−	0.0374243i	−0.834669	−	0.00303551i
$153$	−6.42193	+	6.11833i	−0.519182	+	0.494638i
$154$	9.59671	+	5.22067i	0.773325	+	0.420694i
$155$		−	6.09992i		−	0.489957i
$156$	−0.995650	+	2.71503i	−0.0797158	+	0.217376i
$157$	14.1664	+	8.17895i	1.13060	+	0.652751i	0.944085	−	0.329702i	$-0.106948\pi$
$157$	14.1664	+	8.17895i	1.13060	+	0.652751i	0.186513	+	0.982453i	$0.440281\pi$
$158$	1.01619	−	5.72250i	0.0808434	−	0.455258i
$159$	18.4358	−	10.6439i	1.46206	−	0.844119i
$160$	−3.31895	+	0.564500i	−0.262386	+	0.0446276i
$161$	−5.82956	+	17.4460i	−0.459434	+	1.37493i
$162$	−5.21891	−	14.3931i	−0.410036	−	1.13083i
$163$	−11.0304	−	19.1052i	−0.863969	−	1.49644i	−0.868068	−	0.496446i	$-0.834638\pi$
$163$	−11.0304	−	19.1052i	−0.863969	−	1.49644i	0.00409899	−	0.999992i	$-0.498695\pi$
$164$	18.9924	−	3.30142i	1.48306	−	0.257797i
$165$	−1.97195	+	3.41552i	−0.153516	+	0.265898i
$166$	−5.24468	−	4.41165i	−0.407066	−	0.342411i
$167$			8.88138i			0.687262i	0.939105	+	0.343631i	$0.111657\pi$
$167$			8.88138i			0.687262i	−0.939105	+	0.343631i	$0.888343\pi$
$168$	−5.44133	+	16.0892i	−0.419808	+	1.24131i
$169$	12.5941			0.968780
$170$	−0.214493	−	3.46359i	−0.0164509	−	0.265645i
$171$	−6.77827	−	3.91343i	−0.518347	−	0.299268i
$172$	−6.91958	+	1.20282i	−0.527613	+	0.0917140i
$173$	−7.08687	−	12.2748i	−0.538805	−	0.933238i	−0.998969	−	0.0454035i	$-0.985543\pi$
$173$	−7.08687	−	12.2748i	−0.538805	−	0.933238i	0.460164	−	0.887834i	$-0.347791\pi$
$174$	−5.78122	−	15.9439i	−0.438273	−	1.20870i
$175$	−2.45539	−	12.0439i	−0.185610	−	0.910434i
$176$	2.08381	−	11.4917i	0.157073	−	0.866223i
$177$	23.5465	−	13.5946i	1.76986	−	1.02183i
$178$	−22.7811	−	4.04540i	−1.70751	−	0.303215i
$179$	−0.563903	−	0.325570i	−0.0421481	−	0.0243342i	0.478778	−	0.877936i	$-0.341080\pi$
$179$	−0.563903	−	0.325570i	−0.0421481	−	0.0243342i	−0.520926	+	0.853602i	$0.674413\pi$
$180$	−2.40405	−	0.881610i	−0.179187	−	0.0657113i
$181$	9.47478			0.704255			0.352128	−	0.935952i	$-0.385458\pi$
$181$	9.47478			0.704255			0.352128	+	0.935952i	$0.385458\pi$
$182$	−2.38292	+	0.0604644i	−0.176634	+	0.00448192i
$183$	15.3538			1.13498
$184$	19.6641	+	0.0715140i	1.44965	+	0.00527208i
$185$	−1.99393	+	3.45358i	−0.146596	+	0.253913i
$186$	−5.75206	+	32.3919i	−0.421761	+	2.37509i
$187$	11.5496	+	3.39634i	0.844588	+	0.248365i
$188$	13.3353	−	11.1347i	0.972577	−	0.812079i
$189$	3.81575	−	3.37862i	0.277555	−	0.245758i
$190$	2.87875	−	1.04383i	0.208847	−	0.0757274i
$191$	−6.75459	−	11.6993i	−0.488745	−	0.846531i	0.511171	−	0.859479i	$-0.329212\pi$
$191$	−6.75459	−	11.6993i	−0.488745	−	0.846531i	−0.999916	+	0.0129480i	$0.995878\pi$
$192$	18.1566	+	0.132065i	1.31034	+	0.00953100i
$193$	−13.9179	−	8.03550i	−1.00183	−	0.578408i	−0.0930418	−	0.995662i	$-0.529659\pi$
$193$	−13.9179	−	8.03550i	−1.00183	−	0.578408i	−0.908790	+	0.417255i	$0.862992\pi$
$194$	−3.86004	−	3.24694i	−0.277135	−	0.233117i
$195$		−	0.860520i		−	0.0616232i
$196$	−13.9820	+	0.710016i	−0.998713	+	0.0507154i
$197$	−3.43415			−0.244673			−0.122337	−	0.992489i	$-0.539039\pi$
$197$	−3.43415			−0.244673			−0.122337	+	0.992489i	$0.539039\pi$
$198$	5.71814	−	6.79786i	0.406370	−	0.483103i
$199$	7.26822	+	4.19631i	0.515230	+	0.297468i	0.734981	−	0.678088i	$-0.237191\pi$
$199$	7.26822	+	4.19631i	0.515230	+	0.297468i	−0.219751	+	0.975556i	$0.570524\pi$
$200$	−11.4037	+	6.52874i	−0.806362	+	0.461651i
$201$	−27.2053	+	15.7070i	−1.91892	+	1.10789i
$202$	0.931858	−	0.337890i	0.0655653	−	0.0237738i
$203$	10.4664	−	9.26735i	0.734595	−	0.650440i
$204$	−2.12707	+	18.5947i	−0.148924	+	1.30189i
$205$	−4.96779	+	2.86816i	−0.346966	+	0.200321i
$206$	26.4868	+	4.70345i	1.84542	+	0.327705i
$207$	12.9526	+	7.47817i	0.900266	+	0.519769i
$208$	0.859939	+	2.39879i	0.0596260	+	0.166326i
$209$			10.6229i			0.734805i
$210$	−0.128200	−	5.05242i	−0.00884666	−	0.348650i
$211$	0.352895			0.0242943			0.0121471	−	0.999926i	$-0.496133\pi$
$211$	0.352895			0.0242943			0.0121471	+	0.999926i	$0.496133\pi$
$212$	6.45861	−	17.6119i	0.443579	−	1.20959i
$213$	−11.9893	−	6.92202i	−0.821493	−	0.474289i
$214$	14.9149	+	2.64854i	1.01956	+	0.181050i
$215$	1.80994	−	1.04497i	0.123437	−	0.0712661i
$216$	−4.70856	−	2.74137i	−0.320377	−	0.186527i
$217$	−26.5712	+	5.41707i	−1.80377	+	0.367735i
$218$	6.59181	+	18.1794i	0.446454	+	1.23126i
$219$	8.69359	−	5.01925i	0.587459	−	0.339169i
$220$	0.595190	+	3.42401i	0.0401277	+	0.230847i
$221$	−2.55291	+	0.618233i	−0.171727	+	0.0415869i
$222$	13.8448	−	16.4590i	0.929203	−	1.10466i
$223$	−9.27035			−0.620789			−0.310394	−	0.950608i	$-0.600461\pi$
$223$	−9.27035			−0.620789			−0.310394	+	0.950608i	$0.600461\pi$
$224$	5.40638	+	13.9560i	0.361229	+	0.932477i
$225$	−9.99437			−0.666292
$226$	−6.54240	−	5.50326i	−0.435194	−	0.366071i
$227$	12.4899	−	21.6331i	0.828984	−	1.43584i	−0.0698528	−	0.997557i	$-0.522253\pi$
$227$	12.4899	−	21.6331i	0.828984	−	1.43584i	0.898836	−	0.438284i	$-0.144414\pi$
$228$	−16.2711	+	2.82837i	−1.07758	+	0.187314i
$229$	−7.64709	+	4.41505i	−0.505334	+	0.291755i	−0.730913	−	0.682470i	$-0.760906\pi$
$229$	−7.64709	+	4.41505i	−0.505334	+	0.291755i	0.225580	+	0.974225i	$0.427572\pi$
$230$	−5.50100	+	1.99465i	−0.362725	+	0.131523i
$231$	16.6292	+	5.55665i	1.09412	+	0.365601i
$232$	−12.9153	−	7.51942i	−0.847932	−	0.493674i
$233$	5.66544	−	3.27095i	0.371156	−	0.214287i	−0.302808	−	0.953052i	$-0.597924\pi$
$233$	5.66544	−	3.27095i	0.371156	−	0.214287i	0.673963	+	0.738765i	$0.264591\pi$
$234$	−0.338876	+	1.90833i	−0.0221530	+	0.124751i
$235$	−2.58479	+	4.47699i	−0.168613	+	0.292047i
$236$	8.24903	−	22.4942i	0.536966	−	1.46425i
$237$		−	9.32759i		−	0.605892i
$238$	−14.8969	+	4.01020i	−0.965624	+	0.259943i
$239$	−4.98602			−0.322519			−0.161259	−	0.986912i	$-0.551556\pi$
$239$	−4.98602			−0.322519			−0.161259	+	0.986912i	$0.551556\pi$
$240$	−5.08606	+	1.82330i	−0.328304	+	0.117693i
$241$	16.1379	+	9.31724i	1.03954	+	0.600176i	0.919702	−	0.392618i	$-0.128430\pi$
$241$	16.1379	+	9.31724i	1.03954	+	0.600176i	0.119834	+	0.992794i	$0.461764\pi$
$242$	3.44604	+	0.611938i	0.221520	+	0.0393369i
$243$	−9.39591	−	16.2742i	−0.602748	−	1.04399i
$244$	10.3854	−	8.67158i	0.664858	−	0.555141i
$245$	3.83349	−	1.63085i	0.244913	−	0.104191i
$246$	29.0846	−	10.5460i	1.85437	−	0.672390i
$247$	−1.15891	−	2.00729i	−0.0737397	−	0.127721i
$248$	14.4037	+	25.1588i	0.914634	+	1.59758i
$249$	−9.52533	−	5.49945i	−0.603643	−	0.348514i
$250$	5.22596	−	6.21275i	0.330519	−	0.392929i
$251$			8.70447i			0.549421i	0.961527	+	0.274710i	$0.0885820\pi$
$251$			8.70447i			0.549421i	−0.961527	+	0.274710i	$0.911418\pi$
$252$	−1.70536	+	11.2550i	−0.107427	+	0.708996i
$253$		−	20.2994i		−	1.27621i
$254$	−17.6231	+	20.9507i	−1.10577	+	1.31457i
$255$	−1.31082	−	5.41283i	−0.0820865	−	0.338965i
$256$	12.3559	−	10.1653i	0.772242	−	0.635328i
$257$	7.51635	+	13.0187i	0.468857	+	0.812085i	0.999366	−	0.0355947i	$-0.0113325\pi$
$257$	7.51635	+	13.0187i	0.468857	+	0.812085i	−0.530509	+	0.847679i	$0.677999\pi$
$258$	−10.5965	+	3.84228i	−0.659711	+	0.239210i
$259$	16.8145	+	5.61857i	1.04480	+	0.349121i
$260$	−0.486008	−	0.582062i	−0.0301410	−	0.0360980i
$261$	−5.68341	−	9.84396i	−0.351794	−	0.609326i
$262$	0.420502	+	0.0746716i	0.0259787	+	0.00461323i
$263$	−5.21302	+	9.02922i	−0.321449	+	0.556765i	−0.980787	−	0.195081i	$-0.937503\pi$
