LMFDB - Embedded newform 1323.2.s.d.962.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1323,2,Mod(656,1323)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1323, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1323.656"); 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:traces = [48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

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

Embedding invariants

Embedding label			962.18
Character	$\chi$	$=$	1323.962
Dual form			1323.2.s.d.656.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

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

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

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 $

$2$	1.58658	+	0.916012i	1.12188	+	0.647718i	0.941880	−	0.335948i	$-0.109057\pi$
$2$	1.58658	+	0.916012i	1.12188	+	0.647718i	0.180001	+	0.983667i	$0.442390\pi$
$3$		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	$-0.704084\pi$
$11$		−	5.31595i		−	1.60282i	0.598116	−	0.801410i	$-0.295916\pi$
$12$		0			0
$13$	4.44045	+	2.56370i	1.23156	+	0.711041i	0.967355	−	0.253425i	$-0.0815572\pi$
$13$	4.44045	+	2.56370i	1.23156	+	0.711041i	0.264205	+	0.964467i	$0.414890\pi$
$14$		0			0
$15$		0			0
$16$	2.43652	−	4.22018i	0.609130	−	1.05504i
$17$	0.814931	−	1.41150i	0.197650	−	0.342339i	−0.750116	−	0.661306i	$-0.770002\pi$
$17$	0.814931	−	1.41150i	0.197650	−	0.342339i	0.947766	+	0.318967i	$0.103336\pi$
$18$		0			0
$19$	−2.09039	+	1.20689i	−0.479569	+	0.276879i	−0.720237	−	0.693728i	$-0.755967\pi$
$19$	−2.09039	+	1.20689i	−0.479569	+	0.276879i	0.240668	+	0.970608i	$0.422634\pi$
$20$	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	$-0.950971\pi$
$23$		−	1.47157i		−	0.306843i	0.988161	−	0.153422i	$-0.0490292\pi$
$24$		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	0.236022	−	0.971748i	$-0.424156\pi$
$29$	6.43846	−	3.71724i	1.19559	−	0.690275i	0.959569	+	0.281473i	$0.0908229\pi$
$30$		0			0
$31$	4.90799	−	2.83363i	0.881501	−	0.508935i	0.0103477	−	0.999946i	$-0.496706\pi$
$31$	4.90799	−	2.83363i	0.881501	−	0.508935i	0.871153	+	0.491012i	$0.163373\pi$
$32$	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	0.981347	+	0.192244i	$0.0615763\pi$
$37$	3.99736	+	6.92362i	0.657161	+	1.13824i	−0.324186	+	0.945993i	$0.605090\pi$
$38$	−4.42210			−0.717359
$39$		0			0
$40$		−	0.761288i		−	0.120370i
$41$	−5.99052	+	10.3759i	−0.935562	+	1.62044i	−0.161934	+	0.986802i	$0.551773\pi$
$41$	−5.99052	+	10.3759i	−0.935562	+	1.62044i	−0.773628	+	0.633640i	$0.781560\pi$
$42$		0			0
$43$	−1.51281	−	2.62026i	−0.230701	−	0.399586i	0.727314	−	0.686305i	$-0.240769\pi$
$43$	−1.51281	−	2.62026i	−0.230701	−	0.399586i	−0.958015	+	0.286719i	$0.907435\pi$
$44$	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	−0.731397	−	0.681952i	$-0.761131\pi$
$47$	1.54176	−	2.67041i	0.224889	−	0.389520i	0.956286	+	0.292432i	$0.0944646\pi$
$48$		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	0.633866	−	0.773443i	$-0.281467\pi$
$53$	2.04554	+	1.18100i	0.280977	+	0.162222i	−0.352889	+	0.935665i	$0.614801\pi$
$54$		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	0.753529	−	0.657414i	$-0.228350\pi$
$59$	−1.47918	−	2.56202i	−0.192573	−	0.333546i	−0.946102	+	0.323868i	$0.895017\pi$
$60$		0			0
$61$	9.18018	+	5.30018i	1.17540	+	0.678618i	0.954946	−	0.296779i	$-0.0959124\pi$
$61$	9.18018	+	5.30018i	1.17540	+	0.678618i	0.220455	+	0.975397i	$0.429246\pi$
