LMFDB - Embedded newform 880.2.bo.f.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(81,880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(880, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("880.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.26265625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 $ x^8 - 3x^7 + 2x^6 + x^4 + 8x^2 - 24x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 220)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.1
Root			$-1.21700 + 0.720348i$ of defining polynomial
Character	$\chi$	$=$	880.81
Dual form			880.2.bo.f.641.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.655837 + 2.01846i) q^{3} +(0.809017 - 0.587785i) q^{5} +(-0.0946704 - 0.291365i) q^{7} +(-1.21700 - 0.884205i) q^{9} +O(q^{10})$	\(q+(-0.655837 + 2.01846i) q^{3} +(0.809017 - 0.587785i) q^{5} +(-0.0946704 - 0.291365i) q^{7} +(-1.21700 - 0.884205i) q^{9} +(-2.72130 + 1.89592i) q^{11} +(-2.68616 - 1.95161i) q^{13} +(0.655837 + 2.01846i) q^{15} +(-4.58719 + 3.33279i) q^{17} +(-0.464854 + 1.43067i) q^{19} +0.650198 q^{21} +0.343838 q^{23} +(0.309017 - 0.951057i) q^{25} +(-2.56812 + 1.86585i) q^{27} +(2.15849 + 6.64316i) q^{29} +(-4.80849 - 3.49357i) q^{31} +(-2.04210 - 6.73625i) q^{33} +(-0.247850 - 0.180074i) q^{35} +(1.63842 + 5.04252i) q^{37} +(5.70092 - 4.14196i) q^{39} +(-2.25645 + 6.94464i) q^{41} -4.16046 q^{43} -1.50430 q^{45} +(1.94313 - 5.98035i) q^{47} +(5.58719 - 4.05933i) q^{49} +(-3.71865 - 11.4448i) q^{51} +(-8.63227 - 6.27171i) q^{53} +(-1.08719 + 3.13337i) q^{55} +(-2.58289 - 1.87658i) q^{57} +(0.590371 + 1.81697i) q^{59} +(-8.27850 + 6.01468i) q^{61} +(-0.142413 + 0.438301i) q^{63} -3.32027 q^{65} -10.4137 q^{67} +(-0.225502 + 0.694023i) q^{69} +(9.03760 - 6.56620i) q^{71} +(-0.792610 - 2.43940i) q^{73} +(1.71700 + 1.24748i) q^{75} +(0.810032 + 0.613406i) q^{77} +(1.95737 + 1.42211i) q^{79} +(-3.47644 - 10.6994i) q^{81} +(3.66709 - 2.66430i) q^{83} +(-1.75215 + 5.39256i) q^{85} -14.8246 q^{87} +2.46354 q^{89} +(-0.314331 + 0.967413i) q^{91} +(10.2052 - 7.41453i) q^{93} +(0.464854 + 1.43067i) q^{95} +(-11.1057 - 8.06878i) q^{97} +(4.98822 + 0.0988498i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{3} + 2 q^{5} - q^{7} + 3 q^{9}+O(q^{10}) $ 8 * q + q^3 + 2 * q^5 - q^7 + 3 * q^9	$ 8 q + q^{3} + 2 q^{5} - q^{7} + 3 q^{9} - 5 q^{11} + 6 q^{13} - q^{15} - 13 q^{17} + 7 q^{19} + 28 q^{21} + 22 q^{23} - 2 q^{25} - 2 q^{27} + 3 q^{29} + 2 q^{31} - 15 q^{33} - 4 q^{35} + 16 q^{37} + 17 q^{39} - 12 q^{41} - 10 q^{43} - 8 q^{45} + 18 q^{47} + 21 q^{49} - 21 q^{51} - 23 q^{53} + 15 q^{55} - q^{57} + 9 q^{59} - 34 q^{61} + 29 q^{63} - 6 q^{65} - 26 q^{67} - q^{69} + 26 q^{71} + q^{73} + q^{75} - 10 q^{77} - 19 q^{79} + 12 q^{81} + 7 q^{83} - 12 q^{85} - 94 q^{87} - 8 q^{89} + 18 q^{91} + 49 q^{93} - 7 q^{95} - 24 q^{97} + 20 q^{99}+O(q^{100}) $ 8 * q + q^3 + 2 * q^5 - q^7 + 3 * q^9 - 5 * q^11 + 6 * q^13 - q^15 - 13 * q^17 + 7 * q^19 + 28 * q^21 + 22 * q^23 - 2 * q^25 - 2 * q^27 + 3 * q^29 + 2 * q^31 - 15 * q^33 - 4 * q^35 + 16 * q^37 + 17 * q^39 - 12 * q^41 - 10 * q^43 - 8 * q^45 + 18 * q^47 + 21 * q^49 - 21 * q^51 - 23 * q^53 + 15 * q^55 - q^57 + 9 * q^59 - 34 * q^61 + 29 * q^63 - 6 * q^65 - 26 * q^67 - q^69 + 26 * q^71 + q^73 + q^75 - 10 * q^77 - 19 * q^79 + 12 * q^81 + 7 * q^83 - 12 * q^85 - 94 * q^87 - 8 * q^89 + 18 * q^91 + 49 * q^93 - 7 * q^95 - 24 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$1$

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
$3$	−0.655837	+	2.01846i	−0.378648	+	1.16536i	0.562337	+	0.826908i	$0.309902\pi$
$3$	−0.655837	+	2.01846i	−0.378648	+	1.16536i	−0.940985	+	0.338450i	$0.890098\pi$
$4$		0			0
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$		0			0
$7$	−0.0946704	−	0.291365i	−0.0357820	−	0.110126i	0.931570	−	0.363562i	$-0.118439\pi$
$7$	−0.0946704	−	0.291365i	−0.0357820	−	0.110126i	−0.967352	+	0.253436i	$0.918439\pi$
$8$		0			0
$9$	−1.21700	−	0.884205i	−0.405668	−	0.294735i
$10$		0			0
$11$	−2.72130	+	1.89592i	−0.820504	+	0.571641i
$11$	−2.72130	+	1.89592i	−0.820504	+	0.571641i
$12$		0			0
$13$	−2.68616	−	1.95161i	−0.745006	−	0.541279i	0.149269	−	0.988797i	$-0.452308\pi$
$13$	−2.68616	−	1.95161i	−0.745006	−	0.541279i	−0.894275	+	0.447518i	$0.852308\pi$
$14$		0			0
$15$	0.655837	+	2.01846i	0.169336	+	0.521164i
$16$		0			0
$17$	−4.58719	+	3.33279i	−1.11256	+	0.808320i	−0.983064	−	0.183261i	$-0.941335\pi$
$17$	−4.58719	+	3.33279i	−1.11256	+	0.808320i	−0.129492	+	0.991580i	$0.541335\pi$
$18$		0			0
$19$	−0.464854	+	1.43067i	−0.106645	+	0.328219i	−0.990113	−	0.140272i	$-0.955202\pi$
$19$	−0.464854	+	1.43067i	−0.106645	+	0.328219i	0.883468	+	0.468491i	$0.155202\pi$
$20$		0			0
$21$	0.650198			0.141885
$22$		0			0
$23$	0.343838			0.0716951			0.0358476	−	0.999357i	$-0.488587\pi$
$23$	0.343838			0.0716951			0.0358476	+	0.999357i	$0.488587\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$		0			0
$27$	−2.56812	+	1.86585i	−0.494236	+	0.359083i
$28$		0			0
$29$	2.15849	+	6.64316i	0.400822	+	1.23360i	0.924334	+	0.381586i	$0.124622\pi$
$29$	2.15849	+	6.64316i	0.400822	+	1.23360i	−0.523511	+	0.852019i	$0.675378\pi$
$30$		0			0
$31$	−4.80849	−	3.49357i	−0.863630	−	0.627464i	0.0652397	−	0.997870i	$-0.479219\pi$
$31$	−4.80849	−	3.49357i	−0.863630	−	0.627464i	−0.928870	+	0.370405i	$0.879219\pi$
$32$		0			0
$33$	−2.04210	−	6.73625i	−0.355484	−	1.17263i
$34$		0			0
$35$	−0.247850	−	0.180074i	−0.0418943	−	0.0304380i
$36$		0			0
$37$	1.63842	+	5.04252i	0.269354	+	0.828986i	0.990658	+	0.136368i	$0.0435429\pi$
$37$	1.63842	+	5.04252i	0.269354	+	0.828986i	−0.721304	+	0.692618i	$0.756457\pi$
$38$		0			0
$39$	5.70092	−	4.14196i	0.912878	−	0.663245i
$40$		0			0
$41$	−2.25645	+	6.94464i	−0.352398	+	1.08457i	0.605105	+	0.796146i	$0.293131\pi$
$41$	−2.25645	+	6.94464i	−0.352398	+	1.08457i	−0.957503	+	0.288424i	$0.906869\pi$
$42$		0			0
$43$	−4.16046			−0.634464			−0.317232	−	0.948348i	$-0.602753\pi$
$43$	−4.16046			−0.634464			−0.317232	+	0.948348i	$0.602753\pi$
$44$		0			0
$45$	−1.50430			−0.224248
$46$		0			0
$47$	1.94313	−	5.98035i	0.283435	−	0.872323i	−0.703428	−	0.710766i	$-0.748348\pi$
$47$	1.94313	−	5.98035i	0.283435	−	0.872323i	0.986863	−	0.161557i	$-0.0516516\pi$
$48$		0			0
$49$	5.58719	−	4.05933i	0.798170	−	0.579904i
$50$		0			0
$51$	−3.71865	−	11.4448i	−0.520715	−	1.60259i
$52$		0			0
$53$	−8.63227	−	6.27171i	−1.18573	−	0.861486i	−0.192927	−	0.981213i	$-0.561798\pi$
$53$	−8.63227	−	6.27171i	−1.18573	−	0.861486i	−0.992807	+	0.119727i	$0.961798\pi$
$54$		0			0
$55$	−1.08719	+	3.13337i	−0.146596	+	0.422504i
$56$		0			0
$57$	−2.58289	−	1.87658i	−0.342112	−	0.248559i
$58$		0			0
$59$	0.590371	+	1.81697i	0.0768597	+	0.236550i	0.982103	−	0.188343i	$-0.0603117\pi$
$59$	0.590371	+	1.81697i	0.0768597	+	0.236550i	−0.905244	+	0.424893i	$0.860312\pi$
$60$		0			0
$61$	−8.27850	+	6.01468i	−1.05995	+	0.770101i	−0.974080	−	0.226205i	$-0.927368\pi$
