LMFDB - Embedded newform 160.2.z.a.109.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [160,2,Mod(29,160)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("160.29"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(160, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	160.z (of order $8$, degree $4$, 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:	$1.27760643234$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			109.3
Character	$\chi$	$=$	160.109
Dual form			160.2.z.a.69.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.26433 + 0.633607i) q^{2} +(2.72675 + 1.12946i) q^{3} +(1.19708 - 1.60218i) q^{4} +(-1.63639 + 1.52389i) q^{5} +(-4.16316 + 0.299677i) q^{6} +(0.911488 + 0.911488i) q^{7} +(-0.498360 + 2.78418i) q^{8} +(4.03817 + 4.03817i) q^{9} +(1.10339 - 2.96353i) q^{10} +(-1.71789 - 4.14736i) q^{11} +(5.07375 - 3.01670i) q^{12} +(0.122394 - 0.295486i) q^{13} +(-1.72995 - 0.574901i) q^{14} +(-6.18319 + 2.30703i) q^{15} +(-1.13398 - 3.83589i) q^{16} -1.24150 q^{17} +(-7.66422 - 2.54699i) q^{18} +(5.63014 + 2.33208i) q^{19} +(0.482655 + 4.44601i) q^{20} +(1.45591 + 3.51489i) q^{21} +(4.79979 + 4.15518i) q^{22} +(-2.85230 + 2.85230i) q^{23} +(-4.50351 + 7.02888i) q^{24} +(0.355529 - 4.98734i) q^{25} +(0.0324747 + 0.451143i) q^{26} +(3.06178 + 7.39179i) q^{27} +(2.55150 - 0.369243i) q^{28} +(2.86983 - 6.92838i) q^{29} +(6.35586 - 6.83457i) q^{30} -7.15524 q^{31} +(3.86418 + 4.13136i) q^{32} -13.2491i q^{33} +(1.56967 - 0.786622i) q^{34} +(-2.88055 - 0.102542i) q^{35} +(11.3039 - 1.63586i) q^{36} +(-2.32483 - 5.61264i) q^{37} +(-8.59601 + 0.618768i) q^{38} +(0.667478 - 0.667478i) q^{39} +(-3.42726 - 5.31544i) q^{40} +(1.47276 + 1.47276i) q^{41} +(-4.06782 - 3.52152i) q^{42} +(4.82876 - 2.00014i) q^{43} +(-8.70129 - 2.21236i) q^{44} +(-12.7617 - 0.454292i) q^{45} +(1.79902 - 5.41349i) q^{46} +0.547863 q^{47} +(1.24040 - 11.7403i) q^{48} -5.33838i q^{49} +(2.71051 + 6.53094i) q^{50} +(-3.38526 - 1.40222i) q^{51} +(-0.326907 - 0.549820i) q^{52} +(9.59054 - 3.97253i) q^{53} +(-8.55460 - 7.40573i) q^{54} +(9.13125 + 4.16881i) q^{55} +(-2.99199 + 2.08350i) q^{56} +(12.7180 + 12.7180i) q^{57} +(0.761447 + 10.5781i) q^{58} +(-1.54689 + 0.640744i) q^{59} +(-3.70550 + 12.6683i) q^{60} +(0.461455 - 1.11405i) q^{61} +(9.04662 - 4.53361i) q^{62} +7.36150i q^{63} +(-7.50328 - 2.77504i) q^{64} +(0.250003 + 0.670045i) q^{65} +(8.39472 + 16.7513i) q^{66} +(-14.5683 - 6.03439i) q^{67} +(-1.48618 + 1.98911i) q^{68} +(-10.9990 + 4.55595i) q^{69} +(3.70696 - 1.69549i) q^{70} +(-0.198299 + 0.198299i) q^{71} +(-13.2555 + 9.23053i) q^{72} +(-8.93915 + 8.93915i) q^{73} +(6.49558 + 5.62323i) q^{74} +(6.60243 - 13.1977i) q^{75} +(10.4762 - 6.22882i) q^{76} +(2.21443 - 5.34611i) q^{77} +(-0.420996 + 1.26683i) q^{78} +15.6241i q^{79} +(7.70111 + 4.54895i) q^{80} +6.48118i q^{81} +(-2.79521 - 0.928910i) q^{82} +(-3.23636 + 7.81327i) q^{83} +(7.37435 + 1.87497i) q^{84} +(2.03157 - 1.89190i) q^{85} +(-4.83786 + 5.58838i) q^{86} +(15.6506 - 15.6506i) q^{87} +(12.4031 - 2.71604i) q^{88} +(-0.464872 + 0.464872i) q^{89} +(16.4230 - 7.51156i) q^{90} +(0.380893 - 0.157771i) q^{91} +(1.15546 + 7.98434i) q^{92} +(-19.5106 - 8.08154i) q^{93} +(-0.692682 + 0.347130i) q^{94} +(-12.7669 + 4.76352i) q^{95} +(5.87047 + 15.6296i) q^{96} +11.6763i q^{97} +(3.38243 + 6.74950i) q^{98} +(9.81061 - 23.6849i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9} - 4 q^{10} - 8 q^{11} - 24 q^{14} - 8 q^{16} - 8 q^{19} - 4 q^{20} - 8 q^{21} - 16 q^{24} - 4 q^{25} + 32 q^{26} - 8 q^{29} - 52 q^{30} - 64 q^{31} - 24 q^{34}+ \cdots - 48 q^{99}+O(q^{100}) $ 88 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9 - 4 * q^10 - 8 * q^11 - 24 * q^14 - 8 * q^16 - 8 * q^19 - 4 * q^20 - 8 * q^21 - 16 * q^24 - 4 * q^25 + 32 * q^26 - 8 * q^29 - 52 * q^30 - 64 * q^31 - 24 * q^34 + 20 * q^35 + 72 * q^36 - 8 * q^39 - 56 * q^40 - 8 * q^41 - 8 * q^44 - 16 * q^45 - 8 * q^46 - 44 * q^50 - 48 * q^51 + 24 * q^54 + 28 * q^55 - 56 * q^56 + 24 * q^59 + 32 * q^60 + 24 * q^61 + 64 * q^64 - 8 * q^65 - 8 * q^66 - 40 * q^69 + 80 * q^70 - 40 * q^71 + 128 * q^74 + 28 * q^75 - 8 * q^76 + 48 * q^80 + 200 * q^84 - 24 * q^85 + 24 * q^86 - 8 * q^89 + 80 * q^90 - 8 * q^91 + 120 * q^94 - 8 * q^95 - 56 * q^96 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{8}\right)$

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 $

$2$	−1.26433	+	0.633607i	−0.894020	+	0.448028i
$2$	−1.26433	+	0.633607i	−0.894020	+	0.448028i
$3$	2.72675	+	1.12946i	1.57429	+	0.652092i	0.987496	−	0.157644i	$-0.0503898\pi$
$3$	2.72675	+	1.12946i	1.57429	+	0.652092i	0.586794	+	0.809736i	$0.300390\pi$
$4$	1.19708	−	1.60218i	0.598542	−	0.801092i
$5$	−1.63639	+	1.52389i	−0.731815	+	0.681504i
$5$	−1.63639	+	1.52389i	−0.731815	+	0.681504i
$6$	−4.16316	+	0.299677i	−1.69960	+	0.122343i
$7$	0.911488	+	0.911488i	0.344510	+	0.344510i	0.858060	−	0.513550i	$-0.171670\pi$
$7$	0.911488	+	0.911488i	0.344510	+	0.344510i	−0.513550	+	0.858060i	$0.671670\pi$
$8$	−0.498360	+	2.78418i	−0.176197	+	0.984355i
$9$	4.03817	+	4.03817i	1.34606	+	1.34606i
$10$	1.10339	−	2.96353i	0.348924	−	0.937151i
$11$	−1.71789	−	4.14736i	−0.517964	−	1.25048i	−0.939152	−	0.343502i	$-0.888387\pi$
$11$	−1.71789	−	4.14736i	−0.517964	−	1.25048i	0.421188	−	0.906973i	$-0.361613\pi$
$12$	5.07375	−	3.01670i	1.46466	−	0.870846i
$13$	0.122394	−	0.295486i	0.0339461	−	0.0819531i	−0.905997	−	0.423283i	$-0.860877\pi$
$13$	0.122394	−	0.295486i	0.0339461	−	0.0819531i	0.939943	+	0.341330i	$0.110877\pi$
$14$	−1.72995	−	0.574901i	−0.462349	−	0.153649i
$15$	−6.18319	+	2.30703i	−1.59649	+	0.595673i
$16$	−1.13398	−	3.83589i	−0.283495	−	0.958974i
$17$	−1.24150			−0.301108			−0.150554	−	0.988602i	$-0.548106\pi$
$17$	−1.24150			−0.301108			−0.150554	+	0.988602i	$0.548106\pi$
$18$	−7.66422	−	2.54699i	−1.80647	−	0.600331i
$19$	5.63014	+	2.33208i	1.29164	+	0.535016i	0.919475	−	0.393149i	$-0.128614\pi$
$19$	5.63014	+	2.33208i	1.29164	+	0.535016i	0.372168	+	0.928165i	$0.378614\pi$
$20$	0.482655	+	4.44601i	0.107925	+	0.994159i
$21$	1.45591	+	3.51489i	0.317707	+	0.767011i
$22$	4.79979	+	4.15518i	1.02332	+	0.885887i
$23$	−2.85230	+	2.85230i	−0.594745	+	0.594745i	−0.938909	−	0.344165i	$-0.888162\pi$
$23$	−2.85230	+	2.85230i	−0.594745	+	0.594745i	0.344165	+	0.938909i	$0.388162\pi$
$24$	−4.50351	+	7.02888i	−0.919275	+	1.43476i
$25$	0.355529	−	4.98734i	0.0711058	−	0.997469i
$26$	0.0324747	+	0.451143i	0.00636882	+	0.0884765i
$27$	3.06178	+	7.39179i	0.589239	+	1.42255i
$28$	2.55150	−	0.369243i	0.482188	−	0.0697804i
$29$	2.86983	−	6.92838i	0.532914	−	1.28657i	−0.396672	−	0.917961i	$-0.629835\pi$
$29$	2.86983	−	6.92838i	0.532914	−	1.28657i	0.929585	−	0.368607i	$-0.120165\pi$
$30$	6.35586	−	6.83457i	1.16042	−	1.24782i
$31$	−7.15524			−1.28512			−0.642560	−	0.766236i	$-0.722127\pi$
$31$	−7.15524			−1.28512			−0.642560	+	0.766236i	$0.722127\pi$
$32$	3.86418	+	4.13136i	0.683097	+	0.730327i
$33$		−	13.2491i		−	2.30637i
$34$	1.56967	−	0.786622i	0.269196	−	0.134905i
$35$	−2.88055	−	0.102542i	−0.486903	−	0.0173327i
$36$	11.3039	−	1.63586i	1.88399	−	0.272644i
$37$	−2.32483	−	5.61264i	−0.382200	−	0.922713i	−0.991540	−	0.129803i	$-0.958565\pi$
$37$	−2.32483	−	5.61264i	−0.382200	−	0.922713i	0.609340	−	0.792909i	$-0.291435\pi$
$38$	−8.59601	+	0.618768i	−1.39446	+	0.100377i
$39$	0.667478	−	0.667478i	0.106882	−	0.106882i
$40$	−3.42726	−	5.31544i	−0.541898	−	0.840444i
$41$	1.47276	+	1.47276i	0.230007	+	0.230007i	0.812695	−	0.582689i	$-0.197999\pi$
$41$	1.47276	+	1.47276i	0.230007	+	0.230007i	−0.582689	+	0.812695i	$0.697999\pi$
$42$	−4.06782	−	3.52152i	−0.627678	−	0.543382i
$43$	4.82876	−	2.00014i	0.736378	−	0.305018i	0.0172083	−	0.999852i	$-0.494522\pi$
$43$	4.82876	−	2.00014i	0.736378	−	0.305018i	0.719170	+	0.694834i	$0.244522\pi$
$44$	−8.70129	−	2.21236i	−1.31177	−	0.333526i
$45$	−12.7617	−	0.454292i	−1.90241	−	0.0677219i
$46$	1.79902	−	5.41349i	0.265251	−	0.798176i
$47$	0.547863			0.0799140			0.0399570	−	0.999201i	$-0.487278\pi$
$47$	0.547863			0.0799140			0.0399570	+	0.999201i	$0.487278\pi$
$48$	1.24040	−	11.7403i	0.179036	−	1.69457i
$49$		−	5.33838i		−	0.762625i
$50$	2.71051	+	6.53094i	0.383324	+	0.923614i
$51$	−3.38526	−	1.40222i	−0.474031	−	0.196350i
$52$	−0.326907	−	0.549820i	−0.0453338	−	0.0762463i
$53$	9.59054	−	3.97253i	1.31736	−	0.545669i	0.390338	−	0.920672i	$-0.372358\pi$
$53$	9.59054	−	3.97253i	1.31736	−	0.545669i	0.927024	+	0.375003i	$0.122358\pi$
$54$	−8.55460	−	7.40573i	−1.16413	−	1.00779i
$55$	9.13125	+	4.16881i	1.23126	+	0.562122i
$56$	−2.99199	+	2.08350i	−0.399822	+	0.278419i
$57$	12.7180	+	12.7180i	1.68454	+	1.68454i
$58$	0.761447	+	10.5781i	0.0999829	+	1.38898i
$59$	−1.54689	+	0.640744i	−0.201388	+	0.0834178i	−0.481098	−	0.876667i	$-0.659762\pi$
$59$	−1.54689	+	0.640744i	−0.201388	+	0.0834178i	0.279710	+	0.960085i	$0.409762\pi$
$60$	−3.70550	+	12.6683i	−0.478378	+	1.63547i
$61$	0.461455	−	1.11405i	0.0590832	−	0.142639i	−0.891581	−	0.452861i	$-0.850403\pi$
$61$	0.461455	−	1.11405i	0.0590832	−	0.142639i	0.950664	+	0.310222i	$0.100403\pi$
$62$	9.04662	−	4.53361i	1.14892	−	0.575769i
$63$			7.36150i			0.927462i
$64$	−7.50328	−	2.77504i	−0.937909	−	0.346880i
$65$	0.250003	+	0.670045i	0.0310091	+	0.0831089i
$66$	8.39472	+	16.7513i	1.03332	+	2.06194i
$67$	−14.5683	−	6.03439i	−1.77980	−	0.737218i	−0.992731	−	0.120355i	$-0.961597\pi$
