LMFDB - Embedded newform 798.2.bc.b.103.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(31,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 1, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bc (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,0,28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			103.8
Character	$\chi$	$=$	798.103
Dual form			798.2.bc.b.31.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.82315 + 1.62995i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-1.88485 - 1.85670i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +(-1.62995 + 2.82315i) q^{10} +(-2.71451 - 4.70166i) q^{11} +(0.500000 - 0.866025i) q^{12} +(0.714142 + 1.23693i) q^{13} +(-2.56068 - 0.665524i) q^{14} +(-2.82315 + 1.62995i) q^{15} +(-0.500000 - 0.866025i) q^{16} -7.91573i q^{17} +(0.866025 - 0.500000i) q^{18} +(3.51758 - 2.57423i) q^{19} +3.25990i q^{20} +(-1.88485 - 1.85670i) q^{21} +(-4.70166 - 2.71451i) q^{22} -4.55733 q^{23} -1.00000i q^{24} +(2.81347 - 4.87306i) q^{25} +(1.23693 + 0.714142i) q^{26} +1.00000 q^{27} +(-2.55038 + 0.703979i) q^{28} +(0.0142282 - 0.00821465i) q^{29} +(-1.62995 + 2.82315i) q^{30} +(3.26114 + 5.64846i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-2.71451 - 4.70166i) q^{33} +(-3.95787 - 6.85523i) q^{34} +(8.34755 + 2.16954i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-7.25582 - 4.18915i) q^{37} +(1.75920 - 3.98813i) q^{38} +(0.714142 + 1.23693i) q^{39} +(1.62995 + 2.82315i) q^{40} +(4.82765 - 8.36174i) q^{41} +(-2.56068 - 0.665524i) q^{42} +(-5.98293 + 10.3627i) q^{43} -5.42901 q^{44} +(-2.82315 + 1.62995i) q^{45} +(-3.94676 + 2.27866i) q^{46} +2.99936i q^{47} +(-0.500000 - 0.866025i) q^{48} +(0.105327 + 6.99921i) q^{49} -5.62693i q^{50} -7.91573i q^{51} +1.42828 q^{52} +(0.918586 + 0.530346i) q^{53} +(0.866025 - 0.500000i) q^{54} +(15.3269 + 8.84901i) q^{55} +(-1.85670 + 1.88485i) q^{56} +(3.51758 - 2.57423i) q^{57} +(0.00821465 - 0.0142282i) q^{58} +6.62637 q^{59} +3.25990i q^{60} -3.83790i q^{61} +(5.64846 + 3.26114i) q^{62} +(-1.88485 - 1.85670i) q^{63} -1.00000 q^{64} +(-4.03227 - 2.32803i) q^{65} +(-4.70166 - 2.71451i) q^{66} +(0.307919 + 0.177777i) q^{67} +(-6.85523 - 3.95787i) q^{68} -4.55733 q^{69} +(8.31396 - 2.29490i) q^{70} +(-1.21530 - 0.701655i) q^{71} -1.00000i q^{72} +9.36694i q^{73} -8.37830 q^{74} +(2.81347 - 4.87306i) q^{75} +(-0.470556 - 4.33343i) q^{76} +(-3.61314 + 13.9020i) q^{77} +(1.23693 + 0.714142i) q^{78} +(6.77772 - 3.91312i) q^{79} +(2.82315 + 1.62995i) q^{80} +1.00000 q^{81} -9.65530i q^{82} +6.47715i q^{83} +(-2.55038 + 0.703979i) q^{84} +(12.9022 + 22.3473i) q^{85} +11.9659i q^{86} +(0.0142282 - 0.00821465i) q^{87} +(-4.70166 + 2.71451i) q^{88} -1.34598 q^{89} +(-1.62995 + 2.82315i) q^{90} +(0.950558 - 3.65738i) q^{91} +(-2.27866 + 3.94676i) q^{92} +(3.26114 + 5.64846i) q^{93} +(1.49968 + 2.59752i) q^{94} +(-5.73481 + 13.0009i) q^{95} +(-0.866025 - 0.500000i) q^{96} +(8.67534 - 15.0261i) q^{97} +(3.59082 + 6.00883i) q^{98} +(-2.71451 - 4.70166i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 28 q^{3} + 14 q^{4} + 6 q^{5} - 8 q^{7} + 28 q^{9} + 2 q^{10} + 14 q^{12} + 2 q^{13} - 8 q^{14} + 6 q^{15} - 14 q^{16} + 12 q^{19} - 8 q^{21} - 12 q^{22} + 24 q^{23} + 14 q^{25} + 24 q^{26} + 28 q^{27}+ \cdots + 28 q^{98}+O(q^{100}) $ 28 * q + 28 * q^3 + 14 * q^4 + 6 * q^5 - 8 * q^7 + 28 * q^9 + 2 * q^10 + 14 * q^12 + 2 * q^13 - 8 * q^14 + 6 * q^15 - 14 * q^16 + 12 * q^19 - 8 * q^21 - 12 * q^22 + 24 * q^23 + 14 * q^25 + 24 * q^26 + 28 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 + 4 * q^31 - 4 * q^34 - 10 * q^35 + 14 * q^36 - 24 * q^37 - 6 * q^38 + 2 * q^39 - 2 * q^40 + 4 * q^41 - 8 * q^42 - 14 * q^43 + 6 * q^45 - 12 * q^46 - 14 * q^48 - 24 * q^49 + 4 * q^52 + 24 * q^53 + 18 * q^55 - 4 * q^56 + 12 * q^57 - 2 * q^58 + 44 * q^59 - 12 * q^62 - 8 * q^63 - 28 * q^64 - 24 * q^65 - 12 * q^66 - 18 * q^67 + 6 * q^68 + 24 * q^69 + 6 * q^70 - 6 * q^71 + 12 * q^74 + 14 * q^75 + 40 * q^77 + 24 * q^78 - 24 * q^79 - 6 * q^80 + 28 * q^81 + 2 * q^84 + 28 * q^85 + 18 * q^87 - 12 * q^88 + 16 * q^89 + 2 * q^90 - 20 * q^91 + 12 * q^92 + 4 * q^93 - 18 * q^94 + 26 * q^95 - 40 * q^97 + 28 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−2.82315	+	1.62995i	−1.26255	+	0.728935i	−0.973568	−	0.228398i	$-0.926651\pi$
$5$	−2.82315	+	1.62995i	−1.26255	+	0.728935i	−0.288985	+	0.957334i	$0.593318\pi$
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	−1.88485	−	1.85670i	−0.712407	−	0.701767i
$7$	−1.88485	−	1.85670i	−0.712407	−	0.701767i
$8$		−	1.00000i		−	0.353553i
$9$	1.00000			0.333333
$10$	−1.62995	+	2.82315i	−0.515435	+	0.892760i
$11$	−2.71451	−	4.70166i	−0.818454	−	1.41760i	−0.906821	−	0.421516i	$-0.861498\pi$
$11$	−2.71451	−	4.70166i	−0.818454	−	1.41760i	0.0883666	−	0.996088i	$-0.471835\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	0.714142	+	1.23693i	0.198067	+	0.343063i	0.947902	−	0.318563i	$-0.103200\pi$
$13$	0.714142	+	1.23693i	0.198067	+	0.343063i	−0.749834	+	0.661626i	$0.769867\pi$
$14$	−2.56068	−	0.665524i	−0.684370	−	0.177869i
$15$	−2.82315	+	1.62995i	−0.728935	+	0.420851i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		−	7.91573i		−	1.91985i	−0.280261	−	0.959924i	$-0.590421\pi$
$17$		−	7.91573i		−	1.91985i	0.280261	−	0.959924i	$-0.409579\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	3.51758	−	2.57423i	0.806988	−	0.590568i
$19$	3.51758	−	2.57423i	0.806988	−	0.590568i
$20$			3.25990i			0.728935i
$21$	−1.88485	−	1.85670i	−0.411308	−	0.405165i
$22$	−4.70166	−	2.71451i	−1.00240	−	0.578735i
$23$	−4.55733			−0.950268			−0.475134	−	0.879913i	$-0.657600\pi$
$23$	−4.55733			−0.950268			−0.475134	+	0.879913i	$0.657600\pi$
$24$		−	1.00000i		−	0.204124i
$25$	2.81347	−	4.87306i	0.562693	−	0.974613i
$26$	1.23693	+	0.714142i	0.242582	+	0.140055i
$27$	1.00000			0.192450
$28$	−2.55038	+	0.703979i	−0.481976	+	0.133039i
$29$	0.0142282	−	0.00821465i	0.00264211	−	0.00152542i	−0.498678	−	0.866787i	$-0.666181\pi$
$29$	0.0142282	−	0.00821465i	0.00264211	−	0.00152542i	0.501320	+	0.865262i	$0.332848\pi$
$30$	−1.62995	+	2.82315i	−0.297587	+	0.515435i
$31$	3.26114	+	5.64846i	0.585718	+	1.01449i	0.994786	+	0.101989i	$0.0325207\pi$
$31$	3.26114	+	5.64846i	0.585718	+	1.01449i	−0.409068	+	0.912504i	$0.634146\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−2.71451	−	4.70166i	−0.472535	−	0.818454i
$34$	−3.95787	−	6.85523i	−0.678769	−	1.17566i
$35$	8.34755	+	2.16954i	1.41099	+	0.366719i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−7.25582	−	4.18915i	−1.19285	−	0.688692i	−0.233897	−	0.972261i	$-0.575148\pi$
$37$	−7.25582	−	4.18915i	−1.19285	−	0.688692i	−0.958952	+	0.283570i	$0.908481\pi$
$38$	1.75920	−	3.98813i	0.285380	−	0.646961i
$39$	0.714142	+	1.23693i	0.114354	+	0.198067i
$40$	1.62995	+	2.82315i	0.257718	+	0.446380i
$41$	4.82765	−	8.36174i	0.753953	−	1.30588i	−0.191941	−	0.981406i	$-0.561478\pi$
$41$	4.82765	−	8.36174i	0.753953	−	1.30588i	0.945893	−	0.324478i	$-0.105188\pi$
$42$	−2.56068	−	0.665524i	−0.395121	−	0.102693i
$43$	−5.98293	+	10.3627i	−0.912389	+	1.58030i	−0.101709	+	0.994814i	$0.532431\pi$
$43$	−5.98293	+	10.3627i	−0.912389	+	1.58030i	−0.810680	+	0.585489i	$0.800902\pi$
$44$	−5.42901			−0.818454
$45$	−2.82315	+	1.62995i	−0.420851	+	0.242978i
$46$	−3.94676	+	2.27866i	−0.581918	+	0.335971i
$47$			2.99936i			0.437502i	0.975781	+	0.218751i	$0.0701982\pi$
$47$			2.99936i			0.437502i	−0.975781	+	0.218751i	$0.929802\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	0.105327	+	6.99921i	0.0150468	+	0.999887i
$50$		−	5.62693i		−	0.795768i
$51$		−	7.91573i		−	1.10842i
$52$	1.42828			0.198067
$53$	0.918586	+	0.530346i	0.126178	+	0.0728486i	0.561760	−	0.827300i	$-0.310124\pi$
$53$	0.918586	+	0.530346i	0.126178	+	0.0728486i	−0.435583	+	0.900149i	$0.643458\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	15.3269	+	8.84901i	2.06668	+	1.19320i
$56$	−1.85670	+	1.88485i	−0.248112	+	0.251874i
$57$	3.51758	−	2.57423i	0.465915	−	0.340965i
$58$	0.00821465	−	0.0142282i	0.00107864	−	0.00186825i
$59$	6.62637			0.862679			0.431340	−	0.902190i	$-0.358041\pi$
$59$	6.62637			0.862679			0.431340	+	0.902190i	$0.358041\pi$
$60$			3.25990i			0.420851i
$61$		−	3.83790i		−	0.491392i	−0.969347	−	0.245696i	$-0.920983\pi$
$61$		−	3.83790i		−	0.491392i	0.969347	−	0.245696i	$-0.0790166\pi$
$62$	5.64846	+	3.26114i	0.717355	+	0.414165i
$63$	−1.88485	−	1.85670i	−0.237469	−	0.233922i
$64$	−1.00000			−0.125000
$65$	−4.03227	−	2.32803i	−0.500141	−	0.288757i
$66$	−4.70166	−	2.71451i	−0.578735	−	0.334133i
$67$	0.307919	+	0.177777i	0.0376182	+	0.0217189i	0.518691	−	0.854962i	$-0.326419\pi$
$67$	0.307919	+	0.177777i	0.0376182	+	0.0217189i	−0.481073	+	0.876681i	$0.659753\pi$
$68$	−6.85523	−	3.95787i	−0.831318	−	0.479962i
$69$	−4.55733			−0.548638
