LMFDB - Embedded newform 735.2.g.b.734.20

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			734.20
Character	$\chi$	$=$	735.734
Dual form			735.2.g.b.734.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.51469 q^{2} +(1.66512 + 0.476833i) q^{3} +0.294280 q^{4} +(0.775809 + 2.09717i) q^{5} +(2.52214 + 0.722254i) q^{6} -2.58363 q^{8} +(2.54526 + 1.58797i) q^{9} +(1.17511 + 3.17656i) q^{10} +2.14830i q^{11} +(0.490013 + 0.140323i) q^{12} +3.48097 q^{13} +(0.291817 + 3.86197i) q^{15} -4.50196 q^{16} -3.57718i q^{17} +(3.85528 + 2.40528i) q^{18} -1.22234i q^{19} +(0.228305 + 0.617156i) q^{20} +3.25401i q^{22} -1.51469 q^{23} +(-4.30206 - 1.23196i) q^{24} +(-3.79624 + 3.25401i) q^{25} +5.27259 q^{26} +(3.48097 + 3.85783i) q^{27} +5.95645i q^{29} +(0.442011 + 5.84969i) q^{30} -3.17656i q^{31} -1.65180 q^{32} +(-1.02438 + 3.57718i) q^{33} -5.41832i q^{34} +(0.749020 + 0.467309i) q^{36} -7.80350i q^{37} -1.85147i q^{38} +(5.79624 + 1.65984i) q^{39} +(-2.00441 - 5.41832i) q^{40} +11.8685 q^{41} -2.99294i q^{43} +0.632203i q^{44} +(-1.35561 + 6.56980i) q^{45} -2.29428 q^{46} -6.10167i q^{47} +(-7.49631 - 2.14668i) q^{48} +(-5.75012 + 4.92881i) q^{50} +(1.70572 - 5.95645i) q^{51} +1.02438 q^{52} -11.2260 q^{53} +(5.27259 + 5.84341i) q^{54} +(-4.50535 + 1.66667i) q^{55} +(0.582853 - 2.03535i) q^{57} +9.02216i q^{58} -2.16935 q^{59} +(0.0858759 + 1.13650i) q^{60} -3.39872i q^{61} -4.81149i q^{62} +6.50196 q^{64} +(2.70057 + 7.30019i) q^{65} +(-1.55162 + 5.41832i) q^{66} -10.3176i q^{67} -1.05269i q^{68} +(-2.52214 - 0.722254i) q^{69} -10.3968i q^{71} +(-6.57602 - 4.10273i) q^{72} -6.85557 q^{73} -11.8199i q^{74} +(-7.87282 + 3.60814i) q^{75} -0.359711i q^{76} +(8.77950 + 2.51414i) q^{78} -1.88284 q^{79} +(-3.49266 - 9.44137i) q^{80} +(3.95670 + 8.08360i) q^{81} +17.9771 q^{82} +9.10486i q^{83} +(7.50196 - 2.77521i) q^{85} -4.53337i q^{86} +(-2.84023 + 9.91821i) q^{87} -5.55042i q^{88} +1.77992 q^{89} +(-2.05332 + 9.95121i) q^{90} -0.445743 q^{92} +(1.51469 - 5.28936i) q^{93} -9.24213i q^{94} +(2.56346 - 0.948304i) q^{95} +(-2.75045 - 0.787632i) q^{96} -1.32584 q^{97} +(-3.41144 + 5.46799i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.320114\pi$
$2$	1.51469			1.07105			0.535523	+	0.844521i	$0.320114\pi$
$3$	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	$0.104984\pi$
$11$			2.14830i			0.647737i	−0.946102	+	0.323869i	$0.895016\pi$
$12$	0.490013	+	0.140323i	0.141454	+	0.0405077i
$13$	3.48097			0.965448			0.482724	−	0.875773i	$-0.339647\pi$
$13$	3.48097			0.965448			0.482724	+	0.875773i	$0.339647\pi$
$14$		0			0
$15$	0.291817	+	3.86197i	0.0753468	+	0.997157i
$16$	−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	$-0.955222\pi$
$19$		−	1.22234i		−	0.280425i	0.990121	−	0.140212i	$-0.0447785\pi$
$20$	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	$-0.550478\pi$
$23$	−1.51469			−0.315834			−0.157917	+	0.987452i	$0.550478\pi$
$24$	−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	$0.186533\pi$
$29$			5.95645i			1.10608i	−0.833153	+	0.553042i	$0.813467\pi$
$30$	0.442011	+	5.84969i	0.0806999	+	1.06800i
