LMFDB - Embedded newform 840.2.cq.a.611.50

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			611.50
Character	$\chi$	$=$	840.611
Dual form			840.2.cq.a.11.50

$q$-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} +(0.702074 - 1.58338i) q^{3} +(0.438874 - 1.95125i) 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} +(-2.01418 - 2.22330i) q^{9} +(0.212988 + 1.39808i) q^{10} +(-4.04336 + 2.33444i) q^{11} +(-2.78145 - 2.06483i) 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} +(-4.18850 - 0.675629i) q^{18} +(-0.0249616 + 0.0432347i) q^{19} +(1.47040 + 1.35570i) q^{20} +(1.64832 - 4.27587i) q^{21} +(-2.40255 + 6.15017i) q^{22} +(3.62201 - 6.27350i) q^{23} +(-4.89577 + 0.177248i) 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} +(2.36323 + 0.644317i) q^{30} +(1.01737 - 0.587378i) q^{31} +(-5.50490 + 1.30233i) q^{32} +(0.857558 + 8.04113i) 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} +(0.0106330 + 0.0697967i) q^{38} +(-6.88577 - 3.05317i) q^{39} +(2.82149 + 0.197987i) q^{40} +10.8636i q^{41} +(-1.95750 - 6.17804i) q^{42} +8.18596 q^{43} +(2.78055 + 8.91415i) q^{44} +(2.93253 - 0.632683i) q^{45} +(-1.54289 - 10.1277i) 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} +(-0.355377 - 3.33229i) q^{51} +(-8.48557 - 1.90856i) q^{52} +(7.07548 + 12.2551i) q^{53} +(-4.01042 + 6.15764i) 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} +(3.17892 - 1.37639i) q^{60} +(-1.18119 - 0.681959i) q^{61} +(0.604515 - 1.54747i) q^{62} +(-5.61308 - 5.61189i) q^{63} +(-4.92836 + 6.30169i) q^{64} +(3.76615 + 2.17439i) q^{65} +(8.05128 + 8.12202i) 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} +(-3.15655 + 7.87631i) q^{72} +(-4.51719 - 7.82400i) q^{73} +(5.81929 - 0.886529i) q^{74} +(-1.72228 + 0.183676i) 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} +(3.29064 - 2.27414i) q^{80} +(-0.886135 + 8.95627i) q^{81} +(9.59797 + 11.9965i) q^{82} -11.4677i q^{83} +(-7.61990 - 5.09285i) q^{84} +1.93481i q^{85} +(9.03960 - 7.23225i) q^{86} +(-0.0682880 + 0.154009i) q^{87} +(10.9461 + 7.38712i) 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} +(-0.215774 - 2.02326i) q^{93} +(-1.21644 - 7.98487i) q^{94} +(-0.0249616 - 0.0432347i) q^{95} +(-1.80277 + 9.63068i) 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} - 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 $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

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

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
$3$	0.702074	−	1.58338i	0.405343	−	0.914165i
$3$	0.702074	−	1.58338i	0.405343	−	0.914165i
$4$	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
$6$	−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
$9$	−2.01418	−	2.22330i	−0.671394	−	0.741100i
$10$	0.212988	+	1.39808i	0.0673529	+	0.442113i
$11$	−4.04336	+	2.33444i	−1.21912	+	0.703859i	−0.964730	−	0.263242i	$-0.915208\pi$
$11$	−4.04336	+	2.33444i	−1.21912	+	0.703859i	−0.254390	+	0.967102i	$0.581875\pi$
$12$	−2.78145	−	2.06483i	−0.802936	−	0.596065i
$13$		−	4.34878i		−	1.20613i	−0.797690	−	0.603067i	$-0.793945\pi$
$13$		−	4.34878i		−	1.20613i	0.797690	−	0.603067i	$-0.206055\pi$
$14$	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	$-0.591279\pi$
$17$	1.67559	−	0.967404i	0.406391	−	0.234630i	0.689238	+	0.724535i	$0.257945\pi$
$18$	−4.18850	−	0.675629i	−0.987239	−	0.159247i
$19$	−0.0249616	+	0.0432347i	−0.00572657	+	0.00991872i	−0.868874	−	0.495032i	$-0.835156\pi$
$19$	−0.0249616	+	0.0432347i	−0.00572657	+	0.00991872i	0.863148	+	0.504951i	$0.168490\pi$
$20$	1.47040	+	1.35570i	0.328791	+	0.303144i
$21$	1.64832	−	4.27587i	0.359693	−	0.933071i
$22$	−2.40255	+	6.15017i	−0.512225	+	1.31122i
$23$	3.62201	−	6.27350i	0.755240	−	1.30811i	−0.190014	−	0.981781i	$-0.560853\pi$
$23$	3.62201	−	6.27350i	0.755240	−	1.30811i	0.945255	−	0.326333i	$-0.105813\pi$
$24$	−4.89577	+	0.177248i	−0.999345	+	0.0361806i
$25$	−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	$-0.502875\pi$
$29$	−0.0972660			−0.0180618			−0.00903092	+	0.999959i	$0.502875\pi$
$30$	2.36323	+	0.644317i	0.431465	+	0.117636i
$31$	1.01737	−	0.587378i	0.182725	−	0.105496i	−0.405847	−	0.913941i	$-0.633024\pi$
$31$	1.01737	−	0.587378i	0.182725	−	0.105496i	0.588572	+	0.808445i	$0.299690\pi$
$32$	−5.50490	+	1.30233i	−0.973138	+	0.230221i
$33$	0.857558	+	8.04113i	0.149282	+	1.39978i
$34$	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	$-0.222181\pi$
$37$	3.60469	+	2.08117i	0.592607	+	0.342142i	−0.173521	+	0.984830i	$0.555514\pi$
$38$	0.0106330	+	0.0697967i	0.00172491	+	0.0113225i
$39$	−6.88577	−	3.05317i	−1.10261	−	0.488898i
$40$	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	$0.677622\pi$
$42$	−1.95750	−	6.17804i	−0.302049	−	0.953292i
$43$	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
$45$	2.93253	−	0.632683i	0.437155	−	0.0943148i
$46$	−1.54289	−	10.1277i	−0.227487	−	1.49325i
$47$	2.85565	−	4.94613i	0.416539	−	0.721467i	−0.579050	−	0.815292i	$-0.696576\pi$
$47$	2.85565	−	4.94613i	0.416539	−	0.721467i	0.995589	+	0.0938254i	$0.0299095\pi$
$48$	−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
$51$	−0.355377	−	3.33229i	−0.0497627	−	0.466614i
$52$	−8.48557	−	1.90856i	−1.17674	−	0.264670i
$53$	7.07548	+	12.2551i	0.971892	+	1.68337i	0.689831	+	0.723970i	$0.257685\pi$
$53$	7.07548	+	12.2551i	0.971892	+	1.68337i	0.282061	+	0.959396i	$0.408982\pi$
$54$	−4.01042	+	6.15764i	−0.545748	+	0.837949i
$55$		−	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	−0.537981	+	0.842957i	$0.680813\pi$
$59$	−11.8059	+	6.81613i	−1.53699	+	0.887384i	−0.999013	+	0.0444272i	$0.985854\pi$
$60$	3.17892	−	1.37639i	0.410397	−	0.177692i
$61$	−1.18119	−	0.681959i	−0.151236	−	0.0873160i	0.422472	−	0.906376i	$-0.361162\pi$
$61$	−1.18119	−	0.681959i	−0.151236	−	0.0873160i	−0.573708	+	0.819060i	$0.694496\pi$
$62$	0.604515	−	1.54747i	0.0767735	−	0.196529i
$63$	−5.61308	−	5.61189i	−0.707182	−	0.707032i
$64$	−4.92836	+	6.30169i	−0.616045	+	0.787711i
$65$	3.76615	+	2.17439i	0.467134	+	0.269700i
$66$	8.05128	+	8.12202i	0.991044	+	0.999751i
$67$	1.67973	+	2.90938i	0.205212	+	0.355437i	0.950200	−	0.311640i	$-0.100878\pi$
$67$	1.67973	+	2.90938i	0.205212	+	0.355437i	−0.744989	+	0.667077i	$0.767545\pi$
$68$	−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	$-0.375075\pi$
$71$	6.44542			0.764931			0.382466	+	0.923970i	$0.375075\pi$
$72$	−3.15655	+	7.87631i	−0.372002	+	0.928232i
$73$	−4.51719	−	7.82400i	−0.528697	−	0.915730i	−0.999440	−	0.0334596i	$-0.989347\pi$
$73$	−4.51719	−	7.82400i	−0.528697	−	0.915730i	0.470743	−	0.882270i	$-0.343986\pi$
$74$	5.81929	−	0.886529i	0.676478	−	0.103057i
$75$	−1.72228	+	0.183676i	−0.198872	+	0.0212090i
$76$	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	$-0.152526\pi$
$79$	8.28188	+	4.78155i	0.931785	+	0.537966i	0.0444090	+	0.999013i	$0.485860\pi$
