LMFDB - Embedded newform 735.2.g.b.734.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [735,2,Mod(734,735)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("735.734"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(735, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			734.6
Character	$\chi$	$=$	735.734
Dual form			735.2.g.b.734.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.51469 q^{2} +(-1.66512 + 0.476833i) q^{3} +0.294280 q^{4} +(0.775809 + 2.09717i) q^{5} +(2.52214 - 0.722254i) q^{6} +2.58363 q^{8} +(2.54526 - 1.58797i) q^{9} +(-1.17511 - 3.17656i) q^{10} -2.14830i q^{11} +(-0.490013 + 0.140323i) q^{12} -3.48097 q^{13} +(-2.29182 - 3.12211i) q^{15} -4.50196 q^{16} -3.57718i q^{17} +(-3.85528 + 2.40528i) q^{18} +1.22234i q^{19} +(0.228305 + 0.617156i) q^{20} +3.25401i q^{22} +1.51469 q^{23} +(-4.30206 + 1.23196i) q^{24} +(-3.79624 + 3.25401i) q^{25} +5.27259 q^{26} +(-3.48097 + 3.85783i) q^{27} -5.95645i q^{29} +(3.47139 + 4.72902i) q^{30} +3.17656i q^{31} +1.65180 q^{32} +(1.02438 + 3.57718i) q^{33} +5.41832i q^{34} +(0.749020 - 0.467309i) q^{36} -7.80350i q^{37} -1.85147i q^{38} +(5.79624 - 1.65984i) q^{39} +(2.00441 + 5.41832i) q^{40} +11.8685 q^{41} -2.99294i q^{43} -0.632203i q^{44} +(5.30488 + 4.10588i) q^{45} -2.29428 q^{46} -6.10167i q^{47} +(7.49631 - 2.14668i) q^{48} +(5.75012 - 4.92881i) q^{50} +(1.70572 + 5.95645i) q^{51} -1.02438 q^{52} +11.2260 q^{53} +(5.27259 - 5.84341i) q^{54} +(4.50535 - 1.66667i) q^{55} +(-0.582853 - 2.03535i) q^{57} +9.02216i q^{58} -2.16935 q^{59} +(-0.674437 - 0.918776i) q^{60} +3.39872i q^{61} -4.81149i q^{62} +6.50196 q^{64} +(-2.70057 - 7.30019i) q^{65} +(-1.55162 - 5.41832i) q^{66} -10.3176i q^{67} -1.05269i q^{68} +(-2.52214 + 0.722254i) q^{69} +10.3968i q^{71} +(6.57602 - 4.10273i) q^{72} +6.85557 q^{73} +11.8199i q^{74} +(4.76958 - 7.22849i) q^{75} +0.359711i q^{76} +(-8.77950 + 2.51414i) q^{78} -1.88284 q^{79} +(-3.49266 - 9.44137i) q^{80} +(3.95670 - 8.08360i) q^{81} -17.9771 q^{82} +9.10486i q^{83} +(7.50196 - 2.77521i) q^{85} +4.53337i q^{86} +(2.84023 + 9.91821i) q^{87} -5.55042i q^{88} +1.77992 q^{89} +(-8.03524 - 6.21913i) q^{90} +0.445743 q^{92} +(-1.51469 - 5.28936i) q^{93} +9.24213i q^{94} +(-2.56346 + 0.948304i) q^{95} +(-2.75045 + 0.787632i) q^{96} +1.32584 q^{97} +(-3.41144 - 5.46799i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4} + 12 q^{9} - 24 q^{15} + 24 q^{16} + 24 q^{25} - 36 q^{30} + 84 q^{36} + 24 q^{39} - 72 q^{46} + 24 q^{51} - 24 q^{60} + 24 q^{64} - 96 q^{79} + 12 q^{81} + 48 q^{85} - 48 q^{99}+O(q^{100}) $ 24 * q + 24 * q^4 + 12 * q^9 - 24 * q^15 + 24 * q^16 + 24 * q^25 - 36 * q^30 + 84 * q^36 + 24 * q^39 - 72 * q^46 + 24 * q^51 - 24 * q^60 + 24 * q^64 - 96 * q^79 + 12 * q^81 + 48 * q^85 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.51469			−1.07105			−0.535523	−	0.844521i	$-0.679886\pi$
$2$	−1.51469			−1.07105			−0.535523	+	0.844521i	$0.679886\pi$
$3$	−1.66512	+	0.476833i	−0.961358	+	0.275300i
$3$	−1.66512	+	0.476833i	−0.961358	+	0.275300i
$4$	0.294280			0.147140
$5$	0.775809	+	2.09717i	0.346952	+	0.937883i
$5$	0.775809	+	2.09717i	0.346952	+	0.937883i
$6$	2.52214	−	0.722254i	1.02966	−	0.294859i
$7$		0			0
$7$		0			0
$8$	2.58363			0.913452
$9$	2.54526	−	1.58797i	0.848420	−	0.529323i
$10$	−1.17511	−	3.17656i	−0.371602	−	1.00452i
$11$		−	2.14830i		−	0.647737i	−0.946102	−	0.323869i	$-0.895016\pi$
$11$		−	2.14830i		−	0.647737i	0.946102	−	0.323869i	$-0.104984\pi$
$12$	−0.490013	+	0.140323i	−0.141454	+	0.0405077i
$13$	−3.48097			−0.965448			−0.482724	−	0.875773i	$-0.660353\pi$
$13$	−3.48097			−0.965448			−0.482724	+	0.875773i	$0.660353\pi$
$14$		0			0
$15$	−2.29182	−	3.12211i	−0.591745	−	0.806126i
$16$	−4.50196			−1.12549
$17$		−	3.57718i		−	0.867594i	−0.901011	−	0.433797i	$-0.857173\pi$
$17$		−	3.57718i		−	0.867594i	0.901011	−	0.433797i	$-0.142827\pi$
$18$	−3.85528	+	2.40528i	−0.908697	+	0.566930i
$19$			1.22234i			0.280425i	0.990121	+	0.140212i	$0.0447785\pi$
$19$			1.22234i			0.280425i	−0.990121	+	0.140212i	$0.955222\pi$
$20$	0.228305	+	0.617156i	0.0510506	+	0.138000i
$21$		0			0
$22$			3.25401i			0.693757i
$23$	1.51469			0.315834			0.157917	−	0.987452i	$-0.449522\pi$
$23$	1.51469			0.315834			0.157917	+	0.987452i	$0.449522\pi$
$24$	−4.30206	+	1.23196i	−0.878155	+	0.251473i
$25$	−3.79624	+	3.25401i	−0.759248	+	0.650801i
$26$	5.27259			1.03404
$27$	−3.48097	+	3.85783i	−0.669913	+	0.742439i
$28$		0			0
$29$		−	5.95645i		−	1.10608i	−0.833153	−	0.553042i	$-0.813467\pi$
$29$		−	5.95645i		−	1.10608i	0.833153	−	0.553042i	$-0.186533\pi$
$30$	3.47139	+	4.72902i	0.633786	+	0.863398i
$31$			3.17656i			0.570527i	0.958449	+	0.285263i	$0.0920811\pi$
$31$			3.17656i			0.570527i	−0.958449	+	0.285263i	$0.907919\pi$
$32$	1.65180			0.291999
$33$	1.02438	+	3.57718i	0.178322	+	0.622708i
$34$			5.41832i			0.929234i
$35$		0			0
$36$	0.749020	−	0.467309i	0.124837	−	0.0778848i
$37$		−	7.80350i		−	1.28289i	−0.767170	−	0.641444i	$-0.778336\pi$
$37$		−	7.80350i		−	1.28289i	0.767170	−	0.641444i	$-0.221664\pi$
$38$		−	1.85147i		−	0.300348i
$39$	5.79624	−	1.65984i	0.928141	−	0.265788i
$40$	2.00441	+	5.41832i	0.316925	+	0.856711i
$41$	11.8685			1.85355			0.926773	−	0.375622i	$-0.122571\pi$
$41$	11.8685			1.85355			0.926773	+	0.375622i	$0.122571\pi$
$42$		0			0
$43$		−	2.99294i		−	0.456419i	−0.973612	−	0.228209i	$-0.926713\pi$
$43$		−	2.99294i		−	0.456419i	0.973612	−	0.228209i	$-0.0732871\pi$
$44$		−	0.632203i		−	0.0953082i
$45$	5.30488	+	4.10588i	0.790805	+	0.612068i
$46$	−2.29428			−0.338273
$47$		−	6.10167i		−	0.890020i	−0.895526	−	0.445010i	$-0.853200\pi$
$47$		−	6.10167i		−	0.890020i	0.895526	−	0.445010i	$-0.146800\pi$
$48$	7.49631	−	2.14668i	1.08200	−	0.309847i
$49$		0			0
$50$	5.75012	−	4.92881i	0.813190	−	0.697038i
$51$	1.70572	+	5.95645i	0.238849	+	0.834069i
$52$	−1.02438			−0.142056
$53$	11.2260			1.54201			0.771006	−	0.636828i	$-0.219754\pi$
$53$	11.2260			1.54201			0.771006	+	0.636828i	$0.219754\pi$
$54$	5.27259	−	5.84341i	0.717508	−	0.795187i
$55$	4.50535	−	1.66667i	0.607502	−	0.224734i
$56$		0			0
$57$	−0.582853	−	2.03535i	−0.0772008	−	0.269589i
$58$			9.02216i			1.18467i
$59$	−2.16935			−0.282425			−0.141213	−	0.989979i	$-0.545100\pi$
$59$	−2.16935			−0.282425			−0.141213	+	0.989979i	$0.545100\pi$
$60$	−0.674437	−	0.918776i	−0.0870694	−	0.118613i
$61$			3.39872i			0.435162i	0.976042	+	0.217581i	$0.0698166\pi$
$61$			3.39872i			0.435162i	−0.976042	+	0.217581i	$0.930183\pi$
$62$		−	4.81149i		−	0.611060i
$63$		0			0
$64$	6.50196			0.812745
$65$	−2.70057	−	7.30019i	−0.334964	−	0.905477i
$66$	−1.55162	−	5.41832i	−0.190991	−	0.666949i
$67$		−	10.3176i		−	1.26050i	−0.776392	−	0.630250i	$-0.782952\pi$
$67$		−	10.3176i		−	1.26050i	0.776392	−	0.630250i	$-0.217048\pi$
$68$		−	1.05269i		−	0.127658i
$69$	−2.52214	+	0.722254i	−0.303630	+	0.0869491i
$70$		0			0
$71$			10.3968i			1.23387i	0.787013	+	0.616936i	$0.211626\pi$
$71$			10.3968i			1.23387i	−0.787013	+	0.616936i	$0.788374\pi$
$72$	6.57602	−	4.10273i	0.774991	−	0.483512i
$73$	6.85557			0.802384			0.401192	−	0.915994i	$-0.368596\pi$
$73$	6.85557			0.802384			0.401192	+	0.915994i	$0.368596\pi$
$74$			11.8199i			1.37403i
$75$	4.76958	−	7.22849i	0.550744	−	0.834674i
$76$			0.359711i			0.0412617i
$77$		0			0
$78$	−8.77950	+	2.51414i	−0.994082	+	0.284671i
