LMFDB - Embedded newform 1690.2.c.g.1689.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1690,2,Mod(1689,1690)] 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, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1690.1689"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [18,-18,0,18,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == 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			1689.13
Root			$2.17115i$ of defining polynomial
Character	$\chi$	$=$	1690.1689
Dual form			1690.2.c.g.1689.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +0.956446i q^{3} +1.00000 q^{4} +(-2.19496 + 0.426774i) q^{5} -0.956446i q^{6} -2.15124 q^{7} -1.00000 q^{8} +2.08521 q^{9} +(2.19496 - 0.426774i) q^{10} +1.30608i q^{11} +0.956446i q^{12} +2.15124 q^{14} +(-0.408187 - 2.09936i) q^{15} +1.00000 q^{16} -2.87416i q^{17} -2.08521 q^{18} -2.65614i q^{19} +(-2.19496 + 0.426774i) q^{20} -2.05754i q^{21} -1.30608i q^{22} -5.11025i q^{23} -0.956446i q^{24} +(4.63573 - 1.87351i) q^{25} +4.86373i q^{27} -2.15124 q^{28} -7.96020 q^{29} +(0.408187 + 2.09936i) q^{30} +4.12897i q^{31} -1.00000 q^{32} -1.24919 q^{33} +2.87416i q^{34} +(4.72189 - 0.918093i) q^{35} +2.08521 q^{36} +2.98725 q^{37} +2.65614i q^{38} +(2.19496 - 0.426774i) q^{40} -8.69023i q^{41} +2.05754i q^{42} -3.35303i q^{43} +1.30608i q^{44} +(-4.57696 + 0.889915i) q^{45} +5.11025i q^{46} +7.30423 q^{47} +0.956446i q^{48} -2.37217 q^{49} +(-4.63573 + 1.87351i) q^{50} +2.74898 q^{51} +10.0804i q^{53} -4.86373i q^{54} +(-0.557400 - 2.86679i) q^{55} +2.15124 q^{56} +2.54046 q^{57} +7.96020 q^{58} +14.6950i q^{59} +(-0.408187 - 2.09936i) q^{60} +11.2009 q^{61} -4.12897i q^{62} -4.48579 q^{63} +1.00000 q^{64} +1.24919 q^{66} +11.0454 q^{67} -2.87416i q^{68} +4.88768 q^{69} +(-4.72189 + 0.918093i) q^{70} -14.0739i q^{71} -2.08521 q^{72} +3.83547 q^{73} -2.98725 q^{74} +(1.79191 + 4.43382i) q^{75} -2.65614i q^{76} -2.80969i q^{77} +8.94252 q^{79} +(-2.19496 + 0.426774i) q^{80} +1.60374 q^{81} +8.69023i q^{82} +13.9980 q^{83} -2.05754i q^{84} +(1.22662 + 6.30867i) q^{85} +3.35303i q^{86} -7.61350i q^{87} -1.30608i q^{88} -15.6235i q^{89} +(4.57696 - 0.889915i) q^{90} -5.11025i q^{92} -3.94914 q^{93} -7.30423 q^{94} +(1.13357 + 5.83013i) q^{95} -0.956446i q^{96} -5.05416 q^{97} +2.37217 q^{98} +2.72345i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 18 q^{2} + 18 q^{4} + 2 q^{5} + 2 q^{7} - 18 q^{8} - 16 q^{9} - 2 q^{10} - 2 q^{14} - 14 q^{15} + 18 q^{16} + 16 q^{18} + 2 q^{20} - 22 q^{25} + 2 q^{28} - 30 q^{29} + 14 q^{30} - 18 q^{32} + 28 q^{33}+ \cdots + 20 q^{98}+O(q^{100}) $ 18 * q - 18 * q^2 + 18 * q^4 + 2 * q^5 + 2 * q^7 - 18 * q^8 - 16 * q^9 - 2 * q^10 - 2 * q^14 - 14 * q^15 + 18 * q^16 + 16 * q^18 + 2 * q^20 - 22 * q^25 + 2 * q^28 - 30 * q^29 + 14 * q^30 - 18 * q^32 + 28 * q^33 - 4 * q^35 - 16 * q^36 - 20 * q^37 - 2 * q^40 - 20 * q^45 + 10 * q^47 - 20 * q^49 + 22 * q^50 - 24 * q^51 - 2 * q^56 + 24 * q^57 + 30 * q^58 - 14 * q^60 - 38 * q^61 - 78 * q^63 + 18 * q^64 - 28 * q^66 + 2 * q^67 - 28 * q^69 + 4 * q^70 + 16 * q^72 + 24 * q^73 + 20 * q^74 + 72 * q^75 + 28 * q^79 + 2 * q^80 + 106 * q^81 + 2 * q^83 + 16 * q^85 + 20 * q^90 - 56 * q^93 - 10 * q^94 + 54 * q^95 - 12 * q^97 + 20 * q^98

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$			0.956446i			0.552204i	0.961128	+	0.276102i	$0.0890428\pi$
$3$			0.956446i			0.552204i	−0.961128	+	0.276102i	$0.910957\pi$
$4$	1.00000			0.500000
$5$	−2.19496	+	0.426774i	−0.981617	+	0.190859i
$5$	−2.19496	+	0.426774i	−0.981617	+	0.190859i
$6$		−	0.956446i		−	0.390467i
$7$	−2.15124			−0.813092			−0.406546	−	0.913630i	$-0.633267\pi$
$7$	−2.15124			−0.813092			−0.406546	+	0.913630i	$0.633267\pi$
$8$	−1.00000			−0.353553
$9$	2.08521			0.695070
$10$	2.19496	−	0.426774i	0.694108	−	0.134958i
$11$			1.30608i			0.393797i	0.980424	+	0.196899i	$0.0630870\pi$
$11$			1.30608i			0.393797i	−0.980424	+	0.196899i	$0.936913\pi$
$12$			0.956446i			0.276102i
$13$		0			0
$13$		0			0
$14$	2.15124			0.574943
$15$	−0.408187	−	2.09936i	−0.105393	−	0.542053i
$16$	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	$-0.113323\pi$
$18$	−2.08521			−0.491489
$19$		−	2.65614i		−	0.609360i	−0.952455	−	0.304680i	$-0.901450\pi$
$19$		−	2.65614i		−	0.609360i	0.952455	−	0.304680i	$-0.0985496\pi$
$20$	−2.19496	+	0.426774i	−0.490809	+	0.0954296i
$21$		−	2.05754i		−	0.448993i
$22$		−	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	$-0.178853\pi$
$24$		−	0.956446i		−	0.195234i
$25$	4.63573	−	1.87351i	0.927145	−	0.374702i
$26$		0			0
$27$			4.86373i			0.936025i
$28$	−2.15124			−0.406546
$29$	−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
$31$			4.12897i			0.741585i	0.928716	+	0.370792i	$0.120914\pi$
$31$			4.12897i			0.741585i	−0.928716	+	0.370792i	$0.879086\pi$
$32$	−1.00000			−0.176777
$33$	−1.24919			−0.217457
$34$			2.87416i			0.492914i
$35$	4.72189	−	0.918093i	0.798145	−	0.155186i
$36$	2.08521			0.347535
$37$	2.98725			0.491101			0.245551	−	0.969384i	$-0.421031\pi$
$37$	2.98725			0.491101			0.245551	+	0.969384i	$0.421031\pi$
$38$			2.65614i			0.430883i
$39$		0			0
$40$	2.19496	−	0.426774i	0.347054	−	0.0674789i
$41$		−	8.69023i		−	1.35719i	−0.734514	−	0.678593i	$-0.762590\pi$
$41$		−	8.69023i		−	1.35719i	0.734514	−	0.678593i	$-0.237410\pi$
$42$			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	$-0.0822948\pi$
$44$			1.30608i			0.196899i
$45$	−4.57696	+	0.889915i	−0.682293	+	0.132661i
$46$			5.11025i			0.753465i
$47$	7.30423			1.06543			0.532716	−	0.846294i	$-0.321172\pi$
$47$	7.30423			1.06543			0.532716	+	0.846294i	$0.321172\pi$
$48$			0.956446i			0.138051i
$49$	−2.37217			−0.338882
$50$	−4.63573	+	1.87351i	−0.655591	+	0.264954i
$51$	2.74898			0.384934
$52$		0			0
$53$			10.0804i			1.38465i	0.721586	+	0.692325i	$0.243413\pi$
$53$			10.0804i			1.38465i	−0.721586	+	0.692325i	$0.756587\pi$
$54$		−	4.86373i		−	0.661870i
$55$	−0.557400	−	2.86679i	−0.0751599	−	0.386558i
$56$	2.15124			0.287471
$57$	2.54046			0.336491
$58$	7.96020			1.04523
$59$			14.6950i			1.91313i	0.291522	+	0.956564i	$0.405838\pi$
$59$			14.6950i			1.91313i	−0.291522	+	0.956564i	$0.594162\pi$
$60$	−0.408187	−	2.09936i	−0.0526967	−	0.271027i
$61$	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
$63$	−4.48579			−0.565156
