LMFDB - Embedded newform 990.2.t.b.131.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(131,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.131"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.t (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,24] 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:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.14
Character	$\chi$	$=$	990.131
Dual form			990.2.t.b.461.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(0.216395 + 1.71848i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.38005 + 1.04664i) q^{6} +(-3.44565 + 1.98935i) q^{7} -1.00000 q^{8} +(-2.90635 + 0.743740i) q^{9} +1.00000i q^{10} +(1.94455 - 2.68677i) q^{11} +(-1.59644 - 0.671837i) q^{12} +(-1.91641 - 1.10644i) q^{13} +(-3.44565 - 1.98935i) q^{14} +(-0.671837 + 1.59644i) q^{15} +(-0.500000 - 0.866025i) q^{16} -2.92469 q^{17} +(-2.09727 - 2.14510i) q^{18} +5.09549i q^{19} +(-0.866025 + 0.500000i) q^{20} +(-4.16427 - 5.49080i) q^{21} +(3.29908 + 0.340645i) q^{22} +(-3.45652 - 1.99562i) q^{23} +(-0.216395 - 1.71848i) q^{24} +(0.500000 + 0.866025i) q^{25} -2.21287i q^{26} +(-1.90702 - 4.83356i) q^{27} -3.97869i q^{28} +(1.94708 + 3.37244i) q^{29} +(-1.71848 + 0.216395i) q^{30} +(-0.189484 + 0.328196i) q^{31} +(0.500000 - 0.866025i) q^{32} +(5.03795 + 2.76027i) q^{33} +(-1.46235 - 2.53286i) q^{34} -3.97869 q^{35} +(0.809076 - 2.88884i) q^{36} +4.03169 q^{37} +(-4.41282 + 2.54775i) q^{38} +(1.48669 - 3.53273i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(2.82033 - 4.88496i) q^{41} +(2.67303 - 6.35176i) q^{42} +(-5.34893 + 3.08820i) q^{43} +(1.35454 + 3.02741i) q^{44} +(-2.88884 - 0.809076i) q^{45} -3.99124i q^{46} +(-7.07537 + 4.08496i) q^{47} +(1.38005 - 1.04664i) q^{48} +(4.41500 - 7.64700i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-0.632888 - 5.02603i) q^{51} +(1.91641 - 1.10644i) q^{52} +2.04474i q^{53} +(3.23247 - 4.06831i) q^{54} +(3.02741 - 1.35454i) q^{55} +(3.44565 - 1.98935i) q^{56} +(-8.75650 + 1.10264i) q^{57} +(-1.94708 + 3.37244i) q^{58} +(11.5359 + 6.66026i) q^{59} +(-1.04664 - 1.38005i) q^{60} +(-2.64559 + 1.52743i) q^{61} -0.378968 q^{62} +(8.53470 - 8.34440i) q^{63} +1.00000 q^{64} +(-1.10644 - 1.91641i) q^{65} +(0.128512 + 5.74312i) q^{66} +(-2.41293 + 4.17932i) q^{67} +(1.46235 - 2.53286i) q^{68} +(2.68146 - 6.37179i) q^{69} +(-1.98935 - 3.44565i) q^{70} +11.7114i q^{71} +(2.90635 - 0.743740i) q^{72} -1.49541i q^{73} +(2.01585 + 3.49155i) q^{74} +(-1.38005 + 1.04664i) q^{75} +(-4.41282 - 2.54775i) q^{76} +(-1.35532 + 13.1260i) q^{77} +(3.80278 - 0.478854i) q^{78} +(-9.26757 + 5.35063i) q^{79} -1.00000i q^{80} +(7.89370 - 4.32313i) q^{81} +5.64066 q^{82} +(-3.29598 - 5.70881i) q^{83} +(6.83730 - 0.860968i) q^{84} +(-2.53286 - 1.46235i) q^{85} +(-5.34893 - 3.08820i) q^{86} +(-5.37414 + 4.07580i) q^{87} +(-1.94455 + 2.68677i) q^{88} +13.0159i q^{89} +(-0.743740 - 2.90635i) q^{90} +8.80435 q^{91} +(3.45652 - 1.99562i) q^{92} +(-0.605002 - 0.254605i) q^{93} +(-7.07537 - 4.08496i) q^{94} +(-2.54775 + 4.41282i) q^{95} +(1.59644 + 0.671837i) q^{96} +(-6.50778 - 11.2718i) q^{97} +8.83000 q^{98} +(-3.65328 + 9.25492i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} - 48 q^{8} + 10 q^{9} - 12 q^{11} + 4 q^{12} - 24 q^{13} - 4 q^{15} - 24 q^{16} + 12 q^{17} + 8 q^{18} + 16 q^{21} - 6 q^{22} + 36 q^{23} + 2 q^{24} + 24 q^{25}+ \cdots - 44 q^{99}+O(q^{100}) $ 48 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 - 48 * q^8 + 10 * q^9 - 12 * q^11 + 4 * q^12 - 24 * q^13 - 4 * q^15 - 24 * q^16 + 12 * q^17 + 8 * q^18 + 16 * q^21 - 6 * q^22 + 36 * q^23 + 2 * q^24 + 24 * q^25 - 8 * q^27 - 8 * q^30 + 24 * q^32 + 12 * q^33 + 6 * q^34 - 2 * q^36 - 6 * q^38 + 40 * q^39 + 6 * q^41 + 8 * q^42 - 30 * q^43 + 6 * q^44 - 2 * q^48 + 24 * q^49 - 24 * q^50 - 22 * q^51 + 24 * q^52 - 22 * q^54 - 40 * q^57 - 54 * q^59 - 4 * q^60 + 38 * q^63 + 48 * q^64 - 12 * q^66 - 6 * q^67 - 6 * q^68 + 76 * q^69 - 10 * q^72 + 2 * q^75 - 6 * q^76 - 18 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 - 36 * q^83 - 8 * q^84 - 30 * q^86 + 44 * q^87 + 12 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 - 4 * q^96 + 6 * q^97 + 48 * q^98 - 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.216395	+	1.71848i	0.124936	+	0.992165i
$3$	0.216395	+	1.71848i	0.124936	+	0.992165i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	−1.38005	+	1.04664i	−0.563403	+	0.427290i
$7$	−3.44565	+	1.98935i	−1.30233	+	0.751902i	−0.980804	−	0.194997i	$-0.937530\pi$
$7$	−3.44565	+	1.98935i	−1.30233	+	0.751902i	−0.321529	+	0.946900i	$0.604197\pi$
$8$	−1.00000			−0.353553
$9$	−2.90635	+	0.743740i	−0.968782	+	0.247913i
$10$			1.00000i			0.316228i
$11$	1.94455	−	2.68677i	0.586304	−	0.810091i
$11$	1.94455	−	2.68677i	0.586304	−	0.810091i
$12$	−1.59644	−	0.671837i	−0.460854	−	0.193943i
$13$	−1.91641	−	1.10644i	−0.531515	−	0.306870i	0.210118	−	0.977676i	$-0.432615\pi$
$13$	−1.91641	−	1.10644i	−0.531515	−	0.306870i	−0.741633	+	0.670806i	$0.765948\pi$
$14$	−3.44565	−	1.98935i	−0.920889	−	0.531675i
$15$	−0.671837	+	1.59644i	−0.173467	+	0.412200i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.92469			−0.709342			−0.354671	−	0.934991i	$-0.615407\pi$
$17$	−2.92469			−0.709342			−0.354671	+	0.934991i	$0.615407\pi$
$18$	−2.09727	−	2.14510i	−0.494331	−	0.505605i
$19$			5.09549i			1.16899i	0.811399	+	0.584493i	$0.198706\pi$
$19$			5.09549i			1.16899i	−0.811399	+	0.584493i	$0.801294\pi$
$20$	−0.866025	+	0.500000i	−0.193649	+	0.111803i
$21$	−4.16427	−	5.49080i	−0.908719	−	1.19819i
$22$	3.29908	+	0.340645i	0.703367	+	0.0726258i
$23$	−3.45652	−	1.99562i	−0.720733	−	0.416116i	0.0942892	−	0.995545i	$-0.469942\pi$
$23$	−3.45652	−	1.99562i	−0.720733	−	0.416116i	−0.815023	+	0.579429i	$0.803275\pi$
$24$	−0.216395	−	1.71848i	−0.0441714	−	0.350783i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		−	2.21287i		−	0.433980i
$27$	−1.90702	−	4.83356i	−0.367006	−	0.930219i
$28$		−	3.97869i		−	0.751902i
$29$	1.94708	+	3.37244i	0.361564	+	0.626247i	0.988218	−	0.153050i	$-0.0489096\pi$
$29$	1.94708	+	3.37244i	0.361564	+	0.626247i	−0.626655	+	0.779297i	$0.715576\pi$
$30$	−1.71848	+	0.216395i	−0.313750	+	0.0395081i
$31$	−0.189484	+	0.328196i	−0.0340324	+	0.0589458i	−0.882540	−	0.470237i	$-0.844168\pi$
$31$	−0.189484	+	0.328196i	−0.0340324	+	0.0589458i	0.848508	+	0.529183i	$0.177502\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	5.03795	+	2.76027i	0.876994	+	0.480501i
$34$	−1.46235	−	2.53286i	−0.250790	−	0.434382i
$35$	−3.97869			−0.672522
$36$	0.809076	−	2.88884i	0.134846	−	0.481473i
$37$	4.03169			0.662807			0.331403	−	0.943489i	$-0.392478\pi$
$37$	4.03169			0.662807			0.331403	+	0.943489i	$0.392478\pi$
$38$	−4.41282	+	2.54775i	−0.715855	+	0.413299i
$39$	1.48669	−	3.53273i	0.238061	−	0.565690i
$40$	−0.866025	−	0.500000i	−0.136931	−	0.0790569i
$41$	2.82033	−	4.88496i	0.440462	−	0.762902i	−0.557262	−	0.830337i	$-0.688148\pi$
$41$	2.82033	−	4.88496i	0.440462	−	0.762902i	0.997724	+	0.0674345i	$0.0214814\pi$
$42$	2.67303	−	6.35176i	0.412458	−	0.980098i
$43$	−5.34893	+	3.08820i	−0.815704	+	0.470947i	−0.848933	−	0.528501i	$-0.822754\pi$
$43$	−5.34893	+	3.08820i	−0.815704	+	0.470947i	0.0332290	+	0.999448i	$0.489421\pi$
$44$	1.35454	+	3.02741i	0.204204	+	0.456400i
$45$	−2.88884	−	0.809076i	−0.430643	−	0.120610i
$46$		−	3.99124i		−	0.588476i
$47$	−7.07537	+	4.08496i	−1.03205	+	0.595853i	−0.917571	−	0.397573i	$-0.869853\pi$
$47$	−7.07537	+	4.08496i	−1.03205	+	0.595853i	−0.114477	+	0.993426i	$0.536519\pi$
$48$	1.38005	−	1.04664i	0.199193	−	0.151070i
$49$	4.41500	−	7.64700i	0.630714	−	1.09243i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−0.632888	−	5.02603i	−0.0886220	−	0.703784i
$52$	1.91641	−	1.10644i	0.265758	−	0.153435i
$53$			2.04474i			0.280866i	0.990090	+	0.140433i	$0.0448495\pi$
$53$			2.04474i			0.280866i	−0.990090	+	0.140433i	$0.955151\pi$
$54$	3.23247	−	4.06831i	0.439884	−	0.553626i
$55$	3.02741	−	1.35454i	0.408216	−	0.182645i
$56$	3.44565	−	1.98935i	0.460444	−	0.265838i
$57$	−8.75650	+	1.10264i	−1.15983	+	0.146048i
$58$	−1.94708	+	3.37244i	−0.255664	+	0.442823i
$59$	11.5359	+	6.66026i	1.50185	+	0.867091i	0.999998	+	0.00213609i	$0.000679941\pi$
$59$	11.5359	+	6.66026i	1.50185	+	0.867091i	0.501849	+	0.864955i	$0.332653\pi$
$60$	−1.04664	−	1.38005i	−0.135121	−	0.178164i
$61$	−2.64559	+	1.52743i	−0.338734	+	0.195568i	−0.659712	−	0.751519i	$-0.729322\pi$
$61$	−2.64559	+	1.52743i	−0.338734	+	0.195568i	0.320978	+	0.947087i	$0.395988\pi$
$62$	−0.378968			−0.0481290
$63$	8.53470	−	8.34440i	1.07527	−	1.05130i
$64$	1.00000			0.125000
$65$	−1.10644	−	1.91641i	−0.137237	−	0.237701i
$66$	0.128512	+	5.74312i	0.0158188	+	0.706930i
$67$	−2.41293	+	4.17932i	−0.294787	+	0.510586i	−0.974935	−	0.222489i	$-0.928582\pi$
$67$	−2.41293	+	4.17932i	−0.294787	+	0.510586i	0.680149	+	0.733074i	$0.261915\pi$
$68$	1.46235	−	2.53286i	0.177336	−	0.307154i
$69$	2.68146	−	6.37179i	0.322810	−	0.767074i
