LMFDB - Embedded newform 161.2.g.a.45.10

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			45.10
Character	$\chi$	$=$	161.45
Dual form			161.2.g.a.68.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.292153 + 0.506024i) q^{2} +(0.510598 + 0.294794i) q^{3} +(0.829293 - 1.43638i) q^{4} +(1.76663 + 3.05989i) q^{5} +0.344500i q^{6} +(-2.22044 - 1.43862i) q^{7} +2.13773 q^{8} +(-1.32619 - 2.29703i) q^{9} +(-1.03225 + 1.78791i) q^{10} +(0.243326 + 0.140484i) q^{11} +(0.846870 - 0.488941i) q^{12} +6.20533i q^{13} +(0.0792673 - 1.54390i) q^{14} +2.08316i q^{15} +(-1.03404 - 1.79101i) q^{16} +(1.89785 - 3.28717i) q^{17} +(0.774903 - 1.34217i) q^{18} +(-1.92712 - 3.33788i) q^{19} +5.86020 q^{20} +(-0.709657 - 1.38913i) q^{21} +0.164172i q^{22} +(-2.71326 + 3.95452i) q^{23} +(1.09152 + 0.630191i) q^{24} +(-3.74193 + 6.48121i) q^{25} +(-3.14005 + 1.81291i) q^{26} -3.33258i q^{27} +(-3.90780 + 1.99636i) q^{28} -2.64066 q^{29} +(-1.05413 + 0.608602i) q^{30} +(-4.59366 - 2.65215i) q^{31} +(2.74193 - 4.74916i) q^{32} +(0.0828278 + 0.143462i) q^{33} +2.21785 q^{34} +(0.479323 - 9.33581i) q^{35} -4.39921 q^{36} +(-0.645778 + 0.372840i) q^{37} +(1.12603 - 1.95034i) q^{38} +(-1.82929 + 3.16843i) q^{39} +(3.77658 + 6.54122i) q^{40} -4.20999i q^{41} +(0.495605 - 0.764942i) q^{42} -7.90283i q^{43} +(0.403577 - 0.233005i) q^{44} +(4.68577 - 8.11600i) q^{45} +(-2.79377 - 0.217652i) q^{46} +(-5.41106 + 3.12408i) q^{47} -1.21931i q^{48} +(2.86074 + 6.38875i) q^{49} -4.37287 q^{50} +(1.93808 - 1.11895i) q^{51} +(8.91320 + 5.14604i) q^{52} +(-1.15012 - 0.664023i) q^{53} +(1.68636 - 0.973623i) q^{54} +0.992733i q^{55} +(-4.74672 - 3.07539i) q^{56} -2.27242i q^{57} +(-0.771476 - 1.33624i) q^{58} +(3.11416 + 1.79796i) q^{59} +(2.99221 + 1.72755i) q^{60} +(5.17682 + 8.96652i) q^{61} -3.09934i q^{62} +(-0.359824 + 7.00832i) q^{63} -0.931905 q^{64} +(-18.9876 + 10.9625i) q^{65} +(-0.0483968 + 0.0838258i) q^{66} +(9.69710 + 5.59862i) q^{67} +(-3.14775 - 5.45206i) q^{68} +(-2.55115 + 1.21931i) q^{69} +(4.86418 - 2.48494i) q^{70} +5.77682 q^{71} +(-2.83505 - 4.91045i) q^{72} +(6.45526 + 3.72695i) q^{73} +(-0.377332 - 0.217853i) q^{74} +(-3.82124 + 2.20620i) q^{75} -6.39260 q^{76} +(-0.338188 - 0.661992i) q^{77} -2.13773 q^{78} +(-6.19011 + 3.57386i) q^{79} +(3.65352 - 6.32809i) q^{80} +(-2.99616 + 5.18950i) q^{81} +(2.13036 - 1.22996i) q^{82} +10.3906 q^{83} +(-2.58383 - 0.132660i) q^{84} +13.4112 q^{85} +(3.99902 - 2.30884i) q^{86} +(-1.34831 - 0.778449i) q^{87} +(0.520167 + 0.300318i) q^{88} +(2.79272 + 4.83714i) q^{89} +5.47585 q^{90} +(8.92712 - 13.7786i) q^{91} +(3.43009 + 7.17672i) q^{92} +(-1.56367 - 2.70836i) q^{93} +(-3.16172 - 1.82542i) q^{94} +(6.80901 - 11.7936i) q^{95} +(2.80005 - 1.61661i) q^{96} -10.9371 q^{97} +(-2.39709 + 3.31410i) q^{98} -0.745238i 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 $\left(\mathbb{Z}/161\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.292153	+	0.506024i	0.206583	+	0.357813i	0.950636	−	0.310308i	$-0.100432\pi$
$2$	0.292153	+	0.506024i	0.206583	+	0.357813i	−0.744053	+	0.668121i	$0.767099\pi$
$3$	0.510598	+	0.294794i	0.294794	+	0.170199i	0.640102	−	0.768290i	$-0.278892\pi$
$3$	0.510598	+	0.294794i	0.294794	+	0.170199i	−0.345308	+	0.938489i	$0.612226\pi$
$4$	0.829293	−	1.43638i	0.414647	−	0.718189i
$5$	1.76663	+	3.05989i	0.790059	+	1.36842i	0.925930	+	0.377696i	$0.123283\pi$
$5$	1.76663	+	3.05989i	0.790059	+	1.36842i	−0.135871	+	0.990727i	$0.543383\pi$
$6$			0.344500i			0.140641i
$7$	−2.22044	−	1.43862i	−0.839249	−	0.543748i
$7$	−2.22044	−	1.43862i	−0.839249	−	0.543748i
$8$	2.13773			0.755803
$9$	−1.32619	−	2.29703i	−0.442064	−	0.765678i
$10$	−1.03225	+	1.78791i	−0.326426	+	0.565387i
$11$	0.243326	+	0.140484i	0.0733656	+	0.0423576i	0.536234	−	0.844069i	$-0.319846\pi$
$11$	0.243326	+	0.140484i	0.0733656	+	0.0423576i	−0.462868	+	0.886427i	$0.653180\pi$
$12$	0.846870	−	0.488941i	0.244470	−	0.141145i
$13$			6.20533i			1.72105i	0.509409	+	0.860525i	$0.329864\pi$
$13$			6.20533i			1.72105i	−0.509409	+	0.860525i	$0.670136\pi$
$14$	0.0792673	−	1.54390i	0.0211851	−	0.412623i
$15$			2.08316i			0.537870i
$16$	−1.03404	−	1.79101i	−0.258510	−	0.447753i
$17$	1.89785	−	3.28717i	0.460296	−	0.797257i	−0.538679	−	0.842511i	$-0.681077\pi$
$17$	1.89785	−	3.28717i	0.460296	−	0.797257i	0.998975	+	0.0452544i	$0.0144099\pi$
$18$	0.774903	−	1.34217i	0.182646	−	0.316353i
$19$	−1.92712	−	3.33788i	−0.442113	−	0.765761i	0.555734	−	0.831360i	$-0.312437\pi$
$19$	−1.92712	−	3.33788i	−0.442113	−	0.765761i	−0.997846	+	0.0655991i	$0.979104\pi$
$20$	5.86020			1.31038
$21$	−0.709657	−	1.38913i	−0.154860	−	0.303133i
$22$			0.164172i			0.0350015i
$23$	−2.71326	+	3.95452i	−0.565755	+	0.824574i
$23$	−2.71326	+	3.95452i	−0.565755	+	0.824574i
$24$	1.09152	+	0.630191i	0.222806	+	0.128637i
$25$	−3.74193	+	6.48121i	−0.748386	+	1.29624i
$26$	−3.14005	+	1.81291i	−0.615814	+	0.355540i
$27$		−	3.33258i		−	0.641355i
$28$	−3.90780	+	1.99636i	−0.738505	+	0.377276i
$29$	−2.64066			−0.490358			−0.245179	−	0.969478i	$-0.578847\pi$
$29$	−2.64066			−0.490358			−0.245179	+	0.969478i	$0.578847\pi$
$30$	−1.05413	+	0.608602i	−0.192457	+	0.111115i
$31$	−4.59366	−	2.65215i	−0.825046	−	0.476340i	0.0271077	−	0.999633i	$-0.491370\pi$
$31$	−4.59366	−	2.65215i	−0.825046	−	0.476340i	−0.852153	+	0.523292i	$0.824704\pi$
$32$	2.74193	−	4.74916i	0.484710	−	0.839542i
$33$	0.0828278	+	0.143462i	0.0144185	+	0.0249735i
$34$	2.21785			0.380358
$35$	0.479323	−	9.33581i	0.0810204	−	1.57804i
$36$	−4.39921			−0.733202
$37$	−0.645778	+	0.372840i	−0.106165	+	0.0612945i	−0.552142	−	0.833750i	$-0.686190\pi$
$37$	−0.645778	+	0.372840i	−0.106165	+	0.0612945i	0.445977	+	0.895044i	$0.352856\pi$
$38$	1.12603	−	1.95034i	0.182666	−	0.316387i
$39$	−1.82929	+	3.16843i	−0.292921	+	0.507355i
$40$	3.77658	+	6.54122i	0.597129	+	1.03426i
$41$		−	4.20999i		−	0.657490i	−0.944419	−	0.328745i	$-0.893374\pi$
$41$		−	4.20999i		−	0.657490i	0.944419	−	0.328745i	$-0.106626\pi$
$42$	0.495605	−	0.764942i	0.0764734	−	0.118033i
$43$		−	7.90283i		−	1.20517i	−0.798054	−	0.602585i	$-0.794137\pi$
$43$		−	7.90283i		−	1.20517i	0.798054	−	0.602585i	$-0.205863\pi$
$44$	0.403577	−	0.233005i	0.0608416	−	0.0351269i
$45$	4.68577	−	8.11600i	0.698514	−	1.20986i
$46$	−2.79377	−	0.217652i	−0.411919	−	0.0320911i
$47$	−5.41106	+	3.12408i	−0.789285	+	0.455694i	−0.839711	−	0.543034i	$-0.817275\pi$
$47$	−5.41106	+	3.12408i	−0.789285	+	0.455694i	0.0504259	+	0.998728i	$0.483942\pi$
$48$		−	1.21931i		−	0.175993i
$49$	2.86074	+	6.38875i	0.408677	+	0.912679i
$50$	−4.37287			−0.618417
$51$	1.93808	−	1.11895i	0.271385	−	0.156684i
$52$	8.91320	+	5.14604i	1.23604	+	0.713627i
$53$	−1.15012	−	0.664023i	−0.157981	−	0.0912105i	0.418925	−	0.908021i	$-0.362407\pi$
$53$	−1.15012	−	0.664023i	−0.157981	−	0.0912105i	−0.576906	+	0.816810i	$0.695740\pi$
$54$	1.68636	−	0.973623i	0.229485	−	0.132493i
$55$			0.992733i			0.133860i
$56$	−4.74672	−	3.07539i	−0.634307	−	0.410966i
$57$		−	2.27242i		−	0.300989i
$58$	−0.771476	−	1.33624i	−0.101300	−	0.175456i
$59$	3.11416	+	1.79796i	0.405429	+	0.234075i	0.688824	−	0.724929i	$-0.258127\pi$
$59$	3.11416	+	1.79796i	0.405429	+	0.234075i	−0.283395	+	0.959003i	$0.591461\pi$
$60$	2.99221	+	1.72755i	0.386292	+	0.223026i
$61$	5.17682	+	8.96652i	0.662824	+	1.14805i	0.979870	+	0.199635i	$0.0639757\pi$
$61$	5.17682	+	8.96652i	0.662824	+	1.14805i	−0.317046	+	0.948410i	$0.602691\pi$
$62$		−	3.09934i		−	0.393616i
$63$	−0.359824	+	7.00832i	−0.0453336	+	0.882966i
$64$	−0.931905			−0.116488
$65$	−18.9876	+	10.9625i	−2.35512	+	1.35973i
$66$	−0.0483968	+	0.0838258i	−0.00595724	+	0.0103182i
$67$	9.69710	+	5.59862i	1.18469	+	0.683980i	0.957095	−	0.289776i	$-0.0935807\pi$
$67$	9.69710	+	5.59862i	1.18469	+	0.683980i	0.227594	+	0.973756i	$0.426914\pi$
$68$	−3.14775	−	5.45206i	−0.381721	−	0.661159i
$69$	−2.55115	+	1.21931i	−0.307123	+	0.146788i
$70$	4.86418	−	2.48494i	0.581381	−	0.297007i
$71$	5.77682			0.685582			0.342791	−	0.939412i	$-0.388628\pi$
$71$	5.77682			0.685582			0.342791	+	0.939412i	$0.388628\pi$
$72$	−2.83505	−	4.91045i	−0.334114	−	0.578702i
$73$	6.45526	+	3.72695i	0.755531	+	0.436206i	0.827689	−	0.561187i	$-0.189655\pi$
$73$	6.45526	+	3.72695i	0.755531	+	0.436206i	−0.0721580	+	0.997393i	$0.522989\pi$
$74$	−0.377332	−	0.217853i	−0.0438640	−	0.0253249i
$75$	−3.82124	+	2.20620i	−0.441239	+	0.254750i
$76$	−6.39260			−0.733282
$77$	−0.338188	−	0.661992i	−0.0385401	−	0.0754409i
$78$	−2.13773			−0.242051
$79$	−6.19011	+	3.57386i	−0.696441	+	0.402091i	−0.806021	−	0.591887i	$-0.798383\pi$
