LMFDB - Embedded newform 1323.2.i.d.521.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(521,1323)]

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, 1]))

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

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

chi := DirichletCharacter("1323.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: 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			521.3
Character	$\chi$	$=$	1323.521
Dual form			1323.2.i.d.1097.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.424201i q^{2} +1.82005 q^{4} +(1.80381 - 3.12430i) q^{5} -1.62047i q^{8} +O(q^{10})$	\(q-0.424201i q^{2} +1.82005 q^{4} +(1.80381 - 3.12430i) q^{5} -1.62047i q^{8} +(-1.32533 - 0.765180i) q^{10} +(3.20952 - 1.85302i) q^{11} +(-5.23479 + 3.02231i) q^{13} +2.95270 q^{16} +(0.532108 - 0.921637i) q^{17} +(3.16265 - 1.82596i) q^{19} +(3.28304 - 5.68639i) q^{20} +(-0.786052 - 1.36148i) q^{22} +(0.314574 + 0.181620i) q^{23} +(-4.00749 - 6.94117i) q^{25} +(1.28207 + 2.22060i) q^{26} +(0.857560 + 0.495112i) q^{29} -1.08517i q^{31} -4.49348i q^{32} +(-0.390960 - 0.225721i) q^{34} +(4.00186 + 6.93143i) q^{37} +(-0.774573 - 1.34160i) q^{38} +(-5.06283 - 2.92303i) q^{40} +(-2.09005 - 3.62007i) q^{41} +(-1.89758 + 3.28670i) q^{43} +(5.84149 - 3.37259i) q^{44} +(0.0770432 - 0.133443i) q^{46} -5.67697 q^{47} +(-2.94445 + 1.69998i) q^{50} +(-9.52760 + 5.50076i) q^{52} +(3.92463 + 2.26589i) q^{53} -13.3700i q^{55} +(0.210027 - 0.363778i) q^{58} -11.2549 q^{59} +0.0275117i q^{61} -0.460331 q^{62} +3.99926 q^{64} +21.8067i q^{65} -9.72978 q^{67} +(0.968464 - 1.67743i) q^{68} +5.55775i q^{71} +(1.95561 + 1.12907i) q^{73} +(2.94032 - 1.69759i) q^{74} +(5.75619 - 3.32334i) q^{76} +6.53207 q^{79} +(5.32612 - 9.22511i) q^{80} +(-1.53564 + 0.886601i) q^{82} +(1.52977 - 2.64964i) q^{83} +(-1.91965 - 3.32492i) q^{85} +(1.39422 + 0.804954i) q^{86} +(-3.00276 - 5.20093i) q^{88} +(7.47952 + 12.9549i) q^{89} +(0.572542 + 0.330557i) q^{92} +2.40818i q^{94} -13.1747i q^{95} +(-1.67018 - 0.964277i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4}+O(q^{10}) $ 48 * q - 48 * q^4	$ 48 q - 48 q^{4} - 24 q^{11} + 48 q^{16} - 48 q^{23} - 24 q^{25} + 96 q^{44} - 48 q^{50} + 48 q^{53} - 48 q^{64} - 168 q^{74} + 48 q^{79} - 24 q^{85} + 24 q^{86} + 144 q^{92}+O(q^{100}) $ 48 * q - 48 * q^4 - 24 * q^11 + 48 * q^16 - 48 * q^23 - 24 * q^25 + 96 * q^44 - 48 * q^50 + 48 * q^53 - 48 * q^64 - 168 * q^74 + 48 * q^79 - 24 * q^85 + 24 * q^86 + 144 * q^92

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	0.424201i		−	0.299956i	−0.988689	−	0.149978i	$-0.952080\pi$
$2$		−	0.424201i		−	0.299956i	0.988689	−	0.149978i	$-0.0479202\pi$
$3$		0			0
$3$		0			0
$4$	1.82005			0.910027
$5$	1.80381	−	3.12430i	0.806690	−	1.39723i	−0.108454	−	0.994101i	$-0.534590\pi$
$5$	1.80381	−	3.12430i	0.806690	−	1.39723i	0.915144	−	0.403126i	$-0.132077\pi$
$6$		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
$11$	3.20952	−	1.85302i	0.967706	−	0.558705i	0.0691700	−	0.997605i	$-0.477965\pi$
$11$	3.20952	−	1.85302i	0.967706	−	0.558705i	0.898536	+	0.438899i	$0.144632\pi$
$12$		0			0
$13$	−5.23479	+	3.02231i	−1.45187	+	0.838238i	−0.998588	−	0.0531292i	$-0.983080\pi$
$13$	−5.23479	+	3.02231i	−1.45187	+	0.838238i	−0.453283	+	0.891367i	$0.649747\pi$
$14$		0			0
$15$		0			0
$16$	2.95270			0.738175
$17$	0.532108	−	0.921637i	0.129055	−	0.223530i	−0.794256	−	0.607584i	$-0.792139\pi$
$17$	0.532108	−	0.921637i	0.129055	−	0.223530i	0.923311	+	0.384054i	$0.125472\pi$
$18$		0			0
$19$	3.16265	−	1.82596i	0.725561	−	0.418903i	−0.0912348	−	0.995829i	$-0.529081\pi$
$19$	3.16265	−	1.82596i	0.725561	−	0.418903i	0.816796	+	0.576926i	$0.195748\pi$
$20$	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	0.532438	−	0.846469i	$-0.321276\pi$
$23$	0.314574	+	0.181620i	0.0655933	+	0.0378703i	−0.466845	+	0.884339i	$0.654609\pi$
$24$		0			0
$25$	−4.00749	−	6.94117i	−0.801497	−	1.38823i
$26$	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
$31$		−	1.08517i		−	0.194903i	−0.995240	−	0.0974513i	$-0.968931\pi$
$31$		−	1.08517i		−	0.194903i	0.995240	−	0.0974513i	$-0.0310690\pi$
$32$		−	4.49348i		−	0.794343i
$33$		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	0.981158	+	0.193208i	$0.0618893\pi$
$37$	4.00186	+	6.93143i	0.657902	+	1.13952i	−0.323256	+	0.946312i	$0.604777\pi$
$38$	−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	$-0.272506\pi$
$41$	−2.09005	−	3.62007i	−0.326411	−	0.565360i	−0.981797	+	0.189934i	$0.939173\pi$
$42$		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
$47$	−5.67697			−0.828072			−0.414036	−	0.910261i	$-0.635881\pi$
$47$	−5.67697			−0.828072			−0.414036	+	0.910261i	$0.635881\pi$
$48$		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
$53$	3.92463	+	2.26589i	0.539089	+	0.311243i	0.744710	−	0.667389i	$-0.232588\pi$
$53$	3.92463	+	2.26589i	0.539089	+	0.311243i	−0.205621	+	0.978632i	$0.565921\pi$
$54$		0			0
$55$		−	13.3700i		−	1.80281i
$56$		0			0
$57$		0			0
$58$	0.210027	−	0.363778i	0.0275779	−	0.0477664i
$59$	−11.2549			−1.46527			−0.732633	−	0.680624i	$-0.761709\pi$
$59$	−11.2549			−1.46527			−0.732633	+	0.680624i	$0.761709\pi$
$60$		0			0
