LMFDB - Embedded newform 820.2.s.c.583.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(583,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.583"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.s (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [240,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$120$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			583.14
Character	$\chi$	$=$	820.583
Dual form			820.2.s.c.647.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.33694 - 0.461086i) q^{2} -2.00537 q^{3} +(1.57480 + 1.23289i) q^{4} +(-1.66826 - 1.48893i) q^{5} +(2.68106 + 0.924650i) q^{6} -4.57903i q^{7} +(-1.53694 - 2.37441i) q^{8} +1.02153 q^{9} +(1.54384 + 2.75981i) q^{10} +(2.54798 - 2.54798i) q^{11} +(-3.15806 - 2.47240i) q^{12} -2.88430i q^{13} +(-2.11133 + 6.12187i) q^{14} +(3.34549 + 2.98585i) q^{15} +(0.959984 + 3.88310i) q^{16} -0.355667i q^{17} +(-1.36572 - 0.471012i) q^{18} +(4.98430 - 4.98430i) q^{19} +(-0.791504 - 4.40154i) q^{20} +9.18267i q^{21} +(-4.58132 + 2.23165i) q^{22} +(0.157197 - 0.157197i) q^{23} +(3.08214 + 4.76158i) q^{24} +(0.566202 + 4.96784i) q^{25} +(-1.32991 + 3.85613i) q^{26} +3.96758 q^{27} +(5.64542 - 7.21105i) q^{28} +(-3.65502 + 3.65502i) q^{29} +(-3.09597 - 5.53446i) q^{30} -9.42699i q^{31} +(0.507003 - 5.63409i) q^{32} +(-5.10964 + 5.10964i) q^{33} +(-0.163993 + 0.475504i) q^{34} +(-6.81784 + 7.63903i) q^{35} +(1.60870 + 1.25943i) q^{36} +(3.67243 - 3.67243i) q^{37} +(-8.96189 + 4.36550i) q^{38} +5.78410i q^{39} +(-0.971297 + 6.24953i) q^{40} +(6.25621 + 1.36377i) q^{41} +(4.23400 - 12.2766i) q^{42} +(-4.13136 - 4.13136i) q^{43} +(7.15391 - 0.871186i) q^{44} +(-1.70417 - 1.52098i) q^{45} +(-0.282644 + 0.137681i) q^{46} -3.92076 q^{47} +(-1.92513 - 7.78706i) q^{48} -13.9675 q^{49} +(1.53363 - 6.90275i) q^{50} +0.713245i q^{51} +(3.55601 - 4.54219i) q^{52} -3.52215i q^{53} +(-5.30440 - 1.82940i) q^{54} +(-8.04444 + 0.456947i) q^{55} +(-10.8725 + 7.03770i) q^{56} +(-9.99539 + 9.99539i) q^{57} +(6.57181 - 3.20125i) q^{58} -4.54425 q^{59} +(1.58726 + 8.82673i) q^{60} -8.21966i q^{61} +(-4.34666 + 12.6033i) q^{62} -4.67760i q^{63} +(-3.27563 + 7.29865i) q^{64} +(-4.29451 + 4.81177i) q^{65} +(9.18726 - 4.47528i) q^{66} +7.29388 q^{67} +(0.438497 - 0.560104i) q^{68} +(-0.315239 + 0.315239i) q^{69} +(12.6373 - 7.06929i) q^{70} +(-8.39564 + 8.39564i) q^{71} +(-1.57002 - 2.42552i) q^{72} +(-6.17916 + 6.17916i) q^{73} +(-6.60311 + 3.21650i) q^{74} +(-1.13545 - 9.96237i) q^{75} +(13.9943 - 1.70420i) q^{76} +(-11.6673 - 11.6673i) q^{77} +(2.66697 - 7.73297i) q^{78} +(7.01044 + 7.01044i) q^{79} +(4.18013 - 7.90737i) q^{80} -11.0211 q^{81} +(-7.73534 - 4.70793i) q^{82} +(-1.29454 + 1.29454i) q^{83} +(-11.3212 + 14.4609i) q^{84} +(-0.529561 + 0.593346i) q^{85} +(3.61845 + 7.42827i) q^{86} +(7.32968 - 7.32968i) q^{87} +(-9.96602 - 2.13385i) q^{88} +(10.8817 - 10.8817i) q^{89} +(1.57707 + 2.81922i) q^{90} -13.2073 q^{91} +(0.441360 - 0.0537477i) q^{92} +18.9047i q^{93} +(5.24180 + 1.80781i) q^{94} +(-15.7364 + 0.893871i) q^{95} +(-1.01673 + 11.2985i) q^{96} +13.6157i q^{97} +(18.6737 + 6.44023i) q^{98} +(2.60282 - 2.60282i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{6} - 12 q^{8} + 240 q^{9} - 20 q^{10} + 8 q^{14} + 8 q^{16} - 12 q^{18} - 16 q^{20} - 12 q^{24} - 16 q^{25} - 30 q^{30} - 24 q^{33} + 20 q^{34} - 8 q^{37} - 4 q^{40} - 16 q^{41} + 84 q^{42}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q - 4 * q^6 - 12 * q^8 + 240 * q^9 - 20 * q^10 + 8 * q^14 + 8 * q^16 - 12 * q^18 - 16 * q^20 - 12 * q^24 - 16 * q^25 - 30 * q^30 - 24 * q^33 + 20 * q^34 - 8 * q^37 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 - 224 * q^49 + 12 * q^50 + 28 * q^52 - 48 * q^54 + 24 * q^56 - 8 * q^57 + 28 * q^58 - 26 * q^60 - 40 * q^65 - 8 * q^66 + 96 * q^68 - 16 * q^69 - 14 * q^70 - 96 * q^72 + 72 * q^73 - 112 * q^74 + 20 * q^76 + 56 * q^77 + 4 * q^78 - 60 * q^80 + 48 * q^81 + 20 * q^82 + 32 * q^84 - 16 * q^85 - 8 * q^86 - 16 * q^88 + 64 * q^89 - 76 * q^90 + 20 * q^92 - 48 * q^94 + 24 * q^96 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.33694	−	0.461086i	−0.945357	−	0.326037i
$2$	−1.33694	−	0.461086i	−0.945357	−	0.326037i
$3$	−2.00537			−1.15780			−0.578902	−	0.815397i	$-0.696519\pi$
$3$	−2.00537			−1.15780			−0.578902	+	0.815397i	$0.696519\pi$
$4$	1.57480	+	1.23289i	0.787400	+	0.616443i
$5$	−1.66826	−	1.48893i	−0.746070	−	0.665868i
$5$	−1.66826	−	1.48893i	−0.746070	−	0.665868i
$6$	2.68106	+	0.924650i	1.09454	+	0.377487i
$7$		−	4.57903i		−	1.73071i	−0.501158	−	0.865356i	$-0.667093\pi$
$7$		−	4.57903i		−	1.73071i	0.501158	−	0.865356i	$-0.332907\pi$
$8$	−1.53694	−	2.37441i	−0.543390	−	0.839480i
$9$	1.02153			0.340509
$10$	1.54384	+	2.75981i	0.488205	+	0.872729i
$11$	2.54798	−	2.54798i	0.768243	−	0.768243i	−0.209554	−	0.977797i	$-0.567201\pi$
$11$	2.54798	−	2.54798i	0.768243	−	0.768243i	0.977797	+	0.209554i	$0.0672011\pi$
$12$	−3.15806	−	2.47240i	−0.911654	−	0.713720i
$13$		−	2.88430i		−	0.799961i	−0.916524	−	0.399980i	$-0.869017\pi$
$13$		−	2.88430i		−	0.799961i	0.916524	−	0.399980i	$-0.130983\pi$
$14$	−2.11133	+	6.12187i	−0.564276	+	1.63614i
$15$	3.34549	+	2.98585i	0.863802	+	0.770944i
$16$	0.959984	+	3.88310i	0.239996	+	0.970774i
$17$		−	0.355667i		−	0.0862619i	−0.999069	−	0.0431309i	$-0.986267\pi$
$17$		−	0.355667i		−	0.0862619i	0.999069	−	0.0431309i	$-0.0137333\pi$
$18$	−1.36572	−	0.471012i	−0.321902	−	0.111018i
$19$	4.98430	−	4.98430i	1.14348	−	1.14348i	0.155667	−	0.987810i	$-0.450247\pi$
$19$	4.98430	−	4.98430i	1.14348	−	1.14348i	0.987810	−	0.155667i	$-0.0497528\pi$
$20$	−0.791504	−	4.40154i	−0.176986	−	0.984213i
$21$			9.18267i			2.00382i
$22$	−4.58132	+	2.23165i	−0.976740	+	0.475788i
$23$	0.157197	−	0.157197i	0.0327778	−	0.0327778i	−0.690528	−	0.723306i	$-0.742622\pi$
$23$	0.157197	−	0.157197i	0.0327778	−	0.0327778i	0.723306	+	0.690528i	$0.242622\pi$
$24$	3.08214	+	4.76158i	0.629139	+	0.971953i
$25$	0.566202	+	4.96784i	0.113240	+	0.993568i
$26$	−1.32991	+	3.85613i	−0.260817	+	0.756248i
$27$	3.96758			0.763561
$28$	5.64542	−	7.21105i	1.06688	−	1.36276i
$29$	−3.65502	+	3.65502i	−0.678720	+	0.678720i	−0.959711	−	0.280990i	$-0.909337\pi$
$29$	−3.65502	+	3.65502i	−0.678720	+	0.678720i	0.280990	+	0.959711i	$0.409337\pi$
$30$	−3.09597	−	5.53446i	−0.565245	−	1.01045i
$31$		−	9.42699i		−	1.69314i	−0.532279	−	0.846569i	$-0.678664\pi$
$31$		−	9.42699i		−	1.69314i	0.532279	−	0.846569i	$-0.321336\pi$
$32$	0.507003	−	5.63409i	0.0896263	−	0.995975i
$33$	−5.10964	+	5.10964i	−0.889475	+	0.889475i
$34$	−0.163993	+	0.475504i	−0.0281246	+	0.0815483i
$35$	−6.81784	+	7.63903i	−1.15242	+	1.29123i
$36$	1.60870	+	1.25943i	0.268116	+	0.209904i
$37$	3.67243	−	3.67243i	0.603744	−	0.603744i	−0.337560	−	0.941304i	$-0.609602\pi$
$37$	3.67243	−	3.67243i	0.603744	−	0.603744i	0.941304	+	0.337560i	$0.109602\pi$
$38$	−8.96189	+	4.36550i	−1.45381	+	0.708178i
$39$			5.78410i			0.926197i
$40$	−0.971297	+	6.24953i	−0.153576	+	0.988137i
$41$	6.25621	+	1.36377i	0.977055	+	0.212985i
$41$	6.25621	+	1.36377i	0.977055	+	0.212985i
$42$	4.23400	−	12.2766i	0.653321	−	1.89433i
$43$	−4.13136	−	4.13136i	−0.630026	−	0.630026i	0.318049	−	0.948074i	$-0.396972\pi$
$43$	−4.13136	−	4.13136i	−0.630026	−	0.630026i	−0.948074	+	0.318049i	$0.896972\pi$
$44$	7.15391	−	0.871186i	1.07849	−	0.131336i
$45$	−1.70417	−	1.52098i	−0.254043	−	0.226734i
$46$	−0.282644	+	0.137681i	−0.0416735	+	0.0203000i
$47$	−3.92076			−0.571901			−0.285951	−	0.958244i	$-0.592309\pi$
$47$	−3.92076			−0.571901			−0.285951	+	0.958244i	$0.592309\pi$
$48$	−1.92513	−	7.78706i	−0.277868	−	1.12397i
$49$	−13.9675			−1.99536
$50$	1.53363	−	6.90275i	0.216887	−	0.976197i
$51$			0.713245i			0.0998743i
$52$	3.55601	−	4.54219i	0.493130	−	0.629889i
$53$		−	3.52215i		−	0.483804i	−0.970301	−	0.241902i	$-0.922229\pi$
$53$		−	3.52215i		−	0.483804i	0.970301	−	0.241902i	$-0.0777713\pi$
$54$	−5.30440	−	1.82940i	−0.721838	−	0.248949i
$55$	−8.04444	+	0.456947i	−1.08471	+	0.0616147i
$56$	−10.8725	+	7.03770i	−1.45290	+	0.940452i
$57$	−9.99539	+	9.99539i	−1.32392	+	1.32392i
$58$	6.57181	−	3.20125i	0.862921	−	0.420345i
$59$	−4.54425			−0.591611			−0.295806	−	0.955248i	$-0.595588\pi$
$59$	−4.54425			−0.591611			−0.295806	+	0.955248i	$0.595588\pi$
$60$	1.58726	+	8.82673i	0.204914	+	1.13953i
$61$		−	8.21966i		−	1.05242i	−0.850355	−	0.526210i	$-0.823613\pi$
$61$		−	8.21966i		−	1.05242i	0.850355	−	0.526210i	$-0.176387\pi$
$62$	−4.34666	+	12.6033i	−0.552026	+	1.60062i
$63$		−	4.67760i		−	0.589322i
$64$	−3.27563	+	7.29865i	−0.409454	+	0.912331i
$65$	−4.29451	+	4.81177i	−0.532668	+	0.596826i
$66$	9.18726	−	4.47528i	1.13087	−	0.550869i
$67$	7.29388			0.891090			0.445545	−	0.895260i	$-0.353010\pi$
$67$	7.29388			0.891090			0.445545	+	0.895260i	$0.353010\pi$
$68$	0.438497	−	0.560104i	0.0531755	−	0.0679226i
$69$	−0.315239	+	0.315239i	−0.0379503	+	0.0379503i
