LMFDB - Embedded newform 576.2.bb.e.337.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(49,576)]

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([0, 3, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("576.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bb (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:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			337.2
Character	$\chi$	$=$	576.337
Dual form			576.2.bb.e.241.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71768 + 0.222657i) q^{3} +(-0.798307 - 2.97932i) q^{5} +(1.78208 - 1.02889i) q^{7} +(2.90085 - 0.764906i) q^{9} +O(q^{10})$	\(q+(-1.71768 + 0.222657i) q^{3} +(-0.798307 - 2.97932i) q^{5} +(1.78208 - 1.02889i) q^{7} +(2.90085 - 0.764906i) q^{9} +(0.446347 + 0.119598i) q^{11} +(-5.67550 + 1.52075i) q^{13} +(2.03460 + 4.93977i) q^{15} +0.0443921 q^{17} +(1.10726 + 1.10726i) q^{19} +(-2.83196 + 2.16409i) q^{21} +(-7.89263 - 4.55681i) q^{23} +(-3.90893 + 2.25682i) q^{25} +(-4.81242 + 1.95976i) q^{27} +(1.86402 - 6.95662i) q^{29} +(-0.542236 + 0.939180i) q^{31} +(-0.793310 - 0.106049i) q^{33} +(-4.48803 - 4.48803i) q^{35} +(-0.769054 + 0.769054i) q^{37} +(9.41009 - 3.87585i) q^{39} +(-5.77193 - 3.33242i) q^{41} +(-11.0600 - 2.96351i) q^{43} +(-4.59467 - 8.03193i) q^{45} +(1.22453 + 2.12095i) q^{47} +(-1.38279 + 2.39506i) q^{49} +(-0.0762514 + 0.00988420i) q^{51} +(2.44801 - 2.44801i) q^{53} -1.42529i q^{55} +(-2.14846 - 1.65538i) q^{57} +(0.962265 + 3.59122i) q^{59} +(0.318210 - 1.18758i) q^{61} +(4.38255 - 4.34777i) q^{63} +(9.06158 + 15.6951i) q^{65} +(5.52723 - 1.48102i) q^{67} +(14.5716 + 6.06980i) q^{69} -6.88571i q^{71} +13.1963i q^{73} +(6.21180 - 4.74685i) q^{75} +(0.918480 - 0.246106i) q^{77} +(-3.46441 - 6.00054i) q^{79} +(7.82984 - 4.43775i) q^{81} +(-0.157584 + 0.588112i) q^{83} +(-0.0354385 - 0.132258i) q^{85} +(-1.65285 + 12.3643i) q^{87} +5.30004i q^{89} +(-8.54954 + 8.54954i) q^{91} +(0.722273 - 1.73394i) q^{93} +(2.41495 - 4.18282i) q^{95} +(-5.88304 - 10.1897i) q^{97} +(1.38627 + 0.00552307i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) $ 72 * q - 2 * q^3 + 4 * q^5	$ 72 q - 2 q^{3} + 4 q^{5} + 2 q^{11} - 16 q^{13} + 20 q^{15} - 16 q^{17} - 28 q^{19} - 16 q^{21} - 8 q^{27} + 4 q^{29} - 28 q^{31} - 32 q^{33} + 16 q^{35} + 16 q^{37} + 10 q^{43} + 40 q^{45} + 56 q^{47} + 4 q^{49} + 54 q^{51} - 8 q^{53} + 14 q^{59} - 32 q^{61} + 108 q^{63} - 64 q^{65} + 18 q^{67} + 32 q^{69} - 86 q^{75} - 36 q^{77} - 44 q^{79} - 44 q^{81} - 20 q^{83} - 8 q^{85} + 80 q^{91} - 4 q^{93} - 48 q^{95} + 40 q^{97} - 28 q^{99}+O(q^{100}) $ 72 * q - 2 * q^3 + 4 * q^5 + 2 * q^11 - 16 * q^13 + 20 * q^15 - 16 * q^17 - 28 * q^19 - 16 * q^21 - 8 * q^27 + 4 * q^29 - 28 * q^31 - 32 * q^33 + 16 * q^35 + 16 * q^37 + 10 * q^43 + 40 * q^45 + 56 * q^47 + 4 * q^49 + 54 * q^51 - 8 * q^53 + 14 * q^59 - 32 * q^61 + 108 * q^63 - 64 * q^65 + 18 * q^67 + 32 * q^69 - 86 * q^75 - 36 * q^77 - 44 * q^79 - 44 * q^81 - 20 * q^83 - 8 * q^85 + 80 * q^91 - 4 * q^93 - 48 * q^95 + 40 * q^97 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−1.71768	+	0.222657i	−0.991703	+	0.128551i
$3$	−1.71768	+	0.222657i	−0.991703	+	0.128551i
$4$		0			0
$5$	−0.798307	−	2.97932i	−0.357014	−	1.33239i	−0.877932	−	0.478786i	$-0.841077\pi$
$5$	−0.798307	−	2.97932i	−0.357014	−	1.33239i	0.520918	−	0.853607i	$-0.325590\pi$
$6$		0			0
$7$	1.78208	−	1.02889i	0.673564	−	0.388882i	−0.123862	−	0.992299i	$-0.539528\pi$
$7$	1.78208	−	1.02889i	0.673564	−	0.388882i	0.797426	+	0.603417i	$0.206195\pi$
$8$		0			0
$9$	2.90085	−	0.764906i	0.966949	−	0.254969i
$10$		0			0
$11$	0.446347	+	0.119598i	0.134579	+	0.0360602i	0.325480	−	0.945549i	$-0.394474\pi$
$11$	0.446347	+	0.119598i	0.134579	+	0.0360602i	−0.190901	+	0.981609i	$0.561141\pi$
$12$		0			0
$13$	−5.67550	+	1.52075i	−1.57410	+	0.421779i	−0.937094	−	0.349078i	$-0.886495\pi$
$13$	−5.67550	+	1.52075i	−1.57410	+	0.421779i	−0.637008	+	0.770857i	$0.719828\pi$
$14$		0			0
$15$	2.03460	+	4.93977i	0.525332	+	1.27544i
$16$		0			0
$17$	0.0443921			0.0107667			0.00538333	−	0.999986i	$-0.498286\pi$
$17$	0.0443921			0.0107667			0.00538333	+	0.999986i	$0.498286\pi$
$18$		0			0
$19$	1.10726	+	1.10726i	0.254023	+	0.254023i	0.822618	−	0.568595i	$-0.192513\pi$
$19$	1.10726	+	1.10726i	0.254023	+	0.254023i	−0.568595	+	0.822618i	$0.692513\pi$
$20$		0			0
$21$	−2.83196	+	2.16409i	−0.617984	+	0.472243i
$22$		0			0
$23$	−7.89263	−	4.55681i	−1.64573	−	0.950161i	−0.978743	−	0.205089i	$-0.934252\pi$
$23$	−7.89263	−	4.55681i	−1.64573	−	0.950161i	−0.666984	−	0.745072i	$-0.732415\pi$
$24$		0			0
$25$	−3.90893	+	2.25682i	−0.781786	+	0.451364i
$26$		0			0
$27$	−4.81242	+	1.95976i	−0.926150	+	0.377155i
$28$		0			0
$29$	1.86402	−	6.95662i	0.346140	−	1.29181i	−0.545134	−	0.838349i	$-0.683521\pi$
$29$	1.86402	−	6.95662i	0.346140	−	1.29181i	0.891275	−	0.453464i	$-0.149812\pi$
$30$		0			0
$31$	−0.542236	+	0.939180i	−0.0973884	+	0.168682i	−0.910603	−	0.413282i	$-0.864382\pi$
$31$	−0.542236	+	0.939180i	−0.0973884	+	0.168682i	0.813214	+	0.581964i	$0.197716\pi$
$32$		0			0
$33$	−0.793310	−	0.106049i	−0.138098	−	0.0184608i
$34$		0			0
$35$	−4.48803	−	4.48803i	−0.758615	−	0.758615i
$36$		0			0
$37$	−0.769054	+	0.769054i	−0.126432	+	0.126432i	−0.767491	−	0.641060i	$-0.778495\pi$
$37$	−0.769054	+	0.769054i	−0.126432	+	0.126432i	0.641060	+	0.767491i	$0.278495\pi$
$38$		0			0
$39$	9.41009	−	3.87585i	1.50682	−	0.620632i
$40$		0			0
$41$	−5.77193	−	3.33242i	−0.901423	−	0.520437i	−0.0237617	−	0.999718i	$-0.507564\pi$
$41$	−5.77193	−	3.33242i	−0.901423	−	0.520437i	−0.877662	+	0.479281i	$0.840898\pi$
$42$		0			0
$43$	−11.0600	−	2.96351i	−1.68663	−	0.451932i	−0.717115	−	0.696955i	$-0.754538\pi$
$43$	−11.0600	−	2.96351i	−1.68663	−	0.451932i	−0.969517	+	0.245023i	$0.921204\pi$
$44$		0			0
$45$	−4.59467	−	8.03193i	−0.684932	−	1.19733i
$46$		0			0
$47$	1.22453	+	2.12095i	0.178617	+	0.309373i	0.941407	−	0.337273i	$-0.109504\pi$
$47$	1.22453	+	2.12095i	0.178617	+	0.309373i	−0.762790	+	0.646646i	$0.776171\pi$
$48$		0			0
$49$	−1.38279	+	2.39506i	−0.197541	+	0.342151i
$50$		0			0
$51$	−0.0762514	+	0.00988420i	−0.0106773	+	0.00138406i
$52$		0			0
$53$	2.44801	−	2.44801i	0.336260	−	0.336260i	−0.518698	−	0.854958i	$-0.673583\pi$
$53$	2.44801	−	2.44801i	0.336260	−	0.336260i	0.854958	+	0.518698i	$0.173583\pi$
$54$		0			0
$55$		−	1.42529i		−	0.192186i
$56$		0			0
$57$	−2.14846	−	1.65538i	−0.284570	−	0.219260i
$58$		0			0
$59$	0.962265	+	3.59122i	0.125276	+	0.467537i	0.999849	−	0.0173563i	$-0.00552495\pi$
$59$	0.962265	+	3.59122i	0.125276	+	0.467537i	−0.874573	+	0.484894i	$0.838858\pi$
$60$		0			0
$61$	0.318210	−	1.18758i	0.0407426	−	0.152054i	−0.942558	−	0.334043i	$-0.891587\pi$
$61$	0.318210	−	1.18758i	0.0407426	−	0.152054i	0.983301	+	0.181989i	$0.0582536\pi$
$62$		0			0
$63$	4.38255	−	4.34777i	0.552149	−	0.547767i
$64$		0			0
$65$	9.06158	+	15.6951i	1.12395	+	1.94674i
$66$		0			0
$67$	5.52723	−	1.48102i	0.675258	−	0.180935i	0.0951361	−	0.995464i	$-0.469671\pi$