$79$	−6.19011	+	3.57386i	−0.696441	+	0.402091i	0.109579	+	0.993978i	$0.465050\pi$
$80$	3.65352	−	6.32809i	0.408476	−	0.707502i
$81$	−2.99616	+	5.18950i	−0.332906	+	0.576611i
$82$	2.13036	−	1.22996i	0.235258	−	0.135827i
$83$	10.3906			1.14052			0.570258	−	0.821465i	$-0.306843\pi$
$83$	10.3906			1.14052			0.570258	+	0.821465i	$0.306843\pi$
$84$	−2.58383	−	0.132660i	−0.281919	−	0.0144744i
$85$	13.4112			1.45464
$86$	3.99902	−	2.30884i	0.431226	−	0.248968i
$87$	−1.34831	−	0.778449i	−0.144554	−	0.0834585i
$88$	0.520167	+	0.300318i	0.0554500	+	0.0320140i
$89$	2.79272	+	4.83714i	0.296028	+	0.512736i	0.975224	−	0.221222i	$-0.0710045\pi$
$89$	2.79272	+	4.83714i	0.296028	+	0.512736i	−0.679195	+	0.733957i	$0.737671\pi$
$90$	5.47585			0.577206
$91$	8.92712	−	13.7786i	0.935817	−	1.44439i
$92$	3.43009	+	7.17672i	0.357612	+	0.748225i
$93$	−1.56367	−	2.70836i	−0.162146	−	0.280844i
$94$	−3.16172	−	1.82542i	−0.326106	−	0.188278i
$95$	6.80901	−	11.7936i	0.698590	−	1.20999i
$96$	2.80005	−	1.61661i	0.285779	−	0.164994i
$97$	−10.9371			−1.11049			−0.555247	−	0.831686i	$-0.687376\pi$
$97$	−10.9371			−1.11049			−0.555247	+	0.831686i	$0.687376\pi$
$98$	−2.39709	+	3.31410i	−0.242143	+	0.334774i
$99$		−	0.745238i		−	0.0748992i
$100$	6.20632	+	10.7497i	0.620632	+	1.07497i
$101$	6.34218	+	3.66166i	0.631070	+	0.364349i	0.781166	−	0.624323i	$-0.214625\pi$
$101$	6.34218	+	3.66166i	0.631070	+	0.364349i	−0.150096	+	0.988671i	$0.547958\pi$
$102$	1.13243	+	0.653809i	0.112127	+	0.0647367i
$103$	4.65928	+	8.07011i	0.459093	+	0.795172i	0.998913	−	0.0466083i	$-0.0148413\pi$
$103$	4.65928	+	8.07011i	0.459093	+	0.795172i	−0.539821	+	0.841780i	$0.681508\pi$
$104$			13.2654i			1.30078i
$105$	2.99688	−	4.62554i	0.292465	−	0.451407i
$106$		−	0.775985i		−	0.0753704i
$107$	6.10591	−	3.52525i	0.590280	−	0.340798i	−0.174928	−	0.984581i	$-0.555969\pi$
$107$	6.10591	−	3.52525i	0.590280	−	0.340798i	0.765208	+	0.643783i	$0.222636\pi$
$108$	−4.78684	−	2.76368i	−0.460614	−	0.265935i
$109$	−13.4532	−	7.76720i	−1.28858	−	0.743962i	−0.310180	−	0.950678i	$-0.600389\pi$
$109$	−13.4532	−	7.76720i	−1.28858	−	0.743962i	−0.978401	+	0.206716i	$0.933723\pi$
$110$	−0.502347	+	0.290030i	−0.0478969	+	0.0276533i
$111$	−0.439644			−0.0417291
$112$	−0.280557	+	5.46443i	−0.0265101	+	0.516340i
$113$		−	2.81523i		−	0.264834i	−0.991194	−	0.132417i	$-0.957726\pi$
$113$		−	2.81523i		−	0.264834i	0.991194	−	0.132417i	$-0.0422738\pi$
$114$	1.14990	−	0.663894i	0.107698	−	0.0621793i
$115$	−16.8937	−	1.31612i	−1.57534	−	0.122729i
$116$	−2.18988	+	3.79298i	−0.203325	+	0.352169i
$117$	14.2539	−	8.22947i	1.31777	−	0.760815i
$118$			2.10112i			0.193424i
$119$	−8.94307	+	4.56869i	−0.819809	+	0.418812i
$120$			4.45325i			0.406524i
$121$	−5.46053	−	9.45791i	−0.496412	−	0.859810i
$122$	−3.02485	+	5.23919i	−0.273857	+	0.474334i
$123$	1.24108	−	2.14961i	0.111904	−	0.193824i
$124$	−7.61898	+	4.39882i	−0.684205	+	0.395026i
$125$	−8.77611			−0.784959
$126$	−3.65150	+	1.86542i	−0.325302	+	0.166185i
$127$	6.58438			0.584269			0.292135	−	0.956377i	$-0.405634\pi$
$127$	6.58438			0.584269			0.292135	+	0.956377i	$0.405634\pi$
$128$	−5.75612	−	9.96989i	−0.508774	−	0.881223i
$129$	2.32971	−	4.03517i	0.205119	−	0.355277i
$130$	−11.0946	−	6.40546i	−0.973059	−	0.561796i
$131$	−6.84664	+	3.95291i	−0.598193	+	0.345367i	−0.768330	−	0.640053i	$-0.778912\pi$
$131$	−6.84664	+	3.95291i	−0.598193	+	0.345367i	0.170137	+	0.985420i	$0.445579\pi$
$132$	0.274754			0.0239143
$133$	−0.522870	+	10.1840i	−0.0453385	+	0.883062i
$134$			6.54262i			0.565196i
$135$	10.1973	−	5.88741i	0.877644	−	0.506708i
$136$	4.05710	−	7.02710i	0.347894	−	0.602569i
$137$	18.3156	+	10.5745i	1.56481	+	0.903441i	0.996759	+	0.0804444i	$0.0256340\pi$
$137$	18.3156	+	10.5745i	1.56481	+	0.903441i	0.568046	+	0.822996i	$0.307699\pi$
$138$	−1.36233	−	0.934718i	−0.115969	−	0.0795685i
$139$			0.0766084i			0.00649784i	0.999995	+	0.00324892i	$0.00103416\pi$
$139$			0.0766084i			0.00649784i	−0.999995	+	0.00324892i	$0.998966\pi$
$140$	−13.0122	−	8.43061i	−1.09974	−	0.712516i
$141$	−3.68384			−0.310235
$142$	1.68772	+	2.92321i	0.141630	+	0.245310i
$143$	−0.871752	+	1.50992i	−0.0728996	+	0.126266i
$144$	−2.74267	+	4.75045i	−0.228556	+	0.395871i
$145$	−4.66505	−	8.08011i	−0.387411	−	0.671016i
$146$			4.35536i			0.360452i
$147$	−0.422678	+	4.10541i	−0.0348619	+	0.338609i
$148$			1.23677i			0.101662i
$149$	19.3490	−	11.1712i	1.58513	−	0.915178i	0.591042	−	0.806641i	$-0.298717\pi$
$149$	19.3490	−	11.1712i	1.58513	−	0.915178i	0.994092	−	0.108536i	$-0.0346164\pi$
$150$	−2.23278	−	1.28909i	−0.182305	−	0.105254i
$151$	7.44825	−	12.9007i	0.606130	−	1.04985i	−0.385742	−	0.922607i	$-0.626055\pi$
$151$	7.44825	−	12.9007i	0.606130	−	1.04985i	0.991872	−	0.127241i	$-0.0406121\pi$
$152$	−4.11968	−	7.13549i	−0.334150	−	0.578765i
$153$	−10.0677			−0.813922
$154$	0.236181	−	0.364534i	0.0190320	−	0.0293750i
$155$		−	18.7414i		−	1.50535i
$156$	3.03404	+	5.25511i	0.242918	+	0.420746i
$157$	−9.43980	+	16.3502i	−0.753378	+	1.30489i	0.192798	+	0.981238i	$0.438244\pi$
$157$	−9.43980	+	16.3502i	−0.753378	+	1.30489i	−0.946176	+	0.323651i	$0.895090\pi$
$158$	−3.61692	−	2.08823i	−0.287747	−	0.166131i
$159$	−0.391500	−	0.678097i	−0.0310479	−	0.0537766i
$160$	19.3759			1.53180
$161$	11.7137	−	4.87742i	0.923169	−	0.384395i
$162$	−3.50135			−0.275092
$163$	−0.459659	−	0.796153i	−0.0360033	−	0.0623595i	0.847462	−	0.530856i	$-0.178129\pi$
$163$	−0.459659	−	0.796153i	−0.0360033	−	0.0623595i	−0.883466	+	0.468496i	$0.844796\pi$
$164$	−6.04713	−	3.49131i	−0.472202	−	0.272626i
$165$	−0.292652	+	0.506887i	−0.0227829	+	0.0394611i
$166$	3.03565	+	5.25789i	0.235612	+	0.408092i
$167$		−	24.9470i		−	1.93045i	−0.261413	−	0.965227i	$-0.584189\pi$
$167$		−	24.9470i		−	1.93045i	0.261413	−	0.965227i	$-0.415811\pi$
$168$	−1.51706	−	2.96959i	−0.117044	−	0.229109i
$169$	−25.5061			−1.96201
$170$	3.91811	+	6.78637i	0.300506	+	0.520491i
$171$	−5.11148	+	8.85334i	−0.390884	+	0.677032i
$172$	−11.3515	−	6.55377i	−0.865540	−	0.499720i
$173$	−13.5633	+	7.83077i	−1.03120	+	0.595362i	−0.917328	−	0.398133i	$-0.869658\pi$
$173$	−13.5633	+	7.83077i	−1.03120	+	0.595362i	−0.113870	+	0.993496i	$0.536325\pi$
$174$		−	0.909705i		−	0.0689646i
$175$	17.6328	−	9.00795i	1.33291	−	0.680937i
$176$		−	0.581066i		−	0.0437995i
$177$	1.06006	+	1.83607i	0.0796786	+	0.138007i
$178$	−1.63181	+	2.82637i	−0.122309	+	0.211845i
$179$	−1.55169	+	2.68760i	−0.115978	+	0.200881i	−0.918170	−	0.396186i	$-0.870334\pi$
$179$	−1.55169	+	2.68760i	−0.115978	+	0.200881i	0.802192	+	0.597066i	$0.203667\pi$
$180$	−7.77176	−	13.4611i	−0.579273	−	1.00333i
$181$	2.83745			0.210906			0.105453	−	0.994424i	$-0.466371\pi$
$181$	2.83745			0.210906			0.105453	+	0.994424i	$0.466371\pi$
$182$	9.58038	+	0.491880i	0.710145	+	0.0364606i
$183$			6.10438i			0.451249i
$184$	−5.80024	+	8.45371i	−0.427599	+	0.623216i
$185$	−2.28170	−	1.31734i	−0.167754	−	0.0968526i
$186$	0.913665	−	1.58251i	0.0669932	−	0.116036i
$187$	0.923593	−	0.533237i	0.0675398	−	0.0389941i
$188$			10.3631i			0.755807i
$189$	−4.79431	+	7.39980i	−0.348735	+	0.538256i
$190$	7.95710			0.577268
$191$	−19.1005	+	11.0277i	−1.38207	+	0.797937i	−0.992404	−	0.123021i	$-0.960742\pi$
$191$	−19.1005	+	11.0277i	−1.38207	+	0.797937i	−0.389663	+	0.920958i	$0.627408\pi$
$192$	−0.475829	−	0.274720i	−0.0343400	−	0.0198262i
$193$	−6.80995	+	11.7952i	−0.490191	+	0.849035i	−0.999936	−	0.0112899i	$-0.996406\pi$
$193$	−6.80995	+	11.7952i	−0.490191	+	0.849035i	0.509745	+	0.860325i	$0.329740\pi$
$194$	−3.19531	−	5.53443i	−0.229410	−	0.397349i
$195$	−12.9267			−0.925700
$196$	11.5491	+	1.18905i	0.824932	+	0.0849319i
$197$	2.26953			0.161697			0.0808486	−	0.996726i	$-0.474237\pi$
$197$	2.26953			0.161697			0.0808486	+	0.996726i	$0.474237\pi$
$198$	0.377108	−	0.217724i	0.0267999	−	0.0154729i
$199$	−6.03681	+	10.4561i	−0.427938	+	0.741210i	−0.996690	−	0.0812988i	$-0.974093\pi$
$199$	−6.03681	+	10.4561i	−0.427938	+	0.741210i	0.568752	+	0.822509i	$0.307427\pi$
$200$	−7.99926	+	13.8551i	−0.565633	+	0.979705i
$201$	3.30088	+	5.71729i	0.232826	+	0.403266i
$202$			4.27906i			0.301074i
$203$	5.86343	+	3.79890i	0.411532	+	0.266631i
$204$		−	3.71175i		−	0.259874i
$205$	12.8821	−	7.43747i	0.899724	−	0.519456i
$206$	−2.72245	+	4.71542i	−0.189682	+	0.328539i
$207$	12.6820	+	0.988005i	0.881458	+	0.0686711i
$208$	11.1138	−	6.41656i	0.770604	−	0.444909i
$209$		−	1.08292i		−	0.0749074i
$210$	3.21618	+	0.165127i	0.221938	+	0.0113948i
$211$	−15.0034			−1.03287			−0.516437	−	0.856325i	$-0.672742\pi$