$61$	−8.27850	+	6.01468i	−1.05995	+	0.770101i	−0.0858731	+	0.996306i	$0.527368\pi$
$62$		0			0
$63$	−0.142413	+	0.438301i	−0.0179423	+	0.0552207i
$64$		0			0
$65$	−3.32027			−0.411829
$66$		0			0
$67$	−10.4137			−1.27224			−0.636120	−	0.771590i	$-0.719462\pi$
$67$	−10.4137			−1.27224			−0.636120	+	0.771590i	$0.719462\pi$
$68$		0			0
$69$	−0.225502	+	0.694023i	−0.0271472	+	0.0835505i
$70$		0			0
$71$	9.03760	−	6.56620i	1.07257	−	0.779265i	0.0961943	−	0.995363i	$-0.469333\pi$
$71$	9.03760	−	6.56620i	1.07257	−	0.779265i	0.976372	+	0.216098i	$0.0693330\pi$
$72$		0			0
$73$	−0.792610	−	2.43940i	−0.0927680	−	0.285511i	0.893898	−	0.448271i	$-0.147960\pi$
$73$	−0.792610	−	2.43940i	−0.0927680	−	0.285511i	−0.986666	+	0.162761i	$0.947960\pi$
$74$		0			0
$75$	1.71700	+	1.24748i	0.198263	+	0.144046i
$76$		0			0
$77$	0.810032	+	0.613406i	0.0923117	+	0.0699041i
$78$		0			0
$79$	1.95737	+	1.42211i	0.220221	+	0.160000i	0.692426	−	0.721489i	$-0.256542\pi$
$79$	1.95737	+	1.42211i	0.220221	+	0.160000i	−0.472205	+	0.881489i	$0.656542\pi$
$80$		0			0
$81$	−3.47644	−	10.6994i	−0.386271	−	1.18882i
$82$		0			0
$83$	3.66709	−	2.66430i	0.402516	−	0.292445i	−0.368049	−	0.929806i	$-0.619974\pi$
$83$	3.66709	−	2.66430i	0.402516	−	0.292445i	0.770565	+	0.637361i	$0.219974\pi$
$84$		0			0
$85$	−1.75215	+	5.39256i	−0.190047	+	0.584906i
$86$		0			0
$87$	−14.8246			−1.58936
$88$		0			0
$89$	2.46354			0.261134			0.130567	−	0.991439i	$-0.458320\pi$
$89$	2.46354			0.261134			0.130567	+	0.991439i	$0.458320\pi$
$90$		0			0
$91$	−0.314331	+	0.967413i	−0.0329509	+	0.101412i
$92$		0			0
$93$	10.2052	−	7.41453i	1.05823	−	0.768851i
$94$		0			0
$95$	0.464854	+	1.43067i	0.0476930	+	0.146784i
$96$		0			0
$97$	−11.1057	−	8.06878i	−1.12762	−	0.819261i	−0.142270	−	0.989828i	$-0.545440\pi$
$97$	−11.1057	−	8.06878i	−1.12762	−	0.819261i	−0.985346	+	0.170567i	$0.945440\pi$
$98$		0			0
$99$	4.98822	+	0.0988498i	0.501335	+	0.00993478i
$100$		0			0
$101$	5.79208	+	4.20820i	0.576334	+	0.418731i	0.837401	−	0.546590i	$-0.184074\pi$
$101$	5.79208	+	4.20820i	0.576334	+	0.418731i	−0.261067	+	0.965321i	$0.584074\pi$
$102$		0			0
$103$	3.24201	+	9.97788i	0.319445	+	0.983150i	0.973886	+	0.227037i	$0.0729038\pi$
$103$	3.24201	+	9.97788i	0.319445	+	0.983150i	−0.654441	+	0.756113i	$0.727096\pi$
$104$		0			0
$105$	0.526021	−	0.382177i	0.0513344	−	0.0372966i
$106$		0			0
$107$	−5.27981	+	16.2496i	−0.510419	+	1.57091i	0.281047	+	0.959694i	$0.409318\pi$
$107$	−5.27981	+	16.2496i	−0.510419	+	1.57091i	−0.791466	+	0.611213i	$0.790682\pi$
$108$		0			0
$109$	18.9436			1.81447			0.907235	−	0.420624i	$-0.138189\pi$
$109$	18.9436			1.81447			0.907235	+	0.420624i	$0.138189\pi$
$110$		0			0
$111$	−11.2527			−1.06806
$112$		0			0
$113$	−1.10359	+	3.39651i	−0.103817	+	0.319517i	−0.989451	−	0.144867i	$-0.953724\pi$
$113$	−1.10359	+	3.39651i	−0.103817	+	0.319517i	0.885634	+	0.464385i	$0.153724\pi$
$114$		0			0
$115$	0.278171	−	0.202103i	0.0259395	−	0.0188462i
$116$		0			0
$117$	1.54344	+	4.75023i	0.142691	+	0.439159i
$118$		0			0
$119$	1.40533	+	1.02103i	0.128826	+	0.0935978i
$120$		0			0
$121$	3.81098	−	10.3187i	0.346453	−	0.938067i
$122$		0			0
$123$	−12.5376	−	9.10910i	−1.13048	−	0.821340i
$124$		0			0
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$		0			0
$127$	5.86887	−	4.26398i	0.520778	−	0.378367i	−0.296119	−	0.955151i	$-0.595693\pi$
$127$	5.86887	−	4.26398i	0.520778	−	0.378367i	0.816897	+	0.576784i	$0.195693\pi$
$128$		0			0
$129$	2.72859	−	8.39772i	0.240239	−	0.739378i
$130$		0			0
$131$	21.7731			1.90233			0.951163	−	0.308690i	$-0.0998907\pi$
$131$	21.7731			1.90233			0.951163	+	0.308690i	$0.0998907\pi$
$132$		0			0
$133$	0.460857			0.0399614
$134$		0			0
$135$	−0.980936	+	3.01901i	−0.0844255	+	0.259835i
$136$		0			0
$137$	−1.44579	+	1.05043i	−0.123522	+	0.0897441i	−0.647831	−	0.761784i	$-0.724324\pi$
$137$	−1.44579	+	1.05043i	−0.123522	+	0.0897441i	0.524309	+	0.851528i	$0.324324\pi$
$138$		0			0
$139$	3.99416	+	12.2928i	0.338780	+	1.04266i	0.964830	+	0.262875i	$0.0846707\pi$
$139$	3.99416	+	12.2928i	0.338780	+	1.04266i	−0.626050	+	0.779783i	$0.715329\pi$
$140$		0			0
$141$	10.7967	+	7.84427i	0.909247	+	0.660607i
$142$		0			0
$143$	11.0099	+	0.218180i	0.920697	+	0.0182451i
$144$		0			0
$145$	5.65101	+	4.10570i	0.469291	+	0.340960i
$146$		0			0
$147$	4.52931	+	13.9398i	0.373571	+	1.14973i
$148$		0			0
$149$	−1.69449	+	1.23112i	−0.138818	+	0.100857i	−0.655027	−	0.755605i	$-0.727343\pi$
$149$	−1.69449	+	1.23112i	−0.138818	+	0.100857i	0.516209	+	0.856463i	$0.327343\pi$
$150$		0			0
$151$	−5.46384	+	16.8160i	−0.444641	+	1.36846i	0.438236	+	0.898860i	$0.355603\pi$
$151$	−5.46384	+	16.8160i	−0.444641	+	1.36846i	−0.882877	+	0.469604i	$0.844397\pi$
$152$		0			0
$153$	8.52949			0.689569
$154$		0			0
$155$	−5.94362			−0.477403
$156$		0			0
$157$	−6.29957	+	19.3881i	−0.502760	+	1.54734i	0.301744	+	0.953389i	$0.402431\pi$
$157$	−6.29957	+	19.3881i	−0.502760	+	1.54734i	−0.804504	+	0.593948i	$0.797569\pi$
$158$		0			0
$159$	18.3206	−	13.3107i	1.45292	−	1.05560i
$160$		0			0
$161$	−0.0325513	−	0.100182i	−0.00256540	−	0.00789548i
$162$		0			0
$163$	10.4842	+	7.61725i	0.821189	+	0.596629i	0.917053	−	0.398766i	$-0.130561\pi$
$163$	10.4842	+	7.61725i	0.821189	+	0.596629i	−0.0958636	+	0.995394i	$0.530561\pi$
$164$		0			0
$165$	−5.61157	−	4.24943i	−0.436860	−	0.330817i
$166$		0			0
$167$	4.00909	+	2.91277i	0.310233	+	0.225397i	0.731996	−	0.681309i	$-0.238589\pi$
$167$	4.00909	+	2.91277i	0.310233	+	0.225397i	−0.421764	+	0.906706i	$0.638589\pi$
$168$		0			0
$169$	−0.610551	−	1.87908i	−0.0469655	−	0.144545i
$170$		0			0
$171$	1.83074	−	1.33011i	0.140000	−	0.101716i
$172$		0			0
$173$	−6.59834	+	20.3076i	−0.501663	+	1.54396i	0.304647	+	0.952465i	$0.401462\pi$
$173$	−6.59834	+	20.3076i	−0.501663	+	1.54396i	−0.806310	+	0.591494i	$0.798538\pi$
$174$		0			0
$175$	−0.306360			−0.0231586
$176$		0			0
$177$	−4.05468			−0.304768
$178$		0			0
$179$	6.94425	−	21.3722i	0.519038	−	1.59743i	−0.256776	−	0.966471i	$-0.582660\pi$
$179$	6.94425	−	21.3722i	0.519038	−	1.59743i	0.775813	−	0.630962i	$-0.217340\pi$
$180$		0			0
$181$	−1.44149	+	1.04730i	−0.107145	+	0.0778455i	−0.640068	−	0.768319i	$-0.721094\pi$
$181$	−1.44149	+	1.04730i	−0.107145	+	0.0778455i	0.532923	+	0.846164i	$0.321094\pi$
$182$		0			0
$183$	−6.71104	−	20.6545i	−0.496094	−	1.52682i
$184$		0			0
$185$	4.28943	+	3.11645i	0.315365	+	0.229126i
$186$		0			0
$187$	6.16444	−	17.7665i	0.450788	−	1.29921i
$188$		0			0
$189$	0.786770	+	0.571622i	0.0572291	+	0.0415794i
$190$		0			0
$191$	8.09897	+	24.9261i	0.586021	+	1.80359i	0.595131	+	0.803628i	$0.297100\pi$
$191$	8.09897	+	24.9261i	0.586021	+	1.80359i	−0.00911057	+	0.999958i	$0.502900\pi$
$192$		0			0
$193$	8.15314	−	5.92361i	0.586876	−	0.426390i	−0.254320	−	0.967120i	$-0.581852\pi$
$193$	8.15314	−	5.92361i	0.586876	−	0.426390i	0.841196	+	0.540730i	$0.181852\pi$
$194$		0			0
$195$	2.17756	−	6.70184i	0.155938	−	0.479928i
$196$		0			0
