LMFDB - Embedded newform 1323.2.o.e.881.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(440,1323)]

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, 3]))

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

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

chi := DirichletCharacter("1323.440");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.o (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			881.14
Character	$\chi$	$=$	1323.881
Dual form			1323.2.o.e.440.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.367369 - 0.212101i) q^{2} +(-0.910027 + 1.57621i) q^{4} +(-1.80381 + 3.12430i) q^{5} +1.62047i q^{8} +O(q^{10})$	\(q+(0.367369 - 0.212101i) q^{2} +(-0.910027 + 1.57621i) q^{4} +(-1.80381 + 3.12430i) q^{5} +1.62047i q^{8} +1.53036i q^{10} +(-3.20952 + 1.85302i) q^{11} +(5.23479 + 3.02231i) q^{13} +(-1.47635 - 2.55711i) q^{16} +1.06422 q^{17} +3.65191i q^{19} +(-3.28304 - 5.68639i) q^{20} +(-0.786052 + 1.36148i) q^{22} +(-0.314574 - 0.181620i) q^{23} +(-4.00749 - 6.94117i) q^{25} +2.56413 q^{26} +(0.857560 - 0.495112i) q^{29} +(0.939786 + 0.542586i) q^{31} +(-3.89147 - 2.24674i) q^{32} +(0.390960 - 0.225721i) q^{34} -8.00373 q^{37} +(0.774573 + 1.34160i) q^{38} +(-5.06283 - 2.92303i) q^{40} +(2.09005 - 3.62007i) q^{41} +(-1.89758 - 3.28670i) q^{43} -6.74518i q^{44} -0.154086 q^{46} +(-2.83849 - 4.91640i) q^{47} +(-2.94445 - 1.69998i) q^{50} +(-9.52760 + 5.50076i) q^{52} +4.53177i q^{53} -13.3700i q^{55} +(0.210027 - 0.363778i) q^{58} +(-5.62746 + 9.74705i) q^{59} +(0.0238258 - 0.0137558i) q^{61} +0.460331 q^{62} +3.99926 q^{64} +(-18.8852 + 10.9034i) q^{65} +(4.86489 - 8.42624i) q^{67} +(-0.968464 + 1.67743i) q^{68} -5.55775i q^{71} -2.25814i q^{73} +(-2.94032 + 1.69759i) q^{74} +(-5.75619 - 3.32334i) q^{76} +(-3.26604 - 5.65694i) q^{79} +10.6522 q^{80} -1.77320i q^{82} +(-1.52977 - 2.64964i) q^{83} +(-1.91965 + 3.32492i) q^{85} +(-1.39422 - 0.804954i) q^{86} +(-3.00276 - 5.20093i) q^{88} +14.9590 q^{89} +(0.572542 - 0.330557i) q^{92} +(-2.08554 - 1.20409i) q^{94} +(-11.4097 - 6.58737i) q^{95} +(1.67018 - 0.964277i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4}+O(q^{10}) $ 48 * q + 24 * q^4	$ 48 q + 24 q^{4} + 24 q^{11} - 24 q^{16} + 48 q^{23} - 24 q^{25} - 120 q^{32} - 48 q^{50} - 48 q^{64} - 120 q^{65} + 168 q^{74} - 24 q^{79} - 24 q^{85} - 24 q^{86} + 144 q^{92} - 96 q^{95}+O(q^{100}) $ 48 * q + 24 * q^4 + 24 * q^11 - 24 * q^16 + 48 * q^23 - 24 * q^25 - 120 * q^32 - 48 * q^50 - 48 * q^64 - 120 * q^65 + 168 * q^74 - 24 * q^79 - 24 * q^85 - 24 * q^86 + 144 * q^92 - 96 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.364460	−	0.931219i	$-0.618746\pi$
$2$	0.367369	−	0.212101i	0.259769	−	0.149978i	0.624229	+	0.781241i	$0.285413\pi$
$3$		0			0
$3$		0			0
$4$	−0.910027	+	1.57621i	−0.455013	+	0.788106i
$5$	−1.80381	+	3.12430i	−0.806690	+	1.39723i	0.108454	+	0.994101i	$0.465410\pi$
$5$	−1.80381	+	3.12430i	−0.806690	+	1.39723i	−0.915144	+	0.403126i	$0.867923\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			1.62047i			0.572923i
$9$		0			0
$10$			1.53036i			0.483942i
$11$	−3.20952	+	1.85302i	−0.967706	+	0.558705i	−0.898536	−	0.438899i	$-0.855368\pi$
$11$	−3.20952	+	1.85302i	−0.967706	+	0.558705i	−0.0691700	+	0.997605i	$0.522035\pi$
$12$		0			0
$13$	5.23479	+	3.02231i	1.45187	+	0.838238i	0.998588	−	0.0531292i	$-0.0169195\pi$
$13$	5.23479	+	3.02231i	1.45187	+	0.838238i	0.453283	+	0.891367i	$0.350253\pi$
$14$		0			0
$15$		0			0
$16$	−1.47635	−	2.55711i	−0.369088	−	0.639279i
$17$	1.06422			0.258110			0.129055	−	0.991637i	$-0.458806\pi$
$17$	1.06422			0.258110			0.129055	+	0.991637i	$0.458806\pi$
$18$		0			0
$19$			3.65191i			0.837806i	0.908031	+	0.418903i	$0.137585\pi$
$19$			3.65191i			0.837806i	−0.908031	+	0.418903i	$0.862415\pi$
$20$	−3.28304	−	5.68639i	−0.734109	−	1.27151i
$21$		0			0
$22$	−0.786052	+	1.36148i	−0.167587	+	0.290269i
$23$	−0.314574	−	0.181620i	−0.0655933	−	0.0378703i	0.466845	−	0.884339i	$-0.345391\pi$
$23$	−0.314574	−	0.181620i	−0.0655933	−	0.0378703i	−0.532438	+	0.846469i	$0.678724\pi$
$24$		0			0
$25$	−4.00749	−	6.94117i	−0.801497	−	1.38823i
$26$	2.56413			0.502868
$27$		0			0
$28$		0			0
$29$	0.857560	−	0.495112i	0.159245	−	0.0919401i	−0.418260	−	0.908327i	$-0.637360\pi$
$29$	0.857560	−	0.495112i	0.159245	−	0.0919401i	0.577505	+	0.816387i	$0.304027\pi$
$30$		0			0
$31$	0.939786	+	0.542586i	0.168791	+	0.0974513i	0.582015	−	0.813178i	$-0.302264\pi$
$31$	0.939786	+	0.542586i	0.168791	+	0.0974513i	−0.413225	+	0.910629i	$0.635598\pi$
$32$	−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
$37$	−8.00373			−1.31580			−0.657902	−	0.753103i	$-0.728556\pi$
$37$	−8.00373			−1.31580			−0.657902	+	0.753103i	$0.728556\pi$
$38$	0.774573	+	1.34160i	0.125652	+	0.217636i
$39$		0			0
$40$	−5.06283	−	2.92303i	−0.800504	−	0.462171i
$41$	2.09005	−	3.62007i	0.326411	−	0.565360i	−0.655386	−	0.755294i	$-0.727494\pi$
$41$	2.09005	−	3.62007i	0.326411	−	0.565360i	0.981797	+	0.189934i	$0.0608275\pi$
$42$		0			0
$43$	−1.89758	−	3.28670i	−0.289378	−	0.501217i	0.684284	−	0.729216i	$-0.260115\pi$
$43$	−1.89758	−	3.28670i	−0.289378	−	0.501217i	−0.973661	+	0.227999i	$0.926782\pi$
$44$		−	6.74518i		−	1.01687i
$45$		0			0
$46$	−0.154086			−0.0227188
$47$	−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
$52$	−9.52760	+	5.50076i	−1.32124	+	0.762819i
$53$			4.53177i			0.622487i	0.950330	+	0.311243i	$0.100745\pi$
$53$			4.53177i			0.622487i	−0.950330	+	0.311243i	$0.899255\pi$
$54$		0			0
$55$		−	13.3700i		−	1.80281i
$56$		0			0
$57$		0			0
$58$	0.210027	−	0.363778i	0.0275779	−	0.0477664i
$59$	−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	−0.498474	−	0.866905i	$-0.666106\pi$
