LMFDB - Embedded newform 324.3.k.a.125.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(17,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 11]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("324.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.k (of order $18$, degree $6$, not 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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			125.4
Character	$\chi$	$=$	324.125
Dual form			324.3.k.a.197.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0686711 - 0.188672i) q^{5} +(-1.47862 - 8.38565i) q^{7} +O(q^{10})$	$q+(-0.0686711 - 0.188672i) q^{5} +(-1.47862 - 8.38565i) q^{7} +(-2.58315 + 7.09715i) q^{11} +(-12.5592 - 10.5384i) q^{13} +(-5.21882 - 3.01309i) q^{17} +(-0.189946 - 0.328995i) q^{19} +(-27.6819 - 4.88107i) q^{23} +(19.1202 - 16.0438i) q^{25} +(-26.6332 - 31.7402i) q^{29} +(2.35612 - 13.3622i) q^{31} +(-1.48060 + 0.854825i) q^{35} +(-2.26190 + 3.91773i) q^{37} +(49.3383 - 58.7991i) q^{41} +(1.63966 + 0.596788i) q^{43} +(-75.3795 + 13.2914i) q^{47} +(-22.0879 + 8.03934i) q^{49} +85.8739i q^{53} +1.51642 q^{55} +(-6.23410 - 17.1281i) q^{59} +(-6.51665 - 36.9578i) q^{61} +(-1.12585 + 3.09326i) q^{65} +(-53.9204 - 45.2446i) q^{67} +(38.9179 + 22.4692i) q^{71} +(51.2495 + 88.7667i) q^{73} +(63.3337 + 11.1674i) q^{77} +(64.7058 - 54.2946i) q^{79} +(44.2042 + 52.6805i) q^{83} +(-0.210104 + 1.19156i) q^{85} +(119.245 - 68.8461i) q^{89} +(-69.8014 + 120.900i) q^{91} +(-0.0490285 + 0.0584299i) q^{95} +(112.916 + 41.0979i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 9 q^{5}+O(q^{10}) $ 36 * q + 9 * q^5	$ 36 q + 9 q^{5} - 36 q^{11} + 18 q^{23} - 9 q^{25} + 18 q^{29} + 45 q^{31} + 243 q^{35} + 198 q^{41} + 90 q^{43} + 243 q^{47} + 72 q^{49} - 252 q^{59} - 144 q^{61} - 747 q^{65} + 108 q^{67} - 324 q^{71} - 63 q^{73} - 495 q^{77} + 36 q^{79} + 27 q^{83} - 180 q^{85} + 567 q^{89} + 99 q^{91} + 1044 q^{95} - 216 q^{97}+O(q^{100}) $ 36 * q + 9 * q^5 - 36 * q^11 + 18 * q^23 - 9 * q^25 + 18 * q^29 + 45 * q^31 + 243 * q^35 + 198 * q^41 + 90 * q^43 + 243 * q^47 + 72 * q^49 - 252 * q^59 - 144 * q^61 - 747 * q^65 + 108 * q^67 - 324 * q^71 - 63 * q^73 - 495 * q^77 + 36 * q^79 + 27 * q^83 - 180 * q^85 + 567 * q^89 + 99 * q^91 + 1044 * q^95 - 216 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{5}{18}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.0686711	−	0.188672i	−0.0137342	−	0.0377344i	0.932636	−	0.360818i	$-0.117503\pi$
$5$	−0.0686711	−	0.188672i	−0.0137342	−	0.0377344i	−0.946370	+	0.323084i	$0.895280\pi$
$6$		0			0
$7$	−1.47862	−	8.38565i	−0.211231	−	1.19795i	−0.887328	−	0.461138i	$-0.847441\pi$
$7$	−1.47862	−	8.38565i	−0.211231	−	1.19795i	0.676098	−	0.736812i	$-0.263670\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.58315	+	7.09715i	−0.234832	+	0.645195i	0.765167	+	0.643832i	$0.222656\pi$
$11$	−2.58315	+	7.09715i	−0.234832	+	0.645195i	−0.999999	+	0.00136376i	$0.999566\pi$
$12$		0			0
$13$	−12.5592	−	10.5384i	−0.966094	−	0.810649i	0.0158399	−	0.999875i	$-0.494958\pi$
$13$	−12.5592	−	10.5384i	−0.966094	−	0.810649i	−0.981934	+	0.189226i	$0.939402\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.21882	−	3.01309i	−0.306990	−	0.177241i	0.338589	−	0.940934i	$-0.390050\pi$
$17$	−5.21882	−	3.01309i	−0.306990	−	0.177241i	−0.645579	+	0.763694i	$0.723384\pi$
$18$		0			0
$19$	−0.189946	−	0.328995i	−0.00999714	−	0.0173155i	0.860984	−	0.508633i	$-0.169849\pi$
$19$	−0.189946	−	0.328995i	−0.00999714	−	0.0173155i	−0.870981	+	0.491317i	$0.836516\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−27.6819	−	4.88107i	−1.20356	−	0.212220i	−0.464324	−	0.885665i	$-0.653703\pi$
$23$	−27.6819	−	4.88107i	−1.20356	−	0.212220i	−0.739238	+	0.673445i	$0.764814\pi$
$24$		0			0
$25$	19.1202	−	16.0438i	0.764809	−	0.641751i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−26.6332	−	31.7402i	−0.918387	−	1.09449i	−0.995241	−	0.0974484i	$-0.968932\pi$
$29$	−26.6332	−	31.7402i	−0.918387	−	1.09449i	0.0768538	−	0.997042i	$-0.475513\pi$
$30$		0			0
$31$	2.35612	−	13.3622i	0.0760038	−	0.431039i	−0.922934	−	0.384959i	$-0.874216\pi$
$31$	2.35612	−	13.3622i	0.0760038	−	0.431039i	0.998938	−	0.0460807i	$-0.0146731\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.48060	+	0.854825i	−0.0423029	+	0.0244236i
$36$		0			0
$37$	−2.26190	+	3.91773i	−0.0611325	+	0.105885i	−0.894972	−	0.446122i	$-0.852805\pi$
$37$	−2.26190	+	3.91773i	−0.0611325	+	0.105885i	0.833839	+	0.552007i	$0.186138\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	49.3383	−	58.7991i	1.20337	−	1.43412i	0.332156	−	0.943225i	$-0.392224\pi$
$41$	49.3383	−	58.7991i	1.20337	−	1.43412i	0.871217	−	0.490899i	$-0.163332\pi$
$42$		0			0
$43$	1.63966	+	0.596788i	0.0381317	+	0.0138788i	0.361016	−	0.932560i	$-0.382430\pi$
$43$	1.63966	+	0.596788i	0.0381317	+	0.0138788i	−0.322884	+	0.946439i	$0.604652\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−75.3795	+	13.2914i	−1.60382	+	0.282797i	−0.902708	−	0.430255i	$-0.858424\pi$
$47$	−75.3795	+	13.2914i	−1.60382	+	0.282797i	−0.701112	+	0.713051i	$0.747313\pi$
$48$		0			0
$49$	−22.0879	+	8.03934i	−0.450773	+	0.164068i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			85.8739i			1.62026i	0.586249	+	0.810131i	$0.300604\pi$
$53$			85.8739i			1.62026i	−0.586249	+	0.810131i	$0.699396\pi$
$54$		0			0
$55$	1.51642			0.0275713
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.23410	−	17.1281i	−0.105663	−	0.290306i	0.875583	−	0.483068i	$-0.160478\pi$
$59$	−6.23410	−	17.1281i	−0.105663	−	0.290306i	−0.981246	+	0.192762i	$0.938255\pi$
$60$		0			0
$61$	−6.51665	−	36.9578i	−0.106830	−	0.605865i	−0.990473	−	0.137704i	$-0.956028\pi$
$61$	−6.51665	−	36.9578i	−0.106830	−	0.605865i	0.883643	−	0.468161i	$-0.155083\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.12585	+	3.09326i	−0.0173208	+	0.0475886i
$66$		0			0
$67$	−53.9204	−	45.2446i	−0.804783	−	0.675293i	0.144574	−	0.989494i	$-0.453819\pi$
$67$	−53.9204	−	45.2446i	−0.804783	−	0.675293i	−0.949356	+	0.314201i	$0.898263\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	38.9179	+	22.4692i	0.548139	+	0.316468i	0.748371	−	0.663280i	$-0.230836\pi$
$71$	38.9179	+	22.4692i	0.548139	+	0.316468i	−0.200232	+	0.979748i	$0.564170\pi$
