LMFDB - Embedded newform 864.2.i.e.289.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(289,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("864.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.i (of order $3$, degree $2$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.2
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	864.289
Dual form			864.2.i.e.577.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{5} +(1.72474 - 2.98735i) q^{7} +O(q^{10})$	$q+(-0.500000 - 0.866025i) q^{5} +(1.72474 - 2.98735i) q^{7} +(-0.724745 + 1.25529i) q^{11} +(-2.94949 - 5.10867i) q^{13} -4.89898 q^{17} -4.00000 q^{19} +(2.72474 + 4.71940i) q^{23} +(2.00000 - 3.46410i) q^{25} +(0.0505103 - 0.0874863i) q^{29} +(1.27526 + 2.20881i) q^{31} -3.44949 q^{35} -0.898979 q^{37} +(-5.94949 - 10.3048i) q^{41} +(-1.17423 + 2.03383i) q^{43} +(3.17423 - 5.49794i) q^{47} +(-2.44949 - 4.24264i) q^{49} -8.89898 q^{53} +1.44949 q^{55} +(-7.17423 - 12.4261i) q^{59} +(3.94949 - 6.84072i) q^{61} +(-2.94949 + 5.10867i) q^{65} +(6.17423 + 10.6941i) q^{67} +7.79796 q^{71} -4.89898 q^{73} +(2.50000 + 4.33013i) q^{77} +(6.72474 - 11.6476i) q^{79} +(0.275255 - 0.476756i) q^{83} +(2.44949 + 4.24264i) q^{85} +12.8990 q^{89} -20.3485 q^{91} +(2.00000 + 3.46410i) q^{95} +(1.94949 - 3.37662i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{5} + 2 q^{7}+O(q^{10}) $ 4 * q - 2 * q^5 + 2 * q^7	$ 4 q - 2 q^{5} + 2 q^{7} + 2 q^{11} - 2 q^{13} - 16 q^{19} + 6 q^{23} + 8 q^{25} + 10 q^{29} + 10 q^{31} - 4 q^{35} + 16 q^{37} - 14 q^{41} + 10 q^{43} - 2 q^{47} - 16 q^{53} - 4 q^{55} - 14 q^{59} + 6 q^{61} - 2 q^{65} + 10 q^{67} - 8 q^{71} + 10 q^{77} + 22 q^{79} + 6 q^{83} + 32 q^{89} - 52 q^{91} + 8 q^{95} - 2 q^{97}+O(q^{100}) $ 4 * q - 2 * q^5 + 2 * q^7 + 2 * q^11 - 2 * q^13 - 16 * q^19 + 6 * q^23 + 8 * q^25 + 10 * q^29 + 10 * q^31 - 4 * q^35 + 16 * q^37 - 14 * q^41 + 10 * q^43 - 2 * q^47 - 16 * q^53 - 4 * q^55 - 14 * q^59 + 6 * q^61 - 2 * q^65 + 10 * q^67 - 8 * q^71 + 10 * q^77 + 22 * q^79 + 6 * q^83 + 32 * q^89 - 52 * q^91 + 8 * q^95 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$		0			0
$7$	1.72474	−	2.98735i	0.651892	−	1.12911i	−0.330771	−	0.943711i	$-0.607309\pi$
$7$	1.72474	−	2.98735i	0.651892	−	1.12911i	0.982663	−	0.185399i	$-0.0593579\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.724745	+	1.25529i	−0.218519	+	0.378486i	−0.954355	−	0.298674i	$-0.903456\pi$
$11$	−0.724745	+	1.25529i	−0.218519	+	0.378486i	0.735837	+	0.677159i	$0.236789\pi$
$12$		0			0
$13$	−2.94949	−	5.10867i	−0.818041	−	1.41689i	−0.907123	−	0.420865i	$-0.861727\pi$
$13$	−2.94949	−	5.10867i	−0.818041	−	1.41689i	0.0890821	−	0.996024i	$-0.471607\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.89898			−1.18818			−0.594089	−	0.804400i	$-0.702487\pi$
$17$	−4.89898			−1.18818			−0.594089	+	0.804400i	$0.702487\pi$
$18$		0			0
$19$	−4.00000			−0.917663			−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000			−0.917663			−0.458831	+	0.888523i	$0.651732\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.72474	+	4.71940i	0.568149	+	0.984062i	0.996749	+	0.0805681i	$0.0256735\pi$
$23$	2.72474	+	4.71940i	0.568149	+	0.984062i	−0.428601	+	0.903494i	$0.640993\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.0505103	−	0.0874863i	0.00937952	−	0.0162458i	−0.861298	−	0.508101i	$-0.830348\pi$
$29$	0.0505103	−	0.0874863i	0.00937952	−	0.0162458i	0.870677	+	0.491855i	$0.163681\pi$
$30$		0			0
$31$	1.27526	+	2.20881i	0.229043	+	0.396713i	0.957525	−	0.288352i	$-0.0931072\pi$
$31$	1.27526	+	2.20881i	0.229043	+	0.396713i	−0.728482	+	0.685065i	$0.759774\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−3.44949			−0.583070
$36$		0			0
$37$	−0.898979			−0.147791			−0.0738957	−	0.997266i	$-0.523543\pi$
$37$	−0.898979			−0.147791			−0.0738957	+	0.997266i	$0.523543\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5.94949	−	10.3048i	−0.929154	−	1.60934i	−0.784740	−	0.619825i	$-0.787204\pi$
$41$	−5.94949	−	10.3048i	−0.929154	−	1.60934i	−0.144414	−	0.989517i	$-0.546130\pi$
$42$		0			0
$43$	−1.17423	+	2.03383i	−0.179069	+	0.310157i	−0.941562	−	0.336840i	$-0.890642\pi$
$43$	−1.17423	+	2.03383i	−0.179069	+	0.310157i	0.762493	+	0.646997i	$0.223975\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.17423	−	5.49794i	0.463010	−	0.801956i	−0.536100	−	0.844155i	$-0.680103\pi$
$47$	3.17423	−	5.49794i	0.463010	−	0.801956i	0.999109	+	0.0421984i	$0.0134362\pi$
$48$		0			0
$49$	−2.44949	−	4.24264i	−0.349927	−	0.606092i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−8.89898			−1.22237			−0.611184	−	0.791488i	$-0.709307\pi$
$53$	−8.89898			−1.22237			−0.611184	+	0.791488i	$0.709307\pi$
$54$		0			0
$55$	1.44949			0.195449
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−7.17423	−	12.4261i	−0.934006	−	1.61775i	−0.776397	−	0.630244i	$-0.782955\pi$
$59$	−7.17423	−	12.4261i	−0.934006	−	1.61775i	−0.157609	−	0.987502i	$-0.550378\pi$
$60$		0			0
$61$	3.94949	−	6.84072i	0.505680	−	0.875864i	−0.494298	−	0.869292i	$-0.664575\pi$
$61$	3.94949	−	6.84072i	0.505680	−	0.875864i	0.999978	−	0.00657156i	$-0.00209181\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.94949	+	5.10867i	−0.365839	+	0.633652i
$66$		0			0
$67$	6.17423	+	10.6941i	0.754303	+	1.30649i	0.945720	+	0.324982i	$0.105358\pi$
$67$	6.17423	+	10.6941i	0.754303	+	1.30649i	−0.191417	+	0.981509i	$0.561308\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	7.79796			0.925447			0.462724	−	0.886503i	$-0.346872\pi$
$71$	7.79796			0.925447			0.462724	+	0.886503i	$0.346872\pi$
$72$		0			0
$73$	−4.89898			−0.573382			−0.286691	−	0.958023i	$-0.592555\pi$
$73$	−4.89898			−0.573382			−0.286691	+	0.958023i	$0.592555\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.50000	+	4.33013i	0.284901	+	0.493464i
$78$		0			0
$79$	6.72474	−	11.6476i	0.756593	−	1.31046i	−0.187986	−	0.982172i	$-0.560196\pi$