$70$	12.6373	−	7.06929i	1.51044	−	0.844941i
$71$	−8.39564	+	8.39564i	−0.996379	+	0.996379i	−0.999993	−	0.00361430i	$-0.998850\pi$
$71$	−8.39564	+	8.39564i	−0.996379	+	0.996379i	0.00361430	+	0.999993i	$0.498850\pi$
$72$	−1.57002	−	2.42552i	−0.185029	−	0.285850i
$73$	−6.17916	+	6.17916i	−0.723216	+	0.723216i	−0.969259	−	0.246043i	$-0.920870\pi$
$73$	−6.17916	+	6.17916i	−0.723216	+	0.723216i	0.246043	+	0.969259i	$0.420870\pi$
$74$	−6.60311	+	3.21650i	−0.767596	+	0.373910i
$75$	−1.13545	−	9.96237i	−0.131110	−	1.15036i
$76$	13.9943	−	1.70420i	1.60526	−	0.195485i
$77$	−11.6673	−	11.6673i	−1.32961	−	1.32961i
$78$	2.66697	−	7.73297i	0.301975	−	0.875587i
$79$	7.01044	+	7.01044i	0.788736	+	0.788736i	0.981287	−	0.192551i	$-0.0616761\pi$
$79$	7.01044	+	7.01044i	0.788736	+	0.788736i	−0.192551	+	0.981287i	$0.561676\pi$
$80$	4.18013	−	7.90737i	0.467353	−	0.884071i
$81$	−11.0211			−1.22456
$82$	−7.73534	−	4.70793i	−0.854225	−	0.519903i
$83$	−1.29454	+	1.29454i	−0.142094	+	0.142094i	−0.774576	−	0.632481i	$-0.782037\pi$
$83$	−1.29454	+	1.29454i	−0.142094	+	0.142094i	0.632481	+	0.774576i	$0.282037\pi$
$84$	−11.3212	+	14.4609i	−1.23524	+	1.57781i
$85$	−0.529561	+	0.593346i	−0.0574390	+	0.0643574i
$86$	3.61845	+	7.42827i	0.390187	+	0.801011i
$87$	7.32968	−	7.32968i	0.785825	−	0.785825i
$88$	−9.96602	−	2.13385i	−1.06238	−	0.227469i
$89$	10.8817	−	10.8817i	1.15346	−	1.15346i	0.167606	−	0.985854i	$-0.446396\pi$
$89$	10.8817	−	10.8817i	1.15346	−	1.15346i	0.985854	−	0.167606i	$-0.0536036\pi$
$90$	1.57707	+	2.81922i	0.166238	+	0.297172i
$91$	−13.2073			−1.38450
$92$	0.441360	−	0.0537477i	0.0460149	−	0.00560359i
$93$			18.9047i			1.96032i
$94$	5.24180	+	1.80781i	0.540651	+	0.186461i
$95$	−15.7364	+	0.893871i	−1.61452	+	0.0917093i
$96$	−1.01673	+	11.2985i	−0.103770	+	1.15314i
$97$			13.6157i			1.38247i	0.722631	+	0.691234i	$0.242932\pi$
$97$			13.6157i			1.38247i	−0.722631	+	0.691234i	$0.757068\pi$
$98$	18.6737	+	6.44023i	1.88633	+	0.650562i
$99$	2.60282	−	2.60282i	0.261594	−	0.261594i
$100$	−5.23312	+	8.52141i	−0.523312	+	0.852141i
$101$	−6.41204	+	6.41204i	−0.638022	+	0.638022i	−0.950067	−	0.312045i	$-0.898986\pi$
$101$	−6.41204	+	6.41204i	−0.638022	+	0.638022i	0.312045	+	0.950067i	$0.398986\pi$
$102$	0.328867	−	0.953563i	0.0325627	−	0.0944169i
$103$	3.61313	+	3.61313i	0.356012	+	0.356012i	0.862341	−	0.506329i	$-0.168998\pi$
$103$	3.61313	+	3.61313i	0.356012	+	0.356012i	−0.506329	+	0.862341i	$0.668998\pi$
$104$	−6.84850	+	4.43299i	−0.671551	+	0.434691i
$105$	13.6723	−	15.3191i	1.33428	−	1.49499i
$106$	−1.62401	+	4.70889i	−0.157738	+	0.457368i
$107$	0.400234	+	0.400234i	0.0386921	+	0.0386921i	0.726188	−	0.687496i	$-0.241290\pi$
$107$	0.400234	+	0.400234i	0.0386921	+	0.0386921i	−0.687496	+	0.726188i	$0.741290\pi$
$108$	6.24814	+	4.89157i	0.601228	+	0.470692i
$109$	−2.44951	−	2.44951i	−0.234621	−	0.234621i	0.579998	−	0.814618i	$-0.303053\pi$
$109$	−2.44951	−	2.44951i	−0.234621	−	0.234621i	−0.814618	+	0.579998i	$0.803053\pi$
$110$	10.9656	+	3.09827i	1.04553	+	0.295408i
$111$	−7.36460	+	7.36460i	−0.699017	+	0.699017i
$112$	17.7808	−	4.39580i	1.68013	−	0.415364i
$113$	8.30678	+	8.30678i	0.781436	+	0.781436i	0.980073	−	0.198637i	$-0.0636515\pi$
$113$	8.30678	+	8.30678i	0.781436	+	0.781436i	−0.198637	+	0.980073i	$0.563651\pi$
$114$	17.9719	−	8.75447i	1.68323	−	0.819931i
$115$	−0.496300	+	0.0281913i	−0.0462803	+	0.00262885i
$116$	−10.2621	+	1.24970i	−0.952816	+	0.116032i
$117$		−	2.94639i		−	0.272394i
$118$	6.07538	+	2.09529i	0.559284	+	0.192887i
$119$	−1.62861			−0.149294
$120$	1.94781	−	12.5326i	0.177810	−	1.14407i
$121$		−	1.98435i		−	0.180396i
$122$	−3.78997	+	10.9892i	−0.343128	+	0.994912i
$123$	−12.5460	−	2.73487i	−1.13124	−	0.246595i
$124$	11.6224	−	14.8456i	1.04372	−	1.33318i
$125$	6.45217	−	9.13069i	0.577099	−	0.816674i
$126$	−2.15678	+	6.25365i	−0.192141	+	0.557120i
$127$	−8.10588	−	8.10588i	−0.719280	−	0.719280i	0.249178	−	0.968458i	$-0.419840\pi$
$127$	−8.10588	−	8.10588i	−0.719280	−	0.719280i	−0.968458	+	0.249178i	$0.919840\pi$
$128$	7.74462	−	8.24748i	0.684534	−	0.728981i
$129$	8.28491	+	8.28491i	0.729446	+	0.729446i
$130$	7.96012	−	4.45289i	0.698149	−	0.390545i
$131$	−0.0494153			−0.00431743			−0.00215872	−	0.999998i	$-0.500687\pi$
$131$	−0.0494153			−0.00431743			−0.00215872	+	0.999998i	$0.500687\pi$
$132$	−14.3463	+	1.74705i	−1.24868	+	0.152062i
$133$	−22.8233	−	22.8233i	−1.97903	−	1.97903i
$134$	−9.75146	−	3.36311i	−0.842398	−	0.290528i
$135$	−6.61897	−	5.90743i	−0.569670	−	0.508431i
$136$	−0.844498	+	0.546639i	−0.0724151	+	0.0468739i
$137$			6.06910i			0.518518i	0.965808	+	0.259259i	$0.0834784\pi$
$137$			6.06910i			0.518518i	−0.965808	+	0.259259i	$0.916522\pi$
$138$	0.566807	−	0.276102i	0.0482498	−	0.0235034i
$139$	22.7326			1.92816			0.964079	−	0.265617i	$-0.0855757\pi$
$139$	22.7326			1.92816			0.964079	+	0.265617i	$0.0855757\pi$
$140$	−20.1548	+	3.62432i	−1.70339	+	0.306311i
$141$	7.86259			0.662149
$142$	15.0956	−	7.35333i	1.26679	−	0.617077i
$143$	−7.34912	−	7.34912i	−0.614564	−	0.614564i
$144$	0.980649	+	3.96668i	0.0817208	+	0.330557i
$145$	11.5396	−	0.655482i	0.958310	−	0.0544348i
$146$	11.1103	−	5.41202i	0.919493	−	0.447902i
$147$	28.0101			2.31024
$148$	10.3110	−	1.25565i	0.847561	−	0.103214i
$149$	−6.94868	−	6.94868i	−0.569258	−	0.569258i	0.362663	−	0.931921i	$-0.381868\pi$
$149$	−6.94868	−	6.94868i	−0.569258	−	0.569258i	−0.931921	+	0.362663i	$0.881868\pi$
$150$	−3.07549	+	13.8426i	−0.251113	+	1.13024i
$151$	−6.90006	+	6.90006i	−0.561519	+	0.561519i	−0.929739	−	0.368220i	$-0.879967\pi$
$151$	−6.90006	+	6.90006i	−0.561519	+	0.561519i	0.368220	+	0.929739i	$0.379967\pi$
$152$	−19.4953	−	4.17419i	−1.58128	−	0.338572i
$153$		−	0.363323i		−	0.0293729i
$154$	10.2188	+	20.9780i	0.823452	+	1.69046i
$155$	−14.0361	+	15.7267i	−1.12741	+	1.26320i
$156$	−7.13113	+	9.10879i	−0.570948	+	0.729287i
$157$	13.8336			1.10404			0.552021	−	0.833830i	$-0.313857\pi$
$157$	13.8336			1.10404			0.552021	+	0.833830i	$0.313857\pi$
$158$	−6.14010	−	12.6049i	−0.488480	−	1.00279i
$159$			7.06322i			0.560150i
$160$	−9.23455	+	8.64425i	−0.730055	+	0.683388i
$161$	−0.719810	−	0.719810i	−0.0567290	−	0.0567290i
$162$	14.7345	+	5.08166i	1.15765	+	0.399253i
$163$	12.5958	−	12.5958i	0.986581	−	0.986581i	−0.0133305	−	0.999911i	$-0.504243\pi$
$163$	12.5958	−	12.5958i	0.986581	−	0.986581i	0.999911	+	0.0133305i	$0.00424336\pi$
$164$	8.17090	+	9.86086i	0.638040	+	0.770003i
$165$	16.1321	−	0.916350i	1.25588	−	0.0713378i
$166$	2.32761	−	1.13382i	0.180658	−	0.0880018i
$167$			1.29426i			0.100153i	0.998745	+	0.0500766i	$0.0159465\pi$
$167$			1.29426i			0.100153i	−0.998745	+	0.0500766i	$0.984053\pi$
$168$	21.8034	−	14.1132i	1.68217	−	1.08886i
$169$	4.68082			0.360063
$170$	0.981574	−	0.549092i	0.0752833	−	0.0421135i
$171$	5.09159	−	5.09159i	0.389364	−	0.389364i
$172$	−1.41256	−	11.5995i	−0.107707	−	0.884457i
$173$	−6.93988	+	6.93988i	−0.527629	+	0.527629i	−0.919865	−	0.392236i	$-0.871702\pi$
$173$	−6.93988	+	6.93988i	−0.527629	+	0.527629i	0.392236	+	0.919865i	$0.371702\pi$
$174$	−13.1789	+	6.41971i	−0.999093	+	0.486677i
$175$	22.7479	−	2.59266i	1.71958	−	0.195986i
$176$	12.3400	+	7.44801i	0.930166	+	0.561415i
$177$	9.11292			0.684969
$178$	−19.5656	+	9.53076i	−1.46650	+	0.714361i
$179$	9.42997	−	9.42997i	0.704829	−	0.704829i	−0.260614	−	0.965443i	$-0.583925\pi$
$179$	9.42997	−	9.42997i	0.704829	−	0.704829i	0.965443	+	0.260614i	$0.0839251\pi$
$180$	−0.808542	−	4.49628i	−0.0602651	−	0.335133i
$181$	7.57125	−	7.57125i	0.562766	−	0.562766i	−0.367326	−	0.930092i	$-0.619727\pi$
$181$	7.57125	−	7.57125i	0.562766	−	0.562766i	0.930092	+	0.367326i	$0.119727\pi$
$182$	17.6573	+	6.08970i	1.30885	+	0.451399i
$183$			16.4835i			1.21850i
$184$	−0.614852	−	0.131648i	−0.0453275	−	0.00970518i
$185$	−11.5946	+	0.658604i	−0.852449	+	0.0484215i
$186$	8.71667	−	25.2743i	0.639137	−	1.85320i
$187$	−0.906230	−	0.906230i	−0.0662701	−	0.0662701i
$188$	−6.17440	−	4.83385i	−0.450315	−	0.352544i
$189$		−	18.1677i		−	1.32150i
$190$	21.4507	+	6.06078i	1.55620	+	0.439695i
$191$	−11.2287	−	11.2287i	−0.812479	−	0.812479i	0.172526	−	0.985005i	$-0.444807\pi$
$191$	−11.2287	−	11.2287i	−0.812479	−	0.812479i	−0.985005	+	0.172526i	$0.944807\pi$
$192$	6.56887	−	14.6365i	0.474067	−	1.05630i
$193$		−	3.03867i		−	0.218728i	−0.994002	−	0.109364i	$-0.965119\pi$
$193$		−	3.03867i		−	0.218728i	0.994002	−	0.109364i	$-0.0348815\pi$
$194$	6.27802	−	18.2034i	0.450736	−	1.30692i
$195$	8.61209	−	9.64940i	0.616725	−	0.691008i
$196$	−21.9960	−	17.2204i	−1.57115	−	1.23003i
$197$	2.84117	+	2.84117i	0.202425	+	0.202425i	0.801038	−	0.598613i	$-0.204281\pi$
$197$	2.84117	+	2.84117i	0.202425	+	0.202425i	−0.598613	+	0.801038i	$0.704281\pi$
$198$	−4.67994	+	2.27968i	−0.332589	+	0.162010i
$199$	−3.62341	+	3.62341i	−0.256857	+	0.256857i	−0.823775	−	0.566918i	$-0.808136\pi$
$199$	−3.62341	+	3.62341i	−0.256857	+	0.256857i	0.566918	+	0.823775i	$0.308136\pi$
