LMFDB - Embedded newform 840.2.u.e.629.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(629,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.629"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.u (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [160,0,0,-24,0,0,0,0,-32,0,0,0,0,0,-48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(15)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$160$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			629.19
Character	$\chi$	$=$	840.629
Dual form			840.2.u.e.629.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.25943 - 0.643305i) q^{2} +(1.72207 - 0.185637i) q^{3} +(1.17232 + 1.62039i) q^{4} +(0.799234 + 2.08835i) q^{5} +(-2.28825 - 0.874023i) q^{6} +(-2.00372 - 1.72775i) q^{7} +(-0.434041 - 2.79493i) q^{8} +(2.93108 - 0.639360i) q^{9} +(0.336872 - 3.14428i) q^{10} +2.99129 q^{11} +(2.31962 + 2.57281i) q^{12} +3.88403i q^{13} +(1.41207 + 3.46498i) q^{14} +(1.76402 + 3.44793i) q^{15} +(-1.25135 + 3.79923i) q^{16} -5.87186i q^{17} +(-4.10279 - 1.08035i) q^{18} +0.253401 q^{19} +(-2.44700 + 3.74329i) q^{20} +(-3.77129 - 2.60334i) q^{21} +(-3.76732 - 1.92431i) q^{22} +7.37014 q^{23} +(-1.26629 - 4.73249i) q^{24} +(-3.72245 + 3.33817i) q^{25} +(2.49862 - 4.89166i) q^{26} +(4.92884 - 1.64514i) q^{27} +(0.450635 - 5.27228i) q^{28} +3.74592 q^{29} +(-0.00357650 - 5.47722i) q^{30} +2.69635i q^{31} +(4.02004 - 3.97986i) q^{32} +(5.15123 - 0.555294i) q^{33} +(-3.77740 + 7.39519i) q^{34} +(2.00671 - 5.56535i) q^{35} +(4.47217 + 3.99997i) q^{36} -6.74382 q^{37} +(-0.319141 - 0.163014i) q^{38} +(0.721019 + 6.68859i) q^{39} +(5.48989 - 3.14023i) q^{40} -2.03838 q^{41} +(3.07492 + 5.70481i) q^{42} +10.3418 q^{43} +(3.50674 + 4.84707i) q^{44} +(3.67783 + 5.61013i) q^{45} +(-9.28216 - 4.74125i) q^{46} +9.01566i q^{47} +(-1.44963 + 6.77485i) q^{48} +(1.02978 + 6.92384i) q^{49} +(6.83562 - 1.80951i) q^{50} +(-1.09003 - 10.1118i) q^{51} +(-6.29366 + 4.55332i) q^{52} +1.26942i q^{53} +(-7.26585 - 1.09881i) q^{54} +(2.39074 + 6.24688i) q^{55} +(-3.95923 + 6.35016i) q^{56} +(0.436376 - 0.0470406i) q^{57} +(-4.71771 - 2.40977i) q^{58} +4.83995i q^{59} +(-3.51902 + 6.90047i) q^{60} +6.45642 q^{61} +(1.73458 - 3.39586i) q^{62} +(-6.97771 - 3.78306i) q^{63} +(-7.62322 + 2.42623i) q^{64} +(-8.11124 + 3.10425i) q^{65} +(-6.84482 - 2.61446i) q^{66} -1.43931 q^{67} +(9.51472 - 6.88368i) q^{68} +(12.6919 - 1.36817i) q^{69} +(-6.10752 + 5.71823i) q^{70} -7.63417i q^{71} +(-3.05917 - 7.91464i) q^{72} -14.7411 q^{73} +(8.49335 + 4.33833i) q^{74} +(-5.79065 + 6.43960i) q^{75} +(0.297067 + 0.410610i) q^{76} +(-5.99371 - 5.16820i) q^{77} +(3.39473 - 8.88763i) q^{78} -3.41532 q^{79} +(-8.93425 + 0.423218i) q^{80} +(8.18244 - 3.74803i) q^{81} +(2.56719 + 1.31130i) q^{82} +1.78238 q^{83} +(-0.202702 - 9.16291i) q^{84} +(12.2625 - 4.69299i) q^{85} +(-13.0247 - 6.65292i) q^{86} +(6.45074 - 0.695380i) q^{87} +(-1.29835 - 8.36044i) q^{88} +10.9341 q^{89} +(-1.02293 - 9.43152i) q^{90} +(6.71063 - 7.78251i) q^{91} +(8.64014 + 11.9425i) q^{92} +(0.500542 + 4.64332i) q^{93} +(5.79982 - 11.3546i) q^{94} +(0.202527 + 0.529192i) q^{95} +(6.18400 - 7.59987i) q^{96} +10.8736 q^{97} +(3.15721 - 9.38254i) q^{98} +(8.76771 - 1.91251i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 24 q^{4} - 32 q^{9} - 48 q^{15} - 104 q^{16} - 16 q^{25} - 32 q^{30} + 48 q^{36} - 64 q^{39} - 64 q^{46} + 144 q^{49} + 16 q^{60} - 72 q^{64} + 8 q^{70} - 96 q^{79} + 16 q^{81} - 72 q^{84}+O(q^{100}) $ 160 * q - 24 * q^4 - 32 * q^9 - 48 * q^15 - 104 * q^16 - 16 * q^25 - 32 * q^30 + 48 * q^36 - 64 * q^39 - 64 * q^46 + 144 * q^49 + 16 * q^60 - 72 * q^64 + 8 * q^70 - 96 * q^79 + 16 * q^81 - 72 * q^84

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.25943	−	0.643305i	−0.890550	−	0.454885i
$2$	−1.25943	−	0.643305i	−0.890550	−	0.454885i
$3$	1.72207	−	0.185637i	0.994240	−	0.107177i
$3$	1.72207	−	0.185637i	0.994240	−	0.107177i
$4$	1.17232	+	1.62039i	0.586158	+	0.810196i
$5$	0.799234	+	2.08835i	0.357428	+	0.933941i
$5$	0.799234	+	2.08835i	0.357428	+	0.933941i
$6$	−2.28825	−	0.874023i	−0.934174	−	0.356818i
$7$	−2.00372	−	1.72775i	−0.757335	−	0.653027i
$7$	−2.00372	−	1.72775i	−0.757335	−	0.653027i
$8$	−0.434041	−	2.79493i	−0.153457	−	0.988155i
$9$	2.93108	−	0.639360i	0.977026	−	0.213120i
$10$	0.336872	−	3.14428i	0.106528	−	0.994310i
$11$	2.99129			0.901909			0.450954	−	0.892547i	$-0.351084\pi$
$11$	2.99129			0.901909			0.450954	+	0.892547i	$0.351084\pi$
$12$	2.31962	+	2.57281i	0.669617	+	0.742707i
$13$			3.88403i			1.07724i	0.842550	+	0.538618i	$0.181054\pi$
$13$			3.88403i			1.07724i	−0.842550	+	0.538618i	$0.818946\pi$
$14$	1.41207	+	3.46498i	0.377392	+	0.926054i
$15$	1.76402	+	3.44793i	0.455467	+	0.890253i
$16$	−1.25135	+	3.79923i	−0.312837	+	0.949807i
$17$		−	5.87186i		−	1.42414i	−0.702111	−	0.712068i	$-0.747759\pi$
$17$		−	5.87186i		−	1.42414i	0.702111	−	0.712068i	$-0.252241\pi$
$18$	−4.10279	−	1.08035i	−0.967036	−	0.254641i
$19$	0.253401			0.0581343			0.0290671	−	0.999577i	$-0.490746\pi$
$19$	0.253401			0.0581343			0.0290671	+	0.999577i	$0.490746\pi$
$20$	−2.44700	+	3.74329i	−0.547166	+	0.837024i
$21$	−3.77129	−	2.60334i	−0.822962	−	0.568096i
$22$	−3.76732	−	1.92431i	−0.803195	−	0.410265i
$23$	7.37014			1.53678			0.768390	−	0.639982i	$-0.221058\pi$
$23$	7.37014			1.53678			0.768390	+	0.639982i	$0.221058\pi$
$24$	−1.26629	−	4.73249i	−0.258481	−	0.966016i
$25$	−3.72245	+	3.33817i	−0.744490	+	0.667634i
$26$	2.49862	−	4.89166i	0.490019	−	0.959333i
$27$	4.92884	−	1.64514i	0.948557	−	0.316608i
$28$	0.450635	−	5.27228i	0.0851620	−	0.996367i
$29$	3.74592			0.695599			0.347800	−	0.937569i	$-0.386929\pi$
$29$	3.74592			0.695599			0.347800	+	0.937569i	$0.386929\pi$
$30$	−0.00357650	−	5.47722i	−0.000652976	−	1.00000i
$31$			2.69635i			0.484280i	0.970241	+	0.242140i	$0.0778493\pi$
$31$			2.69635i			0.484280i	−0.970241	+	0.242140i	$0.922151\pi$
$32$	4.02004	−	3.97986i	0.710650	−	0.703546i
$33$	5.15123	−	0.555294i	0.896714	−	0.0966643i
$34$	−3.77740	+	7.39519i	−0.647819	+	1.26826i
$35$	2.00671	−	5.56535i	0.339196	−	0.940716i
$36$	4.47217	+	3.99997i	0.745361	+	0.666661i
$37$	−6.74382			−1.10868			−0.554338	−	0.832291i	$-0.687029\pi$
$37$	−6.74382			−1.10868			−0.554338	+	0.832291i	$0.687029\pi$
$38$	−0.319141	−	0.163014i	−0.0517715	−	0.0264444i
$39$	0.721019	+	6.68859i	0.115455	+	1.07103i
$40$	5.48989	−	3.14023i	0.868029	−	0.496514i
$41$	−2.03838			−0.318342			−0.159171	−	0.987251i	$-0.550882\pi$
$41$	−2.03838			−0.318342			−0.159171	+	0.987251i	$0.550882\pi$
$42$	3.07492	+	5.70481i	0.474470	+	0.880272i
$43$	10.3418			1.57711			0.788553	−	0.614967i	$-0.210831\pi$
$43$	10.3418			1.57711			0.788553	+	0.614967i	$0.210831\pi$
$44$	3.50674	+	4.84707i	0.528661	+	0.730723i
$45$	3.67783	+	5.61013i	0.548258	+	0.836309i
$46$	−9.28216	−	4.74125i	−1.36858	−	0.699059i
$47$			9.01566i			1.31507i	0.753425	+	0.657534i	$0.228400\pi$
$47$			9.01566i			1.31507i	−0.753425	+	0.657534i	$0.771600\pi$
$48$	−1.44963	+	6.77485i	−0.209237	+	0.977865i
$49$	1.02978	+	6.92384i	0.147112	+	0.989120i
$50$	6.83562	−	1.80951i	0.966702	−	0.255903i
$51$	−1.09003	−	10.1118i	−0.152635	−	1.41593i
$52$	−6.29366	+	4.55332i	−0.872773	+	0.631431i
$53$			1.26942i			0.174369i	0.996192	+	0.0871844i	$0.0277869\pi$
$53$			1.26942i			0.174369i	−0.996192	+	0.0871844i	$0.972213\pi$
$54$	−7.26585	−	1.09881i	−0.988757	−	0.149530i
$55$	2.39074	+	6.24688i	0.322368	+	0.842329i
$56$	−3.95923	+	6.35016i	−0.529074	+	0.848576i
$57$	0.436376	−	0.0470406i	0.0577994	−	0.00623068i
$58$	−4.71771	−	2.40977i	−0.619466	−	0.316418i
$59$			4.83995i			0.630108i	0.949074	+	0.315054i	$0.102023\pi$
$59$			4.83995i			0.630108i	−0.949074	+	0.315054i	$0.897977\pi$
$60$	−3.51902	+	6.90047i	−0.454304	+	0.890847i
$61$	6.45642			0.826660			0.413330	−	0.910581i	$-0.364366\pi$
$61$	6.45642			0.826660			0.413330	+	0.910581i	$0.364366\pi$
$62$	1.73458	−	3.39586i	0.220292	−	0.431275i
$63$	−6.97771	−	3.78306i	−0.879109	−	0.476621i
$64$	−7.62322	+	2.42623i	−0.952902	+	0.303278i
$65$	−8.11124	+	3.10425i	−1.00608	+	0.385035i
$66$	−6.84482	−	2.61446i	−0.842540	−	0.321818i
$67$	−1.43931			−0.175840			−0.0879199	−	0.996128i	$-0.528022\pi$
$67$	−1.43931			−0.175840			−0.0879199	+	0.996128i	$0.528022\pi$
$68$	9.51472	−	6.88368i	1.15383	−	0.834769i
$69$	12.6919	−	1.36817i	1.52793	−	0.164708i
$70$	−6.10752	+	5.71823i	−0.729989	+	0.683459i
$71$		−	7.63417i		−	0.906009i	−0.891508	−	0.453005i	$-0.850352\pi$
$71$		−	7.63417i		−	0.906009i	0.891508	−	0.453005i	$-0.149648\pi$
$72$	−3.05917	−	7.91464i	−0.360527	−	0.932749i
$73$	−14.7411			−1.72531			−0.862657	−	0.505790i	$-0.831201\pi$
