LMFDB - Embedded newform 161.2.g.a.68.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [161,2,Mod(45,161)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(161, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("161.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	161.g (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.28559147254$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			68.4
Character	$\chi$	$=$	161.68
Dual form			161.2.g.a.45.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.06863 + 1.85092i) q^{2} +(-2.39984 + 1.38555i) q^{3} +(-1.28394 - 2.22386i) q^{4} +(1.92742 - 3.33839i) q^{5} -5.92256i q^{6} +(-2.36835 - 1.17938i) q^{7} +1.21373 q^{8} +(2.33949 - 4.05212i) q^{9} +(4.11940 + 7.13501i) q^{10} +(-1.51548 + 0.874964i) q^{11} +(6.16253 + 3.55794i) q^{12} -0.204932i q^{13} +(4.71383 - 3.12331i) q^{14} +10.6821i q^{15} +(1.27086 - 2.20120i) q^{16} +(-0.829997 - 1.43760i) q^{17} +(5.00011 + 8.66045i) q^{18} +(2.01267 - 3.48605i) q^{19} -9.89880 q^{20} +(7.31775 - 0.451142i) q^{21} -3.74005i q^{22} +(-4.79290 + 0.167754i) q^{23} +(-2.91275 + 1.68168i) q^{24} +(-4.92989 - 8.53883i) q^{25} +(0.379314 + 0.218997i) q^{26} +4.65264i q^{27} +(0.418059 + 6.78112i) q^{28} -8.95599 q^{29} +(-19.7718 - 11.4153i) q^{30} +(3.78515 - 2.18536i) q^{31} +(3.92989 + 6.80678i) q^{32} +(2.42461 - 4.19955i) q^{33} +3.54784 q^{34} +(-8.50202 + 5.63331i) q^{35} -12.0151 q^{36} +(5.48330 + 3.16579i) q^{37} +(4.30161 + 7.45060i) q^{38} +(0.283944 + 0.491805i) q^{39} +(2.33936 - 4.05189i) q^{40} -5.27084i q^{41} +(-6.98494 + 14.0267i) q^{42} -10.2031i q^{43} +(3.89159 + 2.24681i) q^{44} +(-9.01838 - 15.6203i) q^{45} +(4.81134 - 9.05055i) q^{46} +(-0.416658 - 0.240557i) q^{47} +7.04338i q^{48} +(4.21814 + 5.58635i) q^{49} +21.0729 q^{50} +(3.98373 + 2.30000i) q^{51} +(-0.455740 + 0.263122i) q^{52} +(-6.22805 + 3.59576i) q^{53} +(-8.61169 - 4.97196i) q^{54} +6.74569i q^{55} +(-2.87452 - 1.43144i) q^{56} +11.1546i q^{57} +(9.57065 - 16.5769i) q^{58} +(-2.96207 + 1.71015i) q^{59} +(23.7555 - 13.7153i) q^{60} +(-1.45607 + 2.52199i) q^{61} +9.34135i q^{62} +(-10.3197 + 6.83769i) q^{63} -11.7150 q^{64} +(-0.684144 - 0.394991i) q^{65} +(5.18203 + 8.97554i) q^{66} +(-7.10467 + 4.10188i) q^{67} +(-2.13134 + 3.69159i) q^{68} +(11.2698 - 7.04338i) q^{69} +(-1.34130 - 21.7565i) q^{70} +2.87254 q^{71} +(2.83950 - 4.91816i) q^{72} +(-8.52674 + 4.92292i) q^{73} +(-11.7192 + 6.76611i) q^{74} +(23.6619 + 13.6612i) q^{75} -10.3366 q^{76} +(4.62110 - 0.284893i) q^{77} -1.21373 q^{78} +(-6.64288 - 3.83527i) q^{79} +(-4.89898 - 8.48527i) q^{80} +(0.572014 + 0.990758i) q^{81} +(9.75591 + 5.63258i) q^{82} -0.832284 q^{83} +(-10.3989 - 15.6944i) q^{84} -6.39901 q^{85} +(18.8852 + 10.9034i) q^{86} +(21.4930 - 12.4090i) q^{87} +(-1.83938 + 1.06197i) q^{88} +(1.27673 - 2.21136i) q^{89} +38.5493 q^{90} +(-0.241693 + 0.485351i) q^{91} +(6.52687 + 10.4433i) q^{92} +(-6.05584 + 10.4890i) q^{93} +(0.890507 - 0.514134i) q^{94} +(-7.75853 - 13.4382i) q^{95} +(-18.8622 - 10.8901i) q^{96} +16.3072 q^{97} +(-14.8475 + 1.83770i) q^{98} +8.18789i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{2} - 6 q^{3} - 12 q^{4} + 12 q^{8} + 4 q^{9} + 6 q^{12} + 22 q^{18} - 36 q^{24} - 22 q^{25} - 12 q^{26} - 44 q^{29} - 6 q^{32} - 10 q^{35} - 16 q^{39} + 18 q^{46} - 36 q^{47} + 28 q^{49} + 84 q^{50}+ \cdots - 146 q^{98}+O(q^{100}) $ 28 * q - 4 * q^2 - 6 * q^3 - 12 * q^4 + 12 * q^8 + 4 * q^9 + 6 * q^12 + 22 * q^18 - 36 * q^24 - 22 * q^25 - 12 * q^26 - 44 * q^29 - 6 * q^32 - 10 * q^35 - 16 * q^39 + 18 * q^46 - 36 * q^47 + 28 * q^49 + 84 * q^50 + 72 * q^52 - 30 * q^54 + 14 * q^58 - 54 * q^59 - 68 * q^64 + 38 * q^70 + 16 * q^71 - 4 * q^72 - 18 * q^73 + 96 * q^75 + 20 * q^77 - 12 * q^78 + 22 * q^81 - 52 * q^85 - 18 * q^87 - 28 * q^92 - 10 * q^93 + 84 * q^94 + 56 * q^95 - 84 * q^96 - 146 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/161\mathbb{Z}\right)^\times$.

$n$	$24$	$120$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.06863	+	1.85092i	−0.755636	+	1.30880i	0.189421	+	0.981896i	$0.439339\pi$
$2$	−1.06863	+	1.85092i	−0.755636	+	1.30880i	−0.945057	+	0.326904i	$0.893995\pi$
$3$	−2.39984	+	1.38555i	−1.38555	+	0.799947i	−0.992810	−	0.119702i	$-0.961806\pi$
$3$	−2.39984	+	1.38555i	−1.38555	+	0.799947i	−0.392740	+	0.919650i	$0.628473\pi$
$4$	−1.28394	−	2.22386i	−0.641972	−	1.11193i
$5$	1.92742	−	3.33839i	0.861968	−	1.49297i	−0.00805796	−	0.999968i	$-0.502565\pi$
$5$	1.92742	−	3.33839i	0.861968	−	1.49297i	0.870026	−	0.493005i	$-0.164102\pi$
$6$		−	5.92256i		−	2.41788i
$7$	−2.36835	−	1.17938i	−0.895151	−	0.445763i
$7$	−2.36835	−	1.17938i	−0.895151	−	0.445763i
$8$	1.21373			0.429117
$9$	2.33949	−	4.05212i	0.779832	−	1.35071i
$10$	4.11940	+	7.13501i	1.30267	+	2.25629i
$11$	−1.51548	+	0.874964i	−0.456935	+	0.263811i	−0.710755	−	0.703440i	$-0.751646\pi$
$11$	−1.51548	+	0.874964i	−0.456935	+	0.263811i	0.253820	+	0.967252i	$0.418313\pi$
$12$	6.16253	+	3.55794i	1.77897	+	1.02709i
$13$		−	0.204932i		−	0.0568380i	−0.999596	−	0.0284190i	$-0.990953\pi$
$13$		−	0.204932i		−	0.0568380i	0.999596	−	0.0284190i	$-0.00904727\pi$
$14$	4.71383	−	3.12331i	1.25982	−	0.834739i
$15$			10.6821i			2.75812i
$16$	1.27086	−	2.20120i	0.317716	−	0.550300i
$17$	−0.829997	−	1.43760i	−0.201304	−	0.348669i	0.747645	−	0.664099i	$-0.231185\pi$
$17$	−0.829997	−	1.43760i	−0.201304	−	0.348669i	−0.948949	+	0.315430i	$0.897851\pi$
$18$	5.00011	+	8.66045i	1.17854	+	2.04129i
$19$	2.01267	−	3.48605i	0.461739	−	0.799755i	−0.537309	−	0.843385i	$-0.680559\pi$
$19$	2.01267	−	3.48605i	0.461739	−	0.799755i	0.999048	+	0.0436305i	$0.0138924\pi$
$20$	−9.89880			−2.21344
$21$	7.31775	−	0.451142i	1.59686	−	0.0984473i
$22$		−	3.74005i		−	0.797382i
$23$	−4.79290	+	0.167754i	−0.999388	+	0.0349791i
$23$	−4.79290	+	0.167754i	−0.999388	+	0.0349791i
$24$	−2.91275	+	1.68168i	−0.594562	+	0.343271i
$25$	−4.92989	−	8.53883i	−0.985979	−	1.70777i
$26$	0.379314	+	0.218997i	0.0743896	+	0.0429489i
$27$			4.65264i			0.895402i
$28$	0.418059	+	6.78112i	0.0790057	+	1.28151i
$29$	−8.95599			−1.66309			−0.831543	−	0.555460i	$-0.812542\pi$
$29$	−8.95599			−1.66309			−0.831543	+	0.555460i	$0.812542\pi$
$30$	−19.7718	−	11.4153i	−3.60982	−	2.08413i
$31$	3.78515	−	2.18536i	0.679832	−	0.392501i	−0.119959	−	0.992779i	$-0.538276\pi$
$31$	3.78515	−	2.18536i	0.679832	−	0.392501i	0.799792	+	0.600277i	$0.204943\pi$
$32$	3.92989	+	6.80678i	0.694714	+	1.20328i
$33$	2.42461	−	4.19955i	0.422071	−	0.731048i
$34$	3.54784			0.608450
$35$	−8.50202	+	5.63331i	−1.43710	+	0.952203i
$36$	−12.0151			−2.00252
$37$	5.48330	+	3.16579i	0.901449	+	0.520452i	0.877670	−	0.479265i	$-0.159097\pi$
$37$	5.48330	+	3.16579i	0.901449	+	0.520452i	0.0237791	+	0.999717i	$0.492430\pi$
$38$	4.30161	+	7.45060i	0.697813	+	1.20865i
$39$	0.283944	+	0.491805i	0.0454674	+	0.0787519i
$40$	2.33936	−	4.05189i	0.369885	−	0.640660i
$41$		−	5.27084i		−	0.823166i	−0.911372	−	0.411583i	$-0.864976\pi$
$41$		−	5.27084i		−	0.823166i	0.911372	−	0.411583i	$-0.135024\pi$
$42$	−6.98494	+	14.0267i	−1.07780	+	2.16436i
$43$		−	10.2031i		−	1.55596i	−0.628287	−	0.777981i	$-0.716244\pi$
$43$		−	10.2031i		−	1.55596i	0.628287	−	0.777981i	$-0.283756\pi$
$44$	3.89159	+	2.24681i	0.586679	+	0.338719i
$45$	−9.01838	−	15.6203i	−1.34438	−	2.32853i
$46$	4.81134	−	9.05055i	0.709393	−	1.33443i
$47$	−0.416658	−	0.240557i	−0.0607758	−	0.0350889i	0.469304	−	0.883037i	$-0.344505\pi$
$47$	−0.416658	−	0.240557i	−0.0607758	−	0.0350889i	−0.530080	+	0.847948i	$0.677838\pi$
$48$			7.04338i			1.01662i
$49$	4.21814	+	5.58635i	0.602591	+	0.798050i
$50$	21.0729			2.98016
$51$	3.98373	+	2.30000i	0.557833	+	0.322065i
$52$	−0.455740	+	0.263122i	−0.0631998	+	0.0364884i
$53$	−6.22805	+	3.59576i	−0.855488	+	0.493916i	−0.862499	−	0.506059i	$-0.831102\pi$
$53$	−6.22805	+	3.59576i	−0.855488	+	0.493916i	0.00701084	+	0.999975i	$0.497768\pi$
$54$	−8.61169	−	4.97196i	−1.17190	−	0.676598i
$55$			6.74569i			0.909588i
$56$	−2.87452	−	1.43144i	−0.384124	−	0.191284i
$57$			11.1546i			1.47747i
$58$	9.57065	−	16.5769i	1.25669	−	2.17665i
$59$	−2.96207	+	1.71015i	−0.385629	+	0.222643i	−0.680264	−	0.732967i	$-0.738135\pi$
$59$	−2.96207	+	1.71015i	−0.385629	+	0.222643i	0.294636	+	0.955610i	$0.404802\pi$
$60$	23.7555	−	13.7153i	3.06683	−	1.77063i
$61$	−1.45607	+	2.52199i	−0.186431	+	0.322908i	−0.944058	−	0.329780i	$-0.893025\pi$
$61$	−1.45607	+	2.52199i	−0.186431	+	0.322908i	0.757627	+	0.652688i	$0.226359\pi$
$62$			9.34135i			1.18635i
$63$	−10.3197	+	6.83769i	−1.30016	+	0.861468i
$64$	−11.7150			−1.46437
$65$	−0.684144	−	0.394991i	−0.0848576	−	0.0489926i
$66$	5.18203	+	8.97554i	0.637864	+	1.10481i
$67$	−7.10467	+	4.10188i	−0.867973	+	0.501125i	−0.866674	−	0.498875i	$-0.833747\pi$
