LMFDB - Embedded newform 1120.2.bi.a.463.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1120,2,Mod(463,1120)] 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("1120.463"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1120, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 3, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1120 = 2^{5} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1120.bi (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$8.94324502638$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			463.11
Character	$\chi$	$=$	1120.463
Dual form			1120.2.bi.a.687.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.683238 - 0.683238i) q^{3} +(-2.03938 - 0.917023i) q^{5} +(0.707107 + 0.707107i) q^{7} -2.06637i q^{9} -5.41441 q^{11} +(3.15744 - 3.15744i) q^{13} +(0.766836 + 2.01993i) q^{15} +(-2.46948 + 2.46948i) q^{17} +3.87964i q^{19} -0.966244i q^{21} +(-0.659207 + 0.659207i) q^{23} +(3.31814 + 3.74032i) q^{25} +(-3.46154 + 3.46154i) q^{27} +5.76955 q^{29} +3.09841i q^{31} +(3.69933 + 3.69933i) q^{33} +(-0.793626 - 2.09049i) q^{35} +(-0.680801 - 0.680801i) q^{37} -4.31457 q^{39} -7.39465 q^{41} +(0.0846505 + 0.0846505i) q^{43} +(-1.89491 + 4.21412i) q^{45} +(-2.32683 - 2.32683i) q^{47} +1.00000i q^{49} +3.37448 q^{51} +(-8.08545 + 8.08545i) q^{53} +(11.0420 + 4.96514i) q^{55} +(2.65072 - 2.65072i) q^{57} +7.94305i q^{59} +4.20293i q^{61} +(1.46115 - 1.46115i) q^{63} +(-9.33468 + 3.54378i) q^{65} +(-7.82159 + 7.82159i) q^{67} +0.900790 q^{69} -2.85514i q^{71} +(1.45516 + 1.45516i) q^{73} +(0.288449 - 4.82260i) q^{75} +(-3.82857 - 3.82857i) q^{77} +12.8568 q^{79} -1.46901 q^{81} +(3.88328 + 3.88328i) q^{83} +(7.30077 - 2.77163i) q^{85} +(-3.94197 - 3.94197i) q^{87} +1.96589i q^{89} +4.46530 q^{91} +(2.11695 - 2.11695i) q^{93} +(3.55772 - 7.91206i) q^{95} +(-13.2788 + 13.2788i) q^{97} +11.1882i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 8 q^{17} - 8 q^{25} + 64 q^{43} + 32 q^{51} - 8 q^{65} - 40 q^{73} - 112 q^{75} - 72 q^{81} - 80 q^{83} - 8 q^{97}+O(q^{100}) $ 72 * q + 8 * q^17 - 8 * q^25 + 64 * q^43 + 32 * q^51 - 8 * q^65 - 40 * q^73 - 112 * q^75 - 72 * q^81 - 80 * q^83 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times$.

$n$	$351$	$421$	$801$	$897$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−0.683238	−	0.683238i	−0.394468	−	0.394468i	0.481809	−	0.876276i	$-0.339980\pi$
$3$	−0.683238	−	0.683238i	−0.394468	−	0.394468i	−0.876276	+	0.481809i	$0.839980\pi$
$4$		0			0
$5$	−2.03938	−	0.917023i	−0.912038	−	0.410105i
$5$	−2.03938	−	0.917023i	−0.912038	−	0.410105i
$6$		0			0
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$		0			0
$9$		−	2.06637i		−	0.688791i
$10$		0			0
$11$	−5.41441			−1.63251			−0.816253	−	0.577694i	$-0.803953\pi$
$11$	−5.41441			−1.63251			−0.816253	+	0.577694i	$0.803953\pi$
$12$		0			0
$13$	3.15744	−	3.15744i	0.875717	−	0.875717i	−0.117371	−	0.993088i	$-0.537447\pi$
$13$	3.15744	−	3.15744i	0.875717	−	0.875717i	0.993088	+	0.117371i	$0.0374466\pi$
$14$		0			0
$15$	0.766836	+	2.01993i	0.197996	+	0.521543i
$16$		0			0
$17$	−2.46948	+	2.46948i	−0.598936	+	0.598936i	−0.940029	−	0.341093i	$-0.889203\pi$
$17$	−2.46948	+	2.46948i	−0.598936	+	0.598936i	0.341093	+	0.940029i	$0.389203\pi$
$18$		0			0
$19$			3.87964i			0.890051i	0.895518	+	0.445025i	$0.146805\pi$
$19$			3.87964i			0.890051i	−0.895518	+	0.445025i	$0.853195\pi$
$20$		0			0
$21$		−	0.966244i		−	0.210852i
$22$		0			0
$23$	−0.659207	+	0.659207i	−0.137454	+	0.137454i	−0.772486	−	0.635032i	$-0.780987\pi$
$23$	−0.659207	+	0.659207i	−0.137454	+	0.137454i	0.635032	+	0.772486i	$0.280987\pi$
$24$		0			0
$25$	3.31814	+	3.74032i	0.663627	+	0.748063i
$26$		0			0
$27$	−3.46154	+	3.46154i	−0.666173	+	0.666173i
$28$		0			0
$29$	5.76955			1.07138			0.535689	−	0.844415i	$-0.320052\pi$
$29$	5.76955			1.07138			0.535689	+	0.844415i	$0.320052\pi$
$30$		0			0
$31$			3.09841i			0.556492i	0.960510	+	0.278246i	$0.0897530\pi$
$31$			3.09841i			0.556492i	−0.960510	+	0.278246i	$0.910247\pi$
$32$		0			0
$33$	3.69933	+	3.69933i	0.643971	+	0.643971i
$34$		0			0
$35$	−0.793626	−	2.09049i	−0.134147	−	0.353358i
$36$		0			0
$37$	−0.680801	−	0.680801i	−0.111923	−	0.111923i	0.648927	−	0.760850i	$-0.275218\pi$
$37$	−0.680801	−	0.680801i	−0.111923	−	0.111923i	−0.760850	+	0.648927i	$0.775218\pi$
$38$		0			0
$39$	−4.31457			−0.690884
$40$		0			0
$41$	−7.39465			−1.15485			−0.577425	−	0.816444i	$-0.695942\pi$
$41$	−7.39465			−1.15485			−0.577425	+	0.816444i	$0.695942\pi$
$42$		0			0
$43$	0.0846505	+	0.0846505i	0.0129091	+	0.0129091i	0.713532	−	0.700623i	$-0.247094\pi$
$43$	0.0846505	+	0.0846505i	0.0129091	+	0.0129091i	−0.700623	+	0.713532i	$0.747094\pi$
$44$		0			0
$45$	−1.89491	+	4.21412i	−0.282477	+	0.628203i
$46$		0			0
$47$	−2.32683	−	2.32683i	−0.339403	−	0.339403i	0.516740	−	0.856143i	$-0.327146\pi$
$47$	−2.32683	−	2.32683i	−0.339403	−	0.339403i	−0.856143	+	0.516740i	$0.827146\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	3.37448			0.472522
$52$		0			0
$53$	−8.08545	+	8.08545i	−1.11062	+	1.11062i	−0.117556	+	0.993066i	$0.537506\pi$
$53$	−8.08545	+	8.08545i	−1.11062	+	1.11062i	−0.993066	+	0.117556i	$0.962494\pi$
$54$		0			0
$55$	11.0420	+	4.96514i	1.48891	+	0.669500i
$56$		0			0
$57$	2.65072	−	2.65072i	0.351096	−	0.351096i
$58$		0			0
$59$			7.94305i			1.03410i	0.855956	+	0.517049i	$0.172969\pi$
$59$			7.94305i			1.03410i	−0.855956	+	0.517049i	$0.827031\pi$
$60$		0			0
$61$			4.20293i			0.538130i	0.963122	+	0.269065i	$0.0867147\pi$
$61$			4.20293i			0.538130i	−0.963122	+	0.269065i	$0.913285\pi$
$62$		0			0
$63$	1.46115	−	1.46115i	0.184087	−	0.184087i
$64$		0			0
$65$	−9.33468	+	3.54378i	−1.15782	+	0.439551i
$66$		0			0
$67$	−7.82159	+	7.82159i	−0.955559	+	0.955559i	−0.999054	−	0.0434947i	$-0.986151\pi$
$67$	−7.82159	+	7.82159i	−0.955559	+	0.955559i	0.0434947	+	0.999054i	$0.486151\pi$
$68$		0			0
$69$	0.900790			0.108442
$70$		0			0
$71$		−	2.85514i		−	0.338842i	−0.985544	−	0.169421i	$-0.945810\pi$
$71$		−	2.85514i		−	0.338842i	0.985544	−	0.169421i	$-0.0541898\pi$
$72$		0			0
$73$	1.45516	+	1.45516i	0.170314	+	0.170314i	0.787117	−	0.616803i	$-0.211573\pi$
$73$	1.45516	+	1.45516i	0.170314	+	0.170314i	−0.616803	+	0.787117i	$0.711573\pi$