$67$	−14.5683	−	6.03439i	−1.77980	−	0.737218i	−0.787071	−	0.616863i	$-0.788403\pi$
$68$	−1.48618	+	1.98911i	−0.180225	+	0.241215i
$69$	−10.9990	+	4.55595i	−1.32413	+	0.548472i
$70$	3.70696	−	1.69549i	0.443066	−	0.202650i
$71$	−0.198299	+	0.198299i	−0.0235338	+	0.0235338i	−0.718776	−	0.695242i	$-0.755297\pi$
$71$	−0.198299	+	0.198299i	−0.0235338	+	0.0235338i	0.695242	+	0.718776i	$0.255297\pi$
$72$	−13.2555	+	9.23053i	−1.56217	+	1.08783i
$73$	−8.93915	+	8.93915i	−1.04625	+	1.04625i	−0.0473708	+	0.998877i	$0.515084\pi$
$73$	−8.93915	+	8.93915i	−1.04625	+	1.04625i	−0.998877	+	0.0473708i	$0.984916\pi$
$74$	6.49558	+	5.62323i	0.755095	+	0.653687i
$75$	6.60243	−	13.1977i	0.762383	−	1.52394i
$76$	10.4762	−	6.22882i	1.20170	−	0.714495i
$77$	2.21443	−	5.34611i	0.252358	−	0.609246i
$78$	−0.420996	+	1.26683i	−0.0476685	+	0.143441i
$79$			15.6241i			1.75785i	0.476961	+	0.878924i	$0.341738\pi$
$79$			15.6241i			1.75785i	−0.476961	+	0.878924i	$0.658262\pi$
$80$	7.70111	+	4.54895i	0.861010	+	0.508588i
$81$			6.48118i			0.720131i
$82$	−2.79521	−	0.928910i	−0.308680	−	0.102581i
$83$	−3.23636	+	7.81327i	−0.355237	+	0.857618i	0.640719	+	0.767775i	$0.278636\pi$
$83$	−3.23636	+	7.81327i	−0.355237	+	0.857618i	−0.995956	+	0.0898423i	$0.971364\pi$
$84$	7.37435	+	1.87497i	0.804607	+	0.204576i
$85$	2.03157	−	1.89190i	0.220355	−	0.205206i
$86$	−4.83786	+	5.58838i	−0.521680	+	0.602610i
$87$	15.6506	−	15.6506i	1.67792	−	1.67792i
$88$	12.4031	−	2.71604i	1.32218	−	0.289531i
$89$	−0.464872	+	0.464872i	−0.0492763	+	0.0492763i	−0.731316	−	0.682039i	$-0.761093\pi$
$89$	−0.464872	+	0.464872i	−0.0492763	+	0.0492763i	0.682039	+	0.731316i	$0.261093\pi$
$90$	16.4230	−	7.51156i	1.73113	−	0.791788i
$91$	0.380893	−	0.157771i	0.0399285	−	0.0165389i
$92$	1.15546	+	7.98434i	0.120465	+	0.832425i
$93$	−19.5106	−	8.08154i	−2.02315	−	0.838016i
$94$	−0.692682	+	0.347130i	−0.0714447	+	0.0358037i
$95$	−12.7669	+	4.76352i	−1.30986	+	0.488727i
$96$	5.87047	+	15.6296i	0.599152	+	1.59519i
$97$			11.6763i			1.18555i	0.805369	+	0.592774i	$0.201967\pi$
$97$			11.6763i			1.18555i	−0.805369	+	0.592774i	$0.798033\pi$
$98$	3.38243	+	6.74950i	0.341678	+	0.681802i
$99$	9.81061	−	23.6849i	0.986003	−	2.38042i
$100$	−7.56504	−	6.53989i	−0.756504	−	0.653989i
$101$	5.25789	−	2.17789i	0.523180	−	0.216708i	−0.105433	−	0.994426i	$-0.533623\pi$
$101$	5.25789	−	2.17789i	0.523180	−	0.216708i	0.628613	+	0.777718i	$0.283623\pi$
$102$	5.16855	−	0.372049i	0.511763	−	0.0368383i
$103$	0.141841	+	0.141841i	0.0139760	+	0.0139760i	0.714060	−	0.700084i	$-0.246854\pi$
$103$	0.141841	+	0.141841i	0.0139760	+	0.0139760i	−0.700084	+	0.714060i	$0.746854\pi$
$104$	0.761689	+	0.488026i	0.0746898	+	0.0478549i
$105$	−7.73874	−	3.53307i	−0.755223	−	0.344792i
$106$	−9.60862	+	11.0992i	−0.933272	+	1.07805i
$107$	−11.1859	+	4.63333i	−1.08138	+	0.447921i	−0.850992	−	0.525178i	$-0.823999\pi$
$107$	−11.1859	+	4.63333i	−1.08138	+	0.447921i	−0.230385	+	0.973100i	$0.573999\pi$
$108$	15.5082	+	3.94306i	1.49228	+	0.379421i
$109$	7.48703	+	3.10123i	0.717128	+	0.297044i	0.711250	−	0.702939i	$-0.248129\pi$
$109$	7.48703	+	3.10123i	0.717128	+	0.297044i	0.00587723	+	0.999983i	$0.498129\pi$
$110$	−14.1863	+	0.514854i	−1.35261	+	0.0490894i
$111$		−	17.9301i		−	1.70185i
$112$	2.46276	−	4.52998i	0.232709	−	0.428043i
$113$	−1.74718			−0.164361			−0.0821803	−	0.996617i	$-0.526188\pi$
$113$	−1.74718			−0.164361			−0.0821803	+	0.996617i	$0.526188\pi$
$114$	−24.1380	−	8.02160i	−2.26073	−	0.751291i
$115$	0.320881	−	9.01404i	0.0299223	−	0.840564i
$116$	−7.66510	−	12.8918i	−0.711687	−	1.19698i
$117$	1.68747	−	0.698975i	0.156007	−	0.0646202i
$118$	1.54981	−	1.79024i	0.142672	−	0.164805i
$119$	−1.13161	−	1.13161i	−0.103735	−	0.103735i
$120$	−3.34174	−	18.3648i	−0.305057	−	1.67647i
$121$	−6.47126	+	6.47126i	−0.588296	+	0.588296i
$122$	0.122437	+	1.70091i	0.0110849	+	0.153993i
$123$	2.35243	+	5.67927i	0.212112	+	0.512083i
$124$	−8.56542	+	11.4640i	−0.769198	+	1.02950i
$125$	7.01837	+	8.70301i	0.627742	+	0.778421i
$126$	−4.66430	−	9.30740i	−0.415529	−	0.829169i
$127$		−	4.51490i		−	0.400633i	−0.979731	−	0.200316i	$-0.935803\pi$
$127$		−	4.51490i		−	0.400633i	0.979731	−	0.200316i	$-0.0641970\pi$
$128$	11.2449	−	1.24555i	0.993921	−	0.110092i
$129$	15.4259			1.35817
$130$	−0.740633	−	0.688757i	−0.0649578	−	0.0604080i
$131$	−3.70265	+	8.93898i	−0.323502	+	0.781002i	0.675544	+	0.737320i	$0.263909\pi$
$131$	−3.70265	+	8.93898i	−0.323502	+	0.781002i	−0.999045	+	0.0436823i	$0.986091\pi$
$132$	−21.2275	−	15.8603i	−1.84762	−	1.38046i
$133$	3.00614	+	7.25747i	0.260666	+	0.629303i
$134$	22.2426	−	1.60110i	1.92147	−	0.138314i
$135$	−16.2745	−	7.43002i	−1.40069	−	0.639474i
$136$	0.618713	−	3.45655i	0.0530542	−	0.296397i
$137$	−3.53625	+	3.53625i	−0.302123	+	0.302123i	−0.841844	−	0.539721i	$-0.818530\pi$
$137$	−3.53625	+	3.53625i	−0.302123	+	0.302123i	0.539721	+	0.841844i	$0.318530\pi$
$138$	11.0198	−	12.7293i	0.938066	−	1.08359i
$139$	3.20996	+	7.74953i	0.272265	+	0.657306i	0.999579	−	0.0289983i	$-0.00923175\pi$
$139$	3.20996	+	7.74953i	0.272265	+	0.657306i	−0.727314	+	0.686305i	$0.759232\pi$
$140$	−3.61256	+	4.49242i	−0.305317	+	0.379679i
$141$	1.49389	+	0.618788i	0.125808	+	0.0521113i
$142$	0.125073	−	0.376361i	0.0104959	−	0.0315835i
$143$	−1.43575			−0.120063
$144$	10.9108	−	20.0692i	0.909233	−	1.67244i
$145$	5.86192	+	15.7108i	0.486806	+	1.30471i
$146$	5.63817	−	16.9660i	0.466618	−	1.40411i
$147$	6.02947	−	14.5564i	0.497302	−	1.20059i
$148$	−11.7755	−	2.99400i	−0.967940	−	0.246105i
$149$	−1.31432	−	3.17304i	−0.107673	−	0.259945i	0.860855	−	0.508850i	$-0.169929\pi$
$149$	−1.31432	−	3.17304i	−0.107673	−	0.259945i	−0.968528	+	0.248905i	$0.919929\pi$
$150$	0.0144701	+	20.8696i	0.00118148	+	1.70400i
$151$	1.48714	+	1.48714i	0.121022	+	0.121022i	0.765024	−	0.644002i	$-0.222727\pi$
$151$	1.48714	+	1.48714i	0.121022	+	0.121022i	−0.644002	+	0.765024i	$0.722727\pi$
$152$	−9.29876	+	14.5131i	−0.754229	+	1.17717i
$153$	−5.01339	−	5.01339i	−0.405308	−	0.405308i
$154$	0.587552	+	8.16235i	0.0473463	+	0.657741i
$155$	11.7087	−	10.9038i	0.940469	−	0.875813i
$156$	−0.270395	−	1.86845i	−0.0216489	−	0.149596i
$157$	−7.36408	−	3.05030i	−0.587718	−	0.243441i	0.0689506	−	0.997620i	$-0.478035\pi$
$157$	−7.36408	−	3.05030i	−0.587718	−	0.243441i	−0.656668	+	0.754179i	$0.728035\pi$
$158$	−9.89954	−	19.7541i	−0.787565	−	1.57155i
$159$	30.6378			2.42974
$160$	−12.6190	−	0.871919i	−0.997621	−	0.0689312i
$161$	−5.19967			−0.409791
$162$	−4.10652	−	8.19438i	−0.322639	−	0.643811i
$163$	−0.292636	−	0.121214i	−0.0229210	−	0.00949419i	0.371193	−	0.928556i	$-0.378949\pi$
$163$	−0.292636	−	0.121214i	−0.0229210	−	0.00949419i	−0.394114	+	0.919061i	$0.628949\pi$
$164$	4.12265	−	0.596614i	0.321925	−	0.0465877i
$165$	20.1901	+	21.6807i	1.57180	+	1.68784i
$166$	−0.858699	−	11.9292i	−0.0666480	−	0.925883i
$167$	2.62579	+	2.62579i	0.203190	+	0.203190i	0.801365	−	0.598175i	$-0.204107\pi$
$167$	2.62579	+	2.62579i	0.203190	+	0.203190i	−0.598175	+	0.801365i	$0.704107\pi$
$168$	−10.5116	+	2.30184i	−0.810990	+	0.177591i
$169$	9.12006	+	9.12006i	0.701543	+	0.701543i
$170$	−1.36986	+	3.67922i	−0.105064	+	0.282183i
$171$	13.3181	+	32.1528i	1.01846	+	2.45879i
$172$	2.57584	−	10.1309i	0.196406	−	0.772473i
$173$	−1.46890	+	3.54623i	−0.111678	+	0.269615i	−0.969831	−	0.243780i	$-0.921612\pi$
$173$	−1.46890	+	3.54623i	−0.111678	+	0.269615i	0.858152	+	0.513395i	$0.171612\pi$
$174$	−9.87127	+	29.7039i	−0.748339	+	2.25185i
$175$	4.86997	−	4.22185i	0.368135	−	0.319142i
$176$	−13.9608	+	11.2927i	−1.05233	+	0.851218i
$177$	−4.94168			−0.371440
$178$	0.293207	−	0.882299i	0.0219768	−	0.0661311i
$179$	−7.28940	−	3.01937i	−0.544836	−	0.225678i	0.0932514	−	0.995643i	$-0.470274\pi$
$179$	−7.28940	−	3.01937i	−0.544836	−	0.225678i	−0.638087	+	0.769964i	$0.720274\pi$
$180$	−16.0047	+	19.9028i	−1.19292	+	1.48347i
$181$	−3.39354	−	8.19274i	−0.252240	−	0.608961i	0.746144	−	0.665784i	$-0.231903\pi$
$181$	−3.39354	−	8.19274i	−0.252240	−	0.608961i	−0.998384	+	0.0568230i	$0.981903\pi$
$182$	−0.381612	+	0.440812i	−0.0282869	+	0.0326752i
$183$	2.51654	−	2.51654i	0.186028	−	0.186028i
$184$	−6.51982	−	9.36276i	−0.480648	−	0.690232i
$185$	12.3574	+	5.64167i	0.908532	+	0.414784i
$186$	29.7884	−	2.14426i	2.18419	−	0.157225i
$187$	2.13276	+	5.14894i	0.155963	+	0.376528i
$188$	0.655838	−	0.877777i	0.0478319	−	0.0640184i
$189$	−3.94675	+	9.52830i	−0.287084	+	0.693082i
$190$	13.1235	−	14.1119i	0.952076	−	1.02378i
$191$	4.55654			0.329699			0.164850	−	0.986319i	$-0.447286\pi$
$191$	4.55654			0.329699			0.164850	+	0.986319i	$0.447286\pi$
$192$	−17.3253	−	16.0415i	−1.25034	−	1.15769i
$193$		−	5.56099i		−	0.400289i	−0.979766	−	0.200144i	$-0.935859\pi$
$193$		−	5.56099i		−	0.400289i	0.979766	−	0.200144i	$-0.0641412\pi$
$194$	−7.39819	−	14.7627i	−0.531159	−	1.05990i
$195$	−0.0750908	+	2.10941i	−0.00537737	+	0.151058i
$196$	−8.55306	−	6.39049i	−0.610933	−	0.456463i
$197$	−4.62793	−	11.1728i	−0.329727	−	0.796030i	−0.998612	−	0.0526650i	$-0.983228\pi$
$197$	−4.62793	−	11.1728i	−0.329727	−	0.796030i	0.668886	−	0.743365i	$-0.266772\pi$
$198$	2.60303	+	36.1617i	0.184990	+	2.56990i
$199$	−10.8973	+	10.8973i	−0.772491	+	0.772491i	−0.978541	−	0.206051i	$-0.933939\pi$
$199$	−10.8973	+	10.8973i	−0.772491	+	0.772491i	0.206051	+	0.978541i	$0.433939\pi$