$67$	−7.10467	+	4.10188i	−0.867973	+	0.501125i	−0.00129901	+	0.999999i	$0.500413\pi$
$68$	−2.13134	+	3.69159i	−0.258463	+	0.447671i
$69$	11.2698	−	7.04338i	1.35672	−	0.847923i
$70$	−1.34130	−	21.7565i	−0.160316	−	2.60040i
$71$	2.87254			0.340908			0.170454	−	0.985366i	$-0.445477\pi$
$71$	2.87254			0.340908			0.170454	+	0.985366i	$0.445477\pi$
$72$	2.83950	−	4.91816i	0.334639	−	0.579611i
$73$	−8.52674	+	4.92292i	−0.997980	+	0.576184i	−0.907650	−	0.419728i	$-0.862125\pi$
$73$	−8.52674	+	4.92292i	−0.997980	+	0.576184i	−0.0903298	+	0.995912i	$0.528792\pi$
$74$	−11.7192	+	6.76611i	−1.36234	+	0.786545i
$75$	23.6619	+	13.6612i	2.73224	+	1.57746i
$76$	−10.3366			−1.18569
$77$	4.62110	−	0.284893i	0.526623	−	0.0324666i
$78$	−1.21373			−0.137427
$79$	−6.64288	−	3.83527i	−0.747383	−	0.431502i	0.0773647	−	0.997003i	$-0.475349\pi$
$79$	−6.64288	−	3.83527i	−0.747383	−	0.431502i	−0.824747	+	0.565501i	$0.808683\pi$
$80$	−4.89898	−	8.48527i	−0.547722	−	0.948682i
$81$	0.572014	+	0.990758i	0.0635571	+	0.110084i
$82$	9.75591	+	5.63258i	1.07736	+	0.622014i
$83$	−0.832284			−0.0913551			−0.0456775	−	0.998956i	$-0.514545\pi$
$83$	−0.832284			−0.0913551			−0.0456775	+	0.998956i	$0.514545\pi$
$84$	−10.3989	−	15.6944i	−1.13461	−	1.71240i
$85$	−6.39901			−0.694070
$86$	18.8852	+	10.9034i	2.03644	+	1.17574i
$87$	21.4930	−	12.4090i	2.30429	−	1.33038i
$88$	−1.83938	+	1.06197i	−0.196078	+	0.113206i
$89$	1.27673	−	2.21136i	0.135333	−	0.234404i	−0.790392	−	0.612602i	$-0.790123\pi$
$89$	1.27673	−	2.21136i	0.135333	−	0.234404i	0.925725	+	0.378198i	$0.123456\pi$
$90$	38.5493			4.06345
$91$	−0.241693	+	0.485351i	−0.0253363	+	0.0508786i
$92$	6.52687	+	10.4433i	0.680473	+	1.08879i
$93$	−6.05584	+	10.4890i	−0.627961	+	1.08766i
$94$	0.890507	−	0.514134i	0.0918487	−	0.0530289i
$95$	−7.75853	−	13.4382i	−0.796008	−	1.37873i
$96$	−18.8622	−	10.8901i	−1.92512	−	1.11147i
$97$	16.3072			1.65574			0.827871	−	0.560919i	$-0.189552\pi$
$97$	16.3072			1.65574			0.827871	+	0.560919i	$0.189552\pi$
$98$	−14.8475	+	1.83770i	−1.49983	+	0.185636i
$99$			8.18789i			0.822914i
$100$	−12.6594	+	21.9267i	−1.26594	+	2.19267i
$101$	3.28009	−	1.89376i	0.326381	−	0.188436i	−0.327852	−	0.944729i	$-0.606325\pi$
$101$	3.28009	−	1.89376i	0.326381	−	0.188436i	0.654233	+	0.756293i	$0.272992\pi$
$102$	−8.51426	+	4.91571i	−0.843038	+	0.486728i
$103$	8.15645	−	14.1274i	0.803679	−	1.39201i	−0.113501	−	0.993538i	$-0.536206\pi$
$103$	8.15645	−	14.1274i	0.803679	−	1.39201i	0.917179	−	0.398474i	$-0.130460\pi$
$104$		−	0.248732i		−	0.0243901i
$105$	12.5983	−	25.2990i	1.22947	−	2.46893i
$106$		−	15.3702i		−	1.49288i
$107$	5.70603	+	3.29438i	0.551622	+	0.318479i	0.749776	−	0.661692i	$-0.230161\pi$
$107$	5.70603	+	3.29438i	0.551622	+	0.318479i	−0.198154	+	0.980171i	$0.563495\pi$
$108$	10.3468	−	5.97374i	0.995623	−	0.574823i
$109$	−0.721798	+	0.416730i	−0.0691357	+	0.0399155i	−0.534169	−	0.845377i	$-0.679376\pi$
$109$	−0.721798	+	0.416730i	−0.0691357	+	0.0399155i	0.465034	+	0.885293i	$0.346042\pi$
$110$	−12.4858	−	7.20865i	−1.19047	−	0.687318i
$111$	−17.5454			−1.66534
$112$	−5.60589	+	3.71438i	−0.529707	+	0.350976i
$113$		−	0.292918i		−	0.0275554i	−0.999905	−	0.0137777i	$-0.995614\pi$
$113$		−	0.292918i		−	0.0275554i	0.999905	−	0.0137777i	$-0.00438572\pi$
$114$	−20.6464	−	11.9202i	−1.93371	−	1.11643i
$115$	−8.67790	+	16.3239i	−0.809218	+	1.52221i
$116$	11.4990	+	19.9168i	1.06765	+	1.84923i
$117$	−0.830411	−	0.479438i	−0.0767716	−	0.0443241i
$118$		−	7.31008i		−	0.672948i
$119$	0.270252	+	4.38361i	0.0247739	+	0.401845i
$120$			12.9652i			1.18355i
$121$	−3.96888	+	6.87430i	−0.360807	+	0.624936i
$122$	−3.11201	−	5.39016i	−0.281748	−	0.488002i
$123$	7.30301	+	12.6492i	0.658490	+	1.14054i
$124$	−9.71983	−	5.61175i	−0.872867	−	0.503950i
$125$	−18.7337			−1.67559
$126$	−1.62806	−	26.4080i	−0.145039	−	2.35261i
$127$	14.3002			1.26894			0.634470	−	0.772947i	$-0.281218\pi$
$127$	14.3002			1.26894			0.634470	+	0.772947i	$0.281218\pi$
$128$	4.65919	−	8.06995i	0.411818	−	0.713290i
$129$	14.1369	+	24.4859i	1.24469	+	2.15586i
$130$	1.46219	−	0.844199i	0.128243	−	0.0740411i
$131$	−1.48125	−	0.855202i	−0.129418	−	0.0747194i	0.433893	−	0.900964i	$-0.357139\pi$
$131$	−1.48125	−	0.855202i	−0.129418	−	0.0747194i	−0.563311	+	0.826245i	$0.690473\pi$
$132$	−12.4523			−1.08383
$133$	−8.87808	+	5.88248i	−0.769827	+	0.510076i
$134$		−	17.5336i		−	1.51467i
$135$	15.5323	+	8.96760i	1.33681	+	0.771808i
$136$	−1.00739	−	1.74485i	−0.0863829	−	0.149620i
$137$	13.9951	−	8.08008i	1.19568	−	0.690328i	0.236093	−	0.971730i	$-0.424133\pi$
$137$	13.9951	−	8.08008i	1.19568	−	0.690328i	0.959590	+	0.281403i	$0.0907997\pi$
$138$	0.993532	+	28.3862i	0.0845751	+	2.41640i
$139$			3.58058i			0.303701i	0.988404	+	0.151850i	$0.0485232\pi$
$139$			3.58058i			0.303701i	−0.988404	+	0.151850i	$0.951477\pi$
$140$	23.4438	+	11.6744i	1.98136	+	0.986668i
$141$	1.33322			0.112277
$142$	−3.06968	+	5.31685i	−0.257602	+	0.446180i
$143$	0.179308	+	0.310571i	0.0149945	+	0.0259713i
$144$	−5.94636	−	10.2994i	−0.495530	−	0.858283i
$145$	−17.2620	+	29.8986i	−1.43353	+	2.48294i
$146$		−	21.0431i		−	1.74154i
$147$	−17.8630	−	7.56192i	−1.47332	−	0.623697i
$148$		−	16.2588i		−	1.33646i
$149$	−11.2771	−	6.51085i	−0.923858	−	0.533389i	−0.0389938	−	0.999239i	$-0.512415\pi$
$149$	−11.2771	−	6.51085i	−0.923858	−	0.533389i	−0.884864	+	0.465850i	$0.845749\pi$
$150$	−50.5717	+	29.1976i	−4.12917	+	2.38397i
$151$	3.83347	+	6.63977i	0.311963	+	0.540337i	0.978787	−	0.204879i	$-0.0656800\pi$
$151$	3.83347	+	6.63977i	0.311963	+	0.540337i	−0.666824	+	0.745215i	$0.732347\pi$
$152$	2.44283	−	4.23111i	0.198140	−	0.343188i
$153$	−7.76710			−0.627933
$154$	−4.41093	+	8.85774i	−0.355443	+	0.713777i
$155$		−	16.8484i		−	1.35330i
$156$	0.729136	−	1.26290i	0.0583776	−	0.101113i
$157$	−7.19948	−	12.4699i	−0.574581	−	0.995204i	−0.996087	−	0.0883781i	$-0.971832\pi$
$157$	−7.19948	−	12.4699i	−0.574581	−	0.995204i	0.421506	−	0.906826i	$-0.361502\pi$
$158$	14.1976	−	8.19698i	1.12950	−	0.652116i
$159$	9.96422	−	17.2585i	0.790214	−	1.36869i
$160$	30.2982			2.39528
$161$	11.5491	+	5.25534i	0.910196	+	0.414178i
$162$	−2.44509			−0.192104
$163$	0.164926	−	0.285661i	0.0129180	−	0.0223747i	−0.859494	−	0.511146i	$-0.829221\pi$
$163$	0.164926	−	0.285661i	0.0129180	−	0.0223747i	0.872412	+	0.488771i	$0.162555\pi$
$164$	−11.7216	+	6.76746i	−0.915302	+	0.528450i
$165$	−9.34648	−	16.1886i	−0.727623	−	1.26028i
$166$	0.889405	−	1.54049i	0.0690312	−	0.119566i
$167$		−	10.3335i		−	0.799627i	−0.916596	−	0.399814i	$-0.869075\pi$
$167$		−	10.3335i		−	0.799627i	0.916596	−	0.399814i	$-0.130925\pi$
$168$	8.88173	−	0.547563i	0.685241	−	0.0422454i
$169$	12.9580			0.996769
$170$	6.83818	−	11.8441i	0.524465	−	0.908400i
$171$	−9.41727	−	16.3112i	−0.720157	−	1.24735i
$172$	−22.6903	+	13.1002i	−1.73012	+	0.998884i
$173$	−6.14735	−	3.54917i	−0.467374	−	0.269839i	0.247766	−	0.968820i	$-0.420304\pi$
$173$	−6.14735	−	3.54917i	−0.467374	−	0.269839i	−0.715140	+	0.698981i	$0.753637\pi$
$174$			53.0424i			4.02114i
$175$	1.60520	+	26.0371i	0.121342	+	1.96822i
$176$			4.44784i			0.335268i
$177$	4.73900	−	8.20819i	0.356205	−	0.616965i
$178$	2.72871	+	4.72626i	0.204525	+	0.354248i
$179$	9.81217	+	16.9952i	0.733396	+	1.27028i	0.955423	+	0.295239i	$0.0953993\pi$
$179$	9.81217	+	16.9952i	0.733396	+	1.27028i	−0.222027	+	0.975040i	$0.571267\pi$
$180$	−23.1582	+	40.1111i	−1.72611	+	2.98971i
$181$	−5.51100			−0.409629			−0.204815	−	0.978801i	$-0.565659\pi$
$181$	−5.51100			−0.409629			−0.204815	+	0.978801i	$0.565659\pi$
$182$	−0.640067	−	0.966016i	−0.0474449	−	0.0716058i
$183$		−	8.06985i		−	0.596541i
$184$	−5.81726	+	0.203607i	−0.428854	+	0.0150101i
$185$	21.1372	−	12.2036i	1.55404	−	0.897226i
$186$	−12.9429	−	22.4178i	−0.949020	−	1.64375i
$187$	2.51569	+	1.45244i	0.183966	+	0.106213i
$188$			1.23545i			0.0901044i
$189$	5.48722	−	11.0191i	0.399137	−	0.801520i
$190$	33.1640			2.40597
$191$	18.5510	+	10.7104i	1.34230	+	0.774977i	0.987145	−	0.159830i	$-0.0510947\pi$
$191$	18.5510	+	10.7104i	1.34230	+	0.774977i	0.355155	+	0.934807i	$0.384428\pi$
$192$	28.1141	−	16.2317i	2.02896	−	1.17142i
$193$	−2.72633	−	4.72214i	−0.196246	−	0.339907i	0.751063	−	0.660231i	$-0.229542\pi$
$193$	−2.72633	−	4.72214i	−0.196246	−	0.339907i	−0.947308	+	0.320324i	$0.896208\pi$
$194$	−17.4263	+	30.1833i	−1.25114	+	2.16704i
$195$	2.18912			0.156766
$196$	7.00739	−	16.5531i	0.500528	−	1.18236i
$197$	−6.78385			−0.483329			−0.241665	−	0.970360i	$-0.577693\pi$
$197$	−6.78385			−0.483329			−0.241665	+	0.970360i	$0.577693\pi$
$198$	−15.1552	−	8.74983i	−1.07703	−	0.621824i
$199$	−0.946823	−	1.63995i	−0.0671185	−	0.116253i	0.830513	−	0.556999i	$-0.188047\pi$