$62$	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	0.989428	+	0.145028i	$0.0463273\pi$
$67$	5.07747	+	8.79444i	0.620312	+	1.07441i	−0.369116	+	0.929383i	$0.620339\pi$
$68$	2.21060			0.268075
$69$		0			0
$70$		0			0
$71$		−	4.76597i		−	0.565617i	−0.959176	−	0.282808i	$-0.908734\pi$
$71$		−	4.76597i		−	0.565617i	0.959176	−	0.282808i	$-0.0912661\pi$
$72$		0			0
$73$	−10.2239	−	5.90277i	−1.19662	−	0.690867i	−0.236817	−	0.971554i	$-0.576104\pi$
$73$	−10.2239	−	5.90277i	−1.19662	−	0.690867i	−0.959799	+	0.280687i	$0.909438\pi$
$74$			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	−0.992667	−	0.120881i	$-0.961428\pi$
$79$	−3.48104	+	6.02934i	−0.391648	+	0.678354i	0.601019	+	0.799235i	$0.294762\pi$
$80$	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	0.605949	−	0.795503i	$-0.292793\pi$
$83$	−3.51618	−	6.09021i	−0.385951	−	0.668487i	−0.991901	+	0.127016i	$0.959460\pi$
$84$		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	0.957606	−	0.288082i	$-0.0930176\pi$
$89$	2.16337	+	3.74706i	0.229317	+	0.397188i	−0.728289	+	0.685270i	$0.759684\pi$
$90$		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	−0.999083	−	0.0428048i	$-0.986371\pi$
$97$	−14.3946	+	8.31075i	−1.46156	+	0.843829i	−0.462472	+	0.886634i	$0.653037\pi$
$98$		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	$0.169489\pi$
$103$			10.3043i			1.01532i	−0.861559	+	0.507658i	$0.830511\pi$
$104$	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	−0.487028	−	0.873386i	$-0.661919\pi$
$107$	0.267212	−	0.154275i	0.0258324	−	0.0149143i	0.512861	+	0.858472i	$0.328586\pi$
$108$		0			0
$109$	3.14423	−	5.44596i	0.301162	−	0.521628i	−0.675237	−	0.737601i	$-0.735959\pi$
$109$	3.14423	−	5.44596i	0.301162	−	0.521628i	0.976399	+	0.215972i	$0.0692921\pi$
$110$	3.14358	−	5.44484i	0.299728	−	0.519145i
$111$		0			0
$112$		0			0
$113$	−7.72869	−	4.46216i	−0.727054	−	0.419765i	0.0902895	−	0.995916i	$-0.471221\pi$
$113$	−7.72869	−	4.46216i	−0.727054	−	0.419765i	−0.817343	+	0.576151i	$0.804554\pi$
$114$		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	$-0.983500\pi$
$137$		−	1.21291i		−	0.103626i	0.998657	−	0.0518131i	$-0.0165000\pi$
$138$		0			0
$139$	−6.11754	−	3.53196i	−0.518883	−	0.299577i	0.217594	−	0.976039i	$-0.430179\pi$
$139$	−6.11754	−	3.53196i	−0.518883	−	0.299577i	−0.736478	+	0.676462i	$0.763512\pi$
$140$		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	$0.0916343\pi$
$149$			6.93132i			0.567836i	−0.958849	+	0.283918i	$0.908366\pi$
$150$		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	−0.567201	−	0.823579i	$-0.691974\pi$
$157$	−1.72363	+	0.995139i	−0.137561	+	0.0794208i	0.429640	+	0.903000i	$0.358640\pi$
$158$	−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	0.959122	−	0.282994i	$-0.0913278\pi$
$163$	2.99365	+	5.18515i	0.234480	+	0.406132i	−0.724641	+	0.689126i	$0.757994\pi$
$164$	−16.2500			−1.26891
$165$		0			0
$166$		−	12.8835i		−	0.999951i
$167$	0.697990	−	1.20895i	0.0540121	−	0.0935516i	−0.837755	−	0.546046i	$-0.816132\pi$
$167$	0.697990	−	1.20895i	0.0540121	−	0.0935516i	0.891767	+	0.452494i	$0.149466\pi$
$168$		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	−0.973641	−	0.228085i	$-0.926754\pi$
$173$	−3.80506	+	6.59055i	−0.289293	+	0.501071i	0.684348	+	0.729156i	$0.260087\pi$
$174$		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	0.169883	−	0.985464i	$-0.445661\pi$
$179$	−8.00888	−	4.62393i	−0.598612	−	0.345609i	−0.768495	+	0.639855i	$0.778994\pi$
