LMFDB - Embedded newform 1690.2.b.g.339.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1690,2,Mod(339,1690)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1690, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1690.339"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [18,0,0,-18,0,14,0,0,-16,2,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4947179416$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 29x^{16} + 336x^{14} + 1977x^{12} + 6147x^{10} + 9369x^{8} + 5559x^{6} + 1342x^{4} + 116x^{2} + 1 $ x^18 + 29x^16 + 336x^14 + 1977x^12 + 6147x^10 + 9369x^8 + 5559x^6 + 1342x^4 + 116x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			339.13
Root			$-2.17115i$ of defining polynomial
Character	$\chi$	$=$	1690.339
Dual form			1690.2.b.g.339.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} -0.956446i q^{3} -1.00000 q^{4} +(-0.426774 + 2.19496i) q^{5} +0.956446 q^{6} -2.15124i q^{7} -1.00000i q^{8} +2.08521 q^{9} +(-2.19496 - 0.426774i) q^{10} +1.30608 q^{11} +0.956446i q^{12} +2.15124 q^{14} +(2.09936 + 0.408187i) q^{15} +1.00000 q^{16} -2.87416i q^{17} +2.08521i q^{18} +2.65614 q^{19} +(0.426774 - 2.19496i) q^{20} -2.05754 q^{21} +1.30608i q^{22} -5.11025i q^{23} -0.956446 q^{24} +(-4.63573 - 1.87351i) q^{25} -4.86373i q^{27} +2.15124i q^{28} -7.96020 q^{29} +(-0.408187 + 2.09936i) q^{30} -4.12897 q^{31} +1.00000i q^{32} -1.24919i q^{33} +2.87416 q^{34} +(4.72189 + 0.918093i) q^{35} -2.08521 q^{36} +2.98725i q^{37} +2.65614i q^{38} +(2.19496 + 0.426774i) q^{40} +8.69023 q^{41} -2.05754i q^{42} -3.35303i q^{43} -1.30608 q^{44} +(-0.889915 + 4.57696i) q^{45} +5.11025 q^{46} +7.30423i q^{47} -0.956446i q^{48} +2.37217 q^{49} +(1.87351 - 4.63573i) q^{50} -2.74898 q^{51} -10.0804i q^{53} +4.86373 q^{54} +(-0.557400 + 2.86679i) q^{55} -2.15124 q^{56} -2.54046i q^{57} -7.96020i q^{58} +14.6950 q^{59} +(-2.09936 - 0.408187i) q^{60} +11.2009 q^{61} -4.12897i q^{62} -4.48579i q^{63} -1.00000 q^{64} +1.24919 q^{66} -11.0454i q^{67} +2.87416i q^{68} -4.88768 q^{69} +(-0.918093 + 4.72189i) q^{70} +14.0739 q^{71} -2.08521i q^{72} +3.83547i q^{73} -2.98725 q^{74} +(-1.79191 + 4.43382i) q^{75} -2.65614 q^{76} -2.80969i q^{77} +8.94252 q^{79} +(-0.426774 + 2.19496i) q^{80} +1.60374 q^{81} +8.69023i q^{82} -13.9980i q^{83} +2.05754 q^{84} +(6.30867 + 1.22662i) q^{85} +3.35303 q^{86} +7.61350i q^{87} -1.30608i q^{88} -15.6235 q^{89} +(-4.57696 - 0.889915i) q^{90} +5.11025i q^{92} +3.94914i q^{93} -7.30423 q^{94} +(-1.13357 + 5.83013i) q^{95} +0.956446 q^{96} +5.05416i q^{97} +2.37217i q^{98} +2.72345 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 18 q^{4} + 14 q^{6} - 16 q^{9} + 2 q^{10} + 8 q^{11} - 2 q^{14} + 8 q^{15} + 18 q^{16} - 12 q^{19} + 16 q^{21} - 14 q^{24} + 22 q^{25} - 30 q^{29} - 14 q^{30} - 12 q^{31} - 24 q^{34} - 4 q^{35} + 16 q^{36}+ \cdots - 32 q^{99}+O(q^{100}) $ 18 * q - 18 * q^4 + 14 * q^6 - 16 * q^9 + 2 * q^10 + 8 * q^11 - 2 * q^14 + 8 * q^15 + 18 * q^16 - 12 * q^19 + 16 * q^21 - 14 * q^24 + 22 * q^25 - 30 * q^29 - 14 * q^30 - 12 * q^31 - 24 * q^34 - 4 * q^35 + 16 * q^36 - 2 * q^40 + 54 * q^41 - 8 * q^44 + 20 * q^45 + 22 * q^46 + 20 * q^49 + 8 * q^50 + 24 * q^51 - 68 * q^54 + 2 * q^56 - 40 * q^59 - 8 * q^60 - 38 * q^61 - 18 * q^64 - 28 * q^66 + 28 * q^69 - 6 * q^70 - 20 * q^71 + 20 * q^74 - 72 * q^75 + 12 * q^76 + 28 * q^79 + 106 * q^81 - 16 * q^84 + 56 * q^85 + 82 * q^86 - 86 * q^89 - 20 * q^90 - 10 * q^94 - 54 * q^95 + 14 * q^96 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$1$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		−	0.956446i		−	0.552204i	−0.961128	−	0.276102i	$-0.910957\pi$
$3$		−	0.956446i		−	0.552204i	0.961128	−	0.276102i	$-0.0890428\pi$
$4$	−1.00000			−0.500000
$5$	−0.426774	+	2.19496i	−0.190859	+	0.981617i
$5$	−0.426774	+	2.19496i	−0.190859	+	0.981617i
$6$	0.956446			0.390467
$7$		−	2.15124i		−	0.813092i	−0.913630	−	0.406546i	$-0.866733\pi$
$7$		−	2.15124i		−	0.813092i	0.913630	−	0.406546i	$-0.133267\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.08521			0.695070
$10$	−2.19496	−	0.426774i	−0.694108	−	0.134958i
$11$	1.30608			0.393797			0.196899	−	0.980424i	$-0.436913\pi$
$11$	1.30608			0.393797			0.196899	+	0.980424i	$0.436913\pi$
$12$			0.956446i			0.276102i
$13$		0			0
$13$		0			0
$14$	2.15124			0.574943
$15$	2.09936	+	0.408187i	0.542053	+	0.105393i
$16$	1.00000			0.250000
$17$		−	2.87416i		−	0.697086i	−0.937293	−	0.348543i	$-0.886677\pi$
$17$		−	2.87416i		−	0.697086i	0.937293	−	0.348543i	$-0.113323\pi$
$18$			2.08521i			0.491489i
$19$	2.65614			0.609360			0.304680	−	0.952455i	$-0.401450\pi$
$19$	2.65614			0.609360			0.304680	+	0.952455i	$0.401450\pi$
$20$	0.426774	−	2.19496i	0.0954296	−	0.490809i
$21$	−2.05754			−0.448993
$22$			1.30608i			0.278457i
$23$		−	5.11025i		−	1.06556i	−0.846254	−	0.532780i	$-0.821147\pi$
$23$		−	5.11025i		−	1.06556i	0.846254	−	0.532780i	$-0.178853\pi$
$24$	−0.956446			−0.195234
$25$	−4.63573	−	1.87351i	−0.927145	−	0.374702i
$26$		0			0
$27$		−	4.86373i		−	0.936025i
$28$			2.15124i			0.406546i
$29$	−7.96020			−1.47817			−0.739086	−	0.673611i	$-0.764742\pi$
$29$	−7.96020			−1.47817			−0.739086	+	0.673611i	$0.764742\pi$
$30$	−0.408187	+	2.09936i	−0.0745243	+	0.383290i
$31$	−4.12897			−0.741585			−0.370792	−	0.928716i	$-0.620914\pi$
$31$	−4.12897			−0.741585			−0.370792	+	0.928716i	$0.620914\pi$
$32$			1.00000i			0.176777i
$33$		−	1.24919i		−	0.217457i
$34$	2.87416			0.492914
$35$	4.72189	+	0.918093i	0.798145	+	0.155186i
$36$	−2.08521			−0.347535
$37$			2.98725i			0.491101i	0.969384	+	0.245551i	$0.0789688\pi$
$37$			2.98725i			0.491101i	−0.969384	+	0.245551i	$0.921031\pi$
$38$			2.65614i			0.430883i
$39$		0			0
$40$	2.19496	+	0.426774i	0.347054	+	0.0674789i
$41$	8.69023			1.35719			0.678593	−	0.734514i	$-0.262590\pi$
$41$	8.69023			1.35719			0.678593	+	0.734514i	$0.262590\pi$
$42$		−	2.05754i		−	0.317486i
$43$		−	3.35303i		−	0.511332i	−0.966765	−	0.255666i	$-0.917705\pi$
$43$		−	3.35303i		−	0.511332i	0.966765	−	0.255666i	$-0.0822948\pi$
$44$	−1.30608			−0.196899
$45$	−0.889915	+	4.57696i	−0.132661	+	0.682293i
$46$	5.11025			0.753465
$47$			7.30423i			1.06543i	0.846294	+	0.532716i	$0.178828\pi$
$47$			7.30423i			1.06543i	−0.846294	+	0.532716i	$0.821172\pi$
$48$		−	0.956446i		−	0.138051i
$49$	2.37217			0.338882
$50$	1.87351	−	4.63573i	0.264954	−	0.655591i
$51$	−2.74898			−0.384934
$52$		0			0
$53$		−	10.0804i		−	1.38465i	−0.721586	−	0.692325i	$-0.756587\pi$
$53$		−	10.0804i		−	1.38465i	0.721586	−	0.692325i	$-0.243413\pi$
$54$	4.86373			0.661870
$55$	−0.557400	+	2.86679i	−0.0751599	+	0.386558i
$56$	−2.15124			−0.287471
$57$		−	2.54046i		−	0.336491i
$58$		−	7.96020i		−	1.04523i
$59$	14.6950			1.91313			0.956564	−	0.291522i	$-0.0941615\pi$
$59$	14.6950			1.91313			0.956564	+	0.291522i	$0.0941615\pi$
$60$	−2.09936	−	0.408187i	−0.271027	−	0.0526967i
