LMFDB - Embedded newform 880.2.cm.a.497.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(17,880)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 0, 5, 18])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("880.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.cm (of order $20$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			497.1
Character	$\chi$	$=$	880.497
Dual form			880.2.cm.a.193.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.313634 + 1.98021i) q^{3} +(1.91314 + 1.15755i) q^{5} +(1.78576 - 0.282837i) q^{7} +(-0.969677 - 0.315067i) q^{9} +(-1.72268 + 2.83415i) q^{11} +(-2.00993 + 1.02411i) q^{13} +(-2.89220 + 3.42536i) q^{15} +(2.99738 + 1.52724i) q^{17} +(1.05647 - 0.767569i) q^{19} +3.62488i q^{21} +(3.16488 - 3.16488i) q^{23} +(2.32018 + 4.42908i) q^{25} +(-1.80258 + 3.53776i) q^{27} +(-2.37569 - 1.72604i) q^{29} +(1.23925 - 3.81401i) q^{31} +(-5.07190 - 4.30014i) q^{33} +(3.74380 + 1.52600i) q^{35} +(0.501987 + 3.16942i) q^{37} +(-1.39757 - 4.30127i) q^{39} +(0.766287 + 1.05470i) q^{41} +(-4.55431 - 4.55431i) q^{43} +(-1.49042 - 1.72521i) q^{45} +(7.62854 + 1.20824i) q^{47} +(-3.54845 + 1.15296i) q^{49} +(-3.96433 + 5.45644i) q^{51} +(-2.89146 - 5.67482i) q^{53} +(-6.57637 + 3.42803i) q^{55} +(1.18860 + 2.33276i) q^{57} +(-7.28135 + 10.0219i) q^{59} +(-8.85435 + 2.87695i) q^{61} +(-1.82072 - 0.288374i) q^{63} +(-5.03072 - 0.367324i) q^{65} +(2.46236 + 2.46236i) q^{67} +(5.27449 + 7.25972i) q^{69} +(2.09243 + 6.43984i) q^{71} +(-1.47735 - 9.32763i) q^{73} +(-9.49818 + 3.20531i) q^{75} +(-2.27469 + 5.54835i) q^{77} +(-0.353860 + 1.08907i) q^{79} +(-8.91472 - 6.47692i) q^{81} +(4.75092 - 9.32422i) q^{83} +(3.96654 + 6.39143i) q^{85} +(4.16301 - 4.16301i) q^{87} +3.85743i q^{89} +(-3.29960 + 2.39730i) q^{91} +(7.16385 + 3.65016i) q^{93} +(2.90966 - 0.245553i) q^{95} +(-0.693249 + 0.353228i) q^{97} +(2.56339 - 2.20545i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} - 2 q^{5} + 24 q^{11} - 10 q^{13} - 14 q^{15} + 24 q^{23} + 16 q^{25} + 16 q^{27} + 28 q^{31} + 66 q^{33} + 10 q^{35} - 8 q^{37} + 40 q^{41} - 28 q^{45} + 28 q^{47} - 20 q^{51} - 24 q^{53}+ \cdots - 8 q^{97}+O(q^{100}) $ 32 * q + 4 * q^3 - 2 * q^5 + 24 * q^11 - 10 * q^13 - 14 * q^15 + 24 * q^23 + 16 * q^25 + 16 * q^27 + 28 * q^31 + 66 * q^33 + 10 * q^35 - 8 * q^37 + 40 * q^41 - 28 * q^45 + 28 * q^47 - 20 * q^51 - 24 * q^53 + 64 * q^55 + 30 * q^57 - 60 * q^61 + 30 * q^63 + 8 * q^67 - 24 * q^71 + 50 * q^73 - 34 * q^75 + 70 * q^77 - 12 * q^81 - 90 * q^83 + 30 * q^85 - 20 * q^91 - 8 * q^93 + 40 * q^95 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{10}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.313634	+	1.98021i	−0.181076	+	1.14327i	0.714918	+	0.699208i	$0.246464\pi$
$3$	−0.313634	+	1.98021i	−0.181076	+	1.14327i	−0.895995	+	0.444064i	$0.853536\pi$
$4$		0			0
$5$	1.91314	+	1.15755i	0.855580	+	0.517670i
$5$	1.91314	+	1.15755i	0.855580	+	0.517670i
$6$		0			0
$7$	1.78576	−	0.282837i	0.674955	−	0.106902i	0.190458	−	0.981695i	$-0.439003\pi$
$7$	1.78576	−	0.282837i	0.674955	−	0.106902i	0.484497	+	0.874793i	$0.339003\pi$
$8$		0			0
$9$	−0.969677	−	0.315067i	−0.323226	−	0.105022i
$10$		0			0
$11$	−1.72268	+	2.83415i	−0.519407	+	0.854527i
$11$	−1.72268	+	2.83415i	−0.519407	+	0.854527i
$12$		0			0
$13$	−2.00993	+	1.02411i	−0.557454	+	0.284037i	−0.709933	−	0.704270i	$-0.751275\pi$
$13$	−2.00993	+	1.02411i	−0.557454	+	0.284037i	0.152478	+	0.988307i	$0.451275\pi$
$14$		0			0
$15$	−2.89220	+	3.42536i	−0.746763	+	0.884423i
$16$		0			0
$17$	2.99738	+	1.52724i	0.726972	+	0.370411i	0.777981	−	0.628288i	$-0.216244\pi$
$17$	2.99738	+	1.52724i	0.726972	+	0.370411i	−0.0510094	+	0.998698i	$0.516244\pi$
$18$		0			0
$19$	1.05647	−	0.767569i	0.242370	−	0.176092i	−0.459968	−	0.887935i	$-0.652139\pi$
$19$	1.05647	−	0.767569i	0.242370	−	0.176092i	0.702339	+	0.711843i	$0.252139\pi$
$20$		0			0
$21$			3.62488i			0.791014i
$22$		0			0
$23$	3.16488	−	3.16488i	0.659922	−	0.659922i	−0.295439	−	0.955362i	$-0.595466\pi$
$23$	3.16488	−	3.16488i	0.659922	−	0.659922i	0.955362	+	0.295439i	$0.0954660\pi$
$24$		0			0
$25$	2.32018	+	4.42908i	0.464035	+	0.885817i
$26$		0			0
$27$	−1.80258	+	3.53776i	−0.346907	+	0.680843i
$28$		0			0
$29$	−2.37569	−	1.72604i	−0.441154	−	0.320517i	0.344939	−	0.938625i	$-0.387900\pi$
$29$	−2.37569	−	1.72604i	−0.441154	−	0.320517i	−0.786093	+	0.618108i	$0.787900\pi$
$30$		0			0
$31$	1.23925	−	3.81401i	0.222575	−	0.685016i	−0.775953	−	0.630790i	$-0.782731\pi$
$31$	1.23925	−	3.81401i	0.222575	−	0.685016i	0.998529	−	0.0542261i	$-0.0172692\pi$
$32$		0			0
$33$	−5.07190	−	4.30014i	−0.882905	−	0.748558i
$34$		0			0
$35$	3.74380	+	1.52600i	0.632818	+	0.257940i
$36$		0			0
$37$	0.501987	+	3.16942i	0.0825262	+	0.521050i	0.993972	+	0.109631i	$0.0349668\pi$
$37$	0.501987	+	3.16942i	0.0825262	+	0.521050i	−0.911446	+	0.411419i	$0.865033\pi$
$38$		0			0
$39$	−1.39757	−	4.30127i	−0.223790	−	0.688754i
$40$		0			0
$41$	0.766287	+	1.05470i	0.119674	+	0.164717i	0.864651	−	0.502373i	$-0.167540\pi$
$41$	0.766287	+	1.05470i	0.119674	+	0.164717i	−0.744977	+	0.667090i	$0.767540\pi$
$42$		0			0
$43$	−4.55431	−	4.55431i	−0.694526	−	0.694526i	0.268698	−	0.963224i	$-0.413407\pi$
$43$	−4.55431	−	4.55431i	−0.694526	−	0.694526i	−0.963224	+	0.268698i	$0.913407\pi$
$44$		0			0
$45$	−1.49042	−	1.72521i	−0.222178	−	0.257179i
$46$		0			0
$47$	7.62854	+	1.20824i	1.11274	+	0.176240i	0.685622	−	0.727957i	$-0.259530\pi$
$47$	7.62854	+	1.20824i	1.11274	+	0.176240i	0.427114	+	0.904198i	$0.359530\pi$
$48$		0			0
$49$	−3.54845	+	1.15296i	−0.506921	+	0.164709i
$50$		0			0
$51$	−3.96433	+	5.45644i	−0.555118	+	0.764054i
$52$		0			0
$53$	−2.89146	−	5.67482i	−0.397173	−	0.779496i	0.602656	−	0.798001i	$-0.294109\pi$
$53$	−2.89146	−	5.67482i	−0.397173	−	0.779496i	−0.999829	+	0.0185052i	$0.994109\pi$
$54$		0			0
$55$	−6.57637	+	3.42803i	−0.886757	+	0.462235i
$56$		0			0
$57$	1.18860	+	2.33276i	0.157434	+	0.308981i
$58$		0			0
$59$	−7.28135	+	10.0219i	−0.947952	+	1.30474i	0.00447977	+	0.999990i	$0.498574\pi$
$59$	−7.28135	+	10.0219i	−0.947952	+	1.30474i	−0.952431	+	0.304753i	$0.901426\pi$
$60$		0			0
$61$	−8.85435	+	2.87695i	−1.13368	+	0.368356i	−0.814975	−	0.579496i	$-0.803249\pi$
$61$	−8.85435	+	2.87695i	−1.13368	+	0.368356i	−0.318709	+	0.947853i	$0.603249\pi$
$62$		0			0
$63$	−1.82072	−	0.288374i	−0.229390	−	0.0363318i
$64$		0			0
$65$	−5.03072	−	0.367324i	−0.623984	−	0.0455609i
$66$		0			0
$67$	2.46236	+	2.46236i	0.300825	+	0.300825i	0.841336	−	0.540512i	$-0.181769\pi$
$67$	2.46236	+	2.46236i	0.300825	+	0.300825i	−0.540512	+	0.841336i	$0.681769\pi$
$68$		0			0
$69$	5.27449	+	7.25972i	0.634974	+	0.873967i
$70$		0			0
$71$	2.09243	+	6.43984i	0.248326	+	0.764268i	0.995072	+	0.0991588i	$0.0316152\pi$
$71$	2.09243	+	6.43984i	0.248326	+	0.764268i	−0.746746	+	0.665110i	$0.768385\pi$
$72$		0			0
$73$	−1.47735	−	9.32763i	−0.172911	−	1.09172i	−0.909600	−	0.415485i	$-0.863612\pi$
$73$	−1.47735	−	9.32763i	−0.172911	−	1.09172i	0.736689	−	0.676232i	$-0.236388\pi$
$74$		0			0
$75$	−9.49818	+	3.20531i	−1.09676	+	0.370118i
$76$		0			0
$77$	−2.27469	+	5.54835i	−0.259225	+	0.632293i
