LMFDB - Embedded newform 441.2.s.d.374.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,2,Mod(362,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, 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("441.362"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			374.8
Character	$\chi$	$=$	441.374
Dual form			441.2.s.d.362.8

$q$-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} +(0.108803 + 1.72863i) q^{3} +(0.678156 + 1.17460i) q^{4} +0.645568 q^{5} +(1.41082 - 2.84227i) q^{6} +1.17925i q^{8} +(-2.97632 + 0.376160i) q^{9} +(-1.02425 - 0.591348i) q^{10} +5.31595i q^{11} +(-1.95666 + 1.30008i) q^{12} +(-4.44045 - 2.56370i) q^{13} +(0.0702397 + 1.11595i) q^{15} +(2.43652 - 4.22018i) q^{16} +(0.814931 - 1.41150i) q^{17} +(5.06674 + 2.12954i) q^{18} +(2.09039 - 1.20689i) q^{19} +(0.437796 + 0.758285i) q^{20} +(4.86947 - 8.43418i) q^{22} +1.47157i q^{23} +(-2.03849 + 0.128306i) q^{24} -4.58324 q^{25} +(4.69675 + 8.13502i) q^{26} +(-0.974073 - 5.10404i) q^{27} +(-6.43846 + 3.71724i) q^{29} +(0.910782 - 1.83488i) q^{30} +(-4.90799 + 2.83363i) q^{31} +(-5.68894 + 3.28451i) q^{32} +(-9.18931 + 0.578390i) q^{33} +(-2.58590 + 1.49297i) q^{34} +(-2.46025 - 3.24090i) q^{36} +(3.99736 + 6.92362i) q^{37} -4.42210 q^{38} +(3.94855 - 7.95484i) q^{39} +0.761288i q^{40} +(-5.99052 + 10.3759i) q^{41} +(-1.51281 - 2.62026i) q^{43} +(-6.24412 + 3.60504i) q^{44} +(-1.92142 + 0.242837i) q^{45} +(1.34797 - 2.33476i) q^{46} +(1.54176 - 2.67041i) q^{47} +(7.56023 + 3.75268i) q^{48} +(7.27168 + 4.19830i) q^{50} +(2.52863 + 1.25514i) q^{51} -6.95434i q^{52} +(-2.04554 - 1.18100i) q^{53} +(-3.12991 + 8.99022i) q^{54} +3.43181i q^{55} +(2.31371 + 3.48220i) q^{57} +13.6202 q^{58} +(-1.47918 - 2.56202i) q^{59} +(-1.26316 + 0.839291i) q^{60} +(-9.18018 - 5.30018i) q^{61} +10.3825 q^{62} +2.28853 q^{64} +(-2.86662 - 1.65504i) q^{65} +(15.1094 + 7.49986i) q^{66} +(5.07747 + 8.79444i) q^{67} +2.21060 q^{68} +(-2.54380 + 0.160111i) q^{69} +4.76597i q^{71} +(-0.443587 - 3.50984i) q^{72} +(10.2239 + 5.90277i) q^{73} -14.6465i q^{74} +(-0.498670 - 7.92273i) q^{75} +(2.83523 + 1.63692i) q^{76} +(-13.5514 + 9.00406i) q^{78} +(-3.48104 + 6.02934i) q^{79} +(1.57294 - 2.72441i) q^{80} +(8.71701 - 2.23915i) q^{81} +(19.0089 - 10.9748i) q^{82} +(-3.51618 - 6.09021i) q^{83} +(0.526093 - 0.911221i) q^{85} +5.54300i q^{86} +(-7.12626 - 10.7253i) q^{87} -6.26884 q^{88} +(2.16337 + 3.74706i) q^{89} +(3.27093 + 1.37476i) q^{90} +(-1.72850 + 0.997953i) q^{92} +(-5.43230 - 8.17579i) q^{93} +(-4.89226 + 2.82455i) q^{94} +(1.34949 - 0.779129i) q^{95} +(-6.29668 - 9.47671i) q^{96} +(14.3946 - 8.31075i) q^{97} +(-1.99965 - 15.8220i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4} - 8 q^{9} - 40 q^{15} - 24 q^{16} + 32 q^{18} + 48 q^{25} + 48 q^{30} - 120 q^{32} - 8 q^{36} - 32 q^{39} + 96 q^{44} + 48 q^{50} + 48 q^{53} + 80 q^{57} - 72 q^{60} - 48 q^{64} - 120 q^{65}+ \cdots - 72 q^{99}+O(q^{100}) $ 48 * q + 24 * q^4 - 8 * q^9 - 40 * q^15 - 24 * q^16 + 32 * q^18 + 48 * q^25 + 48 * q^30 - 120 * q^32 - 8 * q^36 - 32 * q^39 + 96 * q^44 + 48 * q^50 + 48 * q^53 + 80 * q^57 - 72 * q^60 - 48 * q^64 - 120 * q^65 + 32 * q^72 - 88 * q^78 - 24 * q^79 + 120 * q^81 - 24 * q^85 - 144 * q^92 + 16 * q^93 - 96 * q^95 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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	$-0.557610\pi$
$2$	−1.58658	−	0.916012i	−1.12188	−	0.647718i	−0.941880	+	0.335948i	$0.890943\pi$
$3$	0.108803	+	1.72863i	0.0628173	+	0.998025i
$3$	0.108803	+	1.72863i	0.0628173	+	0.998025i
$4$	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	$0.453890\pi$
$6$	1.41082	−	2.84227i	0.575966	−	1.16035i
$7$		0			0
$7$		0			0
$8$			1.17925i			0.416928i
$9$	−2.97632	+	0.376160i	−0.992108	+	0.125387i
$10$	−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	$0.704084\pi$
$12$	−1.95666	+	1.30008i	−0.564840	+	0.375301i
$13$	−4.44045	−	2.56370i	−1.23156	−	0.711041i	−0.264205	−	0.964467i	$-0.585110\pi$
$13$	−4.44045	−	2.56370i	−1.23156	−	0.711041i	−0.967355	+	0.253425i	$0.918443\pi$
$14$		0			0
$15$	0.0702397	+	1.11595i	0.0181358	+	0.288137i
$16$	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	$0.103336\pi$
$18$	5.06674	+	2.12954i	1.19424	+	0.501938i
$19$	2.09039	−	1.20689i	0.479569	−	0.276879i	−0.240668	−	0.970608i	$-0.577366\pi$
$19$	2.09039	−	1.20689i	0.479569	−	0.276879i	0.720237	+	0.693728i	$0.244033\pi$
$20$	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	$0.950971\pi$
$24$	−2.03849	+	0.128306i	−0.416105	+	0.0261903i
$25$	−4.58324			−0.916648
$26$	4.69675	+	8.13502i	0.921109	+	1.59541i
$27$	−0.974073	−	5.10404i	−0.187461	−	0.982272i
$28$		0			0
$29$	−6.43846	+	3.71724i	−1.19559	+	0.690275i	−0.959569	−	0.281473i	$-0.909177\pi$
$29$	−6.43846	+	3.71724i	−1.19559	+	0.690275i	−0.236022	+	0.971748i	$0.575844\pi$
$30$	0.910782	−	1.83488i	0.166285	−	0.335002i
$31$	−4.90799	+	2.83363i	−0.881501	+	0.508935i	−0.871153	−	0.491012i	$-0.836627\pi$
$31$	−4.90799	+	2.83363i	−0.881501	+	0.508935i	−0.0103477	+	0.999946i	$0.503294\pi$
$32$	−5.68894	+	3.28451i	−1.00567	+	0.580625i
$33$	−9.18931	+	0.578390i	−1.59965	+	0.100685i
$34$	−2.58590	+	1.49297i	−0.443479	+	0.256043i
$35$		0			0
$36$	−2.46025	−	3.24090i	−0.410042	−	0.540150i
$37$	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
$39$	3.94855	−	7.95484i	0.632274	−	1.27379i
$40$			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
$45$	−1.92142	+	0.242837i	−0.286428	+	0.0362000i
$46$	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	$0.0944646\pi$
$48$	7.56023	+	3.75268i	1.09122	+	0.541652i
$49$		0			0
$50$	7.27168	+	4.19830i	1.02837	+	0.593730i
$51$	2.52863	+	1.25514i	0.354079	+	0.175755i
$52$		−	6.95434i		−	0.964394i
$53$	−2.04554	−	1.18100i	−0.280977	−	0.162222i	0.352889	−	0.935665i	$-0.385199\pi$
$53$	−2.04554	−	1.18100i	−0.280977	−	0.162222i	−0.633866	+	0.773443i	$0.718533\pi$
