LMFDB - Embedded newform 840.2.dc.e.557.78

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(53,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.53"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 6, 6, 9, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.dc (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [704,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$704$
Relative dimension:	$176$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.78
Character	$\chi$	$=$	840.557
Dual form			840.2.dc.e.653.78

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.291371 - 1.38387i) q^{2} +(1.55945 - 0.753731i) q^{3} +(-1.83021 + 0.806441i) q^{4} +(1.66009 - 1.49804i) q^{5} +(-1.49745 - 1.93847i) q^{6} +(-1.00857 + 2.44598i) q^{7} +(1.64928 + 2.29780i) q^{8} +(1.86378 - 2.35082i) q^{9} +(-2.55679 - 1.86086i) q^{10} +(2.73976 - 4.74540i) q^{11} +(-2.24628 + 2.63709i) q^{12} +(-3.67085 - 3.67085i) q^{13} +(3.67878 + 0.683040i) q^{14} +(1.45971 - 3.58737i) q^{15} +(2.69930 - 2.95191i) q^{16} +(1.75160 + 6.53708i) q^{17} +(-3.79628 - 1.89427i) q^{18} +(0.772962 + 1.33881i) q^{19} +(-1.83022 + 4.08048i) q^{20} +(0.270799 + 4.57457i) q^{21} +(-7.36532 - 2.40880i) q^{22} +(0.540699 - 2.01792i) q^{23} +(4.30390 + 2.34019i) q^{24} +(0.511778 - 4.97374i) q^{25} +(-4.01041 + 6.14957i) q^{26} +(1.13459 - 5.07077i) q^{27} +(-0.126652 - 5.28999i) q^{28} -8.14119i q^{29} +(-5.38978 - 0.974792i) q^{30} +(-1.83447 + 3.17740i) q^{31} +(-4.87156 - 2.87539i) q^{32} +(0.695762 - 9.46526i) q^{33} +(8.53611 - 4.32871i) q^{34} +(1.98985 + 5.57140i) q^{35} +(-1.51530 + 5.80550i) q^{36} +(2.67633 + 0.717120i) q^{37} +(1.62752 - 1.45977i) q^{38} +(-8.49135 - 2.95768i) q^{39} +(6.18013 + 1.34386i) q^{40} -5.71150i q^{41} +(6.25171 - 1.70765i) q^{42} +(1.79304 + 1.79304i) q^{43} +(-1.18743 + 10.8945i) q^{44} +(-0.427572 - 6.69456i) q^{45} +(-2.95008 - 0.160296i) q^{46} +(1.86342 + 0.499301i) q^{47} +(1.98449 - 6.63791i) q^{48} +(-4.96559 - 4.93386i) q^{49} +(-7.03214 + 0.740969i) q^{50} +(7.65874 + 8.87402i) q^{51} +(9.67873 + 3.75808i) q^{52} +(0.433517 + 1.61791i) q^{53} +(-7.34789 - 0.0926470i) q^{54} +(-2.56054 - 11.9820i) q^{55} +(-7.28376 + 1.71662i) q^{56} +(2.21450 + 1.50520i) q^{57} +(-11.2664 + 2.37211i) q^{58} +(0.390662 + 0.225549i) q^{59} +(0.221440 + 7.74280i) q^{60} +(-10.7886 + 6.22883i) q^{61} +(4.93162 + 1.61287i) q^{62} +(3.87029 + 6.92971i) q^{63} +(-2.55974 + 7.57943i) q^{64} +(-11.5930 - 0.594866i) q^{65} +(-13.3014 + 1.79506i) q^{66} +(2.47229 + 9.22673i) q^{67} +(-8.47757 - 10.5516i) q^{68} +(-0.677773 - 3.55438i) q^{69} +(7.13032 - 4.37705i) q^{70} +3.18021i q^{71} +(8.47559 + 0.405427i) q^{72} +(2.12875 + 7.94460i) q^{73} +(0.212597 - 3.91265i) q^{74} +(-2.95077 - 8.14205i) q^{75} +(-2.49435 - 1.82695i) q^{76} +(8.84390 + 11.4874i) q^{77} +(-1.61891 + 12.6127i) q^{78} +(-3.04609 + 1.75866i) q^{79} +(0.0590185 - 8.94408i) q^{80} +(-2.05267 - 8.76279i) q^{81} +(-7.90399 + 1.66417i) q^{82} +(4.86400 - 4.86400i) q^{83} +(-4.18474 - 8.15402i) q^{84} +(12.7006 + 8.22815i) q^{85} +(1.95890 - 3.00378i) q^{86} +(-6.13627 - 12.6958i) q^{87} +(15.4226 - 1.53109i) q^{88} +(0.630636 + 1.09229i) q^{89} +(-9.13984 + 2.54231i) q^{90} +(12.6811 - 5.27651i) q^{91} +(0.637741 + 4.12924i) q^{92} +(-0.465864 + 6.33769i) q^{93} +(0.148023 - 2.72421i) q^{94} +(3.28877 + 1.06462i) q^{95} +(-9.76424 - 0.812184i) q^{96} +(4.49246 + 4.49246i) q^{97} +(-5.38100 + 8.30932i) q^{98} +(-6.04926 - 15.2850i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 704 q - 16 q^{6} - 24 q^{7} + 12 q^{10} + 10 q^{12} + 32 q^{15} - 72 q^{16} + 6 q^{18} + 64 q^{22} - 8 q^{25} + 24 q^{28} + 8 q^{30} - 16 q^{31} + 44 q^{33} - 240 q^{36} + 16 q^{40} - 78 q^{42} - 8 q^{46}+ \cdots - 80 q^{97}+O(q^{100}) $ 704 * q - 16 * q^6 - 24 * q^7 + 12 * q^10 + 10 * q^12 + 32 * q^15 - 72 * q^16 + 6 * q^18 + 64 * q^22 - 8 * q^25 + 24 * q^28 + 8 * q^30 - 16 * q^31 + 44 * q^33 - 240 * q^36 + 16 * q^40 - 78 * q^42 - 8 * q^46 - 20 * q^48 - 60 * q^52 + 272 * q^55 + 8 * q^57 - 20 * q^58 - 14 * q^60 + 12 * q^63 - 84 * q^66 + 112 * q^70 - 38 * q^72 + 104 * q^73 - 64 * q^76 - 16 * q^78 - 168 * q^81 - 72 * q^82 - 64 * q^87 + 52 * q^88 - 44 * q^90 + 40 * q^96 - 80 * q^97

Character values

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

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−0.291371	−	1.38387i	−0.206031	−	0.978546i
$2$	−0.291371	−	1.38387i	−0.206031	−	0.978546i
$3$	1.55945	−	0.753731i	0.900350	−	0.435167i
$3$	1.55945	−	0.753731i	0.900350	−	0.435167i
$4$	−1.83021	+	0.806441i	−0.915103	+	0.403221i
$5$	1.66009	−	1.49804i	0.742414	−	0.669942i
$5$	1.66009	−	1.49804i	0.742414	−	0.669942i
$6$	−1.49745	−	1.93847i	−0.611330	−	0.791375i
$7$	−1.00857	+	2.44598i	−0.381202	+	0.924492i
$7$	−1.00857	+	2.44598i	−0.381202	+	0.924492i
$8$	1.64928	+	2.29780i	0.583109	+	0.812394i
$9$	1.86378	−	2.35082i	0.621259	−	0.783605i
$10$	−2.55679	−	1.86086i	−0.808529	−	0.588457i
$11$	2.73976	−	4.74540i	0.826068	−	1.43079i	−0.0750319	−	0.997181i	$-0.523906\pi$
$11$	2.73976	−	4.74540i	0.826068	−	1.43079i	0.901100	−	0.433611i	$-0.142761\pi$
$12$	−2.24628	+	2.63709i	−0.648444	+	0.761262i
$13$	−3.67085	−	3.67085i	−1.01811	−	1.01811i	−0.999833	−	0.0182775i	$-0.994182\pi$
$13$	−3.67085	−	3.67085i	−1.01811	−	1.01811i	−0.0182775	−	0.999833i	$-0.505818\pi$
$14$	3.67878	+	0.683040i	0.983197	+	0.182550i
$15$	1.45971	−	3.58737i	0.376895	−	0.926256i
$16$	2.69930	−	2.95191i	0.674826	−	0.737977i
$17$	1.75160	+	6.53708i	0.424827	+	1.58547i	0.764301	+	0.644859i	$0.223084\pi$
$17$	1.75160	+	6.53708i	0.424827	+	1.58547i	−0.339475	+	0.940615i	$0.610249\pi$
$18$	−3.79628	−	1.89427i	−0.894792	−	0.446484i
$19$	0.772962	+	1.33881i	0.177330	+	0.307144i	0.940965	−	0.338504i	$-0.109921\pi$
$19$	0.772962	+	1.33881i	0.177330	+	0.307144i	−0.763635	+	0.645648i	$0.776587\pi$
$20$	−1.83022	+	4.08048i	−0.409250	+	0.912422i
$21$	0.270799	+	4.57457i	0.0590931	+	0.998252i
$22$	−7.36532	−	2.40880i	−1.57029	−	0.513558i
$23$	0.540699	−	2.01792i	0.112744	−	0.420765i	−0.886365	−	0.462988i	$-0.846777\pi$
$23$	0.540699	−	2.01792i	0.112744	−	0.420765i	0.999108	+	0.0422232i	$0.0134440\pi$
$24$	4.30390	+	2.34019i	0.878529	+	0.477689i
$25$	0.511778	−	4.97374i	0.102356	−	0.994748i
$26$	−4.01041	+	6.14957i	−0.786506	+	1.20603i
$27$	1.13459	−	5.07077i	0.218351	−	0.975870i
$28$	−0.126652	−	5.28999i	−0.0239350	−	0.999714i
$29$		−	8.14119i		−	1.51178i	−0.654698	−	0.755891i	$-0.727204\pi$
$29$		−	8.14119i		−	1.51178i	0.654698	−	0.755891i	$-0.272796\pi$
$30$	−5.38978	−	0.974792i	−0.984036	−	0.177972i
$31$	−1.83447	+	3.17740i	−0.329481	+	0.570677i	−0.982409	−	0.186743i	$-0.940207\pi$
$31$	−1.83447	+	3.17740i	−0.329481	+	0.570677i	0.652928	+	0.757420i	$0.273540\pi$
$32$	−4.87156	−	2.87539i	−0.861179	−	0.508302i
$33$	0.695762	−	9.46526i	0.121117	−	1.64769i
$34$	8.53611	−	4.32871i	1.46393	−	0.742368i
$35$	1.98985	+	5.57140i	0.336346	+	0.941738i
$36$	−1.51530	+	5.80550i	−0.252550	+	0.967584i
$37$	2.67633	+	0.717120i	0.439986	+	0.117894i	0.472010	−	0.881593i	$-0.343529\pi$
$37$	2.67633	+	0.717120i	0.439986	+	0.117894i	−0.0320240	+	0.999487i	$0.510195\pi$
$38$	1.62752	−	1.45977i	0.264019	−	0.236806i
$39$	−8.49135	−	2.95768i	−1.35970	−	0.473607i
$40$	6.18013	+	1.34386i	0.977165	+	0.212483i
$41$		−	5.71150i		−	0.891987i	−0.895036	−	0.445994i	$-0.852850\pi$
$41$		−	5.71150i		−	0.891987i	0.895036	−	0.445994i	$-0.147150\pi$
$42$	6.25171	−	1.70765i	0.964661	−	0.263496i
$43$	1.79304	+	1.79304i	0.273436	+	0.273436i	0.830482	−	0.557046i	$-0.188065\pi$
$43$	1.79304	+	1.79304i	0.273436	+	0.273436i	−0.557046	+	0.830482i	$0.688065\pi$
$44$	−1.18743	+	10.8945i	−0.179012	+	1.64241i
$45$	−0.427572	−	6.69456i	−0.0637387	−	0.997967i
$46$	−2.95008	−	0.160296i	−0.434966	−	0.0236343i
$47$	1.86342	+	0.499301i	0.271807	+	0.0728306i	0.392148	−	0.919902i	$-0.371732\pi$
$47$	1.86342	+	0.499301i	0.271807	+	0.0728306i	−0.120341	+	0.992733i	$0.538399\pi$
$48$	1.98449	−	6.63791i	0.286436	−	0.958099i
$49$	−4.96559	−	4.93386i	−0.709370	−	0.704837i
$50$	−7.03214	+	0.740969i	−0.994494	+	0.104789i
$51$	7.65874	+	8.87402i	1.07244	+	1.24261i
$52$	9.67873	+	3.75808i	1.34220	+	0.521152i
$53$	0.433517	+	1.61791i	0.0595482	+	0.222237i	0.989287	−	0.145982i	$-0.0466343\pi$
$53$	0.433517	+	1.61791i	0.0595482	+	0.222237i	−0.929739	+	0.368219i	$0.879968\pi$
$54$	−7.34789	−	0.0926470i	−0.999921	−	0.0126077i
$55$	−2.56054	−	11.9820i	−0.345263	−	1.61566i
$56$	−7.28376	+	1.71662i	−0.973334	+	0.229393i
$57$	2.21450	+	1.50520i	0.293318	+	0.199369i
$58$	−11.2664	+	2.37211i	−1.47935	+	0.311473i
$59$	0.390662	+	0.225549i	0.0508599	+	0.0293640i	0.525214	−	0.850970i	$-0.323985\pi$
$59$	0.390662	+	0.225549i	0.0508599	+	0.0293640i	−0.474354	+	0.880334i	$0.657318\pi$
$60$	0.221440	+	7.74280i	0.0285878	+	0.999591i
$61$	−10.7886	+	6.22883i	−1.38134	+	0.797520i	−0.992319	−	0.123707i	$-0.960522\pi$
$61$	−10.7886	+	6.22883i	−1.38134	+	0.797520i	−0.389026	+	0.921227i	$0.627188\pi$
$62$	4.93162	+	1.61287i	0.626317	+	0.204835i
$63$	3.87029	+	6.92971i	0.487611	+	0.873061i
$64$	−2.55974	+	7.57943i	−0.319968	+	0.947428i
$65$	−11.5930	−	0.594866i	−1.43793	−	0.0737841i
$66$	−13.3014	+	1.79506i	−1.63729	+	0.220957i
$67$	2.47229	+	9.22673i	0.302039	+	1.12722i	0.935465	+	0.353421i	$0.114982\pi$
$67$	2.47229	+	9.22673i	0.302039	+	1.12722i	−0.633426	+	0.773804i	$0.718352\pi$
$68$	−8.47757	−	10.5516i	−1.02806	−	1.27957i
$69$	−0.677773	−	3.55438i	−0.0815943	−	0.427898i
$70$	7.13032	−	4.37705i	0.852236	−	0.523157i
