LMFDB - Embedded newform 576.2.y.a.335.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(47,576)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			335.7
Character	$\chi$	$=$	576.335
Dual form			576.2.y.a.239.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−1.10465	−	1.33407i	−0.637771	−	0.770226i
$3$	−1.10465	−	1.33407i	−0.637771	−	0.770226i
$4$		0			0
$5$	0.664471	+	0.178044i	0.297161	+	0.0796239i	0.404319	−	0.914618i	$-0.367509\pi$
$5$	0.664471	+	0.178044i	0.297161	+	0.0796239i	−0.107158	+	0.994242i	$0.534175\pi$
$6$		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
$11$	−3.21069	+	0.860301i	−0.968058	+	0.259390i	−0.708008	−	0.706205i	$-0.750406\pi$
$11$	−3.21069	+	0.860301i	−0.968058	+	0.259390i	−0.260051	+	0.965595i	$0.583739\pi$
$12$		0			0
$13$	−4.74727	−	1.27203i	−1.31666	−	0.352797i	−0.468933	−	0.883234i	$-0.655361\pi$
$13$	−4.74727	−	1.27203i	−1.31666	−	0.352797i	−0.847725	+	0.530437i	$0.822028\pi$
$14$		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	0.932891	−	0.360158i	$-0.117277\pi$
$19$	2.49649	+	2.49649i	0.572733	+	0.572733i	−0.360158	+	0.932891i	$0.617277\pi$
$20$		0			0
$21$	2.20525	−	0.374013i	0.481226	−	0.0816163i
$22$		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
$27$	4.55004	−	2.50942i	0.875655	−	0.482937i
$28$		0			0
$29$	−2.95682	+	0.792277i	−0.549067	+	0.147122i	−0.522679	−	0.852530i	$-0.675067\pi$
$29$	−2.95682	+	0.792277i	−0.549067	+	0.147122i	−0.0263884	+	0.999652i	$0.508401\pi$
$30$		0			0
$31$	−5.28160	+	3.04933i	−0.948604	+	0.547677i	−0.892647	−	0.450757i	$-0.851154\pi$
$31$	−5.28160	+	3.04933i	−0.948604	+	0.547677i	−0.0559568	+	0.998433i	$0.517821\pi$
$32$		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	0.747585	−	0.664166i	$-0.231213\pi$
$37$	0.507420	+	0.507420i	0.0834193	+	0.0834193i	−0.664166	+	0.747585i	$0.731213\pi$
$38$		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	$0.110635\pi$
$41$	4.89892	+	8.48518i	0.765083	+	1.32516i	−0.175120	+	0.984547i	$0.556031\pi$
$42$		0			0
$43$	−0.254540	−	0.949956i	−0.0388170	−	0.144867i	0.943798	−	0.330524i	$-0.107225\pi$
$43$	−0.254540	−	0.949956i	−0.0388170	−	0.144867i	−0.982615	+	0.185657i	$0.940559\pi$
$44$		0			0
$45$	−0.896527	+	1.85883i	−0.133646	+	0.277097i
$46$		0			0
$47$	−6.13774	+	10.6309i	−0.895281	+	1.55067i	−0.0618250	+	0.998087i	$0.519692\pi$
$47$	−6.13774	+	10.6309i	−0.895281	+	1.55067i	−0.833456	+	0.552586i	$0.813641\pi$
$48$		0			0
$49$	2.66616	+	4.61793i	0.380880	+	0.659704i
$50$		0			0
$51$	7.45109	−	6.16973i	1.04336	−	0.863935i
$52$		0			0
$53$	−0.601793	+	0.601793i	−0.0826626	+	0.0826626i	−0.747229	−	0.664567i	$-0.768616\pi$
$53$	−0.601793	+	0.601793i	−0.0826626	+	0.0826626i	0.664567	+	0.747229i	$0.268616\pi$
$54$		0			0
$55$	−2.28658			−0.308322
$56$		0			0
$57$	0.572741	−	6.08824i	0.0758614	−	0.806407i
$58$		0			0
$59$	−1.28003	+	4.77715i	−0.166646	+	0.621932i	0.831178	+	0.556006i	$0.187667\pi$
$59$	−1.28003	+	4.77715i	−0.166646	+	0.621932i	−0.997824	+	0.0659263i	$0.979000\pi$
$60$		0			0
$61$	−2.90167	−	10.8292i	−0.371520	−	1.38653i	−0.858363	−	0.513043i	$-0.828518\pi$
$61$	−2.90167	−	10.8292i	−0.371520	−	1.38653i	0.486842	−	0.873490i	$-0.338149\pi$
$62$		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
$67$	0.0295686	−	0.110351i	0.00361238	−	0.0134816i	−0.964096	−	0.265554i	$-0.914445\pi$
$67$	0.0295686	−	0.110351i	0.00361238	−	0.0134816i	0.967708	+	0.252072i	$0.0811120\pi$
$68$		0			0
$69$	−4.43463	−	1.64695i	−0.533866	−	0.198269i
$70$		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	$-0.716274\pi$
$73$		−	13.2931i		−	1.55585i	0.628360	−	0.777923i	$-0.283726\pi$
$74$		0			0
$75$	1.31105	+	7.73022i	0.151387	+	0.892609i
$76$		0			0
$77$	1.11098	−	4.14624i	0.126608	−	0.472507i
$78$		0			0
$79$	−2.50052	−	1.44368i	−0.281331	−	0.162426i	0.352695	−	0.935738i	$-0.385265\pi$
$79$	−2.50052	−	1.44368i	−0.281331	−	0.162426i	−0.634026	+	0.773312i	$0.718599\pi$
$80$		0			0
$81$	−8.37394	−	3.29804i	−0.930438	−	0.366449i
$82$		0			0
$83$	−1.01705	−	3.79568i	−0.111636	−	0.416630i	0.887378	−	0.461043i	$-0.152525\pi$
$83$	−1.01705	−	3.79568i	−0.111636	−	0.416630i	−0.999013	+	0.0444135i	$0.985858\pi$
$84$		0			0
$85$	−0.994419	+	3.71122i	−0.107860	+	0.402539i
$86$		0			0
$87$	4.32321	+	3.06941i	0.463497	+	0.329076i
$88$		0			0
$89$	12.7362			1.35003			0.675017	−	0.737802i	$-0.264136\pi$
$89$	12.7362			1.35003			0.675017	+	0.737802i	$0.264136\pi$
$90$		0			0
$91$	4.48788	−	4.48788i	0.470458	−	0.470458i
$92$		0			0
$93$	9.90236	+	3.67758i	1.02683	+	0.381347i
$94$		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
$99$	−0.739279	−	9.94440i	−0.0743004	−	0.999450i
$100$		0			0
