LMFDB - Embedded newform 990.2.t.a.131.11

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			131.11
Character	$\chi$	$=$	990.131
Dual form			990.2.t.a.461.11

$q$-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} +(-0.234765 - 1.71607i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.36878 + 1.06135i) q^{6} +(3.20594 - 1.85095i) q^{7} +1.00000 q^{8} +(-2.88977 + 0.805744i) q^{9} +1.00000i q^{10} +(3.31504 + 0.102382i) q^{11} +(1.60354 + 0.654721i) q^{12} +(-1.47269 - 0.850259i) q^{13} +(-3.20594 - 1.85095i) q^{14} +(-0.654721 + 1.60354i) q^{15} +(-0.500000 - 0.866025i) q^{16} -6.30104 q^{17} +(2.14268 + 2.09974i) q^{18} -8.13491i q^{19} +(0.866025 - 0.500000i) q^{20} +(-3.92900 - 5.06707i) q^{21} +(-1.56886 - 2.92210i) q^{22} +(5.99664 + 3.46216i) q^{23} +(-0.234765 - 1.71607i) q^{24} +(0.500000 + 0.866025i) q^{25} +1.70052i q^{26} +(2.06113 + 4.76988i) q^{27} +3.70190i q^{28} +(-2.93922 - 5.09088i) q^{29} +(1.71607 - 0.234765i) q^{30} +(4.67635 - 8.09968i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.602562 - 5.71287i) q^{33} +(3.15052 + 5.45686i) q^{34} -3.70190 q^{35} +(0.747091 - 2.90549i) q^{36} -4.24407 q^{37} +(-7.04504 + 4.06746i) q^{38} +(-1.11337 + 2.72685i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(0.847146 - 1.46730i) q^{41} +(-2.42371 + 5.93615i) q^{42} +(-0.116302 + 0.0671471i) q^{43} +(-1.74619 + 2.81972i) q^{44} +(2.90549 + 0.747091i) q^{45} -6.92433i q^{46} +(-5.80744 + 3.35293i) q^{47} +(-1.36878 + 1.06135i) q^{48} +(3.35205 - 5.80591i) q^{49} +(0.500000 - 0.866025i) q^{50} +(1.47926 + 10.8130i) q^{51} +(1.47269 - 0.850259i) q^{52} +11.7272i q^{53} +(3.10027 - 4.16993i) q^{54} +(-2.81972 - 1.74619i) q^{55} +(3.20594 - 1.85095i) q^{56} +(-13.9601 + 1.90979i) q^{57} +(-2.93922 + 5.09088i) q^{58} +(-9.11652 - 5.26343i) q^{59} +(-1.06135 - 1.36878i) q^{60} +(-12.3423 + 7.12584i) q^{61} -9.35271 q^{62} +(-7.77305 + 7.93200i) q^{63} +1.00000 q^{64} +(0.850259 + 1.47269i) q^{65} +(-4.64621 + 3.37827i) q^{66} +(1.52684 - 2.64456i) q^{67} +(3.15052 - 5.45686i) q^{68} +(4.53350 - 11.1034i) q^{69} +(1.85095 + 3.20594i) q^{70} +7.72800i q^{71} +(-2.88977 + 0.805744i) q^{72} -4.82386i q^{73} +(2.12203 + 3.67547i) q^{74} +(1.36878 - 1.06135i) q^{75} +(7.04504 + 4.06746i) q^{76} +(10.8173 - 5.80776i) q^{77} +(2.91820 - 0.399222i) q^{78} +(4.26744 - 2.46381i) q^{79} +1.00000i q^{80} +(7.70155 - 4.65683i) q^{81} -1.69429 q^{82} +(0.208818 + 0.361683i) q^{83} +(6.35271 - 0.869077i) q^{84} +(5.45686 + 3.15052i) q^{85} +(0.116302 + 0.0671471i) q^{86} +(-8.04626 + 6.23905i) q^{87} +(3.31504 + 0.102382i) q^{88} -4.53823i q^{89} +(-0.805744 - 2.88977i) q^{90} -6.29516 q^{91} +(-5.99664 + 3.46216i) q^{92} +(-14.9974 - 6.12341i) q^{93} +(5.80744 + 3.35293i) q^{94} +(-4.06746 + 7.04504i) q^{95} +(1.60354 + 0.654721i) q^{96} +(6.30071 + 10.9132i) q^{97} -6.70409 q^{98} +(-9.66221 + 2.37522i) 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} - 6 q^{11} + 4 q^{12} + 24 q^{13} - 4 q^{15} - 24 q^{16} - 12 q^{17} - 8 q^{18} - 16 q^{21} + 12 q^{22} + 36 q^{23} - 2 q^{24} + 24 q^{25}+ \cdots - 48 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 - 6 * q^11 + 4 * q^12 + 24 * q^13 - 4 * q^15 - 24 * q^16 - 12 * q^17 - 8 * q^18 - 16 * q^21 + 12 * q^22 + 36 * q^23 - 2 * q^24 + 24 * q^25 - 8 * q^27 + 8 * q^30 - 24 * q^32 + 2 * 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 + 8 * q^66 - 6 * q^67 + 6 * q^68 + 76 * q^69 + 10 * q^72 + 2 * q^75 + 6 * q^76 + 6 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 + 36 * q^83 + 8 * q^84 - 30 * q^86 - 44 * q^87 - 6 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 + 4 * q^96 + 6 * q^97 - 48 * q^98 - 48 * 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
$3$	−0.234765	−	1.71607i	−0.135541	−	0.990772i
$3$	−0.234765	−	1.71607i	−0.135541	−	0.990772i
$4$	−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
$6$	−1.36878	+	1.06135i	−0.558800	+	0.433293i
$7$	3.20594	−	1.85095i	1.21173	−	0.699594i	0.248596	−	0.968607i	$-0.420031\pi$
$7$	3.20594	−	1.85095i	1.21173	−	0.699594i	0.963136	+	0.269013i	$0.0866975\pi$
$8$	1.00000			0.353553
$9$	−2.88977	+	0.805744i	−0.963257	+	0.268581i
$10$			1.00000i			0.316228i
$11$	3.31504	+	0.102382i	0.999523	+	0.0308692i
$11$	3.31504	+	0.102382i	0.999523	+	0.0308692i
$12$	1.60354	+	0.654721i	0.462902	+	0.189002i
$13$	−1.47269	−	0.850259i	−0.408451	−	0.235819i	0.281673	−	0.959511i	$-0.409111\pi$
$13$	−1.47269	−	0.850259i	−0.408451	−	0.235819i	−0.690124	+	0.723691i	$0.742444\pi$
$14$	−3.20594	−	1.85095i	−0.856824	−	0.494688i
$15$	−0.654721	+	1.60354i	−0.169048	+	0.414032i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−6.30104			−1.52823			−0.764113	−	0.645082i	$-0.776823\pi$
$17$	−6.30104			−1.52823			−0.764113	+	0.645082i	$0.776823\pi$
$18$	2.14268	+	2.09974i	0.505035	+	0.494914i
$19$		−	8.13491i		−	1.86628i	−0.359517	−	0.933139i	$-0.617058\pi$
$19$		−	8.13491i		−	1.86628i	0.359517	−	0.933139i	$-0.382942\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$	−3.92900	−	5.06707i	−0.857378	−	1.10573i
$22$	−1.56886	−	2.92210i	−0.334481	−	0.622995i
$23$	5.99664	+	3.46216i	1.25039	+	0.721911i	0.971186	−	0.238322i	$-0.0765974\pi$
$23$	5.99664	+	3.46216i	1.25039	+	0.721911i	0.279200	+	0.960233i	$0.409931\pi$
$24$	−0.234765	−	1.71607i	−0.0479212	−	0.350291i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$			1.70052i			0.333499i
$27$	2.06113	+	4.76988i	0.396664	+	0.917964i
$28$			3.70190i			0.699594i
$29$	−2.93922	−	5.09088i	−0.545799	−	0.945352i	−0.998556	−	0.0537180i	$-0.982893\pi$
$29$	−2.93922	−	5.09088i	−0.545799	−	0.945352i	0.452757	−	0.891634i	$-0.350441\pi$
$30$	1.71607	−	0.234765i	0.313310	−	0.0428620i
$31$	4.67635	−	8.09968i	0.839898	−	1.45475i	−0.0500817	−	0.998745i	$-0.515948\pi$
$31$	4.67635	−	8.09968i	0.839898	−	1.45475i	0.889979	−	0.456001i	$-0.150718\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−0.602562	−	5.71287i	−0.104893	−	0.994484i
$34$	3.15052	+	5.45686i	0.540310	+	0.935844i
$35$	−3.70190			−0.625736
$36$	0.747091	−	2.90549i	0.124515	−	0.484248i
$37$	−4.24407			−0.697721			−0.348860	−	0.937175i	$-0.613431\pi$
$37$	−4.24407			−0.697721			−0.348860	+	0.937175i	$0.613431\pi$
$38$	−7.04504	+	4.06746i	−1.14286	+	0.659829i
$39$	−1.11337	+	2.72685i	−0.178281	+	0.436645i
$40$	−0.866025	−	0.500000i	−0.136931	−	0.0790569i
$41$	0.847146	−	1.46730i	0.132302	−	0.229154i	−0.792262	−	0.610182i	$-0.791096\pi$
$41$	0.847146	−	1.46730i	0.132302	−	0.229154i	0.924564	+	0.381028i	$0.124430\pi$
$42$	−2.42371	+	5.93615i	−0.373987	+	0.915968i
$43$	−0.116302	+	0.0671471i	−0.0177359	+	0.0102398i	−0.508842	−	0.860860i	$-0.669926\pi$
$43$	−0.116302	+	0.0671471i	−0.0177359	+	0.0102398i	0.491106	+	0.871100i	$0.336593\pi$
$44$	−1.74619	+	2.81972i	−0.263248	+	0.425089i
$45$	2.90549	+	0.747091i	0.433124	+	0.111370i
$46$		−	6.92433i		−	1.02094i
$47$	−5.80744	+	3.35293i	−0.847102	+	0.489075i	−0.859672	−	0.510846i	$-0.829332\pi$
$47$	−5.80744	+	3.35293i	−0.847102	+	0.489075i	0.0125701	+	0.999921i	$0.495999\pi$
$48$	−1.36878	+	1.06135i	−0.197566	+	0.153192i
$49$	3.35205	−	5.80591i	0.478864	−	0.829416i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	1.47926	+	10.8130i	0.207138	+	1.51412i
$52$	1.47269	−	0.850259i	0.204226	−	0.117910i
$53$			11.7272i			1.61086i	0.592694	+	0.805428i	$0.298064\pi$
$53$			11.7272i			1.61086i	−0.592694	+	0.805428i	$0.701936\pi$
$54$	3.10027	−	4.16993i	0.421894	−	0.567455i
$55$	−2.81972	−	1.74619i	−0.380211	−	0.235456i
$56$	3.20594	−	1.85095i	0.428412	−	0.247344i
$57$	−13.9601	+	1.90979i	−1.84905	+	0.252958i
$58$	−2.93922	+	5.09088i	−0.385938	+	0.668465i
$59$	−9.11652	−	5.26343i	−1.18687	−	0.685240i	−0.229276	−	0.973361i	$-0.573636\pi$
$59$	−9.11652	−	5.26343i	−1.18687	−	0.685240i	−0.957594	+	0.288122i	$0.906969\pi$
$60$	−1.06135	−	1.36878i	−0.137019	−	0.176708i
$61$	−12.3423	+	7.12584i	−1.58027	+	0.912370i	−0.585452	+	0.810707i	$0.699083\pi$
$61$	−12.3423	+	7.12584i	−1.58027	+	0.912370i	−0.994819	+	0.101663i	$0.967584\pi$
$62$	−9.35271			−1.18779
$63$	−7.77305	+	7.93200i	−0.979312	+	0.999338i
$64$	1.00000			0.125000
$65$	0.850259	+	1.47269i	0.105462	+	0.182665i
$66$	−4.64621	+	3.37827i	−0.571909	+	0.415836i
$67$	1.52684	−	2.64456i	0.186533	−	0.323085i	−0.757559	−	0.652767i	$-0.773608\pi$
$67$	1.52684	−	2.64456i	0.186533	−	0.323085i	0.944092	+	0.329682i	$0.106942\pi$
$68$	3.15052	−	5.45686i	0.382057	−	0.661741i
$69$	4.53350	−	11.1034i	0.545770	−	1.33670i
$70$	1.85095	+	3.20594i	0.221231	+	0.383183i
$71$			7.72800i			0.917145i	0.888657	+	0.458573i	$0.151639\pi$
$71$			7.72800i			0.917145i	−0.888657	+	0.458573i	$0.848361\pi$
$72$	−2.88977	+	0.805744i	−0.340563	+	0.0949578i
$73$		−	4.82386i		−	0.564590i	−0.959328	−	0.282295i	$-0.908904\pi$
$73$		−	4.82386i		−	0.564590i	0.959328	−	0.282295i	$-0.0910957\pi$
$74$	2.12203	+	3.67547i	0.246682	+	0.427265i
