LMFDB - Embedded newform 275.2.l.d.31.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,2,Mod(31,275)] 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("275.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([4, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.l (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [100,2,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$25$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.6
Character	$\chi$	$=$	275.31
Dual form			275.2.l.d.71.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.83159 q^{2} +(0.699896 - 2.15406i) q^{3} +1.35471 q^{4} +(1.42132 - 1.72623i) q^{5} +(-1.28192 + 3.94534i) q^{6} +(2.79400 + 2.02996i) q^{7} +1.18190 q^{8} +(-1.72306 - 1.25188i) q^{9} +(-2.60327 + 3.16173i) q^{10} +(3.31036 - 0.203811i) q^{11} +(0.948156 - 2.91812i) q^{12} +(3.62771 + 2.63568i) q^{13} +(-5.11745 - 3.71805i) q^{14} +(-2.72362 - 4.26978i) q^{15} -4.87418 q^{16} +(0.167452 - 0.515364i) q^{17} +(3.15593 + 2.29292i) q^{18} -6.83359 q^{19} +(1.92547 - 2.33854i) q^{20} +(6.32816 - 4.59768i) q^{21} +(-6.06321 + 0.373298i) q^{22} +(0.562574 + 1.73142i) q^{23} +(0.827210 - 2.54589i) q^{24} +(-0.959714 - 4.90703i) q^{25} +(-6.64446 - 4.82748i) q^{26} +(1.59448 - 1.15846i) q^{27} +(3.78506 + 2.75001i) q^{28} -2.59887 q^{29} +(4.98854 + 7.82047i) q^{30} +(-1.07206 + 0.778901i) q^{31} +6.56368 q^{32} +(1.87788 - 7.27334i) q^{33} +(-0.306702 + 0.943933i) q^{34} +(7.47533 - 1.93786i) q^{35} +(-2.33424 - 1.69593i) q^{36} +(-7.31128 + 5.31196i) q^{37} +12.5163 q^{38} +(8.21643 - 5.96959i) q^{39} +(1.67986 - 2.04023i) q^{40} +(-1.66988 - 5.13937i) q^{41} +(-11.5906 + 8.42104i) q^{42} +0.229816 q^{43} +(4.48457 - 0.276105i) q^{44} +(-4.61003 + 1.19508i) q^{45} +(-1.03040 - 3.17125i) q^{46} +(-1.18353 + 3.64254i) q^{47} +(-3.41142 + 10.4993i) q^{48} +(1.52258 + 4.68602i) q^{49} +(1.75780 + 8.98765i) q^{50} +(-0.992924 - 0.721402i) q^{51} +(4.91449 + 3.57059i) q^{52} +(-0.549782 - 1.69206i) q^{53} +(-2.92043 + 2.12182i) q^{54} +(4.35324 - 6.00410i) q^{55} +(3.30224 + 2.39922i) q^{56} +(-4.78280 + 14.7199i) q^{57} +4.76006 q^{58} +(-2.80631 + 2.03890i) q^{59} +(-3.68971 - 5.78431i) q^{60} +(-11.4278 + 8.30277i) q^{61} +(1.96358 - 1.42662i) q^{62} +(-2.27297 - 6.99548i) q^{63} -2.27358 q^{64} +(9.70591 - 2.51610i) q^{65} +(-3.43951 + 13.3218i) q^{66} +(-9.64145 - 7.00493i) q^{67} +(0.226849 - 0.698168i) q^{68} +4.12333 q^{69} +(-13.6917 + 3.54936i) q^{70} +(-2.57203 - 1.86869i) q^{71} +(-2.03649 - 1.47960i) q^{72} +(0.901745 - 2.77528i) q^{73} +(13.3912 - 9.72931i) q^{74} +(-11.2417 - 1.36713i) q^{75} -9.25753 q^{76} +(9.66287 + 6.15044i) q^{77} +(-15.0491 + 10.9338i) q^{78} +(4.64697 + 14.3019i) q^{79} +(-6.92776 + 8.41394i) q^{80} +(-3.35386 - 10.3221i) q^{81} +(3.05854 + 9.41321i) q^{82} +(-4.37159 + 13.4544i) q^{83} +(8.57282 - 6.22852i) q^{84} +(-0.651632 - 1.02155i) q^{85} -0.420928 q^{86} +(-1.81894 + 5.59812i) q^{87} +(3.91253 - 0.240885i) q^{88} +(-0.966770 - 2.97541i) q^{89} +(8.44368 - 2.18889i) q^{90} +(4.78548 + 14.7282i) q^{91} +(0.762124 + 2.34558i) q^{92} +(0.927463 + 2.85444i) q^{93} +(2.16774 - 6.67163i) q^{94} +(-9.71270 + 11.7963i) q^{95} +(4.59389 - 14.1385i) q^{96} +(-0.372622 - 1.14681i) q^{97} +(-2.78874 - 8.58285i) q^{98} +(-5.95908 - 3.79298i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 2 q^{2} - 2 q^{3} + 106 q^{4} + 5 q^{5} + 5 q^{6} + 5 q^{7} - 30 q^{8} - 25 q^{9} - 22 q^{10} - 53 q^{12} - 18 q^{13} - 10 q^{14} + 16 q^{15} + 62 q^{16} + q^{17} - 21 q^{18} + 6 q^{19} + q^{20}+ \cdots - 84 q^{99}+O(q^{100}) $ 100 * q + 2 * q^2 - 2 * q^3 + 106 * q^4 + 5 * q^5 + 5 * q^6 + 5 * q^7 - 30 * q^8 - 25 * q^9 - 22 * q^10 - 53 * q^12 - 18 * q^13 - 10 * q^14 + 16 * q^15 + 62 * q^16 + q^17 - 21 * q^18 + 6 * q^19 + q^20 - 22 * q^21 + 6 * q^22 + 20 * q^23 - 18 * q^24 + q^25 - 37 * q^26 + 10 * q^27 - 64 * q^28 - 28 * q^29 + 15 * q^30 + 9 * q^31 - 98 * q^32 + 13 * q^33 - 14 * q^34 + 13 * q^35 - 30 * q^36 - 21 * q^37 + 18 * q^38 + 44 * q^39 + 9 * q^40 + 28 * q^41 + 31 * q^42 + 82 * q^43 - 4 * q^44 - 25 * q^45 - 16 * q^46 - 10 * q^47 - 72 * q^48 - 26 * q^49 - 46 * q^50 - 14 * q^51 - 23 * q^52 - 5 * q^53 - 22 * q^54 + 32 * q^55 + q^56 - 85 * q^57 + 80 * q^58 - 3 * q^59 + 61 * q^60 + 35 * q^61 + 43 * q^62 - 47 * q^63 - 54 * q^64 - 64 * q^65 - 13 * q^66 - 20 * q^67 + 5 * q^68 + 76 * q^69 - 23 * q^70 + 28 * q^71 - 53 * q^72 + 33 * q^73 - 3 * q^74 - 34 * q^75 - 156 * q^76 + 45 * q^77 + 30 * q^78 + 4 * q^79 - 144 * q^80 - 27 * q^81 - 59 * q^82 - 92 * q^83 + 9 * q^84 - 26 * q^85 - 56 * q^86 + 38 * q^87 + 18 * q^88 + 39 * q^89 + 114 * q^90 - 11 * q^91 - 60 * q^92 - 19 * q^93 + 46 * q^94 - 46 * q^95 + 9 * q^96 + 20 * q^97 + 122 * q^98 - 84 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−1.83159			−1.29513			−0.647564	−	0.762011i	$-0.724212\pi$
$2$	−1.83159			−1.29513			−0.647564	+	0.762011i	$0.724212\pi$
$3$	0.699896	−	2.15406i	0.404085	−	1.24365i	−0.517572	−	0.855640i	$-0.673164\pi$
$3$	0.699896	−	2.15406i	0.404085	−	1.24365i	0.921657	−	0.388006i	$-0.126836\pi$
$4$	1.35471			0.677355
$5$	1.42132	−	1.72623i	0.635632	−	0.771992i
$5$	1.42132	−	1.72623i	0.635632	−	0.771992i
$6$	−1.28192	+	3.94534i	−0.523342	+	1.61068i
$7$	2.79400	+	2.02996i	1.05603	+	0.767253i	0.973350	−	0.229323i	$-0.0736513\pi$
$7$	2.79400	+	2.02996i	1.05603	+	0.767253i	0.0826825	+	0.996576i	$0.473651\pi$
$8$	1.18190			0.417866
$9$	−1.72306	−	1.25188i	−0.574353	−	0.417292i
$10$	−2.60327	+	3.16173i	−0.823225	+	0.999828i
$11$	3.31036	−	0.203811i	0.998110	−	0.0614514i
$11$	3.31036	−	0.203811i	0.998110	−	0.0614514i
$12$	0.948156	−	2.91812i	0.273709	−	0.842390i
$13$	3.62771	+	2.63568i	1.00615	+	0.731007i	0.963397	−	0.268079i	$-0.0863887\pi$
$13$	3.62771	+	2.63568i	1.00615	+	0.731007i	0.0427481	+	0.999086i	$0.486389\pi$
$14$	−5.11745	−	3.71805i	−1.36770	−	0.993690i
$15$	−2.72362	−	4.26978i	−0.703235	−	1.10245i
$16$	−4.87418			−1.21855
$17$	0.167452	−	0.515364i	0.0406130	−	0.124994i	−0.928694	−	0.370846i	$-0.879068\pi$
$17$	0.167452	−	0.515364i	0.0406130	−	0.124994i	0.969307	+	0.245852i	$0.0790677\pi$
$18$	3.15593	+	2.29292i	0.743860	+	0.540446i
$19$	−6.83359			−1.56773			−0.783866	−	0.620930i	$-0.786755\pi$
$19$	−6.83359			−1.56773			−0.783866	+	0.620930i	$0.786755\pi$
$20$	1.92547	−	2.33854i	0.430549	−	0.522913i
$21$	6.32816	−	4.59768i	1.38092	−	1.00330i
$22$	−6.06321	+	0.373298i	−1.29268	+	0.0795874i
$23$	0.562574	+	1.73142i	0.117305	+	0.361027i	0.992421	−	0.122886i	$-0.0392151\pi$
$23$	0.562574	+	1.73142i	0.117305	+	0.361027i	−0.875116	+	0.483913i	$0.839215\pi$
$24$	0.827210	−	2.54589i	0.168854	−	0.519678i
$25$	−0.959714	−	4.90703i	−0.191943	−	0.981406i
$26$	−6.64446	−	4.82748i	−1.30309	−	0.946748i
$27$	1.59448	−	1.15846i	0.306858	−	0.222945i
$28$	3.78506	+	2.75001i	0.715309	+	0.519703i
$29$	−2.59887			−0.482598			−0.241299	−	0.970451i	$-0.577573\pi$
$29$	−2.59887			−0.482598			−0.241299	+	0.970451i	$0.577573\pi$
$30$	4.98854	+	7.82047i	0.910779	+	1.42782i
$31$	−1.07206	+	0.778901i	−0.192549	+	0.139895i	−0.679883	−	0.733321i	$-0.737969\pi$
$31$	−1.07206	+	0.778901i	−0.192549	+	0.139895i	0.487334	+	0.873216i	$0.337969\pi$
$32$	6.56368			1.16030
$33$	1.87788	−	7.27334i	0.326898	−	1.26613i
$34$	−0.306702	+	0.943933i	−0.0525990	+	0.161883i
$35$	7.47533	−	1.93786i	1.26356	−	0.327558i
$36$	−2.33424	−	1.69593i	−0.389041	−	0.282655i
$37$	−7.31128	+	5.31196i	−1.20197	+	0.873280i	−0.994477	−	0.104957i	$-0.966529\pi$
$37$	−7.31128	+	5.31196i	−1.20197	+	0.873280i	−0.207490	+	0.978237i	$0.566529\pi$
$38$	12.5163			2.03041
$39$	8.21643	−	5.96959i	1.31568	−	0.955899i
$40$	1.67986	−	2.04023i	0.265609	−	0.322589i
$41$	−1.66988	−	5.13937i	−0.260792	−	0.802635i	−0.992633	−	0.121160i	$-0.961339\pi$
$41$	−1.66988	−	5.13937i	−0.260792	−	0.802635i	0.731841	−	0.681475i	$-0.238661\pi$
$42$	−11.5906	+	8.42104i	−1.78846	+	1.29940i
$43$	0.229816			0.0350466			0.0175233	−	0.999846i	$-0.494422\pi$
$43$	0.229816			0.0350466			0.0175233	+	0.999846i	$0.494422\pi$
$44$	4.48457	−	0.276105i	0.676075	−	0.0416244i
$45$	−4.61003	+	1.19508i	−0.687223	+	0.178152i
$46$	−1.03040	−	3.17125i	−0.151925	−	0.467576i
$47$	−1.18353	+	3.64254i	−0.172636	+	0.531319i	−0.999518	−	0.0310570i	$-0.990113\pi$
$47$	−1.18353	+	3.64254i	−0.172636	+	0.531319i	0.826882	+	0.562376i	$0.190113\pi$
$48$	−3.41142	+	10.4993i	−0.492396	+	1.51544i
$49$	1.52258	+	4.68602i	0.217512	+	0.669432i
$50$	1.75780	+	8.98765i	0.248591	+	1.27105i
$51$	−0.992924	−	0.721402i	−0.139037	−	0.101016i
$52$	4.91449	+	3.57059i	0.681517	+	0.495151i
$53$	−0.549782	−	1.69206i	−0.0755184	−	0.232422i	0.906171	−	0.422912i	$-0.138992\pi$
$53$	−0.549782	−	1.69206i	−0.0755184	−	0.232422i	−0.981689	+	0.190491i	$0.938992\pi$
$54$	−2.92043	+	2.12182i	−0.397420	+	0.288742i
$55$	4.35324	−	6.00410i	0.586991	−	0.809593i
$56$	3.30224	+	2.39922i	0.441281	+	0.320609i
$57$	−4.78280	+	14.7199i	−0.633497	+	1.94970i
$58$	4.76006			0.625026
$59$	−2.80631	+	2.03890i	−0.365351	+	0.265443i	−0.755280	−	0.655402i	$-0.772499\pi$
$59$	−2.80631	+	2.03890i	−0.365351	+	0.265443i	0.389930	+	0.920845i	$0.372499\pi$
$60$	−3.68971	−	5.78431i	−0.476340	−	0.746751i
