LMFDB - Embedded newform 540.2.n.d.359.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [540,2,Mod(179,540)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(540, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("540.179"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 540 = 2^{2} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	540.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,-2,18,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.31192170915$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			359.17
Character	$\chi$	$=$	540.359
Dual form			540.2.n.d.179.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.745653 + 1.20167i) q^{2} +(-0.888004 + 1.79205i) q^{4} +(-0.0361315 - 2.23578i) q^{5} +(1.44473 - 2.50234i) q^{7} +(-2.81559 + 0.269163i) q^{8} +(2.65972 - 1.71053i) q^{10} +(0.395318 - 0.684712i) q^{11} +(4.04214 - 2.33373i) q^{13} +(4.08425 - 0.129797i) q^{14} +(-2.42290 - 3.18270i) q^{16} +5.89560 q^{17} +4.55505i q^{19} +(4.03871 + 1.92063i) q^{20} +(1.11756 - 0.0355161i) q^{22} +(1.15468 - 0.666656i) q^{23} +(-4.99739 + 0.161564i) q^{25} +(5.81840 + 3.11715i) q^{26} +(3.20140 + 4.81112i) q^{28} +(-2.29484 - 1.32492i) q^{29} +(-2.26893 + 1.30997i) q^{31} +(2.01790 - 5.28470i) q^{32} +(4.39607 + 7.08454i) q^{34} +(-5.64688 - 3.13968i) q^{35} -7.44000i q^{37} +(-5.47365 + 3.39649i) q^{38} +(0.703519 + 6.28531i) q^{40} +(5.91566 - 3.41541i) q^{41} +(-5.95249 + 10.3100i) q^{43} +(0.875994 + 1.31646i) q^{44} +(1.66209 + 0.890449i) q^{46} +(-2.60947 - 1.50658i) q^{47} +(-0.674484 - 1.16824i) q^{49} +(-3.92046 - 5.88472i) q^{50} +(0.592728 + 9.31609i) q^{52} +1.70763 q^{53} +(-1.54515 - 0.859104i) q^{55} +(-3.39423 + 7.43444i) q^{56} +(-0.119034 - 3.74556i) q^{58} +(5.29436 + 9.17010i) q^{59} +(-0.869749 + 1.50645i) q^{61} +(-3.26598 - 1.74972i) q^{62} +(7.85510 - 1.51570i) q^{64} +(-5.36375 - 8.95300i) q^{65} +(-3.76721 - 6.52500i) q^{67} +(-5.23532 + 10.5652i) q^{68} +(-0.437767 - 9.12678i) q^{70} -2.88566 q^{71} +6.50847i q^{73} +(8.94040 - 5.54766i) q^{74} +(-8.16289 - 4.04491i) q^{76} +(-1.14226 - 1.97845i) q^{77} +(3.30854 + 1.91019i) q^{79} +(-7.02826 + 5.53205i) q^{80} +(8.51521 + 4.56194i) q^{82} +(-8.33679 - 4.81325i) q^{83} +(-0.213017 - 13.1812i) q^{85} +(-16.8277 + 0.534782i) q^{86} +(-0.928756 + 2.03427i) q^{88} +0.00741921i q^{89} -13.4864i q^{91} +(0.169319 + 2.66124i) q^{92} +(-0.135354 - 4.25910i) q^{94} +(10.1841 - 0.164581i) q^{95} +(-5.74925 - 3.31933i) q^{97} +(0.900905 - 1.68161i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{4} + 18 q^{5} - 16 q^{10} + 42 q^{14} + 30 q^{16} - 26 q^{25} - 4 q^{34} + 10 q^{40} - 96 q^{41} + 4 q^{46} + 32 q^{49} + 90 q^{50} - 6 q^{56} + 8 q^{61} - 20 q^{64} + 6 q^{65} + 4 q^{70} - 72 q^{74}+ \cdots - 62 q^{94}+O(q^{100}) $ 48 * q - 2 * q^4 + 18 * q^5 - 16 * q^10 + 42 * q^14 + 30 * q^16 - 26 * q^25 - 4 * q^34 + 10 * q^40 - 96 * q^41 + 4 * q^46 + 32 * q^49 + 90 * q^50 - 6 * q^56 + 8 * q^61 - 20 * q^64 + 6 * q^65 + 4 * q^70 - 72 * q^74 - 4 * q^85 - 108 * q^86 - 62 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.745653	+	1.20167i	0.527256	+	0.849706i
$2$	0.745653	+	1.20167i	0.527256	+	0.849706i
$3$		0			0
$3$		0			0
$4$	−0.888004	+	1.79205i	−0.444002	+	0.896026i
$5$	−0.0361315	−	2.23578i	−0.0161585	−	0.999869i
$5$	−0.0361315	−	2.23578i	−0.0161585	−	0.999869i
$6$		0			0
$7$	1.44473	−	2.50234i	0.546056	−	0.945797i	−0.452483	−	0.891773i	$-0.649462\pi$
$7$	1.44473	−	2.50234i	0.546056	−	0.945797i	0.998540	−	0.0540243i	$-0.0172049\pi$
$8$	−2.81559	+	0.269163i	−0.995462	+	0.0951634i
$9$		0			0
$10$	2.65972	−	1.71053i	0.841076	−	0.540917i
$11$	0.395318	−	0.684712i	0.119193	−	0.206448i	−0.800255	−	0.599660i	$-0.795303\pi$
$11$	0.395318	−	0.684712i	0.119193	−	0.206448i	0.919448	+	0.393211i	$0.128636\pi$
$12$		0			0
$13$	4.04214	−	2.33373i	1.12109	−	0.647261i	0.179410	−	0.983774i	$-0.442581\pi$
$13$	4.04214	−	2.33373i	1.12109	−	0.647261i	0.941679	+	0.336514i	$0.109248\pi$
$14$	4.08425	−	0.129797i	1.09156	−	0.0346897i
$15$		0			0
$16$	−2.42290	−	3.18270i	−0.605724	−	0.795675i
$17$	5.89560			1.42989			0.714946	−	0.699179i	$-0.246451\pi$
$17$	5.89560			1.42989			0.714946	+	0.699179i	$0.246451\pi$
$18$		0			0
$19$			4.55505i			1.04500i	0.852639	+	0.522500i	$0.175001\pi$
$19$			4.55505i			1.04500i	−0.852639	+	0.522500i	$0.824999\pi$
$20$	4.03871	+	1.92063i	0.903083	+	0.429466i
$21$		0			0
$22$	1.11756	−	0.0355161i	0.238266	−	0.00757206i
$23$	1.15468	−	0.666656i	0.240768	−	0.139007i	−0.374762	−	0.927121i	$-0.622275\pi$
$23$	1.15468	−	0.666656i	0.240768	−	0.139007i	0.615530	+	0.788114i	$0.288942\pi$
$24$		0			0
$25$	−4.99739	+	0.161564i	−0.999478	+	0.0323128i
$26$	5.81840	+	3.11715i	1.14108	+	0.611324i
$27$		0			0
$28$	3.20140	+	4.81112i	0.605008	+	0.909216i
$29$	−2.29484	−	1.32492i	−0.426140	−	0.246032i	0.271561	−	0.962421i	$-0.412460\pi$
$29$	−2.29484	−	1.32492i	−0.426140	−	0.246032i	−0.697701	+	0.716389i	$0.745794\pi$
$30$		0			0
$31$	−2.26893	+	1.30997i	−0.407512	+	0.235277i	−0.689720	−	0.724076i	$-0.742266\pi$
$31$	−2.26893	+	1.30997i	−0.407512	+	0.235277i	0.282208	+	0.959353i	$0.408933\pi$
$32$	2.01790	−	5.28470i	0.356718	−	0.934212i
$33$		0			0
$34$	4.39607	+	7.08454i	0.753919	+	1.21499i
$35$	−5.64688	−	3.13968i	−0.954497	−	0.530702i
$36$		0			0
$37$		−	7.44000i		−	1.22313i	−0.791195	−	0.611564i	$-0.790541\pi$
$37$		−	7.44000i		−	1.22313i	0.791195	−	0.611564i	$-0.209459\pi$
$38$	−5.47365	+	3.39649i	−0.887944	+	0.550983i
$39$		0			0
$40$	0.703519	+	6.28531i	0.111236	+	0.993794i
$41$	5.91566	−	3.41541i	0.923871	−	0.533397i	0.0390029	−	0.999239i	$-0.487582\pi$
$41$	5.91566	−	3.41541i	0.923871	−	0.533397i	0.884868	+	0.465842i	$0.154249\pi$
$42$		0			0
$43$	−5.95249	+	10.3100i	−0.907746	+	1.57226i	−0.0905567	+	0.995891i	$0.528865\pi$
$43$	−5.95249	+	10.3100i	−0.907746	+	1.57226i	−0.817189	+	0.576370i	$0.804469\pi$
$44$	0.875994	+	1.31646i	0.132061	+	0.198463i
$45$		0			0
$46$	1.66209	+	0.890449i	0.245062	+	0.131290i
$47$	−2.60947	−	1.50658i	−0.380631	−	0.219757i	0.297462	−	0.954734i	$-0.403860\pi$
$47$	−2.60947	−	1.50658i	−0.380631	−	0.219757i	−0.678093	+	0.734976i	$0.737193\pi$
$48$		0			0
$49$	−0.674484	−	1.16824i	−0.0963548	−	0.166891i
$50$	−3.92046	−	5.88472i	−0.554437	−	0.832226i
$51$		0			0
$52$	0.592728	+	9.31609i	0.0821965	+	1.29191i
$53$	1.70763			0.234561			0.117281	−	0.993099i	$-0.462582\pi$
$53$	1.70763			0.234561			0.117281	+	0.993099i	$0.462582\pi$
$54$		0			0
$55$	−1.54515	−	0.859104i	−0.208347	−	0.115842i
$56$	−3.39423	+	7.43444i	−0.453573	+	0.993469i
$57$		0			0
$58$	−0.119034	−	3.74556i	−0.0156299	−	0.491816i
$59$	5.29436	+	9.17010i	0.689267	+	1.19385i	0.972075	+	0.234669i	$0.0754007\pi$
$59$	5.29436	+	9.17010i	0.689267	+	1.19385i	−0.282808	+	0.959176i	$0.591266\pi$
$60$		0			0
$61$	−0.869749	+	1.50645i	−0.111360	+	0.192881i	−0.916319	−	0.400450i	$-0.868854\pi$
$61$	−0.869749	+	1.50645i	−0.111360	+	0.192881i	0.804959	+	0.593331i	$0.202187\pi$
$62$	−3.26598	−	1.74972i	−0.414779	−	0.222214i
$63$		0			0
$64$	7.85510	−	1.51570i	0.981888	−	0.189463i
$65$	−5.36375	−	8.95300i	−0.665291	−	1.11048i
$66$		0			0
$67$	−3.76721	−	6.52500i	−0.460238	−	0.797155i	0.538735	−	0.842476i	$-0.318903\pi$
$67$	−3.76721	−	6.52500i	−0.460238	−	0.797155i	−0.998973	+	0.0453201i	$0.985569\pi$
$68$	−5.23532	+	10.5652i	−0.634875	+	1.28122i
$69$		0			0
$70$	−0.437767	−	9.12678i	−0.0523232	−	1.09086i
$71$	−2.88566			−0.342465			−0.171233	−	0.985231i	$-0.554775\pi$
$71$	−2.88566			−0.342465			−0.171233	+	0.985231i	$0.554775\pi$
$72$		0			0
$73$			6.50847i			0.761759i	0.924625	+	0.380880i	$0.124379\pi$
