LMFDB - Embedded newform 1323.2.i.d.1097.22

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			1097.22
Character	$\chi$	$=$	1323.1097
Dual form			1323.2.i.d.521.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.86894i q^{2} -1.49292 q^{4} +(-1.25287 - 2.17003i) q^{5} -0.947692i q^{8} +(-4.05565 + 2.34153i) q^{10} +(-4.85803 - 2.80479i) q^{11} +(0.384312 + 0.221883i) q^{13} -4.75703 q^{16} +(1.53885 + 2.66536i) q^{17} +(-2.22932 - 1.28710i) q^{19} +(1.87044 + 3.23969i) q^{20} +(-5.24197 + 9.07935i) q^{22} +(6.83476 - 3.94605i) q^{23} +(-0.639351 + 1.10739i) q^{25} +(0.414685 - 0.718255i) q^{26} +(-2.71041 + 1.56485i) q^{29} +10.4669i q^{31} +6.99520i q^{32} +(4.98140 - 2.87601i) q^{34} +(0.708168 - 1.22658i) q^{37} +(-2.40550 + 4.16645i) q^{38} +(-2.05652 + 1.18733i) q^{40} +(-1.64665 + 2.85208i) q^{41} +(-4.75676 - 8.23894i) q^{43} +(7.25268 + 4.18733i) q^{44} +(-7.37492 - 12.7737i) q^{46} -2.14380 q^{47} +(2.06964 + 1.19491i) q^{50} +(-0.573749 - 0.331254i) q^{52} +(-4.20379 + 2.42706i) q^{53} +14.0561i q^{55} +(2.92461 + 5.06558i) q^{58} -7.30991 q^{59} +8.55576i q^{61} +19.5619 q^{62} +3.55953 q^{64} -1.11196i q^{65} -1.86888 q^{67} +(-2.29739 - 3.97919i) q^{68} -2.95338i q^{71} +(7.37804 - 4.25971i) q^{73} +(-2.29241 - 1.32352i) q^{74} +(3.32820 + 1.92154i) q^{76} -0.574261 q^{79} +(5.95992 + 10.3229i) q^{80} +(5.33036 + 3.07748i) q^{82} +(-4.23521 - 7.33560i) q^{83} +(3.85595 - 6.67870i) q^{85} +(-15.3981 + 8.89008i) q^{86} +(-2.65807 + 4.60392i) q^{88} +(-3.78929 + 6.56325i) q^{89} +(-10.2038 + 5.89115i) q^{92} +4.00663i q^{94} +6.45024i q^{95} +(-3.22662 + 1.86289i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	1.86894i		−	1.32154i	−0.750589	−	0.660769i	$-0.770230\pi$
$2$		−	1.86894i		−	1.32154i	0.750589	−	0.660769i	$-0.229770\pi$
$3$		0			0
$3$		0			0
$4$	−1.49292			−0.746462
$5$	−1.25287	−	2.17003i	−0.560299	−	0.970467i	−0.997470	−	0.0710881i	$-0.977353\pi$
$5$	−1.25287	−	2.17003i	−0.560299	−	0.970467i	0.437171	−	0.899378i	$-0.355980\pi$
$6$		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
$11$	−4.85803	−	2.80479i	−1.46475	−	0.845675i	−0.465527	−	0.885034i	$-0.654135\pi$
$11$	−4.85803	−	2.80479i	−1.46475	−	0.845675i	−0.999225	+	0.0393590i	$0.987468\pi$
$12$		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
$16$	−4.75703			−1.18926
$17$	1.53885	+	2.66536i	0.373226	+	0.646446i	0.990060	−	0.140647i	$-0.0449184\pi$
$17$	1.53885	+	2.66536i	0.373226	+	0.646446i	−0.616834	+	0.787093i	$0.711585\pi$
$18$		0			0
$19$	−2.22932	−	1.28710i	−0.511440	−	0.295280i	0.221985	−	0.975050i	$-0.428746\pi$
$19$	−2.22932	−	1.28710i	−0.511440	−	0.295280i	−0.733425	+	0.679770i	$0.762080\pi$
$20$	1.87044	+	3.23969i	0.418242	+	0.724417i
$21$		0			0
$22$	−5.24197	+	9.07935i	−1.11759	+	1.93572i
$23$	6.83476	−	3.94605i	1.42515	−	0.822808i	0.428413	−	0.903583i	$-0.359073\pi$
$23$	6.83476	−	3.94605i	1.42515	−	0.822808i	0.996732	+	0.0807749i	$0.0257395\pi$
$24$		0			0
$25$	−0.639351	+	1.10739i	−0.127870	+	0.221478i
$26$	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
$31$			10.4669i			1.87990i	0.341306	+	0.939952i	$0.389131\pi$
$31$			10.4669i			1.87990i	−0.341306	+	0.939952i	$0.610869\pi$
$32$			6.99520i			1.23659i
$33$		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	−0.801925	−	0.597424i	$-0.796191\pi$
$37$	0.708168	−	1.22658i	0.116422	−	0.201649i	0.918347	+	0.395775i	$0.129524\pi$
$38$	−2.40550	+	4.16645i	−0.390224	+	0.675887i
$39$		0			0
$40$	−2.05652	+	1.18733i	−0.325164	+	0.187734i
$41$	−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
$47$	−2.14380			−0.312706			−0.156353	−	0.987701i	$-0.549974\pi$
$47$	−2.14380			−0.312706			−0.156353	+	0.987701i	$0.549974\pi$
$48$		0			0
$49$		0			0
$50$	2.06964	+	1.19491i	0.292691	+	0.168985i
$51$		0			0
$52$	−0.573749	−	0.331254i	−0.0795647	−	0.0459367i
$53$	−4.20379	+	2.42706i	−0.577435	+	0.333382i	−0.760113	−	0.649791i	$-0.774857\pi$
$53$	−4.20379	+	2.42706i	−0.577435	+	0.333382i	0.182678	+	0.983173i	$0.441523\pi$
$54$		0			0
$55$			14.0561i			1.89532i
$56$		0			0
$57$		0			0
$58$	2.92461	+	5.06558i	0.384020	+	0.665143i
$59$	−7.30991			−0.951669			−0.475835	−	0.879535i	$-0.657854\pi$
$59$	−7.30991			−0.951669			−0.475835	+	0.879535i	$0.657854\pi$
$60$		0			0
$61$			8.55576i			1.09545i	0.836658	+	0.547726i	$0.184506\pi$
$61$			8.55576i			1.09545i	−0.836658	+	0.547726i	$0.815494\pi$
$62$	19.5619			2.48437
$63$		0			0
$64$	3.55953			0.444941
$65$		−	1.11196i		−	0.137921i
$66$		0			0
$67$	−1.86888			−0.228321			−0.114160	−	0.993462i	$-0.536418\pi$
$67$	−1.86888			−0.228321			−0.114160	+	0.993462i	$0.536418\pi$
$68$	−2.29739	−	3.97919i	−0.278599	−	0.482548i
$69$		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	$-0.500528\pi$
$73$	7.37804	−	4.25971i	0.863534	−	0.498562i	0.865194	+	0.501437i	$0.167195\pi$
$74$	−2.29241	−	1.32352i	−0.266487	−	0.153856i
$75$		0			0
$76$	3.32820	+	1.92154i	0.381771	+	0.220415i
