LMFDB - Embedded newform 1323.2.s.d.656.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1323.656");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			656.18
Character	$\chi$	$=$	1323.656
Dual form			1323.2.s.d.962.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.58658 - 0.916012i) q^{2} +(0.678156 - 1.17460i) q^{4} +0.645568 q^{5} +1.17925i q^{8} +O(q^{10})$	\(q+(1.58658 - 0.916012i) q^{2} +(0.678156 - 1.17460i) q^{4} +0.645568 q^{5} +1.17925i q^{8} +(1.02425 - 0.591348i) q^{10} +5.31595i q^{11} +(4.44045 - 2.56370i) q^{13} +(2.43652 + 4.22018i) q^{16} +(0.814931 + 1.41150i) q^{17} +(-2.09039 - 1.20689i) q^{19} +(0.437796 - 0.758285i) q^{20} +(4.86947 + 8.43418i) q^{22} +1.47157i q^{23} -4.58324 q^{25} +(4.69675 - 8.13502i) q^{26} +(6.43846 + 3.71724i) q^{29} +(4.90799 + 2.83363i) q^{31} +(5.68894 + 3.28451i) q^{32} +(2.58590 + 1.49297i) q^{34} +(3.99736 - 6.92362i) q^{37} -4.42210 q^{38} +0.761288i q^{40} +(-5.99052 - 10.3759i) q^{41} +(-1.51281 + 2.62026i) q^{43} +(6.24412 + 3.60504i) q^{44} +(1.34797 + 2.33476i) q^{46} +(1.54176 + 2.67041i) q^{47} +(-7.27168 + 4.19830i) q^{50} -6.95434i q^{52} +(2.04554 - 1.18100i) q^{53} +3.43181i q^{55} +13.6202 q^{58} +(-1.47918 + 2.56202i) q^{59} +(9.18018 - 5.30018i) q^{61} +10.3825 q^{62} +2.28853 q^{64} +(2.86662 - 1.65504i) q^{65} +(5.07747 - 8.79444i) q^{67} +2.21060 q^{68} +4.76597i q^{71} +(-10.2239 + 5.90277i) q^{73} -14.6465i q^{74} +(-2.83523 + 1.63692i) q^{76} +(-3.48104 - 6.02934i) q^{79} +(1.57294 + 2.72441i) q^{80} +(-19.0089 - 10.9748i) q^{82} +(-3.51618 + 6.09021i) q^{83} +(0.526093 + 0.911221i) q^{85} +5.54300i q^{86} -6.26884 q^{88} +(2.16337 - 3.74706i) q^{89} +(1.72850 + 0.997953i) q^{92} +(4.89226 + 2.82455i) q^{94} +(-1.34949 - 0.779129i) q^{95} +(-14.3946 - 8.31075i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4}+O(q^{10}) $ 48 * q + 24 * q^4	$ 48 q + 24 q^{4} - 24 q^{16} + 48 q^{25} + 120 q^{32} - 96 q^{44} - 48 q^{50} - 48 q^{53} - 48 q^{64} + 120 q^{65} - 24 q^{79} - 24 q^{85} + 144 q^{92} + 96 q^{95}+O(q^{100}) $ 48 * q + 24 * q^4 - 24 * q^16 + 48 * q^25 + 120 * q^32 - 96 * q^44 - 48 * q^50 - 48 * q^53 - 48 * q^64 + 120 * q^65 - 24 * q^79 - 24 * q^85 + 144 * q^92 + 96 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.58658	−	0.916012i	1.12188	−	0.647718i	0.180001	−	0.983667i	$-0.442390\pi$
$2$	1.58658	−	0.916012i	1.12188	−	0.647718i	0.941880	+	0.335948i	$0.109057\pi$
$3$		0			0
$3$		0			0
$4$	0.678156	−	1.17460i	0.339078	−	0.587300i
$5$	0.645568			0.288707			0.144353	−	0.989526i	$-0.453890\pi$
$5$	0.645568			0.288707			0.144353	+	0.989526i	$0.453890\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			1.17925i			0.416928i
$9$		0			0
$10$	1.02425	−	0.591348i	0.323895	−	0.187001i
$11$			5.31595i			1.60282i	0.598116	+	0.801410i	$0.295916\pi$
$11$			5.31595i			1.60282i	−0.598116	+	0.801410i	$0.704084\pi$
$12$		0			0
$13$	4.44045	−	2.56370i	1.23156	−	0.711041i	0.264205	−	0.964467i	$-0.414890\pi$
$13$	4.44045	−	2.56370i	1.23156	−	0.711041i	0.967355	+	0.253425i	$0.0815572\pi$
$14$		0			0
$15$		0			0
$16$	2.43652	+	4.22018i	0.609130	+	1.05504i
$17$	0.814931	+	1.41150i	0.197650	+	0.342339i	0.947766	−	0.318967i	$-0.103336\pi$
$17$	0.814931	+	1.41150i	0.197650	+	0.342339i	−0.750116	+	0.661306i	$0.770002\pi$
$18$		0			0
$19$	−2.09039	−	1.20689i	−0.479569	−	0.276879i	0.240668	−	0.970608i	$-0.422634\pi$
$19$	−2.09039	−	1.20689i	−0.479569	−	0.276879i	−0.720237	+	0.693728i	$0.755967\pi$
$20$	0.437796	−	0.758285i	0.0978942	−	0.169558i
$21$		0			0
$22$	4.86947	+	8.43418i	1.03818	+	1.79817i
$23$			1.47157i			0.306843i	0.988161	+	0.153422i	$0.0490292\pi$
$23$			1.47157i			0.306843i	−0.988161	+	0.153422i	$0.950971\pi$
$24$		0			0
$25$	−4.58324			−0.916648
$26$	4.69675	−	8.13502i	0.921109	−	1.59541i
$27$		0			0
$28$		0			0
$29$	6.43846	+	3.71724i	1.19559	+	0.690275i	0.959569	−	0.281473i	$-0.0908229\pi$
$29$	6.43846	+	3.71724i	1.19559	+	0.690275i	0.236022	+	0.971748i	$0.424156\pi$
$30$		0			0
$31$	4.90799	+	2.83363i	0.881501	+	0.508935i	0.871153	−	0.491012i	$-0.163373\pi$
$31$	4.90799	+	2.83363i	0.881501	+	0.508935i	0.0103477	+	0.999946i	$0.496706\pi$
$32$	5.68894	+	3.28451i	1.00567	+	0.580625i
$33$		0			0
$34$	2.58590	+	1.49297i	0.443479	+	0.256043i
$35$		0			0
$36$		0			0
$37$	3.99736	−	6.92362i	0.657161	−	1.13824i	−0.324186	−	0.945993i	$-0.605090\pi$
$37$	3.99736	−	6.92362i	0.657161	−	1.13824i	0.981347	−	0.192244i	$-0.0615763\pi$
$38$	−4.42210			−0.717359
$39$		0			0
$40$			0.761288i			0.120370i
$41$	−5.99052	−	10.3759i	−0.935562	−	1.62044i	−0.773628	−	0.633640i	$-0.781560\pi$
$41$	−5.99052	−	10.3759i	−0.935562	−	1.62044i	−0.161934	−	0.986802i	$-0.551773\pi$
$42$		0			0
$43$	−1.51281	+	2.62026i	−0.230701	+	0.399586i	−0.958015	−	0.286719i	$-0.907435\pi$
$43$	−1.51281	+	2.62026i	−0.230701	+	0.399586i	0.727314	+	0.686305i	$0.240769\pi$
$44$	6.24412	+	3.60504i	0.941336	+	0.543481i
$45$		0			0
$46$	1.34797	+	2.33476i	0.198748	+	0.344241i
$47$	1.54176	+	2.67041i	0.224889	+	0.389520i	0.956286	−	0.292432i	$-0.0944646\pi$
$47$	1.54176	+	2.67041i	0.224889	+	0.389520i	−0.731397	+	0.681952i	$0.761131\pi$
$48$		0			0
$49$		0			0
$50$	−7.27168	+	4.19830i	−1.02837	+	0.593730i
$51$		0			0
$52$		−	6.95434i		−	0.964394i
$53$	2.04554	−	1.18100i	0.280977	−	0.162222i	−0.352889	−	0.935665i	$-0.614801\pi$
$53$	2.04554	−	1.18100i	0.280977	−	0.162222i	0.633866	+	0.773443i	$0.281467\pi$
$54$		0			0
$55$			3.43181i			0.462745i
$56$		0			0
$57$		0			0
$58$	13.6202			1.78841
$59$	−1.47918	+	2.56202i	−0.192573	+	0.333546i	−0.946102	−	0.323868i	$-0.895017\pi$
$59$	−1.47918	+	2.56202i	−0.192573	+	0.333546i	0.753529	+	0.657414i	$0.228350\pi$
$60$		0			0
$61$	9.18018	−	5.30018i	1.17540	−	0.678618i	0.220455	−	0.975397i	$-0.429246\pi$
$61$	9.18018	−	5.30018i	1.17540	−	0.678618i	0.954946	+	0.296779i	$0.0959124\pi$
$62$	10.3825			1.31859
$63$		0			0
$64$	2.28853			0.286066
$65$	2.86662	−	1.65504i	0.355560	−	0.205283i
$66$		0			0
$67$	5.07747	−	8.79444i	0.620312	−	1.07441i	−0.369116	−	0.929383i	$-0.620339\pi$
$67$	5.07747	−	8.79444i	0.620312	−	1.07441i	0.989428	−	0.145028i	$-0.0463273\pi$
$68$	2.21060			0.268075
$69$		0			0
$70$		0			0
$71$			4.76597i			0.565617i	0.959176	+	0.282808i	$0.0912661\pi$
$71$			4.76597i			0.565617i	−0.959176	+	0.282808i	$0.908734\pi$
$72$		0			0
$73$	−10.2239	+	5.90277i	−1.19662	+	0.690867i	−0.959799	−	0.280687i	$-0.909438\pi$
$73$	−10.2239	+	5.90277i	−1.19662	+	0.690867i	−0.236817	+	0.971554i	$0.576104\pi$
$74$		−	14.6465i		−	1.70262i
$75$		0			0
$76$	−2.83523	+	1.63692i	−0.325223	+	0.187767i
$77$		0			0
$78$		0			0
$79$	−3.48104	−	6.02934i	−0.391648	−	0.678354i	0.601019	−	0.799235i	$-0.294762\pi$
$79$	−3.48104	−	6.02934i	−0.391648	−	0.678354i	−0.992667	+	0.120881i	$0.961428\pi$
