LMFDB - Embedded newform 1323.2.i.d.1097.21

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			1097.21
Character	$\chi$	$=$	1323.1097
Dual form			1323.2.i.d.521.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.70883i q^{2} -5.33776 q^{4} +(0.601464 + 1.04177i) q^{5} -9.04141i q^{8} +(-2.82197 + 1.62926i) q^{10} +(-2.15351 - 1.24333i) q^{11} +(-1.63211 - 0.942300i) q^{13} +13.8161 q^{16} +(0.601863 + 1.04246i) q^{17} +(-6.46933 - 3.73507i) q^{19} +(-3.21047 - 5.56070i) q^{20} +(3.36797 - 5.83350i) q^{22} +(2.63359 - 1.52050i) q^{23} +(1.77648 - 3.07696i) q^{25} +(2.55253 - 4.42111i) q^{26} +(0.173847 - 0.100371i) q^{29} -3.50314i q^{31} +19.3427i q^{32} +(-2.82384 + 1.63034i) q^{34} +(-0.865458 + 1.49902i) q^{37} +(10.1177 - 17.5243i) q^{38} +(9.41904 - 5.43809i) q^{40} +(3.36029 - 5.82020i) q^{41} +(0.00656005 + 0.0113623i) q^{43} +(11.4949 + 6.63660i) q^{44} +(4.11878 + 7.13394i) q^{46} +1.43481 q^{47} +(8.33495 + 4.81219i) q^{50} +(8.71182 + 5.02977i) q^{52} +(8.58085 - 4.95416i) q^{53} -2.99128i q^{55} +(0.271887 + 0.470923i) q^{58} -12.2191 q^{59} -11.2457i q^{61} +9.48942 q^{62} -24.7638 q^{64} -2.26704i q^{65} -5.15865 q^{67} +(-3.21260 - 5.56438i) q^{68} +12.0452i q^{71} +(-7.51020 + 4.33602i) q^{73} +(-4.06058 - 2.34438i) q^{74} +(34.5317 + 19.9369i) q^{76} +5.49601 q^{79} +(8.30991 + 14.3932i) q^{80} +(15.7659 + 9.10246i) q^{82} +(1.60854 + 2.78607i) q^{83} +(-0.723998 + 1.25400i) q^{85} +(-0.0307786 + 0.0177700i) q^{86} +(-11.2415 + 19.4708i) q^{88} +(3.98364 - 6.89986i) q^{89} +(-14.0574 + 8.11607i) q^{92} +3.88665i q^{94} -8.98604i q^{95} +(-2.06260 + 1.19084i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4} - 24 q^{11} + 48 q^{16} - 48 q^{23} - 24 q^{25} + 96 q^{44} - 48 q^{50} + 48 q^{53} - 48 q^{64} - 168 q^{74} + 48 q^{79} - 24 q^{85} + 24 q^{86} + 144 q^{92}+O(q^{100}) $ 48 * q - 48 * q^4 - 24 * q^11 + 48 * q^16 - 48 * q^23 - 24 * q^25 + 96 * q^44 - 48 * q^50 + 48 * q^53 - 48 * q^64 - 168 * q^74 + 48 * q^79 - 24 * q^85 + 24 * q^86 + 144 * q^92

Character values

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

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

Coefficient data

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

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

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

$2$			2.70883i			1.91543i	0.287716	+	0.957716i	$0.407104\pi$
$2$			2.70883i			1.91543i	−0.287716	+	0.957716i	$0.592896\pi$
$3$		0			0
$3$		0			0
$4$	−5.33776			−2.66888
$5$	0.601464	+	1.04177i	0.268983	+	0.465892i	0.968599	−	0.248626i	$-0.0799791\pi$
$5$	0.601464	+	1.04177i	0.268983	+	0.465892i	−0.699616	+	0.714519i	$0.746646\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	9.04141i		−	3.19662i
$9$		0			0
$10$	−2.82197	+	1.62926i	−0.892385	+	0.515219i
$11$	−2.15351	−	1.24333i	−0.649309	−	0.374879i	0.138882	−	0.990309i	$-0.455649\pi$
$11$	−2.15351	−	1.24333i	−0.649309	−	0.374879i	−0.788191	+	0.615430i	$0.788982\pi$
$12$		0			0
$13$	−1.63211	−	0.942300i	−0.452666	−	0.261347i	0.256289	−	0.966600i	$-0.417500\pi$
$13$	−1.63211	−	0.942300i	−0.452666	−	0.261347i	−0.708956	+	0.705253i	$0.750833\pi$
$14$		0			0
$15$		0			0
$16$	13.8161			3.45403
$17$	0.601863	+	1.04246i	0.145973	+	0.252833i	0.929736	−	0.368228i	$-0.120035\pi$
$17$	0.601863	+	1.04246i	0.145973	+	0.252833i	−0.783762	+	0.621061i	$0.786702\pi$
$18$		0			0
$19$	−6.46933	−	3.73507i	−1.48417	−	0.856883i	−0.484327	−	0.874887i	$-0.660936\pi$
$19$	−6.46933	−	3.73507i	−1.48417	−	0.856883i	−0.999838	+	0.0180038i	$0.994269\pi$
$20$	−3.21047	−	5.56070i	−0.717883	−	1.24341i
$21$		0			0
$22$	3.36797	−	5.83350i	0.718054	−	1.24371i
$23$	2.63359	−	1.52050i	0.549141	−	0.317047i	−0.199634	−	0.979870i	$-0.563975\pi$
$23$	2.63359	−	1.52050i	0.549141	−	0.317047i	0.748775	+	0.662824i	$0.230642\pi$
$24$		0			0
$25$	1.77648	−	3.07696i	0.355296	−	0.615391i
$26$	2.55253	−	4.42111i	0.500592	−	0.867052i
$27$		0			0
$28$		0			0
$29$	0.173847	−	0.100371i	0.0322826	−	0.0186384i	−0.483772	−	0.875194i	$-0.660734\pi$
$29$	0.173847	−	0.100371i	0.0322826	−	0.0186384i	0.516054	+	0.856556i	$0.327400\pi$
$30$		0			0
$31$		−	3.50314i		−	0.629183i	−0.949227	−	0.314592i	$-0.898132\pi$
$31$		−	3.50314i		−	0.629183i	0.949227	−	0.314592i	$-0.101868\pi$
$32$			19.3427i			3.41934i
$33$		0			0
$34$	−2.82384	+	1.63034i	−0.484285	+	0.279602i
$35$		0			0
$36$		0			0
$37$	−0.865458	+	1.49902i	−0.142280	+	0.246437i	−0.928355	−	0.371695i	$-0.878777\pi$
$37$	−0.865458	+	1.49902i	−0.142280	+	0.246437i	0.786075	+	0.618132i	$0.212110\pi$
$38$	10.1177	−	17.5243i	1.64130	−	2.84282i
$39$		0			0
$40$	9.41904	−	5.43809i	1.48928	−	0.859837i
$41$	3.36029	−	5.82020i	0.524790	−	0.908963i	−0.474793	−	0.880097i	$-0.657477\pi$
$41$	3.36029	−	5.82020i	0.524790	−	0.908963i	0.999583	−	0.0288655i	$-0.00918944\pi$
$42$		0			0
$43$	0.00656005	+	0.0113623i	0.00100040	+	0.00173274i	0.866525	−	0.499133i	$-0.166348\pi$
$43$	0.00656005	+	0.0113623i	0.00100040	+	0.00173274i	−0.865525	+	0.500866i	$0.833015\pi$
$44$	11.4949	+	6.63660i	1.73293	+	1.00051i
$45$		0			0
$46$	4.11878	+	7.13394i	0.607281	+	1.05184i
$47$	1.43481			0.209288			0.104644	−	0.994510i	$-0.466630\pi$
$47$	1.43481			0.209288			0.104644	+	0.994510i	$0.466630\pi$
$48$		0			0
$49$		0			0
$50$	8.33495	+	4.81219i	1.17874	+	0.680546i
$51$		0			0
$52$	8.71182	+	5.02977i	1.20811	+	0.697504i
$53$	8.58085	−	4.95416i	1.17867	−	0.680506i	0.222964	−	0.974827i	$-0.428427\pi$
$53$	8.58085	−	4.95416i	1.17867	−	0.680506i	0.955707	+	0.294321i	$0.0950935\pi$
$54$		0			0
$55$		−	2.99128i		−	0.403344i
$56$		0			0
$57$		0			0
$58$	0.271887	+	0.470923i	0.0357005	+	0.0618352i
$59$	−12.2191			−1.59079			−0.795394	−	0.606092i	$-0.792736\pi$
$59$	−12.2191			−1.59079			−0.795394	+	0.606092i	$0.792736\pi$
$60$		0			0
$61$		−	11.2457i		−	1.43986i	−0.694047	−	0.719930i	$-0.744174\pi$
$61$		−	11.2457i		−	1.43986i	0.694047	−	0.719930i	$-0.255826\pi$
$62$	9.48942			1.20516
$63$		0			0
$64$	−24.7638			−3.09548
$65$		−	2.26704i		−	0.281192i
$66$		0			0
$67$	−5.15865			−0.630229			−0.315115	−	0.949054i	$-0.602043\pi$
$67$	−5.15865			−0.630229			−0.315115	+	0.949054i	$0.602043\pi$
$68$	−3.21260	−	5.56438i	−0.389585	−	0.674781i
$69$		0			0
$70$		0			0
$71$			12.0452i			1.42950i	0.699379	+	0.714751i	$0.253460\pi$
$71$			12.0452i			1.42950i	−0.699379	+	0.714751i	$0.746540\pi$
$72$		0			0
$73$	−7.51020	+	4.33602i	−0.879003	+	0.507493i	−0.870330	−	0.492470i	$-0.836094\pi$
$73$	−7.51020	+	4.33602i	−0.879003	+	0.507493i	−0.00867336	+	0.999962i	$0.502761\pi$
$74$	−4.06058	−	2.34438i	−0.472033	−	0.272528i
$75$		0			0
$76$	34.5317	+	19.9369i	3.96106	+	2.28692i
$77$		0			0
$78$		0			0
$79$	5.49601			0.618350			0.309175	−	0.951005i	$-0.399947\pi$
