LMFDB - Embedded newform 990.2.bh.d.127.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(73,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 15, 14])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.73"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.bh (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,0,0,0,-40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			127.3
Character	$\chi$	$=$	990.127
Dual form			990.2.bh.d.343.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.891007 - 0.453990i) q^{2} +(0.587785 + 0.809017i) q^{4} +(-0.169731 - 2.22962i) q^{5} +(0.743917 - 4.69691i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-0.860994 + 2.06366i) q^{10} +(-2.86962 + 1.66292i) q^{11} +(2.34342 - 4.59923i) q^{13} +(-2.79519 + 3.84725i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-0.748460 - 1.46893i) q^{17} +(-1.69404 - 1.23080i) q^{19} +(1.70403 - 1.44785i) q^{20} +(3.31180 - 0.178892i) q^{22} +(-4.35146 + 4.35146i) q^{23} +(-4.94238 + 0.756869i) q^{25} +(-4.17601 + 3.03405i) q^{26} +(4.23714 - 2.15893i) q^{28} +(5.53644 - 4.02246i) q^{29} +(2.33171 + 7.17628i) q^{31} +(0.707107 - 0.707107i) q^{32} +1.64862i q^{34} +(-10.5986 - 0.861441i) q^{35} +(1.00371 + 0.158971i) q^{37} +(0.950635 + 1.86573i) q^{38} +(-2.17561 + 0.516430i) q^{40} +(-4.45667 + 6.13408i) q^{41} +(8.40230 + 8.40230i) q^{43} +(-3.03205 - 1.34413i) q^{44} +(5.85270 - 1.90166i) q^{46} +(-1.15329 - 7.28159i) q^{47} +(-14.8502 - 4.82511i) q^{49} +(4.74731 + 1.56942i) q^{50} +(5.09829 - 0.807489i) q^{52} +(1.22476 + 0.624046i) q^{53} +(4.19473 + 6.11590i) q^{55} -4.75546 q^{56} +(-6.75916 + 1.07055i) q^{58} +(0.509356 + 0.701068i) q^{59} +(-2.24687 - 0.730053i) q^{61} +(1.18039 - 7.45269i) q^{62} +(-0.951057 + 0.309017i) q^{64} +(-10.6523 - 4.44431i) q^{65} +(-6.82700 - 6.82700i) q^{67} +(0.748460 - 1.46893i) q^{68} +(9.05231 + 5.57920i) q^{70} +(2.92210 - 8.99330i) q^{71} +(-4.47657 - 0.709019i) q^{73} +(-0.822137 - 0.597318i) q^{74} -2.09395i q^{76} +(5.67582 + 14.7154i) q^{77} +(-3.09610 - 9.52881i) q^{79} +(2.17294 + 0.527566i) q^{80} +(6.75573 - 3.44222i) q^{82} +(-4.08300 + 2.08039i) q^{83} +(-3.14812 + 1.91810i) q^{85} +(-3.67194 - 11.3011i) q^{86} +(2.09135 + 2.57415i) q^{88} -13.6217i q^{89} +(-19.8589 - 14.4283i) q^{91} +(-6.07812 - 0.962680i) q^{92} +(-2.27818 + 7.01153i) q^{94} +(-2.45667 + 3.98597i) q^{95} +(0.662306 - 1.29985i) q^{97} +(11.0410 + 11.0410i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 40 q^{7} + 24 q^{16} + 4 q^{22} + 8 q^{25} + 20 q^{28} - 16 q^{31} + 64 q^{37} - 40 q^{46} - 40 q^{52} - 36 q^{55} - 12 q^{58} - 80 q^{61} - 48 q^{67} - 52 q^{70} + 20 q^{73} + 48 q^{82} - 160 q^{85}+ \cdots + 48 q^{97}+O(q^{100}) $ 96 * q - 40 * q^7 + 24 * q^16 + 4 * q^22 + 8 * q^25 + 20 * q^28 - 16 * q^31 + 64 * q^37 - 40 * q^46 - 40 * q^52 - 36 * q^55 - 12 * q^58 - 80 * q^61 - 48 * q^67 - 52 * q^70 + 20 * q^73 + 48 * q^82 - 160 * q^85 + 4 * q^88 + 8 * q^91 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{9}{10}\right)$	$1$

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 $

$2$	−0.891007	−	0.453990i	−0.630037	−	0.321020i
$2$	−0.891007	−	0.453990i	−0.630037	−	0.321020i
$3$		0			0
$3$		0			0
$4$	0.587785	+	0.809017i	0.293893	+	0.404508i
$5$	−0.169731	−	2.22962i	−0.0759059	−	0.997115i
$5$	−0.169731	−	2.22962i	−0.0759059	−	0.997115i
$6$		0			0
$7$	0.743917	−	4.69691i	0.281174	−	1.77526i	−0.292583	−	0.956240i	$-0.594515\pi$
$7$	0.743917	−	4.69691i	0.281174	−	1.77526i	0.573758	−	0.819025i	$-0.305485\pi$
$8$	−0.156434	−	0.987688i	−0.0553079	−	0.349201i
$9$		0			0
$10$	−0.860994	+	2.06366i	−0.272270	+	0.652586i
$11$	−2.86962	+	1.66292i	−0.865222	+	0.501389i
$11$	−2.86962	+	1.66292i	−0.865222	+	0.501389i
$12$		0			0
$13$	2.34342	−	4.59923i	0.649949	−	1.27560i	−0.297204	−	0.954814i	$-0.596054\pi$
$13$	2.34342	−	4.59923i	0.649949	−	1.27560i	0.947153	−	0.320783i	$-0.103946\pi$
$14$	−2.79519	+	3.84725i	−0.747045	+	1.02822i
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	−0.748460	−	1.46893i	−0.181528	−	0.356269i	0.782254	−	0.622959i	$-0.214070\pi$
$17$	−0.748460	−	1.46893i	−0.181528	−	0.356269i	−0.963782	+	0.266690i	$0.914070\pi$
$18$		0			0
$19$	−1.69404	−	1.23080i	−0.388640	−	0.282364i	0.376258	−	0.926515i	$-0.377211\pi$
$19$	−1.69404	−	1.23080i	−0.388640	−	0.282364i	−0.764898	+	0.644151i	$0.777211\pi$
$20$	1.70403	−	1.44785i	0.381033	−	0.323749i
$21$		0			0
$22$	3.31180	−	0.178892i	0.706077	−	0.0381400i
$23$	−4.35146	+	4.35146i	−0.907341	+	0.907341i	−0.996057	−	0.0887157i	$-0.971724\pi$
$23$	−4.35146	+	4.35146i	−0.907341	+	0.907341i	0.0887157	+	0.996057i	$0.471724\pi$
$24$		0			0
$25$	−4.94238	+	0.756869i	−0.988477	+	0.151374i
$26$	−4.17601	+	3.03405i	−0.818984	+	0.595026i
$27$		0			0
$28$	4.23714	−	2.15893i	0.800745	−	0.408000i
$29$	5.53644	−	4.02246i	1.02809	−	0.746951i	0.0601649	−	0.998188i	$-0.480837\pi$
$29$	5.53644	−	4.02246i	1.02809	−	0.746951i	0.967926	+	0.251237i	$0.0808373\pi$
$30$		0			0
$31$	2.33171	+	7.17628i	0.418788	+	1.28890i	0.908818	+	0.417192i	$0.136986\pi$
$31$	2.33171	+	7.17628i	0.418788	+	1.28890i	−0.490030	+	0.871706i	$0.663014\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$			1.64862i			0.282737i
$35$	−10.5986	−	0.861441i	−1.79149	−	0.145610i
$36$		0			0
$37$	1.00371	+	0.158971i	0.165008	+	0.0261347i	0.238392	−	0.971169i	$-0.423380\pi$
$37$	1.00371	+	0.158971i	0.165008	+	0.0261347i	−0.0733836	+	0.997304i	$0.523380\pi$
$38$	0.950635	+	1.86573i	0.154213	+	0.302661i
$39$		0			0
$40$	−2.17561	+	0.516430i	−0.343995	+	0.0816547i
$41$	−4.45667	+	6.13408i	−0.696014	+	0.957982i	0.303971	+	0.952681i	$0.401687\pi$
$41$	−4.45667	+	6.13408i	−0.696014	+	0.957982i	−0.999986	+	0.00530062i	$0.998313\pi$
$42$		0			0
$43$	8.40230	+	8.40230i	1.28134	+	1.28134i	0.939906	+	0.341432i	$0.110912\pi$
$43$	8.40230	+	8.40230i	1.28134	+	1.28134i	0.341432	+	0.939906i	$0.389088\pi$
$44$	−3.03205	−	1.34413i	−0.457098	−	0.202635i
$45$		0			0
$46$	5.85270	−	1.90166i	0.862933	−	0.280384i
$47$	−1.15329	−	7.28159i	−0.168225	−	1.06213i	−0.916878	−	0.399168i	$-0.869299\pi$
$47$	−1.15329	−	7.28159i	−0.168225	−	1.06213i	0.748653	−	0.662962i	$-0.230701\pi$
$48$		0			0
$49$	−14.8502	−	4.82511i	−2.12145	−	0.689301i
$50$	4.74731	+	1.56942i	0.671371	+	0.221949i
$51$		0			0
$52$	5.09829	−	0.807489i	0.707005	−	0.111979i
$53$	1.22476	+	0.624046i	0.168234	+	0.0857193i	0.536080	−	0.844167i	$-0.319905\pi$
$53$	1.22476	+	0.624046i	0.168234	+	0.0857193i	−0.367846	+	0.929887i	$0.619905\pi$
$54$		0			0
$55$	4.19473	+	6.11590i	0.565618	+	0.824668i
$56$	−4.75546			−0.635475
$57$		0			0
$58$	−6.75916	+	1.07055i	−0.887521	+	0.140570i
$59$	0.509356	+	0.701068i	0.0663124	+	0.0912713i	0.840885	−	0.541214i	$-0.182035\pi$
$59$	0.509356	+	0.701068i	0.0663124	+	0.0912713i	−0.774573	+	0.632485i	$0.782035\pi$
$60$		0			0
$61$	−2.24687	−	0.730053i	−0.287683	−	0.0934738i	0.161621	−	0.986853i	$-0.448328\pi$
$61$	−2.24687	−	0.730053i	−0.287683	−	0.0934738i	−0.449304	+	0.893379i	$0.648328\pi$
$62$	1.18039	−	7.45269i	0.149910	−	0.946492i
$63$		0			0
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$	−10.6523	−	4.44431i	−1.32125	−	0.551249i
$66$		0			0
$67$	−6.82700	−	6.82700i	−0.834051	−	0.834051i	0.154017	−	0.988068i	$-0.450779\pi$
$67$	−6.82700	−	6.82700i	−0.834051	−	0.834051i	−0.988068	+	0.154017i	$0.950779\pi$
$68$	0.748460	−	1.46893i	0.0907641	−	0.178134i
$69$		0			0
$70$	9.05231	+	5.57920i	1.08196	+	0.666842i
$71$	2.92210	−	8.99330i	0.346790	−	1.06731i	−0.613829	−	0.789439i	$-0.710372\pi$
$71$	2.92210	−	8.99330i	0.346790	−	1.06731i	0.960619	−	0.277870i	$-0.0896284\pi$
$72$		0			0
$73$	−4.47657	−	0.709019i	−0.523943	−	0.0829845i	−0.111140	−	0.993805i	$-0.535450\pi$