$61$			0.0275117i			0.00352251i	0.999998	+	0.00176126i	$0.000560625\pi$
$61$			0.0275117i			0.00352251i	−0.999998	+	0.00176126i	$0.999439\pi$
$62$	−0.460331			−0.0584621
$63$		0			0
$64$	3.99926			0.499908
$65$			21.8067i			2.70479i
$66$		0			0
$67$	−9.72978			−1.18868			−0.594341	−	0.804213i	$-0.702587\pi$
$67$	−9.72978			−1.18868			−0.594341	+	0.804213i	$0.702587\pi$
$68$	0.968464	−	1.67743i	0.117444	−	0.203418i
$69$		0			0
$70$		0			0
$71$			5.55775i			0.659584i	0.944054	+	0.329792i	$0.106979\pi$
$71$			5.55775i			0.659584i	−0.944054	+	0.329792i	$0.893021\pi$
$72$		0			0
$73$	1.95561	+	1.12907i	0.228887	+	0.132148i	0.610058	−	0.792356i	$-0.291146\pi$
$73$	1.95561	+	1.12907i	0.228887	+	0.132148i	−0.381172	+	0.924504i	$0.624479\pi$
$74$	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
$79$	6.53207			0.734916			0.367458	−	0.930040i	$-0.380228\pi$
$79$	6.53207			0.734916			0.367458	+	0.930040i	$0.380228\pi$
$80$	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	−0.769772	−	0.638319i	$-0.779630\pi$
$83$	1.52977	−	2.64964i	0.167914	−	0.290836i	0.937686	+	0.347483i	$0.112964\pi$
$84$		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
$89$	7.47952	+	12.9549i	0.792827	+	1.37322i	0.924210	+	0.381886i	$0.124725\pi$
$89$	7.47952	+	12.9549i	0.792827	+	1.37322i	−0.131382	+	0.991332i	$0.541942\pi$
$90$		0			0
$91$		0			0
$92$	0.572542	+	0.330557i	0.0596916	+	0.0344630i
$93$		0			0
$94$			2.40818i			0.248385i
$95$		−	13.1747i		−	1.35170i
$96$		0			0
$97$	−1.67018	−	0.964277i	−0.169581	−	0.0979075i	0.412807	−	0.910818i	$-0.364548\pi$
$97$	−1.67018	−	0.964277i	−0.169581	−	0.0979075i	−0.582388	+	0.812911i	$0.697882\pi$
$98$		0			0
$99$		0			0
$100$	−7.29384	−	12.6333i	−0.729384	−	1.26333i
$101$	−3.21811	−	5.57394i	−0.320214	−	0.554627i	0.660318	−	0.750986i	$-0.270422\pi$
$101$	−3.21811	−	5.57394i	−0.320214	−	0.554627i	−0.980532	+	0.196359i	$0.937088\pi$
$102$		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
$107$	−3.43139	+	1.98112i	−0.331725	+	0.191522i	−0.656607	−	0.754233i	$-0.728009\pi$
$107$	−3.43139	+	1.98112i	−0.331725	+	0.191522i	0.324881	+	0.945755i	$0.394676\pi$
$108$		0			0
$109$	8.66263	−	15.0041i	0.829729	−	1.43713i	−0.0685210	−	0.997650i	$-0.521828\pi$
$109$	8.66263	−	15.0041i	0.829729	−	1.43713i	0.898250	−	0.439484i	$-0.144839\pi$
$110$	−5.67156			−0.540762
$111$		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
$115$	1.13487	−	0.655216i	0.105827	−	0.0610992i
$116$	1.56080	+	0.901131i	0.144917	+	0.0836679i
$117$		0			0
$118$			4.77435i			0.439515i
$119$		0			0
$120$		0			0
$121$	1.36734	−	2.36830i	0.124303	−	0.215300i
$122$	0.0116705			0.00105660
$123$		0			0
$124$		−	1.97507i		−	0.177367i
$125$	−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	$0.674277\pi$
$128$		−	10.6835i		−	0.944293i
$129$		0			0
$130$	9.25044			0.811317
$131$	10.5013	−	18.1888i	0.917502	−	1.58916i	0.114305	−	0.993446i	$-0.463536\pi$
$131$	10.5013	−	18.1888i	0.917502	−	1.58916i	0.803197	−	0.595714i	$-0.203131\pi$
$132$		0			0
$133$		0			0
$134$			4.12738i			0.356552i
$135$		0			0
$136$	−1.49349	−	0.862265i	−0.128065	−	0.0739386i
$137$	−9.76185	+	5.63600i	−0.834011	+	0.481516i	−0.855224	−	0.518259i	$-0.826580\pi$
$137$	−9.76185	+	5.63600i	−0.834011	+	0.481516i	0.0212131	+	0.999775i	$0.493247\pi$
$138$		0			0
$139$	−2.80312	+	1.61838i	−0.237758	+	0.137269i	−0.614146	−	0.789193i	$-0.710499\pi$
$139$	−2.80312	+	1.61838i	−0.237758	+	0.137269i	0.376388	+	0.926462i	$0.377166\pi$
$140$		0			0
$141$		0			0
$142$	2.35761			0.197846
$143$	−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
$149$	−15.5066	−	8.95277i	−1.27035	−	0.733439i	−0.295299	−	0.955405i	$-0.595419\pi$
$149$	−15.5066	−	8.95277i	−1.27035	−	0.733439i	−0.975055	+	0.221966i	$0.928753\pi$
$150$		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	$0.560106\pi$
$152$	−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
$157$			7.66976i			0.612113i	0.952013	+	0.306057i	$0.0990097\pi$
$157$			7.66976i			0.612113i	−0.952013	+	0.306057i	$0.900990\pi$
$158$		−	2.77091i		−	0.220442i
$159$		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	0.933562	−	0.358416i	$-0.116683\pi$
$163$	1.99657	+	3.45815i	0.156383	+	0.270864i	−0.777179	+	0.629280i	$0.783350\pi$
$164$	−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	$-0.0596702\pi$
$167$	4.26254	+	7.38293i	0.329845	+	0.571308i	−0.652636	+	0.757672i	$0.726337\pi$
$168$		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
$173$	0.434890			0.0330641			0.0165320	−	0.999863i	$-0.494737\pi$
$173$	0.434890			0.0330641			0.0165320	+	0.999863i	$0.494737\pi$
$174$		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
$179$	15.0838	+	8.70862i	1.12741	+	0.650913i	0.943283	−	0.331989i	$-0.107720\pi$
$179$	15.0838	+	8.70862i	1.12741	+	0.650913i	0.184130	+	0.982902i	$0.441053\pi$
$180$		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
$185$	28.8745			2.12289
$186$		0			0
$187$		−	3.94402i		−	0.288415i
$188$	−10.3324			−0.753567
$189$		0			0
$190$	−5.58874			−0.405450
$191$			0.248866i			0.0180073i	0.999959	+	0.00900367i	$0.00286599\pi$
$191$			0.248866i			0.0180073i	−0.999959	+	0.00900367i	$0.997134\pi$
$192$		0			0