$64$	1.00000			0.125000
$65$		0			0
$66$	1.24919			0.153765
$67$	11.0454			1.34941			0.674706	−	0.738087i	$-0.264270\pi$
$67$	11.0454			1.34941			0.674706	+	0.738087i	$0.264270\pi$
$68$		−	2.87416i		−	0.348543i
$69$	4.88768			0.588407
$70$	−4.72189	+	0.918093i	−0.564374	+	0.109733i
$71$		−	14.0739i		−	1.67026i	−0.550053	−	0.835130i	$-0.685392\pi$
$71$		−	14.0739i		−	1.67026i	0.550053	−	0.835130i	$-0.314608\pi$
$72$	−2.08521			−0.245744
$73$	3.83547			0.448907			0.224454	−	0.974485i	$-0.427940\pi$
$73$	3.83547			0.448907			0.224454	+	0.974485i	$0.427940\pi$
$74$	−2.98725			−0.347261
$75$	1.79191	+	4.43382i	0.206912	+	0.511974i
$76$		−	2.65614i		−	0.304680i
$77$		−	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	$0.332209\pi$
$80$	−2.19496	+	0.426774i	−0.245404	+	0.0477148i
$81$	1.60374			0.178193
$82$			8.69023i			0.959676i
$83$	13.9980			1.53648			0.768239	−	0.640163i	$-0.221133\pi$
$83$	13.9980			1.53648			0.768239	+	0.640163i	$0.221133\pi$
$84$		−	2.05754i		−	0.224496i
$85$	1.22662	+	6.30867i	0.133045	+	0.684272i
$86$			3.35303i			0.361567i
$87$		−	7.61350i		−	0.816253i
$88$		−	1.30608i		−	0.139228i
$89$		−	15.6235i		−	1.65609i	−0.560665	−	0.828043i	$-0.689454\pi$
$89$		−	15.6235i		−	1.65609i	0.560665	−	0.828043i	$-0.310546\pi$
$90$	4.57696	−	0.889915i	0.482454	−	0.0938052i
$91$		0			0
$92$		−	5.11025i		−	0.532780i
$93$	−3.94914			−0.409506
$94$	−7.30423			−0.753374
$95$	1.13357	+	5.83013i	0.116302	+	0.598159i
$96$		−	0.956446i		−	0.0976169i
$97$	−5.05416			−0.513172			−0.256586	−	0.966521i	$-0.582598\pi$
$97$	−5.05416			−0.513172			−0.256586	+	0.966521i	$0.582598\pi$
$98$	2.37217			0.239626
$99$			2.72345i			0.273717i
$100$	4.63573	−	1.87351i	0.463573	−	0.187351i
$101$	2.02811			0.201804			0.100902	−	0.994896i	$-0.467827\pi$
$101$	2.02811			0.201804			0.100902	+	0.994896i	$0.467827\pi$
$102$	−2.74898			−0.272189
$103$			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
$106$		−	10.0804i		−	0.979095i
$107$		−	1.89051i		−	0.182763i	−0.995816	−	0.0913814i	$-0.970872\pi$
$107$		−	1.89051i		−	0.182763i	0.995816	−	0.0913814i	$-0.0291282\pi$
$108$			4.86373i			0.468013i
$109$			4.29397i			0.411287i	0.978627	+	0.205644i	$0.0659288\pi$
$109$			4.29397i			0.411287i	−0.978627	+	0.205644i	$0.934071\pi$
$110$	0.557400	+	2.86679i	0.0531461	+	0.273338i
$111$			2.85715i			0.271188i
$112$	−2.15124			−0.203273
$113$			18.7154i			1.76060i	0.474418	+	0.880300i	$0.342658\pi$
$113$			18.7154i			1.76060i	−0.474418	+	0.880300i	$0.657342\pi$
$114$	−2.54046			−0.237935
$115$	2.18092	+	11.2168i	0.203372	+	1.04597i
$116$	−7.96020			−0.739086
$117$		0			0
$118$		−	14.6950i		−	1.35279i
$119$			6.18300i			0.566795i
$120$	0.408187	+	2.09936i	0.0372622	+	0.191645i
$121$	9.29416			0.844924
$122$	−11.2009			−1.01408
$123$	8.31174			0.749444
$124$			4.12897i			0.370792i
$125$	−9.37569	+	6.09069i	−0.838587	+	0.544768i
$126$	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	$0.713646\pi$
$128$	−1.00000			−0.0883883
$129$	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	$0.377515\pi$
$132$	−1.24919			−0.108728
$133$			5.71399i			0.495466i
$134$	−11.0454			−0.954178
$135$	−2.07572	−	10.6757i	−0.178649	−	0.918819i
$136$			2.87416i			0.246457i
$137$	−6.43023			−0.549372			−0.274686	−	0.961534i	$-0.588574\pi$
$137$	−6.43023			−0.549372			−0.274686	+	0.961534i	$0.588574\pi$
$138$	−4.88768			−0.416067
$139$	−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
$141$			6.98610i			0.588336i
$142$			14.0739i			1.18105i
$143$		0			0
$144$	2.08521			0.173768
$145$	17.4724	−	3.39721i	1.45100	−	0.282123i
$146$	−3.83547			−0.317426
$147$		−	2.26885i		−	0.187132i
$148$	2.98725			0.245551
$149$		−	8.49082i		−	0.695595i	−0.937570	−	0.347798i	$-0.886930\pi$
$149$		−	8.49082i		−	0.695595i	0.937570	−	0.347798i	$-0.113070\pi$
$150$	−1.79191	−	4.43382i	−0.146309	−	0.362020i
$151$		−	2.97802i		−	0.242347i	−0.992631	−	0.121174i	$-0.961334\pi$
$151$		−	2.97802i		−	0.242347i	0.992631	−	0.121174i	$-0.0386658\pi$
$152$			2.65614i			0.215441i
$153$		−	5.99323i		−	0.484524i
$154$			2.80969i			0.226411i
$155$	−1.76214	−	9.06294i	−0.141538	−	0.727953i
$156$		0			0
$157$		−	14.3503i		−	1.14528i	−0.819808	−	0.572639i	$-0.805920\pi$
$157$		−	14.3503i		−	1.14528i	0.819808	−	0.572639i	$-0.194080\pi$
$158$	−8.94252			−0.711428
$159$	−9.64136			−0.764609
$160$	2.19496	−	0.426774i	0.173527	−	0.0337395i
$161$			10.9934i			0.866398i
$162$	−1.60374			−0.126002
$163$	12.7139			0.995833			0.497916	−	0.867225i	$-0.334099\pi$
$163$	12.7139			0.995833			0.497916	+	0.867225i	$0.334099\pi$
$164$		−	8.69023i		−	0.678593i
$165$	2.74193	−	0.533123i	0.213459	−	0.0415036i
$166$	−13.9980			−1.08645
$167$	1.32171			0.102277			0.0511387	−	0.998692i	$-0.483715\pi$
$167$	1.32171			0.102277			0.0511387	+	0.998692i	$0.483715\pi$
$168$			2.05754i			0.158743i
$169$		0			0
$170$	−1.22662	−	6.30867i	−0.0940772	−	0.483853i
$171$		−	5.53861i		−	0.423548i
$172$		−	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	$-0.363928\pi$
$174$			7.61350i			0.577178i
$175$	−9.97256	+	4.03036i	−0.753854	+	0.304667i
$176$			1.30608i			0.0984493i
$177$	−14.0550			−1.05644
$178$			15.6235i			1.17103i
$179$	−0.841778			−0.0629174			−0.0314587	−	0.999505i	$-0.510015\pi$
$179$	−0.841778			−0.0629174			−0.0314587	+	0.999505i	$0.510015\pi$
$180$	−4.57696	+	0.889915i	−0.341147	+	0.0663303i
$181$	6.20054			0.460883			0.230441	−	0.973086i	$-0.425983\pi$
$181$	6.20054			0.460883			0.230441	+	0.973086i	$0.425983\pi$
$182$		0			0
$183$			10.7130i			0.791930i
$184$			5.11025i			0.376732i
$185$	−6.55691	+	1.27488i	−0.482074	+	0.0937313i
$186$	3.94914			0.289565
$187$	3.75387			0.274511
$188$	7.30423			0.532716
$189$		−	10.4630i		−	0.761074i
$190$	−1.13357	−	5.83013i	−0.0822380	−	0.422962i
$191$	−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
$193$	25.9564			1.86838			0.934191	−	0.356774i	$-0.116123\pi$
$193$	25.9564			1.86838			0.934191	+	0.356774i	$0.116123\pi$
$194$	5.05416			0.362868
$195$		0			0
$196$	−2.37217			−0.169441
$197$	5.14709			0.366715			0.183358	−	0.983046i	$-0.441303\pi$
$197$	5.14709			0.366715			0.183358	+	0.983046i	$0.441303\pi$
$198$		−	2.72345i		−	0.193547i
$199$	−9.50447			−0.673754			−0.336877	−	0.941549i	$-0.609371\pi$
$199$	−9.50447			−0.673754			−0.336877	+	0.941549i	$0.609371\pi$