$101$	−1.88240	−	7.02523i	−0.187306	−	0.699037i	−0.994125	−	0.108238i	$-0.965479\pi$
$101$	−1.88240	−	7.02523i	−0.187306	−	0.699037i	0.806819	−	0.590799i	$-0.201187\pi$
$102$		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	$-0.0582764\pi$
$107$	8.28797	+	8.28797i	0.801228	+	0.801228i	−0.182060	+	0.983287i	$0.558276\pi$
$108$		0			0
$109$	−14.3799	+	14.3799i	−1.37735	+	1.37735i	−0.528273	+	0.849074i	$0.677160\pi$
$109$	−14.3799	+	14.3799i	−1.37735	+	1.37735i	−0.849074	+	0.528273i	$0.822840\pi$
$110$		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
$115$	1.81480	−	0.486275i	0.169231	−	0.0453454i
$116$		0			0
$117$	6.40518	−	13.2803i	0.592159	−	1.22776i
$118$		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
$123$	5.90823	−	15.9087i	0.532727	−	1.43444i
$124$		0			0
$125$	−4.63408	−	4.63408i	−0.414485	−	0.414485i
$126$		0			0
$127$		−	17.5157i		−	1.55427i	−0.629333	−	0.777135i	$-0.716672\pi$
$127$		−	17.5157i		−	1.55427i	0.629333	−	0.777135i	$-0.283328\pi$
$128$		0			0
$129$	−0.986131	+	1.38895i	−0.0868240	+	0.122290i
$130$		0			0
$131$	−11.9889	−	3.21241i	−1.04747	−	0.280669i	−0.306266	−	0.951946i	$-0.599080\pi$
$131$	−11.9889	−	3.21241i	−1.04747	−	0.280669i	−0.741207	+	0.671277i	$0.765746\pi$
$132$		0			0
$133$	−4.40397	+	1.18004i	−0.381872	+	0.102322i
$134$		0			0
$135$	3.47016	−	0.857326i	0.298663	−	0.0737869i
$136$		0			0
$137$	−5.00063	+	8.66134i	−0.427232	+	0.739988i	−0.996626	−	0.0820768i	$-0.973845\pi$
$137$	−5.00063	+	8.66134i	−0.427232	+	0.739988i	0.569394	+	0.822065i	$0.307178\pi$
$138$		0			0
$139$	−1.37583	−	0.368654i	−0.116697	−	0.0312688i	0.199998	−	0.979796i	$-0.435906\pi$
$139$	−1.37583	−	0.368654i	−0.116697	−	0.0312688i	−0.316695	+	0.948528i	$0.602573\pi$
$140$		0			0
$141$	20.9624	−	3.55524i	1.76535	−	0.299405i
$142$		0			0
$143$	16.3363			1.36611
$144$		0			0
$145$	−2.10578			−0.174876
$146$		0			0
$147$	3.21546	−	8.65805i	0.265207	−	0.714104i
$148$		0			0
$149$	5.52986	+	1.48172i	0.453024	+	0.121387i	0.478114	−	0.878298i	$-0.341321\pi$
$149$	5.52986	+	1.48172i	0.453024	+	0.121387i	−0.0250901	+	0.999685i	$0.507987\pi$
$150$		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
$155$	−4.05239	+	1.08583i	−0.325496	+	0.0872163i
$156$		0			0
$157$	7.56718	+	2.02762i	0.603927	+	0.161822i	0.547810	−	0.836602i	$-0.315462\pi$
$157$	7.56718	+	2.02762i	0.603927	+	0.161822i	0.0561165	+	0.998424i	$0.482128\pi$
$158$		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	0.872402	−	0.488789i	$-0.162561\pi$
$163$	4.89763	+	4.89763i	0.383612	+	0.383612i	−0.488789	+	0.872402i	$0.662561\pi$
$164$		0			0
$165$	2.52587	+	3.05046i	0.196639	+	0.237478i
$166$		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
$171$	−8.75482	+	5.96130i	−0.669497	+	0.455872i
$172$		0			0
$173$	−7.68601	+	2.05946i	−0.584356	+	0.156578i	−0.538873	−	0.842387i	$-0.681150\pi$
$173$	−7.68601	+	2.05946i	−0.584356	+	0.156578i	−0.0454836	+	0.998965i	$0.514483\pi$
$174$		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	$-0.917045\pi$
$179$	−9.47991	+	9.47991i	−0.708562	+	0.708562i	0.257671	+	0.966233i	$0.417045\pi$
$180$		0			0
$181$	8.00075	+	8.00075i	0.594691	+	0.594691i	0.938895	−	0.344204i	$-0.111851\pi$
$181$	8.00075	+	8.00075i	0.594691	+	0.594691i	−0.344204	+	0.938895i	$0.611851\pi$
$182$		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
$187$	−4.80498	−	17.9324i	−0.351375	−	1.31135i
$188$		0			0
$189$	−0.131462	+	6.70895i	−0.00956248	+	0.488004i
$190$		0			0
$191$	9.22986	−	15.9866i	0.667850	−	1.15675i	−0.310655	−	0.950523i	$-0.600548\pi$
$191$	9.22986	−	15.9866i	0.667850	−	1.15675i	0.978504	−	0.206227i	$-0.0661184\pi$
$192$		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
$195$	0.979182	+	5.77345i	0.0701207	+	0.413445i
$196$		0			0
$197$	−14.3573	+	14.3573i	−1.02292	+	1.02292i	−0.0231869	+	0.999731i	$0.507381\pi$
$197$	−14.3573	+	14.3573i	−1.02292	+	1.02292i	−0.999731	+	0.0231869i	$0.992619\pi$
$198$		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
$203$	1.02314	−	3.81839i	0.0718100	−	0.267999i
$204$		0			0
$205$	1.74445	+	6.51038i	0.121838	+	0.454705i
$206$		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
$211$	−6.87239	+	25.6481i	−0.473115	+	1.76569i	0.155358	+	0.987858i	$0.450347\pi$
$211$	−6.87239	+	25.6481i	−0.473115	+	1.76569i	−0.628473	+	0.777831i	$0.716320\pi$
$212$		0			0
$213$	0.0597536	−	0.0494778i	0.00409425	−	0.00339017i
$214$		0			0
$215$		−	0.676538i		−	0.0461395i
$216$		0			0
$217$		−	7.87574i		−	0.534640i
$218$		0			0
$219$	−17.7340	+	14.6843i	−1.19835	+	0.992273i
$220$		0			0
$221$	7.10457	−	26.5146i	0.477905	−	1.78357i
$222$		0			0
$223$	2.77266	+	1.60079i	0.185671	+	0.107197i	0.589954	−	0.807437i	$-0.299146\pi$