$73$	−14.7411			−1.72531			−0.862657	+	0.505790i	$0.831201\pi$
$74$	8.49335	+	4.33833i	0.987332	+	0.504321i
$75$	−5.79065	+	6.43960i	−0.668646	+	0.743581i
$76$	0.297067	+	0.410610i	0.0340759	+	0.0471002i
$77$	−5.99371	−	5.16820i	−0.683047	−	0.588971i
$78$	3.39473	−	8.88763i	0.384378	−	1.00633i
$79$	−3.41532			−0.384254			−0.192127	−	0.981370i	$-0.561539\pi$
$79$	−3.41532			−0.384254			−0.192127	+	0.981370i	$0.561539\pi$
$80$	−8.93425	+	0.423218i	−0.998880	+	0.0473172i
$81$	8.18244	−	3.74803i	0.909160	−	0.416448i
$82$	2.56719	+	1.31130i	0.283499	+	0.144809i
$83$	1.78238			0.195641			0.0978207	−	0.995204i	$-0.468813\pi$
$83$	1.78238			0.195641			0.0978207	+	0.995204i	$0.468813\pi$
$84$	−0.202702	−	9.16291i	−0.0221165	−	0.999755i
$85$	12.2625	−	4.69299i	1.33006	−	0.509027i
$86$	−13.0247	−	6.65292i	−1.40449	−	0.717402i
$87$	6.45074	−	0.695380i	0.691592	−	0.0745525i
$88$	−1.29835	−	8.36044i	−0.138404	−	0.891226i
$89$	10.9341			1.15902			0.579508	−	0.814966i	$-0.303245\pi$
$89$	10.9341			1.15902			0.579508	+	0.814966i	$0.303245\pi$
$90$	−1.02293	−	9.43152i	−0.107827	−	0.994170i
$91$	6.71063	−	7.78251i	0.703465	−	0.815829i
$92$	8.64014	+	11.9425i	0.900797	+	1.24509i
$93$	0.500542	+	4.64332i	0.0519038	+	0.481490i
$94$	5.79982	−	11.3546i	0.598206	−	1.17113i
$95$	0.202527	+	0.529192i	0.0207788	+	0.0542939i
$96$	6.18400	−	7.59987i	0.631152	−	0.775659i
$97$	10.8736			1.10405			0.552024	−	0.833828i	$-0.313856\pi$
$97$	10.8736			1.10405			0.552024	+	0.833828i	$0.313856\pi$
$98$	3.15721	−	9.38254i	0.318926	−	0.947780i
$99$	8.76771	−	1.91251i	0.881188	−	0.192215i
$100$	−9.77303	−	2.11844i	−0.977303	−	0.211844i
$101$		−	4.39714i		−	0.437531i	−0.975777	−	0.218766i	$-0.929797\pi$
$101$		−	4.39714i		−	0.437531i	0.975777	−	0.218766i	$-0.0702030\pi$
$102$	−5.13214	+	13.4363i	−0.508158	+	1.33039i
$103$	−9.07933			−0.894613			−0.447307	−	0.894381i	$-0.647617\pi$
$103$	−9.07933			−0.894613			−0.447307	+	0.894381i	$0.647617\pi$
$104$	10.8556	−	1.68583i	1.06448	−	0.165309i
$105$	2.42257	−	9.95646i	0.236418	−	0.971651i
$106$	0.816627	−	1.59875i	0.0793178	−	0.155284i
$107$		−	13.9960i		−	1.35304i	−0.736423	−	0.676521i	$-0.763487\pi$
$107$		−	13.9960i		−	1.35304i	0.736423	−	0.676521i	$-0.236513\pi$
$108$	8.44394	+	6.05804i	0.812519	+	0.582935i
$109$		−	11.7924i		−	1.12950i	−0.825261	−	0.564752i	$-0.808972\pi$
$109$		−	11.7924i		−	1.12950i	0.825261	−	0.564752i	$-0.191028\pi$
$110$	1.00768	−	9.40547i	0.0960787	−	0.896777i
$111$	−11.6134	+	1.25190i	−1.10229	+	0.118825i
$112$	9.07145	−	5.45058i	0.857172	−	0.515031i
$113$	−8.64843			−0.813576			−0.406788	−	0.913523i	$-0.633351\pi$
$113$	−8.64843			−0.813576			−0.406788	+	0.913523i	$0.633351\pi$
$114$	−0.579845	−	0.221479i	−0.0543075	−	0.0207434i
$115$	5.89047	+	15.3915i	0.549289	+	1.43526i
$116$	4.39140	+	6.06986i	0.407731	+	0.563572i
$117$	2.48330	+	11.3844i	0.229581	+	1.05249i
$118$	3.11357	−	6.09557i	0.286627	−	0.561143i
$119$	−10.1451	+	11.7656i	−0.929999	+	1.07855i
$120$	8.87106	−	6.42684i	0.809814	−	0.586687i
$121$	−2.05216			−0.186560
$122$	−8.13140	−	4.15345i	−0.736182	−	0.376036i
$123$	−3.51024	+	0.378399i	−0.316508	+	0.0341190i
$124$	−4.36915	+	3.16098i	−0.392362	+	0.283865i
$125$	−9.94639	−	5.10582i	−0.889632	−	0.456678i
$126$	6.35426	+	9.25329i	0.566082	+	0.824349i
$127$			1.83482i			0.162814i	0.996681	+	0.0814068i	$0.0259413\pi$
$127$			1.83482i			0.162814i	−0.996681	+	0.0814068i	$0.974059\pi$
$128$	11.1617	+	1.84840i	0.986564	+	0.163377i
$129$	17.8093	−	1.91981i	1.56802	−	0.169030i
$130$	12.2125	+	1.30842i	1.07111	+	0.114756i
$131$		−	7.74727i		−	0.676882i	−0.940988	−	0.338441i	$-0.890100\pi$
$131$		−	7.74727i		−	0.676882i	0.940988	−	0.338441i	$-0.109900\pi$
$132$	6.93867	+	7.69603i	0.603933	+	0.669854i
$133$	−0.507745	−	0.437813i	−0.0440271	−	0.0379632i
$134$	1.81271	+	0.925917i	0.156594	+	0.0799870i
$135$	7.37494	+	8.97832i	0.634734	+	0.772731i
$136$	−16.4114	+	2.54863i	−1.40727	+	0.218543i
$137$	−12.5120			−1.06897			−0.534485	−	0.845178i	$-0.679494\pi$
$137$	−12.5120			−1.06897			−0.534485	+	0.845178i	$0.679494\pi$
$138$	−16.8647	−	6.44167i	−1.43562	−	0.548352i
$139$	−3.43413			−0.291279			−0.145640	−	0.989338i	$-0.546524\pi$
$139$	−3.43413			−0.291279			−0.145640	+	0.989338i	$0.546524\pi$
$140$	11.3706	−	3.27270i	0.960987	−	0.276594i
$141$	1.67364	+	15.5256i	0.140946	+	1.30749i
$142$	−4.91110	+	9.61468i	−0.412130	+	0.806846i
$143$			11.6183i			0.971569i
$144$	−1.23872	+	11.9359i	−0.103226	+	0.994658i
$145$	2.99386	+	7.82280i	0.248627	+	0.649648i
$146$	18.5653	+	9.48302i	1.53648	+	0.784820i
$147$	3.05868	+	11.7322i	0.252275	+	0.967655i
$148$	−7.90589	−	10.9276i	−0.649860	−	0.898246i
$149$	−12.9889			−1.06409			−0.532047	−	0.846715i	$-0.678577\pi$
$149$	−12.9889			−1.06409			−0.532047	+	0.846715i	$0.678577\pi$
$150$	11.4355	−	4.38505i	0.933707	−	0.358038i
$151$	3.46307			0.281821			0.140911	−	0.990022i	$-0.454997\pi$
$151$	3.46307			0.281821			0.140911	+	0.990022i	$0.454997\pi$
$152$	−0.109987	−	0.708238i	−0.00892110	−	0.0574457i
$153$	−3.75424	−	17.2109i	−0.303512	−	1.39142i
$154$	4.22392	+	10.3648i	0.340373	+	0.835216i
$155$	−5.63095	+	2.15502i	−0.452288	+	0.173095i
$156$	−9.99288	+	9.00948i	−0.800071	+	0.721336i
$157$		−	16.2856i		−	1.29973i	−0.760050	−	0.649864i	$-0.774826\pi$
$157$		−	16.2856i		−	1.29973i	0.760050	−	0.649864i	$-0.225174\pi$
$158$	4.30135	+	2.19709i	0.342197	+	0.174791i
$159$	0.235652	+	2.18604i	0.0186884	+	0.173364i
$160$	11.5243	+	5.21444i	0.911076	+	0.412238i
$161$	−14.7677	−	12.7337i	−1.16386	−	1.00356i
$162$	−12.7163	−	0.543430i	−0.999088	−	0.0426959i
$163$	−9.53016			−0.746459			−0.373230	−	0.927739i	$-0.621750\pi$
$163$	−9.53016			−0.746459			−0.373230	+	0.927739i	$0.621750\pi$
$164$	−2.38963	−	3.30298i	−0.186599	−	0.257919i
$165$	5.27669	+	10.3138i	0.410790	+	0.802927i
$166$	−2.24478	−	1.14661i	−0.174228	−	0.0889944i
$167$			7.92521i			0.613271i	0.951827	+	0.306636i	$0.0992033\pi$
$167$			7.92521i			0.613271i	−0.951827	+	0.306636i	$0.900797\pi$
$168$	−5.63926	+	11.6704i	−0.435078	+	0.900393i
$169$	−2.08571			−0.160439
$170$	−18.4628	−	1.97806i	−1.41603	−	0.151711i
$171$	0.742739	−	0.162015i	0.0567987	−	0.0123896i
$172$	12.1238	+	16.7577i	0.924434	+	1.27777i
$173$	−21.4624			−1.63175			−0.815877	−	0.578225i	$-0.803746\pi$
$173$	−21.4624			−1.63175			−0.815877	+	0.578225i	$0.803746\pi$
$174$	−8.57159	−	3.27402i	−0.649810	−	0.248203i
$175$	13.2263	−	0.257301i	0.999811	−	0.0194501i
$176$	−3.74314	+	11.3646i	−0.282150	+	0.856639i
$177$	0.898473	+	8.33476i	0.0675334	+	0.626479i
$178$	−13.7708	−	7.03399i	−1.03216	−	0.527220i
$179$	15.3694			1.14877			0.574383	−	0.818587i	$-0.305242\pi$
$179$	15.3694			1.14877			0.574383	+	0.818587i	$0.305242\pi$
$180$	−4.77904	+	12.5364i	−0.356208	+	0.934407i
$181$	−1.96261			−0.145880			−0.0729400	−	0.997336i	$-0.523238\pi$
$181$	−1.96261			−0.145880			−0.0729400	+	0.997336i	$0.523238\pi$
$182$	−13.4581	+	5.48453i	−0.997579	+	0.406540i
$183$	11.1184	−	1.19855i	0.821899	−	0.0885993i
$184$	−3.19895	−	20.5990i	−0.235829	−	1.51858i
$185$	−5.38989	−	14.0835i	−0.396272	−	1.03544i
$186$	2.35668	−	6.16993i	0.172800	−	0.452401i
$187$		−	17.5645i		−	1.28444i
$188$	−14.6089	+	10.5692i	−1.06546	+	0.770838i
$189$	−12.7184	−	5.21939i	−0.925128	−	0.379655i
$190$	0.0853637	−	0.796766i	0.00619294	−	0.0578035i
$191$		−	15.9387i		−	1.15328i	−0.816998	−	0.576641i	$-0.804363\pi$
$191$		−	15.9387i		−	1.15328i	0.816998	−	0.576641i	$-0.195637\pi$
$192$	−12.6773	+	5.59329i	−0.914909	+	0.403661i
$193$		−	23.7979i		−	1.71301i	−0.516136	−	0.856507i	$-0.672630\pi$
$193$		−	23.7979i		−	1.71301i	0.516136	−	0.856507i	$-0.327370\pi$
$194$	−13.6945	−	6.99506i	−0.983211	−	0.502216i
$195$	−13.3919	+	6.85149i	−0.959013	+	0.490646i
$196$	−10.0121	+	9.78558i	−0.715151	+	0.698970i
$197$			22.2134i			1.58264i	0.611402	+	0.791320i	$0.290606\pi$
$197$			22.2134i			1.58264i	−0.611402	+	0.791320i	$0.709394\pi$
$198$	−12.2726	−	3.23164i	−0.872178	−	0.229663i
$199$		−	6.08469i		−	0.431332i	−0.976467	−	0.215666i	$-0.930808\pi$
$199$		−	6.08469i		−	0.431332i	0.976467	−	0.215666i	$-0.0691922\pi$
$200$	10.9456	+	8.95507i	0.773973	+	0.633219i
$201$	−2.47860	+	0.267189i	−0.174827	+	0.0188461i
$202$	−2.82870	+	5.53787i	−0.199027	+	0.389644i
$203$	−7.50576	−	6.47200i	−0.526801	−	0.454245i
$204$	15.1072	−	13.6205i	1.05772	−	0.953625i
$205$	−1.62914	−	4.25686i	−0.113784	−	0.297312i
$206$	11.4348	+	5.84078i	0.796698	+	0.406947i
$207$	21.6025	−	4.71218i	1.50147	−	0.327519i
$208$	−14.7563	−	4.86027i	−1.02317	−	0.336999i
$209$	0.757998			0.0524318
$210$	−9.45609	+	10.9810i	−0.652532	+	0.757761i