$78$		0			0
$79$	−0.353860	+	1.08907i	−0.0398123	+	0.122530i	−0.968987	−	0.247110i	$-0.920519\pi$
$79$	−0.353860	+	1.08907i	−0.0398123	+	0.122530i	0.929175	+	0.369640i	$0.120519\pi$
$80$		0			0
$81$	−8.91472	−	6.47692i	−0.990524	−	0.719658i
$82$		0			0
$83$	4.75092	−	9.32422i	0.521482	−	1.02347i	−0.468658	−	0.883380i	$-0.655262\pi$
$83$	4.75092	−	9.32422i	0.521482	−	1.02347i	0.990139	−	0.140086i	$-0.0447378\pi$
$84$		0			0
$85$	3.96654	+	6.39143i	0.430232	+	0.693248i
$86$		0			0
$87$	4.16301	−	4.16301i	0.446321	−	0.446321i
$88$		0			0
$89$			3.85743i			0.408887i	0.978878	+	0.204443i	$0.0655384\pi$
$89$			3.85743i			0.408887i	−0.978878	+	0.204443i	$0.934462\pi$
$90$		0			0
$91$	−3.29960	+	2.39730i	−0.345892	+	0.251305i
$92$		0			0
$93$	7.16385	+	3.65016i	0.742857	+	0.378504i
$94$		0			0
$95$	2.90966	−	0.245553i	0.298525	−	0.0251932i
$96$		0			0
$97$	−0.693249	+	0.353228i	−0.0703888	+	0.0358649i	−0.488831	−	0.872379i	$-0.662576\pi$
$97$	−0.693249	+	0.353228i	−0.0703888	+	0.0358649i	0.418442	+	0.908244i	$0.362576\pi$
$98$		0			0
$99$	2.56339	−	2.20545i	0.257630	−	0.221656i
$100$		0			0
$101$	9.28960	+	3.01837i	0.924350	+	0.300339i	0.732250	−	0.681036i	$-0.238470\pi$
$101$	9.28960	+	3.01837i	0.924350	+	0.300339i	0.192100	+	0.981375i	$0.438470\pi$
$102$		0			0
$103$	−4.61435	+	0.730841i	−0.454665	+	0.0720119i	−0.379567	−	0.925164i	$-0.623927\pi$
$103$	−4.61435	+	0.730841i	−0.454665	+	0.0720119i	−0.0750982	+	0.997176i	$0.523927\pi$
$104$		0			0
$105$	−4.19597	+	6.93489i	−0.409485	+	0.676776i
$106$		0			0
$107$	2.39372	−	15.1133i	0.231410	−	1.46106i	−0.549015	−	0.835813i	$-0.684997\pi$
$107$	2.39372	−	15.1133i	0.231410	−	1.46106i	0.780424	−	0.625250i	$-0.215003\pi$
$108$		0			0
$109$	17.8837			1.71295			0.856476	−	0.516187i	$-0.172649\pi$
$109$	17.8837			1.71295			0.856476	+	0.516187i	$0.172649\pi$
$110$		0			0
$111$	−6.43355			−0.610646
$112$		0			0
$113$	1.16850	−	7.37759i	0.109923	−	0.694025i	−0.869760	−	0.493474i	$-0.835727\pi$
$113$	1.16850	−	7.37759i	0.109923	−	0.694025i	0.979683	−	0.200551i	$-0.0642733\pi$
$114$		0			0
$115$	9.71833	−	2.39135i	0.906239	−	0.222994i
$116$		0			0
$117$	2.27165	−	0.359793i	0.210014	−	0.0332629i
$118$		0			0
$119$	5.78457	+	1.87952i	0.530271	+	0.172295i
$120$		0			0
$121$	−5.06477	−	9.76464i	−0.460433	−	0.887694i
$122$		0			0
$123$	−2.32886	+	1.18662i	−0.209987	+	0.106994i
$124$		0			0
$125$	−0.688059	+	11.1591i	−0.0615419	+	0.998105i
$126$		0			0
$127$	0.183716	+	0.0936079i	0.0163021	+	0.00830635i	0.462123	−	0.886816i	$-0.347088\pi$
$127$	0.183716	+	0.0936079i	0.0163021	+	0.00830635i	−0.445820	+	0.895122i	$0.647088\pi$
$128$		0			0
$129$	10.4469	−	7.59009i	0.919794	−	0.668270i
$130$		0			0
$131$		−	0.551708i		−	0.0482029i	−0.999710	−	0.0241015i	$-0.992328\pi$
$131$		−	0.551708i		−	0.0482029i	0.999710	−	0.0241015i	$-0.00767248\pi$
$132$		0			0
$133$	1.66950	−	1.66950i	0.144764	−	0.144764i
$134$		0			0
$135$	−7.54370	+	4.68165i	−0.649259	+	0.402932i
$136$		0			0
$137$	7.02615	−	13.7896i	0.600284	−	1.17812i	−0.368362	−	0.929682i	$-0.620081\pi$
$137$	7.02615	−	13.7896i	0.600284	−	1.17812i	0.968647	−	0.248442i	$-0.0799186\pi$
$138$		0			0
$139$	−1.15101	−	0.836256i	−0.0976272	−	0.0709303i	0.537901	−	0.843008i	$-0.319218\pi$
$139$	−1.15101	−	0.836256i	−0.0976272	−	0.0709303i	−0.635528	+	0.772078i	$0.719218\pi$
$140$		0			0
$141$	−4.78513	+	14.7271i	−0.402981	+	1.24025i
$142$		0			0
$143$	0.559982	−	7.46065i	0.0468280	−	0.623891i
$144$		0			0
$145$	−2.54705	−	6.05212i	−0.211521	−	0.502601i
$146$		0			0
$147$	−1.17019	−	7.38826i	−0.0965153	−	0.609373i
$148$		0			0
$149$	−7.35615	−	22.6399i	−0.602639	−	1.85473i	−0.512269	−	0.858825i	$-0.671195\pi$
$149$	−7.35615	−	22.6399i	−0.602639	−	1.85473i	−0.0903702	−	0.995908i	$-0.528805\pi$
$150$		0			0
$151$	8.45592	+	11.6386i	0.688133	+	0.947134i	0.999996	−	0.00299311i	$-0.000952737\pi$
$151$	8.45592	+	11.6386i	0.688133	+	0.947134i	−0.311862	+	0.950127i	$0.600953\pi$
$152$		0			0
$153$	−2.42531	−	2.42531i	−0.196075	−	0.196075i
$154$		0			0
$155$	6.78574	−	5.86223i	0.545044	−	0.470866i
$156$		0			0
$157$	13.3277	+	2.11091i	1.06367	+	0.168469i	0.663654	−	0.748040i	$-0.269005\pi$
$157$	13.3277	+	2.11091i	1.06367	+	0.168469i	0.400016	+	0.916508i	$0.369005\pi$
$158$		0			0
$159$	12.1442	−	3.94588i	0.963095	−	0.312928i
$160$		0			0
$161$	4.75657	−	6.54686i	0.374870	−	0.515965i
$162$		0			0
$163$	0.487228	+	0.956239i	0.0381626	+	0.0748984i	0.909300	−	0.416140i	$-0.136617\pi$
$163$	0.487228	+	0.956239i	0.0381626	+	0.0748984i	−0.871138	+	0.491039i	$0.836617\pi$
$164$		0			0
$165$	−4.72563	−	14.0977i	−0.367890	−	1.09750i
$166$		0			0
$167$	0.858874	+	1.68563i	0.0664616	+	0.130438i	0.921847	−	0.387554i	$-0.126680\pi$
$167$	0.858874	+	1.68563i	0.0664616	+	0.130438i	−0.855386	+	0.517992i	$0.826680\pi$
$168$		0			0
$169$	−4.65019	+	6.40044i	−0.357707	+	0.492342i
$170$		0			0
$171$	−1.26627	+	0.411435i	−0.0968339	+	0.0314633i
$172$		0			0
$173$	18.7140	+	2.96401i	1.42280	+	0.225350i	0.819919	−	0.572480i	$-0.194019\pi$
$173$	18.7140	+	2.96401i	1.42280	+	0.225350i	0.602883	+	0.797830i	$0.294019\pi$
$174$		0			0
$175$	5.39599	+	7.25306i	0.407898	+	0.548280i
$176$		0			0
$177$	−17.5618	−	17.5618i	−1.32002	−	1.32002i
$178$		0			0
$179$	9.62961	+	13.2540i	0.719751	+	0.990652i	0.999532	+	0.0305880i	$0.00973800\pi$
$179$	9.62961	+	13.2540i	0.719751	+	0.990652i	−0.279781	+	0.960064i	$0.590262\pi$
$180$		0			0
$181$	4.59306	+	14.1360i	0.341400	+	1.05072i	0.963483	+	0.267769i	$0.0862864\pi$
$181$	4.59306	+	14.1360i	0.341400	+	1.05072i	−0.622084	+	0.782951i	$0.713714\pi$
$182$		0			0
$183$	−2.91994	−	18.4357i	−0.215848	−	1.36281i
$184$		0			0
$185$	−2.70838	+	6.64461i	−0.199124	+	0.488522i
$186$		0			0
$187$	−9.49195	+	5.86407i	−0.694120	+	0.428823i
$188$		0			0
$189$	−2.21837	+	6.82744i	−0.161363	+	0.496623i
$190$		0			0
$191$	−1.54488	−	1.12242i	−0.111784	−	0.0812156i	0.530489	−	0.847692i	$-0.322008\pi$
$191$	−1.54488	−	1.12242i	−0.111784	−	0.0812156i	−0.642273	+	0.766476i	$0.722008\pi$
$192$		0			0
$193$	5.16774	−	10.1423i	0.371982	−	0.730056i	−0.626811	−	0.779171i	$-0.715640\pi$
$193$	5.16774	−	10.1423i	0.371982	−	0.730056i	0.998793	+	0.0491153i	$0.0156402\pi$
$194$		0			0
$195$	2.30518	−	9.84666i	0.165077	−	0.705134i
$196$		0			0
$197$	13.8092	−	13.8092i	0.983863	−	0.983863i	−0.0160086	−	0.999872i	$-0.505096\pi$
$197$	13.8092	−	13.8092i	0.983863	−	0.983863i	0.999872	+	0.0160086i	$0.00509592\pi$
$198$		0			0
$199$		−	22.3508i		−	1.58441i	−0.610258	−	0.792203i	$-0.708934\pi$
$199$		−	22.3508i		−	1.58441i	0.610258	−	0.792203i	$-0.291066\pi$
$200$		0			0
$201$	−5.64825	+	4.10369i	−0.398397	+	0.289452i
$202$		0			0
$203$	−4.73060	−	2.41036i	−0.332023	−	0.169174i
$204$		0			0
$205$	0.245143	+	2.90480i	0.0171215	+	0.202880i
$206$		0			0
$207$	−4.06606	+	2.07176i	−0.282610	+	0.143997i
$208$		0			0
$209$	0.355449	+	4.31646i	0.0245869	+	0.298576i
$210$		0			0
$211$	0.358113	+	0.116358i	0.0246535	+	0.00801042i	0.321318	−	0.946971i	$-0.395874\pi$
$211$	0.358113	+	0.116358i	0.0246535	+	0.00801042i	−0.296664	+	0.954982i	$0.595874\pi$
$212$		0			0