$200$	−4.63573	+	1.87351i	−0.327795	+	0.132477i
$201$			10.5643i			0.745151i
$202$	−2.02811			−0.142697
$203$	17.1243			1.20189
$204$	2.74898			0.192467
$205$	3.70877	+	19.0747i	0.259032	+	1.33224i
$206$		−	3.26212i		−	0.227283i
$207$		−	10.6559i		−	0.740639i
$208$		0			0
$209$	3.46913			0.239964
$210$	−0.878107	−	4.51623i	−0.0605951	−	0.311650i
$211$	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
$213$	13.4609			0.922325
$214$			1.89051i			0.129233i
$215$	1.43099	+	7.35978i	0.0975925	+	0.501933i
$216$		−	4.86373i		−	0.330935i
$217$		−	8.88240i		−	0.602977i
$218$		−	4.29397i		−	0.290824i
$219$			3.66842i			0.247889i
$220$	−0.557400	−	2.86679i	−0.0375799	−	0.193279i
$221$		0			0
$222$		−	2.85715i		−	0.191759i
$223$	−0.669364			−0.0448239			−0.0224120	−	0.999749i	$-0.507135\pi$
$223$	−0.669364			−0.0448239			−0.0224120	+	0.999749i	$0.507135\pi$
$224$	2.15124			0.143736
$225$	9.66647	−	3.90666i	0.644431	−	0.260444i
$226$		−	18.7154i		−	1.24493i
$227$	5.40643			0.358837			0.179419	−	0.983773i	$-0.442578\pi$
$227$	5.40643			0.358837			0.179419	+	0.983773i	$0.442578\pi$
$228$	2.54046			0.168246
$229$			2.23462i			0.147668i	0.997271	+	0.0738340i	$0.0235235\pi$
$229$			2.23462i			0.147668i	−0.997271	+	0.0738340i	$0.976476\pi$
$230$	−2.18092	−	11.2168i	−0.143806	−	0.739614i
$231$	2.68731			0.176812
$232$	7.96020			0.522613
$233$		−	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
$236$			14.6950i			0.956564i
$237$			8.55303i			0.555579i
$238$		−	6.18300i		−	0.400784i
$239$			22.7145i			1.46928i	0.678458	+	0.734639i	$0.262649\pi$
$239$			22.7145i			1.46928i	−0.678458	+	0.734639i	$0.737351\pi$
$240$	−0.408187	−	2.09936i	−0.0263483	−	0.135513i
$241$		−	21.9809i		−	1.41591i	−0.706256	−	0.707956i	$-0.749617\pi$
$241$		−	21.9809i		−	1.41591i	0.706256	−	0.707956i	$-0.250383\pi$
$242$	−9.29416			−0.597451
$243$			16.1251i			1.03442i
$244$	11.2009			0.717062
$245$	5.20683	−	1.01238i	0.332652	−	0.0646787i
$246$	−8.31174			−0.529937
$247$		0			0
$248$		−	4.12897i		−	0.262190i
$249$			13.3883i			0.848450i
$250$	9.37569	−	6.09069i	0.592970	−	0.385209i
$251$	−9.38645			−0.592468			−0.296234	−	0.955115i	$-0.595731\pi$
$251$	−9.38645			−0.592468			−0.296234	+	0.955115i	$0.595731\pi$
$252$	−4.48579			−0.282578
$253$	6.67438			0.419615
$254$		−	17.6498i		−	1.10745i
$255$	−6.03390	+	1.17319i	−0.377858	+	0.0734682i
$256$	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	$0.926195\pi$
$258$	−3.20699			−0.199659
$259$	−6.42630			−0.399311
$260$		0			0
$261$	−16.5987			−1.02743
$262$	−8.59263			−0.530855
$263$		−	20.4624i		−	1.26177i	−0.775877	−	0.630884i	$-0.782692\pi$
$263$		−	20.4624i		−	1.26177i	0.775877	−	0.630884i	$-0.217308\pi$
$264$	1.24919			0.0768825
$265$	−4.30206	−	22.1261i	−0.264273	−	1.35920i
$266$		−	5.71399i		−	0.350347i
$267$	14.9430			0.914498
$268$	11.0454			0.674706
$269$	−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
$271$			1.82589i			0.110915i	0.998461	+	0.0554575i	$0.0176617\pi$
$271$			1.82589i			0.110915i	−0.998461	+	0.0554575i	$0.982338\pi$
$272$		−	2.87416i		−	0.174271i
$273$		0			0
$274$	6.43023			0.388465
$275$	2.44695	+	6.05462i	0.147556	+	0.365107i
$276$	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	$-0.0105565\pi$
$278$	1.79435			0.107618
$279$			8.60977i			0.515454i
$280$	−4.72189	+	0.918093i	−0.282187	+	0.0548666i
$281$		−	2.66535i		−	0.159002i	−0.996835	−	0.0795008i	$-0.974667\pi$
$281$		−	2.66535i		−	0.159002i	0.996835	−	0.0795008i	$-0.0253326\pi$
$282$		−	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	$-0.259876\pi$
$284$		−	14.0739i		−	0.835130i
$285$	−5.57621	+	1.08420i	−0.330306	+	0.0642225i
$286$		0			0
$287$			18.6948i			1.10352i
$288$	−2.08521			−0.122872
$289$	8.73921			0.514071
$290$	−17.4724	+	3.39721i	−1.02601	+	0.199491i
$291$		−	4.83403i		−	0.283376i
$292$	3.83547			0.224454
$293$	8.74457			0.510863			0.255432	−	0.966827i	$-0.417782\pi$
$293$	8.74457			0.510863			0.255432	+	0.966827i	$0.417782\pi$
$294$			2.26885i			0.132322i
$295$	−6.27146	−	32.2550i	−0.365138	−	1.87796i
$296$	−2.98725			−0.173631
$297$	−6.35241			−0.368604
$298$			8.49082i			0.491860i
$299$		0			0
$300$	1.79191	+	4.43382i	0.103456	+	0.255987i
$301$			7.21317i			0.415760i
$302$			2.97802i			0.171366i
$303$			1.93977i			0.111437i
$304$		−	2.65614i		−	0.152340i
$305$	−24.5855	+	4.78025i	−1.40776	+	0.273716i
$306$			5.99323i			0.342610i
$307$	12.4345			0.709674			0.354837	−	0.934928i	$-0.384536\pi$
$307$	12.4345			0.709674			0.354837	+	0.934928i	$0.384536\pi$
$308$		−	2.80969i		−	0.160097i
$309$	−3.12004			−0.177493
$310$	1.76214	+	9.06294i	0.100083	+	0.514740i
$311$	0.269313			0.0152713			0.00763567	−	0.999971i	$-0.497569\pi$
$311$	0.269313			0.0152713			0.00763567	+	0.999971i	$0.497569\pi$
$312$		0			0
$313$		−	10.5866i		−	0.598389i	−0.954192	−	0.299195i	$-0.903282\pi$
$313$		−	10.5866i		−	0.598389i	0.954192	−	0.299195i	$-0.0967180\pi$
$314$			14.3503i			0.809833i
$315$	9.84614	−	1.91442i	0.554767	−	0.107865i
$316$	8.94252			0.503056
$317$	−21.0117			−1.18014			−0.590068	−	0.807354i	$-0.700899\pi$
$317$	−21.0117			−1.18014			−0.590068	+	0.807354i	$0.700899\pi$
$318$	9.64136			0.540661
$319$		−	10.3966i		−	0.582100i
$320$	−2.19496	+	0.426774i	−0.122702	+	0.0238574i
$321$	1.80817			0.100922
$322$		−	10.9934i		−	0.612636i
$323$	−7.63417			−0.424777
$324$	1.60374			0.0890966
$325$		0			0
$326$	−12.7139			−0.704160
$327$	−4.10695			−0.227115
$328$			8.69023i			0.479838i
$329$	−15.7131			−0.866293
$330$	−2.74193	+	0.533123i	−0.150938	+	0.0293475i
$331$			26.6423i			1.46440i	0.681092	+	0.732198i	$0.261505\pi$
$331$			26.6423i			1.46440i	−0.681092	+	0.732198i	$0.738495\pi$
$332$	13.9980			0.768239
$333$	6.22905			0.341350
$334$	−1.32171			−0.0723210
$335$	−24.2443	+	4.71390i	−1.32461	+	0.257548i
$336$		−	2.05754i		−	0.112248i
$337$		−	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
$340$	1.22662	+	6.30867i	0.0665227	+	0.342136i
$341$	−5.39276			−0.292034
$342$			5.53861i			0.299494i
$343$	20.1618			1.08863
$344$			3.35303i			0.180783i
$345$	−10.7283	+	2.08593i	−0.577591	+	0.112303i
$346$			23.9387i			1.28695i
$347$		−	13.6671i		−	0.733686i	−0.930283	−	0.366843i	$-0.880439\pi$
$347$		−	13.6671i		−	0.733686i	0.930283	−	0.366843i	$-0.119561\pi$
