LMFDB - Embedded newform 840.2.cf.a.101.16

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			101.16
Character	$\chi$	$=$	840.101
Dual form			840.2.cf.a.341.16

$q$-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 $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

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

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	−0.670547	−	0.741867i	$-0.733940\pi$
$11$	1.01888	−	1.76474i	0.307203	−	0.532090i	0.977749	+	0.209777i	$0.0672738\pi$
$12$	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	0.418805	+	0.908076i	$0.362449\pi$
$17$	−2.37909	+	4.12071i	−0.577015	+	0.999419i	−0.995820	+	0.0913428i	$0.970884\pi$
$18$	0.595918	+	4.20058i	0.140459	+	0.990086i
$19$	2.28453	+	3.95692i	0.524107	+	0.907780i	0.999606	+	0.0280641i	$0.00893426\pi$
$19$	2.28453	+	3.95692i	0.524107	+	0.907780i	−0.475499	+	0.879716i	$0.657732\pi$
$20$	−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	−0.930293	−	0.366817i	$-0.880448\pi$
$23$	−5.16879	+	2.98420i	−1.07777	+	0.622249i	−0.147474	+	0.989066i	$0.547114\pi$
$24$	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	0.231572	−	0.972818i	$-0.425613\pi$
$31$	−2.75675	−	1.59161i	−0.495128	−	0.285862i	−0.726699	+	0.686956i	$0.758947\pi$
$32$	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	0.612347	−	0.790589i	$-0.290226\pi$
$37$	9.75183	−	5.63022i	1.60319	−	0.925602i	0.990844	−	0.135013i	$-0.0431076\pi$
$38$	−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	$0.167069\pi$
$43$			6.57181i			1.00219i	−0.865392	+	0.501096i	$0.832931\pi$
$44$	−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	0.919413	−	0.393294i	$-0.128665\pi$
$47$	0.816535	+	1.41428i	0.119104	+	0.206294i	−0.800309	+	0.599588i	$0.795331\pi$
$48$	−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	−0.919916	−	0.392117i	$-0.871743\pi$
$53$	−0.876342	+	1.51787i	−0.120375	+	0.208495i	0.799541	+	0.600612i	$0.205076\pi$
$54$	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	0.654338	−	0.756202i	$-0.272947\pi$
$59$	2.50880	+	1.44846i	0.326618	+	0.188573i	−0.327721	+	0.944775i	$0.606281\pi$
$60$	1.20608	+	3.24736i	0.155705	+	0.419233i
$61$	−1.25565	−	2.17484i	−0.160769	−	0.278460i	0.774376	−	0.632726i	$-0.218064\pi$
$61$	−1.25565	−	2.17484i	−0.160769	−	0.278460i	−0.935145	+	0.354266i	$0.884731\pi$
$62$	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	0.555993	−	0.831187i	$-0.312338\pi$
$67$	0.934450	+	0.539505i	0.114161	+	0.0659110i	−0.441832	+	0.897098i	$0.645671\pi$
$68$	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	$-0.923031\pi$
$71$		−	4.03538i		−	0.478911i	0.970907	−	0.239456i	$-0.0769690\pi$
$72$	6.48660	+	5.47028i	0.764454	+	0.644679i
$73$	−9.04253	−	5.22071i	−1.05835	−	0.611038i	−0.133373	−	0.991066i	$-0.542581\pi$
$73$	−9.04253	−	5.22071i	−1.05835	−	0.611038i	−0.924975	+	0.380028i	$0.875914\pi$
$74$	−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	0.597956	−	0.801529i	$-0.295980\pi$
$79$	−3.51232	−	6.08352i	−0.395167	−	0.684449i	−0.993122	+	0.117080i	$0.962647\pi$
$80$	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	$0.0350553\pi$
$83$			2.00260i			0.219814i	−0.993942	+	0.109907i	$0.964945\pi$
$84$	−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	−0.970382	−	0.241576i	$-0.922336\pi$