$75$	1.36878	−	1.06135i	0.158053	−	0.122554i
$76$	7.04504	+	4.06746i	0.808122	+	0.466569i
$77$	10.8173	−	5.80776i	1.23275	−	0.661855i
$78$	2.91820	−	0.399222i	0.330421	−	0.0452030i
$79$	4.26744	−	2.46381i	0.480124	−	0.277200i	−0.240344	−	0.970688i	$-0.577260\pi$
$79$	4.26744	−	2.46381i	0.480124	−	0.277200i	0.720468	+	0.693488i	$0.243927\pi$
$80$			1.00000i			0.111803i
$81$	7.70155	−	4.65683i	0.855728	−	0.517426i
$82$	−1.69429			−0.187103
$83$	0.208818	+	0.361683i	0.0229207	+	0.0396999i	0.877258	−	0.480019i	$-0.159370\pi$
$83$	0.208818	+	0.361683i	0.0229207	+	0.0396999i	−0.854338	+	0.519719i	$0.826037\pi$
$84$	6.35271	−	0.869077i	0.693138	−	0.0948240i
$85$	5.45686	+	3.15052i	0.591879	+	0.341722i
$86$	0.116302	+	0.0671471i	0.0125412	+	0.00724066i
$87$	−8.04626	+	6.23905i	−0.862650	+	0.668897i
$88$	3.31504	+	0.102382i	0.353385	+	0.0109139i
$89$		−	4.53823i		−	0.481051i	−0.970643	−	0.240526i	$-0.922680\pi$
$89$		−	4.53823i		−	0.481051i	0.970643	−	0.240526i	$-0.0773198\pi$
$90$	−0.805744	−	2.88977i	−0.0849329	−	0.304609i
$91$	−6.29516			−0.659912
$92$	−5.99664	+	3.46216i	−0.625193	+	0.360955i
$93$	−14.9974	−	6.12341i	−1.55516	−	0.634969i
$94$	5.80744	+	3.35293i	0.598992	+	0.345828i
$95$	−4.06746	+	7.04504i	−0.417312	+	0.722806i
$96$	1.60354	+	0.654721i	0.163661	+	0.0668222i
$97$	6.30071	+	10.9132i	0.639740	+	1.10806i	0.985490	+	0.169736i	$0.0542914\pi$
$97$	6.30071	+	10.9132i	0.639740	+	1.10806i	−0.345749	+	0.938327i	$0.612375\pi$
$98$	−6.70409			−0.677216
$99$	−9.66221	+	2.37522i	−0.971089	+	0.238718i
$100$	−1.00000			−0.100000
$101$	−3.56165	−	6.16895i	−0.354397	−	0.613834i	0.632617	−	0.774464i	$-0.281981\pi$
$101$	−3.56165	−	6.16895i	−0.354397	−	0.613834i	−0.987015	+	0.160631i	$0.948647\pi$
$102$	8.62470	−	6.68758i	0.853973	−	0.662169i
$103$	1.51569	−	2.62526i	0.149346	−	0.258674i	−0.781640	−	0.623730i	$-0.785617\pi$
$103$	1.51569	−	2.62526i	0.149346	−	0.258674i	0.930986	+	0.365055i	$0.118950\pi$
$104$	−1.47269	−	0.850259i	−0.144409	−	0.0833748i
$105$	0.869077	+	6.35271i	0.0848132	+	0.619961i
$106$	10.1561	−	5.86360i	0.986444	−	0.569523i
$107$	6.00734			0.580751			0.290376	−	0.956913i	$-0.406220\pi$
$107$	6.00734			0.580751			0.290376	+	0.956913i	$0.406220\pi$
$108$	−5.16140	−	0.599952i	−0.496656	−	0.0577304i
$109$			4.74953i			0.454923i	0.973787	+	0.227461i	$0.0730426\pi$
$109$			4.74953i			0.454923i	−0.973787	+	0.227461i	$0.926957\pi$
$110$	−0.102382	+	3.31504i	−0.00976170	+	0.316077i
$111$	0.996358	+	7.28311i	0.0945701	+	0.691282i
$112$	−3.20594	−	1.85095i	−0.302933	−	0.174899i
$113$	9.55200	+	5.51485i	0.898577	+	0.518794i	0.876738	−	0.480968i	$-0.159715\pi$
$113$	9.55200	+	5.51485i	0.898577	+	0.518794i	0.0218388	+	0.999762i	$0.493048\pi$
$114$	8.63396	+	11.1349i	0.808644	+	1.04288i
$115$	−3.46216	−	5.99664i	−0.322848	−	0.559190i
$116$	5.87844			0.545799
$117$	4.94083	+	1.27044i	0.456780	+	0.117452i
$118$			10.5269i			0.969075i
$119$	−20.2008	+	11.6629i	−1.85180	+	1.06914i
$120$	−0.654721	+	1.60354i	−0.0597676	+	0.146382i
$121$	10.9790	+	0.678799i	0.998094	+	0.0617090i
$122$	12.3423	+	7.12584i	1.11742	+	0.645143i
$123$	−2.71687	−	1.10929i	−0.244971	−	0.100021i
$124$	4.67635	+	8.09968i	0.419949	+	0.727373i
$125$		−	1.00000i		−	0.0894427i
$126$	10.7558	+	2.76566i	0.958206	+	0.246384i
$127$		−	11.1622i		−	0.990483i	−0.868755	−	0.495241i	$-0.835080\pi$
$127$		−	11.1622i		−	0.990483i	0.868755	−	0.495241i	$-0.164920\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	0.142533	+	0.183819i	0.0125493	+	0.0161843i
$130$	0.850259	−	1.47269i	0.0745727	−	0.129164i
$131$	3.26700	−	5.65861i	0.285439	−	0.494395i	−0.687276	−	0.726396i	$-0.741194\pi$
$131$	3.26700	−	5.65861i	0.285439	−	0.494395i	0.972716	+	0.232001i	$0.0745272\pi$
$132$	5.24877	+	2.33460i	0.456847	+	0.203201i
$133$	−15.0573	−	26.0801i	−1.30564	−	2.26143i
$134$	−3.05368			−0.263797
$135$	0.599952	−	5.16140i	0.0516356	−	0.444223i
$136$	−6.30104			−0.540310
$137$	−6.06599	+	3.50220i	−0.518252	+	0.299213i	−0.736219	−	0.676743i	$-0.763391\pi$
$137$	−6.06599	+	3.50220i	−0.518252	+	0.299213i	0.217967	+	0.975956i	$0.430057\pi$
$138$	−11.8826	+	1.62559i	−1.01151	+	0.138379i
$139$	−1.05294	−	0.607915i	−0.0893092	−	0.0515627i	0.454680	−	0.890655i	$-0.349754\pi$
$139$	−1.05294	−	0.607915i	−0.0893092	−	0.0515627i	−0.543989	+	0.839092i	$0.683087\pi$
$140$	1.85095	−	3.20594i	0.156434	−	0.270952i
$141$	7.11723	+	9.17880i	0.599379	+	0.772995i
$142$	6.69265	−	3.86400i	0.561634	−	0.324260i
$143$	−4.79499	−	2.96942i	−0.400977	−	0.248316i
$144$	2.14268	+	2.09974i	0.178557	+	0.174979i
$145$			5.87844i			0.488178i
$146$	−4.17758	+	2.41193i	−0.345739	+	0.199613i
$147$	−10.7503	−	4.38931i	−0.886668	−	0.362024i
$148$	2.12203	−	3.67547i	0.174430	−	0.302122i
$149$	−3.54443	+	6.13914i	−0.290371	+	0.502938i	−0.973898	−	0.226988i	$-0.927112\pi$
$149$	−3.54443	+	6.13914i	−0.290371	+	0.502938i	0.683526	+	0.729926i	$0.260445\pi$
$150$	−1.60354	−	0.654721i	−0.130928	−	0.0534578i
$151$	5.98852	−	3.45747i	0.487339	−	0.281365i	−0.236131	−	0.971721i	$-0.575879\pi$
$151$	5.98852	−	3.45747i	0.487339	−	0.281365i	0.723470	+	0.690356i	$0.242546\pi$
$152$		−	8.13491i		−	0.659829i
$153$	18.2086	−	5.07702i	1.47207	−	0.410453i
$154$	−10.4383	−	6.46422i	−0.841145	−	0.520901i
$155$	−8.09968	+	4.67635i	−0.650582	+	0.375614i
$156$	−1.80484	−	2.32763i	−0.144503	−	0.186359i
$157$	5.63065	−	9.75257i	0.449375	−	0.778340i	−0.548971	−	0.835842i	$-0.684980\pi$
$157$	5.63065	−	9.75257i	0.449375	−	0.778340i	0.998345	+	0.0575019i	$0.0183135\pi$
$158$	−4.26744	−	2.46381i	−0.339499	−	0.196010i
$159$	20.1247	−	2.75313i	1.59599	−	0.218338i
$160$	0.866025	−	0.500000i	0.0684653	−	0.0395285i
$161$	25.6332			2.02018
$162$	−7.88371	−	4.34132i	−0.619403	−	0.341087i
$163$	−0.950144			−0.0744210			−0.0372105	−	0.999307i	$-0.511847\pi$
$163$	−0.950144			−0.0744210			−0.0372105	+	0.999307i	$0.511847\pi$
$164$	0.847146	+	1.46730i	0.0661510	+	0.114577i
$165$	−2.33460	+	5.24877i	−0.181749	+	0.408617i
$166$	0.208818	−	0.361683i	0.0162074	−	0.0280720i
$167$	5.34171	−	9.25211i	0.413354	−	0.715950i	−0.581900	−	0.813260i	$-0.697691\pi$
$167$	5.34171	−	9.25211i	0.413354	−	0.715950i	0.995254	+	0.0973102i	$0.0310239\pi$
$168$	−3.92900	−	5.06707i	−0.303129	−	0.390933i
$169$	−5.05412	−	8.75399i	−0.388778	−	0.673384i
$170$		−	6.30104i		−	0.483268i
$171$	6.55466	+	23.5080i	0.501247	+	1.79770i
$172$		−	0.134294i		−	0.0102398i
$173$	−11.6874	−	20.2432i	−0.888576	−	1.53906i	−0.841559	−	0.540165i	$-0.818362\pi$
$173$	−11.6874	−	20.2432i	−0.888576	−	1.53906i	−0.0470165	−	0.998894i	$-0.514971\pi$
$174$	9.42631	+	3.84874i	0.714607	+	0.291772i
$175$	3.20594	+	1.85095i	0.242347	+	0.139919i
$176$	−1.56886	−	2.92210i	−0.118257	−	0.220262i
$177$	−6.89215	+	16.8802i	−0.518046	+	1.26880i
$178$	−3.93022	+	2.26911i	−0.294583	+	0.170077i
$179$		−	20.8131i		−	1.55565i	−0.628483	−	0.777824i	$-0.716324\pi$
$179$		−	20.8131i		−	1.55565i	0.628483	−	0.777824i	$-0.283676\pi$
$180$	−2.09974	+	2.14268i	−0.156506	+	0.159706i
$181$	16.6474			1.23739			0.618697	−	0.785629i	$-0.287661\pi$
$181$	16.6474			1.23739			0.618697	+	0.785629i	$0.287661\pi$
$182$	3.14758	+	5.45177i	0.233314	+	0.404112i
$183$	15.1259	+	19.5073i	1.11814	+	1.44202i
$184$	5.99664	+	3.46216i	0.442078	+	0.255234i
$185$	3.67547	+	2.12203i	0.270226	+	0.156015i
$186$	2.19569	+	16.0499i	0.160995	+	1.17683i
$187$	−20.8882	−	0.645110i	−1.52750	−	0.0471751i
$188$		−	6.70585i		−	0.489075i
$189$	15.4367	+	11.4769i	1.12285	+	0.834823i
$190$	8.13491			0.590169
$191$	13.9415	−	8.04916i	1.00877	−	0.582416i	0.0979422	−	0.995192i	$-0.468774\pi$
$191$	13.9415	−	8.04916i	1.00877	−	0.582416i	0.910833	+	0.412776i	$0.135441\pi$
$192$	−0.234765	−	1.71607i	−0.0169427	−	0.123846i
$193$	8.32495	+	4.80641i	0.599243	+	0.345973i	0.768744	−	0.639557i	$-0.220882\pi$
$193$	8.32495	+	4.80641i	0.599243	+	0.345973i	−0.169501	+	0.985530i	$0.554216\pi$
$194$	6.30071	−	10.9132i	0.452365	−	0.783519i
$195$	2.32763	−	1.80484i	0.166685	−	0.129247i
$196$	3.35205	+	5.80591i	0.239432	+	0.414708i
$197$	−6.51573			−0.464226			−0.232113	−	0.972689i	$-0.574564\pi$
$197$	−6.51573			−0.464226			−0.232113	+	0.972689i	$0.574564\pi$
$198$	6.88810	+	7.18011i	0.489516	+	0.510268i
$199$	−8.85635			−0.627810			−0.313905	−	0.949454i	$-0.601637\pi$
$199$	−8.85635			−0.627810			−0.313905	+	0.949454i	$0.601637\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	−4.89669	−	1.99931i	−0.345386	−	0.141020i
$202$	−3.56165	+	6.16895i	−0.250597	+	0.434046i
$203$	−18.8459	−	10.8807i	−1.32273	−	0.763676i
$204$	−10.1040	−	4.12542i	−0.707419	−	0.288837i
$205$	−1.46730	+	0.847146i	−0.102481	+	0.0591673i
$206$	−3.03139			−0.211207
$207$	−20.1185	−	5.17310i	−1.39834	−	0.359555i
$208$			1.70052i			0.117910i
$209$	0.832865	−	26.9676i	0.0576105	−	1.86539i
$210$	5.06707	−	3.92900i	0.349661	−	0.271127i