$77$		0			0
$78$		0			0
$79$	−0.574261			−0.0646094			−0.0323047	−	0.999478i	$-0.510285\pi$
$79$	−0.574261			−0.0646094			−0.0323047	+	0.999478i	$0.510285\pi$
$80$	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
$86$	−15.3981	+	8.89008i	−1.66042	+	0.958642i
$87$		0			0
$88$	−2.65807	+	4.60392i	−0.283352	+	0.490779i
$89$	−3.78929	+	6.56325i	−0.401664	+	0.695703i	−0.993927	−	0.110042i	$-0.964901\pi$
$89$	−3.78929	+	6.56325i	−0.401664	+	0.695703i	0.592263	+	0.805745i	$0.298235\pi$
$90$		0			0
$91$		0			0
$92$	−10.2038	+	5.89115i	−1.06382	+	0.614195i
$93$		0			0
$94$			4.00663i			0.413252i
$95$			6.45024i			0.661781i
$96$		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
$101$	3.76725	−	6.52506i	0.374855	−	0.649268i	−0.615450	−	0.788176i	$-0.711026\pi$
$101$	3.76725	−	6.52506i	0.374855	−	0.649268i	0.990305	+	0.138908i	$0.0443592\pi$
$102$		0			0
$103$	12.4045	−	7.16173i	1.22225	−	0.705666i	0.256853	−	0.966451i	$-0.417315\pi$
$103$	12.4045	−	7.16173i	1.22225	−	0.705666i	0.965397	+	0.260784i	$0.0839812\pi$
$104$	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	$-0.107305\pi$
$107$	11.6798	+	6.74331i	1.12912	+	0.651900i	0.185410	+	0.982661i	$0.440639\pi$
$108$		0			0
$109$	0.459348	+	0.795613i	0.0439975	+	0.0762059i	0.887186	−	0.461413i	$-0.152657\pi$
$109$	0.459348	+	0.795613i	0.0439975	+	0.0762059i	−0.843188	+	0.537619i	$0.819324\pi$
$110$	26.2700			2.50474
$111$		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
$115$	−17.1261	−	9.88775i	−1.59702	−	0.922037i
$116$	4.04643	−	2.33621i	0.375702	−	0.216912i
$117$		0			0
$118$			13.6618i			1.25767i
$119$		0			0
$120$		0			0
$121$	10.2337	+	17.7252i	0.930332	+	1.61138i
$122$	15.9902			1.44768
$123$		0			0
$124$		−	15.6262i		−	1.40328i
$125$	−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	$0.393929\pi$
$128$			7.33786i			0.648581i
$129$		0			0
$130$	−2.07818			−0.182268
$131$	−3.93150	−	6.80955i	−0.343497	−	0.594953i	0.641583	−	0.767054i	$-0.278278\pi$
$131$	−3.93150	−	6.80955i	−0.343497	−	0.594953i	−0.985079	+	0.172100i	$0.944945\pi$
$132$		0			0
$133$		0			0
$134$			3.49283i			0.301734i
$135$		0			0
$136$	2.52594	−	1.45835i	0.216598	−	0.125053i
$137$	−10.0198	−	5.78491i	−0.856046	−	0.494238i	0.00664016	−	0.999978i	$-0.497886\pi$
$137$	−10.0198	−	5.78491i	−0.856046	−	0.494238i	−0.862686	+	0.505740i	$0.831220\pi$
$138$		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
$142$	−5.51968			−0.463201
$143$	−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
$149$	−13.6315	+	7.87012i	−1.11673	+	0.644746i	−0.940565	−	0.339615i	$-0.889703\pi$
$149$	−13.6315	+	7.87012i	−1.11673	+	0.644746i	−0.176167	+	0.984360i	$0.556370\pi$
$150$		0			0
$151$	0.991353	−	1.71707i	0.0806752	−	0.139734i	−0.822865	−	0.568237i	$-0.807626\pi$
$151$	0.991353	−	1.71707i	0.0806752	−	0.139734i	0.903540	+	0.428503i	$0.140959\pi$
$152$	−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
$157$		−	8.39224i		−	0.669774i	−0.942258	−	0.334887i	$-0.891302\pi$
$157$		−	8.39224i		−	0.669774i	0.942258	−	0.334887i	$-0.108698\pi$
$158$			1.07326i			0.0853837i
$159$		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	−0.844226	−	0.535987i	$-0.819940\pi$
$163$	0.537054	−	0.930204i	0.0420653	−	0.0728592i	0.886291	+	0.463128i	$0.153273\pi$
$164$	2.45832	−	4.25794i	0.191963	−	0.332489i
$165$		0			0
$166$	−13.7098	+	7.91534i	−1.06408	+	0.614349i
$167$	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
$173$	−1.00349			−0.0762938			−0.0381469	−	0.999272i	$-0.512145\pi$
$173$	−1.00349			−0.0762938			−0.0381469	+	0.999272i	$0.512145\pi$
$174$		0			0
$175$		0			0
$176$	23.1098	+	13.3424i	1.74197	+	1.00572i
$177$		0			0
$178$	12.2663	+	7.08195i	0.919398	+	0.530814i
$179$	1.27773	−	0.737695i	0.0955017	−	0.0551379i	−0.451489	−	0.892277i	$-0.649107\pi$
$179$	1.27773	−	0.737695i	0.0955017	−	0.0551379i	0.546990	+	0.837139i	$0.315773\pi$
$180$		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
$184$	−3.73964	−	6.47724i	−0.275690	−	0.477509i
$185$	−3.54896			−0.260925
$186$		0			0
$187$		−	17.2646i		−	1.26251i
$188$	3.20054			0.233423
$189$		0			0
$190$	12.0551			0.874568
$191$		−	13.2237i		−	0.956836i	−0.878132	−	0.478418i	$-0.841210\pi$
$191$		−	13.2237i		−	0.956836i	0.878132	−	0.478418i	$-0.158790\pi$
$192$		0			0
$193$	−1.55571			−0.111982			−0.0559912	−	0.998431i	$-0.517832\pi$
$193$	−1.55571			−0.111982			−0.0559912	+	0.998431i	$0.517832\pi$
$194$	3.48163	+	6.03035i	0.249966	+	0.432954i
$195$		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	$-0.536823\pi$
$199$	9.69273	−	5.59610i	0.687100	−	0.396697i	0.802525	+	0.596619i	$0.203490\pi$
$200$	1.04946	+	0.605908i	0.0742083	+	0.0428442i
$201$		0			0
$202$	−12.1949	−	7.04074i	−0.858032	−	0.495385i
$203$		0			0
$204$		0			0
$205$	8.25213			0.576354
$206$	−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	$-0.0106654\pi$
$212$	6.27594	−	3.62342i	0.431033	−	0.248857i
$213$		0			0