$70$	8.31396	−	2.29490i	0.993708	−	0.274293i
$71$	−1.21530	−	0.701655i	−0.144230	−	0.0832711i	0.426149	−	0.904653i	$-0.359870\pi$
$71$	−1.21530	−	0.701655i	−0.144230	−	0.0832711i	−0.570378	+	0.821382i	$0.693203\pi$
$72$		−	1.00000i		−	0.117851i
$73$			9.36694i			1.09632i	0.836374	+	0.548159i	$0.184671\pi$
$73$			9.36694i			1.09632i	−0.836374	+	0.548159i	$0.815329\pi$
$74$	−8.37830			−0.973957
$75$	2.81347	−	4.87306i	0.324871	−	0.562693i
$76$	−0.470556	−	4.33343i	−0.0539765	−	0.497078i
$77$	−3.61314	+	13.9020i	−0.411755	+	1.58427i
$78$	1.23693	+	0.714142i	0.140055	+	0.0808607i
$79$	6.77772	−	3.91312i	0.762553	−	0.440260i	−0.0676585	−	0.997709i	$-0.521553\pi$
$79$	6.77772	−	3.91312i	0.762553	−	0.440260i	0.830212	+	0.557448i	$0.188219\pi$
$80$	2.82315	+	1.62995i	0.315638	+	0.182234i
$81$	1.00000			0.111111
$82$		−	9.65530i		−	1.06625i
$83$			6.47715i			0.710960i	0.934684	+	0.355480i	$0.115683\pi$
$83$			6.47715i			0.710960i	−0.934684	+	0.355480i	$0.884317\pi$
$84$	−2.55038	+	0.703979i	−0.278269	+	0.0768104i
$85$	12.9022	+	22.3473i	1.39944	+	2.42391i
$86$			11.9659i			1.29031i
$87$	0.0142282	−	0.00821465i	0.00152542	−	0.000880703i
$88$	−4.70166	+	2.71451i	−0.501199	+	0.289367i
$89$	−1.34598			−0.142674			−0.0713369	−	0.997452i	$-0.522727\pi$
$89$	−1.34598			−0.142674			−0.0713369	+	0.997452i	$0.522727\pi$
$90$	−1.62995	+	2.82315i	−0.171812	+	0.297587i
$91$	0.950558	−	3.65738i	0.0996455	−	0.383397i
$92$	−2.27866	+	3.94676i	−0.237567	+	0.411478i
$93$	3.26114	+	5.64846i	0.338164	+	0.585718i
$94$	1.49968	+	2.59752i	0.154680	+	0.267914i
$95$	−5.73481	+	13.0009i	−0.588379	+	1.33387i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	8.67534	−	15.0261i	0.880847	−	1.52567i	0.0304458	−	0.999536i	$-0.490307\pi$
$97$	8.67534	−	15.0261i	0.880847	−	1.52567i	0.850401	−	0.526135i	$-0.176359\pi$
$98$	3.59082	+	6.00883i	0.362728	+	0.606983i
$99$	−2.71451	−	4.70166i	−0.272818	−	0.472535i
$100$	−2.81347	−	4.87306i	−0.281347	−	0.487306i
$101$	−7.52128	−	4.34241i	−0.748395	−	0.432086i	0.0767187	−	0.997053i	$-0.475556\pi$
$101$	−7.52128	−	4.34241i	−0.748395	−	0.432086i	−0.825114	+	0.564967i	$0.808889\pi$
$102$	−3.95787	−	6.85523i	−0.391887	−	0.678769i
$103$	−4.33300	+	7.50497i	−0.426943	+	0.739487i	−0.996600	−	0.0823958i	$-0.973743\pi$
$103$	−4.33300	+	7.50497i	−0.426943	+	0.739487i	0.569657	+	0.821883i	$0.307076\pi$
$104$	1.23693	−	0.714142i	0.121291	−	0.0700274i
$105$	8.34755	+	2.16954i	0.814638	+	0.211725i
$106$	1.06069			0.103024
$107$	−4.39058	−	2.53490i	−0.424453	−	0.245058i	0.272528	−	0.962148i	$-0.412140\pi$
$107$	−4.39058	−	2.53490i	−0.424453	−	0.245058i	−0.696981	+	0.717090i	$0.745474\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$		−	0.410523i		−	0.0393210i	−0.999807	−	0.0196605i	$-0.993741\pi$
$109$		−	0.410523i		−	0.0393210i	0.999807	−	0.0196605i	$-0.00625853\pi$
$110$	17.6980			1.68744
$111$	−7.25582	−	4.18915i	−0.688692	−	0.397616i
$112$	−0.665524	+	2.56068i	−0.0628861	+	0.241961i
$113$		−	3.41761i		−	0.321501i	−0.986995	−	0.160751i	$-0.948609\pi$
$113$		−	3.41761i		−	0.321501i	0.986995	−	0.160751i	$-0.0513915\pi$
$114$	1.75920	−	3.98813i	0.164764	−	0.373523i
$115$	12.8660	−	7.42821i	1.19976	−	0.692684i
$116$		−	0.0164293i		−	0.00152542i
$117$	0.714142	+	1.23693i	0.0660225	+	0.114354i
$118$	5.73860	−	3.31318i	0.528281	−	0.305003i
$119$	−14.6971	+	14.9200i	−1.34729	+	1.36771i
$120$	1.62995	+	2.82315i	0.148793	+	0.257718i
$121$	−9.23708	+	15.9991i	−0.839735	+	1.45446i
$122$	−1.91895	−	3.32372i	−0.173733	−	0.300915i
$123$	4.82765	−	8.36174i	0.435295	−	0.753953i
$124$	6.52228			0.585718
$125$			2.04373i			0.182797i
$126$	−2.56068	−	0.665524i	−0.228123	−	0.0592896i
$127$	12.3881	−	7.15228i	1.09927	−	0.634662i	0.163239	−	0.986587i	$-0.447806\pi$
$127$	12.3881	−	7.15228i	1.09927	−	0.634662i	0.936028	+	0.351925i	$0.114473\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−5.98293	+	10.3627i	−0.526768	+	0.912389i
$130$	−4.65606			−0.408364
$131$	−0.553373	+	0.319490i	−0.0483485	+	0.0279140i	−0.523979	−	0.851731i	$-0.675553\pi$
$131$	−0.553373	+	0.319490i	−0.0483485	+	0.0279140i	0.475631	+	0.879645i	$0.342220\pi$
$132$	−5.42901			−0.472535
$133$	−11.4097	−	1.67906i	−0.989345	−	0.145593i
$134$	0.355554			0.0307152
$135$	−2.82315	+	1.62995i	−0.242978	+	0.140284i
$136$	−7.91573			−0.678769
$137$	6.28064	−	10.8784i	0.536592	−	0.929404i	−0.462493	−	0.886623i	$-0.653045\pi$
$137$	6.28064	−	10.8784i	0.536592	−	0.929404i	0.999084	−	0.0427808i	$-0.0136217\pi$
$138$	−3.94676	+	2.27866i	−0.335971	+	0.193973i
$139$	7.00918	−	4.04675i	0.594511	−	0.343241i	−0.172368	−	0.985033i	$-0.555142\pi$
$139$	7.00918	−	4.04675i	0.594511	−	0.343241i	0.766879	+	0.641791i	$0.221808\pi$
$140$	6.05265	−	6.14442i	0.511543	−	0.519298i
$141$			2.99936i			0.252592i
$142$	−1.40331			−0.117763
$143$	3.87709	−	6.71531i	0.324218	−	0.561562i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−0.0267789	+	0.0463825i	−0.00222387	+	0.00385185i
$146$	4.68347	+	8.11201i	0.387607	+	0.671354i
$147$	0.105327	+	6.99921i	0.00868725	+	0.577285i
$148$	−7.25582	+	4.18915i	−0.596424	+	0.344346i
$149$	−7.79374	−	13.4992i	−0.638488	−	1.10589i	−0.985765	−	0.168131i	$-0.946227\pi$
$149$	−7.79374	−	13.4992i	−0.638488	−	1.10589i	0.347277	−	0.937763i	$-0.387107\pi$
$150$		−	5.62693i		−	0.459437i
$151$	12.8753	−	7.43354i	1.04777	−	0.604933i	0.125749	−	0.992062i	$-0.459867\pi$
$151$	12.8753	−	7.43354i	1.04777	−	0.604933i	0.922025	+	0.387129i	$0.126533\pi$
$152$	−2.57423	−	3.51758i	−0.208797	−	0.285313i
$153$		−	7.91573i		−	0.639949i
$154$	3.82191	+	13.8460i	0.307978	+	1.11574i
$155$	−18.4134	−	10.6310i	−1.47900	−	0.853901i
$156$	1.42828			0.114354
$157$		−	4.08753i		−	0.326220i	−0.986608	−	0.163110i	$-0.947847\pi$
$157$		−	4.08753i		−	0.326220i	0.986608	−	0.163110i	$-0.0521526\pi$
$158$	3.91312	−	6.77772i	0.311311	−	0.539207i
$159$	0.918586	+	0.530346i	0.0728486	+	0.0420592i
$160$	3.25990			0.257718
$161$	8.58988	+	8.46159i	0.676978	+	0.666867i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	5.83332	−	10.1036i	0.456901	−	0.791376i	−0.541894	−	0.840447i	$-0.682293\pi$
$163$	5.83332	−	10.1036i	0.456901	−	0.791376i	0.998795	+	0.0490708i	$0.0156260\pi$
$164$	−4.82765	−	8.36174i	−0.376976	−	0.652942i
$165$	15.3269	+	8.84901i	1.19320	+	0.688894i
$166$	3.23857	+	5.60938i	0.251362	+	0.435372i
$167$	−1.29023	−	2.23474i	−0.0998409	−	0.172929i	0.811778	−	0.583966i	$-0.198500\pi$
$167$	−1.29023	−	2.23474i	−0.0998409	−	0.172929i	−0.911619	+	0.411037i	$0.865167\pi$
$168$	−1.85670	+	1.88485i	−0.143248	+	0.145419i
$169$	5.48000	−	9.49164i	0.421539	−	0.730126i
$170$	22.3473	+	12.9022i	1.71396	+	0.989557i
$171$	3.51758	−	2.57423i	0.268996	−	0.196856i
$172$	5.98293	+	10.3627i	0.456194	+	0.790152i
$173$	8.41289	+	14.5716i	0.639620	+	1.10785i	0.985516	+	0.169582i	$0.0542416\pi$
$173$	8.41289	+	14.5716i	0.639620	+	1.10785i	−0.345896	+	0.938273i	$0.612425\pi$
$174$	0.00821465	−	0.0142282i	0.000622751	−	0.00107864i
$175$	−14.3508	+	3.96124i	−1.08482	+	0.299442i
$176$	−2.71451	+	4.70166i	−0.204614	+	0.354401i
$177$	6.62637			0.498068
$178$	−1.16565	+	0.672991i	−0.0873695	+	0.0504428i
$179$	−8.20242	+	4.73567i	−0.613078	+	0.353960i	−0.774169	−	0.632979i	$-0.781832\pi$
$179$	−8.20242	+	4.73567i	−0.613078	+	0.353960i	0.161091	+	0.986939i	$0.448499\pi$
$180$			3.25990i			0.242978i
$181$	−9.09772	−	15.7577i	−0.676228	−	1.17126i	−0.976108	−	0.217285i	$-0.930280\pi$
$181$	−9.09772	−	15.7577i	−0.676228	−	1.17126i	0.299880	−	0.953977i	$-0.403053\pi$
$182$	−1.00548	−	3.64266i	−0.0745313	−	0.270012i
$183$		−	3.83790i		−	0.283706i
$184$			4.55733i			0.335971i
$185$	27.3124			2.00805
$186$	5.64846	+	3.26114i	0.414165	+	0.239118i
$187$	−37.2171	+	21.4873i	−2.72158	+	1.57131i
$188$	2.59752	+	1.49968i	0.189444	+	0.109376i
$189$	−1.88485	−	1.85670i	−0.137103	−	0.135055i
$190$	1.53396	+	14.1265i	0.111285	+	1.02485i
$191$	−5.00050	+	8.66112i	−0.361824	+	0.626697i	−0.988261	−	0.152775i	$-0.951179\pi$
$191$	−5.00050	+	8.66112i	−0.361824	+	0.626697i	0.626437	+	0.779472i	$0.284512\pi$
$192$	−1.00000			−0.0721688
$193$		−	6.60829i		−	0.475675i	−0.971305	−	0.237837i	$-0.923561\pi$
$193$		−	6.60829i		−	0.475675i	0.971305	−	0.237837i	$-0.0764386\pi$
$194$		−	17.3507i		−	1.24571i
$195$	−4.03227	−	2.32803i	−0.288757	−	0.166714i
$196$	6.11416	+	3.40839i	0.436725	+	0.243456i
$197$	15.5834			1.11027			0.555134	−	0.831761i	$-0.312667\pi$
$197$	15.5834			1.11027			0.555134	+	0.831761i	$0.312667\pi$
$198$	−4.70166	−	2.71451i	−0.334133	−	0.192912i
$199$	7.75390	+	4.47672i	0.549659	+	0.317346i	0.748985	−	0.662587i	$-0.230542\pi$
$199$	7.75390	+	4.47672i	0.549659	+	0.317346i	−0.199325	+	0.979933i	$0.563875\pi$
$200$	−4.87306	−	2.81347i	−0.344578	−	0.198942i
$201$	0.307919	+	0.177777i	0.0217189	+	0.0125394i
