LMFDB - Embedded newform 735.2.g.b.734.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(734,735)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.51469 q^{2} +(-1.66512 - 0.476833i) q^{3} +0.294280 q^{4} +(0.775809 - 2.09717i) q^{5} +(2.52214 + 0.722254i) q^{6} +2.58363 q^{8} +(2.54526 + 1.58797i) q^{9} +(-1.17511 + 3.17656i) q^{10} +2.14830i q^{11} +(-0.490013 - 0.140323i) q^{12} -3.48097 q^{13} +(-2.29182 + 3.12211i) q^{15} -4.50196 q^{16} +3.57718i q^{17} +(-3.85528 - 2.40528i) q^{18} -1.22234i q^{19} +(0.228305 - 0.617156i) q^{20} -3.25401i q^{22} +1.51469 q^{23} +(-4.30206 - 1.23196i) q^{24} +(-3.79624 - 3.25401i) q^{25} +5.27259 q^{26} +(-3.48097 - 3.85783i) q^{27} +5.95645i q^{29} +(3.47139 - 4.72902i) q^{30} -3.17656i q^{31} +1.65180 q^{32} +(1.02438 - 3.57718i) q^{33} -5.41832i q^{34} +(0.749020 + 0.467309i) q^{36} +7.80350i q^{37} +1.85147i q^{38} +(5.79624 + 1.65984i) q^{39} +(2.00441 - 5.41832i) q^{40} +11.8685 q^{41} +2.99294i q^{43} +0.632203i q^{44} +(5.30488 - 4.10588i) q^{45} -2.29428 q^{46} +6.10167i q^{47} +(7.49631 + 2.14668i) q^{48} +(5.75012 + 4.92881i) q^{50} +(1.70572 - 5.95645i) q^{51} -1.02438 q^{52} +11.2260 q^{53} +(5.27259 + 5.84341i) q^{54} +(4.50535 + 1.66667i) q^{55} +(-0.582853 + 2.03535i) q^{57} -9.02216i q^{58} -2.16935 q^{59} +(-0.674437 + 0.918776i) q^{60} -3.39872i q^{61} +4.81149i q^{62} +6.50196 q^{64} +(-2.70057 + 7.30019i) q^{65} +(-1.55162 + 5.41832i) q^{66} +10.3176i q^{67} +1.05269i q^{68} +(-2.52214 - 0.722254i) q^{69} -10.3968i q^{71} +(6.57602 + 4.10273i) q^{72} +6.85557 q^{73} -11.8199i q^{74} +(4.76958 + 7.22849i) q^{75} -0.359711i q^{76} +(-8.77950 - 2.51414i) q^{78} -1.88284 q^{79} +(-3.49266 + 9.44137i) q^{80} +(3.95670 + 8.08360i) q^{81} -17.9771 q^{82} -9.10486i q^{83} +(7.50196 + 2.77521i) q^{85} -4.53337i q^{86} +(2.84023 - 9.91821i) q^{87} +5.55042i q^{88} +1.77992 q^{89} +(-8.03524 + 6.21913i) q^{90} +0.445743 q^{92} +(-1.51469 + 5.28936i) q^{93} -9.24213i q^{94} +(-2.56346 - 0.948304i) q^{95} +(-2.75045 - 0.787632i) q^{96} +1.32584 q^{97} +(-3.41144 + 5.46799i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.104984\pi$
$11$			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	$-0.660353\pi$
$13$	−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	$0.142827\pi$
$17$			3.57718i			0.867594i	−0.901011	+	0.433797i	$0.857173\pi$
$18$	−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	$-0.449522\pi$
$23$	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	$0.186533\pi$
$29$			5.95645i			1.10608i	−0.833153	+	0.553042i	$0.813467\pi$
$30$	3.47139	−	4.72902i	0.633786	−	0.863398i
$31$		−	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	$0.221664\pi$
$37$			7.80350i			1.28289i	−0.767170	+	0.641444i	$0.778336\pi$
$38$			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	$0.0732871\pi$
$43$			2.99294i			0.456419i	−0.973612	+	0.228209i	$0.926713\pi$
$44$			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	$0.146800\pi$
$47$			6.10167i			0.890020i	−0.895526	+	0.445010i	$0.853200\pi$
$48$	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	$-0.930183\pi$
$61$		−	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	$0.217048\pi$
$67$			10.3176i			1.26050i	−0.776392	+	0.630250i	$0.782952\pi$
$68$			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	$-0.368596\pi$
$73$	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	$-0.833446\pi$
$83$		−	9.10486i		−	0.999388i	0.866202	−	0.499694i	$-0.166554\pi$
$84$		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	$-0.860293\pi$
$127$		−	9.57778i		−	0.849891i	0.905219	−	0.424945i	$-0.139707\pi$
$128$	−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	$0.0557858\pi$
$139$			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	$0.966773\pi$
$150$	−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	$-0.949037\pi$
$163$		−	4.07070i		−	0.318842i	0.987211	−	0.159421i	$-0.0509627\pi$
$164$	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	$0.181803\pi$
$167$			13.9722i			1.08120i	−0.841279	+	0.540602i	$0.818197\pi$
$168$		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	$0.124160\pi$
$173$			10.0027i			0.760488i	−0.924886	+	0.380244i	$0.875840\pi$
$174$	−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	$0.792862\pi$
$180$	1.56112	−	1.20828i	0.116359	−	0.0900599i
$181$			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	$-0.730385\pi$