$200$	13.7085	+	3.47535i	0.969335	+	0.245744i
$201$	−32.9085	−	32.9085i	−2.32119	−	2.32119i
$202$	−5.26781	+	6.08502i	−0.370642	+	0.428140i
$203$	8.93095	−	3.69932i	0.626830	−	0.259641i
$204$	−6.29905	+	3.74523i	−0.441021	+	0.262218i
$205$	−4.65433	−	0.165685i	−0.325072	−	0.0115719i
$206$	−0.269207	−	0.0894632i	−0.0187565	−	0.00623320i
$207$	−23.0361			−1.60112
$208$	−1.27225	−	0.134416i	−0.0882144	−	0.00932009i
$209$		−	27.3565i		−	1.89229i
$210$	12.0229	−	0.436339i	0.829661	−	0.0301102i
$211$	11.9158	+	4.93570i	0.820320	+	0.339787i	0.753063	−	0.657948i	$-0.228575\pi$
$211$	11.9158	+	4.93570i	0.820320	+	0.339787i	0.0672564	+	0.997736i	$0.478575\pi$
$212$	5.11596	−	20.1212i	0.351365	−	1.38193i
$213$	−0.764684	+	0.316742i	−0.0523953	+	0.0217028i
$214$	11.2070	−	12.9455i	0.766091	−	0.884938i
$215$	−4.85373	+	10.6315i	−0.331022	+	0.725061i
$216$	−22.1059	+	4.84076i	−1.50412	+	0.329372i
$217$	−6.52192	−	6.52192i	−0.442737	−	0.442737i
$218$	−11.4311	+	0.822845i	−0.774210	+	0.0557301i
$219$	−34.4712	+	14.2784i	−2.32935	+	0.964848i
$220$	17.6101	−	9.63952i	1.18727	−	0.649896i
$221$	−0.151952	+	0.366846i	−0.0102214	+	0.0246767i
$222$	11.3606	+	22.6696i	0.762475	+	1.52148i
$223$			18.1259i			1.21380i	0.794779	+	0.606900i	$0.207587\pi$
$223$			18.1259i			1.21380i	−0.794779	+	0.606900i	$0.792413\pi$
$224$	−0.243526	+	7.28784i	−0.0162713	+	0.486939i
$225$	21.5755	−	18.7041i	1.43836	−	1.24694i
$226$	2.20902	−	1.10702i	0.146942	−	0.0736382i
$227$	−0.0863798	−	0.0357797i	−0.00573323	−	0.00237478i	0.379815	−	0.925062i	$-0.375988\pi$
$227$	−0.0863798	−	0.0357797i	−0.00573323	−	0.00237478i	−0.385548	+	0.922688i	$0.625988\pi$
$228$	35.6011	−	5.15205i	2.35774	−	0.341203i
$229$	−15.7849	+	6.53832i	−1.04310	+	0.432064i	−0.837422	−	0.546556i	$-0.815938\pi$
$229$	−15.7849	+	6.53832i	−1.04310	+	0.432064i	−0.205673	+	0.978621i	$0.565938\pi$
$230$	5.30566	+	11.6001i	0.349845	+	0.764886i
$231$	12.0764	−	12.0764i	0.794569	−	0.794569i
$232$	17.8596	+	11.4429i	1.17254	+	0.751265i
$233$	20.7793	−	20.7793i	1.36130	−	1.36130i	0.489030	−	0.872267i	$-0.337351\pi$
$233$	20.7793	−	20.7793i	1.36130	−	1.36130i	0.872267	−	0.489030i	$-0.162649\pi$
$234$	−1.69066	+	1.95293i	−0.110522	+	0.127667i
$235$	−0.896516	+	0.834882i	−0.0584823	+	0.0544617i
$236$	−0.825171	+	3.24543i	−0.0537141	+	0.211260i
$237$	−17.6468	+	42.6030i	−1.14628	+	2.76736i
$238$	2.14773	+	0.713738i	0.139217	+	0.0462648i
$239$		−	10.9572i		−	0.708766i	−0.935100	−	0.354383i	$-0.884691\pi$
$239$		−	10.9572i		−	0.708766i	0.935100	−	0.354383i	$-0.115309\pi$
$240$	15.8612	+	21.1019i	1.02383	+	1.36212i
$241$		−	1.41493i		−	0.0911434i	−0.998961	−	0.0455717i	$-0.985489\pi$
$241$		−	1.41493i		−	0.0911434i	0.998961	−	0.0455717i	$-0.0145109\pi$
$242$	4.08160	−	12.2821i	0.262375	−	0.789521i
$243$	1.86512	−	4.50280i	0.119647	−	0.288855i
$244$	−1.23251	−	2.07295i	−0.0789035	−	0.132707i
$245$	8.13509	+	8.73566i	0.519732	+	0.558101i
$246$	−6.57269	−	5.68998i	−0.419059	−	0.362780i
$247$	1.37820	−	1.37820i	0.0876925	−	0.0876925i
$248$	3.56588	−	19.9214i	0.226434	−	1.26501i
$249$	−17.6495	+	17.6495i	−1.11849	+	1.11849i
$250$	−14.3879	−	6.55663i	−0.909968	−	0.414678i
$251$	3.03972	−	1.25910i	0.191866	−	0.0794734i	−0.284682	−	0.958622i	$-0.591888\pi$
$251$	3.03972	−	1.25910i	0.191866	−	0.0794734i	0.476548	+	0.879149i	$0.341888\pi$
$252$	11.7945	+	8.81233i	0.742982	+	0.555125i
$253$	16.7294	+	6.92956i	1.05177	+	0.435658i
$254$	2.86068	+	5.70835i	0.179495	+	0.358174i
$255$	7.67642	−	2.86418i	0.480716	−	0.179362i
$256$	−13.4282	+	8.69966i	−0.839261	+	0.543729i
$257$		−	10.8572i		−	0.677255i	−0.940920	−	0.338628i	$-0.890037\pi$
$257$		−	10.8572i		−	0.677255i	0.940920	−	0.338628i	$-0.109963\pi$
$258$	−19.5035	+	9.77395i	−1.21423	+	0.608500i
$259$	2.99680	−	7.23491i	0.186212	−	0.449556i
$260$	1.37281	+	0.401549i	0.0851381	+	0.0249030i
$261$	39.5669	−	16.3891i	2.44913	−	1.01446i
$262$	−0.982418	−	13.6479i	−0.0606940	−	0.843169i
$263$	2.14576	+	2.14576i	0.132313	+	0.132313i	0.770162	−	0.637849i	$-0.220175\pi$
$263$	2.14576	+	2.14576i	0.132313	+	0.132313i	−0.637849	+	0.770162i	$0.720175\pi$
$264$	36.8878	+	6.60282i	2.27029	+	0.406375i
$265$	−9.64014	+	21.1155i	−0.592189	+	1.29712i
$266$	−8.39916	−	7.27116i	−0.514986	−	0.445823i
$267$	−1.79264	+	0.742536i	−0.109708	+	0.0454425i
$268$	−27.1077	+	16.1174i	−1.65586	+	0.984528i
$269$	13.0879	+	5.42120i	0.797986	+	0.330536i	0.744149	−	0.668013i	$-0.232855\pi$
$269$	13.0879	+	5.42120i	0.797986	+	0.330536i	0.0538363	+	0.998550i	$0.482855\pi$
$270$	25.2841	−	0.917617i	1.53874	−	0.0558444i
$271$		−	15.8907i		−	0.965289i	−0.875816	−	0.482644i	$-0.839676\pi$
$271$		−	15.8907i		−	0.965289i	0.875816	−	0.482644i	$-0.160324\pi$
$272$	1.40784	+	4.76226i	0.0853625	+	0.288754i
$273$	1.21680			0.0736439
$274$	2.23041	−	6.71161i	0.134744	−	0.405463i
$275$	−21.2951	+	7.09321i	−1.28414	+	0.427737i
$276$	−5.86731	+	23.0763i	−0.353170	+	1.38903i
$277$	15.0380	−	6.22892i	0.903543	−	0.374260i	0.117962	−	0.993018i	$-0.462364\pi$
$277$	15.0380	−	6.22892i	0.903543	−	0.374260i	0.785581	+	0.618758i	$0.212364\pi$
$278$	−8.96862	−	7.76414i	−0.537902	−	0.465662i
$279$	−28.8941	−	28.8941i	−1.72984	−	1.72984i
$280$	1.72105	−	7.96887i	0.102852	−	0.476231i
$281$	−7.62571	+	7.62571i	−0.454912	+	0.454912i	−0.896981	−	0.442069i	$-0.854245\pi$
$281$	−7.62571	+	7.62571i	−0.454912	+	0.454912i	0.442069	+	0.896981i	$0.354245\pi$
$282$	−2.28084	+	0.164182i	−0.135822	+	0.00977690i
$283$	8.28981	+	20.0134i	0.492778	+	1.18967i	0.953300	+	0.302024i	$0.0976622\pi$
$283$	8.28981	+	20.0134i	0.492778	+	1.18967i	−0.460522	+	0.887648i	$0.652338\pi$
$284$	0.0803309	+	0.555093i	0.00476676	+	0.0329387i
$285$	−40.1924	−	1.43077i	−2.38079	−	0.0847514i
$286$	1.81527	−	0.909700i	0.107339	−	0.0537917i
$287$			2.68481i			0.158479i
$288$	−1.07890	+	32.2874i	−0.0635746	+	1.90255i
$289$	−15.4587			−0.909334
$290$	−17.3659	−	16.1496i	−1.01976	−	0.948335i
$291$	−13.1879	+	31.8383i	−0.773087	+	1.86640i
$292$	3.62124	+	25.0231i	0.211917	+	1.46436i
$293$	−7.30714	−	17.6410i	−0.426888	−	1.03060i	−0.980269	−	0.197670i	$-0.936663\pi$
$293$	−7.30714	−	17.6410i	−0.426888	−	1.03060i	0.553381	−	0.832928i	$-0.313337\pi$
$294$	1.59979	+	22.2245i	0.0933017	+	1.29616i
$295$	1.55489	−	3.40580i	0.0905295	−	0.198293i
$296$	16.7852	−	3.67563i	0.975619	−	0.213642i
$297$	25.3966	−	25.3966i	1.47366	−	1.47366i
$298$	3.67220	+	3.17902i	0.212725	+	0.184156i
$299$	0.493709	+	1.19192i	0.0285519	+	0.0689304i
$300$	−13.2414	−	26.3770i	−0.764495	−	1.52288i
$301$	6.22446	+	2.57825i	0.358772	+	0.148608i
$302$	−2.82251	−	0.937980i	−0.162417	−	0.0539747i
$303$	16.7968			0.964950
$304$	2.56115	−	24.2412i	0.146892	−	1.39033i
$305$	0.942569	+	2.52622i	0.0539713	+	0.144651i
$306$	9.51512	+	3.16208i	0.543943	+	0.180764i
$307$	0.0878173	−	0.212010i	0.00501200	−	0.0121000i	−0.921354	−	0.388725i	$-0.872916\pi$
$307$	0.0878173	−	0.212010i	0.00501200	−	0.0121000i	0.926366	+	0.376625i	$0.122916\pi$
$308$	−5.91459	−	9.94766i	−0.337015	−	0.566821i
$309$	0.226562	+	0.546970i	0.0128887	+	0.0311160i
$310$	−7.89506	+	21.2048i	−0.448409	+	1.20435i
$311$	0.0242199	+	0.0242199i	0.00137338	+	0.00137338i	0.707793	−	0.706420i	$-0.249691\pi$
$311$	0.0242199	+	0.0242199i	0.00137338	+	0.00137338i	−0.706420	+	0.707793i	$0.749691\pi$
$312$	1.52573	+	2.19102i	0.0863775	+	0.124042i
$313$	2.33873	+	2.33873i	0.132193	+	0.132193i	0.770107	−	0.637914i	$-0.220203\pi$
$313$	2.33873	+	2.33873i	0.132193	+	0.132193i	−0.637914	+	0.770107i	$0.720203\pi$
$314$	11.2434	−	0.809333i	0.634499	−	0.0456733i
$315$	−11.2181	−	12.0463i	−0.632068	−	0.678730i
$316$	25.0327	+	18.7034i	1.40820	+	1.05215i
$317$	22.3337	+	9.25092i	1.25438	+	0.519583i	0.908182	−	0.418576i	$-0.137471\pi$
$317$	22.3337	+	9.25092i	1.25438	+	0.519583i	0.346203	+	0.938160i	$0.387471\pi$
$318$	−38.7364	+	19.4123i	−2.17223	+	1.08859i
$319$	−33.6645			−1.88485
$320$	16.5071	−	6.89311i	0.922776	−	0.385336i
$321$	−35.7342			−1.99449
$322$	6.57412	−	3.29455i	0.366361	−	0.183598i
$323$	−6.98981	−	2.89528i	−0.388924	−	0.161097i
$324$	10.3840	+	7.75852i	0.576891	+	0.431029i
$325$	−1.43018	−	0.715477i	−0.0793319	−	0.0396875i
$326$	0.446791	−	0.0321614i	0.0247455	−	0.00178126i
$327$	16.9126	+	16.9126i	0.935267	+	0.935267i
$328$	−4.83439	+	3.36646i	−0.266934	+	0.185882i
$329$	0.499371	+	0.499371i	0.0275312	+	0.0275312i
$330$	−39.2641	−	14.6190i	−2.16142	−	0.804749i
$331$	−7.03076	−	16.9738i	−0.386446	−	0.932962i	−0.990687	−	0.136161i	$-0.956524\pi$
$331$	−7.03076	−	16.9738i	−0.386446	−	0.932962i	0.604241	−	0.796802i	$-0.293476\pi$
$332$	8.64409	+	14.5384i	0.474406	+	0.797897i
$333$	13.2767	−	32.0529i	0.727561	−	1.75649i
$334$	−4.98360	−	1.65616i	−0.272691	−	0.0906210i
$335$	33.0351	−	12.3259i	1.80490	−	0.673434i
$336$	11.8318	−	9.57055i	0.645476	−	0.522116i
$337$	−21.5885			−1.17600			−0.588000	−	0.808861i	$-0.700085\pi$
$337$	−21.5885			−1.17600			−0.588000	+	0.808861i	$0.700085\pi$
$338$	−17.3093	−	5.75227i	−0.941504	−	0.312882i
$339$	−4.76412	−	1.97336i	−0.258751	−	0.107178i
$340$	−0.599215	−	5.51972i	−0.0324970	−	0.299349i
$341$	12.2919	+	29.6753i	0.665645	+	1.60701i
$342$	−37.2109	−	32.2135i	−2.01213	−	1.74191i
$343$	11.2463	−	11.2463i	0.607242	−	0.607242i
$344$	3.16227	+	14.4409i	0.170498	+	0.778601i
$345$	11.0559	−	24.2166i	0.595232	−	1.30378i
