LMFDB - Embedded newform 720.2.u.a.539.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(179,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2, 2]))

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

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

chi := DirichletCharacter("720.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.u (of order $4$, 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			539.15
Character	$\chi$	$=$	720.539
Dual form			720.2.u.a.179.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.638599 + 1.26182i) q^{2} +(-1.18438 - 1.61160i) q^{4} +(-2.14049 + 0.646750i) q^{5} +0.594230i q^{7} +(2.78989 - 0.465314i) q^{8} +O(q^{10})$	\(q+(-0.638599 + 1.26182i) q^{2} +(-1.18438 - 1.61160i) q^{4} +(-2.14049 + 0.646750i) q^{5} +0.594230i q^{7} +(2.78989 - 0.465314i) q^{8} +(0.550835 - 3.11393i) q^{10} +(3.48671 + 3.48671i) q^{11} +(-3.41630 - 3.41630i) q^{13} +(-0.749812 - 0.379475i) q^{14} +(-1.19448 + 3.81749i) q^{16} -5.22898 q^{17} +(-2.52907 - 2.52907i) q^{19} +(3.57746 + 2.68361i) q^{20} +(-6.62621 + 2.17299i) q^{22} -2.90543 q^{23} +(4.16343 - 2.76873i) q^{25} +(6.49240 - 2.12911i) q^{26} +(0.957658 - 0.703795i) q^{28} +(-0.201837 - 0.201837i) q^{29} -7.91354i q^{31} +(-4.05419 - 3.94506i) q^{32} +(3.33922 - 6.59803i) q^{34} +(-0.384318 - 1.27195i) q^{35} +(3.40301 - 3.40301i) q^{37} +(4.80630 - 1.57617i) q^{38} +(-5.67080 + 2.80036i) q^{40} +4.36373 q^{41} +(-2.94210 - 2.94210i) q^{43} +(1.48957 - 9.74875i) q^{44} +(1.85541 - 3.66613i) q^{46} -10.7533i q^{47} +6.64689 q^{49} +(0.834879 + 7.02161i) q^{50} +(-1.45949 + 9.55189i) q^{52} +(-5.71919 - 5.71919i) q^{53} +(-9.71830 - 5.20824i) q^{55} +(0.276504 + 1.65784i) q^{56} +(0.383576 - 0.125789i) q^{58} +(-3.56275 - 3.56275i) q^{59} +(-9.03433 + 9.03433i) q^{61} +(9.98547 + 5.05358i) q^{62} +(7.56697 - 2.59635i) q^{64} +(9.52206 + 5.10307i) q^{65} +(-7.72594 + 7.72594i) q^{67} +(6.19311 + 8.42699i) q^{68} +(1.85039 + 0.327323i) q^{70} -2.31103i q^{71} +2.62944 q^{73} +(2.12083 + 6.46715i) q^{74} +(-1.08045 + 7.07123i) q^{76} +(-2.07191 + 2.07191i) q^{77} -9.07044i q^{79} +(0.0878100 - 8.94384i) q^{80} +(-2.78667 + 5.50624i) q^{82} +(-3.75900 - 3.75900i) q^{83} +(11.1926 - 3.38184i) q^{85} +(5.59122 - 1.83358i) q^{86} +(11.3499 + 8.10511i) q^{88} -17.3168 q^{89} +(2.03007 - 2.03007i) q^{91} +(3.44114 + 4.68238i) q^{92} +(13.5687 + 6.86704i) q^{94} +(7.04915 + 3.77779i) q^{95} +2.43368i q^{97} +(-4.24470 + 8.38718i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q - 8 q^{16} - 16 q^{19} + 72 q^{34} + 8 q^{40} + 8 q^{46} - 96 q^{49} + 64 q^{55} - 32 q^{61} + 48 q^{64} + 24 q^{70} + 40 q^{76} - 88 q^{94}+O(q^{100}) $ 96 * q - 8 * q^16 - 16 * q^19 + 72 * q^34 + 8 * q^40 + 8 * q^46 - 96 * q^49 + 64 * q^55 - 32 * q^61 + 48 * q^64 + 24 * q^70 + 40 * q^76 - 88 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.638599	+	1.26182i	−0.451558	+	0.892242i
$2$	−0.638599	+	1.26182i	−0.451558	+	0.892242i
$3$		0			0
$3$		0			0
$4$	−1.18438	−	1.61160i	−0.592191	−	0.805798i
$5$	−2.14049	+	0.646750i	−0.957258	+	0.289236i
$5$	−2.14049	+	0.646750i	−0.957258	+	0.289236i
$6$		0			0
$7$			0.594230i			0.224598i	0.993674	+	0.112299i	$0.0358214\pi$
$7$			0.594230i			0.224598i	−0.993674	+	0.112299i	$0.964179\pi$
$8$	2.78989	−	0.465314i	0.986375	−	0.164513i
$9$		0			0
$10$	0.550835	−	3.11393i	0.174189	−	0.984712i
$11$	3.48671	+	3.48671i	1.05128	+	1.05128i	0.998612	+	0.0526694i	$0.0167730\pi$
$11$	3.48671	+	3.48671i	1.05128	+	1.05128i	0.0526694	+	0.998612i	$0.483227\pi$
$12$		0			0
$13$	−3.41630	−	3.41630i	−0.947511	−	0.947511i	0.0511786	−	0.998690i	$-0.483702\pi$
$13$	−3.41630	−	3.41630i	−0.947511	−	0.947511i	−0.998690	+	0.0511786i	$0.983702\pi$
$14$	−0.749812	−	0.379475i	−0.200396	−	0.101419i
$15$		0			0
$16$	−1.19448	+	3.81749i	−0.298619	+	0.954372i
$17$	−5.22898			−1.26821			−0.634107	−	0.773246i	$-0.718632\pi$
$17$	−5.22898			−1.26821			−0.634107	+	0.773246i	$0.718632\pi$
$18$		0			0
$19$	−2.52907	−	2.52907i	−0.580209	−	0.580209i	0.354751	−	0.934961i	$-0.384566\pi$
$19$	−2.52907	−	2.52907i	−0.580209	−	0.580209i	−0.934961	+	0.354751i	$0.884566\pi$
$20$	3.57746	+	2.68361i	0.799945	+	0.600073i
$21$		0			0
$22$	−6.62621	+	2.17299i	−1.41271	+	0.463283i
$23$	−2.90543			−0.605824			−0.302912	−	0.953019i	$-0.597959\pi$
$23$	−2.90543			−0.605824			−0.302912	+	0.953019i	$0.597959\pi$
$24$		0			0
$25$	4.16343	−	2.76873i	0.832686	−	0.553746i
$26$	6.49240	−	2.12911i	1.27326	−	0.417553i
$27$		0			0
$28$	0.957658	−	0.703795i	0.180980	−	0.133005i
$29$	−0.201837	−	0.201837i	−0.0374802	−	0.0374802i	0.688118	−	0.725599i	$-0.258437\pi$
$29$	−0.201837	−	0.201837i	−0.0374802	−	0.0374802i	−0.725599	+	0.688118i	$0.758437\pi$
$30$		0			0
$31$		−	7.91354i		−	1.42131i	−0.703538	−	0.710657i	$-0.748398\pi$
$31$		−	7.91354i		−	1.42131i	0.703538	−	0.710657i	$-0.251602\pi$
$32$	−4.05419	−	3.94506i	−0.716687	−	0.697395i
$33$		0			0
$34$	3.33922	−	6.59803i	0.572672	−	1.13155i
$35$	−0.384318	−	1.27195i	−0.0649617	−	0.214998i
$36$		0			0
$37$	3.40301	−	3.40301i	0.559452	−	0.559452i	−0.369699	−	0.929151i	$-0.620539\pi$
$37$	3.40301	−	3.40301i	0.559452	−	0.559452i	0.929151	+	0.369699i	$0.120539\pi$
$38$	4.80630	−	1.57617i	0.779685	−	0.255689i
$39$		0			0
$40$	−5.67080	+	2.80036i	−0.896632	+	0.442777i
$41$	4.36373			0.681500			0.340750	−	0.940154i	$-0.389319\pi$
$41$	4.36373			0.681500			0.340750	+	0.940154i	$0.389319\pi$
$42$		0			0
$43$	−2.94210	−	2.94210i	−0.448666	−	0.448666i	0.446245	−	0.894911i	$-0.352761\pi$
$43$	−2.94210	−	2.94210i	−0.448666	−	0.448666i	−0.894911	+	0.446245i	$0.852761\pi$
$44$	1.48957	−	9.74875i	0.224561	−	1.46968i
$45$		0			0
$46$	1.85541	−	3.66613i	0.273565	−	0.540542i
$47$		−	10.7533i		−	1.56853i	−0.620427	−	0.784264i	$-0.713041\pi$
$47$		−	10.7533i		−	1.56853i	0.620427	−	0.784264i	$-0.286959\pi$
$48$		0			0
$49$	6.64689			0.949556
$50$	0.834879	+	7.02161i	0.118070	+	0.993005i
$51$		0			0
$52$	−1.45949	+	9.55189i	−0.202394	+	1.32461i
$53$	−5.71919	−	5.71919i	−0.785591	−	0.785591i	0.195177	−	0.980768i	$-0.437472\pi$
$53$	−5.71919	−	5.71919i	−0.785591	−	0.785591i	−0.980768	+	0.195177i	$0.937472\pi$
$54$		0			0
$55$	−9.71830	−	5.20824i	−1.31042	−	0.702280i
$56$	0.276504	+	1.65784i	0.0369494	+	0.221538i
$57$		0			0
$58$	0.383576	−	0.125789i	0.0503659	−	0.0165169i
$59$	−3.56275	−	3.56275i	−0.463831	−	0.463831i	0.436078	−	0.899909i	$-0.356367\pi$
$59$	−3.56275	−	3.56275i	−0.463831	−	0.463831i	−0.899909	+	0.436078i	$0.856367\pi$
$60$		0			0
$61$	−9.03433	+	9.03433i	−1.15673	+	1.15673i	−0.171553	+	0.985175i	$0.554878\pi$
$61$	−9.03433	+	9.03433i	−1.15673	+	1.15673i	−0.985175	+	0.171553i	$0.945122\pi$
$62$	9.98547	+	5.05358i	1.26816	+	0.641806i
$63$		0			0
$64$	7.56697	−	2.59635i	0.945871	−	0.324544i
$65$	9.52206	+	5.10307i	1.18107	+	0.632958i
$66$		0			0
$67$	−7.72594	+	7.72594i	−0.943874	+	0.943874i	−0.998507	−	0.0546326i	$-0.982601\pi$
$67$	−7.72594	+	7.72594i	−0.943874	+	0.943874i	0.0546326	+	0.998507i	$0.482601\pi$
$68$	6.19311	+	8.42699i	0.751025	+	1.02192i
$69$		0			0
$70$	1.85039	+	0.327323i	0.221164	+	0.0391225i
$71$		−	2.31103i		−	0.274269i	−0.990552	−	0.137134i	$-0.956211\pi$
$71$		−	2.31103i		−	0.274269i	0.990552	−	0.137134i	$-0.0437892\pi$
$72$		0			0
$73$	2.62944			0.307753			0.153876	−	0.988090i	$-0.450824\pi$