$214$	12.6028	−	21.8287i	0.861511	−	1.49218i
$215$	−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
$220$		−	20.9847i		−	1.41479i
$221$			1.36578i			0.0918721i
$222$		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
$227$	−7.33494	+	12.7045i	−0.486837	+	0.843227i	−0.999885	−	0.0151329i	$-0.995183\pi$
$227$	−7.33494	+	12.7045i	−0.486837	+	0.843227i	0.513048	+	0.858360i	$0.328516\pi$
$228$		0			0
$229$	2.92550	−	1.68904i	0.193322	−	0.111615i	−0.400215	−	0.916421i	$-0.631064\pi$
$229$	2.92550	−	1.68904i	0.193322	−	0.111615i	0.593537	+	0.804807i	$0.297731\pi$
$230$	−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	$-0.282231\pi$
$233$	4.22628	+	2.44005i	0.276873	+	0.159853i	−0.355134	+	0.934815i	$0.615565\pi$
$234$		0			0
$235$	2.68590	+	4.65211i	0.175209	+	0.303470i
$236$	10.9131			0.710385
$237$		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
$241$	−0.666305	−	0.384691i	−0.0429205	−	0.0247801i	0.478386	−	0.878150i	$-0.341222\pi$
$241$	−0.666305	−	0.384691i	−0.0429205	−	0.0247801i	−0.521307	+	0.853369i	$0.674555\pi$
$242$	33.1273	−	19.1260i	2.12950	−	1.22947i
$243$		0			0
$244$		−	12.7731i		−	0.817714i
$245$		0			0
$246$		0			0
$247$	−0.571169	−	0.989293i	−0.0363426	−	0.0629472i
$248$	9.91936			0.629880
$249$		0			0
$250$			17.4271i			1.10218i
$251$	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
$254$		−	13.7787i		−	0.864549i
$255$		0			0
$256$	20.8331			1.30207
$257$	−14.4917	−	25.1004i	−0.903969	−	1.56572i	−0.822295	−	0.569061i	$-0.807307\pi$
$257$	−14.4917	−	25.1004i	−0.903969	−	1.56572i	−0.0816738	−	0.996659i	$-0.526027\pi$
$258$		0			0
$259$		0			0
$260$			1.66007i			0.102953i
$261$		0			0
$262$	−12.7266	+	7.34772i	−0.786254	+	0.453944i
$263$	11.8643	+	6.84988i	0.731586	+	0.422381i	0.819002	−	0.573790i	$-0.194528\pi$
$263$	11.8643	+	6.84988i	0.731586	+	0.422381i	−0.0874160	+	0.996172i	$0.527861\pi$
$264$		0			0
$265$	10.5336	+	6.08156i	0.647072	+	0.373587i
$266$		0			0
$267$		0			0
$268$	2.79010			0.170433
$269$	−5.23973	−	9.07548i	−0.319472	−	0.553342i	0.660906	−	0.750469i	$-0.270172\pi$
$269$	−5.23973	−	9.07548i	−0.319472	−	0.553342i	−0.980378	+	0.197127i	$0.936839\pi$
$270$		0			0
$271$	−5.66907	−	3.27304i	−0.344371	−	0.198823i	0.317832	−	0.948147i	$-0.397045\pi$
$271$	−5.66907	−	3.27304i	−0.344371	−	0.198823i	−0.662203	+	0.749324i	$0.730379\pi$
$272$	−7.32034	−	12.6792i	−0.443861	−	0.768790i
$273$		0			0
$274$	−10.8116	+	18.7263i	−0.653155	+	1.13130i
$275$	6.21198	−	3.58649i	0.374596	−	0.216273i
$276$		0			0
$277$	−11.2156	+	19.4261i	−0.673883	+	1.16720i	0.302911	+	0.953019i	$0.402041\pi$
$277$	−11.2156	+	19.4261i	−0.673883	+	1.16720i	−0.976794	+	0.214181i	$0.931292\pi$
$278$	−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
$283$			18.9713i			1.12772i	0.825869	+	0.563862i	$0.190685\pi$
$283$			18.9713i			1.12772i	−0.825869	+	0.563862i	$0.809315\pi$
$284$			4.40917i			0.261636i
$285$		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
$290$	7.32830	−	12.6930i	0.430333	−	0.745358i
$291$		0			0
$292$	−11.0149	+	6.35943i	−0.644596	+	0.372158i
$293$	−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
$299$	3.50224			0.202540
$300$		0			0
$301$		0			0
$302$	−3.20910	−	1.85278i	−0.184663	−	0.106615i
$303$		0			0
$304$	10.6049	+	6.12275i	0.608233	+	0.351164i
$305$	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
$310$	−24.5085	−	42.4499i	−1.39199	−	2.41099i
$311$	−13.2859			−0.753373			−0.376687	−	0.926341i	$-0.622937\pi$
$311$	−13.2859			−0.753373			−0.376687	+	0.926341i	$0.622937\pi$
$312$		0			0
$313$			31.5495i			1.78329i	0.452740	+	0.891643i	$0.350447\pi$
$313$			31.5495i			1.78329i	−0.452740	+	0.891643i	$0.649553\pi$
$314$	−15.6846			−0.885132
$315$		0			0
$316$	0.857328			0.0482285
$317$		−	20.0709i		−	1.12729i	−0.826016	−	0.563646i	$-0.809398\pi$
$317$		−	20.0709i		−	1.12729i	0.826016	−	0.563646i	$-0.190602\pi$
$318$		0			0
$319$	17.5563			0.982965
$320$	−4.45961	−	7.72428i	−0.249300	−	0.431800i
$321$		0			0
$322$		0			0
$323$		−	7.92259i		−	0.440824i
$324$		0			0
$325$	−0.491421	+	0.283722i	−0.0272591	+	0.0157381i
$326$	−1.73849	−	1.00372i	−0.0962862	−	0.0555909i
$327$		0			0
$328$	2.70289	+	1.56052i	0.149242	+	0.0861651i
$329$		0			0
$330$		0			0
$331$	1.24791			0.0685915			0.0342958	−	0.999412i	$-0.489081\pi$
$331$	1.24791			0.0685915			0.0342958	+	0.999412i	$0.489081\pi$
$332$	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	$0.0498385\pi$
$338$	−20.7224	+	11.9641i	−1.12715	+	0.650759i
$339$		0			0
$340$	−5.75664	+	9.97079i	−0.312198	+	0.540742i
$341$	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
$346$			1.87545i			0.100825i
$347$		−	27.0675i		−	1.45306i	−0.687136	−	0.726529i	$-0.741132\pi$
$347$		−	27.0675i		−	1.45306i	0.687136	−	0.726529i	$-0.258868\pi$
$348$		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
$353$	1.26256	−	2.18682i	0.0671992	−	0.116392i	−0.830468	−	0.557066i	$-0.811927\pi$
