LMFDB - Embedded newform 1323.2.s.d.656.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(656,1323)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1323.656");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 441)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			656.11
Character	$\chi$	$=$	1323.656
Dual form			1323.2.s.d.962.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.367369 + 0.212101i) q^{2} +(-0.910027 + 1.57621i) q^{4} +3.60763 q^{5} -1.62047i q^{8} +O(q^{10})$	\(q+(-0.367369 + 0.212101i) q^{2} +(-0.910027 + 1.57621i) q^{4} +3.60763 q^{5} -1.62047i q^{8} +(-1.32533 + 0.765180i) q^{10} +3.70603i q^{11} +(5.23479 - 3.02231i) q^{13} +(-1.47635 - 2.55711i) q^{16} +(-0.532108 - 0.921637i) q^{17} +(3.16265 + 1.82596i) q^{19} +(-3.28304 + 5.68639i) q^{20} +(-0.786052 - 1.36148i) q^{22} -0.363239i q^{23} +8.01497 q^{25} +(-1.28207 + 2.22060i) q^{26} +(0.857560 + 0.495112i) q^{29} +(-0.939786 - 0.542586i) q^{31} +(3.89147 + 2.24674i) q^{32} +(0.390960 + 0.225721i) q^{34} +(4.00186 - 6.93143i) q^{37} -1.54915 q^{38} -5.84605i q^{40} +(2.09005 + 3.62007i) q^{41} +(-1.89758 + 3.28670i) q^{43} +(-5.84149 - 3.37259i) q^{44} +(0.0770432 + 0.133443i) q^{46} +(-2.83849 - 4.91640i) q^{47} +(-2.94445 + 1.69998i) q^{50} +11.0015i q^{52} +(-3.92463 + 2.26589i) q^{53} +13.3700i q^{55} -0.420055 q^{58} +(-5.62746 + 9.74705i) q^{59} +(-0.0238258 + 0.0137558i) q^{61} +0.460331 q^{62} +3.99926 q^{64} +(18.8852 - 10.9034i) q^{65} +(4.86489 - 8.42624i) q^{67} +1.93693 q^{68} +5.55775i q^{71} +(1.95561 - 1.12907i) q^{73} +3.39519i q^{74} +(-5.75619 + 3.32334i) q^{76} +(-3.26604 - 5.65694i) q^{79} +(-5.32612 - 9.22511i) q^{80} +(-1.53564 - 0.886601i) q^{82} +(-1.52977 + 2.64964i) q^{83} +(-1.91965 - 3.32492i) q^{85} -1.60991i q^{86} +6.00552 q^{88} +(-7.47952 + 12.9549i) q^{89} +(0.572542 + 0.330557i) q^{92} +(2.08554 + 1.20409i) q^{94} +(11.4097 + 6.58737i) q^{95} +(1.67018 + 0.964277i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4}+O(q^{10}) $ 48 * q + 24 * q^4	$ 48 q + 24 q^{4} - 24 q^{16} + 48 q^{25} + 120 q^{32} - 96 q^{44} - 48 q^{50} - 48 q^{53} - 48 q^{64} + 120 q^{65} - 24 q^{79} - 24 q^{85} + 144 q^{92} + 96 q^{95}+O(q^{100}) $ 48 * q + 24 * q^4 - 24 * q^16 + 48 * q^25 + 120 * q^32 - 96 * q^44 - 48 * q^50 - 48 * q^53 - 48 * q^64 + 120 * q^65 - 24 * q^79 - 24 * q^85 + 144 * q^92 + 96 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.367369	+	0.212101i	−0.259769	+	0.149978i	−0.624229	−	0.781241i	$-0.714587\pi$
$2$	−0.367369	+	0.212101i	−0.259769	+	0.149978i	0.364460	+	0.931219i	$0.381254\pi$
$3$		0			0
$3$		0			0
$4$	−0.910027	+	1.57621i	−0.455013	+	0.788106i
$5$	3.60763			1.61338			0.806690	−	0.590975i	$-0.201257\pi$
$5$	3.60763			1.61338			0.806690	+	0.590975i	$0.201257\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	1.62047i		−	0.572923i
$9$		0			0
$10$	−1.32533	+	0.765180i	−0.419106	+	0.241971i
$11$			3.70603i			1.11741i	0.829366	+	0.558705i	$0.188702\pi$
$11$			3.70603i			1.11741i	−0.829366	+	0.558705i	$0.811298\pi$
$12$		0			0
$13$	5.23479	−	3.02231i	1.45187	−	0.838238i	0.453283	−	0.891367i	$-0.350253\pi$
$13$	5.23479	−	3.02231i	1.45187	−	0.838238i	0.998588	+	0.0531292i	$0.0169195\pi$
$14$		0			0
$15$		0			0
$16$	−1.47635	−	2.55711i	−0.369088	−	0.639279i
$17$	−0.532108	−	0.921637i	−0.129055	−	0.223530i	0.794256	−	0.607584i	$-0.207861\pi$
$17$	−0.532108	−	0.921637i	−0.129055	−	0.223530i	−0.923311	+	0.384054i	$0.874528\pi$
$18$		0			0
$19$	3.16265	+	1.82596i	0.725561	+	0.418903i	0.816796	−	0.576926i	$-0.195748\pi$
$19$	3.16265	+	1.82596i	0.725561	+	0.418903i	−0.0912348	+	0.995829i	$0.529081\pi$
$20$	−3.28304	+	5.68639i	−0.734109	+	1.27151i
$21$		0			0
$22$	−0.786052	−	1.36148i	−0.167587	−	0.290269i
$23$		−	0.363239i		−	0.0757406i	−0.999283	−	0.0378703i	$-0.987943\pi$
$23$		−	0.363239i		−	0.0757406i	0.999283	−	0.0378703i	$-0.0120574\pi$
$24$		0			0
$25$	8.01497			1.60299
$26$	−1.28207	+	2.22060i	−0.251434	+	0.435496i
$27$		0			0
$28$		0			0
$29$	0.857560	+	0.495112i	0.159245	+	0.0919401i	0.577505	−	0.816387i	$-0.304027\pi$
$29$	0.857560	+	0.495112i	0.159245	+	0.0919401i	−0.418260	+	0.908327i	$0.637360\pi$
$30$		0			0
$31$	−0.939786	−	0.542586i	−0.168791	−	0.0974513i	0.413225	−	0.910629i	$-0.364402\pi$
$31$	−0.939786	−	0.542586i	−0.168791	−	0.0974513i	−0.582015	+	0.813178i	$0.697736\pi$
$32$	3.89147	+	2.24674i	0.687921	+	0.397171i
$33$		0			0
$34$	0.390960	+	0.225721i	0.0670490	+	0.0387108i
$35$		0			0
$36$		0			0
$37$	4.00186	−	6.93143i	0.657902	−	1.13952i	−0.323256	−	0.946312i	$-0.604777\pi$
$37$	4.00186	−	6.93143i	0.657902	−	1.13952i	0.981158	−	0.193208i	$-0.0618893\pi$
$38$	−1.54915			−0.251305
$39$		0			0
$40$		−	5.84605i		−	0.924342i
$41$	2.09005	+	3.62007i	0.326411	+	0.565360i	0.981797	−	0.189934i	$-0.0608275\pi$
$41$	2.09005	+	3.62007i	0.326411	+	0.565360i	−0.655386	+	0.755294i	$0.727494\pi$
$42$		0			0
$43$	−1.89758	+	3.28670i	−0.289378	+	0.501217i	−0.973661	−	0.227999i	$-0.926782\pi$
$43$	−1.89758	+	3.28670i	−0.289378	+	0.501217i	0.684284	+	0.729216i	$0.260115\pi$
$44$	−5.84149	−	3.37259i	−0.880638	−	0.508437i
$45$		0			0
$46$	0.0770432	+	0.133443i	0.0113594	+	0.0196751i
$47$	−2.83849	−	4.91640i	−0.414036	−	0.717131i	0.581291	−	0.813696i	$-0.302548\pi$
$47$	−2.83849	−	4.91640i	−0.414036	−	0.717131i	−0.995327	+	0.0965648i	$0.969215\pi$
$48$		0			0
$49$		0			0
$50$	−2.94445	+	1.69998i	−0.416408	+	0.240413i
$51$		0			0
$52$			11.0015i			1.52564i
$53$	−3.92463	+	2.26589i	−0.539089	+	0.311243i	−0.744710	−	0.667389i	$-0.767412\pi$
$53$	−3.92463	+	2.26589i	−0.539089	+	0.311243i	0.205621	+	0.978632i	$0.434079\pi$
$54$		0			0
$55$			13.3700i			1.80281i
$56$		0			0
$57$		0			0
$58$	−0.420055			−0.0551559
$59$	−5.62746	+	9.74705i	−0.732633	+	1.26896i	0.223121	+	0.974791i	$0.428376\pi$
$59$	−5.62746	+	9.74705i	−0.732633	+	1.26896i	−0.955754	+	0.294167i	$0.904958\pi$
$60$		0			0
$61$	−0.0238258	+	0.0137558i	−0.00305058	+	0.00176126i	−0.501525	−	0.865143i	$-0.667227\pi$
$61$	−0.0238258	+	0.0137558i	−0.00305058	+	0.00176126i	0.498474	+	0.866905i	$0.333894\pi$
$62$	0.460331			0.0584621
$63$		0			0
$64$	3.99926			0.499908
$65$	18.8852	−	10.9034i	2.34242	−	1.35240i
$66$		0			0
$67$	4.86489	−	8.42624i	0.594341	−	1.02943i	−0.399298	−	0.916821i	$-0.630746\pi$
$67$	4.86489	−	8.42624i	0.594341	−	1.02943i	0.993640	−	0.112608i	$-0.0359204\pi$
$68$	1.93693			0.234887
$69$		0			0
$70$		0			0
$71$			5.55775i			0.659584i	0.944054	+	0.329792i	$0.106979\pi$
$71$			5.55775i			0.659584i	−0.944054	+	0.329792i	$0.893021\pi$
$72$		0			0
$73$	1.95561	−	1.12907i	0.228887	−	0.132148i	−0.381172	−	0.924504i	$-0.624479\pi$
$73$	1.95561	−	1.12907i	0.228887	−	0.132148i	0.610058	+	0.792356i	$0.291146\pi$
$74$			3.39519i			0.394683i
$75$		0			0
$76$	−5.75619	+	3.32334i	−0.660280	+	0.381213i
$77$		0			0
$78$		0			0