$197$	6.84912			0.487979			0.243990	−	0.969778i	$-0.421544\pi$
$197$	6.84912			0.487979			0.243990	+	0.969778i	$0.421544\pi$
$198$		0			0
$199$	−16.7018			−1.18396			−0.591981	−	0.805952i	$-0.701654\pi$
$199$	−16.7018			−1.18396			−0.591981	+	0.805952i	$0.701654\pi$
$200$		0			0
$201$	6.82971	−	21.0197i	0.481731	−	1.48261i
$202$		0			0
$203$	1.73124	−	1.25782i	0.121509	−	0.0882817i
$204$		0			0
$205$	2.25645	+	6.94464i	0.157597	+	0.485034i
$206$		0			0
$207$	−0.418452	−	0.304023i	−0.0290844	−	0.0211311i
$208$		0			0
$209$	−1.44743	−	4.77462i	−0.100121	−	0.330268i
$210$		0			0
$211$	−6.62282	−	4.81176i	−0.455934	−	0.331255i	0.336000	−	0.941862i	$-0.390926\pi$
$211$	−6.62282	−	4.81176i	−0.455934	−	0.331255i	−0.791934	+	0.610607i	$0.790926\pi$
$212$		0			0
$213$	7.32642	+	22.5484i	0.501998	+	1.54499i
$214$		0			0
$215$	−3.36588	+	2.44546i	−0.229551	+	0.166779i
$216$		0			0
$217$	−0.562685	+	1.73177i	−0.0381975	+	0.117560i
$218$		0			0
$219$	5.44366			0.367848
$220$		0			0
$221$	18.8262			1.26639
$222$		0			0
$223$	5.07192	−	15.6098i	0.339641	−	1.04531i	−0.624750	−	0.780825i	$-0.714799\pi$
$223$	5.07192	−	15.6098i	0.339641	−	1.04531i	0.964391	−	0.264482i	$-0.0852010\pi$
$224$		0			0
$225$	−1.21700	+	0.884205i	−0.0811336	+	0.0589470i
$226$		0			0
$227$	5.56261	+	17.1199i	0.369203	+	1.13629i	0.947307	+	0.320327i	$0.103793\pi$
$227$	5.56261	+	17.1199i	0.369203	+	1.13629i	−0.578104	+	0.815963i	$0.696207\pi$
$228$		0			0
$229$	−11.9638	−	8.69221i	−0.790590	−	0.574397i	0.117548	−	0.993067i	$-0.462497\pi$
$229$	−11.9638	−	8.69221i	−0.790590	−	0.574397i	−0.908139	+	0.418670i	$0.862497\pi$
$230$		0			0
$231$	−1.76938	+	1.23272i	−0.116417	+	0.0811071i
$232$		0			0
$233$	20.8466	+	15.1459i	1.36571	+	0.992243i	0.998059	+	0.0622770i	$0.0198362\pi$
$233$	20.8466	+	15.1459i	1.36571	+	0.992243i	0.367646	+	0.929966i	$0.380164\pi$
$234$		0			0
$235$	−1.94313	−	5.98035i	−0.126756	−	0.390115i
$236$		0			0
$237$	−4.15419	+	3.01820i	−0.269844	+	0.196053i
$238$		0			0
$239$	2.42324	−	7.45797i	0.156746	−	0.482416i	−0.841587	−	0.540121i	$-0.818378\pi$
$239$	2.42324	−	7.45797i	0.156746	−	0.482416i	0.998334	+	0.0577054i	$0.0183784\pi$
$240$		0			0
$241$	−23.1921			−1.49394			−0.746969	−	0.664859i	$-0.768492\pi$
$241$	−23.1921			−1.49394			−0.746969	+	0.664859i	$0.768492\pi$
$242$		0			0
$243$	14.3531			0.920751
$244$		0			0
$245$	2.13412	−	6.56813i	0.136344	−	0.419623i
$246$		0			0
$247$	4.04079	−	2.93580i	0.257109	−	0.186801i
$248$		0			0
$249$	2.97276	+	9.14922i	0.188391	+	0.579809i
$250$		0			0
$251$	−9.28896	−	6.74883i	−0.586314	−	0.425982i	0.254681	−	0.967025i	$-0.418030\pi$
$251$	−9.28896	−	6.74883i	−0.586314	−	0.425982i	−0.840995	+	0.541043i	$0.818030\pi$
$252$		0			0
$253$	−0.935687	+	0.651889i	−0.0588261	+	0.0409839i
$254$		0			0
$255$	−9.73554	−	7.07329i	−0.609663	−	0.442946i
$256$		0			0
$257$	−1.40071	−	4.31093i	−0.0873736	−	0.268908i	0.897818	−	0.440367i	$-0.145152\pi$
$257$	−1.40071	−	4.31093i	−0.0873736	−	0.268908i	−0.985191	+	0.171459i	$0.945152\pi$
$258$		0			0
$259$	1.31411	−	0.954755i	0.0816547	−	0.0593256i
$260$		0			0
$261$	3.24702	−	9.99331i	0.200986	−	0.618570i
$262$		0			0
$263$	−3.80101			−0.234380			−0.117190	−	0.993110i	$-0.537389\pi$
$263$	−3.80101			−0.234380			−0.117190	+	0.993110i	$0.537389\pi$
$264$		0			0
$265$	−10.6701			−0.655458
$266$		0			0
$267$	−1.61568	+	4.97255i	−0.0988779	+	0.304315i
$268$		0			0
$269$	15.6148	−	11.3448i	0.952052	−	0.691706i	0.000760692	−	1.00000i	$-0.499758\pi$
$269$	15.6148	−	11.3448i	0.952052	−	0.691706i	0.951291	+	0.308293i	$0.0997579\pi$
$270$		0			0
$271$	4.27539	+	13.1583i	0.259711	+	0.799309i	0.992865	+	0.119246i	$0.0380478\pi$
$271$	4.27539	+	13.1583i	0.259711	+	0.799309i	−0.733153	+	0.680063i	$0.761952\pi$
$272$		0			0
$273$	−1.74653	−	1.26893i	−0.105705	−	0.0767992i
$274$		0			0
$275$	0.962197	+	3.17398i	0.0580227	+	0.191398i
$276$		0			0
$277$	−16.3219	−	11.8586i	−0.980690	−	0.712513i	−0.0228275	−	0.999739i	$-0.507267\pi$
$277$	−16.3219	−	11.8586i	−0.980690	−	0.712513i	−0.957863	+	0.287226i	$0.907267\pi$
$278$		0			0
$279$	2.76292	+	8.50338i	0.165412	+	0.509084i
$280$		0			0
$281$	−8.19508	+	5.95408i	−0.488878	+	0.355190i	−0.804753	−	0.593610i	$-0.797702\pi$
$281$	−8.19508	+	5.95408i	−0.488878	+	0.355190i	0.315875	+	0.948801i	$0.397702\pi$
$282$		0			0
$283$	6.50842	−	20.0309i	0.386885	−	1.19071i	−0.548218	−	0.836336i	$-0.684694\pi$
$283$	6.50842	−	20.0309i	0.386885	−	1.19071i	0.935103	−	0.354375i	$-0.115306\pi$
$284$		0			0
$285$	−3.19263			−0.189115
$286$		0			0
$287$	2.23705			0.132049
$288$		0			0
$289$	4.68153	−	14.4083i	0.275384	−	0.847546i
$290$		0			0
$291$	23.5701	−	17.1246i	1.38170	−	1.00386i
$292$		0			0
$293$	−5.66886	−	17.4470i	−0.331178	−	1.01926i	−0.968574	−	0.248725i	$-0.919988\pi$
$293$	−5.66886	−	17.4470i	−0.331178	−	1.01926i	0.637396	−	0.770537i	$-0.280012\pi$
$294$		0			0
$295$	1.54561	+	1.12295i	0.0899889	+	0.0653808i
$296$		0			0
$297$	3.45114	−	9.94650i	0.200256	−	0.577154i
$298$		0			0
$299$	−0.923603	−	0.671037i	−0.0534133	−	0.0388070i
$300$		0			0
$301$	0.393872	+	1.21221i	0.0227024	+	0.0698709i
$302$		0			0
$303$	−12.2927	+	8.93119i	−0.706199	+	0.513084i
$304$		0			0
$305$	−3.16210	+	9.73196i	−0.181062	+	0.557250i
$306$		0			0
$307$	−21.3397			−1.21792			−0.608962	−	0.793199i	$-0.708414\pi$
$307$	−21.3397			−1.21792			−0.608962	+	0.793199i	$0.708414\pi$
$308$		0			0
$309$	−22.2662			−1.26668
$310$		0			0
$311$	−4.25441	+	13.0937i	−0.241245	+	0.742476i	0.754986	+	0.655741i	$0.227644\pi$
$311$	−4.25441	+	13.0937i	−0.241245	+	0.742476i	−0.996231	+	0.0867356i	$0.972356\pi$
$312$		0			0
$313$	21.2820	−	15.4623i	1.20293	−	0.873978i	0.208358	−	0.978053i	$-0.433188\pi$
$313$	21.2820	−	15.4623i	1.20293	−	0.873978i	0.994570	+	0.104074i	$0.0331880\pi$
$314$		0			0
$315$	0.142413	+	0.438301i	0.00802404	+	0.0246955i
$316$		0			0
$317$	8.43968	+	6.13179i	0.474020	+	0.344396i	0.799006	−	0.601323i	$-0.205360\pi$
$317$	8.43968	+	6.13179i	0.474020	+	0.344396i	−0.324986	+	0.945719i	$0.605360\pi$
$318$		0			0
$319$	−18.4688	−	13.9857i	−1.03406	−	0.783051i
$320$		0			0
$321$	−29.3364	−	21.3142i	−1.63740	−	1.18964i
$322$		0			0
$323$	−2.63576	−	8.11203i	−0.146658	−	0.451365i
$324$		0			0
$325$	−2.68616	+	1.95161i	−0.149001	+	0.108256i
$326$		0			0
$327$	−12.4239	+	38.2369i	−0.687045	+	2.11451i
$328$		0			0
$329$	−1.92642			−0.106207
$330$		0			0
$331$	9.45080			0.519463			0.259732	−	0.965681i	$-0.416366\pi$
$331$	9.45080			0.519463			0.259732	+	0.965681i	$0.416366\pi$
$332$		0			0
$333$	2.46467	−	7.58547i	0.135063	−	0.415681i
$334$		0			0
$335$	−8.42488	+	6.12104i	−0.460301	+	0.334428i
$336$		0			0
$337$	4.95717	+	15.2566i	0.270034	+	0.831080i	0.990491	+	0.137580i	$0.0439324\pi$
$337$	4.95717	+	15.2566i	0.270034	+	0.831080i	−0.720456	+	0.693500i	$0.756068\pi$
$338$		0			0
$339$	−6.13195	−	4.45512i	−0.333042	−	0.241969i
$340$		0			0
$341$	19.7089	+	0.390564i	1.06730	+	0.0211503i
