LMFDB - Embedded newform 540.2.n.d.179.19

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			179.19
Character	$\chi$	$=$	540.179
Dual form			540.2.n.d.359.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00727 + 0.992675i) q^{2} +(0.0291929 + 1.99979i) q^{4} +(-1.64183 + 1.51803i) q^{5} +(1.65751 + 2.87089i) q^{7} +(-1.95573 + 2.04331i) q^{8} +(-3.16067 - 0.100737i) q^{10} +(-1.17952 - 2.04298i) q^{11} +(-3.81058 - 2.20004i) q^{13} +(-1.18030 + 4.53714i) q^{14} +(-3.99830 + 0.116759i) q^{16} +0.889368 q^{17} +3.03537i q^{19} +(-3.08366 - 3.23899i) q^{20} +(0.839925 - 3.22872i) q^{22} +(6.29952 + 3.63703i) q^{23} +(0.391197 - 4.98467i) q^{25} +(-1.65437 - 5.99870i) q^{26} +(-5.69278 + 3.39848i) q^{28} +(-1.03714 + 0.598791i) q^{29} +(0.205172 + 0.118456i) q^{31} +(-4.14327 - 3.85140i) q^{32} +(0.895835 + 0.882853i) q^{34} +(-7.07943 - 2.19737i) q^{35} +11.4975i q^{37} +(-3.01314 + 3.05745i) q^{38} +(0.109183 - 6.32361i) q^{40} +(-2.45213 - 1.41574i) q^{41} +(4.17637 + 7.23369i) q^{43} +(4.05110 - 2.41842i) q^{44} +(2.73494 + 9.91686i) q^{46} +(6.55796 - 3.78624i) q^{47} +(-1.99467 + 3.45488i) q^{49} +(5.34220 - 4.63259i) q^{50} +(4.28837 - 7.68457i) q^{52} -0.772055 q^{53} +(5.03787 + 1.56369i) q^{55} +(-9.10776 - 2.22789i) q^{56} +(-1.63908 - 0.426394i) q^{58} +(-1.06446 + 1.84370i) q^{59} +(1.91303 + 3.31346i) q^{61} +(0.0890754 + 0.322986i) q^{62} +(-0.350216 - 7.99233i) q^{64} +(9.59603 - 2.17247i) q^{65} +(3.17238 - 5.49472i) q^{67} +(0.0259632 + 1.77855i) q^{68} +(-4.94964 - 9.24092i) q^{70} +11.7244 q^{71} -6.10889i q^{73} +(-11.4133 + 11.5811i) q^{74} +(-6.07010 + 0.0886114i) q^{76} +(3.91012 - 6.77253i) q^{77} +(8.94873 - 5.16655i) q^{79} +(6.38727 - 6.26121i) q^{80} +(-1.06459 - 3.86020i) q^{82} +(2.25103 - 1.29963i) q^{83} +(-1.46019 + 1.35008i) q^{85} +(-2.97396 + 11.4321i) q^{86} +(6.48127 + 1.58541i) q^{88} +4.68130i q^{89} -14.5863i q^{91} +(-7.08939 + 12.7039i) q^{92} +(10.3642 + 2.69615i) q^{94} +(-4.60778 - 4.98356i) q^{95} +(5.34684 - 3.08700i) q^{97} +(-5.43875 + 1.49994i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.00727	+	0.992675i	0.712249	+	0.701927i
$2$	1.00727	+	0.992675i	0.712249	+	0.701927i
$3$		0			0
$3$		0			0
$4$	0.0291929	+	1.99979i	0.0145965	+	0.999893i
$5$	−1.64183	+	1.51803i	−0.734248	+	0.678882i
$5$	−1.64183	+	1.51803i	−0.734248	+	0.678882i
$6$		0			0
$7$	1.65751	+	2.87089i	0.626480	+	1.08509i	0.988253	+	0.152828i	$0.0488382\pi$
$7$	1.65751	+	2.87089i	0.626480	+	1.08509i	−0.361773	+	0.932266i	$0.617828\pi$
$8$	−1.95573	+	2.04331i	−0.691456	+	0.722418i
$9$		0			0
$10$	−3.16067	−	0.100737i	−0.999492	−	0.0318558i
$11$	−1.17952	−	2.04298i	−0.355638	−	0.615983i	0.631589	−	0.775303i	$-0.282403\pi$
$11$	−1.17952	−	2.04298i	−0.355638	−	0.615983i	−0.987227	+	0.159320i	$0.949070\pi$
$12$		0			0
$13$	−3.81058	−	2.20004i	−1.05686	−	0.610181i	−0.132301	−	0.991210i	$-0.542237\pi$
$13$	−3.81058	−	2.20004i	−1.05686	−	0.610181i	−0.924563	+	0.381029i	$0.875570\pi$
$14$	−1.18030	+	4.53714i	−0.315448	+	1.21260i
$15$		0			0
$16$	−3.99830	+	0.116759i	−0.999574	+	0.0291898i
$17$	0.889368			0.215703			0.107852	−	0.994167i	$-0.465603\pi$
$17$	0.889368			0.215703			0.107852	+	0.994167i	$0.465603\pi$
$18$		0			0
$19$			3.03537i			0.696363i	0.937427	+	0.348181i	$0.113201\pi$
$19$			3.03537i			0.696363i	−0.937427	+	0.348181i	$0.886799\pi$
$20$	−3.08366	−	3.23899i	−0.689527	−	0.724260i
$21$		0			0
$22$	0.839925	−	3.22872i	0.179073	−	0.688365i
$23$	6.29952	+	3.63703i	1.31354	+	0.758374i	0.982681	−	0.185306i	$-0.0593276\pi$
$23$	6.29952	+	3.63703i	1.31354	+	0.758374i	0.330861	+	0.943680i	$0.392661\pi$
$24$		0			0
$25$	0.391197	−	4.98467i	0.0782393	−	0.996935i
$26$	−1.65437	−	5.99870i	−0.324448	−	1.17644i
$27$		0			0
$28$	−5.69278	+	3.39848i	−1.07583	+	0.642251i
$29$	−1.03714	+	0.598791i	−0.192592	+	0.111193i	−0.593195	−	0.805059i	$-0.702134\pi$
$29$	−1.03714	+	0.598791i	−0.192592	+	0.111193i	0.400604	+	0.916251i	$0.368800\pi$
$30$		0			0
$31$	0.205172	+	0.118456i	0.0368499	+	0.0212753i	0.518312	−	0.855192i	$-0.326561\pi$
$31$	0.205172	+	0.118456i	0.0368499	+	0.0212753i	−0.481462	+	0.876467i	$0.659894\pi$
$32$	−4.14327	−	3.85140i	−0.732434	−	0.680838i
$33$		0			0
$34$	0.895835	+	0.882853i	0.153634	+	0.151408i
$35$	−7.07943	−	2.19737i	−1.19664	−	0.371423i
$36$		0			0
$37$			11.4975i			1.89018i	0.326807	+	0.945091i	$0.394027\pi$
$37$			11.4975i			1.89018i	−0.326807	+	0.945091i	$0.605973\pi$
$38$	−3.01314	+	3.05745i	−0.488796	+	0.495983i
$39$		0			0
$40$	0.109183	−	6.32361i	0.0172633	−	0.999851i
$41$	−2.45213	−	1.41574i	−0.382958	−	0.221101i	0.296146	−	0.955143i	$-0.404298\pi$
$41$	−2.45213	−	1.41574i	−0.382958	−	0.221101i	−0.679105	+	0.734042i	$0.737632\pi$
$42$		0			0
$43$	4.17637	+	7.23369i	0.636891	+	1.10313i	0.986111	+	0.166087i	$0.0531132\pi$
$43$	4.17637	+	7.23369i	0.636891	+	1.10313i	−0.349220	+	0.937041i	$0.613553\pi$
$44$	4.05110	−	2.41842i	0.610726	−	0.364591i
$45$		0			0
$46$	2.73494	+	9.91686i	0.403245	+	1.46216i
$47$	6.55796	−	3.78624i	0.956577	−	0.552280i	0.0614594	−	0.998110i	$-0.480425\pi$
$47$	6.55796	−	3.78624i	0.956577	−	0.552280i	0.895118	+	0.445829i	$0.147091\pi$
$48$		0			0
$49$	−1.99467	+	3.45488i	−0.284954	+	0.493554i
$50$	5.34220	−	4.63259i	0.755501	−	0.655147i
$51$		0			0
$52$	4.28837	−	7.68457i	0.594689	−	1.06566i
$53$	−0.772055			−0.106050			−0.0530249	−	0.998593i	$-0.516886\pi$
$53$	−0.772055			−0.106050			−0.0530249	+	0.998593i	$0.516886\pi$
$54$		0			0
$55$	5.03787	+	1.56369i	0.679306	+	0.210848i
$56$	−9.10776	−	2.22789i	−1.21708	−	0.297715i
$57$		0			0
$58$	−1.63908	−	0.426394i	−0.215222	−	0.0559883i
$59$	−1.06446	+	1.84370i	−0.138581	+	0.240029i	−0.926960	−	0.375161i	$-0.877587\pi$
$59$	−1.06446	+	1.84370i	−0.138581	+	0.240029i	0.788379	+	0.615190i	$0.210921\pi$
$60$		0			0
$61$	1.91303	+	3.31346i	0.244938	+	0.424245i	0.962114	−	0.272647i	$-0.0878990\pi$
$61$	1.91303	+	3.31346i	0.244938	+	0.424245i	−0.717176	+	0.696892i	$0.754566\pi$
$62$	0.0890754	+	0.322986i	0.0113126	+	0.0410193i
$63$		0			0
$64$	−0.350216	−	7.99233i	−0.0437769	−	0.999041i
$65$	9.59603	−	2.17247i	1.19024	−	0.269462i
$66$		0			0
$67$	3.17238	−	5.49472i	0.387567	−	0.671287i	−0.604554	−	0.796564i	$-0.706649\pi$
$67$	3.17238	−	5.49472i	0.387567	−	0.671287i	0.992122	+	0.125277i	$0.0399821\pi$
$68$	0.0259632	+	1.77855i	0.00314851	+	0.215680i
$69$		0			0
$70$	−4.94964	−	9.24092i	−0.591595	−	1.10450i
$71$	11.7244			1.39143			0.695717	−	0.718316i	$-0.255087\pi$
$71$	11.7244			1.39143			0.695717	+	0.718316i	$0.255087\pi$
$72$		0			0
$73$		−	6.10889i		−	0.714992i	−0.933915	−	0.357496i	$-0.883631\pi$
$73$		−	6.10889i		−	0.714992i	0.933915	−	0.357496i	$-0.116369\pi$
$74$	−11.4133	+	11.5811i	−1.32677	+	1.34628i
$75$		0			0
$76$	−6.07010	+	0.0886114i	−0.696288	+	0.0101644i
$77$	3.91012	−	6.77253i	0.445600	−	0.771802i
$78$		0			0
$79$	8.94873	−	5.16655i	1.00681	−	0.581283i	0.0965546	−	0.995328i	$-0.469218\pi$
$79$	8.94873	−	5.16655i	1.00681	−	0.581283i	0.910256	+	0.414045i	$0.135884\pi$
$80$	6.38727	−	6.26121i	0.714118	−	0.700025i
$81$		0			0
$82$	−1.06459	−	3.86020i	−0.117565	−	0.426288i
$83$	2.25103	−	1.29963i	0.247083	−	0.142653i	−0.371345	−	0.928495i	$-0.621103\pi$
$83$	2.25103	−	1.29963i	0.247083	−	0.142653i	0.618428	+	0.785842i	$0.287770\pi$
$84$		0			0
$85$	−1.46019	+	1.35008i	−0.158380	+	0.146437i
$86$	−2.97396	+	11.4321i	−0.320690	+	1.23275i
$87$		0			0
$88$	6.48127	+	1.58541i	0.690906	+	0.169006i
