LMFDB - Embedded newform 576.2.y.a.47.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [576,2,Mod(47,576)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("576.47"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(576, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.y (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			47.5
Character	$\chi$	$=$	576.47
Dual form			576.2.y.a.527.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.33407 + 1.10465i) q^{3} +(0.178044 - 0.664471i) q^{5} +(-0.645693 + 1.11837i) q^{7} +(0.559489 - 2.94737i) q^{9} +(-0.860301 - 3.21069i) q^{11} +(1.27203 - 4.74727i) q^{13} +(0.496485 + 1.08313i) q^{15} +5.58523i q^{17} +(2.49649 - 2.49649i) q^{19} +(-0.374013 - 2.20525i) q^{21} +(2.36529 - 1.36560i) q^{23} +(3.92031 + 2.26339i) q^{25} +(2.50942 + 4.55004i) q^{27} +(-0.792277 - 2.95682i) q^{29} +(5.28160 - 3.04933i) q^{31} +(4.69439 + 3.33295i) q^{33} +(0.628165 + 0.628165i) q^{35} +(0.507420 - 0.507420i) q^{37} +(3.54711 + 7.73835i) q^{39} +(-4.89892 - 8.48518i) q^{41} +(0.949956 - 0.254540i) q^{43} +(-1.85883 - 0.896527i) q^{45} +(6.13774 - 10.6309i) q^{47} +(2.66616 + 4.61793i) q^{49} +(-6.16973 - 7.45109i) q^{51} +(0.601793 + 0.601793i) q^{53} -2.28658 q^{55} +(-0.572741 + 6.08824i) q^{57} +(-4.77715 - 1.28003i) q^{59} +(10.8292 - 2.90167i) q^{61} +(2.93500 + 2.52881i) q^{63} +(-2.92795 - 1.69045i) q^{65} +(-0.110351 - 0.0295686i) q^{67} +(-1.64695 + 4.43463i) q^{69} +0.0447904i q^{71} +13.2931i q^{73} +(-7.73022 + 1.31105i) q^{75} +(4.14624 + 1.11098i) q^{77} +(2.50052 + 1.44368i) q^{79} +(-8.37394 - 3.29804i) q^{81} +(-3.79568 + 1.01705i) q^{83} +(3.71122 + 0.994419i) q^{85} +(4.32321 + 3.06941i) q^{87} -12.7362 q^{89} +(4.48788 + 4.48788i) q^{91} +(-3.67758 + 9.90236i) q^{93} +(-1.21436 - 2.10333i) q^{95} +(4.41066 - 7.63949i) q^{97} +(-9.94440 + 0.739279i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55}+ \cdots - 46 q^{99}+O(q^{100}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.33407	+	1.10465i	−0.770226	+	0.637771i
$3$	−1.33407	+	1.10465i	−0.770226	+	0.637771i
$4$		0			0
$5$	0.178044	−	0.664471i	0.0796239	−	0.297161i	−0.914618	−	0.404319i	$-0.867509\pi$
$5$	0.178044	−	0.664471i	0.0796239	−	0.297161i	0.994242	+	0.107158i	$0.0341752\pi$
$6$		0			0
$7$	−0.645693	+	1.11837i	−0.244049	+	0.422705i	−0.961864	−	0.273529i	$-0.911809\pi$
$7$	−0.645693	+	1.11837i	−0.244049	+	0.422705i	0.717815	+	0.696234i	$0.245142\pi$
$8$		0			0
$9$	0.559489	−	2.94737i	0.186496	−	0.982456i
$10$		0			0
$11$	−0.860301	−	3.21069i	−0.259390	−	0.968058i	−0.965595	−	0.260051i	$-0.916261\pi$
$11$	−0.860301	−	3.21069i	−0.259390	−	0.968058i	0.706205	−	0.708008i	$-0.250406\pi$
$12$		0			0
$13$	1.27203	−	4.74727i	0.352797	−	1.31666i	−0.530437	−	0.847725i	$-0.677972\pi$
$13$	1.27203	−	4.74727i	0.352797	−	1.31666i	0.883234	−	0.468933i	$-0.155361\pi$
$14$		0			0
$15$	0.496485	+	1.08313i	0.128192	+	0.279663i
$16$		0			0
$17$			5.58523i			1.35462i	0.735699	+	0.677308i	$0.236854\pi$
$17$			5.58523i			1.35462i	−0.735699	+	0.677308i	$0.763146\pi$
$18$		0			0
$19$	2.49649	−	2.49649i	0.572733	−	0.572733i	−0.360158	−	0.932891i	$-0.617277\pi$
$19$	2.49649	−	2.49649i	0.572733	−	0.572733i	0.932891	+	0.360158i	$0.117277\pi$
$20$		0			0
$21$	−0.374013	−	2.20525i	−0.0816163	−	0.481226i
$22$		0			0
$23$	2.36529	−	1.36560i	0.493197	−	0.284747i	−0.232703	−	0.972548i	$-0.574757\pi$
$23$	2.36529	−	1.36560i	0.493197	−	0.284747i	0.725900	+	0.687801i	$0.241424\pi$
$24$		0			0
$25$	3.92031	+	2.26339i	0.784061	+	0.452678i
$26$		0			0
$27$	2.50942	+	4.55004i	0.482937	+	0.875655i
$28$		0			0
$29$	−0.792277	−	2.95682i	−0.147122	−	0.549067i	−0.999652	−	0.0263884i	$-0.991599\pi$
$29$	−0.792277	−	2.95682i	−0.147122	−	0.549067i	0.852530	−	0.522679i	$-0.175067\pi$
$30$		0			0
$31$	5.28160	−	3.04933i	0.948604	−	0.547677i	0.0559568	−	0.998433i	$-0.482179\pi$
$31$	5.28160	−	3.04933i	0.948604	−	0.547677i	0.892647	+	0.450757i	$0.148846\pi$
$32$		0			0
$33$	4.69439	+	3.33295i	0.817189	+	0.580192i
$34$		0			0
$35$	0.628165	+	0.628165i	0.106179	+	0.106179i
$36$		0			0
$37$	0.507420	−	0.507420i	0.0834193	−	0.0834193i	−0.664166	−	0.747585i	$-0.731213\pi$
$37$	0.507420	−	0.507420i	0.0834193	−	0.0834193i	0.747585	+	0.664166i	$0.231213\pi$
$38$		0			0
$39$	3.54711	+	7.73835i	0.567992	+	1.23913i
$40$		0			0
$41$	−4.89892	−	8.48518i	−0.765083	−	1.32516i	−0.940203	−	0.340616i	$-0.889365\pi$
$41$	−4.89892	−	8.48518i	−0.765083	−	1.32516i	0.175120	−	0.984547i	$-0.443969\pi$
$42$		0			0
$43$	0.949956	−	0.254540i	0.144867	−	0.0388170i	−0.185657	−	0.982615i	$-0.559441\pi$
$43$	0.949956	−	0.254540i	0.144867	−	0.0388170i	0.330524	+	0.943798i	$0.392775\pi$
$44$		0			0
$45$	−1.85883	−	0.896527i	−0.277097	−	0.133646i
$46$		0			0
$47$	6.13774	−	10.6309i	0.895281	−	1.55067i	0.0618250	−	0.998087i	$-0.480308\pi$
$47$	6.13774	−	10.6309i	0.895281	−	1.55067i	0.833456	−	0.552586i	$-0.186359\pi$
$48$		0			0
$49$	2.66616	+	4.61793i	0.380880	+	0.659704i
$50$		0			0
$51$	−6.16973	−	7.45109i	−0.863935	−	1.04336i
$52$		0			0
$53$	0.601793	+	0.601793i	0.0826626	+	0.0826626i	0.747229	−	0.664567i	$-0.231384\pi$
$53$	0.601793	+	0.601793i	0.0826626	+	0.0826626i	−0.664567	+	0.747229i	$0.731384\pi$
$54$		0			0
$55$	−2.28658			−0.308322
$56$		0			0
$57$	−0.572741	+	6.08824i	−0.0758614	+	0.806407i
$58$		0			0
$59$	−4.77715	−	1.28003i	−0.621932	−	0.166646i	−0.0659263	−	0.997824i	$-0.521000\pi$
$59$	−4.77715	−	1.28003i	−0.621932	−	0.166646i	−0.556006	+	0.831178i	$0.687667\pi$
$60$		0			0
$61$	10.8292	−	2.90167i	1.38653	−	0.371520i	0.513043	−	0.858363i	$-0.328518\pi$
$61$	10.8292	−	2.90167i	1.38653	−	0.371520i	0.873490	+	0.486842i	$0.161851\pi$
$62$		0			0
$63$	2.93500	+	2.52881i	0.369775	+	0.318600i
$64$		0			0
$65$	−2.92795	−	1.69045i	−0.363167	−	0.209675i
$66$		0			0
$67$	−0.110351	−	0.0295686i	−0.0134816	−	0.00361238i	0.252072	−	0.967708i	$-0.418888\pi$
$67$	−0.110351	−	0.0295686i	−0.0134816	−	0.00361238i	−0.265554	+	0.964096i	$0.585555\pi$
$68$		0			0
$69$	−1.64695	+	4.43463i	−0.198269	+	0.533866i
$70$		0			0
$71$			0.0447904i			0.00531565i	0.999996	+	0.00265782i	$0.000846013\pi$
$71$			0.0447904i			0.00531565i	−0.999996	+	0.00265782i	$0.999154\pi$
$72$		0			0
$73$			13.2931i			1.55585i	0.628360	+	0.777923i	$0.283726\pi$
$73$			13.2931i			1.55585i	−0.628360	+	0.777923i	$0.716274\pi$
$74$		0			0
$75$	−7.73022	+	1.31105i	−0.892609	+	0.151387i
$76$		0			0
$77$	4.14624	+	1.11098i	0.472507	+	0.126608i
$78$		0			0
$79$	2.50052	+	1.44368i	0.281331	+	0.162426i	0.634026	−	0.773312i	$-0.281401\pi$
$79$	2.50052	+	1.44368i	0.281331	+	0.162426i	−0.352695	+	0.935738i	$0.614735\pi$
$80$		0			0
$81$	−8.37394	−	3.29804i	−0.930438	−	0.366449i
$82$		0			0
