LMFDB - Embedded newform 1323.2.i.d.1097.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1323,2,Mod(521,1323)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1323, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1323.521"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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			1097.24
Character	$\chi$	$=$	1323.1097
Dual form			1323.2.i.d.521.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.37274i q^{2} -3.62990 q^{4} +(1.71774 + 2.97522i) q^{5} -3.86732i q^{8} +(-7.05942 + 4.07576i) q^{10} +(0.271895 + 0.156979i) q^{11} +(-5.09882 - 2.94381i) q^{13} +1.91636 q^{16} +(0.476712 + 0.825689i) q^{17} +(1.09214 + 0.630546i) q^{19} +(-6.23523 - 10.7997i) q^{20} +(-0.372470 + 0.645137i) q^{22} +(-5.91336 + 3.41408i) q^{23} +(-3.40128 + 5.89118i) q^{25} +(6.98489 - 12.0982i) q^{26} +(-3.43518 + 1.98330i) q^{29} -5.23527i q^{31} -3.18763i q^{32} +(-1.95915 + 1.13111i) q^{34} +(-2.68802 + 4.65579i) q^{37} +(-1.49612 + 2.59136i) q^{38} +(11.5061 - 6.64306i) q^{40} +(-0.0699627 + 0.121179i) q^{41} +(1.44078 + 2.49550i) q^{43} +(-0.986951 - 0.569817i) q^{44} +(-8.10072 - 14.0309i) q^{46} -2.01390 q^{47} +(-13.9783 - 8.07035i) q^{50} +(18.5082 + 10.6857i) q^{52} +(-10.3749 + 5.98997i) q^{53} +1.07860i q^{55} +(-4.70586 - 8.15079i) q^{58} +1.64892 q^{59} +2.97247i q^{61} +12.4219 q^{62} +11.3961 q^{64} -20.2268i q^{65} -1.86812 q^{67} +(-1.73041 - 2.99717i) q^{68} +10.9981i q^{71} +(0.354655 - 0.204760i) q^{73} +(-11.0470 - 6.37798i) q^{74} +(-3.96435 - 2.28882i) q^{76} +10.4665 q^{79} +(3.29181 + 5.70158i) q^{80} +(-0.287526 - 0.166003i) q^{82} +(4.00094 + 6.92984i) q^{83} +(-1.63774 + 2.83664i) q^{85} +(-5.92117 + 3.41859i) q^{86} +(0.607087 - 1.05151i) q^{88} +(-1.05931 + 1.83478i) q^{89} +(21.4649 - 12.3927i) q^{92} -4.77847i q^{94} +4.33246i q^{95} +(10.5054 - 6.06531i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4} - 24 q^{11} + 48 q^{16} - 48 q^{23} - 24 q^{25} + 96 q^{44} - 48 q^{50} + 48 q^{53} - 48 q^{64} - 168 q^{74} + 48 q^{79} - 24 q^{85} + 24 q^{86} + 144 q^{92}+O(q^{100}) $ 48 * q - 48 * q^4 - 24 * q^11 + 48 * q^16 - 48 * q^23 - 24 * q^25 + 96 * q^44 - 48 * q^50 + 48 * q^53 - 48 * q^64 - 168 * q^74 + 48 * q^79 - 24 * q^85 + 24 * q^86 + 144 * q^92

Character values

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

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

Coefficient data

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

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

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

$2$			2.37274i			1.67778i	0.544300	+	0.838890i	$0.316795\pi$
$2$			2.37274i			1.67778i	−0.544300	+	0.838890i	$0.683205\pi$
$3$		0			0
$3$		0			0
$4$	−3.62990			−1.81495
$5$	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
$10$	−7.05942	+	4.07576i	−2.23238	+	1.28887i
$11$	0.271895	+	0.156979i	0.0819795	+	0.0473309i	0.540429	−	0.841389i	$-0.318262\pi$
$11$	0.271895	+	0.156979i	0.0819795	+	0.0473309i	−0.458450	+	0.888720i	$0.651595\pi$
$12$		0			0
$13$	−5.09882	−	2.94381i	−1.41416	−	0.816465i	−0.418383	−	0.908271i	$-0.637403\pi$
$13$	−5.09882	−	2.94381i	−1.41416	−	0.816465i	−0.995777	+	0.0918054i	$0.970736\pi$
$14$		0			0
$15$		0			0
$16$	1.91636			0.479089
$17$	0.476712	+	0.825689i	0.115620	+	0.200259i	0.918027	−	0.396517i	$-0.129781\pi$
$17$	0.476712	+	0.825689i	0.115620	+	0.200259i	−0.802408	+	0.596776i	$0.796448\pi$
$18$		0			0
$19$	1.09214	+	0.630546i	0.250553	+	0.144657i	0.620018	−	0.784588i	$-0.287125\pi$
$19$	1.09214	+	0.630546i	0.250553	+	0.144657i	−0.369464	+	0.929245i	$0.620459\pi$
$20$	−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	$-0.918825\pi$
$23$	−5.91336	+	3.41408i	−1.23302	+	0.711884i	−0.265362	+	0.964149i	$0.585491\pi$
$24$		0			0
$25$	−3.40128	+	5.89118i	−0.680255	+	1.17824i
$26$	6.98489	−	12.0982i	1.36985	−	2.37265i
$27$		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
$31$		−	5.23527i		−	0.940283i	−0.882591	−	0.470141i	$-0.844203\pi$
$31$		−	5.23527i		−	0.940283i	0.882591	−	0.470141i	$-0.155797\pi$
$32$		−	3.18763i		−	0.563498i
$33$		0			0
$34$	−1.95915	+	1.13111i	−0.335991	+	0.193984i
$35$		0			0
$36$		0			0
$37$	−2.68802	+	4.65579i	−0.441908	+	0.765407i	−0.997831	−	0.0658264i	$-0.979032\pi$
$37$	−2.68802	+	4.65579i	−0.441908	+	0.765407i	0.555923	+	0.831234i	$0.312365\pi$
$38$	−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	−0.871437	−	0.490508i	$-0.836811\pi$
$41$	−0.0699627	+	0.121179i	−0.0109263	+	0.0189250i	0.860511	+	0.509433i	$0.170145\pi$
$42$		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	$0.762820\pi$
$44$	−0.986951	−	0.569817i	−0.148788	−	0.0859031i
$45$		0			0
$46$	−8.10072	−	14.0309i	−1.19439	−	2.06874i
$47$	−2.01390			−0.293758			−0.146879	−	0.989154i	$-0.546923\pi$
$47$	−2.01390			−0.293758			−0.146879	+	0.989154i	$0.546923\pi$
$48$		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
$53$	−10.3749	+	5.98997i	−1.42511	+	0.822786i	−0.996729	−	0.0808132i	$-0.974248\pi$
$53$	−10.3749	+	5.98997i	−1.42511	+	0.822786i	−0.428378	+	0.903599i	$0.640915\pi$