$211$			18.8683i			1.29895i	0.760385	+	0.649473i	$0.225010\pi$
$211$			18.8683i			1.29895i	−0.760385	+	0.649473i	$0.774990\pi$
$212$	−2.05696	+	1.48817i	−0.141273	+	0.102208i
$213$	−1.41718	−	13.1466i	−0.0971037	−	0.900790i
$214$	−9.00369	+	17.6269i	−0.615479	+	1.20495i
$215$	8.26550	+	21.5973i	0.563702	+	1.47292i
$216$	−6.73737	−	13.0617i	−0.458420	−	0.888736i
$217$	4.65862	−	5.40274i	0.316248	−	0.366762i
$218$	−7.58609	+	14.8516i	−0.513795	+	1.00588i
$219$	−25.3852	+	2.73649i	−1.71538	+	0.184915i
$220$	−7.31969	+	11.1973i	−0.493494	+	0.754920i
$221$	22.8065			1.53413
$222$	15.4315	+	5.89425i	1.03570	+	0.395596i
$223$	−2.13715			−0.143114			−0.0715569	−	0.997437i	$-0.522797\pi$
$223$	−2.13715			−0.143114			−0.0715569	+	0.997437i	$0.522797\pi$
$224$	−14.9312	+	1.02890i	−0.997634	+	0.0687460i
$225$	−8.77650	+	12.1644i	−0.585100	+	0.810961i
$226$	10.8921	+	5.56358i	0.724530	+	0.370084i
$227$	−1.65229			−0.109666			−0.0548332	−	0.998496i	$-0.517463\pi$
$227$	−1.65229			−0.109666			−0.0548332	+	0.998496i	$0.517463\pi$
$228$	0.587795	+	0.651954i	0.0389277	+	0.0431767i
$229$	−23.2456			−1.53611			−0.768057	−	0.640381i	$-0.778776\pi$
$229$	−23.2456			−1.53611			−0.768057	+	0.640381i	$0.778776\pi$
$230$	2.48279	−	23.1738i	0.163710	−	1.52804i
$231$	−11.2810	−	7.78737i	−0.742237	−	0.512371i
$232$	−1.62588	−	10.4696i	−0.106744	−	0.687360i
$233$	−16.4197			−1.07569			−0.537846	−	0.843043i	$-0.680762\pi$
$233$	−16.4197			−1.07569			−0.537846	+	0.843043i	$0.680762\pi$
$234$	4.19611	−	15.9354i	0.274308	−	1.04173i
$235$	−18.8279	+	7.20562i	−1.22820	+	0.470043i
$236$	−7.84263	+	5.67396i	−0.510512	+	0.369343i
$237$	−5.88144	+	0.634009i	−0.382040	+	0.0411833i
$238$	20.3459	−	8.29149i	1.31883	−	0.537457i
$239$			26.3343i			1.70342i	0.524011	+	0.851712i	$0.324435\pi$
$239$			26.3343i			1.70342i	−0.524011	+	0.851712i	$0.675565\pi$
$240$	−15.3069	+	2.38734i	−0.988055	+	0.154102i
$241$			11.7807i			0.758862i	0.925220	+	0.379431i	$0.123880\pi$
$241$			11.7807i			0.758862i	−0.925220	+	0.379431i	$0.876120\pi$
$242$	2.58455	+	1.32017i	0.166141	+	0.0848636i
$243$	13.3950	−	7.97335i	0.859289	−	0.511490i
$244$	7.56898	+	10.4619i	0.484554	+	0.669757i
$245$	−13.6364	+	7.68432i	−0.871197	+	0.490933i
$246$	4.66433	+	1.78159i	0.297387	+	0.113590i
$247$			0.984219i			0.0626244i
$248$	7.53611	−	1.17033i	0.478544	−	0.0743160i
$249$	3.06939	−	0.330875i	0.194515	−	0.0209683i
$250$	9.24216	+	12.8290i	0.584525	+	0.811375i
$251$		−	11.0385i		−	0.696741i	−0.937357	−	0.348371i	$-0.886735\pi$
$251$		−	11.0385i		−	0.696741i	0.937357	−	0.348371i	$-0.113265\pi$
$252$	−2.05004	−	15.7416i	−0.129140	−	0.991626i
$253$	22.0462			1.38604
$254$	1.18035	−	2.31082i	0.0740615	−	0.144994i
$255$	20.2458	−	10.3581i	1.26784	−	0.648647i
$256$	−12.8683	−	9.50830i	−0.804267	−	0.594269i
$257$		−	7.02676i		−	0.438317i	−0.975689	−	0.219159i	$-0.929669\pi$
$257$		−	7.02676i		−	0.438317i	0.975689	−	0.219159i	$-0.0703313\pi$
$258$	−23.6646	−	9.03895i	−1.47329	−	0.562740i
$259$	13.5127	+	11.6516i	0.839639	+	0.723996i
$260$	−14.5390	−	9.50423i	−0.901673	−	0.589427i
$261$	10.9796	−	2.39499i	0.679618	−	0.148246i
$262$	−4.98386	+	9.75713i	−0.307904	+	0.602797i
$263$	−12.3592			−0.762100			−0.381050	−	0.924554i	$-0.624437\pi$
$263$	−12.3592			−0.762100			−0.381050	+	0.924554i	$0.624437\pi$
$264$	−3.78785	−	14.1563i	−0.233126	−	0.871259i
$265$	−2.65101	+	1.01457i	−0.162850	+	0.0623243i
$266$	0.357821	+	0.878030i	0.0219394	+	0.0538355i
$267$	18.8294	−	2.02978i	1.15234	−	0.124220i
$268$	−1.68733	−	2.33225i	−0.103070	−	0.142465i
$269$		−	1.88627i		−	0.115008i	−0.998345	−	0.0575040i	$-0.981686\pi$
$269$		−	1.88627i		−	0.115008i	0.998345	−	0.0575040i	$-0.0183142\pi$
$270$	−3.51240	−	16.0519i	−0.213758	−	0.976887i
$271$			7.90779i			0.480364i	0.970728	+	0.240182i	$0.0772072\pi$
$271$			7.90779i			0.480364i	−0.970728	+	0.240182i	$0.922793\pi$
$272$	22.3085	+	7.34773i	1.35265	+	0.445522i
$273$	10.1115	−	14.6478i	0.611974	−	0.886525i
$274$	15.7579	+	8.04901i	0.951970	+	0.486258i
$275$	−11.1349	+	9.98544i	−0.671462	+	0.602145i
$276$	17.0959	+	18.9620i	1.02905	+	1.14138i
$277$	−28.8336			−1.73244			−0.866221	−	0.499661i	$-0.833458\pi$
$277$	−28.8336			−1.73244			−0.866221	+	0.499661i	$0.833458\pi$
$278$	4.32504	+	2.20920i	0.259399	+	0.132499i
$279$	1.72394	+	7.90323i	0.103210	+	0.473154i
$280$	−16.4257	−	3.19301i	−0.981625	−	0.190819i
$281$		−	15.8864i		−	0.947704i	−0.880604	−	0.473852i	$-0.842863\pi$
$281$		−	15.8864i		−	0.947704i	0.880604	−	0.473852i	$-0.157137\pi$
$282$	7.87989	−	20.6301i	0.469241	−	1.22850i
$283$			32.1369i			1.91034i	0.296053	+	0.955171i	$0.404329\pi$
$283$			32.1369i			1.91034i	−0.296053	+	0.955171i	$0.595671\pi$
$284$	12.3704	−	8.94966i	0.734045	−	0.531065i
$285$	0.447004	+	0.873711i	0.0264782	+	0.0517542i
$286$	7.47410	−	14.6324i	0.441953	−	0.865231i
$287$	4.08435	+	3.52181i	0.241091	+	0.207886i
$288$	9.23850	−	14.2355i	0.544384	−	0.838836i
$289$	−17.4788			−1.02816
$290$	1.26189	−	11.7782i	0.0741009	−	0.691641i
$291$	18.7252	−	2.01854i	1.09769	−	0.118329i
$292$	−17.2812	−	23.8864i	−1.01131	−	1.39784i
$293$	23.2728			1.35961			0.679807	−	0.733391i	$-0.262064\pi$
$293$	23.2728			1.35961			0.679807	+	0.733391i	$0.262064\pi$
$294$	3.69520	−	16.7435i	0.215508	−	0.976502i
$295$	−10.1075	+	3.86826i	−0.588484	+	0.225219i
$296$	2.92710	+	18.8485i	0.170134	+	1.09554i
$297$	14.7436	−	4.92110i	0.855512	−	0.285551i
$298$	16.3586	+	8.35584i	0.947629	+	0.484041i
$299$			28.6259i			1.65548i
$300$	−17.2232	−	1.83388i	−0.994379	−	0.105879i
$301$	−20.7220	−	17.8680i	−1.19440	−	1.02989i
$302$	−4.36149	−	2.22781i	−0.250976	−	0.128196i
$303$	−0.816270	−	7.57219i	−0.0468935	−	0.435011i
$304$	−0.317093	+	0.962730i	−0.0181865	+	0.0552163i
$305$	5.16019	+	13.4833i	0.295472	+	0.772052i
$306$	−6.34366	+	24.0910i	−0.362643	+	1.37719i
$307$		−	16.8908i		−	0.964009i	−0.876169	−	0.482005i	$-0.839909\pi$
$307$		−	16.8908i		−	0.964009i	0.876169	−	0.482005i	$-0.160091\pi$
$308$	1.34798	−	15.7709i	0.0768084	−	0.898632i
$309$	−15.6353	+	1.68546i	−0.889460	+	0.0958823i
$310$	8.47810	+	0.908326i	0.481524	+	0.0515894i
$311$	−11.2659			−0.638829			−0.319415	−	0.947615i	$-0.603486\pi$
$311$	−11.2659			−0.638829			−0.319415	+	0.947615i	$0.603486\pi$
$312$	18.3812	−	4.91832i	1.04063	−	0.278445i
$313$	−11.2529			−0.636052			−0.318026	−	0.948082i	$-0.603020\pi$
$313$	−11.2529			−0.636052			−0.318026	+	0.948082i	$0.603020\pi$
$314$	−10.4766	+	20.5105i	−0.591228	+	1.15747i
$315$	2.32355	−	17.5955i	0.130917	−	0.991393i
$316$	−4.00384	−	5.53416i	−0.225234	−	0.311321i
$317$		−	16.3815i		−	0.920078i	−0.887899	−	0.460039i	$-0.847835\pi$
$317$		−	16.3815i		−	0.920078i	0.887899	−	0.460039i	$-0.152165\pi$
$318$	1.10951	−	2.90476i	0.0622180	−	0.162891i
$319$	11.2051			0.627367
$320$	−11.1596	−	13.9809i	−0.623838	−	0.781554i
$321$	−2.59817	−	24.1021i	−0.145016	−	1.34525i
$322$	10.4072	+	25.5374i	0.579968	+	1.42314i
$323$		−	1.48794i		−	0.0827911i
$324$	15.6657	+	8.86488i	0.870316	+	0.492494i
$325$	−12.9656	−	14.4581i	−0.719200	−	0.801992i
$326$	12.0025	+	6.13080i	0.664759	+	0.339554i
$327$	−2.18910	−	20.3073i	−0.121057	−	1.12300i
$328$	0.884742	+	5.69713i	0.0488517	+	0.314571i
$329$	15.5768	−	18.0648i	0.858775	−	0.995947i
$330$	−0.0106983	−	16.3840i	−0.000588925	−	0.901909i
$331$			20.4088i			1.12177i	0.827894	+	0.560884i	$0.189539\pi$
$331$			20.4088i			1.12177i	−0.827894	+	0.560884i	$0.810461\pi$
$332$	2.08951	+	2.88815i	0.114677	+	0.158508i
$333$	−19.7667	+	4.31173i	−1.08321	+	0.236281i
$334$	5.09833	−	9.98123i	0.278968	−	0.546148i
$335$	−1.15035	−	3.00579i	−0.0628502	−	0.164224i
$336$	14.6099	−	11.0703i	0.797034	−	0.603934i
$337$			29.0425i			1.58204i	0.611788	+	0.791022i	$0.290450\pi$
$337$			29.0425i			1.58204i	−0.611788	+	0.791022i	$0.709550\pi$
$338$	2.62680	+	1.34175i	0.142879	+	0.0729815i
$339$	−14.8932	+	1.60547i	−0.808890	+	0.0871970i
$340$	21.9801	+	14.3684i	1.19204	+	0.779238i
$341$			8.06559i			0.436776i
$342$	−1.03965	−	0.273762i	−0.0562179	−	0.0148034i
$343$	9.89925	−	15.6526i	0.534509	−	0.845163i
$344$	−4.48876	−	28.9045i	−0.242018	−	1.55843i
$345$	13.0010	+	25.4118i	0.699953	+	1.36812i
$346$	27.0303	+	13.8069i	1.45316	+	0.742261i
$347$			8.45703i			0.453997i	0.973895	+	0.226999i	$0.0728913\pi$
$347$			8.45703i			0.453997i	−0.973895	+	0.226999i	$0.927109\pi$
$348$	8.68911	+	9.63754i	0.465785	+	0.516626i
$349$	−0.270566			−0.0144831			−0.00724153	−	0.999974i	$-0.502305\pi$
$349$	−0.270566			−0.0144831			−0.00724153	+	0.999974i	$0.502305\pi$
$350$	−16.8230	−	8.18447i	−0.899229	−	0.437478i
$351$	6.38978	+	19.1438i	0.341061	+	1.02182i