$73$			6.50847i			0.761759i	−0.924625	+	0.380880i	$0.875621\pi$
$74$	8.94040	−	5.54766i	1.03930	−	0.644902i
$75$		0			0
$76$	−8.16289	−	4.04491i	−0.936347	−	0.463983i
$77$	−1.14226	−	1.97845i	−0.130172	−	0.225465i
$78$		0			0
$79$	3.30854	+	1.91019i	0.372240	+	0.214913i	0.674436	−	0.738333i	$-0.264387\pi$
$79$	3.30854	+	1.91019i	0.372240	+	0.214913i	−0.302197	+	0.953246i	$0.597720\pi$
$80$	−7.02826	+	5.53205i	−0.785783	+	0.618502i
$81$		0			0
$82$	8.51521	+	4.56194i	0.940347	+	0.503782i
$83$	−8.33679	−	4.81325i	−0.915081	−	0.528322i	−0.0330187	−	0.999455i	$-0.510512\pi$
$83$	−8.33679	−	4.81325i	−0.915081	−	0.528322i	−0.882063	+	0.471132i	$0.843845\pi$
$84$		0			0
$85$	−0.213017	−	13.1812i	−0.0231049	−	1.42971i
$86$	−16.8277	+	0.534782i	−1.81457	+	0.0576670i
$87$		0			0
$88$	−0.928756	+	2.03427i	−0.0990057	+	0.216854i
$89$			0.00741921i			0.000786434i	1.00000		0.000393217i	$0.000125165\pi$
$89$			0.00741921i			0.000786434i	−1.00000		0.000393217i	$0.999875\pi$
$90$		0			0
$91$		−	13.4864i		−	1.41376i
$92$	0.169319	+	2.66124i	0.0176528	+	0.277454i
$93$		0			0
$94$	−0.135354	−	4.25910i	−0.0139607	−	0.439293i
$95$	10.1841	−	0.164581i	1.04486	−	0.0168857i
$96$		0			0
$97$	−5.74925	−	3.31933i	−0.583748	−	0.337027i	0.178874	−	0.983872i	$-0.442755\pi$
$97$	−5.74925	−	3.31933i	−0.583748	−	0.337027i	−0.762621	+	0.646845i	$0.776088\pi$
$98$	0.900905	−	1.68161i	0.0910051	−	0.169868i
$99$		0			0
$100$	4.14817	−	9.09905i	0.414817	−	0.909905i
$101$	2.20027	+	1.27033i	0.218935	+	0.126402i	0.605457	−	0.795878i	$-0.292990\pi$
$101$	2.20027	+	1.27033i	0.218935	+	0.126402i	−0.386522	+	0.922280i	$0.626324\pi$
$102$		0			0
$103$	−3.82824	−	6.63071i	−0.377208	−	0.653343i	0.613447	−	0.789736i	$-0.289782\pi$
$103$	−3.82824	−	6.63071i	−0.377208	−	0.653343i	−0.990655	+	0.136393i	$0.956449\pi$
$104$	−10.7529	+	7.65883i	−1.05441	+	0.751010i
$105$		0			0
$106$	1.27330	+	2.05200i	0.123674	+	0.199308i
$107$			13.7118i			1.32557i	0.748808	+	0.662787i	$0.230626\pi$
$107$			13.7118i			1.32557i	−0.748808	+	0.662787i	$0.769374\pi$
$108$		0			0
$109$	−13.2664			−1.27069			−0.635347	−	0.772227i	$-0.719143\pi$
$109$	−13.2664			−1.27069			−0.635347	+	0.772227i	$0.719143\pi$
$110$	−0.119785	−	2.49734i	−0.0114211	−	0.238112i
$111$		0			0
$112$	−11.4646	+	1.46478i	−1.08331	+	0.138409i
$113$	4.62487	+	8.01051i	0.435071	+	0.753565i	0.997301	−	0.0734153i	$-0.0233899\pi$
$113$	4.62487	+	8.01051i	0.435071	+	0.753565i	−0.562230	+	0.826981i	$0.690057\pi$
$114$		0			0
$115$	−1.53221	−	2.55752i	−0.142880	−	0.238490i
$116$	4.41216	−	2.93593i	0.409659	−	0.272594i
$117$		0			0
$118$	−7.07165	+	13.1998i	−0.650998	+	1.21514i
$119$	8.51754	−	14.7528i	0.780802	−	1.35239i
$120$		0			0
$121$	5.18745	+	8.98492i	0.471586	+	0.816811i
$122$	−2.45878	+	0.0781398i	−0.222608	+	0.00707445i
$123$		0			0
$124$	−0.332709	−	5.22929i	−0.0298781	−	0.469604i
$125$	0.541784	+	11.1672i	0.0484587	+	0.998825i
$126$		0			0
$127$	9.77239			0.867159			0.433580	−	0.901115i	$-0.357250\pi$
$127$	9.77239			0.867159			0.433580	+	0.901115i	$0.357250\pi$
$128$	7.67855	+	8.30902i	0.678694	+	0.734421i
$129$		0			0
$130$	6.75903	−	13.1213i	0.592806	−	1.15081i
$131$	−6.61827	−	11.4632i	−0.578241	−	1.00154i	−0.995681	−	0.0928382i	$-0.970406\pi$
$131$	−6.61827	−	11.4632i	−0.578241	−	1.00154i	0.417440	−	0.908704i	$-0.362927\pi$
$132$		0			0
$133$	11.3983	+	6.58082i	0.988359	+	0.570629i
$134$	5.03184	−	9.39231i	0.434685	−	0.811372i
$135$		0			0
$136$	−16.5996	+	1.58688i	−1.42340	+	0.136073i
$137$	1.57622	−	2.73010i	0.134666	−	0.233248i	−0.790804	−	0.612069i	$-0.790337\pi$
$137$	1.57622	−	2.73010i	0.134666	−	0.233248i	0.925470	+	0.378822i	$0.123671\pi$
$138$		0			0
$139$	−2.22556	+	1.28493i	−0.188770	+	0.108986i	−0.591407	−	0.806374i	$-0.701427\pi$
$139$	−2.22556	+	1.28493i	−0.188770	+	0.108986i	0.402637	+	0.915360i	$0.368094\pi$
$140$	10.6409	−	7.33145i	0.899322	−	0.619621i
$141$		0			0
$142$	−2.15170	−	3.46761i	−0.180567	−	0.290995i
$143$		−	3.69027i		−	0.308596i
$144$		0			0
$145$	−2.87932	+	5.17861i	−0.239114	+	0.430060i
$146$	−7.82101	+	4.85306i	−0.647272	+	0.401642i
$147$		0			0
$148$	13.3329	+	6.60675i	1.09595	+	0.543072i
$149$	−8.52719	+	4.92318i	−0.698575	+	0.403322i	−0.806816	−	0.590802i	$-0.798811\pi$
$149$	−8.52719	+	4.92318i	−0.698575	+	0.403322i	0.108242	+	0.994125i	$0.465478\pi$
$150$		0			0
$151$	9.24153	+	5.33560i	0.752065	+	0.434205i	0.826440	−	0.563025i	$-0.190363\pi$
$151$	9.24153	+	5.33560i	0.752065	+	0.434205i	−0.0743744	+	0.997230i	$0.523696\pi$
$152$	−1.22605	−	12.8252i	−0.0994458	−	1.04026i
$153$		0			0
$154$	1.52571	−	2.84784i	0.122945	−	0.229486i
$155$	3.01077	+	5.02549i	0.241831	+	0.403657i
$156$		0			0
$157$	−12.9992	+	7.50509i	−1.03745	+	0.598972i	−0.919110	−	0.394001i	$-0.871091\pi$
$157$	−12.9992	+	7.50509i	−1.03745	+	0.598972i	−0.118340	+	0.992973i	$0.537757\pi$
$158$	0.171614	+	5.40009i	0.0136529	+	0.429608i
$159$		0			0
$160$	−11.8883	−	4.32064i	−0.939854	−	0.341576i
$161$		−	3.85255i		−	0.303624i
$162$		0			0
$163$	4.15873			0.325737			0.162869	−	0.986648i	$-0.447925\pi$
$163$	4.15873			0.325737			0.162869	+	0.986648i	$0.447925\pi$
$164$	0.867455	+	13.6341i	0.0677368	+	1.06464i
$165$		0			0
$166$	−0.432431	−	13.6070i	−0.0335631	−	1.05611i
$167$	0.0288855	−	0.0166770i	0.00223522	−	0.00129051i	−0.498882	−	0.866670i	$-0.666256\pi$
$167$	0.0288855	−	0.0166770i	0.00223522	−	0.00129051i	0.501117	+	0.865379i	$0.332923\pi$
$168$		0			0
$169$	4.39261	−	7.60822i	0.337893	−	0.585248i
$170$	15.6806	−	10.0846i	1.20265	−	0.773453i
$171$		0			0
$172$	−13.1902	−	19.8225i	−1.00575	−	1.51145i
$173$	−11.9161	+	20.6392i	−0.905962	+	1.56917i	−0.0863411	+	0.996266i	$0.527517\pi$
$173$	−11.9161	+	20.6392i	−0.905962	+	1.56917i	−0.819621	+	0.572906i	$0.805816\pi$
$174$		0			0
$175$	−6.81558	+	12.7386i	−0.515210	+	0.962948i
$176$	−3.13705	+	0.400806i	−0.236464	+	0.0302119i
$177$		0			0
$178$	−0.00891541	+	0.00553215i	−0.000668238	+	0.000414652i
$179$	−25.5288			−1.90811			−0.954055	−	0.299631i	$-0.903136\pi$
$179$	−25.5288			−1.90811			−0.954055	+	0.299631i	$0.903136\pi$
$180$		0			0
$181$	25.6109			1.90364			0.951821	−	0.306653i	$-0.0992092\pi$
$181$	25.6109			1.90364			0.951821	+	0.306653i	$0.0992092\pi$
$182$	16.2062	−	10.0562i	1.20128	−	0.745415i
$183$		0			0
$184$	−3.07168	+	2.18783i	−0.226447	+	0.161289i
$185$	−16.6342	+	0.268819i	−1.22297	+	0.0197639i
$186$		0			0
$187$	2.33064	−	4.03678i	0.170433	−	0.295199i
$188$	5.01709	−	3.33846i	0.365909	−	0.243482i
$189$		0			0
$190$	7.79155	+	12.1151i	0.565259	+	0.878925i
$191$	3.85863	−	6.68334i	0.279200	−	0.483589i	−0.691986	−	0.721911i	$-0.743264\pi$
$191$	3.85863	−	6.68334i	0.279200	−	0.483589i	0.971186	+	0.238322i	$0.0765973\pi$
$192$		0			0
$193$	−4.47373	+	2.58291i	−0.322026	+	0.185922i	−0.652295	−	0.757965i	$-0.726194\pi$
$193$	−4.47373	+	2.58291i	−0.322026	+	0.185922i	0.330269	+	0.943887i	$0.392861\pi$
$194$	−0.298215	−	9.38374i	−0.0214106	−	0.673714i
$195$		0			0
$196$	2.69249	−	0.171307i	0.192321	−	0.0122362i
$197$	−8.47116			−0.603545			−0.301773	−	0.953380i	$-0.597578\pi$
$197$	−8.47116			−0.603545			−0.301773	+	0.953380i	$0.597578\pi$
$198$		0			0
$199$			0.555967i			0.0394115i	0.999806	+	0.0197057i	$0.00627293\pi$
$199$			0.555967i			0.0394115i	−0.999806	+	0.0197057i	$0.993727\pi$
$200$	14.0271	−	1.80001i	0.991867	−	0.127280i
$201$		0			0
$202$	0.114128	+	3.59121i	0.00803004	+	0.252677i
$203$	−6.63083	+	3.82831i	−0.465393	+	0.268695i
$204$		0			0
$205$	−7.84983	−	13.1027i	−0.548256	−	0.915131i
$206$	5.11336	−	9.54447i	0.356265	−	0.664995i
$207$		0			0
$208$	−17.2213	−	7.21053i	−1.19408	−	0.499960i
$209$	3.11890	+	1.80070i	0.215739	+	0.124557i
$210$		0			0