$89$			4.68130i			0.496217i	0.968732	+	0.248108i	$0.0798089\pi$
$89$			4.68130i			0.496217i	−0.968732	+	0.248108i	$0.920191\pi$
$90$		0			0
$91$		−	14.5863i		−	1.52906i
$92$	−7.08939	+	12.7039i	−0.739120	+	1.32447i
$93$		0			0
$94$	10.3642	+	2.69615i	1.06898	+	0.278087i
$95$	−4.60778	−	4.98356i	−0.472748	−	0.511303i
$96$		0			0
$97$	5.34684	−	3.08700i	0.542890	−	0.313438i	−0.203360	−	0.979104i	$-0.565186\pi$
$97$	5.34684	−	3.08700i	0.542890	−	0.313438i	0.746249	+	0.665667i	$0.231853\pi$
$98$	−5.43875	+	1.49994i	−0.549397	+	0.151517i
$99$		0			0
$100$	9.97970	+	0.636793i	0.997970	+	0.0636793i
$101$	6.72336	−	3.88174i	0.669000	−	0.386247i	−0.126698	−	0.991941i	$-0.540438\pi$
$101$	6.72336	−	3.88174i	0.669000	−	0.386247i	0.795697	+	0.605694i	$0.207105\pi$
$102$		0			0
$103$	−6.58033	+	11.3975i	−0.648379	+	1.12302i	0.335131	+	0.942171i	$0.391219\pi$
$103$	−6.58033	+	11.3975i	−0.648379	+	1.12302i	−0.983510	+	0.180853i	$0.942114\pi$
$104$	11.9478	−	3.48350i	1.17158	−	0.341585i
$105$		0			0
$106$	−0.777669	−	0.766400i	−0.0755339	−	0.0744393i
$107$			0.252175i			0.0243786i	0.999926	+	0.0121893i	$0.00388008\pi$
$107$			0.252175i			0.0243786i	−0.999926	+	0.0121893i	$0.996120\pi$
$108$		0			0
$109$	0.459068			0.0439708			0.0219854	−	0.999758i	$-0.493001\pi$
$109$	0.459068			0.0439708			0.0219854	+	0.999758i	$0.493001\pi$
$110$	3.52227	+	6.57603i	0.335835	+	0.627000i
$111$		0			0
$112$	−6.96242	−	11.2851i	−0.657886	−	1.06635i
$113$	−8.71557	+	15.0958i	−0.819892	+	1.42009i	0.0858696	+	0.996306i	$0.472633\pi$
$113$	−8.71557	+	15.0958i	−0.819892	+	1.42009i	−0.905761	+	0.423788i	$0.860700\pi$
$114$		0			0
$115$	−15.8638	+	3.59146i	−1.47931	+	0.334905i
$116$	−1.22773	−	2.05657i	−0.113992	−	0.190948i
$117$		0			0
$118$	−2.90240	+	0.800444i	−0.267187	+	0.0736868i
$119$	1.47414	+	2.55328i	0.135134	+	0.234059i
$120$		0			0
$121$	2.71748	−	4.70681i	0.247043	−	0.427891i
$122$	−1.36225	+	5.23657i	−0.123332	+	0.474097i
$123$		0			0
$124$	−0.230897	+	0.413758i	−0.0207352	+	0.0371565i
$125$	6.92458	+	8.77782i	0.619354	+	0.785112i
$126$		0			0
$127$	−10.5666			−0.937635			−0.468817	−	0.883295i	$-0.655320\pi$
$127$	−10.5666			−0.937635			−0.468817	+	0.883295i	$0.655320\pi$
$128$	7.58102	−	8.39810i	0.670074	−	0.742294i
$129$		0			0
$130$	11.8224	+	7.33747i	1.03689	+	0.643538i
$131$	8.12900	−	14.0798i	0.710234	−	1.23016i	−0.254535	−	0.967064i	$-0.581922\pi$
$131$	8.12900	−	14.0798i	0.710234	−	1.23016i	0.964769	−	0.263098i	$-0.0847444\pi$
$132$		0			0
$133$	−8.71423	+	5.03116i	−0.755619	+	0.436257i
$134$	8.64991	−	2.38554i	0.747239	−	0.206079i
$135$		0			0
$136$	−1.73937	+	1.81725i	−0.149149	+	0.155828i
$137$	−6.59587	−	11.4244i	−0.563523	−	0.976051i	−0.997185	−	0.0749753i	$-0.976112\pi$
$137$	−6.59587	−	11.4244i	−0.563523	−	0.976051i	0.433662	−	0.901076i	$-0.357221\pi$
$138$		0			0
$139$	−5.61535	−	3.24202i	−0.476288	−	0.274985i	0.242580	−	0.970131i	$-0.422006\pi$
$139$	−5.61535	−	3.24202i	−0.476288	−	0.274985i	−0.718868	+	0.695146i	$0.755340\pi$
$140$	4.18759	−	14.2215i	0.353916	−	1.20194i
$141$		0			0
$142$	11.8097	+	11.6385i	0.991047	+	0.976685i
$143$			10.3799i			0.868014i
$144$		0			0
$145$	0.793820	−	2.55751i	0.0659232	−	0.212390i
$146$	6.06415	−	6.15332i	0.501872	−	0.509252i
$147$		0			0
$148$	−22.9926	+	0.335646i	−1.88998	+	0.0275900i
$149$	−7.25009	−	4.18584i	−0.593950	−	0.342917i	0.172708	−	0.984973i	$-0.444748\pi$
$149$	−7.25009	−	4.18584i	−0.593950	−	0.342917i	−0.766658	+	0.642056i	$0.778082\pi$
$150$		0			0
$151$	14.2008	−	8.19886i	1.15565	−	0.667214i	0.205391	−	0.978680i	$-0.434153\pi$
$151$	14.2008	−	8.19886i	1.15565	−	0.667214i	0.950257	+	0.311466i	$0.100820\pi$
$152$	−6.20220	−	5.93638i	−0.503065	−	0.481504i
$153$		0			0
$154$	10.6615	−	2.94030i	0.859127	−	0.236936i
$155$	−0.516676	+	0.116972i	−0.0415004	+	0.00939539i
$156$		0			0
$157$	−9.27700	−	5.35608i	−0.740386	−	0.427462i	0.0818239	−	0.996647i	$-0.473925\pi$
$157$	−9.27700	−	5.35608i	−0.740386	−	0.427462i	−0.822209	+	0.569185i	$0.807259\pi$
$158$	14.1425	+	3.67906i	1.12512	+	0.292690i
$159$		0			0
$160$	12.6491	+	0.0337379i	0.999996	+	0.00266722i
$161$			24.1137i			1.90042i
$162$		0			0
$163$	−1.33584			−0.104631			−0.0523153	−	0.998631i	$-0.516660\pi$
$163$	−1.33584			−0.104631			−0.0523153	+	0.998631i	$0.516660\pi$
$164$	2.75959	−	4.94507i	0.215488	−	0.386145i
$165$		0			0
$166$	3.55752	+	0.925458i	0.276117	+	0.0718295i
$167$	−6.20942	−	3.58501i	−0.480500	−	0.277417i	0.240125	−	0.970742i	$-0.422812\pi$
$167$	−6.20942	−	3.58501i	−0.480500	−	0.277417i	−0.720625	+	0.693325i	$0.756145\pi$
$168$		0			0
$169$	3.18034	+	5.50851i	0.244641	+	0.423731i
$170$	−2.81100	−	0.0895921i	−0.215594	−	0.00687140i
$171$		0			0
$172$	−14.3439	+	8.56303i	−1.09371	+	0.652925i
$173$	1.28765	+	2.23027i	0.0978979	+	0.169564i	0.910814	−	0.412816i	$-0.135455\pi$
$173$	1.28765	+	2.23027i	0.0978979	+	0.169564i	−0.812916	+	0.582380i	$0.802121\pi$
$174$		0			0
$175$	14.9589	−	7.13906i	1.13078	−	0.539662i
$176$	4.95460	+	8.03074i	0.373467	+	0.605340i
$177$		0			0
$178$	−4.64701	+	4.71534i	−0.348308	+	0.353430i
$179$	−10.1847			−0.761243			−0.380622	−	0.924731i	$-0.624290\pi$
$179$	−10.1847			−0.761243			−0.380622	+	0.924731i	$0.624290\pi$
$180$		0			0
$181$	4.17537			0.310353			0.155176	−	0.987887i	$-0.450405\pi$
$181$	4.17537			0.310353			0.155176	+	0.987887i	$0.450405\pi$
$182$	14.4795	−	14.6924i	1.07329	−	1.08907i
$183$		0			0
$184$	−19.7518	+	5.75880i	−1.45612	+	0.424545i
$185$	−17.4535	−	18.8770i	−1.28321	−	1.38786i
$186$		0			0
$187$	−1.04902	−	1.81696i	−0.0767123	−	0.132870i
$188$	7.76312	+	13.0040i	0.566184	+	0.948414i
$189$		0			0
$190$	0.305774	−	9.59382i	0.0221832	−	0.696009i
$191$	12.5152	+	21.6770i	0.905570	+	1.56849i	0.820151	+	0.572147i	$0.193889\pi$
$191$	12.5152	+	21.6770i	0.905570	+	1.56849i	0.0854186	+	0.996345i	$0.472777\pi$
$192$		0			0
$193$	16.3830	+	9.45871i	1.17927	+	0.680853i	0.955846	−	0.293868i	$-0.0949425\pi$
$193$	16.3830	+	9.45871i	1.17927	+	0.680853i	0.223426	+	0.974721i	$0.428276\pi$
$194$	8.45011	+	2.19823i	0.606683	+	0.157824i
$195$		0			0
$196$	−6.96725	−	3.88807i	−0.497661	−	0.277719i
$197$	5.25418			0.374345			0.187172	−	0.982327i	$-0.440068\pi$
$197$	5.25418			0.374345			0.187172	+	0.982327i	$0.440068\pi$
$198$		0			0
$199$			18.8487i			1.33615i	0.744095	+	0.668074i	$0.232881\pi$
$199$			18.8487i			1.33615i	−0.744095	+	0.668074i	$0.767119\pi$
$200$	9.42015	+	10.5480i	0.666105	+	0.745858i
$201$		0			0
$202$	10.6256	+	2.76415i	0.747612	+	0.194485i
$203$	−3.43813	−	1.98500i	−0.241309	−	0.139320i
$204$		0			0
$205$	6.17510	−	1.39800i	0.431288	−	0.0976404i
$206$	−17.9421	+	4.94821i	−1.25009	+	0.344758i
$207$		0			0
$208$	15.4927	+	8.35148i	1.07423	+	0.579071i
$209$	6.20122	−	3.58028i	0.428948	−	0.247653i
$210$		0			0
$211$	−3.96081	−	2.28678i	−0.272674	−	0.157428i	0.357428	−	0.933941i	$-0.383654\pi$
$211$	−3.96081	−	2.28678i	−0.272674	−	0.157428i	−0.630102	+	0.776512i	$0.716987\pi$
$212$	−0.0225385	−	1.54395i	−0.00154795	−	0.106039i
$213$		0			0
$214$	−0.250327	+	0.254008i	−0.0171120	+	0.0173636i
$215$	−17.8378	−	5.53663i	−1.21653	−	0.377595i
$216$		0			0
$217$			0.785367i			0.0533142i
$218$	0.462407	+	0.455706i	0.0313181	+	0.0308643i
$219$		0			0
$220$	−2.97998	+	10.1203i	−0.200910	+	0.682311i
$221$	−3.38900	−	1.95664i	−0.227969	−	0.131618i
$222$		0			0
$223$	−11.8767	−	20.5711i	−0.795323	−	1.37754i	−0.922634	−	0.385677i	$-0.873968\pi$
$223$	−11.8767	−	20.5711i	−0.795323	−	1.37754i	0.127310	−	0.991863i	$-0.459366\pi$
