LMFDB - Embedded newform 585.2.dp.a.28.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [585,2,Mod(28,585)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("585.28"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(585, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 1])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$585 = 3^{2} \cdot 5 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	585.dp (of order $12$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [20,6,0,6,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1$ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			28.5
Root			$-2.64975i$ of defining polynomial
Character	$\chi$	$=$	585.28
Dual form			585.2.dp.a.397.5

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.29475 - 1.32488i) q^{2} +(2.51060 - 4.34849i) q^{4} +(-1.81654 - 1.30391i) q^{5} +(0.0561740 - 0.0972962i) q^{7} -8.00544i q^{8} +(-5.89604 - 0.585458i) q^{10} +(-0.479564 + 1.78976i) q^{11} +(2.96279 - 2.05471i) q^{13} -0.297695i q^{14} +(-5.58502 - 9.67354i) q^{16} +(2.63669 - 0.706500i) q^{17} +(-6.72284 + 1.80138i) q^{19} +(-10.2306 + 4.62561i) q^{20} +(1.27073 + 4.74241i) q^{22} +(3.10327 + 0.831519i) q^{23} +(1.59964 + 4.73721i) q^{25} +(4.07664 - 8.64040i) q^{26} +(-0.282061 - 0.488544i) q^{28} +(4.03134 - 2.32749i) q^{29} +(-0.624367 + 0.624367i) q^{31} +(-11.7667 - 6.79350i) q^{32} +(5.11454 - 5.11454i) q^{34} +(-0.228908 + 0.103497i) q^{35} +(-0.737435 - 1.27728i) q^{37} +(-13.0407 + 13.0407i) q^{38} +(-10.4384 + 14.5422i) q^{40} +(5.24069 + 1.40424i) q^{41} +(1.00860 + 3.76415i) q^{43} +(6.57874 + 6.57874i) q^{44} +(8.22291 - 2.20332i) q^{46} +0.345095 q^{47} +(3.49369 + 6.05125i) q^{49} +(9.94700 + 8.75140i) q^{50} +(-1.49651 - 18.0422i) q^{52} +(3.59144 + 3.59144i) q^{53} +(3.20483 - 2.62586i) q^{55} +(-0.778898 - 0.449697i) q^{56} +(6.16729 - 10.6821i) q^{58} +(-0.332494 - 1.24088i) q^{59} +(1.39151 - 2.41016i) q^{61} +(-0.605559 + 2.25998i) q^{62} -13.6621 q^{64} +(-8.06120 - 0.130742i) q^{65} +(0.124992 - 0.0721643i) q^{67} +(3.54747 - 13.2394i) q^{68} +(-0.388167 + 0.540774i) q^{70} +(1.41668 + 5.28713i) q^{71} +9.06221i q^{73} +(-3.38447 - 1.95402i) q^{74} +(-9.04509 + 33.7567i) q^{76} +(0.147197 + 0.147197i) q^{77} -15.1689i q^{79} +(-2.46800 + 24.8547i) q^{80} +(13.8865 - 3.72089i) q^{82} -8.53853 q^{83} +(-5.71087 - 2.15462i) q^{85} +(7.30152 + 7.30152i) q^{86} +(14.3278 + 3.83912i) q^{88} +(-0.549735 - 0.147301i) q^{89} +(-0.0334840 - 0.403690i) q^{91} +(11.4069 - 11.4069i) q^{92} +(0.791908 - 0.457208i) q^{94} +(14.5612 + 5.49370i) q^{95} +(-12.9596 - 7.48223i) q^{97} +(16.0343 + 9.25742i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$20 q + 6 q^{2} + 6 q^{4} - 2 q^{7} - 2 q^{10} + 16 q^{11} - 4 q^{13} - 2 q^{16} - 4 q^{17} - 20 q^{19} + 16 q^{22} + 10 q^{23} + 18 q^{25} + 24 q^{26} + 18 q^{28} - 48 q^{32} + 2 q^{34} - 40 q^{35} - 4 q^{37}+ \cdots + 30 q^{98}+O(q^{100})$ 20 * q + 6 * q^2 + 6 * q^4 - 2 * q^7 - 2 * q^10 + 16 * q^11 - 4 * q^13 - 2 * q^16 - 4 * q^17 - 20 * q^19 + 16 * q^22 + 10 * q^23 + 18 * q^25 + 24 * q^26 + 18 * q^28 - 48 * q^32 + 2 * q^34 - 40 * q^35 - 4 * q^37 + 8 * q^38 - 16 * q^40 - 10 * q^41 + 10 * q^43 + 36 * q^44 + 4 * q^46 + 40 * q^47 + 18 * q^49 - 36 * q^50 - 30 * q^52 + 10 * q^53 - 10 * q^55 + 16 * q^59 - 16 * q^61 + 44 * q^62 + 20 * q^64 + 14 * q^65 + 18 * q^67 - 22 * q^68 - 12 * q^70 + 16 * q^71 - 18 * q^74 - 64 * q^76 + 28 * q^77 + 2 * q^80 + 56 * q^82 - 48 * q^83 - 26 * q^85 - 60 * q^86 + 82 * q^88 + 6 * q^89 + 8 * q^91 + 8 * q^92 - 48 * q^94 + 26 * q^95 + 66 * q^97 + 30 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$ .

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{12}\right)$

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

)

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

$2$	2.29475	−	1.32488i	1.62264	−	0.936830i	0.636425	−	0.771338i	$-0.280412\pi$
$2$	2.29475	−	1.32488i	1.62264	−	0.936830i	0.986211	−	0.165491i	$-0.0529210\pi$
$3$		0			0
$3$		0			0
$4$	2.51060	−	4.34849i	1.25530	−	2.17424i
$5$	−1.81654	−	1.30391i	−0.812382	−	0.583126i
$5$	−1.81654	−	1.30391i	−0.812382	−	0.583126i
$6$		0			0
$7$	0.0561740	−	0.0972962i	0.0212318	−	0.0367745i	−0.855214	−	0.518275i	$-0.826575\pi$
$7$	0.0561740	−	0.0972962i	0.0212318	−	0.0367745i	0.876446	+	0.481500i	$0.159908\pi$
$8$		−	8.00544i		−	2.83035i
$9$		0			0
$10$	−5.89604	−	0.585458i	−1.86449	−	0.185138i
$11$	−0.479564	+	1.78976i	−0.144594	+	0.539632i	0.855179	+	0.518332i	$0.173447\pi$
$11$	−0.479564	+	1.78976i	−0.144594	+	0.539632i	−0.999773	+	0.0212994i	$0.993220\pi$
$12$		0			0
$13$	2.96279	−	2.05471i	0.821731	−	0.569875i
$13$	2.96279	−	2.05471i	0.821731	−	0.569875i
$14$		−	0.297695i		−	0.0795622i
$15$		0			0
$16$	−5.58502	−	9.67354i	−1.39626	−	2.41838i
$17$	2.63669	−	0.706500i	0.639492	−	0.171351i	0.0755186	−	0.997144i	$-0.475939\pi$
$17$	2.63669	−	0.706500i	0.639492	−	0.171351i	0.563973	+	0.825793i	$0.309272\pi$
$18$		0			0
$19$	−6.72284	+	1.80138i	−1.54233	+	0.413265i	−0.927016	−	0.375021i	$-0.877636\pi$
$19$	−6.72284	+	1.80138i	−1.54233	+	0.413265i	−0.615309	+	0.788286i	$0.710969\pi$
$20$	−10.2306	+	4.62561i	−2.28764	+	1.03432i
$21$		0			0
$22$	1.27073	+	4.74241i	0.270920	+	1.01109i
$23$	3.10327	+	0.831519i	0.647077	+	0.173384i	0.567407	−	0.823438i	$-0.307947\pi$
$23$	3.10327	+	0.831519i	0.647077	+	0.173384i	0.0796701	+	0.996821i	$0.474613\pi$
$24$		0			0
$25$	1.59964	+	4.73721i	0.319928	+	0.947442i
$26$	4.07664	−	8.64040i	0.799495	−	1.69452i
$27$		0			0
$28$	−0.282061	−	0.488544i	−0.0533045	−	0.0923261i
$29$	4.03134	−	2.32749i	0.748601	−	0.432205i	−0.0765874	−	0.997063i	$-0.524402\pi$
$29$	4.03134	−	2.32749i	0.748601	−	0.432205i	0.825188	+	0.564858i	$0.191069\pi$
$30$		0			0
$31$	−0.624367	+	0.624367i	−0.112140	+	0.112140i	−0.760950	−	0.648810i	$-0.775267\pi$
$31$	−0.624367	+	0.624367i	−0.112140	+	0.112140i	0.648810	+	0.760950i	$0.275267\pi$
$32$	−11.7667	−	6.79350i	−2.08008	−	1.20093i
$33$		0			0
$34$	5.11454	−	5.11454i	0.877136	−	0.877136i
$35$	−0.228908	+	0.103497i	−0.0386925	+	0.0174941i
$36$		0			0
$37$	−0.737435	−	1.27728i	−0.121234	−	0.209983i	0.799021	−	0.601303i	$-0.205352\pi$
$37$	−0.737435	−	1.27728i	−0.121234	−	0.209983i	−0.920254	+	0.391321i	$0.872018\pi$
$38$	−13.0407	+	13.0407i	−2.11548	+	2.11548i
$39$		0			0
$40$	−10.4384	+	14.5422i	−1.65045	+	2.29932i
$41$	5.24069	+	1.40424i	0.818458	+	0.219305i	0.643672	−	0.765301i	$-0.277410\pi$
$41$	5.24069	+	1.40424i	0.818458	+	0.219305i	0.174786	+	0.984606i	$0.444077\pi$
$42$		0			0
$43$	1.00860	+	3.76415i	0.153810	+	0.574027i	0.999204	+	0.0398840i	$0.0126989\pi$
$43$	1.00860	+	3.76415i	0.153810	+	0.574027i	−0.845394	+	0.534143i	$0.820634\pi$
$44$	6.57874	+	6.57874i	0.991782	+	0.991782i
$45$		0			0
$46$	8.22291	−	2.20332i	1.21240	−	0.324862i
$47$	0.345095			0.0503372			0.0251686	−	0.999683i	$-0.491988\pi$
$47$	0.345095			0.0503372			0.0251686	+	0.999683i	$0.491988\pi$
$48$		0			0
$49$	3.49369	+	6.05125i	0.499098	+	0.864464i
$50$	9.94700	+	8.75140i	1.40672	+	1.23764i
$51$		0			0
$52$	−1.49651	−	18.0422i	−0.207528	−	2.50201i
$53$	3.59144	+	3.59144i	0.493322	+	0.493322i	0.909351	−	0.416029i	$-0.136579\pi$
$53$	3.59144	+	3.59144i	0.493322	+	0.493322i	−0.416029	+	0.909351i	$0.636579\pi$
$54$		0			0
$55$	3.20483	−	2.62586i	0.432139	−	0.354071i
$56$	−0.778898	−	0.449697i	−0.104085	−	0.0600933i
$57$		0			0
$58$	6.16729	−	10.6821i	0.809805	−	1.40262i
$59$	−0.332494	−	1.24088i	−0.0432870	−	0.161549i	0.940899	−	0.338687i	$-0.109983\pi$
$59$	−0.332494	−	1.24088i	−0.0432870	−	0.161549i	−0.984186	+	0.177138i	$0.943316\pi$
