LMFDB - Embedded newform 1323.2.s.d.962.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1323,2,Mod(656,1323)] 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, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1323.656"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.s (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			962.20
Character	$\chi$	$=$	1323.962
Dual form			1323.2.s.d.656.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.61855 + 0.934468i) q^{2} +(0.746462 + 1.29291i) q^{4} +2.50573 q^{5} -0.947692i q^{8} +(4.05565 + 2.34153i) q^{10} +5.60957i q^{11} +(0.384312 + 0.221883i) q^{13} +(2.37851 - 4.11970i) q^{16} +(1.53885 - 2.66536i) q^{17} +(2.22932 - 1.28710i) q^{19} +(1.87044 + 3.23969i) q^{20} +(-5.24197 + 9.07935i) q^{22} +7.89210i q^{23} +1.27870 q^{25} +(0.414685 + 0.718255i) q^{26} +(-2.71041 + 1.56485i) q^{29} +(9.06457 - 5.23343i) q^{31} +(6.05802 - 3.49760i) q^{32} +(4.98140 - 2.87601i) q^{34} +(0.708168 + 1.22658i) q^{37} +4.81100 q^{38} -2.37466i q^{40} +(-1.64665 + 2.85208i) q^{41} +(-4.75676 - 8.23894i) q^{43} +(-7.25268 + 4.18733i) q^{44} +(-7.37492 + 12.7737i) q^{46} +(1.07190 - 1.85659i) q^{47} +(2.06964 + 1.19491i) q^{50} +0.662509i q^{52} +(4.20379 + 2.42706i) q^{53} +14.0561i q^{55} -5.84923 q^{58} +(3.65496 + 6.33057i) q^{59} +(-7.40950 - 4.27788i) q^{61} +19.5619 q^{62} +3.55953 q^{64} +(0.962984 + 0.555979i) q^{65} +(0.934442 + 1.61850i) q^{67} +4.59477 q^{68} -2.95338i q^{71} +(-7.37804 - 4.25971i) q^{73} +2.64704i q^{74} +(3.32820 + 1.92154i) q^{76} +(0.287130 - 0.497324i) q^{79} +(5.95992 - 10.3229i) q^{80} +(-5.33036 + 3.07748i) q^{82} +(-4.23521 - 7.33560i) q^{83} +(3.85595 - 6.67870i) q^{85} -17.7802i q^{86} +5.31615 q^{88} +(-3.78929 - 6.56325i) q^{89} +(-10.2038 + 5.89115i) q^{92} +(3.46984 - 2.00332i) q^{94} +(5.58607 - 3.22512i) q^{95} +(-3.22662 + 1.86289i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4} - 24 q^{16} + 48 q^{25} + 120 q^{32} - 96 q^{44} - 48 q^{50} - 48 q^{53} - 48 q^{64} + 120 q^{65} - 24 q^{79} - 24 q^{85} + 144 q^{92} + 96 q^{95}+O(q^{100}) $ 48 * q + 24 * q^4 - 24 * q^16 + 48 * q^25 + 120 * q^32 - 96 * q^44 - 48 * q^50 - 48 * q^53 - 48 * q^64 + 120 * q^65 - 24 * q^79 - 24 * q^85 + 144 * q^92 + 96 * q^95

Character values

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

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

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 $

$2$	1.61855	+	0.934468i	1.14449	+	0.660769i	0.947537	−	0.319645i	$-0.103564\pi$
$2$	1.61855	+	0.934468i	1.14449	+	0.660769i	0.196948	+	0.980414i	$0.436897\pi$
$3$		0			0
$3$		0			0
$4$	0.746462	+	1.29291i	0.373231	+	0.646455i
$5$	2.50573			1.12060			0.560299	−	0.828290i	$-0.310686\pi$
$5$	2.50573			1.12060			0.560299	+	0.828290i	$0.310686\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	0.947692i		−	0.335060i
$9$		0			0
$10$	4.05565	+	2.34153i	1.28251	+	0.740457i
$11$			5.60957i			1.69135i	0.533698	+	0.845675i	$0.320802\pi$
$11$			5.60957i			1.69135i	−0.533698	+	0.845675i	$0.679198\pi$
$12$		0			0
$13$	0.384312	+	0.221883i	0.106589	+	0.0615392i	0.552347	−	0.833614i	$-0.313732\pi$
$13$	0.384312	+	0.221883i	0.106589	+	0.0615392i	−0.445758	+	0.895154i	$0.647066\pi$
$14$		0			0
$15$		0			0
$16$	2.37851	−	4.11970i	0.594628	−	1.02993i
$17$	1.53885	−	2.66536i	0.373226	−	0.646446i	−0.616834	−	0.787093i	$-0.711585\pi$
$17$	1.53885	−	2.66536i	0.373226	−	0.646446i	0.990060	+	0.140647i	$0.0449184\pi$
$18$		0			0
$19$	2.22932	−	1.28710i	0.511440	−	0.295280i	−0.221985	−	0.975050i	$-0.571254\pi$
$19$	2.22932	−	1.28710i	0.511440	−	0.295280i	0.733425	+	0.679770i	$0.237920\pi$
$20$	1.87044	+	3.23969i	0.418242	+	0.724417i
$21$		0			0
$22$	−5.24197	+	9.07935i	−1.11759	+	1.93572i
$23$			7.89210i			1.64562i	0.568319	+	0.822808i	$0.307594\pi$
$23$			7.89210i			1.64562i	−0.568319	+	0.822808i	$0.692406\pi$
$24$		0			0
$25$	1.27870			0.255741
$26$	0.414685	+	0.718255i	0.0813264	+	0.140861i
$27$		0			0
$28$		0			0
$29$	−2.71041	+	1.56485i	−0.503310	+	0.290586i	−0.730079	−	0.683362i	$-0.760517\pi$
$29$	−2.71041	+	1.56485i	−0.503310	+	0.290586i	0.226770	+	0.973948i	$0.427184\pi$
$30$		0			0
$31$	9.06457	−	5.23343i	1.62805	−	0.939952i	0.643370	−	0.765556i	$-0.277536\pi$
$31$	9.06457	−	5.23343i	1.62805	−	0.939952i	0.984675	−	0.174397i	$-0.0557975\pi$
$32$	6.05802	−	3.49760i	1.07092	−	0.618294i
$33$		0			0
$34$	4.98140	−	2.87601i	0.854303	−	0.493232i
$35$		0			0
$36$		0			0
$37$	0.708168	+	1.22658i	0.116422	+	0.201649i	0.918347	−	0.395775i	$-0.129524\pi$
$37$	0.708168	+	1.22658i	0.116422	+	0.201649i	−0.801925	+	0.597424i	$0.796191\pi$
$38$	4.81100			0.780448
$39$		0			0
$40$		−	2.37466i		−	0.375467i
$41$	−1.64665	+	2.85208i	−0.257163	+	0.445420i	−0.965481	−	0.260474i	$-0.916121\pi$
$41$	−1.64665	+	2.85208i	−0.257163	+	0.445420i	0.708318	+	0.705894i	$0.249455\pi$
$42$		0			0
$43$	−4.75676	−	8.23894i	−0.725398	−	1.25643i	−0.958810	−	0.284049i	$-0.908322\pi$
$43$	−4.75676	−	8.23894i	−0.725398	−	1.25643i	0.233411	−	0.972378i	$-0.425011\pi$
$44$	−7.25268	+	4.18733i	−1.09338	+	0.631264i
$45$		0			0
$46$	−7.37492	+	12.7737i	−1.08737	+	1.88338i
$47$	1.07190	−	1.85659i	0.156353	−	0.270811i	−0.777198	−	0.629256i	$-0.783360\pi$
$47$	1.07190	−	1.85659i	0.156353	−	0.270811i	0.933551	+	0.358445i	$0.116693\pi$
$48$		0			0
$49$		0			0
$50$	2.06964	+	1.19491i	0.292691	+	0.168985i
$51$		0			0
$52$			0.662509i			0.0918734i
$53$	4.20379	+	2.42706i	0.577435	+	0.333382i	0.760113	−	0.649791i	$-0.225143\pi$
$53$	4.20379	+	2.42706i	0.577435	+	0.333382i	−0.182678	+	0.983173i	$0.558477\pi$
$54$		0			0
$55$			14.0561i			1.89532i
$56$		0			0
$57$		0			0
$58$	−5.84923			−0.768041
$59$	3.65496	+	6.33057i	0.475835	+	0.824170i	0.999617	−	0.0276824i	$-0.00881270\pi$
$59$	3.65496	+	6.33057i	0.475835	+	0.824170i	−0.523782	+	0.851852i	$0.675479\pi$
$60$		0			0
$61$	−7.40950	−	4.27788i	−0.948690	−	0.547726i	−0.0560160	−	0.998430i	$-0.517840\pi$
$61$	−7.40950	−	4.27788i	−0.948690	−	0.547726i	−0.892674	+	0.450704i	$0.851173\pi$
$62$	19.5619			2.48437
$63$		0			0
$64$	3.55953			0.444941
$65$	0.962984	+	0.555979i	0.119443	+	0.0689607i
$66$		0			0
$67$	0.934442	+	1.61850i	0.114160	+	0.197731i	0.917444	−	0.397865i	$-0.130249\pi$
$67$	0.934442	+	1.61850i	0.114160	+	0.197731i	−0.803284	+	0.595597i	$0.796916\pi$
$68$	4.59477			0.557198
$69$		0			0
$70$		0			0
$71$		−	2.95338i		−	0.350501i	−0.984524	−	0.175251i	$-0.943926\pi$
$71$		−	2.95338i		−	0.350501i	0.984524	−	0.175251i	$-0.0560736\pi$
$72$		0			0
$73$	−7.37804	−	4.25971i	−0.863534	−	0.498562i	0.00165984	−	0.999999i	$-0.499472\pi$
$73$	−7.37804	−	4.25971i	−0.863534	−	0.498562i	−0.865194	+	0.501437i	$0.832805\pi$
$74$			2.64704i			0.307712i
$75$		0			0
$76$	3.32820	+	1.92154i	0.381771	+	0.220415i
$77$		0			0