$193$		−	20.8195i		−	1.49862i	0.662218	−	0.749311i	$-0.269615\pi$
$194$	−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	$0.344708\pi$
$199$			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	$-0.546099\pi$
$223$	−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	$0.120210\pi$
$227$			11.1112i			0.737478i	−0.929533	+	0.368739i	$0.879790\pi$
$228$	−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	$-0.263835\pi$
$233$	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	$0.0296254\pi$
$239$			2.87353i			0.185873i	−0.995672	+	0.0929365i	$0.970375\pi$
$240$	10.3177	−	14.0556i	0.666003	−	0.907286i
$241$		−	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
$255$	−11.1684	−	8.19825i	−0.699390	−	0.513394i
$256$	6.91732			0.432332
$257$			13.1303i			0.819045i	0.912300	+	0.409522i	$0.134305\pi$
$257$			13.1303i			0.819045i	−0.912300	+	0.409522i	$0.865695\pi$
$258$	−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	$0.254241\pi$
$271$			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	$0.125969\pi$
$277$			12.8318i			0.770987i	−0.922710	+	0.385494i	$0.874031\pi$
$278$		−	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	$-0.562406\pi$
$283$	−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	$-0.965349\pi$
$293$		−	3.71937i		−	0.217288i	0.994081	−	0.108644i	$-0.0346509\pi$
$294$		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	$-0.777347\pi$
$337$		−	23.6381i		−	1.28765i	0.765174	−	0.643824i	$-0.222653\pi$
$338$	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	$0.000163910\pi$
$349$			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	$-0.763503\pi$
$353$		−	25.4200i		−	1.35297i	0.736457	−	0.676484i	$-0.236497\pi$
$354$	−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	$-0.220262\pi$
$360$	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	$0.132007\pi$
$373$			15.5637i			0.805856i	−0.915232	+	0.402928i	$0.867993\pi$
$374$	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	$0.0870967\pi$
$383$			10.5767i			0.540442i	−0.962798	+	0.270221i	$0.912903\pi$
$384$	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	$0.858756\pi$
$390$	−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	$0.246190\pi$
$401$			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
$405$	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	$-0.979361\pi$
$409$		−	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	$-0.539411\pi$
$433$	−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	$-0.869529\pi$
$439$		−	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	$-0.501907\pi$
$443$	−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	$0.238564\pi$
$449$			28.8710i			1.36250i	−0.732049	+	0.681252i	$0.761436\pi$
$450$	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	$-0.809625\pi$
$457$		−	24.0735i		−	1.12611i	0.826419	−	0.563056i	$-0.190375\pi$
$458$		−	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	$0.243901\pi$
$463$			29.8417i			1.38686i	−0.720524	+	0.693430i	$0.756099\pi$
$464$		−	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	$0.0308452\pi$
$467$			4.18164i			0.193503i	−0.995309	+	0.0967515i	$0.969155\pi$
$468$	−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	$-0.680298\pi$
$487$		−	37.2432i		−	1.68765i	0.536618	−	0.843826i	$-0.319702\pi$
$488$		−	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
$495$	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	$0.253251\pi$
$503$			32.0398i			1.42858i	−0.699849	+	0.714291i	$0.746749\pi$
$504$		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	$-0.919148\pi$
$547$		−	11.7540i		−	0.502566i	0.967914	−	0.251283i	$-0.0808525\pi$
$548$	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	$0.134986\pi$
$563$			19.5266i			0.822949i	−0.911421	+	0.411475i	$0.865014\pi$
$564$	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	$0.912857\pi$
$570$	−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	$-0.848573\pi$
$587$		−	22.1920i		−	0.915961i	0.888962	−	0.457981i	$-0.151427\pi$
$588$		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	$-0.958619\pi$
$593$		−	6.31375i		−	0.259275i	0.991561	−	0.129637i	$-0.0413813\pi$
$594$	−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	$-0.138731\pi$
$600$	12.3229	+	18.6758i	0.503078	+	0.762435i
$601$			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	$-0.166622\pi$
$607$	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	$-0.965717\pi$