$213$	−13.4085	+	2.12369i	−0.918733	+	0.145513i
$214$		0			0
$215$	−3.44119	−	13.9848i	−0.234687	−	0.953758i
$216$		0			0
$217$	1.13426	−	7.16142i	0.0769984	−	0.486149i
$218$		0			0
$219$	18.9340			1.27944
$220$		0			0
$221$	−7.58859			−0.510464
$222$		0			0
$223$	−1.19037	+	7.51570i	−0.0797131	+	0.503289i	0.915237	+	0.402916i	$0.132003\pi$
$223$	−1.19037	+	7.51570i	−0.0797131	+	0.503289i	−0.994950	+	0.100372i	$0.967997\pi$
$224$		0			0
$225$	−0.854361	−	5.02579i	−0.0569574	−	0.335053i
$226$		0			0
$227$	8.10167	−	1.28318i	0.537727	−	0.0851676i	0.118336	−	0.992974i	$-0.462244\pi$
$227$	8.10167	−	1.28318i	0.537727	−	0.0851676i	0.419390	+	0.907806i	$0.362244\pi$
$228$		0			0
$229$	7.21772	+	2.34518i	0.476960	+	0.154974i	0.537624	−	0.843184i	$-0.319322\pi$
$229$	7.21772	+	2.34518i	0.476960	+	0.154974i	−0.0606641	+	0.998158i	$0.519322\pi$
$230$		0			0
$231$	−10.2734	−	6.24450i	−0.675943	−	0.410858i
$232$		0			0
$233$	−23.3597	+	11.9023i	−1.53034	+	0.779749i	−0.997777	−	0.0666396i	$-0.978772\pi$
$233$	−23.3597	+	11.9023i	−1.53034	+	0.779749i	−0.532566	+	0.846388i	$0.678772\pi$
$234$		0			0
$235$	13.1958	+	11.1419i	0.860801	+	0.726818i
$236$		0			0
$237$	−2.04560	−	1.04228i	−0.132876	−	0.0677036i
$238$		0			0
$239$	1.84133	−	1.33781i	0.119106	−	0.0865356i	−0.526638	−	0.850090i	$-0.676548\pi$
$239$	1.84133	−	1.33781i	0.119106	−	0.0865356i	0.645744	+	0.763554i	$0.276548\pi$
$240$		0			0
$241$		−	6.29531i		−	0.405517i	−0.979229	−	0.202758i	$-0.935009\pi$
$241$		−	6.29531i		−	0.405517i	0.979229	−	0.202758i	$-0.0649906\pi$
$242$		0			0
$243$	7.19883	−	7.19883i	0.461805	−	0.461805i
$244$		0			0
$245$	−8.12326	−	1.90172i	−0.518976	−	0.121496i
$246$		0			0
$247$	−1.33735	+	2.62470i	−0.0850936	+	0.167006i
$248$		0			0
$249$	16.9738	+	12.3322i	1.07567	+	0.781521i
$250$		0			0
$251$	8.21826	−	25.2932i	0.518732	−	1.59649i	−0.257655	−	0.966237i	$-0.582950\pi$
$251$	8.21826	−	25.2932i	0.518732	−	1.59649i	0.776387	−	0.630256i	$-0.217050\pi$
$252$		0			0
$253$	3.51766	+	14.4218i	0.221153	+	0.906690i
$254$		0			0
$255$	−13.9004	+	5.85000i	−0.870476	+	0.366341i
$256$		0			0
$257$	3.09337	+	19.5307i	0.192959	+	1.21829i	0.873955	+	0.486007i	$0.161547\pi$
$257$	3.09337	+	19.5307i	0.192959	+	1.21829i	−0.680996	+	0.732287i	$0.738453\pi$
$258$		0			0
$259$	1.79286	+	5.51786i	0.111403	+	0.342863i
$260$		0			0
$261$	1.75983	+	2.42220i	0.108931	+	0.149931i
$262$		0			0
$263$	5.91748	+	5.91748i	0.364888	+	0.364888i	0.865609	−	0.500721i	$-0.166932\pi$
$263$	5.91748	+	5.91748i	0.364888	+	0.364888i	−0.500721	+	0.865609i	$0.666932\pi$
$264$		0			0
$265$	1.03710	−	14.2037i	0.0637085	−	0.872526i
$266$		0			0
$267$	−7.63850	−	1.20982i	−0.467469	−	0.0740398i
$268$		0			0
$269$	−9.23539	+	3.00076i	−0.563092	+	0.182960i	−0.576712	−	0.816948i	$-0.695664\pi$
$269$	−9.23539	+	3.00076i	−0.563092	+	0.182960i	0.0136201	+	0.999907i	$0.495664\pi$
$270$		0			0
$271$	−1.79360	+	2.46868i	−0.108954	+	0.149962i	−0.860012	−	0.510274i	$-0.829544\pi$
$271$	−1.79360	+	2.46868i	−0.108954	+	0.149962i	0.751058	+	0.660236i	$0.229544\pi$
$272$		0			0
$273$	−3.71228	−	7.28576i	−0.224677	−	0.440954i
$274$		0			0
$275$	−16.5496	−	1.05417i	−0.997977	−	0.0635687i
$276$		0			0
$277$	−1.08057	−	2.12073i	−0.0649249	−	0.127422i	0.856263	−	0.516540i	$-0.172780\pi$
$277$	−1.08057	−	2.12073i	−0.0649249	−	0.127422i	−0.921188	+	0.389117i	$0.872780\pi$
$278$		0			0
$279$	−2.40334	+	3.30791i	−0.143884	+	0.198039i
$280$		0			0
$281$	26.8503	−	8.72419i	1.60175	−	0.520442i	0.634214	−	0.773157i	$-0.281324\pi$
$281$	26.8503	−	8.72419i	1.60175	−	0.520442i	0.967541	+	0.252716i	$0.0813238\pi$
$282$		0			0
$283$	−16.8040	−	2.66149i	−0.998893	−	0.158209i	−0.364486	−	0.931209i	$-0.618755\pi$
$283$	−16.8040	−	2.66149i	−0.998893	−	0.158209i	−0.634406	+	0.773000i	$0.718755\pi$
$284$		0			0
$285$	−0.426322	+	5.83874i	−0.0252532	+	0.345857i
$286$		0			0
$287$	1.66672	+	1.66672i	0.0983831	+	0.0983831i
$288$		0			0
$289$	−3.34052	−	4.59783i	−0.196501	−	0.270461i
$290$		0			0
$291$	−0.482038	−	1.48356i	−0.0282576	−	0.0869678i
$292$		0			0
$293$	−1.67148	−	10.5533i	−0.0976492	−	0.616533i	−0.987174	−	0.159646i	$-0.948965\pi$
$293$	−1.67148	−	10.5533i	−0.0976492	−	0.616533i	0.889525	−	0.456886i	$-0.151035\pi$
$294$		0			0
$295$	−25.5311	+	10.7448i	−1.48648	+	0.625586i
$296$		0			0
$297$	−6.92127	−	11.2032i	−0.401613	−	0.650076i
$298$		0			0
$299$	−3.12000	+	9.60236i	−0.180434	+	0.555319i
$300$		0			0
$301$	−9.42104	−	6.84479i	−0.543020	−	0.394527i
$302$		0			0
$303$	−8.89053	+	17.4487i	−0.510748	+	1.00240i
$304$		0			0
$305$	−20.2698	−	4.74532i	−1.16064	−	0.271716i
$306$		0			0
$307$	22.9923	−	22.9923i	1.31224	−	1.31224i	0.392474	−	0.919763i	$-0.371619\pi$
$307$	22.9923	−	22.9923i	1.31224	−	1.31224i	0.919763	−	0.392474i	$-0.128381\pi$
$308$		0			0
$309$		−	9.36657i		−	0.532846i
$310$		0			0
$311$	11.2361	−	8.16354i	0.637143	−	0.462912i	−0.221724	−	0.975109i	$-0.571168\pi$
$311$	11.2361	−	8.16354i	0.637143	−	0.462912i	0.858868	+	0.512198i	$0.171168\pi$
$312$		0			0
$313$	−15.4928	−	7.89399i	−0.875707	−	0.446195i	−0.0424612	−	0.999098i	$-0.513520\pi$
$313$	−15.4928	−	7.89399i	−0.875707	−	0.446195i	−0.833245	+	0.552903i	$0.813520\pi$
$314$		0			0
$315$	−3.14949	−	2.65927i	−0.177453	−	0.149833i
$316$		0			0
$317$	14.3960	−	7.33513i	0.808560	−	0.411982i	−0.000287853	−	1.00000i	$-0.500092\pi$
$317$	14.3960	−	7.33513i	0.808560	−	0.411982i	0.808848	+	0.588018i	$0.200092\pi$
$318$		0			0
$319$	8.98439	−	3.75964i	0.503029	−	0.210500i
$320$		0			0
$321$	29.1768	+	9.48011i	1.62849	+	0.529128i
$322$		0			0
$323$	4.33890	−	0.687214i	0.241423	−	0.0382376i
$324$		0			0
$325$	−9.19926	−	6.52603i	−0.510283	−	0.361999i
$326$		0			0
$327$	−5.60894	+	35.4135i	−0.310175	+	1.95837i
$328$		0			0
$329$	13.9645			0.769887
$330$		0			0
$331$	−14.6837			−0.807090			−0.403545	−	0.914960i	$-0.632222\pi$
$331$	−14.6837			−0.807090			−0.403545	+	0.914960i	$0.632222\pi$
$332$		0			0
$333$	0.511816	−	3.23148i	0.0280473	−	0.177084i
$334$		0			0
$335$	1.86053	+	7.56111i	0.101652	+	0.413108i
$336$		0			0
$337$	−13.3250	+	2.11047i	−0.725859	+	0.114965i	−0.508420	−	0.861109i	$-0.669770\pi$
$337$	−13.3250	+	2.11047i	−0.725859	+	0.114965i	−0.217439	+	0.976074i	$0.569770\pi$
$338$		0			0
$339$	14.2427	+	4.62772i	0.773555	+	0.251343i
$340$		0			0
$341$	8.67464	+	10.0825i	0.469758	+	0.545999i
$342$		0			0
$343$	−17.2873	+	8.80832i	−0.933426	+	0.475604i
$344$		0			0
$345$	1.68736	+	19.9943i	0.0908446	+	1.07646i
$346$		0			0
$347$	−10.9022	−	5.55495i	−0.585261	−	0.298205i	0.136177	−	0.990685i	$-0.456518\pi$
$347$	−10.9022	−	5.55495i	−0.585261	−	0.298205i	−0.721438	+	0.692479i	$0.756518\pi$
$348$		0			0
$349$	−16.4807	+	11.9739i	−0.882193	+	0.640951i	−0.933831	−	0.357715i	$-0.883556\pi$
$349$	−16.4807	+	11.9739i	−0.882193	+	0.640951i	0.0516378	+	0.998666i	$0.483556\pi$
$350$		0			0
$351$		−	8.95670i		−	0.478073i
$352$		0			0
$353$	13.7886	−	13.7886i	0.733893	−	0.733893i	−0.237495	−	0.971389i	$-0.576326\pi$
$353$	13.7886	−	13.7886i	0.733893	−	0.733893i	0.971389	+	0.237495i	$0.0763264\pi$
$354$		0			0
$355$	−3.45131	+	14.7424i	−0.183176	+	0.782444i