$61$	0.0238258	−	0.0137558i	0.00305058	−	0.00176126i	0.501525	+	0.865143i	$0.332773\pi$
$62$	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	$-0.0359204\pi$
$68$	−0.968464	+	1.67743i	−0.117444	+	0.203418i
$69$		0			0
$70$		0			0
$71$		−	5.55775i		−	0.659584i	−0.944054	−	0.329792i	$-0.893021\pi$
$71$		−	5.55775i		−	0.659584i	0.944054	−	0.329792i	$-0.106979\pi$
$72$		0			0
$73$		−	2.25814i		−	0.264296i	−0.991230	−	0.132148i	$-0.957813\pi$
$73$		−	2.25814i		−	0.264296i	0.991230	−	0.132148i	$-0.0421874\pi$
$74$	−2.94032	+	1.69759i	−0.341805	+	0.197341i
$75$		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	$0.953105\pi$
$80$	10.6522			1.19096
$81$		0			0
$82$		−	1.77320i		−	0.195817i
$83$	−1.52977	−	2.64964i	−0.167914	−	0.290836i	0.769772	−	0.638319i	$-0.220370\pi$
$83$	−1.52977	−	2.64964i	−0.167914	−	0.290836i	−0.937686	+	0.347483i	$0.887036\pi$
$84$		0			0
$85$	−1.91965	+	3.32492i	−0.208215	+	0.360639i
$86$	−1.39422	−	0.804954i	−0.150343	−	0.0868004i
$87$		0			0
$88$	−3.00276	−	5.20093i	−0.320095	−	0.554421i
$89$	14.9590			1.58565			0.792827	−	0.609446i	$-0.208608\pi$
$89$	14.9590			1.58565			0.792827	+	0.609446i	$0.208608\pi$
$90$		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	−0.412807	−	0.910818i	$-0.635452\pi$
$97$	1.67018	−	0.964277i	0.169581	−	0.0979075i	0.582388	+	0.812911i	$0.302118\pi$
$98$		0			0
$99$		0			0
$100$	14.5877			1.45877
$101$	3.21811	+	5.57394i	0.320214	+	0.554627i	0.980532	−	0.196359i	$-0.0629117\pi$
$101$	3.21811	+	5.57394i	0.320214	+	0.554627i	−0.660318	+	0.750986i	$0.729578\pi$
$102$		0			0
$103$	8.41917	+	4.86081i	0.829565	+	0.478950i	0.853704	−	0.520759i	$-0.174351\pi$
$103$	8.41917	+	4.86081i	0.829565	+	0.478950i	−0.0241385	+	0.999709i	$0.507684\pi$
$104$	−4.89756	+	8.48283i	−0.480246	+	0.831810i
$105$		0			0
$106$	0.961191	+	1.66483i	0.0933591	+	0.161703i
$107$			3.96223i			0.383043i	0.981488	+	0.191522i	$0.0613422\pi$
$107$			3.96223i			0.383043i	−0.981488	+	0.191522i	$0.938658\pi$
$108$		0			0
$109$	−17.3253			−1.65946			−0.829729	−	0.558166i	$-0.811505\pi$
$109$	−17.3253			−1.65946			−0.829729	+	0.558166i	$0.811505\pi$
$110$	−2.83578	−	4.91172i	−0.270381	−	0.468314i
$111$		0			0
$112$		0			0
$113$	8.50273	+	4.90905i	0.799869	+	0.461805i	0.843425	−	0.537246i	$-0.180535\pi$
$113$	8.50273	+	4.90905i	0.799869	+	0.461805i	−0.0435562	+	0.999051i	$0.513869\pi$
$114$		0			0
$115$	1.13487	−	0.655216i	0.105827	−	0.0610992i
$116$			1.80226i			0.167336i
$117$		0			0
$118$			4.77435i			0.439515i
$119$		0			0
$120$		0			0
$121$	1.36734	−	2.36830i	0.124303	−	0.215300i
$122$	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
$131$	−10.5013	+	18.1888i	−0.917502	+	1.58916i	−0.114305	+	0.993446i	$0.536464\pi$
$131$	−10.5013	+	18.1888i	−0.917502	+	1.58916i	−0.803197	+	0.595714i	$0.796869\pi$
$132$		0			0
$133$		0			0
$134$		−	4.12738i		−	0.356552i
$135$		0			0
$136$			1.72453i			0.147877i
$137$	9.76185	−	5.63600i	0.834011	−	0.481516i	−0.0212131	−	0.999775i	$-0.506753\pi$
$137$	9.76185	−	5.63600i	0.834011	−	0.481516i	0.855224	+	0.518259i	$0.173420\pi$
$138$		0			0
$139$	2.80312	+	1.61838i	0.237758	+	0.137269i	0.614146	−	0.789193i	$-0.289501\pi$
$139$	2.80312	+	1.61838i	0.237758	+	0.137269i	−0.376388	+	0.926462i	$0.622834\pi$
$140$		0			0
$141$		0			0
$142$	−1.17880	−	2.04175i	−0.0989229	−	0.171340i
$143$	−22.4015			−1.87331
$144$		0			0
$145$			3.57236i			0.296668i
$146$	−0.478954	−	0.829572i	−0.0396385	−	0.0686559i
$147$		0			0
$148$	7.28360	−	12.6156i	0.598709	−	1.03699i
$149$	15.5066	+	8.95277i	1.27035	+	0.733439i	0.975055	−	0.221966i	$-0.0712472\pi$
$149$	15.5066	+	8.95277i	1.27035	+	0.733439i	0.295299	+	0.955405i	$0.404581\pi$
$150$		0			0
$151$	9.29945	+	16.1071i	0.756778	+	1.31078i	0.944485	+	0.328553i	$0.106561\pi$
$151$	9.29945	+	16.1071i	0.756778	+	1.31078i	−0.187707	+	0.982225i	$0.560106\pi$
$152$	−5.91782			−0.479998
$153$		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	0.210954	−	0.977496i	$-0.432343\pi$
$157$	−6.64220	−	3.83488i	−0.530106	−	0.306057i	−0.741059	+	0.671439i	$0.765676\pi$
$158$	−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
$163$	−3.99313			−0.312766			−0.156383	−	0.987696i	$-0.549983\pi$
$163$	−3.99313			−0.312766			−0.156383	+	0.987696i	$0.549983\pi$
$164$	3.80400	+	6.58872i	0.297042	+	0.514492i
$165$		0			0
$166$	−1.12398	−	0.648930i	−0.0872377	−	0.0503667i
$167$	−4.26254	+	7.38293i	−0.329845	+	0.571308i	−0.982481	−	0.186363i	$-0.940330\pi$
$167$	−4.26254	+	7.38293i	−0.329845	+	0.571308i	0.652636	+	0.757672i	$0.273663\pi$
$168$		0			0
$169$	11.7687	+	20.3840i	0.905285	+	1.56800i
$170$			1.62863i			0.124910i
$171$		0			0
$172$	6.90738			0.526683
$173$	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
$178$	5.49549	−	3.17282i	0.411904	−	0.237813i
$179$			17.4172i			1.30183i	0.759153	+	0.650913i	$0.225614\pi$
$179$			17.4172i			1.30183i	−0.759153	+	0.650913i	$0.774386\pi$
$180$		0			0
$181$			17.7421i			1.31876i	0.751809	+	0.659381i	$0.229182\pi$
$181$			17.7421i			1.31876i	−0.751809	+	0.659381i	$0.770818\pi$
$182$		0			0
$183$		0			0
$184$	0.294309	−	0.509759i	0.0216968	−	0.0375799i
$185$	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	−0.507777	−	0.861488i	$-0.669533\pi$
$191$	−0.215525	+	0.124433i	−0.0155948	+	0.00900367i	0.492182	+	0.870492i	$0.336199\pi$
$192$		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	$0.0701356\pi$
$194$	0.409047	−	0.708491i	0.0293679	−	0.0508667i
$195$		0			0
$196$		0			0
$197$			22.5819i			1.60889i	0.594026	+	0.804446i	$0.297538\pi$
$197$			22.5819i			1.60889i	−0.594026	+	0.804446i	$0.702462\pi$
$198$		0			0
$199$			6.12003i			0.433837i	0.976190	+	0.216919i	$0.0696007\pi$
$199$			6.12003i			0.433837i	−0.976190	+	0.216919i	$0.930399\pi$