$67$	5.52723	−	1.48102i	0.675258	−	0.180935i	0.580122	+	0.814529i	$0.303005\pi$
$68$		0			0
$69$	14.5716	+	6.06980i	1.75422	+	0.730718i
$70$		0			0
$71$		−	6.88571i		−	0.817184i	−0.912717	−	0.408592i	$-0.866020\pi$
$71$		−	6.88571i		−	0.817184i	0.912717	−	0.408592i	$-0.133980\pi$
$72$		0			0
$73$			13.1963i			1.54451i	0.635312	+	0.772255i	$0.280871\pi$
$73$			13.1963i			1.54451i	−0.635312	+	0.772255i	$0.719129\pi$
$74$		0			0
$75$	6.21180	−	4.74685i	0.717276	−	0.548119i
$76$		0			0
$77$	0.918480	−	0.246106i	0.104670	−	0.0280464i
$78$		0			0
$79$	−3.46441	−	6.00054i	−0.389777	−	0.675113i	0.602643	−	0.798011i	$-0.294115\pi$
$79$	−3.46441	−	6.00054i	−0.389777	−	0.675113i	−0.992419	+	0.122898i	$0.960781\pi$
$80$		0			0
$81$	7.82984	−	4.43775i	0.869982	−	0.493084i
$82$		0			0
$83$	−0.157584	+	0.588112i	−0.0172971	+	0.0645537i	−0.974035	−	0.226398i	$-0.927305\pi$
$83$	−0.157584	+	0.588112i	−0.0172971	+	0.0645537i	0.956738	+	0.290951i	$0.0939718\pi$
$84$		0			0
$85$	−0.0354385	−	0.132258i	−0.00384385	−	0.0143454i
$86$		0			0
$87$	−1.65285	+	12.3643i	−0.177205	+	1.32559i
$88$		0			0
$89$			5.30004i			0.561803i	0.959737	+	0.280902i	$0.0906335\pi$
$89$			5.30004i			0.561803i	−0.959737	+	0.280902i	$0.909367\pi$
$90$		0			0
$91$	−8.54954	+	8.54954i	−0.896235	+	0.896235i
$92$		0			0
$93$	0.722273	−	1.73394i	0.0748962	−	0.179802i
$94$		0			0
$95$	2.41495	−	4.18282i	0.247769	−	0.429148i
$96$		0			0
$97$	−5.88304	−	10.1897i	−0.597333	−	1.03461i	−0.993213	−	0.116309i	$-0.962894\pi$
$97$	−5.88304	−	10.1897i	−0.597333	−	1.03461i	0.395880	−	0.918302i	$-0.370439\pi$
$98$		0			0
$99$	1.38627	+	0.00552307i	0.139325	+	0.000555089i
$100$		0			0
$101$	−5.65271	−	1.51464i	−0.562466	−	0.150712i	−0.0336269	−	0.999434i	$-0.510706\pi$
$101$	−5.65271	−	1.51464i	−0.562466	−	0.150712i	−0.528839	+	0.848722i	$0.677372\pi$
$102$		0			0
$103$	1.13680	+	0.656334i	0.112013	+	0.0646705i	0.554960	−	0.831877i	$-0.312734\pi$
$103$	1.13680	+	0.656334i	0.112013	+	0.0646705i	−0.442947	+	0.896548i	$0.646067\pi$
$104$		0			0
$105$	8.70829	+	6.70971i	0.849842	+	0.654800i
$106$		0			0
$107$	2.92966	−	2.92966i	0.283221	−	0.283221i	−0.551171	−	0.834392i	$-0.685819\pi$
$107$	2.92966	−	2.92966i	0.283221	−	0.283221i	0.834392	+	0.551171i	$0.185819\pi$
$108$		0			0
$109$	11.5193	+	11.5193i	1.10335	+	1.10335i	0.994004	+	0.109344i	$0.0348750\pi$
$109$	11.5193	+	11.5193i	1.10335	+	1.10335i	0.109344	+	0.994004i	$0.465125\pi$
$110$		0			0
$111$	1.14975	−	1.49222i	0.109130	−	0.141636i
$112$		0			0
$113$	3.79250	−	6.56880i	0.356768	−	0.617941i	−0.630651	−	0.776067i	$-0.717212\pi$
$113$	3.79250	−	6.56880i	0.356768	−	0.617941i	0.987419	+	0.158126i	$0.0505452\pi$
$114$		0			0
$115$	−7.27547	+	27.1524i	−0.678441	+	2.53198i
$116$		0			0
$117$	−15.3005	+	8.75268i	−1.41454	+	0.809186i
$118$		0			0
$119$	0.0791104	−	0.0456744i	0.00725204	−	0.00418696i
$120$		0			0
$121$	−9.34136	−	5.39324i	−0.849214	−	0.490294i
$122$		0			0
$123$	10.6563	+	4.43888i	0.960847	+	0.400240i
$124$		0			0
$125$	−1.06075	−	1.06075i	−0.0948761	−	0.0948761i
$126$		0			0
$127$	10.6374			0.943915			0.471958	−	0.881621i	$-0.343548\pi$
$127$	10.6374			0.943915			0.471958	+	0.881621i	$0.343548\pi$
$128$		0			0
$129$	19.6574	+	2.62779i	1.73073	+	0.231364i
$130$		0			0
$131$	18.5982	−	4.98338i	1.62493	−	0.435400i	0.672488	−	0.740108i	$-0.265226\pi$
$131$	18.5982	−	4.98338i	1.62493	−	0.435400i	0.952446	+	0.304708i	$0.0985589\pi$
$132$		0			0
$133$	3.11247	+	0.833985i	0.269886	+	0.0723157i
$134$		0			0
$135$	9.68053	+	12.7732i	0.833167	+	1.09935i
$136$		0			0
$137$	8.30213	−	4.79324i	0.709299	−	0.409514i	−0.101502	−	0.994835i	$-0.532365\pi$
$137$	8.30213	−	4.79324i	0.709299	−	0.409514i	0.810802	+	0.585321i	$0.199032\pi$
$138$		0			0
$139$	1.82598	+	6.81465i	0.154878	+	0.578011i	0.999116	+	0.0420428i	$0.0133866\pi$
$139$	1.82598	+	6.81465i	0.154878	+	0.578011i	−0.844238	+	0.535968i	$0.819947\pi$
$140$		0			0
$141$	−2.57560	−	3.37047i	−0.216905	−	0.283845i
$142$		0			0
$143$	−2.71512			−0.227050
$144$		0			0
$145$	−22.2141			−1.84478
$146$		0			0
$147$	1.84191	−	4.42183i	0.151918	−	0.364707i
$148$		0			0
$149$	−5.22476	−	19.4991i	−0.428029	−	1.59743i	−0.757218	−	0.653162i	$-0.773442\pi$
$149$	−5.22476	−	19.4991i	−0.428029	−	1.59743i	0.329189	−	0.944264i	$-0.393225\pi$
$150$		0			0
$151$	3.86699	−	2.23261i	0.314691	−	0.181687i	−0.334333	−	0.942455i	$-0.608511\pi$
$151$	3.86699	−	2.23261i	0.314691	−	0.181687i	0.649024	+	0.760768i	$0.275178\pi$
$152$		0			0
$153$	0.128775	−	0.0339558i	0.0104108	−	0.00274516i
$154$		0			0
$155$	3.23099	+	0.865741i	0.259519	+	0.0695380i
$156$		0			0
$157$	15.9143	−	4.26421i	1.27010	−	0.340321i	0.440029	−	0.897984i	$-0.354968\pi$
$157$	15.9143	−	4.26421i	1.27010	−	0.340321i	0.830068	+	0.557662i	$0.188302\pi$
$158$		0			0
$159$	−3.65983	+	4.74996i	−0.290243	+	0.376696i
$160$		0			0
$161$	−18.7538			−1.47800
$162$		0			0
$163$	−5.24124	−	5.24124i	−0.410525	−	0.410525i	0.471396	−	0.881922i	$-0.343750\pi$
$163$	−5.24124	−	5.24124i	−0.410525	−	0.410525i	−0.881922	+	0.471396i	$0.843750\pi$
$164$		0			0
$165$	0.317350	+	2.44819i	0.0247056	+	0.190591i
$166$		0			0
$167$	−11.2974	−	6.52257i	−0.874220	−	0.504731i	−0.00547195	−	0.999985i	$-0.501742\pi$
$167$	−11.2974	−	6.52257i	−0.874220	−	0.504731i	−0.868748	+	0.495254i	$0.835075\pi$
$168$		0			0
$169$	18.6403	−	10.7620i	1.43387	−	0.827847i
$170$		0			0
$171$	4.05894	+	2.36504i	0.310395	+	0.180859i
$172$		0			0
$173$	−0.371831	+	1.38769i	−0.0282698	+	0.105504i	−0.978619	−	0.205681i	$-0.934059\pi$
$173$	−0.371831	+	1.38769i	−0.0282698	+	0.105504i	0.950349	+	0.311185i	$0.100726\pi$
$174$		0			0
$175$	−4.64402	+	8.04369i	−0.351055	+	0.608046i
$176$		0			0
$177$	−2.45247	−	5.95432i	−0.184339	−	0.447554i
$178$		0			0
$179$	2.50772	+	2.50772i	0.187436	+	0.187436i	0.794587	−	0.607151i	$-0.207688\pi$
$179$	2.50772	+	2.50772i	0.187436	+	0.187436i	−0.607151	+	0.794587i	$0.707688\pi$
$180$		0			0
$181$	10.8795	−	10.8795i	0.808666	−	0.808666i	−0.175766	−	0.984432i	$-0.556240\pi$
$181$	10.8795	−	10.8795i	0.808666	−	0.808666i	0.984432	+	0.175766i	$0.0562403\pi$
$182$		0			0
$183$	−0.282161	+	2.11073i	−0.0208580	+	0.156029i
$184$		0			0
$185$	2.90520	+	1.67732i	0.213594	+	0.123319i
$186$		0			0
$187$	0.0198143	+	0.00530922i	0.00144896	+	0.000388248i
$188$		0			0
$189$	−6.55976	+	8.44387i	−0.477152	+	0.614201i
$190$		0			0
$191$	6.59227	+	11.4182i	0.477000	+	0.826188i	0.999653	−	0.0263575i	$-0.00839081\pi$
$191$	6.59227	+	11.4182i	0.477000	+	0.826188i	−0.522653	+	0.852546i	$0.675057\pi$
$192$		0			0
$193$	8.71808	−	15.1002i	0.627541	−	1.08693i	−0.360503	−	0.932758i	$-0.617395\pi$
$193$	8.71808	−	15.1002i	0.627541	−	1.08693i	0.988044	−	0.154175i	$-0.0492718\pi$
$194$		0			0
$195$	−19.0595	−	24.9416i	−1.36488	−	1.78610i
$196$		0			0
$197$	−8.36275	+	8.36275i	−0.595822	+	0.595822i	−0.939198	−	0.343376i	$-0.888429\pi$
$197$	−8.36275	+	8.36275i	−0.595822	+	0.595822i	0.343376	+	0.939198i	$0.388429\pi$
$198$		0			0
$199$		−	15.6420i		−	1.10883i	−0.832240	−	0.554416i	$-0.812942\pi$