$346$	−0.389741	−	5.41433i	−0.0209526	−	0.291076i
$347$	−5.00934	−	12.0936i	−0.268915	−	0.649219i	0.730518	−	0.682894i	$-0.239279\pi$
$347$	−5.00934	−	12.0936i	−0.268915	−	0.649219i	−0.999433	+	0.0336749i	$0.989279\pi$
$348$	−6.34005	−	43.8102i	−0.339862	−	2.34847i
$349$	11.2976	−	27.2749i	0.604747	−	1.45999i	−0.263896	−	0.964551i	$-0.585008\pi$
$349$	11.2976	−	27.2749i	0.604747	−	1.45999i	0.868643	−	0.495438i	$-0.164992\pi$
$350$	−3.48228	+	8.42347i	−0.186135	+	0.450253i
$351$	2.55891			0.136585
$352$	10.4960	−	23.1234i	0.559437	−	1.23248i
$353$			3.10968i			0.165511i	0.996570	+	0.0827557i	$0.0263721\pi$
$353$			3.10968i			0.165511i	−0.996570	+	0.0827557i	$0.973628\pi$
$354$	6.24794	−	3.13109i	0.332074	−	0.166415i
$355$	0.0223086	−	0.626681i	0.00118402	−	0.0332608i
$356$	0.188319	+	1.30130i	0.00998089	+	0.0689687i
$357$	−1.80752	−	4.36373i	−0.0956639	−	0.230953i
$358$	11.1293	−	0.801125i	0.588204	−	0.0423408i
$359$	11.2439	−	11.2439i	0.593430	−	0.593430i	−0.345126	−	0.938556i	$-0.612164\pi$
$359$	11.2439	−	11.2439i	0.593430	−	0.593430i	0.938556	+	0.345126i	$0.112164\pi$
$360$	7.62477	−	35.3045i	0.401861	−	1.86071i
$361$	12.8249	+	12.8249i	0.674993	+	0.674993i
$362$	9.48155	+	8.20819i	0.498339	+	0.431413i
$363$	−24.9545	+	10.3365i	−1.30977	+	0.542525i
$364$	0.203183	−	0.799126i	0.0106497	−	0.0418856i
$365$	1.00565	−	28.2502i	0.0526380	−	1.47868i
$366$	−1.58725	+	4.77625i	−0.0829670	+	0.249659i
$367$	−20.1341			−1.05099			−0.525495	−	0.850797i	$-0.676120\pi$
$367$	−20.1341			−1.05099			−0.525495	+	0.850797i	$0.676120\pi$
$368$	14.1756	+	7.70666i	0.738952	+	0.401737i
$369$			11.8945i			0.619204i
$370$	−19.1984	+	0.696754i	−0.998080	+	0.0362225i
$371$	12.3626	+	5.12075i	0.641833	+	0.265856i
$372$	−36.3039	+	21.5852i	−1.88227	+	1.11914i
$373$	−30.9540	+	12.8216i	−1.60274	+	0.663876i	−0.991800	−	0.127803i	$-0.959207\pi$
$373$	−30.9540	+	12.8216i	−1.60274	+	0.663876i	−0.610938	+	0.791679i	$0.709207\pi$
$374$	−5.95893	−	5.15865i	−0.308129	−	0.266747i
$375$	9.30767	+	31.6579i	0.480646	+	1.63481i
$376$	−0.273033	+	1.52535i	−0.0140806	+	0.0786638i
$377$	−1.69599	−	1.69599i	−0.0873479	−	0.0873479i
$378$	−1.04719	−	14.5477i	−0.0538614	−	0.748251i
$379$	27.3360	−	11.3229i	1.40416	−	0.581620i	0.453329	−	0.891343i	$-0.350236\pi$
$379$	27.3360	−	11.3229i	1.40416	−	0.581620i	0.950827	+	0.309723i	$0.100236\pi$
$380$	−7.65105	+	26.1573i	−0.392491	+	1.34184i
$381$	5.09939	−	12.3110i	0.261250	−	0.630712i
$382$	−5.76099	+	2.88705i	−0.294758	+	0.147715i
$383$		−	12.4268i		−	0.634980i	−0.948262	−	0.317490i	$-0.897160\pi$
$383$		−	12.4268i		−	0.634980i	0.948262	−	0.317490i	$-0.102840\pi$
$384$	32.0689	+	9.30438i	1.63651	+	0.474812i
$385$	4.52321	+	12.1229i	0.230524	+	0.617838i
$386$	3.52348	+	7.03095i	0.179341	+	0.357866i
$387$	27.5763	+	11.4225i	1.40178	+	0.580636i
$388$	18.7076	+	13.9775i	0.949733	+	0.709600i
$389$	−8.34404	+	3.45622i	−0.423060	+	0.175237i	−0.584048	−	0.811719i	$-0.698532\pi$
$389$	−8.34404	+	3.45622i	−0.423060	+	0.175237i	0.160988	+	0.986956i	$0.448532\pi$
$390$	−1.24160	−	2.71458i	−0.0628709	−	0.137458i
$391$	3.54112	−	3.54112i	0.179082	−	0.179082i
$392$	14.8630	+	2.66043i	0.750694	+	0.134372i
$393$	−20.1924	+	20.1924i	−1.01857	+	1.01857i
$394$	12.9304	+	11.1939i	0.651426	+	0.563940i
$395$	−23.8094	−	25.5671i	−1.19798	−	1.28642i
$396$	−26.2034	−	44.0712i	−1.31677	−	2.21466i
$397$	10.2478	−	24.7404i	0.514323	−	1.24169i	−0.427022	−	0.904241i	$-0.640437\pi$
$397$	10.2478	−	24.7404i	0.514323	−	1.24169i	0.941345	−	0.337445i	$-0.109563\pi$
$398$	6.87324	−	20.6825i	0.344524	−	1.03672i
$399$			23.1846i			1.16068i
$400$	−19.5341	+	4.29178i	−0.976704	+	0.214589i
$401$		−	0.767428i		−	0.0383235i	−0.999816	−	0.0191618i	$-0.993900\pi$
$401$		−	0.767428i		−	0.0383235i	0.999816	−	0.0191618i	$-0.00609976\pi$
$402$	62.4585	+	20.7563i	3.11515	+	1.03523i
$403$	−0.875761	+	2.11427i	−0.0436248	+	0.105320i
$404$	2.80476	−	11.0312i	0.139542	−	0.548824i
$405$	−9.87660	−	10.6057i	−0.490772	−	0.527003i
$406$	−8.94779	+	10.3359i	−0.444071	+	0.512962i
$407$	−19.2838	+	19.2838i	−0.955864	+	0.955864i
$408$	5.59110	−	8.72634i	0.276801	−	0.432018i
$409$	7.98767	−	7.98767i	0.394965	−	0.394965i	−0.481488	−	0.876453i	$-0.659903\pi$
$409$	7.98767	−	7.98767i	0.394965	−	0.394965i	0.876453	+	0.481488i	$0.159903\pi$
$410$	5.98961	−	2.73954i	0.295806	−	0.135296i
$411$	−13.6365	+	5.64844i	−0.672640	+	0.278617i
$412$	0.397052	−	0.0574598i	0.0195613	−	0.00283084i
$413$	−1.99401	−	0.825944i	−0.0981186	−	0.0406421i
$414$	29.1254	−	14.5959i	1.43143	−	0.717347i
$415$	−6.61061	−	17.7174i	−0.324502	−	0.869712i
$416$	1.69371	−	0.636157i	0.0830411	−	0.0311902i
$417$			24.7565i			1.21233i
$418$	17.3333	+	34.5878i	0.847798	+	1.69174i
$419$	−10.2175	+	24.6673i	−0.499159	+	1.20508i	0.450778	+	0.892636i	$0.351147\pi$
$419$	−10.2175	+	24.6673i	−0.499159	+	1.20508i	−0.949937	+	0.312441i	$0.898853\pi$
$420$	−14.9245	+	8.16949i	−0.728243	+	0.398630i
$421$	−16.5677	+	6.86255i	−0.807459	+	0.334460i	−0.747940	−	0.663767i	$-0.768957\pi$
$421$	−16.5677	+	6.86255i	−0.807459	+	0.334460i	−0.0595191	+	0.998227i	$0.518957\pi$
$422$	−18.1929	+	1.30958i	−0.885616	+	0.0637494i
$423$	2.21237	+	2.21237i	0.107569	+	0.107569i
$424$	6.28069	+	28.6815i	0.305017	+	1.39290i
$425$	−0.441389	+	6.19178i	−0.0214105	+	0.300345i
$426$	0.766126	−	0.884978i	0.0371189	−	0.0428773i
$427$	1.43605	−	0.594833i	0.0694955	−	0.0287860i
$428$	−5.96696	+	23.4683i	−0.288424	+	1.13438i
$429$	−3.91492	−	1.62161i	−0.189014	−	0.0782923i
$430$	−0.599442	−	16.5171i	−0.0289077	−	0.796526i
$431$			21.8696i			1.05342i	0.850044	+	0.526712i	$0.176575\pi$
$431$			21.8696i			1.05342i	−0.850044	+	0.526712i	$0.823425\pi$
$432$	24.8821	−	20.1268i	1.19714	−	0.968351i
$433$	14.8749			0.714840			0.357420	−	0.933944i	$-0.383657\pi$
$433$	14.8749			0.714840			0.357420	+	0.933944i	$0.383657\pi$
$434$	12.3782	+	4.11355i	0.594174	+	0.197457i
$435$	−1.76068	+	49.4602i	−0.0844183	+	2.37144i
$436$	13.9313	−	8.28316i	0.667190	−	0.396692i
$437$	−22.7106	+	9.40704i	−1.08640	+	0.450000i
$438$	34.5362	−	39.8939i	1.65020	−	1.90621i
$439$	17.1499	+	17.1499i	0.818521	+	0.818521i	0.985894	−	0.167373i	$-0.0535283\pi$
$439$	17.1499	+	17.1499i	0.818521	+	0.818521i	−0.167373	+	0.985894i	$0.553528\pi$
$440$	−16.1574	+	23.3454i	−0.770272	+	1.11295i
$441$	21.5573	−	21.5573i	1.02654	−	1.02654i
$442$	−0.0403173	−	0.560094i	−0.00191770	−	0.0266409i
$443$	−9.75798	−	23.5578i	−0.463615	−	1.11927i	−0.966902	−	0.255147i	$-0.917876\pi$
$443$	−9.75798	−	23.5578i	−0.463615	−	1.11927i	0.503287	−	0.864119i	$-0.332124\pi$
$444$	−28.7273	−	21.4638i	−1.36334	−	1.01863i
$445$	0.0522978	−	1.46912i	0.00247915	−	0.0696431i
$446$	−11.4847	−	22.9172i	−0.543816	−	1.08516i
$447$		−	10.1365i		−	0.479442i
$448$	−4.30973	−	9.36857i	−0.203616	−	0.442623i
$449$	−28.0149			−1.32211			−0.661053	−	0.750339i	$-0.729890\pi$
$449$	−28.0149			−1.32211			−0.661053	+	0.750339i	$0.729890\pi$
$450$	−15.4276	+	37.3186i	−0.727262	+	1.75921i
$451$	3.57802	−	8.63811i	0.168483	−	0.406753i
$452$	−2.09152	+	2.79930i	−0.0983767	+	0.131668i
$453$	2.37540	+	5.73472i	0.111606	+	0.269441i
$454$	0.131883	−	0.00949337i	0.00618958	−	0.000445546i
$455$	−0.382863	+	0.838613i	−0.0179489	+	0.0393148i
$456$	−41.7473	+	29.0710i	−1.95500	+	1.36138i
$457$	8.38337	−	8.38337i	0.392158	−	0.392158i	−0.483298	−	0.875456i	$-0.660561\pi$
$457$	8.38337	−	8.38337i	0.392158	−	0.392158i	0.875456	+	0.483298i	$0.160561\pi$
$458$	15.8147	−	18.2681i	0.738971	−	0.853610i
$459$	−3.80119	−	9.17689i	−0.177424	−	0.428341i
$460$	−14.0580	−	11.3047i	−0.655459	−	0.527083i
$461$	32.0460	+	13.2739i	1.49253	+	0.618226i	0.971866	−	0.235535i	$-0.0756844\pi$
$461$	32.0460	+	13.2739i	1.49253	+	0.618226i	0.520664	+	0.853762i	$0.325684\pi$
$462$	−7.61692	+	22.9203i	−0.354371	+	1.06635i
$463$	−0.943633			−0.0438543			−0.0219272	−	0.999760i	$-0.506980\pi$
$463$	−0.943633			−0.0438543			−0.0219272	+	0.999760i	$0.506980\pi$
$464$	−29.8309	−	3.15171i	−1.38486	−	0.146314i
$465$	44.2422	−	16.5074i	2.05168	−	0.765511i
$466$	−13.1061	+	39.4379i	−0.607127	+	1.82693i
$467$	7.68569	−	18.5549i	0.355651	−	0.858618i	−0.640250	−	0.768167i	$-0.721169\pi$
$467$	7.68569	−	18.5549i	0.355651	−	0.858618i	0.995901	−	0.0904510i	$-0.0288309\pi$
$468$	0.900163	−	3.54037i	0.0416100	−	0.163654i
$469$	−7.77856	−	18.7791i	−0.359181	−	0.867139i
$470$	0.604509	−	1.62361i	0.0278839	−	0.0748915i
$471$	−16.6348	−	16.6348i	−0.766493	−	0.766493i
$472$	−1.01304	−	4.62614i	−0.0466287	−	0.212936i
$473$	−16.5906	−	16.5906i	−0.762835	−	0.762835i
$474$	−4.68219	−	65.0456i	−0.215060	−	2.98764i
$475$	13.6326	−	27.2503i	0.625505	−	1.25033i
$476$	−3.16768	+	0.458415i	−0.145190	+	0.0210114i
$477$	54.7700	+	22.6865i	2.50775	+	1.03874i
$478$	6.94259	+	13.8536i	0.317547	+	0.633650i
$479$	15.2079			0.694867			0.347434	−	0.937705i	$-0.387053\pi$
$479$	15.2079			0.694867			0.347434	+	0.937705i	$0.387053\pi$
$480$	−33.4241	−	16.6301i	−1.52560	−	0.759059i
$481$	−1.94300			−0.0885934
$482$	0.896507	+	1.78894i	0.0408348	+	0.0814839i
$483$	−14.1782	−	5.87280i	−0.645130	−	0.267222i
$484$	2.62150	+	18.1148i	0.119159	+	0.823399i
$485$	−17.7934	−	19.1069i	−0.807955	−	0.867602i
$486$	0.494870	+	6.87480i	0.0224477	+	0.311847i
$487$	20.4939	+	20.4939i	0.928668	+	0.928668i	0.997620	−	0.0689520i	$-0.0219655\pi$
