LMFDB - Embedded newform 840.2.cq.b.11.15

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			11.15
Character	$\chi$	$=$	840.11
Dual form			840.2.cq.b.611.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.10428 - 0.883495i) q^{2} +(-1.72228 + 0.183676i) q^{3} +(0.438874 + 1.95125i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.06416 + 1.31880i) q^{6} +(2.64252 + 0.130688i) q^{7} +(1.23928 - 2.54247i) q^{8} +(2.93253 - 0.632683i) q^{9} +(0.212988 - 1.39808i) q^{10} +(4.04336 + 2.33444i) q^{11} +(-1.11426 - 3.28000i) q^{12} +4.34878i q^{13} +(-2.80262 - 2.47897i) q^{14} +(-1.02021 - 1.39970i) q^{15} +(-3.61478 + 1.71271i) q^{16} +(-1.67559 - 0.967404i) q^{17} +(-3.79731 - 1.89221i) 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} +(-1.66741 + 4.60649i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.84212 - 4.80228i) q^{26} +(-4.93444 + 1.62829i) q^{27} +(0.904727 + 5.21358i) q^{28} +0.0972660 q^{29} +(-0.110033 + 2.44702i) q^{30} +(1.01737 + 0.587378i) q^{31} +(5.50490 + 1.30233i) q^{32} +(-7.39260 - 3.27790i) q^{33} +(0.995629 + 2.54866i) q^{34} +(1.20808 + 2.35383i) q^{35} +(2.52153 + 5.44443i) q^{36} +(3.60469 - 2.08117i) q^{37} +(-0.0106330 + 0.0697967i) q^{38} +(-0.798764 - 7.48984i) q^{39} +(2.82149 - 0.197987i) q^{40} +10.8636i q^{41} +(5.28224 + 3.75472i) q^{42} +8.18596 q^{43} +(-2.78055 + 8.91415i) q^{44} +(2.01418 + 2.22330i) q^{45} +(-1.54289 + 10.1277i) q^{46} +(-2.85565 - 4.94613i) q^{47} +(5.91110 - 3.61372i) q^{48} +(6.96584 + 0.690692i) q^{49} +(1.31727 - 0.514588i) q^{50} +(3.06354 + 1.35838i) q^{51} +(-8.48557 + 1.90856i) q^{52} +(-7.07548 + 12.2551i) q^{53} +(6.88759 + 2.56146i) q^{54} +4.66887i q^{55} +(3.60710 - 6.55659i) q^{56} +(0.0509321 + 0.0698776i) q^{57} +(-0.107409 - 0.0859340i) q^{58} +(11.8059 + 6.81613i) q^{59} +(2.28343 - 2.60498i) 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} +(5.26750 + 10.1510i) q^{66} +(1.67973 - 2.90938i) q^{67} +(1.15228 - 3.69408i) q^{68} +(7.39041 + 10.1395i) q^{69} +(0.745539 - 3.66663i) q^{70} -6.44542 q^{71} +(2.02565 - 8.23995i) q^{72} +(-4.51719 + 7.82400i) q^{73} +(-5.81929 - 0.886529i) q^{74} +(0.702074 - 1.58338i) q^{75} +(0.0734069 - 0.0676809i) q^{76} +(10.3796 + 6.69722i) q^{77} +(-5.73517 + 8.97659i) q^{78} +(8.28188 - 4.78155i) q^{79} +(-3.29064 - 2.27414i) q^{80} +(8.19942 - 3.71072i) q^{81} +(9.59797 - 11.9965i) q^{82} -11.4677i q^{83} +(-2.51581 - 8.81310i) q^{84} -1.93481i q^{85} +(-9.03960 - 7.23225i) q^{86} +(-0.167520 + 0.0178654i) q^{87} +(10.9461 - 7.38712i) q^{88} +(5.85921 - 3.38281i) q^{89} +(-0.259949 - 4.23467i) q^{90} +(-0.568334 + 11.4917i) q^{91} +(10.6516 - 9.82072i) q^{92} +(-1.86008 - 0.824766i) q^{93} +(-1.21644 + 7.98487i) q^{94} +(0.0249616 - 0.0432347i) q^{95} +(-9.72021 - 1.23187i) q^{96} +6.90641 q^{97} +(-7.08202 - 6.91700i) q^{98} +(13.3342 + 4.28763i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 64 q^{5} + 2 q^{12} + 6 q^{14} + 8 q^{16} - 4 q^{18} - 8 q^{21} + 4 q^{22} + 20 q^{24} - 64 q^{25} + 16 q^{26} - 6 q^{28} + 10 q^{32} + 24 q^{34} + 20 q^{36} + 16 q^{38} + 18 q^{42} - 6 q^{44} + 8 q^{46}+ \cdots - 14 q^{98}+O(q^{100}) $ 128 * q + 64 * q^5 + 2 * q^12 + 6 * q^14 + 8 * q^16 - 4 * q^18 - 8 * q^21 + 4 * q^22 + 20 * q^24 - 64 * q^25 + 16 * q^26 - 6 * q^28 + 10 * q^32 + 24 * q^34 + 20 * q^36 + 16 * q^38 + 18 * q^42 - 6 * q^44 + 8 * q^46 - 44 * q^48 + 8 * q^49 + 20 * q^51 - 6 * q^52 - 16 * q^54 + 18 * q^56 - 8 * q^58 - 2 * q^60 + 20 * q^62 + 28 * q^63 + 22 * q^66 + 32 * q^67 + 2 * q^68 - 40 * q^69 - 6 * q^70 + 48 * q^71 - 54 * q^72 - 8 * q^73 + 26 * q^74 - 24 * q^76 - 84 * q^78 - 8 * q^80 + 4 * q^81 - 12 * q^82 + 6 * q^84 - 46 * q^86 + 36 * q^87 - 20 * q^88 - 8 * q^90 - 24 * q^91 + 40 * q^92 + 12 * q^94 + 22 * 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 $

$2$	−1.10428	−	0.883495i	−0.780845	−	0.624725i
$2$	−1.10428	−	0.883495i	−0.780845	−	0.624725i
$3$	−1.72228	+	0.183676i	−0.994361	+	0.106045i
$3$	−1.72228	+	0.183676i	−0.994361	+	0.106045i
$4$	0.438874	+	1.95125i	0.219437	+	0.975627i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	2.06416	+	1.31880i	0.842691	+	0.538398i
$7$	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
$10$	0.212988	−	1.39808i	0.0673529	−	0.442113i
$11$	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	$0.418125\pi$
$12$	−1.11426	−	3.28000i	−0.321660	−	0.946855i
$13$			4.34878i			1.20613i	0.797690	+	0.603067i	$0.206055\pi$
$13$			4.34878i			1.20613i	−0.797690	+	0.603067i	$0.793945\pi$
$14$	−2.80262	−	2.47897i	−0.749033	−	0.662533i
$15$	−1.02021	−	1.39970i	−0.263417	−	0.361402i
$16$	−3.61478	+	1.71271i	−0.903695	+	0.428177i
$17$	−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	$0.742055\pi$
$18$	−3.79731	−	1.89221i	−0.895034	−	0.445999i
$19$	−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	$-0.894187\pi$
$23$	−3.62201	−	6.27350i	−0.755240	−	1.30811i	0.190014	−	0.981781i	$-0.439147\pi$
$24$	−1.66741	+	4.60649i	−0.340358	+	0.940296i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	3.84212	−	4.80228i	0.753503	−	0.941804i
$27$	−4.93444	+	1.62829i	−0.949633	+	0.313365i
$28$	0.904727	+	5.21358i	0.170977	+	0.985275i
$29$	0.0972660			0.0180618			0.00903092	−	0.999959i	$-0.497125\pi$
$29$	0.0972660			0.0180618			0.00903092	+	0.999959i	$0.497125\pi$
$30$	−0.110033	+	2.44702i	−0.0200892	+	0.446762i
$31$	1.01737	+	0.587378i	0.182725	+	0.105496i	0.588572	−	0.808445i	$-0.299690\pi$
$31$	1.01737	+	0.587378i	0.182725	+	0.105496i	−0.405847	+	0.913941i	$0.633024\pi$
$32$	5.50490	+	1.30233i	0.973138	+	0.230221i
$33$	−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
$36$	2.52153	+	5.44443i	0.420256	+	0.907406i
$37$	3.60469	−	2.08117i	0.592607	−	0.342142i	−0.173521	−	0.984830i	$-0.555514\pi$
$37$	3.60469	−	2.08117i	0.592607	−	0.342142i	0.766128	+	0.642689i	$0.222181\pi$
$38$	−0.0106330	+	0.0697967i	−0.00172491	+	0.0113225i
$39$	−0.798764	−	7.48984i	−0.127905	−	1.19933i
$40$	2.82149	−	0.197987i	0.446117	−	0.0313045i
$41$			10.8636i			1.69662i	0.529504	+	0.848308i	$0.322378\pi$
$41$			10.8636i			1.69662i	−0.529504	+	0.848308i	$0.677622\pi$
$42$	5.28224	+	3.75472i	0.815068	+	0.579366i
$43$	8.18596			1.24835			0.624173	−	0.781286i	$-0.285436\pi$
$43$	8.18596			1.24835			0.624173	+	0.781286i	$0.285436\pi$
$44$	−2.78055	+	8.91415i	−0.419184	+	1.34386i
$45$	2.01418	+	2.22330i	0.300257	+	0.331430i
$46$	−1.54289	+	10.1277i	−0.227487	+	1.49325i
$47$	−2.85565	−	4.94613i	−0.416539	−	0.721467i	0.579050	−	0.815292i	$-0.303424\pi$
$47$	−2.85565	−	4.94613i	−0.416539	−	0.721467i	−0.995589	+	0.0938254i	$0.970090\pi$
$48$	5.91110	−	3.61372i	0.853193	−	0.521595i
$49$	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
$52$	−8.48557	+	1.90856i	−1.17674	+	0.264670i
$53$	−7.07548	+	12.2551i	−0.971892	+	1.68337i	−0.282061	+	0.959396i	$0.591018\pi$
$53$	−7.07548	+	12.2551i	−0.971892	+	1.68337i	−0.689831	+	0.723970i	$0.742315\pi$
$54$	6.88759	+	2.56146i	0.937283	+	0.348570i
$55$			4.66887i			0.629551i
$56$	3.60710	−	6.55659i	0.482019	−	0.876161i
$57$	0.0509321	+	0.0698776i	0.00674612	+	0.00925551i
$58$	−0.107409	−	0.0859340i	−0.0141035	−	0.0112837i
$59$	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	$0.319187\pi$
$60$	2.28343	−	2.60498i	0.294790	−	0.336302i
$61$	−1.18119	+	0.681959i	−0.151236	+	0.0873160i	−0.573708	−	0.819060i	$-0.694496\pi$
$61$	−1.18119	+	0.681959i	−0.151236	+	0.0873160i	0.422472	+	0.906376i	$0.361162\pi$
$62$	−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
$66$	5.26750	+	10.1510i	0.648385	+	1.24951i
