LMFDB - Embedded newform 441.2.s.d.374.24

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			374.24
Character	$\chi$	$=$	441.374
Dual form			441.2.s.d.362.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.34591 + 1.35441i) q^{2} +(1.12982 - 1.31283i) q^{3} +(2.66888 + 4.62263i) q^{4} -1.20293 q^{5} +(4.42857 - 1.54954i) q^{6} +9.04141i q^{8} +(-0.447031 - 2.96651i) q^{9} +(-2.82197 - 1.62926i) q^{10} -2.48666i q^{11} +(9.08406 + 1.71895i) q^{12} +(1.63211 + 0.942300i) q^{13} +(-1.35909 + 1.57924i) q^{15} +(-6.90806 + 11.9651i) q^{16} +(0.601863 - 1.04246i) q^{17} +(2.96918 - 7.56464i) q^{18} +(-6.46933 + 3.73507i) q^{19} +(-3.21047 - 5.56070i) q^{20} +(3.36797 - 5.83350i) q^{22} -3.04101i q^{23} +(11.8698 + 10.2151i) q^{24} -3.55296 q^{25} +(2.55253 + 4.42111i) q^{26} +(-4.39957 - 2.76473i) q^{27} +(-0.173847 + 0.100371i) q^{29} +(-5.32725 + 1.86399i) q^{30} +(3.03381 - 1.75157i) q^{31} +(-16.7513 + 9.67135i) q^{32} +(-3.26456 - 2.80947i) q^{33} +(2.82384 - 1.63034i) q^{34} +(12.5200 - 9.98370i) q^{36} +(-0.865458 - 1.49902i) q^{37} -20.2353 q^{38} +(3.08106 - 1.07805i) q^{39} -10.8762i q^{40} +(3.36029 - 5.82020i) q^{41} +(0.00656005 + 0.0113623i) q^{43} +(11.4949 - 6.63660i) q^{44} +(0.537746 + 3.56850i) q^{45} +(4.11878 - 7.13394i) q^{46} +(-0.717403 + 1.24258i) q^{47} +(7.90329 + 22.5875i) q^{48} +(-8.33495 - 4.81219i) q^{50} +(-0.688572 - 1.96793i) q^{51} +10.0595i q^{52} +(8.58085 + 4.95416i) q^{53} +(-6.57643 - 12.4447i) q^{54} +2.99128i q^{55} +(-2.40565 + 12.7130i) q^{57} -0.543775 q^{58} +(6.10954 + 10.5820i) q^{59} +(-10.9275 - 2.06777i) q^{60} +(-9.73903 - 5.62283i) q^{61} +9.48942 q^{62} -24.7638 q^{64} +(-1.96331 - 1.13352i) q^{65} +(-3.85319 - 11.0124i) q^{66} +(2.57932 + 4.46752i) q^{67} +6.42520 q^{68} +(-3.99231 - 3.43578i) q^{69} -12.0452i q^{71} +(26.8214 - 4.04179i) q^{72} +(-7.51020 - 4.33602i) q^{73} -4.68875i q^{74} +(-4.01420 + 4.66443i) q^{75} +(-34.5317 - 19.9369i) q^{76} +(8.68805 + 1.64401i) q^{78} +(-2.74801 + 4.75969i) q^{79} +(8.30991 - 14.3932i) q^{80} +(-8.60033 + 2.65224i) q^{81} +(15.7659 - 9.10246i) q^{82} +(1.60854 + 2.78607i) q^{83} +(-0.723998 + 1.25400i) q^{85} +0.0355401i q^{86} +(-0.0646460 + 0.341632i) q^{87} +22.4829 q^{88} +(3.98364 + 6.89986i) q^{89} +(-3.57172 + 9.09972i) q^{90} +(14.0574 - 8.11607i) q^{92} +(1.12814 - 5.96182i) q^{93} +(-3.36593 + 1.94332i) q^{94} +(7.78214 - 4.49302i) q^{95} +(-6.22905 + 32.9184i) q^{96} +(2.06260 - 1.19084i) q^{97} +(-7.37671 + 1.11162i) 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 $

$2$	2.34591	+	1.35441i	1.65881	+	0.957716i	0.973264	+	0.229689i	$0.0737707\pi$
$2$	2.34591	+	1.35441i	1.65881	+	0.957716i	0.685548	+	0.728027i	$0.259563\pi$
$3$	1.12982	−	1.31283i	0.652300	−	0.757961i
$3$	1.12982	−	1.31283i	0.652300	−	0.757961i
$4$	2.66888	+	4.62263i	1.33444	+	2.31132i
$5$	−1.20293			−0.537966			−0.268983	−	0.963145i	$-0.586688\pi$
$5$	−1.20293			−0.537966			−0.268983	+	0.963145i	$0.586688\pi$
$6$	4.42857	−	1.54954i	1.80795	−	0.632598i
$7$		0			0
$7$		0			0
$8$			9.04141i			3.19662i
$9$	−0.447031	−	2.96651i	−0.149010	−	0.988836i
$10$	−2.82197	−	1.62926i	−0.892385	−	0.515219i
$11$		−	2.48666i		−	0.749757i	−0.927074	−	0.374879i	$-0.877684\pi$
$11$		−	2.48666i		−	0.749757i	0.927074	−	0.374879i	$-0.122316\pi$
$12$	9.08406	+	1.71895i	2.62234	+	0.496218i
$13$	1.63211	+	0.942300i	0.452666	+	0.261347i	0.708956	−	0.705253i	$-0.249167\pi$
$13$	1.63211	+	0.942300i	0.452666	+	0.261347i	−0.256289	+	0.966600i	$0.582500\pi$
$14$		0			0
$15$	−1.35909	+	1.57924i	−0.350915	+	0.407757i
$16$	−6.90806	+	11.9651i	−1.72702	+	2.99128i
$17$	0.601863	−	1.04246i	0.145973	−	0.252833i	−0.783762	−	0.621061i	$-0.786702\pi$
$17$	0.601863	−	1.04246i	0.145973	−	0.252833i	0.929736	+	0.368228i	$0.120035\pi$
$18$	2.96918	−	7.56464i	0.699843	−	1.78300i
$19$	−6.46933	+	3.73507i	−1.48417	+	0.856883i	−0.999838	−	0.0180038i	$-0.994269\pi$
$19$	−6.46933	+	3.73507i	−1.48417	+	0.856883i	−0.484327	+	0.874887i	$0.660936\pi$
$20$	−3.21047	−	5.56070i	−0.717883	−	1.24341i
$21$		0			0
$22$	3.36797	−	5.83350i	0.718054	−	1.24371i
$23$		−	3.04101i		−	0.634093i	−0.948410	−	0.317047i	$-0.897309\pi$
$23$		−	3.04101i		−	0.634093i	0.948410	−	0.317047i	$-0.102691\pi$
$24$	11.8698	+	10.2151i	2.42292	+	2.08516i
$25$	−3.55296			−0.710593
$26$	2.55253	+	4.42111i	0.500592	+	0.867052i
$27$	−4.39957	−	2.76473i	−0.846698	−	0.532073i
$28$		0			0
$29$	−0.173847	+	0.100371i	−0.0322826	+	0.0186384i	−0.516054	−	0.856556i	$-0.672600\pi$
$29$	−0.173847	+	0.100371i	−0.0322826	+	0.0186384i	0.483772	+	0.875194i	$0.339266\pi$
$30$	−5.32725	+	1.86399i	−0.972618	+	0.340316i
$31$	3.03381	−	1.75157i	0.544889	−	0.314592i	−0.202169	−	0.979351i	$-0.564799\pi$
$31$	3.03381	−	1.75157i	0.544889	−	0.314592i	0.747058	+	0.664759i	$0.231466\pi$
$32$	−16.7513	+	9.67135i	−2.96124	+	1.70967i
$33$	−3.26456	−	2.80947i	−0.568287	−	0.489066i
$34$	2.82384	−	1.63034i	0.484285	−	0.279602i
$35$		0			0
$36$	12.5200	−	9.98370i	2.08667	−	1.66395i
$37$	−0.865458	−	1.49902i	−0.142280	−	0.246437i	0.786075	−	0.618132i	$-0.212110\pi$
$37$	−0.865458	−	1.49902i	−0.142280	−	0.246437i	−0.928355	+	0.371695i	$0.878777\pi$
$38$	−20.2353			−3.28260
$39$	3.08106	−	1.07805i	0.493365	−	0.172627i
$40$		−	10.8762i		−	1.71967i
$41$	3.36029	−	5.82020i	0.524790	−	0.908963i	−0.474793	−	0.880097i	$-0.657477\pi$
$41$	3.36029	−	5.82020i	0.524790	−	0.908963i	0.999583	−	0.0288655i	$-0.00918944\pi$
$42$		0			0
$43$	0.00656005	+	0.0113623i	0.00100040	+	0.00173274i	0.866525	−	0.499133i	$-0.166348\pi$
$43$	0.00656005	+	0.0113623i	0.00100040	+	0.00173274i	−0.865525	+	0.500866i	$0.833015\pi$
$44$	11.4949	−	6.63660i	1.73293	−	1.00051i
$45$	0.537746	+	3.56850i	0.0801624	+	0.531960i
$46$	4.11878	−	7.13394i	0.607281	−	1.05184i
$47$	−0.717403	+	1.24258i	−0.104644	+	0.181249i	−0.913593	−	0.406631i	$-0.866704\pi$
$47$	−0.717403	+	1.24258i	−0.104644	+	0.181249i	0.808949	+	0.587879i	$0.200037\pi$
$48$	7.90329	+	22.5875i	1.14074	+	3.26022i
$49$		0			0
$50$	−8.33495	−	4.81219i	−1.17874	−	0.680546i
$51$	−0.688572	−	1.96793i	−0.0964194	−	0.275565i
$52$			10.0595i			1.39501i
$53$	8.58085	+	4.95416i	1.17867	+	0.680506i	0.955707	−	0.294321i	$-0.0950935\pi$
$53$	8.58085	+	4.95416i	1.17867	+	0.680506i	0.222964	+	0.974827i	$0.428427\pi$
$54$	−6.57643	−	12.4447i	−0.894939	−	1.69351i
$55$			2.99128i			0.403344i
$56$		0			0
$57$	−2.40565	+	12.7130i	−0.318636	+	1.68388i
$58$	−0.543775			−0.0714011
$59$	6.10954	+	10.5820i	0.795394	+	1.37766i	0.922588	+	0.385786i	$0.126070\pi$
$59$	6.10954	+	10.5820i	0.795394	+	1.37766i	−0.127194	+	0.991878i	$0.540597\pi$
$60$	−10.9275	−	2.06777i	−1.41073	−	0.266948i
$61$	−9.73903	−	5.62283i	−1.24696	−	0.719930i	−0.276454	−	0.961027i	$-0.589159\pi$
$61$	−9.73903	−	5.62283i	−1.24696	−	0.719930i	−0.970501	+	0.241097i	$0.922493\pi$
$62$	9.48942			1.20516
$63$		0			0
$64$	−24.7638			−3.09548
$65$	−1.96331	−	1.13352i	−0.243519	−	0.140596i
$66$	−3.85319	−	11.0124i	−0.474295	−	1.35553i
$67$	2.57932	+	4.46752i	0.315115	+	0.545794i	0.979462	−	0.201630i	$-0.0646237\pi$
$67$	2.57932	+	4.46752i	0.315115	+	0.545794i	−0.664347	+	0.747424i	$0.731290\pi$
$68$	6.42520			0.779170
$69$	−3.99231	−	3.43578i	−0.480618	−	0.413619i
$70$		0			0
$71$		−	12.0452i		−	1.42950i	−0.699379	−	0.714751i	$-0.746540\pi$
$71$		−	12.0452i		−	1.42950i	0.699379	−	0.714751i	$-0.253460\pi$
$72$	26.8214	−	4.04179i	3.16093	−	0.476329i
$73$	−7.51020	−	4.33602i	−0.879003	−	0.507493i	−0.00867336	−	0.999962i	$-0.502761\pi$
$73$	−7.51020	−	4.33602i	−0.879003	−	0.507493i	−0.870330	+	0.492470i	$0.836094\pi$
$74$		−	4.68875i		−	0.545057i
$75$	−4.01420	+	4.66443i	−0.463519	+	0.538602i
$76$	−34.5317	−	19.9369i	−3.96106	−	2.28692i
$77$		0			0
$78$	8.68805	+	1.64401i	0.983728	+	0.186148i
$79$	−2.74801	+	4.75969i	−0.309175	+	0.535507i	−0.978182	−	0.207749i	$-0.933386\pi$
$79$	−2.74801	+	4.75969i	−0.309175	+	0.535507i	0.669007	+	0.743256i	$0.266719\pi$
$80$	8.30991	−	14.3932i	0.929076	−	1.60921i
$81$	−8.60033	+	2.65224i	−0.955592	+	0.294693i
$82$	15.7659	−	9.10246i	1.74106	−	1.00520i
$83$	1.60854	+	2.78607i	0.176560	+	0.305811i	0.940700	−	0.339239i	$-0.110170\pi$