$60$		0			0
$61$	1.39151	−	2.41016i	0.178164	−	0.308589i	−0.763088	−	0.646295i	$-0.776318\pi$
$61$	1.39151	−	2.41016i	0.178164	−	0.308589i	0.941252	+	0.337706i	$0.109651\pi$
$62$	−0.605559	+	2.25998i	−0.0769061	+	0.287017i
$63$		0			0
$64$	−13.6621			−1.70776
$65$	−8.06120	−	0.130742i	−0.999869	−	0.0162165i
$66$		0			0
$67$	0.124992	−	0.0721643i	0.0152702	−	0.00881627i	−0.492345	−	0.870400i	$-0.663860\pi$
$67$	0.124992	−	0.0721643i	0.0152702	−	0.00881627i	0.507616	+	0.861584i	$0.330527\pi$
$68$	3.54747	−	13.2394i	0.430194	−	1.60551i
$69$		0			0
$70$	−0.388167	+	0.540774i	−0.0463948	+	0.0646349i
$71$	1.41668	+	5.28713i	0.168129	+	0.627467i	0.997620	+	0.0689472i	$0.0219640\pi$
$71$	1.41668	+	5.28713i	0.168129	+	0.627467i	−0.829491	+	0.558520i	$0.811369\pi$
$72$		0			0
$73$			9.06221i			1.06065i	0.847794	+	0.530326i	$0.177930\pi$
$73$			9.06221i			1.06065i	−0.847794	+	0.530326i	$0.822070\pi$
$74$	−3.38447	−	1.95402i	−0.393436	−	0.227151i
$75$		0			0
$76$	−9.04509	+	33.7567i	−1.03754	+	3.87216i
$77$	0.147197	+	0.147197i	0.0167747	+	0.0167747i
$78$		0			0
$79$		−	15.1689i		−	1.70664i	−0.521388	−	0.853320i	$-0.674586\pi$
$79$		−	15.1689i		−	1.70664i	0.521388	−	0.853320i	$-0.325414\pi$
$80$	−2.46800	+	24.8547i	−0.275931	+	2.77884i
$81$		0			0
$82$	13.8865	−	3.72089i	1.53351	−	0.410903i
$83$	−8.53853			−0.937226			−0.468613	−	0.883404i	$-0.655246\pi$
$83$	−8.53853			−0.937226			−0.468613	+	0.883404i	$0.655246\pi$
$84$		0			0
$85$	−5.71087	−	2.15462i	−0.619431	−	0.233702i
$86$	7.30152	+	7.30152i	0.787343	+	0.787343i
$87$		0			0
$88$	14.3278	+	3.83912i	1.52735	+	0.409251i
$89$	−0.549735	−	0.147301i	−0.0582718	−	0.0156139i	0.229565	−	0.973293i	$-0.426270\pi$
$89$	−0.549735	−	0.147301i	−0.0582718	−	0.0156139i	−0.287837	+	0.957679i	$0.592936\pi$
$90$		0			0
$91$	−0.0334840	−	0.403690i	−0.00351007	−	0.0423182i
$92$	11.4069	−	11.4069i	1.18925	−	1.18925i
$93$		0			0
$94$	0.791908	−	0.457208i	0.0816791	−	0.0471574i
$95$	14.5612	+	5.49370i	1.49394	+	0.563641i
$96$		0			0
$97$	−12.9596	−	7.48223i	−1.31585	−	0.759705i	−0.332790	−	0.943001i	$-0.607990\pi$
$97$	−12.9596	−	7.48223i	−1.31585	−	0.759705i	−0.983058	+	0.183296i	$0.941323\pi$
$98$	16.0343	+	9.25742i	1.61971	+	0.935140i
$99$		0			0
$100$	24.6157	+	4.93722i	2.46157	+	0.493722i
$101$	−7.19717	+	4.15529i	−0.716146	+	0.413467i	−0.813332	−	0.581799i	$-0.802349\pi$
$101$	−7.19717	+	4.15529i	−0.716146	+	0.413467i	0.0971867	+	0.995266i	$0.469016\pi$
$102$		0			0
$103$	−7.72940	+	7.72940i	−0.761600	+	0.761600i	−0.976612	−	0.215011i	$-0.931021\pi$
$103$	−7.72940	+	7.72940i	−0.761600	+	0.761600i	0.215011	+	0.976612i	$0.431021\pi$
$104$	−16.4489	−	23.7185i	−1.61295	−	2.32579i
$105$		0			0
$106$	12.9997	+	3.48325i	1.26264	+	0.338324i
$107$	−7.15177	−	1.91631i	−0.691388	−	0.185257i	−0.104018	−	0.994575i	$-0.533170\pi$
$107$	−7.15177	−	1.91631i	−0.691388	−	0.185257i	−0.587370	+	0.809318i	$0.699837\pi$
$108$		0			0
$109$	3.34544	+	3.34544i	0.320435	+	0.320435i	0.848934	−	0.528499i	$-0.177245\pi$
$109$	3.34544	+	3.34544i	0.320435	+	0.320435i	−0.528499	+	0.848934i	$0.677245\pi$
$110$	3.87535	−	10.2717i	0.369500	−	0.979368i
$111$		0			0
$112$	−1.25493			−0.118580
$113$	5.90688	−	1.58274i	0.555672	−	0.148892i	0.0299550	−	0.999551i	$-0.490464\pi$
$113$	5.90688	−	1.58274i	0.555672	−	0.148892i	0.525717	+	0.850659i	$0.323797\pi$
$114$		0			0
$115$	−4.55300	−	5.55688i	−0.424569	−	0.518181i
$116$		−	23.3736i		−	2.17019i
$117$		0			0
$118$	−2.40701	−	2.40701i	−0.221583	−	0.221583i
$119$	0.0793738	−	0.296227i	0.00727618	−	0.0271551i
$120$		0			0
$121$	6.55303	+	3.78340i	0.595730	+	0.343945i
$122$		−	7.37430i		−	0.667638i
$123$		0			0
$124$	1.14751	+	4.28258i	0.103050	+	0.384587i
$125$	3.27108	−	10.6911i	0.292574	−	0.956243i
$126$		0			0
$127$	−3.01994	+	11.2706i	−0.267976	+	1.00010i	0.692427	+	0.721488i	$0.256541\pi$
$127$	−3.01994	+	11.2706i	−0.267976	+	1.00010i	−0.960403	+	0.278613i	$0.910125\pi$
$128$	−7.81784	+	4.51363i	−0.691006	+	0.398953i
$129$		0			0
$130$	−18.6717	+	10.3801i	−1.63762	+	0.910393i
$131$	−7.46380			−0.652115			−0.326058	−	0.945350i	$-0.605720\pi$
$131$	−7.46380			−0.652115			−0.326058	+	0.945350i	$0.605720\pi$
$132$		0			0
$133$	−0.202381	+	0.755298i	−0.0175487	+	0.0654926i
$134$	0.191218	−	0.331199i	0.0165187	−	0.0286112i
$135$		0			0
$136$	−5.65584	−	21.1079i	−0.484984	−	1.80998i
$137$	−9.24213	+	16.0078i	−0.789608	+	1.36764i	0.136599	+	0.990626i	$0.456383\pi$
$137$	−9.24213	+	16.0078i	−0.789608	+	1.36764i	−0.926207	+	0.377015i	$0.876950\pi$
$138$		0			0
$139$	−9.44862	−	5.45516i	−0.801421	−	0.462701i	0.0425466	−	0.999094i	$-0.486453\pi$
$139$	−9.44862	−	5.45516i	−0.801421	−	0.462701i	−0.843968	+	0.536394i	$0.819786\pi$
$140$	−0.124642	+	1.25524i	−0.0105341	+	0.106087i
$141$		0			0
$142$	10.2557	+	10.2557i	0.860643	+	0.860643i
$143$	2.25659	+	6.28804i	0.188705	+	0.525833i
$144$		0			0
$145$	−10.3579	−	1.02851i	−0.860179	−	0.0854132i
$146$	12.0063	+	20.7955i	0.993650	+	1.72105i
$147$		0			0
$148$	−7.40562			−0.608738
$149$	−13.4468	+	3.60307i	−1.10161	+	0.295175i	−0.763419	−	0.645903i	$-0.776481\pi$
$149$	−13.4468	+	3.60307i	−1.10161	+	0.295175i	−0.338189	+	0.941078i	$0.609814\pi$
$150$		0			0
$151$	−8.49593	−	8.49593i	−0.691389	−	0.691389i	0.271149	−	0.962537i	$-0.412596\pi$
$151$	−8.49593	−	8.49593i	−0.691389	−	0.691389i	−0.962537	+	0.271149i	$0.912596\pi$
$152$	14.4208	+	53.8193i	1.16968	+	4.36532i
$153$		0			0
$154$	0.532801	+	0.142763i	0.0429343	+	0.0115042i
$155$	1.94830	−	0.320070i	0.156492	−	0.0257086i
$156$		0			0
$157$	−5.14491	+	5.14491i	−0.410609	+	0.410609i	−0.881951	−	0.471342i	$-0.843770\pi$
$157$	−5.14491	+	5.14491i	−0.410609	+	0.410609i	0.471342	+	0.881951i	$0.343770\pi$
$158$	−20.0970	−	34.8090i	−1.59883	−	2.76926i
$159$		0			0
$160$	12.5166	+	27.6833i	0.989520	+	2.18856i
$161$	0.255227	−	0.255227i	0.0201147	−	0.0201147i
$162$		0			0
$163$	17.7686	+	10.2587i	1.39175	+	0.803526i	0.993509	−	0.113756i	$-0.0362881\pi$
$163$	17.7686	+	10.2587i	1.39175	+	0.803526i	0.398239	+	0.917282i	$0.369621\pi$
$164$	19.2636	−	19.2636i	1.50423	−	1.50423i
$165$		0			0
$166$	−19.5938	+	11.3125i	−1.52078	+	0.878021i
$167$	−1.27050	−	2.20058i	−0.0983146	−	0.170286i	0.812673	−	0.582721i	$-0.198012\pi$
$167$	−1.27050	−	2.20058i	−0.0983146	−	0.170286i	−0.910987	+	0.412435i	$0.864678\pi$
$168$		0			0
$169$	4.55630	−	12.1754i	0.350484	−	0.936569i
$170$	−15.9597	+	2.62187i	−1.22405	+	0.201088i
$171$		0			0
$172$	18.9005	+	5.06438i	1.44115	+	0.386155i
$173$	−0.0204199	−	0.0762079i	−0.00155249	−	0.00579398i	0.965145	−	0.261715i	$-0.0842880\pi$
$173$	−0.0204199	−	0.0762079i	−0.00155249	−	0.00579398i	−0.966698	+	0.255921i	$0.917621\pi$
$174$		0			0
$175$	0.550771	+	0.110469i	0.0416343	+	0.00835067i
$176$	19.9916	−	5.35675i	1.50693	−	0.403780i
$177$		0			0
$178$	−1.45666	+	0.390312i	−0.109182	+	0.0292551i
$179$	−10.6120	−	18.3806i	−0.793181	−	1.37383i	−0.923988	−	0.382421i	$-0.875090\pi$
$179$	−10.6120	−	18.3806i	−0.793181	−	1.37383i	0.130808	−	0.991408i	$-0.458243\pi$
$180$		0			0
$181$		−	22.5267i		−	1.67440i	−0.546899	−	0.837198i	$-0.684192\pi$
$181$		−	22.5267i		−	1.67440i	0.546899	−	0.837198i	$-0.315808\pi$
$182$	−0.611677	−	0.882008i	−0.0453405	−	0.0653788i
$183$		0			0
$184$	6.65667	−	24.8430i	0.490737	−	1.83145i
$185$	−0.325870	+	3.28177i	−0.0239584	+	0.241281i
$186$		0			0
$187$			5.05785i			0.369866i
$188$	0.866395	−	1.50064i	0.0631883	−	0.109445i
$189$		0			0
$190$	40.6927	−	6.68506i	2.95216	−	0.484985i
$191$	9.80326	−	16.9797i	0.709339	−	1.22861i	−0.255764	−	0.966739i	$-0.582327\pi$