$80$	1.57294	+	2.72441i	0.175860	+	0.304599i
$81$		0			0
$82$	−19.0089	−	10.9748i	−2.09918	−	1.21196i
$83$	−3.51618	+	6.09021i	−0.385951	+	0.668487i	−0.991901	−	0.127016i	$-0.959460\pi$
$83$	−3.51618	+	6.09021i	−0.385951	+	0.668487i	0.605949	+	0.795503i	$0.292793\pi$
$84$		0			0
$85$	0.526093	+	0.911221i	0.0570628	+	0.0988357i
$86$			5.54300i			0.597717i
$87$		0			0
$88$	−6.26884			−0.668261
$89$	2.16337	−	3.74706i	0.229317	−	0.397188i	−0.728289	−	0.685270i	$-0.759684\pi$
$89$	2.16337	−	3.74706i	0.229317	−	0.397188i	0.957606	+	0.288082i	$0.0930176\pi$
$90$		0			0
$91$		0			0
$92$	1.72850	+	0.997953i	0.180209	+	0.104044i
$93$		0			0
$94$	4.89226	+	2.82455i	0.504598	+	0.291330i
$95$	−1.34949	−	0.779129i	−0.138455	−	0.0799370i
$96$		0			0
$97$	−14.3946	−	8.31075i	−1.46156	−	0.843829i	−0.462472	−	0.886634i	$-0.653037\pi$
$97$	−14.3946	−	8.31075i	−1.46156	−	0.843829i	−0.999083	+	0.0428048i	$0.986371\pi$
$98$		0			0
$99$		0			0
$100$	−3.10815	+	5.38348i	−0.310815	+	0.538348i
$101$	4.65154			0.462846			0.231423	−	0.972853i	$-0.425662\pi$
$101$	4.65154			0.462846			0.231423	+	0.972853i	$0.425662\pi$
$102$		0			0
$103$		−	10.3043i		−	1.01532i	−0.861559	−	0.507658i	$-0.830511\pi$
$103$		−	10.3043i		−	1.01532i	0.861559	−	0.507658i	$-0.169489\pi$
$104$	3.02324	+	5.23641i	0.296453	+	0.513472i
$105$		0			0
$106$	2.16361	−	3.74749i	0.210149	−	0.363988i
$107$	0.267212	+	0.154275i	0.0258324	+	0.0149143i	0.512861	−	0.858472i	$-0.328586\pi$
$107$	0.267212	+	0.154275i	0.0258324	+	0.0149143i	−0.487028	+	0.873386i	$0.661919\pi$
$108$		0			0
$109$	3.14423	+	5.44596i	0.301162	+	0.521628i	0.976399	−	0.215972i	$-0.0692921\pi$
$109$	3.14423	+	5.44596i	0.301162	+	0.521628i	−0.675237	+	0.737601i	$0.735959\pi$
$110$	3.14358	+	5.44484i	0.299728	+	0.519145i
$111$		0			0
$112$		0			0
$113$	−7.72869	+	4.46216i	−0.727054	+	0.419765i	−0.817343	−	0.576151i	$-0.804554\pi$
$113$	−7.72869	+	4.46216i	−0.727054	+	0.419765i	0.0902895	+	0.995916i	$0.471221\pi$
$114$		0			0
$115$			0.949998i			0.0885877i
$116$	8.73256	−	5.04174i	0.810797	−	0.468114i
$117$		0			0
$118$			5.41979i			0.498932i
$119$		0			0
$120$		0			0
$121$	−17.2593			−1.56903
$122$	9.71006	−	16.8183i	0.879107	−	1.52266i
$123$		0			0
$124$	6.65676	−	3.84328i	0.597795	−	0.345137i
$125$	−6.18664			−0.553350
$126$		0			0
$127$	−2.49989			−0.221829			−0.110915	−	0.993830i	$-0.535378\pi$
$127$	−2.49989			−0.221829			−0.110915	+	0.993830i	$0.535378\pi$
$128$	−7.74695	+	4.47270i	−0.684740	+	0.395335i
$129$		0			0
$130$	3.03208	−	5.25171i	0.265931	−	0.460605i
$131$	2.53450			0.221440			0.110720	−	0.993852i	$-0.464684\pi$
$131$	2.53450			0.221440			0.110720	+	0.993852i	$0.464684\pi$
$132$		0			0
$133$		0			0
$134$		−	18.6041i		−	1.60715i
$135$		0			0
$136$	−1.66452	+	0.961008i	−0.142731	+	0.0824058i
$137$			1.21291i			0.103626i	0.998657	+	0.0518131i	$0.0165000\pi$
$137$			1.21291i			0.103626i	−0.998657	+	0.0518131i	$0.983500\pi$
$138$		0			0
$139$	−6.11754	+	3.53196i	−0.518883	+	0.299577i	−0.736478	−	0.676462i	$-0.763512\pi$
$139$	−6.11754	+	3.53196i	−0.518883	+	0.299577i	0.217594	+	0.976039i	$0.430179\pi$
$140$		0			0
$141$		0			0
$142$	4.36569	+	7.56159i	0.366360	+	0.634555i
$143$	13.6285	+	23.6052i	1.13967	+	1.97397i
$144$		0			0
$145$	4.15646	+	2.39974i	0.345175	+	0.199287i
$146$	−10.8140	+	18.7304i	−0.894974	+	1.55014i
$147$		0			0
$148$	−5.42166	−	9.39060i	−0.445658	−	0.771902i
$149$		−	6.93132i		−	0.567836i	−0.958849	−	0.283918i	$-0.908366\pi$
$149$		−	6.93132i		−	0.567836i	0.958849	−	0.283918i	$-0.0916343\pi$
$150$		0			0
$151$	6.31878			0.514215			0.257108	−	0.966383i	$-0.417231\pi$
$151$	6.31878			0.514215			0.257108	+	0.966383i	$0.417231\pi$
$152$	1.42323	−	2.46510i	0.115439	−	0.199946i
$153$		0			0
$154$		0			0
$155$	3.16844	+	1.82930i	0.254495	+	0.146933i
$156$		0			0
$157$	−1.72363	−	0.995139i	−0.137561	−	0.0794208i	0.429640	−	0.903000i	$-0.358640\pi$
$157$	−1.72363	−	0.995139i	−0.137561	−	0.0794208i	−0.567201	+	0.823579i	$0.691974\pi$
$158$	−11.0459	−	6.37735i	−0.878765	−	0.507355i
$159$		0			0
$160$	3.67260	+	2.12038i	0.290345	+	0.167631i
$161$		0			0
$162$		0			0
$163$	2.99365	−	5.18515i	0.234480	−	0.406132i	−0.724641	−	0.689126i	$-0.757994\pi$
$163$	2.99365	−	5.18515i	0.234480	−	0.406132i	0.959122	+	0.282994i	$0.0913278\pi$
$164$	−16.2500			−1.26891
$165$		0			0
$166$			12.8835i			0.999951i
$167$	0.697990	+	1.20895i	0.0540121	+	0.0935516i	0.891767	−	0.452494i	$-0.149466\pi$
$167$	0.697990	+	1.20895i	0.0540121	+	0.0935516i	−0.837755	+	0.546046i	$0.816132\pi$
$168$		0			0
$169$	6.64508	−	11.5096i	0.511160	−	0.885355i
$170$	1.66938	+	0.963816i	0.128035	+	0.0739213i
$171$		0			0
$172$	2.05184	+	3.55389i	0.156451	+	0.270982i
$173$	−3.80506	−	6.59055i	−0.289293	−	0.501071i	0.684348	−	0.729156i	$-0.260087\pi$
$173$	−3.80506	−	6.59055i	−0.289293	−	0.501071i	−0.973641	+	0.228085i	$0.926754\pi$
$174$		0			0
$175$		0			0
$176$	−22.4343	+	12.9524i	−1.69105	+	0.976326i
$177$		0			0
$178$		−	7.92669i		−	0.594130i
$179$	−8.00888	+	4.62393i	−0.598612	+	0.345609i	−0.768495	−	0.639855i	$-0.778994\pi$
$179$	−8.00888	+	4.62393i	−0.598612	+	0.345609i	0.169883	+	0.985464i	$0.445661\pi$
$180$		0			0
$181$			11.9634i			0.889234i	0.895721	+	0.444617i	$0.146660\pi$
$181$			11.9634i			0.889234i	−0.895721	+	0.444617i	$0.853340\pi$
$182$		0			0
$183$		0			0
$184$	−1.73535			−0.127932
$185$	2.58057	−	4.46967i	0.189727	−	0.328617i
$186$		0			0
$187$	−7.50347	+	4.33213i	−0.548708	+	0.316797i
$188$	4.18223			0.305020
$189$		0			0
$190$	−2.85477			−0.207107
$191$	−17.5586	+	10.1375i	−1.27050	+	0.733521i	−0.975081	−	0.221847i	$-0.928791\pi$
$191$	−17.5586	+	10.1375i	−1.27050	+	0.733521i	−0.295415	+	0.955369i	$0.595458\pi$
$192$		0			0
$193$	8.44583	−	14.6286i	0.607944	−	1.05299i	−0.383634	−	0.923485i	$-0.625328\pi$
$193$	8.44583	−	14.6286i	0.607944	−	1.05299i	0.991579	−	0.129505i	$-0.0413389\pi$
$194$	−30.4510			−2.18625
$195$		0			0
$196$		0			0
$197$		−	18.7102i		−	1.33305i	−0.745484	−	0.666524i	$-0.767781\pi$
$197$		−	18.7102i		−	1.33305i	0.745484	−	0.666524i	$-0.232219\pi$
$198$		0			0
$199$	15.6271	−	9.02231i	1.10778	−	0.639574i	0.169523	−	0.985526i	$-0.445777\pi$
$199$	15.6271	−	9.02231i	1.10778	−	0.639574i	0.938252	+	0.345952i	$0.112444\pi$
$200$		−	5.40480i		−	0.382177i
$201$		0			0
$202$	7.38004	−	4.26087i	0.519258	−	0.299794i
$203$		0			0
$204$		0			0
$205$	−3.86729	−	6.69834i	−0.270103	−	0.467833i
$206$	−9.43889	−	16.3486i	−0.657639	−	1.13906i
$207$		0			0
$208$	21.6385	+	12.4930i	1.50036	+	0.866234i
$209$	6.41576	−	11.1124i	0.443788	−	0.768663i
$210$		0			0
$211$	−4.03491	−	6.98868i	−0.277775	−	0.481120i	0.693057	−	0.720883i	$-0.256264\pi$
$211$	−4.03491	−	6.98868i	−0.277775	−	0.481120i	−0.970831	+	0.239763i	$0.922930\pi$
$212$		−	3.20360i		−	0.220024i