$73$	2.62944			0.307753			0.153876	+	0.988090i	$0.450824\pi$
$74$	2.12083	+	6.46715i	0.246542	+	0.751791i
$75$		0			0
$76$	−1.08045	+	7.07123i	−0.123936	+	0.811126i
$77$	−2.07191	+	2.07191i	−0.236116	+	0.236116i
$78$		0			0
$79$		−	9.07044i		−	1.02050i	−0.860025	−	0.510252i	$-0.829552\pi$
$79$		−	9.07044i		−	1.02050i	0.860025	−	0.510252i	$-0.170448\pi$
$80$	0.0878100	−	8.94384i	0.00981746	−	0.999952i
$81$		0			0
$82$	−2.78667	+	5.50624i	−0.307737	+	0.608063i
$83$	−3.75900	−	3.75900i	−0.412604	−	0.412604i	0.470041	−	0.882645i	$-0.344239\pi$
$83$	−3.75900	−	3.75900i	−0.412604	−	0.412604i	−0.882645	+	0.470041i	$0.844239\pi$
$84$		0			0
$85$	11.1926	−	3.38184i	1.21401	−	0.366812i
$86$	5.59122	−	1.83358i	0.602917	−	0.197720i
$87$		0			0
$88$	11.3499	+	8.10511i	1.20991	+	0.864008i
$89$	−17.3168			−1.83558			−0.917788	−	0.397070i	$-0.870027\pi$
$89$	−17.3168			−1.83558			−0.917788	+	0.397070i	$0.870027\pi$
$90$		0			0
$91$	2.03007	−	2.03007i	0.212809	−	0.212809i
$92$	3.44114	+	4.68238i	0.358764	+	0.488172i
$93$		0			0
$94$	13.5687	+	6.86704i	1.39951	+	0.708281i
$95$	7.04915	+	3.77779i	0.723227	+	0.387593i
$96$		0			0
$97$			2.43368i			0.247103i	0.992338	+	0.123551i	$0.0394284\pi$
$97$			2.43368i			0.247103i	−0.992338	+	0.123551i	$0.960572\pi$
$98$	−4.24470	+	8.38718i	−0.428779	+	0.847233i
$99$		0			0
$100$	−9.39316	−	3.43053i	−0.939316	−	0.343053i
$101$	−9.22586	+	9.22586i	−0.918007	+	0.918007i	−0.996884	−	0.0788774i	$-0.974866\pi$
$101$	−9.22586	+	9.22586i	−0.918007	+	0.918007i	0.0788774	+	0.996884i	$0.474866\pi$
$102$		0			0
$103$			0.353806i			0.0348615i	0.999848	+	0.0174308i	$0.00554866\pi$
$103$			0.353806i			0.0348615i	−0.999848	+	0.0174308i	$0.994451\pi$
$104$	−11.1207	−	7.94144i	−1.09048	−	0.778723i
$105$		0			0
$106$	10.8689	−	3.56432i	1.05568	−	0.346197i
$107$	−7.83739	+	7.83739i	−0.757670	+	0.757670i	−0.975898	−	0.218228i	$-0.929972\pi$
$107$	−7.83739	+	7.83739i	−0.757670	+	0.757670i	0.218228	+	0.975898i	$0.429972\pi$
$108$		0			0
$109$	5.04082	−	5.04082i	0.482823	−	0.482823i	−0.423209	−	0.906032i	$-0.639096\pi$
$109$	5.04082	−	5.04082i	0.482823	−	0.482823i	0.906032	+	0.423209i	$0.139096\pi$
$110$	12.7780	−	8.93677i	1.21833	−	0.852088i
$111$		0			0
$112$	−2.26847	−	0.709794i	−0.214350	−	0.0670693i
$113$	13.6858			1.28745			0.643724	−	0.765257i	$-0.277388\pi$
$113$	13.6858			1.28745			0.643724	+	0.765257i	$0.277388\pi$
$114$		0			0
$115$	6.21906	−	1.87909i	0.579930	−	0.175226i
$116$	−0.0862275	+	0.564333i	−0.00800602	+	0.0523970i
$117$		0			0
$118$	6.77073	−	2.22038i	0.623296	−	0.204403i
$119$		−	3.10721i		−	0.284838i
$120$		0			0
$121$			13.3142i			1.21039i
$122$	−5.63039	−	17.1690i	−0.509751	−	1.55441i
$123$		0			0
$124$	−12.7534	+	9.37266i	−1.14529	+	0.841690i
$125$	−7.12111	+	8.61915i	−0.636932	+	0.770920i
$126$		0			0
$127$	21.2399			1.88474			0.942369	−	0.334575i	$-0.108593\pi$
$127$	21.2399			1.88474			0.942369	+	0.334575i	$0.108593\pi$
$128$	−1.55613	+	11.2062i	−0.137544	+	0.990496i
$129$		0			0
$130$	−12.5199	+	8.75631i	−1.09807	+	0.767979i
$131$	2.47505	−	2.47505i	0.216246	−	0.216246i	−0.590668	−	0.806914i	$-0.701136\pi$
$131$	2.47505	−	2.47505i	0.216246	−	0.216246i	0.806914	+	0.590668i	$0.201136\pi$
$132$		0			0
$133$	1.50285	−	1.50285i	0.130314	−	0.130314i
$134$	−4.81497	−	14.6825i	−0.415950	−	1.26838i
$135$		0			0
$136$	−14.5883	+	2.43312i	−1.25093	+	0.208638i
$137$		−	1.05127i		−	0.0898162i	−0.998991	−	0.0449081i	$-0.985700\pi$
$137$		−	1.05127i		−	0.0898162i	0.998991	−	0.0449081i	$-0.0142995\pi$
$138$		0			0
$139$	−2.76139	+	2.76139i	−0.234218	+	0.234218i	−0.814451	−	0.580233i	$-0.802962\pi$
$139$	−2.76139	+	2.76139i	−0.234218	+	0.234218i	0.580233	+	0.814451i	$0.302962\pi$
$140$	−1.59468	+	2.12584i	−0.134775	+	0.179666i
$141$		0			0
$142$	2.91610	+	1.47582i	0.244714	+	0.123848i
$143$		−	23.8233i		−	1.99220i
$144$		0			0
$145$	0.562570	+	0.301493i	0.0467189	+	0.0250376i
$146$	−1.67916	+	3.31788i	−0.138968	+	0.274590i
$147$		0			0
$148$	−9.51475	−	1.45381i	−0.782108	−	0.119503i
$149$	−6.00428	+	6.00428i	−0.491890	+	0.491890i	−0.908901	−	0.417011i	$-0.863078\pi$
$149$	−6.00428	+	6.00428i	−0.491890	+	0.491890i	0.417011	+	0.908901i	$0.363078\pi$
$150$		0			0
$151$	−5.86656			−0.477414			−0.238707	−	0.971092i	$-0.576724\pi$
$151$	−5.86656			−0.477414			−0.238707	+	0.971092i	$0.576724\pi$
$152$	−8.23265	−	5.87902i	−0.667756	−	0.476852i
$153$		0			0
$154$	−1.29126	−	3.93749i	−0.104052	−	0.317292i
$155$	5.11809	+	16.9389i	0.411095	+	1.36056i
$156$		0			0
$157$	3.07654	+	3.07654i	0.245535	+	0.245535i	0.819135	−	0.573600i	$-0.194454\pi$
$157$	3.07654	+	3.07654i	0.245535	+	0.245535i	−0.573600	+	0.819135i	$0.694454\pi$
$158$	11.4453	+	5.79238i	0.910537	+	0.460817i
$159$		0			0
$160$	11.2294	+	5.82233i	0.887766	+	0.460296i
$161$		−	1.72649i		−	0.136067i
$162$		0			0
$163$	−11.6108	+	11.6108i	−0.909426	+	0.909426i	−0.996226	−	0.0867995i	$-0.972336\pi$
$163$	−11.6108	+	11.6108i	−0.909426	+	0.909426i	0.0867995	+	0.996226i	$0.472336\pi$
$164$	−5.16832	−	7.03257i	−0.403578	−	0.549151i
$165$		0			0
$166$	7.14368	−	2.34269i	0.554457	−	0.181828i
$167$	−15.2444			−1.17965			−0.589823	−	0.807533i	$-0.700802\pi$
$167$	−15.2444			−1.17965			−0.589823	+	0.807533i	$0.700802\pi$
$168$		0			0
$169$			10.3422i			0.795554i
$170$	−2.88030	+	16.2827i	−0.220909	+	1.24882i
$171$		0			0
$172$	−1.25690	+	8.22604i	−0.0958380	+	0.627230i
$173$	−8.88472	+	8.88472i	−0.675493	+	0.675493i	−0.958977	−	0.283484i	$-0.908510\pi$
$173$	−8.88472	+	8.88472i	−0.675493	+	0.675493i	0.283484	+	0.958977i	$0.408510\pi$
$174$		0			0
$175$	1.64526	+	2.47403i	0.124370	+	0.187019i
$176$	−17.4753	+	9.14567i	−1.31725	+	0.689381i
$177$		0			0
$178$	11.0585	−	21.8507i	0.828869	−	1.63778i
$179$	16.3484	−	16.3484i	1.22193	−	1.22193i	0.254990	−	0.966944i	$-0.417928\pi$
$179$	16.3484	−	16.3484i	1.22193	−	1.22193i	0.966944	−	0.254990i	$-0.0820721\pi$
$180$		0			0
$181$	7.64457	+	7.64457i	0.568216	+	0.568216i	0.931628	−	0.363412i	$-0.118388\pi$
$181$	7.64457	+	7.64457i	0.568216	+	0.568216i	−0.363412	+	0.931628i	$0.618388\pi$
$182$	1.26518	+	3.85798i	0.0937815	+	0.285972i
$183$		0			0
$184$	−8.10583	+	1.35194i	−0.597570	+	0.0996662i
$185$	−5.08323	+	9.48503i	−0.373726	+	0.697353i
$186$		0			0
$187$	−18.2319	−	18.2319i	−1.33325	−	1.33325i
$188$	−17.3299	+	12.7360i	−1.26392	+	0.928869i
$189$		0			0
$190$	−9.26847	+	6.48227i	−0.672405	+	0.470273i
$191$	−23.6358			−1.71023			−0.855113	−	0.518442i	$-0.826512\pi$
$191$	−23.6358			−1.71023			−0.855113	+	0.518442i	$0.826512\pi$
$192$		0			0
$193$			11.6874i			0.841281i	0.907227	+	0.420640i	$0.138195\pi$
$193$			11.6874i			0.841281i	−0.907227	+	0.420640i	$0.861805\pi$
$194$	−3.07087	−	1.55415i	−0.220475	−	0.111581i
$195$		0			0
$196$	−7.87246	−	10.7121i	−0.562318	−	0.765150i
$197$	7.52719	+	7.52719i	0.536290	+	0.536290i	0.922437	−	0.386147i	$-0.126194\pi$
$197$	7.52719	+	7.52719i	0.536290	+	0.536290i	−0.386147	+	0.922437i	$0.626194\pi$
$198$		0			0
$199$	9.24585			0.655421			0.327710	−	0.944778i	$-0.393723\pi$
$199$	9.24585			0.655421			0.327710	+	0.944778i	$0.393723\pi$
$200$	10.3272	−	9.66175i	0.730241	−	0.683189i
$201$		0			0
$202$	−5.74975	−	17.5330i	−0.404551	−	1.23362i
$203$	0.119938	−	0.119938i	0.00841798	−	0.00841798i
$204$		0			0
$205$	−9.34054	+	2.82224i	−0.652371	+	0.197114i
$206$	−0.446439	−	0.225940i	−0.0311049	−	0.0157420i
$207$		0			0