$191$	9.80326	−	16.9797i	0.709339	−	1.22861i	0.965103	−	0.261872i	$-0.0843398\pi$
$192$		0			0
$193$	14.4730	−	8.35601i	1.04179	−	0.601479i	0.121451	−	0.992597i	$-0.461245\pi$
$193$	14.4730	−	8.35601i	1.04179	−	0.601479i	0.920340	+	0.391119i	$0.127912\pi$
$194$	−39.6521			−2.84686
$195$		0			0
$196$	35.0850			2.50607
$197$	−13.1517	+	7.59315i	−0.937021	+	0.540990i	−0.889025	−	0.457858i	$-0.848617\pi$
$197$	−13.1517	+	7.59315i	−0.937021	+	0.540990i	−0.0479960	+	0.998848i	$0.515283\pi$
$198$		0			0
$199$	−6.97357	+	12.0786i	−0.494343	+	0.856228i	−0.999979	−	0.00651960i	$-0.997925\pi$
$199$	−6.97357	+	12.0786i	−0.494343	+	0.856228i	0.505636	+	0.862747i	$0.331258\pi$
$200$	37.9234	−	12.8058i	2.68159	−	0.905508i
$201$		0			0
$202$	−11.0105	+	19.0707i	−0.774696	+	1.34181i
$203$		−	0.522979i		−	0.0367059i
$204$		0			0
$205$	−7.68893	−	9.38424i	−0.537018	−	0.655424i
$206$	−7.49657	+	27.9776i	−0.522311	+	1.94929i
$207$		0			0
$208$	−36.4236	−	17.1851i	−2.52552	−	1.19157i
$209$		−	12.8961i		−	0.892044i
$210$		0			0
$211$	11.8091	+	20.4539i	0.812969	+	1.40810i	0.910777	+	0.412898i	$0.135483\pi$
$211$	11.8091	+	20.4539i	0.812969	+	1.40810i	−0.0978083	+	0.995205i	$0.531183\pi$
$212$	24.6340	−	6.60065i	1.69187	−	0.453335i
$213$		0			0
$214$	−18.9504	+	5.07776i	−1.29543	+	0.347108i
$215$	3.07594	−	8.15285i	0.209777	−	0.556019i
$216$		0			0
$217$	0.0256753	+	0.0958217i	0.00174296	+	0.00650480i
$218$	12.1093	+	3.24467i	0.820143	+	0.219757i
$219$		0			0
$220$	−3.37247	−	20.5286i	−0.227372	−	1.38404i
$221$	6.36032	−	7.51086i	0.427841	−	0.505235i
$222$		0			0
$223$	−4.86319	−	8.42330i	−0.325664	−	0.564066i	0.655983	−	0.754776i	$-0.272254\pi$
$223$	−4.86319	−	8.42330i	−0.325664	−	0.564066i	−0.981646	+	0.190710i	$0.938921\pi$
$224$	−1.32196	+	0.763236i	−0.0883274	+	0.0509958i
$225$		0			0
$226$	11.4579	−	11.4579i	0.762168	−	0.762168i
$227$	−7.94647	−	4.58790i	−0.527426	−	0.304510i	0.212542	−	0.977152i	$-0.431826\pi$
$227$	−7.94647	−	4.58790i	−0.527426	−	0.304510i	−0.739968	+	0.672642i	$0.765159\pi$
$228$		0			0
$229$	12.5270	−	12.5270i	0.827811	−	0.827811i	−0.159403	−	0.987214i	$-0.550957\pi$
$229$	12.5270	−	12.5270i	0.827811	−	0.827811i	0.987214	+	0.159403i	$0.0509569\pi$
$230$	−17.8102	−	6.71950i	−1.17437	−	0.443071i
$231$		0			0
$232$	−18.6326	−	32.2726i	−1.22329	−	2.11880i
$233$	11.8637	−	11.8637i	0.777214	−	0.777214i	−0.202142	−	0.979356i	$-0.564790\pi$
$233$	11.8637	−	11.8637i	0.777214	−	0.777214i	0.979356	+	0.202142i	$0.0647903\pi$
$234$		0			0
$235$	−0.626879	−	0.449972i	−0.0408931	−	0.0293530i
$236$	−6.23072	−	1.66952i	−0.405585	−	0.108676i
$237$		0			0
$238$	−0.210321	−	0.784929i	−0.0136331	−	0.0508794i
$239$	18.2161	+	18.2161i	1.17830	+	1.17830i	0.980177	+	0.198124i	$0.0634848\pi$
$239$	18.2161	+	18.2161i	1.17830	+	1.17830i	0.198124	+	0.980177i	$0.436515\pi$
$240$		0			0
$241$	−5.28403	+	1.41585i	−0.340374	+	0.0912030i	−0.424957	−	0.905213i	$-0.639711\pi$
$241$	−5.28403	+	1.41585i	−0.340374	+	0.0912030i	0.0845830	+	0.996416i	$0.473044\pi$
$242$	20.0501			1.28887
$243$		0			0
$244$	−6.98703	−	12.1019i	−0.447299	−	0.774744i
$245$	1.54385	−	15.5478i	0.0986329	−	0.993312i
$246$		0			0
$247$	−16.2171	+	19.1506i	−1.03187	+	1.21853i
$248$	4.99833	+	4.99833i	0.317394	+	0.317394i
$249$		0			0
$250$	−6.65810	−	28.8673i	−0.421095	−	1.82573i
$251$	−11.3169	−	6.53384i	−0.714319	−	0.412412i	0.0983394	−	0.995153i	$-0.468647\pi$
$251$	−11.3169	−	6.53384i	−0.714319	−	0.412412i	−0.812658	+	0.582741i	$0.801980\pi$
$252$		0			0
$253$	−2.97643	+	5.15533i	−0.187127	+	0.324113i
$254$	8.00209	+	29.8642i	0.502096	+	1.87385i
$255$		0			0
$256$	1.70209	−	2.94811i	0.106381	−	0.184257i
$257$	−4.51603	+	16.8541i	−0.281702	+	1.05133i	0.669513	+	0.742800i	$0.266503\pi$
$257$	−4.51603	+	16.8541i	−0.281702	+	1.05133i	−0.951215	+	0.308528i	$0.900164\pi$
$258$		0			0
$259$	−0.165699			−0.0102960
$260$	−20.8070	+	34.7258i	−1.29039	+	2.15360i
$261$		0			0
$262$	−17.1276	+	9.88862i	−1.05815	+	0.610921i
$263$	−5.39593	+	20.1379i	−0.332727	+	1.24175i	0.573585	+	0.819146i	$0.305552\pi$
$263$	−5.39593	+	20.1379i	−0.332727	+	1.24175i	−0.906312	+	0.422608i	$0.861115\pi$
$264$		0			0
$265$	−1.84108	−	11.2069i	−0.113097	−	0.688434i
$266$	0.536261	+	2.00135i	0.0328803	+	0.122711i
$267$		0			0
$268$		−	0.724703i		−	0.0442683i
$269$	9.15088	+	5.28326i	0.557939	+	0.322126i	0.752318	−	0.658800i	$-0.228936\pi$
$269$	9.15088	+	5.28326i	0.557939	+	0.322126i	−0.194379	+	0.980927i	$0.562269\pi$
$270$		0			0
$271$	−2.04739	+	7.64095i	−0.124370	+	0.464155i	−0.999816	−	0.0191601i	$-0.993901\pi$
$271$	−2.04739	+	7.64095i	−0.124370	+	0.464155i	0.875446	+	0.483315i	$0.160567\pi$
$272$	−21.5603	−	21.5603i	−1.30729	−	1.30729i
$273$		0			0
$274$			48.9787i			2.95891i
$275$	−9.24558	+	0.591174i	−0.557529	+	0.0356491i
$276$		0			0
$277$	9.86609	−	2.64361i	0.592796	−	0.158839i	0.0500653	−	0.998746i	$-0.484057\pi$
$277$	9.86609	−	2.64361i	0.592796	−	0.158839i	0.542731	+	0.839907i	$0.317390\pi$
$278$	−28.9097			−1.73389
$279$		0			0
$280$	0.828536	+	1.83251i	0.0495145	+	0.109513i
$281$	−12.4763	−	12.4763i	−0.744271	−	0.744271i	0.229126	−	0.973397i	$-0.426413\pi$
$281$	−12.4763	−	12.4763i	−0.744271	−	0.744271i	−0.973397	+	0.229126i	$0.926413\pi$
$282$		0			0
$283$	−7.98478	−	2.13952i	−0.474646	−	0.127181i	0.0135626	−	0.999908i	$-0.495683\pi$
$283$	−7.98478	−	2.13952i	−0.474646	−	0.127181i	−0.488208	+	0.872727i	$0.662349\pi$
$284$	26.5478	+	7.11345i	1.57532	+	0.422105i
$285$		0			0
$286$	13.5092	+	11.4398i	0.798816	+	0.676451i
$287$	0.431018	−	0.431018i	0.0254422	−	0.0254422i
$288$		0			0
$289$	−8.26943	+	4.77436i	−0.486437	+	0.280844i
$290$	−25.1316	+	11.3628i	−1.47578	+	0.667247i
$291$		0			0
$292$	39.4069	+	22.7516i	2.30611	+	1.33144i
$293$	5.52378	+	3.18916i	0.322703	+	0.186313i	0.652597	−	0.757705i	$-0.273680\pi$
$293$	5.52378	+	3.18916i	0.322703	+	0.186313i	−0.329894	+	0.944018i	$0.607013\pi$
$294$		0			0
$295$	−1.01401	+	2.68766i	−0.0590380	+	0.156481i
$296$	−10.2251	+	5.90349i	−0.594325	+	0.343133i
$297$		0			0
$298$	−26.0836	+	26.0836i	−1.51098	+	1.51098i
$299$	10.9029	−	3.91272i	0.630531	−	0.226278i
$300$		0			0
$301$	0.422894	+	0.113314i	0.0243752	+	0.00653132i
$302$	−30.7521	−	8.24001i	−1.76959	−	0.474159i
$303$		0			0
$304$	54.9729	+	54.9729i	3.15291	+	3.15291i
$305$	−5.67036	+	2.56376i	−0.324684	+	0.146800i
$306$		0			0
$307$	−26.5460			−1.51506			−0.757530	−	0.652801i	$-0.773594\pi$
$307$	−26.5460			−1.51506			−0.757530	+	0.652801i	$0.773594\pi$
$308$	1.00964	−	0.270532i	0.0575296	−	0.0154150i
$309$		0			0
$310$	4.04683	−	3.31575i	0.229844	−	0.188322i
$311$			3.54417i			0.200972i	0.994938	+	0.100486i	$0.0320397\pi$
$311$			3.54417i			0.200972i	−0.994938	+	0.100486i	$0.967960\pi$
$312$		0			0
$313$	−6.21088	−	6.21088i	−0.351060	−	0.351060i	0.509444	−	0.860504i	$-0.329851\pi$
$313$	−6.21088	−	6.21088i	−0.351060	−	0.351060i	−0.860504	+	0.509444i	$0.829851\pi$
$314$	−4.98993	+	18.6227i	−0.281598	+	1.05094i
$315$		0			0
$316$	−65.9619	−	38.0831i	−3.71065	−	2.14234i
$317$		−	8.52812i		−	0.478987i	−0.970898	−	0.239494i	$-0.923019\pi$
$317$		−	8.52812i		−	0.478987i	0.970898	−	0.239494i	$-0.0769814\pi$
$318$		0			0
$319$	2.23236	+	8.33129i	0.124988	+	0.466463i
$320$	24.8178	+	17.8142i	1.38736	+	0.995842i
$321$		0			0
$322$	0.247539	−	0.923827i	0.0137948	−	0.0514829i
$323$	−16.4534	+	9.49937i	−0.915491	+	0.528559i
$324$		0			0
$325$	14.4730	+	10.7486i	0.802819	+	0.596223i
$326$	54.3663			3.01107
$327$		0			0
$328$	11.2415	−	41.9540i	0.620710	−	2.31652i
$329$	0.0193853	−	0.0335764i	0.00106875	−	0.00185113i