$199$		−	15.6420i		−	1.10883i	0.832240	−	0.554416i	$-0.187058\pi$
$200$		0			0
$201$	−9.16425	+	3.77459i	−0.646396	+	0.266239i
$202$		0			0
$203$	−3.83573	−	14.3151i	−0.269216	−	1.00473i
$204$		0			0
$205$	−5.32059	+	19.8567i	−0.371606	+	1.38685i
$206$		0			0
$207$	−26.3809	−	7.18150i	−1.83360	−	0.499149i
$208$		0			0
$209$	0.361796	+	0.626649i	0.0250259	+	0.0433462i
$210$		0			0
$211$	18.6925	−	5.00865i	1.28685	−	0.344810i	0.450386	−	0.892834i	$-0.351287\pi$
$211$	18.6925	−	5.00865i	1.28685	−	0.344810i	0.836462	+	0.548024i	$0.184620\pi$
$212$		0			0
$213$	1.53315	+	11.8275i	0.105050	+	0.810404i
$214$		0			0
$215$			35.3170i			2.40860i
$216$		0			0
$217$			2.23159i			0.151491i
$218$		0			0
$219$	−2.93825	−	22.6670i	−0.198548	−	1.53170i
$220$		0			0
$221$	−0.251948	+	0.0675091i	−0.0169478	+	0.00454116i
$222$		0			0
$223$	2.07790	+	3.59904i	0.139147	+	0.241009i	0.927174	−	0.374631i	$-0.122231\pi$
$223$	2.07790	+	3.59904i	0.139147	+	0.241009i	−0.788027	+	0.615641i	$0.788897\pi$
$224$		0			0
$225$	−9.61296	+	9.53666i	−0.640864	+	0.635778i
$226$		0			0
$227$	1.66928	−	6.22983i	0.110794	−	0.413488i	−0.888144	−	0.459565i	$-0.848005\pi$
$227$	1.66928	−	6.22983i	0.110794	−	0.413488i	0.998938	+	0.0460768i	$0.0146719\pi$
$228$		0			0
$229$	2.51329	+	9.37974i	0.166083	+	0.619831i	0.997900	+	0.0647799i	$0.0206345\pi$
$229$	2.51329	+	9.37974i	0.166083	+	0.619831i	−0.831816	+	0.555051i	$0.812699\pi$
$230$		0			0
$231$	−1.52286	+	0.627237i	−0.100197	+	0.0412692i
$232$		0			0
$233$		−	22.2096i		−	1.45500i	−0.686108	−	0.727499i	$-0.740682\pi$
$233$		−	22.2096i		−	1.45500i	0.686108	−	0.727499i	$-0.259318\pi$
$234$		0			0
$235$	5.34145	−	5.34145i	0.348438	−	0.348438i
$236$		0			0
$237$	7.28681	+	9.53563i	0.473329	+	0.619406i
$238$		0			0
$239$	4.02723	−	6.97537i	0.260500	−	0.451199i	−0.705875	−	0.708337i	$-0.749446\pi$
$239$	4.02723	−	6.97537i	0.260500	−	0.451199i	0.966375	+	0.257137i	$0.0827792\pi$
$240$		0			0
$241$	5.07653	+	8.79280i	0.327008	+	0.566394i	0.981917	−	0.189314i	$-0.0606263\pi$
$241$	5.07653	+	8.79280i	0.327008	+	0.566394i	−0.654909	+	0.755708i	$0.727293\pi$
$242$		0			0
$243$	−12.4611	+	9.36600i	−0.799377	+	0.600829i
$244$		0			0
$245$	8.23954	+	2.20778i	0.526405	+	0.141050i
$246$		0			0
$247$	−7.96812	−	4.60040i	−0.507000	−	0.292716i
$248$		0			0
$249$	0.139732	−	1.04528i	0.00885516	−	0.0662417i
$250$		0			0
$251$	−11.0682	+	11.0682i	−0.698617	+	0.698617i	−0.964112	−	0.265495i	$-0.914465\pi$
$251$	−11.0682	+	11.0682i	−0.698617	+	0.698617i	0.265495	+	0.964112i	$0.414465\pi$
$252$		0			0
$253$	−2.97786	−	2.97786i	−0.187217	−	0.187217i
$254$		0			0
$255$	0.0903202	+	0.219287i	0.00565607	+	0.0137323i
$256$		0			0
$257$	−10.3807	+	17.9800i	−0.647533	+	1.12156i	0.336177	+	0.941799i	$0.390866\pi$
$257$	−10.3807	+	17.9800i	−0.647533	+	1.12156i	−0.983710	+	0.179761i	$0.942467\pi$
$258$		0			0
$259$	−0.579249	+	2.16179i	−0.0359928	+	0.134327i
$260$		0			0
$261$	0.0860808	−	21.6059i	0.00532827	−	1.33737i
$262$		0			0
$263$	−9.13436	+	5.27373i	−0.563249	+	0.325192i	−0.754448	−	0.656359i	$-0.772096\pi$
$263$	−9.13436	+	5.27373i	−0.563249	+	0.325192i	0.191200	+	0.981551i	$0.438762\pi$
$264$		0			0
$265$	−9.24767	−	5.33914i	−0.568080	−	0.327981i
$266$		0			0
$267$	−1.18009	−	9.10377i	−0.0722203	−	0.557142i
$268$		0			0
$269$	−0.529850	−	0.529850i	−0.0323055	−	0.0323055i	0.690770	−	0.723075i	$-0.257272\pi$
$269$	−0.529850	−	0.529850i	−0.0323055	−	0.0323055i	−0.723075	+	0.690770i	$0.757272\pi$
$270$		0			0
$271$	−14.3682			−0.872804			−0.436402	−	0.899752i	$-0.643747\pi$
$271$	−14.3682			−0.872804			−0.436402	+	0.899752i	$0.643747\pi$
$272$		0			0
$273$	12.7818	−	16.5890i	0.773587	−	1.00401i
$274$		0			0
$275$	−2.01465	+	0.539824i	−0.121488	+	0.0325526i
$276$		0			0
$277$	−8.19567	−	2.19602i	−0.492430	−	0.131946i	0.00405455	−	0.999992i	$-0.498709\pi$
$277$	−8.19567	−	2.19602i	−0.492430	−	0.131946i	−0.496485	+	0.868046i	$0.665376\pi$
$278$		0			0
$279$	−0.854559	+	3.13918i	−0.0511611	+	0.187938i
$280$		0			0
$281$	−6.21827	+	3.59012i	−0.370951	+	0.214169i	−0.673874	−	0.738847i	$-0.735371\pi$
$281$	−6.21827	+	3.59012i	−0.370951	+	0.214169i	0.302923	+	0.953015i	$0.402038\pi$
$282$		0			0
$283$	−3.98753	−	14.8817i	−0.237034	−	0.884623i	−0.977221	−	0.212222i	$-0.931930\pi$
$283$	−3.98753	−	14.8817i	−0.237034	−	0.884623i	0.740187	−	0.672401i	$-0.234737\pi$
$284$		0			0
$285$	−3.21678	+	7.72245i	−0.190546	+	0.457438i
$286$		0			0
$287$	−13.7147			−0.809555
$288$		0			0
$289$	−16.9980			−0.999884
$290$		0			0
$291$	12.3740	+	16.1928i	0.725377	+	0.949239i
$292$		0			0
$293$	4.11281	+	15.3492i	0.240273	+	0.896711i	0.975701	+	0.219108i	$0.0703146\pi$
$293$	4.11281	+	15.3492i	0.240273	+	0.896711i	−0.735428	+	0.677603i	$0.763019\pi$
$294$		0			0
$295$	9.93122	−	5.73379i	0.578218	−	0.333834i
$296$		0			0
$297$	−2.38239	+	0.299175i	−0.138240	+	0.0173599i
$298$		0			0
$299$	51.7244	+	13.8595i	2.99130	+	0.801517i
$300$		0			0
$301$	−22.7589	+	6.09824i	−1.31180	+	0.351496i
$302$		0			0
$303$	10.0468	+	1.34305i	0.577173	+	0.0771563i
$304$		0			0
$305$	−3.79220			−0.217141
$306$		0			0
$307$	−7.37130	−	7.37130i	−0.420702	−	0.420702i	0.464743	−	0.885446i	$-0.346147\pi$
$307$	−7.37130	−	7.37130i	−0.420702	−	0.420702i	−0.885446	+	0.464743i	$0.846147\pi$
$308$		0			0
$309$	−2.09880	−	0.874254i	−0.119397	−	0.0497346i
$310$		0			0
$311$	−6.23360	−	3.59897i	−0.353475	−	0.204079i	0.312740	−	0.949839i	$-0.398753\pi$
$311$	−6.23360	−	3.59897i	−0.353475	−	0.204079i	−0.666215	+	0.745760i	$0.732087\pi$
$312$		0			0
$313$	9.23161	−	5.32987i	0.521801	−	0.301262i	−0.215870	−	0.976422i	$-0.569259\pi$
$313$	9.23161	−	5.32987i	0.521801	−	0.301262i	0.737671	+	0.675160i	$0.235925\pi$
$314$		0			0
$315$	−16.4520	−	9.58617i	−0.926966	−	0.540119i
$316$		0			0
$317$	−3.89052	+	14.5196i	−0.218513	+	0.815503i	0.766387	+	0.642379i	$0.222053\pi$
$317$	−3.89052	+	14.5196i	−0.218513	+	0.815503i	−0.984900	+	0.173123i	$0.944614\pi$
$318$		0			0
$319$	1.66400	−	2.88213i	0.0931662	−	0.161369i
$320$		0			0
$321$	−4.37991	+	5.68453i	−0.244463	+	0.317280i
$322$		0			0
$323$	0.0491536	+	0.0491536i	0.00273498	+	0.00273498i
$324$		0			0
$325$	18.7531	−	18.7531i	1.04023	−	1.04023i
$326$		0			0
$327$	−22.3513	−	17.2216i	−1.23603	−	0.952357i
$328$		0			0
$329$	4.36444	+	2.51981i	0.240619	+	0.138922i
$330$		0			0
$331$	24.3818	+	6.53309i	1.34015	+	0.359091i	0.856488	−	0.516166i	$-0.172641\pi$
$331$	24.3818	+	6.53309i	1.34015	+	0.359091i	0.483658	+	0.875257i	$0.339308\pi$
$332$		0			0
$333$	−1.64265	+	2.81916i	−0.0900169	+	0.154489i
$334$		0			0
$335$	−8.82485	−	15.2851i	−0.482153	−	0.835113i
$336$		0			0
$337$	1.80217	−	3.12146i	0.0981707	−	0.170037i	−0.812757	−	0.582603i	$-0.802034\pi$
$337$	1.80217	−	3.12146i	0.0981707	−	0.170037i	0.910928	+	0.412566i	$0.135368\pi$
$338$		0			0
$339$	−5.05171	+	12.1275i	−0.274371	+	0.658677i
$340$		0			0
$341$	−0.354350	+	0.354350i	−0.0191891	+	0.0191891i
$342$		0			0
$343$			20.0953i			1.08505i
$344$		0			0
$345$	6.45126	−	48.2591i	0.347324	−	2.59818i