$79$	6.72474	−	11.6476i	0.756593	−	1.31046i	0.944579	−	0.328286i	$-0.106471\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.275255	−	0.476756i	0.0302132	−	0.0523308i	−0.850523	−	0.525937i	$-0.823715\pi$
$83$	0.275255	−	0.476756i	0.0302132	−	0.0523308i	0.880737	+	0.473606i	$0.157048\pi$
$84$		0			0
$85$	2.44949	+	4.24264i	0.265684	+	0.460179i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	12.8990			1.36729			0.683645	−	0.729815i	$-0.260394\pi$
$89$	12.8990			1.36729			0.683645	+	0.729815i	$0.260394\pi$
$90$		0			0
$91$	−20.3485			−2.13310
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.00000	+	3.46410i	0.205196	+	0.355409i
$96$		0			0
$97$	1.94949	−	3.37662i	0.197941	−	0.342843i	−0.749920	−	0.661529i	$-0.769908\pi$
$97$	1.94949	−	3.37662i	0.197941	−	0.342843i	0.947861	+	0.318685i	$0.103241\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.39898	−	11.0834i	0.636722	−	1.10284i	−0.349425	−	0.936964i	$-0.613623\pi$
$101$	6.39898	−	11.0834i	0.636722	−	1.10284i	0.986147	−	0.165871i	$-0.0530435\pi$
$102$		0			0
$103$	6.27526	+	10.8691i	0.618319	+	1.07096i	0.989792	+	0.142517i	$0.0455195\pi$
$103$	6.27526	+	10.8691i	0.618319	+	1.07096i	−0.371473	+	0.928444i	$0.621147\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.79796			−0.560510			−0.280255	−	0.959926i	$-0.590419\pi$
$107$	−5.79796			−0.560510			−0.280255	+	0.959926i	$0.590419\pi$
$108$		0			0
$109$	0.898979			0.0861066			0.0430533	−	0.999073i	$-0.486291\pi$
$109$	0.898979			0.0861066			0.0430533	+	0.999073i	$0.486291\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	4.39898	+	7.61926i	0.413821	+	0.716759i	0.995304	−	0.0967994i	$-0.0308605\pi$
$113$	4.39898	+	7.61926i	0.413821	+	0.716759i	−0.581483	+	0.813559i	$0.697527\pi$
$114$		0			0
$115$	2.72474	−	4.71940i	0.254084	−	0.440086i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−8.44949	+	14.6349i	−0.774563	+	1.34158i
$120$		0			0
$121$	4.44949	+	7.70674i	0.404499	+	0.700613i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−9.00000			−0.804984
$126$		0			0
$127$	−8.00000			−0.709885			−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000			−0.709885			−0.354943	+	0.934888i	$0.615500\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.62372	+	11.4726i	0.578717	+	1.00237i	0.995627	+	0.0934200i	$0.0297799\pi$
$131$	6.62372	+	11.4726i	0.578717	+	1.00237i	−0.416909	+	0.908948i	$0.636887\pi$
$132$		0			0
$133$	−6.89898	+	11.9494i	−0.598217	+	1.03614i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.05051	+	8.74774i	−0.431494	+	0.747370i	−0.997002	−	0.0773729i	$-0.975347\pi$
$137$	−5.05051	+	8.74774i	−0.431494	+	0.747370i	0.565508	+	0.824743i	$0.308680\pi$
$138$		0			0
$139$	−1.72474	−	2.98735i	−0.146291	−	0.253383i	0.783563	−	0.621312i	$-0.213400\pi$
$139$	−1.72474	−	2.98735i	−0.146291	−	0.253383i	−0.929854	+	0.367929i	$0.880067\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	8.55051			0.715030
$144$		0			0
$145$	−0.101021			−0.00838930
$146$		0			0
$147$		0			0
$148$		0			0
$149$	2.05051	+	3.55159i	0.167984	+	0.290957i	0.937711	−	0.347416i	$-0.112941\pi$
$149$	2.05051	+	3.55159i	0.167984	+	0.290957i	−0.769727	+	0.638374i	$0.779608\pi$
$150$		0			0
$151$	7.62372	−	13.2047i	0.620410	−	1.07458i	−0.368999	−	0.929430i	$-0.620300\pi$
$151$	7.62372	−	13.2047i	0.620410	−	1.07458i	0.989409	−	0.145152i	$-0.0463671\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.27526	−	2.20881i	0.102431	−	0.177416i
$156$		0			0
$157$	5.39898	+	9.35131i	0.430885	+	0.746316i	0.996950	−	0.0780455i	$-0.0248680\pi$
$157$	5.39898	+	9.35131i	0.430885	+	0.746316i	−0.566064	+	0.824361i	$0.691535\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	18.7980			1.48149
$162$		0			0
$163$	5.79796			0.454131			0.227066	−	0.973879i	$-0.427087\pi$
$163$	5.79796			0.454131			0.227066	+	0.973879i	$0.427087\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.27526	−	3.94086i	−0.176065	−	0.304953i	0.764465	−	0.644666i	$-0.223003\pi$
$167$	−2.27526	−	3.94086i	−0.176065	−	0.304953i	−0.940529	+	0.339713i	$0.889670\pi$
$168$		0			0
$169$	−10.8990	+	18.8776i	−0.838383	+	1.45212i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.50000	−	2.59808i	0.114043	−	0.197528i	−0.803354	−	0.595502i	$-0.796953\pi$
$173$	1.50000	−	2.59808i	0.114043	−	0.197528i	0.917397	+	0.397974i	$0.130287\pi$
$174$		0			0
$175$	−6.89898	−	11.9494i	−0.521514	−	0.903288i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$		0			0
$181$	10.6969			0.795097			0.397549	−	0.917581i	$-0.369861\pi$
$181$	10.6969			0.795097			0.397549	+	0.917581i	$0.369861\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.449490	+	0.778539i	0.0330471	+	0.0572393i
$186$		0			0
$187$	3.55051	−	6.14966i	0.259639	−	0.449708i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.27526	−	10.8691i	0.454062	−	0.786458i	−0.544572	−	0.838714i	$-0.683308\pi$
$191$	6.27526	−	10.8691i	0.454062	−	0.786458i	0.998634	+	0.0522563i	$0.0166413\pi$
$192$		0			0
$193$	−2.05051	−	3.55159i	−0.147599	−	0.255649i	0.782741	−	0.622348i	$-0.213821\pi$
$193$	−2.05051	−	3.55159i	−0.147599	−	0.255649i	−0.930340	+	0.366699i	$0.880488\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	17.5959			1.25366			0.626829	−	0.779157i	$-0.284353\pi$
$197$	17.5959			1.25366			0.626829	+	0.779157i	$0.284353\pi$
$198$		0			0
$199$	7.79796			0.552783			0.276391	−	0.961045i	$-0.410861\pi$
$199$	7.79796			0.552783			0.276391	+	0.961045i	$0.410861\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.174235	−	0.301783i	−0.0122289	−	0.0211810i
$204$		0			0
$205$	−5.94949	+	10.3048i	−0.415530	+	0.719720i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.89898	−	5.02118i	0.200527	−	0.347322i
$210$		0			0
$211$	5.27526	+	9.13701i	0.363164	+	0.629018i	0.988480	−	0.151354i	$-0.0483633\pi$
$211$	5.27526	+	9.13701i	0.363164	+	0.629018i	−0.625316	+	0.780372i	$0.715030\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.34847			0.160164