$330$		0			0
$331$	4.66054	+	17.3934i	0.256166	+	0.956026i	0.967438	+	0.253109i	$0.0814530\pi$
$331$	4.66054	+	17.3934i	0.256166	+	0.956026i	−0.711271	+	0.702917i	$0.751880\pi$
$332$	−21.4368	+	37.1297i	−1.17650	+	2.03776i
$333$		0			0
$334$	−5.83099	−	3.36652i	−0.319058	−	0.184208i
$335$	−0.321149	−	0.0318891i	−0.0175463	−	0.00174229i
$336$		0			0
$337$	−20.0865	−	20.0865i	−1.09418	−	1.09418i	−0.995077	−	0.0991030i	$-0.968403\pi$
$337$	−20.0865	−	20.0865i	−1.09418	−	1.09418i	−0.0991030	−	0.995077i	$-0.531597\pi$
$338$	−5.67532	−	33.9761i	−0.308697	−	1.84805i
$339$		0			0
$340$	−23.7071	+	19.4242i	−1.28570	+	1.05343i
$341$	−0.818040	−	1.41689i	−0.0442994	−	0.0767288i
$342$		0			0
$343$	1.57145			0.0848505
$344$	30.1336	−	8.07428i	1.62470	−	0.435336i
$345$		0			0
$346$	−0.147825	−	0.147825i	−0.00794710	−	0.00794710i
$347$	1.85743	+	6.93201i	0.0997119	+	0.372130i	0.997692	−	0.0679068i	$-0.0216321\pi$
$347$	1.85743	+	6.93201i	0.0997119	+	0.372130i	−0.897980	+	0.440037i	$0.854965\pi$
$348$		0			0
$349$	3.52885	+	0.945552i	0.188895	+	0.0506143i	0.352026	−	0.935990i	$-0.385493\pi$
$349$	3.52885	+	0.945552i	0.188895	+	0.0506143i	−0.163131	+	0.986604i	$0.552159\pi$
$350$	1.41024	−	0.476204i	0.0753806	−	0.0254542i
$351$		0			0
$352$	17.8016	−	17.8016i	0.948827	−	0.948827i
$353$	0.881628	+	1.52702i	0.0469243	+	0.0812753i	0.888534	−	0.458812i	$-0.151725\pi$
$353$	0.881628	+	1.52702i	0.0469243	+	0.0812753i	−0.841609	+	0.540087i	$0.818391\pi$
$354$		0			0
$355$	4.32048	−	11.4515i	0.229307	−	0.607784i
$356$	−2.02070	+	2.02070i	−0.107097	+	0.107097i
$357$		0			0
$358$	−48.7040	−	28.1193i	−2.57409	−	1.48615i
$359$	−8.58021	+	8.58021i	−0.452846	+	0.452846i	−0.896298	−	0.443452i	$-0.853754\pi$
$359$	−8.58021	+	8.58021i	−0.452846	+	0.452846i	0.443452	+	0.896298i	$0.353754\pi$
$360$		0			0
$361$	25.4972	−	14.7208i	1.34196	−	0.774778i
$362$	−29.8451	−	51.6933i	−1.56862	−	2.71694i
$363$		0			0
$364$	−1.83951	−	0.867900i	−0.0964163	−	0.0454903i
$365$	11.8163	−	16.4619i	0.618493	−	0.861654i
$366$		0			0
$367$	13.5337	+	3.62635i	0.706454	+	0.189294i	0.594120	−	0.804377i	$-0.297501\pi$
$367$	13.5337	+	3.62635i	0.706454	+	0.189294i	0.112334	+	0.993670i	$0.464167\pi$
$368$	−9.28811	−	34.6637i	−0.484176	−	1.80697i
$369$		0			0
$370$	3.60015	+	7.96260i	0.187163	+	0.413956i
$371$	0.551179	−	0.147688i	0.0286158	−	0.00766757i
$372$		0			0
$373$	27.9078	−	7.47789i	1.44501	−	0.387190i	0.550727	−	0.834685i	$-0.314350\pi$
$373$	27.9078	−	7.47789i	1.44501	−	0.387190i	0.894286	+	0.447495i	$0.147684\pi$
$374$	6.70103	+	11.6065i	0.346502	+	0.600159i
$375$		0			0
$376$		−	2.76263i		−	0.142472i
$377$	7.16169	−	15.1791i	0.368846	−	0.781765i
$378$		0			0
$379$	2.45278	−	9.15390i	0.125991	−	0.470204i	−0.873882	−	0.486138i	$-0.838405\pi$
$379$	2.45278	−	9.15390i	0.125991	−	0.470204i	0.999873	+	0.0159336i	$0.00507204\pi$
$380$	60.4465	−	49.5265i	3.10084	−	2.54066i
$381$		0			0
$382$		−	51.9525i		−	2.65812i
$383$	−10.5361	+	18.2490i	−0.538369	+	0.932483i	0.460623	+	0.887596i	$0.347626\pi$
$383$	−10.5361	+	18.2490i	−0.538369	+	0.932483i	−0.998992	+	0.0448868i	$0.985707\pi$
$384$		0			0
$385$	−0.0754581	−	0.459322i	−0.00384570	−	0.0234092i
$386$	22.1414	−	38.3500i	1.12697	−	1.95196i
$387$		0			0
$388$	−65.0727	+	37.5698i	−3.30357	+	1.90732i
$389$	−0.0604806			−0.00306649			−0.00153324	−	0.999999i	$-0.500488\pi$
$389$	−0.0604806			−0.00306649			−0.00153324	+	0.999999i	$0.500488\pi$
$390$		0			0
$391$	8.76984			0.443510
$392$	48.4429	−	27.9685i	2.44673	−	1.41262i
$393$		0			0
$394$	−20.1200	+	34.8488i	−1.01363	+	1.75566i
$395$	−19.7789	+	27.5550i	−0.995186	+	1.38644i
$396$		0			0
$397$	−4.10812	+	7.11548i	−0.206181	+	0.357116i	−0.950508	−	0.310699i	$-0.899437\pi$
$397$	−4.10812	+	7.11548i	−0.206181	+	0.357116i	0.744327	+	0.667815i	$0.232770\pi$
$398$			36.9565i			1.85246i
$399$		0			0
$400$	36.8915	−	41.9316i	1.84458	−	2.09658i
$401$	2.32904	−	8.69210i	0.116307	−	0.434063i	−0.883075	−	0.469233i	$-0.844531\pi$
$401$	2.32904	−	8.69210i	0.116307	−	0.434063i	0.999381	+	0.0351698i	$0.0111972\pi$
$402$		0			0
$403$	−0.566974	+	3.13276i	−0.0282430	+	0.156054i
$404$			41.7291i			2.07610i
$405$		0			0
$406$	−0.692882	−	1.20011i	−0.0343872	−	0.0595603i
$407$	2.63966	−	0.707294i	0.130843	−	0.0350593i
$408$		0			0
$409$	34.6013	−	9.27138i	1.71092	−	0.458440i	0.735272	−	0.677772i	$-0.237054\pi$
$409$	34.6013	−	9.27138i	1.71092	−	0.458440i	0.975650	+	0.219332i	$0.0703877\pi$
$410$	−30.0772	−	11.3476i	−1.48541	−	0.560420i
$411$		0			0
$412$	14.2058	+	53.0166i	0.699867	+	2.61194i
$413$	−0.139411	−	0.0373550i	−0.00685995	−	0.00183812i
$414$		0			0
$415$	15.5106	+	11.1335i	0.761385	+	0.546521i
$416$	−48.8209	+	4.04944i	−2.39364	+	0.198540i
$417$		0			0
$418$	−17.0858	−	29.5934i	−0.835693	−	1.44746i
$419$	11.3282	−	6.54037i	0.553421	−	0.319518i	−0.197080	−	0.980387i	$-0.563146\pi$
$419$	11.3282	−	6.54037i	0.553421	−	0.319518i	0.750501	+	0.660870i	$0.229812\pi$
$420$		0			0
$421$	−13.7924	+	13.7924i	−0.672203	+	0.672203i	−0.958223	−	0.286021i	$-0.907667\pi$
$421$	−13.7924	+	13.7924i	−0.672203	+	0.672203i	0.286021	+	0.958223i	$0.407667\pi$
$422$	54.1978	+	31.2911i	2.63831	+	1.52323i
$423$		0			0
$424$	28.7510	−	28.7510i	1.39627	−	1.39627i
$425$	7.56460	+	11.3604i	0.366937	+	0.551061i
$426$		0			0
$427$	−0.156333	−	0.270777i	−0.00756548	−	0.0131038i
$428$	−26.2883	+	26.2883i	−1.27069	+	1.27069i
$429$		0			0
$430$	−3.74299	−	22.7840i	−0.180503	−	1.09874i
$431$	−21.4619	−	5.75070i	−1.03378	−	0.277002i	−0.298249	−	0.954488i	$-0.596403\pi$
$431$	−21.4619	−	5.75070i	−1.03378	−	0.277002i	−0.735535	+	0.677487i	$0.763069\pi$
$432$		0			0
$433$	0.0475058	+	0.177294i	0.00228298	+	0.00852021i	0.967058	−	0.254556i	$-0.0819295\pi$
$433$	0.0475058	+	0.177294i	0.00228298	+	0.00852021i	−0.964775	+	0.263077i	$0.915263\pi$
$434$	0.185871	+	0.185871i	0.00892207	+	0.00892207i
$435$		0			0
$436$	22.9467	−	6.14854i	1.09895	−	0.294462i
$437$	−22.3607			−1.06966
$438$		0			0
$439$	−8.64682	−	14.9767i	−0.412690	−	0.714800i	0.582493	−	0.812836i	$-0.302077\pi$
$439$	−8.64682	−	14.9767i	−0.412690	−	0.714800i	−0.995183	+	0.0980356i	$0.968744\pi$
$440$	−21.0211	−	25.6560i	−1.00214	−	1.22310i
$441$		0			0
$442$	4.64440	−	25.6622i	0.220912	−	1.22063i
$443$	−24.4472	−	24.4472i	−1.16152	−	1.16152i	−0.984143	−	0.177377i	$-0.943239\pi$
$443$	−24.4472	−	24.4472i	−1.16152	−	1.16152i	−0.177377	−	0.984143i	$-0.556761\pi$
$444$		0			0
$445$	0.806549	+	0.984383i	0.0382341	+	0.0466643i
$446$	−22.3197	−	12.8863i	−1.05687	−	0.610183i
$447$		0			0
$448$	−0.767456	+	1.32927i	−0.0362589	+	0.0628022i
$449$	−9.62407	−	35.9175i	−0.454188	−	1.69505i	−0.690465	−	0.723366i	$-0.742594\pi$
$449$	−9.62407	−	35.9175i	−0.454188	−	1.69505i	0.236277	−	0.971686i	$-0.424073\pi$
$450$		0			0
$451$	−5.02649	+	8.70613i	−0.236688	+	0.409956i
$452$	7.94727	−	29.6596i	0.373808	−	1.39507i
$453$		0			0
$454$	−24.3136			−1.14109
$455$	−0.465550	+	0.776980i	−0.0218253	+	0.0364254i
$456$		0			0
$457$	−8.16394	+	4.71345i	−0.381893	+	0.220486i	−0.678642	−	0.734470i	$-0.737431\pi$
$457$	−8.16394	+	4.71345i	−0.381893	+	0.220486i	0.296749	+	0.954956i	$0.404098\pi$
$458$	12.1497	−	45.3433i	0.567718	−	2.11875i
$459$		0			0
$460$	−35.5947	+	5.84755i	−1.65961	+	0.272643i
$461$	8.51149	+	31.7653i	0.396419	+	1.47946i	0.819349	+	0.573295i	$0.194335\pi$
$461$	8.51149	+	31.7653i	0.396419	+	1.47946i	−0.422930	+	0.906162i	$0.638998\pi$
$462$		0			0
$463$			18.6729i			0.867805i	0.900960	+	0.433903i	$0.142864\pi$
$463$			18.6729i			0.867805i	−0.900960	+	0.433903i	$0.857136\pi$
