LMFDB - Embedded newform 840.2.cq.a.11.36

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(11,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 3, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.11"); 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.cq (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [128,0,0,0,-64] 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:	$128$
Relative dimension:	$64$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.36
Character	$\chi$	$=$	840.11
Dual form			840.2.cq.a.611.36

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.212988 + 1.39808i) q^{2} +(-1.72228 + 0.183676i) q^{3} +(-1.90927 + 0.595551i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.623620 - 2.36878i) q^{6} +(-2.64252 - 0.130688i) q^{7} +(-1.23928 - 2.54247i) q^{8} +(2.93253 - 0.632683i) q^{9} +(1.10428 - 0.883495i) q^{10} +(4.04336 + 2.33444i) q^{11} +(3.17892 - 1.37639i) q^{12} -4.34878i q^{13} +(-0.380114 - 3.72230i) q^{14} +(1.02021 + 1.39970i) q^{15} +(3.29064 - 2.27414i) q^{16} +(-1.67559 - 0.967404i) q^{17} +(1.50914 + 3.96516i) q^{18} +(-0.0249616 - 0.0432347i) q^{19} +(1.47040 + 1.35570i) q^{20} +(4.57518 - 0.260285i) q^{21} +(-2.40255 + 6.15017i) q^{22} +(3.62201 + 6.27350i) q^{23} +(2.60139 + 4.15124i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(6.07996 - 0.926240i) q^{26} +(-4.93444 + 1.62829i) q^{27} +(5.12312 - 1.32424i) q^{28} -0.0972660 q^{29} +(-1.73961 + 1.72446i) q^{30} +(-1.01737 - 0.587378i) q^{31} +(3.88030 + 4.11622i) q^{32} +(-7.39260 - 3.27790i) q^{33} +(0.995629 - 2.54866i) q^{34} +(1.20808 + 2.35383i) q^{35} +(-5.22220 + 2.95443i) q^{36} +(-3.60469 + 2.08117i) q^{37} +(0.0551292 - 0.0441068i) q^{38} +(0.798764 + 7.48984i) q^{39} +(-1.58221 + 2.34449i) q^{40} +10.8636i q^{41} +(1.33836 + 6.34104i) q^{42} +8.18596 q^{43} +(-9.11016 - 2.04905i) q^{44} +(-2.01418 - 2.22330i) q^{45} +(-7.99942 + 6.40005i) q^{46} +(2.85565 + 4.94613i) q^{47} +(-5.24971 + 4.52112i) q^{48} +(6.96584 + 0.690692i) q^{49} +(-1.31727 - 0.514588i) q^{50} +(3.06354 + 1.35838i) q^{51} +(2.58992 + 8.30300i) q^{52} +(7.07548 - 12.2551i) q^{53} +(-3.32747 - 6.55194i) q^{54} -4.66887i q^{55} +(2.94256 + 6.88050i) q^{56} +(0.0509321 + 0.0698776i) q^{57} +(-0.0207165 - 0.135986i) q^{58} +(11.8059 + 6.81613i) q^{59} +(-2.78145 - 2.06483i) q^{60} +(1.18119 - 0.681959i) q^{61} +(0.604515 - 1.54747i) q^{62} +(-7.83195 + 1.28863i) q^{63} +(-4.92836 + 6.30169i) q^{64} +(-3.76615 + 2.17439i) q^{65} +(3.00823 - 11.0336i) q^{66} +(1.67973 - 2.90938i) q^{67} +(3.77530 + 0.849136i) q^{68} +(-7.39041 - 10.1395i) q^{69} +(-3.03355 + 2.19034i) q^{70} +6.44542 q^{71} +(-5.24281 - 6.67180i) q^{72} +(-4.51719 + 7.82400i) q^{73} +(-3.67740 - 4.59639i) q^{74} +(0.702074 - 1.58338i) q^{75} +(0.0734069 + 0.0676809i) q^{76} +(-10.3796 - 6.69722i) q^{77} +(-10.3013 + 2.71199i) q^{78} +(-8.28188 + 4.78155i) q^{79} +(-3.61478 - 1.71271i) q^{80} +(8.19942 - 3.71072i) q^{81} +(-15.1883 + 2.31383i) q^{82} -11.4677i q^{83} +(-8.58025 + 3.22171i) q^{84} +1.93481i q^{85} +(1.74351 + 11.4446i) q^{86} +(0.167520 - 0.0178654i) q^{87} +(0.924378 - 13.1732i) q^{88} +(5.85921 - 3.38281i) q^{89} +(2.67936 - 3.28953i) q^{90} +(-0.568334 + 11.4917i) q^{91} +(-10.6516 - 9.82072i) q^{92} +(1.86008 + 0.824766i) q^{93} +(-6.30688 + 5.04590i) q^{94} +(-0.0249616 + 0.0432347i) q^{95} +(-7.43903 - 6.37658i) q^{96} +6.90641 q^{97} +(0.517999 + 9.88593i) q^{98} +(13.3342 + 4.28763i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 64 q^{5} - 12 q^{12} - 6 q^{14} + 8 q^{16} + 14 q^{18} + 8 q^{21} + 4 q^{22} - 64 q^{25} - 16 q^{26} - 6 q^{28} - 10 q^{32} + 24 q^{34} + 20 q^{36} - 16 q^{38} + 16 q^{42} + 6 q^{44} + 8 q^{46}+ \cdots + 14 q^{98}+O(q^{100}) $ 128 * q - 64 * q^5 - 12 * q^12 - 6 * q^14 + 8 * q^16 + 14 * q^18 + 8 * q^21 + 4 * q^22 - 64 * q^25 - 16 * q^26 - 6 * q^28 - 10 * q^32 + 24 * q^34 + 20 * q^36 - 16 * q^38 + 16 * q^42 + 6 * q^44 + 8 * q^46 - 80 * q^48 + 8 * q^49 + 20 * q^51 - 6 * q^52 - 32 * q^54 - 18 * q^56 - 8 * q^58 - 12 * q^60 - 20 * q^62 - 28 * q^63 - 14 * q^66 + 32 * q^67 - 2 * q^68 + 40 * q^69 - 6 * q^70 - 48 * q^71 + 4 * q^72 - 8 * q^73 - 26 * q^74 - 24 * q^76 - 12 * q^78 + 8 * q^80 + 4 * q^81 - 12 * q^82 - 22 * q^84 + 46 * q^86 - 36 * q^87 - 20 * q^88 - 28 * q^90 - 24 * q^91 - 40 * q^92 + 12 * q^94 + 34 * q^96 + 32 * q^97 + 14 * q^98

Character values

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

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

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 $

$2$	0.212988	+	1.39808i	0.150606	+	0.988594i
$2$	0.212988	+	1.39808i	0.150606	+	0.988594i
$3$	−1.72228	+	0.183676i	−0.994361	+	0.106045i
$3$	−1.72228	+	0.183676i	−0.994361	+	0.106045i
$4$	−1.90927	+	0.595551i	−0.954636	+	0.297776i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−0.623620	−	2.36878i	−0.254592	−	0.967049i
$7$	−2.64252	−	0.130688i	−0.998779	−	0.0493955i
$7$	−2.64252	−	0.130688i	−0.998779	−	0.0493955i
$8$	−1.23928	−	2.54247i	−0.438153	−	0.898901i
$9$	2.93253	−	0.632683i	0.977509	−	0.210894i
$10$	1.10428	−	0.883495i	0.349204	−	0.279386i
$11$	4.04336	+	2.33444i	1.21912	+	0.703859i	0.964730	−	0.263242i	$-0.0847919\pi$
$11$	4.04336	+	2.33444i	1.21912	+	0.703859i	0.254390	+	0.967102i	$0.418125\pi$
$12$	3.17892	−	1.37639i	0.917675	−	0.397331i
$13$		−	4.34878i		−	1.20613i	−0.797690	−	0.603067i	$-0.793945\pi$
$13$		−	4.34878i		−	1.20613i	0.797690	−	0.603067i	$-0.206055\pi$
$14$	−0.380114	−	3.72230i	−0.101590	−	0.994826i
$15$	1.02021	+	1.39970i	0.263417	+	0.361402i
$16$	3.29064	−	2.27414i	0.822659	−	0.568534i
$17$	−1.67559	−	0.967404i	−0.406391	−	0.234630i	0.282847	−	0.959165i	$-0.408721\pi$
$17$	−1.67559	−	0.967404i	−0.406391	−	0.234630i	−0.689238	+	0.724535i	$0.742055\pi$
$18$	1.50914	+	3.96516i	0.355707	+	0.934597i
$19$	−0.0249616	−	0.0432347i	−0.00572657	−	0.00991872i	0.863148	−	0.504951i	$-0.168490\pi$
$19$	−0.0249616	−	0.0432347i	−0.00572657	−	0.00991872i	−0.868874	+	0.495032i	$0.835156\pi$
$20$	1.47040	+	1.35570i	0.328791	+	0.303144i
$21$	4.57518	−	0.260285i	0.998386	−	0.0567987i
$22$	−2.40255	+	6.15017i	−0.512225	+	1.31122i
$23$	3.62201	+	6.27350i	0.755240	+	1.30811i	0.945255	+	0.326333i	$0.105813\pi$
$23$	3.62201	+	6.27350i	0.755240	+	1.30811i	−0.190014	+	0.981781i	$0.560853\pi$
$24$	2.60139	+	4.15124i	0.531006	+	0.847368i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	6.07996	−	0.926240i	1.19238	−	0.181651i
$27$	−4.93444	+	1.62829i	−0.949633	+	0.313365i
$28$	5.12312	−	1.32424i	0.968179	−	0.250257i
$29$	−0.0972660			−0.0180618			−0.00903092	−	0.999959i	$-0.502875\pi$
$29$	−0.0972660			−0.0180618			−0.00903092	+	0.999959i	$0.502875\pi$
$30$	−1.73961	+	1.72446i	−0.317608	+	0.314842i
$31$	−1.01737	−	0.587378i	−0.182725	−	0.105496i	0.405847	−	0.913941i	$-0.366976\pi$
$31$	−1.01737	−	0.587378i	−0.182725	−	0.105496i	−0.588572	+	0.808445i	$0.700310\pi$
$32$	3.88030	+	4.11622i	0.685947	+	0.727652i
$33$	−7.39260	−	3.27790i	−1.28689	−	0.570609i
$34$	0.995629	−	2.54866i	0.170749	−	0.437092i
$35$	1.20808	+	2.35383i	0.204203	+	0.397871i
$36$	−5.22220	+	2.95443i	−0.870366	+	0.492406i
$37$	−3.60469	+	2.08117i	−0.592607	+	0.342142i	−0.766128	−	0.642689i	$-0.777819\pi$
$37$	−3.60469	+	2.08117i	−0.592607	+	0.342142i	0.173521	+	0.984830i	$0.444486\pi$
$38$	0.0551292	−	0.0441068i	0.00894313	−	0.00715507i
$39$	0.798764	+	7.48984i	0.127905	+	1.19933i
$40$	−1.58221	+	2.34449i	−0.250169	+	0.370696i
$41$			10.8636i			1.69662i	0.529504	+	0.848308i	$0.322378\pi$
$41$			10.8636i			1.69662i	−0.529504	+	0.848308i	$0.677622\pi$
$42$	1.33836	+	6.34104i	0.206513	+	0.978444i
$43$	8.18596			1.24835			0.624173	−	0.781286i	$-0.285436\pi$
$43$	8.18596			1.24835			0.624173	+	0.781286i	$0.285436\pi$
$44$	−9.11016	−	2.04905i	−1.37341	−	0.308905i
$45$	−2.01418	−	2.22330i	−0.300257	−	0.331430i
$46$	−7.99942	+	6.40005i	−1.17945	+	0.943635i
$47$	2.85565	+	4.94613i	0.416539	+	0.721467i	0.995589	−	0.0938254i	$-0.0299095\pi$
$47$	2.85565	+	4.94613i	0.416539	+	0.721467i	−0.579050	+	0.815292i	$0.696576\pi$
$48$	−5.24971	+	4.52112i	−0.757730	+	0.652568i
$49$	6.96584	+	0.690692i	0.995120	+	0.0986703i
$50$	−1.31727	−	0.514588i	−0.186290	−	0.0727737i
$51$	3.06354	+	1.35838i	0.428981	+	0.190211i
$52$	2.58992	+	8.30300i	0.359157	+	1.15142i
$53$	7.07548	−	12.2551i	0.971892	−	1.68337i	0.282061	−	0.959396i	$-0.408982\pi$
$53$	7.07548	−	12.2551i	0.971892	−	1.68337i	0.689831	−	0.723970i	$-0.257685\pi$
$54$	−3.32747	−	6.55194i	−0.452811	−	0.891607i
$55$		−	4.66887i		−	0.629551i
$56$	2.94256	+	6.88050i	0.393216	+	0.919446i
$57$	0.0509321	+	0.0698776i	0.00674612	+	0.00925551i
$58$	−0.0207165	−	0.135986i	−0.00272021	−	0.0178558i
$59$	11.8059	+	6.81613i	1.53699	+	0.887384i	0.999013	+	0.0444272i	$0.0141463\pi$
$59$	11.8059	+	6.81613i	1.53699	+	0.887384i	0.537981	+	0.842957i	$0.319187\pi$
$60$	−2.78145	−	2.06483i	−0.359084	−	0.266568i
$61$	1.18119	−	0.681959i	0.151236	−	0.0873160i	−0.422472	−	0.906376i	$-0.638838\pi$
$61$	1.18119	−	0.681959i	0.151236	−	0.0873160i	0.573708	+	0.819060i	$0.305504\pi$
$62$	0.604515	−	1.54747i	0.0767735	−	0.196529i
$63$	−7.83195	+	1.28863i	−0.986733	+	0.162352i
$64$	−4.92836	+	6.30169i	−0.616045	+	0.787711i
$65$	−3.76615	+	2.17439i	−0.467134	+	0.269700i
$66$	3.00823	−	11.0336i	0.370288	−	1.35815i