$216$		0			0
$217$	8.79796			0.597244
$218$		0			0
$219$		0			0
$220$		0			0
$221$	14.4495	+	25.0273i	0.971978	+	1.68352i
$222$		0			0
$223$	−8.07321	+	13.9832i	−0.540622	+	0.936385i	0.458246	+	0.888825i	$0.348478\pi$
$223$	−8.07321	+	13.9832i	−0.540622	+	0.936385i	−0.998868	+	0.0475601i	$0.984855\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.82577	+	6.62642i	−0.253925	+	0.439811i	−0.964603	−	0.263706i	$-0.915055\pi$
$227$	−3.82577	+	6.62642i	−0.253925	+	0.439811i	0.710678	+	0.703517i	$0.248388\pi$
$228$		0			0
$229$	0.500000	+	0.866025i	0.0330409	+	0.0572286i	0.882073	−	0.471113i	$-0.156147\pi$
$229$	0.500000	+	0.866025i	0.0330409	+	0.0572286i	−0.849032	+	0.528341i	$0.822814\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$		0			0
$235$	−6.34847			−0.414128
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−7.07321	−	12.2512i	−0.457528	−	0.792462i	0.541301	−	0.840829i	$-0.317932\pi$
$239$	−7.07321	−	12.2512i	−0.457528	−	0.792462i	−0.998830	+	0.0483665i	$0.984598\pi$
$240$		0			0
$241$	−3.50000	+	6.06218i	−0.225455	+	0.390499i	−0.956456	−	0.291877i	$-0.905720\pi$
$241$	−3.50000	+	6.06218i	−0.225455	+	0.390499i	0.731001	+	0.682376i	$0.239053\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2.44949	+	4.24264i	−0.156492	+	0.271052i
$246$		0			0
$247$	11.7980	+	20.4347i	0.750686	+	1.30023i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	21.7980			1.37587			0.687937	−	0.725770i	$-0.258516\pi$
$251$	21.7980			1.37587			0.687937	+	0.725770i	$0.258516\pi$
$252$		0			0
$253$	−7.89898			−0.496605
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−5.39898	−	9.35131i	−0.336779	−	0.583318i	0.647046	−	0.762451i	$-0.276004\pi$
$257$	−5.39898	−	9.35131i	−0.336779	−	0.583318i	−0.983825	+	0.179133i	$0.942671\pi$
$258$		0			0
$259$	−1.55051	+	2.68556i	−0.0963440	+	0.166873i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.72474	+	4.71940i	−0.168015	+	0.291010i	−0.937722	−	0.347387i	$-0.887069\pi$
$263$	−2.72474	+	4.71940i	−0.168015	+	0.291010i	0.769707	+	0.638397i	$0.220402\pi$
$264$		0			0
$265$	4.44949	+	7.70674i	0.273330	+	0.473421i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−7.10102			−0.432957			−0.216478	−	0.976287i	$-0.569457\pi$
$269$	−7.10102			−0.432957			−0.216478	+	0.976287i	$0.569457\pi$
$270$		0			0
$271$	−29.3939			−1.78555			−0.892775	−	0.450502i	$-0.851245\pi$
$271$	−29.3939			−1.78555			−0.892775	+	0.450502i	$0.851245\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.89898	+	5.02118i	0.174815	+	0.302789i
$276$		0			0
$277$	7.39898	−	12.8154i	0.444562	−	0.770003i	−0.553460	−	0.832876i	$-0.686693\pi$
$277$	7.39898	−	12.8154i	0.444562	−	0.770003i	0.998022	+	0.0628725i	$0.0200262\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−5.05051	+	8.74774i	−0.301288	+	0.521846i	−0.976428	−	0.215843i	$-0.930750\pi$
$281$	−5.05051	+	8.74774i	−0.301288	+	0.521846i	0.675140	+	0.737690i	$0.264083\pi$
$282$		0			0
$283$	−1.72474	−	2.98735i	−0.102525	−	0.177579i	0.810199	−	0.586155i	$-0.199359\pi$
$283$	−1.72474	−	2.98735i	−0.102525	−	0.177579i	−0.912725	+	0.408576i	$0.866026\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−41.0454			−2.42283
$288$		0			0
$289$	7.00000			0.411765
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.398979	+	0.691053i	0.0233086	+	0.0403717i	0.877444	−	0.479678i	$-0.159247\pi$
$293$	0.398979	+	0.691053i	0.0233086	+	0.0403717i	−0.854136	+	0.520050i	$0.825913\pi$
$294$		0			0
$295$	−7.17423	+	12.4261i	−0.417700	+	0.723478i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	16.0732	−	27.8396i	0.929538	−	1.61001i
$300$		0			0
$301$	4.05051	+	7.01569i	0.233468	+	0.404378i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−7.89898			−0.452294
$306$		0			0
$307$	21.7980			1.24408			0.622038	−	0.782987i	$-0.286305\pi$
$307$	21.7980			1.24408			0.622038	+	0.782987i	$0.286305\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	7.62372	+	13.2047i	0.432302	+	0.748769i	0.997071	−	0.0764802i	$-0.0243682\pi$
$311$	7.62372	+	13.2047i	0.432302	+	0.748769i	−0.564769	+	0.825249i	$0.691035\pi$
$312$		0			0
$313$	8.50000	−	14.7224i	0.480448	−	0.832161i	−0.519300	−	0.854592i	$-0.673807\pi$
$313$	8.50000	−	14.7224i	0.480448	−	0.832161i	0.999748	+	0.0224310i	$0.00714060\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	12.9495	−	22.4292i	0.727316	−	1.25975i	−0.230698	−	0.973025i	$-0.574101\pi$
$317$	12.9495	−	22.4292i	0.727316	−	1.25975i	0.958014	−	0.286722i	$-0.0925658\pi$
$318$		0			0
$319$	0.0732141	+	0.126811i	0.00409920	+	0.00710003i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	19.5959			1.09035
$324$		0			0
$325$	−23.5959			−1.30887
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−10.9495	−	18.9651i	−0.603665	−	1.04558i
$330$		0			0
$331$	5.62372	−	9.74058i	0.309108	−	0.535390i	−0.669060	−	0.743209i	$-0.733303\pi$
$331$	5.62372	−	9.74058i	0.309108	−	0.535390i	0.978167	+	0.207818i	$0.0666363\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	6.17423	−	10.6941i	0.337334	−	0.584280i
$336$		0			0
$337$	5.39898	+	9.35131i	0.294101	+	0.509398i	0.974775	−	0.223188i	$-0.0716464\pi$
$337$	5.39898	+	9.35131i	0.294101	+	0.509398i	−0.680674	+	0.732586i	$0.738313\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−3.69694			−0.200200
$342$		0			0
$343$	7.24745			0.391325
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.07321	−	5.32296i	−0.164979	−	0.285752i	0.771669	−	0.636024i	$-0.219422\pi$
$347$	−3.07321	−	5.32296i	−0.164979	−	0.285752i	−0.936648	+	0.350273i	$0.886089\pi$
$348$		0			0
$349$	7.39898	−	12.8154i	0.396058	−	0.685993i	−0.597177	−	0.802109i	$-0.703711\pi$
$349$	7.39898	−	12.8154i	0.396058	−	0.685993i	0.993236	+	0.116116i	$0.0370445\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.84847	+	11.8619i	−0.364507	+	0.631345i	−0.988697	−	0.149928i	$-0.952096\pi$
