LMFDB - Embedded newform 280.2.bo.a.257.2

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			257.2
Character	$\chi$	$=$	280.257
Dual form			280.2.bo.a.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.617784 + 2.30560i) q^{3} +(2.21396 + 0.313627i) q^{5} +(2.53563 - 0.755351i) q^{7} +(-2.33607 - 1.34873i) q^{9} +O(q^{10})$	\(q+(-0.617784 + 2.30560i) q^{3} +(2.21396 + 0.313627i) q^{5} +(2.53563 - 0.755351i) q^{7} +(-2.33607 - 1.34873i) q^{9} +(2.18726 + 3.78844i) q^{11} +(-4.36695 - 4.36695i) q^{13} +(-2.09085 + 4.91077i) q^{15} +(1.63513 + 0.438132i) q^{17} +(-3.56560 + 6.17580i) q^{19} +(0.175064 + 6.31281i) q^{21} +(-1.31791 - 4.91851i) q^{23} +(4.80328 + 1.38872i) q^{25} +(-0.510640 + 0.510640i) q^{27} -1.33053i q^{29} +(-1.90109 + 1.09759i) q^{31} +(-10.0859 + 2.70251i) q^{33} +(5.85070 - 0.877077i) q^{35} +(0.839435 - 0.224926i) q^{37} +(12.7663 - 7.37062i) q^{39} -5.69781i q^{41} +(3.40535 - 3.40535i) q^{43} +(-4.74897 - 3.71869i) q^{45} +(-2.63809 - 9.84549i) q^{47} +(5.85889 - 3.83059i) q^{49} +(-2.02031 + 3.49929i) q^{51} +(2.02016 + 0.541299i) q^{53} +(3.65436 + 9.07346i) q^{55} +(-12.0362 - 12.0362i) q^{57} +(-2.56679 - 4.44580i) q^{59} +(6.21535 + 3.58843i) q^{61} +(-6.94217 - 1.65533i) q^{63} +(-8.29868 - 11.0379i) q^{65} +(1.90669 - 7.11586i) q^{67} +12.1543 q^{69} +4.31969 q^{71} +(-3.82176 + 14.2630i) q^{73} +(-6.16922 + 10.2165i) q^{75} +(8.40770 + 7.95396i) q^{77} +(-4.82649 - 2.78658i) q^{79} +(-4.90805 - 8.50099i) q^{81} +(0.272283 + 0.272283i) q^{83} +(3.48271 + 1.48283i) q^{85} +(3.06768 + 0.821982i) q^{87} +(-1.79506 + 3.10913i) q^{89} +(-14.3716 - 7.77441i) q^{91} +(-1.35615 - 5.06123i) q^{93} +(-9.83100 + 12.5547i) q^{95} +(-0.325781 + 0.325781i) q^{97} -11.8001i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

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

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
$3$	−0.617784	+	2.30560i	−0.356678	+	1.33114i	0.521682	+	0.853140i	$0.325305\pi$
$3$	−0.617784	+	2.30560i	−0.356678	+	1.33114i	−0.878360	+	0.478000i	$0.841362\pi$
$4$		0			0
$5$	2.21396	+	0.313627i	0.990115	+	0.140258i
$5$	2.21396	+	0.313627i	0.990115	+	0.140258i
$6$		0			0
$7$	2.53563	−	0.755351i	0.958380	−	0.285496i
$7$	2.53563	−	0.755351i	0.958380	−	0.285496i
$8$		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	−0.970641	−	0.240533i	$-0.922678\pi$
$13$	−4.36695	−	4.36695i	−1.21117	−	1.21117i	−0.240533	−	0.970641i	$-0.577322\pi$
$14$		0			0
$15$	−2.09085	+	4.91077i	−0.539855	+	1.26795i
$16$		0			0
$17$	1.63513	+	0.438132i	0.396577	+	0.106263i	0.451595	−	0.892223i	$-0.350855\pi$
$17$	1.63513	+	0.438132i	0.396577	+	0.106263i	−0.0550183	+	0.998485i	$0.517522\pi$
$18$		0			0
$19$	−3.56560	+	6.17580i	−0.818004	+	1.41682i	0.0891466	+	0.996019i	$0.471586\pi$
$19$	−3.56560	+	6.17580i	−0.818004	+	1.41682i	−0.907151	+	0.420806i	$0.861747\pi$
$20$		0			0
$21$	0.175064	+	6.31281i	0.0382021	+	1.37757i
$22$		0			0
$23$	−1.31791	−	4.91851i	−0.274803	−	1.02558i	−0.955973	−	0.293454i	$-0.905195\pi$
$23$	−1.31791	−	4.91851i	−0.274803	−	1.02558i	0.681170	−	0.732125i	$-0.261471\pi$
$24$		0			0
$25$	4.80328	+	1.38872i	0.960655	+	0.277744i
$26$		0			0
$27$	−0.510640	+	0.510640i	−0.0982727	+	0.0982727i
$28$		0			0
$29$		−	1.33053i		−	0.247074i	−0.992340	−	0.123537i	$-0.960576\pi$
$29$		−	1.33053i		−	0.247074i	0.992340	−	0.123537i	$-0.0394237\pi$
$30$		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
$33$	−10.0859	+	2.70251i	−1.75573	+	0.470446i
$34$		0			0
$35$	5.85070	−	0.877077i	0.988949	−	0.148253i
$36$		0			0
$37$	0.839435	−	0.224926i	0.138002	−	0.0369776i	−0.189157	−	0.981947i	$-0.560575\pi$
$37$	0.839435	−	0.224926i	0.138002	−	0.0369776i	0.327159	+	0.944969i	$0.393909\pi$
$38$		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	−0.398051	−	0.917363i	$-0.630313\pi$
$43$	3.40535	−	3.40535i	0.519312	−	0.519312i	0.917363	+	0.398051i	$0.130313\pi$
$44$		0			0
$45$	−4.74897	−	3.71869i	−0.707934	−	0.554349i
$46$		0			0
$47$	−2.63809	−	9.84549i	−0.384805	−	1.43611i	−0.838474	−	0.544942i	$-0.816552\pi$
$47$	−2.63809	−	9.84549i	−0.384805	−	1.43611i	0.453669	−	0.891170i	$-0.350115\pi$
$48$		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
$53$	2.02016	+	0.541299i	0.277490	+	0.0743531i	0.394880	−	0.918733i	$-0.370786\pi$
$53$	2.02016	+	0.541299i	0.277490	+	0.0743531i	−0.117390	+	0.993086i	$0.537453\pi$
$54$		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	0.649157	−	0.760654i	$-0.275122\pi$
$59$	−2.56679	−	4.44580i	−0.334167	−	0.578794i	−0.983324	+	0.181860i	$0.941788\pi$
$60$		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
$63$	−6.94217	−	1.65533i	−0.874631	−	0.208552i
$64$		0			0
$65$	−8.29868	−	11.0379i	−1.02932	−	1.36908i
$66$		0			0
$67$	1.90669	−	7.11586i	0.232939	−	0.869341i	−0.746128	−	0.665803i	$-0.768089\pi$
$67$	1.90669	−	7.11586i	0.232939	−	0.869341i	0.979067	−	0.203538i	$-0.0652441\pi$
$68$		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
$73$	−3.82176	+	14.2630i	−0.447303	+	1.66936i	0.262481	+	0.964937i	$0.415459\pi$
$73$	−3.82176	+	14.2630i	−0.447303	+	1.66936i	−0.709784	+	0.704420i	$0.751207\pi$
$74$		0			0
$75$	−6.16922	+	10.2165i	−0.712360	+	1.17970i
$76$		0			0
$77$	8.40770	+	7.95396i	0.958146	+	0.906438i
$78$		0			0