$213$		0			0
$214$	0.565272			0.0386412
$215$	−0.976621	+	1.69156i	−0.0666050	+	0.115363i
$216$		0			0
$217$		0			0
$218$	9.97713	+	5.76030i	0.675736	+	0.390137i
$219$		0			0
$220$	4.03101	+	2.32730i	0.271770	+	0.156907i
$221$	7.23732	+	4.17847i	0.486835	+	0.281074i
$222$		0			0
$223$	−20.2450	−	11.6884i	−1.35570	−	0.782716i	−0.366662	−	0.930354i	$-0.619500\pi$
$223$	−20.2450	−	11.6884i	−1.35570	−	0.782716i	−0.989041	+	0.147638i	$0.952833\pi$
$224$		0			0
$225$		0			0
$226$	−8.17479	+	14.1591i	−0.543779	+	0.941852i
$227$	−14.4431			−0.958620			−0.479310	−	0.877646i	$-0.659113\pi$
$227$	−14.4431			−0.958620			−0.479310	+	0.877646i	$0.659113\pi$
$228$		0			0
$229$			13.1137i			0.866578i	0.901255	+	0.433289i	$0.142647\pi$
$229$			13.1137i			0.866578i	−0.901255	+	0.433289i	$0.857353\pi$
$230$	0.870209	+	1.50725i	0.0573799	+	0.0993849i
$231$		0			0
$232$	−4.38357	+	7.59256i	−0.287795	+	0.498476i
$233$	−7.31966	−	4.22601i	−0.479527	−	0.276855i	0.240692	−	0.970601i	$-0.422626\pi$
$233$	−7.31966	−	4.22601i	−0.479527	−	0.276855i	−0.720219	+	0.693746i	$0.755959\pi$
$234$		0			0
$235$	0.995314	+	1.72393i	0.0649271	+	0.112457i
$236$	2.00623	+	3.47489i	0.130594	+	0.226196i
$237$		0			0
$238$		0			0
$239$	24.2111	−	13.9783i	1.56608	−	0.904179i	0.569466	−	0.822015i	$-0.307150\pi$
$239$	24.2111	−	13.9783i	1.56608	−	0.904179i	0.996619	−	0.0821642i	$-0.0261832\pi$
$240$		0			0
$241$			22.4079i			1.44342i	0.692196	+	0.721710i	$0.256643\pi$
$241$			22.4079i			1.44342i	−0.692196	+	0.721710i	$0.743357\pi$
$242$	−27.3833	+	15.8097i	−1.76026	+	1.01629i
$243$		0			0
$244$		−	14.3774i		−	0.920418i
$245$		0			0
$246$		0			0
$247$	−12.3764			−0.787491
$248$	−3.34156	+	5.78775i	−0.212189	+	0.367523i
$249$		0			0
$250$	−9.81559	+	5.66703i	−0.620792	+	0.358415i
$251$	6.39587			0.403704			0.201852	−	0.979416i	$-0.435304\pi$
$251$	6.39587			0.403704			0.201852	+	0.979416i	$0.435304\pi$
$252$		0			0
$253$	−7.82278			−0.491814
$254$	−3.96627	+	2.28993i	−0.248866	+	0.143683i
$255$		0			0
$256$	−10.4826	+	18.1565i	−0.655165	+	1.13478i
$257$	−3.31409			−0.206727			−0.103364	−	0.994644i	$-0.532961\pi$
$257$	−3.31409			−0.206727			−0.103364	+	0.994644i	$0.532961\pi$
$258$		0			0
$259$		0			0
$260$		−	4.48950i		−	0.278427i
$261$		0			0
$262$	4.02118	−	2.32163i	0.248429	−	0.143431i
$263$			22.6901i			1.39913i	0.714567	+	0.699567i	$0.246624\pi$
$263$			22.6901i			1.39913i	−0.714567	+	0.699567i	$0.753376\pi$
$264$		0			0
$265$	1.32054	−	0.762413i	0.0811200	−	0.0468347i
$266$		0			0
$267$		0			0
$268$	−6.88664	−	11.9280i	−0.420668	−	0.728619i
$269$	−1.38050	−	2.39110i	−0.0841707	−	0.145788i	0.820867	−	0.571120i	$-0.193491\pi$
$269$	−1.38050	−	2.39110i	−0.0841707	−	0.145788i	−0.905038	+	0.425332i	$0.860157\pi$
$270$		0			0
$271$	5.27342	+	3.04461i	0.320337	+	0.184947i	0.651543	−	0.758612i	$-0.274122\pi$
$271$	5.27342	+	3.04461i	0.320337	+	0.184947i	−0.331206	+	0.943559i	$0.607455\pi$
$272$	−3.97119	+	6.87830i	−0.240789	+	0.417058i
$273$		0			0
$274$	1.11104	+	1.92438i	0.0671205	+	0.116256i
$275$		−	24.3643i		−	1.46922i
$276$		0			0
$277$	−9.43367			−0.566814			−0.283407	−	0.959000i	$-0.591465\pi$
$277$	−9.43367			−0.566814			−0.283407	+	0.959000i	$0.591465\pi$
$278$	−6.47064	+	11.2075i	−0.388083	+	0.672180i
$279$		0			0
$280$		0			0
$281$	−4.57153	−	2.63938i	−0.272715	−	0.157452i	0.357406	−	0.933949i	$-0.383661\pi$
$281$	−4.57153	−	2.63938i	−0.272715	−	0.157452i	−0.630121	+	0.776497i	$0.716995\pi$
$282$		0			0
$283$	−17.0346	−	9.83496i	−1.01260	−	0.584628i	−0.100651	−	0.994922i	$-0.532093\pi$
$283$	−17.0346	−	9.83496i	−1.01260	−	0.584628i	−0.911953	+	0.410294i	$0.865426\pi$
$284$	5.59811	+	3.23207i	0.332187	+	0.191788i
$285$		0			0
$286$	43.2453	+	24.9677i	2.55715	+	1.47637i
$287$		0			0
$288$		0			0
$289$	7.17178	−	12.4219i	0.421869	−	0.730699i
$290$	8.79274			0.516328
$291$		0			0
$292$			16.0120i			0.937031i
$293$	−9.11647	−	15.7902i	−0.532590	−	0.922473i	−0.999276	−	0.0380495i	$-0.987886\pi$
$293$	−9.11647	−	15.7902i	−0.532590	−	0.922473i	0.466686	−	0.884423i	$-0.345448\pi$
$294$		0			0
$295$	−0.954912	+	1.65396i	−0.0555971	+	0.0962970i
$296$	8.16470	+	4.71389i	0.474563	+	0.273989i
$297$		0			0
$298$	−6.34917	−	10.9971i	−0.367797	−	0.637044i
$299$	3.77265	+	6.53443i	0.218178	+	0.377896i
$300$		0			0
$301$		0			0
$302$	10.0253	−	5.78808i	0.576888	−	0.333067i
$303$		0			0
$304$		−	11.7624i		−	0.674622i
$305$	5.92643	−	3.42163i	0.339347	−	0.195922i
$306$		0			0
$307$		−	26.0447i		−	1.48645i	−0.669042	−	0.743224i	$-0.733296\pi$
$307$		−	26.0447i		−	1.48645i	0.669042	−	0.743224i	$-0.266704\pi$
$308$		0			0
$309$		0			0
$310$	6.70265			0.380685
$311$	14.1433	−	24.4969i	0.801992	−	1.38909i	−0.116311	−	0.993213i	$-0.537107\pi$
$311$	14.1433	−	24.4969i	0.801992	−	1.38909i	0.918303	−	0.395878i	$-0.129560\pi$
$312$		0			0
$313$	−4.82891	+	2.78797i	−0.272946	+	0.157586i	−0.630226	−	0.776412i	$-0.717038\pi$
$313$	−4.82891	+	2.78797i	−0.272946	+	0.157586i	0.357280	+	0.933998i	$0.383704\pi$
$314$	−3.64624			−0.205769
$315$		0			0
$316$	−9.44276			−0.531197
$317$	29.0708	−	16.7841i	1.63278	−	0.942686i	0.649550	−	0.760319i	$-0.274957\pi$
$317$	29.0708	−	16.7841i	1.63278	−	0.942686i	0.983230	−	0.182367i	$-0.0583760\pi$
$318$		0			0
$319$	−19.7607	+	34.2265i	−1.10639	+	1.91632i
$320$	1.47740			0.0825893
$321$		0			0
$322$		0			0
$323$		−	3.93412i		−	0.218901i
$324$		0			0
$325$	−20.3517	+	11.7500i	−1.12891	+	0.651775i
$326$		−	10.9689i		−	0.607509i
$327$		0			0
$328$	12.2358	−	7.06433i	0.675608	−	0.390063i
$329$		0			0
$330$		0			0
$331$	15.1867	+	26.3042i	0.834739	+	1.44581i	0.894243	+	0.447582i	$0.147715\pi$
$331$	15.1867	+	26.3042i	0.834739	+	1.44581i	−0.0595042	+	0.998228i	$0.518952\pi$
$332$	4.76904	+	8.26023i	0.261735	+	0.453339i
$333$		0			0
$334$	2.21483	+	1.27873i	0.121190	+	0.0699692i
$335$	3.27785	−	5.67741i	0.179088	−	0.310190i
$336$		0			0
$337$	1.86121	+	3.22371i	0.101387	+	0.175607i	0.912256	−	0.409620i	$-0.134339\pi$
$337$	1.86121	+	3.22371i	0.101387	+	0.175607i	−0.810870	+	0.585227i	$0.801005\pi$
$338$		−	24.3479i		−	1.32435i
$339$		0			0
$340$	1.42709			0.0773950
$341$	−15.0634	+	26.0906i	−0.815730	+	1.41289i
$342$		0			0
$343$		0			0
$344$	−3.08995	−	1.78398i	−0.166599	−	0.0961858i
$345$		0			0
$346$	−12.0741	−	6.97096i	−0.649105	−	0.374761i
$347$	6.18028	+	3.56818i	0.331775	+	0.191550i	0.656629	−	0.754214i	$-0.271982\pi$
$347$	6.18028	+	3.56818i	0.331775	+	0.191550i	−0.324854	+	0.945764i	$0.605315\pi$
$348$		0			0
$349$	13.2087	+	7.62607i	0.707047	+	0.408214i	0.809967	−	0.586476i	$-0.199485\pi$
$349$	13.2087	+	7.62607i	0.707047	+	0.408214i	−0.102920	+	0.994690i	$0.532818\pi$
$350$		0			0
$351$		0			0
$352$	−17.4603	+	30.2421i	−0.930637	+	1.61191i
$353$	−34.4718			−1.83475			−0.917373	−	0.398028i	$-0.869695\pi$