$211$	21.0649	−	12.1618i	1.45016	−	0.837253i	0.451675	−	0.892183i	$-0.350827\pi$
$211$	21.0649	−	12.1618i	1.45016	−	0.837253i	0.998490	+	0.0549298i	$0.0174935\pi$
$212$	−1.51638	+	3.06016i	−0.104146	+	0.210173i
$213$		0			0
$214$	−16.4771	+	10.2243i	−1.12635	+	0.698917i
$215$	23.2659	+	12.9359i	1.58672	+	0.882222i
$216$		0			0
$217$			7.57019i			0.513898i
$218$	−9.89215	−	15.9418i	−0.669981	−	1.07972i
$219$		0			0
$220$	2.91165	−	2.00609i	0.196304	−	0.135251i
$221$	23.8308	−	13.7587i	1.60304	−	0.925513i
$222$		0			0
$223$	0.169636	−	0.293817i	0.0113596	−	0.0196755i	−0.860290	−	0.509805i	$-0.829717\pi$
$223$	0.169636	−	0.293817i	0.0113596	−	0.0196755i	0.871649	+	0.490130i	$0.163051\pi$
$224$	−10.3088	−	12.6844i	−0.688787	−	0.847515i
$225$		0			0
$226$	−6.17741	+	11.5306i	−0.410915	+	0.767005i
$227$	7.45137	+	4.30205i	0.494565	+	0.285537i	0.726466	−	0.687202i	$-0.241161\pi$
$227$	7.45137	+	4.30205i	0.494565	+	0.285537i	−0.231902	+	0.972739i	$0.574495\pi$
$228$		0			0
$229$	0.358866	+	0.621574i	0.0237145	+	0.0410748i	0.877639	−	0.479322i	$-0.159117\pi$
$229$	0.358866	+	0.621574i	0.0237145	+	0.0410748i	−0.853925	+	0.520397i	$0.825784\pi$
$230$	1.93079	−	3.74824i	0.127313	−	0.247151i
$231$		0			0
$232$	6.81794	+	3.11276i	0.447620	+	0.204363i
$233$	−13.8379			−0.906553			−0.453276	−	0.891370i	$-0.649745\pi$
$233$	−13.8379			−0.906553			−0.453276	+	0.891370i	$0.649745\pi$
$234$		0			0
$235$	−3.27409	+	5.88864i	−0.213578	+	0.384132i
$236$	−21.1347	+	1.34468i	−1.37575	+	0.0875310i
$237$		0			0
$238$	24.0791	−	0.765231i	1.56082	−	0.0496026i
$239$	13.8553	+	23.9980i	0.896223	+	1.55230i	0.832284	+	0.554350i	$0.187033\pi$
$239$	13.8553	+	23.9980i	0.896223	+	1.55230i	0.0639388	+	0.997954i	$0.479634\pi$
$240$		0			0
$241$	−5.71303	+	9.89526i	−0.368009	+	0.637410i	−0.989254	−	0.146206i	$-0.953294\pi$
$241$	−5.71303	+	9.89526i	−0.368009	+	0.637410i	0.621245	+	0.783616i	$0.286627\pi$
$242$	−6.92884	+	12.9332i	−0.445403	+	0.831378i
$243$		0			0
$244$	−1.92729	−	2.89637i	−0.123382	−	0.185421i
$245$	−2.58755	+	1.55021i	−0.165313	+	0.0990390i
$246$		0			0
$247$	10.6303	+	18.4122i	0.676388	+	1.17154i
$248$	6.03578	−	4.29904i	0.383272	−	0.272989i
$249$		0			0
$250$	−13.0153	+	8.97790i	−0.823158	+	0.567812i
$251$	−5.05161			−0.318855			−0.159427	−	0.987210i	$-0.550965\pi$
$251$	−5.05161			−0.318855			−0.159427	+	0.987210i	$0.550965\pi$
$252$		0			0
$253$		−	1.05417i		−	0.0662749i
$254$	7.28681	+	11.7432i	0.457215	+	0.736831i
$255$		0			0
$256$	−4.25914	+	15.4227i	−0.266197	+	0.963919i
$257$	−1.32366	−	2.29265i	−0.0825679	−	0.143012i	0.821784	−	0.569799i	$-0.192979\pi$
$257$	−1.32366	−	2.29265i	−0.0825679	−	0.143012i	−0.904352	+	0.426787i	$0.859645\pi$
$258$		0			0
$259$	−18.6174	−	10.7488i	−1.15683	−	0.667897i
$260$	20.8073	−	1.66181i	1.29041	−	0.103061i
$261$		0			0
$262$	8.83999	−	16.5005i	0.546136	−	1.01940i
$263$	−2.19210	−	1.26561i	−0.135171	−	0.0780408i	0.430890	−	0.902405i	$-0.358200\pi$
$263$	−2.19210	−	1.26561i	−0.135171	−	0.0780408i	−0.566060	+	0.824364i	$0.691533\pi$
$264$		0			0
$265$	−0.0616994	−	3.81788i	−0.00379016	−	0.234531i
$266$	0.591232	+	18.6040i	0.0362508	+	1.14068i
$267$		0			0
$268$	15.0384	−	0.956806i	0.918618	−	0.0584462i
$269$			5.26469i			0.320994i	0.987036	+	0.160497i	$0.0513097\pi$
$269$			5.26469i			0.320994i	−0.987036	+	0.160497i	$0.948690\pi$
$270$		0			0
$271$			16.6468i			1.01122i	0.862761	+	0.505612i	$0.168733\pi$
$271$			16.6468i			1.01122i	−0.862761	+	0.505612i	$0.831267\pi$
$272$	−14.2844	−	18.7639i	−0.866120	−	1.13773i
$273$		0			0
$274$	4.45598	−	0.141611i	0.269196	−	0.00855501i
$275$	−1.86493	+	3.48564i	−0.112460	+	0.210192i
$276$		0			0
$277$	22.8566	+	13.1963i	1.37332	+	0.792888i	0.991345	−	0.131283i	$-0.0419097\pi$
$277$	22.8566	+	13.1963i	1.37332	+	0.792888i	0.381978	+	0.924171i	$0.375243\pi$
$278$	−3.20355	−	1.71627i	−0.192136	−	0.102935i
$279$		0			0
$280$	16.7444	+	7.32012i	1.00067	+	0.437461i
$281$	19.8511	+	11.4611i	1.18422	+	0.683710i	0.956987	−	0.290131i	$-0.0936987\pi$
$281$	19.8511	+	11.4611i	1.18422	+	0.683710i	0.227233	+	0.973840i	$0.427032\pi$
$282$		0			0
$283$	3.25733	+	5.64186i	0.193628	+	0.335374i	0.946450	−	0.322851i	$-0.104641\pi$
$283$	3.25733	+	5.64186i	0.193628	+	0.335374i	−0.752822	+	0.658224i	$0.771308\pi$
$284$	2.56248	−	5.17126i	0.152055	−	0.306858i
$285$		0			0
$286$	4.43447	−	2.75166i	0.262216	−	0.162709i
$287$		−	19.7374i		−	1.16506i
$288$		0			0
$289$	17.7581			1.04459
$290$	−8.36994	+	0.401465i	−0.491500	+	0.0235749i
$291$		0			0
$292$	−11.6635	−	5.77955i	−0.682556	−	0.338223i
$293$	−8.37272	−	14.5020i	−0.489140	−	0.847215i	0.510782	−	0.859710i	$-0.329356\pi$
$293$	−8.37272	−	14.5020i	−0.489140	−	0.847215i	−0.999922	+	0.0124952i	$0.996023\pi$
$294$		0			0
$295$	20.3110	−	12.1683i	1.18255	−	0.708468i
$296$	2.00257	+	20.9480i	0.116397	+	1.21758i
$297$		0			0
$298$	−12.2743	−	6.57586i	−0.711033	−	0.380929i
$299$	3.11159	−	5.38944i	0.179948	−	0.311679i
$300$		0			0
$301$	17.1995	+	29.7903i	0.991360	+	1.71709i
$302$	0.479360	+	15.0837i	0.0275841	+	0.867972i
$303$		0			0
$304$	14.4974	−	11.0364i	0.831481	−	0.632982i
$305$	3.39951	+	1.89013i	0.194655	+	0.108229i
$306$		0			0
$307$	−24.2759			−1.38550			−0.692749	−	0.721179i	$-0.743600\pi$
$307$	−24.2759			−1.38550			−0.692749	+	0.721179i	$0.743600\pi$
$308$	4.55980	−	0.290113i	0.259819	−	0.0165307i
$309$		0			0
$310$	−3.79397	+	7.36521i	−0.215483	+	0.418316i
$311$	3.81664	+	6.61061i	0.216422	+	0.374853i	0.953711	−	0.300723i	$-0.0972281\pi$
$311$	3.81664	+	6.61061i	0.216422	+	0.374853i	−0.737290	+	0.675577i	$0.763895\pi$
$312$		0			0
$313$	3.85836	+	2.22762i	0.218087	+	0.125913i	0.605064	−	0.796177i	$-0.293147\pi$
$313$	3.85836	+	2.22762i	0.218087	+	0.125913i	−0.386977	+	0.922089i	$0.626481\pi$
$314$	−18.7115	−	10.0245i	−1.05595	−	0.565716i
$315$		0			0
$316$	−6.36115	+	4.23282i	−0.357842	+	0.238115i
$317$	−2.47795	+	4.29194i	−0.139176	+	0.241059i	−0.927185	−	0.374604i	$-0.877779\pi$
$317$	−2.47795	+	4.29194i	−0.139176	+	0.241059i	0.788009	+	0.615663i	$0.211112\pi$
$318$		0			0
$319$	−1.81438	+	1.04753i	−0.101586	+	0.0586506i
$320$	−3.67259	−	17.5075i	−0.205304	−	0.978698i
$321$		0			0
$322$	4.62948	−	2.87267i	0.257991	−	0.160087i
$323$			26.8548i			1.49424i
$324$		0			0
$325$	−19.8231	+	12.3156i	−1.09959	+	0.683148i
$326$	3.10097	+	4.99741i	0.171747	+	0.276781i
$327$		0			0
$328$	−15.7368	+	11.2087i	−0.868918	+	0.618895i
$329$	−7.53997	+	4.35320i	−0.415692	+	0.240000i
$330$		0			0
$331$	−23.0250	−	13.2935i	−1.26557	−	0.730676i	−0.291422	−	0.956594i	$-0.594129\pi$
$331$	−23.0250	−	13.2935i	−1.26557	−	0.730676i	−0.974146	+	0.225918i	$0.927462\pi$
$332$	16.0287	−	10.6658i	0.879689	−	0.585360i
$333$		0			0
$334$	0.0415787	+	0.0222754i	0.00227509	+	0.00121886i
$335$	−14.4523	+	8.65839i	−0.789615	+	0.473059i
$336$		0			0
$337$	10.7769	−	6.22205i	0.587056	−	0.338937i	−0.176877	−	0.984233i	$-0.556599\pi$
$337$	10.7769	−	6.22205i	0.587056	−	0.338937i	0.763933	+	0.645296i	$0.223266\pi$
$338$	12.4179	−	0.394640i	0.675445	−	0.0214656i
$339$		0			0
$340$	23.8106	+	11.3233i	1.29131	+	0.614090i
$341$			2.07142i			0.112173i
$342$		0			0
$343$	16.3284			0.881652
$344$	13.9847	−	30.6309i	0.754004	−	1.65151i
$345$		0			0
$346$	−33.6867	+	1.07056i	−1.81101	+	0.0575537i
$347$	14.6546	−	8.46084i	0.786701	−	0.454202i	−0.0520991	−	0.998642i	$-0.516591\pi$
$347$	14.6546	−	8.46084i	0.786701	−	0.454202i	0.838800	+	0.544440i	$0.183258\pi$
$348$		0			0
$349$	−0.955553	+	1.65507i	−0.0511496	+	0.0885937i	−0.890467	−	0.455049i	$-0.849622\pi$
$349$	−0.955553	+	1.65507i	−0.0511496	+	0.0885937i	0.839317	+	0.543642i	$0.182955\pi$
