LMFDB - Embedded newform 280.2.bo.a.33.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(17,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

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

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

chi := DirichletCharacter("280.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bo (of order $12$, degree $4$, 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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			33.2
Character	$\chi$	$=$	280.33
Dual form			280.2.bo.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.30560 - 0.617784i) q^{3} +(1.37859 + 1.76054i) q^{5} +(-0.755351 - 2.53563i) q^{7} +(2.33607 + 1.34873i) q^{9} +O(q^{10})$	\(q+(-2.30560 - 0.617784i) q^{3} +(1.37859 + 1.76054i) q^{5} +(-0.755351 - 2.53563i) q^{7} +(2.33607 + 1.34873i) q^{9} +(2.18726 + 3.78844i) q^{11} +(4.36695 - 4.36695i) q^{13} +(-2.09085 - 4.91077i) q^{15} +(0.438132 - 1.63513i) q^{17} +(3.56560 - 6.17580i) q^{19} +(0.175064 + 6.31281i) q^{21} +(4.91851 - 1.31791i) q^{23} +(-1.19897 + 4.85412i) q^{25} +(0.510640 + 0.510640i) q^{27} +1.33053i q^{29} +(-1.90109 + 1.09759i) q^{31} +(-2.70251 - 10.0859i) q^{33} +(3.42276 - 4.82543i) q^{35} +(-0.224926 - 0.839435i) q^{37} +(-12.7663 + 7.37062i) q^{39} -5.69781i q^{41} +(3.40535 + 3.40535i) q^{43} +(0.845995 + 5.97207i) q^{45} +(-9.84549 + 2.63809i) q^{47} +(-5.85889 + 3.83059i) q^{49} +(-2.02031 + 3.49929i) q^{51} +(-0.541299 + 2.02016i) q^{53} +(-3.65436 + 9.07346i) q^{55} +(-12.0362 + 12.0362i) q^{57} +(2.56679 + 4.44580i) q^{59} +(6.21535 + 3.58843i) q^{61} +(1.65533 - 6.94217i) q^{63} +(13.7084 + 1.66793i) q^{65} +(-7.11586 - 1.90669i) q^{67} -12.1543 q^{69} +4.31969 q^{71} +(-14.2630 - 3.82176i) q^{73} +(5.76315 - 10.4510i) q^{75} +(7.95396 - 8.40770i) q^{77} +(4.82649 + 2.78658i) q^{79} +(-4.90805 - 8.50099i) q^{81} +(-0.272283 + 0.272283i) q^{83} +(3.48271 - 1.48283i) q^{85} +(0.821982 - 3.06768i) q^{87} +(1.79506 - 3.10913i) q^{89} +(-14.3716 - 7.77441i) q^{91} +(5.06123 - 1.35615i) q^{93} +(15.7882 - 2.23653i) q^{95} +(0.325781 + 0.325781i) q^{97} +11.8001i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{7}+O(q^{10}) $ 48 * q - 4 * q^7	$ 48 q - 4 q^{7} + 4 q^{11} + 8 q^{15} - 4 q^{21} - 4 q^{23} - 8 q^{25} - 36 q^{33} + 24 q^{35} + 8 q^{37} - 16 q^{43} + 48 q^{45} + 24 q^{51} + 16 q^{53} - 96 q^{57} - 36 q^{61} - 68 q^{63} + 12 q^{65} - 16 q^{67} - 64 q^{71} - 48 q^{73} - 48 q^{75} + 4 q^{77} - 40 q^{85} - 12 q^{87} - 80 q^{91} + 24 q^{95}+O(q^{100}) $ 48 * q - 4 * q^7 + 4 * q^11 + 8 * q^15 - 4 * q^21 - 4 * q^23 - 8 * q^25 - 36 * q^33 + 24 * q^35 + 8 * q^37 - 16 * q^43 + 48 * q^45 + 24 * q^51 + 16 * q^53 - 96 * q^57 - 36 * q^61 - 68 * q^63 + 12 * q^65 - 16 * q^67 - 64 * q^71 - 48 * q^73 - 48 * q^75 + 4 * q^77 - 40 * q^85 - 12 * q^87 - 80 * q^91 + 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.30560	−	0.617784i	−1.33114	−	0.356678i	−0.478000	−	0.878360i	$-0.658638\pi$
$3$	−2.30560	−	0.617784i	−1.33114	−	0.356678i	−0.853140	+	0.521682i	$0.825305\pi$
$4$		0			0
$5$	1.37859	+	1.76054i	0.616525	+	0.787336i
$5$	1.37859	+	1.76054i	0.616525	+	0.787336i
$6$		0			0
$7$	−0.755351	−	2.53563i	−0.285496	−	0.958380i
$7$	−0.755351	−	2.53563i	−0.285496	−	0.958380i
$8$		0			0
$9$	2.33607	+	1.34873i	0.778688	+	0.449576i
$10$		0			0
$11$	2.18726	+	3.78844i	0.659483	+	1.14226i	0.980750	+	0.195270i	$0.0625583\pi$
$11$	2.18726	+	3.78844i	0.659483	+	1.14226i	−0.321266	+	0.946989i	$0.604108\pi$
$12$		0			0
$13$	4.36695	−	4.36695i	1.21117	−	1.21117i	0.240533	−	0.970641i	$-0.422678\pi$
$13$	4.36695	−	4.36695i	1.21117	−	1.21117i	0.970641	−	0.240533i	$-0.0773224\pi$
$14$		0			0
$15$	−2.09085	−	4.91077i	−0.539855	−	1.26795i
$16$		0			0
$17$	0.438132	−	1.63513i	0.106263	−	0.396577i	−0.892223	−	0.451595i	$-0.850855\pi$
$17$	0.438132	−	1.63513i	0.106263	−	0.396577i	0.998485	+	0.0550183i	$0.0175217\pi$
$18$		0			0
$19$	3.56560	−	6.17580i	0.818004	−	1.41682i	−0.0891466	−	0.996019i	$-0.528414\pi$
$19$	3.56560	−	6.17580i	0.818004	−	1.41682i	0.907151	−	0.420806i	$-0.138253\pi$
$20$		0			0
$21$	0.175064	+	6.31281i	0.0382021	+	1.37757i
$22$		0			0
$23$	4.91851	−	1.31791i	1.02558	−	0.274803i	0.293454	−	0.955973i	$-0.405195\pi$
$23$	4.91851	−	1.31791i	1.02558	−	0.274803i	0.732125	+	0.681170i	$0.238529\pi$
$24$		0			0
$25$	−1.19897	+	4.85412i	−0.239795	+	0.970824i
$26$		0			0
$27$	0.510640	+	0.510640i	0.0982727	+	0.0982727i
$28$		0			0
$29$			1.33053i			0.247074i	0.992340	+	0.123537i	$0.0394237\pi$
$29$			1.33053i			0.247074i	−0.992340	+	0.123537i	$0.960576\pi$
$30$		0			0
$31$	−1.90109	+	1.09759i	−0.341446	+	0.197134i	−0.660911	−	0.750464i	$-0.729830\pi$
$31$	−1.90109	+	1.09759i	−0.341446	+	0.197134i	0.319465	+	0.947598i	$0.396497\pi$
$32$		0			0
$33$	−2.70251	−	10.0859i	−0.470446	−	1.75573i
$34$		0			0
$35$	3.42276	−	4.82543i	0.578551	−	0.815646i
$36$		0			0
$37$	−0.224926	−	0.839435i	−0.0369776	−	0.138002i	0.944969	−	0.327159i	$-0.106091\pi$
$37$	−0.224926	−	0.839435i	−0.0369776	−	0.138002i	−0.981947	+	0.189157i	$0.939425\pi$
$38$		0			0
$39$	−12.7663	+	7.37062i	−2.04424	+	1.18024i
$40$		0			0
$41$		−	5.69781i		−	0.889849i	−0.895568	−	0.444924i	$-0.853231\pi$
$41$		−	5.69781i		−	0.889849i	0.895568	−	0.444924i	$-0.146769\pi$
$42$		0			0
$43$	3.40535	+	3.40535i	0.519312	+	0.519312i	0.917363	−	0.398051i	$-0.130313\pi$
$43$	3.40535	+	3.40535i	0.519312	+	0.519312i	−0.398051	+	0.917363i	$0.630313\pi$
$44$		0			0
$45$	0.845995	+	5.97207i	0.126113	+	0.890264i
$46$		0			0
$47$	−9.84549	+	2.63809i	−1.43611	+	0.384805i	−0.891170	−	0.453669i	$-0.850115\pi$
$47$	−9.84549	+	2.63809i	−1.43611	+	0.384805i	−0.544942	+	0.838474i	$0.683448\pi$
$48$		0			0
$49$	−5.85889	+	3.83059i	−0.836984	+	0.547227i
$50$		0			0
$51$	−2.02031	+	3.49929i	−0.282901	+	0.489998i
$52$		0			0
$53$	−0.541299	+	2.02016i	−0.0743531	+	0.277490i	−0.993086	−	0.117390i	$-0.962547\pi$
$53$	−0.541299	+	2.02016i	−0.0743531	+	0.277490i	0.918733	+	0.394880i	$0.129214\pi$
$54$		0			0
$55$	−3.65436	+	9.07346i	−0.492753	+	1.22347i
$56$		0			0
$57$	−12.0362	+	12.0362i	−1.59423	+	1.59423i
$58$		0			0
$59$	2.56679	+	4.44580i	0.334167	+	0.578794i	0.983324	−	0.181860i	$-0.0582117\pi$
$59$	2.56679	+	4.44580i	0.334167	+	0.578794i	−0.649157	+	0.760654i	$0.724878\pi$
$60$		0			0
$61$	6.21535	+	3.58843i	0.795794	+	0.459452i	0.841998	−	0.539480i	$-0.181379\pi$
$61$	6.21535	+	3.58843i	0.795794	+	0.459452i	−0.0462043	+	0.998932i	$0.514713\pi$
$62$		0			0
$63$	1.65533	−	6.94217i	0.208552	−	0.874631i
$64$		0			0
$65$	13.7084	+	1.66793i	1.70032	+	0.206882i
$66$		0			0
$67$	−7.11586	−	1.90669i	−0.869341	−	0.232939i	−0.203538	−	0.979067i	$-0.565244\pi$
$67$	−7.11586	−	1.90669i	−0.869341	−	0.232939i	−0.665803	+	0.746128i	$0.731911\pi$
$68$		0			0
$69$	−12.1543			−1.46321
$70$		0			0
$71$	4.31969			0.512653			0.256326	−	0.966590i	$-0.417488\pi$
