LMFDB - Embedded newform 504.2.cj.e.37.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(37,504)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("504.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.6
Character	$\chi$	$=$	504.37
Dual form			504.2.cj.e.109.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.867144 - 1.11717i) q^{2} +(-0.496121 + 1.93749i) q^{4} +(-2.93503 - 1.69454i) q^{5} +(-1.85242 - 1.88906i) q^{7} +(2.59471 - 1.12583i) q^{8} +O(q^{10})$	\(q+(-0.867144 - 1.11717i) q^{2} +(-0.496121 + 1.93749i) q^{4} +(-2.93503 - 1.69454i) q^{5} +(-1.85242 - 1.88906i) q^{7} +(2.59471 - 1.12583i) q^{8} +(0.652012 + 4.74833i) q^{10} +(0.0932820 - 0.0538564i) q^{11} +1.50033i q^{13} +(-0.504078 + 3.70755i) q^{14} +(-3.50773 - 1.92246i) q^{16} +(0.214800 + 0.372045i) q^{17} +(4.32799 + 2.49877i) q^{19} +(4.73929 - 4.84589i) q^{20} +(-0.141056 - 0.0575103i) q^{22} +(-4.56401 + 7.90510i) q^{23} +(3.24294 + 5.61694i) q^{25} +(1.67612 - 1.30100i) q^{26} +(4.57905 - 2.65184i) q^{28} +7.95437i q^{29} +(-0.393116 - 0.680897i) q^{31} +(0.894002 + 5.58576i) q^{32} +(0.229373 - 0.562584i) q^{34} +(2.23582 + 8.68345i) q^{35} +(-7.68900 - 4.43925i) q^{37} +(-0.961455 - 7.00187i) q^{38} +(-9.52331 - 1.09248i) q^{40} -8.59425 q^{41} +6.65201i q^{43} +(0.0580670 + 0.207452i) q^{44} +(12.7890 - 1.75610i) q^{46} +(2.87493 - 4.97953i) q^{47} +(-0.137086 + 6.99866i) q^{49} +(3.46295 - 8.49360i) q^{50} +(-2.90687 - 0.744345i) q^{52} +(0.286078 - 0.165167i) q^{53} -0.365048 q^{55} +(-6.93325 - 2.81604i) q^{56} +(8.88635 - 6.89759i) q^{58} +(8.63850 - 4.98744i) q^{59} +(1.76996 + 1.02189i) q^{61} +(-0.419787 + 1.02961i) q^{62} +(5.46500 - 5.84241i) q^{64} +(2.54237 - 4.40351i) q^{65} +(-2.79312 + 1.61261i) q^{67} +(-0.827399 + 0.231594i) q^{68} +(7.76208 - 10.0276i) q^{70} +8.72656 q^{71} +(-4.38649 - 7.59762i) q^{73} +(1.70810 + 12.4394i) q^{74} +(-6.98854 + 7.14574i) q^{76} +(-0.274535 - 0.0764506i) q^{77} +(-0.785733 + 1.36093i) q^{79} +(7.03761 + 11.5865i) q^{80} +(7.45246 + 9.60121i) q^{82} +1.33259i q^{83} -1.45595i q^{85} +(7.43140 - 5.76826i) q^{86} +(0.181406 - 0.244762i) q^{88} +(-3.62404 + 6.27701i) q^{89} +(2.83421 - 2.77924i) q^{91} +(-13.0517 - 12.7646i) q^{92} +(-8.05594 + 1.10619i) q^{94} +(-8.46852 - 14.6679i) q^{95} -19.0450 q^{97} +(7.93754 - 5.91570i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8}+O(q^{10}) $ 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8	$ 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 6 q^{10} - 22 q^{14} - 10 q^{16} + 40 q^{20} - 12 q^{22} + 8 q^{23} + 16 q^{25} - 6 q^{26} - 26 q^{28} - 24 q^{31} + 8 q^{32} - 24 q^{34} + 26 q^{38} - 6 q^{40} - 20 q^{44} + 16 q^{46} + 24 q^{47} + 8 q^{49} - 52 q^{50} + 44 q^{52} - 64 q^{55} - 40 q^{56} + 34 q^{58} - 100 q^{62} - 20 q^{64} - 16 q^{68} + 38 q^{70} + 80 q^{71} + 8 q^{73} - 10 q^{74} - 32 q^{76} + 8 q^{79} + 56 q^{80} + 22 q^{86} + 50 q^{88} - 64 q^{92} - 48 q^{94} - 24 q^{95} - 48 q^{97} + 64 q^{98}+O(q^{100}) $ 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 6 * q^10 - 22 * q^14 - 10 * q^16 + 40 * q^20 - 12 * q^22 + 8 * q^23 + 16 * q^25 - 6 * q^26 - 26 * q^28 - 24 * q^31 + 8 * q^32 - 24 * q^34 + 26 * q^38 - 6 * q^40 - 20 * q^44 + 16 * q^46 + 24 * q^47 + 8 * q^49 - 52 * q^50 + 44 * q^52 - 64 * q^55 - 40 * q^56 + 34 * q^58 - 100 * q^62 - 20 * q^64 - 16 * q^68 + 38 * q^70 + 80 * q^71 + 8 * q^73 - 10 * q^74 - 32 * q^76 + 8 * q^79 + 56 * q^80 + 22 * q^86 + 50 * q^88 - 64 * q^92 - 48 * q^94 - 24 * q^95 - 48 * q^97 + 64 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$1$

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 $

$2$	−0.867144	−	1.11717i	−0.613164	−	0.789956i
$2$	−0.867144	−	1.11717i	−0.613164	−	0.789956i
$3$		0			0
$3$		0			0
$4$	−0.496121	+	1.93749i	−0.248060	+	0.968745i
$5$	−2.93503	−	1.69454i	−1.31259	−	0.757822i	−0.330062	−	0.943959i	$-0.607070\pi$
$5$	−2.93503	−	1.69454i	−1.31259	−	0.757822i	−0.982524	+	0.186137i	$0.940403\pi$
$6$		0			0
$7$	−1.85242	−	1.88906i	−0.700149	−	0.713997i
$7$	−1.85242	−	1.88906i	−0.700149	−	0.713997i
$8$	2.59471	−	1.12583i	0.917367	−	0.398042i
$9$		0			0
$10$	0.652012	+	4.74833i	0.206184	+	1.50155i
$11$	0.0932820	−	0.0538564i	0.0281256	−	0.0162383i	−0.485871	−	0.874030i	$-0.661498\pi$
$11$	0.0932820	−	0.0538564i	0.0281256	−	0.0162383i	0.513997	+	0.857792i	$0.328164\pi$
$12$		0			0
$13$			1.50033i			0.416116i	0.978116	+	0.208058i	$0.0667143\pi$
$13$			1.50033i			0.416116i	−0.978116	+	0.208058i	$0.933286\pi$
$14$	−0.504078	+	3.70755i	−0.134720	+	0.990884i
$15$		0			0
$16$	−3.50773	−	1.92246i	−0.876932	−	0.480614i
$17$	0.214800	+	0.372045i	0.0520967	+	0.0902341i	0.890898	−	0.454204i	$-0.150076\pi$
$17$	0.214800	+	0.372045i	0.0520967	+	0.0902341i	−0.838801	+	0.544438i	$0.816743\pi$
$18$		0			0
$19$	4.32799	+	2.49877i	0.992909	+	0.573256i	0.906143	−	0.422973i	$-0.139013\pi$
$19$	4.32799	+	2.49877i	0.992909	+	0.573256i	0.0867663	+	0.996229i	$0.472347\pi$
$20$	4.73929	−	4.84589i	1.05974	−	1.08357i
$21$		0			0
$22$	−0.141056	−	0.0575103i	−0.0300732	−	0.0122612i
$23$	−4.56401	+	7.90510i	−0.951663	+	1.64833i	−0.209836	+	0.977737i	$0.567293\pi$
$23$	−4.56401	+	7.90510i	−0.951663	+	1.64833i	−0.741827	+	0.670591i	$0.766040\pi$
$24$		0			0
$25$	3.24294	+	5.61694i	0.648588	+	1.12339i
$26$	1.67612	−	1.30100i	0.328714	−	0.255147i
$27$		0			0
$28$	4.57905	−	2.65184i	0.865360	−	0.501151i
$29$			7.95437i			1.47709i	0.674204	+	0.738545i	$0.264487\pi$
$29$			7.95437i			1.47709i	−0.674204	+	0.738545i	$0.735513\pi$
$30$		0			0
$31$	−0.393116	−	0.680897i	−0.0706058	−	0.122293i	0.828561	−	0.559899i	$-0.189160\pi$
$31$	−0.393116	−	0.680897i	−0.0706058	−	0.122293i	−0.899167	+	0.437606i	$0.855827\pi$
$32$	0.894002	+	5.58576i	0.158039	+	0.987433i
$33$		0			0
$34$	0.229373	−	0.562584i	0.0393371	−	0.0964823i
$35$	2.23582	+	8.68345i	0.377923	+	1.46777i
$36$		0			0
$37$	−7.68900	−	4.43925i	−1.26406	−	0.729808i	−0.290206	−	0.956964i	$-0.593724\pi$
$37$	−7.68900	−	4.43925i	−1.26406	−	0.729808i	−0.973858	+	0.227156i	$0.927057\pi$
$38$	−0.961455	−	7.00187i	−0.155969	−	1.13585i
$39$		0			0
$40$	−9.52331	−	1.09248i	−1.50577	−	0.172736i
$41$	−8.59425			−1.34220			−0.671098	−	0.741369i	$-0.734177\pi$
$41$	−8.59425			−1.34220			−0.671098	+	0.741369i	$0.734177\pi$
$42$		0			0
$43$			6.65201i			1.01442i	0.861822	+	0.507211i	$0.169324\pi$
$43$			6.65201i			1.01442i	−0.861822	+	0.507211i	$0.830676\pi$
$44$	0.0580670	+	0.207452i	0.00875394	+	0.0312746i
$45$		0			0
$46$	12.7890	−	1.75610i	1.88563	−	0.258924i
$47$	2.87493	−	4.97953i	0.419352	−	0.726339i	−0.576523	−	0.817081i	$-0.695591\pi$
$47$	2.87493	−	4.97953i	0.419352	−	0.726339i	0.995874	+	0.0907426i	$0.0289241\pi$
$48$		0			0
$49$	−0.137086	+	6.99866i	−0.0195838	+	0.999808i
$50$	3.46295	−	8.49360i	0.489736	−	1.20118i
$51$		0			0
$52$	−2.90687	−	0.744345i	−0.403111	−	0.103222i
$53$	0.286078	−	0.165167i	0.0392959	−	0.0226875i	−0.480223	−	0.877146i	$-0.659444\pi$
$53$	0.286078	−	0.165167i	0.0392959	−	0.0226875i	0.519519	+	0.854459i	$0.326111\pi$
$54$		0			0
$55$	−0.365048			−0.0492230
$56$	−6.93325	−	2.81604i	−0.926494	−	0.376309i
$57$		0			0
$58$	8.88635	−	6.89759i	1.16684	−	0.905698i
$59$	8.63850	−	4.98744i	1.12464	−	0.649310i	0.182057	−	0.983288i	$-0.441725\pi$
$59$	8.63850	−	4.98744i	1.12464	−	0.649310i	0.942581	+	0.333978i	$0.108391\pi$
$60$		0			0
$61$	1.76996	+	1.02189i	0.226620	+	0.130839i	0.609012	−	0.793161i	$-0.291566\pi$
$61$	1.76996	+	1.02189i	0.226620	+	0.130839i	−0.382392	+	0.924000i	$0.624900\pi$
$62$	−0.419787	+	1.02961i	−0.0533130	+	0.130761i
$63$		0			0
$64$	5.46500	−	5.84241i	0.683125	−	0.730302i
$65$	2.54237	−	4.40351i	0.315342	−	0.546189i
$66$		0			0
$67$	−2.79312	+	1.61261i	−0.341234	+	0.197012i	−0.660818	−	0.750546i	$-0.729790\pi$