$223$	2.77266	+	1.60079i	0.185671	+	0.107197i	−0.404284	+	0.914634i	$0.632479\pi$
$224$		0			0
$225$	8.86441	−	10.2882i	0.590960	−	0.685882i
$226$		0			0
$227$	−0.745680	−	2.78291i	−0.0494925	−	0.184708i	0.936754	−	0.349988i	$-0.113814\pi$
$227$	−0.745680	−	2.78291i	−0.0494925	−	0.184708i	−0.986247	+	0.165279i	$0.947148\pi$
$228$		0			0
$229$	4.72334	−	17.6277i	0.312127	−	1.16487i	−0.614508	−	0.788911i	$-0.710645\pi$
$229$	4.72334	−	17.6277i	0.312127	−	1.16487i	0.926635	−	0.375963i	$-0.122688\pi$
$230$		0			0
$231$	−6.75862	+	3.09802i	−0.444684	+	0.203835i
$232$		0			0
$233$	−6.00585			−0.393456			−0.196728	−	0.980458i	$-0.563032\pi$
$233$	−6.00585			−0.393456			−0.196728	+	0.980458i	$0.563032\pi$
$234$		0			0
$235$	−5.97112	+	5.97112i	−0.389513	+	0.389513i
$236$		0			0
$237$	0.836239	+	4.93063i	0.0543196	+	0.320279i
$238$		0			0
$239$	6.00788	+	10.4059i	0.388617	+	0.673105i	0.992264	−	0.124147i	$-0.0396195\pi$
$239$	6.00788	+	10.4059i	0.388617	+	0.673105i	−0.603647	+	0.797252i	$0.706286\pi$
$240$		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
$243$	4.85048	+	14.8146i	0.311158	+	0.950358i
$244$		0			0
$245$	0.949391	+	3.54317i	0.0606543	+	0.226365i
$246$		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	$-0.207912\pi$
$251$	2.95387	+	2.95387i	0.186447	+	0.186447i	−0.607711	+	0.794158i	$0.707912\pi$
$252$		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
$259$	−0.895122	+	0.239847i	−0.0556202	+	0.0149034i
$260$		0			0
$261$	−0.680824	−	9.15810i	−0.0421420	−	0.566872i
$262$		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
$267$	−14.0691	−	16.9910i	−0.861013	−	1.03983i
$268$		0			0
$269$	14.2013	+	14.2013i	0.865871	+	0.865871i	0.992012	−	0.126141i	$-0.0402592\pi$
$269$	14.2013	+	14.2013i	0.865871	+	0.865871i	−0.126141	+	0.992012i	$0.540259\pi$
$270$		0			0
$271$			11.3712i			0.690754i	0.938464	+	0.345377i	$0.112249\pi$
$271$			11.3712i			0.690754i	−0.938464	+	0.345377i	$0.887751\pi$
$272$		0			0
$273$	−10.9447	−	1.02961i	−0.662404	−	0.0623145i
$274$		0			0
$275$	14.5341	+	3.89439i	0.876437	+	0.234841i
$276$		0			0
$277$	−6.77138	+	1.81439i	−0.406853	+	0.109016i	−0.456441	−	0.889754i	$-0.650876\pi$
$277$	−6.77138	+	1.81439i	−0.406853	+	0.109016i	0.0495877	+	0.998770i	$0.484209\pi$
$278$		0			0
$279$	−6.03251	−	17.2729i	−0.361157	−	1.03410i
$280$		0			0
$281$	−5.16379	+	8.94395i	−0.308046	+	0.533552i	−0.977935	−	0.208910i	$-0.933008\pi$
$281$	−5.16379	+	8.94395i	−0.308046	+	0.533552i	0.669889	+	0.742461i	$0.266342\pi$
$282$		0			0
$283$	23.3260	+	6.25018i	1.38659	+	0.371535i	0.873509	−	0.486807i	$-0.161839\pi$
$283$	23.3260	+	6.25018i	1.38659	+	0.371535i	0.513078	+	0.858342i	$0.328505\pi$
$284$		0			0
$285$	1.46455	−	3.94348i	0.0867523	−	0.233592i
$286$		0			0
$287$	−12.6528			−0.746871
$288$		0			0
$289$	−14.1948			−0.834987
$290$		0			0
$291$	−15.0639	+	2.55484i	−0.883060	+	0.149768i
$292$		0			0
$293$	−18.8302	−	5.04554i	−1.10007	−	0.294763i	−0.337278	−	0.941405i	$-0.609506\pi$
$293$	−18.8302	−	5.04554i	−1.10007	−	0.294763i	−0.762794	+	0.646642i	$0.776173\pi$
$294$		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
$299$	−12.9658	+	3.47416i	−0.749829	+	0.200916i
$300$		0			0
$301$	1.22676	+	0.328709i	0.0707093	+	0.0189465i
$302$		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	0.820879	−	0.571101i	$-0.193484\pi$
$307$	4.37646	+	4.37646i	0.249778	+	0.249778i	−0.571101	+	0.820879i	$0.693484\pi$
$308$		0			0
$309$	−11.4657	+	30.8728i	−0.652259	+	1.75629i
$310$		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	0.571550	−	0.820567i	$-0.306342\pi$
$313$	2.59526	+	1.49837i	0.146693	+	0.0846930i	−0.424857	+	0.905260i	$0.639676\pi$
$314$		0			0
$315$	−1.49998	−	2.20288i	−0.0845143	−	0.124118i
$316$		0			0
$317$	9.24401	−	2.47692i	0.519195	−	0.139118i	0.0103009	−	0.999947i	$-0.496721\pi$
$317$	9.24401	−	2.47692i	0.519195	−	0.139118i	0.508894	+	0.860829i	$0.330054\pi$
$318$		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
$331$	3.90856	+	14.5870i	0.214834	+	0.801772i	0.986225	+	0.165410i	$0.0528947\pi$
$331$	3.90856	+	14.5870i	0.214834	+	0.801772i	−0.771391	+	0.636362i	$0.780439\pi$
$332$		0			0
$333$	−1.77945	+	1.21166i	−0.0975131	+	0.0663984i
$334$		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
$339$	4.10183	+	1.52335i	0.222781	+	0.0827372i
$340$		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
$347$	7.41711	−	27.6810i	0.398171	−	1.48599i	−0.418140	−	0.908382i	$-0.637318\pi$
$347$	7.41711	−	27.6810i	0.398171	−	1.48599i	0.816311	−	0.577612i	$-0.196015\pi$
$348$		0			0
$349$	6.18561	+	23.0850i	0.331108	+	1.23571i	0.908027	+	0.418911i	$0.137588\pi$
$349$	6.18561	+	23.0850i	0.331108	+	1.23571i	−0.576919	+	0.816801i	$0.695745\pi$