$54$	−3.12991	+	8.99022i	−0.425927	+	1.22341i
$55$			3.43181i			0.462745i
$56$		0			0
$57$	2.31371	+	3.48220i	0.306458	+	0.461229i
$58$	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	$0.895017\pi$
$60$	−1.26316	+	0.839291i	−0.163073	+	0.108352i
$61$	−9.18018	−	5.30018i	−1.17540	−	0.678618i	−0.220455	−	0.975397i	$-0.570754\pi$
$61$	−9.18018	−	5.30018i	−1.17540	−	0.678618i	−0.954946	+	0.296779i	$0.904088\pi$
$62$	10.3825			1.31859
$63$		0			0
$64$	2.28853			0.286066
$65$	−2.86662	−	1.65504i	−0.355560	−	0.205283i
$66$	15.1094	+	7.49986i	1.85984	+	0.923169i
$67$	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
$69$	−2.54380	+	0.160111i	−0.306237	+	0.0192751i
$70$		0			0
$71$			4.76597i			0.565617i	0.959176	+	0.282808i	$0.0912661\pi$
$71$			4.76597i			0.565617i	−0.959176	+	0.282808i	$0.908734\pi$
$72$	−0.443587	−	3.50984i	−0.0522772	−	0.413638i
$73$	10.2239	+	5.90277i	1.19662	+	0.690867i	0.959799	−	0.280687i	$-0.0905624\pi$
$73$	10.2239	+	5.90277i	1.19662	+	0.690867i	0.236817	+	0.971554i	$0.423896\pi$
$74$		−	14.6465i		−	1.70262i
$75$	−0.498670	−	7.92273i	−0.0575814	−	0.914838i
$76$	2.83523	+	1.63692i	0.325223	+	0.187767i
$77$		0			0
$78$	−13.5514	+	9.00406i	−1.53440	+	1.01951i
$79$	−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
$81$	8.71701	−	2.23915i	0.968556	−	0.248794i
$82$	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
$87$	−7.12626	−	10.7253i	−0.764015	−	1.14987i
$88$	−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	$0.759684\pi$
$90$	3.27093	+	1.37476i	0.344786	+	0.144913i
$91$		0			0
$92$	−1.72850	+	0.997953i	−0.180209	+	0.104044i
$93$	−5.43230	−	8.17579i	−0.563303	−	0.847790i
$94$	−4.89226	+	2.82455i	−0.504598	+	0.291330i
$95$	1.34949	−	0.779129i	0.138455	−	0.0799370i
$96$	−6.29668	−	9.47671i	−0.642652	−	0.967213i
$97$	14.3946	−	8.31075i	1.46156	−	0.843829i	0.462472	−	0.886634i	$-0.346963\pi$
$97$	14.3946	−	8.31075i	1.46156	−	0.843829i	0.999083	+	0.0428048i	$0.0136294\pi$
$98$		0			0
$99$	−1.99965	−	15.8220i	−0.200972	−	1.59017i
$100$	−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	$0.425662\pi$
$102$	−2.86215	−	4.30763i	−0.283395	−	0.426519i
$103$		−	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	$-0.671414\pi$
$107$	−0.267212	+	0.154275i	−0.0258324	+	0.0149143i	0.487028	+	0.873386i	$0.338081\pi$
$108$	5.33463	−	4.60548i	0.513325	−	0.443163i
$109$	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
$111$	−11.5335	+	7.66326i	−1.09471	+	0.727365i
$112$		0			0
$113$	7.72869	+	4.46216i	0.727054	+	0.419765i	0.817343	−	0.576151i	$-0.195446\pi$
$113$	7.72869	+	4.46216i	0.727054	+	0.419765i	−0.0902895	+	0.995916i	$0.528779\pi$
$114$	−0.481137	−	7.64418i	−0.0450626	−	0.715943i
$115$			0.949998i			0.0885877i
$116$	−8.73256	−	5.04174i	−0.810797	−	0.468114i
$117$	14.1806	+	5.96007i	1.31100	+	0.551009i
$118$			5.41979i			0.498932i
$119$		0			0
$120$	−1.31598	+	0.0828302i	−0.120132	+	0.00756133i
$121$	−17.2593			−1.56903
$122$	9.71006	+	16.8183i	0.879107	+	1.52266i
$123$	−18.5879	−	9.22647i	−1.67601	−	0.831923i
$124$	−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
$129$	4.36486	−	2.90018i	0.384305	−	0.255346i
$130$	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	$0.464684\pi$
$132$	−6.91116	−	10.4015i	−0.601540	−	0.905337i
$133$		0			0
$134$		−	18.6041i		−	1.60715i
$135$	−0.628831	−	3.29500i	−0.0541211	−	0.283589i
$136$	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	$0.983500\pi$
$138$	4.18260	+	2.07612i	0.356046	+	0.176731i
$139$	6.11754	+	3.53196i	0.518883	+	0.299577i	0.736478	−	0.676462i	$-0.236488\pi$
$139$	6.11754	+	3.53196i	0.518883	+	0.299577i	−0.217594	+	0.976039i	$0.569821\pi$
$140$		0			0
$141$	4.78390	+	2.37459i	0.402877	+	0.199977i
$142$	4.36569	−	7.56159i	0.366360	−	0.634555i
$143$	13.6285	−	23.6052i	1.13967	−	1.97397i
$144$	−5.66441	+	13.4771i	−0.472035	+	1.12309i
$145$	−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	$-0.0916343\pi$
$150$	−6.46614	+	13.0268i	−0.527958	+	1.06364i
$151$	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
$153$	−1.89455	+	4.50763i	−0.153165	+	0.364420i
$154$		0			0
$155$	−3.16844	+	1.82930i	−0.254495	+	0.146933i
$156$	12.0215	−	0.756652i	0.962489	−	0.0605807i
$157$	1.72363	−	0.995139i	0.137561	−	0.0794208i	−0.429640	−	0.903000i	$-0.641360\pi$
$157$	1.72363	−	0.995139i	0.137561	−	0.0794208i	0.567201	+	0.823579i	$0.308026\pi$
$158$	11.0459	−	6.37735i	0.878765	−	0.507355i
$159$	1.81894	−	3.66448i	0.144252	−	0.290613i
$160$	−3.67260	+	2.12038i	−0.290345	+	0.167631i
$161$		0			0
$162$	−15.8813	−	4.43230i	−1.24775	−	0.348234i
$163$	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
$165$	−5.93233	+	0.373390i	−0.461831	+	0.0290684i
$166$			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
$171$	−5.76770	+	4.37841i	−0.441067	+	0.334826i
$172$	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	$0.260087\pi$
$174$	1.48191	+	23.5442i	0.112343	+	1.78488i
$175$		0			0
$176$	22.4343	+	12.9524i	1.69105	+	0.976326i
$177$	4.26784	−	2.83571i	0.320790	−	0.213145i
$178$		−	7.92669i		−	0.594130i
$179$	8.00888	+	4.62393i	0.598612	+	0.345609i	0.768495	−	0.639855i	$-0.221006\pi$
$179$	8.00888	+	4.62393i	0.598612	+	0.345609i	−0.169883	+	0.985464i	$0.554339\pi$
$180$	−1.58826	−	2.09222i	−0.118382	−	0.155945i
$181$			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
$183$	8.16322	−	16.4458i	0.603443	−	1.21571i
$184$	−1.73535			−0.127932
$185$	2.58057	+	4.46967i	0.189727	+	0.328617i
$186$	1.12965	+	17.9476i	0.0828300	+	1.31598i
$187$	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	$-0.0712087\pi$
$191$	17.5586	+	10.1375i	1.27050	+	0.733521i	0.295415	+	0.955369i	$0.404542\pi$
$192$	0.248999	+	3.95602i	0.0179699	+	0.285501i
$193$	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
$195$	2.54906	−	5.13539i	0.182542	−	0.367753i
$196$		0			0
$197$		−	18.7102i		−	1.33305i	−0.745484	−	0.666524i	$-0.767781\pi$
$197$		−	18.7102i		−	1.33305i	0.745484	−	0.666524i	$-0.232219\pi$