$200$	11.2480	−	6.49401i	0.795351	−	0.459196i
$201$		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
$206$	4.12392			0.287327
$207$		0			0
$208$		−	17.8479i		−	1.23753i
$209$	−6.76705	−	11.7209i	−0.468087	−	0.810750i
$210$		0			0
$211$	1.95472	−	3.38567i	0.134568	−	0.233079i	−0.790864	−	0.611992i	$-0.790369\pi$
$211$	1.95472	−	3.38567i	0.134568	−	0.233079i	0.925432	+	0.378913i	$0.123702\pi$
$212$	−7.14303	−	4.12403i	−0.490586	−	0.283240i
$213$		0			0
$214$	0.840392	+	1.45560i	0.0574480	+	0.0995029i
$215$	13.6915			0.933752
$216$		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	−0.999980	−	0.00640186i	$-0.997962\pi$
$223$	−22.3165	+	12.8845i	−1.49443	+	0.862807i	−0.494446	+	0.869209i	$0.664629\pi$
$224$		0			0
$225$		0			0
$226$	4.16485			0.277042
$227$	−12.3051	−	21.3130i	−0.816718	−	1.41460i	−0.908088	−	0.418779i	$-0.862458\pi$
$227$	−12.3051	−	21.3130i	−0.816718	−	1.41460i	0.0913703	−	0.995817i	$-0.470875\pi$
$228$		0			0
$229$	−3.94267	−	2.27630i	−0.260539	−	0.150422i	0.364042	−	0.931383i	$-0.381397\pi$
$229$	−3.94267	−	2.27630i	−0.260539	−	0.150422i	−0.624580	+	0.780961i	$0.714730\pi$
$230$	0.277943	−	0.481412i	0.0183270	−	0.0317433i
$231$		0			0
$232$	0.802315	+	1.38965i	0.0526746	+	0.0912351i
$233$		−	26.1353i		−	1.71218i	−0.516826	−	0.856090i	$-0.672887\pi$
$233$		−	26.1353i		−	1.71218i	0.516826	−	0.856090i	$-0.327113\pi$
$234$		0			0
$235$	20.4804			1.33599
$236$	−10.2423	−	17.7402i	−0.666716	−	1.15479i
$237$		0			0
$238$		0			0
$239$	−14.8933	−	8.59865i	−0.963367	−	0.556200i	−0.0661594	−	0.997809i	$-0.521075\pi$
$239$	−14.8933	−	8.59865i	−0.963367	−	0.556200i	−0.897208	+	0.441609i	$0.854408\pi$
$240$		0			0
$241$	14.4927	−	8.36738i	0.933559	−	0.538991i	0.0456237	−	0.998959i	$-0.485472\pi$
$241$	14.4927	−	8.36738i	0.933559	−	0.538991i	0.887935	+	0.459968i	$0.152139\pi$
$242$		−	1.16005i		−	0.0745710i
$243$		0			0
$244$			0.0500727i			0.00320558i
$245$		0			0
$246$		0			0
$247$	−11.0372	+	19.1170i	−0.702281	+	1.21639i
$248$	−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
$257$	12.3100	−	21.3216i	0.767878	−	1.33000i	−0.170834	−	0.985300i	$-0.554646\pi$
$257$	12.3100	−	21.3216i	0.767878	−	1.33000i	0.938712	−	0.344703i	$-0.112021\pi$
$258$		0			0
$259$		0			0
$260$		−	39.6894i		−	2.46143i
$261$		0			0
$262$			8.90932i			0.550419i
$263$	26.6568	−	15.3903i	1.64373	−	0.949006i	0.664235	−	0.747524i	$-0.268758\pi$
$263$	26.6568	−	15.3903i	1.64373	−	0.949006i	0.979492	−	0.201482i	$-0.0645757\pi$
$264$		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
$269$	−13.9809			−0.852432			−0.426216	−	0.904622i	$-0.640154\pi$
$269$	−13.9809			−0.852432			−0.426216	+	0.904622i	$0.640154\pi$
$270$		0			0
$271$		−	6.46262i		−	0.392576i	−0.980546	−	0.196288i	$-0.937111\pi$
$271$		−	6.46262i		−	0.392576i	0.980546	−	0.196288i	$-0.0628888\pi$
$272$	−1.57115	−	2.72132i	−0.0952652	−	0.165004i
$273$		0			0
$274$	2.39080	−	4.14099i	0.144433	−	0.250166i
$275$	25.7242	+	14.8519i	1.55123	+	0.895601i
$276$		0			0
$277$	9.55984	+	16.5581i	0.574395	+	0.994881i	0.996107	+	0.0881515i	$0.0280960\pi$
$277$	9.55984	+	16.5581i	0.574395	+	0.994881i	−0.421712	+	0.906730i	$0.638571\pi$
$278$	1.37304			0.0823494
$279$		0			0
$280$		0			0
$281$	−20.0611	+	11.5823i	−1.19674	+	0.690940i	−0.959828	−	0.280591i	$-0.909470\pi$
$281$	−20.0611	+	11.5823i	−1.19674	+	0.690940i	−0.236915	+	0.971530i	$0.576136\pi$
$282$		0			0
$283$	−13.8239	−	7.98126i	−0.821748	−	0.474436i	0.0292708	−	0.999572i	$-0.490681\pi$
$283$	−13.8239	−	7.98126i	−0.821748	−	0.474436i	−0.851019	+	0.525135i	$0.824015\pi$
$284$	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
$289$	−15.8674			−0.933379
$290$	0.757700	+	1.31237i	0.0444937	+	0.0770653i
$291$		0			0
$292$	3.55931	+	2.05497i	0.208293	+	0.120258i
$293$	−3.34849	+	5.79975i	−0.195621	+	0.338825i	−0.947104	−	0.320927i	$-0.896005\pi$
$293$	−3.34849	+	5.79975i	−0.195621	+	0.338825i	0.751483	+	0.659752i	$0.229339\pi$
$294$		0			0
$295$	−20.3018	−	35.1637i	−1.18202	−	2.04731i
$296$		−	12.9698i		−	0.753855i
$297$		0			0
$298$	7.59555			0.439998
$299$	−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
$304$	9.33836	−	5.39150i	0.535591	−	0.309224i
$305$			0.0992519i			0.00568315i
$306$		0			0
$307$			8.59068i			0.490296i	0.969486	+	0.245148i	$0.0788365\pi$
$307$			8.59068i			0.490296i	−0.969486	+	0.245148i	$0.921163\pi$
$308$		0			0
$309$		0			0
$310$	−0.830352	+	1.43821i	−0.0471608	+	0.0816849i
$311$	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	−0.585123	−	0.810945i	$-0.698954\pi$
$313$	−3.10288	+	1.79145i	−0.175385	+	0.101259i	0.409737	+	0.912204i	$0.365620\pi$
$314$	−3.25352			−0.183607
$315$		0			0
$316$	11.8887			0.668793
$317$	7.69566	−	4.44309i	0.432231	−	0.249549i	−0.268065	−	0.963401i	$-0.586384\pi$
$317$	7.69566	−	4.44309i	0.432231	−	0.249549i	0.700297	+	0.713852i	$0.253051\pi$
$318$		0			0
$319$	−1.83490	+	3.17814i	−0.102735	+	0.177942i
$320$	−7.21392	+	12.4949i	−0.403271	+	0.698485i
$321$		0			0
$322$		0			0
$323$			3.88642i			0.216246i
$324$		0			0
$325$		−	48.4474i		−	2.68738i
$326$	−1.46695	+	0.846946i	−0.0812470	+	0.0469080i
$327$		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	$0.976141\pi$
$332$	5.56852			0.305612
$333$		0			0
$334$			3.61635i			0.197878i
$335$	17.5507	+	30.3987i	0.958898	+	1.66086i
$336$		0			0
$337$	−6.79951	+	11.7771i	−0.370393	+	0.641539i	−0.989626	−	0.143668i	$-0.954110\pi$
$337$	−6.79951	+	11.7771i	−0.370393	+	0.641539i	0.619233	+	0.785207i	$0.287444\pi$
$338$	8.64691	+	4.99230i	0.470330	+	0.271545i
$339$		0			0
$340$	−3.49386	−	6.05154i	−0.189481	−	0.328191i
$341$	−4.02168			−0.217786
$342$		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	0.141818	−	0.989893i	$-0.454705\pi$