$353$	−34.4718			−1.83475			−0.917373	+	0.398028i	$0.869695\pi$
$354$		0			0
$355$			3.07676i			0.163297i
$356$	−2.93420	−	5.08219i	−0.155512	−	0.269355i
$357$		0			0
$358$	−8.47115	+	14.6725i	−0.447714	+	0.775464i
$359$	−5.73791	−	3.31278i	−0.302835	−	0.174842i	0.340881	−	0.940107i	$-0.389275\pi$
$359$	−5.73791	−	3.31278i	−0.302835	−	0.174842i	−0.643716	+	0.765265i	$0.722608\pi$
$360$		0			0
$361$	−6.58684	−	11.4087i	−0.346676	−	0.600460i
$362$	10.9586	+	18.9809i	0.575973	+	0.997614i
$363$		0			0
$364$		0			0
$365$	−6.60022	+	3.81064i	−0.345472	+	0.199458i
$366$		0			0
$367$			3.09716i			0.161670i	0.996727	+	0.0808352i	$0.0257587\pi$
$367$			3.09716i			0.161670i	−0.996727	+	0.0808352i	$0.974241\pi$
$368$	−6.21028	+	3.58551i	−0.323733	+	0.186907i
$369$		0			0
$370$		−	9.45532i		−	0.491559i
$371$		0			0
$372$		0			0
$373$	9.69999			0.502246			0.251123	−	0.967955i	$-0.419200\pi$
$373$	9.69999			0.502246			0.251123	+	0.967955i	$0.419200\pi$
$374$	−7.93657	+	13.7465i	−0.410390	+	0.710816i
$375$		0			0
$376$	−3.14909	+	1.81813i	−0.162402	+	0.0937628i
$377$	38.1195			1.96326
$378$		0			0
$379$	7.76103			0.398657			0.199329	−	0.979933i	$-0.436124\pi$
$379$	7.76103			0.398657			0.199329	+	0.979933i	$0.436124\pi$
$380$	−1.83033	+	1.05674i	−0.0938941	+	0.0542098i
$381$		0			0
$382$	−18.5721	+	32.1678i	−0.950231	+	1.64585i
$383$	24.6127			1.25765			0.628825	−	0.777547i	$-0.283536\pi$
$383$	24.6127			1.25765			0.628825	+	0.777547i	$0.283536\pi$
$384$		0			0
$385$		0			0
$386$		−	30.9459i		−	1.57511i
$387$		0			0
$388$	−19.5236	+	11.2720i	−0.991162	+	0.572248i
$389$			6.42681i			0.325852i	0.986638	+	0.162926i	$0.0520932\pi$
$389$			6.42681i			0.325852i	−0.986638	+	0.162926i	$0.947907\pi$
$390$		0			0
$391$	−2.07712	+	1.19923i	−0.105044	+	0.0606474i
$392$		0			0
$393$		0			0
$394$	−17.1388	−	29.6852i	−0.863439	−	1.49552i
$395$	−2.24725	−	3.89235i	−0.113071	−	0.195846i
$396$		0			0
$397$	11.4835	+	6.62998i	0.576338	+	0.332749i	0.759677	−	0.650301i	$-0.225357\pi$
$397$	11.4835	+	6.62998i	0.576338	+	0.332749i	−0.183339	+	0.983050i	$0.558690\pi$
$398$	16.5291	−	28.6292i	0.828528	−	1.43505i
$399$		0			0
$400$	−11.1672	−	19.3421i	−0.558358	−	0.967105i
$401$			15.8052i			0.789273i	0.918837	+	0.394636i	$0.129129\pi$
$401$			15.8052i			0.789273i	−0.918837	+	0.394636i	$0.870871\pi$
$402$		0			0
$403$	29.0582			1.44749
$404$	3.15447	−	5.46370i	0.156941	−	0.271829i
$405$		0			0
$406$		0			0
$407$	36.8056	+	21.2497i	1.82439	+	1.05331i
$408$		0			0
$409$	−4.69257	−	2.70926i	−0.232033	−	0.133964i	0.379477	−	0.925201i	$-0.376104\pi$
$409$	−4.69257	−	2.70926i	−0.232033	−	0.133964i	−0.611509	+	0.791237i	$0.709437\pi$
$410$	−12.2715	−	7.08497i	−0.606048	−	0.349902i
$411$		0			0
$412$	−12.1035	−	6.98795i	−0.596296	−	0.344271i
$413$		0			0
$414$		0			0
$415$	−2.26994	+	3.93165i	−0.111427	+	0.192997i
$416$	33.6820			1.65139
$417$		0			0
$418$		−	23.5077i		−	1.14980i
$419$	−12.2469	−	21.2123i	−0.598302	−	1.03629i	−0.993072	−	0.117509i	$-0.962509\pi$
$419$	−12.2469	−	21.2123i	−0.598302	−	1.03629i	0.394770	−	0.918780i	$-0.370824\pi$
$420$		0			0
$421$	5.99347	−	10.3810i	0.292104	−	0.505939i	−0.682203	−	0.731163i	$-0.738978\pi$
$421$	5.99347	−	10.3810i	0.292104	−	0.505939i	0.974307	+	0.225224i	$0.0723113\pi$
$422$	−12.8034	−	7.39206i	−0.623261	−	0.359840i
$423$		0			0
$424$	1.39269	+	2.41221i	0.0676350	+	0.117147i
$425$	−3.73502	−	6.46925i	−0.181175	−	0.313805i
$426$		0			0
$427$		0			0
$428$	0.362424	−	0.209245i	0.0175184	−	0.0101143i
$429$		0			0
$430$			3.57839i			0.172565i
$431$	26.6926	−	15.4110i	1.28574	−	0.742320i	0.307845	−	0.951437i	$-0.400392\pi$
$431$	26.6926	−	15.4110i	1.28574	−	0.742320i	0.977891	+	0.209117i	$0.0670590\pi$
$432$		0			0
$433$			6.06173i			0.291308i	0.989336	+	0.145654i	$0.0465287\pi$
$433$			6.06173i			0.291308i	−0.989336	+	0.145654i	$0.953471\pi$
$434$		0			0
$435$		0			0
$436$	8.52910			0.408470
$437$	1.77602	−	3.07616i	0.0849585	−	0.147152i
$438$		0			0
$439$	−23.5081	+	13.5724i	−1.12198	+	0.647776i	−0.941906	−	0.335877i	$-0.890967\pi$
$439$	−23.5081	+	13.5724i	−1.12198	+	0.647776i	−0.180075	+	0.983653i	$0.557634\pi$
$440$	−4.04697			−0.192932
$441$		0			0
$442$	15.3101			0.728228
$443$	−4.63465	+	2.67582i	−0.220199	+	0.127132i	−0.606042	−	0.795432i	$-0.707244\pi$
$443$	−4.63465	+	2.67582i	−0.220199	+	0.127132i	0.385843	+	0.922564i	$0.373910\pi$
$444$		0			0
$445$	1.39660	−	2.41899i	0.0662053	−	0.114671i
$446$	−42.8270			−2.02792
$447$		0			0
$448$		0			0
$449$			34.2418i			1.61597i	0.589204	+	0.807985i	$0.299442\pi$
$449$			34.2418i			1.61597i	−0.589204	+	0.807985i	$0.700558\pi$
$450$		0			0
$451$	55.1577	−	31.8453i	2.59727	−	1.49954i
$452$			12.1042i			0.569332i
$453$		0			0
$454$	−22.9151	+	13.2300i	−1.07546	+	0.620916i
$455$		0			0
$456$		0			0
$457$	7.93019	+	13.7355i	0.370958	+	0.642519i	0.989713	−	0.143065i	$-0.0456959\pi$
$457$	7.93019	+	13.7355i	0.370958	+	0.642519i	−0.618755	+	0.785584i	$0.712363\pi$
$458$	12.0123	+	20.8059i	0.561299	+	0.972198i
$459$		0			0
$460$	1.11587	+	0.644247i	0.0520276	+	0.0300382i
$461$	−6.50676	+	11.2700i	−0.303050	+	0.524898i	−0.976825	−	0.214038i	$-0.931338\pi$
$461$	−6.50676	+	11.2700i	−0.303050	+	0.524898i	0.673775	+	0.738936i	$0.264672\pi$
$462$		0			0
$463$	−6.01941	−	10.4259i	−0.279746	−	0.484534i	0.691576	−	0.722304i	$-0.256917\pi$
$463$	−6.01941	−	10.4259i	−0.279746	−	0.484534i	−0.971321	+	0.237770i	$0.923583\pi$
$464$			36.2286i			1.68187i
$465$		0			0
$466$	−15.4843			−0.717297
$467$	10.1728	−	17.6199i	0.470743	−	0.815351i	−0.528697	−	0.848811i	$-0.677319\pi$
$467$	10.1728	−	17.6199i	0.470743	−	0.815351i	0.999440	+	0.0334596i	$0.0106525\pi$
$468$		0			0
$469$		0			0
$470$	3.15829	+	1.82344i	0.145681	+	0.0841090i
$471$		0			0
$472$	−3.02126	−	1.74433i	−0.139065	−	0.0802891i
$473$	−13.9292	−	8.04201i	−0.640464	−	0.369772i
$474$		0			0
$475$	9.58078	+	5.53146i	0.439596	+	0.253801i
$476$		0			0
$477$		0			0
$478$	25.6085	−	44.3553i	1.17131	−	2.02876i
$479$	24.2983			1.11022			0.555109	−	0.831778i	$-0.312676\pi$
$479$	24.2983			1.11022			0.555109	+	0.831778i	$0.312676\pi$
$480$		0			0
$481$		−	40.9920i		−	1.86908i
$482$	20.5259	+	35.5519i	0.934929	+	1.61934i
$483$		0			0
$484$	−11.7045	+	20.2728i	−0.532023	+	0.921491i
$485$	−9.29273	−	5.36516i	−0.421961	−	0.243619i
$486$		0			0
$487$	13.6546	+	23.6504i	0.618747	+	1.07170i	0.989715	+	0.143055i	$0.0456927\pi$
$487$	13.6546	+	23.6504i	0.618747	+	1.07170i	−0.370968	+	0.928646i	$0.620974\pi$
$488$	6.25025	+	10.8257i	0.282935	+	0.490058i
$489$		0			0
$490$		0			0
$491$	13.2899	−	7.67290i	0.599763	−	0.346273i	−0.169185	−	0.985584i	$-0.554114\pi$
$491$	13.2899	−	7.67290i	0.599763	−	0.346273i	0.768948	+	0.639311i	$0.220780\pi$
$492$		0			0
$493$			12.1172i			0.545731i
