LMFDB - Embedded newform 720.2.u.a.179.15

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			179.15
Character	$\chi$	$=$	720.179
Dual form			720.2.u.a.539.15

$q$-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 $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$	$-1$

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	$-0.964179\pi$
$7$		−	0.594230i		−	0.224598i	0.993674	−	0.112299i	$-0.0358214\pi$
$8$	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	0.0526694	−	0.998612i	$-0.483227\pi$
$11$	3.48671	−	3.48671i	1.05128	−	1.05128i	0.998612	−	0.0526694i	$-0.0167730\pi$
$12$		0			0
$13$	−3.41630	+	3.41630i	−0.947511	+	0.947511i	−0.998690	−	0.0511786i	$-0.983702\pi$
$13$	−3.41630	+	3.41630i	−0.947511	+	0.947511i	0.0511786	+	0.998690i	$0.483702\pi$
$14$	−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	−0.934961	−	0.354751i	$-0.884566\pi$
$19$	−2.52907	+	2.52907i	−0.580209	+	0.580209i	0.354751	+	0.934961i	$0.384566\pi$
$20$	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	−0.725599	−	0.688118i	$-0.758437\pi$
$29$	−0.201837	+	0.201837i	−0.0374802	+	0.0374802i	0.688118	+	0.725599i	$0.258437\pi$
$30$		0			0
$31$			7.91354i			1.42131i	0.703538	+	0.710657i	$0.251602\pi$
$31$			7.91354i			1.42131i	−0.703538	+	0.710657i	$0.748398\pi$
$32$	−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	0.929151	−	0.369699i	$-0.120539\pi$
$37$	3.40301	+	3.40301i	0.559452	+	0.559452i	−0.369699	+	0.929151i	$0.620539\pi$
$38$	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	−0.894911	−	0.446245i	$-0.852761\pi$
$43$	−2.94210	+	2.94210i	−0.448666	+	0.448666i	0.446245	+	0.894911i	$0.352761\pi$
$44$	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	$0.286959\pi$
$47$			10.7533i			1.56853i	−0.620427	+	0.784264i	$0.713041\pi$
$48$		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	−0.980768	−	0.195177i	$-0.937472\pi$
$53$	−5.71919	+	5.71919i	−0.785591	+	0.785591i	0.195177	+	0.980768i	$0.437472\pi$
$54$		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	−0.899909	−	0.436078i	$-0.856367\pi$
$59$	−3.56275	+	3.56275i	−0.463831	+	0.463831i	0.436078	+	0.899909i	$0.356367\pi$
$60$		0			0
$61$	−9.03433	−	9.03433i	−1.15673	−	1.15673i	−0.985175	−	0.171553i	$-0.945122\pi$
$61$	−9.03433	−	9.03433i	−1.15673	−	1.15673i	−0.171553	−	0.985175i	$-0.554878\pi$
$62$	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	0.0546326	−	0.998507i	$-0.482601\pi$
$67$	−7.72594	−	7.72594i	−0.943874	−	0.943874i	−0.998507	+	0.0546326i	$0.982601\pi$
$68$	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	$0.0437892\pi$
$71$			2.31103i			0.274269i	−0.990552	+	0.137134i	$0.956211\pi$
$72$		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	$0.170448\pi$
$79$			9.07044i			1.02050i	−0.860025	+	0.510252i	$0.829552\pi$
$80$	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	−0.882645	−	0.470041i	$-0.844239\pi$
$83$	−3.75900	+	3.75900i	−0.412604	+	0.412604i	0.470041	+	0.882645i	$0.344239\pi$
$84$		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	$-0.960572\pi$
$97$		−	2.43368i		−	0.247103i	0.992338	−	0.123551i	$-0.0394284\pi$
$98$	−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	0.0788774	−	0.996884i	$-0.474866\pi$