$72$		0			0
$73$	51.2495	+	88.7667i	0.702047	+	1.21598i	0.967747	+	0.251926i	$0.0810639\pi$
$73$	51.2495	+	88.7667i	0.702047	+	1.21598i	−0.265699	+	0.964056i	$0.585603\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	63.3337	+	11.1674i	0.822516	+	0.145032i
$78$		0			0
$79$	64.7058	−	54.2946i	0.819060	−	0.687273i	−0.133692	−	0.991023i	$-0.542683\pi$
$79$	64.7058	−	54.2946i	0.819060	−	0.687273i	0.952752	+	0.303750i	$0.0982387\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	44.2042	+	52.6805i	0.532580	+	0.634704i	0.963507	−	0.267682i	$-0.0862578\pi$
$83$	44.2042	+	52.6805i	0.532580	+	0.634704i	−0.430927	+	0.902387i	$0.641813\pi$
$84$		0			0
$85$	−0.210104	+	1.19156i	−0.00247181	+	0.0140183i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	119.245	−	68.8461i	1.33983	−	0.773551i	0.353048	−	0.935605i	$-0.385145\pi$
$89$	119.245	−	68.8461i	1.33983	−	0.773551i	0.986782	+	0.162054i	$0.0518118\pi$
$90$		0			0
$91$	−69.8014	+	120.900i	−0.767048	+	1.32857i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.0490285	+	0.0584299i	−0.000516090	+	0.000615052i
$96$		0			0
$97$	112.916	+	41.0979i	1.16408	+	0.423690i	0.850553	−	0.525889i	$-0.176267\pi$
$97$	112.916	+	41.0979i	1.16408	+	0.423690i	0.313526	+	0.949580i	$0.398490\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−13.1189	+	2.31321i	−0.129890	+	0.0229031i	−0.238215	−	0.971212i	$-0.576562\pi$
$101$	−13.1189	+	2.31321i	−0.129890	+	0.0229031i	0.108325	+	0.994116i	$0.465451\pi$
$102$		0			0
$103$	−183.161	+	66.6652i	−1.77826	+	0.647235i	−0.778454	+	0.627702i	$0.783996\pi$
$103$	−183.161	+	66.6652i	−1.77826	+	0.647235i	−0.999809	+	0.0195327i	$0.993782\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			155.702i			1.45516i	0.686024	+	0.727579i	$0.259355\pi$
$107$			155.702i			1.45516i	−0.686024	+	0.727579i	$0.740645\pi$
$108$		0			0
$109$	70.1664			0.643729			0.321864	−	0.946786i	$-0.395691\pi$
$109$	70.1664			0.643729			0.321864	+	0.946786i	$0.395691\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−35.8589	−	98.5216i	−0.317336	−	0.871873i	−0.991123	−	0.132947i	$-0.957556\pi$
$113$	−35.8589	−	98.5216i	−0.317336	−	0.871873i	0.673787	−	0.738925i	$-0.264666\pi$
$114$		0			0
$115$	0.980025	+	5.55800i	0.00852196	+	0.0483304i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−17.5501	+	48.2184i	−0.147480	+	0.405197i
$120$		0			0
$121$	48.9945	+	41.1113i	0.404913	+	0.339763i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−8.68705	−	5.01547i	−0.0694964	−	0.0401238i
$126$		0			0
$127$	77.8451	+	134.832i	0.612954	+	1.06167i	0.990740	+	0.135774i	$0.0433521\pi$
$127$	77.8451	+	134.832i	0.612954	+	1.06167i	−0.377786	+	0.925893i	$0.623315\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	140.642	+	24.7989i	1.07360	+	0.189305i	0.682383	−	0.730994i	$-0.260943\pi$
$131$	140.642	+	24.7989i	1.07360	+	0.189305i	0.391216	+	0.920299i	$0.372055\pi$
$132$		0			0
$133$	−2.47798	+	2.07928i	−0.0186315	+	0.0156336i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−123.444	−	147.114i	−0.901048	−	1.07383i	−0.996919	−	0.0784331i	$-0.975008\pi$
$137$	−123.444	−	147.114i	−0.901048	−	1.07383i	0.0958717	−	0.995394i	$-0.469436\pi$
$138$		0			0
$139$	−12.4043	+	70.3485i	−0.0892398	+	0.506104i	0.907121	+	0.420870i	$0.138275\pi$
$139$	−12.4043	+	70.3485i	−0.0892398	+	0.506104i	−0.996361	+	0.0852345i	$0.972836\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	107.235	−	61.9123i	0.749897	−	0.432953i
$144$		0			0
$145$	−4.15957	+	7.20458i	−0.0286867	+	0.0496868i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	64.1576	−	76.4600i	0.430588	−	0.513155i	−0.506504	−	0.862238i	$-0.669062\pi$
$149$	64.1576	−	76.4600i	0.430588	−	0.513155i	0.937092	+	0.349083i	$0.113507\pi$
$150$		0			0
$151$	−91.0224	−	33.1295i	−0.602797	−	0.219400i	0.0225513	−	0.999746i	$-0.492821\pi$
$151$	−91.0224	−	33.1295i	−0.602797	−	0.219400i	−0.625349	+	0.780345i	$0.715043\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−2.68288	+	0.473063i	−0.0173089	+	0.00305202i
$156$		0			0
$157$	225.856	−	82.2049i	1.43857	−	0.523598i	0.499198	−	0.866488i	$-0.333628\pi$
$157$	225.856	−	82.2049i	1.43857	−	0.523598i	0.939376	+	0.342890i	$0.111406\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			239.348i			1.48663i
$162$		0			0
$163$	−58.5417			−0.359152			−0.179576	−	0.983744i	$-0.557473\pi$
$163$	−58.5417			−0.359152			−0.179576	+	0.983744i	$0.557473\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−22.4027	−	61.5510i	−0.134148	−	0.368569i	0.854371	−	0.519663i	$-0.173943\pi$
$167$	−22.4027	−	61.5510i	−0.134148	−	0.368569i	−0.988519	+	0.151094i	$0.951720\pi$
$168$		0			0
$169$	17.3288	+	98.2765i	0.102537	+	0.581518i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−25.8686	+	71.0734i	−0.149530	+	0.410829i	−0.991731	−	0.128334i	$-0.959037\pi$
$173$	−25.8686	+	71.0734i	−0.149530	+	0.410829i	0.842201	+	0.539163i	$0.181259\pi$
$174$		0			0
$175$	−162.809	−	136.613i	−0.930337	−	0.780646i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−259.614	−	149.888i	−1.45035	−	0.837363i	−0.451854	−	0.892092i	$-0.649237\pi$
$179$	−259.614	−	149.888i	−1.45035	−	0.837363i	−0.998501	+	0.0547292i	$0.982570\pi$
$180$		0			0
$181$	−148.560	−	257.314i	−0.820774	−	1.42162i	−0.905107	−	0.425184i	$-0.860209\pi$
$181$	−148.560	−	257.314i	−0.820774	−	1.42162i	0.0843330	−	0.996438i	$-0.473124\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.894495	+	0.157724i	0.00483511	+	0.000852560i
$186$		0			0
$187$	34.8654	−	29.2555i	0.186446	−	0.156447i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	52.6139	+	62.7028i	0.275466	+	0.328287i	0.885985	−	0.463714i	$-0.153484\pi$
$191$	52.6139	+	62.7028i	0.275466	+	0.328287i	−0.610519	+	0.792001i	$0.709039\pi$
$192$		0			0
$193$	20.4421	−	115.933i	0.105918	−	0.600688i	−0.884932	−	0.465720i	$-0.845796\pi$
$193$	20.4421	−	115.933i	0.105918	−	0.600688i	0.990850	−	0.134968i	$-0.0430933\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	69.8603	−	40.3339i	0.354621	−	0.204740i	−0.312098	−	0.950050i	$-0.601032\pi$
$197$	69.8603	−	40.3339i	0.354621	−	0.204740i	0.666719	+	0.745310i	$0.267698\pi$
$198$		0			0