$202$	−8.68482			−0.611062
$203$	−0.0420702	−	0.0109341i	−0.00295275	−	0.000767424i
$204$	−6.85523	−	3.95787i	−0.479962	−	0.277106i
$205$			31.4753i			2.19833i
$206$			8.66600i			0.603789i
$207$	−4.55733			−0.316756
$208$	0.714142	−	1.23693i	0.0495169	−	0.0857657i
$209$	−21.6516	−	9.55071i	−1.49767	−	0.660637i
$210$	8.31396	−	2.29490i	0.573718	−	0.158363i
$211$	9.87775	+	5.70292i	0.680012	+	0.392605i	0.799860	−	0.600187i	$-0.204907\pi$
$211$	9.87775	+	5.70292i	0.680012	+	0.392605i	−0.119847	+	0.992792i	$0.538241\pi$
$212$	0.918586	−	0.530346i	0.0630888	−	0.0364243i
$213$	−1.21530	−	0.701655i	−0.0832711	−	0.0480766i
$214$	−5.06980			−0.346565
$215$		−	39.0075i		−	2.66029i
$216$		−	1.00000i		−	0.0680414i
$217$	4.34073	−	16.7015i	0.294668	−	1.13377i
$218$	−0.205261	−	0.355523i	−0.0139021	−	0.0240791i
$219$			9.36694i			0.632959i
$220$	15.3269	−	8.84901i	1.03334	−	0.596600i
$221$	9.79121	−	5.65296i	0.658628	−	0.380259i
$222$	−8.37830			−0.562314
$223$	2.62150	−	4.54057i	0.175549	−	0.304059i	−0.764802	−	0.644265i	$-0.777163\pi$
$223$	2.62150	−	4.54057i	0.175549	−	0.304059i	0.940351	+	0.340206i	$0.110497\pi$
$224$	0.703979	+	2.55038i	0.0470366	+	0.170404i
$225$	2.81347	−	4.87306i	0.187564	−	0.324871i
$226$	−1.70880	−	2.95973i	−0.113668	−	0.196879i
$227$	14.1297	+	24.4733i	0.937819	+	1.62435i	0.769528	+	0.638613i	$0.220492\pi$
$227$	14.1297	+	24.4733i	0.937819	+	1.62435i	0.168292	+	0.985737i	$0.446175\pi$
$228$	−0.470556	−	4.33343i	−0.0311633	−	0.286988i
$229$	19.7790	+	11.4194i	1.30703	+	0.754615i	0.981600	−	0.190951i	$-0.0611571\pi$
$229$	19.7790	+	11.4194i	1.30703	+	0.754615i	0.325432	+	0.945566i	$0.394490\pi$
$230$	7.42821	−	12.8660i	0.489802	−	0.848361i
$231$	−3.61314	+	13.9020i	−0.237727	+	0.914682i
$232$	−0.00821465	−	0.0142282i	−0.000539318	−	0.000934127i
$233$	0.411130	+	0.712098i	0.0269340	+	0.0466511i	0.879178	−	0.476493i	$-0.158092\pi$
$233$	0.411130	+	0.712098i	0.0269340	+	0.0466511i	−0.852244	+	0.523144i	$0.824759\pi$
$234$	1.23693	+	0.714142i	0.0808607	+	0.0466849i
$235$	−4.88881	−	8.46766i	−0.318911	−	0.552369i
$236$	3.31318	−	5.73860i	0.215670	−	0.373551i
$237$	6.77772	−	3.91312i	0.440260	−	0.254184i
$238$	−5.26811	+	20.2697i	−0.341481	+	1.31389i
$239$	−15.6050			−1.00941			−0.504703	−	0.863293i	$-0.668398\pi$
$239$	−15.6050			−1.00941			−0.504703	+	0.863293i	$0.668398\pi$
$240$	2.82315	+	1.62995i	0.182234	+	0.105213i
$241$	−6.85020	+	11.8649i	−0.441260	+	0.764285i	−0.997783	−	0.0665470i	$-0.978802\pi$
$241$	−6.85020	+	11.8649i	−0.441260	+	0.764285i	0.556523	+	0.830832i	$0.312135\pi$
$242$			18.4742i			1.18756i
$243$	1.00000			0.0641500
$244$	−3.32372	−	1.91895i	−0.212779	−	0.122848i
$245$	−11.7057	−	19.5882i	−0.747850	−	1.25144i
$246$		−	9.65530i		−	0.615600i
$247$	5.69619	+	2.51264i	0.362440	+	0.159875i
$248$	5.64846	−	3.26114i	0.358678	−	0.207083i
$249$			6.47715i			0.410473i
$250$	1.02186	+	1.76992i	0.0646283	+	0.111940i
$251$	−11.3817	+	6.57124i	−0.718408	+	0.414773i	−0.814167	−	0.580631i	$-0.802806\pi$
$251$	−11.3817	+	6.57124i	−0.718408	+	0.414773i	0.0957582	+	0.995405i	$0.469472\pi$
$252$	−2.55038	+	0.703979i	−0.160659	+	0.0443465i
$253$	12.3709	+	21.4270i	0.777751	+	1.34710i
$254$	7.15228	−	12.3881i	0.448774	−	0.777299i
$255$	12.9022	+	22.3473i	0.807970	+	1.39944i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.7152			−0.793152			−0.396576	−	0.918002i	$-0.629802\pi$
$257$	−12.7152			−0.793152			−0.396576	+	0.918002i	$0.629802\pi$
$258$			11.9659i			0.744962i
$259$	5.89814	+	21.3678i	0.366493	+	1.32773i
$260$	−4.03227	+	2.32803i	−0.250071	+	0.144378i
$261$	0.0142282	−	0.00821465i	0.000880703	−	0.000508474i
$262$	−0.319490	+	0.553373i	−0.0197382	+	0.0341875i
$263$	−6.85177			−0.422498			−0.211249	−	0.977432i	$-0.567753\pi$
$263$	−6.85177			−0.422498			−0.211249	+	0.977432i	$0.567753\pi$
$264$	−4.70166	+	2.71451i	−0.289367	+	0.167066i
$265$	−3.45775			−0.212408
$266$	−10.7206	+	4.25073i	−0.657322	+	0.260629i
$267$	−1.34598			−0.0823728
$268$	0.307919	−	0.177777i	0.0188091	−	0.0108595i
$269$	19.7401			1.20358			0.601789	−	0.798655i	$-0.294455\pi$
$269$	19.7401			1.20358			0.601789	+	0.798655i	$0.294455\pi$
$270$	−1.62995	+	2.82315i	−0.0991955	+	0.171812i
$271$	20.8046	−	12.0115i	1.26379	−	0.729649i	0.289984	−	0.957032i	$-0.406350\pi$
$271$	20.8046	−	12.0115i	1.26379	−	0.729649i	0.973806	+	0.227382i	$0.0730167\pi$
$272$	−6.85523	+	3.95787i	−0.415659	+	0.239981i
$273$	0.950558	−	3.65738i	0.0575304	−	0.221355i
$274$		−	12.5613i		−	0.758855i
$275$	−30.5487			−1.84215
$276$	−2.27866	+	3.94676i	−0.137159	+	0.237567i
$277$	6.93109	+	12.0050i	0.416449	+	0.721311i	0.995579	−	0.0939242i	$-0.0299411\pi$
$277$	6.93109	+	12.0050i	0.416449	+	0.721311i	−0.579130	+	0.815235i	$0.696608\pi$
$278$	4.04675	−	7.00918i	0.242708	−	0.420383i
$279$	3.26114	+	5.64846i	0.195239	+	0.338164i
$280$	2.16954	−	8.34755i	0.129655	−	0.498862i
$281$	27.6265	−	15.9501i	1.64806	−	0.951506i	0.670213	−	0.742169i	$-0.266203\pi$
$281$	27.6265	−	15.9501i	1.64806	−	0.951506i	0.977843	−	0.209337i	$-0.0671307\pi$
$282$	1.49968	+	2.59752i	0.0893047	+	0.154680i
$283$			17.3517i			1.03145i	0.856753	+	0.515727i	$0.172478\pi$
$283$			17.3517i			1.03145i	−0.856753	+	0.515727i	$0.827522\pi$
$284$	−1.21530	+	0.701655i	−0.0721149	+	0.0416355i
$285$	−5.73481	+	13.0009i	−0.339701	+	0.770107i
$286$		−	7.75417i		−	0.458514i
$287$	−24.6246	+	6.79713i	−1.45355	+	0.401222i
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	−45.6589			−2.68582
$290$			0.0535579i			0.00314503i
$291$	8.67534	−	15.0261i	0.508557	−	0.880847i
$292$	8.11201	+	4.68347i	0.474719	+	0.274079i
$293$	0.290543			0.0169737			0.00848684	−	0.999964i	$-0.497299\pi$
$293$	0.290543			0.0169737			0.00848684	+	0.999964i	$0.497299\pi$
$294$	3.59082	+	6.00883i	0.209421	+	0.350442i
$295$	−18.7072	+	10.8006i	−1.08918	+	0.628837i
$296$	−4.18915	+	7.25582i	−0.243489	+	0.421736i
$297$	−2.71451	−	4.70166i	−0.157512	−	0.272818i
$298$	−13.4992	−	7.79374i	−0.781985	−	0.451479i
$299$	−3.25458	−	5.63710i	−0.188217	−	0.326002i
$300$	−2.81347	−	4.87306i	−0.162435	−	0.281347i
$301$	30.5174	−	8.42372i	1.75900	−	0.485535i
$302$	7.43354	−	12.8753i	0.427752	−	0.740888i
$303$	−7.52128	−	4.34241i	−0.432086	−	0.249465i
$304$	−3.98813	−	1.75920i	−0.228735	−	0.100897i
$305$	6.25558	+	10.8350i	0.358193	+	0.620409i
$306$	−3.95787	−	6.85523i	−0.226256	−	0.391887i
$307$	0.0103240	−	0.0178817i	0.000589223	−	0.00102056i	−0.865731	−	0.500510i	$-0.833146\pi$
$307$	0.0103240	−	0.0178817i	0.000589223	−	0.00102056i	0.866320	+	0.499490i	$0.166479\pi$
$308$	10.2329	+	10.0800i	0.583072	+	0.574364i
$309$	−4.33300	+	7.50497i	−0.246496	+	0.426943i
$310$	−21.2620			−1.20760
$311$	10.6122	−	6.12693i	0.601760	−	0.347427i	−0.167973	−	0.985792i	$-0.553722\pi$
$311$	10.6122	−	6.12693i	0.601760	−	0.347427i	0.769734	+	0.638365i	$0.220389\pi$
$312$	1.23693	−	0.714142i	0.0700274	−	0.0404303i
$313$		−	31.7873i		−	1.79673i	−0.439254	−	0.898363i	$-0.644757\pi$
$313$		−	31.7873i		−	1.79673i	0.439254	−	0.898363i	$-0.355243\pi$
$314$	−2.04376	−	3.53990i	−0.115336	−	0.199768i
$315$	8.34755	+	2.16954i	0.470331	+	0.122240i
$316$		−	7.82624i		−	0.440260i
$317$		−	18.0250i		−	1.01239i	−0.862420	−	0.506193i	$-0.831052\pi$
$317$		−	18.0250i		−	1.01239i	0.862420	−	0.506193i	$-0.168948\pi$
$318$	1.06069			0.0594807
$319$	−0.0772450	−	0.0445974i	−0.00432489	−	0.00249698i
$320$	2.82315	−	1.62995i	0.157819	−	0.0911169i
$321$	−4.39058	−	2.53490i	−0.245058	−	0.141484i
$322$	11.6699	+	3.03301i	0.650335	+	0.169023i
$323$	−20.3769	−	27.8442i	−1.13380	−	1.54929i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	8.03686			0.445805
$326$		−	11.6666i		−	0.646156i
$327$		−	0.410523i		−	0.0227020i
$328$	−8.36174	−	4.82765i	−0.461700	−	0.266562i
$329$	5.56892	−	5.65335i	0.307024	−	0.311679i
$330$	17.6980			0.974244
$331$	−13.1068	−	7.56719i	−0.720413	−	0.415930i	0.0944919	−	0.995526i	$-0.469877\pi$
$331$	−13.1068	−	7.56719i	−0.720413	−	0.415930i	−0.814905	+	0.579595i	$0.803211\pi$
$332$	5.60938	+	3.23857i	0.307855	+	0.177740i
$333$	−7.25582	−	4.18915i	−0.397616	−	0.229564i
$334$	−2.23474	−	1.29023i	−0.122280	−	0.0705982i
$335$	−1.15907			−0.0633267
$336$	−0.665524	+	2.56068i	−0.0363073	+	0.139696i
$337$	−18.6266	−	10.7541i	−1.01466	−	0.585812i	−0.102104	−	0.994774i	$-0.532557\pi$
$337$	−18.6266	−	10.7541i	−1.01466	−	0.585812i	−0.912551	+	0.408962i	$0.865891\pi$
$338$		−	10.9600i		−	0.596146i
$339$		−	3.41761i		−	0.185619i
$340$	25.8045			1.39944
$341$	17.7048	−	30.6655i	0.958767	−	1.66063i
$342$	1.75920	−	3.98813i	0.0951266	−	0.215654i
$343$	12.7969	−	13.3880i	0.690968	−	0.722885i
$344$	10.3627	+	5.98293i	0.558722	+	0.322578i
$345$	12.8660	−	7.42821i	0.692684	−	0.399921i
$346$	14.5716	+	8.41289i	0.783371	+	0.452280i
$347$	−15.3746			−0.825352			−0.412676	−	0.910878i	$-0.635406\pi$