$263$	−5.21302	+	9.02922i	−0.321449	+	0.556765i	0.659338	+	0.751846i	$0.270836\pi$
$264$	0.0681661	−	18.7435i	0.00419533	−	1.15358i
$265$			5.58205i			0.342903i
$266$	−7.10342	−	11.6129i	−0.435539	−	0.712030i
$267$	−37.1328			−2.27249
$268$	−9.53081	+	25.9895i	−0.582187	+	1.58756i
$269$	−0.366180	+	0.634242i	−0.0223264	+	0.0386704i	−0.876973	−	0.480540i	$-0.840441\pi$
$269$	−0.366180	+	0.634242i	−0.0223264	+	0.0386704i	0.854646	+	0.519211i	$0.173774\pi$
$270$	1.59632	+	0.283470i	0.0971490	+	0.0172514i
$271$	−6.33178	−	10.9670i	−0.384628	−	0.666195i	0.607089	−	0.794633i	$-0.292337\pi$
$271$	−6.33178	−	10.9670i	−0.384628	−	0.666195i	−0.991718	+	0.128438i	$0.959004\pi$
$272$	9.06321	+	13.7789i	0.549538	+	0.835469i
$273$	−3.74843	+	0.764191i	−0.226865	+	0.0462510i
$274$	1.89999	+	5.23993i	0.114782	+	0.316556i
$275$	6.78239	+	11.7474i	0.408993	+	0.708397i
$276$	31.0924	−	5.40473i	1.87154	−	0.325326i
$277$	−15.2238	+	26.3684i	−0.914709	+	1.58432i	−0.107383	+	0.994218i	$0.534247\pi$
$277$	−15.2238	+	26.3684i	−0.914709	+	1.58432i	−0.807326	+	0.590105i	$0.799086\pi$
$278$	1.50165	−	1.78520i	0.0900630	−	0.107069i
$279$			22.0496i			1.32007i
$280$	−2.94024	−	3.34509i	−0.175713	−	0.199907i
$281$	15.7122			0.937312			0.468656	−	0.883381i	$-0.344738\pi$
$281$	15.7122			0.937312			0.468656	+	0.883381i	$0.344738\pi$
$282$	17.9475	−	21.3364i	1.06876	−	1.27056i
$283$	−9.38772	+	16.2600i	−0.558042	+	0.966557i	0.439618	+	0.898185i	$0.355114\pi$
$283$	−9.38772	+	16.2600i	−0.558042	+	0.966557i	−0.997660	+	0.0683724i	$0.978219\pi$
$284$	−12.0191	+	2.08926i	−0.713202	+	0.123975i
$285$	4.25598	−	2.45719i	0.252103	−	0.145552i
$286$	2.47303	−	0.896715i	0.146233	−	0.0530239i
$287$	16.9054	+	19.0926i	0.997893	+	1.12700i
$288$	11.9971	−	2.04051i	0.706936	−	0.120238i
$289$	−15.1165	+	7.77760i	−0.889206	+	0.457506i
$290$	4.37861	+	0.777542i	0.257121	+	0.0456588i
$291$	−7.01057	−	4.04755i	−0.410967	−	0.237272i
$292$	3.04562	−	8.30506i	0.178231	−	0.486017i
$293$			23.9955i			1.40183i	0.713243	+	0.700917i	$0.247226\pi$
$293$			23.9955i			1.40183i	−0.713243	+	0.700917i	$0.752774\pi$
$294$	−21.8945	+	5.04528i	−1.27691	+	0.294247i
$295$			7.12947i			0.415094i
$296$	0.0689257	−	18.9524i	0.00400622	−	1.10158i
$297$	−2.81222	+	4.87091i	−0.163182	+	0.282639i
$298$	−2.69959	+	15.2023i	−0.156383	+	0.880648i
$299$	2.21456	+	3.83573i	0.128071	+	0.221826i
$300$	−16.1876	+	13.5163i	−0.934594	+	0.780364i
$301$	−6.15920	−	6.95609i	−0.355011	−	0.400942i
$302$	−6.23723	−	17.2015i	−0.358912	−	0.989834i
$303$	1.37767	−	0.795398i	0.0791451	−	0.0456944i
$304$	−9.40846	+	11.1028i	−0.539612	+	0.636789i
$305$	−2.01301	+	3.48664i	−0.115265	+	0.199645i
$306$	0.775336	+	12.5199i	0.0443230	+	0.715718i
$307$			5.19847i			0.296692i	0.988936	+	0.148346i	$0.0473950\pi$
$307$			5.19847i			0.296692i	−0.988936	+	0.148346i	$0.952605\pi$
$308$	14.3864	−	5.63337i	0.819744	−	0.320991i
$309$	43.1731			2.45603
$310$	−6.60162	−	5.55307i	−0.374947	−	0.315393i
$311$	11.5735	+	6.68196i	0.656273	+	0.378899i	0.790855	−	0.612003i	$-0.209636\pi$
$311$	11.5735	+	6.68196i	0.656273	+	0.378899i	−0.134582	+	0.990902i	$0.542969\pi$
$312$	2.03194	+	3.54917i	0.115036	+	0.200932i
$313$	−24.1784	+	13.9594i	−1.36664	+	0.789033i	−0.990498	−	0.137528i	$-0.956084\pi$
$313$	−24.1784	+	13.9594i	−1.36664	+	0.789033i	−0.376147	+	0.926560i	$0.622751\pi$
$314$	21.7480	−	7.88578i	1.22731	−	0.445020i
$315$	−0.676662	−	3.31909i	−0.0381256	−	0.187009i
$316$	−5.26808	−	6.30925i	−0.296353	−	0.354923i
$317$	−5.72445	−	9.91504i	−0.321517	−	0.556884i	0.659284	−	0.751894i	$-0.270860\pi$
$317$	−5.72445	−	9.91504i	−0.321517	−	0.556884i	−0.980801	+	0.195010i	$0.937526\pi$
$318$	5.26372	−	29.6419i	0.295175	−	1.66223i
$319$	−7.71376	+	13.3606i	−0.431888	+	0.748052i
$320$	−2.41048	+	4.10582i	−0.134750	+	0.229522i
$321$	24.3110			1.35691
$322$	13.5739	+	22.1910i	0.756444	+	1.23666i
$323$	−10.3474	−	10.8609i	−0.575746	−	0.604316i
$324$	−20.3279	−	7.45463i	−1.12933	−	0.414146i
$325$	−2.56317	−	1.47985i	−0.142179	−	0.0820872i
$326$	−30.7182	−	5.45484i	−1.70132	−	0.302116i
$327$	15.5172	+	26.8766i	0.858105	+	1.48628i
$328$	13.7168	−	23.5599i	0.757385	−	1.30088i
$329$	21.7972	+	7.28354i	1.20172	+	0.401554i
$330$	1.90127	+	5.24347i	0.104662	+	0.288643i
$331$	26.0183	−	15.0217i	1.43010	−	0.825666i	0.432968	−	0.901409i	$-0.357466\pi$
$331$	26.0183	−	15.0217i	1.43010	−	0.825666i	0.997127	+	0.0757430i	$0.0241329\pi$
$332$	−9.54901	+	1.65989i	−0.524070	+	0.0910981i
$333$	7.20751	−	12.4838i	0.394969	−	0.684107i
$334$	9.61185	+	8.08518i	0.525937	+	0.442401i
$335$		−	8.23729i		−	0.450051i
$336$	12.4590	+	20.5357i	0.679694	+	1.12031i
$337$			4.81722i			0.262411i	0.991355	+	0.131205i	$0.0418847\pi$
$337$			4.81722i			0.262411i	−0.991355	+	0.131205i	$0.958115\pi$
$338$	11.4651	−	13.6300i	0.623619	−	0.741373i
$339$	−11.8822	−	6.86021i	−0.645354	−	0.372596i
$340$	−3.94373	−	2.92095i	−0.213879	−	0.158411i
$341$	25.9172	−	14.9633i	1.40349	−	0.810307i
$342$	−10.4059	+	3.77316i	−0.562687	+	0.204029i
$343$	−10.5083	−	15.2504i	−0.567397	−	0.823444i
$344$	−4.99751	+	8.58369i	−0.269448	+	0.462802i
$345$	−8.13274	+	4.69544i	−0.437852	+	0.252794i
$346$	−19.7359	−	3.50465i	−1.06101	−	0.188411i
$347$	−16.4426	+	28.4794i	−0.882685	+	1.52885i	−0.0343400	+	0.999410i	$0.510933\pi$
$347$	−16.4426	+	28.4794i	−0.882685	+	1.52885i	−0.848345	+	0.529444i	$0.822400\pi$
$348$	−22.5182	−	8.25783i	−1.20710	−	0.442666i
$349$		−	12.2383i		−	0.655102i	−0.944833	−	0.327551i	$-0.893777\pi$
$349$		−	12.2383i		−	0.655102i	0.944833	−	0.327551i	$-0.106223\pi$
$350$	−15.2698	−	8.30686i	−0.816203	−	0.444020i
$351$		−	1.22720i		−	0.0655029i
$352$	−10.5399	−	12.7167i	−0.561780	−	0.677804i
$353$	−6.16964	+	10.6861i	−0.328377	+	0.568765i	−0.982190	−	0.187891i	$-0.939835\pi$
$353$	−6.16964	+	10.6861i	−0.328377	+	0.568765i	0.653813	+	0.756656i	$0.273168\pi$
$354$	6.72290	−	37.8590i	0.357318	−	2.01218i
$355$	3.14380	−	1.81507i	0.166856	−	0.0963341i
$356$	−25.1169	+	20.9720i	−1.33119	+	1.11151i
$357$	−22.4142	+	10.5168i	−1.18629	+	0.556609i
$358$	−0.865697	+	0.313900i	−0.0457535	+	0.0165901i
$359$	−14.6474	−	25.3700i	−0.773059	−	1.33898i	−0.935879	−	0.352322i	$-0.885392\pi$
$359$	−14.6474	−	25.3700i	−0.773059	−	1.33898i	0.162820	−	0.986656i	$-0.447941\pi$
$360$	−3.14265	+	1.79920i	−0.165632	+	0.0948264i
$361$	−2.88153	+	4.99095i	−0.151659	+	0.262682i
$362$	8.62539	−	10.2541i	0.453340	−	0.538942i
$363$	5.61699			0.294816
$364$	−2.10386	+	2.63396i	−0.110272	+	0.138057i
$365$			2.63227i			0.137779i
$366$	13.9773	−	16.6166i	0.730608	−	0.868564i
$367$	−13.2198	−	7.63243i	−0.690065	−	0.398409i	0.113571	−	0.993530i	$-0.463771\pi$
$367$	−13.2198	−	7.63243i	−0.690065	−	0.398409i	−0.803637	+	0.595120i	$0.797104\pi$
$368$	17.9786	−	21.2163i	0.937200	−	1.10598i
$369$	17.9572	−	10.3676i	0.934816	−	0.539716i
$370$	1.92246	+	5.30190i	0.0999438	+	0.275633i
$371$	24.3154	−	4.95718i	1.26239	−	0.257364i
$372$	29.8196	+	35.7131i	1.54608	+	1.85164i
$373$	−10.2346	+	5.90893i	−0.529926	+	0.305953i	−0.740986	−	0.671520i	$-0.765642\pi$
$373$	−10.2346	+	5.90893i	−0.529926	+	0.305953i	0.211061	+	0.977473i	$0.432308\pi$
$374$	14.1899	−	9.40763i	0.733740	−	0.486457i
$375$	6.51454	−	11.2835i	0.336410	−	0.582679i
