LMFDB - Embedded newform 798.2.bc.b.31.8

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)

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")

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);

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			31.8
Character	$\chi$	$=$	798.31
Dual form			798.2.bc.b.103.8

$q$-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 $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

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

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	−0.288985	−	0.957334i	$-0.593318\pi$
$5$	−2.82315	−	1.62995i	−1.26255	−	0.728935i	−0.973568	+	0.228398i	$0.926651\pi$
$6$	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	0.0883666	+	0.996088i	$0.471835\pi$
$11$	−2.71451	+	4.70166i	−0.818454	+	1.41760i	−0.906821	+	0.421516i	$0.861498\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	0.714142	−	1.23693i	0.198067	−	0.343063i	−0.749834	−	0.661626i	$-0.769867\pi$
$13$	0.714142	−	1.23693i	0.198067	−	0.343063i	0.947902	+	0.318563i	$0.103200\pi$
$14$	−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	$0.409579\pi$
$17$			7.91573i			1.91985i	−0.280261	+	0.959924i	$0.590421\pi$
$18$	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	0.501320	−	0.865262i	$-0.332848\pi$
$29$	0.0142282	+	0.00821465i	0.00264211	+	0.00152542i	−0.498678	+	0.866787i	$0.666181\pi$
$30$	−1.62995	−	2.82315i	−0.297587	−	0.515435i
$31$	3.26114	−	5.64846i	0.585718	−	1.01449i	−0.409068	−	0.912504i	$-0.634146\pi$
$31$	3.26114	−	5.64846i	0.585718	−	1.01449i	0.994786	−	0.101989i	$-0.0325207\pi$
$32$	−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	−0.958952	−	0.283570i	$-0.908481\pi$
$37$	−7.25582	+	4.18915i	−1.19285	+	0.688692i	−0.233897	+	0.972261i	$0.575148\pi$
$38$	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	0.945893	+	0.324478i	$0.105188\pi$
$41$	4.82765	+	8.36174i	0.753953	+	1.30588i	−0.191941	+	0.981406i	$0.561478\pi$
$42$	−2.56068	+	0.665524i	−0.395121	+	0.102693i
$43$	−5.98293	−	10.3627i	−0.912389	−	1.58030i	−0.810680	−	0.585489i	$-0.800902\pi$
$43$	−5.98293	−	10.3627i	−0.912389	−	1.58030i	−0.101709	−	0.994814i	$-0.532431\pi$
$44$	−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	$-0.929802\pi$
$47$		−	2.99936i		−	0.437502i	0.975781	−	0.218751i	$-0.0701982\pi$
$48$	−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	−0.435583	−	0.900149i	$-0.643458\pi$
$53$	0.918586	−	0.530346i	0.126178	−	0.0728486i	0.561760	+	0.827300i	$0.310124\pi$
$54$	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	$0.0790166\pi$
$61$			3.83790i			0.491392i	−0.969347	+	0.245696i	$0.920983\pi$
$62$	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	−0.481073	−	0.876681i	$-0.659753\pi$
$67$	0.307919	−	0.177777i	0.0376182	−	0.0217189i	0.518691	+	0.854962i	$0.326419\pi$
$68$	−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	−0.570378	−	0.821382i	$-0.693203\pi$
$71$	−1.21530	+	0.701655i	−0.144230	+	0.0832711i	0.426149	+	0.904653i	$0.359870\pi$
$72$			1.00000i			0.117851i
$73$		−	9.36694i		−	1.09632i	−0.836374	−	0.548159i	$-0.815329\pi$
$73$		−	9.36694i		−	1.09632i	0.836374	−	0.548159i	$-0.184671\pi$
$74$	−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	0.830212	−	0.557448i	$-0.188219\pi$