$199$	−0.946823	−	1.63995i	−0.0671185	−	0.116253i	−0.897632	+	0.440746i	$0.854714\pi$
$200$	−5.98354	−	10.3638i	−0.423100	−	0.732831i
$201$	11.3667	−	19.6877i	0.801747	−	1.38867i
$202$			8.09492i			0.569556i
$203$	21.2109	+	10.5625i	1.48871	+	0.741342i
$204$		−	11.8123i		−	0.827027i
$205$	−17.5961	−	10.1591i	−1.22897	−	0.709543i
$206$	17.4325	+	30.1939i	1.21458	+	2.10371i
$207$	−10.5332	+	19.8139i	−0.732108	+	1.37716i
$208$	−0.451097	−	0.260441i	−0.0312780	−	0.0180583i
$209$			7.04406i			0.487248i
$210$	33.3636	+	50.3538i	2.30231	+	3.47474i
$211$	14.1714			0.975599			0.487800	−	0.872956i	$-0.337800\pi$
$211$	14.1714			0.975599			0.487800	+	0.872956i	$0.337800\pi$
$212$	15.9929	+	9.23352i	1.09840	+	0.634161i
$213$	−6.89364	+	3.98004i	−0.472344	+	0.272708i
$214$	−12.1953	+	7.04094i	−0.833652	+	0.481309i
$215$	−34.0620	−	19.6657i	−2.32301	−	1.34119i
$216$			5.64703i			0.384232i
$217$	−11.5419	+	0.711564i	−0.783515	+	0.0483041i
$218$		−	1.78132i		−	0.120646i
$219$	13.6419	−	23.6284i	0.921833	−	1.59666i
$220$	15.0014	−	8.66109i	1.01140	−	0.583930i
$221$	−0.294610	+	0.170093i	−0.0198176	+	0.0114417i
$222$	18.7496	−	32.4752i	1.25839	−	2.17959i
$223$		−	25.9587i		−	1.73832i	−0.494528	−	0.869162i	$-0.664659\pi$
$223$		−	25.9587i		−	1.73832i	0.494528	−	0.869162i	$-0.335341\pi$
$224$	−1.27959	−	20.7556i	−0.0854965	−	1.38679i
$225$	−46.1338			−3.07559
$226$	0.542169	+	0.313021i	0.0360645	+	0.0208219i
$227$	−0.107801	−	0.186717i	−0.00715502	−	0.0123929i	0.862426	−	0.506184i	$-0.168944\pi$
$227$	−0.107801	−	0.186717i	−0.00715502	−	0.0123929i	−0.869581	+	0.493791i	$0.835611\pi$
$228$	24.8063	−	14.3219i	1.64284	−	0.948492i
$229$	−0.651636	+	1.12867i	−0.0430613	+	0.0745844i	−0.886753	−	0.462244i	$-0.847044\pi$
$229$	−0.651636	+	1.12867i	−0.0430613	+	0.0745844i	0.843691	+	0.536828i	$0.180378\pi$
$230$	−20.9408	−	33.5063i	−1.38079	−	2.20934i
$231$	−10.6952	+	7.08646i	−0.703691	+	0.466255i
$232$	−10.8701			−0.713658
$233$	1.93886	−	3.35821i	0.127019	−	0.220004i	−0.795501	−	0.605952i	$-0.792792\pi$
$233$	1.93886	−	3.35821i	0.127019	−	0.220004i	0.922520	+	0.385948i	$0.126126\pi$
$234$	1.77481	−	1.02469i	0.116023	−	0.0669858i
$235$	−1.60615	+	0.927310i	−0.104774	+	0.0604911i
$236$	7.60626	+	4.39148i	0.495125	+	0.285861i
$237$	21.2558			1.38071
$238$	−8.40253	−	4.18425i	−0.544655	−	0.271224i
$239$	−11.5086			−0.744427			−0.372214	−	0.928147i	$-0.621401\pi$
$239$	−11.5086			−0.744427			−0.372214	+	0.928147i	$0.621401\pi$
$240$	23.5135	+	13.5755i	1.51779	+	0.876298i
$241$	−0.170470	−	0.295263i	−0.0109810	−	0.0190196i	0.860483	−	0.509480i	$-0.170162\pi$
$241$	−0.170470	−	0.295263i	−0.0109810	−	0.0190196i	−0.871464	+	0.490460i	$0.836829\pi$
$242$	−8.48253	−	14.6922i	−0.545278	−	0.944449i
$243$	−14.8334	−	8.56408i	−0.951564	−	0.549386i
$244$	7.47807			0.478734
$245$	26.7795	−	3.31454i	1.71088	−	0.211758i
$246$	−31.2169			−1.99031
$247$	−0.714405	−	0.412462i	−0.0454565	−	0.0262443i
$248$	4.59413	−	2.65242i	0.291727	−	0.168429i
$249$	1.99735	−	1.15317i	0.126577	−	0.0730792i
$250$	20.0194	−	34.6746i	1.26614	−	2.19302i
$251$	−20.2808			−1.28011			−0.640057	−	0.768327i	$-0.721089\pi$
$251$	−20.2808			−1.28011			−0.640057	+	0.768327i	$0.721089\pi$
$252$	28.4560	+	14.1704i	1.79256	+	0.892649i
$253$	7.11677	−	4.44784i	0.447427	−	0.279633i
$254$	−15.2817	+	26.4686i	−0.958857	+	1.66079i
$255$	15.3566	−	8.86615i	0.961669	−	0.555220i
$256$	−1.75706	−	3.04332i	−0.109816	−	0.190207i
$257$	17.7715	+	10.2604i	1.10856	+	0.640026i	0.938455	−	0.345401i	$-0.112257\pi$
$257$	17.7715	+	10.2604i	1.10856	+	0.640026i	0.170102	+	0.985426i	$0.445590\pi$
$258$	−60.4287			−3.76213
$259$	−9.25270	−	13.9646i	−0.574935	−	0.867716i
$260$			2.02858i			0.125807i
$261$	−20.9525	+	36.2908i	−1.29693	+	2.24634i
$262$	3.16583	−	1.82779i	0.195585	−	0.112921i
$263$	6.29979	−	3.63718i	0.388461	−	0.224278i	−0.293032	−	0.956103i	$-0.594664\pi$
$263$	6.29979	−	3.63718i	0.388461	−	0.224278i	0.681493	+	0.731824i	$0.261331\pi$
$264$	2.94281	−	5.09710i	0.181118	−	0.313705i
$265$			27.7222i			1.70296i
$266$	−1.40063	−	22.7188i	−0.0858779	−	1.39298i
$267$			7.07589i			0.433038i
$268$	18.2440	+	10.5332i	1.11443	+	0.643416i
$269$	13.9099	−	8.03088i	0.848101	−	0.489651i	−0.0119088	−	0.999929i	$-0.503791\pi$
$269$	13.9099	−	8.03088i	0.848101	−	0.489651i	0.860010	+	0.510278i	$0.170457\pi$
$270$	−33.1967	+	19.1661i	−2.02029	+	1.16641i
$271$	8.48238	+	4.89730i	0.515268	+	0.297490i	0.734996	−	0.678071i	$-0.237184\pi$
$271$	8.48238	+	4.89730i	0.515268	+	0.297490i	−0.219729	+	0.975561i	$0.570517\pi$
$272$	−4.21925			−0.255830
$273$	−0.0924537	−	1.49964i	−0.00559555	−	0.0907625i
$274$			34.5385i			2.08655i
$275$	14.9423	+	8.62696i	0.901056	+	0.520225i
$276$	−30.1332	−	16.0190i	−1.81381	−	0.964232i
$277$	5.37245	+	9.30536i	0.322800	+	0.559105i	0.981065	−	0.193681i	$-0.0620427\pi$
$277$	5.37245	+	9.30536i	0.322800	+	0.559105i	−0.658265	+	0.752786i	$0.728709\pi$
$278$	−6.62737	−	3.82632i	−0.397483	−	0.229487i
$279$		−	20.4505i		−	1.22434i
$280$	−10.3191	+	6.83729i	−0.616685	+	0.408606i
$281$		−	11.1537i		−	0.665376i	−0.943037	−	0.332688i	$-0.892044\pi$
$281$		−	11.1537i		−	0.665376i	0.943037	−	0.332688i	$-0.107956\pi$
$282$	−1.42472	+	2.46768i	−0.0848406	+	0.146948i
$283$	−8.61689	−	14.9249i	−0.512221	−	0.887193i	−0.999900	−	0.0141696i	$-0.995490\pi$
$283$	−8.61689	−	14.9249i	−0.512221	−	0.887193i	0.487679	−	0.873023i	$-0.337844\pi$
$284$	−3.68818	−	6.38811i	−0.218853	−	0.379065i
$285$	37.2385	+	21.4997i	2.20582	+	1.27353i
$286$	−0.766458			−0.0453216
$287$	−6.21631	+	12.4832i	−0.366937	+	0.736858i
$288$	36.7759			2.16704
$289$	7.12221	−	12.3360i	0.418953	−	0.725649i
$290$	−36.8933	−	63.9011i	−2.16645	−	3.75240i
$291$	−39.1346	+	22.5944i	−2.29411	+	1.32451i
$292$	21.8957	+	12.6415i	1.28135	+	0.739788i
$293$	−8.91155			−0.520618			−0.260309	−	0.965525i	$-0.583824\pi$
$293$	−8.91155			−0.520618			−0.260309	+	0.965525i	$0.583824\pi$
$294$	33.0855	−	24.9822i	1.92959	−	1.45699i
$295$			13.1847i			0.767644i
$296$	6.65522	+	3.84239i	0.386827	+	0.223335i
$297$	−4.07089	−	7.05100i	−0.236217	−	0.409140i
$298$	24.1022	−	13.9154i	1.39620	−	0.806097i
$299$	0.0343782	+	0.982220i	0.00198814	+	0.0568032i
$300$		−	70.1610i		−	4.05075i
$301$	−12.0333	+	24.1646i	−0.693590	+	1.39282i
$302$	−16.3863			−0.942923
$303$	−5.24779	+	9.08944i	−0.301478	+	0.522175i
$304$	−5.11566	−	8.86059i	−0.293403	−	0.508190i
$305$	5.61293	+	9.72188i	0.321396	+	0.556673i
$306$	8.30016	−	14.3763i	0.474489	−	0.821838i
$307$			17.5645i			1.00246i	0.865314	+	0.501230i	$0.167119\pi$
$307$			17.5645i			1.00246i	−0.865314	+	0.501230i	$0.832881\pi$
$308$	−6.56679	−	9.91087i	−0.374178	−	0.564724i
$309$			45.2046i			2.57160i
$310$	31.1851	+	18.0047i	1.77119	+	1.02260i
$311$	2.32221	−	1.34073i	0.131681	−	0.0760259i	−0.432713	−	0.901532i	$-0.642443\pi$
$311$	2.32221	−	1.34073i	0.131681	−	0.0760259i	0.564393	+	0.825506i	$0.309110\pi$
$312$	0.344630	+	0.596917i	0.0195108	+	0.0337938i
$313$	−3.71224	+	6.42979i	−0.209828	+	0.363433i	−0.951660	−	0.307152i	$-0.900624\pi$
$313$	−3.71224	+	6.42979i	−0.209828	+	0.363433i	0.741832	+	0.670586i	$0.233957\pi$
$314$	30.7744			1.73670
$315$	2.93643	+	47.6303i	0.165449	+	2.68367i
$316$			19.6971i			1.10805i
$317$	−0.398442	+	0.690122i	−0.0223787	+	0.0387611i	−0.876998	−	0.480494i	$-0.840457\pi$
$317$	−0.398442	+	0.690122i	−0.0223787	+	0.0387611i	0.854619	+	0.519255i	$0.173791\pi$
$318$	21.2961	+	36.8860i	1.19423	+	2.06846i
$319$	13.5726	−	7.83617i	0.759922	−	0.438741i
$320$	−22.5797	+	39.1091i	−1.26224	+	2.18627i
$321$	−18.2581			−1.01907
$322$	−22.0689	+	15.7605i	−1.22985	+	0.878296i
$323$	−6.68205			−0.371799
$324$	1.46887	−	2.54415i	0.0816038	−	0.141342i
$325$	−1.74988	+	1.01029i	−0.0970660	+	0.0560411i
$326$	0.352491	+	0.610532i	0.0195227	+	0.0338143i
$327$	1.15480	−	2.00017i	0.0638606	−	0.110610i
$328$		−	6.39735i		−	0.353234i
$329$	0.703082	+	1.06112i	0.0387622	+	0.0585015i
$330$	39.9518			2.19927
$331$	−5.96961	+	10.3397i	−0.328119	+	0.568319i	−0.982139	−	0.188159i	$-0.939748\pi$
$331$	−5.96961	+	10.3397i	−0.328119	+	0.568319i	0.654019	+	0.756478i	$0.273081\pi$
$332$	1.06861	+	1.85088i	0.0586474	+	0.101580i
$333$	25.6563	−	14.8127i	1.40596	−	0.811730i
$334$	19.1264	+	11.0427i	1.04655	+	0.604227i
$335$			31.6242i			1.72781i
$336$	8.30680	−	16.6812i	0.453173	−	0.910032i
$337$		−	17.0561i		−	0.929104i	−0.885546	−	0.464552i	$-0.846215\pi$
$337$		−	17.0561i		−	0.929104i	0.885546	−	0.464552i	$-0.153785\pi$
$338$	−13.8473	+	23.9843i	−0.753195	+	1.30457i
$339$	0.405853	+	0.702957i	0.0220429	+	0.0381794i
$340$	8.21597	+	14.2305i	0.445574	+	0.771756i
$341$	−3.82421	+	6.62373i	−0.207093	+	0.358695i
$342$	40.2544			2.17671