$376$	0.0893506	−	24.5686i	0.00460790	−	1.26703i
$377$		−	3.36613i		−	0.173365i
$378$	−0.182828	−	7.20531i	−0.00940365	−	0.370601i
$379$	−1.22762			−0.0630584			−0.0315292	−	0.999503i	$-0.510038\pi$
$379$	−1.22762			−0.0630584			−0.0315292	+	0.999503i	$0.510038\pi$
$380$	1.49099	−	4.06577i	0.0764864	−	0.208570i
$381$	−21.9685	+	38.0505i	−1.12548	+	1.94939i
$382$	−18.8106	−	3.34033i	−0.962433	−	0.170906i
$383$	0.294115	+	0.509422i	0.0150286	+	0.0260303i	0.873442	−	0.486928i	$-0.161883\pi$
$383$	0.294115	+	0.509422i	0.0150286	+	0.0260303i	−0.858413	+	0.512959i	$0.828549\pi$
$384$	16.6719	−	19.5298i	0.850782	−	0.996624i
$385$	−3.44208	+	3.04775i	−0.175425	+	0.155328i
$386$	−21.3666	+	7.74747i	−1.08753	+	0.394336i
$387$	−6.54243	+	3.77727i	−0.332570	+	0.192010i
$388$	−7.02800	+	1.22166i	−0.356792	+	0.0620206i
$389$	−2.84709	−	1.64377i	−0.144353	−	0.0833424i	0.426084	−	0.904684i	$-0.359893\pi$
$389$	−2.84709	−	1.64377i	−0.144353	−	0.0833424i	−0.570437	+	0.821341i	$0.693226\pi$
$390$	−0.931296	−	0.783376i	−0.0471580	−	0.0396678i
$391$	19.7729	+	20.7540i	0.999957	+	1.04958i
$392$	−11.9601	+	15.7783i	−0.604077	+	0.796926i
$393$	0.685413			0.0345745
$394$	−3.12628	+	3.71660i	−0.157500	+	0.187240i
$395$	2.11817	+	1.22293i	0.106577	+	0.0615322i
$396$	−2.15145	−	12.3769i	−0.108114	−	0.621962i
$397$	4.95235	+	8.57772i	0.248551	+	0.430504i	0.963124	−	0.269058i	$-0.0867122\pi$
$397$	4.95235	+	8.57772i	0.248551	+	0.430504i	−0.714573	+	0.699561i	$0.753379\pi$
$398$	11.1581	−	4.04590i	0.559304	−	0.202802i
$399$	−14.4831	−	16.3569i	−0.725061	−	0.818871i
$400$	−3.31565	+	18.2851i	−0.165782	+	0.914253i
$401$	−1.39496	+	0.805383i	−0.0696612	+	0.0402189i	−0.534426	−	0.845215i	$-0.679472\pi$
$401$	−1.39496	+	0.805383i	−0.0696612	+	0.0402189i	0.464765	+	0.885434i	$0.346139\pi$
$402$	−7.76754	+	43.7418i	−0.387410	+	2.18164i
$403$	−3.26484	+	5.65486i	−0.162633	+	0.281689i
$404$	0.482638	−	1.31610i	0.0240121	−	0.0654784i
$405$	6.44289			0.320150
$406$	−0.501486	−	19.7637i	−0.0248883	−	0.980858i
$407$	−19.5647			−0.969784
$408$	18.1877	+	19.2297i	0.900423	+	0.952012i
$409$	−3.83308	+	6.63908i	−0.189533	+	0.328281i	−0.945095	−	0.326796i	$-0.894031\pi$
$409$	−3.83308	+	6.63908i	−0.189533	+	0.328281i	0.755561	+	0.655078i	$0.227364\pi$
$410$	−1.41838	+	7.98741i	−0.0700489	+	0.394470i
$411$	4.47260	+	7.74677i	0.220617	+	0.382120i
$412$	29.2026	−	24.3835i	1.43871	−	1.20129i
$413$	31.0560	−	6.33138i	1.52817	−	0.311547i
$414$	19.8846	−	7.21012i	0.977276	−	0.354358i
$415$	2.49771	−	1.44205i	0.122608	−	0.0707875i
$416$	3.37893	+	1.25308i	0.165666	+	0.0614371i
$417$	1.87192	−	3.24225i	0.0916682	−	0.158774i
$418$	11.4967	+	9.67062i	0.562320	+	0.473005i
$419$	−4.23375			−0.206832			−0.103416	−	0.994638i	$-0.532977\pi$
$419$	−4.23375			−0.206832			−0.103416	+	0.994638i	$0.532977\pi$
$420$	−5.58468	−	4.46074i	−0.272504	−	0.217662i
$421$		−	5.14426i		−	0.250716i	−0.992112	−	0.125358i	$-0.959992\pi$
$421$		−	5.14426i		−	0.250716i	0.992112	−	0.125358i	$-0.0400079\pi$
$422$	0.321258	−	0.381919i	0.0156386	−	0.0185915i
$423$	9.34333	−	16.1831i	0.454288	−	0.786850i
$424$	−13.1808	−	23.0228i	−0.640118	−	1.11809i
$425$	−18.3771	−	5.40408i	−0.891418	−	0.262136i
$426$	−18.4058	+	6.67391i	−0.891765	+	0.323352i
$427$	16.9755	+	5.67235i	0.821502	+	0.274504i
$428$	16.4441	−	13.7305i	0.794858	−	0.663687i
$429$	3.65616	−	2.11088i	0.176521	−	0.101914i
$430$	0.516765	−	2.91009i	0.0249206	−	0.140337i
$431$	−3.74965	−	2.16486i	−0.180614	−	0.104278i	0.406967	−	0.913443i	$-0.366586\pi$
$431$	−3.74965	−	2.16486i	−0.180614	−	0.104278i	−0.587581	+	0.809165i	$0.699920\pi$
$432$	−7.25329	+	2.60022i	−0.348974	+	0.125103i
$433$	24.0799			1.15720			0.578602	−	0.815610i	$-0.303598\pi$
$433$	24.0799			1.15720			0.578602	+	0.815610i	$0.303598\pi$
$434$	−18.3266	+	33.6881i	−0.879703	+	1.61708i
$435$	7.13708			0.342197
$436$	25.6755	+	9.41567i	1.22963	+	0.450929i
$437$	−12.6472	+	21.9056i	−0.604998	+	1.04789i
$438$	2.48216	−	13.9779i	0.118602	−	0.667890i
$439$	−23.6991	+	13.6827i	−1.13110	+	0.653039i	−0.944210	−	0.329343i	$-0.893173\pi$
$439$	−23.6991	+	13.6827i	−1.13110	+	0.653039i	−0.186886	+	0.982382i	$0.559839\pi$
$440$	4.24746	+	2.47291i	0.202490	+	0.117891i
$441$	−13.8570	+	5.89508i	−0.659859	+	0.280718i
$442$	−1.65496	+	3.32569i	−0.0787185	+	0.158187i
$443$	−11.7301	+	6.77238i	−0.557314	+	0.321766i	−0.752067	−	0.659087i	$-0.770943\pi$
$443$	−11.7301	+	6.77238i	−0.557314	+	0.321766i	0.194753	+	0.980852i	$0.437610\pi$
$444$	−5.20912	−	29.9670i	−0.247214	−	1.42217i
$445$	4.86843	−	8.43237i	0.230786	−	0.399733i
$446$	−8.43928	+	10.0328i	−0.399611	+	0.475068i
$447$			24.7796i			1.17203i
$448$	20.0256	+	6.85386i	0.946121	+	0.323815i
$449$			4.73085i			0.223263i	0.993750	+	0.111631i	$0.0356076\pi$
$449$			4.73085i			0.223263i	−0.993750	+	0.111631i	$0.964392\pi$
$450$	−9.09839	+	10.8164i	−0.428902	+	0.509889i
$451$	−24.3723	−	14.0713i	−1.14765	−	0.662594i
$452$	−11.9118	+	2.07060i	−0.560283	+	0.0973929i
$453$	−14.6825	−	25.4309i	−0.689846	−	1.19485i
$454$	−12.0422	−	33.2109i	−0.565169	−	1.55867i
$455$	0.317913	−	0.951411i	0.0149040	−	0.0446028i
$456$	−11.7514	+	20.1842i	−0.550310	+	0.945210i
$457$	−15.1675	−	26.2709i	−0.709506	−	1.22890i	−0.965041	−	0.262100i	$-0.915585\pi$
$457$	−15.1675	−	26.2709i	−0.709506	−	1.22890i	0.255535	−	0.966800i	$-0.417748\pi$
$458$	−2.18336	+	12.2953i	−0.102022	+	0.574521i
$459$	−1.86937	−	7.71929i	−0.0872547	−	0.360306i
$460$	−2.84914	+	7.76927i	−0.132842	+	0.362244i
$461$			31.4208i			1.46341i	0.681619	+	0.731707i	$0.261276\pi$
$461$			31.4208i			1.46341i	−0.681619	+	0.731707i	$0.738724\pi$
$462$	21.1521	−	12.9384i	0.984086	−	0.601951i
$463$	−27.1048			−1.25967			−0.629834	−	0.776730i	$-0.716877\pi$
$463$	−27.1048			−1.25967			−0.629834	+	0.776730i	$0.716877\pi$
$464$	−19.8953	+	7.13225i	−0.923618	+	0.331107i
$465$	−11.9898	−	6.92231i	−0.556013	−	0.321014i
$466$	1.61757	−	9.10912i	0.0749326	−	0.421972i
$467$	−31.2276	+	18.0293i	−1.44504	+	0.834295i	−0.998180	−	0.0603077i	$-0.980792\pi$
$467$	−31.2276	+	18.0293i	−1.44504	+	0.834295i	−0.446862	+	0.894603i	$0.647458\pi$
$468$	1.75679	+	2.10400i	0.0812076	+	0.0972574i
$469$	−35.8817	+	7.31519i	−1.65686	+	0.337784i
$470$	2.49215	+	6.87302i	0.114954	+	0.317029i
$471$	32.1525	−	18.5633i	1.48151	−	0.855350i
$472$	−16.8348	−	29.4051i	−0.774883	−	1.35348i
$473$	8.87966	+	5.12667i	0.408287	+	0.235725i
$474$	−10.0948	−	8.49139i	−0.463668	−	0.390022i
$475$		−	16.9027i		−	0.775548i
$476$	−9.22141	+	19.7729i	−0.422662	+	0.906287i
$477$		−	20.1776i		−	0.923869i
$478$	−4.53903	+	5.39610i	−0.207610	+	0.246812i
$479$	3.81395	+	2.20198i	0.174264	+	0.100611i	0.584595	−	0.811325i	$-0.301254\pi$
$479$	3.81395	+	2.20198i	0.174264	+	0.100611i	−0.410331	+	0.911937i	$0.634587\pi$
$480$	−2.65685	+	7.16422i	−0.121268	+	0.327000i
$481$	3.69690	−	2.13441i	0.168564	−	0.0973205i
$482$	24.7748	−	8.98328i	1.12846	−	0.409177i
$483$	27.6757	+	31.2564i	1.25929	+	1.42222i
$484$	3.79938	−	3.17239i	0.172699	−	0.144200i
$485$	1.83829	−	1.06134i	0.0834726	−	0.0481929i
$486$	−26.1663	−	4.64654i	−1.18693	−	0.210771i
$487$	0.876150	+	0.505845i	0.0397021	+	0.0229220i	0.519720	−	0.854337i	$-0.326036\pi$
$487$	0.876150	+	0.505845i	0.0397021	+	0.0229220i	−0.480018	+	0.877259i	$0.659370\pi$
