LMFDB - Embedded newform 576.2.p.c.95.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(95,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("576.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.p (of order $6$, degree $2$, 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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 11x^{14} + 85x^{12} + 332x^{10} + 940x^{8} + 1064x^{6} + 880x^{4} + 128x^{2} + 16 $ x^16 + 11x^14 + 85x^12 + 332x^10 + 940x^8 + 1064x^6 + 880x^4 + 128*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			95.6
Root			$1.03144 + 1.78651i$ of defining polynomial
Character	$\chi$	$=$	576.95
Dual form			576.2.p.c.479.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.31461 - 1.12774i) q^{3} +(-1.21189 + 2.09905i) q^{5} +(-3.96035 + 2.28651i) q^{7} +(0.456412 - 2.96508i) q^{9} +O(q^{10})$	\(q+(1.31461 - 1.12774i) q^{3} +(-1.21189 + 2.09905i) q^{5} +(-3.96035 + 2.28651i) q^{7} +(0.456412 - 2.96508i) q^{9} +(-3.73910 + 2.15877i) q^{11} +(-1.88322 - 1.08728i) q^{13} +(0.774019 + 4.12613i) q^{15} +3.90660i q^{17} -5.93016 q^{19} +(-2.62774 + 7.47211i) q^{21} +(2.94857 - 5.10707i) q^{23} +(-0.437348 - 0.757509i) q^{25} +(-2.74383 - 4.41264i) q^{27} +(-0.776975 - 1.34576i) q^{29} +(-0.925013 - 0.534057i) q^{31} +(-2.48094 + 7.05467i) q^{33} -11.0840i q^{35} +2.02356i q^{37} +(-3.70186 + 0.694430i) q^{39} +(10.4666 + 6.04289i) q^{41} +(0.995268 + 1.72386i) q^{43} +(5.67074 + 4.55138i) q^{45} +(3.70186 + 6.41181i) q^{47} +(6.95623 - 12.0485i) q^{49} +(4.40562 + 5.13567i) q^{51} +3.97773 q^{53} -10.4647i q^{55} +(-7.79586 + 6.68767i) q^{57} +(0.294283 + 0.169904i) q^{59} +(-8.33093 + 4.80986i) q^{61} +(4.97212 + 12.7863i) q^{63} +(4.56450 - 2.63531i) q^{65} +(-1.71554 + 2.97141i) q^{67} +(-1.88322 - 10.0390i) q^{69} +2.32554 q^{71} -2.37960 q^{73} +(-1.42922 - 0.502617i) q^{75} +(9.87208 - 17.0989i) q^{77} +(-5.38160 + 3.10707i) q^{79} +(-8.58338 - 2.70659i) q^{81} +(-5.40089 + 3.11821i) q^{83} +(-8.20016 - 4.73437i) q^{85} +(-2.53909 - 0.892929i) q^{87} +4.90465i q^{89} +9.94425 q^{91} +(-1.81831 + 0.341096i) q^{93} +(7.18669 - 12.4477i) q^{95} +(-1.32056 - 2.28728i) q^{97} +(4.69435 + 12.0720i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{5} + 6 q^{9}+O(q^{10}) $ 16 * q + 6 * q^5 + 6 * q^9	$ 16 q + 6 q^{5} + 6 q^{9} + 6 q^{13} - 30 q^{21} - 14 q^{25} + 18 q^{29} - 48 q^{33} + 66 q^{45} + 6 q^{49} - 48 q^{53} + 18 q^{57} - 42 q^{61} + 54 q^{65} + 6 q^{69} + 28 q^{73} + 66 q^{77} - 6 q^{81} - 36 q^{85} - 102 q^{93} + 8 q^{97}+O(q^{100}) $ 16 * q + 6 * q^5 + 6 * q^9 + 6 * q^13 - 30 * q^21 - 14 * q^25 + 18 * q^29 - 48 * q^33 + 66 * q^45 + 6 * q^49 - 48 * q^53 + 18 * q^57 - 42 * q^61 + 54 * q^65 + 6 * q^69 + 28 * q^73 + 66 * q^77 - 6 * q^81 - 36 * q^85 - 102 * q^93 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.31461	−	1.12774i	0.758992	−	0.651100i
$3$	1.31461	−	1.12774i	0.758992	−	0.651100i
$4$		0			0
$5$	−1.21189	+	2.09905i	−0.541973	+	0.938725i	0.456818	+	0.889560i	$0.348989\pi$
$5$	−1.21189	+	2.09905i	−0.541973	+	0.938725i	−0.998791	+	0.0491645i	$0.984344\pi$
$6$		0			0
$7$	−3.96035	+	2.28651i	−1.49687	+	0.864218i	−0.999994	−	0.00360263i	$-0.998853\pi$
$7$	−3.96035	+	2.28651i	−1.49687	+	0.864218i	−0.496877	+	0.867821i	$0.665520\pi$
$8$		0			0
$9$	0.456412	−	2.96508i	0.152137	−	0.988359i
$10$		0			0
$11$	−3.73910	+	2.15877i	−1.12738	+	0.650893i	−0.943275	−	0.332013i	$-0.892272\pi$
$11$	−3.73910	+	2.15877i	−1.12738	+	0.650893i	−0.184105	+	0.982907i	$0.558939\pi$
$12$		0			0
$13$	−1.88322	−	1.08728i	−0.522310	−	0.301556i	0.215569	−	0.976489i	$-0.430839\pi$
$13$	−1.88322	−	1.08728i	−0.522310	−	0.301556i	−0.737879	+	0.674933i	$0.764173\pi$
$14$		0			0
$15$	0.774019	+	4.12613i	0.199851	+	1.06536i
$16$		0			0
$17$			3.90660i			0.947490i	0.880662	+	0.473745i	$0.157098\pi$
$17$			3.90660i			0.947490i	−0.880662	+	0.473745i	$0.842902\pi$
$18$		0			0
$19$	−5.93016			−1.36047			−0.680236	−	0.732994i	$-0.738123\pi$
$19$	−5.93016			−1.36047			−0.680236	+	0.732994i	$0.738123\pi$
$20$		0			0
$21$	−2.62774	+	7.47211i	−0.573420	+	1.63055i
$22$		0			0
$23$	2.94857	−	5.10707i	0.614819	−	1.06490i	−0.375597	−	0.926783i	$-0.622562\pi$
$23$	2.94857	−	5.10707i	0.614819	−	1.06490i	0.990416	−	0.138115i	$-0.0441043\pi$
$24$		0			0
$25$	−0.437348	−	0.757509i	−0.0874697	−	0.151502i
$26$		0			0
$27$	−2.74383	−	4.41264i	−0.528050	−	0.849213i
$28$		0			0
$29$	−0.776975	−	1.34576i	−0.144281	−	0.249902i	0.784824	−	0.619719i	$-0.212753\pi$
$29$	−0.776975	−	1.34576i	−0.144281	−	0.249902i	−0.929104	+	0.369818i	$0.879420\pi$
$30$		0			0
$31$	−0.925013	−	0.534057i	−0.166137	−	0.0959194i	0.414626	−	0.909992i	$-0.363912\pi$
$31$	−0.925013	−	0.534057i	−0.166137	−	0.0959194i	−0.580763	+	0.814073i	$0.697246\pi$
$32$		0			0
$33$	−2.48094	+	7.05467i	−0.431876	+	1.22806i
$34$		0			0
$35$		−	11.0840i		−	1.87353i
$36$		0			0
$37$			2.02356i			0.332670i	0.986069	+	0.166335i	$0.0531934\pi$
$37$			2.02356i			0.332670i	−0.986069	+	0.166335i	$0.946807\pi$
$38$		0			0
$39$	−3.70186	+	0.694430i	−0.592772	+	0.111198i
$40$		0			0
$41$	10.4666	+	6.04289i	1.63461	+	0.943741i	0.982647	+	0.185488i	$0.0593866\pi$
$41$	10.4666	+	6.04289i	1.63461	+	0.943741i	0.651961	+	0.758253i	$0.273947\pi$
$42$		0			0
$43$	0.995268	+	1.72386i	0.151777	+	0.262885i	0.931881	−	0.362765i	$-0.118167\pi$
$43$	0.995268	+	1.72386i	0.151777	+	0.262885i	−0.780104	+	0.625650i	$0.784834\pi$
$44$		0			0
$45$	5.67074	+	4.55138i	0.845343	+	0.678479i
$46$		0			0
$47$	3.70186	+	6.41181i	0.539972	+	0.935259i	0.998905	+	0.0467878i	$0.0148985\pi$
$47$	3.70186	+	6.41181i	0.539972	+	0.935259i	−0.458933	+	0.888471i	$0.651768\pi$
$48$		0			0
$49$	6.95623	−	12.0485i	0.993747	−	1.72122i
$50$		0			0
$51$	4.40562	+	5.13567i	0.616911	+	0.719137i
$52$		0			0
$53$	3.97773			0.546383			0.273192	−	0.961960i	$-0.411921\pi$
$53$	3.97773			0.546383			0.273192	+	0.961960i	$0.411921\pi$
$54$		0			0
$55$		−	10.4647i		−	1.41107i
$56$		0			0
$57$	−7.79586	+	6.68767i	−1.03259	+	0.885803i
$58$		0			0
$59$	0.294283	+	0.169904i	0.0383124	+	0.0221197i	0.519034	−	0.854754i	$-0.326292\pi$
$59$	0.294283	+	0.169904i	0.0383124	+	0.0221197i	−0.480721	+	0.876873i	$0.659625\pi$
$60$		0			0
$61$	−8.33093	+	4.80986i	−1.06667	+	0.615840i	−0.927269	−	0.374397i	$-0.877850\pi$
$61$	−8.33093	+	4.80986i	−1.06667	+	0.615840i	−0.139397	+	0.990237i	$0.544516\pi$
$62$		0			0
$63$	4.97212	+	12.7863i	0.626429	+	1.61093i
$64$		0			0
$65$	4.56450	−	2.63531i	0.566156	−	0.326870i
$66$		0			0
$67$	−1.71554	+	2.97141i	−0.209587	+	0.363015i	−0.951584	−	0.307388i	$-0.900545\pi$
$67$	−1.71554	+	2.97141i	−0.209587	+	0.363015i	0.741998	+	0.670402i	$0.233879\pi$
$68$		0			0
$69$	−1.88322	−	10.0390i	−0.226713	−	1.20856i
$70$		0			0
$71$	2.32554			0.275991			0.137996	−	0.990433i	$-0.455934\pi$