$79$	−1.88284			−0.211836			−0.105918	−	0.994375i	$-0.533778\pi$
$79$	−1.88284			−0.211836			−0.105918	+	0.994375i	$0.533778\pi$
$80$	−3.49266	−	9.44137i	−0.390491	−	1.05558i
$81$	3.95670	−	8.08360i	0.439633	−	0.898177i
$82$	−17.9771			−1.98523
$83$			9.10486i			0.999388i	0.866202	+	0.499694i	$0.166554\pi$
$83$			9.10486i			0.999388i	−0.866202	+	0.499694i	$0.833446\pi$
$84$		0			0
$85$	7.50196	−	2.77521i	0.813702	−	0.301014i
$86$			4.53337i			0.488846i
$87$	2.84023	+	9.91821i	0.304505	+	1.06334i
$88$		−	5.55042i		−	0.591677i
$89$	1.77992			0.188672			0.0943358	−	0.995540i	$-0.469927\pi$
$89$	1.77992			0.188672			0.0943358	+	0.995540i	$0.469927\pi$
$90$	−8.03524	−	6.21913i	−0.846989	−	0.655554i
$91$		0			0
$92$	0.445743			0.0464719
$93$	−1.51469	−	5.28936i	−0.157066	−	0.548481i
$94$			9.24213i			0.953253i
$95$	−2.56346	+	0.948304i	−0.263005	+	0.0972940i
$96$	−2.75045	+	0.787632i	−0.280716	+	0.0803874i
$97$	1.32584			0.134618			0.0673092	−	0.997732i	$-0.478559\pi$
$97$	1.32584			0.134618			0.0673092	+	0.997732i	$0.478559\pi$
$98$		0			0
$99$	−3.41144	−	5.46799i	−0.342863	−	0.549553i
$100$	−1.11716	+	0.957590i	−0.111716	+	0.0957590i
$101$	13.4201			1.33535			0.667675	−	0.744453i	$-0.267290\pi$
$101$	13.4201			1.33535			0.667675	+	0.744453i	$0.267290\pi$
$102$	−2.58363	−	9.02216i	−0.255818	−	0.893327i
$103$	5.78683			0.570194			0.285097	−	0.958499i	$-0.407974\pi$
$103$	5.78683			0.570194			0.285097	+	0.958499i	$0.407974\pi$
$104$	−8.99355			−0.881890
$105$		0			0
$106$	−17.0039			−1.65157
$107$	3.88645			0.375717			0.187859	−	0.982196i	$-0.439845\pi$
$107$	3.88645			0.375717			0.187859	+	0.982196i	$0.439845\pi$
$108$	−1.02438	+	1.13528i	−0.0985711	+	0.109243i
$109$	5.20768			0.498805			0.249403	−	0.968400i	$-0.419766\pi$
$109$	5.20768			0.498805			0.249403	+	0.968400i	$0.419766\pi$
$110$	−6.82420	+	2.52449i	−0.650662	+	0.240701i
$111$	3.72097	+	12.9938i	0.353179	+	1.23331i
$112$		0			0
$113$	9.36235			0.880736			0.440368	−	0.897817i	$-0.354848\pi$
$113$	9.36235			0.880736			0.440368	+	0.897817i	$0.354848\pi$
$114$	0.882841	+	3.08292i	0.0826856	+	0.288742i
$115$	1.17511	+	3.17656i	0.109579	+	0.296216i
$116$		−	1.75286i		−	0.162749i
$117$	−8.85998	+	5.52768i	−0.819105	+	0.511034i
$118$	3.28589			0.302490
$119$		0			0
$120$	−5.92121	−	8.06639i	−0.540530	−	0.736357i
$121$	6.38480			0.580436
$122$		−	5.14801i		−	0.466079i
$123$	−19.7625	+	5.65929i	−1.78192	+	0.510281i
$124$			0.934799i			0.0839474i
$125$	−9.76936	−	5.43687i	−0.873798	−	0.486289i
$126$		0			0
$127$			9.57778i			0.849891i	0.905219	+	0.424945i	$0.139707\pi$
$127$			9.57778i			0.849891i	−0.905219	+	0.424945i	$0.860293\pi$
$128$	−13.1520			−1.16249
$129$	1.42713	+	4.98361i	0.125652	+	0.438782i
$130$	4.09052	+	11.0575i	0.358762	+	0.969807i
$131$	−9.45016			−0.825665			−0.412832	−	0.910807i	$-0.635460\pi$
$131$	−9.45016			−0.825665			−0.412832	+	0.910807i	$0.635460\pi$
$132$	0.301455	+	1.05269i	0.0262383	+	0.0916253i
$133$		0			0
$134$			15.6280i			1.35005i
$135$	−10.7911	−	4.30725i	−0.928749	−	0.370709i
$136$		−	9.24213i		−	0.792506i
$137$	10.7055			0.914634			0.457317	−	0.889304i	$-0.348810\pi$
$137$	10.7055			0.914634			0.457317	+	0.889304i	$0.348810\pi$
$138$	3.82026	−	1.09399i	0.325202	−	0.0931265i
$139$		−	4.11136i		−	0.348721i	−0.984682	−	0.174360i	$-0.944214\pi$
$139$		−	4.11136i		−	0.348721i	0.984682	−	0.174360i	$-0.0557858\pi$
$140$		0			0
$141$	2.90948	+	10.1600i	0.245022	+	0.855629i
$142$		−	15.7479i		−	1.32153i
$143$			7.47817i			0.625356i
$144$	−11.4587	+	7.14898i	−0.954888	+	0.595748i
$145$	12.4917	−	4.62107i	1.03738	−	0.383759i
$146$	−10.3841			−0.859390
$147$		0			0
$148$		−	2.29642i		−	0.188764i
$149$		−	2.54374i		−	0.208391i	−0.994557	−	0.104196i	$-0.966773\pi$
$149$		−	2.54374i		−	0.208391i	0.994557	−	0.104196i	$-0.0332268\pi$
$150$	−7.22443	+	10.9489i	−0.589872	+	0.893975i
$151$	−5.61912			−0.457277			−0.228639	−	0.973511i	$-0.573427\pi$
$151$	−5.61912			−0.457277			−0.228639	+	0.973511i	$0.573427\pi$
$152$			3.15808i			0.256154i
$153$	−5.68046	−	9.10486i	−0.459238	−	0.736084i
$154$		0			0
$155$	−6.66178	+	2.46440i	−0.535087	+	0.197946i
$156$	1.70572	−	0.488459i	0.136567	−	0.0391080i
$157$	−13.9239			−1.11125			−0.555623	−	0.831434i	$-0.687520\pi$
$157$	−13.9239			−1.11125			−0.555623	+	0.831434i	$0.687520\pi$
$158$	2.85192			0.226886
$159$	−18.6927	+	5.35294i	−1.48243	+	0.424516i
$160$	1.28148	+	3.46410i	0.101310	+	0.273861i
$161$		0			0
$162$	−5.99317	+	12.2441i	−0.470868	+	0.961990i
$163$			4.07070i			0.318842i	0.987211	+	0.159421i	$0.0509627\pi$
$163$			4.07070i			0.318842i	−0.987211	+	0.159421i	$0.949037\pi$
$164$	3.49266			0.272731
$165$	−6.70724	+	4.92351i	−0.522158	+	0.383295i
$166$		−	13.7910i		−	1.07039i
$167$		−	13.9722i		−	1.08120i	−0.841279	−	0.540602i	$-0.818197\pi$
$167$		−	13.9722i		−	1.08120i	0.841279	−	0.540602i	$-0.181803\pi$
$168$		0			0
$169$	−0.882841			−0.0679109
$170$	−11.3631	+	4.20358i	−0.871512	+	0.322400i
$171$	1.94104	+	3.11118i	0.148435	+	0.237918i
$172$		−	0.880763i		−	0.0671576i
$173$		−	10.0027i		−	0.760488i	−0.924886	−	0.380244i	$-0.875840\pi$
$173$		−	10.0027i		−	0.760488i	0.924886	−	0.380244i	$-0.124160\pi$
$174$	−4.30206	−	15.0230i	−0.326139	−	1.13889i
$175$		0			0
$176$			9.67157i			0.729022i
$177$	3.61223	−	1.03442i	0.271512	−	0.0777516i
$178$	−2.69603			−0.202076
$179$		−	16.2095i		−	1.21155i	−0.795634	−	0.605777i	$-0.792862\pi$
$179$		−	16.2095i		−	1.21155i	0.795634	−	0.605777i	$-0.207138\pi$
$180$	1.56112	+	1.20828i	0.116359	+	0.0900599i
$181$		−	19.4123i		−	1.44290i	−0.692465	−	0.721451i	$-0.743475\pi$
$181$		−	19.4123i		−	1.44290i	0.692465	−	0.721451i	$-0.256525\pi$
$182$		0			0
$183$	−1.62062	−	5.65929i	−0.119800	−	0.418347i
$184$	3.91340			0.288500
$185$	16.3653	−	6.05403i	1.20320	−	0.445101i
$186$	2.29428	+	8.01172i	0.168225	+	0.587448i
$187$	−7.68487			−0.561973
$188$		−	1.79560i		−	0.130958i
$189$		0			0
$190$	3.88284	−	1.43639i	0.281691	−	0.104206i
$191$			12.7038i			0.919212i	0.888123	+	0.459606i	$0.152009\pi$
$191$			12.7038i			0.919212i	−0.888123	+	0.459606i	$0.847991\pi$
$192$	−10.8266	+	3.10035i	−0.781339	+	0.223748i
$193$			20.8195i			1.49862i	0.662218	+	0.749311i	$0.269615\pi$
$193$			20.8195i			1.49862i	−0.662218	+	0.749311i	$0.730385\pi$
$194$	−2.00823			−0.144182
$195$	7.97775	+	10.8680i	0.571298	+	0.778272i
$196$		0			0
$197$	−2.23465			−0.159212			−0.0796062	−	0.996826i	$-0.525366\pi$
$197$	−2.23465			−0.159212			−0.0796062	+	0.996826i	$0.525366\pi$
$198$	5.16727	+	8.28229i	0.367222	+	0.588597i
$199$		−	24.9220i		−	1.76667i	−0.468739	−	0.883337i	$-0.655292\pi$
$199$		−	24.9220i		−	1.76667i	0.468739	−	0.883337i	$-0.344708\pi$
$200$	−9.80809	+	8.40716i	−0.693537	+	0.594476i
$201$	4.91979	+	17.1801i	0.347016	+	1.21179i
$202$	−20.3273			−1.43022
$203$		0			0
$204$	0.501960	+	1.75286i	0.0351442	+	0.122725i
$205$	9.20768	+	24.8902i	0.643092	+	1.73841i
$206$	−8.76525			−0.610704
$207$	3.85528	−	2.40528i	0.267960	−	0.167179i
$208$	15.6712			1.08660
$209$	2.62596			0.181641
$210$		0			0
$211$	−6.61520			−0.455409			−0.227705	−	0.973730i	$-0.573122\pi$
$211$	−6.61520			−0.455409			−0.227705	+	0.973730i	$0.573122\pi$
$212$	3.30360			0.226892
$213$	−4.95754	−	17.3119i	−0.339685	−	1.18619i
$214$	−5.88676			−0.402411
$215$	6.27670	−	2.32195i	0.428067	−	0.158356i
$216$	−8.99355	+	9.96721i	−0.611934	+	0.678183i
