LMFDB - Embedded newform 840.2.cf.a.341.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(101,840)] 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([0, 3, 3, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.101"); 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.cf (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$128$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.16
Character	$\chi$	$=$	840.341
Dual form			840.2.cf.a.101.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.32124 - 0.504319i) q^{2} +(1.35380 + 1.08038i) q^{3} +(1.49132 + 1.33265i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.24383 - 2.11019i) q^{6} +(-2.34427 + 1.22654i) q^{7} +(-1.29831 - 2.51285i) q^{8} +(0.665543 + 2.92524i) q^{9} +(0.892064 + 1.09737i) q^{10} +(1.01888 + 1.76474i) q^{11} +(0.579182 + 3.41534i) q^{12} -5.96019 q^{13} +(3.71590 - 0.438284i) q^{14} +(-0.632233 - 1.61254i) q^{15} +(0.448097 + 3.97482i) q^{16} +(-2.37909 - 4.12071i) q^{17} +(0.595918 - 4.20058i) q^{18} +(2.28453 - 3.95692i) q^{19} +(-0.625201 - 1.89977i) q^{20} +(-4.49880 - 0.872225i) q^{21} +(-0.456180 - 2.84548i) q^{22} +(-5.16879 - 2.98420i) q^{23} +(0.957186 - 4.80456i) q^{24} +(0.500000 + 0.866025i) q^{25} +(7.87482 + 3.00584i) q^{26} +(-2.25937 + 4.67923i) q^{27} +(-5.13061 - 1.29492i) q^{28} -3.53059 q^{29} +(0.0220935 + 2.44939i) q^{30} +(-2.75675 + 1.59161i) q^{31} +(1.41254 - 5.47766i) q^{32} +(-0.527248 + 3.48989i) q^{33} +(1.06519 + 6.64425i) q^{34} +(2.64347 + 0.109922i) q^{35} +(-2.90578 + 5.24942i) q^{36} +(9.75183 + 5.63022i) q^{37} +(-5.01395 + 4.07589i) q^{38} +(-8.06890 - 6.43930i) q^{39} +(-0.132053 + 2.82534i) q^{40} -11.4992 q^{41} +(5.50410 + 3.42125i) q^{42} -6.57181i q^{43} +(-0.832310 + 3.98961i) q^{44} +(0.886245 - 2.86611i) q^{45} +(5.32420 + 6.54955i) q^{46} +(0.816535 - 1.41428i) q^{47} +(-3.68770 + 5.86523i) q^{48} +(3.99121 - 5.75067i) q^{49} +(-0.223864 - 1.39638i) q^{50} +(1.23113 - 8.14895i) q^{51} +(-8.88858 - 7.94284i) q^{52} +(-0.876342 - 1.51787i) q^{53} +(5.34499 - 5.04292i) q^{54} -2.03775i q^{55} +(6.12569 + 4.29836i) q^{56} +(7.36779 - 2.88871i) q^{57} +(4.66474 + 1.78055i) q^{58} +(2.50880 - 1.44846i) q^{59} +(1.20608 - 3.24736i) q^{60} +(-1.25565 + 2.17484i) q^{61} +(4.44500 - 0.712610i) q^{62} +(-5.14814 - 6.04125i) q^{63} +(-4.62878 + 6.52490i) q^{64} +(5.16168 + 2.98010i) q^{65} +(2.45663 - 4.34506i) q^{66} +(0.934450 - 0.539505i) q^{67} +(1.94346 - 9.31581i) q^{68} +(-3.77342 - 9.62429i) q^{69} +(-3.43721 - 1.47838i) q^{70} +4.03538i q^{71} +(6.48660 - 5.47028i) q^{72} +(-9.04253 + 5.22071i) q^{73} +(-10.0450 - 12.3569i) q^{74} +(-0.258740 + 1.71262i) q^{75} +(8.68016 - 2.85658i) q^{76} +(-4.55305 - 2.88735i) q^{77} +(7.41346 + 12.5771i) q^{78} +(-3.51232 + 6.08352i) q^{79} +(1.59935 - 3.66635i) q^{80} +(-8.11410 + 3.89375i) q^{81} +(15.1931 + 5.79926i) q^{82} -2.00260i q^{83} +(-5.54680 - 7.29609i) q^{84} +4.75819i q^{85} +(-3.31429 + 8.68290i) q^{86} +(-4.77971 - 3.81439i) q^{87} +(3.11171 - 4.85146i) q^{88} +(-6.55097 + 11.3466i) q^{89} +(-2.61637 + 3.33985i) q^{90} +(13.9723 - 7.31040i) q^{91} +(-3.73145 - 11.3386i) q^{92} +(-5.45164 - 0.823628i) q^{93} +(-1.79208 + 1.45680i) q^{94} +(-3.95692 + 2.28453i) q^{95} +(7.83026 - 5.88956i) q^{96} +8.84076i q^{97} +(-8.17350 + 5.58515i) q^{98} +(-4.48420 + 4.15497i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 30 q^{12} + 16 q^{16} - 10 q^{18} + 8 q^{22} + 128 q^{25} + 12 q^{28} - 40 q^{36} - 54 q^{42} + 16 q^{46} + 16 q^{49} + 36 q^{52} - 72 q^{54} - 16 q^{58} - 14 q^{60} + 80 q^{63} - 48 q^{64} - 60 q^{66}+ \cdots - 144 q^{96}+O(q^{100}) $ 256 * q + 30 * q^12 + 16 * q^16 - 10 * q^18 + 8 * q^22 + 128 * q^25 + 12 * q^28 - 40 * q^36 - 54 * q^42 + 16 * q^46 + 16 * q^49 + 36 * q^52 - 72 * q^54 - 16 * q^58 - 14 * q^60 + 80 * q^63 - 48 * q^64 - 60 * q^66 - 12 * q^70 - 50 * q^72 + 48 * q^73 - 16 * q^78 + 64 * q^79 - 8 * q^81 - 72 * q^82 - 56 * q^84 - 8 * q^88 - 72 * q^94 - 144 * q^96

Character values

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

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$-1$	$1$

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 $

$2$	−1.32124	−	0.504319i	−0.934254	−	0.356608i
$2$	−1.32124	−	0.504319i	−0.934254	−	0.356608i
$3$	1.35380	+	1.08038i	0.781616	+	0.623760i
$3$	1.35380	+	1.08038i	0.781616	+	0.623760i
$4$	1.49132	+	1.33265i	0.745662	+	0.666324i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	−1.24383	−	2.11019i	−0.507791	−	0.861480i
$7$	−2.34427	+	1.22654i	−0.886051	+	0.463588i
$7$	−2.34427	+	1.22654i	−0.886051	+	0.463588i
$8$	−1.29831	−	2.51285i	−0.459022	−	0.888425i
$9$	0.665543	+	2.92524i	0.221848	+	0.975081i
$10$	0.892064	+	1.09737i	0.282095	+	0.347019i
$11$	1.01888	+	1.76474i	0.307203	+	0.532090i	0.977749	−	0.209777i	$-0.0672738\pi$
$11$	1.01888	+	1.76474i	0.307203	+	0.532090i	−0.670547	+	0.741867i	$0.733940\pi$
$12$	0.579182	+	3.41534i	0.167195	+	0.985924i
$13$	−5.96019			−1.65306			−0.826530	−	0.562892i	$-0.809689\pi$
$13$	−5.96019			−1.65306			−0.826530	+	0.562892i	$0.809689\pi$
$14$	3.71590	−	0.438284i	0.993116	−	0.117136i
$15$	−0.632233	−	1.61254i	−0.163242	−	0.416356i
$16$	0.448097	+	3.97482i	0.112024	+	0.993705i
$17$	−2.37909	−	4.12071i	−0.577015	−	0.999419i	−0.995820	−	0.0913428i	$-0.970884\pi$
$17$	−2.37909	−	4.12071i	−0.577015	−	0.999419i	0.418805	−	0.908076i	$-0.362449\pi$
$18$	0.595918	−	4.20058i	0.140459	−	0.990086i
$19$	2.28453	−	3.95692i	0.524107	−	0.907780i	−0.475499	−	0.879716i	$-0.657732\pi$
$19$	2.28453	−	3.95692i	0.524107	−	0.907780i	0.999606	−	0.0280641i	$-0.00893426\pi$
$20$	−0.625201	−	1.89977i	−0.139799	−	0.424801i
$21$	−4.49880	−	0.872225i	−0.981719	−	0.190335i
$22$	−0.456180	−	2.84548i	−0.0972579	−	0.606658i
$23$	−5.16879	−	2.98420i	−1.07777	−	0.622249i	−0.147474	−	0.989066i	$-0.547114\pi$
$23$	−5.16879	−	2.98420i	−1.07777	−	0.622249i	−0.930293	+	0.366817i	$0.880448\pi$
$24$	0.957186	−	4.80456i	0.195385	−	0.980727i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	7.87482	+	3.00584i	1.54438	+	0.589494i
$27$	−2.25937	+	4.67923i	−0.434817	+	0.900519i
$28$	−5.13061	−	1.29492i	−0.969594	−	0.244717i
$29$	−3.53059			−0.655614			−0.327807	−	0.944745i	$-0.606310\pi$
$29$	−3.53059			−0.655614			−0.327807	+	0.944745i	$0.606310\pi$
$30$	0.0220935	+	2.44939i	0.00403370	+	0.447195i
$31$	−2.75675	+	1.59161i	−0.495128	+	0.285862i	−0.726699	−	0.686956i	$-0.758947\pi$
$31$	−2.75675	+	1.59161i	−0.495128	+	0.285862i	0.231572	+	0.972818i	$0.425613\pi$
$32$	1.41254	−	5.47766i	0.249704	−	0.968322i
$33$	−0.527248	+	3.48989i	−0.0917821	+	0.607511i
$34$	1.06519	+	6.64425i	0.182678	+	1.13948i
$35$	2.64347	+	0.109922i	0.446827	+	0.0185803i
$36$	−2.90578	+	5.24942i	−0.484297	+	0.874904i
$37$	9.75183	+	5.63022i	1.60319	+	0.925602i	0.990844	+	0.135013i	$0.0431076\pi$
$37$	9.75183	+	5.63022i	1.60319	+	0.925602i	0.612347	+	0.790589i	$0.290226\pi$
$38$	−5.01395	+	4.07589i	−0.813371	+	0.661197i
$39$	−8.06890	−	6.43930i	−1.29206	−	1.03111i
$40$	−0.132053	+	2.82534i	−0.0208795	+	0.446726i
$41$	−11.4992			−1.79587			−0.897935	−	0.440128i	$-0.854933\pi$
$41$	−11.4992			−1.79587			−0.897935	+	0.440128i	$0.854933\pi$
$42$	5.50410	+	3.42125i	0.849300	+	0.527910i
$43$		−	6.57181i		−	1.00219i	−0.865392	−	0.501096i	$-0.832931\pi$
$43$		−	6.57181i		−	1.00219i	0.865392	−	0.501096i	$-0.167069\pi$
$44$	−0.832310	+	3.98961i	−0.125475	+	0.601456i
$45$	0.886245	−	2.86611i	0.132114	−	0.427254i
$46$	5.32420	+	6.54955i	0.785010	+	0.965679i
$47$	0.816535	−	1.41428i	0.119104	−	0.206294i	−0.800309	−	0.599588i	$-0.795331\pi$
$47$	0.816535	−	1.41428i	0.119104	−	0.206294i	0.919413	+	0.393294i	$0.128665\pi$
$48$	−3.68770	+	5.86523i	−0.532274	+	0.846572i
$49$	3.99121	−	5.75067i	0.570173	−	0.821525i
$50$	−0.223864	−	1.39638i	−0.0316592	−	0.197478i
$51$	1.23113	−	8.14895i	0.172393	−	1.14108i
$52$	−8.88858	−	7.94284i	−1.23262	−	1.10147i
$53$	−0.876342	−	1.51787i	−0.120375	−	0.208495i	0.799541	−	0.600612i	$-0.205076\pi$
$53$	−0.876342	−	1.51787i	−0.120375	−	0.208495i	−0.919916	+	0.392117i	$0.871743\pi$
$54$	5.34499	−	5.04292i	0.727361	−	0.686255i
$55$		−	2.03775i		−	0.274770i
$56$	6.12569	+	4.29836i	0.818580	+	0.574393i
$57$	7.36779	−	2.88871i	0.975888	−	0.382619i
$58$	4.66474	+	1.78055i	0.612511	+	0.233797i
$59$	2.50880	−	1.44846i	0.326618	−	0.188573i	−0.327721	−	0.944775i	$-0.606281\pi$
$59$	2.50880	−	1.44846i	0.326618	−	0.188573i	0.654338	+	0.756202i	$0.272947\pi$
$60$	1.20608	−	3.24736i	0.155705	−	0.419233i
$61$	−1.25565	+	2.17484i	−0.160769	+	0.278460i	−0.935145	−	0.354266i	$-0.884731\pi$
$61$	−1.25565	+	2.17484i	−0.160769	+	0.278460i	0.774376	+	0.632726i	$0.218064\pi$
$62$	4.44500	−	0.712610i	0.564516	−	0.0905016i
$63$	−5.14814	−	6.04125i	−0.648604	−	0.761126i
$64$	−4.62878	+	6.52490i	−0.578598	+	0.815613i
$65$	5.16168	+	2.98010i	0.640228	+	0.369636i
$66$	2.45663	−	4.34506i	0.302391	−	0.534840i
$67$	0.934450	−	0.539505i	0.114161	−	0.0659110i	−0.441832	−	0.897098i	$-0.645671\pi$
$67$	0.934450	−	0.539505i	0.114161	−	0.0659110i	0.555993	+	0.831187i	$0.312338\pi$
$68$	1.94346	−	9.31581i	0.235679	−	1.12971i
$69$	−3.77342	−	9.62429i	−0.454266	−	1.15863i
$70$	−3.43721	−	1.47838i	−0.410825	−	0.176701i