$211$	−15.0034			−1.03287			−0.516437	+	0.856325i	$0.672742\pi$
$212$	−1.90758	+	1.10134i	−0.131013	+	0.0756403i
$213$	2.94963	+	1.70297i	0.202105	+	0.116686i
$214$	3.56772	+	2.05982i	0.243884	+	0.140807i
$215$	24.1818	−	13.9613i	1.64918	−	0.952156i
$216$		−	7.12417i		−	0.484738i
$217$	6.38452	+	12.4975i	0.433410	+	0.848385i
$218$		−	9.07684i		−	0.614761i
$219$	2.19736	+	3.80594i	0.148484	+	0.257182i
$220$	1.42594	+	0.823267i	0.0961368	+	0.0555046i
$221$	20.3980	+	11.7768i	1.37212	+	0.792193i
$222$	−0.128443	−	0.222470i	−0.00862055	−	0.0149312i
$223$		−	13.7114i		−	0.918184i	−0.888389	−	0.459092i	$-0.848175\pi$
$223$		−	13.7114i		−	0.918184i	0.888389	−	0.459092i	$-0.151825\pi$
$224$	−12.9206	+	6.60065i	−0.863291	+	0.441025i
$225$	19.8501			1.32334
$226$	1.42457	−	0.822477i	0.0947611	−	0.0547103i
$227$	7.52049	−	13.0259i	0.499153	−	0.864558i	−0.500847	−	0.865536i	$-0.666978\pi$
$227$	7.52049	−	13.0259i	0.499153	−	0.864558i	1.00000		0.000978046i	$0.000311322\pi$
$228$	−3.26405	−	1.88450i	−0.216167	−	0.124804i
$229$	−7.81423	−	13.5346i	−0.516379	−	0.894395i	−0.999819	−	0.0190171i	$-0.993946\pi$
$229$	−7.81423	−	13.5346i	−0.516379	−	0.894395i	0.483440	−	0.875377i	$-0.339387\pi$
$230$	−4.26955	−	8.93312i	−0.281526	−	0.589033i
$231$	0.0224729	−	0.437707i	0.00147861	−	0.0287990i
$232$	−5.64502			−0.370614
$233$	11.2032	+	19.4045i	0.733946	+	1.27123i	0.955184	+	0.296011i	$0.0956567\pi$
$233$	11.2032	+	19.4045i	0.733946	+	1.27123i	−0.221239	+	0.975220i	$0.571010\pi$
$234$	8.32862	+	4.80853i	0.544459	+	0.314344i
$235$	−19.1186	−	11.0382i	−1.24716	−	0.720050i
$236$	5.16510	−	2.98207i	0.336219	−	0.194116i
$237$	−4.21421			−0.273742
$238$	−4.92461	−	3.19065i	−0.319215	−	0.206819i
$239$	6.47497			0.418831			0.209416	−	0.977827i	$-0.432844\pi$
$239$	6.47497			0.418831			0.209416	+	0.977827i	$0.432844\pi$
$240$	3.73096	−	2.15407i	0.240833	−	0.139045i
$241$	0.289704	−	0.501783i	0.0186615	−	0.0323227i	−0.856544	−	0.516074i	$-0.827393\pi$
$241$	0.289704	−	0.501783i	0.0186615	−	0.0323227i	0.875205	+	0.483752i	$0.160726\pi$
$242$	3.19062	−	5.52632i	0.205101	−	0.355245i
$243$	−11.7179	+	6.76536i	−0.751707	+	0.433998i
$244$	17.1724			1.09935
$245$	−14.4950	+	20.0401i	−0.926051	+	1.28031i
$246$	1.45034			0.0924703
$247$	20.7126	−	11.9584i	1.31791	−	0.760897i
$248$	−9.82003	−	5.66960i	−0.623572	−	0.360020i
$249$	5.30542	+	3.06308i	0.336217	+	0.194115i
$250$	−2.56397	−	4.44092i	−0.162160	−	0.280869i
$251$	−2.46315			−0.155473			−0.0777364	−	0.996974i	$-0.524769\pi$
$251$	−2.46315			−0.155473			−0.0777364	+	0.996974i	$0.524769\pi$
$252$	9.76820	+	6.32880i	0.615339	+	0.398677i
$253$	−1.21576	+	0.581066i	−0.0764339	+	0.0365313i
$254$	1.92365	+	3.33186i	0.120700	+	0.209059i
$255$	6.84771	+	3.95353i	0.428820	+	0.247579i
$256$	2.43143	−	4.21136i	0.151965	−	0.263210i
$257$	17.1355	−	9.89317i	1.06888	−	0.617119i	0.141006	−	0.990009i	$-0.454966\pi$
$257$	17.1355	−	9.89317i	1.06888	−	0.617119i	0.927876	+	0.372890i	$0.121633\pi$
$258$	2.72252			0.169497
$259$	1.97029	+	0.101159i	0.122428	+	0.00628574i
$260$			36.3645i			2.25523i
$261$	3.50202	+	6.06568i	0.216770	+	0.375456i
$262$	−4.00053	−	2.30971i	−0.247154	−	0.142694i
$263$	−19.8299	−	11.4488i	−1.22276	−	0.705962i	−0.257256	−	0.966343i	$-0.582818\pi$
$263$	−19.8299	−	11.4488i	−1.22276	−	0.705962i	−0.965506	+	0.260381i	$0.916152\pi$
$264$	0.177064	+	0.306684i	0.0108975	+	0.0188751i
$265$		−	4.69232i		−	0.288247i
$266$	−5.30609	+	2.71069i	−0.325337	+	0.166203i
$267$			3.29311i			0.201535i
$268$	16.0835	−	9.28580i	0.982454	−	0.567220i
$269$	13.6840	+	7.90043i	0.834325	+	0.481698i	0.855331	−	0.518081i	$-0.173354\pi$
$269$	13.6840	+	7.90043i	0.834325	+	0.481698i	−0.0210061	+	0.999779i	$0.506687\pi$
$270$	5.95835	+	3.44005i	0.362613	+	0.209355i
$271$	−12.5545	+	7.24833i	−0.762630	+	0.440305i	−0.830239	−	0.557407i	$-0.811796\pi$
$271$	−12.5545	+	7.24833i	−0.762630	+	0.440305i	0.0676092	+	0.997712i	$0.478463\pi$
$272$	−7.84981			−0.475965
$273$	8.62001	−	4.40366i	0.521707	−	0.266521i
$274$			12.3575i			0.746544i
$275$	−1.82102	+	1.05137i	−0.109812	+	0.0633997i
$276$	−0.364258	+	4.67559i	−0.0219257	+	0.281437i
$277$	11.6668	−	20.2076i	0.700993	−	1.21416i	−0.267126	−	0.963662i	$-0.586074\pi$
$277$	11.6668	−	20.2076i	0.700993	−	1.21416i	0.968118	−	0.250493i	$-0.0805928\pi$
$278$	−0.0387657	+	0.0223814i	−0.00232501	+	0.00134235i
$279$			14.0691i			0.842292i
$280$	1.02467	−	19.9575i	0.0612355	−	1.19269i
$281$		−	16.7022i		−	0.996371i	−0.867070	−	0.498185i	$-0.834000\pi$
$281$		−	16.7022i		−	0.996371i	0.867070	−	0.498185i	$-0.166000\pi$
$282$	−1.07624	−	1.86411i	−0.0640894	−	0.111006i
$283$	−6.10516	+	10.5744i	−0.362914	+	0.628585i	−0.988439	−	0.151619i	$-0.951551\pi$
$283$	−6.10516	+	10.5744i	−0.362914	+	0.628585i	0.625525	+	0.780204i	$0.284885\pi$
$284$	4.79067	−	8.29769i	0.284274	−	0.492377i
$285$	6.95333	−	4.01451i	0.411880	−	0.237799i
$286$	−1.01874			−0.0602394
$287$	−6.05658	+	9.34804i	−0.357508	+	0.551797i
$288$	−14.5453			−0.857091
$289$	1.29633	+	2.24531i	0.0762547	+	0.132077i
$290$	2.72582	−	4.72126i	0.160066	−	0.277242i
$291$	−5.58445	−	3.22419i	−0.327367	−	0.189005i
$292$	10.7066	−	6.18146i	0.626557	−	0.361743i
$293$	−12.6527			−0.739177			−0.369588	−	0.929196i	$-0.620501\pi$
$293$	−12.6527			−0.739177			−0.369588	+	0.929196i	$0.620501\pi$
$294$	−2.20092	+	0.985524i	−0.128360	+	0.0574769i
$295$			12.7053i			0.739731i
$296$	−1.38050	+	0.797033i	−0.0802400	+	0.0463266i
$297$	0.468175	−	0.810903i	0.0271663	−	0.0470533i
$298$	11.3058	+	6.52738i	0.654925	+	0.378121i
$299$	−24.5391	−	16.8367i	−1.41913	−	0.973691i
$300$			7.31833i			0.422524i
$301$	−11.3692	+	17.5478i	−0.655309	+	1.01144i
$302$	8.70412			0.500866
$303$	2.15887	+	3.73927i	0.124024	+	0.214815i
$304$	−3.98545	+	6.90300i	−0.228581	+	0.395914i
$305$	−18.2910	+	31.6810i	−1.04734	+	1.81405i
$306$	−2.94130	−	5.09448i	−0.168143	−	0.291232i
$307$			1.54074i			0.0879346i	0.999033	+	0.0439673i	$0.0139997\pi$
$307$			1.54074i			0.0879346i	−0.999033	+	0.0439673i	$0.986000\pi$
$308$	−1.23133	−	0.0632193i	−0.0701614	−	0.00360225i
$309$			5.49411i			0.312549i
$310$	9.48361	−	5.47537i	0.538633	−	0.310980i
$311$	5.04116	+	2.91051i	0.285858	+	0.165040i	0.636072	−	0.771629i	$-0.280558\pi$
$311$	5.04116	+	2.91051i	0.285858	+	0.165040i	−0.350215	+	0.936670i	$0.613891\pi$
$312$	−3.91054	+	6.77326i	−0.221391	+	0.383460i
$313$	−8.37312	−	14.5027i	−0.473277	−	0.819740i	0.526255	−	0.850327i	$-0.323596\pi$
$313$	−8.37312	−	14.5027i	−0.473277	−	0.819740i	−0.999532	+	0.0305870i	$0.990262\pi$
$314$	−11.0315			−0.622542
$315$	−22.0803	+	11.2801i	−1.24409	+	0.635560i
$316$			11.8551i			0.666902i
$317$	−5.79067	−	10.0297i	−0.325236	−	0.563326i	0.656324	−	0.754479i	$-0.272110\pi$
$317$	−5.79067	−	10.0297i	−0.325236	−	0.563326i	−0.981560	+	0.191154i	$0.938777\pi$
$318$	0.228756	−	0.396216i	0.0128280	−	0.0222187i
$319$	−0.642541	−	0.370971i	−0.0359754	−	0.0207704i
$320$	−1.64633	−	2.85152i	−0.0920325	−	0.159405i
$321$	4.15688			0.232015
$322$	5.89029	+	4.50246i	0.328253	+	0.250912i
$323$	−14.6296			−0.814011
$324$	4.96938	+	8.60723i	0.276077	+	0.478179i
$325$	−40.2181	−	23.2199i	−2.23090	−	1.28801i
$326$	0.268582	−	0.465197i	0.0148754	−	0.0257649i
$327$	−4.57944	−	7.93183i	−0.253244	−	0.438631i
$328$		−	8.99984i		−	0.496933i
$329$	16.5093	+	0.847629i	0.910189	+	0.0467313i
$330$	−0.341996			−0.0188263
$331$	−12.3025	−	21.3086i	−0.676208	−	1.17123i	−0.976114	−	0.217258i	$-0.930289\pi$
$331$	−12.3025	−	21.3086i	−0.676208	−	1.17123i	0.299906	−	0.953969i	$-0.403045\pi$
$332$	8.61685	−	14.9248i	0.472911	−	0.819106i
$333$	1.71285	+	0.988916i	0.0938637	+	0.0541923i
$334$	12.6238	−	7.28833i	0.690742	−	0.398800i
$335$			39.5627i			2.16154i
$336$	−1.75413	+	2.70742i	−0.0956957	+	0.147702i
$337$		−	28.2320i		−	1.53789i	−0.639312	−	0.768947i	$-0.720781\pi$
$337$		−	28.2320i		−	1.53789i	0.639312	−	0.768947i	$-0.279219\pi$
$338$	−7.45170	−	12.9067i	−0.405319	−	0.702033i
$339$	0.829911	−	1.43745i	0.0450746	−	0.0780714i
$340$	11.1218	−	19.2635i	0.603163	−	1.04471i
$341$	−0.745171	−	1.29067i	−0.0403533	−	0.0698940i
$342$	−5.97334			−0.323001
$343$	2.83889	−	18.3014i	0.153285	−	0.988182i
$344$		−	16.8942i		−	0.910872i
$345$	−8.23789	−	5.65216i	−0.443513	−	0.304302i
$346$	−7.92512	−	4.57557i	−0.426057	−	0.245984i
$347$	−5.09946	+	8.83253i	−0.273754	+	0.474155i	−0.969820	−	0.243822i	$-0.921599\pi$
$347$	−5.09946	+	8.83253i	−0.273754	+	0.474155i	0.696066	+	0.717977i	$0.254932\pi$
$348$	−2.23629	+	1.29112i	−0.119878	+	0.0692115i
$349$			0.948313i			0.0507620i	0.999678	+	0.0253810i	$0.00807990\pi$