$488$	0.0695855	−	19.1338i	0.00314999	−	0.866146i
$489$	−50.0701			−2.26425
$490$	1.72484	−	5.63343i	0.0779204	−	0.254493i
$491$		−	18.4565i		−	0.832931i	−0.909151	−	0.416466i	$-0.863269\pi$
$491$		−	18.4565i		−	0.832931i	0.909151	−	0.416466i	$-0.136731\pi$
$492$	15.0638	−	41.0774i	0.679130	−	1.85191i
$493$	−5.12757	−	21.1736i	−0.230934	−	0.953610i
$494$	−3.22740	−	0.573113i	−0.145208	−	0.0257856i
$495$	1.86911	+	3.23739i	0.0840100	+	0.145510i
$496$	40.3404	+	7.31497i	1.81134	+	0.328452i
$497$	−10.6983	−	12.0825i	−0.479886	−	0.541974i
$498$	−14.6232	+	5.30233i	−0.655280	+	0.237603i
$499$	−8.41846	−	14.5812i	−0.376862	−	0.652744i	0.613742	−	0.789507i	$-0.289664\pi$
$499$	−8.41846	−	14.5812i	−0.376862	−	0.652744i	−0.990604	+	0.136763i	$0.956330\pi$
$500$	−1.96627	−	11.3116i	−0.0879342	−	0.505869i
$501$	17.4569	+	10.0788i	0.779918	+	0.450286i
$502$	9.42039	+	7.92412i	0.420452	+	0.353671i
$503$		−	22.1991i		−	0.989810i	−0.868947	−	0.494905i	$-0.835203\pi$
$503$		−	22.1991i		−	0.989810i	0.868947	−	0.494905i	$-0.164797\pi$
$504$	10.6282	+	12.0916i	0.473417	+	0.538602i
$505$			0.417134i			0.0185622i
$506$	−21.9689	−	18.4796i	−0.976638	−	0.821516i
$507$	14.2921	−	24.7546i	0.634734	−	1.09939i
$508$	6.63069	+	38.1451i	0.294189	+	1.69241i
$509$	−11.2215	+	6.47872i	−0.497383	+	0.287164i	−0.727632	−	0.685968i	$-0.759379\pi$
$509$	−11.2215	+	6.47872i	−0.497383	+	0.287164i	0.230249	+	0.973132i	$0.426046\pi$
$510$	−7.05133	−	3.50895i	−0.312238	−	0.155379i
$511$	11.4662	−	2.33760i	0.507233	−	0.103410i
$512$	0.246867	−	22.6261i	0.0109101	−	0.999940i
$513$	6.06950	−	3.50423i	0.267975	−	0.154715i
$514$	20.9320	+	3.71704i	0.923270	+	0.163952i
$515$	−5.66037	+	9.80404i	−0.249426	+	0.432018i
$516$	−5.48826	+	14.9659i	−0.241607	+	0.658836i
$517$	−25.3623			−1.11543
$518$	21.3878	−	13.0826i	0.939727	−	0.574817i
$519$	−32.1693			−1.41208
$520$	−1.07237	−	0.00390000i	−0.0470267	−	0.000171026i
$521$	19.7131	+	11.3814i	0.863648	+	0.498627i	0.865232	−	0.501372i	$-0.167171\pi$
$521$	19.7131	+	11.3814i	0.863648	+	0.498627i	−0.00158447	+	0.999999i	$0.500504\pi$
$522$	−15.8275	−	2.81060i	−0.692751	−	0.123017i
$523$	−16.3637	+	9.44761i	−0.715537	+	0.413115i	−0.813108	−	0.582113i	$-0.802226\pi$
$523$	−16.3637	+	9.44761i	−0.715537	+	0.413115i	0.0975711	+	0.995229i	$0.468893\pi$
$524$	0.463618	−	0.387110i	0.0202533	−	0.0169110i
$525$	−26.4595	−	8.84144i	−1.15479	−	0.385872i
$526$	5.02617	+	13.8615i	0.219151	+	0.604392i
$527$	−11.9225	+	40.5434i	−0.519351	+	1.76610i
$528$	−20.2230	−	17.1369i	−0.880095	−	0.745789i
$529$	12.6675	−	21.9408i	0.550762	−	0.953947i
$530$	6.04116	+	5.08163i	0.262411	+	0.220732i
$531$		−	25.7711i		−	1.11837i
$532$	−19.0346	−	2.88413i	−0.825255	−	0.125043i
$533$	6.14045			0.265972
$534$	−33.8039	+	40.1869i	−1.46284	+	1.73906i
$535$	−3.18738	+	5.52071i	−0.137803	+	0.238681i
$536$	19.4506	+	33.9743i	0.840140	+	1.46746i
$537$	−1.27986	+	0.738926i	−0.0552299	+	0.0318870i
$538$	0.353054	+	0.973680i	0.0152213	+	0.0419783i
$539$	16.3328	+	12.2871i	0.703503	+	0.529243i
$540$	1.76000	−	1.46956i	0.0757382	−	0.0632396i
$541$	7.12624	+	12.3430i	0.306381	+	0.530667i	0.977568	−	0.210621i	$-0.0675486\pi$
$541$	7.12624	+	12.3430i	0.306381	+	0.530667i	−0.671187	+	0.741288i	$0.734215\pi$
$542$	−17.6331	−	3.13124i	−0.757407	−	0.134498i
$543$	10.7522	−	18.6233i	0.461420	−	0.799203i
$544$	23.1629	+	2.73501i	0.993101	+	0.117262i
$545$	−8.13777			−0.348584
$546$	−2.58534	+	4.75241i	−0.110642	+	0.203384i
$547$	−30.9907			−1.32507			−0.662534	−	0.749032i	$-0.730519\pi$
$547$	−30.9907			−1.32507			−0.662534	+	0.749032i	$0.730519\pi$
$548$	7.40056	+	2.71392i	0.316136	+	0.115933i
$549$	7.27651	−	12.6033i	0.310554	−	0.537895i
$550$	18.8880	+	3.35408i	0.805387	+	0.143018i
$551$	16.6483	−	9.61189i	0.709241	−	0.409480i
$552$	22.4557	−	38.5699i	0.955780	−	1.64164i
$553$	3.44602	−	10.3128i	0.146540	−	0.438545i
$554$	14.6781	+	40.4804i	0.623614	+	1.71985i
$555$	4.52550	+	7.83839i	0.192097	+	0.332721i
$556$	−0.564996	−	3.25031i	−0.0239612	−	0.137844i
$557$	18.1735	+	10.4925i	0.770037	+	0.444581i	0.832888	−	0.553442i	$-0.186686\pi$
$557$	18.1735	+	10.4925i	0.770037	+	0.444581i	−0.0628507	+	0.998023i	$0.520019\pi$
$558$	23.8631	+	20.0728i	1.01020	+	0.849751i
$559$	−2.23718			−0.0946225
$560$	−6.29687	+	0.136864i	−0.266091	+	0.00578356i
$561$	19.7824	−	18.8472i	0.835215	−	0.795730i
$562$	14.3036	−	17.0045i	0.603362	−	0.717292i
$563$	−20.9915	−	12.1194i	−0.884686	−	0.510774i	−0.0124852	−	0.999922i	$-0.503974\pi$
$563$	−20.9915	−	12.1194i	−0.884686	−	0.510774i	−0.872201	+	0.489148i	$0.837308\pi$
$564$	−6.75275	−	38.8473i	−0.284342	−	1.63576i
$565$	3.11573	−	1.79887i	0.131080	−	0.0756789i
$566$	9.05123	+	24.9622i	0.380452	+	1.04924i
$567$	−5.72165	−	28.0652i	−0.240287	−	1.17863i
$568$	−8.68051	+	14.9096i	−0.364226	+	0.625593i
$569$	16.5412	+	28.6502i	0.693444	+	1.20108i	0.970702	+	0.240285i	$0.0772410\pi$
$569$	16.5412	+	28.6502i	0.693444	+	1.20108i	−0.277258	+	0.960795i	$0.589426\pi$
$570$	1.21515	−	6.84294i	0.0508970	−	0.286619i
$571$	10.2732	−	17.7938i	0.429922	−	0.744647i	−0.566944	−	0.823756i	$-0.691874\pi$
$571$	10.2732	−	17.7938i	0.429922	−	0.744647i	0.996866	+	0.0791096i	$0.0252077\pi$
$572$	1.28086	−	3.49276i	0.0535554	−	0.146039i
$573$	−30.6610			−1.28088
$574$	36.0528	−	0.914804i	1.50481	−	0.0381832i
$575$			32.2993i			1.34697i
$576$	8.71324	−	14.8414i	0.363052	−	0.618393i
$577$	−6.36374	+	11.0223i	−0.264926	+	0.458865i	−0.967544	−	0.252702i	$-0.918681\pi$
$577$	−6.36374	+	11.0223i	−0.264926	+	0.458865i	0.702618	+	0.711567i	$0.252014\pi$
$578$	−5.34405	+	23.4402i	−0.222283	+	0.974982i
$579$	−31.5886	+	18.2377i	−1.31278	+	0.757932i
$580$	4.82757	−	4.03091i	0.200454	−	0.167374i
$581$	−8.49968	−	9.59939i	−0.352626	−	0.398250i
$582$	−10.7625	+	3.90248i	−0.446122	+	0.161763i
$583$	−23.7169	+	13.6929i	−0.982252	+	0.567104i
$584$	−6.21555	−	10.8566i	−0.257201	−	0.449251i
$585$	−0.706365	−	0.407820i	−0.0292046	−	0.0168613i
$586$	25.9691	+	21.8444i	1.07277	+	0.902382i
$587$			18.4291i			0.760652i	0.924853	+	0.380326i	$0.124188\pi$
$587$			18.4291i			0.760652i	−0.924853	+	0.380326i	$0.875812\pi$
$588$	−14.4715	+	28.2883i	−0.596793	+	1.16659i
$589$	−37.2906			−1.53653
$590$	7.71585	+	6.49033i	0.317657	+	0.267203i
$591$	−3.89714	+	6.75005i	−0.160307	+	0.277660i
$592$	−20.4484	−	17.3279i	−0.840424	−	0.712172i
$593$	6.62111	+	11.4681i	0.271896	+	0.470938i	0.969347	−	0.245694i	$-0.0790159\pi$
$593$	6.62111	+	11.4681i	0.271896	+	0.470938i	−0.697451	+	0.716632i	$0.745683\pi$
$594$	2.71142	+	7.47776i	0.111251	+	0.306816i
$595$	0.550466	−	6.46882i	0.0225669	−	0.265196i
$596$	13.9951	+	16.7611i	0.573262	+	0.686561i
$597$	16.4962	−	9.52411i	0.675146	−	0.389796i
$598$	6.16723	+	1.09516i	0.252197	+	0.0447844i
$599$	−7.22383	+	12.5120i	−0.295158	+	0.511228i	−0.975022	−	0.222110i	$-0.928706\pi$
$599$	−7.22383	+	12.5120i	−0.295158	+	0.511228i	0.679864	+	0.733338i	$0.262039\pi$
$600$	−0.108462	+	29.8236i	−0.00442795	+	1.21754i
$601$		−	0.0319037i		−	0.00130138i	−1.00000		0.000650691i	$-0.999793\pi$
$601$		−	0.0319037i		−	0.00130138i	1.00000		0.000650691i	$-0.000207121\pi$
$602$	−13.1353	+	0.333294i	−0.535353	+	0.0135841i
$603$			29.7756i			1.21256i
$604$	−24.2943	−	8.90918i	−0.988523	−	0.362509i