$79$	−3.26604	−	5.65694i	−0.367458	−	0.636456i	0.621710	−	0.783248i	$-0.286438\pi$
$79$	−3.26604	−	5.65694i	−0.367458	−	0.636456i	−0.989167	+	0.146792i	$0.953105\pi$
$80$	−5.32612	−	9.22511i	−0.595479	−	1.03140i
$81$		0			0
$82$	−1.53564	−	0.886601i	−0.169583	−	0.0979087i
$83$	−1.52977	+	2.64964i	−0.167914	+	0.290836i	−0.937686	−	0.347483i	$-0.887036\pi$
$83$	−1.52977	+	2.64964i	−0.167914	+	0.290836i	0.769772	+	0.638319i	$0.220370\pi$
$84$		0			0
$85$	−1.91965	−	3.32492i	−0.208215	−	0.360639i
$86$		−	1.60991i		−	0.173601i
$87$		0			0
$88$	6.00552			0.640190
$89$	−7.47952	+	12.9549i	−0.792827	+	1.37322i	0.131382	+	0.991332i	$0.458058\pi$
$89$	−7.47952	+	12.9549i	−0.792827	+	1.37322i	−0.924210	+	0.381886i	$0.875275\pi$
$90$		0			0
$91$		0			0
$92$	0.572542	+	0.330557i	0.0596916	+	0.0344630i
$93$		0			0
$94$	2.08554	+	1.20409i	0.215107	+	0.124192i
$95$	11.4097	+	6.58737i	1.17061	+	0.675850i
$96$		0			0
$97$	1.67018	+	0.964277i	0.169581	+	0.0979075i	0.582388	−	0.812911i	$-0.302118\pi$
$97$	1.67018	+	0.964277i	0.169581	+	0.0979075i	−0.412807	+	0.910818i	$0.635452\pi$
$98$		0			0
$99$		0			0
$100$	−7.29384	+	12.6333i	−0.729384	+	1.26333i
$101$	−6.43623			−0.640429			−0.320214	−	0.947345i	$-0.603755\pi$
$101$	−6.43623			−0.640429			−0.320214	+	0.947345i	$0.603755\pi$
$102$		0			0
$103$			9.72162i			0.957899i	0.877842	+	0.478950i	$0.158982\pi$
$103$			9.72162i			0.957899i	−0.877842	+	0.478950i	$0.841018\pi$
$104$	−4.89756	−	8.48283i	−0.480246	−	0.831810i
$105$		0			0
$106$	0.961191	−	1.66483i	0.0933591	−	0.161703i
$107$	3.43139	+	1.98112i	0.331725	+	0.191522i	0.656607	−	0.754233i	$-0.271991\pi$
$107$	3.43139	+	1.98112i	0.331725	+	0.191522i	−0.324881	+	0.945755i	$0.605324\pi$
$108$		0			0
$109$	8.66263	+	15.0041i	0.829729	+	1.43713i	0.898250	+	0.439484i	$0.144839\pi$
$109$	8.66263	+	15.0041i	0.829729	+	1.43713i	−0.0685210	+	0.997650i	$0.521828\pi$
$110$	−2.83578	−	4.91172i	−0.270381	−	0.468314i
$111$		0			0
$112$		0			0
$113$	8.50273	−	4.90905i	0.799869	−	0.461805i	−0.0435562	−	0.999051i	$-0.513869\pi$
$113$	8.50273	−	4.90905i	0.799869	−	0.461805i	0.843425	+	0.537246i	$0.180535\pi$
$114$		0			0
$115$		−	1.31043i		−	0.122198i
$116$	−1.56080	+	0.901131i	−0.144917	+	0.0836679i
$117$		0			0
$118$		−	4.77435i		−	0.439515i
$119$		0			0
$120$		0			0
$121$	−2.73468			−0.248607
$122$	0.00583524	−	0.0101069i	0.000528298	−	0.000915039i
$123$		0			0
$124$	1.71046	−	0.987535i	0.153604	−	0.0886833i
$125$	10.8769			0.972858
$126$		0			0
$127$	−11.7328			−1.04112			−0.520560	−	0.853825i	$-0.674277\pi$
$127$	−11.7328			−1.04112			−0.520560	+	0.853825i	$0.674277\pi$
$128$	−9.25214	+	5.34173i	−0.817782	+	0.472146i
$129$		0			0
$130$	−4.62522	+	8.01111i	−0.405659	+	0.702621i
$131$	21.0026			1.83500			0.917502	−	0.397732i	$-0.130203\pi$
$131$	21.0026			1.83500			0.917502	+	0.397732i	$0.130203\pi$
$132$		0			0
$133$		0			0
$134$			4.12738i			0.356552i
$135$		0			0
$136$	−1.49349	+	0.862265i	−0.128065	+	0.0739386i
$137$		−	11.2720i		−	0.963033i	−0.876437	−	0.481516i	$-0.840086\pi$
$137$		−	11.2720i		−	0.963033i	0.876437	−	0.481516i	$-0.159914\pi$
$138$		0			0
$139$	2.80312	−	1.61838i	0.237758	−	0.137269i	−0.376388	−	0.926462i	$-0.622834\pi$
$139$	2.80312	−	1.61838i	0.237758	−	0.137269i	0.614146	+	0.789193i	$0.289501\pi$
$140$		0			0
$141$		0			0
$142$	−1.17880	−	2.04175i	−0.0989229	−	0.171340i
$143$	11.2008	+	19.4003i	0.936656	+	1.62234i
$144$		0			0
$145$	3.09376	+	1.78618i	0.256922	+	0.148334i
$146$	−0.478954	+	0.829572i	−0.0396385	+	0.0686559i
$147$		0			0
$148$	7.28360	+	12.6156i	0.598709	+	1.03699i
$149$			17.9055i			1.46688i	0.679755	+	0.733439i	$0.262086\pi$
$149$			17.9055i			1.46688i	−0.679755	+	0.733439i	$0.737914\pi$
$150$		0			0
$151$	−18.5989			−1.51356			−0.756778	−	0.653672i	$-0.773228\pi$
$151$	−18.5989			−1.51356			−0.756778	+	0.653672i	$0.773228\pi$
$152$	2.95891	−	5.12498i	0.239999	−	0.415691i
$153$		0			0
$154$		0			0
$155$	−3.39040	−	1.95745i	−0.272323	−	0.157226i
$156$		0			0
$157$	6.64220	+	3.83488i	0.530106	+	0.306057i	0.741059	−	0.671439i	$-0.234324\pi$
$157$	6.64220	+	3.83488i	0.530106	+	0.306057i	−0.210954	+	0.977496i	$0.567657\pi$
$158$	2.39968	+	1.38546i	0.190908	+	0.110221i
$159$		0			0
$160$	14.0390	+	8.10540i	1.10988	+	0.640788i
$161$		0			0
$162$		0			0
$163$	1.99657	−	3.45815i	0.156383	−	0.270864i	−0.777179	−	0.629280i	$-0.783350\pi$
$163$	1.99657	−	3.45815i	0.156383	−	0.270864i	0.933562	+	0.358416i	$0.116683\pi$
$164$	−7.60800			−0.594085
$165$		0			0
$166$		−	1.29786i		−	0.100733i
$167$	−4.26254	−	7.38293i	−0.329845	−	0.571308i	0.652636	−	0.757672i	$-0.273663\pi$
$167$	−4.26254	−	7.38293i	−0.329845	−	0.571308i	−0.982481	+	0.186363i	$0.940330\pi$
$168$		0			0
$169$	11.7687	−	20.3840i	0.905285	−	1.56800i
$170$	1.41044	+	0.814316i	0.108176	+	0.0624552i
$171$		0			0
$172$	−3.45369	−	5.98197i	−0.263341	−	0.456121i
$173$	0.217445	+	0.376626i	0.0165320	+	0.0286343i	0.874173	−	0.485615i	$-0.161404\pi$
$173$	0.217445	+	0.376626i	0.0165320	+	0.0286343i	−0.857641	+	0.514249i	$0.828071\pi$
$174$		0			0
$175$		0			0
$176$	9.47675	−	5.47140i	0.714337	−	0.412423i
$177$		0			0
$178$		−	6.34564i		−	0.475626i
$179$	−15.0838	+	8.70862i	−1.12741	+	0.650913i	−0.943283	−	0.331989i	$-0.892280\pi$
$179$	−15.0838	+	8.70862i	−1.12741	+	0.650913i	−0.184130	+	0.982902i	$0.558947\pi$
$180$		0			0
$181$		−	17.7421i		−	1.31876i	−0.751809	−	0.659381i	$-0.770818\pi$
$181$		−	17.7421i		−	1.31876i	0.751809	−	0.659381i	$-0.229182\pi$
$182$		0			0
$183$		0			0
$184$	−0.588618			−0.0433935
$185$	14.4372	−	25.0060i	1.06145	−	1.83848i
$186$		0			0
$187$	3.41562	−	1.97201i	0.249775	−	0.144208i
$188$	10.3324			0.753567
$189$		0			0
$190$	−5.58874			−0.405450
$191$	0.215525	−	0.124433i	0.0155948	−	0.00900367i	−0.492182	−	0.870492i	$-0.663801\pi$
$191$	0.215525	−	0.124433i	0.0155948	−	0.00900367i	0.507777	+	0.861488i	$0.330467\pi$
$192$		0			0
$193$	4.14876	−	7.18586i	0.298634	−	0.517250i	−0.677190	−	0.735809i	$-0.736802\pi$
$193$	4.14876	−	7.18586i	0.298634	−	0.517250i	0.975824	+	0.218559i	$0.0701356\pi$
$194$	−0.818095			−0.0587358
$195$		0			0
$196$		0			0
$197$		−	22.5819i		−	1.60889i	−0.594026	−	0.804446i	$-0.702462\pi$
$197$		−	22.5819i		−	1.60889i	0.594026	−	0.804446i	$-0.297538\pi$
$198$		0			0
$199$	−5.30010	+	3.06002i	−0.375714	+	0.216919i	−0.675952	−	0.736946i	$-0.736267\pi$
$199$	−5.30010	+	3.06002i	−0.375714	+	0.216919i	0.300238	+	0.953864i	$0.402934\pi$
$200$		−	12.9880i		−	0.918392i
$201$		0			0
$202$	2.36447	−	1.36513i	0.166364	−	0.0960500i
$203$		0			0
$204$		0			0
$205$	7.54011	+	13.0599i	0.526624	+	0.912140i
$206$	−2.06196	−	3.57142i	−0.143664	−	0.248833i
$207$		0			0
$208$	−15.4568	−	8.92397i	−1.07173	−	0.618766i
$209$	−6.76705	+	11.7209i	−0.468087	+	0.810750i
$210$		0			0
$211$	1.95472	+	3.38567i	0.134568	+	0.233079i	0.925432	−	0.378913i	$-0.123702\pi$
