LMFDB - Embedded newform 864.2.r.b.721.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(145,864)]

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, 3, 2]))

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

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

chi := DirichletCharacter("864.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.r (of order $6$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + x^{14} + 2 x^{12} - 4 x^{11} - 8 x^{9} + 4 x^{8} - 16 x^{7} - 32 x^{5} + 32 x^{4} + \cdots + 256 $ x^16 - x^15 + x^14 + 2x^12 - 4x^11 - 8x^9 + 4x^8 - 16x^7 - 32x^5 + 32x^4 + 64x^2 - 128*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			721.4
Root			$-1.34532 + 0.436011i$ of defining polynomial
Character	$\chi$	$=$	864.721
Dual form			864.2.r.b.145.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.602794 + 0.348023i) q^{5} +(-0.795065 + 1.37709i) q^{7} +O(q^{10})$	$q+(-0.602794 + 0.348023i) q^{5} +(-0.795065 + 1.37709i) q^{7} +(-2.37222 - 1.36960i) q^{11} +(4.76780 - 2.75269i) q^{13} +5.65175 q^{17} +0.963328i q^{19} +(3.28857 + 5.69597i) q^{23} +(-2.25776 + 3.91055i) q^{25} +(2.85076 + 1.64589i) q^{29} +(3.69844 + 6.40589i) q^{31} -1.10680i q^{35} +6.25538i q^{37} +(0.931886 + 1.61407i) q^{41} +(-2.99838 - 1.73111i) q^{43} +(3.85668 - 6.67997i) q^{47} +(2.23574 + 3.87242i) q^{49} -2.54179i q^{53} +1.90662 q^{55} +(4.62019 - 2.66747i) q^{59} +(-7.93715 - 4.58252i) q^{61} +(-1.91600 + 3.31861i) q^{65} +(5.95780 - 3.43974i) q^{67} +3.68351 q^{71} +2.83201 q^{73} +(3.77214 - 2.17785i) q^{77} +(-2.87870 + 4.98605i) q^{79} +(5.74968 + 3.31958i) q^{83} +(-3.40684 + 1.96694i) q^{85} +2.98701 q^{89} +8.75427i q^{91} +(-0.335261 - 0.580689i) q^{95} +(-1.24837 + 2.16224i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{7}+O(q^{10}) $ 16 * q - 6 * q^7	$ 16 q - 6 q^{7} + 28 q^{17} - 10 q^{23} + 2 q^{25} + 10 q^{31} + 8 q^{41} + 6 q^{47} + 18 q^{49} + 4 q^{55} + 14 q^{65} + 72 q^{71} - 44 q^{73} + 30 q^{79} - 64 q^{89} + 44 q^{95}+O(q^{100}) $ 16 * q - 6 * q^7 + 28 * q^17 - 10 * q^23 + 2 * q^25 + 10 * q^31 + 8 * q^41 + 6 * q^47 + 18 * q^49 + 4 * q^55 + 14 * q^65 + 72 * q^71 - 44 * q^73 + 30 * q^79 - 64 * q^89 + 44 * q^95

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
$5$	−0.602794	+	0.348023i	−0.269578	+	0.155641i	−0.628696	−	0.777651i	$-0.716411\pi$
$5$	−0.602794	+	0.348023i	−0.269578	+	0.155641i	0.359118	+	0.933292i	$0.383078\pi$
$6$		0			0
$7$	−0.795065	+	1.37709i	−0.300506	+	0.520492i	−0.976251	−	0.216644i	$-0.930489\pi$
$7$	−0.795065	+	1.37709i	−0.300506	+	0.520492i	0.675745	+	0.737136i	$0.263822\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.37222	−	1.36960i	−0.715252	−	0.412951i	0.0977506	−	0.995211i	$-0.468835\pi$
$11$	−2.37222	−	1.36960i	−0.715252	−	0.412951i	−0.813003	+	0.582260i	$0.802169\pi$
$12$		0			0
$13$	4.76780	−	2.75269i	1.32235	−	0.763460i	0.338248	−	0.941057i	$-0.390166\pi$
$13$	4.76780	−	2.75269i	1.32235	−	0.763460i	0.984103	+	0.177597i	$0.0568325\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	5.65175			1.37075			0.685375	−	0.728190i	$-0.259638\pi$
$17$	5.65175			1.37075			0.685375	+	0.728190i	$0.259638\pi$
$18$		0			0
$19$			0.963328i			0.221003i	0.993876	+	0.110501i	$0.0352457\pi$
$19$			0.963328i			0.221003i	−0.993876	+	0.110501i	$0.964754\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.28857	+	5.69597i	0.685714	+	1.18769i	0.973212	+	0.229910i	$0.0738432\pi$
$23$	3.28857	+	5.69597i	0.685714	+	1.18769i	−0.287498	+	0.957781i	$0.592823\pi$
$24$		0			0
$25$	−2.25776	+	3.91055i	−0.451552	+	0.782111i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.85076	+	1.64589i	0.529373	+	0.305634i	0.740761	−	0.671768i	$-0.234465\pi$
