LMFDB - Embedded newform 873.2.bo.b.442.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [873,2,Mod(73,873)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(873, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("873.73"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 873 = 3^{2} \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	873.bo (of order $24$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [56] 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:	$6.97094009646$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 97)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			442.4
Character	$\chi$	$=$	873.442
Dual form			873.2.bo.b.397.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.168402 + 0.628486i) q^{2} +(1.36542 - 0.788323i) q^{4} +(-0.240478 + 1.82661i) q^{5} +(2.03717 - 1.56318i) q^{7} +(1.64556 + 1.64556i) q^{8} +(-1.18850 + 0.156468i) q^{10} +(-1.20639 + 4.50229i) q^{11} +(-0.895889 + 6.80495i) q^{13} +(1.32550 + 1.01709i) q^{14} +(0.819554 - 1.41951i) q^{16} +(-3.71898 - 2.85368i) q^{17} +(-4.18366 + 1.73293i) q^{19} +(1.11161 + 2.68366i) q^{20} -3.03279 q^{22} +(3.49421 - 4.55375i) q^{23} +(1.55095 + 0.415576i) q^{25} +(-4.42769 + 0.582916i) q^{26} +(1.54930 - 3.74033i) q^{28} +(2.46586 + 0.324637i) q^{29} +(5.75920 - 1.54317i) q^{31} +(5.52590 + 1.48066i) q^{32} +(1.16721 - 2.81789i) q^{34} +(2.36542 + 4.09703i) q^{35} +(3.26313 + 4.25260i) q^{37} +(-1.79366 - 2.33754i) q^{38} +(-3.40151 + 2.61007i) q^{40} +(-0.301931 - 0.0397499i) q^{41} +(-4.03522 - 2.32974i) q^{43} +(1.90204 + 7.09853i) q^{44} +(3.45040 + 1.42920i) q^{46} -1.31590i q^{47} +(-0.105189 + 0.392572i) q^{49} +1.04473i q^{50} +(4.14124 + 9.99784i) q^{52} +(0.993641 + 3.70832i) q^{53} +(-7.93383 - 3.28630i) q^{55} +(5.92457 + 0.779984i) q^{56} +(0.211227 + 1.60443i) q^{58} +(-6.37251 - 8.30482i) q^{59} +(3.08241 - 5.33890i) q^{61} +(1.93972 + 3.35970i) q^{62} +0.444079i q^{64} +(-12.2146 - 3.27288i) q^{65} +(-2.60485 + 1.07896i) q^{67} +(-7.32758 - 0.964694i) q^{68} +(-2.17658 + 2.17658i) q^{70} +(1.48326 - 0.195275i) q^{71} +(-0.448016 - 0.258662i) q^{73} +(-2.12318 + 2.76698i) q^{74} +(-4.34633 + 5.66425i) q^{76} +(4.58026 + 11.0577i) q^{77} +(3.64268 + 3.64268i) q^{79} +(2.39581 + 1.83837i) q^{80} +(-0.0258635 - 0.196453i) q^{82} +(2.76947 + 2.12509i) q^{83} +(6.10689 - 6.10689i) q^{85} +(0.784665 - 2.92841i) q^{86} +(-9.39395 + 5.42360i) q^{88} +(-3.39457 - 3.39457i) q^{89} +(8.81226 + 15.2633i) q^{91} +(1.18123 - 8.97233i) q^{92} +(0.827025 - 0.221601i) q^{94} +(-2.15931 - 8.05865i) q^{95} +(-9.83979 - 0.422473i) q^{97} -0.264440 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{2} - 12 q^{4} + 16 q^{5} - 16 q^{7} + 16 q^{8} - 24 q^{10} + 24 q^{13} + 32 q^{14} + 12 q^{16} + 4 q^{17} + 20 q^{19} - 4 q^{20} + 20 q^{23} + 52 q^{25} + 20 q^{26} + 32 q^{28} + 8 q^{29} + 12 q^{31}+ \cdots - 96 q^{98}+O(q^{100}) $ 56 * q + 8 * q^2 - 12 * q^4 + 16 * q^5 - 16 * q^7 + 16 * q^8 - 24 * q^10 + 24 * q^13 + 32 * q^14 + 12 * q^16 + 4 * q^17 + 20 * q^19 - 4 * q^20 + 20 * q^23 + 52 * q^25 + 20 * q^26 + 32 * q^28 + 8 * q^29 + 12 * q^31 + 136 * q^32 + 20 * q^34 - 28 * q^35 + 52 * q^37 - 24 * q^38 + 72 * q^40 + 48 * q^41 - 12 * q^43 - 36 * q^44 + 72 * q^46 - 32 * q^49 - 16 * q^52 + 44 * q^53 - 8 * q^55 + 64 * q^56 - 100 * q^58 + 48 * q^59 - 12 * q^61 - 28 * q^62 - 16 * q^65 + 48 * q^67 - 16 * q^68 - 24 * q^70 + 4 * q^71 + 24 * q^73 - 20 * q^74 - 56 * q^76 - 12 * q^77 + 24 * q^79 + 136 * q^80 - 8 * q^82 - 76 * q^83 - 40 * q^85 + 68 * q^86 - 168 * q^88 + 100 * q^89 - 60 * q^91 + 52 * q^92 - 88 * q^94 - 32 * q^95 - 36 * q^97 - 96 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/873\mathbb{Z}\right)^\times$.

$n$	$199$	$389$
$\chi(n)$	$e\left(\frac{13}{24}\right)$	$1$

Coefficient data

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

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

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

$2$	0.168402	+	0.628486i	0.119078	+	0.444406i	0.999560	−	0.0296745i	$-0.00944707\pi$
$2$	0.168402	+	0.628486i	0.119078	+	0.444406i	−0.880481	+	0.474081i	$0.842780\pi$
$3$		0			0
$3$		0			0
$4$	1.36542	−	0.788323i	0.682708	−	0.394162i
$5$	−0.240478	+	1.82661i	−0.107545	+	0.816886i	0.849631	+	0.527378i	$0.176825\pi$
$5$	−0.240478	+	1.82661i	−0.107545	+	0.816886i	−0.957176	+	0.289507i	$0.906508\pi$
$6$		0			0
$7$	2.03717	−	1.56318i	0.769978	−	0.590825i	−0.147291	−	0.989093i	$-0.547055\pi$
$7$	2.03717	−	1.56318i	0.769978	−	0.590825i	0.917269	+	0.398268i	$0.130389\pi$
$8$	1.64556	+	1.64556i	0.581792	+	0.581792i
$9$		0			0
$10$	−1.18850	+	0.156468i	−0.375835	+	0.0494797i
$11$	−1.20639	+	4.50229i	−0.363739	+	1.35749i	0.505383	+	0.862895i	$0.331351\pi$
$11$	−1.20639	+	4.50229i	−0.363739	+	1.35749i	−0.869122	+	0.494598i	$0.835315\pi$
$12$		0			0
$13$	−0.895889	+	6.80495i	−0.248475	+	1.88735i	0.179795	+	0.983704i	$0.442457\pi$
$13$	−0.895889	+	6.80495i	−0.248475	+	1.88735i	−0.428270	+	0.903651i	$0.640877\pi$
$14$	1.32550	+	1.01709i	0.354254	+	0.271829i
$15$		0			0
$16$	0.819554	−	1.41951i	0.204888	−	0.354877i
$17$	−3.71898	−	2.85368i	−0.901986	−	0.692118i	0.0498396	−	0.998757i	$-0.484129\pi$
$17$	−3.71898	−	2.85368i	−0.901986	−	0.692118i	−0.951826	+	0.306639i	$0.900796\pi$
$18$		0			0
$19$	−4.18366	+	1.73293i	−0.959798	+	0.397561i	−0.806905	−	0.590682i	$-0.798859\pi$
$19$	−4.18366	+	1.73293i	−0.959798	+	0.397561i	−0.152893	+	0.988243i	$0.548859\pi$
$20$	1.11161	+	2.68366i	0.248563	+	0.600084i
$21$		0			0
$22$	−3.03279			−0.646592
$23$	3.49421	−	4.55375i	0.728594	−	0.949522i	−0.271322	−	0.962489i	$-0.587461\pi$
$23$	3.49421	−	4.55375i	0.728594	−	0.949522i	0.999916	+	0.0129666i	$0.00412752\pi$
$24$		0			0
$25$	1.55095	+	0.415576i	0.310190	+	0.0831151i
$26$	−4.42769	+	0.582916i	−0.868341	+	0.114319i
$27$		0			0
$28$	1.54930	−	3.74033i	0.292790	−	0.706857i
$29$	2.46586	+	0.324637i	0.457899	+	0.0602836i	0.355948	−	0.934506i	$-0.384158\pi$
$29$	2.46586	+	0.324637i	0.457899	+	0.0602836i	0.101951	+	0.994789i	$0.467491\pi$
$30$		0			0
$31$	5.75920	−	1.54317i	1.03438	−	0.277162i	0.298599	−	0.954379i	$-0.403481\pi$
$31$	5.75920	−	1.54317i	1.03438	−	0.277162i	0.735784	+	0.677217i	$0.236814\pi$
$32$	5.52590	+	1.48066i	0.976850	+	0.261746i
$33$		0			0
$34$	1.16721	−	2.81789i	0.200175	−	0.483265i
$35$	2.36542	+	4.09703i	0.399829	+	0.692524i
$36$		0			0
$37$	3.26313	+	4.25260i	0.536456	+	0.699123i	0.980419	−	0.196922i	$-0.0630947\pi$
$37$	3.26313	+	4.25260i	0.536456	+	0.699123i	−0.443964	+	0.896045i	$0.646428\pi$
$38$	−1.79366	−	2.33754i	−0.290970	−	0.379199i
$39$		0			0
$40$	−3.40151	+	2.61007i	−0.537826	+	0.412688i
$41$	−0.301931	−	0.0397499i	−0.0471537	−	0.00620790i	0.106912	−	0.994268i	$-0.465904\pi$
$41$	−0.301931	−	0.0397499i	−0.0471537	−	0.00620790i	−0.154066	+	0.988061i	$0.549237\pi$
$42$		0			0
$43$	−4.03522	−	2.32974i	−0.615365	−	0.355281i	0.159697	−	0.987166i	$-0.448948\pi$
$43$	−4.03522	−	2.32974i	−0.615365	−	0.355281i	−0.775062	+	0.631885i	$0.782282\pi$
$44$	1.90204	+	7.09853i	0.286744	+	1.07014i
$45$		0			0
$46$	3.45040	+	1.42920i	0.508733	+	0.210724i
$47$		−	1.31590i		−	0.191944i	−0.995384	−	0.0959719i	$-0.969404\pi$
$47$		−	1.31590i		−	0.191944i	0.995384	−	0.0959719i	$-0.0305959\pi$
$48$		0			0
$49$	−0.105189	+	0.392572i	−0.0150270	+	0.0560816i
$50$			1.04473i			0.147748i
$51$		0			0
$52$	4.14124	+	9.99784i	0.574287	+	1.38645i
$53$	0.993641	+	3.70832i	0.136487	+	0.509377i	0.999987	+	0.00502836i	$0.00160058\pi$
$53$	0.993641	+	3.70832i	0.136487	+	0.509377i	−0.863500	+	0.504348i	$0.831733\pi$
$54$		0			0
$55$	−7.93383	−	3.28630i	−1.06980	−	0.443125i
$56$	5.92457	+	0.779984i	0.791704	+	0.104230i
$57$		0			0
$58$	0.211227	+	1.60443i	0.0277355	+	0.210672i
$59$	−6.37251	−	8.30482i	−0.829631	−	1.08120i	−0.995473	−	0.0950434i	$-0.969701\pi$