$199$	87.9561	−	152.345i	0.441991	−	0.765550i	−0.555846	−	0.831285i	$-0.687606\pi$
$199$	87.9561	−	152.345i	0.441991	−	0.765550i	0.997837	+	0.0657347i	$0.0209391\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−226.782	+	270.268i	−1.11715	+	1.33137i
$204$		0			0
$205$	−14.4819	−	5.27097i	−0.0706432	−	0.0257120i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.82559	−	0.498227i	0.0135196	−	0.00238386i
$210$		0			0
$211$	−34.0107	+	12.3789i	−0.161188	+	0.0586678i	−0.421354	−	0.906896i	$-0.638445\pi$
$211$	−34.0107	+	12.3789i	−0.161188	+	0.0586678i	0.260166	+	0.965564i	$0.416223\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	0.350341i		−	0.00162949i
$216$		0			0
$217$	−115.535			−0.532418
$218$		0			0
$219$		0			0
$220$		0			0
$221$	33.7911	+	92.8403i	0.152901	+	0.420092i
$222$		0			0
$223$	−70.0960	−	397.534i	−0.314332	−	1.78266i	−0.575942	−	0.817490i	$-0.695365\pi$
$223$	−70.0960	−	397.534i	−0.314332	−	1.78266i	0.261611	−	0.965174i	$-0.415746\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	59.9958	−	164.837i	0.264299	−	0.726155i	−0.734567	−	0.678536i	$-0.762615\pi$
$227$	59.9958	−	164.837i	0.264299	−	0.726155i	0.998866	−	0.0476187i	$-0.0151632\pi$
$228$		0			0
$229$	102.807	+	86.2654i	0.448939	+	0.376705i	0.839042	−	0.544066i	$-0.183116\pi$
$229$	102.807	+	86.2654i	0.448939	+	0.376705i	−0.390103	+	0.920771i	$0.627561\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−342.572	−	197.784i	−1.47027	−	0.848858i	−0.470823	−	0.882228i	$-0.656043\pi$
$233$	−342.572	−	197.784i	−1.47027	−	0.848858i	−0.999443	+	0.0333693i	$0.989376\pi$
$234$		0			0
$235$	7.68412	+	13.3093i	0.0326984	+	0.0566352i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−442.556	−	78.0346i	−1.85170	−	0.326504i	−0.866668	−	0.498885i	$-0.833743\pi$
$239$	−442.556	−	78.0346i	−1.85170	−	0.326504i	−0.985030	+	0.172380i	$0.944854\pi$
$240$		0			0
$241$	−174.607	+	146.513i	−0.724511	+	0.607937i	−0.928629	−	0.371009i	$-0.879012\pi$
$241$	−174.607	+	146.513i	−0.724511	+	0.607937i	0.204118	+	0.978946i	$0.434567\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3.03360	+	3.61530i	0.0123820	+	0.0147563i
$246$		0			0
$247$	−1.08153	+	6.13365i	−0.00437866	+	0.0248326i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	307.522	−	177.548i	1.22519	−	0.707362i	0.259167	−	0.965832i	$-0.416552\pi$
$251$	307.522	−	177.548i	1.22519	−	0.707362i	0.966019	+	0.258471i	$0.0832186\pi$
$252$		0			0
$253$	106.148	−	183.854i	0.419558	−	0.726697i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	122.816	−	146.366i	0.477883	−	0.569519i	−0.472210	−	0.881486i	$-0.656544\pi$
$257$	122.816	−	146.366i	0.477883	−	0.569519i	0.950093	+	0.311968i	$0.100988\pi$
$258$		0			0
$259$	36.1972	+	13.1747i	0.139758	+	0.0508676i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	59.8335	−	10.5503i	0.227504	−	0.0401150i	−0.0587341	−	0.998274i	$-0.518706\pi$
$263$	59.8335	−	10.5503i	0.227504	−	0.0401150i	0.286238	+	0.958159i	$0.407595\pi$
$264$		0			0
$265$	16.2020	−	5.89705i	0.0611397	−	0.0222530i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			1.02338i			0.00380438i	0.999998	+	0.00190219i	$0.000605486\pi$
$269$			1.02338i			0.00380438i	−0.999998	+	0.00190219i	$0.999395\pi$
$270$		0			0
$271$	264.552			0.976205			0.488102	−	0.872786i	$-0.337689\pi$
$271$	264.552			0.976205			0.488102	+	0.872786i	$0.337689\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	64.4747	+	177.143i	0.234453	+	0.644155i
$276$		0			0
$277$	63.0965	+	357.838i	0.227785	+	1.29183i	0.857288	+	0.514837i	$0.172147\pi$
$277$	63.0965	+	357.838i	0.227785	+	1.29183i	−0.629503	+	0.776998i	$0.716742\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	64.8213	−	178.095i	0.230681	−	0.633790i	−0.769306	−	0.638880i	$-0.779398\pi$
$281$	64.8213	−	178.095i	0.230681	−	0.633790i	0.999987	+	0.00509010i	$0.00162023\pi$
$282$		0			0
$283$	219.711	+	184.359i	0.776364	+	0.651447i	0.942330	−	0.334685i	$-0.108630\pi$
$283$	219.711	+	184.359i	0.776364	+	0.651447i	−0.165966	+	0.986131i	$0.553074\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−566.021	−	326.792i	−1.97220	−	1.13865i
$288$		0			0
$289$	−126.343	−	218.832i	−0.437172	−	0.757203i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−197.305	−	34.7903i	−0.673397	−	0.118738i	−0.173515	−	0.984831i	$-0.555512\pi$
$293$	−197.305	−	34.7903i	−0.673397	−	0.118738i	−0.499883	+	0.866093i	$0.666624\pi$
$294$		0			0
$295$	−2.80348	+	2.35240i	−0.00950334	+	0.00797425i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	296.225	+	353.027i	0.990717	+	1.18069i
$300$		0			0
$301$	2.58003	−	14.6321i	0.00857152	−	0.0486115i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−6.52540	+	3.76744i	−0.0213948	+	0.0123523i
$306$		0			0
$307$	−87.7799	+	152.039i	−0.285928	+	0.495242i	−0.972834	−	0.231505i	$-0.925635\pi$
$307$	−87.7799	+	152.039i	−0.285928	+	0.495242i	0.686906	+	0.726746i	$0.258968\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−92.2362	+	109.923i	−0.296579	+	0.353450i	−0.893670	−	0.448724i	$-0.851879\pi$
$311$	−92.2362	+	109.923i	−0.296579	+	0.353450i	0.597091	+	0.802174i	$0.296323\pi$
$312$		0			0
$313$	−469.902	−	171.030i	−1.50128	−	0.546422i	−0.544891	−	0.838507i	$-0.683429\pi$
$313$	−469.902	−	171.030i	−1.50128	−	0.546422i	−0.956392	+	0.292085i	$0.905651\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	159.214	−	28.0736i	0.502251	−	0.0885604i	0.0832179	−	0.996531i	$-0.473480\pi$
$317$	159.214	−	28.0736i	0.502251	−	0.0885604i	0.419033	+	0.907971i	$0.362369\pi$
$318$		0			0
$319$	294.063	−	107.030i	0.921827	−	0.335518i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			2.28929i			0.00708759i
$324$		0			0
$325$	−409.211			−1.25911
$326$		0			0
$327$		0			0
$328$		0			0
$329$	222.915	+	612.453i	0.677553	+	1.86156i
$330$		0			0
$331$	79.9019	+	453.146i	0.241396	+	1.36902i	0.828717	+	0.559668i	$0.189072\pi$
$331$	79.9019	+	453.146i	0.241396	+	1.36902i	−0.587321	+	0.809354i	$0.699817\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−4.83363	+	13.2803i	−0.0144287	+	0.0396426i
$336$		0			0
$337$	262.855	+	220.561i	0.779984	+	0.654484i	0.943245	−	0.332099i	$-0.107757\pi$
$337$	262.855	+	220.561i	0.779984	+	0.654484i	−0.163261	+	0.986583i	$0.552201\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	88.7474	+	51.2384i	0.260256	+	0.150259i