$71$	2.32554			0.275991			0.137996	+	0.990433i	$0.455934\pi$
$72$		0			0
$73$	−2.37960			−0.278511			−0.139255	−	0.990256i	$-0.544471\pi$
$73$	−2.37960			−0.278511			−0.139255	+	0.990256i	$0.544471\pi$
$74$		0			0
$75$	−1.42922	−	0.502617i	−0.165032	−	0.0580372i
$76$		0			0
$77$	9.87208	−	17.0989i	1.12503	−	1.94861i
$78$		0			0
$79$	−5.38160	+	3.10707i	−0.605478	+	0.349573i	−0.771194	−	0.636601i	$-0.780340\pi$
$79$	−5.38160	+	3.10707i	−0.605478	+	0.349573i	0.165716	+	0.986174i	$0.447007\pi$
$80$		0			0
$81$	−8.58338	−	2.70659i	−0.953709	−	0.300732i
$82$		0			0
$83$	−5.40089	+	3.11821i	−0.592825	+	0.342268i	−0.766214	−	0.642586i	$-0.777862\pi$
$83$	−5.40089	+	3.11821i	−0.592825	+	0.342268i	0.173389	+	0.984853i	$0.444528\pi$
$84$		0			0
$85$	−8.20016	−	4.73437i	−0.889432	−	0.513514i
$86$		0			0
$87$	−2.53909	−	0.892929i	−0.272219	−	0.0957320i
$88$		0			0
$89$			4.90465i			0.519892i	0.965623	+	0.259946i	$0.0837047\pi$
$89$			4.90465i			0.519892i	−0.965623	+	0.259946i	$0.916295\pi$
$90$		0			0
$91$	9.94425			1.04244
$92$		0			0
$93$	−1.81831	+	0.341096i	−0.188550	+	0.0353700i
$94$		0			0
$95$	7.18669	−	12.4477i	0.737339	−	1.27711i
$96$		0			0
$97$	−1.32056	−	2.28728i	−0.134083	−	0.232238i	0.791164	−	0.611604i	$-0.209476\pi$
$97$	−1.32056	−	2.28728i	−0.134083	−	0.232238i	−0.925247	+	0.379366i	$0.876142\pi$
$98$		0			0
$99$	4.69435	+	12.0720i	0.471800	+	1.21328i
$100$		0			0
$101$	7.44830	+	12.9008i	0.741134	+	1.28368i	0.951979	+	0.306162i	$0.0990449\pi$
$101$	7.44830	+	12.9008i	0.741134	+	1.28368i	−0.210846	+	0.977519i	$0.567622\pi$
$102$		0			0
$103$	−15.3451	−	8.85952i	−1.51200	−	0.872955i	−0.999902	−	0.0140288i	$-0.995534\pi$
$103$	−15.3451	−	8.85952i	−1.51200	−	0.872955i	−0.512100	−	0.858926i	$-0.671132\pi$
$104$		0			0
$105$	−12.4998	−	14.5711i	−1.21986	−	1.42200i
$106$		0			0
$107$		−	6.57622i		−	0.635747i	−0.948133	−	0.317874i	$-0.897031\pi$
$107$		−	6.57622i		−	0.635747i	0.948133	−	0.317874i	$-0.102969\pi$
$108$		0			0
$109$		−	1.50658i		−	0.144305i	−0.997394	−	0.0721523i	$-0.977013\pi$
$109$		−	1.50658i		−	0.144305i	0.997394	−	0.0721523i	$-0.0229868\pi$
$110$		0			0
$111$	2.28204	+	2.66019i	0.216602	+	0.252494i
$112$		0			0
$113$	−13.1406	−	7.58671i	−1.23616	−	0.713698i	−0.267853	−	0.963460i	$-0.586314\pi$
$113$	−13.1406	−	7.58671i	−1.23616	−	0.713698i	−0.968307	+	0.249762i	$0.919648\pi$
$114$		0			0
$115$	7.14667	+	12.3784i	0.666431	+	1.15429i
$116$		0			0
$117$	−4.08338	+	5.08764i	−0.377508	+	0.470352i
$118$		0			0
$119$	−8.93247	−	15.4715i	−0.818838	−	1.41827i
$120$		0			0
$121$	3.82056	−	6.61741i	0.347324	−	0.601583i
$122$		0			0
$123$	20.5743	−	3.85952i	1.85512	−	0.348001i
$124$		0			0
$125$	−9.99882			−0.894321
$126$		0			0
$127$			9.14603i			0.811579i	0.913967	+	0.405789i	$0.133003\pi$
$127$			9.14603i			0.811579i	−0.913967	+	0.405789i	$0.866997\pi$
$128$		0			0
$129$	3.25245	+	1.14380i	0.286362	+	0.100706i
$130$		0			0
$131$	6.90748	+	3.98803i	0.603509	+	0.348436i	0.770421	−	0.637536i	$-0.220046\pi$
$131$	6.90748	+	3.98803i	0.603509	+	0.348436i	−0.166912	+	0.985972i	$0.553380\pi$
$132$		0			0
$133$	23.4855	−	13.5593i	2.03645	−	1.17574i
$134$		0			0
$135$	12.5876	−	0.411811i	1.08337	−	0.0354430i
$136$		0			0
$137$	−0.252450	+	0.145752i	−0.0215683	+	0.0124525i	−0.510745	−	0.859732i	$-0.670631\pi$
$137$	−0.252450	+	0.145752i	−0.0215683	+	0.0124525i	0.489177	+	0.872184i	$0.337297\pi$
$138$		0			0
$139$	−7.36792	+	12.7616i	−0.624939	+	1.08243i	0.363613	+	0.931550i	$0.381543\pi$
$139$	−7.36792	+	12.7616i	−0.624939	+	1.08243i	−0.988553	+	0.150876i	$0.951790\pi$
$140$		0			0
$141$	12.0974	+	4.25431i	1.01878	+	0.358278i
$142$		0			0
$143$	9.38870			0.785123
$144$		0			0
$145$	3.76643			0.312785
$146$		0			0
$147$	−4.44286	−	23.6840i	−0.366441	−	1.95342i
$148$		0			0
$149$	7.85810	−	13.6106i	0.643761	−	1.11503i	−0.340826	−	0.940126i	$-0.610707\pi$
$149$	7.85810	−	13.6106i	0.643761	−	1.11503i	0.984586	−	0.174899i	$-0.0559601\pi$
$150$		0			0
$151$	5.59864	−	3.23237i	0.455611	−	0.263047i	−0.254586	−	0.967050i	$-0.581939\pi$
$151$	5.59864	−	3.23237i	0.455611	−	0.263047i	0.710197	+	0.704003i	$0.248606\pi$
$152$		0			0
$153$	11.5834	+	1.78302i	0.936461	+	0.144148i
$154$		0			0
$155$	2.24203	−	1.29443i	0.180084	−	0.103971i
$156$		0			0
$157$	0.316946	+	0.182989i	0.0252950	+	0.0146041i	0.512594	−	0.858631i	$-0.328685\pi$
$157$	0.316946	+	0.182989i	0.0252950	+	0.0146041i	−0.487299	+	0.873235i	$0.662018\pi$
$158$		0			0
$159$	5.22917	−	4.48584i	0.414700	−	0.355750i
$160$		0			0
$161$			26.9677i			2.12535i
$162$		0			0
$163$	−0.884999			−0.0693184			−0.0346592	−	0.999399i	$-0.511035\pi$
$163$	−0.884999			−0.0693184			−0.0346592	+	0.999399i	$0.511035\pi$
$164$		0			0
$165$	−11.8015	−	13.7571i	−0.918746	−	1.07099i
$166$		0			0
$167$	2.41231	−	4.17824i	0.186670	−	0.323322i	−0.757468	−	0.652872i	$-0.773564\pi$
$167$	2.41231	−	4.17824i	0.186670	−	0.323322i	0.944138	+	0.329550i	$0.106897\pi$
$168$		0			0
$169$	−4.13567	−	7.16318i	−0.318128	−	0.551014i
$170$		0			0
$171$	−2.70659	+	17.5834i	−0.206978	+	1.34463i
$172$		0			0
$173$	−0.342062	−	0.592469i	−0.0260065	−	0.0450446i	0.852729	−	0.522353i	$-0.174946\pi$
$173$	−0.342062	−	0.592469i	−0.0260065	−	0.0450446i	−0.878736	+	0.477309i	$0.841612\pi$
$174$		0			0
$175$	3.46410	+	2.00000i	0.261861	+	0.151186i
$176$		0			0
$177$	0.578476	−	0.108516i	0.0434809	−	0.00815656i
$178$		0			0
$179$			12.8030i			0.956942i	0.878103	+	0.478471i	$0.158809\pi$
$179$			12.8030i			0.956942i	−0.878103	+	0.478471i	$0.841191\pi$
$180$		0			0
$181$		−	22.7310i		−	1.68958i	−0.535096	−	0.844791i	$-0.679724\pi$
$181$		−	22.7310i		−	1.68958i	0.535096	−	0.844791i	$-0.320276\pi$
$182$		0			0
$183$	−5.52767	+	15.7182i	−0.408617	+	1.16192i
$184$		0			0
$185$	−4.24755	−	2.45232i	−0.312286	−	0.180298i
$186$		0			0
$187$	−8.43345	−	14.6072i	−0.616715	−	1.06818i
$188$		0			0
$189$	20.9560	+	11.2018i	1.52433	+	0.814811i
$190$		0			0
$191$	10.8885	+	18.8595i	0.787868	+	1.36463i	0.927271	+	0.374391i	$0.122148\pi$
$191$	10.8885	+	18.8595i	0.787868	+	1.36463i	−0.139403	+	0.990236i	$0.544518\pi$
$192$		0			0
$193$	−11.5919	+	20.0778i	−0.834403	+	1.44523i	0.0601127	+	0.998192i	$0.480854\pi$
$193$	−11.5919	+	20.0778i	−0.834403	+	1.44523i	−0.894516	+	0.447037i	$0.852479\pi$
$194$		0			0
$195$	3.02860	−	8.61197i	0.216882	−	0.616716i
$196$		0			0
$197$	−23.9076			−1.70335			−0.851673	−	0.524074i	$-0.824411\pi$
$197$	−23.9076			−1.70335			−0.851673	+	0.524074i	$0.824411\pi$
$198$		0			0
$199$			1.89173i			0.134102i	0.997750	+	0.0670508i	$0.0213589\pi$
$199$			1.89173i			0.134102i	−0.997750	+	0.0670508i	$0.978641\pi$
$200$		0			0
$201$	1.09570	+	5.84093i	0.0772844	+	0.411987i
$202$		0			0
$203$	6.15418	+	3.55312i	0.431939	+	0.249380i