$71$			3.18021i			0.377422i	0.982033	+	0.188711i	$0.0604309\pi$
$71$			3.18021i			0.377422i	−0.982033	+	0.188711i	$0.939569\pi$
$72$	8.47559	+	0.405427i	0.998858	+	0.0477800i
$73$	2.12875	+	7.94460i	0.249151	+	0.929845i	0.971251	+	0.238057i	$0.0765103\pi$
$73$	2.12875	+	7.94460i	0.249151	+	0.929845i	−0.722100	+	0.691789i	$0.756823\pi$
$74$	0.212597	−	3.91265i	0.0247139	−	0.454836i
$75$	−2.95077	−	8.14205i	−0.340726	−	0.940163i
$76$	−2.49435	−	1.82695i	−0.286122	−	0.209565i
$77$	8.84390	+	11.4874i	1.00786	+	1.30911i
$78$	−1.61891	+	12.6127i	−0.183306	+	1.42811i
$79$	−3.04609	+	1.75866i	−0.342712	+	0.197865i	−0.661471	−	0.749971i	$-0.730067\pi$
$79$	−3.04609	+	1.75866i	−0.342712	+	0.197865i	0.318759	+	0.947836i	$0.396734\pi$
$80$	0.0590185	−	8.94408i	0.00659847	−	0.999978i
$81$	−2.05267	−	8.76279i	−0.228074	−	0.973644i
$82$	−7.90399	+	1.66417i	−0.872850	+	0.183777i
$83$	4.86400	−	4.86400i	0.533893	−	0.533893i	−0.387836	−	0.921729i	$-0.626777\pi$
$83$	4.86400	−	4.86400i	0.533893	−	0.533893i	0.921729	+	0.387836i	$0.126777\pi$
$84$	−4.18474	−	8.15402i	−0.456592	−	0.889676i
$85$	12.7006	+	8.22815i	1.37757	+	0.892468i
$86$	1.95890	−	3.00378i	0.211234	−	0.323906i
$87$	−6.13627	−	12.6958i	−0.657878	−	1.36113i
$88$	15.4226	−	1.53109i	1.64405	−	0.163215i
$89$	0.630636	+	1.09229i	0.0668473	+	0.115783i	0.897512	−	0.440990i	$-0.145373\pi$
$89$	0.630636	+	1.09229i	0.0668473	+	0.115783i	−0.830665	+	0.556773i	$0.812039\pi$
$90$	−9.13984	+	2.54231i	−0.963424	+	0.267983i
$91$	12.6811	−	5.27651i	1.32934	−	0.553129i
$92$	0.637741	+	4.12924i	0.0664891	+	0.430503i
$93$	−0.465864	+	6.33769i	−0.0483079	+	0.657188i
$94$	0.148023	−	2.72421i	0.0152674	−	0.280981i
$95$	3.28877	+	1.06462i	0.337420	+	0.109227i
$96$	−9.76424	−	0.812184i	−0.996558	−	0.0828932i
$97$	4.49246	+	4.49246i	0.456140	+	0.456140i	0.897386	−	0.441246i	$-0.145463\pi$
$97$	4.49246	+	4.49246i	0.456140	+	0.456140i	−0.441246	+	0.897386i	$0.645463\pi$
$98$	−5.38100	+	8.30932i	−0.543563	+	0.839369i
$99$	−6.04926	−	15.2850i	−0.607974	−	1.53620i
$100$	3.07437	+	9.51568i	0.307437	+	0.951568i
$101$	−5.37072	+	9.30236i	−0.534407	+	0.925620i	0.464785	+	0.885423i	$0.346132\pi$
$101$	−5.37072	+	9.30236i	−0.534407	+	0.925620i	−0.999192	+	0.0401960i	$0.987202\pi$
$102$	10.0490	−	13.1844i	0.994996	−	1.30545i
$103$	15.3742	+	4.11951i	1.51487	+	0.405907i	0.918048	−	0.396469i	$-0.129765\pi$
$103$	15.3742	+	4.11951i	1.51487	+	0.405907i	0.596818	+	0.802376i	$0.296431\pi$
$104$	2.38060	−	14.4891i	0.233437	−	1.42078i
$105$	7.30241	+	7.18851i	0.712643	+	0.701527i
$106$	2.11267	−	1.07135i	0.205200	−	0.104058i
$107$	0.288524	−	1.07679i	0.0278927	−	0.104097i	−0.950576	−	0.310492i	$-0.899506\pi$
$107$	0.288524	−	1.07679i	0.0278927	−	0.104097i	0.978469	+	0.206395i	$0.0661730\pi$
$108$	2.01275	+	10.1955i	0.193677	+	0.981065i
$109$	−5.51362	+	9.54988i	−0.528109	+	0.914712i	0.471354	+	0.881944i	$0.343766\pi$
$109$	−5.51362	+	9.54988i	−0.528109	+	0.914712i	−0.999463	+	0.0327679i	$0.989568\pi$
$110$	−15.8355	+	7.03468i	−1.50986	+	0.670731i
$111$	4.71412	−	0.898920i	0.447445	−	0.0853217i
$112$	4.49786	+	9.57963i	0.425008	+	0.905190i
$113$	−8.85232	−	8.85232i	−0.832756	−	0.832756i	0.155137	−	0.987893i	$-0.450418\pi$
$113$	−8.85232	−	8.85232i	−0.832756	−	0.832756i	−0.987893	+	0.155137i	$0.950418\pi$
$114$	1.43777	−	3.50316i	0.134659	−	0.328101i
$115$	−2.12530	−	4.15990i	−0.198186	−	0.387913i
$116$	6.56539	+	14.9001i	0.609582	+	1.38344i
$117$	−15.4711	+	1.78784i	−1.43031	+	0.165286i
$118$	0.198303	−	0.606345i	0.0182553	−	0.0558186i
$119$	−17.7561	−	2.30869i	−1.62770	−	0.211638i
$120$	10.6505	−	2.56247i	0.972256	−	0.233921i
$121$	−9.51255	−	16.4762i	−0.864778	−	1.49784i
$122$	11.7634	+	13.1152i	1.06501	+	1.18739i
$123$	−4.30494	−	8.90681i	−0.388163	−	0.803100i
$124$	0.795074	−	7.29468i	0.0713998	−	0.655082i
$125$	−6.60124	−	9.02350i	−0.590433	−	0.807087i
$126$	8.46214	−	7.37511i	0.753867	−	0.657027i
$127$	7.40465	+	7.40465i	0.657056	+	0.657056i	0.954682	−	0.297626i	$-0.0961950\pi$
$127$	7.40465	+	7.40465i	0.657056	+	0.657056i	−0.297626	+	0.954682i	$0.596195\pi$
$128$	11.2348	+	1.33393i	0.993025	+	0.117904i
$129$	4.14763	+	1.44469i	0.365179	+	0.127198i
$130$	2.55465	+	16.2165i	0.224057	+	1.42229i
$131$	8.04871	+	13.9408i	0.703219	+	1.21801i	0.967330	+	0.253519i	$0.0815882\pi$
$131$	8.04871	+	13.9408i	0.703219	+	1.21801i	−0.264111	+	0.964492i	$0.585079\pi$
$132$	6.35979	+	17.8845i	0.553549	+	1.55664i
$133$	−4.05428	+	0.540368i	−0.351550	+	0.0468558i
$134$	12.0483	−	6.10974i	1.04081	−	0.527801i
$135$	−5.71268	−	10.1176i	−0.491669	−	0.870782i
$136$	−12.1320	+	14.8063i	−1.04031	+	1.26963i
$137$	1.26541	+	4.72256i	0.108111	+	0.403476i	0.998680	−	0.0513733i	$-0.0163598\pi$
$137$	1.26541	+	4.72256i	0.108111	+	0.403476i	−0.890568	+	0.454849i	$0.849693\pi$
$138$	−4.72133	+	1.97360i	−0.401906	+	0.168004i
$139$	9.05937			0.768405			0.384203	−	0.923249i	$-0.374476\pi$
$139$	9.05937			0.768405			0.384203	+	0.923249i	$0.374476\pi$
$140$	−8.13484	−	8.59211i	−0.687520	−	0.726166i
$141$	3.28225	−	0.625881i	0.276415	−	0.0527087i
$142$	4.40101	−	0.926623i	0.369325	−	0.0777605i
$143$	−27.4769	+	7.36241i	−2.29773	+	0.615676i
$144$	−1.90848	−	11.8473i	−0.159040	−	0.987272i
$145$	−12.1958	−	13.5151i	−1.01281	−	1.12237i
$146$	10.3741	−	5.26075i	0.858563	−	0.435382i
$147$	−11.4624	−	3.95139i	−0.945403	−	0.325905i
$148$	−5.47655	+	0.845825i	−0.450170	+	0.0695264i
$149$	3.93460	−	2.27164i	0.322335	−	0.186100i	−0.330098	−	0.943947i	$-0.607082\pi$
$149$	3.93460	−	2.27164i	0.322335	−	0.186100i	0.652433	+	0.757847i	$0.273749\pi$
$150$	−10.4078	+	6.45585i	−0.849792	+	0.527118i
$151$	0.00805115	−	0.0139450i	0.000655194	−	0.00113483i	−0.865698	−	0.500567i	$-0.833125\pi$
$151$	0.00805115	−	0.0139450i	0.000655194	−	0.00113483i	0.866353	+	0.499432i	$0.166458\pi$
$152$	−1.80148	+	3.98418i	−0.146119	+	0.323160i
$153$	18.6321	+	8.06596i	1.50631	+	0.652094i
$154$	13.3203	−	15.5859i	1.07338	−	1.25595i
$155$	1.71447	+	8.02285i	0.137710	+	0.644411i
$156$	17.9261	−	1.43462i	1.43524	−	0.114861i
$157$	−1.97547	−	7.37254i	−0.157659	−	0.588393i	−0.998863	−	0.0476741i	$-0.984819\pi$
$157$	−1.97547	−	7.37254i	−0.157659	−	0.588393i	0.841204	−	0.540718i	$-0.181848\pi$
$158$	3.32131	+	3.70298i	0.264229	+	0.294593i
$159$	1.89552	+	2.19629i	0.150324	+	0.174178i
$160$	−12.3947	+	2.52437i	−0.979884	+	0.199569i
$161$	4.39044	+	3.35774i	0.346015	+	0.264627i
$162$	−11.5285	+	5.39385i	−0.905765	+	0.423781i
$163$	4.41943	−	16.4935i	0.346156	−	1.29187i	−0.545099	−	0.838372i	$-0.683508\pi$
$163$	4.41943	−	16.4935i	0.346156	−	1.29187i	0.891255	−	0.453502i	$-0.149825\pi$
$164$	4.60599	+	10.4532i	0.359668	+	0.816260i
$165$	−13.0243	−	16.7554i	−1.01394	−	1.30441i
$166$	−8.14838	−	5.31392i	−0.632437	−	0.412440i
$167$	−2.89921	+	2.89921i	−0.224347	+	0.224347i	−0.810326	−	0.585979i	$-0.800710\pi$
$167$	−2.89921	+	2.89921i	−0.224347	+	0.224347i	0.585979	+	0.810326i	$0.300710\pi$
$168$	−10.0648	+	8.16699i	−0.776517	+	0.630097i
$169$			13.9503i			1.07310i
$170$	7.68612	−	19.9734i	0.589499	−	1.53189i
$171$	4.58792	+	0.678152i	0.350847	+	0.0518596i
$172$	−4.72762	−	1.83565i	−0.360477	−	0.139967i
$173$	−7.32975	−	1.96400i	−0.557271	−	0.149320i	−0.0308185	−	0.999525i	$-0.509811\pi$
$173$	−7.32975	−	1.96400i	−0.557271	−	0.149320i	−0.526452	+	0.850205i	$0.676478\pi$
$174$	−15.7814	+	12.1910i	−1.19639	+	0.924198i
$175$	11.6495	+	6.26814i	0.880618	+	0.473827i
$176$	−6.61254	−	20.8968i	−0.498439	−	1.57516i
$177$	0.779222	+	0.0572782i	0.0585699	+	0.00430529i
$178$	1.32785	−	1.19098i	0.0995263	−	0.0892680i
$179$	3.61023	+	2.08437i	0.269842	+	0.155793i	0.628816	−	0.777554i	$-0.283540\pi$
$179$	3.61023	+	2.08437i	0.269842	+	0.155793i	−0.358974	+	0.933348i	$0.616873\pi$
$180$	6.18132	+	11.9076i	0.460728	+	0.887541i
$181$		−	8.63873i		−	0.642112i	−0.947060	−	0.321056i	$-0.895962\pi$
$181$		−	8.63873i		−	0.642112i	0.947060	−	0.321056i	$-0.104038\pi$
$182$	−10.9969	−	16.0116i	−0.815147	−	1.18686i
$183$	−12.1295	+	17.8453i	−0.896639	+	1.31916i
$184$	5.52853	−	2.08569i	0.407568	−	0.153759i
$185$	5.51721	−	2.81876i	0.405634	−	0.207239i
$186$	8.90630	−	1.20193i	0.653041	−	0.0881294i
$187$	35.8200	+	9.59795i	2.61942	+	0.701871i
$188$	−3.81309	+	0.588913i	−0.278099	+	0.0429509i
$189$	11.2587	+	7.88938i	0.818948	+	0.573868i
$190$	0.515039	−	4.86143i	0.0373649	−	0.352685i
$191$	−2.23198	+	1.28864i	−0.161501	+	0.0932424i	−0.578572	−	0.815631i	$-0.696390\pi$
$191$	−2.23198	+	1.28864i	−0.161501	+	0.0932424i	0.417071	+	0.908874i	$0.363057\pi$
$192$	1.72106	+	13.7491i	0.124207	+	0.992256i
$193$	5.53320	+	20.6502i	0.398288	+	1.48643i	0.816107	+	0.577901i	$0.196128\pi$
$193$	5.53320	+	20.6502i	0.398288	+	1.48643i	−0.417819	+	0.908530i	$0.637205\pi$
$194$	4.90802	−	7.52597i	0.352375	−	0.540333i
$195$	−18.5271	+	7.81034i	−1.32675	+	0.559310i
$196$	13.0669	+	5.02551i	0.933351	+	0.358965i
$197$	4.75973	+	4.75973i	0.339117	+	0.339117i	0.856035	−	0.516918i	$-0.172921\pi$
$197$	4.75973	+	4.75973i	0.339117	+	0.339117i	−0.516918	+	0.856035i	$0.672921\pi$
$198$	−19.3900	+	12.8250i	−1.37798	+	0.911435i
$199$	22.3123	+	12.8820i	1.58168	+	0.913181i	0.994615	+	0.103638i	$0.0330483\pi$
$199$	22.3123	+	12.8820i	1.58168	+	0.913181i	0.587061	+	0.809543i	$0.300285\pi$
$200$	12.2727	−	7.02713i	0.867812	−	0.496893i
$201$	10.8099	+	12.5252i	0.762471	+	0.883459i
$202$	14.4382	+	4.72195i	1.01586	+	0.332235i
$203$	19.9132	+	8.21093i	1.39763	+	0.576294i
$204$	−21.1734	−	10.0649i	−1.48244	−	0.704687i
$205$	−8.55604	−	9.48159i	−0.597580	−	0.662223i