$198$	−11.3205	+	26.9345i	−0.804515	+	1.91415i
$199$	−15.6271	−	9.02231i	−1.10778	−	0.639574i	−0.169523	−	0.985526i	$-0.554223\pi$
$199$	−15.6271	−	9.02231i	−1.10778	−	0.639574i	−0.938252	+	0.345952i	$0.887556\pi$
$200$		−	5.40480i		−	0.382177i
$201$	−14.6499	+	9.73393i	−1.03332	+	0.686578i
$202$	−7.38004	−	4.26087i	−0.519258	−	0.299794i
$203$		0			0
$204$	0.240520	+	3.82131i	0.0168397	+	0.267545i
$205$	−3.86729	+	6.69834i	−0.270103	+	0.467833i
$206$	−9.43889	+	16.3486i	−0.657639	+	1.13906i
$207$	−0.553544	−	4.37986i	−0.0384740	−	0.304421i
$208$	−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
$213$	−8.23860	+	0.518551i	−0.564500	+	0.0355305i
$214$	0.565272			0.0386412
$215$	−0.976621	−	1.69156i	−0.0666050	−	0.115363i
$216$	6.01894	−	1.14868i	0.409537	−	0.0781576i
$217$		0			0
$218$	−9.97713	+	5.76030i	−0.675736	+	0.390137i
$219$	−9.09132	+	18.3156i	−0.614334	+	1.23765i
$220$	−4.03101	+	2.32730i	−0.271770	+	0.156907i
$221$	−7.23732	+	4.17847i	−0.486835	+	0.281074i
$222$	25.3184	−	1.59358i	1.69926	−	0.106954i
$223$	20.2450	−	11.6884i	1.35570	−	0.782716i	0.366662	−	0.930354i	$-0.380500\pi$
$223$	20.2450	−	11.6884i	1.35570	−	0.782716i	0.989041	+	0.147638i	$0.0471671\pi$
$224$		0			0
$225$	13.6412	−	1.72403i	0.909414	−	0.114935i
$226$	−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	$0.659113\pi$
$228$	−2.52115	+	5.07916i	−0.166967	+	0.336375i
$229$			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	$-0.577374\pi$
$233$	7.31966	−	4.22601i	0.479527	−	0.276855i	0.720219	+	0.693746i	$0.244041\pi$
$234$	−17.0391	−	22.4457i	−1.11388	−	1.46732i
$235$	0.995314	−	1.72393i	0.0649271	−	0.112457i
$236$	2.00623	−	3.47489i	0.130594	−	0.226196i
$237$	−10.8013	−	5.36143i	−0.701617	−	0.348262i
$238$		0			0
$239$	−24.2111	−	13.9783i	−1.56608	−	0.904179i	−0.996619	−	0.0821642i	$-0.973817\pi$
$239$	−24.2111	−	13.9783i	−1.56608	−	0.904179i	−0.569466	−	0.822015i	$-0.692850\pi$
$240$	4.88064	+	2.42261i	0.315044	+	0.156379i
$241$			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
$243$	4.81909	+	14.8249i	0.309145	+	0.951015i
$244$		−	14.3774i		−	0.920418i
$245$		0			0
$246$	21.0396	+	31.6652i	1.34143	+	2.01890i
$247$	−12.3764			−0.787491
$248$	−3.34156	−	5.78775i	−0.212189	−	0.367523i
$249$	10.1451	−	6.74081i	0.642923	−	0.427182i
$250$	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
$255$	1.63240	+	0.810278i	0.102225	+	0.0507415i
$256$	−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	$0.532961\pi$
$258$	−9.58180	+	0.603094i	−0.596537	+	0.0375470i
$259$		0			0
$260$		−	4.48950i		−	0.278427i
$261$	17.7647	−	13.4856i	1.09960	−	0.834738i
$262$	−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	$0.753376\pi$
$264$	−0.682068	−	10.8365i	−0.0419784	−	0.666941i
$265$	−1.32054	−	0.762413i	−0.0811200	−	0.0468347i
$266$		0			0
$267$	−6.24191	+	4.14736i	−0.381999	+	0.253814i
$268$	−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	$0.193491\pi$
$270$	−2.02057	+	5.80380i	−0.122968	+	0.353208i
$271$	−5.27342	+	3.04461i	−0.320337	+	0.184947i	−0.651543	−	0.758612i	$-0.725878\pi$
$271$	−5.27342	+	3.04461i	−0.320337	+	0.184947i	0.331206	+	0.943559i	$0.392545\pi$
$272$	−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
$276$	−1.91316	−	2.87936i	−0.115159	−	0.173317i
$277$	−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
$279$	13.5419	−	10.2800i	0.810730	−	0.615446i
$280$		0			0
$281$	4.57153	−	2.63938i	0.272715	−	0.157452i	−0.357406	−	0.933949i	$-0.616339\pi$
$281$	4.57153	−	2.63938i	0.272715	−	0.157452i	0.630121	+	0.776497i	$0.283005\pi$
$282$	−5.41489	−	8.14959i	−0.322452	−	0.485301i
$283$	17.0346	−	9.83496i	1.01260	−	0.584628i	0.100651	−	0.994922i	$-0.467907\pi$
$283$	17.0346	−	9.83496i	1.01260	−	0.584628i	0.911953	+	0.410294i	$0.134574\pi$
$284$	−5.59811	+	3.23207i	−0.332187	+	0.191788i
$285$	1.49366	+	2.24800i	0.0884765	+	0.133160i
$286$	−43.2453	+	24.9677i	−2.55715	+	1.47637i
$287$		0			0
$288$	15.6966	−	11.9157i	0.924933	−	0.702141i
$289$	7.17178	+	12.4219i	0.421869	+	0.730699i
$290$	8.79274			0.516328
$291$	15.9324	+	23.9788i	0.933974	+	1.40566i
$292$			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
$297$	27.1328	−	5.17812i	1.57440	−	0.300465i
$298$	−6.34917	+	10.9971i	−0.367797	+	0.637044i
$299$	3.77265	−	6.53443i	0.218178	−	0.377896i
$300$	8.96787	−	5.95858i	0.517760	−	0.344019i
$301$		0			0
$302$	−10.0253	−	5.78808i	−0.576888	−	0.333067i
$303$	0.506101	+	8.04079i	0.0290747	+	0.461932i
$304$		−	11.7624i		−	0.674622i
$305$	−5.92643	−	3.42163i	−0.339347	−	0.195922i
$306$	7.13489	−	5.41628i	0.407875	−	0.309628i
$307$		−	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
$309$	17.8124	−	1.12114i	1.01331	−	0.0637795i
$310$	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	$0.537107\pi$
$312$	9.38075	+	4.65633i	0.531081	+	0.263613i
$313$	4.82891	+	2.78797i	0.272946	+	0.157586i	0.630226	−	0.776412i	$-0.282962\pi$
$313$	4.82891	+	2.78797i	0.272946	+	0.157586i	−0.357280	+	0.933998i	$0.616296\pi$
$314$	−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	$-0.941624\pi$
$317$	−29.0708	−	16.7841i	−1.63278	−	0.942686i	−0.649550	−	0.760319i	$-0.725043\pi$
$318$	−6.24261	+	4.14782i	−0.350068	+	0.232598i
$319$	−19.7607	−	34.2265i	−1.10639	−	1.91632i
$320$	1.47740			0.0825893
$321$	−0.295758	−	0.445126i	−0.0165076	−	0.0248445i
$322$		0			0
$323$		−	3.93412i		−	0.218901i
$324$	8.54159	+	8.72051i	0.474533	+	0.484473i
$325$	20.3517	+	11.7500i	1.12891	+	0.651775i
$326$		−	10.9689i		−	0.607509i
$327$	9.75615	+	4.84267i	0.539516	+	0.267800i
$328$	−12.2358	−	7.06433i	−0.675608	−	0.390063i
$329$		0			0
$330$	9.75414	+	4.84167i	0.536948	+	0.266525i
$331$	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
$333$	−14.5018	−	19.1033i	−0.794695	−	1.04685i
$334$	−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
$339$	−6.87252	+	13.8455i	−0.373264	+	0.751986i
$340$	1.42709			0.0773950