$29$	2.85076	+	1.64589i	0.529373	+	0.305634i	−0.211388	+	0.977402i	$0.567798\pi$
$30$		0			0
$31$	3.69844	+	6.40589i	0.664259	+	1.15053i	0.979486	+	0.201514i	$0.0645863\pi$
$31$	3.69844	+	6.40589i	0.664259	+	1.15053i	−0.315226	+	0.949017i	$0.602080\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		−	1.10680i		−	0.187084i
$36$		0			0
$37$			6.25538i			1.02838i	0.857677	+	0.514189i	$0.171907\pi$
$37$			6.25538i			1.02838i	−0.857677	+	0.514189i	$0.828093\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.931886	+	1.61407i	0.145536	+	0.252076i	0.929573	−	0.368639i	$-0.120176\pi$
$41$	0.931886	+	1.61407i	0.145536	+	0.252076i	−0.784037	+	0.620714i	$0.786843\pi$
$42$		0			0
$43$	−2.99838	−	1.73111i	−0.457248	−	0.263992i	0.253638	−	0.967299i	$-0.418373\pi$
$43$	−2.99838	−	1.73111i	−0.457248	−	0.263992i	−0.710886	+	0.703307i	$0.751706\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.85668	−	6.67997i	0.562555	−	0.974374i	−0.434717	−	0.900567i	$-0.643152\pi$
$47$	3.85668	−	6.67997i	0.562555	−	0.974374i	0.997273	−	0.0738070i	$-0.0235149\pi$
$48$		0			0
$49$	2.23574	+	3.87242i	0.319392	+	0.553203i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	2.54179i		−	0.349141i	−0.984645	−	0.174571i	$-0.944146\pi$
$53$		−	2.54179i		−	0.349141i	0.984645	−	0.174571i	$-0.0558537\pi$
$54$		0			0
$55$	1.90662			0.257088
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.62019	−	2.66747i	0.601498	−	0.347275i	−0.168133	−	0.985764i	$-0.553774\pi$
$59$	4.62019	−	2.66747i	0.601498	−	0.347275i	0.769631	+	0.638489i	$0.220440\pi$
$60$		0			0
$61$	−7.93715	−	4.58252i	−1.01625	−	0.586731i	−0.103233	−	0.994657i	$-0.532919\pi$
$61$	−7.93715	−	4.58252i	−1.01625	−	0.586731i	−0.913015	+	0.407926i	$0.866252\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.91600	+	3.31861i	−0.237651	+	0.411623i
$66$		0			0
$67$	5.95780	−	3.43974i	0.727861	−	0.420231i	−0.0897783	−	0.995962i	$-0.528616\pi$
$67$	5.95780	−	3.43974i	0.727861	−	0.420231i	0.817639	+	0.575731i	$0.195283\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.68351			0.437153			0.218576	−	0.975820i	$-0.429859\pi$
$71$	3.68351			0.437153			0.218576	+	0.975820i	$0.429859\pi$
$72$		0			0
$73$	2.83201			0.331461			0.165731	−	0.986171i	$-0.447002\pi$
$73$	2.83201			0.331461			0.165731	+	0.986171i	$0.447002\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.77214	−	2.17785i	0.429875	−	0.248189i
$78$		0			0
$79$	−2.87870	+	4.98605i	−0.323879	+	0.560975i	−0.981285	−	0.192562i	$-0.938320\pi$
$79$	−2.87870	+	4.98605i	−0.323879	+	0.560975i	0.657406	+	0.753537i	$0.271654\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.74968	+	3.31958i	0.631110	+	0.364371i	0.781182	−	0.624304i	$-0.214617\pi$
$83$	5.74968	+	3.31958i	0.631110	+	0.364371i	−0.150072	+	0.988675i	$0.547951\pi$
$84$		0			0
$85$	−3.40684	+	1.96694i	−0.369524	+	0.213345i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.98701			0.316622			0.158311	−	0.987389i	$-0.449395\pi$
$89$	2.98701			0.316622			0.158311	+	0.987389i	$0.449395\pi$
$90$		0			0
$91$			8.75427i			0.917697i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.335261	−	0.580689i	−0.0343970	−	0.0595774i
$96$		0			0
$97$	−1.24837	+	2.16224i	−0.126753	+	0.219543i	−0.922417	−	0.386196i	$-0.873789\pi$
$97$	−1.24837	+	2.16224i	−0.126753	+	0.219543i	0.795664	+	0.605738i	$0.207122\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−8.22136	−	4.74661i	−0.818056	−	0.472305i	0.0316896	−	0.999498i	$-0.489911\pi$
$101$	−8.22136	−	4.74661i	−0.818056	−	0.472305i	−0.849746	+	0.527193i	$0.823245\pi$
$102$		0			0
$103$	−7.37220	−	12.7690i	−0.726405	−	1.25817i	−0.958393	−	0.285451i	$-0.907857\pi$