$352$	12.0251	−	11.9049i	0.640942	−	0.634534i
$353$			23.4260i			1.24684i	0.781887	+	0.623420i	$0.214257\pi$
$353$			23.4260i			1.24684i	−0.781887	+	0.623420i	$0.785743\pi$
$354$	4.23023	−	11.0750i	0.224834	−	0.588631i
$355$	15.9429	−	6.10149i	0.846159	−	0.323833i
$356$	12.8183	+	17.7176i	0.679367	+	0.939031i
$357$	−15.2865	+	22.1445i	−0.809046	+	1.17201i
$358$	−19.3567	−	9.88723i	−1.02303	−	0.522556i
$359$		−	16.8560i		−	0.889628i	−0.895623	−	0.444814i	$-0.853270\pi$
$359$		−	16.8560i		−	0.889628i	0.895623	−	0.444814i	$-0.146730\pi$
$360$	14.0836	−	12.7143i	0.742269	−	0.670102i
$361$	−18.9358			−0.996620
$362$	2.47177	+	1.26256i	0.129913	+	0.0663587i
$363$	−3.53398	+	0.380957i	−0.185486	+	0.0199951i
$364$	20.4777	+	1.75028i	1.07332	+	0.0917397i
$365$	−11.7816	−	30.7846i	−0.616676	−	1.61134i
$366$	−14.7739	−	5.64306i	−0.772244	−	0.294968i
$367$	5.27587			0.275398			0.137699	−	0.990474i	$-0.456029\pi$
$367$	5.27587			0.275398			0.137699	+	0.990474i	$0.456029\pi$
$368$	−9.22260	+	28.0008i	−0.480761	+	1.45964i
$369$	−5.97466	+	1.30326i	−0.311028	+	0.0678450i
$370$	−2.27180	+	21.2045i	−0.118105	+	1.10237i
$371$	2.19324	−	2.54357i	0.113867	−	0.132055i
$372$	−6.93721	+	6.25452i	−0.359678	+	0.324282i
$373$	25.2464			1.30721			0.653604	−	0.756837i	$-0.273256\pi$
$373$	25.2464			1.30721			0.653604	+	0.756837i	$0.273256\pi$
$374$	−11.2993	+	22.1212i	−0.584273	+	1.14386i
$375$	−18.0762	−	6.94618i	−0.933453	−	0.358699i
$376$	25.1981	−	3.91317i	1.29949	−	0.201806i
$377$			14.5493i			0.749325i
$378$	12.6603	+	14.7553i	0.651173	+	0.758929i
$379$			4.79359i			0.246230i	0.992392	+	0.123115i	$0.0392885\pi$
$379$			4.79359i			0.246230i	−0.992392	+	0.123115i	$0.960712\pi$
$380$	−0.620073	+	0.948554i	−0.0318091	+	0.0486598i
$381$	0.340609	+	3.15969i	0.0174499	+	0.161876i
$382$	−10.2534	+	20.0736i	−0.524611	+	1.02705i
$383$		−	21.8231i		−	1.11511i	−0.830141	−	0.557554i	$-0.811740\pi$
$383$		−	21.8231i		−	1.11511i	0.830141	−	0.557554i	$-0.188260\pi$
$384$	19.5644	+	1.11106i	0.998391	+	0.0566984i
$385$	6.00265	−	16.6476i	0.305923	−	0.848440i
$386$	−15.3093	+	29.9718i	−0.779225	+	1.52552i
$387$	30.3125	−	6.61212i	1.54087	−	0.336113i
$388$	12.7473	+	17.6195i	0.647148	+	0.894496i
$389$	18.1057			0.917996			0.458998	−	0.888437i	$-0.348209\pi$
$389$	18.1057			0.917996			0.458998	+	0.888437i	$0.348209\pi$
$390$	21.2737	−	0.0138912i	1.07724	−	0.000703410i
$391$		−	43.2764i		−	2.18858i
$392$	18.9046	−	5.88339i	0.954829	−	0.297156i
$393$	−1.43818	−	13.3414i	−0.0725465	−	0.672983i
$394$	14.2900	−	27.9762i	0.719920	−	1.40942i
$395$	−2.72964	−	7.13240i	−0.137343	−	0.358870i
$396$	13.3776	+	11.9651i	0.672248	+	0.601267i
$397$			25.2352i			1.26652i	0.773939	+	0.633260i	$0.218284\pi$
$397$			25.2352i			1.26652i	−0.773939	+	0.633260i	$0.781716\pi$
$398$	−3.91431	+	7.66322i	−0.196207	+	0.384123i
$399$	−0.955649	−	0.659691i	−0.0478423	−	0.0330259i
$400$	−8.02439	−	18.3196i	−0.401219	−	0.915982i
$401$			20.2402i			1.01075i	0.862901	+	0.505373i	$0.168645\pi$
$401$			20.2402i			1.01075i	−0.862901	+	0.505373i	$0.831355\pi$
$402$	3.29350	+	1.25799i	0.164265	+	0.0627429i
$403$	−10.4727			−0.521684
$404$	7.12509	−	5.15484i	0.354486	−	0.256463i
$405$	14.3669	+	14.0923i	0.713897	+	0.700251i
$406$	5.28950	+	12.9795i	0.262513	+	0.644162i
$407$	−20.1727			−0.999925
$408$	−27.7886	+	7.43549i	−1.37574	+	0.368112i
$409$		−	15.0121i		−	0.742301i	−0.928573	−	0.371150i	$-0.878963\pi$
$409$		−	15.0121i		−	0.742301i	0.928573	−	0.371150i	$-0.121037\pi$
$410$	−0.686673	+	6.40925i	−0.0339124	+	0.316530i
$411$	−21.5465	+	2.32268i	−1.06281	+	0.114569i
$412$	−10.6439	−	14.7121i	−0.524385	−	0.724812i
$413$	8.36222	−	9.69791i	0.411478	−	0.477203i
$414$	−30.2381	−	7.96233i	−1.48612	−	0.391327i
$415$	1.42454	+	3.72224i	0.0699278	+	0.182717i
$416$	15.4579	+	15.6140i	0.757885	+	0.765538i
$417$	−5.91383	+	0.637501i	−0.289602	+	0.0312186i
$418$	−0.954644	−	0.487624i	−0.0466931	−	0.0238505i
$419$		−	9.20741i		−	0.449812i	−0.974381	−	0.224906i	$-0.927793\pi$
$419$		−	9.20741i		−	0.449812i	0.974381	−	0.224906i	$-0.0722074\pi$
$420$	18.9734	−	7.74662i	0.925807	−	0.377996i
$421$		−	5.81872i		−	0.283587i	−0.989896	−	0.141793i	$-0.954713\pi$
$421$		−	5.81872i		−	0.283587i	0.989896	−	0.141793i	$-0.0452869\pi$
$422$	12.1381	−	23.7632i	0.590872	−	1.15678i
$423$	5.76425	+	26.4256i	0.280268	+	1.28486i
$424$	3.54794	−	0.550982i	0.172303	−	0.0267581i
$425$	19.6013	+	21.8577i	0.950801	+	1.06025i
$426$	−6.67244	+	17.4689i	−0.323281	+	0.846370i
$427$	−12.9369	−	11.1551i	−0.626059	−	0.539832i
$428$	22.6790	−	16.4077i	1.09623	−	0.793097i
$429$	2.15678	+	20.0075i	0.104130	+	0.965973i
$430$	3.48385	−	32.5175i	0.168006	−	1.56813i
$431$		−	29.8724i		−	1.43890i	−0.694543	−	0.719452i	$-0.744393\pi$
$431$		−	29.8724i		−	1.43890i	0.694543	−	0.719452i	$-0.255607\pi$
$432$	0.0825767	+	20.7844i	0.00397297	+	0.999992i
$433$	2.76341			0.132801			0.0664006	−	0.997793i	$-0.478848\pi$
$433$	2.76341			0.132801			0.0664006	+	0.997793i	$0.478848\pi$
$434$	−9.34280	+	3.80744i	−0.448469	+	0.182763i
$435$	6.60785	+	12.9157i	0.316822	+	0.619259i
$436$	19.1083	−	13.8244i	0.915121	−	0.662069i
$437$	1.86760			0.0893396
$438$	33.7313	+	12.8841i	1.61174	+	0.615624i
$439$		−	36.5869i		−	1.74620i	−0.487543	−	0.873099i	$-0.662107\pi$
$439$		−	36.5869i		−	1.74620i	0.487543	−	0.873099i	$-0.337893\pi$
$440$	16.4219	−	9.39335i	0.782883	−	0.447811i
$441$	7.44520	+	19.6359i	0.354533	+	0.935043i
$442$	−28.7231	−	14.6715i	−1.36622	−	0.697854i
$443$		−	14.6025i		−	0.693784i	−0.937905	−	0.346892i	$-0.887237\pi$
$443$		−	14.6025i		−	0.693784i	0.937905	−	0.346892i	$-0.112763\pi$
$444$	−15.6431	−	17.3506i	−0.742389	−	0.823422i
$445$	8.73894	+	22.8344i	0.414265	+	1.08245i
$446$	2.69158	+	1.37484i	0.127450	+	0.0651004i
$447$	−22.3679	+	2.41122i	−1.05796	+	0.114047i
$448$	19.4667	+	8.30951i	0.919715	+	0.392588i
$449$		−	21.7393i		−	1.02594i	−0.858406	−	0.512971i	$-0.828545\pi$
$449$		−	21.7393i		−	1.02594i	0.858406	−	0.512971i	$-0.171455\pi$
$450$	18.8788	−	9.67424i	0.889955	−	0.456048i
$451$	−6.09740			−0.287115
$452$	−10.1387	−	14.0139i	−0.476884	−	0.659156i
$453$	5.96367	−	0.642874i	0.280198	−	0.0302048i
$454$	2.08094	+	1.06293i	0.0976634	+	0.0498857i
$455$	21.6160	+	7.79412i	1.01337	+	0.365394i
$456$	−0.320880	−	1.19922i	−0.0150266	−	0.0561587i
$457$			0.703722i			0.0329187i	0.999865	+	0.0164594i	$0.00523941\pi$
$457$			0.703722i			0.0329187i	−0.999865	+	0.0164594i	$0.994761\pi$
$458$	29.2762	+	14.9540i	1.36799	+	0.698756i
$459$	−9.66005	−	28.9415i	−0.450892	−	1.35087i
$460$	−18.0347	+	27.5885i	−0.840873	+	1.28632i
$461$		−	26.6508i		−	1.24125i	−0.784107	−	0.620626i	$-0.786879\pi$
$461$		−	26.6508i		−	1.24125i	0.784107	−	0.620626i	$-0.213121\pi$
$462$	9.19798	+	17.0648i	0.427929	+	0.793925i
$463$			39.2373i			1.82351i	0.410733	+	0.911756i	$0.365273\pi$
$463$			39.2373i			1.82351i	−0.410733	+	0.911756i	$0.634727\pi$
$464$	−4.68744	+	14.2316i	−0.217609	+	0.660685i
$465$	−9.29685	+	4.75641i	−0.431131	+	0.220573i
$466$	20.6794	+	10.5629i	0.957957	+	0.489316i
$467$	21.0343			0.973353			0.486677	−	0.873582i	$-0.338209\pi$
$467$	21.0343			0.973353			0.486677	+	0.873582i	$0.338209\pi$
$468$	−15.5360	+	17.3700i	−0.718152	+	0.802931i
$469$	2.88398	+	2.48677i	0.133170	+	0.114828i
$470$	28.3478	+	3.03712i	1.30759	+	0.140092i
$471$	−3.02320	−	28.0449i	−0.139302	−	1.29224i
$472$	13.5273	−	2.10074i	0.622645	−	0.0966944i
$473$	30.9353			1.42241
$474$	7.81511	+	2.98507i	0.358960	+	0.137109i
$475$	−0.943274	+	0.845897i	−0.0432804	+	0.0388124i
$476$	−30.9581	−	2.64607i	−1.41896	−	0.121282i
$477$	0.811619	+	3.72078i	0.0371615	+	0.170363i
$478$	16.9410	−	33.1661i	0.774862	−	1.51698i
$479$	−39.6811			−1.81308			−0.906539	−	0.422123i	$-0.861285\pi$
$479$	−39.6811			−1.81308			−0.906539	+	0.422123i	$0.861285\pi$
$480$	20.8137	+	6.84032i	0.950011	+	0.312216i
$481$		−	26.1932i		−	1.19431i
$482$	7.57859	−	14.8370i	0.345195	−	0.675805i
$483$	−27.7949	−	19.1870i	−1.26471	−	0.873039i
$484$	−2.40579	−	3.32531i	−0.109354	−	0.151151i
$485$	8.69057	+	22.7080i	0.394618	+	1.03112i
$486$	−21.9993	+	1.42479i	−0.997909	+	0.0646297i
$487$		−	27.2901i		−	1.23663i	−0.785929	−	0.618317i	$-0.787815\pi$
$487$		−	27.2901i		−	1.23663i	0.785929	−	0.618317i	$-0.212185\pi$
$488$	−2.80236	−	18.0452i	−0.126857	−	0.816869i
$489$	−16.4116	+	1.76915i	−0.742160	+	0.0800036i
$490$	22.1174	−	0.905477i	0.999163	−	0.0409053i
$491$	30.8380			1.39170			0.695850	−	0.718187i	$-0.255028\pi$
$491$	30.8380			1.39170			0.695850	+	0.718187i	$0.255028\pi$
$492$	−4.72827	−	5.24437i	−0.213167	−	0.236435i
$493$		−	21.9955i		−	0.990628i