$54$		0			0
$55$			1.07860i			0.145438i
$56$		0			0
$57$		0			0
$58$	−4.70586	−	8.15079i	−0.617910	−	1.07025i
$59$	1.64892			0.214671			0.107335	−	0.994223i	$-0.465768\pi$
$59$	1.64892			0.214671			0.107335	+	0.994223i	$0.465768\pi$
$60$		0			0
$61$			2.97247i			0.380585i	0.981727	+	0.190293i	$0.0609437\pi$
$61$			2.97247i			0.380585i	−0.981727	+	0.190293i	$0.939056\pi$
$62$	12.4219			1.57759
$63$		0			0
$64$	11.3961			1.42452
$65$		−	20.2268i		−	2.50883i
$66$		0			0
$67$	−1.86812			−0.228227			−0.114113	−	0.993468i	$-0.536403\pi$
$67$	−1.86812			−0.228227			−0.114113	+	0.993468i	$0.536403\pi$
$68$	−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
$73$	0.354655	−	0.204760i	0.0415092	−	0.0239653i	−0.479102	−	0.877759i	$-0.659038\pi$
$73$	0.354655	−	0.204760i	0.0415092	−	0.0239653i	0.520611	+	0.853794i	$0.325704\pi$
$74$	−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
$79$	10.4665			1.17757			0.588787	−	0.808288i	$-0.299606\pi$
$79$	10.4665			1.17757			0.588787	+	0.808288i	$0.299606\pi$
$80$	3.29181	+	5.70158i	0.368035	+	0.637456i
$81$		0			0
$82$	−0.287526	−	0.166003i	−0.0317519	−	0.0183320i
$83$	4.00094	+	6.92984i	0.439161	+	0.760649i	0.997625	−	0.0688800i	$-0.0219426\pi$
$83$	4.00094	+	6.92984i	0.439161	+	0.760649i	−0.558464	+	0.829529i	$0.688609\pi$
$84$		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
$89$	−1.05931	+	1.83478i	−0.112287	+	0.194487i	−0.916692	−	0.399595i	$-0.869151\pi$
$89$	−1.05931	+	1.83478i	−0.112287	+	0.194487i	0.804405	+	0.594081i	$0.202484\pi$
$90$		0			0
$91$		0			0
$92$	21.4649	−	12.3927i	2.23787	−	1.29203i
$93$		0			0
$94$		−	4.77847i		−	0.492862i
$95$			4.33246i			0.444501i
$96$		0			0
$97$	10.5054	−	6.06531i	1.06666	−	0.615839i	0.139396	−	0.990237i	$-0.455484\pi$
$97$	10.5054	−	6.06531i	1.06666	−	0.615839i	0.927268	+	0.374398i	$0.122150\pi$
$98$		0			0
$99$		0			0
$100$	12.3463	−	21.3844i	1.23463	−	2.13844i
$101$	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	$-0.318983\pi$
$103$	15.6040	−	9.00897i	1.53751	−	0.887680i	0.998984	−	0.0450689i	$-0.0143507\pi$
$104$	−11.3847	+	19.7188i	−1.11636	+	1.93359i
$105$		0			0
$106$	−14.2127	−	24.6170i	−1.38046	−	2.39102i
$107$	−3.11610	−	1.79908i	−0.301245	−	0.173924i	0.341757	−	0.939788i	$-0.388978\pi$
$107$	−3.11610	−	1.79908i	−0.301245	−	0.173924i	−0.643002	+	0.765864i	$0.722311\pi$
$108$		0			0
$109$	3.28109	+	5.68302i	0.314271	+	0.544334i	0.979282	−	0.202499i	$-0.0649064\pi$
$109$	3.28109	+	5.68302i	0.314271	+	0.544334i	−0.665011	+	0.746834i	$0.731573\pi$
$110$	−2.55923			−0.244013
$111$		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
$116$	12.4694	−	7.19918i	1.15775	−	0.668427i
$117$		0			0
$118$			3.91246i			0.360171i
$119$		0			0
$120$		0			0
$121$	−5.45072	−	9.44092i	−0.495520	−	0.858265i
$122$	−7.05289			−0.638539
$123$		0			0
$124$			19.0035i			1.70656i
$125$	−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	$0.466756\pi$
$128$			20.6648i			1.82653i
$129$		0			0
$130$	47.9930			4.20926
$131$	−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
$136$	3.19320	−	1.84360i	0.273815	−	0.158087i
$137$	8.85456	+	5.11218i	0.756496	+	0.436763i	0.828036	−	0.560674i	$-0.189458\pi$
$137$	8.85456	+	5.11218i	0.756496	+	0.436763i	−0.0715401	+	0.997438i	$0.522791\pi$
$138$		0			0
$139$	4.56556	+	2.63593i	0.387246	+	0.223577i	0.680966	−	0.732315i	$-0.261560\pi$
$139$	4.56556	+	2.63593i	0.387246	+	0.223577i	−0.293720	+	0.955891i	$0.594893\pi$
$140$		0			0
$141$		0			0
$142$	−26.0957			−2.18990
$143$	−0.924230	−	1.60081i	−0.0772880	−	0.133867i
$144$		0			0
$145$	−11.8015	−	6.81361i	−0.980062	−	0.565839i
$146$	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	$-0.397667\pi$
$149$	15.8151	−	9.13086i	1.29562	−	0.748029i	0.979645	+	0.200737i	$0.0643338\pi$
$150$		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	$0.777174\pi$
$152$	2.43852	−	4.22365i	0.197790	−	0.342583i
$153$		0			0
$154$		0			0
$155$	15.5761	−	8.99285i	1.25110	−	0.722323i
$156$		0			0
$157$			6.52936i			0.521100i	0.965460	+	0.260550i	$0.0839038\pi$
$157$			6.52936i			0.521100i	−0.965460	+	0.260550i	$0.916096\pi$
$158$			24.8343i			1.97571i
$159$		0			0
$160$	9.48388	−	5.47552i	0.749767	−	0.432878i
$161$		0			0
$162$		0			0
$163$	−12.2623	+	21.2389i	−0.960457	+	1.66356i	−0.239103	+	0.970994i	$0.576853\pi$
$163$	−12.2623	+	21.2389i	−0.960457	+	1.66356i	−0.721354	+	0.692566i	$0.756480\pi$
$164$	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	$0.348839\pi$
$167$	−6.99871	+	12.1221i	−0.541576	+	0.938037i	−0.998814	+	0.0486928i	$0.984494\pi$
$168$		0			0
$169$	10.8320	+	18.7616i	0.833232	+	1.44320i
$170$	−6.73061	−	3.88592i	−0.516214	−	0.298037i
$171$		0			0
$172$	−5.22987	−	9.05840i	−0.398774	−	0.690697i
$173$	−10.8995			−0.828672			−0.414336	−	0.910124i	$-0.635986\pi$
$173$	−10.8995			−0.828672			−0.414336	+	0.910124i	$0.635986\pi$
$174$		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
$179$	−1.38517	+	0.799726i	−0.103532	+	0.0597743i	−0.550872	−	0.834590i	$-0.685705\pi$