$353$	1.26256	−	2.18682i	0.0671992	−	0.116392i	0.897667	+	0.440674i	$0.145260\pi$
$354$		0			0
$355$	−6.40892	+	3.70019i	−0.340150	+	0.196386i
$356$	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	$-0.271906\pi$
$359$	6.29395	+	3.63381i	0.332182	+	0.191785i	−0.324628	+	0.945842i	$0.605239\pi$
$360$		0			0
$361$	−6.18677	−	10.7158i	−0.325619	−	0.563989i
$362$	−28.1163			−1.47776
$363$		0			0
$364$		0			0
$365$	−18.4874	−	10.6737i	−0.967675	−	0.558688i
$366$		0			0
$367$	−11.6714	−	6.73848i	−0.609242	−	0.351746i	0.163427	−	0.986555i	$-0.447745\pi$
$367$	−11.6714	−	6.73848i	−0.609242	−	0.351746i	−0.772669	+	0.634809i	$0.781079\pi$
$368$	−32.5131	+	18.7715i	−1.69486	+	0.978530i
$369$		0			0
$370$			6.63278i			0.344822i
$371$		0			0
$372$		0			0
$373$	−11.8820	−	20.5801i	−0.615224	−	1.06560i	−0.990345	−	0.138624i	$-0.955732\pi$
$373$	−11.8820	−	20.5801i	−0.615224	−	1.06560i	0.375121	−	0.926976i	$-0.377601\pi$
$374$	−32.2664			−1.66846
$375$		0			0
$376$			2.03166i			0.104775i
$377$	−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	$0.316449\pi$
$380$		−	9.62972i		−	0.493994i
$381$		0			0
$382$	−24.7143			−1.26450
$383$	6.47930	+	11.2225i	0.331077	+	0.573442i	0.982723	−	0.185081i	$-0.0592547\pi$
$383$	6.47930	+	11.2225i	0.331077	+	0.573442i	−0.651646	+	0.758523i	$0.725921\pi$
$384$		0			0
$385$		0			0
$386$			2.90752i			0.147989i
$387$		0			0
$388$	4.81710	−	2.78116i	0.244551	−	0.141192i
$389$	9.48037	+	5.47350i	0.480674	+	0.277517i	0.720697	−	0.693250i	$-0.243822\pi$
$389$	9.48037	+	5.47350i	0.480674	+	0.277517i	−0.240023	+	0.970767i	$0.577155\pi$
$390$		0			0
$391$	21.0353	+	12.1447i	1.06380	+	0.614186i
$392$		0			0
$393$		0			0
$394$	−9.27338			−0.467186
$395$	0.719472	+	1.24616i	0.0362006	+	0.0627012i
$396$		0			0
$397$	−25.8856	−	14.9451i	−1.29916	−	0.750071i	−0.318901	−	0.947788i	$-0.603314\pi$
$397$	−25.8856	−	14.9451i	−1.29916	−	0.750071i	−0.980259	+	0.197717i	$0.936647\pi$
$398$	−10.4588	−	18.1151i	−0.524250	−	0.908028i
$399$		0			0
$400$	3.04141	−	5.26788i	0.152071	−	0.263394i
$401$	16.6233	−	9.59744i	0.830126	−	0.479273i	−0.0237698	−	0.999717i	$-0.507567\pi$
$401$	16.6233	−	9.59744i	0.830126	−	0.479273i	0.853896	+	0.520444i	$0.174234\pi$
$402$		0			0
$403$	−2.32242	+	4.02254i	−0.115688	+	0.200377i
$404$	−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
$409$		−	28.8372i		−	1.42591i	−0.701212	−	0.712953i	$-0.747357\pi$
$409$		−	28.8372i		−	1.42591i	0.701212	−	0.712953i	$-0.252643\pi$
$410$		−	15.4227i		−	0.761673i
$411$		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
$416$	−1.55211	+	2.68834i	−0.0760986	+	0.131807i
$417$		0			0
$418$	23.3720	−	13.4938i	1.14316	−	0.660005i
$419$	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
$425$	−3.93546			−0.190898
$426$		0			0
$427$		0			0
$428$	−17.4370	−	10.0673i	−0.842849	−	0.486619i
$429$		0			0
$430$	38.5834	+	22.2762i	1.86066	+	1.07425i
$431$	9.39066	−	5.42170i	0.452332	−	0.261154i	−0.256482	−	0.966549i	$-0.582564\pi$
$431$	9.39066	−	5.42170i	0.452332	−	0.261154i	0.708815	+	0.705395i	$0.249230\pi$
$432$		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
$436$	−0.685771	−	1.18779i	−0.0328425	−	0.0568849i
$437$	−20.3158			−0.971835
$438$		0			0
$439$		−	31.9547i		−	1.52511i	−0.646922	−	0.762557i	$-0.723944\pi$
$439$		−	31.9547i		−	1.52511i	0.646922	−	0.762557i	$-0.276056\pi$
$440$	13.3208			0.635046
$441$		0			0
$442$	2.55255			0.121412
$443$		−	24.7969i		−	1.17814i	−0.808083	−	0.589068i	$-0.799495\pi$
$443$		−	24.7969i		−	1.17814i	0.808083	−	0.589068i	$-0.200505\pi$
$444$		0			0
$445$	18.9899			0.900208
$446$	−2.98724	−	5.17406i	−0.141450	−	0.244999i
$447$		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
$452$	6.12715	+	3.53751i	0.288197	+	0.166390i
$453$		0			0
$454$	23.7439	+	13.7085i	1.11436	+	0.643374i
$455$		0			0
$456$		0			0
$457$	27.3107			1.27754			0.638771	−	0.769397i	$-0.279443\pi$
$457$	27.3107			1.27754			0.638771	+	0.769397i	$0.279443\pi$
$458$	−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	$0.974155\pi$
$464$	12.8935	−	7.44405i	0.598564	−	0.345581i
$465$		0			0
$466$	4.56029	−	7.89866i	0.211251	−	0.365898i
$467$	−7.95241	+	13.7740i	−0.367994	+	0.637384i	−0.989252	−	0.146222i	$-0.953289\pi$
$467$	−7.95241	+	13.7740i	−0.367994	+	0.637384i	0.621258	+	0.783606i	$0.286622\pi$
$468$		0			0
$469$		0			0
$470$	8.69451	−	5.01978i	0.401048	−	0.231545i
$471$		0			0
$472$			6.92754i			0.318866i
$473$			53.3667i			2.45380i
$474$		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
$479$	−6.92685	+	11.9976i	−0.316496	+	0.548187i	−0.979754	−	0.200204i	$-0.935840\pi$
$479$	−6.92685	+	11.9976i	−0.316496	+	0.548187i	0.663259	+	0.748390i	$0.269173\pi$
$480$		0			0
$481$	0.544315	−	0.314261i	0.0248186	−	0.0143290i
$482$	−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	−0.982515	−	0.186182i	$-0.940389\pi$
$487$	−14.3993	−	24.9404i	−0.652496	−	1.13016i	0.330020	−	0.943974i	$-0.392945\pi$