$341$	−15.0634	−	26.0906i	−0.815730	−	1.41289i
$342$	13.1616	−	1.66342i	0.711698	−	0.0899472i
$343$		0			0
$344$	3.08995	−	1.78398i	0.166599	−	0.0961858i
$345$	−1.64219	+	0.103362i	−0.0884128	+	0.00556485i
$346$	12.0741	−	6.97096i	0.649105	−	0.374761i
$347$	−6.18028	+	3.56818i	−0.331775	+	0.191550i	−0.656629	−	0.754214i	$-0.728018\pi$
$347$	−6.18028	+	3.56818i	−0.331775	+	0.191550i	0.324854	+	0.945764i	$0.394685\pi$
$348$	7.76518	−	15.6439i	0.416257	−	0.838602i
$349$	−13.2087	+	7.62607i	−0.707047	+	0.408214i	−0.809967	−	0.586476i	$-0.800515\pi$
$349$	−13.2087	+	7.62607i	−0.707047	+	0.408214i	0.102920	+	0.994690i	$0.467182\pi$
$350$		0			0
$351$	−8.75987	+	25.1615i	−0.467567	+	1.34302i
$352$	−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	$0.869695\pi$
$354$	−9.36881	+	0.589688i	−0.497946	+	0.0313416i
$355$			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	$-0.610725\pi$
$359$	5.73791	−	3.31278i	0.302835	−	0.174842i	0.643716	+	0.765265i	$0.277392\pi$
$360$	−0.286366	−	2.26584i	−0.0150928	−	0.119420i
$361$	−6.58684	+	11.4087i	−0.346676	+	0.600460i
$362$	10.9586	−	18.9809i	0.575973	−	0.997614i
$363$	−1.87786	−	29.8350i	−0.0985622	−	1.56593i
$364$		0			0
$365$	6.60022	+	3.81064i	0.345472	+	0.199458i
$366$	−28.0162	+	18.6150i	−1.46443	+	0.973020i
$367$			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
$369$	13.9267	−	33.1354i	0.724997	−	1.72496i
$370$		−	9.45532i		−	0.491559i
$371$		0			0
$372$	5.91934	−	11.9252i	0.306904	−	0.618295i
$373$	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
$375$	−0.673124	−	10.6944i	−0.0347600	−	0.552257i
$376$	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
$381$	−0.271995	−	4.32138i	−0.0139347	−	0.221391i
$382$	−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	$0.283536\pi$
$384$	−6.88876	+	13.8783i	−0.351541	+	0.708222i
$385$		0			0
$386$		−	30.9459i		−	1.57511i
$387$	5.48824	+	7.22969i	0.278983	+	0.367506i
$388$	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	$0.947907\pi$
$390$	−8.74836	+	5.81274i	−0.442991	+	0.294339i
$391$	2.07712	+	1.19923i	0.105044	+	0.0606474i
$392$		0			0
$393$	0.275761	+	4.38121i	0.0139103	+	0.221003i
$394$	−17.1388	+	29.6852i	−0.863439	+	1.49552i
$395$	−2.24725	+	3.89235i	−0.113071	+	0.195846i
$396$	17.2284	−	13.0786i	0.865762	−	0.657222i
$397$	−11.4835	+	6.62998i	−0.576338	+	0.332749i	−0.759677	−	0.650301i	$-0.774643\pi$
$397$	−11.4835	+	6.62998i	−0.576338	+	0.332749i	0.183339	+	0.983050i	$0.441310\pi$
$398$	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	$0.870871\pi$
$402$	32.1596	−	2.02418i	1.60398	−	0.100957i
$403$	29.0582			1.44749
$404$	3.15447	+	5.46370i	0.156941	+	0.271829i
$405$	5.62742	−	1.44552i	0.279629	−	0.0718286i
$406$		0			0
$407$	−36.8056	+	21.2497i	−1.82439	+	1.05331i
$408$	−1.48012	+	2.98189i	−0.0732771	+	0.147626i
$409$	4.69257	−	2.70926i	0.232033	−	0.133964i	−0.379477	−	0.925201i	$-0.623896\pi$
$409$	4.69257	−	2.70926i	0.232033	−	0.133964i	0.611509	+	0.791237i	$0.290563\pi$
$410$	12.2715	−	7.08497i	0.606048	−	0.349902i
$411$	−2.09668	+	0.131968i	−0.103421	+	0.00650952i
$412$	12.1035	−	6.98795i	0.596296	−	0.344271i
$413$		0			0
$414$	−3.13376	+	7.45605i	−0.154016	+	0.366445i
$415$	−2.26994	−	3.93165i	−0.111427	−	0.192997i
$416$	33.6820			1.65139
$417$	−5.43985	+	10.9593i	−0.266391	+	0.536677i
$418$		−	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
$423$	−3.58429	+	8.52796i	−0.174274	+	0.414644i
$424$	1.39269	−	2.41221i	0.0676350	−	0.117147i
$425$	−3.73502	+	6.46925i	−0.181175	+	0.313805i
$426$	13.5462	+	6.72394i	0.656315	+	0.325776i
$427$		0			0
$428$	−0.362424	−	0.209245i	−0.0175184	−	0.0101143i
$429$	42.2875	+	20.9903i	2.04166	+	1.01342i
$430$			3.57839i			0.172565i
$431$	−26.6926	−	15.4110i	−1.28574	−	0.742320i	−0.307845	−	0.951437i	$-0.599608\pi$
$431$	−26.6926	−	15.4110i	−1.28574	−	0.742320i	−0.977891	+	0.209117i	$0.932941\pi$
$432$	−23.9133	−	8.32533i	−1.15053	−	0.400552i
$433$			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
$435$	−4.60049	−	6.92389i	−0.220577	−	0.331975i
$436$	8.52910			0.408470
$437$	1.77602	+	3.07616i	0.0849585	+	0.147152i
$438$	31.2014	−	20.7314i	1.49086	−	0.990582i
$439$	23.5081	+	13.5724i	1.12198	+	0.647776i	0.941906	−	0.335877i	$-0.109033\pi$
$439$	23.5081	+	13.5724i	1.12198	+	0.647776i	0.180075	+	0.983653i	$0.442366\pi$
$440$	−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	$-0.292756\pi$
$443$	4.63465	+	2.67582i	0.220199	+	0.127132i	−0.385843	+	0.922564i	$0.626090\pi$
$444$	−16.8228	−	8.35033i	−0.798373	−	0.396289i
$445$	1.39660	+	2.41899i	0.0662053	+	0.114671i
$446$	−42.8270			−2.02792
$447$	11.9817	−	0.754147i	0.566714	−	0.0356699i
$448$		0			0
$449$			34.2418i			1.61597i	0.589204	+	0.807985i	$0.299442\pi$
$449$			34.2418i			1.61597i	−0.589204	+	0.807985i	$0.700558\pi$
$450$	−23.2221	−	9.76020i	−1.09470	−	0.460100i
$451$	−55.1577	−	31.8453i	−2.59727	−	1.49954i
$452$			12.1042i			0.569332i
$453$	0.687501	+	10.9228i	0.0323016	+	0.513200i
$454$	22.9151	+	13.2300i	1.07546	+	0.620916i
$455$		0			0
$456$	−4.10640	+	2.72844i	−0.192300	+	0.127771i
$457$	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
$459$	−7.99815	−	2.78453i	−0.373322	−	0.129971i
$460$	−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
$465$	−3.50692	−	5.27803i	−0.162629	−	0.244763i
$466$	−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	$0.677319\pi$
$468$	2.61594	+	20.6984i	0.120922	+	0.956783i
$469$		0			0
$470$	−3.15829	+	1.82344i	−0.145681	+	0.0841090i
$471$	1.90776	+	2.87125i	0.0879051	+	0.132300i
$472$	3.02126	−	1.74433i	0.139065	−	0.0802891i
$473$	13.9292	−	8.04201i	0.640464	−	0.369772i
$474$	12.2259	+	18.4004i	0.561555	+	0.845159i
$475$	−9.58078	+	5.53146i	−0.439596	+	0.253801i
$476$		0			0
$477$	6.53244	+	2.74557i	0.299100	+	0.125711i
$478$	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	$0.312676\pi$
$480$	−4.06494	−	6.11787i	−0.185538	−	0.279241i