$200$	10.9255	−	8.97966i	0.772547	−	0.634958i
$201$	−14.6270			−1.03171
$202$	11.5290	−	5.61599i	0.811177	−	0.395140i
$203$	16.7365	+	16.7365i	1.17467	+	1.17467i
$204$	−0.879350	+	1.12322i	−0.0615668	+	0.0786410i
$205$	−8.40644	−	11.5902i	−0.587132	−	0.809492i
$206$	−3.16456	−	6.49649i	−0.220485	−	0.452632i
$207$	0.160581	−	0.160581i	0.0111611	−	0.0111611i
$208$	11.2000	−	2.76888i	0.776581	−	0.191987i
$209$		−	25.3997i		−	1.75694i
$210$	−25.3424	+	14.1766i	−1.74879	+	0.978276i
$211$	−0.620705	−	0.620705i	−0.0427311	−	0.0427311i	0.685418	−	0.728149i	$-0.259619\pi$
$211$	−0.620705	−	0.620705i	−0.0427311	−	0.0427311i	−0.728149	+	0.685418i	$0.759619\pi$
$212$	4.34241	−	5.54667i	0.298238	−	0.380947i
$213$	16.8364	−	16.8364i	1.15361	−	1.15361i
$214$	−0.350545	−	0.719630i	−0.0239628	−	0.0491929i
$215$	0.740906	+	13.0435i	0.0505294	+	0.889557i
$216$	−6.09793	−	9.42066i	−0.414912	−	0.640995i
$217$	−43.1665			−2.93033
$218$	2.14540	+	4.40428i	0.145305	+	0.298295i
$219$	12.3915	−	12.3915i	0.837342	−	0.837342i
$220$	−13.2317	−	9.19827i	−0.892083	−	0.620148i
$221$	−1.02585			−0.0690061
$222$	13.2417	−	6.45029i	0.888726	−	0.432915i
$223$	−9.89381	+	9.89381i	−0.662538	+	0.662538i	−0.955978	−	0.293439i	$-0.905200\pi$
$223$	−9.89381	+	9.89381i	−0.662538	+	0.662538i	0.293439	+	0.955978i	$0.405200\pi$
$224$	−25.7987	−	2.32158i	−1.72375	−	0.155117i
$225$	0.578390	+	5.07478i	0.0385593	+	0.338318i
$226$	−7.27550	−	14.9358i	−0.483959	−	0.993513i
$227$	18.0133			1.19558			0.597792	−	0.801651i	$-0.296045\pi$
$227$	18.0133			1.19558			0.597792	+	0.801651i	$0.296045\pi$
$228$	−28.0639	+	3.41755i	−1.85858	+	0.226333i
$229$	16.1132	+	16.1132i	1.06479	+	1.06479i	0.997750	+	0.0670419i	$0.0213561\pi$
$229$	16.1132	+	16.1132i	1.06479	+	1.06479i	0.0670419	+	0.997750i	$0.478644\pi$
$230$	0.676521	+	0.191147i	0.0446085	+	0.0126039i
$231$	23.3972	+	23.3972i	1.53942	+	1.53942i
$232$	14.2961	+	3.06096i	0.938582	+	0.200962i
$233$			18.0023i			1.17937i	0.807635	+	0.589683i	$0.200747\pi$
$233$			18.0023i			1.17937i	−0.807635	+	0.589683i	$0.799253\pi$
$234$	−1.35854	+	3.93913i	−0.0888104	+	0.257509i
$235$	6.54085	+	5.83772i	0.426678	+	0.380811i
$236$	−7.15628	−	5.60254i	−0.465834	−	0.364694i
$237$	−14.0586	−	14.0586i	−0.913201	−	0.913201i
$238$	2.17735	+	0.750929i	0.141136	+	0.0486755i
$239$	9.56330	+	9.56330i	0.618599	+	0.618599i	0.945172	−	0.326573i	$-0.105894\pi$
$239$	9.56330	+	9.56330i	0.618599	+	0.618599i	−0.326573	+	0.945172i	$0.605894\pi$
$240$	−8.38273	+	15.8572i	−0.541103	+	1.02358i
$241$			23.9966i			1.54576i	0.634553	+	0.772879i	$0.281184\pi$
$241$			23.9966i			1.54576i	−0.634553	+	0.772879i	$0.718816\pi$
$242$	−0.914959	+	2.65296i	−0.0588158	+	0.170539i
$243$	10.1986			0.654241
$244$	10.1339	−	12.9443i	0.648757	−	0.828675i
$245$	23.3015	+	20.7966i	1.48868	+	1.32865i
$246$	15.5122	+	9.44115i	0.989025	+	0.601946i
$247$	−14.3762	−	14.3762i	−0.914737	−	0.914737i
$248$	−22.3835	+	14.4887i	−1.42136	+	0.920035i
$249$	2.59604	−	2.59604i	0.164517	−	0.164517i
$250$	−12.8362	+	9.23215i	−0.811831	+	0.583893i
$251$	8.46569			0.534350			0.267175	−	0.963648i	$-0.413910\pi$
$251$	8.46569			0.534350			0.267175	+	0.963648i	$0.413910\pi$
$252$	5.76695	−	7.36628i	0.363284	−	0.464032i
$253$		−	0.801068i		−	0.0503627i
$254$	7.09954	+	14.5745i	0.445464	+	0.914489i
$255$	1.06197	−	1.18988i	0.0665031	−	0.0745132i
$256$	−14.1569	+	7.45542i	−0.884804	+	0.465964i
$257$	4.96814			0.309904			0.154952	−	0.987922i	$-0.450478\pi$
$257$	4.96814			0.309904			0.154952	+	0.987922i	$0.450478\pi$
$258$	−7.25635	−	14.8965i	−0.451760	−	0.927413i
$259$	−16.8162	−	16.8162i	−1.04491	−	1.04491i
$260$	−12.6953	+	2.28293i	−0.787332	+	0.141581i
$261$	−3.73370	+	3.73370i	−0.231110	+	0.231110i
$262$	0.0660651	+	0.0227847i	0.00408151	+	0.00140764i
$263$			13.3682i			0.824319i	0.911112	+	0.412159i	$0.135225\pi$
$263$			13.3682i			0.824319i	−0.911112	+	0.412159i	$0.864775\pi$
$264$	19.9856	+	4.27917i	1.23003	+	0.263364i
$265$	−5.24422	+	5.87587i	−0.322150	+	0.360952i
$266$	19.9898	+	41.0368i	1.22565	+	2.51612i
$267$	−21.8219	+	21.8219i	−1.33548	+	1.33548i
$268$	11.4864	+	8.99253i	0.701644	+	0.549306i
$269$		−	19.1500i		−	1.16760i	−0.811899	−	0.583798i	$-0.801566\pi$
$269$		−	19.1500i		−	1.16760i	0.811899	−	0.583798i	$-0.198434\pi$
$270$	6.12530	+	10.9498i	0.372774	+	0.666382i
$271$		−	13.2583i		−	0.805386i	−0.915335	−	0.402693i	$-0.868074\pi$
$271$		−	13.2583i		−	0.805386i	0.915335	−	0.402693i	$-0.131926\pi$
$272$	1.38109	−	0.341435i	0.0837408	−	0.0207025i
$273$	26.4856			1.60298
$274$	2.79838	−	8.11401i	0.169056	−	0.490185i
$275$	14.1006	+	11.2153i	0.850298	+	0.676306i
$276$	−0.885091	+	0.107784i	−0.0532762	+	0.00648785i
$277$	−11.0269	+	11.0269i	−0.662545	+	0.662545i	−0.955979	−	0.293434i	$-0.905202\pi$
$277$	−11.0269	+	11.0269i	−0.662545	+	0.662545i	0.293434	+	0.955979i	$0.405202\pi$
$278$	−30.3921	−	10.4817i	−1.82280	−	0.628651i
$279$		−	9.62992i		−	0.576528i
$280$	28.6168	+	4.44760i	1.71018	+	0.265795i
$281$	0.251867	−	0.251867i	0.0150251	−	0.0150251i	−0.699554	−	0.714579i	$-0.746618\pi$
$281$	0.251867	−	0.251867i	0.0150251	−	0.0150251i	0.714579	+	0.699554i	$0.246618\pi$
$282$	−10.5118	−	3.62533i	−0.625967	−	0.215885i
$283$	−17.1809	+	17.1809i	−1.02130	+	1.02130i	−0.0215286	+	0.999768i	$0.506853\pi$
$283$	−17.1809	+	17.1809i	−1.02130	+	1.02130i	−0.999768	+	0.0215286i	$0.993147\pi$
$284$	−23.5723	+	2.87058i	−1.39876	+	0.170338i
$285$	31.5573	−	1.79255i	1.86929	−	0.106181i
$286$	6.43673	+	13.2139i	0.380612	+	0.781354i
$287$	6.24475	−	28.6474i	0.368616	−	1.69100i
$288$	0.517917	−	5.75537i	0.0305186	−	0.339138i
$289$	16.8735			0.992559
$290$	−15.7299	−	4.44441i	−0.923693	−	0.260985i
$291$		−	27.3046i		−	1.60063i
$292$	−17.3491	+	2.11274i	−1.01528	+	0.123639i
$293$	−25.2668			−1.47610			−0.738052	−	0.674744i	$-0.764254\pi$
$293$	−25.2668			−1.47610			−0.738052	+	0.674744i	$0.764254\pi$
$294$	−37.4478	−	12.9151i	−2.18400	−	0.753223i
$295$	7.58100	+	6.76605i	0.441383	+	0.393935i
$296$	−14.3642	−	3.07554i	−0.834899	−	0.178762i
$297$	10.1093	−	10.1093i	0.586601	−	0.586601i
$298$	6.08600	+	12.4939i	0.352553	+	0.723751i
$299$	−0.453403	−	0.453403i	−0.0262210	−	0.0262210i
$300$	10.4944	−	17.0886i	0.605893	−	0.986612i
$301$	−18.9176	+	18.9176i	−1.09039	+	1.09039i
$302$	12.4065	−	6.04342i	0.713911	−	0.347760i
$303$	12.8585	−	12.8585i	0.738704	−	0.738704i
$304$	24.1394	+	14.5697i	1.38449	+	0.835628i
$305$	−12.2385	+	13.7126i	−0.700772	+	0.785179i
$306$	−0.167523	+	0.485740i	−0.00957666	+	0.0277679i
$307$	−10.4574	+	10.4574i	−0.596834	+	0.596834i	−0.939469	−	0.342635i	$-0.888681\pi$
$307$	−10.4574	+	10.4574i	−0.596834	+	0.596834i	0.342635	+	0.939469i	$0.388681\pi$
$308$	−3.98919	−	32.7580i	−0.227305	−	1.86656i
$309$	−7.24567	−	7.24567i	−0.412192	−	0.412192i
$310$	26.0167	−	14.5538i	1.47765	−	0.826598i
$311$	9.95581	+	9.95581i	0.564542	+	0.564542i	0.930594	−	0.366052i	$-0.119291\pi$
$311$	9.95581	+	9.95581i	0.564542	+	0.564542i	−0.366052	+	0.930594i	$0.619291\pi$
$312$	13.7338	−	8.88981i	0.777524	−	0.503287i
$313$	1.97742			0.111770			0.0558852	−	0.998437i	$-0.482202\pi$
$313$	1.97742			0.111770			0.0558852	+	0.998437i	$0.482202\pi$
$314$	−18.4947	−	6.37849i	−1.04371	−	0.359959i
$315$	−6.96460	+	7.80347i	−0.392411	+	0.439676i
$316$	2.39696	+	19.6831i	0.134840	+	1.10726i
$317$	22.2451			1.24941			0.624704	−	0.780862i	$-0.285220\pi$
$317$	22.2451			1.24941			0.624704	+	0.780862i	$0.285220\pi$
$318$	3.25675	−	9.44308i	0.182630	−	0.529542i
$319$			18.6258i			1.04284i
$320$	16.3318	−	7.29889i	0.912973	−	0.408020i
$321$	−0.802619	−	0.802619i	−0.0447978	−	0.0447978i
$322$	0.630446	+	1.29423i	0.0351334	+	0.0721249i
$323$	−1.77275	−	1.77275i	−0.0986385	−	0.0986385i
$324$	−17.3560	−	13.5877i	−0.964220	−	0.754873i
$325$	14.3287	−	1.63310i	0.794815	−	0.0905878i
$326$	−22.6476	+	11.0321i	−1.25433	+	0.611009i
$327$	4.91218	+	4.91218i	0.271644	+	0.271644i
$328$	−6.37727	−	16.9508i	−0.352126	−	0.935953i
$329$			17.9533i			0.989796i
$330$	−21.9901	−	6.21319i	−1.21052	−	0.342025i
$331$	8.92595	−	8.92595i	0.490614	−	0.490614i	−0.417885	−	0.908500i	$-0.637229\pi$
$331$	8.92595	−	8.92595i	0.490614	−	0.490614i	0.908500	+	0.417885i	$0.137229\pi$
$332$	−3.63466	+	0.442621i	−0.199478	+	0.0242920i
$333$	3.75148	−	3.75148i	0.205580	−	0.205580i
$334$	0.596768	−	1.73035i	0.0326537	−	0.0946805i
$335$	−12.1681	−	10.8600i	−0.664815	−	0.593348i
$336$	−35.6572	+	8.81522i	−1.94526	+	0.480910i
$337$	−24.9002	−	24.9002i	−1.35640	−	1.35640i	−0.878309	−	0.478092i	$-0.841328\pi$
$337$	−24.9002	−	24.9002i	−1.35640	−	1.35640i	−0.478092	−	0.878309i	$-0.658672\pi$
$338$	−6.25796	−	2.15826i	−0.340388	−	0.117394i
$339$	−16.6582	−	16.6582i	−0.904749	−	0.904749i
$340$	−1.56548	+	0.281512i	−0.0849001	+	0.0152671i
$341$	−24.0197	−	24.0197i	−1.30074	−	1.30074i
$342$	−9.15480	+	4.45947i	−0.495035	+	0.241141i