$67$	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	$0.100878\pi$
$68$	1.15228	−	3.69408i	0.139734	−	0.447972i
$69$	7.39041	+	10.1395i	0.889701	+	1.22065i
$70$	0.745539	−	3.66663i	0.0891090	−	0.438246i
$71$	−6.44542			−0.764931			−0.382466	−	0.923970i	$-0.624925\pi$
$71$	−6.44542			−0.764931			−0.382466	+	0.923970i	$0.624925\pi$
$72$	2.02565	−	8.23995i	0.238725	−	0.971087i
$73$	−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	$0.989347\pi$
$74$	−5.81929	−	0.886529i	−0.676478	−	0.103057i
$75$	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
$78$	−5.73517	+	8.97659i	−0.649380	+	1.01640i
$79$	8.28188	−	4.78155i	0.931785	−	0.537966i	0.0444090	−	0.999013i	$-0.485860\pi$
$79$	8.28188	−	4.78155i	0.931785	−	0.537966i	0.887376	+	0.461047i	$0.152526\pi$
$80$	−3.29064	−	2.27414i	−0.367905	−	0.254256i
$81$	8.19942	−	3.71072i	0.911047	−	0.412302i
$82$	9.59797	−	11.9965i	1.05992	−	1.32479i
$83$		−	11.4677i		−	1.25875i	−0.777103	−	0.629373i	$-0.783312\pi$
$83$		−	11.4677i		−	1.25875i	0.777103	−	0.629373i	$-0.216688\pi$
$84$	−2.51581	−	8.81310i	−0.274497	−	0.961588i
$85$		−	1.93481i		−	0.209859i
$86$	−9.03960	−	7.23225i	−0.974765	−	0.779874i
$87$	−0.167520	+	0.0178654i	−0.0179600	+	0.00191537i
$88$	10.9461	−	7.38712i	1.16686	−	0.787470i
$89$	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	$0.216595\pi$
$90$	−0.259949	−	4.23467i	−0.0274010	−	0.446373i
$91$	−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
$94$	−1.21644	+	7.98487i	−0.125466	+	0.823576i
$95$	0.0249616	−	0.0432347i	0.00256100	−	0.00443579i
$96$	−9.72021	−	1.23187i	−0.992065	−	0.125727i
$97$	6.90641			0.701239			0.350620	−	0.936518i	$-0.385971\pi$
$97$	6.90641			0.701239			0.350620	+	0.936518i	$0.385971\pi$
$98$	−7.08202	−	6.91700i	−0.715392	−	0.698723i
$99$	13.3342	+	4.28763i	1.34014	+	0.430923i
$100$	−1.90927	−	0.595551i	−0.190927	−	0.0595551i
$101$	−8.80824	+	15.2563i	−0.876453	+	1.51806i	−0.0212462	+	0.999774i	$0.506763\pi$
$101$	−8.80824	+	15.2563i	−0.876453	+	1.51806i	−0.855207	+	0.518287i	$0.826570\pi$
$102$	−2.18288	−	4.20665i	−0.216138	−	0.416521i
$103$	−1.23715	+	0.714272i	−0.121900	+	0.0703793i	−0.559710	−	0.828688i	$-0.689088\pi$
$103$	−1.23715	+	0.714272i	−0.121900	+	0.0703793i	0.437810	+	0.899068i	$0.355754\pi$
$104$	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	$0.446107\pi$
$108$	−5.34281	−	8.91372i	−0.514112	−	0.857723i
$109$	−8.26788	−	4.77346i	−0.791919	−	0.457215i	0.0487186	−	0.998813i	$-0.484486\pi$
$109$	−8.26788	−	4.77346i	−0.791919	−	0.457215i	−0.840638	+	0.541598i	$0.817820\pi$
$110$	4.12493	−	5.15575i	0.393296	−	0.491581i
$111$	−5.82604	+	4.24645i	−0.552983	+	0.403056i
$112$	−9.77596	+	4.05346i	−0.923742	+	0.383016i
$113$			3.67651i			0.345857i	0.984934	+	0.172928i	$0.0553229\pi$
$113$			3.67651i			0.345857i	−0.984934	+	0.172928i	$0.944677\pi$
$114$	0.00549319	−	0.122163i	0.000514484	−	0.0114416i
$115$	3.62201	−	6.27350i	0.337754	−	0.585007i
$116$	0.0426875	+	0.189791i	0.00396343	+	0.0176216i
$117$	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
$120$	−4.82304	+	0.859229i	−0.440281	+	0.0784365i
$121$	5.39919	+	9.35168i	0.490836	+	0.850153i
$122$	1.90687	+	0.290499i	0.172640	+	0.0263005i
$123$	−1.99538	−	18.7103i	−0.179918	−	1.68705i
$124$	−0.699627	+	2.24293i	−0.0628284	+	0.201421i
$125$	−1.00000			−0.0894427
$126$	−9.78717	−	5.49647i	−0.871911	−	0.489665i
$127$			2.19395i			0.194681i	0.995251	+	0.0973407i	$0.0310336\pi$
$127$			2.19395i			0.194681i	−0.995251	+	0.0973407i	$0.968966\pi$
$128$	−0.125218	+	11.3130i	−0.0110679	+	0.999939i
$129$	−14.0985	+	1.50356i	−1.24131	+	0.132381i
$130$	6.07996	+	0.926240i	0.533247	+	0.0812366i
$131$	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	$0.303523\pi$
$132$	3.15159	−	15.8634i	0.274311	−	1.38073i
$133$	−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
$136$	−4.53613	+	3.06127i	−0.388970	+	0.262501i
$137$	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	$0.511361\pi$
$138$	0.797080	−	17.7262i	0.0678520	−	1.50896i
$139$	−8.15854			−0.691999			−0.345999	−	0.938235i	$-0.612460\pi$
$139$	−8.15854			−0.691999			−0.345999	+	0.938235i	$0.612460\pi$
$140$	−4.06273	+	3.39031i	−0.343364	+	0.286533i
$141$	5.82672	+	7.99413i	0.490698	+	0.673227i
$142$	7.11756	+	5.69450i	0.597292	+	0.477872i
$143$	−10.1520	+	17.5837i	−0.848949	+	1.47042i
$144$	−9.51684	+	7.30957i	−0.793070	+	0.609131i
$145$	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	$-0.910873\pi$
$149$	−8.78701	−	15.2195i	−0.719860	−	1.24683i	0.241195	−	0.970477i	$-0.422461\pi$
$150$	−2.17420	+	1.12822i	−0.177522	+	0.0921185i
$151$	13.3596	+	7.71315i	1.08719	+	0.627688i	0.932826	−	0.360327i	$-0.117335\pi$
$151$	13.3596	+	7.71315i	1.08719	+	0.627688i	0.154361	+	0.988015i	$0.450668\pi$
$152$	−0.140858	+	0.00988414i	−0.0114251	+	0.000801710i
$153$	−5.52578	−	1.77682i	−0.446733	−	0.143647i
$154$	−5.54503	−	16.5659i	−0.446831	−	1.33492i
$155$			1.17476i			0.0943587i
$156$	14.2640	−	4.84568i	1.14203	−	0.387965i
$157$	−13.6657	−	7.88990i	−1.09064	−	0.629682i	−0.156895	−	0.987615i	$-0.550148\pi$
$157$	−13.6657	−	7.88990i	−1.09064	−	0.629682i	−0.933747	+	0.357933i	$0.883482\pi$
$158$	−13.3700	−	2.03683i	−1.06366	−	0.162041i
$159$	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
$162$	−12.3329	−	3.14647i	−0.968962	−	0.247210i
$163$	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	$0.411508\pi$
$164$	−21.1977	+	4.76776i	−1.65526	+	0.372300i
$165$	−0.857558	−	8.04113i	−0.0667608	−	0.626001i
$166$	−10.1317	+	12.6636i	−0.786370	+	0.982885i
$167$	1.69273			0.130987			0.0654936	−	0.997853i	$-0.479138\pi$
$167$	1.69273			0.130987			0.0654936	+	0.997853i	$0.479138\pi$
$168$	−5.00817	+	11.9548i	−0.386389	+	0.922336i
$169$	−5.91189			−0.454761
$170$	−1.70939	+	2.13657i	−0.131104	+	0.163868i
$171$	−0.100554	−	0.110994i	−0.00768958	−	0.00848793i
$172$	3.59260	+	15.9729i	0.273933	+	1.21792i
$173$	1.64079	+	2.84193i	0.124747	+	0.216068i	0.921634	−	0.388060i	$-0.126855\pi$
$173$	1.64079	+	2.84193i	0.124747	+	0.216068i	−0.796887	+	0.604128i	$0.793521\pi$
$174$	0.200773	+	0.128274i	0.0152205	+	0.00972445i
$175$	−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
$178$	−9.45891	−	1.44100i	−0.708975	−	0.108008i
$179$	−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	$0.679481\pi$
$180$	−3.45425	+	4.90593i	−0.257465	+	0.365666i
$181$			26.2498i			1.95113i	0.219710	+	0.975565i	$0.429489\pi$
$181$			26.2498i			1.95113i	−0.219710	+	0.975565i	$0.570511\pi$
$182$	10.7805	−	12.1880i	0.799104	−	0.903434i
$183$	1.90908	−	1.39148i	0.141123	−	0.102861i
$184$	−20.4389	+	1.43422i	−1.50678	+	0.105732i
$185$	3.60469	+	2.08117i	0.265022	+	0.153010i
$186$	1.32538	+	2.55415i	0.0971816	+	0.187279i
$187$	−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	0.759716	−	0.650255i	$-0.225338\pi$
$191$	−2.53297	−	4.38724i	−0.183279	−	0.317449i	−0.942995	+	0.332806i	$0.892005\pi$
$192$	9.64550	+	9.94808i	0.696104	+	0.717941i
$193$	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	$-0.116108\pi$
$194$	−7.62662	−	6.10178i	−0.547559	−	0.438082i
$195$	6.08701	−	4.43667i	0.435900	−	0.317716i
$196$	1.70941	+	13.8952i	0.122101	+	0.992518i
$197$	19.4850			1.38825			0.694124	−	0.719856i	$-0.255792\pi$
$197$	19.4850			1.38825			0.694124	+	0.719856i	$0.255792\pi$
$198$	−10.9366	−	16.5155i	−0.777233	−	1.17370i
$199$	−2.34902	−	1.35621i	−0.166518	−	0.0961390i	0.414425	−	0.910083i	$-0.363983\pi$
$199$	−2.34902	−	1.35621i	−0.166518	−	0.0961390i	−0.580943	+	0.813944i	$0.697316\pi$
$200$	1.58221	+	2.34449i	0.111879	+	0.165780i