$83$	−3.79568	+	1.01705i	−0.416630	+	0.111636i	−0.461043	−	0.887378i	$-0.652525\pi$
$83$	−3.79568	+	1.01705i	−0.416630	+	0.111636i	0.0444135	+	0.999013i	$0.485858\pi$
$84$		0			0
$85$	3.71122	+	0.994419i	0.402539	+	0.107860i
$86$		0			0
$87$	4.32321	+	3.06941i	0.463497	+	0.329076i
$88$		0			0
$89$	−12.7362			−1.35003			−0.675017	−	0.737802i	$-0.735864\pi$
$89$	−12.7362			−1.35003			−0.675017	+	0.737802i	$0.735864\pi$
$90$		0			0
$91$	4.48788	+	4.48788i	0.470458	+	0.470458i
$92$		0			0
$93$	−3.67758	+	9.90236i	−0.381347	+	1.02683i
$94$		0			0
$95$	−1.21436	−	2.10333i	−0.124590	−	0.215797i
$96$		0			0
$97$	4.41066	−	7.63949i	0.447835	−	0.775673i	−0.550410	−	0.834895i	$-0.685529\pi$
$97$	4.41066	−	7.63949i	0.447835	−	0.775673i	0.998245	+	0.0592215i	$0.0188618\pi$
$98$		0			0
$99$	−9.94440	+	0.739279i	−0.999450	+	0.0743004i
$100$		0			0
$101$	−7.02523	+	1.88240i	−0.699037	+	0.187306i	−0.590799	−	0.806819i	$-0.701187\pi$
$101$	−7.02523	+	1.88240i	−0.699037	+	0.187306i	−0.108238	+	0.994125i	$0.534521\pi$
$102$		0			0
$103$	−9.50698	−	16.4666i	−0.936750	−	1.62250i	−0.771483	−	0.636250i	$-0.780485\pi$
$103$	−9.50698	−	16.4666i	−0.936750	−	1.62250i	−0.165267	−	0.986249i	$-0.552849\pi$
$104$		0			0
$105$	−1.53192	−	0.144113i	−0.149500	−	0.0140640i
$106$		0			0
$107$	−8.28797	+	8.28797i	−0.801228	+	0.801228i	−0.983287	−	0.182060i	$-0.941724\pi$
$107$	−8.28797	+	8.28797i	−0.801228	+	0.801228i	0.182060	+	0.983287i	$0.441724\pi$
$108$		0			0
$109$	−14.3799	−	14.3799i	−1.37735	−	1.37735i	−0.849074	−	0.528273i	$-0.822840\pi$
$109$	−14.3799	−	14.3799i	−1.37735	−	1.37735i	−0.528273	−	0.849074i	$-0.677160\pi$
$110$		0			0
$111$	−0.116412	+	1.23746i	−0.0110493	+	0.117454i
$112$		0			0
$113$	−2.18778	+	1.26312i	−0.205809	+	0.118824i	−0.599362	−	0.800478i	$-0.704579\pi$
$113$	−2.18778	+	1.26312i	−0.205809	+	0.118824i	0.393553	+	0.919302i	$0.371246\pi$
$114$		0			0
$115$	−0.486275	−	1.81480i	−0.0453454	−	0.169231i
$116$		0			0
$117$	−13.2803	−	6.40518i	−1.22776	−	0.592159i
$118$		0			0
$119$	−6.24637	−	3.60634i	−0.572604	−	0.330593i
$120$		0			0
$121$	−0.0421101	+	0.0243123i	−0.00382819	+	0.00221021i
$122$		0			0
$123$	15.9087	+	5.90823i	1.43444	+	0.532727i
$124$		0			0
$125$	4.63408	−	4.63408i	0.414485	−	0.414485i
$126$		0			0
$127$			17.5157i			1.55427i	0.629333	+	0.777135i	$0.283328\pi$
$127$			17.5157i			1.55427i	−0.629333	+	0.777135i	$0.716672\pi$
$128$		0			0
$129$	−0.986131	+	1.38895i	−0.0868240	+	0.122290i
$130$		0			0
$131$	−3.21241	+	11.9889i	−0.280669	+	1.04747i	0.671277	+	0.741207i	$0.265746\pi$
$131$	−3.21241	+	11.9889i	−0.280669	+	1.04747i	−0.951946	+	0.306266i	$0.900920\pi$
$132$		0			0
$133$	1.18004	+	4.40397i	0.102322	+	0.381872i
$134$		0			0
$135$	3.47016	−	0.857326i	0.298663	−	0.0737869i
$136$		0			0
$137$	5.00063	−	8.66134i	0.427232	−	0.739988i	−0.569394	−	0.822065i	$-0.692822\pi$
$137$	5.00063	−	8.66134i	0.427232	−	0.739988i	0.996626	+	0.0820768i	$0.0261553\pi$
$138$		0			0
$139$	0.368654	−	1.37583i	0.0312688	−	0.116697i	−0.948528	−	0.316695i	$-0.897427\pi$
$139$	0.368654	−	1.37583i	0.0312688	−	0.116697i	0.979796	+	0.199998i	$0.0640936\pi$
$140$		0			0
$141$	3.55524	+	20.9624i	0.299405	+	1.76535i
$142$		0			0
$143$	−16.3363			−1.36611
$144$		0			0
$145$	−2.10578			−0.174876
$146$		0			0
$147$	−8.65805	−	3.21546i	−0.714104	−	0.265207i
$148$		0			0
$149$	1.48172	−	5.52986i	0.121387	−	0.453024i	−0.878298	−	0.478114i	$-0.841321\pi$
$149$	1.48172	−	5.52986i	0.121387	−	0.453024i	0.999685	+	0.0250901i	$0.00798725\pi$
$150$		0			0
$151$	−8.10127	+	14.0318i	−0.659272	+	1.14189i	0.321533	+	0.946899i	$0.395802\pi$
$151$	−8.10127	+	14.0318i	−0.659272	+	1.14189i	−0.980804	+	0.194994i	$0.937531\pi$
$152$		0			0
$153$	16.4617	+	3.12487i	1.33085	+	0.252631i
$154$		0			0
$155$	−1.08583	−	4.05239i	−0.0872163	−	0.325496i
$156$		0			0
$157$	−2.02762	+	7.56718i	−0.161822	+	0.603927i	0.836602	+	0.547810i	$0.184538\pi$
$157$	−2.02762	+	7.56718i	−0.161822	+	0.603927i	−0.998424	+	0.0561165i	$0.982128\pi$
$158$		0			0
$159$	−1.46761	−	0.138063i	−0.116389	−	0.0109491i
$160$		0			0
$161$			3.52703i			0.277969i
$162$		0			0
$163$	4.89763	−	4.89763i	0.383612	−	0.383612i	−0.488789	−	0.872402i	$-0.662561\pi$
$163$	4.89763	−	4.89763i	0.383612	−	0.383612i	0.872402	+	0.488789i	$0.162561\pi$
$164$		0			0
$165$	3.05046	−	2.52587i	0.237478	−	0.196639i
$166$		0			0
$167$	18.7832	−	10.8445i	1.45349	−	0.839174i	0.454814	−	0.890587i	$-0.349706\pi$
$167$	18.7832	−	10.8445i	1.45349	−	0.839174i	0.998677	+	0.0514129i	$0.0163725\pi$
$168$		0			0
$169$	−9.66023	−	5.57734i	−0.743095	−	0.429026i
$170$		0			0
$171$	−5.96130	−	8.75482i	−0.455872	−	0.669497i
$172$		0			0
$173$	−2.05946	−	7.68601i	−0.156578	−	0.584356i	−0.998965	−	0.0454836i	$-0.985517\pi$
$173$	−2.05946	−	7.68601i	−0.156578	−	0.584356i	0.842387	−	0.538873i	$-0.181150\pi$
$174$		0			0
$175$	−5.06263	+	2.92291i	−0.382699	+	0.220951i
$176$		0			0
$177$	7.78705	−	3.56944i	0.585311	−	0.268295i
$178$		0			0
$179$	9.47991	+	9.47991i	0.708562	+	0.708562i	0.966233	−	0.257671i	$-0.0829551\pi$
$179$	9.47991	+	9.47991i	0.708562	+	0.708562i	−0.257671	+	0.966233i	$0.582955\pi$
$180$		0			0
$181$	8.00075	−	8.00075i	0.594691	−	0.594691i	−0.344204	−	0.938895i	$-0.611851\pi$
$181$	8.00075	−	8.00075i	0.594691	−	0.594691i	0.938895	+	0.344204i	$0.111851\pi$
$182$		0			0
$183$	−11.2415	+	15.8335i	−0.830999	+	1.17045i
$184$		0			0
$185$	−0.246822	−	0.427509i	−0.0181467	−	0.0314311i
$186$		0			0
$187$	17.9324	−	4.80498i	1.31135	−	0.351375i
$188$		0			0
$189$	−6.70895	−	0.131462i	−0.488004	−	0.00956248i
$190$		0			0
$191$	−9.22986	+	15.9866i	−0.667850	+	1.15675i	0.310655	+	0.950523i	$0.399452\pi$
$191$	−9.22986	+	15.9866i	−0.667850	+	1.15675i	−0.978504	+	0.206227i	$0.933882\pi$
$192$		0			0
$193$	2.61643	+	4.53179i	0.188335	+	0.326205i	0.944695	−	0.327950i	$-0.106358\pi$
$193$	2.61643	+	4.53179i	0.188335	+	0.326205i	−0.756360	+	0.654155i	$0.773024\pi$
$194$		0			0
$195$	5.77345	−	0.979182i	0.413445	−	0.0701207i
$196$		0			0
$197$	14.3573	+	14.3573i	1.02292	+	1.02292i	0.999731	+	0.0231869i	$0.00738128\pi$
$197$	14.3573	+	14.3573i	1.02292	+	1.02292i	0.0231869	+	0.999731i	$0.492619\pi$
$198$		0			0
$199$	13.8358			0.980797			0.490399	−	0.871498i	$-0.336851\pi$
$199$	13.8358			0.980797			0.490399	+	0.871498i	$0.336851\pi$
$200$		0			0
$201$	0.179880	−	0.0824533i	0.0126877	−	0.00581581i
$202$		0			0
$203$	3.81839	+	1.02314i	0.267999	+	0.0718100i
$204$		0			0
$205$	−6.51038	+	1.74445i	−0.454705	+	0.121838i
$206$		0			0
$207$	−2.70157	−	7.73541i	−0.187772	−	0.537648i
$208$		0			0
$209$	−10.1632	−	5.86770i	−0.703001	−	0.405878i
$210$		0			0
$211$	25.6481	+	6.87239i	1.76569	+	0.473115i	0.987858	−	0.155358i	$-0.0496531\pi$
$211$	25.6481	+	6.87239i	1.76569	+	0.473115i	0.777831	+	0.628473i	$0.216320\pi$