$83$	1.60854	+	2.78607i	0.176560	+	0.305811i	−0.764140	+	0.645051i	$0.776836\pi$
$84$		0			0
$85$	−0.723998	+	1.25400i	−0.0785286	+	0.136016i
$86$			0.0355401i			0.00383239i
$87$	−0.0646460	+	0.341632i	−0.00693078	+	0.0366268i
$88$	22.4829			2.39669
$89$	3.98364	+	6.89986i	0.422265	+	0.731384i	0.996161	−	0.0875442i	$-0.0279019\pi$
$89$	3.98364	+	6.89986i	0.422265	+	0.731384i	−0.573896	+	0.818928i	$0.694569\pi$
$90$	−3.57172	+	9.09972i	−0.376492	+	0.959195i
$91$		0			0
$92$	14.0574	−	8.11607i	1.46559	−	0.846159i
$93$	1.12814	−	5.96182i	0.116982	−	0.618212i
$94$	−3.36593	+	1.94332i	−0.347170	+	0.200438i
$95$	7.78214	−	4.49302i	0.798430	−	0.460974i
$96$	−6.22905	+	32.9184i	−0.635749	+	3.35972i
$97$	2.06260	−	1.19084i	0.209425	−	0.120912i	−0.391619	−	0.920128i	$-0.628085\pi$
$97$	2.06260	−	1.19084i	0.209425	−	0.120912i	0.601044	+	0.799216i	$0.294751\pi$
$98$		0			0
$99$	−7.37671	+	1.11162i	−0.741387	+	0.111722i
$100$	−9.48242	−	16.4240i	−0.948242	−	1.64240i
$101$	9.46543			0.941846			0.470923	−	0.882174i	$-0.343921\pi$
$101$	9.46543			0.941846			0.470923	+	0.882174i	$0.343921\pi$
$102$	1.05006	−	5.54920i	0.103971	−	0.549453i
$103$			17.2582i			1.70050i	0.526381	+	0.850249i	$0.323549\pi$
$103$			17.2582i			1.70050i	−0.526381	+	0.850249i	$0.676451\pi$
$104$	−8.51973	+	14.7566i	−0.835428	+	1.44700i
$105$		0			0
$106$	13.4200	+	23.2441i	1.30346	+	2.25766i
$107$	−8.55935	+	4.94175i	−0.827464	+	0.477737i	−0.852984	−	0.521938i	$-0.825209\pi$
$107$	−8.55935	+	4.94175i	−0.827464	+	0.477737i	0.0255196	+	0.999674i	$0.491876\pi$
$108$	1.03842	−	27.7163i	0.0999221	−	2.66701i
$109$	−5.20678	+	9.01841i	−0.498719	+	0.863807i	−0.999999	−	0.00147852i	$-0.999529\pi$
$109$	−5.20678	+	9.01841i	−0.498719	+	0.863807i	0.501280	+	0.865285i	$0.332863\pi$
$110$	−4.05143	+	7.01729i	−0.386289	+	0.669072i
$111$	−2.94576	−	0.557417i	−0.279599	−	0.0529077i
$112$		0			0
$113$	−9.56137	−	5.52026i	−0.899458	−	0.519303i	−0.0224339	−	0.999748i	$-0.507142\pi$
$113$	−9.56137	−	5.52026i	−0.899458	−	0.519303i	−0.877024	+	0.480446i	$0.840475\pi$
$114$	−22.8622	+	26.5655i	−2.14124	+	2.48808i
$115$			3.65811i			0.341121i
$116$	−0.927954	−	0.535755i	−0.0861584	−	0.0497436i
$117$	2.06574	−	5.26291i	0.190977	−	0.486556i
$118$			33.0994i			3.04705i
$119$		0			0
$120$	−14.2785	−	12.2881i	−1.30345	−	1.12174i
$121$	4.81650			0.437864
$122$	−15.2313	−	26.3814i	−1.37898	−	2.38846i
$123$	−3.84440	−	10.9872i	−0.346638	−	0.990686i
$124$	16.1937	+	9.34946i	1.45424	+	0.839607i
$125$	10.2886			0.920241
$126$		0			0
$127$	13.8634			1.23018			0.615090	−	0.788457i	$-0.289119\pi$
$127$	13.8634			1.23018			0.615090	+	0.788457i	$0.289119\pi$
$128$	−24.5913	−	14.1978i	−2.17359	−	1.25492i
$129$	0.0223284	+	0.00422514i	0.00196591	+	0.000372003i
$130$	−3.07051	−	5.31828i	−0.269302	−	0.466444i
$131$	12.3595			1.07985			0.539927	−	0.841712i	$-0.318452\pi$
$131$	12.3595			1.07985			0.539927	+	0.841712i	$0.318452\pi$
$132$	4.27445	−	22.5890i	0.372043	−	1.96612i
$133$		0			0
$134$			13.9739i			1.20716i
$135$	5.29237	+	3.32578i	0.455495	+	0.286237i
$136$	9.42529	+	5.44169i	0.808212	+	0.466621i
$137$			11.6614i			0.996301i	0.867091	+	0.498150i	$0.165987\pi$
$137$			11.6614i			0.996301i	−0.867091	+	0.498150i	$0.834013\pi$
$138$	−4.71216	−	13.4673i	−0.401126	−	1.14641i
$139$	8.73893	+	5.04543i	0.741227	+	0.427947i	0.822515	−	0.568743i	$-0.192570\pi$
$139$	8.73893	+	5.04543i	0.741227	+	0.427947i	−0.0812884	+	0.996691i	$0.525903\pi$
$140$		0			0
$141$	0.820757	+	2.34571i	0.0691202	+	0.197545i
$142$	16.3142	−	28.2570i	1.36906	−	2.37128i
$143$	2.34318	−	4.05851i	0.195947	−	0.339390i
$144$	38.5827	+	15.1440i	3.21523	+	1.26200i
$145$	0.209126	−	0.120739i	0.0173670	−	0.0100268i
$146$	−11.7455	−	20.3439i	−0.972067	−	1.68367i
$147$		0			0
$148$	4.61960	−	8.00138i	0.379729	−	0.657710i
$149$		−	4.79212i		−	0.392586i	−0.980545	−	0.196293i	$-0.937110\pi$
$149$		−	4.79212i		−	0.392586i	0.980545	−	0.196293i	$-0.0628904\pi$
$150$	−15.7345	+	5.50546i	−1.28472	+	0.449519i
$151$	−11.3185			−0.921085			−0.460542	−	0.887638i	$-0.652345\pi$
$151$	−11.3185			−0.921085			−0.460542	+	0.887638i	$0.652345\pi$
$152$	−33.7703	−	58.4918i	−2.73913	−	4.74431i
$153$	−3.36151	−	1.31942i	−0.271762	−	0.106669i
$154$		0			0
$155$	−3.64946	+	2.10702i	−0.293132	+	0.169240i
$156$	13.2064	+	11.3654i	1.05736	+	0.909963i
$157$	12.7580	−	7.36581i	1.01820	−	0.587856i	0.104615	−	0.994513i	$-0.466639\pi$
$157$	12.7580	−	7.36581i	1.01820	−	0.587856i	0.913581	+	0.406657i	$0.133306\pi$
$158$	−12.8932	+	7.44388i	−1.02573	+	0.592203i
$159$	16.1987	−	5.66789i	1.28464	−	0.449493i
$160$	20.1506	−	11.6339i	1.59304	−	0.919744i
$161$		0			0
$162$	−23.7679	−	5.42648i	−1.86738	−	0.426345i
$163$	9.07900	+	15.7253i	0.711122	+	1.23170i	0.964436	+	0.264316i	$0.0851460\pi$
$163$	9.07900	+	15.7253i	0.711122	+	1.23170i	−0.253314	+	0.967384i	$0.581521\pi$
$164$	35.8729			2.80120
$165$	3.92703	+	3.37960i	0.305719	+	0.263101i
$166$			8.71452i			0.676378i
$167$	0.599436	−	1.03825i	0.0463857	−	0.0803425i	−0.841900	−	0.539633i	$-0.818563\pi$
$167$	0.599436	−	1.03825i	0.0463857	−	0.0803425i	0.888286	+	0.459291i	$0.151896\pi$
$168$		0			0
$169$	−4.72414	−	8.18245i	−0.363395	−	0.629419i
$170$	−3.39688	+	1.96119i	−0.260529	+	0.150416i
$171$	13.9721	+	17.5216i	1.06847	+	1.33991i
$172$	−0.0350159	+	0.0606494i	−0.00266994	+	0.00462447i
$173$	9.00403	−	15.5954i	0.684564	−	1.18570i	−0.289010	−	0.957326i	$-0.593326\pi$
$173$	9.00403	−	15.5954i	0.684564	−	1.18570i	0.973574	−	0.228373i	$-0.0733405\pi$
$174$	−0.614365	+	0.713882i	−0.0465749	+	0.0541193i
$175$		0			0
$176$	29.7532	+	17.1780i	2.24273	+	1.29484i
$177$	20.7950	+	3.93498i	1.56305	+	0.295771i
$178$			21.5820i			1.61764i
$179$	−13.1137	−	7.57118i	−0.980162	−	0.565897i	−0.0778428	−	0.996966i	$-0.524803\pi$
$179$	−13.1137	−	7.57118i	−0.980162	−	0.565897i	−0.902319	+	0.431069i	$0.858137\pi$
$180$	−15.0607	+	12.0097i	−1.12256	+	0.895149i
$181$			7.98716i			0.593681i	0.954927	+	0.296840i	$0.0959329\pi$
$181$			7.98716i			0.593681i	−0.954927	+	0.296840i	$0.904067\pi$
$182$		0			0
$183$	−18.3851	+	6.43290i	−1.35907	+	0.475534i
$184$	27.4950			2.02696
$185$	1.04108	+	1.80321i	0.0765420	+	0.132575i
$186$	10.7213	−	12.4580i	0.786124	−	0.913462i
$187$	−2.59224	−	1.49663i	−0.189563	−	0.109445i
$188$	−7.65865			−0.558564
$189$		0			0
$190$	24.3416			1.76593
$191$	−13.8711	−	8.00848i	−1.00368	−	0.579473i	−0.0943426	−	0.995540i	$-0.530075\pi$
$191$	−13.8711	−	8.00848i	−1.00368	−	0.579473i	−0.909334	+	0.416067i	$0.863408\pi$
$192$	−27.9786	+	32.5106i	−2.01918	+	2.34625i
$193$	6.85468	+	11.8726i	0.493410	+	0.854612i	0.999971	−	0.00759239i	$-0.00241676\pi$
$193$	6.85468	+	11.8726i	0.493410	+	0.854612i	−0.506561	+	0.862204i	$0.669083\pi$
$194$	6.45158			0.463197
$195$	−3.70630	+	1.29682i	−0.265414	+	0.0928674i
$196$		0			0
$197$		−	18.9248i		−	1.34834i	−0.738577	−	0.674170i	$-0.764502\pi$
$197$		−	18.9248i		−	1.34834i	0.738577	−	0.674170i	$-0.235498\pi$
$198$	−18.8107	−	7.38336i	−1.33682	−	0.524713i
$199$	−21.5055	−	12.4162i	−1.52449	−	0.880163i	−0.999579	−	0.0290036i	$-0.990767\pi$
$199$	−21.5055	−	12.4162i	−1.52449	−	0.880163i	−0.524908	−	0.851159i	$-0.675900\pi$
$200$		−	32.1238i		−	2.27150i
$201$	8.77924	+	1.66127i	0.619240	+	0.117177i
$202$	22.2051	+	12.8201i	1.56235	+	0.902020i
$203$		0			0
$204$	7.25929	−	8.43517i	0.508252	−	0.590580i
$205$	−4.04219	+	7.00129i	−0.282319	+	0.488991i
$206$	−23.3747	+	40.4862i	−1.62859	+	2.82081i
$207$	−9.02116	+	1.35942i	−0.627014	+	0.0944864i
$208$	−22.5495	+	13.0189i	−1.56352	+	0.902701i
$209$	9.28786	+	16.0870i	0.642454	+	1.11276i
$210$		0			0
$211$	3.60761	−	6.24857i	0.248358	−	0.430169i	−0.714712	−	0.699419i	$-0.753442\pi$
$211$	3.60761	−	6.24857i	0.248358	−	0.430169i	0.963070	+	0.269250i	$0.0867757\pi$
$212$			52.8881i			3.63237i
$213$	−15.8133	−	13.6089i	−1.08351	−	0.932464i
$214$	−26.7727			−1.83014
$215$	−0.00789127	−	0.0136681i	−0.000538180	−	0.000932155i
$216$	24.9971	−	39.7784i	1.70084	−	2.70657i
$217$		0			0
$218$	−24.4293	+	14.1043i	−1.65456	+	0.955262i
$219$	−14.1776	+	4.96070i	−0.958033	+	0.335213i