$67$	1.67973	−	2.90938i	0.205212	−	0.355437i	−0.744989	−	0.667077i	$-0.767545\pi$
$67$	1.67973	−	2.90938i	0.205212	−	0.355437i	0.950200	+	0.311640i	$0.100878\pi$
$68$	3.77530	+	0.849136i	0.457823	+	0.102973i
$69$	−7.39041	−	10.1395i	−0.889701	−	1.22065i
$70$	−3.03355	+	2.19034i	−0.362578	+	0.261795i
$71$	6.44542			0.764931			0.382466	−	0.923970i	$-0.375075\pi$
$71$	6.44542			0.764931			0.382466	+	0.923970i	$0.375075\pi$
$72$	−5.24281	−	6.67180i	−0.617871	−	0.786279i
$73$	−4.51719	+	7.82400i	−0.528697	+	0.915730i	0.470743	+	0.882270i	$0.343986\pi$
$73$	−4.51719	+	7.82400i	−0.528697	+	0.915730i	−0.999440	+	0.0334596i	$0.989347\pi$
$74$	−3.67740	−	4.59639i	−0.427489	−	0.534319i
$75$	0.702074	−	1.58338i	0.0810686	−	0.182833i
$76$	0.0734069	+	0.0676809i	0.00842034	+	0.00776353i
$77$	−10.3796	−	6.69722i	−1.18286	−	0.763219i
$78$	−10.3013	+	2.71199i	−1.16639	+	0.307072i
$79$	−8.28188	+	4.78155i	−0.931785	+	0.537966i	−0.887376	−	0.461047i	$-0.847474\pi$
$79$	−8.28188	+	4.78155i	−0.931785	+	0.537966i	−0.0444090	+	0.999013i	$0.514140\pi$
$80$	−3.61478	−	1.71271i	−0.404145	−	0.191486i
$81$	8.19942	−	3.71072i	0.911047	−	0.412302i
$82$	−15.1883	+	2.31383i	−1.67726	+	0.255520i
$83$		−	11.4677i		−	1.25875i	−0.777103	−	0.629373i	$-0.783312\pi$
$83$		−	11.4677i		−	1.25875i	0.777103	−	0.629373i	$-0.216688\pi$
$84$	−8.58025	+	3.22171i	−0.936182	+	0.351517i
$85$			1.93481i			0.209859i
$86$	1.74351	+	11.4446i	0.188008	+	1.23411i
$87$	0.167520	−	0.0178654i	0.0179600	−	0.00191537i
$88$	0.924378	−	13.1732i	0.0985390	−	1.40427i
$89$	5.85921	−	3.38281i	0.621075	−	0.358578i	−0.156213	−	0.987723i	$-0.549929\pi$
$89$	5.85921	−	3.38281i	0.621075	−	0.358578i	0.777287	+	0.629146i	$0.216595\pi$
$90$	2.67936	−	3.28953i	0.282430	−	0.346747i
$91$	−0.568334	+	11.4917i	−0.0595776	+	1.20466i
$92$	−10.6516	−	9.82072i	−1.11050	−	1.02388i
$93$	1.86008	+	0.824766i	0.192882	+	0.0855243i
$94$	−6.30688	+	5.04590i	−0.650505	+	0.520445i
$95$	−0.0249616	+	0.0432347i	−0.00256100	+	0.00443579i
$96$	−7.43903	−	6.37658i	−0.759243	−	0.650807i
$97$	6.90641			0.701239			0.350620	−	0.936518i	$-0.385971\pi$
$97$	6.90641			0.701239			0.350620	+	0.936518i	$0.385971\pi$
$98$	0.517999	+	9.88593i	0.0523258	+	0.998630i
$99$	13.3342	+	4.28763i	1.34014	+	0.430923i
$100$	0.438874	−	1.95125i	0.0438874	−	0.195125i
$101$	8.80824	−	15.2563i	0.876453	−	1.51806i	0.0212462	−	0.999774i	$-0.493237\pi$
$101$	8.80824	−	15.2563i	0.876453	−	1.51806i	0.855207	−	0.518287i	$-0.173430\pi$
$102$	−1.24663	+	4.57240i	−0.123435	+	0.452735i
$103$	1.23715	−	0.714272i	0.121900	−	0.0703793i	−0.437810	−	0.899068i	$-0.644246\pi$
$103$	1.23715	−	0.714272i	0.121900	−	0.0703793i	0.559710	+	0.828688i	$0.310912\pi$
$104$	−11.0567	+	5.38937i	−1.08420	+	0.528471i
$105$	−2.51300	−	3.83208i	−0.245244	−	0.373973i
$106$	18.6406	+	7.28192i	1.81054	+	0.707282i
$107$	−6.21564	+	3.58860i	−0.600889	+	0.346923i	−0.769391	−	0.638778i	$-0.779440\pi$
$107$	−6.21564	+	3.58860i	−0.600889	+	0.346923i	0.168502	+	0.985701i	$0.446107\pi$
$108$	8.45145	−	6.04756i	0.813241	−	0.581927i
$109$	8.26788	+	4.77346i	0.791919	+	0.457215i	0.840638	−	0.541598i	$-0.182180\pi$
$109$	8.26788	+	4.77346i	0.791919	+	0.457215i	−0.0487186	+	0.998813i	$0.515514\pi$
$110$	6.52747	−	0.994416i	0.622370	−	0.0948139i
$111$	5.82604	−	4.24645i	0.552983	−	0.403056i
$112$	−8.99278	+	5.57941i	−0.849738	+	0.527205i
$113$			3.67651i			0.345857i	0.984934	+	0.172928i	$0.0553229\pi$
$113$			3.67651i			0.345857i	−0.984934	+	0.172928i	$0.944677\pi$
$114$	−0.0868467	+	0.0860904i	−0.00813394	+	0.00806310i
$115$	3.62201	−	6.27350i	0.337754	−	0.585007i
$116$	0.185707	−	0.0579269i	0.0172425	−	0.00537837i
$117$	−2.75140	−	12.7529i	−0.254367	−	1.17901i
$118$	−7.01499	+	17.9573i	−0.645782	+	1.65311i
$119$	4.30136	+	2.77537i	0.394305	+	0.254417i
$120$	2.29438	−	4.32849i	0.209448	−	0.395135i
$121$	5.39919	+	9.35168i	0.490836	+	0.850153i
$122$	1.20502	+	1.50615i	0.109097	+	0.136360i
$123$	−1.99538	−	18.7103i	−0.179918	−	1.68705i
$124$	2.29225	+	0.515569i	0.205850	+	0.0462995i
$125$	1.00000			0.0894427
$126$	−3.46973	−	10.6753i	−0.309108	−	0.951027i
$127$		−	2.19395i		−	0.194681i	−0.995251	−	0.0973407i	$-0.968966\pi$
$127$		−	2.19395i		−	0.194681i	0.995251	−	0.0973407i	$-0.0310336\pi$
$128$	−9.85997	−	5.54807i	−0.871506	−	0.490384i
$129$	−14.0985	+	1.50356i	−1.24131	+	0.132381i
$130$	−3.84212	−	4.80228i	−0.336977	−	0.421187i
$131$	1.85389	−	1.07034i	0.161975	−	0.0935164i	−0.416821	−	0.908988i	$-0.636856\pi$
$131$	1.85389	−	1.07034i	0.161975	−	0.0935164i	0.578796	+	0.815472i	$0.303523\pi$
$132$	16.0666	+	1.85573i	1.39842	+	0.161520i
$133$	0.0603112	+	0.117511i	0.00522964	+	0.0101895i
$134$	4.42531	+	1.72874i	0.382289	+	0.149340i
$135$	3.87736	+	3.45920i	0.333710	+	0.297721i
$136$	−0.383067	+	5.45904i	−0.0328478	+	0.468109i
$137$	9.50363	+	5.48692i	0.811950	+	0.468779i	0.847632	−	0.530584i	$-0.178027\pi$
$137$	9.50363	+	5.48692i	0.811950	+	0.468779i	−0.0356828	+	0.999363i	$0.511361\pi$
$138$	12.6018	−	12.4920i	1.07273	−	1.06339i
$139$	−8.15854			−0.691999			−0.345999	−	0.938235i	$-0.612460\pi$
$139$	−8.15854			−0.691999			−0.345999	+	0.938235i	$0.612460\pi$
$140$	−3.70839	−	3.77464i	−0.313416	−	0.319015i
$141$	−5.82672	−	7.99413i	−0.490698	−	0.673227i
$142$	1.37280	+	9.01124i	0.115203	+	0.756206i
$143$	10.1520	−	17.5837i	0.848949	−	1.47042i
$144$	8.21108	−	8.75090i	0.684256	−	0.729242i
$145$	0.0486330	+	0.0842348i	0.00403875	+	0.00699532i
$146$	−11.9007	−	4.64898i	−0.984910	−	0.384753i
$147$	−12.1240	+	0.0898863i	−0.999973	+	0.00741370i
$148$	5.64289	−	6.12029i	0.463842	−	0.503085i
$149$	8.78701	+	15.2195i	0.719860	+	1.24683i	0.961055	+	0.276357i	$0.0891273\pi$
$149$	8.78701	+	15.2195i	0.719860	+	1.24683i	−0.241195	+	0.970477i	$0.577539\pi$
$150$	2.36323	+	0.644317i	0.192957	+	0.0526082i
$151$	−13.3596	−	7.71315i	−1.08719	−	0.627688i	−0.154361	−	0.988015i	$-0.549332\pi$
$151$	−13.3596	−	7.71315i	−1.08719	−	0.627688i	−0.932826	+	0.360327i	$0.882665\pi$
$152$	−0.0789887	+	0.117044i	−0.00640683	+	0.00949353i
$153$	−5.52578	−	1.77682i	−0.446733	−	0.143647i
$154$	7.15254	−	15.9380i	0.576368	−	1.28432i
$155$			1.17476i			0.0943587i
$156$	−5.98564	−	13.8244i	−0.479235	−	1.10684i
$157$	13.6657	+	7.88990i	1.09064	+	0.629682i	0.933747	−	0.357933i	$-0.116518\pi$
$157$	13.6657	+	7.88990i	1.09064	+	0.629682i	0.156895	+	0.987615i	$0.449852\pi$
$158$	−8.44894	−	10.5603i	−0.672162	−	0.840136i
$159$	−9.93503	+	22.4064i	−0.787899	+	1.77694i
$160$	1.62460	−	5.41855i	0.128436	−	0.428374i
$161$	−8.75136	−	17.0512i	−0.689703	−	1.34382i
$162$	6.93428	+	10.6731i	0.544808	+	0.838561i
$163$	12.3840	+	21.4498i	0.969993	+	1.68008i	0.695554	+	0.718474i	$0.255159\pi$
$163$	12.3840	+	21.4498i	0.969993	+	1.68008i	0.274439	+	0.961604i	$0.411508\pi$
$164$	−6.46985	−	20.7416i	−0.505211	−	1.61965i
$165$	0.857558	+	8.04113i	0.0667608	+	0.626001i
$166$	16.0328	−	2.44249i	1.24439	−	0.189574i
$167$	−1.69273			−0.130987			−0.0654936	−	0.997853i	$-0.520862\pi$
$167$	−1.69273			−0.130987			−0.0654936	+	0.997853i	$0.520862\pi$
$168$	−6.33171	−	11.3097i	−0.488502	−	0.872563i
$169$	−5.91189			−0.454761
$170$	−2.70502	+	0.412092i	−0.207466	+	0.0316060i
$171$	−0.100554	−	0.110994i	−0.00768958	−	0.00848793i
$172$	−15.6292	+	4.87516i	−1.19172	+	0.371727i
$173$	−1.64079	−	2.84193i	−0.124747	−	0.216068i	0.796887	−	0.604128i	$-0.206479\pi$
$173$	−1.64079	−	2.84193i	−0.124747	−	0.216068i	−0.921634	+	0.388060i	$0.873145\pi$
$174$	0.0606570	+	0.230401i	0.00459840	+	0.0174667i
$175$	1.43444	−	2.22315i	0.108433	−	0.168054i
$176$	18.6141	−	1.51338i	1.40309	−	0.114075i
$177$	−21.5850	−	9.57085i	−1.62243	−	0.719390i
$178$	5.97740	+	7.47116i	0.448025	+	0.559987i
$179$	−0.932643	−	0.538462i	−0.0697090	−	0.0402465i	0.464740	−	0.885447i	$-0.346148\pi$
$179$	−0.932643	−	0.538462i	−0.0697090	−	0.0402465i	−0.534449	+	0.845200i	$0.679481\pi$
$180$	5.16971	+	3.04534i	0.385328	+	0.226986i
$181$		−	26.2498i		−	1.95113i	−0.219710	−	0.975565i	$-0.570511\pi$
$181$		−	26.2498i		−	1.95113i	0.219710	−	0.975565i	$-0.429489\pi$
$182$	−16.1875	+	1.65303i	−1.19989	+	0.122531i
$183$	−1.90908	+	1.39148i	−0.141123	+	0.102861i
$184$	11.4615	−	16.9835i	0.844955	−	1.25204i
$185$	3.60469	+	2.08117i	0.265022	+	0.153010i
$186$	−0.756915	+	2.77622i	−0.0554997	+	0.203562i
$187$	−4.51669	−	7.82313i	−0.330293	−	0.572084i
$188$	−8.39788	−	7.74282i	−0.612478	−	0.564703i
$189$	13.2522	−	3.65793i	0.963952	−	0.266075i
$190$	−0.0657622	−	0.0256898i	−0.00477089	−	0.00186374i
$191$	2.53297	+	4.38724i	0.183279	+	0.317449i	0.942995	−	0.332806i	$-0.107995\pi$
$191$	2.53297	+	4.38724i	0.183279	+	0.317449i	−0.759716	+	0.650255i	$0.774662\pi$
$192$	7.33057	−	11.7585i	0.529038	−	0.848598i
$193$	10.7811	−	18.6734i	0.776041	−	1.34414i	−0.158166	−	0.987412i	$-0.550558\pi$
$193$	10.7811	−	18.6734i	0.776041	−	1.34414i	0.934208	−	0.356730i	$-0.116108\pi$
$194$	1.47098	+	9.65573i	0.105611	+	0.693241i
$195$	6.08701	−	4.43667i	0.435900	−	0.317716i
$196$	−13.7110	+	2.82979i	−0.979359	+	0.202128i
$197$	−19.4850			−1.38825			−0.694124	−	0.719856i	$-0.744208\pi$
$197$	−19.4850			−1.38825			−0.694124	+	0.719856i	$0.744208\pi$
$198$	−3.15443	+	19.5556i	−0.224175	+	1.38975i
$199$	2.34902	+	1.35621i	0.166518	+	0.0961390i	0.580943	−	0.813944i	$-0.302684\pi$
$199$	2.34902	+	1.35621i	0.166518	+	0.0961390i	−0.414425	+	0.910083i	$0.636017\pi$