$347$	−12.0065	−	6.93198i	−0.644545	−	0.372128i	−0.786363	+	0.617765i	$0.788038\pi$
$348$		0			0
$349$	−1.55204	+	0.896072i	−0.0830789	+	0.0479656i	−0.540964	−	0.841046i	$-0.681940\pi$
$349$	−1.55204	+	0.896072i	−0.0830789	+	0.0479656i	0.457885	+	0.889011i	$0.348607\pi$
$350$		0			0
$351$		0			0
$352$	16.6530			0.887607
$353$	3.88049	+	6.72121i	0.206538	+	0.357734i	0.950622	−	0.310352i	$-0.100447\pi$
$353$	3.88049	+	6.72121i	0.206538	+	0.357734i	−0.744084	+	0.668086i	$0.767114\pi$
$354$		0			0
$355$	17.3641	+	10.0252i	0.921589	+	0.532080i
$356$	−13.6131	+	23.5786i	−0.721494	+	1.24966i
$357$		0			0
$358$	3.69421	+	6.39855i	0.195245	+	0.338174i
$359$			22.5810i			1.19178i	0.803066	+	0.595890i	$0.203201\pi$
$359$			22.5810i			1.19178i	−0.803066	+	0.595890i	$0.796799\pi$
$360$		0			0
$361$	5.66354			0.298081
$362$	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
$367$	−13.5263	+	7.80942i	−0.706068	+	0.407648i	−0.809603	−	0.586977i	$-0.800318\pi$
$367$	−13.5263	+	7.80942i	−0.706068	+	0.407648i	0.103536	+	0.994626i	$0.466984\pi$
$368$			1.07254i			0.0559098i
$369$		0			0
$370$		−	12.2486i		−	0.636773i
$371$		0			0
$372$		0			0
$373$	12.6229	−	21.8635i	0.653589	−	1.13205i	−0.328656	−	0.944450i	$-0.606596\pi$
$373$	12.6229	−	21.8635i	0.653589	−	1.13205i	0.982246	−	0.187600i	$-0.0600709\pi$
$374$	−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
$383$	−5.29503	+	9.17127i	−0.270564	+	0.468630i	−0.969006	−	0.247036i	$-0.920543\pi$
$383$	−5.29503	+	9.17127i	−0.270564	+	0.468630i	0.698443	+	0.715666i	$0.253877\pi$
$384$		0			0
$385$		0			0
$386$		−	3.51982i		−	0.179154i
$387$		0			0
$388$			3.51007i			0.178197i
$389$	11.7642	−	6.79207i	0.596469	−	0.344371i	−0.171182	−	0.985239i	$-0.554759\pi$
$389$	11.7642	−	6.79207i	0.596469	−	0.344371i	0.767651	+	0.640868i	$0.221425\pi$
$390$		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
$395$	23.5653			1.18570
$396$		0			0
$397$			38.9108i			1.95287i	0.215801	+	0.976437i	$0.430764\pi$
$397$			38.9108i			1.95287i	−0.215801	+	0.976437i	$0.569236\pi$
$398$	1.29806	+	2.24831i	0.0650660	+	0.112698i
$399$		0			0
$400$	−11.8329	+	20.4952i	−0.591645	+	1.02476i
$401$	−24.8956	−	14.3735i	−1.24323	−	0.717778i	−0.273477	−	0.961878i	$-0.588174\pi$
$401$	−24.8956	−	14.3735i	−1.24323	−	0.717778i	−0.969750	+	0.244101i	$0.921507\pi$
$402$		0			0
$403$	3.27972	+	5.68065i	0.163375	+	0.282973i
$404$	−11.7143			−0.582807
$405$		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	0.846393	−	0.532559i	$-0.178770\pi$
$409$	16.3485	+	9.43879i	0.808379	+	0.466718i	−0.0380133	+	0.999277i	$0.512103\pi$
$410$	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
$415$	11.0377			0.541818
$416$	−13.5807	−	23.5224i	−0.665848	−	1.15328i
$417$		0			0
$418$	−4.97201	−	2.87059i	−0.243189	−	0.140405i
$419$	−3.31895	+	5.74860i	−0.162142	+	0.280837i	−0.935636	−	0.352965i	$-0.885173\pi$
$419$	−3.31895	+	5.74860i	−0.162142	+	0.280837i	0.773495	+	0.633802i	$0.218507\pi$
$420$		0			0
$421$	−9.70574	−	16.8108i	−0.473029	−	0.819310i	0.526495	−	0.850178i	$-0.323506\pi$
$421$	−9.70574	−	16.8108i	−0.473029	−	0.819310i	−0.999523	+	0.0308686i	$0.990173\pi$
$422$		−	1.65839i		−	0.0807290i
$423$		0			0
$424$	−7.34360			−0.356637
$425$	−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
$430$	5.02983	−	2.90397i	0.242560	−	0.140042i
$431$		−	24.3185i		−	1.17138i	−0.810535	−	0.585690i	$-0.800824\pi$
$431$		−	24.3185i		−	1.17138i	0.810535	−	0.585690i	$-0.199176\pi$
$432$		0			0
$433$			3.32148i			0.159620i	0.996810	+	0.0798101i	$0.0254314\pi$
$433$			3.32148i			0.159620i	−0.996810	+	0.0798101i	$0.974569\pi$
$434$		0			0
$435$		0			0
$436$	15.7664	−	27.3083i	0.755076	−	1.30783i
$437$	0.663259	−	1.14880i	0.0317280	−	0.0549544i
$438$		0			0
$439$	23.3126	−	13.4595i	1.11265	−	0.642389i	0.173136	−	0.984898i	$-0.444610\pi$
$439$	23.3126	−	13.4595i	1.11265	−	0.642389i	0.939515	+	0.342509i	$0.111277\pi$
$440$	21.6657			1.03287
$441$		0			0
$442$	2.72879			0.129795
$443$	−22.8837	+	13.2119i	−1.08724	+	0.627717i	−0.932839	−	0.360292i	$-0.882677\pi$
$443$	−22.8837	+	13.2119i	−1.08724	+	0.627717i	−0.154397	+	0.988009i	$0.549344\pi$
$444$		0			0
$445$	−26.9833	+	46.7365i	−1.27913	+	2.21552i
$446$	−5.46560	+	9.46670i	−0.258804	+	0.448261i
$447$		0			0
$448$		0			0
$449$			19.6314i			0.926464i	0.886237	+	0.463232i	$0.153310\pi$
$449$			19.6314i			0.926464i	−0.886237	+	0.463232i	$0.846690\pi$
$450$		0			0
$451$			15.4916i			0.729470i
$452$	−15.4754	+	8.93474i	−0.727902	+	0.420255i
$453$		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	$0.632247\pi$
$458$	−1.93122			−0.0902399
$459$		0			0
$460$			2.38505i			0.111204i
$461$	7.23618	+	12.5334i	0.337023	+	0.583740i	0.983871	−	0.178878i	$-0.0572468\pi$
$461$	7.23618	+	12.5334i	0.337023	+	0.583740i	−0.646849	+	0.762618i	$0.723913\pi$
$462$		0			0
$463$	−10.0168	+	17.3495i	−0.465519	+	0.806302i	−0.999225	−	0.0393681i	$-0.987466\pi$
$463$	−10.0168	+	17.3495i	−0.465519	+	0.806302i	0.533706	+	0.845670i	$0.320799\pi$
$464$	−2.53212	−	1.46192i	−0.117551	−	0.0678679i
$465$		0			0
$466$	−5.54331	−	9.60130i	−0.256789	−	0.444772i
$467$	23.5630			1.09037			0.545183	−	0.838317i	$-0.316460\pi$
$467$	23.5630			1.09037			0.545183	+	0.838317i	$0.316460\pi$
$468$		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
$478$	−7.29511			−0.333671
$479$	12.4674	+	21.5941i	0.569648	+	0.986660i	0.996601	+	0.0823855i	$0.0262539\pi$
$479$	12.4674	+	21.5941i	0.569648	+	0.986660i	−0.426952	+	0.904274i	$0.640413\pi$
$480$		0			0
$481$	−41.8978	−	24.1897i	−1.91038	−	1.10296i
$482$	3.54945	−	6.14783i	0.161673	−	0.280026i
$483$		0			0
$484$	2.48863	+	4.31043i	0.113119	+	0.195929i