$217$		0			0
$218$	−7.88801			−0.534243
$219$	−11.4154	+	3.26896i	−0.771378	+	0.220896i
$220$	1.32584	−	0.490469i	0.0893879	−	0.0330674i
$221$			12.4521i			0.837617i
$222$	−5.63611	−	19.6815i	−0.378271	−	1.32094i
$223$	−4.31027			−0.288637			−0.144318	−	0.989531i	$-0.546099\pi$
$223$	−4.31027			−0.288637			−0.144318	+	0.989531i	$0.546099\pi$
$224$		0			0
$225$	−4.49515	+	14.3106i	−0.299677	+	0.954041i
$226$	−14.1810			−0.943309
$227$		−	11.1112i		−	0.737478i	−0.929533	−	0.368739i	$-0.879790\pi$
$227$		−	11.1112i		−	0.737478i	0.929533	−	0.368739i	$-0.120210\pi$
$228$	−0.171522	−	0.598963i	−0.0113593	−	0.0396673i
$229$		−	9.97400i		−	0.659101i	−0.944138	−	0.329550i	$-0.893103\pi$
$229$		−	9.97400i		−	0.659101i	0.944138	−	0.329550i	$-0.106897\pi$
$230$	−1.77992	−	4.81149i	−0.117365	−	0.317261i
$231$		0			0
$232$		−	15.3893i		−	1.01036i
$233$	20.6287			1.35143			0.675716	−	0.737162i	$-0.263835\pi$
$233$	20.6287			1.35143			0.675716	+	0.737162i	$0.263835\pi$
$234$	13.4201	−	8.37271i	0.877300	−	0.547341i
$235$	12.7962	−	4.73373i	0.834735	−	0.308795i
$236$	−0.638397			−0.0415561
$237$	3.13516	−	0.897801i	0.203650	−	0.0583184i
$238$		0			0
$239$		−	2.87353i		−	0.185873i	−0.995672	−	0.0929365i	$-0.970375\pi$
$239$		−	2.87353i		−	0.185873i	0.995672	−	0.0929365i	$-0.0296254\pi$
$240$	10.3177	+	14.0556i	0.666003	+	0.907286i
$241$			26.0722i			1.67946i	0.543007	+	0.839728i	$0.317286\pi$
$241$			26.0722i			1.67946i	−0.543007	+	0.839728i	$0.682714\pi$
$242$	−9.67098			−0.621674
$243$	−2.73386	+	15.3469i	−0.175377	+	0.984501i
$244$			1.00018i			0.0640298i
$245$		0			0
$246$	29.9340	−	8.57206i	1.90852	−	0.546534i
$247$		−	4.25494i		−	0.270735i
$248$			8.20706i			0.521149i
$249$	−4.34150	−	15.1607i	−0.275131	−	0.960771i
$250$	14.7975	+	8.23516i	0.935878	+	0.520837i
$251$	−0.161120			−0.0101698			−0.00508489	−	0.999987i	$-0.501619\pi$
$251$	−0.161120			−0.0101698			−0.00508489	+	0.999987i	$0.501619\pi$
$252$		0			0
$253$		−	3.25401i		−	0.204578i
$254$		−	14.5074i		−	0.910272i
$255$	−11.1684	+	8.19825i	−0.699390	+	0.513394i
$256$	6.91732			0.432332
$257$		−	13.1303i		−	0.819045i	−0.912300	−	0.409522i	$-0.865695\pi$
$257$		−	13.1303i		−	0.819045i	0.912300	−	0.409522i	$-0.134305\pi$
$258$	−2.16166	−	7.54861i	−0.134579	−	0.469956i
$259$		0			0
$260$	−0.794725	−	2.14830i	−0.0492867	−	0.133232i
$261$	−9.45866	−	15.1607i	−0.585476	−	0.938424i
$262$	14.3141			0.884325
$263$	17.7305			1.09331			0.546655	−	0.837358i	$-0.315901\pi$
$263$	17.7305			1.09331			0.546655	+	0.837358i	$0.315901\pi$
$264$	2.64663	+	9.24213i	0.162889	+	0.568814i
$265$	8.70925	+	23.5429i	0.535005	+	1.44623i
$266$		0			0
$267$	−2.96379	+	0.848727i	−0.181381	+	0.0519412i
$268$		−	3.03628i		−	0.185470i
$269$	4.40588			0.268631			0.134316	−	0.990939i	$-0.457116\pi$
$269$	4.40588			0.268631			0.134316	+	0.990939i	$0.457116\pi$
$270$	16.3451	+	6.52414i	0.994733	+	0.397046i
$271$		−	23.5890i		−	1.43293i	−0.697623	−	0.716465i	$-0.745759\pi$
$271$		−	23.5890i		−	1.43293i	0.697623	−	0.716465i	$-0.254241\pi$
$272$			16.1043i			0.976469i
$273$		0			0
$274$	−16.2155			−0.979615
$275$	6.99059	+	8.15547i	0.421548	+	0.491793i
$276$	−0.742216	+	0.212545i	−0.0446762	+	0.0127937i
$277$		−	12.8318i		−	0.770987i	−0.922710	−	0.385494i	$-0.874031\pi$
$277$		−	12.8318i		−	0.770987i	0.922710	−	0.385494i	$-0.125969\pi$
$278$			6.22742i			0.373496i
$279$	5.04428	+	8.08517i	0.301993	+	0.484046i
$280$		0			0
$281$		−	21.2397i		−	1.26706i	−0.773719	−	0.633528i	$-0.781606\pi$
$281$		−	21.2397i		−	1.26706i	0.773719	−	0.633528i	$-0.218394\pi$
$282$	−4.40695	−	15.3893i	−0.262430	−	0.916418i
$283$	−6.55412			−0.389602			−0.194801	−	0.980843i	$-0.562406\pi$
$283$	−6.55412			−0.389602			−0.194801	+	0.980843i	$0.562406\pi$
$284$			3.05957i			0.181552i
$285$	3.81629	−	2.80138i	0.226057	−	0.165940i
$286$		−	11.3271i		−	0.669786i
$287$		0			0
$288$	4.20426	−	2.62301i	0.247738	−	0.154562i
$289$	4.20376			0.247280
$290$	−18.9210	+	6.99947i	−1.11108	+	0.411023i
$291$	−2.20768	+	0.632203i	−0.129416	+	0.0370604i
$292$	2.01746			0.118063
$293$			3.71937i			0.217288i	0.994081	+	0.108644i	$0.0346509\pi$
$293$			3.71937i			0.217288i	−0.994081	+	0.108644i	$0.965349\pi$
$294$		0			0
$295$	−1.68300	−	4.54949i	−0.0979881	−	0.264882i
$296$		−	20.1614i		−	1.17186i
$297$	8.28778	+	7.47817i	0.480906	+	0.433928i
$298$			3.85297i			0.223197i
$299$	−5.27259			−0.304922
$300$	1.40359	−	2.12720i	0.0810366	−	0.122814i
$301$		0			0
$302$	8.51121			0.489765
$303$	−22.3461	+	6.39915i	−1.28375	+	0.367622i
$304$		−	5.50294i		−	0.315615i
$305$	−7.12770	+	2.63676i	−0.408131	+	0.150980i
$306$	8.60413	+	13.7910i	0.491865	+	0.788381i
$307$	11.2102			0.639800			0.319900	−	0.947451i	$-0.396351\pi$
$307$	11.2102			0.639800			0.319900	+	0.947451i	$0.396351\pi$
$308$		0			0
$309$	−9.63578	+	2.75935i	−0.548160	+	0.156974i
$310$	10.0905	−	3.73280i	0.573103	−	0.212009i
$311$	−18.9210			−1.07291			−0.536456	−	0.843929i	$-0.680237\pi$
$311$	−18.9210			−1.07291			−0.536456	+	0.843929i	$0.680237\pi$
$312$	14.9754	−	4.28842i	0.847813	−	0.242784i
$313$	−16.3805			−0.925879			−0.462940	−	0.886390i	$-0.653205\pi$
$313$	−16.3805			−0.925879			−0.462940	+	0.886390i	$0.653205\pi$
$314$	21.0903			1.19020
$315$		0			0
$316$	−0.554083			−0.0311696
$317$	−10.1167			−0.568212			−0.284106	−	0.958793i	$-0.591697\pi$
$317$	−10.1167			−0.568212			−0.284106	+	0.958793i	$0.591697\pi$
$318$	28.3136	−	8.10803i	1.58775	−	0.454676i
$319$	−12.7962			−0.716452
$320$	5.04428	+	13.6357i	0.281984	+	0.762259i
$321$	−6.47141	+	1.85319i	−0.361199	+	0.103435i
$322$		0			0
$323$	4.37254			0.243295
$324$	1.16438	−	2.37884i	0.0646877	−	0.132158i
$325$	13.2146	−	11.3271i	0.733014	−	0.628315i
$326$		−	6.16584i		−	0.341494i
$327$	−8.67142	+	2.48319i	−0.479531	+	0.137321i
$328$	30.6638			1.69313
$329$		0			0
$330$	10.1594	−	7.45759i	0.559255	−	0.410527i
$331$	19.2755			1.05948			0.529738	−	0.848161i	$-0.322290\pi$
$331$	19.2755			1.05948			0.529738	+	0.848161i	$0.322290\pi$
$332$			2.67938i			0.147050i
$333$	−12.3917	−	19.8619i	−0.679062	−	1.08843i
$334$			21.1636i			1.15802i
$335$	21.6378	−	8.00452i	1.18220	−	0.437334i
$336$		0			0
$337$			23.6381i			1.28765i	0.765174	+	0.643824i	$0.222653\pi$
$337$			23.6381i			1.28765i	−0.765174	+	0.643824i	$0.777347\pi$
$338$	1.33723			0.0727357
$339$	−15.5895	+	4.46428i	−0.846703	+	0.242466i
$340$	2.20768	−	0.816690i	0.119728	−	0.0442913i
$341$	6.82420			0.369551
$342$	−2.94008	−	4.71247i	−0.158981	−	0.254821i
$343$		0			0
$344$		−	7.73266i		−	0.416917i
$345$	−3.47139	−	4.72902i	−0.186893	−	0.254602i
$346$			15.1509i			0.814518i
$347$	−15.9072			−0.853943			−0.426971	−	0.904265i	$-0.640420\pi$
$347$	−15.9072			−0.853943			−0.426971	+	0.904265i	$0.640420\pi$
$348$	0.835824	+	2.91873i	0.0448049	+	0.156461i
$349$		−	0.0192397i		−	0.00102988i	−1.00000		0.000514938i	$-0.999836\pi$
$349$		−	0.0192397i		−	0.00102988i	1.00000		0.000514938i	$-0.000163910\pi$
$350$		0			0
$351$	12.1172	−	13.4290i	0.646766	−	0.716786i
$352$		−	3.54856i		−	0.189139i
$353$			25.4200i			1.35297i	0.736457	+	0.676484i	$0.236497\pi$
$353$			25.4200i			1.35297i	−0.736457	+	0.676484i	$0.763503\pi$
$354$	−5.47140	+	1.56682i	−0.290802	+	0.0832755i
$355$	−21.8038	+	8.06593i	−1.15723	+	0.428095i
$356$	0.523797			0.0277612
$357$		0			0
$358$			24.5523i			1.29763i