$356$		0			0
$357$	−5.53607	+	10.8652i	−0.293000	+	0.575045i
$358$		0			0
$359$	−13.3648	−	9.71011i	−0.705368	−	0.512480i	0.176308	−	0.984335i	$-0.443585\pi$
$359$	−13.3648	−	9.71011i	−0.705368	−	0.512480i	−0.881676	+	0.471855i	$0.843585\pi$
$360$		0			0
$361$	−5.34436	+	16.4483i	−0.281282	+	0.865697i
$362$		0			0
$363$	20.9245	−	6.96676i	1.09825	−	0.365660i
$364$		0			0
$365$	7.97079	−	19.5551i	0.417210	−	1.02356i
$366$		0			0
$367$	1.00765	+	6.36207i	0.0525990	+	0.332097i	0.999930	+	0.0118406i	$0.00376908\pi$
$367$	1.00765	+	6.36207i	0.0525990	+	0.332097i	−0.947331	+	0.320256i	$0.896231\pi$
$368$		0			0
$369$	−0.410749	−	1.26415i	−0.0213827	−	0.0658092i
$370$		0			0
$371$	−6.76851	−	9.31606i	−0.351404	−	0.483666i
$372$		0			0
$373$	9.69631	+	9.69631i	0.502056	+	0.502056i	0.912076	−	0.410021i	$-0.134478\pi$
$373$	9.69631	+	9.69631i	0.502056	+	0.502056i	−0.410021	+	0.912076i	$0.634478\pi$
$374$		0			0
$375$	−21.8816	−	4.86238i	−1.12996	−	0.251092i
$376$		0			0
$377$	6.54262	+	1.03625i	0.336962	+	0.0533696i
$378$		0			0
$379$	−20.4487	+	6.64419i	−1.05038	+	0.341289i	−0.782818	−	0.622251i	$-0.786218\pi$
$379$	−20.4487	+	6.64419i	−1.05038	+	0.341289i	−0.267563	+	0.963540i	$0.586218\pi$
$380$		0			0
$381$	−0.242982	+	0.334436i	−0.0124484	+	0.0171337i
$382$		0			0
$383$	0.137756	+	0.270362i	0.00703902	+	0.0138148i	0.894499	−	0.447069i	$-0.147532\pi$
$383$	0.137756	+	0.270362i	0.00703902	+	0.0138148i	−0.887460	+	0.460884i	$0.847532\pi$
$384$		0			0
$385$	−10.7743	+	7.98168i	−0.549107	+	0.406784i
$386$		0			0
$387$	2.98130	+	5.85112i	0.151548	+	0.297429i
$388$		0			0
$389$	2.11680	−	2.91353i	0.107326	−	0.147722i	−0.751975	−	0.659191i	$-0.770899\pi$
$389$	2.11680	−	2.91353i	0.107326	−	0.147722i	0.859301	+	0.511470i	$0.170899\pi$
$390$		0			0
$391$	14.3199	−	4.65281i	0.724187	−	0.235303i
$392$		0			0
$393$	1.09249	+	0.173034i	0.0551091	+	0.00872842i
$394$		0			0
$395$	−1.93763	+	1.67393i	−0.0974927	+	0.0842244i
$396$		0			0
$397$	22.1781	+	22.1781i	1.11309	+	1.11309i	0.992731	+	0.120357i	$0.0384039\pi$
$397$	22.1781	+	22.1781i	1.11309	+	1.11309i	0.120357	+	0.992731i	$0.461596\pi$
$398$		0			0
$399$	2.78235	+	3.82957i	0.139292	+	0.191718i
$400$		0			0
$401$	−3.08934	−	9.50802i	−0.154274	−	0.474808i	0.843812	−	0.536639i	$-0.180306\pi$
$401$	−3.08934	−	9.50802i	−0.154274	−	0.474808i	−0.998087	+	0.0618306i	$0.980306\pi$
$402$		0			0
$403$	1.41517	+	8.93502i	0.0704945	+	0.445085i
$404$		0			0
$405$	−9.55773	−	22.7104i	−0.474927	−	1.12849i
$406$		0			0
$407$	−9.84737	−	4.03719i	−0.488116	−	0.200116i
$408$		0			0
$409$	−9.39140	+	28.9037i	−0.464375	+	1.42920i	0.395393	+	0.918512i	$0.370609\pi$
$409$	−9.39140	+	28.9037i	−0.464375	+	1.42920i	−0.859767	+	0.510686i	$0.829391\pi$
$410$		0			0
$411$	25.1026	+	18.2381i	1.23822	+	0.899619i
$412$		0			0
$413$	−10.1682	+	19.9562i	−0.500344	+	0.981981i
$414$		0			0
$415$	19.8824	−	12.3391i	0.975987	−	0.605701i
$416$		0			0
$417$	2.01695	−	2.01695i	0.0987706	−	0.0987706i
$418$		0			0
$419$			7.48185i			0.365512i	0.983158	+	0.182756i	$0.0585019\pi$
$419$			7.48185i			0.365512i	−0.983158	+	0.182756i	$0.941498\pi$
$420$		0			0
$421$	−16.5226	+	12.0043i	−0.805260	+	0.585056i	−0.912453	−	0.409182i	$-0.865814\pi$
$421$	−16.5226	+	12.0043i	−0.805260	+	0.585056i	0.107192	+	0.994238i	$0.465814\pi$
$422$		0			0
$423$	−7.01654	−	3.57511i	−0.341156	−	0.173828i
$424$		0			0
$425$	0.190165	+	16.8191i	0.00922437	+	0.815847i
$426$		0			0
$427$	−14.9981	+	7.64189i	−0.725807	+	0.369817i
$428$		0			0
$429$	14.5980	+	3.44879i	0.704797	+	0.166509i
$430$		0			0
$431$	32.0182	+	10.4034i	1.54226	+	0.501112i	0.952000	−	0.306098i	$-0.0990236\pi$
$431$	32.0182	+	10.4034i	1.54226	+	0.501112i	0.590264	+	0.807210i	$0.299024\pi$
$432$		0			0
$433$	11.4564	−	1.81451i	0.550557	−	0.0871997i	0.125043	−	0.992151i	$-0.460093\pi$
$433$	11.4564	−	1.81451i	0.550557	−	0.0871997i	0.425514	+	0.904952i	$0.360093\pi$
$434$		0			0
$435$	12.7833	−	3.14553i	0.612911	−	0.150816i
$436$		0			0
$437$	0.914330	−	5.77285i	0.0437383	−	0.276153i
$438$		0			0
$439$	10.7242			0.511837			0.255918	−	0.966698i	$-0.417622\pi$
$439$	10.7242			0.511837			0.255918	+	0.966698i	$0.417622\pi$
$440$		0			0
$441$	3.80411			0.181148
$442$		0			0
$443$	6.30958	−	39.8371i	0.299777	−	1.89272i	−0.132835	−	0.991138i	$-0.542408\pi$
$443$	6.30958	−	39.8371i	0.299777	−	1.89272i	0.432612	−	0.901580i	$-0.357592\pi$
$444$		0			0
$445$	−4.46515	+	7.37979i	−0.211669	+	0.349836i
$446$		0			0
$447$	47.1388	−	7.46605i	2.22959	−	0.353132i
$448$		0			0
$449$	3.46337	+	1.12532i	0.163447	+	0.0531070i	0.389597	−	0.920985i	$-0.372614\pi$
$449$	3.46337	+	1.12532i	0.163447	+	0.0531070i	−0.226151	+	0.974092i	$0.572614\pi$
$450$		0			0
$451$	−4.30925	+	0.354856i	−0.202915	+	0.0167095i
$452$		0			0
$453$	−25.6988	+	13.0942i	−1.20744	+	0.615220i
$454$		0			0
$455$	−9.08757	+	0.766921i	−0.426032	+	0.0359538i
$456$		0			0
$457$	−16.1207	−	8.21391i	−0.754094	−	0.384230i	0.0342910	−	0.999412i	$-0.489083\pi$
$457$	−16.1207	−	8.21391i	−0.754094	−	0.384230i	−0.788385	+	0.615182i	$0.789083\pi$
$458$		0			0
$459$	−10.8060	+	7.85105i	−0.504383	+	0.366456i
$460$		0			0
$461$		−	35.5884i		−	1.65751i	−0.559608	−	0.828757i	$-0.689048\pi$
$461$		−	35.5884i		−	1.65751i	0.559608	−	0.828757i	$-0.310952\pi$
$462$		0			0
$463$	4.46802	−	4.46802i	0.207647	−	0.207647i	−0.595620	−	0.803266i	$-0.703093\pi$
$463$	4.46802	−	4.46802i	0.207647	−	0.207647i	0.803266	+	0.595620i	$0.203093\pi$
$464$		0			0
$465$	9.48019	+	15.2757i	0.439633	+	0.708396i
$466$		0			0
$467$	−3.92827	+	7.70967i	−0.181779	+	0.356761i	−0.963857	−	0.266419i	$-0.914160\pi$
$467$	−3.92827	+	7.70967i	−0.181779	+	0.356761i	0.782079	+	0.623180i	$0.214160\pi$
$468$		0			0
$469$	5.09363	+	3.70074i	0.235202	+	0.170884i
$470$		0			0
$471$	−8.36006	+	25.7296i	−0.385211	+	1.18556i
$472$		0			0
$473$	20.7532	−	5.06198i	0.954233	−	0.232750i
$474$		0			0
$475$	5.85082	+	2.89829i	0.268454	+	0.132983i
$476$		0			0
$477$	1.01584	+	6.41374i	0.0465120	+	0.293665i
$478$		0			0
$479$	−4.75378	−	14.6306i	−0.217206	−	0.668490i	−0.998990	−	0.0449410i	$-0.985690\pi$
$479$	−4.75378	−	14.6306i	−0.217206	−	0.668490i	0.781784	−	0.623549i	$-0.214310\pi$
$480$		0			0
$481$	−4.25480	−	5.85623i	−0.194002	−	0.267021i
$482$		0			0
$483$	11.4723	+	11.4723i	0.522008	+	0.522008i
$484$		0			0
$485$	−1.73516	−	0.126694i	−0.0787894	−	0.00575290i
$486$		0			0
$487$	5.87316	+	0.930218i	0.266138	+	0.0421522i	0.288077	−	0.957607i	$-0.406984\pi$
$487$	5.87316	+	0.930218i	0.266138	+	0.0421522i	−0.0219390	+	0.999759i	$0.506984\pi$
$488$		0			0
$489$	−2.04636	+	0.664903i	−0.0925396	+	0.0300679i
$490$		0			0
$491$	−24.0702	+	33.1298i	−1.08627	+	1.49513i	−0.233851	+	0.972272i	$0.575133\pi$
$491$	−24.0702	+	33.1298i	−1.08627	+	1.49513i	−0.852422	+	0.522855i	$0.824867\pi$
$492$		0			0
$493$	−4.48477	−	8.80185i	−0.201984	−	0.396415i
$494$		0			0
$495$	7.45701	−	1.25208i	0.335168	−	0.0562769i
$496$		0			0
$497$	5.55801	+	10.9082i	0.249311	+	0.489300i
$498$		0			0
$499$	−13.6289	+	18.7585i	−0.610111	+	0.839746i	−0.996587	−	0.0825534i	$-0.973692\pi$
