LMFDB - Embedded newform 840.2.cq.b.11.29

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			11.29
Character	$\chi$	$=$	840.11
Dual form			840.2.cq.b.611.29

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.212988 - 1.39808i) q^{2} +(0.702074 + 1.58338i) q^{3} +(-1.90927 + 0.595551i) 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} +(-2.01418 + 2.22330i) q^{9} +(1.10428 - 0.883495i) q^{10} +(-4.04336 - 2.33444i) q^{11} +(-2.28343 - 2.60498i) q^{12} -4.34878i q^{13} +(0.380114 + 3.72230i) q^{14} +(-1.02021 + 1.39970i) q^{15} +(3.29064 - 2.27414i) q^{16} +(1.67559 + 0.967404i) q^{17} +(3.53736 + 2.34246i) 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} +(-3.15563 + 3.74726i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-6.07996 + 0.926240i) q^{26} +(-4.93444 - 1.62829i) q^{27} +(5.12312 - 1.32424i) q^{28} +0.0972660 q^{29} +(2.17420 + 1.12822i) q^{30} +(-1.01737 - 0.587378i) q^{31} +(-3.88030 - 4.11622i) q^{32} +(0.857558 - 8.04113i) 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} +(-0.0551292 + 0.0441068i) q^{38} +(6.88577 - 3.05317i) q^{39} +(-1.58221 + 2.34449i) q^{40} -10.8636i q^{41} +(-5.62695 + 3.21520i) q^{42} +8.18596 q^{43} +(9.11016 + 2.04905i) q^{44} +(-2.93253 - 0.632683i) q^{45} +(-7.99942 + 6.40005i) 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} +(-0.355377 + 3.33229i) q^{51} +(2.58992 + 8.30300i) q^{52} +(-7.07548 + 12.2551i) q^{53} +(-1.22551 + 7.24556i) q^{54} -4.66887i q^{55} +(-2.94256 - 6.88050i) q^{56} +(0.0509321 - 0.0698776i) q^{57} +(-0.0207165 - 0.135986i) q^{58} +(-11.8059 - 6.81613i) q^{59} +(1.11426 - 3.28000i) 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} +(-11.4248 + 0.513730i) q^{66} +(1.67973 - 2.90938i) q^{67} +(-3.77530 - 0.849136i) q^{68} +(7.39041 - 10.1395i) q^{69} +(-3.03355 + 2.19034i) q^{70} -6.44542 q^{71} +(-8.14883 - 2.36571i) q^{72} +(-4.51719 + 7.82400i) q^{73} +(3.67740 + 4.59639i) q^{74} +(-1.72228 - 0.183676i) 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} +(3.61478 + 1.71271i) q^{80} +(-0.886135 - 8.95627i) q^{81} +(-15.1883 + 2.31383i) q^{82} +11.4677i q^{83} +(5.69358 + 7.18214i) q^{84} +1.93481i q^{85} +(-1.74351 - 11.4446i) q^{86} +(0.0682880 + 0.154009i) q^{87} +(0.924378 - 13.1732i) 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} +(0.215774 - 2.02326i) q^{93} +(-6.30688 + 5.04590i) q^{94} +(0.0249616 - 0.0432347i) q^{95} +(3.79328 - 9.03388i) q^{96} +6.90641 q^{97} +(-0.517999 - 9.88593i) q^{98} +(13.3342 - 4.28763i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 64 q^{5} + 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 $

$2$	−0.212988	−	1.39808i	−0.150606	−	0.988594i
$2$	−0.212988	−	1.39808i	−0.150606	−	0.988594i
$3$	0.702074	+	1.58338i	0.405343	+	0.914165i
$3$	0.702074	+	1.58338i	0.405343	+	0.914165i
$4$	−1.90927	+	0.595551i	−0.954636	+	0.297776i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	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
$9$	−2.01418	+	2.22330i	−0.671394	+	0.741100i
$10$	1.10428	−	0.883495i	0.349204	−	0.279386i
$11$	−4.04336	−	2.33444i	−1.21912	−	0.703859i	−0.254390	−	0.967102i	$-0.581875\pi$
$11$	−4.04336	−	2.33444i	−1.21912	−	0.703859i	−0.964730	+	0.263242i	$0.915208\pi$
$12$	−2.28343	−	2.60498i	−0.659171	−	0.751993i
$13$		−	4.34878i		−	1.20613i	−0.797690	−	0.603067i	$-0.793945\pi$
$13$		−	4.34878i		−	1.20613i	0.797690	−	0.603067i	$-0.206055\pi$
$14$	0.380114	+	3.72230i	0.101590	+	0.994826i
$15$	−1.02021	+	1.39970i	−0.263417	+	0.361402i
$16$	3.29064	−	2.27414i	0.822659	−	0.568534i
$17$	1.67559	+	0.967404i	0.406391	+	0.234630i	0.689238	−	0.724535i	$-0.257945\pi$
$17$	1.67559	+	0.967404i	0.406391	+	0.234630i	−0.282847	+	0.959165i	$0.591279\pi$
$18$	3.53736	+	2.34246i	0.833763	+	0.552122i
$19$	−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
$21$	−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	−0.945255	−	0.326333i	$-0.894187\pi$
$23$	−3.62201	−	6.27350i	−0.755240	−	1.30811i	0.190014	−	0.981781i	$-0.439147\pi$
$24$	−3.15563	+	3.74726i	−0.644141	+	0.764907i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−6.07996	+	0.926240i	−1.19238	+	0.181651i
$27$	−4.93444	−	1.62829i	−0.949633	−	0.313365i
$28$	5.12312	−	1.32424i	0.968179	−	0.250257i
$29$	0.0972660			0.0180618			0.00903092	−	0.999959i	$-0.497125\pi$
$29$	0.0972660			0.0180618			0.00903092	+	0.999959i	$0.497125\pi$
$30$	2.17420	+	1.12822i	0.396952	+	0.205983i
$31$	−1.01737	−	0.587378i	−0.182725	−	0.105496i	0.405847	−	0.913941i	$-0.366976\pi$
$31$	−1.01737	−	0.587378i	−0.182725	−	0.105496i	−0.588572	+	0.808445i	$0.700310\pi$
$32$	−3.88030	−	4.11622i	−0.685947	−	0.727652i
$33$	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
$36$	2.52153	−	5.44443i	0.420256	−	0.907406i
$37$	−3.60469	+	2.08117i	−0.592607	+	0.342142i	−0.766128	−	0.642689i	$-0.777819\pi$
$37$	−3.60469	+	2.08117i	−0.592607	+	0.342142i	0.173521	+	0.984830i	$0.444486\pi$
$38$	−0.0551292	+	0.0441068i	−0.00894313	+	0.00715507i
$39$	6.88577	−	3.05317i	1.10261	−	0.488898i
$40$	−1.58221	+	2.34449i	−0.250169	+	0.370696i
$41$		−	10.8636i		−	1.69662i	−0.529504	−	0.848308i	$-0.677622\pi$
$41$		−	10.8636i		−	1.69662i	0.529504	−	0.848308i	$-0.322378\pi$
$42$	−5.62695	+	3.21520i	−0.868257	+	0.496116i
$43$	8.18596			1.24835			0.624173	−	0.781286i	$-0.285436\pi$
$43$	8.18596			1.24835			0.624173	+	0.781286i	$0.285436\pi$
$44$	9.11016	+	2.04905i	1.37341	+	0.308905i
$45$	−2.93253	−	0.632683i	−0.437155	−	0.0943148i
$46$	−7.99942	+	6.40005i	−1.17945	+	0.943635i
$47$	−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
$51$	−0.355377	+	3.33229i	−0.0497627	+	0.466614i
$52$	2.58992	+	8.30300i	0.359157	+	1.15142i
$53$	−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	$0.742315\pi$
$54$	−1.22551	+	7.24556i	−0.166771	+	0.985996i
$55$		−	4.66887i		−	0.629551i
$56$	−2.94256	−	6.88050i	−0.393216	−	0.919446i
$57$	0.0509321	−	0.0698776i	0.00674612	−	0.00925551i
$58$	−0.0207165	−	0.135986i	−0.00272021	−	0.0178558i
$59$	−11.8059	−	6.81613i	−1.53699	−	0.887384i	−0.999013	−	0.0444272i	$-0.985854\pi$
$59$	−11.8059	−	6.81613i	−1.53699	−	0.887384i	−0.537981	−	0.842957i	$-0.680813\pi$
$60$	1.11426	−	3.28000i	0.143851	−	0.423447i
$61$	1.18119	−	0.681959i	0.151236	−	0.0873160i	−0.422472	−	0.906376i	$-0.638838\pi$
$61$	1.18119	−	0.681959i	0.151236	−	0.0873160i	0.573708	+	0.819060i	$0.305504\pi$
$62$	−0.604515	+	1.54747i	−0.0767735	+	0.196529i
$63$	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
$66$	−11.4248	+	0.513730i	−1.40630	+	0.0632358i
$67$	1.67973	−	2.90938i	0.205212	−	0.355437i	−0.744989	−	0.667077i	$-0.767545\pi$
$67$	1.67973	−	2.90938i	0.205212	−	0.355437i	0.950200	+	0.311640i	$0.100878\pi$
$68$	−3.77530	−	0.849136i	−0.457823	−	0.102973i
$69$	7.39041	−	10.1395i	0.889701	−	1.22065i
$70$	−3.03355	+	2.19034i	−0.362578	+	0.261795i
$71$	−6.44542			−0.764931			−0.382466	−	0.923970i	$-0.624925\pi$
$71$	−6.44542			−0.764931			−0.382466	+	0.923970i	$0.624925\pi$
$72$	−8.14883	−	2.36571i	−0.960349	−	0.278802i
$73$	−4.51719	+	7.82400i	−0.528697	+	0.915730i	0.470743	+	0.882270i	$0.343986\pi$
$73$	−4.51719	+	7.82400i	−0.528697	+	0.915730i	−0.999440	+	0.0334596i	$0.989347\pi$
$74$	3.67740	+	4.59639i	0.427489	+	0.534319i
$75$	−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
$78$	−5.73517	−	8.97659i	−0.649380	−	1.01640i
$79$	−8.28188	+	4.78155i	−0.931785	+	0.537966i	−0.887376	−	0.461047i	$-0.847474\pi$
$79$	−8.28188	+	4.78155i	−0.931785	+	0.537966i	−0.0444090	+	0.999013i	$0.514140\pi$
$80$	3.61478	+	1.71271i	0.404145	+	0.191486i
$81$	−0.886135	−	8.95627i	−0.0984594	−	0.995141i
$82$	−15.1883	+	2.31383i	−1.67726	+	0.255520i