$103$	−7.37220	−	12.7690i	−0.726405	−	1.25817i	0.231989	−	0.972719i	$-0.425477\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			7.83384i			0.757325i	0.925535	+	0.378663i	$0.123616\pi$
$107$			7.83384i			0.757325i	−0.925535	+	0.378663i	$0.876384\pi$
$108$		0			0
$109$		−	0.242400i		−	0.0232177i	−0.999933	−	0.0116089i	$-0.996305\pi$
$109$		−	0.242400i		−	0.0232177i	0.999933	−	0.0116089i	$-0.00369529\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−4.34789	−	7.53076i	−0.409015	−	0.708435i	0.585765	−	0.810481i	$-0.300794\pi$
$113$	−4.34789	−	7.53076i	−0.409015	−	0.708435i	−0.994780	+	0.102046i	$0.967461\pi$
$114$		0			0
$115$	−3.96466	−	2.28900i	−0.369706	−	0.213450i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−4.49350	+	7.78298i	−0.411919	+	0.713464i
$120$		0			0
$121$	−1.74837	−	3.02827i	−0.158943	−	0.275297i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	6.62325i		−	0.592401i
$126$		0			0
$127$	1.72754			0.153295			0.0766473	−	0.997058i	$-0.475578\pi$
$127$	1.72754			0.153295			0.0766473	+	0.997058i	$0.475578\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.74968	+	3.31958i	−0.502352	+	0.290033i	−0.729684	−	0.683784i	$-0.760333\pi$
$131$	−5.74968	+	3.31958i	−0.502352	+	0.290033i	0.227332	+	0.973817i	$0.427000\pi$
$132$		0			0
$133$	−1.32659	−	0.765908i	−0.115030	−	0.0664127i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.81325	+	3.14063i	−0.154916	+	0.268322i	−0.933028	−	0.359803i	$-0.882844\pi$
$137$	−1.81325	+	3.14063i	−0.154916	+	0.268322i	0.778112	+	0.628125i	$0.216177\pi$
$138$		0			0
$139$	14.9919	−	8.65556i	1.27159	−	0.734155i	0.296307	−	0.955093i	$-0.404245\pi$
$139$	14.9919	−	8.65556i	1.27159	−	0.734155i	0.975288	+	0.220937i	$0.0709117\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−15.0804			−1.26109
$144$		0			0
$145$	−2.29123			−0.190276
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−18.7251	+	10.8109i	−1.53402	+	0.885665i	−0.534846	+	0.844949i	$0.679631\pi$
$149$	−18.7251	+	10.8109i	−1.53402	+	0.885665i	−0.999171	+	0.0407158i	$0.987036\pi$
$150$		0			0
$151$	6.35019	−	10.9988i	0.516771	−	0.895073i	−0.483039	−	0.875599i	$-0.660467\pi$
$151$	6.35019	−	10.9988i	0.516771	−	0.895073i	0.999810	−	0.0194749i	$-0.00619944\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−4.45880	−	2.57429i	−0.358139	−	0.206772i
$156$		0			0
$157$	15.1285	−	8.73443i	1.20738	−	0.697083i	0.245197	−	0.969473i	$-0.421147\pi$
$157$	15.1285	−	8.73443i	1.20738	−	0.697083i	0.962187	+	0.272390i	$0.0878140\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−10.4585			−0.824245
$162$		0			0
$163$			8.56748i			0.671057i	0.942030	+	0.335528i	$0.108915\pi$
$163$			8.56748i			0.671057i	−0.942030	+	0.335528i	$0.891085\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.97532	−	10.3496i	−0.462384	−	0.800873i	0.536695	−	0.843776i	$-0.319673\pi$
$167$	−5.97532	−	10.3496i	−0.462384	−	0.800873i	−0.999079	+	0.0429032i	$0.986339\pi$
$168$		0			0
$169$	8.65464	−	14.9903i	0.665741	−	1.15310i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	11.2973	+	6.52248i	0.858916	+	0.495895i	0.863649	−	0.504094i	$-0.168173\pi$
$173$	11.2973	+	6.52248i	0.858916	+	0.495895i	−0.00473326	+	0.999989i	$0.501507\pi$
$174$		0			0
$175$	−3.59013	−	6.21829i	−0.271388	−	0.470058i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	3.31875i		−	0.248055i	−0.992279	−	0.124028i	$-0.960419\pi$
$179$		−	3.31875i		−	0.248055i	0.992279	−	0.124028i	$-0.0395811\pi$
$180$		0			0
$181$			14.9128i			1.10846i	0.832363	+	0.554231i	$0.186987\pi$
$181$			14.9128i			1.10846i	−0.832363	+	0.554231i	$0.813013\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.17702	−	3.77070i	−0.160058	−	0.277228i
$186$		0			0