$61$	−11.4278	+	8.30277i	−1.46318	+	1.06306i	−0.480656	+	0.876909i	$0.659601\pi$
$61$	−11.4278	+	8.30277i	−1.46318	+	1.06306i	−0.982521	+	0.186151i	$0.940399\pi$
$62$	1.96358	−	1.42662i	0.249375	−	0.181181i
$63$	−2.27297	−	6.99548i	−0.286367	−	0.881348i
$64$	−2.27358			−0.284198
$65$	9.70591	−	2.51610i	1.20387	−	0.312084i
$66$	−3.43951	+	13.3218i	−0.423374	+	1.63980i
$67$	−9.64145	−	7.00493i	−1.17789	−	0.855788i	−0.185959	−	0.982558i	$-0.559539\pi$
$67$	−9.64145	−	7.00493i	−1.17789	−	0.855788i	−0.991932	+	0.126769i	$0.959539\pi$
$68$	0.226849	−	0.698168i	0.0275094	−	0.0846653i
$69$	4.12333			0.496390
$70$	−13.6917	+	3.54936i	−1.63647	+	0.424229i
$71$	−2.57203	−	1.86869i	−0.305244	−	0.221773i	0.424609	−	0.905377i	$-0.360412\pi$
$71$	−2.57203	−	1.86869i	−0.305244	−	0.221773i	−0.729853	+	0.683604i	$0.760412\pi$
$72$	−2.03649	−	1.47960i	−0.240003	−	0.174372i
$73$	0.901745	−	2.77528i	0.105541	−	0.324823i	−0.884316	−	0.466889i	$-0.845375\pi$
$73$	0.901745	−	2.77528i	0.105541	−	0.324823i	0.989857	+	0.142067i	$0.0453747\pi$
$74$	13.3912	−	9.72931i	1.55670	−	1.13101i
$75$	−11.2417	−	1.36713i	−1.29808	−	0.157863i
$76$	−9.25753			−1.06191
$77$	9.66287	+	6.15044i	1.10119	+	0.700908i
$78$	−15.0491	+	10.9338i	−1.70398	+	1.23801i
$79$	4.64697	+	14.3019i	0.522825	+	1.60909i	0.768577	+	0.639757i	$0.220965\pi$
$79$	4.64697	+	14.3019i	0.522825	+	1.60909i	−0.245752	+	0.969333i	$0.579035\pi$
$80$	−6.92776	+	8.41394i	−0.774547	+	0.940707i
$81$	−3.35386	−	10.3221i	−0.372651	−	1.14690i
$82$	3.05854	+	9.41321i	0.337759	+	1.03952i
$83$	−4.37159	+	13.4544i	−0.479844	+	1.47681i	0.359468	+	0.933158i	$0.382958\pi$
$83$	−4.37159	+	13.4544i	−0.479844	+	1.47681i	−0.839312	+	0.543651i	$0.817042\pi$
$84$	8.57282	−	6.22852i	0.935371	−	0.679587i
$85$	−0.651632	−	1.02155i	−0.0706794	−	0.110803i
$86$	−0.420928			−0.0453898
$87$	−1.81894	+	5.59812i	−0.195011	+	0.600181i
$88$	3.91253	−	0.240885i	0.417077	−	0.0256785i
$89$	−0.966770	−	2.97541i	−0.102477	−	0.315393i	0.886653	−	0.462436i	$-0.153024\pi$
$89$	−0.966770	−	2.97541i	−0.102477	−	0.315393i	−0.989130	+	0.147043i	$0.953024\pi$
$90$	8.44368	−	2.18889i	0.890041	−	0.230729i
$91$	4.78548	+	14.7282i	0.501655	+	1.54394i
$92$	0.762124	+	2.34558i	0.0794569	+	0.244543i
$93$	0.927463	+	2.85444i	0.0961735	+	0.295991i
$94$	2.16774	−	6.67163i	0.223586	−	0.688126i
$95$	−9.71270	+	11.7963i	−0.996502	+	1.21028i
$96$	4.59389	−	14.1385i	0.468862	−	1.44301i
$97$	−0.372622	−	1.14681i	−0.0378340	−	0.116441i	0.930356	−	0.366658i	$-0.119498\pi$
$97$	−0.372622	−	1.14681i	−0.0378340	−	0.116441i	−0.968190	+	0.250217i	$0.919498\pi$
$98$	−2.78874	−	8.58285i	−0.281705	−	0.866999i
$99$	−5.95908	−	3.79298i	−0.598910	−	0.381208i
$100$	−1.30013	−	6.64760i	−0.130013	−	0.664760i
$101$	3.67013	−	11.2955i	0.365191	−	1.12394i	−0.584670	−	0.811271i	$-0.698776\pi$
$101$	3.67013	−	11.2955i	0.365191	−	1.12394i	0.949861	−	0.312672i	$-0.101224\pi$
$102$	1.81863	+	1.32131i	0.180071	+	0.130829i
$103$	14.0604			1.38542			0.692708	−	0.721219i	$-0.256418\pi$
$103$	14.0604			1.38542			0.692708	+	0.721219i	$0.256418\pi$
$104$	4.28760	+	3.11513i	0.420434	+	0.305463i
$105$	1.05769	−	17.4586i	0.103220	−	1.70378i
$106$	1.00697	+	3.09915i	0.0978060	+	0.301016i
$107$	14.9630	−	10.8712i	1.44653	−	1.05096i	0.459900	−	0.887971i	$-0.347885\pi$
$107$	14.9630	−	10.8712i	1.44653	−	1.05096i	0.986627	−	0.162992i	$-0.0521146\pi$
$108$	2.16006	−	1.56937i	0.207852	−	0.151013i
$109$	−0.972933	+	2.99438i	−0.0931901	+	0.286810i	−0.986778	−	0.162079i	$-0.948180\pi$
$109$	−0.972933	+	2.99438i	−0.0931901	+	0.286810i	0.893588	+	0.448889i	$0.148180\pi$
$110$	−7.97334	+	10.9970i	−0.760228	+	1.04853i
$111$	6.32512	+	19.4667i	0.600354	+	1.84770i
$112$	−13.6185	−	9.89439i	−1.28682	−	0.934932i
$113$	−5.83129	−	17.9469i	−0.548562	−	1.68830i	−0.712367	−	0.701807i	$-0.752377\pi$
$113$	−5.83129	−	17.9469i	−0.548562	−	1.68830i	0.163806	−	0.986493i	$-0.447623\pi$
$114$	8.76011	−	26.9609i	0.820460	−	2.52512i
$115$	3.78842	+	1.48977i	0.353272	+	0.138922i
$116$	−3.52072			−0.326890
$117$	−2.95121	−	9.08288i	−0.272839	−	0.839712i
$118$	5.14000	−	3.73443i	0.473175	−	0.343782i
$119$	1.51403	−	1.10001i	0.138791	−	0.100837i
$120$	−3.21905	−	5.04647i	−0.293858	−	0.460677i
$121$	10.9169	−	1.34938i	0.992447	−	0.122670i
$122$	20.9310	−	15.2072i	1.89500	−	1.37680i
$123$	−12.2393			−1.10358
$124$	−1.45234	+	1.05518i	−0.130424	+	0.0947584i
$125$	−9.83470	−	5.31776i	−0.879643	−	0.475635i
$126$	4.16314	+	12.8128i	0.370882	+	1.14146i
$127$	1.77543	−	1.28992i	0.157544	−	0.114462i	−0.506220	−	0.862404i	$-0.668958\pi$
$127$	1.77543	−	1.28992i	0.157544	−	0.114462i	0.663764	+	0.747942i	$0.268958\pi$
$128$	−8.96309			−0.792233
$129$	0.160847	−	0.495037i	0.0141618	−	0.0435855i
$130$	−17.7772	+	4.60846i	−1.55917	+	0.404189i
$131$	−11.0503	−	8.02853i	−0.965471	−	0.701456i	−0.0110560	−	0.999939i	$-0.503519\pi$
$131$	−11.0503	−	8.02853i	−0.965471	−	0.701456i	−0.954415	+	0.298483i	$0.903519\pi$
$132$	2.54399	−	9.85327i	0.221426	−	0.857617i
$133$	−19.0930	−	13.8719i	−1.65558	−	1.20285i
$134$	17.6592	+	12.8301i	1.52552	+	1.10835i
$135$	0.266502	−	4.39897i	0.0229368	−	0.378603i
$136$	0.197912	−	0.609111i	0.0169708	−	0.0522308i
$137$	18.4640			1.57749			0.788744	−	0.614721i	$-0.210732\pi$
$137$	18.4640			1.57749			0.788744	+	0.614721i	$0.210732\pi$
$138$	−7.55224			−0.642889
$139$	−5.65014	+	17.3893i	−0.479238	+	1.47494i	0.360917	+	0.932598i	$0.382464\pi$
$139$	−5.65014	+	17.3893i	−0.479238	+	1.47494i	−0.840155	+	0.542346i	$0.817536\pi$
$140$	10.1269	−	2.62524i	0.855880	−	0.221873i
$141$	7.01789	+	5.09880i	0.591013	+	0.429396i
$142$	4.71090	+	3.42267i	0.395330	+	0.287224i
$143$	12.5462	+	7.98569i	1.04917	+	0.667797i
$144$	8.39850	+	6.10187i	0.699875	+	0.508489i
$145$	−3.69382	+	4.48624i	−0.306755	+	0.372562i
$146$	−1.65162	+	5.08317i	−0.136689	+	0.420687i
$147$	11.1596			0.920429
$148$	−9.90466	+	7.19616i	−0.814158	+	0.591521i
$149$	−0.528222	−	1.62570i	−0.0432736	−	0.133182i	0.927086	−	0.374850i	$-0.122306\pi$
$149$	−0.528222	−	1.62570i	−0.0432736	−	0.133182i	−0.970359	+	0.241667i	$0.922306\pi$
$150$	20.5902	+	2.50402i	1.68118	+	0.204452i
$151$	1.50879	−	1.09620i	0.122784	−	0.0892075i	−0.524699	−	0.851288i	$-0.675822\pi$
$151$	1.50879	−	1.09620i	0.122784	−	0.0892075i	0.647482	+	0.762081i	$0.275822\pi$
$152$	−8.07665			−0.655103
$153$	−0.933700	+	0.678373i	−0.0754852	+	0.0548432i
$154$	−17.6984	−	11.2651i	−1.42618	−	0.907765i
$155$	−0.179185	+	2.95769i	−0.0143925	+	0.237567i
$156$	11.1309	−	8.08706i	0.891184	−	0.647483i
$157$	3.06924	−	2.22993i	0.244952	−	0.177968i	−0.458535	−	0.888677i	$-0.651626\pi$
$157$	3.06924	−	2.22993i	0.244952	−	0.177968i	0.703487	+	0.710709i	$0.251626\pi$
$158$	−8.51133	−	26.1952i	−0.677125	−	2.08398i
$159$	−4.02958			−0.319566
$160$	9.32907	−	11.3304i	0.737527	−	0.895746i
$161$	−1.94289	+	5.97960i	−0.153121	+	0.471259i
$162$	6.14289	+	18.9059i	0.482631	+	1.48539i
$163$	11.7046	+	8.50390i	0.916776	+	0.666077i	0.942719	−	0.333587i	$-0.108259\pi$
$163$	11.7046	+	8.50390i	0.916776	+	0.666077i	−0.0259433	+	0.999663i	$0.508259\pi$
$164$	−2.26221	−	6.96236i	−0.176649	−	0.543669i
$165$	−9.88637	−	13.5794i	−0.769653	−	1.05715i
$166$	8.00694	−	24.6428i	0.621459	−	1.91265i
$167$	−8.35748	+	6.07206i	−0.646721	+	0.469870i	−0.862153	−	0.506648i	$-0.830884\pi$
$167$	−8.35748	+	6.07206i	−0.646721	+	0.469870i	0.215432	+	0.976519i	$0.430884\pi$
$168$	7.47928	−	5.43401i	0.577039	−	0.419243i
$169$	2.19621	+	6.75925i	0.168939	+	0.519942i
$170$	1.19352	+	1.87107i	0.0915389	+	0.143504i
$171$	11.7747	+	8.55480i	0.900432	+	0.654202i
$172$	0.311334			0.0237390
$173$	1.95933	+	1.42354i	0.148965	+	0.108229i	0.659771	−	0.751466i	$-0.270653\pi$
$173$	1.95933	+	1.42354i	0.148965	+	0.108229i	−0.510806	+	0.859696i	$0.670653\pi$
$174$	3.33154	−	10.2534i	0.252564	−	0.777311i
$175$	7.27963	−	15.6584i	0.550289	−	1.18367i
$176$	−16.1353	+	0.993412i	−1.21624	+	0.0748813i
$177$	2.42779	+	7.47197i	0.182484	+	0.561628i
$178$	1.77072	+	5.44972i	0.132721	+	0.408474i
$179$	−5.17830	+	15.9372i	−0.387044	+	1.19120i	0.547942	+	0.836516i	$0.315411\pi$
$179$	−5.17830	+	15.9372i	−0.387044	+	1.19120i	−0.934986	+	0.354684i	$0.884589\pi$
$180$	−6.24526	+	1.61898i	−0.465494	+	0.120672i
$181$	6.04508	−	18.6048i	0.449327	−	1.38289i	−0.428341	−	0.903617i	$-0.640902\pi$
$181$	6.04508	−	18.6048i	0.449327	−	1.38289i	0.877668	−	0.479269i	$-0.159098\pi$
$182$	−8.76503	−	26.9760i	−0.649707	−	1.99959i
$183$	9.88638	+	30.4272i	0.730822	+	2.24924i
$184$	0.664908	+	2.04638i	0.0490177	+	0.150861i
$185$	−1.22201	+	20.1709i	−0.0898440	+	1.48299i
$186$	−1.69873	−	5.22815i	−0.124557	−	0.383347i
$187$	0.449288	−	1.74017i	0.0328552	−	0.127254i
$188$	−1.60334	+	4.93459i	−0.116936	+	0.359892i
$189$	6.80660			0.495107
$190$	17.7896	−	21.6060i	1.29060	−	1.56746i
$191$	−11.1958	+	8.13421i	−0.810098	+	0.588570i	−0.913859	−	0.406032i	$-0.866912\pi$
$191$	−11.1958	+	8.13421i	−0.810098	+	0.588570i	0.103761	+	0.994602i	$0.466912\pi$
$192$	−1.59127	+	4.89742i	−0.114840	+	0.353441i
$193$	3.08766	+	9.50283i	0.222254	+	0.684029i	0.998559	+	0.0536705i	$0.0170921\pi$
$193$	3.08766	+	9.50283i	0.222254	+	0.684029i	−0.776304	+	0.630358i	$0.782908\pi$
$194$	0.682489	+	2.10049i	0.0489999	+	0.150806i