$494$	−19.6361	+	11.3369i	−0.883471	+	0.510072i
$495$		0			0
$496$			27.6168i			1.24003i
$497$		0			0
$498$		0			0
$499$	−10.3101			−0.461542			−0.230771	−	0.973008i	$-0.574125\pi$
$499$	−10.3101			−0.461542			−0.230771	+	0.973008i	$0.574125\pi$
$500$	−4.19551	+	7.26683i	−0.187629	+	0.324982i
$501$		0			0
$502$	10.1476	−	5.85869i	0.452907	−	0.261486i
$503$	−24.6770			−1.10029			−0.550146	−	0.835068i	$-0.685428\pi$
$503$	−24.6770			−1.10029			−0.550146	+	0.835068i	$0.685428\pi$
$504$		0			0
$505$	3.00289			0.133627
$506$	−12.4115	+	7.16576i	−0.551757	+	0.318557i
$507$		0			0
$508$	−1.69531	+	2.93637i	−0.0752174	+	0.130280i
$509$	5.17203			0.229246			0.114623	−	0.993409i	$-0.463434\pi$
$509$	5.17203			0.229246			0.114623	+	0.993409i	$0.463434\pi$
$510$		0			0
$511$		0			0
$512$			20.5181i			0.906778i
$513$		0			0
$514$	−5.25807	+	3.03575i	−0.231924	+	0.133901i
$515$		−	6.65215i		−	0.293129i
$516$		0			0
$517$	−14.1958	+	8.19594i	−0.624330	+	0.360457i
$518$		0			0
$519$		0			0
$520$	1.95171	+	3.38046i	0.0855882	+	0.148243i
$521$	−19.1664	−	33.1972i	−0.839696	−	1.45440i	−0.890149	−	0.455669i	$-0.849400\pi$
$521$	−19.1664	−	33.1972i	−0.839696	−	1.45440i	0.0504538	−	0.998726i	$-0.483933\pi$
$522$		0			0
$523$	23.6468	+	13.6525i	1.03400	+	0.596982i	0.918129	−	0.396282i	$-0.129700\pi$
$523$	23.6468	+	13.6525i	1.03400	+	0.596982i	0.115874	+	0.993264i	$0.463033\pi$
$524$	1.71878	−	2.97702i	0.0750855	−	0.130052i
$525$		0			0
$526$	20.7844	+	35.9997i	0.906245	+	1.56966i
$527$			9.23684i			0.402363i
$528$		0			0
$529$	20.8345			0.905847
$530$	1.39676	−	2.41926i	0.0606714	−	0.105086i
$531$		0			0
$532$		0			0
$533$	−53.2012	−	30.7158i	−2.30440	−	1.33045i
$534$		0			0
$535$	0.172504	+	0.0995952i	0.00745799	+	0.00430588i
$536$	10.3709	+	5.98762i	0.447953	+	0.258626i
$537$		0			0
$538$	−4.38055	−	2.52911i	−0.188859	−	0.109038i
$539$		0			0
$540$		0			0
$541$	−9.78052	+	16.9404i	−0.420498	+	0.728323i	−0.995988	−	0.0894853i	$-0.971478\pi$
$541$	−9.78052	+	16.9404i	−0.420498	+	0.728323i	0.575491	+	0.817808i	$0.304811\pi$
$542$	11.1556			0.479174
$543$		0			0
$544$			10.7066i			0.459042i
$545$	2.02981	+	3.51574i	0.0869476	+	0.150598i
$546$		0			0
$547$	12.6246	−	21.8665i	0.539790	−	0.934944i	−0.459125	−	0.888372i	$-0.651837\pi$
$547$	12.6246	−	21.8665i	0.539790	−	0.934944i	0.998915	−	0.0465723i	$-0.0148298\pi$
$548$	1.42469	+	0.822544i	0.0608597	+	0.0351373i
$549$		0			0
$550$	−22.3180	−	38.6559i	−0.951642	−	1.64829i
$551$	−8.97260	−	15.5410i	−0.382246	−	0.662069i
$552$		0			0
$553$		0			0
$554$	−14.9673	+	8.64136i	−0.635898	+	0.367136i
$555$		0			0
$556$			9.58089i			0.406320i
$557$	28.8204	−	16.6395i	1.22116	−	0.705036i	0.255994	−	0.966678i	$-0.417597\pi$
$557$	28.8204	−	16.6395i	1.22116	−	0.705036i	0.965165	+	0.261642i	$0.0842640\pi$
$558$		0			0
$559$			15.5135i			0.656152i
$560$		0			0
$561$		0			0
$562$	−9.67080			−0.407938
$563$	−15.2587	+	26.4289i	−0.643079	+	1.11385i	0.341663	+	0.939823i	$0.389010\pi$
$563$	−15.2587	+	26.4289i	−0.643079	+	1.11385i	−0.984742	+	0.174023i	$0.944323\pi$
$564$		0			0
$565$	−4.98940	+	2.88063i	−0.209905	+	0.121189i
$566$	−36.0358			−1.51470
$567$		0			0
$568$	−5.62028			−0.235822
$569$	13.4044	−	7.73906i	0.561943	−	0.324438i	−0.191982	−	0.981398i	$-0.561491\pi$
$569$	13.4044	−	7.73906i	0.561943	−	0.324438i	0.753925	+	0.656960i	$0.228158\pi$
$570$		0			0
$571$	12.2042	−	21.1384i	0.510731	−	0.884613i	−0.489191	−	0.872177i	$-0.662708\pi$
$571$	12.2042	−	21.1384i	0.510731	−	0.884613i	0.999923	−	0.0124362i	$-0.00395868\pi$
$572$	36.9689			1.54575
$573$		0			0
$574$		0			0
$575$		−	6.74455i		−	0.281267i
$576$		0			0
$577$	12.6901	−	7.32664i	0.528296	−	0.305012i	−0.212026	−	0.977264i	$-0.568006\pi$
$577$	12.6901	−	7.32664i	0.528296	−	0.305012i	0.740322	+	0.672252i	$0.234673\pi$
$578$		−	26.2777i		−	1.09301i
$579$		0			0
$580$	5.63746	−	3.25479i	0.234083	−	0.135148i
$581$		0			0
$582$		0			0
$583$	6.27811	+	10.8740i	0.260013	+	0.450355i
$584$	−6.96085	−	12.0565i	−0.288042	−	0.498904i
$585$		0			0
$586$	−28.9280	−	16.7016i	−1.19500	−	0.689936i
$587$	−11.6129	+	20.1141i	−0.479314	+	0.830197i	−0.999719	−	0.0237232i	$-0.992448\pi$
$587$	−11.6129	+	20.1141i	−0.479314	+	0.830197i	0.520404	+	0.853920i	$0.325781\pi$
$588$		0			0
$589$	−6.83975	−	11.8468i	−0.281827	−	0.488139i
$590$			3.49884i			0.144045i
$591$		0			0
$592$	38.9586			1.60119
$593$	5.55605	−	9.62337i	0.228160	−	0.395184i	−0.729103	−	0.684404i	$-0.760062\pi$
$593$	5.55605	−	9.62337i	0.228160	−	0.395184i	0.957263	+	0.289220i	$0.0933958\pi$
$594$		0			0
$595$		0			0
$596$	−8.14153	−	4.70051i	−0.333490	−	0.192541i
$597$		0			0
$598$	11.9712	+	6.91159i	0.489540	+	0.282636i
$599$	−13.5581	−	7.82776i	−0.553968	−	0.319833i	0.196753	−	0.980453i	$-0.436960\pi$
$599$	−13.5581	−	7.82776i	−0.553968	−	0.319833i	−0.750721	+	0.660620i	$0.770294\pi$
$600$		0			0
$601$	−30.5665	−	17.6476i	−1.24684	−	0.719861i	−0.276358	−	0.961055i	$-0.589128\pi$
$601$	−30.5665	−	17.6476i	−1.24684	−	0.719861i	−0.970477	+	0.241194i	$0.922461\pi$
$602$		0			0
$603$		0			0
$604$	4.28512	−	7.42205i	0.174359	−	0.301999i
$605$	−11.1421			−0.452990
$606$		0			0
$607$		−	38.8051i		−	1.57505i	−0.616284	−	0.787524i	$-0.711363\pi$
$607$		−	38.8051i		−	1.57505i	0.616284	−	0.787524i	$-0.288637\pi$
$608$	−7.92809	−	13.7318i	−0.321526	−	0.556900i
$609$		0			0
$610$	6.26850	−	10.8574i	0.253804	−	0.439602i
$611$	13.6923	+	7.90523i	0.553929	+	0.319811i
$612$		0			0
$613$	−15.8786	−	27.5025i	−0.641330	−	1.11082i	−0.985136	−	0.171776i	$-0.945049\pi$
$613$	−15.8786	−	27.5025i	−0.641330	−	1.11082i	0.343806	−	0.939041i	$-0.388284\pi$
$614$	−23.8572	−	41.3220i	−0.962800	−	1.66762i
$615$		0			0
$616$		0			0
$617$	−1.25518	+	0.724680i	−0.0505317	+	0.0291745i	−0.525053	−	0.851070i	$-0.675955\pi$
$617$	−1.25518	+	0.724680i	−0.0505317	+	0.0291745i	0.474521	+	0.880244i	$0.342621\pi$
$618$		0			0
$619$		−	29.1666i		−	1.17230i	−0.810201	−	0.586152i	$-0.800642\pi$
$619$		−	29.1666i		−	1.17230i	0.810201	−	0.586152i	$-0.199358\pi$
$620$	4.29740	−	2.48110i	0.172588	−	0.0996435i
$621$		0			0
$622$		−	51.8217i		−	2.07786i
$623$		0			0
$624$		0			0
$625$	18.9223			0.756892
$626$	−5.10764	+	8.84668i	−0.204142	+	0.353585i
$627$		0			0
$628$	−2.33778	+	1.34972i	−0.0932877	+	0.0538597i
$629$	13.0303			0.519551
$630$		0			0
$631$	11.7428			0.467473			0.233736	−	0.972300i	$-0.424905\pi$
$631$	11.7428			0.467473			0.233736	+	0.972300i	$0.424905\pi$
$632$	7.11011	−	4.10503i	0.282825	−	0.163289i
$633$		0			0
$634$	30.7488	−	53.2585i	1.22119	−	2.11516i
$635$	−1.61385			−0.0640436
$636$		0			0
$637$		0			0
$638$			72.4041i			2.86651i
$639$		0			0
$640$	−5.00119	+	2.88744i	−0.197689	+	0.114136i
$641$		−	11.5778i		−	0.457296i	−0.973509	−	0.228648i	$-0.926569\pi$
