LMFDB - Embedded newform 720.2.u.a.179.16

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			179.16
Character	$\chi$	$=$	720.179
Dual form			720.2.u.a.539.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.638599 - 1.26182i) q^{2} +(-1.18438 + 1.61160i) q^{4} +(0.646750 + 2.14049i) q^{5} +0.594230i q^{7} +(2.78989 + 0.465314i) q^{8} +O(q^{10})$	\(q+(-0.638599 - 1.26182i) q^{2} +(-1.18438 + 1.61160i) q^{4} +(0.646750 + 2.14049i) q^{5} +0.594230i q^{7} +(2.78989 + 0.465314i) q^{8} +(2.28790 - 2.18300i) q^{10} +(-3.48671 + 3.48671i) q^{11} +(3.41630 - 3.41630i) q^{13} +(0.749812 - 0.379475i) q^{14} +(-1.19448 - 3.81749i) q^{16} -5.22898 q^{17} +(-2.52907 + 2.52907i) q^{19} +(-4.21561 - 1.49286i) q^{20} +(6.62621 + 2.17299i) q^{22} -2.90543 q^{23} +(-4.16343 + 2.76873i) q^{25} +(-6.49240 - 2.12911i) q^{26} +(-0.957658 - 0.703795i) q^{28} +(0.201837 - 0.201837i) q^{29} +7.91354i q^{31} +(-4.05419 + 3.94506i) q^{32} +(3.33922 + 6.59803i) q^{34} +(-1.27195 + 0.384318i) q^{35} +(-3.40301 - 3.40301i) q^{37} +(4.80630 + 1.57617i) q^{38} +(0.808359 + 6.27268i) q^{40} -4.36373 q^{41} +(2.94210 - 2.94210i) q^{43} +(-1.48957 - 9.74875i) q^{44} +(1.85541 + 3.66613i) q^{46} +10.7533i q^{47} +6.64689 q^{49} +(6.15240 + 3.48539i) q^{50} +(1.45949 + 9.55189i) q^{52} +(-5.71919 + 5.71919i) q^{53} +(-9.71830 - 5.20824i) q^{55} +(-0.276504 + 1.65784i) q^{56} +(-0.383576 - 0.125789i) q^{58} +(3.56275 - 3.56275i) q^{59} +(-9.03433 - 9.03433i) q^{61} +(9.98547 - 5.05358i) q^{62} +(7.56697 + 2.59635i) q^{64} +(9.52206 + 5.10307i) q^{65} +(7.72594 + 7.72594i) q^{67} +(6.19311 - 8.42699i) q^{68} +(1.29720 + 1.35954i) q^{70} -2.31103i q^{71} -2.62944 q^{73} +(-2.12083 + 6.46715i) q^{74} +(-1.08045 - 7.07123i) q^{76} +(-2.07191 - 2.07191i) q^{77} +9.07044i q^{79} +(7.39878 - 5.02573i) q^{80} +(2.78667 + 5.50624i) q^{82} +(-3.75900 + 3.75900i) q^{83} +(-3.38184 - 11.1926i) q^{85} +(-5.59122 - 1.83358i) q^{86} +(-11.3499 + 8.10511i) q^{88} +17.3168 q^{89} +(2.03007 + 2.03007i) q^{91} +(3.44114 - 4.68238i) q^{92} +(13.5687 - 6.86704i) q^{94} +(-7.04915 - 3.77779i) q^{95} +2.43368i q^{97} +(-4.24470 - 8.38718i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	0.646750	+	2.14049i	0.289236	+	0.957258i
$5$	0.646750	+	2.14049i	0.289236	+	0.957258i
$6$		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
$10$	2.28790	−	2.18300i	0.723499	−	0.690325i
$11$	−3.48671	+	3.48671i	−1.05128	+	1.05128i	−0.0526694	+	0.998612i	$0.516773\pi$
$11$	−3.48671	+	3.48671i	−1.05128	+	1.05128i	−0.998612	+	0.0526694i	$0.983227\pi$
$12$		0			0
$13$	3.41630	−	3.41630i	0.947511	−	0.947511i	−0.0511786	−	0.998690i	$-0.516298\pi$
$13$	3.41630	−	3.41630i	0.947511	−	0.947511i	0.998690	+	0.0511786i	$0.0162978\pi$
$14$	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	$0.384566\pi$
$20$	−4.21561	−	1.49286i	−0.942639	−	0.333814i
$21$		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	$-0.741563\pi$
$29$	0.201837	−	0.201837i	0.0374802	−	0.0374802i	0.725599	+	0.688118i	$0.241563\pi$
$30$		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
$35$	−1.27195	+	0.384318i	−0.214998	+	0.0649617i
$36$		0			0
$37$	−3.40301	−	3.40301i	−0.559452	−	0.559452i	0.369699	−	0.929151i	$-0.379461\pi$
$37$	−3.40301	−	3.40301i	−0.559452	−	0.559452i	−0.929151	+	0.369699i	$0.879461\pi$
$38$	4.80630	+	1.57617i	0.779685	+	0.255689i
$39$		0			0
$40$	0.808359	+	6.27268i	0.127813	+	0.991798i
$41$	−4.36373			−0.681500			−0.340750	−	0.940154i	$-0.610681\pi$