$195$	1.37330	−	22.6681i	0.0983439	−	1.62330i
$196$	2.06266	+	6.34820i	0.147333	+	0.453443i
$197$	−13.5084	+	9.81445i	−0.962436	+	0.699251i	−0.953715	−	0.300711i	$-0.902776\pi$
$197$	−13.5084	+	9.81445i	−0.962436	+	0.699251i	−0.00872064	+	0.999962i	$0.502776\pi$
$198$	10.9146	+	6.94716i	0.775665	+	0.493713i
$199$	7.21473			0.511439			0.255719	−	0.966751i	$-0.417688\pi$
$199$	7.21473			0.511439			0.255719	+	0.966751i	$0.417688\pi$
$200$	−1.13429	−	5.79964i	−0.0802065	−	0.410097i
$201$	−21.8370	+	15.8655i	−1.54027	+	1.11907i
$202$	−6.72215	+	20.6887i	−0.472969	+	1.45565i
$203$	−7.26124	−	5.27560i	−0.509639	−	0.370275i
$204$	−1.34512	−	0.977290i	−0.0941775	−	0.0684240i
$205$	−11.2452	−	4.42208i	−0.785396	−	0.308852i
$206$	−25.7529			−1.79429
$207$	1.19818	−	3.68762i	0.0832792	−	0.256307i
$208$	−17.6821	−	12.8468i	−1.22603	−	0.890765i
$209$	−22.6216	+	1.39276i	−1.56477	+	0.0963393i
$210$	−1.93725	+	31.9769i	−0.133683	+	2.20662i
$211$	−22.9119			−1.57732			−0.788661	−	0.614828i	$-0.789225\pi$
$211$	−22.9119			−1.57732			−0.788661	+	0.614828i	$0.789225\pi$
$212$	−0.744796	−	2.29225i	−0.0511528	−	0.157432i
$213$	−5.82543	+	4.23242i	−0.399152	+	0.290001i
$214$	−27.4060	+	19.9116i	−1.87344	+	1.36113i
$215$	0.326641	−	0.396714i	0.0222767	−	0.0270557i
$216$	1.88452	−	1.36919i	0.128226	−	0.0931613i
$217$	−4.57649			−0.310672
$218$	1.78201	−	5.48447i	0.120693	−	0.371455i
$219$	−5.34700	−	3.88482i	−0.361316	−	0.262512i
$220$	5.89738	−	8.13382i	0.397601	−	0.548382i
$221$	1.96580	−	1.42824i	0.132234	−	0.0960737i
$222$	−11.5850	−	35.6550i	−0.777535	−	2.39301i
$223$	8.56345	+	6.22171i	0.573451	+	0.416636i	0.836357	−	0.548185i	$-0.184681\pi$
$223$	8.56345	+	6.22171i	0.573451	+	0.416636i	−0.262906	+	0.964821i	$0.584681\pi$
$224$	18.3389	+	13.3240i	1.22532	+	0.890247i
$225$	−4.48935	+	9.65654i	−0.299290	+	0.643770i
$226$	10.6805	+	32.8712i	0.710457	+	2.18656i
$227$	1.47883	−	4.55138i	0.0981537	−	0.302086i	−0.889909	−	0.456138i	$-0.849232\pi$
$227$	1.47883	−	4.55138i	0.0981537	−	0.302086i	0.988063	+	0.154052i	$0.0492323\pi$
$228$	−6.47931	+	19.9413i	−0.429103	+	1.32064i
$229$	−5.32599	−	16.3917i	−0.351951	−	1.08319i	−0.957756	−	0.287582i	$-0.907149\pi$
$229$	−5.32599	−	16.3917i	−0.351951	−	1.08319i	0.605805	−	0.795613i	$-0.292851\pi$
$230$	−6.93883	−	2.72865i	−0.457533	−	0.179922i
$231$	20.0114	−	16.5097i	1.31665	−	1.08626i
$232$	−3.07162			−0.201661
$233$	3.61514	−	2.62655i	0.236836	−	0.172071i	−0.463037	−	0.886339i	$-0.653240\pi$
$233$	3.61514	−	2.62655i	0.236836	−	0.172071i	0.699872	+	0.714268i	$0.253240\pi$
$234$	5.40539	+	16.6361i	0.353361	+	1.08753i
$235$	4.60567	+	7.22025i	0.300441	+	0.470997i
$236$	−3.80174	+	2.76212i	−0.247472	+	0.179799i
$237$	34.0595			2.21240
$238$	−2.77307	+	2.01476i	−0.179752	+	0.130597i
$239$	6.57589	+	4.77767i	0.425359	+	0.309042i	0.779791	−	0.626041i	$-0.215326\pi$
$239$	6.57589	+	4.77767i	0.425359	+	0.309042i	−0.354431	+	0.935082i	$0.615326\pi$
$240$	13.2754	+	20.8117i	0.856923	+	1.34339i
$241$	0.440040	−	1.35430i	0.0283454	−	0.0872383i	−0.935883	−	0.352311i	$-0.885396\pi$
$241$	0.440040	−	1.35430i	0.0283454	−	0.0872383i	0.964228	+	0.265073i	$0.0853959\pi$
$242$	−19.9953	+	2.47150i	−1.28535	+	0.158874i
$243$	−18.6692			−1.19763
$244$	−15.4813	+	11.2478i	−0.991090	+	0.720069i
$245$	10.2532	+	4.03200i	0.655053	+	0.257595i
$246$	22.4173			1.42927
$247$	−24.7903	−	18.0112i	−1.57737	−	1.14602i
$248$	−1.26708	+	0.920586i	−0.0804595	+	0.0584573i
$249$	25.9218	+	18.8333i	1.64273	+	1.19351i
$250$	18.0131	+	9.73994i	1.13925	+	0.616008i
$251$	1.62139	−	4.99012i	0.102341	−	0.314974i	−0.886756	−	0.462238i	$-0.847047\pi$
$251$	1.62139	−	4.99012i	0.102341	−	0.314974i	0.989097	+	0.147264i	$0.0470467\pi$
$252$	−3.07921	−	9.47685i	−0.193972	−	0.596985i
$253$	2.21520	+	5.61697i	0.139269	+	0.353136i
$254$	−3.25185	+	2.36261i	−0.204039	+	0.148243i
$255$	−2.65656	+	0.688671i	−0.166360	+	0.0431263i
$256$	20.9638			1.31024
$257$	−17.9191	−	13.0190i	−1.11776	−	0.812101i	−0.133893	−	0.990996i	$-0.542748\pi$
$257$	−17.9191	−	13.0190i	−1.11776	−	0.812101i	−0.983868	+	0.178894i	$0.942748\pi$
$258$	−0.294605	+	0.906702i	−0.0183413	+	0.0564488i
$259$	−31.2108			−1.93934
$260$	13.1487	−	3.40859i	0.815447	−	0.211392i
$261$	4.47801	+	3.25346i	0.277182	+	0.201384i
$262$	20.2396	+	14.7049i	1.25041	+	0.908474i
$263$	−3.28610	+	10.1136i	−0.202630	+	0.623630i	0.797173	+	0.603751i	$0.206328\pi$
$263$	−3.28610	+	10.1136i	−0.202630	+	0.623630i	−0.999802	+	0.0198786i	$0.993672\pi$
$264$	2.21948	−	8.59640i	0.136599	−	0.529072i
$265$	−3.70229	−	1.45590i	−0.227430	−	0.0894352i
$266$	34.9706	+	25.4076i	2.14418	+	1.55784i
$267$	−7.08585			−0.433647
$268$	−13.0614	−	9.48965i	−0.797851	−	0.579672i
$269$	3.89980	−	12.0023i	0.237775	−	0.731796i	−0.758966	−	0.651130i	$-0.774295\pi$
$269$	3.89980	−	12.0023i	0.237775	−	0.731796i	0.996741	−	0.0806661i	$-0.0257047\pi$
$270$	−0.488122	+	8.05709i	−0.0297061	+	0.490339i
$271$	23.0883			1.40251			0.701257	−	0.712908i	$-0.252622\pi$
$271$	23.0883			1.40251			0.701257	+	0.712908i	$0.252622\pi$
$272$	−0.816190	+	2.51198i	−0.0494888	+	0.152311i
$273$	35.0747			2.12282
$274$	−33.8185			−2.04305
$275$	−4.17710	−	16.0484i	−0.251889	−	0.967756i
$276$	5.58592			0.336233
$277$	17.2807			1.03830			0.519149	−	0.854684i	$-0.326249\pi$
$277$	17.2807			1.03830			0.519149	+	0.854684i	$0.326249\pi$
$278$	10.3487	−	31.8501i	0.620675	−	1.91024i
$279$	2.82232			0.168968
$280$	8.83513	−	2.29036i	0.528000	−	0.136875i
$281$	3.98653	−	12.2693i	0.237816	−	0.731924i	−0.758919	−	0.651185i	$-0.774272\pi$
$281$	3.98653	−	12.2693i	0.237816	−	0.731924i	0.996735	−	0.0807384i	$-0.0257278\pi$
$282$	−12.8539	−	9.33889i	−0.765437	−	0.556123i
$283$	−11.4934			−0.683210			−0.341605	−	0.939844i	$-0.610970\pi$
$283$	−11.4934			−0.683210			−0.341605	+	0.939844i	$0.610970\pi$
$284$	−3.48436	−	2.53154i	−0.206759	−	0.150219i
$285$	18.6121	+	29.1779i	1.10248	+	1.72835i
$286$	−22.9794	−	14.6265i	−1.35880	−	0.864882i
$287$	5.76707	−	17.7492i	0.340419	−	1.04770i
$288$	−11.3096	−	8.21690i	−0.666424	−	0.484186i
$289$	13.5157	+	9.81975i	0.795043	+	0.577632i
$290$	6.76555	−	8.21693i	0.397287	−	0.482515i
$291$	−2.73110			−0.160100
$292$	1.22160	−	3.75971i	0.0714889	−	0.220020i
$293$	−1.81285	−	1.31712i	−0.105908	−	0.0769467i	0.533571	−	0.845755i	$-0.320850\pi$
$293$	−1.81285	−	1.31712i	−0.105908	−	0.0769467i	−0.639479	+	0.768809i	$0.720850\pi$
$294$	−20.4398			−1.19207
$295$	−0.469048	+	7.74226i	−0.0273090	+	0.450772i
$296$	−8.64123	+	6.27822i	−0.502262	+	0.364914i
$297$	5.04219	−	4.15988i	0.292578	−	0.241381i
$298$	0.967484	+	2.97761i	0.0560448	+	0.172488i
$299$	−2.52263	+	7.76387i	−0.145888	+	0.448996i
$300$	−15.2293	−	1.85206i	−0.879263	−	0.106929i
$301$	0.642105	+	0.466517i	0.0370103	+	0.0268896i
$302$	−2.76348	+	2.00779i	−0.159020	+	0.115535i
$303$	−21.7624	−	15.8113i	−1.25022	−	0.908337i
$304$	33.3081			1.91035
$305$	−1.91004	+	31.5278i	−0.109369	+	1.80528i
$306$	1.71015	−	1.24250i	0.0977629	−	0.0710289i
$307$	4.42308			0.252438			0.126219	−	0.992002i	$-0.459716\pi$
$307$	4.42308			0.252438			0.126219	+	0.992002i	$0.459716\pi$
$308$	13.0904	+	8.33207i	0.745894	+	0.474764i
$309$	9.84083	−	30.2870i	0.559825	−	1.72297i
$310$	0.328194	−	5.41727i	0.0186401	−	0.307680i
$311$	14.1170	+	10.2566i	0.800504	+	0.581600i	0.911062	−	0.412270i	$-0.135264\pi$
$311$	14.1170	+	10.2566i	0.800504	+	0.581600i	−0.110558	+	0.993870i	$0.535264\pi$
$312$	9.71104	−	7.05548i	0.549779	−	0.399438i
$313$	11.3160			0.639619			0.319809	−	0.947482i	$-0.396381\pi$
$313$	11.3160			0.639619			0.319809	+	0.947482i	$0.396381\pi$
$314$	−5.62158	+	4.08432i	−0.317244	+	0.230491i
$315$	−15.3064	−	6.01914i	−0.862417	−	0.339140i
$316$	6.29530	+	19.3749i	0.354138	+	1.08993i
$317$	−11.5761	+	8.41055i	−0.650180	+	0.472383i	−0.863332	−	0.504636i	$-0.831627\pi$
$317$	−11.5761	+	8.41055i	−0.650180	+	0.472383i	0.213153	+	0.977019i	$0.431627\pi$
$318$	7.38052			0.413879
$319$	−8.60319	+	0.529679i	−0.481686	+	0.0296563i
$320$	−3.23148	+	3.92471i	−0.180645	+	0.219398i
$321$	−12.9448	−	39.8399i	−0.722506	−	2.22365i
$322$	3.55857	−	10.9522i	0.198311	−	0.610340i
$323$	−1.14430	+	3.52178i	−0.0636704	+	0.195957i
$324$	−4.54351	−	13.9835i	−0.252417	−	0.776861i
$325$	9.45182	−	20.3308i	0.524293	−	1.12775i
$326$	−21.4380	−	15.5756i	−1.18734	−	0.862654i
$327$	5.76912	+	4.19151i	0.319033	+	0.231791i
$328$	−1.97364	−	6.07425i	−0.108976	−	0.335394i
$329$	−10.7010	+	7.77473i	−0.589965	+	0.428635i
$330$	18.1077	+	24.8718i	0.996799	+	1.36915i
$331$	23.0357	+	16.7364i	1.26616	+	0.919916i	0.999043	−	0.0437492i	$-0.0139303\pi$
$331$	23.0357	+	16.7364i	1.26616	+	0.919916i	0.267113	+	0.963665i	$0.413930\pi$
$332$	−5.92223	+	18.2268i	−0.325025	+	1.00032i
$333$	19.2477			1.05477
$334$	15.3074	−	11.1215i	0.837586	−	0.608542i
$335$	−25.7957	+	6.68711i	−1.40937	+	0.365356i
$336$	−30.8446	+	22.4099i	−1.68271	+	1.22256i
$337$	−21.7327	+	15.7897i	−1.18386	+	0.860122i	−0.992601	−	0.121418i	$-0.961256\pi$
$337$	−21.7327	+	15.7897i	−1.18386	+	0.860122i	−0.191255	+	0.981540i	$0.561256\pi$
$338$	−4.02256	−	12.3802i	−0.218798	−	0.673391i
$339$	−42.7399			−2.32131
$340$	−0.882773	−	1.38391i	−0.0478751	−	0.0750531i