$61$	11.2009			1.43412			0.717062	−	0.697009i	$-0.245486\pi$
$61$	11.2009			1.43412			0.717062	+	0.697009i	$0.245486\pi$
$62$		−	4.12897i		−	0.524380i
$63$		−	4.48579i		−	0.565156i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	1.24919			0.153765
$67$		−	11.0454i		−	1.34941i	−0.738087	−	0.674706i	$-0.764270\pi$
$67$		−	11.0454i		−	1.34941i	0.738087	−	0.674706i	$-0.235730\pi$
$68$			2.87416i			0.348543i
$69$	−4.88768			−0.588407
$70$	−0.918093	+	4.72189i	−0.109733	+	0.564374i
$71$	14.0739			1.67026			0.835130	−	0.550053i	$-0.185392\pi$
$71$	14.0739			1.67026			0.835130	+	0.550053i	$0.185392\pi$
$72$		−	2.08521i		−	0.245744i
$73$			3.83547i			0.448907i	0.974485	+	0.224454i	$0.0720598\pi$
$73$			3.83547i			0.448907i	−0.974485	+	0.224454i	$0.927940\pi$
$74$	−2.98725			−0.347261
$75$	−1.79191	+	4.43382i	−0.206912	+	0.511974i
$76$	−2.65614			−0.304680
$77$		−	2.80969i		−	0.320193i
$78$		0			0
$79$	8.94252			1.00611			0.503056	−	0.864254i	$-0.332209\pi$
$79$	8.94252			1.00611			0.503056	+	0.864254i	$0.332209\pi$
$80$	−0.426774	+	2.19496i	−0.0477148	+	0.245404i
$81$	1.60374			0.178193
$82$			8.69023i			0.959676i
$83$		−	13.9980i		−	1.53648i	−0.640163	−	0.768239i	$-0.721133\pi$
$83$		−	13.9980i		−	1.53648i	0.640163	−	0.768239i	$-0.278867\pi$
$84$	2.05754			0.224496
$85$	6.30867	+	1.22662i	0.684272	+	0.133045i
$86$	3.35303			0.361567
$87$			7.61350i			0.816253i
$88$		−	1.30608i		−	0.139228i
$89$	−15.6235			−1.65609			−0.828043	−	0.560665i	$-0.810546\pi$
$89$	−15.6235			−1.65609			−0.828043	+	0.560665i	$0.810546\pi$
$90$	−4.57696	−	0.889915i	−0.482454	−	0.0938052i
$91$		0			0
$92$			5.11025i			0.532780i
$93$			3.94914i			0.409506i
$94$	−7.30423			−0.753374
$95$	−1.13357	+	5.83013i	−0.116302	+	0.598159i
$96$	0.956446			0.0976169
$97$			5.05416i			0.513172i	0.966521	+	0.256586i	$0.0825978\pi$
$97$			5.05416i			0.513172i	−0.966521	+	0.256586i	$0.917402\pi$
$98$			2.37217i			0.239626i
$99$	2.72345			0.273717
$100$	4.63573	+	1.87351i	0.463573	+	0.187351i
$101$	−2.02811			−0.201804			−0.100902	−	0.994896i	$-0.532173\pi$
$101$	−2.02811			−0.201804			−0.100902	+	0.994896i	$0.532173\pi$
$102$		−	2.74898i		−	0.272189i
$103$			3.26212i			0.321426i	0.987001	+	0.160713i	$0.0513794\pi$
$103$			3.26212i			0.321426i	−0.987001	+	0.160713i	$0.948621\pi$
$104$		0			0
$105$	0.878107	−	4.51623i	0.0856945	−	0.440739i
$106$	10.0804			0.979095
$107$			1.89051i			0.182763i	0.995816	+	0.0913814i	$0.0291282\pi$
$107$			1.89051i			0.182763i	−0.995816	+	0.0913814i	$0.970872\pi$
$108$			4.86373i			0.468013i
$109$	−4.29397			−0.411287			−0.205644	−	0.978627i	$-0.565929\pi$
$109$	−4.29397			−0.411287			−0.205644	+	0.978627i	$0.565929\pi$
$110$	−2.86679	−	0.557400i	−0.273338	−	0.0531461i
$111$	2.85715			0.271188
$112$		−	2.15124i		−	0.203273i
$113$		−	18.7154i		−	1.76060i	−0.474418	−	0.880300i	$-0.657342\pi$
$113$		−	18.7154i		−	1.76060i	0.474418	−	0.880300i	$-0.342658\pi$
$114$	2.54046			0.237935
$115$	11.2168	+	2.18092i	1.04597	+	0.203372i
$116$	7.96020			0.739086
$117$		0			0
$118$			14.6950i			1.35279i
$119$	−6.18300			−0.566795
$120$	0.408187	−	2.09936i	0.0372622	−	0.191645i
$121$	−9.29416			−0.844924
$122$			11.2009i			1.01408i
$123$		−	8.31174i		−	0.749444i
$124$	4.12897			0.370792
$125$	6.09069	−	9.37569i	0.544768	−	0.838587i
$126$	4.48579			0.399626
$127$			17.6498i			1.56617i	0.621918	+	0.783083i	$0.286354\pi$
$127$			17.6498i			1.56617i	−0.621918	+	0.783083i	$0.713646\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−3.20699			−0.282360
$130$		0			0
$131$	8.59263			0.750742			0.375371	−	0.926875i	$-0.377515\pi$
$131$	8.59263			0.750742			0.375371	+	0.926875i	$0.377515\pi$
$132$			1.24919i			0.108728i
$133$		−	5.71399i		−	0.495466i
$134$	11.0454			0.954178
$135$	10.6757	+	2.07572i	0.918819	+	0.178649i
$136$	−2.87416			−0.246457
$137$		−	6.43023i		−	0.549372i	−0.961534	−	0.274686i	$-0.911426\pi$
$137$		−	6.43023i		−	0.549372i	0.961534	−	0.274686i	$-0.0885739\pi$
$138$		−	4.88768i		−	0.416067i
$139$	−1.79435			−0.152195			−0.0760975	−	0.997100i	$-0.524246\pi$
$139$	−1.79435			−0.152195			−0.0760975	+	0.997100i	$0.524246\pi$
$140$	−4.72189	−	0.918093i	−0.399073	−	0.0775931i
$141$	6.98610			0.588336
$142$			14.0739i			1.18105i
$143$		0			0
$144$	2.08521			0.173768
$145$	3.39721	−	17.4724i	0.282123	−	1.45100i
$146$	−3.83547			−0.317426
$147$		−	2.26885i		−	0.187132i
$148$		−	2.98725i		−	0.245551i
$149$	8.49082			0.695595			0.347798	−	0.937570i	$-0.386930\pi$
$149$	8.49082			0.695595			0.347798	+	0.937570i	$0.386930\pi$
$150$	−4.43382	−	1.79191i	−0.362020	−	0.146309i
$151$	−2.97802			−0.242347			−0.121174	−	0.992631i	$-0.538666\pi$
$151$	−2.97802			−0.242347			−0.121174	+	0.992631i	$0.538666\pi$
$152$		−	2.65614i		−	0.215441i
$153$		−	5.99323i		−	0.484524i
$154$	2.80969			0.226411
$155$	1.76214	−	9.06294i	0.141538	−	0.727953i
$156$		0			0
$157$			14.3503i			1.14528i	0.819808	+	0.572639i	$0.194080\pi$
$157$			14.3503i			1.14528i	−0.819808	+	0.572639i	$0.805920\pi$
$158$			8.94252i			0.711428i
$159$	−9.64136			−0.764609
$160$	−2.19496	−	0.426774i	−0.173527	−	0.0337395i
$161$	−10.9934			−0.866398
$162$			1.60374i			0.126002i
$163$			12.7139i			0.995833i	0.867225	+	0.497916i	$0.165901\pi$
$163$			12.7139i			0.995833i	−0.867225	+	0.497916i	$0.834099\pi$
$164$	−8.69023			−0.678593
$165$	2.74193	+	0.533123i	0.213459	+	0.0415036i
$166$	13.9980			1.08645
$167$			1.32171i			0.102277i	0.998692	+	0.0511387i	$0.0162851\pi$
$167$			1.32171i			0.102277i	−0.998692	+	0.0511387i	$0.983715\pi$
$168$			2.05754i			0.158743i
$169$		0			0
$170$	−1.22662	+	6.30867i	−0.0940772	+	0.483853i
$171$	5.53861			0.423548
$172$			3.35303i			0.255666i
$173$		−	23.9387i		−	1.82002i	−0.414581	−	0.910012i	$-0.636072\pi$
$173$		−	23.9387i		−	1.82002i	0.414581	−	0.910012i	$-0.363928\pi$
$174$	−7.61350			−0.577178
$175$	−4.03036	+	9.97256i	−0.304667	+	0.753854i
$176$	1.30608			0.0984493
$177$		−	14.0550i		−	1.05644i
$178$		−	15.6235i		−	1.17103i
$179$	0.841778			0.0629174			0.0314587	−	0.999505i	$-0.489985\pi$
$179$	0.841778			0.0629174			0.0314587	+	0.999505i	$0.489985\pi$
$180$	0.889915	−	4.57696i	0.0663303	−	0.341147i
$181$	−6.20054			−0.460883			−0.230441	−	0.973086i	$-0.574017\pi$
$181$	−6.20054			−0.460883			−0.230441	+	0.973086i	$0.574017\pi$
$182$		0			0
$183$		−	10.7130i		−	0.791930i
$184$	−5.11025			−0.376732
$185$	−6.55691	−	1.27488i	−0.482074	−	0.0937313i
$186$	−3.94914			−0.289565
$187$		−	3.75387i		−	0.274511i
$188$		−	7.30423i		−	0.532716i
$189$	−10.4630			−0.761074
$190$	−5.83013	−	1.13357i	−0.422962	−	0.0822380i
$191$	−10.7222			−0.775829			−0.387915	−	0.921695i	$-0.626804\pi$
$191$	−10.7222			−0.775829			−0.387915	+	0.921695i	$0.626804\pi$
$192$			0.956446i			0.0690255i
$193$			25.9564i			1.86838i	0.356774	+	0.934191i	$0.383877\pi$
$193$			25.9564i			1.86838i	−0.356774	+	0.934191i	$0.616123\pi$
$194$	−5.05416			−0.362868
$195$		0			0