$79$	−4.82649	−	2.78658i	−0.543023	−	0.313514i	0.203280	−	0.979121i	$-0.434840\pi$
$79$	−4.82649	−	2.78658i	−0.543023	−	0.313514i	−0.746303	+	0.665606i	$0.768173\pi$
$80$		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	$-0.243273\pi$
$83$	0.272283	+	0.272283i	0.0298869	+	0.0298869i	−0.692005	+	0.721892i	$0.743273\pi$
$84$		0			0
$85$	3.48271	+	1.48283i	0.377753	+	0.160835i
$86$		0			0
$87$	3.06768	+	0.821982i	0.328890	+	0.0881257i
$88$		0			0
$89$	−1.79506	+	3.10913i	−0.190276	+	0.329567i	−0.945342	−	0.326082i	$-0.894271\pi$
$89$	−1.79506	+	3.10913i	−0.190276	+	0.329567i	0.755066	+	0.655649i	$0.227605\pi$
$90$		0			0
$91$	−14.3716	−	7.77441i	−1.50655	−	0.814980i
$92$		0			0
$93$	−1.35615	−	5.06123i	−0.140627	−	0.524825i
$94$		0			0
$95$	−9.83100	+	12.5547i	−1.00864	+	1.28809i
$96$		0			0
$97$	−0.325781	+	0.325781i	−0.0330781	+	0.0330781i	−0.723452	−	0.690374i	$-0.757446\pi$
$97$	−0.325781	+	0.325781i	−0.0330781	+	0.0330781i	0.690374	+	0.723452i	$0.257446\pi$
$98$		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
$103$	−5.28651	+	1.41652i	−0.520895	+	0.139573i	−0.509681	−	0.860364i	$-0.670236\pi$
$103$	−5.28651	+	1.41652i	−0.520895	+	0.139573i	−0.0112145	+	0.999937i	$0.503570\pi$
$104$		0			0
$105$	−1.59228	+	14.0312i	−0.155391	+	1.36931i
$106$		0			0
$107$	−3.45859	+	0.926726i	−0.334354	+	0.0895900i	−0.422090	−	0.906554i	$-0.638703\pi$
$107$	−3.45859	+	0.926726i	−0.334354	+	0.0895900i	0.0877359	+	0.996144i	$0.472037\pi$
$108$		0			0
$109$	−5.80975	+	3.35426i	−0.556473	+	0.321280i	−0.751729	−	0.659472i	$-0.770780\pi$
$109$	−5.80975	+	3.35426i	−0.556473	+	0.321280i	0.195255	+	0.980752i	$0.437446\pi$
$110$		0			0
$111$			2.07436i			0.196889i
$112$		0			0
$113$	5.75259	−	5.75259i	0.541158	−	0.541158i	−0.382710	−	0.923869i	$-0.625009\pi$
$113$	5.75259	−	5.75259i	0.541158	−	0.541158i	0.923869	+	0.382710i	$0.125009\pi$
$114$		0			0
$115$	−1.37523	−	11.3027i	−0.128241	−	1.05398i
$116$		0			0
$117$	4.31165	+	16.0913i	0.398613	+	1.48764i
$118$		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
$123$	13.1369	+	3.52002i	1.18451	+	0.317389i
$124$		0			0
$125$	10.1987	+	4.58101i	0.912203	+	0.409738i
$126$		0			0
$127$	3.47621	+	3.47621i	0.308464	+	0.308464i	0.844314	−	0.535849i	$-0.180009\pi$
$127$	3.47621	+	3.47621i	0.308464	+	0.308464i	−0.535849	+	0.844314i	$0.680009\pi$
$128$		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
$133$	−4.37616	+	18.3528i	−0.379461	+	1.59139i
$134$		0			0
$135$	−1.29069	+	0.970388i	−0.111085	+	0.0835177i
$136$		0			0
$137$	4.46833	−	16.6760i	0.381756	−	1.42473i	−0.461463	−	0.887160i	$-0.652675\pi$
$137$	4.46833	−	16.6760i	0.381756	−	1.42473i	0.843218	−	0.537571i	$-0.180658\pi$
$138$		0			0
$139$	4.33475			0.367669			0.183834	−	0.982957i	$-0.441149\pi$
$139$	4.33475			0.367669			0.183834	+	0.982957i	$0.441149\pi$
$140$		0			0
$141$	24.3295			2.04892
$142$		0			0
$143$	6.99230	−	26.0956i	0.584725	−	2.18222i
$144$		0			0
$145$	0.417291	−	2.94575i	0.0346541	−	0.244631i
$146$		0			0
$147$	5.21229	+	15.8747i	0.429902	+	1.30933i
$148$		0			0
$149$	2.22537	+	1.28482i	0.182309	+	0.105256i	0.588377	−	0.808587i	$-0.299767\pi$
$149$	2.22537	+	1.28482i	0.182309	+	0.105256i	−0.406068	+	0.913843i	$0.633100\pi$
$150$		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
$157$	−17.5839	−	4.71159i	−1.40335	−	0.376026i	−0.523801	−	0.851841i	$-0.675487\pi$
$157$	−17.5839	−	4.71159i	−1.40335	−	0.376026i	−0.879545	+	0.475815i	$0.842153\pi$
$158$		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
$163$	2.26156	+	8.44026i	0.177139	+	0.661092i	0.996177	+	0.0873531i	$0.0278408\pi$
$163$	2.26156	+	8.44026i	0.177139	+	0.661092i	−0.819038	+	0.573739i	$0.805492\pi$
$164$		0			0
$165$	−23.1774	+	2.82005i	−1.80436	+	0.219540i
$166$		0			0
$167$	−12.3783	+	12.3783i	−0.957862	+	0.957862i	−0.999147	−	0.0412856i	$-0.986855\pi$
$167$	−12.3783	+	12.3783i	−0.957862	+	0.957862i	0.0412856	+	0.999147i	$0.486855\pi$
$168$		0			0
$169$			25.1405i			1.93389i
$170$		0			0
$171$	16.6589	−	9.61804i	1.27394	−	0.735510i
$172$		0			0
$173$	−2.78674	+	0.746705i	−0.211872	+	0.0567709i	−0.363194	−	0.931714i	$-0.618314\pi$
$173$	−2.78674	+	0.746705i	−0.211872	+	0.0567709i	0.151322	+	0.988485i	$0.451647\pi$
$174$		0			0
$175$	13.2283	−	0.106880i	0.999967	−	0.00807938i
$176$		0			0
$177$	11.8360	−	3.17144i	0.889646	−	0.238380i
$178$		0			0
$179$	6.47526	−	3.73849i	0.483984	−	0.279428i	−0.238092	−	0.971243i	$-0.576522\pi$
$179$	6.47526	−	3.73849i	0.483984	−	0.279428i	0.722075	+	0.691815i	$0.243188\pi$
$180$		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
$185$	1.92902	−	0.234709i	0.141825	−	0.0172561i
$186$		0			0
$187$	1.91661	+	7.15290i	0.140157	+	0.523072i
$188$		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
$193$	5.36396	+	1.43727i	0.386106	+	0.103457i	0.446650	−	0.894709i	$-0.352617\pi$
$193$	5.36396	+	1.43727i	0.386106	+	0.103457i	−0.0605441	+	0.998166i	$0.519284\pi$
$194$		0			0
$195$	30.5757	−	12.3144i	2.18957	−	0.881855i
$196$		0			0
$197$	−12.5995	−	12.5995i	−0.897678	−	0.897678i	0.0975523	−	0.995230i	$-0.468899\pi$
$197$	−12.5995	−	12.5995i	−0.897678	−	0.897678i	−0.995230	+	0.0975523i	$0.968899\pi$
$198$		0			0
$199$	−2.02418	−	3.50598i	−0.143490	−	0.248532i	0.785318	−	0.619092i	$-0.212499\pi$