$208$	17.1224	−	8.96099i	1.18722	−	0.621333i
$209$		−	17.6363i		−	1.21993i
$210$		0			0
$211$	−13.2934	−	13.2934i	−0.915154	−	0.915154i	0.0815182	−	0.996672i	$-0.474023\pi$
$211$	−13.2934	−	13.2934i	−0.915154	−	0.915154i	−0.996672	+	0.0815182i	$0.974023\pi$
$212$	−2.44331	+	15.9907i	−0.167807	+	1.09825i
$213$		0			0
$214$	−4.88443	−	14.8943i	−0.333893	−	1.01816i
$215$	8.20035	+	4.39474i	0.559259	+	0.299719i
$216$		0			0
$217$	4.70246			0.319224
$218$	3.14155	+	9.57968i	0.212772	+	0.648818i
$219$		0			0
$220$	3.11660	+	21.8305i	0.210121	+	1.47181i
$221$	17.8637	+	17.8637i	1.20165	+	1.20165i
$222$		0			0
$223$	−22.4740			−1.50497			−0.752487	−	0.658607i	$-0.771146\pi$
$223$	−22.4740			−1.50497			−0.752487	+	0.658607i	$0.771146\pi$
$224$	2.34427	−	2.40912i	0.156633	−	0.160966i
$225$		0			0
$226$	−8.73972	+	17.2690i	−0.581357	+	1.14872i
$227$	20.4123	+	20.4123i	1.35481	+	1.35481i	0.880190	+	0.474622i	$0.157415\pi$
$227$	20.4123	+	20.4123i	1.35481	+	1.35481i	0.474622	+	0.880190i	$0.342585\pi$
$228$		0			0
$229$	−1.13042	−	1.13042i	−0.0747005	−	0.0747005i	0.668769	−	0.743470i	$-0.266821\pi$
$229$	−1.13042	−	1.13042i	−0.0747005	−	0.0747005i	−0.743470	+	0.668769i	$0.766821\pi$
$230$	−1.60041	+	9.04732i	−0.105528	+	0.596562i
$231$		0			0
$232$	−0.657022	−	0.469186i	−0.0431356	−	0.0308036i
$233$		−	6.91098i		−	0.452753i	−0.974040	−	0.226377i	$-0.927312\pi$
$233$		−	6.91098i		−	0.452753i	0.974040	−	0.226377i	$-0.0726880\pi$
$234$		0			0
$235$	6.95469	+	23.0174i	0.453674	+	1.50149i
$236$	−1.52205	+	9.96138i	−0.0990773	+	0.648430i
$237$		0			0
$238$	3.92075	+	1.98426i	0.254144	+	0.128621i
$239$	−3.97843			−0.257343			−0.128672	−	0.991687i	$-0.541071\pi$
$239$	−3.97843			−0.257343			−0.128672	+	0.991687i	$0.541071\pi$
$240$		0			0
$241$	12.1568			0.783086			0.391543	−	0.920160i	$-0.371941\pi$
$241$	12.1568			0.783086			0.391543	+	0.920160i	$0.371941\pi$
$242$	−16.8002	−	8.50246i	−1.07996	−	0.546559i
$243$		0			0
$244$	25.2598	+	3.85958i	1.61709	+	0.247085i
$245$	−14.2276	+	4.29888i	−0.908970	+	0.274645i
$246$		0			0
$247$			17.2801i			1.09951i
$248$	−3.68229	−	22.0779i	−0.233825	−	1.40195i
$249$		0			0
$250$	−6.32828	−	14.4898i	−0.400236	−	0.916412i
$251$	−9.68497	−	9.68497i	−0.611310	−	0.611310i	0.331977	−	0.943287i	$-0.392284\pi$
$251$	−9.68497	−	9.68497i	−0.611310	−	0.611310i	−0.943287	+	0.331977i	$0.892284\pi$
$252$		0			0
$253$	−10.1304	−	10.1304i	−0.636892	−	0.636892i
$254$	−13.5638	+	26.8010i	−0.851068	+	1.68164i
$255$		0			0
$256$	−13.1464	−	9.11981i	−0.821653	−	0.569988i
$257$	22.8387			1.42464			0.712320	−	0.701855i	$-0.247644\pi$
$257$	22.8387			1.42464			0.712320	+	0.701855i	$0.247644\pi$
$258$		0			0
$259$	2.02217	+	2.02217i	0.125652	+	0.125652i
$260$	−3.05367	−	21.3897i	−0.189380	−	1.32653i
$261$		0			0
$262$	1.54250	+	4.70363i	0.0952962	+	0.290591i
$263$	7.69609			0.474562			0.237281	−	0.971441i	$-0.423744\pi$
$263$	7.69609			0.474562			0.237281	+	0.971441i	$0.423744\pi$
$264$		0			0
$265$	15.9408	+	8.54300i	0.979234	+	0.524792i
$266$	0.936609	+	2.85605i	0.0574272	+	0.175116i
$267$		0			0
$268$	21.6016	+	3.30062i	1.31953	+	0.201618i
$269$	−10.3047	−	10.3047i	−0.628286	−	0.628286i	0.319351	−	0.947637i	$-0.396535\pi$
$269$	−10.3047	−	10.3047i	−0.628286	−	0.628286i	−0.947637	+	0.319351i	$0.896535\pi$
$270$		0			0
$271$		−	11.2542i		−	0.683642i	−0.939765	−	0.341821i	$-0.888956\pi$
$271$		−	11.2542i		−	0.683642i	0.939765	−	0.341821i	$-0.111044\pi$
$272$	6.24590	−	19.9616i	0.378713	−	1.21035i
$273$		0			0
$274$	1.32652	+	0.671342i	0.0801378	+	0.0405572i
$275$	24.1704	+	4.86290i	1.45753	+	0.293244i
$276$		0			0
$277$	17.5560	−	17.5560i	1.05484	−	1.05484i	0.0564290	−	0.998407i	$-0.482029\pi$
$277$	17.5560	−	17.5560i	1.05484	−	1.05484i	0.998407	−	0.0564290i	$-0.0179715\pi$
$278$	−1.72096	−	5.24780i	−0.103216	−	0.314742i
$279$		0			0
$280$	−1.66406	−	3.36976i	−0.0994466	−	0.201382i
$281$	13.7416			0.819753			0.409876	−	0.912141i	$-0.365572\pi$
$281$	13.7416			0.819753			0.409876	+	0.912141i	$0.365572\pi$
$282$		0			0
$283$	−4.27900	−	4.27900i	−0.254360	−	0.254360i	0.568395	−	0.822756i	$-0.307564\pi$
$283$	−4.27900	−	4.27900i	−0.254360	−	0.254360i	−0.822756	+	0.568395i	$0.807564\pi$
$284$	−3.72444	+	2.73714i	−0.221005	+	0.162420i
$285$		0			0
$286$	30.0607	+	15.2135i	1.77753	+	0.899594i
$287$			2.59306i			0.153063i
$288$		0			0
$289$	10.3422			0.608365
$290$	−0.739687	+	0.517329i	−0.0434359	+	0.0303786i
$291$		0			0
$292$	−3.11426	−	4.23759i	−0.182248	−	0.247986i
$293$	−11.6595	−	11.6595i	−0.681153	−	0.681153i	0.279107	−	0.960260i	$-0.409962\pi$
$293$	−11.6595	−	11.6595i	−0.681153	−	0.681153i	−0.960260	+	0.279107i	$0.909962\pi$
$294$		0			0
$295$	9.93026	+	5.32184i	0.578162	+	0.309849i
$296$	7.91056	−	11.0775i	0.459792	−	0.643867i
$297$		0			0
$298$	−3.74200	−	11.4107i	−0.216768	−	0.661002i
$299$	9.92582	+	9.92582i	0.574025	+	0.574025i
$300$		0			0
$301$	1.74828	−	1.74828i	0.100769	−	0.100769i
$302$	3.74638	−	7.40255i	0.215580	−	0.425969i
$303$		0			0
$304$	12.6756	−	6.63379i	0.726997	−	0.380474i
$305$	13.4950	−	25.1809i	0.772720	−	1.44185i
$306$		0			0
$307$	4.64313	−	4.64313i	0.264997	−	0.264997i	−0.562083	−	0.827081i	$-0.690000\pi$
$307$	4.64313	−	4.64313i	0.264997	−	0.264997i	0.827081	+	0.562083i	$0.190000\pi$
$308$	5.79300	+	0.885145i	0.330087	+	0.0504358i
$309$		0			0
$310$	−24.6422	−	4.35905i	−1.39959	−	0.247578i
$311$		−	0.760850i		−	0.0431438i	−0.999767	−	0.0215719i	$-0.993133\pi$
$311$		−	0.760850i		−	0.0431438i	0.999767	−	0.0215719i	$-0.00686709\pi$
$312$		0			0
$313$	−31.2608			−1.76697			−0.883483	−	0.468464i	$-0.844808\pi$
$313$	−31.2608			−1.76697			−0.883483	+	0.468464i	$0.844808\pi$
$314$	−5.84672	+	1.91737i	−0.329950	+	0.108203i
$315$		0			0
$316$	−14.6179	+	10.7429i	−0.822320	+	0.604334i
$317$	−3.38359	+	3.38359i	−0.190041	+	0.190041i	−0.795714	−	0.605673i	$-0.792904\pi$
$317$	−3.38359	+	3.38359i	−0.190041	+	0.190041i	0.605673	+	0.795714i	$0.292904\pi$
$318$		0			0
$319$		−	1.40749i		−	0.0788046i
$320$	−14.5179	+	10.4514i	−0.811573	+	0.584252i
$321$		0			0
$322$	2.17853	+	1.10254i	0.121404	+	0.0614420i
$323$	13.2245	+	13.2245i	0.735829	+	0.735829i
$324$		0			0
$325$	−23.6823	−	4.76470i	−1.31366	−	0.264298i
$326$	−7.23608	−	22.0654i	−0.400770	−	1.22209i
$327$		0			0
$328$	12.1743	−	2.03051i	0.672215	−	0.112116i
$329$	6.38993			0.352288
$330$		0			0
$331$	−0.0840779	+	0.0840779i	−0.00462134	+	0.00462134i	−0.709414	−	0.704792i	$-0.751040\pi$
$331$	−0.0840779	+	0.0840779i	−0.00462134	+	0.00462134i	0.704792	+	0.709414i	$0.251040\pi$
$332$	−1.60589	+	10.5101i	−0.0881348	+	0.576815i
$333$		0			0
$334$	9.73504	−	19.2357i	0.532678	−	1.05253i
$335$	11.5406	−	21.5341i	0.630529	−	1.17653i
$336$		0			0
$337$			27.7179i			1.50989i	0.655787	+	0.754946i	$0.272337\pi$
$337$			27.7179i			1.50989i	−0.655787	+	0.754946i	$0.727663\pi$
$338$	−13.0500	−	6.60452i	−0.709826	−	0.359238i
$339$		0			0
$340$	−18.7065	−	14.0325i	−1.01450	−	0.761021i
$341$	27.5922	−	27.5922i	1.49420	−	1.49420i
$342$		0			0
$343$			8.10939i			0.437866i
$344$	−9.57713	−	6.83913i	−0.516364	−	0.368741i
$345$		0			0
$346$	−5.53715	−	16.8847i	−0.297679	−	0.907727i
$347$	11.7819	−	11.7819i	0.632487	−	0.632487i	−0.316204	−	0.948691i	$-0.602408\pi$
$347$	11.7819	−	11.7819i	0.632487	−	0.632487i	0.948691	+	0.316204i	$0.102408\pi$
$348$		0			0