$224$	4.18943	−	18.2786i	0.279918	−	1.22129i
$225$		0			0
$226$	−23.7642	+	6.55386i	−1.58077	+	0.435956i
$227$	−24.1252	+	13.9287i	−1.60124	+	0.924478i	−0.610005	+	0.792398i	$0.708832\pi$
$227$	−24.1252	+	13.9287i	−1.60124	+	0.924478i	−0.991239	+	0.132081i	$0.957834\pi$
$228$		0			0
$229$	8.35991	−	14.4798i	0.552439	−	0.956852i	−0.445659	−	0.895203i	$-0.647031\pi$
$229$	8.35991	−	14.4798i	0.552439	−	0.956852i	0.998098	−	0.0616492i	$-0.0196360\pi$
$230$	−19.5444	−	12.1301i	−1.28872	−	0.799833i
$231$		0			0
$232$	0.804848	−	3.29027i	0.0528409	−	0.216017i
$233$	−1.67938			−0.110020			−0.0550101	−	0.998486i	$-0.517519\pi$
$233$	−1.67938			−0.110020			−0.0550101	+	0.998486i	$0.517519\pi$
$234$		0			0
$235$	−5.01943	+	16.1715i	−0.327432	+	1.05491i
$236$	−3.71808	−	2.07487i	−0.242027	−	0.135063i
$237$		0			0
$238$	−1.04972	+	4.03518i	−0.0680432	+	0.261562i
$239$	−5.41085	+	9.37186i	−0.349999	+	0.606215i	−0.986249	−	0.165267i	$-0.947151\pi$
$239$	−5.41085	+	9.37186i	−0.349999	+	0.606215i	0.636250	+	0.771483i	$0.280485\pi$
$240$		0			0
$241$	−5.45657	−	9.45105i	−0.351488	−	0.608796i	0.635022	−	0.772494i	$-0.280991\pi$
$241$	−5.45657	−	9.45105i	−0.351488	−	0.608796i	−0.986510	+	0.163698i	$0.947658\pi$
$242$	7.40957	−	2.04346i	0.476305	−	0.131359i
$243$		0			0
$244$	−6.57037	+	3.92238i	−0.420625	+	0.251104i
$245$	−1.96968	−	8.70028i	−0.125838	−	0.555841i
$246$		0			0
$247$	6.67794	−	11.5665i	0.424907	−	0.735961i
$248$	−0.643303	+	0.187561i	−0.0408498	+	0.0119101i
$249$		0			0
$250$	−1.73858	+	15.7155i	−0.109958	+	0.993936i
$251$	5.05766			0.319237			0.159618	−	0.987179i	$-0.448974\pi$
$251$	5.05766			0.319237			0.159618	+	0.987179i	$0.448974\pi$
$252$		0			0
$253$		−	17.1598i		−	1.07883i
$254$	−10.6434	−	10.4892i	−0.667829	−	0.658151i
$255$		0			0
$256$	15.9727	−	0.933676i	0.998296	−	0.0583548i
$257$	−6.69541	+	11.5968i	−0.417649	+	0.723388i	−0.995702	−	0.0926101i	$-0.970479\pi$
$257$	−6.69541	+	11.5968i	−0.417649	+	0.723388i	0.578054	+	0.815999i	$0.303812\pi$
$258$		0			0
$259$	−33.0081	+	19.0573i	−2.05103	+	1.18416i
$260$	4.62462	+	19.1266i	0.286807	+	1.18618i
$261$		0			0
$262$	22.1648	−	6.11278i	1.36935	−	0.377649i
$263$	−9.43213	+	5.44564i	−0.581610	+	0.335793i	−0.761773	−	0.647844i	$-0.775671\pi$
$263$	−9.43213	+	5.44564i	−0.581610	+	0.335793i	0.180163	+	0.983637i	$0.442337\pi$
$264$		0			0
$265$	1.26758	−	1.17200i	0.0778669	−	0.0719953i
$266$	−13.7719	−	3.58265i	−0.844410	−	0.219666i
$267$		0			0
$268$	11.0809	+	6.18367i	0.676872	+	0.377728i
$269$		−	21.5020i		−	1.31100i	−0.755195	−	0.655500i	$-0.772458\pi$
$269$		−	21.5020i		−	1.31100i	0.755195	−	0.655500i	$-0.227542\pi$
$270$		0			0
$271$		−	18.9445i		−	1.15080i	−0.817873	−	0.575399i	$-0.804847\pi$
$271$		−	18.9445i		−	1.15080i	0.817873	−	0.575399i	$-0.195153\pi$
$272$	−3.55595	+	0.103842i	−0.215611	+	0.00629634i
$273$		0			0
$274$	4.69686	−	18.0550i	0.283748	−	1.09074i
$275$	−10.6450	+	5.08030i	−0.641920	+	0.306354i
$276$		0			0
$277$	16.1616	−	9.33092i	0.971058	−	0.560641i	0.0714994	−	0.997441i	$-0.477222\pi$
$277$	16.1616	−	9.33092i	0.971058	−	0.560641i	0.899559	+	0.436800i	$0.143888\pi$
$278$	−2.43791	−	8.83982i	−0.146216	−	0.530177i
$279$		0			0
$280$	18.3354	−	10.1680i	1.09575	−	0.607654i
$281$	5.84683	−	3.37567i	0.348792	−	0.201375i	−0.315361	−	0.948972i	$-0.602126\pi$
$281$	5.84683	−	3.37567i	0.348792	−	0.201375i	0.664153	+	0.747596i	$0.268792\pi$
$282$		0			0
$283$	−2.63488	+	4.56374i	−0.156627	+	0.271286i	−0.933650	−	0.358186i	$-0.883395\pi$
$283$	−2.63488	+	4.56374i	−0.156627	+	0.271286i	0.777023	+	0.629472i	$0.216729\pi$
$284$	0.342270	+	23.4464i	0.0203100	+	1.39129i
$285$		0			0
$286$	−10.3039	+	10.4554i	−0.609283	+	0.618242i
$287$		−	9.38639i		−	0.554061i
$288$		0			0
$289$	−16.2090			−0.953472
$290$	3.33837	−	1.78811i	0.196036	−	0.105001i
$291$		0			0
$292$	12.2165	−	0.178336i	0.714916	−	0.0104364i
$293$	11.1453	−	19.3041i	0.651113	−	1.12776i	−0.331741	−	0.943371i	$-0.607636\pi$
$293$	11.1453	−	19.3041i	0.651113	−	1.12776i	0.982853	−	0.184390i	$-0.0590308\pi$
$294$		0			0
$295$	−1.05112	−	4.64292i	−0.0611988	−	0.270321i
$296$	−23.4930	−	22.4861i	−1.36550	−	1.30698i
$297$		0			0
$298$	−3.14763	−	11.4133i	−0.182337	−	0.661153i
$299$	−16.0032	−	27.7184i	−0.925490	−	1.60300i
$300$		0			0
$301$	−13.8448	+	23.9798i	−0.797999	+	1.38217i
$302$	22.4429	+	5.83834i	1.29144	+	0.335959i
$303$		0			0
$304$	−0.354408	−	12.1363i	−0.0203267	−	0.696066i
$305$	−8.17078	−	2.53611i	−0.467857	−	0.145217i
$306$		0			0
$307$	0.415414			0.0237089			0.0118545	−	0.999930i	$-0.496227\pi$
$307$	0.415414			0.0237089			0.0118545	+	0.999930i	$0.496227\pi$
$308$	13.6578	+	7.62170i	0.778224	+	0.434287i
$309$		0			0
$310$	−0.636548	−	0.395069i	−0.0361535	−	0.0224384i
$311$	0.284562	−	0.492876i	0.0161360	−	0.0279484i	−0.857845	−	0.513909i	$-0.828197\pi$
$311$	0.284562	−	0.492876i	0.0161360	−	0.0279484i	0.873981	+	0.485961i	$0.161530\pi$
$312$		0			0
$313$	−24.3028	+	14.0312i	−1.37367	+	0.793091i	−0.991388	−	0.130954i	$-0.958196\pi$
$313$	−24.3028	+	14.0312i	−1.37367	+	0.793091i	−0.382285	+	0.924044i	$0.624863\pi$
$314$	−4.02762	−	14.6041i	−0.227292	−	0.824156i
$315$		0			0
$316$	10.5932	+	17.7447i	0.595917	+	0.998219i
$317$	6.63676	+	11.4952i	0.372758	+	0.645635i	0.989989	−	0.141147i	$-0.0450790\pi$
$317$	6.63676	+	11.4952i	0.372758	+	0.645635i	−0.617231	+	0.786782i	$0.711746\pi$
$318$		0			0
$319$	2.44664	+	1.41257i	0.136986	+	0.0790887i
$320$	12.7076	+	12.5904i	0.710374	+	0.703824i
$321$		0			0
$322$	−23.9370	+	24.2890i	−1.33396	+	1.35357i
$323$			2.69956i			0.150208i
$324$		0			0
$325$	−12.4572	+	18.1338i	−0.690999	+	1.00588i
$326$	−1.34555	−	1.32605i	−0.0745231	−	0.0734431i
$327$		0			0
$328$	7.68850	−	2.24165i	0.424526	−	0.123774i
$329$	21.7398	+	12.5515i	1.19855	+	0.691985i
$330$		0			0
$331$	7.43989	−	4.29542i	0.408933	−	0.236098i	−0.281398	−	0.959591i	$-0.590798\pi$
$331$	7.43989	−	4.29542i	0.408933	−	0.236098i	0.690331	+	0.723493i	$0.257465\pi$
$332$	2.66471	+	4.46364i	0.146245	+	0.244974i
$333$		0			0
$334$	−2.69583	−	9.77502i	−0.147509	−	0.534865i
$335$	3.13263	+	13.8371i	0.171154	+	0.756003i
$336$		0			0
$337$	0.914017	+	0.527708i	0.0497897	+	0.0287461i	0.524688	−	0.851294i	$-0.324182\pi$
$337$	0.914017	+	0.527708i	0.0497897	+	0.0287461i	−0.474899	+	0.880041i	$0.657515\pi$
$338$	−2.26469	+	8.70561i	−0.123183	+	0.473523i
$339$		0			0
$340$	−2.74250	−	2.88065i	−0.148733	−	0.156225i
$341$		−	0.558884i		−	0.0302652i
$342$		0			0
$343$	9.98036			0.538889
$344$	−22.9485	−	5.61355i	−1.23730	−	0.302662i
$345$		0			0
$346$	−0.916922	+	3.52470i	−0.0492940	+	0.189489i
$347$	5.97844	+	3.45165i	0.320939	+	0.185294i	0.651811	−	0.758381i	$-0.274009\pi$
$347$	5.97844	+	3.45165i	0.320939	+	0.185294i	−0.330872	+	0.943676i	$0.607343\pi$
$348$		0			0
$349$	−15.5145	−	26.8719i	−0.830473	−	1.43842i	−0.897663	−	0.440682i	$-0.854737\pi$
$349$	−15.5145	−	26.8719i	−0.830473	−	1.43842i	0.0671899	−	0.997740i	$-0.478597\pi$
$350$	22.1544	+	7.65831i	1.18420	+	0.409354i
$351$		0			0
$352$	−2.98128	+	13.0074i	−0.158903	+	0.693299i
$353$	−7.67847	−	13.2995i	−0.408684	−	0.707861i	0.586059	−	0.810269i	$-0.300679\pi$
$353$	−7.67847	−	13.2995i	−0.408684	−	0.707861i	−0.994743	+	0.102408i	$0.967345\pi$
$354$		0			0
$355$	−19.2495	+	17.7980i	−1.02166	+	0.944619i
$356$	−9.36161	+	0.136661i	−0.496164	+	0.00724301i
$357$		0			0
$358$	−10.2588	−	10.1101i	−0.542194	−	0.534337i