$74$		0			0
$75$	0.288449	−	4.82260i	0.0333073	−	0.556866i
$76$		0			0
$77$	−3.82857	−	3.82857i	−0.436306	−	0.436306i
$78$		0			0
$79$	12.8568			1.44650			0.723249	−	0.690587i	$-0.242648\pi$
$79$	12.8568			1.44650			0.723249	+	0.690587i	$0.242648\pi$
$80$		0			0
$81$	−1.46901			−0.163223
$82$		0			0
$83$	3.88328	+	3.88328i	0.426245	+	0.426245i	0.887347	−	0.461102i	$-0.152546\pi$
$83$	3.88328	+	3.88328i	0.426245	+	0.426245i	−0.461102	+	0.887347i	$0.652546\pi$
$84$		0			0
$85$	7.30077	−	2.77163i	0.791879	−	0.300626i
$86$		0			0
$87$	−3.94197	−	3.94197i	−0.422624	−	0.422624i
$88$		0			0
$89$			1.96589i			0.208384i	0.994557	+	0.104192i	$0.0332256\pi$
$89$			1.96589i			0.208384i	−0.994557	+	0.104192i	$0.966774\pi$
$90$		0			0
$91$	4.46530			0.468091
$92$		0			0
$93$	2.11695	−	2.11695i	0.219518	−	0.219518i
$94$		0			0
$95$	3.55772	−	7.91206i	0.365015	−	0.811760i
$96$		0			0
$97$	−13.2788	+	13.2788i	−1.34826	+	1.34826i	−0.460707	+	0.887552i	$0.652404\pi$
$97$	−13.2788	+	13.2788i	−1.34826	+	1.34826i	−0.887552	+	0.460707i	$0.847596\pi$
$98$		0			0
$99$			11.1882i			1.12446i
$100$		0			0
$101$			12.7251i			1.26619i	0.774073	+	0.633097i	$0.218216\pi$
$101$			12.7251i			1.26619i	−0.774073	+	0.633097i	$0.781784\pi$
$102$		0			0
$103$	−8.27848	+	8.27848i	−0.815703	+	0.815703i	−0.985482	−	0.169779i	$-0.945695\pi$
$103$	−8.27848	+	8.27848i	−0.815703	+	0.815703i	0.169779	+	0.985482i	$0.445695\pi$
$104$		0			0
$105$	−0.886068	+	1.97054i	−0.0864714	+	0.192305i
$106$		0			0
$107$	4.27215	−	4.27215i	0.413004	−	0.413004i	−0.469780	−	0.882784i	$-0.655667\pi$
$107$	4.27215	−	4.27215i	0.413004	−	0.413004i	0.882784	+	0.469780i	$0.155667\pi$
$108$		0			0
$109$	18.5611			1.77783			0.888915	−	0.458073i	$-0.151460\pi$
$109$	18.5611			1.77783			0.888915	+	0.458073i	$0.151460\pi$
$110$		0			0
$111$			0.930298i			0.0883000i
$112$		0			0
$113$	−7.33321	−	7.33321i	−0.689851	−	0.689851i	0.272348	−	0.962199i	$-0.412200\pi$
$113$	−7.33321	−	7.33321i	−0.689851	−	0.689851i	−0.962199	+	0.272348i	$0.912200\pi$
$114$		0			0
$115$	1.94888	−	0.739865i	0.181734	−	0.0689927i
$116$		0			0
$117$	−6.52445	−	6.52445i	−0.603186	−	0.603186i
$118$		0			0
$119$	−3.49237			−0.320145
$120$		0			0
$121$	18.3159			1.66508
$122$		0			0
$123$	5.05230	+	5.05230i	0.455551	+	0.455551i
$124$		0			0
$125$	−3.33698	−	10.6707i	−0.298469	−	0.954419i
$126$		0			0
$127$	−15.8188	−	15.8188i	−1.40369	−	1.40369i	−0.787938	−	0.615754i	$-0.788851\pi$
$127$	−15.8188	−	15.8188i	−1.40369	−	1.40369i	−0.615754	−	0.787938i	$-0.711149\pi$
$128$		0			0
$129$		−	0.115673i		−	0.0101844i
$130$		0			0
$131$	−8.12773			−0.710123			−0.355062	−	0.934843i	$-0.615540\pi$
$131$	−8.12773			−0.710123			−0.355062	+	0.934843i	$0.615540\pi$
$132$		0			0
$133$	−2.74332	+	2.74332i	−0.237876	+	0.237876i
$134$		0			0
$135$	10.2337	−	3.88508i	0.880776	−	0.334374i
$136$		0			0
$137$	4.20821	−	4.20821i	0.359531	−	0.359531i	−0.504109	−	0.863640i	$-0.668179\pi$
$137$	4.20821	−	4.20821i	0.359531	−	0.359531i	0.863640	+	0.504109i	$0.168179\pi$
$138$		0			0
$139$		−	21.7350i		−	1.84354i	−0.387741	−	0.921769i	$-0.626744\pi$
$139$		−	21.7350i		−	1.84354i	0.387741	−	0.921769i	$-0.373256\pi$
$140$		0			0
$141$			3.17956i			0.267767i
$142$		0			0
$143$	−17.0957	+	17.0957i	−1.42961	+	1.42961i
$144$		0			0
$145$	−11.7663	−	5.29081i	−0.977138	−	0.439378i
$146$		0			0
$147$	0.683238	−	0.683238i	0.0563525	−	0.0563525i
$148$		0			0
$149$	13.2830			1.08818			0.544092	−	0.839025i	$-0.316874\pi$
$149$	13.2830			1.08818			0.544092	+	0.839025i	$0.316874\pi$
$150$		0			0
$151$		−	10.5109i		−	0.855365i	−0.903929	−	0.427682i	$-0.859330\pi$
$151$		−	10.5109i		−	0.855365i	0.903929	−	0.427682i	$-0.140670\pi$
$152$		0			0
$153$	5.10286	+	5.10286i	0.412542	+	0.412542i
$154$		0			0
$155$	2.84132	−	6.31884i	0.228220	−	0.507542i
$156$		0			0
$157$	−14.7455	−	14.7455i	−1.17682	−	1.17682i	−0.980549	−	0.196273i	$-0.937116\pi$
$157$	−14.7455	−	14.7455i	−1.17682	−	1.17682i	−0.196273	−	0.980549i	$-0.562884\pi$
$158$		0			0
$159$	11.0486			0.876209
$160$		0			0
$161$	−0.932259			−0.0734723
$162$		0			0
$163$	−6.86932	−	6.86932i	−0.538047	−	0.538047i	0.384908	−	0.922955i	$-0.374233\pi$
$163$	−6.86932	−	6.86932i	−0.538047	−	0.538047i	−0.922955	+	0.384908i	$0.874233\pi$
$164$		0			0
$165$	−4.15197	−	10.9367i	−0.323230	−	0.851422i
$166$		0			0
$167$	3.08533	+	3.08533i	0.238750	+	0.238750i	0.816332	−	0.577583i	$-0.196004\pi$
$167$	3.08533	+	3.08533i	0.238750	+	0.238750i	−0.577583	+	0.816332i	$0.696004\pi$
$168$		0			0
$169$		−	6.93890i		−	0.533762i
$170$		0			0
$171$	8.01678			0.613059
$172$		0			0
$173$	−6.45046	+	6.45046i	−0.490419	+	0.490419i	−0.908438	−	0.418019i	$-0.862725\pi$
$173$	−6.45046	+	6.45046i	−0.490419	+	0.490419i	0.418019	+	0.908438i	$0.362725\pi$
$174$		0			0
$175$	−0.298526	+	4.99108i	−0.0225665	+	0.377290i
$176$		0			0
$177$	5.42700	−	5.42700i	0.407918	−	0.407918i
$178$		0			0
$179$		−	19.1642i		−	1.43240i	−0.697895	−	0.716201i	$-0.745880\pi$
$179$		−	19.1642i		−	1.43240i	0.697895	−	0.716201i	$-0.254120\pi$
$180$		0			0
$181$			13.4361i			0.998700i	0.866400	+	0.499350i	$0.166428\pi$
$181$			13.4361i			0.998700i	−0.866400	+	0.499350i	$0.833572\pi$
$182$		0			0
$183$	2.87160	−	2.87160i	0.212275	−	0.212275i
$184$		0			0
$185$	0.764101	+	2.01272i	0.0561778	+	0.147978i
$186$		0			0
$187$	13.3708	−	13.3708i	0.977767	−	0.977767i
$188$		0			0
$189$	−4.89535			−0.356084
$190$		0			0
$191$		−	0.448780i		−	0.0324726i	−0.999868	−	0.0162363i	$-0.994832\pi$
$191$		−	0.448780i		−	0.0324726i	0.999868	−	0.0162363i	$-0.00516839\pi$
$192$		0			0
$193$	−2.00162	−	2.00162i	−0.144080	−	0.144080i	0.631388	−	0.775467i	$-0.282486\pi$
$193$	−2.00162	−	2.00162i	−0.144080	−	0.144080i	−0.775467	+	0.631388i	$0.782486\pi$
$194$		0			0
$195$	8.79904	+	3.95656i	0.630113	+	0.283335i
$196$		0			0
$197$	9.07212	+	9.07212i	0.646362	+	0.646362i	0.952112	−	0.305750i	$-0.0989072\pi$
$197$	9.07212	+	9.07212i	0.646362	+	0.646362i	−0.305750	+	0.952112i	$0.598907\pi$
$198$		0			0
$199$	−18.1441			−1.28620			−0.643101	−	0.765781i	$-0.722353\pi$
$199$	−18.1441			−1.28620			−0.643101	+	0.765781i	$0.722353\pi$
$200$		0			0
$201$	10.6880			0.753874
$202$		0			0
$203$	4.07969	+	4.07969i	0.286338	+	0.286338i
