LMFDB - Embedded newform 1323.2.o.e.440.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(440,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("1323.440");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.o (of order $6$, degree $2$, 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:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 441)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			440.21
Character	$\chi$	$=$	1323.440
Dual form			1323.2.o.e.881.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.05485 + 1.18637i) q^{2} +(1.81495 + 3.14358i) q^{4} +(1.71774 + 2.97522i) q^{5} +3.86732i q^{8} +O(q^{10})$	\(q+(2.05485 + 1.18637i) q^{2} +(1.81495 + 3.14358i) q^{4} +(1.71774 + 2.97522i) q^{5} +3.86732i q^{8} +8.15151i q^{10} +(-0.271895 - 0.156979i) q^{11} +(-5.09882 + 2.94381i) q^{13} +(-0.958178 + 1.65961i) q^{16} -0.953423 q^{17} +1.26109i q^{19} +(-6.23523 + 10.7997i) q^{20} +(-0.372470 - 0.645137i) q^{22} +(5.91336 - 3.41408i) q^{23} +(-3.40128 + 5.89118i) q^{25} -13.9698 q^{26} +(-3.43518 - 1.98330i) q^{29} +(4.53388 - 2.61764i) q^{31} +(2.76057 - 1.59381i) q^{32} +(-1.95915 - 1.13111i) q^{34} +5.37604 q^{37} +(-1.49612 + 2.59136i) q^{38} +(-11.5061 + 6.64306i) q^{40} +(-0.0699627 - 0.121179i) q^{41} +(1.44078 - 2.49550i) q^{43} -1.13963i q^{44} +16.2014 q^{46} +(1.00695 - 1.74409i) q^{47} +(-13.9783 + 8.07035i) q^{50} +(-18.5082 - 10.6857i) q^{52} +11.9799i q^{53} -1.07860i q^{55} +(-4.70586 - 8.15079i) q^{58} +(-0.824459 - 1.42801i) q^{59} +(2.57423 + 1.48623i) q^{61} +12.4219 q^{62} +11.3961 q^{64} +(-17.5169 - 10.1134i) q^{65} +(0.934059 + 1.61784i) q^{67} +(-1.73041 - 2.99717i) q^{68} -10.9981i q^{71} -0.409520i q^{73} +(11.0470 + 6.37798i) q^{74} +(-3.96435 + 2.28882i) q^{76} +(-5.23325 + 9.06426i) q^{79} -6.58361 q^{80} -0.332007i q^{82} +(4.00094 - 6.92984i) q^{83} +(-1.63774 - 2.83664i) q^{85} +(5.92117 - 3.41859i) q^{86} +(0.607087 - 1.05151i) q^{88} +2.11862 q^{89} +(21.4649 + 12.3927i) q^{92} +(4.13828 - 2.38924i) q^{94} +(-3.75202 + 2.16623i) q^{95} +(10.5054 + 6.06531i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4}+O(q^{10}) $ 48 * q + 24 * q^4	$ 48 q + 24 q^{4} + 24 q^{11} - 24 q^{16} + 48 q^{23} - 24 q^{25} - 120 q^{32} - 48 q^{50} - 48 q^{64} - 120 q^{65} + 168 q^{74} - 24 q^{79} - 24 q^{85} - 24 q^{86} + 144 q^{92} - 96 q^{95}+O(q^{100}) $ 48 * q + 24 * q^4 + 24 * q^11 - 24 * q^16 + 48 * q^23 - 24 * q^25 - 120 * q^32 - 48 * q^50 - 48 * q^64 - 120 * q^65 + 168 * q^74 - 24 * q^79 - 24 * q^85 - 24 * q^86 + 144 * q^92 - 96 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	2.05485	+	1.18637i	1.45300	+	0.838890i	0.998651	−	0.0519328i	$-0.0165382\pi$
$2$	2.05485	+	1.18637i	1.45300	+	0.838890i	0.454350	+	0.890823i	$0.349871\pi$
$3$		0			0
$3$		0			0
$4$	1.81495	+	3.14358i	0.907474	+	1.57179i
$5$	1.71774	+	2.97522i	0.768198	+	1.33056i	0.938539	+	0.345172i	$0.112180\pi$
$5$	1.71774	+	2.97522i	0.768198	+	1.33056i	−0.170342	+	0.985385i	$0.554487\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			3.86732i			1.36730i
$9$		0			0
$10$			8.15151i			2.57773i
$11$	−0.271895	−	0.156979i	−0.0819795	−	0.0473309i	0.458450	−	0.888720i	$-0.348405\pi$
$11$	−0.271895	−	0.156979i	−0.0819795	−	0.0473309i	−0.540429	+	0.841389i	$0.681738\pi$
$12$		0			0
$13$	−5.09882	+	2.94381i	−1.41416	+	0.816465i	−0.995777	−	0.0918054i	$-0.970736\pi$
$13$	−5.09882	+	2.94381i	−1.41416	+	0.816465i	−0.418383	+	0.908271i	$0.637403\pi$
$14$		0			0
$15$		0			0
$16$	−0.958178	+	1.65961i	−0.239545	+	0.414903i
$17$	−0.953423			−0.231239			−0.115620	−	0.993294i	$-0.536885\pi$
$17$	−0.953423			−0.231239			−0.115620	+	0.993294i	$0.536885\pi$
$18$		0			0
$19$			1.26109i			0.289314i	0.989482	+	0.144657i	$0.0462079\pi$
$19$			1.26109i			0.289314i	−0.989482	+	0.144657i	$0.953792\pi$
$20$	−6.23523	+	10.7997i	−1.39424	+	2.41489i
$21$		0			0
$22$	−0.372470	−	0.645137i	−0.0794108	−	0.137544i
$23$	5.91336	−	3.41408i	1.23302	−	0.711884i	0.265362	−	0.964149i	$-0.414509\pi$
$23$	5.91336	−	3.41408i	1.23302	−	0.711884i	0.967658	+	0.252265i	$0.0811754\pi$
$24$		0			0
$25$	−3.40128	+	5.89118i	−0.680255	+	1.17824i
$26$	−13.9698			−2.73970
$27$		0			0
$28$		0			0
$29$	−3.43518	−	1.98330i	−0.637897	−	0.368290i	0.145907	−	0.989298i	$-0.453390\pi$
$29$	−3.43518	−	1.98330i	−0.637897	−	0.368290i	−0.783804	+	0.621008i	$0.786723\pi$
$30$		0			0
$31$	4.53388	−	2.61764i	0.814309	−	0.470141i	−0.0341412	−	0.999417i	$-0.510870\pi$
$31$	4.53388	−	2.61764i	0.814309	−	0.470141i	0.848450	+	0.529276i	$0.177536\pi$
$32$	2.76057	−	1.59381i	0.488004	−	0.281749i
$33$		0			0
$34$	−1.95915	−	1.13111i	−0.335991	−	0.193984i
$35$		0			0
$36$		0			0
$37$	5.37604			0.883816			0.441908	−	0.897060i	$-0.354302\pi$
$37$	5.37604			0.883816			0.441908	+	0.897060i	$0.354302\pi$
$38$	−1.49612	+	2.59136i	−0.242703	+	0.420374i
$39$		0			0
$40$	−11.5061	+	6.64306i	−1.81928	+	1.05036i
$41$	−0.0699627	−	0.121179i	−0.0109263	−	0.0189250i	0.860511	−	0.509433i	$-0.170145\pi$
$41$	−0.0699627	−	0.121179i	−0.0109263	−	0.0189250i	−0.871437	+	0.490508i	$0.836811\pi$
$42$		0			0
$43$	1.44078	−	2.49550i	0.219716	−	0.380560i	−0.735005	−	0.678062i	$-0.762820\pi$
$43$	1.44078	−	2.49550i	0.219716	−	0.380560i	0.954721	+	0.297502i	$0.0961535\pi$
$44$		−	1.13963i		−	0.171806i
$45$		0			0
$46$	16.2014			2.38877
$47$	1.00695	−	1.74409i	0.146879	−	0.254402i	−0.783193	−	0.621778i	$-0.786411\pi$
$47$	1.00695	−	1.74409i	0.146879	−	0.254402i	0.930072	+	0.367376i	$0.119744\pi$
$48$		0			0
$49$		0			0
$50$	−13.9783	+	8.07035i	−1.97682	+	1.14132i
$51$		0			0
$52$	−18.5082	−	10.6857i	−2.56663	−	1.48184i
$53$			11.9799i			1.64557i	0.568351	+	0.822786i	$0.307582\pi$
$53$			11.9799i			1.64557i	−0.568351	+	0.822786i	$0.692418\pi$
$54$		0			0
$55$		−	1.07860i		−	0.145438i
$56$		0			0
$57$		0			0
$58$	−4.70586	−	8.15079i	−0.617910	−	1.07025i
$59$	−0.824459	−	1.42801i	−0.107335	−	0.185910i	0.807355	−	0.590067i	$-0.200899\pi$
$59$	−0.824459	−	1.42801i	−0.107335	−	0.185910i	−0.914690	+	0.404156i	$0.867565\pi$
$60$		0			0
$61$	2.57423	+	1.48623i	0.329597	+	0.190293i	0.655662	−	0.755055i	$-0.272390\pi$
$61$	2.57423	+	1.48623i	0.329597	+	0.190293i	−0.326065	+	0.945347i	$0.605723\pi$
$62$	12.4219			1.57759
$63$		0			0
$64$	11.3961			1.42452
$65$	−17.5169	−	10.1134i	−2.17271	−	1.25441i
$66$		0			0
$67$	0.934059	+	1.61784i	0.114113	+	0.197650i	0.917425	−	0.397909i	$-0.130264\pi$
$67$	0.934059	+	1.61784i	0.114113	+	0.197650i	−0.803312	+	0.595559i	$0.796931\pi$
$68$	−1.73041	−	2.99717i	−0.209844	−	0.363460i
$69$		0			0
$70$		0			0
$71$		−	10.9981i		−	1.30524i	−0.757686	−	0.652619i	$-0.773670\pi$
$71$		−	10.9981i		−	1.30524i	0.757686	−	0.652619i	$-0.226330\pi$
$72$		0			0
$73$		−	0.409520i		−	0.0479307i	−0.999713	−	0.0239653i	$-0.992371\pi$
$73$		−	0.409520i		−	0.0479307i	0.999713	−	0.0239653i	$-0.00762914\pi$