$359$	8.51196			0.449244			0.224622	−	0.974446i	$-0.427885\pi$
$359$	8.51196			0.449244			0.224622	+	0.974446i	$0.427885\pi$
$360$		0			0
$361$	9.78650			0.515079
$362$	4.20573	+	4.14478i	0.221048	+	0.217845i
$363$		0			0
$364$	29.1696	−	0.425818i	1.52890	−	0.0223189i
$365$	9.27346	+	10.0298i	0.485395	+	0.524981i
$366$		0			0
$367$	0.646542	+	1.11984i	0.0337492	+	0.0584553i	0.882407	−	0.470488i	$-0.155922\pi$
$367$	0.646542	+	1.11984i	0.0337492	+	0.0584553i	−0.848657	+	0.528943i	$0.822589\pi$
$368$	−25.6120	−	13.8064i	−1.33512	−	0.719708i
$369$		0			0
$370$	1.15823	−	36.3399i	0.0602133	−	1.88922i
$371$	−1.27969	−	2.21648i	−0.0664381	−	0.115074i
$372$		0			0
$373$	14.1837	+	8.18898i	0.734406	+	0.424010i	0.820032	−	0.572318i	$-0.193956\pi$
$373$	14.1837	+	8.18898i	0.734406	+	0.424010i	−0.0856259	+	0.996327i	$0.527289\pi$
$374$	0.747002	−	2.87152i	0.0386265	−	0.148483i
$375$		0			0
$376$	−5.08917	+	20.8048i	−0.262454	+	1.07293i
$377$	5.26946			0.271391
$378$		0			0
$379$		−	11.7940i		−	0.605818i	−0.953020	−	0.302909i	$-0.902042\pi$
$379$		−	11.7940i		−	0.605818i	0.953020	−	0.302909i	$-0.0979578\pi$
$380$	9.83155	−	9.36005i	0.504348	−	0.480161i
$381$		0			0
$382$	−8.91198	+	34.2582i	−0.455977	+	1.75280i
$383$	−9.75933	−	5.63455i	−0.498678	−	0.287912i	0.229489	−	0.973311i	$-0.426294\pi$
$383$	−9.75933	−	5.63455i	−0.498678	−	0.287912i	−0.728168	+	0.685399i	$0.759628\pi$
$384$		0			0
$385$	3.86113	+	17.0550i	0.196781	+	0.869203i
$386$	7.11268	+	25.7905i	0.362026	+	1.31270i
$387$		0			0
$388$	6.32944	+	10.6024i	0.321328	+	0.538257i
$389$	−17.4583	+	10.0796i	−0.885172	+	0.511054i	−0.872360	−	0.488864i	$-0.837411\pi$
$389$	−17.4583	+	10.0796i	−0.885172	+	0.511054i	−0.0128115	+	0.999918i	$0.504078\pi$
$390$		0			0
$391$	5.60259	+	3.23466i	0.283335	+	0.163584i
$392$	−3.15833	−	10.8326i	−0.159520	−	0.547127i
$393$		0			0
$394$	5.29239	+	5.21569i	0.266627	+	0.262763i
$395$	−6.84932	+	22.0670i	−0.344627	+	1.11031i
$396$		0			0
$397$		−	5.11859i		−	0.256895i	−0.991716	−	0.128447i	$-0.959001\pi$
$397$		−	5.11859i		−	0.256895i	0.991716	−	0.128447i	$-0.0409993\pi$
$398$	−18.7106	+	18.9858i	−0.937879	+	0.951670i
$399$		0			0
$400$	−0.982113	+	19.9759i	−0.0491056	+	0.998794i
$401$	−9.58291	−	5.53269i	−0.478548	−	0.276290i	0.241263	−	0.970460i	$-0.422438\pi$
$401$	−9.58291	−	5.53269i	−0.478548	−	0.276290i	−0.719811	+	0.694170i	$0.755772\pi$
$402$		0			0
$403$	−0.521215	−	0.902771i	−0.0259636	−	0.0449702i
$404$	7.95892	+	13.3320i	0.395971	+	0.663291i
$405$		0			0
$406$	−1.49267	−	5.41238i	−0.0740798	−	0.268612i
$407$	23.4893	−	13.5615i	1.16432	−	0.672221i
$408$		0			0
$409$	−8.08315	+	14.0004i	−0.399686	+	0.692276i	−0.993687	−	0.112188i	$-0.964214\pi$
$409$	−8.08315	+	14.0004i	−0.399686	+	0.692276i	0.594001	+	0.804464i	$0.297548\pi$
$410$	7.60776	+	4.72170i	0.375721	+	0.233188i
$411$		0			0
$412$	−22.9846	−	12.8265i	−1.13237	−	0.631917i
$413$	−7.05742			−0.347273
$414$		0			0
$415$	−1.72293	+	5.55090i	−0.0845753	+	0.272483i
$416$	7.31504	+	23.7914i	0.358650	+	1.16647i
$417$		0			0
$418$	9.80037	+	2.54949i	0.479352	+	0.124699i
$419$	−3.65564	+	6.33176i	−0.178590	+	0.309327i	−0.941398	−	0.337298i	$-0.890487\pi$
$419$	−3.65564	+	6.33176i	−0.178590	+	0.309327i	0.762808	+	0.646625i	$0.223820\pi$
$420$		0			0
$421$	14.9731	+	25.9341i	0.729742	+	1.26395i	0.956992	+	0.290114i	$0.0936932\pi$
$421$	14.9731	+	25.9341i	0.729742	+	1.26395i	−0.227250	+	0.973836i	$0.572973\pi$
$422$	−1.71959	−	6.23521i	−0.0837083	−	0.303525i
$423$		0			0
$424$	1.50993	−	1.57755i	0.0733288	−	0.0766124i
$425$	0.347917	−	4.43321i	0.0168765	−	0.215042i
$426$		0			0
$427$	−6.34172	+	10.9842i	−0.306897	+	0.531562i
$428$	−0.504295	+	0.00736171i	−0.0243760	+	0.000355842i
$429$		0			0
$430$	−12.4715	−	23.2840i	−0.601427	−	1.12286i
$431$	30.7505			1.48120			0.740599	−	0.671947i	$-0.234542\pi$
$431$	30.7505			1.48120			0.740599	+	0.671947i	$0.234542\pi$
$432$		0			0
$433$		−	29.3734i		−	1.41160i	−0.708413	−	0.705798i	$-0.750589\pi$
$433$		−	29.3734i		−	1.41160i	0.708413	−	0.705798i	$-0.249411\pi$
$434$	−0.779614	+	0.791078i	−0.0374227	+	0.0379730i
$435$		0			0
$436$	0.0134016	+	0.918039i	0.000641818	+	0.0439661i
$437$	−11.0398	+	19.1214i	−0.528103	+	0.914701i
$438$		0			0
$439$	6.77418	−	3.91108i	0.323314	−	0.186665i	−0.329555	−	0.944136i	$-0.606899\pi$
$439$	6.77418	−	3.91108i	0.323314	−	0.186665i	0.652869	+	0.757471i	$0.273565\pi$
$440$	−13.0478	+	7.23575i	−0.622031	+	0.344951i
$441$		0			0
$442$	−1.47134	−	5.33505i	−0.0699844	−	0.253763i
$443$	23.1263	−	13.3520i	1.09876	−	0.634371i	0.162867	−	0.986648i	$-0.447926\pi$
$443$	23.1263	−	13.3520i	1.09876	−	0.634371i	0.935896	+	0.352277i	$0.114592\pi$
$444$		0			0
$445$	−7.10634	−	7.68589i	−0.336873	−	0.364346i
$446$	8.45731	−	32.5104i	0.400465	−	1.53941i
$447$		0			0
$448$	22.3646	−	14.2528i	1.05663	−	0.673381i
$449$		−	23.8441i		−	1.12527i	−0.826704	−	0.562637i	$-0.809787\pi$
$449$		−	23.8441i		−	1.12527i	0.826704	−	0.562637i	$-0.190213\pi$
$450$		0			0
$451$			6.67955i			0.314528i
$452$	−30.4428	−	16.9886i	−1.43191	−	0.799076i
$453$		0			0
$454$	−38.1272	−	9.91849i	−1.78940	−	0.465498i
$455$	22.1424	+	23.9483i	1.03805	+	1.12271i
$456$		0			0
$457$	−13.6451	+	7.87798i	−0.638289	+	0.368516i	−0.783955	−	0.620817i	$-0.786801\pi$
$457$	−13.6451	+	7.87798i	−0.638289	+	0.368516i	0.145666	+	0.989334i	$0.453468\pi$
$458$	22.7944	−	6.28641i	1.06511	−	0.293745i
$459$		0			0
$460$	−7.64526	−	31.6195i	−0.356462	−	1.47426i
$461$	−9.24515	+	5.33769i	−0.430590	+	0.248601i	−0.699598	−	0.714537i	$-0.746637\pi$
$461$	−9.24515	+	5.33769i	−0.430590	+	0.248601i	0.269008	+	0.963138i	$0.413304\pi$
$462$		0			0
$463$	3.17644	−	5.50175i	0.147622	−	0.255688i	−0.782726	−	0.622366i	$-0.786172\pi$
$463$	3.17644	−	5.50175i	0.147622	−	0.255688i	0.930348	+	0.366678i	$0.119505\pi$
$464$	4.07687	−	2.51524i	0.189264	−	0.116767i
$465$		0			0
$466$	−1.69160	−	1.66708i	−0.0783617	−	0.0772261i
$467$			7.76191i			0.359179i	0.983742	+	0.179589i	$0.0574769\pi$
$467$			7.76191i			0.359179i	−0.983742	+	0.179589i	$0.942523\pi$
$468$		0			0
$469$	21.0330			0.971213
$470$	−21.1090	+	11.3064i	−0.973685	+	0.521527i
$471$		0			0
$472$	−1.68545	−	5.78081i	−0.0775790	−	0.266083i
$473$	9.85221	−	17.0645i	0.453005	−	0.784628i
$474$		0			0
$475$	15.1303	+	1.18743i	0.694228	+	0.0544829i
$476$	−5.06298	+	3.02249i	−0.232061	+	0.138536i
$477$		0			0
$478$	−14.7534	+	4.06880i	−0.674805	+	0.186103i
$479$	3.56565	+	6.17588i	0.162919	+	0.282183i	0.935914	−	0.352228i	$-0.114576\pi$
$479$	3.56565	+	6.17588i	0.162919	+	0.282183i	−0.772996	+	0.634411i	$0.781243\pi$
$480$		0			0
$481$	25.2950	−	43.8122i	1.15335	−	1.99767i
$482$	3.88558	−	14.9364i	0.176983	−	0.680333i
$483$		0			0
$484$	9.49194	+	5.29697i	0.431452	+	0.240771i
$485$	−4.09245	+	13.1850i	−0.185829	+	0.598699i
$486$		0			0
$487$	15.1089			0.684649			0.342325	−	0.939582i	$-0.388786\pi$
$487$	15.1089			0.684649			0.342325	+	0.939582i	$0.388786\pi$
$488$	−10.5118	−	2.57134i	−0.475846	−	0.116399i
$489$		0			0
$490$	6.65255	−	10.7188i	0.300531	−	0.484226i
$491$	14.7215	−	25.4984i	0.664372	−	1.15073i	−0.315083	−	0.949064i	$-0.602032\pi$
$491$	14.7215	−	25.4984i	0.664372	−	1.15073i	0.979455	−	0.201662i	$-0.0646342\pi$
$492$		0			0
$493$	−0.922396	+	0.532546i	−0.0415426	+	0.0239847i
$494$	18.2083	−	5.02162i	0.819230	−	0.225933i
$495$		0			0
$496$	−0.834168	−	0.449666i	−0.0374552	−	0.0201906i
$497$	19.4333	+	33.6595i	0.871705	+	1.50984i
$498$		0			0