$204$		0			0
$205$	15.0805	+	6.78107i	1.05327	+	0.473610i
$206$		0			0
$207$	1.36217	+	1.36217i	0.0946771	+	0.0946771i
$208$		0			0
$209$		−	21.0060i		−	1.45301i
$210$		0			0
$211$	−13.0722			−0.899929			−0.449964	−	0.893046i	$-0.648563\pi$
$211$	−13.0722			−0.899929			−0.449964	+	0.893046i	$0.648563\pi$
$212$		0			0
$213$	−1.95074	+	1.95074i	−0.133662	+	0.133662i
$214$		0			0
$215$	−0.0950080	−	0.250261i	−0.00647949	−	0.0170677i
$216$		0			0
$217$	−2.19091	+	2.19091i	−0.148729	+	0.148729i
$218$		0			0
$219$		−	1.98844i		−	0.134367i
$220$		0			0
$221$			15.5945i			1.04900i
$222$		0			0
$223$	6.46091	−	6.46091i	0.432655	−	0.432655i	−0.456876	−	0.889531i	$-0.651032\pi$
$223$	6.46091	−	6.46091i	0.432655	−	0.432655i	0.889531	+	0.456876i	$0.151032\pi$
$224$		0			0
$225$	7.72889	−	6.85651i	0.515259	−	0.457100i
$226$		0			0
$227$	−6.74613	+	6.74613i	−0.447756	+	0.447756i	−0.894608	−	0.446852i	$-0.852545\pi$
$227$	−6.74613	+	6.74613i	−0.447756	+	0.447756i	0.446852	+	0.894608i	$0.352545\pi$
$228$		0			0
$229$	−20.4172			−1.34921			−0.674603	−	0.738181i	$-0.735685\pi$
$229$	−20.4172			−1.34921			−0.674603	+	0.738181i	$0.735685\pi$
$230$		0			0
$231$			5.23164i			0.344217i
$232$		0			0
$233$	−9.85773	−	9.85773i	−0.645802	−	0.645802i	0.306174	−	0.951976i	$-0.400951\pi$
$233$	−9.85773	−	9.85773i	−0.645802	−	0.645802i	−0.951976	+	0.306174i	$0.900951\pi$
$234$		0			0
$235$	2.61153	+	6.87905i	0.170358	+	0.448740i
$236$		0			0
$237$	−8.78422	−	8.78422i	−0.570597	−	0.570597i
$238$		0			0
$239$	4.45737			0.288324			0.144162	−	0.989554i	$-0.453951\pi$
$239$	4.45737			0.288324			0.144162	+	0.989554i	$0.453951\pi$
$240$		0			0
$241$	5.85350			0.377057			0.188529	−	0.982068i	$-0.439628\pi$
$241$	5.85350			0.377057			0.188529	+	0.982068i	$0.439628\pi$
$242$		0			0
$243$	11.3883	+	11.3883i	0.730559	+	0.730559i
$244$		0			0
$245$	0.917023	−	2.03938i	0.0585865	−	0.130291i
$246$		0			0
$247$	12.2498	+	12.2498i	0.779433	+	0.779433i
$248$		0			0
$249$		−	5.30641i		−	0.336280i
$250$		0			0
$251$	−4.36889			−0.275762			−0.137881	−	0.990449i	$-0.544029\pi$
$251$	−4.36889			−0.275762			−0.137881	+	0.990449i	$0.544029\pi$
$252$		0			0
$253$	3.56922	−	3.56922i	0.224395	−	0.224395i
$254$		0			0
$255$	−6.88184	−	3.09448i	−0.430958	−	0.193784i
$256$		0			0
$257$	−6.53348	+	6.53348i	−0.407547	+	0.407547i	−0.880882	−	0.473335i	$-0.843050\pi$
$257$	−6.53348	+	6.53348i	−0.407547	+	0.407547i	0.473335	+	0.880882i	$0.343050\pi$
$258$		0			0
$259$		−	0.962798i		−	0.0598254i
$260$		0			0
$261$		−	11.9220i		−	0.737956i
$262$		0			0
$263$	−11.5702	+	11.5702i	−0.713446	+	0.713446i	−0.967254	−	0.253808i	$-0.918317\pi$
$263$	−11.5702	+	11.5702i	−0.713446	+	0.713446i	0.253808	+	0.967254i	$0.418317\pi$
$264$		0			0
$265$	23.9038	−	9.07476i	1.46840	−	0.557458i
$266$		0			0
$267$	1.34317	−	1.34317i	0.0822006	−	0.0822006i
$268$		0			0
$269$	−15.9197			−0.970644			−0.485322	−	0.874336i	$-0.661298\pi$
$269$	−15.9197			−0.970644			−0.485322	+	0.874336i	$0.661298\pi$
$270$		0			0
$271$			20.8120i			1.26424i	0.774872	+	0.632119i	$0.217814\pi$
$271$			20.8120i			1.26424i	−0.774872	+	0.632119i	$0.782186\pi$
$272$		0			0
$273$	−3.05086	−	3.05086i	−0.184647	−	0.184647i
$274$		0			0
$275$	−17.9658	−	20.2516i	−1.08338	−	1.22122i
$276$		0			0
$277$	−14.4770	−	14.4770i	−0.869840	−	0.869840i	0.122615	−	0.992454i	$-0.460872\pi$
$277$	−14.4770	−	14.4770i	−0.869840	−	0.869840i	−0.992454	+	0.122615i	$0.960872\pi$
$278$		0			0
$279$	6.40248			0.383306
$280$		0			0
$281$	22.0154			1.31333			0.656664	−	0.754184i	$-0.271967\pi$
$281$	22.0154			1.31333			0.656664	+	0.754184i	$0.271967\pi$
$282$		0			0
$283$	−0.00141407	−	0.00141407i	−8.40579e−5	−	8.40579e-5i	0.707065	−	0.707149i	$-0.250019\pi$
$283$	−0.00141407	−	0.00141407i	−8.40579e−5	−	8.40579e-5i	−0.707149	+	0.707065i	$0.750019\pi$
$284$		0			0
$285$	−7.83659	+	2.97505i	−0.464199	+	0.176227i
$286$		0			0
$287$	−5.22881	−	5.22881i	−0.308647	−	0.308647i
$288$		0			0
$289$			4.80337i			0.282551i
$290$		0			0
$291$	18.1452			1.06369
$292$		0			0
$293$	13.2135	−	13.2135i	0.771940	−	0.771940i	−0.206505	−	0.978445i	$-0.566209\pi$
$293$	13.2135	−	13.2135i	0.771940	−	0.771940i	0.978445	+	0.206505i	$0.0662091\pi$
$294$		0			0
$295$	7.28397	−	16.1989i	0.424089	−	0.943137i
$296$		0			0
$297$	18.7422	−	18.7422i	1.08753	−	1.08753i
$298$		0			0
$299$			4.16282i			0.240742i
$300$		0			0
$301$			0.119714i			0.00690019i
$302$		0			0
$303$	8.69426	−	8.69426i	0.499472	−	0.499472i
$304$		0			0
$305$	3.85419	−	8.57137i	0.220690	−	0.490795i
$306$		0			0
$307$	15.4316	−	15.4316i	0.880731	−	0.880731i	−0.112878	−	0.993609i	$-0.536007\pi$
$307$	15.4316	−	15.4316i	0.880731	−	0.880731i	0.993609	+	0.112878i	$0.0360069\pi$
$308$		0			0
$309$	11.3123			0.643537
$310$		0			0
$311$		−	22.4892i		−	1.27524i	−0.770349	−	0.637622i	$-0.779918\pi$
$311$		−	22.4892i		−	1.27524i	0.770349	−	0.637622i	$-0.220082\pi$
$312$		0			0
$313$	10.8617	+	10.8617i	0.613942	+	0.613942i	0.943971	−	0.330029i	$-0.107058\pi$
$313$	10.8617	+	10.8617i	0.613942	+	0.613942i	−0.330029	+	0.943971i	$0.607058\pi$
$314$		0			0
$315$	−4.31974	+	1.63993i	−0.243390	+	0.0923994i
$316$		0			0
$317$	−5.29117	−	5.29117i	−0.297182	−	0.297182i	0.542727	−	0.839909i	$-0.317392\pi$
$317$	−5.29117	−	5.29117i	−0.297182	−	0.297182i	−0.839909	+	0.542727i	$0.817392\pi$
$318$		0			0
$319$	−31.2387			−1.74903
$320$		0			0
$321$	−5.83778			−0.325833
$322$		0			0
$323$	−9.58068	−	9.58068i	−0.533083	−	0.533083i
$324$		0			0
$325$	22.2867	+	1.33301i	1.23624	+	0.0739421i
$326$		0			0
$327$	−12.6816	−	12.6816i	−0.701296	−	0.701296i
$328$		0			0
$329$		−	3.29064i		−	0.181419i
$330$		0			0
$331$	6.80525			0.374050			0.187025	−	0.982355i	$-0.440115\pi$
$331$	6.80525			0.374050			0.187025	+	0.982355i	$0.440115\pi$
$332$		0			0
$333$	−1.40679	+	1.40679i	−0.0770915	+	0.0770915i
$334$		0			0
$335$	23.1238	−	8.77861i	1.26339	−	0.479627i
$336$		0			0
$337$	−18.9299	+	18.9299i	−1.03118	+	1.03118i	−0.0316788	+	0.999498i	$0.510085\pi$
$337$	−18.9299	+	18.9299i	−1.03118	+	1.03118i	−0.999498	+	0.0316788i	$0.989915\pi$
$338$		0			0
$339$			10.0207i			0.544247i
$340$		0			0
$341$		−	16.7761i		−	0.908476i
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$		0			0