$347$	−15.3746			−0.825352			−0.412676	+	0.910878i	$0.635406\pi$
$348$		−	0.0164293i		−	0.000880703i
$349$			8.04972i			0.430892i	0.976516	+	0.215446i	$0.0691205\pi$
$349$			8.04972i			0.430892i	−0.976516	+	0.215446i	$0.930880\pi$
$350$	−10.4475	+	10.6059i	−0.558444	+	0.566911i
$351$	0.714142	+	1.23693i	0.0381181	+	0.0660225i
$352$			5.42901i			0.289367i
$353$	24.1432	−	13.9391i	1.28501	−	0.741903i	0.307254	−	0.951628i	$-0.400590\pi$
$353$	24.1432	−	13.9391i	1.28501	−	0.741903i	0.977761	+	0.209724i	$0.0672566\pi$
$354$	5.73860	−	3.31318i	0.305003	−	0.176094i
$355$	4.57464			0.242797
$356$	−0.672991	+	1.16565i	−0.0356685	+	0.0617796i
$357$	−14.6971	+	14.9200i	−0.777856	+	0.789649i
$358$	−4.73567	+	8.20242i	−0.250288	+	0.433511i
$359$	15.5509	+	26.9349i	0.820744	+	1.42157i	0.905129	+	0.425137i	$0.139774\pi$
$359$	15.5509	+	26.9349i	0.820744	+	1.42157i	−0.0843856	+	0.996433i	$0.526893\pi$
$360$	1.62995	+	2.82315i	0.0859058	+	0.148793i
$361$	5.74672	−	18.1101i	0.302459	−	0.953162i
$362$	−15.7577	−	9.09772i	−0.828207	−	0.478166i
$363$	−9.23708	+	15.9991i	−0.484821	+	0.839735i
$364$	−2.69210	−	2.65190i	−0.141105	−	0.138997i
$365$	−15.2676	−	26.4443i	−0.799144	−	1.38416i
$366$	−1.91895	−	3.32372i	−0.100305	−	0.173733i
$367$	−24.4514	−	14.1170i	−1.27635	−	0.736902i	−0.300176	−	0.953884i	$-0.597045\pi$
$367$	−24.4514	−	14.1170i	−1.27635	−	0.736902i	−0.976176	+	0.216982i	$0.930379\pi$
$368$	2.27866	+	3.94676i	0.118784	+	0.205739i
$369$	4.82765	−	8.36174i	0.251318	−	0.435295i
$370$	23.6532	−	13.6562i	1.22967	−	0.709952i
$371$	−0.746705	−	2.70516i	−0.0387670	−	0.140445i
$372$	6.52228			0.338164
$373$	2.20146	+	1.27101i	0.113987	+	0.0658105i	0.555910	−	0.831243i	$-0.312370\pi$
$373$	2.20146	+	1.27101i	0.113987	+	0.0658105i	−0.441923	+	0.897053i	$0.645703\pi$
$374$	−21.4873	+	37.2171i	−1.11108	+	1.92445i
$375$			2.04373i			0.105538i
$376$	2.99936			0.154680
$377$	0.0203219	+	0.0117329i	0.00104663	+	0.000604273i
$378$	−2.56068	−	0.665524i	−0.131707	−	0.0342309i
$379$			0.640519i			0.0329013i	0.999865	+	0.0164506i	$0.00523664\pi$
$379$			0.640519i			0.0329013i	−0.999865	+	0.0164506i	$0.994763\pi$
$380$	8.39171	+	11.4669i	0.430486	+	0.588242i
$381$	12.3881	−	7.15228i	0.634662	−	0.366422i
$382$			10.0010i			0.511696i
$383$	12.8814	+	22.3112i	0.658207	+	1.14005i	0.981079	+	0.193606i	$0.0620182\pi$
$383$	12.8814	+	22.3112i	0.658207	+	1.14005i	−0.322872	+	0.946443i	$0.604648\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$	−12.4590	−	45.1366i	−0.634971	−	2.30037i
$386$	−3.30414	−	5.72294i	−0.168176	−	0.291290i
$387$	−5.98293	+	10.3627i	−0.304130	+	0.526768i
$388$	−8.67534	−	15.0261i	−0.440423	−	0.762836i
$389$	−13.2371	+	22.9273i	−0.671148	+	1.16246i	0.306431	+	0.951893i	$0.400865\pi$
$389$	−13.2371	+	22.9273i	−0.671148	+	1.16246i	−0.977579	+	0.210570i	$0.932468\pi$
$390$	−4.65606			−0.235769
$391$			36.0746i			1.82437i
$392$	6.99921	−	0.105327i	0.353513	−	0.00531983i
$393$	−0.553373	+	0.319490i	−0.0279140	+	0.0161162i
$394$	13.4956	−	7.79168i	0.679898	−	0.392539i
$395$	−12.7564	+	22.0947i	−0.641842	+	1.11170i
$396$	−5.42901			−0.272818
$397$	−26.1732	+	15.1111i	−1.31359	+	0.758403i	−0.982689	−	0.185261i	$-0.940687\pi$
$397$	−26.1732	+	15.1111i	−1.31359	+	0.758403i	−0.330904	+	0.943664i	$0.607354\pi$
$398$	8.95343			0.448795
$399$	−11.4097	−	1.67906i	−0.571198	−	0.0840579i
$400$	−5.62693			−0.281347
$401$	−4.27344	+	2.46727i	−0.213405	+	0.123210i	−0.602893	−	0.797822i	$-0.705985\pi$
$401$	−4.27344	+	2.46727i	−0.213405	+	0.123210i	0.389488	+	0.921032i	$0.372652\pi$
$402$	0.355554			0.0177334
$403$	−4.65784	+	8.06761i	−0.232023	+	0.401876i
$404$	−7.52128	+	4.34241i	−0.374197	+	0.216043i
$405$	−2.82315	+	1.62995i	−0.140284	+	0.0809928i
$406$	−0.0419009	+	0.0115659i	−0.00207951	+	0.000574005i
$407$			45.4859i			2.25465i
$408$	−7.91573			−0.391887
$409$	11.0739	−	19.1805i	0.547567	−	0.948414i	−0.450874	−	0.892588i	$-0.648888\pi$
$409$	11.0739	−	19.1805i	0.547567	−	0.948414i	0.998441	−	0.0558258i	$-0.0177792\pi$
$410$	15.7376	+	27.2584i	0.777227	+	1.34620i
$411$	6.28064	−	10.8784i	0.309801	−	0.536592i
$412$	4.33300	+	7.50497i	0.213472	+	0.369744i
$413$	−12.4897	−	12.3032i	−0.614579	−	0.605400i
$414$	−3.94676	+	2.27866i	−0.193973	+	0.111990i
$415$	−10.5574	−	18.2860i	−0.518243	−	0.897624i
$416$		−	1.42828i		−	0.0700274i
$417$	7.00918	−	4.04675i	0.343241	−	0.198170i
$418$	−23.5262	+	2.55465i	−1.15070	+	0.124952i
$419$			5.34125i			0.260937i	0.991452	+	0.130469i	$0.0416482\pi$
$419$			5.34125i			0.260937i	−0.991452	+	0.130469i	$0.958352\pi$
$420$	6.05265	−	6.14442i	0.295339	−	0.299817i
$421$	−13.7757	−	7.95341i	−0.671387	−	0.387625i	0.125215	−	0.992130i	$-0.460038\pi$
$421$	−13.7757	−	7.95341i	−0.671387	−	0.387625i	−0.796602	+	0.604504i	$0.793371\pi$
$422$	11.4058			0.555228
$423$			2.99936i			0.145834i
$424$	0.530346	−	0.918586i	0.0257559	−	0.0446105i
$425$	−38.5739	−	22.2706i	−1.87111	−	1.08028i
$426$	−1.40331			−0.0679906
$427$	−7.12583	+	7.23387i	−0.344843	+	0.350071i
$428$	−4.39058	+	2.53490i	−0.212227	+	0.122529i
$429$	3.87709	−	6.71531i	0.187187	−	0.324218i
$430$	−19.5037	−	33.7815i	−0.940554	−	1.62909i
$431$	−16.3224	−	9.42372i	−0.786220	−	0.453924i	0.0524101	−	0.998626i	$-0.483310\pi$
$431$	−16.3224	−	9.42372i	−0.786220	−	0.453924i	−0.838630	+	0.544701i	$0.816643\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	3.24657	+	5.62323i	0.156020	+	0.270235i	0.933430	−	0.358759i	$-0.116800\pi$
$433$	3.24657	+	5.62323i	0.156020	+	0.270235i	−0.777410	+	0.628995i	$0.783467\pi$
$434$	−4.59155	−	16.6343i	−0.220401	−	0.798470i
$435$	−0.0267789	+	0.0463825i	−0.00128395	+	0.00222387i
$436$	−0.355523	−	0.205261i	−0.0170265	−	0.00983024i
$437$	−16.0308	+	11.7316i	−0.766855	+	0.561198i
$438$	4.68347	+	8.11201i	0.223785	+	0.387607i
$439$	−12.1661	−	21.0723i	−0.580655	−	1.00572i	−0.995402	−	0.0957877i	$-0.969463\pi$
$439$	−12.1661	−	21.0723i	−0.580655	−	1.00572i	0.414746	−	0.909937i	$-0.363870\pi$
$440$	8.84901	−	15.3269i	0.421860	−	0.730683i
$441$	0.105327	+	6.99921i	0.00501559	+	0.333296i
$442$	5.65296	−	9.79121i	0.268884	−	0.465721i
$443$	−18.4817			−0.878092			−0.439046	−	0.898465i	$-0.644683\pi$
$443$	−18.4817			−0.878092			−0.439046	+	0.898465i	$0.644683\pi$
$444$	−7.25582	+	4.18915i	−0.344346	+	0.198808i
$445$	3.79991	−	2.19388i	0.180133	−	0.104000i
$446$		−	5.24300i		−	0.248263i
$447$	−7.79374	−	13.4992i	−0.368631	−	0.638488i
$448$	1.88485	+	1.85670i	0.0890508	+	0.0877208i
$449$			23.9267i			1.12917i	0.825374	+	0.564586i	$0.190964\pi$
$449$			23.9267i			1.12917i	−0.825374	+	0.564586i	$0.809036\pi$
$450$		−	5.62693i		−	0.265256i
$451$	−52.4187			−2.46830
$452$	−2.95973	−	1.70880i	−0.139214	−	0.0803753i
$453$	12.8753	−	7.43354i	0.604933	−	0.349258i
$454$	24.4733	+	14.1297i	1.14859	+	0.663138i
$455$	3.27777	+	11.8747i	0.153664	+	0.556695i
$456$	−2.57423	−	3.51758i	−0.120549	−	0.164726i
$457$	−13.9074	+	24.0884i	−0.650562	+	1.12681i	0.332424	+	0.943130i	$0.392133\pi$
$457$	−13.9074	+	24.0884i	−0.650562	+	1.12681i	−0.982987	+	0.183677i	$0.941200\pi$
$458$	22.8388			1.06719
$459$		−	7.91573i		−	0.369475i
$460$		−	14.8564i		−	0.692684i
$461$	−4.08758	−	2.35997i	−0.190378	−	0.109915i	0.401782	−	0.915736i	$-0.368391\pi$
$461$	−4.08758	−	2.35997i	−0.190378	−	0.109915i	−0.592159	+	0.805821i	$0.701724\pi$
$462$	3.82191	+	13.8460i	0.177811	+	0.644175i
$463$	−2.63114			−0.122279			−0.0611396	−	0.998129i	$-0.519473\pi$
$463$	−2.63114			−0.122279			−0.0611396	+	0.998129i	$0.519473\pi$
$464$	−0.0142282	−	0.00821465i	−0.000660528	−	0.000381356i
$465$	−18.4134	−	10.6310i	−0.853901	−	0.493000i
$466$	0.712098	+	0.411130i	0.0329873	+	0.0190452i
$467$	−8.01523	−	4.62760i	−0.370901	−	0.214140i	0.302951	−	0.953006i	$-0.402028\pi$
$467$	−8.01523	−	4.62760i	−0.370901	−	0.214140i	−0.673852	+	0.738866i	$0.735361\pi$
$468$	1.42828			0.0660225
$469$	−0.250302	−	0.906795i	−0.0115579	−	0.0418719i
$470$	−8.46766	−	4.88881i	−0.390584	−	0.225504i
$471$		−	4.08753i		−	0.188343i
$472$		−	6.62637i		−	0.305003i
$473$	64.9628			2.98699
$474$	3.91312	−	6.77772i	0.179736	−	0.311311i
$475$	−2.64779	−	24.3839i	−0.121489	−	1.11881i
$476$	5.57251	+	20.1881i	0.255416	+	0.925320i
$477$	0.918586	+	0.530346i	0.0420592	+	0.0242829i
$478$	−13.5144	+	7.80252i	−0.618132	+	0.356879i
$479$	−18.6831	−	10.7867i	−0.853651	−	0.492856i	0.00822987	−	0.999966i	$-0.497380\pi$
$479$	−18.6831	−	10.7867i	−0.853651	−	0.492856i	−0.861881	+	0.507110i	$0.830714\pi$
$480$	3.25990			0.148793
$481$		−	11.9666i		−	0.545629i
$482$			13.7004i			0.624036i
$483$	8.58988	+	8.46159i	0.390853	+	0.385016i
$484$	9.23708	+	15.9991i	0.419867	+	0.727231i
$485$			56.5614i			2.56832i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	−15.9607	+	9.21489i	−0.723246	+	0.417566i	−0.815946	−	0.578128i	$-0.803784\pi$