$79$	6.77772	+	3.91312i	0.762553	+	0.440260i	−0.0676585	+	0.997709i	$0.521553\pi$
$80$	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	$-0.884317\pi$
$83$		−	6.47715i		−	0.710960i	0.934684	−	0.355480i	$-0.115683\pi$
$84$	−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	0.850401	+	0.526135i	$0.176359\pi$
$97$	8.67534	+	15.0261i	0.880847	+	1.52567i	0.0304458	+	0.999536i	$0.490307\pi$
$98$	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	−0.825114	−	0.564967i	$-0.808889\pi$
$101$	−7.52128	+	4.34241i	−0.748395	+	0.432086i	0.0767187	+	0.997053i	$0.475556\pi$
$102$	−3.95787	+	6.85523i	−0.391887	+	0.678769i
$103$	−4.33300	−	7.50497i	−0.426943	−	0.739487i	0.569657	−	0.821883i	$-0.307076\pi$
$103$	−4.33300	−	7.50497i	−0.426943	−	0.739487i	−0.996600	+	0.0823958i	$0.973743\pi$
$104$	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	−0.696981	−	0.717090i	$-0.745474\pi$
$107$	−4.39058	+	2.53490i	−0.424453	+	0.245058i	0.272528	+	0.962148i	$0.412140\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$			0.410523i			0.0393210i	0.999807	+	0.0196605i	$0.00625853\pi$
$109$			0.410523i			0.0393210i	−0.999807	+	0.0196605i	$0.993741\pi$
$110$	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	$0.0513915\pi$
$113$			3.41761i			0.321501i	−0.986995	+	0.160751i	$0.948609\pi$
$114$	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	0.936028	−	0.351925i	$-0.114473\pi$
$127$	12.3881	+	7.15228i	1.09927	+	0.634662i	0.163239	+	0.986587i	$0.447806\pi$
$128$	−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	0.475631	−	0.879645i	$-0.342220\pi$
$131$	−0.553373	−	0.319490i	−0.0483485	−	0.0279140i	−0.523979	+	0.851731i	$0.675553\pi$
$132$	−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	0.999084	+	0.0427808i	$0.0136217\pi$
$137$	6.28064	+	10.8784i	0.536592	+	0.929404i	−0.462493	+	0.886623i	$0.653045\pi$
$138$	−3.94676	−	2.27866i	−0.335971	−	0.193973i
$139$	7.00918	+	4.04675i	0.594511	+	0.343241i	0.766879	−	0.641791i	$-0.221808\pi$
$139$	7.00918	+	4.04675i	0.594511	+	0.343241i	−0.172368	+	0.985033i	$0.555142\pi$
$140$	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	0.347277	+	0.937763i	$0.387107\pi$
$149$	−7.79374	+	13.4992i	−0.638488	+	1.10589i	−0.985765	+	0.168131i	$0.946227\pi$
$150$			5.62693i			0.459437i
$151$	12.8753	+	7.43354i	1.04777	+	0.604933i	0.922025	−	0.387129i	$-0.126533\pi$
$151$	12.8753	+	7.43354i	1.04777	+	0.604933i	0.125749	+	0.992062i	$0.459867\pi$
$152$	−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	$0.0521526\pi$
$157$			4.08753i			0.326220i	−0.986608	+	0.163110i	$0.947847\pi$
$158$	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	0.998795	−	0.0490708i	$-0.0156260\pi$
$163$	5.83332	+	10.1036i	0.456901	+	0.791376i	−0.541894	+	0.840447i	$0.682293\pi$
$164$	−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	−0.911619	−	0.411037i	$-0.865167\pi$
$167$	−1.29023	+	2.23474i	−0.0998409	+	0.172929i	0.811778	+	0.583966i	$0.198500\pi$
$168$	−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	−0.345896	−	0.938273i	$-0.612425\pi$
$173$	8.41289	−	14.5716i	0.639620	−	1.10785i	0.985516	−	0.169582i	$-0.0542416\pi$
$174$	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	0.161091	−	0.986939i	$-0.448499\pi$
$179$	−8.20242	−	4.73567i	−0.613078	−	0.353960i	−0.774169	+	0.632979i	$0.781832\pi$