$350$	−20.3896	+	1.30851i	−1.08987	+	0.0699430i
$351$		0			0
$352$	−2.82078	−	3.47082i	−0.150348	−	0.184995i
$353$	11.0561	−	19.1497i	0.588457	−	1.01924i	−0.405978	−	0.913883i	$-0.633069\pi$
$353$	11.0561	−	19.1497i	0.588457	−	1.01924i	0.994435	−	0.105355i	$-0.0335978\pi$
$354$		0			0
$355$	0.104263	+	6.45170i	0.00553373	+	0.342421i
$356$	−0.0132956	−	0.00658829i	−0.000704665	−	0.000349178i
$357$		0			0
$358$	−19.0356	−	30.6771i	−1.00606	−	1.62133i
$359$	−1.48034			−0.0781296			−0.0390648	−	0.999237i	$-0.512438\pi$
$359$	−1.48034			−0.0781296			−0.0390648	+	0.999237i	$0.512438\pi$
$360$		0			0
$361$	−1.74850			−0.0920262
$362$	19.0968	+	30.7757i	1.00371	+	1.61754i
$363$		0			0
$364$	24.1684	+	11.9760i	1.26677	+	0.627714i
$365$	14.5515	−	0.235161i	0.761660	−	0.0123089i
$366$		0			0
$367$	0.0631149	−	0.109318i	0.00329457	−	0.00570636i	−0.864373	−	0.502850i	$-0.832285\pi$
$367$	0.0631149	−	0.109318i	0.00329457	−	0.00570636i	0.867668	+	0.497144i	$0.165618\pi$
$368$	−4.91944	−	2.05977i	−0.256444	−	0.107373i
$369$		0			0
$370$	−12.7263	−	19.7883i	−0.661611	−	1.02874i
$371$	2.46707	−	4.27308i	0.128084	−	0.221847i
$372$		0			0
$373$	−19.8527	+	11.4620i	−1.02794	+	0.593479i	−0.916393	−	0.400280i	$-0.868913\pi$
$373$	−19.8527	+	11.4620i	−1.02794	+	0.593479i	−0.111543	+	0.993760i	$0.535579\pi$
$374$	6.58871	−	0.209389i	0.340694	−	0.0108272i
$375$		0			0
$376$	7.75273	+	3.53954i	0.399816	+	0.182538i
$377$	−12.3681			−0.636988
$378$		0			0
$379$		−	27.5123i		−	1.41321i	−0.707608	−	0.706605i	$-0.750226\pi$
$379$		−	27.5123i		−	1.41321i	0.707608	−	0.706605i	$-0.249774\pi$
$380$	−8.74857	+	18.3965i	−0.448792	+	0.943722i
$381$		0			0
$382$	10.9083	−	0.346666i	0.558119	−	0.0177370i
$383$	20.5507	−	11.8649i	1.05009	−	0.606270i	0.127416	−	0.991849i	$-0.459332\pi$
$383$	20.5507	−	11.8649i	1.05009	−	0.606270i	0.922675	+	0.385579i	$0.125998\pi$
$384$		0			0
$385$	−4.38209	+	2.62531i	−0.223332	+	0.133798i
$386$	−6.43965	−	3.44998i	−0.327770	−	0.175599i
$387$		0			0
$388$	11.0538	−	7.35537i	0.561170	−	0.373412i
$389$	1.58128	+	0.912954i	0.0801742	+	0.0462886i	0.539551	−	0.841953i	$-0.318594\pi$
$389$	1.58128	+	0.912954i	0.0801742	+	0.0462886i	−0.459377	+	0.888241i	$0.651927\pi$
$390$		0			0
$391$	6.80755	−	3.93034i	0.344272	−	0.198766i
$392$	2.21352	+	3.10774i	0.111800	+	0.156965i
$393$		0			0
$394$	−6.31654	−	10.1795i	−0.318223	−	0.512836i
$395$	4.15120	−	7.46617i	0.208870	−	0.375664i
$396$		0			0
$397$		−	19.0828i		−	0.957737i	−0.877887	−	0.478868i	$-0.841047\pi$
$397$		−	19.0828i		−	0.957737i	0.877887	−	0.478868i	$-0.158953\pi$
$398$	−0.668087	+	0.414558i	−0.0334882	+	0.0207799i
$399$		0			0
$400$	12.6224	+	15.5137i	0.631118	+	0.775687i
$401$	15.1375	−	8.73963i	0.755930	−	0.436436i	−0.0719025	−	0.997412i	$-0.522907\pi$
$401$	15.1375	−	8.73963i	0.755930	−	0.436436i	0.827833	+	0.560975i	$0.189574\pi$
$402$		0			0
$403$	−6.11422	+	10.5901i	−0.304571	+	0.527533i
$404$	−4.23034	+	2.81494i	−0.210467	+	0.140048i
$405$		0			0
$406$	−9.54466	−	5.11346i	−0.473693	−	0.253777i
$407$	−5.09425	−	2.94117i	−0.252513	−	0.145788i
$408$		0			0
$409$	−8.17716	−	14.1633i	−0.404335	−	0.700328i	0.589909	−	0.807470i	$-0.299164\pi$
$409$	−8.17716	−	14.1633i	−0.404335	−	0.700328i	−0.994244	+	0.107142i	$0.965830\pi$
$410$	9.89181	−	19.2029i	0.488522	−	0.948365i
$411$		0			0
$412$	15.2821	−	0.972307i	0.752893	−	0.0479021i
$413$	30.5957			1.50551
$414$		0			0
$415$	−10.4601	+	18.8131i	−0.513467	+	0.923499i
$416$	−4.17642	−	26.0708i	−0.204766	−	1.27822i
$417$		0			0
$418$	0.161778	+	5.09057i	0.00791281	+	0.248988i
$419$	−12.3846	−	21.4508i	−0.605029	−	1.04794i	−0.992047	−	0.125869i	$-0.959828\pi$
$419$	−12.3846	−	21.4508i	−0.605029	−	1.04794i	0.387018	−	0.922072i	$-0.373505\pi$
$420$		0			0
$421$	8.38623	−	14.5254i	0.408720	−	0.707923i	−0.586027	−	0.810292i	$-0.699309\pi$
$421$	8.38623	−	14.5254i	0.408720	−	0.707923i	0.994747	+	0.102368i	$0.0326420\pi$
$422$	30.3215	+	16.2445i	1.47603	+	0.790768i
$423$		0			0
$424$	−4.80799	+	0.459631i	−0.233497	+	0.0223217i
$425$	−29.4626	+	0.952517i	−1.42915	+	0.0462038i
$426$		0			0
$427$	2.51310	+	4.35282i	0.121618	+	0.210648i
$428$	−24.5723	−	12.1762i	−1.18775	−	0.588558i
$429$		0			0
$430$	1.80366	+	37.6036i	0.0869803	+	1.81341i
$431$	15.2488			0.734510			0.367255	−	0.930120i	$-0.380298\pi$
$431$	15.2488			0.734510			0.367255	+	0.930120i	$0.380298\pi$
$432$		0			0
$433$		−	23.5695i		−	1.13268i	−0.824172	−	0.566340i	$-0.808359\pi$
$433$		−	23.5695i		−	1.13268i	0.824172	−	0.566340i	$-0.191641\pi$
$434$	−9.09684	+	5.64473i	−0.436662	+	0.270956i
$435$		0			0
$436$	11.7806	−	23.7741i	0.564191	−	1.13857i
$437$	3.03665	+	5.25964i	0.145263	+	0.251603i
$438$		0			0
$439$	12.8688	+	7.42979i	0.614193	+	0.354605i	0.774605	−	0.632446i	$-0.217949\pi$
$439$	12.8688	+	7.42979i	0.614193	+	0.354605i	−0.160412	+	0.987050i	$0.551282\pi$
$440$	4.58173	+	2.00299i	0.218426	+	0.0954887i
$441$		0			0
$442$	34.3030	+	18.3775i	1.63163	+	0.874128i
$443$	23.5062	+	13.5713i	1.11681	+	0.644791i	0.940585	−	0.339558i	$-0.110278\pi$
$443$	23.5062	+	13.5713i	1.11681	+	0.644791i	0.176226	+	0.984350i	$0.443611\pi$
$444$		0			0
$445$	0.0165877		0.000268067i	0.000786332		1.27076e-5i
$446$	0.479560	−	0.0152404i	0.0227078	−	0.000721652i
$447$		0			0
$448$	7.55568	−	21.8460i	0.356972	−	1.03212i
$449$		−	17.4879i		−	0.825304i	−0.910889	−	0.412652i	$-0.864602\pi$
$449$		−	17.4879i		−	0.825304i	0.910889	−	0.412652i	$-0.135398\pi$
$450$		0			0
$451$		−	5.40069i		−	0.254309i
$452$	−18.4622	+	1.17464i	−0.868386	+	0.0552503i
$453$		0			0
$454$	0.386504	+	12.1619i	0.0181395	+	0.570786i
$455$	−30.1527	+	0.487286i	−1.41358	+	0.0228443i
$456$		0			0
$457$	−5.10627	−	2.94811i	−0.238861	−	0.137907i	0.375792	−	0.926704i	$-0.377371\pi$
$457$	−5.10627	−	2.94811i	−0.238861	−	0.137907i	−0.614653	+	0.788797i	$0.710704\pi$
$458$	−0.479335	+	0.894715i	−0.0223979	+	0.0418073i
$459$		0			0
$460$	5.94383	−	0.474715i	0.277132	−	0.0221337i
$461$	−30.5948	−	17.6639i	−1.42494	−	0.822691i	−0.428227	−	0.903671i	$-0.640862\pi$
$461$	−30.5948	−	17.6639i	−1.42494	−	0.822691i	−0.996716	+	0.0809799i	$0.974195\pi$
$462$		0			0
$463$	−18.6175	−	32.2464i	−0.865227	−	1.49862i	−0.866822	−	0.498618i	$-0.833841\pi$
$463$	−18.6175	−	32.2464i	−0.865227	−	1.49862i	0.00159457	−	0.999999i	$-0.499492\pi$
$464$	1.34332	+	10.5139i	0.0623619	+	0.488097i
$465$		0			0
$466$	−10.3183	−	16.6286i	−0.477985	−	0.770304i
$467$		−	6.98334i		−	0.323151i	−0.986860	−	0.161575i	$-0.948343\pi$
$467$		−	6.98334i		−	0.323151i	0.986860	−	0.161575i	$-0.0516575\pi$
$468$		0			0
$469$	−21.7704			−1.00526
$470$	−9.51751	+	0.456509i	−0.439010	+	0.0210572i
$471$		0			0
$472$	−17.3750	−	24.3942i	−0.799749	−	1.12283i
$473$	4.70625	+	8.15147i	0.216394	+	0.374805i
$474$		0			0
$475$	−0.735933	−	22.7634i	−0.0337669	−	1.04445i
$476$	18.8742	+	28.3644i	0.865097	+	1.30008i
$477$		0			0
$478$	−18.5064	+	34.5436i	−0.846463	+	1.57999i
$479$	−10.2090	+	17.6825i	−0.466460	+	0.807932i	−0.999266	−	0.0383050i	$-0.987804\pi$
$479$	−10.2090	+	17.6825i	−0.466460	+	0.807932i	0.532806	+	0.846237i	$0.321137\pi$
$480$		0			0
$481$	−17.3630	−	30.0735i	−0.791683	−	1.37124i
$482$	−16.1507	+	0.513269i	−0.735646	+	0.0233788i
$483$		0			0
$484$	−20.7079	+	1.31752i	−0.941269	+	0.0598874i
$485$	−7.21355	+	12.9740i	−0.327550	+	0.589117i
$486$		0			0
$487$	−20.8264			−0.943735			−0.471868	−	0.881669i	$-0.656420\pi$
$487$	−20.8264			−0.943735			−0.471868	+	0.881669i	$0.656420\pi$
$488$	2.04338	−	4.47565i	0.0924993	−	0.202603i
$489$		0			0
$490$	−3.79225	−	1.95346i	−0.171316	−	0.0882484i
$491$	−9.31608	−	16.1359i	−0.420429	−	0.728204i	0.575552	−	0.817765i	$-0.304787\pi$