$193$	−8.29752			−0.597268			−0.298634	−	0.954368i	$-0.596531\pi$
$193$	−8.29752			−0.597268			−0.298634	+	0.954368i	$0.596531\pi$
$194$	−0.409047	+	0.708491i	−0.0293679	+	0.0508667i
$195$		0			0
$196$		0			0
$197$		−	22.5819i		−	1.60889i	−0.594026	−	0.804446i	$-0.702462\pi$
$197$		−	22.5819i		−	1.60889i	0.594026	−	0.804446i	$-0.297538\pi$
$198$		0			0
$199$	−5.30010	−	3.06002i	−0.375714	−	0.216919i	0.300238	−	0.953864i	$-0.402934\pi$
$199$	−5.30010	−	3.06002i	−0.375714	−	0.216919i	−0.675952	+	0.736946i	$0.736267\pi$
$200$	−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
$205$	−15.0802			−1.05325
$206$	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	$0.790369\pi$
$212$	7.14303	+	4.12403i	0.490586	+	0.283240i
$213$		0			0
$214$	0.840392	+	1.45560i	0.0574480	+	0.0995029i
$215$	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
$220$		−	24.3341i		−	1.64060i
$221$			6.43277i			0.432715i
$222$		0			0
$223$	22.3165	+	12.8845i	1.49443	+	0.862807i	0.999980	−	0.00640186i	$-0.00203779\pi$
$223$	22.3165	+	12.8845i	1.49443	+	0.862807i	0.494446	+	0.869209i	$0.335371\pi$
$224$		0			0
$225$		0			0
$226$	−2.08243	−	3.60687i	−0.138521	−	0.239925i
$227$	12.3051	+	21.3130i	0.816718	+	1.41460i	0.908088	+	0.418779i	$0.137542\pi$
$227$	12.3051	+	21.3130i	0.816718	+	1.41460i	−0.0913703	+	0.995817i	$0.529125\pi$
$228$		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
$233$	22.6338	−	13.0676i	1.48279	−	0.856090i	0.482983	−	0.875630i	$-0.339553\pi$
$233$	22.6338	−	13.0676i	1.48279	−	0.856090i	0.999809	+	0.0195398i	$0.00622009\pi$
$234$		0			0
$235$	−10.2402	+	17.7365i	−0.667997	+	1.15700i
$236$	−20.4846			−1.33343
$237$		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
$241$	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	$0.152139\pi$
$242$	−1.00464	−	0.580026i	−0.0645804	−	0.0372855i
$243$		0			0
$244$			0.0500727i			0.00320558i
$245$		0			0
$246$		0			0
$247$	−11.0372	+	19.1170i	−0.702281	+	1.21639i
$248$	−1.75849			−0.111664
$249$		0			0
$250$			4.61399i			0.291814i
$251$	5.33468			0.336722			0.168361	−	0.985725i	$-0.446153\pi$
$251$	5.33468			0.336722			0.168361	+	0.985725i	$0.446153\pi$
$252$		0			0
$253$	1.34618			0.0846334
$254$			4.97708i			0.312290i
$255$		0			0
$256$	3.46659			0.216662
$257$	−12.3100	+	21.3216i	−0.767878	+	1.33000i	0.170834	+	0.985300i	$0.445354\pi$
$257$	−12.3100	+	21.3216i	−0.767878	+	1.33000i	−0.938712	+	0.344703i	$0.887979\pi$
$258$		0			0
$259$		0			0
$260$			39.6894i			2.46143i
$261$		0			0
$262$	−7.71569	−	4.45466i	−0.476677	−	0.275210i
$263$	−26.6568	+	15.3903i	−1.64373	+	0.949006i	−0.664235	+	0.747524i	$0.731242\pi$
$263$	−26.6568	+	15.3903i	−1.64373	+	0.949006i	−0.979492	+	0.201482i	$0.935424\pi$
$264$		0			0
$265$	14.1586	−	8.17447i	0.869756	−	0.502154i
$266$		0			0
$267$		0			0
$268$	−17.7087			−1.08173
$269$	−6.99046	+	12.1078i	−0.426216	+	0.738227i	−0.996533	−	0.0831971i	$-0.973487\pi$
$269$	−6.99046	+	12.1078i	−0.426216	+	0.738227i	0.570317	+	0.821424i	$0.306820\pi$
$270$		0			0
$271$	−5.59679	+	3.23131i	−0.339981	+	0.196288i	−0.660264	−	0.751034i	$-0.729555\pi$
$271$	−5.59679	+	3.23131i	−0.339981	+	0.196288i	0.320283	+	0.947322i	$0.396222\pi$
$272$	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	$0.638571\pi$
$278$	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
$283$			15.9625i			0.948873i	0.880290	+	0.474436i	$0.157348\pi$
$283$			15.9625i			0.948873i	−0.880290	+	0.474436i	$0.842652\pi$
$284$			10.1154i			0.600239i
$285$		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
$290$	−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	$-0.103995\pi$
$293$	3.34849	+	5.79975i	0.195621	+	0.338825i	−0.751483	+	0.659752i	$0.770661\pi$
$294$		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
$299$	−2.19564			−0.126977
$300$		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
$305$	0.0859547	+	0.0496259i	0.00492175	+	0.00284157i
$306$		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
$311$	4.23445			0.240114			0.120057	−	0.992767i	$-0.461692\pi$
$311$	4.23445			0.240114			0.120057	+	0.992767i	$0.461692\pi$
$312$		0			0
$313$		−	3.58290i		−	0.202517i	−0.994860	−	0.101259i	$-0.967713\pi$
$313$		−	3.58290i		−	0.202517i	0.994860	−	0.101259i	$-0.0322870\pi$
$314$	3.25352			0.183607
$315$		0			0
$316$	11.8887			0.668793
$317$		−	8.88618i		−	0.499098i	−0.968362	−	0.249549i	$-0.919718\pi$
$317$		−	8.88618i		−	0.499098i	0.968362	−	0.249549i	$-0.0802823\pi$
$318$		0			0
$319$	3.66981			0.205470
$320$	7.21392	−	12.4949i	0.403271	−	0.698485i
$321$		0			0
$322$		0			0
$323$		−	3.88642i		−	0.216246i
$324$		0			0
$325$	41.9567	+	24.2237i	2.32734	+	1.34369i
$326$	1.46695	−	0.846946i	0.0812470	−	0.0469080i
$327$		0			0
$328$	−5.86622	+	3.38686i	−0.323908	+	0.187008i
$329$		0			0
$330$		0			0
$331$	15.7825			0.867486			0.433743	−	0.901037i	$-0.357193\pi$
$331$	15.7825			0.867486			0.433743	+	0.901037i	$0.357193\pi$
$332$	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	$0.954110\pi$
$338$	−8.64691	−	4.99230i	−0.470330	−	0.271545i
$339$		0			0
$340$	−3.49386	−	6.05154i	−0.189481	−	0.328191i
$341$	−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
$346$		−	0.184481i		−	0.00991775i