$89$	−6.55097	−	11.3466i	−0.694402	−	1.20274i	0.275980	−	0.961163i	$-0.410998\pi$
$90$	−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	$-0.851844\pi$
$97$		−	8.84076i		−	0.897643i	0.893621	−	0.448822i	$-0.148156\pi$
$98$	−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	0.961154	−	0.276011i	$-0.0890128\pi$
$101$	12.0870	+	6.97842i	1.20270	+	0.694378i	0.241544	+	0.970390i	$0.422346\pi$
$102$	−5.73629	−	10.1458i	−0.567977	−	1.00458i
$103$	−16.4114	+	9.47511i	−1.61706	+	0.933610i	−0.629385	+	0.777094i	$0.716693\pi$
$103$	−16.4114	+	9.47511i	−1.61706	+	0.933610i	−0.987675	+	0.156517i	$0.949974\pi$
$104$	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	−0.900977	−	0.433867i	$-0.857149\pi$
$107$	−8.54657	−	14.8031i	−0.826228	−	1.43107i	0.0747490	−	0.997202i	$-0.476184\pi$
$108$	−9.60523	−	3.96731i	−0.924264	−	0.381754i
$109$	−2.12001	−	1.22399i	−0.203061	−	0.117237i	0.395022	−	0.918672i	$-0.370737\pi$
$109$	−2.12001	−	1.22399i	−0.203061	−	0.117237i	−0.598082	+	0.801435i	$0.704070\pi$
$110$	−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	$0.0530660\pi$
$113$			3.52795i			0.331881i	−0.986136	+	0.165941i	$0.946934\pi$
$114$	−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	−0.407762	−	0.913088i	$-0.633691\pi$
$131$	2.05006	−	1.18360i	0.179114	−	0.103412i	0.586876	+	0.809676i	$0.300357\pi$
$132$	−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	−0.267109	−	0.963666i	$-0.586068\pi$
$137$	−14.4579	−	8.34728i	−1.23522	−	0.713156i	−0.968114	+	0.250510i	$0.919402\pi$
$138$	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	−0.939331	−	0.343012i	$-0.888553\pi$
$149$	−9.35904	−	16.2103i	−0.766723	−	1.32800i	0.172608	−	0.984991i	$-0.444781\pi$
$150$	1.20556	+	2.13228i	0.0984337	+	0.174100i
$151$	−8.74283	+	15.1430i	−0.711481	+	1.23232i	0.252820	+	0.967513i	$0.418642\pi$
$151$	−8.74283	+	15.1430i	−0.711481	+	1.23232i	−0.964301	+	0.264808i	$0.914691\pi$
$152$	−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	−0.538015	−	0.842935i	$-0.680826\pi$
$157$	5.77625	−	10.0048i	0.460995	−	0.798467i	0.999011	+	0.0444676i	$0.0141592\pi$
$158$	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	−0.490910	−	0.871210i	$-0.663336\pi$
$163$	0.231398	−	0.133598i	0.0181245	−	0.0104642i	0.509035	+	0.860746i	$0.330002\pi$
$164$	−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	0.398104	−	0.917340i	$-0.369668\pi$
$173$	18.3036	−	10.5676i	1.39160	−	0.803438i	0.993492	+	0.113902i	$0.0363350\pi$
$174$	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	−0.898730	−	0.438503i	$-0.855509\pi$
$179$	−0.931323	+	1.61310i	−0.0696104	+	0.120569i	0.829119	+	0.559071i	$0.188842\pi$
$180$	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	−0.415289	−	0.909690i	$-0.636320\pi$
$191$	2.27870	−	1.31561i	0.164881	−	0.0951941i	0.580170	+	0.814496i	$0.302986\pi$
$192$	−13.3158	−	3.83255i	−0.960988	−	0.276590i
$193$	12.0880	−	20.9371i	0.870115	−	1.50708i	0.00823741	−	0.999966i	$-0.497378\pi$
$193$	12.0880	−	20.9371i	0.870115	−	1.50708i	0.861877	−	0.507117i	$-0.169289\pi$
$194$	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	0.999323	−	0.0368015i	$-0.0117169\pi$
$199$	20.6962	+	11.9489i	1.46711	+	0.847038i	0.467790	+	0.883839i	$0.345050\pi$