$613$		−	5.32284i		−	0.214988i	0.994206	−	0.107494i	$-0.0342826\pi$
$614$	−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	$-0.917636\pi$
$619$		−	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	$-0.781440\pi$
$643$	−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	$0.0390867\pi$
$647$			6.23116i			0.244972i	−0.992470	+	0.122486i	$0.960913\pi$
$648$	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	$-0.699150\pi$
$659$		−	41.6170i		−	1.62117i	0.585622	−	0.810584i	$-0.300850\pi$
$660$	−1.97381	−	1.44889i	−0.0768304	−	0.0563981i
$661$		−	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	$0.205805\pi$
$673$			31.2573i			1.20488i	−0.798163	+	0.602441i	$0.794195\pi$
$674$			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	$-0.946297\pi$
$677$		−	8.73789i		−	0.335824i	0.985802	−	0.167912i	$-0.0537025\pi$
$678$	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	$0.141012\pi$
$691$			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
$705$	−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	$0.333989\pi$
$757$			47.7116i			1.73411i	−0.498214	+	0.867054i	$0.666011\pi$
$758$	−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	$0.0614100\pi$
$769$			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	$-0.917076\pi$
$773$		−	14.3228i		−	0.515154i	0.966258	−	0.257577i	$-0.0829240\pi$
$774$	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	$0.231106\pi$
$797$			37.4862i			1.32783i	−0.747809	+	0.663914i	$0.768894\pi$
$798$		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	$-0.148451\pi$
$810$	−30.3276	+	3.06958i	−1.06560	+	0.107854i
$811$		−	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	$0.183166\pi$
$823$			31.2239i			1.08840i	−0.838957	+	0.544198i	$0.816834\pi$
$824$	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	$0.0123949\pi$
$829$			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	$-0.461388\pi$
$853$	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	$0.0928261\pi$
$857$			16.8332i			0.575012i	−0.957779	+	0.287506i	$0.907174\pi$
$858$	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	$-0.276292\pi$
$863$	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	$-0.938077\pi$
$877$		−	11.4496i		−	0.386626i	0.981137	−	0.193313i	$-0.0619233\pi$
$878$			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	$-0.908577\pi$
$883$		−	16.8355i		−	0.566560i	0.959037	−	0.283280i	$-0.0914226\pi$
$884$		−	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	$0.344337\pi$
$887$			52.5834i			1.76558i	−0.469770	+	0.882789i	$0.655663\pi$
$888$	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	$-0.680834\pi$
$907$		−	50.7715i		−	1.68584i	0.538038	−	0.842920i	$-0.319166\pi$
$908$			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
$915$	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	$0.0236998\pi$
$967$			4.62632i			0.148772i	−0.997230	+	0.0743862i	$0.976300\pi$
$968$	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	$0.278196\pi$
$983$			48.0882i			1.53378i	−0.641781	+	0.766888i	$0.721804\pi$
$984$	−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.734.5		24
3.2	odd	2	inner	735.2.g.b.734.18		24
5.4	even	2	inner	735.2.g.b.734.20		24
7.2	even	3		105.2.p.a.59.10	yes	24
7.3	odd	6		105.2.p.a.89.9	yes	24
7.4	even	3		735.2.p.f.509.10		24
7.5	odd	6		735.2.p.f.374.9		24
7.6	odd	2	inner	735.2.g.b.734.8		24
15.14	odd	2	inner	735.2.g.b.734.7		24
21.2	odd	6		105.2.p.a.59.4	yes	24
21.5	even	6		735.2.p.f.374.3		24
21.11	odd	6		735.2.p.f.509.4		24
21.17	even	6		105.2.p.a.89.3	yes	24
21.20	even	2	inner	735.2.g.b.734.19		24
35.2	odd	12		525.2.t.j.101.3		24
35.3	even	12		525.2.t.j.26.4		24
35.4	even	6		735.2.p.f.509.3		24
35.9	even	6		105.2.p.a.59.3	✓	24
35.17	even	12		525.2.t.j.26.9		24
35.19	odd	6		735.2.p.f.374.4		24
35.23	odd	12		525.2.t.j.101.10		24
35.24	odd	6		105.2.p.a.89.4	yes	24
35.34	odd	2	inner	735.2.g.b.734.17		24
105.2	even	12		525.2.t.j.101.9		24
105.17	odd	12		525.2.t.j.26.3		24
105.23	even	12		525.2.t.j.101.4		24
105.38	odd	12		525.2.t.j.26.10		24
105.44	odd	6		105.2.p.a.59.9	yes	24
105.59	even	6		105.2.p.a.89.10	yes	24
105.74	odd	6		735.2.p.f.509.9		24
105.89	even	6		735.2.p.f.374.10		24
105.104	even	2	inner	735.2.g.b.734.6		24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
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

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