$481$		−	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
$486$	5.93388	−	27.9352i	0.269166	−	1.26716i
$487$	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
$489$	−8.63748	+	5.73907i	−0.390601	+	0.259530i
$490$		0			0
$491$	−13.2899	−	7.67290i	−0.599763	−	0.346273i	0.169185	−	0.985584i	$-0.445886\pi$
$491$	−13.2899	−	7.67290i	−0.599763	−	0.346273i	−0.768948	+	0.639311i	$0.779220\pi$
$492$	−1.76805	−	28.0903i	−0.0797098	−	1.26641i
$493$			12.1172i			0.545731i
$494$	19.6361	+	11.3369i	0.883471	+	0.510072i
$495$	−1.29091	−	10.2142i	−0.0580220	−	0.459093i
$496$			27.6168i			1.24003i
$497$		0			0
$498$	−22.2708	+	1.40176i	−0.997976	+	0.0628143i
$499$	−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
$501$	2.16578	+	1.07503i	0.0967598	+	0.0480287i
$502$	−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
$507$	−19.1729	+	12.7392i	−0.851496	+	0.565766i
$508$	−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	$0.463434\pi$
$510$	−1.84771	−	2.78087i	−0.0818181	−	0.123139i
$511$		0			0
$512$			20.5181i			0.906778i
$513$	−8.19620	−	9.49384i	−0.361871	−	0.419163i
$514$	5.25807	+	3.03575i	0.231924	+	0.133901i
$515$		−	6.65215i		−	0.293129i
$516$	6.36661	+	3.16020i	0.280274	+	0.139120i
$517$	14.1958	+	8.19594i	0.624330	+	0.360457i
$518$		0			0
$519$	−11.8066	−	5.86047i	−0.518254	−	0.257246i
$520$	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	$0.849400\pi$
$522$	−40.5380	+	5.12336i	−1.77430	+	0.224243i
$523$	−23.6468	+	13.6525i	−1.03400	+	0.596982i	−0.918129	−	0.396282i	$-0.870300\pi$
$523$	−23.6468	+	13.6525i	−1.03400	+	0.596982i	−0.115874	+	0.993264i	$0.536967\pi$
$524$	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
$528$	−19.9490	+	40.1898i	−0.868170	+	1.74904i
$529$	20.8345			0.905847
$530$	1.39676	+	2.41926i	0.0606714	+	0.105086i
$531$	5.36625	+	7.06898i	0.232875	+	0.306768i
$532$		0			0
$533$	53.2012	−	30.7158i	2.30440	−	1.33045i
$534$	13.7023	−	0.862446i	0.592957	−	0.0373217i
$535$	−0.172504	+	0.0995952i	−0.00745799	+	0.00430588i
$536$	−10.3709	+	5.98762i	−0.447953	+	0.258626i
$537$	−7.12168	+	14.3475i	−0.307323	+	0.619140i
$538$	4.38055	−	2.52911i	0.188859	−	0.109038i
$539$		0			0
$540$	3.44387	−	2.97315i	0.148201	−	0.127944i
$541$	−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
$543$	−20.6803	+	1.30165i	−0.887478	+	0.0558593i
$544$			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
$549$	29.3169	+	12.3218i	1.25121	+	0.525883i
$550$	−22.3180	+	38.6559i	−0.951642	+	1.64829i
$551$	−8.97260	+	15.5410i	−0.382246	+	0.662069i
$552$	−0.188811	−	2.99978i	−0.00803632	−	0.127679i
$553$		0			0
$554$	14.9673	+	8.64136i	0.635898	+	0.367136i
$555$	−7.44564	+	4.94716i	−0.316050	+	0.209995i
$556$			9.58089i			0.406320i
$557$	−28.8204	−	16.6395i	−1.22116	−	0.705036i	−0.255994	−	0.966678i	$-0.582403\pi$
$557$	−28.8204	−	16.6395i	−1.22116	−	0.705036i	−0.965165	+	0.261642i	$0.915736\pi$
$558$	−30.9018	+	3.90550i	−1.30818	+	0.165333i
$559$			15.5135i			0.656152i
$560$		0			0
$561$	−6.67225	+	13.4421i	−0.281703	+	0.567525i
$562$	−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	$-0.389010\pi$
$564$	0.455038	+	7.22952i	0.0191606	+	0.304418i
$565$	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	$-0.438509\pi$
$569$	−13.4044	−	7.73906i	−0.561943	−	0.324438i	−0.753925	+	0.656960i	$0.771842\pi$
$570$	−0.310607	−	4.93484i	−0.0130099	−	0.206698i
$571$	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
$573$	−15.6135	+	31.4553i	−0.652264	+	1.31407i
$574$		0			0
$575$		−	6.74455i		−	0.281267i
$576$	−6.81141	+	0.860853i	−0.283809	+	0.0358689i
$577$	−12.6901	−	7.32664i	−0.528296	−	0.305012i	0.212026	−	0.977264i	$-0.431994\pi$
$577$	−12.6901	−	7.32664i	−0.528296	−	0.305012i	−0.740322	+	0.672252i	$0.765327\pi$
$578$		−	26.2777i		−	1.09301i
$579$	−24.3685	+	16.1914i	−1.01272	+	0.672890i
$580$	−5.63746	−	3.25479i	−0.234083	−	0.135148i
$581$		0			0
$582$	−3.31316	−	52.6385i	−0.137335	−	2.18194i
$583$	6.27811	−	10.8740i	0.260013	−	0.450355i
$584$	−6.96085	+	12.0565i	−0.288042	+	0.498904i
$585$	9.15454	+	3.84763i	0.378493	+	0.159080i
$586$	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
$591$	32.3430	−	2.03572i	1.33041	−	0.0837385i
$592$	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	$0.760062\pi$
$594$	−47.7916	−	16.6385i	−1.96091	−	0.682684i
$595$		0			0
$596$	8.14153	−	4.70051i	0.333490	−	0.192541i
$597$	13.8960	−	27.9951i	0.568724	−	1.14576i
$598$	−11.9712	+	6.91159i	−0.489540	+	0.282636i
$599$	13.5581	−	7.82776i	0.553968	−	0.319833i	−0.196753	−	0.980453i	$-0.563040\pi$
$599$	13.5581	−	7.82776i	0.553968	−	0.319833i	0.750721	+	0.660620i	$0.229706\pi$
$600$	9.34289	−	0.588057i	0.381422	−	0.0240073i
$601$	30.5665	−	17.6476i	1.24684	−	0.719861i	0.276358	−	0.961055i	$-0.410872\pi$
$601$	30.5665	−	17.6476i	1.24684	−	0.719861i	0.970477	+	0.241194i	$0.0775390\pi$
$602$		0			0
$603$	−18.4203	−	24.2652i	−0.750133	−	0.988154i
$604$	4.28512	+	7.42205i	0.174359	+	0.301999i
$605$	−11.1421			−0.452990
$606$	6.56250	−	13.2210i	0.266583	−	0.537065i
$607$		−	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
$612$	−6.57946	+	0.831539i	−0.265959	+	0.0336130i
$613$	−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
$615$	−11.9997	−	5.95632i	−0.483876	−	0.240182i
$616$		0			0
$617$	1.25518	+	0.724680i	0.0505317	+	0.0291745i	0.525053	−	0.851070i	$-0.324045\pi$
$617$	1.25518	+	0.724680i	0.0505317	+	0.0291745i	−0.474521	+	0.880244i	$0.657379\pi$
$618$	−29.2877	−	14.5376i	−1.17813	−	0.584787i
$619$		−	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
$621$	7.51093	−	1.43341i	0.301403	−	0.0575210i
$622$		−	51.8217i		−	2.07786i
$623$		0			0
$624$	−23.9501	−	36.0457i	−0.958771	−	1.44298i
$625$	18.9223			0.756892
$626$	−5.10764	−	8.84668i	−0.204142	−	0.353585i
$627$	−18.5112	+	12.2995i	−0.739267	+	0.491196i
$628$	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
$633$	−12.5198	−	6.21449i	−0.497619	−	0.247004i