$347$		−	13.8640i		−	0.744256i	−0.928181	−	0.372128i	$-0.878628\pi$
$347$		−	13.8640i		−	0.744256i	0.928181	−	0.372128i	$-0.121372\pi$
$348$		0			0
$349$	1.55204	+	0.896072i	0.0830789	+	0.0479656i	0.540964	−	0.841046i	$-0.318060\pi$
$349$	1.55204	+	0.896072i	0.0830789	+	0.0479656i	−0.457885	+	0.889011i	$0.651393\pi$
$350$		0			0
$351$		0			0
$352$	−8.32649	−	14.4219i	−0.443804	−	0.768690i
$353$	−3.88049	−	6.72121i	−0.206538	−	0.357734i	0.744084	−	0.668086i	$-0.232886\pi$
$353$	−3.88049	−	6.72121i	−0.206538	−	0.357734i	−0.950622	+	0.310352i	$0.899553\pi$
$354$		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
$359$	−19.5557	+	11.2905i	−1.03211	+	0.595890i	−0.917589	−	0.397531i	$-0.869867\pi$
$359$	−19.5557	+	11.2905i	−1.03211	+	0.595890i	−0.114523	+	0.993421i	$0.536534\pi$
$360$		0			0
$361$	−2.83177	+	4.90477i	−0.149041	+	0.258146i
$362$	7.52623			0.395570
$363$		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	$0.466984\pi$
$368$	0.928844	+	0.536268i	0.0484193	+	0.0279549i
$369$		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	$-0.0600709\pi$
$374$	−1.67306			−0.0865117
$375$		0			0
$376$			9.19937i			0.474421i
$377$	−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	$0.376132\pi$
$380$		−	23.9787i		−	1.23008i
$381$		0			0
$382$	0.105569			0.00540140
$383$	5.29503	−	9.17127i	0.270564	−	0.468630i	−0.698443	−	0.715666i	$-0.746123\pi$
$383$	5.29503	−	9.17127i	0.270564	−	0.468630i	0.969006	+	0.247036i	$0.0794566\pi$
$384$		0			0
$385$		0			0
$386$			3.51982i			0.179154i
$387$		0			0
$388$	−3.03981	−	1.75504i	−0.154323	−	0.0890984i
$389$	−11.7642	+	6.79207i	−0.596469	+	0.344371i	−0.767651	−	0.640868i	$-0.778575\pi$
$389$	−11.7642	+	6.79207i	−0.596469	+	0.344371i	0.171182	+	0.985239i	$0.445241\pi$
$390$		0			0
$391$	0.334775	−	0.193282i	0.0169303	−	0.00977471i
$392$		0			0
$393$		0			0
$394$	−9.57925			−0.482596
$395$	11.7826	−	20.4081i	0.592849	−	1.02684i
$396$		0			0
$397$	33.6977	−	19.4554i	1.69124	−	0.976437i	0.737719	−	0.675108i	$-0.235903\pi$
$397$	33.6977	−	19.4554i	1.69124	−	0.976437i	0.953520	−	0.301330i	$-0.0974305\pi$
$398$	−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	0.969750	−	0.244101i	$-0.0784928\pi$
$401$	24.8956	+	14.3735i	1.24323	+	0.717778i	0.273477	+	0.961878i	$0.411826\pi$
$402$		0			0
$403$	3.27972	+	5.68065i	0.163375	+	0.282973i
$404$	−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
$409$		−	18.8776i		−	0.933436i	−0.884406	−	0.466718i	$-0.845436\pi$
$409$		−	18.8776i		−	0.933436i	0.884406	−	0.466718i	$-0.154564\pi$
$410$			6.39705i			0.315928i
$411$		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
$416$	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	$-0.114827\pi$
$419$	3.31895	+	5.74860i	0.162142	+	0.280837i	−0.773495	+	0.633802i	$0.781493\pi$
$420$		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
$425$	−8.52965			−0.413749
$426$		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
$431$	−21.0604	−	12.1592i	−1.01444	−	0.585690i	−0.101955	−	0.994789i	$-0.532510\pi$
$431$	−21.0604	−	12.1592i	−1.01444	−	0.585690i	−0.912490	+	0.409099i	$0.865843\pi$
$432$		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
$437$	1.32652			0.0634559
$438$		0			0
$439$			26.9191i			1.28478i	0.766379	+	0.642389i	$0.222057\pi$
$439$			26.9191i			1.28478i	−0.766379	+	0.642389i	$0.777943\pi$
$440$	−21.6657			−1.03287
$441$		0			0
$442$	2.72879			0.129795
$443$			26.4238i			1.25543i	0.778442	+	0.627717i	$0.216010\pi$
$443$			26.4238i			1.25543i	−0.778442	+	0.627717i	$0.783990\pi$
$444$		0			0
$445$	53.9666			2.55826
$446$	5.46560	−	9.46670i	0.258804	−	0.448261i
$447$		0			0
$448$		0			0
$449$		−	19.6314i		−	0.926464i	−0.886237	−	0.463232i	$-0.846690\pi$
$449$		−	19.6314i		−	0.926464i	0.886237	−	0.463232i	$-0.153310\pi$
$450$		0			0
$451$	−13.4161	−	7.74578i	−0.631739	−	0.364735i
$452$	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
$457$	−25.2487			−1.18109			−0.590543	−	0.807006i	$-0.701086\pi$
$457$	−25.2487			−1.18109			−0.590543	+	0.807006i	$0.701086\pi$
$458$	−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	−0.983871	−	0.178878i	$-0.942753\pi$
$461$	−7.23618	+	12.5334i	−0.337023	+	0.583740i	0.646849	+	0.762618i	$0.276087\pi$
$462$		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	$0.987466\pi$
$464$	2.53212	+	1.46192i	0.117551	+	0.0678679i
$465$		0			0
$466$	−5.54331	−	9.60130i	−0.256789	−	0.444772i
$467$	11.7815	+	20.4062i	0.545183	+	0.944285i	0.998595	+	0.0529842i	$0.0168733\pi$
$467$	11.7815	+	20.4062i	0.545183	+	0.944285i	−0.453412	+	0.891301i	$0.649793\pi$
$468$		0			0
$469$		0			0
$470$	7.52386	+	4.34390i	0.347050	+	0.200369i
$471$		0			0
$472$			18.2383i			0.839485i
$473$			14.0650i			0.646707i
$474$		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
$479$	−12.4674	−	21.5941i	−0.569648	−	0.986660i	−0.996601	−	0.0823855i	$-0.973746\pi$
$479$	−12.4674	−	21.5941i	−0.569648	−	0.986660i	0.426952	−	0.904274i	$-0.359587\pi$
$480$		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
$485$	−6.02537	+	3.47875i	−0.273598	+	0.157962i
$486$		0			0
$487$	2.50331	−	4.33586i	0.113436	−	0.196476i	−0.803718	−	0.595011i	$-0.797148\pi$