$78$		0			0
$79$	0.287130	−	0.497324i	0.0323047	−	0.0559533i	−0.849421	−	0.527716i	$-0.823049\pi$
$79$	0.287130	−	0.497324i	0.0323047	−	0.0559533i	0.881726	+	0.471762i	$0.156382\pi$
$80$	5.95992	−	10.3229i	0.666339	−	1.15413i
$81$		0			0
$82$	−5.33036	+	3.07748i	−0.588639	+	0.339851i
$83$	−4.23521	−	7.33560i	−0.464875	−	0.805186i	0.534321	−	0.845281i	$-0.320567\pi$
$83$	−4.23521	−	7.33560i	−0.464875	−	0.805186i	−0.999196	+	0.0400951i	$0.987234\pi$
$84$		0			0
$85$	3.85595	−	6.67870i	0.418236	−	0.724406i
$86$		−	17.7802i		−	1.91728i
$87$		0			0
$88$	5.31615			0.566703
$89$	−3.78929	−	6.56325i	−0.401664	−	0.695703i	0.592263	−	0.805745i	$-0.298235\pi$
$89$	−3.78929	−	6.56325i	−0.401664	−	0.695703i	−0.993927	+	0.110042i	$0.964901\pi$
$90$		0			0
$91$		0			0
$92$	−10.2038	+	5.89115i	−1.06382	+	0.614195i
$93$		0			0
$94$	3.46984	−	2.00332i	0.357887	−	0.206626i
$95$	5.58607	−	3.22512i	0.573119	−	0.330890i
$96$		0			0
$97$	−3.22662	+	1.86289i	−0.327614	+	0.189148i	−0.654781	−	0.755818i	$-0.727239\pi$
$97$	−3.22662	+	1.86289i	−0.327614	+	0.189148i	0.327167	+	0.944966i	$0.393906\pi$
$98$		0			0
$99$		0			0
$100$	0.954503	+	1.65325i	0.0954503	+	0.165325i
$101$	−7.53449			−0.749710			−0.374855	−	0.927083i	$-0.622308\pi$
$101$	−7.53449			−0.749710			−0.374855	+	0.927083i	$0.622308\pi$
$102$		0			0
$103$			14.3235i			1.41133i	0.708545	+	0.705666i	$0.249352\pi$
$103$			14.3235i			1.41133i	−0.708545	+	0.705666i	$0.750648\pi$
$104$	0.210276	−	0.364210i	0.0206193	−	0.0357137i
$105$		0			0
$106$	4.53602	+	7.85662i	0.440577	+	0.763102i
$107$	−11.6798	+	6.74331i	−1.12912	+	0.651900i	−0.943715	−	0.330761i	$-0.892695\pi$
$107$	−11.6798	+	6.74331i	−1.12912	+	0.651900i	−0.185410	+	0.982661i	$0.559361\pi$
$108$		0			0
$109$	0.459348	−	0.795613i	0.0439975	−	0.0762059i	−0.843188	−	0.537619i	$-0.819324\pi$
$109$	0.459348	−	0.795613i	0.0439975	−	0.0762059i	0.887186	+	0.461413i	$0.152657\pi$
$110$	−13.1350	+	22.7504i	−1.25237	+	2.16917i
$111$		0			0
$112$		0			0
$113$	−4.10412	−	2.36952i	−0.386083	−	0.222905i	0.294378	−	0.955689i	$-0.404887\pi$
$113$	−4.10412	−	2.36952i	−0.386083	−	0.222905i	−0.680462	+	0.732784i	$0.738221\pi$
$114$		0			0
$115$			19.7755i			1.84407i
$116$	−4.04643	−	2.33621i	−0.375702	−	0.216912i
$117$		0			0
$118$			13.6618i			1.25767i
$119$		0			0
$120$		0			0
$121$	−20.4673			−1.86066
$122$	−7.99508	−	13.8479i	−0.723841	−	1.25373i
$123$		0			0
$124$	13.5327	+	7.81312i	1.21527	+	0.701639i
$125$	−9.32458			−0.834016
$126$		0			0
$127$	7.37245			0.654200			0.327100	−	0.944990i	$-0.393929\pi$
$127$	7.37245			0.654200			0.327100	+	0.944990i	$0.393929\pi$
$128$	−6.35477	−	3.66893i	−0.561688	−	0.324291i
$129$		0			0
$130$	1.03909	+	1.79976i	0.0911342	+	0.157849i
$131$	7.86300			0.686993			0.343497	−	0.939154i	$-0.388389\pi$
$131$	7.86300			0.686993			0.343497	+	0.939154i	$0.388389\pi$
$132$		0			0
$133$		0			0
$134$			3.49283i			0.301734i
$135$		0			0
$136$	−2.52594	−	1.45835i	−0.216598	−	0.125053i
$137$			11.5698i			0.988477i	0.869326	+	0.494238i	$0.164553\pi$
$137$			11.5698i			0.988477i	−0.869326	+	0.494238i	$0.835447\pi$
$138$		0			0
$139$	−16.9741	−	9.79999i	−1.43972	−	0.831224i	−0.441893	−	0.897068i	$-0.645693\pi$
$139$	−16.9741	−	9.79999i	−1.43972	−	0.831224i	−0.997830	+	0.0658437i	$0.979026\pi$
$140$		0			0
$141$		0			0
$142$	2.75984	−	4.78018i	0.231600	−	0.401144i
$143$	−1.24467	+	2.15583i	−0.104084	+	0.180279i
$144$		0			0
$145$	−6.79156	+	3.92111i	−0.564008	+	0.325630i
$146$	−7.96114	−	13.7891i	−0.658868	−	1.14119i
$147$		0			0
$148$	−1.05724	+	1.83120i	−0.0869047	+	0.150523i
$149$		−	15.7402i		−	1.28949i	−0.764397	−	0.644746i	$-0.776963\pi$
$149$		−	15.7402i		−	1.28949i	0.764397	−	0.644746i	$-0.223037\pi$
$150$		0			0
$151$	−1.98271			−0.161350			−0.0806752	−	0.996740i	$-0.525708\pi$
$151$	−1.98271			−0.161350			−0.0806752	+	0.996740i	$0.525708\pi$
$152$	−1.21977	−	2.11270i	−0.0989364	−	0.171363i
$153$		0			0
$154$		0			0
$155$	22.7134	−	13.1136i	1.82438	−	1.05331i
$156$		0			0
$157$	−7.26790	+	4.19612i	−0.580041	+	0.334887i	−0.761150	−	0.648576i	$-0.775365\pi$
$157$	−7.26790	+	4.19612i	−0.580041	+	0.334887i	0.181108	+	0.983463i	$0.442031\pi$
$158$	0.929468	−	0.536628i	0.0739445	−	0.0426919i
$159$		0			0
$160$	15.1798	−	8.76405i	1.20007	−	0.692859i
$161$		0			0
$162$		0			0
$163$	0.537054	+	0.930204i	0.0420653	+	0.0728592i	0.886291	−	0.463128i	$-0.153273\pi$
$163$	0.537054	+	0.930204i	0.0420653	+	0.0728592i	−0.844226	+	0.535987i	$0.819940\pi$
$164$	−4.91665			−0.383926
$165$		0			0
$166$		−	15.8307i		−	1.22870i
$167$	3.99731	−	6.92354i	0.309321	−	0.535760i	−0.668893	−	0.743359i	$-0.733232\pi$
$167$	3.99731	−	6.92354i	0.309321	−	0.535760i	0.978214	+	0.207599i	$0.0665649\pi$
$168$		0			0
$169$	−6.40154	−	11.0878i	−0.492426	−	0.852907i
$170$	12.4821	−	7.20652i	0.957330	−	0.552715i
$171$		0			0
$172$	7.10148	−	12.3001i	0.541483	−	0.937875i
$173$	0.501744	−	0.869046i	0.0381469	−	0.0660723i	−0.846322	−	0.532672i	$-0.821188\pi$
$173$	0.501744	−	0.869046i	0.0381469	−	0.0660723i	0.884468	+	0.466600i	$0.154521\pi$
$174$		0			0
$175$		0			0
$176$	23.1098	+	13.3424i	1.74197	+	1.00572i
$177$		0			0
$178$		−	14.1639i		−	1.06163i
$179$	−1.27773	−	0.737695i	−0.0955017	−	0.0551379i	0.451489	−	0.892277i	$-0.350893\pi$
$179$	−1.27773	−	0.737695i	−0.0955017	−	0.0551379i	−0.546990	+	0.837139i	$0.684227\pi$
$180$		0			0
$181$		−	15.0440i		−	1.11821i	−0.829096	−	0.559106i	$-0.811145\pi$
$181$		−	15.0440i		−	1.11821i	0.829096	−	0.559106i	$-0.188855\pi$
$182$		0			0
$183$		0			0
$184$	7.47928			0.551380
$185$	1.77448	+	3.07349i	0.130462	+	0.225967i
$186$		0			0
$187$	14.9516	+	8.63229i	1.09337	+	0.631255i
$188$	3.20054			0.233423
$189$		0			0
$190$	12.0551			0.874568
$191$	11.4521	+	6.61187i	0.828644	+	0.478418i	0.853388	−	0.521276i	$-0.174544\pi$
$191$	11.4521	+	6.61187i	0.828644	+	0.478418i	−0.0247439	+	0.999694i	$0.507877\pi$
$192$		0			0
$193$	0.777855	+	1.34728i	0.0559912	+	0.0969796i	0.892662	−	0.450726i	$-0.148835\pi$
$193$	0.777855	+	1.34728i	0.0559912	+	0.0969796i	−0.836671	+	0.547705i	$0.815501\pi$
$194$	−6.96325			−0.499932
$195$		0			0
$196$		0			0
$197$		−	4.96185i		−	0.353517i	−0.984254	−	0.176759i	$-0.943439\pi$
$197$		−	4.96185i		−	0.353517i	0.984254	−	0.176759i	$-0.0565612\pi$
$198$		0			0
$199$	−9.69273	−	5.59610i	−0.687100	−	0.396697i	0.115425	−	0.993316i	$-0.463177\pi$
$199$	−9.69273	−	5.59610i	−0.687100	−	0.396697i	−0.802525	+	0.596619i	$0.796510\pi$
$200$		−	1.21182i		−	0.0856883i
$201$		0			0
$202$	−12.1949	−	7.04074i	−0.858032	−	0.495385i
$203$		0			0
$204$		0			0
$205$	−4.12606	+	7.14655i	−0.288177	+	0.499137i
$206$	−13.3848	+	23.1832i	−0.932565	+	1.61525i
$207$		0			0
$208$	1.82818	−	1.05550i	0.126762	−	0.0731859i
$209$	7.22006	+	12.5055i	0.499422	+	0.865024i
$210$		0			0