$70$	−1.98935	−	3.44565i	−0.237772	−	0.411834i
$71$			11.7114i			1.38989i	0.719063	+	0.694945i	$0.244571\pi$
$71$			11.7114i			1.38989i	−0.719063	+	0.694945i	$0.755429\pi$
$72$	2.90635	−	0.743740i	0.342516	−	0.0876506i
$73$		−	1.49541i		−	0.175024i	−0.996163	−	0.0875120i	$-0.972108\pi$
$73$		−	1.49541i		−	0.175024i	0.996163	−	0.0875120i	$-0.0278916\pi$
$74$	2.01585	+	3.49155i	0.234338	+	0.405884i
$75$	−1.38005	+	1.04664i	−0.159354	+	0.120856i
$76$	−4.41282	−	2.54775i	−0.506186	−	0.292246i
$77$	−1.35532	+	13.1260i	−0.154453	+	1.49585i
$78$	3.80278	−	0.478854i	0.430580	−	0.0542196i
$79$	−9.26757	+	5.35063i	−1.04268	+	0.601993i	−0.920592	−	0.390525i	$-0.872293\pi$
$79$	−9.26757	+	5.35063i	−1.04268	+	0.601993i	−0.122091	+	0.992519i	$0.538960\pi$
$80$		−	1.00000i		−	0.111803i
$81$	7.89370	−	4.32313i	0.877078	−	0.480348i
$82$	5.64066			0.622907
$83$	−3.29598	−	5.70881i	−0.361781	−	0.626623i	0.626473	−	0.779443i	$-0.284498\pi$
$83$	−3.29598	−	5.70881i	−0.361781	−	0.626623i	−0.988254	+	0.152820i	$0.951165\pi$
$84$	6.83730	−	0.860968i	0.746011	−	0.0939393i
$85$	−2.53286	−	1.46235i	−0.274727	−	0.158614i
$86$	−5.34893	−	3.08820i	−0.576790	−	0.333010i
$87$	−5.37414	+	4.07580i	−0.576168	+	0.436971i
$88$	−1.94455	+	2.68677i	−0.207290	+	0.286411i
$89$			13.0159i			1.37968i	0.723962	+	0.689840i	$0.242319\pi$
$89$			13.0159i			1.37968i	−0.723962	+	0.689840i	$0.757681\pi$
$90$	−0.743740	−	2.90635i	−0.0783971	−	0.306356i
$91$	8.80435			0.922946
$92$	3.45652	−	1.99562i	0.360367	−	0.208058i
$93$	−0.605002	−	0.254605i	−0.0627358	−	0.0264013i
$94$	−7.07537	−	4.08496i	−0.729768	−	0.421332i
$95$	−2.54775	+	4.41282i	−0.261393	+	0.452746i
$96$	1.59644	+	0.671837i	0.162936	+	0.0685690i
$97$	−6.50778	−	11.2718i	−0.660765	−	1.14448i	−0.980415	−	0.196943i	$-0.936899\pi$
$97$	−6.50778	−	11.2718i	−0.660765	−	1.14448i	0.319650	−	0.947536i	$-0.396435\pi$
$98$	8.83000			0.891965
$99$	−3.65328	+	9.25492i	−0.367168	+	0.930154i
$100$	−1.00000			−0.100000
$101$	3.90859	+	6.76988i	0.388920	+	0.673628i	0.992304	−	0.123822i	$-0.0395151\pi$
$101$	3.90859	+	6.76988i	0.388920	+	0.673628i	−0.603385	+	0.797450i	$0.706182\pi$
$102$	4.03622	−	3.06111i	0.399646	−	0.303095i
$103$	0.158524	−	0.274571i	0.0156198	−	0.0270543i	−0.858110	−	0.513466i	$-0.828361\pi$
$103$	0.158524	−	0.274571i	0.0156198	−	0.0270543i	0.873730	+	0.486412i	$0.161695\pi$
$104$	1.91641	+	1.10644i	0.187919	+	0.108495i
$105$	−0.860968	−	6.83730i	−0.0840219	−	0.667253i
$106$	−1.77079	+	1.02237i	−0.171995	+	0.0993012i
$107$	16.3196			1.57767			0.788837	−	0.614603i	$-0.210684\pi$
$107$	16.3196			1.57767			0.788837	+	0.614603i	$0.210684\pi$
$108$	5.13949	+	0.765251i	0.494548	+	0.0736363i
$109$		−	15.7731i		−	1.51079i	−0.655268	−	0.755396i	$-0.727444\pi$
$109$		−	15.7731i		−	1.51079i	0.655268	−	0.755396i	$-0.272556\pi$
$110$	2.68677	+	1.94455i	0.256173	+	0.185406i
$111$	0.872437	+	6.92839i	0.0828081	+	0.657613i
$112$	3.44565	+	1.98935i	0.325583	+	0.187976i
$113$	−15.2583	−	8.80939i	−1.43538	−	0.828717i	−0.437856	−	0.899045i	$-0.644262\pi$
$113$	−15.2583	−	8.80939i	−1.43538	−	0.828717i	−0.997524	+	0.0703277i	$0.977596\pi$
$114$	−5.33316	−	7.03203i	−0.499496	−	0.658610i
$115$	−1.99562	−	3.45652i	−0.186093	−	0.322322i
$116$	−3.89416			−0.361564
$117$	6.39264	+	1.79038i	0.591000	+	0.165521i
$118$			13.3205i			1.22625i
$119$	10.0775	−	5.81823i	0.923800	−	0.533356i
$120$	0.671837	−	1.59644i	0.0613300	−	0.145735i
$121$	−3.43745	−	10.4491i	−0.312496	−	0.949919i
$122$	−2.64559	−	1.52743i	−0.239521	−	0.138287i
$123$	9.00501	+	3.78961i	0.811954	+	0.341697i
$124$	−0.189484	−	0.328196i	−0.0170162	−	0.0294729i
$125$			1.00000i			0.0894427i
$126$	11.4938	+	3.21906i	1.02395	+	0.286777i
$127$			0.487775i			0.0432831i	0.999766	+	0.0216415i	$0.00688925\pi$
$127$			0.487775i			0.0432831i	−0.999766	+	0.0216415i	$0.993111\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−6.46450	−	8.52375i	−0.569167	−	0.750475i
$130$	1.10644	−	1.91641i	0.0970409	−	0.168080i
$131$	0.867437	−	1.50245i	0.0757883	−	0.131269i	−0.825640	−	0.564197i	$-0.809186\pi$
$131$	0.867437	−	1.50245i	0.0757883	−	0.131269i	0.901429	+	0.432927i	$0.142519\pi$
$132$	−4.90944	+	2.98286i	−0.427312	+	0.259624i
$133$	−10.1367	−	17.5573i	−0.878963	−	1.52241i
$134$	−4.82587			−0.416891
$135$	0.765251	−	5.13949i	0.0658623	−	0.442337i
$136$	2.92469			0.250790
$137$	−14.0600	+	8.11757i	−1.20123	+	0.693531i	−0.960829	−	0.277143i	$-0.910613\pi$
$137$	−14.0600	+	8.11757i	−1.20123	+	0.693531i	−0.240402	+	0.970673i	$0.577279\pi$
$138$	6.85887	−	0.863683i	0.583865	−	0.0735216i
$139$	19.2708	+	11.1260i	1.63453	+	0.943697i	0.982671	+	0.185356i	$0.0593440\pi$
$139$	19.2708	+	11.1260i	1.63453	+	0.943697i	0.651859	+	0.758340i	$0.273989\pi$
$140$	1.98935	−	3.44565i	0.168130	−	0.291211i
$141$	−8.55100	−	11.2749i	−0.720124	−	0.949519i
$142$	−10.1424	+	5.85571i	−0.851130	+	0.491400i
$143$	−6.69929	+	2.99742i	−0.560222	+	0.250656i
$144$	2.09727	+	2.14510i	0.174773	+	0.178758i
$145$			3.89416i			0.323393i
$146$	1.29506	−	0.747703i	0.107180	−	0.0618803i
$147$	14.0966	+	5.93232i	1.16267	+	0.489289i
$148$	−2.01585	+	3.49155i	−0.165702	+	0.287004i
$149$	−2.77025	+	4.79821i	−0.226947	+	0.393084i	−0.956902	−	0.290411i	$-0.906208\pi$
$149$	−2.77025	+	4.79821i	−0.226947	+	0.393084i	0.729955	+	0.683496i	$0.239541\pi$
$150$	−1.59644	−	0.671837i	−0.130349	−	0.0548552i
$151$	−8.48831	+	4.90073i	−0.690769	+	0.398816i	−0.803900	−	0.594765i	$-0.797245\pi$
$151$	−8.48831	+	4.90073i	−0.690769	+	0.398816i	0.113131	+	0.993580i	$0.463912\pi$
$152$		−	5.09549i		−	0.413299i
$153$	8.50017	−	2.17521i	0.687198	−	0.175855i
$154$	−12.0452	+	5.38928i	−0.970626	+	0.434280i
$155$	−0.328196	+	0.189484i	−0.0263614	+	0.0152197i
$156$	2.31609	+	3.05388i	0.185436	+	0.244506i
$157$	−6.19979	+	10.7384i	−0.494797	+	0.857014i	−0.999982	−	0.00599731i	$-0.998091\pi$
$157$	−6.19979	+	10.7384i	−0.494797	+	0.857014i	0.505185	+	0.863011i	$0.331424\pi$
$158$	−9.26757	−	5.35063i	−0.737288	−	0.425674i
$159$	−3.51384	+	0.442470i	−0.278666	+	0.0350902i
$160$	0.866025	−	0.500000i	0.0684653	−	0.0395285i
$161$	15.8799			1.25151
$162$	7.69079	+	4.67458i	0.604246	+	0.367270i
$163$	5.52581			0.432815			0.216407	−	0.976303i	$-0.430566\pi$
$163$	5.52581			0.432815			0.216407	+	0.976303i	$0.430566\pi$
$164$	2.82033	+	4.88496i	0.220231	+	0.381451i
$165$	2.98286	+	4.90944i	0.232215	+	0.382199i
$166$	3.29598	−	5.70881i	0.255818	−	0.443090i
$167$	−10.5661	+	18.3010i	−0.817630	+	1.41618i	0.0897940	+	0.995960i	$0.471379\pi$
$167$	−10.5661	+	18.3010i	−0.817630	+	1.41618i	−0.907424	+	0.420216i	$0.861954\pi$
$168$	4.16427	+	5.49080i	0.321281	+	0.423624i
$169$	−4.05159	−	7.01757i	−0.311661	−	0.539813i
$170$		−	2.92469i		−	0.224314i
$171$	−3.78972	−	14.8093i	−0.289807	−	1.13249i
$172$		−	6.17641i		−	0.470947i
$173$	4.24528	+	7.35303i	0.322762	+	0.559041i	0.981057	−	0.193720i	$-0.0620552\pi$
$173$	4.24528	+	7.35303i	0.322762	+	0.559041i	−0.658295	+	0.752760i	$0.728722\pi$
$174$	−6.21681	−	2.61624i	−0.471295	−	0.198337i
$175$	−3.44565	−	1.98935i	−0.260467	−	0.150380i
$176$	−3.29908	−	0.340645i	−0.248678	−	0.0256771i
$177$	−8.94921	+	21.2655i	−0.672664	+	1.59841i
$178$	−11.2721	+	6.50793i	−0.844877	+	0.487790i
$179$			24.6690i			1.84384i	0.387376	+	0.921922i	$0.373382\pi$
$179$			24.6690i			1.84384i	−0.387376	+	0.921922i	$0.626618\pi$
$180$	2.14510	−	2.09727i	0.159886	−	0.156321i
$181$	11.3159			0.841106			0.420553	−	0.907268i	$-0.361836\pi$
$181$	11.3159			0.841106			0.420553	+	0.907268i	$0.361836\pi$
$182$	4.40217	+	7.62479i	0.326311	+	0.565187i
$183$	−3.19736	−	4.21587i	−0.236355	−	0.311646i
$184$	3.45652	+	1.99562i	0.254818	+	0.147119i
$185$	3.49155	+	2.01585i	0.256704	+	0.148208i
$186$	−0.0820067	−	0.651250i	−0.00601303	−	0.0477519i
$187$	−5.68721	+	7.85797i	−0.415890	+	0.574632i
$188$		−	8.16993i		−	0.595853i
$189$	16.1865	+	12.8610i	1.17740	+	0.935502i
$190$	−5.09549			−0.369666
$191$	−0.309330	+	0.178592i	−0.0223823	+	0.0129224i	−0.511149	−	0.859492i	$-0.670780\pi$
$191$	−0.309330	+	0.178592i	−0.0223823	+	0.0129224i	0.488767	+	0.872414i	$0.337447\pi$
$192$	0.216395	+	1.71848i	0.0156169	+	0.124021i
$193$	9.64082	+	5.56613i	0.693961	+	0.400659i	0.805094	−	0.593147i	$-0.202115\pi$
$193$	9.64082	+	5.56613i	0.693961	+	0.400659i	−0.111133	+	0.993806i	$0.535448\pi$
$194$	6.50778	−	11.2718i	0.467232	−	0.809269i
$195$	3.05388	−	2.31609i	0.218693	−	0.165859i
$196$	4.41500	+	7.64700i	0.315357	+	0.546215i
$197$	27.4225			1.95377			0.976887	−	0.213756i	$-0.0685698\pi$
$197$	27.4225			1.95377			0.976887	+	0.213756i	$0.0685698\pi$
$198$	−9.84164	+	1.46363i	−0.699415	+	0.104015i
$199$	−0.974271			−0.0690643			−0.0345321	−	0.999404i	$-0.510994\pi$
$199$	−0.974271			−0.0690643			−0.0345321	+	0.999404i	$0.510994\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−7.70423	−	3.24219i	−0.543414	−	0.228687i
$202$	−3.90859	+	6.76988i	−0.275008	+	0.476327i
$203$	−13.4179	−	7.74684i	−0.941753	−	0.543721i
$204$	4.66911	+	1.96492i	0.326903	+	0.137572i