$350$		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
$355$	−0.00797469	+	0.0297620i	−0.000423253	+	0.00157960i
$356$		0			0
$357$	2.08895	+	12.3169i	0.110559	+	0.651877i
$358$		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
$363$	−0.0789513	−	0.0293212i	−0.00414387	−	0.00153897i
$364$		0			0
$365$	2.36677	−	8.83291i	0.123883	−	0.462336i
$366$		0			0
$367$	16.1698	+	9.33562i	0.844055	+	0.487316i	0.858641	−	0.512578i	$-0.171310\pi$
$367$	16.1698	+	9.33562i	0.844055	+	0.487316i	−0.0145854	+	0.999894i	$0.504643\pi$
$368$		0			0
$369$	−27.7498	+	9.69156i	−1.44460	+	0.504522i
$370$		0			0
$371$	−0.284455	−	1.06160i	−0.0147682	−	0.0551156i
$372$		0			0
$373$	−3.09325	+	11.5442i	−0.160163	+	0.597735i	0.838445	+	0.544986i	$0.183465\pi$
$373$	−3.09325	+	11.5442i	−0.160163	+	0.597735i	−0.998608	+	0.0527491i	$0.983202\pi$
$374$		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	−0.981371	−	0.192123i	$-0.938463\pi$
$379$	−15.3650	+	15.3650i	−0.789248	+	0.789248i	0.192123	+	0.981371i	$0.438463\pi$
$380$		0			0
$381$	−23.3672	+	19.3488i	−1.19714	+	0.991269i
$382$		0			0
$383$	−11.1162	−	19.2539i	−0.568013	−	0.983827i	−0.996762	−	0.0804037i	$-0.974379\pi$
$383$	−11.1162	−	19.2539i	−0.568013	−	0.983827i	0.428750	−	0.903423i	$-0.358954\pi$
$384$		0			0
$385$	1.47643	−	2.55725i	0.0752458	−	0.130330i
$386$		0			0
$387$	2.94228	−	0.218733i	0.149565	−	0.0111188i
$388$		0			0
$389$	4.18905	+	15.6338i	0.212393	+	0.792663i	0.987068	+	0.160303i	$0.0512470\pi$
$389$	4.18905	+	15.6338i	0.212393	+	0.792663i	−0.774675	+	0.632360i	$0.782086\pi$
$390$		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	−0.239106	−	0.970993i	$-0.576854\pi$
$397$	14.5828	−	14.5828i	0.731887	−	0.731887i	0.970993	+	0.239106i	$0.0768543\pi$
$398$		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
$403$	28.9521	−	7.75768i	1.44220	−	0.386438i
$404$		0			0
$405$	−4.97705	−	3.68239i	−0.247311	−	0.182979i
$406$		0			0
$407$	−2.06570	−	1.19263i	−0.102393	−	0.0591166i
$408$		0			0
$409$	−12.9975	+	7.50409i	−0.642683	+	0.371053i	−0.785647	−	0.618674i	$-0.787670\pi$
$409$	−12.9975	+	7.50409i	−0.642683	+	0.371053i	0.142964	+	0.989728i	$0.454337\pi$
$410$		0			0
$411$	17.0788	−	2.89658i	0.842435	−	0.142878i
$412$		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
$419$	−22.4191	−	6.00718i	−1.09525	−	0.293470i	−0.334418	−	0.942425i	$-0.608540\pi$
$419$	−22.4191	−	6.00718i	−1.09525	−	0.293470i	−0.760827	+	0.648955i	$0.775206\pi$
$420$		0			0
$421$	−15.1189	+	4.05109i	−0.736849	+	0.197438i	−0.607677	−	0.794184i	$-0.707899\pi$
$421$	−15.1189	+	4.05109i	−0.736849	+	0.197438i	−0.129172	+	0.991622i	$0.541232\pi$
$422$		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
$427$	13.9846	+	3.74717i	0.676764	+	0.181338i
$428$		0			0
$429$	−18.0460	−	21.7938i	−0.871267	−	1.05222i
$430$		0			0
$431$	−1.63818			−0.0789082			−0.0394541	−	0.999221i	$-0.512562\pi$
$431$	−1.63818			−0.0789082			−0.0394541	+	0.999221i	$0.512562\pi$
$432$		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
$435$	2.32615	+	2.80926i	0.111531	+	0.134694i
$436$		0			0
$437$	9.31411	+	2.49571i	0.445554	+	0.119386i
$438$		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
$443$	16.2512	−	4.35450i	0.772119	−	0.206889i	0.148811	−	0.988866i	$-0.452455\pi$
$443$	16.2512	−	4.35450i	0.772119	−	0.206889i	0.623307	+	0.781977i	$0.285789\pi$
$444$		0			0
$445$	8.46284	+	2.26761i	0.401177	+	0.107495i
$446$		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
$453$	27.6685	−	4.69260i	1.29998	−	0.220477i
$454$		0			0
$455$	3.78111	−	2.18303i	0.177261	−	0.102342i
$456$		0			0
$457$	24.8553	+	14.3502i	1.16268	+	0.671275i	0.951945	−	0.306268i	$-0.0990803\pi$
$457$	24.8553	+	14.3502i	1.16268	+	0.671275i	0.210737	+	0.977543i	$0.432414\pi$
$458$		0			0
$459$	14.0157	+	25.4130i	0.654195	+	1.18618i
$460$		0			0
$461$	1.80601	−	0.483918i	0.0841141	−	0.0225383i	−0.216517	−	0.976279i	$-0.569470\pi$
$461$	1.80601	−	0.483918i	0.0841141	−	0.0225383i	0.300631	+	0.953741i	$0.402803\pi$
$462$		0			0
$463$	−4.71990	+	2.72503i	−0.219352	+	0.126643i	−0.605650	−	0.795731i	$-0.707087\pi$
$463$	−4.71990	+	2.72503i	−0.219352	+	0.126643i	0.386298	+	0.922374i	$0.373754\pi$
$464$		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	$-0.655370\pi$
$467$	8.95228	−	8.95228i	0.414262	−	0.414262i	0.883220	+	0.468958i	$0.155370\pi$
$468$		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
$475$	−4.13647	−	15.4375i	−0.189794	−	0.708321i
$476$		0			0
$477$	−1.43701	−	2.11040i	−0.0657961	−	0.0966286i
$478$		0			0
$479$	−4.27809	+	7.40987i	−0.195471	+	0.338566i	−0.947055	−	0.321072i	$-0.895957\pi$