$341$	−3.39017	+	2.79694i	−0.183588	+	0.151463i
$342$	−21.5663	−	15.6689i	−1.16617	−	0.847275i
$343$	2.21215	−	6.80829i	0.119445	−	0.367613i
$344$	0.271620			0.0146448
$345$	5.86056	−	7.11780i	0.315522	−	0.383209i
$346$	−3.58868	−	2.60733i	−0.192929	−	0.140171i
$347$	15.3786	+	11.1732i	0.825568	+	0.599810i	0.918302	−	0.395881i	$-0.129561\pi$
$347$	15.3786	+	11.1732i	0.825568	+	0.599810i	−0.0927340	+	0.995691i	$0.529561\pi$
$348$	−2.46413	+	7.58382i	−0.132091	+	0.406536i
$349$	2.98386	−	2.16790i	0.159722	−	0.116045i	−0.505053	−	0.863088i	$-0.668527\pi$
$349$	2.98386	−	2.16790i	0.159722	−	0.116045i	0.664775	+	0.747043i	$0.268527\pi$
$350$	−13.3333	+	28.6798i	−0.712694	+	1.53300i
$351$	8.83763			0.471718
$352$	21.7281	−	1.33775i	1.15811	−	0.0713023i
$353$	−1.64525	+	1.19534i	−0.0875678	+	0.0636217i	−0.630708	−	0.776020i	$-0.717235\pi$
$353$	−1.64525	+	1.19534i	−0.0875678	+	0.0636217i	0.543140	+	0.839642i	$0.317235\pi$
$354$	−4.44671	−	13.6856i	−0.236340	−	0.727380i
$355$	−6.88146	+	1.78391i	−0.365230	+	0.0946800i
$356$	−1.30969	−	4.03082i	−0.0694136	−	0.213633i
$357$	−1.30981	−	4.03119i	−0.0693227	−	0.213353i
$358$	9.48451	−	29.1903i	0.501272	−	1.54276i
$359$	10.9404	−	7.94868i	0.577414	−	0.419516i	−0.260377	−	0.965507i	$-0.583847\pi$
$359$	10.9404	−	7.94868i	0.577414	−	0.419516i	0.837791	+	0.545991i	$0.183847\pi$
$360$	−5.44862	+	1.41247i	−0.287167	+	0.0744435i
$361$	27.6979			1.45779
$362$	−11.0721	+	34.0764i	−0.581936	+	1.79101i
$363$	4.73408	−	24.4601i	0.248475	−	1.28382i
$364$	6.48294	+	19.9524i	0.339799	+	1.04579i
$365$	−3.50910	−	5.50118i	−0.183675	−	0.287945i
$366$	−18.1078	−	55.7300i	−0.946508	−	2.91305i
$367$	−3.19136	−	9.82200i	−0.166588	−	0.512704i	0.832562	−	0.553932i	$-0.186873\pi$
$367$	−3.19136	−	9.82200i	−0.166588	−	0.512704i	−0.999150	+	0.0412276i	$0.986873\pi$
$368$	−2.74209	−	8.43927i	−0.142941	−	0.439927i
$369$	−3.55655	+	10.9459i	−0.185146	+	0.569822i
$370$	2.23822	−	36.9447i	0.116359	−	1.92067i
$371$	1.89871	−	5.84364i	0.0985763	−	0.303387i
$372$	1.25644	+	3.86694i	0.0651436	+	0.200491i
$373$	−1.66597	−	5.12732i	−0.0862605	−	0.265482i	0.898617	−	0.438733i	$-0.144573\pi$
$373$	−1.66597	−	5.12732i	−0.0862605	−	0.265482i	−0.984878	+	0.173251i	$0.944573\pi$
$374$	−0.822911	+	3.18726i	−0.0425517	+	0.164810i
$375$	−18.3380	+	17.4626i	−0.946972	+	0.901767i
$376$	−1.39882	+	4.30513i	−0.0721388	+	0.222020i
$377$	−9.42794	−	6.84980i	−0.485564	−	0.352783i
$378$	−12.4669			−0.641227
$379$	−7.25908	−	5.27403i	−0.372874	−	0.270909i	0.385528	−	0.922696i	$-0.374019\pi$
$379$	−7.25908	−	5.27403i	−0.372874	−	0.270909i	−0.758402	+	0.651788i	$0.774019\pi$
$380$	−13.1579	+	15.9806i	−0.674985	+	0.819787i
$381$	−1.53596	−	4.72719i	−0.0786894	−	0.242181i
$382$	20.5060	−	14.8985i	1.04918	−	0.762274i
$383$	−0.583507	+	0.423942i	−0.0298158	+	0.0216624i	−0.602593	−	0.798048i	$-0.705866\pi$
$383$	−0.583507	+	0.423942i	−0.0298158	+	0.0216624i	0.572778	+	0.819711i	$0.305866\pi$
$384$	−6.27323	+	19.3070i	−0.320129	+	0.985257i
$385$	24.3511	−	7.93856i	1.24104	−	0.404587i
$386$	−5.65531	−	17.4053i	−0.287848	−	0.885905i
$387$	−0.395986	−	0.287701i	−0.0201291	−	0.0146247i
$388$	−0.504795	−	1.55360i	−0.0256271	−	0.0788720i
$389$	−2.20533	+	6.78730i	−0.111814	+	0.344130i	−0.991269	−	0.131853i	$-0.957907\pi$
$389$	−2.20533	+	6.78730i	−0.111814	+	0.344130i	0.879455	+	0.475982i	$0.157907\pi$
$390$	−2.51531	+	41.5186i	−0.127368	+	2.10238i
$391$	0.986517			0.0498903
$392$	1.79954	+	5.53843i	0.0908907	+	0.279733i
$393$	−25.0280	+	18.1839i	−1.26249	+	0.917256i
$394$	24.7419	−	17.9760i	1.24648	−	0.905619i
$395$	31.2931	+	12.3058i	1.57453	+	0.619173i
$396$	−8.07283	−	5.13838i	−0.405675	−	0.258213i
$397$	−7.51473	+	5.45977i	−0.377153	+	0.274018i	−0.760171	−	0.649723i	$-0.774885\pi$
$397$	−7.51473	+	5.45977i	−0.377153	+	0.274018i	0.383018	+	0.923741i	$0.374885\pi$
$398$	−13.2144			−0.662378
$399$	−43.2440	+	31.4186i	−2.16491	+	1.57290i
$400$	4.67782	+	23.9178i	0.233891	+	1.19589i
$401$	4.04575	+	12.4515i	0.202035	+	0.621800i	0.999822	+	0.0188605i	$0.00600385\pi$
$401$	4.04575	+	12.4515i	0.202035	+	0.621800i	−0.797787	+	0.602939i	$0.793996\pi$
$402$	39.9964	−	29.0591i	1.99484	−	1.44934i
$403$	−5.94207			−0.295996
$404$	4.97196	−	15.3021i	0.247364	−	0.761308i
$405$	−22.5852	−	8.88149i	−1.12227	−	0.441325i
$406$	13.2996	+	9.66272i	0.660048	+	0.479553i
$407$	−23.1203	+	19.0746i	−1.14603	+	0.945492i
$408$	−1.17354	−	0.852628i	−0.0580990	−	0.0422114i
$409$	−24.6911	−	17.9391i	−1.22089	−	0.887032i	−0.224720	−	0.974423i	$-0.572147\pi$
$409$	−24.6911	−	17.9391i	−1.22089	−	0.887032i	−0.996174	+	0.0873915i	$0.972147\pi$
$410$	20.5965	+	8.09943i	1.01719	+	0.400002i
$411$	12.9229	−	39.7726i	0.637439	−	1.96184i
$412$	19.0478			0.938418
$413$	−11.9797			−0.589484
$414$	−2.19457	+	6.75419i	−0.107857	+	0.331950i
$415$	17.0119	+	26.6693i	0.835080	+	1.30914i
$416$	23.8111	+	17.2998i	1.16744	+	0.848191i
$417$	33.5031	+	24.3414i	1.64066	+	1.19201i
$418$	41.4335	−	2.55096i	2.02658	−	0.124772i
$419$	4.21478	+	3.06222i	0.205905	+	0.149599i	0.685959	−	0.727640i	$-0.259383\pi$
$419$	4.21478	+	3.06222i	0.205905	+	0.149599i	−0.480054	+	0.877239i	$0.659383\pi$
$420$	1.43287	−	23.6513i	0.0699167	−	1.15407i
$421$	2.95299	−	9.08836i	0.143920	−	0.442940i	−0.852951	−	0.521991i	$-0.825189\pi$
$421$	2.95299	−	9.08836i	0.143920	−	0.442940i	0.996871	+	0.0790519i	$0.0251893\pi$
$422$	41.9652			2.04283
$423$	6.59930	−	4.79467i	0.320869	−	0.233125i
$424$	−0.649790	−	1.99985i	−0.0315566	−	0.0971212i
$425$	−2.68961	−	0.327089i	−0.130465	−	0.0158662i
$426$	10.6698	−	7.75204i	0.516952	−	0.375588i
$427$	−48.7835			−2.36080
$428$	20.2705	−	14.7274i	0.979812	−	0.711875i
$429$	25.9827	−	21.4361i	1.25445	−	1.03494i
$430$	−0.598272	+	0.726616i	−0.0288512	+	0.0350406i
$431$	7.49442	−	5.44501i	0.360993	−	0.262277i	−0.392473	−	0.919764i	$-0.628380\pi$
$431$	7.49442	−	5.44501i	0.360993	−	0.262277i	0.753466	+	0.657486i	$0.228380\pi$
$432$	−7.77178	+	5.64653i	−0.373920	+	0.271669i
$433$	6.89137	+	21.2095i	0.331178	+	1.01926i	0.968574	+	0.248725i	$0.0800117\pi$
$433$	6.89137	+	21.2095i	0.331178	+	1.01926i	−0.637396	+	0.770537i	$0.719988\pi$
$434$	8.38223			0.402360
$435$	7.07833	+	11.0966i	0.339380	+	0.532041i
$436$	−1.31804	+	4.05652i	−0.0631228	+	0.194272i
$437$	−3.84440	−	11.8318i	−0.183902	−	0.565994i
$438$	9.79349	+	7.11538i	0.467951	+	0.339986i
$439$	−4.22062	−	12.9897i	−0.201439	−	0.619966i	−0.999841	−	0.0178409i	$-0.994321\pi$
$439$	−4.22062	−	12.9897i	−0.201439	−	0.619966i	0.798402	−	0.602125i	$-0.205679\pi$
$440$	5.14512	−	7.09628i	0.245284	−	0.338302i
$441$	3.24282	−	9.98037i	0.154420	−	0.475256i
$442$	−3.60054	+	2.61594i	−0.171260	+	0.124428i
$443$	−30.4283	+	22.1075i	−1.44569	+	1.05036i	−0.458879	+	0.888499i	$0.651749\pi$
$443$	−30.4283	+	22.1075i	−1.44569	+	1.05036i	−0.986814	+	0.161858i	$0.948251\pi$
$444$	8.56871	+	26.3718i	0.406653	+	1.25155i
$445$	−6.51032	−	2.56014i	−0.308619	−	0.121362i
$446$	−15.6847	−	11.3956i	−0.742692	−	0.539597i
$447$	−3.87155			−0.183118
$448$	−6.35238	−	4.61528i	−0.300122	−	0.218051i
$449$	8.79554	−	27.0699i	0.415087	−	1.27751i	−0.497086	−	0.867701i	$-0.665597\pi$
$449$	8.79554	−	27.0699i	0.415087	−	1.27751i	0.912173	−	0.409806i	$-0.134403\pi$
$450$	8.22263	−	17.6868i	0.387618	−	0.833764i
$451$	−6.57537	−	16.6728i	−0.309622	−	0.785092i
$452$	−7.89971	−	24.3128i	−0.371571	−	1.14358i
$453$	−1.30528	−	4.01725i	−0.0613275	−	0.188747i
$454$	−2.70861	+	8.33625i	−0.127122	+	0.391240i
$455$	32.2259	+	12.6726i	1.51077	+	0.594102i
$456$	−5.65281	+	17.3976i	−0.264717	+	0.814716i
$457$	10.7384	+	33.0495i	0.502323	+	1.54599i	0.805225	+	0.592969i	$0.202044\pi$
$457$	10.7384	+	33.0495i	0.502323	+	1.54599i	−0.302902	+	0.953022i	$0.597956\pi$
$458$	9.75501	+	30.0228i	0.455822	+	1.40288i
$459$	−0.330028	−	1.01572i	−0.0154044	−	0.0474099i
$460$	5.13222	+	2.01821i	0.239291	+	0.0940995i
$461$	−8.72857	−	26.8638i	−0.406530	−	1.25117i	−0.919611	−	0.392831i	$-0.871496\pi$
$461$	−8.72857	−	26.8638i	−0.406530	−	1.25117i	0.513081	−	0.858340i	$-0.328504\pi$
$462$	−36.6526	+	30.2389i	−1.70523	+	1.40684i
$463$	−0.215394	+	0.662916i	−0.0100102	+	0.0308083i	−0.955937	−	0.293572i	$-0.905156\pi$
$463$	−0.215394	+	0.662916i	−0.0100102	+	0.0308083i	0.945927	+	0.324381i	$0.105156\pi$
$464$	12.6674			0.588068
$465$	6.24563	+	2.45605i	0.289634	+	0.113897i
$466$	−6.62144	+	4.81076i	−0.306732	+	0.222854i
$467$	1.22898	−	3.78240i	0.0568702	−	0.175029i	−0.918586	−	0.395220i	$-0.870668\pi$
$467$	1.22898	−	3.78240i	0.0568702	−	0.175029i	0.975457	+	0.220192i	$0.0706683\pi$
$468$	−3.99803	−	12.3047i	−0.184809	−	0.568783i
$469$	−12.7185	−	39.1435i	−0.587286	−	1.80748i
$470$	−8.43569	−	13.2245i	−0.389109	−	0.610001i
$471$	−2.65526	−	8.17204i	−0.122348	−	0.376548i
$472$	−3.31679	+	2.40979i	−0.152668	+	0.110920i
$473$	0.760772	−	0.0468390i	0.0349804	−	0.00215366i
$474$	−62.3830			−2.86534
$475$	6.55829	+	33.5326i	0.300915	+	1.53858i
$476$	2.05107	−	1.49019i	0.0940106	−	0.0683027i
$477$	−1.17094	+	3.60377i	−0.0536135	+	0.165005i
$478$	−12.0443	−	8.75071i	−0.550894	−	0.400248i
$479$	7.32030	+	5.31851i	0.334473	+	0.243009i	0.742326	−	0.670039i	$-0.233722\pi$