$200$	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	$-0.889570\pi$
$211$		−	9.87780i		−	0.680016i	0.940423	−	0.340008i	$-0.110430\pi$
$212$	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	$0.0812882\pi$
$223$			7.54448i			0.505216i	−0.967569	+	0.252608i	$0.918712\pi$
$224$	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	0.568067	−	0.822982i	$-0.307691\pi$
$227$	2.09993	+	1.21240i	0.139378	+	0.0804697i	−0.428690	+	0.903452i	$0.641025\pi$
$228$	14.8374	−	5.51067i	0.982631	−	0.364953i
$229$	1.24517	+	2.15670i	0.0822831	+	0.142518i	0.904230	−	0.427045i	$-0.140446\pi$
$229$	1.24517	+	2.15670i	0.0822831	+	0.142518i	−0.821947	+	0.569564i	$0.807112\pi$
$230$	−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	−0.481660	−	0.876358i	$-0.659966\pi$
$233$	0.556527	−	0.321311i	0.0364593	−	0.0210498i	0.518119	+	0.855309i	$0.326632\pi$
$234$	−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	$0.198089\pi$
$239$			18.0234i			1.16584i	−0.812531	+	0.582918i	$0.801911\pi$
$240$	6.12625	+	3.23559i	0.395448	+	0.208856i
$241$	4.22950	+	2.44190i	0.272446	+	0.157297i	0.629999	−	0.776596i	$-0.283055\pi$
$241$	4.22950	+	2.44190i	0.272446	+	0.157297i	−0.357553	+	0.933893i	$0.616389\pi$
$242$	−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	$0.0609484\pi$
$251$			6.03006i			0.380614i	−0.981725	+	0.190307i	$0.939052\pi$
$252$	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	0.771514	−	0.636212i	$-0.219500\pi$
$257$	−2.64867	−	4.58762i	−0.165219	−	0.286168i	−0.936733	+	0.350044i	$0.886166\pi$
$258$	−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	0.580427	−	0.814312i	$-0.302886\pi$
$263$	2.68275	+	1.54889i	0.165426	+	0.0955085i	−0.415001	+	0.909821i	$0.636219\pi$
$264$	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	0.822695	−	0.568483i	$-0.192470\pi$
$269$	12.1651	+	7.02354i	0.741721	+	0.428233i	−0.0809736	+	0.996716i	$0.525803\pi$
$270$	−7.15036	−	1.69480i	−0.435157	−	0.103142i
$271$	−4.54653	+	2.62494i	−0.276182	+	0.159454i	−0.631694	−	0.775218i	$-0.717640\pi$
$271$	−4.54653	+	2.62494i	−0.276182	+	0.159454i	0.355512	+	0.934672i	$0.384307\pi$
$272$	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	0.783046	−	0.621964i	$-0.213665\pi$
$277$	10.5840	+	6.11068i	0.635932	+	0.367155i	−0.147114	+	0.989120i	$0.546998\pi$
$278$	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	$-0.722738\pi$
$281$		−	25.6475i		−	1.53000i	0.644028	−	0.765002i	$-0.277262\pi$
$282$	−4.00002	−	0.0360802i	−0.238198	−	0.00214855i
$283$	−9.08093	+	15.7286i	−0.539805	+	0.934970i	0.459109	+	0.888380i	$0.348169\pi$
$283$	−9.08093	+	15.7286i	−0.539805	+	0.934970i	−0.998914	+	0.0465899i	$0.985165\pi$
$284$	−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	$0.0383365\pi$
$293$			4.11316i			0.240293i	−0.992756	+	0.120147i	$0.961664\pi$
$294$	−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	−0.485558	−	0.874205i	$-0.661383\pi$
$311$	9.06986	−	15.7095i	0.514304	−	0.890801i	0.999862	−	0.0165969i	$-0.00528319\pi$
$312$	−5.70501	−	28.6361i	−0.322983	−	1.62120i
$313$	2.29334	−	1.32406i	0.129627	−	0.0748404i	−0.433784	−	0.901017i	$-0.642822\pi$
$313$	2.29334	−	1.32406i	0.129627	−	0.0748404i	0.563411	+	0.826176i	$0.309489\pi$