$343$			31.9045i			1.72268i
$344$	−3.45988	+	16.1592i	−0.186544	+	0.871244i
$345$	0.995268	−	0.0565341i	0.0535834	−	0.00304369i
$346$	12.4781	−	6.07830i	0.670825	−	0.326771i
$347$	−34.5791			−1.85630			−0.928152	−	0.372200i	$-0.878603\pi$
$347$	−34.5791			−1.85630			−0.928152	+	0.372200i	$0.878603\pi$
$348$	20.5794	−	2.50612i	1.10317	−	0.134342i
$349$	29.6933			1.58945			0.794723	−	0.606972i	$-0.207616\pi$
$349$	29.6933			1.58945			0.794723	+	0.606972i	$0.207616\pi$
$350$	−31.6079	−	7.02252i	−1.68951	−	0.375369i
$351$		−	11.4437i		−	0.610819i
$352$	−13.0637	−	15.6473i	−0.696297	−	0.834006i
$353$	11.2623	+	11.2623i	0.599431	+	0.599431i	0.940161	−	0.340730i	$-0.110674\pi$
$353$	11.2623	+	11.2623i	0.599431	+	0.599431i	−0.340730	+	0.940161i	$0.610674\pi$
$354$	−12.1834	−	4.20184i	−0.647540	−	0.223325i
$355$	26.5066	−	1.50565i	1.40683	−	0.0799117i
$356$	30.5524	−	3.72060i	1.61928	−	0.197192i
$357$	3.26597			0.172854
$358$	−16.9553	+	8.25924i	−0.896115	+	0.436514i
$359$	−7.47454			−0.394491			−0.197246	−	0.980354i	$-0.563200\pi$
$359$	−7.47454			−0.394491			−0.197246	+	0.980354i	$0.563200\pi$
$360$	−0.992206	+	6.38405i	−0.0522938	+	0.336469i
$361$		−	30.6865i		−	1.61508i
$362$	−13.6133	+	6.63128i	−0.715498	+	0.348532i
$363$			3.97937i			0.208863i
$364$	−20.7988	−	16.2831i	−1.09016	−	0.853466i
$365$	19.5088	−	1.10815i	1.02114	−	0.0580035i
$366$	7.60031	−	22.0374i	0.397275	−	1.15191i
$367$	4.33614	−	4.33614i	0.226344	−	0.226344i	−0.584819	−	0.811164i	$-0.698835\pi$
$367$	4.33614	−	4.33614i	0.226344	−	0.226344i	0.811164	+	0.584819i	$0.198835\pi$
$368$	0.761318	+	0.459504i	0.0396864	+	0.0239533i
$369$	6.39088	+	1.39313i	0.332696	+	0.0725233i
$370$	15.8049	+	4.46558i	0.821655	+	0.232154i
$371$	−16.1280			−0.837325
$372$	−23.3073	+	29.7710i	−1.20843	+	1.54356i
$373$	14.1225	+	14.1225i	0.731235	+	0.731235i	0.970864	−	0.239629i	$-0.0770259\pi$
$373$	14.1225	+	14.1225i	0.731235	+	0.731235i	−0.239629	+	0.970864i	$0.577026\pi$
$374$	0.793722	+	1.62942i	0.0410424	+	0.0842554i
$375$	−12.9390	+	18.3105i	−0.668168	+	0.945548i
$376$	6.02597	+	9.30948i	0.310766	+	0.480100i
$377$	10.5422	+	10.5422i	0.542949	+	0.542949i
$378$	−8.37686	+	24.2890i	−0.430859	+	1.24929i
$379$	−30.6121			−1.57244			−0.786219	−	0.617948i	$-0.787964\pi$
$379$	−30.6121			−1.57244			−0.786219	+	0.617948i	$0.787964\pi$
$380$	−25.8837	−	17.9935i	−1.32780	−	0.923046i
$381$	16.2553	+	16.2553i	0.832785	+	0.832785i
$382$	9.83465	+	20.1894i	0.503185	+	1.03298i
$383$		−	30.1532i		−	1.54076i	−0.637586	−	0.770379i	$-0.720067\pi$
$383$		−	30.1532i		−	1.54076i	0.637586	−	0.770379i	$-0.279933\pi$
$384$	−15.5309	+	16.5393i	−0.792556	+	0.844017i
$385$	2.09238	+	36.8357i	0.106637	+	1.87732i
$386$	−1.40109	+	4.06251i	−0.0713136	+	0.206776i
$387$	−4.22029	−	4.22029i	−0.214529	−	0.214529i
$388$	−16.7866	+	21.4420i	−0.852212	+	1.08855i
$389$	24.0016			1.21693			0.608465	−	0.793581i	$-0.291786\pi$
$389$	24.0016			1.21693			0.608465	+	0.793581i	$0.291786\pi$
$390$	−15.9630	+	8.92972i	−0.808319	+	0.452174i
$391$	−0.0559097	−	0.0559097i	−0.00282748	−	0.00282748i
$392$	21.4672	+	33.1646i	1.08426	+	1.67507i
$393$	0.0990961			0.00499874
$394$	−2.48844	−	5.10849i	−0.125366	−	0.257362i
$395$	−1.25723	−	22.1333i	−0.0632583	−	1.11365i
$396$	7.30791	−	0.889939i	0.367236	−	0.0447211i
$397$	−9.87585			−0.495655			−0.247827	−	0.968804i	$-0.579717\pi$
$397$	−9.87585			−0.495655			−0.247827	+	0.968804i	$0.579717\pi$
$398$	6.51498	−	3.17357i	0.326567	−	0.159077i
$399$	45.7692	+	45.7692i	2.29133	+	2.29133i
$400$	−18.7470	+	6.96766i	−0.937352	+	0.348383i
$401$		−	7.13568i		−	0.356339i	−0.984000	−	0.178169i	$-0.942982\pi$
$401$		−	7.13568i		−	0.356339i	0.984000	−	0.178169i	$-0.0570175\pi$
$402$	19.5553	+	6.74429i	0.975331	+	0.336375i
$403$	−27.1903			−1.35444
$404$	−18.0030	+	2.19236i	−0.895682	+	0.109074i
$405$	18.3860	+	16.4095i	0.913609	+	0.815397i
$406$	−14.6586	−	30.0925i	−0.727495	−	1.49347i
$407$		−	18.7145i		−	0.927644i
$408$	1.69354	−	1.09621i	0.0838425	−	0.0542707i
$409$		−	9.89588i		−	0.489320i	−0.969609	−	0.244660i	$-0.921324\pi$
$409$		−	9.89588i		−	0.489320i	0.969609	−	0.244660i	$-0.0786763\pi$
$410$	5.89482	+	19.3714i	0.291125	+	0.956685i
$411$		−	12.1708i		−	0.600342i
$412$	1.23538	+	10.1445i	0.0608626	+	0.499785i
$413$			20.8083i			1.02391i
$414$	−0.288728	+	0.140645i	−0.0141902	+	0.00691231i
$415$	4.08711	−	0.232160i	0.200628	−	0.0113963i
$416$	−16.2504	−	1.46235i	−0.796741	−	0.0716975i
$417$	−45.5874			−2.23243
$418$	−11.7115	+	33.9579i	−0.572827	+	1.66093i
$419$		−	1.35375i		−	0.0661351i	−0.999453	−	0.0330676i	$-0.989472\pi$
$419$		−	1.35375i		−	0.0661351i	0.999453	−	0.0330676i	$-0.0105277\pi$
$420$	40.4179	−	7.26812i	1.97219	−	0.354648i
$421$	−13.5068	−	13.5068i	−0.658282	−	0.658282i	0.296692	−	0.954973i	$-0.404117\pi$
$421$	−13.5068	−	13.5068i	−0.658282	−	0.658282i	−0.954973	+	0.296692i	$0.904117\pi$
$422$	0.543645	+	1.11604i	0.0264642	+	0.0543281i
$423$	−4.00516			−0.194737
$424$	−8.36302	+	5.41333i	−0.406144	+	0.262895i
$425$	1.76690	−	0.201379i	0.0857070	−	0.00976833i
$426$	−30.2722	+	14.7462i	−1.46669	+	0.714454i
$427$	−37.6381			−1.82143
$428$	0.136845	+	1.12373i	0.00661467	+	0.0543176i
$429$	14.7377	+	14.7377i	0.711545	+	0.711545i
$430$	5.02362	−	17.7799i	0.242260	−	0.857423i
$431$	−23.7484			−1.14392			−0.571959	−	0.820282i	$-0.693816\pi$
$431$	−23.7484			−1.14392			−0.571959	+	0.820282i	$0.693816\pi$
$432$	3.80882	+	15.4065i	0.183252	+	0.741245i
$433$	3.02756	+	3.02756i	0.145495	+	0.145495i	0.776102	−	0.630607i	$-0.217194\pi$
$433$	3.02756	+	3.02756i	0.145495	+	0.145495i	−0.630607	+	0.776102i	$0.717194\pi$
$434$	57.7109	+	19.9035i	2.77021	+	0.955397i
$435$	−23.1412	+	1.31449i	−1.10954	+	0.0630248i
$436$	−0.837520	−	6.87745i	−0.0401099	−	0.329370i
$437$		−	1.56703i		−	0.0749614i
$438$	−22.2803	+	10.8531i	−1.06459	+	0.518583i
$439$	2.91251	+	2.91251i	0.139007	+	0.139007i	0.773186	−	0.634179i	$-0.218662\pi$
$439$	2.91251	+	2.91251i	0.139007	+	0.139007i	−0.634179	+	0.773186i	$0.718662\pi$
$440$	13.4488	+	18.3985i	0.641146	+	0.877113i
$441$	−14.2682			−0.679438
$442$	1.37150	+	0.473005i	0.0652354	+	0.0224986i
$443$	−21.8300	−	21.8300i	−1.03717	−	1.03717i	−0.999282	−	0.0378928i	$-0.987935\pi$
$443$	−21.8300	−	21.8300i	−1.03717	−	1.03717i	−0.0378928	−	0.999282i	$-0.512065\pi$
$444$	−20.6775	+	2.51805i	−0.981309	+	0.119501i
$445$	−34.3556	+	1.95150i	−1.62861	+	0.0925099i
$446$	17.7893	−	8.66550i	0.842347	−	0.410323i
$447$	13.9347	+	13.9347i	0.659089	+	0.659089i
$448$	33.4207	+	14.9992i	1.57898	+	0.708646i
$449$	18.1811			0.858019			0.429010	−	0.903300i	$-0.358863\pi$
$449$	18.1811			0.858019			0.429010	+	0.903300i	$0.358863\pi$
$450$	1.56664	−	7.05134i	0.0738520	−	0.332403i
$451$	19.4155	−	12.4658i	0.914241	−	0.586992i
$452$	2.84020	+	23.3228i	0.133592	+	1.09701i
$453$	13.8372	−	13.8372i	0.650128	−	0.650128i
$454$	−24.0826	−	8.30568i	−1.13025	−	0.389805i
$455$	22.0332	+	19.6647i	1.03293	+	0.921894i
$456$	39.0954	+	8.37082i	1.83081	+	0.392000i
$457$			5.06758i			0.237051i	0.992951	+	0.118526i	$0.0378168\pi$
$457$			5.06758i			0.237051i	−0.992951	+	0.118526i	$0.962183\pi$
$458$	−14.1128	−	28.9719i	−0.659447	−	1.35377i
$459$		−	1.41114i		−	0.0658662i
$460$	−0.816330	−	0.567486i	−0.0380616	−	0.0264592i
$461$	12.4732			0.580933			0.290467	−	0.956885i	$-0.406189\pi$
$461$	12.4732			0.580933			0.290467	+	0.956885i	$0.406189\pi$
$462$	−20.4925	−	42.0687i	−0.953396	−	1.95721i
$463$	4.42097			0.205460			0.102730	−	0.994709i	$-0.467242\pi$
$463$	4.42097			0.205460			0.102730	+	0.994709i	$0.467242\pi$
$464$	−17.7016	−	10.6840i	−0.821774	−	0.495994i
$465$	28.1476	−	31.5379i	1.30531	−	1.46254i
$466$	8.30059	−	24.0679i	0.384517	−	1.11492i
$467$	26.1837	+	26.1837i	1.21164	+	1.21164i	0.970488	+	0.241149i	$0.0775241\pi$
$467$	26.1837	+	26.1837i	1.21164	+	1.21164i	0.241149	+	0.970488i	$0.422476\pi$
$468$	3.63256	−	4.63997i	0.167915	−	0.214483i
$469$		−	33.3989i		−	1.54222i
$470$	−6.05302	−	10.8206i	−0.279205	−	0.499115i
$471$	−27.7416			−1.27826
$472$	6.98424	+	10.7899i	0.321476	+	0.496646i
$473$	−21.0532			−0.968026
$474$	12.3132	+	25.2776i	0.565564	+	1.16104i
$475$	27.5833	+	21.9391i	1.26561	+	1.00663i
$476$	−2.56473	−	2.00789i	−0.117554	−	0.0920315i
$477$		−	3.59797i		−	0.164740i
$478$	−8.37602	−	17.1950i	−0.383110	−	0.786483i
$479$	−8.05823	−	8.05823i	−0.368190	−	0.368190i	0.498627	−	0.866817i	$-0.333838\pi$
$479$	−8.05823	−	8.05823i	−0.368190	−	0.368190i	−0.866817	+	0.498627i	$0.833838\pi$
$480$	18.5187	−	17.3350i	0.845261	−	0.791229i
$481$	−10.5924	−	10.5924i	−0.482971	−	0.482971i
$482$	11.0645	−	32.0820i	0.503975	−	1.46129i
$483$	1.44349	+	1.44349i	0.0656810	+	0.0656810i
$484$	2.44648	−	3.12496i	0.111204	−	0.142044i
$485$	20.2728	−	22.7146i	0.920540	−	1.03142i
$486$	−13.6349	−	4.70244i	−0.618492	−	0.213307i
$487$	12.5632	−	12.5632i	0.569293	−	0.569293i	−0.362637	−	0.931930i	$-0.618124\pi$