$491$	−9.31608	−	16.1359i	−0.420429	−	0.728204i	−0.995981	+	0.0895606i	$0.971454\pi$
$492$		0			0
$493$	−13.5294	−	7.81122i	−0.609335	−	0.351800i
$494$	−14.1988	+	26.5031i	−0.638834	+	1.19243i
$495$		0			0
$496$	9.66661	+	4.04740i	0.434044	+	0.181734i
$497$	−4.16900	+	7.22093i	−0.187005	+	0.323903i
$498$		0			0
$499$	4.48667	−	2.59038i	0.200851	−	0.115961i	−0.396201	−	0.918164i	$-0.629672\pi$
$499$	4.48667	−	2.59038i	0.200851	−	0.115961i	0.597052	+	0.802202i	$0.296338\pi$
$500$	−20.4933	−	8.94562i	−0.916489	−	0.400060i
$501$		0			0
$502$	−3.76675	−	6.07035i	−0.168118	−	0.270933i
$503$		−	27.8846i		−	1.24331i	−0.783290	−	0.621657i	$-0.786460\pi$
$503$		−	27.8846i		−	1.24331i	0.783290	−	0.621657i	$-0.213540\pi$
$504$		0			0
$505$	2.76066	−	4.96521i	0.122848	−	0.220949i
$506$	1.26676	−	0.786042i	0.0563142	−	0.0349438i
$507$		0			0
$508$	−8.67792	+	17.5126i	−0.385021	+	0.776997i
$509$	−18.6724	+	10.7805i	−0.827640	+	0.477838i	−0.853044	−	0.521839i	$-0.825246\pi$
$509$	−18.6724	+	10.7805i	−0.827640	+	0.477838i	0.0254039	+	0.999677i	$0.491913\pi$
$510$		0			0
$511$	16.2864	+	9.40298i	0.720470	+	0.415963i
$512$	−21.7088	+	6.38191i	−0.959402	+	0.282043i
$513$		0			0
$514$	1.76801	−	3.30013i	0.0779837	−	0.145562i
$515$	−14.6865	+	8.79867i	−0.647163	+	0.387716i
$516$		0			0
$517$	−2.06315	+	1.19116i	−0.0907371	+	0.0523871i
$518$	−0.965690	−	30.3868i	−0.0424300	−	1.33512i
$519$		0			0
$520$	17.5119	+	23.7643i	0.767950	+	1.04213i
$521$			19.9411i			0.873633i	0.899551	+	0.436817i	$0.143894\pi$
$521$			19.9411i			0.873633i	−0.899551	+	0.436817i	$0.856106\pi$
$522$		0			0
$523$	18.9360			0.828013			0.414006	−	0.910274i	$-0.364129\pi$
$523$	18.9360			0.828013			0.414006	+	0.910274i	$0.364129\pi$
$524$	26.4197	−	1.68093i	1.15415	−	0.0734316i
$525$		0			0
$526$	−0.113705	−	3.57788i	−0.00495776	−	0.156003i
$527$	−13.3767	+	7.72304i	−0.582698	+	0.336421i
$528$		0			0
$529$	−10.6111	+	18.3790i	−0.461354	+	0.799088i
$530$	4.54182	−	2.92096i	0.197284	−	0.126878i
$531$		0			0
$532$	−21.9149	+	14.5826i	−0.950132	+	0.632234i
$533$	15.9413	−	27.6111i	0.690494	−	1.19597i
$534$		0			0
$535$	30.6566	−	0.495430i	1.32540	−	0.0214193i
$536$	12.3632	+	17.3577i	0.534009	+	0.749740i
$537$		0			0
$538$	−6.32640	+	3.92563i	−0.272751	+	0.169246i
$539$	−1.06654			−0.0459393
$540$		0			0
$541$	−13.2697			−0.570511			−0.285255	−	0.958452i	$-0.592078\pi$
$541$	−13.2697			−0.570511			−0.285255	+	0.958452i	$0.592078\pi$
$542$	−20.0039	+	12.4128i	−0.859243	+	0.533174i
$543$		0			0
$544$	11.8967	−	31.1565i	0.510069	−	1.33582i
$545$	0.479336	+	29.6608i	0.0205325	+	1.27053i
$546$		0			0
$547$	−4.51377	+	7.81809i	−0.192995	+	0.334277i	−0.946241	−	0.323461i	$-0.895153\pi$
$547$	−4.51377	+	7.81809i	−0.192995	+	0.334277i	0.753246	+	0.657738i	$0.228487\pi$
$548$	3.49278	+	5.24901i	0.149204	+	0.224227i
$549$		0			0
$550$	−5.57917	+	0.358046i	−0.237897	+	0.0152671i
$551$	6.03510	−	10.4531i	0.257104	−	0.445317i
$552$		0			0
$553$	9.55988	−	5.51940i	0.406527	−	0.234709i
$554$	1.18558	+	37.3059i	0.0503704	+	1.58498i
$555$		0			0
$556$	−0.326350	−	5.12935i	−0.0138403	−	0.217533i
$557$	30.4174			1.28883			0.644414	−	0.764677i	$-0.277101\pi$
$557$	30.4174			1.28883			0.644414	+	0.764677i	$0.277101\pi$
$558$		0			0
$559$			55.5660i			2.35019i
$560$	3.68916	+	25.5794i	0.155896	+	1.08093i
$561$		0			0
$562$	1.02968	+	32.4004i	0.0434345	+	1.36673i
$563$	−39.1934	+	22.6283i	−1.65180	+	0.953669i	−0.675473	+	0.737385i	$0.736060\pi$
$563$	−39.1934	+	22.6283i	−1.65180	+	0.953669i	−0.976330	+	0.216284i	$0.930606\pi$
$564$		0			0
$565$	17.7426	−	10.6296i	0.746437	−	0.447191i
$566$	−4.35080	+	8.12109i	−0.182878	+	0.341355i
$567$		0			0
$568$	8.12485	−	0.776714i	0.340911	−	0.0325902i
$569$	4.42750	+	2.55622i	0.185610	+	0.107162i	0.589926	−	0.807457i	$-0.299157\pi$
$569$	4.42750	+	2.55622i	0.185610	+	0.107162i	−0.404316	+	0.914620i	$0.632490\pi$
$570$		0			0
$571$	−30.6553	+	17.6989i	−1.28289	+	0.740675i	−0.977375	−	0.211514i	$-0.932161\pi$
$571$	−30.6553	+	17.6989i	−1.28289	+	0.740675i	−0.305511	+	0.952189i	$0.598827\pi$
$572$	6.61315	+	3.27697i	0.276510	+	0.137017i
$573$		0			0
$574$	23.7177	−	14.7172i	0.989958	−	0.614284i
$575$	−5.66269	+	3.51810i	−0.236151	+	0.146715i
$576$		0			0
$577$			30.4257i			1.26664i	0.773890	+	0.633320i	$0.218308\pi$
$577$			30.4257i			1.26664i	−0.773890	+	0.633320i	$0.781692\pi$
$578$	13.2414	+	21.3393i	0.550768	+	0.887597i
$579$		0			0
$580$	−6.72349	−	9.75852i	−0.279178	−	0.405200i
$581$	−24.0888	+	13.9077i	−0.999372	+	0.576987i
$582$		0			0
$583$	0.675058	−	1.16924i	0.0279581	−	0.0484248i
$584$	−1.75184	−	18.3252i	−0.0724916	−	0.758302i
$585$		0			0
$586$	11.1834	−	20.8747i	0.461982	−	0.862324i
$587$	−25.3201	−	14.6186i	−1.04507	−	0.603372i	−0.123806	−	0.992306i	$-0.539510\pi$
$587$	−25.3201	−	14.6186i	−1.04507	−	0.603372i	−0.921265	+	0.388934i	$0.872843\pi$
$588$		0			0
$589$	−5.96697	−	10.3351i	−0.245865	−	0.425850i
$590$	29.7672	+	15.3337i	1.22550	+	0.631278i
$591$		0			0
$592$	−23.6793	+	18.0264i	−0.973213	+	0.740879i
$593$	−1.73460			−0.0712314			−0.0356157	−	0.999366i	$-0.511339\pi$
$593$	−1.73460			−0.0712314			−0.0356157	+	0.999366i	$0.511339\pi$
$594$		0			0
$595$	−33.2917	−	18.5103i	−1.36483	−	0.758847i
$596$	−1.25040	−	19.6530i	−0.0512185	−	0.805017i
$597$		0			0
$598$	8.79648	−	0.279551i	0.359715	−	0.0114317i
$599$	−1.94974	−	3.37704i	−0.0796641	−	0.137982i	0.823441	−	0.567402i	$-0.192051\pi$
$599$	−1.94974	−	3.37704i	−0.0796641	−	0.137982i	−0.903105	+	0.429420i	$0.858718\pi$
$600$		0			0
$601$	2.16133	−	3.74354i	0.0881625	−	0.152702i	−0.818572	−	0.574404i	$-0.805234\pi$
$601$	2.16133	−	3.74354i	0.0881625	−	0.152702i	0.906734	+	0.421702i	$0.138567\pi$
$602$	−22.9732	+	42.8812i	−0.936319	+	1.74771i
$603$		0			0
$604$	−17.7682	+	11.8233i	−0.722978	+	0.481082i
$605$	19.9008	−	11.9226i	0.809084	−	0.484723i
$606$		0			0
$607$	6.33497	+	10.9725i	0.257128	+	0.445360i	0.965471	−	0.260509i	$-0.0838903\pi$
$607$	6.33497	+	10.9725i	0.257128	+	0.445360i	−0.708343	+	0.705868i	$0.750557\pi$
$608$	24.0721	+	9.19165i	0.976252	+	0.372771i
$609$		0			0
$610$	0.263543	+	5.49446i	0.0106705	+	0.222464i
$611$	−14.0638			−0.568961
$612$		0			0
$613$		−	47.3059i		−	1.91067i	−0.295527	−	0.955334i	$-0.595495\pi$
$613$		−	47.3059i		−	1.91067i	0.295527	−	0.955334i	$-0.404505\pi$
$614$	−18.1014	−	29.1715i	−0.730512	−	1.17727i
$615$		0			0
$616$	3.74865	+	5.26304i	0.151037	+	0.212054i
$617$	−3.48880	−	6.04277i	−0.140454	−	0.243273i	0.787214	−	0.616680i	$-0.211523\pi$
$617$	−3.48880	−	6.04277i	−0.140454	−	0.243273i	−0.927668	+	0.373407i	$0.878189\pi$
$618$		0			0
$619$	24.9827	+	14.4238i	1.00414	+	0.579741i	0.909471	−	0.415768i	$-0.136487\pi$
$619$	24.9827	+	14.4238i	1.00414	+	0.579741i	0.0946695	+	0.995509i	$0.469821\pi$
$620$	−11.6795	+	0.932805i	−0.469060	+	0.0374624i
$621$		0			0
$622$	−5.09786	+	9.51554i	−0.204406	+	0.381538i
$623$	0.0185654	+	0.0107187i	0.000743807	+	0.000429437i
$624$		0			0
$625$	24.9478	−	1.61480i	0.997912	−	0.0645919i
$626$	0.200134	+	6.29750i	0.00799896	+	0.251699i
$627$		0			0
$628$	−1.90616	−	29.9598i	−0.0760643	−	1.19553i
$629$		−	43.8633i		−	1.74894i
$630$		0			0
$631$		−	31.3427i		−	1.24774i	−0.781530	−	0.623868i	$-0.785560\pi$
$631$		−	31.3427i		−	1.24774i	0.781530	−	0.623868i	$-0.214440\pi$
$632$	−9.82964	−	4.48776i	−0.391002	−	0.178514i
$633$		0			0
$634$	−7.00517	+	0.222624i	−0.278211	+	0.00884151i
$635$	−0.353091	−	21.8489i	−0.0140120	−	0.867046i
$636$		0			0
$637$	−5.45272	−	3.14813i	−0.216045	−	0.124733i
$638$	−2.61169	−	1.39919i	−0.103398	−	0.0553943i
$639$		0			0
$640$	18.2997	−	17.4677i	0.723358	−	0.690473i