$314$	−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	0.511819	−	0.859093i	$-0.328972\pi$
$317$	−8.69014	−	15.0518i	−0.488087	−	0.845392i	−0.999906	+	0.0137016i	$0.995638\pi$
$318$	−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	−0.953099	−	0.302657i	$-0.902126\pi$
$331$	−21.2415	+	12.2638i	−1.16754	+	0.674080i	−0.214441	+	0.976737i	$0.568793\pi$
$332$	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	−0.584764	−	0.811203i	$-0.698813\pi$
$347$	7.64008	−	13.2330i	0.410141	−	0.710385i	0.994905	+	0.100819i	$0.0321462\pi$
$348$	−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	−0.952604	−	0.304212i	$-0.901607\pi$
$353$	−3.99904	+	6.92654i	−0.212847	+	0.368662i	0.739757	+	0.672874i	$0.234940\pi$
$354$	−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	−0.131431	−	0.991325i	$-0.541957\pi$
$359$	12.5311	−	7.23483i	0.661366	−	0.381840i	0.792797	+	0.609485i	$0.208624\pi$
$360$	−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	0.613358	−	0.789805i	$-0.289818\pi$
$367$	4.52199	+	2.61077i	0.236046	+	0.136281i	−0.377312	+	0.926086i	$0.623152\pi$
$368$	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	−0.844451	−	0.535633i	$-0.820073\pi$
$373$	−15.5047	+	8.95166i	−0.802805	+	0.463500i	0.0416461	+	0.999132i	$0.486740\pi$
$374$	−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	$-0.752695\pi$
$379$		−	27.2977i		−	1.40219i	0.713069	−	0.701094i	$-0.247305\pi$
$380$	−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	0.687651	−	0.726041i	$-0.258642\pi$
$383$	−5.57647	−	9.65872i	−0.284944	−	0.493538i	−0.972596	+	0.232503i	$0.925308\pi$
$384$	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	0.0109173	+	0.999940i	$0.496525\pi$
$389$	−16.9720	+	29.3964i	−0.860515	+	1.49046i	−0.871432	+	0.490516i	$0.836808\pi$
$390$	−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	0.796597	−	0.604511i	$-0.206631\pi$
$397$	−2.49505	−	4.32155i	−0.125223	−	0.216892i	−0.921820	+	0.387618i	$0.873298\pi$
$398$	−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	−0.0140306	−	0.999902i	$-0.504466\pi$
$401$	16.9190	−	9.76819i	0.844894	−	0.487800i	0.858925	+	0.512102i	$0.171133\pi$
$402$	−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	−0.224094	−	0.974567i	$-0.571942\pi$
$409$	−23.8669	−	13.7796i	−1.18014	−	0.681355i	−0.956047	+	0.293212i	$0.905276\pi$
$410$	−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	$-0.854654\pi$
$419$		−	18.0506i		−	0.881831i	0.897549	−	0.440915i	$-0.145346\pi$
$420$	1.15563	−	9.09200i	0.0563888	−	0.443644i
$421$		−	16.1056i		−	0.784940i	−0.919765	−	0.392470i	$-0.871621\pi$
$421$		−	16.1056i		−	0.784940i	0.919765	−	0.392470i	$-0.128379\pi$
$422$	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	0.865980	−	0.500078i	$-0.166695\pi$
$431$	17.9764	+	10.3787i	0.865891	+	0.499922i	−8.98140e−5		1.00000i	$0.500029\pi$
$432$	−19.6115	+	6.88386i	−0.943561	+	0.331200i
$433$			17.9802i			0.864072i	0.901856	+	0.432036i	$0.142205\pi$
$433$			17.9802i			0.864072i	−0.901856	+	0.432036i	$0.857795\pi$
$434$	−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	−0.441634	−	0.897195i	$-0.645601\pi$
$439$	2.39995	−	1.38561i	0.114544	−	0.0661318i	0.556177	+	0.831064i	$0.312268\pi$
$440$	−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	0.999156	−	0.0410822i	$-0.0130805\pi$