$211$	13.8138	+	7.97541i	0.950982	+	0.549050i	0.893386	−	0.449290i	$-0.148323\pi$
$211$	13.8138	+	7.97541i	0.950982	+	0.549050i	0.0575960	+	0.998340i	$0.481656\pi$
$212$	−10.1561	−	5.86360i	−0.697521	−	0.402714i
$213$	13.2618	−	1.81426i	0.908681	−	0.124311i
$214$	−3.00367	−	5.20251i	−0.205327	−	0.355636i
$215$	0.134294			0.00915879
$216$	2.06113	+	4.76988i	0.140242	+	0.324549i
$217$		−	34.6228i		−	2.35035i
$218$	4.11322	−	2.37477i	0.278582	−	0.160840i
$219$	−8.27806	+	1.13247i	−0.559380	+	0.0765253i
$220$	2.92210	−	1.56886i	0.197008	−	0.105772i
$221$	9.27949	+	5.35752i	0.624206	+	0.360385i
$222$	5.80918	−	4.50442i	0.389886	−	0.302317i
$223$	10.6625	+	18.4681i	0.714017	+	1.23671i	0.963337	+	0.268293i	$0.0864594\pi$
$223$	10.6625	+	18.4681i	0.714017	+	1.23671i	−0.249321	+	0.968421i	$0.580207\pi$
$224$			3.70190i			0.247344i
$225$	−2.14268	−	2.09974i	−0.142845	−	0.139983i
$226$		−	11.0297i		−	0.733685i
$227$	5.69581	+	9.86544i	0.378045	+	0.654792i	0.990778	−	0.135498i	$-0.0432633\pi$
$227$	5.69581	+	9.86544i	0.378045	+	0.654792i	−0.612733	+	0.790290i	$0.709930\pi$
$228$	5.32610	−	13.0447i	0.352730	−	0.863904i
$229$	2.57721	−	4.46385i	0.170307	−	0.294980i	−0.768220	−	0.640185i	$-0.778857\pi$
$229$	2.57721	−	4.46385i	0.170307	−	0.294980i	0.938527	+	0.345206i	$0.112191\pi$
$230$	−3.46216	+	5.99664i	−0.228288	+	0.395407i
$231$	−12.5060	−	17.1998i	−0.822837	−	1.13167i
$232$	−2.93922	−	5.09088i	−0.192969	−	0.334232i
$233$	−24.7686			−1.62264			−0.811321	−	0.584600i	$-0.801251\pi$
$233$	−24.7686			−1.62264			−0.811321	+	0.584600i	$0.801251\pi$
$234$	−1.37018	−	4.91411i	−0.0895716	−	0.321245i
$235$	6.70585			0.437442
$236$	9.11652	−	5.26343i	0.593435	−	0.342620i
$237$	−5.22990	−	6.74479i	−0.339719	−	0.438121i
$238$	20.2008	+	11.6629i	1.30942	+	0.755995i
$239$	−2.51124	+	4.34960i	−0.162439	+	0.281352i	−0.935743	−	0.352683i	$-0.885269\pi$
$239$	−2.51124	+	4.34960i	−0.162439	+	0.281352i	0.773304	+	0.634035i	$0.218603\pi$
$240$	1.71607	−	0.234765i	0.110772	−	0.0151540i
$241$	6.58899	−	3.80415i	0.424434	−	0.245047i	−0.272539	−	0.962145i	$-0.587863\pi$
$241$	6.58899	−	3.80415i	0.424434	−	0.245047i	0.696973	+	0.717098i	$0.254530\pi$
$242$	−4.90166	−	9.84752i	−0.315091	−	0.633023i
$243$	−9.79949	−	12.1231i	−0.628637	−	0.777699i
$244$		−	14.2517i		−	0.912370i
$245$	−5.80591	+	3.35205i	−0.370926	+	0.214154i
$246$	0.397760	+	2.90752i	0.0253603	+	0.185377i
$247$	−6.91679	+	11.9802i	−0.440105	+	0.762283i
$248$	4.67635	−	8.09968i	0.296949	−	0.514330i
$249$	0.571649	−	0.443256i	0.0362268	−	0.0280902i
$250$	−0.866025	+	0.500000i	−0.0547723	+	0.0316228i
$251$		−	16.3323i		−	1.03088i	−0.856925	−	0.515442i	$-0.827628\pi$
$251$		−	16.3323i		−	1.03088i	0.856925	−	0.515442i	$-0.172372\pi$
$252$	−2.98279	−	10.6977i	−0.187898	−	0.673889i
$253$	19.5247	+	12.0912i	1.22751	+	0.760165i
$254$	−9.66673	+	5.58109i	−0.606544	+	0.350189i
$255$	4.12542	−	10.1040i	0.258344	−	0.632735i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.0935	+	5.82747i	0.629614	+	0.363508i	0.780603	−	0.625028i	$-0.214912\pi$
$257$	10.0935	+	5.82747i	0.629614	+	0.363508i	−0.150988	+	0.988536i	$0.548246\pi$
$258$	0.0879252	−	0.215346i	0.00547399	−	0.0134069i
$259$	−13.6062	+	7.85557i	−0.845451	+	0.488121i
$260$	−1.70052			−0.105462
$261$	12.5956	+	12.3432i	0.779649	+	0.764025i
$262$	−6.53400			−0.403672
$263$	−5.72200	−	9.91079i	−0.352833	−	0.611126i	0.633911	−	0.773406i	$-0.281448\pi$
$263$	−5.72200	−	9.91079i	−0.352833	−	0.611126i	−0.986745	+	0.162280i	$0.948115\pi$
$264$	−0.602562	−	5.71287i	−0.0370851	−	0.351603i
$265$	5.86360	−	10.1561i	0.360198	−	0.623882i
$266$	−15.0573	+	26.0801i	−0.923224	+	1.59907i
$267$	−7.78790	+	1.06542i	−0.476612	+	0.0652024i
$268$	1.52684	+	2.64456i	0.0932665	+	0.161542i
$269$			23.9445i			1.45992i	0.683489	+	0.729961i	$0.260462\pi$
$269$			23.9445i			1.45992i	−0.683489	+	0.729961i	$0.739538\pi$
$270$	−4.76988	+	2.06113i	−0.290286	+	0.125436i
$271$		−	6.48042i		−	0.393657i	−0.980438	−	0.196829i	$-0.936936\pi$
$271$		−	6.48042i		−	0.393657i	0.980438	−	0.196829i	$-0.0630643\pi$
$272$	3.15052	+	5.45686i	0.191028	+	0.330871i
$273$	1.47788	+	10.8029i	0.0894454	+	0.653822i
$274$	6.06599	+	3.50220i	0.366460	+	0.211576i
$275$	1.56886	+	2.92210i	0.0946056	+	0.176209i
$276$	7.34910	+	9.47785i	0.442364	+	0.570499i
$277$	14.3214	−	8.26849i	0.860492	−	0.496805i	−0.00368500	−	0.999993i	$-0.501173\pi$
$277$	14.3214	−	8.26849i	0.860492	−	0.496805i	0.864177	+	0.503188i	$0.167840\pi$
$278$			1.21583i			0.0729207i
$279$	−6.98732	+	27.1742i	−0.418320	+	1.62687i
$280$	−3.70190			−0.221231
$281$	7.80447	+	13.5177i	0.465575	+	0.806400i	0.999227	−	0.0393040i	$-0.0125141\pi$
$281$	7.80447	+	13.5177i	0.465575	+	0.806400i	−0.533652	+	0.845704i	$0.679181\pi$
$282$	4.39046	−	10.7531i	0.261448	−	0.640338i
$283$	21.8952	+	12.6412i	1.30154	+	0.751443i	0.980668	−	0.195680i	$-0.0626915\pi$
$283$	21.8952	+	12.6412i	1.30154	+	0.751443i	0.320870	+	0.947123i	$0.396025\pi$
$284$	−6.69265	−	3.86400i	−0.397136	−	0.229286i
$285$	13.0447	+	5.32610i	0.772699	+	0.315491i
$286$	−0.174102	+	5.63729i	−0.0102949	+	0.333340i
$287$		−	6.27211i		−	0.370231i
$288$	0.747091	−	2.90549i	0.0440227	−	0.171207i
$289$	22.7031			1.33547
$290$	5.09088	−	2.93922i	0.298947	−	0.172597i
$291$	17.2485	−	13.3745i	1.01113	−	0.784025i
$292$	4.17758	+	2.41193i	0.244475	+	0.141147i
$293$	10.3738	−	17.9679i	0.606042	−	1.04970i	−0.385843	−	0.922564i	$-0.626090\pi$
$293$	10.3738	−	17.9679i	0.606042	−	1.04970i	0.991886	−	0.127132i	$-0.0405771\pi$
$294$	1.57388	+	11.5047i	0.0917908	+	0.670966i
$295$	5.26343	+	9.11652i	0.306449	+	0.530785i
$296$	−4.24407			−0.246682
$297$	6.34438	+	16.0234i	0.368138	+	0.929771i
$298$	7.08887			0.410647
$299$	−5.88747	−	10.1974i	−0.340481	−	0.589731i
$300$	0.234765	+	1.71607i	0.0135541	+	0.0990772i
$301$	−0.248572	+	0.430539i	−0.0143275	+	0.0248159i
$302$	−5.98852	−	3.45747i	−0.344600	−	0.198955i
$303$	−9.75019	+	7.56028i	−0.560134	+	0.434327i
$304$	−7.04504	+	4.06746i	−0.404061	+	0.233285i
$305$	14.2517			0.816048
$306$	−13.5011	−	13.2306i	−0.771807	−	0.756341i
$307$			11.7469i			0.670431i	0.942141	+	0.335216i	$0.108809\pi$
$307$			11.7469i			0.670431i	−0.942141	+	0.335216i	$0.891191\pi$
$308$	−0.379007	+	12.2720i	−0.0215959	+	0.699261i
$309$	−4.86095	−	1.98471i	−0.276530	−	0.112906i
$310$	8.09968	+	4.67635i	0.460031	+	0.265599i
$311$	9.13746	+	5.27551i	0.518138	+	0.299147i	0.736172	−	0.676794i	$-0.236631\pi$
$311$	9.13746	+	5.27551i	0.518138	+	0.299147i	−0.218035	+	0.975941i	$0.569965\pi$
$312$	−1.11337	+	2.72685i	−0.0630319	+	0.154377i
$313$	4.93502	+	8.54771i	0.278944	+	0.483145i	0.971123	−	0.238581i	$-0.0766823\pi$
$313$	4.93502	+	8.54771i	0.278944	+	0.483145i	−0.692179	+	0.721726i	$0.743349\pi$
$314$	−11.2613			−0.635512
$315$	10.6977	−	2.98279i	0.602745	−	0.168061i
$316$			4.92761i			0.277200i
$317$	23.9489	−	13.8269i	1.34511	−	0.776598i	0.357555	−	0.933892i	$-0.383611\pi$
$317$	23.9489	−	13.8269i	1.34511	−	0.776598i	0.987552	+	0.157295i	$0.0502772\pi$
$318$	−12.4466	−	16.0519i	−0.697972	−	0.900146i
$319$	−9.22243	−	17.1774i	−0.516357	−	0.961750i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	−1.41031	−	10.3090i	−0.0787159	−	0.575392i
$322$	−12.8166	−	22.1990i	−0.714241	−	1.23710i
$323$			51.2584i			2.85209i
$324$	0.182158	+	8.99816i	0.0101199	+	0.499898i
$325$		−	1.70052i		−	0.0943278i
$326$	0.475072	+	0.822849i	0.0263118	+	0.0455734i
$327$	8.15052	−	1.11502i	0.450725	−	0.0616609i
$328$	0.847146	−	1.46730i	0.0467758	−	0.0810181i
$329$	−12.4122	+	21.4986i	−0.684307	+	1.18525i
$330$	5.71287	−	0.602562i	0.314483	−	0.0331699i
$331$	−11.9098	−	20.6284i	−0.654623	−	1.13384i	−0.981988	−	0.188943i	$-0.939494\pi$
$331$	−11.9098	−	20.6284i	−0.654623	−	1.13384i	0.327365	−	0.944898i	$-0.393839\pi$
$332$	−0.417636			−0.0229207
$333$	12.2644	−	3.41963i	0.672084	−	0.187395i
$334$	−10.6834			−0.584571
$335$	−2.64456	+	1.52684i	−0.144488	+	0.0834201i
$336$	−2.42371	+	5.93615i	−0.132224	+	0.323844i
$337$	19.0990	+	11.0268i	1.04039	+	0.600670i	0.919944	−	0.392049i	$-0.128234\pi$
$337$	19.0990	+	11.0268i	1.04039	+	0.600670i	0.120447	+	0.992720i	$0.461567\pi$
$338$	−5.05412	+	8.75399i	−0.274908	+	0.476154i
$339$	7.22138	−	17.6866i	0.392212	−	0.960603i
$340$	−5.45686	+	3.15052i	−0.295940	+	0.170861i
$341$	16.3316	−	26.3720i	0.884404	−	1.42813i
$342$	17.0812	−	17.4305i	0.923647	−	0.942535i
$343$			1.09542i			0.0591471i
$344$	−0.116302	+	0.0671471i	−0.00627059	+	0.00362033i
$345$	−9.47785	+	7.34910i	−0.510270	+	0.395662i
$346$	−11.6874	+	20.2432i	−0.628318	+	1.08828i
$347$	−1.41366	+	2.44854i	−0.0758895	+	0.131444i	−0.901473	−	0.432836i	$-0.857513\pi$
$347$	−1.41366	+	2.44854i	−0.0758895	+	0.131444i	0.825583	+	0.564280i	$0.190846\pi$
$348$	−1.38005	−	10.0878i	−0.0739784	−	0.540762i
$349$	−15.3832	+	8.88151i	−0.823445	+	0.475416i	−0.851603	−	0.524187i	$-0.824369\pi$