$342$		0			0
$343$	−108.543	−	188.002i	−0.316453	−	0.548112i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	270.540	+	47.7035i	0.779653	+	0.137474i	0.549291	−	0.835631i	$-0.314898\pi$
$347$	270.540	+	47.7035i	0.779653	+	0.137474i	0.230362	+	0.973105i	$0.426009\pi$
$348$		0			0
$349$	−377.022	+	316.359i	−1.08029	+	0.906473i	−0.995945	−	0.0899629i	$-0.971325\pi$
$349$	−377.022	+	316.359i	−1.08029	+	0.906473i	−0.0843479	+	0.996436i	$0.526881\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−71.2407	−	84.9014i	−0.201815	−	0.240514i	0.655639	−	0.755075i	$-0.272399\pi$
$353$	−71.2407	−	84.9014i	−0.201815	−	0.240514i	−0.857454	+	0.514561i	$0.827955\pi$
$354$		0			0
$355$	1.56679	−	8.88570i	0.00441349	−	0.0250302i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	480.926	−	277.663i	1.33963	−	0.773433i	0.352874	−	0.935671i	$-0.385204\pi$
$359$	480.926	−	277.663i	1.33963	−	0.773433i	0.986752	+	0.162237i	$0.0518711\pi$
$360$		0			0
$361$	180.428	−	312.510i	0.499800	−	0.865679i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	13.2284	−	15.7650i	0.0362423	−	0.0431919i
$366$		0			0
$367$	374.715	+	136.385i	1.02102	+	0.371622i	0.797656	−	0.603113i	$-0.206073\pi$
$367$	374.715	+	136.385i	1.02102	+	0.371622i	0.223367	+	0.974734i	$0.428295\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	720.108	−	126.975i	1.94099	−	0.342249i
$372$		0			0
$373$	189.416	−	68.9418i	0.507818	−	0.184830i	−0.0753893	−	0.997154i	$-0.524020\pi$
$373$	189.416	−	68.9418i	0.507818	−	0.184830i	0.583207	+	0.812324i	$0.301798\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			679.305i			1.80187i
$378$		0			0
$379$	135.501			0.357522			0.178761	−	0.983892i	$-0.442791\pi$
$379$	135.501			0.357522			0.178761	+	0.983892i	$0.442791\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−82.3154	−	226.160i	−0.214923	−	0.590495i	0.784643	−	0.619947i	$-0.212846\pi$
$383$	−82.3154	−	226.160i	−0.214923	−	0.590495i	−0.999566	+	0.0294519i	$0.990624\pi$
$384$		0			0
$385$	−2.24221	−	12.7162i	−0.00582392	−	0.0330291i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−34.2832	+	94.1925i	−0.0881317	+	0.242140i	−0.975927	−	0.218100i	$-0.930014\pi$
$389$	−34.2832	+	94.1925i	−0.0881317	+	0.242140i	0.887795	+	0.460240i	$0.152236\pi$
$390$		0			0
$391$	129.760	+	108.882i	0.331867	+	0.278469i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−14.6873	−	8.47971i	−0.0371830	−	0.0214676i
$396$		0			0
$397$	−31.5616	−	54.6663i	−0.0795003	−	0.137699i	0.823534	−	0.567267i	$-0.191999\pi$
$397$	−31.5616	−	54.6663i	−0.0795003	−	0.137699i	−0.903034	+	0.429568i	$0.858666\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	382.225	+	67.3965i	0.953178	+	0.168071i	0.628549	−	0.777770i	$-0.283649\pi$
$401$	382.225	+	67.3965i	0.953178	+	0.168071i	0.324630	+	0.945841i	$0.394760\pi$
$402$		0			0
$403$	−170.408	+	142.989i	−0.422848	+	0.354812i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−21.9619	−	26.1732i	−0.0539604	−	0.0643075i
$408$		0			0
$409$	−90.7835	+	514.859i	−0.221965	+	1.25882i	0.646439	+	0.762966i	$0.276258\pi$
$409$	−90.7835	+	514.859i	−0.221965	+	1.25882i	−0.868404	+	0.495858i	$0.834854\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−134.412	+	77.6028i	−0.325453	+	0.187900i
$414$		0			0
$415$	6.90379	−	11.9577i	0.0166356	−	0.0288138i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−324.985	+	387.301i	−0.775619	+	0.924347i	−0.998727	−	0.0504466i	$-0.983936\pi$
$419$	−324.985	+	387.301i	−0.775619	+	0.924347i	0.223107	+	0.974794i	$0.428380\pi$
$420$		0			0
$421$	−61.4522	−	22.3668i	−0.145967	−	0.0531277i	0.268003	−	0.963418i	$-0.413636\pi$
$421$	−61.4522	−	22.3668i	−0.145967	−	0.0531277i	−0.413971	+	0.910290i	$0.635858\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−148.126	+	26.1187i	−0.348533	+	0.0614557i
$426$		0			0
$427$	−300.279	+	109.293i	−0.703230	+	0.255955i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	449.973i		−	1.04402i	−0.852939	−	0.522010i	$-0.825182\pi$
$431$		−	449.973i		−	1.04402i	0.852939	−	0.522010i	$-0.174818\pi$
$432$		0			0
$433$	57.6415			0.133121			0.0665606	−	0.997782i	$-0.478797\pi$
$433$	57.6415			0.133121			0.0665606	+	0.997782i	$0.478797\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	3.65221	+	10.0344i	0.00835746	+	0.0229619i
$438$		0			0
$439$	−40.0913	−	227.369i	−0.0913241	−	0.517925i	−0.995812	−	0.0914252i	$-0.970858\pi$
$439$	−40.0913	−	227.369i	−0.0913241	−	0.517925i	0.904488	−	0.426499i	$-0.140253\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−97.4032	+	267.613i	−0.219872	+	0.604093i	−0.999762	−	0.0218237i	$-0.993053\pi$
$443$	−97.4032	+	267.613i	−0.219872	+	0.604093i	0.779890	+	0.625917i	$0.215275\pi$
$444$		0			0
$445$	−21.1780	−	17.7705i	−0.0475910	−	0.0399336i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−249.959	−	144.314i	−0.556701	−	0.321412i	0.195119	−	0.980780i	$-0.437491\pi$
$449$	−249.959	−	144.314i	−0.556701	−	0.321412i	−0.751821	+	0.659368i	$0.770824\pi$
$450$		0			0
$451$	289.858	+	502.048i	0.642700	+	1.11319i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	27.6037	+	4.86728i	0.0606675	+	0.0106973i
$456$		0			0
$457$	57.0131	−	47.8396i	0.124755	−	0.104682i	−0.578276	−	0.815842i	$-0.696274\pi$
$457$	57.0131	−	47.8396i	0.124755	−	0.104682i	0.703031	+	0.711160i	$0.251830\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	81.2197	+	96.7939i	0.176182	+	0.209965i	0.846907	−	0.531740i	$-0.178462\pi$
$461$	81.2197	+	96.7939i	0.176182	+	0.209965i	−0.670726	+	0.741705i	$0.734017\pi$
$462$		0			0
$463$	7.85137	−	44.5273i	0.0169576	−	0.0961713i	−0.975154	−	0.221527i	$-0.928896\pi$
$463$	7.85137	−	44.5273i	0.0169576	−	0.0961713i	0.992112	+	0.125355i	$0.0400071\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	395.495	−	228.339i	0.846884	−	0.488949i	−0.0127140	−	0.999919i	$-0.504047\pi$
$467$	395.495	−	228.339i	0.846884	−	0.488949i	0.859598	+	0.510970i	$0.170714\pi$
$468$		0			0
$469$	−299.678	+	519.057i	−0.638972	+	1.10673i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−8.47099	+	10.0953i	−0.0179091	+	0.0213432i
$474$		0			0