$641$	17.6686	+	10.2010i	0.697869	+	0.402915i	0.806553	−	0.591162i	$-0.201330\pi$
$641$	17.6686	+	10.2010i	0.697869	+	0.402915i	−0.108684	+	0.994076i	$0.534664\pi$
$642$		0			0
$643$	−14.8702	−	25.7560i	−0.586424	−	1.01572i	−0.994696	−	0.102856i	$-0.967202\pi$
$643$	−14.8702	−	25.7560i	−0.586424	−	1.01572i	0.408272	−	0.912860i	$-0.366131\pi$
$644$	6.90397	+	3.42108i	0.272055	+	0.134810i
$645$		0			0
$646$	−32.2705	+	20.0243i	−1.26966	+	0.787846i
$647$		−	7.37854i		−	0.290081i	−0.989426	−	0.145040i	$-0.953669\pi$
$647$		−	7.37854i		−	0.290081i	0.989426	−	0.145040i	$-0.0463312\pi$
$648$		0			0
$649$	8.37183			0.328623
$650$	−29.5804	−	14.6376i	−1.16024	−	0.574133i
$651$		0			0
$652$	−3.69297	+	7.45266i	−0.144628	+	0.291869i
$653$	−7.32692	−	12.6906i	−0.286724	−	0.496621i	0.686301	−	0.727317i	$-0.259233\pi$
$653$	−7.32692	−	12.6906i	−0.286724	−	0.496621i	−0.973026	+	0.230696i	$0.925900\pi$
$654$		0			0
$655$	−25.3900	+	15.2112i	−0.992068	+	0.594349i
$656$	−25.2032	−	10.5526i	−0.984021	−	0.412009i
$657$		0			0
$658$	−10.8533	−	5.81455i	−0.423105	−	0.226675i
$659$	3.26655	−	5.65782i	0.127247	−	0.220398i	−0.795362	−	0.606134i	$-0.792719\pi$
$659$	3.26655	−	5.65782i	0.127247	−	0.220398i	0.922609	+	0.385737i	$0.126053\pi$
$660$		0			0
$661$	13.4007	+	23.2106i	0.521225	+	0.902788i	0.999695	+	0.0246846i	$0.00785816\pi$
$661$	13.4007	+	23.2106i	0.521225	+	0.902788i	−0.478470	+	0.878104i	$0.658809\pi$
$662$	−1.19431	−	37.5807i	−0.0464182	−	1.46062i
$663$		0			0
$664$	24.7685	+	11.3082i	0.961205	+	0.438842i
$665$	14.3014	−	25.7218i	0.554584	−	0.997450i
$666$		0			0
$667$	−3.53308			−0.136801
$668$	0.00423568	+	0.0665735i	0.000163883	+	0.00257581i
$669$		0			0
$670$	−21.1809	−	10.9107i	−0.818290	−	0.421518i
$671$	0.687656	+	1.19105i	0.0265466	+	0.0459801i
$672$		0			0
$673$	−16.3504	−	9.43992i	−0.630262	−	0.363882i	0.150591	−	0.988596i	$-0.451882\pi$
$673$	−16.3504	−	9.43992i	−0.630262	−	0.363882i	−0.780854	+	0.624714i	$0.785216\pi$
$674$	15.5127	+	8.31076i	0.597526	+	0.320119i
$675$		0			0
$676$	9.73367	+	14.6279i	0.374372	+	0.562612i
$677$	10.1163	−	17.5219i	0.388800	−	0.673421i	−0.603488	−	0.797372i	$-0.706223\pi$
$677$	10.1163	−	17.5219i	0.388800	−	0.673421i	0.992288	+	0.123950i	$0.0395564\pi$
$678$		0			0
$679$	−16.6122	+	9.59106i	−0.637518	+	0.368071i
$680$	4.14767	+	37.0556i	0.159056	+	1.42102i
$681$		0			0
$682$	−2.48915	+	1.54456i	−0.0953145	+	0.0591441i
$683$		−	15.3795i		−	0.588481i	−0.955731	−	0.294241i	$-0.904933\pi$
$683$		−	15.3795i		−	0.588481i	0.955731	−	0.294241i	$-0.0950667\pi$
$684$		0			0
$685$	−6.16084	−	3.42544i	−0.235393	−	0.130879i
$686$	12.1753	+	19.6213i	0.464856	+	0.749145i
$687$		0			0
$688$	47.2359	−	6.03511i	1.80085	−	0.230086i
$689$	6.90249	−	3.98516i	0.262964	−	0.151822i
$690$		0			0
$691$	13.7773	+	7.95434i	0.524114	+	0.302598i	0.738616	−	0.674126i	$-0.235480\pi$
$691$	13.7773	+	7.95434i	0.524114	+	0.302598i	−0.214502	+	0.976724i	$0.568813\pi$
$692$	−26.4051	−	39.6819i	−1.00377	−	1.50848i
$693$		0			0
$694$	21.0944	+	11.3011i	0.800731	+	0.428984i
$695$	2.95323	+	4.92944i	0.112022	+	0.186984i
$696$		0			0
$697$	34.8763	−	20.1359i	1.32104	−	0.762700i
$698$	−2.70135	+	0.0858486i	−0.102248	+	0.00324942i
$699$		0			0
$700$	−16.7760	−	23.5258i	−0.634072	−	0.889192i
$701$		−	38.9767i		−	1.47213i	−0.676912	−	0.736064i	$-0.736682\pi$
$701$		−	38.9767i		−	1.47213i	0.676912	−	0.736064i	$-0.263318\pi$
$702$		0			0
$703$	33.8896			1.27817
$704$	2.06745	−	5.97767i	0.0779198	−	0.225292i
$705$		0			0
$706$	31.2556	−	0.993301i	1.17632	−	0.0373834i
$707$	6.35758	−	3.67055i	0.239102	−	0.138045i
$708$		0			0
$709$	−6.59388	+	11.4209i	−0.247638	+	0.428922i	−0.962870	−	0.269965i	$-0.912988\pi$
$709$	−6.59388	+	11.4209i	−0.247638	+	0.428922i	0.715232	+	0.698887i	$0.246321\pi$
$710$	−7.67505	+	4.93602i	−0.288039	+	0.185245i
$711$		0			0
$712$	−0.00199697	−	0.0208894i	−7.48398e−5	−	0.000782865i
$713$	−1.74660	+	3.02519i	−0.0654105	+	0.113294i
$714$		0			0
$715$	−8.25061	+	0.133335i	−0.308555	+	0.00498645i
$716$	22.6697	−	45.7489i	0.847205	−	1.70972i
$717$		0			0
$718$	−1.10382	−	1.77888i	−0.0411943	−	0.0663872i
$719$	43.7650			1.63216			0.816079	−	0.577940i	$-0.196143\pi$
$719$	43.7650			1.63216			0.816079	+	0.577940i	$0.196143\pi$
$720$		0			0
$721$	−22.1231			−0.823907
$722$	−1.30377	−	2.10111i	−0.0485214	−	0.0781953i
$723$		0			0
$724$	−22.7426	+	45.8960i	−0.845221	+	1.70571i
$725$	11.6823	+	6.25040i	0.433868	+	0.232134i
$726$		0			0
$727$	4.95811	−	8.58770i	0.183886	−	0.318500i	−0.759314	−	0.650724i	$-0.774466\pi$
$727$	4.95811	−	8.58770i	0.183886	−	0.318500i	0.943201	+	0.332224i	$0.107799\pi$
$728$	3.63005	+	37.9723i	0.134539	+	1.40735i
$729$		0			0
$730$	11.1329	+	17.3107i	0.412049	+	0.640697i
$731$	−35.0935	+	60.7837i	−1.29798	+	2.24816i
$732$		0			0
$733$	−24.2247	+	13.9862i	−0.894761	+	0.516591i	−0.875497	−	0.483224i	$-0.839466\pi$
$733$	−24.2247	+	13.9862i	−0.894761	+	0.516591i	−0.0192642	+	0.999814i	$0.506132\pi$
$734$	0.178426	−	0.00567035i	0.00658581	−	0.000209297i
$735$		0			0
$736$	−1.19304	−	7.44740i	−0.0439761	−	0.274515i
$737$	−5.95699			−0.219428
$738$		0			0
$739$		−	24.2237i		−	0.891082i	−0.895262	−	0.445541i	$-0.853011\pi$
$739$		−	24.2237i		−	0.891082i	0.895262	−	0.445541i	$-0.146989\pi$
$740$	14.2895	−	30.0480i	0.525292	−	1.10459i
$741$		0			0
$742$	6.97439	−	0.221646i	0.256038	−	0.00813687i
$743$	43.9304	−	25.3632i	1.61165	−	0.930486i	0.622660	−	0.782492i	$-0.286052\pi$
$743$	43.9304	−	25.3632i	1.61165	−	0.930486i	0.988988	−	0.147993i	$-0.0472814\pi$
$744$		0			0
$745$	11.3152	+	18.8870i	0.414558	+	0.691967i
$746$	−28.5767	−	15.3097i	−1.04627	−	0.560528i
$747$		0			0
$748$	5.16451	+	7.76131i	0.188833	+	0.283781i
$749$	34.3117	+	19.8099i	1.25372	+	0.723838i
$750$		0			0
$751$	0.581286	−	0.335605i	0.0212114	−	0.0122464i	−0.489357	−	0.872084i	$-0.662768\pi$
$751$	0.581286	−	0.335605i	0.0212114	−	0.0122464i	0.510568	+	0.859837i	$0.329435\pi$
$752$	1.52749	+	11.9555i	0.0557020	+	0.435971i
$753$		0			0
$754$	−9.22229	−	14.8623i	−0.335856	−	0.541253i
$755$	11.5953	−	20.8548i	0.421996	−	0.758983i
$756$		0			0
$757$			17.0611i			0.620095i	0.950721	+	0.310048i	$0.100345\pi$
$757$			17.0611i			0.620095i	−0.950721	+	0.310048i	$0.899655\pi$
$758$	33.0606	−	20.5146i	1.20081	−	0.745123i
$759$		0			0
$760$	−28.6299	+	3.20457i	−1.03852	+	0.116242i
$761$	−6.74677	+	3.89525i	−0.244570	+	0.141203i	−0.617275	−	0.786747i	$-0.711764\pi$
$761$	−6.74677	+	3.89525i	−0.244570	+	0.141203i	0.372705	+	0.927950i	$0.378430\pi$
$762$		0			0
$763$	−19.1664	+	33.1972i	−0.693870	+	1.20182i
$764$	8.55041	+	12.8497i	0.309343	+	0.464886i
$765$		0			0
$766$	29.5814	+	15.8479i	1.06882	+	0.572609i
$767$	42.8011	+	24.7112i	1.54546	+	0.892271i
$768$		0			0
$769$	4.58773	+	7.94618i	0.165438	+	0.286546i	0.936811	−	0.349837i	$-0.113763\pi$
$769$	4.58773	+	7.94618i	0.165438	+	0.286546i	−0.771373	+	0.636383i	$0.780430\pi$
$770$	−6.42227	−	3.30824i	−0.231442	−	0.119221i
$771$		0			0
$772$	−0.656015	−	10.3108i	−0.0236105	−	0.371094i
$773$	−32.0512			−1.15280			−0.576401	−	0.817167i	$-0.695543\pi$
$773$	−32.0512			−1.15280			−0.576401	+	0.817167i	$0.695543\pi$
$774$		0			0
$775$	11.1271	−	6.91299i	0.399696	−	0.248322i
$776$	17.0810	+	7.79839i	0.613171	+	0.279946i
$777$		0			0
$778$	0.0820214	+	2.58092i	0.00294061	+	0.0925305i
$779$	15.5574	+	26.9461i	0.557400	+	0.965445i
$780$		0			0
$781$	−1.14076	+	1.97585i	−0.0408195	+	0.0707014i
$782$	9.79902	+	5.24973i	0.350412	+	0.187730i
$783$		0			0
$784$	−2.08395	+	4.97720i	−0.0744269	+	0.177757i
$785$	17.2494	+	28.7921i	0.615657	+	1.02764i
$786$		0			0
$787$	−1.97855	−	3.42695i	−0.0705276	−	0.122157i	0.828605	−	0.559834i	$-0.189135\pi$