$31$		−	3.17656i		−	0.570527i	−0.958449	−	0.285263i	$-0.907919\pi$
$31$		−	3.17656i		−	0.570527i	0.958449	−	0.285263i	$-0.0920811\pi$
$32$	−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
$45$	−1.35561	+	6.56980i	−0.202082	+	0.979369i
$46$	−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	$-0.780246\pi$
$53$	−11.2260			−1.54201			−0.771006	+	0.636828i	$0.780246\pi$
$54$	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	$0.545100\pi$
$60$	0.0858759	+	1.13650i	0.0110865	+	0.146722i
$61$		−	3.39872i		−	0.435162i	−0.976042	−	0.217581i	$-0.930183\pi$
$61$		−	3.39872i		−	0.435162i	0.976042	−	0.217581i	$-0.0698166\pi$
$62$		−	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	$-0.788374\pi$
$71$		−	10.3968i		−	1.23387i	0.787013	−	0.616936i	$-0.211626\pi$
$72$	−6.57602	−	4.10273i	−0.774991	−	0.483512i
$73$	−6.85557			−0.802384			−0.401192	−	0.915994i	$-0.631404\pi$
$73$	−6.85557			−0.802384			−0.401192	+	0.915994i	$0.631404\pi$
$74$		−	11.8199i		−	1.37403i
$75$	−7.87282	+	3.60814i	−0.909075	+	0.416633i
$76$		−	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	$0.469927\pi$
$90$	−2.05332	+	9.95121i	−0.216439	+	1.04895i
$91$		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	$-0.521441\pi$
$97$	−1.32584			−0.134618			−0.0673092	+	0.997732i	$0.521441\pi$
$98$		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	$-0.592026\pi$
$103$	−5.78683			−0.570194			−0.285097	+	0.958499i	$0.592026\pi$
$104$	−8.99355			−0.881890
$105$		0			0
$106$	−17.0039			−1.65157
$107$	−3.88645			−0.375717			−0.187859	−	0.982196i	$-0.560155\pi$
$107$	−3.88645			−0.375717			−0.187859	+	0.982196i	$0.560155\pi$
$108$	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	$-0.645152\pi$
$113$	−9.36235			−0.880736			−0.440368	+	0.897817i	$0.645152\pi$
$114$	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
$120$	−0.753947	−	9.97793i	−0.0688257	−	0.910856i
$121$	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
$135$	−5.38995	+	10.2931i	−0.463893	+	0.885891i
$136$			9.24213i			0.792506i
$137$	−10.7055			−0.914634			−0.457317	−	0.889304i	$-0.651190\pi$
$137$	−10.7055			−0.914634			−0.457317	+	0.889304i	$0.651190\pi$
$138$	−3.82026	−	1.09399i	−0.325202	−	0.0931265i
$139$			4.11136i			0.348721i	0.984682	+	0.174360i	$0.0557858\pi$
$139$			4.11136i			0.348721i	−0.984682	+	0.174360i	$0.944214\pi$
$140$		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	$0.0332268\pi$
$149$			2.54374i			0.208391i	−0.994557	+	0.104196i	$0.966773\pi$
$150$	−11.9249	+	5.46521i	−0.973661	+	0.446233i
$151$	−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	$-0.312480\pi$
$157$	13.9239			1.11125			0.555623	+	0.831434i	$0.312480\pi$
$158$	−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
$165$	−8.29668	+	0.626910i	−0.645896	+	0.0488049i
$166$			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	$0.207138\pi$
$179$			16.2095i			1.21155i	−0.795634	+	0.605777i	$0.792862\pi$
$180$	−0.398929	+	1.93336i	−0.0297344	+	0.144104i
$181$			19.4123i			1.44290i	0.692465	+	0.721451i	$0.256525\pi$
$181$			19.4123i			1.44290i	−0.692465	+	0.721451i	$0.743475\pi$
$182$		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	$-0.847991\pi$