$349$			0.948313i			0.0507620i	−0.999678	+	0.0253810i	$0.991920\pi$
$350$	9.70971	+	6.29090i	0.519006	+	0.336263i
$351$	20.6797			1.10380
$352$	1.33437	−	0.770397i	0.0711220	−	0.0410623i
$353$	9.51292	+	5.49229i	0.506322	+	0.292325i	0.731320	−	0.682034i	$-0.238904\pi$
$353$	9.51292	+	5.49229i	0.506322	+	0.292325i	−0.224999	+	0.974359i	$0.572238\pi$
$354$	−0.619397	+	1.07283i	−0.0329206	+	0.0570201i
$355$	10.2055	+	17.6764i	0.541650	+	0.938166i
$356$	9.26394			0.490988
$357$	−5.91313	−	0.303595i	−0.312956	−	0.0160679i
$358$	−1.81332			−0.0958369
$359$	9.17457	−	5.29694i	0.484216	−	0.279562i	−0.237956	−	0.971276i	$-0.576477\pi$
$359$	9.17457	−	5.29694i	0.484216	−	0.279562i	0.722172	+	0.691714i	$0.243144\pi$
$360$	10.0169	−	17.3499i	0.527939	−	0.914418i
$361$	2.07239	−	3.58948i	0.109073	−	0.188920i
$362$	0.828969	+	1.43582i	0.0435696	+	0.0754648i
$363$		−	6.43892i		−	0.337956i
$364$	−12.3881	−	24.2492i	−0.649311	−	1.27100i
$365$			26.3365i			1.37851i
$366$	−3.08896	+	1.78341i	−0.161463	+	0.0932205i
$367$	−5.76982	+	9.99363i	−0.301182	+	0.521663i	−0.976404	−	0.215952i	$-0.930715\pi$
$367$	−5.76982	+	9.99363i	−0.301182	+	0.521663i	0.675222	+	0.737615i	$0.264048\pi$
$368$	9.88820	+	0.770353i	0.515458	+	0.0401574i
$369$	−9.67049	+	5.58326i	−0.503425	+	0.290653i
$370$		−	1.53946i		−	0.0800326i
$371$	1.59850	+	3.12901i	0.0829901	+	0.162450i
$372$	−5.18698			−0.268932
$373$	10.1491	−	5.85959i	0.525501	−	0.303398i	−0.213681	−	0.976903i	$-0.568545\pi$
$373$	10.1491	−	5.85959i	0.525501	−	0.303398i	0.739182	+	0.673505i	$0.235212\pi$
$374$	0.539661	+	0.311573i	0.0279052	+	0.0161111i
$375$	−4.48106	−	2.58714i	−0.231401	−	0.133599i
$376$	−11.5674	+	6.67845i	−0.596544	+	0.344415i
$377$		−	16.3861i		−	0.843930i
$378$	−5.14515	−	0.264164i	−0.264638	−	0.0135872i
$379$			14.9631i			0.768602i	0.923208	+	0.384301i	$0.125557\pi$
$379$			14.9631i			0.768602i	−0.923208	+	0.384301i	$0.874443\pi$
$380$	−11.2933	−	19.5606i	−0.579336	−	1.00344i
$381$	3.36197	+	1.94103i	0.172239	+	0.0994422i
$382$	−11.1606	−	6.44356i	−0.571024	−	0.329681i
$383$	13.2712	+	22.9864i	0.678126	+	1.17455i	0.975545	+	0.219801i	$0.0705408\pi$
$383$	13.2712	+	22.9864i	0.678126	+	1.17455i	−0.297419	+	0.954747i	$0.596126\pi$
$384$		−	6.78747i		−	0.346372i
$385$	1.42817	−	2.20431i	0.0727861	−	0.112342i
$386$	−7.95819			−0.405061
$387$	−18.1531	+	10.4807i	−0.922773	+	0.532763i
$388$	−9.07005	+	15.7098i	−0.460462	+	0.797544i
$389$	−9.90203	−	5.71694i	−0.502053	−	0.289860i	0.227508	−	0.973776i	$-0.426942\pi$
$389$	−9.90203	−	5.71694i	−0.502053	−	0.289860i	−0.729561	+	0.683916i	$0.760275\pi$
$390$	−3.77658	−	6.54122i	−0.191234	−	0.331228i
$391$	7.84981	+	16.4240i	0.396982	+	0.830600i
$392$	6.11550	+	13.6575i	0.308879	+	0.689806i
$393$	−4.66117			−0.235125
$394$	0.663050	+	1.14844i	0.0334040	+	0.0578574i
$395$	−21.8712	−	12.6273i	−1.10046	−	0.635351i
$396$	−1.07044	−	0.618020i	−0.0537918	−	0.0310567i
$397$	−10.6091	+	6.12515i	−0.532454	+	0.307412i	−0.742015	−	0.670383i	$-0.766130\pi$
$397$	−10.6091	+	6.12515i	−0.532454	+	0.307412i	0.209561	+	0.977796i	$0.432796\pi$
$398$	−7.05469			−0.353620
$399$	−3.26915	+	5.04577i	−0.163662	+	0.252605i
$400$	15.4772			0.773861
$401$	−7.39823	+	4.27137i	−0.369450	+	0.213302i	−0.673218	−	0.739444i	$-0.735089\pi$
$401$	−7.39823	+	4.27137i	−0.369450	+	0.213302i	0.303768	+	0.952746i	$0.401755\pi$
$402$	−1.92872	+	3.34065i	−0.0961960	+	0.166616i
$403$	16.4575	−	28.5052i	0.819805	−	1.41994i
$404$	10.5190	−	6.07318i	0.523342	−	0.302152i
$405$	−21.1724			−1.05206
$406$	−0.209318	+	4.07690i	−0.0103883	+	0.202333i
$407$	−0.209513			−0.0103852
$408$	4.14309	−	2.39202i	0.205114	−	0.118422i
$409$	−24.2320	−	13.9904i	−1.19820	−	0.691780i	−0.238044	−	0.971254i	$-0.576506\pi$
$409$	−24.2320	−	13.9904i	−1.19820	−	0.691780i	−0.960153	+	0.279475i	$0.909840\pi$
$410$	7.52708	+	4.34576i	0.371736	+	0.214622i
$411$	6.23460	+	10.7986i	0.307530	+	0.532657i
$412$	15.4556			0.761445
$413$	−4.32823	−	8.47237i	−0.212978	−	0.416898i
$414$	3.20512	+	6.70603i	0.157523	+	0.329583i
$415$	18.3563	+	31.7940i	0.901075	+	1.56071i
$416$	29.4701	+	17.0146i	1.44489	+	0.834209i
$417$	−0.0225837	+	0.0391161i	−0.00110593	+	0.00191552i
$418$	0.547985	−	0.316379i	0.0268028	−	0.0154746i
$419$	15.6695			0.765503			0.382751	−	0.923851i	$-0.374977\pi$
$419$	15.6695			0.765503			0.382751	+	0.923851i	$0.374977\pi$
$420$	−4.15873	−	8.14058i	−0.202925	−	0.397220i
$421$		−	34.7278i		−	1.69253i	−0.532764	−	0.846264i	$-0.678847\pi$
$421$		−	34.7278i		−	1.69253i	0.532764	−	0.846264i	$-0.321153\pi$
$422$	−4.38328	−	7.59207i	−0.213375	−	0.369576i
$423$	14.3522	+	8.28627i	0.697829	+	0.402892i
$424$	−2.45865	−	1.41950i	−0.119403	−	0.0689372i
$425$	14.2032	+	24.6007i	0.688959	+	1.19331i
$426$			1.99011i			0.0964212i
$427$	1.40458	−	27.3571i	0.0679725	−	1.32390i
$428$		−	11.6938i		−	0.565244i
$429$	−0.890229	+	0.513974i	−0.0429807	+	0.0248149i
$430$	14.1296	+	8.15770i	0.681388	+	0.393399i
$431$	−7.12545	−	4.11388i	−0.343221	−	0.198159i	0.318475	−	0.947931i	$-0.396829\pi$
$431$	−7.12545	−	4.11388i	−0.343221	−	0.198159i	−0.661695	+	0.749773i	$0.730163\pi$
$432$	−5.96868	+	3.44602i	−0.287168	+	0.165797i
$433$	−0.384659			−0.0184855			−0.00924276	−	0.999957i	$-0.502942\pi$
$433$	−0.384659			−0.0184855			−0.00924276	+	0.999957i	$0.502942\pi$
$434$	−4.45877	+	6.88190i	−0.214028	+	0.330342i
$435$		−	5.50091i		−	0.263749i
$436$	−22.3133	+	12.8826i	−1.06861	+	0.616963i
$437$	18.4285	+	1.43569i	0.881554	+	0.0686786i
$438$	−1.28393	+	2.22383i	−0.0613486	+	0.106259i
$439$	−4.20458	+	2.42751i	−0.200673	+	0.115859i	−0.596970	−	0.802264i	$-0.703629\pi$
$439$	−4.20458	+	2.42751i	−0.200673	+	0.115859i	0.396296	+	0.918123i	$0.370295\pi$
$440$			2.12220i			0.101172i
$441$	10.8813	−	15.0439i	0.518157	−	0.716378i
$442$			13.7625i			0.654616i
$443$	15.5716	+	26.9707i	0.739827	+	1.28142i	0.952573	+	0.304310i	$0.0984260\pi$
$443$	15.5716	+	26.9707i	0.739827	+	1.28142i	−0.212746	+	0.977108i	$0.568241\pi$
$444$	−0.364593	+	0.631494i	−0.0173028	+	0.0299694i
$445$	−9.86739	+	17.0908i	−0.467759	+	0.810183i
$446$	6.93830	−	4.00583i	0.328538	−	0.189682i
$447$	13.1728			0.623050
$448$	2.06924	+	1.34066i	0.0977625	+	0.0633402i
$449$	−15.2127			−0.717931			−0.358965	−	0.933351i	$-0.616870\pi$
$449$	−15.2127			−0.717931			−0.358965	+	0.933351i	$0.616870\pi$
$450$	5.79927	+	10.0446i	0.273380	+	0.473508i
$451$	0.591438	−	1.02440i	0.0278497	−	0.0482371i
$452$	−4.04373	−	2.33465i	−0.190201	−	0.109813i
$453$	7.60612	−	4.39139i	0.357367	−	0.206326i
$454$	8.78854			0.412467
$455$	57.9318	+	2.97436i	2.71588	+	0.139440i
$456$		−	4.85782i		−	0.227488i
$457$	7.23129	−	4.17499i	0.338265	−	0.195298i	−0.321239	−	0.946998i	$-0.604099\pi$
$457$	7.23129	−	4.17499i	0.338265	−	0.195298i	0.659505	+	0.751700i	$0.270766\pi$
$458$	4.56590	−	7.90838i	0.213351	−	0.369534i
$459$	−10.9548	−	6.32473i	−0.511324	−	0.295213i
$460$	−15.9003	+	23.1743i	−0.741354	+	1.08051i
$461$		−	3.94962i		−	0.183952i	−0.995761	−	0.0919762i	$-0.970682\pi$
$461$		−	3.94962i		−	0.183952i	0.995761	−	0.0919762i	$-0.0293184\pi$
$462$	0.228056	−	0.116506i	0.0106101	−	0.00542033i
$463$	24.9864			1.16121			0.580607	−	0.814184i	$-0.302815\pi$
$463$	24.9864			1.16121			0.580607	+	0.814184i	$0.302815\pi$
$464$	2.73054	+	4.72944i	0.126762	+	0.219559i
$465$	5.52486	−	9.56933i	0.256209	−	0.443767i
$466$	−6.54610	+	11.3382i	−0.303242	+	0.525231i
$467$	−1.91655	−	3.31957i	−0.0886876	−	0.153611i	0.818269	−	0.574835i	$-0.194934\pi$
$467$	−1.91655	−	3.31957i	−0.0886876	−	0.153611i	−0.906957	+	0.421224i	$0.861601\pi$
$468$		−	27.2986i		−	1.26188i
$469$	−13.4776	−	26.3819i	−0.622336	−	1.21820i
$470$		−	12.8993i		−	0.595002i
$471$	−9.63989	+	5.56559i	−0.444183	+	0.256449i
$472$	6.65725	+	3.84356i	0.306425	+	0.176914i
$473$	1.11022	−	1.92297i	0.0510482	−	0.0884180i
$474$	−1.23119	−	2.13249i	−0.0565506	−	0.0979485i
$475$	28.8447			1.32348
$476$	−0.854051	+	16.6344i	−0.0391454	+	0.762437i
$477$			3.52249i			0.161284i
$478$	1.89168	+	3.27649i	0.0865236	+	0.149863i
$479$	0.302877	−	0.524598i	0.0138388	−	0.0239695i	−0.859023	−	0.511937i	$-0.828928\pi$
$479$	0.302877	−	0.524598i	0.0138388	−	0.0239695i	0.872862	+	0.487967i	$0.162262\pi$
$480$	9.89327	+	5.71188i	0.451564	+	0.260711i
$481$	−2.31360	−	4.00727i	−0.105491	−	0.182716i
$482$	0.338552			0.0154206
$483$	7.41882	+	0.962724i	0.337568	+	0.0438054i
$484$	−18.1135			−0.823342
$485$	−19.3217	−	33.4662i	−0.877355	−	1.51962i
$486$	−6.84687	−	3.95304i	−0.310580	−	0.179314i
