LMFDB - Embedded newform 1323.2.o.e.881.22

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			881.22
Character	$\chi$	$=$	1323.881
Dual form			1323.2.o.e.440.22

$q$-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 $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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	0.454350	−	0.890823i	$-0.349871\pi$
$2$	2.05485	−	1.18637i	1.45300	−	0.838890i	0.998651	+	0.0519328i	$0.0165382\pi$
$3$		0			0
$3$		0			0
$4$	1.81495	−	3.14358i	0.907474	−	1.57179i
$5$	−1.71774	+	2.97522i	−0.768198	+	1.33056i	0.170342	+	0.985385i	$0.445513\pi$
$5$	−1.71774	+	2.97522i	−0.768198	+	1.33056i	−0.938539	+	0.345172i	$0.887820\pi$
$6$		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	−0.540429	−	0.841389i	$-0.681738\pi$
$11$	−0.271895	+	0.156979i	−0.0819795	+	0.0473309i	0.458450	+	0.888720i	$0.348405\pi$
$12$		0			0
$13$	5.09882	+	2.94381i	1.41416	+	0.816465i	0.995777	−	0.0918054i	$-0.0292638\pi$
$13$	5.09882	+	2.94381i	1.41416	+	0.816465i	0.418383	+	0.908271i	$0.362597\pi$
$14$		0			0
$15$		0			0
$16$	−0.958178	−	1.65961i	−0.239545	−	0.414903i
$17$	0.953423			0.231239			0.115620	−	0.993294i	$-0.463115\pi$
$17$	0.953423			0.231239			0.115620	+	0.993294i	$0.463115\pi$
$18$		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	0.967658	−	0.252265i	$-0.0811754\pi$
$23$	5.91336	+	3.41408i	1.23302	+	0.711884i	0.265362	+	0.964149i	$0.414509\pi$
$24$		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	−0.783804	−	0.621008i	$-0.786723\pi$
$29$	−3.43518	+	1.98330i	−0.637897	+	0.368290i	0.145907	+	0.989298i	$0.453390\pi$
$30$		0			0
$31$	−4.53388	−	2.61764i	−0.814309	−	0.470141i	0.0341412	−	0.999417i	$-0.489130\pi$
$31$	−4.53388	−	2.61764i	−0.814309	−	0.470141i	−0.848450	+	0.529276i	$0.822464\pi$
$32$	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	$-0.829855\pi$
$41$	0.0699627	−	0.121179i	0.0109263	−	0.0189250i	0.871437	+	0.490508i	$0.163189\pi$
$42$		0			0
$43$	1.44078	+	2.49550i	0.219716	+	0.380560i	0.954721	−	0.297502i	$-0.0961535\pi$
$43$	1.44078	+	2.49550i	0.219716	+	0.380560i	−0.735005	+	0.678062i	$0.762820\pi$
$44$			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	$-0.213589\pi$
$47$	−1.00695	−	1.74409i	−0.146879	−	0.254402i	−0.930072	+	0.367376i	$0.880256\pi$
$48$		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	$-0.692418\pi$
$53$		−	11.9799i		−	1.64557i	0.568351	−	0.822786i	$-0.307582\pi$
$54$		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	$-0.799101\pi$
$59$	0.824459	−	1.42801i	0.107335	−	0.185910i	0.914690	+	0.404156i	$0.132435\pi$
$60$		0			0
$61$	−2.57423	+	1.48623i	−0.329597	+	0.190293i	−0.655662	−	0.755055i	$-0.727610\pi$
$61$	−2.57423	+	1.48623i	−0.329597	+	0.190293i	0.326065	+	0.945347i	$0.394277\pi$
$62$	−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	−0.803312	−	0.595559i	$-0.796931\pi$
$67$	0.934059	−	1.61784i	0.114113	−	0.197650i	0.917425	+	0.397909i	$0.130264\pi$
$68$	1.73041	−	2.99717i	0.209844	−	0.363460i
$69$		0			0
$70$		0			0
$71$			10.9981i			1.30524i	0.757686	+	0.652619i	$0.226330\pi$
$71$			10.9981i			1.30524i	−0.757686	+	0.652619i	$0.773670\pi$
$72$		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	−0.994392	−	0.105760i	$-0.966272\pi$
$79$	−5.23325	−	9.06426i	−0.588787	−	1.01981i	0.405605	−	0.914049i	$-0.367061\pi$