$180$		0			0
$181$		−	11.9634i		−	0.889234i	−0.895721	−	0.444617i	$-0.853340\pi$
$181$		−	11.9634i		−	0.889234i	0.895721	−	0.444617i	$-0.146660\pi$
$182$		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	−0.295415	−	0.955369i	$-0.595458\pi$
$191$	−17.5586	−	10.1375i	−1.27050	−	0.733521i	−0.975081	+	0.221847i	$0.928791\pi$
$192$		0			0
$193$	8.44583	+	14.6286i	0.607944	+	1.05299i	0.991579	+	0.129505i	$0.0413389\pi$
$193$	8.44583	+	14.6286i	0.607944	+	1.05299i	−0.383634	+	0.923485i	$0.625328\pi$
$194$	−30.4510			−2.18625
$195$		0			0
$196$		0			0
$197$			18.7102i			1.33305i	0.745484	+	0.666524i	$0.232219\pi$
$197$			18.7102i			1.33305i	−0.745484	+	0.666524i	$0.767781\pi$
$198$		0			0
$199$	15.6271	+	9.02231i	1.10778	+	0.639574i	0.938252	−	0.345952i	$-0.112444\pi$
$199$	15.6271	+	9.02231i	1.10778	+	0.639574i	0.169523	+	0.985526i	$0.445777\pi$
$200$			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	−0.970831	−	0.239763i	$-0.922930\pi$
$211$	−4.03491	+	6.98868i	−0.277775	+	0.481120i	0.693057	+	0.720883i	$0.256264\pi$
$212$			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	−0.989041	−	0.147638i	$-0.952833\pi$
$223$	−20.2450	+	11.6884i	−1.35570	+	0.782716i	−0.366662	+	0.930354i	$0.619500\pi$
$224$		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	$-0.857353\pi$
$229$		−	13.1137i		−	0.866578i	0.901255	−	0.433289i	$-0.142647\pi$
$230$	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	−0.720219	−	0.693746i	$-0.755959\pi$
$233$	−7.31966	+	4.22601i	−0.479527	+	0.276855i	0.240692	+	0.970601i	$0.422626\pi$
$234$		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	0.996619	+	0.0821642i	$0.0261832\pi$
$239$	24.2111	+	13.9783i	1.56608	+	0.904179i	0.569466	+	0.822015i	$0.307150\pi$
$240$		0			0
$241$		−	22.4079i		−	1.44342i	−0.692196	−	0.721710i	$-0.743357\pi$
$241$		−	22.4079i		−	1.44342i	0.692196	−	0.721710i	$-0.256643\pi$
$242$	−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	$-0.753376\pi$
$263$		−	22.6901i		−	1.39913i	0.714567	−	0.699567i	$-0.246624\pi$
$264$		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	−0.905038	−	0.425332i	$-0.860157\pi$
$269$	−1.38050	+	2.39110i	−0.0841707	+	0.145788i	0.820867	+	0.571120i	$0.193491\pi$
$270$		0			0
$271$	5.27342	−	3.04461i	0.320337	−	0.184947i	−0.331206	−	0.943559i	$-0.607455\pi$
$271$	5.27342	−	3.04461i	0.320337	−	0.184947i	0.651543	+	0.758612i	$0.274122\pi$
$272$	−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	−0.630121	−	0.776497i	$-0.716995\pi$
$281$	−4.57153	+	2.63938i	−0.272715	+	0.157452i	0.357406	+	0.933949i	$0.383661\pi$
$282$		0			0
$283$	−17.0346	+	9.83496i	−1.01260	+	0.584628i	−0.911953	−	0.410294i	$-0.865426\pi$
$283$	−17.0346	+	9.83496i	−1.01260	+	0.584628i	−0.100651	+	0.994922i	$0.532093\pi$
$284$	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	0.466686	+	0.884423i	$0.345448\pi$
$293$	−9.11647	+	15.7902i	−0.532590	+	0.922473i	−0.999276	+	0.0380495i	$0.987886\pi$
$294$		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	$0.266704\pi$
$307$			26.0447i			1.48645i	−0.669042	+	0.743224i	$0.733296\pi$
$308$		0			0
$309$		0			0
$310$	6.70265			0.380685
$311$	14.1433	+	24.4969i	0.801992	+	1.38909i	0.918303	+	0.395878i	$0.129560\pi$
$311$	14.1433	+	24.4969i	0.801992	+	1.38909i	−0.116311	+	0.993213i	$0.537107\pi$
$312$		0			0
$313$	−4.82891	−	2.78797i	−0.272946	−	0.157586i	0.357280	−	0.933998i	$-0.383704\pi$