$499$	18.0795	+	10.4382i	0.809351	+	0.467279i	0.846730	−	0.532022i	$-0.178568\pi$
$499$	18.0795	+	10.4382i	0.809351	+	0.467279i	−0.0373795	+	0.999301i	$0.511901\pi$
$500$	−17.3516	+	14.1039i	−0.775988	+	0.630748i
$501$		0			0
$502$	5.09444	+	5.02061i	0.227376	+	0.224081i
$503$		−	22.6713i		−	1.01086i	−0.862867	−	0.505431i	$-0.831333\pi$
$503$		−	22.6713i		−	1.01086i	0.862867	−	0.505431i	$-0.168667\pi$
$504$		0			0
$505$	−5.14603	+	16.5794i	−0.228995	+	0.737773i
$506$	17.0341	−	17.2846i	0.757257	−	0.768392i
$507$		0			0
$508$	−0.308470	−	21.1310i	−0.0136862	−	0.937535i
$509$	23.5593	+	13.6020i	1.04425	+	0.602896i	0.921033	−	0.389484i	$-0.127347\pi$
$509$	23.5593	+	13.6020i	1.04425	+	0.602896i	0.123213	+	0.992380i	$0.460680\pi$
$510$		0			0
$511$	17.5380	−	10.1255i	0.775834	−	0.447928i
$512$	17.0157	+	14.9153i	0.751996	+	0.659168i
$513$		0			0
$514$	−18.2560	+	5.03476i	−0.805236	+	0.222074i
$515$	−6.49787	−	28.7018i	−0.286330	−	1.26475i
$516$		0			0
$517$	−15.4705	−	8.93188i	−0.680390	−	0.392824i
$518$	−52.1658	−	13.5705i	−2.29204	−	0.596254i
$519$		0			0
$520$	−14.3282	+	23.8564i	−0.628335	+	1.04617i
$521$			2.18176i			0.0955847i	0.998857	+	0.0477924i	$0.0152186\pi$
$521$			2.18176i			0.0955847i	−0.998857	+	0.0477924i	$0.984781\pi$
$522$		0			0
$523$	28.8185			1.26014			0.630071	−	0.776537i	$-0.283026\pi$
$523$	28.8185			1.26014			0.630071	+	0.776537i	$0.283026\pi$
$524$	28.3940	+	15.8452i	1.24040	+	0.692203i
$525$		0			0
$526$	−14.9065	−	3.87779i	−0.649953	−	0.169080i
$527$	0.182473	+	0.105351i	0.00794865	+	0.00458916i
$528$		0			0
$529$	14.9560	+	25.9046i	0.650261	+	1.12629i
$530$	2.44021	+	0.0777744i	0.105996	+	0.00337830i
$531$		0			0
$532$	−10.3156	−	17.2797i	−0.447240	−	0.749171i
$533$	6.22935	+	10.7896i	0.269823	+	0.467348i
$534$		0			0
$535$	−0.382807	−	0.414027i	−0.0165502	−	0.0179000i
$536$	5.02308	+	17.2283i	0.216964	+	0.744151i
$537$		0			0
$538$	21.3445	−	21.6584i	0.920227	−	0.933759i
$539$	9.41102			0.405361
$540$		0			0
$541$	3.32257			0.142848			0.0714242	−	0.997446i	$-0.477246\pi$
$541$	3.32257			0.142848			0.0714242	+	0.997446i	$0.477246\pi$
$542$	18.8058	−	19.0823i	0.807777	−	0.819655i
$543$		0			0
$544$	−3.68489	−	3.42531i	−0.157989	−	0.146859i
$545$	−0.753711	+	0.696878i	−0.0322854	+	0.0298510i
$546$		0			0
$547$	13.8697	+	24.0231i	0.593027	+	1.02715i	0.993822	+	0.110986i	$0.0354008\pi$
$547$	13.8697	+	24.0231i	0.593027	+	1.02715i	−0.400795	+	0.916168i	$0.631266\pi$
$548$	22.6538	−	13.5238i	0.967721	−	0.577710i
$549$		0			0
$550$	−15.7655	−	5.44981i	−0.672244	−	0.232381i
$551$	−1.81756	−	3.14810i	−0.0774305	−	0.134114i
$552$		0			0
$553$	29.6652	+	17.1272i	1.26149	+	0.728323i
$554$	25.5417	+	6.64447i	1.08516	+	0.282296i
$555$		0			0
$556$	6.31943	−	11.3241i	0.268003	−	0.480251i
$557$	−30.0401			−1.27284			−0.636419	−	0.771344i	$-0.719585\pi$
$557$	−30.0401			−1.27284			−0.636419	+	0.771344i	$0.719585\pi$
$558$		0			0
$559$		−	36.7527i		−	1.55447i
$560$	28.5622	+	7.95913i	1.20697	+	0.336335i
$561$		0			0
$562$	9.24028	+	2.40378i	0.389778	+	0.101398i
$563$	−1.52959	−	0.883109i	−0.0644645	−	0.0372186i	0.467421	−	0.884035i	$-0.345183\pi$
$563$	−1.52959	−	0.883109i	−0.0644645	−	0.0372186i	−0.531886	+	0.846816i	$0.678516\pi$
$564$		0			0
$565$	−8.60636	−	38.0152i	−0.362072	−	1.59931i
$566$	−7.18435	+	1.98135i	−0.301981	+	0.0832824i
$567$		0			0
$568$	−22.9298	+	23.9566i	−0.962115	+	1.00520i
$569$	−31.9951	+	18.4724i	−1.34131	+	0.774403i	−0.986999	−	0.160726i	$-0.948616\pi$
$569$	−31.9951	+	18.4724i	−1.34131	+	0.774403i	−0.354306	+	0.935129i	$0.615283\pi$
$570$		0			0
$571$	−26.5164	−	15.3092i	−1.10968	−	0.640672i	−0.170930	−	0.985283i	$-0.554677\pi$
$571$	−26.5164	−	15.3092i	−1.10968	−	0.640672i	−0.938745	+	0.344612i	$0.888011\pi$
$572$	−20.7577	+	0.303021i	−0.867922	+	0.0126699i
$573$		0			0
$574$	9.31764	−	9.45465i	0.388911	−	0.394629i
$575$	20.5938	−	29.9783i	0.858819	−	1.25018i
$576$		0			0
$577$		−	23.6405i		−	0.984168i	−0.870548	−	0.492084i	$-0.836235\pi$
$577$		−	23.6405i		−	0.984168i	0.870548	−	0.492084i	$-0.163765\pi$
$578$	−16.3269	−	16.0903i	−0.679109	−	0.669268i
$579$		0			0
$580$	5.13766	+	1.51281i	0.213330	+	0.0628160i
$581$	7.46221	+	4.30831i	0.309585	+	0.178739i
$582$		0			0
$583$	0.910652	+	1.57730i	0.0377154	+	0.0653249i
$584$	12.4824	+	11.9474i	0.516523	+	0.494385i
$585$		0			0
$586$	30.3890	−	8.38091i	1.25536	−	0.346212i
$587$	−0.0513568	+	0.0296509i	−0.00211972	+	0.00122382i	−0.501059	−	0.865413i	$-0.667056\pi$
$587$	−0.0513568	+	0.0296509i	−0.00211972	+	0.00122382i	0.498940	+	0.866637i	$0.333723\pi$
$588$		0			0
$589$	−0.359558	+	0.622773i	−0.0148153	+	0.0256609i
$590$	3.55014	−	5.72010i	0.146157	−	0.235493i
$591$		0			0
$592$	−1.34244	−	45.9705i	−0.0551741	−	1.88938i
$593$	44.6245			1.83251			0.916255	−	0.400596i	$-0.131197\pi$
$593$	44.6245			1.83251			0.916255	+	0.400596i	$0.131197\pi$
$594$		0			0
$595$	−6.29622	−	1.95427i	−0.258120	−	0.0801171i
$596$	8.15914	−	14.6208i	0.334211	−	0.598893i
$597$		0			0
$598$	11.3958	−	43.8059i	0.466007	−	1.79136i
$599$	−11.5001	+	19.9187i	−0.469881	+	0.813857i	−0.999407	−	0.0344362i	$-0.989036\pi$
$599$	−11.5001	+	19.9187i	−0.469881	+	0.813857i	0.529526	+	0.848294i	$0.322370\pi$
$600$		0			0
$601$	0.981232	+	1.69954i	0.0400253	+	0.0693259i	0.885344	−	0.464936i	$-0.153923\pi$
$601$	0.981232	+	1.69954i	0.0400253	+	0.0693259i	−0.845319	+	0.534262i	$0.820589\pi$
$602$	−37.7496	+	10.4109i	−1.53856	+	0.424315i
$603$		0			0
$604$	16.8105	+	28.1593i	0.684011	+	1.14579i
$605$	2.68343	+	11.8530i	0.109097	+	0.481891i
$606$		0			0
$607$	−10.1049	+	17.5023i	−0.410146	+	0.710394i	−0.994905	−	0.100813i	$-0.967856\pi$
$607$	−10.1049	+	17.5023i	−0.410146	+	0.710394i	0.584759	+	0.811207i	$0.301189\pi$
$608$	11.6904	−	12.5764i	0.474110	−	0.510040i
$609$		0			0
$610$	−5.71267	−	10.6655i	−0.231299	−	0.431833i
$611$	−33.3195			−1.34796
$612$		0			0
$613$			24.8672i			1.00438i	0.864758	+	0.502189i	$0.167472\pi$
$613$			24.8672i			1.00438i	−0.864758	+	0.502189i	$0.832528\pi$
$614$	0.418434	+	0.412371i	0.0168866	+	0.0166419i
$615$		0			0
$616$	6.19121	+	21.2349i	0.249451	+	0.855577i
$617$	16.3707	−	28.3549i	0.659059	−	1.14152i	−0.321800	−	0.946808i	$-0.604288\pi$
$617$	16.3707	−	28.3549i	0.659059	−	1.14152i	0.980860	−	0.194717i	$-0.0623788\pi$
$618$		0			0
$619$	11.9754	−	6.91400i	0.481332	−	0.277897i	−0.239640	−	0.970862i	$-0.577029\pi$
$619$	11.9754	−	6.91400i	0.481332	−	0.277897i	0.720971	+	0.692965i	$0.243696\pi$
$620$	−0.249002	−	1.02983i	−0.0100001	−	0.0413588i
$621$		0			0
$622$	0.775897	−	0.213982i	0.0311106	−	0.00857991i
$623$	−13.4395	+	7.75930i	−0.538442	+	0.310870i
$624$		0			0
$625$	−24.6939	−	3.89997i	−0.987757	−	0.155999i
$626$	−38.4079	−	9.99151i	−1.53509	−	0.399341i
$627$		0			0
$628$	10.4402	−	18.7084i	0.416609	−	0.746546i
$629$			10.2255i			0.407719i
$630$		0			0
$631$			0.298908i			0.0118994i	0.999982	+	0.00594968i	$0.00189385\pi$
$631$			0.298908i			0.0118994i	−0.999982	+	0.00594968i	$0.998106\pi$
$632$	−6.94447	+	28.3894i	−0.276236	+	1.12927i
$633$		0			0
$634$	−4.72598	+	18.1669i	−0.187693	+	0.721501i
$635$	17.3485	−	16.0404i	0.688456	−	0.636543i
$636$		0			0
$637$	15.2017	−	8.77672i	0.602314	−	0.347746i
$638$	1.06221	+	3.85156i	0.0420534	+	0.152485i
$639$		0			0
$640$	0.301795	+	25.2964i	0.0119295	+	0.999929i
$641$	−12.2453	+	7.06982i	−0.483660	+	0.279241i	−0.721940	−	0.691955i	$-0.756750\pi$
$641$	−12.2453	+	7.06982i	−0.483660	+	0.279241i	0.238281	+	0.971196i	$0.423416\pi$