$67$	−2.79312	+	1.61261i	−0.341234	+	0.197012i	0.319583	+	0.947558i	$0.396457\pi$
$68$	−0.827399	+	0.231594i	−0.100337	+	0.0280849i
$69$		0			0
$70$	7.76208	−	10.0276i	0.927745	−	1.19853i
$71$	8.72656			1.03565			0.517826	−	0.855486i	$-0.326742\pi$
$71$	8.72656			1.03565			0.517826	+	0.855486i	$0.326742\pi$
$72$		0			0
$73$	−4.38649	−	7.59762i	−0.513399	−	0.889234i	−0.999879	−	0.0155420i	$-0.995053\pi$
$73$	−4.38649	−	7.59762i	−0.513399	−	0.889234i	0.486480	−	0.873692i	$-0.338281\pi$
$74$	1.70810	+	12.4394i	0.198562	+	1.44605i
$75$		0			0
$76$	−6.98854	+	7.14574i	−0.801640	+	0.819673i
$77$	−0.274535	−	0.0764506i	−0.0312862	−	0.00871236i
$78$		0			0
$79$	−0.785733	+	1.36093i	−0.0884018	+	0.153116i	−0.906836	−	0.421484i	$-0.861509\pi$
$79$	−0.785733	+	1.36093i	−0.0884018	+	0.153116i	0.818434	+	0.574601i	$0.194843\pi$
$80$	7.03761	+	11.5865i	0.786828	+	1.29541i
$81$		0			0
$82$	7.45246	+	9.60121i	0.822986	+	1.06028i
$83$			1.33259i			0.146271i	0.997322	+	0.0731355i	$0.0233006\pi$
$83$			1.33259i			0.146271i	−0.997322	+	0.0731355i	$0.976699\pi$
$84$		0			0
$85$		−	1.45595i		−	0.157920i
$86$	7.43140	−	5.76826i	0.801349	−	0.622007i
$87$		0			0
$88$	0.181406	−	0.244762i	0.0193380	−	0.0260917i
$89$	−3.62404	+	6.27701i	−0.384147	+	0.665362i	−0.991650	−	0.128955i	$-0.958838\pi$
$89$	−3.62404	+	6.27701i	−0.384147	+	0.665362i	0.607503	+	0.794317i	$0.292171\pi$
$90$		0			0
$91$	2.83421	−	2.77924i	0.297106	−	0.291343i
$92$	−13.0517	−	12.7646i	−1.36074	−	1.33080i
$93$		0			0
$94$	−8.05594	+	1.10619i	−0.830907	+	0.114095i
$95$	−8.46852	−	14.6679i	−0.868852	−	1.50490i
$96$		0			0
$97$	−19.0450			−1.93373			−0.966864	−	0.255293i	$-0.917828\pi$
$97$	−19.0450			−1.93373			−0.966864	+	0.255293i	$0.917828\pi$
$98$	7.93754	−	5.91570i	0.801812	−	0.597576i
$99$		0			0
$100$	−12.4916	+	3.49648i	−1.24916	+	0.349648i
$101$	2.88397	−	1.66506i	0.286966	−	0.165680i	−0.349607	−	0.936897i	$-0.613685\pi$
$101$	2.88397	−	1.66506i	0.286966	−	0.165680i	0.636573	+	0.771217i	$0.280351\pi$
$102$		0			0
$103$	6.53174	−	11.3133i	0.643591	−	1.11473i	−0.341034	−	0.940051i	$-0.610777\pi$
$103$	6.53174	−	11.3133i	0.643591	−	1.11473i	0.984625	−	0.174682i	$-0.0558896\pi$
$104$	1.68912	+	3.89291i	0.165632	+	0.381732i
$105$		0			0
$106$	−0.432591	−	0.176373i	−0.0420169	−	0.0171309i
$107$	4.00887	+	2.31452i	0.387552	+	0.223753i	0.681099	−	0.732191i	$-0.261502\pi$
$107$	4.00887	+	2.31452i	0.387552	+	0.223753i	−0.293547	+	0.955945i	$0.594836\pi$
$108$		0			0
$109$	−10.3011	+	5.94737i	−0.986670	+	0.569654i	−0.904277	−	0.426946i	$-0.859590\pi$
$109$	−10.3011	+	5.94737i	−0.986670	+	0.569654i	−0.0823930	+	0.996600i	$0.526256\pi$
$110$	0.316549	+	0.407819i	0.0301818	+	0.0388840i
$111$		0			0
$112$	2.86615	+	10.1875i	0.270825	+	0.962628i
$113$	−11.2752			−1.06068			−0.530339	−	0.847786i	$-0.677935\pi$
$113$	−11.2752			−1.06068			−0.530339	+	0.847786i	$0.677935\pi$
$114$		0			0
$115$	26.7910	−	15.4678i	2.49828	−	1.44238i
$116$	−15.4115	−	3.94633i	−1.43092	−	0.366408i
$117$		0			0
$118$	−13.0626	−	5.32581i	−1.20251	−	0.490281i
$119$	0.304914	−	1.09495i	0.0279515	−	0.100374i
$120$		0			0
$121$	−5.49420	+	9.51623i	−0.499473	+	0.865112i
$122$	−0.393193	−	2.86346i	−0.0355981	−	0.259246i
$123$		0			0
$124$	1.51426	−	0.423851i	0.135985	−	0.0380630i
$125$		−	5.03577i		−	0.450413i
$126$		0			0
$127$	−8.12185			−0.720698			−0.360349	−	0.932818i	$-0.617342\pi$
$127$	−8.12185			−0.720698			−0.360349	+	0.932818i	$0.617342\pi$
$128$	−11.2659	−	1.03910i	−0.995773	−	0.0918439i
$129$		0			0
$130$	−7.12406	+	0.978233i	−0.624821	+	0.0857967i
$131$	−9.73136	−	5.61840i	−0.850233	−	0.490882i	0.0104965	−	0.999945i	$-0.496659\pi$
$131$	−9.73136	−	5.61840i	−0.850233	−	0.490882i	−0.860729	+	0.509063i	$0.829992\pi$
$132$		0			0
$133$	−3.29693	−	12.8046i	−0.285880	−	1.11030i
$134$	4.22359	+	1.72202i	0.364863	+	0.148760i
$135$		0			0
$136$	0.976203	+	0.723517i	0.0837087	+	0.0620411i
$137$	3.21986	+	5.57695i	0.275091	+	0.476471i	0.970158	−	0.242473i	$-0.0779587\pi$
$137$	3.21986	+	5.57695i	0.275091	+	0.476471i	−0.695067	+	0.718945i	$0.744625\pi$
$138$		0			0
$139$			11.2139i			0.951154i	0.879674	+	0.475577i	$0.157761\pi$
$139$			11.2139i			0.951154i	−0.879674	+	0.475577i	$0.842239\pi$
$140$	−17.9333	+	0.0238376i	−1.51564	+	0.00201464i
$141$		0			0
$142$	−7.56719	−	9.74901i	−0.635024	−	0.818119i
$143$	0.0808023	+	0.139954i	0.00675703	+	0.0117035i
$144$		0			0
$145$	13.4790	−	23.3463i	1.11937	−	1.93881i
$146$	−4.68408	+	11.4887i	−0.387658	+	0.950809i
$147$		0			0
$148$	12.4157	−	12.6950i	1.02056	−	1.04352i
$149$	−12.9641	−	7.48481i	−1.06206	−	0.613180i	−0.136057	−	0.990701i	$-0.543443\pi$
$149$	−12.9641	−	7.48481i	−1.06206	−	0.613180i	−0.926001	+	0.377521i	$0.876776\pi$
$150$		0			0
$151$	6.69597	+	11.5978i	0.544910	+	0.943813i	0.998613	+	0.0526591i	$0.0167697\pi$
$151$	6.69597	+	11.5978i	0.544910	+	0.943813i	−0.453702	+	0.891153i	$0.649897\pi$
$152$	14.0431	+	1.61097i	1.13904	+	0.130667i
$153$		0			0
$154$	0.152654	+	0.372995i	0.0123012	+	0.0300568i
$155$			2.66461i			0.214026i
$156$		0			0
$157$	−16.2361	+	9.37390i	−1.29578	+	0.748118i	−0.979672	−	0.200605i	$-0.935709\pi$
$157$	−16.2361	+	9.37390i	−1.29578	+	0.748118i	−0.316107	+	0.948724i	$0.602376\pi$
$158$	2.20173	−	0.302328i	0.175160	−	0.0240519i
$159$		0			0
$160$	6.84138	−	17.9093i	0.540859	−	1.41586i
$161$	23.3877	−	6.02188i	1.84321	−	0.474590i
$162$		0			0
$163$	−2.21699	−	1.27998i	−0.173648	−	0.100256i	0.410657	−	0.911790i	$-0.365299\pi$
$163$	−2.21699	−	1.27998i	−0.173648	−	0.100256i	−0.584305	+	0.811534i	$0.698633\pi$
$164$	4.26379	−	16.6513i	0.332946	−	1.30025i
$165$		0			0
$166$	1.48873	−	1.15555i	0.115548	−	0.0896881i
$167$	−5.88750			−0.455589			−0.227794	−	0.973709i	$-0.573151\pi$
$167$	−5.88750			−0.455589			−0.227794	+	0.973709i	$0.573151\pi$
$168$		0			0
$169$	10.7490			0.826847
$170$	−1.62654	+	1.26252i	−0.124750	+	0.0968308i
$171$		0			0
$172$	−12.8882	−	3.30020i	−0.982716	−	0.251638i
$173$	−6.54988	−	3.78157i	−0.497978	−	0.287508i	0.229900	−	0.973214i	$-0.426160\pi$
$173$	−6.54988	−	3.78157i	−0.497978	−	0.287508i	−0.727878	+	0.685707i	$0.759493\pi$
$174$		0			0
$175$	4.60344	−	16.5310i	0.347987	−	1.24963i
$176$	−0.430745	+	0.00958285i	−0.0324686	+	0.000722335i
$177$		0			0
$178$	10.1550	−	1.39443i	0.761152	−	0.104517i
$179$	−9.76120	+	5.63563i	−0.729586	+	0.421227i	−0.818271	−	0.574833i	$-0.805067\pi$
$179$	−9.76120	+	5.63563i	−0.729586	+	0.421227i	0.0886845	+	0.996060i	$0.471734\pi$
$180$		0			0
$181$		−	13.7298i		−	1.02053i	−0.860018	−	0.510264i	$-0.829548\pi$
$181$		−	13.7298i		−	1.02053i	0.860018	−	0.510264i	$-0.170452\pi$
$182$	−5.56254	−	0.756283i	−0.412323	−	0.0560594i
$183$		0			0
$184$	−2.94244	+	25.6497i	−0.216920	+	1.89092i
$185$	15.0450	+	26.0587i	1.10613	+	1.91587i
$186$		0			0
$187$	0.0400740	+	0.0231367i	0.00293050	+	0.00169192i
$188$	8.22146	+	8.04059i	0.599612	+	0.586421i
$189$		0			0
$190$	−9.04306	+	22.1799i	−0.656053	+	1.60910i
$191$	−9.69930	+	16.7997i	−0.701816	+	1.21558i	0.266012	+	0.963970i	$0.414294\pi$
$191$	−9.69930	+	16.7997i	−0.701816	+	1.21558i	−0.967828	+	0.251612i	$0.919039\pi$
$192$		0			0
$193$	−1.27891	−	2.21513i	−0.0920577	−	0.159449i	0.816319	−	0.577601i	$-0.196011\pi$
$193$	−1.27891	−	2.21513i	−0.0920577	−	0.159449i	−0.908377	+	0.418153i	$0.862678\pi$
$194$	16.5148	+	21.2764i	1.18569	+	1.52756i
$195$		0			0
$196$	−13.4918	−	3.73778i	−0.963701	−	0.266985i
$197$			3.83452i			0.273199i	0.990626	+	0.136599i	$0.0436173\pi$
$197$			3.83452i			0.273199i	−0.990626	+	0.136599i	$0.956383\pi$
$198$		0			0
$199$	8.53263	+	14.7789i	0.604862	+	1.04765i	0.992073	+	0.125661i	$0.0401051\pi$
$199$	8.53263	+	14.7789i	0.604862	+	1.04765i	−0.387211	+	0.921991i	$0.626562\pi$
$200$	14.7382	+	10.9233i	1.04215	+	0.772393i
$201$		0			0
$202$	−4.36097	−	1.77803i	−0.306837	−	0.125102i