$494$	0.633153	−	1.23955i	0.0284869	−	0.0557701i
$495$	11.0015	+	16.7815i	0.494479	+	0.754275i
$496$	−10.2441	−	3.37407i	−0.459972	−	0.151500i
$497$	−13.1899	+	15.2967i	−0.591648	+	0.686152i
$498$	−4.07853	−	1.55784i	−0.182763	−	0.0698085i
$499$			13.9363i			0.623873i	0.950103	+	0.311936i	$0.100978\pi$
$499$			13.9363i			0.623873i	−0.950103	+	0.311936i	$0.899022\pi$
$500$	−3.38689	−	22.1027i	−0.151466	−	0.988462i
$501$	1.47121	+	13.6478i	0.0657288	+	0.609739i
$502$	−7.10110	+	13.9021i	−0.316938	+	0.620483i
$503$		−	6.73606i		−	0.300346i	−0.988660	−	0.150173i	$-0.952017\pi$
$503$		−	6.73606i		−	0.300346i	0.988660	−	0.150173i	$-0.0479831\pi$
$504$	−7.54476	+	21.1442i	−0.336070	+	0.941837i
$505$	9.18278	−	3.51434i	0.408628	−	0.156386i
$506$	−27.7657	−	14.1825i	−1.23433	−	0.630488i
$507$	−3.59175	+	0.387184i	−0.159515	+	0.0171955i
$508$	−2.97312	+	2.15099i	−0.131911	+	0.0954345i
$509$		−	5.95889i		−	0.264123i	−0.991242	−	0.132062i	$-0.957840\pi$
$509$		−	5.95889i		−	0.264123i	0.991242	−	0.132062i	$-0.0421597\pi$
$510$	−32.1615	+	0.0210007i	−1.42414	+	0.000929926i
$511$	29.5370	+	25.4689i	1.30664	+	1.12668i
$512$	10.0899	+	20.2532i	0.445915	+	0.895075i
$513$	1.24898	−	0.416881i	0.0551436	−	0.0184058i
$514$	−4.52035	+	8.84970i	−0.199384	+	0.390344i
$515$	−7.25651	−	18.9609i	−0.319760	−	0.835516i
$516$	23.9890	+	26.6074i	1.05606	+	1.17133i
$517$			26.9685i			1.18607i
$518$	−9.52275	−	23.3672i	−0.418406	−	1.02669i
$519$	−36.9598	+	3.98421i	−1.62236	+	0.174887i
$520$	12.1968	+	21.3229i	0.534863	+	0.935072i
$521$	−42.1144			−1.84507			−0.922533	−	0.385919i	$-0.873885\pi$
$521$	−42.1144			−1.84507			−0.922533	+	0.385919i	$0.873885\pi$
$522$	−15.3687	−	4.04690i	−0.672669	−	0.177128i
$523$			1.74549i			0.0763247i	0.999272	+	0.0381624i	$0.0121504\pi$
$523$			1.74549i			0.0763247i	−0.999272	+	0.0381624i	$0.987850\pi$
$524$	12.5536	−	9.08226i	0.548408	−	0.396760i
$525$	22.7288	−	2.89837i	0.991967	−	0.126495i
$526$	15.5655	+	7.95073i	0.678688	+	0.346668i
$527$	15.8326			0.689680
$528$	−4.33628	+	20.2656i	−0.188712	+	0.881945i
$529$	31.3190			1.36169
$530$	3.99143	+	0.427633i	0.173376	+	0.0185752i
$531$	3.09447	+	14.1863i	0.134289	+	0.615632i
$532$	0.114192	−	1.33600i	0.00495083	−	0.0579231i
$533$		−	7.91714i		−	0.342930i
$534$	−25.0200	−	9.55669i	−1.08272	−	0.413559i
$535$	29.2286	−	11.1861i	1.26366	−	0.483616i
$536$	0.624721	+	4.02277i	0.0269838	+	0.173757i
$537$	26.4673	−	2.85313i	1.14215	−	0.123122i
$538$	−1.21345	+	2.37562i	−0.0523154	+	0.102420i
$539$	3.08038	+	20.7112i	0.132681	+	0.892096i
$540$	−5.90264	+	22.4757i	−0.254009	+	0.967202i
$541$			2.88277i			0.123940i	0.998078	+	0.0619699i	$0.0197383\pi$
$541$			2.88277i			0.123940i	−0.998078	+	0.0619699i	$0.980262\pi$
$542$	5.08713	−	9.95930i	0.218511	−	0.427788i
$543$	−3.37977	+	0.364333i	−0.145040	+	0.0156350i
$544$	−23.3692	−	23.6051i	−1.00194	−	1.01206i
$545$	24.6267	−	9.42487i	1.05489	−	0.403717i
$546$	−22.1577	+	11.9431i	−0.948261	+	0.511117i
$547$	38.2217			1.63424			0.817120	−	0.576467i	$-0.195569\pi$
$547$	38.2217			1.63424			0.817120	+	0.576467i	$0.195569\pi$
$548$	−14.6680	−	20.2743i	−0.626585	−	0.866075i
$549$	18.9243	−	4.12798i	0.807669	−	0.176178i
$550$	20.4473	−	5.41278i	0.871877	−	0.230802i
$551$	0.949220			0.0404381
$552$	−9.33275	−	34.8791i	−0.397228	−	1.48456i
$553$	6.84335	+	5.90081i	0.291009	+	0.250928i
$554$	36.3138	+	18.5488i	1.54283	+	0.788063i
$555$	−11.8962	−	23.2522i	−0.504966	−	0.987002i
$556$	−4.02589	−	5.56465i	−0.170736	−	0.235994i
$557$		−	25.2043i		−	1.06794i	−0.845503	−	0.533971i	$-0.820699\pi$
$557$		−	25.2043i		−	1.06794i	0.845503	−	0.533971i	$-0.179301\pi$
$558$	2.91301	−	11.0626i	0.123317	−	0.468316i
$559$			40.1678i			1.69892i
$560$	18.6329	+	14.5881i	0.787386	+	0.616461i
$561$	−3.26061	−	30.2473i	−0.137663	−	1.27704i
$562$	−10.2198	+	20.0078i	−0.431097	+	0.843978i
$563$	−7.30365			−0.307812			−0.153906	−	0.988085i	$-0.549185\pi$
$563$	−7.30365			−0.307812			−0.153906	+	0.988085i	$0.549185\pi$
$564$	−23.1956	+	20.9129i	−0.976710	+	0.880592i
$565$	−6.91212	−	18.0610i	−0.290795	−	0.759832i
$566$	20.6739	−	40.4742i	0.868987	−	1.70126i
$567$	−22.8710	−	6.62718i	−0.960490	−	0.278315i
$568$	−21.3369	+	3.31354i	−0.895278	+	0.139033i
$569$			20.5442i			0.861257i	0.902529	+	0.430629i	$0.141708\pi$
$569$			20.5442i			0.861257i	−0.902529	+	0.430629i	$0.858292\pi$
$570$	−0.000906289	−	1.38794i	−3.79603e−5	−	0.0581343i
$571$			3.06852i			0.128414i	0.997937	+	0.0642068i	$0.0204517\pi$
$571$			3.06852i			0.128414i	−0.997937	+	0.0642068i	$0.979548\pi$
$572$	−18.8262	+	13.6203i	−0.787162	+	0.569494i
$573$	−2.95880	−	27.4476i	−0.123606	−	1.14664i
$574$	−2.87834	−	7.06294i	−0.120140	−	0.294802i
$575$	−27.4350	+	24.6028i	−1.14412	+	1.02601i
$576$	−20.7930	+	11.9854i	−0.866375	+	0.499393i
$577$	−19.0536			−0.793212			−0.396606	−	0.917989i	$-0.629812\pi$
$577$	−19.0536			−0.793212			−0.396606	+	0.917989i	$0.629812\pi$
$578$	22.0132	+	11.2442i	0.915630	+	0.467696i
$579$	−4.41777	−	40.9818i	−0.183596	−	1.70315i
$580$	−9.16625	+	14.0220i	−0.380608	+	0.582233i
$581$	−3.57139	−	3.07950i	−0.148166	−	0.127759i
$582$	−24.8816	−	9.50380i	−1.03137	−	0.393945i
$583$			3.79722i			0.157265i
$584$	6.39824	+	41.2002i	0.264761	+	1.70488i
$585$	−21.7899	+	14.2848i	−0.900903	+	0.590604i
$586$	−29.3105	−	14.9715i	−1.21080	−	0.618468i
$587$	−22.7767			−0.940095			−0.470047	−	0.882641i	$-0.655763\pi$
$587$	−22.7767			−0.940095			−0.470047	+	0.882641i	$0.655763\pi$
$588$	−15.4250	+	18.7101i	−0.636118	+	0.771592i
$589$			0.683260i			0.0281532i
$590$	15.2182	+	1.63044i	0.626523	+	0.0671243i
$591$	4.12363	+	38.2532i	0.169623	+	1.57352i
$592$	8.43885	−	25.6213i	0.346835	−	1.05303i
$593$		−	9.41677i		−	0.386700i	−0.981130	−	0.193350i	$-0.938065\pi$
$593$		−	9.41677i		−	0.386700i	0.981130	−	0.193350i	$-0.0619353\pi$
$594$	−21.7343	−	3.28688i	−0.891769	−	0.134862i
$595$	−32.6790	−	11.7831i	−1.33971	−	0.483060i
$596$	−15.2271	−	21.0472i	−0.623728	−	0.862125i
$597$	−1.12954	−	10.4783i	−0.0462290	−	0.428847i
$598$	18.4152	−	36.0522i	0.753052	−	1.47428i
$599$		−	7.58493i		−	0.309912i	−0.987921	−	0.154956i	$-0.950476\pi$
$599$		−	7.58493i		−	0.309912i	0.987921	−	0.154956i	$-0.0495235\pi$
$600$	20.5116	+	13.3894i	0.837381	+	0.546619i
$601$		−	5.56743i		−	0.227100i	−0.993532	−	0.113550i	$-0.963778\pi$
$601$		−	5.56743i		−	0.227100i	0.993532	−	0.113550i	$-0.0362222\pi$
$602$	14.6033	+	35.8340i	0.595187	+	1.46048i
$603$	−4.21873	+	0.920239i	−0.171800	+	0.0374750i
$604$	4.05982	+	5.61154i	0.165192	+	0.228330i
$605$	−1.64016	−	4.28565i	−0.0666820	−	0.174236i
$606$	−3.84320	+	10.0617i	−0.156119	+	0.408730i
$607$	−39.6108			−1.60775			−0.803876	−	0.594797i	$-0.797233\pi$
$607$	−39.6108			−1.60775			−0.803876	+	0.594797i	$0.797233\pi$
$608$	1.01868	−	1.00850i	0.0413131	−	0.0409001i
$609$	−14.1269	−	9.75191i	−0.572452	−	0.395167i
$610$	2.17499	−	20.3008i	0.0880626	−	0.821956i
$611$	−35.0171			−1.41664
$612$	23.4872	−	26.2600i	0.949416	−	1.06150i
$613$	5.78624			0.233704			0.116852	−	0.993149i	$-0.462720\pi$
$613$	5.78624			0.233704			0.116852	+	0.993149i	$0.462720\pi$
$614$	−10.8659	+	21.2728i	−0.438514	+	0.858498i
$615$	−3.59574	−	7.02821i	−0.144994	−	0.283405i
$616$	−11.8432	+	18.9952i	−0.477176	+	0.765338i
$617$	41.6718			1.67764			0.838821	−	0.544407i	$-0.183245\pi$
$617$	41.6718			1.67764			0.838821	+	0.544407i	$0.183245\pi$
$618$	20.7758	+	7.93555i	0.835724	+	0.319214i
$619$	−14.9019			−0.598957			−0.299479	−	0.954103i	$-0.596813\pi$
$619$	−14.9019			−0.598957			−0.299479	+	0.954103i	$0.596813\pi$
$620$	−10.0932	−	6.59798i	−0.405354	−	0.264981i
$621$	36.3263	−	12.1249i	1.45772	−	0.486556i
$622$	14.1886	+	7.24740i	0.568909	+	0.290594i
$623$	−21.9090	−	18.8914i	−0.877764	−	0.756869i
$624$	−26.3137	−	5.63043i	−1.05339	−	0.225398i
$625$	2.71326	−	24.8523i	0.108531	−	0.994093i
$626$	14.1722	+	7.23905i	0.566436	+	0.289331i
$627$	1.30533	−	0.140712i	0.0521298	−	0.00561951i
$628$	26.3890	−	19.0918i	1.05304	−	0.761847i
$629$			39.5988i			1.57891i
$630$	−14.2456	+	20.6655i	−0.567559	+	0.823333i
$631$	−28.2349			−1.12401			−0.562006	−	0.827133i	$-0.689970\pi$
$631$	−28.2349			−1.12401			−0.562006	+	0.827133i	$0.689970\pi$
$632$	1.48239	+	9.54557i	0.0589663	+	0.379702i
$633$	3.50265	+	32.4926i	0.139218	+	1.29146i
$634$	−10.5383	+	20.6313i	−0.418530	+	0.819375i
$635$	−3.83175	+	1.46645i	−0.152058	+	0.0581942i
$636$	−3.26599	+	2.94458i	−0.129505	+	0.116760i
$637$	−26.8924	+	3.99970i	−1.06552	+	0.158474i
$638$	−14.1121	−	7.20832i	−0.558702	−	0.285380i
$639$	−4.88098	−	22.3763i	−0.193089	−	0.885194i
$640$	5.06070	+	24.7869i	0.200042	+	0.979787i