$443$	9.76606	+	16.9153i	0.464000	+	0.803671i	−0.535156	+	0.844753i	$0.679747\pi$
$444$	−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	$0.120808\pi$
$449$			15.7009i			0.740969i	−0.928839	+	0.370485i	$0.879192\pi$
$450$	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	0.783686	−	0.621158i	$-0.213337\pi$
$457$	−3.12316	−	5.40947i	−0.146095	−	0.253044i	−0.929781	+	0.368113i	$0.880004\pi$
$458$	−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	$-0.986980\pi$
$461$		−	1.75600i		−	0.0817853i	0.999164	−	0.0408926i	$-0.0130202\pi$
$462$	−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	−0.971321	−	0.237774i	$-0.923582\pi$
$467$	−27.0357	+	15.6091i	−1.25106	+	0.722301i	−0.279742	+	0.960075i	$0.590249\pi$
$468$	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	0.203649	+	0.979044i	$0.434720\pi$
$479$	−16.3282	+	28.2812i	−0.746053	+	1.29220i	−0.949701	+	0.313157i	$0.898613\pi$
$480$	−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	−0.771160	−	0.636641i	$-0.780323\pi$
$487$	3.65817	−	6.33613i	0.165767	−	0.287118i	0.936928	+	0.349524i	$0.113657\pi$
$488$	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	−0.734837	−	0.678243i	$-0.762742\pi$
$499$	−11.5016	+	6.64042i	−0.514880	+	0.297266i	0.219957	+	0.975510i	$0.429408\pi$
$500$	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	−0.960084	−	0.279713i	$-0.909761\pi$
$509$	−27.0256	+	15.6032i	−1.19789	+	0.691600i	−0.237803	+	0.971313i	$0.576427\pi$
$510$	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	0.295781	+	0.955256i	$0.404420\pi$
$521$	−15.5073	+	26.8594i	−0.679385	+	1.17673i	−0.975166	+	0.221474i	$0.928913\pi$
$522$	−2.10394	−	14.8305i	−0.0920870	−	0.649115i
$523$	6.50584	+	11.2684i	0.284481	+	0.492735i	0.972483	−	0.232974i	$-0.0748456\pi$
$523$	6.50584	+	11.2684i	0.284481	+	0.492735i	−0.688003	+	0.725708i	$0.741512\pi$
$524$	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	−0.785087	−	0.619385i	$-0.787382\pi$
$541$	−14.9146	+	8.61093i	−0.641228	+	0.370213i	0.143860	+	0.989598i	$0.454049\pi$
$542$	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	$0.105819\pi$
$547$			15.2655i			0.652704i	−0.945248	+	0.326352i	$0.894181\pi$
$548$	−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	−0.496464	−	0.868057i	$-0.665369\pi$
$557$	11.8837	−	20.5831i	0.503527	−	0.872135i	0.999992	−	0.00407777i	$-0.00129800\pi$
$558$	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	0.438371	−	0.898794i	$-0.355556\pi$
$563$	−2.86681	−	1.65515i	−0.120822	−	0.0697565i	−0.559193	+	0.829038i	$0.688889\pi$
$564$	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	−0.528778	−	0.848760i	$-0.677350\pi$
$569$	−1.38637	+	0.800424i	−0.0581199	+	0.0335555i	0.470658	+	0.882315i	$0.344016\pi$
$570$	9.74252	−	5.50828i	0.408069	−	0.230717i
$571$	3.37799	+	1.95028i	0.141364	+	0.0816167i	0.569014	−	0.822328i	$-0.307325\pi$
$571$	3.37799	+	1.95028i	0.141364	+	0.0816167i	−0.427650	+	0.903945i	$0.640658\pi$
$572$	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	−0.221284	−	0.975209i	$-0.571025\pi$
$577$	−28.2601	−	16.3160i	−1.17648	−	0.679243i	−0.955198	+	0.295967i	$0.904358\pi$
$578$	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	$0.192695\pi$