$313$	−4.82891	−	2.78797i	−0.272946	−	0.157586i	−0.630226	+	0.776412i	$0.717038\pi$
$314$	−3.64624			−0.205769
$315$		0			0
$316$	−9.44276			−0.531197
$317$	29.0708	+	16.7841i	1.63278	+	0.942686i	0.983230	+	0.182367i	$0.0583760\pi$
$317$	29.0708	+	16.7841i	1.63278	+	0.942686i	0.649550	+	0.760319i	$0.274957\pi$
$318$		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	−0.0595042	−	0.998228i	$-0.518952\pi$
$331$	15.1867	−	26.3042i	0.834739	−	1.44581i	0.894243	−	0.447582i	$-0.147715\pi$
$332$	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	−0.810870	−	0.585227i	$-0.801005\pi$
$337$	1.86121	−	3.22371i	0.101387	−	0.175607i	0.912256	+	0.409620i	$0.134339\pi$
$338$			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	−0.324854	−	0.945764i	$-0.605315\pi$
$347$	6.18028	−	3.56818i	0.331775	−	0.191550i	0.656629	+	0.754214i	$0.271982\pi$
$348$		0			0
$349$	13.2087	−	7.62607i	0.707047	−	0.408214i	−0.102920	−	0.994690i	$-0.532818\pi$
$349$	13.2087	−	7.62607i	0.707047	−	0.408214i	0.809967	+	0.586476i	$0.199485\pi$
$350$		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	−0.643716	−	0.765265i	$-0.722608\pi$
$359$	−5.73791	+	3.31278i	−0.302835	+	0.174842i	0.340881	+	0.940107i	$0.389275\pi$
$360$		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	$-0.974241\pi$
$367$		−	3.09716i		−	0.161670i	0.996727	−	0.0808352i	$-0.0257587\pi$
$368$	−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	$-0.947907\pi$
$389$		−	6.42681i		−	0.325852i	0.986638	−	0.162926i	$-0.0520932\pi$
$390$		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	−0.183339	−	0.983050i	$-0.558690\pi$
$397$	11.4835	−	6.62998i	0.576338	−	0.332749i	0.759677	+	0.650301i	$0.225357\pi$
$398$	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	$-0.870871\pi$
$401$		−	15.8052i		−	0.789273i	0.918837	−	0.394636i	$-0.129129\pi$
$402$		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	−0.611509	−	0.791237i	$-0.709437\pi$
$409$	−4.69257	+	2.70926i	−0.232033	+	0.133964i	0.379477	+	0.925201i	$0.376104\pi$
$410$	−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	0.394770	+	0.918780i	$0.370824\pi$
$419$	−12.2469	+	21.2123i	−0.598302	+	1.03629i	−0.993072	+	0.117509i	$0.962509\pi$
$420$		0			0
$421$	5.99347	+	10.3810i	0.292104	+	0.505939i	0.974307	−	0.225224i	$-0.0723113\pi$
$421$	5.99347	+	10.3810i	0.292104	+	0.505939i	−0.682203	+	0.731163i	$0.738978\pi$
$422$	−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	0.977891	−	0.209117i	$-0.0670590\pi$
$431$	26.6926	+	15.4110i	1.28574	+	0.742320i	0.307845	+	0.951437i	$0.400392\pi$
$432$		0			0
$433$		−	6.06173i		−	0.291308i	−0.989336	−	0.145654i	$-0.953471\pi$
$433$		−	6.06173i		−	0.291308i	0.989336	−	0.145654i	$-0.0465287\pi$
$434$		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	−0.180075	−	0.983653i	$-0.557634\pi$
$439$	−23.5081	−	13.5724i	−1.12198	−	0.647776i	−0.941906	+	0.335877i	$0.890967\pi$
$440$	−4.04697			−0.192932
$441$		0			0
$442$	15.3101			0.728228
$443$	−4.63465	−	2.67582i	−0.220199	−	0.127132i	0.385843	−	0.922564i	$-0.373910\pi$
$443$	−4.63465	−	2.67582i	−0.220199	−	0.127132i	−0.606042	+	0.795432i	$0.707244\pi$
$444$		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	$-0.700558\pi$
$449$		−	34.2418i		−	1.61597i	0.589204	−	0.807985i	$-0.299442\pi$
$450$		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	−0.618755	−	0.785584i	$-0.712363\pi$
$457$	7.93019	−	13.7355i	0.370958	−	0.642519i	0.989713	+	0.143065i	$0.0456959\pi$