$349$	−15.3832	+	8.88151i	−0.823445	+	0.475416i	0.0281580	+	0.999603i	$0.491036\pi$
$350$		−	3.70190i		−	0.197875i
$351$	1.02023	−	8.77706i	0.0544558	−	0.468485i
$352$	−1.74619	+	2.81972i	−0.0930721	+	0.150292i
$353$	8.18276	−	4.72432i	0.435524	−	0.251450i	−0.266173	−	0.963925i	$-0.585759\pi$
$353$	8.18276	−	4.72432i	0.435524	−	0.251450i	0.701697	+	0.712475i	$0.252426\pi$
$354$	18.0648	−	2.47133i	0.960133	−	0.131350i
$355$	3.86400	−	6.69265i	0.205080	−	0.355209i
$356$	3.93022	+	2.26911i	0.208301	+	0.120263i
$357$	24.7568	+	31.9278i	1.31027	+	1.68980i
$358$	−18.0247	+	10.4066i	−0.952635	+	0.550004i
$359$	15.8662			0.837385			0.418692	−	0.908128i	$-0.362489\pi$
$359$	15.8662			0.837385			0.418692	+	0.908128i	$0.362489\pi$
$360$	2.90549	+	0.747091i	0.153133	+	0.0393751i
$361$	−47.1768			−2.48299
$362$	−8.32372	−	14.4171i	−0.437485	−	0.757746i
$363$	−1.41263	−	19.0001i	−0.0741437	−	0.997248i
$364$	3.14758	−	5.45177i	0.164978	−	0.285750i
$365$	−2.41193	+	4.17758i	−0.126246	+	0.218665i
$366$	9.33087	−	22.8531i	0.487732	−	1.19455i
$367$	−0.928259	−	1.60779i	−0.0484547	−	0.0839261i	0.840781	−	0.541376i	$-0.182096\pi$
$367$	−0.928259	−	1.60779i	−0.0484547	−	0.0839261i	−0.889236	+	0.457450i	$0.848763\pi$
$368$		−	6.92433i		−	0.360955i
$369$	−1.26579	+	4.92274i	−0.0658944	+	0.256268i
$370$		−	4.24407i		−	0.220639i
$371$	21.7065	+	37.5968i	1.12695	+	1.95193i
$372$	12.8018	−	9.92645i	0.663740	−	0.514663i
$373$	12.4567	+	7.19188i	0.644984	+	0.372382i	0.786532	−	0.617550i	$-0.211875\pi$
$373$	12.4567	+	7.19188i	0.644984	+	0.372382i	−0.141548	+	0.989931i	$0.545208\pi$
$374$	9.88543	+	18.4123i	0.511163	+	0.952076i
$375$	−1.71607	+	0.234765i	−0.0886173	+	0.0121232i
$376$	−5.80744	+	3.35293i	−0.299496	+	0.172914i
$377$			9.99639i			0.514840i
$378$	2.22096	−	19.1070i	0.114234	−	0.982759i
$379$	3.35572			0.172372			0.0861860	−	0.996279i	$-0.472532\pi$
$379$	3.35572			0.172372			0.0861860	+	0.996279i	$0.472532\pi$
$380$	−4.06746	−	7.04504i	−0.208656	−	0.361403i
$381$	−19.1550	+	2.62049i	−0.981342	+	0.134252i
$382$	−13.9415	−	8.04916i	−0.713312	−	0.411831i
$383$	9.95383	+	5.74685i	0.508617	+	0.293650i	0.732265	−	0.681020i	$-0.238463\pi$
$383$	9.95383	+	5.74685i	0.508617	+	0.293650i	−0.223648	+	0.974670i	$0.571797\pi$
$384$	−1.36878	+	1.06135i	−0.0698500	+	0.0541616i
$385$	−12.2720	−	0.379007i	−0.625438	−	0.0193160i
$386$		−	9.61282i		−	0.489280i
$387$	0.281983	−	0.287749i	0.0143340	−	0.0146271i
$388$	−12.6014			−0.639740
$389$	30.5931	−	17.6629i	1.55113	−	0.895545i	0.553080	−	0.833128i	$-0.313452\pi$
$389$	30.5931	−	17.6629i	1.55113	−	0.895545i	0.998050	−	0.0624171i	$-0.0198809\pi$
$390$	−2.72685	−	1.11337i	−0.138079	−	0.0563775i
$391$	−37.7851	−	21.8152i	−1.91087	−	1.10324i
$392$	3.35205	−	5.80591i	0.169304	−	0.293243i
$393$	−10.4775	−	4.27795i	−0.528522	−	0.215794i
$394$	3.25786	+	5.64278i	0.164129	+	0.284279i
$395$	−4.92761			−0.247935
$396$	2.77411	−	9.55533i	0.139404	−	0.480173i
$397$	−28.8574			−1.44831			−0.724155	−	0.689637i	$-0.757770\pi$
$397$	−28.8574			−1.44831			−0.724155	+	0.689637i	$0.757770\pi$
$398$	4.42817	+	7.66982i	0.221964	+	0.384453i
$399$	−41.2202	+	31.9621i	−2.06359	+	1.60011i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	−7.66139	−	4.42331i	−0.382592	−	0.220889i	0.296354	−	0.955078i	$-0.404229\pi$
$401$	−7.66139	−	4.42331i	−0.382592	−	0.220889i	−0.678945	+	0.734189i	$0.737563\pi$
$402$	0.716896	+	5.24031i	0.0357555	+	0.261363i
$403$	−13.7737	+	7.95222i	−0.686115	+	0.396129i
$404$	7.12329			0.354397
$405$	−8.99816	+	0.182158i	−0.447122	+	0.00905150i
$406$			21.7614i			1.08000i
$407$	−14.0693	−	0.434515i	−0.697388	−	0.0215381i
$408$	1.47926	+	10.8130i	0.0732344	+	0.535323i
$409$	−22.9860	−	13.2710i	−1.13659	−	0.656208i	−0.191003	−	0.981589i	$-0.561174\pi$
$409$	−22.9860	−	13.2710i	−1.13659	−	0.656208i	−0.945583	+	0.325381i	$0.894507\pi$
$410$	1.46730	+	0.847146i	0.0724648	+	0.0418376i
$411$	7.43409	+	9.58745i	0.366697	+	0.472914i
$412$	1.51569	+	2.62526i	0.0746729	+	0.129337i
$413$	−38.9694			−1.91756
$414$	5.57923	+	20.0097i	0.274204	+	0.983424i
$415$		−	0.417636i		−	0.0205009i
$416$	1.47269	−	0.850259i	0.0722047	−	0.0416874i
$417$	−0.796030	+	1.94963i	−0.0389818	+	0.0954739i
$418$	−23.7711	+	12.7625i	−1.16268	+	0.624235i
$419$	−20.5371	−	11.8571i	−1.00330	−	0.579257i	−0.0940788	−	0.995565i	$-0.529991\pi$
$419$	−20.5371	−	11.8571i	−1.00330	−	0.579257i	−0.909224	+	0.416308i	$0.863324\pi$
$420$	−5.93615	−	2.42371i	−0.289654	−	0.118265i
$421$	10.3493	+	17.9255i	0.504394	+	0.873636i	0.999987	+	0.00508089i	$0.00161730\pi$
$421$	10.3493	+	17.9255i	0.504394	+	0.873636i	−0.495593	+	0.868555i	$0.665049\pi$
$422$		−	15.9508i		−	0.776473i
$423$	14.0806	−	14.3685i	0.684621	−	0.698620i
$424$			11.7272i			0.569523i
$425$	−3.15052	−	5.45686i	−0.152823	−	0.264697i
$426$	−8.20208	−	10.5779i	−0.397392	−	0.512501i
$427$	−26.3792	+	45.6900i	−1.27658	+	2.21110i
$428$	−3.00367	+	5.20251i	−0.145188	+	0.251473i
$429$	−3.97003	+	8.92564i	−0.191675	+	0.430934i
$430$	−0.0671471	−	0.116302i	−0.00323812	−	0.00560859i
$431$	−16.9532			−0.816605			−0.408303	−	0.912847i	$-0.633879\pi$
$431$	−16.9532			−0.816605			−0.408303	+	0.912847i	$0.633879\pi$
$432$	3.10027	−	4.16993i	0.149162	−	0.200626i
$433$	−37.9368			−1.82313			−0.911563	−	0.411161i	$-0.865123\pi$
$433$	−37.9368			−1.82313			−0.911563	+	0.411161i	$0.865123\pi$
$434$	−29.9842	+	17.3114i	−1.43929	+	0.830974i
$435$	10.0878	−	1.38005i	0.483673	−	0.0661683i
$436$	−4.11322	−	2.37477i	−0.196987	−	0.113731i
$437$	28.1644	−	48.7822i	1.34729	−	2.33357i
$438$	5.11978	+	6.60278i	0.244633	+	0.315493i
$439$	19.7502	−	11.4028i	0.942628	−	0.544226i	0.0518447	−	0.998655i	$-0.483490\pi$
$439$	19.7502	−	11.4028i	0.942628	−	0.544226i	0.890783	+	0.454429i	$0.150157\pi$
$440$	−2.81972	−	1.74619i	−0.134425	−	0.0832462i
$441$	−5.00857	+	19.4787i	−0.238503	+	0.927555i
$442$		−	10.7150i		−	0.509662i
$443$	9.65829	−	5.57622i	0.458879	−	0.264934i	−0.252694	−	0.967546i	$-0.581316\pi$
$443$	9.65829	−	5.57622i	0.458879	−	0.264934i	0.711573	+	0.702612i	$0.247983\pi$
$444$	−6.80553	−	2.77868i	−0.322976	−	0.131870i
$445$	−2.26911	+	3.93022i	−0.107566	+	0.186310i
$446$	10.6625	−	18.4681i	0.504886	−	0.874489i
$447$	11.3673	+	4.64123i	0.537654	+	0.219523i
$448$	3.20594	−	1.85095i	0.151467	−	0.0874493i
$449$			28.0037i			1.32158i	0.750572	+	0.660788i	$0.229778\pi$
$449$			28.0037i			1.32158i	−0.750572	+	0.660788i	$0.770222\pi$
$450$	−0.747091	+	2.90549i	−0.0352182	+	0.136966i
$451$	2.95855	−	4.77743i	0.139313	−	0.224961i
$452$	−9.55200	+	5.51485i	−0.449289	+	0.259397i
$453$	−7.33915	−	9.46500i	−0.344823	−	0.444705i
$454$	5.69581	−	9.86544i	0.267318	−	0.463008i
$455$	5.45177	+	3.14758i	0.255583	+	0.147561i
$456$	−13.9601	+	1.90979i	−0.653740	+	0.0894342i
$457$	5.08207	−	2.93413i	0.237729	−	0.137253i	−0.376404	−	0.926456i	$-0.622839\pi$
$457$	5.08207	−	2.93413i	0.237729	−	0.137253i	0.614133	+	0.789203i	$0.289506\pi$
$458$	−5.15442			−0.240850
$459$	−12.9872	−	30.0552i	−0.606192	−	1.40286i
$460$	6.92433			0.322848
$461$	10.4234	+	18.0539i	0.485467	+	0.840854i	0.999861	−	0.0167003i	$-0.00531612\pi$
$461$	10.4234	+	18.0539i	0.485467	+	0.840854i	−0.514393	+	0.857554i	$0.671983\pi$
$462$	−8.64247	+	19.4305i	−0.402084	+	0.903987i
$463$	4.67597	−	8.09902i	0.217311	−	0.376393i	−0.736674	−	0.676248i	$-0.763605\pi$
$463$	4.67597	−	8.09902i	0.217311	−	0.376393i	0.953985	+	0.299855i	$0.0969381\pi$
$464$	−2.93922	+	5.09088i	−0.136450	+	0.236338i
$465$	9.92645	+	12.8018i	0.460328	+	0.593667i
$466$	12.3843	+	21.4502i	0.573691	+	0.993662i
$467$			7.16114i			0.331378i	0.986178	+	0.165689i	$0.0529848\pi$
$467$			7.16114i			0.331378i	−0.986178	+	0.165689i	$0.947015\pi$
$468$	−3.57065	+	3.64367i	−0.165053	+	0.168429i
$469$		−	11.3044i		−	0.521990i
$470$	−3.35293	−	5.80744i	−0.154659	−	0.267877i
$471$	−18.0579	−	7.37301i	−0.832066	−	0.339730i
$472$	−9.11652	−	5.26343i	−0.419622	−	0.242269i
$473$	−0.392421	+	0.210688i	−0.0180436	+	0.00968746i
$474$	−3.22621	+	7.90162i	−0.148185	+	0.362934i
$475$	7.04504	−	4.06746i	0.323249	−	0.186628i
$476$		−	23.3258i		−	1.06914i
$477$	−9.44913	−	33.8889i	−0.432646	−	1.55167i
$478$	5.02249			0.229723
$479$	6.52135	+	11.2953i	0.297968	+	0.516096i	0.975671	−	0.219240i	$-0.0703577\pi$
$479$	6.52135	+	11.2953i	0.297968	+	0.516096i	−0.677703	+	0.735336i	$0.737024\pi$
$480$	−1.06135	−	1.36878i	−0.0484436	−	0.0624758i
$481$	6.25021	+	3.60856i	0.284985	+	0.164536i
$482$	−6.58899	−	3.80415i	−0.300120	−	0.173274i
$483$	−6.01777	−	43.9883i	−0.273818	−	2.00154i
$484$	−6.07738	+	9.16872i	−0.276244	+	0.416760i
$485$		−	12.6014i		−	0.572201i
$486$	−5.59919	+	14.5482i	−0.253984	+	0.659918i
$487$	−7.94167			−0.359872			−0.179936	−	0.983678i	$-0.557589\pi$
$487$	−7.94167			−0.359872			−0.179936	+	0.983678i	$0.557589\pi$
$488$	−12.3423	+	7.12584i	−0.558710	+	0.322571i