$79$	5.49601			0.618350			0.309175	+	0.951005i	$0.399947\pi$
$80$	8.30991	+	14.3932i	0.929076	+	1.60921i
$81$		0			0
$82$	15.7659	+	9.10246i	1.74106	+	1.00520i
$83$	1.60854	+	2.78607i	0.176560	+	0.305811i	0.940700	−	0.339239i	$-0.110170\pi$
$83$	1.60854	+	2.78607i	0.176560	+	0.305811i	−0.764140	+	0.645051i	$0.776836\pi$
$84$		0			0
$85$	−0.723998	+	1.25400i	−0.0785286	+	0.136016i
$86$	−0.0307786	+	0.0177700i	−0.00331894	+	0.00191619i
$87$		0			0
$88$	−11.2415	+	19.4708i	−1.19835	+	2.07559i
$89$	3.98364	−	6.89986i	0.422265	−	0.731384i	−0.573896	−	0.818928i	$-0.694569\pi$
$89$	3.98364	−	6.89986i	0.422265	−	0.731384i	0.996161	+	0.0875442i	$0.0279019\pi$
$90$		0			0
$91$		0			0
$92$	−14.0574	+	8.11607i	−1.46559	+	0.846159i
$93$		0			0
$94$			3.88665i			0.400877i
$95$		−	8.98604i		−	0.921948i
$96$		0			0
$97$	−2.06260	+	1.19084i	−0.209425	+	0.120912i	−0.601044	−	0.799216i	$-0.705249\pi$
$97$	−2.06260	+	1.19084i	−0.209425	+	0.120912i	0.391619	+	0.920128i	$0.371915\pi$
$98$		0			0
$99$		0			0
$100$	−9.48242	+	16.4240i	−0.948242	+	1.64240i
$101$	−4.73272	+	8.19730i	−0.470923	+	0.815662i	−0.999447	−	0.0332561i	$-0.989412\pi$
$101$	−4.73272	+	8.19730i	−0.470923	+	0.815662i	0.528524	+	0.848918i	$0.322746\pi$
$102$		0			0
$103$	−14.9460	+	8.62908i	−1.47267	+	0.850249i	−0.999528	−	0.0307347i	$-0.990215\pi$
$103$	−14.9460	+	8.62908i	−1.47267	+	0.850249i	−0.473147	+	0.880984i	$0.656882\pi$
$104$	−8.51973	+	14.7566i	−0.835428	+	1.44700i
$105$		0			0
$106$	13.4200	+	23.2441i	1.30346	+	2.25766i
$107$	−8.55935	−	4.94175i	−0.827464	−	0.477737i	0.0255196	−	0.999674i	$-0.491876\pi$
$107$	−8.55935	−	4.94175i	−0.827464	−	0.477737i	−0.852984	+	0.521938i	$0.825209\pi$
$108$		0			0
$109$	−5.20678	−	9.01841i	−0.498719	−	0.863807i	0.501280	−	0.865285i	$-0.332863\pi$
$109$	−5.20678	−	9.01841i	−0.498719	−	0.863807i	−0.999999	+	0.00147852i	$0.999529\pi$
$110$	8.10286			0.772578
$111$		0			0
$112$		0			0
$113$	9.56137	+	5.52026i	0.899458	+	0.519303i	0.877024	−	0.480446i	$-0.159525\pi$
$113$	9.56137	+	5.52026i	0.899458	+	0.519303i	0.0224339	+	0.999748i	$0.492858\pi$
$114$		0			0
$115$	3.16802	+	1.82906i	0.295419	+	0.170560i
$116$	−0.927954	+	0.535755i	−0.0861584	+	0.0497436i
$117$		0			0
$118$		−	33.0994i		−	3.04705i
$119$		0			0
$120$		0			0
$121$	−2.40825	−	4.17121i	−0.218932	−	0.379201i
$122$	30.4626			2.75795
$123$		0			0
$124$			18.6989i			1.67921i
$125$	10.2886			0.920241
$126$		0			0
$127$	13.8634			1.23018			0.615090	−	0.788457i	$-0.289119\pi$
$127$	13.8634			1.23018			0.615090	+	0.788457i	$0.289119\pi$
$128$		−	28.3956i		−	2.50984i
$129$		0			0
$130$	6.14102			0.538603
$131$	−6.17975	−	10.7036i	−0.539927	−	0.935181i	−0.998907	−	0.0467344i	$-0.985119\pi$
$131$	−6.17975	−	10.7036i	−0.539927	−	0.935181i	0.458981	−	0.888446i	$-0.348215\pi$
$132$		0			0
$133$		0			0
$134$		−	13.9739i		−	1.20716i
$135$		0			0
$136$	9.42529	−	5.44169i	0.808212	−	0.466621i
$137$	10.0991	+	5.83070i	0.862822	+	0.498150i	0.864956	−	0.501847i	$-0.167346\pi$
$137$	10.0991	+	5.83070i	0.862822	+	0.498150i	−0.00213432	+	0.999998i	$0.500679\pi$
$138$		0			0
$139$	−8.73893	−	5.04543i	−0.741227	−	0.427947i	0.0812884	−	0.996691i	$-0.474097\pi$
$139$	−8.73893	−	5.04543i	−0.741227	−	0.427947i	−0.822515	+	0.568743i	$0.807430\pi$
$140$		0			0
$141$		0			0
$142$	−32.6284			−2.73811
$143$	2.34318	+	4.05851i	0.195947	+	0.339390i
$144$		0			0
$145$	0.209126	+	0.120739i	0.0173670	+	0.0100268i
$146$	−11.7455	−	20.3439i	−0.972067	−	1.68367i
$147$		0			0
$148$	4.61960	−	8.00138i	0.379729	−	0.657710i
$149$	4.15010	−	2.39606i	0.339990	−	0.196293i	−0.320278	−	0.947324i	$-0.603776\pi$
$149$	4.15010	−	2.39606i	0.339990	−	0.196293i	0.660267	+	0.751031i	$0.270443\pi$
$150$		0			0
$151$	5.65924	−	9.80209i	0.460542	−	0.797683i	−0.538446	−	0.842660i	$-0.680988\pi$
$151$	5.65924	−	9.80209i	0.460542	−	0.797683i	0.998988	+	0.0449774i	$0.0143216\pi$
$152$	−33.7703	+	58.4918i	−2.73913	+	4.74431i
$153$		0			0
$154$		0			0
$155$	3.64946	−	2.10702i	0.293132	−	0.169240i
$156$		0			0
$157$		−	14.7316i		−	1.17571i	−0.808966	−	0.587856i	$-0.799972\pi$
$157$		−	14.7316i		−	1.17571i	0.808966	−	0.587856i	$-0.200028\pi$
$158$			14.8878i			1.18441i
$159$		0			0
$160$	−20.1506	+	11.6339i	−1.59304	+	0.919744i
$161$		0			0
$162$		0			0
$163$	9.07900	−	15.7253i	0.711122	−	1.23170i	−0.253314	−	0.967384i	$-0.581521\pi$
$163$	9.07900	−	15.7253i	0.711122	−	1.23170i	0.964436	−	0.264316i	$-0.0851460\pi$
$164$	−17.9364	+	31.0668i	−1.40060	+	2.42591i
$165$		0			0
$166$	−7.54700	+	4.35726i	−0.585761	+	0.338189i
$167$	0.599436	−	1.03825i	0.0463857	−	0.0803425i	−0.841900	−	0.539633i	$-0.818563\pi$
$167$	0.599436	−	1.03825i	0.0463857	−	0.0803425i	0.888286	+	0.459291i	$0.151896\pi$
$168$		0			0
$169$	−4.72414	−	8.18245i	−0.363395	−	0.629419i
$170$	−3.39688	−	1.96119i	−0.260529	−	0.150416i
$171$		0			0
$172$	−0.0350159	−	0.0606494i	−0.00266994	−	0.00462447i
$173$	−18.0081			−1.36913			−0.684564	−	0.728953i	$-0.740007\pi$
$173$	−18.0081			−1.36913			−0.684564	+	0.728953i	$0.740007\pi$
$174$		0			0
$175$		0			0
$176$	−29.7532	−	17.1780i	−2.24273	−	1.29484i
$177$		0			0
$178$	18.6906	+	10.7910i	1.40092	+	0.808819i
$179$	−13.1137	+	7.57118i	−0.980162	+	0.565897i	−0.902319	−	0.431069i	$-0.858137\pi$
$179$	−13.1137	+	7.57118i	−0.980162	+	0.565897i	−0.0778428	+	0.996966i	$0.524803\pi$
$180$		0			0
$181$		−	7.98716i		−	0.593681i	−0.954927	−	0.296840i	$-0.904067\pi$
$181$		−	7.98716i		−	0.593681i	0.954927	−	0.296840i	$-0.0959329\pi$
$182$		0			0
$183$		0			0
$184$	−13.7475	−	23.8114i	−1.01348	−	1.75540i
$185$	−2.08217			−0.153084
$186$		0			0
$187$		−	2.99326i		−	0.218889i
$188$	−7.65865			−0.558564
$189$		0			0
$190$	24.3416			1.76593
$191$		−	16.0170i		−	1.15895i	−0.814991	−	0.579473i	$-0.803258\pi$
$191$		−	16.0170i		−	1.15895i	0.814991	−	0.579473i	$-0.196742\pi$
$192$		0			0
$193$	−13.7094			−0.986821			−0.493410	−	0.869797i	$-0.664250\pi$
$193$	−13.7094			−0.986821			−0.493410	+	0.869797i	$0.664250\pi$
$194$	−3.22579	−	5.58724i	−0.231598	−	0.401140i
$195$		0			0
$196$		0			0
$197$			18.9248i			1.34834i	0.738577	+	0.674170i	$0.235498\pi$
$197$			18.9248i			1.34834i	−0.738577	+	0.674170i	$0.764502\pi$
$198$		0			0
$199$	−21.5055	+	12.4162i	−1.52449	+	0.880163i	−0.524908	+	0.851159i	$0.675900\pi$
$199$	−21.5055	+	12.4162i	−1.52449	+	0.880163i	−0.999579	+	0.0290036i	$0.990767\pi$
$200$	−27.8200	−	16.0619i	−1.96717	−	1.13575i
$201$		0			0
$202$	−22.2051	−	12.8201i	−1.56235	−	0.902020i
$203$		0			0
$204$		0			0
$205$	8.08439			0.564638
$206$	−23.3747	−	40.4862i	−1.62859	−	2.82081i
$207$		0			0
$208$	−22.5495	−	13.0189i	−1.56352	−	0.902701i
$209$	9.28786	+	16.0870i	0.642454	+	1.11276i
$210$		0			0
$211$	3.60761	−	6.24857i	0.248358	−	0.430169i	−0.714712	−	0.699419i	$-0.753442\pi$