$487$	−10.1203	+	17.5288i	−0.458594	+	0.794308i	−0.998887	−	0.0471690i	$-0.984980\pi$
$487$	−10.1203	+	17.5288i	−0.458594	+	0.794308i	0.540293	+	0.841477i	$0.318313\pi$
$488$	11.0667	+	19.1680i	0.500965	+	0.867697i
$489$		−	0.542019i		−	0.0245109i
$490$	−14.3755	−	1.48005i	−0.649420	−	0.0668618i
$491$	9.16948			0.413813			0.206906	−	0.978361i	$-0.433660\pi$
$491$	9.16948			0.413813			0.206906	+	0.978361i	$0.433660\pi$
$492$	−2.05844	−	3.56531i	−0.0928014	−	0.160737i
$493$	−5.01157	+	8.68029i	−0.225710	+	0.390941i
$494$	12.1025	+	6.98739i	0.544518	+	0.314378i
$495$	2.28034	−	1.31656i	0.102494	−	0.0591748i
$496$			10.9697i			0.492555i
$497$	−12.8271	−	8.31065i	−0.575374	−	0.372784i
$498$			3.57956i			0.160404i
$499$	−1.18533	−	2.05305i	−0.0530626	−	0.0919071i	0.838274	−	0.545249i	$-0.183565\pi$
$499$	−1.18533	−	2.05305i	−0.0530626	−	0.0919071i	−0.891337	+	0.453342i	$0.850232\pi$
$500$	−7.27797	+	12.6058i	−0.325481	+	0.563749i
$501$	7.35421	−	12.7379i	0.328562	−	0.569086i
$502$	−0.719618	−	1.24641i	−0.0321181	−	0.0556302i
$503$	−28.6649			−1.27811			−0.639053	−	0.769163i	$-0.720673\pi$
$503$	−28.6649			−1.27811			−0.639053	+	0.769163i	$0.720673\pi$
$504$	−0.769209	+	14.9819i	−0.0342633	+	0.667349i
$505$			25.8751i			1.15143i
$506$	−0.649220	−	0.445441i	−0.0288614	−	0.0198023i
$507$	−13.0234	−	7.51905i	−0.578389	−	0.333933i
$508$	5.46038	−	9.45766i	0.242265	−	0.419616i
$509$	13.1115	−	7.56991i	0.581156	−	0.335530i	−0.180437	−	0.983587i	$-0.557751\pi$
$509$	13.1115	−	7.56991i	0.581156	−	0.335530i	0.761593	+	0.648056i	$0.224418\pi$
$510$			4.62014i			0.204583i
$511$	−8.97188	−	17.5621i	−0.396892	−	0.776903i
$512$	−20.1831			−0.891975
$513$	−11.1237	+	6.42229i	−0.491125	+	0.283551i
$514$	10.0124	+	5.78064i	0.441627	+	0.254973i
$515$	−16.4624	+	28.5137i	−0.725420	+	1.25647i
$516$	−3.86402	−	6.69268i	−0.170104	−	0.294629i
$517$	−1.75554			−0.0772084
$518$	0.524437	+	1.02657i	0.0230424	+	0.0451048i
$519$	−9.23385			−0.405321
$520$	−40.5905	+	23.4349i	−1.78001	+	1.02769i
$521$	−0.362192	+	0.627335i	−0.0158679	+	0.0274840i	−0.873850	−	0.486195i	$-0.838384\pi$
$521$	−0.362192	+	0.627335i	−0.0158679	+	0.0274840i	0.857982	+	0.513679i	$0.171718\pi$
$522$	−2.04625	+	3.54421i	−0.0895621	+	0.155126i
$523$	11.7780	+	20.4000i	0.515014	+	0.892030i	0.999848	+	0.0174243i	$0.00554661\pi$
$523$	11.7780	+	20.4000i	0.515014	+	0.892030i	−0.484834	+	0.874606i	$0.661120\pi$
$524$			13.1125i			0.572821i
$525$	11.6587	+	0.598588i	0.508829	+	0.0261245i
$526$		−	13.3792i		−	0.583360i
$527$	−17.4362	+	10.0668i	−0.759531	+	0.438515i
$528$	0.171295	−	0.296691i	0.00745464	−	0.0129118i
$529$	−8.27640	−	21.4593i	−0.359844	−	0.933013i
$530$	2.37443	−	1.37088i	0.103138	−	0.0595470i
$531$		−	9.53777i		−	0.413904i
$532$	14.1944	+	9.19653i	0.615406	+	0.398720i
$533$	26.1244			1.13157
$534$	−1.66639	+	0.962092i	−0.0721119	+	0.0416338i
$535$	21.5737	+	12.4556i	0.932712	+	0.538502i
$536$	20.7298	+	11.9684i	0.895392	+	0.516955i
$537$	−1.58457	+	0.914855i	−0.0683794	+	0.0394789i
$538$			9.23255i			0.398043i
$539$	−0.201428	+	1.95644i	−0.00867610	+	0.0842698i
$540$		−	19.5296i		−	0.840419i
$541$	9.79429	+	16.9642i	0.421089	+	0.729348i	0.996046	−	0.0888356i	$-0.0283146\pi$
$541$	9.79429	+	16.9642i	0.421089	+	0.729348i	−0.574957	+	0.818184i	$0.694981\pi$
$542$	−7.33566	−	4.23524i	−0.315094	−	0.181919i
$543$	1.44879	+	0.836461i	0.0621737	+	0.0358960i
$544$	−10.4075	−	18.0264i	−0.446220	−	0.772876i
$545$		−	54.8869i		−	2.35110i
$546$	4.74672	+	3.07539i	0.203141	+	0.131615i
$547$	−5.60011			−0.239443			−0.119722	−	0.992808i	$-0.538200\pi$
$547$	−5.60011			−0.239443			−0.119722	+	0.992808i	$0.538200\pi$
$548$	30.3780	−	17.5387i	1.29768	−	0.749217i
$549$	13.7309	−	23.7827i	0.586022	−	1.01502i
$550$	−1.06403	−	0.614320i	−0.0453705	−	0.0261947i
$551$	5.08887	+	8.81418i	0.216793	+	0.375497i
$552$	−5.45369	+	2.60657i	−0.232124	+	0.110943i
$553$	18.8862	+	0.969664i	0.803123	+	0.0412343i
$554$	13.6340			0.579254
$555$	−0.776686	−	1.34526i	−0.0329685	−	0.0571031i
$556$	0.110039	+	0.0635308i	0.00466667	+	0.00269431i
$557$	20.2139	+	11.6705i	0.856491	+	0.494495i	0.862836	−	0.505485i	$-0.168686\pi$
$557$	20.2139	+	11.6705i	0.856491	+	0.494495i	−0.00634468	+	0.999980i	$0.502020\pi$
$558$	−7.11928	+	4.11032i	−0.301383	+	0.174004i
$559$	49.0397			2.07416
$560$	−17.2162	+	8.79513i	−0.727516	+	0.371662i
$561$	0.628779			0.0265471
$562$	8.45173	−	4.87961i	0.356515	−	0.205834i
$563$	−5.20010	+	9.00684i	−0.219158	+	0.379593i	−0.954551	−	0.298048i	$-0.903664\pi$
$563$	−5.20010	+	9.00684i	−0.219158	+	0.379593i	0.735393	+	0.677641i	$0.236998\pi$
$564$	−3.05498	+	5.29138i	−0.128638	+	0.222807i
$565$	8.61427	−	4.97345i	0.362405	−	0.209235i
$566$	−7.13456			−0.299888
$567$	14.1185	−	7.21265i	0.592922	−	0.302903i
$568$	12.3493			0.518165
$569$	−14.4040	+	8.31613i	−0.603845	+	0.348630i	−0.770553	−	0.637376i	$-0.780020\pi$
$569$	−14.4040	+	8.31613i	−0.603845	+	0.348630i	0.166707	+	0.986006i	$0.446686\pi$
$570$	4.06288	+	2.34570i	0.170175	+	0.0982507i
$571$	−10.5156	−	6.07117i	−0.440063	−	0.254071i	0.263561	−	0.964643i	$-0.415103\pi$
$571$	−10.5156	−	6.07117i	−0.440063	−	0.254071i	−0.703625	+	0.710572i	$0.748436\pi$
$572$	1.44588	+	2.50433i	0.0604551	+	0.104711i
$573$	−13.0036			−0.543233
$574$	−6.49978	−	0.333715i	−0.271296	−	0.0139290i
$575$	−15.4772	−	32.3828i	−0.645445	−	1.35045i
$576$	1.23589	+	2.14062i	0.0514953	+	0.0891924i
$577$	0.139215	+	0.0803758i	0.00579560	+	0.00334609i	0.502895	−	0.864348i	$-0.332268\pi$
$577$	0.139215	+	0.0803758i	0.00579560	+	0.00334609i	−0.497099	+	0.867694i	$0.665602\pi$
$578$	−0.757454	+	1.31195i	−0.0315059	+	0.0545699i
$579$	−6.95429	+	4.01506i	−0.289010	+	0.166860i
$580$	−15.4748			−0.642555
$581$	−23.0717	−	14.9481i	−0.957177	−	0.620153i
$582$		−	3.76782i		−	0.156181i
$583$	−0.186570	−	0.323148i	−0.00772693	−	0.0133834i
$584$	13.7996	+	7.96722i	0.571033	+	0.329686i
$585$	50.3625	+	29.0768i	2.08223	+	1.20218i
$586$	−3.69652	−	6.40255i	−0.152702	−	0.264487i
$587$			36.0106i			1.48632i	0.669116	+	0.743158i	$0.266673\pi$
$587$			36.0106i			1.48632i	−0.669116	+	0.743158i	$0.733327\pi$
$588$	5.54640	+	4.01171i	0.228730	+	0.165440i
$589$			20.4441i			0.842384i
$590$	−6.42918	+	3.71189i	−0.264685	+	0.152816i
$591$	1.15882	+	0.669043i	0.0476673	+	0.0275207i
$592$	1.33552	+	0.771063i	0.0548896	+	0.0316905i
$593$	−31.3636	+	18.1078i	−1.28795	+	0.743599i	−0.978288	−	0.207248i	$-0.933549\pi$
$593$	−31.3636	+	18.1078i	−1.28795	+	0.743599i	−0.309662	+	0.950847i	$0.600216\pi$
$594$	0.547115			0.0224484
$595$	−29.7787	−	19.2936i	−1.22081	−	0.790960i
$596$		−	37.0567i		−	1.51790i
$597$	−6.16476	+	3.55923i	−0.252307	+	0.145669i
$598$	1.35060	−	17.3363i	0.0552303	−	0.708933i
$599$	11.7727	−	20.3909i	0.481018	−	0.833148i	−0.518745	−	0.854929i	$-0.673600\pi$
$599$	11.7727	−	20.3909i	0.481018	−	0.833148i	0.999763	+	0.0217813i	$0.00693376\pi$
$600$	−8.16881	+	4.71626i	−0.333490	+	0.192541i
$601$		−	0.940529i		−	0.0383650i	−0.999816	−	0.0191825i	$-0.993894\pi$
$601$		−	0.940529i		−	0.0383650i	0.999816	−	0.0191825i	$-0.00610635\pi$
$602$	−12.2012	−	0.626437i	−0.497282	−	0.0255317i
$603$		−	29.6994i		−	1.20945i
$604$	−12.3536	−	21.3970i	−0.502659	−	0.870631i
$605$	19.2934	−	33.4172i	0.784389	−	1.35860i
$606$	−1.26144	+	2.18488i	−0.0512425	+	0.0887546i
$607$	−6.52117	+	3.76500i	−0.264686	+	0.152816i	−0.626470	−	0.779445i	$-0.715501\pi$
$607$	−6.52117	+	3.76500i	−0.264686	+	0.152816i	0.361784	+	0.932262i	$0.382168\pi$
$608$	−21.1362			−0.857185
$609$	1.87396	+	3.66821i	0.0759367	+	0.148644i
$610$	−21.3751			−0.865453
$611$	−19.3859	−	33.5774i	−0.784271	−	1.35840i
$612$	−8.34904	+	14.4610i	−0.337490	+	0.584550i
$613$	23.3598	+	13.4868i	0.943495	+	0.544727i	0.891054	−	0.453897i	$-0.149967\pi$
$613$	23.3598	+	13.4868i	0.943495	+	0.544727i	0.0524409	+	0.998624i	$0.483300\pi$
$614$	−0.779651	+	0.450132i	−0.0314642	+	0.0181658i
$615$	8.77008			0.353644
$616$	−0.722956	−	1.41516i	−0.0291287	−	0.0570185i
$617$		−	9.25381i		−	0.372544i	−0.982498	−	0.186272i	$-0.940359\pi$
$617$		−	9.25381i		−	0.372544i	0.982498	−	0.186272i	$-0.0596406\pi$
$618$	−2.78015	+	1.60512i	−0.111834	+	0.0645674i
$619$	−15.7588	+	27.2950i	−0.633399	+	1.09708i	0.353453	+	0.935452i	$0.385007\pi$
$619$	−15.7588	+	27.2950i	−0.633399	+	1.09708i	−0.986852	+	0.161627i	$0.948326\pi$
$620$	−26.9198	−	15.5421i	−1.08112	−	0.624187i
$621$	13.1787	+	9.04216i	0.528844	+	0.362849i
$622$			3.40126i			0.136378i
$623$	0.757725	−	14.7583i	0.0303576	−	0.591277i
$624$	7.56625			0.302892
$625$	3.20556	+	5.55219i	0.128222	+	0.222088i