$348$		−	7.61350i		−	0.408127i
$349$			8.18464i			0.438114i	0.975712	+	0.219057i	$0.0702981\pi$
$349$			8.18464i			0.438114i	−0.975712	+	0.219057i	$0.929702\pi$
$350$	9.97256	−	4.03036i	0.533056	−	0.215432i
$351$		0			0
$352$		−	1.30608i		−	0.0696142i
$353$	−21.4420			−1.14124			−0.570621	−	0.821214i	$-0.693297\pi$
$353$	−21.4420			−1.14124			−0.570621	+	0.821214i	$0.693297\pi$
$354$	14.0550			0.747014
$355$	6.00636	+	30.8916i	0.318785	+	1.63956i
$356$		−	15.6235i		−	0.828043i
$357$	−5.91371			−0.312987
$358$	0.841778			0.0444893
$359$		−	7.09493i		−	0.374456i	−0.982316	−	0.187228i	$-0.940050\pi$
$359$		−	7.09493i		−	0.374456i	0.982316	−	0.187228i	$-0.0599503\pi$
$360$	4.57696	−	0.889915i	0.241227	−	0.0469026i
$361$	11.9449			0.628680
$362$	−6.20054			−0.325893
$363$			8.88936i			0.466571i
$364$		0			0
$365$	−8.41871	+	1.63688i	−0.440655	+	0.0856782i
$366$		−	10.7130i		−	0.559979i
$367$		−	23.9033i		−	1.24774i	−0.781526	−	0.623872i	$-0.785559\pi$
$367$		−	23.9033i		−	1.24774i	0.781526	−	0.623872i	$-0.214441\pi$
$368$		−	5.11025i		−	0.266390i
$369$		−	18.1210i		−	0.943340i
$370$	6.55691	−	1.27488i	0.340878	−	0.0662780i
$371$		−	21.6853i		−	1.12585i
$372$	−3.94914			−0.204753
$373$			11.5127i			0.596105i	0.954549	+	0.298053i	$0.0963371\pi$
$373$			11.5127i			0.596105i	−0.954549	+	0.298053i	$0.903663\pi$
$374$	−3.75387			−0.194108
$375$	−5.82542	−	8.96734i	−0.300823	−	0.463071i
$376$	−7.30423			−0.376687
$377$		0			0
$378$			10.4630i			0.538161i
$379$		−	2.64445i		−	0.135836i	−0.997691	−	0.0679180i	$-0.978364\pi$
$379$		−	2.64445i		−	0.135836i	0.997691	−	0.0679180i	$-0.0216356\pi$
$380$	1.13357	+	5.83013i	0.0581510	+	0.299079i
$381$	−16.8811			−0.864843
$382$	10.7222			0.548594
$383$	16.2424			0.829949			0.414975	−	0.909833i	$-0.363790\pi$
$383$	16.2424			0.829949			0.414975	+	0.909833i	$0.363790\pi$
$384$		−	0.956446i		−	0.0488084i
$385$	1.19910	+	6.16716i	0.0611119	+	0.314307i
$386$	−25.9564			−1.32115
$387$		−	6.99178i		−	0.355412i
$388$	−5.05416			−0.256586
$389$	−23.7722			−1.20530			−0.602649	−	0.798006i	$-0.705888\pi$
$389$	−23.7722			−1.20530			−0.602649	+	0.798006i	$0.705888\pi$
$390$		0			0
$391$	−14.6877			−0.742787
$392$	2.37217			0.119813
$393$			8.21839i			0.414563i
$394$	−5.14709			−0.259307
$395$	−19.6285	+	3.81644i	−0.987617	+	0.192026i
$396$			2.72345i			0.136858i
$397$	−34.6274			−1.73790			−0.868949	−	0.494901i	$-0.835204\pi$
$397$	−34.6274			−1.73790			−0.868949	+	0.494901i	$0.835204\pi$
$398$	9.50447			0.476416
$399$	−5.46513			−0.273598
$400$	4.63573	−	1.87351i	0.231786	−	0.0936754i
$401$		−	4.37028i		−	0.218242i	−0.994028	−	0.109121i	$-0.965196\pi$
$401$		−	4.37028i		−	0.218242i	0.994028	−	0.109121i	$-0.0348035\pi$
$402$		−	10.5643i		−	0.526901i
$403$		0			0
$404$	2.02811			0.100902
$405$	−3.52015	+	0.684434i	−0.174917	+	0.0340098i
$406$	−17.1243			−0.849865
$407$			3.90159i			0.193394i
$408$	−2.74898			−0.136095
$409$			11.2279i			0.555186i	0.960699	+	0.277593i	$0.0895366\pi$
$409$			11.2279i			0.555186i	−0.960699	+	0.277593i	$0.910463\pi$
$410$	−3.70877	−	19.0747i	−0.183163	−	0.942034i
$411$		−	6.15017i		−	0.303366i
$412$			3.26212i			0.160713i
$413$		−	31.6125i		−	1.55555i
$414$			10.6559i			0.523711i
$415$	−30.7251	+	5.97398i	−1.50823	+	0.293251i
$416$		0			0
$417$		−	1.71620i		−	0.0840427i
$418$	−3.46913			−0.169681
$419$	−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
$421$			8.92506i			0.434981i	0.976062	+	0.217490i	$0.0697871\pi$
$421$			8.92506i			0.434981i	−0.976062	+	0.217490i	$0.930213\pi$
$422$	−25.8770			−1.25967
$423$	15.2309			0.740550
$424$		−	10.0804i		−	0.489548i
$425$	−5.38476	−	13.3238i	−0.261199	−	0.646300i
$426$	−13.4609			−0.652182
$427$	−24.0958			−1.16608
$428$		−	1.89051i		−	0.0913814i
$429$		0			0
$430$	−1.43099	−	7.35978i	−0.0690083	−	0.354920i
$431$			34.8123i			1.67685i	0.545017	+	0.838425i	$0.316523\pi$
$431$			34.8123i			1.67685i	−0.545017	+	0.838425i	$0.683477\pi$
$432$			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	$-0.365887\pi$
$434$			8.88240i			0.426369i
$435$	3.24925	+	16.7114i	0.155790	+	0.801249i
$436$			4.29397i			0.205644i
$437$	−13.5735			−0.649310
$438$		−	3.66842i		−	0.175284i
$439$	−16.6128			−0.792887			−0.396443	−	0.918059i	$-0.629756\pi$
$439$	−16.6128			−0.792887			−0.396443	+	0.918059i	$0.629756\pi$
$440$	0.557400	+	2.86679i	0.0265730	+	0.136669i
$441$	−4.94648			−0.235547
$442$		0			0
$443$		−	16.5892i		−	0.788177i	−0.919072	−	0.394089i	$-0.871060\pi$
$443$		−	16.5892i		−	0.788177i	0.919072	−	0.394089i	$-0.128940\pi$
$444$			2.85715i			0.135594i
$445$	6.66770	+	34.2930i	0.316079	+	1.62564i
$446$	0.669364			0.0316953
$447$	8.12101			0.384111
$448$	−2.15124			−0.101636
$449$		−	19.4158i		−	0.916287i	−0.888878	−	0.458144i	$-0.848515\pi$
$449$		−	19.4158i		−	0.916287i	0.888878	−	0.458144i	$-0.151485\pi$
$450$	−9.66647	+	3.90666i	−0.455682	+	0.184162i
$451$	11.3501			0.534456
$452$			18.7154i			0.880300i
$453$	2.84831			0.133825
$454$	−5.40643			−0.253736
$455$		0			0
$456$	−2.54046			−0.118968
$457$	−8.84923			−0.413950			−0.206975	−	0.978346i	$-0.566362\pi$
$457$	−8.84923			−0.413950			−0.206975	+	0.978346i	$0.566362\pi$
$458$		−	2.23462i		−	0.104417i
$459$	13.9791			0.652490
$460$	2.18092	+	11.2168i	0.101686	+	0.522986i
$461$		−	17.3352i		−	0.807380i	−0.914896	−	0.403690i	$-0.867727\pi$
$461$		−	17.3352i		−	0.807380i	0.914896	−	0.403690i	$-0.132273\pi$
$462$	−2.68731			−0.125025
$463$	17.0652			0.793088			0.396544	−	0.918016i	$-0.370209\pi$
$463$	17.0652			0.793088			0.396544	+	0.918016i	$0.370209\pi$
$464$	−7.96020			−0.369543
$465$	8.66821	−	1.68539i	0.401979	−	0.0781581i
$466$			0.131688i			0.00610035i
$467$		−	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
$470$	16.0325	−	3.11726i	0.739525	−	0.143788i
$471$	13.7253			0.632427
$472$		−	14.6950i		−	0.676393i
$473$	4.37932			0.201361
$474$		−	8.55303i		−	0.392854i
$475$	−4.97630	−	12.3131i	−0.228328	−	0.564966i
$476$			6.18300i			0.283397i
$477$			21.0198i			0.962429i
$478$		−	22.7145i		−	1.03894i
$479$		−	33.3487i		−	1.52374i	−0.647731	−	0.761870i	$-0.724282\pi$
$479$		−	33.3487i		−	1.52374i	0.647731	−	0.761870i	$-0.275718\pi$
$480$	0.408187	+	2.09936i	0.0186311	+	0.0958224i
$481$		0			0
$482$			21.9809i			1.00120i
$483$	−10.5146			−0.478429