$349$	1.41586	−	1.41586i	0.0757895	−	0.0757895i	−0.668196	−	0.743985i	$-0.732933\pi$
$349$	1.41586	−	1.41586i	0.0757895	−	0.0757895i	0.743985	+	0.668196i	$0.232933\pi$
$350$	−4.17245	+	0.496110i	−0.223027	+	0.0265182i
$351$		0			0
$352$	−0.380509	−	27.8911i	−0.0202812	−	1.48660i
$353$	12.4948			0.665031			0.332515	−	0.943098i	$-0.392103\pi$
$353$	12.4948			0.665031			0.332515	+	0.943098i	$0.392103\pi$
$354$		0			0
$355$	1.49466	+	4.94674i	0.0793283	+	0.262546i
$356$	20.5097	+	27.9077i	1.08701	+	1.47910i
$357$		0			0
$358$	10.1886	+	31.0687i	0.538487	+	1.64203i
$359$		−	1.11928i		−	0.0590733i	−0.999564	−	0.0295366i	$-0.990597\pi$
$359$		−	1.11928i		−	0.0590733i	0.999564	−	0.0295366i	$-0.00940317\pi$
$360$		0			0
$361$		−	6.20757i		−	0.326714i
$362$	−14.5279	+	4.76426i	−0.763569	+	0.250404i
$363$		0			0
$364$	−5.67602	−	0.867271i	−0.297504	−	0.0454574i
$365$	−5.62830	+	1.70059i	−0.294599	+	0.0890130i
$366$		0			0
$367$	12.5630			0.655784			0.327892	−	0.944715i	$-0.393662\pi$
$367$	12.5630			0.655784			0.327892	+	0.944715i	$0.393662\pi$
$368$	3.47047	−	11.0915i	0.180911	−	0.578182i
$369$		0			0
$370$	−8.72226	−	12.4713i	−0.453449	−	0.648350i
$371$	3.39851	−	3.39851i	0.176442	−	0.176442i
$372$		0			0
$373$	−20.4047	+	20.4047i	−1.05652	+	1.05652i	−0.0582111	+	0.998304i	$0.518540\pi$
$373$	−20.4047	+	20.4047i	−1.05652	+	1.05652i	−0.998304	+	0.0582111i	$0.981460\pi$
$374$	34.6483	−	11.3625i	1.79162	−	0.587542i
$375$		0			0
$376$	−5.00366	−	30.0005i	−0.258044	−	1.54716i
$377$			1.37907i			0.0710259i
$378$		0			0
$379$	9.82205	−	9.82205i	0.504525	−	0.504525i	−0.408316	−	0.912841i	$-0.633884\pi$
$379$	9.82205	−	9.82205i	0.504525	−	0.504525i	0.912841	+	0.408316i	$0.133884\pi$
$380$	−2.26062	−	15.8347i	−0.115967	−	0.812304i
$381$		0			0
$382$	15.0938	−	29.8241i	0.772266	−	1.52593i
$383$		−	16.0018i		−	0.817655i	−0.912612	−	0.408827i	$-0.865938\pi$
$383$		−	16.0018i		−	0.817655i	0.912612	−	0.408827i	$-0.134062\pi$
$384$		0			0
$385$	3.09489	−	5.77491i	0.157730	−	0.294316i
$386$	−14.7475	−	7.46360i	−0.750626	−	0.379887i
$387$		0			0
$388$	3.92211	−	2.88241i	0.199115	−	0.146332i
$389$	−1.41189	+	1.41189i	−0.0715855	+	0.0715855i	−0.741993	−	0.670408i	$-0.766119\pi$
$389$	−1.41189	+	1.41189i	−0.0715855	+	0.0715855i	0.670408	+	0.741993i	$0.266119\pi$
$390$		0			0
$391$	15.1924			0.768314
$392$	18.5441	−	3.09289i	0.936618	−	0.156215i
$393$		0			0
$394$	−14.3048	+	4.69110i	−0.720666	+	0.236334i
$395$	5.86631	+	19.4152i	0.295166	+	0.976886i
$396$		0			0
$397$	−11.3004	−	11.3004i	−0.567153	−	0.567153i	0.364177	−	0.931330i	$-0.381350\pi$
$397$	−11.3004	−	11.3004i	−0.567153	−	0.567153i	−0.931330	+	0.364177i	$0.881350\pi$
$398$	−5.90439	+	11.6666i	−0.295960	+	0.584794i
$399$		0			0
$400$	5.59648	+	19.2010i	0.279824	+	0.960051i
$401$			17.8120i			0.889491i	0.895657	+	0.444745i	$0.146706\pi$
$401$			17.8120i			0.889491i	−0.895657	+	0.444745i	$0.853294\pi$
$402$		0			0
$403$	−27.0350	+	27.0350i	−1.34671	+	1.34671i
$404$	25.7953	+	3.94141i	1.28336	+	0.196092i
$405$		0			0
$406$	0.0747478	+	0.227932i	0.00370967	+	0.0113121i
$407$	23.7306			1.17628
$408$		0			0
$409$		−	33.7224i		−	1.66747i	−0.552168	−	0.833733i	$-0.686199\pi$
$409$		−	33.7224i		−	1.66747i	0.552168	−	0.833733i	$-0.313801\pi$
$410$	2.40369	−	13.5884i	0.118710	−	0.671081i
$411$		0			0
$412$	0.570192	−	0.419041i	0.0280913	−	0.0206447i
$413$	2.11709	−	2.11709i	0.104175	−	0.104175i
$414$		0			0
$415$	10.4772	+	5.61498i	0.514308	+	0.275629i
$416$	0.372826	+	27.3278i	0.0182793	+	1.33986i
$417$		0			0
$418$	22.2538	+	11.2625i	1.08847	+	0.550867i
$419$	−10.1570	+	10.1570i	−0.496200	+	0.496200i	−0.910253	−	0.414053i	$-0.864113\pi$
$419$	−10.1570	+	10.1570i	−0.496200	+	0.496200i	0.414053	+	0.910253i	$0.364113\pi$
$420$		0			0
$421$	3.90653	+	3.90653i	0.190393	+	0.190393i	0.795866	−	0.605473i	$-0.207016\pi$
$421$	3.90653	+	3.90653i	0.190393	+	0.190393i	−0.605473	+	0.795866i	$0.707016\pi$
$422$	25.2630	−	8.28471i	1.22978	−	0.403294i
$423$		0			0
$424$	−18.6171	−	13.2947i	−0.904128	−	0.645647i
$425$	−21.7705	+	14.4776i	−1.05602	+	0.702268i
$426$		0			0
$427$	−5.36847	−	5.36847i	−0.259798	−	0.259798i
$428$	21.9132	+	3.34824i	1.05921	+	0.161843i
$429$		0			0
$430$	−10.7821	+	7.54089i	−0.519960	+	0.363654i
$431$	−0.155915			−0.00751015			−0.00375507	−	0.999993i	$-0.501195\pi$
$431$	−0.155915			−0.00751015			−0.00375507	+	0.999993i	$0.501195\pi$
$432$		0			0
$433$			4.49972i			0.216243i	0.994138	+	0.108121i	$0.0344835\pi$
$433$			4.49972i			0.216243i	−0.994138	+	0.108121i	$0.965517\pi$
$434$	−3.00299	+	5.93367i	−0.144148	+	0.284825i
$435$		0			0
$436$	−14.0940	−	2.15350i	−0.674981	−	0.103134i
$437$	7.34805	+	7.34805i	0.351505	+	0.351505i
$438$		0			0
$439$	−22.8807			−1.09204			−0.546018	−	0.837773i	$-0.683857\pi$
$439$	−22.8807			−1.09204			−0.546018	+	0.837773i	$0.683857\pi$
$440$	−29.5365	−	10.0084i	−1.40810	−	0.477130i
$441$		0			0
$442$	−33.9486	+	11.1331i	−1.61477	+	0.529546i
$443$	−23.6054	+	23.6054i	−1.12153	+	1.12153i	−0.130015	+	0.991512i	$0.541502\pi$
$443$	−23.6054	+	23.6054i	−1.12153	+	1.12153i	−0.991512	+	0.130015i	$0.958498\pi$
$444$		0			0
$445$	37.0665	−	11.1996i	1.75712	−	0.530914i
$446$	14.3519	−	28.3582i	0.679583	−	1.34280i
$447$		0			0
$448$	1.54283	+	4.49652i	0.0728918	+	0.212440i
$449$		−	13.5006i		−	0.637132i	−0.947901	−	0.318566i	$-0.896799\pi$
$449$		−	13.5006i		−	0.637132i	0.947901	−	0.318566i	$-0.103201\pi$
$450$		0			0
$451$	15.2150	+	15.2150i	0.716448	+	0.716448i
$452$	−16.2092	−	22.0559i	−0.762416	−	1.03742i
$453$		0			0
$454$	−38.7919	+	12.7214i	−1.82060	+	0.597044i
$455$	−3.03240	+	5.65829i	−0.142161	+	0.265265i
$456$		0			0
$457$	−21.9008			−1.02448			−0.512238	−	0.858844i	$-0.671183\pi$
$457$	−21.9008			−1.02448			−0.512238	+	0.858844i	$0.671183\pi$
$458$	2.14828	−	0.704504i	0.100382	−	0.0329193i
$459$		0			0
$460$	−10.3941	−	7.79704i	−0.484626	−	0.363539i
$461$	20.7061	+	20.7061i	0.964381	+	0.964381i	0.999387	−	0.0350065i	$-0.0111452\pi$
$461$	20.7061	+	20.7061i	0.964381	+	0.964381i	−0.0350065	+	0.999387i	$0.511145\pi$
$462$		0			0
$463$	15.1973			0.706277			0.353139	−	0.935571i	$-0.385114\pi$
$463$	15.1973			0.706277			0.353139	+	0.935571i	$0.385114\pi$
$464$	1.01160	−	0.529422i	0.0469624	−	0.0245778i
$465$		0			0
$466$	8.72041	+	4.41335i	0.403965	+	0.204444i
$467$	−10.4255	−	10.4255i	−0.482432	−	0.482432i	0.423475	−	0.905908i	$-0.360810\pi$
$467$	−10.4255	−	10.4255i	−0.482432	−	0.482432i	−0.905908	+	0.423475i	$0.860810\pi$
$468$		0			0
$469$	−4.59099	−	4.59099i	−0.211992	−	0.211992i
$470$	−33.4850	−	5.92329i	−1.54455	−	0.273221i
$471$		0			0
$472$	−11.5975	−	8.28189i	−0.533818	−	0.381205i
$473$		−	20.5165i		−	0.943349i
$474$		0			0
$475$	−17.5319	−	3.52729i	−0.804421	−	0.161843i
$476$	−5.00757	+	3.68013i	−0.229522	+	0.168678i
$477$		0			0
$478$	2.54062	−	5.02007i	0.116205	−	0.229613i
$479$	−8.69764			−0.397406			−0.198703	−	0.980060i	$-0.563673\pi$
$479$	−8.69764			−0.397406			−0.198703	+	0.980060i	$0.563673\pi$
$480$		0			0
$481$	−23.2514			−1.06017
$482$	−7.76330	+	15.3397i	−0.353609	+	0.698702i
$483$		0			0
$484$	21.4572	−	15.7691i	0.975326	−	0.716779i
$485$	−1.57398	−	5.20928i	−0.0714709	−	0.236541i
$486$		0			0
$487$		−	18.9603i		−	0.859172i	−0.903026	−	0.429586i	$-0.858659\pi$
$487$		−	18.9603i		−	0.859172i	0.903026	−	0.429586i	$-0.141341\pi$
$488$	−21.0010	+	29.4086i	−0.950670	+	1.33126i