$196$	−2.37217			−0.169441
$197$		−	5.14709i		−	0.366715i	−0.983046	−	0.183358i	$-0.941303\pi$
$197$		−	5.14709i		−	0.366715i	0.983046	−	0.183358i	$-0.0586966\pi$
$198$			2.72345i			0.193547i
$199$	9.50447			0.673754			0.336877	−	0.941549i	$-0.390629\pi$
$199$	9.50447			0.673754			0.336877	+	0.941549i	$0.390629\pi$
$200$	−1.87351	+	4.63573i	−0.132477	+	0.327795i
$201$	−10.5643			−0.745151
$202$		−	2.02811i		−	0.142697i
$203$			17.1243i			1.20189i
$204$	2.74898			0.192467
$205$	−3.70877	+	19.0747i	−0.259032	+	1.33224i
$206$	−3.26212			−0.227283
$207$		−	10.6559i		−	0.740639i
$208$		0			0
$209$	3.46913			0.239964
$210$	4.51623	+	0.878107i	0.311650	+	0.0605951i
$211$	25.8770			1.78145			0.890724	−	0.454545i	$-0.150198\pi$
$211$	25.8770			1.78145			0.890724	+	0.454545i	$0.150198\pi$
$212$			10.0804i			0.692325i
$213$		−	13.4609i		−	0.922325i
$214$	−1.89051			−0.129233
$215$	7.35978	+	1.43099i	0.501933	+	0.0975925i
$216$	−4.86373			−0.330935
$217$			8.88240i			0.602977i
$218$		−	4.29397i		−	0.290824i
$219$	3.66842			0.247889
$220$	0.557400	−	2.86679i	0.0375799	−	0.193279i
$221$		0			0
$222$			2.85715i			0.191759i
$223$			0.669364i			0.0448239i	0.999749	+	0.0224120i	$0.00713455\pi$
$223$			0.669364i			0.0448239i	−0.999749	+	0.0224120i	$0.992865\pi$
$224$	2.15124			0.143736
$225$	−9.66647	−	3.90666i	−0.644431	−	0.260444i
$226$	18.7154			1.24493
$227$		−	5.40643i		−	0.358837i	−0.983773	−	0.179419i	$-0.942578\pi$
$227$		−	5.40643i		−	0.358837i	0.983773	−	0.179419i	$-0.0574217\pi$
$228$			2.54046i			0.168246i
$229$	2.23462			0.147668			0.0738340	−	0.997271i	$-0.476476\pi$
$229$	2.23462			0.147668			0.0738340	+	0.997271i	$0.476476\pi$
$230$	−2.18092	+	11.2168i	−0.143806	+	0.739614i
$231$	−2.68731			−0.176812
$232$			7.96020i			0.522613i
$233$		−	0.131688i		−	0.00862719i	−0.999991	−	0.00431360i	$-0.998627\pi$
$233$		−	0.131688i		−	0.00862719i	0.999991	−	0.00431360i	$-0.00137306\pi$
$234$		0			0
$235$	−16.0325	−	3.11726i	−1.04585	−	0.203347i
$236$	−14.6950			−0.956564
$237$		−	8.55303i		−	0.555579i
$238$		−	6.18300i		−	0.400784i
$239$	−22.7145			−1.46928			−0.734639	−	0.678458i	$-0.762649\pi$
$239$	−22.7145			−1.46928			−0.734639	+	0.678458i	$0.762649\pi$
$240$	2.09936	+	0.408187i	0.135513	+	0.0263483i
$241$	−21.9809			−1.41591			−0.707956	−	0.706256i	$-0.750383\pi$
$241$	−21.9809			−1.41591			−0.707956	+	0.706256i	$0.750383\pi$
$242$		−	9.29416i		−	0.597451i
$243$		−	16.1251i		−	1.03442i
$244$	−11.2009			−0.717062
$245$	−1.01238	+	5.20683i	−0.0646787	+	0.332652i
$246$	8.31174			0.529937
$247$		0			0
$248$			4.12897i			0.262190i
$249$	−13.3883			−0.848450
$250$	9.37569	+	6.09069i	0.592970	+	0.385209i
$251$	9.38645			0.592468			0.296234	−	0.955115i	$-0.404269\pi$
$251$	9.38645			0.592468			0.296234	+	0.955115i	$0.404269\pi$
$252$			4.48579i			0.282578i
$253$		−	6.67438i		−	0.419615i
$254$	−17.6498			−1.10745
$255$	1.17319	−	6.03390i	0.0734682	−	0.377858i
$256$	1.00000			0.0625000
$257$			7.36768i			0.459583i	0.973240	+	0.229792i	$0.0738045\pi$
$257$			7.36768i			0.459583i	−0.973240	+	0.229792i	$0.926195\pi$
$258$		−	3.20699i		−	0.199659i
$259$	6.42630			0.399311
$260$		0			0
$261$	−16.5987			−1.02743
$262$			8.59263i			0.530855i
$263$			20.4624i			1.26177i	0.775877	+	0.630884i	$0.217308\pi$
$263$			20.4624i			1.26177i	−0.775877	+	0.630884i	$0.782692\pi$
$264$	−1.24919			−0.0768825
$265$	22.1261	+	4.30206i	1.35920	+	0.264273i
$266$	5.71399			0.350347
$267$			14.9430i			0.914498i
$268$			11.0454i			0.674706i
$269$	−28.7835			−1.75496			−0.877480	−	0.479614i	$-0.840777\pi$
$269$	−28.7835			−1.75496			−0.877480	+	0.479614i	$0.840777\pi$
$270$	−2.07572	+	10.6757i	−0.126324	+	0.649703i
$271$	1.82589			0.110915			0.0554575	−	0.998461i	$-0.482338\pi$
$271$	1.82589			0.110915			0.0554575	+	0.998461i	$0.482338\pi$
$272$		−	2.87416i		−	0.174271i
$273$		0			0
$274$	6.43023			0.388465
$275$	−6.05462	−	2.44695i	−0.365107	−	0.147556i
$276$	4.88768			0.294203
$277$		−	1.10372i		−	0.0663163i	−0.999450	−	0.0331581i	$-0.989443\pi$
$277$		−	1.10372i		−	0.0663163i	0.999450	−	0.0331581i	$-0.0105565\pi$
$278$		−	1.79435i		−	0.107618i
$279$	−8.60977			−0.515454
$280$	0.918093	−	4.72189i	0.0548666	−	0.282187i
$281$	−2.66535			−0.159002			−0.0795008	−	0.996835i	$-0.525333\pi$
$281$	−2.66535			−0.159002			−0.0795008	+	0.996835i	$0.525333\pi$
$282$			6.98610i			0.416016i
$283$		−	24.5173i		−	1.45740i	−0.684831	−	0.728702i	$-0.740124\pi$
$283$		−	24.5173i		−	1.45740i	0.684831	−	0.728702i	$-0.259876\pi$
$284$	−14.0739			−0.835130
$285$	5.57621	+	1.08420i	0.330306	+	0.0642225i
$286$		0			0
$287$		−	18.6948i		−	1.10352i
$288$			2.08521i			0.122872i
$289$	8.73921			0.514071
$290$	17.4724	+	3.39721i	1.02601	+	0.199491i
$291$	4.83403			0.283376
$292$		−	3.83547i		−	0.224454i
$293$			8.74457i			0.510863i	0.966827	+	0.255432i	$0.0822176\pi$
$293$			8.74457i			0.510863i	−0.966827	+	0.255432i	$0.917782\pi$
$294$	2.26885			0.132322
$295$	−6.27146	+	32.2550i	−0.365138	+	1.87796i
$296$	2.98725			0.173631
$297$		−	6.35241i		−	0.368604i
$298$			8.49082i			0.491860i
$299$		0			0
$300$	1.79191	−	4.43382i	0.103456	−	0.255987i
$301$	−7.21317			−0.415760
$302$		−	2.97802i		−	0.171366i
$303$			1.93977i			0.111437i
$304$	2.65614			0.152340
$305$	−4.78025	+	24.5855i	−0.273716	+	1.40776i
$306$	5.99323			0.342610
$307$			12.4345i			0.709674i	0.934928	+	0.354837i	$0.115464\pi$
$307$			12.4345i			0.709674i	−0.934928	+	0.354837i	$0.884536\pi$
$308$			2.80969i			0.160097i
$309$	3.12004			0.177493
$310$	9.06294	+	1.76214i	0.514740	+	0.100083i
$311$	−0.269313			−0.0152713			−0.00763567	−	0.999971i	$-0.502431\pi$
$311$	−0.269313			−0.0152713			−0.00763567	+	0.999971i	$0.502431\pi$
$312$		0			0
$313$			10.5866i			0.598389i	0.954192	+	0.299195i	$0.0967180\pi$
$313$			10.5866i			0.598389i	−0.954192	+	0.299195i	$0.903282\pi$
$314$	−14.3503			−0.809833
$315$	9.84614	+	1.91442i	0.554767	+	0.107865i
$316$	−8.94252			−0.503056
$317$			21.0117i			1.18014i	0.807354	+	0.590068i	$0.200899\pi$
$317$			21.0117i			1.18014i	−0.807354	+	0.590068i	$0.799101\pi$
$318$		−	9.64136i		−	0.540661i
$319$	−10.3966			−0.582100
$320$	0.426774	−	2.19496i	0.0238574	−	0.122702i
$321$	1.80817			0.100922
$322$		−	10.9934i		−	0.612636i
$323$		−	7.63417i		−	0.424777i
$324$	−1.60374			−0.0890966
$325$		0			0
$326$	−12.7139			−0.704160
$327$			4.10695i			0.227115i
$328$		−	8.69023i		−	0.479838i
$329$	15.7131			0.866293
$330$	−0.533123	+	2.74193i	−0.0293475	+	0.150938i
$331$	−26.6423			−1.46440			−0.732198	−	0.681092i	$-0.761505\pi$
$331$	−26.6423			−1.46440			−0.732198	+	0.681092i	$0.761505\pi$
$332$			13.9980i			0.768239i
$333$			6.22905i			0.341350i
$334$	−1.32171			−0.0723210
$335$	24.2443	+	4.71390i	1.32461	+	0.257548i
$336$	−2.05754			−0.112248
$337$		−	3.43601i		−	0.187171i	−0.995611	−	0.0935856i	$-0.970167\pi$
$337$		−	3.43601i		−	0.187171i	0.995611	−	0.0935856i	$-0.0298329\pi$
$338$		0			0