$220$	−13.8276	+	7.98336i	−0.932255	+	0.538238i
$221$	1.96462	−	1.13427i	0.132154	−	0.0762994i
$222$	−6.15552	−	5.29743i	−0.413132	−	0.355540i
$223$	−21.0706	+	12.1651i	−1.41099	+	0.814635i	−0.995482	−	0.0949545i	$-0.969729\pi$
$223$	−21.0706	+	12.1651i	−1.41099	+	0.814635i	−0.415508	+	0.909590i	$0.636396\pi$
$224$		0			0
$225$	1.58828	+	10.5399i	0.105886	+	0.702659i
$226$	−14.9534	−	25.9001i	−0.994688	−	1.72285i
$227$	0.480577			0.0318970			0.0159485	−	0.999873i	$-0.494923\pi$
$227$	0.480577			0.0318970			0.0159485	+	0.999873i	$0.494923\pi$
$228$	−65.1881	+	22.8091i	−4.31719	+	1.51057i
$229$		−	9.01176i		−	0.595514i	−0.954642	−	0.297757i	$-0.903761\pi$
$229$		−	9.01176i		−	0.595514i	0.954642	−	0.297757i	$-0.0962385\pi$
$230$	−4.95460	+	8.58162i	−0.326697	+	0.565855i
$231$		0			0
$232$	−0.907493	−	1.57182i	−0.0595799	−	0.103195i
$233$	9.62742	−	5.55840i	0.630713	−	0.364143i	−0.150315	−	0.988638i	$-0.548029\pi$
$233$	9.62742	−	5.55840i	0.630713	−	0.364143i	0.781028	+	0.624496i	$0.214695\pi$
$234$	11.9742	−	9.54847i	0.782778	−	0.624203i
$235$	0.862985	−	1.49473i	0.0562949	−	0.0975057i
$236$	−32.6112	+	56.4843i	−2.12281	+	3.67682i
$237$	3.14390	+	8.98523i	0.204219	+	0.583653i
$238$		0			0
$239$	12.0446	+	6.95395i	0.779100	+	0.449813i	0.836111	−	0.548560i	$-0.184824\pi$
$239$	12.0446	+	6.95395i	0.779100	+	0.449813i	−0.0570114	+	0.998374i	$0.518157\pi$
$240$	−9.50709	−	27.1711i	−0.613680	−	1.75389i
$241$			12.3761i			0.797217i	0.917121	+	0.398609i	$0.130507\pi$
$241$			12.3761i			0.797217i	−0.917121	+	0.398609i	$0.869493\pi$
$242$	11.2991	+	6.52354i	0.726334	+	0.419349i
$243$	−6.23486	+	14.2873i	−0.399966	+	0.916530i
$244$		−	60.0266i		−	3.84281i
$245$		0			0
$246$	5.86264	−	30.9821i	0.373788	−	1.97534i
$247$	−14.0782			−0.895776
$248$	15.8367	+	27.4299i	1.00563	+	1.74180i
$249$	5.47499	+	1.03602i	0.346963	+	0.0656548i
$250$	24.1362	+	13.9350i	1.52651	+	0.881329i
$251$	−19.7147			−1.24438			−0.622191	−	0.782866i	$-0.713757\pi$
$251$	−19.7147			−1.24438			−0.622191	+	0.782866i	$0.713757\pi$
$252$		0			0
$253$	−7.56196			−0.475416
$254$	32.5224	+	18.7768i	2.04064	+	1.17816i
$255$	0.828303	+	2.36728i	0.0518703	+	0.148245i
$256$	−13.6956	−	23.7214i	−0.855973	−	1.48259i
$257$	11.2405			0.701163			0.350581	−	0.936532i	$-0.385984\pi$
$257$	11.2405			0.701163			0.350581	+	0.936532i	$0.385984\pi$
$258$	0.0466580	+	0.0401538i	0.00290480	+	0.00249987i
$259$		0			0
$260$		−	12.1009i		−	0.750466i
$261$	0.375466	+	0.470850i	0.0232407	+	0.0291449i
$262$	28.9943	+	16.7399i	1.79127	+	1.03419i
$263$		−	3.25794i		−	0.200893i	−0.994942	−	0.100447i	$-0.967973\pi$
$263$		−	3.25794i		−	0.200893i	0.994942	−	0.100447i	$-0.0320272\pi$
$264$	25.4016	−	29.5162i	1.56336	−	1.81660i
$265$	−10.3221	−	5.95949i	−0.634084	−	0.366089i
$266$		0			0
$267$	13.5591	+	2.56575i	0.829804	+	0.157021i
$268$	−13.7678	+	23.8465i	−0.841002	+	1.45666i
$269$	−0.121147	+	0.209832i	−0.00738644	+	0.0127937i	−0.869695	−	0.493590i	$-0.835685\pi$
$269$	−0.121147	+	0.209832i	−0.00738644	+	0.0127937i	0.862309	+	0.506383i	$0.169018\pi$
$270$	7.91098	+	14.9701i	0.481447	+	0.911049i
$271$	−0.929287	+	0.536524i	−0.0564502	+	0.0325915i	−0.527959	−	0.849270i	$-0.677043\pi$
$271$	−0.929287	+	0.536524i	−0.0564502	+	0.0325915i	0.471509	+	0.881861i	$0.343709\pi$
$272$	8.31542	+	14.4027i	0.504196	+	0.873294i
$273$		0			0
$274$	−15.7944	+	27.3567i	−0.954173	+	1.65268i
$275$			8.83502i			0.532772i
$276$	5.22733	−	27.6247i	0.314648	−	1.66281i
$277$	−4.90153			−0.294504			−0.147252	−	0.989099i	$-0.547043\pi$
$277$	−4.90153			−0.294504			−0.147252	+	0.989099i	$0.547043\pi$
$278$	13.6672	+	23.6723i	0.819704	+	1.41977i
$279$	−6.55226	−	8.21682i	−0.392273	−	0.491928i
$280$		0			0
$281$	11.5613	−	6.67494i	0.689691	−	0.398194i	−0.113805	−	0.993503i	$-0.536304\pi$
$281$	11.5613	−	6.67494i	0.689691	−	0.398194i	0.803496	+	0.595310i	$0.202971\pi$
$282$	−1.25164	+	6.61449i	−0.0745340	+	0.393887i
$283$	3.25329	−	1.87829i	0.193388	−	0.111653i	−0.400180	−	0.916437i	$-0.631052\pi$
$283$	3.25329	−	1.87829i	0.193388	−	0.111653i	0.593568	+	0.804784i	$0.297719\pi$
$284$	55.6805	−	32.1472i	3.30403	−	1.90758i
$285$	2.89383	−	15.2929i	0.171415	−	0.905872i
$286$	10.9938	−	6.34729i	0.650078	−	0.375323i
$287$		0			0
$288$	36.1785	+	45.3694i	2.13184	+	2.67342i
$289$	7.77552	+	13.4676i	0.457384	+	0.792212i
$290$	0.654122			0.0384114
$291$	0.766989	−	4.05327i	0.0449617	−	0.237607i
$292$		−	46.2892i		−	2.70887i
$293$	6.38430	−	11.0579i	0.372975	−	0.646011i	−0.617047	−	0.786926i	$-0.711671\pi$
$293$	6.38430	−	11.0579i	0.372975	−	0.646011i	0.990022	+	0.140915i	$0.0450045\pi$
$294$		0			0
$295$	−7.34934	−	12.7294i	−0.427895	−	0.741136i
$296$	13.5532	−	7.82496i	0.787765	−	0.454816i
$297$	−6.87496	+	10.9403i	−0.398926	+	0.634818i
$298$	6.49052	−	11.2419i	0.375986	−	0.651227i
$299$	2.86554	−	4.96326i	0.165718	−	0.287033i
$300$	−32.2753	−	6.10736i	−1.86342	−	0.352609i
$301$		0			0
$302$	−26.5522	−	15.3299i	−1.52791	−	0.882137i
$303$	10.6942	−	12.4265i	0.614366	−	0.713882i
$304$		−	103.208i		−	5.91940i
$305$	11.7154	+	6.76387i	0.670819	+	0.387298i
$306$	−6.09877	−	7.64813i	−0.348644	−	0.437214i
$307$		−	10.7257i		−	0.612148i	−0.952008	−	0.306074i	$-0.900984\pi$
$307$		−	10.7257i		−	0.612148i	0.952008	−	0.306074i	$-0.0990155\pi$
$308$		0			0
$309$	22.6570	+	19.4986i	1.28891	+	1.10923i
$310$	−11.4151			−0.648334
$311$	−9.41743	−	16.3115i	−0.534013	−	0.924938i	−0.999210	−	0.0397310i	$-0.987350\pi$
$311$	−9.41743	−	16.3115i	−0.534013	−	0.924938i	0.465197	−	0.885207i	$-0.345983\pi$
$312$	9.74714	+	27.8572i	0.551823	+	1.57710i
$313$	−22.5774	−	13.0351i	−1.27615	−	0.736787i	−0.300013	−	0.953935i	$-0.596991\pi$
$313$	−22.5774	−	13.0351i	−1.27615	−	0.736787i	−0.976139	+	0.217148i	$0.930324\pi$
$314$	39.9054			2.25199
$315$		0			0
$316$	−29.3364			−1.65030
$317$	−12.0290	−	6.94495i	−0.675616	−	0.390067i	0.122585	−	0.992458i	$-0.460882\pi$
$317$	−12.0290	−	6.94495i	−0.675616	−	0.390067i	−0.798201	+	0.602391i	$0.794215\pi$
$318$	45.6775	+	8.64342i	2.56147	+	0.484699i
$319$	0.249588	+	0.432300i	0.0139743	+	0.0242041i
$320$	29.7891			1.66526
$321$	−3.18284	+	16.8202i	−0.177649	+	0.938813i
$322$		0			0
$323$			8.99200i			0.500328i
$324$	−35.2136	−	32.6776i	−1.95631	−	1.81542i
$325$	−5.79883	−	3.34796i	−0.321661	−	0.185711i
$326$			49.1869i			2.72421i
$327$	5.95691	+	17.0247i	0.329418	+	0.941470i
$328$	52.6228	+	30.3818i	2.90561	+	1.67755i
$329$		0			0
$330$	4.63511	+	13.2471i	0.255154	+	0.729227i
$331$	−2.24230	+	3.88378i	−0.123248	+	0.213472i	−0.921047	−	0.389452i	$-0.872664\pi$
$331$	−2.24230	+	3.88378i	−0.123248	+	0.213472i	0.797799	+	0.602924i	$0.205998\pi$
$332$	−8.58600	+	14.8714i	−0.471218	+	0.816173i
$333$	−4.05996	+	3.23749i	−0.222484	+	0.177413i
$334$	2.81245	−	1.62377i	0.153891	−	0.0888487i
$335$	−3.10274	−	5.37411i	−0.169521	−	0.293619i
$336$		0			0
$337$	−16.4010	+	28.4074i	−0.893420	+	1.54745i	−0.0576723	+	0.998336i	$0.518368\pi$
$337$	−16.4010	+	28.4074i	−0.893420	+	1.54745i	−0.835748	+	0.549113i	$0.814965\pi$
$338$		−	25.5938i		−	1.39212i
$339$	−18.0497	+	6.31555i	−0.980328	+	0.343014i
$340$	−7.72905			−0.419167
$341$	−4.35557	−	7.54407i	−0.235867	−	0.408534i
$342$	9.04581	+	60.0282i	0.489141	+	3.24595i
$343$		0			0
$344$	−0.102732	+	0.0593121i	−0.00553891	+	0.00319789i
$345$	4.80247	+	4.13299i	0.258556	+	0.222513i
$346$	42.2454	−	24.3904i	2.27112	−	1.31123i
$347$	−11.6112	+	6.70374i	−0.623323	+	0.359876i	−0.778162	−	0.628064i	$-0.783848\pi$
$347$	−11.6112	+	6.70374i	−0.623323	+	0.359876i	0.154839	+	0.987940i	$0.450514\pi$
$348$	−1.75177	+	0.612939i	−0.0939048	+	0.0328570i
$349$	19.3276	−	11.1588i	1.03458	−	0.597316i	0.116288	−	0.993215i	$-0.462900\pi$
$349$	19.3276	−	11.1588i	1.03458	−	0.597316i	0.918294	+	0.395899i	$0.129567\pi$
$350$		0			0
$351$	−4.57539	−	8.65807i	−0.244216	−	0.462134i
$352$	24.0494	+	41.6548i	1.28184	+	2.22021i
$353$	−17.2168			−0.916360			−0.458180	−	0.888859i	$-0.651499\pi$
$353$	−17.2168			−0.916360			−0.458180	+	0.888859i	$0.651499\pi$
$354$	43.4538	+	37.3962i	2.30954	+	1.98759i
$355$			14.4895i			0.769024i