$73$	−4.47657	−	0.709019i	−0.523943	−	0.0829845i	−0.412803	+	0.910820i	$0.635450\pi$
$74$	−0.822137	−	0.597318i	−0.0955715	−	0.0694368i
$75$		0			0
$76$		−	2.09395i		−	0.240193i
$77$	5.67582	+	14.7154i	0.646820	+	1.67698i
$78$		0			0
$79$	−3.09610	−	9.52881i	−0.348338	−	1.07207i	−0.959772	−	0.280780i	$-0.909407\pi$
$79$	−3.09610	−	9.52881i	−0.348338	−	1.07207i	0.611434	−	0.791295i	$-0.290593\pi$
$80$	2.17294	+	0.527566i	0.242942	+	0.0589837i
$81$		0			0
$82$	6.75573	−	3.44222i	0.746046	−	0.380129i
$83$	−4.08300	+	2.08039i	−0.448167	+	0.228353i	−0.663482	−	0.748192i	$-0.730922\pi$
$83$	−4.08300	+	2.08039i	−0.448167	+	0.228353i	0.215315	+	0.976545i	$0.430922\pi$
$84$		0			0
$85$	−3.14812	+	1.91810i	−0.341462	+	0.208047i
$86$	−3.67194	−	11.3011i	−0.395955	−	1.21863i
$87$		0			0
$88$	2.09135	+	2.57415i	0.222939	+	0.274405i
$89$		−	13.6217i		−	1.44390i	−0.691944	−	0.721951i	$-0.743246\pi$
$89$		−	13.6217i		−	1.44390i	0.691944	−	0.721951i	$-0.256754\pi$
$90$		0			0
$91$	−19.8589	−	14.4283i	−2.08177	−	1.51250i
$92$	−6.07812	−	0.962680i	−0.633688	−	0.100366i
$93$		0			0
$94$	−2.27818	+	7.01153i	−0.234977	+	0.723184i
$95$	−2.45667	+	3.98597i	−0.252049	+	0.408952i
$96$		0			0
$97$	0.662306	−	1.29985i	0.0672469	−	0.131980i	−0.854936	−	0.518733i	$-0.826404\pi$
$97$	0.662306	−	1.29985i	0.0672469	−	0.131980i	0.922183	+	0.386754i	$0.126404\pi$
$98$	11.0410	+	11.0410i	1.11531	+	1.11531i
$99$		0			0
$100$	−3.51738	−	3.55360i	−0.351738	−	0.355360i
$101$	−8.05097	+	2.61592i	−0.801101	+	0.260294i	−0.680824	−	0.732447i	$-0.738378\pi$
$101$	−8.05097	+	2.61592i	−0.801101	+	0.260294i	−0.120277	+	0.992740i	$0.538378\pi$
$102$		0			0
$103$	−0.981906	+	6.19951i	−0.0967500	+	0.610856i	0.890902	+	0.454195i	$0.150073\pi$
$103$	−0.981906	+	6.19951i	−0.0967500	+	0.610856i	−0.987652	+	0.156661i	$0.949927\pi$
$104$	−4.90920	−	1.59510i	−0.481386	−	0.156412i
$105$		0			0
$106$	−0.807957	−	1.11206i	−0.0784758	−	0.108013i
$107$	6.18271	−	0.979246i	0.597705	−	0.0946672i	0.149751	−	0.988724i	$-0.452153\pi$
$107$	6.18271	−	0.979246i	0.597705	−	0.0946672i	0.447954	+	0.894056i	$0.352153\pi$
$108$		0			0
$109$	−1.60428			−0.153662			−0.0768308	−	0.997044i	$-0.524480\pi$
$109$	−1.60428			−0.153662			−0.0768308	+	0.997044i	$0.524480\pi$
$110$	−0.960975	−	7.35367i	−0.0916254	−	0.701145i
$111$		0			0
$112$	4.23714	+	2.15893i	0.400372	+	0.204000i
$113$	−3.19317	+	0.505749i	−0.300389	+	0.0475769i	−0.304809	−	0.952413i	$-0.598593\pi$
$113$	−3.19317	+	0.505749i	−0.300389	+	0.0475769i	0.00442091	+	0.999990i	$0.498593\pi$
$114$		0			0
$115$	10.4407	+	8.96350i	0.973596	+	0.835851i
$116$	6.50847	+	2.11473i	0.604296	+	0.196348i
$117$		0			0
$118$	−0.135561	−	0.855899i	−0.0124794	−	0.0787919i
$119$	−7.45625	+	2.42268i	−0.683513	+	0.222087i
$120$		0			0
$121$	5.46940	−	9.54388i	0.497219	−	0.867625i
$122$	1.67054	+	1.67054i	0.151244	+	0.151244i
$123$		0			0
$124$	−4.43518	+	6.10451i	−0.398291	+	0.548201i
$125$	2.52640	+	10.8912i	0.225968	+	0.974135i
$126$		0			0
$127$	6.78320	+	13.3128i	0.601911	+	1.18132i	0.968050	+	0.250757i	$0.0806795\pi$
$127$	6.78320	+	13.3128i	0.601911	+	1.18132i	−0.366139	+	0.930560i	$0.619320\pi$
$128$	0.987688	+	0.156434i	0.0873001	+	0.0138270i
$129$		0			0
$130$	7.47357	+	8.79594i	0.655475	+	0.771455i
$131$			13.8516i			1.21022i	0.796142	+	0.605110i	$0.206871\pi$
$131$			13.8516i			1.21022i	−0.796142	+	0.605110i	$0.793129\pi$
$132$		0			0
$133$	−7.04116	+	7.04116i	−0.610546	+	0.610546i
$134$	2.98351	+	9.18229i	0.257736	+	0.793229i
$135$		0			0
$136$	−1.33376	+	0.969037i	−0.114369	+	0.0830942i
$137$	15.3678	−	7.83027i	1.31296	−	0.668986i	0.349523	−	0.936928i	$-0.386344\pi$
$137$	15.3678	−	7.83027i	1.31296	−	0.668986i	0.963435	+	0.267942i	$0.0863436\pi$
$138$		0			0
$139$	−4.25485	+	3.09133i	−0.360891	+	0.262203i	−0.753424	−	0.657535i	$-0.771599\pi$
$139$	−4.25485	+	3.09133i	−0.360891	+	0.262203i	0.392532	+	0.919738i	$0.371599\pi$
$140$	−5.53277	−	9.08077i	−0.467604	−	0.767465i
$141$		0			0
$142$	−6.68649	+	6.68649i	−0.561117	+	0.561117i
$143$	0.923413	+	17.0950i	0.0772197	+	1.42955i
$144$		0			0
$145$	−9.90824	−	11.6614i	−0.822835	−	0.968426i
$146$	3.66677	+	2.66406i	0.303464	+	0.220479i
$147$		0			0
$148$	0.461353	+	0.905456i	0.0379230	+	0.0744281i
$149$	−0.622398	+	1.91554i	−0.0509888	+	0.156927i	−0.973309	−	0.229500i	$-0.926291\pi$
$149$	−0.622398	+	1.91554i	−0.0509888	+	0.156927i	0.922320	+	0.386427i	$0.126291\pi$
$150$		0			0
$151$	11.4348	−	15.7386i	0.930550	−	1.28079i	−0.0290949	−	0.999577i	$-0.509263\pi$
$151$	11.4348	−	15.7386i	0.930550	−	1.28079i	0.959645	−	0.281215i	$-0.0907375\pi$
$152$	−0.950635	+	1.86573i	−0.0771067	+	0.151330i
$153$		0			0
$154$	1.62346	−	15.6883i	0.130822	−	1.26420i
$155$	15.6046	−	6.41687i	1.25339	−	0.515415i
$156$		0			0
$157$	−1.90573	−	12.0323i	−0.152093	−	0.960280i	−0.939177	−	0.343434i	$-0.888410\pi$
$157$	−1.90573	−	12.0323i	−0.152093	−	0.960280i	0.787084	−	0.616846i	$-0.211590\pi$
$158$	−1.56735	+	9.89583i	−0.124691	+	0.787270i
$159$		0			0
$160$	−1.69659	−	1.45656i	−0.134128	−	0.115151i
$161$	17.2013	+	23.6755i	1.35565	+	1.86589i
$162$		0			0
$163$	−13.6534	−	6.95673i	−1.06941	−	0.544893i	−0.171554	−	0.985175i	$-0.554879\pi$
$163$	−13.6534	−	6.95673i	−1.06941	−	0.544893i	−0.897860	+	0.440282i	$0.854879\pi$
$164$	−7.58214			−0.592065
$165$		0			0
$166$	4.58246			0.355668
$167$	−3.63689	−	1.85309i	−0.281431	−	0.143396i	0.307578	−	0.951523i	$-0.400482\pi$
$167$	−3.63689	−	1.85309i	−0.281431	−	0.143396i	−0.589009	+	0.808127i	$0.700482\pi$
$168$		0			0
$169$	−8.02007	−	11.0387i	−0.616928	−	0.849129i
$170$	3.67580	−	0.279822i	0.281921	−	0.0214614i
$171$		0			0
$172$	−1.85886	+	11.7364i	−0.141736	+	0.894888i
$173$	−3.39838	−	21.4565i	−0.258374	−	1.63131i	−0.686176	−	0.727435i	$-0.740712\pi$
$173$	−3.39838	−	21.4565i	−0.258374	−	1.63131i	0.427802	−	0.903872i	$-0.359288\pi$
$174$		0			0
$175$	−0.121780	+	23.7770i	−0.00920568	+	1.79737i
$176$	−0.694769	−	3.24304i	−0.0523702	−	0.244453i
$177$		0			0
$178$	−6.18414	+	12.1371i	−0.463521	+	0.909711i
$179$	−1.45584	+	2.00379i	−0.108815	+	0.149771i	−0.859951	−	0.510377i	$-0.829506\pi$
$179$	−1.45584	+	2.00379i	−0.108815	+	0.149771i	0.751136	+	0.660147i	$0.229506\pi$
$180$		0			0
$181$	−2.64657	+	8.14531i	−0.196718	+	0.605436i	0.803234	+	0.595663i	$0.203111\pi$
$181$	−2.64657	+	8.14531i	−0.196718	+	0.605436i	−0.999952	+	0.00977273i	$0.996889\pi$
$182$	11.1441	+	21.8714i	0.826052	+	1.62122i
$183$		0			0
$184$	4.97860	+	3.61716i	0.367027	+	0.266661i
$185$	0.184086	−	2.26486i	0.0135342	−	0.166516i
$186$		0			0
$187$	4.59051	+	2.97065i	0.335691	+	0.217236i
$188$	5.21305	−	5.21305i	0.380200	−	0.380200i
$189$		0			0
$190$	3.99850	−	2.43622i	0.290082	−	0.176742i
$191$	19.6785	−	14.2973i	1.42389	−	1.03452i	0.432774	−	0.901503i	$-0.357535\pi$
$191$	19.6785	−	14.2973i	1.42389	−	1.03452i	0.991114	−	0.133013i	$-0.0424651\pi$
$192$		0			0
$193$	11.7321	−	5.97781i	0.844496	−	0.430292i	0.0224733	−	0.999747i	$-0.492846\pi$
$193$	11.7321	−	5.97781i	0.844496	−	0.430292i	0.822022	+	0.569455i	$0.192846\pi$
$194$	−1.18024	+	0.857492i	−0.0847361	+	0.0615644i
$195$		0			0
$196$	−4.82511	−	14.8502i	−0.344650	−	1.06073i
$197$	17.3897	−	17.3897i	1.23897	−	1.23897i	0.278543	−	0.960424i	$-0.410149\pi$
$197$	17.3897	−	17.3897i	1.23897	−	1.23897i	0.960424	−	0.278543i	$-0.0898514\pi$
$198$		0			0
$199$			8.21281i			0.582191i	0.956694	+	0.291095i	$0.0940197\pi$
$199$			8.21281i			0.582191i	−0.956694	+	0.291095i	$0.905980\pi$
$200$	1.52071	+	4.76313i	0.107530	+	0.336804i
$201$		0			0
$202$	8.36107	+	1.32426i	0.588283	+	0.0931748i
$203$	−14.7745	−	28.9965i	−1.03696	−	2.03516i