$479$	−4.27809	+	7.40987i	−0.195471	+	0.338566i	0.751584	+	0.659638i	$0.229290\pi$
$480$		0			0
$481$	−1.76341	−	3.05431i	−0.0804045	−	0.139265i
$482$		0			0
$483$	4.70531	−	3.89614i	0.214099	−	0.177281i
$484$		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
$491$	−2.16956	+	8.09692i	−0.0979110	+	0.365409i	−0.997445	−	0.0714425i	$-0.977240\pi$
$491$	−2.16956	+	8.09692i	−0.0979110	+	0.365409i	0.899534	+	0.436851i	$0.143906\pi$
$492$		0			0
$493$	−4.42505	−	16.5145i	−0.199294	−	0.743776i
$494$		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
$499$	8.38567	−	31.2957i	0.375394	−	1.40099i	−0.477374	−	0.878700i	$-0.658411\pi$
$499$	8.38567	−	31.2957i	0.375394	−	1.40099i	0.852768	−	0.522289i	$-0.174922\pi$
$500$		0			0
$501$	−35.2163	−	13.0788i	−1.57335	−	0.584316i
$502$		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
$507$	−3.23063	−	19.0484i	−0.143477	−	0.845971i
$508$		0			0
$509$	−5.54865	+	20.7078i	−0.245940	+	0.917859i	0.726969	+	0.686670i	$0.240928\pi$
$509$	−5.54865	+	20.7078i	−0.245940	+	0.917859i	−0.972909	+	0.231189i	$0.925738\pi$
$510$		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
$515$	−3.38533	−	12.6342i	−0.149175	−	0.556730i
$516$		0			0
$517$	10.5606	−	39.4127i	0.464455	−	1.73337i
$518$		0			0
$519$	11.2378	+	7.97869i	0.493286	+	0.350226i
$520$		0			0
$521$	−20.1534			−0.882938			−0.441469	−	0.897277i	$-0.645542\pi$
$521$	−20.1534			−0.882938			−0.441469	+	0.897277i	$0.645542\pi$
$522$		0			0
$523$	−14.7713	+	14.7713i	−0.645905	+	0.645905i	−0.952001	−	0.306096i	$-0.900977\pi$
$523$	−14.7713	+	14.7713i	−0.645905	+	0.645905i	0.306096	+	0.952001i	$0.400977\pi$
$524$		0			0
$525$	−9.49181	−	3.52511i	−0.414256	−	0.153848i
$526$		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
$531$	−13.3639	−	6.44550i	−0.579942	−	0.279711i
$532$		0			0
$533$	−12.4631	−	46.5131i	−0.539838	−	2.01470i
$534$		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	−0.424857	−	0.905260i	$-0.639676\pi$
$541$	11.1739	−	11.1739i	0.480403	−	0.480403i	0.905260	+	0.424857i	$0.139676\pi$
$542$		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
$547$	−12.0633	+	3.23236i	−0.515791	+	0.138206i	−0.507319	−	0.861758i	$-0.669363\pi$
$547$	−12.0633	+	3.23236i	−0.515791	+	0.138206i	−0.00847177	+	0.999964i	$0.502697\pi$
$548$		0			0
$549$	33.5410	−	2.49348i	1.43149	−	0.106419i
$550$		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
$555$	0.297674	−	0.801527i	0.0126356	−	0.0340229i
$556$		0			0
$557$	4.41323	+	4.41323i	0.186995	+	0.186995i	0.794395	−	0.607401i	$-0.207788\pi$
$557$	4.41323	+	4.41323i	0.186995	+	0.186995i	−0.607401	+	0.794395i	$0.707788\pi$
$558$		0			0
$559$			4.83349i			0.204435i
$560$		0			0
$561$	−18.6153	+	26.2193i	−0.785938	+	1.10698i
$562$		0			0
$563$	33.9300	+	9.09152i	1.42998	+	0.383162i	0.889013	−	0.457882i	$-0.151392\pi$
$563$	33.9300	+	9.09152i	1.42998	+	0.383162i	0.540967	+	0.841044i	$0.318058\pi$
$564$		0			0
$565$	−1.67861	+	0.449782i	−0.0706197	+	0.0189225i
$566$		0			0
$567$	9.09543	−	7.23568i	0.381972	−	0.303870i
$568$		0			0
$569$	10.8432	−	18.7810i	0.454572	−	0.787342i	−0.544091	−	0.839026i	$-0.683126\pi$
$569$	10.8432	−	18.7810i	0.454572	−	0.787342i	0.998663	+	0.0516841i	$0.0164589\pi$
$570$		0			0
$571$	10.0422	+	2.69081i	0.420255	+	0.112607i	0.462748	−	0.886490i	$-0.346863\pi$
$571$	10.0422	+	2.69081i	0.420255	+	0.112607i	−0.0424934	+	0.999097i	$0.513530\pi$
$572$		0			0
$573$	−31.5230	+	5.34633i	−1.31689	+	0.223346i
$574$		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
$579$	3.15548	−	8.49655i	0.131137	−	0.353105i
$580$		0			0
$581$	4.90169	+	1.31340i	0.203356	+	0.0544891i
$582$		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
$587$	2.06941	−	0.554497i	0.0854137	−	0.0228865i	−0.215859	−	0.976425i	$-0.569255\pi$
$587$	2.06941	−	0.554497i	0.0854137	−	0.0228865i	0.301273	+	0.953538i	$0.402589\pi$
$588$		0			0
$589$	−20.7981	−	5.57282i	−0.856969	−	0.229624i
$590$		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
$597$	−15.2838	−	18.4580i	−0.625524	−	0.755436i
$598$		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	0.695800	−	0.718235i	$-0.255050\pi$
$601$	10.3379	+	5.96857i	0.421691	+	0.243463i	−0.274110	+	0.961698i	$0.588383\pi$
$602$		0			0
$603$	0.308703	+	0.148890i	0.0125714	+	0.00606326i
$604$		0			0
$605$	0.0323096	−	0.00865733i	0.00131357	−	0.000351971i
$606$		0			0
$607$	−10.3919	+	5.99979i	−0.421796	+	0.243524i	−0.695845	−	0.718192i	$-0.744970\pi$
$607$	−10.3919	+	5.99979i	−0.421796	+	0.243524i	0.274050	+	0.961716i	$0.411637\pi$
$608$		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	0.237172	−	0.971468i	$-0.423780\pi$
$613$	−18.1803	−	18.1803i	−0.734296	−	0.734296i	−0.971468	+	0.237172i	$0.923780\pi$