$71$			4.03538i			0.478911i	0.970907	+	0.239456i	$0.0769690\pi$
$71$			4.03538i			0.478911i	−0.970907	+	0.239456i	$0.923031\pi$
$72$	6.48660	−	5.47028i	0.764454	−	0.644679i
$73$	−9.04253	+	5.22071i	−1.05835	+	0.611038i	−0.924975	−	0.380028i	$-0.875914\pi$
$73$	−9.04253	+	5.22071i	−1.05835	+	0.611038i	−0.133373	+	0.991066i	$0.542581\pi$
$74$	−10.0450	−	12.3569i	−1.16771	−	1.43646i
$75$	−0.258740	+	1.71262i	−0.0298767	+	0.197756i
$76$	8.68016	−	2.85658i	0.995683	−	0.327672i
$77$	−4.55305	−	2.88735i	−0.518868	−	0.329044i
$78$	7.41346	+	12.5771i	0.839409	+	1.42408i
$79$	−3.51232	+	6.08352i	−0.395167	+	0.684449i	−0.993122	−	0.117080i	$-0.962647\pi$
$79$	−3.51232	+	6.08352i	−0.395167	+	0.684449i	0.597956	+	0.801529i	$0.295980\pi$
$80$	1.59935	−	3.66635i	0.178813	−	0.409910i
$81$	−8.11410	+	3.89375i	−0.901567	+	0.432639i
$82$	15.1931	+	5.79926i	1.67780	+	0.640421i
$83$		−	2.00260i		−	0.219814i	−0.993942	−	0.109907i	$-0.964945\pi$
$83$		−	2.00260i		−	0.219814i	0.993942	−	0.109907i	$-0.0350553\pi$
$84$	−5.54680	−	7.29609i	−0.605206	−	0.796069i
$85$			4.75819i			0.516098i
$86$	−3.31429	+	8.68290i	−0.357389	+	0.936301i
$87$	−4.77971	−	3.81439i	−0.512439	−	0.408946i
$88$	3.11171	−	4.85146i	0.331710	−	0.517168i
$89$	−6.55097	+	11.3466i	−0.694402	+	1.20274i	0.275980	+	0.961163i	$0.410998\pi$
$89$	−6.55097	+	11.3466i	−0.694402	+	1.20274i	−0.970382	+	0.241576i	$0.922336\pi$
$90$	−2.61637	+	3.33985i	−0.275790	+	0.352051i
$91$	13.9723	−	7.31040i	1.46470	−	0.766339i
$92$	−3.73145	−	11.3386i	−0.389031	−	1.18213i
$93$	−5.45164	−	0.823628i	−0.565309	−	0.0854062i
$94$	−1.79208	+	1.45680i	−0.184839	+	0.150258i
$95$	−3.95692	+	2.28453i	−0.405972	+	0.234388i
$96$	7.83026	−	5.88956i	0.799173	−	0.601101i
$97$			8.84076i			0.897643i	0.893621	+	0.448822i	$0.148156\pi$
$97$			8.84076i			0.897643i	−0.893621	+	0.448822i	$0.851844\pi$
$98$	−8.17350	+	5.58515i	−0.825648	+	0.564185i
$99$	−4.48420	+	4.15497i	−0.450679	+	0.417591i
$100$	−0.408445	+	1.95785i	−0.0408445	+	0.195785i
$101$	12.0870	−	6.97842i	1.20270	−	0.694378i	0.241544	−	0.970390i	$-0.422346\pi$
$101$	12.0870	−	6.97842i	1.20270	−	0.694378i	0.961154	+	0.276011i	$0.0890128\pi$
$102$	−5.73629	+	10.1458i	−0.567977	+	1.00458i
$103$	−16.4114	−	9.47511i	−1.61706	−	0.933610i	−0.987675	−	0.156517i	$-0.949974\pi$
$103$	−16.4114	−	9.47511i	−1.61706	−	0.933610i	−0.629385	−	0.777094i	$-0.716693\pi$
$104$	7.73818	+	14.9770i	0.758791	+	1.46862i
$105$	3.45996	+	3.00477i	0.337658	+	0.293236i
$106$	0.392363	+	2.44742i	0.0381097	+	0.237714i
$107$	−8.54657	+	14.8031i	−0.826228	+	1.43107i	0.0747490	+	0.997202i	$0.476184\pi$
$107$	−8.54657	+	14.8031i	−0.826228	+	1.43107i	−0.900977	+	0.433867i	$0.857149\pi$
$108$	−9.60523	+	3.96731i	−0.924264	+	0.381754i
$109$	−2.12001	+	1.22399i	−0.203061	+	0.117237i	−0.598082	−	0.801435i	$-0.704070\pi$
$109$	−2.12001	+	1.22399i	−0.203061	+	0.117237i	0.395022	+	0.918672i	$0.370737\pi$
$110$	−1.02768	+	2.69235i	−0.0979852	+	0.256705i
$111$	7.11922	+	18.1579i	0.675726	+	1.72347i
$112$	−5.92573	−	8.76845i	−0.559929	−	0.828541i
$113$		−	3.52795i		−	0.331881i	−0.986136	−	0.165941i	$-0.946934\pi$
$113$		−	3.52795i		−	0.331881i	0.986136	−	0.165941i	$-0.0530660\pi$
$114$	−11.1914	+	0.100947i	−1.04817	+	0.00945451i
$115$	2.98420	+	5.16879i	0.278278	+	0.481992i
$116$	−5.26526	−	4.70504i	−0.488867	−	0.436852i
$117$	−3.96677	−	17.4350i	−0.366728	−	1.61187i
$118$	−4.04520	+	0.648515i	−0.372391	+	0.0597007i
$119$	10.6314	+	6.74201i	0.974583	+	0.618039i
$120$	−3.23123	+	3.68228i	−0.294969	+	0.336144i
$121$	3.42379	−	5.93017i	0.311253	−	0.539106i
$122$	2.75582	−	2.24023i	0.249500	−	0.202821i
$123$	−15.5676	−	12.4235i	−1.40368	−	1.12019i
$124$	−6.23227	−	1.30017i	−0.559675	−	0.116759i
$125$		−	1.00000i		−	0.0894427i
$126$	3.75518	+	10.5782i	0.334538	+	0.942382i
$127$	6.88062			0.610556			0.305278	−	0.952263i	$-0.401251\pi$
$127$	6.88062			0.610556			0.305278	+	0.952263i	$0.401251\pi$
$128$	9.40634	−	6.28655i	0.831411	−	0.555658i
$129$	7.10007	−	8.89690i	0.625126	−	0.783329i
$130$	−5.31687	−	6.54054i	−0.466321	−	0.573644i
$131$	2.05006	+	1.18360i	0.179114	+	0.103412i	0.586876	−	0.809676i	$-0.300357\pi$
$131$	2.05006	+	1.18360i	0.179114	+	0.103412i	−0.407762	+	0.913088i	$0.633691\pi$
$132$	−5.43709	+	4.50191i	−0.473238	+	0.391841i
$133$	−0.502242	+	12.0782i	−0.0435499	+	1.04731i
$134$	−1.50671	+	0.241552i	−0.130160	+	0.0208669i
$135$	4.29629	−	2.92265i	0.369766	−	0.251542i
$136$	−7.26591	+	11.3283i	−0.623046	+	0.971390i
$137$	−14.4579	+	8.34728i	−1.23522	+	0.713156i	−0.968114	−	0.250510i	$-0.919402\pi$
$137$	−14.4579	+	8.34728i	−1.23522	+	0.713156i	−0.267109	+	0.963666i	$0.586068\pi$
$138$	0.131863	+	14.6190i	0.0112249	+	1.24445i
$139$	−5.83902			−0.495260			−0.247630	−	0.968855i	$-0.579652\pi$
$139$	−5.83902			−0.495260			−0.247630	+	0.968855i	$0.579652\pi$
$140$	3.79578	+	3.68674i	0.320802	+	0.311587i
$141$	2.63339	−	1.03248i	0.221771	−	0.0869505i
$142$	2.03512	−	5.33168i	0.170783	−	0.447425i
$143$	−6.07270	−	10.5182i	−0.507824	−	0.879578i
$144$	−11.3291	+	3.95621i	−0.944091	+	0.329684i
$145$	3.05758	+	1.76530i	0.253918	+	0.146600i
$146$	14.5802	−	2.33746i	1.20667	−	0.193450i
$147$	11.6162	−	3.47322i	0.958090	−	0.286466i
$148$	7.04003	+	21.3922i	0.578687	+	1.75843i
$149$	−9.35904	+	16.2103i	−0.766723	+	1.32800i	0.172608	+	0.984991i	$0.444781\pi$
$149$	−9.35904	+	16.2103i	−0.766723	+	1.32800i	−0.939331	+	0.343012i	$0.888553\pi$
$150$	1.20556	−	2.13228i	0.0984337	−	0.174100i
$151$	−8.74283	−	15.1430i	−0.711481	−	1.23232i	−0.964301	−	0.264808i	$-0.914691\pi$
$151$	−8.74283	−	15.1430i	−0.711481	−	1.23232i	0.252820	−	0.967513i	$-0.418642\pi$
$152$	−12.9092	−	0.603359i	−1.04707	−	0.0489389i
$153$	10.4707	−	9.70194i	0.846506	−	0.784355i
$154$	4.55950	+	6.11105i	0.367415	+	0.492443i
$155$	3.18322			0.255683
$156$	−3.45204	−	20.3561i	−0.276384	−	1.62979i
$157$	5.77625	+	10.0048i	0.460995	+	0.798467i	0.999011	−	0.0444676i	$-0.0141592\pi$
$157$	5.77625	+	10.0048i	0.460995	+	0.798467i	−0.538015	+	0.842935i	$0.680826\pi$
$158$	7.70863	−	6.26642i	0.613266	−	0.498530i
$159$	0.453489	−	3.00167i	0.0359641	−	0.238048i
$160$	−3.96212	+	4.03752i	−0.313233	+	0.319194i
$161$	15.7773	+	0.656061i	1.24342	+	0.0517048i
$162$	12.6843	−	1.05246i	0.996575	−	0.0826893i
$163$	0.231398	+	0.133598i	0.0181245	+	0.0104642i	0.509035	−	0.860746i	$-0.330002\pi$
$163$	0.231398	+	0.133598i	0.0181245	+	0.0104642i	−0.490910	+	0.871210i	$0.663336\pi$
$164$	−17.1490	−	15.3244i	−1.33911	−	1.19663i
$165$	2.20155	−	2.75871i	0.171391	−	0.214765i
$166$	−1.00995	+	2.64591i	−0.0783874	+	0.205362i
$167$	−14.6746			−1.13556			−0.567778	−	0.823182i	$-0.692197\pi$
$167$	−14.6746			−1.13556			−0.567778	+	0.823182i	$0.692197\pi$
$168$	3.64907	+	12.4372i	0.281532	+	0.959552i
$169$	22.5239			1.73261
$170$	2.39965	−	6.28668i	0.184044	−	0.482167i
$171$	13.0954	+	4.04931i	1.00143	+	0.309658i
$172$	8.75791	−	9.80070i	0.667784	−	0.747296i
$173$	18.3036	+	10.5676i	1.39160	+	0.803438i	0.993492	−	0.113902i	$-0.0363350\pi$
$173$	18.3036	+	10.5676i	1.39160	+	0.803438i	0.398104	+	0.917340i	$0.369668\pi$
$174$	4.39145	+	7.45021i	0.332915	+	0.564799i
$175$	−2.23435	−	1.41693i	−0.168901	−	0.107110i
$176$	−6.55799	+	4.84062i	−0.494327	+	0.364876i
$177$	4.96130	+	0.749547i	0.372914	+	0.0563394i
$178$	14.3777	−	11.6878i	1.07765	−	0.876035i
$179$	−0.931323	−	1.61310i	−0.0696104	−	0.120569i	0.829119	−	0.559071i	$-0.188842\pi$
$179$	−0.931323	−	1.61310i	−0.0696104	−	0.120569i	−0.898730	+	0.438503i	$0.855509\pi$
$180$	5.14119	−	3.09324i	0.383202	−	0.230557i
$181$	6.07234			0.451354			0.225677	−	0.974202i	$-0.427541\pi$
$181$	6.07234			0.451354			0.225677	+	0.974202i	$0.427541\pi$
$182$	−22.1475	+	2.61226i	−1.64168	+	0.193634i
$183$	−4.04956	+	1.58772i	−0.299352	+	0.117368i
$184$	−0.788147	+	16.8628i	−0.0581030	+	1.24314i
$185$	−5.63022	−	9.75183i	−0.413942	−	0.716969i
$186$	6.78753	+	3.83757i	0.497686	+	0.281385i
$187$	4.84800	−	8.39698i	0.354521	−	0.614048i
$188$	3.10246	−	1.02100i	0.226270	−	0.0744638i
$189$	−0.442675	−	13.7406i	−0.0321999	−	0.999481i
$190$	6.38016	−	1.02285i	0.462865	−	0.0742053i
$191$	2.27870	+	1.31561i	0.164881	+	0.0951941i	0.580170	−	0.814496i	$-0.302986\pi$
$191$	2.27870	+	1.31561i	0.164881	+	0.0951941i	−0.415289	+	0.909690i	$0.636320\pi$
$192$	−13.3158	+	3.83255i	−0.960988	+	0.276590i
$193$	12.0880	+	20.9371i	0.870115	+	1.50708i	0.861877	+	0.507117i	$0.169289\pi$
$193$	12.0880	+	20.9371i	0.870115	+	1.50708i	0.00823741	+	0.999966i	$0.497378\pi$
$194$	4.45857	−	11.6807i	0.320106	−	0.838627i
$195$	3.76823	+	9.61105i	0.269848	+	0.688261i
$196$	13.6158	−	3.25724i	0.972558	−	0.232660i
$197$	8.33518			0.593857			0.296929	−	0.954900i	$-0.404038\pi$
$197$	8.33518			0.593857			0.296929	+	0.954900i	$0.404038\pi$
$198$	8.02012	−	3.22823i	0.569965	−	0.229420i
$199$	20.6962	−	11.9489i	1.46711	−	0.847038i	0.467790	−	0.883839i	$-0.345050\pi$
$199$	20.6962	−	11.9489i	1.46711	−	0.847038i	0.999323	+	0.0368015i	$0.0117169\pi$
$200$	1.52703	−	2.38079i	0.107978	−	0.168347i
$201$	1.84793	+	0.279183i	0.130343	+	0.0196921i
$202$	−19.4891	+	3.12444i	−1.37125	+	0.219835i
$203$	8.27666	−	4.33040i	0.580908	−	0.303935i