$71$	4.31969			0.512653			0.256326	+	0.966590i	$0.417488\pi$
$72$		0			0
$73$	−14.2630	−	3.82176i	−1.66936	−	0.447303i	−0.704420	−	0.709784i	$-0.748793\pi$
$73$	−14.2630	−	3.82176i	−1.66936	−	0.447303i	−0.964937	+	0.262481i	$0.915459\pi$
$74$		0			0
$75$	5.76315	−	10.4510i	0.665471	−	1.20677i
$76$		0			0
$77$	7.95396	−	8.40770i	0.906438	−	0.958146i
$78$		0			0
$79$	4.82649	+	2.78658i	0.543023	+	0.313514i	0.746303	−	0.665606i	$-0.231827\pi$
$79$	4.82649	+	2.78658i	0.543023	+	0.313514i	−0.203280	+	0.979121i	$0.565160\pi$
$80$		0			0
$81$	−4.90805	−	8.50099i	−0.545339	−	0.944555i
$82$		0			0
$83$	−0.272283	+	0.272283i	−0.0298869	+	0.0298869i	−0.721892	−	0.692005i	$-0.756727\pi$
$83$	−0.272283	+	0.272283i	−0.0298869	+	0.0298869i	0.692005	+	0.721892i	$0.256727\pi$
$84$		0			0
$85$	3.48271	−	1.48283i	0.377753	−	0.160835i
$86$		0			0
$87$	0.821982	−	3.06768i	0.0881257	−	0.328890i
$88$		0			0
$89$	1.79506	−	3.10913i	0.190276	−	0.329567i	−0.755066	−	0.655649i	$-0.772395\pi$
$89$	1.79506	−	3.10913i	0.190276	−	0.329567i	0.945342	+	0.326082i	$0.105729\pi$
$90$		0			0
$91$	−14.3716	−	7.77441i	−1.50655	−	0.814980i
$92$		0			0
$93$	5.06123	−	1.35615i	0.524825	−	0.140627i
$94$		0			0
$95$	15.7882	−	2.23653i	1.61984	−	0.229464i
$96$		0			0
$97$	0.325781	+	0.325781i	0.0330781	+	0.0330781i	0.723452	−	0.690374i	$-0.242554\pi$
$97$	0.325781	+	0.325781i	0.0330781	+	0.0330781i	−0.690374	+	0.723452i	$0.742554\pi$
$98$		0			0
$99$			11.8001i			1.18595i
$100$		0			0
$101$	10.6907	−	6.17228i	1.06376	−	0.614165i	0.137294	−	0.990530i	$-0.456160\pi$
$101$	10.6907	−	6.17228i	1.06376	−	0.614165i	0.926471	+	0.376365i	$0.122826\pi$
$102$		0			0
$103$	−1.41652	−	5.28651i	−0.139573	−	0.520895i	−0.999937	−	0.0112145i	$-0.996430\pi$
$103$	−1.41652	−	5.28651i	−0.139573	−	0.520895i	0.860364	−	0.509681i	$-0.170236\pi$
$104$		0			0
$105$	−10.8726	+	9.01099i	−1.06106	+	0.879382i
$106$		0			0
$107$	0.926726	+	3.45859i	0.0895900	+	0.334354i	0.996144	−	0.0877359i	$-0.0279632\pi$
$107$	0.926726	+	3.45859i	0.0895900	+	0.334354i	−0.906554	+	0.422090i	$0.861297\pi$
$108$		0			0
$109$	5.80975	−	3.35426i	0.556473	−	0.321280i	−0.195255	−	0.980752i	$-0.562554\pi$
$109$	5.80975	−	3.35426i	0.556473	−	0.321280i	0.751729	+	0.659472i	$0.229220\pi$
$110$		0			0
$111$			2.07436i			0.196889i
$112$		0			0
$113$	5.75259	+	5.75259i	0.541158	+	0.541158i	0.923869	−	0.382710i	$-0.125009\pi$
$113$	5.75259	+	5.75259i	0.541158	+	0.541158i	−0.382710	+	0.923869i	$0.625009\pi$
$114$		0			0
$115$	9.10083	+	6.84235i	0.848657	+	0.638052i
$116$		0			0
$117$	16.0913	−	4.31165i	1.48764	−	0.398613i
$118$		0			0
$119$	−4.47703	+	0.124155i	−0.410409	+	0.0113813i
$120$		0			0
$121$	−4.06820	+	7.04634i	−0.369837	+	0.640576i
$122$		0			0
$123$	−3.52002	+	13.1369i	−0.317389	+	1.18451i
$124$		0			0
$125$	−10.1987	+	4.58101i	−0.912203	+	0.409738i
$126$		0			0
$127$	3.47621	−	3.47621i	0.308464	−	0.308464i	−0.535849	−	0.844314i	$-0.680009\pi$
$127$	3.47621	−	3.47621i	0.308464	−	0.308464i	0.844314	+	0.535849i	$0.180009\pi$
$128$		0			0
$129$	−5.74762	−	9.95516i	−0.506049	−	0.876503i
$130$		0			0
$131$	−4.72880	−	2.73018i	−0.413157	−	0.238537i	0.278988	−	0.960295i	$-0.410001\pi$
$131$	−4.72880	−	2.73018i	−0.413157	−	0.238537i	−0.692145	+	0.721758i	$0.743334\pi$
$132$		0			0
$133$	−18.3528	−	4.37616i	−1.59139	−	0.379461i
$134$		0			0
$135$	−0.195036	+	1.60296i	−0.0167860	+	0.137961i
$136$		0			0
$137$	−16.6760	−	4.46833i	−1.42473	−	0.381756i	−0.537571	−	0.843218i	$-0.680658\pi$
$137$	−16.6760	−	4.46833i	−1.42473	−	0.381756i	−0.887160	+	0.461463i	$0.847325\pi$
$138$		0			0
$139$	−4.33475			−0.367669			−0.183834	−	0.982957i	$-0.558851\pi$
$139$	−4.33475			−0.367669			−0.183834	+	0.982957i	$0.558851\pi$
$140$		0			0
$141$	24.3295			2.04892
$142$		0			0
$143$	26.0956	+	6.99230i	2.18222	+	0.584725i
$144$		0			0
$145$	−2.34245	+	1.83426i	−0.194530	+	0.152327i
$146$		0			0
$147$	15.8747	−	5.21229i	1.30933	−	0.429902i
$148$		0			0
$149$	−2.22537	−	1.28482i	−0.182309	−	0.105256i	0.406068	−	0.913843i	$-0.366900\pi$
$149$	−2.22537	−	1.28482i	−0.182309	−	0.105256i	−0.588377	+	0.808587i	$0.700233\pi$
$150$		0			0
$151$	−0.516263	−	0.894194i	−0.0420129	−	0.0727685i	0.844254	−	0.535943i	$-0.180044\pi$
$151$	−0.516263	−	0.894194i	−0.0420129	−	0.0727685i	−0.886267	+	0.463174i	$0.846710\pi$
$152$		0			0
$153$	3.22885	−	3.22885i	0.261037	−	0.261037i
$154$		0			0
$155$	−4.55318	−	1.83380i	−0.365720	−	0.147295i
$156$		0			0
$157$	−4.71159	+	17.5839i	−0.376026	+	1.40335i	0.475815	+	0.879545i	$0.342153\pi$
$157$	−4.71159	+	17.5839i	−0.376026	+	1.40335i	−0.851841	+	0.523801i	$0.824513\pi$
$158$		0			0
$159$	2.49604	−	4.32327i	0.197949	−	0.342857i
$160$		0			0
$161$	−7.05694	−	11.4760i	−0.556164	−	0.904439i
$162$		0			0
$163$	−8.44026	+	2.26156i	−0.661092	+	0.177139i	−0.573739	−	0.819038i	$-0.694508\pi$
$163$	−8.44026	+	2.26156i	−0.661092	+	0.177139i	−0.0873531	+	0.996177i	$0.527841\pi$
$164$		0			0
$165$	14.0309	−	18.6622i	1.09231	−	1.45285i
$166$		0			0
$167$	12.3783	+	12.3783i	0.957862	+	0.957862i	0.999147	−	0.0412856i	$-0.0131454\pi$
$167$	12.3783	+	12.3783i	0.957862	+	0.957862i	−0.0412856	+	0.999147i	$0.513145\pi$
$168$		0			0
$169$		−	25.1405i		−	1.93389i
$170$		0			0
$171$	16.6589	−	9.61804i	1.27394	−	0.735510i
$172$		0			0
$173$	−0.746705	−	2.78674i	−0.0567709	−	0.211872i	0.931714	−	0.363194i	$-0.118314\pi$
$173$	−0.746705	−	2.78674i	−0.0567709	−	0.211872i	−0.988485	+	0.151322i	$0.951647\pi$
$174$		0			0
$175$	13.2139	−	0.626405i	0.998878	−	0.0473518i
$176$		0			0
$177$	−3.17144	−	11.8360i	−0.238380	−	0.889646i
$178$		0			0
$179$	−6.47526	+	3.73849i	−0.483984	+	0.279428i	−0.722075	−	0.691815i	$-0.756812\pi$
$179$	−6.47526	+	3.73849i	−0.483984	+	0.279428i	0.238092	+	0.971243i	$0.423478\pi$
$180$		0			0
$181$			21.7307i			1.61523i	0.589708	+	0.807617i	$0.299243\pi$
$181$			21.7307i			1.61523i	−0.589708	+	0.807617i	$0.700757\pi$
$182$		0			0
$183$	−12.1132	−	12.1132i	−0.895437	−	0.895437i
$184$		0			0
$185$	1.16777	−	1.55323i	0.0858565	−	0.114196i
$186$		0			0
$187$	7.15290	−	1.91661i	0.523072	−	0.140157i
$188$		0			0
$189$	0.909084	−	1.68051i	0.0661261	−	0.122239i
$190$		0			0
$191$	−5.73369	+	9.93104i	−0.414875	+	0.718585i	−0.995415	−	0.0956469i	$-0.969508\pi$
$191$	−5.73369	+	9.93104i	−0.414875	+	0.718585i	0.580540	+	0.814232i	$0.302841\pi$
$192$		0			0
$193$	−1.43727	+	5.36396i	−0.103457	+	0.386106i	−0.998166	−	0.0605441i	$-0.980716\pi$
$193$	−1.43727	+	5.36396i	−0.103457	+	0.386106i	0.894709	+	0.446650i	$0.147383\pi$
$194$		0			0
$195$	−30.5757	−	12.3144i	−2.18957	−	0.881855i
$196$		0			0
$197$	−12.5995	+	12.5995i	−0.897678	+	0.897678i	−0.995230	−	0.0975523i	$-0.968899\pi$
$197$	−12.5995	+	12.5995i	−0.897678	+	0.897678i	0.0975523	+	0.995230i	$0.468899\pi$
$198$		0			0