$641$			23.0269i			0.909506i	0.890618	+	0.454753i	$0.150273\pi$
$641$			23.0269i			0.909506i	−0.890618	+	0.454753i	$0.849727\pi$
$642$	−12.2328	+	32.0263i	−0.482791	+	1.26398i
$643$			19.4192i			0.765818i	0.923786	+	0.382909i	$0.125078\pi$
$643$			19.4192i			0.765818i	−0.923786	+	0.382909i	$0.874922\pi$
$644$	3.32124	−	38.8574i	0.130875	−	1.53120i
$645$	18.2431	+	35.6578i	0.718319	+	1.40402i
$646$	−0.957198	+	1.87395i	−0.0376605	+	0.0737296i
$647$		−	34.9106i		−	1.37248i	−0.727376	−	0.686240i	$-0.759260\pi$
$647$		−	34.9106i		−	1.37248i	0.727376	−	0.686240i	$-0.240740\pi$
$648$	−14.0270	−	21.2425i	−0.551032	−	0.834484i
$649$			14.4777i			0.568300i
$650$	7.02820	+	26.5498i	0.275669	+	1.04137i
$651$	7.01954	−	10.1687i	0.275117	−	0.398544i
$652$	−11.1724	−	15.4426i	−0.437543	−	0.604779i
$653$			18.7225i			0.732669i	0.930483	+	0.366335i	$0.119387\pi$
$653$			18.7225i			0.732669i	−0.930483	+	0.366335i	$0.880613\pi$
$654$	−10.3068	+	26.9839i	−0.403028	+	1.05515i
$655$	16.1791	−	6.19188i	0.632168	−	0.241937i
$656$	2.55072	−	7.74428i	0.0995889	−	0.302363i
$657$	−43.2073	+	9.42487i	−1.68568	+	0.367699i
$658$	−31.2390	+	12.7307i	−1.21782	+	0.496296i
$659$	14.4188			0.561679			0.280839	−	0.959755i	$-0.409387\pi$
$659$	14.4188			0.561679			0.280839	+	0.959755i	$0.409387\pi$
$660$	−10.5264	+	20.6413i	−0.409741	+	0.803463i
$661$	4.56203			0.177442			0.0887212	−	0.996056i	$-0.471722\pi$
$661$	4.56203			0.177442			0.0887212	+	0.996056i	$0.471722\pi$
$662$	13.1291	−	25.7034i	0.510276	−	0.998991i
$663$	39.2745	−	4.23372i	1.52529	−	0.164424i
$664$	−0.773626	−	4.98161i	−0.0300225	−	0.193324i
$665$	0.508503	−	1.41027i	0.0197189	−	0.0546878i
$666$	27.6684	+	7.28568i	1.07213	+	0.282314i
$667$	27.6079			1.06898
$668$	−12.8420	+	9.29086i	−0.496870	+	0.359474i
$669$	−3.68032	+	0.396733i	−0.142290	+	0.0153386i
$670$	−0.484863	+	4.52560i	−0.0187319	+	0.174839i
$671$	19.3131			0.745572
$672$	−25.5217	+	4.54362i	−0.984520	+	0.175274i
$673$			31.4986i			1.21418i	0.794633	+	0.607091i	$0.207663\pi$
$673$			31.4986i			1.21418i	−0.794633	+	0.607091i	$0.792337\pi$
$674$	18.6832	−	36.5769i	0.719648	−	1.40889i
$675$	−12.8556	+	22.5773i	−0.494813	+	0.869000i
$676$	−2.44511	−	3.37967i	−0.0940428	−	0.129987i
$677$	20.6023			0.791810			0.395905	−	0.918291i	$-0.370431\pi$
$677$	20.6023			0.791810			0.395905	+	0.918291i	$0.370431\pi$
$678$	19.7898	+	7.55893i	0.760021	+	0.290299i
$679$	−21.7877	−	18.7869i	−0.836134	−	0.720974i
$680$	−18.4390	−	32.2359i	−0.707104	−	1.23619i
$681$	−2.84537	+	0.306726i	−0.109035	+	0.0117538i
$682$	5.18863	−	10.1580i	0.198683	−	0.388971i
$683$			35.3045i			1.35089i	0.737411	+	0.675444i	$0.236048\pi$
$683$			35.3045i			1.35089i	−0.737411	+	0.675444i	$0.763952\pi$
$684$	1.13325	+	1.01360i	0.0433310	+	0.0387558i
$685$	−9.99999	−	26.1294i	−0.382080	−	0.998354i
$686$	−22.5368	+	13.3451i	−0.860459	+	0.509519i
$687$	−40.0307	+	4.31524i	−1.52727	+	0.164637i
$688$	−12.9411	+	39.2908i	−0.493376	+	1.49795i
$689$	−4.93048			−0.187836
$690$	−0.0263593	−	40.3679i	−0.00100348	−	1.53678i
$691$	0.799384			0.0304100			0.0152050	−	0.999884i	$-0.495160\pi$
$691$	0.799384			0.0304100			0.0152050	+	0.999884i	$0.495160\pi$
$692$	−25.1607	−	34.7775i	−0.956467	−	1.32204i
$693$	−20.8724	−	11.3162i	−0.792876	−	0.429869i
$694$	5.44045	−	10.6510i	0.206517	−	0.404307i
$695$	−2.74468	−	7.17169i	−0.104112	−	0.272038i
$696$	−4.74342	−	17.7275i	−0.179799	−	0.671960i
$697$			11.9691i			0.453362i
$698$	0.340758	+	0.174056i	0.0128979	+	0.00658813i
$699$	−28.2760	+	3.04810i	−1.06950	+	0.115290i
$700$	15.9223	+	21.1301i	0.601806	+	0.798642i
$701$	−9.07828			−0.342882			−0.171441	−	0.985194i	$-0.554842\pi$
$701$	−9.07828			−0.342882			−0.171441	+	0.985194i	$0.554842\pi$
$702$	4.26783	−	28.2208i	0.161079	−	1.06513i
$703$	−1.70889			−0.0644521
$704$	−22.8033	+	7.25755i	−0.859431	+	0.273529i
$705$	−31.0854	+	15.9038i	−1.17074	+	0.598970i
$706$	15.0701	−	29.5033i	0.567169	−	1.11037i
$707$	−7.59714	+	8.81062i	−0.285720	+	0.331358i
$708$	−12.4523	+	11.2269i	−0.467986	+	0.421931i
$709$			1.97120i			0.0740300i	0.999315	+	0.0370150i	$0.0117849\pi$
$709$			1.97120i			0.0740300i	−0.999315	+	0.0370150i	$0.988215\pi$
$710$	−24.0040	−	2.57173i	−0.900854	−	0.0965155i
$711$	−10.0106	+	2.18362i	−0.375426	+	0.0818922i
$712$	−4.74587	−	30.5601i	−0.177859	−	1.14529i
$713$			19.8725i			0.744231i
$714$	33.4979	−	18.0555i	1.25363	−	0.675710i
$715$	−24.2631	+	9.28573i	−0.907388	+	0.347266i
$716$	18.0178	+	24.9045i	0.673358	+	0.930725i
$717$	4.88861	+	45.3496i	0.182568	+	1.69361i
$718$	−10.8436	+	21.2290i	−0.404679	+	0.792258i
$719$	32.9955			1.23052			0.615262	−	0.788323i	$-0.289050\pi$
$719$	32.9955			1.23052			0.615262	+	0.788323i	$0.289050\pi$
$720$	−25.9164	+	6.95269i	−0.965847	+	0.259112i
$721$	18.1924	+	15.6868i	0.677522	+	0.584207i
$722$	23.8483	+	12.1815i	0.887540	+	0.453348i
$723$	2.18693	+	20.2873i	0.0813329	+	0.754491i
$724$	−2.30081	−	3.18021i	−0.0855088	−	0.118191i
$725$	−13.9440	+	12.5045i	−0.517867	+	0.464405i
$726$	4.69586	+	1.79364i	0.174280	+	0.0665682i
$727$	18.0873			0.670822			0.335411	−	0.942072i	$-0.391125\pi$
$727$	18.0873			0.670822			0.335411	+	0.942072i	$0.391125\pi$
$728$	−24.6642	−	15.3778i	−0.914117	−	0.569938i
$729$	21.5870	−	16.2173i	0.799519	−	0.600641i
$730$	−4.96585	+	46.3502i	−0.183795	+	1.71550i
$731$		−	60.7255i		−	2.24601i
$732$	14.9765	+	16.6112i	0.553546	+	0.613966i
$733$			13.9719i			0.516065i	0.966136	+	0.258033i	$0.0830742\pi$
$733$			13.9719i			0.516065i	−0.966136	+	0.258033i	$0.916926\pi$
$734$	−6.64458	−	3.39400i	−0.245256	−	0.125275i
$735$	−22.0564	+	15.7644i	−0.813562	+	0.581478i
$736$	29.6283	−	29.3321i	1.09211	−	1.08120i
$737$	−4.30540			−0.158592
$738$	8.36304	+	2.20216i	0.307848	+	0.0810628i
$739$		−	22.5660i		−	0.830104i	−0.909798	−	0.415052i	$-0.863763\pi$
$739$		−	22.5660i		−	0.830104i	0.909798	−	0.415052i	$-0.136237\pi$
$740$	16.5021	−	25.2440i	0.606630	−	0.927989i
$741$	0.182707	+	1.69490i	0.00671192	+	0.0622637i
$742$	−4.39852	+	1.79252i	−0.161475	+	0.0658053i
$743$	9.63430			0.353448			0.176724	−	0.984260i	$-0.443450\pi$
$743$	9.63430			0.353448			0.176724	+	0.984260i	$0.443450\pi$
$744$	12.7605	−	3.41437i	0.467822	−	0.125177i
$745$	−10.3812	−	27.1255i	−0.380337	−	0.993800i
$746$	−31.7960	−	16.2411i	−1.16413	−	0.594630i
$747$	5.22429	−	1.13958i	0.191147	−	0.0416951i
$748$	28.4613	−	20.5911i	1.04065	−	0.752886i
$749$	−24.1815	+	28.0440i	−0.883573	+	1.02471i
$750$	18.2972	+	20.3768i	0.668120	+	0.744054i
$751$	36.1635			1.31962			0.659812	−	0.751430i	$-0.270636\pi$
$751$	36.1635			1.31962			0.659812	+	0.751430i	$0.270636\pi$
$752$	−34.2525	−	11.2817i	−1.24906	−	0.411401i
$753$	−2.04914	−	19.0090i	−0.0746749	−	0.692728i
$754$	9.35961	−	18.3237i	0.340857	−	0.667311i
$755$	2.76781	+	7.23213i	0.100731	+	0.263204i
$756$	−6.45254	−	26.7276i	−0.234676	−	0.972074i
$757$	−2.68528			−0.0975981			−0.0487991	−	0.998809i	$-0.515539\pi$
$757$	−2.68528			−0.0975981			−0.0487991	+	0.998809i	$0.515539\pi$
$758$	3.08374	−	6.03719i	0.112007	−	0.219280i
$759$	37.9653	−	4.09259i	1.37805	−	0.148552i
$760$	1.39115	−	0.795739i	0.0504622	−	0.0288645i
$761$	−12.1152			−0.439175			−0.219588	−	0.975593i	$-0.570471\pi$
$761$	−12.1152			−0.439175			−0.219588	+	0.975593i	$0.570471\pi$
$762$	1.60367	−	4.19852i	0.0580949	−	0.152096i
$763$	−20.3742	+	23.6286i	−0.737597	+	0.855413i
$764$	25.8269	−	18.6852i	0.934384	−	0.676006i
$765$	32.9419	−	21.5957i	1.19102	−	0.780794i
$766$	−14.0389	+	27.4846i	−0.507246	+	0.993059i
$767$	−18.7985			−0.678776
$768$	−23.9252	−	13.9852i	−0.863326	−	0.504646i
$769$			34.3566i			1.23893i	0.785025	+	0.619465i	$0.212650\pi$
$769$			34.3566i			1.23893i	−0.785025	+	0.619465i	$0.787350\pi$
$770$	−18.2694	+	17.1049i	−0.658383	+	0.616418i
$771$	−1.30443	−	12.1006i	−0.0469777	−	0.435793i
$772$	38.5620	−	27.8987i	1.38788	−	1.00410i
$773$	15.8817			0.571224			0.285612	−	0.958345i	$-0.407803\pi$
$773$	15.8817			0.571224			0.285612	+	0.958345i	$0.407803\pi$
$774$	−42.4301	−	11.1727i	−1.52512	−	0.401595i
$775$	−9.00089	−	10.0370i	−0.323321	−	0.360541i
$776$	−4.71960	−	30.3910i	−0.169424	−	1.09097i
$777$	25.4329	+	17.5565i	0.912399	+	0.629835i
$778$	−22.8028	−	11.6475i	−0.817521	−	0.417583i
$779$	−0.516529			−0.0185066
$780$	−26.8016	−	13.6680i	−0.959653	−	0.489393i
$781$		−	22.8360i		−	0.817138i
$782$	−27.8400	+	54.5036i	−0.995555	+	1.94904i
$783$	18.4630	−	6.16256i	0.659815	−	0.220232i
$784$	−27.5939	−	4.75175i	−0.985495	−	0.169705i
$785$	34.0100	−	13.0160i	1.21387	−	0.464560i
$786$	−6.77129	+	17.7277i	−0.241524	+	0.632326i
$787$		−	11.5166i		−	0.410522i	−0.978707	−	0.205261i	$-0.934196\pi$