$200$	2.82149	+	0.197987i	0.199509	+	0.0139998i
$201$	−2.35859	+	5.31930i	−0.166362	+	0.375194i
$202$	23.2057	+	9.06523i	1.63274	+	0.637828i
$203$	0.257027	+	0.0127115i	0.0180398	+	0.000892173i
$204$	−6.65811	−	0.769024i	−0.466161	−	0.0538424i
$205$	9.40819	−	5.43182i	0.657096	−	0.379375i
$206$	1.26211	+	1.57751i	0.0879354	+	0.109911i
$207$	14.5908	+	16.1056i	1.01413	+	1.11942i
$208$	−9.88972	−	14.3103i	−0.685729	−	0.992238i
$209$		−	0.233085i		−	0.0161228i
$210$	4.82232	−	4.32957i	0.332772	−	0.298769i
$211$	−7.65701			−0.527130			−0.263565	−	0.964642i	$-0.584898\pi$
$211$	−7.65701			−0.527130			−0.263565	+	0.964642i	$0.584898\pi$
$212$	−6.21049	+	27.6121i	−0.426538	+	1.89641i
$213$	−11.1009	+	1.18387i	−0.760618	+	0.0811172i
$214$	−6.34102	−	7.92565i	−0.433463	−	0.541786i
$215$	−4.09298	−	7.08925i	−0.279139	−	0.483483i
$216$	10.2551	+	10.5278i	0.697768	+	0.716324i
$217$	2.61166	+	1.68512i	0.177291	+	0.114393i
$218$	−4.91273	+	12.5759i	−0.332732	+	0.851746i
$219$	6.34280	−	14.3048i	0.428607	−	0.966632i
$220$	2.78055	+	8.91415i	0.187465	+	0.600992i
$221$	−4.20703	+	7.28679i	−0.282995	+	0.490162i
$222$	7.17777	+	7.24084i	0.481741	+	0.485973i
$223$			6.98906i			0.468022i	0.972234	+	0.234011i	$0.0751852\pi$
$223$			6.98906i			0.468022i	−0.972234	+	0.234011i	$0.924815\pi$
$224$	−9.71584	−	11.3843i	−0.649167	−	0.760646i
$225$	−0.918344	+	2.85598i	−0.0612229	+	0.190399i
$226$	−5.14006	+	0.783054i	−0.341912	+	0.0520880i
$227$	13.3146	+	7.68720i	0.883723	+	0.510218i	0.871884	−	0.489712i	$-0.162898\pi$
$227$	13.3146	+	7.68720i	0.883723	+	0.510218i	0.0118388	+	0.999930i	$0.496232\pi$
$228$	−0.138859	−	0.103083i	−0.00919615	−	0.00682682i
$229$	−7.72565	+	4.46041i	−0.510525	+	0.294752i	−0.733050	−	0.680175i	$-0.761904\pi$
$229$	−7.72565	+	4.46041i	−0.510525	+	0.294752i	0.222524	+	0.974927i	$0.428570\pi$
$230$	9.54231	+	3.72768i	0.629202	+	0.245796i
$231$	19.1067	+	9.62804i	1.25713	+	0.633479i
$232$	0.120540	+	0.247296i	0.00791384	+	0.0162358i
$233$	−2.58227	+	1.49088i	−0.169170	+	0.0976706i	−0.582195	−	0.813049i	$-0.697806\pi$
$233$	−2.58227	+	1.49088i	−0.169170	+	0.0976706i	0.413024	+	0.910720i	$0.364472\pi$
$234$	17.2436	−	6.56291i	1.12725	−	0.429031i
$235$	2.85565	−	4.94613i	0.186282	−	0.322650i
$236$	−26.6000	−	5.98283i	−1.73151	−	0.389449i
$237$	13.3855	−	9.75636i	0.869482	−	0.633744i
$238$	−2.96405	+	6.60478i	−0.192131	+	0.428125i
$239$	6.68915			0.432685			0.216343	−	0.976318i	$-0.430587\pi$
$239$	6.68915			0.432685			0.216343	+	0.976318i	$0.430587\pi$
$240$	6.54026	+	2.28582i	0.422172	+	0.147549i
$241$	12.1520	−	21.0478i	0.782776	−	1.35581i	−0.147543	−	0.989056i	$-0.547136\pi$
$241$	12.1520	−	21.0478i	0.782776	−	1.35581i	0.930319	−	0.366752i	$-0.119530\pi$
$242$	−11.9245	+	9.54032i	−0.766533	+	0.613275i
$243$	−13.4402	+	7.89695i	−0.862187	+	0.506589i
$244$	−1.84907	+	2.00550i	−0.118374	+	0.128389i
$245$	−2.88476	−	6.37794i	−0.184301	−	0.407472i
$246$	25.7335	−	6.77479i	1.64071	−	0.431945i
$247$	−0.188018	+	0.108552i	−0.0119633	+	0.00690702i
$248$	−0.232587	+	3.31456i	−0.0147693	+	0.210475i
$249$	2.10634	+	19.7507i	0.133484	+	1.25165i
$250$	0.212988	+	1.39808i	0.0134706	+	0.0884225i
$251$		−	4.12014i		−	0.260061i	−0.991510	−	0.130030i	$-0.958493\pi$
$251$		−	4.12014i		−	0.260061i	0.991510	−	0.130030i	$-0.0415075\pi$
$252$	14.1859	−	7.12467i	0.893626	−	0.448812i
$253$			33.8214i			2.12633i
$254$	3.06732	−	0.467286i	0.192461	−	0.0293201i
$255$	−0.355377	−	3.33229i	−0.0222546	−	0.208676i
$256$	5.65660	−	14.9667i	0.353537	−	0.935420i
$257$	−5.26625	+	3.04047i	−0.328500	+	0.189659i	−0.655175	−	0.755477i	$-0.727405\pi$
$257$	−5.26625	+	3.04047i	−0.328500	+	0.189659i	0.326675	+	0.945137i	$0.394072\pi$
$258$	−5.10493	−	19.3907i	−0.317819	−	1.20721i
$259$	9.79745	−	5.02844i	0.608784	−	0.312452i
$260$	5.89565	−	6.39444i	0.365633	−	0.396566i
$261$	−0.285235	+	0.0615385i	−0.0176556	+	0.00380914i
$262$	1.89129	+	2.36392i	0.116844	+	0.146044i
$263$	−3.88549	+	6.72987i	−0.239590	+	0.414981i	−0.960597	−	0.277946i	$-0.910346\pi$
$263$	−3.88549	+	6.72987i	−0.239590	+	0.414981i	0.721007	+	0.692928i	$0.243680\pi$
$264$	0.827549	+	22.8577i	0.0509321	+	1.40680i
$265$	−14.1510			−0.869287
$266$	−0.151444	+	0.109348i	−0.00928564	+	0.00670459i
$267$	−9.46988	+	6.90236i	−0.579547	+	0.422418i
$268$	−1.47438	+	6.55515i	−0.0900619	+	0.400420i
$269$	−6.80473	+	11.7861i	−0.414892	+	0.718613i	−0.995417	−	0.0956287i	$-0.969514\pi$
$269$	−6.80473	+	11.7861i	−0.414892	+	0.718613i	0.580525	+	0.814242i	$0.302847\pi$
$270$	−4.01042	+	6.15764i	−0.244066	+	0.374742i
$271$	6.21337	−	3.58729i	0.377436	−	0.217913i	−0.299266	−	0.954170i	$-0.596742\pi$
$271$	6.21337	−	3.58729i	0.377436	−	0.217913i	0.676702	+	0.736257i	$0.263409\pi$
$272$	−7.71378	+	0.627153i	−0.467717	+	0.0380267i
$273$	−1.13192	−	19.8964i	−0.0685069	−	1.20419i
$274$	−5.64701	+	14.4555i	−0.341148	+	0.873289i
$275$	−4.04336	+	2.33444i	−0.243824	+	0.140772i
$276$	20.1489	+	14.9576i	1.21282	+	0.900344i
$277$	10.9137	+	6.30101i	0.655738	+	0.378591i	0.790651	−	0.612267i	$-0.209742\pi$
$277$	10.9137	+	6.30101i	0.655738	+	0.378591i	−0.134913	+	0.990857i	$0.543075\pi$
$278$	−1.73768	−	11.4063i	−0.104219	−	0.684106i
$279$	−3.35508	−	1.07883i	−0.200864	−	0.0645879i
$280$	4.48741	−	5.98858i	0.268174	−	0.357886i
$281$			8.26478i			0.493035i	0.969138	+	0.246518i	$0.0792864\pi$
$281$			8.26478i			0.493035i	−0.969138	+	0.246518i	$0.920714\pi$
$282$	9.93543	−	9.84890i	0.591646	−	0.586493i
$283$	−13.3224	+	23.0751i	−0.791937	+	1.37167i	0.132829	+	0.991139i	$0.457594\pi$
$283$	−13.3224	+	23.0751i	−0.791937	+	1.37167i	−0.924766	+	0.380536i	$0.875740\pi$
$284$	−12.3061	+	3.83858i	−0.730231	+	0.227778i
$285$	0.0350497	−	0.0790472i	0.00207617	−	0.00468235i
$286$	26.7457	+	10.4481i	1.58151	+	0.617812i
$287$	1.41975	−	28.7074i	0.0838051	−	1.69454i
$288$	13.9833	+	9.61592i	0.823977	+	0.566624i
$289$	−6.62826	−	11.4805i	−0.389898	−	0.675322i
$290$	−0.107409	+	0.0859340i	−0.00630727	+	0.00504622i
$291$	−11.8948	+	1.26854i	−0.697285	+	0.0743630i
$292$	3.96495	−	17.6284i	0.232031	−	1.03162i
$293$	1.76503			0.103114			0.0515571	−	0.998670i	$-0.483582\pi$
$293$	1.76503			0.103114			0.0515571	+	0.998670i	$0.483582\pi$
$294$	−2.70795	−	16.9312i	−0.157931	−	0.987450i
$295$		−	13.6323i		−	0.793700i
$296$	9.75854	+	6.58567i	0.567204	+	0.382784i
$297$	−23.7529	−	4.93535i	−1.37828	−	0.286378i
$298$	−19.4067	+	15.5266i	−1.12420	+	0.899429i
$299$	27.2821	−	15.7513i	1.57776	−	0.910921i
$300$	−0.397468	+	3.44122i	−0.0229478	+	0.198679i
$301$	−21.6316	−	1.06981i	−1.24682	−	0.0616627i
$302$	7.93819	−	20.3206i	0.456792	−	1.16932i
$303$	−12.3681	+	27.8936i	−0.710528	+	1.60244i
$304$	−0.180461	−	0.0855037i	−0.0103502	−	0.00490397i
$305$	−1.18119	−	0.681959i	−0.0676346	−	0.0390489i
$306$	1.30721	−	8.10394i	0.0747284	−	0.463272i
$307$	−20.6352			−1.17771			−0.588856	−	0.808238i	$-0.700421\pi$
$307$	−20.6352			−1.17771			−0.588856	+	0.808238i	$0.700421\pi$
$308$	23.8060	+	6.60524i	1.35647	+	0.376368i
$309$	−1.99954	+	1.45741i	−0.113750	+	0.0829094i
$310$	−1.64241	+	0.250209i	−0.0932824	+	0.0142109i
$311$	−9.26739	+	16.0516i	−0.525505	+	0.910202i	0.474053	+	0.880496i	$0.342790\pi$
$311$	−9.26739	+	16.0516i	−0.525505	+	0.910202i	−0.999559	+	0.0297058i	$0.990543\pi$
$312$	18.0528	−	11.3129i	1.02204	−	0.640465i
$313$	3.39435	+	5.87919i	0.191860	+	0.332311i	0.945867	−	0.324556i	$-0.105215\pi$
$313$	3.39435	+	5.87919i	0.191860	+	0.332311i	−0.754007	+	0.656867i	$0.771881\pi$
$314$	−8.12009	+	20.7862i	−0.458243	+	1.17304i
$315$	5.03196	+	6.13835i	0.283519	+	0.345857i
$316$	12.9647	−	14.0616i	0.729322	−	0.791024i
$317$	−8.08209	−	13.9986i	−0.453935	−	0.786239i	0.544691	−	0.838637i	$-0.316647\pi$
$317$	−8.08209	−	13.9986i	−0.453935	−	0.786239i	−0.998626	+	0.0523978i	$0.983314\pi$
$318$	−33.4420	−	9.11770i	−1.87533	−	0.511295i
$319$	−0.393282	−	0.227061i	−0.0220195	−	0.0127130i
$320$	7.92160	+	1.11724i	0.442831	+	0.0624555i
$321$	10.0460	−	7.32225i	0.560711	−	0.408688i
$322$	21.9751	−	15.8668i	1.22462	−	0.884224i
$323$			0.0965917i			0.00537450i
$324$	−13.4450	+	11.9679i	−0.746945	+	0.664886i
$325$	3.76615	+	2.17439i	0.208909	+	0.120613i
$326$	−27.3509	+	21.8825i	−1.51483	+	1.21196i
$327$	−15.1164	−	6.70265i	−0.835939	−	0.370657i
$328$	27.6205	−	13.4631i	1.52509	−	0.743376i
$329$	−6.89971	−	13.4435i	−0.380393	−	0.741161i
$330$	−11.0595	+	2.91160i	−0.608806	+	0.160279i
$331$	−14.2409	−	24.6660i	−0.782752	−	1.35577i	−0.930333	−	0.366717i	$-0.880482\pi$
$331$	−14.2409	−	24.6660i	−0.782752	−	1.35577i	0.147580	−	0.989050i	$-0.452852\pi$
$332$	6.82961	+	21.8950i	0.374824	+	1.20164i
$333$	−9.25412	+	8.38370i	−0.507123	+	0.459424i
$334$	−0.360531	−	2.36657i	−0.0197274	−	0.129493i
$335$	−3.35946			−0.183547
$336$	14.4633	−	11.2611i	0.789039	−	0.614343i
$337$	−17.1854			−0.936146			−0.468073	−	0.883690i	$-0.655052\pi$
$337$	−17.1854			−0.936146			−0.468073	+	0.883690i	$0.655052\pi$
$338$	−1.25916	−	8.26531i	−0.0684895	−	0.449574i
$339$	−0.675285	−	6.33199i	−0.0366764	−	0.343907i
$340$	−1.15228	−	3.69408i	−0.0624910	−	0.200339i
$341$	−2.74239	−	4.74997i	−0.148509	−	0.257225i
$342$	0.133762	−	0.164224i	0.00723302	−	0.00888020i
$343$	−18.3171	−	2.73552i	−0.989032	−	0.147704i
$344$	−10.1447	−	20.8126i	−0.546966	−	1.12214i
$345$	−5.08583	+	11.4700i	−0.273812	+	0.617525i