$41$	−4.36373			−0.681500			−0.340750	+	0.940154i	$0.610681\pi$
$42$		0			0
$43$	2.94210	−	2.94210i	0.448666	−	0.448666i	−0.446245	−	0.894911i	$-0.647239\pi$
$43$	2.94210	−	2.94210i	0.448666	−	0.448666i	0.894911	+	0.446245i	$0.147239\pi$
$44$	−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
$50$	6.15240	+	3.48539i	0.870081	+	0.492909i
$51$		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	−0.436078	−	0.899909i	$-0.643633\pi$
$59$	3.56275	−	3.56275i	0.463831	−	0.463831i	0.899909	+	0.436078i	$0.143633\pi$
$60$		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	0.998507	−	0.0546326i	$-0.0173988\pi$
$67$	7.72594	+	7.72594i	0.943874	+	0.943874i	−0.0546326	+	0.998507i	$0.517399\pi$
$68$	6.19311	−	8.42699i	0.751025	−	1.02192i
$69$		0			0
$70$	1.29720	+	1.35954i	0.155046	+	0.162496i
$71$		−	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	$-0.549176\pi$
$73$	−2.62944			−0.307753			−0.153876	+	0.988090i	$0.549176\pi$
$74$	−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	$0.829552\pi$
$80$	7.39878	−	5.02573i	0.827209	−	0.561894i
$81$		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
$85$	−3.38184	−	11.1926i	−0.366812	−	1.21401i
$86$	−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	$-0.129973\pi$
$89$	17.3168			1.83558			0.917788	+	0.397070i	$0.129973\pi$
$90$		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
$100$	0.469017	−	9.98900i	0.0469017	−	0.998900i
$101$	9.22586	+	9.22586i	0.918007	+	0.918007i	0.996884	−	0.0788774i	$-0.0251336\pi$
$101$	9.22586	+	9.22586i	0.918007	+	0.918007i	−0.0788774	+	0.996884i	$0.525134\pi$
$102$		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	0.218228	−	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	$0.639096\pi$
$110$	−0.365771	+	15.5887i	−0.0348749	+	1.48633i
$111$		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
$115$	−1.87909	−	6.21906i	−0.175226	−	0.579930i
$116$	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
$125$	−8.61915	−	7.12111i	−0.770920	−	0.636932i
$126$		0			0
$127$	−21.2399			−1.88474			−0.942369	−	0.334575i	$-0.891407\pi$
$127$	−21.2399			−1.88474			−0.942369	+	0.334575i	$0.891407\pi$
$128$	−1.55613	−	11.2062i	−0.137544	−	0.990496i
$129$		0			0
$130$	0.358385	−	15.2739i	0.0314324	−	1.33961i
$131$	−2.47505	−	2.47505i	−0.216246	−	0.216246i	0.590668	−	0.806914i	$-0.298864\pi$
$131$	−2.47505	−	2.47505i	−0.216246	−	0.216246i	−0.806914	+	0.590668i	$0.798864\pi$
$132$		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	$0.802962\pi$
$140$	0.887104	−	2.50504i	0.0749740	−	0.211715i
$141$		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	$-0.136922\pi$
$149$	6.00428	+	6.00428i	0.491890	+	0.491890i	−0.417011	+	0.908901i	$0.636922\pi$
$150$		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
$155$	−16.9389	+	5.11809i	−1.36056	+	0.411095i
$156$		0			0
$157$	−3.07654	+	3.07654i	−0.245535	+	0.245535i	−0.819135	−	0.573600i	$-0.805546\pi$
$157$	−3.07654	+	3.07654i	−0.245535	+	0.245535i	0.573600	+	0.819135i	$0.305546\pi$
$158$	11.4453	−	5.79238i	0.910537	−	0.460817i
$159$		0			0
$160$	−11.0664	−	6.12651i	−0.874878	−	0.484343i
$161$		−	1.72649i		−	0.136067i
$162$		0			0
$163$	11.6108	+	11.6108i	0.909426	+	0.909426i	0.996226	−	0.0867995i	$-0.0276639\pi$
$163$	11.6108	+	11.6108i	0.909426	+	0.909426i	−0.0867995	+	0.996226i	$0.527664\pi$
$164$	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
$170$	−11.9634	+	11.4149i	−0.917551	+	0.875480i
$171$		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	$-0.917928\pi$