$642$		0			0
$643$	18.2808	−	31.6633i	0.720925	−	1.24868i	−0.239704	−	0.970846i	$-0.577050\pi$
$643$	18.2808	−	31.6633i	0.720925	−	1.24868i	0.960629	−	0.277833i	$-0.0896162\pi$
$644$	−48.2222	+	0.703948i	−1.90022	+	0.0277394i
$645$		0			0
$646$	−2.67979	+	2.71919i	−0.105435	+	0.106985i
$647$			25.4645i			1.00111i	0.865704	+	0.500556i	$0.166871\pi$
$647$			25.4645i			1.00111i	−0.865704	+	0.500556i	$0.833129\pi$
$648$		0			0
$649$	5.02220			0.197139
$650$	−30.5488	+	5.89980i	−1.19822	+	0.231409i
$651$		0			0
$652$	−0.0389969	−	2.67139i	−0.00152724	−	0.104620i
$653$	−11.2123	+	19.4203i	−0.438772	+	0.759976i	−0.997595	−	0.0693112i	$-0.977920\pi$
$653$	−11.2123	+	19.4203i	−0.438772	+	0.759976i	0.558823	+	0.829287i	$0.311253\pi$
$654$		0			0
$655$	8.02715	+	35.4567i	0.313647	+	1.38541i
$656$	9.96964	+	5.37423i	0.389249	+	0.209828i
$657$		0			0
$658$	9.43834	+	34.2233i	0.367945	+	1.33416i
$659$	−3.28193	−	5.68446i	−0.127846	−	0.221435i	0.794996	−	0.606615i	$-0.207473\pi$
$659$	−3.28193	−	5.68446i	−0.127846	−	0.221435i	−0.922842	+	0.385179i	$0.874140\pi$
$660$		0			0
$661$	−9.44856	+	16.3654i	−0.367506	+	0.636540i	−0.989175	−	0.146741i	$-0.953122\pi$
$661$	−9.44856	+	16.3654i	−0.367506	+	0.636540i	0.621669	+	0.783280i	$0.286455\pi$
$662$	11.7579	+	3.05873i	0.456986	+	0.118881i
$663$		0			0
$664$	−1.74687	+	7.14129i	−0.0677915	+	0.277136i
$665$	6.66983	−	21.4887i	0.258645	−	0.833297i
$666$		0			0
$667$	−8.71129			−0.337303
$668$	6.98799	−	12.5222i	0.270373	−	0.484498i
$669$		0			0
$670$	−10.5804	+	17.0474i	−0.408755	+	0.658600i
$671$	4.51290	−	7.81657i	0.174219	−	0.301755i
$672$		0			0
$673$	−27.1258	+	15.6611i	−1.04562	+	0.603690i	−0.921420	−	0.388567i	$-0.872970\pi$
$673$	−27.1258	+	15.6611i	−1.04562	+	0.603690i	−0.124201	+	0.992257i	$0.539637\pi$
$674$	0.396821	+	1.43887i	0.0152850	+	0.0554231i
$675$		0			0
$676$	−10.9230	+	6.52081i	−0.420115	+	0.250800i
$677$	−20.4922	−	35.4936i	−0.787580	−	1.36413i	−0.927446	−	0.373958i	$-0.878000\pi$
$677$	−20.4922	−	35.4936i	−0.787580	−	1.36413i	0.139866	−	0.990171i	$-0.455333\pi$
$678$		0			0
$679$	17.7249	+	10.2335i	0.680219	+	0.392724i
$680$	0.0971038	−	5.62402i	0.00372376	−	0.215671i
$681$		0			0
$682$	0.554790	−	0.562948i	0.0212440	−	0.0215564i
$683$		−	42.0703i		−	1.60978i	−0.593427	−	0.804888i	$-0.702225\pi$
$683$		−	42.0703i		−	1.60978i	0.593427	−	0.804888i	$-0.297775\pi$
$684$		0			0
$685$	28.1718	+	8.74417i	1.07639	+	0.334097i
$686$	10.0529	+	9.90726i	0.383823	+	0.378261i
$687$		0			0
$688$	−17.5430	−	28.4348i	−0.668820	−	1.08407i
$689$	2.94198	+	1.69855i	0.112080	+	0.0647096i
$690$		0			0
$691$	−30.3277	+	17.5097i	−1.15372	+	0.666101i	−0.949791	−	0.312885i	$-0.898705\pi$
$691$	−30.3277	+	17.5097i	−1.15372	+	0.666101i	−0.203930	+	0.978986i	$0.565371\pi$
$692$	−4.42247	+	2.64012i	−0.168117	+	0.100362i
$693$		0			0
$694$	2.59554	+	9.41140i	0.0985255	+	0.357252i
$695$	14.1409	−	3.20140i	0.536395	−	0.121436i
$696$		0			0
$697$	−2.18084	−	1.25911i	−0.0826054	−	0.0476922i
$698$	11.0478	−	42.4682i	0.418164	−	1.60745i
$699$		0			0
$700$	14.7133	+	29.7061i	0.556110	+	1.12279i
$701$		−	41.5315i		−	1.56862i	−0.620366	−	0.784312i	$-0.713016\pi$
$701$		−	41.5315i		−	1.56862i	0.620366	−	0.784312i	$-0.286984\pi$
$702$		0			0
$703$	−34.8993			−1.31625
$704$	−15.9151	+	10.1426i	−0.599824	+	0.382263i
$705$		0			0
$706$	5.46777	−	21.0184i	0.205782	−	0.791039i
$707$	22.2881	+	12.8680i	0.838229	+	0.483952i
$708$		0			0
$709$	5.69139	+	9.85778i	0.213745	+	0.370217i	0.952883	−	0.303337i	$-0.0981006\pi$
$709$	5.69139	+	9.85778i	0.213745	+	0.370217i	−0.739139	+	0.673553i	$0.764767\pi$
$710$	−37.0571	−	1.18108i	−1.39073	−	0.0443252i
$711$		0			0
$712$	−9.56534	−	9.15538i	−0.358476	−	0.343112i
$713$	0.861656	+	1.49243i	0.0322693	+	0.0558920i
$714$		0			0
$715$	−15.7570	−	17.0421i	−0.589279	−	0.637337i
$716$	−0.297322	−	20.3673i	−0.0111115	−	0.761162i
$717$		0			0
$718$	8.57386	+	8.44961i	0.319974	+	0.315337i
$719$	24.0599			0.897282			0.448641	−	0.893712i	$-0.351908\pi$
$719$	24.0599			0.897282			0.448641	+	0.893712i	$0.351908\pi$
$720$		0			0
$721$	−43.6278			−1.62478
$722$	9.85767	+	9.71482i	0.366864	+	0.361548i
$723$		0			0
$724$	0.121891	+	8.34985i	0.00453005	+	0.310320i
$725$	2.57906	+	5.40403i	0.0957837	+	0.200701i
$726$		0			0
$727$	−2.85756	−	4.94944i	−0.105981	−	0.183565i	0.808158	−	0.588966i	$-0.200465\pi$
$727$	−2.85756	−	4.94944i	−0.105981	−	0.183565i	−0.914139	+	0.405402i	$0.867132\pi$
$728$	29.8044	+	28.5270i	1.10462	+	1.05728i
$729$		0			0
$730$	−0.615391	+	19.3082i	−0.0227766	+	0.714629i
$731$	3.71433	+	6.43341i	0.137380	+	0.237948i
$732$		0			0
$733$	22.3900	+	12.9269i	0.826994	+	0.477465i	0.852822	−	0.522201i	$-0.174889\pi$
$733$	22.3900	+	12.9269i	0.826994	+	0.477465i	−0.0258286	+	0.999666i	$0.508222\pi$
$734$	−0.460397	+	1.76979i	−0.0169936	+	0.0653242i
$735$		0			0
$736$	−12.0930	−	39.3312i	−0.445754	−	1.44977i
$737$	−14.9675			−0.551335
$738$		0			0
$739$			18.0774i			0.664989i	0.943105	+	0.332495i	$0.107890\pi$
$739$			18.0774i			0.664989i	−0.943105	+	0.332495i	$0.892110\pi$
$740$	37.2404	−	35.4544i	1.36898	−	1.30333i
$741$		0			0
$742$	0.911255	−	3.50292i	0.0334532	−	0.128596i
$743$	15.5973	+	9.00512i	0.572210	+	0.330366i	0.758032	−	0.652218i	$-0.226161\pi$
$743$	15.5973	+	9.00512i	0.572210	+	0.330366i	−0.185821	+	0.982584i	$0.559495\pi$
$744$		0			0
$745$	18.2576	−	4.13339i	0.668907	−	0.151436i
$746$	6.15788	+	22.3284i	0.225456	+	0.817500i
$747$		0			0
$748$	3.60292	−	2.15087i	0.131736	−	0.0786435i
$749$	−0.723965	+	0.417982i	−0.0264531	+	0.0152727i
$750$		0			0
$751$	35.2487	+	20.3509i	1.28624	+	0.742613i	0.977982	−	0.208689i	$-0.0669195\pi$
$751$	35.2487	+	20.3509i	1.28624	+	0.742613i	0.308262	+	0.951302i	$0.400253\pi$
$752$	−25.7786	+	15.9042i	−0.940049	+	0.579967i
$753$		0			0
$754$	5.30778	+	5.23086i	0.193298	+	0.190497i
$755$	−10.8693	+	35.0184i	−0.395573	+	1.27445i
$756$		0			0
$757$			35.4823i			1.28963i	0.764340	+	0.644813i	$0.223065\pi$
$757$			35.4823i			1.28963i	−0.764340	+	0.644813i	$0.776935\pi$
$758$	11.7076	−	11.8798i	0.425240	−	0.431493i
$759$		0			0
$760$	19.1945	+	0.331411i	0.696259	+	0.0120215i
$761$	34.0009	+	19.6304i	1.23253	+	0.711602i	0.967557	−	0.252654i	$-0.0813033\pi$
$761$	34.0009	+	19.6304i	1.23253	+	0.711602i	0.264974	+	0.964256i	$0.414637\pi$
$762$		0			0
$763$	0.760910	+	1.31794i	0.0275468	+	0.0477125i
$764$	−42.9840	+	25.6606i	−1.55511	+	0.928367i
$765$		0			0
$766$	−4.23702	−	15.3634i	−0.153090	−	0.555101i
$767$	8.11242	−	4.68371i	0.292923	−	0.169119i
$768$		0			0
$769$	−3.27941	+	5.68011i	−0.118259	+	0.204830i	−0.919078	−	0.394076i	$-0.871065\pi$
$769$	−3.27941	+	5.68011i	−0.118259	+	0.204830i	0.800819	+	0.598906i	$0.204398\pi$
$770$	−13.0409	+	21.0119i	−0.469960	+	0.757215i
$771$		0			0
$772$	−18.4371	+	33.0386i	−0.663567	+	1.18908i
$773$	−34.2118			−1.23051			−0.615256	−	0.788327i	$-0.710947\pi$
$773$	−34.2118			−1.23051			−0.615256	+	0.788327i	$0.710947\pi$
$774$		0			0
$775$	0.670727	−	0.976374i	0.0240932	−	0.0350724i
$776$	−4.14930	+	16.9626i	−0.148951	+	0.608922i
$777$		0			0
$778$	−27.5910	−	7.17757i	−0.989185	−	0.257328i
$779$	4.29729	−	7.44313i	0.153967	−	0.266678i
$780$		0			0
$781$	−13.8292	−	23.9528i	−0.494847	−	0.857099i
$782$	2.43237	+	8.81973i	0.0869813	+	0.315393i
$783$		0			0
$784$	7.57191	−	14.0465i	0.270425	−	0.501661i
$785$	23.3619	−	5.28897i	0.833822	−	0.188771i
$786$		0			0