$485$			6.95750i			0.315924i
$486$		0			0
$487$	−5.00662			−0.226871			−0.113436	−	0.993545i	$-0.536186\pi$
$487$	−5.00662			−0.226871			−0.113436	+	0.993545i	$0.536186\pi$
$488$	0.0222909	+	0.0386090i	0.00100906	+	0.00174775i
$489$		0			0
$490$		0			0
$491$	−18.6960	−	10.7942i	−0.843740	−	0.487134i	0.0147936	−	0.999891i	$-0.495291\pi$
$491$	−18.6960	−	10.7942i	−0.843740	−	0.487134i	−0.858534	+	0.512757i	$0.828624\pi$
$492$		0			0
$493$	0.912628	−	0.526906i	0.0411027	−	0.0237307i
$494$			9.36399i			0.421306i
$495$		0			0
$496$		−	3.20419i		−	0.143872i
$497$		0			0
$498$		0			0
$499$	−17.9065	+	31.0149i	−0.801604	+	1.38842i	0.116956	+	0.993137i	$0.462686\pi$
$499$	−17.9065	+	31.0149i	−0.801604	+	1.38842i	−0.918560	+	0.395282i	$0.870647\pi$
$500$	−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
$509$	−9.07094	+	15.7113i	−0.402062	+	0.696392i	−0.993975	−	0.109610i	$-0.965040\pi$
$509$	−9.07094	+	15.7113i	−0.402062	+	0.696392i	0.591912	+	0.806002i	$0.298373\pi$
$510$		0			0
$511$		0			0
$512$			22.8374i			1.00928i
$513$		0			0
$514$		−	10.4438i		−	0.460658i
$515$	−30.3732	+	17.5360i	−1.33840	+	0.772728i
$516$		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
$521$	−0.839387			−0.0367742			−0.0183871	−	0.999831i	$-0.505853\pi$
$521$	−0.839387			−0.0367742			−0.0183871	+	0.999831i	$0.505853\pi$
$522$		0			0
$523$		−	16.2832i		−	0.712015i	−0.934483	−	0.356008i	$-0.884138\pi$
$523$		−	16.2832i		−	0.712015i	0.934483	−	0.356008i	$-0.115862\pi$
$524$	−19.1129	−	33.1045i	−0.834951	−	1.44618i
$525$		0			0
$526$	6.52858	−	11.3078i	0.284660	−	0.493045i
$527$	1.00014	+	0.577428i	0.0435666	+	0.0251532i
$528$		0			0
$529$	−11.4340	−	19.8043i	−0.497132	−	0.861057i
$530$	−6.93524			−0.301247
$531$		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
$541$	−1.86693			−0.0802657			−0.0401328	−	0.999194i	$-0.512778\pi$
$541$	−1.86693			−0.0802657			−0.0401328	+	0.999194i	$0.512778\pi$
$542$	−1.37072	−	2.37417i	−0.0588777	−	0.101979i
$543$		0			0
$544$	−4.14136	−	2.39102i	−0.177559	−	0.102514i
$545$	31.2515	−	54.1292i	1.33867	−	2.31864i
$546$		0			0
$547$	7.55792	+	13.0907i	0.323153	+	0.559718i	0.981137	−	0.193315i	$-0.0619238\pi$
$547$	7.55792	+	13.0907i	0.323153	+	0.559718i	−0.657984	+	0.753032i	$0.728590\pi$
$548$			20.5157i			0.876386i
$549$		0			0
$550$	12.6004			0.537281
$551$	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
$556$	−5.10183	+	2.94554i	−0.216366	+	0.124919i
$557$			6.32176i			0.267862i	0.990991	+	0.133931i	$0.0427600\pi$
$557$			6.32176i			0.267862i	−0.990991	+	0.133931i	$0.957240\pi$
$558$		0			0
$559$		−	22.9402i		−	0.970269i
$560$		0			0
$561$		0			0
$562$	−4.91321	+	8.50992i	−0.207251	+	0.358970i
$563$	−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	−0.755170	−	0.655529i	$-0.772446\pi$
$569$	−13.4785	+	7.78184i	−0.565050	+	0.326232i	0.190120	+	0.981761i	$0.439112\pi$
$570$		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	$-0.173431\pi$
$572$	20.3860	−	35.3096i	0.852382	−	1.47637i
$573$		0			0
$574$		0			0
$575$			2.91135i			0.121412i
$576$		0			0
$577$			40.3472i			1.67968i	0.542837	+	0.839838i	$0.317350\pi$
$577$			40.3472i			1.67968i	−0.542837	+	0.839838i	$0.682650\pi$
$578$	−5.82921	+	3.36549i	−0.242463	+	0.139986i
$579$		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
$584$	3.65926			0.151421
$585$		0			0
$586$			2.84086i			0.117355i
$587$	1.91520	+	3.31723i	0.0790490	+	0.136917i	0.902840	−	0.429977i	$-0.141478\pi$
$587$	1.91520	+	3.31723i	0.0790490	+	0.136917i	−0.823791	+	0.566894i	$0.808145\pi$
$588$		0			0
$589$	−1.98148	+	3.43202i	−0.0816453	+	0.141414i
$590$	−14.9165	−	8.61204i	−0.614102	−	0.354552i
$591$		0			0
$592$	11.8163	+	20.4664i	0.485647	+	0.841166i
$593$	−12.5143			−0.513902			−0.256951	−	0.966424i	$-0.582718\pi$
$593$	−12.5143			−0.513902			−0.256951	+	0.966424i	$0.582718\pi$
$594$		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	0.358565	−	0.933505i	$-0.383266\pi$
$599$	−6.62258	−	3.82355i	−0.270591	−	0.156226i	−0.629156	+	0.777279i	$0.716599\pi$
$600$		0			0
$601$	29.8513	−	17.2346i	1.21766	−	0.703015i	0.253242	−	0.967403i	$-0.418503\pi$
$601$	29.8513	−	17.2346i	1.21766	−	0.703015i	0.964416	+	0.264388i	$0.0851698\pi$
$602$		0			0
$603$		0			0
$604$	−33.8510			−1.37738
$605$	4.93285	+	8.54394i	0.200549	+	0.347361i
$606$		0			0
$607$	10.7472	+	6.20488i	0.436214	+	0.251848i	0.701990	−	0.712186i	$-0.252295\pi$
$607$	10.7472	+	6.20488i	0.436214	+	0.251848i	−0.265776	+	0.964035i	$0.585628\pi$
$608$	8.20490	−	14.2113i	0.332753	−	0.576344i
$609$		0			0
$610$	0.0210514	+	0.0364621i	0.000852346	+	0.00147631i
$611$		−	34.3151i		−	1.38824i
$612$		0			0
$613$	−1.66896			−0.0674088			−0.0337044	−	0.999432i	$-0.510730\pi$
$613$	−1.66896			−0.0674088			−0.0337044	+	0.999432i	$0.510730\pi$
$614$	1.82209	+	3.15595i	0.0735335	+	0.127364i
$615$		0			0
$616$		0			0
$617$	13.5698	+	7.83453i	0.546300	+	0.315406i	0.747628	−	0.664118i	$-0.231193\pi$
$617$	13.5698	+	7.83453i	0.546300	+	0.315406i	−0.201329	+	0.979524i	$0.564526\pi$
$618$		0			0
$619$	−3.10436	+	1.79230i	−0.124775	+	0.0720387i	−0.561088	−	0.827756i	$-0.689617\pi$
$619$	−3.10436	+	1.79230i	−0.124775	+	0.0720387i	0.436314	+	0.899795i	$0.356284\pi$
$620$		−	7.12532i		−	0.286160i
$621$		0			0
$622$		−	1.79626i		−	0.0720234i
$623$		0			0
$624$		0			0
$625$	0.417550	−	0.723218i	0.0167020	−	0.0289287i
$626$	−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
$635$	21.1638	−	36.6568i	0.839861	−	1.45468i
$636$		0			0
$637$		0			0
$638$			1.55674i			0.0616318i
$639$		0			0
$640$			38.5419i			1.52350i
$641$	−20.3567	+	11.7529i	−0.804041	+	0.464213i	−0.844882	−	0.534953i	$-0.820329\pi$