$487$	2.50331	−	4.33586i	0.113436	−	0.196476i	0.917153	+	0.398534i	$0.130481\pi$
$488$	0.0445819			0.00201813
$489$		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
$493$	0.912628	−	0.526906i	0.0411027	−	0.0237307i
$494$	8.10945	+	4.68200i	0.364862	+	0.210653i
$495$		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	$0.870647\pi$
$500$	−19.7965			−0.885327
$501$		0			0
$502$		−	2.26298i		−	0.101002i
$503$	23.9969			1.06997			0.534984	−	0.844862i	$-0.320318\pi$
$503$	23.9969			1.06997			0.534984	+	0.844862i	$0.320318\pi$
$504$		0			0
$505$	−23.2195			−1.03325
$506$		−	0.571049i		−	0.0253862i
$507$		0			0
$508$	−21.3544			−0.947448
$509$	9.07094	−	15.7113i	0.402062	−	0.696392i	−0.591912	−	0.806002i	$-0.701627\pi$
$509$	9.07094	−	15.7113i	0.402062	−	0.696392i	0.993975	+	0.109610i	$0.0349602\pi$
$510$		0			0
$511$		0			0
$512$		−	22.8374i		−	1.00928i
$513$		0			0
$514$	9.04464	+	5.22192i	0.398942	+	0.230329i
$515$	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
$520$	35.3372			1.54964
$521$	−0.419693	+	0.726930i	−0.0183871	+	0.0318474i	−0.875073	−	0.483992i	$-0.839186\pi$
$521$	−0.419693	+	0.726930i	−0.0183871	+	0.0318474i	0.856685	+	0.515839i	$0.172520\pi$
$522$		0			0
$523$	−14.1017	+	8.14160i	−0.616623	+	0.356008i	−0.775553	−	0.631282i	$-0.782529\pi$
$523$	−14.1017	+	8.14160i	−0.616623	+	0.356008i	0.158930	+	0.987290i	$0.449196\pi$
$524$	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
$530$	−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
$535$			14.2943i			0.617995i
$536$			15.7668i			0.681023i
$537$		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	0.885394	−	0.464841i	$-0.153889\pi$
$541$	0.933466	+	1.61681i	0.0401328	+	0.0695121i	−0.845261	+	0.534353i	$0.820555\pi$
$542$	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	−0.657984	−	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
$551$	3.61621			0.154056
$552$		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
$557$	5.47481	+	3.16088i	0.231975	+	0.133931i	0.611483	−	0.791258i	$-0.290573\pi$
$557$	5.47481	+	3.16088i	0.231975	+	0.133931i	−0.379508	+	0.925189i	$0.623907\pi$
$558$		0			0
$559$		−	22.9402i		−	0.970269i
$560$		0			0
$561$		0			0
$562$	−4.91321	+	8.50992i	−0.207251	+	0.358970i
$563$	−9.65091			−0.406737			−0.203369	−	0.979102i	$-0.565189\pi$
$563$	−9.65091			−0.406737			−0.203369	+	0.979102i	$0.565189\pi$
$564$		0			0
$565$		−	35.4200i		−	1.49013i
$566$	6.77132			0.284620
$567$		0			0
$568$	9.00618			0.377891
$569$			15.5637i			0.652463i	0.945290	+	0.326232i	$0.105779\pi$
$569$			15.5637i			0.652463i	−0.945290	+	0.326232i	$0.894221\pi$
$570$		0			0
$571$	−41.8868			−1.75291			−0.876454	−	0.481486i	$-0.840097\pi$
$571$	−41.8868			−1.75291			−0.876454	+	0.481486i	$0.840097\pi$
$572$	−20.3860	+	35.3096i	−0.852382	+	1.47637i
$573$		0			0
$574$		0			0
$575$		−	2.91135i		−	0.121412i
$576$		0			0
$577$	−34.9417	−	20.1736i	−1.45464	−	0.839838i	−0.455903	−	0.890030i	$-0.650683\pi$
$577$	−34.9417	−	20.1736i	−1.45464	−	0.839838i	−0.998740	+	0.0501916i	$0.984017\pi$
$578$	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
$583$	16.7949			0.695573
$584$	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	−0.902840	−	0.429977i	$-0.858522\pi$
$587$	−1.91520	+	3.31723i	−0.0790490	+	0.136917i	0.823791	+	0.566894i	$0.191855\pi$
$588$		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
$593$	−6.25717	−	10.8377i	−0.256951	−	0.445053i	0.708472	−	0.705738i	$-0.249385\pi$
$593$	−6.25717	−	10.8377i	−0.256951	−	0.445053i	−0.965424	+	0.260686i	$0.916051\pi$
$594$		0			0
$595$		0			0
$596$	−28.2229	−	16.2945i	−1.15606	−	0.667449i
$597$		0			0
$598$			0.931394i			0.0380875i
$599$		−	7.64709i		−	0.312452i	−0.987721	−	0.156226i	$-0.950067\pi$
$599$		−	7.64709i		−	0.312452i	0.987721	−	0.156226i	$-0.0499328\pi$
$600$		0			0
$601$	−29.8513	−	17.2346i	−1.21766	−	0.703015i	−0.253242	−	0.967403i	$-0.581497\pi$
$601$	−29.8513	−	17.2346i	−1.21766	−	0.703015i	−0.964416	+	0.264388i	$0.914830\pi$
$602$		0			0
$603$		0			0
$604$	16.9255	+	29.3158i	0.688688	+	1.19284i
$605$	−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
$611$	29.7178	−	17.1576i	1.20225	−	0.694121i
$612$		0			0
$613$	0.834482	−	1.44537i	0.0337044	−	0.0583778i	−0.848681	−	0.528905i	$-0.822603\pi$
$613$	0.834482	−	1.44537i	0.0337044	−	0.0583778i	0.882386	+	0.470527i	$0.155936\pi$
$614$	3.64418			0.147067
$615$		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
$619$	−3.10436	+	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	$0.356284\pi$
$620$	−6.17071	−	3.56266i	−0.247822	−	0.143080i
$621$		0			0
$622$		−	1.79626i		−	0.0720234i
$623$		0			0
$624$		0			0
$625$	0.417550	−	0.723218i	0.0167020	−	0.0289287i
$626$	−1.51987			−0.0607462
$627$		0			0
$628$			13.9594i			0.557039i
$629$	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	$0.347570\pi$
$632$		−	10.5850i		−	0.421050i
$633$		0			0
$634$	−3.76953			−0.149707
$635$	−21.1638	+	36.6568i	−0.839861	+	1.45468i
$636$		0			0
$637$		0			0
$638$		−	1.55674i		−	0.0616318i
$639$		0			0
$640$	−33.3783	−	19.2710i	−1.31939	−	0.761751i
$641$	20.3567	−	11.7529i	0.804041	−	0.464213i	−0.0408415	−	0.999166i	$-0.513004\pi$