$199$	−2.02418	−	3.50598i	−0.143490	−	0.248532i	−0.928809	+	0.370560i	$0.879166\pi$
$200$		0			0
$201$	15.2284	+	8.79213i	1.07413	+	0.620149i
$202$		0			0
$203$	−1.00502	−	3.37375i	−0.0705385	−	0.236790i
$204$		0			0
$205$	1.78699	−	12.6148i	0.124809	−	0.881053i
$206$		0			0
$207$	−3.55500	+	13.2674i	−0.247090	+	0.922151i
$208$		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
$213$	−2.66863	+	9.95948i	−0.182852	+	0.682412i
$214$		0			0
$215$	8.60734	−	6.47132i	0.587016	−	0.441340i
$216$		0			0
$217$	−3.99140	+	4.21909i	−0.270954	+	0.286410i
$218$		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	−0.910854	−	0.412730i	$-0.864575\pi$
$223$	−19.7653	−	19.7653i	−1.32358	−	1.32358i	−0.412730	−	0.910854i	$-0.635425\pi$
$224$		0			0
$225$	−9.34776	−	9.72245i	−0.623184	−	0.648163i
$226$		0			0
$227$	2.83969	+	0.760893i	0.188477	+	0.0505022i	0.351823	−	0.936067i	$-0.385562\pi$
$227$	2.83969	+	0.760893i	0.188477	+	0.0505022i	−0.163346	+	0.986569i	$0.552229\pi$
$228$		0			0
$229$	12.0300	−	20.8366i	0.794965	−	1.37692i	−0.127896	−	0.991788i	$-0.540822\pi$
$229$	12.0300	−	20.8366i	0.794965	−	1.37692i	0.922861	−	0.385133i	$-0.125844\pi$
$230$		0			0
$231$	−23.5328	+	14.4710i	−1.54834	+	0.952120i
$232$		0			0
$233$	−0.636915	−	2.37700i	−0.0417257	−	0.155722i	0.941920	−	0.335838i	$-0.109019\pi$
$233$	−0.636915	−	2.37700i	−0.0417257	−	0.155722i	−0.983645	+	0.180116i	$0.942353\pi$
$234$		0			0
$235$	−2.75283	−	22.6249i	−0.179575	−	1.47589i
$236$		0			0
$237$	9.40647	−	9.40647i	0.611016	−	0.611016i
$238$		0			0
$239$			15.4754i			1.00102i	0.865730	+	0.500511i	$0.166855\pi$
$239$			15.4754i			1.00102i	−0.865730	+	0.500511i	$0.833145\pi$
$240$		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
$243$	20.5394	−	5.50351i	1.31760	−	0.353050i
$244$		0			0
$245$	14.1727	−	6.64328i	0.905464	−	0.424424i
$246$		0			0
$247$	42.5402	−	11.3986i	2.70677	−	0.725276i
$248$		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
$255$	−5.57037	+	7.11367i	−0.348830	+	0.445475i
$256$		0			0
$257$	−5.02024	−	18.7358i	−0.313154	−	1.16871i	−0.925696	−	0.378269i	$-0.876520\pi$
$257$	−5.02024	−	18.7358i	−0.313154	−	1.16871i	0.612542	−	0.790438i	$-0.290147\pi$
$258$		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
$263$	24.5803	+	6.58626i	1.51568	+	0.406126i	0.918318	−	0.395843i	$-0.129547\pi$
$263$	24.5803	+	6.58626i	1.51568	+	0.406126i	0.597366	+	0.801969i	$0.296214\pi$
$264$		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	0.990543	−	0.137205i	$-0.0438120\pi$
$269$	6.17421	+	10.6940i	0.376448	+	0.652027i	−0.614095	+	0.789232i	$0.710479\pi$
$270$		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
$273$	26.8032	−	28.3322i	1.62221	−	1.71474i
$274$		0			0
$275$	5.24493	+	21.2344i	0.316281	+	1.28048i
$276$		0			0
$277$	−4.89207	+	18.2575i	−0.293936	+	1.09698i	0.648123	+	0.761536i	$0.275554\pi$
$277$	−4.89207	+	18.2575i	−0.293936	+	1.09698i	−0.942059	+	0.335448i	$0.891112\pi$
$278$		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
$283$	−6.20653	+	23.1631i	−0.368940	+	1.37690i	0.493061	+	0.869995i	$0.335878\pi$
$283$	−6.20653	+	23.1631i	−0.368940	+	1.37690i	−0.862001	+	0.506907i	$0.830789\pi$
$284$		0			0
$285$	−22.8728	−	30.4225i	−1.35487	−	1.80207i
$286$		0			0
$287$	−4.30385	−	14.4476i	−0.254048	−	0.852813i
$288$		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	$-0.253914\pi$
$293$	−0.297685	−	0.297685i	−0.0173909	−	0.0173909i	−0.715749	+	0.698358i	$0.753914\pi$
$294$		0			0
$295$	−4.28845	−	10.6479i	−0.249683	−	0.619943i
$296$		0			0
$297$	−3.05143	−	0.817629i	−0.177062	−	0.0474436i
$298$		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
$303$	7.62627	+	28.4616i	0.438118	+	1.63508i
$304$		0			0
$305$	12.6351	+	9.89397i	0.723486	+	0.566527i
$306$		0			0
$307$	−5.95890	+	5.95890i	−0.340093	+	0.340093i	−0.856402	−	0.516309i	$-0.827305\pi$
$307$	−5.95890	+	5.95890i	−0.340093	+	0.340093i	0.516309	+	0.856402i	$0.327305\pi$
$308$		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
$313$	−0.295640	+	0.0792166i	−0.0167106	+	0.00447759i	−0.267165	−	0.963651i	$-0.586087\pi$
$313$	−0.295640	+	0.0792166i	−0.0167106	+	0.00447759i	0.250454	+	0.968128i	$0.419420\pi$
$314$		0			0
$315$	−14.8506	−	5.84210i	−0.836734	−	0.329165i
$316$		0			0
$317$	−21.4727	+	5.75358i	−1.20603	+	0.323153i	−0.805201	−	0.593002i	$-0.797943\pi$
$317$	−21.4727	+	5.75358i	−1.20603	+	0.323153i	−0.400824	+	0.916155i	$0.631276\pi$
$318$		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
$325$	−14.9112	−	27.0401i	−0.827125	−	1.49992i
$326$		0			0
$327$	−4.14442	−	15.4672i	−0.229187	−	0.855337i
$328$		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
$333$	−2.26434	−	0.606728i	−0.124085	−	0.0332485i
$334$		0			0
$335$	6.45307	−	15.1563i	0.352569	−	0.828076i
$336$		0			0
$337$	19.3301	+	19.3301i	1.05298	+	1.05298i	0.998516	+	0.0544630i	$0.0173447\pi$
$337$	19.3301	+	19.3301i	1.05298	+	1.05298i	0.0544630	+	0.998516i	$0.482655\pi$
$338$		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
$343$	11.9626	−	14.1385i	0.645918	−	0.763407i
$344$		0			0
$345$	26.9092	+	3.81191i	1.44874	+	0.205227i
$346$		0			0
$347$	−8.43333	+	31.4736i	−0.452725	+	1.68959i	0.241966	+	0.970285i	$0.422208\pi$
$347$	−8.43333	+	31.4736i	−0.452725	+	1.68959i	−0.694691	+	0.719308i	$0.744459\pi$