$614$		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	$-0.890102\pi$
$617$	−18.9672	−	32.8521i	−0.763589	−	1.32257i	0.177401	−	0.984139i	$-0.443231\pi$
$618$		0			0
$619$	−0.000616823	−	0.00230201i	−2.47922e−5	−	9.25258e-5i	0.965913	−	0.258865i	$-0.0833486\pi$
$619$	−0.000616823	−	0.00230201i	−2.47922e−5	−	9.25258e-5i	−0.965938	+	0.258773i	$0.916682\pi$
$620$		0			0
$621$	7.33529	−	12.1490i	0.294355	−	0.487523i
$622$		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
$627$	3.39882	+	20.0401i	0.135736	+	0.800326i
$628$		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
$635$	3.11858	−	11.6387i	0.123757	−	0.461868i
$636$		0			0
$637$	−6.78286	−	25.3140i	−0.268747	−	1.00298i
$638$		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
$643$	−1.76926	+	6.60298i	−0.0697729	+	0.260396i	−0.991997	−	0.126259i	$-0.959703\pi$
$643$	−1.76926	+	6.60298i	−0.0697729	+	0.260396i	0.922224	+	0.386655i	$0.126370\pi$
$644$		0			0
$645$	−0.902549	+	0.747339i	−0.0355378	+	0.0294264i
$646$		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
$651$	−10.5068	+	8.69995i	−0.411793	+	0.340978i
$652$		0			0
$653$	−7.14041	+	26.6484i	−0.279426	+	1.04283i	0.673391	+	0.739286i	$0.264837\pi$
$653$	−7.14041	+	26.6484i	−0.279426	+	1.04283i	−0.952817	+	0.303545i	$0.901830\pi$
$654$		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
$659$	2.71978	+	10.1504i	0.105948	+	0.395402i	0.998451	−	0.0556391i	$-0.0177196\pi$
$659$	2.71978	+	10.1504i	0.105948	+	0.395402i	−0.892503	+	0.451041i	$0.851053\pi$
$660$		0			0
$661$	7.59396	−	28.3410i	0.295371	−	1.10234i	−0.645552	−	0.763717i	$-0.723372\pi$
$661$	7.59396	−	28.3410i	0.295371	−	1.10234i	0.940922	−	0.338622i	$-0.109961\pi$
$662$		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
$669$	−0.927247	−	5.46724i	−0.0358495	−	0.211376i
$670$		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
$675$	−23.5173	−	0.460823i	−0.905182	−	0.0177371i
$676$		0			0
$677$	5.70565	+	21.2938i	0.219286	+	0.818387i	0.984614	+	0.174746i	$0.0559104\pi$
$677$	5.70565	+	21.2938i	0.219286	+	0.818387i	−0.765327	+	0.643641i	$0.777423\pi$
$678$		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	$-0.235509\pi$
$683$	1.68202	+	1.68202i	0.0643609	+	0.0643609i	−0.674194	+	0.738555i	$0.735509\pi$
$684$		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
$691$	−2.22350	+	0.595784i	−0.0845858	+	0.0226647i	−0.300864	−	0.953667i	$-0.597275\pi$
$691$	−2.22350	+	0.595784i	−0.0845858	+	0.0226647i	0.216278	+	0.976332i	$0.430608\pi$
$692$		0			0
$693$	11.5989	+	5.59424i	0.440606	+	0.212508i
$694$		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
$699$	6.63437	+	8.01223i	0.250935	+	0.303050i
$700$		0			0
$701$	−10.2728	−	10.2728i	−0.387997	−	0.387997i	0.485976	−	0.873972i	$-0.338464\pi$
$701$	−10.2728	−	10.2728i	−0.387997	−	0.387997i	−0.873972	+	0.485976i	$0.838464\pi$
$702$		0			0
$703$			2.53353i			0.0955540i
$704$		0			0
$705$	14.5619	+	1.36989i	0.548433	+	0.0515929i
$706$		0			0
$707$	9.07228	+	2.43091i	0.341198	+	0.0914238i
$708$		0			0
$709$	−4.88619	+	1.30925i	−0.183505	+	0.0491700i	−0.349401	−	0.936973i	$-0.613615\pi$
$709$	−4.88619	+	1.30925i	−0.183505	+	0.0491700i	0.165896	+	0.986143i	$0.446948\pi$
$710$		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
$715$	10.8550	+	2.90859i	0.405955	+	0.108775i
$716$		0			0
$717$	7.24566	−	19.5099i	0.270594	−	0.728610i
$718$		0			0
$719$	6.73858			0.251307			0.125653	−	0.992074i	$-0.459897\pi$
$719$	6.73858			0.251307			0.125653	+	0.992074i	$0.459897\pi$
$720$		0			0
$721$	24.5544			0.914452
$722$		0			0
$723$	−5.18867	+	0.880003i	−0.192969	+	0.0327277i
$724$		0			0
$725$	13.3849	+	3.58646i	0.497101	+	0.133198i
$726$		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
$731$	5.30572	−	1.42166i	0.196239	−	0.0525821i
$732$		0			0
$733$	43.6909	+	11.7070i	1.61376	+	0.432406i	0.949161	−	0.314792i	$-0.101935\pi$
$733$	43.6909	+	11.7070i	1.61376	+	0.432406i	0.664601	+	0.747198i	$0.268601\pi$
$734$		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	0.173585	−	0.984819i	$-0.444465\pi$
$739$	−22.0530	−	22.0530i	−0.811234	−	0.811234i	−0.984819	+	0.173585i	$0.944465\pi$
$740$		0			0
$741$	−10.4634	+	28.1740i	−0.384381	+	1.03500i
$742$		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
$747$	11.7563	−	0.873977i	0.430140	−	0.0319772i
$748$		0			0
$749$	−14.6205	+	3.91756i	−0.534222	+	0.143144i
$750$		0			0
$751$	−38.8676	+	22.4402i	−1.41830	+	0.818855i	−0.996149	−	0.0876713i	$-0.972057\pi$
$751$	−38.8676	+	22.4402i	−1.41830	+	0.818855i	−0.422149	+	0.906526i	$0.638724\pi$
$752$		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	0.999994	+	0.00354931i	$0.00112978\pi$