$80$	3.29064	−	2.27414i	0.367905	−	0.254256i
$81$	−0.886135	+	8.95627i	−0.0984594	+	0.995141i
$82$	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	$-0.216688\pi$
$84$	−7.61990	−	5.09285i	−0.831399	−	0.555676i
$85$			1.93481i			0.209859i
$86$	9.03960	−	7.23225i	0.974765	−	0.779874i
$87$	−0.0682880	+	0.154009i	−0.00732124	+	0.0165115i
$88$	10.9461	+	7.38712i	1.16686	+	0.787470i
$89$	−5.85921	−	3.38281i	−0.621075	−	0.358578i	0.156213	−	0.987723i	$-0.450071\pi$
$89$	−5.85921	−	3.38281i	−0.621075	−	0.358578i	−0.777287	+	0.629146i	$0.783405\pi$
$90$	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
$93$	−0.215774	−	2.02326i	−0.0223747	−	0.209803i
$94$	−1.21644	−	7.98487i	−0.125466	−	0.823576i
$95$	−0.0249616	−	0.0432347i	−0.00256100	−	0.00443579i
$96$	−1.80277	+	9.63068i	−0.183994	+	0.982927i
$97$	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	0.855207	+	0.518287i	$0.173430\pi$
$101$	8.80824	+	15.2563i	0.876453	+	1.51806i	0.0212462	+	0.999774i	$0.493237\pi$
$102$	−3.33650	−	3.36581i	−0.330362	−	0.333265i
$103$	−1.23715	−	0.714272i	−0.121900	−	0.0703793i	0.437810	−	0.899068i	$-0.355754\pi$
$103$	−1.23715	−	0.714272i	−0.121900	−	0.0703793i	−0.559710	+	0.828688i	$0.689088\pi$
$104$	−11.0567	+	5.38937i	−1.08420	+	0.528471i
$105$	2.87885	+	3.56542i	0.280947	+	0.347949i
$106$	18.6406	+	7.28192i	1.81054	+	0.707282i
$107$	6.21564	+	3.58860i	0.600889	+	0.346923i	0.769391	−	0.638778i	$-0.220560\pi$
$107$	6.21564	+	3.58860i	0.600889	+	0.346923i	−0.168502	+	0.985701i	$0.553893\pi$
$108$	1.01162	+	10.3430i	0.0973431	+	0.995251i
$109$	−8.26788	+	4.77346i	−0.791919	+	0.457215i	−0.840638	−	0.541598i	$-0.817820\pi$
$109$	−8.26788	+	4.77346i	−0.791919	+	0.457215i	0.0487186	+	0.998813i	$0.484486\pi$
$110$	−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	$0.944677\pi$
$114$	0.117980	+	0.0321663i	0.0110498	+	0.00301265i
$115$	3.62201	+	6.27350i	0.337754	+	0.585007i
$116$	−0.0426875	+	0.189791i	−0.00396343	+	0.0176216i
$117$	−9.66865	+	8.75924i	−0.893867	+	0.809792i
$118$	−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
$122$	−1.90687	+	0.290499i	−0.172640	+	0.0263005i
$123$	17.2013	+	7.62708i	1.55099	+	0.687711i
$124$	−0.699627	−	2.24293i	−0.0628284	−	0.201421i
$125$	1.00000			0.0894427
$126$	−11.1565	−	1.23798i	−0.993900	−	0.110288i
$127$		−	2.19395i		−	0.194681i	−0.995251	−	0.0973407i	$-0.968966\pi$
$127$		−	2.19395i		−	0.194681i	0.995251	−	0.0973407i	$-0.0310336\pi$
$128$	0.125218	+	11.3130i	0.0110679	+	0.999939i
$129$	5.74715	−	12.9615i	0.506008	−	1.14119i
$130$	6.07996	−	0.926240i	0.533247	−	0.0812366i
$131$	−1.85389	−	1.07034i	−0.161975	−	0.0935164i	0.416821	−	0.908988i	$-0.363144\pi$
$131$	−1.85389	−	1.07034i	−0.161975	−	0.0935164i	−0.578796	+	0.815472i	$0.696477\pi$
$132$	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
$135$	1.05707	−	5.08749i	0.0909785	−	0.437862i
$136$	−4.53613	−	3.06127i	−0.388970	−	0.262501i
$137$	−9.50363	+	5.48692i	−0.811950	+	0.468779i	−0.847632	−	0.530584i	$-0.821973\pi$
$137$	−9.50363	+	5.48692i	−0.811950	+	0.468779i	0.0356828	+	0.999363i	$0.488639\pi$
$138$	−17.1193	−	4.66744i	−1.45729	−	0.397319i
$139$	−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
$144$	3.47296	+	11.4864i	0.289414	+	0.957204i
$145$	0.0486330	−	0.0842348i	0.00403875	−	0.00699532i
$146$	−11.9007	−	4.64898i	−0.984910	−	0.384753i
$147$	3.79691	−	11.5145i	0.313164	−	0.949699i
$148$	5.64289	−	6.12029i	0.463842	−	0.503085i
$149$	8.78701	−	15.2195i	0.719860	−	1.24683i	−0.241195	−	0.970477i	$-0.577539\pi$
$149$	8.78701	−	15.2195i	0.719860	−	1.24683i	0.961055	−	0.276357i	$-0.0891273\pi$
$150$	−1.73961	+	1.72446i	−0.142039	+	0.140801i
$151$	13.3596	−	7.71315i	1.08719	−	0.627688i	0.154361	−	0.988015i	$-0.450668\pi$
$151$	13.3596	−	7.71315i	1.08719	−	0.627688i	0.932826	+	0.360327i	$0.117335\pi$
$152$	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
$156$	−8.97949	+	12.0959i	−0.718934	+	0.968449i
$157$	−13.6657	+	7.88990i	−1.09064	+	0.629682i	−0.933747	−	0.357933i	$-0.883482\pi$
$157$	−13.6657	+	7.88990i	−1.09064	+	0.629682i	−0.156895	+	0.987615i	$0.550148\pi$
$158$	13.3700	−	2.03683i	1.06366	−	0.162041i
$159$	24.3720	−	2.59919i	1.93282	−	0.206129i
$160$	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	0.274439	−	0.961604i	$-0.411508\pi$
$163$	12.3840	−	21.4498i	0.969993	−	1.68008i	0.695554	−	0.718474i	$-0.255159\pi$
$164$	21.1977	+	4.76776i	1.65526	+	0.372300i
$165$	−7.39260	−	3.27790i	−0.575513	−	0.255184i
$166$	−10.1317	−	12.6636i	−0.786370	−	0.982885i
$167$	−1.69273			−0.130987			−0.0654936	−	0.997853i	$-0.520862\pi$
$167$	−1.69273			−0.130987			−0.0654936	+	0.997853i	$0.520862\pi$
$168$	−12.9140	+	1.10820i	−0.996338	+	0.0854996i
$169$	−5.91189			−0.454761
$170$	1.70939	+	2.13657i	0.131104	+	0.163868i
$171$	0.146401	−	0.0315855i	0.0111956	−	0.00241540i
$172$	3.59260	−	15.9729i	0.273933	−	1.21792i
$173$	−1.64079	+	2.84193i	−0.124747	+	0.216068i	−0.921634	−	0.388060i	$-0.873145\pi$
$173$	−1.64079	+	2.84193i	−0.124747	+	0.216068i	0.796887	+	0.604128i	$0.206479\pi$
$174$	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
$177$	2.50391	+	23.4786i	0.188205	+	1.76476i
$178$	−9.45891	+	1.44100i	−0.708975	+	0.108008i
$179$	0.932643	−	0.538462i	0.0697090	−	0.0402465i	−0.464740	−	0.885447i	$-0.653852\pi$
$179$	0.932643	−	0.538462i	0.0697090	−	0.0402465i	0.534449	+	0.845200i	$0.320519\pi$
$180$	0.0524836	−	5.99977i	0.00391190	−	0.447196i
$181$		−	26.2498i		−	1.95113i	−0.219710	−	0.975565i	$-0.570511\pi$
$181$		−	26.2498i		−	1.95113i	0.219710	−	0.975565i	$-0.429489\pi$
$182$	−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
$186$	−2.02582	−	2.04362i	−0.148540	−	0.149845i
$187$	−4.51669	+	7.82313i	−0.330293	+	0.572084i
$188$	−8.39788	−	7.74282i	−0.612478	−	0.564703i
$189$	−12.8266	+	4.94767i	−0.932995	+	0.359890i
$190$	−0.0657622	−	0.0256898i	−0.00477089	−	0.00186374i
$191$	2.53297	−	4.38724i	0.183279	−	0.317449i	−0.759716	−	0.650255i	$-0.774662\pi$
$191$	2.53297	−	4.38724i	0.183279	−	0.317449i	0.942995	+	0.332806i	$0.107995\pi$
$192$	6.51789	+	12.2277i	0.470388	+	0.882459i
$193$	10.7811	+	18.6734i	0.776041	+	1.34414i	0.934208	+	0.356730i	$0.116108\pi$
$193$	10.7811	+	18.6734i	0.776041	+	1.34414i	−0.158166	+	0.987412i	$0.550558\pi$
$194$	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	$-0.744208\pi$
$197$	−19.4850			−1.38825			−0.694124	+	0.719856i	$0.744208\pi$
$198$	18.5128	−	7.04597i	1.31565	−	0.500736i
$199$	−2.34902	+	1.35621i	−0.166518	+	0.0961390i	−0.580943	−	0.813944i	$-0.697316\pi$
$199$	−2.34902	+	1.35621i	−0.166518	+	0.0961390i	0.414425	+	0.910083i	$0.363983\pi$
$200$	−1.58221	+	2.34449i	−0.111879	+	0.165780i
$201$	5.78594	−	0.617050i	0.408109	−	0.0435234i
$202$	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
$206$	−1.99722	+	0.304263i	−0.139153	+	0.0211990i