$211$	7.68026	−	13.3026i	0.528731	−	0.915789i	−0.470708	−	0.882289i	$-0.656001\pi$
$211$	7.68026	−	13.3026i	0.528731	−	0.915789i	0.999439	−	0.0334999i	$-0.0106654\pi$
$212$			7.24683i			0.497714i
$213$		0			0
$214$	−25.2056			−1.72302
$215$	−11.9192	−	20.6446i	−0.812880	−	1.40795i
$216$		0			0
$217$		0			0
$218$	1.48695	−	0.858492i	0.100709	−	0.0581444i
$219$		0			0
$220$	−18.1733	+	10.4923i	−1.22524	+	0.707394i
$221$	1.18280	−	0.682888i	0.0795635	−	0.0459360i
$222$		0			0
$223$	2.76845	−	1.59837i	0.185389	−	0.107034i	−0.404433	−	0.914568i	$-0.632531\pi$
$223$	2.76845	−	1.59837i	0.185389	−	0.107034i	0.589822	+	0.807533i	$0.299198\pi$
$224$		0			0
$225$		0			0
$226$	−4.42848	−	7.67035i	−0.294578	−	0.510224i
$227$	14.6699			0.973675			0.486837	−	0.873493i	$-0.338150\pi$
$227$	14.6699			0.973675			0.486837	+	0.873493i	$0.338150\pi$
$228$		0			0
$229$			3.37807i			0.223229i	0.993752	+	0.111615i	$0.0356022\pi$
$229$			3.37807i			0.223229i	−0.993752	+	0.111615i	$0.964398\pi$
$230$	−18.4796	+	32.0076i	−1.21851	+	2.11052i
$231$		0			0
$232$	1.48300	+	2.56863i	0.0973637	+	0.168639i
$233$	−4.22628	+	2.44005i	−0.276873	+	0.159853i	−0.632007	−	0.774963i	$-0.717769\pi$
$233$	−4.22628	+	2.44005i	−0.276873	+	0.159853i	0.355134	+	0.934815i	$0.384435\pi$
$234$		0			0
$235$	2.68590	−	4.65211i	0.175209	−	0.303470i
$236$	−5.45657	+	9.45106i	−0.355193	+	0.615212i
$237$		0			0
$238$		0			0
$239$	−13.6253	−	7.86657i	−0.881347	−	0.508846i	−0.0102448	−	0.999948i	$-0.503261\pi$
$239$	−13.6253	−	7.86657i	−0.881347	−	0.508846i	−0.871102	+	0.491101i	$0.836594\pi$
$240$		0			0
$241$			0.769383i			0.0495603i	0.999693	+	0.0247801i	$0.00788857\pi$
$241$			0.769383i			0.0495603i	−0.999693	+	0.0247801i	$0.992111\pi$
$242$	−33.1273	−	19.1260i	−2.12950	−	1.22947i
$243$		0			0
$244$		−	12.7731i		−	0.817714i
$245$		0			0
$246$		0			0
$247$	1.14234			0.0726852
$248$	−4.95968	−	8.59042i	−0.314940	−	0.545492i
$249$		0			0
$250$	−15.0923	−	8.71353i	−0.954519	−	0.551092i
$251$	1.14544			0.0722996			0.0361498	−	0.999346i	$-0.488491\pi$
$251$	1.14544			0.0722996			0.0361498	+	0.999346i	$0.488491\pi$
$252$		0			0
$253$	−44.2713			−2.78331
$254$	11.9327	+	6.88933i	0.748722	+	0.432275i
$255$		0			0
$256$	−10.4165	−	18.0420i	−0.651033	−	1.12762i
$257$	28.9835			1.80794			0.903969	−	0.427598i	$-0.140640\pi$
$257$	28.9835			1.80794			0.903969	+	0.427598i	$0.140640\pi$
$258$		0			0
$259$		0			0
$260$			1.66007i			0.102953i
$261$		0			0
$262$	12.7266	+	7.34772i	0.786254	+	0.453944i
$263$		−	13.6998i		−	0.844763i	−0.906418	−	0.422381i	$-0.861194\pi$
$263$		−	13.6998i		−	0.844763i	0.906418	−	0.422381i	$-0.138806\pi$
$264$		0			0
$265$	10.5336	+	6.08156i	0.647072	+	0.373587i
$266$		0			0
$267$		0			0
$268$	−1.39505	+	2.41630i	−0.0852163	+	0.147599i
$269$	−5.23973	+	9.07548i	−0.319472	+	0.553342i	−0.980378	−	0.197127i	$-0.936839\pi$
$269$	−5.23973	+	9.07548i	−0.319472	+	0.553342i	0.660906	+	0.750469i	$0.270172\pi$
$270$		0			0
$271$	5.66907	−	3.27304i	0.344371	−	0.198823i	−0.317832	−	0.948147i	$-0.602955\pi$
$271$	5.66907	−	3.27304i	0.344371	−	0.198823i	0.662203	+	0.749324i	$0.269621\pi$
$272$	−7.32034	−	12.6792i	−0.443861	−	0.768790i
$273$		0			0
$274$	−10.8116	+	18.7263i	−0.653155	+	1.13130i
$275$			7.17298i			0.432547i
$276$		0			0
$277$	22.4313			1.34777			0.673883	−	0.738838i	$-0.264625\pi$
$277$	22.4313			1.34777			0.673883	+	0.738838i	$0.264625\pi$
$278$	−18.3156	−	31.7235i	−1.09849	−	1.90265i
$279$		0			0
$280$		0			0
$281$	−19.3552	+	11.1747i	−1.15463	+	0.666627i	−0.950012	−	0.312214i	$-0.898929\pi$
$281$	−19.3552	+	11.1747i	−1.15463	+	0.666627i	−0.204621	+	0.978841i	$0.565596\pi$
$282$		0			0
$283$	16.4296	−	9.48563i	0.976638	−	0.563862i	0.0753848	−	0.997155i	$-0.475981\pi$
$283$	16.4296	−	9.48563i	0.976638	−	0.563862i	0.901254	+	0.433292i	$0.142648\pi$
$284$	3.81845	−	2.20459i	0.226584	−	0.130818i
$285$		0			0
$286$	−4.02910	+	2.32620i	−0.238246	+	0.137551i
$287$		0			0
$288$		0			0
$289$	3.76389	+	6.51924i	0.221405	+	0.383485i
$290$	−14.6566			−0.860665
$291$		0			0
$292$		−	12.7189i		−	0.744315i
$293$	−4.41136	+	7.64069i	−0.257714	+	0.446374i	−0.965629	−	0.259924i	$-0.916303\pi$
$293$	−4.41136	+	7.64069i	−0.257714	+	0.446374i	0.707915	+	0.706298i	$0.249636\pi$
$294$		0			0
$295$	9.15835	+	15.8627i	0.533220	+	0.923563i
$296$	1.16242	−	0.671125i	0.0675644	−	0.0390083i
$297$		0			0
$298$	14.7088	−	25.4763i	0.852056	−	1.47580i
$299$	−1.75112	+	3.03303i	−0.101270	+	0.175405i
$300$		0			0
$301$		0			0
$302$	−3.20910	−	1.85278i	−0.184663	−	0.106615i
$303$		0			0
$304$		−	12.2455i		−	0.702327i
$305$	−18.5662	−	10.7192i	−1.06310	−	0.613781i
$306$		0			0
$307$		−	28.7533i		−	1.64104i	−0.571620	−	0.820519i	$-0.693685\pi$
$307$		−	28.7533i		−	1.64104i	0.571620	−	0.820519i	$-0.306315\pi$
$308$		0			0
$309$		0			0
$310$	49.0169			2.78398
$311$	6.64294	+	11.5059i	0.376687	+	0.652441i	0.990578	−	0.136950i	$-0.0437300\pi$
$311$	6.64294	+	11.5059i	0.376687	+	0.652441i	−0.613891	+	0.789391i	$0.710397\pi$
$312$		0			0
$313$	−27.3227	−	15.7748i	−1.54437	−	0.891643i	−0.998555	−	0.0537372i	$-0.982887\pi$
$313$	−27.3227	−	15.7748i	−1.54437	−	0.891643i	−0.545815	−	0.837905i	$-0.683780\pi$
$314$	−15.6846			−0.885132
$315$		0			0
$316$	0.857328			0.0482285
$317$	17.3819	+	10.0354i	0.976264	+	0.563646i	0.901140	−	0.433528i	$-0.142732\pi$
$317$	17.3819	+	10.0354i	0.976264	+	0.563646i	0.0751236	+	0.997174i	$0.476065\pi$
$318$		0			0
$319$	−8.77816	−	15.2042i	−0.491483	−	0.851273i
$320$	8.91923			0.498600
$321$		0			0
$322$		0			0
$323$		−	7.92259i		−	0.440824i
$324$		0			0
$325$	0.491421	+	0.283722i	0.0272591	+	0.0157381i
$326$			2.00744i			0.111182i
$327$		0			0
$328$	2.70289	+	1.56052i	0.149242	+	0.0861651i
$329$		0			0
$330$		0			0
$331$	−0.623957	+	1.08073i	−0.0342958	+	0.0594020i	−0.882664	−	0.470005i	$-0.844252\pi$
$331$	−0.623957	+	1.08073i	−0.0342958	+	0.0594020i	0.848368	+	0.529407i	$0.177585\pi$
$332$	6.32285	−	10.9515i	0.347011	−	0.601041i
$333$		0			0
$334$	12.9397	−	7.47072i	0.708027	−	0.408780i
$335$	2.34146	+	4.05553i	0.127928	+	0.221577i
$336$		0			0
$337$	6.58745	−	11.4098i	0.358842	−	0.621532i	−0.628926	−	0.777465i	$-0.716505\pi$
$337$	6.58745	−	11.4098i	0.358842	−	0.621532i	0.987768	+	0.155933i	$0.0498385\pi$
$338$		−	23.9281i		−	1.30152i
$339$		0			0
$340$	11.5133			0.624395
$341$	29.3573	+	50.8484i	1.58979	+	2.75359i
$342$		0			0
$343$		0			0
$344$	−7.80798	+	4.50794i	−0.420978	+	0.243052i
$345$		0			0
$346$	1.62419	−	0.937727i	0.0873171	−	0.0504125i
$347$	−23.4411	+	13.5337i	−1.25838	+	0.726529i	−0.972760	−	0.231813i	$-0.925534\pi$
$347$	−23.4411	+	13.5337i	−1.25838	+	0.726529i	−0.285624	+	0.958342i	$0.592201\pi$
$348$		0			0
$349$	−30.3413	+	17.5176i	−1.62413	+	0.937694i	−0.638336	+	0.769758i	$0.720377\pi$