$101$	−9.22586	−	9.22586i	−0.918007	−	0.918007i	−0.996884	+	0.0788774i	$0.974866\pi$
$102$		0			0
$103$		−	0.353806i		−	0.0348615i	−0.999848	−	0.0174308i	$-0.994451\pi$
$103$		−	0.353806i		−	0.0348615i	0.999848	−	0.0174308i	$-0.00554866\pi$
$104$	−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	0.218228	−	0.975898i	$-0.429972\pi$
$107$	−7.83739	−	7.83739i	−0.757670	−	0.757670i	−0.975898	+	0.218228i	$0.929972\pi$
$108$		0			0
$109$	5.04082	+	5.04082i	0.482823	+	0.482823i	0.906032	−	0.423209i	$-0.139096\pi$
$109$	5.04082	+	5.04082i	0.482823	+	0.482823i	−0.423209	+	0.906032i	$0.639096\pi$
$110$	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	0.806914	−	0.590668i	$-0.201136\pi$
$131$	2.47505	+	2.47505i	0.216246	+	0.216246i	−0.590668	+	0.806914i	$0.701136\pi$
$132$		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	$0.0142995\pi$
$137$			1.05127i			0.0898162i	−0.998991	+	0.0449081i	$0.985700\pi$
$138$		0			0
$139$	−2.76139	−	2.76139i	−0.234218	−	0.234218i	0.580233	−	0.814451i	$-0.302962\pi$
$139$	−2.76139	−	2.76139i	−0.234218	−	0.234218i	−0.814451	+	0.580233i	$0.802962\pi$
$140$	−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	0.417011	−	0.908901i	$-0.363078\pi$
$149$	−6.00428	−	6.00428i	−0.491890	−	0.491890i	−0.908901	+	0.417011i	$0.863078\pi$
$150$		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	−0.573600	−	0.819135i	$-0.694454\pi$
$157$	3.07654	−	3.07654i	0.245535	−	0.245535i	0.819135	+	0.573600i	$0.194454\pi$
$158$	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	0.0867995	−	0.996226i	$-0.472336\pi$
$163$	−11.6108	−	11.6108i	−0.909426	−	0.909426i	−0.996226	+	0.0867995i	$0.972336\pi$
$164$	−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	0.283484	−	0.958977i	$-0.408510\pi$
$173$	−8.88472	−	8.88472i	−0.675493	−	0.675493i	−0.958977	+	0.283484i	$0.908510\pi$
$174$		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	0.966944	+	0.254990i	$0.0820721\pi$
$179$	16.3484	+	16.3484i	1.22193	+	1.22193i	0.254990	+	0.966944i	$0.417928\pi$
$180$		0			0
$181$	7.64457	−	7.64457i	0.568216	−	0.568216i	−0.363412	−	0.931628i	$-0.618388\pi$
$181$	7.64457	−	7.64457i	0.568216	−	0.568216i	0.931628	+	0.363412i	$0.118388\pi$
$182$	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	$-0.861805\pi$
$193$		−	11.6874i		−	0.841281i	0.907227	−	0.420640i	$-0.138195\pi$
$194$	−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	−0.386147	−	0.922437i	$-0.626194\pi$
$197$	7.52719	−	7.52719i	0.536290	−	0.536290i	0.922437	+	0.386147i	$0.126194\pi$
$198$		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	−0.996672	−	0.0815182i	$-0.974023\pi$
$211$	−13.2934	+	13.2934i	−0.915154	+	0.915154i	0.0815182	+	0.996672i	$0.474023\pi$
$212$	−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	0.474622	−	0.880190i	$-0.342585\pi$
$227$	20.4123	−	20.4123i	1.35481	−	1.35481i	0.880190	−	0.474622i	$-0.157415\pi$
$228$		0			0
$229$	−1.13042	+	1.13042i	−0.0747005	+	0.0747005i	−0.743470	−	0.668769i	$-0.766821\pi$
$229$	−1.13042	+	1.13042i	−0.0747005	+	0.0747005i	0.668769	+	0.743470i	$0.266821\pi$
$230$	−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	$0.0726880\pi$
$233$			6.91098i			0.452753i	−0.974040	+	0.226377i	$0.927312\pi$