$212$		0			0
$213$	−0.0494778	−	0.0597536i	−0.00339017	−	0.00409425i
$214$		0			0
$215$		−	0.676538i		−	0.0461395i
$216$		0			0
$217$			7.87574i			0.534640i
$218$		0			0
$219$	−14.6843	−	17.7340i	−0.992273	−	1.19835i
$220$		0			0
$221$	26.5146	+	7.10457i	1.78357	+	0.477905i
$222$		0			0
$223$	−2.77266	−	1.60079i	−0.185671	−	0.107197i	0.404284	−	0.914634i	$-0.367521\pi$
$223$	−2.77266	−	1.60079i	−0.185671	−	0.107197i	−0.589954	+	0.807437i	$0.700854\pi$
$224$		0			0
$225$	8.86441	−	10.2882i	0.590960	−	0.685882i
$226$		0			0
$227$	−2.78291	+	0.745680i	−0.184708	+	0.0494925i	−0.349988	−	0.936754i	$-0.613814\pi$
$227$	−2.78291	+	0.745680i	−0.184708	+	0.0494925i	0.165279	+	0.986247i	$0.447148\pi$
$228$		0			0
$229$	−17.6277	−	4.72334i	−1.16487	−	0.312127i	−0.375963	−	0.926635i	$-0.622688\pi$
$229$	−17.6277	−	4.72334i	−1.16487	−	0.312127i	−0.788911	+	0.614508i	$0.789355\pi$
$230$		0			0
$231$	−6.75862	+	3.09802i	−0.444684	+	0.203835i
$232$		0			0
$233$	6.00585			0.393456			0.196728	−	0.980458i	$-0.436968\pi$
$233$	6.00585			0.393456			0.196728	+	0.980458i	$0.436968\pi$
$234$		0			0
$235$	−5.97112	−	5.97112i	−0.389513	−	0.389513i
$236$		0			0
$237$	−4.93063	+	0.836239i	−0.320279	+	0.0543196i
$238$		0			0
$239$	−6.00788	−	10.4059i	−0.388617	−	0.673105i	0.603647	−	0.797252i	$-0.293714\pi$
$239$	−6.00788	−	10.4059i	−0.388617	−	0.673105i	−0.992264	+	0.124147i	$0.960381\pi$
$240$		0			0
$241$	1.51923	−	2.63138i	0.0978622	−	0.169502i	−0.812937	−	0.582351i	$-0.802133\pi$
$241$	1.51923	−	2.63138i	0.0978622	−	0.169502i	0.910800	+	0.412849i	$0.135466\pi$
$242$		0			0
$243$	14.8146	−	4.85048i	0.950358	−	0.311158i
$244$		0			0
$245$	3.54317	−	0.949391i	0.226365	−	0.0606543i
$246$		0			0
$247$	−8.67590	−	15.0271i	−0.552034	−	0.956152i
$248$		0			0
$249$	3.94022	−	5.54972i	0.249701	−	0.351699i
$250$		0			0
$251$	−2.95387	+	2.95387i	−0.186447	+	0.186447i	−0.794158	−	0.607711i	$-0.792088\pi$
$251$	−2.95387	+	2.95387i	−0.186447	+	0.186447i	0.607711	+	0.794158i	$0.292088\pi$
$252$		0			0
$253$	−6.41937	−	6.41937i	−0.403582	−	0.403582i
$254$		0			0
$255$	−6.04952	+	2.77298i	−0.378836	+	0.173651i
$256$		0			0
$257$	1.67398	−	0.966474i	0.104420	−	0.0602870i	−0.446880	−	0.894594i	$-0.647465\pi$
$257$	1.67398	−	0.966474i	0.104420	−	0.0602870i	0.551301	+	0.834307i	$0.314132\pi$
$258$		0			0
$259$	0.239847	+	0.895122i	0.0149034	+	0.0556202i
$260$		0			0
$261$	−9.15810	+	0.680824i	−0.566872	+	0.0421420i
$262$		0			0
$263$	1.51993	+	0.877533i	0.0937230	+	0.0541110i	0.546129	−	0.837701i	$-0.316101\pi$
$263$	1.51993	+	0.877533i	0.0937230	+	0.0541110i	−0.452406	+	0.891812i	$0.649434\pi$
$264$		0			0
$265$	0.507020	−	0.292728i	0.0311460	−	0.0179821i
$266$		0			0
$267$	16.9910	−	14.0691i	1.03983	−	0.861013i
$268$		0			0
$269$	−14.2013	+	14.2013i	−0.865871	+	0.865871i	−0.992012	−	0.126141i	$-0.959741\pi$
$269$	−14.2013	+	14.2013i	−0.865871	+	0.865871i	0.126141	+	0.992012i	$0.459741\pi$
$270$		0			0
$271$		−	11.3712i		−	0.690754i	−0.938464	−	0.345377i	$-0.887751\pi$
$271$		−	11.3712i		−	0.690754i	0.938464	−	0.345377i	$-0.112249\pi$
$272$		0			0
$273$	−10.9447	−	1.02961i	−0.662404	−	0.0623145i
$274$		0			0
$275$	3.89439	−	14.5341i	0.234841	−	0.876437i
$276$		0			0
$277$	1.81439	+	6.77138i	0.109016	+	0.406853i	0.998770	−	0.0495877i	$-0.0157907\pi$
$277$	1.81439	+	6.77138i	0.109016	+	0.406853i	−0.889754	+	0.456441i	$0.849124\pi$
$278$		0			0
$279$	−6.03251	−	17.2729i	−0.361157	−	1.03410i
$280$		0			0
$281$	5.16379	−	8.94395i	0.308046	−	0.533552i	−0.669889	−	0.742461i	$-0.733658\pi$
$281$	5.16379	−	8.94395i	0.308046	−	0.533552i	0.977935	+	0.208910i	$0.0669916\pi$
$282$		0			0
$283$	−6.25018	+	23.3260i	−0.371535	+	1.38659i	0.486807	+	0.873509i	$0.338161\pi$
$283$	−6.25018	+	23.3260i	−0.371535	+	1.38659i	−0.858342	+	0.513078i	$0.828505\pi$
$284$		0			0
$285$	3.94348	+	1.46455i	0.233592	+	0.0867523i
$286$		0			0
$287$	12.6528			0.746871
$288$		0			0
$289$	−14.1948			−0.834987
$290$		0			0
$291$	2.55484	+	15.0639i	0.149768	+	0.883060i
$292$		0			0
$293$	−5.04554	+	18.8302i	−0.294763	+	1.10007i	0.646642	+	0.762794i	$0.276173\pi$
$293$	−5.04554	+	18.8302i	−0.294763	+	1.10007i	−0.941405	+	0.337278i	$0.890494\pi$
$294$		0			0
$295$	−1.70109	+	2.94638i	−0.0990414	+	0.171545i
$296$		0			0
$297$	12.4499	−	11.9713i	0.722416	−	0.694648i
$298$		0			0
$299$	−3.47416	−	12.9658i	−0.200916	−	0.749829i
$300$		0			0
$301$	−0.328709	+	1.22676i	−0.0189465	+	0.0707093i
$302$		0			0
$303$	7.29275	−	10.2717i	0.418958	−	0.590093i
$304$		0			0
$305$		−	7.71230i		−	0.441605i
$306$		0			0
$307$	4.37646	−	4.37646i	0.249778	−	0.249778i	−0.571101	−	0.820879i	$-0.693484\pi$
$307$	4.37646	−	4.37646i	0.249778	−	0.249778i	0.820879	+	0.571101i	$0.193484\pi$
$308$		0			0
$309$	30.8728	+	11.4657i	1.75629	+	0.652259i
$310$		0			0
$311$	2.65273	−	1.53155i	0.150423	−	0.0868465i	−0.422900	−	0.906177i	$-0.638988\pi$
$311$	2.65273	−	1.53155i	0.150423	−	0.0868465i	0.573322	+	0.819330i	$0.305654\pi$
$312$		0			0
$313$	−2.59526	−	1.49837i	−0.146693	−	0.0846930i	0.424857	−	0.905260i	$-0.360324\pi$
$313$	−2.59526	−	1.49837i	−0.146693	−	0.0846930i	−0.571550	+	0.820567i	$0.693658\pi$
$314$		0			0
$315$	2.20288	−	1.49998i	0.124118	−	0.0845143i
$316$		0			0
$317$	2.47692	+	9.24401i	0.139118	+	0.519195i	0.999947	+	0.0103009i	$0.00327892\pi$
$317$	2.47692	+	9.24401i	0.139118	+	0.519195i	−0.860829	+	0.508894i	$0.830054\pi$
$318$		0			0
$319$	−8.81182	+	5.08751i	−0.493367	+	0.284846i
$320$		0			0
$321$	1.90142	−	20.2120i	0.106127	−	1.12813i
$322$		0			0
$323$	13.9434	+	13.9434i	0.775834	+	0.775834i
$324$		0			0
$325$	15.7317	−	15.7317i	0.872636	−	0.872636i
$326$		0			0
$327$	35.0687	+	3.29903i	1.93930	+	0.182437i
$328$		0			0
$329$	7.92619	+	13.7286i	0.436985	+	0.756880i
$330$		0			0
$331$	−14.5870	+	3.90856i	−0.801772	+	0.214834i	−0.636362	−	0.771391i	$-0.719561\pi$
$331$	−14.5870	+	3.90856i	−0.801772	+	0.214834i	−0.165410	+	0.986225i	$0.552895\pi$
$332$		0			0
$333$	−1.21166	−	1.77945i	−0.0663984	−	0.0975131i
$334$		0			0
$335$	−0.0392949	+	0.0680608i	−0.00214691	+	0.00371856i
$336$		0			0
$337$	1.09448	+	1.89569i	0.0596200	+	0.103265i	0.894295	−	0.447478i	$-0.147678\pi$
$337$	1.09448	+	1.89569i	0.0596200	+	0.103265i	−0.834675	+	0.550743i	$0.814344\pi$
$338$		0			0
$339$	1.52335	−	4.10183i	0.0827372	−	0.222781i
$340$		0			0
$341$	−14.3342	−	14.3342i	−0.776242	−	0.776242i
$342$		0			0
$343$	−15.9258			−0.859912
$344$		0			0
$345$	2.65345	+	1.88391i	0.142857	+	0.101426i
$346$		0			0
$347$	27.6810	+	7.41711i	1.48599	+	0.398171i	0.908382	−	0.418140i	$-0.137318\pi$
$347$	27.6810	+	7.41711i	1.48599	+	0.398171i	0.577612	+	0.816311i	$0.303985\pi$
$348$		0			0
$349$	−23.0850	+	6.18561i	−1.23571	+	0.331108i	−0.816801	−	0.576919i	$-0.804255\pi$