$199$	2.02418	+	3.50598i	0.143490	+	0.248532i	0.928809	−	0.370560i	$-0.120834\pi$
$199$	2.02418	+	3.50598i	0.143490	+	0.248532i	−0.785318	+	0.619092i	$0.787501\pi$
$200$		0			0
$201$	15.2284	+	8.79213i	1.07413	+	0.620149i
$202$		0			0
$203$	3.37375	−	1.00502i	0.236790	−	0.0705385i
$204$		0			0
$205$	10.0312	−	7.85495i	0.700610	−	0.548614i
$206$		0			0
$207$	13.2674	+	3.55500i	0.922151	+	0.247090i
$208$		0			0
$209$	31.1955			2.15784
$210$		0			0
$211$	−21.3214			−1.46783			−0.733913	−	0.679244i	$-0.762308\pi$
$211$	−21.3214			−1.46783			−0.733913	+	0.679244i	$0.762308\pi$
$212$		0			0
$213$	−9.95948	−	2.66863i	−0.682412	−	0.182852i
$214$		0			0
$215$	−1.30066	+	10.6898i	−0.0887041	+	0.729041i
$216$		0			0
$217$	4.21909	+	3.99140i	0.286410	+	0.270954i
$218$		0			0
$219$	30.5238	+	17.6229i	2.06260	+	1.19084i
$220$		0			0
$221$	−5.22723	−	9.05383i	−0.351622	−	0.609026i
$222$		0			0
$223$	19.7653	−	19.7653i	1.32358	−	1.32358i	0.412730	−	0.910854i	$-0.364575\pi$
$223$	19.7653	−	19.7653i	1.32358	−	1.32358i	0.910854	−	0.412730i	$-0.135425\pi$
$224$		0			0
$225$	−9.34776	+	9.72245i	−0.623184	+	0.648163i
$226$		0			0
$227$	0.760893	−	2.83969i	0.0505022	−	0.188477i	−0.936067	−	0.351823i	$-0.885562\pi$
$227$	0.760893	−	2.83969i	0.0505022	−	0.188477i	0.986569	+	0.163346i	$0.0522287\pi$
$228$		0			0
$229$	−12.0300	+	20.8366i	−0.794965	+	1.37692i	0.127896	+	0.991788i	$0.459178\pi$
$229$	−12.0300	+	20.8366i	−0.794965	+	1.37692i	−0.922861	+	0.385133i	$0.874156\pi$
$230$		0			0
$231$	−23.5328	+	14.4710i	−1.54834	+	0.952120i
$232$		0			0
$233$	2.37700	−	0.636915i	0.155722	−	0.0417257i	−0.180116	−	0.983645i	$-0.557647\pi$
$233$	2.37700	−	0.636915i	0.155722	−	0.0417257i	0.335838	+	0.941920i	$0.390981\pi$
$234$		0			0
$235$	−18.2174	−	13.6965i	−1.18837	−	0.893460i
$236$		0			0
$237$	−9.40647	−	9.40647i	−0.611016	−	0.611016i
$238$		0			0
$239$		−	15.4754i		−	1.00102i	−0.865730	−	0.500511i	$-0.833145\pi$
$239$		−	15.4754i		−	1.00102i	0.865730	−	0.500511i	$-0.166855\pi$
$240$		0			0
$241$	−13.8765	+	8.01160i	−0.893864	+	0.516073i	−0.875204	−	0.483753i	$-0.839273\pi$
$241$	−13.8765	+	8.01160i	−0.893864	+	0.516073i	−0.0186595	+	0.999826i	$0.505940\pi$
$242$		0			0
$243$	5.50351	+	20.5394i	0.353050	+	1.31760i
$244$		0			0
$245$	−14.8209	−	5.03397i	−0.946873	−	0.321608i
$246$		0			0
$247$	−11.3986	−	42.5402i	−0.725276	−	2.70677i
$248$		0			0
$249$	0.795987	−	0.459563i	0.0504436	−	0.0291237i
$250$		0			0
$251$			0.592810i			0.0374178i	0.999825	+	0.0187089i	$0.00595558\pi$
$251$			0.592810i			0.0374178i	−0.999825	+	0.0187089i	$0.994044\pi$
$252$		0			0
$253$	15.7509	+	15.7509i	0.990249	+	0.990249i
$254$		0			0
$255$	−8.94581	+	1.26725i	−0.560208	+	0.0793582i
$256$		0			0
$257$	−18.7358	+	5.02024i	−1.16871	+	0.313154i	−0.790438	−	0.612542i	$-0.790147\pi$
$257$	−18.7358	+	5.02024i	−1.16871	+	0.313154i	−0.378269	+	0.925696i	$0.623480\pi$
$258$		0			0
$259$	−1.95860	+	1.20440i	−0.121702	+	0.0748377i
$260$		0			0
$261$	−1.79453	+	3.10821i	−0.111078	+	0.192393i
$262$		0			0
$263$	−6.58626	+	24.5803i	−0.406126	+	1.51568i	0.395843	+	0.918318i	$0.370453\pi$
$263$	−6.58626	+	24.5803i	−0.406126	+	1.51568i	−0.801969	+	0.597366i	$0.796214\pi$
$264$		0			0
$265$	−4.30279	+	1.83199i	−0.264318	+	0.112538i
$266$		0			0
$267$	−6.05945	+	6.05945i	−0.370833	+	0.370833i
$268$		0			0
$269$	−6.17421	−	10.6940i	−0.376448	−	0.652027i	0.614095	−	0.789232i	$-0.289521\pi$
$269$	−6.17421	−	10.6940i	−0.376448	−	0.652027i	−0.990543	+	0.137205i	$0.956188\pi$
$270$		0			0
$271$	−10.0880	−	5.82432i	−0.612803	−	0.353802i	0.161259	−	0.986912i	$-0.448445\pi$
$271$	−10.0880	−	5.82432i	−0.612803	−	0.353802i	−0.774062	+	0.633110i	$0.781778\pi$
$272$		0			0
$273$	28.3322	+	26.8032i	1.71474	+	1.62221i
$274$		0			0
$275$	−21.0120	+	6.07497i	−1.26707	+	0.366334i
$276$		0			0
$277$	18.2575	+	4.89207i	1.09698	+	0.293936i	0.761536	−	0.648123i	$-0.224446\pi$
$277$	18.2575	+	4.89207i	1.09698	+	0.293936i	0.335448	+	0.942059i	$0.391112\pi$
$278$		0			0
$279$	−5.92143			−0.354506
$280$		0			0
$281$	21.9795			1.31119			0.655594	−	0.755114i	$-0.272418\pi$
$281$	21.9795			1.31119			0.655594	+	0.755114i	$0.272418\pi$
$282$		0			0
$283$	−23.1631	−	6.20653i	−1.37690	−	0.368940i	−0.506907	−	0.862001i	$-0.669211\pi$
$283$	−23.1631	−	6.20653i	−1.37690	−	0.368940i	−0.869995	+	0.493061i	$0.835878\pi$
$284$		0			0
$285$	−37.7830	−	4.59715i	−2.23807	−	0.272312i
$286$		0			0
$287$	−14.4476	+	4.30385i	−0.852813	+	0.254048i
$288$		0			0
$289$	12.2407	+	7.06720i	0.720044	+	0.415717i
$290$		0			0
$291$	−0.549859	−	0.952384i	−0.0322333	−	0.0558298i
$292$		0			0
$293$	0.297685	−	0.297685i	0.0173909	−	0.0173909i	−0.698358	−	0.715749i	$-0.746086\pi$
$293$	0.297685	−	0.297685i	0.0173909	−	0.0173909i	0.715749	+	0.698358i	$0.246086\pi$
$294$		0			0
$295$	−4.28845	+	10.6479i	−0.249683	+	0.619943i
$296$		0			0
$297$	−0.817629	+	3.05143i	−0.0474436	+	0.177062i
$298$		0			0
$299$	15.7236	−	27.2341i	0.909321	−	1.57499i
$300$		0			0
$301$	6.06250	−	11.2070i	0.349436	−	0.645959i
$302$		0			0
$303$	−28.4616	+	7.62627i	−1.63508	+	0.438118i
$304$		0			0
$305$	2.25086	+	15.8893i	0.128884	+	0.909820i
$306$		0			0
$307$	5.95890	+	5.95890i	0.340093	+	0.340093i	0.856402	−	0.516309i	$-0.172695\pi$
$307$	5.95890	+	5.95890i	0.340093	+	0.340093i	−0.516309	+	0.856402i	$0.672695\pi$
$308$		0			0
$309$			13.0637i			0.743167i
$310$		0			0
$311$	9.70989	−	5.60601i	0.550598	−	0.317888i	−0.198765	−	0.980047i	$-0.563693\pi$
$311$	9.70989	−	5.60601i	0.550598	−	0.317888i	0.749363	+	0.662159i	$0.230360\pi$
$312$		0			0
$313$	−0.0792166	−	0.295640i	−0.00447759	−	0.0167106i	0.963651	−	0.267165i	$-0.0860868\pi$
$313$	−0.0792166	−	0.295640i	−0.00447759	−	0.0167106i	−0.968128	+	0.250454i	$0.919420\pi$
$314$		0			0
$315$	14.5040	−	6.65614i	0.817206	−	0.375031i
$316$		0			0
$317$	5.75358	+	21.4727i	0.323153	+	1.20603i	0.916155	+	0.400824i	$0.131276\pi$
$317$	5.75358	+	21.4727i	0.323153	+	1.20603i	−0.593002	+	0.805201i	$0.702057\pi$
$318$		0			0
$319$	−5.04065	+	2.91022i	−0.282222	+	0.162941i
$320$		0			0
$321$		−	8.54664i		−	0.477027i
$322$		0			0
$323$	−8.53602	−	8.53602i	−0.474957	−	0.474957i
$324$		0			0
$325$	15.9618	+	26.4336i	0.885403	+	1.46627i
$326$		0			0
$327$	−15.4672	+	4.14442i	−0.855337	+	0.229187i
$328$		0			0
$329$	14.1260	+	22.9719i	0.778794	+	1.26648i
$330$		0			0
$331$	7.04614	−	12.2043i	0.387291	−	0.670808i	−0.604793	−	0.796383i	$-0.706744\pi$
$331$	7.04614	−	12.2043i	0.387291	−	0.670808i	0.992084	+	0.125575i	$0.0400775\pi$
$332$		0			0
$333$	0.606728	−	2.26434i	0.0332485	−	0.124085i
$334$		0			0
$335$	−6.45307	−	15.1563i	−0.352569	−	0.828076i
$336$		0			0
$337$	19.3301	−	19.3301i	1.05298	−	1.05298i	0.0544630	−	0.998516i	$-0.482655\pi$
$337$	19.3301	−	19.3301i	1.05298	−	1.05298i	0.998516	−	0.0544630i	$-0.0173447\pi$
$338$		0			0
$339$	−9.70933	−	16.8170i	−0.527338	−	0.913377i
$340$		0			0