$74$	11.0470	+	6.37798i	1.28419	+	0.741425i
$75$		0			0
$76$	−3.96435	+	2.28882i	−0.454742	+	0.262545i
$77$		0			0
$78$		0			0
$79$	−5.23325	+	9.06426i	−0.588787	+	1.01981i	0.405605	+	0.914049i	$0.367061\pi$
$79$	−5.23325	+	9.06426i	−0.588787	+	1.01981i	−0.994392	+	0.105760i	$0.966272\pi$
$80$	−6.58361			−0.736070
$81$		0			0
$82$		−	0.332007i		−	0.0366640i
$83$	4.00094	−	6.92984i	0.439161	−	0.760649i	−0.558464	−	0.829529i	$-0.688609\pi$
$83$	4.00094	−	6.92984i	0.439161	−	0.760649i	0.997625	+	0.0688800i	$0.0219426\pi$
$84$		0			0
$85$	−1.63774	−	2.83664i	−0.177637	−	0.307677i
$86$	5.92117	−	3.41859i	0.638496	−	0.368636i
$87$		0			0
$88$	0.607087	−	1.05151i	0.0647157	−	0.112091i
$89$	2.11862			0.224574			0.112287	−	0.993676i	$-0.464182\pi$
$89$	2.11862			0.224574			0.112287	+	0.993676i	$0.464182\pi$
$90$		0			0
$91$		0			0
$92$	21.4649	+	12.3927i	2.23787	+	1.29203i
$93$		0			0
$94$	4.13828	−	2.38924i	0.426831	−	0.246431i
$95$	−3.75202	+	2.16623i	−0.384949	+	0.222251i
$96$		0			0
$97$	10.5054	+	6.06531i	1.06666	+	0.615839i	0.927268	−	0.374398i	$-0.122150\pi$
$97$	10.5054	+	6.06531i	1.06666	+	0.615839i	0.139396	+	0.990237i	$0.455484\pi$
$98$		0			0
$99$		0			0
$100$	−24.6926			−2.46926
$101$	6.26039	−	10.8433i	0.622932	−	1.07895i	−0.366005	−	0.930613i	$-0.619275\pi$
$101$	6.26039	−	10.8433i	0.622932	−	1.07895i	0.988937	−	0.148337i	$-0.0473920\pi$
$102$		0			0
$103$	−15.6040	+	9.00897i	−1.53751	+	0.887680i	−0.538523	+	0.842611i	$0.681017\pi$
$103$	−15.6040	+	9.00897i	−1.53751	+	0.887680i	−0.998984	+	0.0450689i	$0.985649\pi$
$104$	−11.3847	−	19.7188i	−1.11636	−	1.93359i
$105$		0			0
$106$	−14.2127	+	24.6170i	−1.38046	+	2.39102i
$107$		−	3.59816i		−	0.347848i	−0.984759	−	0.173924i	$-0.944355\pi$
$107$		−	3.59816i		−	0.347848i	0.984759	−	0.173924i	$-0.0556447\pi$
$108$		0			0
$109$	−6.56218			−0.628543			−0.314271	−	0.949333i	$-0.601760\pi$
$109$	−6.56218			−0.628543			−0.314271	+	0.949333i	$0.601760\pi$
$110$	1.27961	−	2.21636i	0.122006	−	0.211321i
$111$		0			0
$112$		0			0
$113$	1.87912	−	1.08491i	0.176773	−	0.102060i	−0.409003	−	0.912533i	$-0.634123\pi$
$113$	1.87912	−	1.08491i	0.176773	−	0.102060i	0.585775	+	0.810473i	$0.300790\pi$
$114$		0			0
$115$	20.3152	+	11.7290i	1.89441	+	1.09374i
$116$		−	14.3984i		−	1.33685i
$117$		0			0
$118$		−	3.91246i		−	0.360171i
$119$		0			0
$120$		0			0
$121$	−5.45072	−	9.44092i	−0.495520	−	0.858265i
$122$	3.52645	+	6.10798i	0.319269	+	0.552991i
$123$		0			0
$124$	16.4575	+	9.50175i	1.47793	+	0.853282i
$125$	−6.19265			−0.553887
$126$		0			0
$127$	2.34967			0.208499			0.104250	−	0.994551i	$-0.466756\pi$
$127$	2.34967			0.208499			0.104250	+	0.994551i	$0.466756\pi$
$128$	17.8962	+	10.3324i	1.58182	+	0.913263i
$129$		0			0
$130$	−23.9965	−	41.5631i	−2.10463	−	3.64533i
$131$	−4.74594	−	8.22021i	−0.414655	−	0.718203i	0.580737	−	0.814091i	$-0.302764\pi$
$131$	−4.74594	−	8.22021i	−0.414655	−	0.718203i	−0.995392	+	0.0958879i	$0.969431\pi$
$132$		0			0
$133$		0			0
$134$			4.43256i			0.382915i
$135$		0			0
$136$		−	3.68719i		−	0.316174i
$137$	−8.85456	−	5.11218i	−0.756496	−	0.436763i	0.0715401	−	0.997438i	$-0.477209\pi$
$137$	−8.85456	−	5.11218i	−0.756496	−	0.436763i	−0.828036	+	0.560674i	$0.810542\pi$
$138$		0			0
$139$	4.56556	−	2.63593i	0.387246	−	0.223577i	−0.293720	−	0.955891i	$-0.594893\pi$
$139$	4.56556	−	2.63593i	0.387246	−	0.223577i	0.680966	+	0.732315i	$0.261560\pi$
$140$		0			0
$141$		0			0
$142$	13.0479	−	22.5996i	1.09495	−	1.89651i
$143$	1.84846			0.154576
$144$		0			0
$145$		−	13.6272i		−	1.13168i
$146$	0.485842	−	0.841504i	0.0402086	−	0.0696433i
$147$		0			0
$148$	9.75724	+	16.9000i	0.802040	+	1.38917i
$149$	−15.8151	+	9.13086i	−1.29562	+	0.748029i	−0.979645	−	0.200737i	$-0.935666\pi$
$149$	−15.8151	+	9.13086i	−1.29562	+	0.748029i	−0.315979	+	0.948766i	$0.602333\pi$
$150$		0			0
$151$	−11.5551	+	20.0140i	−0.940340	+	1.62872i	−0.175517	+	0.984476i	$0.556160\pi$
$151$	−11.5551	+	20.0140i	−0.940340	+	1.62872i	−0.764823	+	0.644240i	$0.777174\pi$
$152$	−4.87705			−0.395581
$153$		0			0
$154$		0			0
$155$	15.5761	+	8.99285i	1.25110	+	0.722323i
$156$		0			0
$157$	−5.65459	+	3.26468i	−0.451286	+	0.260550i	−0.708373	−	0.705838i	$-0.750570\pi$
$157$	−5.65459	+	3.26468i	−0.451286	+	0.260550i	0.257087	+	0.966388i	$0.417237\pi$
$158$	−21.5071	+	12.4172i	−1.71102	+	0.987855i
$159$		0			0
$160$	9.48388	+	5.47552i	0.749767	+	0.432878i
$161$		0			0
$162$		0			0
$163$	24.5246			1.92091			0.960457	−	0.278428i	$-0.0898133\pi$
$163$	24.5246			1.92091			0.960457	+	0.278428i	$0.0898133\pi$
$164$	0.253957	−	0.439867i	0.0198307	−	0.0343478i
$165$		0			0
$166$	16.4427	−	9.49320i	1.27620	−	0.736815i
$167$	−6.99871	−	12.1221i	−0.541576	−	0.938037i	−0.998814	−	0.0486928i	$-0.984494\pi$
$167$	−6.99871	−	12.1221i	−0.541576	−	0.938037i	0.457238	−	0.889345i	$-0.348839\pi$
$168$		0			0
$169$	10.8320	−	18.7616i	0.833232	−	1.44320i
$170$		−	7.77184i		−	0.596073i
$171$		0			0
$172$	10.4597			0.797548
$173$	5.44974	−	9.43923i	0.414336	−	0.717651i	−0.581022	−	0.813888i	$-0.697347\pi$
$173$	5.44974	−	9.43923i	0.414336	−	0.717651i	0.995359	+	0.0962363i	$0.0306805\pi$
$174$		0			0
$175$		0			0
$176$	0.521048	−	0.300827i	0.0392755	−	0.0226757i
$177$		0			0
$178$	4.35346	+	2.51347i	0.326306	+	0.188393i
$179$			1.59945i			0.119549i	0.998212	+	0.0597743i	$0.0190381\pi$
$179$			1.59945i			0.119549i	−0.998212	+	0.0597743i	$0.980962\pi$
$180$		0			0
$181$		−	17.5088i		−	1.30142i	−0.759326	−	0.650710i	$-0.774471\pi$
$181$		−	17.5088i		−	1.30142i	0.759326	−	0.650710i	$-0.225529\pi$
$182$		0			0
$183$		0			0
$184$	13.2033	+	22.8688i	0.973363	+	1.68591i
$185$	9.23466	+	15.9949i	0.678946	+	1.17597i
$186$		0			0
$187$	0.259231	+	0.149667i	0.0189569	+	0.0109447i
$188$	7.31027			0.533156
$189$		0			0
$190$	−10.2798			−0.745775
$191$	13.9107	+	8.03138i	1.00655	+	0.581130i	0.910179	−	0.414216i	$-0.135944\pi$
$191$	13.9107	+	8.03138i	1.00655	+	0.581130i	0.0963679	+	0.995346i	$0.469277\pi$
$192$		0			0
$193$	5.44196	+	9.42575i	0.391721	+	0.678480i	0.992677	−	0.120802i	$-0.0385467\pi$
$193$	5.44196	+	9.42575i	0.391721	+	0.678480i	−0.600956	+	0.799282i	$0.705213\pi$
$194$	14.3914	+	24.9267i	1.03324	+	1.78963i
$195$		0			0
$196$		0			0
$197$			6.50777i			0.463660i	0.972756	+	0.231830i	$0.0744712\pi$
$197$			6.50777i			0.463660i	−0.972756	+	0.231830i	$0.925529\pi$
$198$		0			0
$199$			17.8074i			1.26234i	0.775646	+	0.631168i	$0.217424\pi$
$199$			17.8074i			1.26234i	−0.775646	+	0.631168i	$0.782576\pi$
$200$	−22.7831	−	13.1538i	−1.61101	−	0.930116i
$201$		0			0
$202$	25.7284	−	14.8543i	1.81024	−	1.04514i
$203$		0			0
$204$		0			0
$205$	0.240356	−	0.416308i	0.0167872	−	0.0290762i
$206$	−42.7519			−2.97866
$207$		0			0
$208$		−	11.2828i		−	0.782319i
$209$	0.197965	−	0.342885i	0.0136935	−	0.0237178i
$210$		0			0