$641$	20.3567	−	11.7529i	0.804041	−	0.464213i	0.844882	+	0.534953i	$0.179671\pi$
$642$		0			0
$643$	4.83255	−	2.79007i	0.190577	−	0.110030i	−0.401676	−	0.915782i	$-0.631572\pi$
$643$	4.83255	−	2.79007i	0.190577	−	0.110030i	0.592253	+	0.805752i	$0.298239\pi$
$644$		0			0
$645$		0			0
$646$	−1.64862			−0.0648642
$647$	−1.95089	+	3.37904i	−0.0766974	+	0.132844i	−0.901823	−	0.432105i	$-0.857771\pi$
$647$	−1.95089	+	3.37904i	−0.0766974	+	0.132844i	0.825126	+	0.564949i	$0.191104\pi$
$648$		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
$653$	−5.29484	−	3.05698i	−0.207203	−	0.119629i	0.392808	−	0.919621i	$-0.371504\pi$
$653$	−5.29484	−	3.05698i	−0.207203	−	0.119629i	−0.600011	+	0.799992i	$0.704837\pi$
$654$		0			0
$655$	−37.8847	−	65.6183i	−1.48028	−	2.56392i
$656$	−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
$661$		−	25.1346i		−	0.977624i	−0.872389	−	0.488812i	$-0.837430\pi$
$661$		−	25.1346i		−	0.977624i	0.872389	−	0.488812i	$-0.162570\pi$
$662$		−	6.69496i		−	0.260207i
$663$		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
$668$	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	−0.516895	−	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
$677$	33.6163			1.29198			0.645989	−	0.763346i	$-0.276445\pi$
$677$	33.6163			1.29198			0.645989	+	0.763346i	$0.276445\pi$
$678$		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
$683$	−33.3824	−	19.2734i	−1.27734	−	0.737475i	−0.300984	−	0.953629i	$-0.597315\pi$
$683$	−33.3824	−	19.2734i	−1.27734	−	0.737475i	−0.976359	+	0.216155i	$0.930648\pi$
$684$		0			0
$685$			40.6652i			1.55374i
$686$		0			0
$687$		0			0
$688$	−5.60297	+	9.70464i	−0.213611	+	0.369986i
$689$	−27.3928			−1.04358
$690$		0			0
$691$		−	30.2263i		−	1.14986i	−0.818201	−	0.574932i	$-0.805028\pi$
$691$		−	30.2263i		−	1.14986i	0.818201	−	0.574932i	$-0.194972\pi$
$692$	0.791523			0.0300892
$693$		0			0
$694$	−5.88111			−0.223244
$695$			11.6770i			0.442935i
$696$		0			0
$697$	−4.44852			−0.168500
$698$	0.380115	−	0.658378i	0.0143876	−	0.0249200i
$699$		0			0
$700$		0			0
$701$			29.6057i			1.11819i	0.829103	+	0.559096i	$0.188852\pi$
$701$			29.6057i			1.11819i	−0.829103	+	0.559096i	$0.811148\pi$
$702$		0			0
$703$	25.3130	+	14.6145i	0.954697	+	0.551194i
$704$	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
$709$	3.56401			0.133849			0.0669246	−	0.997758i	$-0.478681\pi$
$709$	3.56401			0.133849			0.0669246	+	0.997758i	$0.478681\pi$
$710$	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
$716$	27.4533	+	15.8501i	1.02598	+	0.592348i
$717$		0			0
$718$	4.78944	+	8.29556i	0.178740	+	0.309588i
$719$	0.806410	+	1.39674i	0.0300740	+	0.0520897i	0.880671	−	0.473729i	$-0.157092\pi$
$719$	0.806410	+	1.39674i	0.0300740	+	0.0520897i	−0.850597	+	0.525819i	$0.823759\pi$
$720$		0			0
$721$		0			0
$722$	2.08061	+	1.20124i	0.0774322	+	0.0447055i
$723$		0			0
$724$			32.2916i			1.20011i
$725$		−	7.93662i		−	0.294759i
$726$		0			0
$727$	−10.4930	−	6.05816i	−0.389166	−	0.224685i	0.292633	−	0.956225i	$-0.405469\pi$
$727$	−10.4930	−	6.05816i	−0.389166	−	0.224685i	−0.681799	+	0.731540i	$0.738802\pi$
$728$		0			0
$729$		0			0
$730$	−1.72789	−	2.99279i	−0.0639519	−	0.110768i
$731$	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
$737$	−31.2279	+	18.0294i	−1.15030	+	0.664123i
$738$		0			0
$739$	10.2317	−	17.7219i	0.376380	−	0.651909i	−0.614153	−	0.789187i	$-0.710502\pi$
$739$	10.2317	−	17.7219i	0.376380	−	0.651909i	0.990533	+	0.137278i	$0.0438354\pi$
$740$	52.5531			1.93189
$741$		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
$745$	−55.9422	+	32.2982i	−2.04956	+	1.18332i
$746$	−9.27453	−	5.35465i	−0.339565	−	0.196048i
$747$		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	$-0.120490\pi$
$752$	−16.7624			−0.611262
$753$		0			0
$754$			2.53907i			0.0924674i
$755$	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	$0.576373\pi$
$758$		−	6.26635i		−	0.227604i
$759$		0			0
$760$	−21.3493			−0.774420
$761$	11.5916	−	20.0773i	0.420196	−	0.727801i	−0.575762	−	0.817617i	$-0.695295\pi$
$761$	11.5916	−	20.0773i	0.420196	−	0.727801i	0.995958	+	0.0898160i	$0.0286279\pi$
$762$		0			0
$763$		0			0
$764$			0.452950i			0.0163872i
$765$		0			0
$766$	−3.89046	−	2.24616i	−0.140568	−	0.0811571i
$767$	58.9172	−	34.0159i	2.12738	−	1.22824i
$768$		0			0
$769$	−11.4527	+	6.61219i	−0.412993	+	0.238442i	−0.692075	−	0.721826i	$-0.743303\pi$
$769$	−11.4527	+	6.61219i	−0.412993	+	0.238442i	0.279082	+	0.960267i	$0.409970\pi$
$770$		0			0
$771$		0			0
$772$	−15.1019			−0.543530
$773$	−9.81595	+	17.0017i	−0.353055	+	0.611509i	−0.986783	−	0.162047i	$-0.948190\pi$
$773$	−9.81595	+	17.0017i	−0.353055	+	0.611509i	0.633728	+	0.773556i	$0.281524\pi$
$774$		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
$779$	−13.2202	−	7.63267i	−0.473662	−	0.273469i
$780$		0			0
$781$	10.2986	+	17.8377i	0.368513	+	0.638284i
$782$	−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
$787$		−	17.1613i		−	0.611733i	−0.952074	−	0.305866i	$-0.901054\pi$
$787$		−	17.1613i		−	0.611733i	0.952074	−	0.305866i	$-0.0989460\pi$
$788$		−	41.1002i		−	1.46413i
$789$		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