$191$		−	12.7038i		−	0.919212i	0.888123	−	0.459606i	$-0.152009\pi$
$192$	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
$195$	1.01581	+	13.4434i	0.0727433	+	0.962703i
$196$		0			0
$197$	2.23465			0.159212			0.0796062	−	0.996826i	$-0.474634\pi$
$197$	2.23465			0.159212			0.0796062	+	0.996826i	$0.474634\pi$
$198$	−5.16727	+	8.28229i	−0.367222	+	0.588597i
$199$			24.9220i			1.76667i	0.468739	+	0.883337i	$0.344708\pi$
$199$			24.9220i			1.76667i	−0.468739	+	0.883337i	$0.655292\pi$
$200$	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	$-0.453901\pi$
$223$	4.31027			0.288637			0.144318	+	0.989531i	$0.453901\pi$
$224$		0			0
$225$	−14.8297	+	2.25398i	−0.988646	+	0.150265i
$226$	−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	$0.106897\pi$
$229$			9.97400i			0.659101i	−0.944138	+	0.329550i	$0.893103\pi$
$230$	−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	$-0.736165\pi$
$233$	−20.6287			−1.35143			−0.675716	+	0.737162i	$0.736165\pi$
$234$	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	$0.0296254\pi$
$239$			2.87353i			0.185873i	−0.995672	+	0.0929365i	$0.970375\pi$
$240$	−1.31375	−	17.3865i	−0.0848020	−	1.12229i
$241$		−	26.0722i		−	1.67946i	−0.543007	−	0.839728i	$-0.682714\pi$
$241$		−	26.0722i		−	1.67946i	0.543007	−	0.839728i	$-0.317286\pi$
$242$	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
$255$	13.8150	−	1.04388i	0.865128	−	0.0653704i
$256$	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	$-0.684099\pi$
$263$	−17.7305			−1.09331			−0.546655	+	0.837358i	$0.684099\pi$
$264$	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	$0.457116\pi$
$270$	−8.16410	+	15.5909i	−0.496851	+	0.948830i
$271$			23.5890i			1.43293i	0.697623	+	0.716465i	$0.254241\pi$
$271$			23.5890i			1.43293i	−0.697623	+	0.716465i	$0.745759\pi$
$272$			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	$0.218394\pi$
$281$			21.2397i			1.26706i	−0.773719	+	0.633528i	$0.781606\pi$
$282$	4.40695	−	15.3893i	0.262430	−	0.916418i
$283$	6.55412			0.389602			0.194801	−	0.980843i	$-0.437594\pi$
$283$	6.55412			0.389602			0.194801	+	0.980843i	$0.437594\pi$
$284$		−	3.05957i		−	0.181552i
$285$	4.72065	−	0.356700i	0.279627	−	0.0211291i
$286$			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
$300$	−2.31682	+	1.06181i	−0.133761	+	0.0613034i
$301$		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	$-0.603649\pi$
$307$	−11.2102			−0.639800			−0.319900	+	0.947451i	$0.603649\pi$
$308$		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	$-0.346795\pi$
$313$	16.3805			0.925879			0.462940	+	0.886390i	$0.346795\pi$
$314$	21.0903			1.19020
$315$		0			0
$316$	−0.554083			−0.0311696
$317$	10.1167			0.568212			0.284106	−	0.958793i	$-0.408303\pi$
$317$	10.1167			0.568212			0.284106	+	0.958793i	$0.408303\pi$
$318$	−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
$330$	−12.5669	+	0.949574i	−0.691785	+	0.0522723i
$331$	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
$345$	−0.442011	−	5.84969i	−0.0237971	−	0.314937i
$346$		−	15.1509i		−	0.814518i
$347$	15.9072			0.853943			0.426971	−	0.904265i	$-0.359580\pi$