$80$	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	$-0.311391\pi$
$83$	−4.00094	−	6.92984i	−0.439161	−	0.760649i	−0.997625	+	0.0688800i	$0.978057\pi$
$84$		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	$-0.535818\pi$
$89$	−2.11862			−0.224574			−0.112287	+	0.993676i	$0.535818\pi$
$90$		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	$-0.877850\pi$
$97$	−10.5054	+	6.06531i	−1.06666	+	0.615839i	−0.139396	+	0.990237i	$0.544516\pi$
$98$		0			0
$99$		0			0
$100$	−24.6926			−2.46926
$101$	−6.26039	−	10.8433i	−0.622932	−	1.07895i	−0.988937	−	0.148337i	$-0.952608\pi$
$101$	−6.26039	−	10.8433i	−0.622932	−	1.07895i	0.366005	−	0.930613i	$-0.380725\pi$
$102$		0			0
$103$	15.6040	+	9.00897i	1.53751	+	0.887680i	0.998984	+	0.0450689i	$0.0143507\pi$
$103$	15.6040	+	9.00897i	1.53751	+	0.887680i	0.538523	+	0.842611i	$0.318983\pi$
$104$	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	$0.0556447\pi$
$107$			3.59816i			0.347848i	−0.984759	+	0.173924i	$0.944355\pi$
$108$		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	0.585775	−	0.810473i	$-0.300790\pi$
$113$	1.87912	+	1.08491i	0.176773	+	0.102060i	−0.409003	+	0.912533i	$0.634123\pi$
$114$		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	$-0.697236\pi$
$131$	4.74594	−	8.22021i	0.414655	−	0.718203i	0.995392	+	0.0958879i	$0.0305690\pi$
$132$		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	−0.828036	−	0.560674i	$-0.810542\pi$
$137$	−8.85456	+	5.11218i	−0.756496	+	0.436763i	0.0715401	+	0.997438i	$0.477209\pi$
$138$		0			0
$139$	−4.56556	−	2.63593i	−0.387246	−	0.223577i	0.293720	−	0.955891i	$-0.405107\pi$
$139$	−4.56556	−	2.63593i	−0.387246	−	0.223577i	−0.680966	+	0.732315i	$0.738440\pi$
$140$		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	−0.315979	−	0.948766i	$-0.602333\pi$
$149$	−15.8151	−	9.13086i	−1.29562	−	0.748029i	−0.979645	+	0.200737i	$0.935666\pi$
$150$		0			0
$151$	−11.5551	−	20.0140i	−0.940340	−	1.62872i	−0.764823	−	0.644240i	$-0.777174\pi$
$151$	−11.5551	−	20.0140i	−0.940340	−	1.62872i	−0.175517	−	0.984476i	$-0.556160\pi$
$152$	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	$-0.249430\pi$
$157$	5.65459	+	3.26468i	0.451286	+	0.260550i	−0.257087	+	0.966388i	$0.582763\pi$
$158$	−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	−0.457238	−	0.889345i	$-0.651161\pi$
$167$	6.99871	−	12.1221i	0.541576	−	0.938037i	0.998814	−	0.0486928i	$-0.0155055\pi$
$168$		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	$-0.302653\pi$
$173$	−5.44974	−	9.43923i	−0.414336	−	0.717651i	−0.995359	+	0.0962363i	$0.969320\pi$
$174$		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	$-0.980962\pi$
$179$		−	1.59945i		−	0.119549i	0.998212	−	0.0597743i	$-0.0190381\pi$
$180$		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	0.0963679	−	0.995346i	$-0.469277\pi$
$191$	13.9107	−	8.03138i	1.00655	−	0.581130i	0.910179	+	0.414216i	$0.135944\pi$
$192$		0			0
$193$	5.44196	−	9.42575i	0.391721	−	0.678480i	−0.600956	−	0.799282i	$-0.705213\pi$
$193$	5.44196	−	9.42575i	0.391721	−	0.678480i	0.992677	+	0.120802i	$0.0385467\pi$
$194$	−14.3914	+	24.9267i	−1.03324	+	1.78963i
$195$		0			0
$196$		0			0
$197$		−	6.50777i		−	0.463660i	−0.972756	−	0.231830i	$-0.925529\pi$
$197$		−	6.50777i		−	0.463660i	0.972756	−	0.231830i	$-0.0744712\pi$