$489$		0			0
$490$	3.66134	−	20.6980i	0.165402	−	0.935039i
$491$	−30.6747	−	30.6747i	−1.38433	−	1.38433i	−0.836758	−	0.547573i	$-0.815552\pi$
$491$	−30.6747	−	30.6747i	−1.38433	−	1.38433i	−0.547573	−	0.836758i	$-0.684448\pi$
$492$		0			0
$493$	1.05540	+	1.05540i	0.0475329	+	0.0475329i
$494$	−21.8044	−	11.0351i	−0.981028	−	0.496492i
$495$		0			0
$496$	30.2099	+	9.45255i	1.35646	+	0.424432i
$497$	1.37328			0.0616002
$498$		0			0
$499$	25.7124	+	25.7124i	1.15105	+	1.15105i	0.986343	+	0.164704i	$0.0526670\pi$
$499$	25.7124	+	25.7124i	1.15105	+	1.15105i	0.164704	+	0.986343i	$0.447333\pi$
$500$	22.3247	+	1.26799i	0.998391	+	0.0567061i
$501$		0			0
$502$	18.4055	−	6.03588i	0.821478	−	0.269395i
$503$	−8.27958			−0.369168			−0.184584	−	0.982817i	$-0.559094\pi$
$503$	−8.27958			−0.369168			−0.184584	+	0.982817i	$0.559094\pi$
$504$		0			0
$505$	13.7811	−	25.7147i	0.613249	−	1.14429i
$506$	19.2520	−	6.31347i	0.855855	−	0.280668i
$507$		0			0
$508$	−25.1562	−	34.2301i	−1.11612	−	1.51872i
$509$	9.07951	+	9.07951i	0.402442	+	0.402442i	0.879093	−	0.476651i	$-0.158149\pi$
$509$	9.07951	+	9.07951i	0.402442	+	0.402442i	−0.476651	+	0.879093i	$0.658149\pi$
$510$		0			0
$511$			1.56249i			0.0691206i
$512$	19.9029	−	10.7646i	0.879591	−	0.475730i
$513$		0			0
$514$	−14.5848	+	28.8184i	−0.643308	+	1.27112i
$515$	−0.228824	−	0.757319i	−0.0100832	−	0.0333715i
$516$		0			0
$517$	37.4936	−	37.4936i	1.64896	−	1.64896i
$518$	−3.84298	+	1.26026i	−0.168851	+	0.0553727i
$519$		0			0
$520$	28.9400	+	9.80626i	1.26910	+	0.430033i
$521$	26.5377			1.16264			0.581320	−	0.813675i	$-0.302537\pi$
$521$	26.5377			1.16264			0.581320	+	0.813675i	$0.302537\pi$
$522$		0			0
$523$	3.66089	+	3.66089i	0.160080	+	0.160080i	0.782602	−	0.622522i	$-0.213892\pi$
$523$	3.66089	+	3.66089i	0.160080	+	0.160080i	−0.622522	+	0.782602i	$0.713892\pi$
$524$	−6.92018	−	1.05737i	−0.302310	−	0.0461916i
$525$		0			0
$526$	−4.91472	+	9.71109i	−0.214292	+	0.423424i
$527$			41.3797i			1.80253i
$528$		0			0
$529$	−14.5585			−0.632977
$530$	−20.9595	+	14.6588i	−0.910423	+	0.636740i
$531$		0			0
$532$	−4.20194	−	0.642038i	−0.182177	−	0.0278359i
$533$	−14.9078	−	14.9078i	−0.645729	−	0.645729i
$534$		0			0
$535$	11.7071	−	21.8447i	0.506140	−	0.944430i
$536$	−17.9595	+	25.1495i	−0.775734	+	1.08629i
$537$		0			0
$538$	19.5832	−	6.42208i	0.844290	−	0.276876i
$539$	23.1758	+	23.1758i	0.998250	+	0.998250i
$540$		0			0
$541$	−25.5381	+	25.5381i	−1.09797	+	1.09797i	−0.103321	+	0.994648i	$0.532947\pi$
$541$	−25.5381	+	25.5381i	−1.09797	+	1.09797i	−0.994648	+	0.103321i	$0.967053\pi$
$542$	14.2007	+	7.18690i	0.609974	+	0.308704i
$543$		0			0
$544$	21.1993	+	20.6286i	0.908912	+	0.884446i
$545$	−7.52970	+	14.0500i	−0.322537	+	0.601836i
$546$		0			0
$547$	10.4273	−	10.4273i	0.445837	−	0.445837i	−0.448131	−	0.893968i	$-0.647910\pi$
$547$	10.4273	−	10.4273i	0.445837	−	0.445837i	0.893968	+	0.448131i	$0.147910\pi$
$548$	−1.69423	+	1.24511i	−0.0723737	+	0.0531884i
$549$		0			0
$550$	−21.5713	+	27.3933i	−0.919804	+	1.16805i
$551$			1.02092i			0.0434928i
$552$		0			0
$553$	5.38993			0.229203
$554$	10.9413	+	33.3637i	0.464849	+	1.41749i
$555$		0			0
$556$	7.72078	+	1.17970i	0.327434	+	0.0500305i
$557$	−22.6374	+	22.6374i	−0.959178	+	0.959178i	−0.999199	−	0.0400207i	$-0.987258\pi$
$557$	−22.6374	+	22.6374i	−0.959178	+	0.959178i	0.0400207	+	0.999199i	$0.487258\pi$
$558$		0			0
$559$			20.1022i			0.850232i
$560$	5.31470	+	0.0521794i	0.224587	+	0.00220498i
$561$		0			0
$562$	−8.77535	+	17.3394i	−0.370166	+	0.731418i
$563$	−14.9776	−	14.9776i	−0.631231	−	0.631231i	0.317146	−	0.948377i	$-0.397276\pi$
$563$	−14.9776	−	14.9776i	−0.631231	−	0.631231i	−0.948377	+	0.317146i	$0.897276\pi$
$564$		0			0
$565$	−29.2943	+	8.85127i	−1.23242	+	0.372376i
$566$	8.13190	−	2.66677i	0.341809	−	0.112093i
$567$		0			0
$568$	−1.07536	−	6.44752i	−0.0451209	−	0.270532i
$569$	18.3967			0.771229			0.385615	−	0.922660i	$-0.373989\pi$
$569$	18.3967			0.771229			0.385615	+	0.922660i	$0.373989\pi$
$570$		0			0
$571$	20.5645	−	20.5645i	0.860599	−	0.860599i	−0.130808	−	0.991408i	$-0.541757\pi$
$571$	20.5645	−	20.5645i	0.860599	−	0.860599i	0.991408	+	0.130808i	$0.0417573\pi$
$572$	−38.3935	+	28.2158i	−1.60531	+	1.17976i
$573$		0			0
$574$	−3.27197	−	1.65593i	−0.136570	−	0.0691170i
$575$	−12.0966	+	8.04435i	−0.504461	+	0.335473i
$576$		0			0
$577$			32.3657i			1.34740i	0.739004	+	0.673701i	$0.235297\pi$
$577$			32.3657i			1.34740i	−0.739004	+	0.673701i	$0.764703\pi$
$578$	−6.60452	+	13.0500i	−0.274712	+	0.542808i
$579$		0			0
$580$	−0.180413	−	1.26372i	−0.00749123	−	0.0524730i
$581$	2.23371	−	2.23371i	0.0926699	−	0.0926699i
$582$		0			0
$583$		−	39.8823i		−	1.65175i
$584$	7.33585	−	1.22352i	0.303560	−	0.0506295i
$585$		0			0
$586$	22.1579	−	7.26642i	0.915333	−	0.300173i
$587$	19.4315	−	19.4315i	0.802026	−	0.802026i	−0.181386	−	0.983412i	$-0.558058\pi$
$587$	19.4315	−	19.4315i	0.802026	−	0.802026i	0.983412	+	0.181386i	$0.0580584\pi$
$588$		0			0
$589$	−20.0139	+	20.0139i	−0.824660	+	0.824660i
$590$	−13.0567	+	9.13169i	−0.537534	+	0.375946i
$591$		0			0
$592$	8.92614	+	17.0558i	0.366862	+	0.700989i
$593$	−6.88255			−0.282633			−0.141316	−	0.989965i	$-0.545133\pi$
$593$	−6.88255			−0.282633			−0.141316	+	0.989965i	$0.545133\pi$
$594$		0			0
$595$	2.00959	+	6.65097i	0.0823852	+	0.272663i
$596$	16.7878	+	2.56511i	0.687657	+	0.105071i
$597$		0			0
$598$	−18.8632	+	6.18598i	−0.771375	+	0.252964i
$599$		−	9.77996i		−	0.399598i	−0.979837	−	0.199799i	$-0.935971\pi$
$599$		−	9.77996i		−	0.399598i	0.979837	−	0.199799i	$-0.0640290\pi$
$600$		0			0
$601$			39.7298i			1.62061i	0.586008	+	0.810305i	$0.300699\pi$
$601$			39.7298i			1.62061i	−0.586008	+	0.810305i	$0.699301\pi$
$602$	1.08957	+	3.32247i	0.0444075	+	0.135414i
$603$		0			0
$604$	6.94825	+	9.45452i	0.282720	+	0.384699i
$605$	−8.61099	−	28.4990i	−0.350086	−	1.15865i
$606$		0			0
$607$	39.5940			1.60707			0.803535	−	0.595257i	$-0.202950\pi$
$607$	39.5940			1.60707			0.803535	+	0.595257i	$0.202950\pi$
$608$	0.276001	+	20.2307i	0.0111933	+	0.820463i
$609$		0			0
$610$	23.1559	+	33.1087i	0.937554	+	1.34053i
$611$	−36.7365	+	36.7365i	−1.48620	+	1.48620i
$612$		0			0
$613$	−22.7872	+	22.7872i	−0.920367	+	0.920367i	−0.997055	−	0.0766879i	$-0.975565\pi$
$613$	−22.7872	+	22.7872i	−0.920367	+	0.920367i	0.0766879	+	0.997055i	$0.475565\pi$
$614$	2.89370	+	8.82389i	0.116780	+	0.356103i
$615$		0			0
$616$	−4.81630	+	6.74447i	−0.194054	+	0.271743i
$617$		−	24.4206i		−	0.983136i	−0.870839	−	0.491568i	$-0.836424\pi$
$617$		−	24.4206i		−	0.983136i	0.870839	−	0.491568i	$-0.163576\pi$
$618$		0			0
$619$	−33.1727	+	33.1727i	−1.33332	+	1.33332i	−0.430945	+	0.902378i	$0.641820\pi$
$619$	−33.1727	+	33.1727i	−1.33332	+	1.33332i	−0.902378	+	0.430945i	$0.858180\pi$
$620$	21.2369	−	28.3104i	0.852893	−	1.13697i
$621$		0			0
$622$	0.960056	+	0.485878i	0.0384947	+	0.0194819i
$623$		−	10.2902i		−	0.412267i
$624$		0			0
$625$	9.66826	−	23.0548i	0.386731	−	0.922193i
$626$	19.9631	−	39.4455i	0.797887	−	1.57656i
$627$		0			0
$628$	1.31434	−	8.60194i	0.0524478	−	0.343255i
$629$	−17.7943	+	17.7943i	−0.709504	+	0.709504i
$630$		0			0
$631$	−1.09691			−0.0436675			−0.0218337	−	0.999762i	$-0.506950\pi$
$631$	−1.09691			−0.0436675			−0.0218337	+	0.999762i	$0.506950\pi$
$632$	−4.22061	−	25.3055i	−0.167887	−	1.00660i