$341$	−8.31635	−	4.80145i	−0.450356	−	0.260013i
$342$		0			0
$343$	14.1385	+	11.9626i	0.763407	+	0.645918i
$344$		0			0
$345$	−16.7558	−	21.3981i	−0.902102	−	1.15203i
$346$		0			0
$347$	31.4736	+	8.43333i	1.68959	+	0.452725i	0.970285	−	0.241966i	$-0.0777922\pi$
$347$	31.4736	+	8.43333i	1.68959	+	0.452725i	0.719308	+	0.694691i	$0.244459\pi$
$348$		0			0
$349$	18.5313			0.991957			0.495978	−	0.868335i	$-0.334810\pi$
$349$	18.5313			0.991957			0.495978	+	0.868335i	$0.334810\pi$
$350$		0			0
$351$	4.45988			0.238051
$352$		0			0
$353$	−26.0688	−	6.98512i	−1.38750	−	0.371780i	−0.513662	−	0.857992i	$-0.671712\pi$
$353$	−26.0688	−	6.98512i	−1.38750	−	0.371780i	−0.873841	+	0.486212i	$0.838378\pi$
$354$		0			0
$355$	5.95508	+	7.60496i	0.316063	+	0.403630i
$356$		0			0
$357$	10.3990	+	2.47959i	0.550371	+	0.131234i
$358$		0			0
$359$	−21.1575	−	12.2153i	−1.11665	−	0.644698i	−0.176106	−	0.984371i	$-0.556350\pi$
$359$	−21.1575	−	12.2153i	−1.11665	−	0.644698i	−0.940543	+	0.339673i	$0.889683\pi$
$360$		0			0
$361$	−15.9270	−	27.5863i	−0.838261	−	1.45191i
$362$		0			0
$363$	13.7328	−	13.7328i	0.720784	−	0.720784i
$364$		0			0
$365$	−12.9345	−	30.3791i	−0.677022	−	1.59012i
$366$		0			0
$367$	−0.168542	+	0.629007i	−0.00879781	+	0.0328339i	−0.970185	−	0.242365i	$-0.922077\pi$
$367$	−0.168542	+	0.629007i	−0.00879781	+	0.0328339i	0.961387	+	0.275199i	$0.0887436\pi$
$368$		0			0
$369$	7.68480	−	13.3105i	0.400055	−	0.692915i
$370$		0			0
$371$	5.53125	−	0.153390i	0.287168	−	0.00796362i
$372$		0			0
$373$	0.0933104	−	0.0250025i	0.00483143	−	0.00129458i	−0.256403	−	0.966570i	$-0.582537\pi$
$373$	0.0933104	−	0.0250025i	0.00483143	−	0.00129458i	0.261234	+	0.965276i	$0.415871\pi$
$374$		0			0
$375$	26.3443	−	4.26136i	1.36041	−	0.220056i
$376$		0			0
$377$	5.81037	+	5.81037i	0.299249	+	0.299249i
$378$		0			0
$379$		−	10.4991i		−	0.539303i	−0.962958	−	0.269651i	$-0.913092\pi$
$379$		−	10.4991i		−	0.539303i	0.962958	−	0.269651i	$-0.0869085\pi$
$380$		0			0
$381$	−10.1623	+	5.86721i	−0.520631	+	0.300586i
$382$		0			0
$383$	2.86065	+	10.6761i	0.146172	+	0.545522i	0.999700	+	0.0244754i	$0.00779155\pi$
$383$	2.86065	+	10.6761i	0.146172	+	0.545522i	−0.853528	+	0.521047i	$0.825542\pi$
$384$		0			0
$385$	25.7673	+	2.41246i	1.31322	+	0.122950i
$386$		0			0
$387$	3.36223	+	12.5480i	0.170912	+	0.637852i
$388$		0			0
$389$	6.30536	−	3.64040i	0.319695	−	0.184576i	−0.331562	−	0.943433i	$-0.607576\pi$
$389$	6.30536	−	3.64040i	0.319695	−	0.184576i	0.651256	+	0.758858i	$0.274242\pi$
$390$		0			0
$391$		−	8.61981i		−	0.435923i
$392$		0			0
$393$	9.21608	+	9.21608i	0.464890	+	0.464890i
$394$		0			0
$395$	1.74789	+	12.3388i	0.0879459	+	0.620831i
$396$		0			0
$397$	23.7390	−	6.36084i	1.19142	−	0.319241i	0.391976	−	0.919976i	$-0.371792\pi$
$397$	23.7390	−	6.36084i	1.19142	−	0.319241i	0.799449	+	0.600734i	$0.205125\pi$
$398$		0			0
$399$	39.6108	+	21.4278i	1.98302	+	1.07273i
$400$		0			0
$401$	−6.84060	+	11.8483i	−0.341603	+	0.591674i	−0.984731	−	0.174085i	$-0.944303\pi$
$401$	−6.84060	+	11.8483i	−0.341603	+	0.591674i	0.643127	+	0.765759i	$0.277637\pi$
$402$		0			0
$403$	−3.50882	+	13.0951i	−0.174787	+	0.652314i
$404$		0			0
$405$	8.20011	−	20.3602i	0.407467	−	1.01171i
$406$		0			0
$407$	2.68818	−	2.68818i	0.133248	−	0.133248i
$408$		0			0
$409$	−6.44604	−	11.1649i	−0.318736	−	0.552067i	0.661489	−	0.749955i	$-0.269925\pi$
$409$	−6.44604	−	11.1649i	−0.318736	−	0.552067i	−0.980225	+	0.197888i	$0.936592\pi$
$410$		0			0
$411$	35.6879	+	20.6044i	1.76035	+	1.01634i
$412$		0			0
$413$	9.33411	−	9.86658i	0.459302	−	0.485503i
$414$		0			0
$415$	−0.854730	−	0.103997i	−0.0419570	−	0.00510501i
$416$		0			0
$417$	9.99421	+	2.67794i	0.489419	+	0.131139i
$418$		0			0
$419$	−8.27208			−0.404117			−0.202059	−	0.979373i	$-0.564763\pi$
$419$	−8.27208			−0.404117			−0.202059	+	0.979373i	$0.564763\pi$
$420$		0			0
$421$	−21.7954			−1.06224			−0.531121	−	0.847296i	$-0.678229\pi$
$421$	−21.7954			−1.06224			−0.531121	+	0.847296i	$0.678229\pi$
$422$		0			0
$423$	−26.5578	−	7.11613i	−1.29128	−	0.345998i
$424$		0			0
$425$	7.41180	+	4.08722i	0.359525	+	0.198259i
$426$		0			0
$427$	4.40419	−	18.4704i	0.213134	−	0.893845i
$428$		0			0
$429$	−55.8463	−	32.2429i	−2.69629	−	1.55670i
$430$		0			0
$431$	−0.922967	−	1.59863i	−0.0444578	−	0.0770031i	0.842940	−	0.538007i	$-0.180823\pi$
$431$	−0.922967	−	1.59863i	−0.0444578	−	0.0770031i	−0.887398	+	0.461004i	$0.847489\pi$
$432$		0			0
$433$	−28.5087	+	28.5087i	−1.37004	+	1.37004i	−0.509670	+	0.860370i	$0.670233\pi$
$433$	−28.5087	+	28.5087i	−1.37004	+	1.37004i	−0.860370	+	0.509670i	$0.829767\pi$
$434$		0			0
$435$	6.53393	−	2.78194i	0.313278	−	0.133384i
$436$		0			0
$437$	9.39827	−	35.0748i	0.449580	−	1.67786i
$438$		0			0
$439$	−10.1088	+	17.5090i	−0.482469	+	0.835660i	−0.999797	−	0.0201265i	$-0.993593\pi$
$439$	−10.1088	+	17.5090i	−0.482469	+	0.835660i	0.517329	+	0.855787i	$0.326926\pi$
$440$		0			0
$441$	−18.8532	+	1.04646i	−0.897770	+	0.0498315i
$442$		0			0
$443$	23.1032	−	6.19049i	1.09767	−	0.294119i	0.335853	−	0.941914i	$-0.390975\pi$
$443$	23.1032	−	6.19049i	1.09767	−	0.294119i	0.761815	+	0.647795i	$0.224309\pi$
$444$		0			0
$445$	7.94838	−	1.12596i	0.376789	−	0.0533754i
$446$		0			0
$447$	4.33708	+	4.33708i	0.205137	+	0.205137i
$448$		0			0
$449$		−	15.9935i		−	0.754782i	−0.926054	−	0.377391i	$-0.876821\pi$
$449$		−	15.9935i		−	0.754782i	0.926054	−	0.377391i	$-0.123179\pi$
$450$		0			0
$451$	21.5858	−	12.4626i	1.01644	−	0.586840i
$452$		0			0
$453$	0.637878	+	2.38059i	0.0299701	+	0.111850i
$454$		0			0
$455$	−6.12539	−	36.0194i	−0.287163	−	1.68862i
$456$		0			0
$457$	3.93478	+	14.6848i	0.184061	+	0.686925i	0.994830	+	0.101558i	$0.0323829\pi$
$457$	3.93478	+	14.6848i	0.184061	+	0.686925i	−0.810769	+	0.585367i	$0.800950\pi$
$458$		0			0
$459$	1.05869	−	0.611235i	0.0494154	−	0.0285300i
$460$		0			0
$461$			24.4079i			1.13679i	0.822756	+	0.568395i	$0.192436\pi$
$461$			24.4079i			1.13679i	−0.822756	+	0.568395i	$0.807564\pi$
$462$		0			0
$463$	5.25987	+	5.25987i	0.244447	+	0.244447i	0.818687	−	0.574240i	$-0.194702\pi$
$463$	5.25987	+	5.25987i	0.244447	+	0.244447i	−0.574240	+	0.818687i	$0.694702\pi$
$464$		0			0
$465$	9.36492	+	7.04090i	0.434288	+	0.326514i
$466$		0			0
$467$	−35.7255	+	9.57262i	−1.65318	+	0.442968i	−0.960501	−	0.278278i	$-0.910236\pi$
$467$	−35.7255	+	9.57262i	−1.65318	+	0.442968i	−0.692679	+	0.721246i	$0.743570\pi$
$468$		0			0
$469$	0.540307	+	19.4834i	0.0249490	+	0.899662i
$470$		0			0
$471$	21.7261	−	37.6307i	1.00109	−	1.73393i
$472$		0			0
$473$	−5.45260	+	20.3494i	−0.250711	+	0.935666i
$474$		0			0
$475$	25.7030	+	24.7124i	1.17933	+	1.13388i
$476$		0			0
$477$	−3.98915	+	3.98915i	−0.182651	+	0.182651i
$478$		0			0
$479$	−11.0150	−	19.0786i	−0.503289	−	0.871722i	−0.999993	−	0.00380219i	$-0.998790\pi$