$343$	−3.40160	−	18.2052i	−0.183669	−	0.982988i
$344$		−	12.3838i		−	0.667689i
$345$	−1.79197	−	51.1984i	−0.0964764	−	2.75643i
$346$	13.1385	−	7.58551i	0.706330	−	0.407800i
$347$	−3.29852	−	5.71320i	−0.177074	−	0.306701i	0.763803	−	0.645449i	$-0.223330\pi$
$347$	−3.29852	−	5.71320i	−0.177074	−	0.306701i	−0.940877	+	0.338748i	$0.889996\pi$
$348$	−55.1915	−	31.8648i	−2.95858	−	1.70814i
$349$		−	36.4610i		−	1.95171i	−0.218417	−	0.975855i	$-0.570089\pi$
$349$		−	36.4610i		−	1.95171i	0.218417	−	0.975855i	$-0.429911\pi$
$350$	−49.9081	−	24.8530i	−2.66770	−	1.32845i
$351$	0.953478			0.0508929
$352$	−11.9114	−	6.87703i	−0.634878	−	0.366547i
$353$	8.67372	−	5.00778i	0.461656	−	0.266537i	−0.251084	−	0.967965i	$-0.580787\pi$
$353$	8.67372	−	5.00778i	0.461656	−	0.266537i	0.712740	+	0.701428i	$0.247454\pi$
$354$	10.1285	+	17.5430i	0.538323	+	0.932402i
$355$	5.53659	−	9.58965i	0.293852	−	0.508966i
$356$	−6.55700			−0.347520
$357$	−6.72227	−	10.1455i	−0.355780	−	0.536958i
$358$	−41.9424			−2.21672
$359$	−3.27783	−	1.89246i	−0.172997	−	0.0998801i	0.411001	−	0.911635i	$-0.365179\pi$
$359$	−3.27783	−	1.89246i	−0.172997	−	0.0998801i	−0.583998	+	0.811755i	$0.698513\pi$
$360$	−10.9458	−	18.9587i	−0.576896	−	0.999213i
$361$	1.39830	+	2.42193i	0.0735947	+	0.127470i
$362$	5.88923	−	10.2004i	0.309531	−	0.536123i
$363$		−	21.9963i		−	1.15451i
$364$	1.38967	−	0.0856739i	0.0728385	−	0.00449053i
$365$			37.9541i			1.98661i
$366$	14.9367	+	8.62369i	0.780752	+	0.450768i
$367$	−4.53149	−	7.84876i	−0.236542	−	0.409702i	0.723178	−	0.690662i	$-0.242681\pi$
$367$	−4.53149	−	7.84876i	−0.236542	−	0.409702i	−0.959720	+	0.280960i	$0.909347\pi$
$368$	−5.72186	+	10.7633i	−0.298273	+	0.561077i
$369$	−21.3581	−	12.3311i	−1.11186	−	0.641931i
$370$			52.1646i			2.71191i
$371$	18.9909	−	1.17080i	0.985960	−	0.0607849i
$372$	31.1014			1.61253
$373$	−19.1866	−	11.0774i	−0.993446	−	0.573566i	−0.0871431	−	0.996196i	$-0.527774\pi$
$373$	−19.1866	−	11.0774i	−0.993446	−	0.573566i	−0.906302	+	0.422630i	$0.861107\pi$
$374$	−5.37669	+	3.10423i	−0.278022	+	0.160516i
$375$	44.9579	−	25.9565i	2.32162	−	1.34039i
$376$	−0.505708	−	0.291971i	−0.0260799	−	0.0150572i
$377$			1.83537i			0.0945265i
$378$	14.5316	+	21.9318i	0.747427	+	1.12805i
$379$			20.0332i			1.02904i	0.857479	+	0.514519i	$0.172029\pi$
$379$			20.0332i			1.02904i	−0.857479	+	0.514519i	$0.827971\pi$
$380$	−19.9230	+	34.5077i	−1.02203	+	1.77021i
$381$	−34.3183	+	19.8137i	−1.75818	+	1.01509i
$382$	−39.6482	+	22.8909i	−2.02858	+	1.17120i
$383$	−8.45906	+	14.6515i	−0.432238	+	0.748658i	−0.997066	−	0.0765509i	$-0.975609\pi$
$383$	−8.45906	+	14.6515i	−0.432238	+	0.748658i	0.564828	+	0.825209i	$0.308943\pi$
$384$			25.8222i			1.31773i
$385$	7.95571	−	15.9761i	0.405461	−	0.814219i
$386$	11.6538			0.593161
$387$	−41.3443	−	23.8702i	−2.10165	−	1.21339i
$388$	−20.9375	−	36.2648i	−1.06294	−	1.84107i
$389$	22.8244	−	13.1777i	1.15724	−	0.668136i	0.206603	−	0.978425i	$-0.433759\pi$
$389$	22.8244	−	13.1777i	1.15724	−	0.668136i	0.950642	+	0.310289i	$0.100426\pi$
$390$	−2.33936	+	4.05189i	−0.118458	+	0.205175i
$391$	4.21925	+	6.75102i	0.213377	+	0.341414i
$392$	5.11966	+	6.78030i	0.258582	+	0.342457i
$393$	4.73970			0.239086
$394$	7.24943	−	12.5564i	0.365221	−	0.632582i
$395$	−25.6072	+	14.7844i	−1.28844	+	0.743881i
$396$	18.2087	−	10.5128i	0.915021	−	0.528288i
$397$	−13.6338	−	7.87148i	−0.684261	−	0.395058i	0.117197	−	0.993109i	$-0.462609\pi$
$397$	−13.6338	−	7.87148i	−0.684261	−	0.395058i	−0.801459	+	0.598050i	$0.795942\pi$
$398$	4.04722			0.202869
$399$	13.1555	−	26.4180i	0.658600	−	1.32256i
$400$	−25.0609			−1.25304
$401$	−33.1621	−	19.1461i	−1.65603	−	0.956112i	−0.974518	−	0.224309i	$-0.927987\pi$
$401$	−33.1621	−	19.1461i	−1.65603	−	0.956112i	−0.681516	−	0.731803i	$-0.738679\pi$
$402$	24.2937	+	42.0778i	1.21166	+	2.09865i
$403$	−0.447850	−	0.775699i	−0.0223090	−	0.0386403i
$404$	−8.42290	−	4.86296i	−0.419055	−	0.241941i
$405$	4.41005			0.219137
$406$	−42.2170	+	27.9723i	−2.09519	+	1.38824i
$407$	−11.0798			−0.549205
$408$	4.83515	+	2.79157i	0.239375	+	0.138204i
$409$	−7.35607	+	4.24703i	−0.363734	+	0.210002i	−0.670718	−	0.741713i	$-0.734014\pi$
$409$	−7.35607	+	4.24703i	−0.363734	+	0.210002i	0.306983	+	0.951715i	$0.400680\pi$
$410$	37.6075	−	21.7127i	1.85730	−	1.07231i
$411$	−22.3907	+	38.7818i	−1.10445	+	1.91297i
$412$	−41.8897			−2.06376
$413$	9.03212	−	0.556834i	0.444442	−	0.0274000i
$414$	−25.4178	−	40.6698i	−1.24922	−	1.99881i
$415$	−1.60416	+	2.77849i	−0.0787452	+	0.136391i
$416$	1.39493	−	0.805363i	0.0683920	−	0.0394861i
$417$	−4.96107	−	8.59282i	−0.242944	−	0.420792i
$418$	−13.0380	−	7.52750i	−0.637710	−	0.368182i
$419$	−9.67094			−0.472456			−0.236228	−	0.971698i	$-0.575911\pi$
$419$	−9.67094			−0.472456			−0.236228	+	0.971698i	$0.575911\pi$
$420$	−72.4369	+	4.46577i	−3.53456	+	0.217907i
$421$			19.7189i			0.961042i	0.876983	+	0.480521i	$0.159553\pi$
$421$			19.7189i			0.961042i	−0.876983	+	0.480521i	$0.840447\pi$
$422$	−15.1440	+	26.2302i	−0.737198	+	1.27686i
$423$	−1.94954	+	1.12557i	−0.0947897	+	0.0547269i
$424$	−7.55914	+	4.36427i	−0.367104	+	0.211948i
$425$	−8.18360	+	14.1744i	−0.396963	+	0.687560i
$426$		−	17.0128i		−	0.824272i
$427$	6.42287	−	4.25570i	0.310825	−	0.205948i
$428$		−	16.9192i		−	0.817819i
$429$	−0.860624	−	0.496881i	−0.0415513	−	0.0239897i
$430$	72.7994	−	42.0308i	3.51070	−	2.02690i
$431$	14.6709	−	8.47027i	0.706674	−	0.407998i	−0.103154	−	0.994665i	$-0.532894\pi$
$431$	14.6709	−	8.47027i	0.706674	−	0.407998i	0.809828	+	0.586667i	$0.199560\pi$
$432$	10.2414	+	5.91288i	0.492740	+	0.284483i
$433$	32.0100			1.53830			0.769152	−	0.639065i	$-0.220679\pi$
$433$	32.0100			1.53830			0.769152	+	0.639065i	$0.220679\pi$
$434$	11.0170	−	22.1236i	0.528832	−	1.06197i
$435$		−	95.6692i		−	4.58699i
$436$	1.85350	+	1.07012i	0.0887664	+	0.0512493i
$437$	−9.06173	+	17.0459i	−0.433481	+	0.815417i
$438$	29.1563	+	50.5002i	1.39314	+	2.41299i
$439$	−22.8492	−	13.1920i	−1.09053	−	0.629620i	−0.156815	−	0.987628i	$-0.550123\pi$
$439$	−22.8492	−	13.1920i	−1.09053	−	0.629620i	−0.933719	+	0.358008i	$0.883456\pi$
$440$			8.18741i			0.390320i
$441$	32.5049	−	4.02317i	1.54785	−	0.191580i
$442$		−	0.727068i		−	0.0345831i
$443$	0.574139	−	0.994438i	0.0272782	−	0.0472472i	−0.852064	−	0.523438i	$-0.824649\pi$
$443$	0.574139	−	0.994438i	0.0272782	−	0.0472472i	0.879342	+	0.476190i	$0.157983\pi$
$444$	22.5273	+	39.0185i	1.06910	+	1.85173i
$445$	−4.92159	−	8.52445i	−0.233306	−	0.404098i
$446$	48.0476	+	27.7403i	2.27512	+	1.31354i
$447$	36.0844			1.70673
$448$	27.7451	+	13.8164i	1.31083	+	0.652762i
$449$	−20.0207			−0.944838			−0.472419	−	0.881374i	$-0.656619\pi$
$449$	−20.0207			−0.944838			−0.472419	+	0.881374i	$0.656619\pi$
$450$	49.3000	−	85.3902i	2.32403	−	4.02533i
$451$	4.61179	+	7.98786i	0.217161	+	0.376133i
$452$	−0.651408	+	0.376090i	−0.0306396	+	0.0176898i
$453$	−18.3994	−	10.6229i	−0.864482	−	0.499109i
$454$	0.460799			0.0216264
$455$	1.15445	+	1.74234i	0.0541213	+	0.0816821i
$456$			13.5387i			0.634006i
$457$	15.0469	+	8.68734i	0.703865	+	0.406377i	0.808785	−	0.588104i	$-0.200125\pi$
$457$	15.0469	+	8.68734i	0.703865	+	0.406377i	−0.104920	+	0.994481i	$0.533459\pi$
$458$	−1.39272	−	2.41226i	−0.0650774	−	0.112717i
$459$	6.68863	−	3.86168i	0.312199	−	0.180248i
$460$	47.4439	−	1.66056i	2.21208	−	0.0774240i
$461$		−	15.2031i		−	0.708081i	−0.935230	−	0.354040i	$-0.884807\pi$
$461$		−	15.2031i		−	0.708081i	0.935230	−	0.354040i	$-0.115193\pi$
$462$	−1.68730	−	27.3688i	−0.0785001	−	1.27331i
$463$	0.731023			0.0339735			0.0169868	−	0.999856i	$-0.494593\pi$
$463$	0.731023			0.0339735			0.0169868	+	0.999856i	$0.494593\pi$
$464$	−11.3818	+	19.7139i	−0.528389	+	0.915196i
$465$	23.3443	+	40.4335i	1.08256	+	1.87506i
$466$	4.14386	+	7.17737i	0.191961	+	0.332485i
$467$	20.5833	−	35.6513i	0.952481	−	1.64975i	0.212451	−	0.977172i	$-0.431855\pi$
$467$	20.5833	−	35.6513i	0.952481	−	1.64975i	0.740030	−	0.672574i	$-0.234811\pi$
$468$			2.46229i			0.113819i
$469$	21.6640	−	1.33559i	1.00035	−	0.0616720i
$470$		−	3.96381i		−	0.182837i
$471$	34.5552	+	19.9505i	1.59222	+	0.919269i
$472$	−3.59514	+	2.07565i	−0.165480	+	0.0955397i
$473$	8.92737	+	15.4627i	0.410481	+	0.710973i
$474$	−22.7146	+	39.3429i	−1.04332	+	1.80708i
$475$	−39.6890			−1.82106
$476$	9.40153	−	6.22931i	0.430919	−	0.285520i
$477$			33.6491i			1.54069i
$478$	12.2984	−	21.3015i	0.562516	−	0.974306i
$479$	−9.59591	−	16.6206i	−0.438448	−	0.759415i	0.559122	−	0.829086i	$-0.311138\pi$
$479$	−9.59591	−	16.6206i	−0.438448	−	0.759415i	−0.997570	+	0.0696707i	$0.977805\pi$
$480$	−72.7109	+	41.9797i	−3.31879	+	1.91610i
$481$	0.648772	−	1.12371i	0.0295815	−	0.0512366i
$482$	0.728679			0.0331904
$483$	−34.9975	+	3.38986i	−1.59244	+	0.154244i