$211$	3.60761	−	6.24857i	0.248358	−	0.430169i	0.963070	+	0.269250i	$0.0867757\pi$
$212$	−45.8025	+	26.4441i	−3.14573	+	1.81619i
$213$		0			0
$214$	13.3863	−	23.1858i	0.915072	−	1.58495i
$215$	−0.00789127	+	0.0136681i	−0.000538180	+	0.000932155i
$216$		0			0
$217$		0			0
$218$	24.4293	−	14.1043i	1.65456	−	0.955262i
$219$		0			0
$220$			15.9667i			1.07648i
$221$		−	2.26854i		−	0.152599i
$222$		0			0
$223$	21.0706	−	12.1651i	1.41099	−	0.814635i	0.415508	−	0.909590i	$-0.363604\pi$
$223$	21.0706	−	12.1651i	1.41099	−	0.814635i	0.995482	+	0.0949545i	$0.0302705\pi$
$224$		0			0
$225$		0			0
$226$	−14.9534	+	25.9001i	−0.994688	+	1.72285i
$227$	−0.240288	+	0.416192i	−0.0159485	+	0.0276236i	−0.873890	−	0.486125i	$-0.838410\pi$
$227$	−0.240288	+	0.416192i	−0.0159485	+	0.0276236i	0.857941	+	0.513748i	$0.171743\pi$
$228$		0			0
$229$	7.80442	−	4.50588i	0.515730	−	0.297757i	−0.219456	−	0.975622i	$-0.570428\pi$
$229$	7.80442	−	4.50588i	0.515730	−	0.297757i	0.735186	+	0.677865i	$0.237095\pi$
$230$	−4.95460	+	8.58162i	−0.326697	+	0.565855i
$231$		0			0
$232$	−0.907493	−	1.57182i	−0.0595799	−	0.103195i
$233$	9.62742	+	5.55840i	0.630713	+	0.364143i	0.781028	−	0.624496i	$-0.214695\pi$
$233$	9.62742	+	5.55840i	0.630713	+	0.364143i	−0.150315	+	0.988638i	$0.548029\pi$
$234$		0			0
$235$	0.862985	+	1.49473i	0.0562949	+	0.0975057i
$236$	65.2225			4.24562
$237$		0			0
$238$		0			0
$239$	−12.0446	−	6.95395i	−0.779100	−	0.449813i	0.0570114	−	0.998374i	$-0.481843\pi$
$239$	−12.0446	−	6.95395i	−0.779100	−	0.449813i	−0.836111	+	0.548560i	$0.815176\pi$
$240$		0			0
$241$	10.7181	+	6.18807i	0.690411	+	0.398609i	0.803766	−	0.594946i	$-0.202827\pi$
$241$	10.7181	+	6.18807i	0.690411	+	0.398609i	−0.113355	+	0.993555i	$0.536160\pi$
$242$	11.2991	−	6.52354i	0.726334	−	0.419349i
$243$		0			0
$244$			60.0266i			3.84281i
$245$		0			0
$246$		0			0
$247$	7.03911	+	12.1921i	0.447888	+	0.775764i
$248$	−31.6734			−2.01126
$249$		0			0
$250$			27.8701i			1.76266i
$251$	−19.7147			−1.24438			−0.622191	−	0.782866i	$-0.713757\pi$
$251$	−19.7147			−1.24438			−0.622191	+	0.782866i	$0.713757\pi$
$252$		0			0
$253$	−7.56196			−0.475416
$254$			37.5537i			2.35633i
$255$		0			0
$256$	27.3911			1.71195
$257$	−5.62025	−	9.73456i	−0.350581	−	0.607225i	0.635770	−	0.771879i	$-0.280683\pi$
$257$	−5.62025	−	9.73456i	−0.350581	−	0.607225i	−0.986351	+	0.164654i	$0.947349\pi$
$258$		0			0
$259$		0			0
$260$			12.1009i			0.750466i
$261$		0			0
$262$	28.9943	−	16.7399i	1.79127	−	1.03419i
$263$	−2.82146	−	1.62897i	−0.173979	−	0.100447i	0.410482	−	0.911869i	$-0.365360\pi$
$263$	−2.82146	−	1.62897i	−0.173979	−	0.100447i	−0.584461	+	0.811422i	$0.698694\pi$
$264$		0			0
$265$	10.3221	+	5.95949i	0.634084	+	0.366089i
$266$		0			0
$267$		0			0
$268$	27.5356			1.68200
$269$	−0.121147	−	0.209832i	−0.00738644	−	0.0127937i	0.862309	−	0.506383i	$-0.169018\pi$
$269$	−0.121147	−	0.209832i	−0.00738644	−	0.0127937i	−0.869695	+	0.493590i	$0.835685\pi$
$270$		0			0
$271$	−0.929287	−	0.536524i	−0.0564502	−	0.0325915i	0.471509	−	0.881861i	$-0.343709\pi$
$271$	−0.929287	−	0.536524i	−0.0564502	−	0.0325915i	−0.527959	+	0.849270i	$0.677043\pi$
$272$	8.31542	+	14.4027i	0.504196	+	0.873294i
$273$		0			0
$274$	−15.7944	+	27.3567i	−0.954173	+	1.65268i
$275$	−7.65136	+	4.41751i	−0.461394	+	0.266386i
$276$		0			0
$277$	2.45076	−	4.24485i	0.147252	−	0.255048i	−0.782959	−	0.622074i	$-0.786290\pi$
$277$	2.45076	−	4.24485i	0.147252	−	0.255048i	0.930211	+	0.367025i	$0.119624\pi$
$278$	13.6672	−	23.6723i	0.819704	−	1.41977i
$279$		0			0
$280$		0			0
$281$	−11.5613	+	6.67494i	−0.689691	+	0.398194i	−0.803496	−	0.595310i	$-0.797029\pi$
$281$	−11.5613	+	6.67494i	−0.689691	+	0.398194i	0.113805	+	0.993503i	$0.463696\pi$
$282$		0			0
$283$		−	3.75657i		−	0.223305i	−0.993747	−	0.111653i	$-0.964386\pi$
$283$		−	3.75657i		−	0.223305i	0.993747	−	0.111653i	$-0.0356144\pi$
$284$		−	64.2943i		−	3.81517i
$285$		0			0
$286$	−10.9938	+	6.34729i	−0.650078	+	0.375323i
$287$		0			0
$288$		0			0
$289$	7.77552	−	13.4676i	0.457384	−	0.792212i
$290$	−0.327061	+	0.566486i	−0.0192057	+	0.0332652i
$291$		0			0
$292$	40.0876	−	23.1446i	2.34595	−	1.35444i
$293$	6.38430	−	11.0579i	0.372975	−	0.646011i	−0.617047	−	0.786926i	$-0.711671\pi$
$293$	6.38430	−	11.0579i	0.372975	−	0.646011i	0.990022	+	0.140915i	$0.0450045\pi$
$294$		0			0
$295$	−7.34934	−	12.7294i	−0.427895	−	0.741136i
$296$	13.5532	+	7.82496i	0.787765	+	0.454816i
$297$		0			0
$298$	6.49052	+	11.2419i	0.375986	+	0.651227i
$299$	−5.73108			−0.331437
$300$		0			0
$301$		0			0
$302$	26.5522	+	15.3299i	1.52791	+	0.882137i
$303$		0			0
$304$	−89.3810	−	51.6042i	−5.12635	−	2.95970i
$305$	11.7154	−	6.76387i	0.670819	−	0.387298i
$306$		0			0
$307$			10.7257i			0.612148i	0.952008	+	0.306074i	$0.0990155\pi$
$307$			10.7257i			0.612148i	−0.952008	+	0.306074i	$0.900984\pi$
$308$		0			0
$309$		0			0
$310$	5.70755	+	9.88576i	0.324167	+	0.561473i
$311$	18.8349			1.06803			0.534013	−	0.845476i	$-0.320683\pi$
$311$	18.8349			1.06803			0.534013	+	0.845476i	$0.320683\pi$
$312$		0			0
$313$		−	26.0702i		−	1.47357i	−0.676125	−	0.736787i	$-0.736342\pi$
$313$		−	26.0702i		−	1.47357i	0.676125	−	0.736787i	$-0.263658\pi$
$314$	39.9054			2.25199
$315$		0			0
$316$	−29.3364			−1.65030
$317$		−	13.8899i		−	0.780134i	−0.920786	−	0.390067i	$-0.872452\pi$
$317$		−	13.8899i		−	0.780134i	0.920786	−	0.390067i	$-0.127548\pi$
$318$		0			0
$319$	−0.499177			−0.0279485
$320$	−14.8946	−	25.7981i	−0.832631	−	1.44216i
$321$		0			0
$322$		0			0
$323$		−	8.99200i		−	0.500328i
$324$		0			0
$325$	−5.79883	+	3.34796i	−0.321661	+	0.185711i
$326$	42.5971	+	24.5935i	2.35924	+	1.36211i
$327$		0			0
$328$	−52.6228	−	30.3818i	−2.90561	−	1.67755i
$329$		0			0
$330$		0			0
$331$	4.48460			0.246496			0.123248	−	0.992376i	$-0.460669\pi$
$331$	4.48460			0.246496			0.123248	+	0.992376i	$0.460669\pi$
$332$	−8.58600	−	14.8714i	−0.471218	−	0.816173i
$333$		0			0
$334$	2.81245	+	1.62377i	0.153891	+	0.0888487i
$335$	−3.10274	−	5.37411i	−0.169521	−	0.293619i
$336$		0			0
$337$	−16.4010	+	28.4074i	−0.893420	+	1.54745i	−0.0576723	+	0.998336i	$0.518368\pi$
$337$	−16.4010	+	28.4074i	−0.893420	+	1.54745i	−0.835748	+	0.549113i	$0.814965\pi$
$338$	22.1649	−	12.7969i	1.20561	−	0.696059i
$339$		0			0
$340$	3.86453	−	6.69356i	0.209583	−	0.363009i
$341$	−4.35557	+	7.54407i	−0.235867	+	0.408534i
$342$		0			0
$343$		0			0
$344$	0.102732	−	0.0593121i	0.00553891	−	0.00319789i
$345$		0			0
$346$		−	48.7807i		−	2.62247i
$347$			13.4075i			0.719751i	0.933000	+	0.359876i	$0.117181\pi$
$347$			13.4075i			0.719751i	−0.933000	+	0.359876i	$0.882819\pi$
$348$		0			0
$349$	−19.3276	+	11.1588i	−1.03458	+	0.597316i	−0.918294	−	0.395899i	$-0.870433\pi$
$349$	−19.3276	+	11.1588i	−1.03458	+	0.597316i	−0.116288	+	0.993215i	$0.537100\pi$