$349$	−23.0850	+	6.18561i	−1.23571	+	0.331108i	−0.418911	+	0.908027i	$0.637588\pi$
$350$		0			0
$351$	24.7923	−	6.12512i	1.32332	−	0.326934i
$352$		0			0
$353$	−0.355770	−	0.205404i	−0.0189357	−	0.0109325i	0.490502	−	0.871440i	$-0.336813\pi$
$353$	−0.355770	−	0.205404i	−0.0189357	−	0.0109325i	−0.509438	+	0.860507i	$0.670147\pi$
$354$		0			0
$355$	0.0297620	+	0.00797469i	0.00157960	+	0.000423253i
$356$		0			0
$357$	12.3169	−	2.08895i	0.651877	−	0.110559i
$358$		0			0
$359$		−	1.19383i		−	0.0630078i	−0.999504	−	0.0315039i	$-0.989970\pi$
$359$		−	1.19383i		−	0.0630078i	0.999504	−	0.0315039i	$-0.0100297\pi$
$360$		0			0
$361$			6.53512i			0.343954i
$362$		0			0
$363$	0.0293212	−	0.0789513i	0.00153897	−	0.00414387i
$364$		0			0
$365$	8.83291	+	2.36677i	0.462336	+	0.123883i
$366$		0			0
$367$	−16.1698	−	9.33562i	−0.844055	−	0.487316i	0.0145854	−	0.999894i	$-0.495357\pi$
$367$	−16.1698	−	9.33562i	−0.844055	−	0.487316i	−0.858641	+	0.512578i	$0.828690\pi$
$368$		0			0
$369$	−27.7498	+	9.69156i	−1.44460	+	0.504522i
$370$		0			0
$371$	−1.06160	+	0.284455i	−0.0551156	+	0.0147682i
$372$		0			0
$373$	11.5442	+	3.09325i	0.597735	+	0.160163i	0.544986	−	0.838445i	$-0.316535\pi$
$373$	11.5442	+	3.09325i	0.597735	+	0.160163i	0.0527491	+	0.998608i	$0.483202\pi$
$374$		0			0
$375$	−1.06314	+	11.3012i	−0.0549006	+	0.583593i
$376$		0			0
$377$	−15.0446			−0.774838
$378$		0			0
$379$	−15.3650	−	15.3650i	−0.789248	−	0.789248i	0.192123	−	0.981371i	$-0.438463\pi$
$379$	−15.3650	−	15.3650i	−0.789248	−	0.789248i	−0.981371	+	0.192123i	$0.938463\pi$
$380$		0			0
$381$	−19.3488	−	23.3672i	−0.991269	−	1.19714i
$382$		0			0
$383$	11.1162	+	19.2539i	0.568013	+	0.983827i	0.996762	+	0.0804037i	$0.0256210\pi$
$383$	11.1162	+	19.2539i	0.568013	+	0.983827i	−0.428750	+	0.903423i	$0.641046\pi$
$384$		0			0
$385$	1.47643	−	2.55725i	0.0752458	−	0.130330i
$386$		0			0
$387$	−0.218733	−	2.94228i	−0.0111188	−	0.149565i
$388$		0			0
$389$	15.6338	−	4.18905i	0.792663	−	0.212393i	0.160303	−	0.987068i	$-0.448753\pi$
$389$	15.6338	−	4.18905i	0.792663	−	0.212393i	0.632360	+	0.774675i	$0.282086\pi$
$390$		0			0
$391$	7.62718	+	13.2107i	0.385723	+	0.668092i
$392$		0			0
$393$	−8.95795	−	19.5426i	−0.451869	−	0.985794i
$394$		0			0
$395$	1.40449	−	1.40449i	0.0706674	−	0.0706674i
$396$		0			0
$397$	14.5828	+	14.5828i	0.731887	+	0.731887i	0.970993	−	0.239106i	$-0.0768543\pi$
$397$	14.5828	+	14.5828i	0.731887	+	0.731887i	−0.239106	+	0.970993i	$0.576854\pi$
$398$		0			0
$399$	−6.43910	−	4.57167i	−0.322358	−	0.228870i
$400$		0			0
$401$	27.9585	−	16.1418i	1.39618	−	0.806085i	0.402191	−	0.915556i	$-0.368249\pi$
$401$	27.9585	−	16.1418i	1.39618	−	0.806085i	0.993990	+	0.109470i	$0.0349155\pi$
$402$		0			0
$403$	−7.75768	−	28.9521i	−0.386438	−	1.44220i
$404$		0			0
$405$	−3.68239	+	4.97705i	−0.182979	+	0.247311i
$406$		0			0
$407$	−2.06570	−	1.19263i	−0.102393	−	0.0591166i
$408$		0			0
$409$	12.9975	−	7.50409i	0.642683	−	0.371053i	−0.142964	−	0.989728i	$-0.545663\pi$
$409$	12.9975	−	7.50409i	0.642683	−	0.371053i	0.785647	+	0.618674i	$0.212330\pi$
$410$		0			0
$411$	2.89658	+	17.0788i	0.142878	+	0.842435i
$412$		0			0
$413$	4.51613	−	4.51613i	0.222224	−	0.222224i
$414$		0			0
$415$			2.70320i			0.132695i
$416$		0			0
$417$	1.02801	+	2.24269i	0.0503417	+	0.109825i
$418$		0			0
$419$	−6.00718	+	22.4191i	−0.293470	+	1.09525i	0.648955	+	0.760827i	$0.275206\pi$
$419$	−6.00718	+	22.4191i	−0.293470	+	1.09525i	−0.942425	+	0.334418i	$0.891460\pi$
$420$		0			0
$421$	4.05109	+	15.1189i	0.197438	+	0.736849i	0.991622	+	0.129172i	$0.0412319\pi$
$421$	4.05109	+	15.1189i	0.197438	+	0.736849i	−0.794184	+	0.607677i	$0.792101\pi$
$422$		0			0
$423$	−27.8991	−	24.0380i	−1.35650	−	1.16877i
$424$		0			0
$425$	−12.6415	+	21.8958i	−0.613205	+	1.06210i
$426$		0			0
$427$	−3.74717	+	13.9846i	−0.181338	+	0.676764i
$428$		0			0
$429$	21.7938	−	18.0460i	1.05222	−	0.871267i
$430$		0			0
$431$	1.63818			0.0789082			0.0394541	−	0.999221i	$-0.487438\pi$
$431$	1.63818			0.0789082			0.0394541	+	0.999221i	$0.487438\pi$
$432$		0			0
$433$	24.1284			1.15954			0.579769	−	0.814781i	$-0.303143\pi$
$433$	24.1284			1.15954			0.579769	+	0.814781i	$0.303143\pi$
$434$		0			0
$435$	2.80926	−	2.32615i	0.134694	−	0.111531i
$436$		0			0
$437$	2.49571	−	9.31411i	0.119386	−	0.445554i
$438$		0			0
$439$	−6.04546	+	10.4711i	−0.288534	+	0.499756i	−0.973460	−	0.228857i	$-0.926501\pi$
$439$	−6.04546	+	10.4711i	−0.288534	+	0.499756i	0.684926	+	0.728613i	$0.259835\pi$
$440$		0			0
$441$	15.1024	−	5.27448i	0.719162	−	0.251166i
$442$		0			0
$443$	4.35450	+	16.2512i	0.206889	+	0.772119i	0.988866	+	0.148811i	$0.0475448\pi$
$443$	4.35450	+	16.2512i	0.206889	+	0.772119i	−0.781977	+	0.623307i	$0.785789\pi$
$444$		0			0
$445$	−2.26761	+	8.46284i	−0.107495	+	0.401177i
$446$		0			0
$447$	4.13185	+	9.01401i	0.195430	+	0.426348i
$448$		0			0
$449$			31.8270i			1.50201i	0.660298	+	0.751004i	$0.270430\pi$
$449$			31.8270i			1.50201i	−0.660298	+	0.751004i	$0.729570\pi$
$450$		0			0
$451$	−23.0287	+	23.0287i	−1.08438	+	1.08438i
$452$		0			0
$453$	−4.69260	−	27.6685i	−0.220477	−	1.29998i
$454$		0			0
$455$	3.78111	−	2.18303i	0.177261	−	0.102342i
$456$		0			0
$457$	−24.8553	−	14.3502i	−1.16268	−	0.671275i	−0.210737	−	0.977543i	$-0.567586\pi$
$457$	−24.8553	−	14.3502i	−1.16268	−	0.671275i	−0.951945	+	0.306268i	$0.900920\pi$
$458$		0			0
$459$	−25.4130	+	14.0157i	−1.18618	+	0.654195i
$460$		0			0
$461$	0.483918	+	1.80601i	0.0225383	+	0.0841141i	0.976279	−	0.216517i	$-0.0694695\pi$
$461$	0.483918	+	1.80601i	0.0225383	+	0.0841141i	−0.953741	+	0.300631i	$0.902803\pi$
$462$		0			0
$463$	4.71990	−	2.72503i	0.219352	−	0.126643i	−0.386298	−	0.922374i	$-0.626246\pi$
$463$	4.71990	−	2.72503i	0.219352	−	0.126643i	0.605650	+	0.795731i	$0.292913\pi$
$464$		0			0
$465$	5.92506	+	4.20670i	0.274768	+	0.195081i
$466$		0			0
$467$	−8.95228	−	8.95228i	−0.414262	−	0.414262i	0.468958	−	0.883220i	$-0.344630\pi$
$467$	−8.95228	−	8.95228i	−0.414262	−	0.414262i	−0.883220	+	0.468958i	$0.844630\pi$
$468$		0			0
$469$	0.104322	−	0.104322i	0.00481713	−	0.00481713i
$470$		0			0
$471$	−5.65411	−	12.3350i	−0.260528	−	0.568365i
$472$		0			0
$473$	−1.63450	−	2.83103i	−0.0751542	−	0.130171i
$474$		0			0
$475$	15.4375	−	4.13647i	0.708321	−	0.189794i
$476$		0			0
$477$	2.11040	−	1.43701i	0.0966286	−	0.0657961i
$478$		0			0
$479$	4.27809	−	7.40987i	0.195471	−	0.338566i	−0.751584	−	0.659638i	$-0.770710\pi$
$479$	4.27809	−	7.40987i	0.195471	−	0.338566i	0.947055	+	0.321072i	$0.104043\pi$
$480$		0			0
$481$	−1.76341	−	3.05431i	−0.0804045	−	0.139265i
$482$		0			0
$483$	−3.89614	−	4.70531i	−0.177281	−	0.214099i
$484$		0			0
$485$	−4.29093	−	4.29093i	−0.194841	−	0.194841i
$486$		0			0