$198$		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	−0.875582	−	0.483069i	$-0.839522\pi$
$211$	−0.282402	+	0.489135i	−0.0194414	+	0.0336735i	0.856141	+	0.516742i	$0.172855\pi$
$212$	−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	$-0.571573\pi$
$223$	7.61261	−	4.39514i	0.509778	−	0.294321i	0.732742	+	0.680506i	$0.238240\pi$
$224$		0			0
$225$		0			0
$226$	5.14842			0.342468
$227$	−8.45329	−	14.6415i	−0.561065	−	0.971793i	−0.997404	−	0.0720104i	$-0.977059\pi$
$227$	−8.45329	−	14.6415i	−0.561065	−	0.971793i	0.436339	−	0.899782i	$-0.356275\pi$
$228$		0			0
$229$	−16.9410	−	9.78088i	−1.11949	−	0.646339i	−0.178221	−	0.983991i	$-0.557034\pi$
$229$	−16.9410	−	9.78088i	−1.11949	−	0.646339i	−0.941271	+	0.337652i	$0.890367\pi$
$230$	−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	$0.223768\pi$
$233$			19.7368i			1.29300i	−0.762914	+	0.646500i	$0.776232\pi$
$234$		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	0.935720	−	0.352744i	$-0.114751\pi$
$239$	16.9761	+	9.80118i	1.09809	+	0.633985i	0.162375	+	0.986729i	$0.448085\pi$
$240$		0			0
$241$	13.8166	−	7.97702i	0.890006	−	0.513845i	0.0160617	−	0.999871i	$-0.494887\pi$
$241$	13.8166	−	7.97702i	0.890006	−	0.513845i	0.873945	+	0.486026i	$0.161554\pi$
$242$			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	$-0.490193\pi$
$251$	0.976065			0.0616087			0.0308044	+	0.999525i	$0.490193\pi$
$252$		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	$-0.708665\pi$
$257$	6.11947	−	10.5992i	0.381722	−	0.661162i	0.991309	+	0.131558i	$0.0419979\pi$
$258$		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	−0.383413	−	0.923577i	$-0.625252\pi$
$263$	3.64436	−	2.10407i	0.224721	−	0.129743i	0.608134	+	0.793834i	$0.291918\pi$
$264$		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	$-0.729575\pi$
$269$	−21.6597			−1.32062			−0.660309	+	0.750994i	$0.729575\pi$
$270$		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	0.891677	+	0.452672i	$0.149529\pi$
$277$	13.9448	+	24.1532i	0.837864	+	1.45122i	−0.0538127	+	0.998551i	$0.517137\pi$
$278$	−12.5087			−0.750225
$279$		0			0
$280$		0			0
$281$	−16.7176	+	9.65190i	−0.997287	+	0.575784i	−0.907444	−	0.420172i	$-0.861970\pi$
$281$	−16.7176	+	9.65190i	−0.997287	+	0.575784i	−0.0898425	+	0.995956i	$0.528636\pi$
$282$		0			0
$283$	15.2703	+	8.81631i	0.907725	+	0.524075i	0.879698	−	0.475532i	$-0.157744\pi$
$283$	15.2703	+	8.81631i	0.907725	+	0.524075i	0.0280263	+	0.999607i	$0.491078\pi$
$284$	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	−0.0777369	−	0.996974i	$-0.524769\pi$
$293$	14.1138	−	24.4458i	0.824536	−	1.42814i	0.902273	−	0.431165i	$-0.141897\pi$
$294$		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	−0.449500	−	0.893280i	$-0.648398\pi$
$311$	9.67914	−	16.7648i	0.548854	−	0.950642i	0.998353	−	0.0573619i	$-0.0182689\pi$
$312$		0			0
$313$	22.9507	−	13.2506i	1.29725	−	0.748967i	0.317321	−	0.948318i	$-0.397217\pi$
$313$	22.9507	−	13.2506i	1.29725	−	0.748967i	0.979928	+	0.199352i	$0.0638836\pi$
$314$	15.4925			0.874291
$315$		0			0
$316$	−37.9923			−2.13724
$317$	7.50458	−	4.33277i	0.421499	−	0.243353i	−0.274219	−	0.961667i	$-0.588419\pi$
$317$	7.50458	−	4.33277i	0.421499	−	0.243353i	0.695719	+	0.718314i	$0.255086\pi$
$318$		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	−0.999326	−	0.0367197i	$-0.988309\pi$