$350$		0			0
$351$		0			0
$352$	24.0494	−	41.6548i	1.28184	−	2.22021i
$353$	8.60842	−	14.9102i	0.458180	−	0.793591i	−0.540685	−	0.841225i	$-0.681835\pi$
$353$	8.60842	−	14.9102i	0.458180	−	0.793591i	0.998865	+	0.0476341i	$0.0151682\pi$
$354$		0			0
$355$	−12.5483	+	7.24476i	−0.665994	+	0.384512i
$356$	−21.2637	+	36.8298i	−1.12697	+	1.95198i
$357$		0			0
$358$	−20.5090	−	35.5227i	−1.08394	−	1.87743i
$359$	5.62867	+	3.24971i	0.297070	+	0.171513i	0.641126	−	0.767436i	$-0.278468\pi$
$359$	5.62867	+	3.24971i	0.297070	+	0.171513i	−0.344056	+	0.938949i	$0.611801\pi$
$360$		0			0
$361$	18.4015	+	31.8722i	0.968497	+	1.67749i
$362$	21.6358			1.13715
$363$		0			0
$364$		0			0
$365$	−9.03424	−	5.21592i	−0.472874	−	0.273014i
$366$		0			0
$367$	−7.79734	−	4.50180i	−0.407018	−	0.234992i	0.282490	−	0.959270i	$-0.408840\pi$
$367$	−7.79734	−	4.50180i	−0.407018	−	0.234992i	−0.689508	+	0.724278i	$0.742173\pi$
$368$	36.3860	−	21.0075i	1.89675	−	1.09509i
$369$		0			0
$370$		−	5.64024i		−	0.293222i
$371$		0			0
$372$		0			0
$373$	−5.75312	−	9.96470i	−0.297885	−	0.515953i	0.677767	−	0.735277i	$-0.262948\pi$
$373$	−5.75312	−	9.96470i	−0.297885	−	0.515953i	−0.975652	+	0.219324i	$0.929615\pi$
$374$	8.10824			0.419267
$375$		0			0
$376$		−	12.9727i		−	0.669015i
$377$	−0.378318			−0.0194844
$378$		0			0
$379$	17.0982			0.878275			0.439138	−	0.898420i	$-0.355284\pi$
$379$	17.0982			0.878275			0.439138	+	0.898420i	$0.355284\pi$
$380$			47.9653i			2.46057i
$381$		0			0
$382$	43.3872			2.21988
$383$	8.10778	+	14.0431i	0.414288	+	0.717569i	0.995353	−	0.0962885i	$-0.0306971\pi$
$383$	8.10778	+	14.0431i	0.414288	+	0.717569i	−0.581065	+	0.813857i	$0.697364\pi$
$384$		0			0
$385$		0			0
$386$		−	37.1363i		−	1.89019i
$387$		0			0
$388$	11.0097	−	6.35643i	0.558931	−	0.322699i
$389$	−16.2358	−	9.37376i	−0.823189	−	0.475269i	0.0283257	−	0.999599i	$-0.490982\pi$
$389$	−16.2358	−	9.37376i	−0.823189	−	0.475269i	−0.851515	+	0.524330i	$0.824316\pi$
$390$		0			0
$391$	3.17012	+	1.83027i	0.160320	+	0.0925607i
$392$		0			0
$393$		0			0
$394$	−51.2642			−2.58265
$395$	3.30565	+	5.72556i	0.166326	+	0.288084i
$396$		0			0
$397$	26.8216	+	15.4854i	1.34614	+	0.777192i	0.987700	−	0.156362i	$-0.0499767\pi$
$397$	26.8216	+	15.4854i	1.34614	+	0.777192i	0.358436	+	0.933554i	$0.383310\pi$
$398$	−33.6334	−	58.2548i	−1.68589	−	2.92005i
$399$		0			0
$400$	24.5441	−	42.5116i	1.22720	−	2.12558i
$401$	−0.801065	+	0.462495i	−0.0400033	+	0.0230959i	−0.519868	−	0.854246i	$-0.674019\pi$
$401$	−0.801065	+	0.462495i	−0.0400033	+	0.0230959i	0.479865	+	0.877342i	$0.340686\pi$
$402$		0			0
$403$	−3.30101	+	5.71752i	−0.164435	+	0.284810i
$404$	25.2621	−	43.7552i	1.25684	−	2.17690i
$405$		0			0
$406$		0			0
$407$	3.72755	−	2.15210i	0.184768	−	0.106676i
$408$		0			0
$409$			7.58159i			0.374885i	0.982276	+	0.187443i	$0.0600199\pi$
$409$			7.58159i			0.374885i	−0.982276	+	0.187443i	$0.939980\pi$
$410$			21.8992i			1.08153i
$411$		0			0
$412$	79.7782	−	46.0599i	3.93039	−	2.26921i
$413$		0			0
$414$		0			0
$415$	−1.93496	+	3.35145i	−0.0949834	+	0.164516i
$416$	18.2266	−	31.5695i	0.893635	−	1.54782i
$417$		0			0
$418$	−43.5770	+	25.1592i	−2.13142	+	1.23058i
$419$	2.85061	−	4.93740i	0.139262	−	0.241208i	−0.787956	−	0.615732i	$-0.788860\pi$
$419$	2.85061	−	4.93740i	0.139262	−	0.241208i	0.927217	+	0.374524i	$0.122194\pi$
$420$		0			0
$421$	−5.86189	−	10.1531i	−0.285691	−	0.494832i	0.687085	−	0.726577i	$-0.258890\pi$
$421$	−5.86189	−	10.1531i	−0.285691	−	0.494832i	−0.972777	+	0.231745i	$0.925557\pi$
$422$	16.9263	+	9.77240i	0.823959	+	0.475713i
$423$		0			0
$424$	−44.7926	−	77.5830i	−2.17532	−	3.76776i
$425$	4.27680			0.207455
$426$		0			0
$427$		0			0
$428$	45.6877	+	26.3778i	2.20840	+	1.27502i
$429$		0			0
$430$	−0.0370245	−	0.0213761i	−0.00178548	−	0.00103085i
$431$	−23.2973	+	13.4507i	−1.12219	+	0.647897i	−0.941959	−	0.335728i	$-0.891018\pi$
$431$	−23.2973	+	13.4507i	−1.12219	+	0.647897i	−0.180231	+	0.983624i	$0.557685\pi$
$432$		0			0
$433$			28.1028i			1.35053i	0.737574	+	0.675266i	$0.235971\pi$
$433$			28.1028i			1.35053i	−0.737574	+	0.675266i	$0.764029\pi$
$434$		0			0
$435$		0			0
$436$	27.7925	+	48.1381i	1.33102	+	2.30539i
$437$	−22.7167			−1.08669
$438$		0			0
$439$		−	9.32629i		−	0.445120i	−0.974919	−	0.222560i	$-0.928559\pi$
$439$		−	9.32629i		−	0.445120i	0.974919	−	0.222560i	$-0.0714412\pi$
$440$	−27.0454			−1.28934
$441$		0			0
$442$	6.14510			0.292292
$443$		−	11.3407i		−	0.538812i	−0.963027	−	0.269406i	$-0.913173\pi$
$443$		−	11.3407i		−	0.538812i	0.963027	−	0.269406i	$-0.0868273\pi$
$444$		0			0
$445$	9.58406			0.454328
$446$	32.9532	+	57.0766i	1.56038	+	2.70265i
$447$		0			0
$448$		0			0
$449$		−	15.3295i		−	0.723444i	−0.932286	−	0.361722i	$-0.882189\pi$
$449$		−	15.3295i		−	0.723444i	0.932286	−	0.361722i	$-0.117811\pi$
$450$		0			0
$451$	−14.4729	+	8.35592i	−0.681501	+	0.393465i
$452$	−51.0363	−	29.4658i	−2.40054	−	1.38596i
$453$		0			0
$454$	−1.12739	−	0.650900i	−0.0529111	−	0.0305483i
$455$		0			0
$456$		0			0
$457$	−9.17299			−0.429094			−0.214547	−	0.976714i	$-0.568828\pi$
$457$	−9.17299			−0.429094			−0.214547	+	0.976714i	$0.568828\pi$
$458$	12.2057	+	21.1408i	0.570333	+	0.987846i
$459$		0			0
$460$	−16.9101	−	9.76305i	−0.788438	−	0.455205i
$461$	16.5365	+	28.6420i	0.770181	+	1.33399i	0.937464	+	0.348083i	$0.113167\pi$
$461$	16.5365	+	28.6420i	0.770181	+	1.33399i	−0.167283	+	0.985909i	$0.553499\pi$
$462$		0			0
$463$	3.91594	−	6.78260i	0.181989	−	0.315214i	−0.760569	−	0.649257i	$-0.775080\pi$
$463$	3.91594	−	6.78260i	0.181989	−	0.315214i	0.942558	+	0.334043i	$0.108413\pi$
$464$	2.40190	−	1.38674i	0.111505	−	0.0643776i
$465$		0			0
$466$	−15.0567	+	26.0790i	−0.697490	+	1.20809i
$467$	−10.3385	+	17.9068i	−0.478408	+	0.828627i	−0.999694	−	0.0247555i	$-0.992119\pi$
$467$	−10.3385	+	17.9068i	−0.478408	+	0.828627i	0.521286	+	0.853382i	$0.325453\pi$
$468$		0			0
$469$		0			0
$470$	−4.04898	+	2.33768i	−0.186765	+	0.107829i
$471$		0			0
$472$			110.478i			5.08515i
$473$		−	0.0326253i		−	0.00150011i
$474$		0			0
$475$	−22.9853	+	13.2706i	−1.05464	+	0.608895i
$476$		0			0
$477$		0			0
$478$	18.8371	−	32.6267i	0.861587	−	1.49231i
$479$	−1.32999	+	2.30361i	−0.0607688	+	0.105255i	−0.894809	−	0.446449i	$-0.852689\pi$
$479$	−1.32999	+	2.30361i	−0.0607688	+	0.105255i	0.834040	+	0.551703i	$0.186022\pi$
$480$		0			0
$481$	2.82505	−	1.63104i	0.128811	−	0.0743691i
$482$	−16.7624	+	29.0334i	−0.763508	+	1.32243i
$483$		0			0
$484$	12.8547	+	22.2649i	0.584303	+	1.01204i
$485$	−2.48116	−	1.43250i	−0.112664	−	0.0650465i
$486$		0			0
$487$	0.521900	+	0.903957i	0.0236495	+	0.0409622i	0.877608	−	0.479379i	$-0.159138\pi$
$487$	0.521900	+	0.903957i	0.0236495	+	0.0409622i	−0.853958	+	0.520341i	$0.825805\pi$
$488$	−101.677			−4.60269
$489$		0			0