$204$		0			0
$205$	−25.3687	+	14.6466i	−1.77183	+	1.02296i
$206$		0			0
$207$	−13.7971	−	11.0737i	−0.958965	−	0.769673i
$208$		0			0
$209$	22.1734	−	12.8018i	1.53377	−	0.885521i
$210$		0			0
$211$	12.6013	−	21.8261i	0.867510	−	1.50257i	0.00297716	−	0.999996i	$-0.499052\pi$
$211$	12.6013	−	21.8261i	0.867510	−	1.50257i	0.864533	−	0.502576i	$-0.167614\pi$
$212$		0			0
$213$	3.05719	−	2.62261i	0.209475	−	0.179698i
$214$		0			0
$215$	−4.82462			−0.329036
$216$		0			0
$217$	4.88450			0.331581
$218$		0			0
$219$	−3.12825	+	2.68356i	−0.211387	+	0.181338i
$220$		0			0
$221$	4.24755	−	7.35697i	0.285721	−	0.494883i
$222$		0			0
$223$	8.41694	−	4.85952i	0.563640	−	0.325418i	−0.190965	−	0.981597i	$-0.561162\pi$
$223$	8.41694	−	4.85952i	0.563640	−	0.325418i	0.754605	+	0.656179i	$0.227828\pi$
$224$		0			0
$225$	−2.44569	+	0.951036i	−0.163046	+	0.0634024i
$226$		0			0
$227$	−8.52577	+	4.92235i	−0.565875	+	0.326708i	−0.755500	−	0.655148i	$-0.772606\pi$
$227$	−8.52577	+	4.92235i	−0.565875	+	0.326708i	0.189625	+	0.981857i	$0.439273\pi$
$228$		0			0
$229$	19.4021	+	11.2018i	1.28213	+	0.740236i	0.977237	−	0.212151i	$-0.0680470\pi$
$229$	19.4021	+	11.2018i	1.28213	+	0.740236i	0.304890	+	0.952388i	$0.401380\pi$
$230$		0			0
$231$	−6.30518	−	33.6116i	−0.414850	−	2.21148i
$232$		0			0
$233$		−	13.3753i		−	0.876247i	−0.898915	−	0.438124i	$-0.855643\pi$
$233$		−	13.3753i		−	0.876247i	0.898915	−	0.438124i	$-0.144357\pi$
$234$		0			0
$235$	−17.9450			−1.17060
$236$		0			0
$237$	−3.57076	+	10.1536i	−0.231946	+	0.659550i
$238$		0			0
$239$	−3.94106	+	6.82611i	−0.254926	+	0.441545i	−0.964875	−	0.262708i	$-0.915384\pi$
$239$	−3.94106	+	6.82611i	−0.254926	+	0.441545i	0.709949	+	0.704253i	$0.248718\pi$
$240$		0			0
$241$	−7.00490	−	12.1328i	−0.451225	−	0.781545i	0.547237	−	0.836978i	$-0.315680\pi$
$241$	−7.00490	−	12.1328i	−0.451225	−	0.781545i	−0.998462	+	0.0554324i	$0.982346\pi$
$242$		0			0
$243$	−14.3361	+	6.12169i	−0.919664	+	0.392706i
$244$		0			0
$245$	16.8604	+	29.2030i	1.07717	+	1.86571i
$246$		0			0
$247$	11.1678	+	6.44771i	0.710588	+	0.410258i
$248$		0			0
$249$	−3.58356	+	10.1900i	−0.227099	+	0.645767i
$250$		0			0
$251$		−	16.2713i		−	1.02704i	−0.858078	−	0.513519i	$-0.828342\pi$
$251$		−	16.2713i		−	1.02704i	0.858078	−	0.513519i	$-0.171658\pi$
$252$		0			0
$253$			25.4611i			1.60073i
$254$		0			0
$255$	−16.1192	+	3.02378i	−1.00942	+	0.189357i
$256$		0			0
$257$	2.06209	+	1.19055i	0.128630	+	0.0742644i	0.562934	−	0.826502i	$-0.309672\pi$
$257$	2.06209	+	1.19055i	0.128630	+	0.0742644i	−0.434304	+	0.900766i	$0.643006\pi$
$258$		0			0
$259$	−4.62687	−	8.01398i	−0.287500	−	0.497965i
$260$		0			0
$261$	−4.34491	+	1.68957i	−0.268943	+	0.104582i
$262$		0			0
$263$	9.42872	+	16.3310i	0.581400	+	1.00701i	0.995314	+	0.0966976i	$0.0308280\pi$
$263$	9.42872	+	16.3310i	0.581400	+	1.00701i	−0.413914	+	0.910316i	$0.635839\pi$
$264$		0			0
$265$	−4.82056	+	8.34946i	−0.296125	+	0.512903i
$266$		0			0
$267$	5.53116	+	6.44771i	0.338502	+	0.394593i
$268$		0			0
$269$	−11.6030			−0.707447			−0.353724	−	0.935350i	$-0.615085\pi$
$269$	−11.6030			−0.707447			−0.353724	+	0.935350i	$0.615085\pi$
$270$		0			0
$271$		−	3.74939i		−	0.227759i	−0.993495	−	0.113880i	$-0.963672\pi$
$271$		−	3.74939i		−	0.227759i	0.993495	−	0.113880i	$-0.0363278\pi$
$272$		0			0
$273$	13.0728	−	11.2145i	0.791204	−	0.678733i
$274$		0			0
$275$	3.27058	+	1.88827i	0.197223	+	0.113867i
$276$		0			0
$277$	−10.1978	+	5.88768i	−0.612724	+	0.353756i	−0.774031	−	0.633148i	$-0.781762\pi$
$277$	−10.1978	+	5.88768i	−0.612724	+	0.353756i	0.161307	+	0.986904i	$0.448429\pi$
$278$		0			0
$279$	−2.00571	+	2.49899i	−0.120079	+	0.149610i
$280$		0			0
$281$	−7.36869	+	4.25431i	−0.439579	+	0.253791i	−0.703419	−	0.710775i	$-0.748344\pi$
$281$	−7.36869	+	4.25431i	−0.439579	+	0.253791i	0.263840	+	0.964566i	$0.415011\pi$
$282$		0			0
$283$	−5.28292	+	9.15028i	−0.314037	+	0.543928i	−0.979232	−	0.202742i	$-0.935015\pi$
$283$	−5.28292	+	9.15028i	−0.314037	+	0.543928i	0.665195	+	0.746669i	$0.268348\pi$
$284$		0			0
$285$	−4.59005	−	24.4686i	−0.271891	−	1.44940i
$286$		0			0
$287$	−55.2684			−3.26239
$288$		0			0
$289$	1.73847			0.102263
$290$		0			0
$291$	−4.31549	−	1.51764i	−0.252978	−	0.0889657i
$292$		0			0
$293$	−13.8498	+	23.9886i	−0.809114	+	1.40143i	0.104364	+	0.994539i	$0.466719\pi$
$293$	−13.8498	+	23.9886i	−0.809114	+	1.40143i	−0.913478	+	0.406888i	$0.866614\pi$
$294$		0			0
$295$	−0.713277	+	0.411811i	−0.0415286	+	0.0239765i
$296$		0			0
$297$	19.7853	+	10.5760i	1.14806	+	0.613682i
$298$		0			0
$299$	−11.1056	+	6.41181i	−0.642252	+	0.370805i
$300$		0			0
$301$	−7.88322	−	4.55138i	−0.454381	−	0.262337i
$302$		0			0
$303$	24.3404	+	8.55986i	1.39832	+	0.491751i
$304$		0			0
$305$		−	23.3161i		−	1.33507i
$306$		0			0
$307$	18.0264			1.02882			0.514411	−	0.857544i	$-0.328011\pi$
$307$	18.0264			1.02882			0.514411	+	0.857544i	$0.328011\pi$
$308$		0			0
$309$	−30.1641	+	5.65847i	−1.71598	+	0.321899i
$310$		0			0
$311$	−14.9599	+	25.9113i	−0.848297	+	1.46929i	0.0344304	+	0.999407i	$0.489038\pi$
$311$	−14.9599	+	25.9113i	−0.848297	+	1.46929i	−0.882727	+	0.469886i	$0.844295\pi$
$312$		0			0
$313$	12.5207	+	21.6865i	0.707713	+	1.22580i	0.965703	+	0.259648i	$0.0836064\pi$
$313$	12.5207	+	21.6865i	0.707713	+	1.22580i	−0.257990	+	0.966148i	$0.583060\pi$
$314$		0			0
$315$	−32.8648	−	5.05885i	−1.85172	−	0.285034i
$316$		0			0
$317$	−9.62738	−	16.6751i	−0.540727	−	0.936567i	−0.998862	−	0.0476846i	$-0.984816\pi$
$317$	−9.62738	−	16.6751i	−0.540727	−	0.936567i	0.458135	−	0.888883i	$-0.348518\pi$
$318$		0			0
$319$	5.81037	+	3.35462i	0.325318	+	0.187823i
$320$		0			0
$321$	−7.41626	−	8.64518i	−0.413935	−	0.482527i
$322$		0			0
$323$		−	23.1668i		−	1.28903i
$324$		0			0
$325$			1.90207i			0.105508i
$326$		0			0
$327$	−1.69903	−	1.98057i	−0.0939567	−	0.109526i
$328$		0			0
$329$	−29.3213	−	16.9287i	−1.61654	−	0.933307i
$330$		0			0
$331$	−3.13258	−	5.42579i	−0.172182	−	0.298228i	0.767000	−	0.641647i	$-0.221748\pi$
$331$	−3.13258	−	5.42579i	−0.172182	−	0.298228i	−0.939183	+	0.343418i	$0.888415\pi$
$332$		0			0
$333$	6.00000	+	0.923574i	0.328798	+	0.0506116i
$334$		0			0
$335$	−4.15809	−	7.20202i	−0.227181	−	0.393489i
$336$		0			0
$337$	−6.71414	+	11.6292i	−0.365743	+	0.633485i	−0.988895	−	0.148616i	$-0.952518\pi$
$337$	−6.71414	+	11.6292i	−0.365743	+	0.633485i	0.623152	+	0.782100i	$0.285852\pi$
$338$		0			0
$339$	−25.8306	+	4.84554i	−1.40292	+	0.263174i
$340$		0			0
$341$	4.61162			0.249733
$342$		0			0
$343$			31.6108i			1.70682i
$344$		0			0
$345$	23.3547	+	8.21322i	1.25738	+	0.442185i
$346$		0			0
$347$	17.2324	+	9.94913i	0.925084	+	0.534097i	0.885253	−	0.465109i	$-0.153985\pi$
$347$	17.2324	+	9.94913i	0.925084	+	0.534097i	0.0398305	+	0.999206i	$0.487318\pi$