$479$	−11.0150	−	19.0786i	−0.503289	−	0.871722i	0.496704	−	0.867920i	$-0.334544\pi$
$480$		0			0
$481$	−4.64801	−	2.68353i	−0.211931	−	0.122359i
$482$		0			0
$483$	9.18076	+	30.8189i	0.417739	+	1.40231i
$484$		0			0
$485$	−0.124431	+	1.02267i	−0.00565010	+	0.0464370i
$486$		0			0
$487$	14.4450	+	3.87053i	0.654566	+	0.175390i	0.570792	−	0.821094i	$-0.306636\pi$
$487$	14.4450	+	3.87053i	0.654566	+	0.175390i	0.0837736	+	0.996485i	$0.473303\pi$
$488$		0			0
$489$	20.8570			0.943187
$490$		0			0
$491$	−13.9698			−0.630449			−0.315224	−	0.949017i	$-0.602080\pi$
$491$	−13.9698			−0.630449			−0.315224	+	0.949017i	$0.602080\pi$
$492$		0			0
$493$	2.17559	+	0.582948i	0.0979838	+	0.0262547i
$494$		0			0
$495$	−20.7744	+	16.2675i	−0.933742	+	0.731168i
$496$		0			0
$497$	−3.26288	−	10.9531i	−0.146360	−	0.491316i
$498$		0			0
$499$	−5.90449	−	3.40896i	−0.264321	−	0.152606i	0.361983	−	0.932185i	$-0.382100\pi$
$499$	−5.90449	−	3.40896i	−0.264321	−	0.152606i	−0.626304	+	0.779579i	$0.715433\pi$
$500$		0			0
$501$	−20.8923	−	36.1865i	−0.933400	−	1.61670i
$502$		0			0
$503$	−13.8531	+	13.8531i	−0.617679	+	0.617679i	−0.944936	−	0.327256i	$-0.893876\pi$
$503$	−13.8531	+	13.8531i	−0.617679	+	0.617679i	0.327256	+	0.944936i	$0.393876\pi$
$504$		0			0
$505$	25.6046	+	10.3123i	1.13939	+	0.458892i
$506$		0			0
$507$	−15.5314	+	57.9640i	−0.689774	+	2.57427i
$508$		0			0
$509$	−22.4079	+	38.8116i	−0.993213	+	1.72030i	−0.395882	+	0.918301i	$0.629561\pi$
$509$	−22.4079	+	38.8116i	−0.993213	+	1.72030i	−0.597332	+	0.801994i	$0.703772\pi$
$510$		0			0
$511$	1.08299	+	39.0525i	0.0479085	+	1.72758i
$512$		0			0
$513$	4.97434	−	1.33287i	0.219623	−	0.0588477i
$514$		0			0
$515$	7.35429	−	9.78176i	0.324069	−	0.431036i
$516$		0			0
$517$	−31.5289	−	31.5289i	−1.38664	−	1.38664i
$518$		0			0
$519$			6.88642i			0.302280i
$520$		0			0
$521$	31.4574	−	18.1620i	1.37818	−	0.795690i	0.386236	−	0.922400i	$-0.373775\pi$
$521$	31.4574	−	18.1620i	1.37818	−	0.795690i	0.991940	+	0.126710i	$0.0404418\pi$
$522$		0			0
$523$	−4.05288	−	15.1255i	−0.177220	−	0.661394i	−0.996163	−	0.0875187i	$-0.972106\pi$
$523$	−4.05288	−	15.1255i	−0.177220	−	0.661394i	0.818943	−	0.573875i	$-0.194560\pi$
$524$		0			0
$525$	−30.8530	−	6.71911i	−1.34654	−	0.293246i
$526$		0			0
$527$	0.961782	+	3.58942i	0.0418959	+	0.156358i
$528$		0			0
$529$	2.53622	−	1.46429i	0.110271	−	0.0636647i
$530$		0			0
$531$			13.8476i			0.600934i
$532$		0			0
$533$	−24.8821	−	24.8821i	−1.07776	−	1.07776i
$534$		0			0
$535$	−4.81139	+	6.39951i	−0.208015	+	0.276675i
$536$		0			0
$537$	17.2389	−	4.61916i	0.743916	−	0.199332i
$538$		0			0
$539$	−27.3269	−	13.8176i	−1.17705	−	0.595165i
$540$		0			0
$541$	−7.57826	+	13.1259i	−0.325815	+	0.564328i	−0.981677	−	0.190553i	$-0.938972\pi$
$541$	−7.57826	+	13.1259i	−0.325815	+	0.564328i	0.655862	+	0.754881i	$0.272305\pi$
$542$		0			0
$543$	13.4249	−	50.1024i	0.576118	−	2.15010i
$544$		0			0
$545$	13.9146	+	5.60412i	0.596035	+	0.240054i
$546$		0			0
$547$	24.0863	−	24.0863i	1.02985	−	1.02985i	0.0303138	−	0.999540i	$-0.490349\pi$
$547$	24.0863	−	24.0863i	1.02985	−	1.02985i	0.999540	−	0.0303138i	$-0.00965066\pi$
$548$		0			0
$549$	9.67964	+	16.7656i	0.413117	+	0.715540i
$550$		0			0
$551$	8.21710	+	4.74414i	0.350060	+	0.202107i
$552$		0			0
$553$	3.42004	−	14.3431i	0.145435	−	0.609929i
$554$		0			0
$555$	−3.65198	+	2.85969i	−0.155018	+	0.121387i
$556$		0			0
$557$	25.2878	+	6.77586i	1.07148	+	0.287102i	0.751101	−	0.660187i	$-0.229523\pi$
$557$	25.2878	+	6.77586i	1.07148	+	0.287102i	0.320379	+	0.947289i	$0.396190\pi$
$558$		0			0
$559$	29.7420			1.25795
$560$		0			0
$561$	−17.6758			−0.746273
$562$		0			0
$563$	4.24428	+	1.13725i	0.178875	+	0.0479294i	0.347145	−	0.937812i	$-0.387151\pi$
$563$	4.24428	+	1.13725i	0.178875	+	0.0479294i	−0.168270	+	0.985741i	$0.553818\pi$
$564$		0			0
$565$	−2.19717	+	18.0581i	−0.0924358	+	0.759711i
$566$		0			0
$567$	−17.8481	+	18.8663i	−0.749550	+	0.792308i
$568$		0			0
$569$	−9.41275	−	5.43445i	−0.394603	−	0.227824i	0.289550	−	0.957163i	$-0.406494\pi$
$569$	−9.41275	−	5.43445i	−0.394603	−	0.227824i	−0.684153	+	0.729339i	$0.739828\pi$
$570$		0			0
$571$	−22.5354	−	39.0325i	−0.943078	−	1.63346i	−0.759555	−	0.650444i	$-0.774583\pi$
$571$	−22.5354	−	39.0325i	−0.943078	−	1.63346i	−0.183523	−	0.983015i	$-0.558750\pi$
$572$		0			0
$573$	19.3548	−	19.3548i	0.808560	−	0.808560i
$574$		0			0
$575$	0.500131	+	25.4551i	0.0208569	+	1.06155i
$576$		0			0
$577$	6.05442	−	22.5954i	0.252049	−	0.940659i	−0.717660	−	0.696394i	$-0.754787\pi$
$577$	6.05442	−	22.5954i	0.252049	−	0.940659i	0.969709	−	0.244265i	$-0.0785467\pi$
$578$		0			0
$579$	6.62753	−	11.4792i	0.275431	−	0.477060i
$580$		0			0
$581$	0.896079	+	0.484740i	0.0371756	+	0.0201104i
$582$		0			0
$583$	−8.83721	+	2.36792i	−0.366000	+	0.0980693i
$584$		0			0
$585$	29.7742	+	22.3853i	1.23101	+	0.925519i
$586$		0			0
$587$	−13.2002	−	13.2002i	−0.544831	−	0.544831i	0.380110	−	0.924941i	$-0.375886\pi$
$587$	−13.2002	−	13.2002i	−0.544831	−	0.544831i	−0.924941	+	0.380110i	$0.875886\pi$
$588$		0			0
$589$			15.6543i			0.645025i
$590$		0			0
$591$	36.8332	−	21.2657i	1.51512	−	0.874753i
$592$		0			0
$593$	−0.815375	−	3.04302i	−0.0334835	−	0.124962i	0.947161	−	0.320758i	$-0.103938\pi$
$593$	−0.815375	−	3.04302i	−0.0334835	−	0.124962i	−0.980645	+	0.195796i	$0.937271\pi$
$594$		0			0
$595$	−6.39058	−	7.71082i	−0.261988	−	0.316113i
$596$		0			0
$597$	−2.50101	−	9.33389i	−0.102360	−	0.382011i
$598$		0			0
$599$	14.3732	−	8.29838i	0.587274	−	0.339063i	−0.176745	−	0.984257i	$-0.556557\pi$
$599$	14.3732	−	8.29838i	0.587274	−	0.339063i	0.764019	+	0.645194i	$0.223223\pi$
$600$		0			0
$601$		−	10.4871i		−	0.427778i	−0.976858	−	0.213889i	$-0.931387\pi$
$601$		−	10.4871i		−	0.427778i	0.976858	−	0.213889i	$-0.0686131\pi$
$602$		0			0
$603$	−14.0515	−	14.0515i	−0.572222	−	0.572222i
$604$		0			0
$605$	−18.0137	+	2.55180i	−0.732362	+	0.103745i
$606$		0			0
$607$	−31.0456	+	8.31863i	−1.26010	+	0.337643i	−0.826230	−	0.563332i	$-0.809519\pi$
$607$	−31.0456	+	8.31863i	−1.26010	+	0.337643i	−0.433870	+	0.900975i	$0.642852\pi$
$608$		0			0
$609$	−8.39940	+	0.232929i	−0.340361	+	0.00943874i
$610$		0			0
$611$	−31.4744	+	54.5152i	−1.27332	+	2.20545i
$612$		0			0
$613$	6.07304	−	22.6649i	0.245288	−	0.915427i	−0.727951	−	0.685630i	$-0.759527\pi$
$613$	6.07304	−	22.6649i	0.245288	−	0.915427i	0.973238	−	0.229797i	$-0.0738064\pi$
$614$		0			0
$615$	−27.9806	+	11.9133i	−1.12829	+	0.480390i
$616$		0			0
$617$	−24.6695	+	24.6695i	−0.993158	+	0.993158i	−0.999977	−	0.00681844i	$-0.997830\pi$
$617$	−24.6695	+	24.6695i	−0.993158	+	0.993158i	0.00681844	+	0.999977i	$0.497830\pi$
$618$		0			0
$619$	12.1208	+	20.9938i	0.487174	+	0.843811i	0.999891	−	0.0147470i	$-0.00469428\pi$
$619$	12.1208	+	20.9938i	0.487174	+	0.843811i	−0.512717	+	0.858558i	$0.671361\pi$
$620$		0			0
$621$	3.18456	+	1.83861i	0.127792	+	0.0737808i