$180$		−	3.25990i		−	0.242978i
$181$	−9.09772	+	15.7577i	−0.676228	+	1.17126i	0.299880	+	0.953977i	$0.403053\pi$
$181$	−9.09772	+	15.7577i	−0.676228	+	1.17126i	−0.976108	+	0.217285i	$0.930280\pi$
$182$	−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	0.626437	−	0.779472i	$-0.284512\pi$
$191$	−5.00050	−	8.66112i	−0.361824	−	0.626697i	−0.988261	+	0.152775i	$0.951179\pi$
$192$	−1.00000			−0.0721688
$193$			6.60829i			0.475675i	0.971305	+	0.237837i	$0.0764386\pi$
$193$			6.60829i			0.475675i	−0.971305	+	0.237837i	$0.923561\pi$
$194$			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	−0.199325	−	0.979933i	$-0.563875\pi$
$199$	7.75390	−	4.47672i	0.549659	−	0.317346i	0.748985	+	0.662587i	$0.230542\pi$
$200$	−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	−0.119847	−	0.992792i	$-0.538241\pi$
$211$	9.87775	−	5.70292i	0.680012	−	0.392605i	0.799860	+	0.600187i	$0.204907\pi$
$212$	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	0.940351	−	0.340206i	$-0.110497\pi$
$223$	2.62150	+	4.54057i	0.175549	+	0.304059i	−0.764802	+	0.644265i	$0.777163\pi$
$224$	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	0.168292	−	0.985737i	$-0.446175\pi$
$227$	14.1297	−	24.4733i	0.937819	−	1.62435i	0.769528	−	0.638613i	$-0.220492\pi$
$228$	−0.470556	+	4.33343i	−0.0311633	+	0.286988i
$229$	19.7790	−	11.4194i	1.30703	−	0.754615i	0.325432	−	0.945566i	$-0.394490\pi$
$229$	19.7790	−	11.4194i	1.30703	−	0.754615i	0.981600	+	0.190951i	$0.0611571\pi$
$230$	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	−0.852244	−	0.523144i	$-0.824759\pi$
$233$	0.411130	−	0.712098i	0.0269340	−	0.0466511i	0.879178	+	0.476493i	$0.158092\pi$
$234$	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	0.556523	−	0.830832i	$-0.312135\pi$
$241$	−6.85020	−	11.8649i	−0.441260	−	0.764285i	−0.997783	+	0.0665470i	$0.978802\pi$
$242$		−	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	0.0957582	−	0.995405i	$-0.469472\pi$
$251$	−11.3817	−	6.57124i	−0.718408	−	0.414773i	−0.814167	+	0.580631i	$0.802806\pi$
$252$	−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	0.973806	−	0.227382i	$-0.0730167\pi$
$271$	20.8046	+	12.0115i	1.26379	+	0.729649i	0.289984	+	0.957032i	$0.406350\pi$
$272$	−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	−0.579130	−	0.815235i	$-0.696608\pi$
$277$	6.93109	−	12.0050i	0.416449	−	0.721311i	0.995579	+	0.0939242i	$0.0299411\pi$
$278$	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	0.977843	+	0.209337i	$0.0671307\pi$
$281$	27.6265	+	15.9501i	1.64806	+	0.951506i	0.670213	+	0.742169i	$0.266203\pi$
$282$	1.49968	−	2.59752i	0.0893047	−	0.154680i
$283$		−	17.3517i		−	1.03145i	−0.856753	−	0.515727i	$-0.827522\pi$
$283$		−	17.3517i		−	1.03145i	0.856753	−	0.515727i	$-0.172478\pi$
$284$	−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	0.866320	−	0.499490i	$-0.166479\pi$
$307$	0.0103240	+	0.0178817i	0.000589223	+	0.00102056i	−0.865731	+	0.500510i	$0.833146\pi$
$308$	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	0.769734	−	0.638365i	$-0.220389\pi$
$311$	10.6122	+	6.12693i	0.601760	+	0.347427i	−0.167973	+	0.985792i	$0.553722\pi$
$312$	1.23693	+	0.714142i	0.0700274	+	0.0404303i
$313$			31.7873i			1.79673i	0.439254	+	0.898363i	$0.355243\pi$