$353$	−6.84847	+	11.8619i	−0.364507	+	0.631345i	0.624190	+	0.781273i	$0.285429\pi$
$354$		0			0
$355$	−3.89898	−	6.75323i	−0.206936	−	0.358424i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.79796			−0.0948926			−0.0474463	−	0.998874i	$-0.515108\pi$
$359$	−1.79796			−0.0948926			−0.0474463	+	0.998874i	$0.515108\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$		0			0
$363$		0			0
$364$		0			0
$365$	2.44949	+	4.24264i	0.128212	+	0.222070i
$366$		0			0
$367$	−2.17423	+	3.76588i	−0.113494	+	0.196578i	−0.917177	−	0.398481i	$-0.869538\pi$
$367$	−2.17423	+	3.76588i	−0.113494	+	0.196578i	0.803683	+	0.595058i	$0.202871\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−15.3485	+	26.5843i	−0.796853	+	1.38019i
$372$		0			0
$373$	−15.8485	−	27.4504i	−0.820603	−	1.42133i	−0.905234	−	0.424913i	$-0.860305\pi$
$373$	−15.8485	−	27.4504i	−0.820603	−	1.42133i	0.0846315	−	0.996412i	$-0.473029\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.595918			−0.0306913
$378$		0			0
$379$	26.0000			1.33553			0.667765	−	0.744372i	$-0.267251\pi$
$379$	26.0000			1.33553			0.667765	+	0.744372i	$0.267251\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−14.2753	−	24.7255i	−0.729431	−	1.26341i	−0.957124	−	0.289679i	$-0.906451\pi$
$383$	−14.2753	−	24.7255i	−0.729431	−	1.26341i	0.227692	−	0.973733i	$-0.426882\pi$
$384$		0			0
$385$	2.50000	−	4.33013i	0.127412	−	0.220684i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−3.39898	+	5.88721i	−0.172335	+	0.298493i	−0.939236	−	0.343273i	$-0.888465\pi$
$389$	−3.39898	+	5.88721i	−0.172335	+	0.298493i	0.766901	+	0.641766i	$0.221798\pi$
$390$		0			0
$391$	−13.3485	−	23.1202i	−0.675061	−	1.16924i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−13.4495			−0.676717
$396$		0			0
$397$	−10.6969			−0.536864			−0.268432	−	0.963299i	$-0.586505\pi$
$397$	−10.6969			−0.536864			−0.268432	+	0.963299i	$0.586505\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−6.84847	−	11.8619i	−0.341996	−	0.592355i	0.642807	−	0.766028i	$-0.277770\pi$
$401$	−6.84847	−	11.8619i	−0.341996	−	0.592355i	−0.984803	+	0.173673i	$0.944436\pi$
$402$		0			0
$403$	7.52270	−	13.0297i	0.374733	−	0.649056i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	0.651531	−	1.12848i	0.0322952	−	0.0559369i
$408$		0			0
$409$	−13.2980	−	23.0327i	−0.657542	−	1.13890i	−0.981250	−	0.192739i	$-0.938263\pi$
$409$	−13.2980	−	23.0327i	−0.657542	−	1.13890i	0.323708	−	0.946157i	$-0.395070\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−49.4949			−2.43548
$414$		0			0
$415$	−0.550510			−0.0270235
$416$		0			0
$417$		0			0
$418$		0			0
$419$	15.6237	+	27.0611i	0.763269	+	1.32202i	0.941157	+	0.337970i	$0.109740\pi$
$419$	15.6237	+	27.0611i	0.763269	+	1.32202i	−0.177888	+	0.984051i	$0.556927\pi$
$420$		0			0
$421$	−0.0505103	+	0.0874863i	−0.00246172	+	0.00426382i	−0.867254	−	0.497867i	$-0.834117\pi$
$421$	−0.0505103	+	0.0874863i	−0.00246172	+	0.00426382i	0.864792	+	0.502130i	$0.167450\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−9.79796	+	16.9706i	−0.475271	+	0.823193i
$426$		0			0
$427$	−13.6237	−	23.5970i	−0.659298	−	1.14194i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	14.2020			0.684088			0.342044	−	0.939684i	$-0.388881\pi$
$431$	14.2020			0.684088			0.342044	+	0.939684i	$0.388881\pi$
$432$		0			0
$433$	−8.49490			−0.408239			−0.204119	−	0.978946i	$-0.565433\pi$
$433$	−8.49490			−0.408239			−0.204119	+	0.978946i	$0.565433\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−10.8990	−	18.8776i	−0.521369	−	0.903037i
$438$		0			0
$439$	−18.1742	+	31.4787i	−0.867409	+	1.50240i	−0.00277364	+	0.999996i	$0.500883\pi$
$439$	−18.1742	+	31.4787i	−0.867409	+	1.50240i	−0.864635	+	0.502400i	$0.832450\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−11.7247	+	20.3079i	−0.557059	+	0.964855i	0.440681	+	0.897664i	$0.354737\pi$
$443$	−11.7247	+	20.3079i	−0.557059	+	0.964855i	−0.997740	+	0.0671913i	$0.978596\pi$
$444$		0			0
$445$	−6.44949	−	11.1708i	−0.305735	−	0.529549i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−11.1010			−0.523890			−0.261945	−	0.965083i	$-0.584364\pi$
$449$	−11.1010			−0.523890			−0.261945	+	0.965083i	$0.584364\pi$
$450$		0			0
$451$	17.2474			0.812151
$452$		0			0
$453$		0			0
$454$		0			0
$455$	10.1742	+	17.6223i	0.476975	+	0.826146i
$456$		0			0
$457$	15.7474	−	27.2754i	0.736635	−	1.27589i	−0.217368	−	0.976090i	$-0.569747\pi$
$457$	15.7474	−	27.2754i	0.736635	−	1.27589i	0.954002	−	0.299799i	$-0.0969195\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	17.8485	−	30.9145i	0.831286	−	1.43983i	−0.0657327	−	0.997837i	$-0.520938\pi$
$461$	17.8485	−	30.9145i	0.831286	−	1.43983i	0.897019	−	0.441992i	$-0.145728\pi$
$462$		0			0
$463$	−15.6237	−	27.0611i	−0.726096	−	1.25764i	−0.958521	−	0.285021i	$-0.907999\pi$
$463$	−15.6237	−	27.0611i	−0.726096	−	1.25764i	0.232425	−	0.972614i	$-0.425334\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	39.5959			1.83228			0.916140	−	0.400858i	$-0.131288\pi$
$467$	39.5959			1.83228			0.916140	+	0.400858i	$0.131288\pi$
$468$		0			0
$469$	42.5959			1.96690
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.70204	−	2.94802i	−0.0782599	−	0.135550i
$474$		0			0
$475$	−8.00000	+	13.8564i	−0.367065	+	0.635776i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−12.5227	+	21.6900i	−0.572177	+	0.991040i	0.424165	+	0.905585i	$0.360568\pi$
$479$	−12.5227	+	21.6900i	−0.572177	+	0.991040i	−0.996342	+	0.0854547i	$0.972766\pi$
$480$		0			0
$481$	2.65153	+	4.59259i	0.120899	+	0.209404i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−3.89898			−0.177044
$486$		0			0
$487$	17.7980			0.806503			0.403251	−	0.915089i	$-0.367880\pi$
$487$	17.7980			0.806503			0.403251	+	0.915089i	$0.367880\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−5.37628	−	9.31198i	−0.242628	−	0.420244i	0.718834	−	0.695182i	$-0.244676\pi$