$479$	7.32030	+	5.31851i	0.334473	+	0.243009i	−0.407853	+	0.913048i	$0.633722\pi$
$480$	−17.8769	−	28.0254i	−0.815967	−	1.27918i
$481$	−40.5238			−1.84773
$482$	−0.805971	+	2.48052i	−0.0367110	+	0.112985i
$483$	11.5206	+	8.37019i	0.524205	+	0.380857i
$484$	14.7893	−	1.82801i	0.672239	−	0.0830915i
$485$	−2.50927	−	0.986754i	−0.113940	−	0.0448062i
$486$	34.1942			1.55108
$487$	4.79711	+	14.7640i	0.217378	+	0.669020i	0.998976	+	0.0452380i	$0.0144046\pi$
$487$	4.79711	+	14.7640i	0.217378	+	0.669020i	−0.781599	+	0.623782i	$0.785595\pi$
$488$	−13.5065	+	9.81308i	−0.611412	+	0.444217i
$489$	26.5099	−	19.2606i	1.19882	−	0.870993i
$490$	−18.7796	−	7.38497i	−0.848377	−	0.333619i
$491$	−17.0862	+	12.4138i	−0.771088	+	0.560228i	−0.902291	−	0.431127i	$-0.858116\pi$
$491$	−17.0862	+	12.4138i	−0.771088	+	0.560228i	0.131203	+	0.991356i	$0.458116\pi$
$492$	−16.5806			−0.747513
$493$	−0.435185	+	1.33936i	−0.0195998	+	0.0603219i
$494$	45.4055	+	32.9890i	2.04289	+	1.48425i
$495$	−15.0173	+	4.89571i	−0.674977	+	0.220046i
$496$	5.22544	−	3.79650i	0.234629	−	0.170468i
$497$	−3.39289	−	10.4423i	−0.152192	−	0.468399i
$498$	−47.4781	−	34.4948i	−2.12754	−	1.54575i
$499$	13.0990	+	9.51699i	0.586393	+	0.426039i	0.841023	−	0.540999i	$-0.181954\pi$
$499$	13.0990	+	9.51699i	0.586393	+	0.426039i	−0.254630	+	0.967038i	$0.581954\pi$
$500$	−13.3232	−	7.20403i	−0.595830	−	0.322174i
$501$	7.23021	+	22.2523i	0.323022	+	0.994160i
$502$	−2.96971	+	9.13984i	−0.132545	+	0.407931i
$503$	8.07083	−	24.8395i	0.359861	−	1.10754i	−0.593277	−	0.804999i	$-0.702166\pi$
$503$	8.07083	−	24.8395i	0.359861	−	1.10754i	0.953137	−	0.302538i	$-0.0978340\pi$
$504$	−2.68643	−	8.26799i	−0.119663	−	0.368285i
$505$	−14.2822	−	22.3899i	−0.635547	−	0.996339i
$506$	−4.05734	−	10.2880i	−0.180371	−	0.457356i
$507$	16.0969			0.714890
$508$	2.40519	−	1.74747i	0.106713	−	0.0775316i
$509$	6.93974	+	21.3583i	0.307599	+	0.946691i	0.978695	+	0.205321i	$0.0658238\pi$
$509$	6.93974	+	21.3583i	0.307599	+	0.946691i	−0.671096	+	0.741370i	$0.734176\pi$
$510$	4.86572	−	1.26136i	0.215458	−	0.0558540i
$511$	8.15319	−	5.92364i	0.360676	−	0.262046i
$512$	−20.4709			−0.904695
$513$	−10.8960	+	7.91642i	−0.481071	+	0.349519i
$514$	32.8204	+	23.8454i	1.44764	+	1.05177i
$515$	19.9843	−	24.2715i	0.880615	−	1.06953i
$516$	0.217901	−	0.670631i	0.00959257	−	0.0295229i
$517$	−3.17553	+	12.2993i	−0.139659	+	0.540924i
$518$	57.1652			2.51170
$519$	4.43771	−	3.22418i	0.194794	−	0.141526i
$520$	11.4715	−	2.97379i	0.503057	−	0.130409i
$521$	29.5830			1.29605			0.648027	−	0.761617i	$-0.275594\pi$
$521$	29.5830			1.29605			0.648027	+	0.761617i	$0.275594\pi$
$522$	−8.20186	−	5.95900i	−0.358985	−	0.260818i
$523$	9.24113	−	6.71407i	0.404086	−	0.293586i	−0.367117	−	0.930175i	$-0.619655\pi$
$523$	9.24113	−	6.71407i	0.404086	−	0.293586i	0.771203	+	0.636589i	$0.219655\pi$
$524$	−14.9700	−	10.8763i	−0.653967	−	0.475134i
$525$	−28.6342	−	26.6400i	−1.24970	−	1.16267i
$526$	6.01878	−	18.5239i	0.262431	−	0.807680i
$527$	0.221898	+	0.682932i	0.00966602	+	0.0297490i
$528$	−9.15314	+	35.4516i	−0.398339	+	1.54283i
$529$	15.9261	−	11.5710i	0.692437	−	0.503085i
$530$	6.78106	+	2.66661i	0.294550	+	0.115830i
$531$	7.38789			0.320607
$532$	−25.8655	−	18.7924i	−1.12141	−	0.814755i
$533$	7.48792	−	23.0454i	0.324338	−	0.998209i
$534$	12.9783			0.561628
$535$	2.50092	−	41.2810i	0.108124	−	1.78473i
$536$	−11.3953	−	8.27915i	−0.492201	−	0.357605i
$537$	30.7053	+	22.3087i	1.32503	+	0.962692i
$538$	−7.14282	+	21.9833i	−0.307949	+	0.947769i
$539$	5.99535	+	15.2021i	0.258238	+	0.654800i
$540$	0.361033	−	5.95933i	0.0155364	−	0.256449i
$541$	14.7114	+	10.6884i	0.632491	+	0.459532i	0.857262	−	0.514880i	$-0.172163\pi$
$541$	14.7114	+	10.6884i	0.632491	+	0.459532i	−0.224771	+	0.974412i	$0.572163\pi$
$542$	−42.2882			−1.81644
$543$	−35.8450	−	26.0429i	−1.53825	−	1.11761i
$544$	1.09910	−	3.38268i	0.0471235	−	0.145031i
$545$	3.78613	+	5.93547i	0.162180	+	0.254248i
$546$	−64.2424			−2.74932
$547$	11.6770	−	35.9383i	0.499275	−	1.53661i	−0.310913	−	0.950438i	$-0.600635\pi$
$547$	11.6770	−	35.9383i	0.499275	−	1.53661i	0.810188	−	0.586171i	$-0.199365\pi$
$548$	25.0134			1.06852
$549$	30.0848			1.28399
$550$	7.65073	+	29.3941i	0.326228	+	1.25337i
$551$	17.7596			0.756585
$552$	4.87338			0.207425
$553$	−16.0487	+	49.3927i	−0.682458	+	2.10039i
$554$	−31.6511			−1.34473
$555$	42.5940	+	16.7498i	1.80801	+	0.710990i
$556$	−7.65430	+	23.5575i	−0.324615	+	0.999061i
$557$	15.8326	+	11.5031i	0.670850	+	0.487401i	0.870310	−	0.492505i	$-0.163919\pi$
$557$	15.8326	+	11.5031i	0.670850	+	0.487401i	−0.199460	+	0.979906i	$0.563919\pi$
$558$	−5.16932			−0.218835
$559$	0.833705	+	0.605722i	0.0352620	+	0.0256193i
$560$	−36.4361	+	9.44548i	−1.53971	+	0.399144i
$561$	−3.43396	−	2.18573i	−0.144982	−	0.0922815i
$562$	−7.30167	+	22.4722i	−0.308003	+	0.947934i
$563$	9.40926	+	6.83622i	0.396553	+	0.288113i	0.768135	−	0.640287i	$-0.221185\pi$
$563$	9.40926	+	6.83622i	0.396553	+	0.288113i	−0.371583	+	0.928400i	$0.621185\pi$
$564$	9.50721	+	6.90739i	0.400326	+	0.290854i
$565$	−39.2685	−	15.4421i	−1.65204	−	0.649653i
$566$	21.0511			0.884844
$567$	11.5828	−	35.6482i	0.486433	−	1.49709i
$568$	−3.03990	−	2.20862i	−0.127551	−	0.0926715i
$569$	−10.4366			−0.437526			−0.218763	−	0.975778i	$-0.570202\pi$
$569$	−10.4366			−0.437526			−0.218763	+	0.975778i	$0.570202\pi$
$570$	−34.0896	−	53.4419i	−1.42786	−	2.23843i
$571$	−28.9592	+	21.0401i	−1.21191	+	0.880501i	−0.995402	−	0.0957809i	$-0.969465\pi$
$571$	−28.9592	+	21.0401i	−1.21191	+	0.880501i	−0.216503	+	0.976282i	$0.569465\pi$
$572$	16.9964	+	10.8183i	0.710657	+	0.452335i
$573$	9.68567	+	29.8094i	0.404625	+	1.24531i
$574$	−10.5629	+	32.5092i	−0.440886	+	1.35691i
$575$	7.95624	−	4.42224i	0.331798	−	0.184420i
$576$	3.91751	+	2.84624i	0.163230	+	0.118593i
$577$	25.4448	−	18.4867i	1.05928	−	0.769612i	0.0853255	−	0.996353i	$-0.472807\pi$
$577$	25.4448	−	18.4867i	1.05928	−	0.769612i	0.973955	+	0.226741i	$0.0728070\pi$
$578$	−24.7552	−	17.9857i	−1.02968	−	0.748108i
$579$	22.6307			0.940499
$580$	−5.00405	+	6.07755i	−0.207782	+	0.252357i
$581$	−39.5260	+	28.7173i	−1.63982	+	1.19140i
$582$	5.00224			0.207349
$583$	−2.16484	−	5.48926i	−0.0896583	−	0.227342i
$584$	1.06578	−	3.28012i	0.0441021	−	0.135732i
$585$	−19.8737	−	7.81520i	−0.821676	−	0.323119i
$586$	3.32040	+	2.41241i	0.137164	+	0.0996558i
$587$	32.9256	−	23.9219i	1.35899	−	0.987361i	0.360477	−	0.932768i	$-0.382614\pi$
$587$	32.9256	−	23.9219i	1.35899	−	0.987361i	0.998509	−	0.0545931i	$-0.0173862\pi$
$588$	15.1180			0.623457
$589$	7.32605	−	5.32269i	0.301865	−	0.219317i
$590$	0.859102	−	14.1806i	0.0353687	−	0.583807i
$591$	11.6864	+	35.9670i	0.480714	+	1.47949i
$592$	35.6365	−	25.8914i	1.46465	−	1.06413i
$593$	9.16418			0.376328			0.188164	−	0.982138i	$-0.439746\pi$
$593$	9.16418			0.376328			0.188164	+	0.982138i	$0.439746\pi$
$594$	−9.23521	+	7.61918i	−0.378925	+	0.312619i
$595$	0.253055	−	4.17701i	0.0103743	−	0.171241i
$596$	−0.715587	−	2.20235i	−0.0293116	−	0.0902118i
$597$	5.04956	−	15.5409i	0.206665	−	0.636049i
$598$	4.62042	−	14.2202i	0.188943	−	0.581507i
$599$	−9.85071	−	30.3174i	−0.402489	−	1.23873i	−0.922974	−	0.384863i	$-0.874249\pi$
$599$	−9.85071	−	30.3174i	−0.402489	−	1.23873i	0.520484	−	0.853871i	$-0.325751\pi$
$600$	−13.2866	−	1.61582i	−0.542425	−	0.0659654i
$601$	−29.8498	−	21.6871i	−1.21760	−	0.884637i	−0.221700	−	0.975115i	$-0.571161\pi$
$601$	−29.8498	−	21.6871i	−1.21760	−	0.884637i	−0.995898	+	0.0904778i	$0.971161\pi$
$602$	−1.17607	−	0.854466i	−0.0479331	−	0.0348254i
$603$	7.84350	+	24.1398i	0.319412	+	0.983049i
$604$	2.04397	−	1.48503i	0.0831681	−	0.0604251i
$605$	13.1871	−	20.7630i	0.536131	−	0.844135i
$606$	39.8598	+	28.9598i	1.61919	+	1.17641i
$607$	0.245303	−	0.754965i	0.00995655	−	0.0306431i	−0.945955	−	0.324298i	$-0.894872\pi$
$607$	0.245303	−	0.754965i	0.00995655	−	0.0306431i	0.955911	+	0.293655i	$0.0948718\pi$
$608$	−44.8535			−1.81905
$609$	−16.4461	+	11.9488i	−0.666428	+	0.484188i
$610$	3.49841	−	57.7459i	0.141647	−	2.33806i
$611$	−13.8941	+	10.0947i	−0.562095	+	0.408386i
$612$	−1.26489	+	0.918999i	−0.0511303	+	0.0371483i
$613$	6.85945	+	21.1112i	0.277051	+	0.852674i	0.988670	+	0.150108i	$0.0479623\pi$
$613$	6.85945	+	21.1112i	0.277051	+	0.852674i	−0.711619	+	0.702566i	$0.752038\pi$
$614$	−8.10125			−0.326940
$615$	−17.3959	+	21.1277i	−0.701469	+	0.851952i
$616$	11.4206	+	7.26924i	0.460148	+	0.292886i
$617$	6.09680	+	4.42958i	0.245448	+	0.178328i	0.703707	−	0.710490i	$-0.251527\pi$
$617$	6.09680	+	4.42958i	0.245448	+	0.178328i	−0.458259	+	0.888819i	$0.651527\pi$
$618$	−18.0243	+	55.4732i	−0.725045	+	2.23146i
$619$	−21.3070			−0.856400			−0.428200	−	0.903684i	$-0.640852\pi$
$619$	−21.3070			−0.856400			−0.428200	+	0.903684i	$0.640852\pi$
$620$	−0.242744	+	4.00681i	−0.00974884	+	0.160918i
$621$	2.90279	+	2.10900i	0.116485	+	0.0846314i
$622$	−25.8566	−	18.7859i	−1.03675	−	0.753246i
$623$	3.33881	−	10.2758i	0.133767	−	0.411691i
$624$	−40.0484	+	29.0968i	−1.60322	+	1.16481i
$625$	−23.1579	+	9.41870i	−0.926316	+	0.376748i
$626$	−20.7262			−0.828388
$627$	−12.8327	+	49.7030i	−0.512488	+	1.98495i
$628$	4.15793	−	3.02091i	0.165919	−	0.120548i
$629$	1.51330	+	4.65746i	0.0603393	+	0.185705i