$331$	−9.66912	−	16.7474i	−0.531463	−	0.920521i	0.467863	−	0.883801i	$-0.345024\pi$
$332$	−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	0.297673	+	0.954668i	$0.403790\pi$
$337$	−12.4451	+	21.5556i	−0.677930	+	1.17421i	−0.975603	+	0.219542i	$0.929544\pi$
$338$	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	0.359247	−	0.933243i	$-0.383034\pi$
$347$	−5.01728	−	2.89673i	−0.269342	−	0.155505i	−0.628588	+	0.777738i	$0.716367\pi$
$348$		0			0
$349$	13.3430	−	7.70360i	0.714236	−	0.412364i	−0.0983918	−	0.995148i	$-0.531370\pi$
$349$	13.3430	−	7.70360i	0.714236	−	0.412364i	0.812627	+	0.582784i	$0.198037\pi$
$350$		0			0
$351$		0			0
$352$	−1.00078			−0.0533417
$353$	8.87263	+	15.3679i	0.472243	+	0.817948i	0.999496	−	0.0317602i	$-0.0101113\pi$
$353$	8.87263	+	15.3679i	0.472243	+	0.817948i	−0.527253	+	0.849708i	$0.676778\pi$
$354$		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	$-0.793242\pi$
$359$		−	22.9197i		−	1.20966i	0.796356	−	0.604828i	$-0.206758\pi$
$360$		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	$-0.708348\pi$
$367$	−4.33253	+	2.50139i	−0.226156	+	0.130571i	0.382641	+	0.923897i	$0.375014\pi$
$368$		−	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	−0.962583	−	0.270988i	$-0.912649\pi$
$373$	−4.76280	+	8.24941i	−0.246608	+	0.427138i	0.715974	+	0.698127i	$0.245983\pi$
$374$	−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	−0.456311	−	0.889821i	$-0.650829\pi$
$383$	10.6160	−	18.3874i	0.542452	−	0.939554i	0.998763	−	0.0497336i	$-0.0158372\pi$
$384$		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	−0.397478	−	0.917612i	$-0.630115\pi$
$389$	3.91419	−	2.25986i	0.198457	−	0.114579i	0.595936	+	0.803032i	$0.296781\pi$
$390$		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	0.248237	−	0.968699i	$-0.420149\pi$
$401$	−9.34292	−	5.39414i	−0.466563	−	0.269370i	−0.714800	+	0.699329i	$0.753482\pi$
$402$		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	$-0.172182\pi$
$409$	16.9860	+	9.80689i	0.839906	+	0.484920i	−0.0173265	+	0.999850i	$0.505515\pi$
$410$	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	$-0.975447\pi$
$419$	−8.83829	+	15.3084i	−0.431779	+	0.747862i	0.565248	+	0.824921i	$0.308780\pi$
$420$		0			0
$421$	−16.9507	−	29.3594i	−0.826124	−	1.43089i	−0.901057	−	0.433701i	$-0.857208\pi$
$421$	−16.9507	−	29.3594i	−0.826124	−	1.43089i	0.0749327	−	0.997189i	$-0.476126\pi$
$422$			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	$0.110482\pi$
$431$			14.1239i			0.680324i	−0.940367	+	0.340162i	$0.889518\pi$
$432$		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	$-0.576417\pi$
$439$	10.1520	−	5.86126i	0.484529	−	0.279743i	0.722302	+	0.691578i	$0.243084\pi$
$440$	−4.17128			−0.198858
$441$		0			0
$442$	13.3191			0.633526
$443$	6.17796	−	3.56685i	0.293524	−	0.169466i	−0.346006	−	0.938232i	$-0.612462\pi$
$443$	6.17796	−	3.56685i	0.293524	−	0.169466i	0.639530	+	0.768766i	$0.279129\pi$
$444$		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	$0.0238656\pi$
$449$			3.17445i			0.149811i	−0.997191	+	0.0749057i	$0.976134\pi$
$450$		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	−0.997066	−	0.0765431i	$-0.975612\pi$
$457$	−12.0745	−	20.9137i	−0.564821	−	0.978299i	0.432245	−	0.901756i	$-0.357722\pi$