$234$		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	−0.943287	−	0.331977i	$-0.892284\pi$
$251$	−9.68497	+	9.68497i	−0.611310	+	0.611310i	0.331977	+	0.943287i	$0.392284\pi$
$252$		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	−0.947637	−	0.319351i	$-0.896535\pi$
$269$	−10.3047	+	10.3047i	−0.628286	+	0.628286i	0.319351	+	0.947637i	$0.396535\pi$
$270$		0			0
$271$			11.2542i			0.683642i	0.939765	+	0.341821i	$0.111044\pi$
$271$			11.2542i			0.683642i	−0.939765	+	0.341821i	$0.888956\pi$
$272$	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	0.998407	+	0.0564290i	$0.0179715\pi$
$277$	17.5560	+	17.5560i	1.05484	+	1.05484i	0.0564290	+	0.998407i	$0.482029\pi$
$278$	−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	−0.822756	−	0.568395i	$-0.807564\pi$
$283$	−4.27900	+	4.27900i	−0.254360	+	0.254360i	0.568395	+	0.822756i	$0.307564\pi$
$284$	−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	−0.960260	−	0.279107i	$-0.909962\pi$
$293$	−11.6595	+	11.6595i	−0.681153	+	0.681153i	0.279107	+	0.960260i	$0.409962\pi$
$294$		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	0.827081	−	0.562083i	$-0.190000\pi$
$307$	4.64313	+	4.64313i	0.264997	+	0.264997i	−0.562083	+	0.827081i	$0.690000\pi$
$308$	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	$0.00686709\pi$
$311$			0.760850i			0.0431438i	−0.999767	+	0.0215719i	$0.993133\pi$
$312$		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	0.605673	−	0.795714i	$-0.292904\pi$
$317$	−3.38359	−	3.38359i	−0.190041	−	0.190041i	−0.795714	+	0.605673i	$0.792904\pi$
$318$		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	0.704792	−	0.709414i	$-0.251040\pi$
$331$	−0.0840779	−	0.0840779i	−0.00462134	−	0.00462134i	−0.709414	+	0.704792i	$0.751040\pi$
$332$	−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	$-0.727663\pi$
$337$		−	27.7179i		−	1.50989i	0.655787	−	0.754946i	$-0.272337\pi$
$338$	−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	0.948691	−	0.316204i	$-0.102408\pi$
$347$	11.7819	+	11.7819i	0.632487	+	0.632487i	−0.316204	+	0.948691i	$0.602408\pi$
$348$		0			0
$349$	1.41586	+	1.41586i	0.0757895	+	0.0757895i	0.743985	−	0.668196i	$-0.232933\pi$
$349$	1.41586	+	1.41586i	0.0757895	+	0.0757895i	−0.668196	+	0.743985i	$0.732933\pi$
$350$	−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	$0.00940317\pi$
$359$			1.11928i			0.0590733i	−0.999564	+	0.0295366i	$0.990597\pi$
$360$		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	−0.998304	−	0.0582111i	$-0.981460\pi$
$373$	−20.4047	−	20.4047i	−1.05652	−	1.05652i	−0.0582111	−	0.998304i	$-0.518540\pi$
$374$	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	0.912841	−	0.408316i	$-0.133884\pi$
$379$	9.82205	+	9.82205i	0.504525	+	0.504525i	−0.408316	+	0.912841i	$0.633884\pi$
$380$	−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	$0.134062\pi$
$383$			16.0018i			0.817655i	−0.912612	+	0.408827i	$0.865938\pi$
$384$		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	0.670408	−	0.741993i	$-0.266119\pi$
$389$	−1.41189	−	1.41189i	−0.0715855	−	0.0715855i	−0.741993	+	0.670408i	$0.766119\pi$
$390$		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	−0.931330	−	0.364177i	$-0.881350\pi$