$488$	8.10822			0.367042
$489$		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
$493$	−8.34181	−	4.81615i	−0.375696	−	0.216908i
$494$	−1.84893	+	1.06748i	−0.0831872	+	0.0480281i
$495$		0			0
$496$		−	49.7911i		−	2.23569i
$497$		0			0
$498$		0			0
$499$	1.73333	+	3.00222i	0.0775946	+	0.134398i	0.902212	−	0.431294i	$-0.141943\pi$
$499$	1.73333	+	3.00222i	0.0775946	+	0.134398i	−0.824617	+	0.565691i	$0.808609\pi$
$500$	13.9209			0.622561
$501$		0			0
$502$		−	2.14076i		−	0.0955467i
$503$	−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
$506$			82.7403i			3.67825i
$507$		0			0
$508$	−11.0065			−0.488335
$509$	17.9062	+	31.0144i	0.793678	+	1.37469i	0.923675	+	0.383176i	$0.125170\pi$
$509$	17.9062	+	31.0144i	0.793678	+	1.37469i	−0.129997	+	0.991514i	$0.541497\pi$
$510$		0			0
$511$		0			0
$512$		−	24.2599i		−	1.07215i
$513$		0			0
$514$	−46.9111	+	27.0841i	−2.06916	+	1.19463i
$515$	−31.0823	−	17.9454i	−1.36965	−	0.790768i
$516$		0			0
$517$	10.4147	+	6.01291i	0.458036	+	0.264447i
$518$		0			0
$519$		0			0
$520$	−1.05379			−0.0462119
$521$	13.4608	+	23.3148i	0.589729	+	1.02144i	0.994268	+	0.106920i	$0.0340989\pi$
$521$	13.4608	+	23.3148i	0.589729	+	1.02144i	−0.404538	+	0.914521i	$0.632568\pi$
$522$		0			0
$523$	−7.82181	−	4.51593i	−0.342024	−	0.197468i	0.319143	−	0.947707i	$-0.396605\pi$
$523$	−7.82181	−	4.51593i	−0.342024	−	0.197468i	−0.661167	+	0.750239i	$0.729938\pi$
$524$	5.86943	+	10.1662i	0.256407	+	0.444110i
$525$		0			0
$526$	12.8020	−	22.1737i	0.558193	−	0.966819i
$527$	−27.8980	+	16.1069i	−1.21526	+	0.701629i
$528$		0			0
$529$	19.6426	−	34.0220i	0.854026	−	1.47922i
$530$	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
$535$		−	33.7939i		−	1.46104i
$536$			1.77113i			0.0765010i
$537$		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	−0.961760	−	0.273892i	$-0.911689\pi$
$541$	−5.66792	+	9.81713i	−0.243683	+	0.422071i	0.718078	+	0.695963i	$0.245022\pi$
$542$	−6.11710	+	10.5951i	−0.262752	+	0.455100i
$543$		0			0
$544$	−18.6447	+	10.7646i	−0.799387	+	0.461526i
$545$	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
$551$	8.05647			0.343217
$552$		0			0
$553$		0			0
$554$	36.3061	+	20.9613i	1.54250	+	0.890562i
$555$		0			0
$556$	25.3410	+	14.6306i	1.07470	+	0.620478i
$557$	6.29167	−	3.63249i	0.266586	−	0.153914i	−0.360749	−	0.932663i	$-0.617479\pi$
$557$	6.29167	−	3.63249i	0.266586	−	0.153914i	0.627335	+	0.778749i	$0.284146\pi$
$558$		0			0
$559$		−	4.22177i		−	0.178562i
$560$		0			0
$561$		0			0
$562$	20.8848	+	36.1736i	0.880973	+	1.52589i
$563$	23.0818			0.972780			0.486390	−	0.873742i	$-0.338313\pi$
$563$	23.0818			0.972780			0.486390	+	0.873742i	$0.338313\pi$
$564$		0			0
$565$			11.8748i			0.499575i
$566$	35.4561			1.49033
$567$		0			0
$568$	−2.79889			−0.117439
$569$			17.9535i			0.752651i	0.926487	+	0.376326i	$0.122813\pi$
$569$			17.9535i			0.752651i	−0.926487	+	0.376326i	$0.877187\pi$
$570$		0			0
$571$	−14.0847			−0.589425			−0.294713	−	0.955586i	$-0.595224\pi$
$571$	−14.0847			−0.589425			−0.294713	+	0.955586i	$0.595224\pi$
$572$	1.85819	+	3.21849i	0.0776950	+	0.134572i
$573$		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	$-0.881919\pi$
$577$	−26.0392	+	15.0337i	−1.08403	+	0.625862i	−0.152046	+	0.988373i	$0.548586\pi$
$578$	−12.1841	−	7.03447i	−0.506790	−	0.292595i
$579$		0			0
$580$	−10.1393	−	5.85392i	−0.421011	−	0.243071i
$581$		0			0
$582$		0			0
$583$	27.2295			1.12773
$584$	−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
$590$	29.6464	−	17.1164i	1.22052	−	0.704670i
$591$		0			0
$592$	−3.36877	+	5.83489i	−0.138456	+	0.239812i
$593$	1.02158	−	1.76943i	0.0419514	−	0.0726620i	−0.844287	−	0.535891i	$-0.819976\pi$
$593$	1.02158	−	1.76943i	0.0419514	−	0.0726620i	0.886239	+	0.463229i	$0.153309\pi$
$594$		0			0
$595$		0			0
$596$	20.3507	−	11.7495i	0.833598	−	0.481278i
$597$		0			0
$598$		−	6.54547i		−	0.267664i
$599$		−	18.2296i		−	0.744840i	−0.928064	−	0.372420i	$-0.878528\pi$
$599$		−	18.2296i		−	0.744840i	0.928064	−	0.372420i	$-0.121472\pi$
$600$		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
$605$	25.6428	−	44.4146i	1.04253	−	1.80571i
$606$		0			0
$607$	17.1730	−	9.91482i	0.697030	−	0.402430i	−0.109211	−	0.994019i	$-0.534832\pi$
$607$	17.1730	−	9.91482i	0.697030	−	0.402430i	0.806240	+	0.591588i	$0.201499\pi$
$608$	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	0.965231	−	0.261400i	$-0.0841840\pi$
$613$	6.34412	+	10.9883i	0.256237	+	0.443815i	−0.708994	+	0.705214i	$0.750851\pi$
$614$	−53.7381			−2.16869
$615$		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
$619$	0.231999	+	0.133945i	0.00932485	+	0.00538370i	0.504655	−	0.863321i	$-0.331620\pi$
$619$	0.231999	+	0.133945i	0.00932485	+	0.00538370i	−0.495330	+	0.868705i	$0.664953\pi$
$620$	−33.9094	+	19.5776i	−1.36183	+	0.786255i
$621$		0			0
$622$			24.8305i			0.995611i
$623$		0			0
$624$		0			0
$625$	14.8792	+	25.7716i	0.595169	+	1.03086i