$205$	4.88496	−	2.82033i	0.341180	−	0.196981i
$206$	0.317047			0.0220897
$207$	11.5301	+	3.22922i	0.801394	+	0.224446i
$208$			2.21287i			0.153435i
$209$	13.6904	+	9.90843i	0.946985	+	0.685381i
$210$	5.49080	−	4.16427i	0.378901	−	0.287362i
$211$	−11.9858	−	6.92003i	−0.825140	−	0.476395i	0.0270459	−	0.999634i	$-0.491390\pi$
$211$	−11.9858	−	6.92003i	−0.825140	−	0.476395i	−0.852186	+	0.523239i	$0.824723\pi$
$212$	−1.77079	−	1.02237i	−0.121619	−	0.0702165i
$213$	−20.1258	+	2.53429i	−1.37900	+	0.173647i
$214$	8.15979	+	14.1332i	0.557792	+	0.966124i
$215$	−6.17641			−0.421228
$216$	1.90702	+	4.83356i	0.129756	+	0.328882i
$217$		−	1.50780i		−	0.102356i
$218$	13.6599	−	7.88657i	0.925168	−	0.534146i
$219$	2.56982	−	0.323598i	0.173653	−	0.0218667i
$220$	−0.340645	+	3.29908i	−0.0229663	+	0.222424i
$221$	5.60490	+	3.23599i	0.377026	+	0.217676i
$222$	−5.56394	+	4.21975i	−0.373427	+	0.283211i
$223$	12.0790	+	20.9214i	0.808867	+	1.40100i	0.913649	+	0.406503i	$0.133252\pi$
$223$	12.0790	+	20.9214i	0.808867	+	1.40100i	−0.104783	+	0.994495i	$0.533415\pi$
$224$			3.97869i			0.265838i
$225$	−2.09727	−	2.14510i	−0.139818	−	0.143007i
$226$		−	17.6188i		−	1.17198i
$227$	11.9134	+	20.6347i	0.790723	+	1.36957i	0.925520	+	0.378699i	$0.123629\pi$
$227$	11.9134	+	20.6347i	0.790723	+	1.36957i	−0.134797	+	0.990873i	$0.543038\pi$
$228$	3.42334	−	8.13467i	0.226716	−	0.538732i
$229$	−4.55299	+	7.88602i	−0.300870	+	0.521123i	−0.976333	−	0.216271i	$-0.930610\pi$
$229$	−4.55299	+	7.88602i	−0.300870	+	0.521123i	0.675463	+	0.737394i	$0.263944\pi$
$230$	1.99562	−	3.45652i	0.131587	−	0.227916i
$231$	−22.8501	+	0.511312i	−1.50343	+	0.0336418i
$232$	−1.94708	−	3.37244i	−0.127832	−	0.221412i
$233$	−4.93934			−0.323587			−0.161793	−	0.986825i	$-0.551728\pi$
$233$	−4.93934			−0.323587			−0.161793	+	0.986825i	$0.551728\pi$
$234$	1.64580	+	6.43138i	0.107589	+	0.420432i
$235$	−8.16993			−0.532947
$236$	−11.5359	+	6.66026i	−0.750923	+	0.433546i
$237$	−11.2004	−	14.7683i	−0.727545	−	0.959303i
$238$	10.0775	+	5.81823i	0.653225	+	0.377140i
$239$	−7.49406	+	12.9801i	−0.484750	+	0.839612i	−0.999847	−	0.0175202i	$-0.994423\pi$
$239$	−7.49406	+	12.9801i	−0.484750	+	0.839612i	0.515096	+	0.857132i	$0.327756\pi$
$240$	1.71848	−	0.216395i	0.110927	−	0.0139682i
$241$	−0.424639	+	0.245165i	−0.0273534	+	0.0157925i	−0.513614	−	0.858021i	$-0.671694\pi$
$241$	−0.424639	+	0.245165i	−0.0273534	+	0.0157925i	0.486261	+	0.873814i	$0.338360\pi$
$242$	7.33047	−	8.20148i	0.471220	−	0.527211i
$243$	9.13737	+	12.6297i	0.586163	+	0.810193i
$244$		−	3.05487i		−	0.195568i
$245$	7.64700	−	4.41500i	0.488549	−	0.282064i
$246$	1.22061	+	9.69337i	0.0778232	+	0.618027i
$247$	5.63784	−	9.76502i	0.358727	−	0.621334i
$248$	0.189484	−	0.328196i	0.0120323	−	0.0208405i
$249$	9.09724	−	6.89944i	0.576514	−	0.437234i
$250$	−0.866025	+	0.500000i	−0.0547723	+	0.0316228i
$251$		−	17.6202i		−	1.11218i	−0.831122	−	0.556090i	$-0.812301\pi$
$251$		−	17.6202i		−	1.11218i	0.831122	−	0.556090i	$-0.187699\pi$
$252$	2.95911	+	11.5635i	0.186407	+	0.728430i
$253$	−12.0831	+	5.40627i	−0.759660	+	0.339890i
$254$	−0.422426	+	0.243888i	−0.0265053	+	0.0153029i
$255$	1.96492	−	4.66911i	0.123048	−	0.292391i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	14.3882	+	8.30701i	0.897509	+	0.518177i	0.876391	−	0.481600i	$-0.159944\pi$
$257$	14.3882	+	8.30701i	0.897509	+	0.518177i	0.0211180	+	0.999777i	$0.493277\pi$
$258$	4.14954	−	9.86029i	0.258339	−	0.613875i
$259$	−13.8918	+	8.02044i	−0.863195	+	0.498366i
$260$	2.21287			0.137237
$261$	−8.16711	−	8.35337i	−0.505532	−	0.517060i
$262$	1.73487			0.107181
$263$	−10.3582	−	17.9410i	−0.638716	−	1.10629i	−0.985715	−	0.168423i	$-0.946133\pi$
$263$	−10.3582	−	17.9410i	−0.638716	−	1.10629i	0.346999	−	0.937865i	$-0.387201\pi$
$264$	−5.03795	−	2.76027i	−0.310064	−	0.169883i
$265$	−1.02237	+	1.77079i	−0.0628036	+	0.108779i
$266$	10.1367	−	17.5573i	0.621521	−	1.07651i
$267$	−22.3675	+	2.81656i	−1.36887	+	0.172371i
$268$	−2.41293	−	4.17932i	−0.147393	−	0.255293i
$269$		−	22.9597i		−	1.39988i	−0.714203	−	0.699938i	$-0.753211\pi$
$269$		−	22.9597i		−	1.39988i	0.714203	−	0.699938i	$-0.246789\pi$
$270$	4.83356	−	1.90702i	0.294161	−	0.116058i
$271$		−	21.1873i		−	1.28704i	−0.765430	−	0.643519i	$-0.777474\pi$
$271$		−	21.1873i		−	1.28704i	0.765430	−	0.643519i	$-0.222526\pi$
$272$	1.46235	+	2.53286i	0.0886678	+	0.153577i
$273$	1.90521	+	15.1301i	0.115309	+	0.915715i
$274$	−14.0600	−	8.11757i	−0.849398	−	0.490400i
$275$	3.29908	+	0.340645i	0.198942	+	0.0205417i
$276$	4.17740	+	5.50811i	0.251450	+	0.331549i
$277$	17.1452	−	9.89877i	1.03015	−	0.594760i	0.113125	−	0.993581i	$-0.463914\pi$
$277$	17.1452	−	9.89877i	1.03015	−	0.594760i	0.917029	+	0.398821i	$0.130581\pi$
$278$			22.2520i			1.33459i
$279$	0.306614	−	1.09478i	0.0183565	−	0.0655427i
$280$	3.97869			0.237772
$281$	0.369015	+	0.639153i	0.0220136	+	0.0381287i	0.876822	−	0.480815i	$-0.159659\pi$
$281$	0.369015	+	0.639153i	0.0220136	+	0.0381287i	−0.854809	+	0.518943i	$0.826326\pi$
$282$	5.48886	−	13.0428i	0.326857	−	0.776690i
$283$	22.3407	+	12.8984i	1.32802	+	0.766731i	0.984993	−	0.172595i	$-0.0552151\pi$
$283$	22.3407	+	12.8984i	1.32802	+	0.766731i	0.343025	+	0.939326i	$0.388548\pi$
$284$	−10.1424	−	5.85571i	−0.601840	−	0.347472i
$285$	−8.13467	−	3.42334i	−0.481856	−	0.202781i
$286$	−5.94548	−	4.30304i	−0.351564	−	0.254444i
$287$			22.4425i			1.32474i
$288$	−0.809076	+	2.88884i	−0.0476752	+	0.170227i
$289$	−8.44617			−0.496834
$290$	−3.37244	+	1.94708i	−0.198037	+	0.114337i
$291$	17.9621	−	13.6227i	1.05296	−	0.798574i
$292$	1.29506	+	0.747703i	0.0757876	+	0.0437560i
$293$	−1.52132	+	2.63500i	−0.0888764	+	0.153939i	−0.907036	−	0.421052i	$-0.861661\pi$
$293$	−1.52132	+	2.63500i	−0.0888764	+	0.153939i	0.818160	+	0.574991i	$0.194994\pi$
$294$	1.91076	+	15.1742i	0.111438	+	0.884976i
$295$	6.66026	+	11.5359i	0.387775	+	0.671646i
$296$	−4.03169			−0.234338
$297$	−16.6949	−	4.27537i	−0.968739	−	0.248082i
$298$	−5.54049			−0.320952
$299$	4.41606	+	7.64883i	0.255387	+	0.442343i
$300$	−0.216395	−	1.71848i	−0.0124936	−	0.0992165i
$301$	12.2870	−	21.2817i	0.708212	−	1.22666i
$302$	−8.48831	−	4.90073i	−0.488447	−	0.282005i
$303$	−10.7881	+	8.18180i	−0.619761	+	0.470032i
$304$	4.41282	−	2.54775i	0.253093	−	0.146123i
$305$	−3.05487			−0.174921
$306$	6.13387	+	6.27376i	0.350650	+	0.358647i
$307$		−	10.9681i		−	0.625984i	−0.949756	−	0.312992i	$-0.898669\pi$
$307$		−	10.9681i		−	0.625984i	0.949756	−	0.312992i	$-0.101331\pi$
$308$	−10.6898	−	7.73677i	−0.609109	−	0.440843i
$309$	0.506149	+	0.213004i	0.0287938	+	0.0121174i
$310$	−0.328196	−	0.189484i	−0.0186403	−	0.0107620i
$311$	−7.69553	−	4.44302i	−0.436374	−	0.251940i	0.265685	−	0.964060i	$-0.414402\pi$
$311$	−7.69553	−	4.44302i	−0.436374	−	0.251940i	−0.702058	+	0.712120i	$0.747735\pi$
$312$	−1.48669	+	3.53273i	−0.0841672	+	0.200001i
$313$	−14.5073	−	25.1273i	−0.819999	−	1.42028i	−0.905682	−	0.423958i	$-0.860641\pi$
$313$	−14.5073	−	25.1273i	−0.819999	−	1.42028i	0.0856830	−	0.996322i	$-0.472693\pi$
$314$	−12.3996			−0.699749
$315$	11.5635	−	2.95911i	0.651527	−	0.166727i
$316$		−	10.7013i		−	0.601993i
$317$	−24.9039	+	14.3783i	−1.39874	+	0.807565i	−0.994261	−	0.106980i	$-0.965882\pi$
$317$	−24.9039	+	14.3783i	−1.39874	+	0.807565i	−0.404483	+	0.914546i	$0.632548\pi$
$318$	−2.14011	−	2.82184i	−0.120011	−	0.158241i
$319$	12.8472	+	1.32653i	0.719303	+	0.0742713i
$320$	0.866025	+	0.500000i	0.0484123	+	0.0279508i
$321$	3.53147	+	28.0449i	0.197107	+	1.56531i
$322$	7.93996	+	13.7524i	0.442477	+	0.766392i
$323$		−	14.9027i		−	0.829211i
$324$	−0.202909	+	8.99771i	−0.0112727	+	0.499873i
$325$		−	2.21287i		−	0.122748i
$326$	2.76290	+	4.78549i	0.153023	+	0.265044i
$327$	27.1058	−	3.41322i	1.49896	−	0.188752i
$328$	−2.82033	+	4.88496i	−0.155727	+	0.269727i
$329$	16.2528	−	28.1507i	0.896047	−	1.55200i
$330$	−2.76027	+	5.03795i	−0.151948	+	0.277330i
$331$	−0.233607	−	0.404619i	−0.0128402	−	0.0222399i	0.859534	−	0.511079i	$-0.170754\pi$
$331$	−0.233607	−	0.404619i	−0.0128402	−	0.0222399i	−0.872374	+	0.488839i	$0.837421\pi$
$332$	6.59197			0.361781
$333$	−11.7175	+	2.99853i	−0.642115	+	0.164319i
$334$	−21.1322			−1.15630
$335$	−4.17932	+	2.41293i	−0.228341	+	0.131833i
$336$	−2.67303	+	6.35176i	−0.145826	+	0.346517i
$337$	20.9970	+	12.1226i	1.14378	+	0.660362i	0.947364	−	0.320159i	$-0.103736\pi$
$337$	20.9970	+	12.1226i	1.14378	+	0.660362i	0.196416	+	0.980521i	$0.437070\pi$
$338$	4.05159	−	7.01757i	0.220378	−	0.381705i
$339$	11.8369	−	28.1274i	0.642894	−	1.52767i
$340$	2.53286	−	1.46235i	0.137364	−	0.0793069i
$341$	0.513326	+	1.14729i	0.0277982	+	0.0621295i
$342$	10.9303	−	10.6866i	0.591045	−	0.577866i
$343$			7.28101i			0.393137i
$344$	5.34893	−	3.08820i	0.288395	−	0.166505i
$345$	5.50811	−	4.17740i	0.296547	−	0.224904i
$346$	−4.24528	+	7.35303i	−0.228227	+	0.395301i
$347$	8.54540	−	14.8011i	0.458741	−	0.794563i	−0.540154	−	0.841566i	$-0.681634\pi$