$458$	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	0.673775	−	0.738936i	$-0.264672\pi$
$461$	−6.50676	−	11.2700i	−0.303050	−	0.524898i	−0.976825	+	0.214038i	$0.931338\pi$
$462$		0			0
$463$	−6.01941	+	10.4259i	−0.279746	+	0.484534i	−0.971321	−	0.237770i	$-0.923583\pi$
$463$	−6.01941	+	10.4259i	−0.279746	+	0.484534i	0.691576	+	0.722304i	$0.256917\pi$
$464$		−	36.2286i		−	1.68187i
$465$		0			0
$466$	−15.4843			−0.717297
$467$	10.1728	+	17.6199i	0.470743	+	0.815351i	0.999440	−	0.0334596i	$-0.0106525\pi$
$467$	10.1728	+	17.6199i	0.470743	+	0.815351i	−0.528697	+	0.848811i	$0.677319\pi$
$468$		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	−0.370968	−	0.928646i	$-0.620974\pi$
$487$	13.6546	−	23.6504i	0.618747	−	1.07170i	0.989715	−	0.143055i	$-0.0456927\pi$
$488$	6.25025	−	10.8257i	0.282935	−	0.490058i
$489$		0			0
$490$		0			0
$491$	13.2899	+	7.67290i	0.599763	+	0.346273i	0.768948	−	0.639311i	$-0.220780\pi$
$491$	13.2899	+	7.67290i	0.599763	+	0.346273i	−0.169185	+	0.985584i	$0.554114\pi$
$492$		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	0.0504538	+	0.998726i	$0.483933\pi$
$521$	−19.1664	+	33.1972i	−0.839696	+	1.45440i	−0.890149	+	0.455669i	$0.849400\pi$
$522$		0			0
$523$	23.6468	−	13.6525i	1.03400	−	0.596982i	0.115874	−	0.993264i	$-0.463033\pi$
$523$	23.6468	−	13.6525i	1.03400	−	0.596982i	0.918129	+	0.396282i	$0.129700\pi$
$524$	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	0.575491	−	0.817808i	$-0.304811\pi$
$541$	−9.78052	−	16.9404i	−0.420498	−	0.728323i	−0.995988	+	0.0894853i	$0.971478\pi$
$542$	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	0.998915	+	0.0465723i	$0.0148298\pi$
$547$	12.6246	+	21.8665i	0.539790	+	0.934944i	−0.459125	+	0.888372i	$0.651837\pi$
$548$	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	0.965165	−	0.261642i	$-0.0842640\pi$
$557$	28.8204	+	16.6395i	1.22116	+	0.705036i	0.255994	+	0.966678i	$0.417597\pi$
$558$		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	−0.984742	−	0.174023i	$-0.944323\pi$
$563$	−15.2587	−	26.4289i	−0.643079	−	1.11385i	0.341663	−	0.939823i	$-0.389010\pi$
$564$		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	0.753925	−	0.656960i	$-0.228158\pi$
$569$	13.4044	+	7.73906i	0.561943	+	0.324438i	−0.191982	+	0.981398i	$0.561491\pi$
$570$		0			0
$571$	12.2042	+	21.1384i	0.510731	+	0.884613i	0.999923	+	0.0124362i	$0.00395868\pi$
$571$	12.2042	+	21.1384i	0.510731	+	0.884613i	−0.489191	+	0.872177i	$0.662708\pi$
$572$	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	0.740322	−	0.672252i	$-0.234673\pi$
$577$	12.6901	+	7.32664i	0.528296	+	0.305012i	−0.212026	+	0.977264i	$0.568006\pi$
$578$			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	0.520404	−	0.853920i	$-0.325781\pi$
$587$	−11.6129	−	20.1141i	−0.479314	−	0.830197i	−0.999719	+	0.0237232i	$0.992448\pi$
$588$		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	0.957263	−	0.289220i	$-0.0933958\pi$
$593$	5.55605	+	9.62337i	0.228160	+	0.395184i	−0.729103	+	0.684404i	$0.760062\pi$
$594$		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	−0.750721	−	0.660620i	$-0.770294\pi$
$599$	−13.5581	+	7.82776i	−0.553968	+	0.319833i	0.196753	+	0.980453i	$0.436960\pi$
$600$		0			0
$601$	−30.5665	+	17.6476i	−1.24684	+	0.719861i	−0.970477	−	0.241194i	$-0.922461\pi$
$601$	−30.5665	+	17.6476i	−1.24684	+	0.719861i	−0.276358	+	0.961055i	$0.589128\pi$