$484$	20.3833			0.926512
$485$	31.4308	−	54.4397i	1.42720	−	2.47198i
$486$	31.7029	−	18.3037i	1.43807	−	0.830271i
$487$	−1.56672	−	2.71364i	−0.0709948	−	0.122967i	0.828343	−	0.560222i	$-0.189284\pi$
$487$	−1.56672	−	2.71364i	−0.0709948	−	0.122967i	−0.899338	+	0.437255i	$0.855951\pi$
$488$	−1.76727	+	3.06101i	−0.0800007	+	0.138565i
$489$			0.914055i			0.0413350i
$490$	−22.4825	+	53.1089i	−1.01565	+	2.39921i
$491$	35.3438			1.59504			0.797522	−	0.603290i	$-0.206144\pi$
$491$	35.3438			1.59504			0.797522	+	0.603290i	$0.206144\pi$
$492$	18.7533	−	32.4817i	0.845464	−	1.46439i
$493$	7.43345	+	12.8751i	0.334786	+	0.579866i
$494$	1.52687	−	0.881539i	0.0686971	−	0.0396623i
$495$	27.3344	+	15.7815i	1.22859	+	0.709326i
$496$		−	11.1092i		−	0.498816i
$497$	−6.80317	−	3.38781i	−0.305164	−	0.151964i
$498$			4.92926i			0.220885i
$499$	−8.70475	+	15.0771i	−0.389678	+	0.674942i	−0.992406	−	0.123005i	$-0.960747\pi$
$499$	−8.70475	+	15.0771i	−0.389678	+	0.674942i	0.602728	+	0.797947i	$0.294080\pi$
$500$	24.0530	+	41.6611i	1.07568	+	1.86314i
$501$	14.3175	+	24.7987i	0.639660	+	1.10792i
$502$	21.6727	−	37.5382i	0.967300	−	1.67541i
$503$	8.82795			0.393619			0.196809	−	0.980442i	$-0.436942\pi$
$503$	8.82795			0.393619			0.196809	+	0.980442i	$0.436942\pi$
$504$	−12.5253	+	8.29907i	−0.557921	+	0.369670i
$505$		−	14.6003i		−	0.649704i
$506$	0.627408	+	17.9257i	0.0278917	+	0.796894i
$507$	−31.0972	+	17.9540i	−1.38107	+	0.797363i
$508$	−18.3607	−	31.8017i	−0.814624	−	1.41097i
$509$	15.3321	+	8.85200i	0.679584	+	0.392358i	0.799698	−	0.600402i	$-0.204993\pi$
$509$	15.3321	+	8.85200i	0.679584	+	0.392358i	−0.120114	+	0.992760i	$0.538326\pi$
$510$			37.8986i			1.67818i
$511$	26.0003	−	1.60293i	1.15018	−	0.0709094i
$512$	26.1474			1.15556
$513$	16.2194	+	9.36425i	0.716102	+	0.413442i
$514$	−37.9824	+	21.9291i	−1.67533	+	0.967253i
$515$	−31.4418	−	54.4588i	−1.38549	−	2.39974i
$516$	36.3021	−	62.8770i	1.59811	−	2.76801i
$517$	0.841916			0.0370274
$518$	35.7351	−	2.20308i	1.57011	−	0.0967979i
$519$	19.6702			0.863427
$520$	−0.830363	−	0.479410i	−0.0364138	−	0.0210235i
$521$	3.42606	+	5.93411i	0.150098	+	0.259978i	0.931263	−	0.364346i	$-0.118708\pi$
$521$	3.42606	+	5.93411i	0.150098	+	0.259978i	−0.781165	+	0.624325i	$0.785374\pi$
$522$	−44.7810	−	77.5629i	−1.96001	−	3.39484i
$523$	−9.90492	+	17.1558i	−0.433112	+	0.750172i	−0.997139	−	0.0755843i	$-0.975918\pi$
$523$	−9.90492	+	17.1558i	−0.433112	+	0.750172i	0.564028	+	0.825756i	$0.309251\pi$
$524$			4.39213i			0.191871i
$525$	−39.9279	−	60.2609i	−1.74260	−	2.63000i
$526$			15.5472i			0.677891i
$527$	−6.28332	−	3.62768i	−0.273706	−	0.158024i
$528$	−6.16270	−	10.6741i	−0.268197	−	0.464531i
$529$	22.9437	−	1.60805i	0.997553	−	0.0699153i
$530$	−51.3116	−	29.6248i	−2.22883	−	1.28682i
$531$			16.0036i			0.694495i
$532$	24.4807	+	12.1908i	1.06137	+	0.528538i
$533$	−1.08017			−0.0467872
$534$	−13.0969	−	7.56152i	−0.566760	−	0.327219i
$535$	21.9958	−	12.6993i	0.950962	−	0.549038i
$536$	−8.62311	+	4.97856i	−0.372462	+	0.215041i
$537$	−47.0953	−	27.1905i	−2.03231	−	1.17336i
$538$			34.3282i			1.47999i
$539$	−11.2804	−	4.77529i	−0.485880	−	0.205687i
$540$		−	46.0556i		−	1.98192i
$541$	5.21528	−	9.03313i	0.224222	−	0.388365i	−0.731863	−	0.681451i	$-0.761349\pi$
$541$	5.21528	−	9.03313i	0.224222	−	0.388365i	0.956086	+	0.293087i	$0.0946825\pi$
$542$	−18.1291	+	10.4668i	−0.778710	+	0.449588i
$543$	13.2255	−	7.63576i	0.567562	−	0.327682i
$544$	6.52360	−	11.2992i	0.279697	−	0.484450i
$545$			3.21286i			0.137624i
$546$	2.87452	+	1.43144i	0.123018	+	0.0612600i
$547$	−28.3266			−1.21116			−0.605580	−	0.795785i	$-0.707059\pi$
$547$	−28.3266			−1.21116			−0.605580	+	0.795785i	$0.707059\pi$
$548$	−35.9379	−	20.7487i	−1.53519	−	0.886342i
$549$	6.81296	+	11.8004i	0.290770	+	0.503628i
$550$	−31.9357	+	18.4381i	−1.36174	+	0.786202i
$551$	−18.0255	+	31.2210i	−0.767911	+	1.33006i
$552$	13.6784	−	8.54873i	0.582191	−	0.363858i
$553$	11.2094	+	16.9177i	0.476673	+	0.719415i
$554$	−22.9647			−0.975676
$555$	−33.8174	+	58.5734i	−1.43547	+	2.48630i
$556$	7.96269	−	4.59726i	0.337693	−	0.194967i
$557$	−21.6038	+	12.4730i	−0.915384	+	0.528497i	−0.882159	−	0.470951i	$-0.843911\pi$
$557$	−21.6038	+	12.4730i	−0.915384	+	0.528497i	−0.0332242	+	0.999448i	$0.510578\pi$
$558$	37.8523	+	21.8540i	1.60242	+	0.925156i
$559$	−2.09095			−0.0884378
$560$	1.59513	+	25.8738i	0.0674067	+	1.09337i
$561$	−8.04968			−0.339858
$562$	20.6447	+	11.9192i	0.870844	+	0.502782i
$563$	−9.04897	−	15.6733i	−0.381368	−	0.660550i	0.609890	−	0.792486i	$-0.291214\pi$
$563$	−9.04897	−	15.6733i	−0.381368	−	0.660550i	−0.991258	+	0.131937i	$0.957880\pi$
$564$	−1.71178	−	2.96488i	−0.0720788	−	0.124844i
$565$	−0.977875	−	0.564576i	−0.0411395	−	0.0237519i
$566$	36.8331			1.54821
$567$	−0.186251	−	3.02108i	−0.00782180	−	0.126873i
$568$	3.48647			0.146289
$569$	12.2131	+	7.05123i	0.511999	+	0.295603i	0.733655	−	0.679522i	$-0.237813\pi$
$569$	12.2131	+	7.05123i	0.511999	+	0.295603i	−0.221656	+	0.975125i	$0.571146\pi$
$570$	−79.5884	+	45.9504i	−3.33359	+	1.92465i
$571$	−28.6167	+	16.5218i	−1.19757	+	0.691418i	−0.960013	−	0.279956i	$-0.909680\pi$
$571$	−28.6167	+	16.5218i	−1.19757	+	0.691418i	−0.237558	+	0.971373i	$0.576347\pi$
$572$	0.460444	−	0.797512i	0.0192521	−	0.0333457i
$573$	−59.3591			−2.47976
$574$	−16.4625	−	24.8458i	−0.687130	−	1.03704i
$575$	25.0609	+	40.0987i	1.04511	+	1.67223i
$576$	−27.4071	+	47.4705i	−1.14196	+	1.97794i
$577$	−8.24985	+	4.76305i	−0.343446	+	0.198288i	−0.661795	−	0.749685i	$-0.730205\pi$
$577$	−8.24985	+	4.76305i	−0.343446	+	0.198288i	0.318349	+	0.947974i	$0.396872\pi$
$578$	15.2220	+	26.3653i	0.633153	+	1.09665i
$579$	13.0855	+	7.55493i	0.543816	+	0.313972i
$580$	88.6535			3.68114
$581$	1.97114	+	0.981577i	0.0817766	+	0.0407227i
$582$		−	96.5802i		−	4.00338i
$583$	6.29233	−	10.8986i	0.260601	−	0.451375i
$584$	−10.3491	+	5.97507i	−0.428250	+	0.247250i
$585$	−3.20110	+	1.84816i	−0.132349	+	0.0764119i
$586$	9.52316	−	16.4946i	0.393398	−	0.681385i
$587$		−	32.6248i		−	1.34657i	−0.739383	−	0.673285i	$-0.764883\pi$
$587$		−	32.6248i		−	1.34657i	0.739383	−	0.673285i	$-0.235117\pi$
$588$	6.11850	+	49.4339i	0.252323	+	2.03862i
$589$		−	17.5936i		−	0.724932i
$590$	−24.4039	−	14.0896i	−1.00469	−	0.580059i
$591$	16.2802	−	9.39936i	0.669677	−	0.386638i
$592$	13.9371	−	8.04656i	0.572809	−	0.330712i
$593$	38.1901	+	22.0491i	1.56828	+	0.905447i	0.996370	+	0.0851318i	$0.0271311\pi$
$593$	38.1901	+	22.0491i	1.56828	+	0.905447i	0.571911	+	0.820316i	$0.306202\pi$
$594$	17.4011			0.713977
$595$	15.1551	+	7.54685i	0.621298	+	0.309391i
$596$			33.4383i			1.36968i
$597$	4.54445	+	2.62374i	0.185992	+	0.107383i
$598$	−1.85475	−	0.985999i	−0.0758464	−	0.0403205i
$599$	−16.9745	−	29.4008i	−0.693561	−	1.20128i	−0.970663	−	0.240443i	$-0.922707\pi$
$599$	−16.9745	−	29.4008i	−0.693561	−	1.20128i	0.277102	−	0.960841i	$-0.410626\pi$
$600$	28.7191	+	16.5810i	1.17245	+	0.676915i
$601$			36.3934i			1.48452i	0.670112	+	0.742260i	$0.266246\pi$
$601$			36.3934i			1.48452i	−0.670112	+	0.742260i	$0.733754\pi$
$602$	−31.8675	−	48.0958i	−1.29882	−	1.96024i
$603$			38.3853i			1.56317i
$604$	9.84392	−	17.0502i	0.400544	−	0.693762i
$605$	15.2994	+	26.4993i	0.622008	+	1.07735i
$606$	−11.2159	−	19.4265i	−0.455615	−	0.789149i
$607$	38.8257	+	22.4160i	1.57589	+	0.909839i	0.995424	+	0.0955520i	$0.0304616\pi$
$607$	38.8257	+	22.4160i	1.57589	+	0.909839i	0.580463	+	0.814287i	$0.302872\pi$
$608$	31.6384			1.28310
$609$	−65.5377	+	4.04043i	−2.65572	+	0.163726i
$610$	−23.9926			−0.971432
$611$	−0.0492980	+	0.0853867i	−0.00199438	+	0.00345437i
$612$	9.97252	+	17.2729i	0.403115	+	0.698216i
$613$	−6.87254	+	3.96787i	−0.277579	+	0.160261i	−0.632327	−	0.774702i	$-0.717900\pi$
$613$	−6.87254	+	3.96787i	−0.277579	+	0.160261i	0.354748	+	0.934962i	$0.384567\pi$
$614$	−32.5106	−	18.7700i	−1.31202	−	0.757496i
$615$	56.3038			2.27039
$616$	5.60874	−	0.345782i	0.225983	−	0.0139319i
$617$		−	17.5849i		−	0.707940i	−0.935257	−	0.353970i	$-0.884831\pi$
$617$		−	17.5849i		−	0.707940i	0.935257	−	0.353970i	$-0.115169\pi$
$618$	−83.6703	−	48.3071i	−3.36571	−	1.94320i
$619$	17.9338	+	31.0622i	0.720820	+	1.24850i	0.960672	+	0.277687i	$0.0895677\pi$
$619$	17.9338	+	31.0622i	0.720820	+	1.24850i	−0.239852	+	0.970809i	$0.577099\pi$
$620$	−37.4684	+	21.6324i	−1.50477	+	0.868778i
$621$	−0.780498	−	22.2996i	−0.0313203	−	0.894854i
$622$			5.73099i			0.229792i
$623$	−5.63177	+	3.73153i	−0.225632	+	0.149500i
$624$	1.44342			0.0577829
$625$	−11.4582	+	19.8462i	−0.458329	+	0.793850i
$626$	−7.93404	−	13.7422i	−0.317108	−	0.549247i
$627$	−9.75989	−	16.9046i	−0.389773	−	0.675106i
$628$	−18.4875	+	32.0212i	−0.737730	+	1.27779i
$629$		−	10.5104i		−	0.419076i