$587$			27.5747i			1.13813i	−0.822293	+	0.569065i	$0.807305\pi$
$588$	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	−0.860900	−	0.508773i	$-0.830099\pi$
$593$	−21.2117	−	36.7398i	−0.871061	−	1.50872i	−0.0101604	−	0.999948i	$-0.503234\pi$
$594$	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	0.486385	−	0.873744i	$-0.338315\pi$
$599$	−0.663420	−	0.383026i	−0.0271066	−	0.0156500i	−0.513492	+	0.858094i	$0.671648\pi$
$600$	4.63946	+	1.57333i	0.189405	+	0.0642310i
$601$			40.3989i			1.64790i	0.566659	+	0.823952i	$0.308236\pi$
$601$			40.3989i			1.64790i	−0.566659	+	0.823952i	$0.691764\pi$
$602$	−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	−0.137564	−	0.990493i	$-0.543927\pi$
$607$	16.0499	−	9.26641i	0.651445	−	0.376112i	0.789010	+	0.614381i	$0.210594\pi$
$608$	−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	0.299138	−	0.954210i	$-0.403301\pi$
$613$	−9.35052	−	5.39852i	−0.377664	−	0.218044i	−0.676801	+	0.736166i	$0.736634\pi$
$614$	−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	$0.206015\pi$
$617$			29.9548i			1.20594i	−0.797765	+	0.602968i	$0.793985\pi$
$618$	0.418677	−	46.4165i	0.0168416	−	1.86714i
$619$	−23.4241	+	40.5717i	−0.941493	+	1.63071i	−0.178868	+	0.983873i	$0.557244\pi$
$619$	−23.4241	+	40.5717i	−0.941493	+	1.63071i	−0.762625	+	0.646841i	$0.776090\pi$
$620$	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	0.705757	−	0.708454i	$-0.250607\pi$
$641$	11.2689	+	6.50611i	0.445095	+	0.256976i	−0.260661	+	0.965430i	$0.583941\pi$
$642$	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	−0.774891	−	0.632095i	$-0.782195\pi$
$647$	4.06889	−	7.04753i	0.159965	−	0.277067i	0.934856	+	0.355028i	$0.115529\pi$
$648$	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	−0.996788	−	0.0800881i	$-0.974480\pi$
$653$	−14.5083	−	25.1290i	−0.567752	−	0.983376i	0.429036	−	0.903288i	$-0.358853\pi$
$654$	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	−0.971953	−	0.235176i	$-0.924433\pi$
$661$	−7.25811	+	12.5714i	−0.282308	+	0.488971i	0.689645	+	0.724148i	$0.257767\pi$
$662$	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	0.122788	−	0.992433i	$-0.460816\pi$
$677$	27.1551	−	15.6780i	1.04365	−	0.602554i	0.920866	+	0.389879i	$0.127483\pi$
$678$	−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	0.202296	+	0.979324i	$0.435160\pi$
$683$	−19.5216	+	33.8123i	−0.746972	+	1.29379i	−0.949268	+	0.314469i	$0.898174\pi$
$684$	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	0.919594	−	0.392869i	$-0.128517\pi$
$691$	3.14293	+	5.44372i	0.119563	+	0.207089i	−0.800032	+	0.599958i	$0.795184\pi$
$692$	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	−0.00571373	−	0.999984i	$-0.501819\pi$
$709$	22.8311	−	13.1816i	0.857441	−	0.495044i	0.863154	+	0.504940i	$0.168485\pi$
$710$	−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	−0.996148	−	0.0876899i	$-0.972052\pi$
$719$	−15.3918	−	26.6593i	−0.574016	−	0.994224i	0.422132	−	0.906534i	$-0.361282\pi$
$720$	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	$0.0516450\pi$
$727$			8.71100i			0.323073i	−0.986867	+	0.161537i	$0.948355\pi$
$728$	−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	−0.781655	−	0.623711i	$-0.785624\pi$
$733$	−25.2052	−	43.6568i	−0.930977	−	1.61250i	−0.149321	−	0.988789i	$-0.547709\pi$