$179$	−16.3484	−	16.3484i	−1.22193	−	1.22193i	−0.254990	−	0.966944i	$-0.582072\pi$
$180$		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
$190$	−0.265311	+	11.3072i	−0.0192477	+	0.820314i
$191$	23.6358			1.71023			0.855113	−	0.518442i	$-0.173488\pi$
$191$	23.6358			1.71023			0.855113	+	0.518442i	$0.173488\pi$
$192$		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	−0.386147	−	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	$0.393723\pi$
$200$	−12.9038	+	5.78715i	−0.912439	+	0.409213i
$201$		0			0
$202$	5.74975	−	17.5330i	0.404551	−	1.23362i
$203$	0.119938	+	0.119938i	0.00841798	+	0.00841798i
$204$		0			0
$205$	−2.82224	−	9.34054i	−0.197114	−	0.652371i
$206$	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
$220$	19.9038	−	9.49342i	1.34191	−	0.640046i
$221$	−17.8637	+	17.8637i	−1.20165	+	1.20165i
$222$		0			0
$223$	22.4740			1.50497			0.752487	−	0.658607i	$-0.228854\pi$
$223$	22.4740			1.50497			0.752487	+	0.658607i	$0.228854\pi$
$224$	−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	$0.266821\pi$
$230$	−6.64735	+	6.34256i	−0.438313	+	0.418216i
$231$		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
$235$	−23.0174	+	6.95469i	−1.50149	+	0.453674i
$236$	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	$-0.458929\pi$
$239$	3.97843			0.257343			0.128672	+	0.991687i	$0.458929\pi$
$240$		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
$245$	4.29888	+	14.2276i	0.274645	+	0.908970i
$246$		0			0
$247$			17.2801i			1.09951i
$248$	−3.68229	+	22.0779i	−0.233825	+	1.40195i
$249$		0			0
$250$	−3.48139	+	15.4234i	−0.220182	+	0.975459i
$251$	9.68497	−	9.68497i	0.611310	−	0.611310i	−0.331977	−	0.943287i	$-0.607716\pi$
$251$	9.68497	−	9.68497i	0.611310	−	0.611310i	0.943287	+	0.331977i	$0.107716\pi$
$252$		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
$260$	−19.5018	+	9.30171i	−1.20945	+	0.576868i
$261$		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	$-0.603465\pi$
$269$	10.3047	−	10.3047i	0.628286	−	0.628286i	0.947637	+	0.319351i	$0.103465\pi$
$270$		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
$275$	4.86290	−	24.1704i	0.293244	−	1.45753i
$276$		0			0
$277$	−17.5560	−	17.5560i	−1.05484	−	1.05484i	−0.998407	−	0.0564290i	$-0.982029\pi$
$277$	−17.5560	−	17.5560i	−1.05484	−	1.05484i	−0.0564290	−	0.998407i	$-0.517971\pi$
$278$	−1.72096	+	5.24780i	−0.103216	+	0.314742i
$279$		0			0
$280$	−3.72742	+	0.480351i	−0.222756	+	0.0287065i
$281$	−13.7416			−0.819753			−0.409876	−	0.912141i	$-0.634428\pi$
$281$	−13.7416			−0.819753			−0.409876	+	0.912141i	$0.634428\pi$
$282$		0			0
$283$	4.27900	−	4.27900i	0.254360	−	0.254360i	−0.568395	−	0.822756i	$-0.692436\pi$
$283$	4.27900	−	4.27900i	0.254360	−	0.254360i	0.822756	+	0.568395i	$0.192436\pi$
$284$	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
$290$	0.0211736	−	0.902396i	0.00124336	−	0.0529905i
$291$		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	0.562083	−	0.827081i	$-0.310000\pi$
$307$	−4.64313	−	4.64313i	−0.264997	−	0.264997i	−0.827081	+	0.562083i	$0.810000\pi$
$308$	5.79300	−	0.885145i	0.330087	−	0.0504358i
$309$		0			0
$310$	17.2753	+	18.1054i	0.981169	+	1.02832i
$311$		−	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	$-0.155192\pi$
$313$	31.2608			1.76697			0.883483	+	0.468464i	$0.155192\pi$
$314$	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
$320$	−0.663537	+	17.8762i	−0.0370928	+	0.999312i
$321$		0			0
$322$	−2.17853	+	1.10254i	−0.121404	+	0.0614420i
$323$	13.2245	−	13.2245i	0.735829	−	0.735829i