$206$	1.22127	−	22.4763i	0.0850898	−	1.56599i
$207$	−3.73601	−	5.03203i	−0.259670	−	0.349750i
$208$	−20.7447	+	0.927265i	−1.43839	+	0.0642943i
$209$	8.47092			0.585945
$210$	7.82027	−	12.2001i	0.539650	−	0.841889i
$211$			14.4275i			0.993229i	0.867971	+	0.496614i	$0.165424\pi$
$211$			14.4275i			0.993229i	−0.867971	+	0.496614i	$0.834576\pi$
$212$	−2.09817	−	2.61150i	−0.144103	−	0.179359i
$213$	2.39703	+	4.95939i	0.164242	+	0.339812i
$214$	−1.57420	−	0.0855359i	−0.107610	−	0.00584711i
$215$	5.66264	+	0.290565i	0.386189	+	0.0198164i
$216$	13.5229	−	5.75608i	0.920114	−	0.391651i
$217$	−5.92165	−	7.69168i	−0.401987	−	0.522145i
$218$	14.8223	+	4.84759i	1.00389	+	0.328320i
$219$	9.30778	+	10.7847i	0.628961	+	0.728763i
$220$	14.3491	+	19.8647i	0.967418	+	1.33928i
$221$	17.5668	−	30.4265i	1.18167	−	2.04671i
$222$	−2.61755	−	6.26182i	−0.175678	−	0.420266i
$223$	5.06769	−	5.06769i	0.339357	−	0.339357i	−0.516768	−	0.856125i	$-0.672865\pi$
$223$	5.06769	−	5.06769i	0.339357	−	0.339357i	0.856125	+	0.516768i	$0.172865\pi$
$224$	11.9464	−	9.01570i	0.798204	−	0.602387i
$225$	−10.7385	−	10.4730i	−0.715900	−	0.698203i
$226$	−9.67117	+	14.8298i	−0.643317	+	0.986463i
$227$	17.6358	−	4.72549i	1.17053	−	0.313641i	0.379364	−	0.925248i	$-0.376143\pi$
$227$	17.6358	−	4.72549i	1.17053	−	0.313641i	0.791162	+	0.611606i	$0.209476\pi$
$228$	−5.26685	−	0.968966i	−0.348805	−	0.0641713i
$229$	−5.06473	−	8.77237i	−0.334687	−	0.579694i	0.648738	−	0.761012i	$-0.275297\pi$
$229$	−5.06473	−	8.77237i	−0.334687	−	0.579694i	−0.983425	+	0.181317i	$0.941964\pi$
$230$	−5.13752	+	4.15322i	−0.338758	+	0.273856i
$231$	22.4501	+	11.2482i	1.47711	+	0.740075i
$232$	18.7068	−	13.4271i	1.22816	−	0.881533i
$233$	−2.40052	+	8.95886i	−0.157263	+	0.586914i	0.841638	+	0.540043i	$0.181592\pi$
$233$	−2.40052	+	8.95886i	−0.157263	+	0.586914i	−0.998901	+	0.0468718i	$0.985075\pi$
$234$	6.98199	+	20.8892i	0.456427	+	1.36557i
$235$	3.84141	−	1.96258i	0.250586	−	0.128025i
$236$	−0.896884	−	0.0977547i	−0.0583822	−	0.00636329i
$237$	−3.42467	+	5.03849i	−0.222457	+	0.327285i
$238$	1.97869	+	25.2449i	0.128260	+	1.63638i
$239$	2.44161			0.157935			0.0789673	−	0.996877i	$-0.474838\pi$
$239$	2.44161			0.157935			0.0789673	+	0.996877i	$0.474838\pi$
$240$	−6.64940	−	13.9923i	−0.429217	−	0.903202i
$241$	−0.114989	+	0.199167i	−0.00740711	+	0.0128295i	−0.869705	−	0.493572i	$-0.835691\pi$
$241$	−0.114989	+	0.199167i	−0.00740711	+	0.0128295i	0.862298	+	0.506401i	$0.169024\pi$
$242$	−20.0293	+	17.9649i	−1.28753	+	1.15482i
$243$	−9.80583	−	12.1180i	−0.629044	−	0.777370i
$244$	14.7223	−	20.1004i	0.942496	−	1.28680i
$245$	−15.6344	−	0.752001i	−0.998845	−	0.0480436i
$246$	−11.0716	+	8.55268i	−0.705897	+	0.545299i
$247$	2.07714	−	7.75199i	0.132165	−	0.493248i
$248$	−10.3266	+	1.02518i	−0.655738	+	0.0650989i
$249$	3.91902	−	11.2513i	0.248358	−	0.713023i
$250$	−10.5640	+	11.7645i	−0.668124	+	0.744050i
$251$	−17.8393			−1.12600			−0.563002	−	0.826455i	$-0.690354\pi$
$251$	−17.8393			−1.12600			−0.563002	+	0.826455i	$0.690354\pi$
$252$	−12.6718	−	9.56162i	−0.798250	−	0.602326i
$253$	−8.09444	−	8.09444i	−0.508893	−	0.508893i
$254$	8.08958	−	12.4046i	0.507586	−	0.778333i
$255$	26.0078	+	3.25857i	1.62867	+	0.204059i
$256$	−1.42751	−	15.9362i	−0.0892194	−	0.996012i
$257$	0.888805	+	0.238155i	0.0554421	+	0.0148557i	0.286434	−	0.958100i	$-0.407530\pi$
$257$	0.888805	+	0.238155i	0.0554421	+	0.0148557i	−0.230991	+	0.972956i	$0.574197\pi$
$258$	0.790764	−	6.16074i	0.0492308	−	0.383551i
$259$	−4.45331	+	5.82297i	−0.276715	+	0.361822i
$260$	21.6973	−	8.26034i	1.34561	−	0.512285i
$261$	−19.1384	−	15.1734i	−1.18464	−	0.939208i
$262$	16.9471	−	15.2003i	1.04700	−	0.939080i
$263$	3.18489	−	0.853389i	0.196389	−	0.0526222i	−0.159284	−	0.987233i	$-0.550919\pi$
$263$	3.18489	−	0.853389i	0.196389	−	0.0526222i	0.355673	+	0.934611i	$0.384252\pi$
$264$	22.8968	−	14.0122i	1.40920	−	0.862389i
$265$	3.14336	+	2.03645i	0.193095	+	0.125098i
$266$	1.92910	+	5.45315i	0.118281	+	0.334354i
$267$	1.80674	+	1.22805i	0.110571	+	0.0751554i
$268$	−11.9656	−	14.8930i	−0.730917	−	0.909738i
$269$	9.35731	+	5.40245i	0.570525	+	0.329393i	0.757359	−	0.652999i	$-0.226489\pi$
$269$	9.35731	+	5.40245i	0.570525	+	0.329393i	−0.186834	+	0.982392i	$0.559823\pi$
$270$	−12.3369	+	10.8536i	−0.750801	+	0.660529i
$271$	−0.680464	−	1.17860i	−0.0413353	−	0.0715948i	0.844618	−	0.535370i	$-0.179828\pi$
$271$	−0.680464	−	1.17860i	−0.0413353	−	0.0715948i	−0.885953	+	0.463775i	$0.846495\pi$
$272$	24.0250	+	12.4750i	1.45673	+	0.756407i
$273$	15.7985	−	17.7866i	0.956168	−	1.07649i
$274$	6.16672	−	3.12718i	0.372545	−	0.188920i
$275$	−22.2002	−	16.0554i	−1.33872	−	0.968179i
$276$	4.10687	+	5.95867i	0.247204	+	0.358670i
$277$	2.24243	+	8.36888i	0.134735	+	0.502837i	0.999999	+	0.00152071i	$0.000484058\pi$
$277$	2.24243	+	8.36888i	0.134735	+	0.502837i	−0.865264	+	0.501316i	$0.832849\pi$
$278$	−2.63964	−	12.5370i	−0.158315	−	0.751920i
$279$	4.05043	+	10.2345i	0.242493	+	0.612721i
$280$	−9.52012	+	13.7611i	−0.568936	+	0.822382i
$281$		−	29.2366i		−	1.74411i	−0.489406	−	0.872056i	$-0.662787\pi$
$281$		−	29.2366i		−	1.74411i	0.489406	−	0.872056i	$-0.337213\pi$
$282$	−1.82249	−	4.35985i	−0.108528	−	0.259625i
$283$	13.7576	−	3.68633i	0.817803	−	0.219130i	0.174417	−	0.984672i	$-0.444196\pi$
$283$	13.7576	−	3.68633i	0.817803	−	0.219130i	0.643386	+	0.765542i	$0.277529\pi$
$284$	−2.56466	−	5.82045i	−0.152184	−	0.345380i
$285$	5.93111	−	0.818632i	0.351329	−	0.0484916i
$286$	18.1946	+	35.8793i	1.07587	+	2.12159i
$287$	13.9702	+	5.76043i	0.824635	+	0.340027i
$288$	−15.8390	+	6.09305i	−0.933324	+	0.359037i
$289$	−24.9428	+	14.4008i	−1.46723	+	0.847103i
$290$	−15.1497	+	20.8153i	−0.889618	+	1.22232i
$291$	10.3919	+	3.61967i	0.609183	+	0.212189i
$292$	−10.3029	−	12.8235i	−0.602932	−	0.750441i
$293$	−21.1885	+	21.1885i	−1.23785	+	1.23785i	−0.276967	+	0.960880i	$0.589329\pi$
$293$	−21.1885	+	21.1885i	−1.23785	+	1.23785i	−0.960880	+	0.276967i	$0.910671\pi$
$294$	−2.12840	+	17.0138i	−0.124131	+	0.992266i
$295$	0.986414	−	0.210795i	0.0574312	−	0.0122730i
$296$	2.76622	+	7.33240i	0.160783	+	0.426187i
$297$	−20.9543	−	19.2768i	−1.21589	−	1.11855i
$298$	−4.29009	−	4.78309i	−0.248518	−	0.277077i
$299$	−9.39229	+	5.42264i	−0.543170	+	0.313599i
$300$	11.9666	+	12.5220i	0.690892	+	0.722958i
$301$	−6.19414	+	2.57733i	−0.357024	+	0.148555i
$302$	−0.0216440	−	0.00707859i	−0.00124547	−	0.000407327i
$303$	−1.36390	+	18.5547i	−0.0783538	+	1.06594i
$304$	6.03850	+	1.33214i	0.346332	+	0.0764036i
$305$	−8.57908	+	26.5022i	−0.491237	+	1.51751i
$306$	5.73341	−	28.1346i	0.327757	−	1.60835i
$307$	−12.2590	+	12.2590i	−0.699658	+	0.699658i	−0.964337	−	0.264679i	$-0.914734\pi$
$307$	−12.2590	+	12.2590i	−0.699658	+	0.699658i	0.264679	+	0.964337i	$0.414734\pi$
$308$	−25.4501	−	13.8923i	−1.45015	−	0.791586i
$309$	27.0803	−	5.16386i	1.54055	−	0.293762i
$310$	10.6031	−	4.71024i	0.602213	−	0.267524i
$311$	22.2027	+	12.8187i	1.25900	+	0.726884i	0.972880	−	0.231309i	$-0.0743010\pi$
$311$	22.2027	+	12.8187i	1.25900	+	0.726884i	0.286120	+	0.958194i	$0.407634\pi$
$312$	−7.20848	−	24.3894i	−0.408100	−	1.38078i
$313$	−8.51951	−	2.28280i	−0.481551	−	0.129031i	0.00987365	−	0.999951i	$-0.496857\pi$
$313$	−8.51951	−	2.28280i	−0.481551	−	0.129031i	−0.491425	+	0.870920i	$0.663524\pi$
$314$	−9.62706	+	4.88194i	−0.543286	+	0.275504i
$315$	16.8060	+	5.70608i	0.946909	+	0.321501i
$316$	4.15672	−	5.67521i	0.233834	−	0.319255i
$317$	−1.51147	+	5.64088i	−0.0848926	+	0.316824i	−0.995294	−	0.0969030i	$-0.969106\pi$
$317$	−1.51147	+	5.64088i	−0.0848926	+	0.316824i	0.910401	+	0.413726i	$0.135773\pi$
$318$	2.48709	−	3.26309i	0.139469	−	0.182985i
$319$	−38.6332	−	22.3049i	−2.16305	−	1.24883i
$320$	7.10486	+	16.4171i	0.397174	+	0.917743i
$321$	−0.361669	−	1.89667i	−0.0201864	−	0.105862i
$322$	3.36743	−	7.05416i	0.187660	−	0.393113i
$323$	−7.39798	+	7.39798i	−0.411634	+	0.411634i
$324$	10.8235	+	14.3824i	0.601304	+	0.799020i
$325$	−20.1365	+	16.3792i	−1.11697	+	0.908554i
$326$	−24.1126	−	1.31018i	−1.33548	−	0.0725643i
$327$	−1.40019	+	19.0484i	−0.0774305	+	1.05338i
$328$	13.1239	−	9.41988i	0.724645	−	0.520126i
$329$	−3.10066	+	4.05430i	−0.170945	+	0.223521i
$330$	−19.3925	+	22.9060i	−1.06752	+	1.26093i
$331$	−26.7273	+	15.4310i	−1.46907	+	0.848166i	−0.999399	−	0.0346774i	$-0.988960\pi$
$331$	−26.7273	+	15.4310i	−1.46907	+	0.848166i	−0.469668	+	0.882843i	$0.655626\pi$
$332$	−4.97958	+	12.8246i	−0.273290	+	0.703843i
$333$	6.67390	−	4.95500i	0.365728	−	0.271533i
$334$	4.85688	+	3.16739i	0.265756	+	0.173312i
$335$	17.9262	+	11.6136i	0.979412	+	0.634518i
$336$	14.2347	+	11.5488i	0.776565	+	0.630038i
$337$	−18.5879	−	18.5879i	−1.01255	−	1.01255i	−0.999920	−	0.0126258i	$-0.995981\pi$
$337$	−18.5879	−	18.5879i	−1.01255	−	1.01255i	−0.0126258	−	0.999920i	$-0.504019\pi$
$338$	19.3054	−	4.06471i	1.05008	−	0.221091i
$339$	−20.4770	−	7.13249i	−1.11216	−	0.387384i
$340$	−29.8802	−	4.81693i	−1.62048	−	0.261234i
$341$	10.0520	+	17.4106i	0.544347	+	0.942836i
$342$	−0.398313	−	6.54669i	−0.0215383	−	0.354005i
$343$	17.0762	−	7.16959i	0.922029	−	0.387121i
$344$	−1.16282	+	7.07727i	−0.0626948	+	0.381581i
$345$	−6.44976	−	4.88526i	−0.347243	−	0.263013i
$346$	−0.582247	+	10.7157i	−0.0313018	+	0.576079i
$347$	−19.1920	+	5.14248i	−1.03028	+	0.276063i	−0.734080	−	0.679063i	$-0.762386\pi$
$347$	−19.1920	+	5.14248i	−1.03028	+	0.276063i	−0.296200	+	0.955126i	$0.595720\pi$
$348$	21.4691	+	18.2874i	1.15086	+	0.980306i
$349$	17.4885			0.936139			0.468070	−	0.883692i	$-0.344950\pi$