$641$		−	11.5778i		−	0.457296i	0.973509	−	0.228648i	$-0.0734305\pi$
$642$		0			0
$643$	13.1240	−	7.57712i	0.517558	−	0.298812i	−0.218377	−	0.975865i	$-0.570076\pi$
$643$	13.1240	−	7.57712i	0.517558	−	0.298812i	0.735935	+	0.677052i	$0.236743\pi$
$644$		0			0
$645$		0			0
$646$	−3.60370	−	6.24180i	−0.141786	−	0.245580i
$647$	6.22057	+	10.7743i	0.244556	+	0.423583i	0.962007	−	0.273026i	$-0.0880246\pi$
$647$	6.22057	+	10.7743i	0.244556	+	0.423583i	−0.717451	+	0.696609i	$0.754691\pi$
$648$		0			0
$649$	−13.6195	−	7.86325i	−0.534614	−	0.308659i
$650$	−21.5264	+	37.2847i	−0.844333	+	1.46243i
$651$		0			0
$652$	−4.06032	−	7.03268i	−0.159014	−	0.275421i
$653$			4.58431i			0.179398i	0.995969	+	0.0896990i	$0.0285905\pi$
$653$			4.58431i			0.179398i	−0.995969	+	0.0896990i	$0.971410\pi$
$654$		0			0
$655$	1.63619			0.0639313
$656$	29.1921	−	50.5621i	1.13976	−	1.97412i
$657$		0			0
$658$		0			0
$659$	−15.6110	−	9.01301i	−0.608118	−	0.351097i	0.164111	−	0.986442i	$-0.447525\pi$
$659$	−15.6110	−	9.01301i	−0.608118	−	0.351097i	−0.772228	+	0.635345i	$0.780858\pi$
$660$		0			0
$661$	0.554932	+	0.320390i	0.0215844	+	0.0124617i	0.510753	−	0.859727i	$-0.329367\pi$
$661$	0.554932	+	0.320390i	0.0215844	+	0.0124617i	−0.489169	+	0.872189i	$0.662700\pi$
$662$	48.1899	+	27.8225i	1.87296	+	1.08135i
$663$		0			0
$664$	−7.18189	−	4.14647i	−0.278711	−	0.160914i
$665$		0			0
$666$		0			0
$667$	−5.47018	+	9.47462i	−0.211806	+	0.366859i
$668$	1.89338			0.0732572
$669$		0			0
$670$		−	12.0102i		−	0.463995i
$671$	28.1755	+	48.8014i	1.08770	+	1.88396i
$672$		0			0
$673$	−11.0695	+	19.1729i	−0.426697	+	0.739061i	−0.996577	−	0.0826667i	$-0.973656\pi$
$673$	−11.0695	+	19.1729i	−0.426697	+	0.739061i	0.569880	+	0.821728i	$0.306990\pi$
$674$	5.90591	+	3.40978i	0.227487	+	0.131340i
$675$		0			0
$676$	−9.01280	−	15.6106i	−0.346646	−	0.600409i
$677$	10.0160	+	17.3482i	0.384947	+	0.666747i	0.991762	−	0.128096i	$-0.0408865\pi$
$677$	10.0160	+	17.3482i	0.384947	+	0.666747i	−0.606815	+	0.794843i	$0.707553\pi$
$678$		0			0
$679$		0			0
$680$	−1.07456	+	0.620397i	−0.0412074	+	0.0237911i
$681$		0			0
$682$			55.1931i			2.11345i
$683$	−18.1316	+	10.4683i	−0.693786	+	0.400558i	−0.805029	−	0.593235i	$-0.797850\pi$
$683$	−18.1316	+	10.4683i	−0.693786	+	0.400558i	0.111243	+	0.993793i	$0.464517\pi$
$684$		0			0
$685$			0.783018i			0.0299176i
$686$		0			0
$687$		0			0
$688$	−14.7440			−0.562108
$689$	6.05543	−	10.4883i	0.230693	−	0.399573i
$690$		0			0
$691$	−1.33430	+	0.770358i	−0.0507591	+	0.0293058i	−0.525165	−	0.851001i	$-0.675996\pi$
$691$	−1.33430	+	0.770358i	−0.0507591	+	0.0293058i	0.474406	+	0.880306i	$0.342663\pi$
$692$	−10.3217			−0.392372
$693$		0			0
$694$	13.0740			0.496282
$695$	−3.94929	+	2.28012i	−0.149805	+	0.0864900i
$696$		0			0
$697$	9.76372	−	16.9113i	0.369827	−	0.640560i
$698$	27.9423			1.05763
$699$		0			0
$700$		0			0
$701$		−	31.6641i		−	1.19593i	−0.801520	−	0.597967i	$-0.795975\pi$
$701$		−	31.6641i		−	1.19593i	0.801520	−	0.597967i	$-0.204025\pi$
$702$		0			0
$703$	−16.7121	+	9.64873i	−0.630309	+	0.363909i
$704$			12.1657i			0.458513i
$705$		0			0
$706$	−54.6922	+	31.5766i	−2.05837	+	1.18840i
$707$		0			0
$708$		0			0
$709$	−11.1762	−	19.3578i	−0.419732	−	0.726996i	0.576181	−	0.817322i	$-0.304542\pi$
$709$	−11.1762	−	19.3578i	−0.419732	−	0.726996i	−0.995912	+	0.0903259i	$0.971209\pi$
$710$	2.81835	+	4.88152i	0.105771	+	0.183200i
$711$		0			0
$712$	4.41873	+	2.55116i	0.165599	+	0.0956086i
$713$	−4.16988	+	7.22244i	−0.156163	+	0.270482i
$714$		0			0
$715$	8.79812	+	15.2388i	0.329031	+	0.569898i
$716$			12.5430i			0.468754i
$717$		0			0
$718$	−12.1382			−0.452994
$719$	−19.4544	+	33.6959i	−0.725525	+	1.25665i	0.233232	+	0.972421i	$0.425070\pi$
$719$	−19.4544	+	33.6959i	−0.725525	+	1.25665i	−0.958757	+	0.284226i	$0.908264\pi$
$720$		0			0
$721$		0			0
$722$	−20.9011	−	12.0672i	−0.777858	−	0.449096i
$723$		0			0
$724$	14.0522	+	8.11306i	0.522247	+	0.301520i
$725$	−29.5090	−	17.0370i	−1.09594	−	0.632739i
$726$		0			0
$727$	11.4647	+	6.61915i	0.425202	+	0.245491i	0.697301	−	0.716779i	$-0.254384\pi$
$727$	11.4647	+	6.61915i	0.425202	+	0.245491i	−0.272098	+	0.962269i	$0.587718\pi$
$728$		0			0
$729$		0			0
$730$	−6.98119	+	12.0918i	−0.258385	+	0.447536i
$731$	−4.93133			−0.182392
$732$		0			0
$733$			32.4727i			1.19941i	0.800222	+	0.599704i	$0.204715\pi$
$733$			32.4727i			1.19941i	−0.800222	+	0.599704i	$0.795285\pi$
$734$	2.83703	+	4.91389i	0.104717	+	0.181375i
$735$		0			0
$736$	−4.83338	+	8.37167i	−0.178161	+	0.308584i
$737$	46.7508	+	26.9916i	1.72209	+	0.994248i
$738$		0			0
$739$	6.91965	+	11.9852i	0.254543	+	0.440882i	0.964771	−	0.263090i	$-0.0847415\pi$
$739$	6.91965	+	11.9852i	0.254543	+	0.440882i	−0.710228	+	0.703972i	$0.751408\pi$
$740$	−3.50005	−	6.06227i	−0.128665	−	0.222854i
$741$		0			0
$742$		0			0
$743$	−31.8593	+	18.3940i	−1.16880	+	0.674810i	−0.953398	−	0.301715i	$-0.902441\pi$
$743$	−31.8593	+	18.3940i	−1.16880	+	0.674810i	−0.215406	+	0.976525i	$0.569108\pi$
$744$		0			0
$745$		−	4.47464i		−	0.163938i
$746$	15.3898	−	8.88530i	0.563461	−	0.325314i
$747$		0			0
$748$			11.7514i			0.429675i
$749$		0			0
$750$		0			0
$751$	−3.65905			−0.133520			−0.0667602	−	0.997769i	$-0.521266\pi$
$751$	−3.65905			−0.133520			−0.0667602	+	0.997769i	$0.521266\pi$
$752$	−7.51308	+	13.0130i	−0.273974	+	0.474537i
$753$		0			0
$754$	60.4797	−	34.9180i	2.20254	−	1.27164i
$755$	4.07921			0.148458
$756$		0			0
$757$	13.8901			0.504842			0.252421	−	0.967617i	$-0.418773\pi$
$757$	13.8901			0.504842			0.252421	+	0.967617i	$0.418773\pi$
$758$	12.3135	−	7.10920i	0.447246	−	0.258218i
$759$		0			0
$760$	0.918790	−	1.59139i	0.0333280	−	0.0577258i
$761$	13.6417			0.494510			0.247255	−	0.968950i	$-0.420471\pi$
$761$	13.6417			0.494510			0.247255	+	0.968950i	$0.420471\pi$
$762$		0			0
$763$		0			0
$764$			27.4991i			0.994884i
$765$		0			0
$766$	39.0500	−	22.5455i	1.41093	−	0.814602i
$767$			15.1687i			0.547709i
$768$		0			0
$769$	22.9328	−	13.2402i	0.826976	−	0.477455i	−0.0258399	−	0.999666i	$-0.508226\pi$
$769$	22.9328	−	13.2402i	0.826976	−	0.477455i	0.852816	+	0.522211i	$0.174893\pi$
$770$		0			0
$771$		0			0
$772$	−11.4552	−	19.8410i	−0.412281	−	0.714092i
$773$	−13.1109	−	22.7087i	−0.471566	−	0.816776i	0.527905	−	0.849303i	$-0.322978\pi$
$773$	−13.1109	−	22.7087i	−0.471566	−	0.816776i	−0.999471	+	0.0325274i	$0.989644\pi$
$774$		0			0
$775$	−22.4945	−	12.9872i	−0.808026	−	0.466514i
$776$	9.80047	−	16.9749i	0.351816	−	0.609364i
$777$		0			0
$778$	5.88703	+	10.1966i	0.211060	+	0.365567i
$779$			28.9196i			1.03615i
$780$		0			0
$781$	−25.3357			−0.906581
$782$	−2.19701	+	3.80533i	−0.0785649	+	0.136078i
$783$		0			0
$784$		0			0
$785$	−1.11272	−	0.642430i	−0.0397148	−	0.0229293i
$786$		0			0
$787$	25.1554	+	14.5235i	0.896694	+	0.517706i	0.876126	−	0.482082i	$-0.160119\pi$