$211$	−0.282402	−	0.489135i	−0.0194414	−	0.0336735i	0.856141	−	0.516742i	$-0.172855\pi$
$211$	−0.282402	−	0.489135i	−0.0194414	−	0.0336735i	−0.875582	+	0.483069i	$0.839522\pi$
$212$	−37.6600	+	21.7430i	−2.58650	+	1.49331i
$213$		0			0
$214$	4.26875	−	7.39370i	0.291806	−	0.505423i
$215$	9.89953			0.675143
$216$		0			0
$217$		0			0
$218$	−13.4843	−	7.78518i	−0.913273	−	0.527279i
$219$		0			0
$220$	3.39066	−	1.95760i	0.228598	−	0.131981i
$221$	4.86134	−	2.80670i	0.327009	−	0.188799i
$222$		0			0
$223$	−7.61261	−	4.39514i	−0.509778	−	0.294321i	0.222964	−	0.974827i	$-0.428427\pi$
$223$	−7.61261	−	4.39514i	−0.509778	−	0.294321i	−0.732742	+	0.680506i	$0.761760\pi$
$224$		0			0
$225$		0			0
$226$	5.14842			0.342468
$227$	8.45329	−	14.6415i	0.561065	−	0.971793i	−0.436339	−	0.899782i	$-0.643725\pi$
$227$	8.45329	−	14.6415i	0.561065	−	0.971793i	0.997404	−	0.0720104i	$-0.0229415\pi$
$228$		0			0
$229$	16.9410	−	9.78088i	1.11949	−	0.646339i	0.178221	−	0.983991i	$-0.442966\pi$
$229$	16.9410	−	9.78088i	1.11949	−	0.646339i	0.941271	+	0.337652i	$0.109633\pi$
$230$	27.8299	+	48.2028i	1.83505	+	3.17840i
$231$		0			0
$232$	7.67007	−	13.2849i	0.503565	−	0.872200i
$233$		−	19.7368i		−	1.29300i	−0.762914	−	0.646500i	$-0.776232\pi$
$233$		−	19.7368i		−	1.29300i	0.762914	−	0.646500i	$-0.223768\pi$
$234$		0			0
$235$	6.91874			0.451329
$236$	2.99270	−	5.18351i	0.194808	−	0.337418i
$237$		0			0
$238$		0			0
$239$	16.9761	−	9.80118i	1.09809	−	0.633985i	0.162375	−	0.986729i	$-0.448085\pi$
$239$	16.9761	−	9.80118i	1.09809	−	0.633985i	0.935720	+	0.352744i	$0.114751\pi$
$240$		0			0
$241$	−13.8166	−	7.97702i	−0.890006	−	0.513845i	−0.0160617	−	0.999871i	$-0.505113\pi$
$241$	−13.8166	−	7.97702i	−0.890006	−	0.513845i	−0.873945	+	0.486026i	$0.838446\pi$
$242$		−	25.8663i		−	1.66275i
$243$		0			0
$244$			10.7897i			0.690743i
$245$		0			0
$246$		0			0
$247$	−3.71241	−	6.43008i	−0.236215	−	0.409136i
$248$	10.1232	+	17.5340i	0.642826	+	1.11341i
$249$		0			0
$250$	−12.7250	−	7.34677i	−0.804798	−	0.464651i
$251$	−0.976065			−0.0616087			−0.0308044	−	0.999525i	$-0.509807\pi$
$251$	−0.976065			−0.0616087			−0.0308044	+	0.999525i	$0.509807\pi$
$252$		0			0
$253$	−2.14375			−0.134776
$254$	4.82822	+	2.78758i	0.302950	+	0.174908i
$255$		0			0
$256$	13.1200	+	22.7244i	0.819998	+	1.42028i
$257$	−6.11947	−	10.5992i	−0.381722	−	0.661162i	0.609587	−	0.792720i	$-0.291335\pi$
$257$	−6.11947	−	10.5992i	−0.381722	−	0.661162i	−0.991309	+	0.131558i	$0.958002\pi$
$258$		0			0
$259$		0			0
$260$		−	73.4212i		−	4.55339i
$261$		0			0
$262$		−	22.5218i		−	1.39140i
$263$	3.64436	+	2.10407i	0.224721	+	0.129743i	0.608134	−	0.793834i	$-0.291918\pi$
$263$	3.64436	+	2.10407i	0.224721	+	0.129743i	−0.383413	+	0.923577i	$0.625252\pi$
$264$		0			0
$265$	−35.6429	+	20.5785i	−2.18953	+	1.26413i
$266$		0			0
$267$		0			0
$268$	−3.39054	+	5.87258i	−0.207110	+	0.358725i
$269$	21.6597			1.32062			0.660309	−	0.750994i	$-0.270425\pi$
$269$	21.6597			1.32062			0.660309	+	0.750994i	$0.270425\pi$
$270$		0			0
$271$			20.6677i			1.25547i	0.778426	+	0.627736i	$0.216018\pi$
$271$			20.6677i			1.25547i	−0.778426	+	0.627736i	$0.783982\pi$
$272$	0.913549	−	1.58231i	0.0553921	−	0.0959419i
$273$		0			0
$274$	−12.1299	−	21.0096i	−0.732793	−	1.26923i
$275$	1.84958	−	1.06786i	0.111534	−	0.0643942i
$276$		0			0
$277$	13.9448	−	24.1532i	0.837864	−	1.45122i	−0.0538127	−	0.998551i	$-0.517137\pi$
$277$	13.9448	−	24.1532i	0.837864	−	1.45122i	0.891677	−	0.452672i	$-0.149529\pi$
$278$	12.5087			0.750225
$279$		0			0
$280$		0			0
$281$	−16.7176	−	9.65190i	−0.997287	−	0.575784i	−0.0898425	−	0.995956i	$-0.528636\pi$
$281$	−16.7176	−	9.65190i	−0.997287	−	0.575784i	−0.907444	+	0.420172i	$0.861970\pi$
$282$		0			0
$283$	−15.2703	+	8.81631i	−0.907725	+	0.524075i	−0.879698	−	0.475532i	$-0.842256\pi$
$283$	−15.2703	+	8.81631i	−0.907725	+	0.524075i	−0.0280263	+	0.999607i	$0.508922\pi$
$284$	34.5735	−	19.9610i	2.05156	−	1.18447i
$285$		0			0
$286$	3.79832	+	2.19296i	0.224599	+	0.129672i
$287$		0			0
$288$		0			0
$289$	−16.0910			−0.946528
$290$	16.1669	−	28.0019i	0.949354	−	1.64433i
$291$		0			0
$292$	1.28736	−	0.743258i	0.0753371	−	0.0434959i
$293$	−14.1138	−	24.4458i	−0.824536	−	1.42814i	−0.902273	−	0.431165i	$-0.858103\pi$
$293$	−14.1138	−	24.4458i	−0.824536	−	1.42814i	0.0777369	−	0.996974i	$-0.475231\pi$
$294$		0			0
$295$	2.83242	−	4.90589i	0.164910	−	0.285632i
$296$			20.7909i			1.20845i
$297$		0			0
$298$	−43.3303			−2.51006
$299$	−20.1008	+	34.8156i	−1.16246	+	2.01344i
$300$		0			0
$301$		0			0
$302$	−47.4880	+	27.4172i	−2.73263	+	1.57768i
$303$		0			0
$304$	−2.09292	−	1.20835i	−0.120037	−	0.0693036i
$305$			10.2119i			0.584730i
$306$		0			0
$307$		−	8.56651i		−	0.488917i	−0.969660	−	0.244458i	$-0.921390\pi$
$307$		−	8.56651i		−	0.488917i	0.969660	−	0.244458i	$-0.0786102\pi$
$308$		0			0
$309$		0			0
$310$	21.3377	+	36.9580i	1.21190	+	2.09907i
$311$	−9.67914	−	16.7648i	−0.548854	−	0.950642i	−0.998353	−	0.0573619i	$-0.981731\pi$
$311$	−9.67914	−	16.7648i	−0.548854	−	0.950642i	0.449500	−	0.893280i	$-0.351602\pi$
$312$		0			0
$313$	−22.9507	−	13.2506i	−1.29725	−	0.748967i	−0.317321	−	0.948318i	$-0.602783\pi$
$313$	−22.9507	−	13.2506i	−1.29725	−	0.748967i	−0.979928	+	0.199352i	$0.936116\pi$
$314$	−15.4925			−0.874291
$315$		0			0
$316$	−37.9923			−2.13724
$317$	7.50458	+	4.33277i	0.421499	+	0.243353i	0.695719	−	0.718314i	$-0.255086\pi$
$317$	7.50458	+	4.33277i	0.421499	+	0.243353i	−0.274219	+	0.961667i	$0.588419\pi$
$318$		0			0
$319$	0.622673	+	1.07850i	0.0348630	+	0.0603844i
$320$	19.5756	+	33.9059i	1.09431	+	1.89540i
$321$		0			0
$322$		0			0
$323$		−	1.20235i		−	0.0669008i
$324$		0			0
$325$		−	40.0508i		−	2.22162i
$326$	50.3944	+	29.0952i	2.79109	+	1.61144i
$327$		0			0
$328$	0.468638	−	0.270568i	0.0258762	−	0.0149396i
$329$		0			0
$330$		0			0
$331$	−9.66912	+	16.7474i	−0.531463	+	0.920521i	0.467863	+	0.883801i	$0.345024\pi$
$331$	−9.66912	+	16.7474i	−0.531463	+	0.920521i	−0.999326	+	0.0367197i	$0.988309\pi$
$332$	29.0460			1.59411
$333$		0			0
$334$		−	33.2122i		−	1.81729i
$335$	−3.20894	+	5.55805i	−0.175323	+	0.303669i
$336$		0			0
$337$	−12.4451	−	21.5556i	−0.677930	−	1.17421i	−0.975603	−	0.219542i	$-0.929544\pi$
$337$	−12.4451	−	21.5556i	−0.677930	−	1.17421i	0.297673	−	0.954668i	$-0.403790\pi$
$338$	44.5164	−	25.7015i	2.42137	−	1.39798i
$339$		0			0
$340$	5.94481	−	10.2967i	0.322403	−	0.558418i
$341$	−1.64365			−0.0890088
$342$		0			0
$343$		0			0
$344$	9.65090	+	5.57195i	0.520341	+	0.300419i
$345$		0			0
$346$	22.3968	−	12.9308i	1.20406	−	0.695165i
$347$	−5.01728	+	2.89673i	−0.269342	+	0.155505i	−0.628588	−	0.777738i	$-0.716367\pi$
$347$	−5.01728	+	2.89673i	−0.269342	+	0.155505i	0.359247	+	0.933243i	$0.383034\pi$
$348$		0			0
$349$	−13.3430	−	7.70360i	−0.714236	−	0.412364i	0.0983918	−	0.995148i	$-0.468630\pi$