$734$	−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	0.709372	−	0.704834i	$-0.248979\pi$
$739$	12.3324	+	7.12009i	0.453653	+	0.261917i	−0.255719	+	0.966751i	$0.582312\pi$
$740$	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	$0.112770\pi$
$743$			18.9124i			0.693827i	−0.937897	+	0.346914i	$0.887230\pi$
$744$	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	0.923293	+	0.384096i	$0.125487\pi$
$751$	21.7669	+	37.7013i	0.794284	+	1.37574i	−0.129009	+	0.991643i	$0.541180\pi$
$752$	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	$-0.923064\pi$
$757$		−	13.1711i		−	0.478711i	0.970932	−	0.239356i	$-0.0769362\pi$
$758$	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	0.938434	−	0.345459i	$-0.112277\pi$
$761$	4.69077	+	8.12465i	0.170040	+	0.294518i	−0.768393	+	0.639978i	$0.778944\pi$
$762$	−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	$0.116968\pi$
$769$			19.9247i			0.718501i	−0.933241	+	0.359251i	$0.883032\pi$
$770$	−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	−0.309984	−	0.950742i	$-0.600324\pi$
$773$	−35.8196	−	20.6805i	−1.28834	−	0.743825i	−0.978359	+	0.206917i	$0.933657\pi$
$774$	−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	−0.529355	−	0.848400i	$-0.677566\pi$
$787$	13.1868	−	22.8402i	0.470059	−	0.814166i	0.999414	+	0.0342346i	$0.0108993\pi$
$788$	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	$0.0667650\pi$
$797$			11.7563i			0.416428i	−0.978083	+	0.208214i	$0.933235\pi$
$798$	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	−0.227551	−	0.973766i	$-0.573072\pi$
$809$	−33.6944	−	19.4535i	−1.18463	−	0.683948i	−0.957082	+	0.289818i	$0.906405\pi$
$810$	−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	0.738654	−	0.674085i	$-0.235462\pi$
$821$	−6.14459	−	10.6427i	−0.214448	−	0.371434i	−0.953102	+	0.302650i	$0.902129\pi$
$822$	35.5975	−	20.1263i	1.24161	−	0.701986i
$823$	−17.1695	+	29.7384i	−0.598489	+	1.03661i	0.394555	+	0.918872i	$0.370899\pi$
$823$	−17.1695	+	29.7384i	−0.598489	+	1.03661i	−0.993044	+	0.117742i	$0.962435\pi$
$824$	−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	0.0466199	+	0.998913i	$0.485155\pi$
$829$	−24.2367	+	41.9791i	−0.841774	+	1.45800i	−0.888394	+	0.459082i	$0.848178\pi$
$830$	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	−0.760423	−	0.649428i	$-0.775008\pi$
$857$	5.33411	−	9.23896i	0.182210	−	0.315597i	0.942633	+	0.333831i	$0.108342\pi$
$858$	−14.6420	−	25.8974i	−0.499870	−	0.884122i
$859$	−8.01206	−	13.8773i	−0.273368	−	0.473487i	0.696354	−	0.717698i	$-0.254804\pi$
$859$	−8.01206	−	13.8773i	−0.273368	−	0.473487i	−0.969722	+	0.244211i	$0.921471\pi$
$860$	−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	−0.488759	−	0.872419i	$-0.662550\pi$
$863$	0.657992	−	0.379892i	0.0223983	−	0.0129317i	0.511157	+	0.859487i	$0.329217\pi$
$864$	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	−0.187087	−	0.982343i	$-0.559905\pi$
$877$	16.8832	−	9.74749i	0.570104	−	0.329149i	0.757191	+	0.653194i	$0.226571\pi$
$878$	−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	$0.0716909\pi$
$883$			13.2723i			0.446649i	−0.974744	+	0.223324i	$0.928309\pi$
$884$	−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	−0.877385	−	0.479788i	$-0.840714\pi$