$787$	25.1554	+	14.5235i	0.896694	+	0.517706i	0.0205676	+	0.999788i	$0.493453\pi$
$788$	−21.9770	−	12.6884i	−0.782899	−	0.452007i
$789$		0			0
$790$	−7.13088	−	4.11702i	−0.253705	−	0.146477i
$791$		0			0
$792$		0			0
$793$	27.1761	−	47.0704i	0.965052	−	1.67152i
$794$	24.2926			0.862111
$795$		0			0
$796$		−	24.4741i		−	0.867462i
$797$	−15.8184	−	27.3983i	−0.560317	−	0.970498i	−0.997469	−	0.0711097i	$-0.977346\pi$
$797$	−15.8184	−	27.3983i	−0.560317	−	0.970498i	0.437151	−	0.899388i	$-0.355987\pi$
$798$		0			0
$799$	−2.51286	+	4.35240i	−0.0888986	+	0.153977i
$800$	−26.0738	−	15.0537i	−0.921848	−	0.532229i
$801$		0			0
$802$	14.4777	+	25.0762i	0.511227	+	0.885470i
$803$	−31.3788	−	54.3497i	−1.10733	−	1.91796i
$804$		0			0
$805$		0			0
$806$	46.1032	−	26.6177i	1.62392	−	0.937569i
$807$		0			0
$808$			5.48534i			0.192974i
$809$	34.5466	−	19.9455i	1.21459	−	0.701245i	0.250836	−	0.968029i	$-0.419294\pi$
$809$	34.5466	−	19.9455i	1.21459	−	0.701245i	0.963756	+	0.266784i	$0.0859610\pi$
$810$		0			0
$811$			28.9516i			1.01663i	0.861172	+	0.508314i	$0.169731\pi$
$811$			28.9516i			1.01663i	−0.861172	+	0.508314i	$0.830269\pi$
$812$		0			0
$813$		0			0
$814$	77.8601			2.72899
$815$	1.93260	−	3.34737i	0.0676961	−	0.117253i
$816$		0			0
$817$	6.32473	−	3.65158i	0.221274	−	0.127753i
$818$	−9.92684			−0.347084
$819$		0			0
$820$	−10.4905			−0.366344
$821$	0.359377	−	0.207486i	0.0125423	−	0.00724132i	−0.493716	−	0.869623i	$-0.664362\pi$
$821$	0.359377	−	0.207486i	0.0125423	−	0.00724132i	0.506258	+	0.862382i	$0.331028\pi$
$822$		0			0
$823$	6.54814	−	11.3417i	0.228254	−	0.395347i	−0.729037	−	0.684475i	$-0.760032\pi$
$823$	6.54814	−	11.3417i	0.228254	−	0.395347i	0.957291	+	0.289127i	$0.0933650\pi$
$824$	12.1514			0.423314
$825$		0			0
$826$		0			0
$827$			35.2637i			1.22624i	0.789990	+	0.613120i	$0.210086\pi$
$827$			35.2637i			1.22624i	−0.789990	+	0.613120i	$0.789914\pi$
$828$		0			0
$829$	−29.0164	+	16.7526i	−1.00778	+	0.581842i	−0.910541	−	0.413419i	$-0.864334\pi$
$829$	−29.0164	+	16.7526i	−1.00778	+	0.581842i	−0.0972388	+	0.995261i	$0.531001\pi$
$830$			8.31716i			0.288693i
$831$		0			0
$832$	10.1621	−	5.86710i	0.352308	−	0.203405i
$833$		0			0
$834$		0			0
$835$	0.450600	+	0.780462i	0.0155937	+	0.0270090i
$836$	−8.70178	−	15.0719i	−0.300957	−	0.521273i
$837$		0			0
$838$	−38.8615	−	22.4367i	−1.34245	−	0.775062i
$839$	22.4984	−	38.9684i	0.776731	−	1.34534i	−0.157085	−	0.987585i	$-0.550210\pi$
$839$	22.4984	−	38.9684i	0.776731	−	1.34534i	0.933816	−	0.357753i	$-0.116457\pi$
$840$		0			0
$841$	13.1358	+	22.7519i	0.452959	+	0.784548i
$842$		−	21.9604i		−	0.756805i
$843$		0			0
$844$	−10.9452			−0.376749
$845$	4.28985	−	7.43024i	0.147575	−	0.255608i
$846$		0			0
$847$		0			0
$848$	9.96802	+	5.75504i	0.342303	+	0.197629i
$849$		0			0
$850$	−11.8518	−	6.84265i	−0.406514	−	0.234701i
$851$	10.1886	+	5.88238i	0.349260	+	0.201645i
$852$		0			0
$853$	15.8457	+	9.14854i	0.542548	+	0.313240i	0.746111	−	0.665822i	$-0.231919\pi$
$853$	15.8457	+	9.14854i	0.542548	+	0.313240i	−0.203563	+	0.979062i	$0.565252\pi$
$854$		0			0
$855$		0			0
$856$	−0.181929	+	0.315111i	−0.00621822	+	0.0107703i
$857$	10.5785			0.361355			0.180678	−	0.983542i	$-0.442171\pi$
$857$	10.5785			0.361355			0.180678	+	0.983542i	$0.442171\pi$
$858$		0			0
$859$			32.6748i			1.11485i	0.830227	+	0.557425i	$0.188210\pi$
$859$			32.6748i			1.11485i	−0.830227	+	0.557425i	$0.811790\pi$
$860$	1.32460	+	2.29428i	0.0451686	+	0.0782343i
$861$		0			0
$862$	28.2332	−	48.9014i	0.961628	−	1.66559i
$863$	−8.09878	−	4.67583i	−0.275686	−	0.159167i	0.355783	−	0.934569i	$-0.384214\pi$
$863$	−8.09878	−	4.67583i	−0.275686	−	0.159167i	−0.631469	+	0.775401i	$0.717548\pi$
$864$		0			0
$865$	−2.45643	−	4.25465i	−0.0835210	−	0.144663i
$866$	5.55262	+	9.61742i	0.188686	+	0.326813i
$867$		0			0
$868$		0			0
$869$	32.0517	−	18.5050i	1.08728	−	0.627741i
$870$		0			0
$871$		−	52.0684i		−	1.76427i
$872$	−6.42216	+	3.70783i	−0.217482	+	0.125563i
$873$		0			0
$874$		−	6.50742i		−	0.220117i
$875$		0			0
$876$		0			0
$877$	1.23815			0.0418095			0.0209048	−	0.999781i	$-0.493345\pi$
$877$	1.23815			0.0418095			0.0209048	+	0.999781i	$0.493345\pi$
$878$	−24.8650	+	43.0674i	−0.839153	+	1.45346i
$879$		0			0
$880$	−14.4828	+	8.36167i	−0.488217	+	0.281872i
$881$	−37.3480			−1.25828			−0.629142	−	0.777290i	$-0.716594\pi$
$881$	−37.3480			−1.25828			−0.629142	+	0.777290i	$0.716594\pi$
$882$		0			0
$883$	3.90708			0.131484			0.0657419	−	0.997837i	$-0.479059\pi$
$883$	3.90708			0.131484			0.0657419	+	0.997837i	$0.479059\pi$
$884$	9.81607	−	5.66731i	0.330150	−	0.190612i
$885$		0			0
$886$	−4.90216	+	8.49079i	−0.164691	+	0.285254i
$887$	14.5116			0.487251			0.243625	−	0.969869i	$-0.421663\pi$
$887$	14.5116			0.487251			0.243625	+	0.969869i	$0.421663\pi$
$888$		0			0
$889$		0			0
$890$		−	5.11722i		−	0.171530i
$891$		0			0
$892$	−27.4585	+	15.8532i	−0.919379	+	0.530804i
$893$		−	7.44295i		−	0.249069i
$894$		0			0
$895$	−5.17028	+	2.98506i	−0.172823	+	0.0997797i
$896$		0			0
$897$		0			0
$898$	31.3659	+	54.3273i	1.04669	+	1.81293i
$899$	21.0666	+	36.4884i	0.702610	+	1.21696i
$900$		0			0
$901$	3.33395	+	1.92486i	0.111070	+	0.0641263i
$902$	58.3414	−	101.050i	1.94256	−	3.36460i
$903$		0			0
$904$	−5.26201	−	9.11407i	−0.175012	−	0.303129i
$905$			7.72320i			0.256728i
$906$		0			0
$907$	−19.2139			−0.637987			−0.318993	−	0.947757i	$-0.603345\pi$
$907$	−19.2139			−0.637987			−0.318993	+	0.947757i	$0.603345\pi$
$908$	−9.79466	+	16.9648i	−0.325047	+	0.562998i
$909$		0			0
$910$		0			0
$911$	−10.1252	−	5.84579i	−0.335463	−	0.193680i	0.322801	−	0.946467i	$-0.395376\pi$
$911$	−10.1252	−	5.84579i	−0.335463	−	0.193680i	−0.658264	+	0.752787i	$0.728709\pi$
$912$		0			0
$913$	−32.3752	−	18.6919i	−1.07146	−	0.618610i
$914$	25.1637	+	14.5283i	0.832342	+	0.480553i
$915$		0			0
$916$	15.4034	+	8.89314i	0.508942	+	0.293838i
$917$		0			0
$918$		0			0
$919$	−19.9930	+	34.6289i	−0.659508	+	1.14230i	0.321236	+	0.946999i	$0.395902\pi$
$919$	−19.9930	+	34.6289i	−0.659508	+	1.14230i	−0.980743	+	0.195301i	$0.937432\pi$
$920$	−1.12029			−0.0369347
$921$		0			0
$922$			23.8411i			0.785164i
$923$	12.2185	+	21.1631i	0.402177	+	0.696591i
$924$		0			0
$925$	−18.3209	+	31.7326i	−0.602386	+	1.04336i
$926$	−19.1005	−	11.0277i	−0.627683	−	0.362393i
$927$		0			0
$928$	24.4187	+	42.2944i	0.801582	+	1.38838i
$929$	6.38359	+	11.0567i	0.209439	+	0.362759i	0.951538	−	0.307532i	$-0.0995030\pi$
$929$	6.38359	+	11.0567i	0.209439	+	0.362759i	−0.742099	+	0.670290i	$0.766170\pi$
$930$		0			0
$931$		0			0
$932$	−9.92775	+	5.73179i	−0.325194	+	0.187751i
$933$		0			0
$934$		−	37.2738i		−	1.21964i
$935$	−4.84400	+	2.79669i	−0.158416	+	0.0914614i
$936$		0			0