$487$	12.5632	−	12.5632i	0.569293	−	0.569293i	0.931930	+	0.362637i	$0.118124\pi$
$488$	−19.5168	+	12.6331i	−0.883486	+	0.571875i
$489$	−25.2593	+	25.2593i	−1.14227	+	1.14227i
$490$	−21.5636	−	38.5477i	−0.974145	−	1.74141i
$491$		−	25.0910i		−	1.13234i	−0.824288	−	0.566170i	$-0.808424\pi$
$491$		−	25.0910i		−	1.13234i	0.824288	−	0.566170i	$-0.191576\pi$
$492$	−16.3857	−	19.7747i	−0.738725	−	0.891513i
$493$	1.29997	+	1.29997i	0.0585477	+	0.0585477i
$494$	12.5914	+	25.8488i	0.566514	+	1.16299i
$495$	−8.21760	+	0.466783i	−0.369354	+	0.0209804i
$496$	36.6059	−	9.04977i	1.64365	−	0.406347i
$497$	38.4439	+	38.4439i	1.72444	+	1.72444i
$498$	−4.66774	+	2.27374i	−0.209166	+	0.101889i
$499$	1.47490	+	1.47490i	0.0660255	+	0.0660255i	0.739348	−	0.673323i	$-0.235134\pi$
$499$	1.47490	+	1.47490i	0.0660255	+	0.0660255i	−0.673323	+	0.739348i	$0.735134\pi$
$500$	21.4180	−	6.42422i	0.957841	−	0.287300i
$501$		−	2.59549i		−	0.115958i
$502$	−11.3181	−	3.90341i	−0.505151	−	0.174218i
$503$	14.2879			0.637064			0.318532	−	0.947912i	$-0.396810\pi$
$503$	14.2879			0.637064			0.318532	+	0.947912i	$0.396810\pi$
$504$	−11.1065	+	7.18919i	−0.494724	+	0.320232i
$505$	20.2440	−	1.14992i	0.900847	−	0.0511707i
$506$	−0.369361	+	1.07098i	−0.0164201	+	0.0476107i
$507$	−9.38679			−0.416882
$508$	−2.77151	−	22.7587i	−0.122966	−	1.00976i
$509$	−26.6826	−	26.6826i	−1.18269	−	1.18269i	−0.979046	−	0.203641i	$-0.934723\pi$
$509$	−26.6826	−	26.6826i	−1.18269	−	1.18269i	−0.203641	−	0.979046i	$-0.565277\pi$
$510$	−1.96842	+	1.10114i	−0.0871632	+	0.0487591i
$511$	28.2946	+	28.2946i	1.25168	+	1.25168i
$512$	22.3644	−	3.43990i	0.988377	−	0.152023i
$513$	19.7756	−	19.7756i	0.873115	−	0.873115i
$514$	−6.64209	−	2.29074i	−0.292970	−	0.101040i
$515$	−0.647969	−	11.4073i	−0.0285529	−	0.502667i
$516$	2.83272	+	23.2614i	0.124704	+	1.02403i
$517$	−9.98999	+	9.98999i	−0.439359	+	0.439359i
$518$	14.7285	+	30.2359i	0.647131	+	1.32849i
$519$	13.9171	−	13.9171i	0.610891	−	0.610891i
$520$	18.0255	+	2.80151i	0.790471	+	0.122854i
$521$	−16.1289	−	16.1289i	−0.706622	−	0.706622i	0.259202	−	0.965823i	$-0.416541\pi$
$521$	−16.1289	−	16.1289i	−0.706622	−	0.706622i	−0.965823	+	0.259202i	$0.916541\pi$
$522$	6.71327	−	3.27016i	0.293832	−	0.143131i
$523$	14.8097	−	14.8097i	0.647582	−	0.647582i	−0.304826	−	0.952408i	$-0.598598\pi$
$523$	14.8097	−	14.8097i	0.647582	−	0.647582i	0.952408	+	0.304826i	$0.0985983\pi$
$524$	−0.0778191	−	0.0609234i	−0.00339954	−	0.00266145i
$525$	−45.6180	+	5.19925i	−1.99093	+	0.226914i
$526$	6.16389	−	17.8724i	0.268759	−	0.779275i
$527$	−3.35287			−0.146053
$528$	−24.7464	−	14.9361i	−1.07695	−	0.650008i
$529$			22.9506i			0.997851i
$530$	9.72046	−	5.43763i	0.422230	−	0.236195i
$531$	−4.64207			−0.201449
$532$	−7.80358	−	64.0805i	−0.338328	−	2.77824i
$533$	3.93352	−	18.0448i	0.170380	−	0.781606i
$534$	39.2363	−	19.1127i	1.69792	−	0.827089i
$535$	−0.0717769	−	1.26361i	−0.00310319	−	0.0546308i
$536$	−11.2103	−	17.3187i	−0.484210	−	0.748052i
$537$	−18.9106	+	18.9106i	−0.816053	+	0.816053i
$538$	−8.82980	+	25.6023i	−0.380680	+	1.10379i
$539$	−35.5889	+	35.5889i	−1.53292	+	1.53292i
$540$	−3.14035	−	17.4635i	−0.135139	−	0.751507i
$541$			11.9694i			0.514607i	0.966331	+	0.257303i	$0.0828339\pi$
$541$			11.9694i			0.514607i	−0.966331	+	0.257303i	$0.917166\pi$
$542$	−6.11323	+	17.7255i	−0.262586	+	0.761377i
$543$	−15.1832	+	15.1832i	−0.651573	+	0.651573i
$544$	−2.00386	−	0.180324i	−0.0859147	−	0.00773134i
$545$	0.439289	+	7.73357i	0.0188171	+	0.331270i
$546$	−35.4095	−	12.2121i	−1.51539	−	0.522631i
$547$	−26.9973			−1.15432			−0.577162	−	0.816630i	$-0.695840\pi$
$547$	−26.9973			−1.15432			−0.577162	+	0.816630i	$0.695840\pi$
$548$	−7.48251	+	9.55762i	−0.319637	+	0.408281i
$549$		−	8.39660i		−	0.358358i
$550$	−13.6804	−	21.4957i	−0.583334	−	0.916579i
$551$			36.4354i			1.55220i
$552$	1.23301	+	0.264003i	0.0524803	+	0.0112367i
$553$	32.1010	−	32.1010i	1.36507	−	1.36507i
$554$	19.8267	−	9.65796i	0.842356	−	0.410327i
$555$	23.2514	−	1.32075i	0.986968	−	0.0560626i
$556$	35.7993	+	28.0268i	1.51823	+	1.18860i
$557$		−	7.41625i		−	0.314237i	−0.987580	−	0.157118i	$-0.949780\pi$
$557$		−	7.41625i		−	0.314237i	0.987580	−	0.157118i	$-0.0502204\pi$
$558$	−4.44022	+	12.8746i	−0.187970	+	0.545025i
$559$	−11.9161	+	11.9161i	−0.503996	+	0.503996i
$560$	−36.2081	−	19.1410i	−1.53007	−	0.808853i
$561$	1.81733	+	1.81733i	0.0767278	+	0.0767278i
$562$	−0.452863	+	0.220598i	−0.0191029	+	0.00930536i
$563$	9.81331			0.413582			0.206791	−	0.978385i	$-0.433698\pi$
$563$	9.81331			0.413582			0.206791	+	0.978385i	$0.433698\pi$
$564$	12.3820	+	9.69367i	0.521376	+	0.408177i
$565$	−1.48972	−	26.2261i	−0.0626728	−	1.10334i
$566$	30.8916	−	15.0479i	1.29847	−	0.632509i
$567$			50.4658i			2.11936i
$568$	32.8383	+	7.03108i	1.37786	+	0.295018i
$569$	−29.9427			−1.25526			−0.627631	−	0.778511i	$-0.715976\pi$
$569$	−29.9427			−1.25526			−0.627631	+	0.778511i	$0.715976\pi$
$570$	−43.0167	−	12.1541i	−1.80177	−	0.509080i
$571$	−17.9920	+	17.9920i	−0.752944	+	0.752944i	−0.975028	−	0.222084i	$-0.928714\pi$
$571$	−17.9920	+	17.9920i	−0.752944	+	0.752944i	0.222084	+	0.975028i	$0.428714\pi$
$572$	−2.51276	−	20.6340i	−0.105064	−	0.862752i
$573$	22.5177	+	22.5177i	0.940691	+	0.940691i
$574$	−21.5577	+	35.4203i	−0.899803	+	1.47842i
$575$	0.869934	+	0.691924i	0.0362788	+	0.0288552i
$576$	−3.34614	+	7.45576i	−0.139423	+	0.310657i
$577$	27.2917			1.13617			0.568084	−	0.822970i	$-0.307685\pi$
$577$	27.2917			1.13617			0.568084	+	0.822970i	$0.307685\pi$
$578$	−22.5588	−	7.78014i	−0.938322	−	0.323611i
$579$			6.09368i			0.253245i
$580$	18.9807	+	13.1947i	0.788129	+	0.547882i
$581$	5.92774	+	5.92774i	0.245924	+	0.245924i
$582$	−12.5898	+	36.5045i	−0.521863	+	1.51316i
$583$	−8.97434	−	8.97434i	−0.371679	−	0.371679i
$584$	24.1689	+	5.17485i	1.00011	+	0.214137i
$585$	−4.38695	+	4.91535i	−0.181378	+	0.203225i
$586$	33.7801	+	11.6502i	1.39544	+	0.481265i
$587$		−	35.6851i		−	1.47288i	−0.676501	−	0.736442i	$-0.736505\pi$
$587$		−	35.6851i		−	1.47288i	0.676501	−	0.736442i	$-0.263495\pi$
$588$	44.1103	+	34.5333i	1.81908	+	1.42413i
$589$	−46.9870	−	46.9870i	−1.93606	−	1.93606i
$590$	−7.01559	−	12.5413i	−0.288827	−	0.516316i
$591$	−5.69761	−	5.69761i	−0.234368	−	0.234368i
$592$	17.7859	+	10.7349i	0.730995	+	0.441203i
$593$	17.6194			0.723541			0.361770	−	0.932267i	$-0.382172\pi$
$593$	17.6194			0.723541			0.361770	+	0.932267i	$0.382172\pi$
$594$	−18.1767	+	8.85423i	−0.745801	+	0.363294i
$595$	2.71695	+	2.42488i	0.111384	+	0.0994103i
$596$	−2.37584	−	19.5097i	−0.0973184	−	0.799148i
$597$	7.26630	−	7.26630i	0.297390	−	0.297390i
$598$	0.397113	+	0.815229i	0.0162392	+	0.0333372i
$599$	−20.7527			−0.847933			−0.423967	−	0.905678i	$-0.639363\pi$
$599$	−20.7527			−0.847933			−0.423967	+	0.905678i	$0.639363\pi$
$600$	−21.9096	+	18.0076i	−0.894457	+	0.735157i
$601$	−17.9460	+	17.9460i	−0.732034	+	0.732034i	−0.971022	−	0.238988i	$-0.923184\pi$
$601$	−17.9460	+	17.9460i	−0.732034	+	0.732034i	0.238988	+	0.971022i	$0.423184\pi$
$602$	34.0143	−	16.5690i	1.38632	−	0.675302i
$603$	7.45089			0.303424
$604$	−19.3732	+	2.35922i	−0.788284	+	0.0959953i
$605$	−2.95456	+	3.31043i	−0.120120	+	0.134588i
$606$	−23.1199	+	11.2622i	−0.939184	+	0.457494i
$607$	31.8391	−	31.8391i	1.29231	−	1.29231i	0.358951	−	0.933356i	$-0.383135\pi$
$607$	31.8391	−	31.8391i	1.29231	−	1.29231i	0.933356	−	0.358951i	$-0.116865\pi$
$608$	−25.5549	−	30.6090i	−1.03639	−	1.24136i
$609$	−33.5628	−	33.5628i	−1.36004	−	1.36004i
$610$	22.6847	−	12.6898i	0.918477	−	0.513796i
$611$			11.3086i			0.457498i
$612$	0.447936	−	0.572161i	0.0181067	−	0.0231282i
$613$	−26.5028	+	26.5028i	−1.07044	+	1.07044i	−0.0731148	+	0.997324i	$0.523294\pi$
$613$	−26.5028	+	26.5028i	−1.07044	+	1.07044i	−0.997324	+	0.0731148i	$0.976706\pi$
$614$	18.8026	−	9.15909i	0.758811	−	0.369631i
$615$	16.8581	+	23.2426i	0.679783	+	0.937232i
$616$	−9.77096	+	45.6347i	−0.393683	+	1.83867i
$617$	0.109186	+	0.109186i	0.00439567	+	0.00439567i	0.709301	−	0.704906i	$-0.249011\pi$
$617$	0.109186	+	0.109186i	0.00439567	+	0.00439567i	−0.704906	+	0.709301i	$0.749011\pi$
$618$	6.34613	+	13.0279i	0.255279	+	0.524058i
$619$	−46.6015			−1.87307			−0.936537	−	0.350569i	$-0.885988\pi$
$619$	−46.6015			−1.87307			−0.936537	+	0.350569i	$0.885988\pi$
$620$	−41.4933	+	7.46150i	−1.66641	+	0.299661i
$621$	0.623692	−	0.623692i	0.0250279	−	0.0250279i
$622$	−8.71980	−	17.9008i	−0.349632	−	0.717756i
$623$	−49.8277	−	49.8277i	−1.99631	−	1.99631i
$624$	−22.4602	+	5.55265i	−0.899128	+	0.222284i
$625$	−24.3588	+	5.62560i	−0.974353	+	0.225024i
$626$	−2.64369	−	0.911761i	−0.105663	−	0.0364413i
$627$			50.9360i			2.03419i
$628$	21.7852	+	17.0553i	0.869323	+	0.680579i
$629$	−1.30616	−	1.30616i	−0.0520801	−	0.0520801i
$630$	12.9093	−	7.22146i	0.514319	−	0.287710i
$631$		−	44.8712i		−	1.78629i	−0.449766	−	0.893147i	$-0.648493\pi$