$187$	−13.4072	−	7.74065i	−0.980432	−	0.566053i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	3.65884	−	6.33729i	0.264744	−	0.458550i	−0.702752	−	0.711434i	$-0.748046\pi$
$191$	3.65884	−	6.33729i	0.264744	−	0.458550i	0.967497	+	0.252884i	$0.0813792\pi$
$192$		0			0
$193$	−10.2354	−	17.7282i	−0.736759	−	1.27610i	−0.953947	−	0.299974i	$-0.903022\pi$
$193$	−10.2354	−	17.7282i	−0.736759	−	1.27610i	0.217189	−	0.976130i	$-0.430311\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			20.5437i			1.46368i	0.681479	+	0.731838i	$0.261337\pi$
$197$			20.5437i			1.46368i	−0.681479	+	0.731838i	$0.738663\pi$
$198$		0			0
$199$	−1.95597			−0.138655			−0.0693275	−	0.997594i	$-0.522085\pi$
$199$	−1.95597			−0.138655			−0.0693275	+	0.997594i	$0.522085\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−4.53308	+	2.61718i	−0.318160	+	0.183690i
$204$		0			0
$205$	−1.12347	−	0.648636i	−0.0784666	−	0.0453027i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.31938	−	2.28523i	0.0912633	−	0.158073i
$210$		0			0
$211$	−9.10981	+	5.25955i	−0.627145	+	0.362082i	−0.779646	−	0.626221i	$-0.784601\pi$
$211$	−9.10981	+	5.25955i	−0.627145	+	0.362082i	0.152501	+	0.988303i	$0.451267\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.40987			0.164352
$216$		0			0
$217$	−11.7620			−0.798456
$218$		0			0
$219$		0			0
$220$		0			0
$221$	26.9464	−	15.5575i	1.81261	−	1.04651i
$222$		0			0
$223$	−1.93129	+	3.34510i	−0.129329	+	0.224004i	−0.923417	−	0.383799i	$-0.874616\pi$
$223$	−1.93129	+	3.34510i	−0.129329	+	0.224004i	0.794088	+	0.607803i	$0.207949\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−13.9183	−	8.03574i	−0.923790	−	0.533351i	−0.0389481	−	0.999241i	$-0.512401\pi$
$227$	−13.9183	−	8.03574i	−0.923790	−	0.533351i	−0.884842	+	0.465891i	$0.845734\pi$
$228$		0			0
$229$	−7.46319	+	4.30888i	−0.493182	+	0.284739i	−0.725893	−	0.687807i	$-0.758573\pi$
$229$	−7.46319	+	4.30888i	−0.493182	+	0.284739i	0.232712	+	0.972546i	$0.425240\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−24.1535			−1.58235			−0.791176	−	0.611589i	$-0.790531\pi$
$233$	−24.1535			−1.58235			−0.791176	+	0.611589i	$0.790531\pi$
$234$		0			0
$235$			5.36886i			0.350226i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−2.01493	−	3.48996i	−0.130335	−	0.225746i	0.793471	−	0.608608i	$-0.208272\pi$
$239$	−2.01493	−	3.48996i	−0.130335	−	0.225746i	−0.923806	+	0.382862i	$0.874939\pi$
$240$		0			0
$241$	2.81649	−	4.87830i	0.181426	−	0.314239i	−0.760940	−	0.648822i	$-0.775262\pi$
$241$	2.81649	−	4.87830i	0.181426	−	0.314239i	0.942366	+	0.334583i	$0.108595\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2.69539	−	1.55618i	−0.172202	−	0.0994209i
$246$		0			0
$247$	2.65175	+	4.59296i	0.168727	+	0.292243i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	13.8828i		−	0.876276i	−0.898908	−	0.438138i	$-0.855638\pi$
$251$		−	13.8828i		−	0.876276i	0.898908	−	0.438138i	$-0.144362\pi$
$252$		0			0
$253$		−	18.0161i		−	1.13267i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.42539	+	9.39705i	0.338427	+	0.586172i	0.984137	−	0.177410i	$-0.0567720\pi$
$257$	5.42539	+	9.39705i	0.338427	+	0.586172i	−0.645710	+	0.763582i	$0.723439\pi$
$258$		0			0
$259$	−8.61423	−	4.97343i	−0.535262	−	0.309034i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−11.6051	+	20.1005i	−0.715598	+	1.23945i	0.247130	+	0.968982i	$0.420513\pi$
$263$	−11.6051	+	20.1005i	−0.715598	+	1.23945i	−0.962728	+	0.270470i	$0.912821\pi$
$264$		0			0
$265$	0.884601	+	1.53217i	0.0543406	+	0.0941207i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			4.01966i			0.245083i	0.992463	+	0.122541i	$0.0391044\pi$
$269$			4.01966i			0.245083i	−0.992463	+	0.122541i	$0.960896\pi$
$270$		0			0
$271$	6.75621			0.410411			0.205205	−	0.978719i	$-0.434214\pi$