$339$	−17.9003			−0.972211
$340$	−6.30867	−	1.22662i	−0.342136	−	0.0665227i
$341$	−5.39276			−0.292034
$342$			5.53861i			0.299494i
$343$		−	20.1618i		−	1.08863i
$344$	−3.35303			−0.180783
$345$	2.08593	−	10.7283i	0.112303	−	0.577591i
$346$	23.9387			1.28695
$347$			13.6671i			0.733686i	0.930283	+	0.366843i	$0.119561\pi$
$347$			13.6671i			0.733686i	−0.930283	+	0.366843i	$0.880439\pi$
$348$		−	7.61350i		−	0.408127i
$349$	8.18464			0.438114			0.219057	−	0.975712i	$-0.429702\pi$
$349$	8.18464			0.438114			0.219057	+	0.975712i	$0.429702\pi$
$350$	−9.97256	−	4.03036i	−0.533056	−	0.215432i
$351$		0			0
$352$			1.30608i			0.0696142i
$353$			21.4420i			1.14124i	0.821214	+	0.570621i	$0.193297\pi$
$353$			21.4420i			1.14124i	−0.821214	+	0.570621i	$0.806703\pi$
$354$	14.0550			0.747014
$355$	−6.00636	+	30.8916i	−0.318785	+	1.63956i
$356$	15.6235			0.828043
$357$			5.91371i			0.312987i
$358$			0.841778i			0.0444893i
$359$	−7.09493			−0.374456			−0.187228	−	0.982316i	$-0.559950\pi$
$359$	−7.09493			−0.374456			−0.187228	+	0.982316i	$0.559950\pi$
$360$	4.57696	+	0.889915i	0.241227	+	0.0469026i
$361$	−11.9449			−0.628680
$362$		−	6.20054i		−	0.325893i
$363$			8.88936i			0.466571i
$364$		0			0
$365$	−8.41871	−	1.63688i	−0.440655	−	0.0856782i
$366$	10.7130			0.559979
$367$			23.9033i			1.24774i	0.781526	+	0.623872i	$0.214441\pi$
$367$			23.9033i			1.24774i	−0.781526	+	0.623872i	$0.785559\pi$
$368$		−	5.11025i		−	0.266390i
$369$	18.1210			0.943340
$370$	1.27488	−	6.55691i	0.0662780	−	0.340878i
$371$	−21.6853			−1.12585
$372$		−	3.94914i		−	0.204753i
$373$		−	11.5127i		−	0.596105i	−0.954549	−	0.298053i	$-0.903663\pi$
$373$		−	11.5127i		−	0.596105i	0.954549	−	0.298053i	$-0.0963371\pi$
$374$	3.75387			0.194108
$375$	−8.96734	−	5.82542i	−0.463071	−	0.300823i
$376$	7.30423			0.376687
$377$		0			0
$378$		−	10.4630i		−	0.538161i
$379$	2.64445			0.135836			0.0679180	−	0.997691i	$-0.478364\pi$
$379$	2.64445			0.135836			0.0679180	+	0.997691i	$0.478364\pi$
$380$	1.13357	−	5.83013i	0.0581510	−	0.299079i
$381$	16.8811			0.864843
$382$		−	10.7222i		−	0.548594i
$383$		−	16.2424i		−	0.829949i	−0.909833	−	0.414975i	$-0.863790\pi$
$383$		−	16.2424i		−	0.829949i	0.909833	−	0.414975i	$-0.136210\pi$
$384$	−0.956446			−0.0488084
$385$	6.16716	+	1.19910i	0.314307	+	0.0611119i
$386$	−25.9564			−1.32115
$387$		−	6.99178i		−	0.355412i
$388$		−	5.05416i		−	0.256586i
$389$	23.7722			1.20530			0.602649	−	0.798006i	$-0.294112\pi$
$389$	23.7722			1.20530			0.602649	+	0.798006i	$0.294112\pi$
$390$		0			0
$391$	−14.6877			−0.742787
$392$		−	2.37217i		−	0.119813i
$393$		−	8.21839i		−	0.414563i
$394$	5.14709			0.259307
$395$	−3.81644	+	19.6285i	−0.192026	+	0.987617i
$396$	−2.72345			−0.136858
$397$		−	34.6274i		−	1.73790i	−0.494901	−	0.868949i	$-0.664796\pi$
$397$		−	34.6274i		−	1.73790i	0.494901	−	0.868949i	$-0.335204\pi$
$398$			9.50447i			0.476416i
$399$	−5.46513			−0.273598
$400$	−4.63573	−	1.87351i	−0.231786	−	0.0936754i
$401$	−4.37028			−0.218242			−0.109121	−	0.994028i	$-0.534804\pi$
$401$	−4.37028			−0.218242			−0.109121	+	0.994028i	$0.534804\pi$
$402$		−	10.5643i		−	0.526901i
$403$		0			0
$404$	2.02811			0.100902
$405$	−0.684434	+	3.52015i	−0.0340098	+	0.174917i
$406$	−17.1243			−0.849865
$407$			3.90159i			0.193394i
$408$			2.74898i			0.136095i
$409$	−11.2279			−0.555186			−0.277593	−	0.960699i	$-0.589537\pi$
$409$	−11.2279			−0.555186			−0.277593	+	0.960699i	$0.589537\pi$
$410$	−19.0747	−	3.70877i	−0.942034	−	0.183163i
$411$	−6.15017			−0.303366
$412$		−	3.26212i		−	0.160713i
$413$		−	31.6125i		−	1.55555i
$414$	10.6559			0.523711
$415$	30.7251	+	5.97398i	1.50823	+	0.293251i
$416$		0			0
$417$			1.71620i			0.0840427i
$418$			3.46913i			0.169681i
$419$	−18.3230			−0.895137			−0.447569	−	0.894250i	$-0.647710\pi$
$419$	−18.3230			−0.895137			−0.447569	+	0.894250i	$0.647710\pi$
$420$	−0.878107	+	4.51623i	−0.0428472	+	0.220370i
$421$	−8.92506			−0.434981			−0.217490	−	0.976062i	$-0.569787\pi$
$421$	−8.92506			−0.434981			−0.217490	+	0.976062i	$0.569787\pi$
$422$			25.8770i			1.25967i
$423$			15.2309i			0.740550i
$424$	−10.0804			−0.489548
$425$	−5.38476	+	13.3238i	−0.261199	+	0.646300i
$426$	13.4609			0.652182
$427$		−	24.0958i		−	1.16608i
$428$		−	1.89051i		−	0.0913814i
$429$		0			0
$430$	−1.43099	+	7.35978i	−0.0690083	+	0.354920i
$431$	−34.8123			−1.67685			−0.838425	−	0.545017i	$-0.816523\pi$
$431$	−34.8123			−1.67685			−0.838425	+	0.545017i	$0.816523\pi$
$432$		−	4.86373i		−	0.234006i
$433$		−	37.9777i		−	1.82509i	−0.408972	−	0.912547i	$-0.634113\pi$
$433$		−	37.9777i		−	1.82509i	0.408972	−	0.912547i	$-0.365887\pi$
$434$	−8.88240			−0.426369
$435$	−16.7114	−	3.24925i	−0.801249	−	0.155790i
$436$	4.29397			0.205644
$437$		−	13.5735i		−	0.649310i
$438$			3.66842i			0.175284i
$439$	16.6128			0.792887			0.396443	−	0.918059i	$-0.370244\pi$
$439$	16.6128			0.792887			0.396443	+	0.918059i	$0.370244\pi$
$440$	2.86679	+	0.557400i	0.136669	+	0.0265730i
$441$	4.94648			0.235547
$442$		0			0
$443$			16.5892i			0.788177i	0.919072	+	0.394089i	$0.128940\pi$
$443$			16.5892i			0.788177i	−0.919072	+	0.394089i	$0.871060\pi$
$444$	−2.85715			−0.135594
$445$	6.66770	−	34.2930i	0.316079	−	1.62564i
$446$	−0.669364			−0.0316953
$447$		−	8.12101i		−	0.384111i
$448$			2.15124i			0.101636i
$449$	−19.4158			−0.916287			−0.458144	−	0.888878i	$-0.651485\pi$
$449$	−19.4158			−0.916287			−0.458144	+	0.888878i	$0.651485\pi$
$450$	3.90666	−	9.66647i	0.184162	−	0.455682i
$451$	11.3501			0.534456
$452$			18.7154i			0.880300i
$453$			2.84831i			0.133825i
$454$	5.40643			0.253736
$455$		0			0
$456$	−2.54046			−0.118968
$457$			8.84923i			0.413950i	0.978346	+	0.206975i	$0.0663618\pi$
$457$			8.84923i			0.413950i	−0.978346	+	0.206975i	$0.933638\pi$
$458$			2.23462i			0.104417i
$459$	−13.9791			−0.652490
$460$	−11.2168	−	2.18092i	−0.522986	−	0.101686i
$461$	17.3352			0.807380			0.403690	−	0.914896i	$-0.367727\pi$
$461$	17.3352			0.807380			0.403690	+	0.914896i	$0.367727\pi$
$462$		−	2.68731i		−	0.125025i
$463$			17.0652i			0.793088i	0.918016	+	0.396544i	$0.129791\pi$
$463$			17.0652i			0.793088i	−0.918016	+	0.396544i	$0.870209\pi$
$464$	−7.96020			−0.369543
$465$	−8.66821	−	1.68539i	−0.401979	−	0.0781581i
$466$	0.131688			0.00610035
$467$		−	22.5357i		−	1.04283i	−0.853303	−	0.521415i	$-0.825404\pi$
$467$		−	22.5357i		−	1.04283i	0.853303	−	0.521415i	$-0.174596\pi$
$468$		0			0
$469$	−23.7613			−1.09720
$470$	3.11726	−	16.0325i	0.143788	−	0.739525i
$471$	13.7253			0.632427
$472$		−	14.6950i		−	0.676393i
$473$		−	4.37932i		−	0.201361i
$474$	8.55303			0.392854
$475$	−12.3131	−	4.97630i	−0.564966	−	0.228328i
$476$	6.18300			0.283397
$477$		−	21.0198i		−	0.962429i
$478$		−	22.7145i		−	1.03894i
$479$	−33.3487			−1.52374			−0.761870	−	0.647731i	$-0.775718\pi$
$479$	−33.3487			−1.52374			−0.761870	+	0.647731i	$0.775718\pi$
$480$	−0.408187	+	2.09936i	−0.0186311	+	0.0958224i