$204$	12.6957	−	10.5121i	0.888877	−	0.735991i
$205$	9.95858	+	5.74959i	0.695538	+	0.401569i
$206$	16.9048	+	20.7954i	1.17781	+	1.44889i
$207$	5.28947	−	17.1061i	0.367643	−	1.18896i
$208$	−2.67074	−	23.6907i	−0.185183	−	1.64266i
$209$	9.31061			0.644028
$210$	−3.05606	−	5.71493i	−0.210888	−	0.394368i
$211$			9.87780i			0.680016i	0.940423	+	0.340008i	$0.110430\pi$
$211$			9.87780i			0.680016i	−0.940423	+	0.340008i	$0.889570\pi$
$212$	0.715875	−	3.43149i	0.0491665	−	0.235676i
$213$	−4.35976	+	5.46309i	−0.298726	+	0.374325i
$214$	18.7575	−	15.2482i	1.28224	−	1.04234i
$215$	−3.28590	+	5.69135i	−0.224097	+	0.388147i
$216$	14.6916	−	0.397640i	0.999634	−	0.0270560i
$217$	4.51040	−	7.11243i	0.306186	−	0.482823i
$218$	3.41832	−	0.548016i	0.231518	−	0.0371163i
$219$	−17.8821	−	2.70161i	−1.20836	−	0.182558i
$220$	2.71561	−	3.03895i	0.183086	−	0.204886i
$221$	14.1799	+	24.5602i	0.953841	+	1.65210i
$222$	−0.248782	−	27.5812i	−0.0166972	−	1.85113i
$223$		−	7.54448i		−	0.505216i	−0.967569	−	0.252608i	$-0.918712\pi$
$223$		−	7.54448i		−	0.505216i	0.967569	−	0.252608i	$-0.0812882\pi$
$224$	3.40718	+	14.5736i	0.227652	+	0.973743i
$225$	−2.20056	+	2.03900i	−0.146704	+	0.135933i
$226$	−1.77921	+	4.66125i	−0.118351	+	0.310062i
$227$	2.09993	−	1.21240i	0.139378	−	0.0804697i	−0.428690	−	0.903452i	$-0.641025\pi$
$227$	2.09993	−	1.21240i	0.139378	−	0.0804697i	0.568067	+	0.822982i	$0.307691\pi$
$228$	14.8374	+	5.51067i	0.982631	+	0.364953i
$229$	1.24517	−	2.15670i	0.0822831	−	0.142518i	−0.821947	−	0.569564i	$-0.807112\pi$
$229$	1.24517	−	2.15670i	0.0822831	−	0.142518i	0.904230	+	0.427045i	$0.140446\pi$
$230$	−1.33611	−	8.33418i	−0.0881007	−	0.549539i
$231$	−3.04447	−	8.82792i	−0.200311	−	0.580835i
$232$	4.58380	+	8.87183i	0.300941	+	0.582464i
$233$	0.556527	+	0.321311i	0.0364593	+	0.0210498i	0.518119	−	0.855309i	$-0.326632\pi$
$233$	0.556527	+	0.321311i	0.0364593	+	0.0210498i	−0.481660	+	0.876358i	$0.659966\pi$
$234$	−3.55178	+	25.0363i	−0.232187	+	1.63667i
$235$	−1.41428	+	0.816535i	−0.0922574	+	0.0532649i
$236$	5.67171	+	1.18323i	0.369197	+	0.0770217i
$237$	−11.3275	+	4.44121i	−0.735801	+	0.288487i
$238$	−10.6465	−	14.2694i	−0.690111	−	0.924950i
$239$		−	18.0234i		−	1.16584i	−0.812531	−	0.582918i	$-0.801911\pi$
$239$		−	18.0234i		−	1.16584i	0.812531	−	0.582918i	$-0.198089\pi$
$240$	6.12625	−	3.23559i	0.395448	−	0.208856i
$241$	4.22950	−	2.44190i	0.272446	−	0.157297i	−0.357553	−	0.933893i	$-0.616389\pi$
$241$	4.22950	−	2.44190i	0.272446	−	0.157297i	0.629999	+	0.776596i	$0.283055\pi$
$242$	−7.51432	+	6.10847i	−0.483039	+	0.392667i
$243$	−15.1916	−	3.49499i	−0.974542	−	0.224204i
$244$	−4.77088	+	1.57006i	−0.305424	+	0.100513i
$245$	−6.33183	+	2.98462i	−0.404525	+	0.190681i
$246$	14.3030	+	24.2654i	0.911927	+	1.54711i
$247$	−13.6162	+	23.5840i	−0.866381	+	1.50062i
$248$	7.57860	+	4.86089i	0.481241	+	0.308667i
$249$	2.16358	−	2.71112i	0.137111	−	0.171810i
$250$	−0.504319	+	1.32124i	−0.0318959	+	0.0835622i
$251$		−	6.03006i		−	0.380614i	−0.981725	−	0.190307i	$-0.939052\pi$
$251$		−	6.03006i		−	0.380614i	0.981725	−	0.190307i	$-0.0609484\pi$
$252$	0.373321	−	15.8701i	0.0235170	−	0.999723i
$253$		−	12.1621i		−	0.764626i
$254$	−9.09092	−	3.47003i	−0.570415	−	0.217729i
$255$	−5.14067	+	6.44163i	−0.321921	+	0.403390i
$256$	−15.5984	+	3.56221i	−0.974901	+	0.222638i
$257$	−2.64867	+	4.58762i	−0.165219	+	0.286168i	−0.936733	−	0.350044i	$-0.886166\pi$
$257$	−2.64867	+	4.58762i	−0.165219	+	0.286168i	0.771514	+	0.636212i	$0.219500\pi$
$258$	−13.8677	+	8.17420i	−0.863368	+	0.508904i
$259$	−29.7666	−	1.23777i	−1.84961	−	0.0769115i
$260$	3.72632	+	11.3230i	0.231096	+	0.702222i
$261$	−2.34976	−	10.3278i	−0.145447	−	0.639277i
$262$	−2.11169	−	2.59770i	−0.130461	−	0.160486i
$263$	2.68275	−	1.54889i	0.165426	−	0.0955085i	−0.415001	−	0.909821i	$-0.636219\pi$
$263$	2.68275	−	1.54889i	0.165426	−	0.0955085i	0.580427	+	0.814312i	$0.302886\pi$
$264$	9.45407	−	3.20606i	0.581858	−	0.197319i
$265$			1.75268i			0.107667i
$266$	6.75483	−	15.7048i	0.414165	−	0.962923i
$267$	−21.1274	+	8.28347i	−1.29298	+	0.506940i
$268$	2.11254	+	0.440716i	0.129044	+	0.0269210i
$269$	12.1651	−	7.02354i	0.741721	−	0.428233i	−0.0809736	−	0.996716i	$-0.525803\pi$
$269$	12.1651	−	7.02354i	0.741721	−	0.428233i	0.822695	+	0.568483i	$0.192470\pi$
$270$	−7.15036	+	1.69480i	−0.435157	+	0.103142i
$271$	−4.54653	−	2.62494i	−0.276182	−	0.159454i	0.355512	−	0.934672i	$-0.384307\pi$
$271$	−4.54653	−	2.62494i	−0.276182	−	0.159454i	−0.631694	+	0.775218i	$0.717640\pi$
$272$	15.3130	−	11.3030i	0.928489	−	0.685342i
$273$	26.8137	+	5.19863i	1.62284	+	0.314636i
$274$	23.3120	−	3.73732i	1.40833	−	0.225780i
$275$	−1.01888	+	1.76474i	−0.0614405	+	0.106418i
$276$	7.19840	−	19.3816i	0.433292	−	1.16663i
$277$	10.5840	−	6.11068i	0.635932	−	0.367155i	−0.147114	−	0.989120i	$-0.546998\pi$
$277$	10.5840	−	6.11068i	0.635932	−	0.367155i	0.783046	+	0.621964i	$0.213665\pi$
$278$	7.71472	+	2.94473i	0.462698	+	0.176613i
$279$	−6.49059	−	7.00489i	−0.388582	−	0.419372i
$280$	−3.15582	−	6.78534i	−0.188596	−	0.405501i
$281$			25.6475i			1.53000i	0.644028	+	0.765002i	$0.277262\pi$
$281$			25.6475i			1.53000i	−0.644028	+	0.765002i	$0.722738\pi$
$282$	−4.00002	+	0.0360802i	−0.238198	+	0.00214855i
$283$	−9.08093	−	15.7286i	−0.539805	−	0.934970i	−0.998914	−	0.0465899i	$-0.985165\pi$
$283$	−9.08093	−	15.7286i	−0.539805	−	0.934970i	0.459109	−	0.888380i	$-0.348169\pi$
$284$	−5.37774	+	6.01806i	−0.319110	+	0.357106i
$285$	−7.82505	−	1.18220i	−0.463516	−	0.0700274i
$286$	2.71892	+	16.9596i	0.160773	+	1.00284i
$287$	26.9572	−	14.1042i	1.59123	−	0.832544i
$288$	16.9636	+	0.486400i	0.999589	+	0.0286614i
$289$	−2.82017	+	4.88468i	−0.165893	+	0.287334i
$290$	−3.14951	−	3.87437i	−0.184946	−	0.227511i
$291$	−9.55141	+	11.9686i	−0.559914	+	0.701612i
$292$	−20.4427	−	4.26475i	−1.19632	−	0.249575i
$293$		−	4.11316i		−	0.240293i	−0.992756	−	0.120147i	$-0.961664\pi$
$293$		−	4.11316i		−	0.240293i	0.992756	−	0.120147i	$-0.0383365\pi$
$294$	−17.0994	−	1.26935i	−0.997256	−	0.0740298i
$295$	−2.89691			−0.168665
$296$	1.48698	−	31.8146i	0.0864288	−	1.84919i
$297$	−10.5597	+	0.780341i	−0.612734	+	0.0452800i
$298$	20.5407	−	16.6977i	1.18989	−	0.967273i
$299$	30.8070	+	17.7864i	1.78161	+	1.02862i
$300$	−2.66818	+	2.20926i	−0.154047	+	0.127551i
$301$	8.06057	+	15.4061i	0.464604	+	0.887992i
$302$	3.91442	+	24.4167i	0.225249	+	1.40502i
$303$	23.9027	+	3.61119i	1.37317	+	0.207458i
$304$	16.7518	+	7.30752i	0.960779	+	0.419115i
$305$	2.17484	−	1.25565i	0.124531	−	0.0718981i
$306$	−18.7271	+	7.53797i	−1.07056	+	0.430917i
$307$	12.4955			0.713158			0.356579	−	0.934265i	$-0.383943\pi$
$307$	12.4955			0.713158			0.356579	+	0.934265i	$0.383943\pi$
$308$	−2.94225	−	10.3736i	−0.167650	−	0.591090i
$309$	−11.9809	−	30.5580i	−0.681572	−	1.73838i
$310$	−4.20579	−	1.60536i	−0.238873	−	0.0911784i
$311$	9.06986	+	15.7095i	0.514304	+	0.890801i	0.999862	+	0.0165969i	$0.00528319\pi$
$311$	9.06986	+	15.7095i	0.514304	+	0.890801i	−0.485558	+	0.874205i	$0.661383\pi$
$312$	−5.70501	+	28.6361i	−0.322983	+	1.62120i
$313$	2.29334	+	1.32406i	0.129627	+	0.0748404i	0.563411	−	0.826176i	$-0.309489\pi$
$313$	2.29334	+	1.32406i	0.129627	+	0.0748404i	−0.433784	+	0.901017i	$0.642822\pi$
$314$	−2.58619	−	16.1317i	−0.145947	−	0.910366i
$315$	1.43779	+	7.80594i	0.0810104	+	0.439815i
$316$	−13.3452	+	4.39181i	−0.750726	+	0.247059i
$317$	−8.69014	+	15.0518i	−0.488087	+	0.845392i	−0.999906	−	0.0137016i	$-0.995638\pi$
$317$	−8.69014	+	15.0518i	−0.488087	+	0.845392i	0.511819	+	0.859093i	$0.328972\pi$
$318$	−2.11297	+	3.73721i	−0.118489	+	0.209573i
$319$	−3.59723	−	6.23059i	−0.201406	−	0.348846i
$320$	7.27110	−	3.33634i	0.406467	−	0.186507i
$321$	−27.5634	+	10.8068i	−1.53844	+	0.603179i
$322$	−20.5146	−	8.82360i	−1.14324	−	0.491720i
$323$	−21.7405			−1.20967
$324$	−17.2898	−	5.00640i	−0.960542	−	0.278133i
$325$	−2.98010	−	5.16168i	−0.165306	−	0.286318i
$326$	−0.238355	−	0.293212i	−0.0132013	−	0.0162395i
$327$	−4.19245	−	0.633391i	−0.231843	−	0.0350266i
$328$	14.9295	+	28.8957i	0.824344	+	1.59550i
$329$	−0.179511	+	4.31696i	−0.00989675	+	0.238002i
$330$	−4.30004	+	2.53461i	−0.236709	+	0.139526i
$331$	−21.2415	−	12.2638i	−1.16754	−	0.674080i	−0.214441	−	0.976737i	$-0.568793\pi$
$331$	−21.2415	−	12.2638i	−1.16754	−	0.674080i	−0.953099	+	0.302657i	$0.902126\pi$
$332$	2.66877	−	2.98653i	0.146468	−	0.163907i
$333$	−9.97950	+	32.2736i	−0.546873	+	1.76858i
$334$	19.3886	+	7.40069i	1.06090	+	0.404947i
$335$	−1.07901			−0.0589526
$336$	1.45104	−	18.2728i	0.0791609	−	0.996862i
$337$	2.04124			0.111193			0.0555967	−	0.998453i	$-0.482294\pi$
$337$	2.04124			0.111193			0.0555967	+	0.998453i	$0.482294\pi$
$338$	−29.7594	−	11.3592i	−1.61870	−	0.617861i
$339$	3.81153	−	4.77613i	0.207014	−	0.259404i
$340$	−6.34099	+	7.09600i	−0.343888	+	0.384835i
$341$	−5.61758	−	3.24331i	−0.304209	−	0.175635i
$342$	−15.2600	−	11.9544i	−0.825166	−	0.646418i
$343$	−2.30306	+	18.3765i	−0.124353	+	0.992238i
$344$	−16.5139	+	8.53224i	−0.890372	+	0.460028i
$345$	−1.54427	+	10.2216i	−0.0831404	+	0.550312i
$346$	−18.8539	−	23.1931i	−1.01359	−	1.24687i
$347$	7.64008	+	13.2330i	0.410141	+	0.710385i	0.994905	−	0.100819i	$-0.0321462\pi$