$271$	6.75621			0.410411			0.205205	+	0.978719i	$0.434214\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	10.7118	−	6.18447i	0.645947	−	0.372938i
$276$		0			0
$277$	−1.83595	−	1.05999i	−0.110312	−	0.0636885i	0.443829	−	0.896111i	$-0.353620\pi$
$277$	−1.83595	−	1.05999i	−0.110312	−	0.0636885i	−0.554141	+	0.832423i	$0.686953\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	13.0580	−	22.6171i	0.778976	−	1.34923i	−0.153557	−	0.988140i	$-0.549073\pi$
$281$	13.0580	−	22.6171i	0.778976	−	1.34923i	0.932533	−	0.361086i	$-0.117594\pi$
$282$		0			0
$283$	−16.5376	+	9.54799i	−0.983058	+	0.567569i	−0.903192	−	0.429237i	$-0.858783\pi$
$283$	−16.5376	+	9.54799i	−0.983058	+	0.567569i	−0.0798661	+	0.996806i	$0.525449\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.96364			−0.174938
$288$		0			0
$289$	14.9423			0.878956
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−5.07116	+	2.92784i	−0.296261	+	0.171046i	−0.640762	−	0.767740i	$-0.721381\pi$
$293$	−5.07116	+	2.92784i	−0.296261	+	0.171046i	0.344501	+	0.938786i	$0.388048\pi$
$294$		0			0
$295$	−1.85668	+	3.21587i	−0.108100	+	0.187235i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	31.3585	+	18.1048i	1.81351	+	1.04703i
$300$		0			0
$301$	4.76780	−	2.75269i	0.274812	−	0.158663i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	6.37929			0.365277
$306$		0			0
$307$		−	13.7071i		−	0.782305i	−0.920326	−	0.391152i	$-0.872077\pi$
$307$		−	13.7071i		−	0.782305i	0.920326	−	0.391152i	$-0.127923\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−9.57980	−	16.5927i	−0.543221	−	0.940886i	−0.998717	−	0.0506479i	$-0.983871\pi$
$311$	−9.57980	−	16.5927i	−0.543221	−	0.940886i	0.455496	−	0.890238i	$-0.349462\pi$
$312$		0			0
$313$	−12.6102	+	21.8416i	−0.712773	+	1.23456i	0.251039	+	0.967977i	$0.419228\pi$
$313$	−12.6102	+	21.8416i	−0.712773	+	1.23456i	−0.963812	+	0.266582i	$0.914106\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.13931	+	1.23513i	0.120156	+	0.0693719i	0.558873	−	0.829253i	$-0.311234\pi$
$317$	2.13931	+	1.23513i	0.120156	+	0.0693719i	−0.438718	+	0.898625i	$0.644567\pi$
$318$		0			0
$319$	−4.50843	−	7.80883i	−0.252424	−	0.437211i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			5.44449i			0.302939i
$324$		0			0
$325$			24.8597i			1.37897i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	6.13262	+	10.6220i	0.338103	+	0.585611i
$330$		0			0
$331$	24.4404	+	14.1107i	1.34336	+	0.775592i	0.987300	−	0.158869i	$-0.0507848\pi$
$331$	24.4404	+	14.1107i	1.34336	+	0.775592i	0.356065	+	0.934461i	$0.384118\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2.39422	+	4.14691i	−0.130810	+	0.226570i
$336$		0			0
$337$	5.60565	+	9.70927i	0.305359	+	0.528897i	0.977341	−	0.211670i	$-0.0678902\pi$
$337$	5.60565	+	9.70927i	0.305359	+	0.528897i	−0.671982	+	0.740567i	$0.734557\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	20.2616i		−	1.09723i
$342$		0			0
$343$	−18.2411			−0.984929
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−17.8303	+	10.2943i	−0.957180	+	0.552628i	−0.895304	−	0.445455i	$-0.853042\pi$
$347$	−17.8303	+	10.2943i	−0.957180	+	0.552628i	−0.0618763	+	0.998084i	$0.519708\pi$
$348$		0			0
$349$	−2.93968	−	1.69723i	−0.157358	−	0.0908505i	0.419253	−	0.907869i	$-0.362292\pi$
$349$	−2.93968	−	1.69723i	−0.157358	−	0.0908505i	−0.576611	+	0.817019i	$0.695625\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.503241	−	0.871639i	0.0267848	−	0.0463926i	−0.852322	−	0.523017i	$-0.824806\pi$
$353$	0.503241	−	0.871639i	0.0267848	−	0.0463926i	0.879107	+	0.476624i	$0.158140\pi$
$354$		0			0
$355$	−2.22040	+	1.28195i	−0.117847	+	0.0680388i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	31.4772			1.66131			0.830653	−	0.556791i	$-0.187968\pi$