$59$	−6.37251	−	8.30482i	−0.829631	−	1.08120i	0.165842	−	0.986152i	$-0.446966\pi$
$60$		0			0
$61$	3.08241	−	5.33890i	0.394663	−	0.683576i	−0.598395	−	0.801201i	$-0.704195\pi$
$61$	3.08241	−	5.33890i	0.394663	−	0.683576i	0.993058	+	0.117625i	$0.0375281\pi$
$62$	1.93972	+	3.35970i	0.246345	+	0.426682i
$63$		0			0
$64$			0.444079i			0.0555098i
$65$	−12.2146	−	3.27288i	−1.51503	−	0.405951i
$66$		0			0
$67$	−2.60485	+	1.07896i	−0.318233	+	0.131816i	−0.536082	−	0.844166i	$-0.680096\pi$
$67$	−2.60485	+	1.07896i	−0.318233	+	0.131816i	0.217849	+	0.975983i	$0.430096\pi$
$68$	−7.32758	−	0.964694i	−0.888600	−	0.116986i
$69$		0			0
$70$	−2.17658	+	2.17658i	−0.260151	+	0.260151i
$71$	1.48326	−	0.195275i	0.176030	−	0.0231748i	−0.0419957	−	0.999118i	$-0.513372\pi$
$71$	1.48326	−	0.195275i	0.176030	−	0.0231748i	0.218026	+	0.975943i	$0.430038\pi$
$72$		0			0
$73$	−0.448016	−	0.258662i	−0.0524364	−	0.0302741i	0.473553	−	0.880766i	$-0.342971\pi$
$73$	−0.448016	−	0.258662i	−0.0524364	−	0.0302741i	−0.525989	+	0.850491i	$0.676305\pi$
$74$	−2.12318	+	2.76698i	−0.246814	+	0.321655i
$75$		0			0
$76$	−4.34633	+	5.66425i	−0.498558	+	0.649734i
$77$	4.58026	+	11.0577i	0.521969	+	1.26015i
$78$		0			0
$79$	3.64268	+	3.64268i	0.409834	+	0.409834i	0.881681	−	0.471847i	$-0.156412\pi$
$79$	3.64268	+	3.64268i	0.409834	+	0.409834i	−0.471847	+	0.881681i	$0.656412\pi$
$80$	2.39581	+	1.83837i	0.267859	+	0.205536i
$81$		0			0
$82$	−0.0258635	−	0.196453i	−0.00285615	−	0.0216946i
$83$	2.76947	+	2.12509i	0.303989	+	0.233259i	0.749479	−	0.662028i	$-0.230304\pi$
$83$	2.76947	+	2.12509i	0.303989	+	0.233259i	−0.445490	+	0.895287i	$0.646971\pi$
$84$		0			0
$85$	6.10689	−	6.10689i	0.662386	−	0.662386i
$86$	0.784665	−	2.92841i	0.0846126	−	0.315779i
$87$		0			0
$88$	−9.39395	+	5.42360i	−1.00140	+	0.578158i
$89$	−3.39457	−	3.39457i	−0.359824	−	0.359824i	0.503924	−	0.863748i	$-0.331889\pi$
$89$	−3.39457	−	3.39457i	−0.359824	−	0.359824i	−0.863748	+	0.503924i	$0.831889\pi$
$90$		0			0
$91$	8.81226	+	15.2633i	0.923776	+	1.60003i
$92$	1.18123	−	8.97233i	0.123152	−	0.935430i
$93$		0			0
$94$	0.827025	−	0.221601i	0.0853011	−	0.0228564i
$95$	−2.15931	−	8.05865i	−0.221541	−	0.826800i
$96$		0			0
$97$	−9.83979	−	0.422473i	−0.999080	−	0.0428956i
$97$	−9.83979	−	0.422473i	−0.999080	−	0.0428956i
$98$	−0.264440			−0.0267124
$99$		0			0
$100$	2.44530	−	0.655216i	0.244530	−	0.0655216i
$101$	12.5712	−	7.25799i	1.25088	−	0.722197i	0.279597	−	0.960117i	$-0.409799\pi$
$101$	12.5712	−	7.25799i	1.25088	−	0.722197i	0.971285	+	0.237921i	$0.0764658\pi$
$102$		0			0
$103$	−8.58601	−	14.8714i	−0.846004	−	1.46532i	−0.884746	−	0.466073i	$-0.845668\pi$
$103$	−8.58601	−	14.8714i	−0.846004	−	1.46532i	0.0387417	−	0.999249i	$-0.487665\pi$
$104$	−12.6722	+	9.72370i	−1.24261	+	0.953487i
$105$		0			0
$106$	−2.16329	+	1.24898i	−0.210118	+	0.121311i
$107$	17.5296	−	2.30781i	1.69465	−	0.223104i	0.779550	−	0.626340i	$-0.215448\pi$
$107$	17.5296	−	2.30781i	1.69465	−	0.223104i	0.915096	+	0.403236i	$0.132115\pi$
$108$		0			0
$109$	5.41614	−	5.41614i	0.518773	−	0.518773i	−0.398427	−	0.917200i	$-0.630444\pi$
$109$	5.41614	−	5.41614i	0.518773	−	0.518773i	0.917200	+	0.398427i	$0.130444\pi$
$110$	0.729318	−	5.53972i	0.0695378	−	0.528192i
$111$		0			0
$112$	−0.549371	−	4.17289i	−0.0519107	−	0.394301i
$113$	−1.49995	+	2.59798i	−0.141103	+	0.244398i	−0.927912	−	0.372799i	$-0.878398\pi$
$113$	−1.49995	+	2.59798i	−0.141103	+	0.244398i	0.786809	+	0.617196i	$0.211732\pi$
$114$		0			0
$115$	7.47765	+	7.47765i	0.697294	+	0.697294i
$116$	3.62285	−	1.50063i	0.336373	−	0.139330i
$117$		0			0
$118$	4.14632	−	5.40358i	0.381699	−	0.497440i
$119$	−12.0370			−1.10343
$120$		0			0
$121$	−9.28901	−	5.36301i	−0.844456	−	0.487547i
$122$	3.87451	+	1.03817i	0.350781	+	0.0939916i
$123$		0			0
$124$	6.64719	−	6.64719i	0.596935	−	0.596935i
$125$	−4.65729	+	11.2437i	−0.416561	+	1.00567i
$126$		0			0
$127$	15.5890	−	6.45717i	1.38330	−	0.572981i	0.437937	−	0.899006i	$-0.355709\pi$
$127$	15.5890	−	6.45717i	1.38330	−	0.572981i	0.945361	+	0.326025i	$0.105709\pi$
$128$	10.7727	−	2.88654i	0.952181	−	0.255136i
$129$		0			0
$130$		−	8.22784i		−	0.721629i
$131$	0.114794	−	0.277138i	0.0100296	−	0.0242136i	−0.918785	−	0.394757i	$-0.870829\pi$
$131$	0.114794	−	0.277138i	0.0100296	−	0.0242136i	0.928815	+	0.370544i	$0.120829\pi$
$132$		0			0
$133$	−5.81396	+	10.0701i	−0.504134	+	0.873186i
$134$	−1.11678	−	1.45541i	−0.0964747	−	0.125728i
$135$		0			0
$136$	−1.42391	−	10.8157i	−0.122099	−	0.927437i
$137$	−9.38782	+	7.20353i	−0.802056	+	0.615439i	−0.926289	−	0.376814i	$-0.877020\pi$
$137$	−9.38782	+	7.20353i	−0.802056	+	0.615439i	0.124233	+	0.992253i	$0.460353\pi$
$138$		0			0
$139$	−14.0413	−	5.81610i	−1.19097	−	0.493315i	−0.302898	−	0.953023i	$-0.597954\pi$
$139$	−14.0413	−	5.81610i	−1.19097	−	0.493315i	−0.888070	+	0.459707i	$0.847954\pi$
$140$	6.45956	+	3.72943i	0.545933	+	0.315194i
$141$		0			0
$142$	0.372511	+	0.899322i	0.0312605	+	0.0754694i
$143$	−29.5571	−	12.2430i	−2.47169	−	1.02381i
$144$		0			0
$145$	−1.18597	+	4.42611i	−0.0984896	+	0.367568i
$146$	0.0871187	−	0.325131i	0.00720999	−	0.0269081i
$147$		0			0
$148$	7.80795	+	3.23416i	0.641810	+	0.265846i
$149$	0.736512	+	1.77810i	0.0603374	+	0.145667i	0.951173	−	0.308659i	$-0.0998801\pi$
$149$	0.736512	+	1.77810i	0.0603374	+	0.145667i	−0.890835	+	0.454326i	$0.849880\pi$
$150$		0			0
$151$	2.45204	+	1.41569i	0.199544	+	0.115207i	0.596443	−	0.802655i	$-0.296580\pi$
$151$	2.45204	+	1.41569i	0.199544	+	0.115207i	−0.396899	+	0.917862i	$0.629914\pi$
$152$	−9.73608	−	4.03282i	−0.789700	−	0.327105i
$153$		0			0
$154$	−6.17830	+	4.74078i	−0.497862	+	0.382023i
$155$	1.43382	+	10.8909i	0.115167	+	0.874780i
$156$		0			0
$157$	−9.94847	−	12.9651i	−0.793974	−	1.03473i	−0.998439	−	0.0558532i	$-0.982212\pi$
$157$	−9.94847	−	12.9651i	−0.793974	−	1.03473i	0.204465	−	0.978874i	$-0.434455\pi$
$158$	−1.67594	+	2.90281i	−0.133331	+	0.230935i
$159$		0			0
$160$	−4.03345	+	9.73760i	−0.318872	+	0.769825i
$161$		−	14.7388i		−	1.16158i
$162$		0			0
$163$	4.60874	−	1.23491i	0.360985	−	0.0967256i	−0.0737680	−	0.997275i	$-0.523502\pi$
$163$	4.60874	−	1.23491i	0.360985	−	0.0967256i	0.434753	+	0.900550i	$0.356836\pi$
$164$	−0.443597	+	0.183744i	−0.0346391	+	0.0143480i
$165$		0			0
$166$	−0.869203	+	2.09844i	−0.0674632	+	0.162871i
$167$	16.9333	−	16.9333i	1.31034	−	1.31034i	0.389169	−	0.921166i	$-0.372762\pi$
$167$	16.9333	−	16.9333i	1.31034	−	1.31034i	0.921166	−	0.389169i	$-0.127238\pi$
$168$		0			0
$169$	−32.9478	−	8.82832i	−2.53444	−	0.679102i
$170$	4.86651	+	2.80968i	0.373244	+	0.215493i
$171$		0			0
$172$	−7.34634			−0.560153
$173$	6.15406	−	8.02013i	0.467885	−	0.609759i	−0.498490	−	0.866895i	$-0.666112\pi$
$173$	6.15406	−	8.02013i	0.467885	−	0.609759i	0.966375	+	0.257136i	$0.0827788\pi$
$174$		0			0
$175$	3.80916	−	1.57781i	0.287946	−	0.119271i
$176$	5.40235	+	5.40235i	0.407217	+	0.407217i
$177$		0			0
$178$	1.56179	−	2.70509i	0.117061	−	0.202755i
$179$	1.14996	+	8.73480i	0.0859519	+	0.652870i	0.979140	+	0.203187i	$0.0651298\pi$
$179$	1.14996	+	8.73480i	0.0859519	+	0.652870i	−0.893188	+	0.449683i	$0.851537\pi$
$180$		0			0
$181$	−2.88152	+	21.8873i	−0.214181	+	1.62687i	0.459731	+	0.888058i	$0.347946\pi$
$181$	−2.88152	+	21.8873i	−0.214181	+	1.62687i	−0.673913	+	0.738811i	$0.735388\pi$
$182$	−8.10875	+	8.10875i	−0.601060	+	0.601060i
$183$		0			0
$184$	13.2434	−	1.74352i	0.976314	−	0.128534i
$185$	−8.55255	+	4.93782i	−0.628796	+	0.363036i
$186$		0			0
$187$	17.3346	−	13.3013i	1.26763	−	0.972690i
$188$	−1.03736	−	1.79675i	−0.0756569	−	0.131042i
$189$		0			0
$190$	4.70112	−	2.71419i	0.341055	−	0.196908i
$191$	−12.0706	+	3.23430i	−0.873397	+	0.234026i	−0.667556	−	0.744559i	$-0.732660\pi$
$191$	−12.0706	+	3.23430i	−0.873397	+	0.234026i	−0.205841	+	0.978585i	$0.565993\pi$
$192$		0			0
$193$	19.1903			1.38135			0.690676	−	0.723165i	$-0.257313\pi$