$458$	−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	$-0.0629505\pi$
$461$	6.87281	+	11.9041i	0.320099	+	0.554427i	−0.660409	+	0.750906i	$0.729617\pi$
$462$		0			0
$463$	10.3157	−	17.8673i	0.479411	−	0.830364i	−0.520310	−	0.853977i	$-0.674184\pi$
$463$	10.3157	−	17.8673i	0.479411	−	0.830364i	0.999721	+	0.0236135i	$0.00751711\pi$
$464$	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	$-0.506863\pi$
$467$	−0.931788			−0.0431180			−0.0215590	+	0.999768i	$0.506863\pi$
$468$		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	0.952340	+	0.305037i	$0.0986690\pi$
$479$	16.2031	+	28.0647i	0.740340	+	1.28231i	−0.212000	+	0.977270i	$0.567998\pi$
$480$		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	0.655804	−	0.754931i	$-0.272330\pi$
$491$	7.31048	+	4.22071i	0.329917	+	0.190478i	−0.325887	+	0.945409i	$0.605663\pi$
$492$		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	−0.709643	−	0.704561i	$-0.751144\pi$
$499$	5.70400	−	9.87961i	0.255346	−	0.442272i	0.964989	+	0.262289i	$0.0844773\pi$
$500$	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	$-0.761087\pi$
$503$	−32.8028			−1.46261			−0.731303	+	0.682053i	$0.761087\pi$
$504$		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	$-0.975712\pi$
$509$	−9.75828	+	16.9018i	−0.432528	+	0.749160i	0.564562	+	0.825390i	$0.309045\pi$
$510$		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	$-0.356717\pi$
$521$	19.8622			0.870177			0.435088	+	0.900388i	$0.356717\pi$
$522$		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	0.930598	−	0.366042i	$-0.119287\pi$
$547$	3.46839	+	6.00743i	0.148298	+	0.256859i	−0.782301	+	0.622901i	$0.785954\pi$
$548$			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	$-0.891220\pi$
$557$		−	15.8186i		−	0.670257i	0.942172	−	0.335128i	$-0.108780\pi$
$558$		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	0.299287	+	0.954163i	$0.403251\pi$
$563$	−16.0561	+	27.8101i	−0.676686	+	1.17205i	−0.975973	+	0.217891i	$0.930082\pi$
$564$		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	−0.982528	−	0.186114i	$-0.940411\pi$
$569$	−31.3107	+	18.0772i	−1.31261	+	0.757837i	−0.330084	+	0.943951i	$0.607077\pi$
$570$		0			0
$571$	−14.1792	+	24.5590i	−0.593380	+	1.02776i	0.400393	+	0.916343i	$0.368873\pi$
$571$	−14.1792	+	24.5590i	−0.593380	+	1.02776i	−0.993773	+	0.111421i	$0.964460\pi$
$572$	−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	$-0.0342270\pi$
$587$	9.79227	+	16.9607i	0.404170	+	0.700043i	−0.590054	+	0.807364i	$0.700894\pi$
$588$		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	$-0.365821\pi$
$593$	19.9275			0.818324			0.409162	+	0.912462i	$0.365821\pi$
$594$		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	0.499453	−	0.866341i	$-0.333534\pi$
$599$	−0.0267639	−	0.0154521i	−0.00109354	−	0.000631357i	−0.500547	+	0.865710i	$0.666868\pi$
$600$		0			0
$601$	−25.8633	+	14.9322i	−1.05499	+	0.609097i	−0.924041	−	0.382293i	$-0.875135\pi$
$601$	−25.8633	+	14.9322i	−1.05499	+	0.609097i	−0.130945	+	0.991390i	$0.541801\pi$
$602$		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	$-0.553226\pi$
$607$	−27.1898	−	15.6980i	−1.10360	−	0.637163i	−0.937164	+	0.348889i	$0.886559\pi$
$608$	−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	−0.153279	−	0.988183i	$-0.548983\pi$