$359$	31.4772			1.66131			0.830653	+	0.556791i	$0.187968\pi$
$360$		0			0
$361$	18.0720			0.951158
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.70712	+	0.985604i	−0.0893546	+	0.0515889i
$366$		0			0
$367$	8.66667	−	15.0111i	0.452397	−	0.783574i	−0.546138	−	0.837695i	$-0.683902\pi$
$367$	8.66667	−	15.0111i	0.452397	−	0.783574i	0.998534	+	0.0541214i	$0.0172358\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.50027	+	2.02088i	0.181725	+	0.104919i
$372$		0			0
$373$	−11.2742	+	6.50917i	−0.583757	+	0.337032i	−0.762625	−	0.646841i	$-0.776090\pi$
$373$	−11.2742	+	6.50917i	−0.583757	+	0.337032i	0.178868	+	0.983873i	$0.442756\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	18.1225			0.933357
$378$		0			0
$379$		−	22.8643i		−	1.17446i	−0.809421	−	0.587229i	$-0.800219\pi$
$379$		−	22.8643i		−	1.17446i	0.809421	−	0.587229i	$-0.199781\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	15.0117	+	26.0010i	0.767061	+	1.32859i	0.939150	+	0.343508i	$0.111615\pi$
$383$	15.0117	+	26.0010i	0.767061	+	1.32859i	−0.172089	+	0.985081i	$0.555052\pi$
$384$		0			0
$385$	−1.51588	+	2.62559i	−0.0772565	+	0.133812i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−32.9474	−	19.0222i	−1.67050	−	0.964463i	−0.967358	−	0.253412i	$-0.918447\pi$
$389$	−32.9474	−	19.0222i	−1.67050	−	0.964463i	−0.703140	−	0.711051i	$-0.748220\pi$
$390$		0			0
$391$	18.5862	+	32.1922i	0.939943	+	1.62803i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	4.00742i		−	0.201635i
$396$		0			0
$397$		−	37.4510i		−	1.87961i	−0.341709	−	0.939806i	$-0.611006\pi$
$397$		−	37.4510i		−	1.87961i	0.341709	−	0.939806i	$-0.388994\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	2.35402	+	4.07728i	0.117554	+	0.203610i	0.918798	−	0.394728i	$-0.129161\pi$
$401$	2.35402	+	4.07728i	0.117554	+	0.203610i	−0.801244	+	0.598338i	$0.795828\pi$
$402$		0			0
$403$	35.2669	+	20.3613i	1.75677	+	1.01427i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	8.56739	−	14.8391i	0.424670	−	0.735549i
$408$		0			0
$409$	5.36377	+	9.29032i	0.265221	+	0.459377i	0.967622	−	0.252405i	$-0.0812216\pi$
$409$	5.36377	+	9.29032i	0.265221	+	0.459377i	−0.702400	+	0.711782i	$0.747888\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			8.48324i			0.417433i
$414$		0			0
$415$	−4.62117			−0.226844
$416$		0			0
$417$		0			0
$418$		0			0
$419$	3.57600	−	2.06460i	0.174699	−	0.100863i	−0.410101	−	0.912040i	$-0.634506\pi$
$419$	3.57600	−	2.06460i	0.174699	−	0.100863i	0.584800	+	0.811178i	$0.301173\pi$
$420$		0			0
$421$	13.7321	+	7.92824i	0.669262	+	0.386399i	0.795797	−	0.605563i	$-0.207052\pi$
$421$	13.7321	+	7.92824i	0.669262	+	0.386399i	−0.126535	+	0.991962i	$0.540386\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−12.7603	+	22.1015i	−0.618965	+	1.07208i
$426$		0			0
$427$	12.6211	−	7.28679i	0.610778	−	0.352633i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	16.1853			0.779619			0.389810	−	0.920895i	$-0.372541\pi$
$431$	16.1853			0.779619			0.389810	+	0.920895i	$0.372541\pi$
$432$		0			0
$433$	−32.8306			−1.57774			−0.788868	−	0.614563i	$-0.789332\pi$
$433$	−32.8306			−1.57774			−0.788868	+	0.614563i	$0.789332\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−5.48709	+	3.16797i	−0.262483	+	0.151545i
$438$		0			0
$439$	−10.9273	+	18.9267i	−0.521533	+	0.903321i	0.478154	+	0.878276i	$0.341306\pi$
$439$	−10.9273	+	18.9267i	−0.521533	+	0.903321i	−0.999686	+	0.0250450i	$0.992027\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−30.4500	−	17.5803i	−1.44672	−	0.835265i	−0.448436	−	0.893815i	$-0.648019\pi$
$443$	−30.4500	−	17.5803i	−1.44672	−	0.835265i	−0.998284	+	0.0585501i	$0.981352\pi$
$444$		0			0