$193$	19.1903			1.38135			0.690676	+	0.723165i	$0.257313\pi$
$194$	−1.39152	−	6.25531i	−0.0999057	−	0.449105i
$195$		0			0
$196$	0.165846	+	0.618947i	0.0118462	+	0.0442105i
$197$	−8.10401	+	2.17146i	−0.577387	+	0.154710i	−0.535682	−	0.844420i	$-0.679946\pi$
$197$	−8.10401	+	2.17146i	−0.577387	+	0.154710i	−0.0417047	+	0.999130i	$0.513279\pi$
$198$		0			0
$199$	−0.349427	+	2.65417i	−0.0247703	+	0.188149i	−0.999357	−	0.0358629i	$-0.988582\pi$
$199$	−0.349427	+	2.65417i	−0.0247703	+	0.188149i	0.974586	+	0.224012i	$0.0719154\pi$
$200$	1.86832	+	3.23603i	0.132110	+	0.228822i
$201$		0			0
$202$	6.67856	+	6.67856i	0.469902	+	0.469902i
$203$	5.53085	−	3.19324i	0.388189	−	0.224121i
$204$		0			0
$205$	0.145215	−	0.541951i	0.0101423	−	0.0378515i
$206$	7.90056	−	7.90056i	0.550458	−	0.550458i
$207$		0			0
$208$	8.92546	+	6.84875i	0.618869	+	0.474875i
$209$	−2.75505	−	20.9267i	−0.190571	−	1.44753i
$210$		0			0
$211$	−12.9112	−	9.90709i	−0.888842	−	0.682032i	0.0598592	−	0.998207i	$-0.480935\pi$
$211$	−12.9112	−	9.90709i	−0.888842	−	0.682032i	−0.948701	+	0.316174i	$0.897601\pi$
$212$	4.28009	+	4.28009i	0.293958	+	0.293958i
$213$		0			0
$214$	4.40244	+	10.6284i	0.300945	+	0.726545i
$215$	5.22590	−	6.81053i	0.356404	−	0.464474i
$216$		0			0
$217$	9.32022	−	12.1463i	0.632698	−	0.824548i
$218$	4.31606	+	2.49188i	0.292320	+	0.168771i
$219$		0			0
$220$	−13.4237	+	1.76726i	−0.905022	+	0.119148i
$221$	22.7509	−	22.7509i	1.53039	−	1.53039i
$222$		0			0
$223$	−2.65411	−	0.349421i	−0.177733	−	0.0233989i	0.0411345	−	0.999154i	$-0.486903\pi$
$223$	−2.65411	−	0.349421i	−0.177733	−	0.0233989i	−0.218867	+	0.975755i	$0.570236\pi$
$224$	13.5717	−	5.62159i	0.906799	−	0.375608i
$225$		0			0
$226$	−1.88539	−	0.505189i	−0.125414	−	0.0336046i
$227$		−	19.1448i		−	1.27069i	−0.772230	−	0.635343i	$-0.780859\pi$
$227$		−	19.1448i		−	1.27069i	0.772230	−	0.635343i	$-0.219141\pi$
$228$		0			0
$229$	−0.644987	−	1.11715i	−0.0426220	−	0.0738234i	0.843927	−	0.536457i	$-0.180238\pi$
$229$	−0.644987	−	1.11715i	−0.0426220	−	0.0738234i	−0.886549	+	0.462634i	$0.846904\pi$
$230$	−3.44034	+	5.95885i	−0.226849	+	0.392915i
$231$		0			0
$232$	3.52351	+	4.59192i	0.231330	+	0.301474i
$233$	−1.99205	−	15.1311i	−0.130504	−	0.991274i	−0.923918	−	0.382591i	$-0.875032\pi$
$233$	−1.99205	−	15.1311i	−0.130504	−	0.991274i	0.793414	−	0.608682i	$-0.208302\pi$
$234$		0			0
$235$	2.40364	+	0.316445i	0.156796	+	0.0206426i
$236$	−15.2480	−	6.31594i	−0.992561	−	0.411132i
$237$		0			0
$238$	−2.02706	−	7.56508i	−0.131395	−	0.490372i
$239$	−0.963943	−	2.32717i	−0.0623523	−	0.150532i	0.889632	−	0.456677i	$-0.150961\pi$
$239$	−0.963943	−	2.32717i	−0.0623523	−	0.150532i	−0.951985	+	0.306146i	$0.900961\pi$
$240$		0			0
$241$		−	17.9879i		−	1.15870i	−0.815078	−	0.579351i	$-0.803306\pi$
$241$		−	17.9879i		−	1.15870i	0.815078	−	0.579351i	$-0.196694\pi$
$242$	1.80629	−	6.74115i	0.116113	−	0.433338i
$243$		0			0
$244$		−	9.71975i		−	0.622244i
$245$	−0.691780	−	0.286545i	−0.0441962	−	0.0183067i
$246$		0			0
$247$	−8.04441	−	30.0221i	−0.511853	−	1.91026i
$248$	12.0165	+	6.93771i	0.763046	+	0.440545i
$249$		0			0
$250$	−7.85080	−	1.03358i	−0.496528	−	0.0653692i
$251$	−7.33293	+	5.62676i	−0.462851	+	0.355158i	−0.813711	−	0.581270i	$-0.802556\pi$
$251$	−7.33293	+	5.62676i	−0.462851	+	0.355158i	0.350860	+	0.936428i	$0.385889\pi$
$252$		0			0
$253$	16.2869	+	21.2256i	1.02395	+	1.33444i
$254$	6.68345	+	8.71005i	0.419357	+	0.546517i
$255$		0			0
$256$	4.07237	+	7.05355i	0.254523	+	0.440847i
$257$	8.51227	−	20.5504i	0.530981	−	1.28190i	−0.399894	−	0.916562i	$-0.630953\pi$
$257$	8.51227	−	20.5504i	0.530981	−	1.28190i	0.930874	−	0.365340i	$-0.119047\pi$
$258$		0			0
$259$	13.2951	+	3.56241i	0.826118	+	0.221358i
$260$	−19.2581	+	5.16018i	−1.19433	+	0.320021i
$261$		0			0
$262$	0.193509	+	0.0254759i	0.0119550	+	0.00157391i
$263$	−0.511663	+	1.23526i	−0.0315505	+	0.0761696i	−0.938869	−	0.344273i	$-0.888125\pi$
$263$	−0.511663	+	1.23526i	−0.0315505	+	0.0761696i	0.907319	+	0.420443i	$0.138125\pi$
$264$		0			0
$265$	−7.01261	+	0.923227i	−0.430781	+	0.0567134i
$266$	−7.30798	−	1.95817i	−0.448081	−	0.120063i
$267$		0			0
$268$	−2.70613	+	3.52670i	−0.165303	+	0.215427i
$269$	−22.6137			−1.37878			−0.689392	−	0.724389i	$-0.742122\pi$
$269$	−22.6137			−1.37878			−0.689392	+	0.724389i	$0.742122\pi$
$270$		0			0
$271$	7.47394	+	18.0437i	0.454010	+	1.09608i	0.970784	+	0.239955i	$0.0771327\pi$
$271$	7.47394	+	18.0437i	0.454010	+	1.09608i	−0.516774	+	0.856122i	$0.672867\pi$
$272$	−7.09873	+	2.94039i	−0.430424	+	0.178287i
$273$		0			0
$274$	−6.10825	−	4.68702i	−0.369013	−	0.283153i
$275$	−3.74209	+	6.48149i	−0.225656	+	0.390848i
$276$		0			0
$277$	−0.0548802	−	0.0421110i	−0.00329743	−	0.00253021i	0.607111	−	0.794617i	$-0.292328\pi$
$277$	−0.0548802	−	0.0421110i	−0.00329743	−	0.00253021i	−0.610409	+	0.792087i	$0.708995\pi$
$278$	1.29075	−	9.80421i	0.0774140	−	0.588017i
$279$		0			0
$280$	−2.84946	+	10.6343i	−0.170288	+	0.635522i
$281$	−4.73339	+	0.623163i	−0.282370	+	0.0371748i	−0.270381	−	0.962753i	$-0.587150\pi$
$281$	−4.73339	+	0.623163i	−0.282370	+	0.0371748i	−0.0119892	+	0.999928i	$0.503816\pi$
$282$		0			0
$283$	−0.779296	−	0.779296i	−0.0463244	−	0.0463244i	0.683565	−	0.729890i	$-0.260429\pi$
$283$	−0.779296	−	0.779296i	−0.0463244	−	0.0463244i	−0.729890	+	0.683565i	$0.760429\pi$
$284$	1.87132	−	1.43592i	0.111043	−	0.0852061i
$285$		0			0
$286$	2.71704	−	20.6380i	0.160662	−	1.22035i
$287$	−0.677220	+	0.390993i	−0.0399751	+	0.0230796i
$288$		0			0
$289$	1.28745	+	4.80483i	0.0757323	+	0.282637i
$290$	−2.98146			−0.175078
$291$		0			0
$292$	−0.815638			−0.0477316
$293$	3.12986	+	11.6808i	0.182849	+	0.682400i	0.995081	+	0.0990660i	$0.0315855\pi$
$293$	3.12986	+	11.6808i	0.182849	+	0.682400i	−0.812232	+	0.583334i	$0.801748\pi$
$294$		0			0
$295$	16.7021	−	9.64298i	0.972436	−	0.561436i
$296$	−1.62822	+	12.3675i	−0.0946383	+	0.718849i
$297$		0			0
$298$	−0.993479	+	0.762323i	−0.0575507	+	0.0441602i
$299$	27.8576	+	27.8576i	1.61105	+	1.61105i
$300$		0			0
$301$	−11.8622	+	1.56169i	−0.683727	+	0.0900143i
$302$	−0.476810	+	1.77948i	−0.0274373	+	0.102397i
$303$		0			0
$304$	−0.968827	+	7.35897i	−0.0555660	+	0.422066i
$305$	9.01084	+	6.91426i	0.515959	+	0.395909i
$306$		0			0
$307$	−5.87053	+	10.1681i	−0.335049	+	0.580321i	−0.983494	−	0.180940i	$-0.942086\pi$
$307$	−5.87053	+	10.1681i	−0.335049	+	0.580321i	0.648445	+	0.761261i	$0.275419\pi$
$308$	14.9710	+	11.4877i	0.853054	+	0.654571i
$309$		0			0
$310$	−6.60333	+	2.73519i	−0.375044	+	0.155348i
$311$	−3.95511	−	9.54848i	−0.224274	−	0.541444i	0.771188	−	0.636607i	$-0.219663\pi$
$311$	−3.95511	−	9.54848i	−0.224274	−	0.541444i	−0.995462	+	0.0951630i	$0.969663\pi$
$312$		0			0
$313$	1.91530			0.108259			0.0541296	−	0.998534i	$-0.482762\pi$
$313$	1.91530			0.108259			0.0541296	+	0.998534i	$0.482762\pi$
$314$	6.47303	−	8.43582i	0.365294	−	0.476061i
$315$		0			0
$316$	7.84539	+	2.10217i	0.441338	+	0.118256i
$317$	−15.2769	+	2.01125i	−0.858038	+	0.112963i	−0.546692	−	0.837334i	$-0.684113\pi$
$317$	−15.2769	+	2.01125i	−0.858038	+	0.112963i	−0.311346	+	0.950297i	$0.600780\pi$
$318$		0			0
$319$	−4.43639	+	10.7104i	−0.248390	+	0.599667i
$320$	−0.811159	−	0.106791i	−0.0453452	−	0.00596981i
$321$		0			0
$322$	9.26314	−	2.48205i	0.516215	−	0.138319i
$323$	20.5042	+	5.49408i	1.14088	+	0.305699i
$324$		0			0
$325$	−4.21745	+	10.1818i	−0.233942	+	0.564786i
$326$	1.55225	+	2.68857i	0.0859709	+	0.148906i
$327$		0			0
$328$	−0.431433	−	0.562255i	−0.0238219	−	0.0310453i
$329$	−2.05698	−	2.68071i	−0.113405	−	0.147793i
$330$		0			0
$331$	−0.448077	+	0.343821i	−0.0246285	+	0.0188981i	−0.621002	−	0.783809i	$-0.713274\pi$
$331$	−0.448077	+	0.343821i	−0.0246285	+	0.0188981i	0.596374	+	0.802707i	$0.296608\pi$
$332$	5.45673	+	0.718393i	0.299477	+	0.0394269i
$333$		0			0
$334$	13.4939	+	7.79072i	0.738354	+	0.426289i