$347$	8.54540	−	14.8011i	0.458741	−	0.794563i	0.998895	+	0.0470035i	$0.0149672\pi$
$348$	−0.842676	−	6.69204i	−0.0451722	−	0.358731i
$349$	−2.99011	+	1.72634i	−0.160057	+	0.0924089i	−0.577889	−	0.816115i	$-0.696123\pi$
$349$	−2.99011	+	1.72634i	−0.160057	+	0.0924089i	0.417832	+	0.908524i	$0.362790\pi$
$350$		−	3.97869i		−	0.212670i
$351$	−1.69340	+	11.3731i	−0.0903872	+	0.607049i
$352$	−1.35454	−	3.02741i	−0.0721970	−	0.161362i
$353$	20.4677	−	11.8170i	1.08938	−	0.628956i	0.155971	−	0.987762i	$-0.450149\pi$
$353$	20.4677	−	11.8170i	1.08938	−	0.628956i	0.933412	+	0.358806i	$0.116816\pi$
$354$	−22.8910	+	2.88249i	−1.21664	+	0.153203i
$355$	−5.85571	+	10.1424i	−0.310789	+	0.538302i
$356$	−11.2721	−	6.50793i	−0.597419	−	0.344920i
$357$	12.1792	+	16.0589i	0.644593	+	0.849927i
$358$	−21.3639	+	12.3345i	−1.12912	+	0.651897i
$359$	4.27322			0.225532			0.112766	−	0.993622i	$-0.464029\pi$
$359$	4.27322			0.225532			0.112766	+	0.993622i	$0.464029\pi$
$360$	2.88884	+	0.809076i	0.152255	+	0.0426420i
$361$	−6.96402			−0.366527
$362$	5.65796	+	9.79988i	0.297376	+	0.515070i
$363$	17.2127	−	8.16832i	0.903435	−	0.428726i
$364$	−4.40217	+	7.62479i	−0.230737	+	0.399647i
$365$	0.747703	−	1.29506i	0.0391365	−	0.0677865i
$366$	2.05237	−	4.87693i	0.107279	−	0.254921i
$367$	−10.6794	−	18.4972i	−0.557460	−	0.965548i	−0.997708	−	0.0676721i	$-0.978443\pi$
$367$	−10.6794	−	18.4972i	−0.557460	−	0.965548i	0.440248	−	0.897876i	$-0.354891\pi$
$368$			3.99124i			0.208058i
$369$	−4.56373	+	16.2950i	−0.237578	+	0.848283i
$370$			4.03169i			0.209598i
$371$	−4.06769	−	7.04544i	−0.211184	−	0.365781i
$372$	0.522995	−	0.396645i	0.0271160	−	0.0205651i
$373$	17.1212	+	9.88495i	0.886504	+	0.511823i	0.872797	−	0.488083i	$-0.162304\pi$
$373$	17.1212	+	9.88495i	0.886504	+	0.511823i	0.0137066	+	0.999906i	$0.495637\pi$
$374$	−9.64881	−	0.996283i	−0.498928	−	0.0515165i
$375$	−1.71848	+	0.216395i	−0.0887419	+	0.0111746i
$376$	7.07537	−	4.08496i	0.364884	−	0.210666i
$377$		−	8.61729i		−	0.443813i
$378$	−3.04470	+	20.4485i	−0.156602	+	1.05176i
$379$	−15.7701			−0.810058			−0.405029	−	0.914304i	$-0.632739\pi$
$379$	−15.7701			−0.810058			−0.405029	+	0.914304i	$0.632739\pi$
$380$	−2.54775	−	4.41282i	−0.130697	−	0.226373i
$381$	−0.838232	+	0.105552i	−0.0429439	+	0.00540759i
$382$	−0.309330	−	0.178592i	−0.0158267	−	0.00913754i
$383$	25.2600	+	14.5839i	1.29073	+	0.745202i	0.978783	−	0.204898i	$-0.0656864\pi$
$383$	25.2600	+	14.5839i	1.29073	+	0.745202i	0.311944	+	0.950100i	$0.399020\pi$
$384$	−1.38005	+	1.04664i	−0.0704254	+	0.0534113i
$385$	−7.73677	+	10.6898i	−0.394302	+	0.544804i
$386$			11.1323i			0.566617i
$387$	13.2490	−	12.9536i	0.673485	−	0.658469i
$388$	13.0156			0.660765
$389$	6.24669	−	3.60653i	0.316720	−	0.182858i	−0.333210	−	0.942853i	$-0.608132\pi$
$389$	6.24669	−	3.60653i	0.316720	−	0.182858i	0.649930	+	0.759994i	$0.274798\pi$
$390$	3.53273	+	1.48669i	0.178887	+	0.0752815i
$391$	10.1092	+	5.83658i	0.511247	+	0.295168i
$392$	−4.41500	+	7.64700i	−0.222991	+	0.386232i
$393$	2.76963	+	1.16555i	0.139709	+	0.0587943i
$394$	13.7113	+	23.7486i	0.690763	+	1.19644i
$395$	−10.7013			−0.538439
$396$	−6.18836	−	7.79129i	−0.310977	−	0.391527i
$397$	−5.88295			−0.295257			−0.147628	−	0.989043i	$-0.547164\pi$
$397$	−5.88295			−0.295257			−0.147628	+	0.989043i	$0.547164\pi$
$398$	−0.487136	−	0.843744i	−0.0244179	−	0.0422931i
$399$	27.9783	−	21.2190i	1.40067	−	1.06228i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	20.7428	+	11.9759i	1.03585	+	0.598046i	0.918654	−	0.395064i	$-0.129277\pi$
$401$	20.7428	+	11.9759i	1.03585	+	0.598046i	0.117192	+	0.993109i	$0.462611\pi$
$402$	−1.04429	−	8.29315i	−0.0520845	−	0.413625i
$403$	0.726257	−	0.419305i	0.0361774	−	0.0208871i
$404$	−7.81719			−0.388920
$405$	8.99771	+	0.202909i	0.447100	+	0.0100826i
$406$		−	15.4937i		−	0.768938i
$407$	7.83983	−	10.8322i	0.388606	−	0.536934i
$408$	0.632888	+	5.02603i	0.0313326	+	0.248825i
$409$	−28.2794	−	16.3271i	−1.39833	−	0.807325i	−0.404110	−	0.914710i	$-0.632419\pi$
$409$	−28.2794	−	16.3271i	−1.39833	−	0.807325i	−0.994217	+	0.107386i	$0.965752\pi$
$410$	4.88496	+	2.82033i	0.241251	+	0.139286i
$411$	−16.9924	−	22.4053i	−0.838173	−	1.10517i
$412$	0.158524	+	0.274571i	0.00780990	+	0.0135271i
$413$	−52.9982			−2.60787
$414$	2.96844	+	11.5999i	0.145891	+	0.570105i
$415$		−	6.59197i		−	0.323587i
$416$	−1.91641	+	1.10644i	−0.0939595	+	0.0542475i
$417$	−14.9497	+	35.5241i	−0.732092	+	1.73962i
$418$	−1.73575	+	16.8105i	−0.0848985	+	0.822226i
$419$	3.41710	+	1.97286i	0.166936	+	0.0963806i	0.581140	−	0.813803i	$-0.302607\pi$
$419$	3.41710	+	1.97286i	0.166936	+	0.0963806i	−0.414204	+	0.910184i	$0.635940\pi$
$420$	6.35176	+	2.67303i	0.309934	+	0.130431i
$421$	−6.89797	−	11.9476i	−0.336187	−	0.582292i	0.647525	−	0.762044i	$-0.275804\pi$
$421$	−6.89797	−	11.9476i	−0.336187	−	0.582292i	−0.983712	+	0.179751i	$0.942471\pi$
$422$		−	13.8401i		−	0.673724i
$423$	17.5253	−	17.1346i	0.852110	−	0.833110i
$424$		−	2.04474i		−	0.0993012i
$425$	−1.46235	−	2.53286i	−0.0709342	−	0.122862i
$426$	−12.2577	−	16.1623i	−0.593886	−	0.783068i
$427$	6.07719	−	10.5260i	0.294096	−	0.509389i
$428$	−8.15979	+	14.1332i	−0.394418	+	0.683153i
$429$	−6.60069	−	10.8640i	−0.318684	−	0.524517i
$430$	−3.08820	−	5.34893i	−0.148926	−	0.257948i
$431$	4.08943			0.196981			0.0984904	−	0.995138i	$-0.468599\pi$
$431$	4.08943			0.196981			0.0984904	+	0.995138i	$0.468599\pi$
$432$	−3.23247	+	4.06831i	−0.155522	+	0.195736i
$433$	11.9242			0.573041			0.286520	−	0.958074i	$-0.407501\pi$
$433$	11.9242			0.573041			0.286520	+	0.958074i	$0.407501\pi$
$434$	1.30579	−	0.753899i	0.0626800	−	0.0361883i
$435$	−6.69204	+	0.842676i	−0.320859	+	0.0404032i
$436$	13.6599	+	7.88657i	0.654192	+	0.377698i
$437$	10.1687	−	17.6126i	0.486433	−	0.842527i
$438$	1.56516	+	2.06373i	0.0747860	+	0.0986090i
$439$	−0.0368928	+	0.0213001i	−0.00176080	+	0.00101660i	−0.500880	−	0.865517i	$-0.666990\pi$
$439$	−0.0368928	+	0.0213001i	−0.00176080	+	0.00101660i	0.499119	+	0.866533i	$0.333657\pi$
$440$	−3.02741	+	1.35454i	−0.144326	+	0.0645749i
$441$	−7.14414	+	25.5085i	−0.340197	+	1.21469i
$442$			6.47198i			0.307841i
$443$	17.5422	−	10.1280i	0.833457	−	0.481197i	−0.0215778	−	0.999767i	$-0.506869\pi$
$443$	17.5422	−	10.1280i	0.833457	−	0.481197i	0.855035	+	0.518571i	$0.173536\pi$
$444$	−6.43638	−	2.70864i	−0.305457	−	0.128546i
$445$	−6.50793	+	11.2721i	−0.308506	+	0.534347i
$446$	−12.0790	+	20.9214i	−0.571955	+	0.990655i
$447$	−8.84509	−	3.72231i	−0.418358	−	0.176059i
$448$	−3.44565	+	1.98935i	−0.162792	+	0.0939878i
$449$		−	26.9788i		−	1.27321i	−0.771191	−	0.636604i	$-0.780339\pi$
$449$		−	26.9788i		−	1.27321i	0.771191	−	0.636604i	$-0.219661\pi$
$450$	0.809076	−	2.88884i	0.0381402	−	0.136181i
$451$	−7.64048	−	17.0766i	−0.359776	−	0.804107i
$452$	15.2583	−	8.80939i	0.717690	−	0.414359i
$453$	−10.2586	−	13.5265i	−0.481992	−	0.635530i
$454$	−11.9134	+	20.6347i	−0.559126	+	0.968434i
$455$	7.62479	+	4.40217i	0.357456	+	0.206377i
$456$	8.75650	−	1.10264i	0.410061	−	0.0516357i
$457$	0.0365469	−	0.0211003i	0.00170959	−	0.000987032i	−0.499145	−	0.866518i	$-0.666352\pi$
$457$	0.0365469	−	0.0211003i	0.00170959	−	0.000987032i	0.500855	+	0.865531i	$0.333019\pi$
$458$	−9.10599			−0.425495
$459$	5.57745	+	14.1367i	0.260333	+	0.659843i
$460$	3.99124			0.186093
$461$	5.90883	+	10.2344i	0.275201	+	0.476663i	0.970186	−	0.242362i	$-0.0779221\pi$
$461$	5.90883	+	10.2344i	0.275201	+	0.476663i	−0.694984	+	0.719025i	$0.744589\pi$
$462$	−11.8679	−	19.5331i	−0.552144	−	0.908764i
$463$	7.36083	−	12.7493i	0.342087	−	0.592511i	−0.642733	−	0.766090i	$-0.722200\pi$
$463$	7.36083	−	12.7493i	0.342087	−	0.592511i	0.984820	+	0.173578i	$0.0555330\pi$
$464$	1.94708	−	3.37244i	0.0903910	−	0.156562i
$465$	−0.396645	−	0.522995i	−0.0183940	−	0.0242533i
$466$	−2.46967	−	4.27759i	−0.114405	−	0.198156i
$467$			9.31007i			0.430819i	0.976524	+	0.215409i	$0.0691086\pi$
$467$			9.31007i			0.430819i	−0.976524	+	0.215409i	$0.930891\pi$
$468$	−4.74684	+	4.64100i	−0.219423	+	0.214530i
$469$		−	19.2006i		−	0.886603i
$470$	−4.08496	−	7.07537i	−0.188425	−	0.326362i
$471$	−19.7952	−	8.33049i	−0.912117	−	0.383849i
$472$	−11.5359	−	6.66026i	−0.530983	−	0.306563i
$473$	−2.10396	+	20.3765i	−0.0967404	+	0.936912i
$474$	7.18951	−	17.0840i	0.330225	−	0.784693i
$475$	−4.41282	+	2.54775i	−0.202474	+	0.116899i
$476$			11.6365i			0.533356i
$477$	−1.52075	−	5.94271i	−0.0696304	−	0.272098i
$478$	−14.9881			−0.685541
$479$	1.01412	+	1.75651i	0.0463365	+	0.0802572i	0.888263	−	0.459334i	$-0.151912\pi$
$479$	1.01412	+	1.75651i	0.0463365	+	0.0802572i	−0.841927	+	0.539592i	$0.818579\pi$
$480$	1.04664	+	1.38005i	0.0477725	+	0.0629904i
$481$	−7.72636	−	4.46082i	−0.352292	−	0.203396i
$482$	−0.424639	−	0.245165i	−0.0193418	−	0.0111670i
$483$	3.43633	+	27.2893i	0.156358	+	1.24171i
$484$	10.7679	+	2.24763i	0.489451	+	0.102165i
$485$		−	13.0156i		−	0.591007i
$486$	−6.36893	+	14.2280i	−0.288900	+	0.645396i
$487$	34.5735			1.56667			0.783337	−	0.621597i	$-0.213516\pi$