$484$	9.29416			0.422462
$485$	11.0937	−	2.15699i	0.503739	−	0.0979437i
$486$		−	16.1251i		−	0.731448i
$487$	−32.8658			−1.48929			−0.744647	−	0.667459i	$-0.767382\pi$
$487$	−32.8658			−1.48929			−0.744647	+	0.667459i	$0.767382\pi$
$488$	−11.2009			−0.507040
$489$			12.1602i			0.549903i
$490$	−5.20683	+	1.01238i	−0.235221	+	0.0457348i
$491$	17.6525			0.796645			0.398322	−	0.917245i	$-0.369593\pi$
$491$	17.6525			0.796645			0.398322	+	0.917245i	$0.369593\pi$
$492$	8.31174			0.374722
$493$			22.8789i			1.03041i
$494$		0			0
$495$	−1.16230	−	5.97787i	−0.0522414	−	0.268685i
$496$			4.12897i			0.185396i
$497$			30.2762i			1.35807i
$498$		−	13.3883i		−	0.599945i
$499$		−	37.3227i		−	1.67079i	−0.549648	−	0.835396i	$-0.685238\pi$
$499$		−	37.3227i		−	1.67079i	0.549648	−	0.835396i	$-0.314762\pi$
$500$	−9.37569	+	6.09069i	−0.419293	+	0.272384i
$501$			1.26415i			0.0564780i
$502$	9.38645			0.418938
$503$			27.1489i			1.21051i	0.796032	+	0.605254i	$0.206928\pi$
$503$			27.1489i			1.21051i	−0.796032	+	0.605254i	$0.793072\pi$
$504$	4.48579			0.199813
$505$	−4.45162	+	0.865544i	−0.198094	+	0.0385162i
$506$	−6.67438			−0.296712
$507$		0			0
$508$			17.6498i			0.783083i
$509$			11.3658i			0.503781i	0.967756	+	0.251890i	$0.0810522\pi$
$509$			11.3658i			0.503781i	−0.967756	+	0.251890i	$0.918948\pi$
$510$	6.03390	−	1.17319i	0.267186	−	0.0519499i
$511$	−8.25101			−0.365003
$512$	−1.00000			−0.0441942
$513$	12.9188			0.570377
$514$		−	7.36768i		−	0.324975i
$515$	−1.39219	−	7.16023i	−0.0613471	−	0.315517i
$516$	3.20699			0.141180
$517$			9.53989i			0.419564i
$518$	6.42630			0.282355
$519$	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	$0.253598\pi$
$522$	16.5987			0.726506
$523$			25.7706i			1.12687i	0.826160	+	0.563435i	$0.190521\pi$
$523$			25.7706i			1.12687i	−0.826160	+	0.563435i	$0.809479\pi$
$524$	8.59263			0.375371
$525$	−3.85482	−	9.53821i	−0.168238	−	0.416282i
$526$			20.4624i			0.892205i
$527$	11.8673			0.516948
$528$	−1.24919			−0.0543641
$529$	−3.11463			−0.135419
$530$	4.30206	+	22.1261i	0.186869	+	0.961097i
$531$			30.6422i			1.32976i
$532$			5.71399i			0.247733i
$533$		0			0
$534$	−14.9430			−0.646648
$535$	0.806822	+	4.14961i	0.0348820	+	0.179403i
$536$	−11.0454			−0.477089
$537$		−	0.805115i		−	0.0347433i
$538$	28.7835			1.24094
$539$		−	3.09824i		−	0.133451i
$540$	−2.07572	−	10.6757i	−0.0893246	−	0.459409i
$541$		−	29.0524i		−	1.24906i	−0.781000	−	0.624531i	$-0.785290\pi$
$541$		−	29.0524i		−	1.24906i	0.781000	−	0.624531i	$-0.214710\pi$
$542$		−	1.82589i		−	0.0784287i
$543$			5.93048i			0.254501i
$544$			2.87416i			0.123229i
$545$	−1.83255	−	9.42510i	−0.0784980	−	0.403727i
$546$		0			0
$547$			14.0848i			0.602221i	0.953589	+	0.301111i	$0.0973574\pi$
$547$			14.0848i			0.602221i	−0.953589	+	0.301111i	$0.902643\pi$
$548$	−6.43023			−0.274686
$549$	23.3562			0.996818
$550$	−2.44695	−	6.05462i	−0.104338	−	0.258170i
$551$			21.1434i			0.900740i
$552$	−4.88768			−0.208033
$553$	−19.2375			−0.818061
$554$			1.10372i			0.0468927i
$555$	−1.21936	−	6.27133i	−0.0517588	−	0.266203i
$556$	−1.79435			−0.0760975
$557$	−1.65529			−0.0701367			−0.0350683	−	0.999385i	$-0.511165\pi$
$557$	−1.65529			−0.0701367			−0.0350683	+	0.999385i	$0.511165\pi$
$558$		−	8.60977i		−	0.364481i
$559$		0			0
$560$	4.72189	−	0.918093i	0.199536	−	0.0387965i
$561$			3.59038i			0.151586i
$562$			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	$0.722752\pi$
$564$			6.98610i			0.294168i
$565$	−7.98726	−	41.0797i	−0.336027	−	1.72823i
$566$			24.5173i			1.03054i
$567$	−3.45002			−0.144887
$568$			14.0739i			0.590526i
$569$	−15.1125			−0.633548			−0.316774	−	0.948501i	$-0.602600\pi$
$569$	−15.1125			−0.633548			−0.316774	+	0.948501i	$0.602600\pi$
$570$	5.57621	−	1.08420i	0.233562	−	0.0454122i
$571$	35.2350			1.47454			0.737269	−	0.675600i	$-0.236115\pi$
$571$	35.2350			1.47454			0.737269	+	0.675600i	$0.236115\pi$
$572$		0			0
$573$		−	10.2552i		−	0.428416i
$574$		−	18.6948i		−	0.780304i
$575$	−9.57409	−	23.6897i	−0.399267	−	0.987929i
$576$	2.08521			0.0868838
$577$	−25.4407			−1.05911			−0.529556	−	0.848275i	$-0.677641\pi$
$577$	−25.4407			−1.05911			−0.529556	+	0.848275i	$0.677641\pi$
$578$	−8.73921			−0.363503
$579$			24.8259i			1.03173i
$580$	17.4724	−	3.39721i	0.725500	−	0.141061i
$581$	−30.1130			−1.24930
$582$			4.83403i			0.200377i
$583$	−13.1658			−0.545271
$584$	−3.83547			−0.158713
$585$		0			0
$586$	−8.74457			−0.361235
$587$	16.4237			0.677877			0.338938	−	0.940809i	$-0.389932\pi$
$587$	16.4237			0.677877			0.338938	+	0.940809i	$0.389932\pi$
$588$		−	2.26885i		−	0.0935660i
$589$	10.9671			0.451892
$590$	6.27146	+	32.2550i	0.258192	+	1.32792i
$591$			4.92291i			0.202502i
$592$	2.98725			0.122775
$593$	−23.1420			−0.950327			−0.475163	−	0.879898i	$-0.657611\pi$
$593$	−23.1420			−0.950327			−0.475163	+	0.879898i	$0.657611\pi$
$594$	6.35241			0.260643
$595$	−2.63875	−	13.5715i	−0.108178	−	0.556376i
$596$		−	8.49082i		−	0.347798i
$597$		−	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	$0.308012\pi$
$600$	−1.79191	−	4.43382i	−0.0731544	−	0.181010i
$601$	−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
$603$	23.0320			0.937936
$604$		−	2.97802i		−	0.121174i
$605$	−20.4003	+	3.96651i	−0.829392	+	0.161262i
$606$		−	1.93977i		−	0.0787979i
$607$		−	37.9308i		−	1.53957i	−0.638306	−	0.769783i	$-0.720365\pi$
$607$		−	37.9308i		−	1.53957i	0.638306	−	0.769783i	$-0.279635\pi$
$608$			2.65614i			0.107721i
$609$			16.3785i			0.663689i
$610$	24.5855	−	4.78025i	0.995438	−	0.193546i
$611$		0			0
$612$		−	5.99323i		−	0.242262i
$613$	−2.38979			−0.0965227			−0.0482614	−	0.998835i	$-0.515368\pi$
$613$	−2.38979			−0.0965227			−0.0482614	+	0.998835i	$0.515368\pi$
$614$	−12.4345			−0.501815
$615$	−18.2440	+	3.54724i	−0.735667	+	0.143038i
$616$			2.80969i			0.113205i
$617$	19.0583			0.767259			0.383630	−	0.923487i	$-0.374674\pi$
$617$	19.0583			0.767259			0.383630	+	0.923487i	$0.374674\pi$
$618$	3.12004			0.125506
$619$			18.6920i			0.751294i	0.926763	+	0.375647i	$0.122579\pi$
$619$			18.6920i			0.751294i	−0.926763	+	0.375647i	$0.877421\pi$
$620$	−1.76214	−	9.06294i	−0.0707692	−	0.363976i
$621$	24.8549			0.997391
$622$	−0.269313			−0.0107985
$623$			33.6098i			1.34655i
$624$		0			0
$625$	17.9799	−	17.3701i	0.719197	−	0.694806i