$207$	−21.2433	+	4.58316i	−1.47651	+	0.318552i
$208$	−7.44819	+	15.7199i	−0.516439	+	1.08998i
$209$		−	0.233085i		−	0.0161228i
$210$	6.32909	+	1.39377i	0.436749	+	0.0961796i
$211$	−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
$213$	4.52517	−	10.2056i	0.310059	−	0.699273i
$214$	10.0343	−	1.52866i	0.685932	−	0.104497i
$215$	−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
$219$	−15.5598	+	1.65939i	−1.05143	+	0.112131i
$220$	−9.11016	−	2.04905i	−0.614207	−	0.138147i
$221$	−4.20703	−	7.28679i	−0.282995	−	0.490162i
$222$	2.68186	−	9.83655i	0.179995	−	0.660186i
$223$			6.98906i			0.468022i	0.972234	+	0.234011i	$0.0751852\pi$
$223$			6.98906i			0.468022i	−0.972234	+	0.234011i	$0.924815\pi$
$224$	−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	$-0.837102\pi$
$227$	−13.3146	+	7.68720i	−0.883723	+	0.510218i	−0.0118388	+	0.999930i	$0.503768\pi$
$228$	0.158702	−	0.0687139i	0.0105103	−	0.00455069i
$229$	7.72565	+	4.46041i	0.510525	+	0.294752i	0.733050	−	0.680175i	$-0.238096\pi$
$229$	7.72565	+	4.46041i	0.510525	+	0.294752i	−0.222524	+	0.974927i	$0.571430\pi$
$230$	9.54231	+	3.72768i	0.629202	+	0.245796i
$231$	3.31700	+	21.1368i	0.218242	+	1.39070i
$232$	0.120540	+	0.247296i	0.00791384	+	0.0162358i
$233$	2.58227	+	1.49088i	0.169170	+	0.0976706i	0.582195	−	0.813049i	$-0.302194\pi$
$233$	2.58227	+	1.49088i	0.169170	+	0.0976706i	−0.413024	+	0.910720i	$0.635528\pi$
$234$	−2.93816	+	18.2149i	−0.192074	+	1.19074i
$235$	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	$-0.430587\pi$
$239$	6.68915			0.432685			0.216343	+	0.976318i	$0.430587\pi$
$240$	−1.29055	−	6.80694i	−0.0833047	−	0.439386i
$241$	12.1520	+	21.0478i	0.782776	+	1.35581i	0.930319	+	0.366752i	$0.119530\pi$
$241$	12.1520	+	21.0478i	0.782776	+	1.35581i	−0.147543	+	0.989056i	$0.547136\pi$
$242$	−2.29993	−	15.0970i	−0.147845	−	0.970475i
$243$	13.5590	+	7.69106i	0.869813	+	0.493381i
$244$	−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
$248$	−2.75420	−	1.85871i	−0.174892	−	0.118028i
$249$	−18.1578	−	8.05119i	−1.15070	−	0.510224i
$250$	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	$-0.0415075\pi$
$252$	−13.4137	+	8.48963i	−0.844981	+	0.534797i
$253$			33.8214i			2.12633i
$254$	−1.93834	−	2.42274i	−0.121622	−	0.152016i
$255$	3.06354	+	1.35838i	0.191846	+	0.0850650i
$256$	10.1333	+	12.3821i	0.633329	+	0.773882i
$257$	5.26625	+	3.04047i	0.328500	+	0.189659i	0.655175	−	0.755477i	$-0.272595\pi$
$257$	5.26625	+	3.04047i	0.328500	+	0.189659i	−0.326675	+	0.945137i	$0.605928\pi$
$258$	−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
$261$	0.195911	+	0.216252i	0.0121266	+	0.0133856i
$262$	−2.99286	+	0.455942i	−0.184900	+	0.0281682i
$263$	−3.88549	−	6.72987i	−0.239590	−	0.414981i	0.721007	−	0.692928i	$-0.243680\pi$
$263$	−3.88549	−	6.72987i	−0.239590	−	0.414981i	−0.960597	+	0.277946i	$0.910346\pi$
$264$	19.3816	−	12.1456i	1.19286	−	0.747507i
$265$	−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	$-0.302847\pi$
$269$	−6.80473	−	11.7861i	−0.414892	−	0.718613i	−0.995417	+	0.0956287i	$0.969514\pi$
$270$	−3.32747	−	6.55194i	−0.202503	−	0.398739i
$271$	−6.21337	−	3.58729i	−0.377436	−	0.217913i	0.299266	−	0.954170i	$-0.403258\pi$
$271$	−6.21337	−	3.58729i	−0.377436	−	0.217913i	−0.676702	+	0.736257i	$0.736591\pi$
$272$	−7.71378	+	0.627153i	−0.467717	+	0.0380267i
$273$	−18.5948	−	7.16817i	−1.12541	−	0.433838i
$274$	−5.64701	+	14.4555i	−0.341148	+	0.873289i
$275$	4.04336	+	2.33444i	0.243824	+	0.140772i
$276$	−23.0281	+	9.97062i	−1.38613	+	0.600161i
$277$	−10.9137	+	6.30101i	−0.655738	+	0.378591i	−0.790651	−	0.612267i	$-0.790258\pi$
$277$	−10.9137	+	6.30101i	−0.655738	+	0.378591i	0.134913	+	0.990857i	$0.456925\pi$
$278$	−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	$0.920714\pi$
$282$	−13.4971	−	3.67988i	−0.803741	−	0.219134i
$283$	−13.3224	−	23.0751i	−0.791937	−	1.37167i	−0.924766	−	0.380536i	$-0.875740\pi$
$283$	−13.3224	−	23.0751i	−0.791937	−	1.37167i	0.132829	−	0.991139i	$-0.457594\pi$
$284$	2.82873	−	12.5767i	0.167854	−	0.746287i
$285$	−0.0859818	+	0.00916965i	−0.00509312	+	0.000543163i
$286$	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
$290$	−0.0207165	−	0.135986i	−0.00121652	−	0.00798537i
$291$	4.84881	−	10.9355i	0.284242	−	0.641048i
$292$	−17.2491	+	5.38043i	−1.00943	+	0.314866i
$293$	1.76503			0.103114			0.0515571	−	0.998670i	$-0.483582\pi$
$293$	1.76503			0.103114			0.0515571	+	0.998670i	$0.483582\pi$
$294$	−5.98013	−	16.0698i	−0.348769	−	0.937209i
$295$		−	13.6323i		−	0.793700i
$296$	0.824089	−	11.7440i	0.0478992	−	0.682605i
$297$	16.1506	−	18.1029i	0.937151	−	1.05044i
$298$	−3.74306	−	24.5699i	−0.216830	−	1.42330i
$299$	−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
$303$	30.3406	−	3.23572i	1.74302	−	0.185887i
$304$	0.164279	−	0.113532i	0.00942204	−	0.00651151i
$305$	1.18119	−	0.681959i	0.0676346	−	0.0390489i
$306$	−7.67183	+	2.91989i	−0.438569	+	0.166919i
$307$	−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	−0.999559	−	0.0297058i	$-0.990543\pi$
$311$	−9.26739	−	16.0516i	−0.525505	−	0.910202i	0.474053	−	0.880496i	$-0.342790\pi$
$312$	0.770813	+	21.2906i	0.0436387	+	1.20534i
$313$	3.39435	−	5.87919i	0.191860	−	0.332311i	−0.754007	−	0.656867i	$-0.771881\pi$
$313$	3.39435	−	5.87919i	0.191860	−	0.332311i	0.945867	+	0.324556i	$0.105215\pi$
$314$	−8.12009	+	20.7862i	−0.458243	+	1.17304i
$315$	7.66658	−	2.05512i	0.431963	−	0.115793i
$316$	12.9647	−	14.0616i	0.729322	−	0.791024i
$317$	−8.08209	+	13.9986i	−0.453935	+	0.786239i	−0.998626	−	0.0523978i	$-0.983314\pi$
$317$	−8.08209	+	13.9986i	−0.453935	+	0.786239i	0.544691	+	0.838637i	$0.316647\pi$
$318$	24.6172	−	24.4028i	1.38046	−	1.36844i
$319$	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
$324$	17.0871	+	5.65974i	0.949281	+	0.314430i
$325$	−3.76615	+	2.17439i	−0.208909	+	0.120613i
$326$	−5.27532	−	34.6279i	−0.292173	−	1.91786i
$327$	1.75354	+	16.4425i	0.0969708	+	0.909273i
$328$	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	0.147580	+	0.989050i	$0.452852\pi$
$331$	−14.2409	+	24.6660i	−0.782752	+	1.35577i	−0.930333	+	0.366717i	$0.880482\pi$
$332$	−22.3764	−	5.03288i	−1.22807	−	0.276215i
$333$	−2.63344	−	12.2062i	−0.144311	−	0.668893i
$334$	−1.86925	+	1.49552i	−0.102281	+	0.0818310i
$335$	−3.35946			−0.183547
$336$	−13.2816	+	12.6332i	−0.724572	+	0.689199i
$337$	−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
$339$	5.82131	+	2.58118i	0.316170	+	0.140191i
$340$	3.77530	+	0.849136i	0.204744	+	0.0460509i
$341$	−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
$345$	12.4762	−	1.33055i	0.671698	−	0.0716343i
$346$	0.698939	+	4.58792i	0.0375752	+	0.246648i
$347$	25.5899	−	14.7743i	1.37374	−	0.793128i	0.382341	−	0.924021i	$-0.375118\pi$
$347$	25.5899	−	14.7743i	1.37374	−	0.793128i	0.991396	+	0.130894i	$0.0417846\pi$
$348$	0.270541	+	0.200838i	0.0145025	+	0.0107660i