$487$	13.1689			0.596738			0.298369	−	0.954451i	$-0.403557\pi$
$487$	13.1689			0.596738			0.298369	+	0.954451i	$0.403557\pi$
$488$		0			0
$489$	−1.12361	+	11.9440i	−0.0508114	+	0.540125i
$490$		0			0
$491$	−8.09692	−	2.16956i	−0.365409	−	0.0979110i	0.0714425	−	0.997445i	$-0.477240\pi$
$491$	−8.09692	−	2.16956i	−0.365409	−	0.0979110i	−0.436851	+	0.899534i	$0.643906\pi$
$492$		0			0
$493$	16.5145	−	4.42505i	0.743776	−	0.199294i
$494$		0			0
$495$	−1.27932	+	6.73939i	−0.0575010	+	0.302913i
$496$		0			0
$497$	−0.0500924	−	0.0289209i	−0.00224695	−	0.00129728i
$498$		0			0
$499$	−31.2957	−	8.38567i	−1.40099	−	0.375394i	−0.522289	−	0.852768i	$-0.674922\pi$
$499$	−31.2957	−	8.38567i	−1.40099	−	0.375394i	−0.878700	+	0.477374i	$0.841589\pi$
$500$		0			0
$501$	−13.0788	+	35.2163i	−0.584316	+	1.57335i
$502$		0			0
$503$			20.8126i			0.927989i	0.885838	+	0.463994i	$0.153584\pi$
$503$			20.8126i			0.927989i	−0.885838	+	0.463994i	$0.846416\pi$
$504$		0			0
$505$			5.00321i			0.222640i
$506$		0			0
$507$	19.0484	−	3.23063i	0.845971	−	0.143477i
$508$		0			0
$509$	−20.7078	−	5.54865i	−0.917859	−	0.245940i	−0.231189	−	0.972909i	$-0.574262\pi$
$509$	−20.7078	−	5.54865i	−0.917859	−	0.245940i	−0.686670	+	0.726969i	$0.740928\pi$
$510$		0			0
$511$	−14.8667	−	8.58329i	−0.657664	−	0.379703i
$512$		0			0
$513$	17.6238	+	5.09438i	0.778111	+	0.224922i
$514$		0			0
$515$	−12.6342	+	3.38533i	−0.556730	+	0.149175i
$516$		0			0
$517$	−39.4127	−	10.5606i	−1.73337	−	0.464455i
$518$		0			0
$519$	11.2378	+	7.97869i	0.493286	+	0.350226i
$520$		0			0
$521$	20.1534			0.882938			0.441469	−	0.897277i	$-0.354458\pi$
$521$	20.1534			0.882938			0.441469	+	0.897277i	$0.354458\pi$
$522$		0			0
$523$	−14.7713	−	14.7713i	−0.645905	−	0.645905i	0.306096	−	0.952001i	$-0.400977\pi$
$523$	−14.7713	−	14.7713i	−0.645905	−	0.645905i	−0.952001	+	0.306096i	$0.900977\pi$
$524$		0			0
$525$	3.52511	−	9.49181i	0.153848	−	0.414256i
$526$		0			0
$527$	17.0312	+	29.4990i	0.741892	+	1.28499i
$528$		0			0
$529$	−7.77028	+	13.4585i	−0.337838	+	0.585153i
$530$		0			0
$531$	−6.44550	+	13.3639i	−0.279711	+	0.579942i
$532$		0			0
$533$	−46.5131	+	12.4631i	−2.01470	+	0.539838i
$534$		0			0
$535$	4.03149	+	6.98274i	0.174296	+	0.301890i
$536$		0			0
$537$	−23.1189	−	2.17487i	−0.997653	−	0.0938525i
$538$		0			0
$539$	12.5330	−	12.5330i	0.539835	−	0.539835i
$540$		0			0
$541$	11.1739	+	11.1739i	0.480403	+	0.480403i	0.905260	−	0.424857i	$-0.139676\pi$
$541$	11.1739	+	11.1739i	0.480403	+	0.480403i	−0.424857	+	0.905260i	$0.639676\pi$
$542$		0			0
$543$	−1.83552	+	19.5116i	−0.0787698	+	0.837324i
$544$		0			0
$545$	−12.1153	+	6.99478i	−0.518963	+	0.299624i
$546$		0			0
$547$	3.23236	+	12.0633i	0.138206	+	0.515791i	0.999964	+	0.00847177i	$0.00269668\pi$
$547$	3.23236	+	12.0633i	0.138206	+	0.515791i	−0.861758	+	0.507319i	$0.830637\pi$
$548$		0			0
$549$	−2.49348	−	33.5410i	−0.106419	−	1.43149i
$550$		0			0
$551$	−9.35956	−	5.40375i	−0.398731	−	0.230207i
$552$		0			0
$553$	−3.22914	+	1.86435i	−0.137317	+	0.0792800i
$554$		0			0
$555$	0.801527	+	0.297674i	0.0340229	+	0.0126356i
$556$		0			0
$557$	−4.41323	+	4.41323i	−0.186995	+	0.186995i	−0.794395	−	0.607401i	$-0.792212\pi$
$557$	−4.41323	+	4.41323i	−0.186995	+	0.186995i	0.607401	+	0.794395i	$0.292212\pi$
$558$		0			0
$559$		−	4.83349i		−	0.204435i
$560$		0			0
$561$	−18.6153	+	26.2193i	−0.785938	+	1.10698i
$562$		0			0
$563$	9.09152	−	33.9300i	0.383162	−	1.42998i	−0.457882	−	0.889013i	$-0.651392\pi$
$563$	9.09152	−	33.9300i	0.383162	−	1.42998i	0.841044	−	0.540967i	$-0.181942\pi$
$564$		0			0
$565$	0.449782	+	1.67861i	0.0189225	+	0.0706197i
$566$		0			0
$567$	9.09543	−	7.23568i	0.381972	−	0.303870i
$568$		0			0
$569$	−10.8432	+	18.7810i	−0.454572	+	0.787342i	−0.998663	−	0.0516841i	$-0.983541\pi$
$569$	−10.8432	+	18.7810i	−0.454572	+	0.787342i	0.544091	+	0.839026i	$0.316874\pi$
$570$		0			0
$571$	−2.69081	+	10.0422i	−0.112607	+	0.420255i	−0.999097	−	0.0424934i	$-0.986470\pi$
$571$	−2.69081	+	10.0422i	−0.112607	+	0.420255i	0.886490	+	0.462748i	$0.153137\pi$
$572$		0			0
$573$	−5.34633	−	31.5230i	−0.223346	−	1.31689i
$574$		0			0
$575$	12.3635			0.515595
$576$		0			0
$577$	−33.2014			−1.38219			−0.691096	−	0.722763i	$-0.742872\pi$
$577$	−33.2014			−1.38219			−0.691096	+	0.722763i	$0.742872\pi$
$578$		0			0
$579$	−8.49655	−	3.15548i	−0.353105	−	0.131137i
$580$		0			0
$581$	1.31340	−	4.90169i	0.0544891	−	0.203356i
$582$		0			0
$583$	1.41444	−	2.44989i	0.0585803	−	0.101464i
$584$		0			0
$585$	−6.62054	+	7.68395i	−0.273726	+	0.317692i
$586$		0			0
$587$	0.554497	+	2.06941i	0.0228865	+	0.0854137i	0.976425	−	0.215859i	$-0.0692552\pi$
$587$	0.554497	+	2.06941i	0.0228865	+	0.0854137i	−0.953538	+	0.301273i	$0.902589\pi$
$588$		0			0
$589$	5.57282	−	20.7981i	0.229624	−	0.856969i
$590$		0			0
$591$	−35.0136	−	3.29384i	−1.44027	−	0.135491i
$592$		0			0
$593$		−	13.9278i		−	0.571945i	−0.958238	−	0.285973i	$-0.907683\pi$
$593$		−	13.9278i		−	0.571945i	0.958238	−	0.285973i	$-0.0923166\pi$
$594$		0			0
$595$	−3.50844	+	3.50844i	−0.143832	+	0.143832i
$596$		0			0
$597$	−18.4580	+	15.2838i	−0.755436	+	0.625524i
$598$		0			0
$599$	−20.2130	+	11.6700i	−0.825881	+	0.476823i	−0.852440	−	0.522825i	$-0.824878\pi$
$599$	−20.2130	+	11.6700i	−0.825881	+	0.476823i	0.0265594	+	0.999647i	$0.491545\pi$
$600$		0			0
$601$	−10.3379	−	5.96857i	−0.421691	−	0.243463i	0.274110	−	0.961698i	$-0.411617\pi$
$601$	−10.3379	−	5.96857i	−0.421691	−	0.243463i	−0.695800	+	0.718235i	$0.744950\pi$
$602$		0			0
$603$	−0.148890	+	0.308703i	−0.00606326	+	0.0125714i
$604$		0			0
$605$	0.00865733	+	0.0323096i	0.000351971	+	0.00131357i
$606$		0			0
$607$	10.3919	−	5.99979i	0.421796	−	0.243524i	−0.274050	−	0.961716i	$-0.588363\pi$
$607$	10.3919	−	5.99979i	0.421796	−	0.243524i	0.695845	+	0.718192i	$0.255030\pi$
$608$		0			0
$609$	−6.22422	+	2.85306i	−0.252218	+	0.115612i
$610$		0			0
$611$	−42.6603	−	42.6603i	−1.72585	−	1.72585i
$612$		0			0
$613$	−18.1803	+	18.1803i	−0.734296	+	0.734296i	−0.971468	−	0.237172i	$-0.923780\pi$
$613$	−18.1803	+	18.1803i	−0.734296	+	0.734296i	0.237172	+	0.971468i	$0.423780\pi$
$614$		0			0
$615$	6.75830	−	9.51893i	0.272521	−	0.383840i
$616$		0			0
$617$	18.9672	+	32.8521i	0.763589	+	1.32257i	0.940989	+	0.338436i	$0.109898\pi$
$617$	18.9672	+	32.8521i	0.763589	+	1.32257i	−0.177401	+	0.984139i	$0.556769\pi$
$618$		0			0
$619$	0.00230201		0.000616823i	9.25258e−5		2.47922e-5i	−0.258773	−	0.965938i	$-0.583318\pi$
$619$	0.00230201		0.000616823i	9.25258e−5		2.47922e-5i	0.258865	+	0.965913i	$0.416651\pi$
$620$		0			0
$621$	12.1490	+	7.33529i	0.487523	+	0.294355i
$622$		0			0
$623$	8.22368	−	14.2438i	0.329475	−	0.570667i
$624$		0			0
$625$	9.06281	+	15.6972i	0.362512	+	0.627890i
$626$		0			0