$487$	20.4939	+	20.4939i	0.928668	+	0.928668i	−0.0689520	+	0.997620i	$0.521966\pi$
$488$	2.87174	+	1.83997i	0.129998	+	0.0832915i
$489$	−0.661039	−	0.661039i	−0.0298932	−	0.0298932i
$490$	−15.8205	−	5.89034i	−0.714695	−	0.266098i
$491$	3.02740	+	7.30880i	0.136625	+	0.329842i	0.977353	−	0.211616i	$-0.0678726\pi$
$491$	3.02740	+	7.30880i	0.136625	+	0.329842i	−0.840728	+	0.541458i	$0.817873\pi$
$492$	11.9153	+	3.02954i	0.537183	+	0.136582i
$493$	−3.56289	+	8.60157i	−0.160464	+	0.387395i
$494$	−0.869266	+	2.61573i	−0.0391101	+	0.117687i
$495$	20.0392	+	53.7080i	0.900695	+	2.41399i
$496$	8.11390	+	27.4467i	0.364325	+	1.23240i
$497$	−0.361495			−0.0162153
$498$	11.1320	−	33.4977i	0.498838	−	1.50107i
$499$	22.2253	+	9.20601i	0.994939	+	0.412117i	0.819939	−	0.572451i	$-0.194007\pi$
$499$	22.2253	+	9.20601i	0.994939	+	0.412117i	0.175000	+	0.984568i	$0.444007\pi$
$500$	22.3454	−	0.826478i	0.999317	−	0.0369612i
$501$	4.19416	+	10.1256i	0.187381	+	0.452379i
$502$	−3.04546	+	3.51791i	−0.135925	+	0.157012i
$503$	−26.2199	+	26.2199i	−1.16909	+	1.16909i	−0.186666	+	0.982424i	$0.559768\pi$
$503$	−26.2199	+	26.2199i	−1.16909	+	1.16909i	−0.982424	+	0.186666i	$0.940232\pi$
$504$	−20.4957	−	3.66867i	−0.912951	−	0.163416i
$505$	−5.28509	+	11.5763i	−0.235183	+	0.515139i
$506$	−25.5422	+	1.83861i	−1.13549	+	0.0817362i
$507$	14.5674	+	35.1688i	0.646961	+	1.56190i
$508$	−7.23370	−	5.40472i	−0.320944	−	0.239796i
$509$	−7.01527	+	16.9364i	−0.310946	+	0.750691i	0.688724	+	0.725023i	$0.258171\pi$
$509$	−7.01527	+	16.9364i	−0.310946	+	0.750691i	−0.999671	+	0.0256674i	$0.991829\pi$
$510$	−7.89079	+	8.48511i	−0.349410	+	0.375727i
$511$	−16.2959			−0.720886
$512$	11.4655	−	19.5075i	0.506710	−	0.862117i
$513$			48.7571i			2.15268i
$514$	6.87922	+	13.7272i	0.303429	+	0.605480i
$515$	−0.448258	−	0.0159571i	−0.0197526	−	0.000703152i
$516$	18.4661	−	24.7151i	0.812924	−	1.08802i
$517$	−0.941170	−	2.27218i	−0.0413926	−	0.0999306i
$518$	0.795137	+	11.0461i	0.0349363	+	0.485340i
$519$	−8.01064	+	8.01064i	−0.351628	+	0.351628i
$520$	−1.99012	+	0.362130i	−0.0872723	+	0.0158804i
$521$	26.5757	+	26.5757i	1.16430	+	1.16430i	0.983523	+	0.180780i	$0.0578624\pi$
$521$	26.5757	+	26.5757i	1.16430	+	1.16430i	0.180780	+	0.983523i	$0.442138\pi$
$522$	−39.6415	+	45.7912i	−1.73506	+	2.00423i
$523$	17.1006	−	7.08330i	0.747757	−	0.309731i	0.0239310	−	0.999714i	$-0.492382\pi$
$523$	17.1006	−	7.08330i	0.747757	−	0.309731i	0.723826	+	0.689982i	$0.242382\pi$
$524$	9.88950	+	16.6330i	0.432025	+	0.726617i
$525$	18.0476	−	6.01150i	0.787661	−	0.262363i
$526$	−4.07253	−	1.35339i	−0.177571	−	0.0590106i
$527$	8.88322			0.386959
$528$	−50.8221	+	15.0242i	−2.21175	+	0.653845i
$529$			6.72882i			0.292557i
$530$	−1.19057	−	32.8051i	−0.0517151	−	1.42496i
$531$	−8.83406	−	3.65919i	−0.383366	−	0.158795i
$532$	15.2264	+	3.87141i	0.660149	+	0.167847i
$533$	0.615438	−	0.254923i	0.0266576	−	0.0110419i
$534$	1.79602	−	2.07464i	0.0777215	−	0.0897786i
$535$	11.2437	−	24.6279i	0.486108	−	1.06476i
$536$	24.0611	−	37.5534i	1.03928	−	1.62206i
$537$	−16.4661	−	16.4661i	−0.710566	−	0.710566i
$538$	−19.9824	+	1.43840i	−0.861504	+	0.0620138i
$539$	−22.1402	+	9.17076i	−0.953645	+	0.395013i
$540$	−31.3862	+	17.1804i	−1.35065	+	0.739326i
$541$	6.41667	−	15.4912i	0.275874	−	0.666019i	−0.723839	−	0.689969i	$-0.757624\pi$
$541$	6.41667	−	15.4912i	0.275874	−	0.666019i	0.999713	+	0.0239498i	$0.00762417\pi$
$542$	10.0684	+	20.0911i	0.432476	+	0.862987i
$543$		−	26.1724i		−	1.12317i
$544$	−4.79737	−	5.12907i	−0.205686	−	0.219907i
$545$	−16.9776	+	6.33459i	−0.727241	+	0.271344i
$546$	−1.53844	+	0.770971i	−0.0658391	+	0.0329945i
$547$	9.78315	+	4.05231i	0.418297	+	0.173264i	0.581897	−	0.813262i	$-0.302311\pi$
$547$	9.78315	+	4.05231i	0.418297	+	0.173264i	−0.163600	+	0.986527i	$0.552311\pi$
$548$	1.43253	+	9.89892i	0.0611948	+	0.422861i
$549$	6.36216	−	2.63529i	0.271530	−	0.112472i
$550$	22.4298	−	22.4609i	0.956409	−	0.957736i
$551$	32.3151	−	32.3151i	1.37667	−	1.37667i
$552$	−7.20310	−	32.8938i	−0.306584	−	1.40005i
$553$	−14.2412	+	14.2412i	−0.605597	+	0.605597i
$554$	−15.0663	+	17.4036i	−0.640106	+	0.739408i
$555$	27.3234	+	29.3405i	1.15981	+	1.24544i
$556$	16.2587	+	4.13389i	0.689524	+	0.175316i
$557$	−13.9446	+	33.6653i	−0.590853	+	1.42644i	0.291827	+	0.956471i	$0.405737\pi$
$557$	−13.9446	+	33.6653i	−0.590853	+	1.42644i	−0.882680	+	0.469974i	$0.844263\pi$
$558$	54.8393	+	18.2243i	2.32153	+	0.771496i
$559$		−	1.67164i		−	0.0707027i
$560$	2.87315	+	11.1658i	0.121413	+	0.471841i
$561$			16.4487i			0.694466i
$562$	4.80974	−	14.4732i	0.202887	−	0.610513i
$563$	−14.4369	+	34.8537i	−0.608441	+	1.46891i	0.256253	+	0.966610i	$0.417512\pi$
$563$	−14.4369	+	34.8537i	−0.608441	+	1.46891i	−0.864695	+	0.502298i	$0.832488\pi$
$564$	2.77972	−	1.65274i	0.117047	−	0.0695928i
$565$	2.85906	−	2.66250i	0.120282	−	0.112012i
$566$	−23.1617	−	20.0511i	−0.973560	−	0.842812i
$567$	−5.90752	+	5.90752i	−0.248093	+	0.248093i
$568$	−0.453276	−	0.650925i	−0.0190190	−	0.0273122i
$569$	16.1912	−	16.1912i	0.678769	−	0.678769i	−0.280953	−	0.959722i	$-0.590650\pi$
$569$	16.1912	−	16.1912i	0.678769	−	0.678769i	0.959722	+	0.280953i	$0.0906504\pi$
$570$	51.7232	−	23.6572i	2.16645	−	0.990892i
$571$	8.05813	−	3.33779i	0.337222	−	0.139682i	−0.207645	−	0.978204i	$-0.566580\pi$
$571$	8.05813	−	3.33779i	0.337222	−	0.139682i	0.544868	+	0.838522i	$0.316580\pi$
$572$	−1.71871	+	2.30033i	−0.0718629	+	0.0961816i
$573$	12.4245	+	5.14641i	0.519043	+	0.214994i
$574$	−1.70111	−	3.39450i	−0.0710031	−	0.141684i
$575$	13.2113	+	15.2395i	0.550949	+	0.635529i
$576$	−19.0934	−	41.5056i	−0.795559	−	1.72940i
$577$		−	37.9507i		−	1.57991i	−0.613167	−	0.789953i	$-0.710105\pi$
$577$		−	37.9507i		−	1.57991i	0.613167	−	0.789953i	$-0.289895\pi$
$578$	19.5449	−	9.79473i	0.812963	−	0.407407i
$579$	6.28090	−	15.1634i	0.261025	−	0.630171i
$580$	32.1888	+	9.41528i	1.33657	+	0.390948i
$581$	−10.0716	+	4.17180i	−0.417841	+	0.173075i
$582$	−3.49912	−	48.6103i	−0.145043	−	2.01496i
$583$	−32.9510	−	32.9510i	−1.36469	−	1.36469i
$584$	−20.4333	−	29.3431i	−0.845534	−	1.21423i
$585$	−1.69620	+	3.71532i	−0.0701293	+	0.153609i
$586$	20.4161	+	17.6743i	0.843383	+	0.730117i
$587$	10.4956	−	4.34742i	0.433200	−	0.179437i	−0.155418	−	0.987849i	$-0.549672\pi$
$587$	10.4956	−	4.34742i	0.433200	−	0.179437i	0.588618	+	0.808411i	$0.299672\pi$
$588$	−16.1043	−	27.0856i	−0.664129	−	1.11699i
$589$	−40.2850	−	16.6866i	−1.65992	−	0.687559i
$590$	0.192032	+	5.29126i	0.00790581	+	0.217838i
$591$		−	35.6925i		−	1.46819i
$592$	−18.8932	+	15.2824i	−0.776505	+	0.628104i
$593$	13.3517			0.548287			0.274144	−	0.961689i	$-0.411606\pi$
$593$	13.3517			0.548287			0.274144	+	0.961689i	$0.411606\pi$
$594$	−16.0183	+	48.2012i	−0.657240	+	1.97772i
$595$	3.57620	+	0.127306i	0.146610	+	0.00521902i
$596$	−6.65714	−	1.69262i	−0.272687	−	0.0693324i
$597$	−42.0223	+	17.4062i	−1.71986	+	0.712389i
$598$	−1.37942	−	1.19417i	−0.0564087	−	0.0488331i
$599$	12.7160	+	12.7160i	0.519560	+	0.519560i	0.917438	−	0.397878i	$-0.130253\pi$
$599$	12.7160	+	12.7160i	0.519560	+	0.519560i	−0.397878	+	0.917438i	$0.630253\pi$
$600$	33.4543	+	24.9595i	1.36577	+	1.01897i
$601$	−15.7021	+	15.7021i	−0.640501	+	0.640501i	−0.950679	−	0.310177i	$-0.899612\pi$
$601$	−15.7021	+	15.7021i	−0.640501	+	0.640501i	0.310177	+	0.950679i	$0.399612\pi$
$602$	−9.50340	+	0.684084i	−0.387330	+	0.0278812i
$603$	−34.4614	−	83.1973i	−1.40338	−	3.38805i
$604$	4.16290	−	0.602439i	0.169386	−	0.0245129i
$605$	0.728012	−	20.4510i	0.0295979	−	0.831450i
$606$	−21.2368	+	10.6426i	−0.862685	+	0.432325i
$607$		−	13.8506i		−	0.562179i	−0.959681	−	0.281090i	$-0.909304\pi$
$607$		−	13.8506i		−	0.562179i	0.959681	−	0.281090i	$-0.0906959\pi$
$608$	12.1212	+	32.2717i	0.491581	+	1.30879i
$609$	28.5307			1.15612
$610$	−2.79236	−	2.59677i	−0.113059	−	0.105140i
$611$	0.0670553	−	0.161886i	0.00271277	−	0.00654920i
$612$	−14.0338	+	2.03092i	−0.567283	+	0.0820950i
$613$	15.7743	+	38.0825i	0.637117	+	1.53814i	0.830503	+	0.557014i	$0.188053\pi$
$613$	15.7743	+	38.0825i	0.637117	+	1.53814i	−0.193385	+	0.981123i	$0.561947\pi$
$614$	0.0233004	+	0.323693i	0.000940329	+	0.0130632i
$615$	−12.5041	−	5.70865i	−0.504212	−	0.230195i
$616$	13.7809	+	8.82965i	0.555249	+	0.355757i
$617$	24.8469	−	24.8469i	1.00030	−	1.00030i	0.000298688	−	1.00000i	$-0.499905\pi$
$617$	24.8469	−	24.8469i	1.00030	−	1.00030i	1.00000		0.000298688i	$-9.50752e-5\pi$
$618$	−0.633015	−	0.548001i	−0.0254636	−	0.0220438i
$619$	−12.7620	−	30.8102i	−0.512948	−	1.23837i	−0.942160	−	0.335162i	$-0.891209\pi$
$619$	−12.7620	−	30.8102i	−0.512948	−	1.23837i	0.429212	−	0.903204i	$-0.358791\pi$
$620$	−3.45351	−	31.8123i	−0.138696	−	1.27761i
$621$	−29.8167	−	12.3505i	−1.19650	−	0.495607i
$622$	−0.0459679	−	0.0152761i	−0.00184315	−	0.000612517i
$623$	−0.847450			−0.0339524
$624$	−3.31728	−	1.80347i	−0.132798	−	0.0721965i
$625$	−24.7472	−	3.54629i	−0.989888	−	0.141852i
$626$	−4.43877	−	1.47510i	−0.177409	−	0.0589569i
$627$	30.8980	−	74.5943i	1.23395	−	2.97901i
$628$	−13.7026	+	8.14714i	−0.546792	+	0.325106i
$629$	2.88628	+	6.96808i	0.115083	+	0.277836i
$630$	21.8160	+	8.12264i	0.869172	+	0.323614i
$631$	−18.8942	−	18.8942i	−0.752165	−	0.752165i	0.222718	−	0.974883i	$-0.428507\pi$
$631$	−18.8942	−	18.8942i	−0.752165	−	0.752165i	−0.974883	+	0.222718i	$0.928507\pi$
$632$	−43.5003	−	7.78642i	−1.73035	−	0.309727i