$602$		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	$0.288637\pi$
$607$			38.8051i			1.57505i	−0.616284	+	0.787524i	$0.711363\pi$
$608$	−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	0.343806	+	0.939041i	$0.388284\pi$
$613$	−15.8786	+	27.5025i	−0.641330	+	1.11082i	−0.985136	+	0.171776i	$0.945049\pi$
$614$	−23.8572	+	41.3220i	−0.962800	+	1.66762i
$615$		0			0
$616$		0			0
$617$	−1.25518	−	0.724680i	−0.0505317	−	0.0291745i	0.474521	−	0.880244i	$-0.342621\pi$
$617$	−1.25518	−	0.724680i	−0.0505317	−	0.0291745i	−0.525053	+	0.851070i	$0.675955\pi$
$618$		0			0
$619$			29.1666i			1.17230i	0.810201	+	0.586152i	$0.199358\pi$
$619$			29.1666i			1.17230i	−0.810201	+	0.586152i	$0.800642\pi$
$620$	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	$0.0734305\pi$
$641$			11.5778i			0.457296i	−0.973509	+	0.228648i	$0.926569\pi$
$642$		0			0
$643$	13.1240	+	7.57712i	0.517558	+	0.298812i	0.735935	−	0.677052i	$-0.236743\pi$
$643$	13.1240	+	7.57712i	0.517558	+	0.298812i	−0.218377	+	0.975865i	$0.570076\pi$
$644$		0			0
$645$		0			0
$646$	−3.60370	+	6.24180i	−0.141786	+	0.245580i
$647$	6.22057	−	10.7743i	0.244556	−	0.423583i	−0.717451	−	0.696609i	$-0.754691\pi$
$647$	6.22057	−	10.7743i	0.244556	−	0.423583i	0.962007	+	0.273026i	$0.0880246\pi$
$648$		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	$-0.971410\pi$
$653$		−	4.58431i		−	0.179398i	0.995969	−	0.0896990i	$-0.0285905\pi$
$654$		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	−0.772228	−	0.635345i	$-0.780858\pi$
$659$	−15.6110	+	9.01301i	−0.608118	+	0.351097i	0.164111	+	0.986442i	$0.447525\pi$
$660$		0			0
$661$	0.554932	−	0.320390i	0.0215844	−	0.0124617i	−0.489169	−	0.872189i	$-0.662700\pi$
$661$	0.554932	−	0.320390i	0.0215844	−	0.0124617i	0.510753	+	0.859727i	$0.329367\pi$
$662$	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	0.569880	−	0.821728i	$-0.306990\pi$
$673$	−11.0695	−	19.1729i	−0.426697	−	0.739061i	−0.996577	+	0.0826667i	$0.973656\pi$
$674$	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	−0.606815	−	0.794843i	$-0.707553\pi$
$677$	10.0160	−	17.3482i	0.384947	−	0.666747i	0.991762	+	0.128096i	$0.0408865\pi$
$678$		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	0.111243	−	0.993793i	$-0.464517\pi$
$683$	−18.1316	−	10.4683i	−0.693786	−	0.400558i	−0.805029	+	0.593235i	$0.797850\pi$
$684$		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	0.474406	−	0.880306i	$-0.342663\pi$
$691$	−1.33430	−	0.770358i	−0.0507591	−	0.0293058i	−0.525165	+	0.851001i	$0.675996\pi$
$692$	−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	$0.204025\pi$
$701$			31.6641i			1.19593i	−0.801520	+	0.597967i	$0.795975\pi$
$702$		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	−0.995912	−	0.0903259i	$-0.971209\pi$
$709$	−11.1762	+	19.3578i	−0.419732	+	0.726996i	0.576181	+	0.817322i	$0.304542\pi$
$710$	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	−0.958757	−	0.284226i	$-0.908264\pi$
$719$	−19.4544	−	33.6959i	−0.725525	−	1.25665i	0.233232	−	0.972421i	$-0.425070\pi$
$720$		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	−0.272098	−	0.962269i	$-0.587718\pi$
$727$	11.4647	−	6.61915i	0.425202	−	0.245491i	0.697301	+	0.716779i	$0.254384\pi$
$728$		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	$-0.795285\pi$
$733$		−	32.4727i		−	1.19941i	0.800222	−	0.599704i	$-0.204715\pi$
$734$	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	−0.710228	−	0.703972i	$-0.751408\pi$