$342$		0			0
$343$	−3.44664	−	2.50413i	−0.186101	−	0.135210i
$344$		0			0
$345$	0.225502	+	0.694023i	0.0121406	+	0.0373649i
$346$		0			0
$347$	−19.2833	+	14.0101i	−1.03518	+	0.752103i	−0.969339	−	0.245727i	$-0.920973\pi$
$347$	−19.2833	+	14.0101i	−1.03518	+	0.752103i	−0.0658419	+	0.997830i	$0.520973\pi$
$348$		0			0
$349$	7.22068	−	22.2230i	0.386514	−	1.18957i	−0.548862	−	0.835913i	$-0.684939\pi$
$349$	7.22068	−	22.2230i	0.386514	−	1.18957i	0.935376	−	0.353655i	$-0.115061\pi$
$350$		0			0
$351$	10.5398			0.562573
$352$		0			0
$353$	0.502597			0.0267506			0.0133753	−	0.999911i	$-0.495742\pi$
$353$	0.502597			0.0267506			0.0133753	+	0.999911i	$0.495742\pi$
$354$		0			0
$355$	3.45206	−	10.6243i	0.183216	−	0.563881i
$356$		0			0
$357$	−2.98258	+	2.16697i	−0.157855	+	0.114688i
$358$		0			0
$359$	2.52152	+	7.76044i	0.133081	+	0.409580i	0.995287	−	0.0969777i	$-0.0309176\pi$
$359$	2.52152	+	7.76044i	0.133081	+	0.409580i	−0.862206	+	0.506558i	$0.830918\pi$
$360$		0			0
$361$	13.5406	+	9.83781i	0.712662	+	0.517780i
$362$		0			0
$363$	18.3286	+	14.4597i	0.962000	+	0.758939i
$364$		0			0
$365$	−2.07508	−	1.50763i	−0.108615	−	0.0789132i
$366$		0			0
$367$	−7.57222	−	23.3049i	−0.395267	−	1.21651i	−0.928754	−	0.370698i	$-0.879119\pi$
$367$	−7.57222	−	23.3049i	−0.395267	−	1.21651i	0.533487	−	0.845808i	$-0.320881\pi$
$368$		0			0
$369$	8.88659	−	6.45649i	0.462617	−	0.336111i
$370$		0			0
$371$	−1.01014	+	3.10889i	−0.0524439	+	0.161406i
$372$		0			0
$373$	10.9745			0.568236			0.284118	−	0.958789i	$-0.408299\pi$
$373$	10.9745			0.568236			0.284118	+	0.958789i	$0.408299\pi$
$374$		0			0
$375$	2.12233			0.109597
$376$		0			0
$377$	7.16679	−	22.0571i	0.369109	−	1.13600i
$378$		0			0
$379$	−20.7307	+	15.0617i	−1.06486	+	0.773669i	−0.974982	−	0.222284i	$-0.928649\pi$
$379$	−20.7307	+	15.0617i	−1.06486	+	0.773669i	−0.0898815	+	0.995952i	$0.528649\pi$
$380$		0			0
$381$	4.75765	+	14.6425i	0.243742	+	0.750160i
$382$		0			0
$383$	2.97611	+	2.16227i	0.152072	+	0.110487i	0.661220	−	0.750192i	$-0.270039\pi$
$383$	2.97611	+	2.16227i	0.152072	+	0.110487i	−0.509147	+	0.860679i	$0.670039\pi$
$384$		0			0
$385$	1.01588	+	0.0201314i	0.0517741	+	0.00102599i
$386$		0			0
$387$	5.06330	+	3.67870i	0.257382	+	0.186999i
$388$		0			0
$389$	6.57725	+	20.2427i	0.333480	+	1.02635i	0.967466	+	0.253001i	$0.0814175\pi$
$389$	6.57725	+	20.2427i	0.333480	+	1.02635i	−0.633986	+	0.773344i	$0.718582\pi$
$390$		0			0
$391$	−1.57725	+	1.14594i	−0.0797649	+	0.0579526i
$392$		0			0
$393$	−14.2796	+	43.9481i	−0.720311	+	2.21689i
$394$		0			0
$395$	2.41944			0.121735
$396$		0			0
$397$	−3.44962			−0.173132			−0.0865658	−	0.996246i	$-0.527589\pi$
$397$	−3.44962			−0.173132			−0.0865658	+	0.996246i	$0.527589\pi$
$398$		0			0
$399$	−0.302247	+	0.930221i	−0.0151313	+	0.0465693i
$400$		0			0
$401$	−6.95524	+	5.05328i	−0.347328	+	0.252349i	−0.747747	−	0.663983i	$-0.768865\pi$
$401$	−6.95524	+	5.05328i	−0.347328	+	0.252349i	0.400419	+	0.916332i	$0.368865\pi$
$402$		0			0
$403$	6.09828	+	18.7686i	0.303777	+	0.934929i
$404$		0			0
$405$	−9.10143	−	6.61257i	−0.452254	−	0.328581i
$406$		0			0
$407$	−14.0188	−	10.6159i	−0.694888	−	0.526212i
$408$		0			0
$409$	−31.4094	−	22.8203i	−1.55310	−	1.12839i	−0.941398	−	0.337298i	$-0.890487\pi$
$409$	−31.4094	−	22.8203i	−1.55310	−	1.12839i	−0.611698	−	0.791092i	$-0.709513\pi$
$410$		0			0
$411$	−1.17204	−	3.60718i	−0.0578126	−	0.177929i
$412$		0			0
$413$	0.473513	−	0.344027i	0.0233001	−	0.0169285i
$414$		0			0
$415$	1.40071	−	4.31093i	0.0687579	−	0.211615i
$416$		0			0
$417$	−27.4319			−1.34335
$418$		0			0
$419$	−5.62952			−0.275020			−0.137510	−	0.990500i	$-0.543910\pi$
$419$	−5.62952			−0.275020			−0.137510	+	0.990500i	$0.543910\pi$
$420$		0			0
$421$	−7.67683	+	23.6269i	−0.374146	+	1.15150i	0.569907	+	0.821709i	$0.306979\pi$
$421$	−7.67683	+	23.6269i	−0.374146	+	1.15150i	−0.944053	+	0.329794i	$0.893021\pi$
$422$		0			0
$423$	−7.65265	+	5.55998i	−0.372085	+	0.270335i
$424$		0			0
$425$	1.75215	+	5.39256i	0.0849917	+	0.261578i
$426$		0			0
$427$	2.53620	+	1.84266i	0.122735	+	0.0891724i
$428$		0			0
$429$	−7.66111	+	22.0800i	−0.369882	+	1.06603i
$430$		0			0
$431$	11.6940	+	8.49616i	0.563278	+	0.409246i	0.832657	−	0.553788i	$-0.186818\pi$
$431$	11.6940	+	8.49616i	0.563278	+	0.409246i	−0.269379	+	0.963034i	$0.586818\pi$
$432$		0			0
$433$	9.59542	+	29.5317i	0.461127	+	1.41920i	0.863789	+	0.503853i	$0.168085\pi$
$433$	9.59542	+	29.5317i	0.461127	+	1.41920i	−0.402663	+	0.915348i	$0.631915\pi$
$434$		0			0
$435$	−11.9933	+	8.71367i	−0.575036	+	0.417788i
$436$		0			0
$437$	−0.159834	+	0.491920i	−0.00764592	+	0.0235317i
$438$		0			0
$439$	26.3444			1.25735			0.628675	−	0.777668i	$-0.283598\pi$
$439$	26.3444			1.25735			0.628675	+	0.777668i	$0.283598\pi$
$440$		0			0
$441$	−10.3889			−0.494710
$442$		0			0
$443$	−8.72725	+	26.8597i	−0.414644	+	1.27614i	0.497925	+	0.867220i	$0.334095\pi$
$443$	−8.72725	+	26.8597i	−0.414644	+	1.27614i	−0.912569	+	0.408923i	$0.865905\pi$
$444$		0			0
$445$	1.99304	−	1.44803i	0.0944793	−	0.0686432i
$446$		0			0
$447$	−1.37366	−	4.22768i	−0.0649717	−	0.199962i
$448$		0			0
$449$	18.8303	+	13.6810i	0.888656	+	0.645646i	0.935527	−	0.353255i	$-0.114925\pi$
$449$	18.8303	+	13.6810i	0.888656	+	0.645646i	−0.0468715	+	0.998901i	$0.514925\pi$
$450$		0			0
$451$	−7.02598	−	23.1765i	−0.330841	−	1.09134i
$452$		0			0
$453$	−30.3590	−	22.0571i	−1.42639	−	1.03633i
$454$		0			0
$455$	0.314331	+	0.967413i	0.0147361	+	0.0453530i
$456$		0			0
$457$	−24.2045	+	17.5856i	−1.13224	+	0.822618i	−0.986019	−	0.166634i	$-0.946710\pi$
$457$	−24.2045	+	17.5856i	−1.13224	+	0.822618i	−0.146218	+	0.989252i	$0.546710\pi$
$458$		0			0
$459$	5.56198	−	17.1180i	0.259611	−	0.799001i
$460$		0			0
$461$	14.7270			0.685904			0.342952	−	0.939353i	$-0.388573\pi$
$461$	14.7270			0.685904			0.342952	+	0.939353i	$0.388573\pi$
$462$		0			0
$463$	19.4047			0.901814			0.450907	−	0.892571i	$-0.351101\pi$
$463$	19.4047			0.901814			0.450907	+	0.892571i	$0.351101\pi$
$464$		0			0
$465$	3.89805	−	11.9970i	0.180768	−	0.556346i
$466$		0			0
$467$	−0.682974	+	0.496210i	−0.0316043	+	0.0229619i	−0.603475	−	0.797382i	$-0.706218\pi$
$467$	−0.682974	+	0.496210i	−0.0316043	+	0.0229619i	0.571871	+	0.820344i	$0.306218\pi$
$468$		0			0
$469$	0.985871	+	3.03420i	0.0455233	+	0.140106i
$470$		0			0
$471$	−35.0025	−	25.4308i	−1.61283	−	1.17179i
$472$		0			0
$473$	11.3219	−	7.88790i	0.520581	−	0.362686i
$474$		0			0
$475$	1.21700	+	0.884205i	0.0558400	+	0.0405701i
$476$		0			0
$477$	4.96003	+	15.2654i	0.227104	+	0.698955i
$478$		0			0
$479$	4.82920	−	3.50862i	0.220652	−	0.160313i	−0.471968	−	0.881616i	$-0.656456\pi$
$479$	4.82920	−	3.50862i	0.220652	−	0.160313i	0.692620	+	0.721303i	$0.256456\pi$
$480$		0			0
$481$	5.43999	−	16.7426i	0.248042	−	0.763395i
$482$		0			0
$483$	0.223563			0.0101724
$484$		0			0
$485$	−13.7274			−0.623331
$486$		0			0
$487$	7.87468	−	24.2358i	0.356836	−	1.09823i	−0.598101	−	0.801421i	$-0.704078\pi$