$356$	−21.2637	+	36.8298i	−1.12697	+	1.95198i
$357$		0			0
$358$	−20.5090	−	35.5227i	−1.08394	−	1.87743i
$359$	5.62867	−	3.24971i	0.297070	−	0.171513i	−0.344056	−	0.938949i	$-0.611801\pi$
$359$	5.62867	−	3.24971i	0.297070	−	0.171513i	0.641126	+	0.767436i	$0.278468\pi$
$360$	−32.2642	+	4.86198i	−1.70047	+	0.256249i
$361$	18.4015	−	31.8722i	0.968497	−	1.67749i
$362$	−10.8179	+	18.7372i	−0.568577	+	0.984805i
$363$	5.44176	−	6.32324i	0.285619	−	0.331884i
$364$		0			0
$365$	9.03424	+	5.21592i	0.472874	+	0.273014i
$366$	−51.8427	−	9.81005i	−2.70986	−	0.512779i
$367$		−	9.00360i		−	0.469984i	−0.971997	−	0.234992i	$-0.924494\pi$
$367$		−	9.00360i		−	0.469984i	0.971997	−	0.234992i	$-0.0755064\pi$
$368$	36.3860	+	21.0075i	1.89675	+	1.09509i
$369$	−18.7678	−	7.36653i	−0.977014	−	0.383486i
$370$			5.64024i			0.293222i
$371$		0			0
$372$	30.5702	−	10.6964i	1.58499	−	0.554583i
$373$	11.5062			0.595771			0.297885	−	0.954602i	$-0.403719\pi$
$373$	11.5062			0.595771			0.297885	+	0.954602i	$0.403719\pi$
$374$	−4.05412	−	7.02194i	−0.209633	−	0.363096i
$375$	11.6242	−	13.5072i	0.600273	−	0.697507i
$376$	−11.2347	−	6.48634i	−0.579384	−	0.334507i
$377$	−0.378318			−0.0194844
$378$		0			0
$379$	17.0982			0.878275			0.439138	−	0.898420i	$-0.355284\pi$
$379$	17.0982			0.878275			0.439138	+	0.898420i	$0.355284\pi$
$380$	41.5391	+	23.9826i	2.13091	+	1.23028i
$381$	15.6631	−	18.2003i	0.802447	−	0.932429i
$382$	−21.6936	−	37.5744i	−1.10994	−	1.92247i
$383$	−16.2156			−0.828577			−0.414288	−	0.910146i	$-0.635970\pi$
$383$	−16.2156			−0.828577			−0.414288	+	0.910146i	$0.635970\pi$
$384$	−46.4229	+	16.2432i	−2.36901	+	0.828909i
$385$		0			0
$386$			37.1363i			1.89019i
$387$	0.0307739	−	0.0245397i	0.00156433	−	0.00124743i
$388$	11.0097	+	6.35643i	0.558931	+	0.322699i
$389$		−	18.7475i		−	0.950537i	−0.879841	−	0.475269i	$-0.842351\pi$
$389$		−	18.7475i		−	0.950537i	0.879841	−	0.475269i	$-0.157649\pi$
$390$	−10.4511	−	1.97763i	−0.529212	−	0.100141i
$391$	−3.17012	−	1.83027i	−0.160320	−	0.0925607i
$392$		0			0
$393$	13.9640	−	16.2259i	0.704388	−	0.818487i
$394$	25.6321	−	44.3961i	1.29133	−	2.23664i
$395$	3.30565	−	5.72556i	0.166326	−	0.288084i
$396$	−24.8261	−	31.1330i	−1.24756	−	1.56449i
$397$	26.8216	−	15.4854i	1.34614	−	0.777192i	0.358436	−	0.933554i	$-0.383310\pi$
$397$	26.8216	−	15.4854i	1.34614	−	0.777192i	0.987700	+	0.156362i	$0.0499767\pi$
$398$	−33.6334	−	58.2548i	−1.68589	−	2.92005i
$399$		0			0
$400$	24.5441	−	42.5116i	1.22720	−	2.12558i
$401$			0.924990i			0.0461918i	0.999733	+	0.0230959i	$0.00735231\pi$
$401$			0.924990i			0.0461918i	−0.999733	+	0.0230959i	$0.992648\pi$
$402$	18.3453	+	15.7879i	0.914981	+	0.787431i
$403$	6.60203			0.328870
$404$	25.2621	+	43.7552i	1.25684	+	2.17690i
$405$	10.3456	−	3.19045i	0.514076	−	0.158535i
$406$		0			0
$407$	−3.72755	+	2.15210i	−0.184768	+	0.106676i
$408$	17.7928	−	6.22566i	0.880877	−	0.308216i
$409$	−6.56585	+	3.79079i	−0.324660	+	0.187443i	−0.653468	−	0.756954i	$-0.726687\pi$
$409$	−6.56585	+	3.79079i	−0.324660	+	0.187443i	0.328808	+	0.944397i	$0.393353\pi$
$410$	−18.9653	+	10.9496i	−0.936629	+	0.540763i
$411$	15.3094	+	13.1752i	0.755157	+	0.649887i
$412$	−79.7782	+	46.0599i	−3.93039	+	2.26921i
$413$		0			0
$414$	−23.0041	−	9.02931i	−1.13059	−	0.443766i
$415$	−1.93496	−	3.35145i	−0.0949834	−	0.164516i
$416$	−36.4533			−1.78727
$417$	16.4972	−	5.77231i	0.807870	−	0.282671i
$418$			50.3184i			2.46115i
$419$	2.85061	−	4.93740i	0.139262	−	0.241208i	−0.787956	−	0.615732i	$-0.788860\pi$
$419$	2.85061	−	4.93740i	0.139262	−	0.241208i	0.927217	+	0.374524i	$0.122194\pi$
$420$		0			0
$421$	−5.86189	−	10.1531i	−0.285691	−	0.494832i	0.687085	−	0.726577i	$-0.258890\pi$
$421$	−5.86189	−	10.1531i	−0.285691	−	0.494832i	−0.972777	+	0.231745i	$0.925557\pi$
$422$	16.9263	−	9.77240i	0.823959	−	0.475713i
$423$	4.00682	+	1.57271i	0.194818	+	0.0764678i
$424$	−44.7926	+	77.5830i	−2.17532	+	3.76776i
$425$	−2.13840	+	3.70381i	−0.103728	+	0.179661i
$426$	−18.6645	−	53.3430i	−0.904300	−	2.58447i
$427$		0			0
$428$	−45.6877	−	26.3778i	−2.20840	−	1.27502i
$429$	−2.68076	−	7.66157i	−0.129428	−	0.369904i
$430$		−	0.0427522i		−	0.00206169i
$431$	−23.2973	−	13.4507i	−1.12219	−	0.647897i	−0.180231	−	0.983624i	$-0.557685\pi$
$431$	−23.2973	−	13.4507i	−1.12219	−	0.647897i	−0.941959	+	0.335728i	$0.891018\pi$
$432$	63.4729	−	33.5425i	3.05384	−	1.61381i
$433$		−	28.1028i		−	1.35053i	−0.737574	−	0.675266i	$-0.764029\pi$
$433$		−	28.1028i		−	1.35053i	0.737574	−	0.675266i	$-0.235971\pi$
$434$		0			0
$435$	0.0777645	−	0.410959i	0.00372852	−	0.0197040i
$436$	−55.5850			−2.66204
$437$	11.3584	+	19.6733i	0.543344	+	0.941099i
$438$	−39.9783	−	7.56497i	−1.91024	−	0.361468i
$439$	−8.07680	−	4.66314i	−0.385485	−	0.222560i	0.294717	−	0.955585i	$-0.404775\pi$
$439$	−8.07680	−	4.66314i	−0.385485	−	0.222560i	−0.680202	+	0.733025i	$0.738108\pi$
$440$	−27.0454			−1.28934
$441$		0			0
$442$	6.14510			0.292292
$443$	−9.82131	−	5.67034i	−0.466624	−	0.269406i	0.248201	−	0.968709i	$-0.420161\pi$
$443$	−9.82131	−	5.67034i	−0.466624	−	0.269406i	−0.714826	+	0.699303i	$0.753494\pi$
$444$	−5.28514	−	15.1048i	−0.250821	−	0.716844i
$445$	−4.79203	−	8.30004i	−0.227164	−	0.393460i
$446$	−65.9063			−3.12076
$447$	−6.29123	−	5.41422i	−0.297565	−	0.256084i
$448$		0			0
$449$			15.3295i			0.723444i	0.932286	+	0.361722i	$0.117811\pi$
$449$			15.3295i			0.723444i	−0.932286	+	0.361722i	$0.882189\pi$
$450$	−10.5494	+	26.8769i	−0.497304	+	1.26699i
$451$	−14.4729	−	8.35592i	−0.681501	−	0.393465i
$452$		−	58.9316i		−	2.77191i
$453$	−12.7878	+	14.8592i	−0.600823	+	0.698147i
$454$	1.12739	+	0.650900i	0.0529111	+	0.0305483i
$455$		0			0
$456$	−114.944	−	21.7505i	−5.38274	−	1.01856i
$457$	4.58649	−	7.94404i	0.214547	−	0.371606i	−0.738585	−	0.674160i	$-0.764506\pi$
$457$	4.58649	−	7.94404i	0.214547	−	0.371606i	0.953132	+	0.302554i	$0.0978391\pi$
$458$	12.2057	−	21.1408i	0.570333	−	0.987846i
$459$	−5.53006	+	2.92238i	−0.258121	+	0.136405i
$460$	−16.9101	+	9.76305i	−0.788438	+	0.455205i
$461$	16.5365	+	28.6420i	0.770181	+	1.33399i	0.937464	+	0.348083i	$0.113167\pi$
$461$	16.5365	+	28.6420i	0.770181	+	1.33399i	−0.167283	+	0.985909i	$0.553499\pi$
$462$		0			0
$463$	3.91594	−	6.78260i	0.181989	−	0.315214i	−0.760569	−	0.649257i	$-0.775080\pi$
$463$	3.91594	−	6.78260i	0.181989	−	0.315214i	0.942558	+	0.334043i	$0.108413\pi$
$464$		−	2.77347i		−	0.128755i
$465$	−1.35707	+	7.17165i	−0.0629326	+	0.332577i
$466$	30.1135			1.39498
$467$	−10.3385	−	17.9068i	−0.478408	−	0.828627i	0.521286	−	0.853382i	$-0.325453\pi$
$467$	−10.3385	−	17.9068i	−0.478408	−	0.828627i	−0.999694	+	0.0247555i	$0.992119\pi$
$468$	29.8417	−	4.49692i	1.37943	−	0.207870i
$469$		0			0
$470$	4.04898	−	2.33768i	0.186765	−	0.107829i
$471$	4.74411	−	25.0710i	0.218597	−	1.15521i
$472$	−95.6765	+	55.2389i	−4.40387	+	2.54257i
$473$	0.0282543	−	0.0163126i	0.00129913	−	0.000750056i
$474$	−4.79439	+	25.3367i	−0.220214	+	1.16375i
$475$	22.9853	−	13.2706i	1.05464	−	0.608895i
$476$		0			0
$477$	10.8606	−	27.6698i	0.497274	−	1.26691i
$478$	18.8371	+	32.6267i	0.861587	+	1.49231i
$479$	2.65998			0.121538			0.0607688	−	0.998152i	$-0.480645\pi$
$479$	2.65998			0.121538			0.0607688	+	0.998152i	$0.480645\pi$
$480$	7.49310	−	39.5985i	0.342012	−	1.80741i
$481$		−	3.26208i		−	0.148738i
$482$	−16.7624	+	29.0334i	−0.763508	+	1.32243i
$483$		0			0
$484$	12.8547	+	22.2649i	0.584303	+	1.01204i
$485$	−2.48116	+	1.43250i	−0.112664	+	0.0650465i
$486$	−33.9774	+	25.0722i	−1.54124	+	1.13730i
$487$	0.521900	−	0.903957i	0.0236495	−	0.0409622i	−0.853958	−	0.520341i	$-0.825805\pi$
$487$	0.521900	−	0.903957i	0.0236495	−	0.0409622i	0.877608	+	0.479379i	$0.159138\pi$
$488$	50.8383	−	88.0546i	2.30134	−	3.98604i
$489$	30.9022	+	5.84753i	1.39745	+	0.264434i
$490$		0			0
$491$	36.0415	+	20.8085i	1.62653	+	0.939076i	0.985118	+	0.171878i	$0.0549835\pi$
$491$	36.0415	+	20.8085i	1.62653	+	0.939076i	0.641410	+	0.767198i	$0.278350\pi$
$492$	40.5297	−	47.0949i	1.82722	−	2.12320i
$493$			0.241638i			0.0108828i
$494$	−33.0263	−	19.0677i	−1.48592	−	0.857898i
$495$	8.87365	−	1.33719i	0.398841	−	0.0601024i