$179$	−1.38517	+	0.799726i	−0.103532	+	0.0597743i	0.447340	+	0.894364i	$0.352371\pi$
$180$		0			0
$181$			17.5088i			1.30142i	0.759326	+	0.650710i	$0.225529\pi$
$181$			17.5088i			1.30142i	−0.759326	+	0.650710i	$0.774471\pi$
$182$		0			0
$183$		0			0
$184$	13.2033	+	22.8688i	0.973363	+	1.68591i
$185$	−18.4693			−1.35789
$186$		0			0
$187$			0.299334i			0.0218895i
$188$	7.31027			0.533156
$189$		0			0
$190$	−10.2798			−0.745775
$191$			16.0628i			1.16226i	0.813811	+	0.581130i	$0.197389\pi$
$191$			16.0628i			1.16226i	−0.813811	+	0.581130i	$0.802611\pi$
$192$		0			0
$193$	−10.8839			−0.783441			−0.391721	−	0.920084i	$-0.628120\pi$
$193$	−10.8839			−0.783441			−0.391721	+	0.920084i	$0.628120\pi$
$194$	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
$199$	−15.4217	+	8.90372i	−1.09321	+	0.631168i	−0.934431	−	0.356145i	$-0.884091\pi$
$199$	−15.4217	+	8.90372i	−1.09321	+	0.631168i	−0.158784	+	0.987313i	$0.550757\pi$
$200$	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
$205$	−0.480711			−0.0335743
$206$	21.3759	+	37.0242i	1.48933	+	2.57960i
$207$		0			0
$208$	−9.77117	−	5.64139i	−0.677508	−	0.391160i
$209$	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
$215$	−4.94977	+	8.57325i	−0.337571	+	0.584691i
$216$		0			0
$217$		0			0
$218$	−13.4843	+	7.78518i	−0.913273	+	0.527279i
$219$		0			0
$220$		−	3.91519i		−	0.263962i
$221$		−	5.61339i		−	0.377598i
$222$		0			0
$223$	−7.61261	+	4.39514i	−0.509778	+	0.294321i	−0.732742	−	0.680506i	$-0.761760\pi$
$223$	−7.61261	+	4.39514i	−0.509778	+	0.294321i	0.222964	+	0.974827i	$0.428427\pi$
$224$		0			0
$225$		0			0
$226$	−2.57421	+	4.45866i	−0.171234	+	0.296586i
$227$	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	−0.941271	−	0.337652i	$-0.890367\pi$
$229$	−16.9410	+	9.78088i	−1.11949	+	0.646339i	−0.178221	+	0.983991i	$0.557034\pi$
$230$	27.8299	−	48.2028i	1.83505	−	3.17840i
$231$		0			0
$232$	7.67007	+	13.2849i	0.503565	+	0.872200i
$233$	−17.0926	−	9.86840i	−1.11977	−	0.646500i	−0.178428	−	0.983953i	$-0.557101\pi$
$233$	−17.0926	−	9.86840i	−1.11977	−	0.646500i	−0.941342	+	0.337453i	$0.890435\pi$
$234$		0			0
$235$	−3.45937	−	5.99180i	−0.225664	−	0.390862i
$236$	−5.98541			−0.389617
$237$		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	0.873945	−	0.486026i	$-0.161554\pi$
$241$	13.8166	+	7.97702i	0.890006	+	0.513845i	0.0160617	+	0.999871i	$0.494887\pi$
$242$	22.4008	−	12.9331i	1.43998	−	0.831373i
$243$		0			0
$244$		−	10.7897i		−	0.690743i
$245$		0			0
$246$		0			0
$247$	−3.71241	−	6.43008i	−0.236215	−	0.409136i
$248$	−20.2465			−1.28565
$249$		0			0
$250$		−	14.6935i		−	0.929301i
$251$	−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
$254$			5.57515i			0.349816i
$255$		0			0
$256$	−26.2399			−1.64000
$257$	−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
$262$	19.5044	−	11.2609i	1.20499	−	0.695700i
$263$	−3.64436	−	2.10407i	−0.224721	−	0.129743i	0.383413	−	0.923577i	$-0.374748\pi$
$263$	−3.64436	−	2.10407i	−0.224721	−	0.129743i	−0.608134	+	0.793834i	$0.708082\pi$
$264$		0			0
$265$	−35.6429	−	20.5785i	−2.18953	−	1.26413i
$266$		0			0
$267$		0			0
$268$	6.78107			0.414220
$269$	−10.8299	−	18.7579i	−0.660309	−	1.14369i	−0.980534	−	0.196348i	$-0.937092\pi$
$269$	−10.8299	−	18.7579i	−0.660309	−	1.14369i	0.320225	−	0.947341i	$-0.396241\pi$
$270$		0			0
$271$	17.8987	+	10.3338i	1.08727	+	0.627736i	0.932849	−	0.360268i	$-0.117315\pi$
$271$	17.8987	+	10.3338i	1.08727	+	0.627736i	0.154423	+	0.988005i	$0.450648\pi$
$272$	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	$-0.149529\pi$
$278$	−6.25437	+	10.8329i	−0.375112	+	0.649714i
$279$		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
$283$			17.6326i			1.04815i	0.851672	+	0.524075i	$0.175589\pi$
$283$			17.6326i			1.04815i	−0.851672	+	0.524075i	$0.824411\pi$
$284$		−	39.9221i		−	2.36894i
$285$		0			0
$286$	3.79832	−	2.19296i	0.224599	−	0.129672i
$287$		0			0
$288$		0			0
$289$	8.04549	−	13.9352i	0.473264	−	0.819718i
$290$	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	$0.475231\pi$
$293$	−14.1138	+	24.4458i	−0.824536	+	1.42814i	−0.902273	+	0.431165i	$0.858103\pi$
$294$		0			0
$295$	2.83242	+	4.90589i	0.164910	+	0.285632i
$296$	18.0054	+	10.3954i	1.04655	+	0.604223i
$297$		0			0
$298$	21.6651	+	37.5251i	1.25503	+	2.17377i
$299$	40.2015			2.32492
$300$		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
$305$	−8.84374	+	5.10593i	−0.506391	+	0.292365i
$306$		0			0
$307$			8.56651i			0.488917i	0.969660	+	0.244458i	$0.0786102\pi$
$307$			8.56651i			0.488917i	−0.969660	+	0.244458i	$0.921390\pi$
$308$		0			0
$309$		0			0
$310$	21.3377	+	36.9580i	1.21190	+	2.09907i
$311$	19.3583			1.09771			0.548854	−	0.835918i	$-0.315064\pi$
$311$	19.3583			1.09771			0.548854	+	0.835918i	$0.315064\pi$
$312$		0			0
$313$		−	26.5012i		−	1.49793i	−0.662608	−	0.748967i	$-0.730550\pi$
$313$		−	26.5012i		−	1.49793i	0.662608	−	0.748967i	$-0.269450\pi$
$314$	−15.4925			−0.874291
$315$		0			0
$316$	−37.9923			−2.13724
$317$			8.66555i			0.486706i	0.969938	+	0.243353i	$0.0782473\pi$
$317$			8.66555i			0.486706i	−0.969938	+	0.243353i	$0.921753\pi$