$201$	−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
$204$	−1.30604	+	6.57389i	−0.0914409	+	0.460265i
$205$	−9.40819	+	5.43182i	−0.657096	+	0.379375i
$206$	1.99722	+	0.304263i	0.139153	+	0.0211990i
$207$	−14.5908	−	16.1056i	−1.01413	−	1.11942i
$208$	−7.44819	−	15.7199i	−0.516439	−	1.08998i
$209$		−	0.233085i		−	0.0161228i
$210$	−0.610561	+	6.45192i	−0.0421327	+	0.445224i
$211$	−7.65701			−0.527130			−0.263565	−	0.964642i	$-0.584898\pi$
$211$	−7.65701			−0.527130			−0.263565	+	0.964642i	$0.584898\pi$
$212$	−27.0180	−	8.42762i	−1.85561	−	0.578811i
$213$	11.1009	−	1.18387i	0.760618	−	0.0811172i
$214$	10.0343	+	1.52866i	0.685932	+	0.104497i
$215$	4.09298	+	7.08925i	0.279139	+	0.483483i
$216$	−1.97527	+	14.5636i	−0.134400	+	0.990927i
$217$	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
$220$	−9.11016	+	2.04905i	−0.614207	+	0.138147i
$221$	4.20703	−	7.28679i	0.282995	−	0.490162i
$222$	10.1853	+	0.457994i	0.683593	+	0.0307386i
$223$		−	6.98906i		−	0.468022i	−0.972234	−	0.234011i	$-0.924815\pi$
$223$		−	6.98906i		−	0.468022i	0.972234	−	0.234011i	$-0.0751852\pi$
$224$	14.3766	+	4.16086i	0.960578	+	0.278009i
$225$	−0.918344	+	2.85598i	−0.0612229	+	0.190399i
$226$	3.24818	−	4.05990i	0.216066	−	0.270060i
$227$	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	$0.496232\pi$
$228$	−0.113996	+	0.130049i	−0.00754958	+	0.00861269i
$229$	7.72565	−	4.46041i	0.510525	−	0.294752i	−0.222524	−	0.974927i	$-0.571430\pi$
$229$	7.72565	−	4.46041i	0.510525	−	0.294752i	0.733050	+	0.680175i	$0.238096\pi$
$230$	−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	$0.364472\pi$
$234$	8.22881	−	16.5136i	0.537934	−	1.07953i
$235$	2.85565	−	4.94613i	0.186282	−	0.322650i
$236$	−8.11870	+	26.0277i	−0.528482	+	1.69426i
$237$	−13.3855	+	9.75636i	−0.869482	+	0.633744i
$238$	2.29789	+	6.86502i	0.148950	+	0.444993i
$239$	−6.68915			−0.432685			−0.216343	−	0.976318i	$-0.569413\pi$
$239$	−6.68915			−0.432685			−0.216343	+	0.976318i	$0.569413\pi$
$240$	6.08512	+	3.31230i	0.392793	+	0.213808i
$241$	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	$-0.119530\pi$
$242$	2.29993	−	15.0970i	0.147845	−	0.970475i
$243$	−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
$246$	−14.3270	+	22.4243i	−0.913454	+	1.42972i
$247$	0.188018	−	0.108552i	0.0119633	−	0.00690702i
$248$	2.75420	−	1.85871i	0.174892	−	0.118028i
$249$	2.10634	+	19.7507i	0.133484	+	1.25165i
$250$	1.10428	+	0.883495i	0.0698409	+	0.0558771i
$251$		−	4.12014i		−	0.260061i	−0.991510	−	0.130030i	$-0.958493\pi$
$251$		−	4.12014i		−	0.260061i	0.991510	−	0.130030i	$-0.0415075\pi$
$252$	5.95168	+	14.7166i	0.374921	+	0.927057i
$253$		−	33.8214i		−	2.12633i
$254$	1.93834	−	2.42274i	0.121622	−	0.152016i
$255$	0.355377	+	3.33229i	0.0222546	+	0.208676i
$256$	10.1333	−	12.3821i	0.633329	−	0.773882i
$257$	−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	$0.394072\pi$
$258$	16.8971	+	10.7956i	1.05197	+	0.672107i
$259$	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
$262$	−2.99286	−	0.455942i	−0.184900	−	0.0281682i
$263$	3.88549	−	6.72987i	0.239590	−	0.414981i	−0.721007	−	0.692928i	$-0.756320\pi$
$263$	3.88549	−	6.72987i	0.239590	−	0.414981i	0.960597	+	0.277946i	$0.0896538\pi$
$264$	−17.4955	+	14.7333i	−1.07677	+	0.906770i
$265$	−14.1510			−0.869287
$266$	−0.0372196	+	0.183050i	−0.00228208	+	0.0112235i
$267$	−9.46988	+	6.90236i	−0.579547	+	0.422418i
$268$	6.41412	+	2.00073i	0.391805	+	0.122214i
$269$	6.80473	−	11.7861i	0.414892	−	0.718613i	−0.580525	−	0.814242i	$-0.697153\pi$
$269$	6.80473	−	11.7861i	0.414892	−	0.718613i	0.995417	+	0.0956287i	$0.0304862\pi$
$270$	1.22551	+	7.24556i	0.0745822	+	0.440951i
$271$	−6.21337	+	3.58729i	−0.377436	+	0.217913i	−0.676702	−	0.736257i	$-0.736591\pi$
$271$	−6.21337	+	3.58729i	−0.377436	+	0.217913i	0.299266	+	0.954170i	$0.403258\pi$
$272$	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
$276$	−16.5412	+	18.8705i	−0.995665	+	1.13587i
$277$	−10.9137	−	6.30101i	−0.655738	−	0.378591i	0.134913	−	0.990857i	$-0.456925\pi$
$277$	−10.9137	−	6.30101i	−0.655738	−	0.378591i	−0.790651	+	0.612267i	$0.790258\pi$
$278$	9.00933	+	7.20803i	0.540343	+	0.432309i
$279$	3.35508	+	1.07883i	0.200864	+	0.0645879i
$280$	7.48172	−	0.154451i	0.447118	−	0.00923019i
$281$			8.26478i			0.493035i	0.969138	+	0.246518i	$0.0792864\pi$
$281$			8.26478i			0.493035i	−0.969138	+	0.246518i	$0.920714\pi$
$282$	0.628431	−	13.9756i	0.0374225	−	0.832237i
$283$	−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	$0.875740\pi$
$284$	−2.82873	−	12.5767i	−0.167854	−	0.746287i
$285$	−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
$288$	16.9672	+	0.336258i	0.999804	+	0.0198142i
$289$	−6.62826	−	11.4805i	−0.389898	−	0.675322i
$290$	0.0207165	−	0.135986i	0.00121652	−	0.00798537i
$291$	−11.8948	+	1.26854i	−0.697285	+	0.0743630i
$292$	−17.2491	−	5.38043i	−1.00943	−	0.314866i
$293$	−1.76503			−0.103114			−0.0515571	−	0.998670i	$-0.516418\pi$
$293$	−1.76503			−0.103114			−0.0515571	+	0.998670i	$0.516418\pi$
$294$	13.4677	+	10.6123i	0.785455	+	0.618919i
$295$			13.6323i			0.793700i
$296$	−0.824089	−	11.7440i	−0.0478992	−	0.682605i
$297$	−23.7529	−	4.93535i	−1.37828	−	0.286378i
$298$	−3.74306	+	24.5699i	−0.216830	+	1.42330i
$299$	27.2821	−	15.7513i	1.57776	−	0.910921i
$300$	3.39770	+	0.675022i	0.196166	+	0.0389724i
$301$	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
$304$	0.164279	+	0.113532i	0.00942204	+	0.00651151i
$305$	−1.18119	−	0.681959i	−0.0676346	−	0.0390489i
$306$	4.53221	+	6.84411i	0.259089	+	0.391252i
$307$	−20.6352			−1.17771			−0.588856	−	0.808238i	$-0.700421\pi$
$307$	−20.6352			−1.17771			−0.588856	+	0.808238i	$0.700421\pi$
$308$	−8.51264	+	23.1925i	−0.485053	+	1.32151i
$309$	1.99954	−	1.45741i	0.113750	−	0.0829094i
$310$	1.03789	−	1.29726i	0.0589482	−	0.0736795i
$311$	9.26739	−	16.0516i	0.525505	−	0.910202i	−0.474053	−	0.880496i	$-0.657210\pi$
$311$	9.26739	−	16.0516i	0.525505	−	0.910202i	0.999559	−	0.0297058i	$-0.00945705\pi$
$312$	−20.0326	−	7.25118i	−1.13412	−	0.410517i
$313$	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	0.998626	−	0.0523978i	$-0.0166864\pi$
$317$	8.08209	+	13.9986i	0.453935	+	0.786239i	−0.544691	+	0.838637i	$0.683353\pi$
$318$	−30.7670	+	15.9654i	−1.72533	+	0.895293i
$319$	0.393282	+	0.227061i	0.0220195	+	0.0127130i
$320$	2.99324	−	7.41893i	0.167327	−	0.414731i
$321$	10.0460	−	7.32225i	0.560711	−	0.408688i
$322$	−5.40069	+	26.5611i	−0.300969	+	1.48019i
$323$			0.0965917i			0.00537450i
$324$	10.8391	+	14.3706i	0.602170	+	0.798368i
$325$	−3.76615	−	2.17439i	−0.208909	−	0.120613i
$326$	5.27532	−	34.6279i	0.292173	−	1.91786i
$327$	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
$330$	−6.15731	+	9.63732i	−0.338949	+	0.530517i
$331$	−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	$-0.452852\pi$
$332$	22.3764	−	5.03288i	1.22807	−	0.276215i
$333$	9.25412	−	8.38370i	0.507123	−	0.459424i
$334$	−1.86925	−	1.49552i	−0.102281	−	0.0818310i
$335$	3.35946			0.183547
$336$	16.0925	−	8.77681i	0.877916	−	0.478814i
$337$	−17.1854			−0.936146			−0.468073	−	0.883690i	$-0.655052\pi$
$337$	−17.1854			−0.936146			−0.468073	+	0.883690i	$0.655052\pi$
$338$	6.52839	+	5.22312i	0.355097	+	0.284100i
$339$	−0.675285	−	6.33199i	−0.0366764	−	0.343907i
$340$	3.77530	−	0.849136i	0.204744	−	0.0460509i
$341$	2.74239	+	4.74997i	0.148509	+	0.257225i
$342$	0.0129775	+	0.211408i	0.000701741	+	0.0114316i
$343$	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
$346$	0.698939	−	4.58792i	0.0375752	−	0.246648i
$347$	−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	$0.958215\pi$