$83$			11.4677i			1.25875i	0.777103	+	0.629373i	$0.216688\pi$
$83$			11.4677i			1.25875i	−0.777103	+	0.629373i	$0.783312\pi$
$84$	5.69358	+	7.18214i	0.621221	+	0.783635i
$85$			1.93481i			0.209859i
$86$	−1.74351	−	11.4446i	−0.188008	−	1.23411i
$87$	0.0682880	+	0.154009i	0.00732124	+	0.0165115i
$88$	0.924378	−	13.1732i	0.0985390	−	1.40427i
$89$	−5.85921	+	3.38281i	−0.621075	+	0.358578i	−0.777287	−	0.629146i	$-0.783405\pi$
$89$	−5.85921	+	3.38281i	−0.621075	+	0.358578i	0.156213	+	0.987723i	$0.450071\pi$
$90$	−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
$93$	0.215774	−	2.02326i	0.0223747	−	0.209803i
$94$	−6.30688	+	5.04590i	−0.650505	+	0.520445i
$95$	0.0249616	−	0.0432347i	0.00256100	−	0.00443579i
$96$	3.79328	−	9.03388i	0.387150	−	0.922017i
$97$	6.90641			0.701239			0.350620	−	0.936518i	$-0.385971\pi$
$97$	6.90641			0.701239			0.350620	+	0.936518i	$0.385971\pi$
$98$	−0.517999	−	9.88593i	−0.0523258	−	0.998630i
$99$	13.3342	−	4.28763i	1.34014	−	0.430923i
$100$	0.438874	−	1.95125i	0.0438874	−	0.195125i
$101$	−8.80824	+	15.2563i	−0.876453	+	1.51806i	−0.0212462	+	0.999774i	$0.506763\pi$
$101$	−8.80824	+	15.2563i	−0.876453	+	1.51806i	−0.855207	+	0.518287i	$0.826570\pi$
$102$	4.73451	−	0.212893i	0.468786	−	0.0210795i
$103$	1.23715	−	0.714272i	0.121900	−	0.0703793i	−0.437810	−	0.899068i	$-0.644246\pi$
$103$	1.23715	−	0.714272i	0.121900	−	0.0703793i	0.559710	+	0.828688i	$0.310912\pi$
$104$	11.0567	−	5.38937i	1.08420	−	0.528471i
$105$	2.87885	−	3.56542i	0.280947	−	0.347949i
$106$	18.6406	+	7.28192i	1.81054	+	0.707282i
$107$	6.21564	−	3.58860i	0.600889	−	0.346923i	−0.168502	−	0.985701i	$-0.553893\pi$
$107$	6.21564	−	3.58860i	0.600889	−	0.346923i	0.769391	+	0.638778i	$0.220560\pi$
$108$	10.3909	+	0.170146i	0.999866	+	0.0163723i
$109$	8.26788	+	4.77346i	0.791919	+	0.457215i	0.840638	−	0.541598i	$-0.182180\pi$
$109$	8.26788	+	4.77346i	0.791919	+	0.457215i	−0.0487186	+	0.998813i	$0.515514\pi$
$110$	−6.52747	+	0.994416i	−0.622370	+	0.0948139i
$111$	−5.82604	−	4.24645i	−0.552983	−	0.403056i
$112$	−8.99278	+	5.57941i	−0.849738	+	0.527205i
$113$		−	3.67651i		−	0.345857i	−0.984934	−	0.172928i	$-0.944677\pi$
$113$		−	3.67651i		−	0.345857i	0.984934	−	0.172928i	$-0.0553229\pi$
$114$	−0.108543	−	0.0563241i	−0.0101659	−	0.00527524i
$115$	3.62201	−	6.27350i	0.337754	−	0.585007i
$116$	−0.185707	+	0.0579269i	−0.0172425	+	0.00537837i
$117$	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
$120$	−4.82304	−	0.859229i	−0.440281	−	0.0784365i
$121$	5.39919	+	9.35168i	0.490836	+	0.850153i
$122$	−1.20502	−	1.50615i	−0.109097	−	0.136360i
$123$	17.2013	−	7.62708i	1.55099	−	0.687711i
$124$	2.29225	+	0.515569i	0.205850	+	0.0462995i
$125$	−1.00000			−0.0894427
$126$	−9.04141	−	6.65228i	−0.805473	−	0.592633i
$127$		−	2.19395i		−	0.194681i	−0.995251	−	0.0973407i	$-0.968966\pi$
$127$		−	2.19395i		−	0.194681i	0.995251	−	0.0973407i	$-0.0310336\pi$
$128$	9.85997	+	5.54807i	0.871506	+	0.490384i
$129$	5.74715	+	12.9615i	0.506008	+	1.14119i
$130$	−3.84212	−	4.80228i	−0.336977	−	0.421187i
$131$	−1.85389	+	1.07034i	−0.161975	+	0.0935164i	−0.578796	−	0.815472i	$-0.696477\pi$
$131$	−1.85389	+	1.07034i	−0.161975	+	0.0935164i	0.416821	+	0.908988i	$0.363144\pi$
$132$	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
$135$	−1.05707	−	5.08749i	−0.0909785	−	0.437862i
$136$	−0.383067	+	5.45904i	−0.0328478	+	0.468109i
$137$	−9.50363	−	5.48692i	−0.811950	−	0.468779i	0.0356828	−	0.999363i	$-0.488639\pi$
$137$	−9.50363	−	5.48692i	−0.811950	−	0.468779i	−0.847632	+	0.530584i	$0.821973\pi$
$138$	−15.7499	−	8.17282i	−1.34072	−	0.695716i
$139$	−8.15854			−0.691999			−0.345999	−	0.938235i	$-0.612460\pi$
$139$	−8.15854			−0.691999			−0.345999	+	0.938235i	$0.612460\pi$
$140$	3.70839	+	3.77464i	0.313416	+	0.319015i
$141$	5.82672	−	7.99413i	0.490698	−	0.673227i
$142$	1.37280	+	9.01124i	0.115203	+	0.756206i
$143$	−10.1520	+	17.5837i	−0.848949	+	1.47042i
$144$	−1.57185	+	11.8966i	−0.130988	+	0.991384i
$145$	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	−0.961055	−	0.276357i	$-0.910873\pi$
$149$	−8.78701	−	15.2195i	−0.719860	−	1.24683i	0.241195	−	0.970477i	$-0.422461\pi$
$150$	0.110033	+	2.44702i	0.00898416	+	0.199798i
$151$	−13.3596	−	7.71315i	−1.08719	−	0.627688i	−0.154361	−	0.988015i	$-0.549332\pi$
$151$	−13.3596	−	7.71315i	−1.08719	−	0.627688i	−0.932826	+	0.360327i	$0.882665\pi$
$152$	0.0789887	−	0.117044i	0.00640683	−	0.00949353i
$153$	−5.52578	+	1.77682i	−0.446733	+	0.143647i
$154$	7.15254	−	15.9380i	0.576368	−	1.28432i
$155$		−	1.17476i		−	0.0943587i
$156$	−11.3285	+	9.93015i	−0.907005	+	0.795049i
$157$	13.6657	+	7.88990i	1.09064	+	0.629682i	0.933747	−	0.357933i	$-0.116518\pi$
$157$	13.6657	+	7.88990i	1.09064	+	0.629682i	0.156895	+	0.987615i	$0.449852\pi$
$158$	8.44894	+	10.5603i	0.672162	+	0.840136i
$159$	−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
$162$	−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	$0.411508\pi$
$164$	6.46985	+	20.7416i	0.505211	+	1.61965i
$165$	7.39260	−	3.27790i	0.575513	−	0.255184i
$166$	16.0328	−	2.44249i	1.24439	−	0.189574i
$167$	1.69273			0.130987			0.0654936	−	0.997853i	$-0.479138\pi$
$167$	1.69273			0.130987			0.0654936	+	0.997853i	$0.479138\pi$
$168$	8.82856	−	9.48982i	0.681138	−	0.732155i
$169$	−5.91189			−0.454761
$170$	2.70502	−	0.412092i	0.207466	−	0.0316060i
$171$	0.146401	+	0.0315855i	0.0111956	+	0.00241540i
$172$	−15.6292	+	4.87516i	−1.19172	+	0.371727i
$173$	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
$177$	2.50391	−	23.4786i	0.188205	−	1.76476i
$178$	5.97740	+	7.47116i	0.448025	+	0.559987i
$179$	0.932643	+	0.538462i	0.0697090	+	0.0402465i	0.534449	−	0.845200i	$-0.320519\pi$
$179$	0.932643	+	0.538462i	0.0697090	+	0.0402465i	−0.464740	+	0.885447i	$0.653852\pi$
$180$	5.97579	−	0.538505i	0.445409	−	0.0401378i
$181$		−	26.2498i		−	1.95113i	−0.219710	−	0.975565i	$-0.570511\pi$
$181$		−	26.2498i		−	1.95113i	0.219710	−	0.975565i	$-0.429489\pi$
$182$	16.1875	−	1.65303i	1.19989	−	0.122531i
$183$	1.90908	+	1.39148i	0.141123	+	0.102861i
$184$	11.4615	−	16.9835i	0.844955	−	1.25204i
$185$	−3.60469	−	2.08117i	−0.265022	−	0.153010i
$186$	−2.87465	+	0.129262i	−0.210779	+	0.00947795i
$187$	−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	$-0.225338\pi$
$191$	−2.53297	−	4.38724i	−0.183279	−	0.317449i	−0.942995	+	0.332806i	$0.892005\pi$
$192$	−13.4380	−	3.37921i	−0.969807	−	0.243873i
$193$	10.7811	−	18.6734i	0.776041	−	1.34414i	−0.158166	−	0.987412i	$-0.550558\pi$
$193$	10.7811	−	18.6734i	0.776041	−	1.34414i	0.934208	−	0.356730i	$-0.116108\pi$
$194$	−1.47098	−	9.65573i	−0.105611	−	0.693241i
$195$	6.08701	+	4.43667i	0.435900	+	0.317716i
$196$	−13.7110	+	2.82979i	−0.979359	+	0.202128i
$197$	19.4850			1.38825			0.694124	−	0.719856i	$-0.255792\pi$
$197$	19.4850			1.38825			0.694124	+	0.719856i	$0.255792\pi$
$198$	−8.83450	−	17.7291i	−0.627841	−	1.25996i
$199$	2.34902	+	1.35621i	0.166518	+	0.0961390i	0.580943	−	0.813944i	$-0.302684\pi$
$199$	2.34902	+	1.35621i	0.166518	+	0.0961390i	−0.414425	+	0.910083i	$0.636017\pi$
$200$	−2.82149	−	0.197987i	−0.199509	−	0.0139998i
$201$	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
$204$	−1.30604	−	6.57389i	−0.0914409	−	0.460265i
$205$	9.40819	−	5.43182i	0.657096	−	0.379375i
$206$	−1.26211	−	1.57751i	−0.0879354	−	0.109911i
$207$	21.2433	+	4.58316i	1.47651	+	0.318552i
$208$	−9.88972	−	14.3103i	−0.685729	−	0.992238i
$209$			0.233085i			0.0161228i
$210$	−5.59791	−	3.26548i	−0.386293	−	0.225340i
$211$	−7.65701			−0.527130			−0.263565	−	0.964642i	$-0.584898\pi$
$211$	−7.65701			−0.527130			−0.263565	+	0.964642i	$0.584898\pi$
$212$	6.21049	−	27.6121i	0.426538	−	1.89641i