$348$		0			0
$349$	15.8218	−	9.13475i	0.846924	−	0.488972i	−0.0126878	−	0.999920i	$-0.504039\pi$
$349$	15.8218	−	9.13475i	0.846924	−	0.488972i	0.859612	+	0.510948i	$0.170705\pi$
$350$		0			0
$351$	0.369466	+	11.2933i	0.0197206	+	0.602789i
$352$		0			0
$353$	−13.9143	+	8.03343i	−0.740584	+	0.427576i	−0.822281	−	0.569081i	$-0.807299\pi$
$353$	−13.9143	+	8.03343i	−0.740584	+	0.427576i	0.0816978	+	0.996657i	$0.473966\pi$
$354$		0			0
$355$	−2.81830	+	4.88144i	−0.149580	+	0.259080i
$356$		0			0
$357$	−29.1905	−	10.2655i	−1.54493	−	0.543309i
$358$		0			0
$359$	7.57725			0.399912			0.199956	−	0.979805i	$-0.435920\pi$
$359$	7.57725			0.399912			0.199956	+	0.979805i	$0.435920\pi$
$360$		0			0
$361$	16.1668			0.850882
$362$		0			0
$363$	−2.44015	−	13.0079i	−0.128075	−	0.682739i
$364$		0			0
$365$	2.88381	−	4.99490i	0.150945	−	0.261445i
$366$		0			0
$367$	1.70047	−	0.981768i	0.0887639	−	0.0512479i	−0.454961	−	0.890511i	$-0.650347\pi$
$367$	1.70047	−	0.981768i	0.0887639	−	0.0512479i	0.543725	+	0.839263i	$0.317013\pi$
$368$		0			0
$369$	22.6947	−	28.2762i	1.18144	−	1.47200i
$370$		0			0
$371$	−15.7532	+	9.09510i	−0.817864	+	0.472194i
$372$		0			0
$373$	26.6400	+	15.3806i	1.37937	+	0.796379i	0.992083	−	0.125582i	$-0.0400797\pi$
$373$	26.6400	+	15.3806i	1.37937	+	0.796379i	0.387285	+	0.921960i	$0.373413\pi$
$374$		0			0
$375$	−13.1446	+	11.2761i	−0.678783	+	0.582293i
$376$		0			0
$377$			3.37914i			0.174035i
$378$		0			0
$379$	33.6044			1.72614			0.863071	−	0.505083i	$-0.168538\pi$
$379$	33.6044			1.72614			0.863071	+	0.505083i	$0.168538\pi$
$380$		0			0
$381$	10.3143	+	12.0235i	0.528419	+	0.615982i
$382$		0			0
$383$	13.3876	−	23.1880i	0.684076	−	1.18485i	−0.289651	−	0.957132i	$-0.593539\pi$
$383$	13.3876	−	23.1880i	0.684076	−	1.18485i	0.973726	−	0.227721i	$-0.0731275\pi$
$384$		0			0
$385$	23.9277	+	41.4440i	1.21947	+	2.11218i
$386$		0			0
$387$	5.56562	−	2.16426i	0.282916	−	0.110016i
$388$		0			0
$389$	11.4260	+	19.7905i	0.579323	+	1.00342i	0.995557	+	0.0941591i	$0.0300162\pi$
$389$	11.4260	+	19.7905i	0.579323	+	1.00342i	−0.416234	+	0.909257i	$0.636650\pi$
$390$		0			0
$391$	19.9513	+	11.5189i	1.00898	+	0.582535i
$392$		0			0
$393$	13.5781	−	2.54711i	0.684925	−	0.128485i
$394$		0			0
$395$		−	15.0617i		−	0.757836i
$396$		0			0
$397$			19.2780i			0.967536i	0.875196	+	0.483768i	$0.160732\pi$
$397$			19.2780i			0.967536i	−0.875196	+	0.483768i	$0.839268\pi$
$398$		0			0
$399$	15.5829	−	44.3108i	0.780121	−	2.21831i
$400$		0			0
$401$	−1.98112	−	1.14380i	−0.0989323	−	0.0571186i	0.449718	−	0.893171i	$-0.351525\pi$
$401$	−1.98112	−	1.14380i	−0.0989323	−	0.0571186i	−0.548650	+	0.836052i	$0.684858\pi$
$402$		0			0
$403$	1.16133	+	2.01149i	0.0578501	+	0.100199i
$404$		0			0
$405$	16.0834	−	14.7369i	0.799189	−	0.732281i
$406$		0			0
$407$	−4.36839	−	7.56627i	−0.216533	−	0.375046i
$408$		0			0
$409$	−7.14113	+	12.3688i	−0.353106	+	0.611598i	−0.986792	−	0.161993i	$-0.948208\pi$
$409$	−7.14113	+	12.3688i	−0.353106	+	0.611598i	0.633686	+	0.773590i	$0.281541\pi$
$410$		0			0
$411$	−0.167504	+	0.476306i	−0.00826236	+	0.0234944i
$412$		0			0
$413$	−1.55395			−0.0764649
$414$		0			0
$415$		−	15.1157i		−	0.741999i
$416$		0			0
$417$	4.70580	+	25.0857i	0.230444	+	1.22845i
$418$		0			0
$419$	18.7485	+	10.8245i	0.915924	+	0.528809i	0.882333	−	0.470627i	$-0.155972\pi$
$419$	18.7485	+	10.8245i	0.915924	+	0.528809i	0.0335917	+	0.999436i	$0.489305\pi$
$420$		0			0
$421$	17.1351	−	9.89297i	0.835115	−	0.482154i	−0.0204860	−	0.999790i	$-0.506521\pi$
$421$	17.1351	−	9.89297i	0.835115	−	0.482154i	0.855601	+	0.517636i	$0.173188\pi$
$422$		0			0
$423$	20.7011	−	8.04988i	1.00652	−	0.391399i
$424$		0			0
$425$	2.95929	−	1.70855i	0.143547	−	0.0828766i
$426$		0			0
$427$	21.9956	−	38.0974i	1.06444	−	1.84366i
$428$		0			0
$429$	12.3425	−	10.5880i	0.595902	−	0.511193i
$430$		0			0
$431$	−17.3865			−0.837480			−0.418740	−	0.908106i	$-0.637528\pi$
$431$	−17.3865			−0.837480			−0.418740	+	0.908106i	$0.637528\pi$
$432$		0			0
$433$	−34.9223			−1.67826			−0.839128	−	0.543933i	$-0.816934\pi$
$433$	−34.9223			−1.67826			−0.839128	+	0.543933i	$0.816934\pi$
$434$		0			0
$435$	4.95140	−	4.24755i	0.237401	−	0.203654i
$436$		0			0
$437$	−17.4855	+	30.2857i	−0.836444	+	1.44876i
$438$		0			0
$439$	18.1634	−	10.4867i	0.866894	−	0.500501i	0.000579038	−	1.00000i	$-0.499816\pi$
$439$	18.1634	−	10.4867i	0.866894	−	0.500501i	0.866315	+	0.499498i	$0.166482\pi$
$440$		0			0
$441$	−32.5500	−	26.1249i	−1.55000	−	1.24404i
$442$		0			0
$443$	−27.2999	+	15.7616i	−1.29706	+	0.748857i	−0.979895	−	0.199514i	$-0.936064\pi$
$443$	−27.2999	+	15.7616i	−1.29706	+	0.748857i	−0.317164	+	0.948371i	$0.602730\pi$
$444$		0			0
$445$	−10.2951	−	5.94389i	−0.488035	−	0.281767i
$446$		0			0
$447$	−5.01887	−	26.7546i	−0.237385	−	1.26545i
$448$		0			0
$449$		−	7.30467i		−	0.344728i	−0.985033	−	0.172364i	$-0.944859\pi$
$449$		−	7.30467i		−	0.344728i	0.985033	−	0.172364i	$-0.0551406\pi$
$450$		0			0
$451$	−52.1808			−2.45710
$452$		0			0
$453$	3.71476	−	10.5631i	0.174535	−	0.496299i
$454$		0			0
$455$	−12.0513	+	20.8735i	−0.564975	+	0.978565i
$456$		0			0
$457$	−8.44587	−	14.6287i	−0.395081	−	0.684300i	0.598031	−	0.801473i	$-0.295950\pi$
$457$	−8.44587	−	14.6287i	−0.395081	−	0.684300i	−0.993112	+	0.117173i	$0.962617\pi$
$458$		0			0
$459$	17.2384	−	10.7190i	0.804621	−	0.500322i
$460$		0			0
$461$	−9.41205	−	16.3021i	−0.438363	−	0.759267i	0.559201	−	0.829032i	$-0.311108\pi$
$461$	−9.41205	−	16.3021i	−0.438363	−	0.759267i	−0.997563	+	0.0697657i	$0.977775\pi$
$462$		0			0
$463$	−2.94364	−	1.69951i	−0.136803	−	0.0789830i	0.430037	−	0.902811i	$-0.358501\pi$
$463$	−2.94364	−	1.69951i	−0.136803	−	0.0789830i	−0.566839	+	0.823828i	$0.691834\pi$
$464$		0			0
$465$	1.48761	−	4.23010i	0.0689864	−	0.196166i
$466$		0			0
$467$			12.8423i			0.594269i	0.954836	+	0.297134i	$0.0960310\pi$
$467$			12.8423i			0.594269i	−0.954836	+	0.297134i	$0.903969\pi$
$468$		0			0
$469$		−	15.6904i		−	0.724515i
$470$		0			0
$471$	0.623024	−	0.116873i	0.0287074	−	0.00538521i
$472$		0			0
$473$	−7.44281	−	4.29711i	−0.342221	−	0.197581i
$474$		0			0
$475$	2.59354	+	4.49215i	0.119000	+	0.206114i
$476$		0			0
$477$	1.81548	−	11.7943i	0.0831252	−	0.540023i
$478$		0			0
$479$	14.3334	+	24.8261i	0.654908	+	1.13433i	0.981917	+	0.189313i	$0.0606260\pi$
$479$	14.3334	+	24.8261i	0.654908	+	1.13433i	−0.327009	+	0.945021i	$0.606041\pi$
$480$		0			0
$481$	2.20016	−	3.81079i	0.100319	−	0.173757i
$482$		0			0
$483$	30.4125	+	35.4521i	1.38382	+	1.61312i
$484$		0			0
$485$	6.40151			0.290677
$486$		0			0
$487$			3.53286i			0.160089i	0.996791	+	0.0800446i	$0.0255063\pi$
$487$			3.53286i			0.160089i	−0.996791	+	0.0800446i	$0.974494\pi$
$488$		0			0
$489$	−1.16343	+	0.998047i	−0.0526121	+	0.0451332i