$627$	20.0401	−	3.39882i	0.800326	−	0.135736i
$628$		0			0
$629$	2.83406	+	2.83406i	0.113001	+	0.113001i
$630$		0			0
$631$	39.2643			1.56309			0.781543	−	0.623852i	$-0.214433\pi$
$631$	39.2643			1.56309			0.781543	+	0.623852i	$0.214433\pi$
$632$		0			0
$633$	−41.8080	+	19.1640i	−1.66172	+	0.761700i
$634$		0			0
$635$	11.6387	+	3.11858i	0.461868	+	0.123757i
$636$		0			0
$637$	25.3140	−	6.78286i	1.00298	−	0.268747i
$638$		0			0
$639$	0.132014	+	0.0250598i	0.00522239	+	0.000991349i
$640$		0			0
$641$	15.2983	+	8.83246i	0.604245	+	0.348861i	0.770710	−	0.637186i	$-0.219902\pi$
$641$	15.2983	+	8.83246i	0.604245	+	0.348861i	−0.166465	+	0.986047i	$0.553235\pi$
$642$		0			0
$643$	6.60298	+	1.76926i	0.260396	+	0.0697729i	0.386655	−	0.922224i	$-0.373630\pi$
$643$	6.60298	+	1.76926i	0.260396	+	0.0697729i	−0.126259	+	0.991997i	$0.540297\pi$
$644$		0			0
$645$	0.747339	+	0.902549i	0.0294264	+	0.0355378i
$646$		0			0
$647$			4.24252i			0.166791i	0.996517	+	0.0833953i	$0.0265764\pi$
$647$			4.24252i			0.166791i	−0.996517	+	0.0833953i	$0.973424\pi$
$648$		0			0
$649$			16.4392i			0.645293i
$650$		0			0
$651$	−8.69995	−	10.5068i	−0.340978	−	0.411793i
$652$		0			0
$653$	−26.6484	−	7.14041i	−1.04283	−	0.279426i	−0.303545	−	0.952817i	$-0.598170\pi$
$653$	−26.6484	−	7.14041i	−1.04283	−	0.279426i	−0.739286	+	0.673391i	$0.764837\pi$
$654$		0			0
$655$	7.39431	+	4.26911i	0.288919	+	0.166808i
$656$		0			0
$657$	39.1798	+	7.43737i	1.52855	+	0.290159i
$658$		0			0
$659$	10.1504	−	2.71978i	0.395402	−	0.105948i	−0.0556391	−	0.998451i	$-0.517720\pi$
$659$	10.1504	−	2.71978i	0.395402	−	0.105948i	0.451041	+	0.892503i	$0.351053\pi$
$660$		0			0
$661$	−28.3410	−	7.59396i	−1.10234	−	0.295371i	−0.338622	−	0.940922i	$-0.609961\pi$
$661$	−28.3410	−	7.59396i	−1.10234	−	0.295371i	−0.763717	+	0.645552i	$0.776628\pi$
$662$		0			0
$663$	−43.2204	+	19.8114i	−1.67854	+	0.769412i
$664$		0			0
$665$	3.13641			0.121625
$666$		0			0
$667$	−5.91179	−	5.91179i	−0.228905	−	0.228905i
$668$		0			0
$669$	5.46724	−	0.927247i	0.211376	−	0.0358495i
$670$		0			0
$671$	−18.6327	−	32.2728i	−0.719307	−	1.24588i
$672$		0			0
$673$	−5.32418	+	9.22175i	−0.205232	+	0.355472i	−0.950207	−	0.311621i	$-0.899128\pi$
$673$	−5.32418	+	9.22175i	−0.205232	+	0.355472i	0.744975	+	0.667093i	$0.232462\pi$
$674$		0			0
$675$	−0.460823	+	23.5173i	−0.0177371	+	0.905182i
$676$		0			0
$677$	21.2938	−	5.70565i	0.818387	−	0.219286i	0.174746	−	0.984614i	$-0.444090\pi$
$677$	21.2938	−	5.70565i	0.818387	−	0.219286i	0.643641	+	0.765327i	$0.277423\pi$
$678$		0			0
$679$	5.69587	+	9.86554i	0.218587	+	0.378605i
$680$		0			0
$681$	2.88889	−	4.06894i	0.110702	−	0.155922i
$682$		0			0
$683$	−1.68202	+	1.68202i	−0.0643609	+	0.0643609i	−0.738555	−	0.674194i	$-0.764491\pi$
$683$	−1.68202	+	1.68202i	−0.0643609	+	0.0643609i	0.674194	+	0.738555i	$0.264491\pi$
$684$		0			0
$685$	−4.86488	−	4.86488i	−0.185877	−	0.185877i
$686$		0			0
$687$	28.7343	−	13.1712i	1.09628	−	0.502514i
$688$		0			0
$689$	3.62237	−	2.09138i	0.138001	−	0.0796751i
$690$		0			0
$691$	0.595784	+	2.22350i	0.0226647	+	0.0845858i	0.976332	−	0.216278i	$-0.0693917\pi$
$691$	0.595784	+	2.22350i	0.0226647	+	0.0845858i	−0.953667	+	0.300864i	$0.902725\pi$
$692$		0			0
$693$	5.59424	−	11.5989i	0.212508	−	0.440606i
$694$		0			0
$695$	−0.848565	−	0.489919i	−0.0321879	−	0.0185837i
$696$		0			0
$697$	47.3917	−	27.3616i	1.79509	−	1.03639i
$698$		0			0
$699$	−8.01223	+	6.63437i	−0.303050	+	0.250935i
$700$		0			0
$701$	10.2728	−	10.2728i	0.387997	−	0.387997i	−0.485976	−	0.873972i	$-0.661536\pi$
$701$	10.2728	−	10.2728i	0.387997	−	0.387997i	0.873972	+	0.485976i	$0.161536\pi$
$702$		0			0
$703$		−	2.53353i		−	0.0955540i
$704$		0			0
$705$	14.5619	+	1.36989i	0.548433	+	0.0515929i
$706$		0			0
$707$	2.43091	−	9.07228i	0.0914238	−	0.341198i
$708$		0			0
$709$	1.30925	+	4.88619i	0.0491700	+	0.183505i	0.986143	−	0.165896i	$-0.0530517\pi$
$709$	1.30925	+	4.88619i	0.0491700	+	0.183505i	−0.936973	+	0.349401i	$0.886385\pi$
$710$		0			0
$711$	5.65406	−	6.56224i	0.212044	−	0.246103i
$712$		0			0
$713$	8.32834	−	14.4251i	0.311899	−	0.540224i
$714$		0			0
$715$	−2.90859	+	10.8550i	−0.108775	+	0.405955i
$716$		0			0
$717$	19.5099	+	7.24566i	0.728610	+	0.270594i
$718$		0			0
$719$	−6.73858			−0.251307			−0.125653	−	0.992074i	$-0.540103\pi$
$719$	−6.73858			−0.251307			−0.125653	+	0.992074i	$0.540103\pi$
$720$		0			0
$721$	24.5544			0.914452
$722$		0			0
$723$	0.880003	+	5.18867i	0.0327277	+	0.192969i
$724$		0			0
$725$	3.58646	−	13.3849i	0.133198	−	0.497101i
$726$		0			0
$727$	4.14056	−	7.17166i	0.153565	−	0.265982i	−0.778971	−	0.627060i	$-0.784258\pi$
$727$	4.14056	−	7.17166i	0.153565	−	0.265982i	0.932536	+	0.361078i	$0.117591\pi$
$728$		0			0
$729$	−14.4057	+	22.8359i	−0.533543	+	0.845773i
$730$		0			0
$731$	1.42166	+	5.30572i	0.0525821	+	0.196239i
$732$		0			0
$733$	−11.7070	+	43.6909i	−0.432406	+	1.61376i	0.314792	+	0.949161i	$0.398065\pi$
$733$	−11.7070	+	43.6909i	−0.432406	+	1.61376i	−0.747198	+	0.664601i	$0.768601\pi$
$734$		0			0
$735$	−3.67810	+	5.18053i	−0.135669	+	0.191087i
$736$		0			0
$737$			0.379742i			0.0139880i
$738$		0			0
$739$	−22.0530	+	22.0530i	−0.811234	+	0.811234i	−0.984819	−	0.173585i	$-0.944465\pi$
$739$	−22.0530	+	22.0530i	−0.811234	+	0.811234i	0.173585	+	0.984819i	$0.444465\pi$
$740$		0			0
$741$	28.1740	+	10.4634i	1.03500	+	0.384381i
$742$		0			0
$743$	−29.9386	+	17.2851i	−1.09834	+	0.634128i	−0.935785	−	0.352571i	$-0.885307\pi$
$743$	−29.9386	+	17.2851i	−1.09834	+	0.634128i	−0.162557	+	0.986699i	$0.551974\pi$
$744$		0			0
$745$	−3.41062	−	1.96912i	−0.124955	−	0.0721431i
$746$		0			0
$747$	0.873977	+	11.7563i	0.0319772	+	0.430140i
$748$		0			0
$749$	−3.91756	−	14.6205i	−0.143144	−	0.534222i
$750$		0			0
$751$	38.8676	−	22.4402i	1.41830	−	0.818855i	0.422149	−	0.906526i	$-0.361276\pi$
$751$	38.8676	−	22.4402i	1.41830	−	0.818855i	0.996149	+	0.0876713i	$0.0279425\pi$
$752$		0			0
$753$	0.677674	−	7.20367i	0.0246958	−	0.262516i
$754$		0			0
$755$	7.88134	+	7.88134i	0.286832	+	0.286832i
$756$		0			0
$757$	27.6111	−	27.6111i	1.00354	−	1.00354i	0.00354931	−	0.999994i	$-0.498870\pi$
$757$	27.6111	−	27.6111i	1.00354	−	1.00354i	0.999994	−	0.00354931i	$-0.00112978\pi$
$758$		0			0
$759$	15.6551	+	1.47272i	0.568243	+	0.0534565i
$760$		0			0
$761$	−17.8578	−	30.9307i	−0.647346	−	1.12124i	−0.983754	−	0.179520i	$-0.942545\pi$
$761$	−17.8578	−	30.9307i	−0.647346	−	1.12124i	0.336408	−	0.941716i	$-0.390788\pi$
$762$		0			0
$763$	25.3672	−	6.79711i	0.918353	−	0.246072i
$764$		0			0
$765$	5.00731	−	10.3820i	0.181040	−	0.375361i
$766$		0			0
$767$	−12.1534	+	21.0502i	−0.438832	+	0.760079i
$768$		0			0
$769$	−22.6077	−	39.1577i	−0.815254	−	1.41206i	−0.909145	−	0.416479i	$-0.863264\pi$