$487$	34.5735			1.56667			0.783337	+	0.621597i	$0.213516\pi$
$488$	2.64559	−	1.52743i	0.119760	−	0.0691437i
$489$	1.19576	+	9.49599i	0.0540739	+	0.429424i
$490$	7.64700	+	4.41500i	0.345456	+	0.199449i
$491$	1.75180	−	3.03420i	0.0790575	−	0.136932i	−0.823786	−	0.566901i	$-0.808142\pi$
$491$	1.75180	−	3.03420i	0.0790575	−	0.136932i	0.902844	+	0.429969i	$0.141476\pi$
$492$	−7.78440	+	5.90376i	−0.350948	+	0.266162i
$493$	−5.69461	−	9.86336i	−0.256472	−	0.444223i
$494$	11.2757			0.507317
$495$	−7.79129	+	6.18836i	−0.350193	+	0.278146i
$496$	0.378968			0.0170162
$497$	−23.2981	−	40.3534i	−1.04506	−	1.81010i
$498$	10.5237	+	4.42872i	0.471579	+	0.198456i
$499$	−6.60606	+	11.4420i	−0.295728	+	0.512216i	−0.975154	−	0.221528i	$-0.928896\pi$
$499$	−6.60606	+	11.4420i	−0.295728	+	0.512216i	0.679426	+	0.733744i	$0.262229\pi$
$500$	−0.866025	−	0.500000i	−0.0387298	−	0.0223607i
$501$	−33.7364	−	14.1974i	−1.50723	−	0.634293i
$502$	15.2596	−	8.81012i	0.681068	−	0.393215i
$503$	−8.74889			−0.390094			−0.195047	−	0.980794i	$-0.562486\pi$
$503$	−8.74889			−0.390094			−0.195047	+	0.980794i	$0.562486\pi$
$504$	−8.53470	+	8.34440i	−0.380166	+	0.371689i
$505$			7.81719i			0.347860i
$506$	−10.7235	−	7.76117i	−0.476719	−	0.345026i
$507$	11.1828	−	8.48115i	0.496646	−	0.376661i
$508$	−0.422426	−	0.243888i	−0.0187421	−	0.0108208i
$509$	−6.09553	−	3.51925i	−0.270180	−	0.155988i	0.358790	−	0.933418i	$-0.383190\pi$
$509$	−6.09553	−	3.51925i	−0.270180	−	0.155988i	−0.628969	+	0.777430i	$0.716523\pi$
$510$	5.02603	−	0.632888i	0.222556	−	0.0280247i
$511$	2.97488	+	5.15264i	0.131601	+	0.227939i
$512$	−1.00000			−0.0441942
$513$	24.6293	−	9.71720i	1.08741	−	0.429025i
$514$			16.6140i			0.732813i
$515$	0.274571	−	0.158524i	0.0120990	−	0.00698539i
$516$	10.6140	−	1.33654i	0.467257	−	0.0588380i
$517$	−2.78305	+	26.9533i	−0.122398	+	1.18540i
$518$	−13.8918	−	8.02044i	−0.610371	−	0.352398i
$519$	−11.7174	+	8.88658i	−0.514336	+	0.390077i
$520$	1.10644	+	1.91641i	0.0485205	+	0.0840399i
$521$		−	18.0730i		−	0.791791i	−0.918295	−	0.395896i	$-0.870434\pi$
$521$		−	18.0730i		−	0.791791i	0.918295	−	0.395896i	$-0.129566\pi$
$522$	3.15067	−	11.2496i	0.137901	−	0.492382i
$523$			43.8273i			1.91644i	0.286040	+	0.958218i	$0.407661\pi$
$523$			43.8273i			1.91644i	−0.286040	+	0.958218i	$0.592339\pi$
$524$	0.867437	+	1.50245i	0.0378942	+	0.0656346i
$525$	2.67303	−	6.35176i	0.116661	−	0.277214i
$526$	10.3582	−	17.9410i	0.451640	−	0.782264i
$527$	0.554183	−	0.959873i	0.0241406	−	0.0418127i
$528$	−0.128512	−	5.74312i	−0.00559279	−	0.249937i
$529$	−3.53500	−	6.12280i	−0.153696	−	0.266209i
$530$	−2.04474			−0.0888177
$531$	−38.4808	−	10.7773i	−1.66993	−	0.467695i
$532$	20.2734			0.878963
$533$	−10.8098	+	6.24104i	−0.468224	+	0.270329i
$534$	−13.6230	−	17.9625i	−0.589523	−	0.777315i
$535$	14.1332	+	8.15979i	0.611030	+	0.352778i
$536$	2.41293	−	4.17932i	0.104223	−	0.180519i
$537$	−42.3931	+	5.33823i	−1.82940	+	0.230362i
$538$	19.8837	−	11.4798i	0.857246	−	0.494931i
$539$	−11.9605	−	26.7321i	−0.515177	−	1.15143i
$540$	4.06831	+	3.23247i	0.175072	+	0.139104i
$541$		−	8.61079i		−	0.370207i	−0.982719	−	0.185103i	$-0.940738\pi$
$541$		−	8.61079i		−	0.370207i	0.982719	−	0.185103i	$-0.0592620\pi$
$542$	18.3488	−	10.5937i	0.788147	−	0.455037i
$543$	2.44871	+	19.4462i	0.105084	+	0.834516i
$544$	−1.46235	+	2.53286i	−0.0626976	+	0.108595i
$545$	7.88657	−	13.6599i	0.337823	−	0.585127i
$546$	−12.1504	+	9.21501i	−0.519991	+	0.394366i
$547$	25.7296	−	14.8550i	1.10012	−	0.635154i	0.163867	−	0.986482i	$-0.447603\pi$
$547$	25.7296	−	14.8550i	1.10012	−	0.635154i	0.936252	+	0.351328i	$0.114270\pi$
$548$		−	16.2351i		−	0.693531i
$549$	6.55300	−	6.40689i	0.279675	−	0.273439i
$550$	1.35454	+	3.02741i	0.0577576	+	0.129089i
$551$	−17.1843	+	9.92133i	−0.732074	+	0.422663i
$552$	−2.68146	+	6.37179i	−0.114131	+	0.271202i
$553$	21.2885	−	36.8728i	0.905281	−	1.56799i
$554$	17.1452	+	9.89877i	0.728429	+	0.420559i
$555$	−2.70864	+	6.43638i	−0.114975	+	0.273209i
$556$	−19.2708	+	11.1260i	−0.817265	+	0.471848i
$557$	−41.7104			−1.76732			−0.883662	−	0.468125i	$-0.844930\pi$
$557$	−41.7104			−1.76732			−0.883662	+	0.468125i	$0.844930\pi$
$558$	1.10141	−	0.281854i	0.0466266	−	0.0119318i
$559$	13.6676			0.578078
$560$	1.98935	+	3.44565i	0.0840652	+	0.145605i
$561$	−14.7345	−	8.07293i	−0.622089	−	0.340840i
$562$	−0.369015	+	0.639153i	−0.0155660	+	0.0269610i
$563$	3.71461	−	6.43389i	0.156552	−	0.271156i	−0.777071	−	0.629413i	$-0.783295\pi$
$563$	3.71461	−	6.43389i	0.156552	−	0.271156i	0.933623	+	0.358257i	$0.116629\pi$
$564$	14.0399	−	1.76793i	0.591185	−	0.0744432i
$565$	−8.80939	−	15.2583i	−0.370614	−	0.641922i
$566$			25.7968i			1.08432i
$567$	−18.5987	+	30.5993i	−0.781073	+	1.28505i
$568$		−	11.7114i		−	0.491400i
$569$	8.18491	+	14.1767i	0.343129	+	0.594318i	0.985012	−	0.172485i	$-0.0551797\pi$
$569$	8.18491	+	14.1767i	0.343129	+	0.594318i	−0.641883	+	0.766803i	$0.721846\pi$
$570$	−1.10264	−	8.75650i	−0.0461844	−	0.366769i
$571$	−27.8338	−	16.0699i	−1.16481	−	0.672503i	−0.212357	−	0.977192i	$-0.568114\pi$
$571$	−27.8338	−	16.0699i	−1.16481	−	0.672503i	−0.952452	+	0.304689i	$0.901447\pi$
$572$	0.753805	−	7.30046i	0.0315182	−	0.305248i
$573$	−0.373843	−	0.492931i	−0.0156175	−	0.0205925i
$574$	−19.4358	+	11.2212i	−0.811233	+	0.468365i
$575$		−	3.99124i		−	0.166446i
$576$	−2.90635	+	0.743740i	−0.121098	+	0.0309892i
$577$	−5.39613			−0.224644			−0.112322	−	0.993672i	$-0.535829\pi$
$577$	−5.39613			−0.224644			−0.112322	+	0.993672i	$0.535829\pi$
$578$	−4.22309	−	7.31460i	−0.175657	−	0.304247i
$579$	−7.47906	+	17.7720i	−0.310819	+	0.738581i
$580$	−3.37244	−	1.94708i	−0.140033	−	0.0808481i
$581$	22.7136	+	13.1137i	0.942319	+	0.544048i
$582$	20.7786	+	8.74434i	0.861302	+	0.362464i
$583$	5.49373	+	3.97609i	0.227527	+	0.164673i
$584$			1.49541i			0.0618803i
$585$	4.64100	+	4.74684i	0.191882	+	0.196258i
$586$	−3.04264			−0.125690
$587$	−23.8986	+	13.7978i	−0.986400	+	0.569498i	−0.904196	−	0.427117i	$-0.859529\pi$
$587$	−23.8986	+	13.7978i	−0.986400	+	0.569498i	−0.0822036	+	0.996616i	$0.526196\pi$
$588$	−12.1858	+	9.24186i	−0.502536	+	0.381128i
$589$	−1.67232	−	0.965515i	−0.0689068	−	0.0397833i
$590$	−6.66026	+	11.5359i	−0.274198	+	0.474926i
$591$	5.93409	+	47.1251i	0.244096	+	1.93847i
$592$	−2.01585	−	3.49155i	−0.0828508	−	0.143502i
$593$	33.4149			1.37219			0.686093	−	0.727514i	$-0.259324\pi$
$593$	33.4149			1.37219			0.686093	+	0.727514i	$0.259324\pi$
$594$	−4.64489	−	16.5959i	−0.190582	−	0.680939i
$595$	11.6365			0.477048
$596$	−2.77025	−	4.79821i	−0.113474	−	0.196542i
$597$	−0.210827	−	1.67427i	−0.00862858	−	0.0685231i
$598$	−4.41606	+	7.64883i	−0.180586	+	0.312784i
$599$	−21.5783	−	12.4583i	−0.881667	−	0.509031i	−0.0104596	−	0.999945i	$-0.503329\pi$
$599$	−21.5783	−	12.4583i	−0.881667	−	0.509031i	−0.871208	+	0.490914i	$0.836663\pi$
$600$	1.38005	−	1.04664i	0.0563403	−	0.0427290i
$601$	34.2219	−	19.7580i	1.39594	−	0.805946i	0.401975	−	0.915651i	$-0.368324\pi$
$601$	34.2219	−	19.7580i	1.39594	−	0.805946i	0.993964	+	0.109705i	$0.0349907\pi$
$602$	24.5740			1.00156
$603$	3.90449	−	13.9412i	0.159003	−	0.567728i
$604$		−	9.80145i		−	0.398816i
$605$	2.24763	−	10.7679i	0.0913794	−	0.437778i
$606$	−12.4797	−	5.25187i	−0.506953	−	0.213343i
$607$	−26.6667	−	15.3960i	−1.08237	−	0.624906i	−0.150834	−	0.988559i	$-0.548196\pi$
$607$	−26.6667	−	15.3960i	−1.08237	−	0.624906i	−0.931534	+	0.363654i	$0.881529\pi$
$608$	4.41282	+	2.54775i	0.178964	+	0.103325i
$609$	10.4092	−	24.7348i	0.421803	−	1.00230i
$610$	−1.52743	−	2.64559i	−0.0618440	−	0.107117i
$611$	18.0790			0.731399
$612$	−2.36630	+	8.44897i	−0.0956519	+	0.341529i
$613$		−	4.39837i		−	0.177648i	−0.996047	−	0.0888242i	$-0.971689\pi$
$613$		−	4.39837i		−	0.177648i	0.996047	−	0.0888242i	$-0.0283109\pi$
$614$	9.49868	−	5.48407i	0.383336	−	0.221319i
$615$	5.90376	+	7.78440i	0.238063	+	0.313897i
$616$	1.35532	−	13.1260i	0.0546075	−	0.528863i
$617$	−0.824104	−	0.475797i	−0.0331772	−	0.0191549i	0.483320	−	0.875444i	$-0.339431\pi$
$617$	−0.824104	−	0.475797i	−0.0331772	−	0.0191549i	−0.516497	+	0.856289i	$0.672764\pi$
$618$	0.0686074	+	0.544840i	0.00275979	+	0.0219167i
$619$	−8.29014	−	14.3589i	−0.333209	−	0.577135i	0.649930	−	0.759994i	$-0.274798\pi$
$619$	−8.29014	−	14.3589i	−0.333209	−	0.577135i	−0.983139	+	0.182859i	$0.941465\pi$
$620$		−	0.378968i		−	0.0152197i
$621$	−3.05430	+	20.5130i	−0.122565	+	0.823156i
$622$		−	8.88604i		−	0.356298i
$623$	−25.8931	−	44.8481i	−1.03738	−	1.79680i
$624$	−3.80278	+	0.478854i	−0.152233	+	0.0191695i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	14.5073	−	25.1273i	0.579827	−	1.00429i
$627$	−14.0649	+	25.6708i	−0.561699	+	1.02519i
$628$	−6.19979	−	10.7384i	−0.247399	−	0.428507i
$629$	−11.7915			−0.470157
$630$	8.34440	+	8.53470i	0.332449	+	0.340030i
$631$	39.6059			1.57669			0.788343	−	0.615237i	$-0.210939\pi$
$631$	39.6059			1.57669			0.788343	+	0.615237i	$0.210939\pi$