$335$	−1.34444	−	5.01751i	−0.0734545	−	0.274136i
$336$		0			0
$337$	−26.5326	−	10.9902i	−1.44532	−	0.598673i	−0.484242	−	0.874934i	$-0.660905\pi$
$337$	−26.5326	−	10.9902i	−1.44532	−	0.598673i	−0.961083	+	0.276261i	$0.910905\pi$
$338$		−	22.1939i		−	1.20719i
$339$		0			0
$340$	3.52424	−	13.1527i	0.191129	−	0.713303i
$341$			27.7913i			1.50498i
$342$		0			0
$343$	7.27794	+	17.5705i	0.392972	+	0.948718i
$344$	−2.80647	−	10.4739i	−0.151315	−	0.564714i
$345$		0			0
$346$	6.07690	+	2.51713i	0.326696	+	0.135322i
$347$	−17.9913	−	2.36860i	−0.965823	−	0.127153i	−0.368915	−	0.929463i	$-0.620271\pi$
$347$	−17.9913	−	2.36860i	−0.965823	−	0.127153i	−0.596908	+	0.802310i	$0.703604\pi$
$348$		0			0
$349$	−0.484723	−	3.68184i	−0.0259466	−	0.197084i	0.973562	−	0.228422i	$-0.0733566\pi$
$349$	−0.484723	−	3.68184i	−0.0259466	−	0.197084i	−0.999509	+	0.0313377i	$0.990023\pi$
$350$	1.63310	+	2.12830i	0.0872929	+	0.113762i
$351$		0			0
$352$	−13.3327	+	23.0930i	−0.710637	+	1.23086i
$353$	12.2720	+	21.2558i	0.653174	+	1.13133i	0.982348	+	0.187061i	$0.0598963\pi$
$353$	12.2720	+	21.2558i	0.653174	+	1.13133i	−0.329174	+	0.944269i	$0.606770\pi$
$354$		0			0
$355$			2.75630i			0.146289i
$356$	−7.31102	−	1.95898i	−0.387483	−	0.103826i
$357$		0			0
$358$	−5.29604	+	2.19369i	−0.279905	+	0.115940i
$359$	10.1476	+	1.33596i	0.535571	+	0.0705093i	0.393461	−	0.919342i	$-0.371278\pi$
$359$	10.1476	+	1.33596i	0.535571	+	0.0705093i	0.142111	+	0.989851i	$0.454611\pi$
$360$		0			0
$361$	1.06494	−	1.06494i	0.0560497	−	0.0560497i
$362$	−14.2411	+	1.87488i	−0.748496	+	0.0985413i
$363$		0			0
$364$	24.0648	+	13.8938i	1.26134	+	0.728234i
$365$	0.580214	−	0.756149i	0.0303698	−	0.0395787i
$366$		0			0
$367$	6.24939	−	8.14436i	0.326216	−	0.425132i	−0.601238	−	0.799070i	$-0.705326\pi$
$367$	6.24939	−	8.14436i	0.326216	−	0.425132i	0.927454	+	0.373937i	$0.121992\pi$
$368$	−3.60039	−	8.69211i	−0.187683	−	0.453107i
$369$		0			0
$370$	−4.54362	−	4.54362i	−0.236211	−	0.236211i
$371$	7.82097	+	6.00124i	0.406044	+	0.311569i
$372$		0			0
$373$	−3.26247	−	24.7809i	−0.168924	−	1.28311i	−0.840354	−	0.542038i	$-0.817653\pi$
$373$	−3.26247	−	24.7809i	−0.168924	−	1.28311i	0.671430	−	0.741068i	$-0.265680\pi$
$374$	11.2789	+	8.65459i	0.583217	+	0.447518i
$375$		0			0
$376$	2.16539	−	2.16539i	0.111671	−	0.111671i
$377$	−4.41828	+	16.4892i	−0.227553	+	0.849239i
$378$		0			0
$379$	−13.0490	+	7.53384i	−0.670281	+	0.386987i	−0.796183	−	0.605056i	$-0.793151\pi$
$379$	−13.0490	+	7.53384i	−0.670281	+	0.386987i	0.125902	+	0.992043i	$0.459818\pi$
$380$	−9.30118	−	9.30118i	−0.477140	−	0.477140i
$381$		0			0
$382$	−4.06543	−	7.04153i	−0.208005	−	0.360276i
$383$	−0.651043	+	4.94516i	−0.0332667	+	0.252686i	−0.999995	−	0.00311909i	$-0.999007\pi$
$383$	−0.651043	+	4.94516i	−0.0332667	+	0.252686i	0.966728	+	0.255805i	$0.0823405\pi$
$384$		0			0
$385$	−21.2996	+	5.70722i	−1.08553	+	0.290867i
$386$	3.23170	+	12.0609i	0.164489	+	0.613881i
$387$		0			0
$388$	−13.7685	+	7.18009i	−0.698987	+	0.364514i
$389$	−22.6518			−1.14849			−0.574247	−	0.818682i	$-0.694705\pi$
$389$	−22.6518			−1.14849			−0.574247	+	0.818682i	$0.694705\pi$
$390$		0			0
$391$	−25.9899	+	6.96396i	−1.31436	+	0.352183i
$392$	−0.819093	+	0.472904i	−0.0413704	+	0.0238852i
$393$		0			0
$394$	−2.72947	−	4.72758i	−0.137509	−	0.238172i
$395$	−7.52975	+	5.77778i	−0.378863	+	0.290712i
$396$		0			0
$397$	15.0132	−	8.66790i	0.753493	−	0.435030i	−0.0734614	−	0.997298i	$-0.523405\pi$
$397$	15.0132	−	8.66790i	0.753493	−	0.435030i	0.826955	+	0.562268i	$0.190071\pi$
$398$	−1.72695	+	0.227357i	−0.0865641	+	0.0113964i
$399$		0			0
$400$	1.86100	−	1.86100i	0.0930499	−	0.0930499i
$401$	−4.31384	+	32.7669i	−0.215423	+	1.63630i	0.452283	+	0.891874i	$0.350610\pi$
$401$	−4.31384	+	32.7669i	−0.215423	+	1.63630i	−0.667706	+	0.744425i	$0.732724\pi$
$402$		0			0
$403$	5.34162	+	40.5736i	0.266085	+	2.02112i
$404$	11.4433	−	19.8203i	0.569325	−	0.986099i
$405$		0			0
$406$	2.93831	+	2.93831i	0.145826	+	0.145826i
$407$	−23.0830	+	9.56131i	−1.14418	+	0.473936i
$408$		0			0
$409$	−16.8319	+	21.9358i	−0.832285	+	1.08466i	0.162900	+	0.986643i	$0.447915\pi$
$409$	−16.8319	+	21.9358i	−0.832285	+	1.08466i	−0.995185	+	0.0980128i	$0.968751\pi$
$410$	0.365063			0.0180292
$411$		0			0
$412$	−23.4469	−	13.5371i	−1.15515	−	0.666925i
$413$	−25.9638	−	6.95698i	−1.27759	−	0.342330i
$414$		0			0
$415$	−4.54771	+	4.54771i	−0.223238	+	0.223238i
$416$	−15.0264	+	36.2770i	−0.736731	+	1.77862i
$417$		0			0
$418$	12.6881	−	5.25560i	0.620597	−	0.257060i
$419$	7.14295	−	1.91395i	0.348956	−	0.0935025i	−0.0800835	−	0.996788i	$-0.525519\pi$
$419$	7.14295	−	1.91395i	0.348956	−	0.0935025i	0.429040	+	0.903286i	$0.358852\pi$
$420$		0			0
$421$		−	23.0464i		−	1.12321i	−0.827405	−	0.561606i	$-0.810184\pi$
$421$		−	23.0464i		−	1.12321i	0.827405	−	0.561606i	$-0.189816\pi$
$422$	4.05219	−	9.78286i	0.197258	−	0.476222i
$423$		0			0
$424$	−4.46715	+	7.73734i	−0.216944	+	0.375758i
$425$	−4.58204	−	5.97143i	−0.222261	−	0.289657i
$426$		0			0
$427$	−2.06623	−	15.6946i	−0.0999920	−	0.759515i
$428$	22.1158	−	16.9701i	1.06901	−	0.820280i
$429$		0			0
$430$	5.16037	+	2.13750i	0.248855	+	0.103079i
$431$	20.3986	+	11.7772i	0.982568	+	0.567286i	0.903044	−	0.429547i	$-0.141327\pi$
$431$	20.3986	+	11.7772i	0.982568	+	0.567286i	0.0795233	+	0.996833i	$0.474660\pi$
$432$		0			0
$433$	−8.83092	−	21.3197i	−0.424387	−	1.02456i	−0.981038	−	0.193814i	$-0.937914\pi$
$433$	−8.83092	−	21.3197i	−0.424387	−	1.02456i	0.556651	−	0.830746i	$-0.312086\pi$
$434$	9.20335	+	3.81215i	0.441775	+	0.182989i
$435$		0			0
$436$	3.12562	−	11.6650i	0.149690	−	0.558650i
$437$	−6.72728	+	25.1066i	−0.321810	+	1.20101i
$438$		0			0
$439$	4.39620	+	1.82097i	0.209819	+	0.0869099i	0.485118	−	0.874449i	$-0.338777\pi$
$439$	4.39620	+	1.82097i	0.209819	+	0.0869099i	−0.275299	+	0.961359i	$0.588777\pi$
$440$	−7.64777	−	18.4634i	−0.364593	−	0.880206i
$441$		0			0
$442$	18.1300	+	10.4673i	0.862354	+	0.497880i
$443$	12.9120	+	5.34832i	0.613467	+	0.254106i	0.667710	−	0.744422i	$-0.267275\pi$
$443$	12.9120	+	5.34832i	0.613467	+	0.254106i	−0.0542434	+	0.998528i	$0.517275\pi$
$444$		0			0
$445$	7.01688	−	5.38424i	0.332632	−	0.255238i
$446$	−0.227353	−	1.72692i	−0.0107655	−	0.0817718i
$447$		0			0
$448$	0.694173	+	0.904664i	0.0327966	+	0.0427413i
$449$	14.1926	−	24.5822i	0.669788	−	1.16011i	−0.308175	−	0.951330i	$-0.599718\pi$
$449$	14.1926	−	24.5822i	0.669788	−	1.16011i	0.977963	−	0.208778i	$-0.0669485\pi$
$450$		0			0
$451$	0.543211	−	1.31143i	0.0255788	−	0.0617527i
$452$			4.72977i			0.222470i
$453$		0			0
$454$	12.0322	−	3.22403i	0.564701	−	0.151311i
$455$	−29.9992	+	12.4261i	−1.40639	+	0.582544i
$456$		0			0
$457$	0.796948	−	1.92400i	0.0372797	−	0.0900010i	−0.904143	−	0.427230i	$-0.859490\pi$
$457$	0.796948	−	1.92400i	0.0372797	−	0.0900010i	0.941423	+	0.337229i	$0.109490\pi$
$458$	0.593496	−	0.593496i	0.0277322	−	0.0277322i
$459$		0			0
$460$	16.1049	+	4.31530i	0.750895	+	0.201202i
$461$	−13.8667	−	8.00593i	−0.645836	−	0.372874i	0.141023	−	0.990006i	$-0.454961\pi$
$461$	−13.8667	−	8.00593i	−0.645836	−	0.372874i	−0.786859	+	0.617133i	$0.788294\pi$
$462$		0			0
$463$	33.6885			1.56564			0.782818	−	0.622250i	$-0.213781\pi$
$463$	33.6885			1.56564			0.782818	+	0.622250i	$0.213781\pi$
$464$	2.48173	−	3.23426i	0.115211	−	0.150147i
$465$		0			0
$466$	9.17423	−	3.80009i	0.424988	−	0.176036i
$467$	24.6282	+	24.6282i	1.13966	+	1.13966i	0.988511	+	0.151148i	$0.0482969\pi$
$467$	24.6282	+	24.6282i	1.13966	+	1.13966i	0.151148	+	0.988511i	$0.451703\pi$
$468$		0			0
$469$	−3.61991	+	6.26987i	−0.167152	+	0.289516i
$470$	0.205897	+	1.56394i	0.00949732	+	0.0721393i
$471$		0			0
$472$	3.17972	−	24.1524i	0.146358	−	1.11170i
$473$	15.3572	−	15.3572i	0.706124	−	0.706124i
$474$		0			0
$475$	−7.20881	+	0.949057i	−0.330763	+	0.0435457i
$476$	−16.4355	+	9.48905i	−0.753321	+	0.434930i