$634$	30.7488	+	53.2585i	1.22119	+	2.11516i
$635$	−1.61385			−0.0640436
$636$	5.53783	−	0.348560i	0.219589	−	0.0138213i
$637$		0			0
$638$			72.4041i			2.86651i
$639$	−1.79277	−	14.1851i	−0.0709207	−	0.561153i
$640$	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	$-0.0734305\pi$
$642$	0.0615032	+	0.977146i	0.00242734	+	0.0385649i
$643$	−13.1240	−	7.57712i	−0.517558	−	0.298812i	0.218377	−	0.975865i	$-0.429924\pi$
$643$	−13.1240	−	7.57712i	−0.517558	−	0.298812i	−0.735935	+	0.677052i	$0.763257\pi$
$644$		0			0
$645$	2.81782	−	1.87226i	0.110951	−	0.0737203i
$646$	−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	$0.0880246\pi$
$648$	2.64052	+	10.2795i	0.103729	+	0.403819i
$649$	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	$0.971410\pi$
$654$	−11.0430	−	16.6200i	−0.431814	−	0.649894i
$655$	1.63619			0.0639313
$656$	29.1921	+	50.5621i	1.13976	+	1.97412i
$657$	−32.6500	−	13.7227i	−1.27380	−	0.535375i
$658$		0			0
$659$	15.6110	−	9.01301i	0.608118	−	0.351097i	−0.164111	−	0.986442i	$-0.552475\pi$
$659$	15.6110	−	9.01301i	0.608118	−	0.351097i	0.772228	+	0.635345i	$0.219142\pi$
$660$	−4.46163	−	6.71490i	−0.173669	−	0.261377i
$661$	−0.554932	+	0.320390i	−0.0215844	+	0.0124617i	−0.510753	−	0.859727i	$-0.670633\pi$
$661$	−0.554932	+	0.320390i	−0.0215844	+	0.0124617i	0.489169	+	0.872189i	$0.337300\pi$
$662$	−48.1899	+	27.8225i	−1.87296	+	1.08135i
$663$	−8.01047	−	12.0560i	−0.311101	−	0.468217i
$664$	7.18189	−	4.14647i	0.278711	−	0.160914i
$665$		0			0
$666$	5.50943	+	43.5927i	0.213486	+	1.68918i
$667$	−5.47018	−	9.47462i	−0.211806	−	0.366859i
$668$	1.89338			0.0732572
$669$	22.4077	+	33.7243i	0.866332	+	1.30386i
$670$		−	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
$675$	4.46441	+	23.3930i	0.171835	+	0.900398i
$676$	−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	$0.0408865\pi$
$678$	23.5865	−	15.6717i	0.905833	−	0.601869i
$679$		0			0
$680$	1.07456	+	0.620397i	0.0412074	+	0.0237911i
$681$	−1.57145	−	24.9667i	−0.0602180	−	0.956727i
$682$			55.1931i			2.11345i
$683$	18.1316	+	10.4683i	0.693786	+	0.400558i	0.805029	−	0.593235i	$-0.202150\pi$
$683$	18.1316	+	10.4683i	0.693786	+	0.400558i	−0.111243	+	0.993793i	$0.535483\pi$
$684$	−9.05429	−	3.80550i	−0.346200	−	0.145507i
$685$			0.783018i			0.0299176i
$686$		0			0
$687$	−22.6688	+	1.42681i	−0.864867	+	0.0544361i
$688$	−14.7440			−0.562108
$689$	6.05543	+	10.4883i	0.230693	+	0.399573i
$690$	2.70015	+	1.34028i	0.102793	+	0.0510235i
$691$	1.33430	+	0.770358i	0.0507591	+	0.0293058i	0.525165	−	0.851001i	$-0.324004\pi$
$691$	1.33430	+	0.770358i	0.0507591	+	0.0293058i	−0.474406	+	0.880306i	$0.657337\pi$
$692$	−10.3217			−0.392372
$693$		0			0
$694$	13.0740			0.496282
$695$	3.94929	+	2.28012i	0.149805	+	0.0864900i
$696$	12.6478	−	8.40366i	0.479413	−	0.318540i
$697$	9.76372	+	16.9113i	0.369827	+	0.640560i
$698$	27.9423			1.05763
$699$	8.10161	+	12.1932i	0.306431	+	0.461189i
$700$		0			0
$701$		−	31.6641i		−	1.19593i	−0.801520	−	0.597967i	$-0.795975\pi$
$701$		−	31.6641i		−	1.19593i	0.801520	−	0.597967i	$-0.204025\pi$
$702$	36.9464	−	31.8965i	1.39445	−	1.20386i
$703$	16.7121	+	9.64873i	0.630309	+	0.363909i
$704$			12.1657i			0.458513i
$705$	3.08834	+	1.53296i	0.116314	+	0.0577346i
$706$	54.6922	+	31.5766i	2.05837	+	1.18840i
$707$		0			0
$708$	6.22509	+	3.08995i	0.233953	+	0.116127i
$709$	−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
$711$	8.09272	−	19.2547i	0.303501	−	0.722108i
$712$	−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
$717$	21.5290	−	43.3729i	0.804016	−	1.61979i
$718$	−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	$-0.425070\pi$
$720$	−3.65677	+	8.70041i	−0.136280	+	0.324245i
$721$		0			0
$722$	20.9011	−	12.0672i	0.777858	−	0.449096i
$723$	−38.7350	+	2.43804i	−1.44057	+	0.0906717i
$724$	−14.0522	+	8.11306i	−0.522247	+	0.301520i
$725$	29.5090	−	17.0370i	1.09594	−	0.632739i
$726$	−24.3498	+	49.0557i	−0.903707	+	1.82063i
$727$	−11.4647	+	6.61915i	−0.425202	+	0.245491i	−0.697301	−	0.716779i	$-0.745616\pi$
$727$	−11.4647	+	6.61915i	−0.425202	+	0.245491i	0.272098	+	0.962269i	$0.412282\pi$
$728$		0			0
$729$	−25.1024	+	9.94341i	−0.929717	+	0.368274i
$730$	−6.98119	−	12.0918i	−0.258385	−	0.447536i
$731$	−4.93133			−0.182392
$732$	24.8532	−	1.56430i	0.918600	−	0.0578182i
$733$			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
$738$	−52.4483	+	39.8149i	−1.93065	+	1.46561i
$739$	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
$741$	−1.34659	−	21.3942i	−0.0494681	−	0.785936i
$742$		0			0
$743$	31.8593	+	18.3940i	1.16880	+	0.674810i	0.953398	−	0.301715i	$-0.0975591\pi$
$743$	31.8593	+	18.3940i	1.16880	+	0.674810i	0.215406	+	0.976525i	$0.430892\pi$
$744$	9.64131	−	6.40605i	0.353468	−	0.234857i
$745$		−	4.47464i		−	0.163938i
$746$	−15.3898	−	8.88530i	−0.563461	−	0.325314i
$747$	12.7562	+	16.8038i	0.466725	+	0.614819i
$748$			11.7514i			0.429675i
$749$		0			0
$750$	−8.72824	+	17.5841i	−0.318710	+	0.642081i
$751$	−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
$753$	0.695888	+	11.0561i	0.0253596	+	0.402906i
$754$	−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
$759$	−0.851141	−	13.5227i	−0.0308944	−	0.490843i
$760$	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	$0.420471\pi$
$762$	−3.52689	+	7.10536i	−0.127766	+	0.257400i
$763$		0			0
$764$			27.4991i			0.994884i
$765$	−1.22306	+	2.90998i	−0.0442198	+	0.105211i
$766$	−39.0500	−	22.5455i	−1.41093	−	0.814602i
$767$			15.1687i			0.547709i
$768$	30.2453	−	20.0961i	1.09138	−	0.725154i
$769$	−22.9328	−	13.2402i	−0.826976	−	0.477455i	0.0258399	−	0.999666i	$-0.491774\pi$
$769$	−22.9328	−	13.2402i	−0.826976	−	0.477455i	−0.852816	+	0.522211i	$0.825107\pi$
$770$		0			0
$771$	−0.360583	−	5.72884i	−0.0129861	−	0.206319i
$772$	−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	$0.322978\pi$
$774$	−2.08505	−	16.4978i	−0.0749457	−	0.593000i
$775$	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