$349$	17.4885			0.936139			0.468070	+	0.883692i	$0.344950\pi$
$350$	5.27998	−	17.9478i	0.282227	−	0.959348i
$351$	−22.7789	+	14.4491i	−1.21585	+	0.771238i
$352$	−26.9918	+	15.2396i	−1.43867	+	0.812275i
$353$	9.83224	−	2.63454i	0.523317	−	0.140222i	0.0125166	−	0.999922i	$-0.496016\pi$
$353$	9.83224	−	2.63454i	0.523317	−	0.140222i	0.510801	+	0.859699i	$0.329349\pi$
$354$	−0.147777	−	1.09503i	−0.00785427	−	0.0582004i
$355$	4.76407	+	5.27943i	0.252851	+	0.280203i
$356$	−2.03507	−	1.49055i	−0.107858	−	0.0789991i
$357$	−29.4300	+	9.78307i	−1.55760	+	0.517775i
$358$	1.83258	−	5.60343i	0.0968550	−	0.296150i
$359$	−4.80594	−	8.32413i	−0.253648	−	0.439331i	0.710880	−	0.703314i	$-0.248297\pi$
$359$	−4.80594	−	8.32413i	−0.253648	−	0.439331i	−0.964527	+	0.263983i	$0.914964\pi$
$360$	14.6776	−	12.0237i	0.773575	−	0.633704i
$361$	8.30506	−	14.3848i	0.437108	−	0.757094i
$362$	−11.9549	+	2.51708i	−0.628336	+	0.132295i
$363$	−27.2530	−	18.5240i	−1.43041	−	0.972256i
$364$	−18.9538	+	19.8837i	−0.993450	+	1.04219i
$365$	15.4352	+	9.99979i	0.807916	+	0.523413i
$366$	28.2298	+	11.5861i	1.47560	+	0.605614i
$367$	−19.5163	+	5.22938i	−1.01874	+	0.272971i	−0.729278	−	0.684217i	$-0.760144\pi$
$367$	−19.5163	+	5.22938i	−1.01874	+	0.272971i	−0.289465	+	0.957189i	$0.593477\pi$
$368$	−4.49719	−	7.04306i	−0.234432	−	0.367145i
$369$	−13.4267	−	10.6450i	−0.698966	−	0.554155i
$370$	−5.50835	−	6.81381i	−0.286366	−	0.354233i
$371$	−4.39460	−	0.571396i	−0.228156	−	0.0296654i
$372$	−4.25835	−	11.9750i	−0.220785	−	0.620873i
$373$	1.17948	−	4.40190i	0.0610714	−	0.227922i	−0.928644	−	0.370972i	$-0.879025\pi$
$373$	1.17948	−	4.40190i	0.0610714	−	0.227922i	0.989715	+	0.143051i	$0.0456912\pi$
$374$	2.84541	−	52.3669i	0.147132	−	2.70783i
$375$	−17.0956	−	9.09615i	−0.882814	−	0.469723i
$376$	1.92601	+	5.10524i	0.0993262	+	0.263283i
$377$	−29.8851	+	29.8851i	−1.53916	+	1.53916i
$378$	7.63744	−	17.8793i	0.392828	−	0.919612i
$379$	−22.9103			−1.17682			−0.588412	−	0.808561i	$-0.700247\pi$
$379$	−22.9103			−1.17682			−0.588412	+	0.808561i	$0.700247\pi$
$380$	−6.87767	+	0.703734i	−0.352817	+	0.0361008i
$381$	17.1283	+	5.96607i	0.877509	+	0.305651i
$382$	2.43364	+	2.71331i	0.124516	+	0.138825i
$383$	−3.59567	+	13.4192i	−0.183730	+	0.685691i	0.811168	+	0.584813i	$0.198832\pi$
$383$	−3.59567	+	13.4192i	−0.183730	+	0.685691i	−0.994899	+	0.100878i	$0.967835\pi$
$384$	18.5255	−	6.38782i	0.945378	−	0.325977i
$385$	31.8902	+	5.82165i	1.62528	+	0.296699i
$386$	26.9650	−	13.6741i	1.37248	−	0.695993i
$387$	7.55694	−	0.873279i	0.384141	−	0.0443913i
$388$	−11.8450	−	4.59922i	−0.601340	−	0.233490i
$389$	−2.93129	−	1.69238i	−0.148623	−	0.0858073i	0.423845	−	0.905735i	$-0.360680\pi$
$389$	−2.93129	−	1.69238i	−0.148623	−	0.0858073i	−0.572467	+	0.819928i	$0.694014\pi$
$390$	16.2068	+	23.3634i	0.820662	+	1.18305i
$391$	14.1384			0.715008
$392$	3.14735	−	19.5472i	0.158965	−	0.987284i
$393$	23.0592	+	15.6734i	1.16318	+	0.790619i
$394$	5.20001	−	7.97371i	0.261973	−	0.401710i
$395$	−2.42224	+	7.48269i	−0.121876	+	0.376495i
$396$	23.3979	+	23.0964i	1.17579	+	1.16064i
$397$	−3.94644	−	1.05745i	−0.198066	−	0.0530717i	0.158422	−	0.987371i	$-0.449359\pi$
$397$	−3.94644	−	1.05745i	−0.198066	−	0.0530717i	−0.356488	+	0.934300i	$0.616026\pi$
$398$	11.3259	−	34.6308i	0.567715	−	1.73588i
$399$	−5.91516	+	3.89851i	−0.296128	+	0.195170i
$400$	−13.3006	−	14.9364i	−0.665029	−	0.746818i
$401$	−18.3584	+	10.5993i	−0.916777	+	0.529302i	−0.882605	−	0.470114i	$-0.844213\pi$
$401$	−18.3584	+	10.5993i	−0.916777	+	0.529302i	−0.0341717	+	0.999416i	$0.510879\pi$
$402$	14.1836	−	18.6090i	0.707412	−	0.928133i
$403$	18.3978	−	4.92968i	0.916460	−	0.245565i
$404$	2.32771	−	21.3564i	0.115808	−	1.06252i
$405$	−16.5346	−	11.4720i	−0.821610	−	0.570050i
$406$	5.56076	−	29.9497i	0.275976	−	1.48638i
$407$	10.7355	−	10.7355i	0.532140	−	0.532140i
$408$	−7.75926	+	32.2340i	−0.384141	+	1.59582i
$409$	−4.25488	−	2.45656i	−0.210390	−	0.121469i	0.391103	−	0.920347i	$-0.372094\pi$
$409$	−4.25488	−	2.45656i	−0.210390	−	0.121469i	−0.601493	+	0.798878i	$0.705427\pi$
$410$	−10.6283	+	14.6031i	−0.524896	+	0.721197i
$411$	5.53289	+	6.41083i	0.272917	+	0.316223i
$412$	−31.4601	+	4.85886i	−1.54993	+	0.239379i
$413$	−0.945696	+	0.728069i	−0.0465346	+	0.0358259i
$414$	−5.87512	+	6.63634i	−0.288747	+	0.326159i
$415$	0.788217	−	15.3611i	0.0386921	−	0.754046i
$416$	7.32764	+	28.4379i	0.359267	+	1.39428i
$417$	14.1276	−	6.82833i	0.691834	−	0.334385i
$418$	−2.46818	−	11.7227i	−0.120723	−	0.573374i
$419$			0.742605i			0.0362786i	0.999835	+	0.0181393i	$0.00577424\pi$
$419$			0.742605i			0.0362786i	−0.999835	+	0.0181393i	$0.994226\pi$
$420$	−19.1620	−	7.26749i	−0.935012	−	0.354617i
$421$		−	36.7020i		−	1.78874i	−0.447323	−	0.894372i	$-0.647623\pi$
$421$		−	36.7020i		−	1.78874i	0.447323	−	0.894372i	$-0.352377\pi$
$422$	19.9658	−	4.20375i	0.971919	−	0.204635i
$423$	4.64676	−	3.44996i	0.225933	−	0.167743i
$424$	−3.00263	+	3.66452i	−0.145821	+	0.177965i
$425$	33.4102	−	5.36649i	1.62063	−	0.260313i
$426$	6.16474	−	4.76220i	0.298683	−	0.230730i
$427$	−4.35449	−	32.6709i	−0.210729	−	1.58106i
$428$	0.340307	+	2.20342i	0.0164494	+	0.106506i
$429$	−37.2996	+	32.1915i	−1.80084	+	1.55422i
$430$	−1.24783	−	7.92104i	−0.0601756	−	0.381986i
$431$	−22.0811	−	12.7485i	−1.06361	−	0.614076i	−0.137182	−	0.990546i	$-0.543805\pi$
$431$	−22.0811	−	12.7485i	−1.06361	−	0.614076i	−0.926429	+	0.376470i	$0.877138\pi$
$432$	−11.9058	−	17.0367i	−0.572820	−	0.819681i
$433$	−16.3796	+	16.3796i	−0.787152	+	0.787152i	−0.981026	−	0.193874i	$-0.937895\pi$
$433$	−16.3796	+	16.3796i	−0.787152	+	0.787152i	0.193874	+	0.981026i	$0.437895\pi$
$434$	−8.91891	+	10.4359i	−0.428121	+	0.500941i
$435$	−29.2055	−	11.8838i	−1.40030	−	0.569783i
$436$	2.38965	−	21.9247i	0.114443	−	1.05000i
$437$	3.11954	−	0.835879i	0.149228	−	0.0399855i
$438$	12.2126	−	16.0231i	0.583543	−	0.765615i
$439$	7.49620	−	4.32793i	0.357774	−	0.206561i	−0.310330	−	0.950629i	$-0.600439\pi$
$439$	7.49620	−	4.32793i	0.357774	−	0.206561i	0.668104	+	0.744068i	$0.267106\pi$
$440$	23.3092	−	25.6454i	1.11122	−	1.22259i
$441$	−20.8533	+	2.47757i	−0.993016	+	0.117980i
$442$	−47.2248	−	15.4447i	−2.24626	−	0.734631i
$443$	−0.550244	−	0.147437i	−0.0261429	−	0.00700497i	0.245724	−	0.969340i	$-0.420974\pi$
$443$	−0.550244	−	0.147437i	−0.0261429	−	0.00700497i	−0.271867	+	0.962335i	$0.587641\pi$
$444$	−7.90289	+	5.44687i	−0.375054	+	0.258497i
$445$	2.68321	+	0.868588i	0.127196	+	0.0411750i
$446$	−8.48961	−	5.53645i	−0.401995	−	0.262159i
$447$	4.42360	−	6.50814i	0.209229	−	0.307824i
$448$	−15.9574	−	13.9054i	−0.753917	−	0.656969i
$449$	26.7279			1.26137			0.630684	−	0.776040i	$-0.282774\pi$
$449$	26.7279			1.26137			0.630684	+	0.776040i	$0.282774\pi$
$450$	−11.3645	+	17.9123i	−0.535726	+	0.844392i
$451$	−27.1034	−	15.6481i	−1.27625	−	0.736842i
$452$	23.3404	+	9.06269i	1.09784	+	0.426273i
$453$	0.00204459	−	0.0278150i	9.60633e−5	−	0.00130686i
$454$	−11.6780	−	23.0288i	−0.548077	−	1.08079i
$455$	13.1473	−	27.7562i	0.616356	−	1.30123i
$456$	0.193683	+	7.57097i	0.00907003	+	0.354543i
$457$	−8.78509	+	32.7864i	−0.410949	+	1.53368i	0.381865	+	0.924218i	$0.375282\pi$
$457$	−8.78509	+	32.7864i	−0.410949	+	1.53368i	−0.792814	+	0.609464i	$0.791385\pi$
$458$	−10.6641	+	9.56496i	−0.498302	+	0.446941i
$459$	35.1354	−	1.46510i	1.63998	−	0.0683850i
$460$	7.24446	+	5.89955i	0.337775	+	0.275068i
$461$	−25.6291			−1.19366			−0.596832	−	0.802366i	$-0.703574\pi$
$461$	−25.6291			−1.19366			−0.596832	+	0.802366i	$0.703574\pi$
$462$	9.02471	−	34.3454i	0.419868	−	1.59789i
$463$	15.7381	−	15.7381i	0.731413	−	0.731413i	−0.239487	−	0.970900i	$-0.576979\pi$
$463$	15.7381	−	15.7381i	0.731413	−	0.731413i	0.970900	+	0.239487i	$0.0769792\pi$
$464$	−24.0320	−	21.9756i	−1.11566	−	1.02019i
$465$	8.72071	+	11.2190i	0.404413	+	0.520269i
$466$	13.0974	+	0.711658i	0.606724	+	0.0329669i
$467$	−2.52196	+	9.41209i	−0.116702	+	0.435540i	−0.999409	−	0.0343858i	$-0.989052\pi$
$467$	−2.52196	+	9.41209i	−0.116702	+	0.435540i	0.882706	+	0.469925i	$0.155719\pi$
$468$	26.8736	−	15.7487i	1.24223	−	0.727983i
$469$	−25.0618	−	3.25860i	−1.15725	−	0.150468i
$470$	−3.83524	−	4.74418i	−0.176906	−	0.218833i
$471$	−8.63756	−	10.0081i	−0.397998	−	0.461151i
$472$	0.126046	+	1.26966i	0.00580175	+	0.0584407i
$473$	13.4212	−	3.59620i	0.617107	−	0.165353i
$474$	7.97047	+	3.27124i	0.366096	+	0.150253i
$475$	7.05447	−	3.15934i	0.323681	−	0.144960i
$476$	34.3592	−	10.0939i	1.57485	−	0.462653i
$477$	4.61139	+	1.99630i	0.211141	+	0.0914045i
$478$	−0.711415	−	3.37888i	−0.0325394	−	0.154546i
$479$	−15.1539	+	26.2473i	−0.692397	+	1.19927i	0.278653	+	0.960392i	$0.410112\pi$
$479$	−15.1539	+	26.2473i	−0.692397	+	1.19927i	−0.971050	+	0.238876i	$0.923221\pi$
$480$	−17.4262	+	13.2789i	−0.795392	+	0.606095i
$481$	−7.19196	−	12.4568i	−0.327925	−	0.567983i
$482$	0.309127	+	0.101099i	0.0140803	+	0.00460493i
$483$	9.37751	+	1.92702i	0.426692	+	0.0876822i
$484$	30.6970	+	22.4836i	1.39532	+	1.02198i
$485$	14.1877	+	0.728009i	0.644232	+	0.0330572i
$486$	−13.9126	+	17.1008i	−0.631089	+	0.775710i
$487$	−0.485850	+	0.130183i	−0.0220160	+	0.00589916i	−0.269810	−	0.962914i	$-0.586961\pi$
$487$	−0.485850	+	0.130183i	−0.0220160	+	0.00589916i	0.247794	+	0.968813i	$0.420294\pi$
$488$	−32.1061	−	14.5170i	−1.45337	−	0.657155i
$489$	−5.53981	−	29.0519i	−0.250519	−	1.31377i
$490$	3.51474	+	21.8551i	0.158780	+	0.987314i
$491$	−2.91832			−0.131702			−0.0658510	−	0.997829i	$-0.520976\pi$
$491$	−2.91832			−0.131702			−0.0658510	+	0.997829i	$0.520976\pi$