$324$		0			0
$325$	−4.76470	+	23.6823i	−0.264298	+	1.31366i
$326$	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	$0.272337\pi$
$337$			27.7179i			1.50989i	−0.655787	+	0.754946i	$0.727663\pi$
$338$	−13.0500	+	6.60452i	−0.709826	+	0.359238i
$339$		0			0
$340$	22.0433	+	7.80615i	1.19547	+	0.423348i
$341$	−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	$0.732933\pi$
$350$	−2.07112	+	3.65594i	−0.110706	+	0.195418i
$351$		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
$355$	4.94674	−	1.49466i	0.262546	−	0.0793283i
$356$	−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
$365$	−1.70059	−	5.62830i	−0.0890130	−	0.294599i
$366$		0			0
$367$	−12.5630			−0.655784			−0.327892	−	0.944715i	$-0.606338\pi$
$367$	−12.5630			−0.655784			−0.327892	+	0.944715i	$0.606338\pi$
$368$	3.47047	+	11.0915i	0.180911	+	0.578182i
$369$		0			0
$370$	−15.2146	−	0.356991i	−0.790967	−	0.0185591i
$371$	−3.39851	−	3.39851i	−0.176442	−	0.176442i
$372$		0			0
$373$	20.4047	+	20.4047i	1.05652	+	1.05652i	0.998304	+	0.0582111i	$0.0185397\pi$
$373$	20.4047	+	20.4047i	1.05652	+	1.05652i	0.0582111	+	0.998304i	$0.481460\pi$
$374$	−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	$0.633884\pi$
$380$	14.4371	−	6.88603i	0.740610	−	0.353246i
$381$		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	0.741993	−	0.670408i	$-0.233881\pi$
$389$	1.41189	+	1.41189i	0.0715855	+	0.0715855i	−0.670408	+	0.741993i	$0.733881\pi$
$390$		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
$395$	−19.4152	+	5.86631i	−0.976886	+	0.295166i
$396$		0			0
$397$	11.3004	−	11.3004i	0.567153	−	0.567153i	−0.364177	−	0.931330i	$-0.618650\pi$
$397$	11.3004	−	11.3004i	0.567153	−	0.567153i	0.931330	+	0.364177i	$0.118650\pi$
$398$	−5.90439	−	11.6666i	−0.295960	−	0.584794i
$399$		0			0
$400$	15.5427	+	12.5867i	0.777136	+	0.629333i
$401$			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	$0.313801\pi$
$409$			33.7224i			1.66747i	−0.552168	+	0.833733i	$0.686199\pi$
$410$	−9.98380	+	9.52602i	−0.493065	+	0.470457i
$411$		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	$-0.135887\pi$
$419$	10.1570	+	10.1570i	0.496200	+	0.496200i	−0.414053	+	0.910253i	$0.635887\pi$
$420$		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
$430$	0.308639	−	13.1538i	0.0148839	−	0.634335i
$431$	0.155915			0.00751015			0.00375507	−	0.999993i	$-0.498805\pi$
$431$	0.155915			0.00751015			0.00375507	+	0.999993i	$0.498805\pi$
$432$		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	$0.683857\pi$
$440$	−24.6895	−	19.0525i	−1.17703	−	0.908292i
$441$		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
$445$	11.1996	+	37.0665i	0.530914	+	1.75712i
$446$	−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	$-0.328817\pi$
$457$	21.9008			1.02448			0.512238	+	0.858844i	$0.328817\pi$
$458$	2.14828	+	0.704504i	0.100382	+	0.0329193i
$459$		0			0
$460$	12.2482	+	4.33741i	0.571073	+	0.202233i
$461$	−20.7061	+	20.7061i	−0.964381	+	0.964381i	−0.999387	−	0.0350065i	$-0.988855\pi$
$461$	−20.7061	+	20.7061i	−0.964381	+	0.964381i	0.0350065	+	0.999387i	$0.488855\pi$
$462$		0			0
$463$	−15.1973			−0.706277			−0.353139	−	0.935571i	$-0.614886\pi$
$463$	−15.1973			−0.706277			−0.353139	+	0.935571i	$0.614886\pi$
$464$	−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
$470$	23.4744	+	24.6025i	1.08280	+	1.13483i
$471$		0			0
$472$	11.5975	−	8.28189i	0.533818	−	0.381205i
$473$			20.5165i			0.943349i
$474$		0			0
$475$	3.52729	−	17.5319i	0.161843	−	0.804421i