$348$		0			0
$349$	−18.5313			−0.991957			−0.495978	−	0.868335i	$-0.665190\pi$
$349$	−18.5313			−0.991957			−0.495978	+	0.868335i	$0.665190\pi$
$350$		0			0
$351$	4.45988			0.238051
$352$		0			0
$353$	−6.98512	+	26.0688i	−0.371780	+	1.38750i	0.486212	+	0.873841i	$0.338378\pi$
$353$	−6.98512	+	26.0688i	−0.371780	+	1.38750i	−0.857992	+	0.513662i	$0.828288\pi$
$354$		0			0
$355$	9.56363	+	1.35477i	0.507585	+	0.0719037i
$356$		0			0
$357$	−2.47959	+	10.3990i	−0.131234	+	0.550371i
$358$		0			0
$359$	21.1575	+	12.2153i	1.11665	+	0.644698i	0.940543	−	0.339673i	$-0.110317\pi$
$359$	21.1575	+	12.2153i	1.11665	+	0.644698i	0.176106	+	0.984371i	$0.443650\pi$
$360$		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
$367$	−0.629007	−	0.168542i	−0.0328339	−	0.00879781i	0.242365	−	0.970185i	$-0.422077\pi$
$367$	−0.629007	−	0.168542i	−0.0328339	−	0.00879781i	−0.275199	+	0.961387i	$0.588744\pi$
$368$		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
$373$	−0.0250025	−	0.0933104i	−0.00129458	−	0.00483143i	0.965276	−	0.261234i	$-0.0841294\pi$
$373$	−0.0250025	−	0.0933104i	−0.00129458	−	0.00483143i	−0.966570	+	0.256403i	$0.917463\pi$
$374$		0			0
$375$	−16.8626	+	20.6842i	−0.870781	+	1.06813i
$376$		0			0
$377$	−5.81037	+	5.81037i	−0.299249	+	0.299249i
$378$		0			0
$379$			10.4991i			0.539303i	0.962958	+	0.269651i	$0.0869085\pi$
$379$			10.4991i			0.539303i	−0.962958	+	0.269651i	$0.913092\pi$
$380$		0			0
$381$	−10.1623	+	5.86721i	−0.520631	+	0.300586i
$382$		0			0
$383$	10.6761	−	2.86065i	0.545522	−	0.146172i	0.0244754	−	0.999700i	$-0.492208\pi$
$383$	10.6761	−	2.86065i	0.545522	−	0.146172i	0.521047	+	0.853528i	$0.325542\pi$
$384$		0			0
$385$	16.1198	+	20.2467i	0.821539	+	1.03187i
$386$		0			0
$387$	−12.5480	+	3.36223i	−0.637852	+	0.170912i
$388$		0			0
$389$	−6.30536	+	3.64040i	−0.319695	+	0.184576i	−0.651256	−	0.758858i	$-0.725758\pi$
$389$	−6.30536	+	3.64040i	−0.319695	+	0.184576i	0.331562	+	0.943433i	$0.392424\pi$
$390$		0			0
$391$		−	8.61981i		−	0.435923i
$392$		0			0
$393$	9.21608	−	9.21608i	0.464890	−	0.464890i
$394$		0			0
$395$	−9.81174	−	7.68310i	−0.493682	−	0.386579i
$396$		0			0
$397$	6.36084	+	23.7390i	0.319241	+	1.19142i	0.919976	+	0.391976i	$0.128208\pi$
$397$	6.36084	+	23.7390i	0.319241	+	1.19142i	−0.600734	+	0.799449i	$0.705125\pi$
$398$		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
$403$	13.0951	+	3.50882i	0.652314	+	0.174787i
$404$		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	0.980225	−	0.197888i	$-0.0634083\pi$
$409$	6.44604	+	11.1649i	0.318736	+	0.552067i	−0.661489	+	0.749955i	$0.730075\pi$
$410$		0			0
$411$	35.6879	+	20.6044i	1.76035	+	1.01634i
$412$		0			0
$413$	−9.86658	−	9.33411i	−0.485503	−	0.459302i
$414$		0			0
$415$	0.517429	+	0.688219i	0.0253996	+	0.0337834i
$416$		0			0
$417$	−2.67794	+	9.99421i	−0.131139	+	0.489419i
$418$		0			0
$419$	8.27208			0.404117			0.202059	−	0.979373i	$-0.435237\pi$
$419$	8.27208			0.404117			0.202059	+	0.979373i	$0.435237\pi$
$420$		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
$423$	−7.11613	+	26.5578i	−0.345998	+	1.29128i
$424$		0			0
$425$	7.24554	+	4.37520i	0.351460	+	0.212228i
$426$		0			0
$427$	18.4704	+	4.40419i	0.893845	+	0.213134i
$428$		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	0.860370	+	0.509670i	$0.170233\pi$
$433$	28.5087	+	28.5087i	1.37004	+	1.37004i	0.509670	+	0.860370i	$0.329767\pi$
$434$		0			0
$435$	6.53393	+	2.78194i	0.313278	+	0.133384i
$436$		0			0
$437$	35.0748	+	9.39827i	1.67786	+	0.449580i
$438$		0			0
$439$	10.1088	−	17.5090i	0.482469	−	0.835660i	−0.517329	−	0.855787i	$-0.673074\pi$
$439$	10.1088	−	17.5090i	0.482469	−	0.835660i	0.999797	+	0.0201265i	$0.00640691\pi$
$440$		0			0
$441$	−18.8532	+	1.04646i	−0.897770	+	0.0498315i
$442$		0			0
$443$	−6.19049	−	23.1032i	−0.294119	−	1.09767i	−0.941914	−	0.335853i	$-0.890975\pi$
$443$	−6.19049	−	23.1032i	−0.294119	−	1.09767i	0.647795	−	0.761815i	$-0.275691\pi$
$444$		0			0
$445$	−4.94930	+	6.32052i	−0.234619	+	0.299621i
$446$		0			0
$447$	−4.33708	+	4.33708i	−0.205137	+	0.205137i
$448$		0			0
$449$			15.9935i			0.754782i	0.926054	+	0.377391i	$0.123179\pi$
$449$			15.9935i			0.754782i	−0.926054	+	0.377391i	$0.876821\pi$
$450$		0			0
$451$	21.5858	−	12.4626i	1.01644	−	0.586840i
$452$		0			0
$453$	2.38059	−	0.637878i	0.111850	−	0.0299701i
$454$		0			0
$455$	−29.3799	−	21.7196i	−1.37735	−	1.01823i
$456$		0			0
$457$	−14.6848	+	3.93478i	−0.686925	+	0.184061i	−0.585367	−	0.810769i	$-0.699050\pi$
$457$	−14.6848	+	3.93478i	−0.686925	+	0.184061i	−0.101558	+	0.994830i	$0.532383\pi$
$458$		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	−0.574240	−	0.818687i	$-0.694702\pi$
$463$	5.25987	−	5.25987i	0.244447	−	0.244447i	0.818687	+	0.574240i	$0.194702\pi$
$464$		0			0
$465$	−1.41514	−	11.6307i	−0.0656254	−	0.539361i
$466$		0			0
$467$	−9.57262	−	35.7255i	−0.442968	−	1.65318i	−0.721246	−	0.692679i	$-0.756430\pi$
$467$	−9.57262	−	35.7255i	−0.442968	−	1.65318i	0.278278	−	0.960501i	$-0.410236\pi$
$468$		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
$473$	20.3494	+	5.45260i	0.935666	+	0.250711i
$474$		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	$0.00121028\pi$
$479$	11.0150	+	19.0786i	0.503289	+	0.871722i	−0.496704	+	0.867920i	$0.665456\pi$