$477$		0			0
$478$	1.30026	−	0.997724i	0.0594725	−	0.0456348i
$479$	7.23977	+	12.5396i	0.330794	+	0.572951i	0.982668	−	0.185376i	$-0.0593503\pi$
$479$	7.23977	+	12.5396i	0.330794	+	0.572951i	−0.651874	+	0.758327i	$0.726017\pi$
$480$		0			0
$481$	−31.8621	+	18.3956i	−1.45279	+	0.838768i
$482$	11.3051	−	3.02920i	0.514935	−	0.137976i
$483$		0			0
$484$	−16.9112			−0.768689
$485$	3.13795	−	17.8719i	0.142487	−	0.811520i
$486$		0			0
$487$	−0.0678582	−	0.253250i	−0.00307495	−	0.0114759i	0.964371	−	0.264552i	$-0.0852242\pi$
$487$	−0.0678582	−	0.253250i	−0.00307495	−	0.0114759i	−0.967446	+	0.253077i	$0.918558\pi$
$488$	13.8577	−	3.71317i	0.627310	−	0.168087i
$489$		0			0
$490$	0.0635919	−	0.483029i	0.00287279	−	0.0218210i
$491$	−7.36871	−	12.7630i	−0.332545	−	0.575986i	0.650465	−	0.759536i	$-0.274574\pi$
$491$	−7.36871	−	12.7630i	−0.332545	−	0.575986i	−0.983010	+	0.183551i	$0.941241\pi$
$492$		0			0
$493$	−8.24410	−	8.24410i	−0.371295	−	0.371295i
$494$	17.5138	−	10.1116i	0.787982	−	0.454942i
$495$		0			0
$496$	2.52943	−	9.43995i	0.113575	−	0.423866i
$497$	2.71640	−	2.71640i	0.121847	−	0.121847i
$498$		0			0
$499$	8.99405	+	6.90137i	0.402629	+	0.308948i	0.790151	−	0.612913i	$-0.210002\pi$
$499$	8.99405	+	6.90137i	0.402629	+	0.308948i	−0.387522	+	0.921860i	$0.626669\pi$
$500$	2.50453	+	19.0238i	0.112006	+	0.850769i
$501$		0			0
$502$	−4.77122	−	3.66109i	−0.212950	−	0.163402i
$503$	18.6554	+	18.6554i	0.831803	+	0.831803i	0.987763	−	0.155960i	$-0.0498471\pi$
$503$	18.6554	+	18.6554i	0.831803	+	0.831803i	−0.155960	+	0.987763i	$0.549847\pi$
$504$		0			0
$505$	10.2344	+	24.7081i	0.455426	+	1.09950i
$506$	−10.5972	+	13.8105i	−0.471103	+	0.613953i
$507$		0			0
$508$	16.1951	−	21.1059i	0.718542	−	0.936422i
$509$	−1.17624	−	0.679104i	−0.0521361	−	0.0301008i	0.473705	−	0.880683i	$-0.342916\pi$
$509$	−1.17624	−	0.679104i	−0.0521361	−	0.0301008i	−0.525841	+	0.850583i	$0.676249\pi$
$510$		0			0
$511$	−1.31702	+	0.173389i	−0.0582616	+	0.00767028i
$512$	12.0251	−	12.0251i	0.531438	−	0.531438i
$513$		0			0
$514$	14.3491	+	1.88910i	0.632913	+	0.0833246i
$515$	29.2290	−	12.1071i	1.28798	−	0.533501i
$516$		0			0
$517$	5.92457	+	1.58748i	0.260562	+	0.0698175i
$518$			8.95570i			0.393491i
$519$		0			0
$520$	−14.7140	−	25.4855i	−0.645253	−	1.11761i
$521$	−17.9897	+	31.1591i	−0.788143	+	1.36510i	0.138960	+	0.990298i	$0.455624\pi$
$521$	−17.9897	+	31.1591i	−0.788143	+	1.36510i	−0.927103	+	0.374806i	$0.877709\pi$
$522$		0			0
$523$	5.97412	+	7.78562i	0.261230	+	0.340442i	0.905492	−	0.424363i	$-0.139502\pi$
$523$	5.97412	+	7.78562i	0.261230	+	0.340442i	−0.644262	+	0.764805i	$0.722835\pi$
$524$	−0.0617322	−	0.468903i	−0.00269679	−	0.0204841i
$525$		0			0
$526$	−0.862511	−	0.113552i	−0.0376073	−	0.00495109i
$527$	−25.8221	−	10.6959i	−1.12483	−	0.465919i
$528$		0			0
$529$	−2.57425	−	9.60724i	−0.111924	−	0.417706i
$530$	−1.76117	−	4.25185i	−0.0765005	−	0.184689i
$531$		0			0
$532$			18.3331i			0.794841i
$533$	0.540993	−	2.01901i	0.0234330	−	0.0874532i
$534$		0			0
$535$			32.5747i			1.40833i
$536$	−6.06192	−	2.51093i	−0.261835	−	0.108456i
$537$		0			0
$538$	−3.80820	−	14.2124i	−0.164183	−	0.612740i
$539$	−1.64057	−	0.947186i	−0.0706645	−	0.0407982i
$540$		0			0
$541$	29.6842	+	3.90800i	1.27622	+	0.168018i	0.738010	−	0.674790i	$-0.235766\pi$
$541$	29.6842	+	3.90800i	1.27622	+	0.168018i	0.538214	+	0.842808i	$0.319099\pi$
$542$	−10.0816	+	7.73587i	−0.433041	+	0.332284i
$543$		0			0
$544$	−16.3254	−	21.2757i	−0.699946	−	0.912187i
$545$	8.59073	+	11.1957i	0.367986	+	0.479569i
$546$		0			0
$547$	18.7032	+	32.3948i	0.799689	+	1.38510i	0.919819	+	0.392344i	$0.128336\pi$
$547$	18.7032	+	32.3948i	0.799689	+	1.38510i	−0.120130	+	0.992758i	$0.538331\pi$
$548$	−7.13957	+	17.2365i	−0.304987	+	0.736305i
$549$		0			0
$550$	−4.70370	−	1.26035i	−0.200566	−	0.0537416i
$551$	−10.8789	+	2.91499i	−0.463457	+	0.124183i
$552$		0			0
$553$	13.1149	+	1.72661i	0.557703	+	0.0734230i
$554$	0.0172242	−	0.0415830i	0.000731788	−	0.00176669i
$555$		0			0
$556$	−23.7572	+	3.12770i	−1.00753	+	0.132644i
$557$	20.1093	+	5.38827i	0.852058	+	0.228308i	0.658314	−	0.752744i	$-0.271270\pi$
$557$	20.1093	+	5.38827i	0.852058	+	0.228308i	0.193745	+	0.981052i	$0.437937\pi$
$558$		0			0
$559$	19.4689	−	25.3723i	0.823445	−	1.07313i
$560$	7.75435			0.327681
$561$		0			0
$562$	−1.18876	−	2.86993i	−0.0501449	−	0.121060i
$563$	24.7691	−	10.2597i	1.04389	−	0.432395i	0.206185	−	0.978513i	$-0.433895\pi$
$563$	24.7691	−	10.2597i	1.04389	−	0.432395i	0.837708	+	0.546119i	$0.183895\pi$
$564$		0			0
$565$	−4.38480	−	3.36458i	−0.184470	−	0.141549i
$566$	0.358541	−	0.621012i	0.0150706	−	0.0261031i
$567$		0			0
$568$	2.76212	+	2.11945i	0.115896	+	0.0889301i
$569$	1.60428	−	12.1857i	0.0672551	−	0.510853i	−0.924350	−	0.381547i	$-0.875392\pi$
$569$	1.60428	−	12.1857i	0.0672551	−	0.510853i	0.991605	−	0.129306i	$-0.0412751\pi$
$570$		0			0
$571$	−8.88361	+	33.1541i	−0.371768	+	1.38746i	0.486243	+	0.873824i	$0.338367\pi$
$571$	−8.88361	+	33.1541i	−0.371768	+	1.38746i	−0.858011	+	0.513632i	$0.828300\pi$
$572$	−50.0092	+	6.58383i	−2.09099	+	0.275284i
$573$		0			0
$574$	−0.359779	−	0.359779i	−0.0150169	−	0.0150169i
$575$	7.31177	−	5.61052i	0.304922	−	0.233975i
$576$		0			0
$577$	−0.560672	+	4.25872i	−0.0233411	+	0.177293i	−0.999144	−	0.0413569i	$-0.986832\pi$
$577$	−0.560672	+	4.25872i	−0.0233411	+	0.177293i	0.975803	+	0.218650i	$0.0701653\pi$
$578$	−2.80296	+	1.61829i	−0.116588	+	0.0673119i
$579$		0			0
$580$	1.86986	+	6.97840i	0.0776416	+	0.289762i
$581$	8.96377			0.371880
$582$		0			0
$583$	−17.8947			−0.741121
$584$	−0.311593	−	1.16288i	−0.0128938	−	0.0481203i
$585$		0			0
$586$	−6.81414	+	3.93415i	−0.281490	+	0.162518i
$587$	5.19854	−	39.4869i	0.214567	−	1.62980i	−0.457432	−	0.889245i	$-0.651231\pi$
$587$	5.19854	−	39.4869i	0.214567	−	1.62980i	0.671998	−	0.740553i	$-0.265436\pi$
$588$		0			0
$589$	−21.4203	+	16.4364i	−0.882609	+	0.677250i
$590$	8.87315	+	8.87315i	0.365302	+	0.365302i
$591$		0			0
$592$	8.71091	−	1.14681i	0.358016	−	0.0471337i
$593$	−1.52959	+	5.70852i	−0.0628129	+	0.234421i	−0.990194	−	0.139696i	$-0.955387\pi$
$593$	−1.52959	+	5.70852i	−0.0628129	+	0.234421i	0.927382	+	0.374117i	$0.122054\pi$
$594$		0			0
$595$	2.89463	−	21.9869i	0.118668	−	0.901376i
$596$	2.40736	+	1.84723i	0.0986094	+	0.0756656i
$597$		0			0
$598$	−12.8168	+	22.1994i	−0.524119	+	0.907801i
$599$	3.83227	+	2.94060i	0.156582	+	0.120150i	0.684081	−	0.729406i	$-0.260203\pi$
$599$	3.83227	+	2.94060i	0.156582	+	0.120150i	−0.527499	+	0.849556i	$0.676870\pi$
$600$		0			0
$601$	37.2453	−	15.4275i	1.51927	−	0.629300i	0.541821	−	0.840494i	$-0.317735\pi$
$601$	37.2453	−	15.4275i	1.51927	−	0.629300i	0.977444	+	0.211193i	$0.0677350\pi$
$602$	−2.97912	−	7.19224i	−0.121420	−	0.293134i
$603$		0			0
$604$	4.46408			0.181641
$605$	12.0299	−	15.6777i	0.489087	−	0.637390i
$606$		0			0
$607$	−15.0955	−	4.04483i	−0.612707	−	0.164174i	−0.0608969	−	0.998144i	$-0.519396\pi$
$607$	−15.0955	−	4.04483i	−0.612707	−	0.164174i	−0.551810	+	0.833970i	$0.686063\pi$
$608$	−25.6844	+	3.38141i	−1.04164	+	0.137134i
$609$		0			0
$610$	−2.82807	+	6.82756i	−0.114505	+	0.276440i
$611$	8.95465	+	1.17890i	0.362266	+	0.0476932i
$612$		0			0
$613$	28.0034	−	7.50348i	1.13104	−	0.303063i	0.355700	−	0.934600i	$-0.384243\pi$
$613$	28.0034	−	7.50348i	1.13104	−	0.303063i	0.775345	+	0.631538i	$0.217576\pi$
$614$	−7.37909	−	1.97722i	−0.297796	−	0.0797941i
$615$		0			0
$616$	−10.6590	+	25.7332i	−0.429465	+	1.03682i
$617$	−4.16949	−	7.22176i	−0.167857	−	0.290737i	0.769809	−	0.638274i	$-0.220351\pi$
$617$	−4.16949	−	7.22176i	−0.167857	−	0.290737i	−0.937666	+	0.347537i	$0.887018\pi$
$618$		0			0
$619$	21.3309	+	27.7990i	0.857362	+	1.11734i	0.991975	+	0.126437i	$0.0403542\pi$
$619$	21.3309	+	27.7990i	0.857362	+	1.11734i	−0.134613	+	0.990898i	$0.542979\pi$
$620$	10.5433	+	13.7403i	0.423430	+	0.551825i