$211$	1.95472	+	3.38567i	0.134568	+	0.233079i	−0.790864	+	0.611992i	$0.790369\pi$
$212$		−	8.24806i		−	0.566479i
$213$		0			0
$214$	−1.68078			−0.114896
$215$	−6.84575	+	11.8572i	−0.466876	+	0.808653i
$216$		0			0
$217$		0			0
$218$	−6.36476	−	3.67470i	−0.431076	−	0.248882i
$219$		0			0
$220$	−21.0739	−	12.1670i	−1.42080	−	0.820302i
$221$	−5.57095	−	3.21639i	−0.374742	−	0.216358i
$222$		0			0
$223$	−22.3165	−	12.8845i	−1.49443	−	0.862807i	−0.494446	−	0.869209i	$-0.664629\pi$
$223$	−22.3165	−	12.8845i	−1.49443	−	0.862807i	−0.999980	+	0.00640186i	$0.997962\pi$
$224$		0			0
$225$		0			0
$226$	−2.08243	+	3.60687i	−0.138521	+	0.239925i
$227$	24.6102			1.63344			0.816718	−	0.577037i	$-0.195791\pi$
$227$	24.6102			1.63344			0.816718	+	0.577037i	$0.195791\pi$
$228$		0			0
$229$		−	4.55260i		−	0.300844i	−0.988622	−	0.150422i	$-0.951937\pi$
$229$		−	4.55260i		−	0.300844i	0.988622	−	0.150422i	$-0.0480633\pi$
$230$	0.277943	+	0.481412i	0.0183270	+	0.0317433i
$231$		0			0
$232$	0.802315	−	1.38965i	0.0526746	−	0.0912351i
$233$	−22.6338	−	13.0676i	−1.48279	−	0.856090i	−0.482983	−	0.875630i	$-0.660447\pi$
$233$	−22.6338	−	13.0676i	−1.48279	−	0.856090i	−0.999809	+	0.0195398i	$0.993780\pi$
$234$		0			0
$235$	−10.2402	−	17.7365i	−0.667997	−	1.15700i
$236$	−10.2423	−	17.7402i	−0.666716	−	1.15479i
$237$		0			0
$238$		0			0
$239$	−14.8933	+	8.59865i	−0.963367	+	0.556200i	−0.897208	−	0.441609i	$-0.854408\pi$
$239$	−14.8933	+	8.59865i	−0.963367	+	0.556200i	−0.0661594	+	0.997809i	$0.521075\pi$
$240$		0			0
$241$		−	16.7348i		−	1.07798i	−0.842312	−	0.538991i	$-0.818806\pi$
$241$		−	16.7348i		−	1.07798i	0.842312	−	0.538991i	$-0.181194\pi$
$242$	1.00464	−	0.580026i	0.0645804	−	0.0372855i
$243$		0			0
$244$		−	0.0500727i		−	0.00320558i
$245$		0			0
$246$		0			0
$247$	22.0744			1.40456
$248$	−0.879245	+	1.52290i	−0.0558321	+	0.0967040i
$249$		0			0
$250$	−3.99583	+	2.30699i	−0.252719	+	0.145907i
$251$	−5.33468			−0.336722			−0.168361	−	0.985725i	$-0.553847\pi$
$251$	−5.33468			−0.336722			−0.168361	+	0.985725i	$0.553847\pi$
$252$		0			0
$253$	1.34618			0.0846334
$254$	4.31028	−	2.48854i	0.270451	−	0.156145i
$255$		0			0
$256$	−1.73330	+	3.00216i	−0.108331	+	0.187635i
$257$	−24.6200			−1.53576			−0.767878	−	0.640596i	$-0.778687\pi$
$257$	−24.6200			−1.53576			−0.767878	+	0.640596i	$0.778687\pi$
$258$		0			0
$259$		0			0
$260$			39.6894i			2.46143i
$261$		0			0
$262$	−7.71569	+	4.45466i	−0.476677	+	0.275210i
$263$		−	30.7806i		−	1.89801i	−0.315258	−	0.949006i	$-0.602091\pi$
$263$		−	30.7806i		−	1.89801i	0.315258	−	0.949006i	$-0.397909\pi$
$264$		0			0
$265$	−14.1586	+	8.17447i	−0.869756	+	0.502154i
$266$		0			0
$267$		0			0
$268$	8.85436	+	15.3362i	0.540866	+	0.936808i
$269$	6.99046	+	12.1078i	0.426216	+	0.738227i	0.996533	−	0.0831971i	$-0.0265131\pi$
$269$	6.99046	+	12.1078i	0.426216	+	0.738227i	−0.570317	+	0.821424i	$0.693180\pi$
$270$		0			0
$271$	−5.59679	−	3.23131i	−0.339981	−	0.196288i	0.320283	−	0.947322i	$-0.396222\pi$
$271$	−5.59679	−	3.23131i	−0.339981	−	0.196288i	−0.660264	+	0.751034i	$0.729555\pi$
$272$	−1.57115	+	2.72132i	−0.0952652	+	0.165004i
$273$		0			0
$274$	2.39080	+	4.14099i	0.144433	+	0.250166i
$275$			29.7037i			1.79120i
$276$		0			0
$277$	−19.1197			−1.14879			−0.574395	−	0.818578i	$-0.694763\pi$
$277$	−19.1197			−1.14879			−0.574395	+	0.818578i	$0.694763\pi$
$278$	−0.686519	+	1.18909i	−0.0411747	+	0.0713167i
$279$		0			0
$280$		0			0
$281$	−20.0611	−	11.5823i	−1.19674	−	0.690940i	−0.236915	−	0.971530i	$-0.576136\pi$
$281$	−20.0611	−	11.5823i	−1.19674	−	0.690940i	−0.959828	+	0.280591i	$0.909470\pi$
$282$		0			0
$283$	13.8239	+	7.98126i	0.821748	+	0.474436i	0.851019	−	0.525135i	$-0.175985\pi$
$283$	13.8239	+	7.98126i	0.821748	+	0.474436i	−0.0292708	+	0.999572i	$0.509319\pi$
$284$	−8.76020	−	5.05770i	−0.519822	−	0.300120i
$285$		0			0
$286$	−8.22963	−	4.75138i	−0.486628	−	0.280955i
$287$		0			0
$288$		0			0
$289$	7.93372	−	13.7416i	0.466690	−	0.808330i
$290$	−1.51540			−0.0889873
$291$		0			0
$292$			4.10994i			0.240516i
$293$	−3.34849	−	5.79975i	−0.195621	−	0.338825i	0.751483	−	0.659752i	$-0.229339\pi$
$293$	−3.34849	−	5.79975i	−0.195621	−	0.338825i	−0.947104	+	0.320927i	$0.896005\pi$
$294$		0			0
$295$	−20.3018	+	35.1637i	−1.18202	+	2.04731i
$296$	−11.2322	−	6.48490i	−0.652857	−	0.376927i
$297$		0			0
$298$	−3.79777	−	6.57794i	−0.219999	−	0.381050i
$299$	−1.09782	−	1.90148i	−0.0634886	−	0.109966i
$300$		0			0
$301$		0			0
$302$	6.83266	−	3.94484i	0.393175	−	0.227000i
$303$		0			0
$304$		−	10.7830i		−	0.618448i
$305$	−0.0859547	+	0.0496259i	−0.00492175	+	0.00284157i
$306$		0			0
$307$		−	8.59068i		−	0.490296i	−0.969486	−	0.245148i	$-0.921163\pi$
$307$		−	8.59068i		−	0.490296i	0.969486	−	0.245148i	$-0.0788365\pi$
$308$		0			0
$309$		0			0
$310$	1.66070			0.0943216
$311$	2.11723	−	3.66714i	0.120057	−	0.207945i	−0.799733	−	0.600356i	$-0.795026\pi$
$311$	2.11723	−	3.66714i	0.120057	−	0.207945i	0.919790	+	0.392411i	$0.128359\pi$
$312$		0			0
$313$	3.10288	−	1.79145i	0.175385	−	0.101259i	−0.409737	−	0.912204i	$-0.634380\pi$
$313$	3.10288	−	1.79145i	0.175385	−	0.101259i	0.585123	+	0.810945i	$0.301046\pi$
$314$	−3.25352			−0.183607
$315$		0			0
$316$	11.8887			0.668793
$317$	−7.69566	+	4.44309i	−0.432231	+	0.249549i	−0.700297	−	0.713852i	$-0.746949\pi$
$317$	−7.69566	+	4.44309i	−0.432231	+	0.249549i	0.268065	+	0.963401i	$0.413616\pi$
$318$		0			0
$319$	−1.83490	+	3.17814i	−0.102735	+	0.177942i
$320$	14.4278			0.806541
$321$		0			0
$322$		0			0
$323$		−	3.88642i		−	0.216246i
$324$		0			0
$325$	41.9567	−	24.2237i	2.32734	−	1.34369i
$326$			1.69389i			0.0938160i
$327$		0			0
$328$	5.86622	−	3.38686i	0.323908	−	0.187008i
$329$		0			0
$330$		0			0
$331$	−7.89126	−	13.6681i	−0.433743	−	0.751265i	0.563449	−	0.826151i	$-0.309474\pi$
$331$	−7.89126	−	13.6681i	−0.433743	−	0.751265i	−0.997192	+	0.0748861i	$0.976141\pi$
$332$	−2.78426	−	4.82248i	−0.152806	−	0.264668i
$333$		0			0
$334$	3.13185	+	1.80817i	0.171367	+	0.0989388i
$335$	17.5507	−	30.3987i	0.958898	−	1.66086i
$336$		0			0
$337$	−6.79951	−	11.7771i	−0.370393	−	0.641539i	0.619233	−	0.785207i	$-0.287444\pi$
$337$	−6.79951	−	11.7771i	−0.370393	−	0.641539i	−0.989626	+	0.143668i	$0.954110\pi$
$338$			9.98459i			0.543090i
$339$		0			0
$340$	6.98771			0.378962
$341$	2.01084	−	3.48288i	0.108893	−	0.188608i
$342$		0			0
$343$		0			0
$344$	5.32600	+	3.07497i	0.287159	+	0.165791i
$345$		0			0
$346$	−0.159765	−	0.0922404i	−0.00858902	−	0.00495887i
$347$	12.0065	+	6.93198i	0.644545	+	0.372128i	0.786363	−	0.617765i	$-0.211962\pi$
$347$	12.0065	+	6.93198i	0.644545	+	0.372128i	−0.141818	+	0.989893i	$0.545295\pi$
$348$		0			0
$349$	−1.55204	−	0.896072i	−0.0830789	−	0.0479656i	0.457885	−	0.889011i	$-0.348607\pi$
$349$	−1.55204	−	0.896072i	−0.0830789	−	0.0479656i	−0.540964	+	0.841046i	$0.681940\pi$