$204$		0			0
$205$	14.4331	+	8.89552i	1.00805	+	0.621290i
$206$	3.68940	−	5.07803i	0.257053	−	0.353803i
$207$		0			0
$208$	3.64997	+	3.64997i	0.253080	+	0.253080i
$209$	6.90797	+	0.714853i	0.477834	+	0.0494474i
$210$		0			0
$211$	−14.9717	+	4.86460i	−1.03069	+	0.334893i	−0.775065	−	0.631882i	$-0.782283\pi$
$211$	−14.9717	+	4.86460i	−1.03069	+	0.334893i	−0.255629	+	0.966775i	$0.582283\pi$
$212$	0.215032	+	1.35766i	0.0147684	+	0.0932442i
$213$		0			0
$214$	−5.95341	−	1.93438i	−0.406966	−	0.132231i
$215$	17.3078	−	20.1600i	1.18038	−	1.37490i
$216$		0			0
$217$	35.4409	−	5.61329i	2.40589	−	0.381055i
$218$	1.42942	+	0.728326i	0.0968125	+	0.0493284i
$219$		0			0
$220$	−2.48226	+	6.98845i	−0.167354	+	0.471161i
$221$	−8.50993			−0.572440
$222$		0			0
$223$	10.3007	−	1.63147i	0.689784	−	0.109251i	0.198305	−	0.980140i	$-0.436456\pi$
$223$	10.3007	−	1.63147i	0.689784	−	0.109251i	0.491479	+	0.870889i	$0.336456\pi$
$224$	−2.79519	−	3.84725i	−0.186761	−	0.257055i
$225$		0			0
$226$	3.07474	+	0.999045i	0.204529	+	0.0664555i
$227$	0.662946	−	4.18568i	0.0440013	−	0.277813i	−0.955871	−	0.293786i	$-0.905085\pi$
$227$	0.662946	−	4.18568i	0.0440013	−	0.277813i	0.999872	+	0.0159731i	$0.00508461\pi$
$228$		0			0
$229$	−12.4353	+	4.04048i	−0.821749	+	0.267002i	−0.689566	−	0.724223i	$-0.742199\pi$
$229$	−12.4353	+	4.04048i	−0.821749	+	0.267002i	−0.132183	+	0.991225i	$0.542199\pi$
$230$	−5.23335	−	12.7265i	−0.345077	−	0.839160i
$231$		0			0
$232$	−4.83902	−	4.83902i	−0.317697	−	0.317697i
$233$	7.33973	−	14.4050i	0.480842	−	0.943705i	−0.515388	−	0.856957i	$-0.672352\pi$
$233$	7.33973	−	14.4050i	0.480842	−	0.943705i	0.996230	−	0.0867486i	$-0.0276477\pi$
$234$		0			0
$235$	−16.0394	+	3.80731i	−1.04630	+	0.248361i
$236$	−0.267784	+	0.824155i	−0.0174313	+	0.0536479i
$237$		0			0
$238$	7.74344	+	1.22644i	0.501933	+	0.0794983i
$239$	2.82823	+	2.05483i	0.182943	+	0.132916i	0.675488	−	0.737371i	$-0.263933\pi$
$239$	2.82823	+	2.05483i	0.182943	+	0.132916i	−0.492544	+	0.870287i	$0.663933\pi$
$240$		0			0
$241$		−	8.19797i		−	0.528078i	−0.964512	−	0.264039i	$-0.914945\pi$
$241$		−	8.19797i		−	0.528078i	0.964512	−	0.264039i	$-0.0850547\pi$
$242$	−9.20610	+	6.02060i	−0.591791	+	0.387019i
$243$		0			0
$244$	−0.730053	−	2.24687i	−0.0467369	−	0.143841i
$245$	−8.23761	+	33.9291i	−0.526282	+	2.16765i
$246$		0			0
$247$	−9.63057	+	4.90702i	−0.612779	+	0.312226i
$248$	6.72317	−	3.42562i	0.426922	−	0.217527i
$249$		0			0
$250$	2.69344	−	10.8511i	0.170348	−	0.686281i
$251$	2.66715	+	8.20863i	0.168349	+	0.518124i	0.999267	−	0.0382697i	$-0.0121846\pi$
$251$	2.66715	+	8.20863i	0.168349	+	0.518124i	−0.830919	+	0.556394i	$0.812185\pi$
$252$		0			0
$253$	5.25089	−	19.7231i	0.330121	−	1.23998i
$254$		−	14.9413i		−	0.937499i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−12.1193	−	1.91952i	−0.755984	−	0.119736i	−0.233467	−	0.972365i	$-0.575007\pi$
$257$	−12.1193	−	1.91952i	−0.755984	−	0.119736i	−0.522517	+	0.852629i	$0.675007\pi$
$258$		0			0
$259$	1.49335	−	4.59606i	0.0927922	−	0.285585i
$260$	−2.66573	−	11.2302i	−0.165321	−	0.696465i
$261$		0			0
$262$	6.28850	−	12.3419i	0.388505	−	0.762483i
$263$	13.4242	+	13.4242i	0.827774	+	0.827774i	0.987208	−	0.159435i	$-0.0509671\pi$
$263$	13.4242	+	13.4242i	0.827774	+	0.827774i	−0.159435	+	0.987208i	$0.550967\pi$
$264$		0			0
$265$	1.18350	−	2.83666i	0.0727021	−	0.174255i
$266$	9.47034	−	3.07710i	0.580664	−	0.188669i
$267$		0			0
$268$	1.51035	−	9.53597i	0.0922593	−	0.582502i
$269$	25.0851	+	8.15065i	1.52947	+	0.496954i	0.948447	−	0.316936i	$-0.102654\pi$
$269$	25.0851	+	8.15065i	1.52947	+	0.496954i	0.581020	+	0.813890i	$0.302654\pi$
$270$		0			0
$271$	17.5795	+	24.1961i	1.06788	+	1.46981i	0.872207	+	0.489137i	$0.162688\pi$
$271$	17.5795	+	24.1961i	1.06788	+	1.46981i	0.195670	+	0.980670i	$0.437312\pi$
$272$	1.62833	−	0.257902i	0.0987318	−	0.0156376i
$273$		0			0
$274$	−17.2477			−1.04197
$275$	12.9241	−	10.3907i	0.779355	−	0.626583i
$276$		0			0
$277$	−4.60192	−	2.34479i	−0.276502	−	0.140885i	0.310241	−	0.950658i	$-0.399590\pi$
$277$	−4.60192	−	2.34479i	−0.276502	−	0.140885i	−0.586743	+	0.809773i	$0.699590\pi$
$278$	5.19453	−	0.822732i	0.311547	−	0.0493442i
$279$		0			0
$280$	0.807147	+	10.6028i	0.0482363	+	0.633641i
$281$	−11.3337	−	3.68254i	−0.676111	−	0.219682i	−0.0492193	−	0.998788i	$-0.515673\pi$
$281$	−11.3337	−	3.68254i	−0.676111	−	0.219682i	−0.626892	+	0.779106i	$0.715673\pi$
$282$		0			0
$283$	2.07850	+	13.1231i	0.123554	+	0.780087i	0.969188	+	0.246324i	$0.0792227\pi$
$283$	2.07850	+	13.1231i	0.123554	+	0.780087i	−0.845634	+	0.533763i	$0.820777\pi$
$284$	8.99330	−	2.92210i	0.533654	−	0.173395i
$285$		0			0
$286$	6.93818	−	15.6509i	0.410263	−	0.925459i
$287$	25.4958	+	25.4958i	1.50497	+	1.50497i
$288$		0			0
$289$	8.39477	−	11.5544i	0.493810	−	0.679671i
$290$	3.53414	+	14.8886i	0.207532	+	0.874290i
$291$		0			0
$292$	−2.05765	−	4.03837i	−0.120415	−	0.236328i
$293$	14.3072	+	2.26604i	0.835837	+	0.132384i	0.559659	−	0.828723i	$-0.310932\pi$
$293$	14.3072	+	2.26604i	0.835837	+	0.132384i	0.276178	+	0.961107i	$0.410932\pi$
$294$		0			0
$295$	1.47666	−	1.25466i	0.0859744	−	0.0730492i
$296$		−	1.01622i		−	0.0590664i
$297$		0			0
$298$	1.42420	−	1.42420i	0.0825016	−	0.0825016i
$299$	9.81604	+	30.2107i	0.567676	+	1.74713i
$300$		0			0
$301$	45.7155	−	33.2142i	2.63500	−	1.91444i
$302$	−17.3337	+	8.83194i	−0.997440	+	0.508221i
$303$		0			0
$304$	1.69404	−	1.23080i	0.0971601	−	0.0705909i
$305$	−1.24638	+	5.13358i	−0.0713673	+	0.293948i
$306$		0			0
$307$	4.77841	−	4.77841i	0.272718	−	0.272718i	−0.557475	−	0.830194i	$-0.688230\pi$
$307$	4.77841	−	4.77841i	0.272718	−	0.272718i	0.830194	+	0.557475i	$0.188230\pi$
$308$	−8.56885	+	13.2413i	−0.488256	+	0.754495i
$309$		0			0
$310$	−16.8170	−	1.36687i	−0.955141	−	0.0776328i
$311$	−4.33101	−	3.14666i	−0.245589	−	0.178431i	0.458181	−	0.888859i	$-0.348501\pi$
$311$	−4.33101	−	3.14666i	−0.245589	−	0.178431i	−0.703770	+	0.710428i	$0.748501\pi$
$312$		0			0
$313$	13.7731	+	27.0312i	0.778500	+	1.52789i	0.847812	+	0.530298i	$0.177920\pi$
$313$	13.7731	+	27.0312i	0.778500	+	1.52789i	−0.0693114	+	0.997595i	$0.522080\pi$
$314$	−3.76452	+	11.5860i	−0.212444	+	0.653837i
$315$		0			0
$316$	5.88913	−	8.10569i	0.331289	−	0.455981i
$317$	−11.5431	+	22.6546i	−0.648325	+	1.27241i	0.299645	+	0.954051i	$0.403132\pi$
$317$	−11.5431	+	22.6546i	−0.648325	+	1.27241i	−0.947970	+	0.318359i	$0.896868\pi$
$318$		0			0
$319$	−9.19844	+	20.7496i	−0.515013	+	1.16175i
$320$	0.850413	+	2.06804i	0.0475395	+	0.115607i
$321$		0			0
$322$	−4.57798	−	28.9043i	−0.255121	−	1.61077i
$323$	−0.540034	+	3.40964i	−0.0300483	+	0.189717i
$324$		0			0
$325$	−8.10109	+	24.5048i	−0.449367	+	1.35928i
$326$	9.00694	+	12.3970i	0.498848	+	0.686606i
$327$		0			0
$328$	6.75573	+	3.44222i	0.373023	+	0.190065i
$329$	−35.0589			−1.93286
$330$		0			0
$331$	−6.21550			−0.341635			−0.170817	−	0.985303i	$-0.554641\pi$
$331$	−6.21550			−0.341635			−0.170817	+	0.985303i	$0.554641\pi$
$332$	−4.08300	−	2.08039i	−0.224084	−	0.114176i
$333$		0			0
$334$	2.39921	+	3.30223i	0.131279	+	0.180690i
$335$	−14.0628	+	16.3803i	−0.768335	+	0.894954i
$336$		0			0
$337$	4.13628	−	26.1154i	0.225318	−	1.42260i	−0.572601	−	0.819834i	$-0.694066\pi$
$337$	4.13628	−	26.1154i	0.225318	−	1.42260i	0.797919	−	0.602765i	$-0.205934\pi$
$338$	2.13448	+	13.4766i	0.116100	+	0.733028i
$339$		0			0
$340$	−3.40220	−	1.41945i	−0.184510	−	0.0769807i
$341$	−18.6247	−	16.7157i	−1.00858	−	0.905207i
$342$		0			0
$343$	−18.5978	+	36.5003i	−1.00419	+	1.97083i
$344$	6.98444	−	9.61326i	0.376576	−	0.518312i
$345$		0			0
$346$	−6.71307	+	20.6607i	−0.360897	+	1.11073i