$313$			31.7873i			1.79673i	−0.439254	+	0.898363i	$0.644757\pi$
$314$	−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	$0.168948\pi$
$317$			18.0250i			1.01239i	−0.862420	+	0.506193i	$0.831052\pi$
$318$	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	−0.814905	−	0.579595i	$-0.803211\pi$
$331$	−13.1068	+	7.56719i	−0.720413	+	0.415930i	0.0944919	+	0.995526i	$0.469877\pi$
$332$	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	−0.912551	−	0.408962i	$-0.865891\pi$
$337$	−18.6266	+	10.7541i	−1.01466	+	0.585812i	−0.102104	+	0.994774i	$0.532557\pi$
$338$			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	$-0.930880\pi$
$349$		−	8.04972i		−	0.430892i	0.976516	−	0.215446i	$-0.0691205\pi$
$350$	−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	0.977761	−	0.209724i	$-0.0672566\pi$
$353$	24.1432	+	13.9391i	1.28501	+	0.741903i	0.307254	+	0.951628i	$0.400590\pi$
$354$	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	−0.0843856	−	0.996433i	$-0.526893\pi$
$359$	15.5509	−	26.9349i	0.820744	−	1.42157i	0.905129	−	0.425137i	$-0.139774\pi$
$360$	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	−0.976176	−	0.216982i	$-0.930379\pi$
$367$	−24.4514	+	14.1170i	−1.27635	+	0.736902i	−0.300176	+	0.953884i	$0.597045\pi$
$368$	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	−0.441923	−	0.897053i	$-0.645703\pi$
$373$	2.20146	−	1.27101i	0.113987	−	0.0658105i	0.555910	+	0.831243i	$0.312370\pi$
$374$	−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	$-0.994763\pi$
$379$		−	0.640519i		−	0.0329013i	0.999865	−	0.0164506i	$-0.00523664\pi$
$380$	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	−0.322872	−	0.946443i	$-0.604648\pi$
$383$	12.8814	−	22.3112i	0.658207	−	1.14005i	0.981079	−	0.193606i	$-0.0620182\pi$
$384$	−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	−0.977579	−	0.210570i	$-0.932468\pi$
$389$	−13.2371	−	22.9273i	−0.671148	−	1.16246i	0.306431	−	0.951893i	$-0.400865\pi$
$390$	−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	−0.330904	−	0.943664i	$-0.607354\pi$
$397$	−26.1732	−	15.1111i	−1.31359	−	0.758403i	−0.982689	+	0.185261i	$0.940687\pi$
$398$	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	0.389488	−	0.921032i	$-0.372652\pi$
$401$	−4.27344	−	2.46727i	−0.213405	−	0.123210i	−0.602893	+	0.797822i	$0.705985\pi$
$402$	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	0.998441	+	0.0558258i	$0.0177792\pi$
$409$	11.0739	+	19.1805i	0.547567	+	0.948414i	−0.450874	+	0.892588i	$0.648888\pi$
$410$	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	$-0.958352\pi$
$419$		−	5.34125i		−	0.260937i	0.991452	−	0.130469i	$-0.0416482\pi$
$420$	6.05265	+	6.14442i	0.295339	+	0.299817i
$421$	−13.7757	+	7.95341i	−0.671387	+	0.387625i	−0.796602	−	0.604504i	$-0.793371\pi$
$421$	−13.7757	+	7.95341i	−0.671387	+	0.387625i	0.125215	+	0.992130i	$0.460038\pi$
$422$	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	−0.838630	−	0.544701i	$-0.816643\pi$
$431$	−16.3224	+	9.42372i	−0.786220	+	0.453924i	0.0524101	+	0.998626i	$0.483310\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	3.24657	−	5.62323i	0.156020	−	0.270235i	−0.777410	−	0.628995i	$-0.783467\pi$
$433$	3.24657	−	5.62323i	0.156020	−	0.270235i	0.933430	+	0.358759i	$0.116800\pi$