$464$	−45.0302	−	25.9982i	−2.09047	−	1.20694i
$465$		0			0
$466$	11.5063	−	42.9421i	0.533019	−	1.98925i
$467$	12.1678	+	12.1678i	0.563057	+	0.563057i	0.930175	−	0.367118i	$-0.119655\pi$
$467$	12.1678	+	12.1678i	0.563057	+	0.563057i	−0.367118	+	0.930175i	$0.619655\pi$
$468$		0			0
$469$		−	0.0162150i		−	0.000748740i
$470$	−2.03469	−	0.202039i	−0.0938533	−	0.00931935i
$471$		0			0
$472$	−9.93381	+	2.66176i	−0.457241	+	0.122517i
$473$	−7.22059			−0.332003
$474$		0			0
$475$	−19.2876	−	28.9659i	−0.884978	−	1.32905i
$476$	−1.08886	−	1.08886i	−0.0499080	−	0.0499080i
$477$		0			0
$478$	65.9355	+	17.6674i	3.01582	+	0.808087i
$479$	31.8403	+	8.53158i	1.45482	+	0.389818i	0.897697	−	0.440612i	$-0.145239\pi$
$479$	31.8403	+	8.53158i	1.45482	+	0.389818i	0.557123	+	0.830430i	$0.311905\pi$
$480$		0			0
$481$	−4.80931	−	2.26908i	−0.219285	−	0.103461i
$482$	−10.2497	+	10.2497i	−0.466862	+	0.466862i
$483$		0			0
$484$	32.9041	−	18.9972i	1.49564	−	0.863508i
$485$	13.7855	+	30.4899i	0.625967	+	1.38448i
$486$		0			0
$487$	28.5670	+	16.4931i	1.29449	+	0.747376i	0.979447	−	0.201701i	$-0.0646469\pi$
$487$	28.5670	+	16.4931i	1.29449	+	0.747376i	0.315045	+	0.949077i	$0.397980\pi$
$488$	−19.2944	−	11.1396i	−0.873415	−	0.504267i
$489$		0			0
$490$	−17.0562	−	37.7238i	−0.770519	−	1.70419i
$491$	18.4427	−	10.6479i	0.832307	−	0.480533i	−0.0223350	−	0.999751i	$-0.507110\pi$
$491$	18.4427	−	10.6479i	0.832307	−	0.480533i	0.854642	+	0.519218i	$0.173777\pi$
$492$		0			0
$493$	8.98502	−	8.98502i	0.404665	−	0.404665i
$494$	−11.8420	+	65.4317i	−0.532795	+	2.94391i
$495$		0			0
$496$	9.52693	+	2.55273i	0.427772	+	0.114621i
$497$	0.593999	+	0.159161i	0.0266445	+	0.00713937i
$498$		0			0
$499$	−14.9199	−	14.9199i	−0.667904	−	0.667904i	0.289326	−	0.957231i	$-0.406569\pi$
$499$	−14.9199	−	14.9199i	−0.667904	−	0.667904i	−0.957231	+	0.289326i	$0.906569\pi$
$500$	−38.2778	−	41.0654i	−1.71184	−	1.83650i
$501$		0			0
$502$	−34.6261			−1.54544
$503$	42.1943	−	11.3059i	1.88135	−	0.504106i	0.881881	−	0.471471i	$-0.156277\pi$
$503$	42.1943	−	11.3059i	1.88135	−	0.504106i	0.999467	−	0.0326345i	$-0.0103897\pi$
$504$		0			0
$505$	18.4921	+	1.83621i	0.822887	+	0.0817102i
$506$			15.7736i			0.701224i
$507$		0			0
$508$	41.4280	+	41.4280i	1.83807	+	1.83807i
$509$	9.67023	−	36.0898i	0.428626	−	1.59965i	−0.327250	−	0.944938i	$-0.606122\pi$
$509$	9.67023	−	36.0898i	0.428626	−	1.59965i	0.755876	−	0.654715i	$-0.227211\pi$
$510$		0			0
$511$	0.881719	+	0.509060i	0.0390049	+	0.0225195i
$512$		−	27.0748i		−	1.19655i
$513$		0			0
$514$	11.9664	+	44.6591i	0.527814	+	1.96983i
$515$	24.1192	−	3.96233i	1.06282	−	0.174601i
$516$		0			0
$517$	−0.165495	+	0.617635i	−0.00727846	+	0.0271636i
$518$	−0.380238	+	0.219530i	−0.0167067	+	0.00964562i
$519$		0			0
$520$	−1.04664	+	64.5334i	−0.0458984	+	2.82998i
$521$	35.6853			1.56340			0.781701	−	0.623653i	$-0.214352\pi$
$521$	35.6853			1.56340			0.781701	+	0.623653i	$0.214352\pi$
$522$		0			0
$523$	−1.11694	+	4.16849i	−0.0488406	+	0.182275i	−0.986037	−	0.166527i	$-0.946745\pi$
$523$	−1.11694	+	4.16849i	−0.0488406	+	0.182275i	0.937196	+	0.348802i	$0.113411\pi$
$524$	−18.7386	+	32.4562i	−0.818600	+	1.41786i
$525$		0			0
$526$	14.2979	+	53.3604i	0.623417	+	2.32662i
$527$	−1.20515	+	2.08738i	−0.0524971	+	0.0909276i
$528$		0			0
$529$	−10.9797	−	6.33914i	−0.477379	−	0.275615i
$530$	−19.0726	−	23.2779i	−0.828461	−	1.01113i
$531$		0			0
$532$	2.77630	+	2.77630i	0.120368	+	0.120368i
$533$	18.4124	−	6.60765i	0.797529	−	0.286209i
$534$		0			0
$535$	10.4928	+	12.8063i	0.453643	+	0.553666i
$536$	−0.577707	−	1.00062i	−0.0249531	−	0.0432201i
$537$		0			0
$538$	27.9987			1.20711
$539$	−12.5057	+	3.35089i	−0.538659	+	0.144333i
$540$		0			0
$541$	−5.42748	−	5.42748i	−0.233345	−	0.233345i	0.580742	−	0.814088i	$-0.302762\pi$
$541$	−5.42748	−	5.42748i	−0.233345	−	0.233345i	−0.814088	+	0.580742i	$0.802762\pi$
$542$	5.42507	+	20.2467i	0.233027	+	0.869668i
$543$		0			0
$544$	−35.8247	−	9.59920i	−1.53597	−	0.411563i
$545$	−1.71498	−	10.4393i	−0.0734616	−	0.447170i
$546$		0			0
$547$	11.6940	−	11.6940i	0.500000	−	0.500000i	−0.411438	−	0.911438i	$-0.634973\pi$
$547$	11.6940	−	11.6940i	0.500000	−	0.500000i	0.911438	+	0.411438i	$0.134973\pi$
$548$	46.4066	+	80.3785i	1.98239	+	3.43360i
$549$		0			0
$550$	−20.4331	+	13.6059i	−0.871270	+	0.580156i
$551$	−22.9093	+	22.9093i	−0.975971	+	0.975971i
$552$		0			0
$553$	−1.47588	−	0.852100i	−0.0627608	−	0.0362350i
$554$	19.1378	−	19.1378i	0.813087	−	0.813087i
$555$		0			0
$556$	−47.4434	+	27.3915i	−2.01205	+	1.16166i
$557$	−2.43751	−	4.22190i	−0.103281	−	0.178888i	0.809754	−	0.586770i	$-0.199601\pi$
$557$	−2.43751	−	4.22190i	−0.103281	−	0.178888i	−0.913034	+	0.407882i	$0.866267\pi$
$558$		0			0
$559$	10.7225	+	9.08000i	0.453514	+	0.384043i
$560$	2.27963	+	1.63632i	0.0963321	+	0.0691470i
$561$		0			0
$562$	−45.1595	−	12.1004i	−1.90494	−	0.510426i
$563$	10.0853	+	37.6390i	0.425047	+	1.58630i	0.763821	+	0.645428i	$0.223321\pi$
$563$	10.0853	+	37.6390i	0.425047	+	1.58630i	−0.338774	+	0.940868i	$0.610012\pi$
$564$		0			0
$565$	−12.7938	−	4.82692i	−0.538241	−	0.203070i
$566$	−21.1577	+	5.66919i	−0.889325	+	0.238294i
$567$		0			0
$568$	42.3258	−	11.3412i	1.77595	−	0.475865i
$569$	−1.84104	−	3.18877i	−0.0771804	−	0.133680i	0.824852	−	0.565349i	$-0.191258\pi$
$569$	−1.84104	−	3.18877i	−0.0771804	−	0.133680i	−0.902032	+	0.431668i	$0.857925\pi$
$570$		0			0
$571$		−	2.96698i		−	0.124164i	−0.998071	−	0.0620821i	$-0.980226\pi$
$571$		−	2.96698i		−	0.124164i	0.998071	−	0.0620821i	$-0.0197741\pi$
$572$	33.0089	+	5.97401i	1.38017	+	0.249786i
$573$		0			0
$574$	0.418034	−	1.56012i	0.0174484	−	0.0651184i
$575$	1.02504	+	16.0310i	0.0427472	+	0.668538i
$576$		0			0
$577$			35.0533i			1.45929i	0.683827	+	0.729644i	$0.260314\pi$
$577$			35.0533i			1.45929i	−0.683827	+	0.729644i	$0.739686\pi$
$578$	−12.6509	+	21.9120i	−0.526207	+	0.911417i
$579$		0			0
$580$	−30.4771	+	42.4591i	−1.26549	+	1.76302i
$581$	−0.479643	+	0.830767i	−0.0198990	+	0.0344660i
$582$		0			0
$583$	−8.15012	+	4.70547i	−0.337543	+	0.194881i
$584$	72.5469			3.00201
$585$		0			0
$586$	16.9010			0.698173
$587$	6.10926	−	3.52719i	0.252156	−	0.145583i	−0.368595	−	0.929590i	$-0.620161\pi$
$587$	6.10926	−	3.52719i	0.252156	−	0.145583i	0.620751	+	0.784008i	$0.286828\pi$
$588$		0			0
$589$	3.07280	−	5.32224i	0.126612	−	0.219299i
$590$	1.23391	+	7.51095i	0.0507992	+	0.309221i
$591$		0			0
$592$	−8.23718	+	14.2672i	−0.338546	+	0.586379i
$593$		−	40.0169i		−	1.64330i	−0.569993	−	0.821649i	$-0.693054\pi$
$593$		−	40.0169i		−	1.64330i	0.569993	−	0.821649i	$-0.306946\pi$
$594$		0			0
$595$	−0.530439	+	0.434612i	−0.0217459	+	0.0178174i
$596$	−18.0917	+	67.5192i	−0.741066	+	2.76570i
$597$		0			0
$598$	19.8356	−	23.4237i	0.811138	−	0.957867i
$599$			13.9207i			0.568784i	0.958708	+	0.284392i	$0.0917918\pi$
$599$			13.9207i			0.568784i	−0.958708	+	0.284392i	$0.908208\pi$
$600$		0			0
$601$	1.15689	+	2.00379i	0.0471906	+	0.0817365i	0.888656	−	0.458575i	$-0.151640\pi$
$601$	1.15689	+	2.00379i	0.0471906	+	0.0817365i	−0.841465	+	0.540311i	$0.818307\pi$
$602$	1.12057	−	0.300255i	0.0456708	−	0.0122375i
$603$		0			0
$604$	−58.2743	+	15.6145i	−2.37115	+	0.635347i
$605$	−6.97065	−	15.4173i	−0.283397	−	0.626801i
$606$		0			0
$607$	6.10830	+	22.7965i	0.247928	+	0.925282i	0.971889	+	0.235440i	$0.0756531\pi$
$607$	6.10830	+	22.7965i	0.247928	+	0.925282i	−0.723960	+	0.689842i	$0.757680\pi$
$608$	91.3432	+	24.4753i	3.70446	+	0.992606i
$609$		0			0
$610$	−9.61542	+	13.3957i	−0.389317	+	0.542377i
$611$	1.02244	−	0.709071i	0.0413637	−	0.0286860i