$349$	−13.3430	−	7.70360i	−0.714236	−	0.412364i	−0.812627	+	0.582784i	$0.801963\pi$
$350$		0			0
$351$		0			0
$352$	−1.00078			−0.0533417
$353$	−8.87263	+	15.3679i	−0.472243	+	0.817948i	−0.999496	−	0.0317602i	$-0.989889\pi$
$353$	−8.87263	+	15.3679i	−0.472243	+	0.817948i	0.527253	+	0.849708i	$0.323222\pi$
$354$		0			0
$355$	32.7218	−	18.8920i	1.73669	−	1.00268i
$356$	3.84519	+	6.66007i	0.203795	+	0.352983i
$357$		0			0
$358$	−1.89754	+	3.28664i	−0.100288	+	0.173704i
$359$			22.9197i			1.20966i	0.796356	+	0.604828i	$0.206758\pi$
$359$			22.9197i			1.20966i	−0.796356	+	0.604828i	$0.793242\pi$
$360$		0			0
$361$	17.4096			0.916297
$362$	20.7719	−	35.9781i	1.09175	−	1.89096i
$363$		0			0
$364$		0			0
$365$	1.21841	−	0.703450i	0.0637745	−	0.0368203i
$366$		0			0
$367$	4.33253	+	2.50139i	0.226156	+	0.130571i	0.608797	−	0.793326i	$-0.291652\pi$
$367$	4.33253	+	2.50139i	0.226156	+	0.130571i	−0.382641	+	0.923897i	$0.624986\pi$
$368$			13.0852i			0.682112i
$369$		0			0
$370$			43.8229i			2.27824i
$371$		0			0
$372$		0			0
$373$	−4.76280	−	8.24941i	−0.246608	−	0.427138i	0.715974	−	0.698127i	$-0.245983\pi$
$373$	−4.76280	−	8.24941i	−0.246608	−	0.427138i	−0.962583	+	0.270988i	$0.912649\pi$
$374$	0.355121	+	0.615088i	0.0183629	+	0.0318055i
$375$		0			0
$376$	6.74497	+	3.89421i	0.347845	+	0.200828i
$377$	23.3538			1.20278
$378$		0			0
$379$	−13.8369			−0.710756			−0.355378	−	0.934723i	$-0.615648\pi$
$379$	−13.8369			−0.710756			−0.355378	+	0.934723i	$0.615648\pi$
$380$	−13.6194	−	7.86319i	−0.698663	−	0.403373i
$381$		0			0
$382$	19.0564	+	33.0066i	0.975009	+	1.68876i
$383$	−10.6160	−	18.3874i	−0.542452	−	0.939554i	−0.998763	−	0.0497336i	$-0.984163\pi$
$383$	−10.6160	−	18.3874i	−0.542452	−	0.939554i	0.456311	−	0.889821i	$-0.349171\pi$
$384$		0			0
$385$		0			0
$386$			25.8247i			1.31444i
$387$		0			0
$388$			44.0329i			2.23543i
$389$	3.91419	+	2.25986i	0.198457	+	0.114579i	0.595936	−	0.803032i	$-0.296781\pi$
$389$	3.91419	+	2.25986i	0.198457	+	0.114579i	−0.397478	+	0.917612i	$0.630115\pi$
$390$		0			0
$391$	−5.63793	+	3.25506i	−0.285122	+	0.164616i
$392$		0			0
$393$		0			0
$394$	−7.72063	+	13.3725i	−0.388960	+	0.673698i
$395$	−35.9575			−1.80922
$396$		0			0
$397$			15.6843i			0.787171i	0.919288	+	0.393586i	$0.128765\pi$
$397$			15.6843i			0.787171i	−0.919288	+	0.393586i	$0.871235\pi$
$398$	−21.1262	+	36.5917i	−1.05896	+	1.83417i
$399$		0			0
$400$	−6.51806	−	11.2896i	−0.325903	−	0.564480i
$401$	−9.34292	+	5.39414i	−0.466563	+	0.269370i	−0.714800	−	0.699329i	$-0.753482\pi$
$401$	−9.34292	+	5.39414i	−0.466563	+	0.269370i	0.248237	+	0.968699i	$0.420149\pi$
$402$		0			0
$403$	−15.4116	+	26.6937i	−0.767708	+	1.32971i
$404$	45.4491			2.26118
$405$		0			0
$406$		0			0
$407$	−1.46172	−	0.843925i	−0.0724548	−	0.0418318i
$408$		0			0
$409$	−16.9860	+	9.80689i	−0.839906	+	0.484920i	−0.857232	−	0.514930i	$-0.827818\pi$
$409$	−16.9860	+	9.80689i	−0.839906	+	0.484920i	0.0173265	+	0.999850i	$0.494485\pi$
$410$	0.987791	−	0.570302i	0.0487835	−	0.0281652i
$411$		0			0
$412$	−56.6409	−	32.7016i	−2.79050	−	1.61109i
$413$		0			0
$414$		0			0
$415$	27.4904			1.34945
$416$	−9.38376	+	16.2532i	−0.460077	+	0.796876i
$417$		0			0
$418$	0.813576	−	0.469718i	0.0397933	−	0.0229747i
$419$	8.83829	+	15.3084i	0.431779	+	0.747862i	0.997027	−	0.0770586i	$-0.0245528\pi$
$419$	8.83829	+	15.3084i	0.431779	+	0.747862i	−0.565248	+	0.824921i	$0.691220\pi$
$420$		0			0
$421$	−16.9507	+	29.3594i	−0.826124	+	1.43089i	0.0749327	+	0.997189i	$0.476126\pi$
$421$	−16.9507	+	29.3594i	−0.826124	+	1.43089i	−0.901057	+	0.433701i	$0.857208\pi$
$422$		−	1.34014i		−	0.0652368i
$423$		0			0
$424$	−46.3303			−2.25000
$425$	3.24286	−	5.61679i	0.157302	−	0.272454i
$426$		0			0
$427$		0			0
$428$	11.3111	−	6.53048i	0.546744	−	0.315663i
$429$		0			0
$430$	20.3421	+	11.7445i	0.980983	+	0.566371i
$431$		−	14.1239i		−	0.680324i	−0.940367	−	0.340162i	$-0.889518\pi$
$431$		−	14.1239i		−	0.680324i	0.940367	−	0.340162i	$-0.110482\pi$
$432$		0			0
$433$			9.10088i			0.437360i	0.975797	+	0.218680i	$0.0701752\pi$
$433$			9.10088i			0.437360i	−0.975797	+	0.218680i	$0.929825\pi$
$434$		0			0
$435$		0			0
$436$	−11.9100	−	20.6288i	−0.570387	−	0.987938i
$437$	4.30546	+	7.45728i	0.205958	+	0.356730i
$438$		0			0
$439$	−10.1520	−	5.86126i	−0.484529	−	0.279743i	0.237773	−	0.971321i	$-0.423583\pi$
$439$	−10.1520	−	5.86126i	−0.484529	−	0.279743i	−0.722302	+	0.691578i	$0.756916\pi$
$440$	4.17128			0.198858
$441$		0			0
$442$	13.3191			0.633526
$443$	6.17796	+	3.56685i	0.293524	+	0.169466i	0.639530	−	0.768766i	$-0.279129\pi$
$443$	6.17796	+	3.56685i	0.293524	+	0.169466i	−0.346006	+	0.938232i	$0.612462\pi$
$444$		0			0
$445$	3.63925	+	6.30337i	0.172517	+	0.298808i
$446$	−10.4285	−	18.0628i	−0.493805	−	0.855296i
$447$		0			0
$448$		0			0
$449$		−	3.17445i		−	0.149811i	−0.997191	−	0.0749057i	$-0.976134\pi$
$449$		−	3.17445i		−	0.149811i	0.997191	−	0.0749057i	$-0.0238656\pi$
$450$		0			0
$451$			0.0439306i			0.00206861i
$452$	6.82100	+	3.93811i	0.320833	+	0.185233i
$453$		0			0
$454$	34.7406	−	20.0575i	1.63045	−	0.941344i
$455$		0			0
$456$		0			0
$457$	−12.0745	+	20.9137i	−0.564821	+	0.978299i	0.432245	+	0.901756i	$0.357722\pi$
$457$	−12.0745	+	20.9137i	−0.564821	+	0.978299i	−0.997066	+	0.0765431i	$0.975612\pi$
$458$	46.4150			2.16883
$459$		0			0
$460$			85.1502i			3.97015i
$461$	−6.87281	+	11.9041i	−0.320099	+	0.554427i	−0.980508	−	0.196478i	$-0.937049\pi$
$461$	−6.87281	+	11.9041i	−0.320099	+	0.554427i	0.660409	+	0.750906i	$0.270383\pi$
$462$		0			0
$463$	10.3157	+	17.8673i	0.479411	+	0.830364i	0.999721	−	0.0236135i	$-0.00751711\pi$
$463$	10.3157	+	17.8673i	0.479411	+	0.830364i	−0.520310	+	0.853977i	$0.674184\pi$
$464$	6.58303	−	3.80071i	0.305610	−	0.176444i
$465$		0			0
$466$	23.4151	−	40.5562i	1.08469	−	1.87873i
$467$	0.931788			0.0431180			0.0215590	−	0.999768i	$-0.493137\pi$
$467$	0.931788			0.0431180			0.0215590	+	0.999768i	$0.493137\pi$
$468$		0			0
$469$		0			0
$470$	14.2170	+	8.20819i	0.655781	+	0.378615i
$471$		0			0
$472$	5.52256	−	3.18845i	0.254196	−	0.146760i
$473$	−0.783481	+	0.452343i	−0.0360245	+	0.0207987i
$474$		0			0
$475$	−7.42932	−	4.28932i	−0.340881	−	0.196808i
$476$		0			0
$477$		0			0
$478$	46.5113			2.12738
$479$	−16.2031	+	28.0647i	−0.740340	+	1.28231i	0.212000	+	0.977270i	$0.432002\pi$
$479$	−16.2031	+	28.0647i	−0.740340	+	1.28231i	−0.952340	+	0.305037i	$0.901331\pi$
$480$		0			0
$481$	−27.4115	+	15.8260i	−1.24986	+	0.721605i
$482$	−18.9274	−	32.7832i	−0.862120	−	1.49324i
$483$		0			0
$484$	19.7855	−	34.2695i	0.899342	−	1.55771i
$485$			41.6746i			1.89234i
$486$		0			0
$487$	−34.3733			−1.55760			−0.778802	−	0.627270i	$-0.784172\pi$
$487$	−34.3733			−1.55760			−0.778802	+	0.627270i	$0.784172\pi$
$488$	−5.74774	+	9.95538i	−0.260188	+	0.450659i
$489$		0			0
$490$		0			0
$491$	7.31048	−	4.22071i	0.329917	−	0.190478i	−0.325887	−	0.945409i	$-0.605663\pi$