$213$	−4.52517	−	10.2056i	−0.310059	−	0.699273i
$214$	−6.34102	−	7.92565i	−0.433463	−	0.541786i
$215$	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
$219$	−15.5598	−	1.65939i	−1.05143	−	0.112131i
$220$	2.78055	+	8.91415i	0.187465	+	0.600992i
$221$	4.20703	−	7.28679i	0.282995	−	0.490162i
$222$	−4.69602	+	9.04973i	−0.315176	+	0.607378i
$223$			6.98906i			0.468022i	0.972234	+	0.234011i	$0.0751852\pi$
$223$			6.98906i			0.468022i	−0.972234	+	0.234011i	$0.924815\pi$
$224$	9.71584	+	11.3843i	0.649167	+	0.760646i
$225$	−0.918344	−	2.85598i	−0.0612229	−	0.190399i
$226$	−5.14006	+	0.783054i	−0.341912	+	0.0520880i
$227$	−13.3146	−	7.68720i	−0.883723	−	0.510218i	−0.0118388	−	0.999930i	$-0.503768\pi$
$227$	−13.3146	−	7.68720i	−0.883723	−	0.510218i	−0.871884	+	0.489712i	$0.837102\pi$
$228$	−0.0556275	+	0.163748i	−0.00368402	+	0.0108445i
$229$	−7.72565	+	4.46041i	−0.510525	+	0.294752i	−0.733050	−	0.680175i	$-0.761904\pi$
$229$	−7.72565	+	4.46041i	−0.510525	+	0.294752i	0.222524	+	0.974927i	$0.428570\pi$
$230$	−9.54231	−	3.72768i	−0.629202	−	0.245796i
$231$	−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	−0.413024	−	0.910720i	$-0.635528\pi$
$233$	2.58227	−	1.49088i	0.169170	−	0.0976706i	0.582195	+	0.813049i	$0.302194\pi$
$234$	10.1868	−	15.3832i	0.665934	−	1.00563i
$235$	2.85565	−	4.94613i	0.186282	−	0.322650i
$236$	26.6000	+	5.98283i	1.73151	+	0.389449i
$237$	−13.3855	−	9.75636i	−0.869482	−	0.633744i
$238$	−2.96405	+	6.60478i	−0.192131	+	0.428125i
$239$	−6.68915			−0.432685			−0.216343	−	0.976318i	$-0.569413\pi$
$239$	−6.68915			−0.432685			−0.216343	+	0.976318i	$0.569413\pi$
$240$	−0.174021	+	6.92602i	−0.0112330	+	0.447072i
$241$	12.1520	−	21.0478i	0.782776	−	1.35581i	−0.147543	−	0.989056i	$-0.547136\pi$
$241$	12.1520	−	21.0478i	0.782776	−	1.35581i	0.930319	−	0.366752i	$-0.119530\pi$
$242$	11.9245	−	9.54032i	0.766533	−	0.613275i
$243$	13.5590	−	7.69106i	0.869813	−	0.493381i
$244$	−1.84907	+	2.00550i	−0.118374	+	0.128389i
$245$	2.88476	+	6.37794i	0.184301	+	0.407472i
$246$	−14.3270	−	22.4243i	−0.913454	−	1.42972i
$247$	−0.188018	+	0.108552i	−0.0119633	+	0.00690702i
$248$	0.232587	−	3.31456i	0.0147693	−	0.210475i
$249$	−18.1578	+	8.05119i	−1.15070	+	0.510224i
$250$	0.212988	+	1.39808i	0.0134706	+	0.0884225i
$251$			4.12014i			0.260061i	0.991510	+	0.130030i	$0.0415075\pi$
$251$			4.12014i			0.260061i	−0.991510	+	0.130030i	$0.958493\pi$
$252$	−7.37473	+	14.0575i	−0.464564	+	0.885539i
$253$			33.8214i			2.12633i
$254$	−3.06732	+	0.467286i	−0.192461	+	0.0293201i
$255$	−3.06354	+	1.35838i	−0.191846	+	0.0850650i
$256$	5.65660	−	14.9667i	0.353537	−	0.935420i
$257$	5.26625	−	3.04047i	0.328500	−	0.189659i	−0.326675	−	0.945137i	$-0.605928\pi$
$257$	5.26625	−	3.04047i	0.328500	−	0.189659i	0.655175	+	0.755477i	$0.272595\pi$
$258$	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
$261$	−0.195911	+	0.216252i	−0.0121266	+	0.0133856i
$262$	1.89129	+	2.36392i	0.116844	+	0.146044i
$263$	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	$0.0896538\pi$
$264$	21.5071	−	7.78491i	1.32367	−	0.479128i
$265$	−14.1510			−0.869287
$266$	0.151444	−	0.109348i	0.00928564	−	0.00670459i
$267$	−9.46988	−	6.90236i	−0.579547	−	0.422418i
$268$	−1.47438	+	6.55515i	−0.0900619	+	0.400420i
$269$	6.80473	−	11.7861i	0.414892	−	0.718613i	−0.580525	−	0.814242i	$-0.697153\pi$
$269$	6.80473	−	11.7861i	0.414892	−	0.718613i	0.995417	+	0.0956287i	$0.0304862\pi$
$270$	−6.88759	+	2.56146i	−0.419166	+	0.155885i
$271$	6.21337	−	3.58729i	0.377436	−	0.217913i	−0.299266	−	0.954170i	$-0.596742\pi$
$271$	6.21337	−	3.58729i	0.377436	−	0.217913i	0.676702	+	0.736257i	$0.263409\pi$
$272$	7.71378	−	0.627153i	0.467717	−	0.0380267i
$273$	−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
$276$	−8.07173	+	23.7604i	−0.485861	+	1.43021i
$277$	10.9137	+	6.30101i	0.655738	+	0.378591i	0.790651	−	0.612267i	$-0.209742\pi$
$277$	10.9137	+	6.30101i	0.655738	+	0.378591i	−0.134913	+	0.990857i	$0.543075\pi$
$278$	1.73768	+	11.4063i	0.104219	+	0.684106i
$279$	3.35508	−	1.07883i	0.200864	−	0.0645879i
$280$	4.48741	−	5.98858i	0.268174	−	0.357886i
$281$		−	8.26478i		−	0.493035i	−0.969138	−	0.246518i	$-0.920714\pi$
$281$		−	8.26478i		−	0.493035i	0.969138	−	0.246518i	$-0.0792864\pi$
$282$	−12.4175	−	6.44358i	−0.739450	−	0.383710i
$283$	−13.3224	+	23.0751i	−0.791937	+	1.37167i	0.132829	+	0.991139i	$0.457594\pi$
$283$	−13.3224	+	23.0751i	−0.791937	+	1.37167i	−0.924766	+	0.380536i	$0.875740\pi$
$284$	12.3061	−	3.83858i	0.730231	−	0.227778i
$285$	0.0859818	+	0.00916965i	0.00509312	+	0.000543163i
$286$	26.7457	+	10.4481i	1.58151	+	0.617812i
$287$	−1.41975	+	28.7074i	−0.0838051	+	1.69454i
$288$	16.9672	−	0.336258i	0.999804	−	0.0198142i
$289$	−6.62826	−	11.4805i	−0.389898	−	0.675322i
$290$	0.107409	−	0.0859340i	0.00630727	−	0.00504622i
$291$	4.84881	+	10.9355i	0.284242	+	0.641048i
$292$	3.96495	−	17.6284i	0.232031	−	1.03162i
$293$	−1.76503			−0.103114			−0.0515571	−	0.998670i	$-0.516418\pi$
$293$	−1.76503			−0.103114			−0.0515571	+	0.998670i	$0.516418\pi$
$294$	15.2895	−	7.76085i	0.891703	−	0.452622i
$295$		−	13.6323i		−	0.793700i
$296$	−9.75854	−	6.58567i	−0.567204	−	0.382784i
$297$	16.1506	+	18.1029i	0.937151	+	1.05044i
$298$	−19.4067	+	15.5266i	−1.12420	+	0.899429i
$299$	−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
$303$	−30.3406	−	3.23572i	−1.74302	−	0.185887i
$304$	−0.180461	−	0.0855037i	−0.0103502	−	0.00490397i
$305$	1.18119	+	0.681959i	0.0676346	+	0.0390489i
$306$	3.66107	+	7.34706i	0.209289	+	0.420003i
$307$	−20.6352			−1.17771			−0.588856	−	0.808238i	$-0.700421\pi$
$307$	−20.6352			−1.17771			−0.588856	+	0.808238i	$0.700421\pi$
$308$	−23.8060	−	6.60524i	−1.35647	−	0.376368i
$309$	1.99954	+	1.45741i	0.113750	+	0.0829094i
$310$	−1.64241	+	0.250209i	−0.0932824	+	0.0142109i
$311$	9.26739	−	16.0516i	0.525505	−	0.910202i	−0.474053	−	0.880496i	$-0.657210\pi$
$311$	9.26739	−	16.0516i	0.525505	−	0.910202i	0.999559	−	0.0297058i	$-0.00945705\pi$
$312$	16.2960	+	13.7232i	0.922580	+	0.776921i
$313$	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
$315$	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	$-0.0166864\pi$
$317$	8.08209	+	13.9986i	0.453935	+	0.786239i	−0.544691	+	0.838637i	$0.683353\pi$
$318$	1.55707	+	34.6277i	0.0873163	+	1.94182i
$319$	−0.393282	−	0.227061i	−0.0220195	−	0.0127130i
$320$	−7.92160	−	1.11724i	−0.442831	−	0.0624555i
$321$	10.0460	+	7.32225i	0.560711	+	0.408688i
$322$	21.9751	−	15.8668i	1.22462	−	0.884224i
$323$		−	0.0965917i		−	0.00537450i
$324$	7.02579	+	16.5722i	0.390322	+	0.920679i
$325$	3.76615	+	2.17439i	0.208909	+	0.120613i
$326$	27.3509	−	21.8825i	1.51483	−	1.21196i
$327$	−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
$330$	−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	$-0.452852\pi$
$332$	−6.82961	−	21.8950i	−0.374824	−	1.20164i
$333$	2.63344	−	12.2062i	0.144311	−	0.668893i
$334$	−0.360531	−	2.36657i	−0.0197274	−	0.129493i
$335$	3.35946			0.183547
$336$	−15.1479	−	10.3218i	−0.826387	−	0.563102i
$337$	−17.1854			−0.936146			−0.468073	−	0.883690i	$-0.655052\pi$
$337$	−17.1854			−0.936146			−0.468073	+	0.883690i	$0.655052\pi$
$338$	1.25916	+	8.26531i	0.0684895	+	0.449574i
$339$	5.82131	−	2.58118i	0.316170	−	0.140191i
$340$	−1.15228	−	3.69408i	−0.0624910	−	0.200339i
$341$	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
$345$	12.4762	+	1.33055i	0.671698	+	0.0716343i
$346$	3.62379	−	2.89926i	0.194816	−	0.155865i
$347$	25.5899	+	14.7743i	1.37374	+	0.793128i	0.991396	−	0.130894i	$-0.0417846\pi$
$347$	25.5899	+	14.7743i	1.37374	+	0.793128i	0.382341	+	0.924021i	$0.375118\pi$
$348$	−0.222100	−	0.253376i	−0.0119058	−	0.0135824i