$632$	9.26757	−	5.35063i	0.368644	−	0.212837i
$633$	9.29826	−	22.0949i	0.369573	−	0.878193i
$634$	−24.9039	−	14.3783i	−0.989061	−	0.571035i
$635$	−0.243888	+	0.422426i	−0.00967839	+	0.0167635i
$636$	1.37373	−	3.26431i	0.0544719	−	0.129438i
$637$	−16.9219	+	9.76984i	−0.670468	+	0.387095i
$638$	5.27478	+	11.7892i	0.208830	+	0.466740i
$639$	−8.71025	−	34.0374i	−0.344572	−	1.34650i
$640$			1.00000i			0.0395285i
$641$	12.7833	−	7.38043i	0.504909	−	0.291509i	−0.225829	−	0.974167i	$-0.572509\pi$
$641$	12.7833	−	7.38043i	0.504909	−	0.291509i	0.730739	+	0.682657i	$0.239176\pi$
$642$	−22.5218	+	17.0808i	−0.888866	+	0.674125i
$643$	14.2301	−	24.6472i	0.561179	−	0.971990i	−0.436215	−	0.899842i	$-0.643681\pi$
$643$	14.2301	−	24.6472i	0.561179	−	0.971990i	0.997394	−	0.0721475i	$-0.0229852\pi$
$644$	−7.93996	+	13.7524i	−0.312878	+	0.541921i
$645$	−1.33654	−	10.6140i	−0.0526263	−	0.417927i
$646$	12.9062	−	7.45137i	0.507786	−	0.293170i
$647$		−	2.94815i		−	0.115904i	−0.998319	−	0.0579518i	$-0.981543\pi$
$647$		−	2.94815i		−	0.115904i	0.998319	−	0.0579518i	$-0.0184570\pi$
$648$	−7.89370	+	4.32313i	−0.310094	+	0.169829i
$649$	40.3267	−	18.0431i	1.58296	−	0.708254i
$650$	1.91641	−	1.10644i	0.0751676	−	0.0433980i
$651$	2.59112	−	0.326280i	0.101554	−	0.0127879i
$652$	−2.76290	+	4.78549i	−0.108204	+	0.187414i
$653$	−13.7076	−	7.91408i	−0.536420	−	0.309702i	0.207207	−	0.978297i	$-0.433563\pi$
$653$	−13.7076	−	7.91408i	−0.536420	−	0.309702i	−0.743627	+	0.668595i	$0.766896\pi$
$654$	16.5088	+	21.7677i	0.645547	+	0.851185i
$655$	1.50245	−	0.867437i	0.0587054	−	0.0338936i
$656$	−5.64066			−0.220231
$657$	1.11219	+	4.34617i	0.0433908	+	0.169560i
$658$	32.5056			1.26720
$659$	−9.59556	−	16.6200i	−0.373790	−	0.647423i	0.616355	−	0.787468i	$-0.288609\pi$
$659$	−9.59556	−	16.6200i	−0.373790	−	0.647423i	−0.990145	+	0.140045i	$0.955275\pi$
$660$	−5.74312	+	0.128512i	−0.223551	+	0.00500234i
$661$	−16.9049	+	29.2801i	−0.657524	+	1.13886i	0.323731	+	0.946149i	$0.395063\pi$
$661$	−16.9049	+	29.2801i	−0.657524	+	1.13886i	−0.981255	+	0.192716i	$0.938270\pi$
$662$	0.233607	−	0.404619i	0.00907938	−	0.0157260i
$663$	−4.34811	+	10.3322i	−0.168867	+	0.401268i
$664$	3.29598	+	5.70881i	0.127909	+	0.221545i
$665$		−	20.2734i		−	0.786168i
$666$	−8.45556	−	8.64839i	−0.327646	−	0.335118i
$667$		−	15.5425i		−	0.601809i
$668$	−10.5661	−	18.3010i	−0.408815	−	0.708088i
$669$	−33.3391	+	25.2847i	−1.28896	+	0.977563i
$670$	−4.17932	−	2.41293i	−0.161461	−	0.0932197i
$671$	−1.04063	+	10.0783i	−0.0401729	+	0.389067i
$672$	−6.83730	+	0.860968i	−0.263755	+	0.0332126i
$673$	−18.9668	+	10.9505i	−0.731116	+	0.422110i	−0.818830	−	0.574035i	$-0.805377\pi$
$673$	−18.9668	+	10.9505i	−0.731116	+	0.422110i	0.0877140	+	0.996146i	$0.472044\pi$
$674$			24.2453i			0.933893i
$675$	3.23247	−	4.06831i	0.124418	−	0.156589i
$676$	8.10319			0.311661
$677$	−7.04655	−	12.2050i	−0.270821	−	0.469076i	0.698251	−	0.715853i	$-0.253962\pi$
$677$	−7.04655	−	12.2050i	−0.270821	−	0.469076i	−0.969072	+	0.246777i	$0.920628\pi$
$678$	30.2775	−	3.81261i	1.16280	−	0.146422i
$679$	44.8471	+	25.8925i	1.72107	+	0.993662i
$680$	2.53286	+	1.46235i	0.0971307	+	0.0560784i
$681$	−32.8823	+	24.9383i	−1.26005	+	0.955636i
$682$	−0.736923	+	1.01820i	−0.0282182	+	0.0389889i
$683$		−	13.9425i		−	0.533496i	−0.963766	−	0.266748i	$-0.914051\pi$
$683$		−	13.9425i		−	0.533496i	0.963766	−	0.266748i	$-0.0859492\pi$
$684$	14.7201	+	4.12264i	0.562835	+	0.157633i
$685$	−16.2351			−0.620313
$686$	−6.30554	+	3.64050i	−0.240746	+	0.138995i
$687$	−14.5372	−	6.11774i	−0.554629	−	0.233406i
$688$	5.34893	+	3.08820i	0.203926	+	0.117737i
$689$	2.26237	−	3.91854i	0.0861895	−	0.149285i
$690$	6.37179	+	2.68146i	0.242570	+	0.102081i
$691$	8.16817	+	14.1477i	0.310732	+	0.538203i	0.978521	−	0.206147i	$-0.0660926\pi$
$691$	8.16817	+	14.1477i	0.310732	+	0.538203i	−0.667789	+	0.744350i	$0.732759\pi$
$692$	−8.49055			−0.322762
$693$	−5.82333	−	39.1568i	−0.221210	−	1.48745i
$694$	17.0908			0.648758
$695$	11.1260	+	19.2708i	0.422034	+	0.730984i
$696$	5.37414	−	4.07580i	0.203706	−	0.154493i
$697$	−8.24861	+	14.2870i	−0.312438	+	0.541159i
$698$	−2.99011	−	1.72634i	−0.113177	−	0.0653429i
$699$	−1.06885	−	8.48815i	−0.0404275	−	0.321051i
$700$	3.44565	−	1.98935i	0.130233	−	0.0751902i
$701$	−10.2733			−0.388016			−0.194008	−	0.981000i	$-0.562149\pi$
$701$	−10.2733			−0.388016			−0.194008	+	0.981000i	$0.562149\pi$
$702$	−10.6961	+	4.21999i	−0.403697	+	0.159273i
$703$			20.5435i			0.774811i
$704$	1.94455	−	2.68677i	0.0732880	−	0.101261i
$705$	−1.76793	−	14.0399i	−0.0665841	−	0.528772i
$706$	20.4677	+	11.8170i	0.770310	+	0.444739i
$707$	−26.9353	−	15.5511i	−1.01301	−	0.584859i
$708$	−13.9418	−	18.3830i	−0.523966	−	0.690874i
$709$	1.35871	+	2.35336i	0.0510274	+	0.0883821i	0.890411	−	0.455158i	$-0.150417\pi$
$709$	1.35871	+	2.35336i	0.0510274	+	0.0883821i	−0.839383	+	0.543540i	$0.817084\pi$
$710$	−11.7114			−0.439522
$711$	22.9553	−	22.4435i	0.860891	−	0.841696i
$712$		−	13.0159i		−	0.487790i
$713$	1.30991	−	0.756277i	0.0490565	−	0.0283228i
$714$	−7.81780	+	18.5770i	−0.292574	+	0.695225i
$715$	−7.30046	−	0.753805i	−0.273022	−	0.0281907i
$716$	−21.3639	−	12.3345i	−0.798408	−	0.460961i
$717$	−23.9277	−	10.0696i	−0.893596	−	0.376055i
$718$	2.13661	+	3.70072i	0.0797376	+	0.138110i
$719$			43.1328i			1.60858i	0.594235	+	0.804291i	$0.297455\pi$
$719$			43.1328i			1.60858i	−0.594235	+	0.804291i	$0.702545\pi$
$720$	0.743740	+	2.90635i	0.0277175	+	0.108313i
$721$			1.26143i			0.0469783i
$722$	−3.48201	−	6.03102i	−0.129587	−	0.224451i
$723$	−0.513201	−	0.676680i	−0.0190861	−	0.0251660i
$724$	−5.65796	+	9.79988i	−0.210276	+	0.364210i
$725$	−1.94708	+	3.37244i	−0.0723128	+	0.125249i
$726$	15.6803	+	10.8225i	0.581952	+	0.401661i
$727$	16.1512	+	27.9747i	0.599016	+	1.03753i	0.992967	+	0.118394i	$0.0377746\pi$
$727$	16.1512	+	27.9747i	0.599016	+	1.03753i	−0.393951	+	0.919131i	$0.628892\pi$
$728$	−8.80435			−0.326311
$729$	−19.7266	+	18.4354i	−0.730613	+	0.682792i
$730$	1.49541			0.0553474
$731$	15.6440	−	9.03205i	0.578613	−	0.334062i
$732$	5.24973	−	0.661057i	0.194036	−	0.0244334i
$733$	46.5487	+	26.8749i	1.71932	+	0.992647i	0.920179	+	0.391498i	$0.128043\pi$
$733$	46.5487	+	26.8749i	1.71932	+	0.992647i	0.799136	+	0.601150i	$0.205290\pi$
$734$	10.6794	−	18.4972i	0.394183	−	0.682746i
$735$	9.24186	+	12.1858i	0.340891	+	0.449481i
$736$	−3.45652	+	1.99562i	−0.127409	+	0.0735595i
$737$	6.53681	+	14.6099i	0.240786	+	0.538162i
$738$	−16.3937	+	4.19519i	−0.603461	+	0.154427i
$739$		−	25.9050i		−	0.952929i	−0.879194	−	0.476465i	$-0.841918\pi$
$739$		−	25.9050i		−	0.952929i	0.879194	−	0.476465i	$-0.158082\pi$
$740$	−3.49155	+	2.01585i	−0.128352	+	0.0741040i
$741$	18.0010	+	7.57541i	0.661283	+	0.278290i
$742$	4.06769	−	7.04544i	0.149330	−	0.258646i
$743$	−17.6520	+	30.5742i	−0.647589	+	1.12166i	0.336108	+	0.941823i	$0.390889\pi$
$743$	−17.6520	+	30.5742i	−0.647589	+	1.12166i	−0.983697	+	0.179833i	$0.942444\pi$
$744$	0.605002	+	0.254605i	0.0221805	+	0.00933427i
$745$	−4.79821	+	2.77025i	−0.175793	+	0.101494i
$746$			19.7699i			0.723827i
$747$	13.8251	+	14.1404i	0.505835	+	0.517371i
$748$	−3.96160	−	8.85426i	−0.144850	−	0.323744i
$749$	−56.2315	+	32.4653i	−2.05466	+	1.18626i
$750$	−1.04664	−	1.38005i	−0.0382180	−	0.0503923i
$751$	−19.3127	+	33.4506i	−0.704731	+	1.22063i	0.262058	+	0.965052i	$0.415599\pi$
$751$	−19.3127	+	33.4506i	−0.704731	+	1.22063i	−0.966789	+	0.255578i	$0.917734\pi$
$752$	7.07537	+	4.08496i	0.258012	+	0.148963i
$753$	30.2800	−	3.81293i	1.10347	−	0.138951i
$754$	7.46279	−	4.30864i	0.271779	−	0.156912i
$755$	−9.80145			−0.356711
$756$	−19.2312	+	7.58745i	−0.699433	+	0.275953i
$757$	−24.0187			−0.872973			−0.436487	−	0.899711i	$-0.643777\pi$
$757$	−24.0187			−0.872973			−0.436487	+	0.899711i	$0.643777\pi$
$758$	−7.88507	−	13.6573i	−0.286399	−	0.496057i
$759$	−11.9053	−	19.5947i	−0.432135	−	0.711244i
$760$	2.54775	−	4.41282i	0.0924164	−	0.160070i
$761$	13.4222	−	23.2478i	0.486553	−	0.842734i	−0.513328	−	0.858193i	$-0.671588\pi$
$761$	13.4222	−	23.2478i	0.486553	−	0.842734i	0.999881	+	0.0154588i	$0.00492087\pi$
$762$	−0.510527	−	0.673154i	−0.0184944	−	0.0243858i
$763$	31.3782	+	54.3487i	1.13597	+	1.96756i
$764$		−	0.357183i		−	0.0129224i
$765$	8.44897	+	2.36630i	0.305473	+	0.0855537i
$766$			29.1678i			1.05387i
$767$	−14.7383	−	25.5275i	−0.532169	−	0.921744i
$768$	−1.59644	−	0.671837i	−0.0576067	−	0.0242428i
$769$	28.9614	+	16.7209i	1.04438	+	0.602971i	0.921070	−	0.389398i	$-0.127317\pi$
$769$	28.9614	+	16.7209i	1.04438	+	0.602971i	0.123307	+	0.992369i	$0.460650\pi$
$770$	−13.1260	−	1.35532i	−0.473030	−	0.0488424i
$771$	−11.1619	+	26.5234i	−0.401986	+	0.955216i
$772$	−9.64082	+	5.56613i	−0.346981	+	0.200329i
$773$		−	31.7570i		−	1.14222i	−0.820874	−	0.571110i	$-0.806513\pi$
$773$		−	31.7570i		−	1.14222i	0.820874	−	0.571110i	$-0.193487\pi$
$774$	17.8427	+	4.99718i	0.641341	+	0.179620i
$775$	−0.378968			−0.0136129
$776$	6.50778	+	11.2718i	0.233616	+	0.404634i