$480$		0			0
$481$	−4.64801	−	2.68353i	−0.211931	−	0.122359i
$482$		0			0
$483$	30.8189	−	9.18076i	1.40231	−	0.417739i
$484$		0			0
$485$	−0.823442	+	0.619094i	−0.0373906	+	0.0281116i
$486$		0			0
$487$	−3.87053	+	14.4450i	−0.175390	+	0.654566i	0.821094	+	0.570792i	$0.193364\pi$
$487$	−3.87053	+	14.4450i	−0.175390	+	0.654566i	−0.996485	+	0.0837736i	$0.973303\pi$
$488$		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
$493$	0.582948	−	2.17559i	0.0262547	−	0.0979838i
$494$		0			0
$495$	3.70082	−	26.1249i	0.166339	−	1.17423i
$496$		0			0
$497$	10.9531	−	3.26288i	0.491316	−	0.146360i
$498$		0			0
$499$	5.90449	+	3.40896i	0.264321	+	0.152606i	0.626304	−	0.779579i	$-0.284567\pi$
$499$	5.90449	+	3.40896i	0.264321	+	0.152606i	−0.361983	+	0.932185i	$0.617900\pi$
$500$		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	$-0.106124\pi$
$503$	13.8531	+	13.8531i	0.617679	+	0.617679i	−0.327256	+	0.944936i	$0.606124\pi$
$504$		0			0
$505$	25.6046	−	10.3123i	1.13939	−	0.458892i
$506$		0			0
$507$	−57.9640	−	15.5314i	−2.57427	−	0.689774i
$508$		0			0
$509$	22.4079	−	38.8116i	0.993213	−	1.72030i	0.395882	−	0.918301i	$-0.370439\pi$
$509$	22.4079	−	38.8116i	0.993213	−	1.72030i	0.597332	−	0.801994i	$-0.296228\pi$
$510$		0			0
$511$	1.08299	+	39.0525i	0.0479085	+	1.72758i
$512$		0			0
$513$	−1.33287	−	4.97434i	−0.0588477	−	0.219623i
$514$		0			0
$515$	−12.1484	+	1.47812i	−0.535322	+	0.0651339i
$516$		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
$523$	−15.1255	+	4.05288i	−0.661394	+	0.177220i	−0.573875	−	0.818943i	$-0.694560\pi$
$523$	−15.1255	+	4.05288i	−0.661394	+	0.177220i	−0.0875187	+	0.996163i	$0.527894\pi$
$524$		0			0
$525$	−7.92583	+	30.5653i	−0.345911	+	1.33398i
$526$		0			0
$527$	−3.58942	+	0.961782i	−0.156358	+	0.0418959i
$528$		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
$535$	−7.94784	+	0.967032i	−0.343615	+	0.0418084i
$536$		0			0
$537$	4.61916	+	17.2389i	0.199332	+	0.743916i
$538$		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
$543$	−50.1024	−	13.4249i	−2.15010	−	0.576118i
$544$		0			0
$545$	−13.9146	+	5.60412i	−0.596035	+	0.240054i
$546$		0			0
$547$	24.0863	+	24.0863i	1.02985	+	1.02985i	0.999540	+	0.0303138i	$0.00965066\pi$
$547$	24.0863	+	24.0863i	1.02985	+	1.02985i	0.0303138	+	0.999540i	$0.490349\pi$
$548$		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
$553$	−14.3431	−	3.42004i	−0.609929	−	0.145435i
$554$		0			0
$555$	−0.650575	+	4.59256i	−0.0276154	+	0.194943i
$556$		0			0
$557$	−6.77586	+	25.2878i	−0.287102	+	1.07148i	0.660187	+	0.751101i	$0.270477\pi$
$557$	−6.77586	+	25.2878i	−0.287102	+	1.07148i	−0.947289	+	0.320379i	$0.896190\pi$
$558$		0			0
$559$	−29.7420			−1.25795
$560$		0			0
$561$	−17.6758			−0.746273
$562$		0			0
$563$	1.13725	−	4.24428i	0.0479294	−	0.178875i	−0.937812	−	0.347145i	$-0.887151\pi$
$563$	1.13725	−	4.24428i	0.0479294	−	0.178875i	0.985741	+	0.168270i	$0.0538180\pi$
$564$		0			0
$565$	14.5402	−	10.9319i	0.611711	−	0.459907i
$566$		0			0
$567$	−18.8663	−	17.8481i	−0.792308	−	0.749550i
$568$		0			0
$569$	9.41275	+	5.43445i	0.394603	+	0.227824i	0.684153	−	0.729339i	$-0.260172\pi$
$569$	9.41275	+	5.43445i	0.394603	+	0.227824i	−0.289550	+	0.957163i	$0.593506\pi$
$570$		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
$577$	22.5954	+	6.05442i	0.940659	+	0.252049i	0.696394	−	0.717660i	$-0.254787\pi$
$577$	22.5954	+	6.05442i	0.940659	+	0.252049i	0.244265	+	0.969709i	$0.421453\pi$
$578$		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
$583$	2.36792	+	8.83721i	0.0980693	+	0.366000i
$584$		0			0
$585$	4.49918	+	36.9778i	0.186018	+	1.52885i
$586$		0			0
$587$	13.2002	−	13.2002i	0.544831	−	0.544831i	−0.380110	−	0.924941i	$-0.624114\pi$
$587$	13.2002	−	13.2002i	0.544831	−	0.544831i	0.924941	+	0.380110i	$0.124114\pi$
$588$		0			0
$589$		−	15.6543i		−	0.645025i
$590$		0			0
$591$	36.8332	−	21.2657i	1.51512	−	0.874753i
$592$		0			0
$593$	−3.04302	+	0.815375i	−0.124962	+	0.0334835i	−0.320758	−	0.947161i	$-0.603938\pi$
$593$	−3.04302	+	0.815375i	−0.124962	+	0.0334835i	0.195796	+	0.980645i	$0.437271\pi$
$594$		0			0
$595$	9.95093	+	1.12924i	0.407948	+	0.0462945i
$596$		0			0
$597$	9.33389	−	2.50101i	0.382011	−	0.102360i
$598$		0			0
$599$	−14.3732	+	8.29838i	−0.587274	+	0.339063i	−0.764019	−	0.645194i	$-0.776777\pi$
$599$	−14.3732	+	8.29838i	−0.587274	+	0.339063i	0.176745	+	0.984257i	$0.443443\pi$
$600$		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
$605$	−11.2168	+	14.3244i	−0.456027	+	0.582371i
$606$		0			0
$607$	−8.31863	−	31.0456i	−0.337643	−	1.26010i	−0.900975	−	0.433870i	$-0.857148\pi$
$607$	−8.31863	−	31.0456i	−0.337643	−	1.26010i	0.563332	−	0.826230i	$-0.309519\pi$
$608$		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
$613$	−22.6649	−	6.07304i	−0.915427	−	0.245288i	−0.229797	−	0.973238i	$-0.573806\pi$
$613$	−22.6649	−	6.07304i	−0.915427	−	0.245288i	−0.685630	+	0.727951i	$0.740473\pi$
$614$		0			0
$615$	27.9806	+	11.9133i	1.12829	+	0.480390i
$616$		0			0
$617$	−24.6695	−	24.6695i	−0.993158	−	0.993158i	0.00681844	−	0.999977i	$-0.497830\pi$
$617$	−24.6695	−	24.6695i	−0.993158	−	0.993158i	−0.999977	+	0.00681844i	$0.997830\pi$
$618$		0			0
$619$	−12.1208	−	20.9938i	−0.487174	−	0.843811i	0.512717	−	0.858558i	$-0.328639\pi$