$490$		0			0
$491$	−36.0415	−	20.8085i	−1.62653	−	0.939076i	−0.985118	−	0.171878i	$-0.945016\pi$
$491$	−36.0415	−	20.8085i	−1.62653	−	0.939076i	−0.641410	−	0.767198i	$-0.721650\pi$
$492$		0			0
$493$	0.209265	+	0.120819i	0.00942480	+	0.00544141i
$494$	−33.0263	+	19.0677i	−1.48592	+	0.857898i
$495$		0			0
$496$		−	48.3999i		−	2.17322i
$497$		0			0
$498$		0			0
$499$	16.1447	+	27.9635i	0.722738	+	1.25182i	0.959898	+	0.280348i	$0.0904499\pi$
$499$	16.1447	+	27.9635i	0.722738	+	1.25182i	−0.237161	+	0.971470i	$0.576217\pi$
$500$	−54.9181			−2.45601
$501$		0			0
$502$		−	53.4038i		−	2.38353i
$503$	−39.9702			−1.78218			−0.891091	−	0.453825i	$-0.850059\pi$
$503$	−39.9702			−1.78218			−0.891091	+	0.453825i	$0.850059\pi$
$504$		0			0
$505$	−11.3862			−0.506681
$506$		−	20.4841i		−	0.910627i
$507$		0			0
$508$	−73.9996			−3.28320
$509$	11.3631	+	19.6815i	0.503661	+	0.872367i	0.999991	+	0.00423260i	$0.00134728\pi$
$509$	11.3631	+	19.6815i	0.503661	+	0.872367i	−0.496330	+	0.868134i	$0.665319\pi$
$510$		0			0
$511$		0			0
$512$			17.4067i			0.769277i
$513$		0			0
$514$	26.3692	−	15.2243i	1.16310	−	0.671515i
$515$	−17.9790	−	10.3802i	−0.792249	−	0.457405i
$516$		0			0
$517$	−3.08988	−	1.78394i	−0.135893	−	0.0784576i
$518$		0			0
$519$		0			0
$520$	−20.4972			−0.898863
$521$	15.0179	+	26.0118i	0.657948	+	1.13960i	0.981146	+	0.193268i	$0.0619087\pi$
$521$	15.0179	+	26.0118i	0.657948	+	1.13960i	−0.323198	+	0.946331i	$0.604758\pi$
$522$		0			0
$523$	−0.675300	−	0.389885i	−0.0295288	−	0.0170485i	0.485163	−	0.874424i	$-0.338760\pi$
$523$	−0.675300	−	0.389885i	−0.0295288	−	0.0170485i	−0.514692	+	0.857375i	$0.672094\pi$
$524$	32.9860	+	57.1334i	1.44100	+	2.49588i
$525$		0			0
$526$	4.41260	−	7.64285i	0.192399	−	0.333244i
$527$	3.65188	−	2.10841i	0.159078	−	0.0918439i
$528$		0			0
$529$	−6.87614	+	11.9098i	−0.298963	+	0.517819i
$530$	−16.1433	+	27.9609i	−0.701218	+	1.21455i
$531$		0			0
$532$		0			0
$533$	−10.9688	+	6.33281i	−0.475110	+	0.274305i
$534$		0			0
$535$		−	11.8891i		−	0.514012i
$536$			46.6415i			2.01460i
$537$		0			0
$538$	0.568399	−	0.328165i	0.0245054	−	0.0141482i
$539$		0			0
$540$		0			0
$541$	−1.02015	+	1.76696i	−0.0438598	+	0.0759674i	−0.887122	−	0.461535i	$-0.847299\pi$
$541$	−1.02015	+	1.76696i	−0.0438598	+	0.0759674i	0.843262	+	0.537503i	$0.180632\pi$
$542$	1.45335	−	2.51728i	0.0624268	−	0.108126i
$543$		0			0
$544$	−20.1640	+	11.6417i	−0.864522	+	0.499132i
$545$	6.26338	−	10.8485i	0.268294	−	0.464699i
$546$		0			0
$547$	−8.93590	−	15.4774i	−0.382071	−	0.661767i	0.609287	−	0.792950i	$-0.291456\pi$
$547$	−8.93590	−	15.4774i	−0.382071	−	0.661767i	−0.991358	+	0.131183i	$0.958123\pi$
$548$	−53.9064	−	31.1229i	−2.30277	−	1.32950i
$549$		0			0
$550$	−11.9663	−	20.7262i	−0.510244	−	0.883769i
$551$	−1.49957			−0.0638837
$552$		0			0
$553$		0			0
$554$	11.4986	+	6.63870i	0.488527	+	0.282051i
$555$		0			0
$556$	46.6463	+	26.9313i	1.97824	+	1.14214i
$557$	37.2049	−	21.4802i	1.57642	−	0.910147i	0.581068	−	0.813855i	$-0.302635\pi$
$557$	37.2049	−	21.4802i	1.57642	−	0.910147i	0.995353	−	0.0962924i	$-0.0306984\pi$
$558$		0			0
$559$		−	0.0247261i		−	0.00104580i
$560$		0			0
$561$		0			0
$562$	−18.0813	−	31.3177i	−0.762713	−	1.32106i
$563$	1.54748			0.0652184			0.0326092	−	0.999468i	$-0.489618\pi$
$563$	1.54748			0.0652184			0.0326092	+	0.999468i	$0.489618\pi$
$564$		0			0
$565$			13.2810i			0.558734i
$566$	10.1759			0.427726
$567$		0			0
$568$	108.906			4.56958
$569$			9.99861i			0.419164i	0.977791	+	0.209582i	$0.0672103\pi$
$569$			9.99861i			0.419164i	−0.977791	+	0.209582i	$0.932790\pi$
$570$		0			0
$571$	−2.79430			−0.116938			−0.0584689	−	0.998289i	$-0.518622\pi$
$571$	−2.79430			−0.116938			−0.0584689	+	0.998289i	$0.518622\pi$
$572$	−12.5073	−	21.6634i	−0.522958	−	0.905790i
$573$		0			0
$574$		0			0
$575$		−	10.8046i		−	0.450582i
$576$		0			0
$577$	−3.23689	+	1.86882i	−0.134754	+	0.0778000i	−0.565861	−	0.824500i	$-0.691456\pi$
$577$	−3.23689	+	1.86882i	−0.134754	+	0.0778000i	0.431108	+	0.902300i	$0.358123\pi$
$578$	36.4814	+	21.0626i	1.51743	+	0.876087i
$579$		0			0
$580$	−1.11626	−	0.644475i	−0.0463503	−	0.0267604i
$581$		0			0
$582$		0			0
$583$	−24.6386			−1.02043
$584$	39.2037	+	67.9028i	1.62226	+	2.80984i
$585$		0			0
$586$	29.9540	+	17.2940i	1.23739	+	0.714407i
$587$	−13.1249	−	22.7331i	−0.541725	−	0.938295i	−0.998805	−	0.0488692i	$-0.984438\pi$
$587$	−13.1249	−	22.7331i	−0.541725	−	0.938295i	0.457081	−	0.889425i	$-0.348895\pi$
$588$		0			0
$589$	−13.0845	+	22.6630i	−0.539136	+	0.933812i
$590$	34.4819	−	19.9081i	1.41960	−	0.819604i
$591$		0			0
$592$	−11.9573	+	20.7106i	−0.491441	+	0.851201i
$593$	1.79833	−	3.11481i	0.0738488	−	0.127910i	−0.826736	−	0.562590i	$-0.809805\pi$
$593$	1.79833	−	3.11481i	0.0738488	−	0.127910i	0.900585	+	0.434680i	$0.143138\pi$
$594$		0			0
$595$		0			0
$596$	−22.1522	+	12.7896i	−0.907391	+	0.523882i
$597$		0			0
$598$		−	15.5245i		−	0.634845i
$599$			23.8330i			0.973789i	0.873461	+	0.486895i	$0.161870\pi$
$599$			23.8330i			0.973789i	−0.873461	+	0.486895i	$0.838130\pi$
$600$		0			0
$601$	14.6034	−	8.43126i	0.595684	−	0.343918i	−0.171658	−	0.985157i	$-0.554912\pi$
$601$	14.6034	−	8.43126i	0.595684	−	0.343918i	0.767342	+	0.641238i	$0.221579\pi$
$602$		0			0
$603$		0			0
$604$	−30.2076	+	52.3212i	−1.22913	+	2.12892i
$605$	2.89695	−	5.01767i	0.117778	−	0.203997i
$606$		0			0
$607$	−9.07737	+	5.24082i	−0.368439	+	0.212718i	−0.672776	−	0.739846i	$-0.734898\pi$
$607$	−9.07737	+	5.24082i	−0.368439	+	0.212718i	0.304337	+	0.952564i	$0.401565\pi$
$608$	72.2463	−	125.134i	2.92997	−	5.07487i
$609$		0			0
$610$	18.3222	+	31.7349i	0.741842	+	1.28491i
$611$	−2.34176	−	1.35202i	−0.0947377	−	0.0546968i
$612$		0			0
$613$	23.9500	+	41.4827i	0.967333	+	1.67547i	0.703213	+	0.710979i	$0.251748\pi$
$613$	23.9500	+	41.4827i	0.967333	+	1.67547i	0.264120	+	0.964490i	$0.414919\pi$
$614$	−29.0541			−1.17253
$615$		0			0
$616$		0			0
$617$	−4.69477	−	2.71053i	−0.189004	−	0.109122i	0.402512	−	0.915415i	$-0.368137\pi$
$617$	−4.69477	−	2.71053i	−0.189004	−	0.109122i	−0.591516	+	0.806293i	$0.701470\pi$
$618$		0			0
$619$	27.9729	+	16.1501i	1.12432	+	0.649129i	0.942501	−	0.334202i	$-0.108467\pi$
$619$	27.9729	+	16.1501i	1.12432	+	0.649129i	0.181823	+	0.983331i	$0.441800\pi$
$620$	−19.4799	+	11.2467i	−0.782332	+	0.451680i
$621$		0			0
$622$			51.0204i			2.04573i
$623$		0			0
$624$		0			0
$625$	−2.69418	−	4.66646i	−0.107767	−	0.186658i
$626$	70.6196			2.82253
$627$		0			0
$628$			78.6338i			3.13783i
$629$	−2.08355			−0.0830765
$630$		0			0
$631$	−18.3539			−0.730656			−0.365328	−	0.930879i	$-0.619043\pi$
$631$	−18.3539			−0.730656			−0.365328	+	0.930879i	$0.619043\pi$
$632$		−	49.6917i		−	1.97663i
$633$		0			0
$634$	37.6253			1.49429