$605$	−0.736436	+	1.27555i	−0.0299404	+	0.0518583i
$606$	0.393346	−	2.21507i	0.0159786	−	0.0899811i
$607$	15.3216	−	8.84591i	0.621883	−	0.359045i	−0.155718	−	0.987801i	$-0.549769\pi$
$607$	15.3216	−	8.84591i	0.621883	−	0.359045i	0.777602	+	0.628757i	$0.216436\pi$
$608$	3.45095	+	20.2897i	0.139955	+	0.822857i
$609$	−6.33813	−	31.0891i	−0.256834	−	1.25979i
$610$	1.94086	+	5.35265i	0.0785832	+	0.216723i
$611$	4.79241	−	2.76690i	0.193880	−	0.111937i
$612$	14.2555	+	10.5584i	0.576245	+	0.426800i
$613$	5.06881	+	2.92648i	0.204727	+	0.118199i	0.598859	−	0.800855i	$-0.295621\pi$
$613$	5.06881	+	2.92648i	0.204727	+	0.118199i	−0.394131	+	0.919054i	$0.628955\pi$
$614$	5.62603	+	4.73243i	0.227048	+	0.190985i
$615$			13.0194i			0.524991i
$616$	7.00002	−	20.6980i	0.282039	−	0.833948i
$617$		−	6.71445i		−	0.270313i	−0.990824	−	0.135157i	$-0.956846\pi$
$617$		−	6.71445i		−	0.270313i	0.990824	−	0.135157i	$-0.0431538\pi$
$618$	39.3027	−	46.7240i	1.58099	−	1.87951i
$619$	11.9934	−	20.7732i	0.482056	−	0.834946i	−0.517731	−	0.855543i	$-0.673223\pi$
$619$	11.9934	−	20.7732i	0.482056	−	0.834946i	0.999788	+	0.0205969i	$0.00655667\pi$
$620$	−12.0196	+	2.08934i	−0.482718	+	0.0839100i
$621$	−11.5982	+	6.69622i	−0.465419	+	0.268710i
$622$	17.7675	−	6.44246i	0.712412	−	0.258319i
$623$	−41.0549	−	13.7185i	−1.64483	−	0.549619i
$624$	5.69086	+	1.03193i	0.227817	+	0.0413102i
$625$	−9.90630	−	17.1582i	−0.396252	−	0.686328i
$626$	−6.90331	+	38.8750i	−0.275912	+	1.55376i
$627$	20.8801	+	12.0551i	0.833871	+	0.481436i
$628$	11.2640	−	30.7156i	0.449481	−	1.22568i
$629$	20.0029	−	19.0572i	0.797567	−	0.759861i
$630$	−4.20808	−	2.28922i	−0.167654	−	0.0912048i
$631$	−8.53906			−0.339935			−0.169967	−	0.985450i	$-0.554366\pi$
$631$	−8.53906			−0.339935			−0.169967	+	0.985450i	$0.554366\pi$
$632$	−11.6240	−	0.0422739i	−0.462377	−	0.00168157i
$633$	0.400472	−	0.693638i	0.0159173	−	0.0275696i
$634$	−15.9418	−	2.83090i	−0.633130	−	0.112429i
$635$	−5.76051	−	9.97750i	−0.228599	−	0.395945i
$636$	−27.2880	−	32.6812i	−1.08204	−	1.29589i
$637$	−4.42667	−	0.539924i	−0.175391	−	0.0213926i
$638$	7.43727	+	20.5111i	0.294445	+	0.812041i
$639$	−11.3640	+	6.56100i	−0.449552	+	0.259549i
$640$	2.24913	+	6.34648i	0.0889045	+	0.250867i
$641$	25.3695	+	14.6471i	1.00204	+	0.578526i	0.908850	−	0.417123i	$-0.136961\pi$
$641$	25.3695	+	14.6471i	1.00204	+	0.578526i	0.0931862	+	0.995649i	$0.470295\pi$
$642$	22.1316	−	26.3105i	0.873463	−	1.03839i
$643$	7.60245			0.299811			0.149906	−	0.988700i	$-0.452103\pi$
$643$	7.60245			0.299811			0.149906	+	0.988700i	$0.452103\pi$
$644$	36.3732	+	5.51128i	1.43330	+	0.217175i
$645$		−	4.74340i		−	0.186771i
$646$	−21.1740	+	1.31126i	−0.833078	+	0.0515909i
$647$	−10.6257	+	18.4043i	−0.417740	+	0.723547i	−0.995712	−	0.0925099i	$-0.970511\pi$
$647$	−10.6257	+	18.4043i	−0.417740	+	0.723547i	0.577972	+	0.816057i	$0.303844\pi$
$648$	−26.5733	+	15.2135i	−1.04390	+	0.597644i
$649$	−30.2915	+	17.4888i	−1.18905	+	0.686496i
$650$	−3.93495	+	1.42681i	−0.154342	+	0.0559639i
$651$	−19.5060	+	58.3749i	−0.764499	+	2.28789i
$652$	−33.8678	+	28.2788i	−1.32637	+	1.10748i
$653$	−14.4891	−	25.0959i	−0.567003	−	0.982078i	−0.996860	−	0.0791809i	$-0.974770\pi$
$653$	−14.4891	−	25.0959i	−0.567003	−	0.982078i	0.429857	−	0.902897i	$-0.358564\pi$
$654$	43.2133	+	7.67370i	1.68977	+	0.300065i
$655$	−0.0898635	+	0.155648i	−0.00351126	+	0.00608168i
$656$	−13.0106	−	36.2928i	−0.507977	−	1.41700i
$657$		−	9.51494i		−	0.371213i
$658$	27.7257	−	16.9594i	1.08086	−	0.661147i
$659$			41.7053i			1.62461i	0.583234	+	0.812304i	$0.301787\pi$
$659$			41.7053i			1.62461i	−0.583234	+	0.812304i	$0.698213\pi$
$660$	7.40556	+	2.71575i	0.288261	+	0.105711i
$661$	−4.56172	−	2.63371i	−0.177430	−	0.102439i	0.408654	−	0.912689i	$-0.365998\pi$
$661$	−4.56172	−	2.63371i	−0.177430	−	0.102439i	−0.586085	+	0.810250i	$0.699331\pi$
$662$	7.42863	−	41.8333i	0.288722	−	1.62590i
$663$	−1.68191	+	5.71949i	−0.0653200	+	0.222127i
$664$	−6.89655	+	11.8455i	−0.267638	+	0.459693i
$665$	5.61330	−	1.14438i	0.217675	−	0.0443773i
$666$	−6.94917	−	19.1649i	−0.269275	−	0.742626i
$667$	−31.8132	+	18.3673i	−1.23181	+	0.711186i
$668$	17.5003	−	3.04205i	0.677108	−	0.117700i
$669$	−10.5202	+	18.2215i	−0.406734	+	0.704483i
$670$	−8.91479	−	7.49883i	−0.344408	−	0.289705i
$671$	−19.7519			−0.762516
$672$	33.5668	+	5.21100i	1.29487	+	0.201019i
$673$		−	30.2531i		−	1.16617i	−0.812411	−	0.583085i	$-0.801845\pi$
$673$		−	30.2531i		−	1.16617i	0.812411	−	0.583085i	$-0.198155\pi$
$674$	5.21342	+	4.38536i	0.200814	+	0.168918i
$675$	4.47466	−	7.75034i	0.172230	−	0.298311i
$676$	−4.31375	−	24.8162i	−0.165913	−	0.954467i
$677$	1.37856	+	2.38773i	0.0529823	+	0.0917680i	0.891300	−	0.453414i	$-0.149794\pi$
$677$	1.37856	+	2.38773i	0.0529823	+	0.0917680i	−0.838318	+	0.545182i	$0.816461\pi$
$678$	−18.2415	+	6.61432i	−0.700559	+	0.254021i
$679$	−6.25570	−	7.06507i	−0.240072	−	0.271133i
$680$	−6.75137	+	1.60900i	−0.258903	+	0.0617023i
$681$	−28.3476	−	49.0994i	−1.08628	−	1.88149i
$682$	7.39976	−	41.6706i	0.283351	−	1.59565i
$683$	0.0664774	−	0.115142i	0.00254369	−	0.00440580i	−0.864751	−	0.502201i	$-0.832524\pi$
$683$	0.0664774	−	0.115142i	0.00254369	−	0.00440580i	0.867294	+	0.497795i	$0.165857\pi$
$684$	−5.38954	+	14.6967i	−0.206074	+	0.561941i
$685$	−2.34559			−0.0896203
$686$	−26.0710	−	2.51060i	−0.995395	−	0.0958552i
$687$			20.0411i			0.764617i
$688$	4.74019	+	13.2227i	0.180718	+	0.504111i
$689$	2.98766	−	5.17478i	0.113821	−	0.197143i
$690$	−2.32202	+	13.0761i	−0.0883980	+	0.497800i
$691$	−22.6115	−	39.1643i	−0.860182	−	1.48988i	−0.871753	−	0.489946i	$-0.837016\pi$
$691$	−22.6115	−	39.1643i	−0.860182	−	1.48988i	0.0115706	−	0.999933i	$-0.496317\pi$
$692$	−21.7596	+	18.1687i	−0.827174	+	0.690671i
$693$	12.4422	−	11.0168i	0.472639	−	0.418494i
$694$	15.8532	+	43.7212i	0.601780	+	1.65964i
$695$	0.490849	+	0.850175i	0.0186190	+	0.0322490i
$696$	−29.4365	+	16.8527i	−1.11579	+	0.638800i
$697$	38.6246	−	9.35365i	1.46301	−	0.354295i
$698$	−13.2449	−	11.1412i	−0.501327	−	0.421700i
$699$		−	14.8477i		−	0.561593i
$700$	−22.8909	+	8.96351i	−0.865196	+	0.338789i
$701$		−	10.7246i		−	0.405064i	−0.979276	−	0.202532i	$-0.935083\pi$
$701$		−	10.7246i		−	0.405064i	0.979276	−	0.202532i	$-0.0649170\pi$
$702$	−1.32813	−	1.11718i	−0.0501271	−	0.0421653i
$703$	21.1128	+	12.1895i	0.796284	+	0.459735i
$704$	−23.3577	−	0.169896i	−0.880326	−	0.00640320i
$705$	5.86655	+	10.1612i	0.220947	+	0.382692i
$706$	5.94849	+	16.4052i	0.223875	+	0.617418i
$707$	1.81704	−	0.370439i	0.0683367	−	0.0139318i
$708$	−34.8526	−	41.7409i	−1.30984	−	1.56872i
$709$	−10.4145	−	18.0384i	−0.391124	−	0.677447i	0.601474	−	0.798892i	$-0.294580\pi$
$709$	−10.4145	−	18.0384i	−0.391124	−	0.677447i	−0.992598	+	0.121446i	$0.961247\pi$
$710$	0.897604	−	5.05473i	0.0336865	−	0.189700i
$711$	−7.65663	−	4.42055i	−0.287146	−	0.165784i
$712$	−0.168291	+	46.2746i	−0.00630697	+	1.73421i
$713$	71.2585			2.66865
$714$	−9.02301	+	33.8317i	−0.337678	+	1.26612i
$715$			1.10702i			0.0414002i
$716$	−0.448371	+	1.22266i	−0.0167564	+	0.0456929i
$717$	−5.65823	+	9.80034i	−0.211311	+	0.366001i
$718$	−40.7909	−	7.24353i	−1.52230	−	0.270326i
$719$	18.6865	−	10.7886i	0.696888	−	0.402348i	−0.109300	−	0.994009i	$-0.534861\pi$
$719$	18.6865	−	10.7886i	0.696888	−	0.402348i	0.806187	+	0.591661i	$0.201527\pi$