$359$			24.1789i			1.27611i	0.769989	+	0.638057i	$0.220262\pi$
$359$			24.1789i			1.27611i	−0.769989	+	0.638057i	$0.779738\pi$
$360$	13.7059	+	10.6081i	0.722362	+	0.559095i
$361$	17.5059			0.921362
$362$			29.4035i			1.54542i
$363$	−10.6315	+	3.04448i	−0.558007	+	0.159794i
$364$		0			0
$365$	5.31861	+	14.3773i	0.278389	+	0.752542i
$366$	2.45474	+	8.57206i	0.128311	+	0.448069i
$367$	9.07272			0.473592			0.236796	−	0.971559i	$-0.423903\pi$
$367$	9.07272			0.473592			0.236796	+	0.971559i	$0.423903\pi$
$368$	−6.81907			−0.355468
$369$	30.2084	−	18.8468i	1.57259	−	0.981125i
$370$	−24.7883	+	9.16996i	−1.28868	+	0.476724i
$371$		0			0
$372$	−0.445743	−	1.55655i	−0.0231107	−	0.0807035i
$373$		−	15.5637i		−	0.805856i	−0.915232	−	0.402928i	$-0.867993\pi$
$373$		−	15.5637i		−	0.805856i	0.915232	−	0.402928i	$-0.132007\pi$
$374$	11.6402			0.601899
$375$	18.8597	+	4.39470i	0.973908	+	0.226941i
$376$		−	15.7645i		−	0.812991i
$377$			20.7342i			1.06787i
$378$		0			0
$379$	34.0984			1.75152			0.875758	−	0.482751i	$-0.160362\pi$
$379$	34.0984			1.75152			0.875758	+	0.482751i	$0.160362\pi$
$380$	−0.754376	+	0.279067i	−0.0386987	+	0.0143159i
$381$	−4.56700	−	15.9482i	−0.233975	−	0.817049i
$382$		−	19.2422i		−	0.984519i
$383$		−	10.5767i		−	0.540442i	−0.962798	−	0.270221i	$-0.912903\pi$
$383$		−	10.5767i		−	0.540442i	0.962798	−	0.270221i	$-0.0870967\pi$
$384$	21.8997	−	6.27133i	1.11757	−	0.320032i
$385$		0			0
$386$		−	31.5351i		−	1.60509i
$387$	−4.75270	−	7.61781i	−0.241593	−	0.387235i
$388$	0.390168			0.0198078
$389$		−	16.9347i		−	0.858624i	−0.903156	−	0.429312i	$-0.858756\pi$
$389$		−	16.9347i		−	0.858624i	0.903156	−	0.429312i	$-0.141244\pi$
$390$	−12.0838	−	16.4616i	−0.611887	−	0.833565i
$391$		−	5.41832i		−	0.274016i
$392$		0			0
$393$	15.7357	−	4.50615i	0.793760	−	0.227305i
$394$	3.38480			0.170524
$395$	−1.46073	−	3.94864i	−0.0734971	−	0.198677i
$396$	−1.00392	−	1.60912i	−0.0504489	−	0.0808614i
$397$	−0.407827			−0.0204682			−0.0102341	−	0.999948i	$-0.503258\pi$
$397$	−0.407827			−0.0204682			−0.0102341	+	0.999948i	$0.503258\pi$
$398$			37.7491i			1.89219i
$399$		0			0
$400$	17.0905	−	14.6494i	0.854526	−	0.732470i
$401$		−	27.9786i		−	1.39719i	−0.715519	−	0.698593i	$-0.753810\pi$
$401$		−	27.9786i		−	1.39719i	0.715519	−	0.698593i	$-0.246190\pi$
$402$	−7.45195	−	26.0225i	−0.371670	−	1.29789i
$403$		−	11.0575i		−	0.550814i
$404$	3.94927			0.196484
$405$	20.0223	+	2.02654i	0.994917	+	0.100700i
$406$		0			0
$407$	−16.7643			−0.830974
$408$	4.40695	+	15.3893i	0.218177	+	0.761882i
$409$			2.62071i			0.129586i	0.997899	+	0.0647929i	$0.0206387\pi$
$409$			2.62071i			0.129586i	−0.997899	+	0.0647929i	$0.979361\pi$
$410$	−13.9468	−	37.7009i	−0.688782	−	1.86192i
$411$	−17.8260	+	5.10475i	−0.879291	+	0.251799i
$412$	1.70295			0.0838984
$413$		0			0
$414$	−5.83954	+	3.64325i	−0.286998	+	0.179056i
$415$	−19.0944	+	7.06364i	−0.937309	+	0.346740i
$416$	−5.74986			−0.281910
$417$	1.96043	+	6.84591i	0.0960027	+	0.335246i
$418$	−3.97751			−0.194546
$419$	8.39649			0.410195			0.205098	−	0.978742i	$-0.434249\pi$
$419$	8.39649			0.410195			0.205098	+	0.978742i	$0.434249\pi$
$420$		0			0
$421$	−7.84952			−0.382562			−0.191281	−	0.981535i	$-0.561264\pi$
$421$	−7.84952			−0.382562			−0.191281	+	0.981535i	$0.561264\pi$
$422$	10.0200			0.487764
$423$	−9.68927	−	15.5303i	−0.471109	−	0.755111i
$424$	29.0039			1.40855
$425$	11.6402	+	13.5798i	0.564632	+	0.658719i
$426$	7.50912	+	26.2222i	0.363818	+	1.27047i
$427$		0			0
$428$	1.14371			0.0552831
$429$	−3.56584	−	12.4521i	−0.172160	−	0.601192i
$430$	−9.50724	+	3.51703i	−0.458480	+	0.169606i
$431$			12.2576i			0.590428i	0.955431	+	0.295214i	$0.0953910\pi$
$431$			12.2576i			0.590428i	−0.955431	+	0.295214i	$0.904609\pi$
$432$	15.6712	−	17.3678i	0.753981	−	0.835608i
$433$	−5.13957			−0.246992			−0.123496	−	0.992345i	$-0.539411\pi$
$433$	−5.13957			−0.246992			−0.123496	+	0.992345i	$0.539411\pi$
$434$		0			0
$435$	−18.5967	+	13.6511i	−0.891643	+	0.654519i
$436$	1.53252			0.0733943
$437$			1.85147i			0.0885677i
$438$	17.2907	−	4.95146i	0.826182	−	0.236590i
$439$			16.6993i			0.797013i	0.917165	+	0.398507i	$0.130471\pi$
$439$			16.6993i			0.797013i	−0.917165	+	0.398507i	$0.869529\pi$
$440$	11.6402	−	4.30607i	0.554924	−	0.205284i
$441$		0			0
$442$		−	18.8610i		−	0.897127i
$443$	−0.252220			−0.0119833			−0.00599167	−	0.999982i	$-0.501907\pi$
$443$	−0.252220			−0.0119833			−0.00599167	+	0.999982i	$0.501907\pi$
$444$	1.09501	+	3.82381i	0.0519668	+	0.181470i
$445$	1.38088	+	3.73280i	0.0654601	+	0.176952i
$446$	6.52871			0.309144
$447$	1.21294	+	4.23563i	0.0573700	+	0.200339i
$448$		0			0
$449$		−	28.8710i		−	1.36250i	−0.732049	−	0.681252i	$-0.761436\pi$
$449$		−	28.8710i		−	1.36250i	0.732049	−	0.681252i	$-0.238564\pi$
$450$	6.80875	−	21.6761i	0.320968	−	1.02182i
$451$		−	25.4971i		−	1.20061i
$452$	2.75516			0.129592
$453$	9.35652	−	2.67938i	0.439607	−	0.125888i
$454$			16.8300i			0.789873i
$455$		0			0
$456$	−1.50588	−	5.25859i	−0.0705193	−	0.246256i
$457$			24.0735i			1.12611i	0.826419	+	0.563056i	$0.190375\pi$
$457$			24.0735i			1.12611i	−0.826419	+	0.563056i	$0.809625\pi$
$458$			15.1075i			0.705927i
$459$	13.8002	+	12.4521i	0.644136	+	0.581213i
$460$	0.345812	+	0.934799i	0.0161235	+	0.0435852i
$461$	−39.8709			−1.85697			−0.928486	−	0.371367i	$-0.878889\pi$
$461$	−39.8709			−1.85697			−0.928486	+	0.371367i	$0.878889\pi$
$462$		0			0
$463$		−	29.8417i		−	1.38686i	−0.720524	−	0.693430i	$-0.756099\pi$
$463$		−	29.8417i		−	1.38686i	0.720524	−	0.693430i	$-0.243901\pi$
$464$			26.8157i			1.24489i
$465$	9.91757	−	7.28009i	0.459916	−	0.337606i
$466$	−31.2461			−1.44745
$467$		−	4.18164i		−	0.193503i	−0.995309	−	0.0967515i	$-0.969155\pi$
$467$		−	4.18164i		−	0.193503i	0.995309	−	0.0967515i	$-0.0308452\pi$
$468$	−2.60732	+	1.62669i	−0.120523	+	0.0751937i
$469$		0			0
$470$	−19.3823	+	7.17013i	−0.894039	+	0.330733i
$471$	23.1850	−	6.63937i	1.06831	−	0.305926i
$472$	−5.60480			−0.257982
$473$	−6.42973			−0.295640
$474$	−4.74879	+	1.35989i	−0.218119	+	0.0624618i
$475$	−3.97751	−	4.64030i	−0.182501	−	0.212912i
$476$		0			0
$477$	28.5731	−	17.8266i	1.30827	−	0.816223i
$478$			4.35250i			0.199079i
$479$	−27.9352			−1.27639			−0.638196	−	0.769874i	$-0.720319\pi$
$479$	−27.9352			−1.27639			−0.638196	+	0.769874i	$0.720319\pi$
$480$	−3.78562	−	5.15710i	−0.172789	−	0.235388i
$481$			27.1638i			1.23856i
$482$		−	39.4912i		−	1.79878i
$483$		0			0
$484$	1.87892			0.0854055
$485$	1.02860	+	2.78050i	0.0467062	+	0.126256i
$486$	4.14094	−	23.2457i	0.187837	−	1.05445i
$487$			37.2432i			1.68765i	0.536618	+	0.843826i	$0.319702\pi$
$487$			37.2432i			1.68765i	−0.536618	+	0.843826i	$0.680298\pi$
$488$			8.78105i			0.397500i
$489$	−1.94104	−	6.77821i	−0.0877770	−	0.306521i
$490$		0			0
$491$		−	5.90572i		−	0.266522i	−0.991081	−	0.133261i	$-0.957455\pi$
$491$		−	5.90572i		−	0.266522i	0.991081	−	0.133261i	$-0.0425448\pi$
$492$	−5.81571	+	1.66542i	−0.262192	+	0.0750828i
$493$	−21.3073			−0.959632
$494$			6.44490i			0.289970i
$495$	8.82067	−	11.3965i	0.396460	−	0.512234i
$496$		−	14.3007i		−	0.642122i
$497$		0			0
$498$	6.57602	+	22.9637i	0.294678	+	1.02903i
$499$	−18.7402			−0.838926			−0.419463	−	0.907772i	$-0.637782\pi$
$499$	−18.7402			−0.838926			−0.419463	+	0.907772i	$0.637782\pi$
$500$	−2.87493	−	1.59996i	−0.128571	−	0.0715526i