$347$	−11.2271	−	22.0344i	−0.602703	−	1.18287i	−0.967757	−	0.251885i	$-0.918950\pi$
$347$	−11.2271	−	22.0344i	−0.602703	−	1.18287i	0.365054	−	0.930986i	$-0.381050\pi$
$348$		0			0
$349$	−24.7447	−	17.9781i	−1.32455	−	0.962345i	−0.999863	−	0.0165246i	$-0.994740\pi$
$349$	−24.7447	−	17.9781i	−1.32455	−	0.962345i	−0.324691	−	0.945820i	$-0.605260\pi$
$350$	10.9030	−	21.1302i	0.582791	−	1.12945i
$351$		0			0
$352$	−0.853265	+	3.20499i	−0.0454792	+	0.170826i
$353$	1.33899	−	1.33899i	0.0712673	−	0.0712673i	−0.670575	−	0.741842i	$-0.733952\pi$
$353$	1.33899	−	1.33899i	0.0712673	−	0.0712673i	0.741842	+	0.670575i	$0.233952\pi$
$354$		0			0
$355$	−20.5476	−	4.98873i	−1.09055	−	0.264774i
$356$	11.0202	−	8.00666i	0.584070	−	0.424352i
$357$		0			0
$358$	2.20687	−	1.12445i	0.116637	−	0.0594293i
$359$	13.2269	−	9.60992i	0.698091	−	0.507192i	−0.181219	−	0.983443i	$-0.558004\pi$
$359$	13.2269	−	9.60992i	0.698091	−	0.507192i	0.879310	+	0.476250i	$0.158004\pi$
$360$		0			0
$361$	−4.51639	−	13.9000i	−0.237705	−	0.731581i
$362$	6.05601	−	6.05601i	0.318297	−	0.318297i
$363$		0			0
$364$		−	24.5469i		−	1.28661i
$365$	−0.821030	+	10.1014i	−0.0429747	+	0.528731i
$366$		0			0
$367$	16.8102	+	2.66247i	0.877483	+	0.138980i	0.578895	−	0.815402i	$-0.303484\pi$
$367$	16.8102	+	2.66247i	0.877483	+	0.138980i	0.298588	+	0.954382i	$0.403484\pi$
$368$	−2.79381	−	5.48315i	−0.145637	−	0.285829i
$369$		0			0
$370$	−1.19225	+	1.93443i	−0.0619820	+	0.100566i
$371$	3.84221	−	5.28834i	0.199477	−	0.274557i
$372$		0			0
$373$	−0.462167	−	0.462167i	−0.0239301	−	0.0239301i	0.695040	−	0.718971i	$-0.255386\pi$
$373$	−0.462167	−	0.462167i	−0.0239301	−	0.0239301i	−0.718971	+	0.695040i	$0.755386\pi$
$374$	−2.74153	−	4.73092i	−0.141761	−	0.244630i
$375$		0			0
$376$	−7.01153	+	2.27818i	−0.361592	+	0.117488i
$377$	−5.52598	−	34.8897i	−0.284602	−	1.79691i
$378$		0			0
$379$	−3.65175	−	1.18653i	−0.187578	−	0.0609478i	0.213722	−	0.976895i	$-0.431441\pi$
$379$	−3.65175	−	1.18653i	−0.187578	−	0.0609478i	−0.401300	+	0.915947i	$0.631441\pi$
$380$	−4.66871	+	0.355408i	−0.239500	+	0.0182321i
$381$		0			0
$382$	−24.0245	+	3.80511i	−1.22920	+	0.194686i
$383$	−32.3357	−	16.4759i	−1.65228	−	0.841877i	−0.996192	−	0.0871894i	$-0.972211\pi$
$383$	−32.3357	−	16.4759i	−1.65228	−	0.841877i	−0.656085	−	0.754687i	$-0.727789\pi$
$384$		0			0
$385$	31.8464	−	15.1526i	1.62304	−	0.772246i
$386$	−13.1673			−0.670195
$387$		0			0
$388$	1.44089	−	0.228215i	0.0731502	−	0.0115859i
$389$	−5.97501	−	8.22390i	−0.302945	−	0.416968i	0.630220	−	0.776417i	$-0.282965\pi$
$389$	−5.97501	−	8.22390i	−0.302945	−	0.416968i	−0.933165	+	0.359449i	$0.882965\pi$
$390$		0			0
$391$	9.64889	+	3.13512i	0.487965	+	0.158550i
$392$	−2.44263	+	15.4221i	−0.123371	+	0.778935i
$393$		0			0
$394$	−23.3891	+	7.59959i	−1.17833	+	0.382862i
$395$	−20.7201	+	8.52044i	−1.04254	+	0.428710i
$396$		0			0
$397$	−3.43344	−	3.43344i	−0.172320	−	0.172320i	0.615678	−	0.787998i	$-0.288882\pi$
$397$	−3.43344	−	3.43344i	−0.172320	−	0.172320i	−0.787998	+	0.615678i	$0.788882\pi$
$398$	3.72854	−	7.31767i	0.186895	−	0.366802i
$399$		0			0
$400$	0.807455	−	4.93437i	0.0403728	−	0.246719i
$401$	4.26805	−	13.1357i	0.213136	−	0.655966i	−0.786144	−	0.618043i	$-0.787926\pi$
$401$	4.26805	−	13.1357i	0.213136	−	0.655966i	0.999281	−	0.0379229i	$-0.0120741\pi$
$402$		0			0
$403$	38.4696	+	6.09298i	1.91631	+	0.303513i
$404$	−6.84856	−	4.97577i	−0.340729	−	0.247554i
$405$		0			0
$406$			32.5436i			1.61511i
$407$	−3.14461	+	1.21289i	−0.155872	+	0.0601209i
$408$		0			0
$409$	10.4918	+	32.2903i	0.518784	+	1.59665i	0.776290	+	0.630376i	$0.217099\pi$
$409$	10.4918	+	32.2903i	0.518784	+	1.59665i	−0.257506	+	0.966277i	$0.582901\pi$
$410$	−8.82148	−	14.4784i	−0.435662	−	0.715039i
$411$		0			0
$412$	−5.59266	+	2.84960i	−0.275530	+	0.140390i
$413$	3.67177	−	1.87086i	0.180676	−	0.0920590i
$414$		0			0
$415$	5.33149	+	8.75042i	0.261712	+	0.429541i
$416$	−1.59510	−	4.90920i	−0.0782060	−	0.240693i
$417$		0			0
$418$	−5.83051	−	3.77309i	−0.285180	−	0.184548i
$419$			15.6273i			0.763444i	0.924277	+	0.381722i	$0.124669\pi$
$419$			15.6273i			0.763444i	−0.924277	+	0.381722i	$0.875331\pi$
$420$		0			0
$421$	1.14190	+	0.829637i	0.0556527	+	0.0404340i	0.615264	−	0.788321i	$-0.289049\pi$
$421$	1.14190	+	0.829637i	0.0556527	+	0.0404340i	−0.559611	+	0.828755i	$0.689049\pi$
$422$	15.5484	+	2.46262i	0.756882	+	0.119878i
$423$		0			0
$424$	0.424768	−	1.30730i	0.0206286	−	0.0634882i
$425$	4.81096	+	6.69355i	0.233366	+	0.324685i
$426$		0			0
$427$	−5.10048	+	10.0103i	−0.246830	+	0.484431i
$428$	4.42633	+	4.42633i	0.213955	+	0.213955i
$429$		0			0
$430$	−24.5738	+	10.1052i	−1.18505	+	0.487314i
$431$	12.5006	−	4.06170i	0.602133	−	0.195645i	0.00794167	−	0.999968i	$-0.497472\pi$
$431$	12.5006	−	4.06170i	0.602133	−	0.195645i	0.594192	+	0.804323i	$0.297472\pi$
$432$		0			0
$433$	3.03796	−	19.1809i	0.145995	−	0.921777i	−0.800564	−	0.599247i	$-0.795467\pi$
$433$	3.03796	−	19.1809i	0.145995	−	0.921777i	0.946559	−	0.322530i	$-0.104533\pi$
$434$	−34.1265	−	11.0884i	−1.63812	−	0.532259i
$435$		0			0
$436$	−0.942969	−	1.29789i	−0.0451600	−	0.0621575i
$437$	12.7273	−	2.01581i	0.608830	−	0.0964292i
$438$		0			0
$439$	−6.60798			−0.315382			−0.157691	−	0.987489i	$-0.550405\pi$
$439$	−6.60798			−0.315382			−0.157691	+	0.987489i	$0.550405\pi$
$440$	5.38440	−	5.09983i	0.256691	−	0.243125i
$441$		0			0
$442$	7.58240	+	3.86343i	0.360658	+	0.183764i
$443$	−14.6857	+	2.32598i	−0.697737	+	0.110511i	−0.495220	−	0.868768i	$-0.664912\pi$
$443$	−14.6857	+	2.32598i	−0.697737	+	0.110511i	−0.202518	+	0.979279i	$0.564912\pi$
$444$		0			0
$445$	−30.3713	+	2.31203i	−1.43974	+	0.109601i
$446$	−9.91863	−	3.22276i	−0.469661	−	0.152602i
$447$		0			0
$448$	0.743917	+	4.69691i	0.0351468	+	0.221908i
$449$	16.2299	−	5.27342i	0.765937	−	0.248868i	0.100112	−	0.994976i	$-0.468080\pi$
$449$	16.2299	−	5.27342i	0.765937	−	0.248868i	0.665825	+	0.746108i	$0.268080\pi$
$450$		0			0
$451$	2.58846	−	25.0135i	0.121886	−	1.17784i
$452$	−2.28606	−	2.28606i	−0.107527	−	0.107527i
$453$		0			0
$454$	−2.49095	+	3.42849i	−0.116906	+	0.160907i
$455$	−28.7989	+	46.7266i	−1.35011	+	2.19057i
$456$		0			0
$457$	6.59994	+	12.9531i	0.308732	+	0.605921i	0.992285	−	0.123980i	$-0.0395659\pi$
$457$	6.59994	+	12.9531i	0.308732	+	0.605921i	−0.683552	+	0.729901i	$0.739566\pi$
$458$	12.9143	+	2.04542i	0.603445	+	0.0955763i
$459$		0			0
$460$	−1.11476	+	13.7153i	−0.0519761	+	0.639478i
$461$		−	1.06440i		−	0.0495742i	−0.999693	−	0.0247871i	$-0.992109\pi$
$461$		−	1.06440i		−	0.0495742i	0.999693	−	0.0247871i	$-0.00789079\pi$
$462$		0			0
$463$	−4.89966	+	4.89966i	−0.227707	+	0.227707i	−0.811734	−	0.584027i	$-0.801476\pi$
$463$	−4.89966	+	4.89966i	−0.227707	+	0.227707i	0.584027	+	0.811734i	$0.301476\pi$
$464$	2.11473	+	6.50847i	0.0981739	+	0.302148i
$465$		0			0
$466$	−13.0795	+	9.50281i	−0.605896	+	0.440209i
$467$	−23.0578	+	11.7486i	−1.06699	+	0.543658i	−0.897110	−	0.441807i	$-0.854338\pi$
$467$	−23.0578	+	11.7486i	−1.06699	+	0.543658i	−0.169879	+	0.985465i	$0.554338\pi$
$468$		0			0
$469$	−37.1445	+	26.9871i	−1.71517	+	1.24615i
$470$	16.0197	+	3.88941i	0.738934	+	0.179405i
$471$		0			0
$472$	0.612756	−	0.612756i	0.0282044	−	0.0282044i
$473$	−38.0837	−	10.1390i	−1.75109	−	0.466194i
$474$		0			0
$475$	9.30416	+	4.80089i	0.426904	+	0.220280i
$476$	−6.34266	−	4.60821i	−0.290715	−	0.211217i
$477$		0			0
$478$	−1.58710	−	3.11486i	−0.0725923	−	0.142470i
$479$	10.6612	−	32.8118i	0.487123	−	1.49921i	−0.341759	−	0.939788i	$-0.611023\pi$
$479$	10.6612	−	32.8118i	0.487123	−	1.49921i	0.828882	−	0.559424i	$-0.188977\pi$
$480$		0			0
$481$	3.08326	−	4.24374i	0.140584	−	0.193498i
$482$	−3.72180	+	7.30444i	−0.169523	+	0.332708i