$203$	15.0263	−	14.7348i	1.05464	−	1.03418i
$204$		0			0
$205$	25.2244	+	14.5633i	1.76175	+	1.01715i
$206$	−18.3028	+	2.51323i	−1.27522	+	0.175105i
$207$		0			0
$208$	2.88432	−	5.26275i	0.199992	−	0.364906i
$209$	0.538298			0.0372349
$210$		0			0
$211$		−	12.8602i		−	0.885331i	−0.896687	−	0.442666i	$-0.854033\pi$
$211$		−	12.8602i		−	0.885331i	0.896687	−	0.442666i	$-0.145967\pi$
$212$	0.178081	+	0.636217i	0.0122306	+	0.0436956i
$213$		0			0
$214$	−0.890563	−	6.48560i	−0.0608776	−	0.443346i
$215$	11.2721	−	19.5239i	0.768751	−	1.33152i
$216$		0			0
$217$	−0.558039	+	2.00393i	−0.0378822	+	0.136035i
$218$	15.5768	+	6.35086i	1.05499	+	0.430135i
$219$		0			0
$220$	0.181108	−	0.707276i	0.0122103	−	0.0476845i
$221$	−0.558189	+	0.322271i	−0.0375479	+	0.0216783i
$222$		0			0
$223$	12.1122			0.811092			0.405546	−	0.914075i	$-0.367081\pi$
$223$	12.1122			0.811092			0.405546	+	0.914075i	$0.367081\pi$
$224$	8.89577	−	12.0360i	0.594374	−	0.804189i
$225$		0			0
$226$	9.77720	+	12.5962i	0.650369	+	0.837889i
$227$	−6.00730	+	3.46832i	−0.398719	+	0.230200i	−0.685931	−	0.727667i	$-0.740605\pi$
$227$	−6.00730	+	3.46832i	−0.398719	+	0.230200i	0.287212	+	0.957867i	$0.407271\pi$
$228$		0			0
$229$	−7.60363	−	4.38996i	−0.502462	−	0.290096i	0.227268	−	0.973832i	$-0.427021\pi$
$229$	−7.60363	−	4.38996i	−0.502462	−	0.290096i	−0.729730	+	0.683736i	$0.760354\pi$
$230$	−40.5118	−	16.5172i	−2.67127	−	1.08911i
$231$		0			0
$232$	8.95530	+	20.6393i	0.587944	+	1.35503i
$233$	8.20486	−	14.2112i	0.537518	−	0.931008i	−0.461519	−	0.887130i	$-0.652695\pi$
$233$	8.20486	−	14.2112i	0.537518	−	0.931008i	0.999037	−	0.0438780i	$-0.0139713\pi$
$234$		0			0
$235$	−16.8760	+	9.74338i	−1.10087	+	0.635588i
$236$	5.37737	+	19.2114i	0.350037	+	1.25055i
$237$		0			0
$238$	−1.48765	+	0.608842i	−0.0964300	+	0.0394654i
$239$	0.816406			0.0528089			0.0264045	−	0.999651i	$-0.491594\pi$
$239$	0.816406			0.0528089			0.0264045	+	0.999651i	$0.491594\pi$
$240$		0			0
$241$	12.0303	+	20.8371i	0.774939	+	1.34223i	0.934829	+	0.355099i	$0.115553\pi$
$241$	12.0303	+	20.8371i	0.774939	+	1.34223i	−0.159890	+	0.987135i	$0.551114\pi$
$242$	15.3955	−	2.11401i	0.989659	−	0.135894i
$243$		0			0
$244$	−2.85801	+	2.92230i	−0.182965	+	0.187081i
$245$	12.2619	−	20.3090i	0.783382	−	1.29749i
$246$		0			0
$247$	−3.74897	+	6.49341i	−0.238541	+	0.413166i
$248$	−1.78660	−	1.32415i	−0.113449	−	0.0840833i
$249$		0			0
$250$	−5.62579	+	4.36674i	−0.355806	+	0.276177i
$251$		−	3.97637i		−	0.250986i	−0.992094	−	0.125493i	$-0.959949\pi$
$251$		−	3.97637i		−	0.250986i	0.992094	−	0.125493i	$-0.0400513\pi$
$252$		0			0
$253$			0.983206i			0.0618136i
$254$	7.04282	+	9.07346i	0.441906	+	0.569319i
$255$		0			0
$256$	8.60831	+	13.4869i	0.538019	+	0.842932i
$257$	10.6451	−	18.4379i	0.664026	−	1.15013i	−0.315523	−	0.948918i	$-0.602180\pi$
$257$	10.6451	−	18.4379i	0.664026	−	1.15013i	0.979548	−	0.201208i	$-0.0644869\pi$
$258$		0			0
$259$	5.85726	+	22.7483i	0.363952	+	1.41351i
$260$	7.27044	+	7.11049i	0.450893	+	0.440974i
$261$		0			0
$262$	2.16180	+	15.7435i	0.133557	+	0.972638i
$263$	3.77491	+	6.53833i	0.232771	+	0.403171i	0.958623	−	0.284680i	$-0.0918874\pi$
$263$	3.77491	+	6.53833i	0.232771	+	0.403171i	−0.725852	+	0.687851i	$0.758554\pi$
$264$		0			0
$265$	−1.11953			−0.0687723
$266$	−11.4459	+	14.7867i	−0.701795	+	0.906628i
$267$		0			0
$268$	−1.73869	−	6.21169i	−0.106207	−	0.379440i
$269$	5.16933	−	2.98451i	0.315179	−	0.181969i	−0.334062	−	0.942551i	$-0.608420\pi$
$269$	5.16933	−	2.98451i	0.315179	−	0.181969i	0.649242	+	0.760582i	$0.275086\pi$
$270$		0			0
$271$	−2.38737	+	4.13504i	−0.145022	+	0.251186i	−0.929381	−	0.369121i	$-0.879659\pi$
$271$	−2.38737	+	4.13504i	−0.145022	+	0.251186i	0.784359	+	0.620307i	$0.212992\pi$
$272$	−0.0382201	−	1.71798i	−0.00231743	−	0.104168i
$273$		0			0
$274$	3.43831	−	8.43314i	0.207716	−	0.509465i
$275$	0.605016	+	0.349306i	0.0364838	+	0.0210640i
$276$		0			0
$277$	7.59525	−	4.38512i	0.456354	−	0.263476i	−0.254156	−	0.967163i	$-0.581798\pi$
$277$	7.59525	−	4.38512i	0.456354	−	0.263476i	0.710510	+	0.703687i	$0.248464\pi$
$278$	12.5278	−	9.72410i	0.751369	−	0.583213i
$279$		0			0
$280$	15.5774	+	20.0138i	0.930928	+	1.19606i
$281$	−13.7147			−0.818151			−0.409076	−	0.912500i	$-0.634149\pi$
$281$	−13.7147			−0.818151			−0.409076	+	0.912500i	$0.634149\pi$
$282$		0			0
$283$	−7.19449	+	4.15374i	−0.427668	+	0.246914i	−0.698353	−	0.715754i	$-0.746083\pi$
$283$	−7.19449	+	4.15374i	−0.427668	+	0.246914i	0.270685	+	0.962668i	$0.412750\pi$
$284$	−4.32943	+	16.9076i	−0.256904	+	1.00328i
$285$		0			0
$286$	0.0862843	−	0.211630i	0.00510210	−	0.0125139i
$287$	15.9202	+	16.2350i	0.939737	+	0.958324i
$288$		0			0
$289$	8.40772	−	14.5626i	0.494572	−	0.856624i
$290$	−37.7700	+	5.18635i	−2.21793	+	0.304553i
$291$		0			0
$292$	16.8965	−	4.72943i	0.988794	−	0.276769i
$293$			9.10732i			0.532056i	0.963965	+	0.266028i	$0.0857113\pi$
$293$			9.10732i			0.532056i	−0.963965	+	0.266028i	$0.914289\pi$
$294$		0			0
$295$	−33.8057			−1.96824
$296$	−24.9486	−	2.86201i	−1.45011	−	0.166351i
$297$		0			0
$298$	2.87995	+	20.9734i	0.166831	+	1.21496i
$299$	−11.8603	−	6.84752i	−0.685896	−	0.396002i
$300$		0			0
$301$	12.5660	−	12.3223i	0.724295	−	0.710246i
$302$	7.15025	−	17.5374i	0.411451	−	1.00917i
$303$		0			0
$304$	−10.3776	−	17.0854i	−0.595198	−	0.979913i
$305$	−3.46326	−	5.99854i	−0.198306	−	0.343475i
$306$		0			0
$307$		−	20.1344i		−	1.14913i	−0.818459	−	0.574565i	$-0.805171\pi$
$307$		−	20.1344i		−	1.14913i	0.818459	−	0.574565i	$-0.194829\pi$
$308$	0.284325	−	0.493981i	0.0162009	−	0.0281472i
$309$		0			0
$310$	2.97681	−	2.31060i	0.169071	−	0.131233i
$311$	1.60500	+	2.77995i	0.0910113	+	0.157636i	0.907937	−	0.419107i	$-0.137657\pi$
$311$	1.60500	+	2.77995i	0.0910113	+	0.157636i	−0.816926	+	0.576743i	$0.804323\pi$
$312$		0			0
$313$	−9.04356	+	15.6639i	−0.511172	+	0.885376i	0.488744	+	0.872427i	$0.337455\pi$
$313$	−9.04356	+	15.6639i	−0.511172	+	0.885376i	−0.999916	+	0.0129488i	$0.995878\pi$
$314$	24.5512	+	10.0099i	1.38551	+	0.564889i
$315$		0			0
$316$	−2.24697	−	2.19753i	−0.126402	−	0.123621i
$317$	15.1458	+	8.74443i	0.850673	+	0.491136i	0.860878	−	0.508812i	$-0.169915\pi$
$317$	15.1458	+	8.74443i	0.850673	+	0.491136i	−0.0102048	+	0.999948i	$0.503248\pi$
$318$		0			0
$319$	0.428394	+	0.742000i	0.0239855	+	0.0415440i
$320$	−25.9402	+	7.88700i	−1.45010	+	0.440897i
$321$		0			0
$322$	−27.0079	−	20.9061i	−1.50509	−	1.16505i
$323$			2.14694i			0.119459i
$324$		0			0
$325$	−8.42725	+	4.86548i	−0.467460	+	0.269888i
$326$	0.492499	+	3.58667i	0.0272770	+	0.198647i
$327$		0			0
$328$	−22.2996	+	9.67569i	−1.23129	+	0.534251i
$329$	−14.7322	+	3.79326i	−0.812212	+	0.209129i
$330$		0			0
$331$	−26.7076	−	15.4196i	−1.46798	−	0.847541i	−0.468626	−	0.883397i	$-0.655251\pi$
$331$	−26.7076	−	15.4196i	−1.46798	−	0.847541i	−0.999357	+	0.0358560i	$0.988584\pi$
$332$	−2.58188	−	0.661127i	−0.141699	−	0.0362841i
$333$		0			0
$334$	5.10532	+	6.57732i	0.279350	+	0.359895i
$335$	10.9305			0.597199
$336$		0			0
$337$	8.73833			0.476007			0.238004	−	0.971264i	$-0.423507\pi$
$337$	8.73833			0.476007			0.238004	+	0.971264i	$0.423507\pi$
$338$	−9.32095	−	12.0084i	−0.506993	−	0.653173i
$339$		0			0
$340$	2.82089	+	0.722327i	0.152984	+	0.0391737i
$341$	−0.0733414	−	0.0423437i	−0.00397166	−	0.00229304i
$342$		0			0
$343$	13.4748	−	12.7055i	0.727572	−	0.686032i
$344$	7.48906	+	17.2600i	0.403783	+	0.930598i
$345$		0			0
$346$	1.45504	+	10.5965i	0.0782236	+	0.569670i
$347$	10.5626	−	6.09832i	0.567030	−	0.327375i	−0.188932	−	0.981990i	$-0.560503\pi$
$347$	10.5626	−	6.09832i	0.567030	−	0.327375i	0.755962	+	0.654615i	$0.227169\pi$
$348$		0			0
$349$		−	5.25279i		−	0.281175i	−0.990068	−	0.140588i	$-0.955101\pi$