$630$	28.0350	+	11.0246i	1.11694	+	0.439229i
$631$	13.7291	+	42.2537i	0.546545	+	1.68209i	0.717288	+	0.696777i	$0.245383\pi$
$631$	13.7291	+	42.2537i	0.546545	+	1.68209i	−0.170743	+	0.985316i	$0.554617\pi$
$632$	5.49228	+	16.9035i	0.218471	+	0.672385i
$633$	−16.0360	+	49.3536i	−0.637372	+	1.96163i
$634$	21.2027	−	15.4046i	0.842066	−	0.611797i
$635$	0.296746	−	4.89818i	0.0117760	−	0.194378i
$636$	−5.45891			−0.216460
$637$	−6.82739	+	21.0126i	−0.270511	+	0.832548i
$638$	15.7575	−	0.970152i	0.623845	−	0.0384087i
$639$	2.09240	+	6.43973i	0.0827739	+	0.254752i
$640$	−12.7394	+	15.4723i	−0.503569	+	0.611597i
$641$	−2.56515	−	7.89472i	−0.101317	−	0.311823i	0.887531	−	0.460748i	$-0.152419\pi$
$641$	−2.56515	−	7.89472i	−0.101317	−	0.311823i	−0.988849	+	0.148925i	$0.952419\pi$
$642$	23.7095	+	72.9702i	0.935738	+	2.87990i
$643$	9.38523	+	28.8848i	0.370117	+	1.13910i	0.946714	+	0.322075i	$0.104380\pi$
$643$	9.38523	+	28.8848i	0.370117	+	1.13910i	−0.576597	+	0.817029i	$0.695620\pi$
$644$	−2.63205	+	8.10062i	−0.103717	+	0.319209i
$645$	−0.625930	−	0.981262i	−0.0246460	−	0.0386372i
$646$	2.09588	−	6.45045i	0.0824612	−	0.253790i
$647$	−4.53615	−	13.9608i	−0.178334	−	0.548857i	0.821436	−	0.570301i	$-0.193174\pi$
$647$	−4.53615	−	13.9608i	−0.178334	−	0.548857i	−0.999770	+	0.0214444i	$0.993174\pi$
$648$	−3.96395	−	12.1998i	−0.155719	−	0.479252i
$649$	−8.87434	+	7.32146i	−0.348348	+	0.287392i
$650$	−17.3118	+	37.2376i	−0.679026	+	1.46058i
$651$	−3.20306	+	9.85801i	−0.125538	+	0.386366i
$652$	15.8564	+	11.5203i	0.620983	+	0.451171i
$653$	46.4203			1.81656			0.908282	−	0.418358i	$-0.137394\pi$
$653$	46.4203			1.81656			0.908282	+	0.418358i	$0.137394\pi$
$654$	−10.5666	−	7.67711i	−0.413188	−	0.300199i
$655$	−29.5651	+	7.66427i	−1.15520	+	0.299468i
$656$	8.13932	+	25.0502i	0.317787	+	0.978048i
$657$	−5.02807	+	3.65311i	−0.196164	+	0.142521i
$658$	19.5998	−	14.2401i	0.764080	−	0.555137i
$659$	11.5715	−	35.6134i	0.450761	−	1.38730i	−0.425279	−	0.905062i	$-0.639824\pi$
$659$	11.5715	−	35.6134i	0.450761	−	1.38730i	0.876040	−	0.482238i	$-0.160176\pi$
$660$	−13.3932	−	18.3961i	−0.521328	−	0.716068i
$661$	−1.95155	−	6.00625i	−0.0759064	−	0.233616i	0.905903	−	0.423485i	$-0.139194\pi$
$661$	−1.95155	−	6.00625i	−0.0759064	−	0.233616i	−0.981809	+	0.189869i	$0.939194\pi$
$662$	−42.1919	−	30.6542i	−1.63983	−	1.19141i
$663$	−1.70065	−	5.23407i	−0.0660478	−	0.203274i
$664$	−5.16680	+	15.9018i	−0.200511	+	0.617108i
$665$	−51.0833	+	13.2425i	−1.98093	+	0.513523i
$666$	−35.2538			−1.36606
$667$	−1.46206	−	4.49975i	−0.0566110	−	0.174231i
$668$	−11.3220	+	8.22589i	−0.438060	+	0.318269i
$669$	19.3954	−	14.0916i	0.749871	−	0.544813i
$670$	47.2470	−	12.2480i	1.82531	−	0.473182i
$671$	−36.1378	+	29.8142i	−1.39509	+	1.15097i
$672$	41.5360	−	30.1777i	1.60229	−	1.16413i
$673$	−24.6899			−0.951727			−0.475863	−	0.879519i	$-0.657864\pi$
$673$	−24.6899			−0.951727			−0.475863	+	0.879519i	$0.657864\pi$
$674$	39.8054	−	28.9203i	1.53325	−	1.11397i
$675$	−7.21483	−	6.71237i	−0.277699	−	0.258359i
$676$	2.97523	+	9.15682i	0.114432	+	0.352186i
$677$	17.9082	−	13.0111i	0.688269	−	0.500057i	−0.187822	−	0.982203i	$-0.560143\pi$
$677$	17.9082	−	13.0111i	0.688269	−	0.500057i	0.876091	+	0.482146i	$0.160143\pi$
$678$	78.2818			3.00639
$679$	1.28688	−	3.96060i	0.0493858	−	0.151994i
$680$	−0.770167	−	1.20738i	−0.0295346	−	0.0463009i
$681$	−8.76891	−	6.37099i	−0.336025	−	0.244137i
$682$	6.20939	−	5.12283i	0.237770	−	0.196163i
$683$	−16.3830	−	11.9030i	−0.626878	−	0.455454i	0.228439	−	0.973558i	$-0.426638\pi$
$683$	−16.3830	−	11.9030i	−0.626878	−	0.455454i	−0.855317	+	0.518104i	$0.826638\pi$
$684$	15.9513	+	11.5893i	0.609912	+	0.443127i
$685$	26.2432	−	31.8731i	1.00270	−	1.21781i
$686$	−4.05174	+	12.4700i	−0.154696	+	0.476106i
$687$	−39.0363			−1.48933
$688$	−1.12016			−0.0427058
$689$	2.46528	−	7.58734i	0.0939195	−	0.289055i
$690$	−10.7341	+	13.0369i	−0.408641	+	0.496305i
$691$	−4.41073	−	3.20459i	−0.167792	−	0.121908i	0.500720	−	0.865609i	$-0.333069\pi$
$691$	−4.41073	−	3.20459i	−0.167792	−	0.121908i	−0.668512	+	0.743701i	$0.733069\pi$
$692$	2.65432	+	1.92848i	0.100902	+	0.0733098i
$693$	−8.95009	−	22.6943i	−0.339986	−	0.862084i
$694$	−28.1673	−	20.4647i	−1.06922	−	0.776831i
$695$	21.9873	+	34.4692i	0.834026	+	1.30749i
$696$	−2.14981	+	6.61644i	−0.0814884	+	0.250795i
$697$	−2.92827			−0.110916
$698$	−5.46519	+	3.97069i	−0.206860	+	0.150293i
$699$	−3.12752	−	9.62553i	−0.118294	−	0.364071i
$700$	9.86179	−	21.2126i	0.372741	−	0.801762i
$701$	−7.05644	+	5.12681i	−0.266518	+	0.193637i	−0.713016	−	0.701148i	$-0.752671\pi$
$701$	−7.05644	+	5.12681i	−0.266518	+	0.193637i	0.446498	+	0.894785i	$0.352671\pi$
$702$	−16.1869			−0.610935
$703$	49.9623	−	36.2997i	1.88436	−	1.36907i
$704$	−7.52636	+	0.463381i	−0.283660	+	0.0174643i
$705$	18.7763	−	4.86746i	0.707157	−	0.183319i
$706$	3.01342	−	2.18938i	0.113411	−	0.0823983i
$707$	33.1837	−	24.1094i	1.24800	−	0.906727i
$708$	3.28895	+	10.1224i	0.123606	+	0.380422i
$709$	10.0517			0.377499			0.188749	−	0.982025i	$-0.439557\pi$
$709$	10.0517			0.377499			0.188749	+	0.982025i	$0.439557\pi$
$710$	12.6040	−	3.26738i	0.473020	−	0.122623i
$711$	9.89720	−	30.4605i	0.371174	−	1.14236i
$712$	−1.14263	−	3.51665i	−0.0428219	−	0.131792i
$713$	−1.95172	−	1.41801i	−0.0730926	−	0.0531049i
$714$	2.39904	+	7.38348i	0.0897817	+	0.276320i
$715$	31.6172	−	10.3074i	1.18242	−	0.385474i
$716$	−7.01509	+	21.5902i	−0.262166	+	0.806865i
$717$	14.8938	−	10.8210i	0.556219	−	0.404117i
$718$	−20.0383	+	14.5587i	−0.747824	+	0.543326i
$719$	−10.7527	−	33.0934i	−0.401008	−	1.23418i	−0.924182	−	0.381951i	$-0.875252\pi$
$719$	−10.7527	−	33.0934i	−0.401008	−	1.23418i	0.523174	−	0.852226i	$-0.324748\pi$
$720$	22.4701	−	5.82502i	0.837412	−	0.217086i
$721$	39.2848	+	28.5421i	1.46304	+	1.06296i
$722$	−50.7312			−1.88802
$723$	−2.60926	−	1.89574i	−0.0970396	−	0.0705034i
$724$	8.18933	−	25.2042i	0.304354	−	0.936705i
$725$	2.49417	+	12.7527i	0.0926313	+	0.473625i
$726$	−8.67087	+	44.8008i	−0.321806	+	1.66271i
$727$	−8.68568	−	26.7318i	−0.322134	−	0.991426i	−0.972718	−	0.231992i	$-0.925476\pi$
$727$	−8.68568	−	26.7318i	−0.322134	−	0.991426i	0.650584	−	0.759434i	$-0.274524\pi$
$728$	5.65598	+	17.4073i	0.209625	+	0.645159i
$729$	−3.00487	+	9.24805i	−0.111292	+	0.342520i
$730$	6.42723	+	10.0759i	0.237882	+	0.372925i
$731$	0.0384831	−	0.118439i	0.00142335	−	0.00438061i
$732$	13.3932	+	41.2200i	0.495026	+	1.52353i
$733$	−3.83192	−	11.7934i	−0.141535	−	0.435600i	0.855014	−	0.518605i	$-0.173548\pi$
$733$	−3.83192	−	11.7934i	−0.141535	−	0.435600i	−0.996549	+	0.0830045i	$0.973548\pi$
$734$	5.84525	+	17.9898i	0.215752	+	0.664017i
$735$	15.8613	−	19.2640i	0.585054	−	0.710564i
$736$	3.69255	+	11.3645i	0.136109	+	0.418901i
$737$	−33.3443	−	21.2238i	−1.22825	−	0.781788i
$738$	6.51413	−	20.0484i	0.239788	−	0.737992i
$739$	−4.96272			−0.182557			−0.0912783	−	0.995825i	$-0.529095\pi$
$739$	−4.96272			−0.182557			−0.0912783	+	0.995825i	$0.529095\pi$
$740$	−1.65547	+	27.3257i	−0.0608563	+	1.00451i
$741$	−56.1477	+	40.7937i	−2.06264	+	1.49859i
$742$	−3.47766	+	10.7031i	−0.127669	+	0.392924i
$743$	−4.80176	−	14.7783i	−0.176159	−	0.542163i	0.823525	−	0.567280i	$-0.192004\pi$
$743$	−4.80176	−	14.7783i	−0.176159	−	0.542163i	−0.999685	+	0.0251169i	$0.992004\pi$
$744$	1.09617	+	3.37367i	0.0401877	+	0.123685i
$745$	−3.55710	−	1.39880i	−0.130322	−	0.0512482i
$746$	3.05136	+	9.39112i	0.111718	+	0.343834i
$747$	24.3757	−	17.7100i	0.891860	−	0.647974i
$748$	0.608655	−	2.35742i	0.0222546	−	0.0861958i
$749$	63.8748			2.33393
$750$	33.5877	−	31.9843i	1.22645	−	1.16790i
$751$	33.9794	−	24.6875i	1.23993	−	0.900860i	0.242333	−	0.970193i	$-0.422087\pi$
$751$	33.9794	−	24.6875i	1.23993	−	0.900860i	0.997594	+	0.0693334i	$0.0220872\pi$
$752$	5.76875	−	17.7544i	0.210365	−	0.647436i
$753$	−9.61420	−	6.98513i	−0.350361	−	0.254552i
$754$	17.2681	+	12.5460i	0.628867	+	0.456899i
$755$	0.252180	−	4.16256i	0.00917776	−	0.151491i
$756$	9.22097			0.335363
$757$	1.77347	−	5.45818i	0.0644579	−	0.198381i	−0.913641	−	0.406522i	$-0.866741\pi$
$757$	1.77347	−	5.45818i	0.0644579	−	0.198381i	0.978099	+	0.208141i	$0.0667414\pi$
$758$	13.2956	+	9.65984i	0.482919	+	0.350861i
$759$	13.6497	−	0.840380i	0.495452	−	0.0305039i
$760$	−11.4795	+	13.9421i	−0.416405	+	0.505734i
$761$	−34.7580			−1.25998			−0.629988	−	0.776605i	$-0.716940\pi$
$761$	−34.7580			−1.25998			−0.629988	+	0.776605i	$0.716940\pi$
$762$	2.81324	+	8.65825i	0.101913	+	0.313655i
$763$	−8.79685	+	6.39129i	−0.318467	+	0.231380i
$764$	−15.1670	+	11.0195i	−0.548724	+	0.398671i
$765$	−0.156059	+	2.57596i	−0.00564233	+	0.0931341i
$766$	1.06874	−	0.776487i	0.0386153	−	0.0280556i
$767$	−15.5544			−0.561636
$768$	14.6725	−	45.1573i	0.529448	−	1.62947i
$769$	−25.9044	−	18.8207i	−0.934137	−	0.678690i	0.0128654	−	0.999917i	$-0.495905\pi$
$769$	−25.9044	−	18.8207i	−0.934137	−	0.678690i	−0.947002	+	0.321227i	$0.895905\pi$
$770$	−44.6011	+	14.5402i	−1.60731	+	0.523991i
$771$	−40.5851	+	29.4868i	−1.46164	+	1.06194i
$772$	4.18288	+	12.8736i	0.150545	+	0.463330i
$773$	−7.94396	−	5.77162i	−0.285724	−	0.207591i	0.435686	−	0.900099i	$-0.356506\pi$