$499$	−13.6289	+	18.7585i	−0.610111	+	0.839746i	0.386475	+	0.922300i	$0.373692\pi$
$500$		0			0
$501$	−3.60727	+	1.17207i	−0.161161	+	0.0523644i
$502$		0			0
$503$	3.30226	+	0.523026i	0.147240	+	0.0233206i	0.229619	−	0.973280i	$-0.426252\pi$
$503$	3.30226	+	0.523026i	0.147240	+	0.0233206i	−0.0823791	+	0.996601i	$0.526252\pi$
$504$		0			0
$505$	14.2784	+	16.5277i	0.635379	+	0.735473i
$506$		0			0
$507$	−11.2157	−	11.2157i	−0.498108	−	0.498108i
$508$		0			0
$509$	−13.0172	−	17.9166i	−0.576977	−	0.794141i	0.416383	−	0.909189i	$-0.363298\pi$
$509$	−13.0172	−	17.9166i	−0.576977	−	0.794141i	−0.993360	+	0.115049i	$0.963298\pi$
$510$		0			0
$511$	−5.27640	−	16.2391i	−0.233414	−	0.718375i
$512$		0			0
$513$	0.811108	+	5.12114i	0.0358113	+	0.226104i
$514$		0			0
$515$	−9.67385	−	3.94312i	−0.426281	−	0.173755i
$516$		0			0
$517$	−16.5658	+	19.5390i	−0.728565	+	0.859323i
$518$		0			0
$519$	−11.7387	+	36.1280i	−0.515272	+	1.58584i
$520$		0			0
$521$	8.59679	+	6.24594i	0.376632	+	0.273639i	0.759956	−	0.649975i	$-0.225221\pi$
$521$	8.59679	+	6.24594i	0.376632	+	0.273639i	−0.383323	+	0.923614i	$0.625221\pi$
$522$		0			0
$523$	−19.6244	+	38.5151i	−0.858116	+	1.68415i	−0.137847	+	0.990454i	$0.544018\pi$
$523$	−19.6244	+	38.5151i	−0.858116	+	1.68415i	−0.720269	+	0.693694i	$0.755982\pi$
$524$		0			0
$525$	−16.0549	+	8.41036i	−0.700694	+	0.367058i
$526$		0			0
$527$	9.53941	−	9.53941i	0.415543	−	0.415543i
$528$		0			0
$529$			2.96712i			0.129005i
$530$		0			0
$531$	10.2181	−	7.42391i	0.443429	−	0.322170i
$532$		0			0
$533$	−2.62032	−	1.33512i	−0.113499	−	0.0578304i
$534$		0			0
$535$	22.0739	−	26.1430i	0.954338	−	1.13026i
$536$		0			0
$537$	−29.2658	+	14.9117i	−1.26291	+	0.643487i
$538$		0			0
$539$	2.84517	−	12.0430i	0.122550	−	0.518728i
$540$		0			0
$541$	−20.0780	−	6.52373i	−0.863220	−	0.280477i	−0.156247	−	0.987718i	$-0.549940\pi$
$541$	−20.0780	−	6.52373i	−0.863220	−	0.280477i	−0.706973	+	0.707241i	$0.749940\pi$
$542$		0			0
$543$	−29.4327	+	4.66168i	−1.26308	+	0.200052i
$544$		0			0
$545$	34.2140	+	20.7012i	1.46557	+	0.886744i
$546$		0			0
$547$	−0.218056	+	1.37675i	−0.00932342	+	0.0588658i	−0.991911	−	0.126932i	$-0.959487\pi$
$547$	−0.218056	+	1.37675i	−0.00932342	+	0.0588658i	0.982588	+	0.185798i	$0.0594870\pi$
$548$		0			0
$549$	9.49230			0.405121
$550$		0			0
$551$	−3.83469			−0.163363
$552$		0			0
$553$	−0.323881	+	2.04490i	−0.0137728	+	0.0869581i
$554$		0			0
$555$	−12.3083	−	7.44713i	−0.522456	−	0.316113i
$556$		0			0
$557$	−3.78516	+	0.599510i	−0.160382	+	0.0254021i	−0.236109	−	0.971727i	$-0.575872\pi$
$557$	−3.78516	+	0.599510i	−0.160382	+	0.0254021i	0.0757269	+	0.997129i	$0.475872\pi$
$558$		0			0
$559$	13.8180	+	4.48973i	0.584438	+	0.189895i
$560$		0			0
$561$	−8.63507	−	20.6352i	−0.364573	−	0.871218i
$562$		0			0
$563$	2.17596	−	1.10871i	0.0917058	−	0.0467264i	−0.407536	−	0.913189i	$-0.633612\pi$
$563$	2.17596	−	1.10871i	0.0917058	−	0.0467264i	0.499242	+	0.866463i	$0.333612\pi$
$564$		0			0
$565$	10.7754	−	12.7617i	0.453324	−	0.536891i
$566$		0			0
$567$	−17.7515	−	9.04483i	−0.745492	−	0.379847i
$568$		0			0
$569$	−5.21403	+	3.78822i	−0.218584	+	0.158810i	−0.691689	−	0.722196i	$-0.743133\pi$
$569$	−5.21403	+	3.78822i	−0.218584	+	0.158810i	0.473105	+	0.881006i	$0.343133\pi$
$570$		0			0
$571$			13.2864i			0.556019i	0.960578	+	0.278009i	$0.0896747\pi$
$571$			13.2864i			0.556019i	−0.960578	+	0.278009i	$0.910325\pi$
$572$		0			0
$573$	2.70715	−	2.70715i	0.113093	−	0.113093i
$574$		0			0
$575$	21.3606	+	6.67444i	0.890797	+	0.278343i
$576$		0			0
$577$	−8.50263	+	16.6874i	−0.353969	+	0.694704i	−0.997496	−	0.0707197i	$-0.977470\pi$
$577$	−8.50263	+	16.6874i	−0.353969	+	0.694704i	0.643527	+	0.765423i	$0.277470\pi$
$578$		0			0
$579$	18.4630	+	13.4141i	0.767295	+	0.557473i
$580$		0			0
$581$	5.84679	−	17.9946i	0.242566	−	0.746540i
$582$		0			0
$583$	21.0643	+	1.58105i	0.872395	+	0.0654803i
$584$		0			0
$585$	4.76244	+	1.94120i	0.196903	+	0.0802588i
$586$		0			0
$587$	1.31860	+	8.32531i	0.0544244	+	0.343622i	0.999842	+	0.0177617i	$0.00565403\pi$
$587$	1.31860	+	8.32531i	0.0544244	+	0.343622i	−0.945418	+	0.325861i	$0.894346\pi$
$588$		0			0
$589$	−1.61829	−	4.98059i	−0.0666805	−	0.205221i
$590$		0			0
$591$	23.0140	+	31.6760i	0.946669	+	1.30298i
$592$		0			0
$593$	4.37233	+	4.37233i	0.179550	+	0.179550i	0.791160	−	0.611610i	$-0.209478\pi$
$593$	4.37233	+	4.37233i	0.179550	+	0.179550i	−0.611610	+	0.791160i	$0.709478\pi$
$594$		0			0
$595$	8.89103	+	10.2917i	0.364497	+	0.421918i
$596$		0			0
$597$	44.2592	+	7.00996i	1.81141	+	0.286899i
$598$		0			0
$599$	−34.7989	+	11.3068i	−1.42184	+	0.461985i	−0.916187	−	0.400750i	$-0.868750\pi$
$599$	−34.7989	+	11.3068i	−1.42184	+	0.461985i	−0.505656	+	0.862735i	$0.668750\pi$
$600$		0			0
$601$	6.33088	−	8.71371i	0.258242	−	0.355440i	−0.660134	−	0.751147i	$-0.729501\pi$
$601$	6.33088	−	8.71371i	0.258242	−	0.355440i	0.918376	+	0.395708i	$0.129501\pi$
$602$		0			0
$603$	−1.61188	−	3.16350i	−0.0656410	−	0.128828i
$604$		0			0
$605$	1.61343	−	24.5438i	0.0655952	−	0.997846i
$606$		0			0
$607$	−15.0249	−	29.4880i	−0.609842	−	1.19688i	−0.965043	−	0.262092i	$-0.915588\pi$
$607$	−15.0249	−	29.4880i	−0.609842	−	1.19688i	0.355201	−	0.934790i	$-0.384412\pi$
$608$		0			0
$609$	6.25669	−	8.61159i	0.253534	−	0.348959i
$610$		0			0
$611$	−16.5702	+	5.38398i	−0.670359	+	0.217813i
$612$		0			0
$613$	−21.3721	−	3.38501i	−0.863213	−	0.136719i	−0.290898	−	0.956754i	$-0.593954\pi$
$613$	−21.3721	−	3.38501i	−0.863213	−	0.136719i	−0.572314	+	0.820034i	$0.693954\pi$
$614$		0			0
$615$	−5.82899	−	0.425611i	−0.235048	−	0.0171623i
$616$		0			0
$617$	−23.2611	−	23.2611i	−0.936455	−	0.936455i	0.0616431	−	0.998098i	$-0.480366\pi$
$617$	−23.2611	−	23.2611i	−0.936455	−	0.936455i	−0.998098	+	0.0616431i	$0.980366\pi$
$618$		0			0
$619$	−24.3484	−	33.5126i	−0.978643	−	1.34699i	−0.937557	−	0.347831i	$-0.886918\pi$
$619$	−24.3484	−	33.5126i	−0.978643	−	1.34699i	−0.0410856	−	0.999156i	$-0.513082\pi$
$620$		0			0
$621$	5.49164	+	16.9015i	0.220372	+	0.678235i
$622$		0			0
$623$	1.09102	+	6.88845i	0.0437109	+	0.275980i
$624$		0			0
$625$	−14.2336	+	20.5525i	−0.569343	+	0.822100i
$626$		0			0
$627$	−8.65895	−	0.649924i	−0.345805	−	0.0259555i
$628$		0			0
$629$	−3.33583	+	10.2666i	−0.133008	+	0.409357i
$630$		0			0
$631$	−25.4513	−	18.4915i	−1.01320	−	0.736134i	−0.0483238	−	0.998832i	$-0.515388\pi$
$631$	−25.4513	−	18.4915i	−1.01320	−	0.736134i	−0.964878	+	0.262697i	$0.915388\pi$
$632$		0			0
$633$	−0.342729	+	0.672644i	−0.0136223	+	0.0267352i
$634$		0			0
$635$	0.243118	+	0.391744i	0.00964783	+	0.0155459i
$636$		0			0
$637$	5.95137	−	5.95137i	0.235802	−	0.235802i
$638$		0			0
$639$		−	6.90382i		−	0.273111i
$640$		0			0
$641$	−16.6022	+	12.0622i	−0.655749	+	0.476430i	−0.865225	−	0.501384i	$-0.832824\pi$
$641$	−16.6022	+	12.0622i	−0.655749	+	0.476430i	0.209476	+	0.977814i	$0.432824\pi$
$642$		0			0
$643$	−15.7020	−	8.00058i	−0.619228	−	0.315512i	0.116086	−	0.993239i	$-0.462965\pi$
$643$	−15.7020	−	8.00058i	−0.619228	−	0.315512i	−0.735314	+	0.677727i	$0.762965\pi$
$644$		0			0
$645$	28.7721	−	2.42815i	1.13290	−	0.0956082i
$646$		0			0