$475$	−8.91013	−	3.24302i	−0.0187582	−	0.00682742i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	370.216	−	65.2790i	0.772893	−	0.136282i	0.226726	−	0.973959i	$-0.427198\pi$
$479$	370.216	−	65.2790i	0.772893	−	0.136282i	0.546166	+	0.837677i	$0.316087\pi$
$480$		0			0
$481$	69.6945	−	25.3667i	0.144895	−	0.0527375i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	24.1263i		−	0.0497449i
$486$		0			0
$487$	51.3988			0.105542			0.0527708	−	0.998607i	$-0.483195\pi$
$487$	51.3988			0.105542			0.0527708	+	0.998607i	$0.483195\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−254.558	−	699.393i	−0.518449	−	1.42443i	−0.872229	−	0.489098i	$-0.837326\pi$
$491$	−254.558	−	699.393i	−0.518449	−	1.42443i	0.353780	−	0.935329i	$-0.384896\pi$
$492$		0			0
$493$	43.3579	+	245.895i	0.0879471	+	0.498773i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	130.875	−	359.575i	0.263329	−	0.723491i
$498$		0			0
$499$	−292.343	−	245.305i	−0.585858	−	0.491593i	0.301007	−	0.953622i	$-0.402677\pi$
$499$	−292.343	−	245.305i	−0.585858	−	0.491593i	−0.886865	+	0.462029i	$0.847122\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−169.431	−	97.8211i	−0.336841	−	0.194475i	0.322033	−	0.946728i	$-0.395634\pi$
$503$	−169.431	−	97.8211i	−0.336841	−	0.194475i	−0.658874	+	0.752253i	$0.728967\pi$
$504$		0			0
$505$	1.33733	+	2.31632i	0.00264817	+	0.00458677i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−429.935	−	75.8091i	−0.844666	−	0.148937i	−0.265463	−	0.964121i	$-0.585525\pi$
$509$	−429.935	−	75.8091i	−0.844666	−	0.148937i	−0.579203	+	0.815184i	$0.696636\pi$
$510$		0			0
$511$	668.588	−	561.012i	1.30839	−	1.09787i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	25.1557	+	29.9794i	0.0488461	+	0.0582125i
$516$		0			0
$517$	100.385	−	569.314i	0.194169	−	1.10119i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−253.777	+	146.518i	−0.487097	+	0.281226i	−0.723369	−	0.690461i	$-0.757408\pi$
$521$	−253.777	+	146.518i	−0.487097	+	0.281226i	0.236272	+	0.971687i	$0.424074\pi$
$522$		0			0
$523$	166.756	−	288.830i	0.318845	−	0.552256i	−0.661402	−	0.750032i	$-0.730038\pi$
$523$	166.756	−	288.830i	0.318845	−	0.552256i	0.980247	+	0.197775i	$0.0633716\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−52.5577	+	62.6358i	−0.0997300	+	0.118854i
$528$		0			0
$529$	245.367	+	89.3062i	0.463831	+	0.168821i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1239.30	+	218.522i	−2.32514	+	0.409985i
$534$		0			0
$535$	29.3766	−	10.6922i	0.0549096	−	0.0199855i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	177.528i		−	0.329365i
$540$		0			0
$541$	−51.1409			−0.0945304			−0.0472652	−	0.998882i	$-0.515051\pi$
$541$	−51.1409			−0.0945304			−0.0472652	+	0.998882i	$0.515051\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−4.81840	−	13.2385i	−0.00884110	−	0.0242907i
$546$		0			0
$547$	−78.2579	−	443.823i	−0.143068	−	0.811376i	−0.968898	−	0.247459i	$-0.920405\pi$
$547$	−78.2579	−	443.823i	−0.143068	−	0.811376i	0.825831	−	0.563918i	$-0.190707\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−5.38353	+	14.7911i	−0.00977047	+	0.0268441i
$552$		0			0
$553$	−550.970	−	462.319i	−0.996330	−	0.836020i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	255.303	+	147.399i	0.458354	+	0.264631i	0.711352	−	0.702836i	$-0.248083\pi$
$557$	255.303	+	147.399i	0.458354	+	0.264631i	−0.252998	+	0.967467i	$0.581417\pi$
$558$		0			0
$559$	−14.3037	−	24.7747i	−0.0255880	−	0.0443196i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	570.607	+	100.613i	1.01351	+	0.178709i	0.655650	−	0.755065i	$-0.272395\pi$
$563$	570.607	+	100.613i	1.01351	+	0.178709i	0.357861	+	0.933775i	$0.383506\pi$
$564$		0			0
$565$	−16.1258	+	13.5312i	−0.0285413	+	0.0239490i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−134.264	−	160.010i	−0.235965	−	0.281212i	0.635047	−	0.772473i	$-0.280981\pi$
$569$	−134.264	−	160.010i	−0.235965	−	0.281212i	−0.871012	+	0.491261i	$0.836536\pi$
$570$		0			0
$571$	−83.0575	+	471.043i	−0.145460	+	0.824943i	0.821537	+	0.570155i	$0.193117\pi$
$571$	−83.0575	+	471.043i	−0.145460	+	0.824943i	−0.966997	+	0.254788i	$0.917994\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−607.596	+	350.795i	−1.05669	+	0.610079i
$576$		0			0
$577$	94.3702	−	163.454i	0.163553	−	0.283282i	−0.772587	−	0.634908i	$-0.781038\pi$
$577$	94.3702	−	163.454i	0.163553	−	0.283282i	0.936141	+	0.351626i	$0.114371\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	376.399	−	448.575i	0.647847	−	0.772074i
$582$		0			0
$583$	−609.460	−	221.825i	−1.04539	−	0.380489i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−563.429	+	99.3478i	−0.959846	+	0.169247i	−0.631556	−	0.775330i	$-0.717583\pi$
$587$	−563.429	+	99.3478i	−0.959846	+	0.169247i	−0.328290	+	0.944577i	$0.606472\pi$
$588$		0			0
$589$	−4.84364	+	1.76294i	−0.00822350	+	0.00299311i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			1075.40i			1.81349i	0.421682	+	0.906744i	$0.361440\pi$
$593$			1075.40i			1.81349i	−0.421682	+	0.906744i	$0.638560\pi$
$594$		0			0
$595$	10.3027			0.0173154
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−145.620	−	400.088i	−0.243106	−	0.667927i	−0.999898	−	0.0142721i	$-0.995457\pi$
$599$	−145.620	−	400.088i	−0.243106	−	0.667927i	0.756793	−	0.653655i	$-0.226765\pi$
$600$		0			0
$601$	−128.421	−	728.311i	−0.213679	−	1.21183i	−0.883185	−	0.469026i	$-0.844605\pi$
$601$	−128.421	−	728.311i	−0.213679	−	1.21183i	0.669506	−	0.742807i	$-0.266506\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	4.39205	−	12.0671i	0.00725959	−	0.0199455i
$606$		0			0
$607$	−379.228	−	318.210i	−0.624758	−	0.524235i	0.274537	−	0.961577i	$-0.411475\pi$
$607$	−379.228	−	318.210i	−0.624758	−	0.524235i	−0.899295	+	0.437342i	$0.855920\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1086.78	+	627.452i	1.77869	+	1.02693i
$612$		0			0
$613$	−521.519	−	903.298i	−0.850766	−	1.47357i	−0.880518	−	0.474012i	$-0.842805\pi$
$613$	−521.519	−	903.298i	−0.850766	−	1.47357i	0.0297525	−	0.999557i	$-0.490528\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−154.839	−	27.3024i	−0.250955	−	0.0442502i	0.0467552	−	0.998906i	$-0.485112\pi$
$617$	−154.839	−	27.3024i	−0.250955	−	0.0442502i	−0.297711	+	0.954656i	$0.596223\pi$
$618$		0			0