$492$	15.0618	+	12.8296i	0.679036	+	0.578404i
$493$	53.2196	−	14.2602i	2.39689	−	0.642245i
$494$	−11.3330	−	0.615789i	−0.509895	−	0.0277057i
$495$	−32.9398	−	16.3125i	−1.48054	−	0.733192i
$496$	4.42758	+	13.9919i	0.198804	+	0.628257i
$497$	−7.77873	−	3.20746i	−0.348924	−	0.143874i
$498$	−16.7123	−	2.14511i	−0.748895	−	0.0961248i
$499$	−7.04700	−	12.2058i	−0.315467	−	0.546405i	0.664069	−	0.747671i	$-0.268828\pi$
$499$	−7.04700	−	12.2058i	−0.315467	−	0.546405i	−0.979537	+	0.201266i	$0.935495\pi$
$500$	19.3586	+	11.1913i	0.865741	+	0.500492i
$501$	−2.33595	+	6.70639i	−0.104362	+	0.299620i
$502$	5.19785	+	24.6873i	0.231991	+	1.10185i
$503$	−4.84934	−	4.84934i	−0.216221	−	0.216221i	0.590683	−	0.806904i	$-0.298859\pi$
$503$	−4.84934	−	4.84934i	−0.216221	−	0.216221i	−0.806904	+	0.590683i	$0.798859\pi$
$504$	−9.53986	+	20.3222i	−0.424939	+	0.905222i
$505$	5.01941	+	23.4883i	0.223361	+	1.04521i
$506$	−8.84318	+	13.5602i	−0.393127	+	0.602822i
$507$	10.5148	+	21.7548i	0.466977	+	0.966163i
$508$	−19.5234	−	7.58061i	−0.866212	−	0.336335i
$509$	30.6916	−	17.7198i	1.36038	−	0.785416i	0.370706	−	0.928750i	$-0.379116\pi$
$509$	30.6916	−	17.7198i	1.36038	−	0.785416i	0.989674	+	0.143335i	$0.0457825\pi$
$510$	−3.06848	−	36.9409i	−0.135875	−	1.63577i
$511$	−21.5793	−	2.80579i	−0.954611	−	0.124121i
$512$	−21.6377	+	6.61884i	−0.956261	+	0.292514i
$513$	7.66579	−	2.40052i	0.338453	−	0.105985i
$514$	0.0706033	−	1.29938i	0.00311418	−	0.0573134i
$515$	31.6937	−	16.1924i	1.39659	−	0.713521i
$516$	−8.75608	+	0.700744i	−0.385465	+	0.0308486i
$517$	7.47470	−	7.47470i	0.328737	−	0.328737i
$518$	9.35582	+	4.46617i	0.411071	+	0.196232i
$519$	−12.9107	+	2.46190i	−0.566718	+	0.108065i
$520$	−17.7532	−	27.6194i	−0.778530	−	1.21119i
$521$	−35.0878	−	20.2580i	−1.53723	−	0.887518i	−0.999000	−	0.0447176i	$-0.985761\pi$
$521$	−35.0878	−	20.2580i	−1.53723	−	0.887518i	−0.538226	−	0.842800i	$-0.680905\pi$
$522$	−15.4216	+	30.9062i	−0.674986	+	1.35273i
$523$	−10.8288	+	40.4136i	−0.473509	+	1.76716i	0.153499	+	0.988149i	$0.450946\pi$
$523$	−10.8288	+	40.4136i	−0.473509	+	1.76716i	−0.627008	+	0.779013i	$0.715721\pi$
$524$	−25.9732	−	19.0237i	−1.13465	−	0.831053i
$525$	22.8913	+	0.994282i	0.999058	+	0.0433940i
$526$	−2.10897	−	4.15883i	−0.0919553	−	0.181334i
$527$	−23.9841	−	6.42653i	−1.04477	−	0.279944i
$528$	−26.0625	−	27.6035i	−1.13423	−	1.20129i
$529$	16.1390	+	9.31783i	0.701694	+	0.405123i
$530$	1.90229	−	4.94337i	0.0826304	−	0.214726i
$531$	1.25833	−	0.498002i	0.0546069	−	0.0216114i
$532$	6.98439	−	4.25852i	0.302812	−	0.184630i
$533$	−20.9661	+	20.9661i	−0.908141	+	0.908141i
$534$	1.17303	−	2.85812i	0.0507620	−	0.123683i
$535$	−1.13409	−	2.21978i	−0.0490310	−	0.0959695i
$536$	−17.1236	+	20.8983i	−0.739629	+	0.902669i
$537$	7.20104	+	0.529326i	0.310748	+	0.0228421i
$538$	4.74985	−	14.5234i	0.204780	−	0.626150i
$539$	−37.0176	+	10.0461i	−1.59446	+	0.432718i
$540$	18.6146	+	13.9103i	0.801045	+	0.598604i
$541$	−0.534833	+	0.308786i	−0.0229943	+	0.0132757i	−0.511453	−	0.859311i	$-0.670893\pi$
$541$	−0.534833	+	0.308786i	−0.0229943	+	0.0132757i	0.488459	+	0.872587i	$0.337559\pi$
$542$	−1.43276	+	1.28509i	−0.0615424	+	0.0551992i
$543$	−6.51128	−	13.4717i	−0.279426	−	0.578125i
$544$	10.2636	−	36.8823i	0.440049	−	1.58132i
$545$	5.15296	+	24.1132i	0.220729	+	1.03290i
$546$	−29.2176	−	16.6806i	−1.25040	−	0.713863i
$547$	5.57234	−	5.57234i	0.238256	−	0.238256i	−0.577872	−	0.816128i	$-0.696117\pi$
$547$	5.57234	−	5.57234i	0.238256	−	0.238256i	0.816128	+	0.577872i	$0.196117\pi$
$548$	−6.12443	−	7.62279i	−0.261623	−	0.325629i
$549$	−5.46481	+	36.9713i	−0.233233	+	1.57789i
$550$	−15.7502	+	35.4004i	−0.671589	+	1.50948i
$551$	10.8995	−	6.29283i	0.464334	−	0.268084i
$552$	7.04941	−	7.41956i	0.300043	−	0.315798i
$553$	−1.22946	−	9.22440i	−0.0522819	−	0.392261i
$554$	10.9281	−	5.54169i	0.464290	−	0.235444i
$555$	6.47924	−	8.55421i	0.275028	−	0.363106i
$556$	−16.5805	+	7.30585i	−0.703170	+	0.309837i
$557$	29.1733	−	7.81696i	1.23611	−	0.331215i	0.419155	−	0.907915i	$-0.362326\pi$
$557$	29.1733	−	7.81696i	1.23611	−	0.331215i	0.816956	+	0.576700i	$0.195660\pi$
$558$	12.9830	−	8.58730i	0.549615	−	0.363529i
$559$		−	13.1640i		−	0.556777i
$560$	21.8175	+	9.16505i	0.921956	+	0.387294i
$561$	63.0939	−	12.0312i	2.66383	−	0.507956i
$562$	−40.4598	+	8.51872i	−1.70669	+	0.359340i
$563$	−1.60556	−	5.99202i	−0.0676662	−	0.252534i	0.923804	−	0.382865i	$-0.125063\pi$
$563$	−1.60556	−	5.99202i	−0.0676662	−	0.252534i	−0.991470	+	0.130331i	$0.958396\pi$
$564$	−5.50245	+	3.79243i	−0.231695	+	0.159690i
$565$	−27.9567	−	1.43453i	−1.17615	−	0.0603512i
$566$	−9.10998	−	17.9646i	−0.382921	−	0.755110i
$567$	23.5038	+	3.81709i	0.987068	+	0.160303i
$568$	−7.30749	+	5.24507i	−0.306615	+	0.220078i
$569$	−2.82664	−	4.89588i	−0.118499	−	0.205246i	0.800674	−	0.599100i	$-0.204475\pi$
$569$	−2.82664	−	4.89588i	−0.118499	−	0.205246i	−0.919173	+	0.393854i	$0.871142\pi$
$570$	−2.86104	−	7.96937i	−0.119836	−	0.333800i
$571$	−16.0259	−	9.25258i	−0.670665	−	0.387208i	0.125664	−	0.992073i	$-0.459894\pi$
$571$	−16.0259	−	9.25258i	−0.670665	−	0.387208i	−0.796328	+	0.604864i	$0.793227\pi$
$572$	44.3510	−	35.6332i	1.85441	−	1.48990i
$573$	−2.50938	+	3.69188i	−0.104831	+	0.154231i
$574$	3.90119	−	21.0114i	0.162832	−	0.876999i
$575$	−9.75987	−	3.72202i	−0.407015	−	0.155219i
$576$	13.0470	+	20.1438i	0.543627	+	0.839327i
$577$	−27.4587	+	7.35754i	−1.14312	+	0.306298i	−0.780205	−	0.625524i	$-0.784885\pi$
$577$	−27.4587	+	7.35754i	−1.14312	+	0.306298i	−0.362915	+	0.931822i	$0.618219\pi$
$578$	27.1964	+	30.3217i	1.13122	+	1.26122i
$579$	24.1934	+	28.0324i	1.00544	+	1.16499i
$580$	33.2199	+	14.9002i	1.37938	+	0.618697i
$581$	6.99155	+	16.8029i	0.290058	+	0.697101i
$582$	1.98126	−	15.4357i	0.0821258	−	0.639831i
$583$	8.86536	+	2.37547i	0.367166	+	0.0983818i
$584$	−14.7442	+	17.9943i	−0.610118	+	0.744610i
$585$	−23.0052	+	26.1443i	−0.951147	+	1.08093i
$586$	35.4959	+	23.1485i	1.46632	+	0.956255i
$587$	−7.31760	−	7.31760i	−0.302029	−	0.302029i	0.539778	−	0.841807i	$-0.318508\pi$
$587$	−7.31760	−	7.31760i	−0.302029	−	0.302029i	−0.841807	+	0.539778i	$0.818508\pi$
$588$	24.1651	−	2.01190i	0.996552	−	0.0829693i
$589$	−5.67190			−0.233707
$590$	−0.579126	−	1.30365i	−0.0238422	−	0.0536705i
$591$	11.0101	+	3.83501i	0.452896	+	0.157751i
$592$	9.34110	−	5.96455i	0.383917	−	0.245141i
$593$	−3.10374	+	11.5833i	−0.127455	+	0.475670i	−0.999915	−	0.0130157i	$-0.995857\pi$
$593$	−3.10374	+	11.5833i	−0.127455	+	0.475670i	0.872460	+	0.488686i	$0.162524\pi$
$594$	−20.5711	+	34.6148i	−0.844042	+	1.42026i
$595$	−32.9352	+	22.7667i	−1.35021	+	0.933344i
$596$	−5.36917	+	7.33059i	−0.219930	+	0.300273i
$597$	44.5045	+	3.27139i	1.82145	+	0.133889i
$598$	10.2409	+	11.4177i	0.418781	+	0.466906i
$599$	7.25087	−	12.5589i	0.296263	−	0.513142i	−0.679015	−	0.734124i	$-0.737593\pi$
$599$	7.25087	−	12.5589i	0.296263	−	0.513142i	0.975278	+	0.220982i	$0.0709263\pi$
$600$	13.8421	−	20.2088i	0.565102	−	0.825021i
$601$	5.76057			0.234978			0.117489	−	0.993074i	$-0.462515\pi$
$601$	5.76057			0.234978			0.117489	+	0.993074i	$0.462515\pi$
$602$	5.37149	+	7.82093i	0.218926	+	0.318757i
$603$	26.2981	+	11.3847i	1.07094	+	0.463619i
$604$	−0.00348944	+	0.0320150i	−0.000141983	+	0.00130267i
$605$	−40.4736	−	13.1018i	−1.64549	−	0.532665i
$606$	26.0747	−	3.51884i	1.05921	−	0.142943i
$607$	−5.58857	+	20.8568i	−0.226833	+	0.846553i	0.754829	+	0.655922i	$0.227720\pi$
$607$	−5.58857	+	20.8568i	−0.226833	+	0.846553i	−0.981662	+	0.190631i	$0.938947\pi$
$608$	0.0840695	−	8.74466i	0.00340947	−	0.354643i
$609$	37.2424	−	2.20462i	1.50914	−	0.0893358i
$610$	39.1753	+	4.15039i	1.58616	+	0.168044i
$611$	−5.00747	−	8.67319i	−0.202580	−	0.350880i
$612$	−40.6052	+	0.263303i	−1.64137	+	0.0106434i
$613$	−29.3425	+	7.86229i	−1.18513	+	0.317555i	−0.796960	−	0.604032i	$-0.793560\pi$
$613$	−29.3425	+	7.86229i	−1.18513	+	0.317555i	−0.388172	+	0.921587i	$0.626893\pi$
$614$	20.5368	+	13.3930i	0.828798	+	0.540496i
$615$	−20.4893	−	8.33713i	−0.826208	−	0.336186i
$616$	−11.8097	+	39.2675i	−0.475826	+	1.58213i
$617$	−18.7170	+	18.7170i	−0.753520	+	0.753520i	−0.975134	−	0.221615i	$-0.928867\pi$
$617$	−18.7170	+	18.7170i	−0.753520	+	0.753520i	0.221615	+	0.975134i	$0.428867\pi$
$618$	−15.0366	−	35.9711i	−0.604859	−	1.44697i
$619$	14.1879	−	24.5742i	0.570260	−	0.987719i	−0.426279	−	0.904592i	$-0.640176\pi$
$619$	14.1879	−	24.5742i	0.570260	−	0.987719i	0.996539	−	0.0831273i	$-0.0264908\pi$
$620$	−9.60780	−	13.3009i	−0.385858	−	0.534175i
$621$	−9.61892	−	5.03126i	−0.385994	−	0.201898i
$622$	11.2703	−	34.4607i	0.451897	−	1.38175i
$623$	−3.30776	+	0.440870i	−0.132523	+	0.0176631i
$624$	−31.6515	+	17.0820i	−1.26707	+	0.683827i
$625$	−24.4762	−	5.09090i	−0.979047	−	0.203636i
$626$	−0.676757	+	12.4551i	−0.0270487	+	0.497804i
$627$	13.2100	−	6.38480i	0.527556	−	0.254984i
$628$	9.56103	+	11.9002i	0.381527	+	0.474868i
$629$			18.7515i			0.747671i
$630$	2.99971	−	24.9199i	0.119511	−	0.992833i
$631$	−2.85043			−0.113474			−0.0567368	−	0.998389i	$-0.518070\pi$
$631$	−2.85043			−0.113474			−0.0567368	+	0.998389i	$0.518070\pi$
$632$	−9.06491	−	4.09877i	−0.360583	−	0.163040i
$633$	10.8744	+	22.4990i	0.432220	+	0.894253i
$634$	8.24666	+	0.448090i	0.327517	+	0.0177959i
$635$	23.3848	+	1.19993i	0.927997	+	0.0476179i
$636$	−5.24037	−	2.49105i	−0.207794	−	0.0987764i
$637$	0.116487	+	36.3394i	0.00461540	+	1.43982i
$638$	−19.6105	+	59.9625i	−0.776388	+	2.37394i
$639$	7.47610	+	5.92721i	0.295750	+	0.234477i
$640$	20.6490	−	14.6157i	0.816224	−	0.577736i