$490$		0			0
$491$	20.4103	+	11.7839i	0.921104	+	0.531800i	0.883987	−	0.467511i	$-0.154849\pi$
$491$	20.4103	+	11.7839i	0.921104	+	0.531800i	0.0371168	+	0.999311i	$0.488183\pi$
$492$		0			0
$493$	5.25735	−	3.03533i	0.236779	−	0.136705i
$494$		0			0
$495$	−31.0288	−	4.77623i	−1.39464	−	0.214676i
$496$		0			0
$497$	−9.20996	+	5.31737i	−0.413123	+	0.238517i
$498$		0			0
$499$	−4.12641	+	7.14715i	−0.184724	+	0.319951i	−0.943483	−	0.331420i	$-0.892472\pi$
$499$	−4.12641	+	7.14715i	−0.184724	+	0.319951i	0.758760	+	0.651371i	$0.225806\pi$
$500$		0			0
$501$	−1.54071	−	8.21322i	−0.0688340	−	0.366940i
$502$		0			0
$503$	18.4591			0.823049			0.411525	−	0.911399i	$-0.364996\pi$
$503$	18.4591			0.823049			0.411525	+	0.911399i	$0.364996\pi$
$504$		0			0
$505$	−36.1061			−1.60670
$506$		0			0
$507$	−13.5150	−	4.75286i	−0.600222	−	0.211082i
$508$		0			0
$509$	12.7057	−	22.0068i	0.563168	−	0.975436i	−0.434049	−	0.900889i	$-0.642916\pi$
$509$	12.7057	−	22.0068i	0.563168	−	0.975436i	0.997218	−	0.0745468i	$-0.0237510\pi$
$510$		0			0
$511$	9.42403	−	5.44097i	0.416895	−	0.240694i
$512$		0			0
$513$	16.2713	+	26.1677i	0.718397	+	1.15533i
$514$		0			0
$515$	37.1932	−	21.4735i	1.63893	−	0.946236i
$516$		0			0
$517$	−27.6832	−	15.9829i	−1.21751	−	0.702928i
$518$		0			0
$519$	−1.11783	−	0.393111i	−0.0490673	−	0.0172556i
$520$		0			0
$521$		−	9.82832i		−	0.430587i	−0.976549	−	0.215293i	$-0.930929\pi$
$521$		−	9.82832i		−	0.430587i	0.976549	−	0.215293i	$-0.0690707\pi$
$522$		0			0
$523$	−3.21054			−0.140387			−0.0701936	−	0.997533i	$-0.522362\pi$
$523$	−3.21054			−0.140387			−0.0701936	+	0.997533i	$0.522362\pi$
$524$		0			0
$525$	6.80943	−	1.27738i	0.297188	−	0.0557493i
$526$		0			0
$527$	2.08635	−	3.61366i	0.0908827	−	0.157413i
$528$		0			0
$529$	−5.88812	−	10.1985i	−0.256005	−	0.443414i
$530$		0			0
$531$	0.638094	−	0.795026i	0.0276909	−	0.0345012i
$532$		0			0
$533$	−13.1406	−	22.7601i	−0.569181	−	0.985851i
$534$		0			0
$535$	13.8038	+	7.96965i	0.596792	+	0.344558i
$536$		0			0
$537$	14.4384	+	16.8310i	0.623065	+	0.726311i
$538$		0			0
$539$			60.0676i			2.58729i
$540$		0			0
$541$		−	13.3394i		−	0.573507i	−0.958004	−	0.286754i	$-0.907424\pi$
$541$		−	13.3394i		−	0.573507i	0.958004	−	0.286754i	$-0.0925761\pi$
$542$		0			0
$543$	−25.6346	−	29.8825i	−1.10009	−	1.28238i
$544$		0			0
$545$	3.16240	+	1.82581i	0.135462	+	0.0782092i
$546$		0			0
$547$	−5.21266	−	9.02859i	−0.222877	−	0.386035i	0.732803	−	0.680441i	$-0.238212\pi$
$547$	−5.21266	−	9.02859i	−0.222877	−	0.386035i	−0.955680	+	0.294406i	$0.904878\pi$
$548$		0			0
$549$	10.4593	+	26.8971i	0.446391	+	1.14794i
$550$		0			0
$551$	4.60759	+	7.98057i	0.196290	+	0.339984i
$552$		0			0
$553$	14.2087	−	24.6102i	0.604215	−	1.04653i
$554$		0			0
$555$	−8.34946	+	1.56627i	−0.354415	+	0.0664845i
$556$		0			0
$557$	−21.2479			−0.900301			−0.450151	−	0.892953i	$-0.648630\pi$
$557$	−21.2479			−0.900301			−0.450151	+	0.892953i	$0.648630\pi$
$558$		0			0
$559$		−	4.32852i		−	0.183077i
$560$		0			0
$561$	−27.5598	−	9.69203i	−1.16357	−	0.409198i
$562$		0			0
$563$	7.30513	+	4.21762i	0.307875	+	0.177752i	0.645975	−	0.763359i	$-0.276451\pi$
$563$	7.30513	+	4.21762i	0.307875	+	0.177752i	−0.338100	+	0.941110i	$0.609784\pi$
$564$		0			0
$565$	31.8498	−	18.3885i	1.33993	−	0.773610i
$566$		0			0
$567$	40.1818	−	8.90691i	1.68748	−	0.374055i
$568$		0			0
$569$	32.1996	−	18.5905i	1.34988	−	0.779353i	0.361646	−	0.932315i	$-0.382215\pi$
$569$	32.1996	−	18.5905i	1.34988	−	0.779353i	0.988232	+	0.152963i	$0.0488815\pi$
$570$		0			0
$571$	1.30606	−	2.26216i	0.0546569	−	0.0946686i	−0.837402	−	0.546587i	$-0.815927\pi$
$571$	1.30606	−	2.26216i	0.0546569	−	0.0946686i	0.892059	+	0.451918i	$0.149260\pi$
$572$		0			0
$573$	35.5828	+	12.5135i	1.48649	+	0.522760i
$574$		0			0
$575$	−5.15821			−0.215112
$576$		0			0
$577$	−10.2993			−0.428765			−0.214383	−	0.976750i	$-0.568774\pi$
$577$	−10.2993			−0.428765			−0.214383	+	0.976750i	$0.568774\pi$
$578$		0			0
$579$	7.40361	+	39.4671i	0.307683	+	1.64020i
$580$		0			0
$581$	14.2596	−	24.6984i	0.591588	−	1.02466i
$582$		0			0
$583$	−14.8731	+	8.58700i	−0.615981	+	0.355637i
$584$		0			0
$585$	−5.73062	−	14.7369i	−0.236932	−	0.609295i
$586$		0			0
$587$	33.0046	−	19.0552i	1.36225	−	0.786493i	0.372324	−	0.928103i	$-0.378561\pi$
$587$	33.0046	−	19.0552i	1.36225	−	0.786493i	0.989923	+	0.141610i	$0.0452278\pi$
$588$		0			0
$589$	5.48547	+	3.16704i	0.226025	+	0.130496i
$590$		0			0
$591$	−31.4292	+	26.9615i	−1.29283	+	1.10905i
$592$		0			0
$593$		−	20.4440i		−	0.839536i	−0.907631	−	0.419768i	$-0.862111\pi$
$593$		−	20.4440i		−	0.839536i	0.907631	−	0.419768i	$-0.137889\pi$
$594$		0			0
$595$	43.3006			1.77515
$596$		0			0
$597$	2.13338	+	2.48690i	0.0873135	+	0.101782i
$598$		0			0
$599$	−2.49234	+	4.31686i	−0.101834	+	0.176382i	−0.912440	−	0.409210i	$-0.865804\pi$
$599$	−2.49234	+	4.31686i	−0.101834	+	0.176382i	0.810606	+	0.585592i	$0.199138\pi$
$600$		0			0
$601$	−1.00184	−	1.73524i	−0.0408661	−	0.0707821i	0.844869	−	0.534973i	$-0.179678\pi$
$601$	−1.00184	−	1.73524i	−0.0408661	−	0.0707821i	−0.885735	+	0.464191i	$0.846345\pi$
$602$		0			0
$603$	8.02746	+	6.44290i	0.326903	+	0.262375i
$604$		0			0
$605$	9.26020	+	16.0391i	0.376481	+	0.652083i
$606$		0			0
$607$	2.75082	+	1.58819i	0.111653	+	0.0644626i	0.554786	−	0.831993i	$-0.312800\pi$
$607$	2.75082	+	1.58819i	0.111653	+	0.0644626i	−0.443134	+	0.896455i	$0.646133\pi$
$608$		0			0
$609$	12.0974	−	2.26934i	0.490210	−	0.0919581i
$610$		0			0
$611$		−	16.0998i		−	0.651327i
$612$		0			0
$613$			4.38768i			0.177217i	0.996067	+	0.0886083i	$0.0282419\pi$
$613$			4.38768i			0.177217i	−0.996067	+	0.0886083i	$0.971758\pi$
$614$		0			0
$615$	−16.8324	+	47.8639i	−0.678749	+	1.93006i
$616$		0			0
$617$	5.29984	+	3.05986i	0.213363	+	0.123185i	0.602874	−	0.797837i	$-0.294022\pi$
$617$	5.29984	+	3.05986i	0.213363	+	0.123185i	−0.389510	+	0.921022i	$0.627356\pi$
$618$		0			0
$619$	18.1785	+	31.4861i	0.730656	+	1.26553i	0.956603	+	0.291394i	$0.0941190\pi$
$619$	18.1785	+	31.4861i	0.730656	+	1.26553i	−0.225947	+	0.974140i	$0.572548\pi$
$620$		0			0
$621$	−30.6260	+	1.00195i	−1.22898	+	0.0402069i
$622$		0			0
$623$	−11.2145	−	19.4241i	−0.449300	−	0.778210i
$624$		0			0
$625$	14.3042	−	24.7756i	0.572168	−	0.991024i
$626$		0			0
$627$	14.7123	−	41.8353i	0.587554	−	1.67074i
$628$		0			0
$629$	−7.90522			−0.315202
$630$		0			0
$631$		−	37.8249i		−	1.50579i	−0.658143	−	0.752893i	$-0.728658\pi$
$631$		−	37.8249i		−	1.50579i	0.658143	−	0.752893i	$-0.271342\pi$
$632$		0			0
$633$	−8.04831	−	42.9039i	−0.319892	−	1.70528i
$634$		0			0
$635$	−19.1980	−	11.0840i	−0.761849	−	0.439854i
$636$		0			0
$637$	−26.2002	+	15.1267i	−1.03809	+	0.599340i
$638$		0			0
$639$	1.06141	−	6.89542i	0.0419886	−	0.272779i