$769$	−22.6077	−	39.1577i	−0.815254	−	1.41206i	0.0938910	−	0.995582i	$-0.470069\pi$
$770$		0			0
$771$	−1.16559	+	3.13851i	−0.0419778	+	0.113031i
$772$		0			0
$773$	5.57961	+	5.57961i	0.200685	+	0.200685i	0.800293	−	0.599609i	$-0.204677\pi$
$773$	5.57961	+	5.57961i	0.200685	+	0.200685i	−0.599609	+	0.800293i	$0.704677\pi$
$774$		0			0
$775$	27.6073			0.991684
$776$		0			0
$777$	−1.30877	−	0.929208i	−0.0469519	−	0.0333352i
$778$		0			0
$779$	−33.4132	−	8.95305i	−1.19715	−	0.320776i
$780$		0			0
$781$	0.143808	−	0.0385333i	0.00514586	−	0.00137883i
$782$		0			0
$783$	11.4655	−	11.0248i	0.409743	−	0.393993i
$784$		0			0
$785$	4.66717	+	2.69459i	0.166578	+	0.0961741i
$786$		0			0
$787$	−8.95529	−	2.39956i	−0.319221	−	0.0855351i	0.0956504	−	0.995415i	$-0.469507\pi$
$787$	−8.95529	−	2.39956i	−0.319221	−	0.0855351i	−0.414872	+	0.909880i	$0.636174\pi$
$788$		0			0
$789$	−2.99706	+	0.508304i	−0.106698	+	0.0180961i
$790$		0			0
$791$		−	3.26235i		−	0.115996i
$792$		0			0
$793$		−	55.1001i		−	1.95666i
$794$		0			0
$795$	−0.353038	+	0.950600i	−0.0125210	+	0.0337143i
$796$		0			0
$797$	−24.5310	−	6.57307i	−0.868934	−	0.232830i	−0.203307	−	0.979115i	$-0.565169\pi$
$797$	−24.5310	−	6.57307i	−0.868934	−	0.232830i	−0.665627	+	0.746285i	$0.731836\pi$
$798$		0			0
$799$	59.3759	+	34.2807i	2.10057	+	1.21276i
$800$		0			0
$801$	−7.12576	+	37.5383i	−0.251776	+	1.32635i
$802$		0			0
$803$	42.6801	−	11.4361i	1.50615	−	0.403571i
$804$		0			0
$805$	2.34361	+	0.627969i	0.0826014	+	0.0221330i
$806$		0			0
$807$	3.25806	−	34.6331i	0.114689	−	1.21914i
$808$		0			0
$809$	33.1931			1.16701			0.583503	−	0.812111i	$-0.301682\pi$
$809$	33.1931			1.16701			0.583503	+	0.812111i	$0.301682\pi$
$810$		0			0
$811$	−7.35128	−	7.35128i	−0.258138	−	0.258138i	0.566158	−	0.824297i	$-0.308429\pi$
$811$	−7.35128	−	7.35128i	−0.258138	−	0.258138i	−0.824297	+	0.566158i	$0.808429\pi$
$812$		0			0
$813$	12.5613	+	15.1700i	0.440543	+	0.532037i
$814$		0			0
$815$	−2.38234	−	4.12633i	−0.0834497	−	0.144539i
$816$		0			0
$817$	1.73610	−	3.00701i	0.0607383	−	0.105202i
$818$		0			0
$819$	15.7384	−	10.7165i	0.549943	−	0.374466i
$820$		0			0
$821$	38.6179	−	10.3476i	1.34777	−	0.361135i	0.488462	−	0.872585i	$-0.337558\pi$
$821$	38.6179	−	10.3476i	1.34777	−	0.361135i	0.859313	+	0.511450i	$0.170891\pi$
$822$		0			0
$823$	−11.8717	−	20.5623i	−0.413821	−	0.716758i	0.581483	−	0.813558i	$-0.302473\pi$
$823$	−11.8717	−	20.5623i	−0.413821	−	0.716758i	−0.995304	+	0.0968000i	$0.969139\pi$
$824$		0			0
$825$	10.8597	+	23.6914i	0.378086	+	0.824829i
$826$		0			0
$827$	−25.1545	+	25.1545i	−0.874708	+	0.874708i	−0.992981	−	0.118273i	$-0.962264\pi$
$827$	−25.1545	+	25.1545i	−0.874708	+	0.874708i	0.118273	+	0.992981i	$0.462264\pi$
$828$		0			0
$829$	6.12372	+	6.12372i	0.212686	+	0.212686i	0.805407	−	0.592722i	$-0.201947\pi$
$829$	6.12372	+	6.12372i	0.212686	+	0.212686i	−0.592722	+	0.805407i	$0.701947\pi$
$830$		0			0
$831$	−9.90054	−	7.02924i	−0.343446	−	0.243842i
$832$		0			0
$833$	−25.7922	+	14.8911i	−0.893646	+	0.515947i
$834$		0			0
$835$	−3.86161	−	14.4117i	−0.133637	−	0.498739i
$836$		0			0
$837$	27.1283	+	16.3794i	0.937692	+	0.566156i
$838$		0			0
$839$	35.2084	+	20.3276i	1.21553	+	0.701786i	0.963958	−	0.266054i	$-0.0857198\pi$
$839$	35.2084	+	20.3276i	1.21553	+	0.701786i	0.251570	+	0.967839i	$0.419053\pi$
$840$		0			0
$841$	16.9997	−	9.81476i	0.586195	−	0.338440i
$842$		0			0
$843$	2.99109	+	17.6361i	0.103019	+	0.607418i
$844$		0			0
$845$	−5.42593	+	5.42593i	−0.186658	+	0.186658i
$846$		0			0
$847$		−	0.0627931i		−	0.00215760i
$848$		0			0
$849$	−17.4289	−	38.0228i	−0.598159	−	1.30494i
$850$		0			0
$851$	0.507262	−	1.89313i	0.0173887	−	0.0648955i
$852$		0			0
$853$	11.1499	+	41.6120i	0.381765	+	1.42477i	0.843203	+	0.537595i	$0.180667\pi$
$853$	11.1499	+	41.6120i	0.381765	+	1.42477i	−0.461437	+	0.887173i	$0.652666\pi$
$854$		0			0
$855$	−6.87870	+	2.40237i	−0.235247	+	0.0821592i
$856$		0			0
$857$	4.72246	−	8.17953i	0.161316	−	0.279408i	−0.774025	−	0.633155i	$-0.781759\pi$
$857$	4.72246	−	8.17953i	0.161316	−	0.279408i	0.935341	+	0.353748i	$0.115093\pi$
$858$		0			0
$859$	5.87045	−	21.9088i	0.200297	−	0.747519i	−0.790535	−	0.612417i	$-0.790197\pi$
$859$	5.87045	−	21.9088i	0.200297	−	0.747519i	0.990832	−	0.135102i	$-0.0431361\pi$
$860$		0			0
$861$	−16.8797	+	13.9769i	−0.575260	+	0.476333i
$862$		0			0
$863$	3.58147			0.121915			0.0609573	−	0.998140i	$-0.480585\pi$
$863$	3.58147			0.121915			0.0609573	+	0.998140i	$0.480585\pi$
$864$		0			0
$865$	−5.47380			−0.186115
$866$		0			0
$867$	18.9368	−	15.6803i	0.643128	−	0.532530i
$868$		0			0
$869$	2.48399	−	9.27039i	0.0842637	−	0.314476i
$870$		0			0
$871$	−0.280740	+	0.486256i	−0.00951252	+	0.0164762i
$872$		0			0
$873$	−20.0487	−	17.2741i	−0.678545	−	0.584638i
$874$		0			0
$875$	2.19044	+	8.17482i	0.0740503	+	0.276359i
$876$		0			0
$877$	4.52743	−	16.8966i	0.152881	−	0.570558i	−0.846397	−	0.532553i	$-0.821233\pi$
$877$	4.52743	−	16.8966i	0.152881	−	0.570558i	0.999278	−	0.0380056i	$-0.0121005\pi$
$878$		0			0
$879$	−14.0697	−	30.6944i	−0.474559	−	1.03530i
$880$		0			0
$881$		−	46.1363i		−	1.55437i	−0.629272	−	0.777185i	$-0.716647\pi$
$881$		−	46.1363i		−	1.55437i	0.629272	−	0.777185i	$-0.283353\pi$
$882$		0			0
$883$	−19.7311	+	19.7311i	−0.664003	+	0.664003i	−0.956321	−	0.292318i	$-0.905573\pi$
$883$	−19.7311	+	19.7311i	−0.664003	+	0.664003i	0.292318	+	0.956321i	$0.405573\pi$
$884$		0			0
$885$	−0.985345	−	5.80979i	−0.0331220	−	0.195294i
$886$		0			0
$887$	−29.7760	+	17.1912i	−0.999780	+	0.577223i	−0.908183	−	0.418573i	$-0.862530\pi$
$887$	−29.7760	+	17.1912i	−0.999780	+	0.577223i	−0.0915965	+	0.995796i	$0.529197\pi$
$888$		0			0
$889$	−19.5891	−	11.3098i	−0.656999	−	0.379318i
$890$		0			0
$891$	−3.38485	+	29.7234i	−0.113397	+	0.995772i
$892$		0			0
$893$	−11.2171	−	41.8626i	−0.375364	−	1.40088i
$894$		0			0
$895$	7.98697	−	4.61128i	0.266975	−	0.154138i
$896$		0			0
$897$	18.9574	+	13.4595i	0.632970	+	0.449399i
$898$		0			0
$899$	−13.2008	−	13.2008i	−0.440272	−	0.440272i
$900$		0			0
$901$	−3.36115	+	3.36115i	−0.111976	+	0.111976i
$902$		0			0
$903$	−0.916621	−	1.99969i	−0.0305033	−	0.0665457i
$904$		0			0
$905$	−3.89178	−	6.74076i	−0.129367	−	0.224070i
$906$		0			0
$907$	53.7121	−	14.3921i	1.78348	−	0.477883i	0.792271	−	0.610170i	$-0.208899\pi$
$907$	53.7121	−	14.3921i	1.78348	−	0.477883i	0.991211	+	0.132287i	$0.0422322\pi$
$908$		0			0
$909$	1.61760	+	21.7591i	0.0536524	+	0.721704i
$910$		0			0
$911$	6.01435	−	10.4172i	0.199264	−	0.345136i	−0.749026	−	0.662541i	$-0.769478\pi$
$911$	6.01435	−	10.4172i	0.199264	−	0.345136i	0.948290	+	0.317405i	$0.102811\pi$
$912$		0			0
$913$	6.53085	+	11.3118i	0.216140	+	0.374365i
$914$		0			0
$915$	8.51940	+	10.2887i	0.281643	+	0.340136i