$487$	7.87468	−	24.2358i	0.356836	−	1.09823i	0.954937	−	0.296808i	$-0.0959221\pi$
$488$		0			0
$489$	−22.2511	+	16.1663i	−1.00623	+	0.731067i
$490$		0			0
$491$	−0.615555	−	1.89448i	−0.0277796	−	0.0854968i	0.936205	−	0.351453i	$-0.114312\pi$
$491$	−0.615555	−	1.89448i	−0.0277796	−	0.0854968i	−0.963985	+	0.265956i	$0.914312\pi$
$492$		0			0
$493$	−32.0417	−	23.2796i	−1.44308	−	1.04846i
$494$		0			0
$495$	4.09366	−	2.85203i	0.183996	−	0.128189i
$496$		0			0
$497$	−2.76876	−	2.01162i	−0.124196	−	0.0902335i
$498$		0			0
$499$	−5.60074	−	17.2373i	−0.250723	−	0.771647i	−0.994642	−	0.103377i	$-0.967035\pi$
$499$	−5.60074	−	17.2373i	−0.250723	−	0.771647i	0.743919	−	0.668270i	$-0.232965\pi$
$500$		0			0
$501$	−8.50862	+	6.18188i	−0.380137	+	0.276186i
$502$		0			0
$503$	0.958726	−	2.95065i	0.0427475	−	0.131563i	−0.927405	−	0.374059i	$-0.877966\pi$
$503$	0.958726	−	2.95065i	0.0427475	−	0.131563i	0.970153	+	0.242495i	$0.0779659\pi$
$504$		0			0
$505$	7.15941			0.318590
$506$		0			0
$507$	4.19328			0.186230
$508$		0			0
$509$	2.02172	−	6.22222i	0.0896112	−	0.275795i	−0.896201	−	0.443649i	$-0.853684\pi$
$509$	2.02172	−	6.22222i	0.0896112	−	0.275795i	0.985812	+	0.167854i	$0.0536837\pi$
$510$		0			0
$511$	−0.635721	+	0.461878i	−0.0281226	+	0.0204323i
$512$		0			0
$513$	−1.47562	−	4.54150i	−0.0651503	−	0.200512i
$514$		0			0
$515$	8.48769	+	6.16667i	0.374012	+	0.271736i
$516$		0			0
$517$	6.05040	+	19.9584i	0.266096	+	0.877768i
$518$		0			0
$519$	−36.6626	−	26.6370i	−1.60931	−	1.16923i
$520$		0			0
$521$	6.20838	+	19.1074i	0.271994	+	0.837112i	0.989999	+	0.141074i	$0.0450555\pi$
$521$	6.20838	+	19.1074i	0.271994	+	0.837112i	−0.718005	+	0.696038i	$0.754944\pi$
$522$		0			0
$523$	−36.9613	+	26.8540i	−1.61620	+	1.17424i	−0.780158	+	0.625582i	$0.784861\pi$
$523$	−36.9613	+	26.8540i	−1.61620	+	1.17424i	−0.836046	+	0.548659i	$0.815139\pi$
$524$		0			0
$525$	0.200922	−	0.618375i	0.00876896	−	0.0269881i
$526$		0			0
$527$	33.7008			1.46803
$528$		0			0
$529$	−22.8818			−0.994860
$530$		0			0
$531$	0.888095	−	2.73327i	0.0385400	−	0.118614i
$532$		0			0
$533$	19.6144	−	14.2507i	0.849593	−	0.617266i
$534$		0			0
$535$	5.27981	+	16.2496i	0.228266	+	0.702531i
$536$		0			0
$537$	38.5846	+	28.0334i	1.66505	+	1.20973i
$538$		0			0
$539$	−7.50827	+	21.6395i	−0.323404	+	0.932080i
$540$		0			0
$541$	−15.9314	−	11.5748i	−0.684943	−	0.497640i	0.190051	−	0.981774i	$-0.439135\pi$
$541$	−15.9314	−	11.5748i	−0.684943	−	0.497640i	−0.874994	+	0.484134i	$0.839135\pi$
$542$		0			0
$543$	−1.16856	−	3.59645i	−0.0501476	−	0.154338i
$544$		0			0
$545$	15.3257	−	11.1348i	0.656481	−	0.476962i
$546$		0			0
$547$	8.28840	−	25.5091i	0.354386	−	1.09069i	−0.601978	−	0.798513i	$-0.705621\pi$
$547$	8.28840	−	25.5091i	0.354386	−	1.09069i	0.956364	−	0.292176i	$-0.0943794\pi$
$548$		0			0
$549$	15.3932			0.656965
$550$		0			0
$551$	−10.5076			−0.447638
$552$		0			0
$553$	0.229050	−	0.704942i	0.00974018	−	0.0299772i
$554$		0			0
$555$	−9.10359	+	6.61415i	−0.386426	+	0.280755i
$556$		0			0
$557$	−6.68924	−	20.5874i	−0.283432	−	0.872315i	−0.986864	−	0.161552i	$-0.948350\pi$
$557$	−6.68924	−	20.5874i	−0.283432	−	0.872315i	0.703432	−	0.710763i	$-0.251650\pi$
$558$		0			0
$559$	11.1757	+	8.11959i	0.472680	+	0.343422i
$560$		0			0
$561$	31.8180	+	24.0946i	1.34336	+	1.01727i
$562$		0			0
$563$	−32.1055	−	23.3260i	−1.35309	−	0.983076i	−0.998851	−	0.0479197i	$-0.984741\pi$
$563$	−32.1055	−	23.3260i	−1.35309	−	0.983076i	−0.354236	−	0.935156i	$-0.615259\pi$
$564$		0			0
$565$	1.10359	+	3.39651i	0.0464286	+	0.142892i
$566$		0			0
$567$	−2.78831	+	2.02583i	−0.117098	+	0.0850767i
$568$		0			0
$569$	0.845992	−	2.60370i	0.0354658	−	0.109153i	−0.931756	−	0.363084i	$-0.881724\pi$
$569$	0.845992	−	2.60370i	0.0354658	−	0.109153i	0.967222	+	0.253931i	$0.0817238\pi$
$570$		0			0
$571$	−38.0562			−1.59260			−0.796302	−	0.604899i	$-0.793213\pi$
$571$	−38.0562			−1.59260			−0.796302	+	0.604899i	$0.793213\pi$
$572$		0			0
$573$	−55.6239			−2.32372
$574$		0			0
$575$	0.106252	−	0.327009i	0.00443100	−	0.0136372i
$576$		0			0
$577$	−6.82060	+	4.95545i	−0.283945	+	0.206298i	−0.720636	−	0.693313i	$-0.756150\pi$
$577$	−6.82060	+	4.95545i	−0.283945	+	0.206298i	0.436691	+	0.899611i	$0.356150\pi$
$578$		0			0
$579$	6.60942	+	20.3417i	0.274678	+	0.845372i
$580$		0			0
$581$	−1.12345	−	0.816234i	−0.0466086	−	0.0338631i
$582$		0			0
$583$	35.3817	+	0.701147i	1.46536	+	0.0290385i
$584$		0			0
$585$	4.04079	+	2.93580i	0.167066	+	0.121380i
$586$		0			0
$587$	−2.99868	−	9.22900i	−0.123769	−	0.380921i	0.869906	−	0.493218i	$-0.164179\pi$
$587$	−2.99868	−	9.22900i	−0.123769	−	0.380921i	−0.993675	+	0.112296i	$0.964179\pi$
$588$		0			0
$589$	7.23341	−	5.25538i	0.298047	−	0.216544i
$590$		0			0
$591$	−4.49190	+	13.8247i	−0.184772	+	0.568670i
$592$		0			0
$593$	−22.3047			−0.915943			−0.457971	−	0.888967i	$-0.651424\pi$
$593$	−22.3047			−0.915943			−0.457971	+	0.888967i	$0.651424\pi$
$594$		0			0
$595$	1.73708			0.0712135
$596$		0			0
$597$	10.9537	−	33.7120i	0.448304	−	1.37974i
$598$		0			0
$599$	16.0325	−	11.6483i	0.655071	−	0.475937i	−0.209924	−	0.977718i	$-0.567322\pi$
$599$	16.0325	−	11.6483i	0.655071	−	0.475937i	0.864995	+	0.501781i	$0.167322\pi$
$600$		0			0
$601$	−5.98586	−	18.4226i	−0.244168	−	0.751473i	−0.995772	−	0.0918582i	$-0.970719\pi$
$601$	−5.98586	−	18.4226i	−0.244168	−	0.751473i	0.751604	−	0.659615i	$-0.229281\pi$
$602$		0			0
$603$	12.6735	+	9.20787i	0.516107	+	0.374973i
$604$		0			0
$605$	−2.98205	−	10.5881i	−0.121238	−	0.430467i
$606$		0			0
$607$	−0.465809	−	0.338430i	−0.0189066	−	0.0137365i	0.578292	−	0.815830i	$-0.303720\pi$
$607$	−0.465809	−	0.338430i	−0.0189066	−	0.0137365i	−0.597198	+	0.802094i	$0.703720\pi$
$608$		0			0
$609$	1.40345	+	4.31937i	0.0568706	+	0.175030i
$610$		0			0
$611$	−16.8909	+	12.2719i	−0.683331	+	0.496469i
$612$		0			0
$613$	9.61609	−	29.5953i	0.388390	−	1.19534i	−0.545601	−	0.838045i	$-0.683698\pi$
$613$	9.61609	−	29.5953i	0.388390	−	1.19534i	0.933991	−	0.357297i	$-0.116302\pi$
$614$		0			0
$615$	−15.4973			−0.624913
$616$		0			0
$617$	18.4917			0.744447			0.372224	−	0.928143i	$-0.378595\pi$
$617$	18.4917			0.744447			0.372224	+	0.928143i	$0.378595\pi$
$618$		0			0
$619$	−2.98840	+	9.19734i	−0.120114	+	0.369672i	−0.992979	−	0.118289i	$-0.962259\pi$
$619$	−2.98840	+	9.19734i	−0.120114	+	0.369672i	0.872865	+	0.487961i	$0.162259\pi$
$620$		0			0
$621$	−0.883018	+	0.641550i	−0.0354343	+	0.0257445i
$622$		0			0
$623$	−0.233224	−	0.717789i	−0.00934392	−	0.0287576i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$		0			0
$627$	10.5867	+	0.209792i	0.422791	+	0.00837830i
$628$		0			0
$629$	−24.3214	−	17.6705i	−0.969757	−	0.704570i
$630$		0			0
$631$	−0.381339	−	1.17364i	−0.0151809	−	0.0467219i	0.943179	−	0.332285i	$-0.107819\pi$
$631$	−0.381339	−	1.17364i	−0.0151809	−	0.0467219i	−0.958360	+	0.285563i	$0.907819\pi$
$632$		0			0