$720$	−0.913734	+	5.03903i	−0.0340528	+	0.187794i
$721$	47.7331	+	15.9500i	1.77768	+	0.594009i
$722$	2.77824	+	7.66205i	0.103396	+	0.285152i
$723$	36.6273	−	21.1468i	1.36218	−	0.786457i
$724$	−3.24530	−	18.6696i	−0.120611	−	0.693850i
$725$	12.2737	−	21.2587i	0.455835	−	0.789529i
$726$	5.11344	−	6.07898i	0.189778	−	0.225612i
$727$	10.7701			0.399442			0.199721	−	0.979853i	$-0.435996\pi$
$727$	10.7701			0.399442			0.199721	+	0.979853i	$0.435996\pi$
$728$	0.935341	+	4.67473i	0.0346661	+	0.173257i
$729$	−10.1731			−0.376783
$730$	2.84876	+	2.39629i	0.105438	+	0.0886906i
$731$	−14.0722	+	3.40785i	−0.520481	+	0.126044i
$732$	−5.25898	−	30.2539i	−0.194378	−	1.11822i
$733$	17.9572	−	10.3676i	0.663264	−	0.382936i	−0.130255	−	0.991480i	$-0.541580\pi$
$733$	17.9572	−	10.3676i	0.663264	−	0.382936i	0.793520	+	0.608545i	$0.208246\pi$
$734$	−20.2948	+	7.35885i	−0.749095	+	0.271620i
$735$	1.14478	−	9.38570i	0.0422259	−	0.346197i
$736$	−6.59442	−	38.7716i	−0.243073	−	1.42914i
$737$	34.9984	−	20.2063i	1.28918	−	0.744310i
$738$	5.12707	−	28.8723i	0.188730	−	1.06281i
$739$	39.8423	+	23.0030i	1.46562	+	0.846177i	0.999262	−	0.0384176i	$-0.0122317\pi$
$739$	39.8423	+	23.0030i	1.46562	+	0.846177i	0.466360	+	0.884595i	$0.345565\pi$
$740$	7.48808	+	2.74602i	0.275267	+	0.100946i
$741$	−5.26062			−0.193254
$742$	16.7707	−	30.8281i	0.615671	−	1.13173i
$743$		−	25.6423i		−	0.940724i	−0.882474	−	0.470362i	$-0.844123\pi$
$743$		−	25.6423i		−	0.940724i	0.882474	−	0.470362i	$-0.155877\pi$
$744$	65.7968	+	0.239289i	2.41223	+	0.00877275i
$745$	−5.62712	−	3.24882i	−0.206162	−	0.119027i
$746$	−2.92213	+	16.4555i	−0.106987	+	0.602480i
$747$	−9.02853	+	5.21263i	−0.330337	+	0.190720i
$748$	2.73637	−	23.9212i	0.100052	−	0.874645i
$749$	26.8788	+	8.98154i	0.982130	+	0.328178i
$750$	−6.28104	−	17.3223i	−0.229351	−	0.632522i
$751$	−16.5534	+	9.55713i	−0.604043	+	0.348744i	−0.770631	−	0.637282i	$-0.780059\pi$
$751$	−16.5534	+	9.55713i	−0.604043	+	0.348744i	0.166587	+	0.986027i	$0.446725\pi$
$752$	−26.5079	−	22.4627i	−0.966645	−	0.819131i
$753$	17.1092	+	9.87800i	0.623494	+	0.359974i
$754$	−3.64299	−	3.06436i	−0.132670	−	0.111597i
$755$	7.70003			0.280233
$756$	−7.96437	−	6.36150i	−0.289661	−	0.231366i
$757$		−	33.3507i		−	1.21215i	−0.795406	−	0.606076i	$-0.792743\pi$
$757$		−	33.3507i		−	1.21215i	0.795406	−	0.606076i	$-0.207257\pi$
$758$	−1.11756	+	1.32859i	−0.0405917	+	0.0482564i
$759$	−39.8997	−	23.0361i	−1.44827	−	0.836158i
$760$	−3.04285	−	5.31491i	−0.110376	−	0.192792i
$761$	−7.10649	−	12.3088i	−0.257610	−	0.446194i	0.707991	−	0.706221i	$-0.249602\pi$
$761$	−7.10649	−	12.3088i	−0.257610	−	0.446194i	−0.965601	+	0.260028i	$0.916268\pi$
$762$	21.1810	+	58.4147i	0.767308	+	2.11614i
$763$	7.22681	+	35.4481i	0.261628	+	1.28331i
$764$	−20.7393	+	17.3168i	−0.750322	+	0.626501i
$765$	−5.06439	−	1.48927i	−0.183103	−	0.0538446i
$766$	0.819069	+	0.145448i	0.0295942	+	0.00525525i
$767$	3.81588	−	6.60930i	0.137784	−	0.238648i
$768$	−5.95878	−	35.8220i	−0.215019	−	1.29262i
$769$	10.5673			0.381068			0.190534	−	0.981681i	$-0.438978\pi$
$769$	10.5673			0.381068			0.190534	+	0.981681i	$0.438978\pi$
$770$	0.164924	+	6.49971i	0.00594344	+	0.234233i
$771$	34.1188			1.22876
$772$	−11.0664	+	30.1768i	−0.398289	+	1.08609i
$773$	12.9269	+	7.46336i	0.464949	+	0.268439i	0.714123	−	0.700020i	$-0.246826\pi$
$773$	12.9269	+	7.46336i	0.464949	+	0.268439i	−0.249174	+	0.968459i	$0.580159\pi$
$774$	−1.86797	+	10.5192i	−0.0671426	+	0.378104i
$775$	−41.2380	+	23.8088i	−1.48131	+	0.855236i
$776$	−5.07580	+	8.71818i	−0.182211	+	0.312964i
$777$	30.1251	−	26.6740i	1.08073	−	0.956925i
$778$	−4.37082	+	1.58485i	−0.156701	+	0.0568196i
$779$	17.5339	+	30.3696i	0.628217	+	1.08810i
$780$	−1.69561	+	0.294745i	−0.0607127	+	0.0105536i
$781$	15.4237	+	8.90486i	0.551903	+	0.318641i
$782$	40.4613	−	2.50569i	1.44689	−	0.0896032i
$783$	10.1783			0.363741
$784$	6.18816	+	27.3076i	0.221006	+	0.975273i
$785$			9.73522i			0.347465i
$786$	0.623967	−	0.741786i	0.0222561	−	0.0264586i
$787$	5.36157	−	9.28652i	0.191119	−	0.331029i	−0.754502	−	0.656298i	$-0.772122\pi$
$787$	5.36157	−	9.28652i	0.191119	−	0.331029i	0.945622	+	0.325269i	$0.105455\pi$
$788$	1.17626	+	6.76683i	0.0419027	+	0.241058i
$789$	11.8317	+	20.4931i	0.421219	+	0.729573i
$790$	3.25179	−	1.17909i	0.115694	−	0.0419503i
$791$	−10.6028	−	11.9746i	−0.376992	−	0.425768i
$792$	−15.3534	−	8.93891i	−0.545560	−	0.317630i
$793$	3.73229	−	2.15484i	0.132537	−	0.0765205i
$794$	13.7916	+	2.44907i	0.489446	+	0.0869144i
$795$	10.9719	+	6.33462i	0.389133	+	0.224666i
$796$	5.77911	−	15.7590i	0.204835	−	0.558563i
$797$		−	38.4821i		−	1.36311i	−0.731768	−	0.681553i	$-0.761305\pi$
$797$		−	38.4821i		−	1.36311i	0.731768	−	0.681553i	$-0.238695\pi$
$798$	−30.8870	+	0.783727i	−1.09339	+	0.0277436i
$799$	25.9304	−	24.7045i	0.917351	−	0.873983i
$800$	16.7706	+	20.2342i	0.592929	+	0.715386i
$801$	−17.5981	+	30.4807i	−0.621797	+	1.07698i
$802$	−0.398284	+	2.24288i	−0.0140639	+	0.0791988i
$803$	−11.1839	+	6.45703i	−0.394672	+	0.227864i
$804$	40.2683	+	48.2268i	1.42015	+	1.70083i
$805$	−10.7264	+	2.18680i	−0.378057	+	0.0770745i
$806$	3.14781	+	8.68128i	0.110877	+	0.305785i
$807$	0.831096	+	1.43950i	0.0292560	+	0.0506728i
$808$	−0.984975	−	1.72045i	−0.0346513	−	0.0605251i
$809$	−10.8450	−	6.26136i	−0.381290	−	0.220138i	0.297089	−	0.954850i	$-0.403984\pi$
$809$	−10.8450	−	6.26136i	−0.381290	−	0.220138i	−0.678379	+	0.734712i	$0.737317\pi$
$810$	5.86529	−	6.97280i	0.206085	−	0.244999i
$811$	1.62747			0.0571483			0.0285741	−	0.999592i	$-0.490903\pi$
$811$	1.62747			0.0571483			0.0285741	+	0.999592i	$0.490903\pi$
$812$	−21.8458	−	17.4492i	−0.766637	−	0.612348i
$813$	−28.7417			−1.00802
$814$	−17.8107	+	21.1738i	−0.624265	+	0.742142i
$815$	6.56463	−	11.3703i	0.229949	−	0.398283i
$816$	37.3685	−	2.17776i	1.30816	−	0.0762370i
$817$	−6.38819	−	11.0647i	−0.223495	−	0.387104i
$818$	3.69568	+	10.1922i	0.129217	+	0.356363i
$819$	−1.14917	+	3.43909i	−0.0401553	+	0.120172i
$820$	7.35313	+	8.80639i	0.256782	+	0.307533i
$821$	−15.6267	−	27.0662i	−0.545375	−	0.944617i	−0.998583	−	0.0532123i	$-0.983054\pi$
$821$	−15.6267	−	27.0662i	−0.545375	−	0.944617i	0.453208	−	0.891405i	$-0.350279\pi$
$822$	12.4556	+	2.21182i	0.434438	+	0.0771463i
$823$	37.9288	+	21.8982i	1.32212	+	0.763324i	0.984066	−	0.177804i	$-0.0568993\pi$
$823$	37.9288	+	21.8982i	1.32212	+	0.763324i	0.338050	+	0.941128i	$0.390233\pi$
$824$	0.195666	−	53.8020i	0.00681636	−	1.87428i
$825$	30.7872			1.07187
$826$	21.4197	−	39.3741i	0.745288	−	1.37000i
$827$	−0.0311276			−0.00108241			−0.000541207	−	1.00000i	$-0.500172\pi$
$827$	−0.0311276			−0.00108241			−0.000541207		1.00000i	$0.500172\pi$
$828$	10.2989	−	28.0838i	0.357910	−	0.975981i
$829$	42.1330	+	24.3255i	1.46334	+	0.844860i	0.999164	−	0.0408828i	$-0.0130170\pi$
$829$	42.1330	+	24.3255i	1.46334	+	0.844860i	0.464176	+	0.885743i	$0.346350\pi$
$830$	0.713134	−	4.01591i	0.0247532	−	0.139394i
$831$	34.5525	+	59.8468i	1.19861	+	2.07606i
$832$	4.43216	−	2.51610i	0.153657	−	0.0872301i
$833$	−28.6670	+	3.34685i	−0.993254	+	0.115962i
$834$	−1.80482	−	4.97747i	−0.0624958	−	0.172356i
$835$	−4.57751	+	2.64283i	−0.158411	+	0.0914588i
$836$	20.9320	−	3.63857i	0.723949	−	0.125843i