$619$	−12.1208	−	20.9938i	−0.487174	−	0.843811i	−0.999891	+	0.0147470i	$0.995306\pi$
$620$		0			0
$621$	3.18456	+	1.83861i	0.127792	+	0.0737808i
$622$		0			0
$623$	−2.20312	+	9.23951i	−0.0882663	+	0.370173i
$624$		0			0
$625$	21.1429	+	13.3408i	0.845717	+	0.533632i
$626$		0			0
$627$	19.2721	−	71.9245i	0.769654	−	2.87239i
$628$		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
$633$	13.1720	−	49.1586i	0.523541	−	1.95388i
$634$		0			0
$635$	6.60598	+	8.78645i	0.262150	+	0.348680i
$636$		0			0
$637$	−42.3135	−	8.85748i	−1.67652	−	0.350946i
$638$		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	$-0.402913\pi$
$643$	−16.5722	−	16.5722i	−0.653545	−	0.653545i	−0.953845	+	0.300300i	$0.902913\pi$
$644$		0			0
$645$	9.60281	+	23.8430i	0.378110	+	0.938816i
$646$		0			0
$647$	−26.5609	−	7.11698i	−1.04422	−	0.279797i	−0.304358	−	0.952558i	$-0.598442\pi$
$647$	−26.5609	−	7.11698i	−1.04422	−	0.279797i	−0.739860	+	0.672760i	$0.765108\pi$
$648$		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
$653$	3.09889	+	11.5652i	0.121269	+	0.452581i	0.999679	−	0.0253256i	$-0.00806226\pi$
$653$	3.09889	+	11.5652i	0.121269	+	0.452581i	−0.878410	+	0.477907i	$0.841396\pi$
$654$		0			0
$655$	−9.61315	−	7.52759i	−0.375617	−	0.294127i
$656$		0			0
$657$	28.1648	−	28.1648i	1.09881	−	1.09881i
$658$		0			0
$659$		−	46.6055i		−	1.81549i	−0.419521	−	0.907746i	$-0.637802\pi$
$659$		−	46.6055i		−	1.81549i	0.419521	−	0.907746i	$-0.362198\pi$
$660$		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
$663$	24.1038	−	6.45860i	0.936115	−	0.250831i
$664$		0			0
$665$	−15.4446	+	39.2601i	−0.598916	+	1.52244i
$666$		0			0
$667$	−6.54423	+	1.75352i	−0.253394	+	0.0678966i
$668$		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	−0.993087	−	0.117383i	$-0.962549\pi$
$673$	−22.7177	+	22.7177i	−0.875704	+	0.875704i	0.117383	+	0.993087i	$0.462549\pi$
$674$		0			0
$675$	−3.16188	+	1.74361i	−0.121701	+	0.0671116i
$676$		0			0
$677$	−2.69961	−	10.0751i	−0.103754	−	0.387216i	0.894447	−	0.447175i	$-0.147570\pi$
$677$	−2.69961	−	10.0751i	−0.103754	−	0.387216i	−0.998201	+	0.0599584i	$0.980903\pi$
$678$		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
$683$	−9.34955	−	2.50520i	−0.357750	−	0.0958589i	0.0754672	−	0.997148i	$-0.475955\pi$
$683$	−9.34955	−	2.50520i	−0.357750	−	0.0958589i	−0.433218	+	0.901289i	$0.642622\pi$
$684$		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
$693$	−8.91320	−	29.9207i	−0.338584	−	1.13659i
$694$		0			0
$695$	9.59699	+	1.35949i	0.364034	+	0.0515686i
$696$		0			0
$697$	2.49639	−	9.31666i	0.0945576	−	0.352894i
$698$		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
$703$	−1.60399	+	5.98618i	−0.0604957	+	0.225773i
$704$		0			0
$705$	53.8647	+	7.63040i	2.02866	+	0.287377i
$706$		0			0
$707$	22.4455	−	23.7259i	0.844149	−	0.892304i
$708$		0			0
$709$	−37.1759	−	21.4635i	−1.39617	−	0.806079i	−0.402182	−	0.915560i	$-0.631748\pi$
$709$	−37.1759	−	21.4635i	−1.39617	−	0.806079i	−0.993989	+	0.109480i	$0.965081\pi$
$710$		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
$717$	−35.6802	−	9.56048i	−1.33250	−	0.357043i
$718$		0			0
$719$	−10.8241	+	18.7480i	−0.403673	+	0.699181i	−0.994166	−	0.107861i	$-0.965600\pi$
$719$	−10.8241	+	18.7480i	−0.403673	+	0.699181i	0.590493	+	0.807042i	$0.298933\pi$
$720$		0			0
$721$	−12.3347	+	7.58494i	−0.459368	+	0.282478i
$722$		0			0
$723$	−9.89888	−	36.9431i	−0.368143	−	1.37393i
$724$		0			0
$725$	1.84773	−	6.39092i	0.0686231	−	0.237353i
$726$		0			0
$727$	−5.06759	+	5.06759i	−0.187947	+	0.187947i	−0.794808	−	0.606861i	$-0.792428\pi$
$727$	−5.06759	+	5.06759i	−0.187947	+	0.187947i	0.606861	+	0.794808i	$0.292428\pi$
$728$		0			0
$729$			21.3073i			0.789159i
$730$		0			0
$731$	7.06019	−	4.07620i	0.261130	−	0.150764i
$732$		0			0
$733$	−30.6035	+	8.20019i	−1.13037	+	0.302881i	−0.775072	−	0.631873i	$-0.782286\pi$
$733$	−30.6035	+	8.20019i	−1.13037	+	0.302881i	−0.355295	+	0.934754i	$0.615620\pi$
$734$		0			0
$735$	6.56107	+	36.7808i	0.242009	+	1.35668i
$736$		0			0
$737$	31.1285	−	8.34085i	1.14663	−	0.307239i
$738$		0			0
$739$	14.6237	−	8.44299i	0.537941	−	0.310580i	−0.206303	−	0.978488i	$-0.566143\pi$
$739$	14.6237	−	8.44299i	0.537941	−	0.310580i	0.744244	+	0.667908i	$0.232810\pi$
$740$		0			0
$741$			105.123i			3.86177i
$742$		0			0
$743$	−23.6519	+	23.6519i	−0.867703	+	0.867703i	−0.992218	−	0.124515i	$-0.960262\pi$
$743$	−23.6519	+	23.6519i	−0.867703	+	0.867703i	0.124515	+	0.992218i	$0.460262\pi$
$744$		0			0
$745$	4.52394	+	3.54248i	0.165744	+	0.129786i
$746$		0			0
$747$	−0.268835	−	1.00331i	−0.00983615	−	0.0367090i
$748$		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
$753$	−1.36678	−	0.366228i	−0.0498083	−	0.0133461i
$754$		0			0
$755$	−0.862545	−	2.14163i	−0.0313912	−	0.0779418i
$756$		0			0
$757$	21.6103	+	21.6103i	0.785439	+	0.785439i	0.980743	−	0.195304i	$-0.0625693\pi$
$757$	21.6103	+	21.6103i	0.785439	+	0.785439i	−0.195304	+	0.980743i	$0.562569\pi$
$758$		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
$763$	−12.1978	+	12.8936i	−0.441589	+	0.466779i
$764$		0			0
$765$	−6.13590	−	8.16121i	−0.221844	−	0.295069i
$766$		0			0
$767$	−8.20558	+	30.6236i	−0.296286	+	1.10576i
$768$		0			0
$769$	24.3594			0.878421			0.439211	−	0.898384i	$-0.355258\pi$