$787$		−	11.5166i		−	0.410522i	0.978707	−	0.205261i	$-0.0658043\pi$
$788$	−35.9945	+	26.0412i	−1.28225	+	0.927678i
$789$	−21.2834	+	2.29432i	−0.757710	+	0.0816799i
$790$	−1.15053	+	10.7387i	−0.0409338	+	0.382067i
$791$	17.3290	+	14.9423i	0.616149	+	0.531287i
$792$	−9.15089	−	23.6750i	−0.325163	−	0.841254i
$793$			25.0770i			0.890509i
$794$	16.2340	−	31.7820i	0.576122	−	1.12790i
$795$	−4.37689	+	2.23928i	−0.155232	+	0.0794192i
$796$	9.85958	−	7.13318i	0.349464	−	0.252829i
$797$	−34.9066			−1.23645			−0.618227	−	0.785999i	$-0.712149\pi$
$797$	−34.9066			−1.23645			−0.618227	+	0.785999i	$0.712149\pi$
$798$	0.779188	+	1.44561i	0.0275830	+	0.0511739i
$799$	52.9387			1.87284
$800$	−1.67898	+	28.2344i	−0.0593609	+	0.998237i
$801$	32.0488	−	6.99086i	1.13239	−	0.247010i
$802$	13.0206	−	25.4910i	0.459774	−	0.900120i
$803$	−44.0949			−1.55608
$804$	−3.33866	−	3.70308i	−0.117745	−	0.130597i
$805$	14.7897	−	41.0174i	0.521269	−	1.44567i
$806$	13.1896	+	6.73716i	0.464586	+	0.237306i
$807$	−0.350161	−	3.24830i	−0.0123263	−	0.114345i
$808$	−12.2897	+	1.90854i	−0.432349	+	0.0671422i
$809$			49.2988i			1.73325i	0.498957	+	0.866627i	$0.333717\pi$
$809$			49.2988i			1.73325i	−0.498957	+	0.866627i	$0.666283\pi$
$810$	−9.02844	−	26.9905i	−0.317227	−	0.948350i
$811$	48.4514			1.70136			0.850679	−	0.525686i	$-0.176191\pi$
$811$	48.4514			1.70136			0.850679	+	0.525686i	$0.176191\pi$
$812$	1.68804	−	19.7495i	0.0592386	−	0.693072i
$813$	1.46798	+	13.6178i	0.0514842	+	0.477597i
$814$	25.4061	+	12.9772i	0.890483	+	0.454851i
$815$	−7.61682	−	19.9023i	−0.266806	−	0.697149i
$816$	39.7810	+	8.51206i	1.39261	+	0.297982i
$817$	2.62062			0.0916839
$818$	−9.65736	+	18.9067i	−0.337662	+	0.661056i
$819$	14.6935	−	27.1017i	0.513434	−	0.947008i
$820$	4.98792	−	7.63025i	0.174186	−	0.266460i
$821$	28.0461			0.978815			0.489408	−	0.872055i	$-0.337213\pi$
$821$	28.0461			0.978815			0.489408	+	0.872055i	$0.337213\pi$
$822$	28.6305	+	10.9357i	0.998603	+	0.381428i
$823$			24.0162i			0.837151i	0.908182	+	0.418576i	$0.137470\pi$
$823$			24.0162i			0.837151i	−0.908182	+	0.418576i	$0.862530\pi$
$824$	3.94081	+	25.3761i	0.137284	+	0.884017i
$825$	−17.3215	+	19.2627i	−0.603058	+	0.670642i
$826$	−16.7703	+	6.83436i	−0.583514	+	0.237798i
$827$			53.9732i			1.87683i	0.345507	+	0.938416i	$0.387707\pi$
$827$			53.9732i			1.87683i	−0.345507	+	0.938416i	$0.612293\pi$
$828$	32.9605	+	29.4803i	1.14546	+	1.02451i
$829$	36.2547			1.25918			0.629590	−	0.776928i	$-0.283223\pi$
$829$	36.2547			1.25918			0.629590	+	0.776928i	$0.283223\pi$
$830$	0.600433	−	5.60430i	0.0208413	−	0.194528i
$831$	−49.6536	+	5.35257i	−1.72246	+	0.185679i
$832$	−9.42354	−	29.6088i	−0.326703	−	1.02650i
$833$	40.6558	−	6.04673i	1.40864	−	0.209507i
$834$	7.85815	+	3.00151i	0.272106	+	0.103934i
$835$	−16.5506	+	6.33410i	−0.572759	+	0.219200i
$836$	0.888614	+	1.22825i	0.0307333	+	0.0424801i
$837$	4.43589	+	13.2899i	0.153327	+	0.459367i
$838$	−5.92318	+	11.5961i	−0.204613	+	0.400580i
$839$	23.0566			0.796004			0.398002	−	0.917385i	$-0.369704\pi$
$839$	23.0566			0.796004			0.398002	+	0.917385i	$0.369704\pi$
$840$	−28.8791	−	2.44937i	−0.996423	−	0.0845114i
$841$	−14.9681			−0.516142
$842$	−3.74321	+	7.32826i	−0.129000	+	0.252548i
$843$	−2.94910	−	27.3576i	−0.101573	−	0.942245i
$844$	−30.5740	+	22.1196i	−1.05240	+	0.761388i
$845$	−1.66697	−	4.35570i	−0.0573455	−	0.149841i
$846$	9.74006	−	36.9893i	0.334870	−	1.27172i
$847$	4.11196	+	3.54562i	0.141289	+	0.121829i
$848$	−4.82283	−	1.58849i	−0.165617	−	0.0545489i
$849$	5.96580	+	55.3422i	0.204746	+	1.89934i
$850$	−10.6252	−	40.1378i	−0.364441	−	1.37672i
$851$	−49.7029			−1.70379
$852$	19.6413	−	17.7084i	0.672899	−	0.606679i
$853$			15.8822i			0.543795i	0.962326	+	0.271898i	$0.0876512\pi$
$853$			15.8822i			0.543795i	−0.962326	+	0.271898i	$0.912349\pi$
$854$	9.11693	+	22.3714i	0.311975	+	0.765532i
$855$	0.931967	+	1.42162i	0.0318726	+	0.0486182i
$856$	−39.1177	+	6.07484i	−1.33702	+	0.207634i
$857$		−	13.4521i		−	0.459515i	−0.973248	−	0.229757i	$-0.926207\pi$
$857$		−	13.4521i		−	0.459515i	0.973248	−	0.229757i	$-0.0737933\pi$
$858$	10.1546	−	26.5855i	0.346674	−	0.907615i
$859$	56.7046			1.93474			0.967369	−	0.253373i	$-0.0815399\pi$
$859$	56.7046			1.93474			0.967369	+	0.253373i	$0.0815399\pi$
$860$	−25.3063	+	38.7122i	−0.862938	+	1.32008i
$861$	7.68732	+	5.30661i	0.261983	+	0.180849i
$862$	−19.2171	+	37.6221i	−0.654536	+	1.28142i
$863$	29.1364			0.991815			0.495908	−	0.868375i	$-0.334835\pi$
$863$	29.1364			0.991815			0.495908	+	0.868375i	$0.334835\pi$
$864$	13.2667	−	26.2296i	0.451344	−	0.892350i
$865$	−17.1535	−	44.8211i	−0.583235	−	1.52396i
$866$	−3.48032	−	1.77772i	−0.118266	−	0.0604093i
$867$	−30.0997	+	3.24470i	−1.02224	+	0.110196i
$868$	14.2159	+	1.21507i	0.482520	+	0.0412422i
$869$	−10.2162			−0.346562
$870$	−0.0133973	−	20.5172i	−0.000454209	−	0.695599i
$871$		−	5.59033i		−	0.189421i
$872$	−32.9588	+	5.11838i	−1.11613	+	0.173330i
$873$	31.8714	−	6.95216i	1.07868	−	0.235295i
$874$	−2.35211	−	1.20144i	−0.0795614	−	0.0406393i
$875$	11.1082	+	27.4155i	0.375526	+	0.926812i
$876$	−34.1937	−	37.9260i	−1.15530	−	1.28140i
$877$	3.83638			0.129545			0.0647726	−	0.997900i	$-0.479368\pi$
$877$	3.83638			0.129545			0.0647726	+	0.997900i	$0.479368\pi$
$878$	−23.5365	+	46.0786i	−0.794320	+	1.55508i
$879$	40.0775	−	4.32029i	1.35178	−	0.145720i
$880$	−26.7250	+	1.26597i	−0.900899	+	0.0426758i
$881$	−14.7572			−0.497183			−0.248591	−	0.968608i	$-0.579968\pi$
$881$	−14.7572			−0.497183			−0.248591	+	0.968608i	$0.579968\pi$
$882$	3.25520	−	29.5195i	0.109608	−	0.993975i
$883$	17.1334			0.576586			0.288293	−	0.957542i	$-0.406912\pi$
$883$	17.1334			0.576586			0.288293	+	0.957542i	$0.406912\pi$
$884$	26.7365	+	36.9555i	0.899244	+	1.24295i
$885$	−16.6878	+	8.53775i	−0.560956	+	0.286993i
$886$	−9.39384	+	18.3907i	−0.315592	+	0.617849i
$887$		−	46.8206i		−	1.57208i	−0.618174	−	0.786042i	$-0.712127\pi$
$887$		−	46.8206i		−	1.57208i	0.618174	−	0.786042i	$-0.287873\pi$
$888$	8.53964	+	31.9151i	0.286572	+	1.07100i
$889$	3.17010	−	3.67646i	0.106322	−	0.123304i
$890$	3.68340	−	34.3800i	0.123468	−	1.15242i
$891$	24.4761	−	11.2115i	0.819979	−	0.375598i
$892$	−2.50541	−	3.46302i	−0.0838874	−	0.115950i
$893$			2.28458i			0.0764505i
$894$	29.7219	+	11.3526i	0.994048	+	0.379688i
$895$	12.2838	+	32.0968i	0.410601	+	1.07288i
$896$	−19.1713	−	22.9883i	−0.640469	−	0.767984i
$897$	5.31401	+	49.2959i	0.177430	+	1.64594i
$898$	−13.9850	+	27.3791i	−0.466686	+	0.913652i
$899$			10.1003i			0.336865i
$900$	−30.0000	+	0.0391785i	−0.999999	+	0.00130595i
$901$	7.45388			0.248325
$902$	7.67923	+	3.92249i	0.255690	+	0.130605i
$903$	−39.0018	−	26.9232i	−1.29790	−	0.895948i
$904$	3.75378	+	24.1717i	0.124849	+	0.803939i
$905$	−1.56859	−	4.09864i	−0.0521417	−	0.136243i
$906$	−7.92438	−	3.02681i	−0.263270	−	0.100559i
$907$	28.6735			0.952087			0.476043	−	0.879422i	$-0.342071\pi$
$907$	28.6735			0.952087			0.476043	+	0.879422i	$0.342071\pi$
$908$	−1.93701	−	2.67736i	−0.0642819	−	0.0888513i
$909$	−2.81135	−	12.8883i	−0.0932467	−	0.427479i
$910$	−22.2098	−	23.7218i	−0.736248	−	0.786371i
$911$		−	1.90619i		−	0.0631550i	−0.999501	−	0.0315775i	$-0.989947\pi$
$911$		−	1.90619i		−	0.0631550i	0.999501	−	0.0315775i	$-0.0100531\pi$
$912$	−0.367339	+	1.71676i	−0.0121638	+	0.0568475i
$913$	5.33162			0.176451
$914$	0.452708	−	0.886287i	0.0149742	−	0.0293158i
$915$	11.3892	+	22.2613i	0.376516	+	0.735937i
$916$	−27.2512	−	37.6671i	−0.900407	−	1.24455i
$917$	−13.3853	+	15.5234i	−0.442022	+	0.512626i
$918$	−6.45209	+	42.6641i	−0.212951	+	1.40812i
$919$	−19.4420			−0.641334			−0.320667	−	0.947192i	$-0.603907\pi$
$919$	−19.4420			−0.641334			−0.320667	+	0.947192i	$0.603907\pi$
$920$	40.4613	−	23.1439i	1.33397	−	0.763033i
$921$	−3.13555	−	29.0872i	−0.103320	−	0.958457i
$922$	−17.1446	+	33.5648i	−0.564627	+	1.10540i
$923$	29.6514			0.975986
$924$	−0.606340	−	27.4090i	−0.0199471	−	0.901688i
$925$	25.1035	−	22.5120i	0.825399	−	0.740190i
$926$	25.2415	−	49.4165i	0.829489	−	1.62393i
$927$	−26.6122	+	5.80497i	−0.874060	+	0.190660i
$928$	15.0587	−	14.9082i	0.494328	−	0.489386i
$929$	−30.4309			−0.998407			−0.499203	−	0.866485i	$-0.666374\pi$
$929$	−30.4309			−0.998407			−0.499203	+	0.866485i	$0.666374\pi$
$930$	14.7685	−	0.00964350i	0.484280	−	0.000316223i
$931$	0.260948	+	1.75451i	0.00855222	+	0.0575018i
$932$	−19.2491	−	26.6064i	−0.630525	−	0.871521i
$933$	−19.4007	+	2.09136i	−0.635150	+	0.0684681i
$934$	−26.4912	−	13.5315i	−0.866820	−	0.442764i
$935$	36.6808	−	14.0381i	1.19959	−	0.459096i
$936$	30.7407	−	11.8819i	1.00479	−	0.388373i