$491$	7.31048	−	4.22071i	0.329917	−	0.190478i	0.655804	+	0.754931i	$0.272330\pi$
$492$		0			0
$493$	3.27518	+	1.89093i	0.147507	+	0.0851631i
$494$		−	17.6172i		−	0.792634i
$495$		0			0
$496$			10.0326i			0.450479i
$497$		0			0
$498$		0			0
$499$	5.70400	+	9.87961i	0.255346	+	0.442272i	0.964989	−	0.262289i	$-0.0844773\pi$
$499$	5.70400	+	9.87961i	0.255346	+	0.442272i	−0.709643	+	0.704561i	$0.751144\pi$
$500$	−11.2393	−	19.4671i	−0.502638	−	0.870595i
$501$		0			0
$502$	−2.00567	−	1.15797i	−0.0895175	−	0.0516830i
$503$	32.8028			1.46261			0.731303	−	0.682053i	$-0.238913\pi$
$503$	32.8028			1.46261			0.731303	+	0.682053i	$0.238913\pi$
$504$		0			0
$505$	43.0149			1.91414
$506$	−4.40509	−	2.54328i	−0.195830	−	0.113063i
$507$		0			0
$508$	4.26453	+	7.38638i	0.189208	+	0.327717i
$509$	9.75828	+	16.9018i	0.432528	+	0.749160i	0.997090	−	0.0762300i	$-0.0242883\pi$
$509$	9.75828	+	16.9018i	0.432528	+	0.749160i	−0.564562	+	0.825390i	$0.690955\pi$
$510$		0			0
$511$		0			0
$512$			20.9310i			0.925027i
$513$		0			0
$514$		−	29.0398i		−	1.28089i
$515$	−53.6073	−	30.9502i	−2.36222	−	1.36383i
$516$		0			0
$517$	−0.547571	+	0.316140i	−0.0240821	+	0.0139038i
$518$		0			0
$519$		0			0
$520$	39.1118	−	67.7436i	1.71517	−	2.97075i
$521$	−19.8622			−0.870177			−0.435088	−	0.900388i	$-0.643283\pi$
$521$	−19.8622			−0.870177			−0.435088	+	0.900388i	$0.643283\pi$
$522$		0			0
$523$			7.75356i			0.339039i	0.985527	+	0.169520i	$0.0542216\pi$
$523$			7.75356i			0.339039i	−0.985527	+	0.169520i	$0.945778\pi$
$524$	17.2273	−	29.8385i	0.752577	−	1.30350i
$525$		0			0
$526$	4.99242	+	8.64713i	0.217680	+	0.377033i
$527$	−4.32271	+	2.49572i	−0.188300	+	0.108715i
$528$		0			0
$529$	11.8118	−	20.4587i	0.513559	−	0.889509i
$530$	−97.6547			−4.24185
$531$		0			0
$532$		0			0
$533$	0.713455	+	0.411913i	0.0309032	+	0.0178419i
$534$		0			0
$535$	10.7053	−	6.18072i	0.462831	−	0.267216i
$536$	−6.25670	+	3.61231i	−0.270248	+	0.156028i
$537$		0			0
$538$	44.5076	+	25.6965i	1.91886	+	1.10785i
$539$		0			0
$540$		0			0
$541$	−18.0923			−0.777850			−0.388925	−	0.921269i	$-0.627153\pi$
$541$	−18.0923			−0.777850			−0.388925	+	0.921269i	$0.627153\pi$
$542$	−24.5195	+	42.4691i	−1.05320	+	1.82420i
$543$		0			0
$544$	−2.63199	+	1.51958i	−0.112846	+	0.0651514i
$545$	−11.2721	−	19.5239i	−0.482845	−	0.836313i
$546$		0			0
$547$	3.46839	−	6.00743i	0.148298	−	0.256859i	−0.782301	−	0.622901i	$-0.785954\pi$
$547$	3.46839	−	6.00743i	0.148298	−	0.256859i	0.930598	+	0.366042i	$0.119287\pi$
$548$		−	37.1134i		−	1.58541i
$549$		0			0
$550$	5.06749			0.216079
$551$	2.50113	−	4.33208i	0.106552	−	0.184553i
$552$		0			0
$553$		0			0
$554$	57.3092	−	33.0875i	2.43483	−	1.40575i
$555$		0			0
$556$	16.5725	+	9.56815i	0.702831	+	0.405780i
$557$			15.8186i			0.670257i	0.942172	+	0.335128i	$0.108780\pi$
$557$			15.8186i			0.670257i	−0.942172	+	0.335128i	$0.891220\pi$
$558$		0			0
$559$			16.9655i			0.717563i
$560$		0			0
$561$		0			0
$562$	−22.9014	−	39.6665i	−0.966039	−	1.67323i
$563$	16.0561	+	27.8101i	0.676686	+	1.17205i	0.975973	+	0.217891i	$0.0699178\pi$
$563$	16.0561	+	27.8101i	0.676686	+	1.17205i	−0.299287	+	0.954163i	$0.596749\pi$
$564$		0			0
$565$	6.45568	+	3.72719i	0.271593	+	0.156804i
$566$	−41.8376			−1.75857
$567$		0			0
$568$	42.5333			1.78466
$569$	−31.3107	−	18.0772i	−1.31261	−	0.757837i	−0.330084	−	0.943951i	$-0.607077\pi$
$569$	−31.3107	−	18.0772i	−1.31261	−	0.757837i	−0.982528	+	0.186114i	$0.940411\pi$
$570$		0			0
$571$	−14.1792	−	24.5590i	−0.593380	−	1.02776i	−0.993773	−	0.111421i	$-0.964460\pi$
$571$	−14.1792	−	24.5590i	−0.593380	−	1.02776i	0.400393	−	0.916343i	$-0.368873\pi$
$572$	3.35486	+	5.81079i	0.140274	+	0.242961i
$573$		0			0
$574$		0			0
$575$			46.4489i			1.93705i
$576$		0			0
$577$		−	41.9836i		−	1.74780i	−0.486105	−	0.873901i	$-0.661583\pi$
$577$		−	41.9836i		−	1.74780i	0.486105	−	0.873901i	$-0.338417\pi$
$578$	−33.0646	−	19.0899i	−1.37531	−	0.794034i
$579$		0			0
$580$	42.8383	−	24.7327i	1.77876	−	1.02697i
$581$		0			0
$582$		0			0
$583$	1.88060	−	3.25729i	0.0778864	−	0.134903i
$584$	1.58375			0.0655359
$585$		0			0
$586$		−	66.9767i		−	2.76678i
$587$	−9.79227	+	16.9607i	−0.404170	+	0.700043i	−0.994225	−	0.107320i	$-0.965773\pi$
$587$	−9.79227	+	16.9607i	−0.404170	+	0.700043i	0.590054	+	0.807364i	$0.299106\pi$
$588$		0			0
$589$	3.30108	+	5.71764i	0.136019	+	0.235591i
$590$	11.6404	−	6.72059i	0.479228	−	0.276682i
$591$		0			0
$592$	−5.15121	+	8.92216i	−0.211713	+	0.366698i
$593$	−19.9275			−0.818324			−0.409162	−	0.912462i	$-0.634179\pi$
$593$	−19.9275			−0.818324			−0.409162	+	0.912462i	$0.634179\pi$
$594$		0			0
$595$		0			0
$596$	−57.4072	−	33.1441i	−2.35149	−	1.35763i
$597$		0			0
$598$	−82.6083	+	47.6939i	−3.37810	+	1.95035i
$599$	−0.0267639	+	0.0154521i	−0.00109354	+	0.000631357i	−0.500547	−	0.865710i	$-0.666868\pi$
$599$	−0.0267639	+	0.0154521i	−0.00109354	+	0.000631357i	0.499453	+	0.866341i	$0.333534\pi$
$600$		0			0
$601$	25.8633	+	14.9322i	1.05499	+	0.609097i	0.924041	−	0.382293i	$-0.124865\pi$
$601$	25.8633	+	14.9322i	1.05499	+	0.609097i	0.130945	+	0.991390i	$0.458199\pi$
$602$		0			0
$603$		0			0
$604$	−83.8876			−3.41334
$605$	18.7258	−	32.4341i	0.761314	−	1.31863i
$606$		0			0
$607$	27.1898	−	15.6980i	1.10360	−	0.637163i	0.166435	−	0.986052i	$-0.446774\pi$
$607$	27.1898	−	15.6980i	1.10360	−	0.637163i	0.937164	+	0.348889i	$0.113441\pi$
$608$	2.00994	+	3.48133i	0.0815140	+	0.141186i
$609$		0			0
$610$	−12.1151	+	20.9839i	−0.490524	+	0.849613i
$611$			11.8571i			0.479687i
$612$		0			0
$613$	−4.46292			−0.180256			−0.0901278	−	0.995930i	$-0.528728\pi$
$613$	−4.46292			−0.180256			−0.0901278	+	0.995930i	$0.528728\pi$
$614$	10.1631	−	17.6029i	0.410148	−	0.710396i
$615$		0			0
$616$		0			0
$617$	−26.9685	+	15.5703i	−1.08571	+	0.626835i	−0.932431	−	0.361348i	$-0.882317\pi$
$617$	−26.9685	+	15.5703i	−1.08571	+	0.626835i	−0.153279	+	0.988183i	$0.548983\pi$
$618$		0			0
$619$	1.13493	+	0.655252i	0.0456167	+	0.0263368i	0.522635	−	0.852557i	$-0.324949\pi$
$619$	1.13493	+	0.655252i	0.0456167	+	0.0263368i	−0.477018	+	0.878893i	$0.658282\pi$
$620$			65.2862i			2.62196i
$621$		0			0
$622$		−	45.9322i		−	1.84171i
$623$		0			0
$624$		0			0
$625$	6.36901	+	11.0315i	0.254761	+	0.441258i
$626$	−31.4402	−	54.4560i	−1.25660	−	2.17650i
$627$		0			0
$628$	−20.5256	−	11.8505i	−0.819060	−	0.472884i
$629$	−5.12565			−0.204373
$630$		0			0
$631$	−28.8892			−1.15006			−0.575030	−	0.818132i	$-0.695010\pi$
$631$	−28.8892			−1.15006			−0.575030	+	0.818132i	$0.695010\pi$
$632$	−35.0544	−	20.2387i	−1.39439	−	0.805051i
$633$		0			0
$634$	10.2805	+	17.8064i	0.408293	+	0.707183i
$635$	4.03612	+	6.99077i	0.160169	+	0.277420i
$636$		0			0
$637$		0			0
$638$			2.95488i			0.116985i
$639$		0			0
$640$			70.9936i			2.80627i