$633$	26.9168	+	26.9168i	1.06985	+	1.06985i
$634$	−34.0987	+	2.45453i	−1.35423	+	0.0974819i
$635$	6.88021	+	7.38813i	0.273033	+	0.293189i
$636$	36.6760	−	49.0874i	1.45430	−	1.94644i
$637$	−1.57742	−	0.653387i	−0.0624995	−	0.0258882i
$638$	42.5632	−	21.3301i	1.68509	−	0.844466i
$639$	−1.60154			−0.0633558
$640$	−16.5030	+	19.1742i	−0.652338	+	0.757928i
$641$	30.1507			1.19088			0.595441	−	0.803399i	$-0.296977\pi$
$641$	30.1507			1.19088			0.595441	+	0.803399i	$0.296977\pi$
$642$	45.1800	−	22.6414i	1.78311	−	0.893586i
$643$	34.8362	+	14.4296i	1.37381	+	0.569049i	0.942818	−	0.333308i	$-0.108165\pi$
$643$	34.8362	+	14.4296i	1.37381	+	0.569049i	0.430988	+	0.902358i	$0.358165\pi$
$644$	−6.22444	+	8.33082i	−0.245277	+	0.328280i
$645$	−25.2427	+	23.5073i	−0.993931	+	0.925600i
$646$	10.6719	−	0.768199i	0.419881	−	0.0302244i
$647$	−28.8534	−	28.8534i	−1.13435	−	1.13435i	−0.989446	−	0.144900i	$-0.953714\pi$
$647$	−28.8534	−	28.8534i	−1.13435	−	1.13435i	−0.144900	−	0.989446i	$-0.546286\pi$
$648$	−18.0447	−	3.22996i	−0.708865	−	0.126885i
$649$	5.31479	+	5.31479i	0.208624	+	0.208624i
$650$	2.26155	−	0.00156806i	0.0887054	−	6.15044e-5i
$651$	−10.4174	−	25.1499i	−0.408291	−	0.985701i
$652$	−0.544516	+	0.323753i	−0.0213249	+	0.0126791i
$653$	−15.0006	+	36.2145i	−0.587017	+	1.41718i	0.299324	+	0.954151i	$0.403239\pi$
$653$	−15.0006	+	36.2145i	−0.587017	+	1.41718i	−0.886341	+	0.463033i	$0.846761\pi$
$654$	−32.0991	−	10.6672i	−1.25517	−	0.417121i
$655$	−7.56304	−	20.2701i	−0.295512	−	0.792017i
$656$	3.97927	−	7.31944i	0.155364	−	0.285776i
$657$	−72.1957			−2.81662
$658$	−0.947777	−	0.314967i	−0.0369482	−	0.0122787i
$659$	−34.7693	−	14.4019i	−1.35442	−	0.561019i	−0.416900	−	0.908953i	$-0.636883\pi$
$659$	−34.7693	−	14.4019i	−1.35442	−	0.561019i	−0.937519	+	0.347934i	$0.886883\pi$
$660$	58.9057	−	6.39474i	2.29290	−	0.248915i
$661$	−15.0853	−	36.4191i	−0.586750	−	1.41654i	−0.886593	−	0.462550i	$-0.846934\pi$
$661$	−15.0853	−	36.4191i	−0.586750	−	1.41654i	0.299843	−	0.953988i	$-0.403066\pi$
$662$	19.6439	+	17.0058i	0.763483	+	0.660948i
$663$	−0.828673	+	0.828673i	−0.0321830	+	0.0321830i
$664$	−20.1406	−	12.9044i	−0.781609	−	0.500789i
$665$	−15.9788	−	7.29501i	−0.619631	−	0.282888i
$666$	3.52270	+	48.9378i	0.136502	+	1.89630i
$667$	11.5762	+	27.9474i	0.448232	+	1.08213i
$668$	7.35030	−	1.06371i	0.284391	−	0.0411560i
$669$	−20.4724	+	49.4248i	−0.791509	+	1.91087i
$670$	−33.9577	+	36.5153i	−1.31190	+	1.41071i
$671$	−5.41309			−0.208970
$672$	−8.89534	+	19.5971i	−0.343145	+	0.755973i
$673$		−	5.61891i		−	0.216593i	−0.994119	−	0.108296i	$-0.965460\pi$
$673$		−	5.61891i		−	0.216593i	0.994119	−	0.108296i	$-0.0345396\pi$
$674$	27.2951	−	13.6786i	1.05137	−	0.526881i
$675$	37.9539	−	12.6421i	1.46085	−	0.486596i
$676$	25.5295	−	3.69453i	0.981903	−	0.142097i
$677$	−6.94816	−	16.7743i	−0.267040	−	0.644690i	0.732302	−	0.680980i	$-0.238446\pi$
$677$	−6.94816	−	16.7743i	−0.267040	−	0.644690i	−0.999341	+	0.0362898i	$0.988446\pi$
$678$	7.27377	−	0.523589i	0.279348	−	0.0201083i
$679$	−10.6428	+	10.6428i	−0.408434	+	0.408434i
$680$	4.25494	+	6.59911i	0.163170	+	0.253064i
$681$	−0.195124	−	0.195124i	−0.00747718	−	0.00747718i
$682$	−34.3436	−	29.7313i	−1.31509	−	1.13847i
$683$	16.7793	−	6.95022i	0.642043	−	0.265943i	−0.0378172	−	0.999285i	$-0.512040\pi$
$683$	16.7793	−	6.95022i	0.642043	−	0.265943i	0.679860	+	0.733342i	$0.262040\pi$
$684$	67.4577	+	17.1515i	2.57931	+	0.655806i
$685$	0.397826	−	11.1755i	0.0152002	−	0.426995i
$686$	−7.09334	+	21.3448i	−0.270825	+	0.814948i
$687$	−50.4262			−1.92388
$688$	−13.1480	−	16.2545i	−0.501264	−	0.619696i
$689$		−	3.32009i		−	0.126485i
$690$	1.36542	+	37.6230i	0.0519808	+	1.43228i
$691$	−18.2182	−	7.54622i	−0.693053	−	0.287072i	0.00821876	−	0.999966i	$-0.497384\pi$
$691$	−18.2182	−	7.54622i	−0.693053	−	0.287072i	−0.701271	+	0.712894i	$0.747384\pi$
$692$	3.92332	+	6.59858i	0.149142	+	0.250840i
$693$	30.5308	−	12.6463i	1.15977	−	0.480392i
$694$	13.9961	+	12.1164i	0.531284	+	0.459933i
$695$	−17.0621	−	7.78961i	−0.647204	−	0.295477i
$696$	35.7744	+	51.3737i	1.35603	+	1.94731i
$697$	−1.82843	−	1.82843i	−0.0692567	−	0.0692567i
$698$	2.99758	+	41.6428i	0.113460	+	1.57620i
$699$	80.1293	−	33.1906i	3.03077	−	1.25539i
$700$	−0.934411	−	12.8565i	−0.0353174	−	0.485929i
$701$	−18.1534	+	43.8263i	−0.685646	+	1.65530i	0.0677272	+	0.997704i	$0.478425\pi$
$701$	−18.1534	+	43.8263i	−0.685646	+	1.65530i	−0.753374	+	0.657593i	$0.771575\pi$
$702$	−3.23532	+	1.62135i	−0.122109	+	0.0611938i
$703$		−	37.0217i		−	1.39630i
$704$	1.38072	+	35.8860i	0.0520379	+	1.35250i
$705$	−3.38754	+	1.26394i	−0.127582	+	0.0476027i
$706$	−1.97031	−	3.93167i	−0.0741537	−	0.147970i
$707$	6.77763	+	2.80739i	0.254899	+	0.105583i
$708$	−5.91561	+	7.91748i	−0.222322	+	0.297557i
$709$	8.80964	−	3.64907i	0.330853	−	0.137044i	−0.211072	−	0.977470i	$-0.567696\pi$
$709$	8.80964	−	3.64907i	0.330853	−	0.137044i	0.541925	+	0.840427i	$0.317696\pi$
$710$	0.368864	+	0.806469i	0.0138432	+	0.0302663i
$711$	−63.0929	+	63.0929i	−2.36617	+	2.36617i
$712$	−1.06261	−	1.52596i	−0.0398230	−	0.0571877i
$713$	20.4089	−	20.4089i	0.764318	−	0.764318i
$714$	5.05019	+	4.37196i	0.188999	+	0.163616i
$715$	2.34944	−	2.18792i	0.0878640	−	0.0818235i
$716$	−13.5636	+	8.06452i	−0.506896	+	0.301385i
$717$	12.3757	−	29.8777i	0.462181	−	1.11580i
$718$	−7.09183	+	21.3403i	−0.264665	+	0.796412i
$719$			10.1525i			0.378626i	0.981917	+	0.189313i	$0.0606261\pi$
$719$			10.1525i			0.378626i	−0.981917	+	0.189313i	$0.939374\pi$
$720$	12.7290	+	49.4679i	0.474380	+	1.84356i
$721$			0.258574i			0.00962978i
$722$	−24.3409	−	8.08900i	−0.905873	−	0.301041i
$723$	1.59810	−	3.85815i	0.0594339	−	0.143486i
$724$	−17.1886	−	4.37032i	−0.638810	−	0.162422i
$725$	−33.5339	−	16.7761i	−1.24542	−	0.623047i
$726$	25.0016	−	28.8802i	0.927895	−	1.07184i
$727$	−8.37341	+	8.37341i	−0.310553	+	0.310553i	−0.845124	−	0.534571i	$-0.820473\pi$
$727$	−8.37341	+	8.37341i	−0.310553	+	0.310553i	0.534571	+	0.845124i	$0.320473\pi$
$728$	0.249441	+	1.13910i	0.00924489	+	0.0422179i
$729$	23.9201	−	23.9201i	0.885929	−	0.885929i
$730$	16.6280	+	36.3549i	0.615431	+	1.34555i
$731$	−5.99489	+	2.48317i	−0.221729	+	0.0918432i
$732$	−1.01945	−	7.04448i	−0.0376799	−	0.260371i
$733$	−28.8577	−	11.9532i	−1.06588	−	0.441503i	−0.220347	−	0.975422i	$-0.570719\pi$
$733$	−28.8577	−	11.9532i	−1.06588	−	0.441503i	−0.845536	+	0.533918i	$0.820719\pi$
$734$	25.4562	−	12.7571i	0.939606	−	0.470873i
$735$	12.3158	+	33.0082i	0.454276	+	1.21753i
$736$	−22.8056	−	0.762060i	−0.840627	−	0.0280899i
$737$			70.7864i			2.60745i
$738$	−7.53646	−	15.0387i	−0.277421	−	0.553581i
$739$	−4.21782	+	10.1827i	−0.155155	+	0.374577i	−0.982274	−	0.187449i	$-0.939978\pi$
$739$	−4.21782	+	10.1827i	−0.155155	+	0.374577i	0.827119	+	0.562026i	$0.189978\pi$
$740$	23.8318	−	13.0452i	0.876074	−	0.479551i
$741$	5.31461	−	2.20138i	0.195237	−	0.0808698i
$742$	−18.8750	+	1.35868i	−0.692922	+	0.0498787i
$743$	−4.04060	−	4.04060i	−0.148235	−	0.148235i	0.629094	−	0.777329i	$-0.283426\pi$
$743$	−4.04060	−	4.04060i	−0.148235	−	0.148235i	−0.777329	+	0.629094i	$0.783426\pi$
$744$	32.2237	−	50.2933i	1.18138	−	1.84384i
$745$	6.98609	+	3.18945i	0.255950	+	0.116852i
$746$	31.0124	−	35.8234i	1.13544	−	1.31159i
$747$	−44.6203	+	18.4823i	−1.63257	+	0.676234i
$748$	10.8026	+	2.74664i	0.394983	+	0.100427i
$749$	−14.4190	−	5.97255i	−0.526859	−	0.218232i
$750$	−31.8267	−	34.1288i	−1.16215	−	1.24621i
$751$			33.7626i			1.23202i	0.787740	+	0.616008i	$0.211251\pi$
$751$			33.7626i			1.23202i	−0.787740	+	0.616008i	$0.788749\pi$
$752$	−0.621266	−	2.10154i	−0.0226552	−	0.0766354i
$753$	9.71066			0.353876
$754$	3.21889	+	1.06971i	0.117225	+	0.0389564i
$755$	−4.69977	−	0.167302i	−0.171042	−	0.00608876i
$756$	10.5415	+	17.7296i	0.383390	+	0.644819i
$757$	21.3445	−	8.84118i	0.775779	−	0.321338i	0.0405684	−	0.999177i	$-0.487083\pi$
$757$	21.3445	−	8.84118i	0.775779	−	0.321338i	0.735211	+	0.677838i	$0.237083\pi$
$758$	−27.3875	+	31.6363i	−0.994760	+	1.14908i
$759$	37.7903	+	37.7903i	1.37170	+	1.37170i
$760$	−6.89995	−	37.9193i	−0.250288	−	1.37548i
$761$	−8.72544	+	8.72544i	−0.316297	+	0.316297i	−0.847343	−	0.531046i	$-0.821799\pi$
$761$	−8.72544	+	8.72544i	−0.316297	+	0.316297i	0.531046	+	0.847343i	$0.321799\pi$
$762$	1.35301	+	18.7963i	0.0490145	+	0.680916i
$763$	3.99761	+	9.65108i	0.144723	+	0.349392i
$764$	5.45456	−	7.30041i	0.197339	−	0.264119i
$765$	15.8437	+	0.564003i	0.572830	+	0.0203916i
$766$	7.87371	+	15.7116i	0.284489	+	0.567684i
$767$			0.535509i			0.0193361i
$768$	−46.4412	+	8.55526i	−1.67580	+	0.308711i
$769$	53.4061			1.92587			0.962937	−	0.269726i	$-0.0869330\pi$
$769$	53.4061			1.92587			0.962937	+	0.269726i	$0.0869330\pi$
$770$	−13.4000	−	12.4614i	−0.482901	−	0.449078i
$771$	12.2628	−	29.6050i	0.441633	−	1.06620i
$772$	−8.90973	−	6.65697i	−0.320668	−	0.239590i
$773$	6.71461	+	16.2105i	0.241508	+	0.583052i	0.997433	−	0.0716065i	$-0.0228126\pi$
$773$	6.71461	+	16.2105i	0.241508	+	0.583052i	−0.755925	+	0.654658i	$0.772813\pi$
$774$	−42.1030	+	3.03071i	−1.51336	+	0.108936i
$775$	−2.54390	+	35.6856i	−0.0913794	+	1.28187i
$776$	−32.5089	−	5.81900i	−1.16700	−	0.208890i
$777$	16.3431	−	16.3431i	0.586304	−	0.586304i
$778$	8.35978	−	9.65666i	0.299713	−	0.346208i
$779$	4.85725	+	11.7264i	0.174029	+	0.420144i