$349$	−30.3413	+	17.5176i	−1.62413	+	0.937694i	−0.985798	+	0.167936i	$0.946290\pi$
$350$		0			0
$351$		0			0
$352$	19.6200	+	33.9829i	1.04575	+	1.81129i
$353$	−2.52512			−0.134398			−0.0671992	−	0.997740i	$-0.521406\pi$
$353$	−2.52512			−0.134398			−0.0671992	+	0.997740i	$0.521406\pi$
$354$		0			0
$355$		−	7.40038i		−	0.392771i
$356$	5.65713	−	9.79843i	0.299827	−	0.519316i
$357$		0			0
$358$	−1.37871	−	2.38799i	−0.0728669	−	0.126209i
$359$	−6.29395	+	3.63381i	−0.332182	+	0.191785i	−0.656809	−	0.754057i	$-0.728094\pi$
$359$	−6.29395	+	3.63381i	−0.332182	+	0.191785i	0.324628	+	0.945842i	$0.394761\pi$
$360$		0			0
$361$	−6.18677	+	10.7158i	−0.325619	+	0.563989i
$362$	14.0581	−	24.3494i	0.738880	−	1.27978i
$363$		0			0
$364$		0			0
$365$	−18.4874	−	10.6737i	−0.967675	−	0.558688i
$366$		0			0
$367$			13.4770i			0.703492i	0.936095	+	0.351746i	$0.114412\pi$
$367$			13.4770i			0.703492i	−0.936095	+	0.351746i	$0.885588\pi$
$368$	32.5131	+	18.7715i	1.69486	+	0.978530i
$369$		0			0
$370$			6.63278i			0.344822i
$371$		0			0
$372$		0			0
$373$	23.7639			1.23045			0.615224	−	0.788352i	$-0.289065\pi$
$373$	23.7639			1.23045			0.615224	+	0.788352i	$0.289065\pi$
$374$	16.1332	+	27.9435i	0.834228	+	1.44492i
$375$		0			0
$376$	−1.75947	−	1.01583i	−0.0907379	−	0.0523875i
$377$	−1.38886			−0.0715297
$378$		0			0
$379$	21.2283			1.09042			0.545211	−	0.838299i	$-0.316449\pi$
$379$	21.2283			1.09042			0.545211	+	0.838299i	$0.316449\pi$
$380$	8.33958	+	4.81486i	0.427812	+	0.246997i
$381$		0			0
$382$	12.3572	+	21.4032i	0.632248	+	1.09509i
$383$	−12.9586			−0.662154			−0.331077	−	0.943604i	$-0.607412\pi$
$383$	−12.9586			−0.662154			−0.331077	+	0.943604i	$0.607412\pi$
$384$		0			0
$385$		0			0
$386$			2.90752i			0.147989i
$387$		0			0
$388$	−4.81710	−	2.78116i	−0.244551	−	0.141192i
$389$		−	10.9470i		−	0.555035i	−0.960721	−	0.277517i	$-0.910488\pi$
$389$		−	10.9470i		−	0.555035i	0.960721	−	0.277517i	$-0.0895116\pi$
$390$		0			0
$391$	21.0353	+	12.1447i	1.06380	+	0.614186i
$392$		0			0
$393$		0			0
$394$	4.63669	−	8.03098i	0.233593	−	0.404595i
$395$	0.719472	−	1.24616i	0.0362006	−	0.0627012i
$396$		0			0
$397$	25.8856	−	14.9451i	1.29916	−	0.750071i	0.318901	−	0.947788i	$-0.396686\pi$
$397$	25.8856	−	14.9451i	1.29916	−	0.750071i	0.980259	+	0.197717i	$0.0633528\pi$
$398$	−10.4588	−	18.1151i	−0.524250	−	0.908028i
$399$		0			0
$400$	3.04141	−	5.26788i	0.152071	−	0.263394i
$401$			19.1949i			0.958547i	0.877666	+	0.479273i	$0.159100\pi$
$401$			19.1949i			0.958547i	−0.877666	+	0.479273i	$0.840900\pi$
$402$		0			0
$403$	4.64483			0.231376
$404$	−5.62421	−	9.74142i	−0.279815	−	0.484654i
$405$		0			0
$406$		0			0
$407$	−6.88060	+	3.97252i	−0.341059	+	0.196910i
$408$		0			0
$409$	−24.9737	+	14.4186i	−1.23487	+	0.712953i	−0.968041	−	0.250790i	$-0.919309\pi$
$409$	−24.9737	+	14.4186i	−1.23487	+	0.712953i	−0.266830	+	0.963744i	$0.585976\pi$
$410$	−13.3565	+	7.71135i	−0.659628	+	0.380837i
$411$		0			0
$412$	−18.5190	+	10.6919i	−0.912363	+	0.526753i
$413$		0			0
$414$		0			0
$415$	−10.6123	−	18.3811i	−0.520938	−	0.902290i
$416$	3.10423			0.152197
$417$		0			0
$418$			26.9877i			1.32001i
$419$	5.06390	−	8.77094i	0.247388	−	0.428488i	−0.715412	−	0.698702i	$-0.753761\pi$
$419$	5.06390	−	8.77094i	0.247388	−	0.428488i	0.962800	+	0.270214i	$0.0870945\pi$
$420$		0			0
$421$	12.7094	+	22.0134i	0.619419	+	1.07287i	0.989592	+	0.143902i	$0.0459651\pi$
$421$	12.7094	+	22.0134i	0.619419	+	1.07287i	−0.370173	+	0.928963i	$0.620702\pi$
$422$	24.8617	−	14.3539i	1.21025	−	0.698738i
$423$		0			0
$424$	2.30010	−	3.98390i	0.111703	−	0.193475i
$425$	1.96773	−	3.40821i	0.0954490	−	0.165322i
$426$		0			0
$427$		0			0
$428$	−17.4370	−	10.0673i	−0.842849	−	0.486619i
$429$		0			0
$430$		−	44.5523i		−	2.14850i
$431$	−9.39066	−	5.42170i	−0.452332	−	0.261154i	0.256482	−	0.966549i	$-0.417436\pi$
$431$	−9.39066	−	5.42170i	−0.452332	−	0.261154i	−0.708815	+	0.705395i	$0.750770\pi$
$432$		0			0
$433$			13.0519i			0.627233i	0.949550	+	0.313616i	$0.101541\pi$
$433$			13.0519i			0.627233i	−0.949550	+	0.313616i	$0.898459\pi$
$434$		0			0
$435$		0			0
$436$	1.37154			0.0656850
$437$	10.1579	+	17.5940i	0.485918	+	0.841634i
$438$		0			0
$439$	27.6736	+	15.9773i	1.32079	+	0.762557i	0.983854	−	0.178972i	$-0.0572772\pi$
$439$	27.6736	+	15.9773i	1.32079	+	0.762557i	0.336933	+	0.941529i	$0.390611\pi$
$440$	13.3208			0.635046
$441$		0			0
$442$	2.55255			0.121412
$443$	21.4748	+	12.3985i	1.02030	+	0.589068i	0.914190	−	0.405286i	$-0.132828\pi$
$443$	21.4748	+	12.3985i	1.02030	+	0.589068i	0.106107	+	0.994355i	$0.466162\pi$
$444$		0			0
$445$	−9.49496	−	16.4458i	−0.450104	−	0.779603i
$446$	5.97449			0.282900
$447$		0			0
$448$		0			0
$449$			13.7710i			0.649892i	0.945733	+	0.324946i	$0.105346\pi$
$449$			13.7710i			0.649892i	−0.945733	+	0.324946i	$0.894654\pi$
$450$		0			0
$451$	−15.9989	−	9.23700i	−0.753361	−	0.434953i
$452$		−	7.07502i		−	0.332781i
$453$		0			0
$454$	23.7439	+	13.7085i	1.11436	+	0.643374i
$455$		0			0
$456$		0			0
$457$	−13.6554	+	23.6518i	−0.638771	+	1.10638i	0.346931	+	0.937890i	$0.387224\pi$
$457$	−13.6554	+	23.6518i	−0.638771	+	1.10638i	−0.985703	+	0.168494i	$0.946110\pi$
$458$	−3.15670	+	5.46757i	−0.147503	+	0.255483i
$459$		0			0
$460$	−25.5680	+	14.7617i	−1.19211	+	0.688266i
$461$	−5.51822	−	9.55784i	−0.257009	−	0.445153i	0.708430	−	0.705781i	$-0.249404\pi$
$461$	−5.51822	−	9.55784i	−0.257009	−	0.445153i	−0.965439	+	0.260628i	$0.916070\pi$
$462$		0			0
$463$	−12.2346	+	21.1910i	−0.568591	+	0.984829i	0.428115	+	0.903724i	$0.359178\pi$
$463$	−12.2346	+	21.1910i	−0.568591	+	0.984829i	−0.996706	+	0.0811042i	$0.974155\pi$
$464$			14.8881i			0.691163i
$465$		0			0
$466$	−9.12059			−0.422503
$467$	−7.95241	−	13.7740i	−0.367994	−	0.637384i	0.621258	−	0.783606i	$-0.286622\pi$
$467$	−7.95241	−	13.7740i	−0.367994	−	0.637384i	−0.989252	+	0.146222i	$0.953289\pi$
$468$		0			0
$469$		0			0
$470$	8.69451	−	5.01978i	0.401048	−	0.231545i
$471$		0			0
$472$	5.99943	−	3.46377i	0.276146	−	0.159433i
$473$	46.2169	−	26.6834i	2.12506	−	1.22690i
$474$		0			0
$475$	2.85063	−	1.64581i	0.130796	−	0.0755151i
$476$		0			0
$477$		0			0
$478$	−14.7021	−	25.4648i	−0.672459	−	1.16473i
$479$	13.8537			0.632991			0.316496	−	0.948594i	$-0.397494\pi$
$479$	13.8537			0.632991			0.316496	+	0.948594i	$0.397494\pi$
$480$		0			0
$481$			0.628521i			0.0286581i
$482$	−0.718964	+	1.24528i	−0.0327479	+	0.0567210i
$483$		0			0
$484$	−15.2781	−	26.4624i	−0.694458	−	1.20284i
$485$	−8.08506	+	4.66791i	−0.367123	+	0.211959i
$486$		0			0
$487$	−14.3993	+	24.9404i	−0.652496	+	1.13016i	0.330020	+	0.943974i	$0.392945\pi$
$487$	−14.3993	+	24.9404i	−0.652496	+	1.13016i	−0.982515	+	0.186182i	$0.940389\pi$
$488$	−4.05411	+	7.02193i	−0.183521	+	0.317868i
$489$		0			0
$490$		0			0