$501$	6.66242	+	23.2655i	0.297655	+	1.03942i
$502$	0.244046			0.0108923
$503$		−	32.0398i		−	1.42858i	−0.699849	−	0.714291i	$-0.746749\pi$
$503$		−	32.0398i		−	1.42858i	0.699849	−	0.714291i	$-0.253251\pi$
$504$		0			0
$505$	10.4114	+	28.1442i	0.463303	+	1.25240i
$506$			4.92881i			0.219112i
$507$	1.47004	−	0.420968i	0.0652867	−	0.0186958i
$508$			2.81855i			0.125053i
$509$	19.1493			0.848778			0.424389	−	0.905480i	$-0.360489\pi$
$509$	19.1493			0.848778			0.424389	+	0.905480i	$0.360489\pi$
$510$	16.9166	−	12.4178i	0.749079	−	0.549869i
$511$		0			0
$512$	15.8265			0.699439
$513$	−4.71559	−	4.25494i	−0.208198	−	0.187860i
$514$			19.8883i			0.877235i
$515$	4.48948	+	12.1360i	0.197830	+	0.534775i
$516$	0.419977	+	1.46658i	0.0184885	+	0.0645625i
$517$	−13.1082			−0.576499
$518$		0			0
$519$	4.76960	+	16.6557i	0.209362	+	0.731102i
$520$	−6.97728	−	18.8610i	−0.305974	−	0.827110i
$521$	3.88209			0.170077			0.0850387	−	0.996378i	$-0.472899\pi$
$521$	3.88209			0.170077			0.0850387	+	0.996378i	$0.472899\pi$
$522$	14.3269	+	22.9637i	0.627072	+	1.00510i
$523$	2.12383			0.0928687			0.0464343	−	0.998921i	$-0.485214\pi$
$523$	2.12383			0.0928687			0.0464343	+	0.998921i	$0.485214\pi$
$524$	−2.78100			−0.121488
$525$		0			0
$526$	−26.8562			−1.17099
$527$	11.3631			0.494986
$528$	−4.61172	−	16.1043i	−0.200700	−	0.700851i
$529$	−20.7057			−0.900249
$530$	−13.1918	−	35.6601i	−0.573015	−	1.54898i
$531$	−5.52156	+	3.44486i	−0.239615	+	0.149494i
$532$		0			0
$533$	−41.3138			−1.78950
$534$	4.48922	−	1.28556i	0.194267	−	0.0556315i
$535$	3.01514	+	8.15055i	0.130356	+	0.352379i
$536$		−	26.6570i		−	1.15141i
$537$	7.72922	+	26.9908i	0.333541	+	1.16474i
$538$	−6.67354			−0.287717
$539$		0			0
$540$	−3.17561	−	1.26754i	−0.136656	−	0.0545462i
$541$	−15.1810			−0.652684			−0.326342	−	0.945252i	$-0.605816\pi$
$541$	−15.1810			−0.652684			−0.326342	+	0.945252i	$0.605816\pi$
$542$			35.7300i			1.53473i
$543$	9.25641	+	32.3238i	0.397231	+	1.38715i
$544$		−	5.90879i		−	0.253337i
$545$	4.04017	+	10.9214i	0.173062	+	0.467821i
$546$		0			0
$547$			11.7540i			0.502566i	0.967914	+	0.251283i	$0.0808525\pi$
$547$			11.7540i			0.502566i	−0.967914	+	0.251283i	$0.919148\pi$
$548$	3.15042			0.134579
$549$	5.39707	+	8.65063i	0.230341	+	0.369200i
$550$	−10.5886	−	12.3530i	−0.451498	−	0.526733i
$551$	7.28081			0.310173
$552$	−6.51629	+	1.86604i	−0.277352	+	0.0794239i
$553$		0			0
$554$			19.4362i			0.825763i
$555$	−24.3634	+	17.8842i	−1.03417	+	0.759142i
$556$		−	1.20989i		−	0.0513108i
$557$	−9.40270			−0.398405			−0.199203	−	0.979958i	$-0.563835\pi$
$557$	−9.40270			−0.398405			−0.199203	+	0.979958i	$0.563835\pi$
$558$	−7.64051	−	12.2465i	−0.323449	−	0.518436i
$559$			10.4183i			0.440649i
$560$		0			0
$561$	12.7962	−	3.66440i	0.540258	−	0.154711i
$562$			32.1716i			1.35708i
$563$		−	19.5266i		−	0.822949i	−0.911421	−	0.411475i	$-0.865014\pi$
$563$		−	19.5266i		−	0.822949i	0.911421	−	0.411475i	$-0.134986\pi$
$564$	0.856203	+	2.98990i	0.0360526	+	0.125897i
$565$	7.26340	+	19.6344i	0.305573	+	0.826027i
$566$	9.92744			0.417281
$567$		0			0
$568$			26.8615i			1.12708i
$569$		−	12.8982i		−	0.540722i	−0.962759	−	0.270361i	$-0.912857\pi$
$569$		−	12.8982i		−	0.540722i	0.962759	−	0.270361i	$-0.0871430\pi$
$570$	−5.78049	+	4.24322i	−0.242118	+	0.177729i
$571$	−41.6642			−1.74359			−0.871796	−	0.489869i	$-0.837045\pi$
$571$	−41.6642			−1.74359			−0.871796	+	0.489869i	$0.837045\pi$
$572$			2.20068i			0.0920151i
$573$	−6.05758	−	21.1533i	−0.253059	−	0.883692i
$574$		0			0
$575$	−5.75012	+	4.92881i	−0.239797	+	0.205545i
$576$	16.5492	−	10.3249i	0.689549	−	0.430205i
$577$	−7.48978			−0.311804			−0.155902	−	0.987773i	$-0.549828\pi$
$577$	−7.48978			−0.311804			−0.155902	+	0.987773i	$0.549828\pi$
$578$	−6.36739			−0.264848
$579$	−9.92744	−	34.6670i	−0.412570	−	1.44071i
$580$	3.67605	−	1.35989i	0.152640	−	0.0564663i
$581$		0			0
$582$	3.34395	−	0.957590i	0.138611	−	0.0396934i
$583$		−	24.1169i		−	0.998819i
$584$	17.7123			0.732939
$585$	−18.4661	−	14.2924i	−0.763481	−	0.590920i
$586$		−	5.63369i		−	0.232726i
$587$			22.1920i			0.915961i	0.888962	+	0.457981i	$0.151427\pi$
$587$			22.1920i			0.915961i	−0.888962	+	0.457981i	$0.848573\pi$
$588$		0			0
$589$	−3.88284			−0.159990
$590$	2.54922	+	6.89106i	0.104950	+	0.283701i
$591$	3.72097	−	1.06556i	0.153060	−	0.0438311i
$592$			35.1310i			1.44388i
$593$			6.31375i			0.259275i	0.991561	+	0.129637i	$0.0413813\pi$
$593$			6.31375i			0.259275i	−0.991561	+	0.129637i	$0.958619\pi$
$594$	−12.5534	−	11.3271i	−0.515072	−	0.464757i
$595$		0			0
$596$		−	0.748572i		−	0.0306627i
$597$	11.8836	+	41.4982i	0.486365	+	1.69841i
$598$	7.98632			0.326585
$599$			20.6648i			0.844339i	0.906517	+	0.422170i	$0.138731\pi$
$599$			20.6648i			0.844339i	−0.906517	+	0.422170i	$0.861269\pi$
$600$	12.3229	−	18.6758i	0.503078	−	0.762435i
$601$		−	12.5956i		−	0.513785i	−0.966440	−	0.256892i	$-0.917301\pi$
$601$		−	12.5956i		−	0.513785i	0.966440	−	0.256892i	$-0.0826986\pi$
$602$		0			0
$603$	−16.3841	−	26.2611i	−0.667213	−	1.06943i
$604$	−1.65360			−0.0672839
$605$	4.95339	+	13.3900i	0.201384	+	0.544381i
$606$	33.8474	−	9.69272i	1.37496	−	0.393740i
$607$	42.6766			1.73219			0.866095	−	0.499879i	$-0.166622\pi$
$607$	42.6766			1.73219			0.866095	+	0.499879i	$0.166622\pi$
$608$			2.01906i			0.0818838i
$609$		0			0
$610$	10.7962	−	3.99387i	0.437127	−	0.161707i
$611$			21.2397i			0.859268i
$612$	−1.67165	−	2.67938i	−0.0675724	−	0.108308i
$613$			5.32284i			0.214988i	0.994206	+	0.107494i	$0.0342826\pi$
$613$			5.32284i			0.214988i	−0.994206	+	0.107494i	$0.965717\pi$
$614$	−16.9800			−0.685255
$615$	−27.2004	−	37.0547i	−1.09683	−	1.49419i
$616$		0			0
$617$	−30.1002			−1.21179			−0.605895	−	0.795545i	$-0.707185\pi$
$617$	−30.1002			−1.21179			−0.605895	+	0.795545i	$0.707185\pi$
$618$	14.5952	−	4.17956i	0.587105	−	0.168127i
$619$			12.7323i			0.511753i	0.966710	+	0.255876i	$0.0823640\pi$
$619$			12.7323i			0.511753i	−0.966710	+	0.255876i	$0.917636\pi$
$620$	−1.96043	+	0.725225i	−0.0787328	+	0.0291258i
$621$	−5.27259	+	5.84341i	−0.211582	+	0.234488i
$622$	28.6594			1.14914
$623$		0			0
$624$	−26.0944	+	7.47254i	−1.04461	+	0.299141i
$625$	3.82288	−	24.7060i	0.152915	−	0.988239i
$626$	24.8113			0.991659
$627$	−4.37254	+	1.25214i	−0.174623	+	0.0500058i
$628$	−4.09753			−0.163509
$629$	−27.9145			−1.11303
$630$		0			0
$631$	−17.4114			−0.693138			−0.346569	−	0.938024i	$-0.612653\pi$
$631$	−17.4114			−0.693138			−0.346569	+	0.938024i	$0.612653\pi$
$632$	−4.86457			−0.193502
$633$	11.0151	−	3.15435i	0.437811	−	0.125374i
$634$	15.3237			0.608581
$635$	−20.0862	+	7.43053i	−0.797098	+	0.294872i
$636$	−5.50089	+	1.57526i	−0.218125	+	0.0624633i
$637$		0			0
$638$	19.3823			0.767353
$639$	16.5098	+	26.4625i	0.653118	+	1.04684i
$640$	−10.2035	−	27.5821i	−0.403328	−	1.09028i
$641$			1.31513i			0.0519444i	0.999663	+	0.0259722i	$0.00826814\pi$
$641$			1.31513i			0.0519444i	−0.999663	+	0.0259722i	$0.991732\pi$
$642$	9.80217	−	2.80700i	0.386861	−	0.110784i
$643$	−39.2223			−1.54678			−0.773389	−	0.633932i	$-0.781440\pi$
$643$	−39.2223			−1.54678			−0.773389	+	0.633932i	$0.781440\pi$
$644$		0			0
$645$	−9.34429	+	6.85927i	−0.367931	+	0.270083i
$646$	−6.62304			−0.260580
$647$		−	6.23116i		−	0.244972i	−0.992470	−	0.122486i	$-0.960913\pi$