$346$		0			0
$347$	4.13293	+	15.4243i	0.221867	+	0.828020i	0.983635	+	0.180170i	$0.0576648\pi$
$347$	4.13293	+	15.4243i	0.221867	+	0.828020i	−0.761768	+	0.647850i	$0.775669\pi$
$348$		0			0
$349$	4.05477	−	15.1326i	0.217047	−	0.810029i	−0.768389	−	0.639983i	$-0.778942\pi$
$349$	4.05477	−	15.1326i	0.217047	−	0.810029i	0.985436	−	0.170047i	$-0.0543918\pi$
$350$		0			0
$351$	24.3326	−	18.4411i	1.29878	−	0.984312i
$352$		0			0
$353$	2.05577	+	3.56070i	0.109418	+	0.189517i	0.915534	−	0.402239i	$-0.131768\pi$
$353$	2.05577	+	3.56070i	0.109418	+	0.189517i	−0.806117	+	0.591756i	$0.798435\pi$
$354$		0			0
$355$	−20.5147	+	5.49691i	−1.08881	+	0.291746i
$356$		0			0
$357$	−0.125717	+	0.0960684i	−0.00665363	+	0.00508448i
$358$		0			0
$359$		−	20.1902i		−	1.06560i	−0.846242	−	0.532800i	$-0.821140\pi$
$359$		−	20.1902i		−	1.06560i	0.846242	−	0.532800i	$-0.178860\pi$
$360$		0			0
$361$		−	16.5479i		−	0.870945i
$362$		0			0
$363$	17.2463	+	7.18394i	0.905196	+	0.377059i
$364$		0			0
$365$	39.3160	−	10.5347i	2.05789	−	0.551411i
$366$		0			0
$367$	−11.2398	−	19.4679i	−0.586714	−	1.01622i	−0.994659	−	0.103212i	$-0.967088\pi$
$367$	−11.2398	−	19.4679i	−0.586714	−	1.01622i	0.407946	−	0.913006i	$-0.366245\pi$
$368$		0			0
$369$	−19.2925	−	5.25187i	−1.00433	−	0.273402i
$370$		0			0
$371$	1.84383	−	6.88128i	0.0957270	−	0.357258i
$372$		0			0
$373$	6.87405	+	25.6543i	0.355925	+	1.32833i	0.879317	+	0.476237i	$0.158000\pi$
$373$	6.87405	+	25.6543i	0.355925	+	1.32833i	−0.523392	+	0.852092i	$0.675334\pi$
$374$		0			0
$375$	2.05821	+	1.58584i	0.106285	+	0.0818925i
$376$		0			0
$377$			42.3171i			2.17944i
$378$		0			0
$379$	6.62881	−	6.62881i	0.340499	−	0.340499i	−0.516056	−	0.856555i	$-0.672600\pi$
$379$	6.62881	−	6.62881i	0.340499	−	0.340499i	0.856555	+	0.516056i	$0.172600\pi$
$380$		0			0
$381$	−18.2716	+	2.36848i	−0.936083	+	0.121341i
$382$		0			0
$383$	−1.98902	+	3.44509i	−0.101634	+	0.176036i	−0.912358	−	0.409393i	$-0.865741\pi$
$383$	−1.98902	+	3.44509i	−0.101634	+	0.176036i	0.810724	+	0.585429i	$0.199074\pi$
$384$		0			0
$385$	−1.46646	−	2.53998i	−0.0747376	−	0.129449i
$386$		0			0
$387$	−34.3502	−	0.136856i	−1.74612	−	0.00695676i
$388$		0			0
$389$	−4.54738	−	1.21847i	−0.230561	−	0.0617787i	0.141688	−	0.989911i	$-0.454747\pi$
$389$	−4.54738	−	1.21847i	−0.230561	−	0.0617787i	−0.372250	+	0.928133i	$0.621414\pi$
$390$		0			0
$391$	−0.350370	−	0.202286i	−0.0177190	−	0.0102301i
$392$		0			0
$393$	−30.8362	+	12.7009i	−1.55548	+	0.640674i
$394$		0			0
$395$	−15.1119	+	15.1119i	−0.760360	+	0.760360i
$396$		0			0
$397$	−18.1361	−	18.1361i	−0.910223	−	0.910223i	0.0860661	−	0.996289i	$-0.472570\pi$
$397$	−18.1361	−	18.1361i	−0.910223	−	0.910223i	−0.996289	+	0.0860661i	$0.972570\pi$
$398$		0			0
$399$	−5.53193	−	0.739506i	−0.276943	−	0.0370216i
$400$		0			0
$401$	−2.47526	+	4.28727i	−0.123608	+	0.214096i	−0.921188	−	0.389118i	$-0.872780\pi$
$401$	−2.47526	+	4.28727i	−0.123608	+	0.214096i	0.797580	+	0.603214i	$0.206113\pi$
$402$		0			0
$403$	1.64921	−	6.15492i	0.0821528	−	0.306599i
$404$		0			0
$405$	−19.4721	−	19.7849i	−0.967576	−	0.983120i
$406$		0			0
$407$	−0.435242	+	0.251287i	−0.0215742	+	0.0124558i
$408$		0			0
$409$	12.4390	+	7.18164i	0.615067	+	0.355109i	0.774946	−	0.632027i	$-0.217777\pi$
$409$	12.4390	+	7.18164i	0.615067	+	0.355109i	−0.159879	+	0.987137i	$0.551110\pi$
$410$		0			0
$411$	−13.1932	+	10.0818i	−0.650771	+	0.497297i
$412$		0			0
$413$	5.40979	+	5.40979i	0.266199	+	0.266199i
$414$		0			0
$415$	1.87798			0.0921862
$416$		0			0
$417$	−4.65378	−	11.2988i	−0.227896	−	0.553305i
$418$		0			0
$419$	−24.4257	+	6.54483i	−1.19327	+	0.319736i	−0.800178	−	0.599763i	$-0.795262\pi$
$419$	−24.4257	+	6.54483i	−1.19327	+	0.319736i	−0.393093	+	0.919499i	$0.628595\pi$
$420$		0			0
$421$	−4.96853	−	1.33131i	−0.242151	−	0.0648842i	0.135702	−	0.990750i	$-0.456671\pi$
$421$	−4.96853	−	1.33131i	−0.242151	−	0.0648842i	−0.377853	+	0.925865i	$0.623338\pi$
$422$		0			0
$423$	5.17452	+	5.21591i	0.251594	+	0.253606i
$424$		0			0
$425$	−0.173526	+	0.100185i	−0.00841723	+	0.00485969i
$426$		0			0
$427$	−0.654803	−	2.44376i	−0.0316882	−	0.118262i
$428$		0			0
$429$	4.66371	−	0.604540i	0.225166	−	0.0291875i
$430$		0			0
$431$	−20.0912			−0.967760			−0.483880	−	0.875134i	$-0.660773\pi$
$431$	−20.0912			−0.967760			−0.483880	+	0.875134i	$0.660773\pi$
$432$		0			0
$433$	21.8262			1.04890			0.524449	−	0.851442i	$-0.324271\pi$
$433$	21.8262			1.04890			0.524449	+	0.851442i	$0.324271\pi$
$434$		0			0
$435$	38.1567	−	4.94611i	1.82947	−	0.237148i
$436$		0			0
$437$	−3.69362	−	13.7848i	−0.176690	−	0.659415i
$438$		0			0
$439$	25.7554	−	14.8699i	1.22924	−	0.709700i	0.262367	−	0.964968i	$-0.415497\pi$
$439$	25.7554	−	14.8699i	1.22924	−	0.709700i	0.966870	+	0.255268i	$0.0821636\pi$
$440$		0			0
$441$	−2.17926	+	8.00541i	−0.103774	+	0.381210i
$442$		0			0
$443$	−33.8185	−	9.06164i	−1.60677	−	0.430532i	−0.659689	−	0.751539i	$-0.729312\pi$
$443$	−33.8185	−	9.06164i	−1.60677	−	0.430532i	−0.947077	+	0.321007i	$0.895979\pi$
$444$		0			0
$445$	15.7905	−	4.23106i	0.748543	−	0.200571i
$446$		0			0
$447$	13.3161	+	32.3298i	0.629828	+	1.52915i
$448$		0			0
$449$	27.6805			1.30633			0.653163	−	0.757217i	$-0.273442\pi$
$449$	27.6805			1.30633			0.653163	+	0.757217i	$0.273442\pi$
$450$		0			0
$451$	−2.17773	−	2.17773i	−0.102545	−	0.102545i
$452$		0			0
$453$	−6.14514	+	4.69591i	−0.288724	+	0.220633i
$454$		0			0
$455$	32.2970	+	18.6467i	1.51411	+	0.874169i
$456$		0			0
$457$	−13.8114	+	7.97402i	−0.646070	+	0.373009i	−0.786949	−	0.617018i	$-0.788341\pi$
$457$	−13.8114	+	7.97402i	−0.646070	+	0.373009i	0.140879	+	0.990027i	$0.455007\pi$
$458$		0			0
$459$	−0.213633	+	0.0869977i	−0.00997155	+	0.00406071i
$460$		0			0
$461$	4.87059	−	18.1773i	0.226846	−	0.846600i	−0.754811	−	0.655943i	$-0.772271\pi$
$461$	4.87059	−	18.1773i	0.226846	−	0.846600i	0.981657	−	0.190658i	$-0.0610620\pi$
$462$		0			0
$463$	−6.07529	+	10.5227i	−0.282343	+	0.489032i	−0.971961	−	0.235141i	$-0.924445\pi$
$463$	−6.07529	+	10.5227i	−0.282343	+	0.489032i	0.689619	+	0.724173i	$0.257778\pi$
$464$		0			0
$465$	−5.74257	−	0.767664i	−0.266305	−	0.0355996i
$466$		0			0
$467$	15.9698	+	15.9698i	0.738992	+	0.738992i	0.972383	−	0.233391i	$-0.0749822\pi$
$467$	15.9698	+	15.9698i	0.738992	+	0.738992i	−0.233391	+	0.972383i	$0.574982\pi$
$468$		0			0
$469$	8.32618	−	8.32618i	0.384467	−	0.384467i
$470$		0			0
$471$	−26.3862	+	10.8680i	−1.21581	+	0.500770i
$472$		0			0
$473$	−4.58216	−	2.64551i	−0.210688	−	0.121641i
$474$		0			0
$475$	−6.82710	−	1.82931i	−0.313249	−	0.0839347i
$476$		0			0
$477$	5.22881	−	8.97380i	0.239411	−	0.410882i
$478$		0			0
$479$	9.27240	+	16.0603i	0.423667	+	0.733813i	0.996295	−	0.0860026i	$-0.0274094\pi$
$479$	9.27240	+	16.0603i	0.423667	+	0.733813i	−0.572628	+	0.819815i	$0.694076\pi$
$480$		0			0
$481$	3.19523	−	5.53430i	0.145690	−	0.252343i
$482$		0			0
$483$	32.2130	−	4.17565i	1.46574	−	0.189999i
$484$		0			0
$485$	−25.6620	+	25.6620i	−1.16525	+	1.16525i
$486$		0			0