$640$		0			0
$641$	−24.7993	+	14.3179i	−0.979513	+	0.565522i	−0.902123	−	0.431479i	$-0.857992\pi$
$641$	−24.7993	+	14.3179i	−0.979513	+	0.565522i	−0.0773901	+	0.997001i	$0.524659\pi$
$642$		0			0
$643$	−9.04767	+	15.6710i	−0.356805	+	0.618005i	−0.987425	−	0.158087i	$-0.949467\pi$
$643$	−9.04767	+	15.6710i	−0.356805	+	0.618005i	0.630620	+	0.776092i	$0.282801\pi$
$644$		0			0
$645$	−6.34250	+	5.44091i	−0.249736	+	0.214236i
$646$		0			0
$647$	0.594123			0.0233574			0.0116787	−	0.999932i	$-0.496282\pi$
$647$	0.594123			0.0233574			0.0116787	+	0.999932i	$0.496282\pi$
$648$		0			0
$649$	−1.46714			−0.0575902
$650$		0			0
$651$	6.42122	−	5.50844i	0.251668	−	0.215893i
$652$		0			0
$653$	2.76584	−	4.79057i	0.108236	−	0.187470i	−0.806820	−	0.590797i	$-0.798813\pi$
$653$	2.76584	−	4.79057i	0.108236	−	0.187470i	0.915056	+	0.403328i	$0.132147\pi$
$654$		0			0
$655$	−16.7422	+	9.66610i	−0.654171	+	0.377686i
$656$		0			0
$657$	−1.08608	+	7.05569i	−0.0423719	+	0.275269i
$658$		0			0
$659$	−2.32903	+	1.34467i	−0.0907262	+	0.0523808i	−0.544677	−	0.838646i	$-0.683348\pi$
$659$	−2.32903	+	1.34467i	−0.0907262	+	0.0523808i	0.453950	+	0.891027i	$0.350014\pi$
$660$		0			0
$661$	31.9642	+	18.4545i	1.24326	+	0.717798i	0.969757	−	0.244072i	$-0.0784834\pi$
$661$	31.9642	+	18.4545i	1.24326	+	0.717798i	0.273506	+	0.961870i	$0.411817\pi$
$662$		0			0
$663$	−2.71286	−	14.4617i	−0.105359	−	0.561646i
$664$		0			0
$665$			65.7297i			2.54889i
$666$		0			0
$667$	−9.16386			−0.354826
$668$		0			0
$669$	5.58474	−	15.8805i	0.215919	−	0.613975i
$670$		0			0
$671$	20.7668	−	35.9691i	0.801692	−	1.38857i
$672$		0			0
$673$	−10.5243	−	18.2287i	−0.405684	−	0.702665i	0.588717	−	0.808339i	$-0.299633\pi$
$673$	−10.5243	−	18.2287i	−0.405684	−	0.702665i	−0.994401	+	0.105674i	$0.966300\pi$
$674$		0			0
$675$	−2.14261	+	4.00834i	−0.0824691	+	0.154281i
$676$		0			0
$677$	−1.23701	−	2.14256i	−0.0475420	−	0.0823451i	0.841275	−	0.540607i	$-0.181805\pi$
$677$	−1.23701	−	2.14256i	−0.0475420	−	0.0823451i	−0.888817	+	0.458262i	$0.848472\pi$
$678$		0			0
$679$	10.4598	+	6.03896i	0.401410	+	0.231754i
$680$		0			0
$681$	−5.65695	+	16.0858i	−0.216775	+	0.616410i
$682$		0			0
$683$		−	1.37923i		−	0.0527749i	−0.999652	−	0.0263875i	$-0.991600\pi$
$683$		−	1.37923i		−	0.0527749i	0.999652	−	0.0263875i	$-0.00840036\pi$
$684$		0			0
$685$		−	0.706542i		−	0.0269956i
$686$		0			0
$687$	38.1389	−	7.15446i	1.45509	−	0.272960i
$688$		0			0
$689$	−7.49092	−	4.32488i	−0.285381	−	0.164765i
$690$		0			0
$691$	−1.71132	−	2.96410i	−0.0651018	−	0.112760i	0.831637	−	0.555319i	$-0.187404\pi$
$691$	−1.71132	−	2.96410i	−0.0651018	−	0.112760i	−0.896739	+	0.442559i	$0.854071\pi$
$692$		0			0
$693$	−46.1940	−	37.0756i	−1.75476	−	1.40839i
$694$		0			0
$695$	−17.8582	−	30.9313i	−0.677400	−	1.17329i
$696$		0			0
$697$	−23.6072	+	40.8888i	−0.894185	+	1.54877i
$698$		0			0
$699$	−15.0839	−	17.5834i	−0.570525	−	0.665064i
$700$		0			0
$701$	21.2981			0.804419			0.402209	−	0.915548i	$-0.368242\pi$
$701$	21.2981			0.804419			0.402209	+	0.915548i	$0.368242\pi$
$702$		0			0
$703$		−	12.0000i		−	0.452589i
$704$		0			0
$705$	−23.5907	+	20.2372i	−0.888476	+	0.762178i
$706$		0			0
$707$	−58.9957	−	34.0612i	−2.21876	−	1.28100i
$708$		0			0
$709$	−15.5213	+	8.96122i	−0.582914	+	0.336546i	−0.762291	−	0.647235i	$-0.775925\pi$
$709$	−15.5213	+	8.96122i	−0.582914	+	0.336546i	0.179377	+	0.983780i	$0.442592\pi$
$710$		0			0
$711$	6.75648	+	17.3750i	0.253388	+	0.651613i
$712$		0			0
$713$	−5.45493	+	3.14941i	−0.204289	+	0.117946i
$714$		0			0
$715$	−11.3781	+	19.7074i	−0.425515	+	0.737014i
$716$		0			0
$717$	2.51711	+	13.4182i	0.0940031	+	0.501111i
$718$		0			0
$719$	24.7546			0.923190			0.461595	−	0.887091i	$-0.347277\pi$
$719$	24.7546			0.923190			0.461595	+	0.887091i	$0.347277\pi$
$720$		0			0
$721$	81.0294			3.01769
$722$		0			0
$723$	−22.8914	−	8.05029i	−0.851341	−	0.299394i
$724$		0			0
$725$	−0.679618	+	1.17713i	−0.0252404	+	0.0437176i
$726$		0			0
$727$	−24.6871	+	14.2531i	−0.915594	+	0.528618i	−0.882227	−	0.470825i	$-0.843956\pi$
$727$	−24.6871	+	14.2531i	−0.915594	+	0.528618i	−0.0333669	+	0.999443i	$0.510623\pi$
$728$		0			0
$729$	−11.9428	+	24.2151i	−0.442326	+	0.896854i
$730$		0			0
$731$	−6.73442	+	3.88812i	−0.249081	+	0.143807i
$732$		0			0
$733$	−10.8260	−	6.25041i	−0.399868	−	0.230864i	0.286559	−	0.958063i	$-0.407489\pi$
$733$	−10.8260	−	6.25041i	−0.399868	−	0.230864i	−0.686427	+	0.727199i	$0.740822\pi$
$734$		0			0
$735$	55.0982	+	19.3765i	2.03233	+	0.714714i
$736$		0			0
$737$		−	14.8138i		−	0.545674i
$738$		0			0
$739$	−6.72166			−0.247260			−0.123630	−	0.992328i	$-0.539454\pi$
$739$	−6.72166			−0.247260			−0.123630	+	0.992328i	$0.539454\pi$
$740$		0			0
$741$	21.9526	−	4.11808i	0.806449	−	0.151281i
$742$		0			0
$743$	−12.3951	+	21.4690i	−0.454733	+	0.787621i	−0.998673	−	0.0515032i	$-0.983599\pi$
$743$	−12.3951	+	21.4690i	−0.454733	+	0.787621i	0.543939	+	0.839124i	$0.316932\pi$
$744$		0			0
$745$	19.0463	+	32.9891i	0.697802	+	1.20863i
$746$		0			0
$747$	6.78070	+	17.4373i	0.248093	+	0.637996i
$748$		0			0
$749$	15.0366	+	26.0441i	0.549425	+	0.951631i
$750$		0			0
$751$	−34.6991	−	20.0335i	−1.26619	−	0.731033i	−0.291922	−	0.956442i	$-0.594295\pi$
$751$	−34.6991	−	20.0335i	−1.26619	−	0.731033i	−0.974264	+	0.225409i	$0.927628\pi$
$752$		0			0
$753$	−18.3498	−	21.3905i	−0.668704	−	0.779513i
$754$		0			0
$755$			15.6691i			0.570257i
$756$		0			0
$757$		−	14.5925i		−	0.530372i	−0.964197	−	0.265186i	$-0.914567\pi$
$757$		−	14.5925i		−	0.530372i	0.964197	−	0.265186i	$-0.0854334\pi$
$758$		0			0
$759$	28.7135	+	33.4715i	1.04223	+	1.21494i
$760$		0			0
$761$	1.95502	+	1.12873i	0.0708693	+	0.0409164i	0.535016	−	0.844842i	$-0.320306\pi$
$761$	1.95502	+	1.12873i	0.0708693	+	0.0409164i	−0.464147	+	0.885758i	$0.653639\pi$
$762$		0			0
$763$	3.44481	+	5.96659i	0.124711	+	0.216005i
$764$		0			0
$765$	−17.7804	+	22.1533i	−0.642852	+	0.800954i
$766$		0			0
$767$	−0.369466	−	0.639933i	−0.0133406	−	0.0231067i
$768$		0			0
$769$	4.55775	−	7.89426i	0.164357	−	0.284674i	−0.772070	−	0.635538i	$-0.780779\pi$
$769$	4.55775	−	7.89426i	0.164357	−	0.284674i	0.936427	+	0.350863i	$0.114112\pi$
$770$		0			0
$771$	4.05348	−	0.760389i	0.145982	−	0.0273847i
$772$		0			0
$773$	49.6226			1.78480			0.892401	−	0.451244i	$-0.149020\pi$
$773$	49.6226			1.78480			0.892401	+	0.451244i	$0.149020\pi$
$774$		0			0
$775$			0.934275i			0.0335602i
$776$		0			0
$777$	−15.1202	−	5.31737i	−0.542435	−	0.190760i
$778$		0			0
$779$	−62.0685	−	35.8353i	−2.22384	−	1.28393i
$780$		0			0
$781$	−8.69544	+	5.02031i	−0.311147	+	0.179641i
$782$		0			0
$783$	−3.80647	+	7.12105i	−0.136032	+	0.254486i
$784$		0			0
$785$	−0.768206	+	0.443524i	−0.0274184	+	0.0158300i
$786$		0			0