$621$		0			0
$622$	5.33503	−	4.09371i	0.213915	−	0.164143i
$623$	−12.2216	−	1.60901i	−0.489649	−	0.0644636i
$624$		0			0
$625$	−12.4652	−	7.19678i	−0.498607	−	0.287871i
$626$	0.322541	+	1.20374i	0.0128913	+	0.0481111i
$627$		0			0
$628$	−23.8045	−	9.86014i	−0.949902	−	0.393462i
$629$		−	25.1273i		−	1.00189i
$630$		0			0
$631$	−8.52777	+	31.8261i	−0.339485	+	1.26698i	0.559439	+	0.828872i	$0.311017\pi$
$631$	−8.52777	+	31.8261i	−0.339485	+	1.26698i	−0.898924	+	0.438104i	$0.855650\pi$
$632$			11.9885i			0.476876i
$633$		0			0
$634$	−3.83671	−	9.26263i	−0.152375	−	0.367866i
$635$	8.04593	+	30.0278i	0.319293	+	1.19162i
$636$		0			0
$637$	−2.57719	−	1.06751i	−0.102112	−	0.0422962i
$638$	−7.47843	−	0.984554i	−0.296074	−	0.0389789i
$639$		0			0
$640$	2.68198	+	20.3717i	0.106015	+	0.805261i
$641$	28.2696	+	36.8416i	1.11658	+	1.45516i	0.874580	+	0.484882i	$0.161137\pi$
$641$	28.2696	+	36.8416i	1.11658	+	1.45516i	0.242002	+	0.970276i	$0.422196\pi$
$642$		0			0
$643$	7.09809	−	12.2942i	0.279921	−	0.484838i	−0.691444	−	0.722430i	$-0.743025\pi$
$643$	7.09809	−	12.2942i	0.279921	−	0.484838i	0.971365	+	0.237593i	$0.0763583\pi$
$644$	−11.6190	−	20.1246i	−0.457851	−	0.793022i
$645$		0			0
$646$			13.8118i			0.543418i
$647$	23.4778	+	6.29085i	0.923007	+	0.247319i	0.688870	−	0.724885i	$-0.258107\pi$
$647$	23.4778	+	6.29085i	0.923007	+	0.247319i	0.234137	+	0.972204i	$0.424774\pi$
$648$		0			0
$649$	45.0785	−	18.6721i	1.76948	−	0.732945i
$650$	−7.10936	−	0.935965i	−0.278852	−	0.0367116i
$651$		0			0
$652$	5.31935	−	5.31935i	0.208322	−	0.208322i
$653$	−45.7350	+	6.02112i	−1.78975	+	0.235625i	−0.951064	−	0.308993i	$-0.900008\pi$
$653$	−45.7350	+	6.02112i	−1.78975	+	0.235625i	−0.838684	+	0.544618i	$0.816675\pi$
$654$		0			0
$655$	0.478617	+	0.276330i	0.0187011	+	0.0107971i
$656$	−0.303874	+	0.396016i	−0.0118643	+	0.0154618i
$657$		0			0
$658$	1.33839	−	1.74422i	0.0521759	−	0.0679969i
$659$	0.236669	+	0.571370i	0.00921933	+	0.0222574i	0.928422	−	0.371527i	$-0.121166\pi$
$659$	0.236669	+	0.571370i	0.00921933	+	0.0222574i	−0.919203	+	0.393784i	$0.871166\pi$
$660$		0			0
$661$	13.1515	+	13.1515i	0.511533	+	0.511533i	0.914996	−	0.403463i	$-0.132194\pi$
$661$	13.1515	+	13.1515i	0.511533	+	0.511533i	−0.403463	+	0.914996i	$0.632194\pi$
$662$	−0.291544	−	0.223710i	−0.0113312	−	0.00869472i
$663$		0			0
$664$	1.06036	+	8.05427i	0.0411501	+	0.312566i
$665$	−16.9960	−	13.0415i	−0.659076	−	0.505726i
$666$		0			0
$667$	10.0946	−	10.0946i	0.390863	−	0.390863i
$668$	9.77206	−	36.4698i	0.378093	−	1.41106i
$669$		0			0
$670$	2.92703	−	1.68992i	0.113081	−	0.0652873i
$671$	20.3187	+	20.3187i	0.784395	+	0.784395i
$672$		0			0
$673$	−7.78897	−	13.4909i	−0.300243	−	0.520036i	0.675948	−	0.736949i	$-0.263734\pi$
$673$	−7.78897	−	13.4909i	−0.300243	−	0.520036i	−0.976191	+	0.216914i	$0.930401\pi$
$674$	2.43901	−	18.5262i	0.0939473	−	0.713601i
$675$		0			0
$676$	−51.9470	+	13.9191i	−1.99796	+	0.535352i
$677$	−5.33904	−	19.9256i	−0.205196	−	0.765801i	−0.989390	−	0.145286i	$-0.953590\pi$
$677$	−5.33904	−	19.9256i	−0.205196	−	0.765801i	0.784194	−	0.620516i	$-0.213077\pi$
$678$		0			0
$679$	−20.7057	+	14.5207i	−0.794613	+	0.557252i
$680$	20.0985			0.770741
$681$		0			0
$682$	−17.4664	+	4.68011i	−0.668824	+	0.179211i
$683$	−13.7545	+	7.94114i	−0.526300	+	0.303859i	−0.739508	−	0.673147i	$-0.764942\pi$
$683$	−13.7545	+	7.94114i	−0.526300	+	0.303859i	0.213209	+	0.977007i	$0.431609\pi$
$684$		0			0
$685$	−10.9005	−	18.8802i	−0.416486	−	0.721375i
$686$	−9.81719	+	7.53299i	−0.374822	+	0.287611i
$687$		0			0
$688$	−6.61416	+	3.81869i	−0.252162	+	0.145586i
$689$	−26.1251	+	3.43944i	−0.995288	+	0.131032i
$690$		0			0
$691$	−7.94975	+	7.94975i	−0.302423	+	0.302423i	−0.841961	−	0.539538i	$-0.818599\pi$
$691$	−7.94975	+	7.94975i	−0.302423	+	0.302423i	0.539538	+	0.841961i	$0.318599\pi$
$692$	2.08040	−	15.8022i	0.0790850	−	0.600710i
$693$		0			0
$694$	−1.54114	−	11.7061i	−0.0585010	−	0.444359i
$695$	14.0004	−	24.2494i	0.531065	−	0.919832i
$696$		0			0
$697$	1.00944	+	1.00944i	0.0382354	+	0.0382354i
$698$	2.23235	−	0.924671i	0.0844958	−	0.0349993i
$699$		0			0
$700$	3.95727	−	5.15722i	0.149571	−	0.194924i
$701$	−47.2986			−1.78645			−0.893223	−	0.449615i	$-0.851561\pi$
$701$	−47.2986			−1.78645			−0.893223	+	0.449615i	$0.851561\pi$
$702$		0			0
$703$	−21.0213	−	12.1366i	−0.792833	−	0.457742i
$704$	−1.99937	−	0.535730i	−0.0753542	−	0.0201911i
$705$		0			0
$706$	−11.2923	+	11.2923i	−0.424992	+	0.424992i
$707$	14.2642	−	34.4368i	0.536459	−	1.29513i
$708$		0			0
$709$	−3.15362	+	1.30627i	−0.118437	+	0.0490581i	−0.441115	−	0.897451i	$-0.645417\pi$
$709$	−3.15362	+	1.30627i	−0.118437	+	0.0490581i	0.322678	+	0.946509i	$0.395417\pi$
$710$	−1.73229	+	0.464166i	−0.0650118	+	0.0174199i
$711$		0			0
$712$		−	11.1719i		−	0.418685i
$713$	13.0967	−	31.6181i	0.490474	−	1.18411i
$714$		0			0
$715$	29.4710	−	51.0452i	1.10215	−	1.90898i
$716$	8.45602	+	11.0201i	0.316016	+	0.411840i
$717$		0			0
$718$	0.869251	+	6.60261i	0.0324401	+	0.246407i
$719$	−27.3220	+	20.9649i	−1.01894	+	0.781860i	−0.976122	−	0.217223i	$-0.930300\pi$
$719$	−27.3220	+	20.9649i	−1.01894	+	0.781860i	−0.0428178	+	0.999083i	$0.513633\pi$
$720$		0			0
$721$	−40.7378	−	16.8741i	−1.51715	−	0.628426i
$722$	0.848641	+	0.489963i	0.0315831	+	0.0182345i
$723$		0			0
$724$	13.3198	+	32.1568i	0.495026	+	1.19510i
$725$	3.68952	+	1.52825i	0.137025	+	0.0567577i
$726$		0			0
$727$	−1.47167	+	5.49235i	−0.0545813	+	0.203700i	−0.987832	−	0.155526i	$-0.950293\pi$
$727$	−1.47167	+	5.49235i	−0.0545813	+	0.203700i	0.933250	+	0.359226i	$0.116959\pi$
$728$	−10.6155	+	39.6176i	−0.393437	+	1.46833i
$729$		0			0
$730$	0.572938	+	0.237319i	0.0212054	+	0.00878356i
$731$	8.35861	+	20.1795i	0.309154	+	0.746365i
$732$		0			0
$733$	−0.385461	−	0.222546i	−0.0142373	−	0.00821993i	0.492864	−	0.870106i	$-0.335950\pi$
$733$	−0.385461	−	0.222546i	−0.0142373	−	0.00821993i	−0.507102	+	0.861886i	$0.669283\pi$
$734$	6.17103	+	2.55612i	0.227777	+	0.0943482i
$735$		0			0
$736$	26.0512	−	19.9898i	0.960261	−	0.736834i
$737$	−1.71536	−	13.0294i	−0.0631861	−	0.479946i
$738$		0			0
$739$	−4.65209	−	6.06272i	−0.171130	−	0.223021i	0.699913	−	0.714228i	$-0.253222\pi$
$739$	−4.65209	−	6.06272i	−0.171130	−	0.223021i	−0.871042	+	0.491208i	$0.836556\pi$
$740$	−7.78519	+	13.4844i	−0.286189	+	0.495695i
$741$		0			0
$742$	−2.45462	+	5.92599i	−0.0901121	+	0.217550i
$743$		−	2.37475i		−	0.0871210i	−0.999051	−	0.0435605i	$-0.986130\pi$
$743$		−	2.37475i		−	0.0871210i	0.999051	−	0.0435605i	$-0.0138701\pi$
$744$		0			0
$745$	−3.42501	+	0.917729i	−0.125483	+	0.0336230i
$746$	15.0250	−	6.22357i	0.550105	−	0.227861i
$747$		0			0
$748$	13.1832	−	31.8271i	0.482027	−	1.16372i
$749$	32.1032	−	32.1032i	1.17302	−	1.17302i
$750$		0			0
$751$	31.6822	+	8.48922i	1.15610	+	0.309776i	0.785407	−	0.618980i	$-0.212454\pi$
$751$	31.6822	+	8.48922i	1.15610	+	0.309776i	0.370693	+	0.928756i	$0.379120\pi$
$752$	−1.86793	−	1.07845i	−0.0681165	−	0.0393271i
$753$		0			0
$754$	−11.1073			−0.404504
$755$	−3.17557	+	4.13849i	−0.115571	+	0.150615i
$756$		0			0
$757$	−18.9849	+	7.86381i	−0.690018	+	0.285815i	−0.700008	−	0.714135i	$-0.746820\pi$
$757$	−18.9849	+	7.86381i	−0.690018	+	0.285815i	0.00998959	+	0.999950i	$0.496820\pi$
$758$	−6.93238	−	6.93238i	−0.251796	−	0.251796i
$759$		0			0
$760$	9.70770	−	16.8142i	0.352135	−	0.609916i
$761$	3.24654	+	24.6599i	0.117687	+	0.893922i	0.943823	+	0.330451i	$0.107201\pi$
$761$	3.24654	+	24.6599i	0.117687	+	0.893922i	−0.826136	+	0.563471i	$0.809466\pi$
$762$		0			0
$763$	2.56722	−	19.5000i	0.0929397	−	0.705947i
$764$	−13.9317	+	13.9317i	−0.504031	+	0.504031i
$765$		0			0
$766$	−3.21760	+	0.423605i	−0.116257	+	0.0153055i
$767$	62.2230	−	35.9245i	2.24674	−	1.29716i
$768$		0			0
$769$	−2.92895	+	2.24746i	−0.105621	+	0.0810456i	−0.660222	−	0.751071i	$-0.729538\pi$