$647$	−5.13354	+	2.61567i	−0.201820	+	0.102833i	−0.551980	−	0.833857i	$-0.686127\pi$
$647$	−5.13354	+	2.61567i	−0.201820	+	0.102833i	0.350159	+	0.936690i	$0.386127\pi$
$648$		0			0
$649$	−15.8602	−	37.9010i	−0.622566	−	1.48774i
$650$		0			0
$651$	13.8253	+	4.49212i	0.541858	+	0.176060i
$652$		0			0
$653$	5.76236	−	0.912669i	0.225499	−	0.0357155i	−0.0426625	−	0.999090i	$-0.513584\pi$
$653$	5.76236	−	0.912669i	0.225499	−	0.0357155i	0.268161	+	0.963374i	$0.413584\pi$
$654$		0			0
$655$	0.638627	−	1.05549i	0.0249532	−	0.0412415i
$656$		0			0
$657$	−1.50628	+	9.51025i	−0.0587654	+	0.371030i
$658$		0			0
$659$	5.21347			0.203088			0.101544	−	0.994831i	$-0.467622\pi$
$659$	5.21347			0.203088			0.101544	+	0.994831i	$0.467622\pi$
$660$		0			0
$661$	4.56016			0.177369			0.0886847	−	0.996060i	$-0.471734\pi$
$661$	4.56016			0.177369			0.0886847	+	0.996060i	$0.471734\pi$
$662$		0			0
$663$	2.38004	−	15.0270i	0.0924330	−	0.583599i
$664$		0			0
$665$	5.12651	−	1.26146i	0.198798	−	0.0489173i
$666$		0			0
$667$	−12.9815	+	2.05606i	−0.502644	+	0.0796110i
$668$		0			0
$669$	−14.5093	−	4.71435i	−0.560962	−	0.182267i
$670$		0			0
$671$	7.09949	−	30.0506i	0.274073	−	1.16009i
$672$		0			0
$673$	−0.498417	+	0.253956i	−0.0192126	+	0.00978930i	−0.463570	−	0.886060i	$-0.653432\pi$
$673$	−0.498417	+	0.253956i	−0.0192126	+	0.00978930i	0.444358	+	0.895849i	$0.353432\pi$
$674$		0			0
$675$	−19.8514	+	0.224449i	−0.764079	+	0.00863905i
$676$		0			0
$677$	−25.9390	−	13.2166i	−0.996918	−	0.507955i	−0.122157	−	0.992511i	$-0.538981\pi$
$677$	−25.9390	−	13.2166i	−0.996918	−	0.507955i	−0.874760	+	0.484556i	$0.838981\pi$
$678$		0			0
$679$	−1.13807	+	0.826858i	−0.0436752	+	0.0317319i
$680$		0			0
$681$			16.4454i			0.630190i
$682$		0			0
$683$	−5.43554	+	5.43554i	−0.207985	+	0.207985i	−0.803411	−	0.595425i	$-0.796984\pi$
$683$	−5.43554	+	5.43554i	−0.207985	+	0.207985i	0.595425	+	0.803411i	$0.296984\pi$
$684$		0			0
$685$	29.4041	−	18.2483i	1.12347	−	0.697231i
$686$		0			0
$687$	−6.90765	+	13.5570i	−0.263543	+	0.517233i
$688$		0			0
$689$	11.6233	+	8.44481i	0.442812	+	0.321722i
$690$		0			0
$691$	2.91716	−	8.97809i	0.110974	−	0.341542i	−0.880112	−	0.474766i	$-0.842533\pi$
$691$	2.91716	−	8.97809i	0.110974	−	0.341542i	0.991086	+	0.133223i	$0.0425328\pi$
$692$		0			0
$693$	3.95382	−	4.66342i	0.150193	−	0.177149i
$694$		0			0
$695$	−1.23403	−	2.93222i	−0.0468094	−	0.111225i
$696$		0			0
$697$	0.686067	+	4.33166i	0.0259866	+	0.164073i
$698$		0			0
$699$	−16.2427	−	49.9899i	−0.614356	−	1.89079i
$700$		0			0
$701$	−11.5843	−	15.9445i	−0.437535	−	0.602215i	0.532127	−	0.846664i	$-0.321393\pi$
$701$	−11.5843	−	15.9445i	−0.437535	−	0.602215i	−0.969662	+	0.244449i	$0.921393\pi$
$702$		0			0
$703$	2.96308	+	2.96308i	0.111755	+	0.111755i
$704$		0			0
$705$	−26.2019	+	22.6360i	−0.986822	+	0.852520i
$706$		0			0
$707$	17.4427	+	2.76266i	0.656001	+	0.103900i
$708$		0			0
$709$	−42.2836	+	13.7388i	−1.58799	+	0.515970i	−0.964100	−	0.265540i	$-0.914450\pi$
$709$	−42.2836	+	13.7388i	−1.58799	+	0.515970i	−0.623893	+	0.781510i	$0.714450\pi$
$710$		0			0
$711$	0.686259	−	0.944555i	0.0257367	−	0.0354236i
$712$		0			0
$713$	−8.14881	−	15.9929i	−0.305175	−	0.598940i
$714$		0			0
$715$	9.70736	−	13.6250i	0.363035	−	0.509547i
$716$		0			0
$717$	2.07163	+	4.06580i	0.0773664	+	0.151840i
$718$		0			0
$719$	14.1002	−	19.4073i	0.525850	−	0.723770i	−0.460641	−	0.887587i	$-0.652380\pi$
$719$	14.1002	−	19.4073i	0.525850	−	0.723770i	0.986491	+	0.163816i	$0.0523804\pi$
$720$		0			0
$721$	−8.03342	+	2.61022i	−0.299180	+	0.0972095i
$722$		0			0
$723$	12.4660	+	1.97442i	0.463616	+	0.0734296i
$724$		0			0
$725$	2.13276	−	14.5268i	0.0792087	−	0.539513i
$726$		0			0
$727$	17.6187	+	17.6187i	0.653441	+	0.653441i	0.953820	−	0.300379i	$-0.0971131\pi$
$727$	17.6187	+	17.6187i	0.653441	+	0.653441i	−0.300379	+	0.953820i	$0.597113\pi$
$728$		0			0
$729$	−7.43339	−	10.2312i	−0.275311	−	0.378933i
$730$		0			0
$731$	−6.69547	−	20.6065i	−0.247641	−	0.762161i
$732$		0			0
$733$	−0.00846331	−	0.0534353i	−0.000312600	−	0.00197368i	0.987532	−	0.157421i	$-0.0503180\pi$
$733$	−0.00846331	−	0.0534353i	−0.000312600	−	0.00197368i	−0.987844	+	0.155448i	$0.950318\pi$
$734$		0			0
$735$	6.31353	−	15.4893i	0.232878	−	0.571331i
$736$		0			0
$737$	−11.2205	+	2.73683i	−0.413313	+	0.100813i
$738$		0			0
$739$	5.95011	−	18.3126i	0.218878	−	0.673638i	−0.779977	−	0.625808i	$-0.784769\pi$
$739$	5.95011	−	18.3126i	0.218878	−	0.673638i	0.998855	−	0.0478303i	$-0.0152307\pi$
$740$		0			0
$741$	−4.77800	−	3.47142i	−0.175524	−	0.127526i
$742$		0			0
$743$	3.38155	−	6.63666i	0.124057	−	0.243475i	−0.820622	−	0.571471i	$-0.806373\pi$
$743$	3.38155	−	6.63666i	0.124057	−	0.243475i	0.944679	+	0.327995i	$0.106373\pi$
$744$		0			0
$745$	12.1334	−	51.8283i	0.444534	−	1.89884i
$746$		0			0
$747$	−7.54462	+	7.54462i	−0.276043	+	0.276043i
$748$		0			0
$749$		−	27.6659i		−	1.01089i
$750$		0			0
$751$	−24.3907	+	17.7209i	−0.890031	+	0.646645i	−0.935886	−	0.352303i	$-0.885399\pi$
$751$	−24.3907	+	17.7209i	−0.890031	+	0.646645i	0.0458552	+	0.998948i	$0.485399\pi$
$752$		0			0
$753$	47.5082	+	24.2066i	1.73130	+	0.882139i
$754$		0			0
$755$	2.70514	+	32.0543i	0.0984500	+	1.16658i
$756$		0			0
$757$	39.6521	−	20.2037i	1.44118	−	0.734318i	0.453566	−	0.891223i	$-0.350152\pi$
$757$	39.6521	−	20.2037i	1.44118	−	0.734318i	0.987614	+	0.156905i	$0.0501516\pi$
$758$		0			0
$759$	−29.6613	+	2.44254i	−1.07664	+	0.0886584i
$760$		0			0
$761$	44.8060	+	14.5584i	1.62422	+	0.527740i	0.972932	−	0.231093i	$-0.0742301\pi$
$761$	44.8060	+	14.5584i	1.62422	+	0.527740i	0.651285	+	0.758833i	$0.274230\pi$
$762$		0			0
$763$	31.9361	−	5.05818i	1.15616	−	0.183118i
$764$		0			0
$765$	−1.83254	−	7.44735i	−0.0662555	−	0.269259i
$766$		0			0
$767$	4.37145	−	27.6003i	0.157844	−	0.996588i
$768$		0			0
$769$	29.7849			1.07407			0.537036	−	0.843559i	$-0.319544\pi$
$769$	29.7849			1.07407			0.537036	+	0.843559i	$0.319544\pi$
$770$		0			0
$771$	−39.6451			−1.42778
$772$		0			0
$773$	−1.11434	+	7.03566i	−0.0400800	+	0.253055i	−0.999590	−	0.0286180i	$-0.990889\pi$
$773$	−1.11434	+	7.03566i	−0.0400800	+	0.253055i	0.959510	+	0.281673i	$0.0908894\pi$
$774$		0			0
$775$	19.7678	−	3.36044i	0.710082	−	0.120711i
$776$		0			0
$777$	−11.4888	+	1.81965i	−0.412158	+	0.0652794i
$778$		0			0
$779$	1.61912	+	0.526083i	0.0580108	+	0.0188489i
$780$		0			0
$781$	−21.8560	−	5.16351i	−0.782070	−	0.184765i
$782$		0			0
$783$	10.3887	−	5.29330i	0.371261	−	0.189167i
$784$		0			0
$785$	23.0543	+	19.4659i	0.822844	+	0.694769i
$786$		0			0
$787$	25.7117	+	13.1008i	0.916524	+	0.466992i	0.847604	−	0.530630i	$-0.178045\pi$
$787$	25.7117	+	13.1008i	0.916524	+	0.466992i	0.0689202	+	0.997622i	$0.478045\pi$
$788$		0			0
$789$	−13.5737	+	9.86191i	−0.483238	+	0.351093i
$790$		0			0
$791$		−	13.5051i		−	0.480187i
$792$		0			0
$793$	14.8503	−	14.8503i	0.527350	−	0.527350i
$794$		0			0
$795$	27.8010	+	6.50843i	0.985999	+	0.230830i
$796$		0			0
$797$	14.0459	−	27.5666i	0.497531	−	0.976460i	−0.496569	−	0.867997i	$-0.665407\pi$
$797$	14.0459	−	27.5666i	0.497531	−	0.976460i	0.994100	−	0.108463i	$-0.0345930\pi$