$739$	6.91965	−	11.9852i	0.254543	−	0.440882i	0.964771	+	0.263090i	$0.0847415\pi$
$740$	−3.50005	+	6.06227i	−0.128665	+	0.222854i
$741$		0			0
$742$		0			0
$743$	−31.8593	−	18.3940i	−1.16880	−	0.674810i	−0.215406	−	0.976525i	$-0.569108\pi$
$743$	−31.8593	−	18.3940i	−1.16880	−	0.674810i	−0.953398	+	0.301715i	$0.902441\pi$
$744$		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	0.852816	−	0.522211i	$-0.174893\pi$
$769$	22.9328	+	13.2402i	0.826976	+	0.477455i	−0.0258399	+	0.999666i	$0.508226\pi$
$770$		0			0
$771$		0			0
$772$	−11.4552	+	19.8410i	−0.412281	+	0.714092i
$773$	−13.1109	+	22.7087i	−0.471566	+	0.816776i	−0.999471	−	0.0325274i	$-0.989644\pi$
$773$	−13.1109	+	22.7087i	−0.471566	+	0.816776i	0.527905	+	0.849303i	$0.322978\pi$
$774$		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	0.0205676	−	0.999788i	$-0.493453\pi$
$787$	25.1554	−	14.5235i	0.896694	−	0.517706i	0.876126	+	0.482082i	$0.160119\pi$
$788$	−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	0.437151	+	0.899388i	$0.355987\pi$
$797$	−15.8184	+	27.3983i	−0.560317	+	0.970498i	−0.997469	+	0.0711097i	$0.977346\pi$
$798$		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	0.963756	−	0.266784i	$-0.0859610\pi$
$809$	34.5466	+	19.9455i	1.21459	+	0.701245i	0.250836	+	0.968029i	$0.419294\pi$
$810$		0			0
$811$		−	28.9516i		−	1.01663i	−0.861172	−	0.508314i	$-0.830269\pi$
$811$		−	28.9516i		−	1.01663i	0.861172	−	0.508314i	$-0.169731\pi$
$812$		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	0.506258	−	0.862382i	$-0.331028\pi$
$821$	0.359377	+	0.207486i	0.0125423	+	0.00724132i	−0.493716	+	0.869623i	$0.664362\pi$
$822$		0			0
$823$	6.54814	+	11.3417i	0.228254	+	0.395347i	0.957291	−	0.289127i	$-0.0933650\pi$
$823$	6.54814	+	11.3417i	0.228254	+	0.395347i	−0.729037	+	0.684475i	$0.760032\pi$
$824$	12.1514			0.423314
$825$		0			0
$826$		0			0
$827$		−	35.2637i		−	1.22624i	−0.789990	−	0.613120i	$-0.789914\pi$
$827$		−	35.2637i		−	1.22624i	0.789990	−	0.613120i	$-0.210086\pi$
$828$		0			0
$829$	−29.0164	−	16.7526i	−1.00778	−	0.581842i	−0.0972388	−	0.995261i	$-0.531001\pi$
$829$	−29.0164	−	16.7526i	−1.00778	−	0.581842i	−0.910541	+	0.413419i	$0.864334\pi$
$830$		−	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	0.933816	+	0.357753i	$0.116457\pi$
$839$	22.4984	+	38.9684i	0.776731	+	1.34534i	−0.157085	+	0.987585i	$0.550210\pi$
$840$		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	−0.203563	−	0.979062i	$-0.565252\pi$
$853$	15.8457	−	9.14854i	0.542548	−	0.313240i	0.746111	+	0.665822i	$0.231919\pi$
$854$		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	$-0.811790\pi$
$859$		−	32.6748i		−	1.11485i	0.830227	−	0.557425i	$-0.188210\pi$
$860$	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	−0.631469	−	0.775401i	$-0.717548\pi$
$863$	−8.09878	+	4.67583i	−0.275686	+	0.159167i	0.355783	+	0.934569i	$0.384214\pi$
$864$		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	−0.658264	−	0.752787i	$-0.728709\pi$
$911$	−10.1252	+	5.84579i	−0.335463	+	0.193680i	0.322801	+	0.946467i	$0.395376\pi$
$912$		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	−0.980743	−	0.195301i	$-0.937432\pi$
$919$	−19.9930	−	34.6289i	−0.659508	−	1.14230i	0.321236	−	0.946999i	$-0.395902\pi$
$920$	−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	−0.742099	−	0.670290i	$-0.766170\pi$
$929$	6.38359	−	11.0567i	0.209439	−	0.362759i	0.951538	+	0.307532i	$0.0995030\pi$