$633$	14.0558	−	10.2122i	0.558669	−	0.405897i
$634$		0			0
$635$	2.24171	−	6.89927i	0.0889595	−	0.273789i
$636$		0			0
$637$	−22.9303			−0.908531
$638$		0			0
$639$	−16.8047			−0.664782
$640$		0			0
$641$	−4.92312	+	15.1518i	−0.194451	+	0.598460i	0.805531	+	0.592553i	$0.201880\pi$
$641$	−4.92312	+	15.1518i	−0.194451	+	0.598460i	−0.999983	+	0.00590646i	$0.998120\pi$
$642$		0			0
$643$	−11.9209	+	8.66107i	−0.470116	+	0.341559i	−0.797487	−	0.603337i	$-0.793838\pi$
$643$	−11.9209	+	8.66107i	−0.470116	+	0.341559i	0.327370	+	0.944896i	$0.393838\pi$
$644$		0			0
$645$	−2.72859	−	8.39772i	−0.107438	−	0.330660i
$646$		0			0
$647$	−3.02156	−	2.19529i	−0.118790	−	0.0863058i	0.526804	−	0.849987i	$-0.323390\pi$
$647$	−3.02156	−	2.19529i	−0.118790	−	0.0863058i	−0.645594	+	0.763681i	$0.723390\pi$
$648$		0			0
$649$	−5.05141	−	3.82524i	−0.198285	−	0.150154i
$650$		0			0
$651$	−3.12647	−	2.27151i	−0.122536	−	0.0890276i
$652$		0			0
$653$	−10.9132	−	33.5874i	−0.427067	−	1.31438i	−0.901002	−	0.433816i	$-0.857167\pi$
$653$	−10.9132	−	33.5874i	−0.427067	−	1.31438i	0.473935	−	0.880560i	$-0.342833\pi$
$654$		0			0
$655$	17.6148	−	12.7979i	0.688268	−	0.500056i
$656$		0			0
$657$	−1.19232	+	3.66959i	−0.0465170	+	0.143164i
$658$		0			0
$659$	40.5715			1.58044			0.790220	−	0.612823i	$-0.209966\pi$
$659$	40.5715			1.58044			0.790220	+	0.612823i	$0.209966\pi$
$660$		0			0
$661$	22.0301			0.856870			0.428435	−	0.903573i	$-0.359065\pi$
$661$	22.0301			0.856870			0.428435	+	0.903573i	$0.359065\pi$
$662$		0			0
$663$	−12.3469	+	37.9999i	−0.479515	+	1.47579i
$664$		0			0
$665$	0.372841	−	0.270885i	0.0144582	−	0.0105045i
$666$		0			0
$667$	0.742172	+	2.28417i	0.0287370	+	0.0884434i
$668$		0			0
$669$	28.1813	+	20.4749i	1.08955	+	0.791606i
$670$		0			0
$671$	11.1250	−	32.0631i	0.429474	−	1.23778i
$672$		0			0
$673$	18.9208	+	13.7468i	0.729345	+	0.529900i	0.889356	−	0.457215i	$-0.151153\pi$
$673$	18.9208	+	13.7468i	0.729345	+	0.529900i	−0.160011	+	0.987115i	$0.551153\pi$
$674$		0			0
$675$	0.980936	+	3.01901i	0.0377562	+	0.116202i
$676$		0			0
$677$	24.6959	−	17.9426i	0.949139	−	0.689590i	−0.00146411	−	0.999999i	$-0.500466\pi$
$677$	24.6959	−	17.9426i	0.949139	−	0.689590i	0.950603	+	0.310409i	$0.100466\pi$
$678$		0			0
$679$	−1.29958	+	3.99970i	−0.0498733	+	0.153494i
$680$		0			0
$681$	−38.2041			−1.46398
$682$		0			0
$683$	22.0885			0.845192			0.422596	−	0.906318i	$-0.361119\pi$
$683$	22.0885			0.845192			0.422596	+	0.906318i	$0.361119\pi$
$684$		0			0
$685$	−0.552243	+	1.69963i	−0.0211001	+	0.0649395i
$686$		0			0
$687$	25.3912	−	18.4478i	0.968734	−	0.703826i
$688$		0			0
$689$	10.9477	+	33.6936i	0.417075	+	1.28362i
$690$		0			0
$691$	13.9069	+	10.1040i	0.529045	+	0.384374i	0.820000	−	0.572363i	$-0.193973\pi$
$691$	13.9069	+	10.1040i	0.529045	+	0.384374i	−0.290956	+	0.956737i	$0.593973\pi$
$692$		0			0
$693$	−0.443435	−	1.46275i	−0.0168447	−	0.0555654i
$694$		0			0
$695$	10.4568	+	7.59734i	0.396651	+	0.288184i
$696$		0			0
$697$	−12.7942	−	39.3766i	−0.484616	−	1.49150i
$698$		0			0
$699$	−44.2434	+	32.1447i	−1.67344	+	1.21582i
$700$		0			0
$701$	10.6808	−	32.8721i	0.403408	−	1.24156i	−0.518808	−	0.854891i	$-0.673624\pi$
$701$	10.6808	−	32.8721i	0.403408	−	1.24156i	0.922217	−	0.386673i	$-0.126376\pi$
$702$		0			0
$703$	−7.97583			−0.300814
$704$		0			0
$705$	13.3455			0.502619
$706$		0			0
$707$	0.677784	−	2.08600i	0.0254907	−	0.0784523i
$708$		0			0
$709$	−17.3833	+	12.6297i	−0.652844	+	0.474319i	−0.864239	−	0.503082i	$-0.832199\pi$
$709$	−17.3833	+	12.6297i	−0.652844	+	0.474319i	0.211395	+	0.977401i	$0.432199\pi$
$710$		0			0
$711$	−1.12469	−	3.46144i	−0.0421791	−	0.129814i
$712$		0			0
$713$	−1.65334	−	1.20122i	−0.0619181	−	0.0449861i
$714$		0			0
$715$	9.03547	−	6.29497i	0.337907	−	0.235418i
$716$		0			0
$717$	13.4644	+	9.78242i	0.502835	+	0.365331i
$718$		0			0
$719$	8.06421	+	24.8191i	0.300744	+	0.925596i	0.981231	+	0.192836i	$0.0617684\pi$
$719$	8.06421	+	24.8191i	0.300744	+	0.925596i	−0.680487	+	0.732760i	$0.738232\pi$
$720$		0			0
$721$	2.60029	−	1.88922i	0.0968398	−	0.0703582i
$722$		0			0
$723$	15.2103	−	46.8124i	0.565676	−	1.74097i
$724$		0			0
$725$	6.98503			0.259418
$726$		0			0
$727$	−11.7639			−0.436300			−0.218150	−	0.975915i	$-0.570002\pi$
$727$	−11.7639			−0.436300			−0.218150	+	0.975915i	$0.570002\pi$
$728$		0			0
$729$	1.01602	−	3.12699i	0.0376303	−	0.115814i
$730$		0			0
$731$	19.0848	−	13.8659i	0.705878	−	0.512850i
$732$		0			0
$733$	−10.1366	−	31.1974i	−0.374405	−	1.15230i	−0.943879	−	0.330291i	$-0.892853\pi$
$733$	−10.1366	−	31.1974i	−0.374405	−	1.15230i	0.569474	−	0.822009i	$-0.307147\pi$
$734$		0			0
$735$	11.8579	+	8.61525i	0.437384	+	0.317778i
$736$		0			0
$737$	28.3389	−	19.7436i	1.04388	−	0.727264i
$738$		0			0
$739$	0.288938	+	0.209926i	0.0106288	+	0.00772224i	0.593087	−	0.805138i	$-0.297909\pi$
$739$	0.288938	+	0.209926i	0.0106288	+	0.00772224i	−0.582458	+	0.812861i	$0.697909\pi$
$740$		0			0
$741$	3.27570	+	10.0816i	0.120336	+	0.370356i
$742$		0			0
$743$	−29.6594	+	21.5488i	−1.08810	+	0.790549i	−0.979077	−	0.203491i	$-0.934771\pi$
$743$	−29.6594	+	21.5488i	−1.08810	+	0.790549i	−0.109020	+	0.994040i	$0.534771\pi$
$744$		0			0
$745$	−0.647238	+	1.99199i	−0.0237130	+	0.0729810i
$746$		0			0
$747$	−6.81865			−0.249481
$748$		0			0
$749$	5.23441			0.191261
$750$		0			0
$751$	13.6834	−	42.1131i	0.499313	−	1.53673i	−0.310811	−	0.950472i	$-0.600601\pi$
$751$	13.6834	−	42.1131i	0.499313	−	1.53673i	0.810125	−	0.586257i	$-0.199399\pi$
$752$		0			0
$753$	19.7143	−	14.3233i	0.718428	−	0.521969i
$754$		0			0
$755$	5.46384	+	16.8160i	0.198849	+	0.611996i
$756$		0			0
$757$	34.7688	+	25.2610i	1.26369	+	0.918126i	0.998933	−	0.0461881i	$-0.0147074\pi$
$757$	34.7688	+	25.2610i	1.26369	+	0.918126i	0.264760	+	0.964314i	$0.414707\pi$
$758$		0			0
$759$	−0.702152	−	2.31618i	−0.0254865	−	0.0840720i
$760$		0			0
$761$	−0.846857	−	0.615278i	−0.0306985	−	0.0223038i	0.572330	−	0.820023i	$-0.306040\pi$
$761$	−0.846857	−	0.615278i	−0.0306985	−	0.0223038i	−0.603029	+	0.797719i	$0.706040\pi$
$762$		0			0
$763$	−1.79340	−	5.51952i	−0.0649254	−	0.199820i
$764$		0			0
$765$	6.90050	−	5.01351i	0.249488	−	0.181264i
$766$		0			0
$767$	1.96019	−	6.03285i	0.0707785	−	0.217834i
$768$		0			0
$769$	52.9156			1.90818			0.954092	−	0.299513i	$-0.0968243\pi$
$769$	52.9156			1.90818			0.954092	+	0.299513i	$0.0968243\pi$
$770$		0			0
$771$	9.62006			0.346458
$772$		0			0
$773$	−11.4526	+	35.2476i	−0.411923	+	1.26777i	0.503051	+	0.864257i	$0.332211\pi$
$773$	−11.4526	+	35.2476i	−0.411923	+	1.26777i	−0.914974	+	0.403512i	$0.867789\pi$
$774$		0			0
$775$	−4.80849	+	3.49357i	−0.172726	+	0.125493i
$776$		0			0
$777$	1.06529	+	3.27864i	0.0382172	+	0.117620i
$778$		0			0
$779$	−8.88659	−	6.45649i	−0.318395	−	0.231328i
$780$		0			0
$781$	−12.1451	+	35.0032i	−0.434585	+	1.25251i
$782$		0			0
$783$	−17.9384	−	13.0330i	−0.641067	−	0.465763i
$784$		0			0
$785$	6.29957	+	19.3881i	0.224841	+	0.691990i