$346$	3.62379	−	2.89926i	0.194816	−	0.155865i
$347$	−25.5899	−	14.7743i	−1.37374	−	0.793128i	−0.382341	−	0.924021i	$-0.624882\pi$
$347$	−25.5899	−	14.7743i	−1.37374	−	0.793128i	−0.991396	+	0.130894i	$0.958215\pi$
$348$	−0.309201	+	0.133876i	−0.0165749	+	0.00717653i
$349$			27.6360i			1.47932i	0.672981	+	0.739659i	$0.265013\pi$
$349$			27.6360i			1.47932i	−0.672981	+	0.739659i	$0.734987\pi$
$350$	3.41366	+	1.53196i	0.182468	+	0.0818868i
$351$	7.08109	+	21.4588i	0.377961	+	1.14538i
$352$	6.08041	+	25.7017i	0.324087	+	1.36990i
$353$	23.5636	+	13.6045i	1.25417	+	0.724093i	0.971934	−	0.235254i	$-0.0755921\pi$
$353$	23.5636	+	13.6045i	1.25417	+	0.724093i	0.282231	+	0.959346i	$0.408925\pi$
$354$	8.78349	−	32.2161i	0.466837	−	1.71227i
$355$	−3.22271	−	5.58190i	−0.171044	−	0.296257i
$356$	−9.17218	+	9.94817i	−0.486125	+	0.527252i
$357$	−7.91794	−	3.98992i	−0.419062	−	0.211169i
$358$	0.554172	−	1.41860i	0.0292889	−	0.0749753i
$359$	−3.74005	−	6.47797i	−0.197393	−	0.341894i	0.750290	−	0.661109i	$-0.229914\pi$
$359$	−3.74005	−	6.47797i	−0.197393	−	0.341894i	−0.947682	+	0.319215i	$0.896581\pi$
$360$	−3.15655	+	7.87631i	−0.166365	+	0.415118i
$361$	9.49875	−	16.4523i	0.499934	−	0.865912i
$362$	36.6994	−	5.59090i	1.92888	−	0.293851i
$363$	−11.0166	−	15.1146i	−0.578223	−	0.793308i
$364$	−5.75882	−	22.2793i	−0.301844	−	1.16775i
$365$	9.03438			0.472881
$366$	−2.35202	−	2.37269i	−0.122942	−	0.124022i
$367$	15.9053	+	9.18291i	0.830248	+	0.479344i	0.853938	−	0.520375i	$-0.174208\pi$
$367$	15.9053	+	9.18291i	0.830248	+	0.479344i	−0.0236896	+	0.999719i	$0.507541\pi$
$368$	26.1855	+	12.4069i	1.36501	+	0.646753i
$369$	6.87324	+	31.8579i	0.357807	+	1.65846i
$370$	−2.14189	+	5.48291i	−0.111351	+	0.285043i
$371$	−20.2987	+	31.4597i	−1.05386	+	1.63330i
$372$	−4.04260	−	0.466927i	−0.209599	−	0.0242091i
$373$	−0.177482	+	0.102469i	−0.00918966	+	0.00530565i	−0.504588	−	0.863360i	$-0.668356\pi$
$373$	−0.177482	+	0.102469i	−0.00918966	+	0.00530565i	0.495398	+	0.868666i	$0.335022\pi$
$374$	9.97539	−	7.98094i	0.515815	−	0.412685i
$375$	−1.72228	+	0.183676i	−0.0889384	+	0.00948496i
$376$	9.03645	−	13.3901i	0.466019	−	0.690540i
$377$			0.422988i			0.0217850i
$378$	7.93664	+	17.7485i	0.408217	+	0.912885i
$379$	10.8141			0.555483			0.277741	−	0.960656i	$-0.410414\pi$
$379$	10.8141			0.555483			0.277741	+	0.960656i	$0.410414\pi$
$380$	0.0219099	−	0.0974126i	0.00112396	−	0.00499716i
$381$	0.402975	+	3.77860i	0.0206450	+	0.193584i
$382$	−5.59423	+	4.47574i	−0.286226	+	0.228999i
$383$	0.773754	+	1.34018i	0.0395370	+	0.0684800i	0.885117	−	0.465369i	$-0.154078\pi$
$383$	0.773754	+	1.34018i	0.0395370	+	0.0684800i	−0.845580	+	0.533849i	$0.820745\pi$
$384$	18.0007	+	7.74431i	0.918595	+	0.395200i
$385$	−0.610166	+	12.3376i	−0.0310970	+	0.628782i
$386$	28.4032	+	11.0957i	1.44569	+	0.564754i
$387$	24.0055	−	5.17912i	1.22027	−	0.263269i
$388$	−13.1862	+	4.11312i	−0.669428	+	0.208812i
$389$	−0.196263	+	0.339937i	−0.00995092	+	0.0172355i	−0.870958	−	0.491357i	$-0.836501\pi$
$389$	−0.196263	+	0.339937i	−0.00995092	+	0.0172355i	0.861007	+	0.508593i	$0.169834\pi$
$390$	7.49929	+	7.56518i	0.379741	+	0.383078i
$391$		−	14.0158i		−	0.708808i
$392$	−6.87658	−	18.5664i	−0.347320	−	0.937747i
$393$	−2.99633	+	2.18395i	−0.151145	+	0.110166i
$394$	−4.15008	−	27.2416i	−0.209078	−	1.37241i
$395$	8.28188	+	4.78155i	0.416707	+	0.240586i
$396$	−28.0122	−	0.245040i	−1.40766	−	0.0123137i
$397$	0.342311	−	0.197633i	0.0171801	−	0.00991894i	−0.491385	−	0.870942i	$-0.663509\pi$
$397$	0.342311	−	0.197633i	0.0171801	−	0.00991894i	0.508565	+	0.861023i	$0.330176\pi$
$398$	−1.39578	+	3.57298i	−0.0699640	+	0.179097i
$399$	−0.125457	−	0.191309i	−0.00628070	−	0.00957744i
$400$	0.324142	+	3.98684i	0.0162071	+	0.199342i
$401$	25.7729	−	14.8800i	1.28704	−	0.743070i	0.308911	−	0.951091i	$-0.400035\pi$
$401$	25.7729	−	14.8800i	1.28704	−	0.743070i	0.978124	+	0.208021i	$0.0667021\pi$
$402$	−7.93917	−	2.16456i	−0.395970	−	0.107958i
$403$	−2.55438	+	4.42431i	−0.127243	+	0.220391i
$404$	−7.73141	+	34.3742i	−0.384652	+	1.71018i
$405$	−7.31329	−	5.24555i	−0.363400	−	0.260653i
$406$	0.0369721	+	0.362053i	0.00183490	+	0.0179684i
$407$	−19.4334			−0.963278
$408$	−0.342941	−	9.47238i	−0.0169781	−	0.468953i
$409$	−5.55525	+	9.62197i	−0.274689	+	0.475776i	−0.970057	−	0.242879i	$-0.921908\pi$
$409$	−5.55525	+	9.62197i	−0.274689	+	0.475776i	0.695367	+	0.718654i	$0.255242\pi$
$410$	9.59797	+	11.9965i	0.474010	+	0.592466i
$411$	−17.3758	−	7.70446i	−0.857083	−	0.380033i
$412$	−1.93668	+	2.10053i	−0.0954133	+	0.103486i
$413$	−30.3065	−	19.5546i	−1.49129	−	0.962221i
$414$	−19.4093	+	23.8294i	−0.953916	+	1.17115i
$415$	−9.93134	+	5.73386i	−0.487510	+	0.281464i
$416$	17.9005	−	16.8746i	0.877646	−	0.827344i
$417$	14.0513	−	1.49852i	0.688097	−	0.0733831i
$418$	0.325872	−	0.0496444i	0.0159389	−	0.00242818i
$419$		−	32.9565i		−	1.61003i	−0.593254	−	0.805016i	$-0.702157\pi$
$419$		−	32.9565i		−	1.61003i	0.593254	−	0.805016i	$-0.297843\pi$
$420$	7.08020	+	5.81986i	0.345478	+	0.283980i
$421$			30.0447i			1.46429i	0.681150	+	0.732144i	$0.261480\pi$
$421$			30.0447i			1.46429i	−0.681150	+	0.732144i	$0.738520\pi$
$422$	−1.63085	−	10.7051i	−0.0793887	−	0.521118i
$423$	11.5036	+	12.6979i	0.559324	+	0.617395i
$424$	−39.9268	−	2.80171i	−1.93902	−	0.136063i
$425$	1.67559	−	0.967404i	0.0812782	−	0.0469260i
$426$	−4.01950	−	15.2678i	−0.194745	−	0.739726i
$427$	−3.21044	+	1.64773i	−0.155364	+	0.0797390i
$428$	9.73015	−	10.5533i	0.470325	−	0.510115i
$429$	−14.2549	+	32.1488i	−0.688231	+	1.55216i
$430$	9.03960	−	7.23225i	0.435928	−	0.348770i
$431$	−13.4451	+	23.2876i	−0.647628	+	1.12173i	0.336060	+	0.941841i	$0.390906\pi$
$431$	−13.4451	+	23.2876i	−0.647628	+	1.12173i	−0.983688	+	0.179884i	$0.942428\pi$
$432$	−12.5345	+	16.5797i	−0.603065	+	0.797692i
$433$	−27.8882			−1.34022			−0.670111	−	0.742261i	$-0.733753\pi$
$433$	−27.8882			−1.34022			−0.670111	+	0.742261i	$0.733753\pi$
$434$	−1.79968	+	4.01022i	−0.0863875	+	0.192497i
$435$	−0.0992317	−	0.136144i	−0.00475780	−	0.00652759i
$436$	−18.6285	−	4.18989i	−0.892142	−	0.200659i
$437$	0.180822	−	0.313193i	0.00864988	−	0.0149820i
$438$	21.3503	+	5.82100i	1.02016	+	0.278138i
$439$	−16.0873	+	9.28803i	−0.767807	+	0.443294i	−0.832092	−	0.554638i	$-0.812857\pi$
$439$	−16.0873	+	9.28803i	−0.767807	+	0.443294i	0.0642846	+	0.997932i	$0.479523\pi$
$440$	−11.8705	+	5.78605i	−0.565904	+	0.275839i
$441$	20.8645	−	2.38170i	0.993548	−	0.113414i
$442$	−11.0836	−	4.32977i	−0.527192	−	0.205946i
$443$	15.5472	−	8.97617i	0.738669	−	0.426471i	−0.0829163	−	0.996557i	$-0.526423\pi$
$443$	15.5472	−	8.97617i	0.738669	−	0.426471i	0.821585	+	0.570086i	$0.193090\pi$
$444$	−8.59451	+	11.5773i	−0.407877	+	0.549436i
$445$	−5.85921	−	3.38281i	−0.277753	−	0.160361i
$446$	−9.77129	+	1.48859i	−0.462684	+	0.0704868i
$447$	−17.9292	−	24.5984i	−0.848021	−	1.16347i
$448$	13.8468	−	16.0083i	0.654202	−	0.756320i
$449$			15.9588i			0.753143i	0.926388	+	0.376571i	$0.122897\pi$
$449$			15.9588i			0.753143i	−0.926388	+	0.376571i	$0.877103\pi$
$450$	−4.18850	−	0.675629i	−0.197448	−	0.0318495i
$451$	−25.3605	+	43.9256i	−1.19418	+	2.06838i
$452$	−2.18955	−	7.01945i	−0.102988	−	0.330167i
$453$	24.4257	+	10.8304i	1.14762	+	0.508857i
$454$	−7.91149	+	20.2522i	−0.371304	+	0.950485i
$455$	10.2363	−	5.25368i	0.479886	−	0.246296i
$456$	0.114543	−	0.216092i	0.00536396	−	0.0101194i
$457$	1.02037	+	1.76733i	0.0477309	+	0.0826723i	0.888904	−	0.458094i	$-0.151468\pi$
$457$	1.02037	+	1.76733i	0.0477309	+	0.0826723i	−0.841173	+	0.540766i	$0.818134\pi$
$458$	−7.88149	−	9.85109i	−0.368278	−	0.460311i
$459$	9.84333	+	2.04524i	0.459447	+	0.0954635i
$460$	−3.17921	+	14.1349i	−0.148231	+	0.659043i
$461$	11.6470			0.542453			0.271226	−	0.962516i	$-0.412571\pi$
$461$	11.6470			0.542453			0.271226	+	0.962516i	$0.412571\pi$
$462$	−9.39129	+	28.7635i	−0.436922	+	1.33820i
$463$		−	18.7737i		−	0.872486i	−0.899829	−	0.436243i	$-0.856309\pi$
$463$		−	18.7737i		−	0.872486i	0.899829	−	0.436243i	$-0.143691\pi$
$464$	−0.320067	+	0.221196i	−0.0148587	+	0.0102688i
$465$	−0.215774	−	2.02326i	−0.0100063	−	0.0938266i
$466$	−2.63436	−	3.29269i	−0.122035	−	0.152531i
$467$	−30.0802	+	17.3668i	−1.39195	+	0.803640i	−0.993531	−	0.113565i	$-0.963773\pi$
$467$	−30.0802	+	17.3668i	−1.39195	+	0.803640i	−0.398415	+	0.917205i	$0.630440\pi$
$468$	12.8482	+	22.7102i	0.593907	+	1.04978i
$469$	−4.81894	+	7.46857i	−0.222518	+	0.344866i
$470$	7.52332	+	2.93897i	0.347025	+	0.135564i
$471$	−24.9854	−	11.0786i	−1.15127	−	0.510475i
$472$	2.69901	−	38.4632i	0.124232	−	1.77041i
$473$	33.0988	+	19.1096i	1.52188	+	0.878660i
$474$	16.4912	+	16.6361i	0.757464	+	0.764119i
$475$	0.0499231			0.00229063
$476$	−9.86534	−	2.73725i	−0.452177	−	0.125462i
$477$	12.9955	−	40.4149i	0.595021	−	1.85047i
$478$	1.42471	+	9.35198i	0.0651648	+	0.427750i
$479$	−0.526981	+	0.912758i	−0.0240784	+	0.0417050i	−0.877814	−	0.479003i	$-0.840998\pi$
$479$	−0.526981	+	0.912758i	−0.0240784	+	0.0417050i	0.853735	+	0.520708i	$0.174332\pi$
$480$	−1.80277	+	9.63068i	−0.0822848	+	0.439578i
$481$	9.05054	+	15.6760i	0.412669	+	0.714763i
$482$	32.0148	+	12.5065i	1.45823	+	0.569655i
$483$	18.2042	+	27.7596i	0.828320	+	1.26311i
$484$	−15.8779	−	14.6394i	−0.721724	−	0.665427i
$485$	−3.45320	−	5.98112i	−0.156802	−	0.271589i