$349$			27.6360i			1.47932i	0.672981	+	0.739659i	$0.265013\pi$
$349$			27.6360i			1.47932i	−0.672981	+	0.739659i	$0.734987\pi$
$350$	−3.54816	−	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	$-0.924408\pi$
$353$	−23.5636	+	13.6045i	−1.25417	+	0.724093i	−0.282231	+	0.959346i	$0.591075\pi$
$354$	23.5083	+	23.7148i	1.24945	+	1.26043i
$355$	−3.22271	+	5.58190i	−0.171044	+	0.296257i
$356$	−9.17218	+	9.94817i	−0.486125	+	0.527252i
$357$	−1.37458	−	8.75921i	−0.0727506	−	0.463586i
$358$	0.554172	−	1.41860i	0.0292889	−	0.0749753i
$359$	−3.74005	+	6.47797i	−0.197393	+	0.341894i	−0.947682	−	0.319215i	$-0.896581\pi$
$359$	−3.74005	+	6.47797i	−0.197393	+	0.341894i	0.750290	+	0.661109i	$0.229914\pi$
$360$	−5.24281	−	6.67180i	−0.276320	−	0.351635i
$361$	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
$366$	−0.878796	+	3.22325i	−0.0459354	+	0.168482i
$367$	−15.9053	+	9.18291i	−0.830248	+	0.479344i	−0.853938	−	0.520375i	$-0.825792\pi$
$367$	−15.9053	+	9.18291i	−0.830248	+	0.479344i	0.0236896	+	0.999719i	$0.492459\pi$
$368$	−23.8374	+	16.4739i	−1.24261	+	0.858760i
$369$	24.1531	−	21.8814i	1.25736	−	1.13910i
$370$	−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	$-0.331644\pi$
$373$	0.177482	+	0.102469i	0.00918966	+	0.00530565i	−0.495398	+	0.868666i	$0.664978\pi$
$374$	1.92401	+	12.6294i	0.0994879	+	0.653051i
$375$	0.702074	−	1.58338i	0.0362550	−	0.0817654i
$376$	−16.1144	−	1.13076i	−0.831035	−	0.0583147i
$377$			0.422988i			0.0217850i
$378$	−9.79288	+	16.7958i	−0.503691	+	0.863884i
$379$	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
$381$	−3.47385	−	1.54031i	−0.177971	−	0.0789127i
$382$	−1.07899	−	7.08261i	−0.0552058	−	0.362378i
$383$	0.773754	−	1.34018i	0.0395370	−	0.0684800i	−0.845580	−	0.533849i	$-0.820745\pi$
$383$	0.773754	−	1.34018i	0.0395370	−	0.0684800i	0.885117	+	0.465369i	$0.154078\pi$
$384$	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
$387$	−16.4880	−	18.1998i	−0.838133	−	0.925150i
$388$	3.03104	−	13.4762i	0.153878	−	0.684148i
$389$	−0.196263	−	0.339937i	−0.00995092	−	0.0172355i	0.861007	−	0.508593i	$-0.169834\pi$
$389$	−0.196263	−	0.339937i	−0.00995092	−	0.0172355i	−0.870958	+	0.491357i	$0.836501\pi$
$390$	2.80199	−	10.2772i	0.141884	−	0.520405i
$391$		−	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
$396$	14.2183	−	24.1367i	0.714496	−	1.21292i
$397$	−0.342311	−	0.197633i	−0.0171801	−	0.00991894i	0.491385	−	0.870942i	$-0.336491\pi$
$397$	−0.342311	−	0.197633i	−0.0171801	−	0.00991894i	−0.508565	+	0.861023i	$0.669824\pi$
$398$	−1.39578	+	3.57298i	−0.0699640	+	0.179097i
$399$	0.143721	+	0.177997i	0.00719506	+	0.00891099i
$400$	0.324142	+	3.98684i	0.0162071	+	0.199342i
$401$	−25.7729	−	14.8800i	−1.28704	−	0.743070i	−0.308911	−	0.951091i	$-0.599965\pi$
$401$	−25.7729	−	14.8800i	−1.28704	−	0.743070i	−0.978124	+	0.208021i	$0.933298\pi$
$402$	5.84415	−	5.79325i	0.291479	−	0.288941i
$403$	−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
$408$	−8.03185	+	5.03319i	−0.397636	+	0.249180i
$409$	−5.55525	−	9.62197i	−0.274689	−	0.475776i	0.695367	−	0.718654i	$-0.255242\pi$
$409$	−5.55525	−	9.62197i	−0.274689	−	0.475776i	−0.970057	+	0.242879i	$0.921908\pi$
$410$	−15.1883	+	2.31383i	−0.750095	+	0.114272i
$411$	2.01563	+	18.9001i	0.0994235	+	0.932272i
$412$	−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
$416$	5.66354	+	23.9396i	0.277678	+	1.17374i
$417$	−5.72790	+	12.9181i	−0.280497	+	0.632601i
$418$	−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	$-0.297843\pi$
$420$	8.22049	−	4.05260i	0.401119	−	0.197747i
$421$			30.0447i			1.46429i	0.681150	+	0.732144i	$0.261480\pi$
$421$			30.0447i			1.46429i	−0.681150	+	0.732144i	$0.738520\pi$
$422$	−8.45549	+	6.76493i	−0.411607	+	0.329312i
$423$	−16.7485	+	3.61344i	−0.814341	+	0.175691i
$424$	22.3898	−	33.1768i	1.08734	−	1.61121i
$425$	−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
$429$	34.9691	−	3.72933i	1.68832	−	0.180054i
$430$	1.74351	+	11.4446i	0.0840797	+	0.551910i
$431$	−13.4451	−	23.2876i	−0.647628	−	1.12173i	−0.983688	−	0.179884i	$-0.942428\pi$
$431$	−13.4451	−	23.2876i	−0.647628	−	1.12173i	0.336060	−	0.941841i	$-0.390906\pi$
$432$	20.6257	+	2.56532i	0.992354	+	0.123424i
$433$	−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
$438$	−15.7163	+	15.5794i	−0.750953	+	0.744413i
$439$	16.0873	+	9.28803i	0.767807	+	0.443294i	0.832092	−	0.554638i	$-0.187143\pi$
$439$	16.0873	+	9.28803i	0.767807	+	0.443294i	−0.0642846	+	0.997932i	$0.520477\pi$
$440$	−11.8705	+	5.78605i	−0.565904	+	0.275839i
$441$	−15.5661	−	14.0960i	−0.741243	−	0.671237i
$442$	−11.0836	−	4.32977i	−0.527192	−	0.205946i
$443$	−15.5472	−	8.97617i	−0.738669	−	0.426471i	0.0829163	−	0.996557i	$-0.473577\pi$
$443$	−15.5472	−	8.97617i	−0.738669	−	0.426471i	−0.821585	+	0.570086i	$0.806910\pi$
$444$	−5.72901	−	13.2317i	−0.271887	−	0.627950i
$445$	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	$0.877103\pi$
$450$	1.50914	+	3.96516i	0.0711414	+	0.186919i
$451$	−25.3605	−	43.9256i	−1.19418	−	2.06838i
$452$	7.17380	+	1.61352i	0.337427	+	0.0758937i
$453$	−2.83344	−	26.5685i	−0.133126	−	1.24830i
$454$	−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	−0.841173	−	0.540766i	$-0.818134\pi$
$457$	1.02037	−	1.76733i	0.0477309	−	0.0826723i	0.888904	+	0.458094i	$0.151468\pi$
$458$	12.4720	−	1.90003i	0.582780	−	0.0887826i
$459$	−6.69289	+	7.50195i	−0.312397	+	0.350161i
$460$	13.8308	−	4.31418i	0.644864	−	0.201150i
$461$	11.6470			0.542453			0.271226	−	0.962516i	$-0.412571\pi$
$461$	11.6470			0.542453			0.271226	+	0.962516i	$0.412571\pi$
$462$	22.3371	+	20.4104i	1.03922	+	0.949578i
$463$		−	18.7737i		−	0.872486i	−0.899829	−	0.436243i	$-0.856309\pi$
$463$		−	18.7737i		−	0.872486i	0.899829	−	0.436243i	$-0.143691\pi$
$464$	0.351595	+	0.166588i	0.0163224	+	0.00773366i
$465$	1.86008	+	0.824766i	0.0862594	+	0.0382476i
$466$	4.16874	−	0.635079i	0.193113	−	0.0294195i
$467$	30.0802	+	17.3668i	1.39195	+	0.803640i	0.993531	−	0.113565i	$-0.0362271\pi$
$467$	30.0802	+	17.3668i	1.39195	+	0.803640i	0.398415	+	0.917205i	$0.369560\pi$
$468$	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
$471$	2.89836	+	27.1773i	0.133549	+	1.25226i
$472$	31.9606	+	21.5690i	1.47111	+	0.992795i
$473$	−33.0988	+	19.1096i	−1.52188	+	0.878660i
$474$	6.16166	−	22.5998i	0.283015	−	1.03804i
$475$	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	$-0.174332\pi$
$479$	−0.526981	−	0.912758i	−0.0240784	−	0.0417050i	−0.877814	+	0.479003i	$0.840998\pi$
$480$	−7.43903	−	6.37658i	−0.339544	−	0.291050i
$481$	9.05054	−	15.6760i	0.412669	−	0.714763i
$482$	32.0148	+	12.5065i	1.45823	+	0.569655i
$483$	−20.8544	−	25.8279i	−0.948909	−	1.17521i
$484$	−15.8779	−	14.6394i	−0.721724	−	0.665427i
$485$	−3.45320	+	5.98112i	−0.156802	+	0.271589i
$486$	21.7680	−	3.48626i	0.987417	−	0.158140i