$345$	−1.83705	−	0.826045i	−0.0989036	−	0.0444728i
$346$		0			0
$347$	−12.1708	+	12.1708i	−0.653362	+	0.653362i	−0.953801	−	0.300439i	$-0.902867\pi$
$347$	−12.1708	+	12.1708i	−0.653362	+	0.653362i	0.300439	+	0.953801i	$0.402867\pi$
$348$		0			0
$349$	15.7645			0.843856			0.421928	−	0.906629i	$-0.361353\pi$
$349$	15.7645			0.843856			0.421928	+	0.906629i	$0.361353\pi$
$350$		0			0
$351$			21.8592i			1.16676i
$352$		0			0
$353$	−12.5792	−	12.5792i	−0.669525	−	0.669525i	0.288081	−	0.957606i	$-0.406983\pi$
$353$	−12.5792	−	12.5792i	−0.669525	−	0.669525i	−0.957606	+	0.288081i	$0.906983\pi$
$354$		0			0
$355$	−2.61823	+	5.82271i	−0.138961	+	0.309037i
$356$		0			0
$357$	2.38612	+	2.38612i	0.126287	+	0.126287i
$358$		0			0
$359$	33.7490			1.78120			0.890602	−	0.454784i	$-0.150284\pi$
$359$	33.7490			1.78120			0.890602	+	0.454784i	$0.150284\pi$
$360$		0			0
$361$	3.94838			0.207810
$362$		0			0
$363$	−12.5141	−	12.5141i	−0.656819	−	0.656819i
$364$		0			0
$365$	−1.63321	−	4.30205i	−0.0854861	−	0.225179i
$366$		0			0
$367$	−2.19334	−	2.19334i	−0.114491	−	0.114491i	0.647540	−	0.762031i	$-0.275798\pi$
$367$	−2.19334	−	2.19334i	−0.114491	−	0.114491i	−0.762031	+	0.647540i	$0.775798\pi$
$368$		0			0
$369$			15.2801i			0.795450i
$370$		0			0
$371$	−11.4346			−0.593652
$372$		0			0
$373$	5.66659	−	5.66659i	0.293405	−	0.293405i	−0.545019	−	0.838424i	$-0.683478\pi$
$373$	5.66659	−	5.66659i	0.293405	−	0.293405i	0.838424	+	0.545019i	$0.183478\pi$
$374$		0			0
$375$	−5.01070	+	9.57060i	−0.258751	+	0.494224i
$376$		0			0
$377$	18.2170	−	18.2170i	0.938225	−	0.938225i
$378$		0			0
$379$			9.13563i			0.469266i	0.972084	+	0.234633i	$0.0753888\pi$
$379$			9.13563i			0.469266i	−0.972084	+	0.234633i	$0.924611\pi$
$380$		0			0
$381$			21.6160i			1.10742i
$382$		0			0
$383$	−7.64787	+	7.64787i	−0.390788	+	0.390788i	−0.874968	−	0.484180i	$-0.839118\pi$
$383$	−7.64787	+	7.64787i	−0.390788	+	0.390788i	0.484180	+	0.874968i	$0.339118\pi$
$384$		0			0
$385$	4.29702	+	11.3188i	0.218996	+	0.576859i
$386$		0			0
$387$	0.174919	−	0.174919i	0.00889165	−	0.00889165i
$388$		0			0
$389$	−27.8987			−1.41452			−0.707261	−	0.706952i	$-0.750070\pi$
$389$	−27.8987			−1.41452			−0.707261	+	0.706952i	$0.750070\pi$
$390$		0			0
$391$		−	3.25579i		−	0.164652i
$392$		0			0
$393$	5.55317	+	5.55317i	0.280121	+	0.280121i
$394$		0			0
$395$	−26.2198	−	11.7899i	−1.31926	−	0.593216i
$396$		0			0
$397$	−8.36699	−	8.36699i	−0.419927	−	0.419927i	0.465251	−	0.885179i	$-0.345964\pi$
$397$	−8.36699	−	8.36699i	−0.419927	−	0.419927i	−0.885179	+	0.465251i	$0.845964\pi$
$398$		0			0
$399$	3.74868			0.187669
$400$		0			0
$401$	−34.4862			−1.72216			−0.861080	−	0.508470i	$-0.830211\pi$
$401$	−34.4862			−1.72216			−0.861080	+	0.508470i	$0.830211\pi$
$402$		0			0
$403$	9.78307	+	9.78307i	0.487329	+	0.487329i
$404$		0			0
$405$	2.99587	+	1.34712i	0.148866	+	0.0669388i
$406$		0			0
$407$	3.68614	+	3.68614i	0.182715	+	0.182715i
$408$		0			0
$409$			24.8534i			1.22892i	0.788947	+	0.614461i	$0.210626\pi$
$409$			24.8534i			1.22892i	−0.788947	+	0.614461i	$0.789374\pi$
$410$		0			0
$411$	−5.75041			−0.283647
$412$		0			0
$413$	−5.61659	+	5.61659i	−0.276374	+	0.276374i
$414$		0			0
$415$	−4.35842	−	11.4805i	−0.213947	−	0.563557i
$416$		0			0
$417$	−14.8502	+	14.8502i	−0.727216	+	0.727216i
$418$		0			0
$419$			1.88796i			0.0922330i	0.998936	+	0.0461165i	$0.0146845\pi$
$419$			1.88796i			0.0922330i	−0.998936	+	0.0461165i	$0.985315\pi$
$420$		0			0
$421$		−	1.78407i		−	0.0869500i	−0.999055	−	0.0434750i	$-0.986157\pi$
$421$		−	1.78407i		−	0.0869500i	0.999055	−	0.0434750i	$-0.0138429\pi$
$422$		0			0
$423$	−4.80810	+	4.80810i	−0.233778	+	0.233778i
$424$		0			0
$425$	−17.4307	−	1.04256i	−0.845512	−	0.0505718i
$426$		0			0
$427$	−2.97192	+	2.97192i	−0.143821	+	0.143821i
$428$		0			0
$429$	23.3609			1.12787
$430$		0			0
$431$			32.0625i			1.54439i	0.635383	+	0.772197i	$0.280842\pi$
$431$			32.0625i			1.54439i	−0.635383	+	0.772197i	$0.719158\pi$
$432$		0			0
$433$	22.4346	+	22.4346i	1.07814	+	1.07814i	0.996677	+	0.0814590i	$0.0259580\pi$
$433$	22.4346	+	22.4346i	1.07814	+	1.07814i	0.0814590	+	0.996677i	$0.474042\pi$
$434$		0			0
$435$	4.42430	+	11.6541i	0.212129	+	0.558770i
$436$		0			0
$437$	−2.55749	−	2.55749i	−0.122341	−	0.122341i
$438$		0			0
$439$	−15.5671			−0.742977			−0.371489	−	0.928438i	$-0.621153\pi$
$439$	−15.5671			−0.742977			−0.371489	+	0.928438i	$0.621153\pi$
$440$		0			0
$441$	2.06637			0.0983987
$442$		0			0
$443$	22.7365	+	22.7365i	1.08025	+	1.08025i	0.996486	+	0.0837592i	$0.0266927\pi$
$443$	22.7365	+	22.7365i	1.08025	+	1.08025i	0.0837592	+	0.996486i	$0.473307\pi$
$444$		0			0
$445$	1.80277	−	4.00919i	0.0854593	−	0.190054i
$446$		0			0
$447$	−9.07544	−	9.07544i	−0.429254	−	0.429254i
$448$		0			0
$449$		−	7.97082i		−	0.376166i	−0.982153	−	0.188083i	$-0.939773\pi$
$449$		−	7.97082i		−	0.376166i	0.982153	−	0.188083i	$-0.0602274\pi$
$450$		0			0
$451$	40.0377			1.88530
$452$		0			0
$453$	−7.18144	+	7.18144i	−0.337414	+	0.337414i
$454$		0			0
$455$	−9.10644	−	4.09478i	−0.426917	−	0.191966i
$456$		0			0
$457$	3.30838	−	3.30838i	0.154759	−	0.154759i	−0.625480	−	0.780240i	$-0.715097\pi$
$457$	3.30838	−	3.30838i	0.154759	−	0.154759i	0.780240	+	0.625480i	$0.215097\pi$
$458$		0			0
$459$		−	17.0964i		−	0.797990i
$460$		0			0
$461$			12.0107i			0.559393i	0.960088	+	0.279697i	$0.0902339\pi$
$461$			12.0107i			0.559393i	−0.960088	+	0.279697i	$0.909766\pi$
$462$		0			0
$463$	−2.07725	+	2.07725i	−0.0965380	+	0.0965380i	−0.753726	−	0.657188i	$-0.771746\pi$
$463$	−2.07725	+	2.07725i	−0.0965380	+	0.0965380i	0.657188	+	0.753726i	$0.271746\pi$
$464$		0			0
$465$	−6.25857	+	2.37598i	−0.290234	+	0.110183i
$466$		0			0
$467$	5.60472	−	5.60472i	0.259356	−	0.259356i	−0.565436	−	0.824792i	$-0.691292\pi$
$467$	5.60472	−	5.60472i	0.259356	−	0.259356i	0.824792	+	0.565436i	$0.191292\pi$
$468$		0			0
$469$	−11.0614			−0.510768
$470$		0			0
$471$			20.1494i			0.928437i
$472$		0			0
$473$	−0.458333	−	0.458333i	−0.0210742	−	0.0210742i
$474$		0			0
$475$	−14.5111	+	12.8732i	−0.665814	+	0.590662i
$476$		0			0
$477$	16.7076	+	16.7076i	0.764986	+	0.764986i
$478$		0			0
$479$	30.2393			1.38167			0.690835	−	0.723013i	$-0.257243\pi$