$347$	7.64008	+	13.2330i	0.410141	+	0.710385i	−0.584764	+	0.811203i	$0.698813\pi$
$348$	−2.04486	−	12.0582i	−0.109616	−	0.646386i
$349$	−26.7402			−1.43137			−0.715686	−	0.698422i	$-0.753886\pi$
$349$	−26.7402			−1.43137			−0.715686	+	0.698422i	$0.753886\pi$
$350$	2.23751	+	2.99892i	0.119600	+	0.160299i
$351$	13.4663	−	27.8891i	0.718778	−	1.48861i
$352$	11.1059	−	3.08828i	0.591945	−	0.164606i
$353$	−3.99904	−	6.92654i	−0.212847	−	0.368662i	0.739757	−	0.672874i	$-0.234940\pi$
$353$	−3.99904	−	6.92654i	−0.212847	−	0.368662i	−0.952604	+	0.304212i	$0.901607\pi$
$354$	−6.17703	−	3.49240i	−0.328305	−	0.185619i
$355$	2.01769	−	3.49474i	0.107088	−	0.185482i
$356$	−24.8907	+	8.19134i	−1.31920	+	0.434140i
$357$	7.10888	+	20.6134i	0.376242	+	1.09098i
$358$	0.416980	+	2.60097i	0.0220381	+	0.137465i
$359$	12.5311	+	7.23483i	0.661366	+	0.381840i	0.792797	−	0.609485i	$-0.208624\pi$
$359$	12.5311	+	7.23483i	0.661366	+	0.381840i	−0.131431	+	0.991325i	$0.541957\pi$
$360$	−8.35270	+	1.49410i	−0.440226	+	0.0787460i
$361$	−0.938162	−	1.62494i	−0.0493770	−	0.0855234i
$362$	−8.02299	−	3.06240i	−0.421679	−	0.160956i
$363$	11.0420	−	4.32926i	0.579553	−	0.227227i
$364$	30.5794	+	7.71799i	1.60280	+	0.404533i
$365$	10.4414			0.546529
$366$	6.15114	−	0.0554832i	0.321525	−	0.00290016i
$367$	4.52199	−	2.61077i	0.236046	−	0.136281i	−0.377312	−	0.926086i	$-0.623152\pi$
$367$	4.52199	−	2.61077i	0.236046	−	0.136281i	0.613358	+	0.789805i	$0.289818\pi$
$368$	9.54556	−	21.8822i	0.497596	−	1.14069i
$369$	−7.65320	−	33.6379i	−0.398410	−	1.75112i
$370$	2.52081	+	15.7239i	0.131051	+	0.817446i
$371$	3.91611	+	2.48343i	0.203314	+	0.128933i
$372$	−7.03256	−	8.49342i	−0.364621	−	0.440363i
$373$	−15.5047	−	8.95166i	−0.802805	−	0.463500i	0.0416461	−	0.999132i	$-0.486740\pi$
$373$	−15.5047	−	8.95166i	−0.802805	−	0.463500i	−0.844451	+	0.535633i	$0.820073\pi$
$374$	−10.6401	+	8.64945i	−0.550187	+	0.447252i
$375$	1.08038	−	1.35380i	0.0557908	−	0.0699099i
$376$	−4.61398	−	0.215652i	−0.237948	−	0.0111214i
$377$	21.0430			1.08377
$378$	−6.34477	+	18.3778i	−0.326340	+	0.945253i
$379$			27.2977i			1.40219i	0.713069	+	0.701094i	$0.247305\pi$
$379$			27.2977i			1.40219i	−0.713069	+	0.701094i	$0.752695\pi$
$380$	−8.94553	−	1.86621i	−0.458896	−	0.0957346i
$381$	9.31497	+	7.43371i	0.477221	+	0.380840i
$382$	−2.34721	−	2.88742i	−0.120094	−	0.147733i
$383$	−5.57647	+	9.65872i	−0.284944	+	0.493538i	−0.972596	−	0.232503i	$-0.925308\pi$
$383$	−5.57647	+	9.65872i	−0.284944	+	0.493538i	0.687651	+	0.726041i	$0.258642\pi$
$384$	19.5262	+	1.65174i	0.996441	+	0.0842898i
$385$	2.49938	+	4.77704i	0.127380	+	0.243461i
$386$	−5.41215	−	33.7590i	−0.275471	−	1.71829i
$387$	19.2241	−	4.37382i	0.977218	−	0.222334i
$388$	−11.7816	+	13.1844i	−0.598121	+	0.669339i
$389$	−16.9720	−	29.3964i	−0.860515	−	1.49046i	−0.871432	−	0.490516i	$-0.836808\pi$
$389$	−16.9720	−	29.3964i	−0.860515	−	1.49046i	0.0109173	−	0.999940i	$-0.496525\pi$
$390$	−0.131682	−	14.5988i	−0.00666795	−	0.739241i
$391$			28.3988i			1.43619i
$392$	−19.6324	−	2.56313i	−0.991585	−	0.129458i
$393$	1.49662	+	3.81721i	0.0754946	+	0.192553i
$394$	−11.0127	−	4.20359i	−0.554814	−	0.211774i
$395$	6.08352	−	3.51232i	0.306095	−	0.176724i
$396$	−12.2245	+	0.220548i	−0.614305	+	0.0110830i
$397$	−2.49505	+	4.32155i	−0.125223	+	0.216892i	−0.921820	−	0.387618i	$-0.873298\pi$
$397$	−2.49505	+	4.32155i	−0.125223	+	0.216892i	0.796597	+	0.604511i	$0.206631\pi$
$398$	−33.3706	+	5.34988i	−1.67272	+	0.268165i
$399$	−13.7290	+	15.8088i	−0.687309	+	0.791429i
$400$	−3.21825	+	2.37547i	−0.160912	+	0.118774i
$401$	16.9190	+	9.76819i	0.844894	+	0.487800i	0.858925	−	0.512102i	$-0.171133\pi$
$401$	16.9190	+	9.76819i	0.844894	+	0.487800i	−0.0140306	+	0.999902i	$0.504466\pi$
$402$	−2.30075	−	1.30081i	−0.114751	−	0.0648786i
$403$	16.4308	−	9.48632i	0.818476	−	0.472547i
$404$	27.3254	+	5.70060i	1.35949	+	0.283615i
$405$	8.97390	+	0.684964i	0.445917	+	0.0340361i
$406$	−13.1193	+	1.54740i	−0.651101	+	0.0767963i
$407$			22.9460i			1.13739i
$408$	−22.0754	+	7.48621i	−1.09290	+	0.370623i
$409$	−23.8669	+	13.7796i	−1.18014	+	0.681355i	−0.956047	−	0.293212i	$-0.905276\pi$
$409$	−23.8669	+	13.7796i	−1.18014	+	0.681355i	−0.224094	+	0.974567i	$0.571942\pi$
$410$	−10.2580	−	12.6189i	−0.506607	−	0.623201i
$411$	−28.5914	−	4.31955i	−1.41031	−	0.213068i
$412$	−11.8477	−	36.0010i	−0.583694	−	1.77364i
$413$	−4.10472	+	6.47271i	−0.201980	+	0.318501i
$414$	−15.6156	+	19.9336i	−0.767463	+	0.979682i
$415$	−1.00130	+	1.73431i	−0.0491520	+	0.0851337i
$416$	−8.41900	+	32.6479i	−0.412775	+	1.60070i
$417$	−7.90487	−	6.30839i	−0.387103	−	0.308923i
$418$	−12.3015	−	4.69552i	−0.601686	−	0.229665i
$419$			18.0506i			0.881831i	0.897549	+	0.440915i	$0.145346\pi$
$419$			18.0506i			0.881831i	−0.897549	+	0.440915i	$0.854654\pi$
$420$	1.15563	+	9.09200i	0.0563888	+	0.443644i
$421$			16.1056i			0.784940i	0.919765	+	0.392470i	$0.128379\pi$
$421$			16.1056i			0.784940i	−0.919765	+	0.392470i	$0.871621\pi$
$422$	4.98156	−	13.0509i	0.242499	−	0.635307i
$423$	4.68055	+	1.44730i	0.227576	+	0.0703701i
$424$	−2.67641	+	4.17278i	−0.129978	+	0.202648i
$425$	2.37909	−	4.12071i	0.115403	−	0.199884i
$426$	8.51540	−	5.01932i	0.412573	−	0.243187i
$427$	0.276047	−	6.63852i	0.0133589	−	0.321260i
$428$	−32.4730	+	10.6866i	−1.56964	+	0.516558i
$429$	3.14250	−	20.8004i	0.151721	−	1.00425i
$430$	7.21171	−	5.86247i	0.347779	−	0.282713i
$431$	17.9764	−	10.3787i	0.865891	−	0.499922i	−8.98140e−5	−	1.00000i	$-0.500029\pi$
$431$	17.9764	−	10.3787i	0.865891	−	0.499922i	0.865980	+	0.500078i	$0.166695\pi$
$432$	−19.6115	−	6.88386i	−0.943561	−	0.331200i
$433$		−	17.9802i		−	0.864072i	−0.901856	−	0.432036i	$-0.857795\pi$
$433$		−	17.9802i		−	0.864072i	0.901856	−	0.432036i	$-0.142205\pi$
$434$	−9.54624	+	7.12251i	−0.458234	+	0.341892i
$435$	2.23215	+	5.69322i	0.107024	+	0.272969i
$436$	−4.79278	−	0.999866i	−0.229532	−	0.0478849i
$437$	−23.6165	+	13.6350i	−1.12973	+	0.652251i
$438$	22.2640	+	12.5878i	1.06382	+	0.601467i
$439$	2.39995	+	1.38561i	0.114544	+	0.0661318i	0.556177	−	0.831064i	$-0.312268\pi$
$439$	2.39995	+	1.38561i	0.114544	+	0.0661318i	−0.441634	+	0.897195i	$0.645601\pi$
$440$	−5.12055	+	2.64563i	−0.244113	+	0.126126i
$441$	19.4784	+	7.84794i	0.927545	+	0.373711i
$442$	−6.34873	−	39.6010i	−0.301978	−	1.88363i
$443$	9.76606	−	16.9153i	0.464000	−	0.803671i	−0.535156	−	0.844753i	$-0.679747\pi$
$443$	9.76606	−	16.9153i	0.464000	−	0.803671i	0.999156	+	0.0410822i	$0.0130805\pi$
$444$	−13.5810	+	36.5667i	−0.644527	+	1.73538i
$445$	11.3466	−	6.55097i	0.537881	−	0.310546i
$446$	−3.80482	+	9.96803i	−0.180164	+	0.472000i
$447$	−30.1836	+	11.8342i	−1.42764	+	0.559738i
$448$	2.84808	−	20.9735i	0.134559	−	0.990906i
$449$		−	15.7009i		−	0.740969i	−0.928839	−	0.370485i	$-0.879192\pi$
$449$		−	15.7009i		−	0.740969i	0.928839	−	0.370485i	$-0.120808\pi$
$450$	3.93577	−	1.58421i	0.185534	−	0.0746804i
$451$	−11.7162	−	20.2931i	−0.551696	−	0.955566i
$452$	4.70151	−	5.26131i	0.221141	−	0.247471i
$453$	4.52424	−	29.9462i	0.212567	−	1.40700i
$454$	−3.38594	+	0.542825i	−0.158910	+	0.0254760i
$455$	−15.7556	−	0.655158i	−0.738633	−	0.0307143i
$456$	−16.8246	−	14.7637i	−0.787882	−	0.691372i
$457$	−3.12316	+	5.40947i	−0.146095	+	0.253044i	−0.929781	−	0.368113i	$-0.880004\pi$
$457$	−3.12316	+	5.40947i	−0.146095	+	0.253044i	0.783686	+	0.621158i	$0.213337\pi$
$458$	−2.73282	+	2.22154i	−0.127696	+	0.103806i
$459$	24.6570	−	1.82211i	1.15089	−	0.0850488i
$460$	−2.43777	+	11.6852i	−0.113661	+	0.544827i
$461$			1.75600i			0.0817853i	0.999164	+	0.0408926i	$0.0130202\pi$
$461$			1.75600i			0.0817853i	−0.999164	+	0.0408926i	$0.986980\pi$
$462$	−0.429638	+	13.1991i	−0.0199886	+	0.614080i
$463$	12.3151			0.572330			0.286165	−	0.958180i	$-0.407619\pi$
$463$	12.3151			0.572330			0.286165	+	0.958180i	$0.407619\pi$
$464$	−1.58205	−	14.0335i	−0.0734446	−	0.651488i
$465$	4.30945	+	3.43910i	0.199846	+	0.159485i
$466$	−0.573259	−	0.705194i	−0.0265557	−	0.0326675i
$467$	−27.0357	−	15.6091i	−1.25106	−	0.722301i	−0.279742	−	0.960075i	$-0.590249\pi$
$467$	−27.0357	−	15.6091i	−1.25106	−	0.722301i	−0.971321	+	0.237774i	$0.923582\pi$
$468$	17.3190	−	31.2876i	0.800572	−	1.44627i
$469$	−1.52888	+	2.41088i	−0.0705971	+	0.111324i
$470$	2.28039	−	0.365586i	0.105187	−	0.0168632i
$471$	−2.98910	+	19.7850i	−0.137730	+	0.911645i
$472$	−6.89694	−	4.42368i	−0.317458	−	0.203616i
$473$	11.5976	−	6.69585i	0.533256	−	0.307876i
$474$	17.2061	−	0.155199i	0.790302	−	0.00712852i
$475$	4.56906			0.209643
$476$	6.87020	+	24.2225i	0.314895	+	1.11024i
$477$	3.85689	−	3.57372i	0.176595	−	0.163629i
$478$	−9.08954	+	23.8131i	−0.415746	+	1.08919i
$479$	−16.3282	−	28.2812i	−0.746053	−	1.29220i	−0.949701	−	0.313157i	$-0.898613\pi$
$479$	−16.3282	−	28.2812i	−0.746053	−	1.29220i	0.203649	−	0.979044i	$-0.434720\pi$
$480$	−9.72599	+	1.18538i	−0.443929	+	0.0541050i
$481$	−58.1228	−	33.5572i	−2.65017	−	1.53008i
$482$	−6.81966	+	1.09331i	−0.310627	+	0.0497989i
$483$	20.6505	+	17.9337i	0.939629	+	0.816011i
$484$	13.0088	−	4.28110i	0.591309	−	0.194596i
$485$	4.42038	−	7.65632i	0.200719	−	0.347656i
$486$	18.3091	+	12.2791i	0.830518	+	0.556992i