$641$	−2.41325	−	1.39329i	−0.0953176	−	0.0550316i	0.451584	−	0.892229i	$-0.350859\pi$
$641$	−2.41325	−	1.39329i	−0.0953176	−	0.0550316i	−0.546901	+	0.837197i	$0.684193\pi$
$642$		0			0
$643$	−0.324584	+	0.187399i	−0.0128004	+	0.00739029i	−0.506387	−	0.862307i	$-0.669019\pi$
$643$	−0.324584	+	0.187399i	−0.0128004	+	0.00739029i	0.493586	+	0.869697i	$0.335686\pi$
$644$		0			0
$645$		0			0
$646$	1.42644	−	2.47066i	0.0561224	−	0.0972069i
$647$	−50.3216			−1.97834			−0.989172	−	0.146758i	$-0.953116\pi$
$647$	−50.3216			−1.97834			−0.989172	+	0.146758i	$0.953116\pi$
$648$		0			0
$649$			0.517690i			0.0203211i
$650$	47.5151	−	82.2986i	1.86370	−	3.22802i
$651$		0			0
$652$	44.5109	+	77.0951i	1.74318	+	3.01928i
$653$	25.0515	−	14.4635i	0.980342	−	0.566000i	0.0779684	−	0.996956i	$-0.475157\pi$
$653$	25.0515	−	14.4635i	0.980342	−	0.566000i	0.902373	+	0.430955i	$0.141823\pi$
$654$		0			0
$655$	16.3046	−	28.2404i	0.637074	−	1.10344i
$656$	0.268147			0.0104694
$657$		0			0
$658$		0			0
$659$	22.8449	+	13.1895i	0.889910	+	0.513790i	0.873913	−	0.486082i	$-0.161574\pi$
$659$	22.8449	+	13.1895i	0.889910	+	0.513790i	0.0159971	+	0.999872i	$0.494908\pi$
$660$		0			0
$661$	10.0533	−	5.80428i	0.391028	−	0.225760i	−0.291577	−	0.956547i	$-0.594180\pi$
$661$	10.0533	−	5.80428i	0.391028	−	0.225760i	0.682606	+	0.730787i	$0.260847\pi$
$662$	−39.7373	+	22.9423i	−1.54443	+	0.891678i
$663$		0			0
$664$	26.7999	+	15.4729i	1.04004	+	0.600466i
$665$		0			0
$666$		0			0
$667$	−27.0846			−1.04872
$668$	25.4046	−	44.0020i	0.982933	−	1.70249i
$669$		0			0
$670$	−13.1878	+	7.61399i	−0.509490	+	0.294154i
$671$	−0.466614	−	0.808199i	−0.0180134	−	0.0312002i
$672$		0			0
$673$	−13.7692	+	23.8490i	−0.530764	+	0.919310i	0.468592	+	0.883415i	$0.344761\pi$
$673$	−13.7692	+	23.8490i	−0.530764	+	0.919310i	−0.999356	+	0.0358949i	$0.988572\pi$
$674$		−	59.0582i		−	2.27484i
$675$		0			0
$676$	78.6382			3.02454
$677$	−2.31563	+	4.01080i	−0.0889970	+	0.154147i	−0.907087	−	0.420942i	$-0.861700\pi$
$677$	−2.31563	+	4.01080i	−0.0889970	+	0.154147i	0.818090	+	0.575090i	$0.195033\pi$
$678$		0			0
$679$		0			0
$680$	10.9702	−	6.33365i	0.420688	−	0.242884i
$681$		0			0
$682$	−3.37747	−	1.94998i	−0.129330	−	0.0746686i
$683$			13.8792i			0.531072i	0.964101	+	0.265536i	$0.0855490\pi$
$683$			13.8792i			0.531072i	−0.964101	+	0.265536i	$0.914451\pi$
$684$		0			0
$685$		−	35.1257i		−	1.34208i
$686$		0			0
$687$		0			0
$688$	2.76104	+	4.78227i	0.105264	+	0.182322i
$689$	−35.2667	−	61.0837i	−1.34355	−	2.32710i
$690$		0			0
$691$	−19.6168	−	11.3258i	−0.746258	−	0.430852i	0.0780825	−	0.996947i	$-0.475120\pi$
$691$	−19.6168	−	11.3258i	−0.746258	−	0.430852i	−0.824340	+	0.566095i	$0.808454\pi$
$692$	39.5640			1.50400
$693$		0			0
$694$	−13.7464			−0.521805
$695$	15.6849	+	9.05569i	0.594963	+	0.343502i
$696$		0			0
$697$	0.0667040	+	0.115535i	0.00252660	+	0.00437619i
$698$	−18.2786	−	31.6595i	−0.691856	−	1.19833i
$699$		0			0
$700$		0			0
$701$			16.3485i			0.617474i	0.951147	+	0.308737i	$0.0999063\pi$
$701$			16.3485i			0.617474i	−0.951147	+	0.308737i	$0.900094\pi$
$702$		0			0
$703$			6.77968i			0.255701i
$704$	−3.09855	−	1.78895i	−0.116781	−	0.0674236i
$705$		0			0
$706$	−36.4639	+	21.0525i	−1.37234	+	0.792320i
$707$		0			0
$708$		0			0
$709$	−7.65356	+	13.2564i	−0.287435	+	0.497853i	−0.973197	−	0.229974i	$-0.926136\pi$
$709$	−7.65356	+	13.2564i	−0.287435	+	0.497853i	0.685761	+	0.727826i	$0.259469\pi$
$710$	89.6514			3.36456
$711$		0			0
$712$			8.19340i			0.307061i
$713$	17.8736	−	30.9580i	0.669372	−	1.15939i
$714$		0			0
$715$	3.17518	+	5.49957i	0.118745	+	0.205672i
$716$	−5.02801	+	2.90292i	−0.187906	+	0.108487i
$717$		0			0
$718$	−27.1913	+	47.0966i	−1.01477	+	1.75763i
$719$	14.9272			0.556690			0.278345	−	0.960481i	$-0.410214\pi$
$719$	14.9272			0.556690			0.278345	+	0.960481i	$0.410214\pi$
$720$		0			0
$721$		0			0
$722$	35.7743	+	20.6543i	1.33138	+	0.768673i
$723$		0			0
$724$	55.0404	−	31.7776i	2.04556	−	1.18101i
$725$	23.3680	−	13.4915i	0.867866	−	0.501063i
$726$		0			0
$727$	−4.62968	−	2.67295i	−0.171705	−	0.0991341i	0.411684	−	0.911326i	$-0.364941\pi$
$727$	−4.62968	−	2.67295i	−0.171705	−	0.0991341i	−0.583390	+	0.812192i	$0.698274\pi$
$728$		0			0
$729$		0			0
$730$	3.33821			0.123553
$731$	−1.37367	+	2.37927i	−0.0508070	+	0.0880004i
$732$		0			0
$733$	16.4099	−	9.47428i	0.606115	−	0.349941i	−0.165328	−	0.986239i	$-0.552868\pi$
$733$	16.4099	−	9.47428i	0.606115	−	0.349941i	0.771443	+	0.636298i	$0.219535\pi$
$734$	5.93514	+	10.2800i	0.219070	+	0.379440i
$735$		0			0
$736$	10.8828	−	18.8496i	0.401145	−	0.694804i
$737$		−	0.586509i		−	0.0216044i
$738$		0			0
$739$	45.6861			1.68059			0.840295	−	0.542130i	$-0.182382\pi$
$739$	45.6861			1.68059			0.840295	+	0.542130i	$0.182382\pi$
$740$	−33.5209	+	58.0598i	−1.23225	+	2.13432i
$741$		0			0
$742$		0			0
$743$	25.0448	−	14.4596i	0.918804	−	0.530472i	0.0355508	−	0.999368i	$-0.488681\pi$
$743$	25.0448	−	14.4596i	0.918804	−	0.530472i	0.883253	+	0.468896i	$0.155348\pi$
$744$		0			0
$745$	−54.3326	−	31.3689i	−1.99059	−	1.14927i
$746$		−	22.6018i		−	0.827510i
$747$		0			0
$748$			1.08655i			0.0397283i
$749$		0			0
$750$		0			0
$751$	−22.1007	−	38.2795i	−0.806465	−	1.39684i	−0.915297	−	0.402779i	$-0.868044\pi$
$751$	−22.1007	−	38.2795i	−0.806465	−	1.39684i	0.108832	−	0.994060i	$-0.465289\pi$
$752$	1.92968	+	3.34230i	0.0703682	+	0.121881i
$753$		0			0
$754$	47.9887	+	27.7063i	1.74765	+	1.00900i
$755$	−79.3947			−2.88947
$756$		0			0
$757$	−27.5029			−0.999611			−0.499805	−	0.866138i	$-0.666595\pi$
$757$	−27.5029			−0.999611			−0.499805	+	0.866138i	$0.666595\pi$
$758$	−28.4329	−	16.4157i	−1.03273	−	0.596246i
$759$		0			0
$760$	−8.37751	−	14.5103i	−0.303884	−	0.526343i
$761$	−2.54651	−	4.41069i	−0.0923109	−	0.159887i	0.816172	−	0.577809i	$-0.196092\pi$
$761$	−2.54651	−	4.41069i	−0.0923109	−	0.159887i	−0.908483	+	0.417921i	$0.862759\pi$
$762$		0			0
$763$		0			0
$764$			58.3061i			2.10944i
$765$		0			0
$766$		−	50.3780i		−	1.82023i
$767$	8.40755	+	4.85410i	0.303579	+	0.175271i
$768$		0			0
$769$	33.4505	−	19.3126i	1.20626	−	0.696432i	0.244316	−	0.969696i	$-0.421436\pi$
$769$	33.4505	−	19.3126i	1.20626	−	0.696432i	0.961939	+	0.273264i	$0.0881031\pi$
$770$		0			0
$771$		0			0
$772$	−19.7537	+	34.2145i	−0.710953	+	1.23141i
$773$	34.3507			1.23551			0.617754	−	0.786371i	$-0.288043\pi$
$773$	34.3507			1.23551			0.617754	+	0.786371i	$0.288043\pi$
$774$		0			0
$775$			35.6132i			1.27926i
$776$	−23.4565	+	40.6279i	−0.842040	+	1.45846i
$777$		0			0
$778$	5.36206	+	9.28736i	0.192239	+	0.332968i
$779$	0.152818	−	0.0882293i	0.00547526	−	0.00316114i
$780$		0			0
$781$	−1.72647	+	2.99034i	−0.0617781	+	0.107003i
$782$	−15.4468			−0.552377
$783$		0			0
$784$		0			0
$785$	−19.4263	−	11.2158i	−0.693353	−	0.400308i
$786$		0			0
$787$	−20.3343	+	11.7400i	−0.724839	+	0.418486i	−0.816531	−	0.577301i	$-0.804106\pi$