$483$		0			0
$484$	10.9360	−	1.18491i	0.497091	−	0.0538596i
$485$	−3.01058	−	1.25606i	−0.136703	−	0.0570349i
$486$		0			0
$487$	−5.92156	−	37.3872i	−0.268331	−	1.69418i	−0.642072	−	0.766644i	$-0.721925\pi$
$487$	−5.92156	−	37.3872i	−0.268331	−	1.69418i	0.373741	−	0.927533i	$-0.378075\pi$
$488$	−0.369577	+	2.33342i	−0.0167300	+	0.105629i
$489$		0			0
$490$	22.7433	−	26.4913i	1.02744	−	1.19675i
$491$	7.89501	+	10.8666i	0.356297	+	0.490401i	0.949112	−	0.314938i	$-0.101984\pi$
$491$	7.89501	+	10.8666i	0.356297	+	0.490401i	−0.592815	+	0.805338i	$0.701984\pi$
$492$		0			0
$493$	−10.0525	−	5.12202i	−0.452743	−	0.230684i
$494$	10.8086			0.486304
$495$		0			0
$496$	−7.54559			−0.338807
$497$	−40.0669	−	20.4151i	−1.79725	−	0.915743i
$498$		0			0
$499$	13.7713	+	18.9545i	0.616487	+	0.848521i	0.997091	−	0.0762166i	$-0.0242841\pi$
$499$	13.7713	+	18.9545i	0.616487	+	0.848521i	−0.380604	+	0.924738i	$0.624284\pi$
$500$	−7.32615	+	8.44556i	−0.327635	+	0.377697i
$501$		0			0
$502$	1.35020	−	8.52480i	0.0602622	−	0.380480i
$503$	−2.07894	−	13.1259i	−0.0926952	−	0.585254i	−0.989691	−	0.143216i	$-0.954256\pi$
$503$	−2.07894	−	13.1259i	−0.0926952	−	0.585254i	0.896996	−	0.442038i	$-0.145744\pi$
$504$		0			0
$505$	7.19899	+	17.5066i	0.320351	+	0.779032i
$506$	−13.6327	+	15.1896i	−0.606047	+	0.675259i
$507$		0			0
$508$	−6.78320	+	13.3128i	−0.300956	+	0.590659i
$509$	−15.3894	+	21.1818i	−0.682125	+	0.938865i	−0.999957	−	0.00928243i	$-0.997045\pi$
$509$	−15.3894	+	21.1818i	−0.682125	+	0.938865i	0.317832	+	0.948147i	$0.397045\pi$
$510$		0			0
$511$	−6.66040	+	20.4986i	−0.294639	+	0.906805i
$512$	0.453990	+	0.891007i	0.0200637	+	0.0393773i
$513$		0			0
$514$	9.92697	+	7.21237i	0.437860	+	0.318124i
$515$	13.9892	+	1.13703i	0.616437	+	0.0501034i
$516$		0			0
$517$	15.4182	+	18.9776i	0.678092	+	0.834632i
$518$	−3.41715	+	3.41715i	−0.150141	+	0.150141i
$519$		0			0
$520$	−2.72321	+	11.2164i	−0.119421	+	0.491870i
$521$	−20.6875	+	15.0303i	−0.906335	+	0.658491i	−0.940085	−	0.340939i	$-0.889255\pi$
$521$	−20.6875	+	15.0303i	−0.906335	+	0.658491i	0.0337502	+	0.999430i	$0.489255\pi$
$522$		0			0
$523$	3.36222	−	1.71313i	0.147019	−	0.0749101i	−0.378933	−	0.925424i	$-0.623709\pi$
$523$	3.36222	−	1.71313i	0.147019	−	0.0749101i	0.525953	+	0.850514i	$0.323709\pi$
$524$	−11.2062	+	8.14177i	−0.489544	+	0.355675i
$525$		0			0
$526$	−5.86661	−	18.0556i	−0.255796	−	0.787260i
$527$	8.79629	−	8.79629i	0.383172	−	0.383172i
$528$		0			0
$529$		−	14.8703i		−	0.646536i
$530$	−2.34233	+	1.99019i	−0.101744	+	0.0864481i
$531$		0			0
$532$	−9.83511	−	1.55773i	−0.426406	−	0.0675361i
$533$	17.7682	+	34.8720i	0.769625	+	1.51047i
$534$		0			0
$535$	−3.23274	−	13.6189i	−0.139763	−	0.588795i
$536$	−5.67497	+	7.81093i	−0.245121	+	0.337381i
$537$		0			0
$538$	−18.6507	−	18.6507i	−0.804088	−	0.804088i
$539$	50.6380	−	10.8484i	2.18113	−	0.467273i
$540$		0			0
$541$	−30.8586	+	10.0266i	−1.32672	+	0.431076i	−0.884796	−	0.465978i	$-0.845702\pi$
$541$	−30.8586	+	10.0266i	−1.32672	+	0.431076i	−0.441920	+	0.897055i	$0.645702\pi$
$542$	−4.67864	−	29.5398i	−0.200965	−	1.26884i
$543$		0			0
$544$	−1.56793	−	0.509453i	−0.0672246	−	0.0218426i
$545$	0.272295	+	3.57692i	0.0116638	+	0.153218i
$546$		0			0
$547$	37.9366	−	6.00856i	1.62205	−	0.256908i	0.721743	−	0.692161i	$-0.243341\pi$
$547$	37.9366	−	6.00856i	1.62205	−	0.256908i	0.900308	+	0.435253i	$0.143341\pi$
$548$	15.3678	+	7.83027i	0.656479	+	0.334493i
$549$		0			0
$550$	−16.2328	+	3.39075i	−0.692168	+	0.144582i
$551$	−14.3298			−0.610469
$552$		0			0
$553$	−47.0592	+	7.45345i	−2.00116	+	0.316953i
$554$	3.03582	+	4.17845i	0.128980	+	0.177525i
$555$		0			0
$556$	−5.00187	−	1.62521i	−0.212127	−	0.0689241i
$557$	4.83457	−	30.5243i	0.204847	−	1.29335i	−0.644126	−	0.764919i	$-0.722779\pi$
$557$	4.83457	−	30.5243i	0.204847	−	1.29335i	0.848974	−	0.528435i	$-0.177221\pi$
$558$		0			0
$559$	58.3343	−	18.9539i	2.46728	−	0.801667i
$560$	4.09442	−	9.81364i	0.173021	−	0.414702i
$561$		0			0
$562$	8.42655	+	8.42655i	0.355453	+	0.355453i
$563$	0.974370	−	1.91231i	0.0410648	−	0.0805942i	−0.869562	−	0.493823i	$-0.835599\pi$
$563$	0.974370	−	1.91231i	0.0410648	−	0.0805942i	0.910627	+	0.413229i	$0.135599\pi$
$564$		0			0
$565$	1.66961	+	7.03371i	0.0702409	+	0.295911i
$566$	4.10581	−	12.6364i	0.172580	−	0.531147i
$567$		0			0
$568$	−9.33970	−	1.47926i	−0.391885	−	0.0620685i
$569$	8.59298	+	6.24316i	0.360236	+	0.261727i	0.753151	−	0.657848i	$-0.228533\pi$
$569$	8.59298	+	6.24316i	0.360236	+	0.261727i	−0.392914	+	0.919575i	$0.628533\pi$
$570$		0			0
$571$			34.9236i			1.46151i	0.682642	+	0.730753i	$0.260831\pi$
$571$			34.9236i			1.46151i	−0.682642	+	0.730753i	$0.739169\pi$
$572$	−13.2873	+	10.7952i	−0.555571	+	0.451371i
$573$		0			0
$574$	−11.1421	−	34.2918i	−0.465061	−	1.43131i
$575$	18.2131	−	24.8000i	0.759538	−	1.03423i
$576$		0			0
$577$	6.70184	−	3.41476i	0.279001	−	0.142158i	−0.308891	−	0.951097i	$-0.599958\pi$
$577$	6.70184	−	3.41476i	0.279001	−	0.142158i	0.587892	+	0.808939i	$0.299958\pi$
$578$	−12.7254	+	6.48391i	−0.529306	+	0.269695i
$579$		0			0
$580$	3.61035	−	14.8703i	0.149912	−	0.617457i
$581$	6.73400	+	20.7251i	0.279373	+	0.859823i
$582$		0			0
$583$	−4.55233	+	0.245902i	−0.188538	+	0.0101842i
$584$			4.53237i			0.187551i
$585$		0			0
$586$	−11.7191	−	8.51440i	−0.484110	−	0.351727i
$587$	−25.9408	−	4.10863i	−1.07069	−	0.169581i	−0.403884	−	0.914810i	$-0.632340\pi$
$587$	−25.9408	−	4.10863i	−1.07069	−	0.169581i	−0.666809	+	0.745229i	$0.732340\pi$
$588$		0			0
$589$	4.88250	−	15.0268i	0.201180	−	0.619168i
$590$	−1.88532	+	0.447521i	−0.0776173	+	0.0184242i
$591$		0			0
$592$	−0.461353	+	0.905456i	−0.0189615	+	0.0372140i
$593$	11.5459	+	11.5459i	0.474133	+	0.474133i	0.903249	−	0.429116i	$-0.141175\pi$
$593$	11.5459	+	11.5459i	0.474133	+	0.474133i	−0.429116	+	0.903249i	$0.641175\pi$
$594$		0			0
$595$	6.66720	+	16.2134i	0.273329	+	0.664683i
$596$	−1.91554	+	0.622398i	−0.0784637	+	0.0254944i
$597$		0			0
$598$	4.96920	−	31.3743i	0.203206	−	1.28299i
$599$	−18.3450	−	5.96065i	−0.749556	−	0.243546i	−0.0907661	−	0.995872i	$-0.528932\pi$
$599$	−18.3450	−	5.96065i	−0.749556	−	0.243546i	−0.658790	+	0.752327i	$0.728932\pi$
$600$		0			0
$601$	−19.1210	−	26.3177i	−0.779960	−	1.07352i	−0.995286	−	0.0969810i	$-0.969081\pi$
$601$	−19.1210	−	26.3177i	−0.779960	−	1.07352i	0.215326	−	0.976542i	$-0.430919\pi$
$602$	−55.8117	+	8.83971i	−2.27472	+	0.360280i
$603$		0			0
$604$	19.4540			0.791573
$605$	−22.2075	−	10.5748i	−0.902864	−	0.429926i
$606$		0			0
$607$	1.69934	+	0.865858i	0.0689742	+	0.0351441i	0.488137	−	0.872767i	$-0.337676\pi$
$607$	1.69934	+	0.865858i	0.0689742	+	0.0351441i	−0.419163	+	0.907911i	$0.637676\pi$
$608$	−2.06817	+	0.327567i	−0.0838755	+	0.0132846i
$609$		0			0
$610$	3.44113	−	4.00821i	0.139327	−	0.162288i
$611$	−36.1924	−	11.7596i	−1.46419	−	0.475743i
$612$		0			0
$613$	−6.67136	−	42.1213i	−0.269454	−	1.70126i	−0.636677	−	0.771131i	$-0.719691\pi$
$613$	−6.67136	−	42.1213i	−0.269454	−	1.70126i	0.367223	−	0.930133i	$-0.380309\pi$
$614$	−6.42695	+	2.08824i	−0.259371	+	0.0842746i
$615$		0			0
$616$	13.6463	−	7.90794i	0.549827	−	0.318620i
$617$	9.44671	+	9.44671i	0.380310	+	0.380310i	0.871214	−	0.490904i	$-0.163333\pi$
$617$	9.44671	+	9.44671i	0.380310	+	0.380310i	−0.490904	+	0.871214i	$0.663333\pi$
$618$		0			0
$619$	−1.06348	+	1.46376i	−0.0427449	+	0.0588333i	−0.829854	−	0.557980i	$-0.811577\pi$
$619$	−1.06348	+	1.46376i	−0.0427449	+	0.0588333i	0.787110	+	0.616813i	$0.211577\pi$
$620$	14.3635	+	8.85264i	0.576852	+	0.355531i
$621$		0			0
$622$	2.43040	+	4.76993i	0.0974502	+	0.191257i
$623$	−63.9801	−	10.1334i	−2.56331	−	0.405988i