$626$	58.9641			2.35668
$627$		0			0
$628$			12.5290i			0.499961i
$629$	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	$0.228994\pi$
$632$			0.544222i			0.0216480i
$633$		0			0
$634$	−37.5112			−1.48976
$635$	−9.23671	−	15.9984i	−0.366547	−	0.634879i
$636$		0			0
$637$		0			0
$638$		−	32.8117i		−	1.29903i
$639$		0			0
$640$	15.9234	−	9.19336i	0.629426	−	0.363400i
$641$	29.7991	+	17.2045i	1.17699	+	0.679537i	0.955317	−	0.295583i	$-0.0955140\pi$
$641$	29.7991	+	17.2045i	1.17699	+	0.679537i	0.221676	+	0.975120i	$0.428847\pi$
$642$		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
$646$	−14.8068			−0.582566
$647$	9.82182	+	17.0119i	0.386136	+	0.668807i	0.991926	−	0.126818i	$-0.0404763\pi$
$647$	9.82182	+	17.0119i	0.386136	+	0.668807i	−0.605790	+	0.795624i	$0.707143\pi$
$648$		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
$653$	2.77600	−	1.60272i	0.108633	−	0.0627194i	−0.444699	−	0.895680i	$-0.646689\pi$
$653$	2.77600	−	1.60272i	0.108633	−	0.0627194i	0.553332	+	0.832961i	$0.313356\pi$
$654$		0			0
$655$	−9.85129	+	17.0629i	−0.384922	+	0.666704i
$656$	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
$661$			32.3882i			1.25976i	0.776694	+	0.629878i	$0.216895\pi$
$661$			32.3882i			1.25976i	−0.776694	+	0.629878i	$0.783105\pi$
$662$		−	2.33227i		−	0.0906463i
$663$		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
$668$	−5.96768	+	10.3363i	−0.230897	+	0.399925i
$669$		0			0
$670$	7.57953	−	4.37605i	0.292823	−	0.169061i
$671$	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
$677$	50.3311			1.93438			0.967190	−	0.254053i	$-0.0817639\pi$
$677$	50.3311			1.93438			0.967190	+	0.254053i	$0.0817639\pi$
$678$		0			0
$679$		0			0
$680$	−6.32935	−	3.65425i	−0.242719	−	0.140134i
$681$		0			0
$682$	−95.0324	−	54.8670i	−3.63898	−	2.10097i
$683$	−11.9031	+	6.87227i	−0.455460	+	0.262960i	−0.710133	−	0.704067i	$-0.751365\pi$
$683$	−11.9031	+	6.87227i	−0.455460	+	0.262960i	0.254673	+	0.967027i	$0.418032\pi$
$684$		0			0
$685$			28.9909i			1.10769i
$686$		0			0
$687$		0			0
$688$	22.6280	+	39.1929i	0.862685	+	1.49421i
$689$	−2.15409			−0.0820643
$690$		0			0
$691$		−	29.3673i		−	1.11719i	−0.829442	−	0.558593i	$-0.811342\pi$
$691$		−	29.3673i		−	1.11719i	0.829442	−	0.558593i	$-0.188658\pi$
$692$	1.49813			0.0569504
$693$		0			0
$694$	−50.5874			−1.92027
$695$			49.1123i			1.86294i
$696$		0			0
$697$	−10.1358			−0.383920
$698$	32.7392	+	56.7060i	1.23920	+	2.14635i
$699$		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
$704$	−17.2923	−	9.98371i	−0.651728	−	0.376275i
$705$		0			0
$706$	−4.08702	−	2.35964i	−0.153817	−	0.0888063i
$707$		0			0
$708$		0			0
$709$	−11.3326			−0.425604			−0.212802	−	0.977095i	$-0.568259\pi$
$709$	−11.3326			−0.425604			−0.212802	+	0.977095i	$0.568259\pi$
$710$	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
$716$	−1.90755	+	1.10132i	−0.0712884	+	0.0411584i
$717$		0			0
$718$	6.79136	−	11.7630i	0.253451	−	0.438991i
$719$	18.0647	−	31.2890i	0.673700	−	1.16688i	−0.303147	−	0.952944i	$-0.598037\pi$
$719$	18.0647	−	31.2890i	0.673700	−	1.16688i	0.976847	−	0.213939i	$-0.0686294\pi$
$720$		0			0
$721$		0			0
$722$	−20.0271	+	11.5627i	−0.745333	+	0.430318i
$723$		0			0
$724$			22.4596i			0.834703i
$725$		−	4.00197i		−	0.148629i
$726$		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
$731$	14.6399	−	25.3570i	0.541475	−	0.937862i
$732$		0			0
$733$	41.4391	−	23.9249i	1.53059	−	0.883685i	0.531253	−	0.847213i	$-0.321721\pi$
$733$	41.4391	−	23.9249i	1.53059	−	0.883685i	0.999335	−	0.0364726i	$-0.0116122\pi$
$734$	−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	0.689652	−	0.724141i	$-0.257764\pi$
$739$	−7.67416	−	13.2920i	−0.282299	−	0.488956i	−0.971951	+	0.235185i	$0.924430\pi$
$740$	5.29833			0.194771
$741$		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
$745$	34.1568	+	19.7204i	1.25141	+	0.722501i
$746$	−38.4630	+	22.2066i	−1.40823	+	0.813042i
$747$		0			0
$748$			25.7747i			0.942417i
$749$		0			0
$750$		0			0
$751$	−16.9449	−	29.3494i	−0.618327	−	1.07097i	−0.989791	−	0.142527i	$-0.954477\pi$
$751$	−16.9449	−	29.3494i	−0.618327	−	1.07097i	0.371463	−	0.928448i	$-0.378856\pi$
$752$	10.1981			0.371887
$753$		0			0
$754$			2.59568i			0.0945293i
$755$	−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	$0.533220\pi$
$758$		−	39.6743i		−	1.44103i
$759$		0			0
$760$	6.11284			0.221736
$761$	13.2666	+	22.9784i	0.480914	+	0.832968i	0.999760	−	0.0218999i	$-0.00697151\pi$
$761$	13.2666	+	22.9784i	0.480914	+	0.832968i	−0.518846	+	0.854868i	$0.673638\pi$
$762$		0			0
$763$		0			0
$764$			19.7420i			0.714242i
$765$		0			0
$766$	20.9741	−	12.1094i	0.757825	−	0.437531i
$767$	−2.80929	−	1.62194i	−0.101438	−	0.0585650i
$768$		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
$772$	2.32256			0.0835906
$773$	11.3009	+	19.5737i	0.406464	+	0.704016i	0.994491	−	0.104826i	$-0.0334284\pi$