$641$	−19.0514	−	10.9994i	−0.752486	−	0.434448i	0.0741052	−	0.997250i	$-0.476390\pi$
$641$	−19.0514	−	10.9994i	−0.752486	−	0.434448i	−0.826592	+	0.562802i	$0.809723\pi$
$642$	−2.51937	+	1.05314i	−0.0994314	+	0.0415640i
$643$	26.1324	+	26.1324i	1.03056	+	1.03056i	0.999518	+	0.0310431i	$0.00988291\pi$
$643$	26.1324	+	26.1324i	1.03056	+	1.03056i	0.0310431	+	0.999518i	$0.490117\pi$
$644$	−10.7432	−	2.60472i	−0.423343	−	0.102640i
$645$	9.04963	−	3.81499i	0.356329	−	0.150215i
$646$	12.3934	+	8.08230i	0.487612	+	0.317994i
$647$	0.795351	+	2.96829i	0.0312685	+	0.116696i	0.979796	−	0.199999i	$-0.0640938\pi$
$647$	0.795351	+	2.96829i	0.0312685	+	0.116696i	−0.948528	+	0.316694i	$0.897427\pi$
$648$	16.7497	−	19.1689i	0.657990	−	0.753026i
$649$	2.14064	−	1.23590i	0.0840275	−	0.0485133i
$650$	28.5339	+	23.0939i	1.11919	+	0.905819i
$651$	−15.0320	−	7.53147i	−0.589150	−	0.295182i
$652$	5.21260	+	33.7506i	0.204141	+	1.32177i
$653$	19.7164	+	5.28299i	0.771561	+	0.206739i	0.623061	−	0.782173i	$-0.285889\pi$
$653$	19.7164	+	5.28299i	0.771561	+	0.206739i	0.148500	+	0.988912i	$0.452555\pi$
$654$	26.7685	−	3.61247i	1.04673	−	0.141259i
$655$	34.2454	+	11.0856i	1.33808	+	0.433152i
$656$	−16.8598	−	15.4171i	−0.658266	−	0.601936i
$657$	22.6438	+	9.80267i	0.883419	+	0.382439i
$658$	6.51407	+	3.10961i	0.253945	+	0.121225i
$659$		−	13.7925i		−	0.537281i	−0.963240	−	0.268641i	$-0.913426\pi$
$659$		−	13.7925i		−	0.537281i	0.963240	−	0.268641i	$-0.0865744\pi$
$660$	37.3494	+	20.1626i	1.45382	+	0.784827i
$661$	29.7372	+	17.1688i	1.15664	+	0.667788i	0.950497	−	0.310733i	$-0.100574\pi$
$661$	29.7372	+	17.1688i	1.15664	+	0.667788i	0.206146	+	0.978521i	$0.433908\pi$
$662$	29.1421	+	32.4910i	1.13264	+	1.26280i
$663$	4.46108	−	60.6893i	0.173254	−	2.35698i
$664$	19.1986	+	3.15438i	0.745049	+	0.122414i
$665$	−5.92096	+	6.97051i	−0.229605	+	0.270305i
$666$	−8.80168	−	7.79208i	−0.341058	−	0.301937i
$667$	−16.4282	−	4.40193i	−0.636104	−	0.170444i
$668$	2.96810	−	7.64418i	0.114839	−	0.295762i
$669$	4.08314	−	11.7225i	0.157863	−	0.453218i
$670$	10.8485	−	28.1914i	0.419116	−	1.08913i
$671$			68.2619i			2.63522i
$672$	11.8345	−	23.0639i	0.456524	−	0.889711i
$673$	4.68092	−	4.68092i	0.180436	−	0.180436i	−0.611110	−	0.791546i	$-0.709277\pi$
$673$	4.68092	−	4.68092i	0.180436	−	0.180436i	0.791546	+	0.611110i	$0.209277\pi$
$674$	−20.3073	+	31.1392i	−0.782207	+	1.19944i
$675$	−24.6400	−	8.23825i	−0.948395	−	0.317090i
$676$	−11.2501	−	25.5319i	−0.432695	−	0.981995i
$677$	−0.382889	+	1.42896i	−0.0147156	+	0.0549194i	−0.972893	−	0.231255i	$-0.925717\pi$
$677$	−0.382889	+	1.42896i	−0.0147156	+	0.0549194i	0.958178	+	0.286174i	$0.0923836\pi$
$678$	−3.90404	+	30.4158i	−0.149934	+	1.16811i
$679$	−15.5194	+	6.45750i	−0.595580	+	0.247816i
$680$	2.04023	+	42.7539i	0.0782391	+	1.63954i
$681$	23.9404	−	20.6618i	0.917396	−	0.791761i
$682$	21.1652	−	18.9836i	0.810456	−	0.726921i
$683$	−8.25789	−	30.8189i	−0.315979	−	1.17925i	−0.923074	−	0.384622i	$-0.874332\pi$
$683$	−8.25789	−	30.8189i	−0.315979	−	1.17925i	0.607095	−	0.794629i	$-0.292335\pi$
$684$	−8.94373	+	2.45873i	−0.341972	+	0.0940120i
$685$	9.17526	+	5.94424i	0.350568	+	0.227118i
$686$	−14.8973	−	21.5423i	−0.568782	−	0.822488i
$687$	−14.5102	−	9.86264i	−0.553599	−	0.376283i
$688$	10.1329	−	0.452927i	0.386311	−	0.0172677i
$689$	4.34772	−	7.53048i	0.165635	−	0.286888i
$690$	−4.88130	+	10.3491i	−0.185828	+	0.393982i
$691$	9.15500	−	5.28564i	0.348273	−	0.201075i	−0.315652	−	0.948875i	$-0.602223\pi$
$691$	9.15500	−	5.28564i	0.348273	−	0.201075i	0.663924	+	0.747800i	$0.268890\pi$
$692$	14.9988	−	2.31649i	0.570169	−	0.0880597i
$693$	43.4879	+	0.619632i	1.65197	+	0.0235379i
$694$	12.7085	+	25.0609i	0.482409	+	0.951299i
$695$	15.0393	−	13.5713i	0.570475	−	0.514787i
$696$	19.0519	−	35.0388i	0.722161	−	1.32814i
$697$	37.3366	−	10.0043i	1.41422	−	0.378940i
$698$	−5.09565	−	24.2019i	−0.192873	−	0.916055i
$699$	3.00908	+	15.7803i	0.113814	+	0.596864i
$700$	−26.3758	−	2.07736i	−0.996913	−	0.0785170i
$701$	46.5380			1.75771			0.878857	−	0.477085i	$-0.158307\pi$
$701$	46.5380			1.75771			0.878857	+	0.477085i	$0.158307\pi$
$702$	26.6329	+	27.3131i	1.00519	+	1.03087i
$703$	1.10861	+	4.13740i	0.0418121	+	0.156045i
$704$	28.9543	+	32.9128i	1.09126	+	1.24045i
$705$	4.51123	−	5.95594i	0.169903	−	0.224314i
$706$	−6.51070	−	12.8389i	−0.245033	−	0.483200i
$707$	−17.3366	−	22.5187i	−0.652011	−	0.846903i
$708$	−1.47233	+	0.523566i	−0.0553335	+	0.0196768i
$709$	−17.4273	−	30.1850i	−0.654496	−	1.13362i	−0.982020	−	0.188777i	$-0.939548\pi$
$709$	−17.4273	−	30.1850i	−0.654496	−	1.13362i	0.327524	−	0.944843i	$-0.393786\pi$
$710$	5.91795	−	8.13115i	0.222097	−	0.305156i
$711$	−1.54295	+	10.4386i	−0.0578651	+	0.391477i
$712$	−1.46977	+	3.25058i	−0.0550821	+	0.121820i
$713$	5.41982	+	5.41982i	0.202974	+	0.202974i
$714$	22.1136	+	37.8768i	0.827579	+	1.41750i
$715$	−34.5849	+	53.3836i	−1.29340	+	1.99643i
$716$	−8.28839	−	0.903383i	−0.309752	−	0.0337610i
$717$	3.80757	−	1.84032i	0.142196	−	0.0687280i
$718$	−10.1192	+	9.07622i	−0.377646	+	0.338721i
$719$	5.42402	+	9.39468i	0.202282	+	0.350363i	0.949263	−	0.314482i	$-0.101831\pi$
$719$	5.42402	+	9.39468i	0.202282	+	0.350363i	−0.746981	+	0.664845i	$0.768498\pi$
$720$	−20.9159	−	16.8085i	−0.779489	−	0.626416i
$721$	−25.5821	+	33.4501i	−0.952728	+	1.24575i
$722$	−22.3266	−	7.30183i	−0.830909	−	0.271746i
$723$	−0.0292015	+	0.397263i	−0.00108602	+	0.0147744i
$724$	6.96663	+	15.8107i	0.258913	+	0.587598i
$725$	−40.4922	−	4.16648i	−1.50384	−	0.154739i
$726$	−17.6941	+	43.1120i	−0.656688	+	1.60004i
$727$	−18.3837	−	18.3837i	−0.681813	−	0.681813i	0.278596	−	0.960408i	$-0.410131\pi$
$727$	−18.3837	−	18.3837i	−0.681813	−	0.681813i	−0.960408	+	0.278596i	$0.910131\pi$
$728$	33.0391	+	20.4361i	1.22451	+	0.757414i
$729$	−24.4254	−	11.5065i	−0.904645	−	0.426165i
$730$	9.34105	−	24.2740i	0.345728	−	0.898421i
$731$	−8.58055	+	14.8620i	−0.317363	+	0.549689i
$732$	7.80830	−	42.4423i	0.288603	−	1.56871i
$733$	13.3642	−	49.8759i	0.493618	−	1.84221i	−0.0440187	−	0.999031i	$-0.514016\pi$
$733$	13.3642	−	49.8759i	0.493618	−	1.84221i	0.537637	−	0.843177i	$-0.319317\pi$
$734$	12.9233	+	25.4844i	0.477007	+	0.940646i
$735$	−24.9479	+	10.6114i	−0.920217	+	0.391409i
$736$	−8.43635	+	8.27568i	−0.310968	+	0.305046i
$737$	50.5580	+	13.5470i	1.86233	+	0.499009i
$738$	−10.8191	+	21.6825i	−0.398258	+	0.798143i
$739$	−18.5436	+	32.1185i	−0.682139	+	1.18150i	0.292188	+	0.956361i	$0.405617\pi$
$739$	−18.5436	+	32.1185i	−0.682139	+	1.18150i	−0.974327	+	0.225138i	$0.927717\pi$
$740$	−7.82447	+	9.60821i	−0.287633	+	0.353205i
$741$	−2.60372	−	13.6545i	−0.0956501	−	0.501609i
$742$	0.489721	+	6.24805i	0.0179782	+	0.229373i
$743$	−31.5394	−	31.5394i	−1.15707	−	1.15707i	−0.985103	−	0.171964i	$-0.944989\pi$
$743$	−31.5394	−	31.5394i	−1.15707	−	1.15707i	−0.171964	−	0.985103i	$-0.555011\pi$
$744$	−15.3311	+	9.38218i	−0.562064	+	0.343967i
$745$	3.12877	−	9.66528i	0.114629	−	0.354109i
$746$	−6.43533	−	0.349670i	−0.235614	−	0.0128023i
$747$	−2.36895	−	20.4998i	−0.0866753	−	0.750047i
$748$	−73.2982	+	11.3205i	−2.68005	+	0.413920i
$749$	2.34280	+	1.79173i	0.0856040	+	0.0654686i
$750$	−7.60674	+	26.3085i	−0.277759	+	0.960651i
$751$	−1.15325	−	1.99749i	−0.0420828	−	0.0728895i	0.844217	−	0.536002i	$-0.180066\pi$
$751$	−1.15325	−	1.99749i	−0.0420828	−	0.0728895i	−0.886300	+	0.463112i	$0.846733\pi$
$752$	6.50382	−	4.15287i	0.237170	−	0.151440i
$753$	−27.8195	+	13.4460i	−1.01380	+	0.490000i
$754$	50.0648	+	32.6495i	1.82325	+	1.18902i
$755$	−0.00752450	−	0.0352108i	−0.000273845	−	0.00128145i
$756$	−26.9680	−	5.35973i	−0.980817	−	0.194931i
$757$	26.5573	−	26.5573i	0.965242	−	0.965242i	−0.0341734	−	0.999416i	$-0.510880\pi$
$757$	26.5573	−	26.5573i	0.965242	−	0.965242i	0.999416	+	0.0341734i	$0.0108799\pi$
$758$	6.67541	+	31.7050i	0.242462	+	1.15158i
$759$	−18.7239	−	6.52185i	−0.679635	−	0.236728i
$760$	2.97783	+	9.31277i	0.108017	+	0.337810i
$761$	−15.3273	+	8.84923i	−0.555614	+	0.320784i	−0.751383	−	0.659866i	$-0.770613\pi$
$761$	−15.3273	+	8.84923i	−0.555614	+	0.320784i	0.195769	+	0.980650i	$0.437280\pi$
$762$	3.26559	−	25.4417i	0.118300	−	0.921656i
$763$	−17.7979	−	23.1179i	−0.644327	−	0.836923i
$764$	3.04578	−	4.15843i	0.110192	−	0.150447i
$765$	43.0139	−	14.5213i	1.55517	−	0.525019i
$766$	19.6182	+	1.06597i	0.708834	+	0.0385152i
$767$	−0.606106	−	2.26202i	−0.0218852	−	0.0816767i
$768$	−14.2377	−	23.7758i	−0.513760	−	0.857934i
$769$			31.9179i			1.15099i	0.817806	+	0.575494i	$0.195190\pi$
$769$			31.9179i			1.15099i	−0.817806	+	0.575494i	$0.804810\pi$
$770$	−1.23548	−	45.8283i	−0.0445235	−	1.65154i
$771$	1.56555	−	0.298530i	0.0563820	−	0.0107513i
$772$	−26.7800	−	33.3319i	−0.963834	−	1.19964i
$773$	−13.1821	−	49.1963i	−0.474127	−	1.76947i	−0.624696	−	0.780868i	$-0.714777\pi$
$773$	−13.1821	−	49.1963i	−0.474127	−	1.76947i	0.150569	−	0.988600i	$-0.451889\pi$
$774$	−3.41038	−	10.2034i	−0.122584	−	0.366753i
$775$	14.8647	+	10.7503i	0.533956	+	0.386162i
$776$	−2.91343	+	17.7321i	−0.104586	+	0.636545i
$777$	−2.55577	+	12.4372i	−0.0916877	+	0.446184i
$778$	−1.48795	+	4.54965i	−0.0533455	+	0.163113i
$779$	7.64662	−	4.41478i	0.273968	−	0.158176i
$780$	27.6098	−	29.2355i	0.988589	−	1.04680i
$781$	15.0914	+	8.71302i	0.540012	+	0.311776i
$782$	−4.11951	−	19.5657i	−0.147314	−	0.699668i
$783$	−41.2821	−	9.23689i	−1.47530	−	0.330100i
$784$	−27.9679	+	1.33998i	−0.998854	+	0.0478563i
$785$	−14.3238	−	9.27974i	−0.511237	−	0.331208i
$786$	14.9712	−	36.4777i	0.534005	−	1.30112i