$837$	−17.0988	−	9.87197i	−0.591020	−	0.341225i
$838$	−3.85420	+	4.58196i	−0.133141	+	0.158281i
$839$		−	44.2839i		−	1.52885i	−0.644712	−	0.764426i	$-0.723023\pi$
$839$		−	44.2839i		−	1.52885i	0.644712	−	0.764426i	$-0.276977\pi$
$840$	−9.91164	+	1.98317i	−0.341984	+	0.0684258i
$841$	−1.08163			−0.0372976
$842$	−5.56736	−	4.68309i	−0.191864	−	0.161390i
$843$	17.8305	−	30.8834i	0.614116	−	1.06368i
$844$	−0.120873	−	0.695362i	−0.00416064	−	0.0239353i
$845$	3.74763	+	6.49109i	0.128922	+	0.223300i
$846$	−9.00843	−	24.8441i	−0.309716	−	0.854159i
$847$	6.21027	+	2.07516i	0.213388	+	0.0713034i
$848$	−36.9156	−	6.69395i	−1.26769	−	0.229871i
$849$	21.3068	+	36.9044i	0.731246	+	1.26655i
$850$	−22.5781	+	14.9689i	−0.774424	+	0.513430i
$851$	−40.3444	−	23.2928i	−1.38299	−	0.798468i
$852$	−9.53294	+	25.9953i	−0.326593	+	0.890583i
$853$	12.9960			0.444974			0.222487	−	0.974936i	$-0.428583\pi$
$853$	12.9960			0.444974			0.222487	+	0.974936i	$0.428583\pi$
$854$	21.5926	−	13.2079i	0.738882	−	0.451963i
$855$		−	4.65807i		−	0.159303i
$856$	0.110181	−	30.2962i	0.00376590	−	1.03550i
$857$	−24.9578	−	14.4094i	−0.852543	−	0.492216i	0.00896479	−	0.999960i	$-0.497146\pi$
$857$	−24.9578	−	14.4094i	−0.852543	−	0.492216i	−0.861508	+	0.507744i	$0.830480\pi$
$858$	1.04389	−	5.87851i	0.0356378	−	0.200689i
$859$	16.7559	−	9.67405i	0.571706	−	0.330074i	−0.186125	−	0.982526i	$-0.559593\pi$
$859$	16.7559	−	9.67405i	0.571706	−	0.330074i	0.757830	+	0.652452i	$0.226260\pi$
$860$	−2.67900	−	3.20847i	−0.0913530	−	0.109408i
$861$	56.7124	−	11.5619i	1.93275	−	0.394030i
$862$	−5.75642	+	2.08727i	−0.196064	+	0.0710926i
$863$	11.9533	+	20.7037i	0.406896	+	0.704764i	0.994540	−	0.104355i	$-0.0332780\pi$
$863$	11.9533	+	20.7037i	0.406896	+	0.704764i	−0.587645	+	0.809119i	$0.699945\pi$
$864$	−3.78896	+	10.2170i	−0.128903	+	0.347588i
$865$	4.21767	−	7.30522i	0.143405	−	0.248385i
$866$	21.9211	−	26.0604i	0.744911	−	0.885568i
$867$	−1.86713	+	38.5387i	−0.0634109	+	1.30884i
$868$	19.7753	+	50.5019i	0.671216	+	1.71415i
$869$			11.9995i			0.407056i
$870$	6.49725	−	7.72408i	0.220277	−	0.261871i
$871$	−4.40882	+	7.63630i	−0.149387	+	0.258746i
$872$	33.5638	−	19.2157i	1.13661	−	0.650724i
$873$	−6.64493	+	3.83645i	−0.224897	+	0.129844i
$874$	12.1939	+	33.6292i	0.412465	+	1.13753i
$875$	11.3712	−	10.0686i	0.384418	−	0.340379i
$876$	−12.8679	−	15.4111i	−0.434767	−	0.520693i
$877$	−11.8806	−	20.5779i	−0.401181	−	0.694865i	0.592688	−	0.805432i	$-0.298067\pi$
$877$	−11.8806	−	20.5779i	−0.401181	−	0.694865i	−0.993869	+	0.110567i	$0.964733\pi$
$878$	−6.76646	+	38.1043i	−0.228357	+	1.28596i
$879$	47.1648	+	27.2306i	1.59083	+	0.918465i
$880$	6.54299	−	2.34559i	0.220564	−	0.0790697i
$881$		−	21.0771i		−	0.710104i	−0.934847	−	0.355052i	$-0.884463\pi$
$881$		−	21.0771i		−	0.710104i	0.934847	−	0.355052i	$-0.115537\pi$
$882$	−6.23484	+	20.3633i	−0.209938	+	0.685669i
$883$			4.08649i			0.137521i	0.997633	+	0.0687606i	$0.0219045\pi$
$883$			4.08649i			0.137521i	−0.997633	+	0.0687606i	$0.978096\pi$
$884$	2.09262	+	4.81862i	0.0703825	+	0.162068i
$885$	14.0134	+	8.09067i	0.471057	+	0.271965i
$886$	−3.34913	+	18.8601i	−0.112516	+	0.633618i
$887$	−17.9535	+	10.3654i	−0.602818	+	0.348037i	−0.770150	−	0.637863i	$-0.779818\pi$
$887$	−17.9535	+	10.3654i	−0.602818	+	0.348037i	0.167331	+	0.985901i	$0.446485\pi$
$888$	−37.1739	−	21.6430i	−1.24747	−	0.726291i
$889$	−38.3463	+	33.9534i	−1.28609	+	1.13876i
$890$	−4.69393	−	12.9453i	−0.157341	−	0.433926i
$891$	15.8046	+	27.3744i	0.529474	+	0.917076i
$892$	3.17528	+	18.2668i	0.106316	+	0.611617i
$893$	27.3692	+	15.8016i	0.915875	+	0.528781i
$894$	26.8176	+	22.5581i	0.896916	+	0.754457i
$895$		−	0.387518i		−	0.0129533i
$896$	25.6479	−	15.4332i	0.856837	−	0.515588i
$897$	10.0525			0.335643
$898$	5.11996	+	4.30674i	0.170855	+	0.143718i
$899$	−46.9009	−	27.0783i	−1.56423	−	0.903110i
$900$	3.42327	+	19.6934i	0.114109	+	0.656448i
$901$	10.9103	−	37.1014i	0.363474	−	1.23603i
$902$	−37.4160	+	13.5670i	−1.24582	+	0.451731i
$903$	−20.6622	+	4.21241i	−0.687596	+	0.140180i
$904$	−8.60300	+	14.7765i	−0.286131	+	0.491458i
$905$	2.81941	+	4.88335i	0.0937202	+	0.162328i
$906$	−40.8888	−	7.26092i	−1.35844	−	0.241228i
$907$	−11.5163	+	19.9469i	−0.382394	+	0.662325i	−0.991404	−	0.130837i	$-0.958233\pi$
$907$	−11.5163	+	19.9469i	−0.382394	+	0.662325i	0.609010	+	0.793162i	$0.291567\pi$
$908$	−46.9051	−	17.2010i	−1.55660	−	0.570834i
$909$		−	1.50783i		−	0.0500115i
$910$	−0.740249	−	1.21018i	−0.0245390	−	0.0401171i
$911$			13.7242i			0.454702i	0.973813	+	0.227351i	$0.0730065\pi$
$911$			13.7242i			0.454702i	−0.973813	+	0.227351i	$0.926993\pi$
$912$	11.1463	+	31.0926i	0.369092	+	1.02958i
$913$	12.2539	+	7.07479i	0.405545	+	0.234141i
$914$	−42.2394	−	7.50075i	−1.39715	−	0.248103i
$915$	4.56882	+	7.91343i	0.151040	+	0.261610i
$916$	11.3189	+	13.5560i	0.373988	+	0.447902i
$917$	0.757808	+	0.253221i	0.0250250	+	0.00836210i
$918$	−10.0560	−	5.00415i	−0.331897	−	0.165162i
$919$	13.1157	+	22.7170i	0.432646	+	0.749365i	0.997100	−	0.0760997i	$-0.0242467\pi$
$919$	13.1157	+	22.7170i	0.432646	+	0.749365i	−0.564454	+	0.825464i	$0.690913\pi$
$920$	5.81456	+	10.1562i	0.191701	+	0.334841i
$921$	10.2179	+	5.89933i	0.336692	+	0.194389i
$922$	34.0051	+	28.6040i	1.11990	+	0.942023i
$923$	−3.88590			−0.127906
$924$	5.25327	−	34.6704i	0.172820	−	1.14057i
$925$	31.1302			1.02356
$926$	−24.6749	+	29.3341i	−0.810868	+	0.963979i
$927$	20.4607	−	35.4390i	0.672017	−	1.16397i
$928$	−10.3929	+	28.0246i	−0.341164	+	0.919951i
$929$	−16.1605	+	9.33029i	−0.530210	+	0.306117i	−0.741102	−	0.671393i	$-0.765696\pi$
$929$	−16.1605	+	9.33029i	−0.530210	+	0.306117i	0.210892	+	0.977509i	$0.432363\pi$
$930$	−18.4066	+	6.67419i	−0.603575	+	0.218855i
$931$	−9.96987	−	23.4353i	−0.326749	−	0.768060i
$932$	−8.38577	−	10.0431i	−0.274685	−	0.328973i
$933$	26.2677	−	15.1657i	0.859965	−	0.496501i
$934$	−8.91597	+	50.2090i	−0.291740	+	1.64289i
$935$	1.68631	+	6.96336i	0.0551481	+	0.227726i
$936$	3.87634	+	0.0140974i	0.126702	+	0.000460789i
$937$	−22.6111			−0.738673			−0.369336	−	0.929296i	$-0.620415\pi$
$937$	−22.6111			−0.738673			−0.369336	+	0.929296i	$0.620415\pi$
$938$	−24.7481	+	45.4922i	−0.808053	+	1.48537i
$939$			63.3657i			2.06786i
$940$	9.70704	+	3.55975i	0.316609	+	0.116106i
$941$	27.5440	−	47.7076i	0.897908	−	1.55522i	0.0677445	−	0.997703i	$-0.478420\pi$
$941$	27.5440	−	47.7076i	0.897908	−	1.55522i	0.830164	−	0.557520i	$-0.188247\pi$
$942$	9.18005	−	51.6961i	0.299102	−	1.68435i
$943$	−33.5055	−	58.0331i	−1.09109	−	1.88982i
$944$	−47.1492	−	8.54961i	−1.53457	−	0.278266i
$945$	2.87681	+	0.961283i	0.0935825	+	0.0312706i
$946$	13.6319	−	4.94291i	0.443212	−	0.160708i
$947$	24.0230	+	41.6091i	0.780644	+	1.35211i	0.931567	+	0.363569i	$0.118442\pi$
$947$	24.0230	+	41.6091i	0.780644	+	1.35211i	−0.150923	+	0.988545i	$0.548225\pi$
$948$	−18.3796	+	3.19489i	−0.596941	+	0.103765i
$949$	1.40886	−	2.44022i	0.0457335	−	0.0792128i
$950$	−18.2929	−	15.3874i	−0.593499	−	0.499232i
$951$	−25.9849			−0.842618
$952$	13.0044	+	27.9801i	0.421475	+	0.906840i
$953$	−21.5882			−0.699309			−0.349655	−	0.936879i	$-0.613701\pi$
$953$	−21.5882			−0.699309			−0.349655	+	0.936879i	$0.613701\pi$
$954$	−21.8372	−	18.3687i	−0.707004	−	0.594709i
$955$	4.01992	−	6.96270i	0.130081	−	0.225308i