$349$		−	5.25279i		−	0.281175i	0.990068	−	0.140588i	$-0.0448992\pi$
$350$	−22.4597	+	9.19198i	−1.20052	+	0.491332i
$351$		0			0
$352$	0.384224	+	0.472904i	0.0204792	+	0.0252059i
$353$	−8.73713	−	15.1332i	−0.465031	−	0.805457i	0.534172	−	0.845376i	$-0.320623\pi$
$353$	−8.73713	−	15.1332i	−0.465031	−	0.805457i	−0.999203	+	0.0399190i	$0.987290\pi$
$354$		0			0
$355$	−25.6127	−	14.7875i	−1.35938	−	0.784839i
$356$	−10.3637	−	10.1357i	−0.549274	−	0.537190i
$357$		0			0
$358$	14.7603	+	6.01798i	0.780107	+	0.318060i
$359$	2.13512	−	3.69813i	0.112687	−	0.195180i	−0.804166	−	0.594405i	$-0.797388\pi$
$359$	2.13512	−	3.69813i	0.112687	−	0.195180i	0.916853	+	0.399225i	$0.130721\pi$
$360$		0			0
$361$	2.98766	+	5.17478i	0.157245	+	0.272357i
$362$	−15.3385	+	11.9057i	−0.806173	+	0.625751i
$363$		0			0
$364$	3.97863	+	6.87009i	0.208537	+	0.360091i
$365$			29.7323i			1.55626i
$366$		0			0
$367$	3.14646	+	5.44983i	0.164244	+	0.284479i	0.936386	−	0.350971i	$-0.114148\pi$
$367$	3.14646	+	5.44983i	0.164244	+	0.284479i	−0.772143	+	0.635449i	$0.780815\pi$
$368$	31.2065	−	18.9548i	1.62675	−	0.988089i
$369$		0			0
$370$	16.0657	−	39.4044i	0.835215	−	2.04854i
$371$	−0.841948	−	0.234460i	−0.0437118	−	0.0121725i
$372$		0			0
$373$	29.3109	+	16.9227i	1.51766	+	0.876222i	0.999784	+	0.0207662i	$0.00661055\pi$
$373$	29.3109	+	16.9227i	1.51766	+	0.876222i	0.517876	+	0.855456i	$0.326723\pi$
$374$	−0.00890236	−	0.0648322i	−0.000460330	−	0.00335239i
$375$		0			0
$376$	1.85348	−	16.1571i	0.0955861	−	0.833239i
$377$	−11.9342			−0.614641
$378$		0			0
$379$			2.56918i			0.131970i	0.997821	+	0.0659850i	$0.0210190\pi$
$379$			2.56918i			0.131970i	−0.997821	+	0.0659850i	$0.978981\pi$
$380$	32.6203	−	9.13061i	1.67339	−	0.468391i
$381$		0			0
$382$	27.1787	−	3.73202i	1.39058	−	0.190947i
$383$	4.40880	−	7.63626i	0.225279	−	0.390195i	−0.731124	−	0.682244i	$-0.761004\pi$
$383$	4.40880	−	7.63626i	0.225279	−	0.390195i	0.956403	+	0.292050i	$0.0943373\pi$
$384$		0			0
$385$	0.676221	+	0.689596i	0.0344634	+	0.0351451i
$386$	−1.36567	+	3.34959i	−0.0695109	+	0.170490i
$387$		0			0
$388$	9.44863	−	36.8995i	0.479681	−	1.87329i
$389$	11.2701	−	6.50678i	0.571416	−	0.329907i	−0.186299	−	0.982493i	$-0.559649\pi$
$389$	11.2701	−	6.50678i	0.571416	−	0.329907i	0.757715	+	0.652586i	$0.226316\pi$
$390$		0			0
$391$	−3.92140			−0.198314
$392$	7.52362	+	18.3138i	0.380000	+	0.924986i
$393$		0			0
$394$	4.28380	−	3.32509i	0.215815	−	0.167515i
$395$	4.61230	−	2.66291i	0.232070	−	0.133986i
$396$		0			0
$397$	−8.49061	−	4.90206i	−0.426132	−	0.246027i	0.271566	−	0.962420i	$-0.412459\pi$
$397$	−8.49061	−	4.90206i	−0.426132	−	0.246027i	−0.697697	+	0.716393i	$0.745792\pi$
$398$	9.11152	−	22.3478i	0.456719	−	1.12020i
$399$		0			0
$400$	−0.577027	−	25.9371i	−0.0288514	−	1.29685i
$401$	−1.25638	+	2.17611i	−0.0627405	+	0.108670i	−0.895689	−	0.444680i	$-0.853317\pi$
$401$	−1.25638	+	2.17611i	−0.0627405	+	0.108670i	0.832949	+	0.553350i	$0.186651\pi$
$402$		0			0
$403$	1.02157	−	0.589804i	0.0508880	−	0.0293802i
$404$	1.79524	+	6.41374i	0.0893166	+	0.319095i
$405$		0			0
$406$	−29.4912	−	4.00962i	−1.46362	−	0.198994i
$407$	−0.956328			−0.0474034
$408$		0			0
$409$	−7.54163	−	13.0625i	−0.372910	−	0.645899i	0.617102	−	0.786883i	$-0.288307\pi$
$409$	−7.54163	−	13.0625i	−0.372910	−	0.645899i	−0.990012	+	0.140985i	$0.954973\pi$
$410$	−5.60355	−	40.8083i	−0.276740	−	2.01538i
$411$		0			0
$412$	18.6789	+	18.2679i	0.920242	+	0.899997i
$413$	−25.4237	−	7.07981i	−1.25102	−	0.348375i
$414$		0			0
$415$	2.25813	−	3.91120i	0.110847	−	0.191993i
$416$	−8.38048	+	1.34130i	−0.410887	+	0.0657625i
$417$		0			0
$418$	−0.466782	−	0.601369i	−0.0228311	−	0.0294139i
$419$			18.2508i			0.891608i	0.895130	+	0.445804i	$0.147082\pi$
$419$			18.2508i			0.891608i	−0.895130	+	0.445804i	$0.852918\pi$
$420$		0			0
$421$			34.3633i			1.67476i	0.546619	+	0.837382i	$0.315915\pi$
$421$			34.3633i			1.67476i	−0.546619	+	0.837382i	$0.684085\pi$
$422$	−14.3670	+	11.1516i	−0.699373	+	0.542853i
$423$		0			0
$424$	0.556338	−	0.750638i	0.0270182	−	0.0364542i
$425$	−1.39317	+	2.41304i	−0.0675785	+	0.117049i
$426$		0			0
$427$	−1.34830	−	5.23652i	−0.0652490	−	0.253413i
$428$	−6.47324	+	6.61886i	−0.312896	+	0.319935i
$429$		0			0
$430$	−31.5859	+	4.33719i	−1.52321	+	0.209158i
$431$	12.8087	+	22.1854i	0.616974	+	1.06863i	0.990035	+	0.140824i	$0.0449751\pi$
$431$	12.8087	+	22.1854i	0.616974	+	1.06863i	−0.373060	+	0.927807i	$0.621692\pi$
$432$		0			0
$433$	3.79352			0.182305			0.0911525	−	0.995837i	$-0.470945\pi$
$433$	3.79352			0.182305			0.0911525	+	0.995837i	$0.470945\pi$
$434$	2.72262	−	1.11427i	0.130690	−	0.0534868i
$435$		0			0
$436$	−6.41235	−	22.9090i	−0.307096	−	1.09714i
$437$	−39.5060	+	22.8088i	−1.88983	+	1.09109i
$438$		0			0
$439$	−4.48040	+	7.76028i	−0.213838	+	0.370378i	−0.952912	−	0.303246i	$-0.901930\pi$
$439$	−4.48040	+	7.76028i	−0.213838	+	0.370378i	0.739075	+	0.673623i	$0.235263\pi$
$440$	−0.947191	+	0.410983i	−0.0451556	+	0.0195928i
$441$		0			0
$442$	0.844061	+	0.344135i	0.0401479	+	0.0163688i
$443$	−11.5331	−	6.65864i	−0.547954	−	0.316361i	0.200342	−	0.979726i	$-0.435795\pi$
$443$	−11.5331	−	6.65864i	−0.547954	−	0.316361i	−0.748296	+	0.663365i	$0.769128\pi$
$444$		0			0
$445$	21.2733	−	12.2822i	1.00845	−	0.582230i
$446$	−10.5030	−	13.5313i	−0.497332	−	0.640727i
$447$		0			0
$448$	−21.1601	+	0.498895i	−0.999722	+	0.0235706i
$449$	−26.7885			−1.26423			−0.632115	−	0.774875i	$-0.717813\pi$
$449$	−26.7885			−1.26423			−0.632115	+	0.774875i	$0.717813\pi$
$450$		0			0
$451$	−0.801689	+	0.462855i	−0.0377501	+	0.0217950i
$452$	5.59385	−	21.8455i	0.263112	−	1.02753i
$453$		0			0
$454$	9.08389	+	3.70362i	0.426328	+	0.173820i
$455$	−13.0280	+	3.35447i	−0.610763	+	0.157260i
$456$		0			0
$457$	−6.83952	+	11.8464i	−0.319939	+	0.554151i	−0.980475	−	0.196643i	$-0.936996\pi$
$457$	−6.83952	+	11.8464i	−0.319939	+	0.554151i	0.660536	+	0.750795i	$0.270329\pi$
$458$	1.68913	+	12.3012i	0.0789280	+	0.574799i
$459$		0			0
$460$	16.6771	+	59.5813i	0.777575	+	2.77799i
$461$		−	28.1071i		−	1.30908i	−0.756028	−	0.654539i	$-0.772863\pi$
$461$		−	28.1071i		−	1.30908i	0.756028	−	0.654539i	$-0.227137\pi$
$462$		0			0
$463$	0.408558			0.0189873			0.00949365	−	0.999955i	$-0.496978\pi$
$463$	0.408558			0.0189873			0.00949365	+	0.999955i	$0.496978\pi$
$464$	15.2919	−	27.9018i	0.709911	−	1.29531i
$465$		0			0
$466$	−22.9911	+	3.15700i	−1.06504	+	0.146245i
$467$	−14.6477	−	8.45683i	−0.677813	−	0.391335i	0.121218	−	0.992626i	$-0.461320\pi$
$467$	−14.6477	−	8.45683i	−0.677813	−	0.391335i	−0.799030	+	0.601291i	$0.794653\pi$
$468$		0			0
$469$	8.22035	+	2.28914i	0.379580	+	0.105703i
$470$	25.5189	+	10.4044i	1.17710	+	0.479920i
$471$		0			0
$472$	16.7993	−	22.6665i	0.773253	−	1.04331i
$473$	0.358253	+	0.620513i	0.0164725	+	0.0285312i
$474$		0			0
$475$			32.4134i			1.48723i
$476$	1.97018	+	1.13400i	0.0903032	+	0.0519767i
$477$		0			0
$478$	−0.707942	−	0.912062i	−0.0323805	−	0.0417167i
$479$	−9.76658	−	16.9162i	−0.446247	−	0.772922i	0.551892	−	0.833916i	$-0.313906\pi$
$479$	−9.76658	−	16.9162i	−0.446247	−	0.772922i	−0.998138	+	0.0609941i	$0.980573\pi$
$480$		0			0
$481$	6.66033	−	11.5360i	0.303685	−	0.525998i
$482$	12.8465	−	31.5086i	0.585141	−	1.43518i
$483$		0			0
$484$	−15.7118	−	15.3662i	−0.714173	−	0.698461i
$485$	55.8977	+	32.2725i	2.53818	+	1.46542i
$486$		0			0
$487$	−17.8306	−	30.8834i	−0.807980	−	1.39946i	−0.914261	−	0.405126i	$-0.867228\pi$
$487$	−17.8306	−	30.8834i	−0.807980	−	1.39946i	0.106281	−	0.994336i	$-0.466106\pi$
$488$	5.74300	+	0.658816i	0.259973	+	0.0298232i
$489$		0			0
$490$	−33.3213	+	3.91228i	−1.50530	+	0.176739i
$491$		−	19.3905i		−	0.875082i	−0.899198	−	0.437541i	$-0.855849\pi$
$491$		−	19.3905i		−	0.875082i	0.899198	−	0.437541i	$-0.144151\pi$
$492$		0			0
$493$	−2.95938	+	1.70860i	−0.133284	+	0.0769514i