$476$	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	$-0.436327\pi$
$479$	8.69764			0.397406			0.198703	+	0.980060i	$0.436327\pi$
$480$		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
$485$	−5.20928	+	1.57398i	−0.236541	+	0.0714709i
$486$		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
$490$	15.2075	−	14.5102i	0.687003	−	0.655502i
$491$	30.6747	−	30.6747i	1.38433	−	1.38433i	0.547573	−	0.836758i	$-0.315552\pi$
$491$	30.6747	−	30.6747i	1.38433	−	1.38433i	0.836758	−	0.547573i	$-0.184448\pi$
$492$		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	$-0.0526670\pi$
$500$	21.6847	−	5.45646i	0.969770	−	0.244020i
$501$		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	$-0.841851\pi$
$509$	−9.07951	+	9.07951i	−0.402442	+	0.402442i	0.476651	+	0.879093i	$0.341851\pi$
$510$		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
$515$	−0.757319	+	0.228824i	−0.0333715	+	0.0100832i
$516$		0			0
$517$	−37.4936	−	37.4936i	−1.64896	−	1.64896i
$518$	−3.84298	−	1.26026i	−0.168851	−	0.0553727i
$519$		0			0
$520$	24.1910	+	18.6678i	1.06084	+	0.818636i
$521$	−26.5377			−1.16264			−0.581320	−	0.813675i	$-0.697463\pi$
$521$	−26.5377			−1.16264			−0.581320	+	0.813675i	$0.697463\pi$
$522$		0			0
$523$	−3.66089	+	3.66089i	−0.160080	+	0.160080i	−0.782602	−	0.622522i	$-0.786108\pi$
$523$	−3.66089	+	3.66089i	−0.160080	+	0.160080i	0.622522	+	0.782602i	$0.286108\pi$
$524$	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
$530$	−0.599968	+	25.5700i	−0.0260609	+	1.11069i
$531$		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	0.448131	−	0.893968i	$-0.352090\pi$
$547$	−10.4273	−	10.4273i	−0.445837	−	0.445837i	−0.893968	+	0.448131i	$0.852090\pi$
$548$	−1.69423	−	1.24511i	−0.0723737	−	0.0531884i
$549$		0			0
$550$	−33.6041	+	9.29909i	−1.43289	+	0.396514i
$551$			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
$560$	2.98644	+	4.39658i	0.126200	+	0.185789i
$561$		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
$565$	8.85127	+	29.2943i	0.372376	+	1.23242i
$566$	−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	$-0.626011\pi$
$569$	−18.3967			−0.771229			−0.385615	+	0.922660i	$0.626011\pi$
$570$		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	$0.235297\pi$
$577$			32.3657i			1.34740i	−0.739004	+	0.673701i	$0.764703\pi$
$578$	−6.60452	−	13.0500i	−0.274712	−	0.542808i
$579$		0			0
$580$	−1.15218	+	0.549552i	−0.0478418	+	0.0228189i
$581$	−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
$590$	0.373748	−	15.9287i	0.0153870	−	0.655775i
$591$		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
$595$	6.65097	−	2.00959i	0.272663	−	0.0823852i
$596$	−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	$-0.699301\pi$
$601$		−	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
$605$	28.4990	−	8.61099i	1.15865	−	0.350086i
$606$		0			0
$607$	−39.5940			−1.60707			−0.803535	−	0.595257i	$-0.797050\pi$
$607$	−39.5940			−1.60707			−0.803535	+	0.595257i	$0.797050\pi$
$608$	0.276001	−	20.2307i	0.0111933	−	0.820463i
$609$		0			0
$610$	−40.3916	−	0.947740i	−1.63541	−	0.0383729i
$611$	36.7365	+	36.7365i	1.48620	+	1.48620i
$612$		0			0
$613$	22.7872	+	22.7872i	0.920367	+	0.920367i	0.997055	−	0.0766879i	$-0.0244345\pi$
$613$	22.7872	+	22.7872i	0.920367	+	0.920367i	−0.0766879	+	0.997055i	$0.524435\pi$
$614$	−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	$-0.641820\pi$
$620$	11.8138	−	33.3604i	0.474455	−	1.33979i
$621$		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
$635$	−13.7369	−	45.4639i	−0.545133	−	1.80418i