$489$	0.223060	+	1.63051i	0.0100871	+	0.0737342i
$490$	5.80591	+	3.35205i	0.262284	+	0.151430i
$491$	9.59045	−	16.6111i	0.432811	−	0.749650i	−0.564303	−	0.825568i	$-0.690855\pi$
$491$	9.59045	−	16.6111i	0.432811	−	0.749650i	0.997114	+	0.0759172i	$0.0241885\pi$
$492$	2.31911	−	1.79823i	0.104553	−	0.0810705i
$493$	18.5201	+	32.0778i	0.834105	+	1.44471i
$494$	13.8336			0.622402
$495$	9.55533	+	2.77411i	0.429480	+	0.124687i
$496$	−9.35271			−0.419949
$497$	14.3042	+	24.7755i	0.641629	+	1.11133i
$498$	−0.669695	−	0.273435i	−0.0300098	−	0.0122529i
$499$	18.8531	−	32.6546i	0.843982	−	1.46182i	−0.0425200	−	0.999096i	$-0.513539\pi$
$499$	18.8531	−	32.6546i	0.843982	−	1.46182i	0.886502	−	0.462724i	$-0.153128\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	−17.1313	−	6.99466i	−0.765370	−	0.312498i
$502$	−14.1442	+	8.16613i	−0.631284	+	0.364472i
$503$	34.9467			1.55820			0.779098	−	0.626902i	$-0.215677\pi$
$503$	34.9467			1.55820			0.779098	+	0.626902i	$0.215677\pi$
$504$	−7.77305	+	7.93200i	−0.346239	+	0.353319i
$505$			7.12329i			0.316982i
$506$	0.708923	−	22.9544i	0.0315155	−	1.02045i
$507$	−13.8359	+	10.7283i	−0.614474	+	0.476462i
$508$	9.66673	+	5.58109i	0.428892	+	0.247621i
$509$	10.1145	+	5.83963i	0.448319	+	0.258837i	0.707120	−	0.707094i	$-0.249994\pi$
$509$	10.1145	+	5.83963i	0.448319	+	0.258837i	−0.258801	+	0.965931i	$0.583327\pi$
$510$	−10.8130	+	1.47926i	−0.478808	+	0.0655028i
$511$	−8.92873	−	15.4650i	−0.394984	−	0.684132i
$512$	1.00000			0.0441942
$513$	38.8026	−	16.7671i	1.71318	−	0.740285i
$514$		−	11.6549i		−	0.514078i
$515$	−2.62526	+	1.51569i	−0.115683	+	0.0667895i
$516$	−0.230458	+	0.0315275i	−0.0101453	+	0.00138792i
$517$	−19.5952	+	10.5205i	−0.861796	+	0.462692i
$518$	13.6062	+	7.85557i	0.597824	+	0.345154i
$519$	−31.9948	+	24.8087i	−1.40442	+	1.08898i
$520$	0.850259	+	1.47269i	0.0372863	+	0.0645818i
$521$			31.3047i			1.37149i	0.727844	+	0.685743i	$0.240523\pi$
$521$			31.3047i			1.37149i	−0.727844	+	0.685743i	$0.759477\pi$
$522$	4.39173	−	17.0797i	0.192221	−	0.747559i
$523$		−	8.03315i		−	0.351265i	−0.984456	−	0.175633i	$-0.943803\pi$
$523$		−	8.03315i		−	0.351265i	0.984456	−	0.175633i	$-0.0561971\pi$
$524$	3.26700	+	5.65861i	0.142720	+	0.247198i
$525$	2.42371	−	5.93615i	0.105780	−	0.259075i
$526$	−5.72200	+	9.91079i	−0.249491	+	0.432131i
$527$	−29.4659	+	51.0364i	−1.28355	+	2.22318i
$528$	−4.64621	+	3.37827i	−0.202200	+	0.147020i
$529$	12.4731	+	21.6041i	0.542311	+	0.939310i
$530$	−11.7272			−0.509397
$531$	30.5856	+	7.86451i	1.32730	+	0.341291i
$532$	30.1147			1.30564
$533$	−2.49517	+	1.44059i	−0.108078	+	0.0623988i
$534$	4.81663	+	6.21181i	0.208436	+	0.268812i
$535$	−5.20251	−	3.00367i	−0.224924	−	0.129860i
$536$	1.52684	−	2.64456i	0.0659494	−	0.114228i
$537$	−35.7167	+	4.88619i	−1.54129	+	0.210855i
$538$	20.7365	−	11.9723i	0.894016	−	0.516160i
$539$	11.7066	−	18.9037i	0.504239	−	0.814239i
$540$	4.16993	+	3.10027i	0.179445	+	0.133415i
$541$		−	20.9687i		−	0.901516i	−0.892646	−	0.450758i	$-0.851154\pi$
$541$		−	20.9687i		−	0.901516i	0.892646	−	0.450758i	$-0.148846\pi$
$542$	−5.61221	+	3.24021i	−0.241065	+	0.139179i
$543$	−3.90823	−	28.5681i	−0.167718	−	1.22598i
$544$	3.15052	−	5.45686i	0.135077	−	0.233961i
$545$	2.37477	−	4.11322i	0.101724	−	0.176191i
$546$	8.61665	−	6.68134i	0.368759	−	0.285935i
$547$	−26.4030	+	15.2438i	−1.12891	+	0.651777i	−0.943661	−	0.330915i	$-0.892643\pi$
$547$	−26.4030	+	15.2438i	−1.12891	+	0.651777i	−0.185250	+	0.982691i	$0.559309\pi$
$548$		−	7.00440i		−	0.299213i
$549$	29.9248	−	30.5368i	1.27716	−	1.30328i
$550$	1.74619	−	2.81972i	0.0744577	−	0.120233i
$551$	−41.4138	+	23.9103i	−1.76429	+	1.01861i
$552$	4.53350	−	11.1034i	0.192959	−	0.472594i
$553$	9.12077	−	15.7976i	0.387855	−	0.671784i
$554$	−14.3214	−	8.26849i	−0.608460	−	0.351294i
$555$	2.77868	−	6.80553i	0.117948	−	0.288879i
$556$	1.05294	−	0.607915i	0.0446546	−	0.0257814i
$557$	30.5744			1.29548			0.647740	−	0.761862i	$-0.275714\pi$
$557$	30.5744			1.29548			0.647740	+	0.761862i	$0.275714\pi$
$558$	27.0272	−	7.53589i	1.14415	−	0.319020i
$559$	0.228370			0.00965901
$560$	1.85095	+	3.20594i	0.0782170	+	0.135476i
$561$	3.79677	+	35.9970i	0.160300	+	1.51980i
$562$	7.80447	−	13.5177i	0.329212	−	0.570211i
$563$	−8.04154	+	13.9284i	−0.338911	+	0.587010i	−0.984228	−	0.176904i	$-0.943392\pi$
$563$	−8.04154	+	13.9284i	−0.338911	+	0.587010i	0.645317	+	0.763914i	$0.276725\pi$
$564$	−11.5077	+	1.57430i	−0.484561	+	0.0662899i
$565$	−5.51485	−	9.55200i	−0.232012	−	0.401856i
$566$		−	25.2825i		−	1.06270i
$567$	16.0712	−	29.1847i	0.674926	−	1.22564i
$568$			7.72800i			0.324260i
$569$	6.32652	+	10.9578i	0.265221	+	0.459377i	0.967622	−	0.252405i	$-0.0812216\pi$
$569$	6.32652	+	10.9578i	0.265221	+	0.459377i	−0.702400	+	0.711782i	$0.747888\pi$
$570$	−1.90979	−	13.9601i	−0.0799923	−	0.584722i
$571$	−6.85184	−	3.95591i	−0.286741	−	0.165550i	0.349730	−	0.936850i	$-0.386273\pi$
$571$	−6.85184	−	3.95591i	−0.286741	−	0.165550i	−0.636471	+	0.771301i	$0.719607\pi$
$572$	4.96909	−	2.66787i	0.207768	−	0.111549i
$573$	−17.0859	−	22.0350i	−0.713773	−	0.920524i
$574$	−5.43180	+	3.13605i	−0.226719	+	0.130896i
$575$			6.92433i			0.288764i
$576$	−2.88977	+	0.805744i	−0.120407	+	0.0335727i
$577$	11.0441			0.459774			0.229887	−	0.973217i	$-0.426164\pi$
$577$	11.0441			0.459774			0.229887	+	0.973217i	$0.426164\pi$
$578$	−11.3515	−	19.6614i	−0.472162	−	0.817808i
$579$	6.29372	−	15.4145i	0.261558	−	0.640606i
$580$	−5.09088	−	2.93922i	−0.211387	−	0.122044i
$581$	1.33892	+	0.773023i	0.0555476	+	0.0320704i
$582$	−20.2069	−	8.25042i	−0.837602	−	0.341991i
$583$	−1.20065	+	38.8762i	−0.0497258	+	1.61009i
$584$		−	4.82386i		−	0.199613i
$585$	−3.64367	−	3.57065i	−0.150647	−	0.147628i
$586$	−20.7475			−0.857073
$587$	11.9704	−	6.91111i	0.494071	−	0.285252i	−0.232191	−	0.972670i	$-0.574589\pi$
$587$	11.9704	−	6.91111i	0.494071	−	0.285252i	0.726262	+	0.687418i	$0.241256\pi$
$588$	9.17640	−	7.11536i	0.378428	−	0.293432i
$589$	−65.8902	−	38.0417i	−2.71496	−	1.56748i
$590$	5.26343	−	9.11652i	0.216692	−	0.375321i
$591$	1.52966	+	11.1814i	0.0629219	+	0.459942i
$592$	2.12203	+	3.67547i	0.0872151	+	0.151061i
$593$	−32.9775			−1.35422			−0.677111	−	0.735881i	$-0.736768\pi$
$593$	−32.9775			−1.35422			−0.677111	+	0.735881i	$0.736768\pi$
$594$	10.7045	−	13.5061i	0.439210	−	0.554161i
$595$	23.3258			0.956266
$596$	−3.54443	−	6.13914i	−0.145186	−	0.251469i
$597$	2.07916	+	15.1981i	0.0850943	+	0.622016i
$598$	−5.88747	+	10.1974i	−0.240757	+	0.417003i
$599$	27.3340	+	15.7813i	1.11684	+	0.644805i	0.940591	−	0.339541i	$-0.110272\pi$
$599$	27.3340	+	15.7813i	1.11684	+	0.644805i	0.176244	+	0.984346i	$0.443605\pi$
$600$	1.36878	−	1.06135i	0.0558800	−	0.0433293i
$601$	−26.3640	+	15.2213i	−1.07541	+	0.620889i	−0.929655	−	0.368431i	$-0.879895\pi$
$601$	−26.3640	+	15.2213i	−1.07541	+	0.620889i	−0.145757	+	0.989320i	$0.546562\pi$
$602$	0.497144			0.0202621
$603$	−2.28137	+	8.87242i	−0.0929047	+	0.361313i
$604$			6.91494i			0.281365i
$605$	−9.16872	−	6.07738i	−0.372762	−	0.247080i
$606$	11.4225	+	4.66377i	0.464007	+	0.189453i
$607$	40.0695	+	23.1341i	1.62637	+	0.938986i	0.985164	+	0.171618i	$0.0548996\pi$
$607$	40.0695	+	23.1341i	1.62637	+	0.938986i	0.641208	+	0.767367i	$0.278434\pi$
$608$	7.04504	+	4.06746i	0.285714	+	0.164957i
$609$	−14.2477	+	34.8953i	−0.577344	+	1.41403i
$610$	−7.12584	−	12.3423i	−0.288517	−	0.499725i
$611$	11.4034			0.461333
$612$	−4.70745	+	18.3076i	−0.190287	+	0.740040i
$613$			34.3945i			1.38918i	0.719405	+	0.694591i	$0.244415\pi$
$613$			34.3945i			1.38918i	−0.719405	+	0.694591i	$0.755585\pi$
$614$	10.1731	−	5.87345i	0.410554	−	0.237033i
$615$	1.79823	+	2.31911i	0.0725116	+	0.0935153i
$616$	10.8173	−	5.80776i	0.435843	−	0.234001i
$617$	−11.0645	−	6.38808i	−0.445439	−	0.257175i	0.260463	−	0.965484i	$-0.416125\pi$
$617$	−11.0645	−	6.38808i	−0.445439	−	0.257175i	−0.705902	+	0.708309i	$0.749458\pi$
$618$	0.711663	+	5.20206i	0.0286273	+	0.209258i
$619$	22.4955	+	38.9633i	0.904170	+	1.56607i	0.822027	+	0.569448i	$0.192843\pi$
$619$	22.4955	+	38.9633i	0.904170	+	1.56607i	0.0821426	+	0.996621i	$0.473824\pi$
$620$		−	9.35271i		−	0.375614i
$621$	−4.15426	+	35.7392i	−0.166705	+	1.43417i
$622$		−	10.5510i		−	0.423058i
$623$	−8.40004	−	14.5493i	−0.336541	−	0.582905i
$624$	2.91820	−	0.399222i	0.116822	−	0.0159817i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	4.93502	−	8.54771i	0.197243	−	0.341635i
$627$	−46.4737	+	4.90179i	−1.85598	+	0.195759i
$628$	5.63065	+	9.75257i	0.224687	+	0.389170i
$629$	26.7420			1.06628
$630$	−7.93200	−	7.77305i	−0.316018	−	0.309686i
$631$	1.04968			0.0417871			0.0208935	−	0.999782i	$-0.493349\pi$
$631$	1.04968			0.0417871			0.0208935	+	0.999782i	$0.493349\pi$
$632$	4.26744	−	2.46381i	0.169750	−	0.0980050i
$633$	10.4433	−	25.5778i	0.415085	−	1.01662i
$634$	−23.9489	−	13.8269i	−0.951134	−	0.549137i