$619$	207.387	−	174.018i	0.335035	−	0.281128i	−0.459713	−	0.888068i	$-0.652048\pi$
$619$	207.387	−	174.018i	0.335035	−	0.281128i	0.794748	+	0.606940i	$0.207603\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−753.636	−	898.149i	−1.20969	−	1.44165i
$624$		0			0
$625$	108.005	−	612.529i	0.172809	−	0.980046i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	23.6090	−	13.6306i	0.0375341	−	0.0216703i
$630$		0			0
$631$	−226.092	+	391.603i	−0.358308	+	0.620608i	−0.987678	−	0.156498i	$-0.949980\pi$
$631$	−226.092	+	391.603i	−0.358308	+	0.620608i	0.629370	+	0.777106i	$0.283313\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	20.0933	−	23.9462i	0.0316430	−	0.0377106i
$636$		0			0
$637$	362.129	+	131.804i	0.568491	+	0.206914i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−682.172	+	120.285i	−1.06423	+	0.187653i	−0.678233	−	0.734847i	$-0.737254\pi$
$641$	−682.172	+	120.285i	−1.06423	+	0.187653i	−0.385998	+	0.922500i	$0.626143\pi$
$642$		0			0
$643$	−738.955	+	268.958i	−1.14923	+	0.418286i	−0.845239	−	0.534389i	$-0.820542\pi$
$643$	−738.955	+	268.958i	−1.14923	+	0.418286i	−0.303992	+	0.952675i	$0.598319\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			62.1427i			0.0960475i	0.998846	+	0.0480237i	$0.0152923\pi$
$647$			62.1427i			0.0960475i	−0.998846	+	0.0480237i	$0.984708\pi$
$648$		0			0
$649$	137.664			0.212117
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−101.323	−	278.384i	−0.155166	−	0.426315i	0.837614	−	0.546262i	$-0.183950\pi$
$653$	−101.323	−	278.384i	−0.155166	−	0.426315i	−0.992780	+	0.119947i	$0.961728\pi$
$654$		0			0
$655$	−4.97914	−	28.2381i	−0.00760174	−	0.0431116i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−94.7068	+	260.205i	−0.143713	+	0.394848i	−0.990576	−	0.136963i	$-0.956266\pi$
$659$	−94.7068	+	260.205i	−0.143713	+	0.394848i	0.846863	+	0.531811i	$0.178488\pi$
$660$		0			0
$661$	489.455	+	410.702i	0.740477	+	0.621334i	0.932966	−	0.359965i	$-0.117212\pi$
$661$	489.455	+	410.702i	0.740477	+	0.621334i	−0.192489	+	0.981299i	$0.561656\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.562467	+	0.324741i	0.000845815	+	0.000488332i
$666$		0			0
$667$	582.332	+	1008.63i	0.873062	+	1.51219i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	279.128	+	49.2179i	0.415989	+	0.0733500i
$672$		0			0
$673$	361.710	−	303.510i	0.537459	−	0.450981i	−0.333209	−	0.942853i	$-0.608132\pi$
$673$	361.710	−	303.510i	0.537459	−	0.450981i	0.870668	+	0.491872i	$0.163687\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	198.994	+	237.152i	0.293935	+	0.350298i	0.892720	−	0.450612i	$-0.148794\pi$
$677$	198.994	+	237.152i	0.293935	+	0.350298i	−0.598785	+	0.800910i	$0.704350\pi$
$678$		0			0
$679$	177.674	−	1007.64i	0.261670	−	1.48401i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−654.635	+	377.954i	−0.958470	+	0.553373i	−0.895702	−	0.444655i	$-0.853326\pi$
$683$	−654.635	+	377.954i	−0.958470	+	0.553373i	−0.0627681	+	0.998028i	$0.519993\pi$
$684$		0			0
$685$	−19.2794	+	33.3929i	−0.0281451	+	0.0487487i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	904.976	−	1078.51i	1.31346	−	1.56533i
$690$		0			0
$691$	711.871	+	259.100i	1.03020	+	0.374963i	0.801158	−	0.598452i	$-0.204217\pi$
$691$	711.871	+	259.100i	1.03020	+	0.374963i	0.229045	+	0.973416i	$0.426440\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	14.1246	−	2.49055i	0.0203232	−	0.00358353i
$696$		0			0
$697$	−434.654	+	158.201i	−0.623608	+	0.226975i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	1368.47i		−	1.95217i	−0.217397	−	0.976083i	$-0.569757\pi$
$701$		−	1368.47i		−	1.95217i	0.217397	−	0.976083i	$-0.430243\pi$
$702$		0			0
$703$	1.71855			0.00244460
$704$		0			0
$705$		0			0
$706$		0			0
$707$	38.7956	+	106.590i	0.0548736	+	0.150764i
$708$		0			0
$709$	70.8018	+	401.537i	0.0998615	+	0.566343i	0.993149	+	0.116857i	$0.0372818\pi$
$709$	70.8018	+	401.537i	0.0998615	+	0.566343i	−0.893287	+	0.449486i	$0.851607\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−130.444	+	358.391i	−0.182951	+	0.502653i
$714$		0			0
$715$	−19.0451	−	15.9807i	−0.0266365	−	0.0223507i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	214.968	+	124.112i	0.298982	+	0.172617i	0.641985	−	0.766717i	$-0.278111\pi$
$719$	214.968	+	124.112i	0.298982	+	0.172617i	−0.343004	+	0.939334i	$0.611444\pi$
$720$		0			0
$721$	829.856	+	1437.35i	1.15098	+	1.99355i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1018.47	−	179.583i	−1.40478	−	0.247701i
$726$		0			0
$727$	229.792	−	192.819i	0.316083	−	0.265225i	−0.470918	−	0.882177i	$-0.656077\pi$
$727$	229.792	−	192.819i	0.316083	−	0.265225i	0.787001	+	0.616952i	$0.211633\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−6.75893	−	8.05498i	−0.00924615	−	0.0110191i
$732$		0			0
$733$	−132.659	+	752.346i	−0.180981	+	1.02639i	0.750031	+	0.661403i	$0.230039\pi$
$733$	−132.659	+	752.346i	−0.180981	+	1.02639i	−0.931011	+	0.364990i	$0.881072\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	460.393	−	265.808i	0.624685	−	0.360662i
$738$		0			0
$739$	−437.913	+	758.487i	−0.592575	+	1.02637i	0.401309	+	0.915943i	$0.368555\pi$
$739$	−437.913	+	758.487i	−0.592575	+	1.02637i	−0.993884	+	0.110427i	$0.964778\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−57.9224	+	69.0292i	−0.0779574	+	0.0929060i	−0.803613	−	0.595152i	$-0.797092\pi$
$743$	−57.9224	+	69.0292i	−0.0779574	+	0.0929060i	0.725656	+	0.688058i	$0.241536\pi$
$744$		0			0
$745$	−18.8317	−	6.85416i	−0.0252774	−	0.00920022i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1305.66	−	230.223i	1.74321	−	0.307374i
$750$		0			0
$751$	−423.400	+	154.105i	−0.563782	+	0.205200i	−0.608159	−	0.793815i	$-0.708092\pi$
$751$	−423.400	+	154.105i	−0.563782	+	0.205200i	0.0443772	+	0.999015i	$0.485870\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			19.4484i			0.0257595i
$756$		0			0
$757$	67.0196			0.0885332			0.0442666	−	0.999020i	$-0.485905\pi$
$757$	67.0196			0.0885332			0.0442666	+	0.999020i	$0.485905\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	309.817	+	851.216i	0.407119	+	1.11855i	0.958698	+	0.284427i	$0.0918034\pi$
$761$	309.817	+	851.216i	0.407119	+	1.11855i	−0.551579	+	0.834123i	$0.685974\pi$
$762$		0			0