$487$	−15.9607	+	9.21489i	−0.723246	+	0.417566i	0.0927001	+	0.995694i	$0.470450\pi$
$488$	−3.83790			−0.173733
$489$	5.83332	−	10.1036i	0.263792	−	0.456901i
$490$	−19.9315	−	11.1110i	−0.900414	−	0.501944i
$491$	−0.412147	+	0.713859i	−0.0185999	+	0.0322160i	−0.875176	−	0.483806i	$-0.839254\pi$
$491$	−0.412147	+	0.713859i	−0.0185999	+	0.0322160i	0.856576	+	0.516022i	$0.172588\pi$
$492$	−4.82765	−	8.36174i	−0.217647	−	0.376976i
$493$	−0.0650250	−	0.112627i	−0.00292858	−	0.00507245i
$494$	6.18936	−	0.672088i	0.278473	−	0.0302387i
$495$	15.3269	+	8.84901i	0.688894	+	0.397733i
$496$	3.26114	−	5.64846i	0.146429	−	0.253623i
$497$	0.987900	+	3.57897i	0.0443134	+	0.160539i
$498$	3.23857	+	5.60938i	0.145124	+	0.251362i
$499$	−12.3352	−	21.3652i	−0.552200	−	0.956438i	−0.998115	−	0.0613633i	$-0.980455\pi$
$499$	−12.3352	−	21.3652i	−0.552200	−	0.956438i	0.445916	−	0.895075i	$-0.352878\pi$
$500$	1.76992	+	1.02186i	0.0791532	+	0.0456991i
$501$	−1.29023	−	2.23474i	−0.0576432	−	0.0998409i
$502$	−6.57124	+	11.3817i	−0.293289	+	0.507991i
$503$	17.9477	−	10.3621i	0.800247	−	0.462023i	−0.0433106	−	0.999062i	$-0.513791\pi$
$503$	17.9477	−	10.3621i	0.800247	−	0.462023i	0.843557	+	0.537039i	$0.180457\pi$
$504$	−1.85670	+	1.88485i	−0.0827040	+	0.0839579i
$505$	28.3116			1.25985
$506$	21.4270	+	12.3709i	0.952547	+	0.549953i
$507$	5.48000	−	9.49164i	0.243375	−	0.421539i
$508$		−	14.3046i		−	0.634662i
$509$	12.6535			0.560858			0.280429	−	0.959875i	$-0.409523\pi$
$509$	12.6535			0.560858			0.280429	+	0.959875i	$0.409523\pi$
$510$	22.3473	+	12.9022i	0.989557	+	0.571321i
$511$	17.3916	−	17.6553i	0.769359	−	0.781024i
$512$			1.00000i			0.0441942i
$513$	3.51758	−	2.57423i	0.155305	−	0.113655i
$514$	−11.0117	+	6.35759i	−0.485704	+	0.280421i
$515$		−	28.2503i		−	1.24486i
$516$	5.98293	+	10.3627i	0.263384	+	0.456194i
$517$	14.1020	−	8.14179i	0.620205	−	0.358075i
$518$	15.7918	+	15.5560i	0.693854	+	0.683491i
$519$	8.41289	+	14.5716i	0.369285	+	0.639620i
$520$	−2.32803	+	4.03227i	−0.102091	+	0.176827i
$521$	0.744122	+	1.28886i	0.0326006	+	0.0564659i	0.881865	−	0.471501i	$-0.156288\pi$
$521$	0.744122	+	1.28886i	0.0326006	+	0.0564659i	−0.849265	+	0.527967i	$0.822954\pi$
$522$	0.00821465	−	0.0142282i	0.000359546	−	0.000622751i
$523$	−25.7520			−1.12605			−0.563027	−	0.826438i	$-0.690363\pi$
$523$	−25.7520			−1.12605			−0.563027	+	0.826438i	$0.690363\pi$
$524$			0.638981i			0.0279140i
$525$	−14.3508	+	3.96124i	−0.626320	+	0.172883i
$526$	−5.93381	+	3.42588i	−0.258726	+	0.149376i
$527$	44.7117	−	25.8143i	1.94767	−	1.12449i
$528$	−2.71451	+	4.70166i	−0.118134	+	0.204614i
$529$	−2.23077			−0.0969901
$530$	−2.99450	+	1.72887i	−0.130073	+	0.0750975i
$531$	6.62637			0.287560
$532$	−7.15894	+	9.04154i	−0.310380	+	0.392001i
$533$	13.7905			0.597334
$534$	−1.16565	+	0.672991i	−0.0504428	+	0.0291232i
$535$	16.5270			0.714526
$536$	0.177777	−	0.307919i	0.00767879	−	0.0133001i
$537$	−8.20242	+	4.73567i	−0.353960	+	0.204359i
$538$	17.0955	−	9.87007i	0.737038	−	0.425529i
$539$	32.6220	−	19.4946i	1.40513	−	0.839692i
$540$			3.25990i			0.140284i
$541$	−23.5459			−1.01232			−0.506158	−	0.862441i	$-0.668935\pi$
$541$	−23.5459			−1.01232			−0.506158	+	0.862441i	$0.668935\pi$
$542$	12.0115	−	20.8046i	0.515940	−	0.893634i
$543$	−9.09772	−	15.7577i	−0.390421	−	0.676228i
$544$	−3.95787	+	6.85523i	−0.169692	+	0.293915i
$545$	0.669131	+	1.15897i	0.0286624	+	0.0496448i
$546$	−1.00548	−	3.64266i	−0.0430307	−	0.155892i
$547$	11.4978	−	6.63826i	0.491610	−	0.283831i	−0.233632	−	0.972325i	$-0.575061\pi$
$547$	11.4978	−	6.63826i	0.491610	−	0.283831i	0.725242	+	0.688494i	$0.241728\pi$
$548$	−6.28064	−	10.8784i	−0.268296	−	0.464702i
$549$		−	3.83790i		−	0.163797i
$550$	−26.4559	+	15.2743i	−1.12808	+	0.651300i
$551$	0.0289024	−	0.0655223i	0.00123128	−	0.00279134i
$552$			4.55733i			0.193973i
$553$	−20.0405	−	5.20855i	−0.852208	−	0.221490i
$554$	12.0050	+	6.93109i	0.510044	+	0.294474i
$555$	27.3124			1.15935
$556$		−	8.09351i		−	0.343241i
$557$	−2.05473	+	3.55890i	−0.0870618	+	0.150795i	−0.906268	−	0.422704i	$-0.861081\pi$
$557$	−2.05473	+	3.55890i	−0.0870618	+	0.150795i	0.819206	+	0.573499i	$0.194414\pi$
$558$	5.64846	+	3.26114i	0.239118	+	0.138055i
$559$	−17.0907			−0.722858
$560$	−2.29490	−	8.31396i	−0.0969772	−	0.351329i
$561$	−37.2171	+	21.4873i	−1.57131	+	0.907195i
$562$	15.9501	−	27.6265i	0.672816	−	1.16535i
$563$	21.1202	+	36.5813i	0.890111	+	1.54172i	0.839742	+	0.542986i	$0.182706\pi$
$563$	21.1202	+	36.5813i	0.890111	+	1.54172i	0.0503688	+	0.998731i	$0.483960\pi$
$564$	2.59752	+	1.49968i	0.109376	+	0.0631480i
$565$	5.57052	+	9.64843i	0.234354	+	0.405912i
$566$	8.67587	+	15.0270i	0.364674	+	0.631634i
$567$	−1.88485	−	1.85670i	−0.0791563	−	0.0779741i
$568$	−0.701655	+	1.21530i	−0.0294408	+	0.0509929i
$569$	−39.1644	−	22.6116i	−1.64186	−	0.947926i	−0.980173	−	0.198143i	$-0.936509\pi$
$569$	−39.1644	−	22.6116i	−1.64186	−	0.947926i	−0.661684	−	0.749783i	$-0.730158\pi$
$570$	1.53396	+	14.1265i	0.0642507	+	0.591695i
$571$	6.52676	+	11.3047i	0.273137	+	0.473086i	0.969663	−	0.244444i	$-0.0786056\pi$
$571$	6.52676	+	11.3047i	0.273137	+	0.473086i	−0.696527	+	0.717531i	$0.745272\pi$
$572$	−3.87709	−	6.71531i	−0.162109	−	0.280781i
$573$	−5.00050	+	8.66112i	−0.208899	+	0.361824i
$574$	−17.9270	+	18.1988i	−0.748259	+	0.759604i
$575$	−12.8219	+	22.2081i	−0.534709	+	0.926144i
$576$	−1.00000			−0.0416667
$577$	−2.77536	+	1.60236i	−0.115540	+	0.0667070i	−0.556656	−	0.830743i	$-0.687916\pi$
$577$	−2.77536	+	1.60236i	−0.115540	+	0.0667070i	0.441116	+	0.897450i	$0.354583\pi$
$578$	−39.5417	+	22.8294i	−1.64472	+	0.949579i
$579$		−	6.60829i		−	0.274631i
$580$	0.0267789	+	0.0463825i	0.00111193	+	0.00192593i
$581$	12.0261	−	12.2085i	0.498928	−	0.506492i
$582$		−	17.3507i		−	0.719208i
$583$		−	5.75851i		−	0.238493i
$584$	9.36694			0.387607
$585$	−4.03227	−	2.32803i	−0.166714	−	0.0962522i
$586$	0.251617	−	0.145271i	0.0103942	−	0.00600110i
$587$	−32.8722	−	18.9788i	−1.35678	−	0.783337i	−0.367591	−	0.929988i	$-0.619817\pi$
$587$	−32.8722	−	18.9788i	−1.35678	−	0.783337i	−0.989188	+	0.146651i	$0.953151\pi$
$588$	6.11416	+	3.40839i	0.252144	+	0.140560i
$589$	26.0117	+	11.4740i	1.07179	+	0.472777i
$590$	−10.8006	+	18.7072i	−0.444655	+	0.770165i
$591$	15.5834			0.641014
$592$			8.37830i			0.344346i
$593$			31.5165i			1.29423i	0.762393	+	0.647114i	$0.224024\pi$
$593$			31.5165i			1.29423i	−0.762393	+	0.647114i	$0.775976\pi$
$594$	−4.70166	−	2.71451i	−0.192912	−	0.111378i
$595$	17.1735	−	66.0770i	0.704045	−	2.70889i
$596$	−15.5875			−0.638488
$597$	7.75390	+	4.47672i	0.317346	+	0.183220i
$598$	−5.63710	−	3.25458i	−0.230518	−	0.133090i
$599$	23.1641	+	13.3738i	0.946460	+	0.546439i	0.891980	−	0.452076i	$-0.149316\pi$
$599$	23.1641	+	13.3738i	0.946460	+	0.546439i	0.0544807	+	0.998515i	$0.482650\pi$
$600$	−4.87306	−	2.81347i	−0.198942	−	0.114859i
$601$	21.9402			0.894958			0.447479	−	0.894294i	$-0.352322\pi$
$601$	21.9402			0.894958			0.447479	+	0.894294i	$0.352322\pi$
$602$	22.2170	−	22.5539i	0.905498	−	0.919227i
$603$	0.307919	+	0.177777i	0.0125394	+	0.00723963i
$604$		−	14.8671i		−	0.604933i
$605$		−	60.2239i		−	2.44845i
$606$	−8.68482			−0.352797
$607$	21.1117	−	36.5666i	0.856898	−	1.48419i	−0.0179749	−	0.999838i	$-0.505722\pi$
$607$	21.1117	−	36.5666i	0.856898	−	1.48419i	0.874873	−	0.484353i	$-0.160945\pi$
$608$	−4.33343	+	0.470556i	−0.175744	+	0.0190836i
$609$	−0.0420702	−	0.0109341i	−0.00170477	−	0.000443072i
$610$	10.8350	+	6.25558i	0.438695	+	0.253281i
$611$	−3.71000	+	2.14197i	−0.150091	+	0.0866549i
$612$	−6.85523	−	3.95787i	−0.277106	−	0.159987i
$613$	22.9790			0.928113			0.464056	−	0.885806i	$-0.346393\pi$
$613$	22.9790			0.928113			0.464056	+	0.885806i	$0.346393\pi$
$614$		−	0.0206481i		−	0.000833288i
$615$			31.4753i			1.26921i
$616$	13.9020	+	3.61314i	0.560126	+	0.145577i
$617$	4.00146	+	6.93074i	0.161093	+	0.279021i	0.935261	−	0.353959i	$-0.115165\pi$
$617$	4.00146	+	6.93074i	0.161093	+	0.279021i	−0.774168	+	0.632980i	$0.781831\pi$
$618$			8.66600i			0.348598i
$619$	5.85957	−	3.38302i	0.235516	−	0.135975i	−0.377598	−	0.925970i	$-0.623250\pi$
$619$	5.85957	−	3.38302i	0.235516	−	0.135975i	0.613114	+	0.789994i	$0.289917\pi$
$620$	−18.4134	+	10.6310i	−0.739500	+	0.426950i
$621$	−4.55733			−0.182879
$622$	6.12693	−	10.6122i	0.245668	−	0.425509i
$623$	2.53698	+	2.49909i	0.101642	+	0.100124i
$624$	0.714142	−	1.23693i	0.0285886	−	0.0495169i
$625$	10.7362	+	18.5956i	0.429446	+	0.743823i
$626$	−15.8937	−	27.5286i	−0.635239	−	1.10027i
$627$	−21.6516	−	9.55071i	−0.864683	−	0.381419i
$628$	−3.53990	−	2.04376i	−0.141258	−	0.0815551i
$629$	−33.1602	+	57.4351i	−1.32218	+	2.29009i
$630$	8.31396	−	2.29490i	0.331236	−	0.0914309i
$631$	17.6332	+	30.5416i	0.701967	+	1.21584i	0.967775	+	0.251817i	$0.0810279\pi$