$635$	−5.58109	+	9.66673i	−0.221479	+	0.383612i
$636$	−7.67805	+	18.8050i	−0.304455	+	0.745668i
$637$	−9.87307	+	5.70022i	−0.391185	+	0.225851i
$638$	−10.2649	+	16.5756i	−0.406389	+	0.656233i
$639$	−6.22679	−	22.3322i	−0.246328	−	0.883447i
$640$			1.00000i			0.0395285i
$641$	19.4193	−	11.2118i	0.767018	−	0.442838i	−0.0647921	−	0.997899i	$-0.520638\pi$
$641$	19.4193	−	11.2118i	0.767018	−	0.442838i	0.831810	+	0.555061i	$0.187305\pi$
$642$	−8.22269	+	6.37586i	−0.324524	+	0.251635i
$643$	10.3829	−	17.9836i	0.409460	−	0.709205i	−0.585370	−	0.810767i	$-0.699051\pi$
$643$	10.3829	−	17.9836i	0.409460	−	0.709205i	0.994829	+	0.101562i	$0.0323839\pi$
$644$	−12.8166	+	22.1990i	−0.505045	+	0.874763i
$645$	−0.0315275	−	0.230458i	−0.00124140	−	0.00907427i
$646$	44.3911	−	25.6292i	1.74654	−	1.00837i
$647$			4.93788i			0.194128i	0.995278	+	0.0970640i	$0.0309451\pi$
$647$			4.93788i			0.194128i	−0.995278	+	0.0970640i	$0.969055\pi$
$648$	7.70155	−	4.65683i	0.302546	−	0.182938i
$649$	−29.6828	−	18.3819i	−1.16515	−	0.721551i
$650$	−1.47269	+	0.850259i	−0.0577637	+	0.0333499i
$651$	−59.4151	+	8.12822i	−2.32866	+	0.318570i
$652$	0.475072	−	0.822849i	0.0186053	−	0.0322252i
$653$	−23.6272	−	13.6412i	−0.924603	−	0.533820i	−0.0395024	−	0.999219i	$-0.512577\pi$
$653$	−23.6272	−	13.6412i	−0.924603	−	0.533820i	−0.885101	+	0.465400i	$0.845911\pi$
$654$	−5.04090	−	6.50104i	−0.197115	−	0.254211i
$655$	−5.65861	+	3.26700i	−0.221100	+	0.127652i
$656$	−1.69429			−0.0661510
$657$	3.88679	+	13.9398i	0.151638	+	0.543845i
$658$	24.8244			0.967757
$659$	−6.36870	−	11.0309i	−0.248089	−	0.429703i	0.714906	−	0.699220i	$-0.246469\pi$
$659$	−6.36870	−	11.0309i	−0.248089	−	0.429703i	−0.962996	+	0.269517i	$0.913136\pi$
$660$	−3.37827	−	4.64621i	−0.131499	−	0.180854i
$661$	−4.16400	+	7.21226i	−0.161961	+	0.280524i	−0.935572	−	0.353136i	$-0.885115\pi$
$661$	−4.16400	+	7.21226i	−0.161961	+	0.280524i	0.773611	+	0.633661i	$0.218448\pi$
$662$	−11.9098	+	20.6284i	−0.462888	+	0.801746i
$663$	7.01536	−	17.1820i	0.272454	−	0.667293i
$664$	0.208818	+	0.361683i	0.00810370	+	0.0140360i
$665$			30.1147i			1.16780i
$666$	−9.09368	−	8.91146i	−0.352373	−	0.345312i
$667$		−	40.7042i		−	1.57607i
$668$	5.34171	+	9.25211i	0.206677	+	0.357975i
$669$	29.1893	−	22.6333i	1.12852	−	0.875054i
$670$	2.64456	+	1.52684i	0.102168	+	0.0589869i
$671$	−41.6449	+	22.3588i	−1.60768	+	0.863153i
$672$	6.35271	−	0.869077i	0.245061	−	0.0335254i
$673$	−40.8988	+	23.6129i	−1.57653	+	0.910211i	−0.581193	+	0.813766i	$0.697414\pi$
$673$	−40.8988	+	23.6129i	−1.57653	+	0.910211i	−0.995338	+	0.0964450i	$0.969253\pi$
$674$		−	22.0537i		−	0.849476i
$675$	−3.10027	+	4.16993i	−0.119330	+	0.160501i
$676$	10.1082			0.388778
$677$	−19.2311	−	33.3093i	−0.739111	−	1.28018i	−0.952896	−	0.303298i	$-0.901912\pi$
$677$	−19.2311	−	33.3093i	−0.739111	−	1.28018i	0.213784	−	0.976881i	$-0.431421\pi$
$678$	−18.9277	+	2.58939i	−0.726914	+	0.0994448i
$679$	40.3994	+	23.3246i	1.55039	+	0.895117i
$680$	5.45686	+	3.15052i	0.209261	+	0.120817i
$681$	15.5926	−	12.0905i	0.597509	−	0.463307i
$682$	−31.0046	−	0.957545i	−1.18723	−	0.0366663i
$683$			1.00073i			0.0382918i	0.999817	+	0.0191459i	$0.00609470\pi$
$683$			1.00073i			0.0382918i	−0.999817	+	0.0191459i	$0.993905\pi$
$684$	−23.6359	−	6.07752i	−0.903741	−	0.232380i
$685$	7.00440			0.267624
$686$	0.948662	−	0.547710i	0.0362201	−	0.0209117i
$687$	−8.26531	−	3.37471i	−0.315341	−	0.128753i
$688$	0.116302	+	0.0671471i	0.00443398	+	0.00255996i
$689$	9.97117	−	17.2706i	0.379871	−	0.657956i
$690$	11.1034	+	4.53350i	0.422700	+	0.172588i
$691$	−9.68498	−	16.7749i	−0.368434	−	0.638146i	0.620887	−	0.783900i	$-0.286773\pi$
$691$	−9.68498	−	16.7749i	−0.368434	−	0.638146i	−0.989321	+	0.145754i	$0.953439\pi$
$692$	23.3748			0.888576
$693$	−26.5801	+	25.4991i	−1.00969	+	0.968631i
$694$	2.82733			0.107324
$695$	0.607915	+	1.05294i	0.0230595	+	0.0399403i
$696$	−8.04626	+	6.23905i	−0.304993	+	0.236491i
$697$	−5.33790	+	9.24551i	−0.202187	+	0.350199i
$698$	15.3832	+	8.88151i	0.582264	+	0.336170i
$699$	5.81479	+	42.5045i	0.219935	+	1.60767i
$700$	−3.20594	+	1.85095i	−0.121173	+	0.0699594i
$701$	24.3953			0.921398			0.460699	−	0.887557i	$-0.347599\pi$
$701$	24.3953			0.921398			0.460699	+	0.887557i	$0.347599\pi$
$702$	−8.11127	+	3.50498i	−0.306140	+	0.132287i
$703$			34.5251i			1.30214i
$704$	3.31504	+	0.102382i	0.124940	+	0.00385865i
$705$	−1.57430	−	11.5077i	−0.0592915	−	0.433405i
$706$	−8.18276	−	4.72432i	−0.307962	−	0.177802i
$707$	−22.8369	−	13.1849i	−0.858869	−	0.495868i
$708$	−11.1726	−	14.4089i	−0.419893	−	0.541519i
$709$	−16.7454	−	29.0038i	−0.628885	−	1.08926i	−0.987776	−	0.155881i	$-0.950178\pi$
$709$	−16.7454	−	29.0038i	−0.628885	−	1.08926i	0.358891	−	0.933380i	$-0.383155\pi$
$710$	−7.72800			−0.290027
$711$	−10.3467	+	10.5583i	−0.388032	+	0.395967i
$712$		−	4.53823i		−	0.170077i
$713$	56.0848	−	32.3806i	2.10039	−	1.21266i
$714$	15.2719	−	37.4039i	0.571537	−	1.39981i
$715$	2.66787	+	4.96909i	0.0997727	+	0.185833i
$716$	18.0247	+	10.4066i	0.673615	+	0.388912i
$717$	8.05376	+	3.28833i	0.300773	+	0.122805i
$718$	−7.93309	−	13.7405i	−0.296060	−	0.512791i
$719$		−	39.1570i		−	1.46031i	−0.683282	−	0.730155i	$-0.739448\pi$
$719$		−	39.1570i		−	1.46031i	0.683282	−	0.730155i	$-0.260552\pi$
$720$	−0.805744	−	2.88977i	−0.0300283	−	0.107695i
$721$		−	11.2219i		−	0.417926i
$722$	23.5884	+	40.8563i	0.877870	+	1.52052i
$723$	−8.07504	−	10.4141i	−0.300314	−	0.387303i
$724$	−8.32372	+	14.4171i	−0.309349	+	0.535808i
$725$	2.93922	−	5.09088i	0.109160	−	0.189070i
$726$	−15.7483	+	10.7234i	−0.584473	+	0.397984i
$727$	18.9732	+	32.8626i	0.703677	+	1.21881i	0.967167	+	0.254143i	$0.0817933\pi$
$727$	18.9732	+	32.8626i	0.703677	+	1.21881i	−0.263489	+	0.964662i	$0.584873\pi$
$728$	−6.29516			−0.233314
$729$	−18.5035	+	19.6627i	−0.685315	+	0.728247i
$730$	4.82386			0.178539
$731$	0.732824	−	0.423096i	0.0271045	−	0.0156488i
$732$	−24.4568	+	3.34579i	−0.903950	+	0.123664i
$733$	−15.5569	−	8.98180i	−0.574609	−	0.331751i	0.184379	−	0.982855i	$-0.440973\pi$
$733$	−15.5569	−	8.98180i	−0.574609	−	0.331751i	−0.758988	+	0.651105i	$0.774306\pi$
$734$	−0.928259	+	1.60779i	−0.0342627	+	0.0593447i
$735$	7.11536	+	9.17640i	0.262454	+	0.338476i
$736$	−5.99664	+	3.46216i	−0.221039	+	0.127617i
$737$	5.33229	−	8.61052i	0.196417	−	0.317173i
$738$	4.89612	−	1.36517i	0.180229	−	0.0502524i
$739$			32.2401i			1.18597i	0.805213	+	0.592985i	$0.202051\pi$
$739$			32.2401i			1.18597i	−0.805213	+	0.592985i	$0.797949\pi$
$740$	−3.67547	+	2.12203i	−0.135113	+	0.0780076i
$741$	22.1827	+	9.05713i	0.814901	+	0.332722i
$742$	21.7065	−	37.5968i	0.796871	−	1.38022i
$743$	5.93755	−	10.2841i	0.217828	−	0.377289i	−0.736316	−	0.676638i	$-0.763436\pi$
$743$	5.93755	−	10.2841i	0.217828	−	0.377289i	0.954144	+	0.299349i	$0.0967696\pi$
$744$	−14.9974	−	6.12341i	−0.549833	−	0.224495i
$745$	6.13914	−	3.54443i	0.224921	−	0.129858i
$746$		−	14.3838i		−	0.526627i
$747$	−0.894859	−	0.876927i	−0.0327412	−	0.0320851i
$748$	11.0028	−	17.7672i	0.402302	−	0.649632i
$749$	19.2592	−	11.1193i	0.703715	−	0.406290i
$750$	1.06135	+	1.36878i	0.0387549	+	0.0499806i
$751$	−8.97230	+	15.5405i	−0.327404	+	0.567080i	−0.981996	−	0.188902i	$-0.939507\pi$
$751$	−8.97230	+	15.5405i	−0.327404	+	0.567080i	0.654592	+	0.755982i	$0.272840\pi$
$752$	5.80744	+	3.35293i	0.211775	+	0.122269i
$753$	−28.0272	+	3.83424i	−1.02137	+	0.139727i
$754$	8.65713	−	4.99820i	0.315274	−	0.182024i
$755$	−6.91494			−0.251661
$756$	−17.6576	+	7.63009i	−0.642202	+	0.277504i
$757$	44.3126			1.61057			0.805285	−	0.592887i	$-0.202012\pi$
$757$	44.3126			1.61057			0.805285	+	0.592887i	$0.202012\pi$
$758$	−1.67786	−	2.90614i	−0.0609427	−	0.105556i
$759$	16.1656	−	36.3442i	0.586772	−	1.31921i
$760$	−4.06746	+	7.04504i	−0.147542	+	0.255551i
$761$	4.67241	−	8.09285i	0.169375	−	0.293366i	−0.768825	−	0.639459i	$-0.779158\pi$
$761$	4.67241	−	8.09285i	0.169375	−	0.293366i	0.938200	+	0.346093i	$0.112492\pi$
$762$	11.8469	+	15.2785i	0.429169	+	0.553482i
$763$	8.79116	+	15.2267i	0.318261	+	0.551245i
$764$			16.0983i			0.582416i
$765$	−18.3076	−	4.70745i	−0.661912	−	0.170198i
$766$		−	11.4937i		−	0.415284i
$767$	8.95056	+	15.5028i	0.323186	+	0.559774i
$768$	1.60354	+	0.654721i	0.0578628	+	0.0236252i
$769$	43.7535	+	25.2611i	1.57779	+	0.910939i	0.995167	+	0.0981981i	$0.0313079\pi$
$769$	43.7535	+	25.2611i	1.57779	+	0.910939i	0.582626	+	0.812741i	$0.302025\pi$
$770$	5.80776	+	10.8173i	0.209297	+	0.389830i
$771$	7.63074	−	18.6892i	0.274814	−	0.673074i
$772$	−8.32495	+	4.80641i	−0.299621	+	0.172986i
$773$		−	10.0301i		−	0.360757i	−0.983597	−	0.180379i	$-0.942268\pi$
$773$		−	10.0301i		−	0.360757i	0.983597	−	0.180379i	$-0.0577323\pi$
$774$	−0.390190	−	0.100330i	−0.0140251	−	0.00360628i
$775$	9.35271			0.335959
$776$	6.30071	+	10.9132i	0.226182	+	0.391759i