$434$	−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	0.414746	+	0.909937i	$0.363870\pi$
$439$	−12.1661	+	21.0723i	−0.580655	+	1.00572i	−0.995402	+	0.0957877i	$0.969463\pi$
$440$	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	$-0.809036\pi$
$449$		−	23.9267i		−	1.12917i	0.825374	−	0.564586i	$-0.190964\pi$
$450$			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	−0.982987	−	0.183677i	$-0.941200\pi$
$457$	−13.9074	−	24.0884i	−0.650562	−	1.12681i	0.332424	−	0.943130i	$-0.392133\pi$
$458$	22.8388			1.06719
$459$			7.91573i			0.369475i
$460$			14.8564i			0.692684i
$461$	−4.08758	+	2.35997i	−0.190378	+	0.109915i	−0.592159	−	0.805821i	$-0.701724\pi$
$461$	−4.08758	+	2.35997i	−0.190378	+	0.109915i	0.401782	+	0.915736i	$0.368391\pi$
$462$	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	−0.673852	−	0.738866i	$-0.735361\pi$
$467$	−8.01523	+	4.62760i	−0.370901	+	0.214140i	0.302951	+	0.953006i	$0.402028\pi$
$468$	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	−0.861881	−	0.507110i	$-0.830714\pi$
$479$	−18.6831	+	10.7867i	−0.853651	+	0.492856i	0.00822987	+	0.999966i	$0.497380\pi$
$480$	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	0.0927001	−	0.995694i	$-0.470450\pi$
$487$	−15.9607	−	9.21489i	−0.723246	−	0.417566i	−0.815946	+	0.578128i	$0.803784\pi$
$488$	−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	0.856576	−	0.516022i	$-0.172588\pi$
$491$	−0.412147	−	0.713859i	−0.0185999	−	0.0322160i	−0.875176	+	0.483806i	$0.839254\pi$
$492$	−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	0.445916	+	0.895075i	$0.352878\pi$
$499$	−12.3352	+	21.3652i	−0.552200	+	0.956438i	−0.998115	+	0.0613633i	$0.980455\pi$
$500$	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	0.843557	−	0.537039i	$-0.180457\pi$
$503$	17.9477	+	10.3621i	0.800247	+	0.462023i	−0.0433106	+	0.999062i	$0.513791\pi$
$504$	−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	−0.849265	−	0.527967i	$-0.822954\pi$
$521$	0.744122	−	1.28886i	0.0326006	−	0.0564659i	0.881865	+	0.471501i	$0.156288\pi$
$522$	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	0.725242	−	0.688494i	$-0.241728\pi$
$547$	11.4978	+	6.63826i	0.491610	+	0.283831i	−0.233632	+	0.972325i	$0.575061\pi$
$548$	−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	0.819206	−	0.573499i	$-0.194414\pi$
$557$	−2.05473	−	3.55890i	−0.0870618	−	0.150795i	−0.906268	+	0.422704i	$0.861081\pi$
$558$	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	0.0503688	−	0.998731i	$-0.483960\pi$
$563$	21.1202	−	36.5813i	0.890111	−	1.54172i	0.839742	−	0.542986i	$-0.182706\pi$
$564$	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	−0.661684	+	0.749783i	$0.730158\pi$
$569$	−39.1644	+	22.6116i	−1.64186	+	0.947926i	−0.980173	+	0.198143i	$0.936509\pi$
$570$	1.53396	−	14.1265i	0.0642507	−	0.591695i
$571$	6.52676	−	11.3047i	0.273137	−	0.473086i	−0.696527	−	0.717531i	$-0.745272\pi$
$571$	6.52676	−	11.3047i	0.273137	−	0.473086i	0.969663	+	0.244444i	$0.0786056\pi$
$572$	−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	0.441116	−	0.897450i	$-0.354583\pi$
$577$	−2.77536	−	1.60236i	−0.115540	−	0.0667070i	−0.556656	+	0.830743i	$0.687916\pi$
$578$	−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	−0.989188	−	0.146651i	$-0.953151\pi$