$347$	15.9072			0.853943			0.426971	+	0.904265i	$0.359580\pi$
$348$	−0.835824	+	2.91873i	−0.0448049	+	0.156461i
$349$			0.0192397i			0.00102988i	1.00000		0.000514938i	$0.000163910\pi$
$349$			0.0192397i			0.00102988i	−1.00000		0.000514938i	$0.999836\pi$
$350$		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	$-0.779738\pi$
$359$		−	24.1789i		−	1.27611i	0.769989	−	0.638057i	$-0.220262\pi$
$360$	3.50239	−	16.9740i	0.184592	−	0.894607i
$361$	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	$-0.576097\pi$
$367$	−9.07272			−0.473592			−0.236796	+	0.971559i	$0.576097\pi$
$368$	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
$375$	−13.6747	−	13.7114i	−0.706158	−	0.708054i
$376$			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	$0.141244\pi$
$389$			16.9347i			0.858624i	−0.903156	+	0.429312i	$0.858756\pi$
$390$	1.53863	+	20.3626i	0.0779115	+	1.03110i
$391$			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	$-0.496742\pi$
$397$	0.407827			0.0204682			0.0102341	+	0.999948i	$0.496742\pi$
$398$			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	$0.246190\pi$
$401$			27.9786i			1.39719i	−0.715519	+	0.698593i	$0.753810\pi$
$402$	7.45195	−	26.0225i	0.371670	−	1.29789i
$403$		−	11.0575i		−	0.550814i
$404$	3.94927			0.196484
$405$	−13.8830	+	14.5692i	−0.689853	+	0.723949i
$406$		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	$-0.979361\pi$
$409$		−	2.62071i		−	0.129586i	0.997899	−	0.0647929i	$-0.0206387\pi$
$410$	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	$-0.904609\pi$
$431$		−	12.2576i		−	0.590428i	0.955431	−	0.295214i	$-0.0953910\pi$
$432$	−15.6712	−	17.3678i	−0.753981	−	0.835608i
$433$	5.13957			0.246992			0.123496	−	0.992345i	$-0.460589\pi$
$433$	5.13957			0.246992			0.123496	+	0.992345i	$0.460589\pi$
$434$		0			0
$435$	−23.0036	+	1.73819i	−1.10294	+	0.0833398i
$436$	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	$-0.869529\pi$
$439$		−	16.6993i		−	0.797013i	0.917165	−	0.398507i	$-0.130471\pi$
$440$	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	$-0.498093\pi$
$443$	0.252220			0.0119833			0.00599167	+	0.999982i	$0.498093\pi$
$444$	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	$0.238564\pi$
$449$			28.8710i			1.36250i	−0.732049	+	0.681252i	$0.761436\pi$
$450$	−22.4624	+	3.41407i	−1.05889	+	0.160941i
$451$			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
$465$	12.2678	−	0.926973i	0.568905	−	0.0429873i
$466$	−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	$0.720319\pi$
$480$	−0.482022	−	6.37920i	−0.0220012	−	0.291169i
$481$		−	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	$0.0425448\pi$
$491$			5.90572i			0.266522i	−0.991081	+	0.133261i	$0.957455\pi$
$492$	5.81571	+	1.66542i	0.262192	+	0.0750828i
$493$	21.3073			0.959632
$494$		−	6.44490i		−	0.289970i
$495$	−14.1139	−	2.91225i	−0.634374	−	0.130896i
$496$			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	$0.360489\pi$
$510$	20.9254	−	1.58116i	0.926592	−	0.0700147i
$511$		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	$-0.514786\pi$
$523$	−2.12383			−0.0928687			−0.0464343	+	0.998921i	$0.514786\pi$