$494$	10.5051	−	1.44250i	0.472647	−	0.0649011i
$495$		0			0
$496$	0.0699485	+	3.14415i	0.00314078	+	0.141177i
$497$	−16.1652	−	16.4850i	−0.725110	−	0.739452i
$498$		0			0
$499$	11.4791	+	6.62747i	0.513876	+	0.296686i	0.734425	−	0.678689i	$-0.237452\pi$
$499$	11.4791	+	6.62747i	0.513876	+	0.296686i	−0.220549	+	0.975376i	$0.570785\pi$
$500$	9.75674	+	2.49835i	0.436335	+	0.111730i
$501$		0			0
$502$	−4.44226	+	3.44809i	−0.198268	+	0.153896i
$503$	−24.7969			−1.10564			−0.552819	−	0.833302i	$-0.686448\pi$
$503$	−24.7969			−1.10564			−0.552819	+	0.833302i	$0.686448\pi$
$504$		0			0
$505$	−11.2861			−0.502223
$506$	1.09840	−	0.852581i	0.0488300	−	0.0379019i
$507$		0			0
$508$	4.02942	−	15.7360i	0.178777	−	0.698172i
$509$	22.7230	+	13.1191i	1.00718	+	0.581495i	0.910365	−	0.413807i	$-0.135801\pi$
$509$	22.7230	+	13.1191i	1.00718	+	0.581495i	0.0968148	+	0.995302i	$0.469135\pi$
$510$		0			0
$511$	−6.22673	+	22.3603i	−0.275455	+	0.989161i
$512$	7.60248	−	21.3120i	0.335985	−	0.941867i
$513$		0			0
$514$	−29.8291	+	4.09595i	−1.31571	+	0.180665i
$515$	−38.3417	+	22.1366i	−1.68954	+	0.975455i
$516$		0			0
$517$		−	0.619334i		−	0.0272383i
$518$	20.3346	−	26.2696i	0.893450	−	1.15422i
$519$		0			0
$520$	1.63908	−	14.2881i	0.0718784	−	0.626575i
$521$	18.4536	+	31.9626i	0.808468	+	1.40031i	0.913925	+	0.405883i	$0.133036\pi$
$521$	18.4536	+	31.9626i	0.808468	+	1.40031i	−0.105457	+	0.994424i	$0.533631\pi$
$522$		0			0
$523$	−3.36834	−	1.94471i	−0.147287	−	0.0850364i	0.424545	−	0.905407i	$-0.360434\pi$
$523$	−3.36834	−	1.94471i	−0.147287	−	0.0850364i	−0.571833	+	0.820370i	$0.693767\pi$
$524$	15.7135	−	16.0670i	0.686449	−	0.701890i
$525$		0			0
$526$	4.03102	−	9.88688i	0.175761	−	0.431089i
$527$	0.168883	−	0.292514i	0.00735665	−	0.0127421i
$528$		0			0
$529$	−30.1604	−	52.2394i	−1.31132	−	2.27128i
$530$	0.970796	+	1.25070i	0.0421687	+	0.0543271i
$531$		0			0
$532$	26.4444	−	0.0351508i	1.14651	−	0.00152398i
$533$		−	12.8942i		−	0.558510i
$534$		0			0
$535$	−7.84410	−	13.5864i	−0.339130	−	0.587391i
$536$	−5.43180	+	7.32884i	−0.234618	+	0.316558i
$537$		0			0
$538$	−7.81675	−	3.18699i	−0.337004	−	0.137401i
$539$	0.364135	+	0.660232i	0.0156844	+	0.0284382i
$540$		0			0
$541$	4.77290	+	2.75564i	0.205203	+	0.118474i	0.599080	−	0.800689i	$-0.295533\pi$
$541$	4.77290	+	2.75564i	0.205203	+	0.118474i	−0.393877	+	0.919163i	$0.628866\pi$
$542$	6.68972	−	0.918592i	0.287348	−	0.0394569i
$543$		0			0
$544$	−1.88612	+	1.53243i	−0.0808668	+	0.0657024i
$545$	40.3122			1.72679
$546$		0			0
$547$			3.62706i			0.155082i	0.996989	+	0.0775409i	$0.0247068\pi$
$547$			3.62706i			0.155082i	−0.996989	+	0.0775409i	$0.975293\pi$
$548$	−12.4027	+	3.47159i	−0.529818	+	0.148299i
$549$		0			0
$550$	−0.134403	−	0.978802i	−0.00573097	−	0.0417363i
$551$	−19.8761	+	34.4264i	−0.846751	+	1.46662i
$552$		0			0
$553$	4.02638	−	1.03672i	0.171219	−	0.0440856i
$554$	−11.4851	−	4.68262i	−0.487954	−	0.198946i
$555$		0			0
$556$	−21.7269	−	5.56347i	−0.921425	−	0.235944i
$557$	−9.16878	+	5.29360i	−0.388494	+	0.224297i	−0.681507	−	0.731811i	$-0.738675\pi$
$557$	−9.16878	+	5.29360i	−0.388494	+	0.224297i	0.293014	+	0.956108i	$0.405342\pi$
$558$		0			0
$559$	−9.98021			−0.422118
$560$	8.85091	−	34.7574i	0.374019	−	1.46877i
$561$		0			0
$562$	11.8926	+	15.3216i	0.501661	+	0.646303i
$563$	35.8149	−	20.6777i	1.50942	−	0.871463i	0.509478	−	0.860484i	$-0.329839\pi$
$563$	35.8149	−	20.6777i	1.50942	−	0.871463i	0.999940	−	0.0109787i	$-0.00349468\pi$
$564$		0			0
$565$	33.0930	+	19.1062i	1.39223	+	0.803805i
$566$	10.8791	+	4.43555i	0.457282	+	0.186440i
$567$		0			0
$568$	22.6428	−	9.82465i	0.950073	−	0.412233i
$569$	−17.7569	+	30.7559i	−0.744408	+	1.28935i	0.206063	+	0.978539i	$0.433935\pi$
$569$	−17.7569	+	30.7559i	−0.744408	+	1.28935i	−0.950471	+	0.310814i	$0.899398\pi$
$570$		0			0
$571$	26.6337	−	15.3770i	1.11459	−	0.643507i	0.174573	−	0.984644i	$-0.444146\pi$
$571$	26.6337	−	15.3770i	1.11459	−	0.643507i	0.940013	+	0.341138i	$0.110812\pi$
$572$	−0.311247	+	0.0871197i	−0.0130139	+	0.00364266i
$573$		0			0
$574$	4.33217	−	31.8636i	0.180821	−	1.32996i
$575$	−59.2033			−2.46895
$576$		0			0
$577$	0.00598449	+	0.0103654i	0.000249138	+	0.000431519i	0.866150	−	0.499784i	$-0.166587\pi$
$577$	0.00598449	+	0.0103654i	0.000249138	+	0.000431519i	−0.865901	+	0.500216i	$0.833254\pi$
$578$	−23.5596	+	3.23506i	−0.979948	+	0.134561i
$579$		0			0
$580$	38.5460	+	37.6980i	1.60054	+	1.56533i
$581$	2.51735	−	2.46852i	0.104437	−	0.102412i
$582$		0			0
$583$	0.0177907	−	0.0308143i	0.000736814	−	0.00127620i
$584$	−19.9353	−	14.7751i	−0.824928	−	0.611399i
$585$		0			0
$586$	10.1744	−	7.89737i	0.420300	−	0.326237i
$587$			45.9133i			1.89505i	0.319688	+	0.947523i	$0.396422\pi$
$587$			45.9133i			1.89505i	−0.319688	+	0.947523i	$0.603578\pi$
$588$		0			0
$589$		−	3.92922i		−	0.161901i
$590$	29.3144	+	37.7666i	1.20686	+	1.55483i
$591$		0			0
$592$	18.4367	+	30.3535i	0.757742	+	1.24752i
$593$	20.1369	−	34.8781i	0.826923	−	1.43227i	−0.0735177	−	0.997294i	$-0.523423\pi$
$593$	20.1369	−	34.8781i	0.826923	−	1.43227i	0.900441	−	0.434979i	$-0.143244\pi$
$594$		0			0
$595$	−2.75038	+	2.69703i	−0.112754	+	0.110567i
$596$	20.9335	−	21.4044i	0.857469	−	0.876757i
$597$		0			0
$598$	2.63473	+	19.1877i	0.107742	+	0.784642i
$599$	−9.26440	−	16.0464i	−0.378533	−	0.655638i	0.612316	−	0.790613i	$-0.290238\pi$
$599$	−9.26440	−	16.0464i	−0.378533	−	0.655638i	−0.990849	+	0.134975i	$0.956905\pi$
$600$		0			0
$601$	−6.16213			−0.251358			−0.125679	−	0.992071i	$-0.540111\pi$
$601$	−6.16213			−0.251358			−0.125679	+	0.992071i	$0.540111\pi$
$602$	−24.6626	−	3.35313i	−1.00517	−	0.136663i
$603$		0			0
$604$	−25.7925	+	7.21948i	−1.04948	+	0.293756i
$605$	32.2513	−	18.6203i	1.31120	−	0.757023i
$606$		0			0
$607$	−21.4265	+	37.1119i	−0.869677	+	1.50632i	−0.00734959	+	0.999973i	$0.502339\pi$
$607$	−21.4265	+	37.1119i	−0.869677	+	1.50632i	−0.862327	+	0.506351i	$0.830994\pi$
$608$	−10.0883	+	26.4090i	−0.409134	+	1.07103i
$609$		0			0
$610$	−3.69822	+	9.07063i	−0.149737	+	0.367259i
$611$	7.47093	+	4.31334i	0.302241	+	0.174499i
$612$		0			0
$613$	14.0140	−	8.09100i	0.566021	−	0.326793i	−0.189537	−	0.981874i	$-0.560699\pi$
$613$	14.0140	−	8.09100i	0.566021	−	0.326793i	0.755559	+	0.655081i	$0.227365\pi$
$614$	−22.4934	+	17.4594i	−0.907761	+	0.704604i
$615$		0			0
$616$	−0.798409	+	0.110714i	−0.0321688	+	0.00446080i
$617$	19.0082			0.765240			0.382620	−	0.923906i	$-0.375022\pi$
$617$	19.0082			0.765240			0.382620	+	0.923906i	$0.375022\pi$
$618$		0			0
$619$	13.0045	−	7.50818i	0.522697	−	0.301779i	−0.215341	−	0.976539i	$-0.569086\pi$
$619$	13.0045	−	7.50818i	0.522697	−	0.301779i	0.738037	+	0.674760i	$0.235753\pi$
$620$	−5.16265	−	1.32197i	−0.207337	−	0.0530915i
$621$		0			0
$622$	1.71389	−	4.20367i	0.0687208	−	0.168552i
$623$	18.5709	−	4.78164i	0.744027	−	0.191573i
$624$		0			0
$625$	7.68139	−	13.3045i	0.307255	−	0.532182i
$626$	25.3413	−	3.47971i	1.01284	−	0.139077i
$627$		0			0
$628$	−10.1068	−	36.1078i	−0.403304	−	1.44086i
$629$		−	3.81420i		−	0.152082i
$630$		0			0
$631$	42.1434			1.67770			0.838852	−	0.544359i	$-0.183227\pi$
$631$	42.1434			1.67770			0.838852	+	0.544359i	$0.183227\pi$
$632$	−0.506566	+	4.41581i	−0.0201501	+	0.175652i
$633$		0			0
$634$	−3.36461	−	24.5031i	−0.133626	−	0.973141i
$635$	23.8379	+	13.7628i	0.945978	+	0.546160i
$636$		0			0
$637$	−10.5003	−	0.205675i	−0.416037	−	0.00814913i
$638$	0.457458	−	1.12201i	0.0181109	−	0.0444207i
$639$		0			0
$640$	31.3050	+	22.1403i	1.23744	+	0.875172i
$641$	−14.4278	−	24.9896i	−0.569862	−	0.987030i	−0.996579	−	0.0826446i	$-0.973663\pi$
$641$	−14.4278	−	24.9896i	−0.569862	−	0.987030i	0.426717	−	0.904385i	$-0.359670\pi$
$642$		0			0
$643$			10.7484i			0.423876i	0.977283	+	0.211938i	$0.0679775\pi$