$487$	3.65817	+	6.33613i	0.165767	+	0.287118i	0.936928	−	0.349524i	$-0.113657\pi$
$487$	3.65817	+	6.33613i	0.165767	+	0.287118i	−0.771160	+	0.636641i	$0.780323\pi$
$488$	7.09526	+	0.331624i	0.321187	+	0.0150119i
$489$	0.168929	+	0.430862i	0.00763925	+	0.0194843i
$490$	9.87103	−	0.750130i	0.445928	−	0.0338874i
$491$	−6.03481			−0.272347			−0.136174	−	0.990685i	$-0.543480\pi$
$491$	−6.03481			−0.272347			−0.136174	+	0.990685i	$0.543480\pi$
$492$	−6.66012	−	39.2736i	−0.300261	−	1.77059i
$493$	8.39961	+	14.5485i	0.378299	+	0.655234i
$494$	29.8841	−	24.2931i	1.34455	−	1.09300i
$495$	5.96092	−	1.35621i	0.267923	−	0.0609572i
$496$	−7.56167	−	10.2444i	−0.339529	−	0.459988i
$497$	−4.94954	−	9.46002i	−0.222017	−	0.424340i
$498$	−4.22587	+	2.49089i	−0.189366	+	0.111620i
$499$	−11.5016	−	6.64042i	−0.514880	−	0.297266i	0.219957	−	0.975510i	$-0.429408\pi$
$499$	−11.5016	−	6.64042i	−0.514880	−	0.297266i	−0.734837	+	0.678243i	$0.762742\pi$
$500$	1.33265	−	1.49132i	0.0595978	−	0.0666941i
$501$	−19.8665	−	15.8542i	−0.887568	−	0.708314i
$502$	−3.04108	+	7.96713i	−0.135730	+	0.355591i
$503$	−13.9171			−0.620531			−0.310266	−	0.950650i	$-0.600418\pi$
$503$	−13.9171			−0.620531			−0.310266	+	0.950650i	$0.600418\pi$
$504$	−8.49685	+	20.7799i	−0.378480	+	0.925610i
$505$	−13.9568			−0.621071
$506$	−6.13359	+	16.0690i	−0.272671	+	0.714355i
$507$	30.4929	+	24.3345i	1.35424	+	1.08073i
$508$	10.2612	+	9.16945i	0.455269	+	0.406828i
$509$	−27.0256	−	15.6032i	−1.19789	−	0.691600i	−0.237803	−	0.971313i	$-0.576427\pi$
$509$	−27.0256	−	15.6032i	−1.19789	−	0.691600i	−0.960084	+	0.279713i	$0.909761\pi$
$510$	10.0407	−	5.91837i	0.444608	−	0.262070i
$511$	14.7947	−	23.3298i	0.654481	−	1.03205i
$512$	22.4057	+	3.16007i	0.990200	+	0.139657i
$513$	13.3538	+	19.6300i	0.589583	+	0.866687i
$514$	5.81314	−	4.72556i	0.256406	−	0.208435i
$515$	9.47511	+	16.4114i	0.417523	+	0.723171i
$516$	22.4450	−	3.80627i	0.988084	−	0.167562i
$517$	3.32779			0.146356
$518$	38.7044	+	16.6473i	1.70058	+	0.731438i
$519$	13.3623	+	34.0813i	0.586541	+	1.49600i
$520$	0.787063	−	16.8396i	0.0345150	−	0.738465i
$521$	−15.5073	−	26.8594i	−0.679385	−	1.17673i	−0.975166	−	0.221474i	$-0.928913\pi$
$521$	−15.5073	−	26.8594i	−0.679385	−	1.17673i	0.295781	−	0.955256i	$-0.404420\pi$
$522$	−2.10394	+	14.8305i	−0.0920870	+	0.649115i
$523$	6.50584	−	11.2684i	0.284481	−	0.492735i	−0.688003	−	0.725708i	$-0.741512\pi$
$523$	6.50584	−	11.2684i	0.284481	−	0.492735i	0.972483	+	0.232974i	$0.0748456\pi$
$524$	1.47998	+	4.49714i	0.0646530	+	0.196458i
$525$	−1.49403	−	4.33219i	−0.0652049	−	0.189072i
$526$	−4.32568	+	0.693482i	−0.188609	+	0.0302372i
$527$	13.1171	+	7.57319i	0.571392	+	0.329893i
$528$	−14.1079	−	0.531911i	−0.613969	−	0.0231484i
$529$	6.31093	+	10.9308i	0.274388	+	0.475254i
$530$	0.883912	−	2.31571i	0.0383947	−	0.100588i
$531$	5.90680	+	6.37484i	0.256333	+	0.276644i
$532$	−16.8449	+	17.3431i	−0.730321	+	0.751921i
$533$	68.5374			2.96868
$534$	32.0918	−	0.289468i	1.38875	−	0.0125265i
$535$	14.8031	−	8.54657i	0.639994	−	0.369500i
$536$	−2.56890	−	1.64768i	−0.110960	−	0.0711691i
$537$	0.481941	−	3.19000i	0.0207973	−	0.137659i
$538$	−19.6151	+	3.14464i	−0.845667	+	0.135575i
$539$	14.2150	+	1.18424i	0.612284	+	0.0510090i
$540$	10.3020	+	1.36683i	0.443329	+	0.0588190i
$541$	−14.9146	−	8.61093i	−0.641228	−	0.370213i	0.143860	−	0.989598i	$-0.454049\pi$
$541$	−14.9146	−	8.61093i	−0.641228	−	0.370213i	−0.785087	+	0.619385i	$0.787382\pi$
$542$	4.68323	+	5.76106i	0.201162	+	0.247459i
$543$	8.22073	+	6.56046i	0.352785	+	0.281536i
$544$	−25.9324	+	7.21120i	−1.11184	+	0.309178i
$545$	2.44798			0.104860
$546$	−32.8055	−	20.3913i	−1.40394	−	0.872667i
$547$		−	15.2655i		−	0.652704i	−0.945248	−	0.326352i	$-0.894181\pi$
$547$		−	15.2655i		−	0.652704i	0.945248	−	0.326352i	$-0.105819\pi$
$548$	−32.6854	−	6.81881i	−1.39625	−	0.291285i
$549$	−7.19763	−	2.22562i	−0.307188	−	0.0949871i
$550$	2.23617	−	1.81780i	0.0953505	−	0.0775114i
$551$	−8.06575	+	13.9703i	−0.343612	+	0.595154i
$552$	−19.2853	+	21.9773i	−0.820836	+	0.935417i
$553$	0.772164	−	18.5694i	0.0328358	−	0.789651i
$554$	−17.0657	+	2.73593i	−0.725052	+	0.116238i
$555$	2.91353	−	19.2848i	0.123672	−	0.818595i
$556$	−8.70788	−	7.78137i	−0.369296	−	0.330003i
$557$	11.8837	+	20.5831i	0.503527	+	0.872135i	0.999992	+	0.00407777i	$0.00129800\pi$
$557$	11.8837	+	20.5831i	0.503527	+	0.872135i	−0.496464	+	0.868057i	$0.665369\pi$
$558$	5.04290	+	12.5284i	0.213483	+	0.530371i
$559$			39.1692i			1.65668i
$560$	0.747607	+	10.5566i	0.0315922	+	0.446096i
$561$	15.6352	−	6.13013i	0.660118	−	0.258814i
$562$	12.9345	−	33.8864i	0.545611	−	1.42941i
$563$	−2.86681	+	1.65515i	−0.120822	+	0.0697565i	−0.559193	−	0.829038i	$-0.688889\pi$
$563$	−2.86681	+	1.65515i	−0.120822	+	0.0697565i	0.438371	+	0.898794i	$0.355556\pi$
$564$	5.30317	+	1.96962i	0.223304	+	0.0829359i
$565$	−1.76397	+	3.05529i	−0.0742109	+	0.128537i
$566$	4.06579	+	25.3609i	0.170898	+	1.06600i
$567$	14.2458	−	19.0803i	0.598268	−	0.801296i
$568$	10.1403	−	5.23917i	0.425477	−	0.219831i
$569$	−1.38637	−	0.800424i	−0.0581199	−	0.0335555i	0.470658	−	0.882315i	$-0.344016\pi$
$569$	−1.38637	−	0.800424i	−0.0581199	−	0.0335555i	−0.528778	+	0.848760i	$0.677350\pi$
$570$	9.74252	+	5.50828i	0.408069	+	0.230717i
$571$	3.37799	−	1.95028i	0.141364	−	0.0816167i	−0.427650	−	0.903945i	$-0.640658\pi$
$571$	3.37799	−	1.95028i	0.141364	−	0.0816167i	0.569014	+	0.822328i	$0.307325\pi$
$572$	4.96073	−	23.7788i	0.207418	−	0.994243i
$573$	1.66354	+	4.24294i	0.0694954	+	0.177251i
$574$	−42.7298	+	5.03991i	−1.78351	+	0.210362i
$575$		−	5.96840i		−	0.248900i
$576$	−22.1676	−	9.19771i	−0.923650	−	0.383238i
$577$	−28.2601	+	16.3160i	−1.17648	+	0.679243i	−0.955198	−	0.295967i	$-0.904358\pi$
$577$	−28.2601	+	16.3160i	−1.17648	+	0.679243i	−0.221284	+	0.975209i	$0.571025\pi$
$578$	6.18955	−	5.03155i	0.257451	−	0.209285i
$579$	−6.25531	+	41.4043i	−0.259962	+	1.72070i
$580$	2.20733	+	6.70731i	0.0916543	+	0.278506i
$581$	2.45627	+	4.69464i	0.101903	+	0.194767i
$582$	18.6557	−	10.9964i	0.773302	−	0.455815i
$583$	1.78577	−	3.09304i	0.0739589	−	0.128101i
$584$	24.8588	+	15.9444i	1.02867	+	0.659783i
$585$	−5.28219	+	17.0826i	−0.218392	+	0.706277i
$586$	−2.07434	+	5.43445i	−0.0856903	+	0.224495i
$587$		−	27.5747i		−	1.13813i	−0.822293	−	0.569065i	$-0.807305\pi$
$587$		−	27.5747i		−	1.13813i	0.822293	−	0.569065i	$-0.192695\pi$
$588$	21.9521	+	10.3007i	0.905291	+	0.424792i
$589$			14.5444i			0.599290i
$590$	3.82750	+	1.46097i	0.157576	+	0.0601471i
$591$	11.2842	+	9.00519i	0.464168	+	0.370424i
$592$	−18.0094	+	41.2847i	−0.740180	+	1.69679i
$593$	−21.2117	+	36.7398i	−0.871061	+	1.50872i	−0.0101604	+	0.999948i	$0.503234\pi$
$593$	−21.2117	+	36.7398i	−0.871061	+	1.50872i	−0.860900	+	0.508773i	$0.830099\pi$
$594$	14.3454	+	4.29443i	0.588597	+	0.176203i
$595$	−5.83610	−	11.1545i	−0.239257	−	0.457289i
$596$	−35.5601	+	11.7026i	−1.45660	+	0.479356i
$597$	40.9279	+	6.18334i	1.67507	+	0.253067i
$598$	−31.7332	−	39.0366i	−1.29767	−	1.59633i
$599$	−0.663420	+	0.383026i	−0.0271066	+	0.0156500i	−0.513492	−	0.858094i	$-0.671648\pi$
$599$	−0.663420	+	0.383026i	−0.0271066	+	0.0156500i	0.486385	+	0.873744i	$0.338315\pi$
$600$	4.63946	−	1.57333i	0.189405	−	0.0642310i
$601$		−	40.3989i		−	1.64790i	−0.566659	−	0.823952i	$-0.691764\pi$
$601$		−	40.3989i		−	1.64790i	0.566659	−	0.823952i	$-0.308236\pi$
$602$	−2.88032	−	24.4202i	−0.117393	−	0.995292i
$603$	2.20010	+	2.37443i	0.0895950	+	0.0966943i
$604$	7.14193	−	34.2343i	0.290601	−	1.39297i
$605$	−5.93017	+	3.42379i	−0.241096	+	0.139197i
$606$	−29.7599	−	16.8258i	−1.20891	−	0.683502i
$607$	16.0499	+	9.26641i	0.651445	+	0.376112i	0.789010	−	0.614381i	$-0.210594\pi$
$607$	16.0499	+	9.26641i	0.651445	+	0.376112i	−0.137564	+	0.990493i	$0.543927\pi$
$608$	−18.4477	−	18.1032i	−0.748152	−	0.734181i
$609$	15.8834	+	3.07947i	0.643629	+	0.124786i
$610$	−3.50673	+	0.562189i	−0.141983	+	0.0227624i
$611$	−4.86671	+	8.42938i	−0.196886	+	0.341016i
$612$	28.5445	−	0.514984i	1.15384	−	0.0208170i
$613$	−9.35052	+	5.39852i	−0.377664	+	0.218044i	−0.676801	−	0.736166i	$-0.736634\pi$
$613$	−9.35052	+	5.39852i	−0.377664	+	0.218044i	0.299138	+	0.954210i	$0.403301\pi$
$614$	−16.5095	−	6.30174i	−0.666271	−	0.254317i
$615$	7.27016	+	18.5429i	0.293161	+	0.747721i
$616$	−1.34420	+	15.1898i	−0.0541592	+	0.612013i
$617$		−	29.9548i		−	1.20594i	−0.797765	−	0.602968i	$-0.793985\pi$
$617$		−	29.9548i		−	1.20594i	0.797765	−	0.602968i	$-0.206015\pi$
$618$	0.418677	+	46.4165i	0.0168416	+	1.86714i
$619$	−23.4241	−	40.5717i	−0.941493	−	1.63071i	−0.762625	−	0.646841i	$-0.776090\pi$
$619$	−23.4241	−	40.5717i	−0.941493	−	1.63071i	−0.178868	−	0.983873i	$-0.557244\pi$
$620$	4.74722	+	4.24212i	0.190653	+	0.170368i
$621$	25.6420	−	17.4436i	1.02898	−	0.699986i
$622$	−4.06084	−	25.3300i	−0.162825	−	1.01564i
$623$	1.44020	−	34.6346i	0.0577002	−	1.38760i
$624$	21.9794	−	34.9579i	0.879880	−	1.39944i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−2.36230	−	2.90597i	−0.0944163	−	0.116146i
$627$	12.6047	+	10.0590i	0.503383	+	0.401719i
$628$	−4.71857	+	22.6181i	−0.188291	+	0.902559i
$629$		−	53.5793i		−	2.13635i
$630$	2.03703	−	11.0386i	0.0811571	−	0.439788i
$631$	10.8582			0.432258			0.216129	−	0.976365i	$-0.430657\pi$