$773$	−7.94396	−	5.77162i	−0.285724	−	0.207591i	−0.721410	+	0.692508i	$0.756506\pi$
$774$	0.725283	+	0.526949i	0.0260698	+	0.0189408i
$775$	4.85097	+	4.51313i	0.174252	+	0.162117i
$776$	−0.440403	−	1.35542i	−0.0158096	−	0.0486568i
$777$	−21.8443	+	67.2298i	−0.783659	+	2.41186i
$778$	4.03925	−	12.4315i	0.144814	−	0.445692i
$779$	11.4113	+	35.1204i	0.408852	+	1.25832i
$780$	1.86042	−	30.7087i	0.0666137	−	1.09955i
$781$	−8.89521	−	5.66183i	−0.318296	−	0.202596i
$782$	−1.80689			−0.0646143
$783$	−4.14385	+	3.01068i	−0.148089	+	0.107593i
$784$	−7.42133	−	22.8405i	−0.265048	−	0.815733i
$785$	0.512994	−	8.46764i	0.0183095	−	0.302223i
$786$	45.8409	−	33.3054i	1.63509	−	1.18796i
$787$	24.5179			0.873969			0.436984	−	0.899469i	$-0.356047\pi$
$787$	24.5179			0.873969			0.436984	+	0.899469i	$0.356047\pi$
$788$	−18.3000	+	13.2957i	−0.651911	+	0.473641i
$789$	19.4853	+	14.1569i	0.693695	+	0.503999i
$790$	−57.3161	−	22.5392i	−2.03922	−	0.801908i
$791$	20.1388	−	61.9808i	0.716053	−	2.20379i
$792$	−7.04307	−	4.48293i	−0.250265	−	0.159294i
$793$	−63.3401			−2.24927
$794$	13.7639	−	10.0000i	0.488462	−	0.354888i
$795$	−5.72731	+	6.95596i	−0.203127	+	0.246703i
$796$	9.77387			0.346426
$797$	−10.3939	−	7.55159i	−0.368170	−	0.267491i	0.388282	−	0.921541i	$-0.373069\pi$
$797$	−10.3939	−	7.55159i	−0.368170	−	0.267491i	−0.756452	+	0.654050i	$0.773069\pi$
$798$	79.2052	−	57.5460i	2.80383	−	2.03710i
$799$	1.67905	+	1.21990i	0.0594005	+	0.0431570i
$800$	−6.29925	−	32.2082i	−0.222712	−	1.13873i
$801$	−2.05904	+	6.33708i	−0.0727527	+	0.223910i
$802$	−7.41014	−	22.8061i	−0.261661	−	0.805310i
$803$	2.41946	−	9.37097i	0.0853810	−	0.330694i
$804$	−29.5828	+	21.4932i	−1.04331	+	0.758006i
$805$	7.56068	+	11.8528i	0.266479	+	0.417755i
$806$	10.8834			0.383352
$807$	−23.1243	−	16.8008i	−0.814014	−	0.591416i
$808$	4.33774	−	13.3502i	0.152601	−	0.469658i
$809$	−23.0001			−0.808642			−0.404321	−	0.914617i	$-0.632492\pi$
$809$	−23.0001			−0.808642			−0.404321	+	0.914617i	$0.632492\pi$
$810$	41.3668	+	16.2672i	1.45348	+	0.571572i
$811$	7.45441	+	5.41595i	0.261760	+	0.190180i	0.710922	−	0.703270i	$-0.248278\pi$
$811$	7.45441	+	5.41595i	0.261760	+	0.190180i	−0.449163	+	0.893450i	$0.648278\pi$
$812$	−9.83688	−	7.14691i	−0.345207	−	0.250807i
$813$	16.1594	−	49.7335i	0.566735	−	1.74423i
$814$	42.3468	−	34.9368i	1.48426	−	1.22453i
$815$	31.3156	−	8.11807i	1.09694	−	0.284364i
$816$	4.83969	+	3.51624i	0.169423	+	0.123093i
$817$	−1.57047			−0.0549437
$818$	45.2238	+	32.8570i	1.58121	+	1.14882i
$819$	10.1922	−	31.3684i	0.356145	−	1.09610i
$820$	−15.2339	−	5.99064i	−0.531992	−	0.209202i
$821$	−29.0196			−1.01279			−0.506396	−	0.862301i	$-0.669023\pi$
$821$	−29.0196			−1.01279			−0.506396	+	0.862301i	$0.669023\pi$
$822$	−23.6694	+	72.8469i	−0.825565	+	2.54083i
$823$	−22.8813			−0.797593			−0.398797	−	0.917039i	$-0.630572\pi$
$823$	−22.8813			−0.797593			−0.398797	+	0.917039i	$0.630572\pi$
$824$	16.6181			0.578918
$825$	−37.4928	−	2.23450i	−1.30533	−	0.0777952i
$826$	21.9419			0.763457
$827$	28.2267			0.981539			0.490769	−	0.871290i	$-0.336716\pi$
$827$	28.2267			0.981539			0.490769	+	0.871290i	$0.336716\pi$
$828$	1.62319	−	4.99565i	0.0564096	−	0.173611i
$829$	−48.2239			−1.67488			−0.837442	−	0.546526i	$-0.815950\pi$
$829$	−48.2239			−1.67488			−0.837442	+	0.546526i	$0.815950\pi$
$830$	−31.1587	−	48.8471i	−1.08153	−	1.69551i
$831$	12.0947	−	37.2237i	0.419561	−	1.29127i
$832$	−8.24789	−	5.99244i	−0.285944	−	0.207750i
$833$	2.66996			0.0925088
$834$	−61.3639	−	44.5835i	−2.12486	−	1.54380i
$835$	−1.39687	+	23.0572i	−0.0483408	+	0.797928i
$836$	−30.6457	+	1.88679i	−1.05990	+	0.0652559i
$837$	−0.807062	+	2.48388i	−0.0278962	+	0.0858555i
$838$	−7.71973	−	5.60871i	−0.266674	−	0.193750i
$839$	−16.3929	−	11.9102i	−0.565946	−	0.411184i	0.267684	−	0.963507i	$-0.413742\pi$
$839$	−16.3929	−	11.9102i	−0.565946	−	0.411184i	−0.833630	+	0.552323i	$0.813742\pi$
$840$	1.25009	−	20.6344i	0.0431322	−	0.711954i
$841$	−22.2459			−0.767099
$842$	−5.40865	+	16.6461i	−0.186394	+	0.573663i
$843$	−23.6386	−	17.1744i	−0.814155	−	0.591519i
$844$	−31.0390			−1.06841
$845$	14.7895	+	5.81588i	0.508775	+	0.200072i
$846$	−12.0872	+	8.78186i	−0.415566	+	0.301927i
$847$	33.2411	+	18.3908i	1.14218	+	0.631914i
$848$	2.67974	+	8.24739i	0.0920226	+	0.283216i
$849$	−8.04416	+	24.7574i	−0.276075	+	0.849671i
$850$	4.92626	+	0.599092i	0.168969	+	0.0205487i
$851$	−13.3104	−	9.67056i	−0.456274	−	0.331502i
$852$	−7.89176	+	5.73370i	−0.270367	+	0.196433i
$853$	41.7884	+	30.3610i	1.43081	+	1.03954i	0.989866	+	0.142005i	$0.0453550\pi$
$853$	41.7884	+	30.3610i	1.43081	+	1.03954i	0.440940	+	0.897536i	$0.354645\pi$
$854$	89.3512			3.05754
$855$	31.5031	−	8.16666i	1.07738	−	0.279294i
$856$	17.6848	−	12.8488i	0.604455	−	0.439162i
$857$	−14.9119			−0.509381			−0.254690	−	0.967023i	$-0.581974\pi$
$857$	−14.9119			−0.509381			−0.254690	+	0.967023i	$0.581974\pi$
$858$	−47.5895	+	39.2620i	−1.62468	+	1.34038i
$859$	−12.4779	+	38.4030i	−0.425740	+	1.31029i	0.476543	+	0.879151i	$0.341890\pi$
$859$	−12.4779	+	38.4030i	−0.425740	+	1.31029i	−0.902284	+	0.431143i	$0.858110\pi$
$860$	0.442504	−	0.537433i	0.0150893	−	0.0183263i
$861$	−34.1965	−	24.8452i	−1.16541	−	0.846722i
$862$	−13.7267	+	9.97302i	−0.467533	+	0.339682i
$863$	5.70529			0.194210			0.0971051	−	0.995274i	$-0.469042\pi$
$863$	5.70529			0.194210			0.0971051	+	0.995274i	$0.469042\pi$
$864$	10.4656	−	7.60374i	0.356049	−	0.258684i
$865$	5.24218	−	1.35895i	0.178239	−	0.0462057i
$866$	−12.6221	−	38.8470i	−0.428918	−	1.32007i
$867$	30.6119	−	22.2409i	1.03963	−	0.755339i
$868$	−6.19981			−0.210435
$869$	18.2980	+	46.3973i	0.620718	+	1.57392i
$870$	−12.9646	−	20.3244i	−0.439540	−	0.689061i
$871$	−16.5136	−	50.8237i	−0.559542	−	1.72209i
$872$	−1.14991	+	3.53907i	−0.0389410	+	0.119848i
$873$	−0.793617	+	2.44250i	−0.0268598	+	0.0826661i
$874$	7.04135	+	21.6710i	0.238177	+	0.733034i
$875$	−16.6833	−	34.8219i	−0.563999	−	1.17719i
$876$	−7.24363	−	5.26280i	−0.244740	−	0.177814i
$877$	−37.8543	−	27.5028i	−1.27825	−	0.928703i	−0.278752	−	0.960363i	$-0.589921\pi$
$877$	−37.8543	−	27.5028i	−1.27825	−	0.928703i	−0.999499	+	0.0316600i	$0.989921\pi$
$878$	7.73043	+	23.7918i	0.260889	+	0.802935i
$879$	−4.10595	+	2.98315i	−0.138490	+	0.100619i
$880$	−21.2185	+	29.2651i	−0.715275	+	0.986526i
$881$	36.9156	+	26.8207i	1.24372	+	0.903614i	0.997840	−	0.0656869i	$-0.0209238\pi$
$881$	36.9156	+	26.8207i	1.24372	+	0.903614i	0.245878	+	0.969301i	$0.420924\pi$
$882$	−5.93950	+	18.2799i	−0.199993	+	0.615517i
$883$	54.4590			1.83269			0.916345	−	0.400389i	$-0.131125\pi$
$883$	54.4590			1.83269			0.916345	+	0.400389i	$0.131125\pi$
$884$	2.66309	−	1.93485i	0.0895695	−	0.0650760i
$885$	16.3490	+	6.42913i	0.549565	+	0.216113i
$886$	55.7321	−	40.4917i	1.87236	−	1.36035i
$887$	13.5430	−	9.83958i	0.454730	−	0.330381i	−0.336730	−	0.941601i	$-0.609321\pi$
$887$	13.5430	−	9.83958i	0.454730	−	0.330381i	0.791460	+	0.611220i	$0.209321\pi$
$888$	7.47569	+	23.0078i	0.250868	+	0.772092i
$889$	7.57904			0.254193
$890$	11.9242	+	4.68912i	0.399701	+	0.157180i
$891$	−13.2062	−	33.4864i	−0.442426	−	1.12184i
$892$	11.6010	+	8.42861i	0.388430	+	0.282211i
$893$	8.08778	−	24.8916i	0.270647	−	0.832966i
$894$	7.09108			0.237161
$895$	20.1512	+	31.5907i	0.673579	+	1.05596i
$896$	−25.0429	−	18.1947i	−0.836624	−	0.607843i
$897$	14.9582	+	10.8678i	0.499441	+	0.362865i
$898$	−16.1098	+	49.5809i	−0.537591	+	1.65453i
$899$	2.78616	−	2.02426i	0.0929235	−	0.0675129i
$900$	−6.08176	+	13.0818i	−0.202725	+	0.436061i
$901$	−0.964086			−0.0321184
$902$	12.0434	+	30.5377i	0.401000	+	1.01679i
$903$	1.45431	−	1.05662i	0.0483964	−	0.0351621i
$904$	−6.89203	−	21.2115i	−0.229225	−	0.705483i
$905$	−23.5242	−	36.8786i	−0.781970	−	1.22588i
$906$	2.39074	+	7.35793i	0.0794269	+	0.244451i
$907$	7.33289	+	22.5683i	0.243485	+	0.749369i	0.995882	+	0.0906591i	$0.0288974\pi$
$907$	7.33289	+	22.5683i	0.243485	+	0.749369i	−0.752397	+	0.658709i	$0.771103\pi$
$908$	2.00339	−	6.16580i	0.0664849	−	0.204619i
$909$	−20.4644	+	14.8682i	−0.678761	+	0.493149i
$910$	−59.0245	−	23.2110i	−1.95664	−	0.769437i
$911$	−18.0297			−0.597349			−0.298675	−	0.954355i	$-0.596545\pi$
$911$	−18.0297			−0.597349			−0.298675	+	0.954355i	$0.596545\pi$
$912$	23.3122	−	71.7477i	0.771945	−	2.37580i
$913$	−11.7294	+	45.4297i	−0.388185	+	1.50350i
$914$	−19.6684	−	60.5331i	−0.650572	−	2.00226i
$915$	66.5758	+	26.1805i	2.20093	+	0.865501i
$916$	−7.21517	−	22.2060i	−0.238396	−	0.733707i
$917$	−14.5770	−	44.8634i	−0.481375	−	1.48152i
$918$	0.604475	+	1.86038i	0.0199507	+	0.0614018i
$919$	−1.84733	+	5.68550i	−0.0609379	+	0.187547i	−0.976891	−	0.213737i	$-0.931436\pi$
$919$	−1.84733	+	5.68550i	−0.0609379	+	0.187547i	0.915953	+	0.401285i	$0.131436\pi$
$920$	4.47756	+	1.76077i	0.147621	+	0.0580508i
$921$	3.09569	−	9.52756i	0.102007	−	0.313944i
$922$	15.9871	+	49.2033i	0.526508	+	1.62043i
$923$	−4.40531	−	13.5581i	−0.145002	−	0.446272i
$924$	27.1097	−	22.3659i	0.891842	−	0.735783i
$925$	33.0827	+	30.7787i	1.08775	+	1.01200i
$926$	0.394513	−	1.21419i	0.0129645	−	0.0399007i
$927$	−24.2269	−	17.6019i	−0.795717	−	0.578122i
$928$	−17.0581			−0.559961
$929$	22.7838	+	16.5534i	0.747513	+	0.543100i	0.895055	−	0.445956i	$-0.147136\pi$