$486$	−13.9032	−	17.1085i	−0.630661	−	0.776058i
$487$	11.5870	+	6.68977i	0.525058	+	0.303142i	0.739002	−	0.673704i	$-0.235298\pi$
$487$	11.5870	+	6.68977i	0.525058	+	0.303142i	−0.213944	+	0.976846i	$0.568631\pi$
$488$	−3.19769	−	2.15800i	−0.144753	−	0.0976881i
$489$	−25.2687	−	34.6680i	−1.14269	−	1.56774i
$490$	8.30247	−	5.39157i	0.375067	−	0.243566i
$491$		−	22.2153i		−	1.00256i	−0.865285	−	0.501281i	$-0.832862\pi$
$491$		−	22.2153i		−	1.00256i	0.865285	−	0.501281i	$-0.167138\pi$
$492$	14.9527	+	34.5347i	0.674118	+	1.55694i
$493$	0.162978	+	0.0940955i	0.00734017	+	0.00423785i
$494$	−0.191811	−	0.239745i	−0.00862998	−	0.0107866i
$495$	−2.95392	−	13.6916i	−0.132769	−	0.615392i
$496$	−4.68357	+	0.380788i	−0.210298	+	0.0170979i
$497$	−17.0322	−	0.842340i	−0.763997	−	0.0377841i
$498$	−27.1645	+	7.15150i	−1.21727	+	0.320466i
$499$	−12.7742	−	22.1255i	−0.571850	−	0.990473i	−0.996376	−	0.0850571i	$-0.972893\pi$
$499$	−12.7742	−	22.1255i	−0.571850	−	0.990473i	0.424526	−	0.905416i	$-0.360441\pi$
$500$	−1.90927	+	0.595551i	−0.0853852	+	0.0266339i
$501$	2.91536	−	0.310913i	0.130249	−	0.0138906i
$502$	5.76029	−	0.877541i	0.257094	−	0.0391666i
$503$	10.7214			0.478044			0.239022	−	0.971014i	$-0.423173\pi$
$503$	10.7214			0.478044			0.239022	+	0.971014i	$0.423173\pi$
$504$	12.9823	+	18.3156i	0.578278	+	0.815840i
$505$	−17.6165			−0.783923
$506$	−47.2851	+	7.20356i	−2.10208	+	0.320237i
$507$	10.1820	−	1.08587i	0.452196	−	0.0482251i
$508$	1.30661	+	4.18884i	0.0579714	+	0.185850i
$509$	−1.09583	−	1.89804i	−0.0485719	−	0.0841290i	0.840717	−	0.541474i	$-0.182134\pi$
$509$	−1.09583	−	1.89804i	−0.0485719	−	0.0841290i	−0.889289	+	0.457345i	$0.848800\pi$
$510$	4.58313	−	1.20659i	0.202944	−	0.0534285i
$511$	12.9593	−	20.0847i	0.573284	−	0.888497i
$512$	22.1295	+	4.72065i	0.977996	+	0.208625i
$513$	0.193570	+	0.172694i	0.00854632	+	0.00762463i
$514$	−5.37248	−	6.71507i	−0.236970	−	0.296189i
$515$	−1.23715	−	0.714272i	−0.0545155	−	0.0314746i
$516$	26.0225	−	11.2671i	1.14558	−	0.496007i
$517$			26.6653i			1.17274i
$518$	9.11692	+	12.6266i	0.400574	+	0.554783i
$519$	3.34790	+	4.59324i	0.146956	+	0.201621i
$520$	10.1957	+	6.88067i	0.447109	+	0.301737i
$521$	−6.24945	−	3.60812i	−0.273793	−	0.158075i	0.356817	−	0.934174i	$-0.383862\pi$
$521$	−6.24945	−	3.60812i	−0.273793	−	0.158075i	−0.630610	+	0.776100i	$0.717195\pi$
$522$	−0.146788	−	0.385675i	−0.00642472	−	0.0168805i
$523$	−2.50192	−	4.33345i	−0.109401	−	0.189489i	0.806127	−	0.591743i	$-0.201560\pi$
$523$	−2.50192	−	4.33345i	−0.109401	−	0.189489i	−0.915528	+	0.402254i	$0.868227\pi$
$524$	−2.90214	+	3.14766i	−0.126780	+	0.137506i
$525$	−2.06218	+	4.09236i	−0.0900007	+	0.178605i
$526$	−10.2365	−	3.99885i	−0.446332	−	0.174358i
$527$	1.13646	+	1.96841i	0.0495051	+	0.0857454i
$528$	−31.7808	+	6.02542i	−1.38308	+	0.262223i
$529$	−14.7378	+	25.5267i	−0.640776	+	1.10986i
$530$	−3.01399	−	19.7842i	−0.130919	−	0.859372i
$531$	38.9335	+	12.5191i	1.68957	+	0.543282i
$532$	−0.185134	−	0.188442i	−0.00802658	−	0.00816998i
$533$	47.2436			2.04635
$534$	−11.6670	−	11.7696i	−0.504883	−	0.509318i
$535$	6.21564	+	3.58860i	0.268726	+	0.155149i
$536$	−9.47867	−	0.665130i	−0.409416	−	0.0287292i
$537$	1.70518	+	0.756080i	0.0735839	+	0.0326273i
$538$	−17.9273	−	7.00326i	−0.772902	−	0.301932i
$539$	26.5531	+	19.0540i	1.14372	+	0.820716i
$540$	−9.46307	−	4.29539i	−0.407226	−	0.184844i
$541$	17.4623	−	10.0819i	0.750764	−	0.433454i	−0.0752056	−	0.997168i	$-0.523961\pi$
$541$	17.4623	−	10.0819i	0.750764	−	0.433454i	0.825970	+	0.563714i	$0.190628\pi$
$542$	6.33871	+	7.92276i	0.272271	+	0.340312i
$543$	4.82144	+	45.2096i	0.206908	+	1.94013i
$544$	−2.51976	−	10.6509i	−0.108034	−	0.456655i
$545$		−	9.54692i		−	0.408945i
$546$	27.5758	−	5.82023i	1.18013	−	0.249083i
$547$	23.5095			1.00519			0.502597	−	0.864521i	$-0.332378\pi$
$547$	23.5095			1.00519			0.502597	+	0.864521i	$0.332378\pi$
$548$	−21.4127	−	4.81613i	−0.914707	−	0.205735i
$549$	3.03240	−	2.74718i	0.129420	−	0.117247i
$550$	−4.12493	−	5.15575i	−0.175887	−	0.219842i
$551$	0.00242791	+	0.00420526i	0.000103432	+	0.000179150i
$552$	−16.6205	+	31.3556i	−0.707417	+	1.33458i
$553$	22.5099	−	11.5530i	0.957220	−	0.491283i
$554$	−6.48484	+	16.6002i	−0.275515	+	0.705277i
$555$	−6.59055	−	2.92227i	−0.279753	−	0.124043i
$556$	15.5769	−	4.85883i	0.660607	−	0.206060i
$557$	−1.11240	+	1.92673i	−0.0471338	+	0.0816381i	−0.888630	−	0.458625i	$-0.848342\pi$
$557$	−1.11240	+	1.92673i	−0.0471338	+	0.0816381i	0.841496	+	0.540263i	$0.181675\pi$
$558$	0.793699	−	4.92046i	0.0336000	−	0.208300i
$559$		−	35.5989i		−	1.50567i
$560$	9.32830	+	4.99827i	0.394193	+	0.211216i
$561$	9.21594	+	12.6441i	0.389097	+	0.533833i
$562$	−11.5548	+	1.76030i	−0.487412	+	0.0742539i
$563$	25.8072	+	14.8998i	1.08764	+	0.627952i	0.932948	−	0.360010i	$-0.117227\pi$
$563$	25.8072	+	14.8998i	1.08764	+	0.627952i	0.154696	+	0.987962i	$0.450560\pi$
$564$	15.8857	+	11.7929i	0.668909	+	0.496569i
$565$	3.18395	−	1.83825i	0.133950	−	0.0773359i
$566$	−35.0985	−	13.7111i	−1.47530	−	0.576322i
$567$	−22.1521	+	8.73409i	−0.930301	+	0.366797i
$568$	−7.98770	−	16.3873i	−0.335157	−	0.687597i
$569$	−24.7640	+	14.2975i	−1.03816	+	0.599382i	−0.919312	−	0.393531i	$-0.871254\pi$
$569$	−24.7640	+	14.2975i	−1.03816	+	0.599382i	−0.118848	+	0.992912i	$0.537920\pi$
$570$	0.117980	+	0.0321663i	0.00494163	+	0.00134730i
$571$	1.45649	−	2.52271i	0.0609522	−	0.105572i	−0.833939	−	0.551856i	$-0.813920\pi$
$571$	1.45649	−	2.52271i	0.0609522	−	0.105572i	0.894891	+	0.446284i	$0.147253\pi$
$572$	−8.91085	+	39.6181i	−0.372581	+	1.65651i
$573$	−5.16833	−	7.09083i	−0.215910	−	0.296223i
$574$	40.4377	−	4.12942i	1.68784	−	0.172359i
$575$	−7.24401			−0.302096
$576$	−10.4656	+	21.5980i	−0.436065	+	0.899915i
$577$	18.4445	−	31.9468i	0.767855	−	1.32996i	−0.170869	−	0.985294i	$-0.554657\pi$
$577$	18.4445	−	31.9468i	0.767855	−	1.32996i	0.938724	−	0.344670i	$-0.112009\pi$
$578$	14.6389	−	11.7121i	0.608899	−	0.487158i
$579$	−15.1383	+	34.1412i	−0.629125	+	1.41886i
$580$	−0.143020	−	0.131864i	−0.00593857	−	0.00547534i
$581$	−1.49869	+	30.3037i	−0.0621763	+	1.25721i
$582$	−4.30698	−	16.3597i	−0.178530	−	0.678133i
$583$	57.2175	−	33.0345i	2.36971	−	1.36815i
$584$	25.4904	+	1.78869i	1.05480	+	0.0740166i
$585$	−9.66865	+	8.75924i	−0.399749	+	0.362150i
$586$	0.375931	+	2.46766i	0.0155296	+	0.101938i
$587$			5.63165i			0.232443i	0.993223	+	0.116221i	$0.0370782\pi$
$587$			5.63165i			0.232443i	−0.993223	+	0.116221i	$0.962922\pi$
$588$	23.0945	−	7.39209i	0.952402	−	0.304845i
$589$			0.0586475i			0.00241653i
$590$	19.0590	−	2.90351i	0.784647	−	0.119536i
$591$	33.5587	−	3.57891i	1.38042	−	0.147217i
$592$	−7.12886	+	15.0459i	−0.292994	+	0.618383i
$593$	15.8168	−	9.13183i	0.649518	−	0.374999i	−0.138754	−	0.990327i	$-0.544310\pi$
$593$	15.8168	−	9.13183i	0.649518	−	0.374999i	0.788271	+	0.615328i	$0.210976\pi$
$594$	1.84094	−	34.2597i	0.0755347	−	1.40569i
$595$	0.252856	−	5.11277i	0.0103661	−	0.209603i
$596$	−25.8408	−	23.8251i	−1.05848	−	0.975916i
$597$	−4.29478	−	1.90432i	−0.175774	−	0.0779385i
$598$	27.8324	+	34.7877i	1.13815	+	1.42258i
$599$	10.2239	−	17.7083i	0.417736	−	0.723540i	−0.577975	−	0.816054i	$-0.696157\pi$
$599$	10.2239	−	17.7083i	0.417736	−	0.723540i	0.995711	+	0.0925144i	$0.0294904\pi$
$600$	−4.89577	+	0.177248i	−0.199869	+	0.00723613i
$601$	−24.8401			−1.01325			−0.506624	−	0.862167i	$-0.669107\pi$
$601$	−24.8401			−1.01325			−0.506624	+	0.862167i	$0.669107\pi$
$602$	−3.11160	−	30.4706i	−0.126819	−	1.24189i
$603$	3.08514	−	9.59456i	0.125636	−	0.390721i
$604$	30.1006	+	6.77020i	1.22478	+	0.275476i
$605$	5.39919	−	9.35168i	0.219508	−	0.380200i
$606$	−41.6318	−	11.3506i	−1.69118	−	0.461087i
$607$	−2.92576	+	1.68919i	−0.118753	+	0.0685620i	−0.558200	−	0.829706i	$-0.688508\pi$
$607$	−2.92576	+	1.68919i	−0.118753	+	0.0685620i	0.439447	+	0.898269i	$0.355174\pi$
$608$	0.0811051	−	0.270511i	0.00328925	−	0.0109707i
$609$	−0.445009	+	0.0253168i	−0.0180327	+	0.00102589i
$610$	0.701856	−	1.79665i	0.0284173	−	0.0727442i
$611$	21.5096	−	12.4186i	0.870186	−	0.502402i
$612$	11.6084	+	0.101546i	0.469242	+	0.00410475i
$613$	−21.7109	−	12.5348i	−0.876893	−	0.506275i	−0.00726042	−	0.999974i	$-0.502311\pi$
$613$	−21.7109	−	12.5348i	−0.876893	−	0.506275i	−0.869633	+	0.493699i	$0.835644\pi$
$614$	−4.39505	−	28.8497i	−0.177370	−	1.16428i
$615$	−15.2059	+	11.0832i	−0.613160	+	0.446917i
$616$	−4.16427	+	34.6896i	−0.167783	+	1.39768i
$617$		−	18.0681i		−	0.727395i	−0.931517	−	0.363697i	$-0.881514\pi$
$617$		−	18.0681i		−	0.727395i	0.931517	−	0.363697i	$-0.118486\pi$
$618$	−2.46346	−	2.48511i	−0.0990950	−	0.0999657i
$619$	18.3452	−	31.7748i	0.737355	−	1.27714i	−0.216327	−	0.976321i	$-0.569408\pi$
$619$	18.3452	−	31.7748i	0.737355	−	1.27714i	0.953682	−	0.300815i	$-0.0972588\pi$
$620$	−0.699627	−	2.24293i	−0.0280977	−	0.0900782i
$621$	−28.0876	−	25.0585i	−1.12712	−	1.00556i
$622$	−24.4153	−	9.53777i	−0.978964	−	0.382430i
$623$	−15.9252	+	8.17343i	−0.638029	+	0.327462i
$624$	19.6614	+	22.8298i	0.787084	+	0.913925i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−7.49663	+	5.99778i	−0.299626	+	0.239720i
$627$	0.0428120	+	0.401438i	0.00170975	+	0.0160319i
$628$	−30.7904	−	6.92534i	−1.22867	−	0.276351i
$629$	8.05332			0.321107
$630$	−7.51017	+	8.34250i	−0.299212	+	0.332373i
$631$			25.3603i			1.00958i	0.863243	+	0.504789i	$0.168430\pi$