$491$	−5.37628	−	9.31198i	−0.242628	−	0.420244i	−0.961462	+	0.274938i	$0.911343\pi$
$492$		0			0
$493$	−0.247449	+	0.428594i	−0.0111445	+	0.0193029i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	13.4495	−	23.2952i	0.603292	−	1.04493i
$498$		0			0
$499$	−0.825765	−	1.43027i	−0.0369663	−	0.0640276i	0.846950	−	0.531672i	$-0.178436\pi$
$499$	−0.825765	−	1.43027i	−0.0369663	−	0.0640276i	−0.883917	+	0.467644i	$0.845103\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−39.7980			−1.77450			−0.887252	−	0.461286i	$-0.847388\pi$
$503$	−39.7980			−1.77450			−0.887252	+	0.461286i	$0.847388\pi$
$504$		0			0
$505$	−12.7980			−0.569502
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−7.74745	−	13.4190i	−0.343400	−	0.594786i	0.641662	−	0.766987i	$-0.278245\pi$
$509$	−7.74745	−	13.4190i	−0.343400	−	0.594786i	−0.985062	+	0.172202i	$0.944912\pi$
$510$		0			0
$511$	−8.44949	+	14.6349i	−0.373783	+	0.647412i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	6.27526	−	10.8691i	0.276521	−	0.478948i
$516$		0			0
$517$	4.60102	+	7.96920i	0.202353	+	0.350485i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$		0			0
$523$	−13.5959			−0.594508			−0.297254	−	0.954798i	$-0.596071\pi$
$523$	−13.5959			−0.594508			−0.297254	+	0.954798i	$0.596071\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−6.24745	−	10.8209i	−0.272143	−	0.471366i
$528$		0			0
$529$	−3.34847	+	5.79972i	−0.145586	+	0.252162i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−35.0959	+	60.7879i	−1.52017	+	2.63302i
$534$		0			0
$535$	2.89898	+	5.02118i	0.125334	+	0.217085i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	7.10102			0.305863
$540$		0			0
$541$	29.5959			1.27243			0.636214	−	0.771513i	$-0.280500\pi$
$541$	29.5959			1.27243			0.636214	+	0.771513i	$0.280500\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−0.449490	−	0.778539i	−0.0192540	−	0.0333489i
$546$		0			0
$547$	−3.27526	+	5.67291i	−0.140040	+	0.242556i	−0.927511	−	0.373795i	$-0.878056\pi$
$547$	−3.27526	+	5.67291i	−0.140040	+	0.242556i	0.787472	+	0.616351i	$0.211390\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.202041	+	0.349945i	−0.00860724	+	0.0149082i
$552$		0			0
$553$	−23.1969	−	40.1783i	−0.986434	−	1.70855i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	18.6969			0.792215			0.396107	−	0.918204i	$-0.370361\pi$
$557$	18.6969			0.792215			0.396107	+	0.918204i	$0.370361\pi$
$558$		0			0
$559$	13.8536			0.585944
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−2.17423	−	3.76588i	−0.0916331	−	0.158713i	0.816565	−	0.577253i	$-0.195875\pi$
$563$	−2.17423	−	3.76588i	−0.0916331	−	0.158713i	−0.908198	+	0.418540i	$0.862542\pi$
$564$		0			0
$565$	4.39898	−	7.61926i	0.185066	−	0.320545i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−0.500000	+	0.866025i	−0.0209611	+	0.0363057i	−0.876316	−	0.481737i	$-0.840006\pi$
$569$	−0.500000	+	0.866025i	−0.0209611	+	0.0363057i	0.855355	+	0.518043i	$0.173339\pi$
$570$		0			0
$571$	−1.82577	−	3.16232i	−0.0764059	−	0.132339i	0.825291	−	0.564708i	$-0.191011\pi$
$571$	−1.82577	−	3.16232i	−0.0764059	−	0.132339i	−0.901697	+	0.432369i	$0.857678\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	21.7980			0.909038
$576$		0			0
$577$	−19.1010			−0.795186			−0.397593	−	0.917562i	$-0.630154\pi$
$577$	−19.1010			−0.795186			−0.397593	+	0.917562i	$0.630154\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−0.949490	−	1.64456i	−0.0393915	−	0.0682280i
$582$		0			0
$583$	6.44949	−	11.1708i	0.267111	−	0.462649i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	14.9722	−	25.9326i	0.617969	−	1.07035i	−0.371887	−	0.928278i	$-0.621289\pi$
$587$	14.9722	−	25.9326i	0.617969	−	1.07035i	0.989856	−	0.142075i	$-0.0453774\pi$
$588$		0			0
$589$	−5.10102	−	8.83523i	−0.210184	−	0.364049i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−28.8990			−1.18674			−0.593369	−	0.804930i	$-0.702203\pi$
$593$	−28.8990			−1.18674			−0.593369	+	0.804930i	$0.702203\pi$
$594$		0			0
$595$	16.8990			0.692791
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−14.2753	−	24.7255i	−0.583271	−	1.01026i	−0.995089	−	0.0989888i	$-0.968439\pi$
$599$	−14.2753	−	24.7255i	−0.583271	−	1.01026i	0.411817	−	0.911266i	$-0.364894\pi$
$600$		0			0
$601$	−5.15153	+	8.92271i	−0.210135	+	0.363965i	−0.951757	−	0.306854i	$-0.900724\pi$
$601$	−5.15153	+	8.92271i	−0.210135	+	0.363965i	0.741621	+	0.670819i	$0.234057\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	4.44949	−	7.70674i	0.180897	−	0.313324i
$606$		0			0
$607$	12.9722	+	22.4685i	0.526525	+	0.911968i	0.999522	+	0.0309043i	$0.00983872\pi$
$607$	12.9722	+	22.4685i	0.526525	+	0.911968i	−0.472997	+	0.881064i	$0.656828\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−37.4495			−1.51504
$612$		0			0
$613$	−26.6969			−1.07828			−0.539140	−	0.842216i	$-0.681250\pi$
$613$	−26.6969			−1.07828			−0.539140	+	0.842216i	$0.681250\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	11.8485	+	20.5222i	0.477001	+	0.826191i	0.999653	−	0.0263559i	$-0.00839032\pi$
$617$	11.8485	+	20.5222i	0.477001	+	0.826191i	−0.522651	+	0.852547i	$0.675057\pi$
$618$		0			0
$619$	−13.0732	+	22.6435i	−0.525457	+	0.910118i	0.474104	+	0.880469i	$0.342772\pi$
$619$	−13.0732	+	22.6435i	−0.525457	+	0.910118i	−0.999560	+	0.0296488i	$0.990561\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	22.2474	−	38.5337i	0.891325	−	1.54382i
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	4.40408			0.175602
$630$		0			0
$631$	6.20204			0.246899			0.123450	−	0.992351i	$-0.460604\pi$
$631$	6.20204			0.246899			0.123450	+	0.992351i	$0.460604\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	4.00000	+	6.92820i	0.158735	+	0.274937i
$636$		0			0
$637$	−14.4495	+	25.0273i	−0.572510	+	0.991616i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	13.2980	−	23.0327i	0.525238	−	0.909739i	−0.474330	−	0.880347i	$-0.657310\pi$