$624$		0			0
$625$	23.8543	−	7.48147i	0.954172	−	0.299259i
$626$		−	30.3378i		−	1.21254i
$627$		0			0
$628$	8.61416	−	8.61416i	0.343742	−	0.343742i
$629$	−0.517715	−	1.59336i	−0.0206426	−	0.0635315i
$630$		0			0
$631$	2.40387	−	1.74651i	0.0956964	−	0.0695275i	−0.538908	−	0.842365i	$-0.681163\pi$
$631$	2.40387	−	1.74651i	0.0956964	−	0.0695275i	0.634605	+	0.772837i	$0.281163\pi$
$632$	−8.92716	+	4.54861i	−0.355103	+	0.180934i
$633$		0			0
$634$	20.5699	−	14.9449i	0.816937	−	0.593540i
$635$	28.5311	−	17.3835i	1.13222	−	0.689844i
$636$		0			0
$637$	−56.9920	+	56.9920i	−2.25810	+	2.25810i
$638$	17.6160	−	14.3120i	0.697423	−	0.566617i
$639$		0			0
$640$	0.181148	−	2.22872i	0.00716050	−	0.0880978i
$641$	21.7906	+	15.8318i	0.860678	+	0.625319i	0.928069	−	0.372407i	$-0.121468\pi$
$641$	21.7906	+	15.8318i	0.860678	+	0.625319i	−0.0673914	+	0.997727i	$0.521468\pi$
$642$		0			0
$643$	3.86084	+	7.57733i	0.152257	+	0.298821i	0.954518	−	0.298152i	$-0.0963701\pi$
$643$	3.86084	+	7.57733i	0.152257	+	0.298821i	−0.802262	+	0.596972i	$0.796370\pi$
$644$	−9.04324	+	27.8322i	−0.356354	+	1.09674i
$645$		0			0
$646$	2.02912	−	2.79284i	0.0798346	−	0.109883i
$647$	−16.7208	+	32.8165i	−0.657364	+	1.29015i	0.285949	+	0.958245i	$0.407691\pi$
$647$	−16.7208	+	32.8165i	−0.657364	+	1.29015i	−0.943313	+	0.331905i	$0.892309\pi$
$648$		0			0
$649$	−2.62747	−	1.16478i	−0.103137	−	0.0457216i
$650$	18.3431	−	18.1561i	0.719475	−	0.712142i
$651$		0			0
$652$	−2.39713	−	15.1349i	−0.0938787	−	0.592727i
$653$	6.41284	−	40.4891i	0.250954	−	1.58446i	−0.464354	−	0.885650i	$-0.653713\pi$
$653$	6.41284	−	40.4891i	0.250954	−	1.58446i	0.715307	−	0.698810i	$-0.246287\pi$
$654$		0			0
$655$	30.8838	−	2.35104i	1.20673	−	0.0918628i
$656$	−4.45667	−	6.13408i	−0.174004	−	0.239495i
$657$		0			0
$658$	31.2377	+	15.9164i	1.21777	+	0.620487i
$659$	31.1223			1.21235			0.606176	−	0.795331i	$-0.292703\pi$
$659$	31.1223			1.21235			0.606176	+	0.795331i	$0.292703\pi$
$660$		0			0
$661$	−14.6020			−0.567950			−0.283975	−	0.958832i	$-0.591653\pi$
$661$	−14.6020			−0.567950			−0.283975	+	0.958832i	$0.591653\pi$
$662$	5.53805	+	2.82178i	0.215242	+	0.109671i
$663$		0			0
$664$	2.69350	+	3.70728i	0.104528	+	0.143871i
$665$	16.8942	+	14.5040i	0.655129	+	0.562441i
$666$		0			0
$667$	−6.58802	+	41.5951i	−0.255089	+	1.61057i
$668$	−0.638531	−	4.03152i	−0.0247055	−	0.155984i
$669$		0			0
$670$	19.9666	−	8.21060i	0.771377	−	0.317203i
$671$	7.66169	−	1.64139i	0.295776	−	0.0633653i
$672$		0			0
$673$	17.5210	−	34.3870i	0.675387	−	1.32552i	−0.257824	−	0.966192i	$-0.583006\pi$
$673$	17.5210	−	34.3870i	0.675387	−	1.32552i	0.933211	−	0.359329i	$-0.116994\pi$
$674$	−15.5416	+	21.3912i	−0.598641	+	0.823958i
$675$		0			0
$676$	4.21640	−	12.9767i	0.162169	−	0.499105i
$677$	−8.95622	−	17.5776i	−0.344215	−	0.675561i	0.652390	−	0.757883i	$-0.273766\pi$
$677$	−8.95622	−	17.5776i	−0.344215	−	0.675561i	−0.996606	+	0.0823224i	$0.973766\pi$
$678$		0			0
$679$	−5.61257	−	4.07777i	−0.215391	−	0.156490i
$680$	2.38696	+	2.80931i	0.0915358	+	0.107732i
$681$		0			0
$682$	9.00595	+	23.3493i	0.344856	+	0.894089i
$683$	4.29467	−	4.29467i	0.164331	−	0.164331i	−0.620151	−	0.784482i	$-0.712929\pi$
$683$	4.29467	−	4.29467i	0.164331	−	0.164331i	0.784482	+	0.620151i	$0.212929\pi$
$684$		0			0
$685$	−20.0669	−	32.9352i	−0.766717	−	1.25839i
$686$	33.1416	−	24.0788i	1.26535	−	0.919332i
$687$		0			0
$688$	−10.5875	+	5.39461i	−0.403645	+	0.205668i
$689$	5.74026	−	4.17054i	0.218687	−	0.158885i
$690$		0			0
$691$	7.82815	+	24.0926i	0.297797	+	0.916524i	0.982268	+	0.187484i	$0.0600333\pi$
$691$	7.82815	+	24.0926i	0.297797	+	0.916524i	−0.684471	+	0.729040i	$0.739967\pi$
$692$	15.3612	−	15.3612i	0.583944	−	0.583944i
$693$		0			0
$694$			24.7298i			0.938732i
$695$	7.61465	+	8.96198i	0.288840	+	0.339947i
$696$		0			0
$697$	12.3462	+	1.95544i	0.467645	+	0.0740678i
$698$	13.8858	+	27.2525i	0.525586	+	1.03152i
$699$		0			0
$700$	−19.3076	+	13.8772i	−0.729757	+	0.524510i
$701$	−2.80274	+	3.85764i	−0.105858	+	0.145701i	−0.858659	−	0.512547i	$-0.828702\pi$
$701$	−2.80274	+	3.85764i	−0.105858	+	0.145701i	0.752801	+	0.658248i	$0.228702\pi$
$702$		0			0
$703$	−1.50466	−	1.50466i	−0.0567494	−	0.0567494i
$704$	2.21530	−	2.46829i	0.0834922	−	0.0930272i
$705$		0			0
$706$	−1.80094	+	0.585161i	−0.0677793	+	0.0220228i
$707$	6.29748	+	39.7607i	0.236841	+	1.49535i
$708$		0			0
$709$	23.3542	+	7.58823i	0.877085	+	0.284982i	0.712746	−	0.701422i	$-0.247451\pi$
$709$	23.3542	+	7.58823i	0.877085	+	0.284982i	0.164338	+	0.986404i	$0.447451\pi$
$710$	16.0432	+	13.7734i	0.602091	+	0.516907i
$711$		0			0
$712$	−13.4540	+	2.13091i	−0.504211	+	0.0798592i
$713$	−41.3736	−	21.0809i	−1.54945	−	0.789486i
$714$		0			0
$715$	37.9585	−	4.96040i	1.41957	−	0.185508i
$716$	−2.47682			−0.0925633
$717$		0			0
$718$	−16.1481	+	2.55761i	−0.602641	+	0.0954490i
$719$	−18.9442	−	26.0744i	−0.706498	−	0.972411i	−0.999865	−	0.0164110i	$-0.994776\pi$
$719$	−18.9442	−	26.0744i	−0.706498	−	0.972411i	0.293368	−	0.956000i	$-0.405224\pi$
$720$		0			0
$721$	28.3881	+	9.22384i	1.05723	+	0.343514i
$722$	−2.28635	+	14.4354i	−0.0850890	+	0.537231i
$723$		0			0
$724$	−8.14531	+	2.64657i	−0.302718	+	0.0983591i
$725$	−24.3187	+	24.0709i	−0.903175	+	0.893970i
$726$		0			0
$727$	−7.06662	−	7.06662i	−0.262087	−	0.262087i	0.563815	−	0.825901i	$-0.309333\pi$
$727$	−7.06662	−	7.06662i	−0.262087	−	0.262087i	−0.825901	+	0.563815i	$0.809333\pi$
$728$	−11.1441	+	21.8714i	−0.413026	+	0.810609i
$729$		0			0
$730$	5.31748	−	8.62766i	0.196809	−	0.319324i
$731$	6.05365	−	18.6312i	0.223902	−	0.689100i
$732$		0			0
$733$	0.681210	+	0.107893i	0.0251610	+	0.00398512i	0.169002	−	0.985616i	$-0.445945\pi$
$733$	0.681210	+	0.107893i	0.0251610	+	0.00398512i	−0.143841	+	0.989601i	$0.545945\pi$
$734$	−13.7692	−	10.0039i	−0.508231	−	0.369252i
$735$		0			0
$736$			6.15389i			0.226835i
$737$	30.9436	+	8.23813i	1.13982	+	0.303455i
$738$		0			0
$739$	−9.33968	−	28.7446i	−0.343566	−	1.05739i	−0.962347	−	0.271823i	$-0.912373\pi$
$739$	−9.33968	−	28.7446i	−0.343566	−	1.05739i	0.618782	−	0.785563i	$-0.287627\pi$
$740$	1.94051	−	1.18232i	0.0713347	−	0.0434631i
$741$		0			0
$742$	−5.82429	+	2.96762i	−0.213816	+	0.108945i
$743$	10.2773	−	5.23656i	0.377039	−	0.192111i	−0.255193	−	0.966890i	$-0.582139\pi$
$743$	10.2773	−	5.23656i	0.377039	−	0.192111i	0.632232	+	0.774779i	$0.282139\pi$
$744$		0			0
$745$	4.37657	+	1.06258i	0.160345	+	0.0389300i
$746$	0.201975	+	0.621614i	0.00739481	+	0.0227589i
$747$		0			0
$748$	0.294926	+	5.45991i	0.0107836	+	0.199634i
$749$		−	29.7681i		−	1.08770i
$750$		0			0
$751$	−21.3255	−	15.4939i	−0.778178	−	0.565379i	0.126254	−	0.991998i	$-0.459705\pi$
$751$	−21.3255	−	15.4939i	−0.778178	−	0.565379i	−0.904432	+	0.426619i	$0.859705\pi$
$752$	7.28159	+	1.15329i	0.265532	+	0.0420562i
$753$		0			0
$754$	−10.9159	+	33.5957i	−0.397533	+	1.22348i
$755$	−37.0320	−	22.8239i	−1.34773	−	0.830646i
$756$		0			0
$757$	−20.2523	+	39.7474i	−0.736083	+	1.44464i	0.153633	+	0.988128i	$0.450903\pi$
$757$	−20.2523	+	39.7474i	−0.736083	+	1.44464i	−0.889715	+	0.456516i	$0.849097\pi$
$758$	2.71506	+	2.71506i	0.0986156	+	0.0986156i
$759$		0			0
$760$	4.32121	+	1.80288i	0.156747	+	0.0653974i
$761$	29.4770	−	9.57767i	1.06854	−	0.347190i	0.278622	−	0.960401i	$-0.410122\pi$
$761$	29.4770	−	9.57767i	1.06854	−	0.347190i	0.789920	+	0.613210i	$0.210122\pi$
$762$		0			0
$763$	−1.19345	+	7.53514i	−0.0432057	+	0.272790i
$764$	23.1335	+	7.51653i	0.836940	+	0.271938i
$765$		0			0
$766$	21.3314	+	29.3602i	0.770736	+	1.06083i
$767$	4.41801	−	0.699744i	0.159525	−	0.0252663i
$768$		0			0
$769$	32.4773			1.17116			0.585581	−	0.810614i	$-0.300866\pi$