$631$		−	44.8712i		−	1.78629i	0.449766	−	0.893147i	$-0.351507\pi$
$632$	5.87102	−	27.4203i	0.233537	−	1.09072i
$633$	1.24475	+	1.24475i	0.0494742	+	0.0494742i
$634$	−29.7402	−	10.2569i	−1.18114	−	0.407353i
$635$	1.45369	+	25.5918i	0.0576878	+	1.01558i
$636$	−8.70815	+	11.1232i	−0.345301	+	0.441062i
$637$			40.2865i			1.59621i
$638$	8.58810	−	24.9015i	0.340006	−	0.985860i
$639$	−8.57637	+	8.57637i	−0.339276	+	0.339276i
$640$	−25.1999	+	2.22781i	−0.996115	+	0.0880618i
$641$	27.0398	−	27.0398i	1.06801	−	1.06801i	0.0704963	−	0.997512i	$-0.477542\pi$
$641$	27.0398	−	27.0398i	1.06801	−	1.06801i	0.997512	−	0.0704963i	$-0.0224583\pi$
$642$	0.702974	+	1.44313i	0.0277442	+	0.0569557i
$643$	20.5246			0.809410			0.404705	−	0.914447i	$-0.367374\pi$
$643$	20.5246			0.809410			0.404705	+	0.914447i	$0.367374\pi$
$644$	−0.246112	−	2.02100i	−0.00969819	−	0.0796385i
$645$	−1.48579	−	26.1570i	−0.0585031	−	1.02993i
$646$	1.55266	+	3.18745i	0.0610888	+	0.125408i
$647$	16.2726	−	16.2726i	0.639743	−	0.639743i	−0.310749	−	0.950492i	$-0.600580\pi$
$647$	16.2726	−	16.2726i	0.639743	−	0.639743i	0.950492	+	0.310749i	$0.100580\pi$
$648$	16.9387	+	26.1685i	0.665415	+	1.02800i
$649$	−11.5786	+	11.5786i	−0.454501	+	0.454501i
$650$	−19.9096	−	4.42343i	−0.780919	−	0.173501i
$651$	86.5650			3.39275
$652$	35.3651	−	4.30668i	1.38500	−	0.168662i
$653$			25.6831i			1.00506i	0.864561	+	0.502528i	$0.167597\pi$
$653$			25.6831i			1.00506i	−0.864561	+	0.502528i	$0.832403\pi$
$654$	−4.30234	−	8.83222i	−0.168235	−	0.345367i
$655$	0.0824377	+	0.0735757i	0.00322111	+	0.00287484i
$656$	0.710209	+	25.6026i	0.0277290	+	0.999615i
$657$	−6.31218	+	6.31218i	−0.246261	+	0.246261i
$658$	8.27800	−	24.0024i	0.322710	−	0.935710i
$659$	8.02251	+	8.02251i	0.312513	+	0.312513i	0.845882	−	0.533370i	$-0.179075\pi$
$659$	8.02251	+	8.02251i	0.312513	+	0.312513i	−0.533370	+	0.845882i	$0.679075\pi$
$660$	26.5346	+	18.4460i	1.03286	+	0.718009i
$661$		−	7.81677i		−	0.304037i	−0.988378	−	0.152019i	$-0.951423\pi$
$661$		−	7.81677i		−	0.304037i	0.988378	−	0.152019i	$-0.0485774\pi$
$662$	−16.0491	+	7.81779i	−0.623764	+	0.303847i
$663$	2.05721			0.0798955
$664$	5.06340	+	1.08414i	0.196498	+	0.0420727i
$665$	4.09306	+	72.0574i	0.158722	+	2.79426i
$666$	−6.74525	+	3.28574i	−0.261373	+	0.127320i
$667$			1.14912i			0.0444940i
$668$	−1.59568	+	2.03821i	−0.0617387	+	0.0788606i
$669$	19.8408	−	19.8408i	0.767089	−	0.767089i
$670$	11.2606	+	20.1297i	0.435034	+	0.777680i
$671$	−20.9435	−	20.9435i	−0.808515	−	0.808515i
$672$	51.7360	+	4.65564i	1.99576	+	0.179595i
$673$	4.92470			0.189833			0.0949166	−	0.995485i	$-0.469742\pi$
$673$	4.92470			0.189833			0.0949166	+	0.995485i	$0.469742\pi$
$674$	21.8089	+	44.7712i	0.840047	+	1.72452i
$675$	2.24645	+	19.7103i	0.0864660	+	0.758650i
$676$	7.37135	+	5.77092i	0.283513	+	0.221958i
$677$	18.9928	+	18.9928i	0.729954	+	0.729954i	0.970610	−	0.240656i	$-0.0773626\pi$
$677$	18.9928	+	18.9928i	0.729954	+	0.729954i	−0.240656	+	0.970610i	$0.577363\pi$
$678$	14.5901	+	29.9518i	0.560329	+	1.15029i
$679$	62.3468			2.39265
$680$	2.22275	+	0.345458i	0.0852385	+	0.0132477i
$681$	−36.1234			−1.38425
$682$	21.0377	+	43.1880i	0.805575	+	1.65376i
$683$		−	15.7812i		−	0.603850i	−0.953332	−	0.301925i	$-0.902371\pi$
$683$		−	15.7812i		−	0.603850i	0.953332	−	0.301925i	$-0.0976292\pi$
$684$	14.2956	−	1.74088i	0.546606	−	0.0665643i
$685$	9.03644	−	10.1249i	0.345265	−	0.386851i
$686$	14.7107	−	42.6543i	0.561658	−	1.62855i
$687$	−32.3131	−	32.3131i	−1.23282	−	1.23282i
$688$	12.0764	−	20.0085i	0.460409	−	0.762816i
$689$	−10.1589			−0.387024
$690$	−1.35668	−	0.383322i	−0.0516478	−	0.0145928i
$691$	6.86743	+	6.86743i	0.261249	+	0.261249i	0.825562	−	0.564312i	$-0.190859\pi$
$691$	6.86743	+	6.86743i	0.261249	+	0.261249i	−0.564312	+	0.825562i	$0.690859\pi$
$692$	−19.4850	+	2.37284i	−0.740708	+	0.0902017i
$693$	−11.9184	−	11.9184i	−0.452743	−	0.452743i
$694$	46.2301	+	15.9440i	1.75487	+	0.605224i
$695$	−37.9240	−	33.8472i	−1.43854	−	1.28390i
$696$	−28.6689	−	6.13838i	−1.08669	−	0.232675i
$697$	0.485048	−	2.22513i	0.0183725	−	0.0842826i
$698$	−39.6981	−	13.6912i	−1.50259	−	0.518218i
$699$		−	36.1013i		−	1.36547i
$700$	39.0198	+	23.9626i	1.47481	+	0.905703i
$701$	4.06136			0.153395			0.0766977	−	0.997054i	$-0.475562\pi$
$701$	4.06136			0.153395			0.0766977	+	0.997054i	$0.475562\pi$
$702$	−5.27653	+	15.2995i	−0.199150	+	0.577442i
$703$		−	36.6090i		−	1.38073i
$704$	10.2505	+	26.9430i	0.386332	+	1.01545i
$705$	−13.1169	−	11.7068i	−0.494010	−	0.440904i
$706$	−9.86408	−	20.2499i	−0.371240	−	0.762113i
$707$	29.3609	+	29.3609i	1.10423	+	1.10423i
$708$	14.3510	+	11.2352i	0.539345	+	0.422245i
$709$	−22.1251	+	22.1251i	−0.830924	+	0.830924i	−0.987643	−	0.156719i	$-0.949908\pi$
$709$	−22.1251	+	22.1251i	−0.830924	+	0.830924i	0.156719	+	0.987643i	$0.449908\pi$
$710$	−36.1319	−	10.2089i	−1.35601	−	0.383132i
$711$	7.16135	+	7.16135i	0.268571	+	0.268571i
$712$	−42.5622	−	9.11310i	−1.59509	−	0.341528i
$713$	−1.48189	−	1.48189i	−0.0554974	−	0.0554974i
$714$	−4.36640	−	1.50589i	−0.163408	−	0.0563567i
$715$	1.31797	+	23.2026i	0.0492894	+	0.867727i
$716$	26.4764	−	3.22423i	0.989469	−	0.120495i
$717$	−19.1780	−	19.1780i	−0.716215	−	0.716215i
$718$	9.99299	+	3.44641i	0.372935	+	0.128619i
$719$	0.908376	−	0.908376i	0.0338767	−	0.0338767i	−0.689966	−	0.723842i	$-0.742374\pi$
$719$	0.908376	−	0.908376i	0.0338767	−	0.0338767i	0.723842	+	0.689966i	$0.242374\pi$
$720$	4.27012	−	8.07758i	0.159138	−	0.301034i
$721$	16.5446	−	16.5446i	0.616154	−	0.616154i
$722$	−14.1491	+	41.0259i	−0.526576	+	1.52683i
$723$		−	48.1222i		−	1.78968i
$724$	21.2577	−	2.58871i	0.790035	−	0.0962086i
$725$	−20.2270	−	16.0881i	−0.751213	−	0.597496i
$726$	1.83483	−	5.32017i	0.0680971	−	0.197450i
$727$		−	32.0189i		−	1.18752i	−0.804644	−	0.593758i	$-0.797644\pi$
$727$		−	32.0189i		−	1.18752i	0.804644	−	0.593758i	$-0.202356\pi$
$728$	20.2988	+	31.3595i	0.752324	+	1.16226i
$729$	12.6111			0.467080
$730$	−26.5930	−	7.51370i	−0.984250	−	0.278094i
$731$	−1.46939	+	1.46939i	−0.0543472	+	0.0543472i
$732$	−20.3223	+	25.9582i	−0.751133	+	0.959443i
$733$	22.3532	−	22.3532i	0.825634	−	0.825634i	−0.161276	−	0.986909i	$-0.551561\pi$
$733$	22.3532	−	22.3532i	0.825634	−	0.825634i	0.986909	+	0.161276i	$0.0515608\pi$
$734$	−7.79647	+	3.79781i	−0.287773	+	0.140180i
$735$	−46.7282	−	41.7050i	−1.72360	−	1.53831i
$736$	−0.805962	−	0.965361i	−0.0297082	−	0.0355837i
$737$	18.5846	−	18.5846i	0.684574	−	0.684574i
$738$	−7.90185	−	4.80927i	−0.290871	−	0.177032i
$739$	−19.2570			−0.708380			−0.354190	−	0.935174i	$-0.615243\pi$
$739$	−19.2570			−0.708380			−0.354190	+	0.935174i	$0.615243\pi$
$740$	−19.0711	−	13.2576i	−0.701067	−	0.487359i
$741$	28.8297	+	28.8297i	1.05909	+	1.05909i
$742$	21.5621	+	7.43641i	0.791571	+	0.272999i
$743$	25.8253	+	25.8253i	0.947437	+	0.947437i	0.998686	−	0.0512490i	$-0.0163202\pi$
$743$	25.8253	+	25.8253i	0.947437	+	0.947437i	−0.0512490	+	0.998686i	$0.516320\pi$
$744$	44.8874	−	29.0553i	1.64565	−	1.06522i
$745$	1.24616	+	21.9383i	0.0456557	+	0.803757i
$746$	−12.3692	−	25.3926i	−0.452868	−	0.929688i
$747$	−1.32241	+	1.32241i	−0.0483844	+	0.0483844i
$748$	−0.309852	−	2.54441i	−0.0113293	−	0.0930328i
$749$	1.83268	−	1.83268i	0.0669648	−	0.0669648i
$750$	25.7413	−	18.5139i	0.939941	−	0.676033i
$751$	3.98264	−	3.98264i	0.145328	−	0.145328i	−0.630699	−	0.776028i	$-0.717232\pi$
$751$	3.98264	−	3.98264i	0.145328	−	0.145328i	0.776028	+	0.630699i	$0.217232\pi$
$752$	−3.76387	−	15.2247i	−0.137254	−	0.555187i
$753$	−16.9769			−0.618672
$754$	−9.23337	−	18.9551i	−0.336259	−	0.690303i
$755$	21.7848	−	1.23744i	0.792829	−	0.0450350i
$756$	22.3987	−	28.6104i	0.814632	−	1.04055i
$757$			2.43172i			0.0883822i	0.999023	+	0.0441911i	$0.0140710\pi$
$757$			2.43172i			0.0883822i	−0.999023	+	0.0441911i	$0.985929\pi$
$758$	40.9264	+	14.1148i	1.48652	+	0.512673i
$759$			1.60644i			0.0583101i
$760$	26.3083	+	35.9908i	0.954302	+	1.30552i
$761$	18.3270			0.664353			0.332176	−	0.943217i	$-0.392217\pi$
$761$	18.3270			0.664353			0.332176	+	0.943217i	$0.392217\pi$
$762$	−14.2372	−	29.2274i	−0.515760	−	1.05880i
$763$	−11.2164	+	11.2164i	−0.406060	+	0.406060i
$764$	−3.83924	−	31.5266i	−0.138899	−	1.14059i
$765$	−0.540961	+	0.606118i	−0.0195585	+	0.0219142i
$766$	−13.9032	+	40.3130i	−0.502344	+	1.45657i
$767$			13.1070i			0.473266i
$768$	28.3898	−	14.9509i	1.02443	−	0.539495i
$769$			44.0139i			1.58718i	0.608453	+	0.793590i	$0.291791\pi$
$769$			44.0139i			1.58718i	−0.608453	+	0.793590i	$0.708209\pi$
$770$	14.1871	−	50.2118i	0.511267	−	1.80951i
$771$	−9.96299			−0.358808
$772$	3.74634	−	4.78530i	0.134834	−	0.172227i
$773$	−0.849292			−0.0305469			−0.0152735	−	0.999883i	$-0.504862\pi$
$773$	−0.849292			−0.0305469			−0.0152735	+	0.999883i	$0.504862\pi$
$774$	3.69634	+	7.58817i	0.132862	+	0.272751i
$775$	46.8318	−	5.33758i	1.68225	−	0.191732i
$776$	32.3293	−	20.9265i	1.16055	−	0.751219i