$794$	−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	$-0.297468\pi$
$797$	−11.2772	−	19.5326i	−0.399458	−	0.691882i	−0.993659	+	0.112435i	$0.964135\pi$
$798$		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
$803$	8.36875			0.295327
$804$		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
$809$	41.7578	+	24.1089i	1.46813	+	0.847624i	0.999363	−	0.0356994i	$-0.0113659\pi$
$809$	41.7578	+	24.1089i	1.46813	+	0.847624i	0.468765	+	0.883323i	$0.344699\pi$
$810$		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
$815$	14.4057			0.504611
$816$		0			0
$817$			13.8596i			0.484885i
$818$	−8.00789			−0.279989
$819$		0			0
$820$	−27.4468			−0.958484
$821$		−	40.0425i		−	1.39749i	−0.715370	−	0.698746i	$-0.753742\pi$
$821$		−	40.0425i		−	1.39749i	0.715370	−	0.698746i	$-0.246258\pi$
$822$		0			0
$823$	9.97844			0.347827			0.173913	−	0.984761i	$-0.444359\pi$
$823$	9.97844			0.347827			0.173913	+	0.984761i	$0.444359\pi$
$824$	7.87680	−	13.6430i	0.274401	−	0.475277i
$825$		0			0
$826$		0			0
$827$		−	20.8802i		−	0.726077i	−0.931774	−	0.363038i	$-0.881739\pi$
$827$		−	20.8802i		−	0.726077i	0.931774	−	0.363038i	$-0.118261\pi$
$828$		0			0
$829$	−13.9123	−	8.03228i	−0.483195	−	0.278973i	0.238552	−	0.971130i	$-0.423327\pi$
$829$	−13.9123	−	8.03228i	−0.483195	−	0.278973i	−0.721747	+	0.692157i	$0.756661\pi$
$830$	−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
$835$	30.7553			1.06433
$836$	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	−0.986590	−	0.163216i	$-0.947813\pi$
$839$	−10.1943	+	17.6570i	−0.351946	+	0.609589i	0.634644	+	0.772805i	$0.281147\pi$
$840$		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
$845$	−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
$850$			3.61829i			0.124106i
$851$			2.90727i			0.0996598i
$852$		0			0
$853$	−7.80792	−	4.50790i	−0.267338	−	0.154348i	0.360339	−	0.932821i	$-0.382661\pi$
$853$	−7.80792	−	4.50790i	−0.267338	−	0.154348i	−0.627677	+	0.778474i	$0.715994\pi$
$854$		0			0
$855$		0			0
$856$	3.21034	+	5.56047i	0.109727	+	0.190053i
$857$	−16.1658	−	28.0000i	−0.552213	−	0.956461i	−0.998115	−	0.0613789i	$-0.980450\pi$
$857$	−16.1658	−	28.0000i	−0.552213	−	0.956461i	0.445902	−	0.895082i	$-0.352883\pi$
$858$		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
$863$	5.30668	−	3.06381i	0.180641	−	0.104293i	−0.406953	−	0.913449i	$-0.633409\pi$
$863$	5.30668	−	3.06381i	0.180641	−	0.104293i	0.587594	+	0.809156i	$0.300075\pi$
$864$		0			0
$865$	0.784460	−	1.35873i	0.0266725	−	0.0461980i
$866$	1.40898			0.0478789
$867$		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
$872$	−24.3137	−	14.0375i	−0.823367	−	0.475371i
$873$		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	$0.154496\pi$
$878$	11.4191			0.385376
$879$		0			0
$880$		−	39.4776i		−	1.33079i
$881$	−19.2955			−0.650083			−0.325041	−	0.945700i	$-0.605378\pi$
$881$	−19.2955			−0.650083			−0.325041	+	0.945700i	$0.605378\pi$
$882$		0			0
$883$	−0.833572			−0.0280519			−0.0140260	−	0.999902i	$-0.504465\pi$
$883$	−0.833572			−0.0280519			−0.0140260	+	0.999902i	$0.504465\pi$
$884$			11.7080i			0.393782i
$885$		0			0
$886$	11.2090			0.376574
$887$	−28.7740	+	49.8380i	−0.966136	+	1.67340i	−0.259604	+	0.965715i	$0.583592\pi$
$887$	−28.7740	+	49.8380i	−0.966136	+	1.67340i	−0.706532	+	0.707681i	$0.749741\pi$
$888$		0			0
$889$		0			0
$890$		−	22.8927i		−	0.767365i
$891$		0			0
$892$	40.6173	+	23.4504i	1.35997	+	0.785177i
$893$	−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
$898$	−8.32767			−0.277898
$899$	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
$905$	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	$0.779638\pi$
$908$	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
$913$		−	11.3387i		−	0.375258i
$914$			10.7105i			0.354273i
$915$		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	0.690487	−	0.723345i	$-0.257396\pi$
$919$	−8.52434	−	14.7646i	−0.281192	−	0.487039i	−0.971679	+	0.236306i	$0.924063\pi$
$920$	−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
$926$	−7.35970	+	4.24912i	−0.241855	+	0.139635i
$927$		0			0
$928$	2.22478	−	3.85343i	0.0730319	−	0.126495i
$929$	−8.65022			−0.283804			−0.141902	−	0.989881i	$-0.545322\pi$
$929$	−8.65022			−0.283804			−0.141902	+	0.989881i	$0.545322\pi$
$930$		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
$935$	−12.3223	−	7.11427i	−0.402981	−	0.232661i
$936$		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
$941$	41.0943			1.33964			0.669818	−	0.742525i	$-0.266372\pi$
$941$	41.0943			1.33964			0.669818	+	0.742525i	$0.266372\pi$
$942$		0			0
$943$		−	1.51837i		−	0.0494451i
$944$	−33.2324			−1.08162
$945$		0			0
$946$	5.96637			0.193983
$947$		−	33.7362i		−	1.09628i	−0.836387	−	0.548139i	$-0.815336\pi$
$947$		−	33.7362i		−	1.09628i	0.836387	−	0.548139i	$-0.184664\pi$
$948$		0			0
$949$	−13.6496			−0.443085
$950$	−6.20818	+	10.7529i	−0.201420	+	0.348869i
$951$		0			0
$952$		0			0
$953$			18.7823i			0.608420i	0.952605	+	0.304210i	$0.0983925\pi$
$953$			18.7823i			0.608420i	−0.952605	+	0.304210i	$0.901608\pi$
$954$		0			0
$955$	0.777532	+	0.448908i	0.0251603	+	0.0145263i
$956$	−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
$961$	29.8224			0.962013