$786$		0			0
$787$	1.50000	−	1.08981i	0.0534692	−	0.0388477i	−0.560730	−	0.827999i	$-0.689479\pi$
$787$	1.50000	−	1.08981i	0.0534692	−	0.0388477i	0.614199	+	0.789151i	$0.289479\pi$
$788$		0			0
$789$	2.49284	−	7.67218i	0.0887475	−	0.273137i
$790$		0			0
$791$	1.09410			0.0389019
$792$		0			0
$793$	33.9756			1.20651
$794$		0			0
$795$	6.99783	−	21.5371i	0.248188	−	0.763843i
$796$		0			0
$797$	−0.0383291	+	0.0278477i	−0.00135769	+	0.000986417i	−0.588464	−	0.808524i	$-0.700267\pi$
$797$	−0.0383291	+	0.0278477i	−0.00135769	+	0.000986417i	0.587106	+	0.809510i	$0.300267\pi$
$798$		0			0
$799$	11.0177	+	33.9090i	0.389779	+	1.19962i
$800$		0			0
$801$	−2.99813	−	2.17827i	−0.105934	−	0.0769655i
$802$		0			0
$803$	6.78184	+	5.13563i	0.239326	+	0.181233i
$804$		0			0
$805$	−0.0852203	−	0.0619162i	−0.00300362	−	0.00218226i
$806$		0			0
$807$	12.6583	+	38.9582i	0.445593	+	1.37139i
$808$		0			0
$809$	−44.2731	+	32.1663i	−1.55656	+	1.13091i	−0.617801	+	0.786335i	$0.711976\pi$
$809$	−44.2731	+	32.1663i	−1.55656	+	1.13091i	−0.938760	+	0.344573i	$0.888024\pi$
$810$		0			0
$811$	−13.1648	+	40.5172i	−0.462280	+	1.42275i	0.400091	+	0.916476i	$0.368979\pi$
$811$	−13.1648	+	40.5172i	−0.462280	+	1.42275i	−0.862371	+	0.506277i	$0.831021\pi$
$812$		0			0
$813$	−29.3634			−1.02982
$814$		0			0
$815$	12.9592			0.453942
$816$		0			0
$817$	1.93401	−	5.95226i	0.0676624	−	0.208243i
$818$		0			0
$819$	1.23793	−	0.899412i	0.0432569	−	0.0314280i
$820$		0			0
$821$	1.51704	+	4.66898i	0.0529452	+	0.162948i	0.974033	−	0.226407i	$-0.0726979\pi$
$821$	1.51704	+	4.66898i	0.0529452	+	0.162948i	−0.921088	+	0.389355i	$0.872698\pi$
$822$		0			0
$823$	−7.51286	−	5.45841i	−0.261882	−	0.190268i	0.449094	−	0.893484i	$-0.351747\pi$
$823$	−7.51286	−	5.45841i	−0.261882	−	0.190268i	−0.710976	+	0.703216i	$0.751747\pi$
$824$		0			0
$825$	−7.03760	−	0.139462i	−0.245018	−	0.00485544i
$826$		0			0
$827$	−26.5271	−	19.2730i	−0.922436	−	0.670189i	0.0216929	−	0.999765i	$-0.493094\pi$
$827$	−26.5271	−	19.2730i	−0.922436	−	0.670189i	−0.944129	+	0.329575i	$0.893094\pi$
$828$		0			0
$829$	3.36118	+	10.3447i	0.116739	+	0.359285i	0.992306	−	0.123812i	$-0.0395119\pi$
$829$	3.36118	+	10.3447i	0.116739	+	0.359285i	−0.875567	+	0.483097i	$0.839512\pi$
$830$		0			0
$831$	34.6406	−	25.1679i	1.20167	−	0.873064i
$832$		0			0
$833$	−12.1006	+	37.2418i	−0.419261	+	1.29035i
$834$		0			0
$835$	4.95551			0.171492
$836$		0			0
$837$	18.8673			0.652149
$838$		0			0
$839$	−4.82985	+	14.8647i	−0.166745	+	0.513188i	−0.999161	−	0.0409637i	$-0.986957\pi$
$839$	−4.82985	+	14.8647i	−0.166745	+	0.513188i	0.832416	+	0.554152i	$0.186957\pi$
$840$		0			0
$841$	−16.0110	+	11.6327i	−0.552104	+	0.401127i
$842$		0			0
$843$	−6.64342	−	20.4463i	−0.228811	−	0.704209i
$844$		0			0
$845$	−1.59844	−	1.16134i	−0.0549881	−	0.0399512i
$846$		0			0
$847$	−3.36731	−	0.133510i	−0.115702	−	0.00458746i
$848$		0			0
$849$	36.1630	+	26.2740i	1.24111	+	0.901720i
$850$		0			0
$851$	0.563349	+	1.73381i	0.0193114	+	0.0594343i
$852$		0			0
$853$	−7.15097	+	5.19549i	−0.244845	+	0.177890i	−0.703439	−	0.710756i	$-0.748353\pi$
$853$	−7.15097	+	5.19549i	−0.244845	+	0.177890i	0.458594	+	0.888646i	$0.348353\pi$
$854$		0			0
$855$	0.699280	−	2.15216i	0.0239149	−	0.0736024i
$856$		0			0
$857$	−51.6469			−1.76422			−0.882112	−	0.471040i	$-0.843879\pi$
$857$	−51.6469			−1.76422			−0.882112	+	0.471040i	$0.843879\pi$
$858$		0			0
$859$	14.0705			0.480078			0.240039	−	0.970763i	$-0.422840\pi$
$859$	14.0705			0.480078			0.240039	+	0.970763i	$0.422840\pi$
$860$		0			0
$861$	−1.46714	+	4.51539i	−0.0499999	+	0.153884i
$862$		0			0
$863$	34.2045	−	24.8510i	1.16433	−	0.845938i	0.174014	−	0.984743i	$-0.444326\pi$
$863$	34.2045	−	24.8510i	1.16433	−	0.845938i	0.990320	+	0.138806i	$0.0443263\pi$
$864$		0			0
$865$	6.59834	+	20.3076i	0.224350	+	0.690479i
$866$		0			0
$867$	26.0122	+	18.8990i	0.883420	+	0.641843i
$868$		0			0
$869$	−8.02281	−	0.158985i	−0.272155	−	0.00539321i
$870$		0			0
$871$	27.9729	+	20.3235i	0.947826	+	0.688636i
$872$		0			0
$873$	6.38125	+	19.6395i	0.215973	+	0.664696i
$874$		0			0
$875$	−0.247850	+	0.180074i	−0.00837887	+	0.00608760i
$876$		0			0
$877$	5.06926	−	15.6016i	0.171177	−	0.526828i	−0.828261	−	0.560342i	$-0.810670\pi$
$877$	5.06926	−	15.6016i	0.171177	−	0.526828i	0.999438	+	0.0335137i	$0.0106698\pi$
$878$		0			0
$879$	38.9338			1.31321
$880$		0			0
$881$	−15.6436			−0.527045			−0.263522	−	0.964653i	$-0.584884\pi$
$881$	−15.6436			−0.527045			−0.263522	+	0.964653i	$0.584884\pi$
$882$		0			0
$883$	2.34202	−	7.20799i	0.0788152	−	0.242568i	−0.903884	−	0.427778i	$-0.859296\pi$
$883$	2.34202	−	7.20799i	0.0788152	−	0.242568i	0.982699	+	0.185210i	$0.0592965\pi$
$884$		0			0
$885$	−3.28030	+	2.38328i	−0.110266	+	0.0801130i
$886$		0			0
$887$	−1.63187	−	5.02238i	−0.0547929	−	0.168635i	0.919915	−	0.392118i	$-0.128257\pi$
$887$	−1.63187	−	5.02238i	−0.0547929	−	0.168635i	−0.974708	+	0.223483i	$0.928257\pi$
$888$		0			0
$889$	−1.79798	−	1.30631i	−0.0603025	−	0.0438123i
$890$		0			0
$891$	29.7456	+	22.5252i	0.996514	+	0.754622i
$892$		0			0
$893$	7.65265	+	5.55998i	0.256086	+	0.186058i
$894$		0			0
$895$	−6.94425	−	21.3722i	−0.232121	−	0.714394i
$896$		0			0
$897$	1.96019	−	1.42416i	0.0654489	−	0.0475514i
$898$		0			0
$899$	12.8293	−	39.4844i	0.427880	−	1.31688i
$900$		0			0
$901$	60.5001			2.01555
$902$		0			0
$903$	−2.70512			−0.0900208
$904$		0			0
$905$	−0.550600	+	1.69457i	−0.0183026	+	0.0563295i
$906$		0			0
$907$	18.3680	−	13.3452i	0.609901	−	0.443119i	−0.239479	−	0.970902i	$-0.576976\pi$
$907$	18.3680	−	13.3452i	0.609901	−	0.443119i	0.849379	+	0.527783i	$0.176976\pi$
$908$		0			0
$909$	−3.32808	−	10.2428i	−0.110385	−	0.339732i
$910$		0			0
$911$	−8.03484	−	5.83766i	−0.266206	−	0.193410i	0.446672	−	0.894698i	$-0.352609\pi$
$911$	−8.03484	−	5.83766i	−0.266206	−	0.193410i	−0.712879	+	0.701287i	$0.752609\pi$
$912$		0			0
$913$	−4.92798	+	14.2029i	−0.163092	+	0.470047i
$914$		0			0
$915$	−17.5697	−	12.7652i	−0.580837	−	0.422003i
$916$		0			0
$917$	−2.06127	−	6.34393i	−0.0680691	−	0.209495i
$918$		0			0
$919$	−9.49295	+	6.89703i	−0.313143	+	0.227512i	−0.733244	−	0.679965i	$-0.761995\pi$
$919$	−9.49295	+	6.89703i	−0.313143	+	0.227512i	0.420101	+	0.907477i	$0.361995\pi$
$920$		0			0
$921$	13.9954	−	43.0734i	0.461164	−	1.41932i
$922$		0			0
$923$	−37.0911			−1.22087
$924$		0			0
$925$	5.30202			0.174329
$926$		0			0
$927$	4.87695	−	15.0097i	0.160180	−	0.492984i
$928$		0			0
$929$	−8.86447	+	6.44041i	−0.290834	+	0.211303i	−0.723629	−	0.690189i	$-0.757527\pi$
$929$	−8.86447	+	6.44041i	−0.290834	+	0.211303i	0.432795	+	0.901492i	$0.357527\pi$
$930$		0			0
$931$	3.21035	+	9.88044i	0.105215	+	0.323818i
$932$		0			0
$933$	−23.6389	−	17.1747i	−0.773904	−	0.562274i
$934$		0			0
$935$	−5.45573	−	17.9967i	−0.178421	−	0.588556i
$936$		0			0
$937$	8.69826	+	6.31966i	0.284160	+	0.206454i	0.720730	−	0.693216i	$-0.243807\pi$