$348$	−0.108380	−	0.319033i	−0.00580977	−	0.0171019i
$349$		−	27.6360i		−	1.47932i	−0.672981	−	0.739659i	$-0.734987\pi$
$349$		−	27.6360i		−	1.47932i	0.672981	−	0.739659i	$-0.265013\pi$
$350$	3.54816	−	1.18766i	0.189657	−	0.0634830i
$351$	−7.08109	−	21.4588i	−0.377961	−	1.14538i
$352$	19.2181	+	18.1166i	1.02433	+	0.965620i
$353$	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	$0.408925\pi$
$354$	15.3801	+	29.6392i	0.817445	+	1.57530i
$355$	−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	0.947682	−	0.319215i	$-0.103419\pi$
$359$	3.74005	+	6.47797i	0.197393	+	0.341894i	−0.750290	+	0.661109i	$0.770086\pi$
$360$	8.14883	−	2.36571i	0.429481	−	0.124684i
$361$	9.49875	−	16.4523i	0.499934	−	0.865912i
$362$	23.1915	−	28.9871i	1.21892	−	1.52353i
$363$	−11.0166	−	15.1146i	−0.578223	−	0.793308i
$364$	−22.6727	+	3.93446i	−1.18837	+	0.206222i
$365$	−9.03438			−0.472881
$366$	−3.33753	−	0.150076i	−0.174456	−	0.00784460i
$367$	−15.9053	−	9.18291i	−0.830248	−	0.479344i	0.0236896	−	0.999719i	$-0.492459\pi$
$367$	−15.9053	−	9.18291i	−0.830248	−	0.479344i	−0.853938	+	0.520375i	$0.825792\pi$
$368$	23.8374	+	16.4739i	1.24261	+	0.858760i
$369$	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
$372$	0.792986	−	3.99147i	0.0411144	−	0.206948i
$373$	0.177482	−	0.102469i	0.00918966	−	0.00530565i	−0.495398	−	0.868666i	$-0.664978\pi$
$373$	0.177482	−	0.102469i	0.00918966	−	0.00530565i	0.504588	+	0.863360i	$0.331644\pi$
$374$	−1.92401	+	12.6294i	−0.0994879	+	0.653051i
$375$	1.72228	−	0.183676i	0.0889384	−	0.00948496i
$376$	−16.1144	+	1.13076i	−0.831035	+	0.0583147i
$377$			0.422988i			0.0217850i
$378$	17.8659	+	7.66883i	0.918921	+	0.394442i
$379$	10.8141			0.555483			0.277741	−	0.960656i	$-0.410414\pi$
$379$	10.8141			0.555483			0.277741	+	0.960656i	$0.410414\pi$
$380$	0.0953168	+	0.0297318i	0.00488965	+	0.00152521i
$381$	−0.402975	−	3.77860i	−0.0206450	−	0.193584i
$382$	−1.07899	+	7.08261i	−0.0552058	+	0.362378i
$383$	−0.773754	−	1.34018i	−0.0395370	−	0.0684800i	0.845580	−	0.533849i	$-0.179255\pi$
$383$	−0.773754	−	1.34018i	−0.0395370	−	0.0684800i	−0.885117	+	0.465369i	$0.845922\pi$
$384$	−1.86226	−	19.5072i	−0.0950332	−	0.995474i
$385$	−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
$388$	3.03104	+	13.4762i	0.153878	+	0.684148i
$389$	0.196263	−	0.339937i	0.00995092	−	0.0172355i	−0.861007	−	0.508593i	$-0.830166\pi$
$389$	0.196263	−	0.339937i	0.00995092	−	0.0172355i	0.870958	+	0.491357i	$0.163499\pi$
$390$	−10.6415	−	0.478509i	−0.538855	−	0.0242303i
$391$			14.0158i			0.708808i
$392$	10.3887	−	16.8545i	0.524709	−	0.851282i
$393$	−2.99633	+	2.18395i	−0.151145	+	0.110166i
$394$	−21.5169	−	17.2149i	−1.08401	−	0.867273i
$395$	8.28188	+	4.78155i	0.416707	+	0.240586i
$396$	−2.51421	+	27.9002i	−0.126344	+	1.40204i
$397$	−0.342311	+	0.197633i	−0.0171801	+	0.00991894i	−0.508565	−	0.861023i	$-0.669824\pi$
$397$	−0.342311	+	0.197633i	−0.0171801	+	0.00991894i	0.491385	+	0.870942i	$0.336491\pi$
$398$	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	$0.0667021\pi$
$402$	7.30412	−	3.79020i	0.364296	−	0.189038i
$403$	−2.55438	+	4.42431i	−0.127243	+	0.220391i
$404$	−33.6347	−	10.4915i	−1.67339	−	0.521972i
$405$	7.31329	+	5.24555i	0.363400	+	0.260653i
$406$	−0.272600	−	0.241120i	−0.0135289	−	0.0119666i
$407$	19.4334			0.963278
$408$	7.25023	−	6.10555i	0.358940	−	0.302270i
$409$	−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	$0.255242\pi$
$410$	15.1883	+	2.31383i	0.750095	+	0.114272i
$411$	−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
$414$	1.88307	+	30.6760i	0.0925480	+	1.50764i
$415$	9.93134	−	5.73386i	0.487510	−	0.281464i
$416$	−5.66354	+	23.9396i	−0.277678	+	1.17374i
$417$	14.0513	−	1.49852i	0.688097	−	0.0733831i
$418$	−0.205929	+	0.257391i	−0.0100723	+	0.0125894i
$419$		−	32.9565i		−	1.61003i	−0.593254	−	0.805016i	$-0.702157\pi$
$419$		−	32.9565i		−	1.61003i	0.593254	−	0.805016i	$-0.297843\pi$
$420$	6.37446	−	6.58530i	0.311042	−	0.321330i
$421$		−	30.0447i		−	1.46429i	−0.681150	−	0.732144i	$-0.738520\pi$
$421$		−	30.0447i		−	1.46429i	0.681150	−	0.732144i	$-0.261480\pi$
$422$	8.45549	+	6.76493i	0.411607	+	0.329312i
$423$	−11.5036	−	12.6979i	−0.559324	−	0.617395i
$424$	22.3898	+	33.1768i	1.08734	+	1.61121i
$425$	1.67559	−	0.967404i	0.0812782	−	0.0469260i
$426$	−13.3044	−	8.50023i	−0.644600	−	0.411837i
$427$	−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
$430$	1.74351	−	11.4446i	0.0840797	−	0.551910i
$431$	13.4451	−	23.2876i	0.647628	−	1.12173i	−0.336060	−	0.941841i	$-0.609094\pi$
$431$	13.4451	−	23.2876i	0.647628	−	1.12173i	0.983688	−	0.179884i	$-0.0575723\pi$
$432$	15.0481	−	14.3372i	0.724003	−	0.689797i
$433$	−27.8882			−1.34022			−0.670111	−	0.742261i	$-0.733753\pi$
$433$	−27.8882			−1.34022			−0.670111	+	0.742261i	$0.733753\pi$
$434$	−1.39521	−	4.16823i	−0.0669722	−	0.200081i
$435$	−0.0992317	−	0.136144i	−0.00475780	−	0.00652759i
$436$	5.68568	−	18.2277i	0.272295	−	0.872947i
$437$	−0.180822	+	0.313193i	−0.00864988	+	0.0149820i
$438$	−19.6425	+	10.1927i	−0.938555	+	0.487028i
$439$	16.0873	−	9.28803i	0.767807	−	0.443294i	−0.0642846	−	0.997932i	$-0.520477\pi$
$439$	16.0873	−	9.28803i	0.767807	−	0.443294i	0.832092	+	0.554638i	$0.187143\pi$
$440$	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	$0.193090\pi$
$444$	−10.8428	−	9.50442i	−0.514577	−	0.451060i
$445$	5.85921	+	3.38281i	0.277753	+	0.160361i
$446$	−6.17480	+	7.71789i	−0.292385	+	0.365453i
$447$	17.9292	+	24.5984i	0.848021	+	1.16347i
$448$	−12.1997	−	17.2964i	−0.576383	−	0.817179i
$449$			15.9588i			0.753143i	0.926388	+	0.376571i	$0.122897\pi$
$449$			15.9588i			0.753143i	−0.926388	+	0.376571i	$0.877103\pi$
$450$	3.53736	−	2.34246i	0.166753	−	0.110424i
$451$	−25.3605	+	43.9256i	−1.19418	+	2.06838i
$452$	−7.17380	+	1.61352i	−0.337427	+	0.0758937i
$453$	−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
$456$	0.240781	−	0.0428954i	0.0112756	−	0.00200876i
$457$	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	$0.818134\pi$
$458$	−12.4720	−	1.90003i	−0.582780	−	0.0887826i
$459$	9.84333	+	2.04524i	0.459447	+	0.0954635i
$460$	13.8308	+	4.31418i	0.644864	+	0.201150i
$461$	−11.6470			−0.542453			−0.271226	−	0.962516i	$-0.587429\pi$
$461$	−11.6470			−0.542453			−0.271226	+	0.962516i	$0.587429\pi$
$462$	12.5929	+	27.5128i	0.585874	+	1.28001i
$463$			18.7737i			0.872486i	0.899829	+	0.436243i	$0.143691\pi$
$463$			18.7737i			0.872486i	−0.899829	+	0.436243i	$0.856309\pi$
$464$	−0.351595	+	0.166588i	−0.0163224	+	0.00773366i
$465$	−0.215774	−	2.02326i	−0.0100063	−	0.0938266i
$466$	4.16874	+	0.635079i	0.193113	+	0.0294195i
$467$	−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	$0.630440\pi$
$468$	−23.6766	+	10.9656i	−1.09445	+	0.506885i
$469$	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
$472$	31.9606	−	21.5690i	1.47111	−	0.992795i
$473$	33.0988	+	19.1096i	1.52188	+	0.878660i
$474$	23.4011	+	1.05226i	1.07485	+	0.0483317i
$475$	0.0499231			0.00229063
$476$	3.52769	−	9.61108i	0.161691	−	0.440523i
$477$	−12.9955	+	40.4149i	−0.595021	+	1.85047i
$478$	7.38670	+	5.90983i	0.337860	+	0.270309i
$479$	0.526981	−	0.912758i	0.0240784	−	0.0417050i	−0.853735	−	0.520708i	$-0.825668\pi$
$479$	0.526981	−	0.912758i	0.0240784	−	0.0417050i	0.877814	+	0.479003i	$0.159002\pi$
$480$	−3.79328	−	9.03388i	−0.173139	−	0.412338i
$481$	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
$486$	21.8186	+	3.15387i	0.989714	+	0.143063i
$487$	−11.5870	−	6.68977i	−0.525058	−	0.303142i	0.213944	−	0.976846i	$-0.431369\pi$