$587$	−32.8722	+	18.9788i	−1.35678	+	0.783337i	−0.367591	+	0.929988i	$0.619817\pi$
$588$	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	$-0.775976\pi$
$593$		−	31.5165i		−	1.29423i	0.762393	−	0.647114i	$-0.224024\pi$
$594$	−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	0.0544807	−	0.998515i	$-0.482650\pi$
$599$	23.1641	−	13.3738i	0.946460	−	0.546439i	0.891980	+	0.452076i	$0.149316\pi$
$600$	−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	0.874873	+	0.484353i	$0.160945\pi$
$607$	21.1117	+	36.5666i	0.856898	+	1.48419i	−0.0179749	+	0.999838i	$0.505722\pi$
$608$	−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	−0.774168	−	0.632980i	$-0.781831\pi$
$617$	4.00146	−	6.93074i	0.161093	−	0.279021i	0.935261	+	0.353959i	$0.115165\pi$
$618$		−	8.66600i		−	0.348598i
$619$	5.85957	+	3.38302i	0.235516	+	0.135975i	0.613114	−	0.789994i	$-0.289917\pi$
$619$	5.85957	+	3.38302i	0.235516	+	0.135975i	−0.377598	+	0.925970i	$0.623250\pi$
$620$	−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	−0.265808	−	0.964026i	$-0.585639\pi$
$631$	17.6332	−	30.5416i	0.701967	−	1.21584i	0.967775	−	0.251817i	$-0.0810279\pi$
$632$	−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	$0.104739\pi$
$641$			16.3625i			0.646281i	−0.946351	+	0.323141i	$0.895261\pi$
$642$	−5.06980			−0.200089
$643$	15.4748	−	8.93438i	0.610266	−	0.352337i	−0.162803	−	0.986659i	$-0.552054\pi$
$643$	15.4748	−	8.93438i	0.610266	−	0.352337i	0.773070	+	0.634321i	$0.218720\pi$
$644$	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	0.138079	−	0.990421i	$-0.455907\pi$
$647$	−16.5491	−	9.55462i	−0.650612	−	0.375631i	−0.788691	+	0.614790i	$0.789241\pi$
$648$			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	0.967566	+	0.252619i	$0.0812920\pi$
$653$	17.9531	+	31.0956i	0.702558	+	1.21687i	−0.265008	+	0.964246i	$0.585375\pi$
$654$	−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	0.974370	+	0.224950i	$0.0722220\pi$
$659$	42.5206	+	24.5493i	1.65637	+	0.956305i	0.681998	+	0.731354i	$0.261111\pi$
$660$	15.3269	+	8.84901i	0.596600	+	0.344447i
$661$	4.89940	+	8.48600i	0.190564	+	0.330067i	0.945437	−	0.325804i	$-0.105635\pi$
$661$	4.89940	+	8.48600i	0.190564	+	0.330067i	−0.754873	+	0.655871i	$0.772302\pi$
$662$	−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	$-0.884648\pi$
$673$		−	18.3935i		−	0.709017i	0.935053	−	0.354508i	$-0.115352\pi$
$674$	−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	−0.775868	−	0.630895i	$-0.782688\pi$
$677$	−24.3099	−	42.1060i	−0.934305	−	1.61826i	−0.158437	−	0.987369i	$-0.550646\pi$
$678$	−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	0.994909	−	0.100777i	$-0.0321329\pi$
$683$	36.7209	+	21.2008i	1.40509	+	0.811228i	0.410179	+	0.912005i	$0.365466\pi$
$684$	−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	−0.121334	−	0.992612i	$-0.538717\pi$
$691$	17.8127	−	10.2841i	0.677626	−	0.391227i	0.798960	+	0.601384i	$0.205384\pi$
$692$	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	0.803729	−	0.594995i	$-0.202846\pi$
$701$	−3.00286	−	5.20110i	−0.113416	−	0.196443i	−0.917146	+	0.398552i	$0.869513\pi$
$702$	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	−0.190879	−	0.981614i	$-0.561134\pi$
$719$	−30.4722	−	17.5931i	−1.13642	−	0.656113i	−0.945542	+	0.325501i	$0.894467\pi$