$318$		0			0
$319$	−1.24535			−0.0697260
$320$	19.5756	+	33.9059i	1.09431	+	1.89540i
$321$		0			0
$322$		0			0
$323$			1.20235i			0.0669008i
$324$		0			0
$325$	34.6850	−	20.0254i	1.92398	−	1.11081i
$326$	−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
$331$	19.3382			1.06293			0.531463	−	0.847081i	$-0.321642\pi$
$331$	19.3382			1.06293			0.531463	+	0.847081i	$0.321642\pi$
$332$	−14.5230	−	25.1546i	−0.797054	−	1.38054i
$333$		0			0
$334$	−28.7626	−	16.6061i	−1.57382	−	0.908646i
$335$	−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
$341$	0.821826	−	1.42345i	0.0445044	−	0.0770839i
$342$		0			0
$343$		0			0
$344$	9.65090	−	5.57195i	0.520341	−	0.300419i
$345$		0			0
$346$		−	25.8616i		−	1.39033i
$347$			5.79346i			0.311009i	0.987835	+	0.155505i	$0.0497003\pi$
$347$			5.79346i			0.311009i	−0.987835	+	0.155505i	$0.950300\pi$
$348$		0			0
$349$	−13.3430	+	7.70360i	−0.714236	+	0.412364i	−0.812627	−	0.582784i	$-0.801963\pi$
$349$	−13.3430	+	7.70360i	−0.714236	+	0.412364i	0.0983918	+	0.995148i	$0.468630\pi$
$350$		0			0
$351$		0			0
$352$	0.500390	−	0.866700i	0.0266709	−	0.0461953i
$353$	−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
$359$	19.8490	+	11.4599i	1.04759	+	0.604828i	0.921974	−	0.387251i	$-0.126575\pi$
$359$	19.8490	+	11.4599i	1.04759	+	0.604828i	0.125618	+	0.992079i	$0.459909\pi$
$360$		0			0
$361$	−8.70482	−	15.0772i	−0.458149	−	0.793537i
$362$	−41.5439			−2.18350
$363$		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	0.382641	−	0.923897i	$-0.375014\pi$
$367$	−4.33253	−	2.50139i	−0.226156	−	0.130571i	−0.608797	+	0.793326i	$0.708348\pi$
$368$	−11.3321	+	6.54259i	−0.590726	+	0.341056i
$369$		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	$0.912649\pi$
$374$	−0.710243			−0.0367258
$375$		0			0
$376$			7.78842i			0.401657i
$377$	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	$0.615648\pi$
$380$		−	15.7264i		−	0.806746i
$381$		0			0
$382$	−38.1127			−1.95002
$383$	−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
$388$	−38.1336	+	22.0165i	−1.93594	+	1.11772i
$389$	−3.91419	−	2.25986i	−0.198457	−	0.114579i	0.397478	−	0.917612i	$-0.369885\pi$
$389$	−3.91419	−	2.25986i	−0.198457	−	0.114579i	−0.595936	+	0.803032i	$0.703219\pi$
$390$		0			0
$391$	−5.63793	−	3.25506i	−0.285122	−	0.164616i
$392$		0			0
$393$		0			0
$394$	15.4413			0.777919
$395$	17.9788	+	31.1401i	0.904610	+	1.56683i
$396$		0			0
$397$	13.5830	+	7.84214i	0.681710	+	0.393586i	0.800499	−	0.599334i	$-0.204568\pi$
$397$	13.5830	+	7.84214i	0.681710	+	0.393586i	−0.118789	+	0.992920i	$0.537901\pi$
$398$	−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	$-0.579851\pi$
$401$	9.34292	−	5.39414i	0.466563	−	0.269370i	0.714800	+	0.699329i	$0.246518\pi$
$402$		0			0
$403$	−15.4116	+	26.6937i	−0.767708	+	1.32971i
$404$	−22.7246	+	39.3601i	−1.13059	+	1.95824i
$405$		0			0
$406$		0			0
$407$	−1.46172	+	0.843925i	−0.0724548	+	0.0418318i
$408$		0			0
$409$			19.6138i			0.969839i	0.874559	+	0.484920i	$0.161151\pi$
$409$			19.6138i			0.969839i	−0.874559	+	0.484920i	$0.838849\pi$
$410$		−	1.14060i		−	0.0563304i
$411$		0			0
$412$	−56.6409	+	32.7016i	−2.79050	+	1.61109i
$413$		0			0
$414$		0			0
$415$	−13.7452	+	23.8074i	−0.674724	+	1.16866i
$416$	−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	−0.565248	−	0.824921i	$-0.691220\pi$
$419$	8.83829	−	15.3084i	0.431779	−	0.747862i	0.997027	+	0.0770586i	$0.0245528\pi$
$420$		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	$-0.476126\pi$
$422$	−1.16059	−	0.670068i	−0.0564967	−	0.0326184i
$423$		0			0
$424$	23.1652	+	40.1232i	1.12500	+	1.94856i
$425$	−6.48571			−0.314603
$426$		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
$431$	12.2317	−	7.06195i	0.589178	−	0.340162i	−0.175594	−	0.984463i	$-0.556185\pi$
$431$	12.2317	−	7.06195i	0.589178	−	0.340162i	0.764772	+	0.644300i	$0.222851\pi$
$432$		0			0
$433$		−	9.10088i		−	0.437360i	−0.975797	−	0.218680i	$-0.929825\pi$
$433$		−	9.10088i		−	0.437360i	0.975797	−	0.218680i	$-0.0701752\pi$
$434$		0			0
$435$		0			0
$436$	−11.9100	−	20.6288i	−0.570387	−	0.987938i
$437$	−8.61093			−0.411917
$438$		0			0
$439$		−	11.7225i		−	0.559486i	−0.960075	−	0.279743i	$-0.909751\pi$
$439$		−	11.7225i		−	0.559486i	0.960075	−	0.279743i	$-0.0902492\pi$
$440$	4.17128			0.198858
$441$		0			0
$442$	13.3191			0.633526
$443$			7.13370i			0.338932i	0.985536	+	0.169466i	$0.0542043\pi$
$443$			7.13370i			0.338932i	−0.985536	+	0.169466i	$0.945796\pi$
$444$		0			0
$445$	−7.27850			−0.345034
$446$	−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
$451$	−0.0380450	+	0.0219653i	−0.00179147	+	0.00103431i
$452$	−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
$457$	24.1490			1.12964			0.564821	−	0.825213i	$-0.308945\pi$
$457$	24.1490			1.12964			0.564821	+	0.825213i	$0.308945\pi$
$458$	−23.2075	−	40.1966i	−1.08442	−	1.87826i
$459$		0			0
$460$	73.7422	+	42.5751i	3.43825	+	1.98507i
$461$	−6.87281	−	11.9041i	−0.320099	−	0.554427i	0.660409	−	0.750906i	$-0.270383\pi$
$461$	−6.87281	−	11.9041i	−0.320099	−	0.554427i	−0.980508	+	0.196478i	$0.937049\pi$