$630$	−91.2980	−	45.4641i	−3.63740	−	1.81133i
$631$		−	44.9970i		−	1.79130i	−0.444755	−	0.895652i	$-0.646709\pi$
$631$		−	44.9970i		−	1.79130i	0.444755	−	0.895652i	$-0.353291\pi$
$632$	−8.06263	−	4.65496i	−0.320714	−	0.185165i
$633$	−34.0091	+	19.6352i	−1.35174	+	0.780428i
$634$	−0.851575	−	1.47497i	−0.0338204	−	0.0585786i
$635$	27.5625	−	47.7397i	1.09379	−	1.89449i
$636$	−51.1740			−2.02918
$637$	1.14482	−	0.864433i	0.0453596	−	0.0342501i
$638$			33.4959i			1.32611i
$639$	6.72029	−	11.6399i	0.265850	−	0.460467i
$640$	−17.9604	−	31.1084i	−0.709948	−	1.22967i
$641$	−30.2125	+	17.4432i	−1.19332	+	0.688964i	−0.959058	−	0.283209i	$-0.908601\pi$
$641$	−30.2125	+	17.4432i	−1.19332	+	0.688964i	−0.234263	+	0.972173i	$0.575268\pi$
$642$	19.5112	−	33.7943i	0.770044	−	1.33375i
$643$	−1.84376			−0.0727106			−0.0363553	−	0.999339i	$-0.511575\pi$
$643$	−1.84376			−0.0727106			−0.0363553	+	0.999339i	$0.511575\pi$
$644$	−3.14127	−	32.4311i	−0.123783	−	1.27796i
$645$	108.991			4.29153
$646$	7.14065	−	12.3680i	0.280945	−	0.486611i
$647$	19.2967	−	11.1410i	0.758632	−	0.437997i	−0.0701722	−	0.997535i	$-0.522355\pi$
$647$	19.2967	−	11.1410i	0.758632	−	0.437997i	0.828804	+	0.559538i	$0.189022\pi$
$648$	0.694268	+	1.20251i	0.0272734	+	0.0472390i
$649$	2.99264	−	5.18340i	0.117471	−	0.203466i
$650$		−	4.31853i		−	0.169387i
$651$	26.7128	−	17.6995i	1.04696	−	0.693699i
$652$	−0.847026			−0.0331721
$653$	9.39204	−	16.2675i	0.367539	−	0.636596i	−0.621641	−	0.783302i	$-0.713534\pi$
$653$	9.39204	−	16.2675i	0.367539	−	0.636596i	0.989180	+	0.146706i	$0.0468672\pi$
$654$	2.46811	+	4.27490i	0.0965108	+	0.167162i
$655$	−5.71000	+	3.29667i	−0.223108	+	0.128811i
$656$	−11.6022	−	6.69852i	−0.452989	−	0.261533i
$657$			46.0685i			1.79731i
$658$	−2.71539	+	0.167405i	−0.105857	+	0.00652612i
$659$		−	37.4963i		−	1.46065i	−0.683100	−	0.730325i	$-0.739369\pi$
$659$		−	37.4963i		−	1.46065i	0.683100	−	0.730325i	$-0.260631\pi$
$660$	−24.0007	+	41.5705i	−0.934227	+	1.61813i
$661$	−16.1735	−	28.0133i	−0.629076	−	1.08959i	−0.987737	−	0.156124i	$-0.950100\pi$
$661$	−16.1735	−	28.0133i	−0.629076	−	1.08959i	0.358661	−	0.933468i	$-0.383233\pi$
$662$	−12.7586	−	22.0986i	−0.495877	−	0.858885i
$663$	0.471346	−	0.816394i	0.0183055	−	0.0317061i
$664$	−1.01016			−0.0392020
$665$	2.52622	+	40.9765i	0.0979626	+	1.58900i
$666$			63.3171i			2.45349i
$667$	42.9251	−	1.50240i	1.66207	−	0.0581732i
$668$	−22.9801	+	13.2676i	−0.889128	+	0.513338i
$669$	35.9671	+	62.2968i	1.39057	+	2.40853i
$670$	−58.5339	−	33.7946i	−2.26136	−	1.30560i
$671$		−	5.09605i		−	0.196731i
$672$	31.8288	+	48.0373i	1.22782	+	1.85308i
$673$	−35.4082			−1.36489			−0.682443	−	0.730939i	$-0.739082\pi$
$673$	−35.4082			−1.36489			−0.682443	+	0.730939i	$0.739082\pi$
$674$	31.5695	+	18.2267i	1.21601	+	0.702064i
$675$	39.7281	−	22.9370i	1.52914	−	0.882847i
$676$	−16.6373	−	28.8167i	−0.639898	−	1.10834i
$677$	−21.7250	+	37.6288i	−0.834960	+	1.44619i	0.0591026	+	0.998252i	$0.481176\pi$
$677$	−21.7250	+	37.6288i	−0.834960	+	1.44619i	−0.894063	+	0.447942i	$0.852157\pi$
$678$	−1.73483			−0.0666256
$679$	−38.6210	−	19.2323i	−1.48214	−	0.738068i
$680$	−7.76664			−0.297837
$681$	0.517412	+	0.298728i	0.0198273	+	0.0114473i
$682$	−8.17334	−	14.1566i	−0.312974	−	0.542086i
$683$	16.4252	+	28.4493i	0.628494	+	1.08858i	0.987854	+	0.155384i	$0.0496616\pi$
$683$	16.4252	+	28.4493i	0.628494	+	1.08858i	−0.359360	+	0.933199i	$0.617005\pi$
$684$	−24.1825	+	41.8853i	−0.924641	+	1.60153i
$685$		−	62.2948i		−	2.38016i
$686$	37.3315	+	13.1585i	1.42532	+	0.502395i
$687$		−	3.61149i		−	0.137787i
$688$	−22.4591	−	12.9668i	−0.856246	−	0.494354i
$689$	0.736889	+	1.27633i	0.0280732	+	0.0486242i
$690$	96.6792	+	51.3954i	3.68052	+	1.95659i
$691$	−3.00191	−	1.73316i	−0.114198	−	0.0659323i	0.441813	−	0.897107i	$-0.354335\pi$
$691$	−3.00191	−	1.73316i	−0.114198	−	0.0659323i	−0.556011	+	0.831175i	$0.687669\pi$
$692$			18.2278i			0.692915i
$693$	9.65661	−	19.3918i	0.366824	−	0.736632i
$694$	14.0996			0.535213
$695$	11.9534	+	6.90128i	0.453417	+	0.261780i
$696$	26.0866	−	15.0611i	0.988808	−	0.570889i
$697$	−7.57734	+	4.37478i	−0.287012	+	0.165707i
$698$	67.4864	+	38.9633i	2.55440	+	1.47478i
$699$			10.7456i			0.406435i
$700$	55.8418	−	36.9999i	2.11062	−	1.39847i
$701$		−	36.7209i		−	1.38693i	−0.720491	−	0.693464i	$-0.756083\pi$
$701$		−	36.7209i		−	1.38693i	0.720491	−	0.693464i	$-0.243917\pi$
$702$	−1.01892	+	1.76481i	−0.0384565	+	0.0666086i
$703$	22.0722	−	12.7434i	0.832468	−	0.480626i
$704$	17.7538	−	10.2502i	0.669122	−	0.386318i
$705$	2.56967	−	4.45080i	0.0967793	−	0.167627i
$706$			21.4059i			0.805620i
$707$	−10.0018	+	0.616618i	−0.376158	+	0.0231903i
$708$	−24.3384			−0.914694
$709$	12.5304	+	7.23444i	0.470590	+	0.271695i	0.716486	−	0.697601i	$-0.245749\pi$
$709$	12.5304	+	7.23444i	0.470590	+	0.271695i	−0.245897	+	0.969296i	$0.579082\pi$
$710$	11.8331	+	20.4956i	0.444090	+	0.769186i
$711$	−31.0820	+	17.9452i	−1.16567	+	0.672997i
$712$	1.54960	−	2.68399i	0.0580737	−	0.100587i
$713$	−17.7752	+	11.1092i	−0.665687	+	0.416041i
$714$	25.9622	−	1.60058i	0.971611	−	0.0599003i
$715$	1.38241			0.0516992
$716$	25.1966	−	43.6417i	0.941640	−	1.63097i
$717$	27.6187	−	15.9457i	1.03144	−	0.595502i
$718$	7.00559	−	4.04468i	0.261446	−	0.150946i
$719$	21.2999	+	12.2975i	0.794354	+	0.458620i	0.841493	−	0.540268i	$-0.181677\pi$
$719$	21.2999	+	12.2975i	0.794354	+	0.458620i	−0.0471393	+	0.998888i	$0.515010\pi$
$720$	−45.8445			−1.70852
$721$	−35.9788	+	23.8390i	−1.33992	+	0.887811i
$722$	−5.97706			−0.222443
$723$	0.818204	+	0.472390i	0.0304293	+	0.0175684i
$724$	7.07582	+	12.2557i	0.262971	+	0.455478i
$725$	44.1521	+	76.4737i	1.63977	+	2.84016i
$726$	40.7135	+	23.5059i	1.51102	+	0.872387i
$727$	−25.3332			−0.939557			−0.469779	−	0.882784i	$-0.655666\pi$
$727$	−25.3332			−0.939557			−0.469779	+	0.882784i	$0.655666\pi$
$728$	−0.293349	+	0.589083i	−0.0108722	+	0.0218329i
$729$	44.0317			1.63080
$730$	−70.2501	−	40.5589i	−2.60007	−	1.50115i
$731$	−14.6680	+	8.46857i	−0.542515	+	0.313221i
$732$	−17.9462	+	10.3612i	−0.663310	+	0.382962i
$733$	6.83443	−	11.8376i	0.252436	−	0.437231i	−0.711760	−	0.702422i	$-0.752102\pi$
$733$	6.83443	−	11.8376i	0.252436	−	0.437231i	0.964196	+	0.265191i	$0.0854351\pi$
$734$	19.3699			0.714958
$735$	−59.6742	+	45.0587i	−2.20112	+	1.66202i
$736$	−19.9774	−	31.9649i	−0.736378	−	1.17824i
$737$	7.17799	−	12.4326i	0.264405	−	0.457963i
$738$	45.6478	−	26.3548i	1.68032	−	0.970133i
$739$	7.37651	+	12.7765i	0.271349	+	0.469990i	0.969208	−	0.246245i	$-0.0791969\pi$
$739$	7.37651	+	12.7765i	0.271349	+	0.469990i	−0.697858	+	0.716236i	$0.745864\pi$
$740$	−54.2781	−	31.3375i	−1.99530	−	1.15199i
$741$	2.28594			0.0839763
$742$	−18.1272	+	36.4019i	−0.665472	+	1.33636i
$743$			28.7849i			1.05602i	0.849240	+	0.528008i	$0.177061\pi$
$743$			28.7849i			1.05602i	−0.849240	+	0.528008i	$0.822939\pi$
$744$	−7.35012	+	12.7308i	−0.269469	+	0.466733i
$745$	−43.4715	+	25.0983i	−1.59267	+	0.919529i
$746$	41.0068	−	23.6753i	1.50137	−	0.866814i
$747$	−1.94712	+	3.37252i	−0.0712416	+	0.123394i
$748$		−	7.45938i		−	0.272742i
$749$	−9.62854	−	14.5318i	−0.351819	−	0.530980i
$750$			110.952i			4.05138i
$751$	4.42625	+	2.55549i	0.161516	+	0.0932513i	0.578579	−	0.815626i	$-0.303607\pi$
$751$	4.42625	+	2.55549i	0.161516	+	0.0932513i	−0.417063	+	0.908877i	$0.636941\pi$
$752$	−1.05903	+	0.611431i	−0.0386189	+	0.0222966i
$753$	48.6708	−	28.1001i	1.77366	−	1.02402i
$754$	−3.39713	−	1.96134i	−0.123716	−	0.0714277i
$755$	29.5548			1.07561
$756$	−31.5501	+	1.94508i	−1.14747	+	0.0707419i
$757$			23.5243i			0.855004i	0.904014	+	0.427502i	$0.140606\pi$
$757$			23.5243i			0.855004i	−0.904014	+	0.427502i	$0.859394\pi$
$758$	−37.0800	−	21.4081i	−1.34680	−	0.777578i
$759$	−10.9164	+	20.5347i	−0.396241	+	0.745364i
$760$	−9.41672	−	16.3102i	−0.341580	−	0.591635i
$761$	7.69396	+	4.44211i	0.278906	+	0.161026i	0.632928	−	0.774211i	$-0.281853\pi$
$761$	7.69396	+	4.44211i	0.278906	+	0.161026i	−0.354022	+	0.935237i	$0.615186\pi$
$762$		−	84.6940i		−	3.06814i
$763$	2.20095	−	0.135690i	0.0796798	−	0.00491230i
$764$		−	55.0062i		−	1.99005i
$765$	−14.9705	+	25.9296i	−0.541258	+	0.937486i
$766$	−18.0792	−	31.3141i	−0.653229	−	1.13143i
$767$	0.350465	+	0.607024i	0.0126546	+	0.0219184i
$768$	8.43333	+	4.86899i	0.304312	+	0.175694i
$769$	−5.85712			−0.211213			−0.105607	−	0.994408i	$-0.533678\pi$
$769$	−5.85712			−0.211213			−0.105607	+	0.994408i	$0.533678\pi$
$770$	21.0689	+	31.7980i	0.759269	+	1.14592i
$771$	−56.8651			−2.04795
$772$	−7.00091	+	12.1259i	−0.251968	+	0.436422i
$773$	20.5386	+	35.5739i	0.738721	+	1.27950i	0.953071	+	0.302746i	$0.0979033\pi$
$773$	20.5386	+	35.5739i	0.738721	+	1.27950i	−0.214350	+	0.976757i	$0.568763\pi$