$641$	−20.3567	+	11.7529i	−0.804041	+	0.464213i	0.0408415	+	0.999166i	$0.486996\pi$
$642$		0			0
$643$	−4.83255	−	2.79007i	−0.190577	−	0.110030i	0.401676	−	0.915782i	$-0.368428\pi$
$643$	−4.83255	−	2.79007i	−0.190577	−	0.110030i	−0.592253	+	0.805752i	$0.701761\pi$
$644$		0			0
$645$		0			0
$646$	0.824312	+	1.42775i	0.0324321	+	0.0561741i
$647$	−3.90178			−0.153395			−0.0766974	−	0.997054i	$-0.524438\pi$
$647$	−3.90178			−0.153395			−0.0766974	+	0.997054i	$0.524438\pi$
$648$		0			0
$649$		−	41.7111i		−	1.63730i
$650$	−10.2757	−	17.7981i	−0.403047	−	0.698098i
$651$		0			0
$652$	3.63386	−	6.29402i	0.142313	−	0.246493i
$653$	5.29484	+	3.05698i	0.207203	+	0.119629i	0.600011	−	0.799992i	$-0.295163\pi$
$653$	5.29484	+	3.05698i	0.207203	+	0.119629i	−0.392808	+	0.919621i	$0.628496\pi$
$654$		0			0
$655$	−37.8847	−	65.6183i	−1.48028	−	2.56392i
$656$	−12.3426			−0.481896
$657$		0			0
$658$		0			0
$659$	−24.7031	+	14.2623i	−0.962296	+	0.555582i	−0.896879	−	0.442276i	$-0.854171\pi$
$659$	−24.7031	+	14.2623i	−0.962296	+	0.555582i	−0.0654174	+	0.997858i	$0.520838\pi$
$660$		0			0
$661$	21.7672	+	12.5673i	0.846648	+	0.488812i	0.859518	−	0.511105i	$-0.170764\pi$
$661$	21.7672	+	12.5673i	0.846648	+	0.488812i	−0.0128707	+	0.999917i	$0.504097\pi$
$662$	−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
$667$	−0.359688			−0.0139272
$668$	−7.75804	−	13.4373i	−0.300168	−	0.519906i
$669$		0			0
$670$	12.8952	+	7.44503i	0.498184	+	0.287627i
$671$	−0.0509796	+	0.0882993i	−0.00196805	+	0.00340875i
$672$		0			0
$673$	12.5278	+	21.6988i	0.482912	+	0.836428i	0.999808	−	0.0196203i	$-0.00624575\pi$
$673$	12.5278	+	21.6988i	0.482912	+	0.836428i	−0.516895	+	0.856049i	$0.672912\pi$
$674$			5.76872i			0.222203i
$675$		0			0
$676$	−42.8393			−1.64767
$677$	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
$682$	−1.47744	+	0.853001i	−0.0565742	+	0.0326631i
$683$		−	38.5467i		−	1.47495i	−0.675375	−	0.737475i	$-0.736018\pi$
$683$		−	38.5467i		−	1.47495i	0.675375	−	0.737475i	$-0.263982\pi$
$684$		0			0
$685$			40.6652i			1.55374i
$686$		0			0
$687$		0			0
$688$	−5.60297	+	9.70464i	−0.213611	+	0.369986i
$689$	−13.6964	+	23.7229i	−0.521792	+	0.903770i
$690$		0			0
$691$	−26.1768	+	15.1132i	−0.995812	+	0.574932i	−0.907006	−	0.421117i	$-0.861638\pi$
$691$	−26.1768	+	15.1132i	−0.995812	+	0.574932i	−0.0888052	+	0.996049i	$0.528305\pi$
$692$	−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
$698$	−0.380115	+	0.658378i	−0.0143876	+	0.0249200i
$699$		0			0
$700$		0			0
$701$		−	29.6057i		−	1.11819i	−0.829103	−	0.559096i	$-0.811148\pi$
$701$		−	29.6057i		−	1.11819i	0.829103	−	0.559096i	$-0.188852\pi$
$702$		0			0
$703$		−	29.2289i		−	1.10239i
$704$	−12.8357	+	7.41070i	−0.483764	+	0.279301i
$705$		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	$0.854652\pi$
$710$	8.50536			0.319200
$711$		0			0
$712$			24.2407i			0.908458i
$713$	−0.197088	−	0.341367i	−0.00738102	−	0.0127843i
$714$		0			0
$715$	40.4082	−	69.9891i	1.51118	−	2.61744i
$716$	−27.4533	−	15.8501i	−1.02598	−	0.592348i
$717$		0			0
$718$	4.78944	+	8.29556i	0.178740	+	0.309588i
$719$	1.61282			0.0601480			0.0300740	−	0.999548i	$-0.490426\pi$
$719$	1.61282			0.0601480			0.0300740	+	0.999548i	$0.490426\pi$
$720$		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	−0.292633	−	0.956225i	$-0.594531\pi$
$727$	10.4930	−	6.05816i	0.389166	−	0.224685i	0.681799	+	0.731540i	$0.261198\pi$
$728$		0			0
$729$		0			0
$730$	3.45577			0.127904
$731$	−2.01943	−	3.49775i	−0.0746913	−	0.129369i
$732$		0			0
$733$	34.9931	+	20.2033i	1.29250	+	0.746225i	0.979097	−	0.203396i	$-0.0651977\pi$
$733$	34.9931	+	20.2033i	1.29250	+	0.746225i	0.313403	+	0.949620i	$0.398531\pi$
$734$	−3.31277	+	5.73788i	−0.122276	+	0.211789i
$735$		0			0
$736$	0.816104	+	1.41353i	0.0300820	+	0.0521035i
$737$			36.0589i			1.32825i
$738$		0			0
$739$	−20.4634			−0.752760			−0.376380	−	0.926465i	$-0.622831\pi$
$739$	−20.4634			−0.752760			−0.376380	+	0.926465i	$0.622831\pi$
$740$	26.2765	+	45.5123i	0.965944	+	1.67306i
$741$		0			0
$742$		0			0
$743$	−37.1209	−	21.4318i	−1.36184	−	0.786256i	−0.371967	−	0.928246i	$-0.621317\pi$
$743$	−37.1209	−	21.4318i	−1.36184	−	0.786256i	−0.989868	+	0.141990i	$0.954650\pi$
$744$		0			0
$745$	−55.9422	+	32.2982i	−2.04956	+	1.18332i
$746$		−	10.7093i		−	0.392095i
$747$		0			0
$748$		−	7.17832i		−	0.262465i
$749$		0			0
$750$		0			0
$751$	21.5028	−	37.2440i	0.784649	−	1.35905i	−0.144559	−	0.989496i	$-0.546177\pi$
$751$	21.5028	−	37.2440i	0.784649	−	1.35905i	0.929209	−	0.369556i	$-0.120490\pi$
$752$	−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
$761$	−11.5916	+	20.0773i	−0.420196	+	0.727801i	−0.995958	−	0.0898160i	$-0.971372\pi$
$761$	−11.5916	+	20.0773i	−0.420196	+	0.727801i	0.575762	+	0.817617i	$0.304705\pi$
$762$		0			0
$763$		0			0
$764$		−	0.452950i		−	0.0163872i
$765$		0			0
$766$			4.49232i			0.162314i
$767$	−58.9172	+	34.0159i	−2.12738	+	1.22824i
$768$		0			0
$769$	11.4527	+	6.61219i	0.412993	+	0.238442i	0.692075	−	0.721826i	$-0.256697\pi$
$769$	11.4527	+	6.61219i	0.412993	+	0.238442i	−0.279082	+	0.960267i	$0.590030\pi$
$770$		0			0
$771$		0			0
$772$	7.55096	+	13.0787i	0.271765	+	0.470711i
$773$	−19.6319			−0.706110			−0.353055	−	0.935603i	$-0.614857\pi$
$773$	−19.6319			−0.706110			−0.353055	+	0.935603i	$0.614857\pi$
$774$		0			0
$775$		−	8.69762i		−	0.312428i
$776$	1.56258	+	2.70647i	0.0560935	+	0.0971567i
$777$		0			0
$778$	2.88120	−	4.99039i	0.103296	−	0.178914i
$779$	13.2202	+	7.63267i	0.473662	+	0.273469i
$780$		0			0
$781$	10.2986	+	17.8377i	0.368513	+	0.638284i
$782$	−0.163981			−0.00586395
$783$		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	0.740925	−	0.671588i	$-0.234387\pi$
$787$	14.8621	+	8.58063i	0.529776	+	0.305866i	−0.211149	+	0.977454i	$0.567721\pi$