$631$	17.6332	+	30.5416i	0.701967	+	1.21584i	−0.265808	+	0.964026i	$0.585639\pi$
$632$	−3.91312	−	6.77772i	−0.155656	−	0.269603i
$633$	9.87775	+	5.70292i	0.392605	+	0.226671i
$634$	−9.01251	−	15.6101i	−0.357932	−	0.619957i
$635$	−23.3157	+	40.3840i	−0.925255	+	1.60259i
$636$	0.918586	−	0.530346i	0.0364243	−	0.0210296i
$637$	−8.58232	+	5.12871i	−0.340044	+	0.203207i
$638$	−0.0891949			−0.00353126
$639$	−1.21530	−	0.701655i	−0.0480766	−	0.0277570i
$640$	1.62995	−	2.82315i	0.0644294	−	0.111595i
$641$		−	16.3625i		−	0.646281i	−0.946351	−	0.323141i	$-0.895261\pi$
$641$		−	16.3625i		−	0.646281i	0.946351	−	0.323141i	$-0.104739\pi$
$642$	−5.06980			−0.200089
$643$	15.4748	+	8.93438i	0.610266	+	0.352337i	0.773070	−	0.634321i	$-0.218720\pi$
$643$	15.4748	+	8.93438i	0.610266	+	0.352337i	−0.162803	+	0.986659i	$0.552054\pi$
$644$	11.6229	−	3.20826i	0.458006	−	0.126423i
$645$		−	39.0075i		−	1.53592i
$646$	−31.5690	−	13.9254i	−1.24207	−	0.547886i
$647$	−16.5491	+	9.55462i	−0.650612	+	0.375631i	−0.788691	−	0.614790i	$-0.789241\pi$
$647$	−16.5491	+	9.55462i	−0.650612	+	0.375631i	0.138079	+	0.990421i	$0.455907\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−17.9873	−	31.1549i	−0.706064	−	1.22294i
$650$	6.96012	−	4.01843i	0.272998	−	0.157616i
$651$	4.34073	−	16.7015i	0.170127	−	0.654582i
$652$	−5.83332	−	10.1036i	−0.228451	−	0.395688i
$653$	17.9531	−	31.0956i	0.702558	−	1.21687i	−0.265008	−	0.964246i	$-0.585375\pi$
$653$	17.9531	−	31.0956i	0.702558	−	1.21687i	0.967566	−	0.252619i	$-0.0812920\pi$
$654$	−0.205261	−	0.355523i	−0.00802636	−	0.0139021i
$655$	1.04151	−	1.80394i	0.0406950	−	0.0704858i
$656$	−9.65530			−0.376976
$657$			9.36694i			0.365439i
$658$	1.99615	−	7.68041i	0.0778180	−	0.299413i
$659$	42.5206	−	24.5493i	1.65637	−	0.956305i	0.681998	−	0.731354i	$-0.261111\pi$
$659$	42.5206	−	24.5493i	1.65637	−	0.956305i	0.974370	−	0.224950i	$-0.0722220\pi$
$660$	15.3269	−	8.84901i	0.596600	−	0.344447i
$661$	4.89940	−	8.48600i	0.190564	−	0.330067i	−0.754873	−	0.655871i	$-0.772302\pi$
$661$	4.89940	−	8.48600i	0.190564	−	0.330067i	0.945437	+	0.325804i	$0.105635\pi$
$662$	−15.1344			−0.588214
$663$	9.79121	−	5.65296i	0.380259	−	0.219543i
$664$	6.47715			0.251362
$665$	34.9481	−	13.8570i	1.35523	−	0.537350i
$666$	−8.37830			−0.324652
$667$	−0.0648426	+	0.0374369i	−0.00251071	+	0.00144956i
$668$	−2.58046			−0.0998409
$669$	2.62150	−	4.54057i	0.101353	−	0.175549i
$670$	−1.00378	+	0.579534i	−0.0387795	+	0.0223894i
$671$	−18.0445	+	10.4180i	−0.696600	+	0.402182i
$672$	0.703979	+	2.55038i	0.0271566	+	0.0983829i
$673$			18.3935i			0.709017i	0.935053	+	0.354508i	$0.115352\pi$
$673$			18.3935i			0.709017i	−0.935053	+	0.354508i	$0.884648\pi$
$674$	−21.5081			−0.828463
$675$	2.81347	−	4.87306i	0.108290	−	0.187564i
$676$	−5.48000	−	9.49164i	−0.210769	−	0.365063i
$677$	−24.3099	+	42.1060i	−0.934305	+	1.61826i	−0.158437	+	0.987369i	$0.550646\pi$
$677$	−24.3099	+	42.1060i	−0.934305	+	1.61826i	−0.775868	+	0.630895i	$0.782688\pi$
$678$	−1.70880	−	2.95973i	−0.0656262	−	0.113668i
$679$	−44.2507	+	12.2145i	−1.69819	+	0.468750i
$680$	22.3473	−	12.9022i	0.856981	−	0.494778i
$681$	14.1297	+	24.4733i	0.541450	+	0.937819i
$682$		−	35.4095i		−	1.35590i
$683$	36.7209	−	21.2008i	1.40509	−	0.811228i	0.410179	−	0.912005i	$-0.365466\pi$
$683$	36.7209	−	21.2008i	1.40509	−	0.811228i	0.994909	+	0.100777i	$0.0321329\pi$
$684$	−0.470556	−	4.33343i	−0.0179922	−	0.165693i
$685$			40.9485i			1.56456i
$686$	4.38843	−	17.9928i	0.167551	−	0.686969i
$687$	19.7790	+	11.4194i	0.754615	+	0.435677i
$688$	11.9659			0.456194
$689$			1.51497i			0.0577158i
$690$	7.42821	−	12.8660i	0.282787	−	0.489802i
$691$	17.8127	+	10.2841i	0.677626	+	0.391227i	0.798960	−	0.601384i	$-0.205384\pi$
$691$	17.8127	+	10.2841i	0.677626	+	0.391227i	−0.121334	+	0.992612i	$0.538717\pi$
$692$	16.8258			0.639620
$693$	−3.61314	+	13.9020i	−0.137252	+	0.528092i
$694$	−13.3148	+	7.68730i	−0.505423	+	0.291806i
$695$	−13.1920	+	22.8492i	−0.500401	+	0.866720i
$696$	−0.00821465	−	0.0142282i	−0.000311376	−	0.000539318i
$697$	−66.1893	−	38.2144i	−2.50710	−	1.44747i
$698$	4.02486	+	6.97126i	0.152343	+	0.263866i
$699$	0.411130	+	0.712098i	0.0155504	+	0.0269340i
$700$	−3.74486	+	14.4088i	−0.141542	+	0.544600i
$701$	−3.00286	+	5.20110i	−0.113416	+	0.196443i	−0.917146	−	0.398552i	$-0.869513\pi$
$701$	−3.00286	+	5.20110i	−0.113416	+	0.196443i	0.803729	+	0.594995i	$0.202846\pi$
$702$	1.23693	+	0.714142i	0.0466849	+	0.0269536i
$703$	−36.3067	+	3.94246i	−1.36933	+	0.148693i
$704$	2.71451	+	4.70166i	0.102307	+	0.177201i
$705$	−4.88881	−	8.46766i	−0.184123	−	0.318911i
$706$	13.9391	−	24.1432i	0.524605	−	0.908642i
$707$	6.11393	+	22.1496i	0.229938	+	0.833020i
$708$	3.31318	−	5.73860i	0.124517	−	0.215670i
$709$	26.2048			0.984140			0.492070	−	0.870556i	$-0.336240\pi$
$709$	26.2048			0.984140			0.492070	+	0.870556i	$0.336240\pi$
$710$	3.96176	−	2.28732i	0.148682	−	0.0858417i
$711$	6.77772	−	3.91312i	0.254184	−	0.146753i
$712$			1.34598i			0.0504428i
$713$	−14.8621	−	25.7419i	−0.556589	−	0.964041i
$714$	−5.26811	+	20.2697i	−0.197154	+	0.758573i
$715$			25.2778i			0.945336i
$716$			9.47134i			0.353960i
$717$	−15.6050			−0.582781
$718$	26.9349	+	15.5509i	1.00520	+	0.580353i
$719$	−30.4722	+	17.5931i	−1.13642	+	0.656113i	−0.945542	−	0.325501i	$-0.894467\pi$
$719$	−30.4722	+	17.5931i	−1.13642	+	0.656113i	−0.190879	+	0.981614i	$0.561134\pi$
$720$	2.82315	+	1.62995i	0.105213	+	0.0607446i
$721$	22.1015	−	6.10068i	0.823105	−	0.227201i
$722$	−4.07824	−	18.5572i	−0.151776	−	0.690626i
$723$	−6.85020	+	11.8649i	−0.254762	+	0.441260i
$724$	−18.1954			−0.676228
$725$		−	0.0924466i		−	0.00343338i
$726$			18.4742i			0.685640i
$727$	3.49969	+	2.02055i	0.129796	+	0.0749379i	0.563492	−	0.826121i	$-0.309457\pi$
$727$	3.49969	+	2.02055i	0.129796	+	0.0749379i	−0.433696	+	0.901059i	$0.642791\pi$
$728$	−3.65738	−	0.950558i	−0.135551	−	0.0352300i
$729$	1.00000			0.0370370
$730$	−26.4443	−	15.2676i	−0.978748	−	0.565080i
$731$	82.0287	+	47.3593i	3.03394	+	1.75165i
$732$	−3.32372	−	1.91895i	−0.122848	−	0.0709264i
$733$	37.8955	+	21.8790i	1.39970	+	0.808118i	0.994361	−	0.106047i	$-0.0338195\pi$
$733$	37.8955	+	21.8790i	1.39970	+	0.808118i	0.405341	+	0.914166i	$0.367153\pi$
$734$	−28.2340			−1.04214
$735$	−11.7057	−	19.5882i	−0.431771	−	0.722520i
$736$	3.94676	+	2.27866i	0.145480	+	0.0839926i
$737$		−	1.93031i		−	0.0711037i
$738$		−	9.65530i		−	0.355417i
$739$	−44.7886			−1.64758			−0.823788	−	0.566898i	$-0.808143\pi$
$739$	−44.7886			−1.64758			−0.823788	+	0.566898i	$0.808143\pi$
$740$	13.6562	−	23.6532i	0.502012	−	0.869510i
$741$	5.69619	+	2.51264i	0.209255	+	0.0923040i
$742$	−1.99925	−	1.96939i	−0.0733947	−	0.0722985i
$743$	−30.5144	−	17.6175i	−1.11946	−	0.646323i	−0.178201	−	0.983994i	$-0.557028\pi$
$743$	−30.5144	−	17.6175i	−1.11946	−	0.646323i	−0.941264	+	0.337671i	$0.890361\pi$
$744$	5.64846	−	3.26114i	0.207083	−	0.119559i
$745$	44.0059	+	25.4068i	1.61225	+	0.930833i
$746$	2.54202			0.0930700
$747$			6.47715i			0.236987i
$748$			42.9746i			1.57131i
$749$	3.56903	+	12.9299i	0.130410	+	0.472448i
$750$	1.02186	+	1.76992i	0.0373132	+	0.0646283i
$751$		−	32.3777i		−	1.18148i	−0.806862	−	0.590740i	$-0.798836\pi$
$751$		−	32.3777i		−	1.18148i	0.806862	−	0.590740i	$-0.201164\pi$
$752$	2.59752	−	1.49968i	0.0947220	−	0.0546878i
$753$	−11.3817	+	6.57124i	−0.414773	+	0.239469i
$754$	0.0234657			0.000854571
$755$	−24.2326	+	41.9721i	−0.881914	+	1.52752i
$756$	−2.55038	+	0.703979i	−0.0927563	+	0.0256035i
$757$	19.0424	−	32.9825i	0.692109	−	1.19877i	−0.279036	−	0.960281i	$-0.590015\pi$
$757$	19.0424	−	32.9825i	0.692109	−	1.19877i	0.971145	−	0.238488i	$-0.0766518\pi$
$758$	0.320260	+	0.554706i	0.0116324	+	0.0201478i
$759$	12.3709	+	21.4270i	0.449035	+	0.777751i
$760$	13.0009	+	5.73481i	0.471593	+	0.208023i
$761$	−3.67671	−	2.12275i	−0.133281	−	0.0769497i	0.431877	−	0.901932i	$-0.357851\pi$
$761$	−3.67671	−	2.12275i	−0.133281	−	0.0769497i	−0.565158	+	0.824983i	$0.691185\pi$
$762$	7.15228	−	12.3881i	0.259100	−	0.448774i
$763$	−0.762218	+	0.773775i	−0.0275942	+	0.0280125i
$764$	5.00050	+	8.66112i	0.180912	+	0.313348i
$765$	12.9022	+	22.3473i	0.466482	+	0.807970i
$766$	22.3112	+	12.8814i	0.806136	+	0.465423i
$767$	4.73217	+	8.19635i	0.170869	+	0.295953i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	28.3003	−	16.3392i	1.02054	−	0.589207i	0.106277	−	0.994337i	$-0.466107\pi$
$769$	28.3003	−	16.3392i	1.02054	−	0.589207i	0.914259	+	0.405130i	$0.132774\pi$
$770$	−33.3581	−	32.8599i	−1.20214	−	1.18419i
$771$	−12.7152			−0.457926
$772$	−5.72294	−	3.30414i	−0.205973	−	0.118919i
$773$	−17.8527	+	30.9218i	−0.642118	+	1.11218i	0.342841	+	0.939394i	$0.388611\pi$
$773$	−17.8527	+	30.9218i	−0.642118	+	1.11218i	−0.984959	+	0.172788i	$0.944722\pi$