$631$	10.8582			0.432258			0.216129	+	0.976365i	$0.430657\pi$
$632$	19.8470	+	0.927626i	0.789472	+	0.0368990i
$633$	−10.6718	+	13.3725i	−0.424166	+	0.531511i
$634$	19.0726	−	15.5043i	0.757470	−	0.615755i
$635$	−5.95879	−	3.44031i	−0.236467	−	0.136525i
$636$	4.67648	−	3.87213i	0.185434	−	0.153540i
$637$	−23.7884	+	34.2751i	−0.942530	+	1.35803i
$638$	1.61058	+	10.0462i	0.0637637	+	0.397734i
$639$	−11.8045	+	2.68572i	−0.466977	+	0.106245i
$640$	−11.2894	+	0.741138i	−0.446253	+	0.0292961i
$641$	11.2689	−	6.50611i	0.445095	−	0.256976i	−0.260661	−	0.965430i	$-0.583941\pi$
$641$	11.2689	−	6.50611i	0.445095	−	0.256976i	0.705757	+	0.708454i	$0.250607\pi$
$642$	41.8678	−	0.377647i	1.65239	−	0.0149045i
$643$	−19.0866			−0.752702			−0.376351	−	0.926477i	$-0.622821\pi$
$643$	−19.0866			−0.752702			−0.376351	+	0.926477i	$0.622821\pi$
$644$	22.6547	+	22.0040i	0.892722	+	0.867078i
$645$	−10.5973	+	4.15491i	−0.417268	+	0.163599i
$646$	28.7242	+	10.9641i	1.13014	+	0.431378i
$647$	4.06889	+	7.04753i	0.159965	+	0.277067i	0.934856	−	0.355028i	$-0.115529\pi$
$647$	4.06889	+	7.04753i	0.159965	+	0.277067i	−0.774891	+	0.632095i	$0.782195\pi$
$648$	20.3190	+	15.3342i	0.798206	+	0.602384i
$649$	5.11231	+	2.95159i	0.200676	+	0.115860i
$650$	1.33427	+	8.32271i	0.0523346	+	0.326444i
$651$	13.7903	−	4.75584i	0.540486	−	0.186396i
$652$	0.167051	+	0.507609i	0.00654220	+	0.0198795i
$653$	−14.5083	+	25.1290i	−0.567752	+	0.983376i	0.429036	+	0.903288i	$0.358853\pi$
$653$	−14.5083	+	25.1290i	−0.567752	+	0.983376i	−0.996788	+	0.0800881i	$0.974480\pi$
$654$	5.21978	+	2.95119i	0.204110	+	0.115401i
$655$	−1.18360	−	2.05006i	−0.0462471	−	0.0801023i
$656$	−5.15274	−	45.7072i	−0.201181	−	1.78457i
$657$	−21.2900	−	22.9770i	−0.830604	−	0.896418i
$658$	2.41430	−	5.61319i	0.0941194	−	0.218825i
$659$	27.4722			1.07016			0.535082	−	0.844800i	$-0.320281\pi$
$659$	27.4722			1.07016			0.535082	+	0.844800i	$0.320281\pi$
$660$	6.95961	−	1.18023i	0.270903	−	0.0459403i
$661$	−7.25811	−	12.5714i	−0.282308	−	0.488971i	0.689645	−	0.724148i	$-0.257767\pi$
$661$	−7.25811	−	12.5714i	−0.282308	−	0.488971i	−0.971953	+	0.235176i	$0.924433\pi$
$662$	21.8802	+	26.9159i	0.850398	+	1.04612i
$663$	−7.33780	+	48.5693i	−0.284976	+	1.88628i
$664$	−5.03223	+	2.60000i	−0.195288	+	0.100900i
$665$	6.47404	−	10.2089i	0.251052	−	0.395883i
$666$	29.4615	−	37.6082i	1.14161	−	1.45729i
$667$	18.2489	+	10.5360i	0.706600	+	0.407956i
$668$	−21.8846	−	19.5561i	−0.846741	−	0.756648i
$669$	8.15093	−	10.2137i	0.315133	−	0.394885i
$670$	1.42563	+	0.544165i	0.0550767	+	0.0210229i
$671$	−5.11739			−0.197555
$672$	−11.1325	+	23.4108i	−0.429445	+	0.903093i
$673$	−34.6701			−1.33643			−0.668217	−	0.743966i	$-0.732942\pi$
$673$	−34.6701			−1.33643			−0.668217	+	0.743966i	$0.732942\pi$
$674$	−2.69696	−	1.02944i	−0.103883	−	0.0396524i
$675$	−5.18202	+	0.382942i	−0.199456	+	0.0147394i
$676$	33.5905	+	30.0165i	1.29194	+	1.15448i
$677$	27.1551	+	15.6780i	1.04365	+	0.602554i	0.920866	−	0.389879i	$-0.127483\pi$
$677$	27.1551	+	15.6780i	1.04365	+	0.602554i	0.122788	+	0.992433i	$0.460816\pi$
$678$	−7.44463	+	4.38816i	−0.285909	+	0.168526i
$679$	−10.8435	−	20.7251i	−0.416136	−	0.795358i
$680$	11.9566	−	6.17760i	0.458514	−	0.236900i
$681$	4.15274	+	0.627392i	0.159133	+	0.0240417i
$682$	5.78648	+	7.11823i	0.221576	+	0.272571i
$683$	−19.5216	−	33.8123i	−0.746972	−	1.29379i	−0.949268	−	0.314469i	$-0.898174\pi$
$683$	−19.5216	−	33.8123i	−0.746972	−	1.29379i	0.202296	−	0.979324i	$-0.435160\pi$
$684$	14.1332	+	23.4904i	0.540397	+	0.898179i
$685$	16.6946			0.637866
$686$	12.3105	−	23.1182i	0.470017	−	0.882657i
$687$	4.01577	−	1.57447i	0.153211	−	0.0600699i
$688$	26.1218	−	2.94480i	0.995883	−	0.112270i
$689$	5.22317	+	9.04679i	0.198987	+	0.344655i
$690$	7.19528	−	12.7263i	0.273920	−	0.484483i
$691$	3.14293	−	5.44372i	0.119563	−	0.207089i	−0.800032	−	0.599958i	$-0.795184\pi$
$691$	3.14293	−	5.44372i	0.119563	−	0.207089i	0.919594	+	0.392869i	$0.128517\pi$
$692$	13.2137	+	40.1519i	0.502310	+	1.52635i
$693$	5.41595	−	15.2404i	0.205735	−	0.578936i
$694$	−3.42068	−	21.3369i	−0.129847	−	0.809939i
$695$	5.05674	+	2.91951i	0.191813	+	0.110743i
$696$	−3.37943	+	16.9629i	−0.128097	+	0.642979i
$697$	27.3576	+	47.3848i	1.03624	+	1.79483i
$698$	35.3301	+	13.4856i	1.33727	+	0.510438i
$699$	0.406286	+	1.03625i	0.0153672	+	0.0391947i
$700$	−1.44387	−	5.09070i	−0.0545732	−	0.192410i
$701$	−34.1452			−1.28965			−0.644823	−	0.764332i	$-0.723069\pi$
$701$	−34.1452			−1.28965			−0.644823	+	0.764332i	$0.723069\pi$
$702$	−31.8572	+	30.0568i	−1.20237	+	1.13442i
$703$	44.5567	−	25.7248i	1.68049	−	0.970230i
$704$	−16.2309	−	1.52055i	−0.611727	−	0.0573080i
$705$	−2.79682	−	0.422540i	−0.105334	−	0.0159138i
$706$	1.79048	+	11.1684i	0.0673857	+	0.420327i
$707$	−19.7758	+	31.1844i	−0.743747	+	1.17281i
$708$	6.40002	+	7.72948i	0.240527	+	0.290492i
$709$	22.8311	+	13.1816i	0.857441	+	0.495044i	0.863154	−	0.504940i	$-0.168485\pi$
$709$	22.8311	+	13.1816i	0.857441	+	0.495044i	−0.00571373	+	0.999984i	$0.501819\pi$
$710$	−4.42831	+	3.59981i	−0.166191	+	0.135099i
$711$	−20.1334	−	6.22555i	−0.755060	−	0.233476i
$712$	37.0175	+	1.73015i	1.38729	+	0.0648403i
$713$	18.9988			0.711510
$714$	1.00321	−	30.8203i	0.0375443	−	1.15342i
$715$			12.1454i			0.454212i
$716$	0.760789	−	3.64678i	0.0284320	−	0.136287i
$717$	19.4722	−	24.4000i	0.727202	−	0.911236i
$718$	−12.9079	−	15.8786i	−0.481717	−	0.592584i
$719$	−15.3918	+	26.6593i	−0.574016	+	0.994224i	0.422132	+	0.906534i	$0.361282\pi$
$719$	−15.3918	+	26.6593i	−0.574016	+	0.994224i	−0.996148	+	0.0876899i	$0.972052\pi$
$720$	11.7894	+	2.23837i	0.439365	+	0.0834192i
$721$	50.0943	+	2.08305i	1.86561	+	0.0775769i
$722$	0.420042	+	2.62007i	0.0156323	+	0.0975088i
$723$	8.36408	+	1.26364i	0.311063	+	0.0469951i
$724$	9.05583	+	8.09230i	0.336557	+	0.300748i
$725$	−1.76530	−	3.05758i	−0.0655614	−	0.113556i
$726$	−16.7724	+	0.151287i	−0.622481	+	0.00561478i
$727$		−	8.71100i		−	0.323073i	−0.986867	−	0.161537i	$-0.948355\pi$
$727$		−	8.71100i		−	0.323073i	0.986867	−	0.161537i	$-0.0516450\pi$
$728$	−36.5103	−	25.6191i	−1.35316	−	0.949506i
$729$	−16.7905	−	21.1443i	−0.621869	−	0.783121i
$730$	−13.7956	−	5.26581i	−0.510597	−	0.194896i
$731$	−27.0805	+	15.6349i	−1.00161	+	0.578279i
$732$	−8.15508	−	3.02883i	−0.301420	−	0.111949i
$733$	−25.2052	+	43.6568i	−0.930977	+	1.61250i	−0.149321	+	0.988789i	$0.547709\pi$
$733$	−25.2052	+	43.6568i	−0.930977	+	1.61250i	−0.781655	+	0.623711i	$0.785624\pi$
$734$	−7.29128	+	1.16892i	−0.269126	+	0.0431456i
$735$	−11.7966	−	2.80022i	−0.435123	−	0.103288i
$736$	−23.6476	+	24.0976i	−0.871660	+	0.888248i
$737$	1.90418	+	1.09938i	0.0701412	+	0.0404961i
$738$	−6.85257	+	48.3032i	−0.252246	+	1.77807i
$739$	12.3324	−	7.12009i	0.453653	−	0.261917i	−0.255719	−	0.966751i	$-0.582312\pi$
$739$	12.3324	−	7.12009i	0.453653	−	0.261917i	0.709372	+	0.704834i	$0.248979\pi$
$740$	4.59927	−	22.0462i	0.169073	−	0.810436i
$741$	−43.9135	+	17.2173i	−1.61320	+	0.632492i
$742$	−3.92166	−	5.25616i	−0.143969	−	0.192960i
$743$		−	18.9124i		−	0.693827i	−0.937897	−	0.346914i	$-0.887230\pi$
$743$		−	18.9124i		−	0.693827i	0.937897	−	0.346914i	$-0.112770\pi$
$744$	5.00827	+	14.7685i	0.183612	+	0.541438i
$745$	16.2103	−	9.35904i	0.593901	−	0.342889i
$746$	15.9709	+	19.6466i	0.584736	+	0.719313i
$747$	5.85810	−	1.33282i	0.214337	−	0.0487653i
$748$	18.4202	−	6.06195i	0.673508	−	0.221647i
$749$	1.87892	−	45.1851i	0.0686541	−	1.65103i
$750$	−2.11019	+	1.24383i	−0.0770531	+	0.0454182i
$751$	21.7669	−	37.7013i	0.794284	−	1.37574i	−0.129009	−	0.991643i	$-0.541180\pi$
$751$	21.7669	−	37.7013i	0.794284	−	1.37574i	0.923293	−	0.384096i	$-0.125487\pi$
$752$	5.98740	+	2.61185i	0.218338	+	0.0952442i
$753$	6.51478	−	8.16349i	0.237412	−	0.297494i
$754$	−27.8028	−	10.6124i	−1.01252	−	0.386481i
$755$			17.4857i			0.636368i
$756$	17.6512	−	21.0816i	0.641968	−	0.766731i
$757$			13.1711i			0.478711i	0.970932	+	0.239356i	$0.0769362\pi$
$757$			13.1711i			0.478711i	−0.970932	+	0.239356i	$0.923064\pi$
$758$	13.7667	−	36.0667i	0.500031	−	1.31000i
$759$	13.1398	−	16.4651i	0.476943	−	0.597644i
$760$	10.8780	+	6.97711i	0.394586	+	0.253086i
$761$	4.69077	−	8.12465i	0.170040	−	0.294518i	−0.768393	−	0.639978i	$-0.778944\pi$
$761$	4.69077	−	8.12465i	0.170040	−	0.294518i	0.938434	+	0.345459i	$0.112277\pi$
$762$	−8.55831	−	14.5194i	−0.310035	−	0.525982i
$763$	3.46862	−	5.46964i	0.125572	−	0.198014i
$764$	1.64504	+	4.99870i	0.0595154	+	0.180847i
$765$	−13.9189	+	3.16678i	−0.503237	+	0.114495i
$766$	12.2389	−	9.94913i	0.442210	−	0.359477i
$767$	−14.9529	+	8.63308i	−0.539919	+	0.311722i
$768$	−24.9657	−	12.0298i	−0.900871	−	0.434087i
$769$		−	19.9247i		−	0.718501i	−0.933241	−	0.359251i	$-0.883032\pi$
$769$		−	19.9247i		−	0.718501i	0.933241	−	0.359251i	$-0.116968\pi$
$770$	−0.893114	−	7.57208i	−0.0321856	−	0.272879i
$771$	−8.54215	+	3.34915i	−0.307638	+	0.120617i
$772$	−9.87459	+	47.3330i	−0.355394	+	1.70355i
$773$	−35.8196	+	20.6805i	−1.28834	+	0.743825i	−0.978359	−	0.206917i	$-0.933657\pi$
$773$	−35.8196	+	20.6805i	−1.28834	+	0.743825i	−0.309984	+	0.950742i	$0.600324\pi$
$774$	−27.6054	−	3.91626i	−0.992256	−	0.140767i