$496$			48.3999i			2.17322i
$497$		0			0
$498$	11.4407	+	9.84581i	0.512668	+	0.441201i
$499$	−32.2895			−1.44548			−0.722738	−	0.691122i	$-0.757117\pi$
$499$	−32.2895			−1.44548			−0.722738	+	0.691122i	$0.757117\pi$
$500$	27.4590	+	47.5604i	1.22800	+	2.12697i
$501$	−0.685795	−	1.95999i	−0.0306391	−	0.0875660i
$502$	−46.2490	−	26.7019i	−2.06420	−	1.19176i
$503$	−39.9702			−1.78218			−0.891091	−	0.453825i	$-0.850059\pi$
$503$	−39.9702			−1.78218			−0.891091	+	0.453825i	$0.850059\pi$
$504$		0			0
$505$	−11.3862			−0.506681
$506$	−17.7397	−	10.2420i	−0.788626	−	0.455314i
$507$	−16.0796	−	3.04269i	−0.714118	−	0.135130i
$508$	36.9998	+	64.0856i	1.64160	+	2.84334i
$509$	−22.7262			−1.00732			−0.503661	−	0.863901i	$-0.668014\pi$
$509$	−22.7262			−1.00732			−0.503661	+	0.863901i	$0.668014\pi$
$510$	−1.26315	+	6.67529i	−0.0559330	+	0.295587i
$511$		0			0
$512$		−	17.4067i		−	0.769277i
$513$	38.7887	+	1.45326i	1.71256	+	0.0641630i
$514$	26.3692	+	15.2243i	1.16310	+	0.671515i
$515$		−	20.7603i		−	0.914810i
$516$	0.0400606	+	0.114493i	0.00176357	+	0.00504025i
$517$	3.08988	+	1.78394i	0.135893	+	0.0784576i
$518$		0			0
$519$	−10.3012	−	29.4407i	−0.452173	−	1.29230i
$520$	10.2486	−	17.7511i	0.449432	−	0.778439i
$521$	15.0179	−	26.0118i	0.657948	−	1.13960i	−0.323198	−	0.946331i	$-0.604758\pi$
$521$	15.0179	−	26.0118i	0.657948	−	1.13960i	0.981146	−	0.193268i	$-0.0619087\pi$
$522$	0.243084	+	1.61311i	0.0106395	+	0.0706040i
$523$	−0.675300	+	0.389885i	−0.0295288	+	0.0170485i	−0.514692	−	0.857375i	$-0.672094\pi$
$523$	−0.675300	+	0.389885i	−0.0295288	+	0.0170485i	0.485163	+	0.874424i	$0.338760\pi$
$524$	32.9860	+	57.1334i	1.44100	+	2.49588i
$525$		0			0
$526$	4.41260	−	7.64285i	0.192399	−	0.333244i
$527$		−	4.21683i		−	0.183688i
$528$	56.1675	−	19.6528i	2.44438	−	0.855279i
$529$	13.7523			0.597926
$530$	−16.1433	−	27.9609i	−0.701218	−	1.21455i
$531$	28.6605	−	22.8545i	1.24376	−	0.991800i
$532$		0			0
$533$	10.9688	−	6.33281i	0.475110	−	0.274305i
$534$	28.3334	+	24.3837i	1.22611	+	1.05519i
$535$	10.2963	−	5.94457i	0.445147	−	0.257006i
$536$	−40.3927	+	23.3207i	−1.74470	+	1.00730i
$537$	−24.7557	+	8.66194i	−1.06829	+	0.373790i
$538$	−0.568399	+	0.328165i	−0.0245054	+	0.0141482i
$539$		0			0
$540$	−1.24915	+	33.3408i	−0.0537547	+	1.43476i
$541$	−1.02015	−	1.76696i	−0.0438598	−	0.0759674i	0.843262	−	0.537503i	$-0.180632\pi$
$541$	−1.02015	−	1.76696i	−0.0438598	−	0.0759674i	−0.887122	+	0.461535i	$0.847299\pi$
$542$	−2.90670			−0.124854
$543$	10.4858	+	9.02402i	0.449987	+	0.387258i
$544$			23.2833i			0.998264i
$545$	6.26338	−	10.8485i	0.268294	−	0.464699i
$546$		0			0
$547$	−8.93590	−	15.4774i	−0.382071	−	0.661767i	0.609287	−	0.792950i	$-0.291456\pi$
$547$	−8.93590	−	15.4774i	−0.382071	−	0.661767i	−0.991358	+	0.131183i	$0.958123\pi$
$548$	−53.9064	+	31.1229i	−2.30277	+	1.32950i
$549$	−12.3265	+	31.4045i	−0.526083	+	1.34031i
$550$	−11.9663	+	20.7262i	−0.510244	+	0.883769i
$551$	0.749783	−	1.29866i	0.0319418	−	0.0553249i
$552$	31.0643	−	36.0962i	1.32218	−	1.53635i
$553$		0			0
$554$	−11.4986	−	6.63870i	−0.488527	−	0.282051i
$555$	3.54354	+	0.670533i	0.150415	+	0.0284625i
$556$			53.8625i			2.28428i
$557$	37.2049	+	21.4802i	1.57642	+	0.910147i	0.995353	+	0.0962924i	$0.0306984\pi$
$557$	37.2049	+	21.4802i	1.57642	+	0.910147i	0.581068	+	0.813855i	$0.302635\pi$
$558$	−4.24206	−	28.1504i	−0.179581	−	1.19170i
$559$			0.0247261i			0.00104580i
$560$		0			0
$561$	−4.89357	+	1.71225i	−0.206607	+	0.0722911i
$562$	36.1625			1.52543
$563$	−0.773739	−	1.34016i	−0.0326092	−	0.0564808i	0.849260	−	0.527975i	$-0.177048\pi$
$563$	−0.773739	−	1.34016i	−0.0326092	−	0.0564808i	−0.881869	+	0.471494i	$0.843715\pi$
$564$	−8.65286	+	10.0545i	−0.364351	+	0.423370i
$565$	11.5016	+	6.64048i	0.483878	+	0.279367i
$566$	10.1759			0.427726
$567$		0			0
$568$	108.906			4.56958
$569$	8.65905	+	4.99931i	0.363006	+	0.209582i	0.670399	−	0.742001i	$-0.266123\pi$
$569$	8.65905	+	4.99931i	0.363006	+	0.209582i	−0.307392	+	0.951583i	$0.599456\pi$
$570$	27.5016	−	31.9564i	1.15191	−	1.33850i
$571$	1.39715	+	2.41994i	0.0584689	+	0.101271i	0.893778	−	0.448509i	$-0.148045\pi$
$571$	1.39715	+	2.41994i	0.0584689	+	0.101271i	−0.835309	+	0.549780i	$0.814711\pi$
$572$	25.0147			1.04592
$573$	−26.1855	+	9.16224i	−1.09392	+	0.382758i
$574$		0			0
$575$			10.8046i			0.450582i
$576$	11.0702	+	73.4621i	0.461258	+	3.06092i
$577$	−3.23689	−	1.86882i	−0.134754	−	0.0778000i	0.431108	−	0.902300i	$-0.358123\pi$
$577$	−3.23689	−	1.86882i	−0.134754	−	0.0778000i	−0.565861	+	0.824500i	$0.691456\pi$
$578$			42.1251i			1.75217i
$579$	23.3313	+	4.41490i	0.969614	+	0.183477i
$580$	1.11626	+	0.644475i	0.0463503	+	0.0267604i
$581$		0			0
$582$	7.28910	−	8.46981i	0.302143	−	0.351085i
$583$	12.3193	−	21.3377i	0.510214	−	0.883717i
$584$	39.2037	−	67.9028i	1.62226	−	2.80984i
$585$	−2.48493	+	6.33090i	−0.102739	+	0.261751i
$586$	29.9540	−	17.2940i	1.23739	−	0.714407i
$587$	−13.1249	−	22.7331i	−0.541725	−	0.938295i	−0.998805	−	0.0488692i	$-0.984438\pi$
$587$	−13.1249	−	22.7331i	−0.541725	−	0.938295i	0.457081	−	0.889425i	$-0.348895\pi$
$588$		0			0
$589$	−13.0845	+	22.6630i	−0.539136	+	0.933812i
$590$		−	39.8162i		−	1.63921i
$591$	−24.8450	−	21.3816i	−1.02199	−	0.879521i
$592$	23.9145			0.982882
$593$	1.79833	+	3.11481i	0.0738488	+	0.127910i	0.900585	−	0.434680i	$-0.143138\pi$
$593$	1.79833	+	3.11481i	0.0738488	+	0.127910i	−0.826736	+	0.562590i	$0.809805\pi$
$594$	−30.9457	+	16.3534i	−1.26972	+	0.670987i
$595$		0			0
$596$	22.1522	−	12.7896i	0.907391	−	0.523882i
$597$	−40.5977	+	14.2050i	−1.66155	+	0.581372i
$598$	13.4446	−	7.76226i	0.549792	−	0.317422i
$599$	−20.6400	+	11.9165i	−0.843326	+	0.486895i	−0.858394	−	0.512992i	$-0.828537\pi$
$599$	−20.6400	+	11.9165i	−0.843326	+	0.486895i	0.0150672	+	0.999886i	$0.495204\pi$
$600$	−42.1730	−	36.2940i	−1.72171	−	1.48170i
$601$	−14.6034	+	8.43126i	−0.595684	+	0.343918i	−0.767342	−	0.641238i	$-0.778421\pi$
$601$	−14.6034	+	8.43126i	−0.595684	+	0.343918i	0.171658	+	0.985157i	$0.445088\pi$
$602$		0			0
$603$	12.0999	−	9.64870i	0.492746	−	0.392925i
$604$	−30.2076	−	52.3212i	−1.22913	−	2.12892i
$605$	−5.79391			−0.235556
$606$	41.9183	−	14.6671i	1.70281	−	0.595809i
$607$			10.4816i			0.425437i	0.977114	+	0.212718i	$0.0682317\pi$
$607$			10.4816i			0.425437i	−0.977114	+	0.212718i	$0.931768\pi$
$608$	72.2463	−	125.134i	2.92997	−	5.07487i
$609$		0			0
$610$	18.3222	+	31.7349i	0.741842	+	1.28491i
$611$	−2.34176	+	1.35202i	−0.0947377	+	0.0546968i
$612$	−2.87226	−	19.0604i	−0.116104	−	0.770471i
$613$	23.9500	−	41.4827i	0.967333	−	1.67547i	0.264120	−	0.964490i	$-0.414919\pi$
$613$	23.9500	−	41.4827i	0.967333	−	1.67547i	0.703213	−	0.710979i	$-0.251748\pi$
$614$	14.5270	−	25.1616i	0.586264	−	1.01544i
$615$	4.62454	+	13.2169i	0.186480	+	0.532956i
$616$		0			0
$617$	4.69477	+	2.71053i	0.189004	+	0.109122i	0.591516	−	0.806293i	$-0.298530\pi$
$617$	4.69477	+	2.71053i	0.189004	+	0.109122i	−0.402512	+	0.915415i	$0.631863\pi$
$618$	26.7422	+	76.4289i	1.07573	+	3.07442i
$619$			32.3003i			1.29826i	0.760678	+	0.649129i	$0.224866\pi$
$619$			32.3003i			1.29826i	−0.760678	+	0.649129i	$0.775134\pi$
$620$	−19.4799	−	11.2467i	−0.782332	−	0.451680i
$621$	−8.40757	+	13.3791i	−0.337384	+	0.536886i
$622$		−	51.0204i		−	2.04573i
$623$		0			0
$624$	−8.38513	+	44.3126i	−0.335674	+	1.77392i
$625$	5.38836			0.215534
$626$	−35.3098	−	61.1584i	−1.41126	−	2.44438i
$627$	31.6131	+	5.98205i	1.26250	+	0.238900i
$628$	68.0989	+	39.3169i	2.71744	+	1.56892i
$629$	−2.08355			−0.0830765
$630$		0			0
$631$	−18.3539			−0.730656			−0.365328	−	0.930879i	$-0.619043\pi$
$631$	−18.3539			−0.730656			−0.365328	+	0.930879i	$0.619043\pi$
$632$	−43.0343	−	24.8459i	−1.71181	−	0.988315i
$633$	−4.12735	−	11.7959i	−0.164047	−	0.468845i
$634$	−18.8127	−	32.5845i	−0.747147	−	1.29410i
$635$	−16.6767			−0.661795
$636$	69.4330	+	59.7539i	2.75320	+	2.36940i
$637$		0			0
$638$			1.35218i			0.0535335i
$639$	−35.7322	+	5.38457i	−1.41354	+	0.213010i
$640$	29.5816	+	17.0789i	1.16931	+	0.675104i
$641$			10.4732i			0.413665i	0.978376	+	0.206833i	$0.0663155\pi$
$641$			10.4732i			0.413665i	−0.978376	+	0.206833i	$0.933684\pi$