$487$			6.58835i			0.298547i	0.988796	+	0.149273i	$0.0476934\pi$
$487$			6.58835i			0.298547i	−0.988796	+	0.149273i	$0.952307\pi$
$488$		0			0
$489$	10.1698	+	7.83577i	0.459893	+	0.354346i
$490$		0			0
$491$	−1.30320	−	4.86361i	−0.0588126	−	0.219491i	0.930265	−	0.366889i	$-0.119577\pi$
$491$	−1.30320	−	4.86361i	−0.0588126	−	0.219491i	−0.989077	+	0.147397i	$0.952910\pi$
$492$		0			0
$493$	0.0827478	−	0.308819i	0.00372678	−	0.0139085i
$494$		0			0
$495$	−1.09021	−	4.13454i	−0.0490013	−	0.185834i
$496$		0			0
$497$	−7.08461	−	12.2709i	−0.317788	−	0.550425i
$498$		0			0
$499$	20.9744	−	5.62008i	0.938944	−	0.251589i	0.243279	−	0.969956i	$-0.421777\pi$
$499$	20.9744	−	5.62008i	0.938944	−	0.251589i	0.695664	+	0.718367i	$0.255110\pi$
$500$		0			0
$501$	20.8576	+	8.68824i	0.931851	+	0.388162i
$502$		0			0
$503$		−	9.04140i		−	0.403136i	−0.979475	−	0.201568i	$-0.935396\pi$
$503$		−	9.04140i		−	0.403136i	0.979475	−	0.201568i	$-0.0646037\pi$
$504$		0			0
$505$			18.0504i			0.803232i
$506$		0			0
$507$	−29.6219	+	22.6361i	−1.31556	+	1.00530i
$508$		0			0
$509$	−14.1941	+	3.80331i	−0.629144	+	0.168579i	−0.559281	−	0.828978i	$-0.688923\pi$
$509$	−14.1941	+	3.80331i	−0.629144	+	0.168579i	−0.0698626	+	0.997557i	$0.522256\pi$
$510$		0			0
$511$	13.5775	+	23.5169i	0.600633	+	1.04033i
$512$		0			0
$513$	−7.49856	−	3.15864i	−0.331070	−	0.139457i
$514$		0			0
$515$	1.04791	−	3.91086i	0.0461765	−	0.172333i
$516$		0			0
$517$	0.292904	+	1.09313i	0.0128819	+	0.0480760i
$518$		0			0
$519$	0.329708	−	2.46640i	0.0144726	−	0.108263i
$520$		0			0
$521$			7.25761i			0.317962i	0.987282	+	0.158981i	$0.0508208\pi$
$521$			7.25761i			0.317962i	−0.987282	+	0.158981i	$0.949179\pi$
$522$		0			0
$523$	19.0736	−	19.0736i	0.834028	−	0.834028i	−0.154037	−	0.988065i	$-0.549227\pi$
$523$	19.0736	−	19.0736i	0.834028	−	0.834028i	0.988065	+	0.154037i	$0.0492274\pi$
$524$		0			0
$525$	6.18597	−	14.8505i	0.269978	−	0.648129i
$526$		0			0
$527$	−0.0240710	+	0.0416922i	−0.00104855	+	0.00181614i
$528$		0			0
$529$	30.0291	+	52.0119i	1.30561	+	2.26139i
$530$		0			0
$531$	5.53833	+	9.68155i	0.240343	+	0.420143i
$532$		0			0
$533$	37.8264	+	10.1355i	1.63844	+	0.439019i
$534$		0			0
$535$	−11.0672	−	6.38963i	−0.478476	−	0.276248i
$536$		0			0
$537$	−4.86582	−	3.74910i	−0.209976	−	0.161786i
$538$		0			0
$539$	−0.903648	+	0.903648i	−0.0389229	+	0.0389229i
$540$		0			0
$541$	12.1246	+	12.1246i	0.521279	+	0.521279i	0.917957	−	0.396679i	$-0.129837\pi$
$541$	12.1246	+	12.1246i	0.521279	+	0.521279i	−0.396679	+	0.917957i	$0.629837\pi$
$542$		0			0
$543$	−16.2651	+	21.1099i	−0.698001	+	0.905911i
$544$		0			0
$545$	25.1237	−	43.5156i	1.07618	−	1.86400i
$546$		0			0
$547$	9.94693	−	37.1224i	0.425300	−	1.58724i	−0.337967	−	0.941158i	$-0.609739\pi$
$547$	9.94693	−	37.1224i	0.425300	−	1.58724i	0.763267	−	0.646083i	$-0.223594\pi$
$548$		0			0
$549$	0.0146950	−	3.68838i	0.000627167	−	0.157416i
$550$		0			0
$551$	9.76675	−	5.63884i	0.416078	−	0.240223i
$552$		0			0
$553$	−12.3477	−	7.12897i	−0.525079	−	0.303155i
$554$		0			0
$555$	−5.36367	−	2.23423i	−0.227675	−	0.0948379i
$556$		0			0
$557$	−7.00897	−	7.00897i	−0.296979	−	0.296979i	0.542850	−	0.839830i	$-0.317345\pi$
$557$	−7.00897	−	7.00897i	−0.296979	−	0.296979i	−0.839830	+	0.542850i	$0.817345\pi$
$558$		0			0
$559$	67.2778			2.84555
$560$		0			0
$561$	−0.0352167	−	0.00470776i	−0.00148685	−	0.000198762i
$562$		0			0
$563$	6.06076	−	1.62398i	0.255430	−	0.0684424i	−0.128831	−	0.991667i	$-0.541123\pi$
$563$	6.06076	−	1.62398i	0.255430	−	0.0684424i	0.384262	+	0.923224i	$0.374456\pi$
$564$		0			0
$565$	−22.5981	−	6.05515i	−0.950711	−	0.254742i
$566$		0			0
$567$	9.38748	−	15.9644i	0.394237	−	0.670444i
$568$		0			0
$569$	5.33529	−	3.08033i	0.223667	−	0.129134i	−0.383980	−	0.923341i	$-0.625447\pi$
$569$	5.33529	−	3.08033i	0.223667	−	0.129134i	0.607647	+	0.794207i	$0.292113\pi$
$570$		0			0
$571$	4.83727	+	18.0529i	0.202433	+	0.755491i	0.990217	+	0.139539i	$0.0445620\pi$
$571$	4.83727	+	18.0529i	0.202433	+	0.755491i	−0.787783	+	0.615952i	$0.788771\pi$
$572$		0			0
$573$	−13.8657	−	18.1449i	−0.579250	−	0.758015i
$574$		0			0
$575$	41.1357			1.71548
$576$		0			0
$577$	11.2964			0.470277			0.235138	−	0.971962i	$-0.424446\pi$
$577$	11.2964			0.470277			0.235138	+	0.971962i	$0.424446\pi$
$578$		0			0
$579$	−11.6127	+	27.8784i	−0.482608	+	1.15859i
$580$		0			0
$581$	0.324272	+	1.21020i	0.0134531	+	0.0502076i
$582$		0			0
$583$	1.38544	−	0.799884i	0.0573790	−	0.0331278i
$584$		0			0
$585$	38.2916	+	38.5979i	1.58316	+	1.59583i
$586$		0			0
$587$	−37.0905	−	9.93836i	−1.53089	−	0.410200i	−0.607579	−	0.794259i	$-0.707859\pi$
$587$	−37.0905	−	9.93836i	−1.53089	−	0.410200i	−0.923309	+	0.384059i	$0.874526\pi$
$588$		0			0
$589$	−1.64031	+	0.439521i	−0.0675879	+	0.0181101i
$590$		0			0
$591$	12.5025	−	16.2266i	0.514285	−	0.667471i
$592$		0			0
$593$	7.39166			0.303539			0.151770	−	0.988416i	$-0.451503\pi$
$593$	7.39166			0.303539			0.151770	+	0.988416i	$0.451503\pi$
$594$		0			0
$595$	−0.199233	−	0.199233i	−0.00816776	−	0.00816776i
$596$		0			0
$597$	3.48280	+	26.8679i	0.142541	+	1.09963i
$598$		0			0
$599$	22.9017	+	13.2223i	0.935739	+	0.540249i	0.888622	−	0.458640i	$-0.151663\pi$
$599$	22.9017	+	13.2223i	0.935739	+	0.540249i	0.0471171	+	0.998889i	$0.484997\pi$
$600$		0			0
$601$	33.6284	−	19.4154i	1.37173	−	0.791970i	0.380587	−	0.924745i	$-0.375722\pi$
$601$	33.6284	−	19.4154i	1.37173	−	0.791970i	0.991146	+	0.132775i	$0.0423887\pi$
$602$		0			0
$603$	14.9008	−	8.52401i	0.606808	−	0.347125i
$604$		0			0
$605$	−8.61091	+	32.1364i	−0.350083	+	1.30653i
$606$		0			0
$607$	−1.86964	+	3.23831i	−0.0758863	+	0.131439i	−0.901471	−	0.432839i	$-0.857512\pi$
$607$	−1.86964	+	3.23831i	−0.0758863	+	0.131439i	0.825585	+	0.564278i	$0.190845\pi$
$608$		0			0
$609$	9.77592	+	23.7348i	0.396140	+	0.961782i
$610$		0			0
$611$	−10.1753	−	10.1753i	−0.411648	−	0.411648i
$612$		0			0
$613$	−4.21378	+	4.21378i	−0.170193	+	0.170193i	−0.787064	−	0.616871i	$-0.788400\pi$
$613$	−4.21378	+	4.21378i	−0.170193	+	0.170193i	0.616871	+	0.787064i	$0.288400\pi$
$614$		0			0
$615$	4.71784	−	35.2921i	0.190242	−	1.42312i
$616$		0			0
$617$	19.3833	+	11.1910i	0.780343	+	0.450531i	0.836552	−	0.547888i	$-0.184568\pi$
$617$	19.3833	+	11.1910i	0.780343	+	0.450531i	−0.0562088	+	0.998419i	$0.517901\pi$
$618$		0			0
$619$	−15.3149	−	4.10361i	−0.615557	−	0.164938i	−0.0624496	−	0.998048i	$-0.519891\pi$
$619$	−15.3149	−	4.10361i	−0.615557	−	0.164938i	−0.553107	+	0.833110i	$0.686558\pi$
$620$		0			0
$621$	46.9129	+	6.46164i	1.88255	+	0.259297i
$622$		0			0
$623$	5.45314	+	9.44511i	0.218475	+	0.378410i
$624$		0			0
$625$	−13.5976	+	23.5518i	−0.543905	+	0.942071i
$626$		0			0
$627$	−0.760977	−	0.995826i	−0.0303905	−	0.0397694i
$628$		0			0
$629$	−0.0341399	+	0.0341399i	−0.00136125	+	0.00136125i
$630$		0			0
$631$			38.2887i			1.52425i	0.647429	+	0.762125i	$0.275844\pi$
$631$			38.2887i			1.52425i	−0.647429	+	0.762125i	$0.724156\pi$
$632$		0			0
$633$	−30.9926	+	12.7653i	−1.23185	+	0.507374i
$634$		0			0