$487$	−11.5870	+	6.68977i	−0.525058	+	0.303142i	−0.739002	−	0.673704i	$-0.764702\pi$
$487$	−11.5870	+	6.68977i	−0.525058	+	0.303142i	0.213944	+	0.976846i	$0.431369\pi$
$488$	−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	$-0.167138\pi$
$492$	22.4316	−	30.2167i	1.01129	−	1.36227i
$493$	−0.162978	+	0.0940955i	−0.00734017	+	0.00423785i
$494$	0.303530	−	0.0462408i	0.0136565	−	0.00208047i
$495$	−10.3803	+	9.40397i	−0.466560	+	0.422677i
$496$	−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	0.424526	+	0.905416i	$0.360441\pi$
$499$	−12.7742	+	22.1255i	−0.571850	+	0.990473i	−0.996376	+	0.0850571i	$0.972893\pi$
$500$	0.438874	−	1.95125i	0.0196270	−	0.0872627i
$501$	−1.18842	+	2.68023i	−0.0530947	+	0.119744i
$502$	−3.64012	−	4.54979i	−0.162466	−	0.203067i
$503$	10.7214			0.478044			0.239022	−	0.971014i	$-0.423173\pi$
$503$	10.7214			0.478044			0.239022	+	0.971014i	$0.423173\pi$
$504$	−7.31190	+	21.2258i	−0.325698	+	0.945474i
$505$	−17.6165			−0.783923
$506$	29.8810	+	37.3483i	1.32837	+	1.66033i
$507$	−4.15058	+	9.36076i	−0.184334	+	0.415726i
$508$	−4.28095	−	0.962866i	−0.189936	−	0.0427203i
$509$	−1.09583	+	1.89804i	−0.0485719	+	0.0841290i	−0.889289	−	0.457345i	$-0.848800\pi$
$509$	−1.09583	+	1.89804i	−0.0485719	+	0.0841290i	0.840717	+	0.541474i	$0.182134\pi$
$510$	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
$513$	0.0527725	−	0.253984i	0.00232996	−	0.0112136i
$514$	8.50166	−	1.29517i	0.374992	−	0.0571275i
$515$	1.23715	−	0.714272i	0.0545155	−	0.0314746i
$516$	−22.7689	−	16.9026i	−1.00234	−	0.744095i
$517$			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	$-0.616138\pi$
$521$	6.24945	−	3.60812i	0.273793	−	0.158075i	0.630610	+	0.776100i	$0.282805\pi$
$522$	0.407398	+	0.0657157i	0.0178313	+	0.00287630i
$523$	−2.50192	+	4.33345i	−0.109401	+	0.189489i	−0.915528	−	0.402254i	$-0.868227\pi$
$523$	−2.50192	+	4.33345i	−0.109401	+	0.189489i	0.806127	+	0.591743i	$0.201560\pi$
$524$	−2.90214	+	3.14766i	−0.126780	+	0.137506i
$525$	−4.52717	+	0.710449i	−0.197582	+	0.0310065i
$526$	−10.2365	−	3.99885i	−0.446332	−	0.174358i
$527$	1.13646	−	1.96841i	0.0495051	−	0.0857454i
$528$	10.6722	−	30.5357i	0.464449	−	1.32889i
$529$	−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
$534$	−4.35921	+	15.9887i	−0.188641	+	0.691900i
$535$	−6.21564	+	3.58860i	−0.268726	+	0.155149i
$536$	5.31536	−	7.87621i	0.229588	−	0.340200i
$537$	−0.197804	−	1.85477i	−0.00853589	−	0.0800392i
$538$	−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	$-0.476039\pi$
$541$	−17.4623	−	10.0819i	−0.750764	−	0.433454i	−0.825970	+	0.563714i	$0.809372\pi$
$542$	−10.0307	+	1.52810i	−0.430854	+	0.0656377i
$543$	−41.5634	−	18.4293i	−1.78365	−	0.790877i
$544$	−7.96410	+	7.50764i	−0.341458	+	0.321887i
$545$		−	9.54692i		−	0.408945i
$546$	−26.8669	+	8.51274i	−1.14980	+	0.364312i
$547$	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
$549$	0.862928	+	3.99973i	0.0368289	+	0.170704i
$550$	6.52747	−	0.994416i	0.278332	−	0.0424021i
$551$	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
$555$	0.764519	+	7.16872i	0.0324520	+	0.304295i
$556$	−3.58057	+	15.9194i	−0.151850	+	0.675132i
$557$	−1.11240	−	1.92673i	−0.0471338	−	0.0816381i	0.841496	−	0.540263i	$-0.181675\pi$
$557$	−1.11240	−	1.92673i	−0.0471338	−	0.0816381i	−0.888630	+	0.458625i	$0.848342\pi$
$558$	−4.65810	+	1.77287i	−0.197193	+	0.0750515i
$559$		−	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	$-0.882773\pi$
$563$	−25.8072	+	14.8998i	−1.08764	+	0.627952i	−0.154696	+	0.987962i	$0.549440\pi$
$564$	−18.1558	+	7.86100i	−0.764495	+	0.331008i
$565$	−3.18395	−	1.83825i	−0.133950	−	0.0773359i
$566$	−35.0985	−	13.7111i	−1.47530	−	0.576322i
$567$	−1.17115	+	23.7829i	−0.0491838	+	0.998790i
$568$	−7.98770	−	16.3873i	−0.335157	−	0.687597i
$569$	24.7640	+	14.2975i	1.03816	+	0.599382i	0.919312	−	0.393531i	$-0.128746\pi$
$569$	24.7640	+	14.2975i	1.03816	+	0.599382i	0.118848	+	0.992912i	$0.462080\pi$
$570$	−0.0868467	+	0.0860904i	−0.00363761	+	0.00360593i
$571$	1.45649	+	2.52271i	0.0609522	+	0.105572i	0.894891	−	0.446284i	$-0.147253\pi$
$571$	1.45649	+	2.52271i	0.0609522	+	0.105572i	−0.833939	+	0.551856i	$0.813920\pi$
$572$	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
$576$	23.9372	−	1.73553i	0.997382	−	0.0723139i
$577$	18.4445	+	31.9468i	0.767855	+	1.32996i	0.938724	+	0.344670i	$0.112009\pi$
$577$	18.4445	+	31.9468i	0.767855	+	1.32996i	−0.170869	+	0.985294i	$0.554657\pi$
$578$	2.82348	+	18.5337i	0.117441	+	0.770901i
$579$	37.1363	−	3.96045i	1.54333	−	0.164591i
$580$	−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
$584$	−14.2942	+	21.1810i	−0.591500	+	0.876475i
$585$	−2.75140	−	12.7529i	−0.113756	−	0.527268i
$586$	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	$0.962922\pi$
$588$	−20.8013	−	12.4621i	−0.857832	−	0.513930i
$589$			0.0586475i			0.00241653i
$590$	−12.0440	−	15.0538i	−0.495845	−	0.619757i
$591$	−13.6799	+	30.8521i	−0.562716	+	1.26909i
$592$	−9.46572	−	13.6967i	−0.389039	−	0.562932i
$593$	−15.8168	−	9.13183i	−0.649518	−	0.374999i	0.138754	−	0.990327i	$-0.455690\pi$
$593$	−15.8168	−	9.13183i	−0.649518	−	0.374999i	−0.788271	+	0.615328i	$0.789024\pi$
$594$	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
$597$	0.498204	+	4.67155i	0.0203901	+	0.191194i
$598$	−44.0433	+	6.70969i	−1.80106	+	0.274380i
$599$	10.2239	+	17.7083i	0.417736	+	0.723540i	0.995711	−	0.0925144i	$-0.0294904\pi$
$599$	10.2239	+	17.7083i	0.417736	+	0.723540i	−0.577975	+	0.816054i	$0.696157\pi$
$600$	2.60139	+	4.15124i	0.106201	+	0.169474i
$601$	−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
$606$	30.6458	−	30.3789i	1.24490	−	1.23406i
$607$	2.92576	+	1.68919i	0.118753	+	0.0685620i	0.558200	−	0.829706i	$-0.311492\pi$
$607$	2.92576	+	1.68919i	0.118753	+	0.0685620i	−0.439447	+	0.898269i	$0.644826\pi$
$608$	0.0811051	−	0.270511i	0.00328925	−	0.0109707i
$609$	−0.160325	+	0.415896i	−0.00649671	+	0.0168530i
$610$	0.701856	−	1.79665i	0.0284173	−	0.0727442i
$611$	−21.5096	−	12.4186i	−0.870186	−	0.502402i
$612$	−5.89214	+	10.0024i	−0.238176	+	0.404323i
$613$	21.7109	−	12.5348i	0.876893	−	0.506275i	0.00726042	−	0.999974i	$-0.497689\pi$
$613$	21.7109	−	12.5348i	0.876893	−	0.506275i	0.869633	+	0.493699i	$0.164356\pi$
$614$	−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	$-0.118486\pi$
$618$	−0.920434	+	3.37598i	−0.0370253	+	0.135802i
$619$	18.3452	+	31.7748i	0.737355	+	1.27714i	0.953682	+	0.300815i	$0.0972588\pi$
$619$	18.3452	+	31.7748i	0.737355	+	1.27714i	−0.216327	+	0.976321i	$0.569408\pi$
$620$	2.29225	+	0.515569i	0.0920588	+	0.0207058i
$621$	−7.65746	+	36.8539i	−0.307283	+	1.47889i
$622$	−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
$626$	−1.44591	−	9.49116i	−0.0577904	−	0.379343i
$627$	−0.369062	−	0.163643i	−0.0147389	−	0.00653527i
$628$	9.39767	+	30.1279i	0.375008	+	1.20223i