$636$		0			0
$637$	22.7078	−	22.7078i	0.899714	−	0.899714i
$638$	1.77601	−	0.898825i	0.0703127	−	0.0355848i
$639$		0			0
$640$	22.9803	−	10.5785i	0.908377	−	0.418151i
$641$		−	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	−0.907998	−	0.418973i	$-0.862390\pi$
$643$	−33.6486	−	33.6486i	−1.32697	−	1.32697i	−0.418973	−	0.907998i	$-0.637610\pi$
$644$	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
$650$	32.9256	−	9.11131i	1.29145	−	0.357375i
$651$		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	0.941508	−	0.336991i	$-0.109409\pi$
$659$	15.5185	+	15.5185i	0.604517	+	0.604517i	−0.336991	+	0.941508i	$0.609409\pi$
$660$		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
$670$	34.5420	+	0.810485i	1.33447	+	0.0313118i
$671$	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	−0.745718	−	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
$680$	−4.22689	−	32.7997i	−0.162094	−	1.25781i
$681$		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
$685$	−2.25024	+	0.679911i	−0.0859773	+	0.0259780i
$686$	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
$700$	5.93576	+	0.278704i	0.224351	+	0.0105340i
$701$	22.6892	−	22.6892i	0.856960	−	0.856960i	−0.134018	−	0.990979i	$-0.542788\pi$
$701$	22.6892	−	22.6892i	0.856960	−	0.856960i	0.990979	+	0.134018i	$0.0427881\pi$
$702$		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	$0.308295\pi$
$710$	−5.04498	−	5.28742i	−0.189335	−	0.198433i
$711$		0			0
$712$	48.3119	+	8.05775i	1.81057	+	0.301977i
$713$		−	22.9923i		−	0.861067i
$714$		0			0
$715$	−50.9935	+	15.4077i	−1.90705	+	0.576215i
$716$	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	$-0.807466\pi$
$719$	−44.1136			−1.64516			−0.822580	+	0.568649i	$0.807466\pi$
$720$		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
$725$	−0.281502	+	1.39917i	−0.0104547	+	0.0519638i
$726$		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
$730$	−6.01591	+	5.74007i	−0.222659	+	0.212450i
$731$	−15.3842	+	15.3842i	−0.569004	+	0.569004i
$732$		0			0
$733$	−1.73352	+	1.73352i	−0.0640290	+	0.0640290i	−0.738396	−	0.674367i	$-0.764417\pi$
$733$	−1.73352	+	1.73352i	−0.0640290	+	0.0640290i	0.674367	+	0.738396i	$0.264417\pi$
$734$	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	$0.144669\pi$
$740$	9.26554	+	19.4260i	0.340608	+	0.714114i
$741$		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
$755$	−3.79420	−	12.5573i	−0.138085	−	0.457008i
$756$		0			0
$757$	−0.105334	−	0.105334i	−0.00382842	−	0.00382842i	0.705190	−	0.709018i	$-0.250862\pi$
$757$	−0.105334	−	0.105334i	−0.00382842	−	0.00382842i	−0.709018	+	0.705190i	$0.750862\pi$
$758$	6.12131	−	18.6660i	0.222336	−	0.677981i
$759$		0			0
$760$	−17.9085	−	13.8197i	−0.649609	−	0.501292i
$761$	−19.6399			−0.711944			−0.355972	−	0.934497i	$-0.615850\pi$
$761$	−19.6399			−0.711944			−0.355972	+	0.934497i	$0.615850\pi$
$762$		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	$0.499477\pi$
$770$	−9.26329	−	0.217352i	−0.333826	−	0.00783282i
$771$		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	0.382397	−	0.923998i	$-0.375099\pi$
$787$	−15.1938	−	15.1938i	−0.541601	−	0.541601i	−0.923998	+	0.382397i	$0.875099\pi$
$788$	3.21571	+	21.0458i	0.114555	+	0.749727i
$789$		0			0
$790$	19.8008	+	20.7523i	0.704480	+	0.738334i
$791$			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
$800$	5.95653	−	27.6500i	0.210595	−	0.977573i
$801$		0			0
$802$	22.4756	−	11.3748i	0.793641	−	0.401656i
$803$	9.16809	−	9.16809i	0.323535	−	0.323535i
$804$		0			0