$780$	3.28978	+	2.64545i	0.117793	+	0.0947225i
$781$	1.16308	+	0.481762i	0.0416181	+	0.0172388i
$782$	−2.23348	+	6.72084i	−0.0798691	+	0.240337i
$783$	59.9999			2.14422
$784$	−20.4775	+	6.05362i	−0.731338	+	0.216201i
$785$	16.6988	−	6.23056i	0.596006	−	0.222378i
$786$	12.7359	−	38.3240i	0.454274	−	1.36697i
$787$	−6.48796	+	15.6633i	−0.231271	+	0.558337i	−0.996327	−	0.0856258i	$-0.972711\pi$
$787$	−6.48796	+	15.6633i	−0.231271	+	0.558337i	0.765056	+	0.643963i	$0.222711\pi$
$788$	−23.4409	−	5.96000i	−0.835048	−	0.212316i
$789$	3.42741	+	8.27449i	0.122019	+	0.294580i
$790$	46.3025	+	17.2396i	1.64737	+	0.613356i
$791$	−1.59253	−	1.59253i	−0.0566239	−	0.0566239i
$792$	61.0537	+	39.1181i	2.16945	+	1.39000i
$793$	−0.272707	−	0.272707i	−0.00968411	−	0.00968411i
$794$	2.71904	+	37.7732i	0.0964950	+	1.34052i
$795$	−50.1353	+	46.6886i	−1.77812	+	1.65587i
$796$	4.41450	+	30.5045i	0.156468	+	1.08120i
$797$	39.1279	+	16.2073i	1.38598	+	0.574093i	0.946074	−	0.323950i	$-0.105011\pi$
$797$	39.1279	+	16.2073i	1.38598	+	0.574093i	0.439908	+	0.898043i	$0.355011\pi$
$798$	−14.6899	−	29.3131i	−0.520019	−	1.03767i
$799$	−0.680171			−0.0240627
$800$	21.9783	−	17.8032i	0.777051	−	0.629438i
$801$	−3.75446			−0.132657
$802$	0.486248	+	0.970286i	0.0171700	+	0.0342620i
$803$	52.4304	+	21.7174i	1.85023	+	0.766389i
$804$	−92.1198	+	13.3312i	−3.24881	+	0.470156i
$805$	8.50867	−	7.92371i	0.299891	−	0.279274i
$806$	−0.232364	−	3.22804i	−0.00818469	−	0.113703i
$807$	29.5645	+	29.5645i	1.04072	+	1.04072i
$808$	3.44331	+	15.7243i	0.121135	+	0.553178i
$809$	−28.1061	−	28.1061i	−0.988159	−	0.988159i	0.0117718	−	0.999931i	$-0.496253\pi$
$809$	−28.1061	−	28.1061i	−0.988159	−	0.988159i	−0.999931	+	0.0117718i	$0.996253\pi$
$810$	19.2072	+	7.15130i	0.674872	+	0.251271i
$811$	8.84424	+	21.3519i	0.310563	+	0.749766i	0.999684	+	0.0251201i	$0.00799683\pi$
$811$	8.84424	+	21.3519i	0.310563	+	0.749766i	−0.689121	+	0.724646i	$0.742003\pi$
$812$	4.76411	−	18.7374i	0.167187	−	0.657554i
$813$	17.9478	−	43.3299i	0.629457	−	1.51964i
$814$	12.1628	−	36.5996i	0.426307	−	1.28281i
$815$	0.663581	−	0.247592i	0.0232442	−	0.00867275i
$816$	−1.53995	+	14.5756i	−0.0539090	+	0.510247i
$817$	31.8511			1.11433
$818$	−5.03804	+	15.1601i	−0.176151	+	0.530062i
$819$	2.17522	+	0.901006i	0.0760084	+	0.0314837i
$820$	−5.83708	+	7.25875i	−0.203840	+	0.253487i
$821$	−20.1061	−	48.5404i	−0.701708	−	1.69407i	−0.719748	−	0.694235i	$-0.755743\pi$
$821$	−20.1061	−	48.5404i	−0.701708	−	1.69407i	0.0180408	−	0.999837i	$-0.494257\pi$
$822$	13.6622	−	15.7817i	0.476526	−	0.550451i
$823$	−10.8798	+	10.8798i	−0.379244	+	0.379244i	−0.870829	−	0.491585i	$-0.836418\pi$
$823$	−10.8798	+	10.8798i	−0.379244	+	0.379244i	0.491585	+	0.870829i	$0.336418\pi$
$824$	−0.465599	+	0.324223i	−0.0162199	+	0.0112949i
$825$	−66.0778	−	4.71044i	−2.30053	−	0.163996i
$826$	3.04442	−	0.219147i	0.105929	−	0.00762509i
$827$	−5.55410	−	13.4088i	−0.193135	−	0.466269i	0.797413	−	0.603434i	$-0.206201\pi$
$827$	−5.55410	−	13.4088i	−0.193135	−	0.466269i	−0.990548	+	0.137164i	$0.956201\pi$
$828$	−27.5762	+	36.9081i	−0.958339	+	1.28265i
$829$	10.5438	−	25.4550i	0.366202	−	0.884090i	−0.628163	−	0.778082i	$-0.716193\pi$
$829$	10.5438	−	25.4550i	0.366202	−	0.884090i	0.994365	−	0.106008i	$-0.0338070\pi$
$830$	19.5839	+	18.2122i	0.679766	+	0.632154i
$831$	48.0401			1.66649
$832$	−1.73835	+	1.87746i	−0.0602663	+	0.0650894i
$833$			6.62759i			0.229632i
$834$	−15.6859	−	31.3005i	−0.543159	−	1.08385i
$835$	−8.29823	−	0.295400i	−0.287172	−	0.0102227i
$836$	−43.8301	−	32.7480i	−1.51590	−	1.13261i
$837$	−21.9078	−	52.8900i	−0.757243	−	1.82815i
$838$	−2.71100	−	37.6616i	−0.0936501	−	1.30100i
$839$	1.44842	−	1.44842i	0.0500049	−	0.0500049i	−0.681662	−	0.731667i	$-0.738743\pi$
$839$	1.44842	−	1.44842i	0.0500049	−	0.0500049i	0.731667	+	0.681662i	$0.238743\pi$
$840$	13.6934	−	19.7853i	0.472466	−	0.682657i
$841$	−19.2604	−	19.2604i	−0.664152	−	0.664152i
$842$	16.5989	−	19.1740i	0.572036	−	0.660778i
$843$	−29.4063	+	12.1805i	−1.01281	+	0.419519i
$844$	22.1721	−	13.1829i	0.763196	−	0.453774i
$845$	−28.8219	−	1.02600i	−0.991503	−	0.0352955i
$846$	−4.19894	−	1.39540i	−0.144363	−	0.0479748i
$847$	−11.7970			−0.405348
$848$	−26.1137	−	32.2835i	−0.896748	−	1.10862i
$849$			63.9345i			2.19423i
$850$	−3.36509	−	8.10815i	−0.115422	−	0.278107i
$851$	22.6400	+	9.37780i	0.776090	+	0.321467i
$852$	−0.407911	+	1.60433i	−0.0139748	+	0.0549635i
$853$	31.6324	−	13.1026i	1.08307	−	0.448624i	0.231488	−	0.972838i	$-0.425641\pi$
$853$	31.6324	−	13.1026i	1.08307	−	0.448624i	0.851587	+	0.524214i	$0.175641\pi$
$854$	−1.43876	+	1.66196i	−0.0492334	+	0.0568712i
$855$	−70.7910	−	32.3192i	−2.42100	−	1.10529i
$856$	−7.32544	−	33.4525i	−0.250378	−	1.14338i
$857$	16.8902	+	16.8902i	0.576960	+	0.576960i	0.934064	−	0.357105i	$-0.116236\pi$
$857$	16.8902	+	16.8902i	0.576960	+	0.576960i	−0.357105	+	0.934064i	$0.616236\pi$
$858$	5.97724	−	0.430261i	0.204060	−	0.0146889i
$859$	0.400211	−	0.165773i	0.0136550	−	0.00565609i	−0.375845	−	0.926682i	$-0.622648\pi$
$859$	0.400211	−	0.165773i	0.0136550	−	0.00565609i	0.389500	+	0.921026i	$0.372648\pi$
$860$	11.2233	+	20.5033i	0.382710	+	0.699158i
$861$	−3.03238	+	7.32080i	−0.103343	+	0.249492i
$862$	−13.8568	−	27.6505i	−0.471963	−	0.941781i
$863$		−	23.3310i		−	0.794198i	−0.917776	−	0.397099i	$-0.870017\pi$
$863$		−	23.3310i		−	0.794198i	0.917776	−	0.397099i	$-0.129983\pi$
$864$	−18.7068	+	41.2125i	−0.636419	+	1.40208i
$865$	−3.00038	−	8.04145i	−0.102016	−	0.273417i
$866$	−18.8068	+	9.42481i	−0.639081	+	0.320268i
$867$	−42.1520	−	17.4599i	−1.43156	−	0.592970i
$868$	−18.2566	+	2.64202i	−0.619669	+	0.0896761i
$869$	64.7988	−	26.8405i	2.19815	−	0.910503i
$870$	−29.1123	−	63.6499i	−0.986998	−	2.15793i
$871$	−3.56616	+	3.56616i	−0.120835	+	0.120835i
$872$	−12.3656	+	19.2997i	−0.418752	+	0.653570i
$873$	−47.1509	+	47.1509i	−1.59582	+	1.59582i
$874$	22.7534	−	26.2833i	0.769647	−	0.889045i
$875$	−1.53553	+	14.3299i	−0.0519105	+	0.484438i
$876$	−18.3882	+	72.3217i	−0.621281	+	2.44352i
$877$	−2.09166	+	5.04970i	−0.0706302	+	0.170516i	−0.955252	−	0.295792i	$-0.904416\pi$
$877$	−2.09166	+	5.04970i	−0.0706302	+	0.170516i	0.884622	+	0.466309i	$0.154416\pi$
$878$	−32.5496	−	10.8169i	−1.09849	−	0.365054i
$879$		−	56.3557i		−	1.90083i
$880$	5.63646	−	39.7539i	0.190005	−	1.34010i
$881$		−	32.8605i		−	1.10710i	−0.832817	−	0.553548i	$-0.813273\pi$
$881$		−	32.8605i		−	1.10710i	0.832817	−	0.553548i	$-0.186727\pi$
$882$	−13.5968	+	40.9145i	−0.457827	+	1.37766i
$883$	8.80508	−	21.2573i	0.296315	−	0.715367i	−0.703674	−	0.710523i	$-0.748458\pi$
$883$	8.80508	−	21.2573i	0.296315	−	0.715367i	0.999988	−	0.00484333i	$-0.00154169\pi$
$884$	0.405854	+	0.682600i	0.0136503	+	0.0229583i
$885$	8.08651	−	7.53058i	0.271825	−	0.253138i
$886$	27.2638	+	23.6023i	0.915944	+	0.792934i
$887$	24.3944	−	24.3944i	0.819083	−	0.819083i	−0.166892	−	0.985975i	$-0.553373\pi$
$887$	24.3944	−	24.3944i	0.819083	−	0.819083i	0.985975	+	0.166892i	$0.0533731\pi$
$888$	49.9205	+	8.93562i	1.67522	+	0.299860i
$889$	4.11528	−	4.11528i	0.138022	−	0.138022i
$890$	0.864725	+	1.89060i	0.0289856	+	0.0633730i
$891$	26.8798	−	11.1340i	0.900507	−	0.373002i
$892$	29.0410	+	21.6982i	0.972364	+	0.726510i
$893$	3.08455	+	1.27766i	0.103220	+	0.0427553i
$894$	6.42259	+	12.8160i	0.214804	+	0.428631i
$895$	16.5295	−	6.16738i	0.552519	−	0.206153i
$896$	11.3849	+	9.11433i	0.380344	+	0.304488i
$897$			3.80769i			0.127135i
$898$	35.4202	−	17.7505i	1.18199	−	0.592340i
$899$	−20.5343	+	49.5742i	−0.684857	+	1.65339i
$900$	−4.13973	−	56.9582i	−0.137991	−	1.89861i
$901$	−11.9066	+	4.93189i	−0.396668	+	0.164305i
$902$	0.949352	+	13.1885i	0.0316099	+	0.439130i
$903$	14.0605	+	14.0605i	0.467905	+	0.467905i
$904$	0.870723	−	4.86445i	0.0289598	−	0.161789i
$905$	18.0380	+	8.23511i	0.599602	+	0.273744i
$906$	−6.63686	−	5.74554i	−0.220495	−	0.190883i
$907$	−52.4650	+	21.7317i	−1.74207	+	0.721590i	−0.743468	+	0.668771i	$0.766821\pi$
$907$	−52.4650	+	21.7317i	−1.74207	+	0.721590i	−0.998604	+	0.0528190i	$0.983179\pi$
$908$	−0.160729	+	0.0955649i	−0.00533399	+	0.00317143i
$909$	30.0270	+	12.4376i	0.995932	+	0.412529i
$910$	−0.0472841	−	1.30287i	−0.00156745	−	0.0431898i
$911$			41.9451i			1.38970i	0.719153	+	0.694852i	$0.244530\pi$
$911$			41.9451i			1.38970i	−0.719153	+	0.694852i	$0.755470\pi$
$912$	34.3630	−	63.2069i	1.13787	−	2.09299i
$913$	37.9641			1.25643
$914$	−5.28762	+	15.9112i	−0.174899	+	0.526294i
$915$	−0.283110	+	7.95297i	−0.00935931	+	0.262917i
$916$	−8.42026	+	33.1172i	−0.278213	+	1.09422i
$917$	−11.5227	+	4.77286i	−0.380513	+	0.157614i
$918$	10.6205	+	9.19420i	0.350529	+	0.303454i
$919$	−6.98997	−	6.98997i	−0.230578	−	0.230578i	0.582356	−	0.812934i	$-0.302131\pi$
$919$	−6.98997	−	6.98997i	−0.230578	−	0.230578i	−0.812934	+	0.582356i	$0.802131\pi$
$920$	24.9368	+	5.38563i	0.822141	+	0.177559i
$921$	0.478912	−	0.478912i	0.0157807	−	0.0157807i
$922$	−48.9273	+	3.52194i	−1.61133	+	0.115989i
$923$	0.0343240	+	0.0828655i	0.00112979	+	0.00272755i
$924$	−4.89214	−	33.8051i	−0.160940	−	1.11210i
$925$	−28.8187	+	9.59928i	−0.947554	+	0.315622i
$926$	1.19307	−	0.597892i	0.0392066	−	0.0196480i
$927$			1.14556i			0.0376251i
$928$	39.7131	−	14.9162i	1.30365	−	0.489649i
$929$	−5.01602			−0.164570			−0.0822851	−	0.996609i	$-0.526222\pi$
$929$	−5.01602			−0.164570			−0.0822851	+	0.996609i	$0.526222\pi$