$787$	−14.0286	−	52.3553i	−0.500064	−	1.86626i	−0.499585	−	0.866265i	$-0.666514\pi$
$787$	−14.0286	−	52.3553i	−0.500064	−	1.86626i	−0.000479613	−	1.00000i	$-0.500153\pi$
$788$	−12.5497	−	4.87284i	−0.447066	−	0.173588i
$789$	4.32346	−	3.73137i	0.153919	−	0.132840i
$790$	11.0609	+	1.17183i	0.393528	+	0.0416919i
$791$	30.5807	−	12.7244i	1.08733	−	0.452428i
$792$	25.1450	−	39.1093i	0.893488	−	1.38969i
$793$	62.4686	+	16.7384i	2.21832	+	0.594398i
$794$	−0.313490	+	5.76948i	−0.0111254	+	0.204751i
$795$	6.43685	+	0.806487i	0.228292	+	0.0286031i
$796$	−51.2246	−	5.58316i	−1.81561	−	0.197890i
$797$	−25.6557	−	25.6557i	−0.908771	−	0.908771i	0.0874025	−	0.996173i	$-0.472143\pi$
$797$	−25.6557	−	25.6557i	−0.908771	−	0.908771i	−0.996173	+	0.0874025i	$0.972143\pi$
$798$	7.11855	+	7.04991i	0.251994	+	0.249564i
$799$			13.0559i			0.461884i
$800$	−16.7946	+	22.7583i	−0.593779	+	0.804628i
$801$	3.74315	+	0.553284i	0.132258	+	0.0195493i
$802$	20.0171	+	22.3174i	0.706830	+	0.788056i
$803$	43.5326	+	11.6645i	1.53623	+	0.411632i
$804$	−29.8852	−	14.2061i	−1.05397	−	0.501011i
$805$	12.3185	−	1.00290i	0.434171	−	0.0353476i
$806$	−12.1826	−	24.0238i	−0.429115	−	0.846204i
$807$	18.6643	+	1.37195i	0.657013	+	0.0482950i
$808$	−30.2328	+	3.00138i	−1.06359	+	0.105588i
$809$	25.9471	−	44.9417i	0.912251	−	1.58007i	0.101374	−	0.994848i	$-0.467676\pi$
$809$	25.9471	−	44.9417i	0.912251	−	1.58007i	0.810877	−	0.585217i	$-0.198991\pi$
$810$	−11.0581	+	26.2244i	−0.388543	+	0.921431i
$811$		−	44.3391i		−	1.55696i	−0.627672	−	0.778478i	$-0.715992\pi$
$811$		−	44.3391i		−	1.55696i	0.627672	−	0.778478i	$-0.284008\pi$
$812$	−43.0668	+	1.03110i	−1.51135	+	0.0361845i
$813$	−1.94950	−	1.32508i	−0.0683719	−	0.0464726i
$814$	−17.9846	−	11.7286i	−0.630360	−	0.411086i
$815$	−17.3713	−	34.0012i	−0.608489	−	1.19101i
$816$	46.8686	+	1.34577i	1.64073	+	0.0471114i
$817$	−1.01459	+	3.78649i	−0.0354959	+	0.132473i
$818$	−2.15981	+	6.60398i	−0.0755160	+	0.230903i
$819$	11.2306	−	39.6452i	0.392431	−	1.38531i
$820$	23.3057	+	10.4533i	0.813869	+	0.365046i
$821$	−19.3548	−	33.5235i	−0.675487	−	1.16998i	−0.976326	−	0.216303i	$-0.930600\pi$
$821$	−19.3548	−	33.5235i	−0.675487	−	1.16998i	0.300839	−	0.953675i	$-0.402733\pi$
$822$	7.25965	−	9.52474i	0.253209	−	0.332213i
$823$	3.78214	+	14.1151i	0.131837	+	0.492023i	0.999991	−	0.00427245i	$-0.00135997\pi$
$823$	3.78214	+	14.1151i	0.131837	+	0.492023i	−0.868154	+	0.496295i	$0.834693\pi$
$824$	15.8906	+	42.1211i	0.553576	+	1.46736i
$825$	−46.7217	−	8.30465i	−1.62664	−	0.289131i
$826$	1.28310	+	1.09658i	0.0446449	+	0.0381550i
$827$	14.2805	+	14.2805i	0.496580	+	0.496580i	0.910372	−	0.413791i	$-0.135796\pi$
$827$	14.2805	+	14.2805i	0.496580	+	0.496580i	−0.413791	+	0.910372i	$0.635796\pi$
$828$	10.8957	+	6.19678i	0.378652	+	0.215353i
$829$	−14.3677	+	24.8855i	−0.499010	+	0.864310i	−0.999999	−	0.00114291i	$-0.999636\pi$
$829$	−14.3677	+	24.8855i	−0.499010	+	0.864310i	0.500989	+	0.865453i	$0.332970\pi$
$830$	−21.4875	+	3.38499i	−0.745841	+	0.117495i
$831$	9.80485	+	11.3607i	0.340127	+	0.394097i
$832$	37.2194	−	18.4265i	1.29035	−	0.638824i
$833$	23.5552	−	41.1026i	0.816141	−	1.42412i
$834$	−13.5659	−	17.5613i	−0.469750	−	0.608097i
$835$	−0.469820	+	9.15605i	−0.0162588	+	0.316858i
$836$	−15.5035	+	6.83130i	−0.536200	+	0.236265i
$837$	14.0305	+	12.9072i	0.484964	+	0.446138i
$838$	1.02767	−	0.216374i	0.0355003	−	0.00747451i
$839$	11.6154			0.401008			0.200504	−	0.979693i	$-0.435742\pi$
$839$	11.6154			0.401008			0.200504	+	0.979693i	$0.435742\pi$
$840$	−4.47401	+	28.6353i	−0.154368	+	0.988013i
$841$	−37.2790			−1.28548
$842$	−50.7908	+	10.6939i	−1.75037	+	0.368536i
$843$	−22.0366	−	45.5931i	−0.758980	−	1.57031i
$844$	−11.6349	−	26.4052i	−0.400490	−	0.908906i
$845$	20.8980	+	23.1587i	0.718913	+	0.796682i
$846$	−6.12824	−	5.42530i	−0.210693	−	0.186526i
$847$	49.8945	−	6.65010i	1.71439	−	0.228500i
$848$	5.94611	+	3.08753i	0.204190	+	0.106026i
$849$	18.6758	−	16.1182i	0.640951	−	0.553174i
$850$	−17.1613	−	44.6717i	−0.588628	−	1.53223i
$851$	2.89418	−	5.01286i	0.0992111	−	0.171839i
$852$	−8.38651	−	7.14364i	−0.287317	−	0.244737i
$853$	8.74516	+	8.74516i	0.299429	+	0.299429i	0.840790	−	0.541361i	$-0.182091\pi$
$853$	8.74516	+	8.74516i	0.299429	+	0.299429i	−0.541361	+	0.840790i	$0.682091\pi$
$854$	−43.9436	+	15.5454i	−1.50372	+	0.531954i
$855$	8.63225	−	5.74708i	0.295217	−	0.196546i
$856$	2.95010	−	1.11295i	0.100832	−	0.0380400i
$857$	10.0772	+	37.6085i	0.344229	+	1.28468i	0.893510	+	0.449043i	$0.148235\pi$
$857$	10.0772	+	37.6085i	0.344229	+	1.28468i	−0.549281	+	0.835638i	$0.685098\pi$
$858$	55.4170	+	42.2382i	1.89190	+	1.44199i
$859$	7.82265	+	13.5492i	0.266905	+	0.462294i	0.968061	−	0.250714i	$-0.0806655\pi$
$859$	7.82265	+	13.5492i	0.266905	+	0.462294i	−0.701156	+	0.713008i	$0.747332\pi$
$860$	−10.5981	+	4.03480i	−0.361393	+	0.137585i
$861$	26.1277	−	1.54667i	0.890428	−	0.0527103i
$862$	−11.2086	+	34.2720i	−0.381765	+	1.16731i
$863$	−11.0696	+	41.3123i	−0.376814	+	1.40629i	0.473863	+	0.880599i	$0.342859\pi$
$863$	−11.0696	+	41.3123i	−0.376814	+	1.40629i	−0.850677	+	0.525689i	$0.823807\pi$
$864$	−20.1077	+	21.4402i	−0.684077	+	0.729410i
$865$	−15.1102	+	7.71982i	−0.513761	+	0.262482i
$866$	27.4398	+	17.8947i	0.932441	+	0.608087i
$867$	−28.0428	+	41.2575i	−0.952385	+	1.40118i
$868$	17.0407	+	9.30190i	0.578400	+	0.315727i
$869$			19.2732i			0.653800i
$870$	−7.93597	+	43.8793i	−0.269055	+	1.48765i
$871$	24.7945	−	42.9453i	0.840130	−	1.45515i
$872$	−31.0372	+	3.08124i	−1.05105	+	0.104344i
$873$	18.9339	−	2.18800i	0.640815	−	0.0740525i
$874$	−2.06570	−	4.07350i	−0.0698732	−	0.137788i
$875$	28.7291	−	7.04568i	0.971219	−	0.238187i
$876$	−25.7324	−	12.2321i	−0.869417	−	0.413283i
$877$	43.2584	+	11.5911i	1.46073	+	0.391403i	0.899743	−	0.436420i	$-0.143754\pi$
$877$	43.2584	+	11.5911i	1.46073	+	0.391403i	0.560991	+	0.827822i	$0.310420\pi$
$878$	−8.17349	−	9.11275i	−0.275842	−	0.307540i
$879$	−17.0720	+	49.0129i	−0.575825	+	1.65316i
$880$	−42.2815	−	24.7847i	−1.42531	−	0.835491i
$881$		−	3.07405i		−	0.103567i	−0.998658	−	0.0517837i	$-0.983509\pi$
$881$		−	3.07405i		−	0.103567i	0.998658	−	0.0517837i	$-0.0164906\pi$
$882$	9.50471	+	28.1365i	0.320040	+	0.947404i
$883$	8.38235	+	8.38235i	0.282088	+	0.282088i	0.833941	−	0.551853i	$-0.186079\pi$
$883$	8.38235	+	8.38235i	0.282088	+	0.282088i	−0.551853	+	0.833941i	$0.686079\pi$
$884$	−7.61357	+	69.8533i	−0.256072	+	2.34942i
$885$	1.37938	−	1.07222i	0.0463674	−	0.0360421i
$886$	−0.0437093	+	0.804427i	−0.00146844	+	0.0270252i
$887$	−20.1435	−	5.39744i	−0.676354	−	0.181228i	−0.0957386	−	0.995407i	$-0.530521\pi$
$887$	−20.1435	−	5.39744i	−0.676354	−	0.181228i	−0.580615	+	0.814178i	$0.697188\pi$
$888$	9.84045	+	9.34953i	0.330224	+	0.313750i
$889$	−25.5797	+	10.6435i	−0.857914	+	0.356972i
$890$	0.420205	−	3.96630i	0.0140853	−	0.132951i
$891$	−47.2068	−	14.2672i	−1.58149	−	0.477970i
$892$	−5.18812	+	13.3617i	−0.173711	+	0.447383i
$893$	0.771882	+	2.88070i	0.0258300	+	0.0963990i
$894$	−10.2953	−	4.22542i	−0.344328	−	0.141319i
$895$	9.11576	−	1.94802i	0.304706	−	0.0651153i
$896$	−14.5938	+	26.1347i	−0.487544	+	0.873098i
$897$	−10.5596	+	15.5356i	−0.352575	+	0.518719i
$898$	−7.78775	−	36.9880i	−0.259880	−	1.23431i
$899$	25.8678	+	14.9348i	0.862739	+	0.498103i
$900$	28.0996	+	10.5078i	0.936652	+	0.350261i
$901$	−9.81705	+	5.66787i	−0.327053	+	0.188824i
$902$	−13.7579	+	42.0670i	−0.458088	+	1.40068i
$903$	−7.71684	+	8.68794i	−0.256800	+	0.289117i
$904$	5.74087	−	34.9408i	0.190938	−	1.16211i
$905$	−12.9411	−	14.3410i	−0.430178	−	0.476712i
$906$	−0.0390881	+	0.00527503i	−0.00129862	+	0.000175251i
$907$	8.74895	+	32.6515i	0.290504	+	1.08418i	0.944723	+	0.327871i	$0.106331\pi$
$907$	8.74895	+	32.6515i	0.290504	+	1.08418i	−0.654218	+	0.756306i	$0.727002\pi$
$908$	−28.4662	+	22.8708i	−0.944685	+	0.758994i
$909$	11.8583	+	29.9631i	0.393315	+	0.993813i
$910$	−42.2418	−	10.1069i	−1.40030	−	0.335039i
$911$		−	36.6652i		−	1.21477i	−0.794407	−	0.607386i	$-0.792218\pi$
$911$		−	36.6652i		−	1.21477i	0.794407	−	0.607386i	$-0.207782\pi$
$912$	10.4208	−	2.47400i	0.345068	−	0.0819222i
$913$	−9.75544	−	36.4078i	−0.322858	−	1.20492i
$914$	47.9319	+	2.60443i	1.58545	+	0.0861467i
$915$	6.59685	+	47.7952i	0.218085	+	1.58006i
$916$	16.3439	+	11.9708i	0.540018	+	0.395527i
$917$	−42.2165	+	5.62675i	−1.39411	+	0.185812i
$918$	−12.2650	−	48.1960i	−0.404804	−	1.59070i
$919$	−9.08681	+	5.24627i	−0.299746	+	0.173059i	−0.642329	−	0.766429i	$-0.722032\pi$
$919$	−9.08681	+	5.24627i	−0.299746	+	0.173059i	0.342583	+	0.939488i	$0.388698\pi$
$920$	6.05339	−	11.7444i	0.199574	−	0.387200i
$921$	−9.87731	+	28.3573i	−0.325469	+	0.934404i
$922$	7.46757	+	35.4673i	0.245931	+	1.16805i
$923$	11.6741	−	11.6741i	0.384257	−	0.384257i
$924$	−50.1592	−	2.48178i	−1.65012	−	0.0816445i
$925$	4.93646	−	12.9444i	0.162310	−	0.425608i
$926$	−26.3652	−	17.1939i	−0.866414	−	0.565027i
$927$	38.3383	−	28.4641i	1.25920	−	0.934883i
$928$	−23.4091	+	39.6603i	−0.768442	+	1.30191i
$929$	−5.13924	−	8.90142i	−0.168613	−	0.292046i	0.769319	−	0.638864i	$-0.220595\pi$
$929$	−5.13924	−	8.90142i	−0.168613	−	0.292046i	−0.937932	+	0.346818i	$0.887262\pi$
$930$	12.9847	−	15.3372i	0.425785	−	0.502928i
$931$	2.76728	−	10.4617i	0.0906940	−	0.342867i
$932$	−2.83135	−	18.3324i	−0.0927440	−	0.600499i
$933$	44.2859	+	3.25532i	1.44986	+	0.106574i
$934$	13.7600	+	0.747660i	0.450240	+	0.0244642i
$935$	73.8424	−	37.7263i	2.41491	−	1.23378i
$936$	−29.6244	−	32.6009i	−0.968302	−	1.06559i
$937$	−7.60794	−	7.60794i	−0.248541	−	0.248541i	0.571831	−	0.820372i	$-0.306233\pi$