$798$		0			0
$799$	21.0204	+	15.2722i	0.743647	+	0.540291i
$800$		0			0
$801$	1.21535	−	3.74046i	0.0429423	−	0.132163i
$802$		0			0
$803$	28.9809	+	11.8815i	1.02271	+	0.419288i
$804$		0			0
$805$	16.6783	−	7.01908i	0.587831	−	0.247390i
$806$		0			0
$807$	−3.04559	−	19.2291i	−0.107210	−	0.676897i
$808$		0			0
$809$	6.07857	+	18.7079i	0.213711	+	0.657735i	0.999243	+	0.0389136i	$0.0123897\pi$
$809$	6.07857	+	18.7079i	0.213711	+	0.657735i	−0.785531	+	0.618822i	$0.787610\pi$
$810$		0			0
$811$	−24.8398	−	34.1891i	−0.872243	−	1.20054i	−0.978509	−	0.206202i	$-0.933890\pi$
$811$	−24.8398	−	34.1891i	−0.872243	−	1.20054i	0.106266	−	0.994338i	$-0.466110\pi$
$812$		0			0
$813$	−4.32597	−	4.32597i	−0.151718	−	0.151718i
$814$		0			0
$815$	−0.174757	+	2.39340i	−0.00612147	+	0.0838373i
$816$		0			0
$817$	−8.30723	−	1.31574i	−0.290633	−	0.0460318i
$818$		0			0
$819$	3.95486	−	1.28501i	0.138194	−	0.0449019i
$820$		0			0
$821$	−31.2544	+	43.0180i	−1.09079	+	1.50134i	−0.243726	+	0.969844i	$0.578370\pi$
$821$	−31.2544	+	43.0180i	−1.09079	+	1.50134i	−0.847061	+	0.531496i	$0.821630\pi$
$822$		0			0
$823$	−0.635792	−	1.24781i	−0.0221623	−	0.0434960i	0.879660	−	0.475603i	$-0.157770\pi$
$823$	−0.635792	−	1.24781i	−0.0221623	−	0.0434960i	−0.901822	+	0.432107i	$0.857770\pi$
$824$		0			0
$825$	7.27797	−	32.4409i	0.253387	−	1.12945i
$826$		0			0
$827$	7.84783	+	15.4022i	0.272896	+	0.535588i	0.986259	−	0.165206i	$-0.0528290\pi$
$827$	7.84783	+	15.4022i	0.272896	+	0.535588i	−0.713363	+	0.700794i	$0.752829\pi$
$828$		0			0
$829$	21.0969	−	29.0374i	0.732727	−	1.00851i	−0.266277	−	0.963897i	$-0.585794\pi$
$829$	21.0969	−	29.0374i	0.732727	−	1.00851i	0.999004	−	0.0446158i	$-0.0142064\pi$
$830$		0			0
$831$	4.53838	−	1.47461i	0.157435	−	0.0511536i
$832$		0			0
$833$	−12.3969	−	1.96348i	−0.429527	−	0.0680304i
$834$		0			0
$835$	−0.308058	+	4.21903i	−0.0106608	+	0.146006i
$836$		0			0
$837$	11.2592	+	11.2592i	0.389176	+	0.389176i
$838$		0			0
$839$	−2.91587	−	4.01335i	−0.100667	−	0.138556i	0.755712	−	0.654904i	$-0.227291\pi$
$839$	−2.91587	−	4.01335i	−0.100667	−	0.138556i	−0.856379	+	0.516348i	$0.827291\pi$
$840$		0			0
$841$	−6.29681	−	19.3796i	−0.217131	−	0.668261i
$842$		0			0
$843$	8.85453	+	55.9053i	0.304966	+	1.92548i
$844$		0			0
$845$	−16.3053	+	6.86210i	−0.560918	+	0.236063i
$846$		0			0
$847$	−11.8063	−	16.0048i	−0.405668	−	0.549932i
$848$		0			0
$849$	10.5406	−	32.4406i	0.361752	−	1.11336i
$850$		0			0
$851$	11.6196	+	8.44211i	0.398313	+	0.289392i
$852$		0			0
$853$	−12.0658	+	23.6804i	−0.413125	+	0.810803i	0.586875	+	0.809678i	$0.300358\pi$
$853$	−12.0658	+	23.6804i	−0.413125	+	0.810803i	−0.999999	+	0.00112492i	$0.999642\pi$
$854$		0			0
$855$	−2.89880	−	0.678632i	−0.0991368	−	0.0232087i
$856$		0			0
$857$	−1.04396	+	1.04396i	−0.0356609	+	0.0356609i	−0.724712	−	0.689051i	$-0.758027\pi$
$857$	−1.04396	+	1.04396i	−0.0356609	+	0.0356609i	0.689051	+	0.724712i	$0.258027\pi$
$858$		0			0
$859$		−	13.9402i		−	0.475633i	−0.971310	−	0.237816i	$-0.923568\pi$
$859$		−	13.9402i		−	0.475633i	0.971310	−	0.237816i	$-0.0764316\pi$
$860$		0			0
$861$	−3.82318	+	2.77770i	−0.130294	+	0.0946638i
$862$		0			0
$863$	45.7166	+	23.2938i	1.55621	+	0.792929i	0.999291	−	0.0376382i	$-0.0119834\pi$
$863$	45.7166	+	23.2938i	1.55621	+	0.792929i	0.556919	+	0.830567i	$0.311983\pi$
$864$		0			0
$865$	32.3715	+	27.3329i	1.10066	+	0.929347i
$866$		0			0
$867$	10.1524	−	5.17288i	0.344792	−	0.175680i
$868$		0			0
$869$	−2.47699	−	2.87900i	−0.0840262	−	0.0976635i
$870$		0			0
$871$	−7.47089	−	2.42744i	−0.253141	−	0.0822507i
$872$		0			0
$873$	0.783518	−	0.124097i	0.0265181	−	0.00420005i
$874$		0			0
$875$	1.92751	+	20.1222i	0.0651617	+	0.680254i
$876$		0			0
$877$	1.04392	−	6.59105i	0.0352507	−	0.222564i	−0.963774	−	0.266720i	$-0.914060\pi$
$877$	1.04392	−	6.59105i	0.0352507	−	0.222564i	0.999025	+	0.0441563i	$0.0140600\pi$
$878$		0			0
$879$	21.4220			0.722546
$880$		0			0
$881$	−14.4573			−0.487080			−0.243540	−	0.969891i	$-0.578309\pi$
$881$	−14.4573			−0.487080			−0.243540	+	0.969891i	$0.578309\pi$
$882$		0			0
$883$	1.63650	−	10.3324i	0.0550725	−	0.347714i	−0.944730	−	0.327849i	$-0.893676\pi$
$883$	1.63650	−	10.3324i	0.0550725	−	0.347714i	0.999803	−	0.0198651i	$-0.00632367\pi$
$884$		0			0
$885$	−13.2695	−	53.9267i	−0.446050	−	1.81272i
$886$		0			0
$887$	−9.76140	+	1.54605i	−0.327756	+	0.0519114i	−0.318144	−	0.948042i	$-0.603060\pi$
$887$	−9.76140	+	1.54605i	−0.327756	+	0.0519114i	−0.00961170	+	0.999954i	$0.503060\pi$
$888$		0			0
$889$	0.354548	+	0.115200i	0.0118912	+	0.00386368i
$890$		0			0
$891$	33.7137	−	14.1080i	1.12945	−	0.472635i
$892$		0			0
$893$	8.98671	−	4.57896i	0.300729	−	0.153229i
$894$		0			0
$895$	3.08061	+	36.5034i	0.102973	+	1.22018i
$896$		0			0
$897$	−18.0361	−	9.18986i	−0.602208	−	0.306840i
$898$		0			0
$899$	−9.52719	+	6.92191i	−0.317750	+	0.230859i
$900$		0			0
$901$		−	21.4256i		−	0.713789i
$902$		0			0
$903$	16.5088	−	16.5088i	0.549380	−	0.549380i
$904$		0			0
$905$	−7.57591	+	32.3607i	−0.251832	+	1.07571i
$906$		0			0
$907$	−5.25319	+	10.3100i	−0.174429	+	0.342337i	−0.961625	−	0.274366i	$-0.911532\pi$
$907$	−5.25319	+	10.3100i	−0.174429	+	0.342337i	0.787196	+	0.616703i	$0.211532\pi$
$908$		0			0
$909$	−8.05692	−	5.85370i	−0.267231	−	0.194155i
$910$		0			0
$911$	2.69510	−	8.29465i	0.0892925	−	0.274814i	−0.896432	−	0.443182i	$-0.853850\pi$
$911$	2.69510	−	8.29465i	0.0892925	−	0.274814i	0.985724	+	0.168368i	$0.0538496\pi$
$912$		0			0
$913$	18.2419	+	29.5274i	0.603718	+	0.977215i
$914$		0			0
$915$	15.7540	−	38.6500i	0.520811	−	1.27773i
$916$		0			0
$917$	−0.156043	−	0.985219i	−0.00515301	−	0.0325348i
$918$		0			0
$919$	−1.78507	−	5.49388i	−0.0588840	−	0.181226i	0.917288	−	0.398224i	$-0.130373\pi$
$919$	−1.78507	−	5.49388i	−0.0588840	−	0.181226i	−0.976172	+	0.216998i	$0.930373\pi$
$920$		0			0
$921$	38.3182	+	52.7405i	1.26263	+	1.73786i
$922$		0			0
$923$	−10.8007	−	10.8007i	−0.355511	−	0.355511i
$924$		0			0
$925$	−12.8729	+	9.57696i	−0.423260	+	0.314889i
$926$		0			0
$927$	4.70469	+	0.745150i	0.154522	+	0.0244739i
$928$		0			0
$929$	−17.2514	+	5.60532i	−0.566000	+	0.183905i	−0.578019	−	0.816023i	$-0.696174\pi$
$929$	−17.2514	+	5.60532i	−0.566000	+	0.183905i	0.0120191	+	0.999928i	$0.496174\pi$
$930$		0			0
$931$	−2.86384	+	3.94174i	−0.0938587	+	0.129185i
$932$		0			0
$933$	12.6414	+	24.8102i	0.413862	+	0.812251i
$934$		0			0
$935$	−24.9473	+	0.231399i	−0.815864	+	0.00756755i
$936$		0			0
$937$	−14.5907	−	28.6359i	−0.476659	−	0.935496i	−0.996686	−	0.0813459i	$-0.974078\pi$
$937$	−14.5907	−	28.6359i	−0.476659	−	0.935496i	0.520027	−	0.854150i	$-0.325922\pi$
$938$		0			0
$939$	20.4908	−	28.2032i	0.668692	−	0.920376i
$940$		0			0
$941$	−4.95612	+	1.61034i	−0.161565	+	0.0524956i	−0.388683	−	0.921372i	$-0.627070\pi$
$941$	−4.95612	+	1.61034i	−0.161565	+	0.0524956i	0.227118	+	0.973867i	$0.427070\pi$
$942$		0			0
$943$	5.76321	+	0.912803i	0.187676	+	0.0297250i
$944$		0			0
$945$	−12.1471	+	10.4940i	−0.395146	+	0.341368i
$946$		0			0
$947$	0.545091	+	0.545091i	0.0177131	+	0.0177131i	0.715908	−	0.698195i	$-0.246013\pi$