$930$	−45.4777	+	48.9030i	−1.49127	+	1.60359i
$931$	12.4495	−	30.0558i	0.408017	−	0.985040i
$932$	−8.41768	−	58.1668i	−0.275730	−	1.90532i
$933$	0.0386863	+	0.0933969i	0.00126653	+	0.00305768i
$934$	2.03923	+	28.3293i	0.0667257	+	0.926963i
$935$	−11.3364	−	5.17557i	−0.370741	−	0.169259i
$936$	1.10510	+	5.04657i	0.0361213	+	0.164952i
$937$	−1.46017	+	1.46017i	−0.0477018	+	0.0477018i	−0.730555	−	0.682854i	$-0.760739\pi$
$937$	−1.46017	+	1.46017i	−0.0477018	+	0.0477018i	0.682854	+	0.730555i	$0.260739\pi$
$938$	21.7333	+	18.8145i	0.709617	+	0.614316i
$939$	3.73564	+	9.01863i	0.121908	+	0.294312i
$940$	0.264429	+	2.43581i	0.00862471	+	0.0794473i
$941$	33.8941	+	14.0394i	1.10492	+	0.457671i	0.859184	−	0.511667i	$-0.170972\pi$
$941$	33.8941	+	14.0394i	1.10492	+	0.457671i	0.245731	+	0.969338i	$0.420972\pi$
$942$	31.5719	+	10.4920i	1.02867	+	0.341849i
$943$	−8.40150			−0.273590
$944$	4.21197	+	5.20713i	0.137088	+	0.169478i
$945$	−8.06165	−	21.6064i	−0.262246	−	0.702856i
$946$	31.4879	+	10.4641i	1.02376	+	0.340218i
$947$	−22.5830	+	54.5203i	−0.733850	+	1.77167i	−0.104534	+	0.994521i	$0.533335\pi$
$947$	−22.5830	+	54.5203i	−0.733850	+	1.77167i	−0.629316	+	0.777150i	$0.716665\pi$
$948$	47.1332	+	79.2727i	1.53082	+	2.57466i
$949$	1.54729	+	3.73550i	0.0502273	+	0.121259i
$950$	0.0298776	+	43.0912i	0.000969356	+	1.39806i
$951$	50.4499	+	50.4499i	1.63595	+	1.63595i
$952$	3.71455	−	2.58666i	0.120389	−	0.0838340i
$953$	0.626016	+	0.626016i	0.0202787	+	0.0202787i	0.717173	−	0.696895i	$-0.245436\pi$
$953$	0.626016	+	0.626016i	0.0202787	+	0.0202787i	−0.696895	+	0.717173i	$0.745436\pi$
$954$	−83.6220	+	6.01937i	−2.70736	+	0.194884i
$955$	−7.45626	+	6.94365i	−0.241279	+	0.224691i
$956$	−17.5555	−	13.1167i	−0.567786	−	0.424226i
$957$	−91.7948	−	38.0226i	−2.96730	−	1.22910i
$958$	−19.2279	+	9.63584i	−0.621225	+	0.311320i
$959$	−6.44651			−0.208169
$960$	52.7963	−	0.151700i	1.70399	−	0.00489608i
$961$	20.1975			0.651531
$962$	2.45661	−	1.23110i	0.0792042	−	0.0396923i
$963$	−63.8806	−	26.4602i	−2.05852	−	0.852669i
$964$	−2.26697	−	1.69378i	−0.0730142	−	0.0545531i
$965$	8.47433	+	9.09994i	0.272798	+	0.292937i
$966$	21.6470	−	1.55822i	0.696482	−	0.0501350i
$967$	27.0620	+	27.0620i	0.870256	+	0.870256i	0.992500	−	0.122244i	$-0.0390090\pi$
$967$	27.0620	+	27.0620i	0.870256	+	0.870256i	−0.122244	+	0.992500i	$0.539009\pi$
$968$	−14.7921	−	21.2421i	−0.475436	−	0.682748i
$969$	−15.7894	−	15.7894i	−0.507228	−	0.507228i
$970$	34.6031	+	12.8836i	1.11104	+	0.413666i
$971$	9.10702	+	21.9863i	0.292258	+	0.705574i	1.00000		0.000897824i	$-0.000285786\pi$
$971$	9.10702	+	21.9863i	0.292258	+	0.705574i	−0.707741	+	0.706472i	$0.750286\pi$
$972$	−4.98160	−	8.37849i	−0.159785	−	0.268740i
$973$	−4.13776	+	9.98944i	−0.132651	+	0.320247i
$974$	−38.8963	−	12.9261i	−1.24632	−	0.414178i
$975$	−3.09163	−	3.56625i	−0.0990115	−	0.114211i
$976$	−4.79666	−	0.506780i	−0.153537	−	0.0162216i
$977$	−49.6811			−1.58944			−0.794719	−	0.606977i	$-0.792382\pi$
$977$	−49.6811			−1.58944			−0.794719	+	0.606977i	$0.792382\pi$
$978$	1.25461	+	0.416935i	0.0401181	+	0.0133321i
$979$	2.72659	+	1.12939i	0.0871421	+	0.0360955i
$980$	23.7345	−	2.57659i	0.758171	−	0.0823063i
$981$	17.7106	+	42.7572i	0.565457	+	1.36513i
$982$	−8.45856	−	7.32259i	−0.269924	−	0.233673i
$983$	1.50245	−	1.50245i	0.0479207	−	0.0479207i	−0.682740	−	0.730661i	$-0.739212\pi$
$983$	1.50245	−	1.50245i	0.0479207	−	0.0479207i	0.730661	+	0.682740i	$0.239212\pi$
$984$	−16.9844	+	3.71926i	−0.541444	+	0.118566i
$985$	24.5992	+	11.2306i	0.783796	+	0.357837i
$986$	−0.945335	−	13.1327i	−0.0301056	−	0.418231i
$987$	0.797642	+	1.92568i	0.0253892	+	0.0612950i
$988$	−0.558306	−	3.85794i	−0.0177621	−	0.122737i
$989$	−8.06806	+	19.4780i	−0.256549	+	0.619365i
$990$	−59.3660	−	55.2079i	−1.88678	−	1.75462i
$991$	14.4312			0.458423			0.229211	−	0.973377i	$-0.426385\pi$
$991$	14.4312			0.458423			0.229211	+	0.973377i	$0.426385\pi$
$992$	−27.6491	−	29.5608i	−0.877861	−	0.938558i
$993$		−	54.2242i		−	1.72075i
$994$	0.457051	−	0.229046i	0.0144968	−	0.00726490i
$995$	1.22594	−	34.4385i	0.0388650	−	1.09178i
$996$	7.14980	+	49.4057i	0.226550	+	1.56548i
$997$	−16.7174	−	40.3594i	−0.529445	−	1.27819i	−0.931887	−	0.362748i	$-0.881838\pi$
$997$	−16.7174	−	40.3594i	−0.529445	−	1.27819i	0.402442	−	0.915446i	$-0.368162\pi$
$998$	−33.9332	+	2.44262i	−1.07414	+	0.0773197i
$999$	34.3693	−	34.3693i	1.08740	−	1.08740i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.2.z.a.109.3	yes	88
4.3	odd	2		640.2.z.a.529.2		88
5.2	odd	4		800.2.y.f.301.9		88
5.3	odd	4		800.2.y.f.301.14		88
5.4	even	2	inner	160.2.z.a.109.20	yes	88
20.19	odd	2		640.2.z.a.529.21		88
32.5	even	8	inner	160.2.z.a.69.20	yes	88
32.27	odd	8		640.2.z.a.369.21		88
160.37	odd	8		800.2.y.f.101.9		88
160.59	odd	8		640.2.z.a.369.2		88
160.69	even	8	inner	160.2.z.a.69.3	✓	88
160.133	odd	8		800.2.y.f.101.14		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.z.a.69.3	✓	88	160.69	even	8	inner
160.2.z.a.69.20	yes	88	32.5	even	8	inner
160.2.z.a.109.3	yes	88	1.1	even	1	trivial
160.2.z.a.109.20	yes	88	5.4	even	2	inner
640.2.z.a.369.2		88	160.59	odd	8
640.2.z.a.369.21		88	32.27	odd	8
640.2.z.a.529.2		88	4.3	odd	2
640.2.z.a.529.21		88	20.19	odd	2
800.2.y.f.101.9		88	160.37	odd	8
800.2.y.f.101.14		88	160.133	odd	8
800.2.y.f.301.9		88	5.2	odd	4
800.2.y.f.301.14		88	5.3	odd	4

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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	160.z (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26433 + 0.633607i) q^{2} +(2.72675 + 1.12946i) q^{3} +(1.19708 - 1.60218i) q^{4} +(-1.63639 + 1.52389i) q^{5} +(-4.16316 + 0.299677i) q^{6} +(0.911488 + 0.911488i) q^{7} +(-0.498360 + 2.78418i) q^{8} +(4.03817 + 4.03817i) q^{9} +(1.10339 - 2.96353i) q^{10} +(-1.71789 - 4.14736i) q^{11} +(5.07375 - 3.01670i) q^{12} +(0.122394 - 0.295486i) q^{13} +(-1.72995 - 0.574901i) q^{14} +(-6.18319 + 2.30703i) q^{15} +(-1.13398 - 3.83589i) q^{16} -1.24150 q^{17} +(-7.66422 - 2.54699i) q^{18} +(5.63014 + 2.33208i) q^{19} +(0.482655 + 4.44601i) q^{20} +(1.45591 + 3.51489i) q^{21} +(4.79979 + 4.15518i) q^{22} +(-2.85230 + 2.85230i) q^{23} +(-4.50351 + 7.02888i) q^{24} +(0.355529 - 4.98734i) q^{25} +(0.0324747 + 0.451143i) q^{26} +(3.06178 + 7.39179i) q^{27} +(2.55150 - 0.369243i) q^{28} +(2.86983 - 6.92838i) q^{29} +(6.35586 - 6.83457i) q^{30} -7.15524 q^{31} +(3.86418 + 4.13136i) q^{32} -13.2491i q^{33} +(1.56967 - 0.786622i) q^{34} +(-2.88055 - 0.102542i) q^{35} +(11.3039 - 1.63586i) q^{36} +(-2.32483 - 5.61264i) q^{37} +(-8.59601 + 0.618768i) q^{38} +(0.667478 - 0.667478i) q^{39} +(-3.42726 - 5.31544i) q^{40} +(1.47276 + 1.47276i) q^{41} +(-4.06782 - 3.52152i) q^{42} +(4.82876 - 2.00014i) q^{43} +(-8.70129 - 2.21236i) q^{44} +(-12.7617 - 0.454292i) q^{45} +(1.79902 - 5.41349i) q^{46} +0.547863 q^{47} +(1.24040 - 11.7403i) q^{48} -5.33838i q^{49} +(2.71051 + 6.53094i) q^{50} +(-3.38526 - 1.40222i) q^{51} +(-0.326907 - 0.549820i) q^{52} +(9.59054 - 3.97253i) q^{53} +(-8.55460 - 7.40573i) q^{54} +(9.13125 + 4.16881i) q^{55} +(-2.99199 + 2.08350i) q^{56} +(12.7180 + 12.7180i) q^{57} +(0.761447 + 10.5781i) q^{58} +(-1.54689 + 0.640744i) q^{59} +(-3.70550 + 12.6683i) q^{60} +(0.461455 - 1.11405i) q^{61} +(9.04662 - 4.53361i) q^{62} +7.36150i q^{63} +(-7.50328 - 2.77504i) q^{64} +(0.250003 + 0.670045i) q^{65} +(8.39472 + 16.7513i) q^{66} +(-14.5683 - 6.03439i) q^{67} +(-1.48618 + 1.98911i) q^{68} +(-10.9990 + 4.55595i) q^{69} +(3.70696 - 1.69549i) q^{70} +(-0.198299 + 0.198299i) q^{71} +(-13.2555 + 9.23053i) q^{72} +(-8.93915 + 8.93915i) q^{73} +(6.49558 + 5.62323i) q^{74} +(6.60243 - 13.1977i) q^{75} +(10.4762 - 6.22882i) q^{76} +(2.21443 - 5.34611i) q^{77} +(-0.420996 + 1.26683i) q^{78} +15.6241i q^{79} +(7.70111 + 4.54895i) q^{80} +6.48118i q^{81} +(-2.79521 - 0.928910i) q^{82} +(-3.23636 + 7.81327i) q^{83} +(7.37435 + 1.87497i) q^{84} +(2.03157 - 1.89190i) q^{85} +(-4.83786 + 5.58838i) q^{86} +(15.6506 - 15.6506i) q^{87} +(12.4031 - 2.71604i) q^{88} +(-0.464872 + 0.464872i) q^{89} +(16.4230 - 7.51156i) q^{90} +(0.380893 - 0.157771i) q^{91} +(1.15546 + 7.98434i) q^{92} +(-19.5106 - 8.08154i) q^{93} +(-0.692682 + 0.347130i) q^{94} +(-12.7669 + 4.76352i) q^{95} +(5.87047 + 15.6296i) q^{96} +11.6763i q^{97} +(3.38243 + 6.74950i) q^{98} +(9.81061 - 23.6849i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9} - 4 q^{10} - 8 q^{11} - 24 q^{14} - 8 q^{16} - 8 q^{19} - 4 q^{20} - 8 q^{21} - 16 q^{24} - 4 q^{25} + 32 q^{26} - 8 q^{29} - 52 q^{30} - 64 q^{31} - 24 q^{34}+ \cdots - 48 q^{99}+O(q^{100}) \) 88 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9 - 4 * q^10 - 8 * q^11 - 24 * q^14 - 8 * q^16 - 8 * q^19 - 4 * q^20 - 8 * q^21 - 16 * q^24 - 4 * q^25 + 32 * q^26 - 8 * q^29 - 52 * q^30 - 64 * q^31 - 24 * q^34 + 20 * q^35 + 72 * q^36 - 8 * q^39 - 56 * q^40 - 8 * q^41 - 8 * q^44 - 16 * q^45 - 8 * q^46 - 44 * q^50 - 48 * q^51 + 24 * q^54 + 28 * q^55 - 56 * q^56 + 24 * q^59 + 32 * q^60 + 24 * q^61 + 64 * q^64 - 8 * q^65 - 8 * q^66 - 40 * q^69 + 80 * q^70 - 40 * q^71 + 128 * q^74 + 28 * q^75 - 8 * q^76 + 48 * q^80 + 200 * q^84 - 24 * q^85 + 24 * q^86 - 8 * q^89 + 80 * q^90 - 8 * q^91 + 120 * q^94 - 8 * q^95 - 56 * q^96 - 48 * q^99

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