$350$		0			0
$351$		0			0
$352$	−8.32649	+	14.4219i	−0.443804	+	0.768690i
$353$	−7.76098			−0.413075			−0.206538	−	0.978439i	$-0.566220\pi$
$353$	−7.76098			−0.413075			−0.206538	+	0.978439i	$0.566220\pi$
$354$		0			0
$355$			20.0503i			1.06416i
$356$	−13.6131	−	23.5786i	−0.721494	−	1.24966i
$357$		0			0
$358$	3.69421	−	6.39855i	0.195245	−	0.338174i
$359$	19.5557	+	11.2905i	1.03211	+	0.595890i	0.917589	−	0.397531i	$-0.130133\pi$
$359$	19.5557	+	11.2905i	1.03211	+	0.595890i	0.114523	+	0.993421i	$0.463466\pi$
$360$		0			0
$361$	−2.83177	−	4.90477i	−0.149041	−	0.258146i
$362$	3.76312	+	6.51791i	0.197785	+	0.342574i
$363$		0			0
$364$		0			0
$365$	7.05511	−	4.07327i	0.369281	−	0.213205i
$366$		0			0
$367$			15.6188i			0.815297i	0.913139	+	0.407648i	$0.133651\pi$
$367$			15.6188i			0.815297i	−0.913139	+	0.407648i	$0.866349\pi$
$368$	−0.928844	+	0.536268i	−0.0484193	+	0.0279549i
$369$		0			0
$370$			12.2486i			0.636773i
$371$		0			0
$372$		0			0
$373$	−25.2458			−1.30718			−0.653589	−	0.756850i	$-0.726738\pi$
$373$	−25.2458			−1.30718			−0.653589	+	0.756850i	$0.726738\pi$
$374$	−0.836528	+	1.44891i	−0.0432558	+	0.0749213i
$375$		0			0
$376$	−7.96689	+	4.59969i	−0.410861	+	0.237211i
$377$	5.98553			0.308271
$378$		0			0
$379$	14.7721			0.758792			0.379396	−	0.925234i	$-0.376132\pi$
$379$	14.7721			0.758792			0.379396	+	0.925234i	$0.376132\pi$
$380$	−20.7662	+	11.9894i	−1.06528	+	0.615041i
$381$		0			0
$382$	−0.0527847	+	0.0914258i	−0.00270070	+	0.00467775i
$383$	10.5901			0.541127			0.270564	−	0.962702i	$-0.412790\pi$
$383$	10.5901			0.541127			0.270564	+	0.962702i	$0.412790\pi$
$384$		0			0
$385$		0			0
$386$			3.51982i			0.179154i
$387$		0			0
$388$	−3.03981	+	1.75504i	−0.154323	+	0.0890984i
$389$		−	13.5841i		−	0.688743i	−0.938834	−	0.344371i	$-0.888092\pi$
$389$		−	13.5841i		−	0.688743i	0.938834	−	0.344371i	$-0.111908\pi$
$390$		0			0
$391$	−0.334775	+	0.193282i	−0.0169303	+	0.00977471i
$392$		0			0
$393$		0			0
$394$	4.78963	+	8.29588i	0.241298	+	0.417940i
$395$	−11.7826	−	20.4081i	−0.592849	−	1.02684i
$396$		0			0
$397$	33.6977	+	19.4554i	1.69124	+	0.976437i	0.953520	+	0.301330i	$0.0974305\pi$
$397$	33.6977	+	19.4554i	1.69124	+	0.976437i	0.737719	+	0.675108i	$0.235903\pi$
$398$	1.29806	−	2.24831i	0.0650660	−	0.112698i
$399$		0			0
$400$	−11.8329	−	20.4952i	−0.591645	−	1.02476i
$401$		−	28.7470i		−	1.43556i	−0.696272	−	0.717778i	$-0.745159\pi$
$401$		−	28.7470i		−	1.43556i	0.696272	−	0.717778i	$-0.254841\pi$
$402$		0			0
$403$	−6.55945			−0.326749
$404$	5.85714	−	10.1449i	0.291404	−	0.504726i
$405$		0			0
$406$		0			0
$407$	25.6881	+	14.8310i	1.27331	+	0.735147i
$408$		0			0
$409$	−16.3485	−	9.43879i	−0.808379	−	0.466718i	0.0380133	−	0.999277i	$-0.487897\pi$
$409$	−16.3485	−	9.43879i	−0.808379	−	0.466718i	−0.846393	+	0.532559i	$0.821230\pi$
$410$	−5.54001	−	3.19852i	−0.273601	−	0.157964i
$411$		0			0
$412$	−15.3233	−	8.84693i	−0.754927	−	0.435857i
$413$		0			0
$414$		0			0
$415$	−5.51884	+	9.55891i	−0.270909	+	0.469228i
$416$	27.1614			1.33170
$417$		0			0
$418$		−	5.74118i		−	0.280810i
$419$	−3.31895	−	5.74860i	−0.162142	−	0.280837i	0.773495	−	0.633802i	$-0.218507\pi$
$419$	−3.31895	−	5.74860i	−0.162142	−	0.280837i	−0.935636	+	0.352965i	$0.885173\pi$
$420$		0			0
$421$	−9.70574	+	16.8108i	−0.473029	+	0.819310i	−0.999523	−	0.0308686i	$-0.990173\pi$
$421$	−9.70574	+	16.8108i	−0.473029	+	0.819310i	0.526495	+	0.850178i	$0.323506\pi$
$422$	−1.43621	−	0.829194i	−0.0699134	−	0.0403645i
$423$		0			0
$424$	3.67180	+	6.35975i	0.178318	+	0.308857i
$425$	−4.26483	−	7.38690i	−0.206874	−	0.358317i
$426$		0			0
$427$		0			0
$428$	−6.24532	+	3.60574i	−0.301879	+	0.174290i
$429$		0			0
$430$		−	5.80795i		−	0.280084i
$431$	21.0604	−	12.1592i	1.01444	−	0.585690i	0.101955	−	0.994789i	$-0.467490\pi$
$431$	21.0604	−	12.1592i	1.01444	−	0.585690i	0.912490	+	0.409099i	$0.134157\pi$
$432$		0			0
$433$		−	3.32148i		−	0.159620i	−0.996810	−	0.0798101i	$-0.974569\pi$
$433$		−	3.32148i		−	0.159620i	0.996810	−	0.0798101i	$-0.0254314\pi$
$434$		0			0
$435$		0			0
$436$	−31.5329			−1.51015
$437$	0.663259	−	1.14880i	0.0317280	−	0.0549544i
$438$		0			0
$439$	−23.3126	+	13.4595i	−1.11265	+	0.642389i	−0.939515	−	0.342509i	$-0.888723\pi$
$439$	−23.3126	+	13.4595i	−1.11265	+	0.642389i	−0.173136	+	0.984898i	$0.555390\pi$
$440$	21.6657			1.03287
$441$		0			0
$442$	2.72879			0.129795
$443$	22.8837	−	13.2119i	1.08724	−	0.627717i	0.154397	−	0.988009i	$-0.450656\pi$
$443$	22.8837	−	13.2119i	1.08724	−	0.627717i	0.932839	+	0.360292i	$0.117323\pi$
$444$		0			0
$445$	−26.9833	+	46.7365i	−1.27913	+	2.21552i
$446$	10.9312			0.517607
$447$		0			0
$448$		0			0
$449$		−	19.6314i		−	0.926464i	−0.886237	−	0.463232i	$-0.846690\pi$
$449$		−	19.6314i		−	0.926464i	0.886237	−	0.463232i	$-0.153310\pi$
$450$		0			0
$451$	−13.4161	+	7.74578i	−0.631739	+	0.364735i
$452$			17.8695i			0.840509i
$453$		0			0
$454$	−9.04102	+	5.21983i	−0.424316	+	0.244979i
$455$		0			0
$456$		0			0
$457$	12.6244	+	21.8660i	0.590543	+	1.02285i	0.994159	+	0.107922i	$0.0344196\pi$
$457$	12.6244	+	21.8660i	0.590543	+	1.02285i	−0.403617	+	0.914928i	$0.632247\pi$
$458$	0.965609	+	1.67248i	0.0451199	+	0.0781500i
$459$		0			0
$460$	2.06552	+	1.19253i	0.0963053	+	0.0556019i
$461$	7.23618	−	12.5334i	0.337023	−	0.583740i	−0.646849	−	0.762618i	$-0.723913\pi$
$461$	7.23618	−	12.5334i	0.337023	−	0.583740i	0.983871	+	0.178878i	$0.0572468\pi$
$462$		0			0
$463$	−10.0168	−	17.3495i	−0.465519	−	0.806302i	0.533706	−	0.845670i	$-0.320799\pi$
$463$	−10.0168	−	17.3495i	−0.465519	−	0.806302i	−0.999225	+	0.0393681i	$0.987466\pi$
$464$		−	2.92384i		−	0.135736i
$465$		0			0
$466$	11.0866			0.513578
$467$	−11.7815	+	20.4062i	−0.545183	+	0.944285i	0.453412	+	0.891301i	$0.350207\pi$
$467$	−11.7815	+	20.4062i	−0.545183	+	0.944285i	−0.998595	+	0.0529842i	$0.983127\pi$
$468$		0			0
$469$		0			0
$470$	7.52386	+	4.34390i	0.347050	+	0.200369i
$471$		0			0
$472$	15.7948	+	9.11914i	0.727015	+	0.419742i
$473$	−12.1806	−	7.03248i	−0.560065	−	0.323354i
$474$		0			0
$475$	25.3485	+	14.6350i	1.16307	+	0.671499i
$476$		0			0
$477$		0			0
$478$	3.64756	−	6.31775i	0.166835	−	0.288967i
$479$	−24.9347			−1.13930			−0.569648	−	0.821889i	$-0.692921\pi$
$479$	−24.9347			−1.13930			−0.569648	+	0.821889i	$0.692921\pi$
$480$		0			0
$481$		−	48.3795i		−	2.20591i
$482$	3.54945	+	6.14783i	0.161673	+	0.280026i
$483$		0			0
$484$	2.48863	−	4.31043i	0.113119	−	0.195929i
$485$	6.02537	+	3.47875i	0.273598	+	0.157962i
$486$		0			0
$487$	2.50331	+	4.33586i	0.113436	+	0.196476i	0.917153	−	0.398534i	$-0.130481\pi$
$487$	2.50331	+	4.33586i	0.113436	+	0.196476i	−0.803718	+	0.595011i	$0.797148\pi$
$488$	0.0222909	+	0.0386090i	0.00100906	+	0.00174775i
$489$		0			0
$490$		0			0
$491$	−18.6960	+	10.7942i	−0.843740	+	0.487134i	−0.858534	−	0.512757i	$-0.828624\pi$