$763$	−103.749	−	588.391i	−0.135975	−	0.771155i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−102.207	+	280.813i	−0.133256	+	0.366118i
$768$		0			0
$769$	−706.730	−	593.017i	−0.919024	−	0.771153i	0.0547901	−	0.998498i	$-0.482551\pi$
$769$	−706.730	−	593.017i	−0.919024	−	0.771153i	−0.973814	+	0.227345i	$0.926995\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1317.32	+	760.554i	1.70416	+	0.983900i	0.941443	+	0.337172i	$0.109470\pi$
$773$	1317.32	+	760.554i	1.70416	+	0.983900i	0.762721	+	0.646728i	$0.223863\pi$
$774$		0			0
$775$	−169.331	−	293.290i	−0.218491	−	0.378438i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−28.7162	−	5.06344i	−0.0368629	−	0.00649993i
$780$		0			0
$781$	−259.998	+	218.164i	−0.332904	+	0.279340i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−31.0196	−	36.9677i	−0.0395154	−	0.0470926i
$786$		0			0
$787$	−136.517	+	774.228i	−0.173465	+	0.983771i	0.766435	+	0.642322i	$0.222029\pi$
$787$	−136.517	+	774.228i	−0.173465	+	0.983771i	−0.939900	+	0.341449i	$0.889082\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−773.146	+	446.376i	−0.977429	+	0.564319i
$792$		0			0
$793$	−307.633	+	532.836i	−0.387936	+	0.671924i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	442.583	−	527.450i	0.555311	−	0.661794i	−0.413236	−	0.910624i	$-0.635602\pi$
$797$	442.583	−	527.450i	0.555311	−	0.661794i	0.968547	+	0.248830i	$0.0800461\pi$
$798$		0			0
$799$	433.441	+	157.759i	0.542479	+	0.197446i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−762.375	+	134.427i	−0.949409	+	0.167406i
$804$		0			0
$805$	45.1584	−	16.4363i	0.0560973	−	0.0204178i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	267.972i		−	0.331238i	−0.986190	−	0.165619i	$-0.947038\pi$
$809$		−	267.972i		−	0.331238i	0.986190	−	0.165619i	$-0.0529623\pi$
$810$		0			0
$811$	457.328			0.563906			0.281953	−	0.959428i	$-0.409018\pi$
$811$	457.328			0.563906			0.281953	+	0.959428i	$0.409018\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	4.02012	+	11.0452i	0.00493266	+	0.0135524i
$816$		0			0
$817$	−0.115106	−	0.652799i	−0.000140889	−	0.000799019i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−71.1226	+	195.408i	−0.0866292	+	0.238012i	−0.975441	−	0.220260i	$-0.929309\pi$
$821$	−71.1226	+	195.408i	−0.0866292	+	0.238012i	0.888812	+	0.458272i	$0.151532\pi$
$822$		0			0
$823$	−239.194	−	200.707i	−0.290636	−	0.243873i	0.485798	−	0.874071i	$-0.338529\pi$
$823$	−239.194	−	200.707i	−0.290636	−	0.243873i	−0.776434	+	0.630198i	$0.782974\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	905.439	+	522.755i	1.09485	+	0.632111i	0.934863	−	0.355009i	$-0.115522\pi$
$827$	905.439	+	522.755i	1.09485	+	0.632111i	0.159985	+	0.987119i	$0.448856\pi$
$828$		0			0
$829$	370.655	+	641.994i	0.447111	+	0.774419i	0.998197	−	0.0600295i	$-0.0191195\pi$
$829$	370.655	+	641.994i	0.447111	+	0.774419i	−0.551085	+	0.834449i	$0.685786\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	139.496	+	24.5969i	0.167462	+	0.0295281i
$834$		0			0
$835$	−10.0745	+	8.45355i	−0.0120653	+	0.0101240i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	54.1406	+	64.5222i	0.0645299	+	0.0769037i	0.797344	−	0.603525i	$-0.206238\pi$
$839$	54.1406	+	64.5222i	0.0645299	+	0.0769037i	−0.732814	+	0.680429i	$0.761793\pi$
$840$		0			0
$841$	−152.076	+	862.466i	−0.180828	+	1.02552i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	17.3521	−	10.0182i	0.0205350	−	0.0118559i
$846$		0			0
$847$	272.301	−	471.639i	0.321488	−	0.556834i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	81.7366	−	97.4099i	0.0960477	−	0.114465i
$852$		0			0
$853$	−16.4245	−	5.97804i	−0.0192550	−	0.00700825i	0.332375	−	0.943147i	$-0.392150\pi$
$853$	−16.4245	−	5.97804i	−0.0192550	−	0.00700825i	−0.351630	+	0.936139i	$0.614372\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	749.943	−	132.235i	0.875079	−	0.154300i	0.281971	−	0.959423i	$-0.409012\pi$
$857$	749.943	−	132.235i	0.875079	−	0.154300i	0.593108	+	0.805123i	$0.297901\pi$
$858$		0			0
$859$	889.121	−	323.614i	1.03507	−	0.376733i	0.232058	−	0.972702i	$-0.425454\pi$
$859$	889.121	−	323.614i	1.03507	−	0.376733i	0.803008	+	0.595969i	$0.203232\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			357.864i			0.414675i	0.978270	+	0.207337i	$0.0664798\pi$
$863$			357.864i			0.414675i	−0.978270	+	0.207337i	$0.933520\pi$
$864$		0			0
$865$	15.1860			0.0175561
$866$		0			0
$867$		0			0
$868$		0			0
$869$	218.192	+	599.478i	0.251084	+	0.689848i
$870$		0			0
$871$	200.391	+	1136.47i	0.230070	+	1.30479i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−29.2132	+	80.2625i	−0.0333865	+	0.0917286i
$876$		0			0
$877$	833.488	+	699.380i	0.950386	+	0.797468i	0.979362	−	0.202112i	$-0.0647804\pi$
$877$	833.488	+	699.380i	0.950386	+	0.797468i	−0.0289766	+	0.999580i	$0.509225\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	668.191	+	385.780i	0.758446	+	0.437889i	0.828738	−	0.559638i	$-0.189060\pi$
$881$	668.191	+	385.780i	0.758446	+	0.437889i	−0.0702915	+	0.997526i	$0.522393\pi$
$882$		0			0
$883$	−605.002	−	1047.89i	−0.685166	−	1.18674i	−0.973385	−	0.229178i	$-0.926396\pi$
$883$	−605.002	−	1047.89i	−0.685166	−	1.18674i	0.288219	−	0.957565i	$-0.406937\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1334.02	+	235.224i	1.50397	+	0.265190i	0.864110	−	0.503303i	$-0.167882\pi$
$887$	1334.02	+	235.224i	1.50397	+	0.265190i	0.639858	+	0.768493i	$0.278993\pi$
$888$		0			0
$889$	1015.55	−	852.146i	1.14235	−	0.958545i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	18.6908	+	22.2749i	0.0209304	+	0.0249439i
$894$		0			0
$895$	−10.4518	+	59.2748i	−0.0116779	+	0.0662289i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−486.871	+	281.095i	−0.541569	+	0.312675i
$900$		0			0
$901$	258.746	−	448.161i	0.287176	−	0.497404i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−38.3461	+	45.6991i	−0.0423714	+	0.0504963i
$906$		0			0
$907$	−1446.41	−	526.450i	−1.59472	−	0.580430i	−0.616381	−	0.787448i	$-0.711402\pi$
$907$	−1446.41	−	526.450i	−1.59472	−	0.580430i	−0.978337	+	0.207019i	$0.933624\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−309.888	+	54.6416i	−0.340162	+	0.0599798i	−0.341120	−	0.940020i	$-0.610806\pi$
$911$	−309.888	+	54.6416i	−0.340162	+	0.0599798i	0.000957797		1.00000i	$0.499695\pi$