$626$	4.89247	−	8.47400i	0.195542	−	0.338689i
$627$	0.319239	−	0.552938i	0.0127492	−	0.0220822i
$628$	15.6567	+	27.1183i	0.624772	+	1.08214i
$629$			2.83038i			0.112855i
$630$	−12.1588	−	7.87768i	−0.484419	−	0.313854i
$631$			14.2570i			0.567562i	0.958889	+	0.283781i	$0.0915889\pi$
$631$			14.2570i			0.567562i	−0.958889	+	0.283781i	$0.908411\pi$
$632$	−13.2328	+	7.63996i	−0.526373	+	0.303901i
$633$	−7.66069	−	4.42290i	−0.304485	−	0.175795i
$634$	3.38352	−	5.86043i	0.134377	−	0.232748i
$635$	11.6321	+	20.1474i	0.461607	+	0.799527i
$636$	−1.29867			−0.0514957
$637$	−39.6443	+	17.7518i	−1.57077	+	0.703353i
$638$		−	0.433521i		−	0.0171633i
$639$	−7.66118	−	13.2695i	−0.303071	−	0.524935i
$640$	20.3378	−	35.2261i	0.803923	−	1.39244i
$641$	−1.75707	−	1.01444i	−0.0694000	−	0.0400681i	0.464898	−	0.885364i	$-0.346091\pi$
$641$	−1.75707	−	1.01444i	−0.0694000	−	0.0400681i	−0.534298	+	0.845296i	$0.679424\pi$
$642$	1.21445	+	2.10348i	0.0479304	+	0.0830178i
$643$	−42.6136			−1.68052			−0.840259	−	0.542186i	$-0.817597\pi$
$643$	−42.6136			−1.68052			−0.840259	+	0.542186i	$0.817597\pi$
$644$	2.70827	−	20.8701i	0.106721	−	0.822398i
$645$	16.4629			0.648225
$646$	−4.27407	−	7.40291i	−0.168161	−	0.291264i
$647$	−19.6353	−	11.3365i	−0.771944	−	0.445682i	0.0616237	−	0.998099i	$-0.480372\pi$
$647$	−19.6353	−	11.3365i	−0.771944	−	0.445682i	−0.833568	+	0.552417i	$0.813705\pi$
$648$	−6.40499	+	11.0938i	−0.251612	+	0.435804i
$649$	0.505171	+	0.874981i	0.0198297	+	0.0343460i
$650$		−	27.1351i		−	1.06433i
$651$	−0.424258	+	8.26331i	−0.0166280	+	0.323864i
$652$	−1.52477			−0.0597145
$653$	−11.5925	−	20.0788i	−0.453650	−	0.785745i	0.544959	−	0.838463i	$-0.316545\pi$
$653$	−11.5925	−	20.0788i	−0.453650	−	0.785745i	−0.998609	+	0.0527172i	$0.983212\pi$
$654$	2.67580	−	4.63462i	0.104632	−	0.181228i
$655$	−24.1909	−	13.9666i	−0.945216	−	0.545721i
$656$	−7.54013	+	4.35330i	−0.294393	+	0.169968i
$657$		−	19.7706i		−	0.771325i
$658$	4.39433	+	8.60175i	0.171309	+	0.335331i
$659$			33.6441i			1.31059i	0.755375	+	0.655293i	$0.227455\pi$
$659$			33.6441i			1.31059i	−0.755375	+	0.655293i	$0.772545\pi$
$660$	0.485388	+	0.840716i	0.0188937	+	0.0327248i
$661$	20.7572	−	35.9526i	0.807363	−	1.39839i	−0.107321	−	0.994224i	$-0.534227\pi$
$661$	20.7572	−	35.9526i	0.807363	−	1.39839i	0.914684	−	0.404170i	$-0.132439\pi$
$662$	7.18845	−	12.4508i	0.279387	−	0.483912i
$663$	6.94345	+	12.0264i	0.269661	+	0.467067i
$664$	22.2123			0.862006
$665$	−32.0855	+	16.3913i	−1.24422	+	0.635629i
$666$			1.15566i			0.0447809i
$667$	7.16480	−	10.4425i	0.277422	−	0.404336i
$668$	−35.8333	−	20.6883i	−1.38643	−	0.800456i
$669$	4.04204	−	7.00101i	0.156274	−	0.270675i
$670$	−20.0197	+	11.5584i	−0.773427	+	0.446538i
$671$			2.90905i			0.112303i
$672$	−8.54303	−	0.438620i	−0.329555	−	0.0169201i
$673$	20.9048			0.805820			0.402910	−	0.915239i	$-0.367999\pi$
$673$	20.9048			0.805820			0.402910	+	0.915239i	$0.367999\pi$
$674$	14.2861	−	8.24806i	0.550279	−	0.317704i
$675$	21.5991	+	12.4703i	0.831351	+	0.479981i
$676$	−21.1521	+	36.6365i	−0.813541	+	1.40909i
$677$	−8.38910	−	14.5303i	−0.322419	−	0.558446i	0.658567	−	0.752522i	$-0.271163\pi$
$677$	−8.38910	−	14.5303i	−0.322419	−	0.558446i	−0.980987	+	0.194075i	$0.937829\pi$
$678$	0.969844			0.0372466
$679$	24.2852	+	15.7343i	0.931980	+	0.603828i
$680$	28.6695			1.09943
$681$	7.67990	−	4.43399i	0.294294	−	0.169911i
$682$	0.435408	−	0.754149i	0.0166726	−	0.0288779i
$683$	−22.4827	+	38.9412i	−0.860276	+	1.49004i	0.0113861	+	0.999935i	$0.496376\pi$
$683$	−22.4827	+	38.9412i	−0.860276	+	1.49004i	−0.871662	+	0.490107i	$0.836958\pi$
$684$	8.47783	+	14.6840i	0.324158	+	0.561458i
$685$			74.7248i			2.85509i
$686$	10.0903	−	3.91026i	0.385251	−	0.149295i
$687$		−	9.21435i		−	0.351549i
$688$	−14.1541	+	8.17185i	−0.539618	+	0.311549i
$689$	4.12048	−	7.13688i	0.156978	−	0.271894i
$690$	0.453404	−	5.81987i	0.0172608	−	0.221559i
$691$	−9.13371	+	5.27335i	−0.347463	+	0.200608i	−0.663567	−	0.748117i	$-0.730958\pi$
$691$	−9.13371	+	5.27335i	−0.347463	+	0.200608i	0.316104	+	0.948724i	$0.397625\pi$
$692$			25.9760i			0.987460i
$693$	−1.07211	+	1.65476i	−0.0407263	+	0.0628591i
$694$	−5.95930			−0.226212
$695$	−0.234413	+	0.135338i	−0.00889178	+	0.00513367i
$696$	−2.88234	−	1.66412i	−0.109255	−	0.0630782i
$697$	−13.8390	−	7.98993i	−0.524188	−	0.302640i
$698$	−0.479869	+	0.277053i	−0.0181633	+	0.0104866i
$699$			13.2105i			0.499668i
$700$	1.68390	−	32.7975i	0.0636456	−	1.23963i
$701$			13.2757i			0.501417i	0.968063	+	0.250709i	$0.0806636\pi$
$701$			13.2757i			0.501417i	−0.968063	+	0.250709i	$0.919336\pi$
$702$	6.04165	+	10.4644i	0.228027	+	0.394955i
$703$	2.48899	+	1.43702i	0.0938740	+	0.0541982i
$704$	−0.226757	−	0.130918i	−0.00854622	−	0.00493416i
$705$	−6.50796	−	11.2721i	−0.245104	−	0.424532i
$706$			6.41835i			0.241558i
$707$	−8.81471	−	17.2545i	−0.331511	−	0.648922i
$708$	3.51639			0.132154
$709$	14.6710	−	8.47030i	0.550980	−	0.318109i	−0.198537	−	0.980093i	$-0.563619\pi$
$709$	14.6710	−	8.47030i	0.550980	−	0.318109i	0.749517	+	0.661985i	$0.230286\pi$
$710$	−5.96312	+	10.3284i	−0.223792	+	0.387619i
$711$	16.4186	+	9.47926i	0.615744	+	0.355500i
$712$	5.97010	+	10.3405i	0.223739	+	0.387527i
$713$	22.9518	−	10.9697i	0.859551	−	0.410819i
$714$	−1.57391	−	3.08088i	−0.0589022	−	0.115299i
$715$	−6.16024			−0.230380
$716$	2.57360	+	4.45761i	0.0961801	+	0.166589i
$717$	3.30611	+	1.90878i	0.123469	+	0.0712848i
$718$	5.36076	+	3.09504i	0.200062	+	0.115506i
$719$	39.6639	−	22.8999i	1.47921	−	0.854023i	0.479489	−	0.877548i	$-0.340822\pi$
$719$	39.6639	−	22.8999i	1.47921	−	0.854023i	0.999723	+	0.0235246i	$0.00748879\pi$
$720$	−19.3811			−0.722291
$721$	1.26416	−	24.6222i	0.0470798	−	0.916977i
$722$	2.42182			0.0901308
$723$	0.295845	−	0.170806i	0.0110026	−	0.00635235i
$724$	2.35307	−	4.07564i	0.0874513	−	0.151470i
$725$	9.88115	−	17.1147i	0.366977	−	0.635623i
$726$	3.25825	−	1.88115i	0.120925	−	0.0698160i
$727$	−27.5793			−1.02286			−0.511429	−	0.859325i	$-0.670884\pi$
$727$	−27.5793			−1.02286			−0.511429	+	0.859325i	$0.670884\pi$
$728$	19.0838	−	29.4550i	0.707293	−	1.09167i
$729$	9.99940			0.370348
$730$	−13.3269	+	7.69428i	−0.493250	+	0.284778i
$731$	−25.9780	−	14.9984i	−0.960830	−	0.554736i
$732$	8.76820	+	5.06232i	0.324082	+	0.187109i
$733$	−6.51715	−	11.2880i	−0.240717	−	0.416933i	0.720202	−	0.693764i	$-0.244049\pi$
$733$	−6.51715	−	11.2880i	−0.240717	−	0.416933i	−0.960919	+	0.276831i	$0.910716\pi$
$734$	−6.74269			−0.248877
$735$	−13.3088	+	5.95938i	−0.490902	+	0.219815i
$736$	11.3411	+	23.7287i	0.418037	+	0.874653i
$737$	1.57304	+	2.72458i	0.0579436	+	0.100361i
$738$	−5.65053	−	3.26233i	−0.207999	−	0.120088i
$739$	14.3324	−	24.8245i	0.527227	−	0.913184i	−0.472269	−	0.881454i	$-0.656565\pi$
$739$	14.3324	−	24.8245i	0.527227	−	0.913184i	0.999496	−	0.0317300i	$-0.0101017\pi$
$740$	−3.78439	+	2.18492i	−0.139117	+	0.0803192i
$741$	14.1011			0.518017
$742$	−1.11635	+	1.72303i	−0.0409825	+	0.0632545i
$743$		−	22.7481i		−	0.834547i	−0.908781	−	0.417274i	$-0.862986\pi$
$743$		−	22.7481i		−	0.834547i	0.908781	−	0.417274i	$-0.137014\pi$
$744$	−3.34272	−	5.78977i	−0.122550	−	0.212263i
$745$	68.3650	+	39.4705i	2.50470	+	1.44609i
$746$	5.93019	+	3.42380i	0.217120	+	0.125354i
$747$	−13.7799	−	23.8676i	−0.504182	−	0.873268i
$748$		−	1.76884i		−	0.0646751i
$749$	−18.6293	−	0.956474i	−0.680700	−	0.0349488i
$750$		−	3.02337i		−	0.110398i
$751$	−25.1903	+	14.5437i	−0.919209	+	0.530705i	−0.883383	−	0.468653i	$-0.844740\pi$
$751$	−25.1903	+	14.5437i	−0.919209	+	0.530705i	−0.0358263	+	0.999358i	$0.511406\pi$
$752$	11.1905	+	6.46085i	0.408076	+	0.235603i
$753$	−1.25768	−	0.726122i	−0.0458324	−	0.0264614i
$754$	8.29179	−	4.78727i	0.301969	−	0.174342i
$755$	52.6331			1.91551
$756$	6.65301	+	13.0230i	0.241968	+	0.473644i
$757$			31.5963i			1.14839i	0.818720	+	0.574193i	$0.194684\pi$
$757$			31.5963i			1.14839i	−0.818720	+	0.574193i	$0.805316\pi$
$758$	−7.57168	+	4.37151i	−0.275016	+	0.158780i
$759$	−0.792057	−	0.0617062i	−0.0287498	−	0.00223979i
$760$	14.5559	−	25.2115i	0.527997	−	0.914517i
$761$	2.63578	−	1.52177i	0.0955468	−	0.0551640i	−0.451465	−	0.892289i	$-0.649099\pi$
$761$	2.63578	−	1.52177i	0.0955468	−	0.0551640i	0.547012	+	0.837125i	$0.315765\pi$
$762$			2.26832i			0.0821725i
$763$	18.6980	+	36.6006i	0.676912	+	1.32503i
$764$			36.5808i			1.32345i
$765$	−17.7858	−	30.8059i	−0.643047	−	1.11379i
$766$	−7.75443	+	13.4311i	−0.280179	+	0.485284i
$767$	−11.1569	+	19.3244i	−0.402854	+	0.697763i
$768$	2.48297	−	1.43354i	0.0895964	−	0.0517285i