$524$	−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
$540$	−1.58616	+	3.02906i	−0.0682573	+	0.130350i
$541$	−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
$555$	30.1369	−	2.27719i	1.27924	−	0.0966614i
$556$			1.20989i			0.0513108i
$557$	9.40270			0.398405			0.199203	−	0.979958i	$-0.436165\pi$
$557$	9.40270			0.398405			0.199203	+	0.979958i	$0.436165\pi$
$558$	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	$0.0871430\pi$
$569$			12.8982i			0.540722i	−0.962759	+	0.270361i	$0.912857\pi$
$570$	7.15032	−	0.540289i	0.299494	−	0.0226302i
$571$	−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	$-0.450172\pi$
$577$	7.48978			0.311804			0.155902	+	0.987773i	$0.450172\pi$
$578$	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
$585$	−4.71883	+	22.8693i	−0.195100	+	0.945529i
$586$			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	$-0.861269\pi$
$599$		−	20.6648i		−	0.844339i	0.906517	−	0.422170i	$-0.138731\pi$
$600$	20.3405	−	9.32212i	0.830397	−	0.380574i
$601$			12.5956i			0.513785i	0.966440	+	0.256892i	$0.0826986\pi$
$601$			12.5956i			0.513785i	−0.966440	+	0.256892i	$0.917301\pi$
$602$		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	$-0.833378\pi$
$607$	−42.6766			−1.73219			−0.866095	+	0.499879i	$0.833378\pi$
$608$			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
$615$	3.46342	+	45.8358i	0.139659	+	1.84828i
$616$		0			0
$617$	30.1002			1.21179			0.605895	−	0.795545i	$-0.292815\pi$
$617$	30.1002			1.21179			0.605895	+	0.795545i	$0.292815\pi$
$618$	−14.5952	−	4.17956i	−0.587105	−	0.168127i
$619$		−	12.7323i		−	0.511753i	−0.966710	−	0.255876i	$-0.917636\pi$
$619$		−	12.7323i		−	0.511753i	0.966710	−	0.255876i	$-0.0823640\pi$
$620$	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	$-0.991732\pi$
$641$		−	1.31513i		−	0.0519444i	0.999663	−	0.0259722i	$-0.00826814\pi$
$642$	−9.80217	−	2.80700i	−0.386861	−	0.110784i
$643$	39.2223			1.54678			0.773389	−	0.633932i	$-0.218560\pi$
$643$	39.2223			1.54678			0.773389	+	0.633932i	$0.218560\pi$
$644$		0			0
$645$	11.5587	−	0.873390i	0.455121	−	0.0343897i
$646$	−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	$-0.620320\pi$
$653$	−18.8618			−0.738120			−0.369060	+	0.929406i	$0.620320\pi$
$654$	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	$-0.699150\pi$
$659$		−	41.6170i		−	1.62117i	0.585622	−	0.810584i	$-0.300850\pi$
$660$	−2.44155	+	0.184487i	−0.0950373	+	0.00718116i
$661$		−	3.77854i		−	0.146968i	−0.997296	−	0.0734842i	$-0.976588\pi$
$661$		−	3.77854i		−	0.146968i	0.997296	−	0.0734842i	$-0.0234118\pi$
$662$	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
$675$	−25.7680	−	3.31814i	−0.991811	−	0.127715i
$676$	−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	$-0.362591\pi$
$683$	21.8692			0.836801			0.418401	+	0.908263i	$0.362591\pi$
$684$	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
$690$	−0.669509	−	8.86045i	−0.0254878	−	0.337312i
$691$			22.5359i			0.857306i	0.903469	+	0.428653i	$0.141012\pi$
$691$			22.5359i			0.857306i	−0.903469	+	0.428653i	$0.858988\pi$
$692$		−	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	$-0.766104\pi$