$774$	88.3637	−	51.0168i	3.17617	−	1.83376i
$775$	−37.3207	−	21.5471i	−1.34060	−	0.773996i
$776$	19.7924			0.710506
$777$	41.5536	+	20.6927i	1.49073	+	0.742345i
$778$			56.3284i			2.01947i
$779$	−18.3744	−	10.6085i	−0.658331	−	0.380088i
$780$	−2.81070	−	4.86828i	−0.100639	−	0.174312i
$781$	−4.35328	+	2.51337i	−0.155773	+	0.0899353i
$782$	−17.0044	+	0.595164i	−0.608078	+	0.0212830i
$783$		−	41.6691i		−	1.48913i
$784$	17.6574	−	2.18547i	0.630620	−	0.0780527i
$785$	−55.5057			−1.98108
$786$	−5.06499	+	8.77282i	−0.180662	+	0.312916i
$787$	−14.2477	−	24.6778i	−0.507876	−	0.879667i	−0.999958	−	0.00911848i	$-0.997097\pi$
$787$	−14.2477	−	24.6778i	−0.507876	−	0.879667i	0.492082	−	0.870549i	$-0.336236\pi$
$788$	8.71009	+	15.0863i	0.310284	+	0.537428i
$789$	−10.0790	+	17.4573i	−0.358822	+	0.621497i
$790$		−	63.1961i		−	2.24841i
$791$	−0.345461	+	0.693732i	−0.0122832	+	0.0246663i
$792$			9.93785i			0.353126i
$793$	0.516838	+	0.298397i	0.0183535	+	0.0105964i
$794$	29.1390	−	16.8234i	1.03411	−	0.597041i
$795$	−38.4105	−	66.5289i	−1.36228	−	2.35954i
$796$	−2.43134	+	4.21120i	−0.0861764	+	0.149262i
$797$	35.2018			1.24691			0.623455	−	0.781859i	$-0.285728\pi$
$797$	35.2018			1.24691			0.623455	+	0.781859i	$0.285728\pi$
$798$	34.8394	+	52.5810i	1.23330	+	1.86135i
$799$			0.798648i			0.0282541i
$800$	38.7479	−	67.1134i	1.36995	−	2.37282i
$801$	−5.97381	−	10.3469i	−0.211074	−	0.365591i
$802$	70.8760	−	40.9203i	2.50272	−	1.44495i
$803$	8.61475	−	14.9212i	0.304008	−	0.526557i
$804$	−58.3769			−2.05880
$805$	39.8043	−	28.4261i	1.40292	−	1.00189i
$806$	1.91435			0.0674300
$807$	−22.2544	+	38.5457i	−0.783390	+	1.35687i
$808$	3.98112	−	2.29850i	0.140055	−	0.0808611i
$809$	−8.24264	−	14.2767i	−0.289796	−	0.501941i	0.683965	−	0.729515i	$-0.260254\pi$
$809$	−8.24264	−	14.2767i	−0.289796	−	0.501941i	−0.973761	+	0.227574i	$0.926921\pi$
$810$	−4.71271	+	8.16265i	−0.165588	+	0.286806i
$811$			3.18946i			0.111997i	0.998431	+	0.0559985i	$0.0178342\pi$
$811$			3.18946i			0.111997i	−0.998431	+	0.0559985i	$0.982166\pi$
$812$	−3.74413	−	60.7316i	−0.131393	−	2.13126i
$813$	−27.1418			−0.951905
$814$	11.8402	−	20.5078i	0.414999	−	0.718799i
$815$	−0.635765	−	1.10118i	−0.0222699	−	0.0385726i
$816$	10.1255	−	5.84599i	0.354465	−	0.204650i
$817$	−35.5686	−	20.5356i	−1.24439	−	0.718448i
$818$		−	18.1540i		−	0.634740i
$819$	1.40126	+	2.11484i	0.0489641	+	0.0738987i
$820$			52.1749i			1.82203i
$821$	−0.356735	+	0.617882i	−0.0124501	+	0.0215642i	−0.872183	−	0.489179i	$-0.837296\pi$
$821$	−0.356735	+	0.617882i	−0.0124501	+	0.0215642i	0.859733	+	0.510743i	$0.170630\pi$
$822$	−47.8548	−	82.8869i	−1.66913	−	2.89101i
$823$	−8.49394	−	14.7119i	−0.296080	−	0.512826i	0.679155	−	0.733994i	$-0.262346\pi$
$823$	−8.49394	−	14.7119i	−0.296080	−	0.512826i	−0.975236	+	0.221169i	$0.929013\pi$
$824$	9.89969	−	17.1468i	0.344872	−	0.597336i
$825$	−47.8123			−1.66461
$826$	−8.62135	+	17.3128i	−0.299975	+	0.602390i
$827$			24.4522i			0.850285i	0.905127	+	0.425142i	$0.139776\pi$
$827$			24.4522i			0.850285i	−0.905127	+	0.425142i	$0.860224\pi$
$828$	57.5872	−	2.01558i	2.00129	−	0.0700463i
$829$	−3.16909	+	1.82968i	−0.110067	+	0.0635473i	−0.554023	−	0.832501i	$-0.686908\pi$
$829$	−3.16909	+	1.82968i	−0.110067	+	0.0635473i	0.443956	+	0.896049i	$0.353575\pi$
$830$	−3.42851	−	5.93836i	−0.119005	−	0.206123i
$831$	−25.7861	−	14.8876i	−0.894509	−	0.516445i
$832$			2.40078i			0.0832320i
$833$	4.52988	−	10.7006i	0.156951	−	0.370755i
$834$	21.2062			0.734311
$835$	−34.4971	−	19.9169i	−1.19382	−	0.689254i
$836$	15.6650	−	9.04418i	0.541785	−	0.312799i
$837$	10.1677	+	17.6109i	0.351447	+	0.608723i
$838$	10.3347	−	17.9002i	0.357005	−	0.618351i
$839$	−51.2893			−1.77070			−0.885351	−	0.464923i	$-0.846082\pi$
$839$	−51.2893			−1.77070			−0.885351	+	0.464923i	$0.846082\pi$
$840$	15.2908	−	30.7061i	0.527584	−	1.05946i
$841$	51.2098			1.76586
$842$	−36.4982	−	21.0723i	−1.25781	−	0.726198i
$843$	15.4540	+	26.7672i	0.532265	+	0.921911i
$844$	−18.1953	−	31.5152i	−0.626307	−	1.08480i
$845$	24.9755	−	43.2589i	0.859184	−	1.48815i
$846$		−	4.81126i		−	0.165414i
$847$	17.5071	−	11.5999i	0.601550	−	0.398578i
$848$			18.2789i			0.627700i
$849$	41.3584	+	23.8783i	1.41942	+	0.819500i
$850$	−17.4905	−	30.2944i	−0.599919	−	1.03909i
$851$	−26.8120	−	14.2534i	−0.919102	−	0.488602i
$852$	17.7021	+	10.2203i	0.606464	+	0.350142i
$853$			37.4884i			1.28358i	0.766881	+	0.641790i	$0.221808\pi$
$853$			37.4884i			1.28358i	−0.766881	+	0.641790i	$0.778192\pi$
$854$	1.01329	+	16.4360i	0.0346740	+	0.562429i
$855$	−72.6041			−2.48301
$856$	6.92555	+	3.99847i	0.236710	+	0.136665i
$857$	24.2615	−	14.0074i	0.828756	−	0.478483i	−0.0246704	−	0.999696i	$-0.507854\pi$
$857$	24.2615	−	14.0074i	0.828756	−	0.478483i	0.853427	+	0.521213i	$0.174520\pi$
$858$	1.83938	−	1.06197i	0.0627953	−	0.0362549i
$859$	27.1045	+	15.6488i	0.924793	+	0.533929i	0.885161	−	0.465285i	$-0.154048\pi$
$859$	27.1045	+	15.6488i	0.924793	+	0.533929i	0.0396317	+	0.999214i	$0.487382\pi$
$860$			100.999i			3.44403i
$861$	−2.37790	−	38.5706i	−0.0810385	−	1.31448i
$862$			36.2064i			1.23319i
$863$	18.7314	−	32.4438i	0.637625	−	1.10440i	−0.348328	−	0.937373i	$-0.613250\pi$
$863$	18.7314	−	32.4438i	0.637625	−	1.10440i	0.985953	−	0.167025i	$-0.0534162\pi$
$864$	−31.6695	+	18.2844i	−1.07742	+	0.622048i
$865$	−23.6970	+	13.6815i	−0.805724	+	0.465185i
$866$	−34.2069	+	59.2481i	−1.16240	+	2.01333i
$867$			39.4727i			1.34056i
$868$	16.4016	+	24.7539i	0.556706	+	0.840203i
$869$	13.4229			0.455340
$870$	177.076	+	102.235i	6.00345	+	3.46609i
$871$	0.840608	+	1.45598i	0.0284829	+	0.0493339i
$872$	−0.876065	+	0.505796i	−0.0296673	+	0.0171284i
$873$	38.1505	−	66.0787i	1.29120	−	2.23642i
$874$	−21.8670	−	34.9884i	−0.739663	−	1.18350i
$875$	44.3679	+	22.0941i	1.49991	+	0.746917i
$876$	−70.0617			−2.36717
$877$	−26.9369	+	46.6560i	−0.909593	+	1.57546i	−0.0949631	+	0.995481i	$0.530273\pi$
$877$	−26.9369	+	46.6560i	−0.909593	+	1.57546i	−0.814630	+	0.579981i	$0.803060\pi$
$878$	48.8348	−	28.1948i	1.64809	−	0.951527i
$879$	21.3863	−	12.3474i	0.721342	−	0.416467i
$880$	14.8486	+	8.57285i	0.500547	+	0.288991i
$881$	−4.08101			−0.137493			−0.0687464	−	0.997634i	$-0.521900\pi$
$881$	−4.08101			−0.137493			−0.0687464	+	0.997634i	$0.521900\pi$
$882$	−27.2891	+	64.4633i	−0.918873	+	2.17059i
$883$	30.2362			1.01753			0.508764	−	0.860906i	$-0.330103\pi$
$883$	30.2362			1.01753			0.508764	+	0.860906i	$0.330103\pi$
$884$	0.756526	+	0.436781i	0.0254447	+	0.0146905i
$885$	−18.2681	−	31.6412i	−0.614075	−	1.06361i
$886$	1.22709	+	2.12537i	0.0412247	+	0.0714034i
$887$	34.5006	+	19.9189i	1.15842	+	0.668812i	0.950924	−	0.309425i	$-0.100137\pi$
$887$	34.5006	+	19.9189i	1.15842	+	0.668812i	0.207492	+	0.978237i	$0.433470\pi$
$888$	−21.2953			−0.714624
$889$	−33.8679	−	16.8654i	−1.13589	−	0.565646i
$890$	21.0375			0.705177
$891$	−1.73375	−	1.00098i	−0.0580829	−	0.0335342i
$892$	−57.7284	+	33.3295i	−1.93289	+	1.11596i
$893$	−1.67719	+	0.968327i	−0.0561251	+	0.0324038i
$894$	−38.5609	+	66.7895i	−1.28967	+	2.23377i
$895$	75.6487			2.52866
$896$	−20.5521	+	13.6175i	−0.686598	+	0.454929i
$897$	−1.44342	−	2.30954i	−0.0481943	−	0.0771133i
$898$	21.3948	−	37.0569i	0.713953	−	1.23660i
$899$	−33.8997	+	19.5720i	−1.13062	+	0.652764i
$900$	59.2333	+	102.595i	1.97444	+	3.41983i
$901$	10.3385	+	5.96895i	0.344426	+	0.198855i
$902$	−19.7132			−0.656378
$903$	−4.60306	−	74.6639i	−0.153180	−	2.48466i
$904$		−	0.355522i		−	0.0118245i
$905$	−10.6220	+	18.3979i	−0.353088	+	0.611566i
$906$	39.3244	−	22.7040i	1.30647	−	0.754289i
$907$	−26.4224	+	15.2550i	−0.877340	+	0.506532i	−0.869780	−	0.493439i	$-0.835740\pi$
$907$	−26.4224	+	15.2550i	−0.877340	+	0.506532i	−0.00755954	+	0.999971i	$0.502406\pi$
$908$	−0.276822	+	0.479469i	−0.00918665	+	0.0159117i
$909$		−	17.7218i		−	0.587794i
$910$	−4.45861	+	0.274876i	−0.147802	+	0.00911204i
$911$		−	6.86165i		−	0.227337i	−0.993519	−	0.113668i	$-0.963740\pi$
$911$		−	6.86165i		−	0.227337i	0.993519	−	0.113668i	$-0.0362601\pi$
$912$	24.5536	+	14.1760i	0.813050	+	0.469415i
$913$	1.26131	−	0.728218i	0.0417433	−	0.0241005i
$914$	−32.1592	+	18.5671i	−1.06373	+	0.614146i
$915$	−26.9403	−	15.5540i	−0.890619	−	0.514199i
$916$	3.34666			0.110577
$917$	2.49952	+	3.77237i	0.0825413	+	0.124575i
$918$			16.5069i			0.544807i
$919$	22.6047	+	13.0508i	0.745659	+	0.430506i	0.824123	−	0.566411i	$-0.191668\pi$
$919$	22.6047	+	13.0508i	0.745659	+	0.430506i	−0.0784645	+	0.996917i	$0.525002\pi$
$920$	−10.5326	+	19.8127i	−0.347249	+	0.653206i
$921$	−24.3365	−	42.1521i	−0.801916	−	1.38896i
$922$	28.1398	+	16.2465i	0.926737	+	0.535052i
$923$		−	0.588676i		−	0.0193765i
$924$	29.4913	+	14.6859i	0.970192	+	0.483131i