$787$	−20.3343	+	11.7400i	−0.724839	+	0.418486i	0.0916921	+	0.995787i	$0.470772\pi$
$788$	−20.4577	+	11.8113i	−0.728776	+	0.420759i
$789$		0			0
$790$	−73.8874	−	42.6589i	−2.62880	−	1.51774i
$791$		0			0
$792$		0			0
$793$	−17.5007			−0.621470
$794$	−18.6074	+	32.2289i	−0.660350	+	1.14376i
$795$		0			0
$796$	−55.9791	+	32.3196i	−1.98413	+	1.14554i
$797$	5.82399	+	10.0875i	0.206296	+	0.357316i	0.950545	−	0.310587i	$-0.100526\pi$
$797$	5.82399	+	10.0875i	0.206296	+	0.357316i	−0.744249	+	0.667903i	$0.767192\pi$
$798$		0			0
$799$	−0.960052	+	1.66286i	−0.0339642	+	0.0588277i
$800$			21.6840i			0.766645i
$801$		0			0
$802$	−25.5978			−0.903889
$803$	−0.0642859	+	0.111347i	−0.00226860	+	0.00392933i
$804$		0			0
$805$		0			0
$806$	−63.3373	+	36.5678i	−2.23096	+	1.28805i
$807$		0			0
$808$	41.9346	+	24.2109i	1.47525	+	0.851738i
$809$		−	15.9029i		−	0.559117i	−0.960129	−	0.279559i	$-0.909812\pi$
$809$		−	15.9029i		−	0.559117i	0.960129	−	0.279559i	$-0.0901881\pi$
$810$		0			0
$811$			3.56109i			0.125047i	0.998044	+	0.0625233i	$0.0199148\pi$
$811$			3.56109i			0.125047i	−0.998044	+	0.0625233i	$0.980085\pi$
$812$		0			0
$813$		0			0
$814$	−2.00241	−	3.46828i	−0.0701846	−	0.121563i
$815$	42.1269	+	72.9660i	1.47564	+	2.55589i
$816$		0			0
$817$	3.14705	+	1.81695i	0.110101	+	0.0635671i
$818$	−46.5384			−1.62718
$819$		0			0
$820$	1.74493			0.0609357
$821$	0.113440	+	0.0654949i	0.00395910	+	0.00228579i	0.501978	−	0.864880i	$-0.332606\pi$
$821$	0.113440	+	0.0654949i	0.00395910	+	0.00228579i	−0.498019	+	0.867166i	$0.665939\pi$
$822$		0			0
$823$	−23.0144	−	39.8621i	−0.802231	−	1.38950i	−0.918145	−	0.396245i	$-0.870313\pi$
$823$	−23.0144	−	39.8621i	−0.802231	−	1.38950i	0.115914	−	0.993259i	$-0.463020\pi$
$824$	−34.8406	−	60.3456i	−1.21373	−	2.10224i
$825$		0			0
$826$		0			0
$827$		−	40.5836i		−	1.41123i	−0.708595	−	0.705615i	$-0.750671\pi$
$827$		−	40.5836i		−	1.41123i	0.708595	−	0.705615i	$-0.249329\pi$
$828$		0			0
$829$			30.1296i			1.04645i	0.852196	+	0.523223i	$0.175270\pi$
$829$			30.1296i			1.04645i	−0.852196	+	0.523223i	$0.824730\pi$
$830$	56.4887	+	32.6137i	1.96075	+	1.13204i
$831$		0			0
$832$	−58.1068	+	33.5480i	−2.01449	+	1.16307i
$833$		0			0
$834$		0			0
$835$	24.0439	−	41.6453i	0.832075	−	1.44120i
$836$	1.43718			0.0497060
$837$		0			0
$838$			41.9419i			1.44886i
$839$	−5.81551	+	10.0728i	−0.200774	+	0.347750i	−0.948778	−	0.315944i	$-0.897679\pi$
$839$	−5.81551	+	10.0728i	−0.200774	+	0.347750i	0.748004	+	0.663694i	$0.231012\pi$
$840$		0			0
$841$	−6.63302	−	11.4887i	−0.228725	−	0.396163i
$842$	−69.6622	+	40.2195i	−2.40072	+	1.38606i
$843$		0			0
$844$	1.02509	−	1.77551i	0.0352851	−	0.0611156i
$845$	74.4264			2.56035
$846$		0			0
$847$		0			0
$848$	−19.8821	−	11.4789i	−0.682754	−	0.394188i
$849$		0			0
$850$	13.3272	−	7.69446i	0.457119	−	0.263918i
$851$	31.7905	−	18.3542i	1.08976	−	0.629175i
$852$		0			0
$853$	20.6854	+	11.9427i	0.708254	+	0.408911i	0.810414	−	0.585857i	$-0.199242\pi$
$853$	20.6854	+	11.9427i	0.708254	+	0.408911i	−0.102160	+	0.994768i	$0.532575\pi$
$854$		0			0
$855$		0			0
$856$	13.9153			0.475614
$857$	17.3362	−	30.0271i	0.592193	−	1.02571i	−0.401744	−	0.915752i	$-0.631596\pi$
$857$	17.3362	−	30.0271i	0.592193	−	1.02571i	0.993936	−	0.109956i	$-0.0350709\pi$
$858$		0			0
$859$	−26.3932	+	15.2381i	−0.900525	+	0.519918i	−0.877371	−	0.479813i	$-0.840704\pi$
$859$	−26.3932	+	15.2381i	−0.900525	+	0.519918i	−0.0231546	+	0.999732i	$0.507371\pi$
$860$	17.9671	+	31.1200i	0.612674	+	1.06118i
$861$		0			0
$862$	16.7562	−	29.0225i	0.570717	−	0.988512i
$863$		−	33.4052i		−	1.13713i	−0.822639	−	0.568564i	$-0.807499\pi$
$863$		−	33.4052i		−	1.13713i	0.822639	−	0.568564i	$-0.192501\pi$
$864$		0			0
$865$	37.4450			1.27317
$866$	−10.7970	+	18.7010i	−0.366898	+	0.635485i
$867$		0			0
$868$		0			0
$869$	2.84579	−	1.64302i	0.0965369	−	0.0557356i
$870$		0			0
$871$	−9.52520	−	5.49938i	−0.322749	−	0.186339i
$872$		−	25.3781i		−	0.859410i
$873$		0			0
$874$			20.4315i			0.691106i
$875$		0			0
$876$		0			0
$877$	27.7600	+	48.0817i	0.937389	+	1.62360i	0.770318	+	0.637660i	$0.220097\pi$
$877$	27.7600	+	48.0817i	0.937389	+	1.62360i	0.167070	+	0.985945i	$0.446569\pi$
$878$	−13.9073	−	24.0881i	−0.469347	−	0.812933i
$879$		0			0
$880$	1.79005	+	1.03349i	0.0603426	+	0.0348388i
$881$	19.9850			0.673313			0.336656	−	0.941628i	$-0.390704\pi$
$881$	19.9850			0.673313			0.336656	+	0.941628i	$0.390704\pi$
$882$		0			0
$883$	35.5837			1.19749			0.598743	−	0.800941i	$-0.295667\pi$
$883$	35.5837			1.19749			0.598743	+	0.800941i	$0.295667\pi$
$884$	17.6462	+	10.1880i	0.593504	+	0.342660i
$885$		0			0
$886$	8.46321	+	14.6587i	0.284327	+	0.492469i
$887$	−17.8317	−	30.8853i	−0.598729	−	1.03703i	−0.993009	−	0.118038i	$-0.962339\pi$
$887$	−17.8317	−	30.8853i	−0.598729	−	1.03703i	0.394280	−	0.918990i	$-0.370994\pi$
$888$		0			0
$889$		0			0
$890$			17.2700i			0.578892i
$891$		0			0
$892$		−	31.9078i		−	1.06835i
$893$	2.19946	+	1.26986i	0.0736021	+	0.0424942i
$894$		0			0
$895$	−4.75872	+	2.74745i	−0.159066	+	0.0918370i
$896$		0			0
$897$		0			0
$898$	3.76607	−	6.52302i	0.125675	−	0.217676i
$899$	−20.7663			−0.692594
$900$		0			0
$901$		−	11.4220i		−	0.380521i
$902$	−0.0521180	+	0.0902710i	−0.00173534	+	0.00300569i
$903$		0			0
$904$	4.19569	+	7.26715i	0.139547	+	0.241702i
$905$	52.0925	−	30.0756i	1.73161	−	0.999748i
$906$		0			0
$907$	−18.6215	+	32.2533i	−0.618315	+	1.07095i	0.371478	+	0.928442i	$0.378851\pi$
$907$	−18.6215	+	32.2533i	−0.618315	+	1.07095i	−0.989793	+	0.142512i	$0.954482\pi$
$908$	61.3692			2.03661
$909$		0			0
$910$		0			0
$911$	18.8068	+	10.8581i	0.623098	+	0.359746i	0.778074	−	0.628172i	$-0.216197\pi$
$911$	18.8068	+	10.8581i	0.623098	+	0.359746i	−0.154976	+	0.987918i	$0.549530\pi$
$912$		0			0
$913$	−2.17567	+	1.25613i	−0.0720043	+	0.0415717i
$914$	−49.6227	+	28.6497i	−1.64137	+	0.947647i
$915$		0			0
$916$	61.4940	+	35.5036i	2.03182	+	1.17307i
$917$		0			0
$918$		0			0
$919$	34.2046			1.12831			0.564153	−	0.825671i	$-0.309203\pi$
$919$	34.2046			1.12831			0.564153	+	0.825671i	$0.309203\pi$
$920$	−45.3598	+	78.5656i	−1.49547	+	2.59023i
$921$		0			0
$922$	−28.2452	+	16.3074i	−0.930208	+	0.537056i
$923$	32.3764	+	56.0776i	1.06568	+	1.84582i
$924$		0			0
$925$	−18.2854	+	31.6713i	−0.601221	+	1.04135i
$926$			48.9529i			1.60869i
$927$		0			0
$928$	−12.6441			−0.415062
$929$	−23.4757	+	40.6611i	−0.770213	+	1.33405i	0.167233	+	0.985917i	$0.446517\pi$
$929$	−23.4757	+	40.6611i	−0.770213	+	1.33405i	−0.937446	+	0.348131i	$0.886816\pi$
$930$		0			0
$931$		0			0
$932$	62.0442	−	35.8213i	2.03233	−	1.17336i
$933$		0			0
$934$	1.91469	+	1.10545i	0.0626505	+	0.0361713i
$935$			1.02836i			0.0336309i
$936$		0			0
$937$		−	28.8826i		−	0.943555i	−0.881718	−	0.471777i	$-0.843613\pi$
$937$		−	28.8826i		−	0.943555i	0.881718	−	0.471777i	$-0.156387\pi$