$930$		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	$-0.937500\pi$
$937$		−	11.9436i		−	0.390179i	0.980785	−	0.195090i	$-0.0624997\pi$
$938$		0			0
$939$		0			0
$940$	2.69991			0.0880614
$941$	−12.5159	−	21.6781i	−0.408006	−	0.706686i	0.586661	−	0.809833i	$-0.300442\pi$
$941$	−12.5159	−	21.6781i	−0.408006	−	0.706686i	−0.994666	+	0.103146i	$0.967109\pi$
$942$		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	−0.0375955	−	0.999293i	$-0.511970\pi$
$947$	−28.3671	−	16.3777i	−0.921806	−	0.532205i	−0.884211	+	0.467088i	$0.845303\pi$
$948$		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	$-0.964990\pi$
$953$		−	6.77705i		−	0.219530i	0.993958	−	0.109765i	$-0.0350099\pi$
$954$		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	−0.309739	−	0.950822i	$-0.600242\pi$
$967$	20.7901	−	36.0096i	0.668566	−	1.15799i	0.978305	−	0.207169i	$-0.0664249\pi$
$968$			20.3531i			0.654173i
$969$		0			0
$970$	−19.6582			−0.631187
$971$	−20.6257	−	35.7248i	−0.661910	−	1.14646i	−0.980113	−	0.198439i	$-0.936413\pi$
$971$	−20.6257	−	35.7248i	−0.661910	−	1.14646i	0.318203	−	0.948023i	$-0.396921\pi$
$972$		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	−0.435230	−	0.900319i	$-0.643333\pi$
$977$	3.96507	−	2.28924i	0.126854	−	0.0732391i	0.562084	+	0.827080i	$0.310000\pi$
$978$		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	−0.307862	−	0.951431i	$-0.599614\pi$
$991$	21.0927	−	36.5337i	0.670032	−	1.16053i	0.977894	−	0.209099i	$-0.0670531\pi$
$992$	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	$0.0489765\pi$
$997$			9.67834i			0.306516i	−0.988186	+	0.153258i	$0.951023\pi$
$998$	−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.962.18		48
3.2	odd	2		441.2.s.d.374.7		48
7.2	even	3		1323.2.i.d.1097.17		48
7.3	odd	6		1323.2.o.e.881.7		48
7.4	even	3		1323.2.o.e.881.8		48
7.5	odd	6		1323.2.i.d.1097.15		48
7.6	odd	2	inner	1323.2.s.d.962.17		48
9.2	odd	6		1323.2.i.d.521.15		48
9.7	even	3		441.2.i.d.227.7		48
21.2	odd	6		441.2.i.d.68.18		48
21.5	even	6		441.2.i.d.68.17		48
21.11	odd	6		441.2.o.e.293.17	yes	48
21.17	even	6		441.2.o.e.293.18	yes	48
21.20	even	2		441.2.s.d.374.8		48
63.2	odd	6	inner	1323.2.s.d.656.17		48
63.11	odd	6		1323.2.o.e.440.7		48
63.16	even	3		441.2.s.d.362.8		48
63.20	even	6		1323.2.i.d.521.17		48
63.25	even	3		441.2.o.e.146.18	yes	48
63.34	odd	6		441.2.i.d.227.8		48
63.38	even	6		1323.2.o.e.440.8		48
63.47	even	6	inner	1323.2.s.d.656.18		48
63.52	odd	6		441.2.o.e.146.17	✓	48
63.61	odd	6		441.2.s.d.362.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.17		48	21.5	even	6
441.2.i.d.68.18		48	21.2	odd	6
441.2.i.d.227.7		48	9.7	even	3
441.2.i.d.227.8		48	63.34	odd	6
441.2.o.e.146.17	✓	48	63.52	odd	6
441.2.o.e.146.18	yes	48	63.25	even	3
441.2.o.e.293.17	yes	48	21.11	odd	6
441.2.o.e.293.18	yes	48	21.17	even	6
441.2.s.d.362.7		48	63.61	odd	6
441.2.s.d.362.8		48	63.16	even	3
441.2.s.d.374.7		48	3.2	odd	2
441.2.s.d.374.8		48	21.20	even	2
1323.2.i.d.521.15		48	9.2	odd	6
1323.2.i.d.521.17		48	63.20	even	6
1323.2.i.d.1097.15		48	7.5	odd	6
1323.2.i.d.1097.17		48	7.2	even	3
1323.2.o.e.440.7		48	63.11	odd	6
1323.2.o.e.440.8		48	63.38	even	6
1323.2.o.e.881.7		48	7.3	odd	6
1323.2.o.e.881.8		48	7.4	even	3
1323.2.s.d.656.17		48	63.2	odd	6	inner
1323.2.s.d.656.18		48	63.47	even	6	inner
1323.2.s.d.962.17		48	7.6	odd	2	inner
1323.2.s.d.962.18		48	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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