$491$	33.5627	+	19.3774i	1.51466	+	0.874492i	0.999852	+	0.0171884i	$0.00547151\pi$
$491$	33.5627	+	19.3774i	1.51466	+	0.874492i	0.514812	+	0.857303i	$0.327862\pi$
$492$		0			0
$493$			9.63230i			0.433817i
$494$	1.84893	+	1.06748i	0.0831872	+	0.0480281i
$495$		0			0
$496$		−	49.7911i		−	2.23569i
$497$		0			0
$498$		0			0
$499$	−3.46667			−0.155189			−0.0775946	−	0.996985i	$-0.524724\pi$
$499$	−3.46667			−0.155189			−0.0775946	+	0.996985i	$0.524724\pi$
$500$	−6.96045	−	12.0558i	−0.311281	−	0.539154i
$501$		0			0
$502$	1.85395	+	1.07038i	0.0827458	+	0.0477733i
$503$	−28.2202			−1.25828			−0.629138	−	0.777293i	$-0.716592\pi$
$503$	−28.2202			−1.25828			−0.629138	+	0.777293i	$0.716592\pi$
$504$		0			0
$505$	−18.8794			−0.840124
$506$	−71.6552	−	41.3701i	−3.18546	−	1.83913i
$507$		0			0
$508$	5.50326	+	9.53193i	0.244168	+	0.422911i
$509$	−35.8124			−1.58736			−0.793678	−	0.608338i	$-0.791836\pi$
$509$	−35.8124			−1.58736			−0.793678	+	0.608338i	$0.791836\pi$
$510$		0			0
$511$		0			0
$512$		−	24.2599i		−	1.07215i
$513$		0			0
$514$	46.9111	+	27.0841i	2.06916	+	1.19463i
$515$			35.8908i			1.58154i
$516$		0			0
$517$	10.4147	+	6.01291i	0.458036	+	0.264447i
$518$		0			0
$519$		0			0
$520$	0.526897	−	0.912612i	0.0231060	−	0.0400207i
$521$	13.4608	−	23.3148i	0.589729	−	1.02144i	−0.404538	−	0.914521i	$-0.632568\pi$
$521$	13.4608	−	23.3148i	0.589729	−	1.02144i	0.994268	−	0.106920i	$-0.0340989\pi$
$522$		0			0
$523$	7.82181	−	4.51593i	0.342024	−	0.197468i	−0.319143	−	0.947707i	$-0.603395\pi$
$523$	7.82181	−	4.51593i	0.342024	−	0.197468i	0.661167	+	0.750239i	$0.270062\pi$
$524$	5.86943	+	10.1662i	0.256407	+	0.444110i
$525$		0			0
$526$	12.8020	−	22.1737i	0.558193	−	0.966819i
$527$		−	32.2139i		−	1.40326i
$528$		0			0
$529$	−39.2852			−1.70805
$530$	11.3661	+	19.6866i	0.493710	+	0.855131i
$531$		0			0
$532$		0			0
$533$	−1.26565	+	0.730726i	−0.0548216	+	0.0316513i
$534$		0			0
$535$	−29.2664	+	16.8969i	−1.26530	+	0.730518i
$536$	1.53384	−	0.885563i	0.0662518	−	0.0382505i
$537$		0			0
$538$	−16.9615	+	9.79273i	−0.731262	+	0.422195i
$539$		0			0
$540$		0			0
$541$	−5.66792	−	9.81713i	−0.243683	−	0.422071i	0.718078	−	0.695963i	$-0.245022\pi$
$541$	−5.66792	−	9.81713i	−0.243683	−	0.422071i	−0.961760	+	0.273892i	$0.911689\pi$
$542$	12.2342			0.525504
$543$		0			0
$544$		−	21.5291i		−	0.923053i
$545$	1.15100	−	1.99360i	0.0493035	−	0.0853962i
$546$		0			0
$547$	19.4246	+	33.6444i	0.830537	+	1.43853i	0.897613	+	0.440784i	$0.145300\pi$
$547$	19.4246	+	33.6444i	0.830537	+	1.43853i	−0.0670762	+	0.997748i	$0.521367\pi$
$548$	−14.9587	+	8.63644i	−0.639006	+	0.368930i
$549$		0			0
$550$	−6.70292	+	11.6098i	−0.285813	+	0.495043i
$551$	−4.02823	+	6.97711i	−0.171609	+	0.297235i
$552$		0			0
$553$		0			0
$554$	36.3061	+	20.9613i	1.54250	+	0.890562i
$555$		0			0
$556$		−	29.2613i		−	1.24096i
$557$	−6.29167	−	3.63249i	−0.266586	−	0.153914i	0.360749	−	0.932663i	$-0.382521\pi$
$557$	−6.29167	−	3.63249i	−0.266586	−	0.153914i	−0.627335	+	0.778749i	$0.715854\pi$
$558$		0			0
$559$		−	4.22177i		−	0.178562i
$560$		0			0
$561$		0			0
$562$	−41.7697			−1.76195
$563$	−11.5409	−	19.9894i	−0.486390	−	0.842453i	0.513487	−	0.858097i	$-0.328353\pi$
$563$	−11.5409	−	19.9894i	−0.486390	−	0.842453i	−0.999878	+	0.0156446i	$0.995020\pi$
$564$		0			0
$565$	−10.2838	−	5.93738i	−0.432644	−	0.249787i
$566$	35.4561			1.49033
$567$		0			0
$568$	−2.79889			−0.117439
$569$	−15.5482	−	8.97677i	−0.651815	−	0.376326i	0.137336	−	0.990525i	$-0.456146\pi$
$569$	−15.5482	−	8.97677i	−0.651815	−	0.376326i	−0.789151	+	0.614199i	$0.789479\pi$
$570$		0			0
$571$	7.04234	+	12.1977i	0.294713	+	0.510457i	0.974918	−	0.222564i	$-0.0714427\pi$
$571$	7.04234	+	12.1977i	0.294713	+	0.510457i	−0.680205	+	0.733022i	$0.738109\pi$
$572$	−3.71639			−0.155390
$573$		0			0
$574$		0			0
$575$			10.0916i			0.420851i
$576$		0			0
$577$	26.0392	+	15.0337i	1.08403	+	0.625862i	0.931979	−	0.362511i	$-0.118081\pi$
$577$	26.0392	+	15.0337i	1.08403	+	0.625862i	0.152046	+	0.988373i	$0.451414\pi$
$578$			14.0689i			0.585190i
$579$		0			0
$580$	−10.1393	−	5.85392i	−0.421011	−	0.243071i
$581$		0			0
$582$		0			0
$583$	−13.6148	+	23.5815i	−0.563866	+	0.976644i
$584$	−4.03690	+	6.99211i	−0.167048	+	0.289336i
$585$		0			0
$586$	−14.2800	+	8.24455i	−0.589900	+	0.340579i
$587$	18.0979	+	31.3465i	0.746981	+	1.29381i	0.949264	+	0.314481i	$0.101831\pi$
$587$	18.0979	+	31.3465i	0.746981	+	1.29381i	−0.202283	+	0.979327i	$0.564836\pi$
$588$		0			0
$589$	13.4719	−	23.3339i	0.555098	−	0.961459i
$590$			34.2327i			1.40934i
$591$		0			0
$592$	6.73755			0.276911
$593$	1.02158	+	1.76943i	0.0419514	+	0.0726620i	0.886239	−	0.463229i	$-0.153309\pi$
$593$	1.02158	+	1.76943i	0.0419514	+	0.0726620i	−0.844287	+	0.535891i	$0.819976\pi$
$594$		0			0
$595$		0			0
$596$	20.3507	−	11.7495i	0.833598	−	0.481278i
$597$		0			0
$598$	−5.66854	+	3.27273i	−0.231804	+	0.133832i
$599$	−15.7873	+	9.11478i	−0.645050	+	0.372420i	−0.786557	−	0.617517i	$-0.788139\pi$
$599$	−15.7873	+	9.11478i	−0.645050	+	0.372420i	0.141507	+	0.989937i	$0.454805\pi$
$600$		0			0
$601$	32.1713	−	18.5741i	1.31230	−	0.757654i	0.329820	−	0.944044i	$-0.393012\pi$
$601$	32.1713	−	18.5741i	1.31230	−	0.757654i	0.982476	+	0.186390i	$0.0596787\pi$
$602$		0			0
$603$		0			0
$604$	−1.48002	−	2.56346i	−0.0602210	−	0.104306i
$605$	−51.2856			−2.08506
$606$		0			0
$607$			19.8296i			0.804860i	0.915451	+	0.402430i	$0.131834\pi$
$607$			19.8296i			0.804860i	−0.915451	+	0.402430i	$0.868166\pi$
$608$	9.00349	−	15.5945i	0.365140	−	0.632440i
$609$		0			0
$610$	−20.0336	−	34.6991i	−0.811135	−	1.40493i
$611$	0.823890	−	0.475673i	0.0333310	−	0.0192437i
$612$		0			0
$613$	6.34412	−	10.9883i	0.256237	−	0.443815i	−0.708994	−	0.705214i	$-0.750851\pi$
$613$	6.34412	−	10.9883i	0.256237	−	0.443815i	0.965231	+	0.261400i	$0.0841840\pi$
$614$	26.8690	−	46.5385i	1.08435	−	1.87814i
$615$		0			0
$616$		0			0
$617$	−4.37247	−	2.52445i	−0.176029	−	0.101630i	0.409397	−	0.912357i	$-0.365739\pi$
$617$	−4.37247	−	2.52445i	−0.176029	−	0.101630i	−0.585426	+	0.810726i	$0.699073\pi$
$618$		0			0
$619$		−	0.267890i		−	0.0107674i	−0.999986	−	0.00538370i	$-0.998286\pi$
$619$		−	0.267890i		−	0.0107674i	0.999986	−	0.00538370i	$-0.00171369\pi$
$620$	33.9094	+	19.5776i	1.36183	+	0.786255i
$621$		0			0
$622$			24.8305i			0.995611i
$623$		0			0
$624$		0			0
$625$	−29.7584			−1.19034
$626$	−29.4820	−	51.0644i	−1.17834	−	2.04094i
$627$		0			0
$628$	−10.8504	−	6.26449i	−0.432979	−	0.249981i
$629$	4.35905			0.173807
$630$		0			0
$631$	37.7899			1.50439			0.752197	−	0.658938i	$-0.228994\pi$
$631$	37.7899			1.50439			0.752197	+	0.658938i	$0.228994\pi$
$632$	−0.471310	−	0.272111i	−0.0187477	−	0.0108240i
$633$		0			0
$634$	18.7556	+	32.4856i	0.744880	+	1.29017i
$635$	18.4734			0.733095
$636$		0			0
$637$		0			0