$629$	8.05332			0.321107
$630$	6.65037	−	9.04282i	0.264957	−	0.360275i
$631$			25.3603i			1.00958i	0.863243	+	0.504789i	$0.168430\pi$
$631$			25.3603i			1.00958i	−0.863243	+	0.504789i	$0.831570\pi$
$632$	1.89337	−	26.9822i	0.0753143	−	1.07329i
$633$	−5.37579	+	12.1240i	−0.213668	+	0.481884i
$634$	3.44278	+	22.5989i	0.136730	+	0.897515i
$635$	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
$639$	−12.9823	−	14.3301i	−0.513570	−	0.566891i
$640$	−9.85997	−	5.54807i	−0.389749	−	0.219307i
$641$	0.00835292	−	0.00482256i	0.000329921	−	0.000190480i	−0.499835	−	0.866121i	$-0.666606\pi$
$641$	0.00835292	−	0.00482256i	0.000329921	−	0.000190480i	0.500165	+	0.865930i	$0.333273\pi$
$642$	4.62439	−	16.9614i	0.182510	−	0.669412i
$643$	−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	−0.972833	−	0.231506i	$-0.925635\pi$
$647$	−17.4723	−	30.2629i	−0.686907	−	1.18976i	0.285927	−	0.958252i	$-0.407699\pi$
$648$	23.8693	−	8.84637i	0.937673	−	0.347518i
$649$	31.8236	−	55.1201i	1.24919	−	2.16366i
$650$	−2.23783	+	5.72852i	−0.0877749	+	0.224691i
$651$	−0.834604	−	5.31832i	−0.0327107	−	0.208441i
$652$	−36.4190	−	33.5782i	−1.42628	−	1.31502i
$653$	16.9633	−	29.3812i	0.663823	−	1.14978i	−0.315780	−	0.948833i	$-0.602266\pi$
$653$	16.9633	−	29.3812i	0.663823	−	1.14978i	0.979603	−	0.200943i	$-0.0644007\pi$
$654$	16.4633	+	16.6079i	0.643765	+	0.649421i
$655$	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	$0.891980\pi$
$660$	−9.64043	+	12.9863i	−0.375253	+	0.505489i
$661$	2.24461	−	1.29593i	0.0873051	−	0.0504056i	−0.455712	−	0.890127i	$-0.650615\pi$
$661$	2.24461	−	1.29593i	0.0873051	−	0.0504056i	0.543017	+	0.839722i	$0.317282\pi$
$662$	6.06631	+	39.8200i	0.235774	+	1.54765i
$663$	−14.4914	+	1.54546i	−0.562799	+	0.0600205i
$664$	−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
$668$	−0.742894	+	3.30294i	−0.0287434	+	0.127795i
$669$	11.0663	+	4.90684i	0.427849	+	0.189710i
$670$	−3.70979	+	2.96806i	−0.143322	+	0.114666i
$671$	6.36797			0.245833
$672$	−3.50524	+	25.6849i	−0.135218	+	0.990816i
$673$	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
$675$	3.87736	+	3.45920i	0.149240	+	0.133145i
$676$	−2.59457	+	11.5356i	−0.0997912	+	0.443677i
$677$	11.4771	−	19.8789i	0.441100	−	0.764008i	−0.556671	−	0.830733i	$-0.687922\pi$
$677$	11.4771	−	19.8789i	0.441100	−	0.764008i	0.997771	+	0.0667247i	$0.0212549\pi$
$678$	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
$681$	2.82390	+	26.4791i	0.108212	+	1.01468i
$682$	1.16820	+	7.66819i	0.0447326	+	0.293630i
$683$	20.8080	−	12.0135i	0.796197	−	0.459685i	−0.0459426	−	0.998944i	$-0.514629\pi$
$683$	20.8080	−	12.0135i	0.796197	−	0.459685i	0.842140	+	0.539260i	$0.181296\pi$
$684$	0.00262015	−	0.299527i	0.000100184	−	0.0114527i
$685$		−	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
$690$	12.6018	−	12.4920i	0.479740	−	0.475562i
$691$	−0.769690	+	1.33314i	−0.0292804	+	0.0507151i	−0.880294	−	0.474428i	$-0.842655\pi$
$691$	−0.769690	+	1.33314i	−0.0292804	+	0.0507151i	0.851014	+	0.525143i	$0.175988\pi$
$692$	4.82523	+	4.44885i	0.183428	+	0.169120i
$693$	35.7963	+	9.58753i	1.35979	+	0.364200i
$694$	15.2054	−	38.9236i	0.577189	−	1.47752i
$695$	4.07927	−	7.06551i	0.154736	−	0.268010i
$696$	0.476192	−	0.0172402i	0.0180500	−	0.000653489i
$697$	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	$-0.450904\pi$
$701$	8.13507			0.307257			0.153629	+	0.988129i	$0.450904\pi$
$702$	26.7782	+	17.4404i	1.01068	+	0.658246i
$703$	−0.179957	+	0.103898i	−0.00678721	+	0.00391860i
$704$	5.21624	−	36.9850i	0.196595	−	1.39392i
$705$	9.83648	−	1.04903i	0.370463	−	0.0395086i
$706$	−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	$-0.399418\pi$
$709$	−9.50630	−	5.48847i	−0.357017	−	0.206124i	−0.667771	+	0.744367i	$0.732752\pi$
$710$	1.37280	+	9.01124i	0.0515203	+	0.338186i
$711$	−6.05041	−	28.0440i	−0.226908	−	1.05173i
$712$	−1.33951	+	19.0891i	−0.0502002	+	0.715396i
$713$		−	8.50994i		−	0.318700i
$714$	−9.25664	−	8.45819i	−0.346421	−	0.316540i
$715$	−20.3039			−0.759323
$716$	−0.641363	−	2.05614i	−0.0239689	−	0.0768415i
$717$	4.69628	−	10.5915i	0.175386	−	0.395545i
$718$	1.59318	+	10.4578i	0.0594568	+	0.390282i
$719$	−3.69133	+	6.39358i	−0.137664	+	0.238440i	−0.926612	−	0.376019i	$-0.877293\pi$
$719$	−3.69133	+	6.39358i	−0.137664	+	0.238440i	0.788948	+	0.614460i	$0.210626\pi$
$720$	−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
$723$	41.8582	−	4.46403i	1.55672	−	0.166019i
$724$	−51.2200	−	11.5203i	−1.90358	−	0.428150i
$725$	0.0486330	+	0.0842348i	0.00180618	+	0.00312840i
$726$	−25.5191	−	6.95758i	−0.947102	−	0.258220i
$727$		−	16.3757i		−	0.607343i	−0.952777	−	0.303671i	$-0.901788\pi$
$727$		−	16.3757i		−	0.607343i	0.952777	−	0.303671i	$-0.0982125\pi$
$728$	−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
$732$	1.87729	+	4.33579i	0.0693867	+	0.160255i
$733$	35.2796	+	20.3687i	1.30308	+	0.752334i	0.980931	−	0.194355i	$-0.0622614\pi$
$733$	35.2796	+	20.3687i	1.30308	+	0.752334i	0.322149	+	0.946689i	$0.395595\pi$
$734$	−9.45083	+	24.1927i	−0.348837	+	0.892970i
$735$	8.07338	+	9.04547i	0.297791	+	0.333647i
$736$	−11.7686	+	39.2520i	−0.433797	+	1.44685i
$737$	−13.5835	−	7.84244i	−0.500355	−	0.288880i
$738$	7.33979	−	45.5023i	0.270181	−	1.67496i
$739$	6.49315	+	11.2465i	0.238854	+	0.413708i	0.960386	−	0.278674i	$-0.0898948\pi$
$739$	6.49315	+	11.2465i	0.238854	+	0.413708i	−0.721531	+	0.692382i	$0.756561\pi$
$740$	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	$-0.603048\pi$
$743$	−17.3420			−0.636216			−0.318108	+	0.948054i	$0.603048\pi$
$744$	−4.87669	+	3.05600i	−0.178788	+	0.112038i
$745$	8.78701	+	15.2195i	0.321931	+	0.557601i
$746$	0.286521	−	0.0436495i	0.0104903	−	0.00159812i
$747$	−25.4962	+	23.0981i	−0.932857	+	0.845115i
$748$	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	$-0.595106\pi$
$751$	−34.7814	−	20.0811i	−1.26919	−	0.732768i	−0.974835	+	0.222927i	$0.928439\pi$
$752$	−18.7938	+	12.9883i	−0.685340	+	0.473634i
$753$	−6.52374	−	2.89264i	−0.237738	−	0.105414i
$754$	0.373708	+	0.467098i	0.0136096	+	0.0170107i
$755$			15.4263i			0.561421i
$756$	4.02493	+	27.1993i	0.146385	+	0.989228i
$757$			15.4831i			0.562742i	0.959599	+	0.281371i	$0.0907892\pi$
$757$			15.4831i			0.562742i	−0.959599	+	0.281371i	$0.909211\pi$
$758$	11.9418	−	9.55420i	0.433746	−	0.347024i
$759$	53.5521	+	23.7451i	1.94382	+	0.861893i
$760$	−0.0789887	+	0.117044i	−0.00286522	+	0.00424564i
$761$	−6.62479	−	3.82482i	−0.240148	−	0.138650i	0.375097	−	0.926986i	$-0.377610\pi$
$761$	−6.62479	−	3.82482i	−0.240148	−	0.138650i	−0.615245	+	0.788336i	$0.710943\pi$
$762$	−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
$765$	4.30166	−	3.89706i	0.155527	−	0.140898i
$766$	−0.329601	−	2.16354i	−0.0119090	−	0.0781720i
$767$	29.6418	+	51.3412i	1.07030	+	1.85382i
$768$	26.7199	−	7.35164i	0.964172	−	0.265279i