$631$			25.3603i			1.00958i	−0.863243	+	0.504789i	$0.831570\pi$
$632$	22.4206	+	15.1308i	0.891842	+	0.601871i
$633$	13.1875	−	1.40641i	0.524158	−	0.0558996i
$634$	17.8498	−	14.2810i	0.708906	−	0.567170i
$635$	−1.90001	+	1.09697i	−0.0753998	+	0.0435321i
$636$	5.62455	−	48.6966i	0.223028	−	1.93095i
$637$	3.00367	−	30.2929i	0.119010	−	1.20025i
$638$	0.233686	−	0.598202i	0.00925172	−	0.0236830i
$639$	18.9014	−	4.07791i	0.747727	−	0.161320i
$640$	0.125218	+	11.3130i	0.00494969	+	0.447186i
$641$	−0.00835292	−	0.00482256i	−0.000329921	−	0.000190480i	0.499835	−	0.866121i	$-0.333394\pi$
$641$	−0.00835292	−	0.00482256i	−0.000329921	−	0.000190480i	−0.500165	+	0.865930i	$0.666727\pi$
$642$	12.3768	+	12.4855i	0.488473	+	0.492765i
$643$	−0.999165			−0.0394032			−0.0197016	−	0.999806i	$-0.506272\pi$
$643$	−0.999165			−0.0394032			−0.0197016	+	0.999806i	$0.506272\pi$
$644$	26.8636	+	27.3435i	1.05857	+	1.07749i
$645$	8.35139	+	11.4579i	0.328836	+	0.451155i
$646$	−0.135043	+	0.0205729i	−0.00531320	+	0.000809430i
$647$	−17.4723	+	30.2629i	−0.686907	+	1.18976i	0.285927	+	0.958252i	$0.407699\pi$
$647$	−17.4723	+	30.2629i	−0.686907	+	1.18976i	−0.972833	+	0.231506i	$0.925635\pi$
$648$	−19.5958	−	16.2482i	−0.769796	−	0.638290i
$649$	31.8236	+	55.1201i	1.24919	+	2.16366i
$650$	−2.23783	+	5.72852i	−0.0877749	+	0.224691i
$651$	−4.80753	−	2.42255i	−0.188422	−	0.0949474i
$652$	−36.4190	−	33.5782i	−1.42628	−	1.31502i
$653$	16.9633	+	29.3812i	0.663823	+	1.14978i	0.979603	+	0.200943i	$0.0644007\pi$
$653$	16.9633	+	29.3812i	0.663823	+	1.14978i	−0.315780	+	0.948833i	$0.602266\pi$
$654$	6.15124	−	22.5616i	0.240533	−	0.882227i
$655$	−1.85389	−	1.07034i	−0.0724375	−	0.0418218i
$656$	24.7054	+	35.7483i	0.964584	+	1.39574i
$657$	−8.29666	+	25.8020i	−0.323684	+	1.00663i
$658$	17.3255	−	12.5097i	0.675418	−	0.487678i
$659$			17.0907i			0.665758i	0.942969	+	0.332879i	$0.108020\pi$
$659$			17.0907i			0.665758i	−0.942969	+	0.332879i	$0.891980\pi$
$660$	−6.42621	−	14.8420i	−0.250140	−	0.577723i
$661$	−2.24461	−	1.29593i	−0.0873051	−	0.0504056i	0.455712	−	0.890127i	$-0.349385\pi$
$661$	−2.24461	−	1.29593i	−0.0873051	−	0.0504056i	−0.543017	+	0.839722i	$0.682718\pi$
$662$	31.4520	−	25.1636i	1.22242	−	0.978010i
$663$	5.90729	−	13.3226i	0.229420	−	0.517409i
$664$	−29.1564	+	14.2117i	−1.13149	+	0.551523i
$665$	0.0716117	−	0.110986i	0.00277698	−	0.00430387i
$666$	−13.6921	−	11.1524i	−0.530559	−	0.432147i
$667$	−0.352298	−	0.610198i	−0.0136410	−	0.0236270i
$668$	3.23188	−	1.00811i	0.125045	−	0.0390048i
$669$	−1.28372	−	12.0372i	−0.0496315	−	0.465383i
$670$	−0.715526	−	4.69680i	−0.0276432	−	0.181453i
$671$	6.36797			0.245833
$672$	18.8245	+	17.8225i	0.726169	+	0.687516i
$673$	36.8310			1.41973			0.709866	−	0.704337i	$-0.248756\pi$
$673$	36.8310			1.41973			0.709866	+	0.704337i	$0.248756\pi$
$674$	−3.66028	−	24.0266i	−0.140989	−	0.925468i
$675$	1.05707	−	5.08749i	0.0406868	−	0.195818i
$676$	11.2874	−	3.52083i	0.434131	−	0.135417i
$677$	11.4771	+	19.8789i	0.441100	+	0.764008i	0.997771	−	0.0667247i	$-0.0212549\pi$
$677$	11.4771	+	19.8789i	0.441100	+	0.764008i	−0.556671	+	0.830733i	$0.687922\pi$
$678$	8.70882	−	2.29275i	0.334460	−	0.0880524i
$679$	−18.2503	−	0.902585i	−0.700383	−	0.0346380i
$680$	4.91920	−	2.39777i	0.188643	−	0.0919504i
$681$	−24.3435	−	10.7940i	−0.932846	−	0.413626i
$682$	6.05675	−	4.84578i	0.231925	−	0.185555i
$683$	−20.8080	−	12.0135i	−0.796197	−	0.459685i	0.0459426	−	0.998944i	$-0.485371\pi$
$683$	−20.8080	−	12.0135i	−0.796197	−	0.459685i	−0.842140	+	0.539260i	$0.818704\pi$
$684$	0.258088	+	0.152033i	0.00986825	+	0.00581312i
$685$		−	10.9738i		−	0.419289i
$686$	−0.0768491	−	26.1915i	−0.00293411	−	0.999996i
$687$	12.4865	−	9.10110i	0.476390	−	0.347229i
$688$	26.9370	−	18.6160i	1.02696	−	0.709728i
$689$	−53.2947	−	30.7697i	−2.03037	−	1.17223i
$690$	−17.1193	−	4.66744i	−0.651719	−	0.177686i
$691$	−0.769690	−	1.33314i	−0.0292804	−	0.0507151i	0.851014	−	0.525143i	$-0.175988\pi$
$691$	−0.769690	−	1.33314i	−0.0292804	−	0.0507151i	−0.880294	+	0.474428i	$0.842655\pi$
$692$	4.82523	+	4.44885i	0.183428	+	0.169120i
$693$	−34.6757	−	13.0728i	−1.31722	−	0.496594i
$694$	15.2054	−	38.9236i	0.577189	−	1.47752i
$695$	4.07927	+	7.06551i	0.154736	+	0.268010i
$696$	−0.253026	−	0.403774i	−0.00959094	−	0.0153050i
$697$	10.5095	−	18.2030i	0.398077	−	0.689489i
$698$	−38.6374	+	5.88614i	−1.46245	+	0.222794i
$699$	4.17357	−	3.04201i	0.157859	−	0.115060i
$700$	−1.41474	+	5.09887i	−0.0534721	+	0.192719i
$701$	8.13507			0.307257			0.153629	−	0.988129i	$-0.450904\pi$
$701$	8.13507			0.307257			0.153629	+	0.988129i	$0.450904\pi$
$702$	−28.4930	+	14.4704i	−1.07540	+	0.546151i
$703$	0.179957	+	0.103898i	0.00678721	+	0.00391860i
$704$	−34.6380	+	13.9751i	−1.30547	+	0.526706i
$705$	−4.00976	+	9.04315i	−0.151016	+	0.340585i
$706$	−14.0014	+	35.8415i	−0.526949	+	1.34891i
$707$	−25.2698	+	39.1640i	−0.950368	+	1.47292i
$708$	46.9116	+	5.41838i	1.76305	+	0.203635i
$709$	9.50630	−	5.48847i	0.357017	−	0.206124i	−0.310755	−	0.950490i	$-0.600582\pi$
$709$	9.50630	−	5.48847i	0.357017	−	0.206124i	0.667771	+	0.744367i	$0.267248\pi$
$710$	7.11756	−	5.69450i	0.267117	−	0.213711i
$711$	−21.2616	+	19.2618i	−0.797374	+	0.722375i
$712$	−15.8619	−	10.7046i	−0.594451	−	0.401173i
$713$		−	8.50994i		−	0.318700i
$714$	3.89180	−	11.9197i	0.145647	−	0.446085i
$715$	−20.3039			−0.759323
$716$	2.10135	+	0.472633i	0.0785312	+	0.0176631i
$717$	−11.5206	+	1.22863i	−0.430245	+	0.0458841i
$718$	8.26014	−	6.60864i	0.308266	−	0.246632i
$719$	−3.69133	−	6.39358i	−0.137664	−	0.238440i	0.788948	−	0.614460i	$-0.210626\pi$
$719$	−3.69133	−	6.39358i	−0.137664	−	0.238440i	−0.926612	+	0.376019i	$0.877293\pi$
$720$	−11.6840	−	2.73555i	−0.435438	−	0.101948i
$721$	−3.36255	+	1.72580i	−0.125228	+	0.0642720i
$722$	25.0248	+	9.77589i	0.931328	+	0.363821i
$723$	−17.0632	+	38.4823i	−0.634585	+	1.43117i
$724$	15.6331	+	50.1180i	0.580999	+	1.86262i
$725$	0.0486330	−	0.0842348i	0.00180618	−	0.00312840i
$726$	18.7850	−	18.6214i	0.697176	−	0.691104i
$727$		−	16.3757i		−	0.607343i	−0.952777	−	0.303671i	$-0.901788\pi$
$727$		−	16.3757i		−	0.607343i	0.952777	−	0.303671i	$-0.0982125\pi$
$728$	29.9218	−	12.7965i	1.10898	−	0.474272i
$729$	21.6973	−	16.0694i	0.803604	−	0.595164i
$730$	1.92422	+	12.6308i	0.0712185	+	0.467487i
$731$	−13.7163	−	7.91913i	−0.507317	−	0.292900i
$732$	2.81626	−	3.79368i	0.104092	−	0.140218i
$733$	−35.2796	+	20.3687i	−1.30308	+	0.752334i	−0.980931	−	0.194355i	$-0.937739\pi$
$733$	−35.2796	+	20.3687i	−1.30308	+	0.752334i	−0.322149	+	0.946689i	$0.604405\pi$
$734$	−9.45083	+	24.1927i	−0.348837	+	0.892970i
$735$	6.13986	+	10.4548i	0.226472	+	0.385630i
$736$	−11.7686	+	39.2520i	−0.433797	+	1.44685i
$737$	13.5835	−	7.84244i	0.500355	−	0.288880i
$738$	−43.0761	+	16.3947i	−1.58565	+	0.603498i
$739$	6.49315	−	11.2465i	0.238854	−	0.413708i	−0.721531	−	0.692382i	$-0.756561\pi$
$739$	6.49315	−	11.2465i	0.238854	−	0.413708i	0.960386	+	0.278674i	$0.0898948\pi$
$740$	−8.12177	−	1.82674i	−0.298562	−	0.0671522i
$741$	0.303882	−	0.221492i	0.0111634	−	0.00813672i
$742$	−48.3066	−	21.6787i	−1.77339	−	0.795851i
$743$	−17.3420			−0.636216			−0.318108	−	0.948054i	$-0.603048\pi$
$743$	−17.3420			−0.636216			−0.318108	+	0.948054i	$0.603048\pi$
$744$	−0.208223	−	5.75134i	−0.00763384	−	0.210854i
$745$	8.78701	−	15.2195i	0.321931	−	0.557601i
$746$	−0.181062	−	0.226310i	−0.00662915	−	0.00828578i
$747$	−7.25543	−	33.6294i	−0.265462	−	1.23044i
$748$	13.2827	+	12.2466i	0.485662	+	0.447779i
$749$	16.8940	−	8.67065i	0.617292	−	0.316819i
$750$	−0.623620	−	2.36878i	−0.0227714	−	0.0864955i
$751$	34.7814	−	20.0811i	1.26919	−	0.732768i	0.294357	−	0.955696i	$-0.404894\pi$
$751$	34.7814	−	20.0811i	1.26919	−	0.732768i	0.974835	+	0.222927i	$0.0715612\pi$
$752$	20.6451	+	9.78178i	0.752849	+	0.356705i
$753$	0.756768	+	7.09604i	0.0275782	+	0.258594i
$754$	−0.591373	+	0.0900916i	−0.0215365	+	0.00328094i
$755$			15.4263i			0.561421i
$756$	−23.1235	+	14.8763i	−0.840993	+	0.541046i
$757$			15.4831i			0.562742i	0.959599	+	0.281371i	$0.0907892\pi$
$757$			15.4831i			0.562742i	−0.959599	+	0.281371i	$0.909211\pi$
$758$	2.30328	+	15.1190i	0.0836588	+	0.549147i
$759$	−6.21216	−	58.2500i	−0.225487	−	2.11434i
$760$	0.140858	+	0.00988414i	0.00510944	+	0.000358535i
$761$	6.62479	−	3.82482i	0.240148	−	0.138650i	−0.375097	−	0.926986i	$-0.622390\pi$
$761$	6.62479	−	3.82482i	0.240148	−	0.138650i	0.615245	+	0.788336i	$0.289057\pi$
$762$	−5.19697	+	1.36819i	−0.188266	+	0.0495643i
$763$	−21.2242	−	13.6945i	−0.768368	−	0.495774i
$764$	−7.44896	−	6.86791i	−0.269494	−	0.248472i
$765$	1.22412	+	5.67388i	0.0442582	+	0.205139i
$766$	−1.70888	+	1.36722i	−0.0617445	+	0.0493995i
$767$	29.6418	−	51.3412i	1.07030	−	1.85382i
$768$	−6.99325	+	26.8159i	−0.252347	+	0.967637i
$769$	28.5801			1.03063			0.515313	−	0.857002i	$-0.327676\pi$
$769$	28.5801			1.03063			0.515313	+	0.857002i	$0.327676\pi$
$770$	−17.3789	+	1.77470i	−0.626294	+	0.0639559i
$771$	8.51152	−	6.20384i	0.306535	−	0.223426i
$772$	−9.46309	+	42.0733i	−0.340584	+	1.51425i
$773$	2.80047	−	4.85056i	0.100726	−	0.174463i	−0.811258	−	0.584688i	$-0.801217\pi$
$773$	2.80047	−	4.85056i	0.100726	−	0.174463i	0.911984	+	0.410226i	$0.134550\pi$
$774$	12.3537	+	32.4586i	0.444046	+	1.16670i
$775$	1.01737	−	0.587378i	0.0365450	−	0.0210992i