$617$	−26.9685	−	15.5703i	−1.08571	−	0.626835i	−0.932431	+	0.361348i	$0.882317\pi$
$618$		0			0
$619$	−1.13493	+	0.655252i	−0.0456167	+	0.0263368i	−0.522635	−	0.852557i	$-0.675051\pi$
$619$	−1.13493	+	0.655252i	−0.0456167	+	0.0263368i	0.477018	+	0.878893i	$0.341718\pi$
$620$		−	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	−0.546901	−	0.837197i	$-0.684193\pi$
$641$	−2.41325	+	1.39329i	−0.0953176	+	0.0550316i	0.451584	+	0.892229i	$0.350859\pi$
$642$		0			0
$643$	0.324584	+	0.187399i	0.0128004	+	0.00739029i	0.506387	−	0.862307i	$-0.330981\pi$
$643$	0.324584	+	0.187399i	0.0128004	+	0.00739029i	−0.493586	+	0.869697i	$0.664314\pi$
$644$		0			0
$645$		0			0
$646$	1.42644	+	2.47066i	0.0561224	+	0.0972069i
$647$	50.3216			1.97834			0.989172	−	0.146758i	$-0.0468837\pi$
$647$	50.3216			1.97834			0.989172	+	0.146758i	$0.0468837\pi$
$648$		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	0.902373	−	0.430955i	$-0.141823\pi$
$653$	25.0515	+	14.4635i	0.980342	+	0.566000i	0.0779684	+	0.996956i	$0.475157\pi$
$654$		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	0.0159971	−	0.999872i	$-0.494908\pi$
$659$	22.8449	−	13.1895i	0.889910	−	0.513790i	0.873913	+	0.486082i	$0.161574\pi$
$660$		0			0
$661$	−10.0533	−	5.80428i	−0.391028	−	0.225760i	0.291577	−	0.956547i	$-0.405820\pi$
$661$	−10.0533	−	5.80428i	−0.391028	−	0.225760i	−0.682606	+	0.730787i	$0.739153\pi$
$662$	−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	−0.999356	−	0.0358949i	$-0.988572\pi$
$673$	−13.7692	−	23.8490i	−0.530764	−	0.919310i	0.468592	−	0.883415i	$-0.344761\pi$
$674$			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	$-0.138300\pi$
$677$	2.31563	+	4.01080i	0.0889970	+	0.154147i	−0.818090	+	0.575090i	$0.804967\pi$
$678$		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	$-0.914451\pi$
$683$		−	13.8792i		−	0.531072i	0.964101	−	0.265536i	$-0.0855490\pi$
$684$		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	$-0.524880\pi$
$691$	19.6168	−	11.3258i	0.746258	−	0.430852i	0.824340	+	0.566095i	$0.191546\pi$
$692$	−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	$-0.900094\pi$
$701$		−	16.3485i		−	0.617474i	0.951147	−	0.308737i	$-0.0999063\pi$
$702$		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	0.685761	−	0.727826i	$-0.259469\pi$
$709$	−7.65356	−	13.2564i	−0.287435	−	0.497853i	−0.973197	+	0.229974i	$0.926136\pi$
$710$	−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	$-0.589786\pi$
$719$	−14.9272			−0.556690			−0.278345	+	0.960481i	$0.589786\pi$
$720$		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	$-0.635059\pi$
$727$	4.62968	−	2.67295i	0.171705	−	0.0991341i	0.583390	+	0.812192i	$0.301726\pi$
$728$		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	$-0.447132\pi$
$733$	−16.4099	−	9.47428i	−0.606115	−	0.349941i	−0.771443	+	0.636298i	$0.780465\pi$
$734$	−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	0.883253	−	0.468896i	$-0.155348\pi$
$743$	25.0448	+	14.4596i	0.918804	+	0.530472i	0.0355508	+	0.999368i	$0.488681\pi$
$744$		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	0.108832	+	0.994060i	$0.465289\pi$
$751$	−22.1007	+	38.2795i	−0.806465	+	1.39684i	−0.915297	+	0.402779i	$0.868044\pi$
$752$	−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	$-0.803908\pi$
$761$	2.54651	−	4.41069i	0.0923109	−	0.159887i	0.908483	+	0.417921i	$0.137241\pi$