$622$		0			0
$623$	−9.23951	−	2.20312i	−0.370173	−	0.0882663i
$624$		0			0
$625$	−22.1249	−	11.6399i	−0.884997	−	0.465597i
$626$		0			0
$627$	−71.9245	−	19.2721i	−2.87239	−	0.769654i
$628$		0			0
$629$	−1.47113			−0.0586579
$630$		0			0
$631$	25.2348			1.00458			0.502291	−	0.864699i	$-0.332491\pi$
$631$	25.2348			1.00458			0.502291	+	0.864699i	$0.332491\pi$
$632$		0			0
$633$	49.1586	+	13.1720i	1.95388	+	0.523541i
$634$		0			0
$635$	10.9123	+	1.32772i	0.433040	+	0.0526890i
$636$		0			0
$637$	−8.85748	+	42.3135i	−0.350946	+	1.67652i
$638$		0			0
$639$	10.0911	+	5.82608i	0.399197	+	0.230476i
$640$		0			0
$641$	18.0215	+	31.2142i	0.711808	+	1.23289i	0.964178	+	0.265257i	$0.0854568\pi$
$641$	18.0215	+	31.2142i	0.711808	+	1.23289i	−0.252370	+	0.967631i	$0.581210\pi$
$642$		0			0
$643$	16.5722	−	16.5722i	0.653545	−	0.653545i	−0.300300	−	0.953845i	$-0.597087\pi$
$643$	16.5722	−	16.5722i	0.653545	−	0.653545i	0.953845	+	0.300300i	$0.0970868\pi$
$644$		0			0
$645$	9.60281	−	23.8430i	0.378110	−	0.938816i
$646$		0			0
$647$	−7.11698	+	26.5609i	−0.279797	+	1.04422i	0.672760	+	0.739860i	$0.265108\pi$
$647$	−7.11698	+	26.5609i	−0.279797	+	1.04422i	−0.952558	+	0.304358i	$0.901558\pi$
$648$		0			0
$649$	−11.2285	+	19.4483i	−0.440755	+	0.763411i
$650$		0			0
$651$	−7.26172	−	11.8091i	−0.284609	−	0.462834i
$652$		0			0
$653$	−11.5652	+	3.09889i	−0.452581	+	0.121269i	−0.477907	−	0.878410i	$-0.658604\pi$
$653$	−11.5652	+	3.09889i	−0.452581	+	0.121269i	0.0253256	+	0.999679i	$0.491938\pi$
$654$		0			0
$655$	−1.71251	−	12.0890i	−0.0669134	−	0.472357i
$656$		0			0
$657$	−28.1648	−	28.1648i	−1.09881	−	1.09881i
$658$		0			0
$659$			46.6055i			1.81549i	0.419521	+	0.907746i	$0.362198\pi$
$659$			46.6055i			1.81549i	−0.419521	+	0.907746i	$0.637802\pi$
$660$		0			0
$661$	2.27963	−	1.31614i	0.0886673	−	0.0511921i	−0.455011	−	0.890486i	$-0.650365\pi$
$661$	2.27963	−	1.31614i	0.0886673	−	0.0511921i	0.543678	+	0.839294i	$0.317031\pi$
$662$		0			0
$663$	6.45860	+	24.1038i	0.250831	+	0.936115i
$664$		0			0
$665$	−17.5967	−	38.3438i	−0.682370	−	1.48691i
$666$		0			0
$667$	1.75352	+	6.54423i	0.0678966	+	0.253394i
$668$		0			0
$669$	−57.7816	+	33.3602i	−2.23397	+	1.28978i
$670$		0			0
$671$			31.3953i			1.21200i
$672$		0			0
$673$	−22.7177	−	22.7177i	−0.875704	−	0.875704i	0.117383	−	0.993087i	$-0.462549\pi$
$673$	−22.7177	−	22.7177i	−0.875704	−	0.875704i	−0.993087	+	0.117383i	$0.962549\pi$
$674$		0			0
$675$	−3.09095	+	1.86646i	−0.118971	+	0.0718402i
$676$		0			0
$677$	−10.0751	+	2.69961i	−0.387216	+	0.103754i	−0.447175	−	0.894447i	$-0.647570\pi$
$677$	−10.0751	+	2.69961i	−0.387216	+	0.103754i	0.0599584	+	0.998201i	$0.480903\pi$
$678$		0			0
$679$	0.579983	−	1.07214i	0.0222577	−	0.0411450i
$680$		0			0
$681$	−3.50863	+	6.07713i	−0.134451	+	0.232876i
$682$		0			0
$683$	2.50520	−	9.34955i	0.0958589	−	0.357750i	−0.901289	−	0.433218i	$-0.857378\pi$
$683$	2.50520	−	9.34955i	0.0958589	−	0.357750i	0.997148	+	0.0754672i	$0.0240448\pi$
$684$		0			0
$685$	−15.1228	−	35.5188i	−0.577812	−	1.35710i
$686$		0			0
$687$	40.6089	−	40.6089i	1.54933	−	1.54933i
$688$		0			0
$689$	6.45809	+	11.1857i	0.246034	+	0.426143i
$690$		0			0
$691$	19.8093	+	11.4369i	0.753583	+	0.435081i	0.826987	−	0.562221i	$-0.190053\pi$
$691$	19.8093	+	11.4369i	0.753583	+	0.435081i	−0.0734041	+	0.997302i	$0.523386\pi$
$692$		0			0
$693$	29.9207	−	8.91320i	1.13659	−	0.338584i
$694$		0			0
$695$	−5.97585	−	7.63149i	−0.226677	−	0.289479i
$696$		0			0
$697$	−9.31666	−	2.49639i	−0.352894	−	0.0945576i
$698$		0			0
$699$	−5.87389			−0.222171
$700$		0			0
$701$	−47.3309			−1.78766			−0.893831	−	0.448403i	$-0.851993\pi$
$701$	−47.3309			−1.78766			−0.893831	+	0.448403i	$0.851993\pi$
$702$		0			0
$703$	−5.98618	−	1.60399i	−0.225773	−	0.0604957i
$704$		0			0
$705$	33.5405	+	42.8330i	1.26321	+	1.61319i
$706$		0			0
$707$	−23.7259	−	22.4455i	−0.892304	−	0.844149i
$708$		0			0
$709$	37.1759	+	21.4635i	1.39617	+	0.806079i	0.993989	−	0.109480i	$-0.0349187\pi$
$709$	37.1759	+	21.4635i	1.39617	+	0.806079i	0.402182	+	0.915560i	$0.368252\pi$
$710$		0			0
$711$	7.51667	+	13.0192i	0.281897	+	0.488260i
$712$		0			0
$713$	−7.90399	+	7.90399i	−0.296007	+	0.296007i
$714$		0			0
$715$	23.6650	+	55.5818i	0.885020	+	2.07864i
$716$		0			0
$717$	−9.56048	+	35.6802i	−0.357043	+	1.33250i
$718$		0			0
$719$	10.8241	−	18.7480i	0.403673	−	0.699181i	−0.590493	−	0.807042i	$-0.701067\pi$
$719$	10.8241	−	18.7480i	0.403673	−	0.699181i	0.994166	+	0.107861i	$0.0344002\pi$
$720$		0			0
$721$	−12.3347	+	7.58494i	−0.459368	+	0.282478i
$722$		0			0
$723$	36.9431	−	9.89888i	1.37393	−	0.368143i
$724$		0			0
$725$	−6.45856	−	1.59527i	−0.239865	−	0.0592470i
$726$		0			0
$727$	5.06759	+	5.06759i	0.187947	+	0.187947i	0.794808	−	0.606861i	$-0.207572\pi$
$727$	5.06759	+	5.06759i	0.187947	+	0.187947i	−0.606861	+	0.794808i	$0.707572\pi$
$728$		0			0
$729$		−	21.3073i		−	0.789159i
$730$		0			0
$731$	7.06019	−	4.07620i	0.261130	−	0.150764i
$732$		0			0
$733$	−8.20019	−	30.6035i	−0.302881	−	1.13037i	−0.934754	−	0.355295i	$-0.884380\pi$
$733$	−8.20019	−	30.6035i	−0.302881	−	1.13037i	0.631873	−	0.775072i	$-0.282286\pi$
$734$		0			0
$735$	31.0612	+	20.7624i	1.14571	+	0.765834i
$736$		0			0
$737$	−8.34085	−	31.1285i	−0.307239	−	1.14663i
$738$		0			0
$739$	−14.6237	+	8.44299i	−0.537941	+	0.310580i	−0.744244	−	0.667908i	$-0.767190\pi$
$739$	−14.6237	+	8.44299i	−0.537941	+	0.310580i	0.206303	+	0.978488i	$0.433857\pi$
$740$		0			0
$741$			105.123i			3.86177i
$742$		0			0
$743$	−23.6519	−	23.6519i	−0.867703	−	0.867703i	0.124515	−	0.992218i	$-0.460262\pi$
$743$	−23.6519	−	23.6519i	−0.867703	−	0.867703i	−0.992218	+	0.124515i	$0.960262\pi$
$744$		0			0
$745$	−0.805907	−	5.68908i	−0.0295262	−	0.208432i
$746$		0			0
$747$	−1.00331	+	0.268835i	−0.0367090	+	0.00983615i
$748$		0			0
$749$	8.06971	−	4.96229i	0.294861	−	0.181318i
$750$		0			0
$751$	4.13856	−	7.16820i	0.151018	−	0.261571i	−0.780584	−	0.625051i	$-0.785078\pi$
$751$	4.13856	−	7.16820i	0.151018	−	0.261571i	0.931602	+	0.363480i	$0.118411\pi$
$752$		0			0
$753$	0.366228	−	1.36678i	0.0133461	−	0.0498083i
$754$		0			0
$755$	0.862545	−	2.14163i	0.0313912	−	0.0779418i
$756$		0			0
$757$	21.6103	−	21.6103i	0.785439	−	0.785439i	−0.195304	−	0.980743i	$-0.562569\pi$
$757$	21.6103	−	21.6103i	0.785439	−	0.785439i	0.980743	+	0.195304i	$0.0625693\pi$
$758$		0			0
$759$	−26.5846	−	46.0459i	−0.964960	−	1.67136i
$760$		0			0
$761$	−18.9354	−	10.9324i	−0.686408	−	0.396298i	0.115857	−	0.993266i	$-0.463038\pi$
$761$	−18.9354	−	10.9324i	−0.686408	−	0.396298i	−0.802265	+	0.596968i	$0.796372\pi$
$762$		0			0
$763$	−12.8936	−	12.1978i	−0.466779	−	0.441589i
$764$		0			0
$765$	10.1358	+	1.23324i	0.366459	+	0.0445880i
$766$		0			0
$767$	30.6236	+	8.20558i	1.10576	+	0.296286i
$768$		0			0
$769$	−24.3594			−0.878421			−0.439211	−	0.898384i	$-0.644742\pi$