$775$	−2.75675	−	1.59161i	−0.0990255	−	0.0571724i
$776$	22.2155	−	11.4780i	0.797489	−	0.412038i
$777$	−38.9607	−	33.8350i	−1.39771	−	1.21383i
$778$	7.59886	+	47.3988i	0.272432	+	1.69933i
$779$	−26.2702	+	45.5014i	−0.941229	+	1.63026i
$780$	−7.18849	+	19.3549i	−0.257389	+	0.693017i
$781$	−7.12141	+	4.11155i	−0.254824	+	0.147123i
$782$	14.3221	−	37.5215i	0.512156	−	1.34177i
$783$	7.97693	−	16.5205i	0.285072	−	0.590393i
$784$	24.6464	+	13.2875i	0.880227	+	0.474553i
$785$		−	11.5525i		−	0.412327i
$786$	−0.0522998	−	5.79820i	−0.00186547	−	0.206815i
$787$	13.1868	+	22.8402i	0.470059	+	0.814166i	0.999414	−	0.0342346i	$-0.0108993\pi$
$787$	13.1868	+	22.8402i	0.470059	+	0.814166i	−0.529355	+	0.848400i	$0.677566\pi$
$788$	12.4305	+	11.1079i	0.442817	+	0.395701i
$789$	5.30530	+	0.801519i	0.188874	+	0.0285348i
$790$	−9.80909	+	1.57257i	−0.348992	+	0.0559494i
$791$	4.32716	+	8.27046i	0.153856	+	0.294064i
$792$	16.2627	+	5.87366i	0.577869	+	0.208712i
$793$	7.48390	−	12.9625i	0.265761	−	0.460311i
$794$	5.47599	−	4.45148i	0.194335	−	0.157977i
$795$	−1.89357	+	2.37278i	−0.0671580	+	0.0841539i
$796$	46.7884	+	9.76098i	1.65837	+	0.345969i
$797$		−	11.7563i		−	0.416428i	−0.978083	−	0.208214i	$-0.933235\pi$
$797$		−	11.7563i		−	0.416428i	0.978083	−	0.208214i	$-0.0667650\pi$
$798$	26.1119	−	13.9633i	0.924351	−	0.494297i
$799$	−7.77045			−0.274899
$800$	5.45006	−	1.51554i	0.192689	−	0.0535823i
$801$	−37.5516	−	11.6115i	−1.32682	−	0.410273i
$802$	−17.4277	−	21.4386i	−0.615393	−	0.757025i
$803$	−18.4264	−	10.6385i	−0.650255	−	0.375425i
$804$	2.38381	+	2.87899i	0.0840705	+	0.101534i
$805$	−13.3355	−	8.45681i	−0.470014	−	0.298063i
$806$	−26.4931	+	4.24730i	−0.933178	+	0.149605i
$807$	24.0573	+	3.63454i	0.846856	+	0.127942i
$808$	−33.2283	−	21.3125i	−1.16897	−	0.749773i
$809$	−33.6944	+	19.4535i	−1.18463	+	0.683948i	−0.957082	−	0.289818i	$-0.906405\pi$
$809$	−33.6944	+	19.4535i	−1.18463	+	0.683948i	−0.227551	+	0.973766i	$0.573072\pi$
$810$	−11.5112	−	5.43071i	−0.404462	−	0.190816i
$811$	43.0594			1.51202			0.756011	−	0.654559i	$-0.227146\pi$
$811$	43.0594			1.51202			0.756011	+	0.654559i	$0.227146\pi$
$812$	18.1141	+	4.57184i	0.635680	+	0.160440i
$813$	−3.31914	−	8.46563i	−0.116407	−	0.296903i
$814$	11.5721	−	30.3170i	0.405602	−	1.06261i
$815$	−0.133598	−	0.231398i	−0.00467972	−	0.00810551i
$816$	32.9423	+	1.24202i	1.15321	+	0.0434794i
$817$	−26.0041	−	15.0135i	−0.909770	−	0.525256i
$818$	38.4831	−	6.16950i	1.34553	−	0.215712i
$819$	30.6839	+	36.0070i	1.07218	+	1.25819i
$820$	7.18930	+	21.8458i	0.251061	+	0.762888i
$821$	−6.14459	+	10.6427i	−0.214448	+	0.371434i	−0.953102	−	0.302650i	$-0.902129\pi$
$821$	−6.14459	+	10.6427i	−0.214448	+	0.371434i	0.738654	+	0.674085i	$0.235462\pi$
$822$	35.5975	+	20.1263i	1.24161	+	0.701986i
$823$	−17.1695	−	29.7384i	−0.598489	−	1.03661i	−0.993044	−	0.117742i	$-0.962435\pi$
$823$	−17.1695	−	29.7384i	−0.598489	−	1.03661i	0.394555	−	0.918872i	$-0.370899\pi$
$824$	−2.50244	+	53.5409i	−0.0871766	+	1.86518i
$825$	−3.28595	+	1.28833i	−0.114402	+	0.0448540i
$826$	8.68761	−	6.48188i	0.302281	−	0.225534i
$827$	40.4065			1.40507			0.702537	−	0.711648i	$-0.252051\pi$
$827$	40.4065			1.40507			0.702537	+	0.711648i	$0.252051\pi$
$828$	30.6847	−	18.4617i	1.06637	−	0.641589i
$829$	−24.2367	−	41.9791i	−0.841774	−	1.45800i	−0.888394	−	0.459082i	$-0.848178\pi$
$829$	−24.2367	−	41.9791i	−0.841774	−	1.45800i	0.0466199	−	0.998913i	$-0.485155\pi$
$830$	2.19760	−	1.78645i	0.0762797	−	0.0620086i
$831$	20.9305	+	3.16216i	0.726071	+	0.109694i
$832$	27.5884	−	38.8897i	0.956457	−	1.34826i
$833$	−33.1923	−	2.76523i	−1.15005	−	0.0958095i
$834$	7.26275	+	12.3214i	0.251488	+	0.426656i
$835$	12.7086	+	7.33730i	0.439799	+	0.253918i
$836$	13.8851	+	12.4078i	0.480228	+	0.429132i
$837$	−1.21899	−	16.4955i	−0.0421345	−	0.570169i
$838$	9.10328	−	23.8491i	0.314467	−	0.823854i
$839$	−17.4232			−0.601514			−0.300757	−	0.953701i	$-0.597239\pi$
$839$	−17.4232			−0.601514			−0.300757	+	0.953701i	$0.597239\pi$
$840$	3.05842	−	12.5955i	0.105525	−	0.434585i
$841$	−16.5349			−0.570170
$842$	8.12237	−	21.2793i	0.279915	−	0.733333i
$843$	−27.7092	+	34.7216i	−0.954355	+	1.19588i
$844$	−13.1636	+	14.7310i	−0.453111	+	0.507062i
$845$	−19.5063	−	11.2620i	−0.671037	−	0.387423i
$846$	−5.45421	−	4.27271i	−0.187520	−	0.146899i
$847$	−0.752701	+	18.1013i	−0.0258631	+	0.621969i
$848$	5.64057	−	4.16345i	0.193698	−	0.142974i
$849$	4.69920	−	31.1043i	0.161276	−	1.06750i
$850$	−5.22150	+	4.24461i	−0.179096	+	0.145589i
$851$	−33.6034	−	58.2028i	−1.15191	−	1.99517i
$852$	−13.7822	+	2.33722i	−0.472170	+	0.0800718i
$853$	23.2615			0.796458			0.398229	−	0.917286i	$-0.369625\pi$
$853$	23.2615			0.796458			0.398229	+	0.917286i	$0.369625\pi$
$854$	−3.71266	+	8.63183i	−0.127044	+	0.295375i
$855$	−9.31631	−	10.0545i	−0.318611	−	0.343857i
$856$	48.2940	+	2.25720i	1.65065	+	0.0771497i
$857$	5.33411	+	9.23896i	0.182210	+	0.315597i	0.942633	−	0.333831i	$-0.108342\pi$
$857$	5.33411	+	9.23896i	0.182210	+	0.315597i	−0.760423	+	0.649428i	$0.775008\pi$
$858$	−14.6420	+	25.8974i	−0.499870	+	0.884122i
$859$	−8.01206	+	13.8773i	−0.273368	+	0.473487i	−0.969722	−	0.244211i	$-0.921471\pi$
$859$	−8.01206	+	13.8773i	−0.273368	+	0.473487i	0.696354	+	0.717698i	$0.254804\pi$
$860$	−12.4849	+	4.10870i	−0.425732	+	0.140105i
$861$	51.7325	+	10.0299i	1.76304	+	0.341817i
$862$	−28.9851	+	4.64682i	−0.987238	+	0.158271i
$863$	0.657992	+	0.379892i	0.0223983	+	0.0129317i	0.511157	−	0.859487i	$-0.329217\pi$
$863$	0.657992	+	0.379892i	0.0223983	+	0.0129317i	−0.488759	+	0.872419i	$0.662550\pi$
$864$	22.4398	+	18.9857i	0.763417	+	0.645906i
$865$	−10.5676	−	18.3036i	−0.359309	−	0.622341i
$866$	−9.06775	+	23.7560i	−0.308135	+	0.807263i
$867$	−9.09528	+	3.56601i	−0.308892	+	0.121108i
$868$	16.2048	−	4.59616i	0.550028	−	0.156004i
$869$	−14.3145			−0.485585
$870$	−0.0780031	−	8.64780i	−0.00264455	−	0.293188i
$871$	−5.56950	+	3.21555i	−0.188715	+	0.108955i
$872$	5.82813	+	3.73815i	0.197366	+	0.126590i
$873$	−25.8614	+	5.88391i	−0.875275	+	0.199140i
$874$	38.0794	−	6.10478i	1.28805	−	0.206497i
$875$	1.22654	+	2.34427i	0.0414646	+	0.0792508i
$876$	−23.0678	−	27.8596i	−0.779388	−	0.941288i
$877$	16.8832	+	9.74749i	0.570104	+	0.329149i	0.757191	−	0.653194i	$-0.226571\pi$
$877$	16.8832	+	9.74749i	0.570104	+	0.329149i	−0.187087	+	0.982343i	$0.559905\pi$
$878$	−2.47211	−	3.04106i	−0.0834297	−	0.102631i
$879$	4.44379	−	5.56839i	0.149885	−	0.187817i
$880$	8.09970	−	0.913109i	0.273041	−	0.0307809i
$881$	−33.7707			−1.13776			−0.568881	−	0.822420i	$-0.692624\pi$
$881$	−33.7707			−1.13776			−0.568881	+	0.822420i	$0.692624\pi$
$882$	−21.7777	−	20.1923i	−0.733295	−	0.679911i
$883$		−	13.2723i		−	0.446649i	−0.974744	−	0.223324i	$-0.928309\pi$
$883$		−	13.2723i		−	0.446649i	0.974744	−	0.223324i	$-0.0716909\pi$
$884$	−11.5834	+	55.5240i	−0.389592	+	1.86748i
$885$	−3.92184	−	3.12977i	−0.131831	−	0.105206i
$886$	−21.4340	+	17.4239i	−0.720089	+	0.585367i
$887$	−25.4403	+	44.0638i	−0.854201	+	1.47952i	0.0231839	+	0.999731i	$0.492620\pi$
$887$	−25.4403	+	44.0638i	−0.854201	+	1.47952i	−0.877385	+	0.479788i	$0.840714\pi$
$888$	36.3850	−	41.4641i	1.22100	−	1.39144i
$889$	−16.1300	+	8.43934i	−0.540984	+	0.283046i
$890$	−18.2953	+	2.93306i	−0.613261	+	0.0983163i
$891$	−15.1387	−	10.3521i	−0.507167	−	0.346807i
$892$	10.0541	−	11.2513i	0.336637	−	0.376720i
$893$	−3.73080	−	6.46193i	−0.124846	−	0.216240i
$894$	45.8479	−	0.413548i	1.53338	−	0.0138311i
$895$			1.86265i			0.0622614i
$896$	−14.3403	+	26.2746i	−0.479077	+	0.877773i
$897$	22.4903	+	57.3626i	0.750930	+	1.91528i
$898$	−7.91824	+	20.7445i	−0.264235	+	0.692254i
$899$	9.73297	−	5.61933i	0.324613	−	0.187415i
$900$	−5.99902	+	0.108231i	−0.199967	+	0.00360771i
$901$	−4.16980	+	7.22230i	−0.138916	+	0.240610i
$902$	5.24569	+	32.7207i	0.174663	+	1.08948i
$903$	−5.73210	+	29.5653i	−0.190752	+	0.983870i
$904$	−8.86518	+	4.58037i	−0.294852	+	0.152341i
$905$	−5.25880	−	3.03617i	−0.174809	−	0.100926i
$906$	−21.0800	+	37.2843i	−0.700337	+	1.23869i
$907$	−45.1723	+	26.0802i	−1.49992	+	0.865979i	−1.00000		9.22087e-5i	$-0.999971\pi$
$907$	−45.1723	+	26.0802i	−1.49992	+	0.865979i	−0.499920	+	0.866072i	$0.666637\pi$
$908$	4.74738	+	0.990396i	0.157547	+	0.0328674i
$909$	28.4580	+	30.7129i	0.943891	+	1.01868i
$910$	20.4864	+	8.81146i	0.679118	+	0.292097i
$911$			30.4779i			1.00978i	0.863184	+	0.504890i	$0.168467\pi$
$911$			30.4779i			1.00978i	−0.863184	+	0.504890i	$0.831533\pi$
$912$	14.7836	+	27.9912i	0.489533	+	0.926882i
$913$	3.53408	−	2.04040i	0.116961	−	0.0675275i
$914$	6.85453	−	5.57212i	0.226728	−	0.184309i
$915$	4.30088	+	0.649772i	0.142183	+	0.0214808i
$916$	4.73107	−	1.55696i	0.156319	−	0.0514434i
$917$	−6.25762	−	0.260208i	−0.206645	−	0.00859283i
$918$	−33.4967	−	10.0276i	−1.10555	−	0.330959i
$919$	−6.70571	+	11.6146i	−0.221201	+	0.383131i	−0.955173	−	0.296048i	$-0.904331\pi$
$919$	−6.70571	+	11.6146i	−0.221201	+	0.383131i	0.733972	+	0.679180i	$0.237664\pi$
$920$	9.11395	−	14.2095i	0.300478	−	0.468474i
$921$	16.9164	+	13.5000i	0.557416	+	0.444839i
$922$	0.885587	−	2.32009i	0.0291652	−	0.0764082i
$923$		−	24.0516i		−	0.791669i
$924$	7.22423	−	17.2225i	0.237660	−	0.566579i