$635$	−8.49189	−	31.6922i	−0.336990	−	1.25767i
$636$		0			0
$637$	4.20574	−	15.6960i	0.166638	−	0.621900i
$638$		0			0
$639$	−5.26692	−	19.9744i	−0.208356	−	0.790175i
$640$		0			0
$641$	−8.82135	−	15.2790i	−0.348422	−	0.603485i	0.637547	−	0.770412i	$-0.279949\pi$
$641$	−8.82135	−	15.2790i	−0.348422	−	0.603485i	−0.985969	+	0.166926i	$0.946616\pi$
$642$		0			0
$643$	27.9805	−	7.49737i	1.10345	−	0.295667i	0.339278	−	0.940686i	$-0.389817\pi$
$643$	27.9805	−	7.49737i	1.10345	−	0.295667i	0.764167	+	0.645019i	$0.223150\pi$
$644$		0			0
$645$	−7.86358	−	60.6634i	−0.309628	−	2.38862i
$646$		0			0
$647$		−	5.73725i		−	0.225555i	−0.993620	−	0.112777i	$-0.964025\pi$
$647$		−	5.73725i		−	0.225555i	0.993620	−	0.112777i	$-0.0359747\pi$
$648$		0			0
$649$			1.71802i			0.0674380i
$650$		0			0
$651$	−0.496880	−	3.83317i	−0.0194742	−	0.150234i
$652$		0			0
$653$	−37.5980	+	10.0743i	−1.47132	+	0.394239i	−0.903384	−	0.428832i	$-0.858925\pi$
$653$	−37.5980	+	10.0743i	−1.47132	+	0.394239i	−0.567938	+	0.823072i	$0.692259\pi$
$654$		0			0
$655$	−29.6942	−	51.4318i	−1.16025	−	2.00961i
$656$		0			0
$657$	10.0939	+	38.2805i	0.393802	+	1.49346i
$658$		0			0
$659$	−10.2644	+	38.3072i	−0.399844	+	1.49224i	0.413528	+	0.910492i	$0.364297\pi$
$659$	−10.2644	+	38.3072i	−0.399844	+	1.49224i	−0.813371	+	0.581745i	$0.802370\pi$
$660$		0			0
$661$	−1.47348	−	5.49909i	−0.0573116	−	0.213890i	0.931331	−	0.364173i	$-0.118648\pi$
$661$	−1.47348	−	5.49909i	−0.0573116	−	0.213890i	−0.988643	+	0.150283i	$0.951982\pi$
$662$		0			0
$663$	0.417734	−	0.172057i	0.0162234	−	0.00668214i
$664$		0			0
$665$		−	9.93883i		−	0.385411i
$666$		0			0
$667$	−46.4121	+	46.4121i	−1.79708	+	1.79708i
$668$		0			0
$669$	−4.37052	−	5.71933i	−0.168974	−	0.221122i
$670$		0			0
$671$	0.284064	−	0.492013i	0.0109662	−	0.0189940i
$672$		0			0
$673$	−2.23206	−	3.86604i	−0.0860396	−	0.149025i	0.819794	−	0.572658i	$-0.194088\pi$
$673$	−2.23206	−	3.86604i	−0.0860396	−	0.149025i	−0.905834	+	0.423633i	$0.860754\pi$
$674$		0			0
$675$	14.3886	−	18.5213i	0.553817	−	0.712886i
$676$		0			0
$677$	−8.06369	−	2.16066i	−0.309913	−	0.0830409i	0.100511	−	0.994936i	$-0.467952\pi$
$677$	−8.06369	−	2.16066i	−0.309913	−	0.0830409i	−0.410423	+	0.911895i	$0.634619\pi$
$678$		0			0
$679$	−20.9681	−	12.1060i	−0.804683	−	0.464584i
$680$		0			0
$681$	−1.48017	+	11.0725i	−0.0567203	+	0.424300i
$682$		0			0
$683$	−3.00972	+	3.00972i	−0.115164	+	0.115164i	−0.762340	−	0.647177i	$-0.775950\pi$
$683$	−3.00972	+	3.00972i	−0.115164	+	0.115164i	0.647177	+	0.762340i	$0.275950\pi$
$684$		0			0
$685$	−20.9082	−	20.9082i	−0.798863	−	0.798863i
$686$		0			0
$687$	−6.40550	−	15.5518i	−0.244385	−	0.593338i
$688$		0			0
$689$	−10.1709	+	17.6165i	−0.387480	+	0.671135i
$690$		0			0
$691$	−7.65924	+	28.5847i	−0.291371	+	1.08741i	0.652686	+	0.757629i	$0.273642\pi$
$691$	−7.65924	+	28.5847i	−0.291371	+	1.08741i	−0.944057	+	0.329783i	$0.893024\pi$
$692$		0			0
$693$	2.47612	−	1.41647i	0.0940601	−	0.0538071i
$694$		0			0
$695$	18.8453	−	10.8804i	0.714844	−	0.412715i
$696$		0			0
$697$	−0.256228	−	0.147933i	−0.00970532	−	0.00560337i
$698$		0			0
$699$	4.94511	+	38.1490i	0.187041	+	1.44293i
$700$		0			0
$701$	−1.29990	−	1.29990i	−0.0490966	−	0.0490966i	0.682132	−	0.731229i	$-0.261053\pi$
$701$	−1.29990	−	1.29990i	−0.0490966	−	0.0490966i	−0.731229	+	0.682132i	$0.761053\pi$
$702$		0			0
$703$	−1.70309			−0.0642331
$704$		0			0
$705$	−7.98559	+	10.3642i	−0.300755	+	0.390339i
$706$		0			0
$707$	−11.6320	+	3.11678i	−0.437466	+	0.117219i
$708$		0			0
$709$	−36.6010	−	9.80720i	−1.37458	−	0.368317i	−0.505429	−	0.862868i	$-0.668666\pi$
$709$	−36.6010	−	9.80720i	−1.37458	−	0.368317i	−0.869149	+	0.494551i	$0.835333\pi$
$710$		0			0
$711$	−14.6396	−	14.7567i	−0.549027	−	0.553419i
$712$		0			0
$713$	8.55933	−	4.94173i	0.320550	−	0.185069i
$714$		0			0
$715$	2.16750	+	8.08922i	0.0810599	+	0.302520i
$716$		0			0
$717$	−5.36438	+	12.8782i	−0.200337	+	0.480943i
$718$		0			0
$719$	−5.11125			−0.190617			−0.0953087	−	0.995448i	$-0.530384\pi$
$719$	−5.11125			−0.190617			−0.0953087	+	0.995448i	$0.530384\pi$
$720$		0			0
$721$	2.70117			0.100597
$722$		0			0
$723$	−10.6776	−	13.9729i	−0.397105	−	0.519658i
$724$		0			0
$725$	8.41353	+	31.3997i	0.312471	+	1.16616i
$726$		0			0
$727$	−18.6355	+	10.7592i	−0.691154	+	0.399038i	−0.804044	−	0.594570i	$-0.797322\pi$
$727$	−18.6355	+	10.7592i	−0.691154	+	0.399038i	0.112890	+	0.993607i	$0.463989\pi$
$728$		0			0
$729$	19.3187	−	18.8623i	0.715508	−	0.698605i
$730$		0			0
$731$	−0.490976	−	0.131557i	−0.0181594	−	0.00486580i
$732$		0			0
$733$	2.98220	−	0.799079i	0.110150	−	0.0295147i	−0.203323	−	0.979112i	$-0.565174\pi$
$733$	2.98220	−	0.799079i	0.110150	−	0.0295147i	0.313473	+	0.949597i	$0.398507\pi$
$734$		0			0
$735$	−14.6445	−	1.95767i	−0.540169	−	0.0722096i
$736$		0			0
$737$	2.64419			0.0973999
$738$		0			0
$739$	−23.9990	−	23.9990i	−0.882818	−	0.882818i	0.111002	−	0.993820i	$-0.464594\pi$
$739$	−23.9990	−	23.9990i	−0.882818	−	0.882818i	−0.993820	+	0.111002i	$0.964594\pi$
$740$		0			0
$741$	14.7110	+	6.12786i	0.540422	+	0.225112i
$742$		0			0
$743$	14.4499	+	8.34266i	0.530116	+	0.306062i	0.741064	−	0.671435i	$-0.234322\pi$
$743$	14.4499	+	8.34266i	0.530116	+	0.306062i	−0.210948	+	0.977497i	$0.567655\pi$
$744$		0			0
$745$	−53.9230	+	31.1325i	−1.97559	+	1.14061i
$746$		0			0
$747$	−0.00727726	+	1.82656i	−0.000266261	+	0.0668304i
$748$		0			0
$749$	2.20661	−	8.23519i	0.0806278	−	0.300907i
$750$		0			0
$751$	−17.1635	+	29.7281i	−0.626305	+	1.08479i	0.361982	+	0.932185i	$0.382100\pi$
$751$	−17.1635	+	29.7281i	−0.626305	+	1.08479i	−0.988287	+	0.152607i	$0.951233\pi$
$752$		0			0
$753$	16.5472	−	21.4760i	0.603012	−	0.782628i
$754$		0			0
$755$	−9.73869	−	9.73869i	−0.354427	−	0.354427i
$756$		0			0
$757$	−24.0162	+	24.0162i	−0.872884	+	0.872884i	−0.992786	−	0.119902i	$-0.961742\pi$
$757$	−24.0162	+	24.0162i	−0.872884	+	0.872884i	0.119902	+	0.992786i	$0.461742\pi$
$758$		0			0
$759$	5.77806	+	4.45198i	0.209730	+	0.161596i
$760$		0			0
$761$	−13.2713	−	7.66221i	−0.481086	−	0.277755i	0.239783	−	0.970826i	$-0.422924\pi$
$761$	−13.2713	−	7.66221i	−0.481086	−	0.277755i	−0.720869	+	0.693072i	$0.756257\pi$
$762$		0			0
$763$	32.3804	+	8.67629i	1.17225	+	0.314103i
$764$		0			0
$765$	−0.203967	−	0.356554i	−0.00737444	−	0.0128912i
$766$		0			0
$767$	−10.9227	−	18.9186i	−0.394395	−	0.683112i
$768$		0			0
$769$	20.6394	−	35.7485i	0.744276	−	1.28912i	−0.206256	−	0.978498i	$-0.566128\pi$
$769$	20.6394	−	35.7485i	0.744276	−	1.28912i	0.950532	−	0.310626i	$-0.100539\pi$
$770$		0			0
$771$	13.8274	−	33.1952i	0.497983	−	1.19550i
$772$		0			0
$773$	36.3711	−	36.3711i	1.30818	−	1.30818i	0.385448	−	0.922730i	$-0.374047\pi$
$773$	36.3711	−	36.3711i	1.30818	−	1.30818i	0.922730	−	0.385448i	$-0.125953\pi$
$774$		0			0
$775$		−	4.89492i		−	0.175831i
$776$		0			0
$777$	0.513628	−	3.84223i	0.0184263	−	0.137839i
$778$		0			0
$779$	−2.70117	−	10.0809i	−0.0967793	−	0.361185i
$780$		0			0
$781$	0.823519	−	3.07342i	0.0294678	−	0.109975i
$782$		0			0