$777$	16.6749	+	21.5050i	0.598210	+	0.771488i
$778$	−30.5931	−	17.6629i	−1.09681	−	0.633246i
$779$	−11.9364	−	6.89146i	−0.427664	−	0.246912i
$780$	0.399222	+	2.91820i	0.0142944	+	0.104488i
$781$	−0.791205	+	25.6187i	−0.0283115	+	0.916708i
$782$			43.6304i			1.56022i
$783$	18.2248	−	24.5127i	0.651300	−	0.876011i
$784$	−6.70409			−0.239432
$785$	−9.75257	+	5.63065i	−0.348084	+	0.200966i
$786$	1.53395	+	11.2128i	0.0547143	+	0.399947i
$787$	−7.93744	−	4.58268i	−0.282939	−	0.163355i	0.351814	−	0.936070i	$-0.385565\pi$
$787$	−7.93744	−	4.58268i	−0.282939	−	0.163355i	−0.634753	+	0.772715i	$0.718898\pi$
$788$	3.25786	−	5.64278i	0.116057	−	0.201016i
$789$	−15.6643	+	12.1460i	−0.557662	+	0.432410i
$790$	2.46381	+	4.26744i	0.0876583	+	0.151829i
$791$	40.8309			1.45178
$792$	−9.66221	+	2.37522i	−0.343332	+	0.0843997i
$793$	24.2352			0.860618
$794$	14.4287	+	24.9912i	0.512055	+	0.886905i
$795$	−18.8050	−	7.67805i	−0.666946	−	0.272312i
$796$	4.42817	−	7.66982i	0.156952	−	0.271850i
$797$	9.12825	+	5.27020i	0.323339	+	0.186680i	0.652880	−	0.757461i	$-0.273561\pi$
$797$	9.12825	+	5.27020i	0.323339	+	0.186680i	−0.329541	+	0.944141i	$0.606894\pi$
$798$	48.2901	+	19.7167i	1.70945	+	0.697964i
$799$	36.5929	−	21.1269i	1.29456	−	0.747416i
$800$	−1.00000			−0.0353553
$801$	3.65665	+	13.1144i	0.129201	+	0.463376i
$802$			8.84662i			0.312385i
$803$	0.493874	−	15.9913i	0.0174284	−	0.564321i
$804$	4.17980	−	3.24101i	0.147410	−	0.114301i
$805$	−22.1990	−	12.8166i	−0.782412	−	0.451726i
$806$	13.7737	+	7.95222i	0.485156	+	0.280105i
$807$	41.0904	−	5.62133i	1.44645	−	0.197880i
$808$	−3.56165	−	6.16895i	−0.125298	−	0.217023i
$809$	20.8254			0.732181			0.366091	−	0.930579i	$-0.380696\pi$
$809$	20.8254			0.732181			0.366091	+	0.930579i	$0.380696\pi$
$810$	4.65683	+	7.70155i	0.163624	+	0.270605i
$811$			1.67047i			0.0586583i	0.999570	+	0.0293291i	$0.00933710\pi$
$811$			1.67047i			0.0586583i	−0.999570	+	0.0293291i	$0.990663\pi$
$812$	18.8459	−	10.8807i	0.661363	−	0.381838i
$813$	−11.1208	+	1.52137i	−0.390025	+	0.0533569i
$814$	6.65834	+	12.4016i	0.233375	+	0.434676i
$815$	0.822849	+	0.475072i	0.0288231	+	0.0166410i
$816$	8.62470	−	6.68758i	0.301925	−	0.234112i
$817$	0.546236	+	0.946108i	0.0191104	+	0.0331001i
$818$			26.5420i			0.928018i
$819$	18.1916	−	5.07228i	0.635665	−	0.177240i
$820$		−	1.69429i		−	0.0591673i
$821$	1.60676	+	2.78300i	0.0560764	+	0.0971272i	0.892701	−	0.450650i	$-0.148808\pi$
$821$	1.60676	+	2.78300i	0.0560764	+	0.0971272i	−0.836624	+	0.547777i	$0.815474\pi$
$822$	4.58593	−	11.2318i	0.159953	−	0.391755i
$823$	22.1840	−	38.4238i	0.773286	−	1.33937i	−0.162467	−	0.986714i	$-0.551945\pi$
$823$	22.1840	−	38.4238i	0.773286	−	1.33937i	0.935753	−	0.352656i	$-0.114721\pi$
$824$	1.51569	−	2.62526i	0.0528017	−	0.0914552i
$825$	4.64621	−	3.37827i	0.161760	−	0.117616i
$826$	19.4847	+	33.7485i	0.677959	+	1.17426i
$827$	−39.7226			−1.38129			−0.690646	−	0.723193i	$-0.742674\pi$
$827$	−39.7226			−1.38129			−0.690646	+	0.723193i	$0.742674\pi$
$828$	14.5393	−	14.8366i	0.505276	−	0.515608i
$829$	2.66747			0.0926450			0.0463225	−	0.998927i	$-0.485250\pi$
$829$	2.66747			0.0926450			0.0463225	+	0.998927i	$0.485250\pi$
$830$	−0.361683	+	0.208818i	−0.0125542	+	0.00724817i
$831$	−17.5514	−	22.6354i	−0.608853	−	0.785213i
$832$	−1.47269	−	0.850259i	−0.0510564	−	0.0294774i
$833$	−21.1214	+	36.5833i	−0.731812	+	1.26754i
$834$	2.08645	−	0.285434i	0.0722477	−	0.00988378i
$835$	−9.25211	+	5.34171i	−0.320183	+	0.184858i
$836$	22.9382	+	14.2051i	0.793334	+	0.491293i
$837$	48.2731	+	5.61117i	1.66856	+	0.193950i
$838$			23.7142i			0.819193i
$839$	−15.3125	+	8.84066i	−0.528645	+	0.305213i	−0.740465	−	0.672095i	$-0.765394\pi$
$839$	−15.3125	+	8.84066i	−0.528645	+	0.305213i	0.211819	+	0.977309i	$0.432061\pi$
$840$	0.869077	+	6.35271i	0.0299860	+	0.219189i
$841$	−2.77801	+	4.81166i	−0.0957936	+	0.165919i
$842$	10.3493	−	17.9255i	0.356660	−	0.617754i
$843$	21.3651	−	16.5665i	0.735854	−	0.570580i
$844$	−13.8138	+	7.97541i	−0.475491	+	0.274525i
$845$			10.1082i			0.347734i
$846$	−19.4838	−	5.00988i	−0.669866	−	0.172243i
$847$	36.4546	−	18.1455i	1.25259	−	0.623486i
$848$	10.1561	−	5.86360i	0.348760	−	0.201357i
$849$	16.5530	−	40.5414i	0.568096	−	1.39138i
$850$	−3.15052	+	5.45686i	−0.108062	+	0.187169i
$851$	−25.4502	−	14.6937i	−0.872421	−	0.503692i
$852$	−5.05969	+	12.3922i	−0.173342	+	0.424548i
$853$	28.7935	−	16.6240i	0.985872	−	0.569194i	0.0818343	−	0.996646i	$-0.473922\pi$
$853$	28.7935	−	16.6240i	0.985872	−	0.569194i	0.904038	+	0.427452i	$0.140589\pi$
$854$	52.7583			1.80535
$855$	6.07752	−	23.6359i	0.207847	−	0.808330i
$856$	6.00734			0.205327
$857$	13.1719	+	22.8143i	0.449942	+	0.779323i	0.998382	−	0.0568672i	$-0.0181112\pi$
$857$	13.1719	+	22.8143i	0.449942	+	0.779323i	−0.548439	+	0.836190i	$0.684778\pi$
$858$	9.71485	−	1.02467i	0.331659	−	0.0349816i
$859$	0.521587	−	0.903414i	0.0177963	−	0.0308241i	−0.856990	−	0.515333i	$-0.827668\pi$
$859$	0.521587	−	0.903414i	0.0177963	−	0.0308241i	0.874786	+	0.484509i	$0.161002\pi$
$860$	−0.0671471	+	0.116302i	−0.00228970	+	0.00396587i
$861$	−10.7634	+	1.47247i	−0.366814	+	0.0501816i
$862$	8.47658	+	14.6819i	0.288713	+	0.500066i
$863$			3.30108i			0.112370i	0.998420	+	0.0561850i	$0.0178937\pi$
$863$			3.30108i			0.112370i	−0.998420	+	0.0561850i	$0.982106\pi$
$864$	−5.16140	−	0.599952i	−0.175594	−	0.0204108i
$865$			23.3748i			0.794766i
$866$	18.9684	+	32.8542i	0.644572	+	1.11643i
$867$	−5.32988	−	38.9600i	−0.181012	−	1.32315i
$868$	29.9842	+	17.3114i	1.01773	+	0.587588i
$869$	14.3990	−	7.73072i	0.488452	−	0.262247i
$870$	−6.23905	−	8.04626i	−0.211524	−	0.272794i
$871$	−4.49713	+	2.59642i	−0.152379	+	0.0879762i
$872$			4.74953i			0.160840i
$873$	−27.0008	−	26.4598i	−0.913839	−	0.895527i
$874$	−56.3288			−1.90535
$875$	−1.85095	−	3.20594i	−0.0625736	−	0.108381i
$876$	3.15828	−	7.73525i	0.106708	−	0.261350i
$877$	0.652792	+	0.376890i	0.0220432	+	0.0127267i	0.510981	−	0.859592i	$-0.329282\pi$
$877$	0.652792	+	0.376890i	0.0220432	+	0.0127267i	−0.488938	+	0.872319i	$0.662616\pi$
$878$	−19.7502	−	11.4028i	−0.666539	−	0.384826i
$879$	−33.2695	−	13.5839i	−1.12215	−	0.458172i
$880$	−0.102382	+	3.31504i	−0.00345128	+	0.111750i
$881$			29.9005i			1.00737i	0.863887	+	0.503686i	$0.168023\pi$
$881$			29.9005i			1.00737i	−0.863887	+	0.503686i	$0.831977\pi$
$882$	19.3733	−	5.40178i	0.652333	−	0.181887i
$883$	−31.4539			−1.05851			−0.529253	−	0.848464i	$-0.677528\pi$
$883$	−31.4539			−1.05851			−0.529253	+	0.848464i	$0.677528\pi$
$884$	−9.27949	+	5.35752i	−0.312103	+	0.180193i
$885$	14.4089	−	11.1726i	0.484350	−	0.375564i
$886$	−9.65829	−	5.57622i	−0.324477	−	0.187337i
$887$	2.45480	−	4.25184i	0.0824241	−	0.142763i	−0.821867	−	0.569680i	$-0.807067\pi$
$887$	2.45480	−	4.25184i	0.0824241	−	0.142763i	0.904291	+	0.426917i	$0.140400\pi$
$888$	0.996358	+	7.28311i	0.0334356	+	0.244405i
$889$	−20.6607	−	35.7853i	−0.692936	−	1.20020i
$890$	4.53823			0.152122
$891$	26.0078	−	14.6491i	0.871293	−	0.490763i
$892$	−21.3251			−0.714017
$893$	27.2758	+	47.2430i	0.912749	+	1.58093i
$894$	−1.66422	−	12.1650i	−0.0556597	−	0.406857i
$895$	−10.4066	+	18.0247i	−0.347853	+	0.602500i
$896$	−3.20594	−	1.85095i	−0.107103	−	0.0618360i
$897$	−16.1173	+	12.4973i	−0.538139	+	0.417272i
$898$	24.2519	−	14.0019i	0.809297	−	0.467248i
$899$	−54.9793			−1.83366
$900$	2.88977	−	0.805744i	0.0963257	−	0.0268581i
$901$		−	73.8936i		−	2.46175i
$902$	−5.61665	−	0.173464i	−0.187014	−	0.00577573i
$903$	0.797190	+	0.325491i	0.0265288	+	0.0108317i
$904$	9.55200	+	5.51485i	0.317695	+	0.183421i
$905$	−14.4171	−	8.32372i	−0.479241	−	0.276690i
$906$	−4.52736	+	11.0884i	−0.150411	+	0.368387i
$907$	−2.20442	−	3.81816i	−0.0731964	−	0.126780i	0.827104	−	0.562049i	$-0.189987\pi$
$907$	−2.20442	−	3.81816i	−0.0731964	−	0.126780i	−0.900301	+	0.435269i	$0.856653\pi$
$908$	−11.3916			−0.378045
$909$	15.2629	+	14.9571i	0.506240	+	0.496095i
$910$		−	6.29516i		−	0.208682i
$911$	25.1448	−	14.5174i	0.833084	−	0.480981i	−0.0218233	−	0.999762i	$-0.506947\pi$
$911$	25.1448	−	14.5174i	0.833084	−	0.480981i	0.854907	+	0.518780i	$0.173614\pi$
$912$	8.63396	+	11.1349i	0.285899	+	0.368712i
$913$	0.655210	+	1.22037i	0.0216843	+	0.0403885i
$914$	−5.08207	−	2.93413i	−0.168100	−	0.0970525i
$915$	−3.34579	−	24.4568i	−0.110608	−	0.808518i
$916$	2.57721	+	4.46385i	0.0851533	+	0.147490i
$917$		−	24.1883i		−	0.798766i
$918$	−19.5349	+	26.2749i	−0.644749	+	0.867200i
$919$			5.48992i			0.181096i	0.995892	+	0.0905478i	$0.0288618\pi$
$919$			5.48992i			0.181096i	−0.995892	+	0.0905478i	$0.971138\pi$
$920$	−3.46216	−	5.99664i	−0.114144	−	0.197703i
$921$	20.1585	−	2.75776i	0.664244	−	0.0908713i
$922$	10.4234	−	18.0539i	0.343277	−	0.594574i
$923$	6.57081	−	11.3810i	0.216281	−	0.374609i
$924$	21.1485	−	2.23063i	0.695735	−	0.0733822i
$925$	−2.12203	−	3.67547i	−0.0697721	−	0.120849i