$491$	−18.6960	+	10.7942i	−0.843740	+	0.487134i	0.0147936	+	0.999891i	$0.495291\pi$
$492$		0			0
$493$		−	1.05381i		−	0.0474613i
$494$	−8.10945	+	4.68200i	−0.364862	+	0.210653i
$495$		0			0
$496$			3.20419i			0.143872i
$497$		0			0
$498$		0			0
$499$	35.8130			1.60321			0.801604	−	0.597855i	$-0.203980\pi$
$499$	35.8130			1.60321			0.801604	+	0.597855i	$0.203980\pi$
$500$	−9.89826	+	17.1443i	−0.442664	+	0.766716i
$501$		0			0
$502$	1.95979	−	1.13149i	0.0874699	−	0.0505008i
$503$	−23.9969			−1.06997			−0.534984	−	0.844862i	$-0.679682\pi$
$503$	−23.9969			−1.06997			−0.534984	+	0.844862i	$0.679682\pi$
$504$		0			0
$505$	−23.2195			−1.03325
$506$	−0.494543	+	0.285525i	−0.0219851	+	0.0126931i
$507$		0			0
$508$	10.6772	−	18.4934i	0.473724	−	0.820514i
$509$	18.1419			0.804124			0.402062	−	0.915612i	$-0.368294\pi$
$509$	18.1419			0.804124			0.402062	+	0.915612i	$0.368294\pi$
$510$		0			0
$511$		0			0
$512$		−	22.8374i		−	1.00928i
$513$		0			0
$514$	9.04464	−	5.22192i	0.398942	−	0.230329i
$515$			35.0720i			1.54546i
$516$		0			0
$517$	18.2203	−	10.5195i	0.801330	−	0.462648i
$518$		0			0
$519$		0			0
$520$	−17.6686	−	30.6029i	−0.774819	−	1.34203i
$521$	0.419693	+	0.726930i	0.0183871	+	0.0318474i	0.875073	−	0.483992i	$-0.160814\pi$
$521$	0.419693	+	0.726930i	0.0183871	+	0.0318474i	−0.856685	+	0.515839i	$0.827480\pi$
$522$		0			0
$523$	−14.1017	−	8.14160i	−0.616623	−	0.356008i	0.158930	−	0.987290i	$-0.449196\pi$
$523$	−14.1017	−	8.14160i	−0.616623	−	0.356008i	−0.775553	+	0.631282i	$0.782529\pi$
$524$	−19.1129	+	33.1045i	−0.834951	+	1.44618i
$525$		0			0
$526$	6.52858	+	11.3078i	0.284660	+	0.493045i
$527$			1.15486i			0.0503063i
$528$		0			0
$529$	22.8681			0.994263
$530$	3.46762	−	6.00609i	0.150624	−	0.260888i
$531$		0			0
$532$		0			0
$533$	21.8819	+	12.6335i	0.947812	+	0.547219i
$534$		0			0
$535$	12.3792	+	7.14713i	0.535199	+	0.308997i
$536$	−13.6545	−	7.88342i	−0.589784	−	0.340512i
$537$		0			0
$538$	−5.13615	−	2.96536i	−0.221435	−	0.127846i
$539$		0			0
$540$		0			0
$541$	0.933466	−	1.61681i	0.0401328	−	0.0695121i	−0.845261	−	0.534353i	$-0.820555\pi$
$541$	0.933466	−	1.61681i	0.0401328	−	0.0695121i	0.885394	+	0.464841i	$0.153889\pi$
$542$	2.74145			0.117755
$543$		0			0
$544$		−	4.78203i		−	0.205028i
$545$	31.2515	+	54.1292i	1.33867	+	2.31864i
$546$		0			0
$547$	7.55792	−	13.0907i	0.323153	−	0.559718i	−0.657984	−	0.753032i	$-0.728590\pi$
$547$	7.55792	−	13.0907i	0.323153	−	0.559718i	0.981137	+	0.193315i	$0.0619238\pi$
$548$	17.7671	+	10.2578i	0.758972	+	0.438193i
$549$		0			0
$550$	−6.30018	−	10.9122i	−0.268641	−	0.465299i
$551$	1.80811	+	3.13173i	0.0770279	+	0.133416i
$552$		0			0
$553$		0			0
$554$	7.02398	−	4.05529i	0.298420	−	0.172293i
$555$		0			0
$556$			5.89108i			0.249838i
$557$	−5.47481	+	3.16088i	−0.231975	+	0.133931i	−0.611483	−	0.791258i	$-0.709427\pi$
$557$	−5.47481	+	3.16088i	−0.231975	+	0.133931i	0.379508	+	0.925189i	$0.376093\pi$
$558$		0			0
$559$			22.9402i			0.970269i
$560$		0			0
$561$		0			0
$562$	9.82641			0.414502
$563$	−4.82545	+	8.35793i	−0.203369	+	0.352245i	−0.949612	−	0.313429i	$-0.898522\pi$
$563$	−4.82545	+	8.35793i	−0.203369	+	0.352245i	0.746243	+	0.665673i	$0.231856\pi$
$564$		0			0
$565$	30.6747	−	17.7100i	1.29049	−	0.745066i
$566$	−6.77132			−0.284620
$567$		0			0
$568$	9.00618			0.377891
$569$	13.4785	−	7.78184i	0.565050	−	0.326232i	−0.190120	−	0.981761i	$-0.560888\pi$
$569$	13.4785	−	7.78184i	0.565050	−	0.326232i	0.755170	+	0.655529i	$0.227554\pi$
$570$		0			0
$571$	20.9434	−	36.2750i	0.876454	−	1.51806i	0.0212481	−	0.999774i	$-0.493236\pi$
$571$	20.9434	−	36.2750i	0.876454	−	1.51806i	0.855206	−	0.518288i	$-0.173431\pi$
$572$	−40.7720			−1.70476
$573$		0			0
$574$		0			0
$575$		−	2.91135i		−	0.121412i
$576$		0			0
$577$	−34.9417	+	20.1736i	−1.45464	+	0.839838i	−0.998740	−	0.0501916i	$-0.984017\pi$
$577$	−34.9417	+	20.1736i	−1.45464	+	0.839838i	−0.455903	+	0.890030i	$0.650683\pi$
$578$			6.73099i			0.279972i
$579$		0			0
$580$	−5.63080	+	3.25094i	−0.233806	+	0.134988i
$581$		0			0
$582$		0			0
$583$	−8.39744	−	14.5448i	−0.347787	−	0.602384i
$584$	−1.82963	−	3.16901i	−0.0757106	−	0.131135i
$585$		0			0
$586$	2.46026	+	1.42043i	0.101632	+	0.0586775i
$587$	1.91520	−	3.31723i	0.0790490	−	0.136917i	−0.823791	−	0.566894i	$-0.808145\pi$
$587$	1.91520	−	3.31723i	0.0790490	−	0.136917i	0.902840	+	0.429977i	$0.141478\pi$
$588$		0			0
$589$	−1.98148	−	3.43202i	−0.0816453	−	0.141414i
$590$		−	17.2241i		−	0.709104i
$591$		0			0
$592$	−23.6326			−0.971294
$593$	6.25717	−	10.8377i	0.256951	−	0.445053i	−0.708472	−	0.705738i	$-0.750615\pi$
$593$	6.25717	−	10.8377i	0.256951	−	0.445053i	0.965424	+	0.260686i	$0.0839487\pi$
$594$		0			0
$595$		0			0
$596$	−28.2229	−	16.2945i	−1.15606	−	0.667449i
$597$		0			0
$598$	0.806611	+	0.465697i	0.0329848	+	0.0190438i
$599$	6.62258	+	3.82355i	0.270591	+	0.156226i	0.629156	−	0.777279i	$-0.283401\pi$
$599$	6.62258	+	3.82355i	0.270591	+	0.156226i	−0.358565	+	0.933505i	$0.616734\pi$
$600$		0			0
$601$	29.8513	+	17.2346i	1.21766	+	0.703015i	0.964416	−	0.264388i	$-0.0851698\pi$
$601$	29.8513	+	17.2346i	1.21766	+	0.703015i	0.253242	+	0.967403i	$0.418503\pi$
$602$		0			0
$603$		0			0
$604$	16.9255	−	29.3158i	0.688688	−	1.19284i
$605$	−9.86569			−0.401097
$606$		0			0
$607$			12.4098i			0.503696i	0.967767	+	0.251848i	$0.0810384\pi$
$607$			12.4098i			0.503696i	−0.967767	+	0.251848i	$0.918962\pi$
$608$	8.20490	+	14.2113i	0.332753	+	0.576344i
$609$		0			0
$610$	0.0210514	−	0.0364621i	0.000852346	−	0.00147631i
$611$	−29.7178	−	17.1576i	−1.20225	−	0.694121i
$612$		0			0
$613$	0.834482	+	1.44537i	0.0337044	+	0.0583778i	0.882386	−	0.470527i	$-0.155936\pi$
$613$	0.834482	+	1.44537i	0.0337044	+	0.0583778i	−0.848681	+	0.528905i	$0.822603\pi$
$614$	1.82209	+	3.15595i	0.0735335	+	0.127364i
$615$		0			0
$616$		0			0
$617$	13.5698	−	7.83453i	0.546300	−	0.315406i	−0.201329	−	0.979524i	$-0.564526\pi$
$617$	13.5698	−	7.83453i	0.546300	−	0.315406i	0.747628	+	0.664118i	$0.231193\pi$
$618$		0			0
$619$			3.58460i			0.144077i	0.997402	+	0.0720387i	$0.0229505\pi$
$619$			3.58460i			0.144077i	−0.997402	+	0.0720387i	$0.977049\pi$
$620$	6.17071	−	3.56266i	0.247822	−	0.143080i
$621$		0			0
$622$			1.79626i			0.0720234i
$623$		0			0
$624$		0			0
$625$	−0.835100			−0.0334040
$626$	−0.759935	+	1.31625i	−0.0303731	+	0.0526078i
$627$		0			0
$628$	−12.0892	+	6.97968i	−0.482410	+	0.278520i
$629$	−8.51769			−0.339622
$630$		0			0
$631$	23.1493			0.921557			0.460779	−	0.887515i	$-0.347570\pi$
$631$	23.1493			0.921557			0.460779	+	0.887515i	$0.347570\pi$
$632$	−9.16691	+	5.29252i	−0.364640	+	0.210525i
$633$		0			0
$634$	1.88476	−	3.26451i	0.0748536	−	0.129650i
$635$	−42.3277			−1.67972
$636$		0			0
$637$		0			0
$638$		−	1.55674i		−	0.0616318i
$639$		0			0
$640$	−33.3783	+	19.2710i	−1.31939	+	0.761751i