$633$		0			0
$634$	−2.10872	−	6.43024i	−0.0837481	−	0.255377i
$635$	−45.4639	+	13.7369i	−1.80418	+	0.545133i
$636$		0			0
$637$	−22.7078	−	22.7078i	−0.899714	−	0.899714i
$638$	1.77601	+	0.898825i	0.0703127	+	0.0355848i
$639$		0			0
$640$	−3.91672	−	24.9932i	−0.154822	−	0.987942i
$641$		−	37.4511i		−	1.47923i	−0.673030	−	0.739615i	$-0.735007\pi$
$641$		−	37.4511i		−	1.47923i	0.673030	−	0.739615i	$-0.264993\pi$
$642$		0			0
$643$	33.6486	−	33.6486i	1.32697	−	1.32697i	0.418973	−	0.907998i	$-0.362390\pi$
$643$	33.6486	−	33.6486i	1.32697	−	1.32697i	0.907998	−	0.418973i	$-0.137610\pi$
$644$	−2.78241	+	2.04483i	−0.109642	+	0.0805775i
$645$		0			0
$646$	−25.1320	+	8.24177i	−0.988807	+	0.324268i
$647$	−35.0053			−1.37620			−0.688099	−	0.725617i	$-0.741555\pi$
$647$	−35.0053			−1.37620			−0.688099	+	0.725617i	$0.741555\pi$
$648$		0			0
$649$		−	24.8445i		−	0.975234i
$650$	21.1357	−	26.8401i	0.829011	−	1.05276i
$651$		0			0
$652$	32.4635	+	4.96028i	1.27137	+	0.194259i
$653$	29.4066	−	29.4066i	1.15077	−	1.15077i	0.164370	−	0.986399i	$-0.447441\pi$
$653$	29.4066	−	29.4066i	1.15077	−	1.15077i	0.986399	−	0.164370i	$-0.0525590\pi$
$654$		0			0
$655$	−3.69709	+	6.89857i	−0.144457	+	0.269549i
$656$	−5.21238	+	16.6585i	−0.203509	+	0.650405i
$657$		0			0
$658$	−4.08060	+	8.06294i	−0.159078	+	0.314326i
$659$	−15.5185	+	15.5185i	−0.604517	+	0.604517i	−0.941508	−	0.336991i	$-0.890591\pi$
$659$	−15.5185	+	15.5185i	−0.604517	+	0.604517i	0.336991	+	0.941508i	$0.390591\pi$
$660$		0			0
$661$	−28.6602	−	28.6602i	−1.11475	−	1.11475i	−0.992499	−	0.122253i	$-0.960988\pi$
$661$	−28.6602	−	28.6602i	−1.11475	−	1.11475i	−0.122253	−	0.992499i	$-0.539012\pi$
$662$	−0.0523992	−	0.159783i	−0.00203655	−	0.00621016i
$663$		0			0
$664$	−12.2363	−	8.73808i	−0.474861	−	0.339103i
$665$	−2.24487	+	4.18881i	−0.0870525	+	0.162435i
$666$		0			0
$667$	0.586424	+	0.586424i	0.0227064	+	0.0227064i
$668$	18.0552	+	24.5678i	0.698575	+	0.950555i
$669$		0			0
$670$	19.8023	+	28.3138i	0.765031	+	1.09386i
$671$	−63.0001			−2.43209
$672$		0			0
$673$		−	18.9415i		−	0.730143i	−0.930979	−	0.365071i	$-0.881045\pi$
$673$		−	18.9415i		−	0.730143i	0.930979	−	0.365071i	$-0.118955\pi$
$674$	−34.9751	−	17.7007i	−1.34719	−	0.681804i
$675$		0			0
$676$	16.6674	−	12.2491i	0.641055	−	0.471120i
$677$	−2.06741	−	2.06741i	−0.0794572	−	0.0794572i	0.666261	−	0.745718i	$-0.267894\pi$
$677$	−2.06741	−	2.06741i	−0.0794572	−	0.0794572i	−0.745718	+	0.666261i	$0.767894\pi$
$678$		0			0
$679$	−1.44617			−0.0554987
$680$	29.6525	−	14.6430i	1.13712	−	0.561535i
$681$		0			0
$682$	17.1960	+	52.4368i	0.658471	+	2.00791i
$683$	16.5476	−	16.5476i	0.633174	−	0.633174i	−0.315688	−	0.948863i	$-0.602235\pi$
$683$	16.5476	−	16.5476i	0.633174	−	0.633174i	0.948863	+	0.315688i	$0.102235\pi$
$684$		0			0
$685$	0.679911	+	2.25024i	0.0259780	+	0.0859773i
$686$	−10.2326	−	5.17865i	−0.390682	−	0.197722i
$687$		0			0
$688$	14.7457	−	7.71716i	0.562175	−	0.294214i
$689$			39.0769i			1.48871i
$690$		0			0
$691$	2.10025	+	2.10025i	0.0798972	+	0.0798972i	0.745926	−	0.666029i	$-0.232007\pi$
$691$	2.10025	+	2.10025i	0.0798972	+	0.0798972i	−0.666029	+	0.745926i	$0.732007\pi$
$692$	24.8415	+	3.79567i	0.944332	+	0.144290i
$693$		0			0
$694$	7.34275	+	22.3906i	0.278727	+	0.849936i
$695$	4.12481	−	7.69666i	0.156463	−	0.291951i
$696$		0			0
$697$	−22.8178			−0.864287
$698$	0.882397	+	2.69074i	0.0333992	+	0.101846i
$699$		0			0
$700$	2.03852	−	5.58170i	0.0770488	−	0.210968i
$701$	−22.6892	−	22.6892i	−0.856960	−	0.856960i	0.134018	−	0.990979i	$-0.457212\pi$
$701$	−22.6892	−	22.6892i	−0.856960	−	0.856960i	−0.990979	+	0.134018i	$0.957212\pi$
$702$		0			0
$703$	−17.2129			−0.649199
$704$	35.4365	+	17.3311i	1.33556	+	0.653189i
$705$		0			0
$706$	−7.97917	+	15.7662i	−0.300300	+	0.593368i
$707$	−5.48228	−	5.48228i	−0.206182	−	0.206182i
$708$		0			0
$709$	−6.85782	−	6.85782i	−0.257551	−	0.257551i	0.566506	−	0.824057i	$-0.308295\pi$
$709$	−6.85782	−	6.85782i	−0.257551	−	0.257551i	−0.824057	+	0.566506i	$0.808295\pi$
$710$	−7.19639	−	1.27300i	−0.270076	−	0.0477747i
$711$		0			0
$712$	−48.3119	+	8.05775i	−1.81057	+	0.301977i
$713$			22.9923i			0.861067i
$714$		0			0
$715$	15.4077	+	50.9935i	0.576215	+	1.90705i
$716$	−45.7096	−	6.98423i	−1.70825	−	0.261013i
$717$		0			0
$718$	1.41233	+	0.714771i	0.0527077	+	0.0266750i
$719$	44.1136			1.64516			0.822580	−	0.568649i	$-0.192534\pi$
$719$	44.1136			1.64516			0.822580	+	0.568649i	$0.192534\pi$
$720$		0			0
$721$	−0.210242			−0.00782982
$722$	7.83284	+	3.96415i	0.291508	+	0.147530i
$723$		0			0
$724$	3.26586	−	21.3740i	0.121375	−	0.794360i
$725$	−1.39917	−	0.281502i	−0.0519638	−	0.0104547i
$726$		0			0
$727$			49.5060i			1.83608i	0.396491	+	0.918039i	$0.370228\pi$
$727$			49.5060i			1.83608i	−0.396491	+	0.918039i	$0.629772\pi$
$728$	4.71904	−	6.60828i	0.174899	−	0.244919i
$729$		0			0
$730$	1.44839	−	8.18790i	0.0536072	−	0.303048i
$731$	15.3842	+	15.3842i	0.569004	+	0.569004i
$732$		0			0
$733$	1.73352	+	1.73352i	0.0640290	+	0.0640290i	0.738396	−	0.674367i	$-0.235583\pi$
$733$	1.73352	+	1.73352i	0.0640290	+	0.0640290i	−0.674367	+	0.738396i	$0.735583\pi$
$734$	−8.02273	+	15.8523i	−0.296124	+	0.585118i
$735$		0			0
$736$	11.7792	+	11.4621i	0.434186	+	0.422499i
$737$	−53.8762			−1.98455
$738$		0			0
$739$	12.4907	+	12.4907i	0.459479	+	0.459479i	0.898484	−	0.439005i	$-0.144669\pi$
$739$	12.4907	+	12.4907i	0.459479	+	0.459479i	−0.439005	+	0.898484i	$0.644669\pi$
$740$	21.3065	−	3.04179i	0.783243	−	0.111819i
$741$		0			0
$742$	2.11803	+	6.45860i	0.0777552	+	0.237103i
$743$	16.6402			0.610469			0.305235	−	0.952277i	$-0.401265\pi$
$743$	16.6402			0.610469			0.305235	+	0.952277i	$0.401265\pi$
$744$		0			0
$745$	8.96886	−	16.7354i	0.328593	−	0.613138i
$746$	−12.7166	−	38.7775i	−0.465589	−	1.41975i
$747$		0			0
$748$	−7.78891	+	50.9760i	−0.284791	+	1.86387i
$749$	−4.65721	−	4.65721i	−0.170171	−	0.170171i
$750$		0			0
$751$		−	40.3813i		−	1.47353i	−0.676146	−	0.736767i	$-0.736351\pi$
$751$		−	40.3813i		−	1.47353i	0.676146	−	0.736767i	$-0.263649\pi$
$752$	41.0506	+	12.8446i	1.49696	+	0.468393i
$753$		0			0
$754$	−1.74014	−	0.880675i	−0.0633723	−	0.0320723i
$755$	12.5573	−	3.79420i	0.457008	−	0.138085i
$756$		0			0
$757$	0.105334	−	0.105334i	0.00382842	−	0.00382842i	−0.705190	−	0.709018i	$-0.749138\pi$
$757$	0.105334	−	0.105334i	0.00382842	−	0.00382842i	0.709018	+	0.705190i	$0.249138\pi$
$758$	6.12131	+	18.6660i	0.222336	+	0.677981i
$759$		0			0
$760$	21.4242	+	7.25954i	0.777137	+	0.263331i
$761$	19.6399			0.711944			0.355972	−	0.934497i	$-0.384150\pi$
$761$	19.6399			0.711944			0.355972	+	0.934497i	$0.384150\pi$
$762$		0			0
$763$	2.99541	+	2.99541i	0.108441	+	0.108441i
$764$	27.9938	+	38.0913i	1.01278	+	1.37810i
$765$		0			0
$766$	20.1914	+	10.2188i	0.729546	+	0.369218i
$767$			24.3429i			0.878970i
$768$		0			0
$769$	0.0910921			0.00328487			0.00164243	−	0.999999i	$-0.499477\pi$
$769$	0.0910921			0.00328487			0.00164243	+	0.999999i	$0.499477\pi$
$770$	5.31050	+	7.59305i	0.191377	+	0.273635i
$771$		0			0
$772$	18.8354	−	13.8424i	0.677902	−	0.498199i
$773$	−7.00151	−	7.00151i	−0.251827	−	0.251827i	0.569892	−	0.821719i	$-0.306985\pi$
$773$	−7.00151	−	7.00151i	−0.251827	−	0.251827i	−0.821719	+	0.569892i	$0.806985\pi$
$774$		0			0
$775$	−21.9105	−	32.9475i	−0.787047	−	1.18351i
$776$	1.13243	+	6.78970i	0.0406517	+	0.243736i