$769$	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	$-0.134550\pi$
$773$	2.80047	+	4.85056i	0.100726	+	0.174463i	−0.811258	+	0.584688i	$0.801217\pi$
$774$	−34.2869	−	5.53067i	−1.23242	−	0.198796i
$775$	−1.01737	−	0.587378i	−0.0365450	−	0.0210992i
$776$	−8.55899	−	17.5594i	−0.307250	−	0.630345i
$777$	14.8405	−	11.9827i	0.532399	−	0.429878i
$778$	−0.517062	−	0.201989i	−0.0185376	−	0.00724166i
$779$	−0.469686	−	0.271173i	−0.0168282	−	0.00971579i
$780$	−5.98564	−	13.8244i	−0.214320	−	0.494994i
$781$	−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
$786$	−1.37928	+	5.05894i	−0.0491973	+	0.180446i
$787$	6.53353	+	11.3164i	0.232895	+	0.403386i	0.958659	−	0.284558i	$-0.0918467\pi$
$787$	6.53353	+	11.3164i	0.232895	+	0.403386i	−0.725764	+	0.687944i	$0.758513\pi$
$788$	−8.55144	+	38.0201i	−0.304633	+	1.35441i
$789$	−13.3838	+	1.42734i	−0.476477	+	0.0508146i
$790$	−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
$794$	−0.552616	+	0.0841873i	−0.0196116	+	0.00298769i
$795$	−9.93503	+	22.4064i	−0.352359	+	0.794671i
$796$	1.61538	+	5.17874i	0.0572557	+	0.183555i
$797$	48.8011			1.72863			0.864313	−	0.502955i	$-0.167754\pi$
$797$	48.8011			1.72863			0.864313	+	0.502955i	$0.167754\pi$
$798$	0.315968	+	0.0695816i	0.0111851	+	0.00246316i
$799$		−	11.0503i		−	0.390930i
$800$	3.88030	+	4.11622i	0.137189	+	0.145530i
$801$	4.28050	+	19.8404i	0.151244	+	0.701026i
$802$	−41.6069	+	6.33852i	−1.46919	+	0.223821i
$803$	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
$807$	−23.4394	+	2.49972i	−0.825104	+	0.0879945i
$808$	27.8729	−	41.3016i	0.980566	−	1.45299i
$809$	16.1767	−	9.33961i	0.568742	−	0.328363i	−0.187905	−	0.982187i	$-0.560170\pi$
$809$	16.1767	−	9.33961i	0.568742	−	0.328363i	0.756647	+	0.653824i	$0.226836\pi$
$810$	−12.7103	+	0.668692i	−0.446596	+	0.0234954i
$811$	−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
$816$	−4.42263	+	12.6542i	−0.154823	+	0.442984i
$817$	−0.204334	+	0.353917i	−0.00714875	+	0.0123820i
$818$	−14.6355	−	5.71733i	−0.511719	−	0.199902i
$819$	−24.4049	+	24.4101i	−0.852776	+	0.852956i
$820$	−14.7279	+	15.9739i	−0.514319	+	0.557832i
$821$	5.05691	−	8.75882i	0.176487	−	0.305685i	−0.764188	−	0.644994i	$-0.776860\pi$
$821$	5.05691	−	8.75882i	0.176487	−	0.305685i	0.940675	+	0.339309i	$0.110193\pi$
$822$	18.9239	+	19.0902i	0.660048	+	0.665847i
$823$	−15.8881	+	9.17301i	−0.553825	+	0.319751i	−0.750663	−	0.660685i	$-0.770266\pi$
$823$	−15.8881	+	9.17301i	−0.553825	+	0.319751i	0.196838	+	0.980436i	$0.436933\pi$
$824$	−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	$-0.215611\pi$
$828$	−0.380192	+	43.4624i	−0.0132126	+	1.51042i
$829$	5.64247	−	3.25768i	0.195971	−	0.113144i	−0.398804	−	0.917036i	$-0.630575\pi$
$829$	5.64247	−	3.25768i	0.195971	−	0.113144i	0.594775	+	0.803892i	$0.297241\pi$
$830$	16.0328	−	2.44249i	0.556507	−	0.0847801i
$831$	2.31468	+	21.7042i	0.0802954	+	0.752912i
$832$	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
$836$	−0.454807	−	0.102295i	−0.0157298	−	0.00353794i
$837$	−4.06372	+	4.55495i	−0.140463	+	0.157442i
$838$	−29.1169	−	36.3933i	−1.00583	−	1.25718i
$839$	40.0265			1.38187			0.690934	−	0.722918i	$-0.257200\pi$
$839$	40.0265			1.38187			0.690934	+	0.722918i	$0.257200\pi$
$840$	5.49728	−	11.7380i	0.189674	−	0.404998i
$841$	−28.9905			−0.999674
$842$	26.5443	+	33.1778i	0.914778	+	1.14338i
$843$	13.0863	+	5.80249i	0.450716	+	0.199848i
$844$	−3.36046	+	14.9408i	−0.115672	+	0.514282i
$845$	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
$849$	−45.8901	+	4.89401i	−1.57494	+	0.167962i
$850$	−2.70502	+	0.412092i	−0.0927815	+	0.0141346i
$851$	26.1124	−	15.0760i	0.895121	−	0.516798i
$852$	−17.9276	−	13.3087i	−0.614191	−	0.455949i
$853$			1.81968i			0.0623048i	0.999515	+	0.0311524i	$0.00991772\pi$
$853$			1.81968i			0.0623048i	−0.999515	+	0.0311524i	$0.990082\pi$
$854$	−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	$-0.822683\pi$
$857$	−23.8693	+	13.7810i	−0.815361	+	0.470749i	0.0334528	+	0.999440i	$0.489350\pi$
$858$	35.3209	−	35.0133i	1.20583	−	1.19533i
$859$	−4.80173	+	8.31684i	−0.163833	+	0.283767i	−0.936240	−	0.351361i	$-0.885719\pi$
$859$	−4.80173	+	8.31684i	−0.163833	+	0.283767i	0.772407	+	0.635127i	$0.219052\pi$
$860$	12.0366	+	11.0977i	0.410445	+	0.378429i
$861$	46.4515	+	17.9067i	1.58306	+	0.610260i
$862$	−35.4217	−	13.8374i	−1.20647	−	0.471303i
$863$	−18.8317	+	32.6174i	−0.641038	+	1.11031i	0.344164	+	0.938910i	$0.388162\pi$
$863$	−18.8317	+	32.6174i	−0.641038	+	1.11031i	−0.985201	+	0.171400i	$0.945171\pi$
$864$	25.0430	−	15.3899i	0.851981	−	0.523574i
$865$	−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
$870$	−0.229862	−	0.0626701i	−0.00779305	−	0.00212472i
$871$	12.6522	−	7.30477i	0.428705	−	0.247513i
$872$	22.3826	+	15.1052i	0.757972	+	0.511527i
$873$	−13.9108	−	15.3550i	−0.470808	−	0.519689i
$874$	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	$-0.246987\pi$
$877$	13.7440	+	7.93509i	0.464101	+	0.267949i	−0.249666	+	0.968332i	$0.580321\pi$
$878$	25.9709	−	3.95649i	0.876475	−	0.133525i
$879$	1.23918	−	2.79471i	0.0417966	−	0.0942633i
$880$	−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	$0.948037\pi$
$882$	−29.6431	−	1.81336i	−0.998134	−	0.0610591i
$883$	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
$885$	−21.5850	−	9.57085i	−0.725573	−	0.321721i
$886$	−25.0989	+	3.82364i	−0.843213	+	0.128458i
$887$	18.4017	−	31.8726i	0.617867	−	1.07018i	−0.372007	−	0.928230i	$-0.621330\pi$
$887$	18.4017	−	31.8726i	0.617867	−	1.07018i	0.989874	−	0.141947i	$-0.0453364\pi$
$888$	−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
$891$	−17.3249	−	38.2821i	−0.580405	−	1.28250i
$892$	13.6374	+	3.06732i	0.456615	+	0.102701i
$893$	0.142563	+	0.246926i	0.00477068	+	0.00826307i
$894$	−41.5315	−	11.3232i	−1.38902	−	0.378706i
$895$			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
$900$	5.16971	+	3.04534i	0.172324	+	0.101511i
$901$	23.7113	+	13.6897i	0.789937	+	0.456070i
$902$	−66.8132	−	26.1004i	−2.22464	−	0.869048i
$903$	13.4931	−	35.0021i	0.449021	−	1.16480i
$904$	9.34743	−	4.55623i	0.310891	−	0.151538i
$905$	22.7330	+	13.1249i	0.755670	+	0.436286i
$906$	−26.6020	−	26.8358i	−0.883793	−	0.891558i
$907$	14.7384	+	25.5277i	0.489381	+	0.847632i	0.999925	−	0.0122192i	$-0.00388959\pi$
$907$	14.7384	+	25.5277i	0.489381	+	0.847632i	−0.510545	+	0.859851i	$0.670556\pi$
$908$	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	$-0.746449\pi$
$911$	−42.2061			−1.39835			−0.699175	+	0.714950i	$0.746449\pi$
$912$	−0.0644283	−	0.339824i	−0.00213343	−	0.0112527i
$913$	26.7707	+	46.3682i	0.885980	+	1.53456i
$914$	−0.434654	−	2.85312i	−0.0143771	−	0.0943729i
$915$	−0.250519	−	2.34906i	−0.00828189	−	0.0776574i
$916$	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	$-0.427529\pi$
$919$	−15.3124	−	8.84063i	−0.505110	−	0.291626i	−0.730821	+	0.682569i	$0.760863\pi$