$937$			11.9436i			0.390179i	0.980785	+	0.195090i	$0.0624997\pi$
$937$			11.9436i			0.390179i	−0.980785	+	0.195090i	$0.937500\pi$
$938$		0			0
$939$		0			0
$940$	2.69991			0.0880614
$941$	−12.5159	+	21.6781i	−0.408006	+	0.706686i	−0.994666	−	0.103146i	$-0.967109\pi$
$941$	−12.5159	+	21.6781i	−0.408006	+	0.706686i	0.586661	+	0.809833i	$0.300442\pi$
$942$		0			0
$943$	15.2688	−	8.81546i	0.497221	−	0.287071i
$944$	−14.4162			−0.469208
$945$		0			0
$946$	−29.4663			−0.958032
$947$	−28.3671	+	16.3777i	−0.921806	+	0.532205i	−0.884211	−	0.467088i	$-0.845303\pi$
$947$	−28.3671	+	16.3777i	−0.921806	+	0.532205i	−0.0375955	+	0.999293i	$0.511970\pi$
$948$		0			0
$949$	−30.2658	+	52.4219i	−0.982470	+	1.70169i
$950$	20.2676			0.657566
$951$		0			0
$952$		0			0
$953$			6.77705i			0.219530i	0.993958	+	0.109765i	$0.0350099\pi$
$953$			6.77705i			0.219530i	−0.993958	+	0.109765i	$0.964990\pi$
$954$		0			0
$955$	−11.3353	+	6.54443i	−0.366801	+	0.211773i
$956$		−	37.9178i		−	1.22635i
$957$		0			0
$958$	38.5512	−	22.2575i	1.24553	−	0.719109i
$959$		0			0
$960$		0			0
$961$	0.558897	+	0.968037i	0.0180289	+	0.0312270i
$962$	−37.5492	−	65.0371i	−1.21063	−	2.09688i
$963$		0			0
$964$	26.3203	+	15.1960i	0.847721	+	0.489432i
$965$	5.45236	−	9.44377i	0.175518	−	0.304006i
$966$		0			0
$967$	20.7901	+	36.0096i	0.668566	+	1.15799i	0.978305	+	0.207169i	$0.0664249\pi$
$967$	20.7901	+	36.0096i	0.668566	+	1.15799i	−0.309739	+	0.950822i	$0.600242\pi$
$968$		−	20.3531i		−	0.654173i
$969$		0			0
$970$	−19.6582			−0.631187
$971$	−20.6257	+	35.7248i	−0.661910	+	1.14646i	0.318203	+	0.948023i	$0.396921\pi$
$971$	−20.6257	+	35.7248i	−0.661910	+	1.14646i	−0.980113	+	0.198439i	$0.936413\pi$
$972$		0			0
$973$		0			0
$974$	43.3281	+	25.0155i	1.38832	+	0.801547i
$975$		0			0
$976$	44.7354	+	25.8280i	1.43195	+	0.826734i
$977$	3.96507	+	2.28924i	0.126854	+	0.0732391i	0.562084	−	0.827080i	$-0.310000\pi$
$977$	3.96507	+	2.28924i	0.126854	+	0.0732391i	−0.435230	+	0.900319i	$0.643333\pi$
$978$		0			0
$979$	19.9192	+	11.5004i	0.636621	+	0.367553i
$980$		0			0
$981$		0			0
$982$	14.0569	−	24.3473i	0.448575	−	0.776955i
$983$	24.4801			0.780794			0.390397	−	0.920647i	$-0.372338\pi$
$983$	24.4801			0.780794			0.390397	+	0.920647i	$0.372338\pi$
$984$		0			0
$985$		−	12.0787i		−	0.384860i
$986$	11.0995	+	19.2249i	0.353480	+	0.612245i
$987$		0			0
$988$	−8.39312	+	14.5373i	−0.267021	+	0.462494i
$989$	−3.85589	−	2.22620i	−0.122610	−	0.0707890i
$990$		0			0
$991$	21.0927	+	36.5337i	0.670032	+	1.16053i	0.977894	+	0.209099i	$0.0670531\pi$
$991$	21.0927	+	36.5337i	0.670032	+	1.16053i	−0.307862	+	0.951431i	$0.599614\pi$
$992$	18.6142	+	32.2407i	0.591001	+	1.02364i
$993$		0			0
$994$		0			0
$995$	10.0884	−	5.82452i	0.319822	−	0.184650i
$996$		0			0
$997$		−	9.67834i		−	0.306516i	−0.988186	−	0.153258i	$-0.951023\pi$
$997$		−	9.67834i		−	0.306516i	0.988186	−	0.153258i	$-0.0489765\pi$
$998$	−16.3578	+	9.44415i	−0.517796	+	0.298949i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.s.d.656.18		48
3.2	odd	2		441.2.s.d.362.7		48
7.2	even	3		1323.2.o.e.440.8		48
7.3	odd	6		1323.2.i.d.521.15		48
7.4	even	3		1323.2.i.d.521.17		48
7.5	odd	6		1323.2.o.e.440.7		48
7.6	odd	2	inner	1323.2.s.d.656.17		48
9.4	even	3		441.2.i.d.68.17		48
9.5	odd	6		1323.2.i.d.1097.15		48
21.2	odd	6		441.2.o.e.146.17	✓	48
21.5	even	6		441.2.o.e.146.18	yes	48
21.11	odd	6		441.2.i.d.227.8		48
21.17	even	6		441.2.i.d.227.7		48
21.20	even	2		441.2.s.d.362.8		48
63.4	even	3		441.2.s.d.374.8		48
63.5	even	6		1323.2.o.e.881.8		48
63.13	odd	6		441.2.i.d.68.18		48
63.23	odd	6		1323.2.o.e.881.7		48
63.31	odd	6		441.2.s.d.374.7		48
63.32	odd	6	inner	1323.2.s.d.962.17		48
63.40	odd	6		441.2.o.e.293.17	yes	48
63.41	even	6		1323.2.i.d.1097.17		48
63.58	even	3		441.2.o.e.293.18	yes	48
63.59	even	6	inner	1323.2.s.d.962.18		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.17		48	9.4	even	3
441.2.i.d.68.18		48	63.13	odd	6
441.2.i.d.227.7		48	21.17	even	6
441.2.i.d.227.8		48	21.11	odd	6
441.2.o.e.146.17	✓	48	21.2	odd	6
441.2.o.e.146.18	yes	48	21.5	even	6
441.2.o.e.293.17	yes	48	63.40	odd	6
441.2.o.e.293.18	yes	48	63.58	even	3
441.2.s.d.362.7		48	3.2	odd	2
441.2.s.d.362.8		48	21.20	even	2
441.2.s.d.374.7		48	63.31	odd	6
441.2.s.d.374.8		48	63.4	even	3
1323.2.i.d.521.15		48	7.3	odd	6
1323.2.i.d.521.17		48	7.4	even	3
1323.2.i.d.1097.15		48	9.5	odd	6
1323.2.i.d.1097.17		48	63.41	even	6
1323.2.o.e.440.7		48	7.5	odd	6
1323.2.o.e.440.8		48	7.2	even	3
1323.2.o.e.881.7		48	63.23	odd	6
1323.2.o.e.881.8		48	63.5	even	6
1323.2.s.d.656.17		48	7.6	odd	2	inner
1323.2.s.d.656.18		48	1.1	even	1	trivial
1323.2.s.d.962.17		48	63.32	odd	6	inner
1323.2.s.d.962.18		48	63.59	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.58658 - 0.916012i) q^{2} +(0.678156 - 1.17460i) q^{4} +0.645568 q^{5} +1.17925i q^{8} +O(q^{10})\)	\(q+(1.58658 - 0.916012i) q^{2} +(0.678156 - 1.17460i) q^{4} +0.645568 q^{5} +1.17925i q^{8} +(1.02425 - 0.591348i) q^{10} +5.31595i q^{11} +(4.44045 - 2.56370i) q^{13} +(2.43652 + 4.22018i) q^{16} +(0.814931 + 1.41150i) q^{17} +(-2.09039 - 1.20689i) q^{19} +(0.437796 - 0.758285i) q^{20} +(4.86947 + 8.43418i) q^{22} +1.47157i q^{23} -4.58324 q^{25} +(4.69675 - 8.13502i) q^{26} +(6.43846 + 3.71724i) q^{29} +(4.90799 + 2.83363i) q^{31} +(5.68894 + 3.28451i) q^{32} +(2.58590 + 1.49297i) q^{34} +(3.99736 - 6.92362i) q^{37} -4.42210 q^{38} +0.761288i q^{40} +(-5.99052 - 10.3759i) q^{41} +(-1.51281 + 2.62026i) q^{43} +(6.24412 + 3.60504i) q^{44} +(1.34797 + 2.33476i) q^{46} +(1.54176 + 2.67041i) q^{47} +(-7.27168 + 4.19830i) q^{50} -6.95434i q^{52} +(2.04554 - 1.18100i) q^{53} +3.43181i q^{55} +13.6202 q^{58} +(-1.47918 + 2.56202i) q^{59} +(9.18018 - 5.30018i) q^{61} +10.3825 q^{62} +2.28853 q^{64} +(2.86662 - 1.65504i) q^{65} +(5.07747 - 8.79444i) q^{67} +2.21060 q^{68} +4.76597i q^{71} +(-10.2239 + 5.90277i) q^{73} -14.6465i q^{74} +(-2.83523 + 1.63692i) q^{76} +(-3.48104 - 6.02934i) q^{79} +(1.57294 + 2.72441i) q^{80} +(-19.0089 - 10.9748i) q^{82} +(-3.51618 + 6.09021i) q^{83} +(0.526093 + 0.911221i) q^{85} +5.54300i q^{86} -6.26884 q^{88} +(2.16337 - 3.74706i) q^{89} +(1.72850 + 0.997953i) q^{92} +(4.89226 + 2.82455i) q^{94} +(-1.34949 - 0.779129i) q^{95} +(-14.3946 - 8.31075i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4}+O(q^{10}) \) 48 * q + 24 * q^4	\( 48 q + 24 q^{4} - 24 q^{16} + 48 q^{25} + 120 q^{32} - 96 q^{44} - 48 q^{50} - 48 q^{53} - 48 q^{64} + 120 q^{65} - 24 q^{79} - 24 q^{85} + 144 q^{92} + 96 q^{95}+O(q^{100}) \) 48 * q + 24 * q^4 - 24 * q^16 + 48 * q^25 + 120 * q^32 - 96 * q^44 - 48 * q^50 - 48 * q^53 - 48 * q^64 + 120 * q^65 - 24 * q^79 - 24 * q^85 + 144 * q^92 + 96 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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