$783$	4.66284	+	37.1312i	0.166636	+	1.32696i
$784$		0			0
$785$	−25.4089	−	44.0096i	−0.906883	−	1.57077i
$786$		0			0
$787$	−29.8060	+	7.98650i	−1.06247	+	0.284688i	−0.747396	−	0.664379i	$-0.768696\pi$
$787$	−29.8060	+	7.98650i	−1.06247	+	0.284688i	−0.315074	+	0.949067i	$0.602029\pi$
$788$		0			0
$789$	14.5157	−	11.0924i	0.516772	−	0.394900i
$790$		0			0
$791$		−	15.6082i		−	0.554963i
$792$		0			0
$793$			7.22401i			0.256532i
$794$		0			0
$795$	17.0733	+	7.11188i	0.605528	+	0.252232i
$796$		0			0
$797$	−25.7854	+	6.90917i	−0.913364	+	0.244735i	−0.684747	−	0.728781i	$-0.740087\pi$
$797$	−25.7854	+	6.90917i	−0.913364	+	0.244735i	−0.228617	+	0.973516i	$0.573420\pi$
$798$		0			0
$799$	0.0543596	+	0.0941536i	0.00192311	+	0.00333092i
$800$		0			0
$801$	4.05403	+	15.3746i	0.143242	+	0.543235i
$802$		0			0
$803$	−1.57826	+	5.89013i	−0.0556954	+	0.207858i
$804$		0			0
$805$	14.9712	+	55.8735i	0.527667	+	1.96928i
$806$		0			0
$807$	1.02809	+	0.792137i	0.0361904	+	0.0278846i
$808$		0			0
$809$		−	41.9379i		−	1.47446i	−0.675644	−	0.737228i	$-0.736134\pi$
$809$		−	41.9379i		−	1.47446i	0.675644	−	0.737228i	$-0.263866\pi$
$810$		0			0
$811$	−0.250947	+	0.250947i	−0.00881196	+	0.00881196i	−0.711499	−	0.702687i	$-0.751983\pi$
$811$	−0.250947	+	0.250947i	−0.00881196	+	0.00881196i	0.702687	+	0.711499i	$0.251983\pi$
$812$		0			0
$813$	24.6799	−	3.19917i	0.865562	−	0.112200i
$814$		0			0
$815$	−11.4312	+	19.7994i	−0.400418	+	0.693544i
$816$		0			0
$817$	−8.96490	−	15.5277i	−0.313642	−	0.543244i
$818$		0			0
$819$	−18.2613	+	31.3405i	−0.638102	+	1.09513i
$820$		0			0
$821$	18.7959	+	5.03635i	0.655982	+	0.175770i	0.571432	−	0.820650i	$-0.306388\pi$
$821$	18.7959	+	5.03635i	0.655982	+	0.175770i	0.0845497	+	0.996419i	$0.473055\pi$
$822$		0			0
$823$	−34.7295	−	20.0511i	−1.21059	−	0.698936i	−0.247705	−	0.968836i	$-0.579676\pi$
$823$	−34.7295	−	20.0511i	−1.21059	−	0.698936i	−0.962889	+	0.269899i	$0.913010\pi$
$824$		0			0
$825$	3.34033	−	1.37582i	0.116295	−	0.0478999i
$826$		0			0
$827$	39.0429	−	39.0429i	1.35765	−	1.35765i	0.480853	−	0.876801i	$-0.340327\pi$
$827$	39.0429	−	39.0429i	1.35765	−	1.35765i	0.876801	−	0.480853i	$-0.159673\pi$
$828$		0			0
$829$	−18.5103	−	18.5103i	−0.642891	−	0.642891i	0.308374	−	0.951265i	$-0.400215\pi$
$829$	−18.5103	−	18.5103i	−0.642891	−	0.642891i	−0.951265	+	0.308374i	$0.900215\pi$
$830$		0			0
$831$	14.5665	+	1.94724i	0.505306	+	0.0675491i
$832$		0			0
$833$	−0.0613849	+	0.106322i	−0.00212686	+	0.00368383i
$834$		0			0
$835$	−10.4140	+	38.8656i	−0.360392	+	1.34500i
$836$		0			0
$837$	0.768900	−	5.58238i	0.0265771	−	0.192955i
$838$		0			0
$839$	9.12331	−	5.26735i	0.314972	−	0.181849i	−0.334177	−	0.942510i	$-0.608458\pi$
$839$	9.12331	−	5.26735i	0.314972	−	0.181849i	0.649149	+	0.760661i	$0.275125\pi$
$840$		0			0
$841$	−19.8053	−	11.4346i	−0.682942	−	0.394297i
$842$		0			0
$843$	9.88163	−	7.55121i	0.340341	−	0.260078i
$844$		0			0
$845$	−46.9442	−	46.9442i	−1.61493	−	1.61493i
$846$		0			0
$847$	−22.1961			−0.762667
$848$		0			0
$849$	10.1628	+	24.6741i	0.348787	+	0.846812i
$850$		0			0
$851$	9.57429	−	2.56542i	0.328203	−	0.0879416i
$852$		0			0
$853$	−31.7237	−	8.50035i	−1.08620	−	0.291046i	−0.329067	−	0.944307i	$-0.606734\pi$
$853$	−31.7237	−	8.50035i	−1.08620	−	0.291046i	−0.757133	+	0.653260i	$0.773401\pi$
$854$		0			0
$855$	3.80594	−	13.9809i	0.130161	−	0.478138i
$856$		0			0
$857$	−32.9302	+	19.0123i	−1.12487	+	0.649447i	−0.942641	−	0.333808i	$-0.891666\pi$
$857$	−32.9302	+	19.0123i	−1.12487	+	0.649447i	−0.182234	+	0.983255i	$0.558333\pi$
$858$		0			0
$859$	−11.2230	−	41.8849i	−0.382925	−	1.42910i	−0.841412	−	0.540395i	$-0.818275\pi$
$859$	−11.2230	−	41.8849i	−0.382925	−	1.42910i	0.458487	−	0.888701i	$-0.348392\pi$
$860$		0			0
$861$	23.5575	−	3.05368i	0.802838	−	0.104069i
$862$		0			0
$863$	19.8437			0.675487			0.337744	−	0.941238i	$-0.390336\pi$
$863$	19.8437			0.675487			0.337744	+	0.941238i	$0.390336\pi$
$864$		0			0
$865$	4.43121			0.150666
$866$		0			0
$867$	29.1972	−	3.78473i	0.991588	−	0.128536i
$868$		0			0
$869$	−0.828675	−	3.09266i	−0.0281109	−	0.104911i
$870$		0			0
$871$	−29.1176	+	16.8110i	−0.986611	+	0.569620i
$872$		0			0
$873$	−24.8600	−	25.0589i	−0.841384	−	0.848115i
$874$		0			0
$875$	−2.98173	−	0.798951i	−0.100801	−	0.0270095i
$876$		0			0
$877$	49.5131	−	13.2670i	1.67194	−	0.447995i	0.706307	−	0.707906i	$-0.250360\pi$
$877$	49.5131	−	13.2670i	1.67194	−	0.447995i	0.965633	+	0.259911i	$0.0836931\pi$
$878$		0			0
$879$	−10.4821	−	25.4493i	−0.353552	−	0.858384i
$880$		0			0
$881$	−31.7902			−1.07104			−0.535519	−	0.844523i	$-0.679884\pi$
$881$	−31.7902			−1.07104			−0.535519	+	0.844523i	$0.679884\pi$
$882$		0			0
$883$	−28.7423	−	28.7423i	−0.967255	−	0.967255i	0.0322259	−	0.999481i	$-0.489740\pi$
$883$	−28.7423	−	28.7423i	−0.967255	−	0.967255i	−0.999481	+	0.0322259i	$0.989740\pi$
$884$		0			0
$885$	−15.7820	+	12.0601i	−0.530506	+	0.405395i
$886$		0			0
$887$	−23.1996	−	13.3943i	−0.778966	−	0.449736i	0.0570976	−	0.998369i	$-0.481815\pi$
$887$	−23.1996	−	13.3943i	−0.778966	−	0.449736i	−0.836064	+	0.548632i	$0.815149\pi$
$888$		0			0
$889$	18.9567	−	10.9447i	0.635787	−	0.367072i
$890$		0			0
$891$	4.02557	−	1.04434i	0.134862	−	0.0349868i
$892$		0			0
$893$	−0.992572	+	3.70433i	−0.0332151	+	0.123961i
$894$		0			0
$895$	5.46938	−	9.47324i	0.182821	−	0.316655i
$896$		0			0
$897$	−91.9319	−	12.2894i	−3.06952	−	0.410332i
$898$		0			0
$899$	5.52278	+	5.52278i	0.184195	+	0.184195i
$900$		0			0
$901$	0.108672	−	0.108672i	0.00362040	−	0.00362040i
$902$		0			0
$903$	37.7347	−	15.5422i	1.25573	−	0.517213i
$904$		0			0
$905$	−41.0986	−	23.7283i	−1.36616	−	0.788756i
$906$		0			0
$907$	15.9995	+	4.28704i	0.531253	+	0.142349i	0.514467	−	0.857510i	$-0.327990\pi$
$907$	15.9995	+	4.28704i	0.531253	+	0.142349i	0.0167863	+	0.999859i	$0.494657\pi$
$908$		0			0
$909$	−17.5562	−	0.0699463i	−0.582303	−	0.00231997i
$910$		0			0
$911$	−0.940538	−	1.62906i	−0.0311614	−	0.0539731i	0.850024	−	0.526744i	$-0.176587\pi$
$911$	−0.940538	−	1.62906i	−0.0311614	−	0.0539731i	−0.881186	+	0.472771i	$0.843254\pi$
$912$		0			0
$913$	−0.140674	+	0.243655i	−0.00465564	+	0.00806381i
$914$		0			0
$915$	6.51378	−	0.844358i	0.215339	−	0.0279136i
$916$		0			0
$917$	28.0162	−	28.0162i	0.925177	−	0.925177i
$918$		0			0
$919$			58.7898i			1.93930i	0.244501	+	0.969649i	$0.421376\pi$
$919$			58.7898i			1.93930i	−0.244501	+	0.969649i	$0.578624\pi$
$920$		0			0
$921$	14.3028	+	11.0203i	0.471293	+	0.363130i
$922$		0			0
$923$	10.4714	+	39.0799i	0.344671	+	1.28633i
$924$		0			0
$925$	1.27056	−	4.74180i	0.0417758	−	0.155909i
$926$		0			0
$927$	3.79973	+	1.03438i	0.124799	+	0.0339734i
$928$		0			0
$929$	17.0265	+	29.4908i	0.558622	+	0.967562i	0.997612	+	0.0690699i	$0.0220032\pi$
$929$	17.0265	+	29.4908i	0.558622	+	0.967562i	−0.438990	+	0.898492i	$0.644664\pi$
$930$		0			0
$931$	−4.18306	+	1.12085i	−0.137094	+	0.0367343i
$932$		0			0
$933$	11.5087	+	4.79393i	0.376777	+	0.156946i
$934$		0			0
$935$		−	0.0632715i		−	0.00206920i