$769$	32.4773			1.17116			0.585581	+	0.810614i	$0.300866\pi$
$770$	−35.2544	−	0.956913i	−1.27048	−	0.0344847i
$771$		0			0
$772$	11.7321	+	5.97781i	0.422248	+	0.215146i
$773$	46.5712	−	7.37615i	1.67505	−	0.265302i	0.754606	−	0.656178i	$-0.227828\pi$
$773$	46.5712	−	7.37615i	1.67505	−	0.265302i	0.920443	+	0.390876i	$0.127828\pi$
$774$		0			0
$775$	−16.9557	−	33.7031i	−0.609068	−	1.21065i
$776$	−1.38745	−	0.450810i	−0.0498066	−	0.0161832i
$777$		0			0
$778$	1.59020	+	10.0401i	0.0570115	+	0.359957i
$779$	15.0996	−	4.90615i	0.540999	−	0.175781i
$780$		0			0
$781$	6.56982	+	30.6666i	0.235087	+	1.09734i
$782$	−7.17391	−	7.17391i	−0.256539	−	0.256539i
$783$		0			0
$784$	9.17790	−	12.6323i	0.327782	−	0.451153i
$785$	−26.5039	+	6.29128i	−0.945965	+	0.224546i
$786$		0			0
$787$	−3.44617	−	6.76350i	−0.122843	−	0.241093i	0.821393	−	0.570363i	$-0.193197\pi$
$787$	−3.44617	−	6.76350i	−0.122843	−	0.241093i	−0.944236	+	0.329270i	$0.893197\pi$
$788$	24.2900	+	3.84716i	0.865296	+	0.137049i
$789$		0			0
$790$	22.3299	+	1.81495i	0.794464	+	0.0645732i
$791$			15.3743i			0.546647i
$792$		0			0
$793$	−8.62306	+	8.62306i	−0.306214	+	0.306214i
$794$	1.50047	+	4.61797i	0.0532497	+	0.163886i
$795$		0			0
$796$	−6.64430	+	4.82737i	−0.235501	+	0.171102i
$797$	11.0724	−	5.64165i	0.392203	−	0.199838i	−0.246757	−	0.969077i	$-0.579365\pi$
$797$	11.0724	−	5.64165i	0.392203	−	0.199838i	0.638960	+	0.769240i	$0.279365\pi$
$798$		0			0
$799$	−9.83299	+	7.14409i	−0.347866	+	0.252740i
$800$	−2.95961	+	4.02998i	−0.104638	+	0.142481i
$801$		0			0
$802$	−9.76634	+	9.76634i	−0.344862	+	0.344862i
$803$	14.0251	−	5.40956i	0.494935	−	0.190899i
$804$		0			0
$805$	49.8678	−	42.3707i	1.75761	−	1.49337i
$806$	−31.5105	−	22.8937i	−1.10991	−	0.806396i
$807$		0			0
$808$	3.84316	+	7.54263i	0.135202	+	0.265349i
$809$	−12.2225	+	37.6170i	−0.429721	+	1.32254i	0.468680	+	0.883368i	$0.344730\pi$
$809$	−12.2225	+	37.6170i	−0.429721	+	1.32254i	−0.898401	+	0.439177i	$0.855270\pi$
$810$		0			0
$811$	11.4987	−	15.8266i	0.403775	−	0.555749i	−0.557911	−	0.829900i	$-0.688397\pi$
$811$	11.4987	−	15.8266i	0.403775	−	0.555749i	0.961686	+	0.274152i	$0.0883971\pi$
$812$	14.7745	−	28.9965i	0.518482	−	1.01758i
$813$		0			0
$814$	3.35251	+	0.346926i	0.117505	+	0.0121597i
$815$	−13.1935	+	31.6225i	−0.462147	+	1.10769i
$816$		0			0
$817$	−3.89236	−	24.5754i	−0.136176	−	0.859783i
$818$	5.31127	−	33.5340i	0.185704	−	1.17249i
$819$		0			0
$820$	1.28692	+	16.9053i	0.0449412	+	0.590357i
$821$	7.06218	+	9.72026i	0.246472	+	0.339239i	0.914272	−	0.405102i	$-0.132764\pi$
$821$	7.06218	+	9.72026i	0.246472	+	0.339239i	−0.667800	+	0.744341i	$0.732764\pi$
$822$		0			0
$823$	−15.0651	−	7.67607i	−0.525137	−	0.267571i	0.171262	−	0.985226i	$-0.445216\pi$
$823$	−15.0651	−	7.67607i	−0.525137	−	0.267571i	−0.696399	+	0.717655i	$0.745216\pi$
$824$	6.27679			0.218662
$825$		0			0
$826$	−4.12092			−0.143385
$827$	12.4573	+	6.34731i	0.433183	+	0.220718i	0.656964	−	0.753922i	$-0.271840\pi$
$827$	12.4573	+	6.34731i	0.433183	+	0.220718i	−0.223781	+	0.974639i	$0.571840\pi$
$828$		0			0
$829$	−12.7391	−	17.5339i	−0.442448	−	0.608977i	0.528306	−	0.849054i	$-0.322827\pi$
$829$	−12.7391	−	17.5339i	−0.442448	−	0.608977i	−0.970754	+	0.240077i	$0.922827\pi$
$830$	−0.777783	−	10.2171i	−0.0269973	−	0.354641i
$831$		0			0
$832$	−0.807489	+	5.09829i	−0.0279946	+	0.176751i
$833$	4.02697	+	25.4253i	0.139526	+	0.880934i
$834$		0			0
$835$	−3.51438	+	8.42340i	−0.121620	+	0.291504i
$836$	3.48207	+	6.00884i	0.120430	+	0.207820i
$837$		0			0
$838$	7.09465	−	13.9240i	0.245081	−	0.480998i
$839$	−9.09171	+	12.5137i	−0.313881	+	0.432020i	−0.936587	−	0.350436i	$-0.886033\pi$
$839$	−9.09171	+	12.5137i	−0.313881	+	0.432020i	0.622706	+	0.782456i	$0.286033\pi$
$840$		0			0
$841$	5.51048	−	16.9595i	0.190017	−	0.584811i
$842$	−0.640791	−	1.25762i	−0.0220831	−	0.0433405i
$843$		0			0
$844$	−12.7357	−	9.25302i	−0.438380	−	0.318502i
$845$	−23.2508	+	19.7553i	−0.799851	+	0.679602i
$846$		0			0
$847$	−40.7580	−	32.7892i	−1.40046	−	1.12665i
$848$	−0.971974	+	0.971974i	−0.0333777	+	0.0333777i
$849$		0			0
$850$	−1.24779	−	8.14813i	−0.0427989	−	0.279479i
$851$	−5.05934	+	3.67583i	−0.173432	+	0.126006i
$852$		0			0
$853$	−3.89903	+	1.98665i	−0.133500	+	0.0680218i	−0.519465	−	0.854492i	$-0.673869\pi$
$853$	−3.89903	+	1.98665i	−0.133500	+	0.0680218i	0.385965	+	0.922514i	$0.373869\pi$
$854$	9.08913	−	6.60364i	0.311024	−	0.225972i
$855$		0			0
$856$	−1.93438	−	5.95341i	−0.0661157	−	0.203483i
$857$	−1.64475	+	1.64475i	−0.0561834	+	0.0561834i	−0.734640	−	0.678457i	$-0.762649\pi$
$857$	−1.64475	+	1.64475i	−0.0561834	+	0.0561834i	0.678457	+	0.734640i	$0.262649\pi$
$858$		0			0
$859$			8.87969i			0.302971i	0.988459	+	0.151486i	$0.0484057\pi$
$859$			8.87969i			0.302971i	−0.988459	+	0.151486i	$0.951594\pi$
$860$	26.4831	+	2.15252i	0.903065	+	0.0734002i
$861$		0			0
$862$	−12.9821	−	2.05616i	−0.442172	−	0.0700332i
$863$	−4.09217	−	8.03134i	−0.139299	−	0.273390i	0.810809	−	0.585311i	$-0.199028\pi$
$863$	−4.09217	−	8.03134i	−0.139299	−	0.273390i	−0.950108	+	0.311921i	$0.899028\pi$
$864$		0			0
$865$	−47.2630	+	11.2189i	−1.60699	+	0.381454i
$866$	−11.4148	+	15.7111i	−0.387891	+	0.533886i
$867$		0			0
$868$	25.3729	+	25.3729i	0.861213	+	0.861213i
$869$	24.7303	+	22.1955i	0.838916	+	0.752930i
$870$		0			0
$871$	−47.3975	+	15.4004i	−1.60600	+	0.521822i
$872$	0.250964	+	1.58452i	0.00849871	+	0.0536588i
$873$		0			0
$874$	−12.2553	−	3.98198i	−0.414541	−	0.134692i
$875$	53.0342	−	3.76416i	1.79288	−	0.127252i
$876$		0			0
$877$	5.34492	−	0.846552i	0.180485	−	0.0285860i	−0.0655376	−	0.997850i	$-0.520876\pi$
$877$	5.34492	−	0.846552i	0.180485	−	0.0285860i	0.246023	+	0.969264i	$0.420876\pi$
$878$	5.88775	+	2.99996i	0.198702	+	0.101244i
$879$		0			0
$880$	−7.11281	+	2.09951i	−0.239773	+	0.0707745i
$881$	38.3930			1.29349			0.646747	−	0.762704i	$-0.276129\pi$
$881$	38.3930			1.29349			0.646747	+	0.762704i	$0.276129\pi$
$882$		0			0
$883$	8.11968	−	1.28603i	0.273249	−	0.0432784i	−0.0183061	−	0.999832i	$-0.505827\pi$
$883$	8.11968	−	1.28603i	0.273249	−	0.0432784i	0.291555	+	0.956554i	$0.405827\pi$
$884$	−5.00201	−	6.88468i	−0.168236	−	0.231557i
$885$		0			0
$886$	14.1410	+	4.59469i	0.475076	+	0.154362i
$887$	−7.14889	+	45.1363i	−0.240036	+	1.51553i	0.513481	+	0.858101i	$0.328356\pi$
$887$	−7.14889	+	45.1363i	−0.240036	+	1.51553i	−0.753517	+	0.657428i	$0.771644\pi$
$888$		0			0
$889$	67.5750	−	21.9565i	2.26639	−	0.736396i
$890$	28.1106	+	11.7282i	0.942271	+	0.393131i
$891$		0			0
$892$	7.37447	+	7.37447i	0.246915	+	0.246915i
$893$	−7.00842	+	13.7548i	−0.234528	+	0.460287i
$894$		0			0
$895$	4.71479	+	2.90586i	0.157598	+	0.0971323i
$896$	1.46952	−	4.52271i	0.0490931	−	0.151093i
$897$		0			0
$898$	−16.8550	−	2.66958i	−0.562460	−	0.0890849i
$899$	41.7757	+	30.3518i	1.39330	+	1.01229i
$900$		0			0
$901$		−	2.26616i		−	0.0754969i
$902$	−13.6622	+	21.1121i	−0.454903	+	0.702955i
$903$		0			0
$904$	0.999045	+	3.07474i	0.0332277	+	0.102264i
$905$	18.6101	+	4.51833i	0.618622	+	0.150194i
$906$		0			0
$907$	−18.8390	+	9.59897i	−0.625540	+	0.318728i	−0.737870	−	0.674942i	$-0.764168\pi$
$907$	−18.8390	+	9.59897i	−0.625540	+	0.318728i	0.112331	+	0.993671i	$0.464168\pi$
$908$	3.77595	−	1.92394i	0.125309	−	0.0638484i
$909$		0			0
$910$	46.8734	−	28.5592i	1.55384	−	0.946729i
$911$	5.76951	+	17.7567i	0.191153	+	0.588307i	1.00000		0.000288399i	$9.18004e-5\pi$
$911$	5.76951	+	17.7567i	0.191153	+	0.588307i	−0.808847	+	0.588019i	$0.799908\pi$
$912$		0			0
$913$	8.25712	−	12.7596i	0.273271	−	0.422282i
$914$		−	14.5376i		−	0.480862i
$915$		0			0
$916$	−10.5781	−	7.68545i	−0.349511	−	0.253934i
$917$	65.0597	+	10.3044i	2.14846	+	0.340283i