$774$			11.9659i			0.430104i
$775$	36.7004			1.31832
$776$	−15.0261	−	8.67534i	−0.539406	−	0.311426i
$777$	5.89814	+	21.3678i	0.211595	+	0.766565i
$778$			26.4742i			0.949147i
$779$	−4.54336	−	41.8405i	−0.162783	−	1.49909i
$780$	−4.03227	+	2.32803i	−0.144378	+	0.0833569i
$781$			7.61858i			0.272614i
$782$	18.0373	+	31.2415i	0.645012	+	1.11719i
$783$	0.0142282	−	0.00821465i	0.000508474	−	0.000293568i
$784$	6.00883	−	3.59082i	0.214601	−	0.128244i
$785$	6.66246	+	11.5397i	0.237794	+	0.411870i
$786$	−0.319490	+	0.553373i	−0.0113958	+	0.0197382i
$787$	17.3443	+	30.0412i	0.618257	+	1.07085i	0.989804	+	0.142439i	$0.0454944\pi$
$787$	17.3443	+	30.0412i	0.618257	+	1.07085i	−0.371546	+	0.928415i	$0.621172\pi$
$788$	7.79168	−	13.4956i	0.277567	−	0.480760i
$789$	−6.85177			−0.243929
$790$			25.5127i			0.907702i
$791$	−6.34547	+	6.44168i	−0.225619	+	0.229040i
$792$	−4.70166	+	2.71451i	−0.167066	+	0.0964558i
$793$	4.74721	−	2.74080i	0.168578	−	0.0973288i
$794$	−15.1111	+	26.1732i	−0.536272	+	0.928851i
$795$	−3.45775			−0.122634
$796$	7.75390	−	4.47672i	0.274830	−	0.158673i
$797$	41.0322			1.45343			0.726717	−	0.686937i	$-0.241045\pi$
$797$	41.0322			1.45343			0.726717	+	0.686937i	$0.241045\pi$
$798$	−10.7206	+	4.25073i	−0.379505	+	0.150474i
$799$	23.7422			0.839937
$800$	−4.87306	+	2.81347i	−0.172289	+	0.0994710i
$801$	−1.34598			−0.0475579
$802$	−2.46727	+	4.27344i	−0.0871223	+	0.150900i
$803$	44.0402	−	25.4266i	1.55414	−	0.897285i
$804$	0.307919	−	0.177777i	0.0108595	−	0.00626971i
$805$	−38.0425	−	9.88730i	−1.34082	−	0.348482i
$806$			9.31567i			0.328130i
$807$	19.7401			0.694886
$808$	−4.34241	+	7.52128i	−0.152765	+	0.264598i
$809$	4.51845	+	7.82618i	0.158860	+	0.275154i	0.934458	−	0.356074i	$-0.115885\pi$
$809$	4.51845	+	7.82618i	0.158860	+	0.275154i	−0.775598	+	0.631227i	$0.782551\pi$
$810$	−1.62995	+	2.82315i	−0.0572706	+	0.0991955i
$811$	27.2870	+	47.2625i	0.958177	+	1.65961i	0.726925	+	0.686717i	$0.240949\pi$
$811$	27.2870	+	47.2625i	0.958177	+	1.65961i	0.231252	+	0.972894i	$0.425718\pi$
$812$	−0.0305043	+	0.0309668i	−0.00107049	+	0.00108672i
$813$	20.8046	−	12.0115i	0.729649	−	0.421263i
$814$	22.7429	+	39.3919i	0.797139	+	1.38069i
$815$			38.0321i			1.33221i
$816$	−6.85523	+	3.95787i	−0.239981	+	0.138553i
$817$	5.63061	+	51.8532i	0.196990	+	1.81411i
$818$		−	22.1477i		−	0.774376i
$819$	0.950558	−	3.65738i	0.0332152	−	0.127799i
$820$	27.2584	+	15.7376i	0.951905	+	0.549583i
$821$	11.6560			0.406796			0.203398	−	0.979096i	$-0.434802\pi$
$821$	11.6560			0.406796			0.203398	+	0.979096i	$0.434802\pi$
$822$		−	12.5613i		−	0.438125i
$823$	−6.83386	+	11.8366i	−0.238213	+	0.412597i	−0.960202	−	0.279308i	$-0.909895\pi$
$823$	−6.83386	+	11.8366i	−0.238213	+	0.412597i	0.721988	+	0.691905i	$0.243228\pi$
$824$	7.50497	+	4.33300i	0.261448	+	0.150947i
$825$	−30.5487			−1.06357
$826$	−16.9680	−	4.41001i	−0.590392	−	0.153444i
$827$	17.3079	−	9.99271i	0.601854	−	0.347481i	−0.167917	−	0.985801i	$-0.553704\pi$
$827$	17.3079	−	9.99271i	0.601854	−	0.347481i	0.769771	+	0.638321i	$0.220371\pi$
$828$	−2.27866	+	3.94676i	−0.0791890	+	0.137159i
$829$	0.850088	+	1.47239i	0.0295248	+	0.0511384i	0.880410	−	0.474213i	$-0.157267\pi$
$829$	0.850088	+	1.47239i	0.0295248	+	0.0511384i	−0.850885	+	0.525351i	$0.823934\pi$
$830$	−18.2860	−	10.5574i	−0.634716	−	0.366453i
$831$	6.93109	+	12.0050i	0.240437	+	0.416449i
$832$	−0.714142	−	1.23693i	−0.0247584	−	0.0428829i
$833$	55.4039	−	0.833743i	1.91963	−	0.0288875i
$834$	4.04675	−	7.00918i	0.140128	−	0.242708i
$835$	7.28503	+	4.20601i	0.252109	+	0.145555i
$836$	−19.0970	+	13.9755i	−0.660483	+	0.483353i
$837$	3.26114	+	5.64846i	0.112721	+	0.195239i
$838$	2.67063	+	4.62566i	0.0922552	+	0.159791i
$839$	7.36695	−	12.7599i	0.254335	−	0.440522i	−0.710379	−	0.703819i	$-0.751477\pi$
$839$	7.36695	−	12.7599i	0.254335	−	0.440522i	0.964715	+	0.263297i	$0.0848100\pi$
$840$	2.16954	−	8.34755i	0.0748563	−	0.288018i
$841$	−14.4999	+	25.1145i	−0.499995	+	0.866017i
$842$	−15.9068			−0.548185
$843$	27.6265	−	15.9501i	0.951506	−	0.549352i
$844$	9.87775	−	5.70292i	0.340006	−	0.196303i
$845$			35.7285i			1.22910i
$846$	1.49968	+	2.59752i	0.0515601	+	0.0893047i
$847$	47.1160	−	13.0054i	1.61893	−	0.446871i
$848$		−	1.06069i		−	0.0364243i
$849$			17.3517i			0.595510i
$850$	−44.5413			−1.52775
$851$	33.0671	+	19.0913i	1.13353	+	0.654442i
$852$	−1.21530	+	0.701655i	−0.0416355	+	0.0240383i
$853$	−45.3823	−	26.2015i	−1.55386	−	0.897122i	−0.997822	−	0.0659665i	$-0.978987\pi$
$853$	−45.3823	−	26.2015i	−1.55386	−	0.897122i	−0.556040	−	0.831156i	$-0.687680\pi$
$854$	−2.55421	+	9.82762i	−0.0874034	+	0.336294i
$855$	−5.73481	+	13.0009i	−0.196126	+	0.444622i
$856$	−2.53490	+	4.39058i	−0.0866412	+	0.150067i
$857$	4.73219			0.161649			0.0808243	−	0.996728i	$-0.474245\pi$
$857$	4.73219			0.161649			0.0808243	+	0.996728i	$0.474245\pi$
$858$		−	7.75417i		−	0.264723i
$859$		−	28.0357i		−	0.956566i	−0.878206	−	0.478283i	$-0.841259\pi$
$859$		−	28.0357i		−	0.956566i	0.878206	−	0.478283i	$-0.158741\pi$
$860$	−33.7815	−	19.5037i	−1.15194	−	0.665072i
$861$	−24.6246	+	6.79713i	−0.839206	+	0.231646i
$862$	−18.8474			−0.641946
$863$	2.68371	+	1.54944i	0.0913545	+	0.0527436i	0.544981	−	0.838448i	$-0.316537\pi$
$863$	2.68371	+	1.54944i	0.0913545	+	0.0527436i	−0.453627	+	0.891192i	$0.649870\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	−47.5018	−	27.4252i	−1.61511	−	0.932483i
$866$	5.62323	+	3.24657i	0.191085	+	0.110323i
$867$	−45.6589			−1.55066
$868$	−12.2935	−	12.1099i	−0.417269	−	0.411037i
$869$	−36.7963	−	21.2444i	−1.24823	−	0.720666i
$870$			0.0535579i			0.00181578i
$871$			0.507832i			0.0172072i
$872$	−0.410523			−0.0139021
$873$	8.67534	−	15.0261i	0.293616	−	0.508557i
$874$	−8.01725	+	18.1752i	−0.271187	+	0.614786i
$875$	3.79459	−	3.85212i	0.128281	−	0.130226i
$876$	8.11201	+	4.68347i	0.274079	+	0.158240i
$877$	−23.1777	+	13.3817i	−0.782656	+	0.451867i	−0.837371	−	0.546635i	$-0.815908\pi$
$877$	−23.1777	+	13.3817i	−0.782656	+	0.451867i	0.0547148	+	0.998502i	$0.482575\pi$
$878$	−21.0723	−	12.1661i	−0.711155	−	0.410585i
$879$	0.290543			0.00979976
$880$		−	17.6980i		−	0.596600i
$881$		−	21.2925i		−	0.717362i	−0.933460	−	0.358681i	$-0.883227\pi$
$881$		−	21.2925i		−	0.717362i	0.933460	−	0.358681i	$-0.116773\pi$
$882$	3.59082	+	6.00883i	0.120909	+	0.202328i
$883$	8.65145	+	14.9847i	0.291144	+	0.504277i	0.974081	−	0.226201i	$-0.0726307\pi$
$883$	8.65145	+	14.9847i	0.291144	+	0.504277i	−0.682936	+	0.730478i	$0.739297\pi$
$884$		−	11.3059i		−	0.380259i
$885$	−18.7072	+	10.8006i	−0.628837	+	0.363059i
$886$	−16.0056	+	9.24085i	−0.537719	+	0.310452i
$887$	7.36403			0.247260			0.123630	−	0.992328i	$-0.460546\pi$
$887$	7.36403			0.247260			0.123630	+	0.992328i	$0.460546\pi$
$888$	−4.18915	+	7.25582i	−0.140579	+	0.243489i
$889$	−36.6294	−	9.52003i	−1.22851	−	0.319291i
$890$	2.19388	−	3.79991i	0.0735391	−	0.127373i
$891$	−2.71451	−	4.70166i	−0.0909394	−	0.157512i
$892$	−2.62150	−	4.54057i	−0.0877743	−	0.152030i
$893$	7.72104	+	10.5505i	0.258375	+	0.353059i
$894$	−13.4992	−	7.79374i	−0.451479	−	0.260662i
$895$	15.4378	−	26.7390i	0.516029	−	0.893788i
$896$	2.56068	+	0.665524i	0.0855463	+	0.0222336i
$897$	−3.25458	−	5.63710i	−0.108667	−	0.188217i
$898$	11.9634	+	20.7211i	0.399223	+	0.691474i
$899$	0.0928003	+	0.0535783i	0.00309506	+	0.00178694i
$900$	−2.81347	−	4.87306i	−0.0937822	−	0.162435i
$901$	4.19808	−	7.27129i	0.139858	−	0.242242i
$902$	−45.3960	+	26.2094i	−1.51152	+	0.872677i
$903$	30.5174	−	8.42372i	1.01556	−	0.280324i
$904$	−3.41761			−0.113668
$905$	51.3685	+	29.6576i	1.70755	+	0.985853i
$906$	7.43354	−	12.8753i	0.246963	−	0.427752i
$907$			37.3776i			1.24110i	0.784165	+	0.620552i	$0.213091\pi$
$907$			37.3776i			1.24110i	−0.784165	+	0.620552i	$0.786909\pi$
$908$	28.2593			0.937819
$909$	−7.52128	−	4.34241i	−0.249465	−	0.144029i
$910$	8.77598	+	8.64491i	0.290921	+	0.286576i
$911$		−	36.3987i		−	1.20594i	−0.797763	−	0.602971i	$-0.793984\pi$
$911$		−	36.3987i		−	1.20594i	0.797763	−	0.602971i	$-0.206016\pi$
$912$	−3.98813	−	1.75920i	−0.132060	−	0.0582529i
$913$	30.4534	−	17.5823i	1.00786	−	0.581888i
$914$			27.8149i			0.920034i
$915$	6.25558	+	10.8350i	0.206803	+	0.358193i
$916$	19.7790	−	11.4194i	0.653516	−	0.377307i
$917$	1.63622	+	0.425257i	0.0540329	+	0.0140432i
$918$	−3.95787	−	6.85523i	−0.130629	−	0.226256i
$919$	−5.31989	+	9.21432i	−0.175487	+	0.303952i	−0.940330	−	0.340265i	$-0.889483\pi$
$919$	−5.31989	+	9.21432i	−0.175487	+	0.303952i	0.764843	+	0.644217i	$0.222817\pi$
$920$	−7.42821	−	12.8660i	−0.244901	−	0.424181i
$921$	0.0103240	−	0.0178817i	0.000340188	−	0.000589223i
$922$	−4.71994			−0.155443
$923$		−	2.00432i		−	0.0659732i
$924$	10.2329	+	10.0800i	0.336637	+	0.331609i
$925$	−40.8280	+	23.5720i	−1.34242	+	0.775044i