$481$		0			0
$482$		−	21.9809i		−	1.00120i
$483$			10.5146i			0.478429i
$484$	9.29416			0.422462
$485$	−11.0937	−	2.15699i	−0.503739	−	0.0979437i
$486$	16.1251			0.731448
$487$			32.8658i			1.48929i	0.667459	+	0.744647i	$0.267382\pi$
$487$			32.8658i			1.48929i	−0.667459	+	0.744647i	$0.732618\pi$
$488$		−	11.2009i		−	0.507040i
$489$	12.1602			0.549903
$490$	−5.20683	−	1.01238i	−0.235221	−	0.0457348i
$491$	−17.6525			−0.796645			−0.398322	−	0.917245i	$-0.630407\pi$
$491$	−17.6525			−0.796645			−0.398322	+	0.917245i	$0.630407\pi$
$492$			8.31174i			0.374722i
$493$			22.8789i			1.03041i
$494$		0			0
$495$	−1.16230	+	5.97787i	−0.0522414	+	0.268685i
$496$	−4.12897			−0.185396
$497$		−	30.2762i		−	1.35807i
$498$		−	13.3883i		−	0.599945i
$499$	37.3227			1.67079			0.835396	−	0.549648i	$-0.185238\pi$
$499$	37.3227			1.67079			0.835396	+	0.549648i	$0.185238\pi$
$500$	−6.09069	+	9.37569i	−0.272384	+	0.419293i
$501$	1.26415			0.0564780
$502$			9.38645i			0.418938i
$503$		−	27.1489i		−	1.21051i	−0.796032	−	0.605254i	$-0.793072\pi$
$503$		−	27.1489i		−	1.21051i	0.796032	−	0.605254i	$-0.206928\pi$
$504$	−4.48579			−0.199813
$505$	0.865544	−	4.45162i	0.0385162	−	0.198094i
$506$	6.67438			0.296712
$507$		0			0
$508$		−	17.6498i		−	0.783083i
$509$	−11.3658			−0.503781			−0.251890	−	0.967756i	$-0.581052\pi$
$509$	−11.3658			−0.503781			−0.251890	+	0.967756i	$0.581052\pi$
$510$	6.03390	+	1.17319i	0.267186	+	0.0519499i
$511$	8.25101			0.365003
$512$			1.00000i			0.0441942i
$513$		−	12.9188i		−	0.570377i
$514$	−7.36768			−0.324975
$515$	−7.16023	−	1.39219i	−0.315517	−	0.0613471i
$516$	3.20699			0.141180
$517$			9.53989i			0.419564i
$518$			6.42630i			0.282355i
$519$	−22.8961			−1.00503
$520$		0			0
$521$	31.9131			1.39814			0.699069	−	0.715054i	$-0.253598\pi$
$521$	31.9131			1.39814			0.699069	+	0.715054i	$0.253598\pi$
$522$		−	16.5987i		−	0.726506i
$523$		−	25.7706i		−	1.12687i	−0.826160	−	0.563435i	$-0.809479\pi$
$523$		−	25.7706i		−	1.12687i	0.826160	−	0.563435i	$-0.190521\pi$
$524$	−8.59263			−0.375371
$525$	9.53821	+	3.85482i	0.416282	+	0.168238i
$526$	−20.4624			−0.892205
$527$			11.8673i			0.516948i
$528$		−	1.24919i		−	0.0543641i
$529$	−3.11463			−0.135419
$530$	−4.30206	+	22.1261i	−0.186869	+	0.961097i
$531$	30.6422			1.32976
$532$			5.71399i			0.247733i
$533$		0			0
$534$	−14.9430			−0.646648
$535$	−4.14961	−	0.806822i	−0.179403	−	0.0348820i
$536$	−11.0454			−0.477089
$537$		−	0.805115i		−	0.0347433i
$538$		−	28.7835i		−	1.24094i
$539$	3.09824			0.133451
$540$	−10.6757	−	2.07572i	−0.459409	−	0.0893246i
$541$	−29.0524			−1.24906			−0.624531	−	0.781000i	$-0.714710\pi$
$541$	−29.0524			−1.24906			−0.624531	+	0.781000i	$0.714710\pi$
$542$			1.82589i			0.0784287i
$543$			5.93048i			0.254501i
$544$	2.87416			0.123229
$545$	1.83255	−	9.42510i	0.0784980	−	0.403727i
$546$		0			0
$547$		−	14.0848i		−	0.602221i	−0.953589	−	0.301111i	$-0.902643\pi$
$547$		−	14.0848i		−	0.602221i	0.953589	−	0.301111i	$-0.0973574\pi$
$548$			6.43023i			0.274686i
$549$	23.3562			0.996818
$550$	2.44695	−	6.05462i	0.104338	−	0.258170i
$551$	−21.1434			−0.900740
$552$			4.88768i			0.208033i
$553$		−	19.2375i		−	0.818061i
$554$	1.10372			0.0468927
$555$	−1.21936	+	6.27133i	−0.0517588	+	0.266203i
$556$	1.79435			0.0760975
$557$		−	1.65529i		−	0.0701367i	−0.999385	−	0.0350683i	$-0.988835\pi$
$557$		−	1.65529i		−	0.0701367i	0.999385	−	0.0350683i	$-0.0111649\pi$
$558$		−	8.60977i		−	0.364481i
$559$		0			0
$560$	4.72189	+	0.918093i	0.199536	+	0.0387965i
$561$	−3.59038			−0.151586
$562$		−	2.66535i		−	0.112431i
$563$			36.3020i			1.52995i	0.644061	+	0.764974i	$0.277248\pi$
$563$			36.3020i			1.52995i	−0.644061	+	0.764974i	$0.722752\pi$
$564$	−6.98610			−0.294168
$565$	41.0797	+	7.98726i	1.72823	+	0.336027i
$566$	24.5173			1.03054
$567$		−	3.45002i		−	0.144887i
$568$		−	14.0739i		−	0.590526i
$569$	15.1125			0.633548			0.316774	−	0.948501i	$-0.397400\pi$
$569$	15.1125			0.633548			0.316774	+	0.948501i	$0.397400\pi$
$570$	−1.08420	+	5.57621i	−0.0454122	+	0.233562i
$571$	−35.2350			−1.47454			−0.737269	−	0.675600i	$-0.763885\pi$
$571$	−35.2350			−1.47454			−0.737269	+	0.675600i	$0.763885\pi$
$572$		0			0
$573$			10.2552i			0.428416i
$574$	18.6948			0.780304
$575$	−9.57409	+	23.6897i	−0.399267	+	0.987929i
$576$	−2.08521			−0.0868838
$577$			25.4407i			1.05911i	0.848275	+	0.529556i	$0.177641\pi$
$577$			25.4407i			1.05911i	−0.848275	+	0.529556i	$0.822359\pi$
$578$			8.73921i			0.363503i
$579$	24.8259			1.03173
$580$	−3.39721	+	17.4724i	−0.141061	+	0.725500i
$581$	−30.1130			−1.24930
$582$			4.83403i			0.200377i
$583$		−	13.1658i		−	0.545271i
$584$	3.83547			0.158713
$585$		0			0
$586$	−8.74457			−0.361235
$587$		−	16.4237i		−	0.677877i	−0.940809	−	0.338938i	$-0.889932\pi$
$587$		−	16.4237i		−	0.677877i	0.940809	−	0.338938i	$-0.110068\pi$
$588$			2.26885i			0.0935660i
$589$	−10.9671			−0.451892
$590$	−32.2550	−	6.27146i	−1.32792	−	0.258192i
$591$	−4.92291			−0.202502
$592$			2.98725i			0.122775i
$593$		−	23.1420i		−	0.950327i	−0.879898	−	0.475163i	$-0.842389\pi$
$593$		−	23.1420i		−	0.950327i	0.879898	−	0.475163i	$-0.157611\pi$
$594$	6.35241			0.260643
$595$	2.63875	−	13.5715i	0.108178	−	0.556376i
$596$	−8.49082			−0.347798
$597$		−	9.09052i		−	0.372050i
$598$		0			0
$599$	27.7657			1.13448			0.567238	−	0.823554i	$-0.308012\pi$
$599$	27.7657			1.13448			0.567238	+	0.823554i	$0.308012\pi$
$600$	4.43382	+	1.79191i	0.181010	+	0.0731544i
$601$	−13.2621			−0.540974			−0.270487	−	0.962724i	$-0.587185\pi$
$601$	−13.2621			−0.540974			−0.270487	+	0.962724i	$0.587185\pi$
$602$		−	7.21317i		−	0.293987i
$603$		−	23.0320i		−	0.937936i
$604$	2.97802			0.121174
$605$	3.96651	−	20.4003i	0.161262	−	0.829392i
$606$	−1.93977			−0.0787979
$607$			37.9308i			1.53957i	0.638306	+	0.769783i	$0.279635\pi$
$607$			37.9308i			1.53957i	−0.638306	+	0.769783i	$0.720365\pi$
$608$			2.65614i			0.107721i
$609$	16.3785			0.663689
$610$	−24.5855	−	4.78025i	−0.995438	−	0.193546i
$611$		0			0
$612$			5.99323i			0.242262i
$613$			2.38979i			0.0965227i	0.998835	+	0.0482614i	$0.0153680\pi$
$613$			2.38979i			0.0965227i	−0.998835	+	0.0482614i	$0.984632\pi$
$614$	−12.4345			−0.501815
$615$	18.2440	+	3.54724i	0.735667	+	0.143038i
$616$	−2.80969			−0.113205
$617$		−	19.0583i		−	0.767259i	−0.923487	−	0.383630i	$-0.874674\pi$
$617$		−	19.0583i		−	0.767259i	0.923487	−	0.383630i	$-0.125326\pi$
$618$			3.12004i			0.125506i
$619$	18.6920			0.751294			0.375647	−	0.926763i	$-0.377421\pi$
$619$	18.6920			0.751294			0.375647	+	0.926763i	$0.377421\pi$
$620$	−1.76214	+	9.06294i	−0.0707692	+	0.363976i
$621$	−24.8549			−0.997391
$622$		−	0.269313i		−	0.0107985i
$623$			33.6098i			1.34655i
$624$		0			0
$625$	17.9799	+	17.3701i	0.719197	+	0.694806i
$626$	−10.5866			−0.423125
$627$		−	3.31803i		−	0.132509i
$628$		−	14.3503i		−	0.572639i
$629$	8.58584			0.342340