$777$	33.7227	+	33.7227i	1.20980	+	1.20980i
$778$	−32.0886	−	11.0668i	−1.15043	−	0.396764i
$779$	37.9803	−	24.3854i	1.36078	−	0.873697i
$780$	25.4589	−	4.57813i	0.911576	−	0.163924i
$781$			42.7838i			1.53092i
$782$	0.0489686	+	0.100527i	0.00175111	+	0.00359484i
$783$	−14.5016	+	14.5016i	−0.518244	+	0.518244i
$784$	−13.4086	−	54.2372i	−0.478879	−	1.93704i
$785$	−23.0781	−	20.5972i	−0.823693	−	0.735146i
$786$	−0.132485	−	0.0456918i	−0.00472559	−	0.00162977i
$787$	−7.06534	+	7.06534i	−0.251852	+	0.251852i	−0.821730	−	0.569878i	$-0.806991\pi$
$787$	−7.06534	+	7.06534i	−0.251852	+	0.251852i	0.569878	+	0.821730i	$0.306991\pi$
$788$	0.971433	+	7.97711i	0.0346059	+	0.284173i
$789$		−	26.8083i		−	0.954399i
$790$	−8.52451	+	30.1705i	−0.303288	+	1.07342i
$791$	38.0370	−	38.0370i	1.35244	−	1.35244i
$792$	−10.1805	−	2.17978i	−0.361750	−	0.0774552i
$793$	−23.7080			−0.841894
$794$	13.2034	+	4.55362i	0.468571	+	0.161602i
$795$	10.5166	−	11.7833i	0.372986	−	0.417911i
$796$	−10.1734	+	1.23889i	−0.360587	+	0.0439114i
$797$	2.90820	−	2.90820i	0.103014	−	0.103014i	−0.653722	−	0.756735i	$-0.726793\pi$
$797$	2.90820	−	2.90820i	0.103014	−	0.103014i	0.756735	+	0.653722i	$0.226793\pi$
$798$	−40.0870	−	82.2941i	−1.41906	−	2.91318i
$799$			1.39448i			0.0493333i
$800$	28.2763	−	0.671321i	0.999718	−	0.0237348i
$801$	11.1160	−	11.1160i	0.392763	−	0.392763i
$802$	−3.29016	+	9.53995i	−0.116180	+	0.336868i
$803$			31.4887i			1.11121i
$804$	−23.0345	−	18.0334i	−0.812365	−	0.635988i
$805$	0.129089	+	2.27258i	0.00454978	+	0.0800978i
$806$	36.3517	+	12.5371i	1.28043	+	0.441599i
$807$			38.4029i			1.35185i
$808$	25.0797	+	5.36988i	0.882302	+	0.188912i
$809$	−35.3334	+	35.3334i	−1.24226	+	1.24226i	−0.283193	+	0.959063i	$0.591394\pi$
$809$	−35.3334	+	35.3334i	−1.24226	+	1.24226i	−0.959063	+	0.283193i	$0.908606\pi$
$810$	−17.0147	−	30.4161i	−0.597837	−	1.06871i
$811$	21.1131			0.741383			0.370691	−	0.928756i	$-0.379121\pi$
$811$	21.1131			0.741383			0.370691	+	0.928756i	$0.379121\pi$
$812$	5.72241	+	46.9907i	0.200817	+	1.64905i
$813$			26.5879i			0.932479i
$814$	−8.62901	+	25.0201i	−0.302447	+	0.876955i
$815$	−39.7674	+	2.25890i	−1.39299	+	0.0791258i
$816$	−2.76960	+	0.684704i	−0.0969553	+	0.0239694i
$817$	−41.1838			−1.44084
$818$	−4.56286	+	13.2302i	−0.159536	+	0.462582i
$819$	−13.4916			−0.471435
$820$	1.05088	−	28.6164i	0.0366982	−	0.999326i
$821$	25.4002			0.886472			0.443236	−	0.896405i	$-0.353830\pi$
$821$	25.4002			0.886472			0.443236	+	0.896405i	$0.353830\pi$
$822$	−5.61180	+	16.2716i	−0.195734	+	0.567538i
$823$	31.0979			1.08400			0.542002	−	0.840377i	$-0.317667\pi$
$823$	31.0979			1.08400			0.542002	+	0.840377i	$0.317667\pi$
$824$	3.02588	−	14.1322i	0.105412	−	0.492319i
$825$	−28.2770	−	22.4908i	−0.984478	−	0.783029i
$826$	9.59440	−	27.8193i	0.333832	−	0.967958i
$827$		−	24.5973i		−	0.855333i	−0.903937	−	0.427667i	$-0.859336\pi$
$827$		−	24.5973i		−	0.855333i	0.903937	−	0.427667i	$-0.140664\pi$
$828$	0.450860	−	0.0549047i	0.0156685	−	0.00190807i
$829$	31.6535			1.09937			0.549686	−	0.835371i	$-0.314747\pi$
$829$	31.6535			1.09937			0.549686	+	0.835371i	$0.314747\pi$
$830$	−5.57125	−	1.57413i	−0.193381	−	0.0546388i
$831$	22.1132	−	22.1132i	0.767097	−	0.767097i
$832$	21.0515	+	9.44790i	0.729829	+	0.327547i
$833$			4.96779i			0.172124i
$834$	60.9475	+	21.0197i	2.11044	+	0.727854i
$835$	1.92706	−	2.15917i	0.0666888	−	0.0747213i
$836$	31.3150	−	39.9995i	1.08305	−	1.38341i
$837$		−	37.4024i		−	1.29281i
$838$	−0.624197	+	1.80988i	−0.0215625	+	0.0625213i
$839$	−1.55280	+	1.55280i	−0.0536087	+	0.0536087i	−0.733403	−	0.679794i	$-0.762069\pi$
$839$	−1.55280	+	1.55280i	−0.0536087	+	0.0536087i	0.679794	+	0.733403i	$0.262069\pi$
$840$	−57.3873	−	8.91911i	−1.98005	−	0.307738i
$841$			2.28166i			0.0786779i
$842$	11.8299	+	24.2855i	0.407687	+	0.836935i
$843$	−0.505088	+	0.505088i	−0.0173961	+	0.0173961i
$844$	−0.212227	−	1.74275i	−0.00730517	−	0.0599878i
$845$	−7.80884	−	6.96939i	−0.268632	−	0.239754i
$846$	5.35464	+	1.84672i	0.184096	+	0.0634916i
$847$	−9.08642			−0.312213
$848$	13.6768	−	3.38121i	0.469664	−	0.116111i
$849$	34.4541	−	34.4541i	1.18246	−	1.18246i
$850$	−2.45508	−	0.545460i	−0.0842085	−	0.0187091i
$851$		−	1.15459i		−	0.0395788i
$852$	47.2713	−	5.75659i	1.61949	−	0.197217i
$853$	1.64231	−	1.64231i	0.0562316	−	0.0562316i	−0.678432	−	0.734663i	$-0.737340\pi$
$853$	1.64231	−	1.64231i	0.0562316	−	0.0562316i	0.734663	+	0.678432i	$0.237340\pi$
$854$	50.3197	+	17.3544i	1.72191	+	0.593855i
$855$	−16.0751	+	0.913113i	−0.549757	+	0.0312278i
$856$	0.335183	−	1.56545i	0.0114563	−	0.0535061i
$857$	11.7972	−	11.7972i	0.402986	−	0.402986i	−0.476298	−	0.879284i	$-0.658022\pi$
$857$	11.7972	−	11.7972i	0.402986	−	0.402986i	0.879284	+	0.476298i	$0.158022\pi$
$858$	−12.9081	−	26.4988i	−0.440674	−	0.904654i
$859$			35.1075i			1.19785i	0.800804	+	0.598926i	$0.204406\pi$
$859$			35.1075i			1.19785i	−0.800804	+	0.598926i	$0.795594\pi$
$860$	−14.9143	+	21.4543i	−0.508574	+	0.731585i
$861$	−12.5231	+	57.4487i	−0.426785	+	1.95785i
$862$	31.7501	+	10.9500i	1.08141	+	0.372960i
$863$	13.6822	+	13.6822i	0.465746	+	0.465746i	0.900533	−	0.434787i	$-0.143176\pi$
$863$	13.6822	+	13.6822i	0.465746	+	0.465746i	−0.434787	+	0.900533i	$0.643176\pi$
$864$	2.01158	−	22.3537i	0.0684352	−	0.760488i
$865$	21.9105	−	1.24458i	0.744980	−	0.0423170i
$866$	−2.65169	−	5.44362i	−0.0901080	−	0.184982i
$867$	−33.8377			−1.14919
$868$	−67.9786	−	53.2194i	−2.30734	−	1.80638i
$869$	35.7248			1.21188
$870$	31.5444	+	8.91270i	1.06946	+	0.302169i
$871$		−	21.0377i		−	0.712837i
$872$	−2.05139	+	9.58089i	−0.0694688	+	0.324450i
$873$			13.9088i			0.470742i
$874$	−0.722538	+	2.09503i	−0.0244402	+	0.0708653i
$875$	−41.8097	−	29.5447i	−1.41343	−	0.998792i
$876$	34.7915	−	4.23683i	1.17550	−	0.143149i
$877$	29.1768	−	29.1768i	0.985231	−	0.985231i	−0.0146619	−	0.999893i	$-0.504667\pi$
$877$	29.1768	−	29.1768i	0.985231	−	0.985231i	0.999893	+	0.0146619i	$0.00466718\pi$
$878$	−2.55093	−	5.23677i	−0.0860896	−	0.176732i
$879$	50.6694			1.70904
$880$	−9.49690	−	30.7987i	−0.320141	−	1.03822i
$881$			7.04428i			0.237328i	0.992934	+	0.118664i	$0.0378611\pi$
$881$			7.04428i			0.237328i	−0.992934	+	0.118664i	$0.962139\pi$
$882$	19.0757	+	6.57887i	0.642311	+	0.221522i
$883$		−	0.316090i		−	0.0106373i	−0.999986	−	0.00531864i	$-0.998307\pi$
$883$		−	0.316090i		−	0.0106373i	0.999986	−	0.00531864i	$-0.00169298\pi$
$884$	−1.61551	−	1.26476i	−0.0543354	−	0.0425383i
$885$	−15.2028	−	13.5685i	−0.511035	−	0.456099i
$886$	19.1198	+	39.2508i	0.642343	+	1.31866i
$887$	−9.84344			−0.330510			−0.165255	−	0.986251i	$-0.552845\pi$
$887$	−9.84344			−0.330510			−0.165255	+	0.986251i	$0.552845\pi$
$888$	28.8055	+	6.16762i	0.966649	+	0.206972i
$889$	−37.1171	+	37.1171i	−1.24487	+	1.24487i
$890$	46.8311	+	13.2319i	1.56978	+	0.443534i
$891$	−28.0814	+	28.0814i	−0.940762	+	0.940762i
$892$	−27.7787	+	3.38282i	−0.930100	+	0.113265i
$893$	−19.5422	+	19.5422i	−0.653956	+	0.653956i
$894$	−12.2047	−	25.0549i	−0.408187	−	0.837962i
$895$	−29.7722	+	1.69115i	−0.995174	+	0.0565287i
$896$	−37.7655	−	35.4628i	−1.26166	−	1.18473i
$897$	0.909243	+	0.909243i	0.0303587	+	0.0303587i
$898$	−24.3070	−	8.38305i	−0.811134	−	0.279746i
$899$	34.4558	+	34.4558i	1.14917	+	1.14917i
$900$	−5.34577	+	8.70484i	−0.178192	+	0.290161i
$901$	−1.25271			−0.0417339
$902$	−31.7051	+	7.71377i	−1.05567	+	0.256840i
$903$	37.9369	−	37.9369i	1.26246	−	1.26246i
$904$	6.95667	−	32.4907i	0.231375	−	1.08062i
$905$	−23.9038	+	1.35781i	−0.794591	+	0.0451350i
$906$	−24.8796	+	12.1193i	−0.826569	+	0.402637i
$907$	−2.65862	+	2.65862i	−0.0882781	+	0.0882781i	−0.749867	−	0.661589i	$-0.769882\pi$
$907$	−2.65862	+	2.65862i	−0.0882781	+	0.0882781i	0.661589	+	0.749867i	$0.269882\pi$
$908$	28.3673	+	22.2083i	0.941403	+	0.737010i
$909$	−6.55007	+	6.55007i	−0.217252	+	0.217252i
$910$	−20.3899	−	36.4497i	−0.675920	−	1.20829i
$911$	19.4337			0.643867			0.321933	−	0.946762i	$-0.395667\pi$
$911$	19.4337			0.643867			0.321933	+	0.946762i	$0.395667\pi$
$912$	−48.4085	−	29.2176i	−1.60296	−	0.967492i
$913$			6.59692i			0.218326i
$914$	2.33659	−	6.77503i	0.0772875	−	0.224098i
$915$	24.5427	−	27.4988i	0.811357	−	0.909082i
$916$	5.50932	+	45.2409i	0.182033	+	1.49480i
$917$			0.226274i			0.00747223i
$918$	−0.650656	+	1.88660i	−0.0214748	+	0.0622671i
$919$	24.2342	−	24.2342i	0.799412	−	0.799412i	−0.183591	−	0.983003i	$-0.558772\pi$
$919$	24.2342	−	24.2342i	0.799412	−	0.799412i	0.983003	+	0.183591i	$0.0587721\pi$
$920$	0.829722	+	1.13509i	0.0273551	+	0.0374229i
$921$	20.9709	−	20.9709i	0.691016	−	0.691016i
$922$	−16.6758	−	5.75120i	−0.549189	−	0.189406i
$923$	24.2155	+	24.2155i	0.797064	+	0.797064i
$924$	7.99982	+	65.6920i	0.263175	+	2.16111i
$925$	20.3234	+	16.1647i	0.668228	+	0.531492i
$926$	−5.91055	−	2.03845i	−0.194233	−	0.0669875i
$927$	3.69090	+	3.69090i	0.121225	+	0.121225i