$479$	30.2393			1.38167			0.690835	+	0.723013i	$0.257243\pi$
$480$		0			0
$481$	−4.29918			−0.196026
$482$		0			0
$483$	0.636955	+	0.636955i	0.0289824	+	0.0289824i
$484$		0			0
$485$	39.2575	−	14.9036i	1.78259	−	0.676736i
$486$		0			0
$487$	−5.59965	−	5.59965i	−0.253745	−	0.253745i	0.568759	−	0.822504i	$-0.307424\pi$
$487$	−5.59965	−	5.59965i	−0.253745	−	0.253745i	−0.822504	+	0.568759i	$0.807424\pi$
$488$		0			0
$489$			9.38676i			0.424484i
$490$		0			0
$491$	−11.2713			−0.508667			−0.254333	−	0.967117i	$-0.581856\pi$
$491$	−11.2713			−0.508667			−0.254333	+	0.967117i	$0.581856\pi$
$492$		0			0
$493$	−14.2478	+	14.2478i	−0.641687	+	0.641687i
$494$		0			0
$495$	10.2598	−	22.8170i	0.461145	−	1.02555i
$496$		0			0
$497$	2.01889	−	2.01889i	0.0905594	−	0.0905594i
$498$		0			0
$499$			7.04115i			0.315205i	0.987503	+	0.157603i	$0.0503765\pi$
$499$			7.04115i			0.315205i	−0.987503	+	0.157603i	$0.949623\pi$
$500$		0			0
$501$		−	4.21602i		−	0.188358i
$502$		0			0
$503$	−13.7302	+	13.7302i	−0.612199	+	0.612199i	−0.943518	−	0.331320i	$-0.892506\pi$
$503$	−13.7302	+	13.7302i	−0.612199	+	0.612199i	0.331320	+	0.943518i	$0.392506\pi$
$504$		0			0
$505$	11.6692	−	25.9513i	0.519273	−	1.15482i
$506$		0			0
$507$	−4.74092	+	4.74092i	−0.210552	+	0.210552i
$508$		0			0
$509$	−4.91505			−0.217856			−0.108928	−	0.994050i	$-0.534742\pi$
$509$	−4.91505			−0.217856			−0.108928	+	0.994050i	$0.534742\pi$
$510$		0			0
$511$			2.05791i			0.0910366i
$512$		0			0
$513$	−13.4295	−	13.4295i	−0.592928	−	0.592928i
$514$		0			0
$515$	24.4745	−	9.29140i	1.07848	−	0.409428i
$516$		0			0
$517$	12.5984	+	12.5984i	0.554078	+	0.554078i
$518$		0			0
$519$	8.81439			0.386909
$520$		0			0
$521$	6.55084			0.286998			0.143499	−	0.989650i	$-0.454165\pi$
$521$	6.55084			0.286998			0.143499	+	0.989650i	$0.454165\pi$
$522$		0			0
$523$	−18.1480	−	18.1480i	−0.793556	−	0.793556i	0.188514	−	0.982070i	$-0.439633\pi$
$523$	−18.1480	−	18.1480i	−0.793556	−	0.793556i	−0.982070	+	0.188514i	$0.939633\pi$
$524$		0			0
$525$	3.61406	−	3.20613i	0.157730	−	0.139927i
$526$		0			0
$527$	−7.65146	−	7.65146i	−0.333303	−	0.333303i
$528$		0			0
$529$			22.1309i			0.962213i
$530$		0			0
$531$	16.4133			0.712277
$532$		0			0
$533$	−23.3482	+	23.3482i	−1.01132	+	1.01132i
$534$		0			0
$535$	−12.6302	+	4.79487i	−0.546051	+	0.207300i
$536$		0			0
$537$	−13.0937	+	13.0937i	−0.565036	+	0.565036i
$538$		0			0
$539$		−	5.41441i		−	0.233215i
$540$		0			0
$541$			7.99669i			0.343805i	0.985114	+	0.171902i	$0.0549913\pi$
$541$			7.99669i			0.343805i	−0.985114	+	0.171902i	$0.945009\pi$
$542$		0			0
$543$	9.18008	−	9.18008i	0.393955	−	0.393955i
$544$		0			0
$545$	−37.8531	−	17.0209i	−1.62145	−	0.729097i
$546$		0			0
$547$	−11.2540	+	11.2540i	−0.481186	+	0.481186i	−0.905510	−	0.424324i	$-0.860512\pi$
$547$	−11.2540	+	11.2540i	−0.481186	+	0.481186i	0.424324	+	0.905510i	$0.360512\pi$
$548$		0			0
$549$	8.68482			0.370659
$550$		0			0
$551$			22.3838i			0.953581i
$552$		0			0
$553$	9.09110	+	9.09110i	0.386593	+	0.386593i
$554$		0			0
$555$	0.853105	−	1.89723i	0.0362123	−	0.0805329i
$556$		0			0
$557$	1.87320	+	1.87320i	0.0793700	+	0.0793700i	0.745677	−	0.666307i	$-0.232126\pi$
$557$	1.87320	+	1.87320i	0.0793700	+	0.0793700i	−0.666307	+	0.745677i	$0.732126\pi$
$558$		0			0
$559$	0.534558			0.0226094
$560$		0			0
$561$	−18.2708			−0.771395
$562$		0			0
$563$	−18.2779	−	18.2779i	−0.770322	−	0.770322i	0.207840	−	0.978163i	$-0.433357\pi$
$563$	−18.2779	−	18.2779i	−0.770322	−	0.770322i	−0.978163	+	0.207840i	$0.933357\pi$
$564$		0			0
$565$	8.23048	+	21.6799i	0.346259	+	0.912082i
$566$		0			0
$567$	−1.03875	−	1.03875i	−0.0436233	−	0.0436233i
$568$		0			0
$569$			0.0832566i			0.00349030i	0.999998	+	0.00174515i	$0.000555499\pi$
$569$			0.0832566i			0.00349030i	−0.999998	+	0.00174515i	$0.999445\pi$
$570$		0			0
$571$	7.17301			0.300181			0.150091	−	0.988672i	$-0.452043\pi$
$571$	7.17301			0.300181			0.150091	+	0.988672i	$0.452043\pi$
$572$		0			0
$573$	−0.306623	+	0.306623i	−0.0128094	+	0.0128094i
$574$		0			0
$575$	−4.65298	−	0.278304i	−0.194043	−	0.0116061i
$576$		0			0
$577$	−3.54999	+	3.54999i	−0.147788	+	0.147788i	−0.777129	−	0.629341i	$-0.783325\pi$
$577$	−3.54999	+	3.54999i	−0.147788	+	0.147788i	0.629341	+	0.777129i	$0.283325\pi$
$578$		0			0
$579$			2.73517i			0.113670i
$580$		0			0
$581$			5.49179i			0.227838i
$582$		0			0
$583$	43.7780	−	43.7780i	1.81310	−	1.81310i
$584$		0			0
$585$	7.32276	+	19.2889i	0.302759	+	0.797498i
$586$		0			0
$587$	−18.7905	+	18.7905i	−0.775568	+	0.775568i	−0.979074	−	0.203505i	$-0.934767\pi$
$587$	−18.7905	+	18.7905i	−0.775568	+	0.775568i	0.203505	+	0.979074i	$0.434767\pi$
$588$		0			0
$589$	−12.0207			−0.495306
$590$		0			0
$591$		−	12.3968i		−	0.509937i
$592$		0			0
$593$	−7.24799	−	7.24799i	−0.297639	−	0.297639i	0.542449	−	0.840088i	$-0.317497\pi$
$593$	−7.24799	−	7.24799i	−0.297639	−	0.297639i	−0.840088	+	0.542449i	$0.817497\pi$
$594$		0			0
$595$	7.12226	+	3.20258i	0.291984	+	0.131293i
$596$		0			0
$597$	12.3967	+	12.3967i	0.507365	+	0.507365i
$598$		0			0
$599$	20.5332			0.838963			0.419482	−	0.907764i	$-0.362212\pi$
$599$	20.5332			0.838963			0.419482	+	0.907764i	$0.362212\pi$
$600$		0			0
$601$	−27.1276			−1.10656			−0.553280	−	0.832995i	$-0.686624\pi$
$601$	−27.1276			−1.10656			−0.553280	+	0.832995i	$0.686624\pi$
$602$		0			0
$603$	16.1623	+	16.1623i	0.658180	+	0.658180i
$604$		0			0
$605$	−37.3530	−	16.7961i	−1.51861	−	0.682857i
$606$		0			0
$607$	−12.6435	−	12.6435i	−0.513185	−	0.513185i	0.402316	−	0.915501i	$-0.368205\pi$
$607$	−12.6435	−	12.6435i	−0.513185	−	0.513185i	−0.915501	+	0.402316i	$0.868205\pi$
$608$		0			0
$609$		−	5.57479i		−	0.225902i
$610$		0			0
$611$	−14.6937			−0.594442
$612$		0			0
$613$	−0.474128	+	0.474128i	−0.0191498	+	0.0191498i	−0.716617	−	0.697467i	$-0.754310\pi$
$613$	−0.474128	+	0.474128i	−0.0191498	+	0.0191498i	0.697467	+	0.716617i	$0.254310\pi$
$614$		0			0
$615$	−5.67048	−	14.9366i	−0.228656	−	0.602304i
$616$		0			0
$617$	−34.0848	+	34.0848i	−1.37220	+	1.37220i	−0.515032	+	0.857171i	$0.672220\pi$
$617$	−34.0848	+	34.0848i	−1.37220	+	1.37220i	−0.857171	+	0.515032i	$0.827780\pi$
$618$		0			0
$619$			29.0177i			1.16632i	0.812357	+	0.583161i	$0.198184\pi$