$773$	11.3009	+	19.5737i	0.406464	+	0.704016i	−0.588027	+	0.808841i	$0.700095\pi$
$774$		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
$779$	7.34180	−	4.23879i	0.263047	−	0.151870i
$780$		0			0
$781$	−8.28359	+	14.3476i	−0.296410	+	0.513398i
$782$	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
$787$			26.1960i			0.933787i	0.884314	+	0.466893i	$0.154627\pi$
$787$			26.1960i			0.933787i	−0.884314	+	0.466893i	$0.845373\pi$
$788$			7.40767i			0.263887i
$789$		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
$794$	−27.9314	+	48.3785i	−0.991247	+	1.71689i
$795$		0			0
$796$	−14.4705	+	8.35456i	−0.512894	+	0.296120i
$797$	−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
$803$	−47.7904			−1.68648
$804$		0			0
$805$		0			0
$806$	7.51788	+	4.34045i	0.264806	+	0.152886i
$807$		0			0
$808$	−6.18375	−	3.57019i	−0.217543	−	0.125599i
$809$	−22.9399	+	13.2443i	−0.806522	+	0.465646i	−0.845747	−	0.533585i	$-0.820845\pi$
$809$	−22.9399	+	13.2443i	−0.806522	+	0.465646i	0.0392244	+	0.999230i	$0.487511\pi$
$810$		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
$814$	7.42439	+	12.8594i	0.260225	+	0.450722i
$815$	−2.69143			−0.0942766
$816$		0			0
$817$			24.4896i			0.856783i
$818$	−53.8949			−1.88439
$819$		0			0
$820$	−12.3198			−0.430226
$821$			13.5669i			0.473489i	0.971572	+	0.236744i	$0.0760804\pi$
$821$			13.5669i			0.473489i	−0.971572	+	0.236744i	$0.923920\pi$
$822$		0			0
$823$	14.6971			0.512310			0.256155	−	0.966636i	$-0.417544\pi$
$823$	14.6971			0.512310			0.256155	+	0.966636i	$0.417544\pi$
$824$	−6.78711	−	11.7556i	−0.236440	−	0.409527i
$825$		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	$-0.551045\pi$
$829$	17.7189	−	10.2300i	0.615402	−	0.355302i	0.775077	+	0.631867i	$0.217711\pi$
$830$	34.3530	+	19.8337i	1.19241	+	0.688439i
$831$		0			0
$832$	1.36797	+	0.789798i	0.0474258	+	0.0273813i
$833$		0			0
$834$		0			0
$835$	−20.0324			−0.693249
$836$	−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
$842$	41.1416	−	23.7531i	1.41783	−	0.818586i
$843$		0			0
$844$	−11.4661	+	19.8598i	−0.394678	+	0.683602i
$845$	−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
$850$			7.35513i			0.252279i
$851$		−	11.1779i		−	0.383172i
$852$		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
$857$	−9.16200	+	15.8691i	−0.312968	+	0.542077i	−0.979003	−	0.203844i	$-0.934657\pi$
$857$	−9.16200	+	15.8691i	−0.312968	+	0.542077i	0.666035	+	0.745920i	$0.267990\pi$
$858$		0			0
$859$	−33.4579	+	19.3169i	−1.14157	+	0.659085i	−0.946819	−	0.321768i	$-0.895723\pi$
$859$	−33.4579	+	19.3169i	−1.14157	+	0.659085i	−0.194750	+	0.980853i	$0.562390\pi$
$860$	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	$-0.241593\pi$
$863$	14.4626	+	8.35001i	0.492314	+	0.284238i	−0.233220	+	0.972424i	$0.574926\pi$
$864$		0			0
$865$	1.25724	+	2.17760i	0.0427473	+	0.0740405i
$866$	24.3931			0.828912
$867$		0			0
$868$		0			0
$869$	2.78978	+	1.61068i	0.0946367	+	0.0546385i
$870$		0			0
$871$	−0.718235	−	0.414673i	−0.0243365	−	0.0140507i
$872$	0.753996	−	0.435320i	0.0255335	−	0.0147418i
$873$		0			0
$874$			37.9689i			1.28432i
$875$		0			0
$876$		0			0
$877$	−16.7617	−	29.0321i	−0.566002	−	0.980345i	−0.996956	−	0.0779707i	$-0.975156\pi$
$877$	−16.7617	−	29.0321i	−0.566002	−	0.980345i	0.430953	−	0.902374i	$-0.358177\pi$
$878$	−59.7213			−2.01549
$879$		0			0
$880$		−	66.8652i		−	2.25403i
$881$	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	$0.722277\pi$
$884$		−	2.03900i		−	0.0685790i
$885$		0			0
$886$	−46.3439			−1.55695
$887$	−17.5914	−	30.4692i	−0.590662	−	1.02306i	−0.994143	−	0.108069i	$-0.965533\pi$
$887$	−17.5914	−	30.4692i	−0.590662	−	1.02306i	0.403481	−	0.914988i	$-0.367800\pi$
$888$		0			0
$889$		0			0
$890$		−	35.4910i		−	1.18966i
$891$		0			0
$892$	−4.13309	+	2.38624i	−0.138386	+	0.0798972i
$893$	4.77921	+	2.75928i	0.159930	+	0.0923358i
$894$		0			0
$895$	−3.20164	−	1.84847i	−0.107019	−	0.0617875i
$896$		0			0
$897$		0			0
$898$	25.7371			0.858857
$899$	−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
$905$	−32.6459	+	18.8481i	−1.08519	+	0.626533i
$906$		0			0
$907$	21.2977	−	36.8887i	0.707179	−	1.22487i	−0.258720	−	0.965952i	$-0.583301\pi$
$907$	21.2977	−	36.8887i	0.707179	−	1.22487i	0.965899	−	0.258918i	$-0.0833660\pi$
$908$	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
$913$			47.5154i			1.57253i
$914$		−	51.0420i		−	1.68832i
$915$		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	0.267137	−	0.963658i	$-0.413922\pi$
$919$	29.3486	−	50.8333i	0.968121	−	1.67684i	0.700984	−	0.713177i	$-0.252744\pi$
$920$	−9.37054	+	16.2303i	−0.308938	+	0.535096i
$921$		0			0
$922$	−17.8630	+	10.3132i	−0.588287	+	0.339647i
$923$	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
$929$	−14.3823			−0.471868			−0.235934	−	0.971769i	$-0.575815\pi$
$929$	−14.3823			−0.471868			−0.235934	+	0.971769i	$0.575815\pi$
$930$		0			0
$931$		0			0
$932$	−6.30952	−	3.64281i	−0.206675	−	0.119324i