$787$	−1.97855	−	3.42695i	−0.0705276	−	0.122157i	−0.899133	+	0.437676i	$0.855802\pi$
$788$	7.52243	−	15.1808i	0.267975	−	0.540792i
$789$		0			0
$790$	12.0672	−	0.578805i	0.429332	−	0.0205930i
$791$	26.7267			0.950293
$792$		0			0
$793$			8.11904i			0.288316i
$794$	22.9311	−	14.2291i	0.813795	−	0.504972i
$795$		0			0
$796$	−0.996321	−	0.493701i	−0.0353137	−	0.0174988i
$797$	4.99178	+	8.64602i	0.176818	+	0.306258i	0.940789	−	0.338993i	$-0.110086\pi$
$797$	4.99178	+	8.64602i	0.176818	+	0.306258i	−0.763971	+	0.645251i	$0.776753\pi$
$798$		0			0
$799$	−15.3844	−	8.88219i	−0.544261	−	0.314229i
$800$	−9.23043	+	26.7357i	−0.326345	+	0.945251i
$801$		0			0
$802$	21.7894	+	11.6735i	0.769412	+	0.412205i
$803$	4.45643	+	2.57292i	0.157264	+	0.0907963i
$804$		0			0
$805$	−8.61344	+	0.139199i	−0.303584	+	0.00490611i
$806$	−17.2849	+	0.549313i	−0.608835	+	0.0193487i
$807$		0			0
$808$	−6.53698	−	2.98449i	−0.229970	−	0.104994i
$809$			37.9989i			1.33597i	0.744174	+	0.667986i	$0.232843\pi$
$809$			37.9989i			1.33597i	−0.744174	+	0.667986i	$0.767157\pi$
$810$		0			0
$811$			21.3193i			0.748622i	0.927303	+	0.374311i	$0.122121\pi$
$811$			21.3193i			0.748622i	−0.927303	+	0.374311i	$0.877879\pi$
$812$	−0.972326	−	15.2824i	−0.0341219	−	0.536306i
$813$		0			0
$814$	−0.264240	−	8.31469i	−0.00926161	−	0.291430i
$815$	−0.150261	−	9.29799i	−0.00526343	−	0.325695i
$816$		0			0
$817$	−46.9626	−	27.1139i	−1.64301	−	0.948595i
$818$	10.9222	−	20.3871i	0.381885	−	0.712818i
$819$		0			0
$820$	30.4514	−	2.43205i	1.06341	−	0.0849310i
$821$	4.11744	+	2.37721i	0.143700	+	0.0829651i	0.570126	−	0.821557i	$-0.306894\pi$
$821$	4.11744	+	2.37721i	0.143700	+	0.0829651i	−0.426426	+	0.904522i	$0.640228\pi$
$822$		0			0
$823$	−20.4702	−	35.4554i	−0.713546	−	1.23590i	−0.963518	−	0.267644i	$-0.913755\pi$
$823$	−20.4702	−	35.4554i	−0.713546	−	1.23590i	0.249972	−	0.968253i	$-0.419578\pi$
$824$	12.5635	+	17.6389i	0.437670	+	0.614482i
$825$		0			0
$826$	22.8137	+	36.7658i	0.793792	+	1.27925i
$827$			26.4974i			0.921406i	0.887554	+	0.460703i	$0.152403\pi$
$827$			26.4974i			0.921406i	−0.887554	+	0.460703i	$0.847597\pi$
$828$		0			0
$829$	38.1524			1.32509			0.662544	−	0.749023i	$-0.269477\pi$
$829$	38.1524			1.32509			0.662544	+	0.749023i	$0.269477\pi$
$830$	−30.4067	+	1.45846i	−1.05543	+	0.0506239i
$831$		0			0
$832$	28.2142	−	24.4584i	0.978151	−	0.847942i
$833$	−3.97649	−	6.88748i	−0.137777	−	0.238637i
$834$		0			0
$835$	−0.0383298	−	0.0639789i	−0.00132646	−	0.00221408i
$836$	−5.99653	+	3.99020i	−0.207394	+	0.138004i
$837$		0			0
$838$	16.5421	−	30.8771i	0.571437	−	1.06663i
$839$	8.60385	−	14.9023i	0.297038	−	0.514485i	−0.678419	−	0.734675i	$-0.737335\pi$
$839$	8.60385	−	14.9023i	0.297038	−	0.514485i	0.975457	+	0.220190i	$0.0706679\pi$
$840$		0			0
$841$	−10.9891	−	19.0338i	−0.378936	−	0.656337i
$842$	23.7079	−	0.753434i	0.817027	−	0.0259650i
$843$		0			0
$844$	3.08889	+	48.5490i	0.106324	+	1.67113i
$845$	−17.1690	−	9.54600i	−0.590631	−	0.328392i
$846$		0			0
$847$	29.9778			1.03005
$848$	−4.13742	−	5.43488i	−0.142079	−	0.186634i
$849$		0			0
$850$	−23.1135	−	34.6940i	−0.792785	−	1.18999i
$851$	−4.95992	−	8.59084i	−0.170024	−	0.294490i
$852$		0			0
$853$	37.6416	+	21.7324i	1.28882	+	0.744102i	0.978444	−	0.206511i	$-0.0662109\pi$
$853$	37.6416	+	21.7324i	1.28882	+	0.744102i	0.310378	+	0.950613i	$0.399544\pi$
$854$	−3.35674	+	6.26561i	−0.114865	+	0.214405i
$855$		0			0
$856$	−3.69072	−	38.6069i	−0.126146	−	1.31956i
$857$	−6.72648	+	11.6506i	−0.229772	+	0.397977i	−0.957741	−	0.287634i	$-0.907131\pi$
$857$	−6.72648	+	11.6506i	−0.229772	+	0.397977i	0.727968	+	0.685611i	$0.240465\pi$
$858$		0			0
$859$	−1.00899	+	0.582541i	−0.0344263	+	0.0198760i	−0.517114	−	0.855916i	$-0.672994\pi$
$859$	−1.00899	+	0.582541i	−0.0344263	+	0.0198760i	0.482688	+	0.875792i	$0.339660\pi$
$860$	−43.8421	+	30.2066i	−1.49500	+	1.03004i
$861$		0			0
$862$	11.3703	+	18.3240i	0.387275	+	0.624118i
$863$			0.0600669i			0.00204470i	0.999999	+	0.00102235i	$0.000325424\pi$
$863$			0.0600669i			0.00204470i	−0.999999	+	0.00102235i	$0.999675\pi$
$864$		0			0
$865$	46.5753	+	25.8959i	1.58361	+	0.880488i
$866$	28.3227	−	17.5747i	0.962446	−	0.597212i
$867$		0			0
$868$	−13.5662	−	6.72236i	−0.460466	−	0.228172i
$869$	2.61585	−	1.51026i	0.0887367	−	0.0512321i
$870$		0			0
$871$	−30.4552	−	17.5833i	−1.03193	−	0.595788i
$872$	37.3528	−	3.57083i	1.26493	−	0.120924i
$873$		0			0
$874$	−4.05604	+	7.57091i	−0.137198	+	0.256090i
$875$	28.7269	+	14.7779i	0.971147	+	0.499583i
$876$		0			0
$877$	5.64252	−	3.25771i	0.190534	−	0.110005i	−0.401698	−	0.915772i	$-0.631580\pi$
$877$	5.64252	−	3.25771i	0.190534	−	0.110005i	0.592233	+	0.805767i	$0.298247\pi$
$878$	0.667506	+	21.0040i	0.0225272	+	0.708851i
$879$		0			0
$880$	1.00946	+	6.99925i	0.0340288	+	0.235945i
$881$		−	12.1468i		−	0.409237i	−0.978842	−	0.204619i	$-0.934405\pi$
$881$		−	12.1468i		−	0.409237i	0.978842	−	0.204619i	$-0.0655954\pi$
$882$		0			0
$883$	30.7337			1.03427			0.517135	−	0.855904i	$-0.326998\pi$
$883$	30.7337			1.03427			0.517135	+	0.855904i	$0.326998\pi$
$884$	3.49448	+	54.9239i	0.117532	+	1.84729i
$885$		0			0
$886$	1.21927	+	38.3660i	0.0409621	+	1.28893i
$887$	−48.2108	+	27.8345i	−1.61876	+	0.934592i	−0.631519	+	0.775361i	$0.717568\pi$
$887$	−48.2108	+	27.8345i	−1.61876	+	0.934592i	−0.987241	+	0.159231i	$0.949099\pi$
$888$		0			0
$889$	14.1185	−	24.4539i	0.473518	−	0.820157i
$890$	0.0126908	+	0.0197330i	0.000425396	+	0.000661451i
$891$		0			0
$892$	0.375899	+	0.564907i	0.0125860	+	0.0189145i
$893$	6.86255	−	11.8863i	0.229647	−	0.397760i
$894$		0			0
$895$	0.922394	+	57.0766i	0.0308322	+	1.90786i
$896$	31.8855	−	7.21008i	1.06522	−	0.240872i
$897$		0			0
$898$	21.0146	−	13.0399i	0.701267	−	0.435147i
$899$	6.94243			0.231543
$900$		0			0
$901$	10.0675			0.335397
$902$	6.48983	−	4.02704i	0.216088	−	0.134086i
$903$		0			0
$904$	−15.1779	−	21.3095i	−0.504809	−	0.708743i
$905$	−0.925361	−	57.2602i	−0.0307600	−	1.90339i
$906$		0			0
$907$	8.31258	−	14.3978i	0.276015	−	0.478072i	−0.694376	−	0.719612i	$-0.744319\pi$
$907$	8.31258	−	14.3978i	0.276015	−	0.478072i	0.970391	+	0.241541i	$0.0776528\pi$
$908$	−14.3263	+	9.53299i	−0.475436	+	0.316363i
$909$		0			0
$910$	−23.0690	−	35.8701i	−0.764729	−	1.18908i
$911$	−9.29200	+	16.0942i	−0.307858	+	0.533225i	−0.977893	−	0.209104i	$-0.932945\pi$
$911$	−9.29200	+	16.0942i	−0.307858	+	0.533225i	0.670036	+	0.742329i	$0.266279\pi$
$912$		0			0
$913$	−6.59137	+	3.80553i	−0.218143	+	0.125945i
$914$	−0.264863	−	8.33430i	−0.00876090	−	0.275674i
$915$		0			0
$916$	−1.43257	+	0.0911458i	−0.0473334	+	0.00301154i
$917$	−38.2464			−1.26301
$918$		0			0
$919$		−	31.1617i		−	1.02793i	−0.857811	−	0.513965i	$-0.828176\pi$
$919$		−	31.1617i		−	1.02793i	0.857811	−	0.513965i	$-0.171824\pi$
$920$	5.00248	+	6.78853i	0.164927	+	0.223811i
$921$		0			0
$922$	−1.58696	−	49.9359i	−0.0522637	−	1.64455i
$923$	−11.6643	+	6.73437i	−0.383934	+	0.221664i
$924$		0			0
$925$	1.20204	+	37.1806i	0.0395227	+	1.22249i
$926$	24.8672	−	46.4166i	0.817189	−	1.52534i
$927$		0			0
$928$	−11.6326	+	9.45396i	−0.381858	+	0.310341i
$929$	−24.5849	−	14.1941i	−0.806604	−	0.465693i	0.0391715	−	0.999233i	$-0.487528\pi$
$929$	−24.5849	−	14.1941i	−0.806604	−	0.465693i	−0.845775	+	0.533540i	$0.820861\pi$
$930$		0			0
$931$	5.32140	−	3.07231i	0.174402	−	0.100691i
$932$	12.2881	−	24.7983i	0.402511	−	0.812295i
$933$		0			0
$934$	8.39165	−	5.20715i	0.274583	−	0.170383i
$935$	−9.10955	−	5.06493i	−0.297914	−	0.165641i
$936$		0			0
$937$			25.1998i			0.823241i	0.911355	+	0.411620i	$0.135037\pi$