$349$			27.6360i			1.47932i	0.672981	+	0.739659i	$0.265013\pi$
$349$			27.6360i			1.47932i	−0.672981	+	0.739659i	$0.734987\pi$
$350$	−3.41366	−	1.53196i	−0.182468	−	0.0818868i
$351$	−7.08109	+	21.4588i	−0.377961	+	1.14538i
$352$	6.08041	+	25.7017i	0.324087	+	1.36990i
$353$	−23.5636	−	13.6045i	−1.25417	−	0.724093i	−0.282231	−	0.959346i	$-0.591075\pi$
$353$	−23.5636	−	13.6045i	−1.25417	−	0.724093i	−0.971934	+	0.235254i	$0.924408\pi$
$354$	−33.3583	+	1.50000i	−1.77298	+	0.0797240i
$355$	−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	$-0.103419\pi$
$359$	3.74005	+	6.47797i	0.197393	+	0.341894i	−0.750290	+	0.661109i	$0.770086\pi$
$360$	−2.02565	−	8.23995i	−0.106761	−	0.434283i
$361$	9.49875	−	16.4523i	0.499934	−	0.865912i
$362$	−36.6994	+	5.59090i	−1.92888	+	0.293851i
$363$	−11.0166	+	15.1146i	−0.578223	+	0.793308i
$364$	−5.75882	−	22.2793i	−0.301844	−	1.16775i
$365$	−9.03438			−0.472881
$366$	1.53880	−	2.96543i	0.0804342	−	0.155005i
$367$	15.9053	+	9.18291i	0.830248	+	0.479344i	0.853938	−	0.520375i	$-0.174208\pi$
$367$	15.9053	+	9.18291i	0.830248	+	0.479344i	−0.0236896	+	0.999719i	$0.507541\pi$
$368$	−26.1855	−	12.4069i	−1.36501	−	0.646753i
$369$	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
$372$	0.792986	+	3.99147i	0.0411144	+	0.206948i
$373$	−0.177482	+	0.102469i	−0.00918966	+	0.00530565i	−0.504588	−	0.863360i	$-0.668356\pi$
$373$	−0.177482	+	0.102469i	−0.00918966	+	0.00530565i	0.495398	+	0.868666i	$0.335022\pi$
$374$	−9.97539	+	7.98094i	−0.515815	+	0.412685i
$375$	−0.702074	−	1.58338i	−0.0362550	−	0.0817654i
$376$	9.03645	−	13.3901i	0.466019	−	0.690540i
$377$		−	0.422988i		−	0.0217850i
$378$	4.18535	−	18.9864i	0.215271	−	0.976554i
$379$	10.8141			0.555483			0.277741	−	0.960656i	$-0.410414\pi$
$379$	10.8141			0.555483			0.277741	+	0.960656i	$0.410414\pi$
$380$	−0.0219099	+	0.0974126i	−0.00112396	+	0.00499716i
$381$	3.47385	−	1.54031i	0.177971	−	0.0789127i
$382$	−5.59423	+	4.47574i	−0.286226	+	0.228999i
$383$	−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
$387$	−16.4880	+	18.1998i	−0.838133	+	0.925150i
$388$	−13.1862	+	4.11312i	−0.669428	+	0.208812i
$389$	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	$0.163499\pi$
$390$	4.90637	−	9.45510i	0.248444	−	0.478777i
$391$		−	14.0158i		−	0.708808i
$392$	6.87658	+	18.5664i	0.347320	+	0.937747i
$393$	−2.99633	−	2.18395i	−0.151145	−	0.110166i
$394$	−4.15008	−	27.2416i	−0.209078	−	1.37241i
$395$	−8.28188	−	4.78155i	−0.416707	−	0.240586i
$396$	−22.9052	+	16.1275i	−1.15103	+	0.810436i
$397$	0.342311	−	0.197633i	0.0171801	−	0.00991894i	−0.491385	−	0.870942i	$-0.663509\pi$
$397$	0.342311	−	0.197633i	0.0171801	−	0.00991894i	0.508565	+	0.861023i	$0.330176\pi$
$398$	1.39578	−	3.57298i	0.0699640	−	0.179097i
$399$	−0.143721	+	0.177997i	−0.00719506	+	0.00891099i
$400$	0.324142	+	3.98684i	0.0162071	+	0.199342i
$401$	−25.7729	+	14.8800i	−1.28704	+	0.743070i	−0.978124	−	0.208021i	$-0.933298\pi$
$401$	−25.7729	+	14.8800i	−1.28704	+	0.743070i	−0.308911	+	0.951091i	$0.599965\pi$
$402$	−0.369651	−	8.22065i	−0.0184365	−	0.410009i
$403$	−2.55438	+	4.42431i	−0.127243	+	0.220391i
$404$	7.73141	−	34.3742i	0.384652	−	1.71018i
$405$	7.31329	−	5.24555i	0.363400	−	0.260653i
$406$	0.0369721	+	0.362053i	0.00183490	+	0.0179684i
$407$	19.4334			0.963278
$408$	−8.91268	+	3.22611i	−0.441243	+	0.159716i
$409$	−5.55525	+	9.62197i	−0.274689	+	0.475776i	−0.970057	−	0.242879i	$-0.921908\pi$
$409$	−5.55525	+	9.62197i	−0.274689	+	0.475776i	0.695367	+	0.718654i	$0.255242\pi$
$410$	−9.59797	−	11.9965i	−0.474010	−	0.592466i
$411$	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
$414$	1.88307	−	30.6760i	0.0925480	−	1.50764i
$415$	−9.93134	+	5.73386i	−0.487510	+	0.281464i
$416$	−17.9005	+	16.8746i	−0.877646	+	0.827344i
$417$	−5.72790	−	12.9181i	−0.280497	−	0.632601i
$418$	0.325872	−	0.0496444i	0.0159389	−	0.00242818i
$419$			32.9565i			1.61003i	0.593254	+	0.805016i	$0.297843\pi$
$419$			32.9565i			1.61003i	−0.593254	+	0.805016i	$0.702157\pi$
$420$	−3.37312	+	8.52186i	−0.164591	+	0.415824i
$421$			30.0447i			1.46429i	0.681150	+	0.732144i	$0.261480\pi$
$421$			30.0447i			1.46429i	−0.681150	+	0.732144i	$0.738520\pi$
$422$	1.63085	+	10.7051i	0.0793887	+	0.521118i
$423$	16.7485	+	3.61344i	0.814341	+	0.175691i
$424$	−39.9268	−	2.80171i	−1.93902	−	0.136063i
$425$	−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
$429$	−34.9691	−	3.72933i	−1.68832	−	0.180054i
$430$	9.03960	−	7.23225i	0.435928	−	0.348770i
$431$	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	$-0.0575723\pi$
$432$	−19.9404	+	5.86346i	−0.959383	+	0.282106i
$433$	−27.8882			−1.34022			−0.670111	−	0.742261i	$-0.733753\pi$
$433$	−27.8882			−1.34022			−0.670111	+	0.742261i	$0.733753\pi$
$434$	1.79968	−	4.01022i	0.0863875	−	0.192497i
$435$	−0.0992317	+	0.136144i	−0.00475780	+	0.00652759i
$436$	−18.6285	−	4.18989i	−0.892142	−	0.200659i
$437$	−0.180822	+	0.313193i	−0.00864988	+	0.0149820i
$438$	0.994080	+	22.1073i	0.0474990	+	1.05633i
$439$	−16.0873	+	9.28803i	−0.767807	+	0.443294i	−0.832092	−	0.554638i	$-0.812857\pi$
$439$	−16.0873	+	9.28803i	−0.767807	+	0.443294i	0.0642846	+	0.997932i	$0.479523\pi$
$440$	11.8705	−	5.78605i	0.565904	−	0.275839i
$441$	−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	−0.821585	−	0.570086i	$-0.806910\pi$
$443$	−15.5472	+	8.97617i	−0.738669	+	0.426471i	0.0829163	+	0.996557i	$0.473577\pi$
$444$	13.6525	+	4.63793i	0.647917	+	0.220107i
$445$	−5.85921	−	3.38281i	−0.277753	−	0.160361i
$446$	9.77129	−	1.48859i	0.462684	−	0.0704868i
$447$	17.9292	−	24.5984i	0.848021	−	1.16347i
$448$	13.8468	−	16.0083i	0.654202	−	0.756320i
$449$		−	15.9588i		−	0.753143i	−0.926388	−	0.376571i	$-0.877103\pi$
$449$		−	15.9588i		−	0.753143i	0.926388	−	0.376571i	$-0.122897\pi$
$450$	−3.79731	+	1.89221i	−0.179007	+	0.0891997i
$451$	−25.3605	+	43.9256i	−1.19418	+	2.06838i
$452$	2.18955	+	7.01945i	0.102988	+	0.330167i
$453$	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
$456$	0.240781	+	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	$0.818134\pi$
$458$	7.88149	+	9.85109i	0.368278	+	0.460311i
$459$	−6.69289	−	7.50195i	−0.312397	−	0.350161i
$460$	−3.17921	+	14.1349i	−0.148231	+	0.659043i
$461$	−11.6470			−0.542453			−0.271226	−	0.962516i	$-0.587429\pi$
$461$	−11.6470			−0.542453			−0.271226	+	0.962516i	$0.587429\pi$
$462$	30.2575	+	0.135544i	1.40770	+	0.00630606i
$463$		−	18.7737i		−	0.872486i	−0.899829	−	0.436243i	$-0.856309\pi$
$463$		−	18.7737i		−	0.872486i	0.899829	−	0.436243i	$-0.143691\pi$
$464$	0.320067	−	0.221196i	0.0148587	−	0.0102688i
$465$	1.86008	−	0.824766i	0.0862594	−	0.0382476i
$466$	−2.63436	−	3.29269i	−0.122035	−	0.152531i
$467$	30.0802	−	17.3668i	1.39195	−	0.803640i	0.398415	−	0.917205i	$-0.369560\pi$
$467$	30.0802	−	17.3668i	1.39195	−	0.803640i	0.993531	+	0.113565i	$0.0362271\pi$
$468$	−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
$471$	−2.89836	+	27.1773i	−0.133549	+	1.25226i
$472$	2.69901	−	38.4632i	0.124232	−	1.77041i
$473$	−33.0988	−	19.1096i	−1.52188	−	0.878660i
$474$	−10.7892	+	20.7920i	−0.495567	+	0.955010i
$475$	0.0499231			0.00229063
$476$	9.86534	+	2.73725i	0.452177	+	0.125462i
$477$	−12.9955	−	40.4149i	−0.595021	−	1.85047i
$478$	1.42471	+	9.35198i	0.0651648	+	0.427750i
$479$	0.526981	−	0.912758i	0.0240784	−	0.0417050i	−0.853735	−	0.520708i	$-0.825668\pi$
$479$	0.526981	−	0.912758i	0.0240784	−	0.0417050i	0.877814	+	0.479003i	$0.159002\pi$
$480$	9.72021	−	1.23187i	0.443665	−	0.0562267i
$481$	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
$486$	−13.6407	−	17.3186i	−0.618753	−	0.785586i
$487$	11.5870	+	6.68977i	0.525058	+	0.303142i	0.739002	−	0.673704i	$-0.235298\pi$