$805$	3.69555	−	1.11661i	0.130251	−	0.0393554i
$806$	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	$-0.412581\pi$
$809$	15.4272			0.542391			0.271195	+	0.962524i	$0.412581\pi$
$810$		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
$820$	18.3958	+	6.51445i	0.642408	+	0.227494i
$821$	−2.62118	−	2.62118i	−0.0914799	−	0.0914799i	0.659886	−	0.751366i	$-0.270605\pi$
$821$	−2.62118	−	2.62118i	−0.0914799	−	0.0914799i	−0.751366	+	0.659886i	$0.770605\pi$
$822$		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	0.999739	−	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	$0.671049\pi$
$830$	−0.394335	+	16.8061i	−0.0136876	+	0.583349i
$831$		0			0
$832$	34.7209	−	16.9811i	1.20373	−	0.588714i
$833$	−34.7564			−1.20424
$834$		0			0
$835$	−9.85930	−	32.6305i	−0.341195	−	1.12922i
$836$	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
$845$	22.1374	−	6.68882i	0.761550	−	0.230102i
$846$		0			0
$847$	7.91172			0.271850
$848$	28.6644	+	15.0015i	0.984339	+	0.515154i
$849$		0			0
$850$	−32.1708	−	18.2250i	−1.10345	−	0.625113i
$851$	9.88722	+	9.88722i	0.338930	+	0.338930i
$852$		0			0
$853$	−16.8340	−	16.8340i	−0.576384	−	0.576384i	0.357521	−	0.933905i	$-0.383622\pi$
$853$	−16.8340	−	16.8340i	−0.576384	−	0.576384i	−0.933905	+	0.357521i	$0.883622\pi$
$854$	−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	$0.698837\pi$
$860$	−16.7949	+	8.01059i	−0.572701	+	0.273159i
$861$		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
$875$	4.23158	−	5.12176i	0.143053	−	0.173147i
$876$		0			0
$877$	−27.4457	+	27.4457i	−0.926776	+	0.926776i	−0.997496	−	0.0707206i	$-0.977470\pi$
$877$	−27.4457	+	27.4457i	−0.926776	+	0.926776i	0.0707206	+	0.997496i	$0.477470\pi$
$878$	14.6116	+	28.8713i	0.493117	+	0.974360i
$879$		0			0
$880$	−8.27412	+	43.3206i	−0.278921	+	1.46034i
$881$			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	$-0.257734\pi$
$883$	−1.02098	−	1.02098i	−0.0343587	−	0.0343587i	−0.724077	+	0.689719i	$0.757734\pi$
$884$	−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
$890$	39.6192	−	37.8026i	1.32804	−	1.26715i
$891$		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	$-0.358738\pi$
$907$	40.1300	−	40.1300i	1.33249	−	1.33249i	0.903132	−	0.429363i	$-0.141262\pi$
$908$	8.72040	+	57.0723i	0.289397	+	1.89401i
$909$		0			0
$910$	9.07624	+	0.212963i	0.300874	+	0.00705965i
$911$	18.2944			0.606119			0.303060	−	0.952972i	$-0.401992\pi$
$911$	18.2944			0.606119			0.303060	+	0.952972i	$0.401992\pi$
$912$		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	$0.556948\pi$
$920$	−2.34863	−	18.2248i	−0.0774321	−	0.600855i
$921$		0			0
$922$	39.3503	+	12.9045i	1.29593	+	0.424987i
$923$	−7.89517	−	7.89517i	−0.259873	−	0.259873i
$924$		0			0
$925$	23.5902	+	4.74618i	0.775642	+	0.156053i
$926$	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	$-0.451337\pi$
$937$	9.32301			0.304570			0.152285	+	0.988337i	$0.451337\pi$
$938$	8.72480	+	2.86120i	0.284875	+	0.0934215i
$939$		0			0
$940$	16.0532	−	45.3317i	0.523597	−	1.47856i
$941$	−35.3372	+	35.3372i	−1.15196	+	1.15196i	−0.165802	+	0.986159i	$0.553021\pi$
$941$	−35.3372	+	35.3372i	−1.15196	+	1.15196i	−0.986159	+	0.165802i	$0.946979\pi$
$942$		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
$950$	−24.3747	+	6.74507i	−0.790819	+	0.218839i
$951$		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
$955$	15.2865	+	50.5923i	0.494658	+	1.63713i
$956$	−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
$965$	−25.0169	+	7.55886i	−0.805323	+	0.243328i