$933$		0			0
$934$	25.7427	+	14.8626i	0.842327	+	0.486318i
$935$	−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
$940$	−4.00985	−	6.94526i	−0.130787	−	0.226529i
$941$	−14.8880			−0.485335			−0.242667	−	0.970110i	$-0.578022\pi$
$941$	−14.8880			−0.485335			−0.242667	+	0.970110i	$0.578022\pi$
$942$		0			0
$943$			25.9910i			0.846384i
$944$	34.7734			1.13178
$945$		0			0
$946$	99.7390			3.24280
$947$		−	41.9552i		−	1.36336i	−0.731650	−	0.681681i	$-0.761249\pi$
$947$		−	41.9552i		−	1.36336i	0.731650	−	0.681681i	$-0.238751\pi$
$948$		0			0
$949$	3.78063			0.122724
$950$	−3.07592	−	5.32765i	−0.0997960	−	0.172852i
$951$		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
$956$	20.3415	+	11.7442i	0.657892	+	0.379834i
$957$		0			0
$958$	22.4228	+	12.9458i	0.724449	+	0.418261i
$959$		0			0
$960$		0			0
$961$	−78.5553			−2.53404
$962$	−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	$0.288080\pi$
$968$	16.7980	−	9.69835i	0.539909	−	0.311717i
$969$		0			0
$970$	8.72403	−	15.1105i	0.280112	−	0.485168i
$971$	−21.6869	+	37.5628i	−0.695965	+	1.20545i	0.273890	+	0.961761i	$0.411690\pi$
$971$	−21.6869	+	37.5628i	−0.695965	+	1.20545i	−0.969854	+	0.243685i	$0.921644\pi$
$972$		0			0
$973$		0			0
$974$	−46.6120	+	26.9114i	−1.49354	+	0.862298i
$975$		0			0
$976$		−	40.7000i		−	1.30277i
$977$		−	12.0331i		−	0.384974i	−0.981300	−	0.192487i	$-0.938345\pi$
$977$		−	12.0331i		−	0.384974i	0.981300	−	0.192487i	$-0.0616553\pi$
$978$		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
$983$	−3.14829	+	5.45300i	−0.100415	+	0.173924i	−0.911856	−	0.410511i	$-0.865350\pi$
$983$	−3.14829	+	5.45300i	−0.100415	+	0.173924i	0.811441	+	0.584435i	$0.198684\pi$
$984$		0			0
$985$	−10.7674	+	6.21654i	−0.343077	+	0.198075i
$986$	−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	−0.999254	−	0.0386256i	$-0.987702\pi$
$991$	−16.7814	−	29.0662i	−0.533078	−	0.923317i	0.466176	−	0.884692i	$-0.345631\pi$
$992$	−73.2178			−2.32467
$993$		0			0
$994$		0			0
$995$	−24.2874	−	14.0223i	−0.769963	−	0.444538i
$996$		0			0
$997$	9.74838	+	5.62823i	0.308734	+	0.178248i	0.646360	−	0.763033i	$-0.276290\pi$
$997$	9.74838	+	5.62823i	0.308734	+	0.178248i	−0.337626	+	0.941280i	$0.609624\pi$
$998$	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.i.d.1097.22		48
3.2	odd	2		441.2.i.d.68.19		48
7.2	even	3		1323.2.o.e.881.5		48
7.3	odd	6		1323.2.s.d.962.19		48
7.4	even	3		1323.2.s.d.962.20		48
7.5	odd	6		1323.2.o.e.881.6		48
7.6	odd	2	inner	1323.2.i.d.1097.7		48
9.2	odd	6		1323.2.s.d.656.19		48
9.7	even	3		441.2.s.d.362.5		48
21.2	odd	6		441.2.o.e.293.20	yes	48
21.5	even	6		441.2.o.e.293.19	yes	48
21.11	odd	6		441.2.s.d.374.6		48
21.17	even	6		441.2.s.d.374.5		48
21.20	even	2		441.2.i.d.68.20		48
63.2	odd	6		1323.2.o.e.440.6		48
63.11	odd	6	inner	1323.2.i.d.521.7		48
63.16	even	3		441.2.o.e.146.19	✓	48
63.20	even	6		1323.2.s.d.656.20		48
63.25	even	3		441.2.i.d.227.6		48
63.34	odd	6		441.2.s.d.362.6		48
63.38	even	6	inner	1323.2.i.d.521.22		48
63.47	even	6		1323.2.o.e.440.5		48
63.52	odd	6		441.2.i.d.227.5		48
63.61	odd	6		441.2.o.e.146.20	yes	48

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

\(f(q)\)	\(=\)	\(q-1.86894i q^{2} -1.49292 q^{4} +(-1.25287 - 2.17003i) q^{5} -0.947692i q^{8} +(-4.05565 + 2.34153i) q^{10} +(-4.85803 - 2.80479i) q^{11} +(0.384312 + 0.221883i) q^{13} -4.75703 q^{16} +(1.53885 + 2.66536i) q^{17} +(-2.22932 - 1.28710i) q^{19} +(1.87044 + 3.23969i) q^{20} +(-5.24197 + 9.07935i) q^{22} +(6.83476 - 3.94605i) q^{23} +(-0.639351 + 1.10739i) q^{25} +(0.414685 - 0.718255i) q^{26} +(-2.71041 + 1.56485i) q^{29} +10.4669i q^{31} +6.99520i q^{32} +(4.98140 - 2.87601i) q^{34} +(0.708168 - 1.22658i) q^{37} +(-2.40550 + 4.16645i) q^{38} +(-2.05652 + 1.18733i) q^{40} +(-1.64665 + 2.85208i) q^{41} +(-4.75676 - 8.23894i) q^{43} +(7.25268 + 4.18733i) q^{44} +(-7.37492 - 12.7737i) q^{46} -2.14380 q^{47} +(2.06964 + 1.19491i) q^{50} +(-0.573749 - 0.331254i) q^{52} +(-4.20379 + 2.42706i) q^{53} +14.0561i q^{55} +(2.92461 + 5.06558i) q^{58} -7.30991 q^{59} +8.55576i q^{61} +19.5619 q^{62} +3.55953 q^{64} -1.11196i q^{65} -1.86888 q^{67} +(-2.29739 - 3.97919i) q^{68} -2.95338i q^{71} +(7.37804 - 4.25971i) q^{73} +(-2.29241 - 1.32352i) q^{74} +(3.32820 + 1.92154i) q^{76} -0.574261 q^{79} +(5.95992 + 10.3229i) q^{80} +(5.33036 + 3.07748i) q^{82} +(-4.23521 - 7.33560i) q^{83} +(3.85595 - 6.67870i) q^{85} +(-15.3981 + 8.89008i) q^{86} +(-2.65807 + 4.60392i) q^{88} +(-3.78929 + 6.56325i) q^{89} +(-10.2038 + 5.89115i) q^{92} +4.00663i q^{94} +6.45024i q^{95} +(-3.22662 + 1.86289i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} - 24 q^{11} + 48 q^{16} - 48 q^{23} - 24 q^{25} + 96 q^{44} - 48 q^{50} + 48 q^{53} - 48 q^{64} - 168 q^{74} + 48 q^{79} - 24 q^{85} + 24 q^{86} + 144 q^{92}+O(q^{100}) \) 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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