$487$	−11.5870	−	6.68977i	−0.525058	−	0.303142i	−0.739002	+	0.673704i	$0.764702\pi$
$488$	0.270039	+	3.84828i	0.0122241	+	0.174204i
$489$	−25.2687	−	34.6680i	−1.14269	−	1.56774i
$490$	2.44929	−	9.59171i	0.110648	−	0.433309i
$491$		−	22.2153i		−	1.00256i	−0.865285	−	0.501281i	$-0.832862\pi$
$491$		−	22.2153i		−	1.00256i	0.865285	−	0.501281i	$-0.167138\pi$
$492$	35.6328	−	12.1049i	1.60645	−	0.545733i
$493$	−0.162978	−	0.0940955i	−0.00734017	−	0.00423785i
$494$	−0.303530	−	0.0462408i	−0.0136565	−	0.00208047i
$495$	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
$498$	15.1236	−	23.6712i	0.677706	−	1.06073i
$499$	−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	$-0.360441\pi$
$500$	−0.438874	−	1.95125i	−0.0196270	−	0.0872627i
$501$	−2.91536	+	0.310913i	−0.130249	+	0.0138906i
$502$	−3.64012	+	4.54979i	−0.162466	+	0.203067i
$503$	−10.7214			−0.478044			−0.239022	−	0.971014i	$-0.576827\pi$
$503$	−10.7214			−0.478044			−0.239022	+	0.971014i	$0.576827\pi$
$504$	6.42968	−	21.5095i	0.286401	−	0.958110i
$505$	−17.6165			−0.783923
$506$	−29.8810	+	37.3483i	−1.32837	+	1.66033i
$507$	10.1820	−	1.08587i	0.452196	−	0.0482251i
$508$	−4.28095	+	0.962866i	−0.189936	+	0.0427203i
$509$	1.09583	+	1.89804i	0.0485719	+	0.0841290i	0.889289	−	0.457345i	$-0.151200\pi$
$509$	1.09583	+	1.89804i	0.0485719	+	0.0841290i	−0.840717	+	0.541474i	$0.817866\pi$
$510$	2.55163	−	3.99376i	0.112988	−	0.176847i
$511$	−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
$514$	8.50166	+	1.29517i	0.374992	+	0.0571275i
$515$	−1.23715	−	0.714272i	−0.0545155	−	0.0314746i
$516$	−9.12131	−	26.8500i	−0.401543	−	1.18200i
$517$		−	26.6653i		−	1.17274i
$518$	−15.2617	−	3.10318i	−0.670562	−	0.136346i
$519$	−3.34790	−	4.59324i	−0.146956	−	0.201621i
$520$	0.861003	+	12.2700i	0.0377575	+	0.538077i
$521$	−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	$0.717195\pi$
$522$	−0.369349	−	0.184048i	−0.0161660	−	0.00805556i
$523$	−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
$528$	32.3367	−	0.812484i	1.40727	−	0.0353588i
$529$	−14.7378	+	25.5267i	−0.640776	+	1.10986i
$530$	15.6266	+	12.5023i	0.678778	+	0.543065i
$531$	38.9335	+	12.5191i	1.68957	+	0.543282i
$532$	0.202824	−	0.169255i	0.00879355	−	0.00733813i
$533$	−47.2436			−2.04635
$534$	16.5556	+	0.744443i	0.716431	+	0.0322152i
$535$	−6.21564	−	3.58860i	−0.268726	−	0.155149i
$536$	−5.31536	−	7.87621i	−0.229588	−	0.340200i
$537$	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
$540$	5.04810	−	9.08387i	0.217236	−	0.390907i
$541$	−17.4623	+	10.0819i	−0.750764	+	0.433454i	−0.825970	−	0.563714i	$-0.809372\pi$
$541$	−17.4623	+	10.0819i	−0.750764	+	0.433454i	0.0752056	+	0.997168i	$0.476039\pi$
$542$	10.0307	+	1.52810i	0.430854	+	0.0656377i
$543$	−4.82144	−	45.2096i	−0.206908	−	1.94013i
$544$	−7.96410	−	7.50764i	−0.341458	−	0.321887i
$545$		−	9.54692i		−	0.408945i
$546$	−16.3284	+	22.9713i	−0.698793	+	0.983081i
$547$	23.5095			1.00519			0.502597	−	0.864521i	$-0.332378\pi$
$547$	23.5095			1.00519			0.502597	+	0.864521i	$0.332378\pi$
$548$	−6.53548	+	20.9520i	−0.279182	+	0.895027i
$549$	−3.03240	+	2.74718i	−0.129420	+	0.117247i
$550$	6.52747	+	0.994416i	0.278332	+	0.0424021i
$551$	−0.00242791	−	0.00420526i	−0.000103432	−	0.000179150i
$552$	34.9382	−	6.22426i	1.48707	−	0.264922i
$553$	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
$556$	−3.58057	−	15.9194i	−0.151850	−	0.675132i
$557$	1.11240	−	1.92673i	0.0471338	−	0.0816381i	−0.841496	−	0.540263i	$-0.818325\pi$
$557$	1.11240	−	1.92673i	0.0471338	−	0.0816381i	0.888630	+	0.458625i	$0.151658\pi$
$558$	−2.75182	−	4.15553i	−0.116494	−	0.175918i
$559$			35.5989i			1.50567i
$560$	−8.39838	−	6.43950i	−0.354896	−	0.272119i
$561$	9.21594	+	12.6441i	0.389097	+	0.533833i
$562$	7.30189	−	9.12664i	0.308012	−	0.384984i
$563$	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	$0.450560\pi$
$564$	−13.0414	+	14.8778i	−0.549141	+	0.626469i
$565$	−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	$0.537920\pi$
$570$	0.108543	−	0.0563241i	0.00454635	−	0.00235916i
$571$	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	$0.147253\pi$
$572$	−38.7657	−	12.0920i	−1.62087	−	0.505592i
$573$	5.16833	+	7.09083i	0.215910	+	0.296223i
$574$	26.9306	−	30.4467i	1.12406	−	1.27082i
$575$	7.24401			0.302096
$576$	−18.4395	−	15.3618i	−0.768313	−	0.640074i
$577$	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	$-0.112009\pi$
$578$	−2.82348	+	18.5337i	−0.117441	+	0.770901i
$579$	−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
$582$	14.2559	+	9.10817i	0.590928	+	0.377546i
$583$	−57.2175	+	33.0345i	−2.36971	+	1.36815i
$584$	14.2942	+	21.1810i	0.591500	+	0.876475i
$585$	−9.66865	+	8.75924i	−0.399749	+	0.362150i
$586$	1.94909	+	1.55939i	0.0805161	+	0.0644180i
$587$			5.63165i			0.232443i	0.993223	+	0.116221i	$0.0370782\pi$
$587$			5.63165i			0.232443i	−0.993223	+	0.116221i	$0.962922\pi$
$588$	−5.49630	−	23.6176i	−0.226664	−	0.973973i
$589$		−	0.0586475i		−	0.00241653i
$590$	12.0440	−	15.0538i	0.495845	−	0.619757i
$591$	−33.5587	+	3.57891i	−1.38042	+	0.147217i
$592$	−9.46572	+	13.6967i	−0.389039	+	0.562932i
$593$	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	$0.210976\pi$
$594$	21.8695	+	26.4356i	0.897316	+	1.08466i
$595$	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
$598$	−44.0433	−	6.70969i	−1.80106	−	0.274380i
$599$	−10.2239	+	17.7083i	−0.417736	+	0.723540i	−0.995711	−	0.0925144i	$-0.970510\pi$
$599$	−10.2239	+	17.7083i	−0.417736	+	0.723540i	0.577975	+	0.816054i	$0.303843\pi$
$600$	−3.15563	−	3.74726i	−0.128828	−	0.152981i
$601$	−24.8401			−1.01325			−0.506624	−	0.862167i	$-0.669107\pi$
$601$	−24.8401			−1.01325			−0.506624	+	0.862167i	$0.669107\pi$
$602$	−22.9422	−	20.2927i	−0.935053	−	0.827071i
$603$	3.08514	−	9.59456i	0.125636	−	0.390721i
$604$	−9.18715	+	29.4530i	−0.373820	+	1.19843i
$605$	−5.39919	+	9.35168i	−0.219508	+	0.380200i
$606$	−38.3017	+	19.8752i	−1.55590	+	0.807376i
$607$	2.92576	−	1.68919i	0.118753	−	0.0685620i	−0.439447	−	0.898269i	$-0.644826\pi$
$607$	2.92576	−	1.68919i	0.118753	−	0.0685620i	0.558200	+	0.829706i	$0.311492\pi$
$608$	−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
$612$	1.04190	−	11.5620i	0.0421165	−	0.467366i
$613$	21.7109	+	12.5348i	0.876893	+	0.506275i	0.869633	−	0.493699i	$-0.164356\pi$
$613$	21.7109	+	12.5348i	0.876893	+	0.506275i	0.00726042	+	0.999974i	$0.497689\pi$
$614$	22.7870	+	18.2311i	0.919610	+	0.735746i
$615$	15.2059	−	11.0832i	0.613160	−	0.446917i
$616$	29.8908	−	18.0901i	1.20433	−	0.728871i
$617$		−	18.0681i		−	0.727395i	−0.931517	−	0.363697i	$-0.881514\pi$
$617$		−	18.0681i		−	0.727395i	0.931517	−	0.363697i	$-0.118486\pi$
$618$	−3.49567	−	0.157187i	−0.140616	−	0.00632298i
$619$	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	$-0.0972588\pi$
$620$	−2.29225	+	0.515569i	−0.0920588	+	0.0207058i
$621$	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
$624$	15.7153	+	25.7061i	0.629114	+	1.02907i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	1.44591	−	9.49116i	0.0577904	−	0.379343i
$627$	0.0428120	+	0.401438i	0.00170975	+	0.0160319i
$628$	9.39767	−	30.1279i	0.375008	−	1.20223i
$629$	−8.05332			−0.321107
$630$	−0.133500	−	11.2242i	−0.00531877	−	0.447182i
$631$		−	25.3603i		−	1.00958i	−0.863243	−	0.504789i	$-0.831570\pi$
$631$		−	25.3603i		−	1.00958i	0.863243	−	0.504789i	$-0.168430\pi$
$632$	−1.89337	−	26.9822i	−0.0753143	−	1.07329i
$633$	13.1875	−	1.40641i	0.524158	−	0.0558996i
$634$	3.44278	−	22.5989i	0.136730	−	0.897515i
$635$	−1.90001	+	1.09697i	−0.0753998	+	0.0435321i