$612$		0			0
$613$	5.32964	+	9.23121i	0.215262	+	0.372845i	0.953354	−	0.301856i	$-0.0976060\pi$
$613$	5.32964	+	9.23121i	0.215262	+	0.372845i	−0.738091	+	0.674701i	$0.764273\pi$
$614$	−60.9165	+	35.1702i	−2.45839	+	1.41935i
$615$		0			0
$616$	1.17838	−	1.17838i	0.0474783	−	0.0474783i
$617$	11.8892	+	6.86421i	0.478639	+	0.276343i	0.719849	−	0.694130i	$-0.244211\pi$
$617$	11.8892	+	6.86421i	0.478639	+	0.276343i	−0.241210	+	0.970473i	$0.577544\pi$
$618$		0			0
$619$	16.8604	−	16.8604i	0.677679	−	0.677679i	−0.281796	−	0.959474i	$-0.590930\pi$
$619$	16.8604	−	16.8604i	0.677679	−	0.677679i	0.959474	+	0.281796i	$0.0909301\pi$
$620$	3.49959	−	9.27574i	0.140547	−	0.372523i
$621$		0			0
$622$	4.69560	+	8.13301i	0.188276	+	0.326104i
$623$	−0.0452127	+	0.0452127i	−0.00181141	+	0.00181141i
$624$		0			0
$625$	−19.8823	+	15.1557i	−0.795292	+	0.606227i
$626$	−22.4811	−	6.02379i	−0.898526	−	0.240759i
$627$		0			0
$628$	9.45576	+	35.2894i	0.377326	+	1.40820i
$629$	−2.84678	−	2.84678i	−0.113509	−	0.113509i
$630$		0			0
$631$	29.5533	−	7.91879i	1.17650	−	0.315242i	0.382962	−	0.923764i	$-0.374904\pi$
$631$	29.5533	−	7.91879i	1.17650	−	0.315242i	0.793537	+	0.608522i	$0.208237\pi$
$632$	−121.434			−4.83038
$633$		0			0
$634$	−11.2987	−	19.5700i	−0.448729	−	0.777222i
$635$	20.1816	−	16.5357i	0.800884	−	0.656200i
$636$		0			0
$637$	22.7847	+	10.7501i	0.902761	+	0.425933i
$638$	16.1607	+	16.1607i	0.639807	+	0.639807i
$639$		0			0
$640$	20.0868	+	1.99456i	0.794001	+	0.0788418i
$641$	13.2495	+	7.64957i	0.523322	+	0.302140i	0.738293	−	0.674480i	$-0.235632\pi$
$641$	13.2495	+	7.64957i	0.523322	+	0.302140i	−0.214971	+	0.976620i	$0.568966\pi$
$642$		0			0
$643$	−11.1740	+	19.3539i	−0.440660	+	0.763245i	−0.997739	−	0.0672147i	$-0.978589\pi$
$643$	−11.1740	+	19.3539i	−0.440660	+	0.763245i	0.557079	+	0.830460i	$0.311922\pi$
$644$	−0.469078	−	1.75062i	−0.0184843	−	0.0689842i
$645$		0			0
$646$	−25.1710	+	43.5974i	−0.990340	+	1.71532i
$647$	−1.21024	+	4.51668i	−0.0475795	+	0.177569i	−0.985627	−	0.168939i	$-0.945966\pi$
$647$	−1.21024	+	4.51668i	−0.0475795	+	0.177569i	0.938047	+	0.346508i	$0.112633\pi$
$648$		0			0
$649$	2.38033			0.0934361
$650$	47.4526	+	5.49035i	1.86124	+	0.215349i
$651$		0			0
$652$	89.2199	−	51.5111i	3.49412	−	2.01733i
$653$	−6.34274	+	23.6714i	−0.248211	+	0.926335i	0.723532	+	0.690291i	$0.242518\pi$
$653$	−6.34274	+	23.6714i	−0.248211	+	0.926335i	−0.971742	+	0.236044i	$0.924149\pi$
$654$		0			0
$655$	13.5583	+	9.73212i	0.529766	+	0.380265i
$656$	−15.6854	−	58.5387i	−0.612412	−	2.28555i
$657$		0			0
$658$		−	0.102733i		−	0.00400494i
$659$	−35.2803	−	20.3691i	−1.37433	−	0.793467i	−0.382856	−	0.923808i	$-0.625059\pi$
$659$	−35.2803	−	20.3691i	−1.37433	−	0.793467i	−0.991469	+	0.130341i	$0.958393\pi$
$660$		0			0
$661$	4.42523	−	16.5152i	0.172122	−	0.642367i	−0.824902	−	0.565275i	$-0.808770\pi$
$661$	4.42523	−	16.5152i	0.172122	−	0.642367i	0.997024	−	0.0770916i	$-0.0245634\pi$
$662$	33.7389	+	33.7389i	1.31130	+	1.31130i
$663$		0			0
$664$			68.3547i			2.65268i
$665$	1.35247	−	1.10814i	0.0524467	−	0.0429719i
$666$		0			0
$667$	14.4457	−	3.87071i	0.559340	−	0.149875i
$668$	−12.7589			−0.493657
$669$		0			0
$670$	−0.779208	+	0.352306i	−0.0301034	+	0.0136107i
$671$	3.64628	+	3.64628i	0.140763	+	0.140763i
$672$		0			0
$673$	−23.0041	−	6.16392i	−0.886742	−	0.237602i	−0.213428	−	0.976959i	$-0.568463\pi$
$673$	−23.0041	−	6.16392i	−0.886742	−	0.237602i	−0.673314	+	0.739357i	$0.735130\pi$
$674$	−72.7057	−	19.4814i	−2.80052	−	0.750396i
$675$		0			0
$676$	−41.5055	−	50.3805i	−1.59636	−	1.93771i
$677$	−26.1344	+	26.1344i	−1.00443	+	1.00443i	−0.00443504	+	0.999990i	$0.501412\pi$
$677$	−26.1344	+	26.1344i	−1.00443	+	1.00443i	−0.999990	+	0.00443504i	$0.998588\pi$
$678$		0			0
$679$	−1.45598	+	0.840613i	−0.0558756	+	0.0322598i
$680$	−17.2487	+	45.7180i	−0.661457	+	1.75321i
$681$		0			0
$682$	−3.75440	−	2.16761i	−0.143764	−	0.0830019i
$683$	23.1988	+	13.3938i	0.887676	+	0.512500i	0.873181	−	0.487395i	$-0.162053\pi$
$683$	23.1988	+	13.3938i	0.887676	+	0.512500i	0.0144941	+	0.999895i	$0.495386\pi$
$684$		0			0
$685$	37.6615	−	17.0280i	1.43897	−	0.650606i
$686$	3.60610	−	2.08198i	0.137682	−	0.0794905i
$687$		0			0
$688$	30.7796	−	30.7796i	1.17346	−	1.17346i
$689$	18.0201	+	3.26131i	0.686510	+	0.124246i
$690$		0			0
$691$	−38.9899	−	10.4473i	−1.48325	−	0.397435i	−0.575796	−	0.817593i	$-0.695308\pi$
$691$	−38.9899	−	10.4473i	−1.48325	−	0.397435i	−0.907451	+	0.420158i	$0.861975\pi$
$692$	−0.382655	−	0.102532i	−0.0145464	−	0.00389769i
$693$		0			0
$694$	13.4464	+	13.4464i	0.510419	+	0.510419i
$695$	10.0508	+	22.2297i	0.381247	+	0.843219i
$696$		0			0
$697$	14.8102			0.560976
$698$	9.35058	−	2.50548i	0.353925	−	0.0948339i
$699$		0			0
$700$	1.86314	−	2.11768i	0.0704200	−	0.0800406i
$701$			24.9781i			0.943410i	0.881756	+	0.471705i	$0.156361\pi$
$701$			24.9781i			0.943410i	−0.881756	+	0.471705i	$0.843639\pi$
$702$		0			0
$703$	7.25852	+	7.25852i	0.273760	+	0.273760i
$704$	6.55185	−	24.4519i	0.246932	−	0.921564i
$705$		0			0
$706$	4.04624	+	2.33610i	0.152282	+	0.0879202i
$707$			0.933677i			0.0351145i
$708$		0			0
$709$	−2.64139	−	9.85779i	−0.0991993	−	0.370217i	0.898423	−	0.439130i	$-0.144713\pi$
$709$	−2.64139	−	9.85779i	−0.0991993	−	0.370217i	−0.997623	+	0.0689135i	$0.978047\pi$
$710$	−5.25742	−	32.0025i	−0.197307	−	1.20103i
$711$		0			0
$712$	−1.17921	+	4.40087i	−0.0441927	+	0.164930i
$713$	−2.45675	+	1.41841i	−0.0920061	+	0.0531198i
$714$		0			0
$715$	4.09985	−	14.3649i	0.153326	−	0.537216i
$716$	−106.570			−3.98272
$717$		0			0
$718$	−8.32175	+	31.0572i	−0.310565	+	1.15904i
$719$	14.2117	−	24.6153i	0.530005	−	0.917996i	−0.469382	−	0.882995i	$-0.655523\pi$
$719$	14.2117	−	24.6153i	0.530005	−	0.917996i	0.999387	−	0.0350008i	$-0.0111434\pi$
$720$		0			0
$721$	0.317850	+	1.18623i	0.0118373	+	0.0441776i
$722$	39.0065	−	67.5612i	1.45167	−	2.51437i
$723$		0			0
$724$	−97.9570	−	56.5555i	−3.64054	−	2.10187i
$725$	17.4745	+	15.3741i	0.648987	+	0.570981i
$726$		0			0
$727$	−8.56116	−	8.56116i	−0.317516	−	0.317516i	0.530296	−	0.847812i	$-0.322081\pi$
$727$	−8.56116	−	8.56116i	−0.317516	−	0.317516i	−0.847812	+	0.530296i	$0.822081\pi$
$728$	−3.23172	+	0.268054i	−0.119775	+	0.00993473i
$729$		0			0
$730$	5.30555	−	53.4311i	0.196367	−	1.97757i
$731$	5.31873	+	9.21232i	0.196720	+	0.340730i
$732$		0			0
$733$	−17.2200			−0.636036			−0.318018	−	0.948085i	$-0.603017\pi$
$733$	−17.2200			−0.636036			−0.318018	+	0.948085i	$0.603017\pi$
$734$	35.8610	−	9.60893i	1.32365	−	0.354672i
$735$		0			0
$736$	−30.8663	−	30.8663i	−1.13775	−	1.13775i
$737$	0.0692148	+	0.258313i	0.00254956	+	0.00951508i
$738$		0			0
$739$	−15.7497	−	4.22013i	−0.579364	−	0.155240i	−0.0427762	−	0.999085i	$-0.513620\pi$
$739$	−15.7497	−	4.22013i	−0.579364	−	0.155240i	−0.536588	+	0.843845i	$0.680287\pi$
$740$	13.4526	+	9.65626i	0.494528	+	0.354971i
$741$		0			0
$742$	1.06915	−	1.06915i	0.0392498	−	0.0392498i
$743$	−16.5599	−	28.6826i	−0.607525	−	1.05226i	−0.991647	−	0.128982i	$-0.958829\pi$
$743$	−16.5599	−	28.6826i	−0.607525	−	1.05226i	0.384122	−	0.923282i	$-0.374504\pi$
$744$		0			0
$745$	29.1248	+	10.9883i	1.06705	+	0.402581i
$746$	54.1344	−	54.1344i	1.98200	−	1.98200i
$747$		0			0
$748$	21.9940	+	12.6982i	0.804179	+	0.464293i
$749$	−0.588194	+	0.588194i	−0.0214921	+	0.0214921i
$750$		0			0
$751$	18.9961	−	10.9674i	0.693176	−	0.400205i	−0.111625	−	0.993750i	$-0.535605\pi$
$751$	18.9961	−	10.9674i	0.693176	−	0.400205i	0.804801	+	0.593545i	$0.202272\pi$
$752$	−1.92736	−	3.33829i	−0.0702836	−	0.121735i
$753$		0			0