$487$	11.5870	+	6.68977i	0.525058	+	0.303142i	−0.213944	+	0.976846i	$0.568631\pi$
$488$	3.19769	+	2.15800i	0.144753	+	0.0976881i
$489$	−25.2687	+	34.6680i	−1.14269	+	1.56774i
$490$	8.30247	−	5.39157i	0.375067	−	0.243566i
$491$			22.2153i			1.00256i	0.865285	+	0.501281i	$0.167138\pi$
$491$			22.2153i			1.00256i	−0.865285	+	0.501281i	$0.832862\pi$
$492$	−28.2996	+	24.8064i	−1.27584	+	1.11836i
$493$	0.162978	+	0.0940955i	0.00734017	+	0.00423785i
$494$	0.191811	+	0.239745i	0.00862998	+	0.0107866i
$495$	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
$498$	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	$-0.360441\pi$
$500$	1.90927	−	0.595551i	0.0853852	−	0.0266339i
$501$	1.18842	+	2.68023i	0.0530947	+	0.119744i
$502$	5.76029	−	0.877541i	0.257094	−	0.0391666i
$503$	−10.7214			−0.478044			−0.239022	−	0.971014i	$-0.576827\pi$
$503$	−10.7214			−0.478044			−0.239022	+	0.971014i	$0.576827\pi$
$504$	21.2243	+	7.31640i	0.945405	+	0.325898i
$505$	−17.6165			−0.783923
$506$	47.2851	−	7.20356i	2.10208	−	0.320237i
$507$	−4.15058	−	9.36076i	−0.184334	−	0.415726i
$508$	1.30661	+	4.18884i	0.0579714	+	0.185850i
$509$	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
$513$	0.0527725	+	0.253984i	0.00232996	+	0.0112136i
$514$	−5.37248	−	6.71507i	−0.236970	−	0.296189i
$515$	1.23715	+	0.714272i	0.0545155	+	0.0314746i
$516$	−18.6921	−	21.3243i	−0.822874	−	0.938748i
$517$			26.6653i			1.17274i
$518$	−9.11692	−	12.6266i	−0.400574	−	0.554783i
$519$	−3.34790	+	4.59324i	−0.146956	+	0.201621i
$520$	10.1957	+	6.88067i	0.447109	+	0.301737i
$521$	6.24945	+	3.60812i	0.273793	+	0.158075i	0.630610	−	0.776100i	$-0.282805\pi$
$521$	6.24945	+	3.60812i	0.273793	+	0.158075i	−0.356817	+	0.934174i	$0.616138\pi$
$522$	0.344064	+	0.227841i	0.0150593	+	0.00997235i
$523$	−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
$525$	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
$528$	−15.4647	−	28.4107i	−0.673016	−	1.23641i
$529$	−14.7378	+	25.5267i	−0.640776	+	1.10986i
$530$	3.01399	+	19.7842i	0.130919	+	0.859372i
$531$	38.9335	−	12.5191i	1.68957	−	0.543282i
$532$	−0.185134	−	0.188442i	−0.00802658	−	0.00816998i
$533$	−47.2436			−2.04635
$534$	−7.63310	+	14.7098i	−0.330316	+	0.636555i
$535$	6.21564	+	3.58860i	0.268726	+	0.155149i
$536$	9.47867	+	0.665130i	0.409416	+	0.0287292i
$537$	−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
$540$	5.04810	+	9.08387i	0.217236	+	0.390907i
$541$	17.4623	−	10.0819i	0.750764	−	0.433454i	−0.0752056	−	0.997168i	$-0.523961\pi$
$541$	17.4623	−	10.0819i	0.750764	−	0.433454i	0.825970	+	0.563714i	$0.190628\pi$
$542$	−6.33871	−	7.92276i	−0.272271	−	0.340312i
$543$	41.5634	−	18.4293i	1.78365	−	0.790877i
$544$	−2.51976	−	10.6509i	−0.108034	−	0.456655i
$545$			9.54692i			0.408945i
$546$	13.9822	+	24.4703i	0.598382	+	1.04723i
$547$	23.5095			1.00519			0.502597	−	0.864521i	$-0.332378\pi$
$547$	23.5095			1.00519			0.502597	+	0.864521i	$0.332378\pi$
$548$	21.4127	+	4.81613i	0.914707	+	0.205735i
$549$	−0.862928	+	3.99973i	−0.0368289	+	0.170704i
$550$	−4.12493	−	5.15575i	−0.175887	−	0.219842i
$551$	−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
$555$	0.764519	−	7.16872i	0.0324520	−	0.304295i
$556$	15.5769	−	4.85883i	0.660607	−	0.206060i
$557$	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	$0.151658\pi$
$558$	−2.22289	−	4.46091i	−0.0941023	−	0.188845i
$559$		−	35.5989i		−	1.50567i
$560$	−9.32830	−	4.99827i	−0.394193	−	0.211216i
$561$	9.21594	−	12.6441i	0.389097	−	0.533833i
$562$	−11.5548	+	1.76030i	−0.487412	+	0.0742539i
$563$	−25.8072	−	14.8998i	−1.08764	−	0.627952i	−0.154696	−	0.987962i	$-0.549440\pi$
$563$	−25.8072	−	14.8998i	−1.08764	−	0.627952i	−0.932948	+	0.360010i	$0.882773\pi$
$564$	−6.36389	+	18.7331i	−0.267968	+	0.788805i
$565$	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	0.118848	−	0.992912i	$-0.462080\pi$
$569$	24.7640	−	14.2975i	1.03816	−	0.599382i	0.919312	+	0.393531i	$0.128746\pi$
$570$	−0.00549319	−	0.122163i	−0.000230084	−	0.00511683i
$571$	1.45649	−	2.52271i	0.0609522	−	0.105572i	−0.833939	−	0.551856i	$-0.813920\pi$
$571$	1.45649	−	2.52271i	0.0609522	−	0.105572i	0.894891	+	0.446284i	$0.147253\pi$
$572$	8.91085	−	39.6181i	0.372581	−	1.65651i
$573$	5.16833	−	7.09083i	0.215910	−	0.296223i
$574$	40.4377	−	4.12942i	1.68784	−	0.172359i
$575$	7.24401			0.302096
$576$	−4.08394	−	23.6500i	−0.170164	−	0.985416i
$577$	18.4445	−	31.9468i	0.767855	−	1.32996i	−0.170869	−	0.985294i	$-0.554657\pi$
$577$	18.4445	−	31.9468i	0.767855	−	1.32996i	0.938724	−	0.344670i	$-0.112009\pi$
$578$	−14.6389	+	11.7121i	−0.608899	+	0.487158i
$579$	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
$582$	14.2559	−	9.10817i	0.590928	−	0.377546i
$583$	57.2175	−	33.0345i	2.36971	−	1.36815i
$584$	−25.4904	−	1.78869i	−1.05480	−	0.0740166i
$585$	−2.75140	+	12.7529i	−0.113756	+	0.527268i
$586$	0.375931	+	2.46766i	0.0155296	+	0.101938i
$587$		−	5.63165i		−	0.232443i	−0.993223	−	0.116221i	$-0.962922\pi$
$587$		−	5.63165i		−	0.232443i	0.993223	−	0.116221i	$-0.0370782\pi$
$588$	−14.1068	−	19.7230i	−0.581755	−	0.813364i
$589$			0.0586475i			0.00241653i
$590$	−19.0590	+	2.90351i	−0.784647	+	0.119536i
$591$	13.6799	+	30.8521i	0.562716	+	1.26909i
$592$	−7.12886	+	15.0459i	−0.292994	+	0.618383i
$593$	−15.8168	+	9.13183i	−0.649518	+	0.374999i	−0.788271	−	0.615328i	$-0.789024\pi$
$593$	−15.8168	+	9.13183i	−0.649518	+	0.374999i	0.138754	+	0.990327i	$0.455690\pi$
$594$	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
$597$	−0.498204	+	4.67155i	−0.0203901	+	0.191194i
$598$	27.8324	+	34.7877i	1.13815	+	1.42258i
$599$	−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	$0.303843\pi$
$600$	−1.66741	−	4.60649i	−0.0680716	−	0.188059i
$601$	−24.8401			−1.01325			−0.506624	−	0.862167i	$-0.669107\pi$
$601$	−24.8401			−1.01325			−0.506624	+	0.862167i	$0.669107\pi$
$602$	3.11160	+	30.4706i	0.126819	+	1.24189i
$603$	3.08514	+	9.59456i	0.125636	+	0.390721i
$604$	30.1006	+	6.77020i	1.22478	+	0.275476i
$605$	−5.39919	+	9.35168i	−0.219508	+	0.380200i
$606$	1.93840	+	43.1078i	0.0787419	+	1.75114i
$607$	−2.92576	+	1.68919i	−0.118753	+	0.0685620i	−0.558200	−	0.829706i	$-0.688508\pi$
$607$	−2.92576	+	1.68919i	−0.118753	+	0.0685620i	0.439447	+	0.898269i	$0.355174\pi$
$608$	−0.0811051	+	0.270511i	−0.00328925	+	0.0109707i
$609$	−0.160325	−	0.415896i	−0.00649671	−	0.0168530i
$610$	0.701856	−	1.79665i	0.0284173	−	0.0727442i
$611$	−21.5096	+	12.4186i	−0.870186	+	0.502402i
$612$	9.49203	−	6.68332i	0.383693	−	0.270157i
$613$	−21.7109	−	12.5348i	−0.876893	−	0.506275i	−0.00726042	−	0.999974i	$-0.502311\pi$
$613$	−21.7109	−	12.5348i	−0.876893	−	0.506275i	−0.869633	+	0.493699i	$0.835644\pi$
$614$	4.39505	+	28.8497i	0.177370	+	1.16428i
$615$	15.2059	+	11.0832i	0.613160	+	0.446917i
$616$	−4.16427	+	34.6896i	−0.167783	+	1.39768i
$617$			18.0681i			0.727395i	0.931517	+	0.363697i	$0.118486\pi$
$617$			18.0681i			0.727395i	−0.931517	+	0.363697i	$0.881514\pi$
$618$	1.61171	−	3.10593i	0.0648324	−	0.124939i
$619$	18.3452	−	31.7748i	0.737355	−	1.27714i	−0.216327	−	0.976321i	$-0.569408\pi$
$619$	18.3452	−	31.7748i	0.737355	−	1.27714i	0.953682	−	0.300815i	$-0.0972588\pi$
$620$	0.699627	+	2.24293i	0.0280977	+	0.0900782i
$621$	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
$624$	15.7153	−	25.7061i	0.629114	−	1.02907i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	7.49663	−	5.99778i	0.299626	−	0.239720i
$627$	−0.369062	+	0.163643i	−0.0147389	+	0.00653527i
$628$	−30.7904	−	6.92534i	−1.22867	−	0.276351i
$629$	−8.05332			−0.321107
$630$	1.24034	−	11.1562i	0.0494164	−	0.444475i
$631$			25.3603i			1.00958i	0.863243	+	0.504789i	$0.168430\pi$