$636$	48.0807	+	9.55221i	1.90652	+	0.378770i
$637$	−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
$640$	−9.85997	+	5.54807i	−0.389749	+	0.219307i
$641$	−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	$0.666727\pi$
$642$	−17.5627	−	0.789729i	−0.693146	−	0.0311681i
$643$	−0.999165			−0.0394032			−0.0197016	−	0.999806i	$-0.506272\pi$
$643$	−0.999165			−0.0394032			−0.0197016	+	0.999806i	$0.506272\pi$
$644$	29.4305	−	24.5594i	1.15972	−	0.967777i
$645$	−8.35139	−	11.4579i	−0.328836	−	0.451155i
$646$	0.0853382	−	0.106664i	0.00335759	−	0.00419665i
$647$	17.4723	−	30.2629i	0.686907	−	1.18976i	−0.285927	−	0.958252i	$-0.592301\pi$
$647$	17.4723	−	30.2629i	0.686907	−	1.18976i	0.972833	−	0.231506i	$-0.0743653\pi$
$648$	0.726993	−	25.4455i	0.0285590	−	0.999592i
$649$	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	$-0.935599\pi$
$653$	−16.9633	−	29.3812i	−0.663823	−	1.14978i	0.315780	−	0.948833i	$-0.397734\pi$
$654$	−10.7710	−	20.7569i	−0.421180	−	0.811658i
$655$	1.85389	+	1.07034i	0.0724375	+	0.0418218i
$656$	−18.6062	−	39.2697i	−0.726451	−	1.53322i
$657$	−8.29666	+	25.8020i	−0.323684	+	1.00663i
$658$	−4.25800	+	20.9412i	−0.165994	+	0.816373i
$659$			17.0907i			0.665758i	0.942969	+	0.332879i	$0.108020\pi$
$659$			17.0907i			0.665758i	−0.942969	+	0.332879i	$0.891980\pi$
$660$	15.3139	−	5.20235i	0.596094	−	0.202501i
$661$	2.24461	+	1.29593i	0.0873051	+	0.0504056i	0.543017	−	0.839722i	$-0.317282\pi$
$661$	2.24461	+	1.29593i	0.0873051	+	0.0504056i	−0.455712	+	0.890127i	$0.650615\pi$
$662$	−6.06631	+	39.8200i	−0.235774	+	1.54765i
$663$	−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
$666$	−17.6261	+	1.08199i	−0.682998	+	0.0419264i
$667$	−0.352298	−	0.610198i	−0.0136410	−	0.0236270i
$668$	0.742894	+	3.30294i	0.0287434	+	0.127795i
$669$	1.28372	+	12.0372i	0.0496315	+	0.465383i
$670$	−3.70979	−	2.96806i	−0.143322	−	0.114666i
$671$	−6.36797			−0.245833
$672$	−25.5249	−	4.52555i	−0.984644	−	0.174577i
$673$	36.8310			1.41973			0.709866	−	0.704337i	$-0.248756\pi$
$673$	36.8310			1.41973			0.709866	+	0.704337i	$0.248756\pi$
$674$	18.9775	+	15.1832i	0.730985	+	0.584834i
$675$	1.05707	−	5.08749i	0.0406868	−	0.195818i
$676$	−2.59457	−	11.5356i	−0.0997912	−	0.443677i
$677$	−11.4771	−	19.8789i	−0.441100	−	0.764008i	0.556671	−	0.830733i	$-0.312078\pi$
$677$	−11.4771	−	19.8789i	−0.441100	−	0.764008i	−0.997771	+	0.0667247i	$0.978745\pi$
$678$	−4.84858	+	7.58891i	−0.186209	+	0.291450i
$679$	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
$682$	1.16820	−	7.66819i	0.0447326	−	0.293630i
$683$	−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	$0.818704\pi$
$684$	0.172447	−	0.244919i	0.00659368	−	0.00936472i
$685$			10.9738i			0.419289i
$686$	−17.8104	−	19.2039i	−0.680005	−	0.733207i
$687$	−12.4865	+	9.10110i	−0.476390	+	0.347229i
$688$	−29.5904	+	14.0201i	−1.12812	+	0.534513i
$689$	−53.2947	−	30.7697i	−2.03037	−	1.17223i
$690$	15.7499	−	8.17282i	0.599588	−	0.311134i
$691$	−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
$696$	−0.162182	+	0.448055i	−0.00614749	+	0.0169835i
$697$	10.5095	−	18.2030i	0.398077	−	0.689489i
$698$	−24.4162	+	30.5179i	−0.924168	+	1.15512i
$699$	4.17357	−	3.04201i	0.157859	−	0.115060i
$700$	−4.96746	−	1.82328i	−0.187752	−	0.0689133i
$701$	−8.13507			−0.307257			−0.153629	−	0.988129i	$-0.549096\pi$
$701$	−8.13507			−0.307257			−0.153629	+	0.988129i	$0.549096\pi$
$702$	−11.1392	+	29.9526i	−0.420422	+	1.13049i
$703$	−0.179957	−	0.103898i	−0.00678721	−	0.00391860i
$704$	−5.21624	−	36.9850i	−0.196595	−	1.39392i
$705$	−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
$708$	9.20206	−	46.3183i	0.345835	−	1.74075i
$709$	−9.50630	+	5.48847i	−0.357017	+	0.206124i	−0.667771	−	0.744367i	$-0.732752\pi$
$709$	−9.50630	+	5.48847i	−0.357017	+	0.206124i	0.310755	+	0.950490i	$0.399418\pi$
$710$	−1.37280	+	9.01124i	−0.0515203	+	0.338186i
$711$	21.2616	−	19.2618i	0.797374	−	0.722375i
$712$	−1.33951	−	19.0891i	−0.0502002	−	0.715396i
$713$		−	8.50994i		−	0.318700i
$714$	−5.21856	−	11.4014i	−0.195300	−	0.426688i
$715$	−20.3039			−0.759323
$716$	0.641363	−	2.05614i	0.0239689	−	0.0768415i
$717$	11.5206	−	1.22863i	0.430245	−	0.0458841i
$718$	1.59318	−	10.4578i	0.0594568	−	0.390282i
$719$	3.69133	+	6.39358i	0.137664	+	0.238440i	0.926612	−	0.376019i	$-0.122707\pi$
$719$	3.69133	+	6.39358i	0.137664	+	0.238440i	−0.788948	+	0.614460i	$0.789374\pi$
$720$	−11.0887	−	4.58704i	−0.413251	−	0.170949i
$721$	−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
$724$	−51.2200	+	11.5203i	−1.90358	+	0.428150i
$725$	−0.0486330	+	0.0842348i	−0.00180618	+	0.00312840i
$726$	−1.18818	+	26.4238i	−0.0440975	+	0.980681i
$727$			16.3757i			0.607343i	0.952777	+	0.303671i	$0.0982125\pi$
$727$			16.3757i			0.607343i	−0.952777	+	0.303671i	$0.901788\pi$
$728$	28.5131	+	15.6865i	1.05677	+	0.581380i
$729$	21.6973	−	16.0694i	0.803604	−	0.595164i
$730$	9.97649	+	7.98183i	0.369247	+	0.295421i
$731$	−13.7163	−	7.91913i	−0.507317	−	0.292900i
$732$	3.55298	+	3.11442i	0.131322	+	0.115112i
$733$	35.2796	−	20.3687i	1.30308	−	0.752334i	0.322149	−	0.946689i	$-0.395595\pi$
$733$	35.2796	−	20.3687i	1.30308	−	0.752334i	0.980931	+	0.194355i	$0.0622614\pi$
$734$	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
$738$	20.5563	−	41.2526i	0.756688	−	1.51853i
$739$	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	$0.0898948\pi$
$740$	−2.47888	+	7.94703i	−0.0911255	+	0.292138i
$741$	−0.303882	+	0.221492i	−0.0111634	+	0.00813672i
$742$	50.2099	−	16.8065i	1.84327	−	0.616987i
$743$	17.3420			0.636216			0.318108	−	0.948054i	$-0.396952\pi$
$743$	17.3420			0.636216			0.318108	+	0.948054i	$0.396952\pi$
$744$	−4.40212	+	3.70710i	−0.161389	+	0.135909i
$745$	8.78701	−	15.2195i	0.321931	−	0.557601i
$746$	−0.286521	−	0.0436495i	−0.0104903	−	0.00159812i
$747$	−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
$750$	−2.06416	−	1.31880i	−0.0753726	−	0.0481558i
$751$	−34.7814	+	20.0811i	−1.26919	+	0.732768i	−0.974835	−	0.222927i	$-0.928439\pi$
$751$	−34.7814	+	20.0811i	−1.26919	+	0.732768i	−0.294357	+	0.955696i	$0.595106\pi$
$752$	18.7938	+	12.9883i	0.685340	+	0.473634i
$753$	0.756768	+	7.09604i	0.0275782	+	0.258594i
$754$	0.373708	−	0.467098i	0.0136096	−	0.0170107i
$755$			15.4263i			0.561421i
$756$	−12.9536	−	24.2529i	−0.471117	−	0.882071i
$757$		−	15.4831i		−	0.562742i	−0.959599	−	0.281371i	$-0.909211\pi$
$757$		−	15.4831i		−	0.562742i	0.959599	−	0.281371i	$-0.0907892\pi$
$758$	−11.9418	−	9.55420i	−0.433746	−	0.347024i
$759$	6.21216	+	58.2500i	0.225487	+	2.11434i
$760$	−0.0789887	−	0.117044i	−0.00286522	−	0.00424564i
$761$	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	$0.289057\pi$
$762$	−2.89338	+	4.52866i	−0.104816	+	0.164056i
$763$	−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
$766$	−0.329601	+	2.16354i	−0.0119090	+	0.0781720i
$767$	−29.6418	+	51.3412i	−1.07030	+	1.85382i
$768$	−15.1781	+	23.1868i	−0.547692	+	0.836680i
$769$	28.5801			1.03063			0.515313	−	0.857002i	$-0.327676\pi$
$769$	28.5801			1.03063			0.515313	+	0.857002i	$0.327676\pi$
$770$	11.5740	−	13.0851i	0.417098	−	0.471554i
$771$	8.51152	−	6.20384i	0.306535	−	0.223426i
$772$	41.1681	+	12.8414i	1.48167	+	0.462172i
$773$	−2.80047	+	4.85056i	−0.100726	+	0.174463i	−0.911984	−	0.410226i	$-0.865450\pi$
$773$	−2.80047	+	4.85056i	−0.100726	+	0.174463i	0.811258	+	0.584688i	$0.198783\pi$
$774$	−31.0846	−	15.4896i	−1.11731	−	0.556761i
$775$	−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
$780$	11.3285	+	9.93015i	0.405625	+	0.355557i
$781$	−26.0612	−	15.0464i	−0.932543	−	0.538404i