$777$	−16.7891	−	22.1372i	−0.602305	−	0.794168i
$778$	6.24669	+	3.60653i	0.223955	+	0.129300i
$779$	24.8913	+	14.3710i	0.891822	+	0.514894i
$780$	0.478854	+	3.80278i	0.0171457	+	0.136161i
$781$	31.4659	+	22.7734i	1.12594	+	0.814898i
$782$			11.6732i			0.417431i
$783$	12.5878	−	15.8426i	0.449850	−	0.566170i
$784$	−8.83000			−0.315357
$785$	−10.7384	+	6.19979i	−0.383268	+	0.221280i
$786$	0.375418	+	2.98135i	0.0133907	+	0.106341i
$787$	−5.05960	−	2.92116i	−0.180355	−	0.104128i	0.407104	−	0.913382i	$-0.366539\pi$
$787$	−5.05960	−	2.92116i	−0.180355	−	0.104128i	−0.587460	+	0.809253i	$0.699872\pi$
$788$	−13.7113	+	23.7486i	−0.488444	+	0.846009i
$789$	28.5897	−	21.6827i	1.01782	−	0.771926i
$790$	−5.35063	−	9.26757i	−0.190367	−	0.329725i
$791$	70.0997			2.49246
$792$	3.65328	−	9.25492i	0.129814	−	0.328859i
$793$	6.76004			0.240056
$794$	−2.94148	−	5.09479i	−0.104389	−	0.180807i
$795$	−3.26431	−	1.37373i	−0.115773	−	0.0487211i
$796$	0.487136	−	0.843744i	0.0172661	−	0.0299057i
$797$	20.6654	+	11.9312i	0.732008	+	0.422625i	0.819156	−	0.573571i	$-0.194442\pi$
$797$	20.6654	+	11.9312i	0.732008	+	0.422625i	−0.0871486	+	0.996195i	$0.527775\pi$
$798$	32.3653	+	13.6204i	1.14572	+	0.482157i
$799$	20.6933	−	11.9473i	0.732075	−	0.422664i
$800$	1.00000			0.0353553
$801$	−9.68042	−	37.8286i	−0.342041	−	1.33661i
$802$			23.9517i			0.845764i
$803$	−4.01781	−	2.90789i	−0.141785	−	0.102617i
$804$	6.65994	−	5.05096i	0.234878	−	0.178134i
$805$	13.7524	+	7.93996i	0.484709	+	0.279847i
$806$	0.726257	+	0.419305i	0.0255813	+	0.0147694i
$807$	39.4557	−	4.96835i	1.38891	−	0.174894i
$808$	−3.90859	−	6.76988i	−0.137504	−	0.238164i
$809$	−35.2716			−1.24008			−0.620042	−	0.784568i	$-0.712885\pi$
$809$	−35.2716			−1.24008			−0.620042	+	0.784568i	$0.712885\pi$
$810$	4.32313	+	7.89370i	0.151899	+	0.277356i
$811$		−	29.0595i		−	1.02042i	−0.860051	−	0.510208i	$-0.829568\pi$
$811$		−	29.0595i		−	1.02042i	0.860051	−	0.510208i	$-0.170432\pi$
$812$	13.4179	−	7.74684i	0.470877	−	0.271861i
$813$	36.4100	−	4.58483i	1.27695	−	0.160797i
$814$	13.3009	+	1.37338i	0.466196	+	0.0481369i
$815$	4.78549	+	2.76290i	0.167628	+	0.0967803i
$816$	−4.03622	+	3.06111i	−0.141296	+	0.107160i
$817$	−15.7359	−	27.2554i	−0.550530	−	0.953546i
$818$		−	32.6543i		−	1.14173i
$819$	−25.5885	+	6.54814i	−0.894134	+	0.228811i
$820$			5.64066i			0.196981i
$821$	20.5652	+	35.6200i	0.717731	+	1.24315i	0.961897	+	0.273412i	$0.0881524\pi$
$821$	20.5652	+	35.6200i	0.717731	+	1.24315i	−0.244166	+	0.969733i	$0.578514\pi$
$822$	10.9074	−	25.9185i	0.380438	−	0.904012i
$823$	−19.2130	+	33.2778i	−0.669722	+	1.15999i	0.308260	+	0.951302i	$0.400253\pi$
$823$	−19.2130	+	33.2778i	−0.669722	+	1.15999i	−0.977982	+	0.208690i	$0.933080\pi$
$824$	−0.158524	+	0.274571i	−0.00552243	+	0.00956514i
$825$	0.128512	+	5.74312i	0.00447423	+	0.199950i
$826$	−26.4991	−	45.8978i	−0.922022	−	1.59699i
$827$	−10.2130			−0.355140			−0.177570	−	0.984108i	$-0.556824\pi$
$827$	−10.2130			−0.355140			−0.177570	+	0.984108i	$0.556824\pi$
$828$	−8.56161	+	8.37071i	−0.297537	+	0.290902i
$829$	−37.9429			−1.31781			−0.658905	−	0.752226i	$-0.728980\pi$
$829$	−37.9429			−1.31781			−0.658905	+	0.752226i	$0.728980\pi$
$830$	5.70881	−	3.29598i	0.198156	−	0.114405i
$831$	20.7210	+	27.3216i	0.718802	+	0.947776i
$832$	−1.91641	−	1.10644i	−0.0664394	−	0.0383588i
$833$	−12.9125	+	22.3651i	−0.447392	+	0.774906i
$834$	−38.2397	+	4.81522i	−1.32413	+	0.166738i
$835$	−18.3010	+	10.5661i	−0.633333	+	0.365655i
$836$	−15.4262	+	6.90202i	−0.533525	+	0.238711i
$837$	1.94771	+	0.290006i	0.0673226	+	0.0100241i
$838$			3.94572i			0.136303i
$839$	7.22783	−	4.17299i	0.249533	−	0.144068i	−0.370018	−	0.929025i	$-0.620648\pi$
$839$	7.22783	−	4.17299i	0.249533	−	0.144068i	0.619550	+	0.784957i	$0.287315\pi$
$840$	0.860968	+	6.83730i	0.0297062	+	0.235909i
$841$	6.91775	−	11.9819i	0.238543	−	0.413169i
$842$	6.89797	−	11.9476i	0.237720	−	0.411743i
$843$	−1.01852	+	0.772454i	−0.0350796	+	0.0266047i
$844$	11.9858	−	6.92003i	0.412570	−	0.238197i
$845$		−	8.10319i		−	0.278758i
$846$	23.6016	+	6.61009i	0.811440	+	0.227260i
$847$	32.6312	+	29.1657i	1.12122	+	1.00214i
$848$	1.77079	−	1.02237i	0.0608093	−	0.0351083i
$849$	−17.3313	+	41.1832i	−0.594807	+	1.41340i
$850$	1.46235	−	2.53286i	0.0501581	−	0.0868763i
$851$	−13.9356	−	8.04573i	−0.477707	−	0.275804i
$852$	7.86816	−	18.6966i	0.269559	−	0.640536i
$853$	42.7598	−	24.6874i	1.46407	−	0.845280i	0.464872	−	0.885378i	$-0.346100\pi$
$853$	42.7598	−	24.6874i	1.46407	−	0.845280i	0.999196	+	0.0400982i	$0.0127671\pi$
$854$	12.1544			0.415914
$855$	4.12264	−	14.7201i	0.140991	−	0.503415i
$856$	−16.3196			−0.557792
$857$	3.95232	+	6.84561i	0.135009	+	0.233842i	0.925601	−	0.378501i	$-0.123560\pi$
$857$	3.95232	+	6.84561i	0.135009	+	0.233842i	−0.790592	+	0.612343i	$0.790227\pi$
$858$	6.10812	−	11.1483i	0.208528	−	0.380598i
$859$	2.58920	−	4.48462i	0.0883422	−	0.153013i	−0.818468	−	0.574552i	$-0.805176\pi$
$859$	2.58920	−	4.48462i	0.0883422	−	0.153013i	0.906811	+	0.421538i	$0.138510\pi$
$860$	3.08820	−	5.34893i	0.105307	−	0.182397i
$861$	−38.5669	+	4.85643i	−1.31436	+	0.165507i
$862$	2.04471	+	3.54155i	0.0696432	+	0.120626i
$863$			41.4051i			1.40945i	0.709482	+	0.704723i	$0.248929\pi$
$863$			41.4051i			1.40945i	−0.709482	+	0.704723i	$0.751071\pi$
$864$	−5.13949	−	0.765251i	−0.174849	−	0.0260344i
$865$			8.49055i			0.288687i
$866$	5.96210	+	10.3267i	0.202600	+	0.350914i
$867$	−1.82771	−	14.5146i	−0.0620722	−	0.492941i
$868$	1.30579	+	0.753899i	0.0443215	+	0.0255890i
$869$	−3.64534	+	35.3044i	−0.123660	+	1.19762i
$870$	−4.07580	−	5.37414i	−0.138182	−	0.182200i
$871$	9.24831	−	5.33952i	0.313367	−	0.180923i
$872$			15.7731i			0.534146i
$873$	27.2972	+	27.9197i	0.923869	+	0.944939i
$874$	20.3373			0.687920
$875$	−1.98935	−	3.44565i	−0.0672522	−	0.116484i
$876$	−1.00467	+	2.38733i	−0.0339446	+	0.0806605i
$877$	−12.6351	−	7.29489i	−0.426658	−	0.246331i	0.271264	−	0.962505i	$-0.412558\pi$
$877$	−12.6351	−	7.29489i	−0.426658	−	0.246331i	−0.697922	+	0.716174i	$0.745892\pi$
$878$	−0.0368928	−	0.0213001i	−0.00124507	−	0.000718842i
$879$	−4.85741	−	2.04416i	−0.163836	−	0.0689477i
$880$	−2.68677	−	1.94455i	−0.0905710	−	0.0655508i
$881$			0.886652i			0.0298721i	0.999888	+	0.0149360i	$0.00475447\pi$
$881$			0.886652i			0.0298721i	−0.999888	+	0.0149360i	$0.995246\pi$
$882$	−25.6630	+	6.56722i	−0.864119	+	0.221130i
$883$	3.01922			0.101605			0.0508025	−	0.998709i	$-0.483822\pi$
$883$	3.01922			0.101605			0.0508025	+	0.998709i	$0.483822\pi$
$884$	−5.60490	+	3.23599i	−0.188513	+	0.108838i
$885$	−18.3830	+	13.9418i	−0.617937	+	0.468649i
$886$	17.5422	+	10.1280i	0.589343	+	0.340257i
$887$	−20.4182	+	35.3653i	−0.685576	+	1.18745i	0.287680	+	0.957727i	$0.407116\pi$
$887$	−20.4182	+	35.3653i	−0.685576	+	1.18745i	−0.973256	+	0.229725i	$0.926217\pi$
$888$	−0.872437	−	6.92839i	−0.0292771	−	0.232501i
$889$	−0.970354	−	1.68070i	−0.0325446	−	0.0563690i
$890$	−13.0159			−0.436293
$891$	3.73444	−	29.6151i	0.125109	−	0.992143i
$892$	−24.1579			−0.808867
$893$	−20.8149	−	36.0525i	−0.696544	−	1.20645i
$894$	−1.19893	−	9.52122i	−0.0400983	−	0.318437i
$895$	−12.3345	+	21.3639i	−0.412296	+	0.714118i
$896$	−3.44565	−	1.98935i	−0.115111	−	0.0664594i
$897$	−12.1888	+	9.24407i	−0.406971	+	0.308651i
$898$	23.3643	−	13.4894i	0.779677	−	0.450147i
$899$	−1.47576			−0.0492195
$900$	2.90635	−	0.743740i	0.0968782	−	0.0247913i
$901$		−	5.98023i		−	0.199230i
$902$	10.9686	−	15.1552i	0.365213	−	0.504612i
$903$	39.2311	+	16.5097i	1.30553	+	0.549410i
$904$	15.2583	+	8.80939i	0.507484	+	0.292996i
$905$	9.79988	+	5.65796i	0.325759	+	0.188077i
$906$	6.58498	−	15.6475i	0.218771	−	0.519853i
$907$	−22.0179	−	38.1360i	−0.731091	−	1.26629i	−0.956417	−	0.292003i	$-0.905678\pi$
$907$	−22.0179	−	38.1360i	−0.731091	−	1.26629i	0.225327	−	0.974283i	$-0.427655\pi$
$908$	−23.8269			−0.790723
$909$	−16.3948	−	16.7686i	−0.543780	−	0.556181i
$910$			8.80435i			0.291861i
$911$	−46.6225	+	26.9175i	−1.54467	+	0.891818i	−0.546139	+	0.837694i	$0.683903\pi$
$911$	−46.6225	+	26.9175i	−1.54467	+	0.891818i	−0.998534	+	0.0541232i	$0.982764\pi$
$912$	5.33316	+	7.03203i	0.176599	+	0.232854i
$913$	−21.7475	−	2.24552i	−0.719736	−	0.0743159i
$914$	0.0365469	+	0.0211003i	0.00120886	+	0.000697937i
$915$	−0.661057	−	5.24973i	−0.0218539	−	0.173551i
$916$	−4.55299	−	7.88602i	−0.150435	−	0.260561i
$917$			6.90253i			0.227942i
$918$	−9.45399	+	11.8985i	−0.312028	+	0.392711i
$919$		−	11.5211i		−	0.380045i	−0.981780	−	0.190022i	$-0.939144\pi$
$919$		−	11.5211i		−	0.380045i	0.981780	−	0.190022i	$-0.0608560\pi$
$920$	1.99562	+	3.45652i	0.0657936	+	0.113958i
$921$	18.8485	−	2.37345i	0.621080	−	0.0782077i
$922$	−5.90883	+	10.2344i	−0.194597	+	0.337052i
$923$	12.9579	−	22.4438i	0.426516	−	0.738747i
$924$	10.9823	−	20.0445i	0.361290	−	0.659414i
$925$	2.01585	+	3.49155i	0.0662807	+	0.114801i
$926$	14.7217			0.483784
$927$	−0.256515	+	0.915899i	−0.00842507	+	0.0300821i
$928$	3.89416			0.127832