$956$	1.70781	+	9.82470i	0.0552345	+	0.317754i
$957$	17.5075	+	30.3238i	0.565936	+	0.980230i
$958$	5.85512	−	2.12306i	0.189170	−	0.0685928i
$959$	2.08302	+	10.2174i	0.0672641	+	0.329936i
$960$	5.33479	+	9.39733i	0.172180	+	0.303297i
$961$	37.0268	+	64.1323i	1.19441	+	2.06879i
$962$	1.05552	−	5.94402i	0.0340314	−	0.191643i
$963$	11.5215	−	19.9559i	0.371276	−	0.643069i
$964$	12.8316	−	34.9904i	0.413278	−	1.12696i
$965$		−	9.56447i		−	0.307891i
$966$	59.0218	−	1.49762i	1.89899	−	0.0481852i
$967$	−25.0095			−0.804251			−0.402126	−	0.915584i	$-0.631729\pi$
$967$	−25.0095			−0.804251			−0.402126	+	0.915584i	$0.631729\pi$
$968$	0.0254570	−	6.99986i	0.000818218	−	0.224984i
$969$	−33.0902	+	8.01341i	−1.06301	+	0.257428i
$970$	0.524861	−	2.95568i	0.0168523	−	0.0949011i
$971$	−42.8915	+	24.7634i	−1.37645	+	0.794696i	−0.991731	−	0.128337i	$-0.959036\pi$
$971$	−42.8915	+	24.7634i	−1.37645	+	0.794696i	−0.384722	+	0.923032i	$0.625703\pi$
$972$	−28.8492	+	24.0884i	−0.925340	+	0.772637i
$973$	3.26746	−	2.89314i	0.104750	−	0.0927499i
$974$	1.34505	−	0.487714i	0.0430983	−	0.0156274i
$975$	−5.81748	+	3.35872i	−0.186308	+	0.107565i
$976$	−20.6441	−	17.4938i	−0.660803	−	0.559962i
$977$	−17.3392	+	30.0323i	−0.554729	+	0.960820i	0.443195	+	0.896425i	$0.353845\pi$
$977$	−17.3392	+	30.0323i	−0.554729	+	0.960820i	−0.997925	+	0.0643944i	$0.979488\pi$
$978$	−45.5814	+	54.1883i	−1.45753	+	1.73275i
$979$	47.7696			1.52672
$980$	−4.52656	−	6.99511i	−0.144596	−	0.223451i
$981$	29.4159			0.939176
$982$	−19.9745	−	16.8019i	−0.637413	−	0.536171i
$983$	−6.60932	−	3.81589i	−0.210805	−	0.121708i	0.390881	−	0.920441i	$-0.372171\pi$
$983$	−6.60932	−	3.81589i	−0.210805	−	0.121708i	−0.601685	+	0.798733i	$0.705504\pi$
$984$	−30.7425	−	53.6976i	−0.980035	−	1.71182i
$985$	−1.02190	−	1.76998i	−0.0325604	−	0.0563962i
$986$	−27.5829	−	13.7261i	−0.878420	−	0.437128i
$987$	39.0522	−	34.5784i	1.24305	−	1.10064i
$988$	−3.55832	+	2.97111i	−0.113205	+	0.0945237i
$989$	12.2072	+	21.1435i	0.388166	+	0.672323i
$990$	5.20520	+	0.924324i	0.165432	+	0.0293769i
$991$	−3.35295	−	1.93583i	−0.106510	−	0.0614936i	0.445799	−	0.895133i	$-0.352920\pi$
$991$	−3.35295	−	1.93583i	−0.106510	−	0.0614936i	−0.552309	+	0.833640i	$0.686253\pi$
$992$	44.6406	−	36.9991i	1.41734	−	1.17472i
$993$		−	68.1876i		−	2.16387i
$994$	−22.8155	+	0.578922i	−0.723664	+	0.0183623i
$995$			4.99477i			0.158345i
$996$	−7.57379	+	20.6529i	−0.239985	+	0.654411i
$997$	14.0843	−	24.3947i	0.446055	−	0.772589i	−0.552070	−	0.833797i	$-0.686162\pi$
$997$	14.0843	−	24.3947i	0.446055	−	0.772589i	0.998125	+	0.0612083i	$0.0194954\pi$
$998$	−23.4442	−	4.16316i	−0.742114	−	0.131782i
$999$	6.45386	+	11.1784i	0.204191	+	0.353669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	952.2.z.c.781.102	yes	272
7.2	even	3	inner	952.2.z.c.373.8	yes	272
8.5	even	2	inner	952.2.z.c.781.7	yes	272
17.16	even	2	inner	952.2.z.c.781.101	yes	272
56.37	even	6	inner	952.2.z.c.373.101	yes	272
119.16	even	6	inner	952.2.z.c.373.7	✓	272
136.101	even	2	inner	952.2.z.c.781.8	yes	272
952.373	even	6	inner	952.2.z.c.373.102	yes	272

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
952.2.z.c.373.7	✓	272	119.16	even	6	inner
952.2.z.c.373.8	yes	272	7.2	even	3	inner
952.2.z.c.373.101	yes	272	56.37	even	6	inner
952.2.z.c.373.102	yes	272	952.373	even	6	inner
952.2.z.c.781.7	yes	272	8.5	even	2	inner
952.2.z.c.781.8	yes	272	136.101	even	2	inner
952.2.z.c.781.101	yes	272	17.16	even	2	inner
952.2.z.c.781.102	yes	272	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 952 = 2^{3} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	952.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.910352 - 1.08225i) q^{2} +(1.13482 - 1.96557i) q^{3} +(-0.342520 - 1.97045i) q^{4} +(0.297569 + 0.515405i) q^{5} +(-1.09414 - 3.01751i) q^{6} +(1.98085 - 1.75392i) q^{7} +(-2.44433 - 1.42311i) q^{8} +(-1.07563 - 1.86305i) q^{9} +(0.828689 + 0.147156i) q^{10} +(-1.45989 + 2.52861i) q^{11} +(-4.26175 - 1.56286i) q^{12} -0.637068i q^{13} +(-0.0949104 - 3.74045i) q^{14} +1.35075 q^{15} +(-3.76536 + 1.34984i) q^{16} +(-0.970435 - 4.00728i) q^{17} +(-2.99549 - 0.531930i) q^{18} +(3.15083 - 1.81913i) q^{19} +(0.913658 - 0.762883i) q^{20} +(-1.19954 - 5.88387i) q^{21} +(1.40757 + 3.88189i) q^{22} +(-6.02090 + 3.47617i) q^{23} +(-5.57110 + 3.18952i) q^{24} +(2.32290 - 4.02339i) q^{25} +(-0.689466 - 0.579956i) q^{26} +1.92632 q^{27} +(-4.13450 - 3.30241i) q^{28} +5.28378 q^{29} +(1.22966 - 1.46185i) q^{30} +(-8.87639 - 5.12478i) q^{31} +(-1.96694 + 5.30388i) q^{32} +(3.31343 + 5.73904i) q^{33} +(-5.22030 - 2.59778i) q^{34} +(1.49342 + 0.499026i) q^{35} +(-3.30263 + 2.75762i) q^{36} +(3.35036 + 5.80299i) q^{37} +(0.899610 - 5.06602i) q^{38} +(-1.25220 - 0.722958i) q^{39} +(0.00612179 - 1.68330i) q^{40} +9.63861i q^{41} +(-7.45981 - 4.05819i) q^{42} -3.51167i q^{43} +(5.48255 + 2.01055i) q^{44} +(0.640151 - 1.10877i) q^{45} +(-1.71906 + 9.68065i) q^{46} +(4.34318 + 7.52260i) q^{47} +(-1.61981 + 8.93289i) q^{48} +(0.847514 - 6.94850i) q^{49} +(-2.23964 - 6.17666i) q^{50} +(-8.97783 - 2.64008i) q^{51} +(-1.25531 + 0.218209i) q^{52} +(8.12280 + 4.68970i) q^{53} +(1.75363 - 2.08476i) q^{54} -1.73768 q^{55} +(-7.33787 + 1.46820i) q^{56} -8.25754i q^{57} +(4.81010 - 5.71836i) q^{58} +(10.3746 + 5.98976i) q^{59} +(-0.462659 - 2.66159i) q^{60} +(3.38243 + 5.85854i) q^{61} +(-13.6269 + 4.94109i) q^{62} +(-5.39831 - 1.80384i) q^{63} +(3.94950 + 6.95711i) q^{64} +(0.328348 - 0.189572i) q^{65} +(9.22745 + 1.63858i) q^{66} +(-11.9866 - 6.92048i) q^{67} +(-7.56375 + 3.28477i) q^{68} +15.7793i q^{69} +(1.89961 - 1.16196i) q^{70} -6.09967i q^{71} +(-0.0221286 + 6.08466i) q^{72} +(3.83038 + 2.21147i) q^{73} +(9.33027 + 1.65684i) q^{74} +(-5.27216 - 9.13165i) q^{75} +(-4.66373 - 5.58546i) q^{76} +(1.54316 + 7.56933i) q^{77} +(-1.92236 + 0.697044i) q^{78} +(3.55913 - 2.05486i) q^{79} +(-1.81617 - 1.53902i) q^{80} +(5.41293 - 9.37546i) q^{81} +(10.4314 + 8.77452i) q^{82} -4.84610i q^{83} +(-11.1830 + 4.37899i) q^{84} +(1.77660 - 1.69261i) q^{85} +(-3.80050 - 3.19686i) q^{86} +(5.99614 - 10.3856i) q^{87} +(7.16696 - 4.10317i) q^{88} +(-8.18033 - 14.1687i) q^{89} +(-0.617206 - 1.70218i) q^{90} +(-1.11737 - 1.26193i) q^{91} +(8.91191 + 10.6732i) q^{92} +(-20.1462 + 11.6314i) q^{93} +(12.0951 + 2.14782i) q^{94} +(1.87518 + 1.08264i) q^{95} +(8.19300 + 9.88510i) q^{96} -3.56669i q^{97} +(-6.74847 - 7.24280i) q^{98} +6.28124 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 272 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 132 q^{9} - 40 q^{15} - 26 q^{16} - 6 q^{17} + 6 q^{18} - 112 q^{25} - 8 q^{26} - 2 q^{30} + 44 q^{32} - 28 q^{33} - 56 q^{34} + 40 q^{36} - 42 q^{38} + 12 q^{42}+ \cdots + 14 q^{98}+O(q^{100}) \) 272 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 132 * q^9 - 40 * q^15 - 26 * q^16 - 6 * q^17 + 6 * q^18 - 112 * q^25 - 8 * q^26 - 2 * q^30 + 44 * q^32 - 28 * q^33 - 56 * q^34 + 40 * q^36 - 42 * q^38 + 12 * q^42 + 28 * q^47 - 60 * q^49 + 72 * q^50 - 38 * q^52 + 232 * q^55 - 6 * q^60 + 40 * q^64 + 48 * q^66 + 32 * q^68 + 86 * q^70 - 36 * q^72 - 148 * q^76 - 168 * q^81 - 34 * q^84 + 22 * q^86 + 16 * q^87 - 72 * q^89 + 62 * q^94 + 14 * q^98

Introduction

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