$631$			25.3603i			1.00958i	−0.863243	+	0.504789i	$0.831570\pi$
$632$	−22.4206	−	15.1308i	−0.891842	−	0.601871i
$633$	−5.37579	−	12.1240i	−0.213668	−	0.481884i
$634$	17.8498	−	14.2810i	0.708906	−	0.567170i
$635$	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
$639$	12.9823	−	14.3301i	0.513570	−	0.566891i
$640$	0.125218	+	11.3130i	0.00494969	+	0.447186i
$641$	0.00835292	+	0.00482256i	0.000329921	+	0.000190480i	0.500165	−	0.865930i	$-0.333273\pi$
$641$	0.00835292	+	0.00482256i	0.000329921	+	0.000190480i	−0.499835	+	0.866121i	$0.666606\pi$
$642$	8.09745	−	15.6046i	0.319581	−	0.615866i
$643$	−0.999165			−0.0394032			−0.0197016	−	0.999806i	$-0.506272\pi$
$643$	−0.999165			−0.0394032			−0.0197016	+	0.999806i	$0.506272\pi$
$644$	−26.8636	−	27.3435i	−1.05857	−	1.07749i
$645$	−8.35139	+	11.4579i	−0.328836	+	0.451155i
$646$	−0.135043	+	0.0205729i	−0.00531320	+	0.000809430i
$647$	17.4723	−	30.2629i	0.686907	−	1.18976i	−0.285927	−	0.958252i	$-0.592301\pi$
$647$	17.4723	−	30.2629i	0.686907	−	1.18976i	0.972833	−	0.231506i	$-0.0743653\pi$
$648$	21.6729	−	13.3523i	0.851393	−	0.524529i
$649$	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	−0.979603	−	0.200943i	$-0.935599\pi$
$653$	−16.9633	−	29.3812i	−0.663823	−	1.14978i	0.315780	−	0.948833i	$-0.397734\pi$
$654$	23.3615	−	1.05048i	0.913506	−	0.0410769i
$655$	−1.85389	−	1.07034i	−0.0724375	−	0.0418218i
$656$	−24.7054	−	35.7483i	−0.964584	−	1.39574i
$657$	−8.29666	−	25.8020i	−0.323684	−	1.00663i
$658$	17.3255	−	12.5097i	0.675418	−	0.487678i
$659$		−	17.0907i		−	0.665758i	−0.942969	−	0.332879i	$-0.891980\pi$
$659$		−	17.0907i		−	0.665758i	0.942969	−	0.332879i	$-0.108020\pi$
$660$	−12.1623	+	10.6611i	−0.473418	+	0.414982i
$661$	−2.24461	−	1.29593i	−0.0873051	−	0.0504056i	0.455712	−	0.890127i	$-0.349385\pi$
$661$	−2.24461	−	1.29593i	−0.0873051	−	0.0504056i	−0.543017	+	0.839722i	$0.682718\pi$
$662$	−31.4520	+	25.1636i	−1.22242	+	0.978010i
$663$	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
$666$	−17.6261	−	1.08199i	−0.682998	−	0.0419264i
$667$	−0.352298	−	0.610198i	−0.0136410	−	0.0236270i
$668$	−3.23188	+	1.00811i	−0.125045	+	0.0390048i
$669$	−11.0663	+	4.90684i	−0.427849	+	0.189710i
$670$	−0.715526	−	4.69680i	−0.0276432	−	0.181453i
$671$	−6.36797			−0.245833
$672$	−11.2044	+	23.3765i	−0.432221	+	0.901768i
$673$	36.8310			1.41973			0.709866	−	0.704337i	$-0.248756\pi$
$673$	36.8310			1.41973			0.709866	+	0.704337i	$0.248756\pi$
$674$	3.66028	+	24.0266i	0.140989	+	0.925468i
$675$	3.87736	−	3.45920i	0.149240	−	0.133145i
$676$	11.2874	−	3.52083i	0.434131	−	0.135417i
$677$	−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
$681$	2.82390	−	26.4791i	0.108212	−	1.01468i
$682$	6.05675	−	4.84578i	0.231925	−	0.185555i
$683$	20.8080	+	12.0135i	0.796197	+	0.459685i	0.842140	−	0.539260i	$-0.181296\pi$
$683$	20.8080	+	12.0135i	0.796197	+	0.459685i	−0.0459426	+	0.998944i	$0.514629\pi$
$684$	−0.298330	+	0.0268839i	−0.0114069	+	0.00102793i
$685$		−	10.9738i		−	0.419289i
$686$	0.0768491	+	26.1915i	0.00293411	+	0.999996i
$687$	−12.4865	−	9.10110i	−0.476390	−	0.347229i
$688$	26.9370	−	18.6160i	1.02696	−	0.709728i
$689$	53.2947	+	30.7697i	2.03037	+	1.17223i
$690$	−0.797080	−	17.7262i	−0.0303443	−	0.674826i
$691$	−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
$693$	−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
$696$	−0.306936	+	0.364481i	−0.0116344	+	0.0138156i
$697$	10.5095	−	18.2030i	0.398077	−	0.689489i
$698$	38.6374	−	5.88614i	1.46245	−	0.222794i
$699$	4.17357	+	3.04201i	0.157859	+	0.115060i
$700$	−1.41474	+	5.09887i	−0.0534721	+	0.192719i
$701$	−8.13507			−0.307257			−0.153629	−	0.988129i	$-0.549096\pi$
$701$	−8.13507			−0.307257			−0.153629	+	0.988129i	$0.549096\pi$
$702$	31.5093	+	5.32948i	1.18924	+	0.201148i
$703$	0.179957	+	0.103898i	0.00678721	+	0.00391860i
$704$	34.6380	−	13.9751i	1.30547	−	0.526706i
$705$	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
$708$	9.20206	+	46.3183i	0.345835	+	1.74075i
$709$	9.50630	−	5.48847i	0.357017	−	0.206124i	−0.310755	−	0.950490i	$-0.600582\pi$
$709$	9.50630	−	5.48847i	0.357017	−	0.206124i	0.667771	+	0.744367i	$0.267248\pi$
$710$	−7.11756	+	5.69450i	−0.267117	+	0.213711i
$711$	6.05041	−	28.0440i	0.226908	−	1.05173i
$712$	−15.8619	−	10.7046i	−0.594451	−	0.401173i
$713$			8.50994i			0.318700i
$714$	−12.5389	−	0.0561701i	−0.469255	−	0.00210211i
$715$	−20.3039			−0.759323
$716$	−2.10135	−	0.472633i	−0.0785312	−	0.0176631i
$717$	−4.69628	−	10.5915i	−0.175386	−	0.395545i
$718$	8.26014	−	6.60864i	0.308266	−	0.246632i
$719$	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
$723$	41.8582	+	4.46403i	1.55672	+	0.166019i
$724$	15.6331	+	50.1180i	0.580999	+	1.86262i
$725$	−0.0486330	+	0.0842348i	−0.00180618	+	0.00312840i
$726$	23.4778	+	12.1829i	0.871343	+	0.452151i
$727$		−	16.3757i		−	0.607343i	−0.952777	−	0.303671i	$-0.901788\pi$
$727$		−	16.3757i		−	0.607343i	0.952777	−	0.303671i	$-0.0982125\pi$
$728$	−29.9218	+	12.7965i	−1.10898	+	0.474272i
$729$	21.6973	+	16.0694i	0.803604	+	0.595164i
$730$	1.92422	+	12.6308i	0.0712185	+	0.467487i
$731$	13.7163	+	7.91913i	0.507317	+	0.292900i
$732$	−4.47366	−	1.51976i	−0.165351	−	0.0561721i
$733$	−35.2796	+	20.3687i	−1.30308	+	0.752334i	−0.980931	−	0.194355i	$-0.937739\pi$
$733$	−35.2796	+	20.3687i	−1.30308	+	0.752334i	−0.322149	+	0.946689i	$0.604405\pi$
$734$	9.45083	−	24.1927i	0.348837	−	0.892970i
$735$	−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
$738$	25.4476	−	38.4286i	0.936740	−	1.41458i
$739$	6.49315	−	11.2465i	0.238854	−	0.413708i	−0.721531	−	0.692382i	$-0.756561\pi$
$739$	6.49315	−	11.2465i	0.238854	−	0.413708i	0.960386	+	0.278674i	$0.0898948\pi$
$740$	8.12177	+	1.82674i	0.298562	+	0.0671522i
$741$	−0.303882	−	0.221492i	−0.0111634	−	0.00813672i
$742$	−48.3066	−	21.6787i	−1.77339	−	0.795851i
$743$	17.3420			0.636216			0.318108	−	0.948054i	$-0.396952\pi$
$743$	17.3420			0.636216			0.318108	+	0.948054i	$0.396952\pi$
$744$	5.41150	−	1.95880i	0.198395	−	0.0718129i
$745$	8.78701	−	15.2195i	0.321931	−	0.557601i
$746$	0.181062	+	0.226310i	0.00662915	+	0.00828578i
$747$	−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
$750$	−2.06416	+	1.31880i	−0.0753726	+	0.0481558i
$751$	34.7814	−	20.0811i	1.26919	−	0.732768i	0.294357	−	0.955696i	$-0.404894\pi$
$751$	34.7814	−	20.0811i	1.26919	−	0.732768i	0.974835	+	0.222927i	$0.0715612\pi$
$752$	−20.6451	−	9.78178i	−0.752849	−	0.356705i
$753$	−6.52374	+	2.89264i	−0.237738	+	0.105414i
$754$	−0.591373	+	0.0900916i	−0.0215365	+	0.00328094i
$755$		−	15.4263i		−	0.561421i
$756$	−27.4360	−	1.80758i	−0.997837	−	0.0657412i
$757$			15.4831i			0.562742i	0.959599	+	0.281371i	$0.0907892\pi$
$757$			15.4831i			0.562742i	−0.959599	+	0.281371i	$0.909211\pi$
$758$	−2.30328	−	15.1190i	−0.0836588	−	0.549147i
$759$	−53.5521	+	23.7451i	−1.94382	+	0.861893i
$760$	0.140858	+	0.00988414i	0.00510944	+	0.000358535i
$761$	−6.62479	+	3.82482i	−0.240148	+	0.138650i	−0.615245	−	0.788336i	$-0.710943\pi$
$761$	−6.62479	+	3.82482i	−0.240148	+	0.138650i	0.375097	+	0.926986i	$0.377610\pi$
$762$	−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
$765$	−4.30166	−	3.89706i	−0.155527	−	0.140898i
$766$	−1.70888	+	1.36722i	−0.0617445	+	0.0493995i
$767$	−29.6418	+	51.3412i	−1.07030	+	1.85382i
$768$	27.6694	−	1.55122i	0.998432	−	0.0559747i
$769$	28.5801			1.03063			0.515313	−	0.857002i	$-0.327676\pi$
$769$	28.5801			1.03063			0.515313	+	0.857002i	$0.327676\pi$
$770$	17.3789	−	1.77470i	0.626294	−	0.0639559i
$771$	8.51152	+	6.20384i	0.306535	+	0.223426i
$772$	−9.46309	+	42.0733i	−0.340584	+	1.51425i
$773$	−2.80047	+	4.85056i	−0.100726	+	0.174463i	−0.911984	−	0.410226i	$-0.865450\pi$