$641$	13.2980	−	23.0327i	0.525238	−	0.909739i	0.999568	−	0.0293915i	$-0.00935696\pi$
$642$		0			0
$643$	2.17423	+	3.76588i	0.0857434	+	0.148512i	0.905708	−	0.423903i	$-0.139340\pi$
$643$	2.17423	+	3.76588i	0.0857434	+	0.148512i	−0.819964	+	0.572415i	$0.806007\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	9.79796			0.385198			0.192599	−	0.981278i	$-0.438308\pi$
$647$	9.79796			0.385198			0.192599	+	0.981278i	$0.438308\pi$
$648$		0			0
$649$	20.7980			0.816391
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−8.50000	−	14.7224i	−0.332631	−	0.576133i	0.650396	−	0.759595i	$-0.274603\pi$
$653$	−8.50000	−	14.7224i	−0.332631	−	0.576133i	−0.983027	+	0.183462i	$0.941270\pi$
$654$		0			0
$655$	6.62372	−	11.4726i	0.258810	−	0.448273i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−3.82577	+	6.62642i	−0.149031	+	0.258129i	−0.930869	−	0.365352i	$-0.880949\pi$
$659$	−3.82577	+	6.62642i	−0.149031	+	0.258129i	0.781839	+	0.623481i	$0.214282\pi$
$660$		0			0
$661$	15.1969	+	26.3219i	0.591092	+	1.02380i	0.994086	+	0.108599i	$0.0346365\pi$
$661$	15.1969	+	26.3219i	0.591092	+	1.02380i	−0.402993	+	0.915203i	$0.632030\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	13.7980			0.535062
$666$		0			0
$667$	0.550510			0.0213158
$668$		0			0
$669$		0			0
$670$		0			0
$671$	5.72474	+	9.91555i	0.221001	+	0.382786i
$672$		0			0
$673$	−13.6464	+	23.6363i	−0.526031	+	0.911113i	0.473509	+	0.880789i	$0.342987\pi$
$673$	−13.6464	+	23.6363i	−0.526031	+	0.911113i	−0.999540	+	0.0303237i	$0.990346\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	12.1969	−	21.1257i	0.468766	−	0.811927i	−0.530596	−	0.847625i	$-0.678032\pi$
$677$	12.1969	−	21.1257i	0.468766	−	0.811927i	0.999363	+	0.0356974i	$0.0113653\pi$
$678$		0			0
$679$	−6.72474	−	11.6476i	−0.258072	−	0.446994i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−17.3939			−0.665558			−0.332779	−	0.943005i	$-0.607986\pi$
$683$	−17.3939			−0.665558			−0.332779	+	0.943005i	$0.607986\pi$
$684$		0			0
$685$	10.1010			0.385940
$686$		0			0
$687$		0			0
$688$		0			0
$689$	26.2474	+	45.4619i	0.999948	+	1.73196i
$690$		0			0
$691$	−18.9722	+	32.8608i	−0.721736	+	1.25008i	0.238567	+	0.971126i	$0.423322\pi$
$691$	−18.9722	+	32.8608i	−0.721736	+	1.25008i	−0.960303	+	0.278958i	$0.910011\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.72474	+	2.98735i	−0.0654233	+	0.113316i
$696$		0			0
$697$	29.1464	+	50.4831i	1.10400	+	1.91218i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	12.4949			0.471926			0.235963	−	0.971762i	$-0.424176\pi$
$701$	12.4949			0.471926			0.235963	+	0.971762i	$0.424176\pi$
$702$		0			0
$703$	3.59592			0.135623
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−22.0732	−	38.2319i	−0.830149	−	1.43786i
$708$		0			0
$709$	2.50000	−	4.33013i	0.0938895	−	0.162621i	−0.815255	−	0.579102i	$-0.803403\pi$
$709$	2.50000	−	4.33013i	0.0938895	−	0.162621i	0.909145	+	0.416481i	$0.136737\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−6.94949	+	12.0369i	−0.260260	+	0.450784i
$714$		0			0
$715$	−4.27526	−	7.40496i	−0.159885	−	0.276930i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	31.1918			1.16326			0.581630	−	0.813454i	$-0.302415\pi$
$719$	31.1918			1.16326			0.581630	+	0.813454i	$0.302415\pi$
$720$		0			0
$721$	43.2929			1.61231
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.202041	−	0.349945i	−0.00750362	−	0.0129966i
$726$		0			0
$727$	−9.27526	+	16.0652i	−0.344000	+	0.595826i	−0.985172	−	0.171572i	$-0.945115\pi$
$727$	−9.27526	+	16.0652i	−0.344000	+	0.595826i	0.641171	+	0.767398i	$0.278449\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	5.75255	−	9.96371i	0.212766	−	0.368521i
$732$		0			0
$733$	5.94949	+	10.3048i	0.219749	+	0.380617i	0.954731	−	0.297470i	$-0.0961427\pi$
$733$	5.94949	+	10.3048i	0.219749	+	0.380617i	−0.734982	+	0.678087i	$0.762809\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−17.8990			−0.659317
$738$		0			0
$739$	14.0000			0.514998			0.257499	−	0.966279i	$-0.417102\pi$
$739$	14.0000			0.514998			0.257499	+	0.966279i	$0.417102\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	17.7247	+	30.7002i	0.650258	+	1.12628i	0.983060	+	0.183283i	$0.0586725\pi$
$743$	17.7247	+	30.7002i	0.650258	+	1.12628i	−0.332802	+	0.942997i	$0.607994\pi$
$744$		0			0
$745$	2.05051	−	3.55159i	0.0751249	−	0.130120i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−10.0000	+	17.3205i	−0.365392	+	0.632878i
$750$		0			0
$751$	−21.3207	−	36.9285i	−0.778002	−	1.34754i	−0.933092	−	0.359639i	$-0.882900\pi$
$751$	−21.3207	−	36.9285i	−0.778002	−	1.34754i	0.155090	−	0.987900i	$-0.450433\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−15.2474			−0.554911
$756$		0			0
$757$	−42.0000			−1.52652			−0.763258	−	0.646094i	$-0.776401\pi$
$757$	−42.0000			−1.52652			−0.763258	+	0.646094i	$0.776401\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−12.6464	−	21.9043i	−0.458433	−	0.794029i	0.540446	−	0.841379i	$-0.318256\pi$
$761$	−12.6464	−	21.9043i	−0.458433	−	0.794029i	−0.998878	+	0.0473502i	$0.984922\pi$
$762$		0			0
$763$	1.55051	−	2.68556i	0.0561322	−	0.0972239i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−42.3207	+	73.3015i	−1.52811	+	2.64677i
$768$		0			0
$769$	18.2980	+	31.6930i	0.659841	+	1.14288i	0.980656	+	0.195737i	$0.0627098\pi$
$769$	18.2980	+	31.6930i	0.659841	+	1.14288i	−0.320815	+	0.947142i	$0.603957\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	36.4949			1.31263			0.656315	−	0.754487i	$-0.272114\pi$
$773$	36.4949			1.31263			0.656315	+	0.754487i	$0.272114\pi$
$774$		0			0
$775$	10.2020			0.366468
$776$		0			0
$777$		0			0
$778$		0			0
$779$	23.7980	+	41.2193i	0.852650	+	1.47683i
$780$		0			0
$781$	−5.65153	+	9.78874i	−0.202228	+	0.350269i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	5.39898	−	9.35131i	0.192698	−	0.333762i
$786$		0			0
$787$	−10.6237	−	18.4008i	−0.378695	−	0.655919i	0.612178	−	0.790720i	$-0.290294\pi$