$626$			10.5866i			0.423125i
$627$			3.31803i			0.132509i
$628$		−	14.3503i		−	0.572639i
$629$		−	8.58584i		−	0.342340i
$630$	−9.84614	+	1.91442i	−0.392279	+	0.0762723i
$631$		−	21.5119i		−	0.856377i	−0.903689	−	0.428188i	$-0.859152\pi$
$631$		−	21.5119i		−	0.856377i	0.903689	−	0.428188i	$-0.140848\pi$
$632$	−8.94252			−0.355714
$633$			24.7500i			0.983723i
$634$	21.0117			0.834482
$635$	−7.53248	−	38.7406i	−0.298917	−	1.53738i
$636$	−9.64136			−0.382305
$637$		0			0
$638$			10.3966i			0.411607i
$639$		−	29.3470i		−	1.16095i
$640$	2.19496	−	0.426774i	0.0867635	−	0.0168697i
$641$	−34.3509			−1.35678			−0.678390	−	0.734702i	$-0.737322\pi$
$641$	−34.3509			−1.35678			−0.678390	+	0.734702i	$0.737322\pi$
$642$	−1.80817			−0.0713629
$643$	31.1063			1.22671			0.613356	−	0.789807i	$-0.289819\pi$
$643$	31.1063			1.22671			0.613356	+	0.789807i	$0.289819\pi$
$644$			10.9934i			0.433199i
$645$	−7.03923	+	1.36866i	−0.277169	+	0.0538910i
$646$	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	$-0.0289010\pi$
$648$	−1.60374			−0.0630008
$649$	−19.1928			−0.753385
$650$		0			0
$651$	8.49554			0.332966
$652$	12.7139			0.497916
$653$		−	15.0219i		−	0.587853i	−0.955828	−	0.293926i	$-0.905038\pi$
$653$		−	15.0219i		−	0.587853i	0.955828	−	0.293926i	$-0.0949621\pi$
$654$	4.10695			0.160594
$655$	−18.8605	+	3.66711i	−0.736941	+	0.143286i
$656$		−	8.69023i		−	0.339297i
$657$	7.99776			0.312022
$658$	15.7131			0.612562
$659$	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
$661$			14.5505i			0.565949i	0.959127	+	0.282974i	$0.0913212\pi$
$661$			14.5505i			0.565949i	−0.959127	+	0.282974i	$0.908679\pi$
$662$		−	26.6423i		−	1.03548i
$663$		0			0
$664$	−13.9980			−0.543227
$665$	−2.43859	−	12.5420i	−0.0945643	−	0.486358i
$666$	−6.22905			−0.241371
$667$			40.6786i			1.57508i
$668$	1.32171			0.0511387
$669$		−	0.640210i		−	0.0247520i
$670$	24.2443	−	4.71390i	0.936638	−	0.182114i
$671$			14.6292i			0.564754i
$672$			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	$0.978462\pi$
$674$			3.43601i			0.132350i
$675$	9.11224	+	22.5469i	0.350730	+	0.867832i
$676$		0			0
$677$		−	33.5349i		−	1.28885i	−0.764668	−	0.644425i	$-0.777097\pi$
$677$		−	33.5349i		−	1.28885i	0.764668	−	0.644425i	$-0.222903\pi$
$678$	17.9003			0.687457
$679$	10.8727			0.417256
$680$	−1.22662	−	6.30867i	−0.0470386	−	0.241927i
$681$			5.17096i			0.198152i
$682$	5.39276			0.206499
$683$	39.6392			1.51675			0.758376	−	0.651817i	$-0.225993\pi$
$683$	39.6392			1.51675			0.758376	+	0.651817i	$0.225993\pi$
$684$		−	5.53861i		−	0.211774i
$685$	14.1141	−	2.74426i	0.539273	−	0.104853i
$686$	−20.1618			−0.769780
$687$	−2.13730			−0.0815429
$688$		−	3.35303i		−	0.127833i
$689$		0			0
$690$	10.7283	−	2.08593i	0.408418	−	0.0794102i
$691$		−	17.6727i		−	0.672300i	−0.941808	−	0.336150i	$-0.890875\pi$
$691$		−	17.6727i		−	0.672300i	0.941808	−	0.336150i	$-0.109125\pi$
$692$		−	23.9387i		−	0.910012i
$693$		−	5.85879i		−	0.222557i
$694$			13.6671i			0.518794i
$695$	3.93854	−	0.765783i	0.149397	−	0.0290478i
$696$			7.61350i			0.288589i
$697$	−24.9771			−0.946075
$698$		−	8.18464i		−	0.309793i
$699$	0.125953			0.00476397
$700$	−9.97256	+	4.03036i	−0.376927	+	0.152333i
$701$	46.5635			1.75868			0.879340	−	0.476194i	$-0.157984\pi$
$701$	46.5635			1.75868			0.879340	+	0.476194i	$0.157984\pi$
$702$		0			0
$703$		−	7.93456i		−	0.299258i
$704$			1.30608i			0.0492247i
$705$	−2.98149	−	15.3342i	−0.112289	−	0.577521i
$706$	21.4420			0.806980
$707$	−4.36294			−0.164085
$708$	−14.0550			−0.528219
$709$			26.2769i			0.986849i	0.869789	+	0.493425i	$0.164255\pi$
$709$			26.2769i			0.986849i	−0.869789	+	0.493425i	$0.835745\pi$
$710$	−6.00636	−	30.8916i	−0.225415	−	1.15934i
$711$	18.6470			0.699318
$712$			15.6235i			0.585515i
$713$	21.1001			0.790203
$714$	5.91371			0.221315
$715$		0			0
$716$	−0.841778			−0.0314587
$717$	−21.7252			−0.811342
$718$			7.09493i			0.264780i
$719$	11.3458			0.423128			0.211564	−	0.977364i	$-0.432144\pi$
$719$	11.3458			0.423128			0.211564	+	0.977364i	$0.432144\pi$
$720$	−4.57696	+	0.889915i	−0.170573	+	0.0331652i
$721$		−	7.01759i		−	0.261349i
$722$	−11.9449			−0.444544
$723$	21.0235			0.781873
$724$	6.20054			0.230441
$725$	−36.9013	+	14.9135i	−1.37048	+	0.553874i
$726$		−	8.88936i		−	0.329915i
$727$			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
$730$	8.41871	−	1.63688i	0.311590	−	0.0605836i
$731$	−9.63714			−0.356443
$732$			10.7130i			0.395965i
$733$	−32.4103			−1.19710			−0.598550	−	0.801085i	$-0.704256\pi$
$733$	−32.4103			−1.19710			−0.598550	+	0.801085i	$0.704256\pi$
$734$			23.9033i			0.882289i
$735$	0.968289	+	4.98005i	0.0357159	+	0.183692i
$736$			5.11025i			0.188366i
$737$			14.4262i			0.531395i
$738$			18.1210i			0.667042i
$739$			19.0620i			0.701208i	0.936524	+	0.350604i	$0.114024\pi$
$739$			19.0620i			0.701208i	−0.936524	+	0.350604i	$0.885976\pi$
$740$	−6.55691	+	1.27488i	−0.241037	+	0.0468656i
$741$		0			0
$742$			21.6853i			0.796094i
$743$	−25.4983			−0.935441			−0.467721	−	0.883876i	$-0.654925\pi$
$743$	−25.4983			−0.935441			−0.467721	+	0.883876i	$0.654925\pi$
$744$	3.94914			0.144782
$745$	3.62366	+	18.6370i	0.132761	+	0.682808i
$746$		−	11.5127i		−	0.421510i
$747$	29.1887			1.06796
$748$	3.75387			0.137255
$749$			4.06694i			0.148603i
$750$	5.82542	+	8.96734i	0.212714	+	0.327441i
$751$	19.5176			0.712209			0.356104	−	0.934446i	$-0.384105\pi$
$751$	19.5176			0.712209			0.356104	+	0.934446i	$0.384105\pi$
$752$	7.30423			0.266358
$753$		−	8.97763i		−	0.327163i
$754$		0			0
$755$	1.27094	+	6.53663i	0.0462543	+	0.237893i
$756$		−	10.4630i		−	0.380537i
$757$		−	23.6562i		−	0.859801i	−0.902876	−	0.429900i	$-0.858549\pi$
$757$		−	23.6562i		−	0.859801i	0.902876	−	0.429900i	$-0.141451\pi$
$758$			2.64445i			0.0960506i
$759$			6.38368i			0.231713i
$760$	−1.13357	−	5.83013i	−0.0411190	−	0.211481i
$761$			16.2681i			0.589717i	0.955541	+	0.294859i	$0.0952725\pi$
$761$			16.2681i			0.589717i	−0.955541	+	0.294859i	$0.904727\pi$
$762$	16.8811			0.611537
$763$		−	9.23735i		−	0.334414i
$764$	−10.7222			−0.387915
$765$	2.55776	+	13.1549i	0.0924758	+	0.475617i
$766$	−16.2424			−0.586863
$767$		0			0
$768$			0.956446i			0.0345128i
$769$		−	30.6878i		−	1.10663i	−0.832973	−	0.553314i	$-0.813363\pi$
$769$		−	30.6878i		−	1.10663i	0.832973	−	0.553314i	$-0.186637\pi$