$769$	44.5932			1.60807			0.804036	−	0.594580i	$-0.202682\pi$
$769$	44.5932			1.60807			0.804036	+	0.594580i	$0.202682\pi$
$770$	1.53268	+	0.0786913i	0.0552338	+	0.00283584i
$771$	11.6658			0.420133
$772$	11.2949	+	19.5633i	0.406512	+	0.704099i
$773$	−8.35221	+	14.4665i	−0.300408	+	0.520322i	−0.976228	−	0.216744i	$-0.930456\pi$
$773$	−8.35221	+	14.4665i	−0.300408	+	0.520322i	0.675820	+	0.737067i	$0.263790\pi$
$774$	−10.6070	−	6.12393i	−0.381259	−	0.220120i
$775$	34.3783	−	19.8483i	1.23491	−	0.712973i
$776$	−23.3806			−0.839315
$777$	0.976204	+	0.632481i	0.0350211	+	0.0226901i
$778$		−	6.68088i		−	0.239521i
$779$	−14.0524	+	8.11317i	−0.503480	+	0.290684i
$780$	−10.7200	+	18.5676i	−0.383838	+	0.664828i
$781$	1.40565	+	0.811552i	0.0502981	+	0.0290396i
$782$	−6.01762	+	8.77053i	−0.215189	+	0.313634i
$783$			8.80019i			0.314493i
$784$	8.48420	−	11.7298i	0.303007	−	0.418923i
$785$	−66.7064			−2.38085
$786$	−1.36178	−	2.35866i	−0.0485729	−	0.0841307i
$787$	1.51592	−	2.62565i	0.0540367	−	0.0935943i	−0.837742	−	0.546067i	$-0.816125\pi$
$787$	1.51592	−	2.62565i	0.0540367	−	0.0935943i	0.891778	+	0.452472i	$0.149458\pi$
$788$	1.88210	−	3.25990i	0.0670472	−	0.116129i
$789$	−6.75006	−	11.6914i	−0.240308	−	0.416226i
$790$		−	14.7565i		−	0.525012i
$791$	−4.05004	+	6.25105i	−0.144003	+	0.222262i
$792$		−	1.59312i		−	0.0566091i
$793$	−55.6402	+	32.1239i	−1.97584	+	1.14075i
$794$	−6.19895	−	3.57896i	−0.219992	−	0.127013i
$795$	1.38327	−	2.39589i	0.0490594	−	0.0849734i
$796$	10.0126	+	17.3423i	0.354886	+	0.614681i
$797$	−2.93351			−0.103910			−0.0519551	−	0.998649i	$-0.516545\pi$
$797$	−2.93351			−0.103910			−0.0519551	+	0.998649i	$0.516545\pi$
$798$	−3.50837	−	0.180128i	−0.124195	−	0.00637648i
$799$			23.7161i			0.839017i
$800$	20.5202	+	35.5421i	0.725500	+	1.25660i
$801$	7.40738	−	12.8300i	0.261727	−	0.453324i
$802$	−4.32283	−	2.49579i	−0.152645	−	0.0881294i
$803$	1.04716	+	1.81373i	0.0369533	+	0.0640050i
$804$	10.9496			0.386162
$805$	35.6181	+	27.2260i	1.25537	+	0.959590i
$806$	19.2324			0.677433
$807$	4.65800	+	8.06789i	0.163969	+	0.284003i
$808$	13.5579	+	7.82765i	0.476965	+	0.275376i
$809$	24.7227	−	42.8209i	0.869203	−	1.50550i	0.00639114	−	0.999980i	$-0.497966\pi$
$809$	24.7227	−	42.8209i	0.869203	−	1.50550i	0.862812	−	0.505525i	$-0.168701\pi$
$810$	−6.18557	−	10.7137i	−0.217339	−	0.376442i
$811$		−	23.8421i		−	0.837210i	−0.908168	−	0.418605i	$-0.862519\pi$
$811$		−	23.8421i		−	0.837210i	0.908168	−	0.418605i	$-0.137481\pi$
$812$	10.3192	−	5.27169i	0.362132	−	0.185000i
$813$	−8.54705			−0.299758
$814$	−0.0612098	−	0.106019i	−0.00214540	−	0.00371595i
$815$	1.62409	−	2.81301i	0.0568894	−	0.0985354i
$816$	−4.00810	−	2.31408i	−0.140311	−	0.0810089i
$817$	−26.3787	+	15.2297i	−0.922873	+	0.532821i
$818$		−	16.3493i		−	0.571641i
$819$	−43.4890	−	2.23283i	−1.51963	−	0.0780214i
$820$		−	24.6714i		−	0.861562i
$821$	15.9293	+	27.5904i	0.555938	+	0.962913i	0.997830	+	0.0658446i	$0.0209741\pi$
$821$	15.9293	+	27.5904i	0.555938	+	0.962913i	−0.441892	+	0.897068i	$0.645693\pi$
$822$	−3.64291	+	6.30971i	−0.127061	+	0.220076i
$823$	18.7653	−	32.5024i	0.654117	−	1.13296i	−0.327998	−	0.944678i	$-0.606374\pi$
$823$	18.7653	−	32.5024i	0.654117	−	1.13296i	0.982114	−	0.188285i	$-0.0602928\pi$
$824$	9.96031	+	17.2518i	0.346984	+	0.600994i
$825$	−1.23974			−0.0431624
$826$	3.02271	−	4.66542i	0.105174	−	0.162331i
$827$			13.6994i			0.476373i	0.971219	+	0.238187i	$0.0765530\pi$
$827$			13.6994i			0.476373i	−0.971219	+	0.238187i	$0.923447\pi$
$828$	11.9362	−	17.3968i	0.414812	−	0.604579i
$829$	−9.99397	−	5.77002i	−0.347105	−	0.200401i	0.316305	−	0.948658i	$-0.397558\pi$
$829$	−9.99397	−	5.77002i	−0.347105	−	0.200401i	−0.663409	+	0.748257i	$0.730891\pi$
$830$	−10.7257	+	18.5775i	−0.372295	+	0.644833i
$831$	11.9141	−	6.87863i	0.413297	−	0.238617i
$832$		−	5.78278i		−	0.200482i
$833$	26.4302	+	2.72115i	0.915752	+	0.0942824i
$834$	−0.0263916			−0.000913865
$835$	76.3348	−	44.0719i	2.64168	−	1.52517i
$836$	−1.55549	−	0.898061i	−0.0537976	−	0.0310601i
$837$	−8.83849	+	15.3087i	−0.305503	+	0.529147i
$838$	4.57788	+	7.92912i	0.158140	+	0.273907i
$839$	25.1844			0.869463			0.434732	−	0.900560i	$-0.356843\pi$
$839$	25.1844			0.869463			0.434732	+	0.900560i	$0.356843\pi$
$840$	6.40653	−	9.88818i	0.221046	−	0.341175i
$841$	−22.0269			−0.759549
$842$	17.5731	−	10.1458i	0.605609	−	0.349648i
$843$	4.92371	−	8.52812i	0.169582	−	0.293724i
$844$	−12.4422	+	21.5505i	−0.428278	+	0.741799i
$845$	−45.0598	−	78.0459i	−1.55010	−	2.68486i
$846$			9.68343i			0.332923i
$847$	−1.48156	+	28.8564i	−0.0509069	+	0.991517i
$848$			2.74650i			0.0943154i
$849$	−6.23456	+	3.59952i	−0.213970	+	0.123535i
$850$	−8.29905	+	14.3744i	−0.284655	+	0.493037i
$851$	0.277763	−	3.56535i	0.00952160	−	0.122219i
$852$	4.89222	−	2.82452i	0.167605	−	0.0967665i
$853$		−	6.71783i		−	0.230014i	−0.993365	−	0.115007i	$-0.963311\pi$
$853$		−	6.71783i		−	0.230014i	0.993365	−	0.115007i	$-0.0366891\pi$
$854$	14.2537	−	7.28172i	0.487752	−	0.249175i
$855$	−36.1203			−1.23529
$856$	13.0528	−	7.53604i	0.446136	−	0.257577i
$857$	44.8509	+	25.8947i	1.53208	+	0.884544i	0.999266	+	0.0383095i	$0.0121973\pi$
$857$	44.8509	+	25.8947i	1.53208	+	0.884544i	0.532810	+	0.846235i	$0.321136\pi$
$858$	−0.520167	−	0.300318i	−0.0177582	−	0.0102527i
$859$	39.3726	−	22.7318i	1.34338	−	0.775598i	0.356074	−	0.934458i	$-0.384115\pi$
$859$	39.3726	−	22.7318i	1.34338	−	0.775598i	0.987301	+	0.158859i	$0.0507817\pi$
$860$		−	46.3122i		−	1.57923i
$861$	−5.84822	+	2.98765i	−0.199307	+	0.101819i
$862$		−	4.80753i		−	0.163745i
$863$	6.96967	+	12.0718i	0.237250	+	0.410930i	0.959924	−	0.280259i	$-0.0904205\pi$
$863$	6.96967	+	12.0718i	0.237250	+	0.410930i	−0.722674	+	0.691189i	$0.757087\pi$
$864$	−15.8270	−	9.13770i	−0.538444	−	0.310871i
$865$	−47.9225	−	27.6681i	−1.62941	−	0.940743i
$866$	−0.112379	−	0.194647i	−0.00381880	−	0.00661436i
$867$			1.52860i			0.0519140i
$868$	23.2458	+	1.19349i	0.789012	+	0.0405098i
$869$	−2.00829			−0.0681264
$870$	2.78359	−	1.60711i	0.0943727	−	0.0544861i
$871$	−34.7413	+	60.1737i	−1.17716	+	2.03891i
$872$	−28.7593	−	16.6042i	−0.973914	−	0.562289i
$873$	14.5047	+	25.1229i	0.490910	+	0.850280i
$874$	4.65744	+	9.74470i	0.157540	+	0.329619i
$875$	19.4869	+	12.6255i	0.658776	+	0.426820i
$876$	7.28902			0.246273
$877$	15.1632	+	26.2635i	0.512026	+	0.886855i	0.999903	+	0.0139426i	$0.00443821\pi$
$877$	15.1632	+	26.2635i	0.512026	+	0.886855i	−0.487877	+	0.872913i	$0.662228\pi$
$878$	−2.45676	−	1.41841i	−0.0829116	−	0.0478691i
$879$	−6.46042	−	3.72993i	−0.217905	−	0.125807i
$880$	1.77799	−	1.02653i	0.0599362	−	0.0346042i
$881$	17.2441			0.580968			0.290484	−	0.956880i	$-0.406184\pi$
$881$	17.2441			0.580968			0.290484	+	0.956880i	$0.406184\pi$
$882$	10.7916	+	1.11106i	0.363372	+	0.0374114i
$883$	2.24713			0.0756221			0.0378110	−	0.999285i	$-0.487962\pi$
$883$	2.24713			0.0756221			0.0378110	+	0.999285i	$0.487962\pi$
$884$	33.8318	−	19.5328i	1.13789	−	0.656960i
$885$	−3.74544	+	6.48729i	−0.125902	+	0.218068i
$886$	−9.09856	+	15.7592i	−0.305672	+	0.529440i
$887$	−35.9318	+	20.7452i	−1.20647	+	0.696557i	−0.961987	−	0.273096i	$-0.911952\pi$
$887$	−35.9318	+	20.7452i	−1.20647	+	0.696557i	−0.244485	+	0.969653i	$0.578619\pi$
$888$	−0.939842			−0.0315390
$889$	−14.6202	−	9.47243i	−0.490347	−	0.317695i
$890$	−11.5312			−0.386525
$891$	−1.45809	+	0.841827i	−0.0488477	+	0.0282022i
$892$	−19.6948	−	11.3708i	−0.659429	−	0.380722i
$893$	20.8556	+	12.0410i	0.697905	+	0.402936i
$894$	3.84846	+	6.66573i	0.128712	+	0.222935i
$895$	−10.9650			−0.366519
$896$	−1.56176	+	30.4185i	−0.0521747	+	1.01621i
$897$	−7.56625	−	15.8308i	−0.252630	−	0.528573i
$898$	−4.44443	−	7.69798i	−0.148313	−	0.256885i
$899$	12.1303	+	7.00342i	0.404567	+	0.233577i
$900$	16.4615	−	28.5122i	0.548718	−	0.950408i
$901$	−4.36552	+	2.52043i	−0.145436	+	0.0839677i
$902$	0.691161			0.0230132
$903$	−10.9781	+	5.60830i	−0.365327	+	0.186633i
$904$		−	6.01821i		−	0.200163i
$905$	5.01270	+	8.68226i	0.166628	+	0.288608i
$906$	4.44430	+	2.56592i	0.147652	+	0.0852470i
$907$	−34.5803	−	19.9649i	−1.14822	−	0.662925i	−0.199767	−	0.979843i	$-0.564019\pi$
$907$	−34.5803	−	19.9649i	−1.14822	−	0.662925i	−0.948453	+	0.316918i	$0.897352\pi$
$908$	−12.4734	−	21.6045i	−0.413944	−	0.716972i
$909$		−	19.4243i		−	0.644262i
$910$	15.4199	+	30.1838i	0.511163	+	1.00058i
$911$			39.5814i			1.31139i	0.755026	+	0.655695i	$0.227624\pi$
$911$			39.5814i			1.31139i	−0.755026	+	0.655695i	$0.772376\pi$
$912$	−4.06992	+	2.34977i	−0.134769	+	0.0778086i
$913$	2.52830	+	1.45972i	0.0836746	+	0.0483096i