$788$	−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
$793$	0.166298			0.00590540
$794$	8.25299	+	14.2946i	0.292888	+	0.507297i
$795$		0			0
$796$	−9.64647	−	5.56939i	−0.341910	−	0.197402i
$797$	11.2772	−	19.5326i	0.399458	−	0.691882i	−0.594201	−	0.804317i	$-0.702532\pi$
$797$	11.2772	−	19.5326i	0.399458	−	0.691882i	0.993659	+	0.112435i	$0.0358650\pi$
$798$		0			0
$799$	−3.02076	−	5.23211i	−0.106867	−	0.185099i
$800$			36.0151i			1.27333i
$801$		0			0
$802$	−12.1945			−0.430603
$803$	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
$808$	−9.03240	+	5.21486i	−0.317759	+	0.183458i
$809$			48.2178i			1.69525i	0.530598	+	0.847624i	$0.321967\pi$
$809$			48.2178i			1.69525i	−0.530598	+	0.847624i	$0.678033\pi$
$810$		0			0
$811$		−	11.2304i		−	0.394354i	−0.980368	−	0.197177i	$-0.936823\pi$
$811$		−	11.2304i		−	0.394354i	0.980368	−	0.197177i	$-0.0631774\pi$
$812$		0			0
$813$		0			0
$814$	6.29134	−	10.8969i	0.220511	−	0.381937i
$815$	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	0.247447	−	0.968902i	$-0.420409\pi$
$821$	34.6778	−	20.0212i	1.21026	−	0.698746i	0.962817	+	0.270156i	$0.0870752\pi$
$822$		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	$0.222308\pi$
$824$	−7.87680	+	13.6430i	−0.274401	+	0.475277i
$825$		0			0
$826$		0			0
$827$			20.8802i			0.726077i	0.931774	+	0.363038i	$0.118261\pi$
$827$			20.8802i			0.726077i	−0.931774	+	0.363038i	$0.881739\pi$
$828$		0			0
$829$			16.0646i			0.557945i	0.960299	+	0.278973i	$0.0899939\pi$
$829$			16.0646i			0.557945i	−0.960299	+	0.278973i	$0.910006\pi$
$830$	4.05490	−	2.34110i	0.140748	−	0.0812607i
$831$		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
$836$	24.6328			0.851943
$837$		0			0
$838$			2.81581i			0.0972705i
$839$	10.1943	+	17.6570i	0.351946	+	0.609589i	0.986590	−	0.163216i	$-0.0521866\pi$
$839$	10.1943	+	17.6570i	0.351946	+	0.609589i	−0.634644	+	0.772805i	$0.718853\pi$
$840$		0			0
$841$	−14.0097	+	24.2656i	−0.483094	+	0.836743i
$842$	−7.13117	−	4.11719i	−0.245756	−	0.141888i
$843$		0			0
$844$	3.55769	+	6.16210i	0.122461	+	0.212108i
$845$	−84.9142			−2.92114
$846$		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	−0.360339	−	0.932821i	$-0.617339\pi$
$853$	7.80792	−	4.50790i	0.267338	−	0.154348i	0.627677	+	0.778474i	$0.284006\pi$
$854$		0			0
$855$		0			0
$856$	−6.42068			−0.219454
$857$	16.1658	+	28.0000i	0.552213	+	0.956461i	0.998115	+	0.0613789i	$0.0195498\pi$
$857$	16.1658	+	28.0000i	0.552213	+	0.956461i	−0.445902	+	0.895082i	$0.647117\pi$
$858$		0			0
$859$	38.1416	+	22.0211i	1.30138	+	0.751349i	0.980640	−	0.195819i	$-0.0627366\pi$
$859$	38.1416	+	22.0211i	1.30138	+	0.751349i	0.320735	+	0.947169i	$0.396070\pi$
$860$	−12.4596	+	21.5807i	−0.424870	+	0.735896i
$861$		0			0
$862$	−5.15796	−	8.93385i	−0.175681	−	0.304288i
$863$		−	6.12763i		−	0.208587i	−0.994547	−	0.104293i	$-0.966742\pi$
$863$		−	6.12763i		−	0.208587i	0.994547	−	0.104293i	$-0.0332581\pi$
$864$		0			0
$865$	−1.56892			−0.0533449
$866$	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
$871$	50.9334	−	29.4064i	1.72581	−	0.996398i
$872$		−	28.0751i		−	0.950742i
$873$		0			0
$874$		−	0.562710i		−	0.0190340i
$875$		0			0
$876$		0			0
$877$	1.13204	−	1.96075i	0.0382263	−	0.0662099i	−0.846279	−	0.532740i	$-0.821163\pi$
$877$	1.13204	−	1.96075i	0.0382263	−	0.0662099i	0.884506	+	0.466530i	$0.154496\pi$
$878$	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
$887$	28.7740	−	49.8380i	0.966136	−	1.67340i	0.259604	−	0.965715i	$-0.416408\pi$
$887$	28.7740	−	49.8380i	0.966136	−	1.67340i	0.706532	−	0.707681i	$-0.250259\pi$
$888$		0			0
$889$		0			0
$890$			22.8927i			0.767365i
$891$		0			0
$892$		−	46.9008i		−	1.57035i
$893$	17.9543	−	10.3659i	0.600817	−	0.346882i
$894$		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
$899$	1.07456			0.0358387
$900$		0			0
$901$			4.82278i			0.160670i
$902$	3.28577	+	5.69112i	0.109404	+	0.189494i
$903$		0			0
$904$	−7.95498	+	13.7784i	−0.264579	+	0.458263i
$905$	−55.4317	−	32.0035i	−1.84261	−	1.06383i
$906$		0			0
$907$	5.05621	+	8.75761i	0.167889	+	0.290792i	0.937677	−	0.347507i	$-0.112972\pi$
$907$	5.05621	+	8.75761i	0.167889	+	0.290792i	−0.769789	+	0.638299i	$0.779638\pi$
$908$	44.7918			1.48647
$909$		0			0
$910$		0			0
$911$	16.9986	−	9.81416i	0.563190	−	0.325158i	−0.191235	−	0.981544i	$-0.561249\pi$
$911$	16.9986	−	9.81416i	0.563190	−	0.325158i	0.754425	+	0.656387i	$0.227916\pi$
$912$		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
$919$	17.0487			0.562384			0.281192	−	0.959652i	$-0.409270\pi$
$919$	17.0487			0.562384			0.281192	+	0.959652i	$0.409270\pi$
$920$	1.06176	+	1.83902i	0.0350051	+	0.0606306i
$921$		0			0
$922$	5.31670	+	3.06960i	0.175096	+	0.101092i
$923$	16.7972	−	29.0937i	0.552888	−	0.957630i
$924$		0			0
$925$	32.0748	+	55.5552i	1.05461	+	1.82664i
$926$			8.49825i			0.279270i
$927$		0			0
$928$	−4.44956			−0.146064
$929$	−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
$934$	8.65632	−	4.99773i	0.283244	−	0.163531i
$935$		−	14.2285i		−	0.465323i
$936$		0			0
$937$		−	34.9586i		−	1.14205i	−0.820933	−	0.571025i	$-0.806546\pi$
$937$		−	34.9586i		−	1.14205i	0.820933	−	0.571025i	$-0.193454\pi$
$938$		0			0
$939$		0			0
$940$	−18.6377	+	32.2815i	−0.607895	+	1.05291i
$941$	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	0.0565088	−	0.998402i	$-0.482003\pi$
$947$	29.2164	−	16.8681i	0.949405	−	0.548139i	0.892896	+	0.450263i	$0.148670\pi$
$948$		0			0
$949$	6.82481	−	11.8209i	0.221543	−	0.383723i
$950$	6.20818	−	10.7529i	0.201420	−	0.348869i
$951$		0			0
$952$		0			0
$953$		−	18.7823i		−	0.608420i	−0.952605	−	0.304210i	$-0.901608\pi$
$953$		−	18.7823i		−	0.608420i	0.952605	−	0.304210i	$-0.0983925\pi$