$630$	−1.91442	+	9.84614i	−0.0762723	+	0.392279i
$631$	−21.5119			−0.856377			−0.428188	−	0.903689i	$-0.640848\pi$
$631$	−21.5119			−0.856377			−0.428188	+	0.903689i	$0.640848\pi$
$632$		−	8.94252i		−	0.355714i
$633$		−	24.7500i		−	0.983723i
$634$	−21.0117			−0.834482
$635$	−38.7406	−	7.53248i	−1.53738	−	0.298917i
$636$	9.64136			0.382305
$637$		0			0
$638$		−	10.3966i		−	0.411607i
$639$	29.3470			1.16095
$640$	2.19496	+	0.426774i	0.0867635	+	0.0168697i
$641$	34.3509			1.35678			0.678390	−	0.734702i	$-0.262678\pi$
$641$	34.3509			1.35678			0.678390	+	0.734702i	$0.262678\pi$
$642$			1.80817i			0.0713629i
$643$		−	31.1063i		−	1.22671i	−0.789807	−	0.613356i	$-0.789819\pi$
$643$		−	31.1063i		−	1.22671i	0.789807	−	0.613356i	$-0.210181\pi$
$644$	10.9934			0.433199
$645$	1.36866	−	7.03923i	0.0538910	−	0.277169i
$646$	7.63417			0.300362
$647$		−	4.61263i		−	0.181341i	−0.995881	−	0.0906705i	$-0.971099\pi$
$647$		−	4.61263i		−	0.181341i	0.995881	−	0.0906705i	$-0.0289010\pi$
$648$		−	1.60374i		−	0.0630008i
$649$	19.1928			0.753385
$650$		0			0
$651$	8.49554			0.332966
$652$		−	12.7139i		−	0.497916i
$653$			15.0219i			0.587853i	0.955828	+	0.293926i	$0.0949621\pi$
$653$			15.0219i			0.587853i	−0.955828	+	0.293926i	$0.905038\pi$
$654$	−4.10695			−0.160594
$655$	−3.66711	+	18.8605i	−0.143286	+	0.736941i
$656$	8.69023			0.339297
$657$			7.99776i			0.312022i
$658$			15.7131i			0.612562i
$659$	37.6385			1.46619			0.733095	−	0.680126i	$-0.238075\pi$
$659$	37.6385			1.46619			0.733095	+	0.680126i	$0.238075\pi$
$660$	−2.74193	−	0.533123i	−0.106730	−	0.0207518i
$661$	14.5505			0.565949			0.282974	−	0.959127i	$-0.408679\pi$
$661$	14.5505			0.565949			0.282974	+	0.959127i	$0.408679\pi$
$662$		−	26.6423i		−	1.03548i
$663$		0			0
$664$	−13.9980			−0.543227
$665$	12.5420	+	2.43859i	0.486358	+	0.0945643i
$666$	−6.22905			−0.241371
$667$			40.6786i			1.57508i
$668$		−	1.32171i		−	0.0511387i
$669$	0.640210			0.0247520
$670$	−4.71390	+	24.2443i	−0.182114	+	0.936638i
$671$	14.6292			0.564754
$672$		−	2.05754i		−	0.0793715i
$673$			3.50799i			0.135223i	0.997712	+	0.0676115i	$0.0215378\pi$
$673$			3.50799i			0.135223i	−0.997712	+	0.0676115i	$0.978462\pi$
$674$	3.43601			0.132350
$675$	−9.11224	+	22.5469i	−0.350730	+	0.867832i
$676$		0			0
$677$			33.5349i			1.28885i	0.764668	+	0.644425i	$0.222903\pi$
$677$			33.5349i			1.28885i	−0.764668	+	0.644425i	$0.777097\pi$
$678$		−	17.9003i		−	0.687457i
$679$	10.8727			0.417256
$680$	1.22662	−	6.30867i	0.0470386	−	0.241927i
$681$	−5.17096			−0.198152
$682$		−	5.39276i		−	0.206499i
$683$			39.6392i			1.51675i	0.651817	+	0.758376i	$0.274007\pi$
$683$			39.6392i			1.51675i	−0.651817	+	0.758376i	$0.725993\pi$
$684$	−5.53861			−0.211774
$685$	14.1141	+	2.74426i	0.539273	+	0.104853i
$686$	20.1618			0.769780
$687$		−	2.13730i		−	0.0815429i
$688$		−	3.35303i		−	0.127833i
$689$		0			0
$690$	10.7283	+	2.08593i	0.408418	+	0.0794102i
$691$	17.6727			0.672300			0.336150	−	0.941808i	$-0.390875\pi$
$691$	17.6727			0.672300			0.336150	+	0.941808i	$0.390875\pi$
$692$			23.9387i			0.910012i
$693$		−	5.85879i		−	0.222557i
$694$	−13.6671			−0.518794
$695$	0.765783	−	3.93854i	0.0290478	−	0.149397i
$696$	7.61350			0.288589
$697$		−	24.9771i		−	0.946075i
$698$			8.18464i			0.309793i
$699$	−0.125953			−0.00476397
$700$	4.03036	−	9.97256i	0.152333	−	0.376927i
$701$	−46.5635			−1.75868			−0.879340	−	0.476194i	$-0.842016\pi$
$701$	−46.5635			−1.75868			−0.879340	+	0.476194i	$0.842016\pi$
$702$		0			0
$703$			7.93456i			0.299258i
$704$	−1.30608			−0.0492247
$705$	−2.98149	+	15.3342i	−0.112289	+	0.577521i
$706$	−21.4420			−0.806980
$707$			4.36294i			0.164085i
$708$			14.0550i			0.528219i
$709$	26.2769			0.986849			0.493425	−	0.869789i	$-0.335745\pi$
$709$	26.2769			0.986849			0.493425	+	0.869789i	$0.335745\pi$
$710$	−30.8916	−	6.00636i	−1.15934	−	0.225415i
$711$	18.6470			0.699318
$712$			15.6235i			0.585515i
$713$			21.1001i			0.790203i
$714$	−5.91371			−0.221315
$715$		0			0
$716$	−0.841778			−0.0314587
$717$			21.7252i			0.811342i
$718$		−	7.09493i		−	0.264780i
$719$	−11.3458			−0.423128			−0.211564	−	0.977364i	$-0.567856\pi$
$719$	−11.3458			−0.423128			−0.211564	+	0.977364i	$0.567856\pi$
$720$	−0.889915	+	4.57696i	−0.0331652	+	0.170573i
$721$	7.01759			0.261349
$722$		−	11.9449i		−	0.444544i
$723$			21.0235i			0.781873i
$724$	6.20054			0.230441
$725$	36.9013	+	14.9135i	1.37048	+	0.553874i
$726$	−8.88936			−0.329915
$727$			33.1374i			1.22900i	0.788918	+	0.614499i	$0.210642\pi$
$727$			33.1374i			1.22900i	−0.788918	+	0.614499i	$0.789358\pi$
$728$		0			0
$729$	−10.6116			−0.393020
$730$	1.63688	−	8.41871i	0.0605836	−	0.311590i
$731$	−9.63714			−0.356443
$732$			10.7130i			0.395965i
$733$			32.4103i			1.19710i	0.801085	+	0.598550i	$0.204256\pi$
$733$			32.4103i			1.19710i	−0.801085	+	0.598550i	$0.795744\pi$
$734$	−23.9033			−0.882289
$735$	4.98005	+	0.968289i	0.183692	+	0.0357159i
$736$	5.11025			0.188366
$737$		−	14.4262i		−	0.531395i
$738$			18.1210i			0.667042i
$739$	19.0620			0.701208			0.350604	−	0.936524i	$-0.385976\pi$
$739$	19.0620			0.701208			0.350604	+	0.936524i	$0.385976\pi$
$740$	6.55691	+	1.27488i	0.241037	+	0.0468656i
$741$		0			0
$742$		−	21.6853i		−	0.796094i
$743$			25.4983i			0.935441i	0.883876	+	0.467721i	$0.154925\pi$
$743$			25.4983i			0.935441i	−0.883876	+	0.467721i	$0.845075\pi$
$744$	3.94914			0.144782
$745$	−3.62366	+	18.6370i	−0.132761	+	0.682808i
$746$	11.5127			0.421510
$747$		−	29.1887i		−	1.06796i
$748$			3.75387i			0.137255i
$749$	4.06694			0.148603
$750$	5.82542	−	8.96734i	0.212714	−	0.327441i
$751$	−19.5176			−0.712209			−0.356104	−	0.934446i	$-0.615895\pi$
$751$	−19.5176			−0.712209			−0.356104	+	0.934446i	$0.615895\pi$
$752$			7.30423i			0.266358i
$753$		−	8.97763i		−	0.327163i
$754$		0			0
$755$	1.27094	−	6.53663i	0.0462543	−	0.237893i
$756$	10.4630			0.380537
$757$			23.6562i			0.859801i	0.902876	+	0.429900i	$0.141451\pi$
$757$			23.6562i			0.859801i	−0.902876	+	0.429900i	$0.858549\pi$
$758$			2.64445i			0.0960506i
$759$	−6.38368			−0.231713
$760$	5.83013	+	1.13357i	0.211481	+	0.0411190i
$761$	16.2681			0.589717			0.294859	−	0.955541i	$-0.404727\pi$
$761$	16.2681			0.589717			0.294859	+	0.955541i	$0.404727\pi$
$762$			16.8811i			0.611537i
$763$			9.23735i			0.334414i
$764$	10.7222			0.387915
$765$	13.1549	+	2.55776i	0.475617	+	0.0924758i
$766$	16.2424			0.586863
$767$		0			0
$768$		−	0.956446i		−	0.0345128i
$769$	30.6878			1.10663			0.553314	−	0.832973i	$-0.313363\pi$
$769$	30.6878			1.10663			0.553314	+	0.832973i	$0.313363\pi$
$770$	−1.19910	+	6.16716i	−0.0432126	+	0.222249i
$771$	7.04679			0.253784
$772$		−	25.9564i		−	0.934191i
$773$		−	37.4115i		−	1.34560i	−0.739826	−	0.672798i	$-0.765092\pi$
$773$		−	37.4115i		−	1.34560i	0.739826	−	0.672798i	$-0.234908\pi$
$774$	6.99178			0.251314
$775$	19.1408	+	7.73566i	0.687557	+	0.277873i
$776$	5.05416			0.181434