$647$		−	6.23116i		−	0.244972i	0.992470	−	0.122486i	$-0.0390867\pi$
$648$	10.2227	−	20.8850i	0.401584	−	0.820442i
$649$			4.66042i			0.182937i
$650$	−20.0160	+	17.1570i	−0.785092	+	0.672954i
$651$		0			0
$652$			1.19793i			0.0469144i
$653$	18.8618			0.738120			0.369060	−	0.929406i	$-0.379680\pi$
$653$	18.8618			0.738120			0.369060	+	0.929406i	$0.379680\pi$
$654$	13.1345	−	3.76127i	0.513599	−	0.147077i
$655$	−7.33152	−	19.8186i	−0.286466	−	0.774377i
$656$	−53.4314			−2.08615
$657$	17.4492	−	10.8864i	0.680759	−	0.424721i
$658$		0			0
$659$			41.6170i			1.62117i	0.585622	+	0.810584i	$0.300850\pi$
$659$			41.6170i			1.62117i	−0.585622	+	0.810584i	$0.699150\pi$
$660$	−1.97381	+	1.44889i	−0.0768304	+	0.0563981i
$661$			3.77854i			0.146968i	0.997296	+	0.0734842i	$0.0234118\pi$
$661$			3.77854i			0.146968i	−0.997296	+	0.0734842i	$0.976588\pi$
$662$	−29.1963			−1.13475
$663$	−5.93756	−	20.7342i	−0.230596	−	0.805250i
$664$			23.5236i			0.912894i
$665$		0			0
$666$	18.7696	+	30.0846i	0.727307	+	1.16576i
$667$		−	9.02216i		−	0.349339i
$668$		−	4.11175i		−	0.159088i
$669$	7.17712	−	2.05528i	0.277484	−	0.0794617i
$670$	−32.7746	+	12.1244i	−1.26619	+	0.468405i
$671$	7.30148			0.281871
$672$		0			0
$673$		−	31.2573i		−	1.20488i	−0.798163	−	0.602441i	$-0.794195\pi$
$673$		−	31.2573i		−	1.20488i	0.798163	−	0.602441i	$-0.205805\pi$
$674$		−	35.8043i		−	1.37913i
$675$	0.661201	−	25.9723i	0.0254496	−	0.999676i
$676$	−0.259803			−0.00999242
$677$			8.73789i			0.335824i	0.985802	+	0.167912i	$0.0537025\pi$
$677$			8.73789i			0.335824i	−0.985802	+	0.167912i	$0.946297\pi$
$678$	23.6132	−	6.76199i	0.906858	−	0.259693i
$679$		0			0
$680$	19.3823	−	7.17013i	0.743278	−	0.274962i
$681$	5.29820	+	18.5015i	0.203027	+	0.708981i
$682$	−10.3365			−0.395807
$683$	−21.8692			−0.836801			−0.418401	−	0.908263i	$-0.637409\pi$
$683$	−21.8692			−0.836801			−0.418401	+	0.908263i	$0.637409\pi$
$684$	0.571211	+	0.915559i	0.0218408	+	0.0350073i
$685$	8.30544	+	22.4513i	0.317334	+	0.857819i
$686$		0			0
$687$	4.75594	+	16.6079i	0.181450	+	0.633632i
$688$			13.4741i			0.513695i
$689$	−39.0774			−1.48873
$690$	5.25807	+	7.16300i	0.200171	+	0.272691i
$691$		−	22.5359i		−	0.857306i	−0.903469	−	0.428653i	$-0.858988\pi$
$691$		−	22.5359i		−	0.857306i	0.903469	−	0.428653i	$-0.141012\pi$
$692$		−	2.94359i		−	0.111898i
$693$		0			0
$694$	24.0944			0.914612
$695$	8.62221	−	3.18963i	0.327059	−	0.120989i
$696$	7.33811	+	25.6250i	0.278151	+	0.971313i
$697$		−	42.4557i		−	1.60813i
$698$			0.0291421i			0.00110305i
$699$	−34.3493	+	9.83646i	−1.29921	+	0.372049i
$700$		0			0
$701$			35.5019i			1.34089i	0.741960	+	0.670444i	$0.233896\pi$
$701$			35.5019i			1.34089i	−0.741960	+	0.670444i	$0.766104\pi$
$702$	−18.3537	+	20.3407i	−0.692716	+	0.767711i
$703$	9.53855			0.359753
$704$		−	13.9682i		−	0.526445i
$705$	−19.0501	+	13.9839i	−0.717468	+	0.526665i
$706$		−	38.5033i		−	1.44909i
$707$		0			0
$708$	1.06301	−	0.304409i	0.0399503	−	0.0114404i
$709$	4.06780			0.152769			0.0763847	−	0.997078i	$-0.475662\pi$
$709$	4.06780			0.152769			0.0763847	+	0.997078i	$0.475662\pi$
$710$	33.0260	−	12.2174i	1.23944	−	0.458510i
$711$	−4.79232	+	2.98990i	−0.179726	+	0.112130i
$712$	4.59867			0.172342
$713$			4.81149i			0.180192i
$714$		0			0
$715$	−15.6830	+	5.80164i	−0.586511	+	0.216969i
$716$		−	4.77014i		−	0.178268i
$717$	1.37019	+	4.78477i	0.0511708	+	0.178691i
$718$		−	36.6235i		−	1.36678i
$719$	−30.5405			−1.13897			−0.569484	−	0.822002i	$-0.692857\pi$
$719$	−30.5405			−1.13897			−0.569484	+	0.822002i	$0.692857\pi$
$720$	−23.8824	−	18.4845i	−0.890043	−	0.688877i
$721$		0			0
$722$	−26.5159			−0.986821
$723$	−12.4321	−	43.4133i	−0.462354	−	1.61456i
$724$		−	5.71265i		−	0.212309i
$725$	19.3823	+	22.6121i	0.719841	+	0.839792i
$726$	16.1034	−	4.61145i	0.597652	−	0.171147i
$727$	23.4181			0.868528			0.434264	−	0.900786i	$-0.357008\pi$
$727$	23.4181			0.868528			0.434264	+	0.900786i	$0.357008\pi$
$728$		0			0
$729$	−2.76568	−	26.8580i	−0.102433	−	0.994740i
$730$	−8.05604	−	21.7771i	−0.298168	−	0.806007i
$731$	−10.7063			−0.395986
$732$	−0.476918	−	1.66542i	−0.0176274	−	0.0615556i
$733$	−16.8907			−0.623871			−0.311935	−	0.950103i	$-0.600977\pi$
$733$	−16.8907			−0.623871			−0.311935	+	0.950103i	$0.600977\pi$
$734$	−13.7423			−0.507239
$735$		0			0
$736$	2.50196			0.0922235
$737$	−22.1654			−0.816473
$738$	−45.7563	+	28.5470i	−1.68431	+	1.05083i
$739$	27.6642			1.01764			0.508822	−	0.860872i	$-0.330081\pi$
$739$	27.6642			1.01764			0.508822	+	0.860872i	$0.330081\pi$
$740$	4.81597	−	1.78158i	0.177039	−	0.0654922i
$741$	2.02890	+	7.08499i	0.0745333	+	0.260274i
$742$		0			0
$743$	40.1701			1.47370			0.736850	−	0.676056i	$-0.236312\pi$
$743$	40.1701			1.47370			0.736850	+	0.676056i	$0.236312\pi$
$744$	−3.91340	−	13.6658i	−0.143472	−	0.501011i
$745$	5.33465	−	1.97346i	0.195446	−	0.0723018i
$746$			23.5741i			0.863109i
$747$	14.4583	+	23.1742i	0.529000	+	0.847901i
$748$	−2.26151			−0.0826888
$749$		0			0
$750$	−28.5665	−	6.65659i	−1.04310	−	0.243064i
$751$	−49.6376			−1.81130			−0.905650	−	0.424026i	$-0.860617\pi$
$751$	−49.6376			−1.81130			−0.905650	+	0.424026i	$0.860617\pi$
$752$			27.4695i			1.00171i
$753$	0.268284	−	0.0768272i	0.00977680	−	0.00279974i
$754$		−	31.4059i		−	1.14373i
$755$	−4.35936	−	11.7842i	−0.158654	−	0.428873i
$756$		0			0
$757$		−	47.7116i		−	1.73411i	−0.498214	−	0.867054i	$-0.666011\pi$
$757$		−	47.7116i		−	1.73411i	0.498214	−	0.867054i	$-0.333989\pi$
$758$	−51.6484			−1.87595
$759$	1.55162	+	5.41832i	0.0563202	+	0.196672i
$760$	−6.62304	+	2.45007i	−0.240243	+	0.0888734i
$761$	19.8342			0.718990			0.359495	−	0.933147i	$-0.382949\pi$
$761$	19.8342			0.718990			0.359495	+	0.933147i	$0.382949\pi$
$762$	6.91759	+	24.1565i	0.250598	+	0.875098i
$763$		0			0
$764$			3.73847i			0.135253i
$765$	14.6875	−	18.9765i	0.531027	−	0.686098i
$766$			16.0203i			0.578838i
$767$	7.55144			0.272667
$768$	−11.5182	+	3.29841i	−0.415626	+	0.119021i
$769$		−	10.6337i		−	0.383461i	−0.981448	−	0.191731i	$-0.938590\pi$
$769$		−	10.6337i		−	0.383461i	0.981448	−	0.191731i	$-0.0614100\pi$
$770$		0			0
$771$	6.26096	+	21.8635i	0.225483	+	0.787396i
$772$			6.12678i			0.220508i
$773$			14.3228i			0.515154i	0.966258	+	0.257577i	$0.0829240\pi$
$773$			14.3228i			0.515154i	−0.966258	+	0.257577i	$0.917076\pi$
$774$	7.19886	+	11.5386i	0.258758	+	0.414747i
$775$	−10.3365	−	12.0590i	−0.371300	−	0.433171i
$776$	3.42548			0.122967
$777$		0			0
$778$			25.6508i			0.919626i
$779$			14.5074i			0.519780i
$780$	2.34769	+	3.19823i	0.0840609	+	0.114515i
$781$	22.3354			0.799225
$782$			8.20706i			0.293484i
$783$	22.9789	+	20.7342i	0.821200	+	0.740980i
$784$		0			0
$785$	−10.8023	−	29.2007i	−0.385550	−	1.04222i
$786$	−23.8346	+	6.82541i	−0.850153	+	0.243454i
$787$	36.9341			1.31656			0.658280	−	0.752773i	$-0.271284\pi$
$787$	36.9341			1.31656			0.658280	+	0.752773i	$0.271284\pi$
$788$	−0.657614			−0.0234265
$789$	−29.5235	+	8.45450i	−1.05106	+	0.300988i
$790$	2.21254	+	5.98095i	0.0787188	+	0.212793i
$791$		0			0
$792$	−8.81391	−	14.1273i	−0.313189	−	0.501991i
$793$		−	11.8309i		−	0.420126i
$794$	0.617730			0.0219224
$795$	−25.7280	−	35.0489i	−0.912477	−	1.24306i
$796$		−	7.33405i		−	0.259949i
$797$		−	37.4862i		−	1.32783i	−0.747809	−	0.663914i	$-0.768894\pi$
$797$		−	37.4862i		−	1.32783i	0.747809	−	0.663914i	$-0.231106\pi$
$798$		0			0