$928$	18.7396	+	22.4458i	0.615157	+	0.736820i
$929$	−33.4285	−	33.4285i	−1.09675	−	1.09675i	−0.994788	−	0.101966i	$-0.967487\pi$
$929$	−33.4285	−	33.4285i	−1.09675	−	1.09675i	−0.101966	−	0.994788i	$-0.532513\pi$
$930$	−52.1733	+	29.1857i	−1.71083	+	0.957038i
$931$	−69.6183	+	69.6183i	−2.28165	+	2.28165i
$932$	−22.1947	+	28.3499i	−0.727012	+	0.928633i
$933$	−19.9651	−	19.9651i	−0.653629	−	0.653629i
$934$	−22.9330	−	47.0789i	−0.750391	−	1.54047i
$935$	0.162521	+	2.86114i	0.00531500	+	0.0935693i
$936$	−6.99593	+	4.52842i	−0.228669	+	0.148016i
$937$			22.0009i			0.718739i	0.933195	+	0.359370i	$0.117008\pi$
$937$			22.0009i			0.718739i	−0.933195	+	0.359370i	$0.882992\pi$
$938$	−15.3998	+	44.6522i	−0.502821	+	1.45795i
$939$	−3.96547			−0.129408
$940$	3.10329	+	17.2574i	0.101218	+	0.562873i
$941$		−	33.6199i		−	1.09598i	−0.836486	−	0.547988i	$-0.815394\pi$
$941$		−	33.6199i		−	1.09598i	0.836486	−	0.547988i	$-0.184606\pi$
$942$	37.0887	+	12.7913i	1.20842	+	0.416762i
$943$	1.19784	−	0.769076i	0.0390070	−	0.0250446i
$944$	−4.36241	−	17.6458i	−0.141984	−	0.574321i
$945$	−27.0503	+	30.3085i	−0.879947	+	0.985934i
$946$	28.1468	+	9.70733i	0.915130	+	0.315613i
$947$	21.4622	+	21.4622i	0.697429	+	0.697429i	0.963855	−	0.266426i	$-0.0858428\pi$
$947$	21.4622	+	21.4622i	0.697429	+	0.697429i	−0.266426	+	0.963855i	$0.585843\pi$
$948$	−4.80680	−	39.4720i	−0.156118	−	1.28199i
$949$	17.8226	+	17.8226i	0.578545	+	0.578545i
$950$	−26.7613	−	42.0494i	−0.868253	−	1.36426i
$951$	−44.6097			−1.44657
$952$	2.50307	+	3.86698i	0.0811251	+	0.125330i
$953$	−14.3244	−	14.3244i	−0.464014	−	0.464014i	0.435955	−	0.899969i	$-0.356411\pi$
$953$	−14.3244	−	14.3244i	−0.464014	−	0.464014i	−0.899969	+	0.435955i	$0.856411\pi$
$954$	−1.65897	+	4.81025i	−0.0537112	+	0.155738i
$955$	2.01372	+	35.4511i	0.0651626	+	1.14717i
$956$	3.26982	+	26.8507i	0.105753	+	0.868415i
$957$		−	37.3517i		−	1.20741i
$958$	7.05781	+	14.4889i	0.228027	+	0.468115i
$959$	27.7906			0.897406
$960$	−32.7513	+	14.6370i	−1.05704	+	0.472407i
$961$	−57.8682			−1.86672
$962$	9.27735	+	19.0454i	0.299114	+	0.614047i
$963$	0.408850	+	0.408850i	0.0131750	+	0.0131750i
$964$	−29.5851	+	37.7899i	−0.952872	+	1.21713i
$965$	−4.52436	+	5.06931i	−0.145644	+	0.163187i
$966$	−1.26428	−	2.59542i	−0.0406775	−	0.0835064i
$967$	−12.7871			−0.411206			−0.205603	−	0.978636i	$-0.565916\pi$
$967$	−12.7871			−0.411206			−0.205603	+	0.978636i	$0.565916\pi$
$968$	−4.71167	+	3.04983i	−0.151439	+	0.0980254i
$969$	3.55503	+	3.55503i	0.114204	+	0.114204i
$970$	−37.5768	+	21.0205i	−1.20652	+	0.674927i
$971$	−11.2873	+	11.2873i	−0.362226	+	0.362226i	−0.864632	−	0.502406i	$-0.832448\pi$
$971$	−11.2873	+	11.2873i	−0.362226	+	0.362226i	0.502406	+	0.864632i	$0.332448\pi$
$972$	16.0608	+	12.5737i	0.515149	+	0.403303i
$973$		−	104.093i		−	3.33708i
$974$	−22.5889	+	11.0035i	−0.723795	+	0.352574i
$975$	−28.7345	+	3.27497i	−0.920239	+	0.104883i
$976$	31.9177	−	7.89075i	1.02166	−	0.252577i
$977$	−19.1640			−0.613111			−0.306555	−	0.951853i	$-0.599176\pi$
$977$	−19.1640			−0.613111			−0.306555	+	0.951853i	$0.599176\pi$
$978$	45.4169	−	22.1234i	1.45227	−	0.707428i
$979$		−	55.4527i		−	1.77228i
$980$	11.0553	+	61.4786i	0.353150	+	1.96386i
$981$	−2.50224	−	2.50224i	−0.0798903	−	0.0798903i
$982$	−11.5691	+	33.5451i	−0.369185	+	1.07047i
$983$	11.1165	−	11.1165i	0.354563	−	0.354563i	−0.507241	−	0.861804i	$-0.669335\pi$
$983$	11.1165	−	11.1165i	0.354563	−	0.354563i	0.861804	+	0.507241i	$0.169335\pi$
$984$	12.7888	+	33.9927i	0.407692	+	1.08365i
$985$	−0.509528	−	8.97010i	−0.0162349	−	0.285811i
$986$	−1.13858	−	2.33737i	−0.0362597	−	0.0744372i
$987$		−	36.0030i		−	1.14599i
$988$	−4.91542	−	40.3639i	−0.156380	−	1.28415i
$989$	−1.29887			−0.0413018
$990$	11.2016	+	3.16496i	0.356012	+	0.100589i
$991$	−16.2263	+	16.2263i	−0.515446	+	0.515446i	−0.916190	−	0.400744i	$-0.868752\pi$
$991$	−16.2263	+	16.2263i	−0.515446	+	0.515446i	0.400744	+	0.916190i	$0.368752\pi$
$992$	−53.1125	−	4.77952i	−1.68632	−	0.151750i
$993$	−17.8999	+	17.8999i	−0.568035	+	0.568035i
$994$	−33.6711	−	69.1230i	−1.06798	−	2.19245i
$995$	11.4398	−	0.649814i	0.362666	−	0.0206005i
$996$	7.28886	−	0.887620i	0.230956	−	0.0281253i
$997$	−51.4430			−1.62922			−0.814608	−	0.580012i	$-0.803048\pi$
$997$	−51.4430			−1.62922			−0.814608	+	0.580012i	$0.803048\pi$
$998$	−1.29179	−	2.65190i	−0.0408909	−	0.0839445i
$999$	14.5707	−	14.5707i	0.460995	−	0.460995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.s.c.583.14	yes	240
4.3	odd	2	inner	820.2.s.c.583.45	yes	240
5.2	odd	4		820.2.j.c.747.76	yes	240
20.7	even	4		820.2.j.c.747.107	yes	240
41.32	even	4		820.2.j.c.483.107	yes	240
164.155	odd	4		820.2.j.c.483.76	✓	240
205.32	odd	4	inner	820.2.s.c.647.45	yes	240
820.647	even	4	inner	820.2.s.c.647.14	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.j.c.483.76	✓	240	164.155	odd	4
820.2.j.c.483.107	yes	240	41.32	even	4
820.2.j.c.747.76	yes	240	5.2	odd	4
820.2.j.c.747.107	yes	240	20.7	even	4
820.2.s.c.583.14	yes	240	1.1	even	1	trivial
820.2.s.c.583.45	yes	240	4.3	odd	2	inner
820.2.s.c.647.14	yes	240	820.647	even	4	inner
820.2.s.c.647.45	yes	240	205.32	odd	4	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:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33694 - 0.461086i) q^{2} -2.00537 q^{3} +(1.57480 + 1.23289i) q^{4} +(-1.66826 - 1.48893i) q^{5} +(2.68106 + 0.924650i) q^{6} -4.57903i q^{7} +(-1.53694 - 2.37441i) q^{8} +1.02153 q^{9} +(1.54384 + 2.75981i) q^{10} +(2.54798 - 2.54798i) q^{11} +(-3.15806 - 2.47240i) q^{12} -2.88430i q^{13} +(-2.11133 + 6.12187i) q^{14} +(3.34549 + 2.98585i) q^{15} +(0.959984 + 3.88310i) q^{16} -0.355667i q^{17} +(-1.36572 - 0.471012i) q^{18} +(4.98430 - 4.98430i) q^{19} +(-0.791504 - 4.40154i) q^{20} +9.18267i q^{21} +(-4.58132 + 2.23165i) q^{22} +(0.157197 - 0.157197i) q^{23} +(3.08214 + 4.76158i) q^{24} +(0.566202 + 4.96784i) q^{25} +(-1.32991 + 3.85613i) q^{26} +3.96758 q^{27} +(5.64542 - 7.21105i) q^{28} +(-3.65502 + 3.65502i) q^{29} +(-3.09597 - 5.53446i) q^{30} -9.42699i q^{31} +(0.507003 - 5.63409i) q^{32} +(-5.10964 + 5.10964i) q^{33} +(-0.163993 + 0.475504i) q^{34} +(-6.81784 + 7.63903i) q^{35} +(1.60870 + 1.25943i) q^{36} +(3.67243 - 3.67243i) q^{37} +(-8.96189 + 4.36550i) q^{38} +5.78410i q^{39} +(-0.971297 + 6.24953i) q^{40} +(6.25621 + 1.36377i) q^{41} +(4.23400 - 12.2766i) q^{42} +(-4.13136 - 4.13136i) q^{43} +(7.15391 - 0.871186i) q^{44} +(-1.70417 - 1.52098i) q^{45} +(-0.282644 + 0.137681i) q^{46} -3.92076 q^{47} +(-1.92513 - 7.78706i) q^{48} -13.9675 q^{49} +(1.53363 - 6.90275i) q^{50} +0.713245i q^{51} +(3.55601 - 4.54219i) q^{52} -3.52215i q^{53} +(-5.30440 - 1.82940i) q^{54} +(-8.04444 + 0.456947i) q^{55} +(-10.8725 + 7.03770i) q^{56} +(-9.99539 + 9.99539i) q^{57} +(6.57181 - 3.20125i) q^{58} -4.54425 q^{59} +(1.58726 + 8.82673i) q^{60} -8.21966i q^{61} +(-4.34666 + 12.6033i) q^{62} -4.67760i q^{63} +(-3.27563 + 7.29865i) q^{64} +(-4.29451 + 4.81177i) q^{65} +(9.18726 - 4.47528i) q^{66} +7.29388 q^{67} +(0.438497 - 0.560104i) q^{68} +(-0.315239 + 0.315239i) q^{69} +(12.6373 - 7.06929i) q^{70} +(-8.39564 + 8.39564i) q^{71} +(-1.57002 - 2.42552i) q^{72} +(-6.17916 + 6.17916i) q^{73} +(-6.60311 + 3.21650i) q^{74} +(-1.13545 - 9.96237i) q^{75} +(13.9943 - 1.70420i) q^{76} +(-11.6673 - 11.6673i) q^{77} +(2.66697 - 7.73297i) q^{78} +(7.01044 + 7.01044i) q^{79} +(4.18013 - 7.90737i) q^{80} -11.0211 q^{81} +(-7.73534 - 4.70793i) q^{82} +(-1.29454 + 1.29454i) q^{83} +(-11.3212 + 14.4609i) q^{84} +(-0.529561 + 0.593346i) q^{85} +(3.61845 + 7.42827i) q^{86} +(7.32968 - 7.32968i) q^{87} +(-9.96602 - 2.13385i) q^{88} +(10.8817 - 10.8817i) q^{89} +(1.57707 + 2.81922i) q^{90} -13.2073 q^{91} +(0.441360 - 0.0537477i) q^{92} +18.9047i q^{93} +(5.24180 + 1.80781i) q^{94} +(-15.7364 + 0.893871i) q^{95} +(-1.01673 + 11.2985i) q^{96} +13.6157i q^{97} +(18.6737 + 6.44023i) q^{98} +(2.60282 - 2.60282i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{6} - 12 q^{8} + 240 q^{9} - 20 q^{10} + 8 q^{14} + 8 q^{16} - 12 q^{18} - 16 q^{20} - 12 q^{24} - 16 q^{25} - 30 q^{30} - 24 q^{33} + 20 q^{34} - 8 q^{37} - 4 q^{40} - 16 q^{41} + 84 q^{42}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q - 4 * q^6 - 12 * q^8 + 240 * q^9 - 20 * q^10 + 8 * q^14 + 8 * q^16 - 12 * q^18 - 16 * q^20 - 12 * q^24 - 16 * q^25 - 30 * q^30 - 24 * q^33 + 20 * q^34 - 8 * q^37 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 - 224 * q^49 + 12 * q^50 + 28 * q^52 - 48 * q^54 + 24 * q^56 - 8 * q^57 + 28 * q^58 - 26 * q^60 - 40 * q^65 - 8 * q^66 + 96 * q^68 - 16 * q^69 - 14 * q^70 - 96 * q^72 + 72 * q^73 - 112 * q^74 + 20 * q^76 + 56 * q^77 + 4 * q^78 - 60 * q^80 + 48 * q^81 + 20 * q^82 + 32 * q^84 - 16 * q^85 - 8 * q^86 - 16 * q^88 + 64 * q^89 - 76 * q^90 + 20 * q^92 - 48 * q^94 + 24 * q^96 - 12 * q^98

Introduction

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