$787$	17.1621	−	29.7257i	0.611765	−	1.05961i	−0.379178	−	0.925324i	$-0.623793\pi$
$787$	17.1621	−	29.7257i	0.611765	−	1.05961i	0.990943	−	0.134284i	$-0.0428733\pi$
$788$		0			0
$789$	30.8122	+	10.8358i	1.09694	+	0.385766i
$790$		0			0
$791$	69.3883			2.46716
$792$		0			0
$793$	20.9186			0.742840
$794$		0			0
$795$	3.07884	+	16.4126i	0.109195	+	0.582096i
$796$		0			0
$797$	−14.9392	+	25.8755i	−0.529174	+	0.916557i	0.470247	+	0.882535i	$0.344165\pi$
$797$	−14.9392	+	25.8755i	−0.529174	+	0.916557i	−0.999421	+	0.0340219i	$0.989168\pi$
$798$		0			0
$799$	−25.0484	+	14.4617i	−0.886148	+	0.511618i
$800$		0			0
$801$	14.5427	+	2.23854i	0.513840	+	0.0790949i
$802$		0			0
$803$	8.89755	−	5.13700i	0.313988	−	0.181281i
$804$		0			0
$805$	−56.6066	−	32.6818i	−1.99512	−	1.15188i
$806$		0			0
$807$	−15.2534	+	13.0852i	−0.536947	+	0.460619i
$808$		0			0
$809$			3.31248i			0.116461i	0.998303	+	0.0582303i	$0.0185458\pi$
$809$			3.31248i			0.116461i	−0.998303	+	0.0582303i	$0.981454\pi$
$810$		0			0
$811$	−31.5697			−1.10856			−0.554281	−	0.832329i	$-0.687007\pi$
$811$	−31.5697			−1.10856			−0.554281	+	0.832329i	$0.687007\pi$
$812$		0			0
$813$	−4.22834	−	4.92900i	−0.148294	−	0.172868i
$814$		0			0
$815$	1.07252	−	1.85766i	0.0375687	−	0.0650709i
$816$		0			0
$817$	−5.90210	−	10.2227i	−0.206488	−	0.357648i
$818$		0			0
$819$	4.53867	−	29.4855i	0.158594	−	1.03031i
$820$		0			0
$821$	4.94041	+	8.55703i	0.172421	+	0.298643i	0.939266	−	0.343190i	$-0.111508\pi$
$821$	4.94041	+	8.55703i	0.172421	+	0.298643i	−0.766845	+	0.641833i	$0.778174\pi$
$822$		0			0
$823$	−25.4921	−	14.7178i	−0.888597	−	0.513032i	−0.0151139	−	0.999886i	$-0.504811\pi$
$823$	−25.4921	−	14.7178i	−0.888597	−	0.513032i	−0.873483	+	0.486854i	$0.838144\pi$
$824$		0			0
$825$	6.42901	−	1.20601i	0.223829	−	0.0419880i
$826$		0			0
$827$		−	25.9774i		−	0.903324i	−0.892189	−	0.451662i	$-0.850831\pi$
$827$		−	25.9774i		−	0.903324i	0.892189	−	0.451662i	$-0.149169\pi$
$828$		0			0
$829$			35.0365i			1.21687i	0.793604	+	0.608434i	$0.208202\pi$
$829$			35.0365i			1.21687i	−0.793604	+	0.608434i	$0.791798\pi$
$830$		0			0
$831$	−6.76634	+	19.2404i	−0.234722	+	0.667443i
$832$		0			0
$833$	47.0689	+	27.1752i	1.63084	+	0.941565i
$834$		0			0
$835$	5.84690	+	10.1271i	0.202340	+	0.350464i
$836$		0			0
$837$	0.181477	+	5.54711i	0.00627277	+	0.191736i
$838$		0			0
$839$	−23.9724	−	41.5214i	−0.827618	−	1.43348i	−0.899902	−	0.436093i	$-0.856362\pi$
$839$	−23.9724	−	41.5214i	−0.827618	−	1.43348i	0.0722833	−	0.997384i	$-0.476971\pi$
$840$		0			0
$841$	13.2926	−	23.0235i	0.458366	−	0.793913i
$842$		0			0
$843$	−4.88922	+	13.9027i	−0.168394	+	0.478835i
$844$		0			0
$845$	20.0479			0.689668
$846$		0			0
$847$			34.9430i			1.20066i
$848$		0			0
$849$	3.37414	+	17.9868i	0.115800	+	0.617306i
$850$		0			0
$851$	10.3344	+	5.96659i	0.354260	+	0.204532i
$852$		0			0
$853$	−42.4065	+	24.4834i	−1.45197	+	0.838295i	−0.998593	−	0.0530245i	$-0.983114\pi$
$853$	−42.4065	+	24.4834i	−1.45197	+	0.838295i	−0.453376	+	0.891319i	$0.649781\pi$
$854$		0			0
$855$	−33.6283	−	26.9904i	−1.15007	−	0.923051i
$856$		0			0
$857$	41.0598	−	23.7059i	1.40258	−	0.809777i	0.407919	−	0.913018i	$-0.366255\pi$
$857$	41.0598	−	23.7059i	1.40258	−	0.809777i	0.994656	+	0.103241i	$0.0329213\pi$
$858$		0			0
$859$	1.42404	−	2.46650i	0.0485875	−	0.0841560i	−0.840709	−	0.541487i	$-0.817861\pi$
$859$	1.42404	−	2.46650i	0.0485875	−	0.0841560i	0.889296	+	0.457331i	$0.151195\pi$
$860$		0			0
$861$	−72.6566	+	62.3284i	−2.47613	+	2.12414i
$862$		0			0
$863$	−23.5015			−0.800002			−0.400001	−	0.916515i	$-0.630990\pi$
$863$	−23.5015			−0.800002			−0.400001	+	0.916515i	$0.630990\pi$
$864$		0			0
$865$	1.65817			0.0563793
$866$		0			0
$867$	2.28541	−	1.96054i	0.0776167	−	0.0665834i
$868$		0			0
$869$	13.4149	−	23.2353i	0.455069	−	0.788203i
$870$		0			0
$871$	6.46147	−	3.73053i	0.218939	−	0.126404i
$872$		0			0
$873$	−7.38470	+	2.87163i	−0.249934	+	0.0971900i
$874$		0			0
$875$	39.5988	−	22.8624i	1.33868	−	0.772889i
$876$		0			0
$877$	35.5743	+	20.5388i	1.20126	+	0.693547i	0.960835	−	0.277121i	$-0.0893803\pi$
$877$	35.5743	+	20.5388i	1.20126	+	0.693547i	0.240424	+	0.970668i	$0.422714\pi$
$878$		0			0
$879$	8.84571	+	47.1546i	0.298358	+	1.59049i
$880$		0			0
$881$			28.4932i			0.959960i	0.877279	+	0.479980i	$0.159356\pi$
$881$			28.4932i			0.959960i	−0.877279	+	0.479980i	$0.840644\pi$
$882$		0			0
$883$	25.6755			0.864048			0.432024	−	0.901862i	$-0.357800\pi$
$883$	25.6755			0.864048			0.432024	+	0.901862i	$0.357800\pi$
$884$		0			0
$885$	−0.473268	+	1.34576i	−0.0159087	+	0.0452373i
$886$		0			0
$887$	−15.2134	+	26.3504i	−0.510817	+	0.884761i	0.489104	+	0.872225i	$0.337324\pi$
$887$	−15.2134	+	26.3504i	−0.510817	+	0.884761i	−0.999921	+	0.0125359i	$0.996010\pi$
$888$		0			0
$889$	−20.9125	−	36.2214i	−0.701381	−	1.21483i
$890$		0			0
$891$	37.9370	−	8.40931i	1.27094	−	0.281723i
$892$		0			0
$893$	−21.9526	−	38.0230i	−0.734616	−	1.27239i
$894$		0			0
$895$	−26.8742	−	15.5158i	−0.898305	−	0.518637i
$896$		0			0
$897$	−7.36869	+	20.9532i	−0.246033	+	0.699608i
$898$		0			0
$899$			1.65980i			0.0553573i
$900$		0			0
$901$			15.5394i			0.517692i
$902$		0			0
$903$	−15.4961	+	2.90691i	−0.515679	+	0.0967359i
$904$		0			0
$905$	47.7136	+	27.5475i	1.58605	+	0.915708i
$906$		0			0
$907$	−18.9318	−	32.7908i	−0.628620	−	1.08880i	−0.987829	−	0.155545i	$-0.950287\pi$
$907$	−18.9318	−	32.7908i	−0.628620	−	1.08880i	0.359209	−	0.933257i	$-0.383047\pi$
$908$		0			0
$909$	41.6515	−	16.1967i	1.38149	−	0.537211i
$910$		0			0
$911$	13.5579	+	23.4830i	0.449193	+	0.778026i	0.998334	−	0.0577043i	$-0.0183781\pi$
$911$	13.5579	+	23.4830i	0.449193	+	0.778026i	−0.549140	+	0.835730i	$0.685045\pi$
$912$		0			0
$913$	13.4630	−	23.3186i	0.445559	−	0.771732i
$914$		0			0
$915$	−26.2944	−	30.6516i	−0.869267	−	1.01331i
$916$		0			0
$917$	−36.4747			−1.20450
$918$		0			0
$919$			20.1170i			0.663598i	0.943350	+	0.331799i	$0.107656\pi$
$919$			20.1170i			0.663598i	−0.943350	+	0.331799i	$0.892344\pi$
$920$		0			0
$921$	23.6978	−	20.3291i	0.780868	−	0.669866i
$922$		0			0
$923$	−4.37950	−	2.52851i	−0.144153	−	0.0832268i
$924$		0			0
$925$	1.53286	−	0.884999i	0.0504002	−	0.0290986i
$926$		0			0
$927$	−33.2729	+	41.4560i	−1.09282	+	1.36159i
$928$		0			0
$929$	−17.3881	+	10.0390i	−0.570486	+	0.329370i	−0.757343	−	0.653017i	$-0.773503\pi$
$929$	−17.3881	+	10.0390i	−0.570486	+	0.329370i	0.186858	+	0.982387i	$0.440170\pi$
$930$		0			0
$931$	−41.2515	+	71.4497i	−1.35196	+	2.34167i
$932$		0			0
$933$	9.55469	+	50.9341i	0.312807	+	1.66751i
$934$		0			0
$935$	40.8816			1.33697
$936$		0			0
$937$	−20.9648			−0.684891			−0.342446	−	0.939538i	$-0.611255\pi$
$937$	−20.9648			−0.684891			−0.342446	+	0.939538i	$0.611255\pi$
$938$		0			0
$939$	40.9166	+	14.3893i	1.33526	+	0.469576i