$641$			23.5059i			0.928426i	0.885724	+	0.464213i	$0.153663\pi$
$641$			23.5059i			0.928426i	−0.885724	+	0.464213i	$0.846337\pi$
$642$		0			0
$643$	−4.83255	+	2.79007i	−0.190577	+	0.110030i	−0.592253	−	0.805752i	$-0.701761\pi$
$643$	−4.83255	+	2.79007i	−0.190577	+	0.110030i	0.401676	+	0.915782i	$0.368428\pi$
$644$		0			0
$645$		0			0
$646$	0.824312	+	1.42775i	0.0324321	+	0.0561741i
$647$	1.95089	+	3.37904i	0.0766974	+	0.132844i	0.901823	−	0.432105i	$-0.142229\pi$
$647$	1.95089	+	3.37904i	0.0766974	+	0.132844i	−0.825126	+	0.564949i	$0.808896\pi$
$648$		0			0
$649$	−36.1229	−	20.8556i	−1.41795	−	0.818652i
$650$	−10.2757	+	17.7981i	−0.403047	+	0.698098i
$651$		0			0
$652$	3.63386	+	6.29402i	0.142313	+	0.246493i
$653$			6.11395i			0.239257i	0.992819	+	0.119629i	$0.0381704\pi$
$653$			6.11395i			0.239257i	−0.992819	+	0.119629i	$0.961830\pi$
$654$		0			0
$655$	75.7694			2.96056
$656$	6.17129	−	10.6890i	0.240948	−	0.417335i
$657$		0			0
$658$		0			0
$659$	−24.7031	−	14.2623i	−0.962296	−	0.555582i	−0.0654174	−	0.997858i	$-0.520838\pi$
$659$	−24.7031	−	14.2623i	−0.962296	−	0.555582i	−0.896879	+	0.442276i	$0.854171\pi$
$660$		0			0
$661$	−21.7672	−	12.5673i	−0.846648	−	0.488812i	0.0128707	−	0.999917i	$-0.495903\pi$
$661$	−21.7672	−	12.5673i	−0.846648	−	0.488812i	−0.859518	+	0.511105i	$0.829236\pi$
$662$	5.79801	+	3.34748i	0.225346	+	0.130104i
$663$		0			0
$664$	4.29366	+	2.47895i	0.166626	+	0.0962018i
$665$		0			0
$666$		0			0
$667$	0.179844	−	0.311499i	0.00696360	−	0.0120613i
$668$	15.5161			0.600335
$669$		0			0
$670$			14.8901i			0.575253i
$671$	−0.0509796	−	0.0882993i	−0.00196805	−	0.00340875i
$672$		0			0
$673$	12.5278	−	21.6988i	0.482912	−	0.836428i	−0.516895	−	0.856049i	$-0.672912\pi$
$673$	12.5278	−	21.6988i	0.482912	−	0.836428i	0.999808	+	0.0196203i	$0.00624575\pi$
$674$	4.99586	+	2.88436i	0.192433	+	0.111101i
$675$		0			0
$676$	21.4197	+	37.0999i	0.823833	+	1.42692i
$677$	16.8081	+	29.1126i	0.645989	+	1.11889i	0.984072	+	0.177770i	$0.0568883\pi$
$677$	16.8081	+	29.1126i	0.645989	+	1.11889i	−0.338083	+	0.941116i	$0.609778\pi$
$678$		0			0
$679$		0			0
$680$	−5.38794	+	3.11073i	−0.206618	+	0.119291i
$681$		0			0
$682$			1.70600i			0.0653262i
$683$	33.3824	−	19.2734i	1.27734	−	0.737475i	0.300984	−	0.953629i	$-0.402685\pi$
$683$	33.3824	−	19.2734i	1.27734	−	0.737475i	0.976359	+	0.216155i	$0.0693515\pi$
$684$		0			0
$685$		−	40.6652i		−	1.55374i
$686$		0			0
$687$		0			0
$688$	11.2059			0.427223
$689$	−13.6964	+	23.7229i	−0.521792	+	0.903770i
$690$		0			0
$691$	26.1768	−	15.1132i	0.995812	−	0.574932i	0.0888052	−	0.996049i	$-0.471695\pi$
$691$	26.1768	−	15.1132i	0.995812	−	0.574932i	0.907006	+	0.421117i	$0.138362\pi$
$692$	−0.791523			−0.0300892
$693$		0			0
$694$	−5.88111			−0.223244
$695$	10.1126	−	5.83852i	0.383593	−	0.221468i
$696$		0			0
$697$	2.22426	−	3.85253i	0.0842499	−	0.145925i
$698$	0.760229			0.0287751
$699$		0			0
$700$		0			0
$701$			29.6057i			1.11819i	0.829103	+	0.559096i	$0.188852\pi$
$701$			29.6057i			1.11819i	−0.829103	+	0.559096i	$0.811148\pi$
$702$		0			0
$703$	25.3130	−	14.6145i	0.954697	−	0.551194i
$704$			14.8214i			0.558602i
$705$		0			0
$706$	2.85114	−	1.64611i	0.107304	−	0.0619521i
$707$		0			0
$708$		0			0
$709$	−1.78201	−	3.08652i	−0.0669246	−	0.115917i	0.830622	−	0.556837i	$-0.187985\pi$
$709$	−1.78201	−	3.08652i	−0.0669246	−	0.115917i	−0.897546	+	0.440921i	$0.854652\pi$
$710$	−4.25268	−	7.36586i	−0.159600	−	0.276436i
$711$		0			0
$712$	20.9931	+	12.1203i	0.786748	+	0.454229i
$713$	−0.197088	+	0.341367i	−0.00738102	+	0.0127843i
$714$		0			0
$715$	40.4082	+	69.9891i	1.51118	+	2.61744i
$716$		−	31.7003i		−	1.18470i
$717$		0			0
$718$	−9.57889			−0.357481
$719$	−0.806410	+	1.39674i	−0.0300740	+	0.0520897i	−0.880671	−	0.473729i	$-0.842908\pi$
$719$	−0.806410	+	1.39674i	−0.0300740	+	0.0520897i	0.850597	+	0.525819i	$0.176241\pi$
$720$		0			0
$721$		0			0
$722$	2.08061	+	1.20124i	0.0774322	+	0.0447055i
$723$		0			0
$724$	27.9654	+	16.1458i	1.03933	+	0.600055i
$725$	6.87332	+	3.96831i	0.255269	+	0.147379i
$726$		0			0
$727$	10.4930	+	6.05816i	0.389166	+	0.224685i	0.681799	−	0.731540i	$-0.261198\pi$
$727$	10.4930	+	6.05816i	0.389166	+	0.224685i	−0.292633	+	0.956225i	$0.594531\pi$
$728$		0			0
$729$		0			0
$730$	−1.72789	+	2.99279i	−0.0639519	+	0.110768i
$731$	4.03886			0.149383
$732$		0			0
$733$			40.4065i			1.49245i	0.665694	+	0.746225i	$0.268136\pi$
$733$			40.4065i			1.49245i	−0.665694	+	0.746225i	$0.731864\pi$
$734$	−3.31277	−	5.73788i	−0.122276	−	0.211789i
$735$		0			0
$736$	0.816104	−	1.41353i	0.0300820	−	0.0521035i
$737$	31.2279	+	18.0294i	1.15030	+	0.664123i
$738$		0			0
$739$	10.2317	+	17.7219i	0.376380	+	0.651909i	0.990533	−	0.137278i	$-0.0438354\pi$
$739$	10.2317	+	17.7219i	0.376380	+	0.651909i	−0.614153	+	0.789187i	$0.710502\pi$
$740$	26.2765	+	45.5123i	0.965944	+	1.67306i
$741$		0			0
$742$		0			0
$743$	−37.1209	+	21.4318i	−1.36184	+	0.786256i	−0.989868	−	0.141990i	$-0.954650\pi$
$743$	−37.1209	+	21.4318i	−1.36184	+	0.786256i	−0.371967	+	0.928246i	$0.621317\pi$
$744$		0			0
$745$			64.5965i			2.36663i
$746$	9.27453	−	5.35465i	0.339565	−	0.196048i
$747$		0			0
$748$			7.17832i			0.262465i
$749$		0			0
$750$		0			0
$751$	−43.0056			−1.56930			−0.784649	−	0.619940i	$-0.787157\pi$
$751$	−43.0056			−1.56930			−0.784649	+	0.619940i	$0.787157\pi$
$752$	−8.38120	+	14.5167i	−0.305631	+	0.529368i
$753$		0			0
$754$	−2.19890	+	1.26953i	−0.0800792	+	0.0462337i
$755$	−67.0979			−2.44194
$756$		0			0
$757$	−13.0766			−0.475276			−0.237638	−	0.971354i	$-0.576373\pi$
$757$	−13.0766			−0.475276			−0.237638	+	0.971354i	$0.576373\pi$
$758$	−5.42682	+	3.13317i	−0.197111	+	0.113802i
$759$		0			0
$760$	10.6746	−	18.4890i	0.387210	−	0.670667i
$761$	23.1833			0.840393			0.420196	−	0.907433i	$-0.361961\pi$
$761$	23.1833			0.840393			0.420196	+	0.907433i	$0.361961\pi$
$762$		0			0
$763$		0			0
$764$			0.452950i			0.0163872i
$765$		0			0
$766$	−3.89046	+	2.24616i	−0.140568	+	0.0811571i
$767$			68.0317i			2.45648i
$768$		0			0
$769$	11.4527	−	6.61219i	0.412993	−	0.238442i	−0.279082	−	0.960267i	$-0.590030\pi$
$769$	11.4527	−	6.61219i	0.412993	−	0.238442i	0.692075	+	0.721826i	$0.256697\pi$
$770$		0			0
$771$		0			0
$772$	7.55096	+	13.0787i	0.271765	+	0.470711i
$773$	9.81595	+	17.0017i	0.353055	+	0.611509i	0.986783	−	0.162047i	$-0.0518095\pi$
$773$	9.81595	+	17.0017i	0.353055	+	0.611509i	−0.633728	+	0.773556i	$0.718476\pi$
$774$		0			0
$775$	−7.53236	−	4.34881i	−0.270570	−	0.156214i
$776$	1.56258	−	2.70647i	0.0560935	−	0.0971567i
$777$		0			0
$778$	2.88120	+	4.99039i	0.103296	+	0.178914i
$779$			15.2653i			0.546938i
$780$		0			0
$781$	−20.5972			−0.737026
$782$	0.0819906	−	0.142012i	0.00293198	−	0.00507833i
$783$		0			0
$784$		0			0
$785$	23.9626	+	13.8348i	0.855262	+	0.493786i
$786$		0			0