$936$		0			0
$937$			23.8098i			0.777833i	0.921273	+	0.388916i	$0.127151\pi$
$937$			23.8098i			0.777833i	−0.921273	+	0.388916i	$0.872849\pi$
$938$		0			0
$939$	−14.6702	+	11.2105i	−0.478744	+	0.365841i
$940$		0			0
$941$	−13.1052	+	3.51153i	−0.427217	+	0.114473i	−0.466020	−	0.884774i	$-0.654312\pi$
$941$	−13.1052	+	3.51153i	−0.427217	+	0.114473i	0.0388023	+	0.999247i	$0.487646\pi$
$942$		0			0
$943$	30.3705	+	52.6032i	0.988998	+	1.71300i
$944$		0			0
$945$	30.3937	+	12.8028i	0.988707	+	0.416476i
$946$		0			0
$947$	−5.14006	+	19.1830i	−0.167030	+	0.623363i	0.830743	+	0.556656i	$0.187916\pi$
$947$	−5.14006	+	19.1830i	−0.167030	+	0.623363i	−0.997773	+	0.0667069i	$0.978751\pi$
$948$		0			0
$949$	−20.0682	−	74.8957i	−0.651442	−	2.43122i
$950$		0			0
$951$	3.44978	−	25.8063i	0.111867	−	0.836826i
$952$		0			0
$953$		−	13.2336i		−	0.428678i	−0.976759	−	0.214339i	$-0.931240\pi$
$953$		−	13.2336i		−	0.428678i	0.976759	−	0.214339i	$-0.0687598\pi$
$954$		0			0
$955$	28.7557	−	28.7557i	0.930512	−	0.930512i
$956$		0			0
$957$	−2.21649	+	5.32108i	−0.0716491	+	0.172006i
$958$		0			0
$959$	9.86339	−	17.0839i	0.318506	−	0.551668i
$960$		0			0
$961$	14.9120	+	25.8283i	0.481031	+	0.833170i
$962$		0			0
$963$	6.25759	−	10.7394i	0.201648	−	0.346073i
$964$		0			0
$965$	−51.9479	−	13.9194i	−1.67226	−	0.448081i
$966$		0			0
$967$	45.2656	+	26.1341i	1.45564	+	0.840417i	0.998793	−	0.0491262i	$-0.0156437\pi$
$967$	45.2656	+	26.1341i	1.45564	+	0.840417i	0.456852	+	0.889543i	$0.348977\pi$
$968$		0			0
$969$	−0.0953746	−	0.0734858i	−0.00306387	−	0.00236070i
$970$		0			0
$971$	33.2081	−	33.2081i	1.06570	−	1.06570i	0.0680139	−	0.997684i	$-0.478334\pi$
$971$	33.2081	−	33.2081i	1.06570	−	1.06570i	0.997684	−	0.0680139i	$-0.0216662\pi$
$972$		0			0
$973$	10.2655	+	10.2655i	0.329098	+	0.329098i
$974$		0			0
$975$	−28.0363	+	36.3873i	−0.897881	+	1.16533i
$976$		0			0
$977$	15.0366	−	26.0441i	0.481063	−	0.833226i	−0.518701	−	0.854956i	$-0.673584\pi$
$977$	15.0366	−	26.0441i	0.481063	−	0.833226i	0.999764	+	0.0217300i	$0.00691743\pi$
$978$		0			0
$979$	−0.633876	+	2.36566i	−0.0202588	+	0.0756067i
$980$		0			0
$981$	42.2269	+	24.6045i	1.34820	+	0.785562i
$982$		0			0
$983$	−18.8575	+	10.8874i	−0.601460	+	0.347253i	−0.769616	−	0.638507i	$-0.779552\pi$
$983$	−18.8575	+	10.8874i	−0.601460	+	0.347253i	0.168155	+	0.985760i	$0.446219\pi$
$984$		0			0
$985$	31.5914	+	18.2393i	1.00658	+	0.581152i
$986$		0			0
$987$	−8.05776	−	3.35646i	−0.256481	−	0.106837i
$988$		0			0
$989$	73.7882	+	73.7882i	2.34633	+	2.34633i
$990$		0			0
$991$	−21.5288			−0.683884			−0.341942	−	0.939721i	$-0.611085\pi$
$991$	−21.5288			−0.683884			−0.341942	+	0.939721i	$0.611085\pi$
$992$		0			0
$993$	−43.3348	−	5.79298i	−1.37519	−	0.183835i
$994$		0			0
$995$	−46.6025	+	12.4871i	−1.47740	+	0.395868i
$996$		0			0
$997$	30.6713	+	8.21836i	0.971371	+	0.260278i	0.709407	−	0.704799i	$-0.248963\pi$
$997$	30.6713	+	8.21836i	0.971371	+	0.260278i	0.261964	+	0.965078i	$0.415630\pi$
$998$		0			0
$999$	2.19385	−	5.20817i	0.0694103	−	0.164779i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bb.e.337.2		72
3.2	odd	2		1728.2.bc.e.145.16		72
4.3	odd	2		144.2.x.e.13.14	✓	72
9.2	odd	6		1728.2.bc.e.721.3		72
9.7	even	3	inner	576.2.bb.e.529.9		72
12.11	even	2		432.2.y.e.253.5		72
16.5	even	4	inner	576.2.bb.e.49.9		72
16.11	odd	4		144.2.x.e.85.11	yes	72
36.7	odd	6		144.2.x.e.61.11	yes	72
36.11	even	6		432.2.y.e.397.8		72
48.5	odd	4		1728.2.bc.e.1009.3		72
48.11	even	4		432.2.y.e.37.8		72
144.11	even	12		432.2.y.e.181.5		72
144.43	odd	12		144.2.x.e.133.14	yes	72
144.101	odd	12		1728.2.bc.e.1585.16		72
144.133	even	12	inner	576.2.bb.e.241.2		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.14	✓	72	4.3	odd	2
144.2.x.e.61.11	yes	72	36.7	odd	6
144.2.x.e.85.11	yes	72	16.11	odd	4
144.2.x.e.133.14	yes	72	144.43	odd	12
432.2.y.e.37.8		72	48.11	even	4
432.2.y.e.181.5		72	144.11	even	12
432.2.y.e.253.5		72	12.11	even	2
432.2.y.e.397.8		72	36.11	even	6
576.2.bb.e.49.9		72	16.5	even	4	inner
576.2.bb.e.241.2		72	144.133	even	12	inner
576.2.bb.e.337.2		72	1.1	even	1	trivial
576.2.bb.e.529.9		72	9.7	even	3	inner
1728.2.bc.e.145.16		72	3.2	odd	2
1728.2.bc.e.721.3		72	9.2	odd	6
1728.2.bc.e.1009.3		72	48.5	odd	4
1728.2.bc.e.1585.16		72	144.101	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.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.71768 + 0.222657i) q^{3} +(-0.798307 - 2.97932i) q^{5} +(1.78208 - 1.02889i) q^{7} +(2.90085 - 0.764906i) q^{9} +O(q^{10})\)	\(q+(-1.71768 + 0.222657i) q^{3} +(-0.798307 - 2.97932i) q^{5} +(1.78208 - 1.02889i) q^{7} +(2.90085 - 0.764906i) q^{9} +(0.446347 + 0.119598i) q^{11} +(-5.67550 + 1.52075i) q^{13} +(2.03460 + 4.93977i) q^{15} +0.0443921 q^{17} +(1.10726 + 1.10726i) q^{19} +(-2.83196 + 2.16409i) q^{21} +(-7.89263 - 4.55681i) q^{23} +(-3.90893 + 2.25682i) q^{25} +(-4.81242 + 1.95976i) q^{27} +(1.86402 - 6.95662i) q^{29} +(-0.542236 + 0.939180i) q^{31} +(-0.793310 - 0.106049i) q^{33} +(-4.48803 - 4.48803i) q^{35} +(-0.769054 + 0.769054i) q^{37} +(9.41009 - 3.87585i) q^{39} +(-5.77193 - 3.33242i) q^{41} +(-11.0600 - 2.96351i) q^{43} +(-4.59467 - 8.03193i) q^{45} +(1.22453 + 2.12095i) q^{47} +(-1.38279 + 2.39506i) q^{49} +(-0.0762514 + 0.00988420i) q^{51} +(2.44801 - 2.44801i) q^{53} -1.42529i q^{55} +(-2.14846 - 1.65538i) q^{57} +(0.962265 + 3.59122i) q^{59} +(0.318210 - 1.18758i) q^{61} +(4.38255 - 4.34777i) q^{63} +(9.06158 + 15.6951i) q^{65} +(5.52723 - 1.48102i) q^{67} +(14.5716 + 6.06980i) q^{69} -6.88571i q^{71} +13.1963i q^{73} +(6.21180 - 4.74685i) q^{75} +(0.918480 - 0.246106i) q^{77} +(-3.46441 - 6.00054i) q^{79} +(7.82984 - 4.43775i) q^{81} +(-0.157584 + 0.588112i) q^{83} +(-0.0354385 - 0.132258i) q^{85} +(-1.65285 + 12.3643i) q^{87} +5.30004i q^{89} +(-8.54954 + 8.54954i) q^{91} +(0.722273 - 1.73394i) q^{93} +(2.41495 - 4.18282i) q^{95} +(-5.88304 - 10.1897i) q^{97} +(1.38627 + 0.00552307i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) \) 72 * q - 2 * q^3 + 4 * q^5	\( 72 q - 2 q^{3} + 4 q^{5} + 2 q^{11} - 16 q^{13} + 20 q^{15} - 16 q^{17} - 28 q^{19} - 16 q^{21} - 8 q^{27} + 4 q^{29} - 28 q^{31} - 32 q^{33} + 16 q^{35} + 16 q^{37} + 10 q^{43} + 40 q^{45} + 56 q^{47} + 4 q^{49} + 54 q^{51} - 8 q^{53} + 14 q^{59} - 32 q^{61} + 108 q^{63} - 64 q^{65} + 18 q^{67} + 32 q^{69} - 86 q^{75} - 36 q^{77} - 44 q^{79} - 44 q^{81} - 20 q^{83} - 8 q^{85} + 80 q^{91} - 4 q^{93} - 48 q^{95} + 40 q^{97} - 28 q^{99}+O(q^{100}) \) 72 * q - 2 * q^3 + 4 * q^5 + 2 * q^11 - 16 * q^13 + 20 * q^15 - 16 * q^17 - 28 * q^19 - 16 * q^21 - 8 * q^27 + 4 * q^29 - 28 * q^31 - 32 * q^33 + 16 * q^35 + 16 * q^37 + 10 * q^43 + 40 * q^45 + 56 * q^47 + 4 * q^49 + 54 * q^51 - 8 * q^53 + 14 * q^59 - 32 * q^61 + 108 * q^63 - 64 * q^65 + 18 * q^67 + 32 * q^69 - 86 * q^75 - 36 * q^77 - 44 * q^79 - 44 * q^81 - 20 * q^83 - 8 * q^85 + 80 * q^91 - 4 * q^93 - 48 * q^95 + 40 * q^97 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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