$937$	8.69826	+	6.31966i	0.284160	+	0.206454i	−0.436570	+	0.899670i	$0.643807\pi$
$938$		0			0
$939$	17.2524	+	53.0975i	0.563012	+	1.73277i
$940$		0			0
$941$	−28.7229	+	20.8684i	−0.936339	+	0.680290i	−0.947537	−	0.319647i	$-0.896436\pi$
$941$	−28.7229	+	20.8684i	−0.936339	+	0.680290i	0.0111977	+	0.999937i	$0.496436\pi$
$942$		0			0
$943$	−0.775853	+	2.38783i	−0.0252652	+	0.0777584i
$944$		0			0
$945$	0.972501			0.0316355
$946$		0			0
$947$	46.7444			1.51899			0.759495	−	0.650513i	$-0.225446\pi$
$947$	46.7444			1.51899			0.759495	+	0.650513i	$0.225446\pi$
$948$		0			0
$949$	−2.63168	+	8.09949i	−0.0854280	+	0.262920i
$950$		0			0
$951$	−17.9118	+	13.0137i	−0.580831	+	0.421998i
$952$		0			0
$953$	10.5357	+	32.4257i	0.341286	+	1.05037i	0.963542	+	0.267557i	$0.0862162\pi$
$953$	10.5357	+	32.4257i	0.341286	+	1.05037i	−0.622256	+	0.782814i	$0.713784\pi$
$954$		0			0
$955$	21.2034	+	15.4052i	0.686125	+	0.498499i
$956$		0			0
$957$	40.3422	−	28.1062i	1.30408	−	0.908544i
$958$		0			0
$959$	0.442932	+	0.321809i	0.0143030	+	0.0103917i
$960$		0			0
$961$	1.33701	+	4.11488i	0.0431292	+	0.132738i
$962$		0			0
$963$	20.7935	−	15.1074i	0.670062	−	0.486829i
$964$		0			0
$965$	3.11422	−	9.58459i	0.100250	−	0.308539i
$966$		0			0
$967$	−20.9490			−0.673675			−0.336837	−	0.941563i	$-0.609357\pi$
$967$	−20.9490			−0.673675			−0.336837	+	0.941563i	$0.609357\pi$
$968$		0			0
$969$	18.1024			0.581534
$970$		0			0
$971$	−6.76006	+	20.8053i	−0.216941	+	0.667675i	0.782070	+	0.623191i	$0.214164\pi$
$971$	−6.76006	+	20.8053i	−0.216941	+	0.667675i	−0.999010	+	0.0444834i	$0.985836\pi$
$972$		0			0
$973$	3.20356	−	2.32752i	0.102701	−	0.0746169i
$974$		0			0
$975$	−2.17756	−	6.70184i	−0.0697377	−	0.214631i
$976$		0			0
$977$	20.3733	+	14.8021i	0.651799	+	0.473560i	0.863884	−	0.503691i	$-0.168025\pi$
$977$	20.3733	+	14.8021i	0.651799	+	0.473560i	−0.212084	+	0.977251i	$0.568025\pi$
$978$		0			0
$979$	−6.70403	+	4.67067i	−0.214262	+	0.149275i
$980$		0			0
$981$	−23.0545	−	16.7500i	−0.736072	−	0.534788i
$982$		0			0
$983$	−4.46922	−	13.7548i	−0.142546	−	0.438711i	0.854141	−	0.520041i	$-0.174083\pi$
$983$	−4.46922	−	13.7548i	−0.142546	−	0.438711i	−0.996687	+	0.0813298i	$0.974083\pi$
$984$		0			0
$985$	5.54105	−	4.02581i	0.176553	−	0.128273i
$986$		0			0
$987$	1.26342	−	3.88841i	0.0402151	−	0.123769i
$988$		0			0
$989$	−1.43052			−0.0454880
$990$		0			0
$991$	−31.2980			−0.994214			−0.497107	−	0.867689i	$-0.665604\pi$
$991$	−31.2980			−0.994214			−0.497107	+	0.867689i	$0.665604\pi$
$992$		0			0
$993$	−6.19819	+	19.0761i	−0.196694	+	0.605361i
$994$		0			0
$995$	−13.5121	+	9.81709i	−0.428361	+	0.311223i
$996$		0			0
$997$	3.13608	+	9.65187i	0.0993207	+	0.305678i	0.988356	−	0.152162i	$-0.0486234\pi$
$997$	3.13608	+	9.65187i	0.0993207	+	0.305678i	−0.889035	+	0.457839i	$0.848623\pi$
$998$		0			0
$999$	−13.6163	−	9.89279i	−0.430799	−	0.312994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bo.f.81.1		8
4.3	odd	2		220.2.m.a.81.2	✓	8
11.3	even	5	inner	880.2.bo.f.641.1		8
11.5	even	5		9680.2.a.ck.1.2		4
11.6	odd	10		9680.2.a.cl.1.2		4
12.11	even	2		1980.2.z.c.1621.1		8
20.3	even	4		1100.2.cb.c.1049.4		16
20.7	even	4		1100.2.cb.c.1049.1		16
20.19	odd	2		1100.2.n.c.301.1		8
44.3	odd	10		220.2.m.a.201.2	yes	8
44.27	odd	10		2420.2.a.n.1.3		4
44.39	even	10		2420.2.a.m.1.3		4
132.47	even	10		1980.2.z.c.1081.1		8
220.3	even	20		1100.2.cb.c.949.1		16
220.47	even	20		1100.2.cb.c.949.4		16
220.179	odd	10		1100.2.n.c.201.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.m.a.81.2	✓	8	4.3	odd	2
220.2.m.a.201.2	yes	8	44.3	odd	10
880.2.bo.f.81.1		8	1.1	even	1	trivial
880.2.bo.f.641.1		8	11.3	even	5	inner
1100.2.n.c.201.1		8	220.179	odd	10
1100.2.n.c.301.1		8	20.19	odd	2
1100.2.cb.c.949.1		16	220.3	even	20
1100.2.cb.c.949.4		16	220.47	even	20
1100.2.cb.c.1049.1		16	20.7	even	4
1100.2.cb.c.1049.4		16	20.3	even	4
1980.2.z.c.1081.1		8	132.47	even	10
1980.2.z.c.1621.1		8	12.11	even	2
2420.2.a.m.1.3		4	44.39	even	10
2420.2.a.n.1.3		4	44.27	odd	10
9680.2.a.ck.1.2		4	11.5	even	5
9680.2.a.cl.1.2		4	11.6	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.655837 + 2.01846i) q^{3} +(0.809017 - 0.587785i) q^{5} +(-0.0946704 - 0.291365i) q^{7} +(-1.21700 - 0.884205i) q^{9} +O(q^{10})\)	\(q+(-0.655837 + 2.01846i) q^{3} +(0.809017 - 0.587785i) q^{5} +(-0.0946704 - 0.291365i) q^{7} +(-1.21700 - 0.884205i) q^{9} +(-2.72130 + 1.89592i) q^{11} +(-2.68616 - 1.95161i) q^{13} +(0.655837 + 2.01846i) q^{15} +(-4.58719 + 3.33279i) q^{17} +(-0.464854 + 1.43067i) q^{19} +0.650198 q^{21} +0.343838 q^{23} +(0.309017 - 0.951057i) q^{25} +(-2.56812 + 1.86585i) q^{27} +(2.15849 + 6.64316i) q^{29} +(-4.80849 - 3.49357i) q^{31} +(-2.04210 - 6.73625i) q^{33} +(-0.247850 - 0.180074i) q^{35} +(1.63842 + 5.04252i) q^{37} +(5.70092 - 4.14196i) q^{39} +(-2.25645 + 6.94464i) q^{41} -4.16046 q^{43} -1.50430 q^{45} +(1.94313 - 5.98035i) q^{47} +(5.58719 - 4.05933i) q^{49} +(-3.71865 - 11.4448i) q^{51} +(-8.63227 - 6.27171i) q^{53} +(-1.08719 + 3.13337i) q^{55} +(-2.58289 - 1.87658i) q^{57} +(0.590371 + 1.81697i) q^{59} +(-8.27850 + 6.01468i) q^{61} +(-0.142413 + 0.438301i) q^{63} -3.32027 q^{65} -10.4137 q^{67} +(-0.225502 + 0.694023i) q^{69} +(9.03760 - 6.56620i) q^{71} +(-0.792610 - 2.43940i) q^{73} +(1.71700 + 1.24748i) q^{75} +(0.810032 + 0.613406i) q^{77} +(1.95737 + 1.42211i) q^{79} +(-3.47644 - 10.6994i) q^{81} +(3.66709 - 2.66430i) q^{83} +(-1.75215 + 5.39256i) q^{85} -14.8246 q^{87} +2.46354 q^{89} +(-0.314331 + 0.967413i) q^{91} +(10.2052 - 7.41453i) q^{93} +(0.464854 + 1.43067i) q^{95} +(-11.1057 - 8.06878i) q^{97} +(4.98822 + 0.0988498i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{3} + 2 q^{5} - q^{7} + 3 q^{9}+O(q^{10}) \) 8 * q + q^3 + 2 * q^5 - q^7 + 3 * q^9	\( 8 q + q^{3} + 2 q^{5} - q^{7} + 3 q^{9} - 5 q^{11} + 6 q^{13} - q^{15} - 13 q^{17} + 7 q^{19} + 28 q^{21} + 22 q^{23} - 2 q^{25} - 2 q^{27} + 3 q^{29} + 2 q^{31} - 15 q^{33} - 4 q^{35} + 16 q^{37} + 17 q^{39} - 12 q^{41} - 10 q^{43} - 8 q^{45} + 18 q^{47} + 21 q^{49} - 21 q^{51} - 23 q^{53} + 15 q^{55} - q^{57} + 9 q^{59} - 34 q^{61} + 29 q^{63} - 6 q^{65} - 26 q^{67} - q^{69} + 26 q^{71} + q^{73} + q^{75} - 10 q^{77} - 19 q^{79} + 12 q^{81} + 7 q^{83} - 12 q^{85} - 94 q^{87} - 8 q^{89} + 18 q^{91} + 49 q^{93} - 7 q^{95} - 24 q^{97} + 20 q^{99}+O(q^{100}) \) 8 * q + q^3 + 2 * q^5 - q^7 + 3 * q^9 - 5 * q^11 + 6 * q^13 - q^15 - 13 * q^17 + 7 * q^19 + 28 * q^21 + 22 * q^23 - 2 * q^25 - 2 * q^27 + 3 * q^29 + 2 * q^31 - 15 * q^33 - 4 * q^35 + 16 * q^37 + 17 * q^39 - 12 * q^41 - 10 * q^43 - 8 * q^45 + 18 * q^47 + 21 * q^49 - 21 * q^51 - 23 * q^53 + 15 * q^55 - q^57 + 9 * q^59 - 34 * q^61 + 29 * q^63 - 6 * q^65 - 26 * q^67 - q^69 + 26 * q^71 + q^73 + q^75 - 10 * q^77 - 19 * q^79 + 12 * q^81 + 7 * q^83 - 12 * q^85 - 94 * q^87 - 8 * q^89 + 18 * q^91 + 49 * q^93 - 7 * q^95 - 24 * q^97 + 20 * q^99

Introduction

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