$769$	−24.3594			−0.878421			−0.439211	+	0.898384i	$0.644742\pi$
$770$		0			0
$771$	46.2987			1.66741
$772$		0			0
$773$	17.9762	+	4.81671i	0.646560	+	0.173245i	0.567173	−	0.823599i	$-0.308037\pi$
$773$	17.9762	+	4.81671i	0.646560	+	0.173245i	0.0793867	+	0.996844i	$0.474704\pi$
$774$		0			0
$775$	−3.04850	−	10.5441i	−0.109505	−	0.378755i
$776$		0			0
$777$	5.25982	−	1.56687i	0.188695	−	0.0562111i
$778$		0			0
$779$	−35.1885	−	20.3161i	−1.26076	−	0.727900i
$780$		0			0
$781$	9.44827	+	16.3649i	0.338086	+	0.585582i
$782$		0			0
$783$	−0.679423	+	0.679423i	−0.0242806	+	0.0242806i
$784$		0			0
$785$	−37.4524	+	15.9461i	−1.33673	+	0.569139i
$786$		0			0
$787$	6.78612	−	25.3262i	0.241899	−	0.902780i	−0.733018	−	0.680210i	$-0.761889\pi$
$787$	6.78612	−	25.3262i	0.241899	−	0.902780i	0.974917	−	0.222570i	$-0.0714446\pi$
$788$		0			0
$789$	30.3706	−	52.6034i	1.08122	−	1.87273i
$790$		0			0
$791$	10.2412	−	18.9317i	0.364137	−	0.673134i
$792$		0			0
$793$	42.8126	−	11.4716i	1.52032	−	0.407369i
$794$		0			0
$795$	11.0523	−	1.56565i	0.391984	−	0.0555279i
$796$		0			0
$797$	−12.0225	−	12.0225i	−0.425859	−	0.425859i	0.461356	−	0.887215i	$-0.347363\pi$
$797$	−12.0225	−	12.0225i	−0.425859	−	0.425859i	−0.887215	+	0.461356i	$0.847363\pi$
$798$		0			0
$799$			17.2545i			0.610420i
$800$		0			0
$801$	8.38674	−	4.84208i	0.296331	−	0.171087i
$802$		0			0
$803$	−16.7183	−	62.3937i	−0.589978	−	2.20183i
$804$		0			0
$805$	10.4754	−	28.2448i	0.369208	−	0.995497i
$806$		0			0
$807$	7.62865	+	28.4705i	0.268541	+	1.00221i
$808$		0			0
$809$	34.2965	−	19.8011i	1.20580	−	0.696169i	0.243961	−	0.969785i	$-0.421553\pi$
$809$	34.2965	−	19.8011i	1.20580	−	0.696169i	0.961839	+	0.273616i	$0.0882196\pi$
$810$		0			0
$811$			25.3370i			0.889703i	0.895604	+	0.444852i	$0.146744\pi$
$811$			25.3370i			0.889703i	−0.895604	+	0.444852i	$0.853256\pi$
$812$		0			0
$813$	19.6608	+	19.6608i	0.689533	+	0.689533i
$814$		0			0
$815$	−15.6172	−	11.7416i	−0.547047	−	0.411291i
$816$		0			0
$817$	33.1729	−	8.88865i	1.16057	−	0.310974i
$818$		0			0
$819$	−23.0874	−	37.5449i	−0.806738	−	1.31192i
$820$		0			0
$821$	24.0406	−	41.6395i	0.839022	−	1.45323i	−0.0516917	−	0.998663i	$-0.516461\pi$
$821$	24.0406	−	41.6395i	0.839022	−	1.45323i	0.890713	−	0.454565i	$-0.150205\pi$
$822$		0			0
$823$	−1.00438	+	3.74840i	−0.0350105	+	0.130661i	−0.981219	−	0.192896i	$-0.938212\pi$
$823$	−1.00438	+	3.74840i	−0.0350105	+	0.130661i	0.946209	+	0.323557i	$0.104879\pi$
$824$		0			0
$825$	52.1984	−	1.02557i	1.81731	−	0.0357057i
$826$		0			0
$827$	16.8597	−	16.8597i	0.586268	−	0.586268i	−0.350351	−	0.936619i	$-0.613938\pi$
$827$	16.8597	−	16.8597i	0.586268	−	0.586268i	0.936619	+	0.350351i	$0.113938\pi$
$828$		0			0
$829$	−8.10906	−	14.0453i	−0.281639	−	0.487813i	0.690149	−	0.723667i	$-0.257545\pi$
$829$	−8.10906	−	14.0453i	−0.281639	−	0.487813i	−0.971789	+	0.235853i	$0.924211\pi$
$830$		0			0
$831$	−39.0722	−	22.5583i	−1.35540	−	0.782540i
$832$		0			0
$833$	3.69655	+	11.2583i	0.128078	+	0.390078i
$834$		0			0
$835$	−4.72783	+	38.8571i	−0.163613	+	1.34470i
$836$		0			0
$837$	−1.53125	−	0.410297i	−0.0529277	−	0.0141819i
$838$		0			0
$839$	−2.13469			−0.0736978			−0.0368489	−	0.999321i	$-0.511732\pi$
$839$	−2.13469			−0.0736978			−0.0368489	+	0.999321i	$0.511732\pi$
$840$		0			0
$841$	27.2297			0.938955
$842$		0			0
$843$	−50.6760	−	13.5786i	−1.74537	−	0.467671i
$844$		0			0
$845$	44.2608	−	34.6585i	1.52262	−	1.19229i
$846$		0			0
$847$	20.9399	+	4.99302i	0.719502	+	0.171562i
$848$		0			0
$849$	49.5705	+	28.6196i	1.70126	+	0.982220i
$850$		0			0
$851$	−2.21260	−	3.83233i	−0.0758469	−	0.131371i
$852$		0			0
$853$	12.2640	−	12.2640i	0.419910	−	0.419910i	−0.465263	−	0.885173i	$-0.654040\pi$
$853$	12.2640	−	12.2640i	0.419910	−	0.419910i	0.885173	+	0.465263i	$0.154040\pi$
$854$		0			0
$855$	39.8988	+	16.0693i	1.36451	+	0.549559i
$856$		0			0
$857$	−7.15985	+	26.7209i	−0.244576	+	0.912769i	0.729021	+	0.684492i	$0.239976\pi$
$857$	−7.15985	+	26.7209i	−0.244576	+	0.912769i	−0.973596	+	0.228277i	$0.926691\pi$
$858$		0			0
$859$	−10.3098	+	17.8570i	−0.351765	+	0.609274i	−0.986559	−	0.163407i	$-0.947752\pi$
$859$	−10.3098	+	17.8570i	−0.351765	+	0.609274i	0.634794	+	0.772681i	$0.281085\pi$
$860$		0			0
$861$	35.9692	−	0.997482i	1.22583	−	0.0339941i
$862$		0			0
$863$	28.5311	−	7.64489i	0.971211	−	0.260235i	0.261872	−	0.965103i	$-0.415660\pi$
$863$	28.5311	−	7.64489i	0.971211	−	0.260235i	0.709339	+	0.704868i	$0.248994\pi$
$864$		0			0
$865$	3.87676	−	5.15638i	0.131814	−	0.175322i
$866$		0			0
$867$	−23.8563	−	23.8563i	−0.810202	−	0.810202i
$868$		0			0
$869$			24.3799i			0.827030i
$870$		0			0
$871$	−39.4010	+	22.7482i	−1.33505	+	0.770793i
$872$		0			0
$873$	0.321656	+	1.20044i	0.0108864	+	0.0406286i
$874$		0			0
$875$	19.3194	+	22.4000i	0.653115	+	0.757259i
$876$		0			0
$877$	1.00650	+	3.75632i	0.0339872	+	0.126842i	0.980835	−	0.194840i	$-0.0624186\pi$
$877$	1.00650	+	3.75632i	0.0339872	+	0.126842i	−0.946848	+	0.321681i	$0.895752\pi$
$878$		0			0
$879$	−0.870248	+	0.502438i	−0.0293527	+	0.0169468i
$880$		0			0
$881$			17.0033i			0.572854i	0.958102	+	0.286427i	$0.0924676\pi$
$881$			17.0033i			0.572854i	−0.958102	+	0.286427i	$0.907532\pi$
$882$		0			0
$883$	−19.1776	−	19.1776i	−0.645377	−	0.645377i	0.306496	−	0.951872i	$-0.400844\pi$
$883$	−19.1776	−	19.1776i	−0.645377	−	0.645377i	−0.951872	+	0.306496i	$0.900844\pi$
$884$		0			0
$885$	16.4655	−	21.9004i	0.553483	−	0.736174i
$886$		0			0
$887$	20.3195	−	5.44459i	0.682262	−	0.182812i	0.0989899	−	0.995088i	$-0.468439\pi$
$887$	20.3195	−	5.44459i	0.682262	−	0.182812i	0.583272	+	0.812277i	$0.301772\pi$
$888$		0			0
$889$	−11.4402	−	6.18865i	−0.383691	−	0.207561i
$890$		0			0
$891$	21.4704	−	37.1877i	0.719284	−	1.24584i
$892$		0			0
$893$	−18.8127	+	70.2101i	−0.629544	+	2.34949i
$894$		0			0
$895$	−15.5085	−	6.24607i	−0.518391	−	0.208783i
$896$		0			0
$897$	−53.0772	+	53.0772i	−1.77220	+	1.77220i
$898$		0			0
$899$	−1.46039	−	2.52946i	−0.0487066	−	0.0843623i
$900$		0			0
$901$	3.06605	+	1.77019i	0.102145	+	0.0589735i
$902$		0			0
$903$	−20.9012	+	22.0935i	−0.695548	+	0.735226i
$904$		0			0
$905$	−38.2577	+	29.9578i	−1.27173	+	0.995831i
$906$		0			0
$907$	23.1357	+	6.19919i	0.768208	+	0.205841i	0.621580	−	0.783351i	$-0.286491\pi$
$907$	23.1357	+	6.19919i	0.768208	+	0.205841i	0.146629	+	0.989192i	$0.453158\pi$
$908$		0			0
$909$	33.2989			1.10446
$910$		0			0
$911$	−36.5580			−1.21122			−0.605611	−	0.795761i	$-0.707071\pi$
$911$	−36.5580			−1.21122			−0.605611	+	0.795761i	$0.707071\pi$
$912$		0			0
$913$	−1.62708	−	0.435975i	−0.0538485	−	0.0144287i
$914$		0			0
$915$	4.62659	−	38.0250i	0.152950	−	1.25707i
$916$		0			0
$917$	−3.35082	+	14.0528i	−0.110654	+	0.464063i
$918$		0			0
$919$	−18.5274	−	10.6968i	−0.611161	−	0.352854i	0.162259	−	0.986748i	$-0.448122\pi$