$397$	−11.3004	+	11.3004i	−0.567153	+	0.567153i	0.364177	+	0.931330i	$0.381350\pi$
$398$	−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	$-0.853294\pi$
$401$		−	17.8120i		−	0.889491i	0.895657	−	0.444745i	$-0.146706\pi$
$402$		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	$0.313801\pi$
$409$			33.7224i			1.66747i	−0.552168	+	0.833733i	$0.686199\pi$
$410$	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	0.414053	−	0.910253i	$-0.364113\pi$
$419$	−10.1570	−	10.1570i	−0.496200	−	0.496200i	−0.910253	+	0.414053i	$0.864113\pi$
$420$		0			0
$421$	3.90653	−	3.90653i	0.190393	−	0.190393i	−0.605473	−	0.795866i	$-0.707016\pi$
$421$	3.90653	−	3.90653i	0.190393	−	0.190393i	0.795866	+	0.605473i	$0.207016\pi$
$422$	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	$-0.965517\pi$
$433$		−	4.49972i		−	0.216243i	0.994138	−	0.108121i	$-0.0344835\pi$
$434$	−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	−0.991512	−	0.130015i	$-0.958498\pi$
$443$	−23.6054	−	23.6054i	−1.12153	−	1.12153i	−0.130015	−	0.991512i	$-0.541502\pi$
$444$		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	$0.103201\pi$
$449$			13.5006i			0.637132i	−0.947901	+	0.318566i	$0.896799\pi$
$450$		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	−0.0350065	−	0.999387i	$-0.511145\pi$
$461$	20.7061	−	20.7061i	0.964381	−	0.964381i	0.999387	+	0.0350065i	$0.0111452\pi$
$462$		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	−0.905908	−	0.423475i	$-0.860810\pi$
$467$	−10.4255	+	10.4255i	−0.482432	+	0.482432i	0.423475	+	0.905908i	$0.360810\pi$
$468$		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	$0.141341\pi$
$487$			18.9603i			0.859172i	−0.903026	+	0.429586i	$0.858659\pi$
$488$	−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	−0.547573	+	0.836758i	$0.684448\pi$
$491$	−30.6747	+	30.6747i	−1.38433	+	1.38433i	−0.836758	+	0.547573i	$0.815552\pi$
$492$		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	0.164704	−	0.986343i	$-0.447333\pi$
$499$	25.7124	−	25.7124i	1.15105	−	1.15105i	0.986343	−	0.164704i	$-0.0526670\pi$
$500$	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	−0.476651	−	0.879093i	$-0.658149\pi$
$509$	9.07951	−	9.07951i	0.402442	−	0.402442i	0.879093	+	0.476651i	$0.158149\pi$
$510$		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	−0.622522	−	0.782602i	$-0.713892\pi$
$523$	3.66089	−	3.66089i	0.160080	−	0.160080i	0.782602	+	0.622522i	$0.213892\pi$
$524$	−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	−0.994648	−	0.103321i	$-0.967053\pi$
$541$	−25.5381	−	25.5381i	−1.09797	−	1.09797i	−0.103321	−	0.994648i	$-0.532947\pi$
$542$	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	0.893968	−	0.448131i	$-0.147910\pi$
$547$	10.4273	+	10.4273i	0.445837	+	0.445837i	−0.448131	+	0.893968i	$0.647910\pi$
$548$	−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	0.0400207	−	0.999199i	$-0.487258\pi$
$557$	−22.6374	−	22.6374i	−0.959178	−	0.959178i	−0.999199	+	0.0400207i	$0.987258\pi$
$558$		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	−0.948377	−	0.317146i	$-0.897276\pi$
$563$	−14.9776	+	14.9776i	−0.631231	+	0.631231i	0.317146	+	0.948377i	$0.397276\pi$