$462$		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
$467$	−0.465894	+	0.806952i	−0.0215590	+	0.0373413i	−0.876604	−	0.481213i	$-0.840196\pi$
$467$	−0.465894	+	0.806952i	−0.0215590	+	0.0373413i	0.855045	+	0.518554i	$0.173530\pi$
$468$		0			0
$469$		0			0
$470$	14.2170	−	8.20819i	0.655781	−	0.378615i
$471$		0			0
$472$		−	6.37690i		−	0.293521i
$473$			0.904685i			0.0415975i
$474$		0			0
$475$	−7.42932	+	4.28932i	−0.340881	+	0.196808i
$476$		0			0
$477$		0			0
$478$	−23.2556	+	40.2800i	−1.06369	+	1.84236i
$479$	−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
$485$	36.0912	+	20.8373i	1.63882	+	0.946172i
$486$		0			0
$487$	17.1867	+	29.7682i	0.778802	+	1.34892i	0.932633	+	0.360828i	$0.117506\pi$
$487$	17.1867	+	29.7682i	0.778802	+	1.34892i	−0.153830	+	0.988097i	$0.549161\pi$
$488$	11.4955			0.520376
$489$		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
$494$	15.2569	−	8.80859i	0.686441	−	0.396317i
$495$		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	$0.751144\pi$
$500$	22.4787			1.00528
$501$		0			0
$502$		−	2.31595i		−	0.103366i
$503$	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
$506$		−	5.08656i		−	0.226125i
$507$		0			0
$508$	−8.52905			−0.378415
$509$	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
$514$	25.1492	−	14.5199i	1.10928	−	0.640446i
$515$	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
$520$	−78.2236			−3.43033
$521$	9.93108	+	17.2011i	0.435088	+	0.753595i	0.997303	−	0.0733964i	$-0.0233838\pi$
$521$	9.93108	+	17.2011i	0.435088	+	0.753595i	−0.562215	+	0.826991i	$0.690050\pi$
$522$		0			0
$523$	6.71478	+	3.87678i	0.293617	+	0.169520i	0.639572	−	0.768731i	$-0.279112\pi$
$523$	6.71478	+	3.87678i	0.293617	+	0.169520i	−0.345955	+	0.938251i	$0.612445\pi$
$524$	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
$530$	48.8274	−	84.5715i	2.12092	−	3.67355i
$531$		0			0
$532$		0			0
$533$	0.713455	−	0.411913i	0.0309032	−	0.0178419i
$534$		0			0
$535$		−	12.3614i		−	0.534432i
$536$			7.22461i			0.312056i
$537$		0			0
$538$	44.5076	−	25.6965i	1.91886	−	1.10785i
$539$		0			0
$540$		0			0
$541$	9.04616	−	15.6684i	0.388925	−	0.673638i	−0.603380	−	0.797454i	$-0.706180\pi$
$541$	9.04616	−	15.6684i	0.388925	−	0.673638i	0.992305	+	0.123816i	$0.0395133\pi$
$542$	−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	$0.785954\pi$
$548$	−32.1411	−	18.5567i	−1.37300	−	0.792703i
$549$		0			0
$550$	−2.53375	−	4.38858i	−0.108039	−	0.187130i
$551$	−5.00225			−0.213103
$552$		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
$557$	−13.6993	+	7.90931i	−0.580459	+	0.335128i	−0.761316	−	0.648381i	$-0.775446\pi$
$557$	−13.6993	+	7.90931i	−0.580459	+	0.335128i	0.180857	+	0.983509i	$0.442113\pi$
$558$		0			0
$559$		−	16.9655i		−	0.717563i
$560$		0			0
$561$		0			0
$562$	−22.9014	−	39.6665i	−0.966039	−	1.67323i
$563$	−32.1123			−1.35337			−0.676686	−	0.736272i	$-0.736584\pi$
$563$	−32.1123			−1.35337			−0.676686	+	0.736272i	$0.736584\pi$
$564$		0			0
$565$			7.45438i			0.313608i
$566$	−41.8376			−1.75857
$567$		0			0
$568$	42.5333			1.78466
$569$		−	36.1545i		−	1.51567i	−0.652444	−	0.757837i	$-0.726256\pi$
$569$		−	36.1545i		−	1.51567i	0.652444	−	0.757837i	$-0.273744\pi$
$570$		0			0
$571$	28.3583			1.18676			0.593380	−	0.804923i	$-0.297793\pi$
$571$	28.3583			1.18676			0.593380	+	0.804923i	$0.297793\pi$
$572$	3.35486	+	5.81079i	0.140274	+	0.242961i
$573$		0			0
$574$		0			0
$575$		−	46.4489i		−	1.93705i
$576$		0			0
$577$	36.3589	−	20.9918i	1.51364	−	0.873901i	0.513768	−	0.857929i	$-0.328249\pi$
$577$	36.3589	−	20.9918i	1.51364	−	0.873901i	0.999872	−	0.0159713i	$-0.00508404\pi$
$578$	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
$583$	−3.76119			−0.155773
$584$	−0.791873	−	1.37156i	−0.0327679	−	0.0567557i
$585$		0			0
$586$	−58.0035	−	33.4884i	−2.39610	−	1.38339i
$587$	−9.79227	−	16.9607i	−0.404170	−	0.700043i	0.590054	−	0.807364i	$-0.299106\pi$
$587$	−9.79227	−	16.9607i	−0.404170	−	0.700043i	−0.994225	+	0.107320i	$0.965773\pi$
$588$		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
$593$	9.96374	−	17.2577i	0.409162	−	0.708689i	−0.585634	−	0.810575i	$-0.699154\pi$
$593$	9.96374	−	17.2577i	0.409162	−	0.708689i	0.994796	+	0.101886i	$0.0324878\pi$
$594$		0			0
$595$		0			0
$596$	−57.4072	+	33.1441i	−2.35149	+	1.35763i
$597$		0			0
$598$			95.3878i			3.90070i
$599$			0.0309043i			0.00126271i	1.00000		0.000631357i	$0.000200967\pi$
$599$			0.0309043i			0.00126271i	−1.00000		0.000631357i	$0.999799\pi$
$600$		0			0
$601$	25.8633	−	14.9322i	1.05499	−	0.609097i	0.130945	−	0.991390i	$-0.458199\pi$
$601$	25.8633	−	14.9322i	1.05499	−	0.609097i	0.924041	+	0.382293i	$0.124865\pi$
$602$		0			0
$603$		0			0
$604$	41.9438	−	72.6488i	1.70667	−	2.95604i
$605$	18.7258	−	32.4341i	0.761314	−	1.31863i
$606$		0			0
$607$	−27.1898	+	15.6980i	−1.10360	+	0.637163i	−0.937164	−	0.348889i	$-0.886559\pi$
$607$	−27.1898	+	15.6980i	−1.10360	+	0.637163i	−0.166435	+	0.986052i	$0.553226\pi$
$608$	2.00994	−	3.48133i	0.0815140	−	0.141186i
$609$		0			0