$619$			29.0177i			1.16632i	−0.812357	+	0.583161i	$0.801816\pi$
$620$		0			0
$621$		−	4.56374i		−	0.183136i
$622$		0			0
$623$	−1.39009	+	1.39009i	−0.0556929	+	0.0556929i
$624$		0			0
$625$	−2.97994	+	24.8218i	−0.119197	+	0.992871i
$626$		0			0
$627$	−14.3521	+	14.3521i	−0.573167	+	0.573167i
$628$		0			0
$629$	3.36244			0.134069
$630$		0			0
$631$			24.5158i			0.975960i	0.872855	+	0.487980i	$0.162266\pi$
$631$			24.5158i			0.975960i	−0.872855	+	0.487980i	$0.837734\pi$
$632$		0			0
$633$	8.93144	+	8.93144i	0.354993	+	0.354993i
$634$		0			0
$635$	17.7543	+	46.7668i	0.704559	+	1.85588i
$636$		0			0
$637$	3.15744	+	3.15744i	0.125102	+	0.125102i
$638$		0			0
$639$	−5.89978			−0.233392
$640$		0			0
$641$	−42.5065			−1.67891			−0.839453	−	0.543432i	$-0.817125\pi$
$641$	−42.5065			−1.67891			−0.839453	+	0.543432i	$0.817125\pi$
$642$		0			0
$643$	3.14215	+	3.14215i	0.123914	+	0.123914i	0.766344	−	0.642430i	$-0.222074\pi$
$643$	3.14215	+	3.14215i	0.123914	+	0.123914i	−0.642430	+	0.766344i	$0.722074\pi$
$644$		0			0
$645$	−0.106075	+	0.235901i	−0.00417669	+	0.00928858i
$646$		0			0
$647$	−10.1457	−	10.1457i	−0.398867	−	0.398867i	0.478966	−	0.877833i	$-0.341012\pi$
$647$	−10.1457	−	10.1457i	−0.398867	−	0.398867i	−0.877833	+	0.478966i	$0.841012\pi$
$648$		0			0
$649$		−	43.0070i		−	1.68817i
$650$		0			0
$651$	2.99382			0.117337
$652$		0			0
$653$	5.20264	−	5.20264i	0.203595	−	0.203595i	−0.597943	−	0.801538i	$-0.704015\pi$
$653$	5.20264	−	5.20264i	0.203595	−	0.203595i	0.801538	+	0.597943i	$0.204015\pi$
$654$		0			0
$655$	16.5755	+	7.45332i	0.647660	+	0.291225i
$656$		0			0
$657$	3.00691	−	3.00691i	0.117311	−	0.117311i
$658$		0			0
$659$		−	45.6133i		−	1.77684i	−0.459032	−	0.888420i	$-0.651804\pi$
$659$		−	45.6133i		−	1.77684i	0.459032	−	0.888420i	$-0.348196\pi$
$660$		0			0
$661$		−	45.1240i		−	1.75512i	−0.479465	−	0.877561i	$-0.659169\pi$
$661$		−	45.1240i		−	1.75512i	0.479465	−	0.877561i	$-0.340831\pi$
$662$		0			0
$663$	10.6547	−	10.6547i	0.413795	−	0.413795i
$664$		0			0
$665$	8.11036	−	3.07898i	0.314506	−	0.119398i
$666$		0			0
$667$	−3.80333	+	3.80333i	−0.147265	+	0.147265i
$668$		0			0
$669$	−8.82868			−0.341337
$670$		0			0
$671$		−	22.7564i		−	0.878501i
$672$		0			0
$673$	5.25412	+	5.25412i	0.202532	+	0.202532i	0.801084	−	0.598552i	$-0.204257\pi$
$673$	5.25412	+	5.25412i	0.202532	+	0.202532i	−0.598552	+	0.801084i	$0.704257\pi$
$674$		0			0
$675$	−24.4331	−	1.46139i	−0.940430	−	0.0562490i
$676$		0			0
$677$	26.8547	+	26.8547i	1.03211	+	1.03211i	0.999467	+	0.0326441i	$0.0103928\pi$
$677$	26.8547	+	26.8547i	1.03211	+	1.03211i	0.0326441	+	0.999467i	$0.489607\pi$
$678$		0			0
$679$	−18.7791			−0.720675
$680$		0			0
$681$	9.21842			0.353251
$682$		0			0
$683$	−11.7713	−	11.7713i	−0.450416	−	0.450416i	0.445077	−	0.895492i	$-0.353176\pi$
$683$	−11.7713	−	11.7713i	−0.450416	−	0.450416i	−0.895492	+	0.445077i	$0.853176\pi$
$684$		0			0
$685$	−12.4412	+	4.72311i	−0.475352	+	0.180461i
$686$		0			0
$687$	13.9498	+	13.9498i	0.532218	+	0.532218i
$688$		0			0
$689$			51.0587i			1.94518i
$690$		0			0
$691$	−32.1658			−1.22364			−0.611822	−	0.790995i	$-0.709563\pi$
$691$	−32.1658			−1.22364			−0.611822	+	0.790995i	$0.709563\pi$
$692$		0			0
$693$	−7.91125	+	7.91125i	−0.300523	+	0.300523i
$694$		0			0
$695$	−19.9315	+	44.3259i	−0.756044	+	1.68138i
$696$		0			0
$697$	18.2609	−	18.2609i	0.691681	−	0.691681i
$698$		0			0
$699$			13.4704i			0.509496i
$700$		0			0
$701$		−	36.5604i		−	1.38087i	−0.723396	−	0.690433i	$-0.757420\pi$
$701$		−	36.5604i		−	1.38087i	0.723396	−	0.690433i	$-0.242580\pi$
$702$		0			0
$703$	2.64126	−	2.64126i	0.0996171	−	0.0996171i
$704$		0			0
$705$	2.91573	−	6.48432i	0.109813	−	0.244214i
$706$		0			0
$707$	−8.99799	+	8.99799i	−0.338404	+	0.338404i
$708$		0			0
$709$	−13.0843			−0.491390			−0.245695	−	0.969347i	$-0.579016\pi$
$709$	−13.0843			−0.491390			−0.245695	+	0.969347i	$0.579016\pi$
$710$		0			0
$711$		−	26.5668i		−	0.996335i
$712$		0			0
$713$	−2.04250	−	2.04250i	−0.0764921	−	0.0764921i
$714$		0			0
$715$	50.5418	−	19.1875i	1.89016	−	0.717571i
$716$		0			0
$717$	−3.04545	−	3.04545i	−0.113734	−	0.113734i
$718$		0			0
$719$	−18.4708			−0.688843			−0.344422	−	0.938815i	$-0.611925\pi$
$719$	−18.4708			−0.688843			−0.344422	+	0.938815i	$0.611925\pi$
$720$		0			0
$721$	−11.7075			−0.436012
$722$		0			0
$723$	−3.99933	−	3.99933i	−0.148737	−	0.148737i
$724$		0			0
$725$	19.1442	+	21.5799i	0.710996	+	0.801459i
$726$		0			0
$727$	25.3587	+	25.3587i	0.940503	+	0.940503i	0.998327	−	0.0578241i	$-0.0184162\pi$
$727$	25.3587	+	25.3587i	0.940503	+	0.940503i	−0.0578241	+	0.998327i	$0.518416\pi$
$728$		0			0
$729$		−	11.1548i		−	0.413140i
$730$		0			0
$731$	−0.418085			−0.0154634
$732$		0			0
$733$	24.6327	−	24.6327i	0.909830	−	0.909830i	−0.0864280	−	0.996258i	$-0.527545\pi$
$733$	24.6327	−	24.6327i	0.909830	−	0.909830i	0.996258	+	0.0864280i	$0.0275453\pi$
$734$		0			0
$735$	−2.01993	+	0.766836i	−0.0745061	+	0.0282852i
$736$		0			0
$737$	42.3493	−	42.3493i	1.55996	−	1.55996i
$738$		0			0
$739$			23.4559i			0.862838i	0.902152	+	0.431419i	$0.141987\pi$
$739$			23.4559i			0.862838i	−0.902152	+	0.431419i	$0.858013\pi$
$740$		0			0
$741$		−	16.7390i		−	0.614922i
$742$		0			0
$743$	9.17537	−	9.17537i	0.336612	−	0.336612i	−0.518479	−	0.855090i	$-0.673502\pi$
$743$	9.17537	−	9.17537i	0.336612	−	0.336612i	0.855090	+	0.518479i	$0.173502\pi$
$744$		0			0
$745$	−27.0891	−	12.1808i	−0.992466	−	0.446270i
$746$		0			0
$747$	8.02430	−	8.02430i	0.293594	−	0.293594i
$748$		0			0
$749$	6.04173			0.220760
$750$		0			0
$751$		−	34.6985i		−	1.26617i	−0.774084	−	0.633083i	$-0.781789\pi$
$751$		−	34.6985i		−	1.26617i	0.774084	−	0.633083i	$-0.218211\pi$
$752$		0			0
$753$	2.98499	+	2.98499i	0.108779	+	0.108779i
$754$		0			0
$755$	−9.63874	+	21.4357i	−0.350790	+	0.780126i
$756$		0			0
$757$	−11.2942	−	11.2942i	−0.410495	−	0.410495i	0.471416	−	0.881911i	$-0.343743\pi$
$757$	−11.2942	−	11.2942i	−0.410495	−	0.410495i	−0.881911	+	0.471416i	$0.843743\pi$
$758$		0			0
$759$	−4.87725			−0.177033
$760$		0			0
$761$	51.7952			1.87757			0.938787	−	0.344499i	$-0.111951\pi$
$761$	51.7952			1.87757			0.938787	+	0.344499i	$0.111951\pi$
$762$		0			0
$763$	13.1247	+	13.1247i	0.475145	+	0.475145i
$764$		0			0