$966$		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
$970$	5.31272	+	5.56803i	0.170581	+	0.178779i
$971$	26.7823	−	26.7823i	0.859484	−	0.859484i	−0.131793	−	0.991277i	$-0.542073\pi$
$971$	26.7823	−	26.7823i	0.859484	−	0.859484i	0.991277	+	0.131793i	$0.0420734\pi$
$972$		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
$980$	−28.0207	−	9.92290i	−0.895088	−	0.316975i
$981$		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
$995$	5.97976	+	19.7907i	0.189571	+	0.627407i
$996$		0			0
$997$	6.59897	+	6.59897i	0.208991	+	0.208991i	0.803839	−	0.594847i	$-0.202787\pi$
$997$	6.59897	+	6.59897i	0.208991	+	0.208991i	−0.594847	+	0.803839i	$0.702787\pi$
$998$	−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.179.16	yes	96
3.2	odd	2	inner	720.2.u.a.179.33	yes	96
4.3	odd	2		2880.2.u.a.2159.30		96
5.4	even	2	inner	720.2.u.a.179.34	yes	96
12.11	even	2		2880.2.u.a.2159.19		96
15.14	odd	2	inner	720.2.u.a.179.15	✓	96
16.5	even	4		2880.2.u.a.719.6		96
16.11	odd	4	inner	720.2.u.a.539.15	yes	96
20.19	odd	2		2880.2.u.a.2159.43		96
48.5	odd	4		2880.2.u.a.719.43		96
48.11	even	4	inner	720.2.u.a.539.34	yes	96
60.59	even	2		2880.2.u.a.2159.6		96
80.59	odd	4	inner	720.2.u.a.539.33	yes	96
80.69	even	4		2880.2.u.a.719.19		96
240.59	even	4	inner	720.2.u.a.539.16	yes	96
240.149	odd	4		2880.2.u.a.719.30		96

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

\(f(q)\)	\(=\)	\(q+(-0.638599 - 1.26182i) q^{2} +(-1.18438 + 1.61160i) q^{4} +(0.646750 + 2.14049i) q^{5} +0.594230i q^{7} +(2.78989 + 0.465314i) q^{8} +O(q^{10})\)	\(q+(-0.638599 - 1.26182i) q^{2} +(-1.18438 + 1.61160i) q^{4} +(0.646750 + 2.14049i) q^{5} +0.594230i q^{7} +(2.78989 + 0.465314i) q^{8} +(2.28790 - 2.18300i) q^{10} +(-3.48671 + 3.48671i) q^{11} +(3.41630 - 3.41630i) q^{13} +(0.749812 - 0.379475i) q^{14} +(-1.19448 - 3.81749i) q^{16} -5.22898 q^{17} +(-2.52907 + 2.52907i) q^{19} +(-4.21561 - 1.49286i) q^{20} +(6.62621 + 2.17299i) q^{22} -2.90543 q^{23} +(-4.16343 + 2.76873i) q^{25} +(-6.49240 - 2.12911i) q^{26} +(-0.957658 - 0.703795i) q^{28} +(0.201837 - 0.201837i) q^{29} +7.91354i q^{31} +(-4.05419 + 3.94506i) q^{32} +(3.33922 + 6.59803i) q^{34} +(-1.27195 + 0.384318i) q^{35} +(-3.40301 - 3.40301i) q^{37} +(4.80630 + 1.57617i) q^{38} +(0.808359 + 6.27268i) q^{40} -4.36373 q^{41} +(2.94210 - 2.94210i) q^{43} +(-1.48957 - 9.74875i) q^{44} +(1.85541 + 3.66613i) q^{46} +10.7533i q^{47} +6.64689 q^{49} +(6.15240 + 3.48539i) q^{50} +(1.45949 + 9.55189i) q^{52} +(-5.71919 + 5.71919i) q^{53} +(-9.71830 - 5.20824i) q^{55} +(-0.276504 + 1.65784i) q^{56} +(-0.383576 - 0.125789i) q^{58} +(3.56275 - 3.56275i) q^{59} +(-9.03433 - 9.03433i) q^{61} +(9.98547 - 5.05358i) q^{62} +(7.56697 + 2.59635i) q^{64} +(9.52206 + 5.10307i) q^{65} +(7.72594 + 7.72594i) q^{67} +(6.19311 - 8.42699i) q^{68} +(1.29720 + 1.35954i) q^{70} -2.31103i q^{71} -2.62944 q^{73} +(-2.12083 + 6.46715i) q^{74} +(-1.08045 - 7.07123i) q^{76} +(-2.07191 - 2.07191i) q^{77} +9.07044i q^{79} +(7.39878 - 5.02573i) q^{80} +(2.78667 + 5.50624i) q^{82} +(-3.75900 + 3.75900i) q^{83} +(-3.38184 - 11.1926i) q^{85} +(-5.59122 - 1.83358i) q^{86} +(-11.3499 + 8.10511i) q^{88} +17.3168 q^{89} +(2.03007 + 2.03007i) q^{91} +(3.44114 - 4.68238i) q^{92} +(13.5687 - 6.86704i) q^{94} +(-7.04915 - 3.77779i) q^{95} +2.43368i q^{97} +(-4.24470 - 8.38718i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 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

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