$916$		0			0
$917$	−11.3338	−	11.3338i	−0.374275	−	0.374275i
$918$		0			0
$919$	11.8860			0.392084			0.196042	−	0.980595i	$-0.437191\pi$
$919$	11.8860			0.392084			0.196042	+	0.980595i	$0.437191\pi$
$920$		0			0
$921$	−1.00404	+	10.6730i	−0.0330844	+	0.351687i
$922$		0			0
$923$	0.212633	+	0.0569747i	0.00699889	+	0.00187535i
$924$		0			0
$925$	3.13773	−	0.840752i	0.103168	−	0.0276438i
$926$		0			0
$927$	−53.8521	+	18.8077i	−1.76873	+	0.617725i
$928$		0			0
$929$	−3.44934	−	1.99148i	−0.113169	−	0.0653382i	0.442347	−	0.896844i	$-0.354146\pi$
$929$	−3.44934	−	1.99148i	−0.113169	−	0.0653382i	−0.555516	+	0.831506i	$0.687479\pi$
$930$		0			0
$931$	18.1846	+	4.87255i	0.595977	+	0.159692i
$932$		0			0
$933$	−1.84710	+	4.97355i	−0.0604712	+	0.162827i
$934$		0			0
$935$		−	12.7711i		−	0.417659i
$936$		0			0
$937$			26.0017i			0.849438i	0.905325	+	0.424719i	$0.139627\pi$
$937$			26.0017i			0.849438i	−0.905325	+	0.424719i	$0.860373\pi$
$938$		0			0
$939$	5.11744	−	0.867921i	0.167001	−	0.0283235i
$940$		0			0
$941$	−41.3717	−	11.0855i	−1.34868	−	0.361378i	−0.489033	−	0.872265i	$-0.662650\pi$
$941$	−41.3717	−	11.0855i	−1.34868	−	0.361378i	−0.859648	+	0.510888i	$0.829317\pi$
$942$		0			0
$943$	−23.1747	−	13.3799i	−0.754673	−	0.435710i
$944$		0			0
$945$	−1.28184	+	4.43450i	−0.0416984	+	0.144254i
$946$		0			0
$947$	−17.6066	+	4.71769i	−0.572139	+	0.153304i	−0.533277	−	0.845940i	$-0.679040\pi$
$947$	−17.6066	+	4.71769i	−0.572139	+	0.153304i	−0.0388617	+	0.999245i	$0.512373\pi$
$948$		0			0
$949$	63.1062	+	16.9093i	2.04851	+	0.548898i
$950$		0			0
$951$	−13.5158	−	9.59602i	−0.438280	−	0.311172i
$952$		0			0
$953$	16.9031			0.547545			0.273772	−	0.961795i	$-0.411729\pi$
$953$	16.9031			0.547545			0.273772	+	0.961795i	$0.411729\pi$
$954$		0			0
$955$	8.97930	+	8.97930i	0.290563	+	0.290563i
$956$		0			0
$957$	6.13567	−	16.5211i	0.198338	−	0.534051i
$958$		0			0
$959$	6.45774	+	11.1851i	0.208531	+	0.361187i
$960$		0			0
$961$	3.09688	−	5.36395i	0.0998993	−	0.173031i
$962$		0			0
$963$	19.7907	+	29.0647i	0.637745	+	0.936597i
$964$		0			0
$965$	3.47708	−	0.931682i	0.111931	−	0.0299919i
$966$		0			0
$967$	−1.50617	−	2.60876i	−0.0484351	−	0.0838921i	0.840791	−	0.541359i	$-0.182090\pi$
$967$	−1.50617	−	2.60876i	−0.0484351	−	0.0838921i	−0.889227	+	0.457467i	$0.848757\pi$
$968$		0			0
$969$	−34.0042	−	3.19889i	−1.09237	−	0.102763i
$970$		0			0
$971$	35.4934	−	35.4934i	1.13904	−	1.13904i	0.150413	−	0.988623i	$-0.451940\pi$
$971$	35.4934	−	35.4934i	1.13904	−	1.13904i	0.988623	−	0.150413i	$-0.0480604\pi$
$972$		0			0
$973$	1.30066	+	1.30066i	0.0416972	+	0.0416972i
$974$		0			0
$975$	−3.60914	+	38.3652i	−0.115585	+	1.22867i
$976$		0			0
$977$	8.03784	−	4.64065i	0.257153	−	0.148467i	−0.365882	−	0.930661i	$-0.619233\pi$
$977$	8.03784	−	4.64065i	0.257153	−	0.148467i	0.623035	+	0.782194i	$0.285899\pi$
$978$		0			0
$979$	10.9570	+	40.8920i	0.350186	+	1.30691i
$980$		0			0
$981$	−50.4283	+	34.3375i	−1.61005	+	1.09631i
$982$		0			0
$983$	−11.0480	−	6.37856i	−0.352376	−	0.203444i	0.313355	−	0.949636i	$-0.398547\pi$
$983$	−11.0480	−	6.37856i	−0.352376	−	0.203444i	−0.665731	+	0.746192i	$0.731880\pi$
$984$		0			0
$985$	12.0963	−	6.98379i	0.385420	−	0.222522i
$986$		0			0
$987$	−25.7394	−	9.55919i	−0.819294	−	0.304273i
$988$		0			0
$989$	1.89932	−	1.89932i	0.0603949	−	0.0603949i
$990$		0			0
$991$			6.60967i			0.209963i	0.994474	+	0.104982i	$0.0334784\pi$
$991$			6.60967i			0.209963i	−0.994474	+	0.104982i	$0.966522\pi$
$992$		0			0
$993$	15.1424	−	21.3278i	0.480530	−	0.676817i
$994$		0			0
$995$	2.46340	−	9.19352i	0.0780949	−	0.291454i
$996$		0			0
$997$	−9.80194	−	36.5814i	−0.310431	−	1.15854i	−0.928169	−	0.372159i	$-0.878618\pi$
$997$	−9.80194	−	36.5814i	−0.310431	−	1.15854i	0.617738	−	0.786384i	$-0.288049\pi$
$998$		0			0
$999$	3.58211	+	1.03545i	0.113333	+	0.0327602i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.y.a.47.5		88
3.2	odd	2		1728.2.z.a.1007.10		88
4.3	odd	2		144.2.u.a.83.8	yes	88
9.4	even	3		1728.2.z.a.1583.10		88
9.5	odd	6	inner	576.2.y.a.239.7		88
12.11	even	2		432.2.v.a.35.15		88
16.5	even	4		144.2.u.a.11.15	✓	88
16.11	odd	4	inner	576.2.y.a.335.7		88
36.23	even	6		144.2.u.a.131.15	yes	88
36.31	odd	6		432.2.v.a.179.8		88
48.5	odd	4		432.2.v.a.251.8		88
48.11	even	4		1728.2.z.a.143.10		88
144.5	odd	12		144.2.u.a.59.8	yes	88
144.59	even	12	inner	576.2.y.a.527.5		88
144.85	even	12		432.2.v.a.395.15		88
144.139	odd	12		1728.2.z.a.719.10		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.15	✓	88	16.5	even	4
144.2.u.a.59.8	yes	88	144.5	odd	12
144.2.u.a.83.8	yes	88	4.3	odd	2
144.2.u.a.131.15	yes	88	36.23	even	6
432.2.v.a.35.15		88	12.11	even	2
432.2.v.a.179.8		88	36.31	odd	6
432.2.v.a.251.8		88	48.5	odd	4
432.2.v.a.395.15		88	144.85	even	12
576.2.y.a.47.5		88	1.1	even	1	trivial
576.2.y.a.239.7		88	9.5	odd	6	inner
576.2.y.a.335.7		88	16.11	odd	4	inner
576.2.y.a.527.5		88	144.59	even	12	inner
1728.2.z.a.143.10		88	48.11	even	4
1728.2.z.a.719.10		88	144.139	odd	12
1728.2.z.a.1007.10		88	3.2	odd	2
1728.2.z.a.1583.10		88	9.4	even	3

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.33407 + 1.10465i) q^{3} +(0.178044 - 0.664471i) q^{5} +(-0.645693 + 1.11837i) q^{7} +(0.559489 - 2.94737i) q^{9} +(-0.860301 - 3.21069i) q^{11} +(1.27203 - 4.74727i) q^{13} +(0.496485 + 1.08313i) q^{15} +5.58523i q^{17} +(2.49649 - 2.49649i) q^{19} +(-0.374013 - 2.20525i) q^{21} +(2.36529 - 1.36560i) q^{23} +(3.92031 + 2.26339i) q^{25} +(2.50942 + 4.55004i) q^{27} +(-0.792277 - 2.95682i) q^{29} +(5.28160 - 3.04933i) q^{31} +(4.69439 + 3.33295i) q^{33} +(0.628165 + 0.628165i) q^{35} +(0.507420 - 0.507420i) q^{37} +(3.54711 + 7.73835i) q^{39} +(-4.89892 - 8.48518i) q^{41} +(0.949956 - 0.254540i) q^{43} +(-1.85883 - 0.896527i) q^{45} +(6.13774 - 10.6309i) q^{47} +(2.66616 + 4.61793i) q^{49} +(-6.16973 - 7.45109i) q^{51} +(0.601793 + 0.601793i) q^{53} -2.28658 q^{55} +(-0.572741 + 6.08824i) q^{57} +(-4.77715 - 1.28003i) q^{59} +(10.8292 - 2.90167i) q^{61} +(2.93500 + 2.52881i) q^{63} +(-2.92795 - 1.69045i) q^{65} +(-0.110351 - 0.0295686i) q^{67} +(-1.64695 + 4.43463i) q^{69} +0.0447904i q^{71} +13.2931i q^{73} +(-7.73022 + 1.31105i) q^{75} +(4.14624 + 1.11098i) q^{77} +(2.50052 + 1.44368i) q^{79} +(-8.37394 - 3.29804i) q^{81} +(-3.79568 + 1.01705i) q^{83} +(3.71122 + 0.994419i) q^{85} +(4.32321 + 3.06941i) q^{87} -12.7362 q^{89} +(4.48788 + 4.48788i) q^{91} +(-3.67758 + 9.90236i) q^{93} +(-1.21436 - 2.10333i) q^{95} +(4.41066 - 7.63949i) q^{97} +(-9.94440 + 0.739279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55}+ \cdots - 46 q^{99}+O(q^{100}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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