$947$	0.545091	+	0.545091i	0.0177131	+	0.0177131i	−0.698195	+	0.715908i	$0.746013\pi$
$948$		0			0
$949$	12.5219	+	17.2349i	0.406478	+	0.559469i
$950$		0			0
$951$	10.0100	+	30.8076i	0.324596	+	0.999004i
$952$		0			0
$953$	2.12456	+	13.4139i	0.0688211	+	0.434519i	0.997908	+	0.0646568i	$0.0205953\pi$
$953$	2.12456	+	13.4139i	0.0688211	+	0.434519i	−0.929086	+	0.369863i	$0.879405\pi$
$954$		0			0
$955$	−1.65631	−	3.93562i	−0.0535970	−	0.127354i
$956$		0			0
$957$	4.62705	+	18.9701i	0.149571	+	0.613216i
$958$		0			0
$959$	8.64682	−	26.6122i	0.279221	−	0.859352i
$960$		0			0
$961$	12.0686	+	8.76834i	0.389309	+	0.282850i
$962$		0			0
$963$	−7.08285	+	13.9009i	−0.228242	+	0.447950i
$964$		0			0
$965$	21.6267	−	13.4216i	0.696189	−	0.432057i
$966$		0			0
$967$	−28.7882	+	28.7882i	−0.925767	+	0.925767i	−0.997429	−	0.0716619i	$-0.977170\pi$
$967$	−28.7882	+	28.7882i	−0.925767	+	0.925767i	0.0716619	+	0.997429i	$0.477170\pi$
$968$		0			0
$969$			8.80745i			0.282936i
$970$		0			0
$971$	−23.7651	+	17.2663i	−0.762657	+	0.554103i	−0.899724	−	0.436459i	$-0.856232\pi$
$971$	−23.7651	+	17.2663i	−0.762657	+	0.554103i	0.137067	+	0.990562i	$0.456232\pi$
$972$		0			0
$973$	−2.29195	−	1.16781i	−0.0734765	−	0.0374382i
$974$		0			0
$975$	15.8081	−	16.1696i	0.506264	−	0.517843i
$976$		0			0
$977$	−20.8453	+	10.6212i	−0.666901	+	0.339803i	−0.754450	−	0.656357i	$-0.772096\pi$
$977$	−20.8453	+	10.6212i	−0.666901	+	0.339803i	0.0875496	+	0.996160i	$0.472096\pi$
$978$		0			0
$979$	−10.9325	−	6.64511i	−0.349405	−	0.212379i
$980$		0			0
$981$	−17.3414	−	5.63458i	−0.553670	−	0.179898i
$982$		0			0
$983$	20.6008	−	3.26285i	0.657064	−	0.104069i	0.181005	−	0.983482i	$-0.442065\pi$
$983$	20.6008	−	3.26285i	0.657064	−	0.104069i	0.476059	+	0.879413i	$0.342065\pi$
$984$		0			0
$985$	42.4036	−	10.4341i	1.35109	−	0.332457i
$986$		0			0
$987$	−4.37973	+	27.6526i	−0.139408	+	0.880190i
$988$		0			0
$989$	−28.8277			−0.916666
$990$		0			0
$991$	6.50787			0.206729			0.103365	−	0.994644i	$-0.467039\pi$
$991$	6.50787			0.206729			0.103365	+	0.994644i	$0.467039\pi$
$992$		0			0
$993$	4.60531	−	29.0768i	0.146145	−	0.922724i
$994$		0			0
$995$	25.8721	−	42.7601i	0.820200	−	1.35559i
$996$		0			0
$997$	26.0805	−	4.13075i	0.825978	−	0.130822i	0.270886	−	0.962611i	$-0.412683\pi$
$997$	26.0805	−	4.13075i	0.825978	−	0.130822i	0.555092	+	0.831789i	$0.312683\pi$
$998$		0			0
$999$	−12.1175	−	3.93723i	−0.383382	−	0.124568i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.cm.a.497.1		32
4.3	odd	2		55.2.l.a.2.1	✓	32
5.3	odd	4	inner	880.2.cm.a.673.1		32
11.6	odd	10	inner	880.2.cm.a.17.1		32
12.11	even	2		495.2.bj.a.442.4		32
20.3	even	4		55.2.l.a.13.1	yes	32
20.7	even	4		275.2.bm.b.68.4		32
20.19	odd	2		275.2.bm.b.57.4		32
44.3	odd	10		605.2.m.d.282.1		32
44.7	even	10		605.2.e.b.362.1		32
44.15	odd	10		605.2.e.b.362.16		32
44.19	even	10		605.2.m.c.282.4		32
44.27	odd	10		605.2.m.e.457.4		32
44.31	odd	10		605.2.m.c.602.1		32
44.35	even	10		605.2.m.d.602.4		32
44.39	even	10		55.2.l.a.17.1	yes	32
44.43	even	2		605.2.m.e.112.4		32
55.28	even	20	inner	880.2.cm.a.193.1		32
60.23	odd	4		495.2.bj.a.343.4		32
132.83	odd	10		495.2.bj.a.127.4		32
220.3	even	20		605.2.m.d.403.4		32
220.39	even	10		275.2.bm.b.182.4		32
220.43	odd	4		605.2.m.e.233.4		32
220.63	odd	20		605.2.m.c.403.1		32
220.83	odd	20		55.2.l.a.28.1	yes	32
220.103	even	20		605.2.e.b.483.1		32
220.123	odd	20		605.2.m.d.118.1		32
220.127	odd	20		275.2.bm.b.193.4		32
220.163	even	20		605.2.m.c.118.4		32
220.183	odd	20		605.2.e.b.483.16		32
220.203	even	20		605.2.m.e.578.4		32
660.83	even	20		495.2.bj.a.28.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.2.1	✓	32	4.3	odd	2
55.2.l.a.13.1	yes	32	20.3	even	4
55.2.l.a.17.1	yes	32	44.39	even	10
55.2.l.a.28.1	yes	32	220.83	odd	20
275.2.bm.b.57.4		32	20.19	odd	2
275.2.bm.b.68.4		32	20.7	even	4
275.2.bm.b.182.4		32	220.39	even	10
275.2.bm.b.193.4		32	220.127	odd	20
495.2.bj.a.28.4		32	660.83	even	20
495.2.bj.a.127.4		32	132.83	odd	10
495.2.bj.a.343.4		32	60.23	odd	4
495.2.bj.a.442.4		32	12.11	even	2
605.2.e.b.362.1		32	44.7	even	10
605.2.e.b.362.16		32	44.15	odd	10
605.2.e.b.483.1		32	220.103	even	20
605.2.e.b.483.16		32	220.183	odd	20
605.2.m.c.118.4		32	220.163	even	20
605.2.m.c.282.4		32	44.19	even	10
605.2.m.c.403.1		32	220.63	odd	20
605.2.m.c.602.1		32	44.31	odd	10
605.2.m.d.118.1		32	220.123	odd	20
605.2.m.d.282.1		32	44.3	odd	10
605.2.m.d.403.4		32	220.3	even	20
605.2.m.d.602.4		32	44.35	even	10
605.2.m.e.112.4		32	44.43	even	2
605.2.m.e.233.4		32	220.43	odd	4
605.2.m.e.457.4		32	44.27	odd	10
605.2.m.e.578.4		32	220.203	even	20
880.2.cm.a.17.1		32	11.6	odd	10	inner
880.2.cm.a.193.1		32	55.28	even	20	inner
880.2.cm.a.497.1		32	1.1	even	1	trivial
880.2.cm.a.673.1		32	5.3	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:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.cm (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.313634 + 1.98021i) q^{3} +(1.91314 + 1.15755i) q^{5} +(1.78576 - 0.282837i) q^{7} +(-0.969677 - 0.315067i) q^{9} +(-1.72268 + 2.83415i) q^{11} +(-2.00993 + 1.02411i) q^{13} +(-2.89220 + 3.42536i) q^{15} +(2.99738 + 1.52724i) q^{17} +(1.05647 - 0.767569i) q^{19} +3.62488i q^{21} +(3.16488 - 3.16488i) q^{23} +(2.32018 + 4.42908i) q^{25} +(-1.80258 + 3.53776i) q^{27} +(-2.37569 - 1.72604i) q^{29} +(1.23925 - 3.81401i) q^{31} +(-5.07190 - 4.30014i) q^{33} +(3.74380 + 1.52600i) q^{35} +(0.501987 + 3.16942i) q^{37} +(-1.39757 - 4.30127i) q^{39} +(0.766287 + 1.05470i) q^{41} +(-4.55431 - 4.55431i) q^{43} +(-1.49042 - 1.72521i) q^{45} +(7.62854 + 1.20824i) q^{47} +(-3.54845 + 1.15296i) q^{49} +(-3.96433 + 5.45644i) q^{51} +(-2.89146 - 5.67482i) q^{53} +(-6.57637 + 3.42803i) q^{55} +(1.18860 + 2.33276i) q^{57} +(-7.28135 + 10.0219i) q^{59} +(-8.85435 + 2.87695i) q^{61} +(-1.82072 - 0.288374i) q^{63} +(-5.03072 - 0.367324i) q^{65} +(2.46236 + 2.46236i) q^{67} +(5.27449 + 7.25972i) q^{69} +(2.09243 + 6.43984i) q^{71} +(-1.47735 - 9.32763i) q^{73} +(-9.49818 + 3.20531i) q^{75} +(-2.27469 + 5.54835i) q^{77} +(-0.353860 + 1.08907i) q^{79} +(-8.91472 - 6.47692i) q^{81} +(4.75092 - 9.32422i) q^{83} +(3.96654 + 6.39143i) q^{85} +(4.16301 - 4.16301i) q^{87} +3.85743i q^{89} +(-3.29960 + 2.39730i) q^{91} +(7.16385 + 3.65016i) q^{93} +(2.90966 - 0.245553i) q^{95} +(-0.693249 + 0.353228i) q^{97} +(2.56339 - 2.20545i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} - 2 q^{5} + 24 q^{11} - 10 q^{13} - 14 q^{15} + 24 q^{23} + 16 q^{25} + 16 q^{27} + 28 q^{31} + 66 q^{33} + 10 q^{35} - 8 q^{37} + 40 q^{41} - 28 q^{45} + 28 q^{47} - 20 q^{51} - 24 q^{53}+ \cdots - 8 q^{97}+O(q^{100}) \) 32 * q + 4 * q^3 - 2 * q^5 + 24 * q^11 - 10 * q^13 - 14 * q^15 + 24 * q^23 + 16 * q^25 + 16 * q^27 + 28 * q^31 + 66 * q^33 + 10 * q^35 - 8 * q^37 + 40 * q^41 - 28 * q^45 + 28 * q^47 - 20 * q^51 - 24 * q^53 + 64 * q^55 + 30 * q^57 - 60 * q^61 + 30 * q^63 + 8 * q^67 - 24 * q^71 + 50 * q^73 - 34 * q^75 + 70 * q^77 - 12 * q^81 - 90 * q^83 + 30 * q^85 - 20 * q^91 - 8 * q^93 + 40 * q^95 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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