$925$		−	62.4279i		−	2.05262i
$926$	−0.781193	+	1.35307i	−0.0256716	+	0.0444645i
$927$	−38.1639	−	66.1019i	−1.25347	−	2.17107i
$928$	−35.1961	−	60.9614i	−1.15537	−	2.00116i
$929$	−19.4884	−	11.2516i	−0.639394	−	0.369155i	0.144987	−	0.989434i	$-0.453686\pi$
$929$	−19.4884	−	11.2516i	−0.639394	−	0.369155i	−0.784381	+	0.620279i	$0.787019\pi$
$930$	−99.7857			−3.27210
$931$	27.9640	−	3.46115i	0.916484	−	0.113434i
$932$	−9.95757			−0.326171
$933$	−3.71530	+	6.43509i	−0.121633	+	0.210675i
$934$	43.9919	+	76.1962i	1.43946	+	2.49322i
$935$	9.69759	−	5.59890i	0.317145	−	0.183104i
$936$	−1.00789	−	0.581906i	−0.0329440	−	0.0190202i
$937$	−25.6250			−0.837132			−0.418566	−	0.908186i	$-0.637467\pi$
$937$	−25.6250			−0.837132			−0.418566	+	0.908186i	$0.637467\pi$
$938$	−20.6787	+	41.5256i	−0.675184	+	1.35586i
$939$		−	20.5740i		−	0.671407i
$940$	4.12441	+	2.38123i	0.134523	+	0.0776671i
$941$	22.5938	+	39.1336i	0.736537	+	1.27572i	0.954046	+	0.299661i	$0.0968737\pi$
$941$	22.5938	+	39.1336i	0.736537	+	1.27572i	−0.217509	+	0.976058i	$0.569793\pi$
$942$	−73.8536	+	42.6394i	−2.40628	+	1.38927i
$943$	0.884202	+	25.2626i	0.0287936	+	0.822663i
$944$			8.69348i			0.282949i
$945$	−26.2098	−	39.5569i	−0.852604	−	1.28679i
$946$	−38.1602			−1.24070
$947$	−1.93187	+	3.34609i	−0.0627772	+	0.108733i	−0.895706	−	0.444647i	$-0.853329\pi$
$947$	−1.93187	+	3.34609i	−0.0627772	+	0.108733i	0.832929	+	0.553380i	$0.186662\pi$
$948$	−27.2913	−	47.2699i	−0.886380	−	1.53526i
$949$	1.00887	+	1.74741i	0.0327492	+	0.0567232i
$950$	42.4129	−	73.4614i	1.37606	−	2.38340i
$951$		−	2.20824i		−	0.0716072i
$952$	0.328011	+	5.32050i	0.0106309	+	0.172438i
$953$			46.4045i			1.50319i	0.659626	+	0.751594i	$0.270715\pi$
$953$			46.4045i			1.50319i	−0.659626	+	0.751594i	$0.729285\pi$
$954$	−62.2819	−	35.9584i	−2.01645	−	1.16420i
$955$	71.5109	−	41.2869i	2.31404	−	1.33601i
$956$	14.7764	+	25.5934i	0.477901	+	0.827749i
$957$	−21.7148	+	37.6111i	−0.701940	+	1.21580i
$958$	41.0180			1.32523
$959$	−42.6747	+	2.63092i	−1.37804	+	0.0849568i
$960$		−	125.141i		−	4.03891i
$961$	−5.94844	+	10.3030i	−0.191885	+	0.332355i
$962$	1.38660	+	2.40165i	0.0447056	+	0.0774324i
$963$	26.6984	−	15.4143i	0.860345	−	0.496720i
$964$	−0.437749	+	0.758203i	−0.0140989	+	0.0244201i
$965$	−21.0191			−0.676630
$966$	31.1251	−	68.4002i	1.00143	−	2.20074i
$967$	−48.6298			−1.56383			−0.781914	−	0.623386i	$-0.785757\pi$
$967$	−48.6298			−1.56383			−0.781914	+	0.623386i	$0.785757\pi$
$968$	−4.81713	+	8.34351i	−0.154828	+	0.268171i
$969$	16.0359	−	9.25831i	0.515146	−	0.297420i
$970$	67.1758	+	116.352i	2.15688	+	3.73583i
$971$	17.8488	−	30.9150i	0.572795	−	0.992109i	−0.423483	−	0.905904i	$-0.639193\pi$
$971$	17.8488	−	30.9150i	0.572795	−	0.992109i	0.996277	−	0.0862053i	$-0.0274741\pi$
$972$			43.9832i			1.41076i
$973$	4.22285	−	8.48005i	0.135378	−	0.271858i
$974$	6.69698			0.214585
$975$	2.79963	−	4.84910i	0.0896598	−	0.155295i
$976$	3.70094	+	6.41022i	0.118464	+	0.205186i
$977$	20.4258	−	11.7928i	0.653479	−	0.377286i	−0.136309	−	0.990666i	$-0.543524\pi$
$977$	20.4258	−	11.7928i	0.653479	−	0.377286i	0.789788	+	0.613380i	$0.210191\pi$
$978$	−1.69185	−	0.976788i	−0.0540993	−	0.0312342i
$979$			4.46837i			0.142810i
$980$	−41.7545	−	55.2981i	−1.33380	−	1.76643i
$981$			3.89975i			0.124510i
$982$	−37.7695	+	65.4187i	−1.20527	+	2.08759i
$983$	−5.05628	−	8.75774i	−0.161270	−	0.279329i	0.774054	−	0.633119i	$-0.218226\pi$
$983$	−5.05628	−	8.75774i	−0.161270	−	0.279329i	−0.935325	+	0.353791i	$0.884892\pi$
$984$	8.86384	+	15.3526i	0.282569	+	0.489424i
$985$	−13.0753	+	22.6471i	−0.416615	+	0.721598i
$986$	−31.7745			−1.01190
$987$	−3.15752	−	1.57237i	−0.100505	−	0.0500490i
$988$			2.11831i			0.0673925i
$989$	1.71161	+	48.9025i	0.0544261	+	1.55501i
$990$	−58.4207	+	33.7292i	−1.85673	+	1.07198i
$991$	−17.7089	−	30.6727i	−0.562541	−	0.974350i	−0.997274	−	0.0737905i	$-0.976490\pi$
$991$	−17.7089	−	30.6727i	−0.562541	−	0.974350i	0.434732	−	0.900560i	$-0.356843\pi$
$992$	29.7504	+	17.1764i	0.944578	+	0.545352i
$993$		−	33.0847i		−	1.04991i
$994$	13.5406	−	8.97183i	0.429483	−	0.284569i
$995$	−7.29970			−0.231416
$996$	−5.12897	−	2.96121i	−0.162518	−	0.0938296i
$997$	46.7706	−	27.0030i	1.48124	−	0.855195i	0.481467	−	0.876464i	$-0.340104\pi$
$997$	46.7706	−	27.0030i	1.48124	−	0.855195i	0.999774	+	0.0212694i	$0.00677078\pi$
$998$	−18.6043	−	32.2236i	−0.588910	−	1.02002i
$999$	−14.7293	+	25.5119i	−0.466014	+	0.807159i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.2.g.a.68.4	yes	28
7.2	even	3		1127.2.c.c.1126.23		28
7.3	odd	6	inner	161.2.g.a.45.3	✓	28
7.5	odd	6		1127.2.c.c.1126.21		28
23.22	odd	2	inner	161.2.g.a.68.3	yes	28
161.45	even	6	inner	161.2.g.a.45.4	yes	28
161.68	even	6		1127.2.c.c.1126.22		28
161.114	odd	6		1127.2.c.c.1126.24		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.2.g.a.45.3	✓	28	7.3	odd	6	inner
161.2.g.a.45.4	yes	28	161.45	even	6	inner
161.2.g.a.68.3	yes	28	23.22	odd	2	inner
161.2.g.a.68.4	yes	28	1.1	even	1	trivial
1127.2.c.c.1126.21		28	7.5	odd	6
1127.2.c.c.1126.22		28	161.68	even	6
1127.2.c.c.1126.23		28	7.2	even	3
1127.2.c.c.1126.24		28	161.114	odd	6

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	161.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06863 + 1.85092i) q^{2} +(-2.39984 + 1.38555i) q^{3} +(-1.28394 - 2.22386i) q^{4} +(1.92742 - 3.33839i) q^{5} -5.92256i q^{6} +(-2.36835 - 1.17938i) q^{7} +1.21373 q^{8} +(2.33949 - 4.05212i) q^{9} +(4.11940 + 7.13501i) q^{10} +(-1.51548 + 0.874964i) q^{11} +(6.16253 + 3.55794i) q^{12} -0.204932i q^{13} +(4.71383 - 3.12331i) q^{14} +10.6821i q^{15} +(1.27086 - 2.20120i) q^{16} +(-0.829997 - 1.43760i) q^{17} +(5.00011 + 8.66045i) q^{18} +(2.01267 - 3.48605i) q^{19} -9.89880 q^{20} +(7.31775 - 0.451142i) q^{21} -3.74005i q^{22} +(-4.79290 + 0.167754i) q^{23} +(-2.91275 + 1.68168i) q^{24} +(-4.92989 - 8.53883i) q^{25} +(0.379314 + 0.218997i) q^{26} +4.65264i q^{27} +(0.418059 + 6.78112i) q^{28} -8.95599 q^{29} +(-19.7718 - 11.4153i) q^{30} +(3.78515 - 2.18536i) q^{31} +(3.92989 + 6.80678i) q^{32} +(2.42461 - 4.19955i) q^{33} +3.54784 q^{34} +(-8.50202 + 5.63331i) q^{35} -12.0151 q^{36} +(5.48330 + 3.16579i) q^{37} +(4.30161 + 7.45060i) q^{38} +(0.283944 + 0.491805i) q^{39} +(2.33936 - 4.05189i) q^{40} -5.27084i q^{41} +(-6.98494 + 14.0267i) q^{42} -10.2031i q^{43} +(3.89159 + 2.24681i) q^{44} +(-9.01838 - 15.6203i) q^{45} +(4.81134 - 9.05055i) q^{46} +(-0.416658 - 0.240557i) q^{47} +7.04338i q^{48} +(4.21814 + 5.58635i) q^{49} +21.0729 q^{50} +(3.98373 + 2.30000i) q^{51} +(-0.455740 + 0.263122i) q^{52} +(-6.22805 + 3.59576i) q^{53} +(-8.61169 - 4.97196i) q^{54} +6.74569i q^{55} +(-2.87452 - 1.43144i) q^{56} +11.1546i q^{57} +(9.57065 - 16.5769i) q^{58} +(-2.96207 + 1.71015i) q^{59} +(23.7555 - 13.7153i) q^{60} +(-1.45607 + 2.52199i) q^{61} +9.34135i q^{62} +(-10.3197 + 6.83769i) q^{63} -11.7150 q^{64} +(-0.684144 - 0.394991i) q^{65} +(5.18203 + 8.97554i) q^{66} +(-7.10467 + 4.10188i) q^{67} +(-2.13134 + 3.69159i) q^{68} +(11.2698 - 7.04338i) q^{69} +(-1.34130 - 21.7565i) q^{70} +2.87254 q^{71} +(2.83950 - 4.91816i) q^{72} +(-8.52674 + 4.92292i) q^{73} +(-11.7192 + 6.76611i) q^{74} +(23.6619 + 13.6612i) q^{75} -10.3366 q^{76} +(4.62110 - 0.284893i) q^{77} -1.21373 q^{78} +(-6.64288 - 3.83527i) q^{79} +(-4.89898 - 8.48527i) q^{80} +(0.572014 + 0.990758i) q^{81} +(9.75591 + 5.63258i) q^{82} -0.832284 q^{83} +(-10.3989 - 15.6944i) q^{84} -6.39901 q^{85} +(18.8852 + 10.9034i) q^{86} +(21.4930 - 12.4090i) q^{87} +(-1.83938 + 1.06197i) q^{88} +(1.27673 - 2.21136i) q^{89} +38.5493 q^{90} +(-0.241693 + 0.485351i) q^{91} +(6.52687 + 10.4433i) q^{92} +(-6.05584 + 10.4890i) q^{93} +(0.890507 - 0.514134i) q^{94} +(-7.75853 - 13.4382i) q^{95} +(-18.8622 - 10.8901i) q^{96} +16.3072 q^{97} +(-14.8475 + 1.83770i) q^{98} +8.18789i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{2} - 6 q^{3} - 12 q^{4} + 12 q^{8} + 4 q^{9} + 6 q^{12} + 22 q^{18} - 36 q^{24} - 22 q^{25} - 12 q^{26} - 44 q^{29} - 6 q^{32} - 10 q^{35} - 16 q^{39} + 18 q^{46} - 36 q^{47} + 28 q^{49} + 84 q^{50}+ \cdots - 146 q^{98}+O(q^{100}) \) 28 * q - 4 * q^2 - 6 * q^3 - 12 * q^4 + 12 * q^8 + 4 * q^9 + 6 * q^12 + 22 * q^18 - 36 * q^24 - 22 * q^25 - 12 * q^26 - 44 * q^29 - 6 * q^32 - 10 * q^35 - 16 * q^39 + 18 * q^46 - 36 * q^47 + 28 * q^49 + 84 * q^50 + 72 * q^52 - 30 * q^54 + 14 * q^58 - 54 * q^59 - 68 * q^64 + 38 * q^70 + 16 * q^71 - 4 * q^72 - 18 * q^73 + 96 * q^75 + 20 * q^77 - 12 * q^78 + 22 * q^81 - 52 * q^85 - 18 * q^87 - 28 * q^92 - 10 * q^93 + 84 * q^94 + 56 * q^95 - 84 * q^96 - 146 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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