$937$	47.3032			1.54533			0.772664	−	0.634815i	$-0.218924\pi$
$937$	47.3032			1.54533			0.772664	+	0.634815i	$0.218924\pi$
$938$	−2.03241	−	4.98718i	−0.0663605	−	0.162837i
$939$	−19.3783	+	2.08895i	−0.632388	+	0.0681704i
$940$	−33.7482	−	22.0613i	−1.10074	−	0.719560i
$941$			9.65922i			0.314881i	0.987528	+	0.157441i	$0.0503243\pi$
$941$			9.65922i			0.314881i	−0.987528	+	0.157441i	$0.949676\pi$
$942$	−14.2340	+	37.2654i	−0.463767	+	1.21417i
$943$	−15.0232			−0.489221
$944$	−18.3881	−	6.05646i	−0.598481	−	0.197121i
$945$	0.734961	−	30.7321i	0.0239083	−	0.999714i
$946$	−38.9608	−	19.9008i	−1.26672	−	0.647032i
$947$			8.12123i			0.263905i	0.991256	+	0.131952i	$0.0421246\pi$
$947$			8.12123i			0.263905i	−0.991256	+	0.131952i	$0.957875\pi$
$948$	−7.92225	−	8.78698i	−0.257303	−	0.285388i
$949$		−	57.2549i		−	1.85857i
$950$	1.73216	−	0.458533i	0.0561985	−	0.0148768i
$951$	−3.04101	−	28.2102i	−0.0986115	−	0.914778i
$952$	37.2873	+	23.2480i	1.20849	+	0.753473i
$953$	−20.6108			−0.667651			−0.333825	−	0.942635i	$-0.608340\pi$
$953$	−20.6108			−0.667651			−0.333825	+	0.942635i	$0.608340\pi$
$954$	1.37142	−	5.20817i	0.0444014	−	0.168621i
$955$	33.2856	−	12.7387i	1.07710	−	0.412215i
$956$	−42.6719	+	30.8721i	−1.38011	+	0.998476i
$957$	19.2961	−	2.08008i	0.623753	−	0.0672396i
$958$	49.9755	+	25.5271i	1.61464	+	0.824743i
$959$	25.0705	+	21.6175i	0.809567	+	0.698066i
$960$	−21.8129	−	22.0044i	−0.704010	−	0.710190i
$961$	23.7297			0.765473
$962$	−16.8502	+	32.9885i	−0.543273	+	1.06359i
$963$	−8.94848	−	41.0233i	−0.288361	−	1.32196i
$964$	−19.0894	+	13.8107i	−0.614827	+	0.444813i
$965$	49.6985	−	19.0201i	1.59985	−	0.612280i
$966$	22.6626	+	42.0453i	0.729156	+	1.35278i
$967$		−	21.1743i		−	0.680920i	−0.940259	−	0.340460i	$-0.889417\pi$
$967$		−	21.1743i		−	0.680920i	0.940259	−	0.340460i	$-0.110583\pi$
$968$	0.890724	+	5.73565i	0.0286290	+	0.184351i
$969$	−0.276216	−	2.56234i	−0.00887333	−	0.0823142i
$970$	3.66301	−	34.1897i	0.117612	−	1.09777i
$971$		−	21.3754i		−	0.685970i	−0.939341	−	0.342985i	$-0.888562\pi$
$971$		−	21.3754i		−	0.685970i	0.939341	−	0.342985i	$-0.111438\pi$
$972$	28.6231	+	12.3579i	0.918087	+	0.396378i
$973$	6.88104	+	5.93331i	0.220596	+	0.190213i
$974$	−17.5559	+	34.3700i	−0.562527	+	1.10128i
$975$	−25.0116	−	22.4911i	−0.801012	−	0.720291i
$976$	−8.07922	+	24.5294i	−0.258610	+	0.785168i
$977$	21.9942			0.703657			0.351829	−	0.936064i	$-0.385560\pi$
$977$	21.9942			0.703657			0.351829	+	0.936064i	$0.385560\pi$
$978$	21.8074	+	8.32958i	0.697323	+	0.266350i
$979$	32.7072			1.04533
$980$	−28.4378	−	13.0879i	−0.908412	−	0.418077i
$981$	−7.53958	−	34.5644i	−0.240720	−	1.10356i
$982$	−38.8383	−	19.8383i	−1.23938	−	0.633065i
$983$		−	1.36406i		−	0.0435066i	−0.999763	−	0.0217533i	$-0.993075\pi$
$983$		−	1.36406i		−	0.0435066i	0.999763	−	0.0217533i	$-0.00692484\pi$
$984$	2.58119	+	9.64663i	0.0822852	+	0.307523i
$985$	−46.3895	+	17.7537i	−1.47809	+	0.565681i
$986$	−14.1498	+	27.7018i	−0.450622	+	0.882203i
$987$	23.4709	−	34.0006i	0.747086	−	1.08225i
$988$	−1.59482	+	1.15382i	−0.0507380	+	0.0367078i
$989$	76.2203			2.42367
$990$	−3.05989	−	28.2124i	−0.0972498	−	0.896650i
$991$	−11.1590			−0.354477			−0.177238	−	0.984168i	$-0.556716\pi$
$991$	−11.1590			−0.354477			−0.177238	+	0.984168i	$0.556716\pi$
$992$	10.7311	+	10.8395i	0.340713	+	0.344153i
$993$	3.78862	+	35.1454i	0.120228	+	1.11531i
$994$	26.4522	−	10.7800i	0.839013	−	0.341920i
$995$	12.7070	−	4.86309i	0.402838	−	0.154170i
$996$	4.13444	+	4.58572i	0.131005	+	0.145304i
$997$			18.8707i			0.597642i	0.954309	+	0.298821i	$0.0965934\pi$
$997$			18.8707i			0.597642i	−0.954309	+	0.298821i	$0.903407\pi$
$998$	8.96527	−	17.5517i	0.283791	−	0.555590i
$999$	−33.2392	+	11.0945i	−1.05164	+	0.351016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.u.e.629.19	yes	160
3.2	odd	2	inner	840.2.u.e.629.141	yes	160
5.4	even	2	inner	840.2.u.e.629.142	yes	160
7.6	odd	2	inner	840.2.u.e.629.18	yes	160
8.5	even	2	inner	840.2.u.e.629.22	yes	160
15.14	odd	2	inner	840.2.u.e.629.20	yes	160
21.20	even	2	inner	840.2.u.e.629.144	yes	160
24.5	odd	2	inner	840.2.u.e.629.140	yes	160
35.34	odd	2	inner	840.2.u.e.629.143	yes	160
40.29	even	2	inner	840.2.u.e.629.139	yes	160
56.13	odd	2	inner	840.2.u.e.629.23	yes	160
105.104	even	2	inner	840.2.u.e.629.17	✓	160
120.29	odd	2	inner	840.2.u.e.629.21	yes	160
168.125	even	2	inner	840.2.u.e.629.137	yes	160
280.69	odd	2	inner	840.2.u.e.629.138	yes	160
840.629	even	2	inner	840.2.u.e.629.24	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.u.e.629.17	✓	160	105.104	even	2	inner
840.2.u.e.629.18	yes	160	7.6	odd	2	inner
840.2.u.e.629.19	yes	160	1.1	even	1	trivial
840.2.u.e.629.20	yes	160	15.14	odd	2	inner
840.2.u.e.629.21	yes	160	120.29	odd	2	inner
840.2.u.e.629.22	yes	160	8.5	even	2	inner
840.2.u.e.629.23	yes	160	56.13	odd	2	inner
840.2.u.e.629.24	yes	160	840.629	even	2	inner
840.2.u.e.629.137	yes	160	168.125	even	2	inner
840.2.u.e.629.138	yes	160	280.69	odd	2	inner
840.2.u.e.629.139	yes	160	40.29	even	2	inner
840.2.u.e.629.140	yes	160	24.5	odd	2	inner
840.2.u.e.629.141	yes	160	3.2	odd	2	inner
840.2.u.e.629.142	yes	160	5.4	even	2	inner
840.2.u.e.629.143	yes	160	35.34	odd	2	inner
840.2.u.e.629.144	yes	160	21.20	even	2	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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.u (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25943 - 0.643305i) q^{2} +(1.72207 - 0.185637i) q^{3} +(1.17232 + 1.62039i) q^{4} +(0.799234 + 2.08835i) q^{5} +(-2.28825 - 0.874023i) q^{6} +(-2.00372 - 1.72775i) q^{7} +(-0.434041 - 2.79493i) q^{8} +(2.93108 - 0.639360i) q^{9} +(0.336872 - 3.14428i) q^{10} +2.99129 q^{11} +(2.31962 + 2.57281i) q^{12} +3.88403i q^{13} +(1.41207 + 3.46498i) q^{14} +(1.76402 + 3.44793i) q^{15} +(-1.25135 + 3.79923i) q^{16} -5.87186i q^{17} +(-4.10279 - 1.08035i) q^{18} +0.253401 q^{19} +(-2.44700 + 3.74329i) q^{20} +(-3.77129 - 2.60334i) q^{21} +(-3.76732 - 1.92431i) q^{22} +7.37014 q^{23} +(-1.26629 - 4.73249i) q^{24} +(-3.72245 + 3.33817i) q^{25} +(2.49862 - 4.89166i) q^{26} +(4.92884 - 1.64514i) q^{27} +(0.450635 - 5.27228i) q^{28} +3.74592 q^{29} +(-0.00357650 - 5.47722i) q^{30} +2.69635i q^{31} +(4.02004 - 3.97986i) q^{32} +(5.15123 - 0.555294i) q^{33} +(-3.77740 + 7.39519i) q^{34} +(2.00671 - 5.56535i) q^{35} +(4.47217 + 3.99997i) q^{36} -6.74382 q^{37} +(-0.319141 - 0.163014i) q^{38} +(0.721019 + 6.68859i) q^{39} +(5.48989 - 3.14023i) q^{40} -2.03838 q^{41} +(3.07492 + 5.70481i) q^{42} +10.3418 q^{43} +(3.50674 + 4.84707i) q^{44} +(3.67783 + 5.61013i) q^{45} +(-9.28216 - 4.74125i) q^{46} +9.01566i q^{47} +(-1.44963 + 6.77485i) q^{48} +(1.02978 + 6.92384i) q^{49} +(6.83562 - 1.80951i) q^{50} +(-1.09003 - 10.1118i) q^{51} +(-6.29366 + 4.55332i) q^{52} +1.26942i q^{53} +(-7.26585 - 1.09881i) q^{54} +(2.39074 + 6.24688i) q^{55} +(-3.95923 + 6.35016i) q^{56} +(0.436376 - 0.0470406i) q^{57} +(-4.71771 - 2.40977i) q^{58} +4.83995i q^{59} +(-3.51902 + 6.90047i) q^{60} +6.45642 q^{61} +(1.73458 - 3.39586i) q^{62} +(-6.97771 - 3.78306i) q^{63} +(-7.62322 + 2.42623i) q^{64} +(-8.11124 + 3.10425i) q^{65} +(-6.84482 - 2.61446i) q^{66} -1.43931 q^{67} +(9.51472 - 6.88368i) q^{68} +(12.6919 - 1.36817i) q^{69} +(-6.10752 + 5.71823i) q^{70} -7.63417i q^{71} +(-3.05917 - 7.91464i) q^{72} -14.7411 q^{73} +(8.49335 + 4.33833i) q^{74} +(-5.79065 + 6.43960i) q^{75} +(0.297067 + 0.410610i) q^{76} +(-5.99371 - 5.16820i) q^{77} +(3.39473 - 8.88763i) q^{78} -3.41532 q^{79} +(-8.93425 + 0.423218i) q^{80} +(8.18244 - 3.74803i) q^{81} +(2.56719 + 1.31130i) q^{82} +1.78238 q^{83} +(-0.202702 - 9.16291i) q^{84} +(12.2625 - 4.69299i) q^{85} +(-13.0247 - 6.65292i) q^{86} +(6.45074 - 0.695380i) q^{87} +(-1.29835 - 8.36044i) q^{88} +10.9341 q^{89} +(-1.02293 - 9.43152i) q^{90} +(6.71063 - 7.78251i) q^{91} +(8.64014 + 11.9425i) q^{92} +(0.500542 + 4.64332i) q^{93} +(5.79982 - 11.3546i) q^{94} +(0.202527 + 0.529192i) q^{95} +(6.18400 - 7.59987i) q^{96} +10.8736 q^{97} +(3.15721 - 9.38254i) q^{98} +(8.76771 - 1.91251i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 24 q^{4} - 32 q^{9} - 48 q^{15} - 104 q^{16} - 16 q^{25} - 32 q^{30} + 48 q^{36} - 64 q^{39} - 64 q^{46} + 144 q^{49} + 16 q^{60} - 72 q^{64} + 8 q^{70} - 96 q^{79} + 16 q^{81} - 72 q^{84}+O(q^{100}) \) 160 * q - 24 * q^4 - 32 * q^9 - 48 * q^15 - 104 * q^16 - 16 * q^25 - 32 * q^30 + 48 * q^36 - 64 * q^39 - 64 * q^46 + 144 * q^49 + 16 * q^60 - 72 * q^64 + 8 * q^70 - 96 * q^79 + 16 * q^81 - 72 * q^84

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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