$777$		0			0
$778$	−0.879918	−	2.68318i	−0.0315466	−	0.0961966i
$779$	−11.0362	−	11.0362i	−0.395413	−	0.395413i
$780$		0			0
$781$	8.05788	−	8.05788i	0.288334	−	0.288334i
$782$	−9.70187	+	19.1701i	−0.346938	+	0.685522i
$783$		0			0
$784$	−7.93956	+	25.3744i	−0.283556	+	0.906230i
$785$	−8.57507	−	4.59556i	−0.306057	−	0.164023i
$786$		0			0
$787$	15.1938	−	15.1938i	0.541601	−	0.541601i	−0.382397	−	0.923998i	$-0.624901\pi$
$787$	15.1938	−	15.1938i	0.541601	−	0.541601i	0.923998	+	0.382397i	$0.124901\pi$
$788$	3.21571	−	21.0458i	0.114555	−	0.749727i
$789$		0			0
$790$	−28.2448	−	4.99632i	−1.00490	−	0.177761i
$791$			8.13249i			0.289158i
$792$		0			0
$793$	61.7280			2.19202
$794$	21.4756	−	7.04268i	0.762140	−	0.249935i
$795$		0			0
$796$	−10.9506	−	14.9006i	−0.388134	−	0.528137i
$797$	7.48483	−	7.48483i	0.265126	−	0.265126i	−0.562007	−	0.827133i	$-0.689970\pi$
$797$	7.48483	−	7.48483i	0.265126	−	0.265126i	0.827133	+	0.562007i	$0.189970\pi$
$798$		0			0
$799$			56.2287i			1.98923i
$800$	−27.8022	−	5.20001i	−0.982955	−	0.183848i
$801$		0			0
$802$	−22.4756	−	11.3748i	−0.793641	−	0.401656i
$803$	9.16809	+	9.16809i	0.323535	+	0.323535i
$804$		0			0
$805$	1.11661	+	3.69555i	0.0393554	+	0.130251i
$806$	−16.8488	−	51.3779i	−0.593474	−	1.80971i
$807$		0			0
$808$	−21.4462	+	30.0320i	−0.754474	+	1.05652i
$809$	−15.4272			−0.542391			−0.271195	−	0.962524i	$-0.587419\pi$
$809$	−15.4272			−0.542391			−0.271195	+	0.962524i	$0.587419\pi$
$810$		0			0
$811$	7.22410	−	7.22410i	0.253672	−	0.253672i	−0.568802	−	0.822474i	$-0.692593\pi$
$811$	7.22410	−	7.22410i	0.253672	−	0.253672i	0.822474	+	0.568802i	$0.192593\pi$
$812$	−0.335343	−	0.0512390i	−0.0117682	−	0.00179814i
$813$		0			0
$814$	−15.1544	+	29.9438i	−0.531160	+	1.04953i
$815$	17.3435	−	32.3621i	0.607517	−	1.13359i
$816$		0			0
$817$			14.8816i			0.520640i
$818$	42.5516	+	21.5351i	1.48778	+	0.752957i
$819$		0			0
$820$	15.6111	+	11.7105i	0.545163	+	0.408950i
$821$	2.62118	−	2.62118i	0.0914799	−	0.0914799i	−0.659886	−	0.751366i	$-0.729395\pi$
$821$	2.62118	−	2.62118i	0.0914799	−	0.0914799i	0.751366	+	0.659886i	$0.229395\pi$
$822$		0			0
$823$			31.3537i			1.09292i	0.837485	+	0.546461i	$0.184025\pi$
$823$			31.3537i			1.09292i	−0.837485	+	0.546461i	$0.815975\pi$
$824$	0.164631	+	0.987079i	0.00573519	+	0.0343865i
$825$		0			0
$826$	1.31942	+	4.02337i	0.0459084	+	0.139991i
$827$	28.0938	−	28.0938i	0.976915	−	0.976915i	−0.0228240	−	0.999739i	$-0.507266\pi$
$827$	28.0938	−	28.0938i	0.976915	−	0.976915i	0.999739	+	0.0228240i	$0.00726574\pi$
$828$		0			0
$829$	9.99625	−	9.99625i	0.347184	−	0.347184i	−0.511876	−	0.859060i	$-0.671049\pi$
$829$	9.99625	−	9.99625i	0.347184	−	0.347184i	0.859060	+	0.511876i	$0.171049\pi$
$830$	−13.7759	+	9.63469i	−0.478167	+	0.334425i
$831$		0			0
$832$	−34.7209	−	16.9811i	−1.20373	−	0.588714i
$833$	−34.7564			−1.20424
$834$		0			0
$835$	32.6305	−	9.85930i	1.12922	−	0.341195i
$836$	−28.4225	+	20.8881i	−0.983014	+	0.722430i
$837$		0			0
$838$	−6.33004	−	19.3025i	−0.218668	−	0.666794i
$839$			53.0820i			1.83260i	0.400498	+	0.916298i	$0.368837\pi$
$839$			53.0820i			1.83260i	−0.400498	+	0.916298i	$0.631163\pi$
$840$		0			0
$841$		−	28.9185i		−	0.997190i
$842$	−7.42405	+	2.43463i	−0.255850	+	0.0839030i
$843$		0			0
$844$	−5.67910	+	37.1680i	−0.195483	+	1.27937i
$845$	−6.68882	−	22.1374i	−0.230102	−	0.761550i
$846$		0			0
$847$	−7.91172			−0.271850
$848$	28.6644	−	15.0015i	0.984339	−	0.515154i
$849$		0			0
$850$	−4.36556	−	36.7158i	−0.149738	−	1.25934i
$851$	−9.88722	+	9.88722i	−0.338930	+	0.338930i
$852$		0			0
$853$	16.8340	−	16.8340i	0.576384	−	0.576384i	−0.357521	−	0.933905i	$-0.616378\pi$
$853$	16.8340	−	16.8340i	0.576384	−	0.576384i	0.933905	+	0.357521i	$0.116378\pi$
$854$	10.2023	−	3.34575i	0.349117	−	0.114489i
$855$		0			0
$856$	−18.2186	+	25.5123i	−0.622699	+	0.871993i
$857$		−	26.8832i		−	0.918312i	−0.888356	−	0.459156i	$-0.848152\pi$
$857$		−	26.8832i		−	0.918312i	0.888356	−	0.459156i	$-0.151848\pi$
$858$		0			0
$859$	6.63355	−	6.63355i	0.226334	−	0.226334i	−0.584825	−	0.811159i	$-0.698837\pi$
$859$	6.63355	−	6.63355i	0.226334	−	0.226334i	0.811159	+	0.584825i	$0.198837\pi$
$860$	−2.62980	−	18.4207i	−0.0896756	−	0.628141i
$861$		0			0
$862$	0.0995670	−	0.196736i	0.00339127	−	0.00670087i
$863$			11.6526i			0.396659i	0.980135	+	0.198329i	$0.0635516\pi$
$863$			11.6526i			0.396659i	−0.980135	+	0.198329i	$0.936448\pi$
$864$		0			0
$865$	13.2715	−	24.7639i	0.451244	−	0.841998i
$866$	−5.67783	−	2.87351i	−0.192941	−	0.0976460i
$867$		0			0
$868$	−5.56952	−	7.57847i	−0.189042	−	0.257230i
$869$	31.6260	−	31.6260i	1.07284	−	1.07284i
$870$		0			0
$871$	52.7882			1.78866
$872$	11.7178	−	16.4089i	0.396814	−	0.555676i
$873$		0			0
$874$	−13.9644	+	4.57946i	−0.472352	+	0.154903i
$875$	−5.12176	−	4.23158i	−0.173147	−	0.143053i
$876$		0			0
$877$	27.4457	+	27.4457i	0.926776	+	0.926776i	0.997496	−	0.0707206i	$-0.0225299\pi$
$877$	27.4457	+	27.4457i	0.926776	+	0.926776i	−0.0707206	+	0.997496i	$0.522530\pi$
$878$	14.6116	−	28.8713i	0.493117	−	0.974360i
$879$		0			0
$880$	31.4907	−	30.8784i	1.06155	−	1.04091i
$881$			22.3792i			0.753973i	0.926219	+	0.376986i	$0.123040\pi$
$881$			22.3792i			0.753973i	−0.926219	+	0.376986i	$0.876960\pi$
$882$		0			0
$883$	1.02098	−	1.02098i	0.0343587	−	0.0343587i	−0.689719	−	0.724077i	$-0.742266\pi$
$883$	1.02098	−	1.02098i	0.0343587	−	0.0343587i	0.724077	+	0.689719i	$0.242266\pi$
$884$	7.63163	−	49.9466i	0.256679	−	1.67989i
$885$		0			0
$886$	−14.7114	−	44.8602i	−0.494239	−	1.50711i
$887$	−21.7448			−0.730118			−0.365059	−	0.930984i	$-0.618951\pi$
$887$	−21.7448			−0.730118			−0.365059	+	0.930984i	$0.618951\pi$
$888$		0			0
$889$			12.6214i			0.423308i
$890$	−9.53869	+	53.9234i	−0.319738	+	1.80751i
$891$		0			0
$892$	26.6179	+	36.2191i	0.891232	+	1.21270i
$893$	−27.1959	+	27.1959i	−0.910075	+	0.910075i
$894$		0			0
$895$	−24.4203	+	45.5669i	−0.816279	+	1.52313i
$896$	−6.65905	−	0.924698i	−0.222463	−	0.0308920i
$897$		0			0
$898$	17.0353	+	8.62146i	0.568475	+	0.287702i
$899$	−1.59725	+	1.59725i	−0.0532712	+	0.0532712i
$900$		0			0
$901$	29.9055	+	29.9055i	0.996297	+	0.996297i
$902$	−28.9150	+	9.48234i	−0.962763	+	0.315727i
$903$		0			0
$904$	38.1818	−	6.36818i	1.26991	−	0.211803i
$905$	−21.3073	−	11.4190i	−0.708278	−	0.379581i
$906$		0			0
$907$	−40.1300	−	40.1300i	−1.33249	−	1.33249i	−0.903132	−	0.429363i	$-0.858738\pi$
$907$	−40.1300	−	40.1300i	−1.33249	−	1.33249i	−0.429363	−	0.903132i	$-0.641262\pi$
$908$	8.72040	−	57.0723i	0.289397	−	1.89401i
$909$		0			0
$910$	−5.20326	−	7.43973i	−0.172486	−	0.246624i
$911$	−18.2944			−0.606119			−0.303060	−	0.952972i	$-0.598008\pi$
$911$	−18.2944			−0.606119			−0.303060	+	0.952972i	$0.598008\pi$
$912$		0			0
$913$		−	26.2131i		−	0.867525i
$914$	13.9858	−	27.6349i	0.462610	−	0.914080i
$915$		0			0
$916$	−0.482932	+	3.16064i	−0.0159565	+	0.104430i
$917$	1.47075	+	1.47075i	0.0485684	+	0.0485684i
$918$		0			0
$919$	−10.7894			−0.355908			−0.177954	−	0.984039i	$-0.556948\pi$
$919$	−10.7894			−0.355908			−0.177954	+	0.984039i	$0.556948\pi$
$920$	16.4761	−	8.13627i	0.543201	−	0.268245i
$921$		0			0
$922$	−39.3503	+	12.9045i	−1.29593	+	0.424987i
$923$	−7.89517	+	7.89517i	−0.259873	+	0.259873i
$924$		0			0
$925$	4.74618	−	23.5902i	0.156053	−	0.775642i
$926$	−9.70497	+	19.1762i	−0.318925	+	0.630170i