$720$	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	−0.433696	−	0.901059i	$-0.642791\pi$
$727$	3.49969	−	2.02055i	0.129796	−	0.0749379i	0.563492	+	0.826121i	$0.309457\pi$
$728$	−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	0.405341	−	0.914166i	$-0.367153\pi$
$733$	37.8955	−	21.8790i	1.39970	−	0.808118i	0.994361	+	0.106047i	$0.0338195\pi$
$734$	−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	−0.941264	−	0.337671i	$-0.890361\pi$
$743$	−30.5144	+	17.6175i	−1.11946	+	0.646323i	−0.178201	+	0.983994i	$0.557028\pi$
$744$	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	$0.201164\pi$
$751$			32.3777i			1.18148i	−0.806862	+	0.590740i	$0.798836\pi$
$752$	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	0.971145	+	0.238488i	$0.0766518\pi$
$757$	19.0424	+	32.9825i	0.692109	+	1.19877i	−0.279036	+	0.960281i	$0.590015\pi$
$758$	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	−0.565158	−	0.824983i	$-0.691185\pi$
$761$	−3.67671	+	2.12275i	−0.133281	+	0.0769497i	0.431877	+	0.901932i	$0.357851\pi$
$762$	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	0.914259	−	0.405130i	$-0.132774\pi$
$769$	28.3003	+	16.3392i	1.02054	+	0.589207i	0.106277	+	0.994337i	$0.466107\pi$
$770$	−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	−0.984959	−	0.172788i	$-0.944722\pi$
$773$	−17.8527	−	30.9218i	−0.642118	−	1.11218i	0.342841	−	0.939394i	$-0.388611\pi$
$774$		−	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	−0.371546	−	0.928415i	$-0.621172\pi$
$787$	17.3443	−	30.0412i	0.618257	−	1.07085i	0.989804	−	0.142439i	$-0.0454944\pi$
$788$	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	−0.775598	−	0.631227i	$-0.782551\pi$
$809$	4.51845	−	7.82618i	0.158860	−	0.275154i	0.934458	+	0.356074i	$0.115885\pi$
$810$	−1.62995	−	2.82315i	−0.0572706	−	0.0991955i
$811$	27.2870	−	47.2625i	0.958177	−	1.65961i	0.231252	−	0.972894i	$-0.425718\pi$
$811$	27.2870	−	47.2625i	0.958177	−	1.65961i	0.726925	−	0.686717i	$-0.240949\pi$
$812$	−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	0.721988	−	0.691905i	$-0.243228\pi$
$823$	−6.83386	−	11.8366i	−0.238213	−	0.412597i	−0.960202	+	0.279308i	$0.909895\pi$
$824$	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	0.769771	−	0.638321i	$-0.220371\pi$
$827$	17.3079	+	9.99271i	0.601854	+	0.347481i	−0.167917	+	0.985801i	$0.553704\pi$
$828$	−2.27866	−	3.94676i	−0.0791890	−	0.137159i
$829$	0.850088	−	1.47239i	0.0295248	−	0.0511384i	−0.850885	−	0.525351i	$-0.823934\pi$
$829$	0.850088	−	1.47239i	0.0295248	−	0.0511384i	0.880410	+	0.474213i	$0.157267\pi$
$830$	−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	0.964715	−	0.263297i	$-0.0848100\pi$
$839$	7.36695	+	12.7599i	0.254335	+	0.440522i	−0.710379	+	0.703819i	$0.751477\pi$
$840$	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	−0.556040	+	0.831156i	$0.687680\pi$
$853$	−45.3823	+	26.2015i	−1.55386	+	0.897122i	−0.997822	+	0.0659665i	$0.978987\pi$
$854$	−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	$0.158741\pi$
$859$			28.0357i			0.956566i	−0.878206	+	0.478283i	$0.841259\pi$
$860$	−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	−0.453627	−	0.891192i	$-0.649870\pi$
$863$	2.68371	−	1.54944i	0.0913545	−	0.0527436i	0.544981	+	0.838448i	$0.316537\pi$