$782$	12.3829	−	15.4774i	0.442810	−	0.553469i
$783$	−0.479953	+	0.158378i	−0.0171521	+	0.00565995i
$784$	−26.3629	+	9.43375i	−0.941533	+	0.336920i
$785$		−	15.7798i		−	0.563205i
$786$	5.23830	+	0.235546i	0.186844	+	0.00840166i
$787$	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	$0.0918467\pi$
$788$	8.55144	+	38.0201i	0.304633	+	1.35441i
$789$	−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
$792$	27.4261	−	28.5884i	0.974543	−	1.01584i
$793$	−2.96569	−	5.13673i	−0.105315	−	0.182411i
$794$	0.552616	+	0.0841873i	0.0196116	+	0.00298769i
$795$	24.3720	−	2.59919i	0.864385	−	0.0921836i
$796$	1.61538	−	5.17874i	0.0572557	−	0.183555i
$797$	−48.8011			−1.72863			−0.864313	−	0.502955i	$-0.832246\pi$
$797$	−48.8011			−1.72863			−0.864313	+	0.502955i	$0.832246\pi$
$798$	0.0304811	−	0.322100i	0.00107902	−	0.0114022i
$799$			11.0503i			0.390930i
$800$	−3.88030	+	4.11622i	−0.137189	+	0.145530i
$801$	15.0420	−	13.6272i	0.531484	−	0.481494i
$802$	−41.6069	−	6.33852i	−1.46919	−	0.223821i
$803$	−36.5293	+	21.0902i	−1.28909	+	0.744256i
$804$	−11.4144	−	2.26771i	−0.402556	−	0.0799759i
$805$	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
$808$	27.8729	+	41.3016i	0.980566	+	1.45299i
$809$	−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	$0.773164\pi$
$810$	−3.44151	−	12.2538i	−0.120922	−	0.430555i
$811$	−44.7323			−1.57076			−0.785381	−	0.619013i	$-0.787533\pi$
$811$	−44.7323			−1.57076			−0.785381	+	0.619013i	$0.787533\pi$
$812$	0.0879992	+	0.507104i	0.00308817	+	0.0177959i
$813$	10.0423	−	7.31958i	0.352199	−	0.256709i
$814$	−21.4599	−	17.1693i	−0.752171	−	0.601784i
$815$	−12.3840	+	21.4498i	−0.433794	+	0.751354i
$816$	−13.4005	+	0.336698i	−0.469112	+	0.0117868i
$817$	−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	0.764188	−	0.644994i	$-0.223140\pi$
$821$	−5.05691	−	8.75882i	−0.176487	−	0.305685i	−0.940675	+	0.339309i	$0.889807\pi$
$822$	12.3809	+	23.8593i	0.431833	+	0.832188i
$823$	−15.8881	−	9.17301i	−0.553825	−	0.319751i	0.196838	−	0.980436i	$-0.436933\pi$
$823$	−15.8881	−	9.17301i	−0.553825	−	0.319751i	−0.750663	+	0.660685i	$0.770266\pi$
$824$	0.282833	+	4.03062i	0.00985297	+	0.140413i
$825$	6.53504	−	4.76323i	0.227521	−	0.165834i
$826$	−16.1905	−	48.3695i	−0.563338	−	1.68299i
$827$		−	36.0470i		−	1.25348i	−0.779229	−	0.626739i	$-0.784389\pi$
$827$		−	36.0470i		−	1.25348i	0.779229	−	0.626739i	$-0.215611\pi$
$828$	25.0226	−	35.5386i	0.869597	−	1.23505i
$829$	5.64247	+	3.25768i	0.195971	+	0.113144i	0.594775	−	0.803892i	$-0.297241\pi$
$829$	5.64247	+	3.25768i	0.195971	+	0.113144i	−0.398804	+	0.917036i	$0.630575\pi$
$830$	−16.0328	−	2.44249i	−0.556507	−	0.0847801i
$831$	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
$834$	−16.8406	−	10.7595i	−0.583141	−	0.372571i
$835$	0.846364	+	1.46595i	0.0292896	+	0.0507311i
$836$	0.454807	−	0.102295i	0.0157298	−	0.00353794i
$837$	−5.97656	−	1.24180i	−0.206580	−	0.0429231i
$838$	−29.1169	+	36.3933i	−1.00583	+	1.25718i
$839$	−40.0265			−1.38187			−0.690934	−	0.722918i	$-0.742800\pi$
$839$	−40.0265			−1.38187			−0.690934	+	0.722918i	$0.742800\pi$
$840$	−12.8573	+	1.64022i	−0.443618	+	0.0565929i
$841$	−28.9905			−0.999674
$842$	−26.5443	+	33.1778i	−0.914778	+	1.14338i
$843$	−1.51804	−	14.2343i	−0.0522840	−	0.490255i
$844$	−3.36046	−	14.9408i	−0.115672	−	0.514282i
$845$	−2.95594	−	5.11984i	−0.101688	−	0.176128i
$846$	1.48465	+	24.1855i	0.0510432	+	0.831513i
$847$	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
$850$	−2.70502	−	0.412092i	−0.0927815	−	0.0141346i
$851$	−26.1124	−	15.0760i	−0.895121	−	0.516798i
$852$	7.18190	+	21.1410i	0.246048	+	0.724279i
$853$		−	1.81968i		−	0.0623048i	−0.999515	−	0.0311524i	$-0.990082\pi$
$853$		−	1.81968i		−	0.0623048i	0.999515	−	0.0311524i	$-0.00991772\pi$
$854$	5.00098	+	1.01686i	0.171130	+	0.0347961i
$855$	0.0458466	−	0.142580i	0.00156792	−	0.00487612i
$856$	1.42100	+	20.2504i	0.0485686	+	0.692145i
$857$	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	$0.510650\pi$
$858$	−44.1447	+	22.9072i	−1.50707	+	0.782040i
$859$	−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	$0.0548292\pi$
$863$	18.8317	+	32.6174i	0.641038	+	1.11031i	−0.344164	+	0.938910i	$0.611838\pi$
$864$	−29.2842	+	2.53733i	−0.996267	+	0.0863219i
$865$	−1.64079	+	2.84193i	−0.0557885	+	0.0966286i
$866$	30.7964	+	24.6391i	1.04651	+	0.837270i
$867$	13.5244	+	18.5552i	0.459314	+	0.630168i
$868$	−2.14190	+	5.83555i	−0.0727010	+	0.198072i
$869$	44.6489			1.51461
$870$	−0.0107025	+	0.238012i	−0.000362848	+	0.00806935i
$871$	12.6522	+	7.30477i	0.428705	+	0.247513i
$872$	−22.3826	+	15.1052i	−0.757972	+	0.511527i
$873$	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
$876$	30.6961	+	6.09840i	1.03712	+	0.206046i
$877$	13.7440	−	7.93509i	0.464101	−	0.267949i	−0.249666	−	0.968332i	$-0.580321\pi$
$877$	13.7440	−	7.93509i	0.464101	−	0.267949i	0.713767	+	0.700383i	$0.246987\pi$
$878$	−25.9709	−	3.95649i	−0.876475	−	0.133525i
$879$	3.03988	−	0.324193i	0.102533	−	0.0109348i
$880$	−7.99642	−	16.8770i	−0.269559	−	0.568922i
$881$			9.64780i			0.325043i	0.986705	+	0.162521i	$0.0519626\pi$
$881$			9.64780i			0.325043i	−0.986705	+	0.162521i	$0.948037\pi$
$882$	−25.1445	−	15.8036i	−0.846659	−	0.532136i
$883$	12.6173			0.424607			0.212303	−	0.977204i	$-0.431903\pi$
$883$	12.6173			0.424607			0.212303	+	0.977204i	$0.431903\pi$
$884$	16.0647	+	5.01100i	0.540315	+	0.168538i
$885$	−2.50391	−	23.4786i	−0.0841680	−	0.789225i
$886$	−25.0989	−	3.82364i	−0.843213	−	0.128458i
$887$	−18.4017	−	31.8726i	−0.617867	−	1.07018i	−0.989874	−	0.141947i	$-0.954664\pi$
$887$	−18.4017	−	31.8726i	−0.617867	−	1.07018i	0.372007	−	0.928230i	$-0.378670\pi$
$888$	3.57640	+	20.0751i	0.120016	+	0.673676i
$889$	−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
$892$	13.6374	−	3.06732i	0.456615	−	0.102701i
$893$	−0.142563	+	0.246926i	−0.00477068	+	0.00826307i
$894$	1.93372	−	43.0039i	0.0646734	−	1.43827i
$895$		−	1.07692i		−	0.0359976i
$896$	−1.80937	+	29.8785i	−0.0604468	+	0.998171i
$897$	−44.0943	+	32.1393i	−1.47227	+	1.07310i
$898$	14.0995	−	17.6230i	0.470507	−	0.588088i
$899$	0.0989553	+	0.0571319i	0.00330035	+	0.00190546i
$900$	−5.97579	−	0.538505i	−0.199193	−	0.0179502i
$901$	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
$906$	17.4042	+	33.5398i	0.578217	+	1.11429i
$907$	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	$0.00388959\pi$
$908$	−9.15624	+	29.3539i	−0.303861	+	0.974144i
$909$	−16.1780	+	50.3124i	−0.536590	+	1.66876i
$910$	15.9454	+	3.24219i	0.528584	+	0.107477i
$911$	42.2061			1.39835			0.699175	−	0.714950i	$-0.253551\pi$
$911$	42.2061			1.39835			0.699175	+	0.714950i	$0.253551\pi$
$912$	−0.303788	−	0.165360i	−0.0100594	−	0.00547563i
$913$	26.7707	−	46.3682i	0.885980	−	1.53456i
$914$	0.434654	−	2.85312i	0.0143771	−	0.0943729i
$915$	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
$918$	−9.06284	−	10.9550i	−0.299118	−	0.361570i
$919$	−15.3124	+	8.84063i	−0.505110	+	0.291626i	−0.730821	−	0.682569i	$-0.760863\pi$
$919$	−15.3124	+	8.84063i	−0.505110	+	0.291626i	0.225711	+	0.974194i	$0.427529\pi$
$920$	−11.4615	−	16.9835i	−0.377875	−	0.559929i
$921$	35.5396	−	3.79018i	1.17107	−	0.124891i
$922$	12.8615	+	10.2900i	0.423571	+	0.338884i
$923$		−	28.0297i		−	0.922610i
$924$	10.4013	−	41.5076i	0.342178	−	1.36550i
$925$			4.16233i			0.136857i
$926$	16.5864	−	20.7314i	0.545064	−	0.681276i
$927$	−3.17608	+	2.87735i	−0.104316	+	0.0945045i
$928$	0.535440	+	0.126672i	0.0175767	+	0.00415822i
$929$	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	$0.290085\pi$