$799$	−21.8268			−0.772177
$800$	−6.27062	+	5.37496i	−0.221700	+	0.190034i
$801$	4.53037	−	2.82647i	0.160073	−	0.0998683i
$802$			42.3789i			1.49645i
$803$		−	14.7278i		−	0.519734i
$804$	1.44780	+	5.05578i	0.0510599	+	0.178303i
$805$		0			0
$806$			16.7487i			0.589947i
$807$	−7.33633	+	2.10087i	−0.258251	+	0.0739542i
$808$	34.6726			1.21978
$809$			25.5786i			0.899297i	0.893206	+	0.449649i	$0.148451\pi$
$809$			25.5786i			0.899297i	−0.893206	+	0.449649i	$0.851549\pi$
$810$	−30.3276	−	3.06958i	−1.06560	−	0.107854i
$811$			7.28791i			0.255913i	0.991780	+	0.127957i	$0.0408418\pi$
$811$			7.28791i			0.255913i	−0.991780	+	0.127957i	$0.959158\pi$
$812$		0			0
$813$	11.2480	+	39.2786i	0.394485	+	1.37756i
$814$	25.3926			0.890012
$815$	−8.53694	+	3.15808i	−0.299036	+	0.110623i
$816$	−7.67908	−	26.8157i	−0.268822	−	0.938736i
$817$	3.65840			0.127991
$818$		−	3.96956i		−	0.138792i
$819$		0			0
$820$	2.70964	+	7.32470i	0.0946247	+	0.255790i
$821$		−	0.00842044i		−	0.000293875i	−1.00000		0.000146938i	$-0.999953\pi$
$821$		−	0.00842044i		−	0.000293875i	1.00000		0.000146938i	$-4.67717e-5\pi$
$822$	27.0008	−	7.73210i	0.941761	−	0.269688i
$823$		−	31.2239i		−	1.08840i	−0.838957	−	0.544198i	$-0.816834\pi$
$823$		−	31.2239i		−	1.08840i	0.838957	−	0.544198i	$-0.183166\pi$
$824$	14.9511			0.520845
$825$	−15.5290	−	10.2465i	−0.540650	−	0.356737i
$826$		0			0
$827$	38.3189			1.33248			0.666239	−	0.745738i	$-0.267903\pi$
$827$	38.3189			1.33248			0.666239	+	0.745738i	$0.267903\pi$
$828$	1.13453	−	0.707827i	0.0394277	−	0.0245987i
$829$		−	2.24176i		−	0.0778595i	−0.999242	−	0.0389298i	$-0.987605\pi$
$829$		−	2.24176i		−	0.0778595i	0.999242	−	0.0389298i	$-0.0123949\pi$
$830$	28.9221	−	10.6992i	1.00390	−	0.371375i
$831$	6.11862	+	21.3665i	0.212253	+	0.741195i
$832$	−22.6331			−0.784663
$833$		0			0
$834$	−2.96944	−	10.3694i	−0.102823	−	0.359064i
$835$	29.3021	−	10.8398i	1.01404	−	0.375126i
$836$	0.772768			0.0267268
$837$	−12.2546	−	11.0575i	−0.423581	−	0.382203i
$838$	−12.7181			−0.439338
$839$	−20.6544			−0.713069			−0.356535	−	0.934282i	$-0.616042\pi$
$839$	−20.6544			−0.713069			−0.356535	+	0.934282i	$0.616042\pi$
$840$		0			0
$841$	−6.47924			−0.223422
$842$	11.8896			0.409742
$843$	10.1278	+	35.3668i	0.348820	+	1.21810i
$844$	−1.94672			−0.0670090
$845$	−0.684916	−	1.85147i	−0.0235618	−	0.0636924i
$846$	14.6762	+	23.5236i	0.504579	+	0.808759i
$847$		0			0
$848$	−50.5391			−1.73552
$849$	10.9134	−	3.12522i	0.374547	−	0.107257i
$850$	−17.6312	−	20.5692i	−0.604747	−	0.705519i
$851$		−	11.8199i		−	0.405180i
$852$	−1.45891	−	5.09456i	−0.0499813	−	0.174537i
$853$	7.06831			0.242014			0.121007	−	0.992652i	$-0.461388\pi$
$853$	7.06831			0.242014			0.121007	+	0.992652i	$0.461388\pi$
$854$		0			0
$855$	−5.01879	+	6.48438i	−0.171639	+	0.221761i
$856$	10.0412			0.343200
$857$		−	16.8332i		−	0.575012i	−0.957779	−	0.287506i	$-0.907174\pi$
$857$		−	16.8332i		−	0.575012i	0.957779	−	0.287506i	$-0.0928261\pi$
$858$	5.40114	+	18.8610i	0.184392	+	0.643904i
$859$			35.1835i			1.20045i	0.799832	+	0.600223i	$0.204922\pi$
$859$			35.1835i			1.20045i	−0.799832	+	0.600223i	$0.795078\pi$
$860$	1.84711	−	0.683304i	0.0629859	−	0.0233005i
$861$		0			0
$862$		−	18.5665i		−	0.632376i
$863$	37.9758			1.29271			0.646356	−	0.763036i	$-0.276292\pi$
$863$	37.9758			1.29271			0.646356	+	0.763036i	$0.276292\pi$
$864$	−5.74986	+	6.37236i	−0.195614	+	0.216792i
$865$	20.9773	−	7.76016i	0.713249	−	0.263853i
$866$	7.78484			0.264540
$867$	−6.99977	+	2.00449i	−0.237725	+	0.0680761i
$868$		0			0
$869$			4.04491i			0.137214i
$870$	28.1682	−	20.6771i	0.954991	−	0.701020i
$871$			35.9154i			1.21695i
$872$	13.4547			0.455635
$873$	3.37460	−	2.10539i	0.114213	−	0.0712566i
$874$		−	2.80440i		−	0.0948601i
$875$		0			0
$876$	−3.35932	+	0.961992i	−0.113501	+	0.0325027i
$877$			11.4496i			0.386626i	0.981137	+	0.193313i	$0.0619233\pi$
$877$			11.4496i			0.386626i	−0.981137	+	0.193313i	$0.938077\pi$
$878$		−	25.2942i		−	0.853638i
$879$	−1.77352	−	6.19321i	−0.0598194	−	0.208892i
$880$	−20.2829	+	7.50329i	−0.683737	+	0.252936i
$881$	23.6698			0.797455			0.398728	−	0.917069i	$-0.369452\pi$
$881$	23.6698			0.797455			0.398728	+	0.917069i	$0.369452\pi$
$882$		0			0
$883$			16.8355i			0.566560i	0.959037	+	0.283280i	$0.0914226\pi$
$883$			16.8355i			0.566560i	−0.959037	+	0.283280i	$0.908577\pi$
$884$			3.66440i			0.123247i
$885$	4.97175	+	6.77295i	0.167124	+	0.227670i
$886$	0.382035			0.0128347
$887$		−	52.5834i		−	1.76558i	−0.469770	−	0.882789i	$-0.655663\pi$
$887$		−	52.5834i		−	1.76558i	0.469770	−	0.882789i	$-0.344337\pi$
$888$	9.61362	+	33.5712i	0.322612	+	1.12657i
$889$		0			0
$890$	−2.09160	−	5.65403i	−0.0701107	−	0.189524i
$891$	−17.3660	−	8.50018i	−0.581783	−	0.284767i
$892$	−1.26843			−0.0424701
$893$	7.45833			0.249584
$894$	−1.83722	−	6.41566i	−0.0614460	−	0.214572i
$895$	33.9941	−	12.5755i	1.13630	−	0.420352i
$896$		0			0
$897$	8.77950	−	2.51414i	0.293139	−	0.0839448i
$898$			43.7305i			1.45931i
$899$	18.9210			0.631050
$900$	−1.32284	+	4.21133i	−0.0440945	+	0.140378i
$901$		−	40.1575i		−	1.33784i
$902$			38.6201i			1.28591i
$903$		0			0
$904$	24.1889			0.804510
$905$	40.7108	−	15.0602i	1.35327	−	0.500619i
$906$	−14.1722	+	4.05843i	−0.470840	+	0.134832i
$907$			50.7715i			1.68584i	0.538038	+	0.842920i	$0.319166\pi$
$907$			50.7715i			1.68584i	−0.538038	+	0.842920i	$0.680834\pi$
$908$		−	3.26981i		−	0.108513i
$909$	34.1577	−	21.3107i	1.13294	−	0.706832i
$910$		0			0
$911$			16.1165i			0.533963i	0.963702	+	0.266981i	$0.0860262\pi$
$911$			16.1165i			0.533963i	−0.963702	+	0.266981i	$0.913974\pi$
$912$	2.62398	+	9.16306i	0.0868887	+	0.303419i
$913$	19.5600			0.647341
$914$		−	36.4639i		−	1.20612i
$915$	10.6112	−	7.78925i	0.350795	−	0.257505i
$916$		−	2.93515i		−	0.0969802i
$917$		0			0
$918$	−20.9029	−	18.8610i	−0.689900	−	0.622506i
$919$	39.7441			1.31104			0.655519	−	0.755179i	$-0.272450\pi$
$919$	39.7441			1.31104			0.655519	+	0.755179i	$0.272450\pi$
$920$	3.03605	+	8.20706i	0.100096	+	0.270579i
$921$	−18.6663	+	5.34539i	−0.615077	+	0.176137i
$922$	60.3920			1.98890
$923$		−	36.1909i		−	1.19124i
$924$		0			0
$925$	25.3926	+	29.6240i	0.834905	+	0.974030i
$926$			45.2008i			1.48539i
$927$	14.7290	−	9.18932i	0.483764	−	0.301817i
$928$		−	9.83885i		−	0.322976i
$929$	36.5187			1.19814			0.599069	−	0.800697i	$-0.295537\pi$
$929$	36.5187			1.19814			0.599069	+	0.800697i	$0.295537\pi$
$930$	−15.0220	+	11.0271i	−0.492591	+	0.361592i
$931$		0			0
$932$	6.07063			0.198850
$933$	31.5058	−	9.02216i	1.03145	−	0.295372i
$934$			6.33388i			0.207251i
$935$	−5.96199	−	16.1165i	−0.194978	−	0.527065i
$936$	−22.8909	+	14.2815i	−0.748214	+	0.466805i
$937$	7.60980			0.248601			0.124301	−	0.992245i	$-0.460331\pi$
$937$	7.60980			0.248601			0.124301	+	0.992245i	$0.460331\pi$
$938$		0			0
$939$	27.2755	−	7.81075i	0.890102	−	0.254894i
$940$	3.76568	−	1.39304i	0.122823	−	0.0454361i
$941$	22.0242			0.717969			0.358985	−	0.933343i	$-0.383123\pi$
$941$	22.0242			0.717969			0.358985	+	0.933343i	$0.383123\pi$
$942$	−35.1180	+	10.0566i	−1.14421	+	0.327661i
$943$	17.9771			0.585413
$944$	9.76632			0.317867
$945$		0			0
$946$	9.73904			0.316644
$947$	−49.2583			−1.60068			−0.800339	−	0.599547i	$-0.795347\pi$
$947$	−49.2583			−1.60068			−0.800339	+	0.599547i	$0.795347\pi$
$948$	0.922616	−	0.264205i	0.0299652	−	0.00858099i