$926$	−2.27863	+	1.31557i	−0.0748805	+	0.0432322i
$927$	−4.33300	+	7.50497i	−0.142314	+	0.246496i
$928$	−0.0164293			−0.000539318
$929$	23.4366	−	13.5312i	0.768931	−	0.443943i	−0.0635619	−	0.997978i	$-0.520246\pi$
$929$	23.4366	−	13.5312i	0.768931	−	0.443943i	0.832493	+	0.554035i	$0.186913\pi$
$930$	−21.2620			−0.697207
$931$	18.3880	+	24.3491i	0.602644	+	0.798010i
$932$	0.822260			0.0269340
$933$	10.6122	−	6.12693i	0.347427	−	0.200587i
$934$	−9.25519			−0.302839
$935$	70.0464	−	121.324i	2.29076	−	3.96772i
$936$	1.23693	−	0.714142i	0.0404303	−	0.0233425i
$937$	1.99565	−	1.15219i	0.0651949	−	0.0376403i	−0.467048	−	0.884232i	$-0.654683\pi$
$937$	1.99565	−	1.15219i	0.0651949	−	0.0376403i	0.532243	+	0.846592i	$0.321349\pi$
$938$	−0.670166	−	0.660157i	−0.0218817	−	0.0215549i
$939$		−	31.7873i		−	1.03734i
$940$	−9.77761			−0.318911
$941$	−4.09800	+	7.09795i	−0.133591	+	0.231386i	−0.925058	−	0.379825i	$-0.875984\pi$
$941$	−4.09800	+	7.09795i	−0.133591	+	0.231386i	0.791467	+	0.611211i	$0.209318\pi$
$942$	−2.04376	−	3.53990i	−0.0665895	−	0.115336i
$943$	−22.0012	+	38.1072i	−0.716457	+	1.24094i
$944$	−3.31318	−	5.73860i	−0.107835	−	0.186776i
$945$	8.34755	+	2.16954i	0.271546	+	0.0705752i
$946$	56.2595	−	32.4814i	1.82915	−	1.05606i
$947$	−0.0654400	−	0.113345i	−0.00212651	−	0.00368323i	0.864960	−	0.501840i	$-0.167344\pi$
$947$	−0.0654400	−	0.113345i	−0.00212651	−	0.00368323i	−0.867087	+	0.498157i	$0.834010\pi$
$948$		−	7.82624i		−	0.254184i
$949$	−11.5863	+	6.68933i	−0.376106	+	0.217145i
$950$	−14.4850	−	19.7932i	−0.469955	−	0.642175i
$951$		−	18.0250i		−	0.584501i
$952$	14.9200	+	14.6971i	0.483559	+	0.476337i
$953$	−0.270295	−	0.156055i	−0.00875572	−	0.00505511i	0.495616	−	0.868542i	$-0.334942\pi$
$953$	−0.270295	−	0.156055i	−0.00875572	−	0.00505511i	−0.504371	+	0.863487i	$0.668276\pi$
$954$	1.06069			0.0343412
$955$		−	32.6022i		−	1.05498i
$956$	−7.80252	+	13.5144i	−0.252351	+	0.437086i
$957$	−0.0772450	−	0.0445974i	−0.00249698	−	0.00144163i
$958$	−21.5734			−0.697003
$959$	−32.0360	+	8.84288i	−1.03450	+	0.285551i
$960$	2.82315	−	1.62995i	0.0911169	−	0.0526064i
$961$	−5.77006	+	9.99404i	−0.186131	+	0.322389i
$962$	−5.98329	−	10.3634i	−0.192909	−	0.334128i
$963$	−4.39058	−	2.53490i	−0.141484	−	0.0816861i
$964$	6.85020	+	11.8649i	0.220630	+	0.382143i
$965$	10.7712	+	18.6562i	0.346736	+	0.600565i
$966$	11.6699	+	3.03301i	0.375471	+	0.0975855i
$967$	7.84452	−	13.5871i	0.252263	−	0.436932i	−0.711886	−	0.702295i	$-0.752159\pi$
$967$	7.84452	−	13.5871i	0.252263	−	0.436932i	0.964148	+	0.265363i	$0.0854919\pi$
$968$	15.9991	+	9.23708i	0.514230	+	0.296891i
$969$	−20.3769	−	27.8442i	−0.654600	−	0.894485i
$970$	28.2807	+	48.9836i	0.908039	+	1.57277i
$971$	15.2678	+	26.4446i	0.489967	+	0.848647i	0.999933	−	0.0115470i	$-0.00367560\pi$
$971$	15.2678	+	26.4446i	0.489967	+	0.848647i	−0.509967	+	0.860194i	$0.670342\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−20.7249	−	5.38643i	−0.664409	−	0.172681i
$974$	−9.21489	+	15.9607i	−0.295264	+	0.511412i
$975$	8.03686			0.257385
$976$	−3.32372	+	1.91895i	−0.106390	+	0.0614241i
$977$	−14.7729	+	8.52914i	−0.472627	+	0.272871i	−0.717339	−	0.696725i	$-0.754640\pi$
$977$	−14.7729	+	8.52914i	−0.472627	+	0.272871i	0.244712	+	0.969596i	$0.421307\pi$
$978$		−	11.6666i		−	0.373058i
$979$	3.65368	+	6.32835i	0.116772	+	0.202255i
$980$	−22.8167	+	0.343356i	−0.728853	+	0.0109681i
$981$		−	0.410523i		−	0.0131070i
$982$			0.824293i			0.0263043i
$983$	15.1889			0.484450			0.242225	−	0.970220i	$-0.422123\pi$
$983$	15.1889			0.484450			0.242225	+	0.970220i	$0.422123\pi$
$984$	−8.36174	−	4.82765i	−0.266562	−	0.153900i
$985$	−43.9942	+	25.4001i	−1.40177	+	0.809314i
$986$	−0.112627	−	0.0650250i	−0.00358676	−	0.00207082i
$987$	5.56892	−	5.65335i	0.177261	−	0.179948i
$988$	5.02410	−	3.67673i	0.159838	−	0.116972i
$989$	27.2662	−	47.2264i	0.867014	−	1.50171i
$990$	17.6980			0.562480
$991$			19.0549i			0.605298i	0.953102	+	0.302649i	$0.0978710\pi$
$991$			19.0549i			0.605298i	−0.953102	+	0.302649i	$0.902129\pi$
$992$		−	6.52228i		−	0.207083i
$993$	−13.1068	−	7.56719i	−0.415930	−	0.240138i
$994$	2.64503	+	2.60552i	0.0838952	+	0.0826422i
$995$	−29.1873			−0.925299
$996$	5.60938	+	3.23857i	0.177740	+	0.102618i
$997$	−43.8655	−	25.3257i	−1.38923	−	0.802074i	−0.396005	−	0.918249i	$-0.629604\pi$
$997$	−43.8655	−	25.3257i	−1.38923	−	0.802074i	−0.993229	+	0.116174i	$0.962937\pi$
$998$	−21.3652	−	12.3352i	−0.676304	−	0.390464i
$999$	−7.25582	−	4.18915i	−0.229564	−	0.132539i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bc.b.103.8	yes	28
7.3	odd	6		798.2.m.b.787.14	yes	28
19.12	odd	6		798.2.m.b.145.1	✓	28
133.31	even	6	inner	798.2.bc.b.31.8	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.m.b.145.1	✓	28	19.12	odd	6
798.2.m.b.787.14	yes	28	7.3	odd	6
798.2.bc.b.31.8	yes	28	133.31	even	6	inner
798.2.bc.b.103.8	yes	28	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.82315 + 1.62995i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-1.88485 - 1.85670i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +(-1.62995 + 2.82315i) q^{10} +(-2.71451 - 4.70166i) q^{11} +(0.500000 - 0.866025i) q^{12} +(0.714142 + 1.23693i) q^{13} +(-2.56068 - 0.665524i) q^{14} +(-2.82315 + 1.62995i) q^{15} +(-0.500000 - 0.866025i) q^{16} -7.91573i q^{17} +(0.866025 - 0.500000i) q^{18} +(3.51758 - 2.57423i) q^{19} +3.25990i q^{20} +(-1.88485 - 1.85670i) q^{21} +(-4.70166 - 2.71451i) q^{22} -4.55733 q^{23} -1.00000i q^{24} +(2.81347 - 4.87306i) q^{25} +(1.23693 + 0.714142i) q^{26} +1.00000 q^{27} +(-2.55038 + 0.703979i) q^{28} +(0.0142282 - 0.00821465i) q^{29} +(-1.62995 + 2.82315i) q^{30} +(3.26114 + 5.64846i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-2.71451 - 4.70166i) q^{33} +(-3.95787 - 6.85523i) q^{34} +(8.34755 + 2.16954i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-7.25582 - 4.18915i) q^{37} +(1.75920 - 3.98813i) q^{38} +(0.714142 + 1.23693i) q^{39} +(1.62995 + 2.82315i) q^{40} +(4.82765 - 8.36174i) q^{41} +(-2.56068 - 0.665524i) q^{42} +(-5.98293 + 10.3627i) q^{43} -5.42901 q^{44} +(-2.82315 + 1.62995i) q^{45} +(-3.94676 + 2.27866i) q^{46} +2.99936i q^{47} +(-0.500000 - 0.866025i) q^{48} +(0.105327 + 6.99921i) q^{49} -5.62693i q^{50} -7.91573i q^{51} +1.42828 q^{52} +(0.918586 + 0.530346i) q^{53} +(0.866025 - 0.500000i) q^{54} +(15.3269 + 8.84901i) q^{55} +(-1.85670 + 1.88485i) q^{56} +(3.51758 - 2.57423i) q^{57} +(0.00821465 - 0.0142282i) q^{58} +6.62637 q^{59} +3.25990i q^{60} -3.83790i q^{61} +(5.64846 + 3.26114i) q^{62} +(-1.88485 - 1.85670i) q^{63} -1.00000 q^{64} +(-4.03227 - 2.32803i) q^{65} +(-4.70166 - 2.71451i) q^{66} +(0.307919 + 0.177777i) q^{67} +(-6.85523 - 3.95787i) q^{68} -4.55733 q^{69} +(8.31396 - 2.29490i) q^{70} +(-1.21530 - 0.701655i) q^{71} -1.00000i q^{72} +9.36694i q^{73} -8.37830 q^{74} +(2.81347 - 4.87306i) q^{75} +(-0.470556 - 4.33343i) q^{76} +(-3.61314 + 13.9020i) q^{77} +(1.23693 + 0.714142i) q^{78} +(6.77772 - 3.91312i) q^{79} +(2.82315 + 1.62995i) q^{80} +1.00000 q^{81} -9.65530i q^{82} +6.47715i q^{83} +(-2.55038 + 0.703979i) q^{84} +(12.9022 + 22.3473i) q^{85} +11.9659i q^{86} +(0.0142282 - 0.00821465i) q^{87} +(-4.70166 + 2.71451i) q^{88} -1.34598 q^{89} +(-1.62995 + 2.82315i) q^{90} +(0.950558 - 3.65738i) q^{91} +(-2.27866 + 3.94676i) q^{92} +(3.26114 + 5.64846i) q^{93} +(1.49968 + 2.59752i) q^{94} +(-5.73481 + 13.0009i) q^{95} +(-0.866025 - 0.500000i) q^{96} +(8.67534 - 15.0261i) q^{97} +(3.59082 + 6.00883i) q^{98} +(-2.71451 - 4.70166i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{3} + 14 q^{4} + 6 q^{5} - 8 q^{7} + 28 q^{9} + 2 q^{10} + 14 q^{12} + 2 q^{13} - 8 q^{14} + 6 q^{15} - 14 q^{16} + 12 q^{19} - 8 q^{21} - 12 q^{22} + 24 q^{23} + 14 q^{25} + 24 q^{26} + 28 q^{27}+ \cdots + 28 q^{98}+O(q^{100}) \) 28 * q + 28 * q^3 + 14 * q^4 + 6 * q^5 - 8 * q^7 + 28 * q^9 + 2 * q^10 + 14 * q^12 + 2 * q^13 - 8 * q^14 + 6 * q^15 - 14 * q^16 + 12 * q^19 - 8 * q^21 - 12 * q^22 + 24 * q^23 + 14 * q^25 + 24 * q^26 + 28 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 + 4 * q^31 - 4 * q^34 - 10 * q^35 + 14 * q^36 - 24 * q^37 - 6 * q^38 + 2 * q^39 - 2 * q^40 + 4 * q^41 - 8 * q^42 - 14 * q^43 + 6 * q^45 - 12 * q^46 - 14 * q^48 - 24 * q^49 + 4 * q^52 + 24 * q^53 + 18 * q^55 - 4 * q^56 + 12 * q^57 - 2 * q^58 + 44 * q^59 - 12 * q^62 - 8 * q^63 - 28 * q^64 - 24 * q^65 - 12 * q^66 - 18 * q^67 + 6 * q^68 + 24 * q^69 + 6 * q^70 - 6 * q^71 + 12 * q^74 + 14 * q^75 + 40 * q^77 + 24 * q^78 - 24 * q^79 - 6 * q^80 + 28 * q^81 + 2 * q^84 + 28 * q^85 + 18 * q^87 - 12 * q^88 + 16 * q^89 + 2 * q^90 - 20 * q^91 + 12 * q^92 + 4 * q^93 - 18 * q^94 + 26 * q^95 - 40 * q^97 + 28 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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