$787$	−8.68943	+	15.0505i	−0.309745	+	0.536494i	−0.978306	−	0.207163i	$-0.933577\pi$
$787$	−8.68943	+	15.0505i	−0.309745	+	0.536494i	0.668562	+	0.743657i	$0.266910\pi$
$788$	0.153385	+	10.5072i	0.00546411	+	0.374305i
$789$		0			0
$790$	−28.8045	+	15.4283i	−1.02482	+	0.548915i
$791$	−57.7846			−2.05458
$792$		0			0
$793$		−	16.8349i		−	0.597826i
$794$	5.08109	−	5.15581i	0.180321	−	0.182973i
$795$		0			0
$796$	−37.6934	+	0.550249i	−1.33601	+	0.0195030i
$797$	−3.50633	+	6.07314i	−0.124201	+	0.215122i	−0.921420	−	0.388568i	$-0.872970\pi$
$797$	−3.50633	+	6.07314i	−0.124201	+	0.215122i	0.797220	+	0.603689i	$0.206303\pi$
$798$		0			0
$799$	5.83244	−	3.36736i	0.206337	−	0.119129i
$800$	−20.8188	+	19.1462i	−0.736056	+	0.676921i
$801$		0			0
$802$	−4.16042	−	15.0856i	−0.146910	−	0.532692i
$803$	−12.4804	+	7.20555i	−0.440423	+	0.254278i
$804$		0			0
$805$	−36.6052	−	39.5905i	−1.29016	−	1.39538i
$806$	0.371153	−	1.42673i	0.0130733	−	0.0502545i
$807$		0			0
$808$	−5.21752	+	21.3295i	−0.183552	+	0.750371i
$809$		−	38.9234i		−	1.36847i	−0.729261	−	0.684236i	$-0.760136\pi$
$809$		−	38.9234i		−	1.36847i	0.729261	−	0.684236i	$-0.239864\pi$
$810$		0			0
$811$			35.7891i			1.25673i	0.777920	+	0.628363i	$0.216275\pi$
$811$			35.7891i			1.25673i	−0.777920	+	0.628363i	$0.783725\pi$
$812$	3.86922	−	6.93347i	0.135783	−	0.243317i
$813$		0			0
$814$	37.1223	+	9.65706i	1.30114	+	0.338480i
$815$	2.19321	−	2.02783i	0.0768248	−	0.0710319i
$816$		0			0
$817$	−21.9570	+	12.6769i	−0.768177	+	0.443507i
$818$	−22.0398	+	6.07829i	−0.770604	+	0.212523i
$819$		0			0
$820$	2.97597	+	12.3081i	0.103925	+	0.429817i
$821$	27.8765	−	16.0945i	0.972895	−	0.561701i	0.0727775	−	0.997348i	$-0.476814\pi$
$821$	27.8765	−	16.0945i	0.972895	−	0.561701i	0.900118	+	0.435647i	$0.143480\pi$
$822$		0			0
$823$	−8.65813	+	14.9963i	−0.301804	+	0.522739i	−0.976545	−	0.215315i	$-0.930922\pi$
$823$	−8.65813	+	14.9963i	−0.301804	+	0.522739i	0.674741	+	0.738055i	$0.264255\pi$
$824$	−10.4192	−	35.7360i	−0.362969	−	1.24492i
$825$		0			0
$826$	−7.10874	−	7.00572i	−0.247345	−	0.243760i
$827$		−	15.5363i		−	0.540249i	−0.962825	−	0.270124i	$-0.912935\pi$
$827$		−	15.5363i		−	0.540249i	0.962825	−	0.270124i	$-0.0870648\pi$
$828$		0			0
$829$	−27.4645			−0.953882			−0.476941	−	0.878935i	$-0.658254\pi$
$829$	−27.4645			−0.953882			−0.476941	+	0.878935i	$0.658254\pi$
$830$	−7.24570	+	3.88096i	−0.251502	+	0.134710i
$831$		0			0
$832$	−16.2489	+	31.2259i	−0.563330	+	1.08256i
$833$	−1.77400	+	3.07266i	−0.0614654	+	0.106461i
$834$		0			0
$835$	15.6369	−	3.54009i	0.541139	−	0.122510i
$836$	7.34082	+	12.2966i	0.253888	+	0.425287i
$837$		0			0
$838$	−9.96761	+	2.74894i	−0.344325	+	0.0949605i
$839$	6.91476	+	11.9767i	0.238724	+	0.413482i	0.960348	−	0.278803i	$-0.0899376\pi$
$839$	6.91476	+	11.9767i	0.238724	+	0.413482i	−0.721624	+	0.692285i	$0.756604\pi$
$840$		0			0
$841$	−13.7829	+	23.8727i	−0.475272	+	0.823196i
$842$	−10.6622	+	40.9861i	−0.367443	+	1.41247i
$843$		0			0
$844$	4.45744	−	7.98754i	0.153431	−	0.274943i
$845$	−13.5836	−	4.21619i	−0.467291	−	0.145041i
$846$		0			0
$847$	18.0170			0.619070
$848$	3.08690	−	0.0901446i	0.106005	−	0.00309558i
$849$		0			0
$850$	4.75118	−	4.12007i	0.162964	−	0.141317i
$851$	−41.8169	+	72.4290i	−1.43346	+	2.48283i
$852$		0			0
$853$	31.2866	−	18.0633i	1.07123	−	0.618476i	0.142714	−	0.989764i	$-0.454417\pi$
$853$	31.2866	−	18.0633i	1.07123	−	0.618476i	0.928518	+	0.371288i	$0.121084\pi$
$854$	−17.2916	+	4.76879i	−0.591705	+	0.163185i
$855$		0			0
$856$	−0.515270	−	0.493186i	−0.0176116	−	0.0168568i
$857$	−3.70493	−	6.41713i	−0.126558	−	0.219205i	0.795783	−	0.605582i	$-0.207060\pi$
$857$	−3.70493	−	6.41713i	−0.126558	−	0.219205i	−0.922341	+	0.386377i	$0.873726\pi$
$858$		0			0
$859$	−35.7586	−	20.6452i	−1.22007	−	0.704407i	−0.255136	−	0.966905i	$-0.582120\pi$
$859$	−35.7586	−	20.6452i	−1.22007	−	0.704407i	−0.964932	+	0.262499i	$0.915453\pi$
$860$	10.5513	−	35.8335i	0.359798	−	1.22191i
$861$		0			0
$862$	30.9741	+	30.5252i	1.05498	+	1.03969i
$863$			46.7922i			1.59282i	0.604754	+	0.796412i	$0.293271\pi$
$863$			46.7922i			1.59282i	−0.604754	+	0.796412i	$0.706729\pi$
$864$		0			0
$865$	−5.49970	−	1.70704i	−0.186995	−	0.0580410i
$866$	29.1583	−	29.5870i	0.990838	−	1.00541i
$867$		0			0
$868$	−1.57057	+	0.0229272i	−0.0533085	+	0.000778199i
$869$	−21.1104	−	12.1881i	−0.716120	−	0.413452i
$870$		0			0
$871$	−24.1772	+	13.9587i	−0.819213	+	0.472973i
$872$	−0.897815	+	0.938018i	−0.0304039	+	0.0317653i
$873$		0			0
$874$	−30.1014	+	8.30157i	−1.01819	+	0.280805i
$875$	−13.7226	+	34.4290i	−0.463909	+	1.16391i
$876$		0			0
$877$	−12.2576	−	7.07692i	−0.413909	−	0.238970i	0.278559	−	0.960419i	$-0.410143\pi$
$877$	−12.2576	−	7.07692i	−0.413909	−	0.238970i	−0.692468	+	0.721449i	$0.743477\pi$
$878$	10.7059	+	2.78504i	0.361306	+	0.0939907i
$879$		0			0
$880$	−20.3255	−	5.66388i	−0.685171	−	0.190929i
$881$			13.5705i			0.457200i	0.973520	+	0.228600i	$0.0734148\pi$
$881$			13.5705i			0.457200i	−0.973520	+	0.228600i	$0.926585\pi$
$882$		0			0
$883$	46.0353			1.54921			0.774606	−	0.632444i	$-0.217948\pi$
$883$	46.0353			1.54921			0.774606	+	0.632444i	$0.217948\pi$
$884$	3.81393	−	6.83441i	0.128276	−	0.229866i
$885$		0			0
$886$	36.5486	+	9.50783i	1.22788	+	0.319422i
$887$	−17.1621	−	9.90855i	−0.576247	−	0.332696i	0.183393	−	0.983040i	$-0.441292\pi$
$887$	−17.1621	−	9.90855i	−0.576247	−	0.332696i	−0.759641	+	0.650343i	$0.774625\pi$
$888$		0			0
$889$	−17.5143	−	30.3356i	−0.587409	−	1.01742i
$890$	0.471580	−	14.7961i	0.0158074	−	0.495965i
$891$		0			0
$892$	40.7910	−	24.3514i	1.36578	−	0.815346i
$893$	11.4927	+	19.9059i	0.384587	+	0.666125i
$894$		0			0
$895$	16.7216	−	15.4607i	0.558941	−	0.516794i
$896$	36.6756	+	7.84436i	1.22525	+	0.262062i
$897$		0			0
$898$	23.6695	−	24.0175i	0.789860	−	0.801475i
$899$	−0.283722			−0.00946265
$900$		0			0
$901$	−0.686641			−0.0228753
$902$	−6.63062	+	6.72812i	−0.220776	+	0.224022i
$903$		0			0
$904$	−13.8001	−	47.3320i	−0.458983	−	1.57424i
$905$	−6.85524	+	6.33832i	−0.227876	+	0.210693i
$906$		0			0
$907$	−24.4653	−	42.3752i	−0.812358	−	1.40705i	−0.911209	−	0.411943i	$-0.864850\pi$
$907$	−24.4653	−	42.3752i	−0.812358	−	1.40705i	0.0988513	−	0.995102i	$-0.468483\pi$
$908$	−28.5587	−	47.8386i	−0.947752	−	1.58758i
$909$		0			0
$910$	−1.46938	+	46.1026i	−0.0487095	+	1.52829i
$911$	−16.0978	−	27.8822i	−0.533343	−	0.923778i	−0.999242	−	0.0389396i	$-0.987602\pi$
$911$	−16.0978	−	27.8822i	−0.533343	−	0.923778i	0.465898	−	0.884838i	$-0.345731\pi$
$912$		0			0
$913$	−5.31026	−	3.06588i	−0.175744	−	0.101466i
$914$	−21.5646	−	5.60985i	−0.713292	−	0.185557i
$915$		0			0
$916$	29.2006	+	16.2953i	0.964814	+	0.538413i
$917$	53.8956			1.77979
$918$		0			0
$919$			37.8553i			1.24873i	0.781133	+	0.624365i	$0.214642\pi$
$919$			37.8553i			1.24873i	−0.781133	+	0.624365i	$0.785358\pi$
$920$	23.6870	−	39.4386i	0.780937	−	1.30025i
$921$		0			0
$922$	−14.6110	−	3.80093i	−0.481187	−	0.125177i
$923$	−44.6768	−	25.7942i	−1.47056	−	0.849026i
$924$		0			0
$925$	57.3114	+	4.49779i	1.88439	+	0.147887i
$926$	8.66098	−	2.38859i	0.284618	−	0.0784939i
$927$		0			0
$928$	6.60333	+	1.51347i	0.216765	+	0.0496822i
$929$	−14.4535	+	8.34474i	−0.474205	+	0.273782i	−0.717998	−	0.696045i	$-0.754941\pi$
$929$	−14.4535	+	8.34474i	−0.474205	+	0.273782i	0.243794	+	0.969827i	$0.421608\pi$
$930$		0			0
$931$	−10.4868	−	6.05458i	−0.343693	−	0.198431i
$932$	−0.0490261	−	3.35841i	−0.00160590	−	0.110008i
$933$		0			0