$642$	−30.2482	+	35.1479i	−1.19380	+	1.38718i
$643$	3.37572	+	1.94897i	0.133125	+	0.0768600i	0.565084	−	0.825034i	$-0.308844\pi$
$643$	3.37572	+	1.94897i	0.133125	+	0.0768600i	−0.431958	+	0.901894i	$0.642177\pi$
$644$		0			0
$645$	−0.0268595	−	0.00508254i	−0.00105759	−	0.000200125i
$646$	−12.1789	+	21.0945i	−0.479172	+	0.829950i
$647$	−6.20269	+	10.7434i	−0.243853	+	0.422366i	−0.961809	−	0.273723i	$-0.911745\pi$
$647$	−6.20269	+	10.7434i	−0.243853	+	0.422366i	0.717955	+	0.696089i	$0.245078\pi$
$648$	−23.9800	−	77.7591i	−0.942023	−	3.05467i
$649$	26.3140	−	15.1924i	1.03291	−	0.596353i
$650$	−9.06905	−	15.7081i	−0.355717	−	0.616120i
$651$		0			0
$652$	−48.4615	+	83.9377i	−1.89790	+	3.28726i
$653$			14.1738i			0.554664i	0.960774	+	0.277332i	$0.0894502\pi$
$653$			14.1738i			0.554664i	−0.960774	+	0.277332i	$0.910550\pi$
$654$	−9.08417	+	48.0067i	−0.355219	+	1.87721i
$655$	−14.8676			−0.580925
$656$	46.4263	+	80.4126i	1.81264	+	3.13959i
$657$	−9.50554	+	24.2174i	−0.370846	+	0.944811i
$658$		0			0
$659$	−17.2962	+	9.98594i	−0.673763	+	0.388997i	−0.797501	−	0.603318i	$-0.793845\pi$
$659$	−17.2962	+	9.98594i	−0.673763	+	0.388997i	0.123738	+	0.992315i	$0.460512\pi$
$660$	−5.14186	+	27.1730i	−0.200146	+	1.05771i
$661$	21.0493	−	12.1528i	0.818721	−	0.472689i	−0.0312540	−	0.999511i	$-0.509950\pi$
$661$	21.0493	−	12.1528i	0.818721	−	0.472689i	0.849975	+	0.526823i	$0.176617\pi$
$662$	−10.5205	+	6.07401i	−0.408891	+	0.236073i
$663$	0.730552	−	3.86072i	0.0283723	−	0.149938i
$664$	−25.1900	+	14.5435i	−0.977563	+	0.564396i
$665$		0			0
$666$	−13.9092	+	2.09602i	−0.538971	+	0.0812190i
$667$	0.305228	+	0.528670i	0.0118185	+	0.0204702i
$668$	6.39929			0.247596
$669$	−7.83520	+	41.4063i	−0.302926	+	1.60086i
$670$		−	16.8096i		−	0.649411i
$671$	−13.9821	+	24.2177i	−0.539773	+	0.934914i
$672$		0			0
$673$	−1.82521	−	3.16135i	−0.0703566	−	0.121861i	0.828701	−	0.559692i	$-0.189080\pi$
$673$	−1.82521	−	3.16135i	−0.0703566	−	0.121861i	−0.899058	+	0.437830i	$0.855747\pi$
$674$	−76.9508	+	44.4275i	−2.96403	+	1.71129i
$675$	15.6315	+	9.82300i	0.601658	+	0.378087i
$676$	25.2163	−	43.6759i	0.969858	−	1.67984i
$677$	−0.968676	+	1.67780i	−0.0372292	+	0.0644829i	−0.884040	−	0.467412i	$-0.845187\pi$
$677$	−0.968676	+	1.67780i	−0.0372292	+	0.0644829i	0.846810	+	0.531895i	$0.178520\pi$
$678$	−50.8970	−	9.63109i	−1.95469	−	0.369880i
$679$		0			0
$680$	−11.3379	−	6.54597i	−0.434790	−	0.251026i
$681$	0.542963	−	0.630914i	0.0208064	−	0.0241767i
$682$		−	23.5970i		−	0.903575i
$683$	−16.8815	−	9.74656i	−0.645954	−	0.372942i	0.140950	−	0.990017i	$-0.454984\pi$
$683$	−16.8815	−	9.74656i	−0.645954	−	0.372942i	−0.786905	+	0.617075i	$0.788318\pi$
$684$	−43.7062	+	111.351i	−1.67115	+	4.25761i
$685$		−	14.0278i		−	0.535976i
$686$		0			0
$687$	−11.8309	−	10.1816i	−0.451377	−	0.388454i
$688$	−0.181269			−0.00691081
$689$	9.33660	+	16.1715i	0.355696	+	0.616084i
$690$	5.66840	+	16.2002i	0.215792	+	0.616731i
$691$	35.7855	+	20.6608i	1.36134	+	0.785972i	0.989803	−	0.142444i	$-0.0454960\pi$
$691$	35.7855	+	20.6608i	1.36134	+	0.785972i	0.371541	+	0.928416i	$0.378829\pi$
$692$	96.1226			3.65403
$693$		0			0
$694$	−36.3186			−1.37863
$695$	−10.5123	−	6.06929i	−0.398755	−	0.230221i
$696$	−3.08884	−	0.584491i	−0.117082	−	0.0221551i
$697$	−4.04488	−	7.00593i	−0.153211	−	0.265369i
$698$	60.4545			2.28824
$699$	3.58001	−	18.9191i	0.135408	−	0.715586i
$700$		0			0
$701$		−	27.3333i		−	1.03236i	−0.856479	−	0.516182i	$-0.827353\pi$
$701$		−	27.3333i		−	1.03236i	0.856479	−	0.516182i	$-0.172647\pi$
$702$	0.993152	−	26.5081i	0.0374841	−	1.00048i
$703$	11.1979	+	6.46508i	0.422335	+	0.243835i
$704$			61.5793i			2.32086i
$705$	−0.987313	−	2.82172i	−0.0371843	−	0.106272i
$706$	−40.3893	−	23.3187i	−1.52007	−	0.877613i
$707$		0			0
$708$	37.3094	+	106.630i	1.40217	+	4.00739i
$709$	−1.35635	+	2.34926i	−0.0509387	+	0.0882283i	−0.890370	−	0.455237i	$-0.849555\pi$
$709$	−1.35635	+	2.34926i	−0.0509387	+	0.0882283i	0.839432	+	0.543465i	$0.182888\pi$
$710$	−19.6248	+	33.9912i	−0.736506	+	1.27567i
$711$	15.3481	+	6.02425i	0.575598	+	0.225927i
$712$	−62.3845	+	36.0177i	−2.33796	+	1.34982i
$713$	−5.32654	−	9.22584i	−0.199480	−	0.345510i
$714$		0			0
$715$	−2.81868	+	4.88210i	−0.105413	+	0.182580i
$716$		−	80.8262i		−	3.02062i
$717$	22.7375	−	7.95578i	0.849148	−	0.297114i
$718$	17.6058			0.657044
$719$	−8.13931	−	14.0977i	−0.303545	−	0.525756i	0.673391	−	0.739286i	$-0.264837\pi$
$719$	−8.13931	−	14.0977i	−0.303545	−	0.525756i	−0.976936	+	0.213531i	$0.931504\pi$
$720$	−46.4123	−	18.2172i	−1.72968	−	0.678915i
$721$		0			0
$722$	86.3365	−	49.8464i	3.21311	−	1.85509i
$723$	16.2477	+	13.9828i	0.604260	+	0.520025i
$724$	−36.9217	+	21.3167i	−1.37218	+	0.792231i
$725$	0.617673	−	0.356614i	0.0229398	−	0.0132443i
$726$	21.3302	−	7.46337i	0.791638	−	0.276992i
$727$	−0.980123	+	0.565874i	−0.0363508	+	0.0209871i	−0.518065	−	0.855341i	$-0.673348\pi$
$727$	−0.980123	+	0.565874i	−0.0363508	+	0.0209871i	0.481714	+	0.876328i	$0.340014\pi$
$728$		0			0
$729$	11.7125	+	24.3273i	0.433796	+	0.901011i
$730$	14.1290	+	24.4722i	0.522939	+	0.905757i
$731$	0.0157930			0.000584125
$732$	−78.8046	−	67.8190i	−2.91270	−	2.50666i
$733$		−	38.3459i		−	1.41634i	−0.706043	−	0.708169i	$-0.749522\pi$
$733$		−	38.3459i		−	1.41634i	0.706043	−	0.708169i	$-0.250478\pi$
$734$	12.1946	−	21.1217i	0.450111	−	0.779615i
$735$		0			0
$736$	29.4106	+	50.9407i	1.08409	+	1.87770i
$737$	11.1092	−	6.41391i	0.409213	−	0.236259i
$738$	−34.0504	−	42.7007i	−1.25341	−	1.57183i
$739$	−5.36489	+	9.29226i	−0.197351	+	0.341821i	−0.947669	−	0.319256i	$-0.896567\pi$
$739$	−5.36489	+	9.29226i	−0.197351	+	0.341821i	0.750318	+	0.661077i	$0.229900\pi$
$740$	−5.55705	+	9.62509i	−0.204281	+	0.353825i
$741$	−15.9058	+	18.4823i	−0.584314	+	0.678963i
$742$		0			0
$743$	−11.3308	−	6.54185i	−0.415687	−	0.239997i	0.277543	−	0.960713i	$-0.410480\pi$
$743$	−11.3308	−	6.54185i	−0.415687	−	0.239997i	−0.693230	+	0.720716i	$0.743813\pi$
$744$	53.9033	+	10.2000i	1.97619	+	0.373949i
$745$			5.76458i			0.211198i
$746$	26.9927	+	15.5842i	0.988272	+	0.570579i
$747$	7.54584	−	6.01721i	0.276088	−	0.220158i
$748$		−	15.9773i		−	0.584188i
$749$		0			0
$750$	45.5637	−	15.9426i	1.66375	−	0.582142i
$751$	26.3354			0.960991			0.480495	−	0.876997i	$-0.340457\pi$
$751$	26.3354			0.960991			0.480495	+	0.876997i	$0.340457\pi$
$752$	−9.91173	−	17.1676i	−0.361444	−	0.626039i
$753$	−22.2740	+	25.8820i	−0.811710	+	0.943193i
$754$	−0.887501	−	0.512399i	−0.0323209	−	0.0186605i
$755$	13.6153			0.495512
$756$		0			0
$757$	−32.6280			−1.18588			−0.592942	−	0.805245i	$-0.702034\pi$
$757$	−32.6280			−1.18588			−0.592942	+	0.805245i	$0.702034\pi$
$758$	40.1109	+	23.1580i	1.45689	+	0.841138i
$759$	−8.54362	+	9.92754i	−0.310114	+	0.360347i
$760$	40.6232	+	70.3615i	1.47356	+	2.55228i
$761$	25.3454			0.918770			0.459385	−	0.888237i	$-0.348070\pi$
$761$	25.3454			0.918770			0.459385	+	0.888237i	$0.348070\pi$
$762$	61.3951	−	21.4820i	2.22411	−	0.778210i
$763$		0			0
$764$		−	85.4946i		−	3.09309i
$765$	4.04366	+	1.58717i	0.146199	+	0.0573842i
$766$	−38.0403	−	21.9626i	−1.37445	−	0.793541i
$767$			23.0281i			0.831496i
$768$	−46.6156	−	8.82093i	−1.68210	−	0.318298i
$769$	−11.4964	−	6.63744i	−0.414570	−	0.239352i	0.278181	−	0.960529i	$-0.410268\pi$
$769$	−11.4964	−	6.63744i	−0.414570	−	0.239352i	−0.692752	+	0.721176i	$0.743602\pi$
$770$		0			0
$771$	12.6997	−	14.7568i	0.457368	−	0.531454i
$772$	−36.5886	+	63.3733i	−1.31685	+	2.28085i
$773$	8.00680	−	13.8682i	0.287985	−	0.498804i	−0.685344	−	0.728219i	$-0.740348\pi$
$773$	8.00680	−	13.8682i	0.287985	−	0.498804i	0.973329	+	0.229416i	$0.0736815\pi$
$774$	0.105430	−	0.0158875i	0.00378960	−	0.000571065i
$775$	−10.7790	+	6.22327i	−0.387194	+	0.223546i
$776$	10.7669	+	18.6488i	0.386509	+	0.669454i
$777$		0			0
$778$	25.3919	−	43.9801i	0.910344	−	1.57676i
$779$			50.2037i			1.79873i
$780$	−15.8864	−	13.6718i	−0.568824	−	0.489529i
$781$	−29.9524			−1.07178
$782$	−4.95789	−	8.58731i	−0.177294	−	0.307082i
$783$	1.04235	+	0.0390528i	0.0372506	+	0.00139563i
$784$		0			0