$949$	−23.8640			−0.774660
$950$	6.02469	+	7.02861i	0.195467	+	0.228038i
$951$	16.8456	−	4.82399i	0.546255	−	0.156429i
$952$		0			0
$953$	−10.2538			−0.332154			−0.166077	−	0.986113i	$-0.553110\pi$
$953$	−10.2538			−0.332154			−0.166077	+	0.986113i	$0.553110\pi$
$954$	−43.2794	+	27.0017i	−1.40122	+	0.874213i
$955$	−26.6419	+	9.85570i	−0.862113	+	0.318923i
$956$		−	0.845623i		−	0.0273494i
$957$	21.3073	−	6.10167i	0.688767	−	0.197239i
$958$	42.3131			1.36708
$959$		0			0
$960$	−14.9013	−	20.2998i	−0.480937	−	0.655174i
$961$	20.9095			0.674499
$962$		−	41.1446i		−	1.32656i
$963$	9.89203	−	6.17157i	0.318766	−	0.198876i
$964$			7.67253i			0.247115i
$965$	−43.6621	+	16.1520i	−1.40553	+	0.519951i
$966$		0			0
$967$		−	4.62632i		−	0.148772i	−0.997230	−	0.0743862i	$-0.976300\pi$
$967$		−	4.62632i		−	0.148772i	0.997230	−	0.0743862i	$-0.0236998\pi$
$968$	16.4960			0.530201
$969$	−7.28081	+	2.08497i	−0.233893	+	0.0669790i
$970$	−1.55800	−	4.21160i	−0.0500245	−	0.135226i
$971$	25.2886			0.811549			0.405775	−	0.913973i	$-0.367002\pi$
$971$	25.2886			0.811549			0.405775	+	0.913973i	$0.367002\pi$
$972$	−0.804521	+	4.51628i	−0.0258050	+	0.144860i
$973$		0			0
$974$		−	56.4119i		−	1.80755i
$975$	−16.6028	+	25.1622i	−0.531715	+	0.805834i
$976$		−	15.3009i		−	0.489770i
$977$	24.1098			0.771340			0.385670	−	0.922637i	$-0.373970\pi$
$977$	24.1098			0.771340			0.385670	+	0.922637i	$0.373970\pi$
$978$	2.94008	+	10.2669i	0.0940133	+	0.328298i
$979$		−	3.82381i		−	0.122210i
$980$		0			0
$981$	13.2549	−	8.26964i	0.423196	−	0.264029i
$982$			8.94533i			0.285457i
$983$		−	48.0882i		−	1.53378i	−0.641781	−	0.766888i	$-0.721804\pi$
$983$		−	48.0882i		−	1.53378i	0.641781	−	0.766888i	$-0.278196\pi$
$984$	−51.0590	+	14.6215i	−1.62770	+	0.466117i
$985$	−1.73366	−	4.68644i	−0.0552391	−	0.149323i
$986$	32.2739			1.02781
$987$		0			0
$988$		−	1.25214i		−	0.0398360i
$989$		−	4.53337i		−	0.144153i
$990$	−13.3606	+	17.2621i	−0.424627	+	0.548626i
$991$	29.7175			0.944007			0.472003	−	0.881597i	$-0.343531\pi$
$991$	29.7175			0.944007			0.472003	+	0.881597i	$0.343531\pi$
$992$			5.24703i			0.166593i
$993$	−32.0960	+	9.19119i	−1.01854	+	0.291674i
$994$		0			0
$995$	52.2656	−	19.3347i	1.65693	−	0.612952i
$996$	−1.27762	−	4.46150i	−0.0404829	−	0.141368i
$997$	−26.7483			−0.847128			−0.423564	−	0.905866i	$-0.639221\pi$
$997$	−26.7483			−0.847128			−0.423564	+	0.905866i	$0.639221\pi$
$998$	28.3856			0.898529
$999$	30.1046	+	27.1638i	0.952466	+	0.859423i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.g.b.734.6		24
3.2	odd	2	inner	735.2.g.b.734.17		24
5.4	even	2	inner	735.2.g.b.734.19		24
7.2	even	3		735.2.p.f.374.10		24
7.3	odd	6		735.2.p.f.509.9		24
7.4	even	3		105.2.p.a.89.10	yes	24
7.5	odd	6		105.2.p.a.59.9	yes	24
7.6	odd	2	inner	735.2.g.b.734.7		24
15.14	odd	2	inner	735.2.g.b.734.8		24
21.2	odd	6		735.2.p.f.374.4		24
21.5	even	6		105.2.p.a.59.3	✓	24
21.11	odd	6		105.2.p.a.89.4	yes	24
21.17	even	6		735.2.p.f.509.3		24
21.20	even	2	inner	735.2.g.b.734.20		24
35.4	even	6		105.2.p.a.89.3	yes	24
35.9	even	6		735.2.p.f.374.3		24
35.12	even	12		525.2.t.j.101.4		24
35.18	odd	12		525.2.t.j.26.3		24
35.19	odd	6		105.2.p.a.59.4	yes	24
35.24	odd	6		735.2.p.f.509.4		24
35.32	odd	12		525.2.t.j.26.10		24
35.33	even	12		525.2.t.j.101.9		24
35.34	odd	2	inner	735.2.g.b.734.18		24
105.32	even	12		525.2.t.j.26.4		24
105.44	odd	6		735.2.p.f.374.9		24
105.47	odd	12		525.2.t.j.101.10		24
105.53	even	12		525.2.t.j.26.9		24
105.59	even	6		735.2.p.f.509.10		24
105.68	odd	12		525.2.t.j.101.3		24
105.74	odd	6		105.2.p.a.89.9	yes	24
105.89	even	6		105.2.p.a.59.10	yes	24
105.104	even	2	inner	735.2.g.b.734.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.p.a.59.3	✓	24	21.5	even	6
105.2.p.a.59.4	yes	24	35.19	odd	6
105.2.p.a.59.9	yes	24	7.5	odd	6
105.2.p.a.59.10	yes	24	105.89	even	6
105.2.p.a.89.3	yes	24	35.4	even	6
105.2.p.a.89.4	yes	24	21.11	odd	6
105.2.p.a.89.9	yes	24	105.74	odd	6
105.2.p.a.89.10	yes	24	7.4	even	3
525.2.t.j.26.3		24	35.18	odd	12
525.2.t.j.26.4		24	105.32	even	12
525.2.t.j.26.9		24	105.53	even	12
525.2.t.j.26.10		24	35.32	odd	12
525.2.t.j.101.3		24	105.68	odd	12
525.2.t.j.101.4		24	35.12	even	12
525.2.t.j.101.9		24	35.33	even	12
525.2.t.j.101.10		24	105.47	odd	12
735.2.g.b.734.5		24	105.104	even	2	inner
735.2.g.b.734.6		24	1.1	even	1	trivial
735.2.g.b.734.7		24	7.6	odd	2	inner
735.2.g.b.734.8		24	15.14	odd	2	inner
735.2.g.b.734.17		24	3.2	odd	2	inner
735.2.g.b.734.18		24	35.34	odd	2	inner
735.2.g.b.734.19		24	5.4	even	2	inner
735.2.g.b.734.20		24	21.20	even	2	inner
735.2.p.f.374.3		24	35.9	even	6
735.2.p.f.374.4		24	21.2	odd	6
735.2.p.f.374.9		24	105.44	odd	6
735.2.p.f.374.10		24	7.2	even	3
735.2.p.f.509.3		24	21.17	even	6
735.2.p.f.509.4		24	35.24	odd	6
735.2.p.f.509.9		24	7.3	odd	6
735.2.p.f.509.10		24	105.59	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.51469 q^{2} +(-1.66512 + 0.476833i) q^{3} +0.294280 q^{4} +(0.775809 + 2.09717i) q^{5} +(2.52214 - 0.722254i) q^{6} +2.58363 q^{8} +(2.54526 - 1.58797i) q^{9} +(-1.17511 - 3.17656i) q^{10} -2.14830i q^{11} +(-0.490013 + 0.140323i) q^{12} -3.48097 q^{13} +(-2.29182 - 3.12211i) q^{15} -4.50196 q^{16} -3.57718i q^{17} +(-3.85528 + 2.40528i) q^{18} +1.22234i q^{19} +(0.228305 + 0.617156i) q^{20} +3.25401i q^{22} +1.51469 q^{23} +(-4.30206 + 1.23196i) q^{24} +(-3.79624 + 3.25401i) q^{25} +5.27259 q^{26} +(-3.48097 + 3.85783i) q^{27} -5.95645i q^{29} +(3.47139 + 4.72902i) q^{30} +3.17656i q^{31} +1.65180 q^{32} +(1.02438 + 3.57718i) q^{33} +5.41832i q^{34} +(0.749020 - 0.467309i) q^{36} -7.80350i q^{37} -1.85147i q^{38} +(5.79624 - 1.65984i) q^{39} +(2.00441 + 5.41832i) q^{40} +11.8685 q^{41} -2.99294i q^{43} -0.632203i q^{44} +(5.30488 + 4.10588i) q^{45} -2.29428 q^{46} -6.10167i q^{47} +(7.49631 - 2.14668i) q^{48} +(5.75012 - 4.92881i) q^{50} +(1.70572 + 5.95645i) q^{51} -1.02438 q^{52} +11.2260 q^{53} +(5.27259 - 5.84341i) q^{54} +(4.50535 - 1.66667i) q^{55} +(-0.582853 - 2.03535i) q^{57} +9.02216i q^{58} -2.16935 q^{59} +(-0.674437 - 0.918776i) q^{60} +3.39872i q^{61} -4.81149i q^{62} +6.50196 q^{64} +(-2.70057 - 7.30019i) q^{65} +(-1.55162 - 5.41832i) q^{66} -10.3176i q^{67} -1.05269i q^{68} +(-2.52214 + 0.722254i) q^{69} +10.3968i q^{71} +(6.57602 - 4.10273i) q^{72} +6.85557 q^{73} +11.8199i q^{74} +(4.76958 - 7.22849i) q^{75} +0.359711i q^{76} +(-8.77950 + 2.51414i) q^{78} -1.88284 q^{79} +(-3.49266 - 9.44137i) q^{80} +(3.95670 - 8.08360i) q^{81} -17.9771 q^{82} +9.10486i q^{83} +(7.50196 - 2.77521i) q^{85} +4.53337i q^{86} +(2.84023 + 9.91821i) q^{87} -5.55042i q^{88} +1.77992 q^{89} +(-8.03524 - 6.21913i) q^{90} +0.445743 q^{92} +(-1.51469 - 5.28936i) q^{93} +9.24213i q^{94} +(-2.56346 + 0.948304i) q^{95} +(-2.75045 + 0.787632i) q^{96} +1.32584 q^{97} +(-3.41144 - 5.46799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} + 12 q^{9} - 24 q^{15} + 24 q^{16} + 24 q^{25} - 36 q^{30} + 84 q^{36} + 24 q^{39} - 72 q^{46} + 24 q^{51} - 24 q^{60} + 24 q^{64} - 96 q^{79} + 12 q^{81} + 48 q^{85} - 48 q^{99}+O(q^{100}) \) 24 * q + 24 * q^4 + 12 * q^9 - 24 * q^15 + 24 * q^16 + 24 * q^25 - 36 * q^30 + 84 * q^36 + 24 * q^39 - 72 * q^46 + 24 * q^51 - 24 * q^60 + 24 * q^64 - 96 * q^79 + 12 * q^81 + 48 * q^85 - 48 * q^99

Introduction

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