$635$	8.33836	+	14.4425i	0.330898	+	0.573132i
$636$		0			0
$637$		0			0
$638$		−	1.35218i		−	0.0535335i
$639$		0			0
$640$	29.5816	−	17.0789i	1.16931	−	0.675104i
$641$	9.07003	+	5.23658i	0.358245	+	0.206833i	0.668310	−	0.743882i	$-0.267018\pi$
$641$	9.07003	+	5.23658i	0.358245	+	0.206833i	−0.310066	+	0.950715i	$0.600351\pi$
$642$		0			0
$643$	−3.37572	−	1.94897i	−0.133125	−	0.0768600i	0.431958	−	0.901894i	$-0.357823\pi$
$643$	−3.37572	−	1.94897i	−0.133125	−	0.0768600i	−0.565084	+	0.825034i	$0.691156\pi$
$644$		0			0
$645$		0			0
$646$	24.3578			0.958344
$647$	−6.20269	−	10.7434i	−0.243853	−	0.422366i	0.717955	−	0.696089i	$-0.245078\pi$
$647$	−6.20269	−	10.7434i	−0.243853	−	0.422366i	−0.961809	+	0.273723i	$0.911745\pi$
$648$		0			0
$649$	26.3140	+	15.1924i	1.03291	+	0.596353i
$650$	−9.06905	−	15.7081i	−0.355717	−	0.616120i
$651$		0			0
$652$	−48.4615	+	83.9377i	−1.89790	+	3.28726i
$653$	−12.2749	+	7.08690i	−0.480353	+	0.277332i	−0.720564	−	0.693389i	$-0.756117\pi$
$653$	−12.2749	+	7.08690i	−0.480353	+	0.277332i	0.240211	+	0.970721i	$0.422784\pi$
$654$		0			0
$655$	7.43379	−	12.8757i	0.290462	−	0.503095i
$656$	46.4263	−	80.4126i	1.81264	−	3.13959i
$657$		0			0
$658$		0			0
$659$	17.2962	−	9.98594i	0.673763	−	0.388997i	−0.123738	−	0.992315i	$-0.539488\pi$
$659$	17.2962	−	9.98594i	0.673763	−	0.388997i	0.797501	+	0.603318i	$0.206155\pi$
$660$		0			0
$661$		−	24.3056i		−	0.945378i	−0.881229	−	0.472689i	$-0.843283\pi$
$661$		−	24.3056i		−	0.945378i	0.881229	−	0.472689i	$-0.156717\pi$
$662$			12.1480i			0.472146i
$663$		0			0
$664$	25.1900	−	14.5435i	0.977563	−	0.564396i
$665$		0			0
$666$		0			0
$667$	0.305228	−	0.528670i	0.0118185	−	0.0204702i
$668$	−3.19964	+	5.54194i	−0.123798	+	0.214424i
$669$		0			0
$670$	14.5575	−	8.40480i	0.562407	−	0.324706i
$671$	−13.9821	+	24.2177i	−0.539773	+	0.934914i
$672$		0			0
$673$	−1.82521	−	3.16135i	−0.0703566	−	0.121861i	0.828701	−	0.559692i	$-0.189080\pi$
$673$	−1.82521	−	3.16135i	−0.0703566	−	0.121861i	−0.899058	+	0.437830i	$0.855747\pi$
$674$	−76.9508	−	44.4275i	−2.96403	−	1.71129i
$675$		0			0
$676$	25.2163	+	43.6759i	0.969858	+	1.67984i
$677$	1.93735			0.0744585			0.0372292	−	0.999307i	$-0.488147\pi$
$677$	1.93735			0.0744585			0.0372292	+	0.999307i	$0.488147\pi$
$678$		0			0
$679$		0			0
$680$	11.3379	+	6.54597i	0.434790	+	0.251026i
$681$		0			0
$682$	−20.4356	−	11.7985i	−0.782519	−	0.451788i
$683$	−16.8815	+	9.74656i	−0.645954	+	0.372942i	−0.786905	−	0.617075i	$-0.788318\pi$
$683$	−16.8815	+	9.74656i	−0.645954	+	0.372942i	0.140950	+	0.990017i	$0.454984\pi$
$684$		0			0
$685$			14.0278i			0.535976i
$686$		0			0
$687$		0			0
$688$	0.0906345	+	0.156983i	0.00345541	+	0.00598494i
$689$	−18.6732			−0.711393
$690$		0			0
$691$			41.3215i			1.57194i	0.618261	+	0.785972i	$0.287837\pi$
$691$			41.3215i			1.57194i	−0.618261	+	0.785972i	$0.712163\pi$
$692$	96.1226			3.65403
$693$		0			0
$694$	−36.3186			−1.37863
$695$		−	12.1386i		−	0.460442i
$696$		0			0
$697$	8.08975			0.306421
$698$	−30.2273	−	52.3552i	−1.14412	−	1.98167i
$699$		0			0
$700$		0			0
$701$			27.3333i			1.03236i	0.856479	+	0.516182i	$0.172647\pi$
$701$			27.3333i			1.03236i	−0.856479	+	0.516182i	$0.827353\pi$
$702$		0			0
$703$	11.1979	−	6.46508i	0.422335	−	0.243835i
$704$	53.3293	+	30.7897i	2.00992	+	1.16043i
$705$		0			0
$706$	40.3893	+	23.3187i	1.52007	+	0.877613i
$707$		0			0
$708$		0			0
$709$	2.71269			0.101877			0.0509387	−	0.998702i	$-0.483779\pi$
$709$	2.71269			0.101877			0.0509387	+	0.998702i	$0.483779\pi$
$710$	−19.6248	−	33.9912i	−0.736506	−	1.27567i
$711$		0			0
$712$	−62.3845	−	36.0177i	−2.33796	−	1.34982i
$713$	−5.32654	−	9.22584i	−0.199480	−	0.345510i
$714$		0			0
$715$	−2.81868	+	4.88210i	−0.105413	+	0.182580i
$716$	69.9976	−	40.4131i	2.61593	−	1.51031i
$717$		0			0
$718$	−8.80292	+	15.2471i	−0.328522	+	0.569017i
$719$	−8.13931	+	14.0977i	−0.303545	+	0.525756i	−0.976936	−	0.213531i	$-0.931504\pi$
$719$	−8.13931	+	14.0977i	−0.303545	+	0.525756i	0.673391	+	0.739286i	$0.264837\pi$
$720$		0			0
$721$		0			0
$722$	−86.3365	+	49.8464i	−3.21311	+	1.85509i
$723$		0			0
$724$			42.6335i			1.58446i
$725$		−	0.713227i		−	0.0264886i
$726$		0			0
$727$	0.980123	−	0.565874i	0.0363508	−	0.0209871i	−0.481714	−	0.876328i	$-0.659986\pi$
$727$	0.980123	−	0.565874i	0.0363508	−	0.0209871i	0.518065	+	0.855341i	$0.326652\pi$
$728$		0			0
$729$		0			0
$730$	14.1290	−	24.4722i	0.522939	−	0.905757i
$731$	−0.00789650	+	0.0136771i	−0.000292063	+	0.000505867i
$732$		0			0
$733$	33.2085	−	19.1729i	1.22658	−	0.708169i	0.260270	−	0.965536i	$-0.416188\pi$
$733$	33.2085	−	19.1729i	1.22658	−	0.708169i	0.966314	+	0.257367i	$0.0828549\pi$
$734$	12.1946	−	21.1217i	0.450111	−	0.779615i
$735$		0			0
$736$	29.4106	+	50.9407i	1.08409	+	1.87770i
$737$	11.1092	+	6.41391i	0.409213	+	0.236259i
$738$		0			0
$739$	−5.36489	−	9.29226i	−0.197351	−	0.341821i	0.750318	−	0.661077i	$-0.229900\pi$
$739$	−5.36489	−	9.29226i	−0.197351	−	0.341821i	−0.947669	+	0.319256i	$0.896567\pi$
$740$	11.1141			0.408562
$741$		0			0
$742$		0			0
$743$	11.3308	+	6.54185i	0.415687	+	0.239997i	0.693230	−	0.720716i	$-0.256187\pi$
$743$	11.3308	+	6.54185i	0.415687	+	0.239997i	−0.277543	+	0.960713i	$0.589520\pi$
$744$		0			0
$745$	4.99228	+	2.88229i	0.182903	+	0.105599i
$746$	26.9927	−	15.5842i	0.988272	−	0.570579i
$747$		0			0
$748$			15.9773i			0.584188i
$749$		0			0
$750$		0			0
$751$	−13.1677	−	22.8071i	−0.480495	−	0.832242i	0.519254	−	0.854620i	$-0.326210\pi$
$751$	−13.1677	−	22.8071i	−0.480495	−	0.832242i	−0.999750	+	0.0223774i	$0.992876\pi$
$752$	19.8235			0.722887
$753$		0			0
$754$		−	1.02480i		−	0.0373209i
$755$	13.6153			0.495512
$756$		0			0
$757$	−32.6280			−1.18588			−0.592942	−	0.805245i	$-0.702034\pi$
$757$	−32.6280			−1.18588			−0.592942	+	0.805245i	$0.702034\pi$
$758$			46.3161i			1.68228i
$759$		0			0
$760$	−81.2465			−2.94712
$761$	−12.6727	−	21.9498i	−0.459385	−	0.795679i	0.539543	−	0.841958i	$-0.318597\pi$
$761$	−12.6727	−	21.9498i	−0.459385	−	0.795679i	−0.998929	+	0.0462793i	$0.985264\pi$
$762$		0			0
$763$		0			0
$764$			85.4946i			3.09309i
$765$		0			0
$766$	−38.0403	+	21.9626i	−1.37445	+	0.793541i
$767$	19.9429	+	11.5140i	0.720097	+	0.415748i
$768$		0			0
$769$	11.4964	+	6.63744i	0.414570	+	0.239352i	0.692752	−	0.721176i	$-0.256398\pi$
$769$	11.4964	+	6.63744i	0.414570	+	0.239352i	−0.278181	+	0.960529i	$0.589732\pi$
$770$		0			0
$771$		0			0
$772$	73.1772			2.63370
$773$	8.00680	+	13.8682i	0.287985	+	0.498804i	0.973329	−	0.229416i	$-0.0736815\pi$
$773$	8.00680	+	13.8682i	0.287985	+	0.498804i	−0.685344	+	0.728219i	$0.740348\pi$
$774$		0			0
$775$	−10.7790	−	6.22327i	−0.387194	−	0.223546i
$776$	10.7669	+	18.6488i	0.386509	+	0.669454i
$777$		0			0
$778$	25.3919	−	43.9801i	0.910344	−	1.57676i