$701$		−	35.5019i		−	1.34089i	0.741960	−	0.670444i	$-0.233896\pi$
$702$	18.3537	+	20.3407i	0.692716	+	0.767711i
$703$	−9.53855			−0.359753
$704$			13.9682i			0.526445i
$705$	23.5645	−	1.78057i	0.887490	−	0.0670601i
$706$			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	$0.692857\pi$
$720$	6.10289	−	29.5770i	0.227441	−	1.10227i
$721$		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	$-0.642992\pi$
$727$	−23.4181			−0.868528			−0.434264	+	0.900786i	$0.642992\pi$
$728$		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	$-0.399023\pi$
$733$	16.8907			0.623871			0.311935	+	0.950103i	$0.399023\pi$
$734$	−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	$-0.763688\pi$
$743$	−40.1701			−1.47370			−0.736850	+	0.676056i	$0.763688\pi$
$744$	−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
$750$	−20.7129	−	20.7685i	−0.756328	−	0.758359i
$751$	−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
$765$	23.5014	+	4.84925i	0.849695	+	0.175325i
$766$		−	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	$0.0614100\pi$
$769$			10.6337i			0.383461i	−0.981448	+	0.191731i	$0.938590\pi$
$770$		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
$780$	0.298932	+	3.95613i	0.0107035	+	0.141652i
$781$	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	$-0.728716\pi$
$787$	−36.9341			−1.31656			−0.658280	+	0.752773i	$0.728716\pi$
$788$	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
$795$	−3.27594	−	43.3546i	−0.116186	−	1.53763i
$796$			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	$-0.851549\pi$
$809$		−	25.5786i		−	0.899297i	0.893206	−	0.449649i	$-0.148451\pi$
$810$	−21.0285	+	22.0678i	−0.738865	+	0.775383i
$811$		−	7.28791i		−	0.255913i	−0.991780	−	0.127957i	$-0.959158\pi$
$811$		−	7.28791i		−	0.255913i	0.991780	−	0.127957i	$-0.0408418\pi$
$812$		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	$4.67717e-5\pi$
$821$			0.00842044i			0.000293875i	−1.00000		0.000146938i	$0.999953\pi$
$822$	−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
$825$	−7.75138	−	16.9132i	−0.269868	−	0.588842i
$826$		0			0
$827$	−38.3189			−1.33248			−0.666239	−	0.745738i	$-0.732097\pi$
$827$	−38.3189			−1.33248			−0.666239	+	0.745738i	$0.732097\pi$
$828$	−1.13453	−	0.707827i	−0.0394277	−	0.0245987i
$829$			2.24176i			0.0778595i	0.999242	+	0.0389298i	$0.0123949\pi$
$829$			2.24176i			0.0778595i	−0.999242	+	0.0389298i	$0.987605\pi$
$830$	−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	$-0.538612\pi$
$853$	−7.06831			−0.242014			−0.121007	+	0.992652i	$0.538612\pi$
$854$		0			0
$855$	8.03055	+	1.65702i	0.274639	+	0.0566687i
$856$	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	$-0.795078\pi$
$859$		−	35.1835i		−	1.20045i	0.799832	−	0.600223i	$-0.204922\pi$
$860$	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	$-0.723708\pi$
$863$	−37.9758			−1.29271			−0.646356	+	0.763036i	$0.723708\pi$
$864$	−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
$870$	−34.8433	+	2.63282i	−1.18130	+	0.0892608i
$871$		−	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
$885$	−0.633052	−	8.37797i	−0.0212798	−	0.281622i