$770$	−1.19910	−	6.16716i	−0.0432126	−	0.222249i
$771$	−7.04679			−0.253784
$772$	25.9564			0.934191
$773$	37.4115			1.34560			0.672798	−	0.739826i	$-0.265092\pi$
$773$	37.4115			1.34560			0.672798	+	0.739826i	$0.265092\pi$
$774$			6.99178i			0.251314i
$775$	7.73566	+	19.1408i	0.277873	+	0.687557i
$776$	5.05416			0.181434
$777$		−	6.14640i		−	0.220501i
$778$	23.7722			0.852275
$779$	−23.0825			−0.827016
$780$		0			0
$781$	18.3816			0.657744
$782$	14.6877			0.525230
$783$		−	38.7163i		−	1.38361i
$784$	−2.37217			−0.0847204
$785$	6.12433	+	31.4983i	0.218587	+	1.12422i
$786$		−	8.21839i		−	0.293140i
$787$	8.05503			0.287131			0.143565	−	0.989641i	$-0.454143\pi$
$787$	8.05503			0.287131			0.143565	+	0.989641i	$0.454143\pi$
$788$	5.14709			0.183358
$789$	19.5712			0.696754
$790$	19.6285	−	3.81644i	0.698351	−	0.135783i
$791$		−	40.2613i		−	1.43153i
$792$		−	2.72345i		−	0.0967735i
$793$		0			0
$794$	34.6274			1.22888
$795$	21.1624	−	4.11468i	0.750554	−	0.145933i
$796$	−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	$-0.0278971\pi$
$798$	5.46513			0.193463
$799$		−	20.9935i		−	0.742697i
$800$	−4.63573	+	1.87351i	−0.163898	+	0.0662385i
$801$		−	32.5783i		−	1.15110i
$802$			4.37028i			0.154320i
$803$			5.00942i			0.176779i
$804$			10.5643i			0.372576i
$805$	−4.69168	−	24.1300i	−0.165360	−	0.850472i
$806$		0			0
$807$		−	27.5298i		−	0.969096i
$808$	−2.02811			−0.0713485
$809$	−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
$811$			11.0393i			0.387644i	0.981037	+	0.193822i	$0.0620884\pi$
$811$			11.0393i			0.387644i	−0.981037	+	0.193822i	$0.937912\pi$
$812$	17.1243			0.600945
$813$	−1.74636			−0.0612477
$814$		−	3.90159i		−	0.136750i
$815$	−27.9066	+	5.42598i	−0.977527	+	0.190064i
$816$	2.74898			0.0962335
$817$	−8.90612			−0.311586
$818$		−	11.2279i		−	0.392575i
$819$		0			0
$820$	3.70877	+	19.0747i	0.129516	+	0.666119i
$821$		−	4.13968i		−	0.144476i	−0.997387	−	0.0722379i	$-0.976986\pi$
$821$		−	4.13968i		−	0.144476i	0.997387	−	0.0722379i	$-0.0230141\pi$
$822$			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	$0.839103\pi$
$824$		−	3.26212i		−	0.113641i
$825$	−5.79092	+	2.34037i	−0.201614	+	0.0814813i
$826$			31.6125i			1.09994i
$827$	6.46886			0.224944			0.112472	−	0.993655i	$-0.464123\pi$
$827$	6.46886			0.224944			0.112472	+	0.993655i	$0.464123\pi$
$828$		−	10.6559i		−	0.370320i
$829$	13.9415			0.484208			0.242104	−	0.970250i	$-0.422162\pi$
$829$	13.9415			0.484208			0.242104	+	0.970250i	$0.422162\pi$
$830$	30.7251	−	5.97398i	1.06648	−	0.207360i
$831$	1.05565			0.0366201
$832$		0			0
$833$			6.81800i			0.236230i
$834$			1.71620i			0.0594272i
$835$	−2.90112	+	0.564074i	−0.100397	+	0.0195206i
$836$	3.46913			0.119982
$837$	−20.0822			−0.694142
$838$	18.3230			0.632958
$839$			41.0483i			1.41714i	0.705639	+	0.708571i	$0.250660\pi$
$839$			41.0483i			1.41714i	−0.705639	+	0.708571i	$0.749340\pi$
$840$	−0.878107	−	4.51623i	−0.0302976	−	0.155825i
$841$	34.3648			1.18499
$842$		−	8.92506i		−	0.307578i
$843$	2.54927			0.0878014
$844$	25.8770			0.890724
$845$		0			0
$846$	−15.2309			−0.523648
$847$	−19.9940			−0.687001
$848$			10.0804i			0.346162i
$849$	23.4495			0.804785
$850$	5.38476	+	13.3238i	0.184696	+	0.457003i
$851$		−	15.2656i		−	0.523298i
$852$	13.4609			0.461162
$853$	−41.4242			−1.41834			−0.709168	−	0.705039i	$-0.750929\pi$
$853$	−41.4242			−1.41834			−0.709168	+	0.705039i	$0.750929\pi$
$854$	24.0958			0.824540
$855$	2.36374	+	12.1571i	0.0808381	+	0.415762i
$856$			1.89051i			0.0646164i
$857$			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	$0.405834\pi$
$860$	1.43099	+	7.35978i	0.0487963	+	0.250966i
$861$	−17.8805			−0.609367
$862$		−	34.8123i		−	1.18571i
$863$	12.3756			0.421269			0.210635	−	0.977565i	$-0.432447\pi$
$863$	12.3756			0.421269			0.210635	+	0.977565i	$0.432447\pi$
$864$		−	4.86373i		−	0.165467i
$865$	10.2164	+	52.5445i	0.347369	+	1.78657i
$866$			37.9777i			1.29054i
$867$			8.35858i			0.283872i
$868$		−	8.88240i		−	0.301488i
$869$			11.6796i			0.396204i
$870$	−3.24925	−	16.7114i	−0.110160	−	0.566568i
$871$		0			0
$872$		−	4.29397i		−	0.145412i
$873$	−10.5390			−0.356691
$874$	13.5735			0.459132
$875$	20.1693	−	13.1025i	0.681848	−	0.442946i
$876$			3.66842i			0.123944i
$877$	−29.3663			−0.991629			−0.495814	−	0.868429i	$-0.665130\pi$
$877$	−29.3663			−0.991629			−0.495814	+	0.868429i	$0.665130\pi$
$878$	16.6128			0.560656
$879$			8.36371i			0.282101i
$880$	−0.557400	−	2.86679i	−0.0187900	−	0.0966396i
$881$	−6.22016			−0.209563			−0.104781	−	0.994495i	$-0.533414\pi$
$881$	−6.22016			−0.209563			−0.104781	+	0.994495i	$0.533414\pi$
$882$	4.94648			0.166557
$883$		−	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
$886$			16.5892i			0.557325i
$887$		−	36.5930i		−	1.22867i	−0.789044	−	0.614337i	$-0.789424\pi$
$887$		−	36.5930i		−	1.22867i	0.789044	−	0.614337i	$-0.210576\pi$
$888$		−	2.85715i		−	0.0958796i
$889$		−	37.9689i		−	1.27344i
$890$	−6.66770	−	34.2930i	−0.223502	−	1.14950i
$891$			2.09461i			0.0701720i
$892$	−0.669364			−0.0224120
$893$		−	19.4011i		−	0.649232i
$894$	−8.12101			−0.271607
$895$	1.84767	−	0.359249i	0.0617608	−	0.0120084i
$896$	2.15124			0.0718678
$897$		0			0
$898$			19.4158i			0.647913i
$899$		−	32.8674i		−	1.09619i
$900$	9.66647	−	3.90666i	0.322216	−	0.130222i
$901$	28.9727			0.965220
$902$	−11.3501			−0.377918
$903$	−6.89901			−0.229585
$904$		−	18.7154i		−	0.622466i
$905$	−13.6100	+	2.64623i	−0.452410	+	0.0879637i
$906$	−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	$0.967009\pi$
$908$	5.40643			0.179419
$909$	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	$0.212163\pi$
$912$	2.54046			0.0841229
$913$			18.2825i			0.605061i
$914$	8.84923			0.292707
$915$	−4.57205	−	23.5147i	−0.151147	−	0.777372i
$916$			2.23462i			0.0738340i
$917$	−18.4848			−0.610422
$918$	−13.9791			−0.461380
$919$	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
$921$			11.8929i			0.391885i
$922$			17.3352i			0.570904i
$923$		0			0
$924$	2.68731			0.0884061
$925$	13.8481	−	5.59664i	0.455322	−	0.184016i
$926$	−17.0652			−0.560798
$927$			6.80220i			0.223414i
$928$	7.96020			0.261306
$929$			7.11857i			0.233553i	0.993158	+	0.116776i	$0.0372561\pi$
$929$			7.11857i			0.233553i	−0.993158	+	0.116776i	$0.962744\pi$