$754$	−3.67617	−	44.3207i	−0.133878	−	1.61407i
$755$	4.35528	+	26.5111i	0.158505	+	0.964838i
$756$		0			0
$757$	−2.84678	−	0.762791i	−0.103468	−	0.0277241i	0.206714	−	0.978401i	$-0.433723\pi$
$757$	−2.84678	−	0.762791i	−0.103468	−	0.0277241i	−0.310181	+	0.950677i	$0.600390\pi$
$758$	−6.49926	−	24.2556i	−0.236064	−	0.881002i
$759$		0			0
$760$	43.9794	−	116.568i	1.59530	−	4.22838i
$761$	21.2875	−	5.70396i	0.771670	−	0.206768i	0.148561	−	0.988903i	$-0.452536\pi$
$761$	21.2875	−	5.70396i	0.771670	−	0.206768i	0.623109	+	0.782135i	$0.285869\pi$
$762$		0			0
$763$	0.513426	−	0.137572i	0.0185873	−	0.00498044i
$764$	−49.2241	−	85.2587i	−1.78087	−	3.08455i
$765$		0			0
$766$			55.8361i			2.01744i
$767$	−3.53477	−	2.99330i	−0.127633	−	0.108082i
$768$		0			0
$769$	−5.46718	+	20.4038i	−0.197152	+	0.735780i	0.794548	+	0.607202i	$0.207708\pi$
$769$	−5.46718	+	20.4038i	−0.197152	+	0.735780i	−0.991699	+	0.128578i	$0.958959\pi$
$770$	−0.781703	−	0.954059i	−0.0281706	−	0.0343819i
$771$		0			0
$772$		−	83.9143i		−	3.02014i
$773$	9.34781	−	16.1909i	0.336217	−	0.582346i	−0.647500	−	0.762065i	$-0.724186\pi$
$773$	9.34781	−	16.1909i	0.336217	−	0.582346i	0.983718	+	0.179719i	$0.0575189\pi$
$774$		0			0
$775$	−3.95652	−	1.95899i	−0.142122	−	0.0703691i
$776$	−59.8985	+	103.747i	−2.15023	+	3.72431i
$777$		0			0
$778$	−0.138788	+	0.0801293i	−0.00497579	+	0.00287278i
$779$	−37.7619			−1.35296
$780$		0			0
$781$	−10.1421			−0.362912
$782$	20.1246	−	11.6190i	0.719656	−	0.415493i
$783$		0			0
$784$	39.0246	−	67.5927i	1.39374	−	2.41402i
$785$	16.0544	−	2.63744i	0.573008	−	0.0941344i
$786$		0			0
$787$	21.6615	−	37.5189i	0.772150	−	1.33740i	−0.164232	−	0.986422i	$-0.552515\pi$
$787$	21.6615	−	37.5189i	0.772150	−	1.33740i	0.936382	−	0.350981i	$-0.114152\pi$
$788$			76.2534i			2.71642i
$789$		0			0
$790$	−8.88078	+	89.4366i	−0.315964	+	3.18201i
$791$	0.177818	−	0.663626i	0.00632248	−	0.0235958i
$792$		0			0
$793$	−0.829444	−	9.99995i	−0.0294544	−	0.355109i
$794$			21.7710i			0.772625i
$795$		0			0
$796$	35.0157	+	60.6489i	1.24110	+	2.14964i
$797$	33.9650	−	9.10089i	1.20310	−	0.322370i	0.399050	−	0.916929i	$-0.369340\pi$
$797$	33.9650	−	9.10089i	1.20310	−	0.322370i	0.804052	+	0.594559i	$0.202673\pi$
$798$		0			0
$799$	0.909909	−	0.243809i	0.0321903	−	0.00862535i
$800$	13.3597	−	66.6084i	0.472338	−	2.35496i
$801$		0			0
$802$	−6.17139	−	23.0319i	−0.217919	−	0.813286i
$803$	−16.2191	−	4.34591i	−0.572361	−	0.153364i
$804$		0			0
$805$	−0.796423	+	0.130837i	−0.0280702	+	0.00461141i
$806$	2.84946	+	7.94010i	0.100368	+	0.279678i
$807$		0			0
$808$	33.2649	+	57.6165i	1.17026	+	2.02694i
$809$	17.8779	−	10.3218i	0.628554	−	0.362896i	−0.151638	−	0.988436i	$-0.548455\pi$
$809$	17.8779	−	10.3218i	0.628554	−	0.362896i	0.780192	+	0.625540i	$0.215121\pi$
$810$		0			0
$811$	−22.0471	+	22.0471i	−0.774178	+	0.774178i	−0.978834	−	0.204656i	$-0.934392\pi$
$811$	−22.0471	+	22.0471i	−0.774178	+	0.774178i	0.204656	+	0.978834i	$0.434392\pi$
$812$	−2.27416	−	1.31299i	−0.0798075	−	0.0460769i
$813$		0			0
$814$	5.12029	−	5.12029i	0.179466	−	0.179466i
$815$	−18.9010	−	41.8041i	−0.662074	−	1.46433i
$816$		0			0
$817$	−13.5613	−	23.4889i	−0.474450	−	0.821772i
$818$	67.1180	−	67.1180i	2.34672	−	2.34672i
$819$		0			0
$820$	−60.1111	+	9.87512i	−2.09917	+	0.344854i
$821$	−35.4477	−	9.49818i	−1.23713	−	0.331489i	−0.419780	−	0.907626i	$-0.637893\pi$
$821$	−35.4477	−	9.49818i	−1.23713	−	0.331489i	−0.817353	+	0.576137i	$0.804559\pi$
$822$		0			0
$823$	6.11025	+	22.8038i	0.212990	+	0.794889i	0.986865	+	0.161550i	$0.0516494\pi$
$823$	6.11025	+	22.8038i	0.212990	+	0.794889i	−0.773875	+	0.633339i	$0.781684\pi$
$824$	61.8772	+	61.8772i	2.15559	+	2.15559i
$825$		0			0
$826$	−0.369404	+	0.0989816i	−0.0128532	+	0.00344401i
$827$	4.44429			0.154543			0.0772716	−	0.997010i	$-0.475379\pi$
$827$	4.44429			0.154543			0.0772716	+	0.997010i	$0.475379\pi$
$828$		0			0
$829$	−14.6685	−	25.4065i	−0.509457	−	0.882406i	−0.999940	−	0.0109548i	$-0.996513\pi$
$829$	−14.6685	−	25.4065i	−0.509457	−	0.882406i	0.490483	−	0.871451i	$-0.336820\pi$
$830$	50.3435	+	4.99895i	1.74745	+	0.173516i
$831$		0			0
$832$	−40.4780	+	28.0718i	−1.40332	+	0.973213i
$833$	13.4870	+	13.4870i	0.467296	+	0.467296i
$834$		0			0
$835$	−0.561431	+	5.65406i	−0.0194291	+	0.195667i
$836$	−56.0786	−	32.3770i	−1.93952	−	1.11978i
$837$		0			0
$838$	17.3304	−	30.0171i	0.598668	−	1.03692i
$839$	2.19656	+	8.19766i	0.0758336	+	0.283015i	0.993421	−	0.114519i	$-0.0365327\pi$
$839$	2.19656	+	8.19766i	0.0758336	+	0.283015i	−0.917587	+	0.397534i	$0.869866\pi$
$840$		0			0
$841$	−3.66554	+	6.34891i	−0.126398	+	0.218928i
$842$	−13.3770	+	49.9236i	−0.461001	+	1.72048i
$843$		0			0
$844$	118.591			4.08208
$845$	−24.1523	+	16.1761i	−0.830865	+	0.556475i
$846$		0			0
$847$	0.736220	−	0.425057i	0.0252968	−	0.0146051i
$848$	14.6837	−	54.8002i	0.504239	−	1.88185i
$849$		0			0
$850$	32.4101	+	16.0472i	1.11166	+	0.550415i
$851$	−1.22638	−	4.57693i	−0.0420399	−	0.156895i
$852$		0			0
$853$		−	34.3415i		−	1.17583i	−0.808923	−	0.587915i	$-0.799949\pi$
$853$		−	34.3415i		−	1.17583i	0.808923	−	0.587915i	$-0.200051\pi$
$854$	−0.717491	−	0.414244i	−0.0245521	−	0.0141751i
$855$		0			0
$856$	−15.3409	+	57.2531i	−0.524342	+	1.95687i
$857$	−24.6090	−	24.6090i	−0.840626	−	0.840626i	0.148314	−	0.988940i	$-0.452615\pi$
$857$	−24.6090	−	24.6090i	−0.840626	−	0.840626i	−0.988940	+	0.148314i	$0.952615\pi$
$858$		0			0
$859$			12.8606i			0.438798i	0.975635	+	0.219399i	$0.0704097\pi$
$859$			12.8606i			0.438798i	−0.975635	+	0.219399i	$0.929590\pi$
$860$	−27.7301	−	33.8442i	−0.945588	−	1.15408i
$861$		0			0
$862$	−56.8688	+	15.2379i	−1.93696	+	0.519007i
$863$	2.75373			0.0937379			0.0468690	−	0.998901i	$-0.485076\pi$
$863$	2.75373			0.0937379			0.0468690	+	0.998901i	$0.485076\pi$
$864$		0			0
$865$	−0.0622747	+	0.165060i	−0.00211740	+	0.00561222i
$866$	0.343907	+	0.343907i	0.0116864	+	0.0116864i
$867$		0			0
$868$	0.481140	+	0.128921i	0.0163309	+	0.00437586i
$869$	27.1487	+	7.27447i	0.920957	+	0.246770i
$870$		0			0
$871$	0.222049	−	0.470631i	0.00752385	−	0.0159467i
$872$	26.7817	−	26.7817i	0.906944	−	0.906944i
$873$		0			0
$874$	−51.3123	+	29.6252i	−1.73566	+	1.00209i
$875$	−0.856456	−	0.918826i	−0.0289535	−	0.0310620i
$876$		0			0
$877$	−40.9311	−	23.6316i	−1.38214	−	0.797981i	−0.389730	−	0.920929i	$-0.627432\pi$
$877$	−40.9311	−	23.6316i	−1.38214	−	0.797981i	−0.992413	+	0.122948i	$0.960765\pi$
$878$	−39.6847	−	22.9119i	−1.33929	−	0.773241i
$879$		0			0
$880$	−43.3004	−	16.3365i	−1.45965	−	0.550705i
$881$	−35.7854	+	20.6607i	−1.20564	+	0.696077i	−0.961804	−	0.273739i	$-0.911739\pi$
$881$	−35.7854	+	20.6607i	−1.20564	+	0.696077i	−0.243837	+	0.969816i	$0.578406\pi$
$882$		0			0
$883$	13.4808	−	13.4808i	0.453666	−	0.453666i	−0.442903	−	0.896569i	$-0.646051\pi$
$883$	13.4808	−	13.4808i	0.453666	−	0.453666i	0.896569	+	0.442903i	$0.146051\pi$
$884$	−16.6927	−	46.5145i	−0.561435	−	1.56445i
$885$		0			0
$886$	−88.4897	−	23.7108i	−2.97287	−	0.796578i
$887$	22.1438	+	5.93341i	0.743516	+	0.199225i	0.610640	−	0.791908i	$-0.290912\pi$
$887$	22.1438	+	5.93341i	0.743516	+	0.199225i	0.132876	+	0.991133i	$0.457579\pi$
$888$		0			0
$889$	0.926941	+	0.926941i	0.0310886	+	0.0310886i
$890$	3.15502	+	1.19034i	0.105757	+	0.0399003i
$891$		0			0
$892$	−48.8381			−1.63522
$893$	−2.32002	+	0.621647i	−0.0776364	+	0.0208026i
$894$		0			0
$895$	−4.68942	+	47.2262i	−0.156750	+	1.57860i
$896$			1.01420i			0.0338819i
$897$		0			0
$898$	−69.6712	−	69.6712i	−2.32496	−	2.32496i
$899$	−1.06382	+	3.97024i	−0.0354805	+	0.132415i