$787$	−10.6237	−	18.4008i	−0.378695	−	0.655919i	−0.990873	+	0.134801i	$0.956960\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	30.3485			1.07907
$792$		0			0
$793$	−46.5959			−1.65467
$794$		0			0
$795$		0			0
$796$		0			0
$797$	23.8485	+	41.3068i	0.844756	+	1.46316i	0.885833	+	0.464005i	$0.153588\pi$
$797$	23.8485	+	41.3068i	0.844756	+	1.46316i	−0.0410767	+	0.999156i	$0.513079\pi$
$798$		0			0
$799$	−15.5505	+	26.9343i	−0.550138	+	0.952866i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	3.55051	−	6.14966i	0.125295	−	0.217017i
$804$		0			0
$805$	−9.39898	−	16.2795i	−0.331270	−	0.573777i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	32.4949			1.14246			0.571230	−	0.820790i	$-0.306466\pi$
$809$	32.4949			1.14246			0.571230	+	0.820790i	$0.306466\pi$
$810$		0			0
$811$	−8.40408			−0.295107			−0.147554	−	0.989054i	$-0.547140\pi$
$811$	−8.40408			−0.295107			−0.147554	+	0.989054i	$0.547140\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−2.89898	−	5.02118i	−0.101547	−	0.175884i
$816$		0			0
$817$	4.69694	−	8.13534i	0.164325	−	0.284619i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	7.64643	−	13.2440i	0.266862	−	0.462219i	−0.701188	−	0.712977i	$-0.747346\pi$
$821$	7.64643	−	13.2440i	0.266862	−	0.462219i	0.968050	+	0.250758i	$0.0806798\pi$
$822$		0			0
$823$	5.27526	+	9.13701i	0.183884	+	0.318496i	0.943200	−	0.332226i	$-0.107800\pi$
$823$	5.27526	+	9.13701i	0.183884	+	0.318496i	−0.759316	+	0.650722i	$0.774466\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−28.0000			−0.973655			−0.486828	−	0.873498i	$-0.661846\pi$
$827$	−28.0000			−0.973655			−0.486828	+	0.873498i	$0.661846\pi$
$828$		0			0
$829$	−23.1010			−0.802332			−0.401166	−	0.916005i	$-0.631395\pi$
$829$	−23.1010			−0.802332			−0.401166	+	0.916005i	$0.631395\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	12.0000	+	20.7846i	0.415775	+	0.720144i
$834$		0			0
$835$	−2.27526	+	3.94086i	−0.0787385	+	0.136379i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	15.1742	−	26.2825i	0.523873	−	0.907374i	−0.475741	−	0.879585i	$-0.657820\pi$
$839$	15.1742	−	26.2825i	0.523873	−	0.907374i	0.999614	−	0.0277888i	$-0.00884660\pi$
$840$		0			0
$841$	14.4949	+	25.1059i	0.499824	+	0.865721i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	21.7980			0.749873
$846$		0			0
$847$	30.6969			1.05476
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−2.44949	−	4.24264i	−0.0839674	−	0.145436i
$852$		0			0
$853$	3.94949	−	6.84072i	0.135228	−	0.234222i	−0.790457	−	0.612518i	$-0.790157\pi$
$853$	3.94949	−	6.84072i	0.135228	−	0.234222i	0.925685	+	0.378296i	$0.123490\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−13.9495	+	24.1612i	−0.476505	+	0.825332i	−0.999638	−	0.0269199i	$-0.991430\pi$
$857$	−13.9495	+	24.1612i	−0.476505	+	0.825332i	0.523132	+	0.852252i	$0.324763\pi$
$858$		0			0
$859$	−10.7247	−	18.5758i	−0.365924	−	0.633798i	0.623000	−	0.782222i	$-0.285914\pi$
$859$	−10.7247	−	18.5758i	−0.365924	−	0.633798i	−0.988924	+	0.148423i	$0.952580\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−17.7980			−0.605850			−0.302925	−	0.953014i	$-0.597963\pi$
$863$	−17.7980			−0.605850			−0.302925	+	0.953014i	$0.597963\pi$
$864$		0			0
$865$	−3.00000			−0.102003
$866$		0			0
$867$		0			0
$868$		0			0
$869$	9.74745	+	16.8831i	0.330660	+	0.572719i
$870$		0			0
$871$	36.4217	−	63.0842i	1.23410	−	2.13753i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−15.5227	+	26.8861i	−0.524763	+	0.908916i
$876$		0			0
$877$	13.9495	+	24.1612i	0.471041	+	0.815867i	0.999451	−	0.0331224i	$-0.0105451\pi$
$877$	13.9495	+	24.1612i	0.471041	+	0.815867i	−0.528411	+	0.848989i	$0.677212\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	24.4949			0.825254			0.412627	−	0.910900i	$-0.364611\pi$
$881$	24.4949			0.825254			0.412627	+	0.910900i	$0.364611\pi$
$882$		0			0
$883$	−39.5959			−1.33251			−0.666254	−	0.745725i	$-0.732103\pi$
$883$	−39.5959			−1.33251			−0.666254	+	0.745725i	$0.732103\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	17.4217	+	30.1752i	0.584963	+	1.01319i	0.994880	+	0.101063i	$0.0322243\pi$
$887$	17.4217	+	30.1752i	0.584963	+	1.01319i	−0.409917	+	0.912123i	$0.634442\pi$
$888$		0			0
$889$	−13.7980	+	23.8988i	−0.462769	+	0.801539i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−12.6969	+	21.9917i	−0.424887	+	0.735926i
$894$		0			0
$895$	6.00000	+	10.3923i	0.200558	+	0.347376i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.257654			0.00859324
$900$		0			0
$901$	43.5959			1.45239
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−5.34847	−	9.26382i	−0.177789	−	0.307940i
$906$		0			0
$907$	12.6237	−	21.8649i	0.419164	−	0.726013i	−0.576692	−	0.816962i	$-0.695657\pi$
$907$	12.6237	−	21.8649i	0.419164	−	0.726013i	0.995856	+	0.0909487i	$0.0289899\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	21.7702	−	37.7070i	0.721277	−	1.24929i	−0.239211	−	0.970968i	$-0.576889\pi$
$911$	21.7702	−	37.7070i	0.721277	−	1.24929i	0.960488	−	0.278321i	$-0.0897780\pi$
$912$		0			0
$913$	0.398979	+	0.691053i	0.0132043	+	0.0228705i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	45.6969			1.50905
$918$		0			0
$919$	9.79796			0.323205			0.161602	−	0.986856i	$-0.448334\pi$
$919$	9.79796			0.323205			0.161602	+	0.986856i	$0.448334\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−23.0000	−	39.8372i	−0.757054	−	1.31126i
$924$		0			0
$925$	−1.79796	+	3.11416i	−0.0591165	+	0.102393i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	23.8485	−	41.3068i	0.782443	−	1.35523i	−0.148072	−	0.988977i	$-0.547307\pi$
$929$	23.8485	−	41.3068i	0.782443	−	1.35523i	0.930515	−	0.366254i	$-0.119360\pi$
$930$		0			0
$931$	9.79796	+	16.9706i	0.321115	+	0.556188i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−7.10102			−0.232228
$936$		0			0
$937$	56.4949			1.84561			0.922804	−	0.385270i	$-0.125892\pi$