$886$	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
$900$	−4.36409	+	0.663301i	−0.145470	+	0.0221100i
$901$			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	$-0.913974\pi$
$911$		−	16.1165i		−	0.533963i	0.963702	−	0.266981i	$-0.0860262\pi$
$912$	−2.62398	+	9.16306i	−0.0868887	+	0.303419i
$913$	−19.5600			−0.647341
$914$			36.4639i			1.20612i
$915$	13.1258	−	0.991804i	0.433925	−	0.0327880i
$916$			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	$0.295537\pi$
$930$	18.5819	−	1.40407i	0.609323	−	0.0460414i
$931$		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	$-0.539669\pi$
$937$	−7.60980			−0.248601			−0.124301	+	0.992245i	$0.539669\pi$
$938$		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	$-0.204653\pi$
$947$	49.2583			1.60068			0.800339	+	0.599547i	$0.204653\pi$
$948$	−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	$-0.446890\pi$
$953$	10.2538			0.332154			0.166077	+	0.986113i	$0.446890\pi$
$954$	−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
$960$	1.89738	+	25.1104i	0.0612377	+	0.810435i
$961$	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
$975$	−27.4051	+	12.5598i	−0.877664	+	0.402237i
$976$			15.3009i			0.489770i
$977$	−24.1098			−0.771340			−0.385670	−	0.922637i	$-0.626030\pi$
$977$	−24.1098			−0.771340			−0.385670	+	0.922637i	$0.626030\pi$
$978$	−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
$990$	−21.3782	−	4.41115i	−0.679443	−	0.140196i
$991$	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	$-0.360779\pi$
$997$	26.7483			0.847128			0.423564	+	0.905866i	$0.360779\pi$
$998$	−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.734.20		24
3.2	odd	2	inner	735.2.g.b.734.7		24
5.4	even	2	inner	735.2.g.b.734.5		24
7.2	even	3		105.2.p.a.59.3	✓	24
7.3	odd	6		105.2.p.a.89.4	yes	24
7.4	even	3		735.2.p.f.509.3		24
7.5	odd	6		735.2.p.f.374.4		24
7.6	odd	2	inner	735.2.g.b.734.17		24
15.14	odd	2	inner	735.2.g.b.734.18		24
21.2	odd	6		105.2.p.a.59.9	yes	24
21.5	even	6		735.2.p.f.374.10		24
21.11	odd	6		735.2.p.f.509.9		24
21.17	even	6		105.2.p.a.89.10	yes	24
21.20	even	2	inner	735.2.g.b.734.6		24
35.2	odd	12		525.2.t.j.101.10		24
35.3	even	12		525.2.t.j.26.9		24
35.4	even	6		735.2.p.f.509.10		24
35.9	even	6		105.2.p.a.59.10	yes	24
35.17	even	12		525.2.t.j.26.4		24
35.19	odd	6		735.2.p.f.374.9		24
35.23	odd	12		525.2.t.j.101.3		24
35.24	odd	6		105.2.p.a.89.9	yes	24
35.34	odd	2	inner	735.2.g.b.734.8		24
105.2	even	12		525.2.t.j.101.4		24
105.17	odd	12		525.2.t.j.26.10		24
105.23	even	12		525.2.t.j.101.9		24
105.38	odd	12		525.2.t.j.26.3		24
105.44	odd	6		105.2.p.a.59.4	yes	24
105.59	even	6		105.2.p.a.89.3	yes	24
105.74	odd	6		735.2.p.f.509.4		24
105.89	even	6		735.2.p.f.374.3		24
105.104	even	2	inner	735.2.g.b.734.19		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.p.a.59.3	✓	24	7.2	even	3
105.2.p.a.59.4	yes	24	105.44	odd	6
105.2.p.a.59.9	yes	24	21.2	odd	6
105.2.p.a.59.10	yes	24	35.9	even	6
105.2.p.a.89.3	yes	24	105.59	even	6
105.2.p.a.89.4	yes	24	7.3	odd	6
105.2.p.a.89.9	yes	24	35.24	odd	6
105.2.p.a.89.10	yes	24	21.17	even	6
525.2.t.j.26.3		24	105.38	odd	12
525.2.t.j.26.4		24	35.17	even	12