$929$	6.58112	−	3.79961i	0.215920	−	0.124661i	−0.388140	−	0.921600i	$-0.626882\pi$
$929$	6.58112	−	3.79961i	0.215920	−	0.124661i	0.604059	+	0.796939i	$0.293549\pi$
$930$	0.254605	−	0.605002i	0.00834882	−	0.0198388i
$931$	38.9652	+	22.4966i	1.27703	+	0.737296i
$932$	2.46967	−	4.27759i	0.0808967	−	0.140117i
$933$	5.96997	−	14.1861i	0.195448	−	0.464431i
$934$	−8.06276	+	4.65503i	−0.263821	+	0.152317i
$935$	−8.85426	+	3.96160i	−0.289565	+	0.129558i
$936$	−6.39264	−	1.79038i	−0.208950	−	0.0585205i
$937$		−	26.9281i		−	0.879702i	−0.898071	−	0.439851i	$-0.855031\pi$
$937$		−	26.9281i		−	0.879702i	0.898071	−	0.439851i	$-0.144969\pi$
$938$	16.6282	−	9.60032i	0.542931	−	0.313462i
$939$	40.0415	−	30.3679i	1.30670	−	0.991018i
$940$	4.08496	−	7.07537i	0.133237	−	0.230773i
$941$	−27.1520	+	47.0287i	−0.885131	+	1.53309i	−0.0395676	+	0.999217i	$0.512598\pi$
$941$	−27.1520	+	47.0287i	−0.885131	+	1.53309i	−0.845563	+	0.533875i	$0.820735\pi$
$942$	−2.68320	−	21.3084i	−0.0874235	−	0.694266i
$943$	−19.4970	+	11.2566i	−0.634911	+	0.366566i
$944$		−	13.3205i		−	0.433546i
$945$	7.58745	+	19.2312i	0.246820	+	0.625592i
$946$	−18.6985	+	8.36616i	−0.607942	+	0.272007i
$947$	−9.73707	+	5.62170i	−0.316412	+	0.182681i	−0.649792	−	0.760112i	$-0.725144\pi$
$947$	−9.73707	+	5.62170i	−0.316412	+	0.182681i	0.333380	+	0.942793i	$0.391811\pi$
$948$	18.3899	−	2.31570i	0.597277	−	0.0752104i
$949$	−1.65457	+	2.86580i	−0.0537097	+	0.0930279i
$950$	−4.41282	−	2.54775i	−0.143171	−	0.0826598i
$951$	−30.0979	−	39.6855i	−0.975991	−	1.28689i
$952$	−10.0775	+	5.81823i	−0.326613	+	0.188570i
$953$	24.1737			0.783064			0.391532	−	0.920164i	$-0.371945\pi$
$953$	24.1737			0.783064			0.391532	+	0.920164i	$0.371945\pi$
$954$	4.38616	−	4.28837i	0.142007	−	0.138841i
$955$	−0.357183			−0.0115582
$956$	−7.49406	−	12.9801i	−0.242375	−	0.419806i
$957$	0.500448	+	22.3647i	0.0161772	+	0.722947i
$958$	−1.01412	+	1.75651i	−0.0327649	+	0.0567504i
$959$	32.2973	−	55.9406i	1.04293	−	1.80642i
$960$	−0.671837	+	1.59644i	−0.0216834	+	0.0515250i
$961$	15.4282	+	26.7224i	0.497684	+	0.862013i
$962$		−	8.92163i		−	0.287645i
$963$	−47.4304	+	12.1375i	−1.52842	+	0.391126i
$964$		−	0.490330i		−	0.0157925i
$965$	5.56613	+	9.64082i	0.179180	+	0.310349i
$966$	−21.9151	+	16.6206i	−0.705106	+	0.534759i
$967$	−33.1392	−	19.1329i	−1.06569	−	0.615274i	−0.138686	−	0.990336i	$-0.544288\pi$
$967$	−33.1392	−	19.1329i	−1.06569	−	0.615274i	−0.927000	+	0.375062i	$0.877621\pi$
$968$	3.43745	+	10.4491i	0.110484	+	0.335847i
$969$	25.6101	−	3.22487i	0.822714	−	0.103598i
$970$	11.2718	−	6.50778i	0.361916	−	0.208952i
$971$		−	36.2801i		−	1.16428i	−0.813087	−	0.582142i	$-0.802215\pi$
$971$		−	36.2801i		−	1.16428i	0.813087	−	0.582142i	$-0.197785\pi$
$972$	−15.5063	+	1.59836i	−0.497365	+	0.0512675i
$973$	−88.5340			−2.83827
$974$	17.2868	+	29.9415i	0.553903	+	0.959389i
$975$	3.80278	−	0.478854i	0.121786	−	0.0153356i
$976$	2.64559	+	1.52743i	0.0846834	+	0.0488920i
$977$	36.8926	+	21.3000i	1.18030	+	0.681446i	0.956084	−	0.293093i	$-0.0946846\pi$
$977$	36.8926	+	21.3000i	1.18030	+	0.681446i	0.224216	+	0.974540i	$0.428018\pi$
$978$	−7.62589	+	5.78355i	−0.243849	+	0.184938i
$979$	34.9706	+	25.3100i	1.11767	+	0.808911i
$980$			8.83000i			0.282064i
$981$	11.7311	+	45.8422i	0.374546	+	1.46363i
$982$	3.50359			0.111804
$983$	−26.8425	+	15.4975i	−0.856144	+	0.494295i	−0.862719	−	0.505683i	$-0.831240\pi$
$983$	−26.8425	+	15.4975i	−0.856144	+	0.494295i	0.00657501	+	0.999978i	$0.497907\pi$
$984$	−9.00501	−	3.78961i	−0.287069	−	0.120808i
$985$	23.7486	+	13.7113i	0.756693	+	0.436877i
$986$	5.69461	−	9.86336i	0.181353	−	0.314113i
$987$	51.8934	+	21.8385i	1.65179	+	0.695126i
$988$	5.63784	+	9.76502i	0.179364	+	0.310667i
$989$	24.6515			0.783873
$990$	−9.25492	−	3.65328i	−0.294141	−	0.116109i
$991$	39.7460			1.26257			0.631287	−	0.775549i	$-0.282527\pi$
$991$	39.7460			1.26257			0.631287	+	0.775549i	$0.282527\pi$
$992$	0.189484	+	0.328196i	0.00601613	+	0.0104202i
$993$	0.644778	−	0.489006i	0.0204614	−	0.0155181i
$994$	23.2981	−	40.3534i	0.738970	−	1.27993i
$995$	−0.843744	−	0.487136i	−0.0267485	−	0.0154432i
$996$	1.42647	+	11.3282i	0.0451993	+	0.358947i
$997$	−10.1943	+	5.88569i	−0.322857	+	0.186402i	−0.652666	−	0.757646i	$-0.726349\pi$
$997$	−10.1943	+	5.88569i	−0.322857	+	0.186402i	0.329808	+	0.944048i	$0.393016\pi$
$998$	−13.2121			−0.418223
$999$	−7.68852	−	19.4874i	−0.243254	−	0.616555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.t.b.131.14	yes	48
3.2	odd	2		2970.2.t.a.2771.3		48
9.2	odd	6		990.2.t.a.461.14	yes	48
9.7	even	3		2970.2.t.b.791.3		48
11.10	odd	2		990.2.t.a.131.14	✓	48
33.32	even	2		2970.2.t.b.2771.3		48
99.43	odd	6		2970.2.t.a.791.3		48
99.65	even	6	inner	990.2.t.b.461.14	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.t.a.131.14	✓	48	11.10	odd	2
990.2.t.a.461.14	yes	48	9.2	odd	6
990.2.t.b.131.14	yes	48	1.1	even	1	trivial
990.2.t.b.461.14	yes	48	99.65	even	6	inner
2970.2.t.a.791.3		48	99.43	odd	6
2970.2.t.a.2771.3		48	3.2	odd	2
2970.2.t.b.791.3		48	9.7	even	3
2970.2.t.b.2771.3		48	33.32	even	2

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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.216395 + 1.71848i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.38005 + 1.04664i) q^{6} +(-3.44565 + 1.98935i) q^{7} -1.00000 q^{8} +(-2.90635 + 0.743740i) q^{9} +1.00000i q^{10} +(1.94455 - 2.68677i) q^{11} +(-1.59644 - 0.671837i) q^{12} +(-1.91641 - 1.10644i) q^{13} +(-3.44565 - 1.98935i) q^{14} +(-0.671837 + 1.59644i) q^{15} +(-0.500000 - 0.866025i) q^{16} -2.92469 q^{17} +(-2.09727 - 2.14510i) q^{18} +5.09549i q^{19} +(-0.866025 + 0.500000i) q^{20} +(-4.16427 - 5.49080i) q^{21} +(3.29908 + 0.340645i) q^{22} +(-3.45652 - 1.99562i) q^{23} +(-0.216395 - 1.71848i) q^{24} +(0.500000 + 0.866025i) q^{25} -2.21287i q^{26} +(-1.90702 - 4.83356i) q^{27} -3.97869i q^{28} +(1.94708 + 3.37244i) q^{29} +(-1.71848 + 0.216395i) q^{30} +(-0.189484 + 0.328196i) q^{31} +(0.500000 - 0.866025i) q^{32} +(5.03795 + 2.76027i) q^{33} +(-1.46235 - 2.53286i) q^{34} -3.97869 q^{35} +(0.809076 - 2.88884i) q^{36} +4.03169 q^{37} +(-4.41282 + 2.54775i) q^{38} +(1.48669 - 3.53273i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(2.82033 - 4.88496i) q^{41} +(2.67303 - 6.35176i) q^{42} +(-5.34893 + 3.08820i) q^{43} +(1.35454 + 3.02741i) q^{44} +(-2.88884 - 0.809076i) q^{45} -3.99124i q^{46} +(-7.07537 + 4.08496i) q^{47} +(1.38005 - 1.04664i) q^{48} +(4.41500 - 7.64700i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-0.632888 - 5.02603i) q^{51} +(1.91641 - 1.10644i) q^{52} +2.04474i q^{53} +(3.23247 - 4.06831i) q^{54} +(3.02741 - 1.35454i) q^{55} +(3.44565 - 1.98935i) q^{56} +(-8.75650 + 1.10264i) q^{57} +(-1.94708 + 3.37244i) q^{58} +(11.5359 + 6.66026i) q^{59} +(-1.04664 - 1.38005i) q^{60} +(-2.64559 + 1.52743i) q^{61} -0.378968 q^{62} +(8.53470 - 8.34440i) q^{63} +1.00000 q^{64} +(-1.10644 - 1.91641i) q^{65} +(0.128512 + 5.74312i) q^{66} +(-2.41293 + 4.17932i) q^{67} +(1.46235 - 2.53286i) q^{68} +(2.68146 - 6.37179i) q^{69} +(-1.98935 - 3.44565i) q^{70} +11.7114i q^{71} +(2.90635 - 0.743740i) q^{72} -1.49541i q^{73} +(2.01585 + 3.49155i) q^{74} +(-1.38005 + 1.04664i) q^{75} +(-4.41282 - 2.54775i) q^{76} +(-1.35532 + 13.1260i) q^{77} +(3.80278 - 0.478854i) q^{78} +(-9.26757 + 5.35063i) q^{79} -1.00000i q^{80} +(7.89370 - 4.32313i) q^{81} +5.64066 q^{82} +(-3.29598 - 5.70881i) q^{83} +(6.83730 - 0.860968i) q^{84} +(-2.53286 - 1.46235i) q^{85} +(-5.34893 - 3.08820i) q^{86} +(-5.37414 + 4.07580i) q^{87} +(-1.94455 + 2.68677i) q^{88} +13.0159i q^{89} +(-0.743740 - 2.90635i) q^{90} +8.80435 q^{91} +(3.45652 - 1.99562i) q^{92} +(-0.605002 - 0.254605i) q^{93} +(-7.07537 - 4.08496i) q^{94} +(-2.54775 + 4.41282i) q^{95} +(1.59644 + 0.671837i) q^{96} +(-6.50778 - 11.2718i) q^{97} +8.83000 q^{98} +(-3.65328 + 9.25492i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} - 48 q^{8} + 10 q^{9} - 12 q^{11} + 4 q^{12} - 24 q^{13} - 4 q^{15} - 24 q^{16} + 12 q^{17} + 8 q^{18} + 16 q^{21} - 6 q^{22} + 36 q^{23} + 2 q^{24} + 24 q^{25}+ \cdots - 44 q^{99}+O(q^{100}) \) 48 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 - 48 * q^8 + 10 * q^9 - 12 * q^11 + 4 * q^12 - 24 * q^13 - 4 * q^15 - 24 * q^16 + 12 * q^17 + 8 * q^18 + 16 * q^21 - 6 * q^22 + 36 * q^23 + 2 * q^24 + 24 * q^25 - 8 * q^27 - 8 * q^30 + 24 * q^32 + 12 * q^33 + 6 * q^34 - 2 * q^36 - 6 * q^38 + 40 * q^39 + 6 * q^41 + 8 * q^42 - 30 * q^43 + 6 * q^44 - 2 * q^48 + 24 * q^49 - 24 * q^50 - 22 * q^51 + 24 * q^52 - 22 * q^54 - 40 * q^57 - 54 * q^59 - 4 * q^60 + 38 * q^63 + 48 * q^64 - 12 * q^66 - 6 * q^67 - 6 * q^68 + 76 * q^69 - 10 * q^72 + 2 * q^75 - 6 * q^76 - 18 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 - 36 * q^83 - 8 * q^84 - 30 * q^86 + 44 * q^87 + 12 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 - 4 * q^96 + 6 * q^97 + 48 * q^98 - 44 * q^99

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