$769$	−2.92895	+	2.24746i	−0.105621	+	0.0810456i	0.554601	+	0.832117i	$0.312871\pi$
$770$	−7.17381	−	12.4254i	−0.258526	−	0.447781i
$771$		0			0
$772$	26.2028	−	15.1282i	0.943059	−	0.544476i
$773$	−28.0857	+	7.52555i	−1.01017	+	0.270675i	−0.725702	−	0.688009i	$-0.758485\pi$
$773$	−28.0857	+	7.52555i	−1.01017	+	0.270675i	−0.284472	+	0.958684i	$0.591818\pi$
$774$		0			0
$775$	9.57353			0.343891
$776$	−15.4967	−	16.8871i	−0.556300	−	0.606213i
$777$		0			0
$778$	−3.81462	−	14.2364i	−0.136761	−	0.510398i
$779$	1.33206	−	0.356924i	0.0477260	−	0.0127881i
$780$		0			0
$781$	−0.910198	+	6.91364i	−0.0325695	+	0.247390i
$782$	−8.75350	−	15.1615i	−0.313024	−	0.542174i
$783$		0			0
$784$	0.471050	+	0.471050i	0.0168232	+	0.0168232i
$785$	26.0746	−	15.0542i	0.930642	−	0.537306i
$786$		0			0
$787$	13.5084	−	50.4142i	0.481524	−	1.79707i	−0.113703	−	0.993515i	$-0.536271\pi$
$787$	13.5084	−	50.4142i	0.481524	−	1.79707i	0.595227	−	0.803558i	$-0.297062\pi$
$788$	−9.35353	+	9.35353i	−0.333206	+	0.333206i
$789$		0			0
$790$	−4.89928	−	3.75935i	−0.174309	−	0.133752i
$791$	1.00546	+	7.63721i	0.0357500	+	0.271548i
$792$		0			0
$793$	33.5695	+	25.7587i	1.19209	+	0.914720i
$794$	7.97592	+	7.97592i	0.283055	+	0.283055i
$795$		0			0
$796$	1.61523	+	3.89950i	0.0572502	+	0.138214i
$797$	−15.6896	+	20.4471i	−0.555754	+	0.724273i	−0.983757	−	0.179505i	$-0.942551\pi$
$797$	−15.6896	+	20.4471i	−0.555754	+	0.724273i	0.428003	+	0.903777i	$0.359217\pi$
$798$		0			0
$799$	−3.75516	+	4.89382i	−0.132848	+	0.173131i
$800$	7.95506	+	4.59286i	0.281254	+	0.162382i
$801$		0			0
$802$	−21.3200	+	2.80683i	−0.752834	+	0.0991125i
$803$	1.70506	−	1.70506i	0.0601701	−	0.0601701i
$804$		0			0
$805$	26.9221	+	3.54436i	0.948880	+	0.124922i
$806$	−24.6004	+	10.1898i	−0.866512	+	0.358921i
$807$		0			0
$808$	32.6300	+	8.74319i	1.14792	+	0.307584i
$809$			9.38194i			0.329852i	0.986306	+	0.164926i	$0.0527385\pi$
$809$			9.38194i			0.329852i	−0.986306	+	0.164926i	$0.947262\pi$
$810$		0			0
$811$	−3.98845	−	6.90820i	−0.140053	−	0.242580i	0.787463	−	0.616362i	$-0.211394\pi$
$811$	−3.98845	−	6.90820i	−0.140053	−	0.242580i	−0.927517	+	0.373782i	$0.878061\pi$
$812$	5.03460	−	8.72019i	0.176680	−	0.306019i
$813$		0			0
$814$	−9.89638	−	12.8972i	−0.346868	−	0.452047i
$815$	1.14740	+	8.71535i	0.0401916	+	0.305286i
$816$		0			0
$817$	20.9193	+	2.75407i	0.731872	+	0.0963528i
$818$	−16.6209	−	6.88459i	−0.581135	−	0.240714i
$819$		0			0
$820$	−0.228953	−	0.854465i	−0.00799540	−	0.0298392i
$821$	−18.6782	−	45.0931i	−0.651873	−	1.57376i	−0.810057	−	0.586351i	$-0.800564\pi$
$821$	−18.6782	−	45.0931i	−0.651873	−	1.57376i	0.158184	−	0.987410i	$-0.449436\pi$
$822$		0			0
$823$		−	26.2841i		−	0.916205i	−0.888899	−	0.458102i	$-0.848529\pi$
$823$		−	26.2841i		−	0.916205i	0.888899	−	0.458102i	$-0.151471\pi$
$824$	10.3430	−	38.6005i	0.360314	−	1.34471i
$825$		0			0
$826$		−	17.4894i		−	0.608535i
$827$	−11.1060	−	4.60025i	−0.386193	−	0.159966i	0.181135	−	0.983458i	$-0.442023\pi$
$827$	−11.1060	−	4.60025i	−0.386193	−	0.159966i	−0.567328	+	0.823492i	$0.692023\pi$
$828$		0			0
$829$	8.02358	+	29.9444i	0.278670	+	1.04001i	0.953342	+	0.301894i	$0.0976187\pi$
$829$	8.02358	+	29.9444i	0.278670	+	1.04001i	−0.674671	+	0.738118i	$0.735715\pi$
$830$	−3.62401	−	2.09233i	−0.125791	−	0.0726257i
$831$		0			0
$832$	−3.02193	−	0.397845i	−0.104767	−	0.0137928i
$833$	1.51147	−	1.15979i	0.0523693	−	0.0401844i
$834$		0			0
$835$	26.8584	+	35.0026i	0.929474	+	1.21131i
$836$	−20.2588	−	26.4017i	−0.700664	−	0.913123i
$837$		0			0
$838$	2.40578	+	4.16693i	0.0831062	+	0.143944i
$839$	−17.8123	+	43.0027i	−0.614948	+	1.48462i	0.242555	+	0.970138i	$0.422015\pi$
$839$	−17.8123	+	43.0027i	−0.614948	+	1.48462i	−0.857503	+	0.514479i	$0.827985\pi$
$840$		0			0
$841$	−22.0368	−	5.90473i	−0.759888	−	0.203611i
$842$	14.4843	−	3.88106i	0.499162	−	0.133750i
$843$		0			0
$844$	−25.4391	−	3.34912i	−0.875650	−	0.115282i
$845$	24.0491	−	58.0597i	0.827315	−	1.99732i
$846$		0			0
$847$	−27.3066	+	3.59499i	−0.938267	+	0.123525i
$848$	6.07833	+	1.62868i	0.208731	+	0.0559292i
$849$		0			0
$850$	2.98133	−	3.88535i	0.102259	−	0.133266i
$851$	30.7673			1.05469
$852$		0			0
$853$	3.70404	+	8.94233i	0.126824	+	0.306180i	0.974519	−	0.224303i	$-0.0720106\pi$
$853$	3.70404	+	8.94233i	0.126824	+	0.306180i	−0.847696	+	0.530483i	$0.822011\pi$
$854$	9.51587	−	3.94160i	0.325626	−	0.134879i
$855$		0			0
$856$	32.6435	+	25.0482i	1.11573	+	0.856131i
$857$	11.8805	−	20.5776i	0.405830	−	0.702918i	−0.588588	−	0.808433i	$-0.700316\pi$
$857$	11.8805	−	20.5776i	0.405830	−	0.702918i	0.994418	+	0.105515i	$0.0336492\pi$
$858$		0			0
$859$	−35.9075	−	27.5528i	−1.22515	−	0.940089i	−0.225729	−	0.974190i	$-0.572477\pi$
$859$	−35.9075	−	27.5528i	−1.22515	−	0.940089i	−0.999418	+	0.0341011i	$0.989143\pi$
$860$	1.76663	−	13.4189i	0.0602417	−	0.457581i
$861$		0			0
$862$	−3.96660	+	14.8035i	−0.135103	+	0.504211i
$863$	−5.29619	+	0.697257i	−0.180284	+	0.0237349i	−0.220128	−	0.975471i	$-0.570647\pi$
$863$	−5.29619	+	0.697257i	−0.180284	+	0.0237349i	0.0398434	+	0.999206i	$0.487314\pi$
$864$		0			0
$865$	13.1698	+	13.1698i	0.447785	+	0.447785i
$866$	11.9120	−	9.14040i	0.404786	−	0.310603i
$867$		0			0
$868$	3.15073	−	23.9322i	0.106943	−	0.812311i
$869$	−20.7949	+	12.0060i	−0.705419	+	0.407274i
$870$		0			0
$871$	−5.00864	−	18.6925i	−0.169711	−	0.633372i
$872$	17.8251			0.603635
$873$		0			0
$874$	−16.9120			−0.572057
$875$	8.08818	+	30.1855i	0.273430	+	1.02046i
$876$		0			0
$877$	−29.3124	+	16.9235i	−0.989809	+	0.571467i	−0.905217	−	0.424949i	$-0.860292\pi$
$877$	−29.3124	+	16.9235i	−0.989809	+	0.571467i	−0.0845918	+	0.996416i	$0.526959\pi$
$878$	−0.404121	+	3.06960i	−0.0136384	+	0.103594i
$879$		0			0
$880$	−11.1671	+	8.56885i	−0.376444	+	0.288856i
$881$	−1.46742	−	1.46742i	−0.0494388	−	0.0494388i	0.681955	−	0.731394i	$-0.261130\pi$
$881$	−1.46742	−	1.46742i	−0.0494388	−	0.0494388i	−0.731394	+	0.681955i	$0.761130\pi$
$882$		0			0
$883$	−8.83185	+	1.16274i	−0.297215	+	0.0391292i	−0.277659	−	0.960680i	$-0.589559\pi$
$883$	−8.83185	+	1.16274i	−0.297215	+	0.0391292i	−0.0195561	+	0.999809i	$0.506225\pi$
$884$	13.1294	−	48.9996i	0.441590	−	1.64803i
$885$		0			0
$886$	−1.18693	+	9.01566i	−0.0398758	+	0.302887i
$887$	−4.75673	−	3.64996i	−0.159715	−	0.122554i	0.525812	−	0.850601i	$-0.323762\pi$
$887$	−4.75673	−	3.64996i	−0.159715	−	0.122554i	−0.685527	+	0.728047i	$0.740428\pi$
$888$		0			0
$889$	21.6637	−	37.5227i	0.726578	−	1.25847i
$890$	4.56558	+	3.50329i	0.153039	+	0.117431i
$891$		0			0
$892$	−3.89942	+	1.61519i	−0.130562	+	0.0540807i
$893$	2.28036	+	5.50528i	0.0763094	+	0.184227i
$894$		0			0
$895$	−16.2316			−0.542564
$896$	17.4337	−	22.7200i	0.582418	−	0.759021i
$897$		0			0
$898$	17.8396	+	4.78012i	0.595317	+	0.159515i
$899$	14.7024	−	1.93560i	0.490351	−	0.0645560i
$900$		0			0
$901$	6.88701	−	16.6267i	0.229440	−	0.553916i
$902$	0.915691	+	0.120553i	0.0304892	+	0.00401398i
$903$		0			0
$904$	−6.74337	+	1.80688i	−0.224281	+	0.0600960i
$905$	−39.2866	−	10.5268i	−1.30593	−	0.349923i
$906$		0			0
$907$	10.2346	−	24.7084i	0.339833	−	0.820430i	−0.657898	−	0.753107i	$-0.728554\pi$
$907$	10.2346	−	24.7084i	0.339833	−	0.820430i	0.997731	−	0.0673230i	$-0.0214458\pi$
$908$	−15.0923	−	26.1406i	−0.500856	−	0.867507i
$909$		0			0
$910$	−12.8616	−	16.7615i	−0.426357	−	0.555639i
$911$	−3.56682	−	4.64837i	−0.118174	−	0.154007i	0.730520	−	0.682891i	$-0.239278\pi$
$911$	−3.56682	−	4.64837i	−0.118174	−	0.154007i	−0.848694	+	0.528883i	$0.822611\pi$
$912$		0			0
$913$	−12.9088	+	9.90529i	−0.427220	+	0.327817i
$914$	1.34342	+	0.176864i	0.0444362	+	0.00585014i
$915$		0			0
$916$	−1.76135	−	1.01692i	−0.0581967	−	0.0335999i
$917$	−0.199359	−	0.744020i	−0.00658343	−	0.0245697i
$918$		0			0
$919$	−27.5470	−	11.4104i	−0.908693	−	0.376393i	−0.121137	−	0.992636i	$-0.538654\pi$