$610$	−12.1151	−	20.9839i	−0.490524	−	0.849613i
$611$	10.2685	+	5.92855i	0.415421	+	0.239843i
$612$		0			0
$613$	2.23146	+	3.86500i	0.0901278	+	0.156106i	0.907565	−	0.419912i	$-0.137939\pi$
$613$	2.23146	+	3.86500i	0.0901278	+	0.156106i	−0.817437	+	0.576018i	$0.804606\pi$
$614$	−20.3261			−0.820295
$615$		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	0.477018	−	0.878893i	$-0.341718\pi$
$619$	−1.13493	−	0.655252i	−0.0456167	−	0.0263368i	−0.522635	+	0.852557i	$0.675051\pi$
$620$	−56.5395	+	32.6431i	−2.27068	+	1.31098i
$621$		0			0
$622$			45.9322i			1.84171i
$623$		0			0
$624$		0			0
$625$	6.36901	+	11.0315i	0.254761	+	0.441258i
$626$	62.8803			2.51320
$627$		0			0
$628$		−	23.7009i		−	0.945769i
$629$	−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	$0.695010\pi$
$632$		−	40.4773i		−	1.61010i
$633$		0			0
$634$	−20.5611			−0.816585
$635$	4.03612	+	6.99077i	0.160169	+	0.277420i
$636$		0			0
$637$		0			0
$638$		−	2.95488i		−	0.116985i
$639$		0			0
$640$	−61.4822	+	35.4968i	−2.43030	+	1.40313i
$641$	2.41325	+	1.39329i	0.0953176	+	0.0550316i	0.546901	−	0.837197i	$-0.315807\pi$
$641$	2.41325	+	1.39329i	0.0953176	+	0.0550316i	−0.451584	+	0.892229i	$0.649141\pi$
$642$		0			0
$643$	−0.324584	−	0.187399i	−0.0128004	−	0.00739029i	0.493586	−	0.869697i	$-0.335686\pi$
$643$	−0.324584	−	0.187399i	−0.0128004	−	0.00739029i	−0.506387	+	0.862307i	$0.669019\pi$
$644$		0			0
$645$		0			0
$646$	−2.85287			−0.112245
$647$	25.1608	+	43.5798i	0.989172	+	1.71330i	0.621682	+	0.783270i	$0.286450\pi$
$647$	25.1608	+	43.5798i	0.989172	+	1.71330i	0.367490	+	0.930027i	$0.380217\pi$
$648$		0			0
$649$	0.448333	+	0.258845i	0.0175986	+	0.0101606i
$650$	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	$-0.858177\pi$
$653$	−25.0515	+	14.4635i	−0.980342	+	0.566000i	−0.0779684	+	0.996956i	$0.524843\pi$
$654$		0			0
$655$	16.3046	−	28.2404i	0.637074	−	1.10344i
$656$	−0.134073	+	0.232222i	−0.00523469	+	0.00906674i
$657$		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
$661$		−	11.6086i		−	0.451521i	−0.974183	−	0.225760i	$-0.927513\pi$
$661$		−	11.6086i		−	0.451521i	0.974183	−	0.225760i	$-0.0724866\pi$
$662$			45.8846i			1.78336i
$663$		0			0
$664$	26.7999	−	15.4729i	1.04004	−	0.600466i
$665$		0			0
$666$		0			0
$667$	13.5423	−	23.4559i	0.524360	−	0.908218i
$668$	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	$-0.344761\pi$
$674$	−51.1459	−	29.5291i	−1.97007	−	1.13742i
$675$		0			0
$676$	−39.3191	−	68.1026i	−1.51227	−	2.61933i
$677$	4.63127			0.177994			0.0889970	−	0.996032i	$-0.471634\pi$
$677$	4.63127			0.177994			0.0889970	+	0.996032i	$0.471634\pi$
$678$		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
$683$	−12.0197	+	6.93959i	−0.459922	+	0.265536i	−0.712012	−	0.702168i	$-0.752216\pi$
$683$	−12.0197	+	6.93959i	−0.459922	+	0.265536i	0.252089	+	0.967704i	$0.418882\pi$
$684$		0			0
$685$			35.1257i			1.34208i
$686$		0			0
$687$		0			0
$688$	2.76104	+	4.78227i	0.105264	+	0.182322i
$689$	70.5333			2.68711
$690$		0			0
$691$		−	22.6515i		−	0.861704i	−0.902423	−	0.430852i	$-0.858213\pi$
$691$		−	22.6515i		−	0.861704i	0.902423	−	0.430852i	$-0.141787\pi$
$692$	39.5640			1.50400
$693$		0			0
$694$	−13.7464			−0.521805
$695$			18.1114i			0.687004i
$696$		0			0
$697$	−0.133408			−0.00505319
$698$	−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
$703$	−5.87138	+	3.38984i	−0.221443	+	0.127850i
$704$	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
$709$	15.3071			0.574871			0.287435	−	0.957800i	$-0.407197\pi$
$709$	15.3071			0.574871			0.287435	+	0.957800i	$0.407197\pi$
$710$	−44.8257	−	77.6404i	−1.68228	−	2.91379i
$711$		0			0
$712$	7.09569	+	4.09670i	0.265922	+	0.153530i
$713$	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
$719$	−7.46359	+	12.9273i	−0.278345	+	0.482108i	−0.970974	−	0.239187i	$-0.923119\pi$
$719$	−7.46359	+	12.9273i	−0.278345	+	0.482108i	0.692629	+	0.721294i	$0.256453\pi$
$720$		0			0
$721$		0			0
$722$	35.7743	−	20.6543i	1.33138	−	0.768673i
$723$		0			0
$724$		−	63.5552i		−	2.36201i
$725$		−	26.9830i		−	1.00213i
$726$		0			0
$727$	−4.62968	+	2.67295i	−0.171705	+	0.0991341i	−0.583390	−	0.812192i	$-0.698274\pi$
$727$	−4.62968	+	2.67295i	−0.171705	+	0.0991341i	0.411684	+	0.911326i	$0.364941\pi$
$728$		0			0
$729$		0			0
$730$	−1.66910	+	2.89097i	−0.0617763	+	0.107000i
$731$	−1.37367	+	2.37927i	−0.0508070	+	0.0880004i
$732$		0			0
$733$	−16.4099	+	9.47428i	−0.606115	+	0.349941i	−0.771443	−	0.636298i	$-0.780465\pi$
$733$	−16.4099	+	9.47428i	−0.606115	+	0.349941i	0.165328	+	0.986239i	$0.447132\pi$
$734$	5.93514	−	10.2800i	0.219070	−	0.379440i
$735$		0			0
$736$	10.8828	+	18.8496i	0.401145	+	0.694804i
$737$	−0.507932	−	0.293255i	−0.0187099	−	0.0108022i
$738$		0			0
$739$	−22.8430	−	39.5653i	−0.840295	−	1.45543i	−0.889646	−	0.456651i	$-0.849049\pi$
$739$	−22.8430	−	39.5653i	−0.840295	−	1.45543i	0.0493510	−	0.998781i	$-0.484285\pi$
$740$	67.0417			2.46450
$741$		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
$746$	19.5737	−	11.3009i	0.716644	−	0.413755i
$747$		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	$-0.465289\pi$