$564$		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	0.991408	−	0.130808i	$-0.0417573\pi$
$571$	20.5645	+	20.5645i	0.860599	+	0.860599i	−0.130808	+	0.991408i	$0.541757\pi$
$572$	−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	$-0.764703\pi$
$577$		−	32.3657i		−	1.34740i	0.739004	−	0.673701i	$-0.235297\pi$
$578$	−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	0.983412	−	0.181386i	$-0.0580584\pi$
$587$	19.4315	+	19.4315i	0.802026	+	0.802026i	−0.181386	+	0.983412i	$0.558058\pi$
$588$		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	$0.0640290\pi$
$599$			9.77996i			0.399598i	−0.979837	+	0.199799i	$0.935971\pi$
$600$		0			0
$601$		−	39.7298i		−	1.62061i	−0.586008	−	0.810305i	$-0.699301\pi$
$601$		−	39.7298i		−	1.62061i	0.586008	−	0.810305i	$-0.300699\pi$
$602$	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	0.0766879	−	0.997055i	$-0.475565\pi$
$613$	−22.7872	−	22.7872i	−0.920367	−	0.920367i	−0.997055	+	0.0766879i	$0.975565\pi$
$614$	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	$0.163576\pi$
$617$			24.4206i			0.983136i	−0.870839	+	0.491568i	$0.836424\pi$
$618$		0			0
$619$	−33.1727	−	33.1727i	−1.33332	−	1.33332i	−0.902378	−	0.430945i	$-0.858180\pi$
$619$	−33.1727	−	33.1727i	−1.33332	−	1.33332i	−0.430945	−	0.902378i	$-0.641820\pi$
$620$	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	$0.264993\pi$
$641$			37.4511i			1.47923i	−0.673030	+	0.739615i	$0.735007\pi$
$642$		0			0
$643$	33.6486	+	33.6486i	1.32697	+	1.32697i	0.907998	+	0.418973i	$0.137610\pi$
$643$	33.6486	+	33.6486i	1.32697	+	1.32697i	0.418973	+	0.907998i	$0.362390\pi$
$644$	−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	0.986399	+	0.164370i	$0.0525590\pi$
$653$	29.4066	+	29.4066i	1.15077	+	1.15077i	0.164370	+	0.986399i	$0.447441\pi$
$654$		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	0.336991	−	0.941508i	$-0.390591\pi$
$659$	−15.5185	−	15.5185i	−0.604517	−	0.604517i	−0.941508	+	0.336991i	$0.890591\pi$
$660$		0			0
$661$	−28.6602	+	28.6602i	−1.11475	+	1.11475i	−0.122253	+	0.992499i	$0.539012\pi$
$661$	−28.6602	+	28.6602i	−1.11475	+	1.11475i	−0.992499	+	0.122253i	$0.960988\pi$
$662$	−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	$0.118955\pi$
$673$			18.9415i			0.730143i	−0.930979	+	0.365071i	$0.881045\pi$
$674$	−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	−0.745718	−	0.666261i	$-0.767894\pi$
$677$	−2.06741	+	2.06741i	−0.0794572	+	0.0794572i	0.666261	+	0.745718i	$0.267894\pi$
$678$		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	0.948863	−	0.315688i	$-0.102235\pi$
$683$	16.5476	+	16.5476i	0.633174	+	0.633174i	−0.315688	+	0.948863i	$0.602235\pi$
$684$		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	−0.666029	−	0.745926i	$-0.732007\pi$
$691$	2.10025	−	2.10025i	0.0798972	−	0.0798972i	0.745926	+	0.666029i	$0.232007\pi$
$692$	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	−0.990979	−	0.134018i	$-0.957212\pi$
$701$	−22.6892	+	22.6892i	−0.856960	+	0.856960i	0.134018	+	0.990979i	$0.457212\pi$
$702$		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	−0.824057	−	0.566506i	$-0.808295\pi$
$709$	−6.85782	+	6.85782i	−0.257551	+	0.257551i	0.566506	+	0.824057i	$0.308295\pi$