$765$	−5.72722	−	15.0861i	−0.207068	−	0.545439i
$766$		0			0
$767$	25.0797	+	25.0797i	0.905577	+	0.905577i
$768$		0			0
$769$			7.52971i			0.271528i	0.990741	+	0.135764i	$0.0433490\pi$
$769$			7.52971i			0.271528i	−0.990741	+	0.135764i	$0.956651\pi$
$770$		0			0
$771$	8.92784			0.321528
$772$		0			0
$773$	−6.95427	+	6.95427i	−0.250128	+	0.250128i	−0.821023	−	0.570895i	$-0.806596\pi$
$773$	−6.95427	+	6.95427i	−0.250128	+	0.250128i	0.570895	+	0.821023i	$0.306596\pi$
$774$		0			0
$775$	−11.5891	+	10.2810i	−0.416291	+	0.369303i
$776$		0			0
$777$	−0.657820	+	0.657820i	−0.0235992	+	0.0235992i
$778$		0			0
$779$		−	28.6886i		−	1.02788i
$780$		0			0
$781$			15.4589i			0.553162i
$782$		0			0
$783$	−19.9715	+	19.9715i	−0.713724	+	0.713724i
$784$		0			0
$785$	16.5498	+	43.5938i	0.590686	+	1.55593i
$786$		0			0
$787$	12.5412	−	12.5412i	0.447047	−	0.447047i	−0.447325	−	0.894372i	$-0.647623\pi$
$787$	12.5412	−	12.5412i	0.447047	−	0.447047i	0.894372	+	0.447325i	$0.147623\pi$
$788$		0			0
$789$	15.8103			0.562863
$790$		0			0
$791$		−	10.3707i		−	0.368741i
$792$		0			0
$793$	13.2705	+	13.2705i	0.471250	+	0.471250i
$794$		0			0
$795$	−22.5322	−	10.1318i	−0.799136	−	0.359338i
$796$		0			0
$797$	21.9527	+	21.9527i	0.777606	+	0.777606i	0.979423	−	0.201817i	$-0.0646846\pi$
$797$	21.9527	+	21.9527i	0.777606	+	0.777606i	−0.201817	+	0.979423i	$0.564685\pi$
$798$		0			0
$799$	11.4921			0.406562
$800$		0			0
$801$	4.06226			0.143533
$802$		0			0
$803$	−7.87885	−	7.87885i	−0.278039	−	0.278039i
$804$		0			0
$805$	1.90123	+	0.854903i	0.0670095	+	0.0301314i
$806$		0			0
$807$	10.8770	+	10.8770i	0.382887	+	0.382887i
$808$		0			0
$809$			15.6233i			0.549285i	0.961546	+	0.274642i	$0.0885595\pi$
$809$			15.6233i			0.549285i	−0.961546	+	0.274642i	$0.911441\pi$
$810$		0			0
$811$	−12.8151			−0.450000			−0.225000	−	0.974359i	$-0.572238\pi$
$811$	−12.8151			−0.450000			−0.225000	+	0.974359i	$0.572238\pi$
$812$		0			0
$813$	14.2195	−	14.2195i	0.498700	−	0.498700i
$814$		0			0
$815$	7.70982	+	20.3085i	0.270063	+	0.711375i
$816$		0			0
$817$	−0.328414	+	0.328414i	−0.0114897	+	0.0114897i
$818$		0			0
$819$		−	9.22697i		−	0.322416i
$820$		0			0
$821$			1.83369i			0.0639962i	0.999488	+	0.0319981i	$0.0101871\pi$
$821$			1.83369i			0.0639962i	−0.999488	+	0.0319981i	$0.989813\pi$
$822$		0			0
$823$	9.77602	−	9.77602i	0.340770	−	0.340770i	−0.515886	−	0.856657i	$-0.672537\pi$
$823$	9.77602	−	9.77602i	0.340770	−	0.340770i	0.856657	+	0.515886i	$0.172537\pi$
$824$		0			0
$825$	−1.56178	+	26.1116i	−0.0543743	+	0.909088i
$826$		0			0
$827$	−9.46776	+	9.46776i	−0.329226	+	0.329226i	−0.852292	−	0.523066i	$-0.824788\pi$
$827$	−9.46776	+	9.46776i	−0.329226	+	0.329226i	0.523066	+	0.852292i	$0.324788\pi$
$828$		0			0
$829$	29.4393			1.02247			0.511234	−	0.859442i	$-0.329189\pi$
$829$	29.4393			1.02247			0.511234	+	0.859442i	$0.329189\pi$
$830$		0			0
$831$			19.7825i			0.686247i
$832$		0			0
$833$	−2.46948	−	2.46948i	−0.0855623	−	0.0855623i
$834$		0			0
$835$	−3.46284	−	9.12147i	−0.119836	−	0.315661i
$836$		0			0
$837$	−10.7253	−	10.7253i	−0.370720	−	0.370720i
$838$		0			0
$839$	−8.19787			−0.283022			−0.141511	−	0.989937i	$-0.545196\pi$
$839$	−8.19787			−0.283022			−0.141511	+	0.989937i	$0.545196\pi$
$840$		0			0
$841$	4.28771			0.147852
$842$		0			0
$843$	−15.0417	−	15.0417i	−0.518065	−	0.518065i
$844$		0			0
$845$	−6.36314	+	14.1511i	−0.218899	+	0.486811i
$846$		0			0
$847$	12.9513	+	12.9513i	0.445011	+	0.445011i
$848$		0			0
$849$			0.00193230i			6.63162e-5i
$850$		0			0
$851$	0.897577			0.0307685
$852$		0			0
$853$	−12.0948	+	12.0948i	−0.414118	+	0.414118i	−0.883170	−	0.469053i	$-0.844595\pi$
$853$	−12.0948	+	12.0948i	−0.414118	+	0.414118i	0.469053	+	0.883170i	$0.344595\pi$
$854$		0			0
$855$	−16.3493	−	7.35158i	−0.559133	−	0.251419i
$856$		0			0
$857$	13.0039	−	13.0039i	0.444205	−	0.444205i	−0.449218	−	0.893422i	$-0.648297\pi$
$857$	13.0039	−	13.0039i	0.444205	−	0.444205i	0.893422	+	0.449218i	$0.148297\pi$
$858$		0			0
$859$			46.0549i			1.57137i	0.618624	+	0.785687i	$0.287690\pi$
$859$			46.0549i			1.57137i	−0.618624	+	0.785687i	$0.712310\pi$
$860$		0			0
$861$			7.14504i			0.243502i
$862$		0			0
$863$	−8.93749	+	8.93749i	−0.304236	+	0.304236i	−0.842669	−	0.538433i	$-0.819017\pi$
$863$	−8.93749	+	8.93749i	−0.304236	+	0.304236i	0.538433	+	0.842669i	$0.319017\pi$
$864$		0			0
$865$	19.0701	−	7.23971i	0.648405	−	0.246158i
$866$		0			0
$867$	3.28185	−	3.28185i	0.111457	−	0.111457i
$868$		0			0
$869$	−69.6118			−2.36142
$870$		0			0
$871$			49.3924i			1.67360i
$872$		0			0
$873$	27.4390	+	27.4390i	0.928669	+	0.928669i
$874$		0			0
$875$	5.18574	−	9.90495i	0.175310	−	0.334848i
$876$		0			0
$877$	−5.94628	−	5.94628i	−0.200792	−	0.200792i	0.599547	−	0.800339i	$-0.295347\pi$
$877$	−5.94628	−	5.94628i	−0.200792	−	0.200792i	−0.800339	+	0.599547i	$0.795347\pi$
$878$		0			0
$879$	−18.0559			−0.609011
$880$		0			0
$881$	23.6599			0.797122			0.398561	−	0.917142i	$-0.369510\pi$
$881$	23.6599			0.797122			0.398561	+	0.917142i	$0.369510\pi$
$882$		0			0
$883$	−21.7857	−	21.7857i	−0.733148	−	0.733148i	0.238094	−	0.971242i	$-0.423477\pi$
$883$	−21.7857	−	21.7857i	−0.733148	−	0.733148i	−0.971242	+	0.238094i	$0.923477\pi$
$884$		0			0
$885$	−16.0444	+	6.09102i	−0.539326	+	0.204747i
$886$		0			0
$887$	−34.7838	−	34.7838i	−1.16793	−	1.16793i	−0.982695	−	0.185230i	$-0.940697\pi$
$887$	−34.7838	−	34.7838i	−1.16793	−	1.16793i	−0.185230	−	0.982695i	$-0.559303\pi$
$888$		0			0
$889$		−	22.3712i		−	0.750305i
$890$		0			0
$891$	7.95383			0.266463
$892$		0			0
$893$	9.02727	−	9.02727i	0.302086	−	0.302086i
$894$		0			0
$895$	−17.5740	+	39.0831i	−0.587435	+	1.30640i
$896$		0			0
$897$	2.84419	−	2.84419i	0.0949648	−	0.0949648i
$898$		0			0
$899$			17.8765i			0.596213i
$900$		0			0
$901$		−	39.9337i		−	1.33038i
$902$		0			0
$903$	0.0817930	−	0.0817930i	0.00272190	−	0.00272190i
$904$		0			0
$905$	12.3213	−	27.4014i	0.409572	−	0.910853i
$906$		0			0
$907$	−6.75591	+	6.75591i	−0.224326	+	0.224326i	−0.810317	−	0.585991i	$-0.800705\pi$
$907$	−6.75591	+	6.75591i	−0.224326	+	0.224326i	0.585991	+	0.810317i	$0.300705\pi$
$908$		0			0
$909$	26.2948			0.872142
$910$		0			0
$911$		−	24.7078i		−	0.818605i	−0.912399	−	0.409302i	$-0.865772\pi$