$638$		−	32.8117i		−	1.29903i
$639$		0			0
$640$	−15.9234	−	9.19336i	−0.629426	−	0.363400i
$641$		−	34.4090i		−	1.35907i	−0.733641	−	0.679537i	$-0.762181\pi$
$641$		−	34.4090i		−	1.35907i	0.733641	−	0.679537i	$-0.237819\pi$
$642$		0			0
$643$	−0.676278	−	0.390449i	−0.0266698	−	0.0153978i	0.486606	−	0.873622i	$-0.338235\pi$
$643$	−0.676278	−	0.390449i	−0.0266698	−	0.0153978i	−0.513276	+	0.858224i	$0.671568\pi$
$644$		0			0
$645$		0			0
$646$	7.40341	−	12.8231i	0.291283	−	0.504517i
$647$	9.82182	−	17.0119i	0.386136	−	0.668807i	−0.605790	−	0.795624i	$-0.707143\pi$
$647$	9.82182	−	17.0119i	0.386136	−	0.668807i	0.991926	+	0.126818i	$0.0404763\pi$
$648$		0			0
$649$	−35.5118	+	20.5027i	−1.39396	+	0.804803i
$650$	0.530259	+	0.918435i	0.0207985	+	0.0360240i
$651$		0			0
$652$	−0.801781	+	1.38872i	−0.0314001	+	0.0543867i
$653$			3.20545i			0.125439i	0.998031	+	0.0627194i	$0.0199773\pi$
$653$			3.20545i			0.125439i	−0.998031	+	0.0627194i	$0.980023\pi$
$654$		0			0
$655$	19.7026			0.769843
$656$	7.83315	+	13.5674i	0.305833	+	0.529719i
$657$		0			0
$658$		0			0
$659$	24.2959	−	14.0273i	0.946435	−	0.546425i	0.0544636	−	0.998516i	$-0.482655\pi$
$659$	24.2959	−	14.0273i	0.946435	−	0.546425i	0.891972	+	0.452091i	$0.149322\pi$
$660$		0			0
$661$	28.0490	−	16.1941i	1.09098	−	0.629878i	0.157143	−	0.987576i	$-0.449772\pi$
$661$	28.0490	−	16.1941i	1.09098	−	0.629878i	0.933837	+	0.357698i	$0.116438\pi$
$662$	−2.01981	+	1.16614i	−0.0785020	+	0.0453232i
$663$		0			0
$664$	−6.95189	+	4.01367i	−0.269785	+	0.155761i
$665$		0			0
$666$		0			0
$667$	−12.3500	−	21.3908i	−0.478193	−	0.828255i
$668$	11.9354			0.461793
$669$		0			0
$670$			8.75209i			0.338123i
$671$	23.9971	−	41.5641i	0.926397	−	1.60457i
$672$		0			0
$673$	−10.3088	−	17.8554i	−0.397375	−	0.688273i	0.596026	−	0.802965i	$-0.296745\pi$
$673$	−10.3088	−	17.8554i	−0.397375	−	0.688273i	−0.993401	+	0.114692i	$0.963412\pi$
$674$	21.3242	−	12.3115i	0.821378	−	0.474223i
$675$		0			0
$676$	9.55701	−	16.5532i	0.367577	−	0.636663i
$677$	−25.1655	+	43.5880i	−0.967190	+	1.67522i	−0.263578	+	0.964638i	$0.584903\pi$
$677$	−25.1655	+	43.5880i	−0.967190	+	1.67522i	−0.703612	+	0.710585i	$0.748431\pi$
$678$		0			0
$679$		0			0
$680$	−6.32935	−	3.65425i	−0.242719	−	0.140134i
$681$		0			0
$682$			109.734i			4.20193i
$683$	11.9031	+	6.87227i	0.455460	+	0.262960i	0.710133	−	0.704067i	$-0.248635\pi$
$683$	11.9031	+	6.87227i	0.455460	+	0.262960i	−0.254673	+	0.967027i	$0.581968\pi$
$684$		0			0
$685$			28.9909i			1.10769i
$686$		0			0
$687$		0			0
$688$	−45.2560			−1.72537
$689$	1.07705	+	1.86550i	0.0410321	+	0.0710698i
$690$		0			0
$691$	25.4328	+	14.6837i	0.967511	+	0.558593i	0.898476	−	0.439022i	$-0.144675\pi$
$691$	25.4328	+	14.6837i	0.967511	+	0.558593i	0.0690343	+	0.997614i	$0.478008\pi$
$692$	1.49813			0.0569504
$693$		0			0
$694$	−50.5874			−1.92027
$695$	−42.5325	−	24.5562i	−1.61335	−	0.931468i
$696$		0			0
$697$	5.06789	+	8.77784i	0.191960	+	0.332484i
$698$	−65.4785			−2.47840
$699$		0			0
$700$		0			0
$701$			44.2011i			1.66945i	0.550666	+	0.834726i	$0.314374\pi$
$701$			44.2011i			1.66945i	−0.550666	+	0.834726i	$0.685626\pi$
$702$		0			0
$703$	3.15746	+	1.82296i	0.119086	+	0.0687542i
$704$			19.9674i			0.752551i
$705$		0			0
$706$	−4.08702	−	2.35964i	−0.153817	−	0.0888063i
$707$		0			0
$708$		0			0
$709$	5.66629	−	9.81430i	0.212802	−	0.368584i	−0.739788	−	0.672840i	$-0.765074\pi$
$709$	5.66629	−	9.81430i	0.212802	−	0.368584i	0.952590	+	0.304256i	$0.0984077\pi$
$710$	6.91542	−	11.9779i	0.259531	−	0.449521i
$711$		0			0
$712$	−6.21994	+	3.59108i	−0.233102	+	0.134581i
$713$	41.3028	+	71.5385i	1.54680	+	2.67914i
$714$		0			0
$715$	−3.11881	+	5.40193i	−0.116637	+	0.202021i
$716$		−	2.20265i		−	0.0823168i
$717$		0			0
$718$	−13.5827			−0.506903
$719$	18.0647	+	31.2890i	0.673700	+	1.16688i	0.976847	+	0.213939i	$0.0686294\pi$
$719$	18.0647	+	31.2890i	0.673700	+	1.16688i	−0.303147	+	0.952944i	$0.598037\pi$
$720$		0			0
$721$		0			0
$722$	−20.0271	+	11.5627i	−0.745333	+	0.430318i
$723$		0			0
$724$	19.4505	−	11.2298i	0.722874	−	0.417351i
$725$	−3.46580	+	2.00098i	−0.128717	+	0.0743146i
$726$		0			0
$727$	6.20547	−	3.58273i	0.230148	−	0.132876i	−0.380492	−	0.924784i	$-0.624245\pi$
$727$	6.20547	−	3.58273i	0.230148	−	0.132876i	0.610640	+	0.791908i	$0.290912\pi$
$728$		0			0
$729$		0			0
$730$	−19.9485	−	34.5518i	−0.738327	−	1.27882i
$731$	−29.2797			−1.08295
$732$		0			0
$733$			47.8498i			1.76737i	0.468081	+	0.883685i	$0.344945\pi$
$733$			47.8498i			1.76737i	−0.468081	+	0.883685i	$0.655055\pi$
$734$	−12.5938	+	21.8131i	−0.464846	+	0.805136i
$735$		0			0
$736$	27.6034	+	47.8105i	1.01747	+	1.76232i
$737$	−9.07910	+	5.24182i	−0.334433	+	0.193085i
$738$		0			0
$739$	−7.67416	+	13.2920i	−0.282299	+	0.488956i	−0.971951	−	0.235185i	$-0.924430\pi$
$739$	−7.67416	+	13.2920i	−0.282299	+	0.488956i	0.689652	+	0.724141i	$0.257764\pi$
$740$	−2.64917	+	4.58849i	−0.0973853	+	0.168676i
$741$		0			0
$742$		0			0
$743$	−34.9422	−	20.1739i	−1.28191	−	0.740109i	−0.304709	−	0.952445i	$-0.598559\pi$
$743$	−34.9422	−	20.1739i	−1.28191	−	0.740109i	−0.977197	+	0.212337i	$0.931893\pi$
$744$		0			0
$745$		−	39.4409i		−	1.44500i
$746$	38.4630	+	22.2066i	1.40823	+	0.813042i
$747$		0			0
$748$			25.7747i			0.942417i
$749$		0			0
$750$		0			0
$751$	33.8898			1.23665			0.618327	−	0.785921i	$-0.287811\pi$
$751$	33.8898			1.23665			0.618327	+	0.785921i	$0.287811\pi$
$752$	−5.09906	−	8.83183i	−0.185944	−	0.322064i
$753$		0			0
$754$	−2.24793	−	1.29784i	−0.0818647	−	0.0472646i
$755$	−4.96814			−0.180809
$756$		0			0
$757$	−5.73237			−0.208346			−0.104173	−	0.994559i	$-0.533220\pi$
$757$	−5.73237			−0.208346			−0.104173	+	0.994559i	$0.533220\pi$
$758$	34.3589	+	19.8371i	1.24797	+	0.720517i
$759$		0			0
$760$	−3.05642	−	5.29387i	−0.110868	−	0.192029i
$761$	−26.5332			−0.961828			−0.480914	−	0.876768i	$-0.659695\pi$
$761$	−26.5332			−0.961828			−0.480914	+	0.876768i	$0.659695\pi$
$762$		0			0
$763$		0			0
$764$			19.7420i			0.714242i
$765$		0			0
$766$	−20.9741	−	12.1094i	−0.757825	−	0.437531i
$767$			3.24389i			0.117130i
$768$		0			0
$769$	−23.3944	−	13.5068i	−0.843623	−	0.487066i	0.0148711	−	0.999889i	$-0.495266\pi$
$769$	−23.3944	−	13.5068i	−0.843623	−	0.487066i	−0.858494	+	0.512823i	$0.828600\pi$
$770$		0			0
$771$		0			0
$772$	−1.16128	+	2.01139i	−0.0417953	+	0.0723916i
$773$	11.3009	−	19.5737i	0.406464	−	0.704016i	−0.588027	−	0.808841i	$-0.700095\pi$
$773$	11.3009	−	19.5737i	0.406464	−	0.704016i	0.994491	+	0.104826i	$0.0334284\pi$
$774$		0			0
$775$	11.5909	−	6.69201i	0.416357	−	0.240384i
$776$	1.76545	+	3.05784i	0.0633758	+	0.109770i
$777$		0			0
$778$	10.2296	−	17.7182i	0.366750	−	0.635229i
$779$			8.47758i			0.303741i
$780$		0			0
$781$	16.5672			0.592821
$782$	22.6978	+	39.3137i	0.811670	+	1.40585i