$787$	−14.8621	−	8.58063i	−0.529776	−	0.305866i	0.211149	−	0.977454i	$-0.432279\pi$
$787$	−14.8621	−	8.58063i	−0.529776	−	0.305866i	−0.740925	+	0.671588i	$0.765613\pi$
$788$	35.5938	+	20.5501i	1.26798	+	0.732067i
$789$		0			0
$790$	8.65715	+	4.99821i	0.308008	+	0.177828i
$791$		0			0
$792$		0			0
$793$	−0.0831488	+	0.144018i	−0.00295270	+	0.00511423i
$794$	−16.5060			−0.585776
$795$		0			0
$796$		−	11.1388i		−	0.394804i
$797$	11.2772	+	19.5326i	0.399458	+	0.691882i	0.993659	−	0.112435i	$-0.0358650\pi$
$797$	11.2772	+	19.5326i	0.399458	+	0.691882i	−0.594201	+	0.804317i	$0.702532\pi$
$798$		0			0
$799$	−3.02076	+	5.23211i	−0.106867	+	0.185099i
$800$	31.1900	+	18.0076i	1.10273	+	0.636663i
$801$		0			0
$802$	6.09725	+	10.5607i	0.215301	+	0.372913i
$803$	4.18438	+	7.24755i	0.147663	+	0.255761i
$804$		0			0
$805$		0			0
$806$	2.40974	−	1.39126i	0.0848794	−	0.0490051i
$807$		0			0
$808$			10.4297i			0.366916i
$809$	−41.7578	+	24.1089i	−1.46813	+	0.847624i	−0.999363	−	0.0356994i	$-0.988634\pi$
$809$	−41.7578	+	24.1089i	−1.46813	+	0.847624i	−0.468765	+	0.883323i	$0.655301\pi$
$810$		0			0
$811$			11.2304i			0.394354i	0.980368	+	0.197177i	$0.0631774\pi$
$811$			11.2304i			0.394354i	−0.980368	+	0.197177i	$0.936823\pi$
$812$		0			0
$813$		0			0
$814$	−12.5827			−0.441023
$815$	7.20287	−	12.4757i	0.252305	−	0.437006i
$816$		0			0
$817$	−12.0027	+	6.92978i	−0.419922	+	0.242442i
$818$	8.00789			0.279989
$819$		0			0
$820$	−27.4468			−0.958484
$821$	−34.6778	+	20.0212i	−1.21026	+	0.698746i	−0.962817	−	0.270156i	$-0.912925\pi$
$821$	−34.6778	+	20.0212i	−1.21026	+	0.698746i	−0.247447	+	0.968902i	$0.579591\pi$
$822$		0			0
$823$	−4.98922	+	8.64158i	−0.173913	+	0.301227i	−0.939785	−	0.341767i	$-0.888975\pi$
$823$	−4.98922	+	8.64158i	−0.173913	+	0.301227i	0.765871	+	0.642994i	$0.222308\pi$
$824$	15.7536			0.548803
$825$		0			0
$826$		0			0
$827$		−	20.8802i		−	0.726077i	−0.931774	−	0.363038i	$-0.881739\pi$
$827$		−	20.8802i		−	0.726077i	0.931774	−	0.363038i	$-0.118261\pi$
$828$		0			0
$829$	−13.9123	+	8.03228i	−0.483195	+	0.278973i	−0.721747	−	0.692157i	$-0.756661\pi$
$829$	−13.9123	+	8.03228i	−0.483195	+	0.278973i	0.238552	+	0.971130i	$0.423327\pi$
$830$		−	4.68219i		−	0.162521i
$831$		0			0
$832$	20.9353	−	12.0870i	0.725801	−	0.419042i
$833$		0			0
$834$		0			0
$835$	−15.3776	−	26.6349i	−0.532165	−	0.921737i
$836$	−12.3164	−	21.3326i	−0.425971	−	0.737804i
$837$		0			0
$838$	2.43856	+	1.40790i	0.0842387	+	0.0486352i
$839$	10.1943	−	17.6570i	0.351946	−	0.609589i	−0.634644	−	0.772805i	$-0.718853\pi$
$839$	10.1943	−	17.6570i	0.351946	−	0.609589i	0.986590	+	0.163216i	$0.0521866\pi$
$840$		0			0
$841$	−14.0097	−	24.2656i	−0.483094	−	0.836743i
$842$		−	8.23437i		−	0.283775i
$843$		0			0
$844$	−7.11538			−0.244922
$845$	42.4571	−	73.5378i	1.46057	−	2.52978i
$846$		0			0
$847$		0			0
$848$	11.5883	+	6.69048i	0.397942	+	0.229752i
$849$		0			0
$850$	3.13353	+	1.80914i	0.107479	+	0.0620531i
$851$	−2.51777	−	1.45363i	−0.0863079	−	0.0498299i
$852$		0			0
$853$	7.80792	+	4.50790i	0.267338	+	0.154348i	0.627677	−	0.778474i	$-0.284006\pi$
$853$	7.80792	+	4.50790i	0.267338	+	0.154348i	−0.360339	+	0.932821i	$0.617339\pi$
$854$		0			0
$855$		0			0
$856$	3.21034	−	5.56047i	0.109727	−	0.190053i
$857$	−32.3316			−1.10443			−0.552213	−	0.833703i	$-0.686216\pi$
$857$	−32.3316			−1.10443			−0.552213	+	0.833703i	$0.686216\pi$
$858$		0			0
$859$			44.0422i			1.50270i	0.659905	+	0.751349i	$0.270597\pi$
$859$			44.0422i			1.50270i	−0.659905	+	0.751349i	$0.729403\pi$
$860$	−12.4596	−	21.5807i	−0.424870	−	0.735896i
$861$		0			0
$862$	−5.15796	+	8.93385i	−0.175681	+	0.304288i
$863$	−5.30668	−	3.06381i	−0.180641	−	0.104293i	0.406953	−	0.913449i	$-0.366591\pi$
$863$	−5.30668	−	3.06381i	−0.180641	−	0.104293i	−0.587594	+	0.809156i	$0.699925\pi$
$864$		0			0
$865$	0.784460	+	1.35873i	0.0266725	+	0.0461980i
$866$	0.704488	+	1.22021i	0.0239395	+	0.0414644i
$867$		0			0
$868$		0			0
$869$	20.9648	−	12.1040i	0.711182	−	0.410601i
$870$		0			0
$871$		−	58.8128i		−	1.99280i
$872$	24.3137	−	14.0375i	0.823367	−	0.475371i
$873$		0			0
$874$			0.562710i			0.0190340i
$875$		0			0
$876$		0			0
$877$	−2.26408			−0.0764526			−0.0382263	−	0.999269i	$-0.512171\pi$
$877$	−2.26408			−0.0764526			−0.0382263	+	0.999269i	$0.512171\pi$
$878$	5.70956	−	9.88924i	0.192688	−	0.333746i
$879$		0			0
$880$	34.1886	−	19.7388i	1.15250	−	0.665394i
$881$	19.2955			0.650083			0.325041	−	0.945700i	$-0.394622\pi$
$881$	19.2955			0.650083			0.325041	+	0.945700i	$0.394622\pi$
$882$		0			0
$883$	−0.833572			−0.0280519			−0.0140260	−	0.999902i	$-0.504465\pi$
$883$	−0.833572			−0.0280519			−0.0140260	+	0.999902i	$0.504465\pi$
$884$	10.1394	−	5.85400i	0.341026	−	0.196891i
$885$		0			0
$886$	−5.60451	+	9.70729i	−0.188287	+	0.326123i
$887$	−57.5480			−1.93227			−0.966136	−	0.258034i	$-0.916925\pi$
$887$	−57.5480			−1.93227			−0.966136	+	0.258034i	$0.916925\pi$
$888$		0			0
$889$		0			0
$890$		−	22.8927i		−	0.767365i
$891$		0			0
$892$	40.6173	−	23.4504i	1.35997	−	0.785177i
$893$		−	20.7318i		−	0.693763i
$894$		0			0
$895$	−54.4166	+	31.4174i	−1.81895	+	1.05017i
$896$		0			0
$897$		0			0
$898$	4.16384	+	7.21198i	0.138949	+	0.240667i
$899$	−0.537282	−	0.930600i	−0.0179194	−	0.0310372i
$900$		0			0
$901$	4.17665	+	2.41139i	0.139144	+	0.0803350i
$902$	3.28577	−	5.69112i	0.109404	−	0.189494i
$903$		0			0
$904$	−7.95498	−	13.7784i	−0.264579	−	0.458263i
$905$		−	64.0070i		−	2.12766i
$906$		0			0
$907$	−10.1124			−0.335777			−0.167889	−	0.985806i	$-0.553695\pi$
$907$	−10.1124			−0.335777			−0.167889	+	0.985806i	$0.553695\pi$
$908$	−22.3959	+	38.7909i	−0.743235	+	1.28732i
$909$		0			0
$910$		0			0
$911$	16.9986	+	9.81416i	0.563190	+	0.325158i	0.754425	−	0.656387i	$-0.227916\pi$
$911$	16.9986	+	9.81416i	0.563190	+	0.325158i	−0.191235	+	0.981544i	$0.561249\pi$
$912$		0			0
$913$	−9.81965	−	5.66937i	−0.324983	−	0.187629i
$914$	−9.27560	−	5.35527i	−0.306810	−	0.177137i
$915$		0			0
$916$	7.17586	+	4.14299i	0.237097	+	0.136888i
$917$		0			0
$918$		0			0
$919$	−8.52434	+	14.7646i	−0.281192	+	0.487039i	−0.971679	−	0.236306i	$-0.924063\pi$
$919$	−8.52434	+	14.7646i	−0.281192	+	0.487039i	0.690487	+	0.723345i	$0.257396\pi$
$920$	−2.12352			−0.0700102
$921$		0			0
$922$			6.13919i			0.202184i
$923$	16.7972	+	29.0937i	0.552888	+	0.957630i
$924$		0			0
$925$	32.0748	−	55.5552i	1.05461	−	1.82664i
$926$	7.35970	+	4.24912i	0.241855	+	0.139635i
$927$		0			0
$928$	2.22478	+	3.85343i	0.0730319	+	0.126495i
$929$	−4.32511	−	7.49131i	−0.141902	−	0.245782i	0.786311	−	0.617831i	$-0.211989\pi$
$929$	−4.32511	−	7.49131i	−0.141902	−	0.245782i	−0.928213	+	0.372049i	$0.878655\pi$
$930$		0			0
$931$		0			0
$932$	41.1948	−	23.7838i	1.34938	−	0.779065i
$933$		0			0
$934$		−	9.99546i		−	0.327061i
$935$	12.3223	−	7.11427i	0.402981	−	0.232661i
$936$		0			0
$937$			34.9586i			1.14205i	0.820933	+	0.571025i	$0.193454\pi$