$643$			10.7484i			0.423876i	−0.977283	+	0.211938i	$0.932022\pi$
$644$	0.0642033	+	48.3009i	0.00252996	+	1.90332i
$645$		0			0
$646$	2.39849	−	1.86171i	0.0943673	−	0.0732479i
$647$	−6.75381	−	11.6979i	−0.265520	−	0.459894i	0.702180	−	0.711999i	$-0.252210\pi$
$647$	−6.75381	−	11.6979i	−0.265520	−	0.459894i	−0.967700	+	0.252106i	$0.918877\pi$
$648$		0			0
$649$	0.537211	−	0.930478i	0.0210874	−	0.0365244i
$650$	12.7432	+	5.19557i	0.499829	+	0.203787i
$651$		0			0
$652$	3.57983	−	3.66036i	0.140197	−	0.143351i
$653$	−7.85026	−	4.53235i	−0.307204	−	0.177364i	0.338470	−	0.940977i	$-0.390090\pi$
$653$	−7.85026	−	4.53235i	−0.307204	−	0.177364i	−0.645675	+	0.763613i	$0.723424\pi$
$654$		0			0
$655$	19.0412	+	32.9804i	0.744002	+	1.28865i
$656$	30.1463	+	16.5221i	1.17701	+	0.645079i
$657$		0			0
$658$	17.0126	+	13.1690i	0.663222	+	0.513381i
$659$			31.5929i			1.23068i	0.788261	+	0.615341i	$0.210982\pi$
$659$			31.5929i			1.23068i	−0.788261	+	0.615341i	$0.789018\pi$
$660$		0			0
$661$	−9.26579	+	5.34961i	−0.360398	+	0.208076i	−0.669255	−	0.743033i	$-0.733387\pi$
$661$	−9.26579	+	5.34961i	−0.360398	+	0.208076i	0.308858	+	0.951108i	$0.400053\pi$
$662$	5.93305	+	43.2079i	0.230594	+	1.67932i
$663$		0			0
$664$	1.50028	+	3.45769i	0.0582221	+	0.134184i
$665$	−12.0213	+	43.1687i	−0.466166	+	1.67401i
$666$		0			0
$667$	−62.8801	−	36.3039i	−2.43473	−	1.40569i
$668$	2.92091	−	11.4070i	0.113014	−	0.441349i
$669$		0			0
$670$	−9.47835	−	12.2112i	−0.366181	−	0.471761i
$671$	0.220141			0.00849843
$672$		0			0
$673$	21.8493			0.842230			0.421115	−	0.907007i	$-0.361639\pi$
$673$	21.8493			0.842230			0.421115	+	0.907007i	$0.361639\pi$
$674$	−7.57739	−	9.76217i	−0.291870	−	0.376025i
$675$		0			0
$676$	−5.33281	+	20.8261i	−0.205108	+	0.801004i
$677$	−3.24311	−	1.87241i	−0.124643	−	0.0719625i	0.436382	−	0.899761i	$-0.356260\pi$
$677$	−3.24311	−	1.87241i	−0.124643	−	0.0719625i	−0.561025	+	0.827799i	$0.689593\pi$
$678$		0			0
$679$	35.2793	+	35.9771i	1.35390	+	1.38068i
$680$	−1.63916	−	3.77776i	−0.0628588	−	0.144871i
$681$		0			0
$682$	0.0162927	+	0.118653i	0.000623878	+	0.00454344i
$683$	−24.2667	+	14.0104i	−0.928541	+	0.536093i	−0.886350	−	0.463016i	$-0.846767\pi$
$683$	−24.2667	+	14.0104i	−0.928541	+	0.536093i	−0.0421911	+	0.999110i	$0.513434\pi$
$684$		0			0
$685$		−	21.8247i		−	0.833880i
$686$	−25.8788	−	4.03612i	−0.988055	−	0.154100i
$687$		0			0
$688$	12.7882	−	23.3334i	0.487546	−	0.889579i
$689$	0.247806	+	0.429212i	0.00944064	+	0.0163517i
$690$		0			0
$691$	−14.0726	−	8.12481i	−0.535346	−	0.309082i	0.207845	−	0.978162i	$-0.433355\pi$
$691$	−14.0726	−	8.12481i	−0.535346	−	0.309082i	−0.743191	+	0.669080i	$0.766688\pi$
$692$	10.5763	−	10.8142i	0.402050	−	0.411094i
$693$		0			0
$694$	−15.9721	−	6.51205i	−0.606294	−	0.247194i
$695$	19.0025	−	32.9133i	0.720805	−	1.24847i
$696$		0			0
$697$	−1.84605	−	3.19744i	−0.0699240	−	0.121112i
$698$	−5.86824	+	4.55493i	−0.222116	+	0.172407i
$699$		0			0
$700$	29.7448	+	17.1205i	1.12425	+	0.647094i
$701$		−	6.77821i		−	0.256010i	−0.991774	−	0.128005i	$-0.959143\pi$
$701$		−	6.77821i		−	0.256010i	0.991774	−	0.128005i	$-0.0408573\pi$
$702$		0			0
$703$	−22.1853	−	38.4260i	−0.836734	−	1.44927i
$704$	0.195135	−	0.839317i	0.00735442	−	0.0316330i
$705$		0			0
$706$	−9.32990	+	22.8835i	−0.351135	+	0.861230i
$707$	−8.48773	−	2.36360i	−0.319214	−	0.0888923i
$708$		0			0
$709$	−18.2622	−	10.5437i	−0.685851	−	0.395976i	0.116205	−	0.993225i	$-0.462927\pi$
$709$	−18.2622	−	10.5437i	−0.685851	−	0.395976i	−0.802056	+	0.597249i	$0.796260\pi$
$710$	5.68982	+	41.4366i	0.213535	+	1.55509i
$711$		0			0
$712$	−2.33644	+	20.3671i	−0.0875616	+	0.763288i
$713$	7.17675			0.268772
$714$		0			0
$715$		−	0.547692i		−	0.0204825i
$716$	−6.07624	−	21.7082i	−0.227080	−	0.811273i
$717$		0			0
$718$	−5.98288	+	0.821534i	−0.223279	+	0.0306594i
$719$	9.43045	−	16.3340i	0.351697	−	0.609156i	−0.634850	−	0.772635i	$-0.718938\pi$
$719$	9.43045	−	16.3340i	0.351697	−	0.609156i	0.986547	+	0.163479i	$0.0522715\pi$
$720$		0			0
$721$	−33.4710	+	8.61814i	−1.24653	+	0.320956i
$722$	3.19036	−	7.82499i	0.118733	−	0.291216i
$723$		0			0
$724$	26.6014	+	6.81165i	0.988632	+	0.253153i
$725$	−44.6792	+	25.7955i	−1.65934	+	0.958022i
$726$		0			0
$727$	−5.67246			−0.210380			−0.105190	−	0.994452i	$-0.533545\pi$
$727$	−5.67246			−0.210380			−0.105190	+	0.994452i	$0.533545\pi$
$728$	4.22498	−	10.4022i	0.156588	−	0.385529i
$729$		0			0
$730$	33.2160	−	25.7822i	1.22938	−	0.954243i
$731$	−2.47485	+	1.42885i	−0.0915355	+	0.0528480i
$732$		0			0
$733$	−17.9878	−	10.3853i	−0.664394	−	0.383588i	0.129555	−	0.991572i	$-0.458645\pi$
$733$	−17.9878	−	10.3853i	−0.664394	−	0.383588i	−0.793949	+	0.607984i	$0.791978\pi$
$734$	3.35993	−	8.24091i	0.124017	−	0.304177i
$735$		0			0
$736$	−48.2363	−	18.4263i	−1.77801	−	0.679203i
$737$	−0.173699	+	0.300855i	−0.00639828	+	0.0110821i
$738$		0			0
$739$	−35.6239	+	20.5675i	−1.31045	+	0.756586i	−0.982170	−	0.187996i	$-0.939801\pi$
$739$	−35.6239	+	20.5675i	−1.31045	+	0.756586i	−0.328276	+	0.944582i	$0.606467\pi$
$740$	−57.9525	+	16.2212i	−2.13038	+	0.596304i
$741$		0			0
$742$	0.468160	+	1.14391i	0.0171867	+	0.0419941i
$743$	−2.47186			−0.0906839			−0.0453419	−	0.998972i	$-0.514438\pi$
$743$	−2.47186			−0.0906839			−0.0453419	+	0.998972i	$0.514438\pi$
$744$		0			0
$745$	25.3666	+	43.9363i	0.929362	+	1.60970i
$746$	−6.51136	−	47.4195i	−0.238398	−	1.73615i
$747$		0			0
$748$	−0.0647087	+	0.0661643i	−0.00236598	+	0.00241921i
$749$	−3.05384	−	11.8605i	−0.111585	−	0.433372i
$750$		0			0
$751$	−10.9291	+	18.9297i	−0.398808	+	0.690755i	−0.993579	−	0.113140i	$-0.963909\pi$
$751$	−10.9291	+	18.9297i	−0.398808	+	0.690755i	0.594771	+	0.803895i	$0.297243\pi$
$752$	−19.6574	+	11.9399i	−0.716832	+	0.435403i
$753$		0			0
$754$	10.3487	+	13.3325i	0.376876	+	0.485539i
$755$		−	45.3864i		−	1.65178i
$756$		0			0
$757$			48.6072i			1.76666i	0.468753	+	0.883329i	$0.344703\pi$
$757$			48.6072i			1.76666i	−0.468753	+	0.883329i	$0.655297\pi$
$758$	2.87020	−	2.22785i	0.104251	−	0.0809192i
$759$		0			0
$760$	−38.4869	−	28.5248i	−1.39607	−	1.03470i
$761$	−3.92491	+	6.79815i	−0.142278	+	0.246433i	−0.928354	−	0.371697i	$-0.878776\pi$
$761$	−3.92491	+	6.79815i	−0.142278	+	0.246433i	0.786076	+	0.618130i	$0.212109\pi$
$762$		0			0
$763$	30.3170	+	8.44244i	1.09755	+	0.305637i
$764$	−27.7372	−	27.1269i	−1.00350	−	0.981419i
$765$		0			0
$766$	−12.3540	+	1.69638i	−0.446370	+	0.0612928i
$767$	7.48280	+	12.9606i	0.270188	+	0.467980i
$768$		0			0
$769$	24.0398			0.866898			0.433449	−	0.901178i	$-0.357297\pi$
$769$	24.0398			0.866898			0.433449	+	0.901178i	$0.357297\pi$
$770$	0.184012	−	1.35343i	0.00663135	−	0.0487743i
$771$		0			0
$772$	4.92628	−	1.37889i	0.177301	−	0.0496275i
$773$	16.6890	−	9.63541i	0.600262	−	0.346562i	−0.168882	−	0.985636i	$-0.554016\pi$
$773$	16.6890	−	9.63541i	0.600262	−	0.346562i	0.769145	+	0.639075i	$0.220682\pi$
$774$		0			0
$775$	2.54970	−	4.41622i	0.0915881	−	0.158635i
$776$	−49.4162	+	21.4415i	−1.77394	+	0.769705i
$777$		0			0
$778$	−17.0419	−	6.94823i	−0.610983	−	0.249106i
$779$	−37.1958	−	21.4750i	−1.33268	−	0.769422i
$780$		0			0
$781$	0.814031	−	0.469981i	0.0291283	−	0.0168172i
$782$	3.40042	+	4.38086i	0.121599	+	0.156659i
$783$		0			0
$784$	13.9355	−	24.2858i	0.497696	−	0.867352i
$785$	63.5378			2.26776
$786$		0			0
$787$	36.8732	−	21.2888i	1.31439	−	0.758863i	0.331569	−	0.943431i	$-0.392422\pi$
$787$	36.8732	−	21.2888i	1.31439	−	0.758863i	0.982820	+	0.184568i	$0.0590886\pi$
$788$	−7.42935	−	1.90239i	−0.264660	−	0.0677698i
$789$		0			0
$790$	−6.97445	−	2.84358i	−0.248140	−	0.101170i
$791$	20.8863	+	21.2994i	0.742632	+	0.757321i
$792$		0			0
$793$	−1.53317	+	2.65552i	−0.0544443	+	0.0943003i
$794$	1.88617	+	13.7362i	0.0669378	+	0.487480i
$795$		0			0