$938$		0			0
$939$		0			0
$940$	12.5572	+	21.7496i	0.409569	+	0.709395i
$941$	−0.727044	−	1.25928i	−0.0237009	−	0.0410512i	0.853932	−	0.520385i	$-0.174212\pi$
$941$	−0.727044	−	1.25928i	−0.0237009	−	0.0410512i	−0.877633	+	0.479334i	$0.840878\pi$
$942$		0			0
$943$	−0.827428	−	0.477716i	−0.0269448	−	0.0155566i
$944$	3.15992			0.102847
$945$		0			0
$946$	−2.14658			−0.0697914
$947$	36.9596	+	21.3386i	1.20102	+	0.693412i	0.960783	−	0.277301i	$-0.0894401\pi$
$947$	36.9596	+	21.3386i	1.20102	+	0.693412i	0.240241	+	0.970713i	$0.422773\pi$
$948$		0			0
$949$	1.20555	+	2.08807i	0.0391338	+	0.0677817i
$950$	−10.1774	−	17.6279i	−0.330200	−	0.571923i
$951$		0			0
$952$		0			0
$953$		−	10.8171i		−	0.350401i	−0.984533	−	0.175200i	$-0.943943\pi$
$953$		−	10.8171i		−	0.350401i	0.984533	−	0.175200i	$-0.0560574\pi$
$954$		0			0
$955$			55.1833i			1.78569i
$956$	61.6216	+	35.5773i	1.99299	+	1.15065i
$957$		0			0
$958$	−66.5902	+	38.4458i	−2.15143	+	1.24213i
$959$		0			0
$960$		0			0
$961$	−1.79596	+	3.11070i	−0.0579342	+	0.100345i
$962$	−75.1022			−2.42139
$963$		0			0
$964$		−	57.9115i		−	1.86521i
$965$	−18.6958	+	32.3820i	−0.601838	+	1.04241i
$966$		0			0
$967$	−22.4942	−	38.9611i	−0.723365	−	1.25290i	−0.959643	−	0.281219i	$-0.909261\pi$
$967$	−22.4942	−	38.9611i	−0.723365	−	1.25290i	0.236279	−	0.971685i	$-0.424072\pi$
$968$	36.5111	−	21.0797i	1.17351	−	0.677526i
$969$		0			0
$970$	−49.4415	+	85.6351i	−1.58747	+	2.74958i
$971$	−6.80343			−0.218332			−0.109166	−	0.994024i	$-0.534818\pi$
$971$	−6.80343			−0.218332			−0.109166	+	0.994024i	$0.534818\pi$
$972$		0			0
$973$		0			0
$974$	−70.6321	−	40.7795i	−2.26320	−	1.30666i
$975$		0			0
$976$	−4.93315	+	2.84815i	−0.157906	+	0.0911672i
$977$	29.2645	−	16.8959i	0.936254	−	0.540546i	0.0474698	−	0.998873i	$-0.484884\pi$
$977$	29.2645	−	16.8959i	0.936254	−	0.540546i	0.888784	+	0.458326i	$0.151551\pi$
$978$		0			0
$979$	−0.576044	−	0.332579i	−0.0184104	−	0.0106293i
$980$		0			0
$981$		0			0
$982$	20.0293			0.639160
$983$	−23.4913	+	40.6881i	−0.749256	+	1.29775i	0.198923	+	0.980015i	$0.436256\pi$
$983$	−23.4913	+	40.6881i	−0.749256	+	1.29775i	−0.948180	+	0.317735i	$0.897078\pi$
$984$		0			0
$985$	−19.3620	+	11.1787i	−0.616926	+	0.356182i
$986$	4.48668	+	7.77116i	0.142885	+	0.247484i
$987$		0			0
$988$	13.4757	−	23.3405i	0.428718	−	0.742562i
$989$		−	19.6757i		−	0.625651i
$990$		0			0
$991$	0.600897			0.0190881			0.00954406	−	0.999954i	$-0.496962\pi$
$991$	0.600897			0.0190881			0.00954406	+	0.999954i	$0.496962\pi$
$992$	8.34405	−	14.4523i	0.264924	−	0.458861i
$993$		0			0
$994$		0			0
$995$	−52.9810	+	30.5886i	−1.67961	+	0.969723i
$996$		0			0
$997$	41.9387	+	24.2133i	1.32821	+	0.766844i	0.985023	−	0.172423i	$-0.0551594\pi$
$997$	41.9387	+	24.2133i	1.32821	+	0.766844i	0.343189	+	0.939266i	$0.388493\pi$
$998$			27.0682i			0.856829i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.o.e.440.21		48
3.2	odd	2		441.2.o.e.146.3	✓	48
7.2	even	3		1323.2.i.d.521.24		48
7.3	odd	6		1323.2.s.d.656.4		48
7.4	even	3		1323.2.s.d.656.3		48
7.5	odd	6		1323.2.i.d.521.4		48
7.6	odd	2	inner	1323.2.o.e.440.22		48
9.4	even	3		441.2.o.e.293.4	yes	48
9.5	odd	6	inner	1323.2.o.e.881.22		48
21.2	odd	6		441.2.i.d.227.22		48
21.5	even	6		441.2.i.d.227.21		48
21.11	odd	6		441.2.s.d.362.21		48
21.17	even	6		441.2.s.d.362.22		48
21.20	even	2		441.2.o.e.146.4	yes	48
63.4	even	3		441.2.i.d.68.3		48
63.5	even	6		1323.2.s.d.962.3		48
63.13	odd	6		441.2.o.e.293.3	yes	48
63.23	odd	6		1323.2.s.d.962.4		48
63.31	odd	6		441.2.i.d.68.4		48
63.32	odd	6		1323.2.i.d.1097.4		48
63.40	odd	6		441.2.s.d.374.21		48
63.41	even	6	inner	1323.2.o.e.881.21		48
63.58	even	3		441.2.s.d.374.22		48
63.59	even	6		1323.2.i.d.1097.24		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.3		48	63.4	even	3
441.2.i.d.68.4		48	63.31	odd	6
441.2.i.d.227.21		48	21.5	even	6
441.2.i.d.227.22		48	21.2	odd	6
441.2.o.e.146.3	✓	48	3.2	odd	2
441.2.o.e.146.4	yes	48	21.20	even	2
441.2.o.e.293.3	yes	48	63.13	odd	6
441.2.o.e.293.4	yes	48	9.4	even	3
441.2.s.d.362.21		48	21.11	odd	6
441.2.s.d.362.22		48	21.17	even	6
441.2.s.d.374.21		48	63.40	odd	6
441.2.s.d.374.22		48	63.58	even	3
1323.2.i.d.521.4		48	7.5	odd	6
1323.2.i.d.521.24		48	7.2	even	3
1323.2.i.d.1097.4		48	63.32	odd	6
1323.2.i.d.1097.24		48	63.59	even	6
1323.2.o.e.440.21		48	1.1	even	1	trivial
1323.2.o.e.440.22		48	7.6	odd	2	inner
1323.2.o.e.881.21		48	63.41	even	6	inner
1323.2.o.e.881.22		48	9.5	odd	6	inner
1323.2.s.d.656.3		48	7.4	even	3
1323.2.s.d.656.4		48	7.3	odd	6
1323.2.s.d.962.3		48	63.5	even	6
1323.2.s.d.962.4		48	63.23	odd	6

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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.05485 + 1.18637i) q^{2} +(1.81495 + 3.14358i) q^{4} +(1.71774 + 2.97522i) q^{5} +3.86732i q^{8} +O(q^{10})\)	\(q+(2.05485 + 1.18637i) q^{2} +(1.81495 + 3.14358i) q^{4} +(1.71774 + 2.97522i) q^{5} +3.86732i q^{8} +8.15151i q^{10} +(-0.271895 - 0.156979i) q^{11} +(-5.09882 + 2.94381i) q^{13} +(-0.958178 + 1.65961i) q^{16} -0.953423 q^{17} +1.26109i q^{19} +(-6.23523 + 10.7997i) q^{20} +(-0.372470 - 0.645137i) q^{22} +(5.91336 - 3.41408i) q^{23} +(-3.40128 + 5.89118i) q^{25} -13.9698 q^{26} +(-3.43518 - 1.98330i) q^{29} +(4.53388 - 2.61764i) q^{31} +(2.76057 - 1.59381i) q^{32} +(-1.95915 - 1.13111i) q^{34} +5.37604 q^{37} +(-1.49612 + 2.59136i) q^{38} +(-11.5061 + 6.64306i) q^{40} +(-0.0699627 - 0.121179i) q^{41} +(1.44078 - 2.49550i) q^{43} -1.13963i q^{44} +16.2014 q^{46} +(1.00695 - 1.74409i) q^{47} +(-13.9783 + 8.07035i) q^{50} +(-18.5082 - 10.6857i) q^{52} +11.9799i q^{53} -1.07860i q^{55} +(-4.70586 - 8.15079i) q^{58} +(-0.824459 - 1.42801i) q^{59} +(2.57423 + 1.48623i) q^{61} +12.4219 q^{62} +11.3961 q^{64} +(-17.5169 - 10.1134i) q^{65} +(0.934059 + 1.61784i) q^{67} +(-1.73041 - 2.99717i) q^{68} -10.9981i q^{71} -0.409520i q^{73} +(11.0470 + 6.37798i) q^{74} +(-3.96435 + 2.28882i) q^{76} +(-5.23325 + 9.06426i) q^{79} -6.58361 q^{80} -0.332007i q^{82} +(4.00094 - 6.92984i) q^{83} +(-1.63774 - 2.83664i) q^{85} +(5.92117 - 3.41859i) q^{86} +(0.607087 - 1.05151i) q^{88} +2.11862 q^{89} +(21.4649 + 12.3927i) q^{92} +(4.13828 - 2.38924i) q^{94} +(-3.75202 + 2.16623i) q^{95} +(10.5054 + 6.06531i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4}+O(q^{10}) \) 48 * q + 24 * q^4	\( 48 q + 24 q^{4} + 24 q^{11} - 24 q^{16} + 48 q^{23} - 24 q^{25} - 120 q^{32} - 48 q^{50} - 48 q^{64} - 120 q^{65} + 168 q^{74} - 24 q^{79} - 24 q^{85} - 24 q^{86} + 144 q^{92} - 96 q^{95}+O(q^{100}) \) 48 * q + 24 * q^4 + 24 * q^11 - 24 * q^16 + 48 * q^23 - 24 * q^25 - 120 * q^32 - 48 * q^50 - 48 * q^64 - 120 * q^65 + 168 * q^74 - 24 * q^79 - 24 * q^85 - 24 * q^86 + 144 * q^92 - 96 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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