$779$	−43.4777	+	25.1019i	−1.55775	+	0.899367i
$780$		0			0
$781$	14.9762	−	25.9395i	0.535890	−	0.928189i
$782$	−4.95789	+	8.58731i	−0.177294	+	0.307082i
$783$		0			0
$784$		0			0
$785$	15.3469	−	8.86054i	0.547755	−	0.316246i
$786$		0			0
$787$			4.90354i			0.174792i	0.996174	+	0.0873961i	$0.0278546\pi$
$787$			4.90354i			0.174792i	−0.996174	+	0.0873961i	$0.972145\pi$
$788$		−	101.016i		−	3.59855i
$789$		0			0
$790$	−15.5096	+	8.95445i	−0.551806	+	0.318585i
$791$		0			0
$792$		0			0
$793$	−10.5968	+	18.3542i	−0.376303	+	0.651776i
$794$	−41.9474	+	72.6551i	−1.48866	+	2.57843i
$795$		0			0
$796$	114.791	−	66.2748i	4.06867	−	2.34905i
$797$	−21.3994	+	37.0649i	−0.758006	+	1.31290i	0.185860	+	0.982576i	$0.440493\pi$
$797$	−21.3994	+	37.0649i	−0.758006	+	1.31290i	−0.943866	+	0.330328i	$0.892841\pi$
$798$		0			0
$799$	0.863557	+	1.49572i	0.0305505	+	0.0529149i
$800$	59.5167	+	34.3620i	2.10423	+	1.21488i
$801$		0			0
$802$	−1.25282	−	2.16995i	−0.0442386	−	0.0766235i
$803$	21.5644			0.760993
$804$		0			0
$805$		0			0
$806$	−15.4878	−	8.94188i	−0.545534	−	0.314964i
$807$		0			0
$808$	74.1152	+	42.7904i	2.60736	+	1.50536i
$809$	−30.5649	+	17.6467i	−1.07461	+	0.620424i	−0.929436	−	0.368983i	$-0.879706\pi$
$809$	−30.5649	+	17.6467i	−1.07461	+	0.620424i	−0.145169	+	0.989407i	$0.546373\pi$
$810$		0			0
$811$		−	21.0223i		−	0.738193i	−0.929391	−	0.369096i	$-0.879667\pi$
$811$		−	21.0223i		−	0.738193i	0.929391	−	0.369096i	$-0.120333\pi$
$812$		0			0
$813$		0			0
$814$	5.82968	+	10.0973i	0.204330	+	0.353910i
$815$	21.8428			0.765119
$816$		0			0
$817$		−	0.0980089i		−	0.00342890i
$818$	−20.5372			−0.718067
$819$		0			0
$820$	−43.1525			−1.50695
$821$			34.4820i			1.20343i	0.798710	+	0.601716i	$0.205516\pi$
$821$			34.4820i			1.20343i	−0.798710	+	0.601716i	$0.794484\pi$
$822$		0			0
$823$	−38.9899			−1.35910			−0.679552	−	0.733628i	$-0.737826\pi$
$823$	−38.9899			−1.35910			−0.679552	+	0.733628i	$0.737826\pi$
$824$	78.0191	+	135.133i	2.71792	+	4.70758i
$825$		0			0
$826$		0			0
$827$		−	47.2537i		−	1.64317i	−0.570086	−	0.821585i	$-0.693090\pi$
$827$		−	47.2537i		−	1.64317i	0.570086	−	0.821585i	$-0.306910\pi$
$828$		0			0
$829$	42.5588	−	24.5713i	1.47813	−	0.853397i	0.478432	−	0.878124i	$-0.341205\pi$
$829$	42.5588	−	24.5713i	1.47813	−	0.853397i	0.999694	+	0.0247275i	$0.00787180\pi$
$830$	−9.07850	−	5.24147i	−0.315119	−	0.181934i
$831$		0			0
$832$	40.4174	+	23.3350i	1.40122	+	0.808995i
$833$		0			0
$834$		0			0
$835$	1.44216			0.0499079
$836$	−49.5763	−	85.8687i	−1.71463	−	2.96983i
$837$		0			0
$838$	13.3746	+	7.72182i	0.462017	+	0.266746i
$839$	26.0780	+	45.1684i	0.900312	+	1.55939i	0.827090	+	0.562070i	$0.189995\pi$
$839$	26.0780	+	45.1684i	0.900312	+	1.55939i	0.0732219	+	0.997316i	$0.476672\pi$
$840$		0			0
$841$	−14.4799	+	25.0798i	−0.499305	+	0.864822i
$842$	27.5030	−	15.8789i	0.947816	−	0.547222i
$843$		0			0
$844$	−19.2565	+	33.3533i	−0.662838	+	1.14807i
$845$	5.68280	−	9.84290i	0.195494	−	0.338606i
$846$		0			0
$847$		0			0
$848$	118.554	−	68.4472i	4.07116	−	2.35049i
$849$		0			0
$850$			11.5851i			0.397366i
$851$			5.26372i			0.180438i
$852$		0			0
$853$	13.4028	−	7.73808i	0.458902	−	0.264947i	−0.252681	−	0.967550i	$-0.581312\pi$
$853$	13.4028	−	7.73808i	0.458902	−	0.264947i	0.711582	+	0.702603i	$0.247979\pi$
$854$		0			0
$855$		0			0
$856$	−44.6804	+	77.3886i	−1.52714	+	2.64509i
$857$	24.4356	−	42.3238i	0.834706	−	1.44575i	−0.0595642	−	0.998224i	$-0.518971\pi$
$857$	24.4356	−	42.3238i	0.834706	−	1.44575i	0.894270	−	0.447528i	$-0.147696\pi$
$858$		0			0
$859$	−8.45000	+	4.87861i	−0.288310	+	0.166456i	−0.637180	−	0.770715i	$-0.719899\pi$
$859$	−8.45000	+	4.87861i	−0.288310	+	0.166456i	0.348869	+	0.937171i	$0.386566\pi$
$860$	0.0421217	−	0.0729569i	0.00143634	−	0.00248781i
$861$		0			0
$862$	−36.4356	−	63.1083i	−1.24100	−	2.14948i
$863$	23.9462	+	13.8253i	0.815138	+	0.470620i	0.848737	−	0.528815i	$-0.177363\pi$
$863$	23.9462	+	13.8253i	0.815138	+	0.470620i	−0.0335987	+	0.999435i	$0.510697\pi$
$864$		0			0
$865$	−10.8312	−	18.7602i	−0.368272	−	0.637866i
$866$	−76.1256			−2.58685
$867$		0			0
$868$		0			0
$869$	−11.8357	−	6.83337i	−0.401500	−	0.231806i
$870$		0			0
$871$	8.41949	+	4.86100i	0.285284	+	0.164709i
$872$	−81.5391	+	47.0766i	−2.76126	+	1.59422i
$873$		0			0
$874$		−	61.5357i		−	2.08148i
$875$		0			0
$876$		0			0
$877$	0.932622	+	1.61535i	0.0314924	+	0.0545465i	0.881342	−	0.472479i	$-0.156641\pi$
$877$	0.932622	+	1.61535i	0.0314924	+	0.0545465i	−0.849850	+	0.527025i	$0.823307\pi$
$878$	25.2633			0.852596
$879$		0			0
$880$		−	41.3279i		−	1.39316i
$881$	0.0273875			0.000922707			0.000461353	−	1.00000i	$-0.499853\pi$
$881$	0.0273875			0.000922707			0.000461353		1.00000i	$0.499853\pi$
$882$		0			0
$883$	36.2074			1.21848			0.609239	−	0.792987i	$-0.291475\pi$
$883$	36.2074			1.21848			0.609239	+	0.792987i	$0.291475\pi$
$884$			12.1089i			0.407267i
$885$		0			0
$886$	30.7199			1.03206
$887$	−12.6626	−	21.9323i	−0.425170	−	0.736415i	0.571267	−	0.820765i	$-0.306452\pi$
$887$	−12.6626	−	21.9323i	−0.425170	−	0.736415i	−0.996436	+	0.0843491i	$0.973119\pi$
$888$		0			0
$889$		0			0
$890$			25.9616i			0.870235i
$891$		0			0
$892$	−112.470	+	64.9343i	−3.76576	+	2.17416i
$893$	−9.28223	−	5.35910i	−0.310618	−	0.179335i
$894$		0			0
$895$	−15.7748	−	9.10759i	−0.527294	−	0.304433i
$896$		0			0
$897$		0			0
$898$	41.5250			1.38571
$899$	−0.351613	−	0.609012i	−0.0117270	−	0.0203117i
$900$		0			0
$901$	10.3290	+	5.96345i	0.344109	+	0.198671i
$902$	−22.6348	−	39.2046i	−0.753655	−	1.30537i
$903$		0			0
$904$	49.9110	−	86.4483i	1.66001	−	2.87523i
$905$	8.32075	−	4.80399i	0.276591	−	0.159690i
$906$		0			0
$907$	19.4060	−	33.6122i	0.644366	−	1.11608i	−0.340081	−	0.940396i	$-0.610455\pi$
$907$	19.4060	−	33.6122i	0.644366	−	1.11608i	0.984447	−	0.175679i	$-0.0562121\pi$
$908$	1.28260	−	2.22153i	0.0425646	−	0.0737240i
$909$		0			0
$910$		0			0
$911$	43.6110	−	25.1788i	1.44490	−	0.834211i	0.446725	−	0.894671i	$-0.352590\pi$
$911$	43.6110	−	25.1788i	1.44490	−	0.834211i	0.998171	+	0.0604602i	$0.0192568\pi$
$912$		0			0
$913$		−	7.99980i		−	0.264755i
$914$		−	24.8481i		−	0.821901i
$915$		0			0
$916$	−41.6581	+	24.0513i	−1.37642	+	0.794677i
$917$		0			0
$918$		0			0
$919$	1.49845	−	2.59539i	0.0494293	−	0.0856140i	−0.840252	−	0.542196i	$-0.817593\pi$
$919$	1.49845	−	2.59539i	0.0494293	−	0.0856140i	0.889681	+	0.456582i	$0.150926\pi$
$920$	16.5372	−	28.6434i	0.545217	−	0.944343i
$921$		0			0
$922$	−77.5863	+	44.7945i	−2.55517	+	1.47523i
$923$	11.3502	−	19.6591i	0.373596	−	0.647088i
$924$		0			0
$925$	3.07494	+	5.32595i	0.101103	+	0.175116i
$926$	18.3729	+	10.6076i	0.603771	+	0.348588i
$927$		0			0
$928$	1.94144	+	3.36268i	0.0637310	+	0.110385i
$929$	32.2215			1.05715			0.528577	−	0.848885i	$-0.322726\pi$