$927$		0			0
$928$	0.0220268	+	1.61455i	0.000723065	+	0.0530001i
$929$			13.5504i			0.444573i	0.974981	+	0.222286i	$0.0713520\pi$
$929$			13.5504i			0.444573i	−0.974981	+	0.222286i	$0.928648\pi$
$930$		0			0
$931$	−16.8105	−	16.8105i	−0.550941	−	0.550941i
$932$	−11.1377	+	8.18524i	−0.364827	+	0.268116i
$933$		0			0
$934$	19.8127	−	6.49736i	0.648292	−	0.212600i
$935$	50.8168	+	27.2338i	1.66189	+	0.890640i
$936$		0			0
$937$	−9.32301			−0.304570			−0.152285	−	0.988337i	$-0.548663\pi$
$937$	−9.32301			−0.304570			−0.152285	+	0.988337i	$0.548663\pi$
$938$	8.72480	−	2.86120i	0.284875	−	0.0934215i
$939$		0			0
$940$	28.8576	−	38.4695i	0.941232	−	1.25474i
$941$	35.3372	+	35.3372i	1.15196	+	1.15196i	0.986159	+	0.165802i	$0.0530214\pi$
$941$	35.3372	+	35.3372i	1.15196	+	1.15196i	0.165802	+	0.986159i	$0.446979\pi$
$942$		0			0
$943$	−12.6785			−0.412869
$944$	17.8564	−	9.34514i	0.581176	−	0.304158i
$945$		0			0
$946$	25.8881	+	13.1018i	0.841695	+	0.425976i
$947$	−38.0391	−	38.0391i	−1.23611	−	1.23611i	−0.961580	−	0.274525i	$-0.911479\pi$
$947$	−38.0391	−	38.0391i	−1.23611	−	1.23611i	−0.274525	−	0.961580i	$-0.588521\pi$
$948$		0			0
$949$	−8.98296	−	8.98296i	−0.291599	−	0.291599i
$950$	15.6467	−	19.8696i	0.507646	−	0.644656i
$951$		0			0
$952$	−1.44583	−	8.66878i	−0.0468597	−	0.280957i
$953$			14.7622i			0.478194i	0.970996	+	0.239097i	$0.0768514\pi$
$953$			14.7622i			0.478194i	−0.970996	+	0.239097i	$0.923149\pi$
$954$		0			0
$955$	50.5923	−	15.2865i	1.63713	−	0.494658i
$956$	4.71199	+	6.41162i	0.152397	+	0.207367i
$957$		0			0
$958$	5.55431	−	10.9749i	0.179452	−	0.354582i
$959$	0.624697			0.0201725
$960$		0			0
$961$	−31.6242			−1.02013
$962$	14.8483	−	29.3391i	0.478730	−	0.945931i
$963$		0			0
$964$	−14.3983	−	19.5918i	−0.463737	−	0.631009i
$965$	−7.55886	−	25.0169i	−0.243328	−	0.805323i
$966$		0			0
$967$			19.8012i			0.636765i	0.947962	+	0.318383i	$0.103140\pi$
$967$			19.8012i			0.636765i	−0.947962	+	0.318383i	$0.896860\pi$
$968$	6.19531	+	37.1453i	0.199125	+	1.19389i
$969$		0			0
$970$	7.57832	+	1.34056i	0.243325	+	0.0430426i
$971$	−26.7823	−	26.7823i	−0.859484	−	0.859484i	0.131793	−	0.991277i	$-0.457927\pi$
$971$	−26.7823	−	26.7823i	−0.859484	−	0.859484i	−0.991277	+	0.131793i	$0.957927\pi$
$972$		0			0
$973$	−1.64090	−	1.64090i	−0.0526048	−	0.0526048i
$974$	23.9245	+	12.1080i	0.766590	+	0.387966i
$975$		0			0
$976$	−23.6972	−	45.2798i	−0.758527	−	1.44937i
$977$	−21.7382			−0.695467			−0.347734	−	0.937593i	$-0.613049\pi$
$977$	−21.7382			−0.695467			−0.347734	+	0.937593i	$0.613049\pi$
$978$		0			0
$979$	−60.3786	−	60.3786i	−1.92971	−	1.92971i
$980$	23.7790	+	17.8377i	0.759592	+	0.569803i
$981$		0			0
$982$	58.2949	−	19.1171i	1.86026	−	0.610053i
$983$	−20.7762			−0.662658			−0.331329	−	0.943515i	$-0.607497\pi$
$983$	−20.7762			−0.662658			−0.331329	+	0.943515i	$0.607497\pi$
$984$		0			0
$985$	−20.9801	−	11.2437i	−0.668482	−	0.358254i
$986$	−2.00571	+	0.657749i	−0.0638748	+	0.0209470i
$987$		0			0
$988$	27.8486	−	20.4663i	0.885982	−	0.651120i
$989$	8.54807	+	8.54807i	0.271813	+	0.271813i
$990$		0			0
$991$		−	0.442922i		−	0.0140699i	−0.999975	−	0.00703494i	$-0.997761\pi$
$991$		−	0.442922i		−	0.0140699i	0.999975	−	0.00703494i	$-0.00223931\pi$
$992$	−31.2194	+	32.0830i	−0.991218	+	1.01864i
$993$		0			0
$994$	−0.876977	+	1.73284i	−0.0278160	+	0.0549622i
$995$	−19.7907	+	5.97976i	−0.627407	+	0.189571i
$996$		0			0
$997$	−6.59897	+	6.59897i	−0.208991	+	0.208991i	−0.803839	−	0.594847i	$-0.797213\pi$
$997$	−6.59897	+	6.59897i	−0.208991	+	0.208991i	0.594847	+	0.803839i	$0.297213\pi$
$998$	−48.8644	+	16.0245i	−1.54678	+	0.507248i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.u.a.539.15	yes	96
3.2	odd	2	inner	720.2.u.a.539.34	yes	96
4.3	odd	2		2880.2.u.a.719.6		96
5.4	even	2	inner	720.2.u.a.539.33	yes	96
12.11	even	2		2880.2.u.a.719.43		96
15.14	odd	2	inner	720.2.u.a.539.16	yes	96
16.3	odd	4	inner	720.2.u.a.179.16	yes	96
16.13	even	4		2880.2.u.a.2159.30		96
20.19	odd	2		2880.2.u.a.719.19		96
48.29	odd	4		2880.2.u.a.2159.19		96
48.35	even	4	inner	720.2.u.a.179.33	yes	96
60.59	even	2		2880.2.u.a.719.30		96
80.19	odd	4	inner	720.2.u.a.179.34	yes	96
80.29	even	4		2880.2.u.a.2159.43		96
240.29	odd	4		2880.2.u.a.2159.6		96
240.179	even	4	inner	720.2.u.a.179.15	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.u.a.179.15	✓	96	240.179	even	4	inner
720.2.u.a.179.16	yes	96	16.3	odd	4	inner
720.2.u.a.179.33	yes	96	48.35	even	4	inner
720.2.u.a.179.34	yes	96	80.19	odd	4	inner
720.2.u.a.539.15	yes	96	1.1	even	1	trivial
720.2.u.a.539.16	yes	96	15.14	odd	2	inner
720.2.u.a.539.33	yes	96	5.4	even	2	inner
720.2.u.a.539.34	yes	96	3.2	odd	2	inner
2880.2.u.a.719.6		96	4.3	odd	2
2880.2.u.a.719.19		96	20.19	odd	2
2880.2.u.a.719.30		96	60.59	even	2
2880.2.u.a.719.43		96	12.11	even	2
2880.2.u.a.2159.6		96	240.29	odd	4
2880.2.u.a.2159.19		96	48.29	odd	4
2880.2.u.a.2159.30		96	16.13	even	4
2880.2.u.a.2159.43		96	80.29	even	4

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.638599 + 1.26182i) q^{2} +(-1.18438 - 1.61160i) q^{4} +(-2.14049 + 0.646750i) q^{5} +0.594230i q^{7} +(2.78989 - 0.465314i) q^{8} +O(q^{10})\)	\(q+(-0.638599 + 1.26182i) q^{2} +(-1.18438 - 1.61160i) q^{4} +(-2.14049 + 0.646750i) q^{5} +0.594230i q^{7} +(2.78989 - 0.465314i) q^{8} +(0.550835 - 3.11393i) q^{10} +(3.48671 + 3.48671i) q^{11} +(-3.41630 - 3.41630i) q^{13} +(-0.749812 - 0.379475i) q^{14} +(-1.19448 + 3.81749i) q^{16} -5.22898 q^{17} +(-2.52907 - 2.52907i) q^{19} +(3.57746 + 2.68361i) q^{20} +(-6.62621 + 2.17299i) q^{22} -2.90543 q^{23} +(4.16343 - 2.76873i) q^{25} +(6.49240 - 2.12911i) q^{26} +(0.957658 - 0.703795i) q^{28} +(-0.201837 - 0.201837i) q^{29} -7.91354i q^{31} +(-4.05419 - 3.94506i) q^{32} +(3.33922 - 6.59803i) q^{34} +(-0.384318 - 1.27195i) q^{35} +(3.40301 - 3.40301i) q^{37} +(4.80630 - 1.57617i) q^{38} +(-5.67080 + 2.80036i) q^{40} +4.36373 q^{41} +(-2.94210 - 2.94210i) q^{43} +(1.48957 - 9.74875i) q^{44} +(1.85541 - 3.66613i) q^{46} -10.7533i q^{47} +6.64689 q^{49} +(0.834879 + 7.02161i) q^{50} +(-1.45949 + 9.55189i) q^{52} +(-5.71919 - 5.71919i) q^{53} +(-9.71830 - 5.20824i) q^{55} +(0.276504 + 1.65784i) q^{56} +(0.383576 - 0.125789i) q^{58} +(-3.56275 - 3.56275i) q^{59} +(-9.03433 + 9.03433i) q^{61} +(9.98547 + 5.05358i) q^{62} +(7.56697 - 2.59635i) q^{64} +(9.52206 + 5.10307i) q^{65} +(-7.72594 + 7.72594i) q^{67} +(6.19311 + 8.42699i) q^{68} +(1.85039 + 0.327323i) q^{70} -2.31103i q^{71} +2.62944 q^{73} +(2.12083 + 6.46715i) q^{74} +(-1.08045 + 7.07123i) q^{76} +(-2.07191 + 2.07191i) q^{77} -9.07044i q^{79} +(0.0878100 - 8.94384i) q^{80} +(-2.78667 + 5.50624i) q^{82} +(-3.75900 - 3.75900i) q^{83} +(11.1926 - 3.38184i) q^{85} +(5.59122 - 1.83358i) q^{86} +(11.3499 + 8.10511i) q^{88} -17.3168 q^{89} +(2.03007 - 2.03007i) q^{91} +(3.44114 + 4.68238i) q^{92} +(13.5687 + 6.86704i) q^{94} +(7.04915 + 3.77779i) q^{95} +2.43368i q^{97} +(-4.24470 + 8.38718i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 8 q^{16} - 16 q^{19} + 72 q^{34} + 8 q^{40} + 8 q^{46} - 96 q^{49} + 64 q^{55} - 32 q^{61} + 48 q^{64} + 24 q^{70} + 40 q^{76} - 88 q^{94}+O(q^{100}) \) 96 * q - 8 * q^16 - 16 * q^19 + 72 * q^34 + 8 * q^40 + 8 * q^46 - 96 * q^49 + 64 * q^55 - 32 * q^61 + 48 * q^64 + 24 * q^70 + 40 * q^76 - 88 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more