$773$	−2.80047	+	4.85056i	−0.100726	+	0.174463i	0.811258	+	0.584688i	$0.198783\pi$
$774$	28.9567	+	19.1753i	1.04083	+	0.689240i
$775$	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
$780$	−14.2640	−	4.84568i	−0.510734	−	0.173503i
$781$	26.0612	+	15.0464i	0.932543	+	0.538404i
$782$	−19.5952	+	2.98520i	−0.700723	+	0.106750i
$783$	−0.479953	−	0.158378i	−0.0171521	−	0.00565995i
$784$	24.4928	−	13.5685i	0.874743	−	0.484588i
$785$			15.7798i			0.563205i
$786$	−2.41516	+	4.65428i	−0.0861460	+	0.166013i
$787$	6.53353	−	11.3164i	0.232895	−	0.403386i	−0.725764	−	0.687944i	$-0.758513\pi$
$787$	6.53353	−	11.3164i	0.232895	−	0.403386i	0.958659	+	0.284558i	$0.0918467\pi$
$788$	−37.2021	+	11.6043i	−1.32527	+	0.413386i
$789$	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
$792$	27.4261	+	28.5884i	0.974543	+	1.01584i
$793$	−2.96569	−	5.13673i	−0.105315	−	0.182411i
$794$	−0.349216	−	0.436486i	−0.0123932	−	0.0154903i
$795$	−9.93503	−	22.4064i	−0.352359	−	0.794671i
$796$	−5.29261	−	1.19041i	−0.187592	−	0.0421929i
$797$	−48.8011			−1.72863			−0.864313	−	0.502955i	$-0.832246\pi$
$797$	−48.8011			−1.72863			−0.864313	+	0.502955i	$0.832246\pi$
$798$	0.279465	+	0.163023i	0.00989296	+	0.00577095i
$799$		−	11.0503i		−	0.390930i
$800$	5.50490	−	1.30233i	0.194628	−	0.0460443i
$801$	4.28050	−	19.8404i	0.151244	−	0.701026i
$802$	26.2928	+	32.8633i	0.928430	+	1.16045i
$803$	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
$807$	23.4394	+	2.49972i	0.825104	+	0.0879945i
$808$	−49.7047	−	3.48784i	−1.74861	−	0.122702i
$809$	16.1767	+	9.33961i	0.568742	+	0.328363i	0.756647	−	0.653824i	$-0.226836\pi$
$809$	16.1767	+	9.33961i	0.568742	+	0.328363i	−0.187905	+	0.982187i	$0.560170\pi$
$810$	−8.89136	−	9.10734i	−0.312411	−	0.319999i
$811$	−44.7323			−1.57076			−0.785381	−	0.619013i	$-0.787533\pi$
$811$	−44.7323			−1.57076			−0.785381	+	0.619013i	$0.787533\pi$
$812$	0.498306	−	0.128803i	0.0174871	−	0.00452011i
$813$	10.0423	+	7.31958i	0.352199	+	0.256709i
$814$	−4.13909	−	27.1695i	−0.145075	−	0.952291i
$815$	−12.3840	+	21.4498i	−0.433794	+	0.751354i
$816$	6.40867	+	11.7735i	0.224348	+	0.412156i
$817$	−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	$-0.223140\pi$
$821$	−5.05691	−	8.75882i	−0.176487	−	0.305685i	−0.940675	+	0.339309i	$0.889807\pi$
$822$	−26.8532	+	1.20749i	−0.936612	+	0.0421159i
$823$	15.8881	+	9.17301i	0.553825	+	0.319751i	0.750663	−	0.660685i	$-0.229734\pi$
$823$	15.8881	+	9.17301i	0.553825	+	0.319751i	−0.196838	+	0.980436i	$0.563067\pi$
$824$	3.34920	+	2.26025i	0.116675	+	0.0787396i
$825$	6.53504	+	4.76323i	0.227521	+	0.165834i
$826$	20.8841	−	46.5359i	0.726650	−	1.61919i
$827$			36.0470i			1.25348i	0.779229	+	0.626739i	$0.215611\pi$
$827$			36.0470i			1.25348i	−0.779229	+	0.626739i	$0.784389\pi$
$828$	−43.2887	+	3.90094i	−1.50438	+	0.135567i
$829$	−5.64247	−	3.25768i	−0.195971	−	0.113144i	0.398804	−	0.917036i	$-0.369425\pi$
$829$	−5.64247	−	3.25768i	−0.195971	−	0.113144i	−0.594775	+	0.803892i	$0.702759\pi$
$830$	10.1317	+	12.6636i	0.351675	+	0.439559i
$831$	−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
$834$	−16.8406	+	10.7595i	−0.583141	+	0.372571i
$835$	0.846364	+	1.46595i	0.0292896	+	0.0507311i
$836$	−0.138814	−	0.445022i	−0.00480098	−	0.0153914i
$837$	4.06372	+	4.55495i	0.140463	+	0.157442i
$838$	46.0759	−	7.01936i	1.59167	−	0.242480i
$839$	−40.0265			−1.38187			−0.690934	−	0.722918i	$-0.742800\pi$
$839$	−40.0265			−1.38187			−0.690934	+	0.722918i	$0.742800\pi$
$840$	12.6327	+	2.90085i	0.435870	+	0.100089i
$841$	−28.9905			−0.999674
$842$	42.0050	−	6.39917i	1.44759	−	0.220530i
$843$	13.0863	−	5.80249i	0.450716	−	0.199848i
$844$	14.6193	−	4.56014i	0.503217	−	0.156966i
$845$	−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
$849$	−45.8901	−	4.89401i	−1.57494	−	0.167962i
$850$	1.70939	+	2.13657i	0.0586317	+	0.0732838i
$851$	26.1124	+	15.0760i	0.895121	+	0.516798i
$852$	14.7177	+	16.7902i	0.504220	+	0.575223i
$853$			1.81968i			0.0623048i	0.999515	+	0.0311524i	$0.00991772\pi$
$853$			1.81968i			0.0623048i	−0.999515	+	0.0311524i	$0.990082\pi$
$854$	2.98744	+	4.13751i	0.102228	+	0.141583i
$855$	0.0458466	+	0.142580i	0.00156792	+	0.00487612i
$856$	16.8269	+	11.3558i	0.575130	+	0.388134i
$857$	−23.8693	−	13.7810i	−0.815361	−	0.470749i	0.0334528	−	0.999440i	$-0.489350\pi$
$857$	−23.8693	−	13.7810i	−0.815361	−	0.470749i	−0.848814	+	0.528691i	$0.822683\pi$
$858$	2.23410	+	49.6840i	0.0762709	+	1.69618i
$859$	−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
$861$	−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	0.985201	+	0.171400i	$0.0548292\pi$
$863$	18.8317	+	32.6174i	0.641038	+	1.11031i	−0.344164	+	0.938910i	$0.611838\pi$
$864$	12.4447	+	26.6295i	0.423377	+	0.905954i
$865$	−1.64079	+	2.84193i	−0.0557885	+	0.0966286i
$866$	5.93987	+	38.9900i	0.201845	+	1.32494i
$867$	13.5244	−	18.5552i	0.459314	−	0.630168i
$868$	−5.98993	−	1.66197i	−0.203312	−	0.0564110i
$869$	44.6489			1.51461
$870$	0.211475	+	0.109737i	0.00716968	+	0.00372044i
$871$	−12.6522	−	7.30477i	−0.428705	−	0.247513i
$872$	−1.89017	+	26.9365i	−0.0640092	+	0.912186i
$873$	−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
$876$	30.6961	−	6.09840i	1.03712	−	0.206046i
$877$	−13.7440	+	7.93509i	−0.464101	+	0.267949i	−0.713767	−	0.700383i	$-0.753013\pi$
$877$	−13.7440	+	7.93509i	−0.464101	+	0.267949i	0.249666	+	0.968332i	$0.419679\pi$
$878$	16.4119	+	20.5132i	0.553873	+	0.692287i
$879$	−1.23918	−	2.79471i	−0.0417966	−	0.0942633i
$880$	−10.6177	−	15.3636i	−0.357921	−	0.517906i
$881$		−	9.64780i		−	0.325043i	−0.986705	−	0.162521i	$-0.948037\pi$
$881$		−	9.64780i		−	0.325043i	0.986705	−	0.162521i	$-0.0519626\pi$
$882$	23.0227	+	18.7604i	0.775216	+	0.631696i
$883$	12.6173			0.424607			0.212303	−	0.977204i	$-0.431903\pi$
$883$	12.6173			0.424607			0.212303	+	0.977204i	$0.431903\pi$
$884$	−3.69271	+	16.4180i	−0.124199	+	0.552196i
$885$	21.5850	−	9.57085i	0.725573	−	0.321721i
$886$	15.8608	+	19.8244i	0.532854	+	0.666015i
$887$	−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
$891$	−17.3249	+	38.2821i	−0.580405	+	1.28250i
$892$	−4.16234	−	13.3440i	−0.139366	−	0.446791i
$893$	−0.142563	+	0.246926i	−0.00477068	+	0.00826307i
$894$	−38.2094	−	19.8273i	−1.27791	−	0.663124i
$895$			1.07692i			0.0359976i
$896$	−25.3301	−	15.9495i	−0.846220	−	0.532834i
$897$	−44.0943	−	32.1393i	−1.47227	−	1.07310i
$898$	−22.3117	+	3.39904i	−0.744553	+	0.113428i
$899$	−0.0989553	−	0.0571319i	−0.00330035	−	0.00190546i
$900$	3.45425	+	4.90593i	0.115142	+	0.163531i
$901$	−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
$906$	−37.7484	+	1.69740i	−1.25411	+	0.0563924i
$907$	14.7384	−	25.5277i	0.489381	−	0.847632i	−0.510545	−	0.859851i	$-0.670556\pi$
$907$	14.7384	−	25.5277i	0.489381	−	0.847632i	0.999925	+	0.0122192i	$0.00388959\pi$
$908$	29.9994	+	6.74742i	0.995564	+	0.223921i
$909$	−16.1780	−	50.3124i	−0.536590	−	1.66876i
$910$	9.52530	+	13.1922i	0.315761	+	0.437318i
$911$	42.2061			1.39835			0.699175	−	0.714950i	$-0.253551\pi$
$911$	42.2061			1.39835			0.699175	+	0.714950i	$0.253551\pi$
$912$	0.00868768	−	0.345768i	0.000287678	−	0.0114495i
$913$	26.7707	−	46.3682i	0.885980	−	1.53456i
$914$	2.25355	−	1.80298i	0.0745408	−	0.0596373i
$915$	−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
$918$	−9.06284	+	10.9550i	−0.299118	+	0.361570i
$919$	15.3124	−	8.84063i	0.505110	−	0.291626i	−0.225711	−	0.974194i	$-0.572471\pi$
$919$	15.3124	−	8.84063i	0.505110	−	0.291626i	0.730821	+	0.682569i	$0.239137\pi$
$920$	20.4389	+	1.43422i	0.673850	+	0.0472849i
$921$	−14.4874	−	32.6733i	−0.477377	−	1.07662i
$922$	2.48067	+	16.2834i	0.0816964	+	0.536266i