$926$	−9.35194			−0.307324
$927$	−2.26472	+	8.80766i	−0.0743832	+	0.289281i
$928$	5.87844			0.192969
$929$	−4.67701	+	2.70027i	−0.153448	+	0.0885930i	−0.574758	−	0.818324i	$-0.694904\pi$
$929$	−4.67701	+	2.70027i	−0.153448	+	0.0885930i	0.421310	+	0.906917i	$0.361570\pi$
$930$	6.12341	−	14.9974i	0.200795	−	0.491785i
$931$	−47.2306	−	27.2686i	−1.54792	−	0.893693i
$932$	12.3843	−	21.4502i	0.405661	−	0.702625i
$933$	6.90798	−	16.9190i	0.226157	−	0.553903i
$934$	6.20173	−	3.58057i	0.202927	−	0.117160i
$935$	17.7672	+	11.0028i	0.581049	+	0.359830i
$936$	4.94083	+	1.27044i	0.161496	+	0.0415257i
$937$			44.5644i			1.45586i	0.685653	+	0.727928i	$0.259517\pi$
$937$			44.5644i			1.45586i	−0.685653	+	0.727928i	$0.740483\pi$
$938$	−9.78991	+	5.65221i	−0.319652	+	0.184551i
$939$	13.5099	−	10.4755i	0.440878	−	0.341856i
$940$	−3.35293	+	5.80744i	−0.109360	+	0.189418i
$941$	2.75946	−	4.77952i	0.0899558	−	0.155808i	−0.817536	−	0.575877i	$-0.804661\pi$
$941$	2.75946	−	4.77952i	0.0899558	−	0.155808i	0.907492	+	0.420069i	$0.137994\pi$
$942$	2.64376	+	19.3251i	0.0861382	+	0.629647i
$943$	10.1601	−	5.86592i	0.330857	−	0.191021i
$944$			10.5269i			0.342620i
$945$	−7.63009	−	17.6576i	−0.248207	−	0.574403i
$946$	0.378672	+	0.234503i	0.0123117	+	0.00762434i
$947$	−9.64627	+	5.56928i	−0.313462	+	0.180977i	−0.648475	−	0.761236i	$-0.724593\pi$
$947$	−9.64627	+	5.56928i	−0.313462	+	0.180977i	0.335013	+	0.942214i	$0.391259\pi$
$948$	8.45611	−	1.15683i	0.274642	−	0.0375721i
$949$	−4.10153	+	7.10406i	−0.133141	+	0.230607i
$950$	−7.04504	−	4.06746i	−0.228571	−	0.131966i
$951$	−29.3503	−	37.8519i	−0.951749	−	1.22743i
$952$	−20.2008	+	11.6629i	−0.654711	+	0.377997i
$953$	25.6900			0.832181			0.416090	−	0.909323i	$-0.363400\pi$
$953$	25.6900			0.832181			0.416090	+	0.909323i	$0.363400\pi$
$954$	−24.6241	+	25.1277i	−0.797235	+	0.813538i
$955$	−16.0983			−0.520929
$956$	−2.51124	−	4.34960i	−0.0812194	−	0.140676i
$957$	−27.3125	+	19.8590i	−0.882887	+	0.641949i
$958$	6.52135	−	11.2953i	0.210695	−	0.364935i
$959$	−12.9648	+	22.4557i	−0.418655	+	0.725133i
$960$	−0.654721	+	1.60354i	−0.0211310	+	0.0517540i
$961$	−28.2366	−	48.9071i	−0.910857	−	1.57765i
$962$		−	7.21712i		−	0.232689i
$963$	−17.3598	+	4.84038i	−0.559413	+	0.155979i
$964$			7.60831i			0.245047i
$965$	−4.80641	−	8.32495i	−0.154724	−	0.267989i
$966$	−35.0861	+	27.2057i	−1.12888	+	0.875328i
$967$	5.92658	+	3.42171i	0.190586	+	0.110035i	0.592257	−	0.805749i	$-0.298237\pi$
$967$	5.92658	+	3.42171i	0.190586	+	0.110035i	−0.401671	+	0.915784i	$0.631570\pi$
$968$	10.9790	+	0.678799i	0.352880	+	0.0218174i
$969$	87.9628	−	12.0337i	2.82577	−	0.386577i
$970$	−10.9132	+	6.30071i	−0.350400	+	0.202304i
$971$			17.2318i			0.552996i	0.961015	+	0.276498i	$0.0891739\pi$
$971$			17.2318i			0.552996i	−0.961015	+	0.276498i	$0.910826\pi$
$972$	15.3987	−	2.42505i	0.493913	−	0.0777834i
$973$	−4.50089			−0.144292
$974$	3.97084	+	6.87769i	0.127234	+	0.220375i
$975$	−2.91820	+	0.399222i	−0.0934573	+	0.0127853i
$976$	12.3423	+	7.12584i	0.395068	+	0.228092i
$977$	−30.1833	−	17.4263i	−0.965649	−	0.557518i	−0.0677422	−	0.997703i	$-0.521580\pi$
$977$	−30.1833	−	17.4263i	−0.965649	−	0.557518i	−0.897907	+	0.440185i	$0.854913\pi$
$978$	1.30053	−	1.00843i	0.0415865	−	0.0322461i
$979$	0.464631	−	15.0444i	0.0148497	−	0.480822i
$980$		−	6.70409i		−	0.214154i
$981$	−3.82691	−	13.7251i	−0.122184	−	0.438208i
$982$	−19.1809			−0.612087
$983$	−47.4751	+	27.4097i	−1.51422	+	0.874235i	−0.514358	+	0.857575i	$0.671970\pi$
$983$	−47.4751	+	27.4097i	−1.51422	+	0.874235i	−0.999861	+	0.0166598i	$0.994697\pi$
$984$	−2.71687	−	1.10929i	−0.0866105	−	0.0353628i
$985$	5.64278	+	3.25786i	0.179794	+	0.103804i
$986$	18.5201	−	32.0778i	0.589801	−	1.02157i
$987$	39.8069	+	16.2531i	1.26707	+	0.517341i
$988$	−6.91679	−	11.9802i	−0.220052	−	0.381142i
$989$	−0.929897			−0.0295690
$990$	−2.37522	−	9.66221i	−0.0754894	−	0.307085i
$991$	−2.80826			−0.0892074			−0.0446037	−	0.999005i	$-0.514203\pi$
$991$	−2.80826			−0.0892074			−0.0446037	+	0.999005i	$0.514203\pi$
$992$	4.67635	+	8.09968i	0.148474	+	0.257165i
$993$	−32.6037	+	25.2809i	−1.03465	+	0.802264i
$994$	14.3042	−	24.7755i	0.453700	−	0.785832i
$995$	7.66982	+	4.42817i	0.243150	+	0.140383i
$996$	0.0980461	+	0.716691i	0.00310671	+	0.0227092i
$997$	−28.6772	+	16.5568i	−0.908216	+	0.524359i	−0.879857	−	0.475239i	$-0.842362\pi$
$997$	−28.6772	+	16.5568i	−0.908216	+	0.524359i	−0.0283596	+	0.999598i	$0.509028\pi$
$998$	−37.7063			−1.19357
$999$	−8.74757	−	20.2437i	−0.276761	−	0.640482i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.t.a.131.11	✓	48
3.2	odd	2		2970.2.t.b.2771.13		48
9.2	odd	6		990.2.t.b.461.11	yes	48
9.7	even	3		2970.2.t.a.791.13		48
11.10	odd	2		990.2.t.b.131.11	yes	48
33.32	even	2		2970.2.t.a.2771.13		48
99.43	odd	6		2970.2.t.b.791.13		48
99.65	even	6	inner	990.2.t.a.461.11	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.t.a.131.11	✓	48	1.1	even	1	trivial
990.2.t.a.461.11	yes	48	99.65	even	6	inner
990.2.t.b.131.11	yes	48	11.10	odd	2
990.2.t.b.461.11	yes	48	9.2	odd	6
2970.2.t.a.791.13		48	9.7	even	3
2970.2.t.a.2771.13		48	33.32	even	2
2970.2.t.b.791.13		48	99.43	odd	6
2970.2.t.b.2771.13		48	3.2	odd	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} +(-0.234765 - 1.71607i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.36878 + 1.06135i) q^{6} +(3.20594 - 1.85095i) q^{7} +1.00000 q^{8} +(-2.88977 + 0.805744i) q^{9} +1.00000i q^{10} +(3.31504 + 0.102382i) q^{11} +(1.60354 + 0.654721i) q^{12} +(-1.47269 - 0.850259i) q^{13} +(-3.20594 - 1.85095i) q^{14} +(-0.654721 + 1.60354i) q^{15} +(-0.500000 - 0.866025i) q^{16} -6.30104 q^{17} +(2.14268 + 2.09974i) q^{18} -8.13491i q^{19} +(0.866025 - 0.500000i) q^{20} +(-3.92900 - 5.06707i) q^{21} +(-1.56886 - 2.92210i) q^{22} +(5.99664 + 3.46216i) q^{23} +(-0.234765 - 1.71607i) q^{24} +(0.500000 + 0.866025i) q^{25} +1.70052i q^{26} +(2.06113 + 4.76988i) q^{27} +3.70190i q^{28} +(-2.93922 - 5.09088i) q^{29} +(1.71607 - 0.234765i) q^{30} +(4.67635 - 8.09968i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.602562 - 5.71287i) q^{33} +(3.15052 + 5.45686i) q^{34} -3.70190 q^{35} +(0.747091 - 2.90549i) q^{36} -4.24407 q^{37} +(-7.04504 + 4.06746i) q^{38} +(-1.11337 + 2.72685i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(0.847146 - 1.46730i) q^{41} +(-2.42371 + 5.93615i) q^{42} +(-0.116302 + 0.0671471i) q^{43} +(-1.74619 + 2.81972i) q^{44} +(2.90549 + 0.747091i) q^{45} -6.92433i q^{46} +(-5.80744 + 3.35293i) q^{47} +(-1.36878 + 1.06135i) q^{48} +(3.35205 - 5.80591i) q^{49} +(0.500000 - 0.866025i) q^{50} +(1.47926 + 10.8130i) q^{51} +(1.47269 - 0.850259i) q^{52} +11.7272i q^{53} +(3.10027 - 4.16993i) q^{54} +(-2.81972 - 1.74619i) q^{55} +(3.20594 - 1.85095i) q^{56} +(-13.9601 + 1.90979i) q^{57} +(-2.93922 + 5.09088i) q^{58} +(-9.11652 - 5.26343i) q^{59} +(-1.06135 - 1.36878i) q^{60} +(-12.3423 + 7.12584i) q^{61} -9.35271 q^{62} +(-7.77305 + 7.93200i) q^{63} +1.00000 q^{64} +(0.850259 + 1.47269i) q^{65} +(-4.64621 + 3.37827i) q^{66} +(1.52684 - 2.64456i) q^{67} +(3.15052 - 5.45686i) q^{68} +(4.53350 - 11.1034i) q^{69} +(1.85095 + 3.20594i) q^{70} +7.72800i q^{71} +(-2.88977 + 0.805744i) q^{72} -4.82386i q^{73} +(2.12203 + 3.67547i) q^{74} +(1.36878 - 1.06135i) q^{75} +(7.04504 + 4.06746i) q^{76} +(10.8173 - 5.80776i) q^{77} +(2.91820 - 0.399222i) q^{78} +(4.26744 - 2.46381i) q^{79} +1.00000i q^{80} +(7.70155 - 4.65683i) q^{81} -1.69429 q^{82} +(0.208818 + 0.361683i) q^{83} +(6.35271 - 0.869077i) q^{84} +(5.45686 + 3.15052i) q^{85} +(0.116302 + 0.0671471i) q^{86} +(-8.04626 + 6.23905i) q^{87} +(3.31504 + 0.102382i) q^{88} -4.53823i q^{89} +(-0.805744 - 2.88977i) q^{90} -6.29516 q^{91} +(-5.99664 + 3.46216i) q^{92} +(-14.9974 - 6.12341i) q^{93} +(5.80744 + 3.35293i) q^{94} +(-4.06746 + 7.04504i) q^{95} +(1.60354 + 0.654721i) q^{96} +(6.30071 + 10.9132i) q^{97} -6.70409 q^{98} +(-9.66221 + 2.37522i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{6} + 48 q^{8} + 10 q^{9} - 6 q^{11} + 4 q^{12} + 24 q^{13} - 4 q^{15} - 24 q^{16} - 12 q^{17} - 8 q^{18} - 16 q^{21} + 12 q^{22} + 36 q^{23} - 2 q^{24} + 24 q^{25}+ \cdots - 48 q^{99}+O(q^{100}) \) 48 * q - 24 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^6 + 48 * q^8 + 10 * q^9 - 6 * q^11 + 4 * q^12 + 24 * q^13 - 4 * q^15 - 24 * q^16 - 12 * q^17 - 8 * q^18 - 16 * q^21 + 12 * q^22 + 36 * q^23 - 2 * q^24 + 24 * q^25 - 8 * q^27 + 8 * q^30 - 24 * q^32 + 2 * 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 + 8 * q^66 - 6 * q^67 + 6 * q^68 + 76 * q^69 + 10 * q^72 + 2 * q^75 + 6 * q^76 + 6 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 + 36 * q^83 + 8 * q^84 - 30 * q^86 - 44 * q^87 - 6 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 + 4 * q^96 + 6 * q^97 - 48 * q^98 - 48 * q^99

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