$914$	4.22529	+	2.43947i	0.139760	+	0.0806905i
$915$	−18.6787	+	10.7842i	−0.617499	+	0.356513i
$916$	−25.9212			−0.856459
$917$	20.8893	+	1.07251i	0.689826	+	0.0354173i
$918$		−	7.39116i		−	0.243945i
$919$	32.1711	−	18.5740i	1.06123	−	0.612700i	0.135455	−	0.990783i	$-0.456750\pi$
$919$	32.1711	−	18.5740i	1.06123	−	0.612700i	0.925771	+	0.378084i	$0.123417\pi$
$920$	−36.1142	−	2.81352i	−1.19065	−	0.0927591i
$921$	−0.454200	+	0.786698i	−0.0149664	+	0.0259226i
$922$	1.99861	−	1.15390i	0.0658206	−	0.0380015i
$923$			35.8471i			1.17992i
$924$	−0.610076	−	0.395267i	−0.0200700	−	0.0130033i
$925$		−	5.58057i		−	0.183488i
$926$	7.29984	+	12.6437i	0.239888	+	0.415498i
$927$	12.3582	−	21.4051i	0.405897	−	0.703034i
$928$	−7.24050	+	12.5409i	−0.237681	+	0.411676i
$929$	−25.2242	+	14.5632i	−0.827580	+	0.477803i	−0.853023	−	0.521873i	$-0.825234\pi$
$929$	−25.2242	+	14.5632i	−0.827580	+	0.477803i	0.0254435	+	0.999676i	$0.491900\pi$
$930$	6.45642			0.211714
$931$	15.8119	−	21.8607i	0.518213	−	0.716456i
$932$	37.1629			1.21731
$933$	1.71600	+	2.97220i	0.0561794	+	0.0973056i
$934$	1.11985	−	1.93965i	0.0366428	−	0.0634671i
$935$	3.26329	+	1.88406i	0.106721	+	0.0616153i
$936$	30.4710	−	17.5924i	0.995975	−	0.575026i
$937$	−8.29853			−0.271101			−0.135551	−	0.990770i	$-0.543280\pi$
$937$	−8.29853			−0.271101			−0.135551	+	0.990770i	$0.543280\pi$
$938$	9.41235	−	14.5275i	0.307324	−	0.474340i
$939$		−	9.87338i		−	0.322206i
$940$	−31.7099	+	18.3077i	−1.03426	+	0.597132i
$941$	4.15468	−	7.19611i	0.135439	−	0.234587i	−0.790326	−	0.612686i	$-0.790089\pi$
$941$	4.15468	−	7.19611i	0.135439	−	0.234587i	0.925765	+	0.378100i	$0.123422\pi$
$942$	−5.63265	−	3.25201i	−0.183522	−	0.105956i
$943$	16.6485	+	11.4228i	0.542149	+	0.371978i
$944$		−	7.43665i		−	0.242042i
$945$	−31.1123	−	1.59738i	−1.01208	−	0.0519628i
$946$	1.29742			0.0421828
$947$	1.92168	+	3.32845i	0.0624462	+	0.108160i	0.895558	−	0.444944i	$-0.146776\pi$
$947$	1.92168	+	3.32845i	0.0624462	+	0.108160i	−0.833112	+	0.553104i	$0.813443\pi$
$948$	−3.49481	+	6.05319i	−0.113506	+	0.196599i
$949$	−23.1269	+	40.0570i	−0.750732	+	1.30031i
$950$	8.42706	+	14.5961i	0.273410	+	0.473560i
$951$		−	6.82821i		−	0.221420i
$952$	−19.1179	+	9.76666i	−0.619615	+	0.316539i
$953$		−	31.2541i		−	1.01242i	−0.862411	−	0.506209i	$-0.831046\pi$
$953$		−	31.2541i		−	1.01242i	0.862411	−	0.506209i	$-0.168954\pi$
$954$	−1.78246	+	1.02911i	−0.0577094	+	0.0333186i
$955$	−67.4870	−	38.9636i	−2.18383	−	1.26083i
$956$	5.36965	−	9.30051i	0.173667	−	0.300800i
$957$	−0.218720	−	0.378834i	−0.00707021	−	0.0122460i
$958$	0.353946			0.0114355
$959$	−25.4560	−	49.8293i	−0.822017	−	1.60907i
$960$		−	1.94131i		−	0.0626555i
$961$	−1.43219	−	2.48063i	−0.0461998	−	0.0800204i
$962$	1.35185	−	2.34147i	0.0435854	−	0.0754921i
$963$	−16.1952	−	9.35032i	−0.521884	−	0.301310i
$964$	−0.480500	−	0.832250i	−0.0154759	−	0.0268050i
$965$	−48.1225			−1.54912
$966$	1.68027	+	4.03537i	0.0540618	+	0.129836i
$967$	−37.6191			−1.20975			−0.604874	−	0.796321i	$-0.706776\pi$
$967$	−37.6191			−1.20975			−0.604874	+	0.796321i	$0.706776\pi$
$968$	−11.6732	−	20.2185i	−0.375190	−	0.649848i
$969$	−7.46982	−	4.31271i	−0.239965	−	0.138544i
$970$	11.2898	−	19.5545i	0.362494	−	0.627858i
$971$	−24.6877	−	42.7603i	−0.792266	−	1.37224i	−0.924561	−	0.381034i	$-0.875568\pi$
$971$	−24.6877	−	42.7603i	−0.792266	−	1.37224i	0.132295	−	0.991210i	$-0.457765\pi$
$972$			22.4419i			0.719823i
$973$	0.110210	−	0.170105i	0.00353318	−	0.00545330i
$974$	−11.8267			−0.378952
$975$	−13.6902	−	23.7121i	−0.438437	−	0.759394i
$976$	10.7061	−	18.5435i	0.342693	−	0.593562i
$977$	45.6640	+	26.3641i	1.46092	+	0.843463i	0.999054	−	0.0434867i	$-0.0138466\pi$
$977$	45.6640	+	26.3641i	1.46092	+	0.843463i	0.461866	+	0.886949i	$0.347180\pi$
$978$	0.274274	−	0.158352i	0.00877033	−	0.00506355i
$979$			1.56934i			0.0501562i
$980$	16.7645	+	37.4394i	0.535522	+	1.19596i
$981$			41.2032i			1.31552i
$982$	2.67889	+	4.63998i	0.0854869	+	0.148068i
$983$	−15.9723	+	27.6649i	−0.509438	+	0.882373i	0.490502	+	0.871440i	$0.336813\pi$
$983$	−15.9723	+	27.6649i	−0.509438	+	0.882373i	−0.999940	+	0.0109329i	$0.996520\pi$
$984$	2.65310	−	4.59530i	0.0845776	−	0.146493i
$985$	4.00941	+	6.94450i	0.127750	+	0.221270i
$986$	−5.85658			−0.186512
$987$	8.17975	+	5.29964i	0.260364	+	0.168690i
$988$		−	39.6682i		−	1.26201i
$989$	31.2519	+	21.4425i	0.993752	+	0.681831i
$990$	1.33242	+	0.769272i	0.0423470	+	0.0244491i
$991$	−17.1798	+	29.7562i	−0.545733	+	0.945237i	0.452827	+	0.891598i	$0.350415\pi$
$991$	−17.1798	+	29.7562i	−0.545733	+	0.945237i	−0.998560	+	0.0536391i	$0.982918\pi$
$992$	−25.1910	+	14.5440i	−0.799815	+	0.461773i
$993$		−	14.5068i		−	0.460361i
$994$	0.457913	−	8.91880i	0.0145241	−	0.282887i
$995$	−42.6591			−1.35239
$996$	8.79949	−	5.08039i	0.278823	−	0.160978i
$997$	−7.50207	−	4.33132i	−0.237593	−	0.137174i	0.376477	−	0.926426i	$-0.377135\pi$
$997$	−7.50207	−	4.33132i	−0.237593	−	0.137174i	−0.614070	+	0.789252i	$0.710469\pi$
$998$	0.692595	−	1.19961i	0.0219237	−	0.0379730i
$999$	1.24252	+	2.15210i	0.0393115	+	0.0680896i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.2.g.a.45.10	yes	28
7.3	odd	6		1127.2.c.c.1126.10		28
7.4	even	3		1127.2.c.c.1126.9		28
7.5	odd	6	inner	161.2.g.a.68.9	yes	28
23.22	odd	2	inner	161.2.g.a.45.9	✓	28
161.45	even	6		1127.2.c.c.1126.12		28
161.68	even	6	inner	161.2.g.a.68.10	yes	28
161.137	odd	6		1127.2.c.c.1126.11		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.2.g.a.45.9	✓	28	23.22	odd	2	inner
161.2.g.a.45.10	yes	28	1.1	even	1	trivial
161.2.g.a.68.9	yes	28	7.5	odd	6	inner
161.2.g.a.68.10	yes	28	161.68	even	6	inner
1127.2.c.c.1126.9		28	7.4	even	3
1127.2.c.c.1126.10		28	7.3	odd	6
1127.2.c.c.1126.11		28	161.137	odd	6
1127.2.c.c.1126.12		28	161.45	even	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+(0.292153 + 0.506024i) q^{2} +(0.510598 + 0.294794i) q^{3} +(0.829293 - 1.43638i) q^{4} +(1.76663 + 3.05989i) q^{5} +0.344500i q^{6} +(-2.22044 - 1.43862i) q^{7} +2.13773 q^{8} +(-1.32619 - 2.29703i) q^{9} +(-1.03225 + 1.78791i) q^{10} +(0.243326 + 0.140484i) q^{11} +(0.846870 - 0.488941i) q^{12} +6.20533i q^{13} +(0.0792673 - 1.54390i) q^{14} +2.08316i q^{15} +(-1.03404 - 1.79101i) q^{16} +(1.89785 - 3.28717i) q^{17} +(0.774903 - 1.34217i) q^{18} +(-1.92712 - 3.33788i) q^{19} +5.86020 q^{20} +(-0.709657 - 1.38913i) q^{21} +0.164172i q^{22} +(-2.71326 + 3.95452i) q^{23} +(1.09152 + 0.630191i) q^{24} +(-3.74193 + 6.48121i) q^{25} +(-3.14005 + 1.81291i) q^{26} -3.33258i q^{27} +(-3.90780 + 1.99636i) q^{28} -2.64066 q^{29} +(-1.05413 + 0.608602i) q^{30} +(-4.59366 - 2.65215i) q^{31} +(2.74193 - 4.74916i) q^{32} +(0.0828278 + 0.143462i) q^{33} +2.21785 q^{34} +(0.479323 - 9.33581i) q^{35} -4.39921 q^{36} +(-0.645778 + 0.372840i) q^{37} +(1.12603 - 1.95034i) q^{38} +(-1.82929 + 3.16843i) q^{39} +(3.77658 + 6.54122i) q^{40} -4.20999i q^{41} +(0.495605 - 0.764942i) q^{42} -7.90283i q^{43} +(0.403577 - 0.233005i) q^{44} +(4.68577 - 8.11600i) q^{45} +(-2.79377 - 0.217652i) q^{46} +(-5.41106 + 3.12408i) q^{47} -1.21931i q^{48} +(2.86074 + 6.38875i) q^{49} -4.37287 q^{50} +(1.93808 - 1.11895i) q^{51} +(8.91320 + 5.14604i) q^{52} +(-1.15012 - 0.664023i) q^{53} +(1.68636 - 0.973623i) q^{54} +0.992733i q^{55} +(-4.74672 - 3.07539i) q^{56} -2.27242i q^{57} +(-0.771476 - 1.33624i) q^{58} +(3.11416 + 1.79796i) q^{59} +(2.99221 + 1.72755i) q^{60} +(5.17682 + 8.96652i) q^{61} -3.09934i q^{62} +(-0.359824 + 7.00832i) q^{63} -0.931905 q^{64} +(-18.9876 + 10.9625i) q^{65} +(-0.0483968 + 0.0838258i) q^{66} +(9.69710 + 5.59862i) q^{67} +(-3.14775 - 5.45206i) q^{68} +(-2.55115 + 1.21931i) q^{69} +(4.86418 - 2.48494i) q^{70} +5.77682 q^{71} +(-2.83505 - 4.91045i) q^{72} +(6.45526 + 3.72695i) q^{73} +(-0.377332 - 0.217853i) q^{74} +(-3.82124 + 2.20620i) q^{75} -6.39260 q^{76} +(-0.338188 - 0.661992i) q^{77} -2.13773 q^{78} +(-6.19011 + 3.57386i) q^{79} +(3.65352 - 6.32809i) q^{80} +(-2.99616 + 5.18950i) q^{81} +(2.13036 - 1.22996i) q^{82} +10.3906 q^{83} +(-2.58383 - 0.132660i) q^{84} +13.4112 q^{85} +(3.99902 - 2.30884i) q^{86} +(-1.34831 - 0.778449i) q^{87} +(0.520167 + 0.300318i) q^{88} +(2.79272 + 4.83714i) q^{89} +5.47585 q^{90} +(8.92712 - 13.7786i) q^{91} +(3.43009 + 7.17672i) q^{92} +(-1.56367 - 2.70836i) q^{93} +(-3.16172 - 1.82542i) q^{94} +(6.80901 - 11.7936i) q^{95} +(2.80005 - 1.61661i) q^{96} -10.9371 q^{97} +(-2.39709 + 3.31410i) q^{98} -0.745238i 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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