$930$	−8.66821	+	1.68539i	−0.284242	+	0.0552661i
$931$			6.30082i			0.206501i
$932$		−	0.131688i		−	0.00431360i
$933$			0.257583i			0.00843290i
$934$			22.5357i			0.737392i
$935$	−8.23962	+	1.60206i	−0.269464	+	0.0523929i
$936$		0			0
$937$		−	5.13448i		−	0.167736i	−0.996477	−	0.0838680i	$-0.973273\pi$
$937$		−	5.13448i		−	0.167736i	0.996477	−	0.0838680i	$-0.0267274\pi$
$938$	23.7613			0.775834
$939$	10.1255			0.330433
$940$	−16.0325	+	3.11726i	−0.522923	+	0.101674i
$941$			44.3630i			1.44619i	0.690748	+	0.723096i	$0.257281\pi$
$941$			44.3630i			1.44619i	−0.690748	+	0.723096i	$0.742719\pi$
$942$	−13.7253			−0.447193
$943$	−44.4092			−1.44616
$944$			14.6950i			0.478282i
$945$	4.46536	+	22.9660i	0.145258	+	0.747084i
$946$	−4.37932			−0.142384
$947$	54.3234			1.76527			0.882637	−	0.470056i	$-0.155766\pi$
$947$	54.3234			1.76527			0.882637	+	0.470056i	$0.155766\pi$
$948$			8.55303i			0.277790i
$949$		0			0
$950$	4.97630	+	12.3131i	0.161453	+	0.399491i
$951$		−	20.0966i		−	0.651676i
$952$		−	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	$-0.209818\pi$
$954$		−	21.0198i		−	0.680540i
$955$	23.5348	−	4.57595i	0.761567	−	0.148074i
$956$			22.7145i			0.734639i
$957$	9.94383			0.321438
$958$			33.3487i			1.07745i
$959$	13.8330			0.446690
$960$	−0.408187	−	2.09936i	−0.0131742	−	0.0677567i
$961$	13.9516			0.450052
$962$		0			0
$963$		−	3.94212i		−	0.127033i
$964$		−	21.9809i		−	0.707956i
$965$	−56.9733	+	11.0775i	−1.83404	+	0.356598i
$966$	10.5146			0.338300
$967$	8.18366			0.263169			0.131584	−	0.991305i	$-0.457994\pi$
$967$	8.18366			0.263169			0.131584	+	0.991305i	$0.457994\pi$
$968$	−9.29416			−0.298726
$969$		−	7.30167i		−	0.234563i
$970$	−11.0937	+	2.15699i	−0.356197	+	0.0692567i
$971$	−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
$973$	3.86008			0.123748
$974$	32.8658			1.05309
$975$		0			0
$976$	11.2009			0.358531
$977$	2.67273			0.0855082			0.0427541	−	0.999086i	$-0.486387\pi$
$977$	2.67273			0.0855082			0.0427541	+	0.999086i	$0.486387\pi$
$978$		−	12.1602i		−	0.388840i
$979$	20.4055			0.652162
$980$	5.20683	−	1.01238i	0.166326	−	0.0323394i
$981$			8.95383i			0.285874i
$982$	−17.6525			−0.563313
$983$	−5.29656			−0.168934			−0.0844670	−	0.996426i	$-0.526919\pi$
$983$	−5.29656			−0.168934			−0.0844670	+	0.996426i	$0.526919\pi$
$984$	−8.31174			−0.264969
$985$	−11.2977	+	2.19665i	−0.359974	+	0.0699910i
$986$		−	22.8789i		−	0.728612i
$987$		−	15.0288i		−	0.478371i
$988$		0			0
$989$	−17.1348			−0.544855
$990$	1.16230	+	5.97787i	0.0369402	+	0.189989i
$991$	−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
$993$	−25.4820			−0.808646
$994$		−	30.2762i		−	0.960304i
$995$	20.8620	−	4.05627i	0.661369	−	0.128592i
$996$			13.3883i			0.424225i
$997$			19.6903i			0.623597i	0.950148	+	0.311799i	$0.100931\pi$
$997$			19.6903i			0.623597i	−0.950148	+	0.311799i	$0.899069\pi$
$998$			37.3227i			1.18143i
$999$			14.5292i			0.459683i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1690.2.b.f.339.4	✓	18	65.44	odd	4
1690.2.b.f.339.15	yes	18	13.5	odd	4
1690.2.b.g.339.6	yes	18	13.8	odd	4
1690.2.b.g.339.13	yes	18	65.34	odd	4
1690.2.c.g.1689.6		18	65.64	even	2	inner
1690.2.c.g.1689.13		18	1.1	even	1	trivial
1690.2.c.h.1689.6		18	5.4	even	2
1690.2.c.h.1689.13		18	13.12	even	2
8450.2.a.ct.1.4		9	65.8	even	4
8450.2.a.cw.1.6		9	65.57	even	4
8450.2.a.cx.1.4		9	65.18	even	4
8450.2.a.da.1.6		9	65.47	even	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.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.956446i q^{3} +1.00000 q^{4} +(-2.19496 + 0.426774i) q^{5} -0.956446i q^{6} -2.15124 q^{7} -1.00000 q^{8} +2.08521 q^{9} +(2.19496 - 0.426774i) q^{10} +1.30608i q^{11} +0.956446i q^{12} +2.15124 q^{14} +(-0.408187 - 2.09936i) q^{15} +1.00000 q^{16} -2.87416i q^{17} -2.08521 q^{18} -2.65614i q^{19} +(-2.19496 + 0.426774i) q^{20} -2.05754i q^{21} -1.30608i q^{22} -5.11025i q^{23} -0.956446i q^{24} +(4.63573 - 1.87351i) q^{25} +4.86373i q^{27} -2.15124 q^{28} -7.96020 q^{29} +(0.408187 + 2.09936i) q^{30} +4.12897i q^{31} -1.00000 q^{32} -1.24919 q^{33} +2.87416i q^{34} +(4.72189 - 0.918093i) q^{35} +2.08521 q^{36} +2.98725 q^{37} +2.65614i q^{38} +(2.19496 - 0.426774i) q^{40} -8.69023i q^{41} +2.05754i q^{42} -3.35303i q^{43} +1.30608i q^{44} +(-4.57696 + 0.889915i) q^{45} +5.11025i q^{46} +7.30423 q^{47} +0.956446i q^{48} -2.37217 q^{49} +(-4.63573 + 1.87351i) q^{50} +2.74898 q^{51} +10.0804i q^{53} -4.86373i q^{54} +(-0.557400 - 2.86679i) q^{55} +2.15124 q^{56} +2.54046 q^{57} +7.96020 q^{58} +14.6950i q^{59} +(-0.408187 - 2.09936i) q^{60} +11.2009 q^{61} -4.12897i q^{62} -4.48579 q^{63} +1.00000 q^{64} +1.24919 q^{66} +11.0454 q^{67} -2.87416i q^{68} +4.88768 q^{69} +(-4.72189 + 0.918093i) q^{70} -14.0739i q^{71} -2.08521 q^{72} +3.83547 q^{73} -2.98725 q^{74} +(1.79191 + 4.43382i) q^{75} -2.65614i q^{76} -2.80969i q^{77} +8.94252 q^{79} +(-2.19496 + 0.426774i) q^{80} +1.60374 q^{81} +8.69023i q^{82} +13.9980 q^{83} -2.05754i q^{84} +(1.22662 + 6.30867i) q^{85} +3.35303i q^{86} -7.61350i q^{87} -1.30608i q^{88} -15.6235i q^{89} +(4.57696 - 0.889915i) q^{90} -5.11025i q^{92} -3.94914 q^{93} -7.30423 q^{94} +(1.13357 + 5.83013i) q^{95} -0.956446i q^{96} -5.05416 q^{97} +2.37217 q^{98} +2.72345i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 18 q^{2} + 18 q^{4} + 2 q^{5} + 2 q^{7} - 18 q^{8} - 16 q^{9} - 2 q^{10} - 2 q^{14} - 14 q^{15} + 18 q^{16} + 16 q^{18} + 2 q^{20} - 22 q^{25} + 2 q^{28} - 30 q^{29} + 14 q^{30} - 18 q^{32} + 28 q^{33}+ \cdots + 20 q^{98}+O(q^{100}) \) 18 * q - 18 * q^2 + 18 * q^4 + 2 * q^5 + 2 * q^7 - 18 * q^8 - 16 * q^9 - 2 * q^10 - 2 * q^14 - 14 * q^15 + 18 * q^16 + 16 * q^18 + 2 * q^20 - 22 * q^25 + 2 * q^28 - 30 * q^29 + 14 * q^30 - 18 * q^32 + 28 * q^33 - 4 * q^35 - 16 * q^36 - 20 * q^37 - 2 * q^40 - 20 * q^45 + 10 * q^47 - 20 * q^49 + 22 * q^50 - 24 * q^51 - 2 * q^56 + 24 * q^57 + 30 * q^58 - 14 * q^60 - 38 * q^61 - 78 * q^63 + 18 * q^64 - 28 * q^66 + 2 * q^67 - 28 * q^69 + 4 * q^70 + 16 * q^72 + 24 * q^73 + 20 * q^74 + 72 * q^75 + 28 * q^79 + 2 * q^80 + 106 * q^81 + 2 * q^83 + 16 * q^85 + 20 * q^90 - 56 * q^93 - 10 * q^94 + 54 * q^95 - 12 * q^97 + 20 * q^98

Introduction

L-functions

Modular forms

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