$783$		0			0
$784$		0			0
$785$	−18.2114	+	10.5144i	−0.649993	+	0.375274i
$786$		0			0
$787$	22.6864	−	13.0980i	0.808683	−	0.466893i	−0.0378153	−	0.999285i	$-0.512040\pi$
$787$	22.6864	−	13.0980i	0.808683	−	0.466893i	0.846498	+	0.532391i	$0.178707\pi$
$788$	6.41523	−	3.70383i	0.228533	−	0.131944i
$789$		0			0
$790$	2.32900	−	1.34465i	0.0828620	−	0.0478404i
$791$		0			0
$792$		0			0
$793$	−1.89838	−	3.28808i	−0.0674133	−	0.116763i
$794$	55.8627			1.98249
$795$		0			0
$796$		−	16.7091i		−	0.592239i
$797$	−5.96560	+	10.3327i	−0.211312	+	0.366004i	−0.952126	−	0.305707i	$-0.901107\pi$
$797$	−5.96560	+	10.3327i	−0.211312	+	0.366004i	0.740813	+	0.671711i	$0.234440\pi$
$798$		0			0
$799$	−3.29899	−	5.71402i	−0.116710	−	0.202147i
$800$	7.74640	−	4.47239i	0.273877	−	0.158123i
$801$		0			0
$802$	−17.9370	+	31.0678i	−0.633378	+	1.09704i
$803$	23.8952	−	41.3877i	0.843242	−	1.46054i
$804$		0			0
$805$		0			0
$806$	7.51788	+	4.34045i	0.264806	+	0.152886i
$807$		0			0
$808$			7.14038i			0.251198i
$809$	22.9399	+	13.2443i	0.806522	+	0.465646i	0.845747	−	0.533585i	$-0.179155\pi$
$809$	22.9399	+	13.2443i	0.806522	+	0.465646i	−0.0392244	+	0.999230i	$0.512489\pi$
$810$		0			0
$811$		−	13.7419i		−	0.482544i	−0.970458	−	0.241272i	$-0.922435\pi$
$811$		−	13.7419i		−	0.482544i	0.970458	−	0.241272i	$-0.0775646\pi$
$812$		0			0
$813$		0			0
$814$	−14.8488			−0.520449
$815$	1.34571	+	2.33084i	0.0471383	+	0.0816459i
$816$		0			0
$817$	−21.2086	−	12.2448i	−0.741996	−	0.428391i
$818$	−53.8949			−1.88439
$819$		0			0
$820$	−12.3198			−0.430226
$821$	−11.7493	−	6.78346i	−0.410053	−	0.236744i	0.280759	−	0.959778i	$-0.409414\pi$
$821$	−11.7493	−	6.78346i	−0.410053	−	0.236744i	−0.690813	+	0.723034i	$0.742747\pi$
$822$		0			0
$823$	−7.34857	−	12.7281i	−0.256155	−	0.443674i	0.709053	−	0.705155i	$-0.249122\pi$
$823$	−7.34857	−	12.7281i	−0.256155	−	0.443674i	−0.965209	+	0.261481i	$0.915789\pi$
$824$	13.5742			0.472881
$825$		0			0
$826$		0			0
$827$			40.8787i			1.42149i	0.703449	+	0.710746i	$0.251642\pi$
$827$			40.8787i			1.42149i	−0.703449	+	0.710746i	$0.748358\pi$
$828$		0			0
$829$	−17.7189	−	10.2300i	−0.615402	−	0.355302i	0.159675	−	0.987170i	$-0.448955\pi$
$829$	−17.7189	−	10.2300i	−0.615402	−	0.355302i	−0.775077	+	0.631867i	$0.782289\pi$
$830$		−	39.6675i		−	1.37688i
$831$		0			0
$832$	1.36797	+	0.789798i	0.0474258	+	0.0273813i
$833$		0			0
$834$		0			0
$835$	10.0162	−	17.3486i	0.346625	−	0.600372i
$836$	−10.7790	+	18.6698i	−0.372800	+	0.645708i
$837$		0			0
$838$	16.3923	−	9.46412i	0.566264	−	0.326932i
$839$	−27.3475	−	47.3673i	−0.944141	−	1.63530i	−0.757462	−	0.652880i	$-0.773561\pi$
$839$	−27.3475	−	47.3673i	−0.944141	−	1.63530i	−0.186680	−	0.982421i	$-0.559773\pi$
$840$		0			0
$841$	−9.60247	+	16.6320i	−0.331120	+	0.573516i
$842$			47.5062i			1.63717i
$843$		0			0
$844$	22.9321			0.789356
$845$	−16.0405	−	27.7830i	−0.551812	−	0.955766i
$846$		0			0
$847$		0			0
$848$	19.9975	−	11.5456i	0.686718	−	0.396477i
$849$		0			0
$850$	6.36973	−	3.67756i	0.218480	−	0.126139i
$851$	−9.68031	+	5.58893i	−0.331837	+	0.191586i
$852$		0			0
$853$	11.0684	−	6.39037i	0.378976	−	0.218802i	−0.298396	−	0.954442i	$-0.596452\pi$
$853$	11.0684	−	6.39037i	0.378976	−	0.218802i	0.677373	+	0.735640i	$0.263118\pi$
$854$		0			0
$855$		0			0
$856$	6.39058	+	11.0688i	0.218426	+	0.378324i
$857$	18.3240			0.625936			0.312968	−	0.949764i	$-0.398677\pi$
$857$	18.3240			0.625936			0.312968	+	0.949764i	$0.398677\pi$
$858$		0			0
$859$		−	38.6339i		−	1.31817i	−0.752068	−	0.659085i	$-0.770944\pi$
$859$		−	38.6339i		−	1.31817i	0.752068	−	0.659085i	$-0.229056\pi$
$860$	17.7944	−	30.8208i	0.606784	−	1.05098i
$861$		0			0
$862$	−10.1328	−	17.5505i	−0.345125	−	0.597774i
$863$	−14.4626	+	8.35001i	−0.492314	+	0.284238i	−0.725534	−	0.688186i	$-0.758407\pi$
$863$	−14.4626	+	8.35001i	−0.492314	+	0.284238i	0.233220	+	0.972424i	$0.425074\pi$
$864$		0			0
$865$	1.25724	−	2.17760i	0.0427473	−	0.0740405i
$866$	−12.1966	+	21.1251i	−0.414456	+	0.717859i
$867$		0			0
$868$		0			0
$869$	2.78978	+	1.61068i	0.0946367	+	0.0546385i
$870$		0			0
$871$			0.829346i			0.0281013i
$872$	−0.753996	−	0.435320i	−0.0255335	−	0.0147418i
$873$		0			0
$874$			37.9689i			1.28432i
$875$		0			0
$876$		0			0
$877$	33.5234			1.13200			0.566002	−	0.824404i	$-0.308489\pi$
$877$	33.5234			1.13200			0.566002	+	0.824404i	$0.308489\pi$
$878$	29.8606	+	51.7201i	1.00775	+	1.74547i
$879$		0			0
$880$	57.9070	+	33.4326i	1.95204	+	1.12701i
$881$	28.6657			0.965771			0.482885	−	0.875684i	$-0.339589\pi$
$881$	28.6657			0.965771			0.482885	+	0.875684i	$0.339589\pi$
$882$		0			0
$883$	−38.2091			−1.28584			−0.642919	−	0.765935i	$-0.722277\pi$
$883$	−38.2091			−1.28584			−0.642919	+	0.765935i	$0.722277\pi$
$884$	1.76583	+	1.01950i	0.0593912	+	0.0342895i
$885$		0			0
$886$	23.1719	+	40.1350i	0.778476	+	1.34836i
$887$	35.1828			1.18132			0.590662	−	0.806919i	$-0.298867\pi$
$887$	35.1828			1.18132			0.590662	+	0.806919i	$0.298867\pi$
$888$		0			0
$889$		0			0
$890$		−	35.4910i		−	1.18966i
$891$		0			0
$892$	4.13309	+	2.38624i	0.138386	+	0.0798972i
$893$		−	5.51856i		−	0.184672i
$894$		0			0
$895$	−3.20164	−	1.84847i	−0.107019	−	0.0617875i
$896$		0			0
$897$		0			0
$898$	−12.8685	+	22.2890i	−0.429429	+	0.743792i
$899$	−16.3791	+	28.3695i	−0.546274	+	0.946174i
$900$		0			0
$901$	12.9380	−	7.46975i	0.431027	−	0.248854i
$902$	−17.2634	−	29.9010i	−0.574807	−	0.995595i
$903$		0			0
$904$	−2.24557	+	3.88944i	−0.0746866	+	0.129361i
$905$		−	37.6963i		−	1.25307i
$906$		0			0
$907$	−42.5954			−1.41436			−0.707179	−	0.707034i	$-0.750033\pi$
$907$	−42.5954			−1.41436			−0.707179	+	0.707034i	$0.750033\pi$
$908$	10.9505	+	18.9669i	0.363406	+	0.629437i
$909$		0			0
$910$		0			0
$911$	43.5221	−	25.1275i	1.44195	−	0.832510i	0.443970	−	0.896042i	$-0.353570\pi$
$911$	43.5221	−	25.1275i	1.44195	−	0.832510i	0.997980	+	0.0635313i	$0.0202363\pi$
$912$		0			0
$913$	41.1496	−	23.7577i	1.36185	−	0.786265i
$914$	−44.2037	+	25.5210i	−1.46213	+	0.844160i
$915$		0			0
$916$	−4.36754	+	2.52160i	−0.144308	+	0.0833161i
$917$		0			0
$918$		0			0
$919$	29.3486	+	50.8333i	0.968121	+	1.67684i	0.700984	+	0.713177i	$0.252744\pi$
$919$	29.3486	+	50.8333i	0.968121	+	1.67684i	0.267137	+	0.963658i	$0.413922\pi$
$920$	18.7411			0.617875
$921$		0			0
$922$		−	20.6264i		−	0.679295i
$923$	0.655304	−	1.13502i	0.0215696	−	0.0373596i
$924$		0			0
$925$	0.905536	+	1.56843i	0.0297738	+	0.0515698i
$926$	−39.6046	+	22.8657i	−1.30149	+	0.751415i
$927$		0			0
$928$	−10.9465	+	18.9598i	−0.359335	+	0.622387i
$929$	7.19115	−	12.4554i	0.235934	−	0.408650i	−0.723610	−	0.690209i	$-0.757518\pi$
$929$	7.19115	−	12.4554i	0.235934	−	0.408650i	0.959544	+	0.281560i	$0.0908518\pi$
$930$		0			0
$931$		0			0
$932$	−6.30952	−	3.64281i	−0.206675	−	0.119324i