$887$	−25.4403	−	44.0638i	−0.854201	−	1.47952i	0.0231839	−	0.999731i	$-0.492620\pi$
$888$	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	−0.499920	−	0.866072i	$-0.666637\pi$
$907$	−45.1723	−	26.0802i	−1.49992	−	0.865979i	−1.00000		9.22087e-5i	$0.999971\pi$
$908$	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	$-0.831533\pi$
$911$		−	30.4779i		−	1.00978i	0.863184	−	0.504890i	$-0.168467\pi$
$912$	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	0.733972	−	0.679180i	$-0.237664\pi$
$919$	−6.70571	−	11.6146i	−0.221201	−	0.383131i	−0.955173	+	0.296048i	$0.904331\pi$
$920$	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	−0.994622	−	0.103573i	$-0.966973\pi$
$929$	−17.8917	−	30.9893i	−0.587008	−	1.01673i	0.407614	−	0.913154i	$-0.366361\pi$
$930$	−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	$0.0521558\pi$
$937$			9.98636i			0.326240i	−0.986606	+	0.163120i	$0.947844\pi$
$938$	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	0.268556	−	0.963264i	$-0.413453\pi$
$941$	−13.2328	−	7.63995i	−0.431377	−	0.249055i	−0.699933	+	0.714209i	$0.746787\pi$
$942$	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	0.958604	+	0.284743i	$0.0919081\pi$
$947$	22.3383	+	38.6910i	0.725896	+	1.25729i	−0.232708	+	0.972547i	$0.574759\pi$
$948$	−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	$0.0470169\pi$
$953$			9.08658i			0.294343i	−0.989111	+	0.147172i	$0.952983\pi$
$954$	−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	−0.179750	−	0.983712i	$-0.557529\pi$
$971$	18.1448	−	10.4759i	0.582295	−	0.336188i	0.762045	+	0.647524i	$0.224196\pi$
$972$	−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	0.704665	−	0.709540i	$-0.251097\pi$
$977$	13.8318	+	7.98578i	0.442518	+	0.255488i	−0.262147	+	0.965028i	$0.584431\pi$
$978$	−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	−0.230577	−	0.973054i	$-0.574061\pi$
$983$	22.8061	−	39.5013i	0.727401	−	1.25990i	0.957978	−	0.286841i	$-0.0926053\pi$
$984$	−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	−0.900440	−	0.434980i	$-0.856755\pi$
$991$	−2.31430	+	4.00849i	−0.0735163	+	0.127334i	0.826924	+	0.562314i	$0.190089\pi$
$992$	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	0.372263	+	0.928127i	$0.378582\pi$
$997$	−19.5025	+	33.7793i	−0.617650	+	1.06980i	−0.989913	+	0.141674i	$0.954752\pi$
$998$	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.101.16	✓	256
3.2	odd	2	inner	840.2.cf.a.101.113	yes	256
7.5	odd	6	inner	840.2.cf.a.341.101	yes	256
8.5	even	2	inner	840.2.cf.a.101.28	yes	256
21.5	even	6	inner	840.2.cf.a.341.28	yes	256
24.5	odd	2	inner	840.2.cf.a.101.101	yes	256
56.5	odd	6	inner	840.2.cf.a.341.113	yes	256
168.5	even	6	inner	840.2.cf.a.341.16	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cf.a.101.16	✓	256	1.1	even	1	trivial
840.2.cf.a.101.28	yes	256	8.5	even	2	inner
840.2.cf.a.101.101	yes	256	24.5	odd	2	inner
840.2.cf.a.101.113	yes	256	3.2	odd	2	inner
840.2.cf.a.341.16	yes	256	168.5	even	6	inner
840.2.cf.a.341.28	yes	256	21.5	even	6	inner
840.2.cf.a.341.101	yes	256	7.5	odd	6	inner
840.2.cf.a.341.113	yes	256	56.5	odd	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.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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more