$762$		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	$-0.578564\pi$
$769$	−33.4505	−	19.3126i	−1.20626	−	0.696432i	−0.961939	+	0.273264i	$0.911897\pi$
$770$		0			0
$771$		0			0
$772$	−19.7537	−	34.2145i	−0.710953	−	1.23141i
$773$	−34.3507			−1.23551			−0.617754	−	0.786371i	$-0.711957\pi$
$773$	−34.3507			−1.23551			−0.617754	+	0.786371i	$0.711957\pi$
$774$		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	$-0.195894\pi$
$787$	20.3343	+	11.7400i	0.724839	+	0.418486i	−0.0916921	+	0.995787i	$0.529228\pi$
$788$	−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	$-0.899474\pi$
$797$	−5.82399	+	10.0875i	−0.206296	+	0.357316i	0.744249	+	0.667903i	$0.232808\pi$
$798$		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	$0.0901881\pi$
$809$			15.9029i			0.559117i	−0.960129	+	0.279559i	$0.909812\pi$
$810$		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	−0.498019	−	0.867166i	$-0.665939\pi$
$821$	0.113440	−	0.0654949i	0.00395910	−	0.00228579i	0.501978	+	0.864880i	$0.332606\pi$
$822$		0			0
$823$	−23.0144	+	39.8621i	−0.802231	+	1.38950i	0.115914	+	0.993259i	$0.463020\pi$
$823$	−23.0144	+	39.8621i	−0.802231	+	1.38950i	−0.918145	+	0.396245i	$0.870313\pi$
$824$	34.8406	−	60.3456i	1.21373	−	2.10224i
$825$		0			0
$826$		0			0
$827$			40.5836i			1.41123i	0.708595	+	0.705615i	$0.249329\pi$
$827$			40.5836i			1.41123i	−0.708595	+	0.705615i	$0.750671\pi$
$828$		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	$-0.102321\pi$
$839$	5.81551	+	10.0728i	0.200774	+	0.347750i	−0.748004	+	0.663694i	$0.768988\pi$
$840$		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	$-0.800758\pi$
$853$	−20.6854	+	11.9427i	−0.708254	+	0.408911i	0.102160	+	0.994768i	$0.467425\pi$
$854$		0			0
$855$		0			0
$856$	13.9153			0.475614
$857$	−17.3362	−	30.0271i	−0.592193	−	1.02571i	−0.993936	−	0.109956i	$-0.964929\pi$
$857$	−17.3362	−	30.0271i	−0.592193	−	1.02571i	0.401744	−	0.915752i	$-0.368404\pi$
$858$		0			0
$859$	26.3932	+	15.2381i	0.900525	+	0.519918i	0.877371	−	0.479813i	$-0.159296\pi$
$859$	26.3932	+	15.2381i	0.900525	+	0.519918i	0.0231546	+	0.999732i	$0.492629\pi$
$860$	−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	$0.192501\pi$
$863$			33.4052i			1.13713i	−0.822639	+	0.568564i	$0.807499\pi$
$864$		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	0.167070	−	0.985945i	$-0.446569\pi$
$877$	27.7600	−	48.0817i	0.937389	−	1.62360i	0.770318	−	0.637660i	$-0.220097\pi$
$878$	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	$-0.609296\pi$
$881$	−19.9850			−0.673313			−0.336656	+	0.941628i	$0.609296\pi$
$882$		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	−0.394280	−	0.918990i	$-0.629006\pi$
$887$	17.8317	−	30.8853i	0.598729	−	1.03703i	0.993009	−	0.118038i	$-0.0376606\pi$
$888$		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	−0.989793	−	0.142512i	$-0.954482\pi$
$907$	−18.6215	−	32.2533i	−0.618315	−	1.07095i	0.371478	−	0.928442i	$-0.378851\pi$
$908$	−61.3692			−2.03661
$909$		0			0
$910$		0			0
$911$	18.8068	−	10.8581i	0.623098	−	0.359746i	−0.154976	−	0.987918i	$-0.549530\pi$
$911$	18.8068	−	10.8581i	0.623098	−	0.359746i	0.778074	+	0.628172i	$0.216197\pi$
$912$		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	0.937446	+	0.348131i	$0.113184\pi$