$937$			25.1998i			0.823241i	−0.911355	+	0.411620i	$0.864963\pi$
$938$	−16.2331	−	26.1607i	−0.530031	−	0.854179i
$939$		0			0
$940$	−7.64533	−	11.0965i	−0.249363	−	0.361927i
$941$	−35.0946	+	20.2619i	−1.14405	+	0.660519i	−0.947431	−	0.319960i	$-0.896330\pi$
$941$	−35.0946	+	20.2619i	−1.14405	+	0.660519i	−0.196622	+	0.980479i	$0.562997\pi$
$942$		0			0
$943$	4.55381	−	7.88742i	0.148292	−	0.256850i
$944$	16.3580	−	39.0686i	0.532407	−	1.27157i
$945$		0			0
$946$	−6.28612	+	11.7335i	−0.204379	+	0.381489i
$947$	−0.518242	−	0.299207i	−0.0168406	−	0.00972293i	0.491556	−	0.870846i	$-0.336428\pi$
$947$	−0.518242	−	0.299207i	−0.0168406	−	0.00972293i	−0.508397	+	0.861123i	$0.669762\pi$
$948$		0			0
$949$	15.1890	+	26.3082i	0.493057	+	0.853999i
$950$	26.8052	−	17.8579i	0.869676	−	0.579387i
$951$		0			0
$952$	−20.0110	+	43.8305i	−0.648560	+	1.42055i
$953$	−2.50405			−0.0811142			−0.0405571	−	0.999177i	$-0.512913\pi$
$953$	−2.50405			−0.0811142			−0.0405571	+	0.999177i	$0.512913\pi$
$954$		0			0
$955$	−15.0819	−	8.38555i	−0.488038	−	0.271350i
$956$	−55.3092	+	3.51900i	−1.78883	+	0.113813i
$957$		0			0
$958$	−28.8608	+	0.917193i	−0.932449	+	0.0296332i
$959$	−4.55443	−	7.88850i	−0.147070	−	0.254733i
$960$		0			0
$961$	−12.0680	+	20.9023i	−0.389289	+	0.674269i
$962$	23.1916	−	43.2889i	0.747728	−	1.39569i
$963$		0			0
$964$	−12.6596	−	19.0251i	−0.407739	−	0.612756i
$965$	5.93646	+	9.90894i	0.191101	+	0.318980i
$966$		0			0
$967$	−18.5754	−	32.1736i	−0.597346	−	1.03463i	−0.993211	−	0.116325i	$-0.962889\pi$
$967$	−18.5754	−	32.1736i	−0.597346	−	1.03463i	0.395866	−	0.918308i	$-0.370445\pi$
$968$	−17.0241	−	23.9016i	−0.547176	−	0.768226i
$969$		0			0
$970$	−20.9692	+	1.00579i	−0.673280	+	0.0322940i
$971$	14.7960			0.474826			0.237413	−	0.971409i	$-0.423701\pi$
$971$	14.7960			0.474826			0.237413	+	0.971409i	$0.423701\pi$
$972$		0			0
$973$			7.42550i			0.238051i
$974$	−15.5293	−	25.0264i	−0.497590	−	0.801898i
$975$		0			0
$976$	6.90189	−	0.881822i	0.220924	−	0.0282264i
$977$	16.1759	+	28.0175i	0.517514	+	0.896360i	0.999793	+	0.0203428i	$0.00647578\pi$
$977$	16.1759	+	28.0175i	0.517514	+	0.896360i	−0.482279	+	0.876018i	$0.660191\pi$
$978$		0			0
$979$	0.00508002	+	0.00293295i	0.000162358	+	9.37374e-5i
$980$	−0.480289	−	6.01362i	−0.0153423	−	0.192098i
$981$		0			0
$982$	12.4434	−	23.2266i	0.397086	−	0.741191i
$983$	−2.93257	−	1.69312i	−0.0935346	−	0.0540022i	0.452503	−	0.891763i	$-0.350531\pi$
$983$	−2.93257	−	1.69312i	−0.0935346	−	0.0540022i	−0.546038	+	0.837761i	$0.683864\pi$
$984$		0			0
$985$	0.306076	+	18.9396i	0.00975239	+	0.603467i
$986$	−0.701774	−	22.0823i	−0.0223490	−	0.703245i
$987$		0			0
$988$	−42.4353	+	2.69991i	−1.35005	+	0.0858954i
$989$			15.8731i			0.504734i
$990$		0			0
$991$			39.7022i			1.26118i	0.776116	+	0.630591i	$0.217187\pi$
$991$			39.7022i			1.26118i	−0.776116	+	0.630591i	$0.782813\pi$
$992$	2.34430	+	14.6340i	0.0744317	+	0.464630i
$993$		0			0
$994$	−11.7858	+	0.374551i	−0.373822	+	0.0118800i
$995$	1.24302	−	0.0200879i	0.0394063	−	0.000636830i
$996$		0			0
$997$	−17.8325	−	10.2956i	−0.564760	−	0.326064i	0.190294	−	0.981727i	$-0.439056\pi$
$997$	−17.8325	−	10.2956i	−0.564760	−	0.326064i	−0.755054	+	0.655663i	$0.772389\pi$
$998$	6.45827	+	3.45995i	0.204433	+	0.109523i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.n.d.359.17		48
3.2	odd	2		180.2.n.d.119.8	yes	48
4.3	odd	2	inner	540.2.n.d.359.1		48
5.4	even	2	inner	540.2.n.d.359.8		48
9.4	even	3		180.2.n.d.59.1	✓	48
9.5	odd	6	inner	540.2.n.d.179.24		48
12.11	even	2		180.2.n.d.119.24	yes	48
15.2	even	4		900.2.r.g.551.20		48
15.8	even	4		900.2.r.g.551.5		48
15.14	odd	2		180.2.n.d.119.17	yes	48
20.19	odd	2	inner	540.2.n.d.359.24		48
36.23	even	6	inner	540.2.n.d.179.8		48
36.31	odd	6		180.2.n.d.59.17	yes	48
45.4	even	6		180.2.n.d.59.24	yes	48
45.13	odd	12		900.2.r.g.851.13		48
45.14	odd	6	inner	540.2.n.d.179.1		48
45.22	odd	12		900.2.r.g.851.12		48
60.23	odd	4		900.2.r.g.551.13		48
60.47	odd	4		900.2.r.g.551.12		48
60.59	even	2		180.2.n.d.119.1	yes	48
180.59	even	6	inner	540.2.n.d.179.17		48
180.67	even	12		900.2.r.g.851.20		48
180.103	even	12		900.2.r.g.851.5		48
180.139	odd	6		180.2.n.d.59.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.d.59.1	✓	48	9.4	even	3
180.2.n.d.59.8	yes	48	180.139	odd	6
180.2.n.d.59.17	yes	48	36.31	odd	6
180.2.n.d.59.24	yes	48	45.4	even	6
180.2.n.d.119.1	yes	48	60.59	even	2
180.2.n.d.119.8	yes	48	3.2	odd	2
180.2.n.d.119.17	yes	48	15.14	odd	2
180.2.n.d.119.24	yes	48	12.11	even	2
540.2.n.d.179.1		48	45.14	odd	6	inner
540.2.n.d.179.8		48	36.23	even	6	inner
540.2.n.d.179.17		48	180.59	even	6	inner
540.2.n.d.179.24		48	9.5	odd	6	inner
540.2.n.d.359.1		48	4.3	odd	2	inner
540.2.n.d.359.8		48	5.4	even	2	inner
540.2.n.d.359.17		48	1.1	even	1	trivial
540.2.n.d.359.24		48	20.19	odd	2	inner
900.2.r.g.551.5		48	15.8	even	4
900.2.r.g.551.12		48	60.47	odd	4
900.2.r.g.551.13		48	60.23	odd	4
900.2.r.g.551.20		48	15.2	even	4
900.2.r.g.851.5		48	180.103	even	12
900.2.r.g.851.12		48	45.22	odd	12
900.2.r.g.851.13		48	45.13	odd	12
900.2.r.g.851.20		48	180.67	even	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

Level:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.745653 + 1.20167i) q^{2} +(-0.888004 + 1.79205i) q^{4} +(-0.0361315 - 2.23578i) q^{5} +(1.44473 - 2.50234i) q^{7} +(-2.81559 + 0.269163i) q^{8} +(2.65972 - 1.71053i) q^{10} +(0.395318 - 0.684712i) q^{11} +(4.04214 - 2.33373i) q^{13} +(4.08425 - 0.129797i) q^{14} +(-2.42290 - 3.18270i) q^{16} +5.89560 q^{17} +4.55505i q^{19} +(4.03871 + 1.92063i) q^{20} +(1.11756 - 0.0355161i) q^{22} +(1.15468 - 0.666656i) q^{23} +(-4.99739 + 0.161564i) q^{25} +(5.81840 + 3.11715i) q^{26} +(3.20140 + 4.81112i) q^{28} +(-2.29484 - 1.32492i) q^{29} +(-2.26893 + 1.30997i) q^{31} +(2.01790 - 5.28470i) q^{32} +(4.39607 + 7.08454i) q^{34} +(-5.64688 - 3.13968i) q^{35} -7.44000i q^{37} +(-5.47365 + 3.39649i) q^{38} +(0.703519 + 6.28531i) q^{40} +(5.91566 - 3.41541i) q^{41} +(-5.95249 + 10.3100i) q^{43} +(0.875994 + 1.31646i) q^{44} +(1.66209 + 0.890449i) q^{46} +(-2.60947 - 1.50658i) q^{47} +(-0.674484 - 1.16824i) q^{49} +(-3.92046 - 5.88472i) q^{50} +(0.592728 + 9.31609i) q^{52} +1.70763 q^{53} +(-1.54515 - 0.859104i) q^{55} +(-3.39423 + 7.43444i) q^{56} +(-0.119034 - 3.74556i) q^{58} +(5.29436 + 9.17010i) q^{59} +(-0.869749 + 1.50645i) q^{61} +(-3.26598 - 1.74972i) q^{62} +(7.85510 - 1.51570i) q^{64} +(-5.36375 - 8.95300i) q^{65} +(-3.76721 - 6.52500i) q^{67} +(-5.23532 + 10.5652i) q^{68} +(-0.437767 - 9.12678i) q^{70} -2.88566 q^{71} +6.50847i q^{73} +(8.94040 - 5.54766i) q^{74} +(-8.16289 - 4.04491i) q^{76} +(-1.14226 - 1.97845i) q^{77} +(3.30854 + 1.91019i) q^{79} +(-7.02826 + 5.53205i) q^{80} +(8.51521 + 4.56194i) q^{82} +(-8.33679 - 4.81325i) q^{83} +(-0.213017 - 13.1812i) q^{85} +(-16.8277 + 0.534782i) q^{86} +(-0.928756 + 2.03427i) q^{88} +0.00741921i q^{89} -13.4864i q^{91} +(0.169319 + 2.66124i) q^{92} +(-0.135354 - 4.25910i) q^{94} +(10.1841 - 0.164581i) q^{95} +(-5.74925 - 3.31933i) q^{97} +(0.900905 - 1.68161i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{4} + 18 q^{5} - 16 q^{10} + 42 q^{14} + 30 q^{16} - 26 q^{25} - 4 q^{34} + 10 q^{40} - 96 q^{41} + 4 q^{46} + 32 q^{49} + 90 q^{50} - 6 q^{56} + 8 q^{61} - 20 q^{64} + 6 q^{65} + 4 q^{70} - 72 q^{74}+ \cdots - 62 q^{94}+O(q^{100}) \) 48 * q - 2 * q^4 + 18 * q^5 - 16 * q^10 + 42 * q^14 + 30 * q^16 - 26 * q^25 - 4 * q^34 + 10 * q^40 - 96 * q^41 + 4 * q^46 + 32 * q^49 + 90 * q^50 - 6 * q^56 + 8 * q^61 - 20 * q^64 + 6 * q^65 + 4 * q^70 - 72 * q^74 - 4 * q^85 - 108 * q^86 - 62 * q^94

Introduction

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