$864$	−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	0.0547148	−	0.998502i	$-0.482575\pi$
$877$	−23.1777	−	13.3817i	−0.782656	−	0.451867i	−0.837371	+	0.546635i	$0.815908\pi$
$878$	−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	$0.116773\pi$
$881$			21.2925i			0.717362i	−0.933460	+	0.358681i	$0.883227\pi$
$882$	3.59082	−	6.00883i	0.120909	−	0.202328i
$883$	8.65145	−	14.9847i	0.291144	−	0.504277i	−0.682936	−	0.730478i	$-0.739297\pi$
$883$	8.65145	−	14.9847i	0.291144	−	0.504277i	0.974081	+	0.226201i	$0.0726307\pi$
$884$			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	$-0.786909\pi$
$907$		−	37.3776i		−	1.24110i	0.784165	−	0.620552i	$-0.213091\pi$
$908$	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	$0.206016\pi$
$911$			36.3987i			1.20594i	−0.797763	+	0.602971i	$0.793984\pi$
$912$	−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	0.764843	−	0.644217i	$-0.222817\pi$
$919$	−5.31989	−	9.21432i	−0.175487	−	0.303952i	−0.940330	+	0.340265i	$0.889483\pi$
$920$	−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	0.832493	−	0.554035i	$-0.186913\pi$
$929$	23.4366	+	13.5312i	0.768931	+	0.443943i	−0.0635619	+	0.997978i	$0.520246\pi$
$930$	−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	0.532243	−	0.846592i	$-0.321349\pi$
$937$	1.99565	+	1.15219i	0.0651949	+	0.0376403i	−0.467048	+	0.884232i	$0.654683\pi$
$938$	−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	0.791467	−	0.611211i	$-0.209318\pi$
$941$	−4.09800	−	7.09795i	−0.133591	−	0.231386i	−0.925058	+	0.379825i	$0.875984\pi$
$942$	−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	−0.867087	−	0.498157i	$-0.834010\pi$
$947$	−0.0654400	+	0.113345i	−0.00212651	+	0.00368323i	0.864960	+	0.501840i	$0.167344\pi$
$948$			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	−0.504371	−	0.863487i	$-0.668276\pi$
$953$	−0.270295	+	0.156055i	−0.00875572	+	0.00505511i	0.495616	+	0.868542i	$0.334942\pi$
$954$	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	0.964148	−	0.265363i	$-0.0854919\pi$
$967$	7.84452	+	13.5871i	0.252263	+	0.436932i	−0.711886	+	0.702295i	$0.752159\pi$
$968$	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	−0.509967	−	0.860194i	$-0.670342\pi$
$971$	15.2678	−	26.4446i	0.489967	−	0.848647i	0.999933	+	0.0115470i	$0.00367560\pi$
$972$	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	0.244712	−	0.969596i	$-0.421307\pi$
$977$	−14.7729	−	8.52914i	−0.472627	−	0.272871i	−0.717339	+	0.696725i	$0.754640\pi$
$978$			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	$-0.902129\pi$
$991$		−	19.0549i		−	0.605298i	0.953102	−	0.302649i	$-0.0978710\pi$
$992$			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	−0.993229	−	0.116174i	$-0.962937\pi$
$997$	−43.8655	+	25.3257i	−1.38923	+	0.802074i	−0.396005	+	0.918249i	$0.629604\pi$
$998$	−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.31.8	yes	28
7.5	odd	6		798.2.m.b.145.1	✓	28
19.8	odd	6		798.2.m.b.787.14	yes	28
133.103	even	6	inner	798.2.bc.b.103.8	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.m.b.145.1	✓	28	7.5	odd	6
798.2.m.b.787.14	yes	28	19.8	odd	6
798.2.bc.b.31.8	yes	28	1.1	even	1	trivial
798.2.bc.b.103.8	yes	28	133.103	even	6	inner

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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