$919$	−18.5274	−	10.6968i	−0.611161	−	0.352854i	−0.773420	+	0.633894i	$0.781455\pi$
$920$		0			0
$921$	−10.0575	−	17.4202i	−0.331407	−	0.574014i
$922$		0			0
$923$	18.8639	−	18.8639i	0.620912	−	0.620912i
$924$		0			0
$925$	4.34440	−	0.0853567i	0.142843	−	0.00280651i
$926$		0			0
$927$	3.82099	−	14.2601i	0.125498	−	0.468364i
$928$		0			0
$929$	−3.04513	+	5.27431i	−0.0999073	+	0.173045i	−0.911646	−	0.410976i	$-0.865188\pi$
$929$	−3.04513	+	5.27431i	−0.0999073	+	0.173045i	0.811739	+	0.584021i	$0.198521\pi$
$930$		0			0
$931$	2.76650	+	49.8416i	0.0906684	+	1.63349i
$932$		0			0
$933$	−25.8505	+	6.92661i	−0.846306	+	0.226767i
$934$		0			0
$935$	13.2352	+	9.95071i	0.432837	+	0.325423i
$936$		0			0
$937$	−35.5732	−	35.5732i	−1.16213	−	1.16213i	−0.984009	−	0.178117i	$-0.943000\pi$
$937$	−35.5732	−	35.5732i	−1.16213	−	1.16213i	−0.178117	−	0.984009i	$-0.557000\pi$
$938$		0			0
$939$			0.730567i			0.0238412i
$940$		0			0
$941$	42.4670	−	24.5184i	1.38439	−	0.799276i	0.391711	−	0.920088i	$-0.371883\pi$
$941$	42.4670	−	24.5184i	1.38439	−	0.799276i	0.992675	+	0.120813i	$0.0385500\pi$
$942$		0			0
$943$	−7.50920	−	28.0247i	−0.244533	−	0.912610i
$944$		0			0
$945$	4.21185	−	0.716259i	0.137012	−	0.0232999i
$946$		0			0
$947$	15.1647	+	56.5955i	0.492787	+	1.83911i	0.542086	+	0.840323i	$0.317635\pi$
$947$	15.1647	+	56.5955i	0.492787	+	1.83911i	−0.0492986	+	0.998784i	$0.515699\pi$
$948$		0			0
$949$	−78.9752	+	45.5964i	−2.56364	+	1.48012i
$950$		0			0
$951$		−	53.0619i		−	1.72065i
$952$		0			0
$953$	13.5252	+	13.5252i	0.438125	+	0.438125i	0.891381	−	0.453255i	$-0.149737\pi$
$953$	13.5252	+	13.5252i	0.438125	+	0.438125i	−0.453255	+	0.891381i	$0.649737\pi$
$954$		0			0
$955$	−25.3884	+	3.59648i	−0.821548	+	0.116379i
$956$		0			0
$957$	13.4196	−	3.59577i	0.433794	−	0.116235i
$958$		0			0
$959$	1.26621	+	45.6595i	0.0408881	+	1.47442i
$960$		0			0
$961$	−13.0906	+	22.6735i	−0.422277	+	0.731404i
$962$		0			0
$963$	−2.49980	+	9.32939i	−0.0805550	+	0.300635i
$964$		0			0
$965$	−11.4248	+	4.86434i	−0.367779	+	0.156589i
$966$		0			0
$967$	−16.2564	+	16.2564i	−0.522770	+	0.522770i	−0.918407	−	0.395637i	$-0.870524\pi$
$967$	−16.2564	+	16.2564i	−0.522770	+	0.522770i	0.395637	+	0.918407i	$0.370524\pi$
$968$		0			0
$969$	14.4072	+	24.9541i	0.462828	+	0.801641i
$970$		0			0
$971$	37.5172	+	21.6605i	1.20398	+	0.695120i	0.961438	−	0.275020i	$-0.0886845\pi$
$971$	37.5172	+	21.6605i	1.20398	+	0.695120i	0.242545	+	0.970140i	$0.422018\pi$
$972$		0			0
$973$	3.27426	+	10.9914i	0.104968	+	0.352367i
$974$		0			0
$975$	−20.4714	−	70.8062i	−0.655610	−	2.26761i
$976$		0			0
$977$	1.74652	+	0.467979i	0.0558761	+	0.0149720i	0.286649	−	0.958036i	$-0.407459\pi$
$977$	1.74652	+	0.467979i	0.0558761	+	0.0149720i	−0.230773	+	0.973008i	$0.574125\pi$
$978$		0			0
$979$	15.7050			0.501934
$980$		0			0
$981$	18.0959			0.577759
$982$		0			0
$983$	18.0205	+	4.82857i	0.574763	+	0.154007i	0.534480	−	0.845181i	$-0.320507\pi$
$983$	18.0205	+	4.82857i	0.574763	+	0.154007i	0.0402830	+	0.999188i	$0.487174\pi$
$984$		0			0
$985$	−39.5515	−	4.81232i	−1.26021	−	0.153333i
$986$		0			0
$987$	−18.3774	−	61.6908i	−0.584958	−	1.96364i
$988$		0			0
$989$	21.2372	+	12.2613i	0.675304	+	0.389887i
$990$		0			0
$991$	−8.46732	−	14.6658i	−0.268973	−	0.465875i	0.699624	−	0.714511i	$-0.253351\pi$
$991$	−8.46732	−	14.6658i	−0.268973	−	0.465875i	−0.968597	+	0.248636i	$0.920018\pi$
$992$		0			0
$993$	−23.7852	+	23.7852i	−0.754801	+	0.754801i
$994$		0			0
$995$	−3.38189	+	8.39695i	−0.107213	+	0.266201i
$996$		0			0
$997$	3.11510	−	11.6257i	0.0986561	−	0.368190i	−0.898892	−	0.438170i	$-0.855627\pi$
$997$	3.11510	−	11.6257i	0.0986561	−	0.368190i	0.997548	+	0.0699801i	$0.0222936\pi$
$998$		0			0
$999$	0.313793	−	0.543505i	0.00992797	−	0.0171957i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bo.a.33.2	yes	48
4.3	odd	2		560.2.ci.e.33.11		48
5.2	odd	4	inner	280.2.bo.a.257.2	yes	48
7.3	odd	6	inner	280.2.bo.a.73.2	yes	48
20.7	even	4		560.2.ci.e.257.11		48
28.3	even	6		560.2.ci.e.353.11		48
35.17	even	12	inner	280.2.bo.a.17.2	✓	48
140.87	odd	12		560.2.ci.e.17.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bo.a.17.2	✓	48	35.17	even	12	inner
280.2.bo.a.33.2	yes	48	1.1	even	1	trivial
280.2.bo.a.73.2	yes	48	7.3	odd	6	inner
280.2.bo.a.257.2	yes	48	5.2	odd	4	inner
560.2.ci.e.17.11		48	140.87	odd	12
560.2.ci.e.33.11		48	4.3	odd	2
560.2.ci.e.257.11		48	20.7	even	4
560.2.ci.e.353.11		48	28.3	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.30560 - 0.617784i) q^{3} +(1.37859 + 1.76054i) q^{5} +(-0.755351 - 2.53563i) q^{7} +(2.33607 + 1.34873i) q^{9} +O(q^{10})\)	\(q+(-2.30560 - 0.617784i) q^{3} +(1.37859 + 1.76054i) q^{5} +(-0.755351 - 2.53563i) q^{7} +(2.33607 + 1.34873i) q^{9} +(2.18726 + 3.78844i) q^{11} +(4.36695 - 4.36695i) q^{13} +(-2.09085 - 4.91077i) q^{15} +(0.438132 - 1.63513i) q^{17} +(3.56560 - 6.17580i) q^{19} +(0.175064 + 6.31281i) q^{21} +(4.91851 - 1.31791i) q^{23} +(-1.19897 + 4.85412i) q^{25} +(0.510640 + 0.510640i) q^{27} +1.33053i q^{29} +(-1.90109 + 1.09759i) q^{31} +(-2.70251 - 10.0859i) q^{33} +(3.42276 - 4.82543i) q^{35} +(-0.224926 - 0.839435i) q^{37} +(-12.7663 + 7.37062i) q^{39} -5.69781i q^{41} +(3.40535 + 3.40535i) q^{43} +(0.845995 + 5.97207i) q^{45} +(-9.84549 + 2.63809i) q^{47} +(-5.85889 + 3.83059i) q^{49} +(-2.02031 + 3.49929i) q^{51} +(-0.541299 + 2.02016i) q^{53} +(-3.65436 + 9.07346i) q^{55} +(-12.0362 + 12.0362i) q^{57} +(2.56679 + 4.44580i) q^{59} +(6.21535 + 3.58843i) q^{61} +(1.65533 - 6.94217i) q^{63} +(13.7084 + 1.66793i) q^{65} +(-7.11586 - 1.90669i) q^{67} -12.1543 q^{69} +4.31969 q^{71} +(-14.2630 - 3.82176i) q^{73} +(5.76315 - 10.4510i) q^{75} +(7.95396 - 8.40770i) q^{77} +(4.82649 + 2.78658i) q^{79} +(-4.90805 - 8.50099i) q^{81} +(-0.272283 + 0.272283i) q^{83} +(3.48271 - 1.48283i) q^{85} +(0.821982 - 3.06768i) q^{87} +(1.79506 - 3.10913i) q^{89} +(-14.3716 - 7.77441i) q^{91} +(5.06123 - 1.35615i) q^{93} +(15.7882 - 2.23653i) q^{95} +(0.325781 + 0.325781i) q^{97} +11.8001i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{7}+O(q^{10}) \) 48 * q - 4 * q^7	\( 48 q - 4 q^{7} + 4 q^{11} + 8 q^{15} - 4 q^{21} - 4 q^{23} - 8 q^{25} - 36 q^{33} + 24 q^{35} + 8 q^{37} - 16 q^{43} + 48 q^{45} + 24 q^{51} + 16 q^{53} - 96 q^{57} - 36 q^{61} - 68 q^{63} + 12 q^{65} - 16 q^{67} - 64 q^{71} - 48 q^{73} - 48 q^{75} + 4 q^{77} - 40 q^{85} - 12 q^{87} - 80 q^{91} + 24 q^{95}+O(q^{100}) \) 48 * q - 4 * q^7 + 4 * q^11 + 8 * q^15 - 4 * q^21 - 4 * q^23 - 8 * q^25 - 36 * q^33 + 24 * q^35 + 8 * q^37 - 16 * q^43 + 48 * q^45 + 24 * q^51 + 16 * q^53 - 96 * q^57 - 36 * q^61 - 68 * q^63 + 12 * q^65 - 16 * q^67 - 64 * q^71 - 48 * q^73 - 48 * q^75 + 4 * q^77 - 40 * q^85 - 12 * q^87 - 80 * q^91 + 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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