$752$	−3.85936			−0.140736
$753$		0			0
$754$			55.4126i			2.01801i
$755$	−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	$0.666595\pi$
$758$		−	32.8315i		−	1.19249i
$759$		0			0
$760$	16.7550			0.607768
$761$	−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
$766$	43.6286	−	25.1890i	1.57637	−	0.910115i
$767$	−8.40755	−	4.85410i	−0.303579	−	0.175271i
$768$		0			0
$769$	33.4505	+	19.3126i	1.20626	+	0.696432i	0.961939	−	0.273264i	$-0.0881031\pi$
$769$	33.4505	+	19.3126i	1.20626	+	0.696432i	0.244316	+	0.969696i	$0.421436\pi$
$770$		0			0
$771$		0			0
$772$	39.5075			1.42191
$773$	−17.1754	−	29.7486i	−0.617754	−	1.06998i	−0.989895	−	0.141806i	$-0.954709\pi$
$773$	−17.1754	−	29.7486i	−0.617754	−	1.06998i	0.372140	−	0.928177i	$-0.378624\pi$
$774$		0			0
$775$	30.8420	+	17.8066i	1.10788	+	0.639632i
$776$	−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
$782$	7.72341	−	13.3773i	0.276189	−	0.478373i
$783$		0			0
$784$		0			0
$785$	−19.4263	+	11.2158i	−0.693353	+	0.400308i
$786$		0			0
$787$			23.4800i			0.836972i	0.908223	+	0.418486i	$0.137439\pi$
$787$			23.4800i			0.836972i	−0.908223	+	0.418486i	$0.862561\pi$
$788$			23.6225i			0.841518i
$789$		0			0
$790$	−73.8874	+	42.6589i	−2.62880	+	1.51774i
$791$		0			0
$792$		0			0
$793$	8.75037	−	15.1561i	0.310735	−	0.538209i
$794$	−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	−0.744249	−	0.667903i	$-0.767192\pi$
$797$	5.82399	−	10.0875i	0.206296	−	0.357316i	0.950545	+	0.310587i	$0.100526\pi$
$798$		0			0
$799$	−0.960052	−	1.66286i	−0.0339642	−	0.0588277i
$800$	18.7789	+	10.8420i	0.663934	+	0.383323i
$801$		0			0
$802$	12.7989	+	22.1683i	0.451945	+	0.782791i
$803$	0.128572			0.00453720
$804$		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
$809$	13.7723	−	7.95147i	0.484210	−	0.279559i	−0.237959	−	0.971275i	$-0.576479\pi$
$809$	13.7723	−	7.95147i	0.484210	−	0.279559i	0.722169	+	0.691716i	$0.243145\pi$
$810$		0			0
$811$		−	3.56109i		−	0.125047i	−0.998044	−	0.0625233i	$-0.980085\pi$
$811$		−	3.56109i		−	0.125047i	0.998044	−	0.0625233i	$-0.0199148\pi$
$812$		0			0
$813$		0			0
$814$	−2.00241	−	3.46828i	−0.0701846	−	0.121563i
$815$	−84.2539			−2.95128
$816$		0			0
$817$			3.63390i			0.127134i
$818$	−46.5384			−1.62718
$819$		0			0
$820$	1.74493			0.0609357
$821$			0.130990i			0.00457157i	0.999997	+	0.00228579i	$0.000727589\pi$
$821$			0.130990i			0.00457157i	−0.999997	+	0.00228579i	$0.999272\pi$
$822$		0			0
$823$	46.0287			1.60446			0.802231	−	0.597014i	$-0.203646\pi$
$823$	46.0287			1.60446			0.802231	+	0.597014i	$0.203646\pi$
$824$	−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
$829$	−26.0930	+	15.0648i	−0.906248	+	0.523223i	−0.879222	−	0.476412i	$-0.841937\pi$
$829$	−26.0930	+	15.0648i	−0.906248	+	0.523223i	−0.0270260	+	0.999635i	$0.508604\pi$
$830$	−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
$835$	−48.0879			−1.66415
$836$	−0.718591	−	1.24464i	−0.0248530	−	0.0430466i
$837$		0			0
$838$	36.3228	+	20.9710i	1.25475	+	0.724430i
$839$	−5.81551	−	10.0728i	−0.200774	−	0.347750i	0.748004	−	0.663694i	$-0.231012\pi$
$839$	−5.81551	−	10.0728i	−0.200774	−	0.347750i	−0.948778	+	0.315944i	$0.897679\pi$
$840$		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
$845$	−37.2132	+	64.4552i	−1.28017	+	2.21732i
$846$		0			0
$847$		0			0
$848$	−19.8821	+	11.4789i	−0.682754	+	0.394188i
$849$		0			0
$850$		−	15.3889i		−	0.527835i
$851$		−	36.7085i		−	1.25835i
$852$		0			0
$853$	20.6854	−	11.9427i	0.708254	−	0.408911i	−0.102160	−	0.994768i	$-0.532575\pi$
$853$	20.6854	−	11.9427i	0.708254	−	0.408911i	0.810414	+	0.585857i	$0.199242\pi$
$854$		0			0
$855$		0			0
$856$	−6.95763	+	12.0510i	−0.237807	+	0.411894i
$857$	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	0.0231546	−	0.999732i	$-0.492629\pi$
$859$	26.3932	−	15.2381i	0.900525	−	0.519918i	0.877371	+	0.479813i	$0.159296\pi$
$860$	17.9671	−	31.1200i	0.612674	−	1.06118i
$861$		0			0
$862$	16.7562	+	29.0225i	0.570717	+	0.988512i
$863$	−28.9298	−	16.7026i	−0.984781	−	0.568564i	−0.0810708	−	0.996708i	$-0.525834\pi$
$863$	−28.9298	−	16.7026i	−0.984781	−	0.568564i	−0.903710	+	0.428145i	$0.859167\pi$
$864$		0			0
$865$	−18.7225	−	32.4283i	−0.636584	−	1.10260i
$866$	21.5940			0.733795
$867$		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
$872$	21.9780	−	12.6890i	0.744271	−	0.429705i
$873$		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	$0.446569\pi$
$878$	27.8145			0.938694
$879$		0			0
$880$			2.06697i			0.0696777i
$881$	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	$0.295667\pi$
$884$			20.3760i			0.685320i
$885$		0			0
$886$	−16.9264			−0.568654
$887$	−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
$892$	27.6330	−	15.9539i	0.925221	−	0.534177i
$893$	−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
$898$	−7.53214			−0.251351
$899$	10.3831	+	17.9841i	0.346297	+	0.599804i
$900$		0			0
$901$	−9.89171	−	5.71098i	−0.329541	−	0.190260i
$902$	−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	$0.954482\pi$