$445$	−1.80055	+	1.03955i	−0.0853543	+	0.0492793i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−3.21851			−0.151891			−0.0759453	−	0.997112i	$-0.524197\pi$
$449$	−3.21851			−0.151891			−0.0759453	+	0.997112i	$0.524197\pi$
$450$		0			0
$451$		−	5.10526i		−	0.240397i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−3.04669	−	5.27703i	−0.142831	−	0.247391i
$456$		0			0
$457$	4.05512	−	7.02368i	0.189691	−	0.328554i	−0.755456	−	0.655199i	$-0.772585\pi$
$457$	4.05512	−	7.02368i	0.189691	−	0.328554i	0.945147	+	0.326645i	$0.105918\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	18.1813	+	10.4970i	0.846789	+	0.488894i	0.859566	−	0.511024i	$-0.170734\pi$
$461$	18.1813	+	10.4970i	0.846789	+	0.488894i	−0.0127771	+	0.999918i	$0.504067\pi$
$462$		0			0
$463$	4.45005	+	7.70772i	0.206812	+	0.358208i	0.950708	−	0.310086i	$-0.100358\pi$
$463$	4.45005	+	7.70772i	0.206812	+	0.358208i	−0.743897	+	0.668294i	$0.767025\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			26.0527i			1.20557i	0.797902	+	0.602787i	$0.205943\pi$
$467$			26.0527i			1.20557i	−0.797902	+	0.602787i	$0.794057\pi$
$468$		0			0
$469$			10.9392i			0.505128i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	4.74188	+	8.21317i	0.218032	+	0.377642i
$474$		0			0
$475$	−3.76715	−	2.17496i	−0.172849	−	0.0997942i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	8.71143	−	15.0886i	0.398035	−	0.689418i	−0.595448	−	0.803394i	$-0.703025\pi$
$479$	8.71143	−	15.0886i	0.398035	−	0.689418i	0.993483	+	0.113976i	$0.0363588\pi$
$480$		0			0
$481$	17.2191	+	29.8244i	0.785125	+	1.35988i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	1.73785i		−	0.0789118i
$486$		0			0
$487$	29.7367			1.34750			0.673750	−	0.738959i	$-0.264682\pi$
$487$	29.7367			1.34750			0.673750	+	0.738959i	$0.264682\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	20.6346	−	11.9134i	0.931229	−	0.537645i	0.0440286	−	0.999030i	$-0.485981\pi$
$491$	20.6346	−	11.9134i	0.931229	−	0.537645i	0.887200	+	0.461385i	$0.152647\pi$
$492$		0			0
$493$	16.1118	+	9.30215i	0.725639	+	0.418948i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−2.92863	+	5.07254i	−0.131367	+	0.227534i
$498$		0			0
$499$	16.8622	−	9.73540i	0.754856	−	0.435816i	−0.0725899	−	0.997362i	$-0.523126\pi$
$499$	16.8622	−	9.73540i	0.754856	−	0.435816i	0.827446	+	0.561546i	$0.189793\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	1.23494			0.0550631			0.0275316	−	0.999621i	$-0.491235\pi$
$503$	1.23494			0.0550631			0.0275316	+	0.999621i	$0.491235\pi$
$504$		0			0
$505$	6.60772			0.294040
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−0.392870	+	0.226823i	−0.0174136	+	0.0100538i	−0.508682	−	0.860955i	$-0.669867\pi$
$509$	−0.392870	+	0.226823i	−0.0174136	+	0.0100538i	0.491268	+	0.871009i	$0.336534\pi$
$510$		0			0
$511$	−2.25163	+	3.89993i	−0.0996061	+	0.172523i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	8.88784	+	5.13140i	0.391645	+	0.226116i
$516$		0			0
$517$	−18.2978	+	10.5643i	−0.804737	+	0.464615i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	29.0873			1.27434			0.637170	−	0.770724i	$-0.280105\pi$
$521$	29.0873			1.27434			0.637170	+	0.770724i	$0.280105\pi$
$522$		0			0
$523$		−	2.95874i		−	0.129377i	−0.997906	−	0.0646883i	$-0.979395\pi$
$523$		−	2.95874i		−	0.129377i	0.997906	−	0.0646883i	$-0.0206053\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	20.9026	+	36.2044i	0.910534	+	1.57709i
$528$		0			0
$529$	−10.1294	+	17.5446i	−0.440407	+	0.762808i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	8.88610	+	5.13039i	0.384900	+	0.222222i
$534$		0			0
$535$	−2.72636	−	4.72219i	−0.117871	−	0.204158i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	12.2483i		−	0.527573i
$540$		0			0
$541$		−	14.9753i		−	0.643838i	−0.946767	−	0.321919i	$-0.895672\pi$