$918$		0			0
$919$	3.04475	−	9.37076i	0.100437	−	0.309113i	−0.888196	−	0.459466i	$-0.848041\pi$
$919$	3.04475	−	9.37076i	0.100437	−	0.309113i	0.988632	+	0.150353i	$0.0480409\pi$
$920$	7.21987	−	11.7143i	0.238032	−	0.386209i
$921$		0			0
$922$	−0.483229	+	0.948390i	−0.0159143	+	0.0312336i
$923$	−34.5145	−	34.5145i	−1.13606	−	1.13606i
$924$		0			0
$925$	−5.08102	−	0.0260237i	−0.167063	−	0.000855655i
$926$	6.59003	−	2.14123i	0.216562	−	0.0703652i
$927$		0			0
$928$	1.07055	−	6.75916i	0.0351424	−	0.221880i
$929$	16.0572	+	5.21732i	0.526821	+	0.171175i	0.560339	−	0.828264i	$-0.310671\pi$
$929$	16.0572	+	5.21732i	0.526821	+	0.171175i	−0.0335176	+	0.999438i	$0.510671\pi$
$930$		0			0
$931$	19.2181	+	26.4514i	0.629848	+	0.866911i
$932$	15.9681	−	2.52910i	0.523053	−	0.0828434i
$933$		0			0
$934$	25.8784			0.846767
$935$	5.84427	−	10.7393i	0.191128	−	0.351212i
$936$		0			0
$937$	19.9944	+	10.1876i	0.653188	+	0.332816i	0.748987	−	0.662585i	$-0.230541\pi$
$937$	19.9944	+	10.1876i	0.653188	+	0.332816i	−0.0957989	+	0.995401i	$0.530541\pi$
$938$	45.3479	−	7.18240i	1.48066	−	0.234514i
$939$		0			0
$940$	−12.5079	−	10.7383i	−0.407963	−	0.350244i
$941$	11.4644	+	3.72500i	0.373728	+	0.121431i	0.489857	−	0.871803i	$-0.337049\pi$
$941$	11.4644	+	3.72500i	0.373728	+	0.121431i	−0.116130	+	0.993234i	$0.537049\pi$
$942$		0			0
$943$	−7.29917	−	46.0852i	−0.237694	−	1.50074i
$944$	−0.824155	+	0.267784i	−0.0268239	+	0.00871563i
$945$		0			0
$946$	29.3298	+	26.3236i	0.953595	+	0.855854i
$947$	7.00199	+	7.00199i	0.227534	+	0.227534i	0.811662	−	0.584128i	$-0.198563\pi$
$947$	7.00199	+	7.00199i	0.227534	+	0.227534i	−0.584128	+	0.811662i	$0.698563\pi$
$948$		0			0
$949$	−13.7515	+	18.9273i	−0.446391	+	0.614405i
$950$	−6.11051	−	8.50163i	−0.198251	−	0.275829i
$951$		0			0
$952$	3.55927	+	6.98546i	0.115357	+	0.226400i
$953$	7.86508	+	1.24571i	0.254775	+	0.0403524i	0.282515	−	0.959263i	$-0.408831\pi$
$953$	7.86508	+	1.24571i	0.254775	+	0.0403524i	−0.0277404	+	0.999615i	$0.508831\pi$
$954$		0			0
$955$	−35.2175	−	41.4489i	−1.13961	−	1.34125i
$956$			3.49589i			0.113065i
$957$		0			0
$958$	−24.3955	+	24.3955i	−0.788182	+	0.788182i
$959$	−25.3457	−	78.0061i	−0.818456	−	2.51895i
$960$		0			0
$961$	−20.9826	+	15.2447i	−0.676857	+	0.491765i
$962$	−4.67382	+	2.38143i	−0.150690	+	0.0767803i
$963$		0			0
$964$	6.63230	−	4.81865i	0.213612	−	0.155198i
$965$	−15.3195	−	25.1435i	−0.493153	−	0.809397i
$966$		0			0
$967$	13.9164	−	13.9164i	0.447521	−	0.447521i	−0.447008	−	0.894530i	$-0.647511\pi$
$967$	13.9164	−	13.9164i	0.447521	−	0.447521i	0.894530	+	0.447008i	$0.147511\pi$
$968$	−10.2820	−	3.90907i	−0.330475	−	0.125642i
$969$		0			0
$970$	2.11220	+	2.48593i	0.0678187	+	0.0798185i
$971$	−21.8763	−	15.8940i	−0.702043	−	0.510064i	0.178554	−	0.983930i	$-0.442858\pi$
$971$	−21.8763	−	15.8940i	−0.702043	−	0.510064i	−0.880597	+	0.473866i	$0.842858\pi$
$972$		0			0
$973$	11.3544	+	22.2843i	0.364006	+	0.714402i
$974$	−11.6973	+	36.0006i	−0.374806	+	1.15353i
$975$		0			0
$976$	1.38864	−	1.91130i	0.0444494	−	0.0611794i
$977$	22.5857	−	44.3269i	0.722580	−	1.41814i	−0.178255	−	0.983984i	$-0.557045\pi$
$977$	22.5857	−	44.3269i	0.722580	−	1.41814i	0.900836	−	0.434160i	$-0.142955\pi$
$978$		0			0
$979$	22.6518	+	39.0892i	0.723956	+	1.24930i
$980$	−32.2912	+	13.2787i	−1.03150	+	0.424171i
$981$		0			0
$982$	−2.10120	−	13.2664i	−0.0670519	−	0.423349i
$983$	−6.21533	+	39.2421i	−0.198238	+	1.25163i	0.665005	+	0.746839i	$0.268429\pi$
$983$	−6.21533	+	39.2421i	−0.198238	+	1.25163i	−0.863243	+	0.504788i	$0.831571\pi$
$984$		0			0
$985$	−41.7240	−	35.8209i	−1.32944	−	1.14135i
$986$	6.63152	+	9.12750i	0.211191	+	0.290679i
$987$		0			0
$988$	−9.63057	−	4.90702i	−0.306389	−	0.156113i
$989$	−73.1245			−2.32522
$990$		0			0
$991$	−30.6185			−0.972628			−0.486314	−	0.873784i	$-0.661659\pi$
$991$	−30.6185			−0.972628			−0.486314	+	0.873784i	$0.661659\pi$
$992$	6.72317	+	3.42562i	0.213461	+	0.108764i
$993$		0			0
$994$	26.4316	+	36.3800i	0.838360	+	1.15390i
$995$	18.3114	−	1.39397i	0.580511	−	0.0441917i
$996$		0			0
$997$	2.95332	−	18.6466i	0.0935327	−	0.590542i	−0.895753	−	0.444552i	$-0.853363\pi$
$997$	2.95332	−	18.6466i	0.0935327	−	0.590542i	0.989286	−	0.145991i	$-0.0466370\pi$
$998$	−3.66512	−	23.1406i	−0.116017	−	0.732504i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.bh.d.127.3	✓	96
3.2	odd	2	inner	990.2.bh.d.127.10	yes	96
5.3	odd	4	inner	990.2.bh.d.523.5	yes	96
11.2	odd	10	inner	990.2.bh.d.937.5	yes	96
15.8	even	4	inner	990.2.bh.d.523.8	yes	96
33.2	even	10	inner	990.2.bh.d.937.8	yes	96
55.13	even	20	inner	990.2.bh.d.343.3	yes	96
165.68	odd	20	inner	990.2.bh.d.343.10	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.bh.d.127.3	✓	96	1.1	even	1	trivial
990.2.bh.d.127.10	yes	96	3.2	odd	2	inner
990.2.bh.d.343.3	yes	96	55.13	even	20	inner
990.2.bh.d.343.10	yes	96	165.68	odd	20	inner
990.2.bh.d.523.5	yes	96	5.3	odd	4	inner
990.2.bh.d.523.8	yes	96	15.8	even	4	inner
990.2.bh.d.937.5	yes	96	11.2	odd	10	inner
990.2.bh.d.937.8	yes	96	33.2	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.bh (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.891007 - 0.453990i) q^{2} +(0.587785 + 0.809017i) q^{4} +(-0.169731 - 2.22962i) q^{5} +(0.743917 - 4.69691i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-0.860994 + 2.06366i) q^{10} +(-2.86962 + 1.66292i) q^{11} +(2.34342 - 4.59923i) q^{13} +(-2.79519 + 3.84725i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-0.748460 - 1.46893i) q^{17} +(-1.69404 - 1.23080i) q^{19} +(1.70403 - 1.44785i) q^{20} +(3.31180 - 0.178892i) q^{22} +(-4.35146 + 4.35146i) q^{23} +(-4.94238 + 0.756869i) q^{25} +(-4.17601 + 3.03405i) q^{26} +(4.23714 - 2.15893i) q^{28} +(5.53644 - 4.02246i) q^{29} +(2.33171 + 7.17628i) q^{31} +(0.707107 - 0.707107i) q^{32} +1.64862i q^{34} +(-10.5986 - 0.861441i) q^{35} +(1.00371 + 0.158971i) q^{37} +(0.950635 + 1.86573i) q^{38} +(-2.17561 + 0.516430i) q^{40} +(-4.45667 + 6.13408i) q^{41} +(8.40230 + 8.40230i) q^{43} +(-3.03205 - 1.34413i) q^{44} +(5.85270 - 1.90166i) q^{46} +(-1.15329 - 7.28159i) q^{47} +(-14.8502 - 4.82511i) q^{49} +(4.74731 + 1.56942i) q^{50} +(5.09829 - 0.807489i) q^{52} +(1.22476 + 0.624046i) q^{53} +(4.19473 + 6.11590i) q^{55} -4.75546 q^{56} +(-6.75916 + 1.07055i) q^{58} +(0.509356 + 0.701068i) q^{59} +(-2.24687 - 0.730053i) q^{61} +(1.18039 - 7.45269i) q^{62} +(-0.951057 + 0.309017i) q^{64} +(-10.6523 - 4.44431i) q^{65} +(-6.82700 - 6.82700i) q^{67} +(0.748460 - 1.46893i) q^{68} +(9.05231 + 5.57920i) q^{70} +(2.92210 - 8.99330i) q^{71} +(-4.47657 - 0.709019i) q^{73} +(-0.822137 - 0.597318i) q^{74} -2.09395i q^{76} +(5.67582 + 14.7154i) q^{77} +(-3.09610 - 9.52881i) q^{79} +(2.17294 + 0.527566i) q^{80} +(6.75573 - 3.44222i) q^{82} +(-4.08300 + 2.08039i) q^{83} +(-3.14812 + 1.91810i) q^{85} +(-3.67194 - 11.3011i) q^{86} +(2.09135 + 2.57415i) q^{88} -13.6217i q^{89} +(-19.8589 - 14.4283i) q^{91} +(-6.07812 - 0.962680i) q^{92} +(-2.27818 + 7.01153i) q^{94} +(-2.45667 + 3.98597i) q^{95} +(0.662306 - 1.29985i) q^{97} +(11.0410 + 11.0410i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 40 q^{7} + 24 q^{16} + 4 q^{22} + 8 q^{25} + 20 q^{28} - 16 q^{31} + 64 q^{37} - 40 q^{46} - 40 q^{52} - 36 q^{55} - 12 q^{58} - 80 q^{61} - 48 q^{67} - 52 q^{70} + 20 q^{73} + 48 q^{82} - 160 q^{85}+ \cdots + 48 q^{97}+O(q^{100}) \) 96 * q - 40 * q^7 + 24 * q^16 + 4 * q^22 + 8 * q^25 + 20 * q^28 - 16 * q^31 + 64 * q^37 - 40 * q^46 - 40 * q^52 - 36 * q^55 - 12 * q^58 - 80 * q^61 - 48 * q^67 - 52 * q^70 + 20 * q^73 + 48 * q^82 - 160 * q^85 + 4 * q^88 + 8 * q^91 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more