$780$	7.76069	−	0.488471i	0.277877	−	0.0174901i
$781$	−25.3357			−0.906581
$782$	−2.19701	−	3.80533i	−0.0785649	−	0.136078i
$783$	25.2445	+	29.2412i	0.902164	+	1.04500i
$784$		0			0
$785$	1.11272	−	0.642430i	0.0397148	−	0.0229293i
$786$	3.57572	−	7.20374i	0.127542	−	0.256949i
$787$	−25.1554	+	14.5235i	−0.896694	+	0.517706i	−0.876126	−	0.482082i	$-0.839881\pi$
$787$	−25.1554	+	14.5235i	−0.896694	+	0.517706i	−0.0205676	+	0.999788i	$0.506547\pi$
$788$	21.9770	−	12.6884i	0.782899	−	0.452007i
$789$	−39.2229	+	2.46875i	−1.39637	+	0.0878899i
$790$	7.13088	−	4.11702i	0.253705	−	0.146477i
$791$		0			0
$792$	18.6581	−	2.35809i	0.662987	−	0.0837909i
$793$	27.1761	+	47.0704i	0.965052	+	1.67152i
$794$	24.2926			0.862111
$795$	1.17425	−	2.36568i	0.0416464	−	0.0839019i
$796$		−	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
$801$	−7.84838	−	10.3387i	−0.277309	−	0.365300i
$802$	14.4777	−	25.0762i	0.511227	−	0.885470i
$803$	−31.3788	+	54.3497i	−1.10733	+	1.91796i
$804$	−21.3684	−	10.6066i	−0.753605	−	0.374068i
$805$		0			0
$806$	−46.1032	−	26.6177i	−1.62392	−	0.937569i
$807$	−4.28353	−	2.12622i	−0.150787	−	0.0748465i
$808$			5.48534i			0.192974i
$809$	−34.5466	−	19.9455i	−1.21459	−	0.701245i	−0.250836	−	0.968029i	$-0.580706\pi$
$809$	−34.5466	−	19.9455i	−1.21459	−	0.701245i	−0.963756	+	0.266784i	$0.914039\pi$
$810$	−10.2525	−	2.86135i	−0.360235	−	0.100538i
$811$			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
$813$	−5.83676	−	8.78452i	−0.204704	−	0.308087i
$814$	77.8601			2.72899
$815$	1.93260	+	3.34737i	0.0676961	+	0.117253i
$816$	11.4580	−	7.61310i	0.401109	−	0.266512i
$817$	−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	$-0.335638\pi$
$821$	−0.359377	−	0.207486i	−0.0125423	−	0.00724132i	−0.506258	+	0.862382i	$0.668972\pi$
$822$	3.44743	+	1.71120i	0.120243	+	0.0596851i
$823$	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
$825$	42.1168	−	2.65090i	1.46632	−	0.0922926i
$826$		0			0
$827$			35.2637i			1.22624i	0.789990	+	0.613120i	$0.210086\pi$
$827$			35.2637i			1.22624i	−0.789990	+	0.613120i	$0.789914\pi$
$828$	4.76920	−	3.62042i	0.165741	−	0.125818i
$829$	29.0164	+	16.7526i	1.00778	+	0.581842i	0.910541	−	0.413419i	$-0.135666\pi$
$829$	29.0164	+	16.7526i	1.00778	+	0.581842i	0.0972388	+	0.995261i	$0.468999\pi$
$830$			8.31716i			0.288693i
$831$	−1.02641	−	16.3073i	−0.0356058	−	0.565695i
$832$	−10.1621	−	5.86710i	−0.352308	−	0.203405i
$833$		0			0
$834$	18.6696	−	12.4048i	0.646474	−	0.429542i
$835$	0.450600	−	0.780462i	0.0155937	−	0.0270090i
$836$	−8.70178	+	15.0719i	−0.300957	+	0.521273i
$837$	19.2437	+	22.2904i	0.665159	+	0.770468i
$838$	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
$843$	5.05990	+	7.61532i	0.174272	+	0.262285i
$844$	−10.9452			−0.376749
$845$	4.28985	+	7.43024i	0.147575	+	0.255608i
$846$	13.4985	−	10.2470i	0.464087	−	0.352301i
$847$		0			0
$848$	−9.96802	+	5.75504i	−0.342303	+	0.197629i
$849$	18.8544	+	28.3765i	0.647082	+	0.973880i
$850$	11.8518	−	6.84265i	0.406514	−	0.234701i
$851$	−10.1886	+	5.88238i	−0.349260	+	0.201645i
$852$	−6.19615	−	9.32541i	−0.212277	−	0.319483i
$853$	−15.8457	+	9.14854i	−0.542548	+	0.313240i	−0.746111	−	0.665822i	$-0.768081\pi$
$853$	−15.8457	+	9.14854i	−0.542548	+	0.313240i	0.203563	+	0.979062i	$0.434748\pi$
$854$		0			0
$855$	−3.72345	+	2.82657i	−0.127339	+	0.0966665i
$856$	−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	$0.442171\pi$
$858$	−47.8651	−	72.0386i	−1.63409	−	2.45936i
$859$			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	$-0.615786\pi$
$863$	8.09878	−	4.67583i	0.275686	−	0.159167i	0.631469	+	0.775401i	$0.282452\pi$
$864$	22.3057	+	25.8372i	0.758856	+	0.879000i
$865$	−2.45643	+	4.25465i	−0.0835210	+	0.144663i
$866$	5.55262	−	9.61742i	0.188686	−	0.326813i
$867$	−20.6925	+	13.7489i	−0.702755	+	0.466937i
$868$		0			0
$869$	−32.0517	−	18.5050i	−1.08728	−	0.627741i
$870$	0.956675	+	15.1994i	0.0324343	+	0.515308i
$871$		−	52.0684i		−	1.76427i
$872$	6.42216	+	3.70783i	0.217482	+	0.125563i
$873$	−39.7170	+	30.1502i	−1.34422	+	1.02043i
$874$		−	6.50742i		−	0.220117i
$875$		0			0
$876$	−27.6788	+	1.74215i	−0.935181	+	0.0588618i
$877$	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
$879$	−28.2873	−	14.0410i	−0.954107	−	0.473591i
$880$	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
$885$	2.75518	−	1.83064i	0.0926144	−	0.0615364i
$886$	−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	$0.421663\pi$
$888$	−9.03691	−	13.6009i	−0.303259	−	0.456415i
$889$		0			0
$890$		−	5.11722i		−	0.171530i
$891$	11.9032	+	46.3392i	0.398772	+	1.55242i
$892$	27.4585	+	15.8532i	0.919379	+	0.530804i
$893$		−	7.44295i		−	0.249069i
$894$	−19.7007	−	9.77885i	−0.658890	−	0.327054i
$895$	5.17028	+	2.98506i	0.172823	+	0.0997797i
$896$		0			0
$897$	11.7061	+	5.81056i	0.390855	+	0.194009i
$898$	31.3659	−	54.3273i	1.04669	−	1.81293i
$899$	21.0666	−	36.4884i	0.702610	−	1.21696i
$900$	11.2759	+	14.8538i	0.375864	+	0.495127i
$901$	−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
$906$	8.91468	−	17.9597i	0.296170	−	0.596671i
$907$	−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
$909$	−13.8445	+	1.74972i	−0.459193	+	0.0580346i
$910$		0			0
$911$	10.1252	−	5.84579i	0.335463	−	0.193680i	−0.322801	−	0.946467i	$-0.604624\pi$
$911$	10.1252	−	5.84579i	0.335463	−	0.193680i	0.658264	+	0.752787i	$0.271291\pi$
$912$	20.3329	−	1.27979i	0.673290	−	0.0423780i
$913$	32.3752	−	18.6919i	1.07146	−	0.618610i
$914$	−25.1637	+	14.5283i	−0.832342	+	0.480553i
$915$	5.26992	−	10.6169i	0.174218	−	0.350984i
$916$	−15.4034	+	8.89314i	−0.508942	+	0.293838i
$917$		0			0
$918$	10.1390	+	11.7443i	0.334638	+	0.387619i
$919$	−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
$921$	45.0216	−	2.83374i	1.48351	−	0.0933747i
$922$			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
$927$	3.87608	+	30.6690i	0.127307	+	1.00730i