$757$	27.6111	+	27.6111i	1.00354	+	1.00354i	0.00354931	+	0.999994i	$0.498870\pi$
$758$		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	$0.0574545\pi$
$761$	17.8578	+	30.9307i	0.647346	+	1.12124i	−0.336408	+	0.941716i	$0.609212\pi$
$762$		0			0
$763$	−6.79711	−	25.3672i	−0.246072	−	0.918353i
$764$		0			0
$765$	−10.3820	−	5.00731i	−0.375361	−	0.181040i
$766$		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
$771$	−3.13851	−	1.16559i	−0.113031	−	0.0419778i
$772$		0			0
$773$	−5.57961	+	5.57961i	−0.200685	+	0.200685i	−0.800293	−	0.599609i	$-0.795323\pi$
$773$	−5.57961	+	5.57961i	−0.200685	+	0.200685i	0.599609	+	0.800293i	$0.295323\pi$
$774$		0			0
$775$	27.6073			0.991684
$776$		0			0
$777$	1.30877	+	0.929208i	0.0469519	+	0.0333352i
$778$		0			0
$779$	−8.95305	+	33.4132i	−0.320776	+	1.19715i
$780$		0			0
$781$	−0.0385333	−	0.143808i	−0.00137883	−	0.00514586i
$782$		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
$787$	2.39956	−	8.95529i	0.0855351	−	0.319221i	−0.909880	−	0.414872i	$-0.863826\pi$
$787$	2.39956	−	8.95529i	0.0855351	−	0.319221i	0.995415	+	0.0956504i	$0.0304931\pi$
$788$		0			0
$789$	−0.508304	−	2.99706i	−0.0180961	−	0.106698i
$790$		0			0
$791$		−	3.26235i		−	0.115996i
$792$		0			0
$793$			55.1001i			1.95666i
$794$		0			0
$795$	0.950600	+	0.353038i	0.0337143	+	0.0125210i
$796$		0			0
$797$	−6.57307	+	24.5310i	−0.232830	+	0.868934i	0.746285	+	0.665627i	$0.231836\pi$
$797$	−6.57307	+	24.5310i	−0.232830	+	0.868934i	−0.979115	+	0.203307i	$0.934831\pi$
$798$		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
$803$	11.4361	+	42.6801i	0.403571	+	1.50615i
$804$		0			0
$805$	−0.627969	+	2.34361i	−0.0221330	+	0.0826014i
$806$		0			0
$807$	3.25806	−	34.6331i	0.114689	−	1.21914i
$808$		0			0
$809$	−33.1931			−1.16701			−0.583503	−	0.812111i	$-0.698318\pi$
$809$	−33.1931			−1.16701			−0.583503	+	0.812111i	$0.698318\pi$
$810$		0			0
$811$	−7.35128	+	7.35128i	−0.258138	+	0.258138i	−0.824297	−	0.566158i	$-0.808429\pi$
$811$	−7.35128	+	7.35128i	−0.258138	+	0.258138i	0.566158	+	0.824297i	$0.308429\pi$
$812$		0			0
$813$	15.1700	−	12.5613i	0.532037	−	0.440543i
$814$		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
$819$	10.7165	+	15.7384i	0.374466	+	0.549943i
$820$		0			0
$821$	10.3476	+	38.6179i	0.361135	+	1.34777i	0.872585	+	0.488462i	$0.162442\pi$
$821$	10.3476	+	38.6179i	0.361135	+	1.34777i	−0.511450	+	0.859313i	$0.670891\pi$
$822$		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	$-0.0377357\pi$
$827$	25.1545	+	25.1545i	0.874708	+	0.874708i	−0.118273	+	0.992981i	$0.537736\pi$
$828$		0			0
$829$	6.12372	−	6.12372i	0.212686	−	0.212686i	−0.592722	−	0.805407i	$-0.701947\pi$
$829$	6.12372	−	6.12372i	0.212686	−	0.212686i	0.805407	+	0.592722i	$0.201947\pi$
$830$		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
$835$	14.4117	−	3.86161i	0.498739	−	0.133637i
$836$		0			0
$837$	−16.3794	+	27.1283i	−0.566156	+	0.937692i
$838$		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
$843$	17.6361	−	2.99109i	0.607418	−	0.103019i
$844$		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
$851$	1.89313	+	0.507262i	0.0648955	+	0.0173887i
$852$		0			0
$853$	−41.6120	+	11.1499i	−1.42477	+	0.381765i	−0.887173	−	0.461437i	$-0.847334\pi$
$853$	−41.6120	+	11.1499i	−1.42477	+	0.381765i	−0.537595	+	0.843203i	$0.680667\pi$
$854$		0			0
$855$	−6.87870	+	2.40237i	−0.235247	+	0.0821592i
$856$		0			0
$857$	−4.72246	+	8.17953i	−0.161316	+	0.279408i	−0.935341	−	0.353748i	$-0.884907\pi$
$857$	−4.72246	+	8.17953i	−0.161316	+	0.279408i	0.774025	+	0.633155i	$0.218241\pi$
$858$		0			0
$859$	−21.9088	−	5.87045i	−0.747519	−	0.200297i	−0.135102	−	0.990832i	$-0.543136\pi$
$859$	−21.9088	−	5.87045i	−0.747519	−	0.200297i	−0.612417	+	0.790535i	$0.709803\pi$
$860$		0			0
$861$	13.9769	+	16.8797i	0.476333	+	0.575260i
$862$		0			0
$863$	−3.58147			−0.121915			−0.0609573	−	0.998140i	$-0.519415\pi$
$863$	−3.58147			−0.121915			−0.0609573	+	0.998140i	$0.519415\pi$
$864$		0			0
$865$	−5.47380			−0.186115
$866$		0			0
$867$	15.6803	+	18.9368i	0.532530	+	0.643128i
$868$		0			0
$869$	9.27039	+	2.48399i	0.314476	+	0.0842637i
$870$		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
$875$	8.17482	−	2.19044i	0.276359	−	0.0740503i
$876$		0			0
$877$	−16.8966	−	4.52743i	−0.570558	−	0.152881i	−0.0380056	−	0.999278i	$-0.512100\pi$
$877$	−16.8966	−	4.52743i	−0.570558	−	0.152881i	−0.532553	+	0.846397i	$0.678767\pi$
$878$		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	0.292318	−	0.956321i	$-0.405573\pi$
$883$	−19.7311	−	19.7311i	−0.664003	−	0.664003i	−0.956321	+	0.292318i	$0.905573\pi$
$884$		0			0
$885$	5.80979	−	0.985345i	0.195294	−	0.0331220i