$911$		−	24.7078i		−	0.818605i	0.912399	−	0.409302i	$-0.134228\pi$
$912$		0			0
$913$	−21.0257	−	21.0257i	−0.695848	−	0.695848i
$914$		0			0
$915$	−8.48961	+	3.22296i	−0.280658	+	0.106548i
$916$		0			0
$917$	−5.74717	−	5.74717i	−0.189788	−	0.189788i
$918$		0			0
$919$	1.05781			0.0348938			0.0174469	−	0.999848i	$-0.494446\pi$
$919$	1.05781			0.0348938			0.0174469	+	0.999848i	$0.494446\pi$
$920$		0			0
$921$	−21.0870			−0.694839
$922$		0			0
$923$	−9.01493	−	9.01493i	−0.296730	−	0.296730i
$924$		0			0
$925$	0.287420	−	4.80540i	0.00945033	−	0.158001i
$926$		0			0
$927$	17.1064	+	17.1064i	0.561849	+	0.561849i
$928$		0			0
$929$		−	17.9400i		−	0.588591i	−0.955714	−	0.294296i	$-0.904915\pi$
$929$		−	17.9400i		−	0.588591i	0.955714	−	0.294296i	$-0.0950850\pi$
$930$		0			0
$931$	−3.87964			−0.127150
$932$		0			0
$933$	−15.3655	+	15.3655i	−0.503043	+	0.503043i
$934$		0			0
$935$	−39.5294	+	15.0068i	−1.29275	+	0.490773i
$936$		0			0
$937$	7.24822	−	7.24822i	0.236789	−	0.236789i	−0.578730	−	0.815519i	$-0.696452\pi$
$937$	7.24822	−	7.24822i	0.236789	−	0.236789i	0.815519	+	0.578730i	$0.196452\pi$
$938$		0			0
$939$		−	14.8423i		−	0.484360i
$940$		0			0
$941$		−	31.3685i		−	1.02259i	−0.859407	−	0.511293i	$-0.829167\pi$
$941$		−	31.3685i		−	1.02259i	0.859407	−	0.511293i	$-0.170833\pi$
$942$		0			0
$943$	4.87460	−	4.87460i	0.158739	−	0.158739i
$944$		0			0
$945$	9.98348	+	4.48915i	0.324763	+	0.146032i
$946$		0			0
$947$	−10.5999	+	10.5999i	−0.344450	+	0.344450i	−0.858037	−	0.513587i	$-0.828316\pi$
$947$	−10.5999	+	10.5999i	−0.344450	+	0.344450i	0.513587	+	0.858037i	$0.328316\pi$
$948$		0			0
$949$	9.18919			0.298294
$950$		0			0
$951$			7.23026i			0.234457i
$952$		0			0
$953$	6.64018	+	6.64018i	0.215097	+	0.215097i	0.806428	−	0.591332i	$-0.201398\pi$
$953$	6.64018	+	6.64018i	0.215097	+	0.215097i	−0.591332	+	0.806428i	$0.701398\pi$
$954$		0			0
$955$	−0.411541	+	0.915232i	−0.0133172	+	0.0296162i
$956$		0			0
$957$	21.3435	+	21.3435i	0.689936	+	0.689936i
$958$		0			0
$959$	5.95131			0.192178
$960$		0			0
$961$	21.3998			0.690317
$962$		0			0
$963$	−8.82784	−	8.82784i	−0.284473	−	0.284473i
$964$		0			0
$965$	2.24653	+	5.91760i	0.0723184	+	0.190494i
$966$		0			0
$967$	29.9303	+	29.9303i	0.962495	+	0.962495i	0.999322	−	0.0368270i	$-0.0117251\pi$
$967$	29.9303	+	29.9303i	0.962495	+	0.962495i	−0.0368270	+	0.999322i	$0.511725\pi$
$968$		0			0
$969$			13.0918i			0.420568i
$970$		0			0
$971$	27.5224			0.883237			0.441618	−	0.897203i	$-0.354405\pi$
$971$	27.5224			0.883237			0.441618	+	0.897203i	$0.354405\pi$
$972$		0			0
$973$	15.3690	−	15.3690i	0.492706	−	0.492706i
$974$		0			0
$975$	−14.3163	−	16.1379i	−0.458490	−	0.516825i
$976$		0			0
$977$	16.9569	−	16.9569i	0.542499	−	0.542499i	−0.381762	−	0.924261i	$-0.624682\pi$
$977$	16.9569	−	16.9569i	0.542499	−	0.542499i	0.924261	+	0.381762i	$0.124682\pi$
$978$		0			0
$979$		−	10.6441i		−	0.340188i
$980$		0			0
$981$		−	38.3541i		−	1.22455i
$982$		0			0
$983$	29.2243	−	29.2243i	0.932109	−	0.932109i	−0.0657283	−	0.997838i	$-0.520937\pi$
$983$	29.2243	−	29.2243i	0.932109	−	0.932109i	0.997838	+	0.0657283i	$0.0209371\pi$
$984$		0			0
$985$	−10.1821	−	26.8208i	−0.324430	−	0.854583i
$986$		0			0
$987$	−2.24829	+	2.24829i	−0.0715638	+	0.0715638i
$988$		0			0
$989$	−0.111604			−0.00354881
$990$		0			0
$991$		−	17.2817i		−	0.548972i	−0.961591	−	0.274486i	$-0.911492\pi$
$991$		−	17.2817i		−	0.548972i	0.961591	−	0.274486i	$-0.0885077\pi$
$992$		0			0
$993$	−4.64961	−	4.64961i	−0.147551	−	0.147551i
$994$		0			0
$995$	37.0027	+	16.6386i	1.17307	+	0.527478i
$996$		0			0
$997$	1.00560	+	1.00560i	0.0318476	+	0.0318476i	0.722851	−	0.691004i	$-0.242831\pi$
$997$	1.00560	+	1.00560i	0.0318476	+	0.0318476i	−0.691004	+	0.722851i	$0.742831\pi$
$998$		0			0
$999$	4.71324			0.149120

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1120.2.bi.a.463.11		72
4.3	odd	2		280.2.w.a.43.6	✓	72
5.2	odd	4	inner	1120.2.bi.a.687.12		72
8.3	odd	2	inner	1120.2.bi.a.463.12		72
8.5	even	2		280.2.w.a.43.14	yes	72
20.7	even	4		280.2.w.a.267.14	yes	72
40.27	even	4	inner	1120.2.bi.a.687.11		72
40.37	odd	4		280.2.w.a.267.6	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.w.a.43.6	✓	72	4.3	odd	2
280.2.w.a.43.14	yes	72	8.5	even	2
280.2.w.a.267.6	yes	72	40.37	odd	4
280.2.w.a.267.14	yes	72	20.7	even	4
1120.2.bi.a.463.11		72	1.1	even	1	trivial
1120.2.bi.a.463.12		72	8.3	odd	2	inner
1120.2.bi.a.687.11		72	40.27	even	4	inner
1120.2.bi.a.687.12		72	5.2	odd	4	inner

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:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.bi (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.683238 - 0.683238i) q^{3} +(-2.03938 - 0.917023i) q^{5} +(0.707107 + 0.707107i) q^{7} -2.06637i q^{9} -5.41441 q^{11} +(3.15744 - 3.15744i) q^{13} +(0.766836 + 2.01993i) q^{15} +(-2.46948 + 2.46948i) q^{17} +3.87964i q^{19} -0.966244i q^{21} +(-0.659207 + 0.659207i) q^{23} +(3.31814 + 3.74032i) q^{25} +(-3.46154 + 3.46154i) q^{27} +5.76955 q^{29} +3.09841i q^{31} +(3.69933 + 3.69933i) q^{33} +(-0.793626 - 2.09049i) q^{35} +(-0.680801 - 0.680801i) q^{37} -4.31457 q^{39} -7.39465 q^{41} +(0.0846505 + 0.0846505i) q^{43} +(-1.89491 + 4.21412i) q^{45} +(-2.32683 - 2.32683i) q^{47} +1.00000i q^{49} +3.37448 q^{51} +(-8.08545 + 8.08545i) q^{53} +(11.0420 + 4.96514i) q^{55} +(2.65072 - 2.65072i) q^{57} +7.94305i q^{59} +4.20293i q^{61} +(1.46115 - 1.46115i) q^{63} +(-9.33468 + 3.54378i) q^{65} +(-7.82159 + 7.82159i) q^{67} +0.900790 q^{69} -2.85514i q^{71} +(1.45516 + 1.45516i) q^{73} +(0.288449 - 4.82260i) q^{75} +(-3.82857 - 3.82857i) q^{77} +12.8568 q^{79} -1.46901 q^{81} +(3.88328 + 3.88328i) q^{83} +(7.30077 - 2.77163i) q^{85} +(-3.94197 - 3.94197i) q^{87} +1.96589i q^{89} +4.46530 q^{91} +(2.11695 - 2.11695i) q^{93} +(3.55772 - 7.91206i) q^{95} +(-13.2788 + 13.2788i) q^{97} +11.1882i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 8 q^{17} - 8 q^{25} + 64 q^{43} + 32 q^{51} - 8 q^{65} - 40 q^{73} - 112 q^{75} - 72 q^{81} - 80 q^{83} - 8 q^{97}+O(q^{100}) \) 72 * q + 8 * q^17 - 8 * q^25 + 64 * q^43 + 32 * q^51 - 8 * q^65 - 40 * q^73 - 112 * q^75 - 72 * q^81 - 80 * q^83 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more