$929$	22.7838	+	16.5534i	0.747513	+	0.543100i	−0.147542	+	0.989056i	$0.547136\pi$
$930$	−11.4394	−	4.49847i	−0.375113	−	0.147511i
$931$	−10.4047	−	32.0223i	−0.341000	−	1.04949i
$932$	4.89747	−	3.55822i	0.160422	−	0.116553i
$933$	31.9738	−	23.2303i	1.04678	−	0.760527i
$934$	−2.25098	+	6.92779i	−0.0736542	+	0.226684i
$935$	−2.36534	−	3.24890i	−0.0773549	−	0.106250i
$936$	−3.48804	−	10.7351i	−0.114010	−	0.350887i
$937$	−3.20776	−	2.33058i	−0.104793	−	0.0761366i	0.534155	−	0.845387i	$-0.320630\pi$
$937$	−3.20776	−	2.33058i	−0.104793	−	0.0761366i	−0.638948	+	0.769250i	$0.720630\pi$
$938$	23.2950	+	71.6948i	0.760610	+	2.34092i
$939$	7.92003	−	24.3753i	0.258460	−	0.795459i
$940$	6.23935	+	9.78135i	0.203505	+	0.319032i
$941$	17.2829			0.563406			0.281703	−	0.959502i	$-0.409101\pi$
$941$	17.2829			0.563406			0.281703	+	0.959502i	$0.409101\pi$
$942$	4.86333	+	14.9678i	0.158456	+	0.487677i
$943$	7.95900	−	5.78255i	0.259181	−	0.188306i
$944$	13.6785	−	9.93799i	0.445196	−	0.323454i
$945$	9.67434	−	11.7497i	0.314706	−	0.382219i
$946$	−1.39342	+	0.0857897i	−0.0453040	+	0.00278927i
$947$	−24.9568	+	18.1322i	−0.810987	+	0.589216i	−0.914117	−	0.405452i	$-0.867114\pi$
$947$	−24.9568	+	18.1322i	−0.810987	+	0.589216i	0.103130	+	0.994668i	$0.467114\pi$
$948$	46.1408			1.49858
$949$	10.5860	−	7.69121i	0.343637	−	0.249667i
$950$	−12.0121	−	61.4179i	−0.389723	−	1.99266i
$951$	10.0147	+	30.8221i	0.324750	+	0.999476i
$952$	1.78944	−	1.30010i	0.0579960	−	0.0421365i
$953$	−19.0811			−0.618097			−0.309048	−	0.951046i	$-0.600011\pi$
$953$	−19.0811			−0.618097			−0.309048	+	0.951046i	$0.600011\pi$
$954$	2.14467	−	6.60062i	0.0694363	−	0.213703i
$955$	−1.87127	+	30.8877i	−0.0605528	+	0.999503i
$956$	8.90843	+	6.47235i	0.288119	+	0.209331i
$957$	−4.88038	+	18.9025i	−0.157760	+	0.611030i
$958$	−13.4078	−	9.74132i	−0.433185	−	0.314728i
$959$	51.5885	+	37.4812i	1.66588	+	1.21033i
$960$	6.19236	+	9.70768i	0.199858	+	0.313314i
$961$	−9.03689	+	27.8127i	−0.291513	+	0.897183i
$962$	74.2229			2.39304
$963$	−39.3916			−1.26938
$964$	0.596126	−	1.83469i	0.0191999	−	0.0590913i
$965$	20.7926	+	8.17655i	0.669337	+	0.263212i
$966$	−21.1009	−	15.3307i	−0.678912	−	0.493258i
$967$	−0.793547	−	0.576545i	−0.0255187	−	0.0185405i	0.574953	−	0.818187i	$-0.305020\pi$
$967$	−0.793547	−	0.576545i	−0.0255187	−	0.0185405i	−0.600472	+	0.799646i	$0.705020\pi$
$968$	12.9028	−	1.59483i	0.414710	−	0.0512599i
$969$	6.78523	+	4.92976i	0.217973	+	0.158367i
$970$	4.59595	+	1.80733i	0.147567	+	0.0580297i
$971$	−9.10862	+	28.0335i	−0.292310	+	0.899637i	0.691802	+	0.722087i	$0.256817\pi$
$971$	−9.10862	+	28.0335i	−0.292310	+	0.899637i	−0.984112	+	0.177550i	$0.943183\pi$
$972$	−25.2913			−0.811219
$973$	−51.0861	+	37.1163i	−1.63775	+	1.18989i
$974$	−8.78632	−	27.0415i	−0.281532	−	0.866466i
$975$	−37.1784	−	34.5892i	−1.19066	−	1.10774i
$976$	55.7011	−	40.4692i	1.78295	−	1.29539i
$977$	20.0758			0.642282			0.321141	−	0.947031i	$-0.395934\pi$
$977$	20.0758			0.642282			0.321141	+	0.947031i	$0.395934\pi$
$978$	−48.5552	+	35.2774i	−1.55262	+	1.12805i
$979$	−3.80677	−	9.65263i	−0.121665	−	0.308500i
$980$	13.8901	+	5.46220i	0.443704	+	0.174483i
$981$	5.42501	−	3.94150i	0.173207	−	0.125842i
$982$	31.2948	−	22.7370i	0.998657	−	0.725567i
$983$	14.6355	+	45.0433i	0.466799	+	1.43666i	0.856706	+	0.515805i	$0.172507\pi$
$983$	14.6355	+	45.0433i	0.466799	+	1.43666i	−0.389907	+	0.920854i	$0.627493\pi$
$984$	−14.4656			−0.461147
$985$	−2.25781	+	37.2681i	−0.0719397	+	1.18746i
$986$	0.797080	−	2.45316i	0.0253842	−	0.0781245i
$987$	9.25764	+	28.4921i	0.294674	+	0.906913i
$988$	−33.5836	−	24.3999i	−1.06844	−	0.776265i
$989$	0.129288	+	0.397909i	0.00411113	+	0.0126528i
$990$	27.5055	−	8.96691i	0.874181	−	0.284987i
$991$	12.3774	−	38.0936i	0.393180	−	1.21008i	−0.537190	−	0.843461i	$-0.680514\pi$
$991$	12.3774	−	38.0936i	0.393180	−	1.21008i	0.930370	−	0.366622i	$-0.119486\pi$
$992$	−7.03669	+	5.11245i	−0.223415	+	0.162320i
$993$	52.1738	−	37.9064i	1.65568	−	1.20292i
$994$	6.21438	+	19.1259i	0.197108	+	0.606636i
$995$	10.2544	−	12.4543i	0.325087	−	0.394827i
$996$	35.1165	+	25.5137i	1.11271	+	0.808431i
$997$	−45.1205			−1.42898			−0.714490	−	0.699645i	$-0.753341\pi$
$997$	−45.1205			−1.42898			−0.714490	+	0.699645i	$0.753341\pi$
$998$	−23.9920	−	17.4312i	−0.759453	−	0.551775i
$999$	−5.50401	+	16.9396i	−0.174139	+	0.535946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.l.d.31.6	yes	100
11.5	even	5		275.2.k.d.181.20	✓	100
25.21	even	5		275.2.k.d.196.20	yes	100
275.71	even	5	inner	275.2.l.d.71.6	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.2.k.d.181.20	✓	100	11.5	even	5
275.2.k.d.196.20	yes	100	25.21	even	5
275.2.l.d.31.6	yes	100	1.1	even	1	trivial
275.2.l.d.71.6	yes	100	275.71	even	5	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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.l (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-1.83159 q^{2} +(0.699896 - 2.15406i) q^{3} +1.35471 q^{4} +(1.42132 - 1.72623i) q^{5} +(-1.28192 + 3.94534i) q^{6} +(2.79400 + 2.02996i) q^{7} +1.18190 q^{8} +(-1.72306 - 1.25188i) q^{9} +(-2.60327 + 3.16173i) q^{10} +(3.31036 - 0.203811i) q^{11} +(0.948156 - 2.91812i) q^{12} +(3.62771 + 2.63568i) q^{13} +(-5.11745 - 3.71805i) q^{14} +(-2.72362 - 4.26978i) q^{15} -4.87418 q^{16} +(0.167452 - 0.515364i) q^{17} +(3.15593 + 2.29292i) q^{18} -6.83359 q^{19} +(1.92547 - 2.33854i) q^{20} +(6.32816 - 4.59768i) q^{21} +(-6.06321 + 0.373298i) q^{22} +(0.562574 + 1.73142i) q^{23} +(0.827210 - 2.54589i) q^{24} +(-0.959714 - 4.90703i) q^{25} +(-6.64446 - 4.82748i) q^{26} +(1.59448 - 1.15846i) q^{27} +(3.78506 + 2.75001i) q^{28} -2.59887 q^{29} +(4.98854 + 7.82047i) q^{30} +(-1.07206 + 0.778901i) q^{31} +6.56368 q^{32} +(1.87788 - 7.27334i) q^{33} +(-0.306702 + 0.943933i) q^{34} +(7.47533 - 1.93786i) q^{35} +(-2.33424 - 1.69593i) q^{36} +(-7.31128 + 5.31196i) q^{37} +12.5163 q^{38} +(8.21643 - 5.96959i) q^{39} +(1.67986 - 2.04023i) q^{40} +(-1.66988 - 5.13937i) q^{41} +(-11.5906 + 8.42104i) q^{42} +0.229816 q^{43} +(4.48457 - 0.276105i) q^{44} +(-4.61003 + 1.19508i) q^{45} +(-1.03040 - 3.17125i) q^{46} +(-1.18353 + 3.64254i) q^{47} +(-3.41142 + 10.4993i) q^{48} +(1.52258 + 4.68602i) q^{49} +(1.75780 + 8.98765i) q^{50} +(-0.992924 - 0.721402i) q^{51} +(4.91449 + 3.57059i) q^{52} +(-0.549782 - 1.69206i) q^{53} +(-2.92043 + 2.12182i) q^{54} +(4.35324 - 6.00410i) q^{55} +(3.30224 + 2.39922i) q^{56} +(-4.78280 + 14.7199i) q^{57} +4.76006 q^{58} +(-2.80631 + 2.03890i) q^{59} +(-3.68971 - 5.78431i) q^{60} +(-11.4278 + 8.30277i) q^{61} +(1.96358 - 1.42662i) q^{62} +(-2.27297 - 6.99548i) q^{63} -2.27358 q^{64} +(9.70591 - 2.51610i) q^{65} +(-3.43951 + 13.3218i) q^{66} +(-9.64145 - 7.00493i) q^{67} +(0.226849 - 0.698168i) q^{68} +4.12333 q^{69} +(-13.6917 + 3.54936i) q^{70} +(-2.57203 - 1.86869i) q^{71} +(-2.03649 - 1.47960i) q^{72} +(0.901745 - 2.77528i) q^{73} +(13.3912 - 9.72931i) q^{74} +(-11.2417 - 1.36713i) q^{75} -9.25753 q^{76} +(9.66287 + 6.15044i) q^{77} +(-15.0491 + 10.9338i) q^{78} +(4.64697 + 14.3019i) q^{79} +(-6.92776 + 8.41394i) q^{80} +(-3.35386 - 10.3221i) q^{81} +(3.05854 + 9.41321i) q^{82} +(-4.37159 + 13.4544i) q^{83} +(8.57282 - 6.22852i) q^{84} +(-0.651632 - 1.02155i) q^{85} -0.420928 q^{86} +(-1.81894 + 5.59812i) q^{87} +(3.91253 - 0.240885i) q^{88} +(-0.966770 - 2.97541i) q^{89} +(8.44368 - 2.18889i) q^{90} +(4.78548 + 14.7282i) q^{91} +(0.762124 + 2.34558i) q^{92} +(0.927463 + 2.85444i) q^{93} +(2.16774 - 6.67163i) q^{94} +(-9.71270 + 11.7963i) q^{95} +(4.59389 - 14.1385i) q^{96} +(-0.372622 - 1.14681i) q^{97} +(-2.78874 - 8.58285i) q^{98} +(-5.95908 - 3.79298i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 2 q^{2} - 2 q^{3} + 106 q^{4} + 5 q^{5} + 5 q^{6} + 5 q^{7} - 30 q^{8} - 25 q^{9} - 22 q^{10} - 53 q^{12} - 18 q^{13} - 10 q^{14} + 16 q^{15} + 62 q^{16} + q^{17} - 21 q^{18} + 6 q^{19} + q^{20}+ \cdots - 84 q^{99}+O(q^{100}) \) 100 * q + 2 * q^2 - 2 * q^3 + 106 * q^4 + 5 * q^5 + 5 * q^6 + 5 * q^7 - 30 * q^8 - 25 * q^9 - 22 * q^10 - 53 * q^12 - 18 * q^13 - 10 * q^14 + 16 * q^15 + 62 * q^16 + q^17 - 21 * q^18 + 6 * q^19 + q^20 - 22 * q^21 + 6 * q^22 + 20 * q^23 - 18 * q^24 + q^25 - 37 * q^26 + 10 * q^27 - 64 * q^28 - 28 * q^29 + 15 * q^30 + 9 * q^31 - 98 * q^32 + 13 * q^33 - 14 * q^34 + 13 * q^35 - 30 * q^36 - 21 * q^37 + 18 * q^38 + 44 * q^39 + 9 * q^40 + 28 * q^41 + 31 * q^42 + 82 * q^43 - 4 * q^44 - 25 * q^45 - 16 * q^46 - 10 * q^47 - 72 * q^48 - 26 * q^49 - 46 * q^50 - 14 * q^51 - 23 * q^52 - 5 * q^53 - 22 * q^54 + 32 * q^55 + q^56 - 85 * q^57 + 80 * q^58 - 3 * q^59 + 61 * q^60 + 35 * q^61 + 43 * q^62 - 47 * q^63 - 54 * q^64 - 64 * q^65 - 13 * q^66 - 20 * q^67 + 5 * q^68 + 76 * q^69 - 23 * q^70 + 28 * q^71 - 53 * q^72 + 33 * q^73 - 3 * q^74 - 34 * q^75 - 156 * q^76 + 45 * q^77 + 30 * q^78 + 4 * q^79 - 144 * q^80 - 27 * q^81 - 59 * q^82 - 92 * q^83 + 9 * q^84 - 26 * q^85 - 56 * q^86 + 38 * q^87 + 18 * q^88 + 39 * q^89 + 114 * q^90 - 11 * q^91 - 60 * q^92 - 19 * q^93 + 46 * q^94 - 46 * q^95 + 9 * q^96 + 20 * q^97 + 122 * q^98 - 84 * q^99

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