$937$	−7.60794	−	7.60794i	−0.248541	−	0.248541i	−0.820372	+	0.571831i	$0.806233\pi$
$938$	2.79281	+	35.6318i	0.0911886	+	1.16342i
$939$	−15.0064	+	2.86151i	−0.489715	+	0.0933820i
$940$	−5.44786	+	6.68980i	−0.177689	+	0.218197i
$941$	2.75537	−	4.77244i	0.0898224	−	0.155577i	−0.817614	−	0.575767i	$-0.804703\pi$
$941$	2.75537	−	4.77244i	0.0898224	−	0.155577i	0.907436	+	0.420190i	$0.138037\pi$
$942$	−11.3333	+	14.8694i	−0.369257	+	0.484470i
$943$	−11.5253	−	3.08820i	−0.375317	−	0.100566i
$944$	1.72032	−	0.544373i	0.0559915	−	0.0177178i
$945$	30.5089	−	3.76884i	0.992456	−	0.122600i
$946$	−8.88723	−	17.5254i	−0.288949	−	0.569800i
$947$	−7.42874	+	27.7244i	−0.241402	+	0.900923i	0.733756	+	0.679413i	$0.237765\pi$
$947$	−7.42874	+	27.7244i	−0.241402	+	0.900923i	−0.975158	+	0.221510i	$0.928901\pi$
$948$	2.20462	−	11.9833i	0.0716026	−	0.389198i
$949$	21.3491	−	36.9778i	0.693022	−	1.20035i
$950$	−6.42759	−	8.84195i	−0.208539	−	0.286871i
$951$	1.89465	+	9.93592i	0.0614381	+	0.322194i
$952$	−23.9800	−	44.6077i	−0.777195	−	1.44574i
$953$	22.9136	+	22.9136i	0.742245	+	0.742245i	0.973010	−	0.230764i	$-0.0741227\pi$
$953$	22.9136	+	22.9136i	0.742245	+	0.742245i	−0.230764	+	0.973010i	$0.574123\pi$
$954$	1.41900	−	6.96323i	0.0459419	−	0.225443i
$955$	−1.77486	+	5.48284i	−0.0574332	+	0.177421i
$956$	−4.46865	+	1.96902i	−0.144526	+	0.0636825i
$957$	−77.0585	−	5.66433i	−2.49095	−	0.183102i
$958$	40.7382	+	13.3233i	1.31619	+	0.430457i
$959$	−12.8275	−	1.66786i	−0.414222	−	0.0538581i
$960$	23.4538	+	20.2465i	0.756967	+	0.653453i
$961$	8.76944	+	15.1891i	0.282885	+	0.489971i
$962$	−15.1432	+	13.5823i	−0.488235	+	0.437912i
$963$	−1.99358	−	2.68516i	−0.0642423	−	0.0865281i
$964$	0.0498373	−	0.457249i	0.00160515	−	0.0147270i
$965$	40.1203	+	25.9921i	1.29152	+	0.836717i
$966$	−0.0655951	−	13.5388i	−0.00211049	−	0.435602i
$967$	−20.7126	−	20.7126i	−0.666072	−	0.666072i	0.290733	−	0.956804i	$-0.406101\pi$
$967$	−20.7126	−	20.7126i	−0.666072	−	0.666072i	−0.956804	+	0.290733i	$0.906101\pi$
$968$	22.1701	−	49.0318i	0.712575	−	1.57594i
$969$	−5.96070	+	17.1129i	−0.191485	+	0.549745i
$970$	−3.12643	−	19.8461i	−0.100384	−	0.637221i
$971$	−8.33342	−	14.4339i	−0.267432	−	0.463206i	0.700766	−	0.713391i	$-0.252842\pi$
$971$	−8.33342	−	14.4339i	−0.267432	−	0.463206i	−0.968198	+	0.250185i	$0.919508\pi$
$972$	27.7191	+	14.2706i	0.889091	+	0.457730i
$973$	−9.13697	+	22.1590i	−0.292918	+	0.710384i
$974$	0.321720	+	0.634423i	0.0103086	+	0.0203282i
$975$	−19.0564	+	40.7201i	−0.610293	+	1.30409i
$976$	−10.7349	+	48.6606i	−0.343616	+	1.55759i
$977$	−8.21516	−	30.6594i	−0.262826	−	0.980880i	−0.963568	−	0.267465i	$-0.913814\pi$
$977$	−8.21516	−	30.6594i	−0.262826	−	0.980880i	0.700741	−	0.713415i	$-0.252853\pi$
$978$	−38.5900	+	16.1313i	−1.23397	+	0.515822i
$979$	6.91117			0.220882
$980$	29.2206	−	11.2319i	0.933418	−	0.358790i
$981$	12.1738	+	30.7604i	0.388680	+	0.982103i
$982$	0.850315	+	4.03859i	0.0271347	+	0.128876i
$983$	15.0123	−	4.02253i	0.478817	−	0.128299i	−0.0113345	−	0.999936i	$-0.503608\pi$
$983$	15.0123	−	4.02253i	0.478817	−	0.128299i	0.490152	+	0.871637i	$0.336941\pi$
$984$	13.3660	−	24.5817i	0.426092	−	0.783637i
$985$	15.0318	+	0.771321i	0.478954	+	0.0245763i
$986$	−35.2409	−	69.4941i	−1.12230	−	2.21314i
$987$	−1.77948	+	8.65954i	−0.0566414	+	0.275636i
$988$	2.44993	+	15.8628i	0.0779428	+	0.504664i
$989$	4.58770	−	2.64871i	0.145880	−	0.0842241i
$990$	−12.9767	+	50.3375i	−0.412426	+	1.59983i
$991$	2.84805	−	4.93296i	0.0904712	−	0.156701i	−0.817238	−	0.576300i	$-0.804496\pi$
$991$	2.84805	−	4.93296i	0.0904712	−	0.156701i	0.907709	+	0.419599i	$0.137829\pi$
$992$	18.0730	−	10.2041i	0.573818	−	0.323979i
$993$	−30.0491	+	44.2092i	−0.953580	+	1.40294i
$994$	−2.17221	+	11.6993i	−0.0688984	+	0.371080i
$995$	56.3380	−	12.0394i	1.78604	−	0.381673i
$996$	1.90091	+	23.7527i	0.0602328	+	0.752632i
$997$	3.22843	+	12.0486i	0.102245	+	0.381584i	0.998018	−	0.0629276i	$-0.0200437\pi$
$997$	3.22843	+	12.0486i	0.102245	+	0.381584i	−0.895773	+	0.444512i	$0.853377\pi$
$998$	−14.8379	+	13.3086i	−0.469687	+	0.421275i
$999$	6.67288	−	12.7574i	0.211121	−	0.403627i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.dc.e.557.78	yes	704
3.2	odd	2	inner	840.2.dc.e.557.99	yes	704
5.3	odd	4	inner	840.2.dc.e.53.11	✓	704
7.2	even	3	inner	840.2.dc.e.317.40	yes	704
8.5	even	2	inner	840.2.dc.e.557.49	yes	704
15.8	even	4	inner	840.2.dc.e.53.166	yes	704
21.2	odd	6	inner	840.2.dc.e.317.137	yes	704
24.5	odd	2	inner	840.2.dc.e.557.128	yes	704
35.23	odd	12	inner	840.2.dc.e.653.128	yes	704
40.13	odd	4	inner	840.2.dc.e.53.137	yes	704
56.37	even	6	inner	840.2.dc.e.317.166	yes	704
105.23	even	12	inner	840.2.dc.e.653.49	yes	704
120.53	even	4	inner	840.2.dc.e.53.40	yes	704
168.149	odd	6	inner	840.2.dc.e.317.11	yes	704
280.93	odd	12	inner	840.2.dc.e.653.99	yes	704
840.653	even	12	inner	840.2.dc.e.653.78	yes	704

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.dc.e.53.11	✓	704	5.3	odd	4	inner
840.2.dc.e.53.40	yes	704	120.53	even	4	inner
840.2.dc.e.53.137	yes	704	40.13	odd	4	inner
840.2.dc.e.53.166	yes	704	15.8	even	4	inner
840.2.dc.e.317.11	yes	704	168.149	odd	6	inner
840.2.dc.e.317.40	yes	704	7.2	even	3	inner
840.2.dc.e.317.137	yes	704	21.2	odd	6	inner
840.2.dc.e.317.166	yes	704	56.37	even	6	inner
840.2.dc.e.557.49	yes	704	8.5	even	2	inner
840.2.dc.e.557.78	yes	704	1.1	even	1	trivial
840.2.dc.e.557.99	yes	704	3.2	odd	2	inner
840.2.dc.e.557.128	yes	704	24.5	odd	2	inner
840.2.dc.e.653.49	yes	704	105.23	even	12	inner
840.2.dc.e.653.78	yes	704	840.653	even	12	inner
840.2.dc.e.653.99	yes	704	280.93	odd	12	inner
840.2.dc.e.653.128	yes	704	35.23	odd	12	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.dc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.291371 - 1.38387i) q^{2} +(1.55945 - 0.753731i) q^{3} +(-1.83021 + 0.806441i) q^{4} +(1.66009 - 1.49804i) q^{5} +(-1.49745 - 1.93847i) q^{6} +(-1.00857 + 2.44598i) q^{7} +(1.64928 + 2.29780i) q^{8} +(1.86378 - 2.35082i) q^{9} +(-2.55679 - 1.86086i) q^{10} +(2.73976 - 4.74540i) q^{11} +(-2.24628 + 2.63709i) q^{12} +(-3.67085 - 3.67085i) q^{13} +(3.67878 + 0.683040i) q^{14} +(1.45971 - 3.58737i) q^{15} +(2.69930 - 2.95191i) q^{16} +(1.75160 + 6.53708i) q^{17} +(-3.79628 - 1.89427i) q^{18} +(0.772962 + 1.33881i) q^{19} +(-1.83022 + 4.08048i) q^{20} +(0.270799 + 4.57457i) q^{21} +(-7.36532 - 2.40880i) q^{22} +(0.540699 - 2.01792i) q^{23} +(4.30390 + 2.34019i) q^{24} +(0.511778 - 4.97374i) q^{25} +(-4.01041 + 6.14957i) q^{26} +(1.13459 - 5.07077i) q^{27} +(-0.126652 - 5.28999i) q^{28} -8.14119i q^{29} +(-5.38978 - 0.974792i) q^{30} +(-1.83447 + 3.17740i) q^{31} +(-4.87156 - 2.87539i) q^{32} +(0.695762 - 9.46526i) q^{33} +(8.53611 - 4.32871i) q^{34} +(1.98985 + 5.57140i) q^{35} +(-1.51530 + 5.80550i) q^{36} +(2.67633 + 0.717120i) q^{37} +(1.62752 - 1.45977i) q^{38} +(-8.49135 - 2.95768i) q^{39} +(6.18013 + 1.34386i) q^{40} -5.71150i q^{41} +(6.25171 - 1.70765i) q^{42} +(1.79304 + 1.79304i) q^{43} +(-1.18743 + 10.8945i) q^{44} +(-0.427572 - 6.69456i) q^{45} +(-2.95008 - 0.160296i) q^{46} +(1.86342 + 0.499301i) q^{47} +(1.98449 - 6.63791i) q^{48} +(-4.96559 - 4.93386i) q^{49} +(-7.03214 + 0.740969i) q^{50} +(7.65874 + 8.87402i) q^{51} +(9.67873 + 3.75808i) q^{52} +(0.433517 + 1.61791i) q^{53} +(-7.34789 - 0.0926470i) q^{54} +(-2.56054 - 11.9820i) q^{55} +(-7.28376 + 1.71662i) q^{56} +(2.21450 + 1.50520i) q^{57} +(-11.2664 + 2.37211i) q^{58} +(0.390662 + 0.225549i) q^{59} +(0.221440 + 7.74280i) q^{60} +(-10.7886 + 6.22883i) q^{61} +(4.93162 + 1.61287i) q^{62} +(3.87029 + 6.92971i) q^{63} +(-2.55974 + 7.57943i) q^{64} +(-11.5930 - 0.594866i) q^{65} +(-13.3014 + 1.79506i) q^{66} +(2.47229 + 9.22673i) q^{67} +(-8.47757 - 10.5516i) q^{68} +(-0.677773 - 3.55438i) q^{69} +(7.13032 - 4.37705i) q^{70} +3.18021i q^{71} +(8.47559 + 0.405427i) q^{72} +(2.12875 + 7.94460i) q^{73} +(0.212597 - 3.91265i) q^{74} +(-2.95077 - 8.14205i) q^{75} +(-2.49435 - 1.82695i) q^{76} +(8.84390 + 11.4874i) q^{77} +(-1.61891 + 12.6127i) q^{78} +(-3.04609 + 1.75866i) q^{79} +(0.0590185 - 8.94408i) q^{80} +(-2.05267 - 8.76279i) q^{81} +(-7.90399 + 1.66417i) q^{82} +(4.86400 - 4.86400i) q^{83} +(-4.18474 - 8.15402i) q^{84} +(12.7006 + 8.22815i) q^{85} +(1.95890 - 3.00378i) q^{86} +(-6.13627 - 12.6958i) q^{87} +(15.4226 - 1.53109i) q^{88} +(0.630636 + 1.09229i) q^{89} +(-9.13984 + 2.54231i) q^{90} +(12.6811 - 5.27651i) q^{91} +(0.637741 + 4.12924i) q^{92} +(-0.465864 + 6.33769i) q^{93} +(0.148023 - 2.72421i) q^{94} +(3.28877 + 1.06462i) q^{95} +(-9.76424 - 0.812184i) q^{96} +(4.49246 + 4.49246i) q^{97} +(-5.38100 + 8.30932i) q^{98} +(-6.04926 - 15.2850i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 704 q - 16 q^{6} - 24 q^{7} + 12 q^{10} + 10 q^{12} + 32 q^{15} - 72 q^{16} + 6 q^{18} + 64 q^{22} - 8 q^{25} + 24 q^{28} + 8 q^{30} - 16 q^{31} + 44 q^{33} - 240 q^{36} + 16 q^{40} - 78 q^{42} - 8 q^{46}+ \cdots - 80 q^{97}+O(q^{100}) \) 704 * q - 16 * q^6 - 24 * q^7 + 12 * q^10 + 10 * q^12 + 32 * q^15 - 72 * q^16 + 6 * q^18 + 64 * q^22 - 8 * q^25 + 24 * q^28 + 8 * q^30 - 16 * q^31 + 44 * q^33 - 240 * q^36 + 16 * q^40 - 78 * q^42 - 8 * q^46 - 20 * q^48 - 60 * q^52 + 272 * q^55 + 8 * q^57 - 20 * q^58 - 14 * q^60 + 12 * q^63 - 84 * q^66 + 112 * q^70 - 38 * q^72 + 104 * q^73 - 64 * q^76 - 16 * q^78 - 168 * q^81 - 72 * q^82 - 64 * q^87 + 52 * q^88 - 44 * q^90 + 40 * q^96 - 80 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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