$769$	24.3594			0.878421			0.439211	+	0.898384i	$0.355258\pi$
$770$		0			0
$771$	46.2987			1.66741
$772$		0			0
$773$	4.81671	−	17.9762i	0.173245	−	0.646560i	−0.823599	−	0.567173i	$-0.808037\pi$
$773$	4.81671	−	17.9762i	0.173245	−	0.646560i	0.996844	−	0.0793867i	$-0.0252962\pi$
$774$		0			0
$775$	−10.6557	+	2.63197i	−0.382764	+	0.0945433i
$776$		0			0
$777$	1.56687	+	5.25982i	0.0562111	+	0.188695i
$778$		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
$787$	25.3262	+	6.78612i	0.902780	+	0.241899i	0.680210	−	0.733018i	$-0.261889\pi$
$787$	25.3262	+	6.78612i	0.902780	+	0.241899i	0.222570	+	0.974917i	$0.428555\pi$
$788$		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
$793$	−11.4716	−	42.8126i	−0.407369	−	1.52032i
$794$		0			0
$795$	−6.88204	+	8.78873i	−0.244081	+	0.311704i
$796$		0			0
$797$	12.0225	−	12.0225i	0.425859	−	0.425859i	−0.461356	−	0.887215i	$-0.652637\pi$
$797$	12.0225	−	12.0225i	0.425859	−	0.425859i	0.887215	+	0.461356i	$0.152637\pi$
$798$		0			0
$799$		−	17.2545i		−	0.610420i
$800$		0			0
$801$	8.38674	−	4.84208i	0.296331	−	0.171087i
$802$		0			0
$803$	−62.3937	+	16.7183i	−2.20183	+	0.589978i
$804$		0			0
$805$	−12.0246	−	27.6208i	−0.423812	−	0.973506i
$806$		0			0
$807$	−28.4705	+	7.62865i	−1.00221	+	0.268541i
$808$		0			0
$809$	−34.2965	+	19.8011i	−1.20580	+	0.696169i	−0.961839	−	0.273616i	$-0.911780\pi$
$809$	−34.2965	+	19.8011i	−1.20580	+	0.696169i	−0.243961	+	0.969785i	$0.578447\pi$
$810$		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
$815$	2.35992	+	19.3957i	0.0826644	+	0.679402i
$816$		0			0
$817$	8.88865	+	33.1729i	0.310974	+	1.16057i
$818$		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
$823$	3.74840	+	1.00438i	0.130661	+	0.0350105i	0.323557	−	0.946209i	$-0.395121\pi$
$823$	3.74840	+	1.00438i	0.130661	+	0.0350105i	−0.192896	+	0.981219i	$0.561788\pi$
$824$		0			0
$825$	−52.1984	−	1.02557i	−1.81731	−	0.0357057i
$826$		0			0
$827$	16.8597	+	16.8597i	0.586268	+	0.586268i	0.936619	−	0.350351i	$-0.113938\pi$
$827$	16.8597	+	16.8597i	0.586268	+	0.586268i	−0.350351	+	0.936619i	$0.613938\pi$
$828$		0			0
$829$	8.10906	+	14.0453i	0.281639	+	0.487813i	0.971789	−	0.235853i	$-0.0757885\pi$
$829$	8.10906	+	14.0453i	0.281639	+	0.487813i	−0.690149	+	0.723667i	$0.742455\pi$
$830$		0			0
$831$	−39.0722	−	22.5583i	−1.35540	−	0.782540i
$832$		0			0
$833$	11.2583	−	3.69655i	0.390078	−	0.128078i
$834$		0			0
$835$	−31.2873	+	23.5230i	−1.08274	+	0.814045i
$836$		0			0
$837$	0.410297	−	1.53125i	0.0141819	−	0.0529277i
$838$		0			0
$839$	2.13469			0.0736978			0.0368489	−	0.999321i	$-0.488268\pi$
$839$	2.13469			0.0736978			0.0368489	+	0.999321i	$0.488268\pi$
$840$		0			0
$841$	27.2297			0.938955
$842$		0			0
$843$	−13.5786	+	50.6760i	−0.467671	+	1.74537i
$844$		0			0
$845$	−7.88474	+	55.6602i	−0.271243	+	1.91477i
$846$		0			0
$847$	−4.99302	+	20.9399i	−0.171562	+	0.719502i
$848$		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	$-0.345960\pi$
$853$	−12.2640	−	12.2640i	−0.419910	−	0.419910i	−0.885173	+	0.465263i	$0.845960\pi$
$854$		0			0
$855$	39.8988	−	16.0693i	1.36451	−	0.549559i
$856$		0			0
$857$	−26.7209	−	7.15985i	−0.912769	−	0.244576i	−0.228277	−	0.973596i	$-0.573309\pi$
$857$	−26.7209	−	7.15985i	−0.912769	−	0.244576i	−0.684492	+	0.729021i	$0.739976\pi$
$858$		0			0
$859$	10.3098	−	17.8570i	0.351765	−	0.609274i	−0.634794	−	0.772681i	$-0.718915\pi$
$859$	10.3098	−	17.8570i	0.351765	−	0.609274i	0.986559	+	0.163407i	$0.0522484\pi$
$860$		0			0
$861$	35.9692	−	0.997482i	1.22583	−	0.0339941i
$862$		0			0
$863$	−7.64489	−	28.5311i	−0.260235	−	0.971211i	−0.965103	−	0.261872i	$-0.915660\pi$
$863$	−7.64489	−	28.5311i	−0.260235	−	0.971211i	0.704868	−	0.709339i	$-0.251006\pi$
$864$		0			0
$865$	−6.40393	+	0.779181i	−0.217740	+	0.0264930i
$866$		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
$873$	1.20044	−	0.321656i	0.0406286	−	0.0108864i
$874$		0			0
$875$	29.3206	+	3.91213i	0.991216	+	0.132254i
$876$		0			0
$877$	−3.75632	+	1.00650i	−0.126842	+	0.0339872i	−0.321681	−	0.946848i	$-0.604248\pi$
$877$	−3.75632	+	1.00650i	−0.126842	+	0.0339872i	0.194840	+	0.980835i	$0.437581\pi$
$878$		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	−0.951872	−	0.306496i	$-0.900844\pi$
$883$	−19.1776	+	19.1776i	−0.645377	+	0.645377i	0.306496	+	0.951872i	$0.400844\pi$
$884$		0			0
$885$	27.1991	−	3.30937i	0.914287	−	0.111243i
$886$		0			0
$887$	5.44459	+	20.3195i	0.182812	+	0.682262i	0.995088	+	0.0989899i	$0.0315612\pi$
$887$	5.44459	+	20.3195i	0.182812	+	0.682262i	−0.812277	+	0.583272i	$0.801772\pi$
$888$		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
$893$	70.2101	+	18.8127i	2.34949	+	0.629544i
$894$		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
$903$	22.0935	+	20.9012i	0.735226	+	0.695548i
$904$		0			0
$905$	−6.81534	+	48.1111i	−0.226550	+	1.59927i
$906$		0			0
$907$	−6.19919	+	23.1357i	−0.205841	+	0.768208i	0.783351	+	0.621580i	$0.213509\pi$
$907$	−6.19919	+	23.1357i	−0.205841	+	0.768208i	−0.989192	+	0.146629i	$0.953158\pi$
$908$		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
$913$	−0.435975	+	1.62708i	−0.0144287	+	0.0538485i
$914$		0			0
$915$	−30.6173	+	23.0192i	−1.01218	+	0.760993i
$916$		0			0
$917$	−14.0528	−	3.35082i	−0.464063	−	0.110654i