$710$	−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	$-0.629772\pi$
$727$		−	49.5060i		−	1.83608i	0.396491	−	0.918039i	$-0.370228\pi$
$728$	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	−0.674367	−	0.738396i	$-0.735583\pi$
$733$	1.73352	−	1.73352i	0.0640290	−	0.0640290i	0.738396	+	0.674367i	$0.235583\pi$
$734$	−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	−0.439005	−	0.898484i	$-0.644669\pi$
$739$	12.4907	−	12.4907i	0.459479	−	0.459479i	0.898484	+	0.439005i	$0.144669\pi$
$740$	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	$0.263649\pi$
$751$			40.3813i			1.47353i	−0.676146	+	0.736767i	$0.736351\pi$
$752$	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	0.709018	−	0.705190i	$-0.249138\pi$
$757$	0.105334	+	0.105334i	0.00382842	+	0.00382842i	−0.705190	+	0.709018i	$0.749138\pi$
$758$	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	−0.821719	−	0.569892i	$-0.806985\pi$
$773$	−7.00151	+	7.00151i	−0.251827	+	0.251827i	0.569892	+	0.821719i	$0.306985\pi$
$774$		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	0.923998	−	0.382397i	$-0.124901\pi$
$787$	15.1938	+	15.1938i	0.541601	+	0.541601i	−0.382397	+	0.923998i	$0.624901\pi$
$788$	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	0.827133	−	0.562007i	$-0.189970\pi$
$797$	7.48483	+	7.48483i	0.265126	+	0.265126i	−0.562007	+	0.827133i	$0.689970\pi$
$798$		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	0.822474	−	0.568802i	$-0.192593\pi$
$811$	7.22410	+	7.22410i	0.253672	+	0.253672i	−0.568802	+	0.822474i	$0.692593\pi$
$812$	−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	0.751366	−	0.659886i	$-0.229395\pi$
$821$	2.62118	+	2.62118i	0.0914799	+	0.0914799i	−0.659886	+	0.751366i	$0.729395\pi$
$822$		0			0
$823$		−	31.3537i		−	1.09292i	−0.837485	−	0.546461i	$-0.815975\pi$
$823$		−	31.3537i		−	1.09292i	0.837485	−	0.546461i	$-0.184025\pi$
$824$	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	0.999739	−	0.0228240i	$-0.00726574\pi$
$827$	28.0938	+	28.0938i	0.976915	+	0.976915i	−0.0228240	+	0.999739i	$0.507266\pi$
$828$		0			0
$829$	9.99625	+	9.99625i	0.347184	+	0.347184i	0.859060	−	0.511876i	$-0.171049\pi$
$829$	9.99625	+	9.99625i	0.347184	+	0.347184i	−0.511876	+	0.859060i	$0.671049\pi$
$830$	−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	$-0.631163\pi$
$839$		−	53.0820i		−	1.83260i	0.400498	−	0.916298i	$-0.368837\pi$
$840$		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	0.933905	−	0.357521i	$-0.116378\pi$
$853$	16.8340	+	16.8340i	0.576384	+	0.576384i	−0.357521	+	0.933905i	$0.616378\pi$
$854$	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	$0.151848\pi$
$857$			26.8832i			0.918312i	−0.888356	+	0.459156i	$0.848152\pi$
$858$		0			0
$859$	6.63355	+	6.63355i	0.226334	+	0.226334i	0.811159	−	0.584825i	$-0.198837\pi$
$859$	6.63355	+	6.63355i	0.226334	+	0.226334i	−0.584825	+	0.811159i	$0.698837\pi$
$860$	−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	$-0.936448\pi$
$863$		−	11.6526i		−	0.396659i	0.980135	−	0.198329i	$-0.0635516\pi$
$864$		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	−0.0707206	−	0.997496i	$-0.522530\pi$
$877$	27.4457	−	27.4457i	0.926776	−	0.926776i	0.997496	+	0.0707206i	$0.0225299\pi$