$962$	−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	$-0.357995\pi$
$968$	−3.83776	−	2.21573i	−0.123350	−	0.0712163i
$969$		0			0
$970$	1.47569	+	2.55597i	0.0473816	+	0.0820673i
$971$	−19.7981	−	34.2913i	−0.635351	−	1.10046i	−0.986441	−	0.164118i	$-0.947522\pi$
$971$	−19.7981	−	34.2913i	−0.635351	−	1.10046i	0.351090	−	0.936342i	$-0.385811\pi$
$972$		0			0
$973$		0			0
$974$	−1.83928	−	1.06191i	−0.0589342	−	0.0340257i
$975$		0			0
$976$			0.0812338i			0.00260023i
$977$			35.0294i			1.12069i	0.828259	+	0.560345i	$0.189331\pi$
$977$			35.0294i			1.12069i	−0.828259	+	0.560345i	$0.810669\pi$
$978$		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
$983$	−22.0865	−	38.2550i	−0.704451	−	1.22015i	−0.966889	−	0.255197i	$-0.917860\pi$
$983$	−22.0865	−	38.2550i	−0.704451	−	1.22015i	0.262438	−	0.964949i	$-0.415474\pi$
$984$		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
$989$	−1.19386	+	0.689274i	−0.0379625	+	0.0219176i
$990$		0			0
$991$	−13.4443	+	23.2862i	−0.427073	+	0.739712i	−0.996611	−	0.0822528i	$-0.973789\pi$
$991$	−13.4443	+	23.2862i	−0.427073	+	0.739712i	0.569539	+	0.821964i	$0.307122\pi$
$992$	−4.87620			−0.154819
$993$		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	$0.497539\pi$
$998$	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.i.d.521.3		48
3.2	odd	2		441.2.i.d.227.13		48
7.2	even	3		1323.2.s.d.656.12		48
7.3	odd	6		1323.2.o.e.440.14		48
7.4	even	3		1323.2.o.e.440.13		48
7.5	odd	6		1323.2.s.d.656.11		48
7.6	odd	2	inner	1323.2.i.d.521.19		48
9.4	even	3		441.2.s.d.374.13		48
9.5	odd	6		1323.2.s.d.962.11		48
21.2	odd	6		441.2.s.d.362.14		48
21.5	even	6		441.2.s.d.362.13		48
21.11	odd	6		441.2.o.e.146.11	✓	48
21.17	even	6		441.2.o.e.146.12	yes	48
21.20	even	2		441.2.i.d.227.14		48
63.4	even	3		441.2.o.e.293.12	yes	48
63.5	even	6	inner	1323.2.i.d.1097.3		48
63.13	odd	6		441.2.s.d.374.14		48
63.23	odd	6	inner	1323.2.i.d.1097.19		48
63.31	odd	6		441.2.o.e.293.11	yes	48
63.32	odd	6		1323.2.o.e.881.14		48
63.40	odd	6		441.2.i.d.68.11		48
63.41	even	6		1323.2.s.d.962.12		48
63.58	even	3		441.2.i.d.68.12		48
63.59	even	6		1323.2.o.e.881.13		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.11		48	63.40	odd	6
441.2.i.d.68.12		48	63.58	even	3
441.2.i.d.227.13		48	3.2	odd	2
441.2.i.d.227.14		48	21.20	even	2
441.2.o.e.146.11	✓	48	21.11	odd	6
441.2.o.e.146.12	yes	48	21.17	even	6
441.2.o.e.293.11	yes	48	63.31	odd	6
441.2.o.e.293.12	yes	48	63.4	even	3
441.2.s.d.362.13		48	21.5	even	6
441.2.s.d.362.14		48	21.2	odd	6
441.2.s.d.374.13		48	9.4	even	3
441.2.s.d.374.14		48	63.13	odd	6
1323.2.i.d.521.3		48	1.1	even	1	trivial
1323.2.i.d.521.19		48	7.6	odd	2	inner
1323.2.i.d.1097.3		48	63.5	even	6	inner
1323.2.i.d.1097.19		48	63.23	odd	6	inner
1323.2.o.e.440.13		48	7.4	even	3
1323.2.o.e.440.14		48	7.3	odd	6
1323.2.o.e.881.13		48	63.59	even	6
1323.2.o.e.881.14		48	63.32	odd	6
1323.2.s.d.656.11		48	7.5	odd	6
1323.2.s.d.656.12		48	7.2	even	3
1323.2.s.d.962.11		48	9.5	odd	6
1323.2.s.d.962.12		48	63.41	even	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.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.424201i q^{2} +1.82005 q^{4} +(1.80381 - 3.12430i) q^{5} -1.62047i q^{8} +O(q^{10})\)	\(q-0.424201i q^{2} +1.82005 q^{4} +(1.80381 - 3.12430i) q^{5} -1.62047i q^{8} +(-1.32533 - 0.765180i) q^{10} +(3.20952 - 1.85302i) q^{11} +(-5.23479 + 3.02231i) q^{13} +2.95270 q^{16} +(0.532108 - 0.921637i) q^{17} +(3.16265 - 1.82596i) q^{19} +(3.28304 - 5.68639i) q^{20} +(-0.786052 - 1.36148i) q^{22} +(0.314574 + 0.181620i) q^{23} +(-4.00749 - 6.94117i) q^{25} +(1.28207 + 2.22060i) q^{26} +(0.857560 + 0.495112i) q^{29} -1.08517i q^{31} -4.49348i q^{32} +(-0.390960 - 0.225721i) q^{34} +(4.00186 + 6.93143i) q^{37} +(-0.774573 - 1.34160i) q^{38} +(-5.06283 - 2.92303i) q^{40} +(-2.09005 - 3.62007i) q^{41} +(-1.89758 + 3.28670i) q^{43} +(5.84149 - 3.37259i) q^{44} +(0.0770432 - 0.133443i) q^{46} -5.67697 q^{47} +(-2.94445 + 1.69998i) q^{50} +(-9.52760 + 5.50076i) q^{52} +(3.92463 + 2.26589i) q^{53} -13.3700i q^{55} +(0.210027 - 0.363778i) q^{58} -11.2549 q^{59} +0.0275117i q^{61} -0.460331 q^{62} +3.99926 q^{64} +21.8067i q^{65} -9.72978 q^{67} +(0.968464 - 1.67743i) q^{68} +5.55775i q^{71} +(1.95561 + 1.12907i) q^{73} +(2.94032 - 1.69759i) q^{74} +(5.75619 - 3.32334i) q^{76} +6.53207 q^{79} +(5.32612 - 9.22511i) q^{80} +(-1.53564 + 0.886601i) q^{82} +(1.52977 - 2.64964i) q^{83} +(-1.91965 - 3.32492i) q^{85} +(1.39422 + 0.804954i) q^{86} +(-3.00276 - 5.20093i) q^{88} +(7.47952 + 12.9549i) q^{89} +(0.572542 + 0.330557i) q^{92} +2.40818i q^{94} -13.1747i q^{95} +(-1.67018 - 0.964277i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4}+O(q^{10}) \) 48 * q - 48 * q^4	\( 48 q - 48 q^{4} - 24 q^{11} + 48 q^{16} - 48 q^{23} - 24 q^{25} + 96 q^{44} - 48 q^{50} + 48 q^{53} - 48 q^{64} - 168 q^{74} + 48 q^{79} - 24 q^{85} + 24 q^{86} + 144 q^{92}+O(q^{100}) \) 48 * q - 48 * q^4 - 24 * q^11 + 48 * q^16 - 48 * q^23 - 24 * q^25 + 96 * q^44 - 48 * q^50 + 48 * q^53 - 48 * q^64 - 168 * q^74 + 48 * q^79 - 24 * q^85 + 24 * q^86 + 144 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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