$933$		0			0
$934$		−	29.7251i		−	0.972636i
$935$	37.4646	+	21.6302i	1.22522	+	0.707384i
$936$		0			0
$937$			44.2981i			1.44716i	0.690243	+	0.723578i	$0.257504\pi$
$937$			44.2981i			1.44716i	−0.690243	+	0.723578i	$0.742496\pi$
$938$		0			0
$939$		0			0
$940$	8.01969			0.261573
$941$	7.44400	+	12.8934i	0.242667	+	0.420312i	0.961473	−	0.274899i	$-0.0886443\pi$
$941$	7.44400	+	12.8934i	0.242667	+	0.420312i	−0.718806	+	0.695211i	$0.755311\pi$
$942$		0			0
$943$	−22.5089	−	12.9955i	−0.732990	−	0.423192i
$944$	34.7734			1.13178
$945$		0			0
$946$	99.7390			3.24280
$947$	36.3343	+	20.9776i	1.18071	+	0.681681i	0.956178	−	0.292787i	$-0.0945827\pi$
$947$	36.3343	+	20.9776i	1.18071	+	0.681681i	0.224528	+	0.974468i	$0.427916\pi$
$948$		0			0
$949$	−1.89031	−	3.27412i	−0.0613622	−	0.106282i
$950$	6.15184			0.199592
$951$		0			0
$952$		0			0
$953$		−	13.9821i		−	0.452926i	−0.974020	−	0.226463i	$-0.927284\pi$
$953$		−	13.9821i		−	0.452926i	0.974020	−	0.226463i	$-0.0727162\pi$
$954$		0			0
$955$	28.6959	+	16.5676i	0.928578	+	0.536115i
$956$		−	23.4884i		−	0.759669i
$957$		0			0
$958$	22.4228	+	12.9458i	0.724449	+	0.418261i
$959$		0			0
$960$		0			0
$961$	39.2776	−	68.0309i	1.26702	−	2.19454i
$962$	−0.587333	+	1.01729i	−0.0189364	+	0.0327988i
$963$		0			0
$964$	−0.994743	+	0.574315i	−0.0320385	+	0.0184974i
$965$	1.94910	+	3.37593i	0.0627436	+	0.108675i
$966$		0			0
$967$	−11.5757	+	20.0497i	−0.372249	+	0.644754i	−0.989911	−	0.141690i	$-0.954746\pi$
$967$	−11.5757	+	20.0497i	−0.372249	+	0.644754i	0.617662	+	0.786443i	$0.288080\pi$
$968$			19.3967i			0.623433i
$969$		0			0
$970$	−17.4481			−0.560223
$971$	−21.6869	−	37.5628i	−0.695965	−	1.20545i	−0.969854	−	0.243685i	$-0.921644\pi$
$971$	−21.6869	−	37.5628i	−0.695965	−	1.20545i	0.273890	−	0.961761i	$-0.411690\pi$
$972$		0			0
$973$		0			0
$974$	−46.6120	+	26.9114i	−1.49354	+	0.862298i
$975$		0			0
$976$	−35.2472	+	20.3500i	−1.12824	+	0.651387i
$977$	−10.4210	+	6.01657i	−0.333397	+	0.192487i	−0.657348	−	0.753587i	$-0.728322\pi$
$977$	−10.4210	+	6.01657i	−0.333397	+	0.192487i	0.323951	+	0.946074i	$0.394989\pi$
$978$		0			0
$979$	36.8170	−	21.2563i	1.17668	−	0.679355i
$980$		0			0
$981$		0			0
$982$	36.2152	+	62.7266i	1.15567	+	2.00169i
$983$	6.29658			0.200830			0.100415	−	0.994946i	$-0.467983\pi$
$983$	6.29658			0.200830			0.100415	+	0.994946i	$0.467983\pi$
$984$		0			0
$985$		−	12.4331i		−	0.396151i
$986$	−9.00108	+	15.5903i	−0.286653	+	0.496497i
$987$		0			0
$988$	0.852712	+	1.47694i	0.0271284	+	0.0469877i
$989$	65.0225	−	37.5408i	2.06760	−	1.19373i
$990$		0			0
$991$	−16.7814	+	29.0662i	−0.533078	+	0.923317i	0.466176	+	0.884692i	$0.345631\pi$
$991$	−16.7814	+	29.0662i	−0.533078	+	0.923317i	−0.999254	+	0.0386256i	$0.987702\pi$
$992$	36.6089	−	63.4085i	1.16233	−	2.01322i
$993$		0			0
$994$		0			0
$995$	−24.2874	−	14.0223i	−0.769963	−	0.444538i
$996$		0			0
$997$		−	11.2565i		−	0.356495i	−0.983986	−	0.178248i	$-0.942957\pi$
$997$		−	11.2565i		−	0.356495i	0.983986	−	0.178248i	$-0.0570428\pi$
$998$	−5.61096	−	3.23949i	−0.177612	−	0.102544i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.s.d.962.20		48
3.2	odd	2		441.2.s.d.374.6		48
7.2	even	3		1323.2.i.d.1097.22		48
7.3	odd	6		1323.2.o.e.881.6		48
7.4	even	3		1323.2.o.e.881.5		48
7.5	odd	6		1323.2.i.d.1097.7		48
7.6	odd	2	inner	1323.2.s.d.962.19		48
9.2	odd	6		1323.2.i.d.521.7		48
9.7	even	3		441.2.i.d.227.6		48
21.2	odd	6		441.2.i.d.68.19		48
21.5	even	6		441.2.i.d.68.20		48
21.11	odd	6		441.2.o.e.293.20	yes	48
21.17	even	6		441.2.o.e.293.19	yes	48
21.20	even	2		441.2.s.d.374.5		48
63.2	odd	6	inner	1323.2.s.d.656.19		48
63.11	odd	6		1323.2.o.e.440.6		48
63.16	even	3		441.2.s.d.362.5		48
63.20	even	6		1323.2.i.d.521.22		48
63.25	even	3		441.2.o.e.146.19	✓	48
63.34	odd	6		441.2.i.d.227.5		48
63.38	even	6		1323.2.o.e.440.5		48
63.47	even	6	inner	1323.2.s.d.656.20		48
63.52	odd	6		441.2.o.e.146.20	yes	48
63.61	odd	6		441.2.s.d.362.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.19		48	21.2	odd	6
441.2.i.d.68.20		48	21.5	even	6
441.2.i.d.227.5		48	63.34	odd	6
441.2.i.d.227.6		48	9.7	even	3
441.2.o.e.146.19	✓	48	63.25	even	3
441.2.o.e.146.20	yes	48	63.52	odd	6
441.2.o.e.293.19	yes	48	21.17	even	6
441.2.o.e.293.20	yes	48	21.11	odd	6
441.2.s.d.362.5		48	63.16	even	3
441.2.s.d.362.6		48	63.61	odd	6
441.2.s.d.374.5		48	21.20	even	2
441.2.s.d.374.6		48	3.2	odd	2
1323.2.i.d.521.7		48	9.2	odd	6
1323.2.i.d.521.22		48	63.20	even	6
1323.2.i.d.1097.7		48	7.5	odd	6
1323.2.i.d.1097.22		48	7.2	even	3
1323.2.o.e.440.5		48	63.38	even	6
1323.2.o.e.440.6		48	63.11	odd	6
1323.2.o.e.881.5		48	7.4	even	3
1323.2.o.e.881.6		48	7.3	odd	6
1323.2.s.d.656.19		48	63.2	odd	6	inner
1323.2.s.d.656.20		48	63.47	even	6	inner
1323.2.s.d.962.19		48	7.6	odd	2	inner
1323.2.s.d.962.20		48	1.1	even	1	trivial

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.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.61855 + 0.934468i) q^{2} +(0.746462 + 1.29291i) q^{4} +2.50573 q^{5} -0.947692i q^{8} +(4.05565 + 2.34153i) q^{10} +5.60957i q^{11} +(0.384312 + 0.221883i) q^{13} +(2.37851 - 4.11970i) q^{16} +(1.53885 - 2.66536i) q^{17} +(2.22932 - 1.28710i) q^{19} +(1.87044 + 3.23969i) q^{20} +(-5.24197 + 9.07935i) q^{22} +7.89210i q^{23} +1.27870 q^{25} +(0.414685 + 0.718255i) q^{26} +(-2.71041 + 1.56485i) q^{29} +(9.06457 - 5.23343i) q^{31} +(6.05802 - 3.49760i) q^{32} +(4.98140 - 2.87601i) q^{34} +(0.708168 + 1.22658i) q^{37} +4.81100 q^{38} -2.37466i q^{40} +(-1.64665 + 2.85208i) q^{41} +(-4.75676 - 8.23894i) q^{43} +(-7.25268 + 4.18733i) q^{44} +(-7.37492 + 12.7737i) q^{46} +(1.07190 - 1.85659i) q^{47} +(2.06964 + 1.19491i) q^{50} +0.662509i q^{52} +(4.20379 + 2.42706i) q^{53} +14.0561i q^{55} -5.84923 q^{58} +(3.65496 + 6.33057i) q^{59} +(-7.40950 - 4.27788i) q^{61} +19.5619 q^{62} +3.55953 q^{64} +(0.962984 + 0.555979i) q^{65} +(0.934442 + 1.61850i) q^{67} +4.59477 q^{68} -2.95338i q^{71} +(-7.37804 - 4.25971i) q^{73} +2.64704i q^{74} +(3.32820 + 1.92154i) q^{76} +(0.287130 - 0.497324i) q^{79} +(5.95992 - 10.3229i) q^{80} +(-5.33036 + 3.07748i) q^{82} +(-4.23521 - 7.33560i) q^{83} +(3.85595 - 6.67870i) q^{85} -17.7802i q^{86} +5.31615 q^{88} +(-3.78929 - 6.56325i) q^{89} +(-10.2038 + 5.89115i) q^{92} +(3.46984 - 2.00332i) q^{94} +(5.58607 - 3.22512i) q^{95} +(-3.22662 + 1.86289i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} - 24 q^{16} + 48 q^{25} + 120 q^{32} - 96 q^{44} - 48 q^{50} - 48 q^{53} - 48 q^{64} + 120 q^{65} - 24 q^{79} - 24 q^{85} + 144 q^{92} + 96 q^{95}+O(q^{100}) \) 48 * q + 24 * q^4 - 24 * q^16 + 48 * q^25 + 120 * q^32 - 96 * q^44 - 48 * q^50 - 48 * q^53 - 48 * q^64 + 120 * q^65 - 24 * q^79 - 24 * q^85 + 144 * q^92 + 96 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more