$912$		0			0
$913$	−488.067	+	177.642i	−0.534575	+	0.194569i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	1216.04i		−	1.32611i
$918$		0			0
$919$	−956.851			−1.04119			−0.520594	−	0.853805i	$-0.674289\pi$
$919$	−956.851			−1.04119			−0.520594	+	0.853805i	$0.674289\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−251.987	−	692.329i	−0.273009	−	0.750086i
$924$		0			0
$925$	19.6071	+	111.197i	0.0211969	+	0.120213i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	373.128	−	1025.16i	0.401645	−	1.10351i	−0.559827	−	0.828610i	$-0.689132\pi$
$929$	373.128	−	1025.16i	0.401645	−	1.10351i	0.961472	−	0.274902i	$-0.0886454\pi$
$930$		0			0
$931$	6.84040	+	5.73978i	0.00734737	+	0.00616518i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−7.91394	−	4.56912i	−0.00846411	−	0.00488676i
$936$		0			0
$937$	−223.525	−	387.156i	−0.238554	−	0.413187i	0.721746	−	0.692158i	$-0.243340\pi$
$937$	−223.525	−	387.156i	−0.238554	−	0.413187i	−0.960299	+	0.278971i	$0.910007\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.45674	+	0.256863i	0.00154808	+	0.000272968i	0.174422	−	0.984671i	$-0.444194\pi$
$941$	1.45674	+	0.256863i	0.00154808	+	0.000272968i	−0.172874	+	0.984944i	$0.555305\pi$
$942$		0			0
$943$	−1652.78	+	1386.85i	−1.75268	+	1.47068i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	997.650	+	1188.95i	1.05348	+	1.25549i	0.965784	+	0.259347i	$0.0835074\pi$
$947$	997.650	+	1188.95i	1.05348	+	1.25549i	0.0877005	+	0.996147i	$0.472048\pi$
$948$		0			0
$949$	291.809	−	1654.93i	0.307491	−	1.74387i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1466.92	+	846.929i	−1.53927	+	0.888698i	−0.540388	+	0.841416i	$0.681723\pi$
$953$	−1466.92	+	846.929i	−1.53927	+	0.888698i	−0.998882	+	0.0472820i	$0.984944\pi$
$954$		0			0
$955$	8.21723	−	14.2327i	0.00860443	−	0.0149033i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1051.12	+	1252.68i	−1.09606	+	1.30624i
$960$		0			0
$961$	730.047	+	265.715i	0.759674	+	0.276499i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−23.2771	+	4.10438i	−0.0241213	+	0.00425324i
$966$		0			0
$967$	557.509	−	202.917i	0.576535	−	0.209841i	−0.0372622	−	0.999306i	$-0.511864\pi$
$967$	557.509	−	202.917i	0.576535	−	0.209841i	0.613797	+	0.789464i	$0.289641\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	597.827i		−	0.615682i	−0.951438	−	0.307841i	$-0.900394\pi$
$971$		−	597.827i		−	0.615682i	0.951438	−	0.307841i	$-0.0996065\pi$
$972$		0			0
$973$	608.259			0.625138
$974$		0			0
$975$		0			0
$976$		0			0
$977$	44.3601	+	121.878i	0.0454044	+	0.124748i	0.960322	−	0.278892i	$-0.0899672\pi$
$977$	44.3601	+	121.878i	0.0454044	+	0.124748i	−0.914918	+	0.403640i	$0.867745\pi$
$978$		0			0
$979$	180.583	+	1024.14i	0.184457	+	1.04611i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	145.726	−	400.380i	0.148246	−	0.407304i	−0.843236	−	0.537543i	$-0.819352\pi$
$983$	145.726	−	400.380i	0.148246	−	0.407304i	0.991483	+	0.130240i	$0.0415747\pi$
$984$		0			0
$985$	−12.4073	−	10.4109i	−0.0125962	−	0.0105695i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−42.4761	−	24.5236i	−0.0429485	−	0.0247963i
$990$		0			0
$991$	−194.763	−	337.340i	−0.196532	−	0.340403i	0.750870	−	0.660450i	$-0.229635\pi$
$991$	−194.763	−	337.340i	−0.196532	−	0.340403i	−0.947402	+	0.320047i	$0.896301\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−34.7832	−	6.13322i	−0.0349580	−	0.00616404i
$996$		0			0
$997$	−505.149	+	423.871i	−0.506669	+	0.425146i	−0.859955	−	0.510369i	$-0.829509\pi$
$997$	−505.149	+	423.871i	−0.506669	+	0.425146i	0.353286	+	0.935515i	$0.385064\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.k.a.125.4		36
3.2	odd	2		108.3.k.a.5.3	✓	36
12.11	even	2		432.3.bc.b.113.4		36
27.4	even	9		2916.3.c.b.1457.19		36
27.11	odd	18	inner	324.3.k.a.197.4		36
27.16	even	9		108.3.k.a.65.3	yes	36
27.23	odd	18		2916.3.c.b.1457.18		36
108.43	odd	18		432.3.bc.b.65.4		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.5.3	✓	36	3.2	odd	2
108.3.k.a.65.3	yes	36	27.16	even	9
324.3.k.a.125.4		36	1.1	even	1	trivial
324.3.k.a.197.4		36	27.11	odd	18	inner
432.3.bc.b.65.4		36	108.43	odd	18
432.3.bc.b.113.4		36	12.11	even	2
2916.3.c.b.1457.18		36	27.23	odd	18
2916.3.c.b.1457.19		36	27.4	even	9

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.k (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0686711 - 0.188672i) q^{5} +(-1.47862 - 8.38565i) q^{7} +O(q^{10})\)	\(q+(-0.0686711 - 0.188672i) q^{5} +(-1.47862 - 8.38565i) q^{7} +(-2.58315 + 7.09715i) q^{11} +(-12.5592 - 10.5384i) q^{13} +(-5.21882 - 3.01309i) q^{17} +(-0.189946 - 0.328995i) q^{19} +(-27.6819 - 4.88107i) q^{23} +(19.1202 - 16.0438i) q^{25} +(-26.6332 - 31.7402i) q^{29} +(2.35612 - 13.3622i) q^{31} +(-1.48060 + 0.854825i) q^{35} +(-2.26190 + 3.91773i) q^{37} +(49.3383 - 58.7991i) q^{41} +(1.63966 + 0.596788i) q^{43} +(-75.3795 + 13.2914i) q^{47} +(-22.0879 + 8.03934i) q^{49} +85.8739i q^{53} +1.51642 q^{55} +(-6.23410 - 17.1281i) q^{59} +(-6.51665 - 36.9578i) q^{61} +(-1.12585 + 3.09326i) q^{65} +(-53.9204 - 45.2446i) q^{67} +(38.9179 + 22.4692i) q^{71} +(51.2495 + 88.7667i) q^{73} +(63.3337 + 11.1674i) q^{77} +(64.7058 - 54.2946i) q^{79} +(44.2042 + 52.6805i) q^{83} +(-0.210104 + 1.19156i) q^{85} +(119.245 - 68.8461i) q^{89} +(-69.8014 + 120.900i) q^{91} +(-0.0490285 + 0.0584299i) q^{95} +(112.916 + 41.0979i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 9 q^{5}+O(q^{10}) \) 36 * q + 9 * q^5	\( 36 q + 9 q^{5} - 36 q^{11} + 18 q^{23} - 9 q^{25} + 18 q^{29} + 45 q^{31} + 243 q^{35} + 198 q^{41} + 90 q^{43} + 243 q^{47} + 72 q^{49} - 252 q^{59} - 144 q^{61} - 747 q^{65} + 108 q^{67} - 324 q^{71} - 63 q^{73} - 495 q^{77} + 36 q^{79} + 27 q^{83} - 180 q^{85} + 567 q^{89} + 99 q^{91} + 1044 q^{95} - 216 q^{97}+O(q^{100}) \) 36 * q + 9 * q^5 - 36 * q^11 + 18 * q^23 - 9 * q^25 + 18 * q^29 + 45 * q^31 + 243 * q^35 + 198 * q^41 + 90 * q^43 + 243 * q^47 + 72 * q^49 - 252 * q^59 - 144 * q^61 - 747 * q^65 + 108 * q^67 - 324 * q^71 - 63 * q^73 - 495 * q^77 + 36 * q^79 + 27 * q^83 - 180 * q^85 + 567 * q^89 + 99 * q^91 + 1044 * q^95 - 216 * q^97

Introduction

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