$908$	−30.6846	+	53.1472i	−1.01830	+	1.76375i
$909$		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
$913$			2.51225i			0.0831434i
$914$			57.2993i			1.89529i
$915$		0			0
$916$	61.4940	−	35.5036i	2.03182	−	1.17307i
$917$		0			0
$918$		0			0
$919$	−17.1023	+	29.6220i	−0.564153	+	0.977141i	0.432975	+	0.901406i	$0.357464\pi$
$919$	−17.1023	+	29.6220i	−0.564153	+	0.977141i	−0.997128	+	0.0757353i	$0.975870\pi$
$920$	−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
$926$	42.3945	+	24.4764i	1.39317	+	0.804346i
$927$		0			0
$928$	6.32203	+	10.9501i	0.207531	+	0.359454i
$929$	46.9514			1.54043			0.770213	−	0.637786i	$-0.220150\pi$
$929$	46.9514			1.54043			0.770213	+	0.637786i	$0.220150\pi$
$930$		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
$935$	−0.890585	+	0.514179i	−0.0291252	+	0.0168155i
$936$		0			0
$937$			28.8826i			0.943555i	0.881718	+	0.471777i	$0.156387\pi$
$937$			28.8826i			0.943555i	−0.881718	+	0.471777i	$0.843613\pi$
$938$		0			0
$939$		0			0
$940$	12.5572	+	21.7496i	0.409569	+	0.709395i
$941$	1.45409			0.0474019			0.0237009	−	0.999719i	$-0.492455\pi$
$941$	1.45409			0.0474019			0.0237009	+	0.999719i	$0.492455\pi$
$942$		0			0
$943$		−	0.955432i		−	0.0311131i
$944$	3.15992			0.102847
$945$		0			0
$946$	−2.14658			−0.0697914
$947$			42.6772i			1.38682i	0.720542	+	0.693412i	$0.243893\pi$
$947$			42.6772i			1.38682i	−0.720542	+	0.693412i	$0.756107\pi$
$948$		0			0
$949$	−2.41110			−0.0782675
$950$	−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
$955$	−47.7902	+	27.5917i	−1.54645	+	0.892845i
$956$	−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
$961$	3.59192			0.115868
$962$	37.5511	+	65.0404i	1.21070	+	2.09699i
$963$		0			0
$964$	−50.1529	−	28.9558i	−1.61532	−	0.932603i
$965$	−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
$971$	3.40171	−	5.89194i	0.109166	−	0.189081i	−0.806267	−	0.591552i	$-0.798515\pi$
$971$	3.40171	−	5.89194i	0.109166	−	0.189081i	0.915433	+	0.402471i	$0.131849\pi$
$972$		0			0
$973$		0			0
$974$	−70.6321	+	40.7795i	−2.26320	+	1.30666i
$975$		0			0
$976$			5.69631i			0.182334i
$977$		−	33.7917i		−	1.08109i	−0.841314	−	0.540546i	$-0.818218\pi$
$977$		−	33.7917i		−	1.08109i	0.841314	−	0.540546i	$-0.181782\pi$
$978$		0			0
$979$	−0.576044	+	0.332579i	−0.0184104	+	0.0106293i
$980$		0			0
$981$		0			0
$982$	−10.0146	+	17.3459i	−0.319580	+	0.553529i
$983$	−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
$989$	−17.0397	−	9.83785i	−0.541829	−	0.312825i
$990$		0			0
$991$	−0.300449	−	0.520392i	−0.00954406	−	0.0165308i	0.861214	−	0.508243i	$-0.169705\pi$
$991$	−0.300449	−	0.520392i	−0.00954406	−	0.0165308i	−0.870758	+	0.491712i	$0.836371\pi$
$992$	−16.6881			−0.529848
$993$		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	−0.343189	−	0.939266i	$-0.611507\pi$
$997$	−41.9387	−	24.2133i	−1.32821	−	0.766844i	−0.985023	+	0.172423i	$0.944841\pi$
$998$	−23.4418	+	13.5341i	−0.742036	+	0.428415i
$999$		0			0

Twists

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

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

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

\(f(q)\)	\(=\)	\(q+2.37274i q^{2} -3.62990 q^{4} +(1.71774 + 2.97522i) q^{5} -3.86732i q^{8} +(-7.05942 + 4.07576i) q^{10} +(0.271895 + 0.156979i) q^{11} +(-5.09882 - 2.94381i) q^{13} +1.91636 q^{16} +(0.476712 + 0.825689i) q^{17} +(1.09214 + 0.630546i) q^{19} +(-6.23523 - 10.7997i) q^{20} +(-0.372470 + 0.645137i) q^{22} +(-5.91336 + 3.41408i) q^{23} +(-3.40128 + 5.89118i) q^{25} +(6.98489 - 12.0982i) q^{26} +(-3.43518 + 1.98330i) q^{29} -5.23527i q^{31} -3.18763i q^{32} +(-1.95915 + 1.13111i) q^{34} +(-2.68802 + 4.65579i) q^{37} +(-1.49612 + 2.59136i) q^{38} +(11.5061 - 6.64306i) q^{40} +(-0.0699627 + 0.121179i) q^{41} +(1.44078 + 2.49550i) q^{43} +(-0.986951 - 0.569817i) q^{44} +(-8.10072 - 14.0309i) q^{46} -2.01390 q^{47} +(-13.9783 - 8.07035i) q^{50} +(18.5082 + 10.6857i) q^{52} +(-10.3749 + 5.98997i) q^{53} +1.07860i q^{55} +(-4.70586 - 8.15079i) q^{58} +1.64892 q^{59} +2.97247i q^{61} +12.4219 q^{62} +11.3961 q^{64} -20.2268i q^{65} -1.86812 q^{67} +(-1.73041 - 2.99717i) q^{68} +10.9981i q^{71} +(0.354655 - 0.204760i) q^{73} +(-11.0470 - 6.37798i) q^{74} +(-3.96435 - 2.28882i) q^{76} +10.4665 q^{79} +(3.29181 + 5.70158i) q^{80} +(-0.287526 - 0.166003i) q^{82} +(4.00094 + 6.92984i) q^{83} +(-1.63774 + 2.83664i) q^{85} +(-5.92117 + 3.41859i) q^{86} +(0.607087 - 1.05151i) q^{88} +(-1.05931 + 1.83478i) q^{89} +(21.4649 - 12.3927i) q^{92} -4.77847i q^{94} +4.33246i q^{95} +(10.5054 - 6.06531i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} - 24 q^{11} + 48 q^{16} - 48 q^{23} - 24 q^{25} + 96 q^{44} - 48 q^{50} + 48 q^{53} - 48 q^{64} - 168 q^{74} + 48 q^{79} - 24 q^{85} + 24 q^{86} + 144 q^{92}+O(q^{100}) \) 48 * q - 48 * q^4 - 24 * q^11 + 48 * q^16 - 48 * q^23 - 24 * q^25 + 96 * q^44 - 48 * q^50 + 48 * q^53 - 48 * q^64 - 168 * q^74 + 48 * q^79 - 24 * q^85 + 24 * q^86 + 144 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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