$929$	32.2215			1.05715			0.528577	+	0.848885i	$0.322726\pi$
$930$		0			0
$931$		0			0
$932$	−51.3888	−	29.6694i	−1.68330	−	0.971852i
$933$		0			0
$934$	−48.5064	−	28.0052i	−1.58718	−	0.916358i
$935$	3.11828	−	1.80034i	0.101979	−	0.0588774i
$936$		0			0
$937$		−	3.07038i		−	0.100305i	−0.998742	−	0.0501525i	$-0.984029\pi$
$937$		−	3.07038i		−	0.100305i	0.998742	−	0.0501525i	$-0.0159708\pi$
$938$		0			0
$939$		0			0
$940$	−4.60640	−	7.97852i	−0.150244	−	0.260231i
$941$	−38.8272			−1.26573			−0.632865	−	0.774263i	$-0.718121\pi$
$941$	−38.8272			−1.26573			−0.632865	+	0.774263i	$0.718121\pi$
$942$		0			0
$943$		−	20.4373i		−	0.665532i
$944$	−168.820			−5.49464
$945$		0			0
$946$	0.0883763			0.00287336
$947$		−	18.7513i		−	0.609337i	−0.952459	−	0.304668i	$-0.901454\pi$
$947$		−	18.7513i		−	0.609337i	0.952459	−	0.304668i	$-0.0985456\pi$
$948$		0			0
$949$	16.3433			0.530527
$950$	−35.9477	−	62.2632i	−1.16630	−	2.02008i
$951$		0			0
$952$		0			0
$953$			47.6453i			1.54338i	0.635997	+	0.771692i	$0.280589\pi$
$953$			47.6453i			1.54338i	−0.635997	+	0.771692i	$0.719411\pi$
$954$		0			0
$955$	16.6859	−	9.63362i	0.539944	−	0.311737i
$956$	64.2911	+	37.1185i	2.07932	+	1.20050i
$957$		0			0
$958$	−6.24009	−	3.60272i	−0.201608	−	0.116398i
$959$		0			0
$960$		0			0
$961$	18.7280			0.604129
$962$	4.41821	+	7.65257i	0.142449	+	0.246729i
$963$		0			0
$964$	−57.2104	−	33.0304i	−1.84262	−	1.06384i
$965$	−8.24569	−	14.2819i	−0.265438	−	0.459752i
$966$		0			0
$967$	25.8005	−	44.6878i	0.829689	−	1.43706i	−0.0685936	−	0.997645i	$-0.521851\pi$
$967$	25.8005	−	44.6878i	0.829689	−	1.43706i	0.898282	−	0.439419i	$-0.144815\pi$
$968$	−37.7137	+	21.7740i	−1.21216	+	0.699843i
$969$		0			0
$970$	3.88040	−	6.72104i	0.124592	−	0.215800i
$971$	−14.1933	+	24.5836i	−0.455485	+	0.788924i	−0.998716	−	0.0506597i	$-0.983868\pi$
$971$	−14.1933	+	24.5836i	−0.455485	+	0.788924i	0.543231	+	0.839584i	$0.317201\pi$
$972$		0			0
$973$		0			0
$974$	−2.44867	+	1.41374i	−0.0784603	+	0.0452991i
$975$		0			0
$976$		−	155.372i		−	4.97332i
$977$			41.1908i			1.31781i	0.752227	+	0.658904i	$0.228980\pi$
$977$			41.1908i			1.31781i	−0.752227	+	0.658904i	$0.771020\pi$
$978$		0			0
$979$	−17.1576	+	9.90597i	−0.548361	+	0.316596i
$980$		0			0
$981$		0			0
$982$	56.3668	−	97.6302i	1.79874	−	3.11550i
$983$	−26.4017	+	45.7291i	−0.842085	+	1.45853i	0.0460447	+	0.998939i	$0.485338\pi$
$983$	−26.4017	+	45.7291i	−0.842085	+	1.45853i	−0.888129	+	0.459594i	$0.847995\pi$
$984$		0			0
$985$	−19.7153	+	11.3826i	−0.628181	+	0.362680i
$986$	−0.327278	+	0.566862i	−0.0104227	+	0.0180526i
$987$		0			0
$988$	−37.5731	−	65.0784i	−1.19536	−	2.07042i
$989$	0.0345529	+	0.0199491i	0.00109872	+	0.000634346i
$990$		0			0
$991$	−8.24486	−	14.2805i	−0.261907	−	0.453636i	0.704842	−	0.709364i	$-0.251018\pi$
$991$	−8.24486	−	14.2805i	−0.261907	−	0.453636i	−0.966749	+	0.255729i	$0.917685\pi$
$992$	67.7603			2.15139
$993$		0			0
$994$		0			0
$995$	−25.8696	−	14.9358i	−0.820122	−	0.473498i
$996$		0			0
$997$	−42.4857	−	24.5291i	−1.34553	−	0.776845i	−0.357921	−	0.933752i	$-0.616514\pi$
$997$	−42.4857	−	24.5291i	−1.34553	−	0.776845i	−0.987613	+	0.156907i	$0.949848\pi$
$998$	−75.7484	+	43.7333i	−2.39777	+	1.38435i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.i.d.1097.21		48
3.2	odd	2		441.2.i.d.68.1		48
7.2	even	3		1323.2.o.e.881.24		48
7.3	odd	6		1323.2.s.d.962.1		48
7.4	even	3		1323.2.s.d.962.2		48
7.5	odd	6		1323.2.o.e.881.23		48
7.6	odd	2	inner	1323.2.i.d.1097.6		48
9.2	odd	6		1323.2.s.d.656.1		48
9.7	even	3		441.2.s.d.362.24		48
21.2	odd	6		441.2.o.e.293.2	yes	48
21.5	even	6		441.2.o.e.293.1	yes	48
21.11	odd	6		441.2.s.d.374.23		48
21.17	even	6		441.2.s.d.374.24		48
21.20	even	2		441.2.i.d.68.2		48
63.2	odd	6		1323.2.o.e.440.23		48
63.11	odd	6	inner	1323.2.i.d.521.6		48
63.16	even	3		441.2.o.e.146.1	✓	48
63.20	even	6		1323.2.s.d.656.2		48
63.25	even	3		441.2.i.d.227.24		48
63.34	odd	6		441.2.s.d.362.23		48
63.38	even	6	inner	1323.2.i.d.521.21		48
63.47	even	6		1323.2.o.e.440.24		48
63.52	odd	6		441.2.i.d.227.23		48
63.61	odd	6		441.2.o.e.146.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.1		48	3.2	odd	2
441.2.i.d.68.2		48	21.20	even	2
441.2.i.d.227.23		48	63.52	odd	6
441.2.i.d.227.24		48	63.25	even	3
441.2.o.e.146.1	✓	48	63.16	even	3
441.2.o.e.146.2	yes	48	63.61	odd	6
441.2.o.e.293.1	yes	48	21.5	even	6
441.2.o.e.293.2	yes	48	21.2	odd	6
441.2.s.d.362.23		48	63.34	odd	6
441.2.s.d.362.24		48	9.7	even	3
441.2.s.d.374.23		48	21.11	odd	6
441.2.s.d.374.24		48	21.17	even	6
1323.2.i.d.521.6		48	63.11	odd	6	inner
1323.2.i.d.521.21		48	63.38	even	6	inner
1323.2.i.d.1097.6		48	7.6	odd	2	inner
1323.2.i.d.1097.21		48	1.1	even	1	trivial
1323.2.o.e.440.23		48	63.2	odd	6
1323.2.o.e.440.24		48	63.47	even	6
1323.2.o.e.881.23		48	7.5	odd	6
1323.2.o.e.881.24		48	7.2	even	3
1323.2.s.d.656.1		48	9.2	odd	6
1323.2.s.d.656.2		48	63.20	even	6
1323.2.s.d.962.1		48	7.3	odd	6
1323.2.s.d.962.2		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)

\(f(q)\)	\(=\)	\(q+2.70883i q^{2} -5.33776 q^{4} +(0.601464 + 1.04177i) q^{5} -9.04141i q^{8} +(-2.82197 + 1.62926i) q^{10} +(-2.15351 - 1.24333i) q^{11} +(-1.63211 - 0.942300i) q^{13} +13.8161 q^{16} +(0.601863 + 1.04246i) q^{17} +(-6.46933 - 3.73507i) q^{19} +(-3.21047 - 5.56070i) q^{20} +(3.36797 - 5.83350i) q^{22} +(2.63359 - 1.52050i) q^{23} +(1.77648 - 3.07696i) q^{25} +(2.55253 - 4.42111i) q^{26} +(0.173847 - 0.100371i) q^{29} -3.50314i q^{31} +19.3427i q^{32} +(-2.82384 + 1.63034i) q^{34} +(-0.865458 + 1.49902i) q^{37} +(10.1177 - 17.5243i) q^{38} +(9.41904 - 5.43809i) q^{40} +(3.36029 - 5.82020i) q^{41} +(0.00656005 + 0.0113623i) q^{43} +(11.4949 + 6.63660i) q^{44} +(4.11878 + 7.13394i) q^{46} +1.43481 q^{47} +(8.33495 + 4.81219i) q^{50} +(8.71182 + 5.02977i) q^{52} +(8.58085 - 4.95416i) q^{53} -2.99128i q^{55} +(0.271887 + 0.470923i) q^{58} -12.2191 q^{59} -11.2457i q^{61} +9.48942 q^{62} -24.7638 q^{64} -2.26704i q^{65} -5.15865 q^{67} +(-3.21260 - 5.56438i) q^{68} +12.0452i q^{71} +(-7.51020 + 4.33602i) q^{73} +(-4.06058 - 2.34438i) q^{74} +(34.5317 + 19.9369i) q^{76} +5.49601 q^{79} +(8.30991 + 14.3932i) q^{80} +(15.7659 + 9.10246i) q^{82} +(1.60854 + 2.78607i) q^{83} +(-0.723998 + 1.25400i) q^{85} +(-0.0307786 + 0.0177700i) q^{86} +(-11.2415 + 19.4708i) q^{88} +(3.98364 - 6.89986i) q^{89} +(-14.0574 + 8.11607i) q^{92} +3.88665i q^{94} -8.98604i q^{95} +(-2.06260 + 1.19084i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} - 24 q^{11} + 48 q^{16} - 48 q^{23} - 24 q^{25} + 96 q^{44} - 48 q^{50} + 48 q^{53} - 48 q^{64} - 168 q^{74} + 48 q^{79} - 24 q^{85} + 24 q^{86} + 144 q^{92}+O(q^{100}) \) 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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