$923$			28.0297i			0.922610i
$924$	−6.25499	−	42.3313i	−0.205774	−	1.39260i
$925$		−	4.16233i		−	0.136857i
$926$	−26.2471	+	3.99857i	−0.862534	+	0.131401i
$927$	−0.903815	+	4.18924i	−0.0296852	+	0.137593i
$928$	−0.377421	−	0.400368i	−0.0123895	−	0.0131427i
$929$	−7.15076	+	4.12849i	−0.234609	+	0.135452i	−0.612696	−	0.790318i	$-0.709915\pi$
$929$	−7.15076	+	4.12849i	−0.234609	+	0.135452i	0.378088	+	0.925770i	$0.376582\pi$
$930$	−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
$933$	31.9222	+	3.40438i	1.04508	+	0.111455i
$934$	−30.6870	−	38.3557i	−1.00411	−	1.25504i
$935$	4.51669	−	7.82313i	0.147712	−	0.255844i
$936$	−10.2880	+	35.4375i	−0.336272	+	1.15831i
$937$	35.5033			1.15984			0.579922	−	0.814672i	$-0.303083\pi$
$937$	35.5033			1.15984			0.579922	+	0.814672i	$0.303083\pi$
$938$	11.4681	+	5.14656i	0.374445	+	0.168041i
$939$	−6.92590	+	9.50217i	−0.226018	+	0.310092i
$940$	−2.50654	+	11.1442i	−0.0817542	+	0.363483i
$941$	24.0272	−	41.6163i	0.783263	−	1.35665i	−0.146768	−	0.989171i	$-0.546887\pi$
$941$	24.0272	−	41.6163i	0.783263	−	1.35665i	0.930031	−	0.367481i	$-0.119780\pi$
$942$	38.6134	−	1.73630i	1.25809	−	0.0565717i
$943$	−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	0.303835	−	0.952725i	$-0.401733\pi$
$947$	39.4156	−	22.7566i	1.28084	−	0.739491i	0.977001	+	0.213234i	$0.0683996\pi$
$948$	31.3670	+	10.6558i	1.01875	+	0.346084i
$949$	34.0249	+	19.6443i	1.10449	+	0.637680i
$950$	−0.0106330	−	0.0697967i	−0.000344982	−	0.00226450i
$951$	−16.4909	+	22.6251i	−0.534753	+	0.733668i
$952$	1.72570	−	14.3756i	0.0559301	−	0.465915i
$953$		−	43.5506i		−	1.41074i	−0.708838	−	0.705371i	$-0.750780\pi$
$953$		−	43.5506i		−	1.41074i	0.708838	−	0.705371i	$-0.249220\pi$
$954$	−53.7355	+	26.7766i	−1.73975	+	0.866925i
$955$	2.53297	−	4.38724i	0.0819651	−	0.141968i
$956$	12.7714	−	3.98373i	0.413057	−	0.128843i
$957$	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
$960$	−3.79254	−	13.3273i	−0.122404	−	0.430136i
$961$	−14.8100	−	25.6516i	−0.477741	−	0.827472i
$962$	19.9887	−	15.9922i	0.644461	−	0.515609i
$963$	−4.54090	+	21.0473i	−0.146328	+	0.678241i
$964$	−10.6663	+	47.4231i	−0.343540	+	1.52739i
$965$	21.5622			0.694112
$966$	40.5513	+	23.6552i	1.30472	+	0.761093i
$967$		−	6.03768i		−	0.194159i	−0.995277	−	0.0970793i	$-0.969050\pi$
$967$		−	6.03768i		−	0.194159i	0.995277	−	0.0970793i	$-0.0309500\pi$
$968$	−17.0853	+	25.3167i	−0.549142	+	0.813709i
$969$	0.152941	−	0.0678145i	0.00491318	−	0.00217852i
$970$	7.62662	−	6.10178i	0.244876	−	0.195916i
$971$	10.4645	−	6.04167i	0.335821	−	0.193886i	−0.322602	−	0.946535i	$-0.604557\pi$
$971$	10.4645	−	6.04167i	0.335821	−	0.193886i	0.658422	+	0.752649i	$0.271224\pi$
$972$	−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
$975$	−0.798764	+	7.48984i	−0.0255809	+	0.239867i
$976$	2.33599	−	4.93027i	0.0747733	−	0.157814i
$977$	−14.8395	−	8.56761i	−0.474759	−	0.274102i	0.243471	−	0.969908i	$-0.421714\pi$
$977$	−14.8395	−	8.56761i	−0.474759	−	0.274102i	−0.718230	+	0.695806i	$0.755047\pi$
$978$	53.8507	+	27.9438i	1.72195	+	0.893544i
$979$	31.5879			1.00955
$980$	−9.30619	−	10.4592i	−0.297275	−	0.334107i
$981$	−27.2659	+	8.76736i	−0.870532	+	0.279920i
$982$	31.0588	−	4.73160i	0.991126	−	0.150991i
$983$	−23.4193	+	40.5633i	−0.746958	+	1.29377i	0.202316	+	0.979320i	$0.435153\pi$
$983$	−23.4193	+	40.5633i	−0.746958	+	1.29377i	−0.949274	+	0.314449i	$0.898180\pi$
$984$	40.7089	+	34.2817i	1.29775	+	1.09286i
$985$	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
$990$	10.9366	−	16.5155i	0.347589	−	0.524896i
$991$	−53.5716	−	30.9296i	−1.70176	−	0.982510i	−0.943983	−	0.329994i	$-0.892953\pi$
$991$	−53.5716	−	30.9296i	−1.70176	−	0.982510i	−0.757775	−	0.652516i	$-0.773713\pi$
$992$	1.52992	+	6.46692i	0.0485750	+	0.205325i
$993$	29.0575	−	39.8662i	0.922111	−	1.26511i
$994$	−2.44999	−	23.9918i	−0.0777091	−	0.760974i
$995$			2.71242i			0.0859893i
$996$	29.8732	−	26.1858i	0.946568	−	0.829728i
$997$	−8.10927	−	4.68189i	−0.256823	−	0.148277i	0.366061	−	0.930591i	$-0.380706\pi$
$997$	−8.10927	−	4.68189i	−0.256823	−	0.148277i	−0.622884	+	0.782314i	$0.714039\pi$
$998$	−28.2125	+	22.5718i	−0.893051	+	0.714498i
$999$	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.b.11.29	yes	128
3.2	odd	2		840.2.cq.a.11.36	✓	128
7.2	even	3	inner	840.2.cq.b.611.15	yes	128
8.3	odd	2		840.2.cq.a.11.50	yes	128
21.2	odd	6		840.2.cq.a.611.50	yes	128
24.11	even	2	inner	840.2.cq.b.11.15	yes	128
56.51	odd	6		840.2.cq.a.611.36	yes	128
168.107	even	6	inner	840.2.cq.b.611.29	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cq.a.11.36	✓	128	3.2	odd	2
840.2.cq.a.11.50	yes	128	8.3	odd	2
840.2.cq.a.611.36	yes	128	56.51	odd	6
840.2.cq.a.611.50	yes	128	21.2	odd	6
840.2.cq.b.11.15	yes	128	24.11	even	2	inner
840.2.cq.b.11.29	yes	128	1.1	even	1	trivial
840.2.cq.b.611.15	yes	128	7.2	even	3	inner
840.2.cq.b.611.29	yes	128	168.107	even	6	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+(-0.212988 - 1.39808i) q^{2} +(0.702074 + 1.58338i) q^{3} +(-1.90927 + 0.595551i) 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} +(-2.01418 + 2.22330i) q^{9} +(1.10428 - 0.883495i) q^{10} +(-4.04336 - 2.33444i) q^{11} +(-2.28343 - 2.60498i) q^{12} -4.34878i q^{13} +(0.380114 + 3.72230i) q^{14} +(-1.02021 + 1.39970i) q^{15} +(3.29064 - 2.27414i) q^{16} +(1.67559 + 0.967404i) q^{17} +(3.53736 + 2.34246i) 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} +(-3.15563 + 3.74726i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-6.07996 + 0.926240i) q^{26} +(-4.93444 - 1.62829i) q^{27} +(5.12312 - 1.32424i) q^{28} +0.0972660 q^{29} +(2.17420 + 1.12822i) q^{30} +(-1.01737 - 0.587378i) q^{31} +(-3.88030 - 4.11622i) q^{32} +(0.857558 - 8.04113i) 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} +(-0.0551292 + 0.0441068i) q^{38} +(6.88577 - 3.05317i) q^{39} +(-1.58221 + 2.34449i) q^{40} -10.8636i q^{41} +(-5.62695 + 3.21520i) q^{42} +8.18596 q^{43} +(9.11016 + 2.04905i) q^{44} +(-2.93253 - 0.632683i) q^{45} +(-7.99942 + 6.40005i) 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} +(-0.355377 + 3.33229i) q^{51} +(2.58992 + 8.30300i) q^{52} +(-7.07548 + 12.2551i) q^{53} +(-1.22551 + 7.24556i) q^{54} -4.66887i q^{55} +(-2.94256 - 6.88050i) q^{56} +(0.0509321 - 0.0698776i) q^{57} +(-0.0207165 - 0.135986i) q^{58} +(-11.8059 - 6.81613i) q^{59} +(1.11426 - 3.28000i) 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} +(-11.4248 + 0.513730i) q^{66} +(1.67973 - 2.90938i) q^{67} +(-3.77530 - 0.849136i) q^{68} +(7.39041 - 10.1395i) q^{69} +(-3.03355 + 2.19034i) q^{70} -6.44542 q^{71} +(-8.14883 - 2.36571i) q^{72} +(-4.51719 + 7.82400i) q^{73} +(3.67740 + 4.59639i) q^{74} +(-1.72228 - 0.183676i) 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} +(3.61478 + 1.71271i) q^{80} +(-0.886135 - 8.95627i) q^{81} +(-15.1883 + 2.31383i) q^{82} +11.4677i q^{83} +(5.69358 + 7.18214i) q^{84} +1.93481i q^{85} +(-1.74351 - 11.4446i) q^{86} +(0.0682880 + 0.154009i) q^{87} +(0.924378 - 13.1732i) 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} +(0.215774 - 2.02326i) q^{93} +(-6.30688 + 5.04590i) q^{94} +(0.0249616 - 0.0432347i) q^{95} +(3.79328 - 9.03388i) q^{96} +6.90641 q^{97} +(-0.517999 - 9.88593i) q^{98} +(13.3342 - 4.28763i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 64 q^{5} + 2 q^{12} + 6 q^{14} + 8 q^{16} - 4 q^{18} - 8 q^{21} + 4 q^{22} + 20 q^{24} - 64 q^{25} + 16 q^{26} - 6 q^{28} + 10 q^{32} + 24 q^{34} + 20 q^{36} + 16 q^{38} + 18 q^{42} - 6 q^{44} + 8 q^{46}+ \cdots - 14 q^{98}+O(q^{100}) \) 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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