525.2.t.j.26.9		24	35.3	even	12
525.2.t.j.26.10		24	105.17	odd	12
525.2.t.j.101.3		24	35.23	odd	12
525.2.t.j.101.4		24	105.2	even	12
525.2.t.j.101.9		24	105.23	even	12
525.2.t.j.101.10		24	35.2	odd	12
735.2.g.b.734.5		24	5.4	even	2	inner
735.2.g.b.734.6		24	21.20	even	2	inner
735.2.g.b.734.7		24	3.2	odd	2	inner
735.2.g.b.734.8		24	35.34	odd	2	inner
735.2.g.b.734.17		24	7.6	odd	2	inner
735.2.g.b.734.18		24	15.14	odd	2	inner
735.2.g.b.734.19		24	105.104	even	2	inner
735.2.g.b.734.20		24	1.1	even	1	trivial
735.2.p.f.374.3		24	105.89	even	6
735.2.p.f.374.4		24	7.5	odd	6
735.2.p.f.374.9		24	35.19	odd	6
735.2.p.f.374.10		24	21.5	even	6
735.2.p.f.509.3		24	7.4	even	3
735.2.p.f.509.4		24	105.74	odd	6
735.2.p.f.509.9		24	21.11	odd	6
735.2.p.f.509.10		24	35.4	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)

\(f(q)\)	\(=\)	\(q+1.51469 q^{2} +(1.66512 + 0.476833i) q^{3} +0.294280 q^{4} +(0.775809 + 2.09717i) q^{5} +(2.52214 + 0.722254i) q^{6} -2.58363 q^{8} +(2.54526 + 1.58797i) q^{9} +(1.17511 + 3.17656i) q^{10} +2.14830i q^{11} +(0.490013 + 0.140323i) q^{12} +3.48097 q^{13} +(0.291817 + 3.86197i) q^{15} -4.50196 q^{16} -3.57718i q^{17} +(3.85528 + 2.40528i) q^{18} -1.22234i q^{19} +(0.228305 + 0.617156i) q^{20} +3.25401i q^{22} -1.51469 q^{23} +(-4.30206 - 1.23196i) q^{24} +(-3.79624 + 3.25401i) q^{25} +5.27259 q^{26} +(3.48097 + 3.85783i) q^{27} +5.95645i q^{29} +(0.442011 + 5.84969i) q^{30} -3.17656i q^{31} -1.65180 q^{32} +(-1.02438 + 3.57718i) q^{33} -5.41832i q^{34} +(0.749020 + 0.467309i) q^{36} -7.80350i q^{37} -1.85147i q^{38} +(5.79624 + 1.65984i) q^{39} +(-2.00441 - 5.41832i) q^{40} +11.8685 q^{41} -2.99294i q^{43} +0.632203i q^{44} +(-1.35561 + 6.56980i) q^{45} -2.29428 q^{46} -6.10167i q^{47} +(-7.49631 - 2.14668i) q^{48} +(-5.75012 + 4.92881i) q^{50} +(1.70572 - 5.95645i) q^{51} +1.02438 q^{52} -11.2260 q^{53} +(5.27259 + 5.84341i) q^{54} +(-4.50535 + 1.66667i) q^{55} +(0.582853 - 2.03535i) q^{57} +9.02216i q^{58} -2.16935 q^{59} +(0.0858759 + 1.13650i) q^{60} -3.39872i q^{61} -4.81149i q^{62} +6.50196 q^{64} +(2.70057 + 7.30019i) q^{65} +(-1.55162 + 5.41832i) q^{66} -10.3176i q^{67} -1.05269i q^{68} +(-2.52214 - 0.722254i) q^{69} -10.3968i q^{71} +(-6.57602 - 4.10273i) q^{72} -6.85557 q^{73} -11.8199i q^{74} +(-7.87282 + 3.60814i) q^{75} -0.359711i q^{76} +(8.77950 + 2.51414i) q^{78} -1.88284 q^{79} +(-3.49266 - 9.44137i) q^{80} +(3.95670 + 8.08360i) q^{81} +17.9771 q^{82} +9.10486i q^{83} +(7.50196 - 2.77521i) q^{85} -4.53337i q^{86} +(-2.84023 + 9.91821i) q^{87} -5.55042i q^{88} +1.77992 q^{89} +(-2.05332 + 9.95121i) q^{90} -0.445743 q^{92} +(1.51469 - 5.28936i) q^{93} -9.24213i q^{94} +(2.56346 - 0.948304i) q^{95} +(-2.75045 - 0.787632i) q^{96} -1.32584 q^{97} +(-3.41144 + 5.46799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} + 12 q^{9} - 24 q^{15} + 24 q^{16} + 24 q^{25} - 36 q^{30} + 84 q^{36} + 24 q^{39} - 72 q^{46} + 24 q^{51} - 24 q^{60} + 24 q^{64} - 96 q^{79} + 12 q^{81} + 48 q^{85} - 48 q^{99}+O(q^{100}) \) 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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