$776$	−8.55899	−	17.5594i	−0.307250	−	0.630345i
$777$	−15.9504	+	10.4600i	−0.572217	+	0.375249i
$778$	−0.517062	−	0.201989i	−0.0185376	−	0.00724166i
$779$	0.469686	−	0.271173i	0.0168282	−	0.00971579i
$780$	−8.97949	+	12.0959i	−0.321517	+	0.433104i
$781$	26.0612	+	15.0464i	0.932543	+	0.538404i
$782$	19.5952	−	2.98520i	0.700723	−	0.106750i
$783$	0.479953	−	0.158378i	0.0171521	−	0.00565995i
$784$	24.4928	−	13.5685i	0.874743	−	0.484588i
$785$		−	15.7798i		−	0.563205i
$786$	−3.69153	−	3.72396i	−0.131672	−	0.132829i
$787$	6.53353	−	11.3164i	0.232895	−	0.403386i	−0.725764	−	0.687944i	$-0.758513\pi$
$787$	6.53353	−	11.3164i	0.232895	−	0.403386i	0.958659	+	0.284558i	$0.0918467\pi$
$788$	37.2021	−	11.6043i	1.32527	−	0.413386i
$789$	5.45581	−	12.3044i	0.194232	−	0.438049i
$790$	−4.92105	+	12.5972i	−0.175083	+	0.448187i
$791$	0.480476	−	9.71525i	0.0170838	−	0.345435i
$792$	−5.62368	−	39.2155i	−0.199829	−	1.39346i
$793$	−2.96569	−	5.13673i	−0.105315	−	0.182411i
$794$	0.349216	+	0.436486i	0.0123932	+	0.0154903i
$795$	24.3720	−	2.59919i	0.864385	−	0.0921836i
$796$	−5.29261	−	1.19041i	−0.187592	−	0.0421929i
$797$	48.8011			1.72863			0.864313	−	0.502955i	$-0.167754\pi$
$797$	48.8011			1.72863			0.864313	+	0.502955i	$0.167754\pi$
$798$	0.240745	−	0.216146i	0.00852229	−	0.00765148i
$799$		−	11.0503i		−	0.390930i
$800$	−5.50490	+	1.30233i	−0.194628	+	0.0460443i
$801$	15.0420	−	13.6272i	0.531484	−	0.481494i
$802$	26.2928	+	32.8633i	0.928430	+	1.16045i
$803$	−36.5293	+	21.0902i	−1.28909	+	0.744256i
$804$	1.33528	−	11.5606i	0.0470915	−	0.407713i
$805$	−10.3911	+	16.1045i	−0.366238	+	0.567609i
$806$	−6.72961	−	2.62890i	−0.237040	−	0.0925992i
$807$	9.55485	−	21.5489i	0.336347	−	0.758559i
$808$	−49.7047	−	3.48784i	−1.74861	−	0.122702i
$809$	−16.1767	−	9.33961i	−0.568742	−	0.328363i	0.187905	−	0.982187i	$-0.439830\pi$
$809$	−16.1767	−	9.33961i	−0.568742	−	0.328363i	−0.756647	+	0.653824i	$0.773164\pi$
$810$	5.77607	−	11.3418i	0.202950	−	0.398511i
$811$	−44.7323			−1.57076			−0.785381	−	0.619013i	$-0.787533\pi$
$811$	−44.7323			−1.57076			−0.785381	+	0.619013i	$0.787533\pi$
$812$	−0.498306	+	0.128803i	−0.0174871	+	0.00452011i
$813$	−10.0423	+	7.31958i	−0.352199	+	0.256709i
$814$	−4.13909	−	27.1695i	−0.145075	−	0.952291i
$815$	12.3840	−	21.4498i	0.433794	−	0.751354i
$816$	13.1701	−	2.49697i	0.461047	−	0.0874114i
$817$	−0.204334	−	0.353917i	−0.00714875	−	0.0123820i
$818$	−14.6355	−	5.71733i	−0.511719	−	0.199902i
$819$	5.60398	+	34.0594i	0.195819	+	1.19013i
$820$	−14.7279	+	15.9739i	−0.514319	+	0.557832i
$821$	5.05691	+	8.75882i	0.176487	+	0.305685i	0.940675	−	0.339309i	$-0.110193\pi$
$821$	5.05691	+	8.75882i	0.176487	+	0.305685i	−0.764188	+	0.644994i	$0.776860\pi$
$822$	7.07063	−	25.9337i	0.246617	−	0.904542i
$823$	15.8881	+	9.17301i	0.553825	+	0.319751i	0.750663	−	0.660685i	$-0.229734\pi$
$823$	15.8881	+	9.17301i	0.553825	+	0.319751i	−0.196838	+	0.980436i	$0.563067\pi$
$824$	−3.34920	−	2.26025i	−0.116675	−	0.0787396i
$825$	6.53504	−	4.76323i	0.227521	−	0.165834i
$826$	20.8841	−	46.5359i	0.726650	−	1.61919i
$827$		−	36.0470i		−	1.25348i	−0.779229	−	0.626739i	$-0.784389\pi$
$827$		−	36.0470i		−	1.25348i	0.779229	−	0.626739i	$-0.215611\pi$
$828$	−37.4494	−	22.0605i	−1.30146	−	0.766654i
$829$	−5.64247	−	3.25768i	−0.195971	−	0.113144i	0.398804	−	0.917036i	$-0.369425\pi$
$829$	−5.64247	−	3.25768i	−0.195971	−	0.113144i	−0.594775	+	0.803892i	$0.702759\pi$
$830$	−10.1317	−	12.6636i	−0.351675	−	0.439559i
$831$	−19.9538	−	8.84755i	−0.692189	−	0.306918i
$832$	27.4047	+	21.4323i	0.950086	+	0.743033i
$833$	−11.0037	−	7.89610i	−0.381257	−	0.273584i
$834$	5.08783	+	19.3258i	0.176177	+	0.669196i
$835$	0.846364	+	1.46595i	0.0292896	+	0.0507311i
$836$	0.138814	+	0.445022i	0.00480098	+	0.0153914i
$837$	5.97656	+	1.24180i	0.206580	+	0.0429231i
$838$	46.0759	−	7.01936i	1.59167	−	0.242480i
$839$	40.0265			1.38187			0.690934	−	0.722918i	$-0.257200\pi$
$839$	40.0265			1.38187			0.690934	+	0.722918i	$0.257200\pi$
$840$	−6.62864	+	11.1383i	−0.228710	+	0.384307i
$841$	−28.9905			−0.999674
$842$	−42.0050	+	6.39917i	−1.44759	+	0.220530i
$843$	−1.51804	−	14.2343i	−0.0522840	−	0.490255i
$844$	14.6193	−	4.56014i	0.503217	−	0.156966i
$845$	2.95594	+	5.11984i	0.101688	+	0.176128i
$846$	−15.3026	+	18.7875i	−0.526115	+	0.645927i
$847$	−13.0453	−	25.4176i	−0.448243	−	0.873360i
$848$	−4.58692	−	56.4177i	−0.157516	−	1.93739i
$849$	18.7067	−	42.1890i	0.642012	−	1.44792i
$850$	1.70939	+	2.13657i	0.0586317	+	0.0732838i
$851$	−26.1124	−	15.0760i	−0.895121	−	0.516798i
$852$	20.4895	−	8.87145i	0.701959	−	0.303931i
$853$			1.81968i			0.0623048i	0.999515	+	0.0311524i	$0.00991772\pi$
$853$			1.81968i			0.0623048i	−0.999515	+	0.0311524i	$0.990082\pi$
$854$	−2.98744	−	4.13751i	−0.102228	−	0.141583i
$855$	−0.0458466	+	0.142580i	−0.00156792	+	0.00487612i
$856$	16.8269	+	11.3558i	0.575130	+	0.388134i
$857$	23.8693	+	13.7810i	0.815361	+	0.470749i	0.848814	−	0.528691i	$-0.177317\pi$
$857$	23.8693	+	13.7810i	0.815361	+	0.470749i	−0.0334528	+	0.999440i	$0.510650\pi$
$858$	−47.9828	−	13.0821i	−1.63811	−	0.446617i
$859$	−4.80173	−	8.31684i	−0.163833	−	0.283767i	0.772407	−	0.635127i	$-0.219052\pi$
$859$	−4.80173	−	8.31684i	−0.163833	−	0.283767i	−0.936240	+	0.351361i	$0.885719\pi$
$860$	12.0366	+	11.0977i	0.410445	+	0.378429i
$861$	2.82764	+	49.7031i	0.0963656	+	1.69388i
$862$	−35.4217	−	13.8374i	−1.20647	−	0.471303i
$863$	−18.8317	−	32.6174i	−0.641038	−	1.11031i	−0.985201	−	0.171400i	$-0.945171\pi$
$863$	−18.8317	−	32.6174i	−0.641038	−	1.11031i	0.344164	−	0.938910i	$-0.388162\pi$
$864$	−25.8495	−	13.9930i	−0.879418	−	0.476050i
$865$	−1.64079	+	2.84193i	−0.0557885	+	0.0966286i
$866$	−5.93987	−	38.9900i	−0.201845	−	1.32494i
$867$	13.5244	+	18.5552i	0.459314	+	0.630168i
$868$	−5.98993	−	1.66197i	−0.203312	−	0.0564110i
$869$	−44.6489			−1.51461
$870$	0.169205	−	0.167731i	0.00573658	−	0.00568662i
$871$	−12.6522	−	7.30477i	−0.428705	−	0.247513i
$872$	1.89017	−	26.9365i	0.0640092	−	0.912186i
$873$	20.2532	−	4.36957i	0.685468	−	0.147887i
$874$	0.476382	+	0.186097i	0.0161139	+	0.00629484i
$875$	−2.64252	−	0.130688i	−0.0893335	−	0.00441806i
$876$	−3.59087	+	31.0893i	−0.121324	+	1.05041i
$877$	−13.7440	+	7.93509i	−0.464101	+	0.267949i	−0.713767	−	0.700383i	$-0.753013\pi$
$877$	−13.7440	+	7.93509i	−0.464101	+	0.267949i	0.249666	+	0.968332i	$0.419679\pi$
$878$	−16.4119	−	20.5132i	−0.553873	−	0.692287i
$879$	−3.03988	+	0.324193i	−0.102533	+	0.0109348i
$880$	−10.6177	−	15.3636i	−0.357921	−	0.517906i
$881$			9.64780i			0.325043i	0.986705	+	0.162521i	$0.0519626\pi$
$881$			9.64780i			0.325043i	−0.986705	+	0.162521i	$0.948037\pi$
$882$	7.77371	+	28.6630i	0.261754	+	0.965135i
$883$	12.6173			0.424607			0.212303	−	0.977204i	$-0.431903\pi$
$883$	12.6173			0.424607			0.212303	+	0.977204i	$0.431903\pi$
$884$	3.69271	−	16.4180i	0.124199	−	0.552196i
$885$	2.50391	+	23.4786i	0.0841680	+	0.789225i
$886$	15.8608	+	19.8244i	0.532854	+	0.666015i
$887$	18.4017	+	31.8726i	0.617867	+	1.07018i	0.989874	+	0.141947i	$0.0453364\pi$
$887$	18.4017	+	31.8726i	0.617867	+	1.07018i	−0.372007	+	0.928230i	$0.621330\pi$
$888$	−18.0166	−	9.54999i	−0.604598	−	0.320477i
$889$	−0.286723	+	5.79755i	−0.00961638	+	0.194444i
$890$	3.48151	−	8.91216i	0.116701	−	0.298736i
$891$	41.8157	+	4.13725i	1.40088	+	0.138603i
$892$	−4.16234	−	13.3440i	−0.139366	−	0.446791i
$893$	0.142563	−	0.246926i	0.00477068	−	0.00826307i
$894$	30.5719	−	30.3057i	1.02248	−	1.01357i
$895$			1.07692i			0.0359976i
$896$	25.3301	+	15.9495i	0.846220	+	0.532834i
$897$	−44.0943	+	32.1393i	−1.47227	+	1.07310i
$898$	−22.3117	+	3.39904i	−0.744553	+	0.113428i
$899$	0.0989553	+	0.0571319i	0.00330035	+	0.00190546i
$900$	0.0524836	−	5.99977i	0.00174945	−	0.199992i
$901$	−23.7113	+	13.6897i	−0.789937	+	0.456070i
$902$	−66.8132	−	26.1004i	−2.22464	−	0.869048i
$903$	37.4522	−	2.13068i	1.24633	−	0.0709045i
$904$	9.34743	−	4.55623i	0.310891	−	0.151538i
$905$	−22.7330	+	13.1249i	−0.755670	+	0.436286i
$906$	−9.93943	+	36.4559i	−0.330215	+	1.21117i
$907$	14.7384	−	25.5277i	0.489381	−	0.847632i	−0.510545	−	0.859851i	$-0.670556\pi$
$907$	14.7384	−	25.5277i	0.489381	−	0.847632i	0.999925	+	0.0122192i	$0.00388959\pi$
$908$	−29.9994	−	6.74742i	−0.995564	−	0.223921i
$909$	16.1780	−	50.3124i	0.536590	−	1.66876i
$910$	9.52530	+	13.1922i	0.315761	+	0.437318i
$911$	−42.2061			−1.39835			−0.699175	−	0.714950i	$-0.746449\pi$
$911$	−42.2061			−1.39835			−0.699175	+	0.714950i	$0.746449\pi$
$912$	0.326510	+	0.114115i	0.0108118	+	0.00377874i
$913$	26.7707	−	46.3682i	0.885980	−	1.53456i
$914$	−2.25355	+	1.80298i	−0.0745408	+	0.0596373i
$915$	2.15960	+	0.957573i	0.0713942	+	0.0316564i
$916$	12.0940	−	13.1172i	0.399596	−	0.433403i
$917$	−5.03883	+	2.58613i	−0.166397	+	0.0854014i
$918$	−0.762896	+	14.1974i	−0.0251793	+	0.468584i
$919$	15.3124	−	8.84063i	0.505110	−	0.291626i	−0.225711	−	0.974194i	$-0.572471\pi$
$919$	15.3124	−	8.84063i	0.505110	−	0.291626i	0.730821	+	0.682569i	$0.239137\pi$
$920$	−20.4389	−	1.43422i	−0.673850	−	0.0472849i
$921$	35.5396	−	3.79018i	1.17107	−	0.124891i
$922$	2.48067	+	16.2834i	0.0816964	+	0.536266i
$923$		−	28.0297i		−	0.922610i
$924$	−42.2139	−	7.00352i	−1.38874	−	0.230399i
$925$		−	4.16233i		−	0.136857i
$926$	26.2471	−	3.99857i	0.862534	−	0.131401i
$927$	3.17608	−	2.87735i	0.104316	−	0.0945045i