$785$	−15.3469	+	8.86054i	−0.547755	+	0.316246i
$786$	54.7348	−	19.1515i	1.95233	−	0.683113i
$787$	−4.24659	+	2.45177i	−0.151375	+	0.0873961i	−0.573774	−	0.819014i	$-0.694521\pi$
$787$	−4.24659	+	2.45177i	−0.151375	+	0.0873961i	0.422400	+	0.906410i	$0.361188\pi$
$788$	87.4826	−	50.5081i	3.11644	−	1.79928i
$789$	−4.27711	−	3.68087i	−0.152269	−	0.131043i
$790$	15.5096	−	8.95445i	0.551806	−	0.318585i
$791$		0			0
$792$	−10.0506	−	66.6958i	−0.357131	−	2.36993i
$793$	−10.5968	−	18.3542i	−0.376303	−	0.651776i
$794$	83.8948			2.97732
$795$	−19.4859	+	6.81806i	−0.691094	+	0.241812i
$796$		−	132.550i		−	4.69809i
$797$	−21.3994	+	37.0649i	−0.758006	+	1.31290i	0.185860	+	0.982576i	$0.440493\pi$
$797$	−21.3994	+	37.0649i	−0.758006	+	1.31290i	−0.943866	+	0.330328i	$0.892841\pi$
$798$		0			0
$799$	0.863557	+	1.49572i	0.0305505	+	0.0529149i
$800$	59.5167	−	34.3620i	2.10423	−	1.21488i
$801$	18.6877	−	14.9019i	0.660297	−	0.526534i
$802$	−1.25282	+	2.16995i	−0.0442386	+	0.0766235i
$803$	−10.7822	+	18.6754i	−0.380496	+	0.659039i
$804$	15.7513	+	45.0169i	0.555505	+	1.58763i
$805$		0			0
$806$	15.4878	+	8.94188i	0.545534	+	0.314964i
$807$	0.138600	+	0.396116i	0.00487895	+	0.0139440i
$808$			85.5809i			3.01072i
$809$	−30.5649	−	17.6467i	−1.07461	−	0.620424i	−0.145169	−	0.989407i	$-0.546373\pi$
$809$	−30.5649	−	17.6467i	−1.07461	−	0.620424i	−0.929436	+	0.368983i	$0.879706\pi$
$810$	28.5910	+	6.52767i	1.00459	+	0.229359i
$811$			21.0223i			0.738193i	0.929391	+	0.369096i	$0.120333\pi$
$811$			21.0223i			0.738193i	−0.929391	+	0.369096i	$0.879667\pi$
$812$		0			0
$813$	−0.345560	+	1.82617i	−0.0121193	+	0.0640465i
$814$	−11.6594			−0.408660
$815$	−10.9214	−	18.9164i	−0.382559	−	0.662612i
$816$	28.3032	+	5.35573i	0.990810	+	0.187488i
$817$	−0.0848782	−	0.0490044i	−0.00296951	−	0.00171445i
$818$	−20.5372			−0.718067
$819$		0			0
$820$	−43.1525			−1.50695
$821$	29.8623	+	17.2410i	1.04220	+	0.601716i	0.920456	−	0.390845i	$-0.127817\pi$
$821$	29.8623	+	17.2410i	1.04220	+	0.601716i	0.121746	+	0.992561i	$0.461151\pi$
$822$	18.0698	+	51.6433i	0.630258	+	1.80127i
$823$	19.4950	+	33.7663i	0.679552	+	1.17702i	0.975116	+	0.221695i	$0.0711590\pi$
$823$	19.4950	+	33.7663i	0.679552	+	1.17702i	−0.295564	+	0.955323i	$0.595508\pi$
$824$	−156.038			−5.43585
$825$	11.5989	+	9.98195i	0.403820	+	0.347527i
$826$		0			0
$827$			47.2537i			1.64317i	0.570086	+	0.821585i	$0.306910\pi$
$827$			47.2537i			1.64317i	−0.570086	+	0.821585i	$0.693090\pi$
$828$	−30.3605	−	38.0734i	−1.05510	−	1.32314i
$829$	42.5588	+	24.5713i	1.47813	+	0.853397i	0.999694	−	0.0247275i	$-0.00787180\pi$
$829$	42.5588	+	24.5713i	1.47813	+	0.853397i	0.478432	+	0.878124i	$0.341205\pi$
$830$		−	10.4829i		−	0.363868i
$831$	−5.53782	+	6.43486i	−0.192105	+	0.223223i
$832$	−40.4174	−	23.3350i	−1.40122	−	0.808995i
$833$		0			0
$834$	46.5190	+	8.80266i	1.61082	+	0.304811i
$835$	−0.721079	+	1.24894i	−0.0249540	+	0.0432215i
$836$	−49.5763	+	85.8687i	−1.71463	+	2.96983i
$837$	−18.1901	−	0.681511i	−0.628742	−	0.0235565i
$838$	13.3746	−	7.72182i	0.462017	−	0.266746i
$839$	26.0780	+	45.1684i	0.900312	+	1.55939i	0.827090	+	0.562070i	$0.189995\pi$
$839$	26.0780	+	45.1684i	0.900312	+	1.55939i	0.0732219	+	0.997316i	$0.476672\pi$
$840$		0			0
$841$	−14.4799	+	25.0798i	−0.499305	+	0.864822i
$842$		−	31.7577i		−	1.09444i
$843$	4.29914	−	22.7195i	0.148070	−	0.782501i
$844$	38.5131			1.32568
$845$	5.68280	+	9.84290i	0.195494	+	0.338606i
$846$	7.26956	+	9.11634i	0.249932	+	0.313426i
$847$		0			0
$848$	−118.554	+	68.4472i	−4.07116	+	2.35049i
$849$	1.20975	−	6.39313i	0.0415186	−	0.219411i
$850$	−10.0330	+	5.79255i	−0.344129	+	0.198683i
$851$	−4.55852	+	2.63186i	−0.156264	+	0.0902190i
$852$	20.7051	−	109.419i	0.709345	−	3.74864i
$853$	−13.4028	+	7.73808i	−0.458902	+	0.264947i	−0.711582	−	0.702603i	$-0.752021\pi$
$853$	−13.4028	+	7.73808i	−0.458902	+	0.264947i	0.252681	+	0.967550i	$0.418688\pi$
$854$		0			0
$855$	−16.8074	−	21.0772i	−0.574802	−	0.720827i
$856$	−44.6804	−	77.3886i	−1.52714	−	2.64509i
$857$	−48.8713			−1.66941			−0.834706	−	0.550696i	$-0.814362\pi$
$857$	−48.8713			−1.66941			−0.834706	+	0.550696i	$0.814362\pi$
$858$	4.08811	−	21.6043i	0.139566	−	0.737557i
$859$			9.75722i			0.332912i	0.986049	+	0.166456i	$0.0532324\pi$
$859$			9.75722i			0.332912i	−0.986049	+	0.166456i	$0.946768\pi$
$860$	0.0421217	−	0.0729569i	0.00143634	−	0.00248781i
$861$		0			0
$862$	−36.4356	−	63.1083i	−1.24100	−	2.14948i
$863$	23.9462	−	13.8253i	0.815138	−	0.470620i	−0.0335987	−	0.999435i	$-0.510697\pi$
$863$	23.9462	−	13.8253i	0.815138	−	0.470620i	0.848737	+	0.528815i	$0.177363\pi$
$864$	100.437	+	3.76298i	3.41694	+	0.128019i
$865$	−10.8312	+	18.7602i	−0.368272	+	0.637866i
$866$	38.0628	−	65.9267i	1.29343	−	2.24028i
$867$	26.4655	+	5.00799i	0.898817	+	0.170080i
$868$		0			0
$869$	11.8357	+	6.83337i	0.401500	+	0.231806i
$870$	0.739038	−	0.858749i	0.0250557	−	0.0291143i
$871$			9.72199i			0.329417i
$872$	−81.5391	−	47.0766i	−2.76126	−	1.59422i
$873$	−4.45469	−	5.58638i	−0.150768	−	0.189070i
$874$			61.5357i			2.08148i
$875$		0			0
$876$	−60.7697	−	52.2983i	−2.05322	−	1.76700i
$877$	−1.86524			−0.0629848			−0.0314924	−	0.999504i	$-0.510026\pi$
$877$	−1.86524			−0.0629848			−0.0314924	+	0.999504i	$0.510026\pi$
$878$	−12.6317	−	21.8787i	−0.426298	−	0.738370i
$879$	−7.30407	−	20.8749i	−0.246360	−	0.704093i
$880$	−35.7910	−	20.6639i	−1.20651	−	0.696581i
$881$	0.0273875			0.000922707			0.000461353	−	1.00000i	$-0.499853\pi$
$881$	0.0273875			0.000922707			0.000461353		1.00000i	$0.499853\pi$
$882$		0			0
$883$	36.2074			1.21848			0.609239	−	0.792987i	$-0.291475\pi$
$883$	36.2074			1.21848			0.609239	+	0.792987i	$0.291475\pi$
$884$	10.4866	+	6.05447i	0.352704	+	0.203634i
$885$	−25.0149	−	4.73350i	−0.840868	−	0.159115i
$886$	−15.3600	−	26.6043i	−0.516028	−	0.893787i
$887$	25.3253			0.850339			0.425170	−	0.905114i	$-0.360214\pi$
$887$	25.3253			0.850339			0.425170	+	0.905114i	$0.360214\pi$
$888$	5.03984	−	26.6338i	0.169126	−	0.893772i
$889$		0			0
$890$		−	25.9616i		−	0.870235i
$891$	6.59523	+	21.3861i	0.220948	+	0.716462i
$892$	−112.470	−	64.9343i	−3.76576	−	2.17416i
$893$		−	10.7182i		−	0.358671i
$894$	−7.42560	−	21.2222i	−0.248349	−	0.709778i
$895$	15.7748	+	9.10759i	0.527294	+	0.304433i
$896$		0			0
$897$	−3.27837	−	9.36953i	−0.109462	−	0.312840i
$898$	−20.7625	+	35.9617i	−0.692854	+	1.20006i
$899$	−0.351613	+	0.609012i	−0.0117270	+	0.0203117i
$900$	−44.4831	+	35.4717i	−1.48277	+	1.18239i
$901$	10.3290	−	5.96345i	0.344109	−	0.198671i
$902$	−22.6348	−	39.2046i	−0.753655	−	1.30537i
$903$		0			0
$904$	49.9110	−	86.4483i	1.66001	−	2.87523i
$905$		−	9.60798i		−	0.319380i
$906$	−50.1246	+	17.5385i	−1.66528	+	0.582676i
$907$	−38.8120			−1.28873			−0.644366	−	0.764717i	$-0.722879\pi$
$907$	−38.8120			−1.28873			−0.644366	+	0.764717i	$0.722879\pi$
$908$	1.28260	+	2.22153i	0.0425646	+	0.0737240i
$909$	−4.23134	−	28.0793i	−0.140345	−	0.931331i
$910$		0			0
$911$	−43.6110	+	25.1788i	−1.44490	+	0.834211i	−0.998171	−	0.0604602i	$-0.980743\pi$
$911$	−43.6110	+	25.1788i	−1.44490	+	0.834211i	−0.446725	+	0.894671i	$0.647410\pi$
$912$	−135.495	−	116.606i	−4.48668	−	3.86122i
$913$	6.92803	−	3.99990i	0.229284	−	0.132377i
$914$	21.5190	−	12.4240i	0.711787	−	0.410950i
$915$	22.1160	−	7.73832i	0.731132	−	0.255821i
$916$	41.6581	−	24.0513i	1.37642	−	0.794677i
$917$		0			0
$918$	−16.9312	−	0.634343i	−0.558812	−	0.0209364i
$919$	1.49845	+	2.59539i	0.0494293	+	0.0856140i	0.889681	−	0.456582i	$-0.150926\pi$
$919$	1.49845	+	2.59539i	0.0494293	+	0.0856140i	−0.840252	+	0.542196i	$0.817593\pi$
$920$	−33.0745			−1.09043
$921$	−14.0810	−	12.1181i	−0.463985	−	0.399304i
$922$			89.5890i			2.95046i
$923$	11.3502	−	19.6591i	0.373596	−	0.647088i
$924$		0			0
$925$	3.07494	+	5.32595i	0.101103	+	0.175116i
$926$	18.3729	−	10.6076i	0.603771	−	0.348588i
$927$	51.1965	−	7.71493i	1.68151	−	0.253392i
$928$	1.94144	−	3.36268i	0.0637310	−	0.110385i
$929$	−16.1108	+	27.9047i	−0.528577	+	0.915522i	0.470868	+	0.882204i	$0.343941\pi$
$929$	−16.1108	+	27.9047i	−0.528577	+	0.915522i	−0.999445	+	0.0333184i	$0.989392\pi$
$930$	−12.8970	+	14.9860i	−0.422908	+	0.491412i