$954$		0			0
$955$		−	0.897817i		−	0.0290527i
$956$	27.1066	−	15.6500i	0.876690	−	0.506157i
$957$		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
$962$	−20.5226			−0.661676
$963$		0			0
$964$			30.4582i			0.980992i
$965$	14.9672	+	25.9239i	0.481810	+	0.834520i
$966$		0			0
$967$	−17.5860	+	30.4599i	−0.565529	+	0.979525i	0.431471	+	0.902127i	$0.357995\pi$
$967$	−17.5860	+	30.4599i	−0.565529	+	0.979525i	−0.997000	+	0.0773981i	$0.975339\pi$
$968$	3.83776	+	2.21573i	0.123350	+	0.0712163i
$969$		0			0
$970$	1.47569	+	2.55597i	0.0473816	+	0.0820673i
$971$	−39.5962			−1.27070			−0.635351	−	0.772223i	$-0.719145\pi$
$971$	−39.5962			−1.27070			−0.635351	+	0.772223i	$0.719145\pi$
$972$		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	0.899403	−	0.437121i	$-0.144002\pi$
$977$	30.3364	+	17.5147i	0.970546	+	0.560345i	0.0711433	+	0.997466i	$0.477335\pi$
$978$		0			0
$979$	−48.0113	+	27.7193i	−1.53445	+	0.885914i
$980$		0			0
$981$		0			0
$982$	−9.15779			−0.292237
$983$	22.0865	+	38.2550i	0.704451	+	1.22015i	0.966889	+	0.255197i	$0.0821403\pi$
$983$	22.0865	+	38.2550i	0.704451	+	1.22015i	−0.262438	+	0.964949i	$0.584526\pi$
$984$		0			0
$985$	−70.5524	−	40.7335i	−2.24799	−	1.29788i
$986$	0.223514	−	0.387138i	0.00711814	−	0.0123290i
$987$		0			0
$988$	−20.0883	−	34.7940i	−0.639094	−	1.10694i
$989$			1.37855i			0.0438353i
$990$		0			0
$991$	26.8886			0.854146			0.427073	−	0.904217i	$-0.359545\pi$
$991$	26.8886			0.854146			0.427073	+	0.904217i	$0.359545\pi$
$992$	−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
$997$	−26.9780	+	15.5757i	−0.854401	+	0.493289i	−0.862133	−	0.506681i	$-0.830872\pi$
$997$	−26.9780	+	15.5757i	−0.854401	+	0.493289i	0.00773220	+	0.999970i	$0.497539\pi$
$998$			15.1919i			0.480891i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.o.e.881.14		48
3.2	odd	2		441.2.o.e.293.12	yes	48
7.2	even	3		1323.2.s.d.962.11		48
7.3	odd	6		1323.2.i.d.1097.3		48
7.4	even	3		1323.2.i.d.1097.19		48
7.5	odd	6		1323.2.s.d.962.12		48
7.6	odd	2	inner	1323.2.o.e.881.13		48
9.2	odd	6	inner	1323.2.o.e.440.13		48
9.7	even	3		441.2.o.e.146.11	✓	48
21.2	odd	6		441.2.s.d.374.13		48
21.5	even	6		441.2.s.d.374.14		48
21.11	odd	6		441.2.i.d.68.12		48
21.17	even	6		441.2.i.d.68.11		48
21.20	even	2		441.2.o.e.293.11	yes	48
63.2	odd	6		1323.2.i.d.521.3		48
63.11	odd	6		1323.2.s.d.656.12		48
63.16	even	3		441.2.i.d.227.13		48
63.20	even	6	inner	1323.2.o.e.440.14		48
63.25	even	3		441.2.s.d.362.14		48
63.34	odd	6		441.2.o.e.146.12	yes	48
63.38	even	6		1323.2.s.d.656.11		48
63.47	even	6		1323.2.i.d.521.19		48
63.52	odd	6		441.2.s.d.362.13		48
63.61	odd	6		441.2.i.d.227.14		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.11		48	21.17	even	6
441.2.i.d.68.12		48	21.11	odd	6
441.2.i.d.227.13		48	63.16	even	3
441.2.i.d.227.14		48	63.61	odd	6
441.2.o.e.146.11	✓	48	9.7	even	3
441.2.o.e.146.12	yes	48	63.34	odd	6
441.2.o.e.293.11	yes	48	21.20	even	2
441.2.o.e.293.12	yes	48	3.2	odd	2
441.2.s.d.362.13		48	63.52	odd	6
441.2.s.d.362.14		48	63.25	even	3
441.2.s.d.374.13		48	21.2	odd	6
441.2.s.d.374.14		48	21.5	even	6
1323.2.i.d.521.3		48	63.2	odd	6
1323.2.i.d.521.19		48	63.47	even	6
1323.2.i.d.1097.3		48	7.3	odd	6
1323.2.i.d.1097.19		48	7.4	even	3
1323.2.o.e.440.13		48	9.2	odd	6	inner
1323.2.o.e.440.14		48	63.20	even	6	inner
1323.2.o.e.881.13		48	7.6	odd	2	inner
1323.2.o.e.881.14		48	1.1	even	1	trivial
1323.2.s.d.656.11		48	63.38	even	6
1323.2.s.d.656.12		48	63.11	odd	6
1323.2.s.d.962.11		48	7.2	even	3
1323.2.s.d.962.12		48	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.367369 - 0.212101i) q^{2} +(-0.910027 + 1.57621i) q^{4} +(-1.80381 + 3.12430i) q^{5} +1.62047i q^{8} +O(q^{10})\)	\(q+(0.367369 - 0.212101i) q^{2} +(-0.910027 + 1.57621i) q^{4} +(-1.80381 + 3.12430i) q^{5} +1.62047i q^{8} +1.53036i q^{10} +(-3.20952 + 1.85302i) q^{11} +(5.23479 + 3.02231i) q^{13} +(-1.47635 - 2.55711i) q^{16} +1.06422 q^{17} +3.65191i q^{19} +(-3.28304 - 5.68639i) q^{20} +(-0.786052 + 1.36148i) q^{22} +(-0.314574 - 0.181620i) q^{23} +(-4.00749 - 6.94117i) q^{25} +2.56413 q^{26} +(0.857560 - 0.495112i) q^{29} +(0.939786 + 0.542586i) q^{31} +(-3.89147 - 2.24674i) q^{32} +(0.390960 - 0.225721i) q^{34} -8.00373 q^{37} +(0.774573 + 1.34160i) q^{38} +(-5.06283 - 2.92303i) q^{40} +(2.09005 - 3.62007i) q^{41} +(-1.89758 - 3.28670i) q^{43} -6.74518i q^{44} -0.154086 q^{46} +(-2.83849 - 4.91640i) q^{47} +(-2.94445 - 1.69998i) q^{50} +(-9.52760 + 5.50076i) q^{52} +4.53177i q^{53} -13.3700i q^{55} +(0.210027 - 0.363778i) q^{58} +(-5.62746 + 9.74705i) q^{59} +(0.0238258 - 0.0137558i) q^{61} +0.460331 q^{62} +3.99926 q^{64} +(-18.8852 + 10.9034i) q^{65} +(4.86489 - 8.42624i) q^{67} +(-0.968464 + 1.67743i) q^{68} -5.55775i q^{71} -2.25814i q^{73} +(-2.94032 + 1.69759i) q^{74} +(-5.75619 - 3.32334i) q^{76} +(-3.26604 - 5.65694i) q^{79} +10.6522 q^{80} -1.77320i q^{82} +(-1.52977 - 2.64964i) q^{83} +(-1.91965 + 3.32492i) q^{85} +(-1.39422 - 0.804954i) q^{86} +(-3.00276 - 5.20093i) q^{88} +14.9590 q^{89} +(0.572542 - 0.330557i) q^{92} +(-2.08554 - 1.20409i) q^{94} +(-11.4097 - 6.58737i) q^{95} +(1.67018 - 0.964277i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4}+O(q^{10}) \) 48 * q + 24 * q^4	\( 48 q + 24 q^{4} + 24 q^{11} - 24 q^{16} + 48 q^{23} - 24 q^{25} - 120 q^{32} - 48 q^{50} - 48 q^{64} - 120 q^{65} + 168 q^{74} - 24 q^{79} - 24 q^{85} - 24 q^{86} + 144 q^{92} - 96 q^{95}+O(q^{100}) \) 48 * q + 24 * q^4 + 24 * q^11 - 24 * q^16 + 48 * q^23 - 24 * q^25 - 120 * q^32 - 48 * q^50 - 48 * q^64 - 120 * q^65 + 168 * q^74 - 24 * q^79 - 24 * q^85 - 24 * q^86 + 144 * q^92 - 96 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more