$796$	−32.8673	+	9.19973i	−1.16495	+	0.326076i
$797$			14.7345i			0.521923i	0.965349	+	0.260962i	$0.0840396\pi$
$797$			14.7345i			0.521923i	−0.965349	+	0.260962i	$0.915960\pi$
$798$		0			0
$799$	2.47014			0.0873873
$800$	−28.4757	+	23.1358i	−1.00677	+	0.817976i
$801$		0			0
$802$	3.52054	−	0.483419i	0.124314	−	0.0170701i
$803$	−0.818361	−	0.472481i	−0.0288793	−	0.0166735i
$804$		0			0
$805$	−78.8479	−	21.9570i	−2.77902	−	0.773882i
$806$	−1.54476	−	0.629819i	−0.0544118	−	0.0221844i
$807$		0			0
$808$	5.60848	−	7.56722i	0.197306	−	0.266214i
$809$	−6.93906	−	12.0188i	−0.243964	−	0.422558i	0.717876	−	0.696171i	$-0.245115\pi$
$809$	−6.93906	−	12.0188i	−0.243964	−	0.422558i	−0.961840	+	0.273613i	$0.911781\pi$
$810$		0			0
$811$			44.9188i			1.57731i	0.614835	+	0.788656i	$0.289223\pi$
$811$			44.9188i			1.57731i	−0.614835	+	0.788656i	$0.710777\pi$
$812$	21.0937	+	36.4235i	0.740244	+	1.27821i
$813$		0			0
$814$	0.829274	+	1.06838i	0.0290661	+	0.0374466i
$815$	4.33795	+	7.51355i	0.151952	+	0.263188i
$816$		0			0
$817$	−16.6218	+	28.7898i	−0.581524	+	1.00723i
$818$	−8.05329	+	19.7523i	−0.281577	+	0.690624i
$819$		0			0
$820$	−40.7306	+	41.6468i	−1.42237	+	1.45437i
$821$	4.28623	+	2.47466i	0.149591	+	0.0863661i	0.572927	−	0.819606i	$-0.305808\pi$
$821$	4.28623	+	2.47466i	0.149591	+	0.0863661i	−0.423336	+	0.905973i	$0.639141\pi$
$822$		0			0
$823$	−4.28025	−	7.41361i	−0.149200	−	0.258422i	0.781732	−	0.623615i	$-0.214337\pi$
$823$	−4.28025	−	7.41361i	−0.149200	−	0.258422i	−0.930932	+	0.365192i	$0.881003\pi$
$824$	4.21105	−	36.7083i	0.146699	−	1.27880i
$825$		0			0
$826$	14.1367	+	34.5417i	0.491879	+	1.20186i
$827$		−	8.43880i		−	0.293446i	−0.989178	−	0.146723i	$-0.953127\pi$
$827$		−	8.43880i		−	0.293446i	0.989178	−	0.146723i	$-0.0468726\pi$
$828$		0			0
$829$	−35.8643	+	20.7062i	−1.24562	+	0.719158i	−0.970232	−	0.242176i	$-0.922139\pi$
$829$	−35.8643	+	20.7062i	−1.24562	+	0.719158i	−0.275385	+	0.961334i	$0.588805\pi$
$830$	−6.32759	+	0.868867i	−0.219634	+	0.0301588i
$831$		0			0
$832$	8.76554	+	8.19930i	0.303890	+	0.284259i
$833$	−2.63326	+	1.45231i	−0.0912370	+	0.0503195i
$834$		0			0
$835$	17.2800	+	9.97662i	0.597999	+	0.345255i
$836$	−0.267061	+	1.04295i	−0.00923650	+	0.0360711i
$837$		0			0
$838$	20.3891	−	15.8261i	0.704331	−	0.546702i
$839$	33.1939			1.14598			0.572990	−	0.819563i	$-0.305783\pi$
$839$	33.1939			1.14598			0.572990	+	0.819563i	$0.305783\pi$
$840$		0			0
$841$	−34.2720			−1.18179
$842$	38.3895	−	29.7979i	1.32299	−	1.02690i
$843$		0			0
$844$	24.9165	+	6.38020i	0.857660	+	0.219616i
$845$	−31.5487	−	18.2146i	−1.08531	−	0.626603i
$846$		0			0
$847$	28.1543	−	7.24919i	0.967393	−	0.249085i
$848$	−1.32101	+	0.0293888i	−0.0453638	+	0.00100922i
$849$		0			0
$850$	3.90384	−	0.536052i	0.133901	−	0.0183864i
$851$	70.1854	−	40.5216i	2.40593	−	1.38906i
$852$		0			0
$853$			7.36144i			0.252051i	0.992027	+	0.126025i	$0.0402221\pi$
$853$			7.36144i			0.252051i	−0.992027	+	0.126025i	$0.959778\pi$
$854$	−4.68089	+	6.04710i	−0.160177	+	0.206927i
$855$		0			0
$856$	13.0076	+	1.49218i	0.444591	+	0.0510018i
$857$	−16.7624	−	29.0332i	−0.572591	−	0.991757i	−0.996299	−	0.0859578i	$-0.972605\pi$
$857$	−16.7624	−	29.0332i	−0.572591	−	0.991757i	0.423708	−	0.905799i	$-0.360728\pi$
$858$		0			0
$859$	16.1210	+	9.30748i	0.550043	+	0.317567i	0.749139	−	0.662413i	$-0.230467\pi$
$859$	16.1210	+	9.30748i	0.550043	+	0.317567i	−0.199097	+	0.979980i	$0.563801\pi$
$860$	32.2349	+	31.5258i	1.09920	+	1.07502i
$861$		0			0
$862$	13.6777	−	33.5474i	0.465865	−	1.14263i
$863$	−1.08784	+	1.88420i	−0.0370307	+	0.0641390i	−0.883947	−	0.467588i	$-0.845123\pi$
$863$	−1.08784	+	1.88420i	−0.0370307	+	0.0641390i	0.846916	+	0.531727i	$0.178457\pi$
$864$		0			0
$865$	12.8161	+	22.1981i	0.435759	+	0.754757i
$866$	−3.28953	−	4.23799i	−0.111783	−	0.144013i
$867$		0			0
$868$	−3.60573	−	2.07539i	−0.122387	−	0.0704432i
$869$			0.169267i			0.00574199i
$870$		0			0
$871$	−2.41945	−	4.19060i	−0.0819798	−	0.141993i
$872$	−20.0327	+	27.0290i	−0.678392	+	0.915319i
$873$		0			0
$874$	59.7386	+	24.3562i	2.02069	+	0.823862i
$875$	−9.51286	+	9.32835i	−0.321593	+	0.315356i
$876$		0			0
$877$	26.2726	+	15.1685i	0.887161	+	0.512203i	0.873013	−	0.487697i	$-0.162163\pi$
$877$	26.2726	+	15.1685i	0.887161	+	0.512203i	0.0141482	+	0.999900i	$0.495496\pi$
$878$	12.5547	−	1.72393i	0.423700	−	0.0581799i
$879$		0			0
$880$	1.28049	+	0.701789i	0.0431652	+	0.0236573i
$881$	−10.1482			−0.341902			−0.170951	−	0.985280i	$-0.554684\pi$
$881$	−10.1482			−0.341902			−0.170951	+	0.985280i	$0.554684\pi$
$882$		0			0
$883$		−	16.3012i		−	0.548578i	−0.961647	−	0.274289i	$-0.911558\pi$
$883$		−	16.3012i		−	0.548578i	0.961647	−	0.274289i	$-0.0884424\pi$
$884$	−0.347467	−	1.24137i	−0.0116866	−	0.0417518i
$885$		0			0
$886$	2.56206	+	18.6584i	0.0860740	+	0.626841i
$887$	6.02108	−	10.4288i	0.202168	−	0.350165i	−0.747059	−	0.664758i	$-0.768535\pi$
$887$	6.02108	−	10.4288i	0.202168	−	0.350165i	0.949227	+	0.314593i	$0.101868\pi$
$888$		0			0
$889$	15.0451	+	15.3427i	0.504596	+	0.514576i
$890$	−32.1683	−	13.1154i	−1.07828	−	0.439630i
$891$		0			0
$892$	−6.00911	+	23.4672i	−0.201200	+	0.785741i
$893$	24.8853	−	14.3676i	0.832756	−	0.480792i
$894$		0			0
$895$	38.1992			1.27686
$896$	18.9062	+	23.2068i	0.631613	+	0.775284i
$897$		0			0
$898$	23.2295	+	29.9272i	0.775179	+	0.998685i
$899$	5.41611	−	3.12699i	0.180637	−	0.104291i
$900$		0			0
$901$	0.122899	+	0.0709560i	0.00409437	+	0.00236389i
$902$	1.21227	+	0.494258i	0.0403641	+	0.0164570i
$903$		0			0
$904$	−29.2557	+	12.6940i	−0.973031	+	0.422195i
$905$	−23.2657	+	40.2974i	−0.773379	+	1.33953i
$906$		0			0
$907$	31.2195	−	18.0246i	1.03663	−	0.598496i	0.117750	−	0.993043i	$-0.462432\pi$
$907$	31.2195	−	18.0246i	1.03663	−	0.598496i	0.918876	+	0.394547i	$0.129098\pi$
$908$	−3.73948	−	13.3598i	−0.124099	−	0.443360i
$909$		0			0
$910$	15.0447	+	11.6457i	0.498726	+	0.386050i
$911$	36.9774			1.22512			0.612558	−	0.790426i	$-0.290141\pi$
$911$	36.9774			1.22512			0.612558	+	0.790426i	$0.290141\pi$
$912$		0			0
$913$	0.0717687	+	0.124307i	0.00237520	+	0.00411396i
$914$	19.1653	−	2.63166i	0.633930	−	0.0870475i
$915$		0			0
$916$	12.2778	−	12.5540i	0.405670	−	0.414796i
$917$	7.41306	+	28.7907i	0.244801	+	0.950754i
$918$		0			0
$919$	4.10501	−	7.11009i	0.135412	−	0.234540i	−0.790343	−	0.612665i	$-0.790098\pi$
$919$	4.10501	−	7.11009i	0.135412	−	0.234540i	0.925755	+	0.378125i	$0.123431\pi$
$920$	52.1007	−	70.2967i	1.71771	−	2.31761i
$921$		0			0
$922$	−31.4003	+	24.3729i	−1.03411	+	0.802679i
$923$			13.0927i			0.430952i
$924$		0			0
$925$		−	57.5848i		−	1.89338i
$926$	−0.354279	−	0.456427i	−0.0116423	−	0.0149991i
$927$		0			0
$928$	−44.4312	+	7.11122i	−1.45853	+	0.233437i
$929$	−12.0428	+	20.8588i	−0.395112	+	0.684355i	−0.993116	−	0.117139i	$-0.962628\pi$
$929$	−12.0428	+	20.8588i	−0.395112	+	0.684355i	0.598003	+	0.801494i	$0.295961\pi$
$930$		0			0
$931$	−18.0813	+	29.9476i	−0.592591	+	0.981492i
$932$	23.4635	+	22.9473i	0.768572	+	0.751664i
$933$		0			0
$934$	3.25395	+	23.6972i	0.106473	+	0.775395i
$935$	−0.0784123	−	0.135814i	−0.00256435	−	0.00444159i
$936$		0			0
$937$	25.0333			0.817802			0.408901	−	0.912579i	$-0.365912\pi$
$937$	25.0333			0.817802			0.408901	+	0.912579i	$0.365912\pi$
$938$	−4.57088	−	11.1685i	−0.149244	−	0.364665i
$939$		0			0
$940$	−10.5051	−	37.5310i	−0.342640	−	1.22413i
$941$	−12.5109	+	7.22317i	−0.407844	+	0.235469i	−0.689863	−	0.723940i	$-0.742329\pi$
$941$	−12.5109	+	7.22317i	−0.407844	+	0.235469i	0.282019	+	0.959409i	$0.408996\pi$
$942$		0			0
$943$	39.2243	−	67.9384i	1.27732	−	2.21238i
$944$	−39.8897	+	0.887432i	−1.29830	+	0.0288835i
$945$		0			0
$946$	0.382559	−	0.938303i	0.0124381	−	0.0305069i
$947$	−5.53236	−	3.19411i	−0.179777	−	0.103795i	0.407411	−	0.913245i	$-0.366432\pi$