$929$	23.4757	+	40.6611i	0.770213	+	1.33405i	−0.167233	+	0.985917i	$0.553483\pi$
$930$		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	$-0.825788\pi$
$941$	0.727044	−	1.25928i	0.0237009	−	0.0410512i	0.877633	+	0.479334i	$0.159122\pi$
$942$		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	0.240241	−	0.970713i	$-0.422773\pi$
$947$	36.9596	−	21.3386i	1.20102	−	0.693412i	0.960783	+	0.277301i	$0.0894401\pi$
$948$		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	$0.0560574\pi$
$953$			10.8171i			0.350401i	−0.984533	+	0.175200i	$0.943943\pi$
$954$		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	0.236279	+	0.971685i	$0.424072\pi$
$967$	−22.4942	+	38.9611i	−0.723365	+	1.25290i	−0.959643	+	0.281219i	$0.909261\pi$
$968$	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	$-0.465182\pi$
$971$	6.80343			0.218332			0.109166	+	0.994024i	$0.465182\pi$
$972$		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	0.888784	−	0.458326i	$-0.151551\pi$
$977$	29.2645	+	16.8959i	0.936254	+	0.540546i	0.0474698	+	0.998873i	$0.484884\pi$
$978$		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	0.948180	+	0.317735i	$0.102922\pi$
$983$	23.4913	+	40.6881i	0.749256	+	1.29775i	−0.198923	+	0.980015i	$0.563744\pi$
$984$		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	$-0.944841\pi$
$997$	−41.9387	+	24.2133i	−1.32821	+	0.766844i	−0.343189	+	0.939266i	$0.611507\pi$
$998$		−	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.881.22		48
3.2	odd	2		441.2.o.e.293.4	yes	48
7.2	even	3		1323.2.s.d.962.4		48
7.3	odd	6		1323.2.i.d.1097.24		48
7.4	even	3		1323.2.i.d.1097.4		48
7.5	odd	6		1323.2.s.d.962.3		48
7.6	odd	2	inner	1323.2.o.e.881.21		48
9.2	odd	6	inner	1323.2.o.e.440.21		48
9.7	even	3		441.2.o.e.146.3	✓	48
21.2	odd	6		441.2.s.d.374.22		48
21.5	even	6		441.2.s.d.374.21		48
21.11	odd	6		441.2.i.d.68.3		48
21.17	even	6		441.2.i.d.68.4		48
21.20	even	2		441.2.o.e.293.3	yes	48
63.2	odd	6		1323.2.i.d.521.24		48
63.11	odd	6		1323.2.s.d.656.3		48
63.16	even	3		441.2.i.d.227.22		48
63.20	even	6	inner	1323.2.o.e.440.22		48
63.25	even	3		441.2.s.d.362.21		48
63.34	odd	6		441.2.o.e.146.4	yes	48
63.38	even	6		1323.2.s.d.656.4		48
63.47	even	6		1323.2.i.d.521.4		48
63.52	odd	6		441.2.s.d.362.22		48
63.61	odd	6		441.2.i.d.227.21		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.3		48	21.11	odd	6
441.2.i.d.68.4		48	21.17	even	6
441.2.i.d.227.21		48	63.61	odd	6
441.2.i.d.227.22		48	63.16	even	3
441.2.o.e.146.3	✓	48	9.7	even	3
441.2.o.e.146.4	yes	48	63.34	odd	6
441.2.o.e.293.3	yes	48	21.20	even	2
441.2.o.e.293.4	yes	48	3.2	odd	2
441.2.s.d.362.21		48	63.25	even	3
441.2.s.d.362.22		48	63.52	odd	6
441.2.s.d.374.21		48	21.5	even	6
441.2.s.d.374.22		48	21.2	odd	6
1323.2.i.d.521.4		48	63.47	even	6
1323.2.i.d.521.24		48	63.2	odd	6
1323.2.i.d.1097.4		48	7.4	even	3
1323.2.i.d.1097.24		48	7.3	odd	6
1323.2.o.e.440.21		48	9.2	odd	6	inner
1323.2.o.e.440.22		48	63.20	even	6	inner
1323.2.o.e.881.21		48	7.6	odd	2	inner
1323.2.o.e.881.22		48	1.1	even	1	trivial
1323.2.s.d.656.3		48	63.11	odd	6
1323.2.s.d.656.4		48	63.38	even	6
1323.2.s.d.962.3		48	7.5	odd	6
1323.2.s.d.962.4		48	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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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