$900$		0			0
$901$	12.0069	+	6.93217i	0.400007	+	0.230944i
$902$			26.6379i			0.886946i
$903$		0			0
$904$	−12.6705	−	47.2871i	−0.421416	−	1.57275i
$905$	−29.3728	+	40.9207i	−0.976384	+	1.36025i
$906$		0			0
$907$	−6.24222	+	23.2963i	−0.207270	+	0.773541i	0.781476	+	0.623935i	$0.214467\pi$
$907$	−6.24222	+	23.2963i	−0.207270	+	0.773541i	−0.988746	+	0.149606i	$0.952200\pi$
$908$	−39.9008	+	23.0367i	−1.32416	+	0.764501i
$909$		0			0
$910$	−0.0389211	+	2.39977i	−0.00129022	+	0.0795518i
$911$	−58.5135			−1.93864			−0.969320	−	0.245803i	$-0.920948\pi$
$911$	−58.5135			−1.93864			−0.969320	+	0.245803i	$0.920948\pi$
$912$		0			0
$913$	4.09477	−	15.2819i	0.135517	−	0.505757i
$914$	−12.4895	+	21.6324i	−0.413116	+	0.715537i
$915$		0			0
$916$	−23.0233	−	85.9241i	−0.760711	−	2.83901i
$917$	−0.419271	+	0.726199i	−0.0138456	+	0.0239812i
$918$		0			0
$919$	38.8451	+	22.4272i	1.28138	+	0.739806i	0.977101	−	0.212776i	$-0.0682506\pi$
$919$	38.8451	+	22.4272i	1.28138	+	0.739806i	0.304281	+	0.952582i	$0.401584\pi$
$920$	−44.4852	+	36.4487i	−1.46663	+	1.20168i
$921$		0			0
$922$	61.6169	+	61.6169i	2.02924	+	2.02924i
$923$	15.0609	+	12.7538i	0.495735	+	0.419797i
$924$		0			0
$925$	4.87109	−	5.53657i	0.160160	−	0.182041i
$926$	24.7394	+	42.8498i	0.812986	+	1.40813i
$927$		0			0
$928$	−63.2473			−2.07619
$929$	27.1090	−	7.26384i	0.889418	−	0.238319i	0.214952	−	0.976625i	$-0.431040\pi$
$929$	27.1090	−	7.26384i	0.889418	−	0.238319i	0.674466	+	0.738306i	$0.264374\pi$
$930$		0			0
$931$	−34.3881	−	34.3881i	−1.12702	−	1.12702i
$932$	−21.8041	−	81.3738i	−0.714215	−	2.66549i
$933$		0			0
$934$	44.0428	+	11.8012i	1.44113	+	0.386148i
$935$	6.59497	−	9.18779i	0.215679	−	0.300473i
$936$		0			0
$937$	20.7545	−	20.7545i	0.678019	−	0.678019i	−0.281533	−	0.959552i	$-0.590843\pi$
$937$	20.7545	−	20.7545i	0.678019	−	0.678019i	0.959552	+	0.281533i	$0.0908428\pi$
$938$	−0.0214829	−	0.0372095i	−0.000701442	−	0.00121493i
$939$		0			0
$940$	−3.53054	+	1.59627i	−0.115153	+	0.0520647i
$941$	6.70533	−	6.70533i	0.218588	−	0.218588i	−0.589315	−	0.807903i	$-0.700602\pi$
$941$	6.70533	−	6.70533i	0.218588	−	0.218588i	0.807903	+	0.589315i	$0.200602\pi$
$942$		0			0
$943$	15.0956	+	8.71547i	0.491582	+	0.283815i
$944$	−10.1467	+	10.1467i	−0.330249	+	0.330249i
$945$		0			0
$946$	−16.5695	+	9.56639i	−0.538720	+	0.311030i
$947$	2.25542	+	3.90651i	0.0732915	+	0.126945i	0.900342	−	0.435183i	$-0.143316\pi$
$947$	2.25542	+	3.90651i	0.0732915	+	0.126945i	−0.827051	+	0.562128i	$0.809983\pi$
$948$		0			0
$949$	18.6203	+	26.8495i	0.604439	+	0.871570i
$950$	−82.6367	−	40.9160i	−2.68109	−	1.32749i
$951$		0			0
$952$	−2.37143	−	0.635422i	−0.0768584	−	0.0205941i
$953$	1.48646	+	5.54756i	0.0481513	+	0.179703i	0.985813	−	0.167845i	$-0.0536809\pi$
$953$	1.48646	+	5.54756i	0.0481513	+	0.179703i	−0.937662	+	0.347548i	$0.887014\pi$
$954$		0			0
$955$	−39.9481	+	18.0618i	−1.29269	+	0.584467i
$956$	124.946	−	33.4791i	4.04103	−	1.08279i
$957$		0			0
$958$	84.3690	−	22.6066i	2.72584	−	0.730386i
$959$	1.03833	+	1.79845i	0.0335296	+	0.0580749i
$960$		0			0
$961$			30.2203i			0.974849i
$962$	−14.0424	+	1.16475i	−0.452746	+	0.0375529i
$963$		0			0
$964$	−7.10927	+	26.5322i	−0.228974	+	0.854543i
$965$	−37.1863	−	3.69249i	−1.19707	−	0.118865i
$966$		0			0
$967$			17.6414i			0.567310i	0.958926	+	0.283655i	$0.0915470\pi$
$967$			17.6414i			0.567310i	−0.958926	+	0.283655i	$0.908453\pi$
$968$	30.2877	−	52.4599i	0.973485	−	1.68612i
$969$		0			0
$970$	72.0297	+	51.7028i	2.31273	+	1.66008i
$971$	16.6987	−	28.9229i	0.535886	−	0.928181i	−0.463234	−	0.886236i	$-0.653311\pi$
$971$	16.6987	−	28.9229i	0.535886	−	0.928181i	0.999120	−	0.0419454i	$-0.0133556\pi$
$972$		0			0
$973$	−1.06153	+	0.612876i	−0.0340312	+	0.0196479i
$974$	87.4056			2.80065
$975$		0			0
$976$	−31.0864			−0.995050
$977$	−13.2886	+	7.67217i	−0.425139	+	0.245454i	−0.697274	−	0.716805i	$-0.745604\pi$
$977$	−13.2886	+	7.67217i	−0.425139	+	0.245454i	0.272134	+	0.962259i	$0.412270\pi$
$978$		0			0
$979$	0.527266	−	0.913252i	0.0168515	−	0.0291877i
$980$	−63.7334	−	45.7477i	−2.03589	−	1.46136i
$981$		0			0
$982$	28.2143	−	48.8686i	0.900354	−	1.55946i
$983$			4.80751i			0.153336i	0.997057	+	0.0766679i	$0.0244281\pi$
$983$			4.80751i			0.153336i	−0.997057	+	0.0766679i	$0.975572\pi$
$984$		0			0
$985$	33.7914	+	3.35539i	1.07668	+	0.106911i
$986$	8.71437	−	32.5225i	0.277522	−	1.03573i
$987$		0			0
$988$	42.5617	+	118.599i	1.35407	+	3.77315i
$989$			12.5198i			0.398108i
$990$		0			0
$991$	−0.219558	−	0.380286i	−0.00697450	−	0.0120802i	0.862517	−	0.506028i	$-0.168887\pi$
$991$	−0.219558	−	0.380286i	−0.00697450	−	0.0120802i	−0.869492	+	0.493948i	$0.835553\pi$
$992$	11.5884	−	3.10509i	0.367931	−	0.0985867i
$993$		0			0
$994$	1.57395	−	0.421739i	0.0499227	−	0.0133767i
$995$	28.4171	−	12.8483i	0.900884	−	0.407319i
$996$		0			0
$997$	−1.70003	−	6.34461i	−0.0538406	−	0.200936i	0.933766	−	0.357883i	$-0.116501\pi$
$997$	−1.70003	−	6.34461i	−0.0538406	−	0.200936i	−0.987607	+	0.156947i	$0.949835\pi$
$998$	−54.0044	−	14.4704i	−1.70948	−	0.458053i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.dp.a.28.5		20
3.2	odd	2		65.2.t.a.28.1	yes	20
5.2	odd	4		585.2.cf.a.262.5		20
13.7	odd	12		585.2.cf.a.163.5		20
15.2	even	4		65.2.o.a.2.1	✓	20
15.8	even	4		325.2.s.b.132.5		20
15.14	odd	2		325.2.x.b.93.5		20
39.2	even	12		845.2.k.d.268.1		20
39.5	even	4		845.2.o.f.258.5		20
39.8	even	4		845.2.o.e.258.1		20
39.11	even	12		845.2.k.e.268.10		20
39.17	odd	6		845.2.t.e.188.1		20
39.20	even	12		65.2.o.a.33.1	yes	20
39.23	odd	6		845.2.f.d.408.10		20
39.29	odd	6		845.2.f.e.408.1		20
39.32	even	12		845.2.o.g.488.5		20
39.35	odd	6		845.2.t.f.188.5		20
39.38	odd	2		845.2.t.g.418.5		20
65.7	even	12	inner	585.2.dp.a.397.5		20
195.2	odd	12		845.2.f.d.437.1		20
195.17	even	12		845.2.o.f.357.5		20
195.32	odd	12		845.2.t.g.657.5		20
195.47	odd	4		845.2.t.f.427.5		20
195.59	even	12		325.2.s.b.293.5		20
195.62	even	12		845.2.k.d.577.1		20
195.77	even	4		845.2.o.g.587.5		20
195.98	odd	12		325.2.x.b.7.5		20
195.107	even	12		845.2.k.e.577.10		20
195.122	odd	4		845.2.t.e.427.1		20
195.137	odd	12		65.2.t.a.7.1	yes	20
195.152	even	12		845.2.o.e.357.1		20
195.167	odd	12		845.2.f.e.437.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.1	✓	20	15.2	even	4
65.2.o.a.33.1	yes	20	39.20	even	12
65.2.t.a.7.1	yes	20	195.137	odd	12
65.2.t.a.28.1	yes	20	3.2	odd	2
325.2.s.b.132.5		20	15.8	even	4
325.2.s.b.293.5		20	195.59	even	12
325.2.x.b.7.5		20	195.98	odd	12
325.2.x.b.93.5		20	15.14	odd	2
585.2.cf.a.163.5		20	13.7	odd	12
585.2.cf.a.262.5		20	5.2	odd	4
585.2.dp.a.28.5		20	1.1	even	1	trivial
585.2.dp.a.397.5		20	65.7	even	12	inner
845.2.f.d.408.10		20	39.23	odd	6
845.2.f.d.437.1		20	195.2	odd	12
845.2.f.e.408.1		20	39.29	odd	6
845.2.f.e.437.10		20	195.167	odd	12
845.2.k.d.268.1		20	39.2	even	12
845.2.k.d.577.1		20	195.62	even	12
845.2.k.e.268.10		20	39.11	even	12
845.2.k.e.577.10		20	195.107	even	12
845.2.o.e.258.1		20	39.8	even	4
845.2.o.e.357.1		20	195.152	even	12
845.2.o.f.258.5		20	39.5	even	4
845.2.o.f.357.5		20	195.17	even	12
845.2.o.g.488.5		20	39.32	even	12
845.2.o.g.587.5		20	195.77	even	4
845.2.t.e.188.1		20	39.17	odd	6
845.2.t.e.427.1		20	195.122	odd	4
845.2.t.f.188.5		20	39.35	odd	6
845.2.t.f.427.5		20	195.47	odd	4
845.2.t.g.418.5		20	39.38	odd	2
845.2.t.g.657.5		20	195.32	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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	585.2.dp.a.28.5

Level	$585$
Weight	$2$
Character	585.28
Analytic conductor	$4.671$
Analytic rank	$0$
Dimension	$20$
Inner twists	$2$