$937$			34.9586i			1.14205i	−0.820933	+	0.571025i	$0.806546\pi$
$938$		0			0
$939$		0			0
$940$	37.2754			1.21579
$941$	20.5472	−	35.5887i	0.669818	−	1.16016i	−0.308136	−	0.951342i	$-0.599705\pi$
$941$	20.5472	−	35.5887i	0.669818	−	1.16016i	0.977955	−	0.208817i	$-0.0669614\pi$
$942$		0			0
$943$	1.31495	−	0.759187i	0.0428207	−	0.0247225i
$944$	33.2324			1.08162
$945$		0			0
$946$	5.96637			0.193983
$947$	−29.2164	+	16.8681i	−0.949405	+	0.548139i	−0.892896	−	0.450263i	$-0.851330\pi$
$947$	−29.2164	+	16.8681i	−0.949405	+	0.548139i	−0.0565088	+	0.998402i	$0.517997\pi$
$948$		0			0
$949$	6.82481	−	11.8209i	0.221543	−	0.383723i
$950$	−12.4164			−0.402840
$951$		0			0
$952$		0			0
$953$			18.7823i			0.608420i	0.952605	+	0.304210i	$0.0983925\pi$
$953$			18.7823i			0.608420i	−0.952605	+	0.304210i	$0.901608\pi$
$954$		0			0
$955$	0.777532	−	0.448908i	0.0251603	−	0.0145263i
$956$		−	31.3000i		−	1.01231i
$957$		0			0
$958$	9.16024	−	5.28867i	0.295954	−	0.170869i
$959$		0			0
$960$		0			0
$961$	−14.9112	−	25.8270i	−0.481006	−	0.833128i
$962$	10.2613	+	17.7731i	0.330838	+	0.573028i
$963$		0			0
$964$	26.3776	+	15.2291i	0.849564	+	0.490496i
$965$	14.9672	−	25.9239i	0.481810	−	0.834520i
$966$		0			0
$967$	−17.5860	−	30.4599i	−0.565529	−	0.979525i	−0.997000	−	0.0773981i	$-0.975339\pi$
$967$	−17.5860	−	30.4599i	−0.565529	−	0.979525i	0.431471	−	0.902127i	$-0.357995\pi$
$968$			4.43146i			0.142433i
$969$		0			0
$970$	−2.95138			−0.0947631
$971$	19.7981	−	34.2913i	0.635351	−	1.10046i	−0.351090	−	0.936342i	$-0.614189\pi$
$971$	19.7981	−	34.2913i	0.635351	−	1.10046i	0.986441	−	0.164118i	$-0.0524779\pi$
$972$		0			0
$973$		0			0
$974$	−1.83928	−	1.06191i	−0.0589342	−	0.0340257i
$975$		0			0
$976$	0.0703505	+	0.0406169i	0.00225187	+	0.00130012i
$977$	−30.3364	−	17.5147i	−0.970546	−	0.560345i	−0.0711433	−	0.997466i	$-0.522665\pi$
$977$	−30.3364	−	17.5147i	−0.970546	−	0.560345i	−0.899403	+	0.437121i	$0.855998\pi$
$978$		0			0
$979$	−48.0113	−	27.7193i	−1.53445	−	0.885914i
$980$		0			0
$981$		0			0
$982$	4.57890	−	7.93088i	0.146118	−	0.253085i
$983$	−44.1731			−1.40890			−0.704451	−	0.709752i	$-0.748807\pi$
$983$	−44.1731			−1.40890			−0.704451	+	0.709752i	$0.748807\pi$
$984$		0			0
$985$		−	81.4669i		−	2.59575i
$986$	0.223514	+	0.387138i	0.00711814	+	0.0123290i
$987$		0			0
$988$	−20.0883	+	34.7940i	−0.639094	+	1.10694i
$989$	1.19386	+	0.689274i	0.0379625	+	0.0219176i
$990$		0			0
$991$	−13.4443	−	23.2862i	−0.427073	−	0.739712i	0.569539	−	0.821964i	$-0.307122\pi$
$991$	−13.4443	−	23.2862i	−0.427073	−	0.739712i	−0.996611	+	0.0822528i	$0.973789\pi$
$992$	−2.43810	−	4.22291i	−0.0774097	−	0.134078i
$993$		0			0
$994$		0			0
$995$	−19.1208	+	11.0394i	−0.606170	+	0.349972i
$996$		0			0
$997$			31.1515i			0.986578i	0.869866	+	0.493289i	$0.164205\pi$
$997$			31.1515i			0.986578i	−0.869866	+	0.493289i	$0.835795\pi$
$998$	−13.1566	+	7.59595i	−0.416464	+	0.240446i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.s.d.656.11		48
3.2	odd	2		441.2.s.d.362.13		48
7.2	even	3		1323.2.o.e.440.14		48
7.3	odd	6		1323.2.i.d.521.3		48
7.4	even	3		1323.2.i.d.521.19		48
7.5	odd	6		1323.2.o.e.440.13		48
7.6	odd	2	inner	1323.2.s.d.656.12		48
9.4	even	3		441.2.i.d.68.11		48
9.5	odd	6		1323.2.i.d.1097.3		48
21.2	odd	6		441.2.o.e.146.12	yes	48
21.5	even	6		441.2.o.e.146.11	✓	48
21.11	odd	6		441.2.i.d.227.14		48
21.17	even	6		441.2.i.d.227.13		48
21.20	even	2		441.2.s.d.362.14		48
63.4	even	3		441.2.s.d.374.14		48
63.5	even	6		1323.2.o.e.881.14		48
63.13	odd	6		441.2.i.d.68.12		48
63.23	odd	6		1323.2.o.e.881.13		48
63.31	odd	6		441.2.s.d.374.13		48
63.32	odd	6	inner	1323.2.s.d.962.12		48
63.40	odd	6		441.2.o.e.293.12	yes	48
63.41	even	6		1323.2.i.d.1097.19		48
63.58	even	3		441.2.o.e.293.11	yes	48
63.59	even	6	inner	1323.2.s.d.962.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.11		48	9.4	even	3
441.2.i.d.68.12		48	63.13	odd	6
441.2.i.d.227.13		48	21.17	even	6
441.2.i.d.227.14		48	21.11	odd	6
441.2.o.e.146.11	✓	48	21.5	even	6
441.2.o.e.146.12	yes	48	21.2	odd	6
441.2.o.e.293.11	yes	48	63.58	even	3
441.2.o.e.293.12	yes	48	63.40	odd	6
441.2.s.d.362.13		48	3.2	odd	2
441.2.s.d.362.14		48	21.20	even	2
441.2.s.d.374.13		48	63.31	odd	6
441.2.s.d.374.14		48	63.4	even	3
1323.2.i.d.521.3		48	7.3	odd	6
1323.2.i.d.521.19		48	7.4	even	3
1323.2.i.d.1097.3		48	9.5	odd	6
1323.2.i.d.1097.19		48	63.41	even	6
1323.2.o.e.440.13		48	7.5	odd	6
1323.2.o.e.440.14		48	7.2	even	3
1323.2.o.e.881.13		48	63.23	odd	6
1323.2.o.e.881.14		48	63.5	even	6
1323.2.s.d.656.11		48	1.1	even	1	trivial
1323.2.s.d.656.12		48	7.6	odd	2	inner
1323.2.s.d.962.11		48	63.59	even	6	inner
1323.2.s.d.962.12		48	63.32	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.367369 + 0.212101i) q^{2} +(-0.910027 + 1.57621i) q^{4} +3.60763 q^{5} -1.62047i q^{8} +O(q^{10})\)	\(q+(-0.367369 + 0.212101i) q^{2} +(-0.910027 + 1.57621i) q^{4} +3.60763 q^{5} -1.62047i q^{8} +(-1.32533 + 0.765180i) q^{10} +3.70603i q^{11} +(5.23479 - 3.02231i) q^{13} +(-1.47635 - 2.55711i) q^{16} +(-0.532108 - 0.921637i) q^{17} +(3.16265 + 1.82596i) q^{19} +(-3.28304 + 5.68639i) q^{20} +(-0.786052 - 1.36148i) q^{22} -0.363239i q^{23} +8.01497 q^{25} +(-1.28207 + 2.22060i) q^{26} +(0.857560 + 0.495112i) q^{29} +(-0.939786 - 0.542586i) q^{31} +(3.89147 + 2.24674i) q^{32} +(0.390960 + 0.225721i) q^{34} +(4.00186 - 6.93143i) q^{37} -1.54915 q^{38} -5.84605i q^{40} +(2.09005 + 3.62007i) q^{41} +(-1.89758 + 3.28670i) q^{43} +(-5.84149 - 3.37259i) q^{44} +(0.0770432 + 0.133443i) q^{46} +(-2.83849 - 4.91640i) q^{47} +(-2.94445 + 1.69998i) q^{50} +11.0015i q^{52} +(-3.92463 + 2.26589i) q^{53} +13.3700i q^{55} -0.420055 q^{58} +(-5.62746 + 9.74705i) q^{59} +(-0.0238258 + 0.0137558i) q^{61} +0.460331 q^{62} +3.99926 q^{64} +(18.8852 - 10.9034i) q^{65} +(4.86489 - 8.42624i) q^{67} +1.93693 q^{68} +5.55775i q^{71} +(1.95561 - 1.12907i) q^{73} +3.39519i q^{74} +(-5.75619 + 3.32334i) q^{76} +(-3.26604 - 5.65694i) q^{79} +(-5.32612 - 9.22511i) q^{80} +(-1.53564 - 0.886601i) q^{82} +(-1.52977 + 2.64964i) q^{83} +(-1.91965 - 3.32492i) q^{85} -1.60991i q^{86} +6.00552 q^{88} +(-7.47952 + 12.9549i) q^{89} +(0.572542 + 0.330557i) q^{92} +(2.08554 + 1.20409i) q^{94} +(11.4097 + 6.58737i) q^{95} +(1.67018 + 0.964277i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4}+O(q^{10}) \) 48 * q + 24 * q^4	\( 48 q + 24 q^{4} - 24 q^{16} + 48 q^{25} + 120 q^{32} - 96 q^{44} - 48 q^{50} - 48 q^{53} - 48 q^{64} + 120 q^{65} - 24 q^{79} - 24 q^{85} + 144 q^{92} + 96 q^{95}+O(q^{100}) \) 48 * q + 24 * q^4 - 24 * q^16 + 48 * q^25 + 120 * q^32 - 96 * q^44 - 48 * q^50 - 48 * q^53 - 48 * q^64 + 120 * q^65 - 24 * q^79 - 24 * q^85 + 144 * q^92 + 96 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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