$940$		0			0
$941$	−20.4621	+	35.4415i	−0.667046	+	1.15536i	0.311680	+	0.950187i	$0.399108\pi$
$941$	−20.4621	+	35.4415i	−0.667046	+	1.15536i	−0.978726	+	0.205171i	$0.934225\pi$
$942$		0			0
$943$	61.7229	−	35.6358i	2.00998	−	1.16046i
$944$		0			0
$945$	−48.9096	+	30.4125i	−1.59103	+	0.989319i
$946$		0			0
$947$	−50.7982	+	29.3284i	−1.65072	+	0.953044i	−0.673944	+	0.738782i	$0.735401\pi$
$947$	−50.7982	+	29.3284i	−1.65072	+	0.953044i	−0.976776	+	0.214262i	$0.931266\pi$
$948$		0			0
$949$	4.48129	+	2.58728i	0.145469	+	0.0839866i
$950$		0			0
$951$	−31.4614	−	11.0641i	−1.02021	−	0.358779i
$952$		0			0
$953$		−	8.47068i		−	0.274392i	−0.990544	−	0.137196i	$-0.956191\pi$
$953$		−	8.47068i		−	0.274392i	0.990544	−	0.137196i	$-0.0438091\pi$
$954$		0			0
$955$	−52.7828			−1.70801
$956$		0			0
$957$	11.4215	−	2.14256i	0.369205	−	0.0692590i
$958$		0			0
$959$	0.666527	−	1.15446i	0.0215233	−	0.0372794i
$960$		0			0
$961$	−14.9296	−	25.8588i	−0.481599	−	0.834154i
$962$		0			0
$963$	−19.4990	−	3.00146i	−0.628347	−	0.0967208i
$964$		0			0
$965$	−28.0962	−	48.6640i	−0.904448	−	1.56655i
$966$		0			0
$967$	−46.1228	−	26.6290i	−1.48321	−	0.856331i	−0.483391	−	0.875404i	$-0.660595\pi$
$967$	−46.1228	−	26.6290i	−1.48321	−	0.856331i	−0.999818	+	0.0190733i	$0.993928\pi$
$968$		0			0
$969$	−26.1260	−	30.4553i	−0.839289	−	0.978365i
$970$		0			0
$971$		−	30.2916i		−	0.972105i	−0.873930	−	0.486052i	$-0.838436\pi$
$971$		−	30.2916i		−	0.972105i	0.873930	−	0.486052i	$-0.161564\pi$
$972$		0			0
$973$		−	67.3872i		−	2.16034i
$974$		0			0
$975$	2.14504	+	2.50049i	0.0686962	+	0.0800797i
$976$		0			0
$977$	38.7617	+	22.3791i	1.24010	+	0.715970i	0.969114	−	0.246614i	$-0.0793179\pi$
$977$	38.7617	+	22.3791i	1.24010	+	0.715970i	0.270983	+	0.962584i	$0.412651\pi$
$978$		0			0
$979$	−10.5880	−	18.3390i	−0.338394	−	0.586115i
$980$		0			0
$981$	−4.46714	−	0.687622i	−0.142625	−	0.0219541i
$982$		0			0
$983$	6.22310	+	10.7787i	0.198486	+	0.343788i	0.948038	−	0.318158i	$-0.103064\pi$
$983$	6.22310	+	10.7787i	0.198486	+	0.343788i	−0.749552	+	0.661946i	$0.769731\pi$
$984$		0			0
$985$	28.9733	−	50.1833i	0.923167	−	1.59897i
$986$		0			0
$987$	−57.6373	+	10.8121i	−1.83461	+	0.344154i
$988$		0			0
$989$	11.7385			0.373262
$990$		0			0
$991$		−	8.02185i		−	0.254822i	−0.991850	−	0.127411i	$-0.959333\pi$
$991$		−	8.02185i		−	0.254822i	0.991850	−	0.127411i	$-0.0406668\pi$
$992$		0			0
$993$	−10.2370	−	3.60008i	−0.324862	−	0.114245i
$994$		0			0
$995$	−3.97085	−	2.29257i	−0.125884	−	0.0726794i
$996$		0			0
$997$	−7.14910	+	4.12754i	−0.226414	+	0.130720i	−0.608917	−	0.793234i	$-0.708396\pi$
$997$	−7.14910	+	4.12754i	−0.226414	+	0.130720i	0.382502	+	0.923954i	$0.375062\pi$
$998$		0			0
$999$	8.92922	−	5.55229i	0.282508	−	0.175667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.p.c.95.6	yes	16
3.2	odd	2		1728.2.p.a.287.7		16
4.3	odd	2	inner	576.2.p.c.95.3	yes	16
8.3	odd	2		576.2.p.a.95.6	yes	16
8.5	even	2		576.2.p.a.95.3	✓	16
9.2	odd	6		576.2.p.a.479.6	yes	16
9.4	even	3		5184.2.f.a.2591.14		16
9.5	odd	6		5184.2.f.f.2591.2		16
9.7	even	3		1728.2.p.c.1439.2		16
12.11	even	2		1728.2.p.a.287.8		16
24.5	odd	2		1728.2.p.c.287.1		16
24.11	even	2		1728.2.p.c.287.2		16
36.7	odd	6		1728.2.p.c.1439.1		16
36.11	even	6		576.2.p.a.479.3	yes	16
36.23	even	6		5184.2.f.f.2591.4		16
36.31	odd	6		5184.2.f.a.2591.16		16
72.5	odd	6		5184.2.f.a.2591.13		16
72.11	even	6	inner	576.2.p.c.479.6	yes	16
72.13	even	6		5184.2.f.f.2591.1		16
72.29	odd	6	inner	576.2.p.c.479.3	yes	16
72.43	odd	6		1728.2.p.a.1439.7		16
72.59	even	6		5184.2.f.a.2591.15		16
72.61	even	6		1728.2.p.a.1439.8		16
72.67	odd	6		5184.2.f.f.2591.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
576.2.p.a.95.3	✓	16	8.5	even	2
576.2.p.a.95.6	yes	16	8.3	odd	2
576.2.p.a.479.3	yes	16	36.11	even	6
576.2.p.a.479.6	yes	16	9.2	odd	6
576.2.p.c.95.3	yes	16	4.3	odd	2	inner
576.2.p.c.95.6	yes	16	1.1	even	1	trivial
576.2.p.c.479.3	yes	16	72.29	odd	6	inner
576.2.p.c.479.6	yes	16	72.11	even	6	inner
1728.2.p.a.287.7		16	3.2	odd	2
1728.2.p.a.287.8		16	12.11	even	2
1728.2.p.a.1439.7		16	72.43	odd	6
1728.2.p.a.1439.8		16	72.61	even	6
1728.2.p.c.287.1		16	24.5	odd	2
1728.2.p.c.287.2		16	24.11	even	2
1728.2.p.c.1439.1		16	36.7	odd	6
1728.2.p.c.1439.2		16	9.7	even	3
5184.2.f.a.2591.13		16	72.5	odd	6
5184.2.f.a.2591.14		16	9.4	even	3
5184.2.f.a.2591.15		16	72.59	even	6
5184.2.f.a.2591.16		16	36.31	odd	6
5184.2.f.f.2591.1		16	72.13	even	6
5184.2.f.f.2591.2		16	9.5	odd	6
5184.2.f.f.2591.3		16	72.67	odd	6
5184.2.f.f.2591.4		16	36.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.31461 - 1.12774i) q^{3} +(-1.21189 + 2.09905i) q^{5} +(-3.96035 + 2.28651i) q^{7} +(0.456412 - 2.96508i) q^{9} +O(q^{10})\)	\(q+(1.31461 - 1.12774i) q^{3} +(-1.21189 + 2.09905i) q^{5} +(-3.96035 + 2.28651i) q^{7} +(0.456412 - 2.96508i) q^{9} +(-3.73910 + 2.15877i) q^{11} +(-1.88322 - 1.08728i) q^{13} +(0.774019 + 4.12613i) q^{15} +3.90660i q^{17} -5.93016 q^{19} +(-2.62774 + 7.47211i) q^{21} +(2.94857 - 5.10707i) q^{23} +(-0.437348 - 0.757509i) q^{25} +(-2.74383 - 4.41264i) q^{27} +(-0.776975 - 1.34576i) q^{29} +(-0.925013 - 0.534057i) q^{31} +(-2.48094 + 7.05467i) q^{33} -11.0840i q^{35} +2.02356i q^{37} +(-3.70186 + 0.694430i) q^{39} +(10.4666 + 6.04289i) q^{41} +(0.995268 + 1.72386i) q^{43} +(5.67074 + 4.55138i) q^{45} +(3.70186 + 6.41181i) q^{47} +(6.95623 - 12.0485i) q^{49} +(4.40562 + 5.13567i) q^{51} +3.97773 q^{53} -10.4647i q^{55} +(-7.79586 + 6.68767i) q^{57} +(0.294283 + 0.169904i) q^{59} +(-8.33093 + 4.80986i) q^{61} +(4.97212 + 12.7863i) q^{63} +(4.56450 - 2.63531i) q^{65} +(-1.71554 + 2.97141i) q^{67} +(-1.88322 - 10.0390i) q^{69} +2.32554 q^{71} -2.37960 q^{73} +(-1.42922 - 0.502617i) q^{75} +(9.87208 - 17.0989i) q^{77} +(-5.38160 + 3.10707i) q^{79} +(-8.58338 - 2.70659i) q^{81} +(-5.40089 + 3.11821i) q^{83} +(-8.20016 - 4.73437i) q^{85} +(-2.53909 - 0.892929i) q^{87} +4.90465i q^{89} +9.94425 q^{91} +(-1.81831 + 0.341096i) q^{93} +(7.18669 - 12.4477i) q^{95} +(-1.32056 - 2.28728i) q^{97} +(4.69435 + 12.0720i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{5} + 6 q^{9}+O(q^{10}) \) 16 * q + 6 * q^5 + 6 * q^9	\( 16 q + 6 q^{5} + 6 q^{9} + 6 q^{13} - 30 q^{21} - 14 q^{25} + 18 q^{29} - 48 q^{33} + 66 q^{45} + 6 q^{49} - 48 q^{53} + 18 q^{57} - 42 q^{61} + 54 q^{65} + 6 q^{69} + 28 q^{73} + 66 q^{77} - 6 q^{81} - 36 q^{85} - 102 q^{93} + 8 q^{97}+O(q^{100}) \) 16 * q + 6 * q^5 + 6 * q^9 + 6 * q^13 - 30 * q^21 - 14 * q^25 + 18 * q^29 - 48 * q^33 + 66 * q^45 + 6 * q^49 - 48 * q^53 + 18 * q^57 - 42 * q^61 + 54 * q^65 + 6 * q^69 + 28 * q^73 + 66 * q^77 - 6 * q^81 - 36 * q^85 - 102 * q^93 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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