$928$	−0.377421	−	0.400368i	−0.0123895	−	0.0131427i
$929$	7.15076	−	4.12849i	0.234609	−	0.135452i	−0.378088	−	0.925770i	$-0.623418\pi$
$929$	7.15076	−	4.12849i	0.234609	−	0.135452i	0.612696	+	0.790318i	$0.290085\pi$
$930$	2.78273	−	0.732602i	0.0912494	−	0.0240230i
$931$	−0.144016	−	0.318407i	−0.00471995	−	0.0104354i
$932$	4.04237	−	4.38436i	0.132412	−	0.143615i
$933$	13.0128	−	29.3476i	0.426020	−	0.960797i
$934$	−30.6870	−	38.3557i	−1.00411	−	1.25504i
$935$	−4.51669	+	7.82313i	−0.147712	+	0.255844i
$936$	−29.0142	+	22.7998i	−0.948359	+	0.745236i
$937$	35.5033			1.15984			0.579922	−	0.814672i	$-0.303083\pi$
$937$	35.5033			1.15984			0.579922	+	0.814672i	$0.303083\pi$
$938$	−11.4681	−	5.14656i	−0.374445	−	0.168041i
$939$	−6.92590	−	9.50217i	−0.226018	−	0.310092i
$940$	−2.50654	+	11.1442i	−0.0817542	+	0.363483i
$941$	−24.0272	+	41.6163i	−0.783263	+	1.35665i	0.146768	+	0.989171i	$0.453113\pi$
$941$	−24.0272	+	41.6163i	−0.783263	+	1.35665i	−0.930031	+	0.367481i	$0.880220\pi$
$942$	10.1672	−	37.2913i	0.331265	−	1.21502i
$943$	−68.1530	+	39.3482i	−2.21937	+	1.28135i
$944$	54.3497	−	4.41878i	1.76893	−	0.143819i
$945$	−9.79394	−	9.64774i	−0.318597	−	0.313841i
$946$	−19.6671	+	50.3450i	−0.639434	+	1.63686i
$947$	−39.4156	+	22.7566i	−1.28084	+	0.739491i	−0.977001	−	0.213234i	$-0.931600\pi$
$947$	−39.4156	+	22.7566i	−1.28084	+	0.739491i	−0.303835	+	0.952725i	$0.598267\pi$
$948$	−19.7462	+	26.5993i	−0.641325	+	0.863905i
$949$	34.0249	+	19.6443i	1.10449	+	0.637680i
$950$	0.0106330	+	0.0697967i	0.000344982	+	0.00226450i
$951$	16.4909	+	22.6251i	0.534753	+	0.733668i
$952$	1.72570	−	14.3756i	0.0559301	−	0.465915i
$953$			43.5506i			1.41074i	0.708838	+	0.705371i	$0.249220\pi$
$953$			43.5506i			1.41074i	−0.708838	+	0.705371i	$0.750780\pi$
$954$	59.2713	+	9.56080i	1.91898	+	0.309542i
$955$	2.53297	−	4.38724i	0.0819651	−	0.141968i
$956$	−12.7714	+	3.98373i	−0.413057	+	0.128843i
$957$	0.719049	+	0.318828i	0.0232435	+	0.0103062i
$958$	−1.38835	−	0.542356i	−0.0448556	−	0.0175227i
$959$	−24.3965	−	15.7413i	−0.787803	−	0.508314i
$960$	−13.8485	−	0.469197i	−0.446957	−	0.0151433i
$961$	−14.8100	−	25.6516i	−0.477741	−	0.827472i
$962$	−19.9887	+	15.9922i	−0.644461	+	0.515609i
$963$	−15.9571	+	14.4562i	−0.514210	+	0.465845i
$964$	−10.6663	+	47.4231i	−0.343540	+	1.52739i
$965$	−21.5622			−0.694112
$966$	−34.9330	+	31.3635i	−1.12395	+	1.00910i
$967$		−	6.03768i		−	0.194159i	−0.995277	−	0.0970793i	$-0.969050\pi$
$967$		−	6.03768i		−	0.194159i	0.995277	−	0.0970793i	$-0.0309500\pi$
$968$	17.0853	−	25.3167i	0.549142	−	0.813709i
$969$	−0.0177415	−	0.166358i	−0.000569940	−	0.00534420i
$970$	7.62662	−	6.10178i	0.244876	−	0.195916i
$971$	−10.4645	+	6.04167i	−0.335821	+	0.193886i	−0.658422	−	0.752649i	$-0.728776\pi$
$971$	−10.4645	+	6.04167i	−0.335821	+	0.193886i	0.322602	+	0.946535i	$0.395443\pi$
$972$	20.9579	−	23.0817i	0.672225	−	0.740347i
$973$	21.5591	+	1.06622i	0.691154	+	0.0341816i
$974$	−6.88495	+	17.6244i	−0.220608	+	0.564724i
$975$	−6.88577	−	3.05317i	−0.220521	−	0.0977796i
$976$	2.33599	−	4.93027i	0.0747733	−	0.157814i
$977$	14.8395	+	8.56761i	0.474759	+	0.274102i	0.718230	−	0.695806i	$-0.244953\pi$
$977$	14.8395	+	8.56761i	0.474759	+	0.274102i	−0.243471	+	0.969908i	$0.578286\pi$
$978$	43.0868	−	42.7116i	1.37776	−	1.36577i
$979$	31.5879			1.00955
$980$	9.30619	+	10.4592i	0.297275	+	0.334107i
$981$	27.2659	+	8.76736i	0.870532	+	0.279920i
$982$	31.0588	−	4.73160i	0.991126	−	0.150991i
$983$	23.4193	−	40.5633i	0.746958	−	1.29377i	−0.202316	−	0.979320i	$-0.564847\pi$
$983$	23.4193	−	40.5633i	0.746958	−	1.29377i	0.949274	−	0.314449i	$-0.101820\pi$
$984$	−45.0976	+	28.2605i	−1.43766	+	0.900913i
$985$	9.74249	+	16.8745i	0.310422	+	0.537666i
$986$	−0.0968409	+	0.247898i	−0.00308404	+	0.00789469i
$987$	14.3525	+	21.8861i	0.456845	+	0.696643i
$988$	0.294329	−	0.319230i	0.00936386	−	0.0101561i
$989$	29.6496	+	51.3546i	0.942802	+	1.63298i
$990$	18.5128	−	7.04597i	0.588377	−	0.223936i
$991$	−53.5716	−	30.9296i	−1.70176	−	0.982510i	−0.943983	−	0.329994i	$-0.892953\pi$
$991$	−53.5716	−	30.9296i	−1.70176	−	0.982510i	−0.757775	−	0.652516i	$-0.773713\pi$
$992$	−1.52992	−	6.46692i	−0.0485750	−	0.205325i
$993$	29.0575	+	39.8662i	0.922111	+	1.26511i
$994$	−2.44999	−	23.9918i	−0.0777091	−	0.760974i
$995$		−	2.71242i		−	0.0859893i
$996$	−15.7841	−	36.4550i	−0.500139	−	1.15512i
$997$	−8.10927	−	4.68189i	−0.256823	−	0.148277i	0.366061	−	0.930591i	$-0.380706\pi$
$997$	−8.10927	−	4.68189i	−0.256823	−	0.148277i	−0.622884	+	0.782314i	$0.714039\pi$
$998$	28.2125	−	22.5718i	0.893051	−	0.714498i
$999$	14.3983	−	16.1389i	0.455543	−	0.510611i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.cq.a.11.36	✓	128
3.2	odd	2		840.2.cq.b.11.29	yes	128
7.2	even	3	inner	840.2.cq.a.611.50	yes	128
8.3	odd	2		840.2.cq.b.11.15	yes	128
21.2	odd	6		840.2.cq.b.611.15	yes	128
24.11	even	2	inner	840.2.cq.a.11.50	yes	128
56.51	odd	6		840.2.cq.b.611.29	yes	128
168.107	even	6	inner	840.2.cq.a.611.36	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cq.a.11.36	✓	128	1.1	even	1	trivial
840.2.cq.a.11.50	yes	128	24.11	even	2	inner
840.2.cq.a.611.36	yes	128	168.107	even	6	inner
840.2.cq.a.611.50	yes	128	7.2	even	3	inner
840.2.cq.b.11.15	yes	128	8.3	odd	2
840.2.cq.b.11.29	yes	128	3.2	odd	2
840.2.cq.b.611.15	yes	128	21.2	odd	6
840.2.cq.b.611.29	yes	128	56.51	odd	6

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.cq (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.212988 + 1.39808i) q^{2} +(-1.72228 + 0.183676i) q^{3} +(-1.90927 + 0.595551i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.623620 - 2.36878i) q^{6} +(-2.64252 - 0.130688i) q^{7} +(-1.23928 - 2.54247i) q^{8} +(2.93253 - 0.632683i) q^{9} +(1.10428 - 0.883495i) q^{10} +(4.04336 + 2.33444i) q^{11} +(3.17892 - 1.37639i) q^{12} -4.34878i q^{13} +(-0.380114 - 3.72230i) q^{14} +(1.02021 + 1.39970i) q^{15} +(3.29064 - 2.27414i) q^{16} +(-1.67559 - 0.967404i) q^{17} +(1.50914 + 3.96516i) q^{18} +(-0.0249616 - 0.0432347i) q^{19} +(1.47040 + 1.35570i) q^{20} +(4.57518 - 0.260285i) q^{21} +(-2.40255 + 6.15017i) q^{22} +(3.62201 + 6.27350i) q^{23} +(2.60139 + 4.15124i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(6.07996 - 0.926240i) q^{26} +(-4.93444 + 1.62829i) q^{27} +(5.12312 - 1.32424i) q^{28} -0.0972660 q^{29} +(-1.73961 + 1.72446i) q^{30} +(-1.01737 - 0.587378i) q^{31} +(3.88030 + 4.11622i) q^{32} +(-7.39260 - 3.27790i) q^{33} +(0.995629 - 2.54866i) q^{34} +(1.20808 + 2.35383i) q^{35} +(-5.22220 + 2.95443i) q^{36} +(-3.60469 + 2.08117i) q^{37} +(0.0551292 - 0.0441068i) q^{38} +(0.798764 + 7.48984i) q^{39} +(-1.58221 + 2.34449i) q^{40} +10.8636i q^{41} +(1.33836 + 6.34104i) q^{42} +8.18596 q^{43} +(-9.11016 - 2.04905i) q^{44} +(-2.01418 - 2.22330i) q^{45} +(-7.99942 + 6.40005i) q^{46} +(2.85565 + 4.94613i) q^{47} +(-5.24971 + 4.52112i) q^{48} +(6.96584 + 0.690692i) q^{49} +(-1.31727 - 0.514588i) q^{50} +(3.06354 + 1.35838i) q^{51} +(2.58992 + 8.30300i) q^{52} +(7.07548 - 12.2551i) q^{53} +(-3.32747 - 6.55194i) q^{54} -4.66887i q^{55} +(2.94256 + 6.88050i) q^{56} +(0.0509321 + 0.0698776i) q^{57} +(-0.0207165 - 0.135986i) q^{58} +(11.8059 + 6.81613i) q^{59} +(-2.78145 - 2.06483i) q^{60} +(1.18119 - 0.681959i) q^{61} +(0.604515 - 1.54747i) q^{62} +(-7.83195 + 1.28863i) q^{63} +(-4.92836 + 6.30169i) q^{64} +(-3.76615 + 2.17439i) q^{65} +(3.00823 - 11.0336i) q^{66} +(1.67973 - 2.90938i) q^{67} +(3.77530 + 0.849136i) q^{68} +(-7.39041 - 10.1395i) q^{69} +(-3.03355 + 2.19034i) q^{70} +6.44542 q^{71} +(-5.24281 - 6.67180i) q^{72} +(-4.51719 + 7.82400i) q^{73} +(-3.67740 - 4.59639i) q^{74} +(0.702074 - 1.58338i) q^{75} +(0.0734069 + 0.0676809i) q^{76} +(-10.3796 - 6.69722i) q^{77} +(-10.3013 + 2.71199i) q^{78} +(-8.28188 + 4.78155i) q^{79} +(-3.61478 - 1.71271i) q^{80} +(8.19942 - 3.71072i) q^{81} +(-15.1883 + 2.31383i) q^{82} -11.4677i q^{83} +(-8.58025 + 3.22171i) q^{84} +1.93481i q^{85} +(1.74351 + 11.4446i) q^{86} +(0.167520 - 0.0178654i) q^{87} +(0.924378 - 13.1732i) q^{88} +(5.85921 - 3.38281i) q^{89} +(2.67936 - 3.28953i) q^{90} +(-0.568334 + 11.4917i) q^{91} +(-10.6516 - 9.82072i) q^{92} +(1.86008 + 0.824766i) q^{93} +(-6.30688 + 5.04590i) q^{94} +(-0.0249616 + 0.0432347i) q^{95} +(-7.43903 - 6.37658i) q^{96} +6.90641 q^{97} +(0.517999 + 9.88593i) q^{98} +(13.3342 + 4.28763i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 64 q^{5} - 12 q^{12} - 6 q^{14} + 8 q^{16} + 14 q^{18} + 8 q^{21} + 4 q^{22} - 64 q^{25} - 16 q^{26} - 6 q^{28} - 10 q^{32} + 24 q^{34} + 20 q^{36} - 16 q^{38} + 16 q^{42} + 6 q^{44} + 8 q^{46}+ \cdots + 14 q^{98}+O(q^{100}) \) 128 * q - 64 * q^5 - 12 * q^12 - 6 * q^14 + 8 * q^16 + 14 * q^18 + 8 * q^21 + 4 * q^22 - 64 * q^25 - 16 * q^26 - 6 * q^28 - 10 * q^32 + 24 * q^34 + 20 * q^36 - 16 * q^38 + 16 * q^42 + 6 * q^44 + 8 * q^46 - 80 * q^48 + 8 * q^49 + 20 * q^51 - 6 * q^52 - 32 * q^54 - 18 * q^56 - 8 * q^58 - 12 * q^60 - 20 * q^62 - 28 * q^63 - 14 * q^66 + 32 * q^67 - 2 * q^68 + 40 * q^69 - 6 * q^70 - 48 * q^71 + 4 * q^72 - 8 * q^73 - 26 * q^74 - 24 * q^76 - 12 * q^78 + 8 * q^80 + 4 * q^81 - 12 * q^82 - 22 * q^84 + 46 * q^86 - 36 * q^87 - 20 * q^88 - 28 * q^90 - 24 * q^91 - 40 * q^92 + 12 * q^94 + 34 * q^96 + 32 * q^97 + 14 * q^98

Introduction

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