$928$	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	$0.0995030\pi$
$930$	0.729267	+	11.5864i	0.0239136	+	0.379933i
$931$		0			0
$932$	9.92775	+	5.73179i	0.325194	+	0.187751i
$933$	−40.8072	+	27.1138i	−1.33597	+	0.887667i
$934$		−	37.2738i		−	1.21964i
$935$	4.84400	+	2.79669i	0.158416	+	0.0914614i
$936$	−7.02842	+	16.7225i	−0.229731	+	0.546591i
$937$			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
$939$	−4.29398	+	8.65074i	−0.140129	+	0.282306i
$940$	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	$0.967109\pi$
$942$	−0.396721	−	6.30300i	−0.0129259	−	0.205363i
$943$	−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	$-0.154697\pi$
$947$	28.3671	+	16.3777i	0.921806	+	0.532205i	0.0375955	+	0.999293i	$0.488030\pi$
$948$	−1.02740	−	16.3230i	−0.0333684	−	0.530148i
$949$	−30.2658	−	52.4219i	−0.982470	−	1.70169i
$950$	20.2676			0.657566
$951$	25.8504	−	52.0789i	0.838258	−	1.68877i
$952$		0			0
$953$			6.77705i			0.219530i	0.993958	+	0.109765i	$0.0350099\pi$
$953$			6.77705i			0.219530i	−0.993958	+	0.109765i	$0.964990\pi$
$954$	−7.84926	−	10.3399i	−0.254129	−	0.334766i
$955$	11.3353	+	6.54443i	0.366801	+	0.211773i
$956$		−	37.9178i		−	1.22635i
$957$	57.0150	−	37.8829i	1.84303	−	1.22458i
$958$	−38.5512	−	22.2575i	−1.24553	−	0.719109i
$959$		0			0
$960$	0.160746	+	2.55388i	0.00518804	+	0.0824262i
$961$	0.558897	−	0.968037i	0.0180289	−	0.0312270i
$962$	−37.5492	+	65.0371i	−1.21063	+	2.09688i
$963$	0.737279	−	0.559688i	0.0237585	−	0.0180357i
$964$	−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
$969$	6.80064	−	0.428044i	0.218468	−	0.0137507i
$970$	−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	$-0.396921\pi$
$972$	−14.1452	+	15.7141i	−0.453707	+	0.504029i
$973$		0			0
$974$	−43.3281	+	25.0155i	−1.38832	+	0.801547i
$975$	−18.0972	+	36.4589i	−0.579573	+	1.16762i
$976$	−44.7354	+	25.8280i	−1.43195	+	0.826734i
$977$	−3.96507	+	2.28924i	−0.126854	+	0.0732391i	−0.562084	−	0.827080i	$-0.690000\pi$
$977$	−3.96507	+	2.28924i	−0.126854	+	0.0732391i	0.435230	+	0.900319i	$0.356667\pi$
$978$	18.9611	−	1.19344i	0.606309	−	0.0381621i
$979$	−19.9192	+	11.5004i	−0.636621	+	0.367553i
$980$		0			0
$981$	−7.30968	+	17.3917i	−0.233380	+	0.555273i
$982$	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	$0.372338\pi$
$984$	10.8803	−	21.9198i	0.346852	−	0.698777i
$985$		−	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
$990$	−7.30818	+	17.3881i	−0.232269	+	0.552630i
$991$	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
$993$	47.1226	+	23.3903i	1.49539	+	0.742268i
$994$		0			0
$995$	−10.0884	−	5.82452i	−0.319822	−	0.184650i
$996$	14.7978	+	7.34518i	0.468885	+	0.232741i
$997$		−	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
$999$	31.4447	−	27.1468i	0.994867	−	0.858886i

Twists

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

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

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.58658 - 0.916012i) q^{2} +(0.108803 + 1.72863i) q^{3} +(0.678156 + 1.17460i) q^{4} +0.645568 q^{5} +(1.41082 - 2.84227i) q^{6} +1.17925i q^{8} +(-2.97632 + 0.376160i) q^{9} +(-1.02425 - 0.591348i) q^{10} +5.31595i q^{11} +(-1.95666 + 1.30008i) q^{12} +(-4.44045 - 2.56370i) q^{13} +(0.0702397 + 1.11595i) q^{15} +(2.43652 - 4.22018i) q^{16} +(0.814931 - 1.41150i) q^{17} +(5.06674 + 2.12954i) q^{18} +(2.09039 - 1.20689i) q^{19} +(0.437796 + 0.758285i) q^{20} +(4.86947 - 8.43418i) q^{22} +1.47157i q^{23} +(-2.03849 + 0.128306i) q^{24} -4.58324 q^{25} +(4.69675 + 8.13502i) q^{26} +(-0.974073 - 5.10404i) q^{27} +(-6.43846 + 3.71724i) q^{29} +(0.910782 - 1.83488i) q^{30} +(-4.90799 + 2.83363i) q^{31} +(-5.68894 + 3.28451i) q^{32} +(-9.18931 + 0.578390i) q^{33} +(-2.58590 + 1.49297i) q^{34} +(-2.46025 - 3.24090i) q^{36} +(3.99736 + 6.92362i) q^{37} -4.42210 q^{38} +(3.94855 - 7.95484i) q^{39} +0.761288i q^{40} +(-5.99052 + 10.3759i) q^{41} +(-1.51281 - 2.62026i) q^{43} +(-6.24412 + 3.60504i) q^{44} +(-1.92142 + 0.242837i) q^{45} +(1.34797 - 2.33476i) q^{46} +(1.54176 - 2.67041i) q^{47} +(7.56023 + 3.75268i) q^{48} +(7.27168 + 4.19830i) q^{50} +(2.52863 + 1.25514i) q^{51} -6.95434i q^{52} +(-2.04554 - 1.18100i) q^{53} +(-3.12991 + 8.99022i) q^{54} +3.43181i q^{55} +(2.31371 + 3.48220i) q^{57} +13.6202 q^{58} +(-1.47918 - 2.56202i) q^{59} +(-1.26316 + 0.839291i) q^{60} +(-9.18018 - 5.30018i) q^{61} +10.3825 q^{62} +2.28853 q^{64} +(-2.86662 - 1.65504i) q^{65} +(15.1094 + 7.49986i) q^{66} +(5.07747 + 8.79444i) q^{67} +2.21060 q^{68} +(-2.54380 + 0.160111i) q^{69} +4.76597i q^{71} +(-0.443587 - 3.50984i) q^{72} +(10.2239 + 5.90277i) q^{73} -14.6465i q^{74} +(-0.498670 - 7.92273i) q^{75} +(2.83523 + 1.63692i) q^{76} +(-13.5514 + 9.00406i) q^{78} +(-3.48104 + 6.02934i) q^{79} +(1.57294 - 2.72441i) q^{80} +(8.71701 - 2.23915i) q^{81} +(19.0089 - 10.9748i) q^{82} +(-3.51618 - 6.09021i) q^{83} +(0.526093 - 0.911221i) q^{85} +5.54300i q^{86} +(-7.12626 - 10.7253i) q^{87} -6.26884 q^{88} +(2.16337 + 3.74706i) q^{89} +(3.27093 + 1.37476i) q^{90} +(-1.72850 + 0.997953i) q^{92} +(-5.43230 - 8.17579i) q^{93} +(-4.89226 + 2.82455i) q^{94} +(1.34949 - 0.779129i) q^{95} +(-6.29668 - 9.47671i) q^{96} +(14.3946 - 8.31075i) q^{97} +(-1.99965 - 15.8220i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} - 8 q^{9} - 40 q^{15} - 24 q^{16} + 32 q^{18} + 48 q^{25} + 48 q^{30} - 120 q^{32} - 8 q^{36} - 32 q^{39} + 96 q^{44} + 48 q^{50} + 48 q^{53} + 80 q^{57} - 72 q^{60} - 48 q^{64} - 120 q^{65}+ \cdots - 72 q^{99}+O(q^{100}) \) 48 * q + 24 * q^4 - 8 * q^9 - 40 * q^15 - 24 * q^16 + 32 * q^18 + 48 * q^25 + 48 * q^30 - 120 * q^32 - 8 * q^36 - 32 * q^39 + 96 * q^44 + 48 * q^50 + 48 * q^53 + 80 * q^57 - 72 * q^60 - 48 * q^64 - 120 * q^65 + 32 * q^72 - 88 * q^78 - 24 * q^79 + 120 * q^81 - 24 * q^85 - 144 * q^92 + 16 * q^93 - 96 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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