$920$	11.4615	−	16.9835i	0.377875	−	0.559929i
$921$	−14.4874	+	32.6733i	−0.477377	+	1.07662i
$922$	12.8615	−	10.2900i	0.423571	−	0.338884i
$923$		−	28.0297i		−	0.922610i
$924$	42.6990	+	2.80408i	1.40469	+	0.0922474i
$925$		−	4.16233i		−	0.136857i
$926$	−16.5864	−	20.7314i	−0.545064	−	0.681276i
$927$	0.903815	+	4.18924i	0.0296852	+	0.137593i
$928$	0.535440	−	0.126672i	0.0175767	−	0.00415822i
$929$	−7.15076	−	4.12849i	−0.234609	−	0.135452i	0.378088	−	0.925770i	$-0.376582\pi$
$929$	−7.15076	−	4.12849i	−0.234609	−	0.135452i	−0.612696	+	0.790318i	$0.709915\pi$
$930$	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
$933$	−31.9222	+	3.40438i	−1.04508	+	0.111455i
$934$	48.5605	−	7.39786i	1.58895	−	0.242065i
$935$	−4.51669	−	7.82313i	−0.147712	−	0.255844i
$936$	34.2523	+	13.7271i	1.11957	+	0.448685i
$937$	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	−0.930031	−	0.367481i	$-0.880220\pi$
$941$	−24.0272	−	41.6163i	−0.783263	−	1.35665i	0.146768	−	0.989171i	$-0.453113\pi$
$942$	27.2116	+	27.4507i	0.886602	+	0.894392i
$943$	68.1530	+	39.3482i	2.21937	+	1.28135i
$944$	54.3497	−	4.41878i	1.76893	−	0.143819i
$945$	2.12847	−	13.5820i	0.0692391	−	0.441821i
$946$	−19.6671	+	50.3450i	−0.639434	+	1.63686i
$947$	39.4156	+	22.7566i	1.28084	+	0.739491i	0.977001	−	0.213234i	$-0.0683996\pi$
$947$	39.4156	+	22.7566i	1.28084	+	0.739491i	0.303835	+	0.952725i	$0.401733\pi$
$948$	−13.1626	−	30.4003i	−0.427501	−	0.987356i
$949$	−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	$0.750780\pi$
$954$	−21.3558	−	56.1109i	−0.691418	−	1.81666i
$955$	2.53297	+	4.38724i	0.0819651	+	0.141968i
$956$	2.93569	−	13.0522i	0.0949470	−	0.422139i
$957$	−0.0834112	−	0.782128i	−0.00269630	−	0.0252826i
$958$	−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
$962$	−3.85532	−	25.3068i	−0.124300	−	0.815924i
$963$	−4.54090	−	21.0473i	−0.146328	−	0.678241i
$964$	46.4028	−	14.4742i	1.49453	−	0.466183i
$965$	−21.5622			−0.694112
$966$	−45.8480	−	10.0965i	−1.47514	−	0.324850i
$967$		−	6.03768i		−	0.194159i	−0.995277	−	0.0970793i	$-0.969050\pi$
$967$		−	6.03768i		−	0.194159i	0.995277	−	0.0970793i	$-0.0309500\pi$
$968$	−30.4675	−	2.13794i	−0.979264	−	0.0687161i
$969$	0.152941	+	0.0678145i	0.00491318	+	0.00217852i
$970$	1.47098	+	9.65573i	0.0472305	+	0.310027i
$971$	10.4645	+	6.04167i	0.335821	+	0.193886i	0.658422	−	0.752649i	$-0.271224\pi$
$971$	10.4645	+	6.04167i	0.335821	+	0.193886i	−0.322602	+	0.946535i	$0.604557\pi$
$972$	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
$975$	0.798764	+	7.48984i	0.0255809	+	0.239867i
$976$	3.10174	+	4.48816i	0.0992842	+	0.143663i
$977$	−14.8395	+	8.56761i	−0.474759	+	0.274102i	−0.718230	−	0.695806i	$-0.755047\pi$
$977$	−14.8395	+	8.56761i	−0.474759	+	0.274102i	0.243471	+	0.969908i	$0.421714\pi$
$978$	−58.5327	−	15.9585i	−1.87167	−	0.510297i
$979$	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	0.949274	+	0.314449i	$0.101820\pi$
$983$	23.4193	+	40.5633i	0.746958	+	1.29377i	−0.202316	+	0.979320i	$0.564847\pi$
$984$	−1.92556	−	53.1859i	−0.0613846	−	1.69550i
$985$	9.74249	−	16.8745i	0.310422	−	0.537666i
$986$	−0.0968409	+	0.247898i	−0.00308404	+	0.00789469i
$987$	−16.4420	−	20.3632i	−0.523354	−	0.648167i
$988$	0.294329	−	0.319230i	0.00936386	−	0.0101561i
$989$	29.6496	−	51.3546i	0.942802	−	1.63298i
$990$	−3.15443	+	19.5556i	−0.100254	+	0.621517i
$991$	53.5716	−	30.9296i	1.70176	−	0.982510i	0.757775	−	0.652516i	$-0.226287\pi$
$991$	53.5716	−	30.9296i	1.70176	−	0.982510i	0.943983	−	0.329994i	$-0.107047\pi$
$992$	−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
$996$	−23.6789	+	31.8969i	−0.750294	+	1.01069i
$997$	8.10927	−	4.68189i	0.256823	−	0.148277i	−0.366061	−	0.930591i	$-0.619294\pi$
$997$	8.10927	−	4.68189i	0.256823	−	0.148277i	0.622884	+	0.782314i	$0.285961\pi$
$998$	5.44149	+	35.7187i	0.172247	+	1.13065i
$999$	−21.1758	−	4.39990i	−0.669974	−	0.139207i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cq.a.11.36	✓	128	7.4	even	3	inner
840.2.cq.a.11.50	yes	128	168.11	even	6	inner
840.2.cq.a.611.36	yes	128	24.11	even	2	inner
840.2.cq.a.611.50	yes	128	1.1	even	1	trivial
840.2.cq.b.11.15	yes	128	56.11	odd	6
840.2.cq.b.11.29	yes	128	21.11	odd	6
840.2.cq.b.611.15	yes	128	3.2	odd	2
840.2.cq.b.611.29	yes	128	8.3	odd	2

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} +(0.702074 - 1.58338i) q^{3} +(0.438874 - 1.95125i) 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} +(-2.01418 - 2.22330i) q^{9} +(0.212988 + 1.39808i) q^{10} +(-4.04336 + 2.33444i) q^{11} +(-2.78145 - 2.06483i) 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} +(-4.18850 - 0.675629i) q^{18} +(-0.0249616 + 0.0432347i) q^{19} +(1.47040 + 1.35570i) q^{20} +(1.64832 - 4.27587i) q^{21} +(-2.40255 + 6.15017i) q^{22} +(3.62201 - 6.27350i) q^{23} +(-4.89577 + 0.177248i) 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} +(2.36323 + 0.644317i) q^{30} +(1.01737 - 0.587378i) q^{31} +(-5.50490 + 1.30233i) q^{32} +(0.857558 + 8.04113i) 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} +(0.0106330 + 0.0697967i) q^{38} +(-6.88577 - 3.05317i) q^{39} +(2.82149 + 0.197987i) q^{40} +10.8636i q^{41} +(-1.95750 - 6.17804i) q^{42} +8.18596 q^{43} +(2.78055 + 8.91415i) q^{44} +(2.93253 - 0.632683i) q^{45} +(-1.54289 - 10.1277i) 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} +(-0.355377 - 3.33229i) q^{51} +(-8.48557 - 1.90856i) q^{52} +(7.07548 + 12.2551i) q^{53} +(-4.01042 + 6.15764i) 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} +(3.17892 - 1.37639i) q^{60} +(-1.18119 - 0.681959i) q^{61} +(0.604515 - 1.54747i) q^{62} +(-5.61308 - 5.61189i) q^{63} +(-4.92836 + 6.30169i) q^{64} +(3.76615 + 2.17439i) q^{65} +(8.05128 + 8.12202i) 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} +(-3.15655 + 7.87631i) q^{72} +(-4.51719 - 7.82400i) q^{73} +(5.81929 - 0.886529i) q^{74} +(-1.72228 + 0.183676i) 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} +(3.29064 - 2.27414i) q^{80} +(-0.886135 + 8.95627i) q^{81} +(9.59797 + 11.9965i) q^{82} -11.4677i q^{83} +(-7.61990 - 5.09285i) q^{84} +1.93481i q^{85} +(9.03960 - 7.23225i) q^{86} +(-0.0682880 + 0.154009i) q^{87} +(10.9461 + 7.38712i) 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} +(-0.215774 - 2.02326i) q^{93} +(-1.21644 - 7.98487i) q^{94} +(-0.0249616 - 0.0432347i) q^{95} +(-1.80277 + 9.63068i) q^{96} +6.90641 q^{97} +(7.08202 - 6.91700i) q^{98} +(13.3342 + 4.28763i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 64 q^{5} - 12 q^{12} - 6 q^{14} + 8 q^{16} + 14 q^{18} + 8 q^{21} + 4 q^{22} - 64 q^{25} - 16 q^{26} - 6 q^{28} - 10 q^{32} + 24 q^{34} + 20 q^{36} - 16 q^{38} + 16 q^{42} + 6 q^{44} + 8 q^{46}+ \cdots + 14 q^{98}+O(q^{100}) \) 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

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