$934$	−7.70506	+	7.81836i	−0.252117	+	0.255824i
$935$	4.48052	+	1.39070i	0.146529	+	0.0454806i
$936$		0			0
$937$			41.7514i			1.36396i	0.731372	+	0.681979i	$0.238880\pi$
$937$			41.7514i			1.36396i	−0.731372	+	0.681979i	$0.761120\pi$
$938$	21.1859	+	20.8789i	0.691745	+	0.681721i
$939$		0			0
$940$	−32.4861	−	9.56570i	−1.05958	−	0.311999i
$941$	−9.78882	−	5.65158i	−0.319106	−	0.184236i	0.331888	−	0.943319i	$-0.392314\pi$
$941$	−9.78882	−	5.65158i	−0.319106	−	0.184236i	−0.650994	+	0.759083i	$0.725648\pi$
$942$		0			0
$943$	−10.2982	−	17.8369i	−0.335354	−	0.580851i
$944$	4.04076	−	7.49595i	0.131516	−	0.243972i
$945$		0			0
$946$	26.8634	−	7.40858i	0.873404	−	0.240874i
$947$	−4.45025	+	2.56935i	−0.144614	+	0.0834928i	−0.570561	−	0.821255i	$-0.693274\pi$
$947$	−4.45025	+	2.56935i	−0.144614	+	0.0834928i	0.425947	+	0.904748i	$0.359941\pi$
$948$		0			0
$949$	−13.4398	+	23.2784i	−0.436274	+	0.755649i
$950$	14.0616	+	16.2156i	0.456220	+	0.526103i
$951$		0			0
$952$	−8.10015	−	1.98142i	−0.262527	−	0.0642181i
$953$	−22.9718			−0.744131			−0.372066	−	0.928206i	$-0.621350\pi$
$953$	−22.9718			−0.744131			−0.372066	+	0.928206i	$0.621350\pi$
$954$		0			0
$955$	−53.4541	−	16.5915i	−1.72973	−	0.536887i
$956$	−18.8997	−	10.5470i	−0.611260	−	0.341113i
$957$		0			0
$958$	−2.53907	+	9.76032i	−0.0820336	+	0.315342i
$959$	21.8654	−	37.8720i	0.706072	−	1.22295i
$960$		0			0
$961$	−15.4719	−	26.7982i	−0.499095	−	0.864457i
$962$	68.9703	−	19.0211i	2.22369	−	0.613265i
$963$		0			0
$964$	18.7408	−	11.1879i	0.603601	−	0.360337i
$965$	−41.2566	+	9.34019i	−1.32810	+	0.300671i
$966$		0			0
$967$	21.0871	−	36.5239i	0.678115	−	1.17453i	−0.297433	−	0.954743i	$-0.596131\pi$
$967$	21.0871	−	36.5239i	0.678115	−	1.17453i	0.975548	−	0.219787i	$-0.0705361\pi$
$968$	4.30280	+	14.7579i	0.138297	+	0.474337i
$969$		0			0
$970$	−17.2106	+	9.21838i	−0.552599	+	0.295984i
$971$	29.9678			0.961712			0.480856	−	0.876799i	$-0.340326\pi$
$971$	29.9678			0.961712			0.480856	+	0.876799i	$0.340326\pi$
$972$		0			0
$973$		−	21.4947i		−	0.689090i
$974$	15.2188	+	14.9982i	0.487641	+	0.480574i
$975$		0			0
$976$	−8.03573	−	13.0248i	−0.257217	−	0.416915i
$977$	18.5590	−	32.1452i	0.593756	−	1.02842i	−0.399965	−	0.916530i	$-0.630978\pi$
$977$	18.5590	−	32.1452i	0.593756	−	1.02842i	0.993721	−	0.111885i	$-0.0356888\pi$
$978$		0			0
$979$	9.56383	−	5.52168i	0.305661	−	0.176474i
$980$	17.3412	−	4.19293i	0.553945	−	0.133938i
$981$		0			0
$982$	40.1402	−	11.0701i	1.28092	−	0.353262i
$983$	−24.8903	+	14.3704i	−0.793876	+	0.458345i	−0.841325	−	0.540529i	$-0.818224\pi$
$983$	−24.8903	+	14.3704i	−0.793876	+	0.458345i	0.0474493	+	0.998874i	$0.484891\pi$
$984$		0			0
$985$	−8.62646	+	7.97598i	−0.274862	+	0.254136i
$986$	−1.45775	−	0.379221i	−0.0464242	−	0.0120769i
$987$		0			0
$988$	23.3255	+	13.0168i	0.742084	+	0.414119i
$989$			60.7584i			1.93201i
$990$		0			0
$991$			5.20653i			0.165391i	0.996575	+	0.0826954i	$0.0263529\pi$
$991$			5.20653i			0.165391i	−0.996575	+	0.0826954i	$0.973647\pi$
$992$	−0.393862	−	1.28099i	−0.0125051	−	0.0406716i
$993$		0			0
$994$	−13.8383	+	53.1953i	−0.438925	+	1.68725i
$995$	−28.6128	−	30.9463i	−0.907087	−	0.981064i
$996$		0			0
$997$	18.1724	−	10.4918i	0.575525	−	0.332279i	−0.183828	−	0.982958i	$-0.558849\pi$
$997$	18.1724	−	10.4918i	0.575525	−	0.332279i	0.759353	+	0.650679i	$0.225516\pi$
$998$	7.84924	+	28.4612i	0.248463	+	0.900924i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.n.d.179.19		48
3.2	odd	2		180.2.n.d.59.6	✓	48
4.3	odd	2	inner	540.2.n.d.179.15		48
5.4	even	2	inner	540.2.n.d.179.6		48
9.2	odd	6	inner	540.2.n.d.359.10		48
9.7	even	3		180.2.n.d.119.15	yes	48
12.11	even	2		180.2.n.d.59.10	yes	48
15.2	even	4		900.2.r.g.851.18		48
15.8	even	4		900.2.r.g.851.7		48
15.14	odd	2		180.2.n.d.59.19	yes	48
20.19	odd	2	inner	540.2.n.d.179.10		48
36.7	odd	6		180.2.n.d.119.19	yes	48
36.11	even	6	inner	540.2.n.d.359.6		48
45.7	odd	12		900.2.r.g.551.22		48
45.29	odd	6	inner	540.2.n.d.359.15		48
45.34	even	6		180.2.n.d.119.10	yes	48
45.43	odd	12		900.2.r.g.551.3		48
60.23	odd	4		900.2.r.g.851.3		48
60.47	odd	4		900.2.r.g.851.22		48
60.59	even	2		180.2.n.d.59.15	yes	48
180.7	even	12		900.2.r.g.551.18		48
180.43	even	12		900.2.r.g.551.7		48
180.79	odd	6		180.2.n.d.119.6	yes	48
180.119	even	6	inner	540.2.n.d.359.19		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.d.59.6	✓	48	3.2	odd	2
180.2.n.d.59.10	yes	48	12.11	even	2
180.2.n.d.59.15	yes	48	60.59	even	2
180.2.n.d.59.19	yes	48	15.14	odd	2
180.2.n.d.119.6	yes	48	180.79	odd	6
180.2.n.d.119.10	yes	48	45.34	even	6
180.2.n.d.119.15	yes	48	9.7	even	3
180.2.n.d.119.19	yes	48	36.7	odd	6
540.2.n.d.179.6		48	5.4	even	2	inner
540.2.n.d.179.10		48	20.19	odd	2	inner
540.2.n.d.179.15		48	4.3	odd	2	inner
540.2.n.d.179.19		48	1.1	even	1	trivial
540.2.n.d.359.6		48	36.11	even	6	inner
540.2.n.d.359.10		48	9.2	odd	6	inner
540.2.n.d.359.15		48	45.29	odd	6	inner
540.2.n.d.359.19		48	180.119	even	6	inner
900.2.r.g.551.3		48	45.43	odd	12
900.2.r.g.551.7		48	180.43	even	12
900.2.r.g.551.18		48	180.7	even	12
900.2.r.g.551.22		48	45.7	odd	12
900.2.r.g.851.3		48	60.23	odd	4
900.2.r.g.851.7		48	15.8	even	4
900.2.r.g.851.18		48	15.2	even	4
900.2.r.g.851.22		48	60.47	odd	4

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)

\(f(q)\)	\(=\)	\(q+(1.00727 + 0.992675i) q^{2} +(0.0291929 + 1.99979i) q^{4} +(-1.64183 + 1.51803i) q^{5} +(1.65751 + 2.87089i) q^{7} +(-1.95573 + 2.04331i) q^{8} +(-3.16067 - 0.100737i) q^{10} +(-1.17952 - 2.04298i) q^{11} +(-3.81058 - 2.20004i) q^{13} +(-1.18030 + 4.53714i) q^{14} +(-3.99830 + 0.116759i) q^{16} +0.889368 q^{17} +3.03537i q^{19} +(-3.08366 - 3.23899i) q^{20} +(0.839925 - 3.22872i) q^{22} +(6.29952 + 3.63703i) q^{23} +(0.391197 - 4.98467i) q^{25} +(-1.65437 - 5.99870i) q^{26} +(-5.69278 + 3.39848i) q^{28} +(-1.03714 + 0.598791i) q^{29} +(0.205172 + 0.118456i) q^{31} +(-4.14327 - 3.85140i) q^{32} +(0.895835 + 0.882853i) q^{34} +(-7.07943 - 2.19737i) q^{35} +11.4975i q^{37} +(-3.01314 + 3.05745i) q^{38} +(0.109183 - 6.32361i) q^{40} +(-2.45213 - 1.41574i) q^{41} +(4.17637 + 7.23369i) q^{43} +(4.05110 - 2.41842i) q^{44} +(2.73494 + 9.91686i) q^{46} +(6.55796 - 3.78624i) q^{47} +(-1.99467 + 3.45488i) q^{49} +(5.34220 - 4.63259i) q^{50} +(4.28837 - 7.68457i) q^{52} -0.772055 q^{53} +(5.03787 + 1.56369i) q^{55} +(-9.10776 - 2.22789i) q^{56} +(-1.63908 - 0.426394i) q^{58} +(-1.06446 + 1.84370i) q^{59} +(1.91303 + 3.31346i) q^{61} +(0.0890754 + 0.322986i) q^{62} +(-0.350216 - 7.99233i) q^{64} +(9.59603 - 2.17247i) q^{65} +(3.17238 - 5.49472i) q^{67} +(0.0259632 + 1.77855i) q^{68} +(-4.94964 - 9.24092i) q^{70} +11.7244 q^{71} -6.10889i q^{73} +(-11.4133 + 11.5811i) q^{74} +(-6.07010 + 0.0886114i) q^{76} +(3.91012 - 6.77253i) q^{77} +(8.94873 - 5.16655i) q^{79} +(6.38727 - 6.26121i) q^{80} +(-1.06459 - 3.86020i) q^{82} +(2.25103 - 1.29963i) q^{83} +(-1.46019 + 1.35008i) q^{85} +(-2.97396 + 11.4321i) q^{86} +(6.48127 + 1.58541i) q^{88} +4.68130i q^{89} -14.5863i q^{91} +(-7.08939 + 12.7039i) q^{92} +(10.3642 + 2.69615i) q^{94} +(-4.60778 - 4.98356i) q^{95} +(5.34684 - 3.08700i) q^{97} +(-5.43875 + 1.49994i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{4} + 18 q^{5} - 16 q^{10} + 42 q^{14} + 30 q^{16} - 26 q^{25} - 4 q^{34} + 10 q^{40} - 96 q^{41} + 4 q^{46} + 32 q^{49} + 90 q^{50} - 6 q^{56} + 8 q^{61} - 20 q^{64} + 6 q^{65} + 4 q^{70} - 72 q^{74}+ \cdots - 62 q^{94}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more