$886$		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
$891$	29.7234	+	3.38485i	0.995772	+	0.113397i
$892$		0			0
$893$	−41.8626	+	11.2171i	−1.40088	+	0.375364i
$894$		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
$907$	−14.3921	−	53.7121i	−0.477883	−	1.78348i	−0.610170	−	0.792271i	$-0.708899\pi$
$907$	−14.3921	−	53.7121i	−0.477883	−	1.78348i	0.132287	−	0.991211i	$-0.457768\pi$
$908$		0			0
$909$	21.7591	−	1.61760i	0.721704	−	0.0536524i
$910$		0			0
$911$	−6.01435	+	10.4172i	−0.199264	+	0.345136i	−0.948290	−	0.317405i	$-0.897189\pi$
$911$	−6.01435	+	10.4172i	−0.199264	+	0.345136i	0.749026	+	0.662541i	$0.230522\pi$
$912$		0			0
$913$	6.53085	+	11.3118i	0.216140	+	0.374365i
$914$		0			0
$915$	−10.2887	+	8.51940i	−0.340136	+	0.281643i
$916$		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
$923$	0.0569747	−	0.212633i	0.00187535	−	0.00699889i
$924$		0			0
$925$	−0.840752	−	3.13773i	−0.0276438	−	0.103168i
$926$		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
$931$	−4.87255	+	18.1846i	−0.159692	+	0.595977i
$932$		0			0
$933$	−4.97355	−	1.84710i	−0.162827	−	0.0604712i
$934$		0			0
$935$		−	12.7711i		−	0.417659i
$936$		0			0
$937$		−	26.0017i		−	0.849438i	−0.905325	−	0.424719i	$-0.860373\pi$
$937$		−	26.0017i		−	0.849438i	0.905325	−	0.424719i	$-0.139627\pi$
$938$		0			0
$939$	−0.867921	−	5.11744i	−0.0283235	−	0.167001i
$940$		0			0
$941$	−11.0855	+	41.3717i	−0.361378	+	1.34868i	0.510888	+	0.859648i	$0.329317\pi$
$941$	−11.0855	+	41.3717i	−0.361378	+	1.34868i	−0.872265	+	0.489033i	$0.837350\pi$
$942$		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
$947$	−4.71769	−	17.6066i	−0.153304	−	0.572139i	−0.999245	−	0.0388617i	$-0.987627\pi$
$947$	−4.71769	−	17.6066i	−0.153304	−	0.572139i	0.845940	−	0.533277i	$-0.179040\pi$
$948$		0			0
$949$	−16.9093	+	63.1062i	−0.548898	+	2.04851i
$950$		0			0
$951$	−13.5158	−	9.59602i	−0.438280	−	0.311172i
$952$		0			0
$953$	−16.9031			−0.547545			−0.273772	−	0.961795i	$-0.588271\pi$
$953$	−16.9031			−0.547545			−0.273772	+	0.961795i	$0.588271\pi$
$954$		0			0
$955$	8.97930	−	8.97930i	0.290563	−	0.290563i
$956$		0			0
$957$	−16.5211	−	6.13567i	−0.534051	−	0.198338i
$958$		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
$963$	−29.0647	+	19.7907i	−0.936597	+	0.637745i
$964$		0			0
$965$	0.931682	+	3.47708i	0.0299919	+	0.111931i
$966$		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	−0.988623	−	0.150413i	$-0.951940\pi$
$971$	−35.4934	−	35.4934i	−1.13904	−	1.13904i	−0.150413	−	0.988623i	$-0.548060\pi$
$972$		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
$979$	−40.8920	+	10.9570i	−1.30691	+	0.350186i
$980$		0			0
$981$	−34.3375	−	50.4283i	−1.09631	−	1.61005i
$982$		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
$987$	−9.55919	+	25.7394i	−0.304273	+	0.819294i
$988$		0			0
$989$	−1.89932	−	1.89932i	−0.0603949	−	0.0603949i
$990$		0			0
$991$		−	6.60967i		−	0.209963i	−0.994474	−	0.104982i	$-0.966522\pi$
$991$		−	6.60967i		−	0.209963i	0.994474	−	0.104982i	$-0.0334784\pi$
$992$		0			0
$993$	15.1424	−	21.3278i	0.480530	−	0.676817i
$994$		0			0
$995$	9.19352	+	2.46340i	0.291454	+	0.0780949i
$996$		0			0
$997$	36.5814	−	9.80194i	1.15854	−	0.310431i	0.372159	−	0.928169i	$-0.378618\pi$
$997$	36.5814	−	9.80194i	1.15854	−	0.310431i	0.786384	+	0.617738i	$0.211951\pi$
$998$		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.335.7		88
3.2	odd	2		1728.2.z.a.143.10		88
4.3	odd	2		144.2.u.a.11.15	✓	88
9.4	even	3		1728.2.z.a.719.10		88
9.5	odd	6	inner	576.2.y.a.527.5		88
12.11	even	2		432.2.v.a.251.8		88
16.3	odd	4	inner	576.2.y.a.47.5		88
16.13	even	4		144.2.u.a.83.8	yes	88
36.23	even	6		144.2.u.a.59.8	yes	88
36.31	odd	6		432.2.v.a.395.15		88
48.29	odd	4		432.2.v.a.35.15		88
48.35	even	4		1728.2.z.a.1007.10		88
144.13	even	12		432.2.v.a.179.8		88
144.67	odd	12		1728.2.z.a.1583.10		88
144.77	odd	12		144.2.u.a.131.15	yes	88
144.131	even	12	inner	576.2.y.a.239.7		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.15	✓	88	4.3	odd	2
144.2.u.a.59.8	yes	88	36.23	even	6
144.2.u.a.83.8	yes	88	16.13	even	4
144.2.u.a.131.15	yes	88	144.77	odd	12
432.2.v.a.35.15		88	48.29	odd	4
432.2.v.a.179.8		88	144.13	even	12
432.2.v.a.251.8		88	12.11	even	2
432.2.v.a.395.15		88	36.31	odd	6
576.2.y.a.47.5		88	16.3	odd	4	inner
576.2.y.a.239.7		88	144.131	even	12	inner
576.2.y.a.335.7		88	1.1	even	1	trivial
576.2.y.a.527.5		88	9.5	odd	6	inner
1728.2.z.a.143.10		88	3.2	odd	2
1728.2.z.a.719.10		88	9.4	even	3
1728.2.z.a.1007.10		88	48.35	even	4
1728.2.z.a.1583.10		88	144.67	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

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

Related objects

Downloads

Learn more