$931$		0			0
$932$	51.3888	+	29.6694i	1.68330	+	0.971852i
$933$	−32.0541	−	6.06550i	−1.04940	−	0.198576i
$934$		−	56.0104i		−	1.83272i
$935$	3.11828	+	1.80034i	0.101979	+	0.0588774i
$936$	47.5841	+	18.6772i	1.55534	+	0.610482i
$937$			3.07038i			0.100305i	0.998742	+	0.0501525i	$0.0159708\pi$
$937$			3.07038i			0.100305i	−0.998742	+	0.0501525i	$0.984029\pi$
$938$		0			0
$939$	−42.6212	+	14.9130i	−1.39089	+	0.486668i
$940$	9.21280			0.300489
$941$	19.4136	+	33.6253i	0.632865	+	1.09615i	0.986963	+	0.160946i	$0.0514543\pi$
$941$	19.4136	+	33.6253i	0.632865	+	1.09615i	−0.354099	+	0.935208i	$0.615212\pi$
$942$	45.0858	−	52.3890i	1.46898	−	1.70692i
$943$	−17.6993	−	10.2187i	−0.576367	−	0.332766i
$944$	−168.820			−5.49464
$945$		0			0
$946$	0.0883763			0.00287336
$947$	−16.2391	−	9.37567i	−0.527701	−	0.304668i	0.212379	−	0.977187i	$-0.431879\pi$
$947$	−16.2391	−	9.37567i	−0.527701	−	0.304668i	−0.740080	+	0.672519i	$0.765212\pi$
$948$	−33.1447	+	38.5136i	−1.07649	+	1.25086i
$949$	−8.17166	−	14.1537i	−0.265263	−	0.459450i
$950$	71.8953			2.33259
$951$	−22.7081	+	7.94549i	−0.736360	+	0.257650i
$952$		0			0
$953$		−	47.6453i		−	1.54338i	−0.635997	−	0.771692i	$-0.719411\pi$
$953$		−	47.6453i		−	1.54338i	0.635997	−	0.771692i	$-0.280589\pi$
$954$	62.9545	−	50.2012i	2.03823	−	1.62532i
$955$	16.6859	+	9.63362i	0.539944	+	0.311737i
$956$			74.2370i			2.40099i
$957$	0.849524	+	0.160753i	0.0274612	+	0.00519640i
$958$	6.24009	+	3.60272i	0.201608	+	0.116398i
$959$		0			0
$960$	33.6562	−	39.1080i	1.08625	−	1.26220i
$961$	−9.36399	+	16.2189i	−0.302064	+	0.523191i
$962$	4.41821	−	7.65257i	0.142449	−	0.246729i
$963$	18.4860	+	23.1823i	0.595704	+	0.747038i
$964$	−57.2104	+	33.0304i	−1.84262	+	1.06384i
$965$	−8.24569	−	14.2819i	−0.265438	−	0.459752i
$966$		0			0
$967$	25.8005	−	44.6878i	0.829689	−	1.43706i	−0.0685936	−	0.997645i	$-0.521851\pi$
$967$	25.8005	−	44.6878i	0.829689	−	1.43706i	0.898282	−	0.439419i	$-0.144815\pi$
$968$			43.5480i			1.39969i
$969$	11.8049	+	10.1593i	0.379229	+	0.326364i
$970$	−7.76079			−0.249184
$971$	−14.1933	−	24.5836i	−0.455485	−	0.788924i	0.543231	−	0.839584i	$-0.317201\pi$
$971$	−14.1933	−	24.5836i	−0.455485	−	0.788924i	−0.998716	+	0.0506597i	$0.983868\pi$
$972$	−82.6849	+	9.30958i	−2.65212	+	0.298605i
$973$		0			0
$974$	2.44867	−	1.41374i	0.0784603	−	0.0452991i
$975$	−10.9469	+	3.83029i	−0.350582	+	0.122667i
$976$	134.556	−	77.6858i	4.30702	−	2.48666i
$977$	−35.6722	+	20.5954i	−1.14126	+	0.658904i	−0.946741	−	0.321995i	$-0.895647\pi$
$977$	−35.6722	+	20.5954i	−1.14126	+	0.658904i	−0.194515	+	0.980900i	$0.562313\pi$
$978$	64.5739	+	55.5722i	2.06485	+	1.77700i
$979$	17.1576	−	9.90597i	0.548361	−	0.316596i
$980$		0			0
$981$	29.0808	+	11.4144i	0.928477	+	0.364435i
$982$	56.3668	+	97.6302i	1.79874	+	3.11550i
$983$	52.8035			1.68417			0.842085	−	0.539346i	$-0.181328\pi$
$983$	52.8035			1.68417			0.842085	+	0.539346i	$0.181328\pi$
$984$	99.3402	−	34.7588i	3.16685	−	1.10807i
$985$			22.7652i			0.725361i
$986$	−0.327278	+	0.566862i	−0.0104227	+	0.0180526i
$987$		0			0
$988$	−37.5731	−	65.0784i	−1.19536	−	2.07042i
$989$	0.0345529	−	0.0199491i	0.00109872	−	0.000634346i
$990$	22.6279	+	8.88166i	0.719163	+	0.282278i
$991$	−8.24486	+	14.2805i	−0.261907	+	0.453636i	−0.966749	−	0.255729i	$-0.917685\pi$
$991$	−8.24486	+	14.2805i	−0.261907	+	0.453636i	0.704842	+	0.709364i	$0.251018\pi$
$992$	−33.8801	+	58.6821i	−1.07570	+	1.86316i
$993$	2.56534	+	7.33171i	0.0814087	+	0.232665i
$994$		0			0
$995$	25.8696	+	14.9358i	0.820122	+	0.473498i
$996$	9.82296	+	28.0739i	0.311252	+	0.889554i
$997$		−	49.0582i		−	1.55369i	−0.629692	−	0.776845i	$-0.716819\pi$
$997$		−	49.0582i		−	1.55369i	0.629692	−	0.776845i	$-0.283181\pi$
$998$	−75.7484	−	43.7333i	−2.39777	−	1.38435i
$999$	−0.336737	+	8.98779i	−0.0106539	+	0.284361i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.s.d.374.24		48
3.2	odd	2		1323.2.s.d.962.1		48
7.2	even	3		441.2.i.d.68.2		48
7.3	odd	6		441.2.o.e.293.2	yes	48
7.4	even	3		441.2.o.e.293.1	yes	48
7.5	odd	6		441.2.i.d.68.1		48
7.6	odd	2	inner	441.2.s.d.374.23		48
9.2	odd	6		441.2.i.d.227.23		48
9.7	even	3		1323.2.i.d.521.21		48
21.2	odd	6		1323.2.i.d.1097.6		48
21.5	even	6		1323.2.i.d.1097.21		48
21.11	odd	6		1323.2.o.e.881.23		48
21.17	even	6		1323.2.o.e.881.24		48
21.20	even	2		1323.2.s.d.962.2		48
63.2	odd	6	inner	441.2.s.d.362.23		48
63.11	odd	6		441.2.o.e.146.2	yes	48
63.16	even	3		1323.2.s.d.656.2		48
63.20	even	6		441.2.i.d.227.24		48
63.25	even	3		1323.2.o.e.440.24		48
63.34	odd	6		1323.2.i.d.521.6		48
63.38	even	6		441.2.o.e.146.1	✓	48
63.47	even	6	inner	441.2.s.d.362.24		48
63.52	odd	6		1323.2.o.e.440.23		48
63.61	odd	6		1323.2.s.d.656.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.1		48	7.5	odd	6
441.2.i.d.68.2		48	7.2	even	3
441.2.i.d.227.23		48	9.2	odd	6
441.2.i.d.227.24		48	63.20	even	6
441.2.o.e.146.1	✓	48	63.38	even	6
441.2.o.e.146.2	yes	48	63.11	odd	6
441.2.o.e.293.1	yes	48	7.4	even	3
441.2.o.e.293.2	yes	48	7.3	odd	6
441.2.s.d.362.23		48	63.2	odd	6	inner
441.2.s.d.362.24		48	63.47	even	6	inner
441.2.s.d.374.23		48	7.6	odd	2	inner
441.2.s.d.374.24		48	1.1	even	1	trivial
1323.2.i.d.521.6		48	63.34	odd	6
1323.2.i.d.521.21		48	9.7	even	3
1323.2.i.d.1097.6		48	21.2	odd	6
1323.2.i.d.1097.21		48	21.5	even	6
1323.2.o.e.440.23		48	63.52	odd	6
1323.2.o.e.440.24		48	63.25	even	3
1323.2.o.e.881.23		48	21.11	odd	6
1323.2.o.e.881.24		48	21.17	even	6
1323.2.s.d.656.1		48	63.61	odd	6
1323.2.s.d.656.2		48	63.16	even	3
1323.2.s.d.962.1		48	3.2	odd	2
1323.2.s.d.962.2		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+(2.34591 + 1.35441i) q^{2} +(1.12982 - 1.31283i) q^{3} +(2.66888 + 4.62263i) q^{4} -1.20293 q^{5} +(4.42857 - 1.54954i) q^{6} +9.04141i q^{8} +(-0.447031 - 2.96651i) q^{9} +(-2.82197 - 1.62926i) q^{10} -2.48666i q^{11} +(9.08406 + 1.71895i) q^{12} +(1.63211 + 0.942300i) q^{13} +(-1.35909 + 1.57924i) q^{15} +(-6.90806 + 11.9651i) q^{16} +(0.601863 - 1.04246i) q^{17} +(2.96918 - 7.56464i) q^{18} +(-6.46933 + 3.73507i) q^{19} +(-3.21047 - 5.56070i) q^{20} +(3.36797 - 5.83350i) q^{22} -3.04101i q^{23} +(11.8698 + 10.2151i) q^{24} -3.55296 q^{25} +(2.55253 + 4.42111i) q^{26} +(-4.39957 - 2.76473i) q^{27} +(-0.173847 + 0.100371i) q^{29} +(-5.32725 + 1.86399i) q^{30} +(3.03381 - 1.75157i) q^{31} +(-16.7513 + 9.67135i) q^{32} +(-3.26456 - 2.80947i) q^{33} +(2.82384 - 1.63034i) q^{34} +(12.5200 - 9.98370i) q^{36} +(-0.865458 - 1.49902i) q^{37} -20.2353 q^{38} +(3.08106 - 1.07805i) q^{39} -10.8762i q^{40} +(3.36029 - 5.82020i) q^{41} +(0.00656005 + 0.0113623i) q^{43} +(11.4949 - 6.63660i) q^{44} +(0.537746 + 3.56850i) q^{45} +(4.11878 - 7.13394i) q^{46} +(-0.717403 + 1.24258i) q^{47} +(7.90329 + 22.5875i) q^{48} +(-8.33495 - 4.81219i) q^{50} +(-0.688572 - 1.96793i) q^{51} +10.0595i q^{52} +(8.58085 + 4.95416i) q^{53} +(-6.57643 - 12.4447i) q^{54} +2.99128i q^{55} +(-2.40565 + 12.7130i) q^{57} -0.543775 q^{58} +(6.10954 + 10.5820i) q^{59} +(-10.9275 - 2.06777i) q^{60} +(-9.73903 - 5.62283i) q^{61} +9.48942 q^{62} -24.7638 q^{64} +(-1.96331 - 1.13352i) q^{65} +(-3.85319 - 11.0124i) q^{66} +(2.57932 + 4.46752i) q^{67} +6.42520 q^{68} +(-3.99231 - 3.43578i) q^{69} -12.0452i q^{71} +(26.8214 - 4.04179i) q^{72} +(-7.51020 - 4.33602i) q^{73} -4.68875i q^{74} +(-4.01420 + 4.66443i) q^{75} +(-34.5317 - 19.9369i) q^{76} +(8.68805 + 1.64401i) q^{78} +(-2.74801 + 4.75969i) q^{79} +(8.30991 - 14.3932i) q^{80} +(-8.60033 + 2.65224i) q^{81} +(15.7659 - 9.10246i) q^{82} +(1.60854 + 2.78607i) q^{83} +(-0.723998 + 1.25400i) q^{85} +0.0355401i q^{86} +(-0.0646460 + 0.341632i) q^{87} +22.4829 q^{88} +(3.98364 + 6.89986i) q^{89} +(-3.57172 + 9.09972i) q^{90} +(14.0574 - 8.11607i) q^{92} +(1.12814 - 5.96182i) q^{93} +(-3.36593 + 1.94332i) q^{94} +(7.78214 - 4.49302i) q^{95} +(-6.22905 + 32.9184i) q^{96} +(2.06260 - 1.19084i) q^{97} +(-7.37671 + 1.11162i) 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

Fields

Representations

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Database

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