$918$		0			0
$919$	18.5274	+	10.6968i	0.611161	+	0.352854i	0.773420	−	0.633894i	$-0.218545\pi$
$919$	18.5274	+	10.6968i	0.611161	+	0.352854i	−0.162259	+	0.986748i	$0.551878\pi$
$920$		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
$927$	14.2601	+	3.82099i	0.468364	+	0.125498i
$928$		0			0
$929$	3.04513	−	5.27431i	0.0999073	−	0.173045i	−0.811739	−	0.584021i	$-0.801479\pi$
$929$	3.04513	−	5.27431i	0.0999073	−	0.173045i	0.911646	+	0.410976i	$0.134812\pi$
$930$		0			0
$931$	2.76650	+	49.8416i	0.0906684	+	1.63349i
$932$		0			0
$933$	6.92661	+	25.8505i	0.226767	+	0.846306i
$934$		0			0
$935$	1.99997	+	16.4374i	0.0654061	+	0.537560i
$936$		0			0
$937$	35.5732	−	35.5732i	1.16213	−	1.16213i	0.178117	−	0.984009i	$-0.443000\pi$
$937$	35.5732	−	35.5732i	1.16213	−	1.16213i	0.984009	−	0.178117i	$-0.0570004\pi$
$938$		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
$943$	−28.0247	+	7.50920i	−0.912610	+	0.244533i
$944$		0			0
$945$	−2.53973	+	3.43547i	−0.0826175	+	0.111756i
$946$		0			0
$947$	−56.5955	+	15.1647i	−1.83911	+	0.492787i	−0.998784	−	0.0492986i	$-0.984301\pi$
$947$	−56.5955	+	15.1647i	−1.83911	+	0.492787i	−0.840323	+	0.542086i	$0.817635\pi$
$948$		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	−0.453255	−	0.891381i	$-0.649737\pi$
$953$	13.5252	−	13.5252i	0.438125	−	0.438125i	0.891381	+	0.453255i	$0.149737\pi$
$954$		0			0
$955$	−15.8088	+	20.1887i	−0.511561	+	0.653292i
$956$		0			0
$957$	3.59577	+	13.4196i	0.116235	+	0.433794i
$958$		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
$963$	9.32939	+	2.49980i	0.300635	+	0.0805550i
$964$		0			0
$965$	11.4248	+	4.86434i	0.367779	+	0.156589i
$966$		0			0
$967$	−16.2564	−	16.2564i	−0.522770	−	0.522770i	0.395637	−	0.918407i	$-0.370524\pi$
$967$	−16.2564	−	16.2564i	−0.522770	−	0.522770i	−0.918407	+	0.395637i	$0.870524\pi$
$968$		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
$973$	10.9914	−	3.27426i	0.352367	−	0.104968i
$974$		0			0
$975$	71.5557	−	17.6743i	2.29162	−	0.566032i
$976$		0			0
$977$	−0.467979	+	1.74652i	−0.0149720	+	0.0558761i	−0.973008	−	0.230773i	$-0.925875\pi$
$977$	−0.467979	+	1.74652i	−0.0149720	+	0.0558761i	0.958036	+	0.286649i	$0.0925413\pi$
$978$		0			0
$979$	−15.7050			−0.501934
$980$		0			0
$981$	18.0959			0.577759
$982$		0			0
$983$	4.82857	−	18.0205i	0.154007	−	0.574763i	−0.845181	−	0.534480i	$-0.820507\pi$
$983$	4.82857	−	18.0205i	0.154007	−	0.574763i	0.999188	−	0.0402830i	$-0.0128259\pi$
$984$		0			0
$985$	−23.9433	−	31.8464i	−0.762898	−	1.01471i
$986$		0			0
$987$	61.6908	−	18.3774i	1.96364	−	0.584958i
$988$		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
$997$	11.6257	+	3.11510i	0.368190	+	0.0986561i	0.438170	−	0.898892i	$-0.355627\pi$
$997$	11.6257	+	3.11510i	0.368190	+	0.0986561i	−0.0699801	+	0.997548i	$0.522294\pi$
$998$		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.257.2	yes	48
4.3	odd	2		560.2.ci.e.257.11		48
5.3	odd	4	inner	280.2.bo.a.33.2	yes	48
7.3	odd	6	inner	280.2.bo.a.17.2	✓	48
20.3	even	4		560.2.ci.e.33.11		48
28.3	even	6		560.2.ci.e.17.11		48
35.3	even	12	inner	280.2.bo.a.73.2	yes	48
140.3	odd	12		560.2.ci.e.353.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bo.a.17.2	✓	48	7.3	odd	6	inner
280.2.bo.a.33.2	yes	48	5.3	odd	4	inner
280.2.bo.a.73.2	yes	48	35.3	even	12	inner
280.2.bo.a.257.2	yes	48	1.1	even	1	trivial
560.2.ci.e.17.11		48	28.3	even	6
560.2.ci.e.33.11		48	20.3	even	4
560.2.ci.e.257.11		48	4.3	odd	2
560.2.ci.e.353.11		48	140.3	odd	12

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)

\(f(q)\)	\(=\)	\(q+(-0.617784 + 2.30560i) q^{3} +(2.21396 + 0.313627i) q^{5} +(2.53563 - 0.755351i) q^{7} +(-2.33607 - 1.34873i) q^{9} +O(q^{10})\)	\(q+(-0.617784 + 2.30560i) q^{3} +(2.21396 + 0.313627i) q^{5} +(2.53563 - 0.755351i) q^{7} +(-2.33607 - 1.34873i) q^{9} +(2.18726 + 3.78844i) q^{11} +(-4.36695 - 4.36695i) q^{13} +(-2.09085 + 4.91077i) q^{15} +(1.63513 + 0.438132i) q^{17} +(-3.56560 + 6.17580i) q^{19} +(0.175064 + 6.31281i) q^{21} +(-1.31791 - 4.91851i) q^{23} +(4.80328 + 1.38872i) q^{25} +(-0.510640 + 0.510640i) q^{27} -1.33053i q^{29} +(-1.90109 + 1.09759i) q^{31} +(-10.0859 + 2.70251i) q^{33} +(5.85070 - 0.877077i) q^{35} +(0.839435 - 0.224926i) q^{37} +(12.7663 - 7.37062i) q^{39} -5.69781i q^{41} +(3.40535 - 3.40535i) q^{43} +(-4.74897 - 3.71869i) q^{45} +(-2.63809 - 9.84549i) q^{47} +(5.85889 - 3.83059i) q^{49} +(-2.02031 + 3.49929i) q^{51} +(2.02016 + 0.541299i) q^{53} +(3.65436 + 9.07346i) q^{55} +(-12.0362 - 12.0362i) q^{57} +(-2.56679 - 4.44580i) q^{59} +(6.21535 + 3.58843i) q^{61} +(-6.94217 - 1.65533i) q^{63} +(-8.29868 - 11.0379i) q^{65} +(1.90669 - 7.11586i) q^{67} +12.1543 q^{69} +4.31969 q^{71} +(-3.82176 + 14.2630i) q^{73} +(-6.16922 + 10.2165i) q^{75} +(8.40770 + 7.95396i) q^{77} +(-4.82649 - 2.78658i) q^{79} +(-4.90805 - 8.50099i) q^{81} +(0.272283 + 0.272283i) q^{83} +(3.48271 + 1.48283i) q^{85} +(3.06768 + 0.821982i) q^{87} +(-1.79506 + 3.10913i) q^{89} +(-14.3716 - 7.77441i) q^{91} +(-1.35615 - 5.06123i) q^{93} +(-9.83100 + 12.5547i) q^{95} +(-0.325781 + 0.325781i) q^{97} -11.8001i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{7}+O(q^{10}) \) 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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