$947$	−5.53236	−	3.19411i	−0.179777	−	0.103795i	−0.587188	+	0.809450i	$0.699765\pi$
$948$		0			0
$949$	11.3989	−	6.58117i	0.370025	−	0.213634i
$950$	36.2111	−	28.1071i	1.17484	−	0.911914i
$951$		0			0
$952$	−0.441571	−	3.18436i	−0.0143114	−	0.103206i
$953$	−18.8800			−0.611583			−0.305791	−	0.952099i	$-0.598921\pi$
$953$	−18.8800			−0.611583			−0.305791	+	0.952099i	$0.598921\pi$
$954$		0			0
$955$	56.9355	−	32.8717i	1.84239	−	1.06370i
$956$	−0.405036	+	1.58178i	−0.0130998	+	0.0511584i
$957$		0			0
$958$	−10.4292	+	25.5797i	−0.336952	+	0.826443i
$959$	4.57067	−	16.4134i	0.147595	−	0.530015i
$960$		0			0
$961$	15.1909	−	26.3114i	0.490030	−	0.848756i
$962$	−18.6631	+	2.56271i	−0.601724	+	0.0826251i
$963$		0			0
$964$	−46.3401	+	12.9708i	−1.49251	+	0.417763i
$965$			8.66864i			0.279053i
$966$		0			0
$967$	−23.9119			−0.768954			−0.384477	−	0.923135i	$-0.625618\pi$
$967$	−23.9119			−0.768954			−0.384477	+	0.923135i	$0.625618\pi$
$968$	−3.54214	+	30.8774i	−0.113849	+	0.992436i
$969$		0			0
$970$	−12.4176	−	90.4320i	−0.398704	−	2.90360i
$971$	29.6865	+	17.1395i	0.952685	+	0.550033i	0.893914	−	0.448239i	$-0.147948\pi$
$971$	29.6865	+	17.1395i	0.952685	+	0.550033i	0.0587710	+	0.998271i	$0.481282\pi$
$972$		0			0
$973$	21.1838	−	20.7729i	0.679121	−	0.665949i
$974$	−19.0403	+	46.7001i	−0.610089	+	1.49637i
$975$		0			0
$976$	−4.24400	−	6.98717i	−0.135847	−	0.223654i
$977$	−1.82067	−	3.15350i	−0.0582485	−	0.100889i	0.835431	−	0.549596i	$-0.185218\pi$
$977$	−1.82067	−	3.15350i	−0.0582485	−	0.100889i	−0.893679	+	0.448706i	$0.851885\pi$
$978$		0			0
$979$			0.780710i			0.0249516i
$980$	33.2651	+	33.8329i	1.06261	+	1.08075i
$981$		0			0
$982$	−21.6624	+	16.8144i	−0.691276	+	0.536569i
$983$	22.4101	+	38.8154i	0.714771	+	1.23802i	0.963048	+	0.269331i	$0.0868025\pi$
$983$	22.4101	+	38.8154i	0.714771	+	1.23802i	−0.248277	+	0.968689i	$0.579864\pi$
$984$		0			0
$985$	6.49776	−	11.2544i	0.207036	−	0.358597i
$986$	4.47500	+	1.82452i	0.142513	+	0.0581045i
$987$		0			0
$988$	−10.7210	−	10.4851i	−0.341079	−	0.333576i
$989$	−52.5848	−	30.3599i	−1.67210	−	0.965388i
$990$		0			0
$991$	−23.9629	−	41.5050i	−0.761208	−	1.31845i	−0.942228	−	0.334972i	$-0.891273\pi$
$991$	−23.9629	−	41.5050i	−0.761208	−	1.31845i	0.181020	−	0.983479i	$-0.442060\pi$
$992$	3.45189	−	2.80458i	0.109597	−	0.0890455i
$993$		0			0
$994$	−4.39886	+	32.3541i	−0.139523	+	1.02621i
$995$		−	57.8356i		−	1.83351i
$996$		0			0
$997$	38.4617	−	22.2059i	1.21810	−	0.703268i	0.253585	−	0.967313i	$-0.418390\pi$
$997$	38.4617	−	22.2059i	1.21810	−	0.703268i	0.964510	+	0.264045i	$0.0850568\pi$
$998$	−2.55007	−	18.5711i	−0.0807209	−	0.587857i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cj.e.37.6		32
3.2	odd	2		168.2.bc.a.37.11	yes	32
4.3	odd	2		2016.2.cr.e.1297.3		32
7.4	even	3	inner	504.2.cj.e.109.16		32
8.3	odd	2		2016.2.cr.e.1297.14		32
8.5	even	2	inner	504.2.cj.e.37.16		32
12.11	even	2		672.2.bk.a.625.15		32
21.2	odd	6		1176.2.c.e.589.11		16
21.5	even	6		1176.2.c.f.589.11		16
21.11	odd	6		168.2.bc.a.109.1	yes	32
24.5	odd	2		168.2.bc.a.37.1	✓	32
24.11	even	2		672.2.bk.a.625.2		32
28.11	odd	6		2016.2.cr.e.1873.14		32
56.11	odd	6		2016.2.cr.e.1873.3		32
56.53	even	6	inner	504.2.cj.e.109.6		32
84.11	even	6		672.2.bk.a.529.2		32
84.23	even	6		4704.2.c.e.2353.10		16
84.47	odd	6		4704.2.c.f.2353.7		16
168.5	even	6		1176.2.c.f.589.12		16
168.11	even	6		672.2.bk.a.529.15		32
168.53	odd	6		168.2.bc.a.109.11	yes	32
168.107	even	6		4704.2.c.e.2353.7		16
168.131	odd	6		4704.2.c.f.2353.10		16
168.149	odd	6		1176.2.c.e.589.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.bc.a.37.1	✓	32	24.5	odd	2
168.2.bc.a.37.11	yes	32	3.2	odd	2
168.2.bc.a.109.1	yes	32	21.11	odd	6
168.2.bc.a.109.11	yes	32	168.53	odd	6
504.2.cj.e.37.6		32	1.1	even	1	trivial
504.2.cj.e.37.16		32	8.5	even	2	inner
504.2.cj.e.109.6		32	56.53	even	6	inner
504.2.cj.e.109.16		32	7.4	even	3	inner
672.2.bk.a.529.2		32	84.11	even	6
672.2.bk.a.529.15		32	168.11	even	6
672.2.bk.a.625.2		32	24.11	even	2
672.2.bk.a.625.15		32	12.11	even	2
1176.2.c.e.589.11		16	21.2	odd	6
1176.2.c.e.589.12		16	168.149	odd	6
1176.2.c.f.589.11		16	21.5	even	6
1176.2.c.f.589.12		16	168.5	even	6
2016.2.cr.e.1297.3		32	4.3	odd	2
2016.2.cr.e.1297.14		32	8.3	odd	2
2016.2.cr.e.1873.3		32	56.11	odd	6
2016.2.cr.e.1873.14		32	28.11	odd	6
4704.2.c.e.2353.7		16	168.107	even	6
4704.2.c.e.2353.10		16	84.23	even	6
4704.2.c.f.2353.7		16	84.47	odd	6
4704.2.c.f.2353.10		16	168.131	odd	6

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.867144 - 1.11717i) q^{2} +(-0.496121 + 1.93749i) q^{4} +(-2.93503 - 1.69454i) q^{5} +(-1.85242 - 1.88906i) q^{7} +(2.59471 - 1.12583i) q^{8} +O(q^{10})\)	\(q+(-0.867144 - 1.11717i) q^{2} +(-0.496121 + 1.93749i) q^{4} +(-2.93503 - 1.69454i) q^{5} +(-1.85242 - 1.88906i) q^{7} +(2.59471 - 1.12583i) q^{8} +(0.652012 + 4.74833i) q^{10} +(0.0932820 - 0.0538564i) q^{11} +1.50033i q^{13} +(-0.504078 + 3.70755i) q^{14} +(-3.50773 - 1.92246i) q^{16} +(0.214800 + 0.372045i) q^{17} +(4.32799 + 2.49877i) q^{19} +(4.73929 - 4.84589i) q^{20} +(-0.141056 - 0.0575103i) q^{22} +(-4.56401 + 7.90510i) q^{23} +(3.24294 + 5.61694i) q^{25} +(1.67612 - 1.30100i) q^{26} +(4.57905 - 2.65184i) q^{28} +7.95437i q^{29} +(-0.393116 - 0.680897i) q^{31} +(0.894002 + 5.58576i) q^{32} +(0.229373 - 0.562584i) q^{34} +(2.23582 + 8.68345i) q^{35} +(-7.68900 - 4.43925i) q^{37} +(-0.961455 - 7.00187i) q^{38} +(-9.52331 - 1.09248i) q^{40} -8.59425 q^{41} +6.65201i q^{43} +(0.0580670 + 0.207452i) q^{44} +(12.7890 - 1.75610i) q^{46} +(2.87493 - 4.97953i) q^{47} +(-0.137086 + 6.99866i) q^{49} +(3.46295 - 8.49360i) q^{50} +(-2.90687 - 0.744345i) q^{52} +(0.286078 - 0.165167i) q^{53} -0.365048 q^{55} +(-6.93325 - 2.81604i) q^{56} +(8.88635 - 6.89759i) q^{58} +(8.63850 - 4.98744i) q^{59} +(1.76996 + 1.02189i) q^{61} +(-0.419787 + 1.02961i) q^{62} +(5.46500 - 5.84241i) q^{64} +(2.54237 - 4.40351i) q^{65} +(-2.79312 + 1.61261i) q^{67} +(-0.827399 + 0.231594i) q^{68} +(7.76208 - 10.0276i) q^{70} +8.72656 q^{71} +(-4.38649 - 7.59762i) q^{73} +(1.70810 + 12.4394i) q^{74} +(-6.98854 + 7.14574i) q^{76} +(-0.274535 - 0.0764506i) q^{77} +(-0.785733 + 1.36093i) q^{79} +(7.03761 + 11.5865i) q^{80} +(7.45246 + 9.60121i) q^{82} +1.33259i q^{83} -1.45595i q^{85} +(7.43140 - 5.76826i) q^{86} +(0.181406 - 0.244762i) q^{88} +(-3.62404 + 6.27701i) q^{89} +(2.83421 - 2.77924i) q^{91} +(-13.0517 - 12.7646i) q^{92} +(-8.05594 + 1.10619i) q^{94} +(-8.46852 - 14.6679i) q^{95} -19.0450 q^{97} +(7.93754 - 5.91570i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8}+O(q^{10}) \) 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8	\( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 6 q^{10} - 22 q^{14} - 10 q^{16} + 40 q^{20} - 12 q^{22} + 8 q^{23} + 16 q^{25} - 6 q^{26} - 26 q^{28} - 24 q^{31} + 8 q^{32} - 24 q^{34} + 26 q^{38} - 6 q^{40} - 20 q^{44} + 16 q^{46} + 24 q^{47} + 8 q^{49} - 52 q^{50} + 44 q^{52} - 64 q^{55} - 40 q^{56} + 34 q^{58} - 100 q^{62} - 20 q^{64} - 16 q^{68} + 38 q^{70} + 80 q^{71} + 8 q^{73} - 10 q^{74} - 32 q^{76} + 8 q^{79} + 56 q^{80} + 22 q^{86} + 50 q^{88} - 64 q^{92} - 48 q^{94} - 24 q^{95} - 48 q^{97} + 64 q^{98}+O(q^{100}) \) 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 6 * q^10 - 22 * q^14 - 10 * q^16 + 40 * q^20 - 12 * q^22 + 8 * q^23 + 16 * q^25 - 6 * q^26 - 26 * q^28 - 24 * q^31 + 8 * q^32 - 24 * q^34 + 26 * q^38 - 6 * q^40 - 20 * q^44 + 16 * q^46 + 24 * q^47 + 8 * q^49 - 52 * q^50 + 44 * q^52 - 64 * q^55 - 40 * q^56 + 34 * q^58 - 100 * q^62 - 20 * q^64 - 16 * q^68 + 38 * q^70 + 80 * q^71 + 8 * q^73 - 10 * q^74 - 32 * q^76 + 8 * q^79 + 56 * q^80 + 22 * q^86 + 50 * q^88 - 64 * q^92 - 48 * q^94 - 24 * q^95 - 48 * q^97 + 64 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more