$878$	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	$-0.876960\pi$
$881$		−	22.3792i		−	0.753973i	0.926219	−	0.376986i	$-0.123040\pi$
$882$		0			0
$883$	1.02098	+	1.02098i	0.0343587	+	0.0343587i	0.724077	−	0.689719i	$-0.242266\pi$
$883$	1.02098	+	1.02098i	0.0343587	+	0.0343587i	−0.689719	+	0.724077i	$0.742266\pi$
$884$	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	−0.429363	+	0.903132i	$0.641262\pi$
$907$	−40.1300	+	40.1300i	−1.33249	+	1.33249i	−0.903132	+	0.429363i	$0.858738\pi$
$908$	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	$-0.928648\pi$
$929$		−	13.5504i		−	0.444573i	0.974981	−	0.222286i	$-0.0713520\pi$
$930$		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	0.165802	−	0.986159i	$-0.446979\pi$
$941$	35.3372	−	35.3372i	1.15196	−	1.15196i	0.986159	−	0.165802i	$-0.0530214\pi$
$942$		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	−0.274525	+	0.961580i	$0.588521\pi$
$947$	−38.0391	+	38.0391i	−1.23611	+	1.23611i	−0.961580	+	0.274525i	$0.911479\pi$
$948$		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	$-0.923149\pi$
$953$		−	14.7622i		−	0.478194i	0.970996	−	0.239097i	$-0.0768514\pi$
$954$		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	$-0.896860\pi$
$967$		−	19.8012i		−	0.636765i	0.947962	−	0.318383i	$-0.103140\pi$
$968$	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	−0.991277	−	0.131793i	$-0.957927\pi$
$971$	−26.7823	+	26.7823i	−0.859484	+	0.859484i	0.131793	+	0.991277i	$0.457927\pi$
$972$		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	$0.00223931\pi$
$991$			0.442922i			0.0140699i	−0.999975	+	0.00703494i	$0.997761\pi$
$992$	−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	0.594847	−	0.803839i	$-0.297213\pi$
$997$	−6.59897	−	6.59897i	−0.208991	−	0.208991i	−0.803839	+	0.594847i	$0.797213\pi$
$998$	−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.179.15	✓	96
3.2	odd	2	inner	720.2.u.a.179.34	yes	96
4.3	odd	2		2880.2.u.a.2159.6		96
5.4	even	2	inner	720.2.u.a.179.33	yes	96
12.11	even	2		2880.2.u.a.2159.43		96
15.14	odd	2	inner	720.2.u.a.179.16	yes	96
16.5	even	4		2880.2.u.a.719.30		96
16.11	odd	4	inner	720.2.u.a.539.16	yes	96
20.19	odd	2		2880.2.u.a.2159.19		96
48.5	odd	4		2880.2.u.a.719.19		96
48.11	even	4	inner	720.2.u.a.539.33	yes	96
60.59	even	2		2880.2.u.a.2159.30		96
80.59	odd	4	inner	720.2.u.a.539.34	yes	96
80.69	even	4		2880.2.u.a.719.43		96
240.59	even	4	inner	720.2.u.a.539.15	yes	96
240.149	odd	4		2880.2.u.a.719.6		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.u.a.179.15	✓	96	1.1	even	1	trivial
720.2.u.a.179.16	yes	96	15.14	odd	2	inner
720.2.u.a.179.33	yes	96	5.4	even	2	inner
720.2.u.a.179.34	yes	96	3.2	odd	2	inner
720.2.u.a.539.15	yes	96	240.59	even	4	inner
720.2.u.a.539.16	yes	96	16.11	odd	4	inner
720.2.u.a.539.33	yes	96	48.11	even	4	inner
720.2.u.a.539.34	yes	96	80.59	odd	4	inner
2880.2.u.a.719.6		96	240.149	odd	4
2880.2.u.a.719.19		96	48.5	odd	4
2880.2.u.a.719.30		96	16.5	even	4
2880.2.u.a.719.43		96	80.69	even	4
2880.2.u.a.2159.6		96	4.3	odd	2
2880.2.u.a.2159.19		96	20.19	odd	2
2880.2.u.a.2159.30		96	60.59	even	2
2880.2.u.a.2159.43		96	12.11	even	2

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