$919$	−27.5470	−	11.4104i	−0.908693	−	0.376393i	−0.787556	+	0.616243i	$0.788654\pi$
$920$			24.6098i			0.811360i
$921$		0			0
$922$	2.69643	−	10.0632i	0.0888023	−	0.331415i
$923$			10.2684i			0.337990i
$924$		0			0
$925$	3.29368	+	7.95164i	0.108295	+	0.261448i
$926$	5.67322	+	21.1727i	0.186433	+	0.695779i
$927$		0			0
$928$	13.1454	+	5.44501i	0.431520	+	0.178741i
$929$	9.73141	+	1.28116i	0.319277	+	0.0420336i	0.288462	−	0.957491i	$-0.406856\pi$
$929$	9.73141	+	1.28116i	0.319277	+	0.0420336i	0.0308155	+	0.999525i	$0.490190\pi$
$930$		0			0
$931$	−0.240223	−	1.82467i	−0.00787298	−	0.0598012i
$932$	−14.6482	−	19.0899i	−0.479818	−	0.625311i
$933$		0			0
$934$	−11.3310	+	19.6259i	−0.370763	+	0.642180i
$935$	20.1278	+	34.8623i	0.658248	+	1.14012i
$936$		0			0
$937$		−	8.35265i		−	0.272869i	−0.990649	−	0.136435i	$-0.956436\pi$
$937$		−	8.35265i		−	0.272869i	0.990649	−	0.136435i	$-0.0435644\pi$
$938$	−4.55012	−	1.21920i	−0.148567	−	0.0398084i
$939$		0			0
$940$	3.53143	−	1.46277i	0.115183	−	0.0477102i
$941$	21.1006	+	2.77794i	0.687859	+	0.0905583i	0.466350	−	0.884600i	$-0.345569\pi$
$941$	21.1006	+	2.77794i	0.687859	+	0.0905583i	0.221508	+	0.975158i	$0.428902\pi$
$942$		0			0
$943$	−1.23602	+	1.23602i	−0.0402504	+	0.0402504i
$944$	−17.0114	+	2.23959i	−0.553673	+	0.0728925i
$945$		0			0
$946$	12.2380	+	7.06559i	0.397890	+	0.229722i
$947$	−11.9169	+	15.5304i	−0.387247	+	0.504670i	−0.945778	−	0.324814i	$-0.894698\pi$
$947$	−11.9169	+	15.5304i	−0.387247	+	0.504670i	0.558531	+	0.829484i	$0.311365\pi$
$948$		0			0
$949$	2.16156	−	2.81700i	0.0701672	−	0.0914437i
$950$	−1.81045	−	4.37081i	−0.0587387	−	0.141808i
$951$		0			0
$952$	−19.8076	−	19.8076i	−0.641967	−	0.641967i
$953$	2.45474	+	1.88359i	0.0795167	+	0.0610153i	0.647755	−	0.761849i	$-0.275708\pi$
$953$	2.45474	+	1.88359i	0.0795167	+	0.0610153i	−0.568238	+	0.822864i	$0.692375\pi$
$954$		0			0
$955$	−3.00511	−	22.8261i	−0.0972430	−	0.738634i
$956$	−3.15074	−	2.41765i	−0.101902	−	0.0781924i
$957$		0			0
$958$	−6.66180	+	6.66180i	−0.215233	+	0.215233i
$959$	−7.86421	+	29.3496i	−0.253949	+	0.947749i
$960$		0			0
$961$	3.94022	−	2.27489i	0.127104	−	0.0733835i
$962$	−16.9270	−	16.9270i	−0.545749	−	0.545749i
$963$		0			0
$964$	−14.1803	−	24.5610i	−0.456716	−	0.791055i
$965$	−4.61485	+	35.0533i	−0.148557	+	1.12841i
$966$		0			0
$967$	32.8964	−	8.81457i	1.05788	−	0.283457i	0.312374	−	0.949959i	$-0.398876\pi$
$967$	32.8964	−	8.81457i	1.05788	−	0.283457i	0.745503	+	0.666502i	$0.232209\pi$
$968$	−6.46045	−	24.1107i	−0.207647	−	0.774948i
$969$		0			0
$970$	11.7607	−	1.03751i	0.377612	−	0.0333124i
$971$	2.42672			0.0778773			0.0389386	−	0.999242i	$-0.487602\pi$
$971$	2.42672			0.0778773			0.0389386	+	0.999242i	$0.487602\pi$
$972$		0			0
$973$	−37.6961	+	10.1007i	−1.20848	+	0.323812i
$974$	0.147737	−	0.0852958i	0.00473379	−	0.00273306i
$975$		0			0
$976$	−5.05241	−	8.75103i	−0.161724	−	0.280114i
$977$	4.04485	−	3.10372i	0.129406	−	0.0992969i	−0.542030	−	0.840359i	$-0.682344\pi$
$977$	4.04485	−	3.10372i	0.129406	−	0.0992969i	0.671437	+	0.741062i	$0.265678\pi$
$978$		0			0
$979$	19.3785	−	11.1882i	0.619340	−	0.357576i
$980$	−1.17046	+	0.154094i	−0.0373889	+	0.00492234i
$981$		0			0
$982$	6.78045	−	6.78045i	0.216373	−	0.216373i
$983$	−7.06322	+	53.6505i	−0.225282	+	1.71118i	0.388284	+	0.921540i	$0.373068\pi$
$983$	−7.06322	+	53.6505i	−0.225282	+	1.71118i	−0.613565	+	0.789644i	$0.710265\pi$
$984$		0			0
$985$	−2.01758	−	15.3251i	−0.0642856	−	0.488297i
$986$	3.79297	−	6.56962i	0.120793	−	0.209219i
$987$		0			0
$988$	−34.6511	−	34.6511i	−1.10240	−	1.10240i
$989$	−24.7089	+	10.2348i	−0.785699	+	0.325447i
$990$		0			0
$991$	−10.6820	+	13.9210i	−0.339324	+	0.442215i	−0.931581	−	0.363534i	$-0.881570\pi$
$991$	−10.6820	+	13.9210i	−0.339324	+	0.442215i	0.592257	+	0.805749i	$0.298237\pi$
$992$	34.1097			1.08298
$993$		0			0
$994$	2.16467	+	1.24977i	0.0686591	+	0.0396403i
$995$	−4.76410	−	1.27654i	−0.151032	−	0.0404689i
$996$		0			0
$997$	5.15026	−	5.15026i	0.163110	−	0.163110i	−0.620833	−	0.783943i	$-0.713205\pi$
$997$	5.15026	−	5.15026i	0.163110	−	0.163110i	0.783943	+	0.620833i	$0.213205\pi$
$998$	−2.82280	+	6.81484i	−0.0893541	+	0.215720i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	873.2.bo.b.442.4		56
3.2	odd	2		97.2.i.a.54.4	yes	56
97.9	even	24	inner	873.2.bo.b.397.4		56
291.191	odd	48		9409.2.a.m.1.24		56
291.197	odd	48		9409.2.a.m.1.23		56
291.203	odd	24		97.2.i.a.9.4	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
97.2.i.a.9.4	✓	56	291.203	odd	24
97.2.i.a.54.4	yes	56	3.2	odd	2
873.2.bo.b.397.4		56	97.9	even	24	inner
873.2.bo.b.442.4		56	1.1	even	1	trivial
9409.2.a.m.1.23		56	291.197	odd	48
9409.2.a.m.1.24		56	291.191	odd	48

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:	\( N \)	\(=\)	\( 873 = 3^{2} \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	873.bo (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.168402 + 0.628486i) q^{2} +(1.36542 - 0.788323i) q^{4} +(-0.240478 + 1.82661i) q^{5} +(2.03717 - 1.56318i) q^{7} +(1.64556 + 1.64556i) q^{8} +(-1.18850 + 0.156468i) q^{10} +(-1.20639 + 4.50229i) q^{11} +(-0.895889 + 6.80495i) q^{13} +(1.32550 + 1.01709i) q^{14} +(0.819554 - 1.41951i) q^{16} +(-3.71898 - 2.85368i) q^{17} +(-4.18366 + 1.73293i) q^{19} +(1.11161 + 2.68366i) q^{20} -3.03279 q^{22} +(3.49421 - 4.55375i) q^{23} +(1.55095 + 0.415576i) q^{25} +(-4.42769 + 0.582916i) q^{26} +(1.54930 - 3.74033i) q^{28} +(2.46586 + 0.324637i) q^{29} +(5.75920 - 1.54317i) q^{31} +(5.52590 + 1.48066i) q^{32} +(1.16721 - 2.81789i) q^{34} +(2.36542 + 4.09703i) q^{35} +(3.26313 + 4.25260i) q^{37} +(-1.79366 - 2.33754i) q^{38} +(-3.40151 + 2.61007i) q^{40} +(-0.301931 - 0.0397499i) q^{41} +(-4.03522 - 2.32974i) q^{43} +(1.90204 + 7.09853i) q^{44} +(3.45040 + 1.42920i) q^{46} -1.31590i q^{47} +(-0.105189 + 0.392572i) q^{49} +1.04473i q^{50} +(4.14124 + 9.99784i) q^{52} +(0.993641 + 3.70832i) q^{53} +(-7.93383 - 3.28630i) q^{55} +(5.92457 + 0.779984i) q^{56} +(0.211227 + 1.60443i) q^{58} +(-6.37251 - 8.30482i) q^{59} +(3.08241 - 5.33890i) q^{61} +(1.93972 + 3.35970i) q^{62} +0.444079i q^{64} +(-12.2146 - 3.27288i) q^{65} +(-2.60485 + 1.07896i) q^{67} +(-7.32758 - 0.964694i) q^{68} +(-2.17658 + 2.17658i) q^{70} +(1.48326 - 0.195275i) q^{71} +(-0.448016 - 0.258662i) q^{73} +(-2.12318 + 2.76698i) q^{74} +(-4.34633 + 5.66425i) q^{76} +(4.58026 + 11.0577i) q^{77} +(3.64268 + 3.64268i) q^{79} +(2.39581 + 1.83837i) q^{80} +(-0.0258635 - 0.196453i) q^{82} +(2.76947 + 2.12509i) q^{83} +(6.10689 - 6.10689i) q^{85} +(0.784665 - 2.92841i) q^{86} +(-9.39395 + 5.42360i) q^{88} +(-3.39457 - 3.39457i) q^{89} +(8.81226 + 15.2633i) q^{91} +(1.18123 - 8.97233i) q^{92} +(0.827025 - 0.221601i) q^{94} +(-2.15931 - 8.05865i) q^{95} +(-9.83979 - 0.422473i) q^{97} -0.264440 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{2} - 12 q^{4} + 16 q^{5} - 16 q^{7} + 16 q^{8} - 24 q^{10} + 24 q^{13} + 32 q^{14} + 12 q^{16} + 4 q^{17} + 20 q^{19} - 4 q^{20} + 20 q^{23} + 52 q^{25} + 20 q^{26} + 32 q^{28} + 8 q^{29} + 12 q^{31}+ \cdots - 96 q^{98}+O(q^{100}) \) 56 * q + 8 * q^2 - 12 * q^4 + 16 * q^5 - 16 * q^7 + 16 * q^8 - 24 * q^10 + 24 * q^13 + 32 * q^14 + 12 * q^16 + 4 * q^17 + 20 * q^19 - 4 * q^20 + 20 * q^23 + 52 * q^25 + 20 * q^26 + 32 * q^28 + 8 * q^29 + 12 * q^31 + 136 * q^32 + 20 * q^34 - 28 * q^35 + 52 * q^37 - 24 * q^38 + 72 * q^40 + 48 * q^41 - 12 * q^43 - 36 * q^44 + 72 * q^46 - 32 * q^49 - 16 * q^52 + 44 * q^53 - 8 * q^55 + 64 * q^56 - 100 * q^58 + 48 * q^59 - 12 * q^61 - 28 * q^62 - 16 * q^65 + 48 * q^67 - 16 * q^68 - 24 * q^70 + 4 * q^71 + 24 * q^73 - 20 * q^74 - 56 * q^76 - 12 * q^77 + 24 * q^79 + 136 * q^80 - 8 * q^82 - 76 * q^83 - 40 * q^85 + 68 * q^86 - 168 * q^88 + 100 * q^89 - 60 * q^91 + 52 * q^92 - 88 * q^94 - 32 * q^95 - 36 * q^97 - 96 * q^98

Introduction

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