$777$		−	6.14640i		−	0.220501i
$778$			23.7722i			0.852275i
$779$	23.0825			0.827016
$780$		0			0
$781$	18.3816			0.657744
$782$		−	14.6877i		−	0.525230i
$783$			38.7163i			1.38361i
$784$	2.37217			0.0847204
$785$	−31.4983	−	6.12433i	−1.12422	−	0.218587i
$786$	8.21839			0.293140
$787$			8.05503i			0.287131i	0.989641	+	0.143565i	$0.0458567\pi$
$787$			8.05503i			0.287131i	−0.989641	+	0.143565i	$0.954143\pi$
$788$			5.14709i			0.183358i
$789$	19.5712			0.696754
$790$	−19.6285	−	3.81644i	−0.698351	−	0.135783i
$791$	−40.2613			−1.43153
$792$		−	2.72345i		−	0.0967735i
$793$		0			0
$794$	34.6274			1.22888
$795$	4.11468	−	21.1624i	0.145933	−	0.750554i
$796$	−9.50447			−0.336877
$797$		−	4.94210i		−	0.175058i	−0.996162	−	0.0875290i	$-0.972103\pi$
$797$		−	4.94210i		−	0.175058i	0.996162	−	0.0875290i	$-0.0278971\pi$
$798$		−	5.46513i		−	0.193463i
$799$	20.9935			0.742697
$800$	1.87351	−	4.63573i	0.0662385	−	0.163898i
$801$	−32.5783			−1.15110
$802$		−	4.37028i		−	0.154320i
$803$			5.00942i			0.176779i
$804$	10.5643			0.372576
$805$	4.69168	−	24.1300i	0.165360	−	0.850472i
$806$		0			0
$807$			27.5298i			0.969096i
$808$			2.02811i			0.0713485i
$809$	−14.0553			−0.494160			−0.247080	−	0.968995i	$-0.579471\pi$
$809$	−14.0553			−0.494160			−0.247080	+	0.968995i	$0.579471\pi$
$810$	−3.52015	−	0.684434i	−0.123685	−	0.0240486i
$811$	−11.0393			−0.387644			−0.193822	−	0.981037i	$-0.562088\pi$
$811$	−11.0393			−0.387644			−0.193822	+	0.981037i	$0.562088\pi$
$812$		−	17.1243i		−	0.600945i
$813$		−	1.74636i		−	0.0612477i
$814$	−3.90159			−0.136750
$815$	−27.9066	−	5.42598i	−0.977527	−	0.190064i
$816$	−2.74898			−0.0962335
$817$		−	8.90612i		−	0.311586i
$818$		−	11.2279i		−	0.392575i
$819$		0			0
$820$	3.70877	−	19.0747i	0.129516	−	0.666119i
$821$	4.13968			0.144476			0.0722379	−	0.997387i	$-0.476986\pi$
$821$	4.13968			0.144476			0.0722379	+	0.997387i	$0.476986\pi$
$822$		−	6.15017i		−	0.214512i
$823$			27.7827i			0.968445i	0.874945	+	0.484222i	$0.160897\pi$
$823$			27.7827i			0.968445i	−0.874945	+	0.484222i	$0.839103\pi$
$824$	3.26212			0.113641
$825$	−2.34037	+	5.79092i	−0.0814813	+	0.201614i
$826$	31.6125			1.09994
$827$			6.46886i			0.224944i	0.993655	+	0.112472i	$0.0358769\pi$
$827$			6.46886i			0.224944i	−0.993655	+	0.112472i	$0.964123\pi$
$828$			10.6559i			0.370320i
$829$	−13.9415			−0.484208			−0.242104	−	0.970250i	$-0.577838\pi$
$829$	−13.9415			−0.484208			−0.242104	+	0.970250i	$0.577838\pi$
$830$	−5.97398	+	30.7251i	−0.207360	+	1.06648i
$831$	−1.05565			−0.0366201
$832$		0			0
$833$		−	6.81800i		−	0.236230i
$834$	−1.71620			−0.0594272
$835$	−2.90112	−	0.564074i	−0.100397	−	0.0195206i
$836$	−3.46913			−0.119982
$837$			20.0822i			0.694142i
$838$		−	18.3230i		−	0.632958i
$839$	41.0483			1.41714			0.708571	−	0.705639i	$-0.249340\pi$
$839$	41.0483			1.41714			0.708571	+	0.705639i	$0.249340\pi$
$840$	−4.51623	−	0.878107i	−0.155825	−	0.0302976i
$841$	34.3648			1.18499
$842$		−	8.92506i		−	0.307578i
$843$			2.54927i			0.0878014i
$844$	−25.8770			−0.890724
$845$		0			0
$846$	−15.2309			−0.523648
$847$			19.9940i			0.687001i
$848$		−	10.0804i		−	0.346162i
$849$	−23.4495			−0.804785
$850$	−13.3238	−	5.38476i	−0.457003	−	0.184696i
$851$	15.2656			0.523298
$852$			13.4609i			0.461162i
$853$		−	41.4242i		−	1.41834i	−0.705039	−	0.709168i	$-0.749071\pi$
$853$		−	41.4242i		−	1.41834i	0.705039	−	0.709168i	$-0.250929\pi$
$854$	24.0958			0.824540
$855$	−2.36374	+	12.1571i	−0.0808381	+	0.415762i
$856$	1.89051			0.0646164
$857$			48.9642i			1.67259i	0.548282	+	0.836293i	$0.315282\pi$
$857$			48.9642i			1.67259i	−0.548282	+	0.836293i	$0.684718\pi$
$858$		0			0
$859$	17.0890			0.583068			0.291534	−	0.956560i	$-0.405834\pi$
$859$	17.0890			0.583068			0.291534	+	0.956560i	$0.405834\pi$
$860$	−7.35978	−	1.43099i	−0.250966	−	0.0487963i
$861$	−17.8805			−0.609367
$862$		−	34.8123i		−	1.18571i
$863$		−	12.3756i		−	0.421269i	−0.977565	−	0.210635i	$-0.932447\pi$
$863$		−	12.3756i		−	0.421269i	0.977565	−	0.210635i	$-0.0675530\pi$
$864$	4.86373			0.165467
$865$	52.5445	+	10.2164i	1.78657	+	0.347369i
$866$	37.9777			1.29054
$867$		−	8.35858i		−	0.283872i
$868$		−	8.88240i		−	0.301488i
$869$	11.6796			0.396204
$870$	3.24925	−	16.7114i	0.110160	−	0.566568i
$871$		0			0
$872$			4.29397i			0.145412i
$873$			10.5390i			0.356691i
$874$	13.5735			0.459132
$875$	−20.1693	−	13.1025i	−0.681848	−	0.442946i
$876$	−3.66842			−0.123944
$877$			29.3663i			0.991629i	0.868429	+	0.495814i	$0.165130\pi$
$877$			29.3663i			0.991629i	−0.868429	+	0.495814i	$0.834870\pi$
$878$			16.6128i			0.560656i
$879$	8.36371			0.282101
$880$	−0.557400	+	2.86679i	−0.0187900	+	0.0966396i
$881$	6.22016			0.209563			0.104781	−	0.994495i	$-0.466586\pi$
$881$	6.22016			0.209563			0.104781	+	0.994495i	$0.466586\pi$
$882$			4.94648i			0.166557i
$883$		−	32.4762i		−	1.09291i	−0.837488	−	0.546456i	$-0.815977\pi$
$883$		−	32.4762i		−	1.09291i	0.837488	−	0.546456i	$-0.184023\pi$
$884$		0			0
$885$	30.8502	+	5.99831i	1.03702	+	0.201631i
$886$	−16.5892			−0.557325
$887$			36.5930i			1.22867i	0.789044	+	0.614337i	$0.210576\pi$
$887$			36.5930i			1.22867i	−0.789044	+	0.614337i	$0.789424\pi$
$888$		−	2.85715i		−	0.0958796i
$889$	37.9689			1.27344
$890$	34.2930	+	6.66770i	1.14950	+	0.223502i
$891$	2.09461			0.0701720
$892$		−	0.669364i		−	0.0224120i
$893$			19.4011i			0.649232i
$894$	8.12101			0.271607
$895$	−0.359249	+	1.84767i	−0.0120084	+	0.0617608i
$896$	−2.15124			−0.0718678
$897$		0			0
$898$		−	19.4158i		−	0.647913i
$899$	32.8674			1.09619
$900$	9.66647	+	3.90666i	0.322216	+	0.130222i
$901$	−28.9727			−0.965220
$902$			11.3501i			0.377918i
$903$			6.89901i			0.229585i
$904$	−18.7154			−0.622466
$905$	2.64623	−	13.6100i	0.0879637	−	0.452410i
$906$	−2.84831			−0.0946288
$907$			6.23158i			0.206916i	0.994634	+	0.103458i	$0.0329908\pi$
$907$			6.23158i			0.206916i	−0.994634	+	0.103458i	$0.967009\pi$
$908$			5.40643i			0.179419i
$909$	−4.22903			−0.140268
$910$		0			0
$911$	47.4457			1.57195			0.785973	−	0.618261i	$-0.212163\pi$
$911$	47.4457			1.57195			0.785973	+	0.618261i	$0.212163\pi$
$912$		−	2.54046i		−	0.0841229i
$913$		−	18.2825i		−	0.605061i
$914$	−8.84923			−0.292707
$915$	23.5147	+	4.57205i	0.777372	+	0.151147i
$916$	−2.23462			−0.0738340
$917$		−	18.4848i		−	0.610422i
$918$		−	13.9791i		−	0.461380i
$919$	52.7882			1.74132			0.870661	−	0.491883i	$-0.163691\pi$
$919$	52.7882			1.74132			0.870661	+	0.491883i	$0.163691\pi$
$920$	2.18092	−	11.2168i	0.0719029	−	0.369807i
$921$	11.8929			0.391885
$922$			17.3352i			0.570904i
$923$		0			0
$924$	2.68731			0.0884061
$925$	5.59664	−	13.8481i	0.184016	−	0.455322i
$926$	−17.0652			−0.560798
$927$			6.80220i			0.223414i
$928$		−	7.96020i		−	0.261306i
$929$	−7.11857			−0.233553			−0.116776	−	0.993158i	$-0.537256\pi$
$929$	−7.11857			−0.233553			−0.116776	+	0.993158i	$0.537256\pi$
$930$	1.68539	−	8.66821i	0.0552661	−	0.284242i