$930$	−1.54927	+	2.42489i	−0.0508025	+	0.0795152i
$931$	−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
$934$	48.5605	+	7.39786i	1.58895	+	0.242065i
$935$	4.51669	−	7.82313i	0.147712	−	0.255844i
$936$	35.8337	+	8.80910i	1.17126	+	0.287934i
$937$	35.5033			1.15984			0.579922	−	0.814672i	$-0.303083\pi$
$937$	35.5033			1.15984			0.579922	+	0.814672i	$0.303083\pi$
$938$	−11.9199	+	3.98989i	−0.389199	+	0.130275i
$939$	−6.92590	−	9.50217i	−0.226018	−	0.310092i
$940$	10.9044	+	3.40137i	0.355663	+	0.110940i
$941$	24.0272	−	41.6163i	0.783263	−	1.35665i	−0.146768	−	0.989171i	$-0.546887\pi$
$941$	24.0272	−	41.6163i	0.783263	−	1.35665i	0.930031	−	0.367481i	$-0.119780\pi$
$942$	−17.8030	−	34.3084i	−0.580054	−	1.11783i
$943$	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	$0.598267\pi$
$948$	−24.9117	−	21.8367i	−0.809094	−	0.709223i
$949$	−34.0249	−	19.6443i	−1.10449	−	0.637680i
$950$	−0.0551292	−	0.0441068i	−0.00178863	−	0.00143101i
$951$	−16.4909	−	22.6251i	−0.534753	−	0.733668i
$952$	−12.3869	+	7.49664i	−0.401462	+	0.242968i
$953$			43.5506i			1.41074i	0.708838	+	0.705371i	$0.249220\pi$
$953$			43.5506i			1.41074i	−0.708838	+	0.705371i	$0.750780\pi$
$954$	50.0570	−	33.1480i	1.62066	−	1.07321i
$955$	2.53297	−	4.38724i	0.0819651	−	0.141968i
$956$	−2.93569	−	13.0522i	−0.0949470	−	0.422139i
$957$	−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
$960$	−3.79254	+	13.3273i	−0.122404	+	0.430136i
$961$	−14.8100	−	25.6516i	−0.477741	−	0.827472i
$962$	3.85532	−	25.3068i	0.124300	−	0.815924i
$963$	−15.9571	+	14.4562i	−0.514210	+	0.465845i
$964$	46.4028	+	14.4742i	1.49453	+	0.466183i
$965$	21.5622			0.694112
$966$	4.42291	−	46.7377i	0.142305	−	1.50376i
$967$			6.03768i			0.194159i	0.995277	+	0.0970793i	$0.0309500\pi$
$967$			6.03768i			0.194159i	−0.995277	+	0.0970793i	$0.969050\pi$
$968$	30.4675	−	2.13794i	0.979264	−	0.0687161i
$969$	−0.0177415	−	0.166358i	−0.000569940	−	0.00534420i
$970$	1.47098	−	9.65573i	0.0472305	−	0.310027i
$971$	−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	$0.395443\pi$
$972$	−21.3075	−	22.7594i	−0.683438	−	0.730009i
$973$	−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
$976$	3.10174	−	4.48816i	0.0992842	−	0.143663i
$977$	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	$0.578286\pi$
$978$	−2.72531	+	60.6080i	−0.0871458	+	1.93803i
$979$	31.5879			1.00955
$980$	−11.1789	+	8.42802i	−0.357098	+	0.269223i
$981$	−27.2659	−	8.76736i	−0.870532	−	0.279920i
$982$	−19.6271	+	24.5319i	−0.626325	+	0.782845i
$983$	−23.4193	+	40.5633i	−0.746958	+	1.29377i	0.202316	+	0.979320i	$0.435153\pi$
$983$	−23.4193	+	40.5633i	−0.746958	+	1.29377i	−0.949274	+	0.314449i	$0.898180\pi$
$984$	−50.0433	−	18.1141i	−1.59532	−	0.577457i
$985$	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
$990$	8.83450	−	17.7291i	0.280779	−	0.563469i
$991$	53.5716	+	30.9296i	1.70176	+	0.982510i	0.943983	+	0.329994i	$0.107047\pi$
$991$	53.5716	+	30.9296i	1.70176	+	0.982510i	0.757775	+	0.652516i	$0.226287\pi$
$992$	4.83555	+	4.55841i	0.153529	+	0.144730i
$993$	29.0575	+	39.8662i	0.922111	+	1.26511i
$994$	18.0641	+	15.9780i	0.572959	+	0.506792i
$995$		−	2.71242i		−	0.0859893i
$996$	−37.6142	+	12.7781i	−1.19185	+	0.404888i
$997$	8.10927	+	4.68189i	0.256823	+	0.148277i	0.622884	−	0.782314i	$-0.285961\pi$
$997$	8.10927	+	4.68189i	0.256823	+	0.148277i	−0.366061	+	0.930591i	$0.619294\pi$
$998$	−5.44149	+	35.7187i	−0.172247	+	1.13065i
$999$	−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.b.11.15	yes	128
3.2	odd	2		840.2.cq.a.11.50	yes	128
7.2	even	3	inner	840.2.cq.b.611.29	yes	128
8.3	odd	2		840.2.cq.a.11.36	✓	128
21.2	odd	6		840.2.cq.a.611.36	yes	128
24.11	even	2	inner	840.2.cq.b.11.29	yes	128
56.51	odd	6		840.2.cq.a.611.50	yes	128
168.107	even	6	inner	840.2.cq.b.611.15	yes	128

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

\(f(q)\)	\(=\)	\(q+(-1.10428 - 0.883495i) q^{2} +(-1.72228 + 0.183676i) q^{3} +(0.438874 + 1.95125i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.06416 + 1.31880i) q^{6} +(2.64252 + 0.130688i) q^{7} +(1.23928 - 2.54247i) q^{8} +(2.93253 - 0.632683i) q^{9} +(0.212988 - 1.39808i) q^{10} +(4.04336 + 2.33444i) q^{11} +(-1.11426 - 3.28000i) q^{12} +4.34878i q^{13} +(-2.80262 - 2.47897i) q^{14} +(-1.02021 - 1.39970i) q^{15} +(-3.61478 + 1.71271i) q^{16} +(-1.67559 - 0.967404i) q^{17} +(-3.79731 - 1.89221i) 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} +(-1.66741 + 4.60649i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.84212 - 4.80228i) q^{26} +(-4.93444 + 1.62829i) q^{27} +(0.904727 + 5.21358i) q^{28} +0.0972660 q^{29} +(-0.110033 + 2.44702i) q^{30} +(1.01737 + 0.587378i) q^{31} +(5.50490 + 1.30233i) q^{32} +(-7.39260 - 3.27790i) q^{33} +(0.995629 + 2.54866i) q^{34} +(1.20808 + 2.35383i) q^{35} +(2.52153 + 5.44443i) q^{36} +(3.60469 - 2.08117i) q^{37} +(-0.0106330 + 0.0697967i) q^{38} +(-0.798764 - 7.48984i) q^{39} +(2.82149 - 0.197987i) q^{40} +10.8636i q^{41} +(5.28224 + 3.75472i) q^{42} +8.18596 q^{43} +(-2.78055 + 8.91415i) q^{44} +(2.01418 + 2.22330i) q^{45} +(-1.54289 + 10.1277i) q^{46} +(-2.85565 - 4.94613i) q^{47} +(5.91110 - 3.61372i) q^{48} +(6.96584 + 0.690692i) q^{49} +(1.31727 - 0.514588i) q^{50} +(3.06354 + 1.35838i) q^{51} +(-8.48557 + 1.90856i) q^{52} +(-7.07548 + 12.2551i) q^{53} +(6.88759 + 2.56146i) q^{54} +4.66887i q^{55} +(3.60710 - 6.55659i) q^{56} +(0.0509321 + 0.0698776i) q^{57} +(-0.107409 - 0.0859340i) q^{58} +(11.8059 + 6.81613i) q^{59} +(2.28343 - 2.60498i) 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} +(5.26750 + 10.1510i) q^{66} +(1.67973 - 2.90938i) q^{67} +(1.15228 - 3.69408i) q^{68} +(7.39041 + 10.1395i) q^{69} +(0.745539 - 3.66663i) q^{70} -6.44542 q^{71} +(2.02565 - 8.23995i) q^{72} +(-4.51719 + 7.82400i) q^{73} +(-5.81929 - 0.886529i) q^{74} +(0.702074 - 1.58338i) q^{75} +(0.0734069 - 0.0676809i) q^{76} +(10.3796 + 6.69722i) q^{77} +(-5.73517 + 8.97659i) q^{78} +(8.28188 - 4.78155i) q^{79} +(-3.29064 - 2.27414i) q^{80} +(8.19942 - 3.71072i) q^{81} +(9.59797 - 11.9965i) q^{82} -11.4677i q^{83} +(-2.51581 - 8.81310i) q^{84} -1.93481i q^{85} +(-9.03960 - 7.23225i) q^{86} +(-0.167520 + 0.0178654i) q^{87} +(10.9461 - 7.38712i) q^{88} +(5.85921 - 3.38281i) q^{89} +(-0.259949 - 4.23467i) q^{90} +(-0.568334 + 11.4917i) q^{91} +(10.6516 - 9.82072i) q^{92} +(-1.86008 - 0.824766i) q^{93} +(-1.21644 + 7.98487i) q^{94} +(0.0249616 - 0.0432347i) q^{95} +(-9.72021 - 1.23187i) q^{96} +6.90641 q^{97} +(-7.08202 - 6.91700i) q^{98} +(13.3342 + 4.28763i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 64 q^{5} + 2 q^{12} + 6 q^{14} + 8 q^{16} - 4 q^{18} - 8 q^{21} + 4 q^{22} + 20 q^{24} - 64 q^{25} + 16 q^{26} - 6 q^{28} + 10 q^{32} + 24 q^{34} + 20 q^{36} + 16 q^{38} + 18 q^{42} - 6 q^{44} + 8 q^{46}+ \cdots - 14 q^{98}+O(q^{100}) \) 128 * q + 64 * q^5 + 2 * q^12 + 6 * q^14 + 8 * q^16 - 4 * q^18 - 8 * q^21 + 4 * q^22 + 20 * q^24 - 64 * q^25 + 16 * q^26 - 6 * q^28 + 10 * q^32 + 24 * q^34 + 20 * q^36 + 16 * q^38 + 18 * q^42 - 6 * q^44 + 8 * q^46 - 44 * q^48 + 8 * q^49 + 20 * q^51 - 6 * q^52 - 16 * q^54 + 18 * q^56 - 8 * q^58 - 2 * q^60 + 20 * q^62 + 28 * q^63 + 22 * q^66 + 32 * q^67 + 2 * q^68 - 40 * q^69 - 6 * q^70 + 48 * q^71 - 54 * q^72 - 8 * q^73 + 26 * q^74 - 24 * q^76 - 84 * q^78 - 8 * q^80 + 4 * q^81 - 12 * q^82 + 6 * q^84 - 46 * q^86 + 36 * q^87 - 20 * q^88 - 8 * q^90 - 24 * q^91 + 40 * q^92 + 12 * q^94 + 22 * q^96 + 32 * q^97 - 14 * q^98

Introduction

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