$925$			11.2604i			0.370241i
$926$	−16.2711	−	6.21073i	−0.534702	−	0.204097i
$927$	16.7945	−	54.3134i	0.551605	−	1.78388i
$928$	−4.98709	+	19.3394i	−0.163709	+	0.634846i
$929$	−17.8917	+	30.9893i	−0.587008	+	1.01673i	0.407614	+	0.913154i	$0.366361\pi$
$929$	−17.8917	+	30.9893i	−0.587008	+	1.01673i	−0.994622	+	0.103573i	$0.966973\pi$
$930$	−3.95939	−	6.71720i	−0.129833	−	0.220266i
$931$	−13.6369	−	28.9305i	−0.446932	−	0.948159i
$932$	0.401767	+	1.22083i	0.0131603	+	0.0399897i
$933$	−4.69347	+	31.0664i	−0.153657	+	1.01707i
$934$	27.8486	+	34.2579i	0.911233	+	1.12095i
$935$	−8.39698	+	4.84800i	−0.274611	+	0.158547i
$936$	−38.6614	+	32.6039i	−1.26369	+	1.06569i
$937$		−	9.98636i		−	0.326240i	−0.986606	−	0.163120i	$-0.947844\pi$
$937$		−	9.98636i		−	0.326240i	0.986606	−	0.163120i	$-0.0521558\pi$
$938$	3.23587	−	2.41430i	0.105655	−	0.0788297i
$939$	1.67423	+	4.27020i	0.0546364	+	0.139353i
$940$	−3.19730	−	0.667019i	−0.104285	−	0.0217558i
$941$	−13.2328	+	7.63995i	−0.431377	+	0.249055i	−0.699933	−	0.714209i	$-0.746787\pi$
$941$	−13.2328	+	7.63995i	−0.431377	+	0.249055i	0.268556	+	0.963264i	$0.413453\pi$
$942$	13.9273	−	24.6332i	0.453775	−	0.802593i
$943$	59.4369	+	34.3159i	1.93553	+	1.11748i
$944$	6.88154	+	9.32298i	0.223975	+	0.303437i
$945$	−6.48693	+	12.1210i	−0.211020	+	0.394298i
$946$	−18.6999	+	2.99793i	−0.607988	+	0.0974710i
$947$	22.3383	−	38.6910i	0.725896	−	1.25729i	−0.232708	−	0.972547i	$-0.574759\pi$
$947$	22.3383	−	38.6910i	0.725896	−	1.25729i	0.958604	−	0.284743i	$-0.0919081\pi$
$948$	−22.8115	−	8.47230i	−0.740885	−	0.275168i
$949$	53.8952	−	31.1164i	1.74951	−	1.01008i
$950$	−6.03680	−	2.30427i	−0.195860	−	0.0747602i
$951$	−28.0264	+	10.9884i	−0.908818	+	0.356323i
$952$	3.13872	−	35.4684i	0.101727	−	1.14954i
$953$		−	9.08658i		−	0.294343i	−0.989111	−	0.147172i	$-0.952983\pi$
$953$		−	9.08658i		−	0.294343i	0.989111	−	0.147172i	$-0.0470169\pi$
$954$	−6.89816	+	2.77662i	−0.223336	+	0.0898964i
$955$	−1.31561	−	2.27870i	−0.0425721	−	0.0737370i
$956$	24.0188	−	26.8787i	0.776825	−	0.869320i
$957$	1.86150	−	12.3214i	0.0601736	−	0.398293i
$958$	7.31059	+	45.6007i	0.236194	+	1.47329i
$959$	23.6550	−	37.3015i	0.763860	−	1.20453i
$960$	13.4481	+	3.33884i	0.434036	+	0.107760i
$961$	−10.4335	+	18.0714i	−0.336566	+	0.582949i
$962$	59.8703	+	73.6494i	1.93030	+	2.37455i
$963$	−48.9908	−	15.1487i	−1.57871	−	0.488160i
$964$	9.56175	+	1.99477i	0.307963	+	0.0642471i
$965$		−	24.1760i		−	0.778254i
$966$	−18.2398	−	34.1090i	−0.586857	−	1.09744i
$967$	25.2632			0.812411			0.406205	−	0.913782i	$-0.366852\pi$
$967$	25.2632			0.812411			0.406205	+	0.913782i	$0.366852\pi$
$968$	−19.3467	−	0.904244i	−0.621828	−	0.0290635i
$969$	−29.4322	−	23.4880i	−0.945498	−	0.754544i
$970$	−9.70159	+	7.88652i	−0.311499	+	0.253221i
$971$	18.1448	+	10.4759i	0.582295	+	0.336188i	0.762045	−	0.647524i	$-0.224196\pi$
$971$	18.1448	+	10.4759i	0.582295	+	0.336188i	−0.179750	+	0.983712i	$0.557529\pi$
$972$	−17.9980	−	25.4572i	−0.577287	−	0.816541i
$973$	13.6883	−	7.16179i	0.438825	−	0.229596i
$974$	−1.63787	−	10.2164i	−0.0524806	−	0.327355i
$975$	1.54214	−	10.2075i	0.0493880	−	0.326902i
$976$	−9.20727	−	4.01643i	−0.294717	−	0.128563i
$977$	13.8318	−	7.98578i	0.442518	−	0.255488i	−0.262147	−	0.965028i	$-0.584431\pi$
$977$	13.8318	−	7.98578i	0.442518	−	0.255488i	0.704665	+	0.709540i	$0.251097\pi$
$978$	−0.00590327	−	0.654465i	−0.000188766	−	0.0209275i
$979$	−26.6985			−0.853288
$980$	−13.4203	−	3.98705i	−0.428695	−	0.127362i
$981$	−4.99143	−	5.38694i	−0.159364	−	0.171992i
$982$	7.97340	+	3.04347i	0.254442	+	0.0971211i
$983$	22.8061	+	39.5013i	0.727401	+	1.25990i	0.957978	+	0.286841i	$0.0926053\pi$
$983$	22.8061	+	39.5013i	0.727401	+	1.25990i	−0.230577	+	0.973054i	$0.574061\pi$
$984$	−11.0069	+	55.2485i	−0.350886	+	1.76126i
$985$	−7.21848	−	4.16759i	−0.230000	−	0.132790i
$986$	−3.76075	−	23.4581i	−0.119767	−	0.747059i
$987$	−4.90700	+	5.65036i	−0.156191	+	0.179853i
$988$	−51.7355	+	17.0258i	−1.64592	+	0.541662i
$989$	−19.6116	+	33.9683i	−0.623613	+	1.08013i
$990$	−8.55974	−	1.21433i	−0.272046	−	0.0385940i
$991$	−2.31430	−	4.00849i	−0.0735163	−	0.127334i	0.826924	−	0.562314i	$-0.190089\pi$
$991$	−2.31430	−	4.00849i	−0.0735163	−	0.127334i	−0.900440	+	0.434980i	$0.856755\pi$
$992$	4.82429	+	17.3488i	0.153171	+	0.550824i
$993$	−15.5072	−	39.5517i	−0.492105	−	1.25514i
$994$	1.76864	+	14.9951i	0.0560979	+	0.475614i
$995$	−23.8979			−0.757614
$996$	6.83957	−	1.15987i	0.216720	−	0.0367519i
$997$	−19.5025	−	33.7793i	−0.617650	−	1.06980i	−0.989913	−	0.141674i	$-0.954752\pi$
$997$	−19.5025	−	33.7793i	−0.617650	−	1.06980i	0.372263	−	0.928127i	$-0.378582\pi$
$998$	11.8474	+	14.5740i	0.375022	+	0.461332i
$999$	−48.3781	+	32.9103i	−1.53062	+	1.04124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.cf.a.341.16	yes	256
3.2	odd	2	inner	840.2.cf.a.341.113	yes	256
7.3	odd	6	inner	840.2.cf.a.101.101	yes	256
8.5	even	2	inner	840.2.cf.a.341.28	yes	256
21.17	even	6	inner	840.2.cf.a.101.28	yes	256
24.5	odd	2	inner	840.2.cf.a.341.101	yes	256
56.45	odd	6	inner	840.2.cf.a.101.113	yes	256
168.101	even	6	inner	840.2.cf.a.101.16	✓	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cf.a.101.16	✓	256	168.101	even	6	inner
840.2.cf.a.101.28	yes	256	21.17	even	6	inner
840.2.cf.a.101.101	yes	256	7.3	odd	6	inner
840.2.cf.a.101.113	yes	256	56.45	odd	6	inner
840.2.cf.a.341.16	yes	256	1.1	even	1	trivial
840.2.cf.a.341.28	yes	256	8.5	even	2	inner
840.2.cf.a.341.101	yes	256	24.5	odd	2	inner
840.2.cf.a.341.113	yes	256	3.2	odd	2	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.cf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32124 - 0.504319i) q^{2} +(1.35380 + 1.08038i) q^{3} +(1.49132 + 1.33265i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.24383 - 2.11019i) q^{6} +(-2.34427 + 1.22654i) q^{7} +(-1.29831 - 2.51285i) q^{8} +(0.665543 + 2.92524i) q^{9} +(0.892064 + 1.09737i) q^{10} +(1.01888 + 1.76474i) q^{11} +(0.579182 + 3.41534i) q^{12} -5.96019 q^{13} +(3.71590 - 0.438284i) q^{14} +(-0.632233 - 1.61254i) q^{15} +(0.448097 + 3.97482i) q^{16} +(-2.37909 - 4.12071i) q^{17} +(0.595918 - 4.20058i) q^{18} +(2.28453 - 3.95692i) q^{19} +(-0.625201 - 1.89977i) q^{20} +(-4.49880 - 0.872225i) q^{21} +(-0.456180 - 2.84548i) q^{22} +(-5.16879 - 2.98420i) q^{23} +(0.957186 - 4.80456i) q^{24} +(0.500000 + 0.866025i) q^{25} +(7.87482 + 3.00584i) q^{26} +(-2.25937 + 4.67923i) q^{27} +(-5.13061 - 1.29492i) q^{28} -3.53059 q^{29} +(0.0220935 + 2.44939i) q^{30} +(-2.75675 + 1.59161i) q^{31} +(1.41254 - 5.47766i) q^{32} +(-0.527248 + 3.48989i) q^{33} +(1.06519 + 6.64425i) q^{34} +(2.64347 + 0.109922i) q^{35} +(-2.90578 + 5.24942i) q^{36} +(9.75183 + 5.63022i) q^{37} +(-5.01395 + 4.07589i) q^{38} +(-8.06890 - 6.43930i) q^{39} +(-0.132053 + 2.82534i) q^{40} -11.4992 q^{41} +(5.50410 + 3.42125i) q^{42} -6.57181i q^{43} +(-0.832310 + 3.98961i) q^{44} +(0.886245 - 2.86611i) q^{45} +(5.32420 + 6.54955i) q^{46} +(0.816535 - 1.41428i) q^{47} +(-3.68770 + 5.86523i) q^{48} +(3.99121 - 5.75067i) q^{49} +(-0.223864 - 1.39638i) q^{50} +(1.23113 - 8.14895i) q^{51} +(-8.88858 - 7.94284i) q^{52} +(-0.876342 - 1.51787i) q^{53} +(5.34499 - 5.04292i) q^{54} -2.03775i q^{55} +(6.12569 + 4.29836i) q^{56} +(7.36779 - 2.88871i) q^{57} +(4.66474 + 1.78055i) q^{58} +(2.50880 - 1.44846i) q^{59} +(1.20608 - 3.24736i) q^{60} +(-1.25565 + 2.17484i) q^{61} +(4.44500 - 0.712610i) q^{62} +(-5.14814 - 6.04125i) q^{63} +(-4.62878 + 6.52490i) q^{64} +(5.16168 + 2.98010i) q^{65} +(2.45663 - 4.34506i) q^{66} +(0.934450 - 0.539505i) q^{67} +(1.94346 - 9.31581i) q^{68} +(-3.77342 - 9.62429i) q^{69} +(-3.43721 - 1.47838i) q^{70} +4.03538i q^{71} +(6.48660 - 5.47028i) q^{72} +(-9.04253 + 5.22071i) q^{73} +(-10.0450 - 12.3569i) q^{74} +(-0.258740 + 1.71262i) q^{75} +(8.68016 - 2.85658i) q^{76} +(-4.55305 - 2.88735i) q^{77} +(7.41346 + 12.5771i) q^{78} +(-3.51232 + 6.08352i) q^{79} +(1.59935 - 3.66635i) q^{80} +(-8.11410 + 3.89375i) q^{81} +(15.1931 + 5.79926i) q^{82} -2.00260i q^{83} +(-5.54680 - 7.29609i) q^{84} +4.75819i q^{85} +(-3.31429 + 8.68290i) q^{86} +(-4.77971 - 3.81439i) q^{87} +(3.11171 - 4.85146i) q^{88} +(-6.55097 + 11.3466i) q^{89} +(-2.61637 + 3.33985i) q^{90} +(13.9723 - 7.31040i) q^{91} +(-3.73145 - 11.3386i) q^{92} +(-5.45164 - 0.823628i) q^{93} +(-1.79208 + 1.45680i) q^{94} +(-3.95692 + 2.28453i) q^{95} +(7.83026 - 5.88956i) q^{96} +8.84076i q^{97} +(-8.17350 + 5.58515i) q^{98} +(-4.48420 + 4.15497i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 30 q^{12} + 16 q^{16} - 10 q^{18} + 8 q^{22} + 128 q^{25} + 12 q^{28} - 40 q^{36} - 54 q^{42} + 16 q^{46} + 16 q^{49} + 36 q^{52} - 72 q^{54} - 16 q^{58} - 14 q^{60} + 80 q^{63} - 48 q^{64} - 60 q^{66}+ \cdots - 144 q^{96}+O(q^{100}) \) 256 * q + 30 * q^12 + 16 * q^16 - 10 * q^18 + 8 * q^22 + 128 * q^25 + 12 * q^28 - 40 * q^36 - 54 * q^42 + 16 * q^46 + 16 * q^49 + 36 * q^52 - 72 * q^54 - 16 * q^58 - 14 * q^60 + 80 * q^63 - 48 * q^64 - 60 * q^66 - 12 * q^70 - 50 * q^72 + 48 * q^73 - 16 * q^78 + 64 * q^79 - 8 * q^81 - 72 * q^82 - 56 * q^84 - 8 * q^88 - 72 * q^94 - 144 * q^96

Introduction

L-functions

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