$931$	6.30082			0.206501
$932$			0.131688i			0.00431360i
$933$			0.257583i			0.00843290i
$934$	22.5357			0.737392
$935$	8.23962	+	1.60206i	0.269464	+	0.0523929i
$936$		0			0
$937$			5.13448i			0.167736i	0.996477	+	0.0838680i	$0.0267274\pi$
$937$			5.13448i			0.167736i	−0.996477	+	0.0838680i	$0.973273\pi$
$938$		−	23.7613i		−	0.775834i
$939$	10.1255			0.330433
$940$	16.0325	+	3.11726i	0.522923	+	0.101674i
$941$	−44.3630			−1.44619			−0.723096	−	0.690748i	$-0.757281\pi$
$941$	−44.3630			−1.44619			−0.723096	+	0.690748i	$0.757281\pi$
$942$			13.7253i			0.447193i
$943$		−	44.4092i		−	1.44616i
$944$	14.6950			0.478282
$945$	4.46536	−	22.9660i	0.145258	−	0.747084i
$946$	4.37932			0.142384
$947$			54.3234i			1.76527i	0.470056	+	0.882637i	$0.344234\pi$
$947$			54.3234i			1.76527i	−0.470056	+	0.882637i	$0.655766\pi$
$948$			8.55303i			0.277790i
$949$		0			0
$950$	4.97630	−	12.3131i	0.161453	−	0.399491i
$951$	20.0966			0.651676
$952$			6.18300i			0.200392i
$953$		−	37.8138i		−	1.22491i	−0.790506	−	0.612454i	$-0.790182\pi$
$953$		−	37.8138i		−	1.22491i	0.790506	−	0.612454i	$-0.209818\pi$
$954$	21.0198			0.680540
$955$	4.57595	−	23.5348i	0.148074	−	0.761567i
$956$	22.7145			0.734639
$957$			9.94383i			0.321438i
$958$		−	33.3487i		−	1.07745i
$959$	−13.8330			−0.446690
$960$	−2.09936	−	0.408187i	−0.0677567	−	0.0131742i
$961$	−13.9516			−0.450052
$962$		0			0
$963$			3.94212i			0.127033i
$964$	21.9809			0.707956
$965$	−56.9733	−	11.0775i	−1.83404	−	0.356598i
$966$	−10.5146			−0.338300
$967$		−	8.18366i		−	0.263169i	−0.991305	−	0.131584i	$-0.957994\pi$
$967$		−	8.18366i		−	0.263169i	0.991305	−	0.131584i	$-0.0420065\pi$
$968$			9.29416i			0.298726i
$969$	−7.30167			−0.234563
$970$	2.15699	−	11.0937i	0.0692567	−	0.356197i
$971$	−19.0931			−0.612727			−0.306364	−	0.951915i	$-0.599112\pi$
$971$	−19.0931			−0.612727			−0.306364	+	0.951915i	$0.599112\pi$
$972$			16.1251i			0.517212i
$973$			3.86008i			0.123748i
$974$	−32.8658			−1.05309
$975$		0			0
$976$	11.2009			0.358531
$977$		−	2.67273i		−	0.0855082i	−0.999086	−	0.0427541i	$-0.986387\pi$
$977$		−	2.67273i		−	0.0855082i	0.999086	−	0.0427541i	$-0.0136132\pi$
$978$			12.1602i			0.388840i
$979$	−20.4055			−0.652162
$980$	1.01238	−	5.20683i	0.0323394	−	0.166326i
$981$	−8.95383			−0.285874
$982$		−	17.6525i		−	0.563313i
$983$		−	5.29656i		−	0.168934i	−0.996426	−	0.0844670i	$-0.973081\pi$
$983$		−	5.29656i		−	0.168934i	0.996426	−	0.0844670i	$-0.0269188\pi$
$984$	−8.31174			−0.264969
$985$	11.2977	+	2.19665i	0.359974	+	0.0699910i
$986$	−22.8789			−0.728612
$987$		−	15.0288i		−	0.478371i
$988$		0			0
$989$	−17.1348			−0.544855
$990$	−5.97787	−	1.16230i	−0.189989	−	0.0369402i
$991$	−26.1528			−0.830773			−0.415386	−	0.909645i	$-0.636354\pi$
$991$	−26.1528			−0.830773			−0.415386	+	0.909645i	$0.636354\pi$
$992$		−	4.12897i		−	0.131095i
$993$			25.4820i			0.808646i
$994$	30.2762			0.960304
$995$	−4.05627	+	20.8620i	−0.128592	+	0.661369i
$996$	13.3883			0.424225
$997$		−	19.6903i		−	0.623597i	−0.950148	−	0.311799i	$-0.899069\pi$
$997$		−	19.6903i		−	0.623597i	0.950148	−	0.311799i	$-0.100931\pi$
$998$			37.3227i			1.18143i
$999$	14.5292			0.459683

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.b.g.339.13	yes	18
5.2	odd	4		8450.2.a.ct.1.4		9
5.3	odd	4		8450.2.a.da.1.6		9
5.4	even	2	inner	1690.2.b.g.339.6	yes	18
13.5	odd	4		1690.2.c.h.1689.6		18
13.8	odd	4		1690.2.c.g.1689.6		18
13.12	even	2		1690.2.b.f.339.4	✓	18
65.12	odd	4		8450.2.a.cx.1.4		9
65.34	odd	4		1690.2.c.h.1689.13		18
65.38	odd	4		8450.2.a.cw.1.6		9
65.44	odd	4		1690.2.c.g.1689.13		18
65.64	even	2		1690.2.b.f.339.15	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1690.2.b.f.339.4	✓	18	13.12	even	2
1690.2.b.f.339.15	yes	18	65.64	even	2
1690.2.b.g.339.6	yes	18	5.4	even	2	inner
1690.2.b.g.339.13	yes	18	1.1	even	1	trivial
1690.2.c.g.1689.6		18	13.8	odd	4
1690.2.c.g.1689.13		18	65.44	odd	4
1690.2.c.h.1689.6		18	13.5	odd	4
1690.2.c.h.1689.13		18	65.34	odd	4
8450.2.a.ct.1.4		9	5.2	odd	4
8450.2.a.cw.1.6		9	65.38	odd	4
8450.2.a.cx.1.4		9	65.12	odd	4
8450.2.a.da.1.6		9	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -0.956446i q^{3} -1.00000 q^{4} +(-0.426774 + 2.19496i) q^{5} +0.956446 q^{6} -2.15124i q^{7} -1.00000i q^{8} +2.08521 q^{9} +(-2.19496 - 0.426774i) q^{10} +1.30608 q^{11} +0.956446i q^{12} +2.15124 q^{14} +(2.09936 + 0.408187i) q^{15} +1.00000 q^{16} -2.87416i q^{17} +2.08521i q^{18} +2.65614 q^{19} +(0.426774 - 2.19496i) q^{20} -2.05754 q^{21} +1.30608i q^{22} -5.11025i q^{23} -0.956446 q^{24} +(-4.63573 - 1.87351i) q^{25} -4.86373i q^{27} +2.15124i q^{28} -7.96020 q^{29} +(-0.408187 + 2.09936i) q^{30} -4.12897 q^{31} +1.00000i q^{32} -1.24919i q^{33} +2.87416 q^{34} +(4.72189 + 0.918093i) q^{35} -2.08521 q^{36} +2.98725i q^{37} +2.65614i q^{38} +(2.19496 + 0.426774i) q^{40} +8.69023 q^{41} -2.05754i q^{42} -3.35303i q^{43} -1.30608 q^{44} +(-0.889915 + 4.57696i) q^{45} +5.11025 q^{46} +7.30423i q^{47} -0.956446i q^{48} +2.37217 q^{49} +(1.87351 - 4.63573i) q^{50} -2.74898 q^{51} -10.0804i q^{53} +4.86373 q^{54} +(-0.557400 + 2.86679i) q^{55} -2.15124 q^{56} -2.54046i q^{57} -7.96020i q^{58} +14.6950 q^{59} +(-2.09936 - 0.408187i) q^{60} +11.2009 q^{61} -4.12897i q^{62} -4.48579i q^{63} -1.00000 q^{64} +1.24919 q^{66} -11.0454i q^{67} +2.87416i q^{68} -4.88768 q^{69} +(-0.918093 + 4.72189i) q^{70} +14.0739 q^{71} -2.08521i q^{72} +3.83547i q^{73} -2.98725 q^{74} +(-1.79191 + 4.43382i) q^{75} -2.65614 q^{76} -2.80969i q^{77} +8.94252 q^{79} +(-0.426774 + 2.19496i) q^{80} +1.60374 q^{81} +8.69023i q^{82} -13.9980i q^{83} +2.05754 q^{84} +(6.30867 + 1.22662i) q^{85} +3.35303 q^{86} +7.61350i q^{87} -1.30608i q^{88} -15.6235 q^{89} +(-4.57696 - 0.889915i) q^{90} +5.11025i q^{92} +3.94914i q^{93} -7.30423 q^{94} +(-1.13357 + 5.83013i) q^{95} +0.956446 q^{96} +5.05416i q^{97} +2.37217i q^{98} +2.72345 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 18 q^{4} + 14 q^{6} - 16 q^{9} + 2 q^{10} + 8 q^{11} - 2 q^{14} + 8 q^{15} + 18 q^{16} - 12 q^{19} + 16 q^{21} - 14 q^{24} + 22 q^{25} - 30 q^{29} - 14 q^{30} - 12 q^{31} - 24 q^{34} - 4 q^{35} + 16 q^{36}+ \cdots - 32 q^{99}+O(q^{100}) \) 18 * q - 18 * q^4 + 14 * q^6 - 16 * q^9 + 2 * q^10 + 8 * q^11 - 2 * q^14 + 8 * q^15 + 18 * q^16 - 12 * q^19 + 16 * q^21 - 14 * q^24 + 22 * q^25 - 30 * q^29 - 14 * q^30 - 12 * q^31 - 24 * q^34 - 4 * q^35 + 16 * q^36 - 2 * q^40 + 54 * q^41 - 8 * q^44 + 20 * q^45 + 22 * q^46 + 20 * q^49 + 8 * q^50 + 24 * q^51 - 68 * q^54 + 2 * q^56 - 40 * q^59 - 8 * q^60 - 38 * q^61 - 18 * q^64 - 28 * q^66 + 28 * q^69 - 6 * q^70 - 20 * q^71 + 20 * q^74 - 72 * q^75 + 12 * q^76 + 28 * q^79 + 106 * q^81 - 16 * q^84 + 56 * q^85 + 82 * q^86 - 86 * q^89 - 20 * q^90 - 10 * q^94 - 54 * q^95 + 14 * q^96 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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