$937$	56.4949			1.84561			0.922804	+	0.385270i	$0.125892\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	3.50000	+	6.06218i	0.114097	+	0.197621i	0.917418	−	0.397924i	$-0.130269\pi$
$941$	3.50000	+	6.06218i	0.114097	+	0.197621i	−0.803322	+	0.595545i	$0.796936\pi$
$942$		0			0
$943$	32.4217	−	56.1560i	1.05580	−	1.82869i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	10.3763	−	17.9722i	0.337184	−	0.584019i	−0.646718	−	0.762729i	$-0.723859\pi$
$947$	10.3763	−	17.9722i	0.337184	−	0.584019i	0.983902	+	0.178710i	$0.0571923\pi$
$948$		0			0
$949$	14.4495	+	25.0273i	0.469050	+	0.812419i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−43.1010			−1.39618			−0.698090	−	0.716011i	$-0.745966\pi$
$953$	−43.1010			−1.39618			−0.698090	+	0.716011i	$0.745966\pi$
$954$		0			0
$955$	−12.5505			−0.406125
$956$		0			0
$957$		0			0
$958$		0			0
$959$	17.4217	+	30.1752i	0.562575	+	0.974409i
$960$		0			0
$961$	12.2474	−	21.2132i	0.395079	−	0.684297i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−2.05051	+	3.55159i	−0.0660083	+	0.114330i
$966$		0			0
$967$	−7.62372	−	13.2047i	−0.245162	−	0.424634i	0.717015	−	0.697058i	$-0.245508\pi$
$967$	−7.62372	−	13.2047i	−0.245162	−	0.424634i	−0.962177	+	0.272424i	$0.912175\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−10.0000			−0.320915			−0.160458	−	0.987043i	$-0.551297\pi$
$971$	−10.0000			−0.320915			−0.160458	+	0.987043i	$0.551297\pi$
$972$		0			0
$973$	−11.8990			−0.381464
$974$		0			0
$975$		0			0
$976$		0			0
$977$	6.60102	+	11.4333i	0.211185	+	0.365784i	0.952086	−	0.305831i	$-0.0989343\pi$
$977$	6.60102	+	11.4333i	0.211185	+	0.365784i	−0.740900	+	0.671615i	$0.765601\pi$
$978$		0			0
$979$	−9.34847	+	16.1920i	−0.298778	+	0.517499i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−9.82577	+	17.0187i	−0.313393	+	0.542813i	−0.979095	−	0.203405i	$-0.934799\pi$
$983$	−9.82577	+	17.0187i	−0.313393	+	0.542813i	0.665701	+	0.746218i	$0.268132\pi$
$984$		0			0
$985$	−8.79796	−	15.2385i	−0.280326	−	0.485539i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−12.7980			−0.406951
$990$		0			0
$991$	21.3939			0.679599			0.339799	−	0.940498i	$-0.389641\pi$
$991$	21.3939			0.679599			0.339799	+	0.940498i	$0.389641\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−3.89898	−	6.75323i	−0.123606	−	0.214092i
$996$		0			0
$997$	−16.1969	+	28.0539i	−0.512962	+	0.888477i	0.486925	+	0.873444i	$0.338119\pi$
$997$	−16.1969	+	28.0539i	−0.512962	+	0.888477i	−0.999887	+	0.0150327i	$0.995215\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.i.e.289.2		4
3.2	odd	2		288.2.i.c.97.1	✓	4
4.3	odd	2		864.2.i.c.289.1		4
8.3	odd	2		1728.2.i.k.1153.1		4
8.5	even	2		1728.2.i.m.1153.2		4
9.2	odd	6		2592.2.a.j.1.1		2
9.4	even	3	inner	864.2.i.e.577.2		4
9.5	odd	6		288.2.i.c.193.2	yes	4
9.7	even	3		2592.2.a.o.1.1		2
12.11	even	2		288.2.i.e.97.2	yes	4
24.5	odd	2		576.2.i.m.385.2		4
24.11	even	2		576.2.i.i.385.1		4
36.7	odd	6		2592.2.a.s.1.2		2
36.11	even	6		2592.2.a.n.1.2		2
36.23	even	6		288.2.i.e.193.1	yes	4
36.31	odd	6		864.2.i.c.577.1		4
72.5	odd	6		576.2.i.m.193.1		4
72.11	even	6		5184.2.a.by.1.2		2
72.13	even	6		1728.2.i.m.577.2		4
72.29	odd	6		5184.2.a.bu.1.1		2
72.43	odd	6		5184.2.a.bn.1.2		2
72.59	even	6		576.2.i.i.193.2		4
72.61	even	6		5184.2.a.bj.1.1		2
72.67	odd	6		1728.2.i.k.577.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.i.c.97.1	✓	4	3.2	odd	2
288.2.i.c.193.2	yes	4	9.5	odd	6
288.2.i.e.97.2	yes	4	12.11	even	2
288.2.i.e.193.1	yes	4	36.23	even	6
576.2.i.i.193.2		4	72.59	even	6
576.2.i.i.385.1		4	24.11	even	2
576.2.i.m.193.1		4	72.5	odd	6
576.2.i.m.385.2		4	24.5	odd	2
864.2.i.c.289.1		4	4.3	odd	2
864.2.i.c.577.1		4	36.31	odd	6
864.2.i.e.289.2		4	1.1	even	1	trivial
864.2.i.e.577.2		4	9.4	even	3	inner
1728.2.i.k.577.1		4	72.67	odd	6
1728.2.i.k.1153.1		4	8.3	odd	2
1728.2.i.m.577.2		4	72.13	even	6
1728.2.i.m.1153.2		4	8.5	even	2
2592.2.a.j.1.1		2	9.2	odd	6
2592.2.a.n.1.2		2	36.11	even	6
2592.2.a.o.1.1		2	9.7	even	3
2592.2.a.s.1.2		2	36.7	odd	6
5184.2.a.bj.1.1		2	72.61	even	6
5184.2.a.bn.1.2		2	72.43	odd	6
5184.2.a.bu.1.1		2	72.29	odd	6
5184.2.a.by.1.2		2	72.11	even	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{5} +(1.72474 - 2.98735i) q^{7} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{5} +(1.72474 - 2.98735i) q^{7} +(-0.724745 + 1.25529i) q^{11} +(-2.94949 - 5.10867i) q^{13} -4.89898 q^{17} -4.00000 q^{19} +(2.72474 + 4.71940i) q^{23} +(2.00000 - 3.46410i) q^{25} +(0.0505103 - 0.0874863i) q^{29} +(1.27526 + 2.20881i) q^{31} -3.44949 q^{35} -0.898979 q^{37} +(-5.94949 - 10.3048i) q^{41} +(-1.17423 + 2.03383i) q^{43} +(3.17423 - 5.49794i) q^{47} +(-2.44949 - 4.24264i) q^{49} -8.89898 q^{53} +1.44949 q^{55} +(-7.17423 - 12.4261i) q^{59} +(3.94949 - 6.84072i) q^{61} +(-2.94949 + 5.10867i) q^{65} +(6.17423 + 10.6941i) q^{67} +7.79796 q^{71} -4.89898 q^{73} +(2.50000 + 4.33013i) q^{77} +(6.72474 - 11.6476i) q^{79} +(0.275255 - 0.476756i) q^{83} +(2.44949 + 4.24264i) q^{85} +12.8990 q^{89} -20.3485 q^{91} +(2.00000 + 3.46410i) q^{95} +(1.94949 - 3.37662i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{5} + 2 q^{7}+O(q^{10}) \) 4 * q - 2 * q^5 + 2 * q^7	\( 4 q - 2 q^{5} + 2 q^{7} + 2 q^{11} - 2 q^{13} - 16 q^{19} + 6 q^{23} + 8 q^{25} + 10 q^{29} + 10 q^{31} - 4 q^{35} + 16 q^{37} - 14 q^{41} + 10 q^{43} - 2 q^{47} - 16 q^{53} - 4 q^{55} - 14 q^{59} + 6 q^{61} - 2 q^{65} + 10 q^{67} - 8 q^{71} + 10 q^{77} + 22 q^{79} + 6 q^{83} + 32 q^{89} - 52 q^{91} + 8 q^{95} - 2 q^{97}+O(q^{100}) \) 4 * q - 2 * q^5 + 2 * q^7 + 2 * q^11 - 2 * q^13 - 16 * q^19 + 6 * q^23 + 8 * q^25 + 10 * q^29 + 10 * q^31 - 4 * q^35 + 16 * q^37 - 14 * q^41 + 10 * q^43 - 2 * q^47 - 16 * q^53 - 4 * q^55 - 14 * q^59 + 6 * q^61 - 2 * q^65 + 10 * q^67 - 8 * q^71 + 10 * q^77 + 22 * q^79 + 6 * q^83 + 32 * q^89 - 52 * q^91 + 8 * q^95 - 2 * q^97

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