$541$		−	14.9753i		−	0.643838i	0.946767	−	0.321919i	$-0.104328\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.0843608	+	0.146117i	0.00361362	+	0.00625897i
$546$		0			0
$547$	−15.7731	−	9.10661i	−0.674409	−	0.389370i	0.123336	−	0.992365i	$-0.460641\pi$
$547$	−15.7731	−	9.10661i	−0.674409	−	0.389370i	−0.797745	+	0.602995i	$0.793974\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.58553	+	2.74622i	−0.0675459	+	0.116993i
$552$		0			0
$553$	−4.57750	−	7.92846i	−0.194655	−	0.337153i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	35.7359i		−	1.51418i	−0.653310	−	0.757090i	$-0.726620\pi$
$557$		−	35.7359i		−	1.51418i	0.653310	−	0.757090i	$-0.273380\pi$
$558$		0			0
$559$	−19.0609			−0.806190
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−8.04256	+	4.64337i	−0.338953	+	0.195695i	−0.659809	−	0.751433i	$-0.729363\pi$
$563$	−8.04256	+	4.64337i	−0.338953	+	0.195695i	0.320856	+	0.947128i	$0.396030\pi$
$564$		0			0
$565$	5.24176	+	3.02633i	0.220523	+	0.127319i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.66727	−	9.81599i	0.237584	−	0.411508i	−0.722436	−	0.691437i	$-0.756978\pi$
$569$	5.66727	−	9.81599i	0.237584	−	0.411508i	0.960021	+	0.279930i	$0.0903111\pi$
$570$		0			0
$571$	−37.7843	+	21.8148i	−1.58122	+	0.912920i	−0.586543	+	0.809918i	$0.699511\pi$
$571$	−37.7843	+	21.8148i	−1.58122	+	0.912920i	−0.994681	+	0.103002i	$0.967155\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−29.6992			−1.23854
$576$		0			0
$577$	6.98123			0.290632			0.145316	−	0.989385i	$-0.453580\pi$
$577$	6.98123			0.290632			0.145316	+	0.989385i	$0.453580\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−9.14274	+	5.27856i	−0.379305	+	0.218992i
$582$		0			0
$583$	−3.48124	+	6.02968i	−0.144178	+	0.249724i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	7.34574	+	4.24107i	0.303191	+	0.175048i	0.643876	−	0.765130i	$-0.277325\pi$
$587$	7.34574	+	4.24107i	0.303191	+	0.175048i	−0.340684	+	0.940178i	$0.610659\pi$
$588$		0			0
$589$	−6.17097	+	3.56281i	−0.254270	+	0.146803i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	9.40869			0.386368			0.193184	−	0.981163i	$-0.438119\pi$
$593$	9.40869			0.386368			0.193184	+	0.981163i	$0.438119\pi$
$594$		0			0
$595$		−	6.25538i		−	0.256445i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−14.9623	−	25.9155i	−0.611344	−	1.05888i	−0.991014	−	0.133757i	$-0.957296\pi$
$599$	−14.9623	−	25.9155i	−0.611344	−	1.05888i	0.379670	−	0.925122i	$-0.376038\pi$
$600$		0			0
$601$	1.81973	−	3.15186i	0.0742282	−	0.128567i	−0.826522	−	0.562904i	$-0.809684\pi$
$601$	1.81973	−	3.15186i	0.0742282	−	0.128567i	0.900750	+	0.434337i	$0.143017\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2.10782	+	1.21695i	0.0856950	+	0.0494760i
$606$		0			0
$607$	−3.63358	−	6.29355i	−0.147482	−	0.255447i	0.782814	−	0.622256i	$-0.213784\pi$
$607$	−3.63358	−	6.29355i	−0.147482	−	0.255447i	−0.930296	+	0.366809i	$0.880450\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	42.4651i		−	1.71795i
$612$		0			0
$613$		−	32.6469i		−	1.31859i	−0.751882	−	0.659297i	$-0.770854\pi$
$613$		−	32.6469i		−	1.31859i	0.751882	−	0.659297i	$-0.229146\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−15.6751	−	27.1501i	−0.631056	−	1.09302i	−0.987336	−	0.158642i	$-0.949288\pi$
$617$	−15.6751	−	27.1501i	−0.631056	−	1.09302i	0.356280	−	0.934379i	$-0.384045\pi$
$618$		0			0
$619$	−1.72589	−	0.996445i	−0.0693695	−	0.0400505i	0.464914	−	0.885356i	$-0.346085\pi$
$619$	−1.72589	−	0.996445i	−0.0693695	−	0.0400505i	−0.534284	+	0.845305i	$0.679419\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−2.37486	+	4.11339i	−0.0951469	+	0.164799i
$624$		0			0
$625$	−8.98375	−	15.5603i	−0.359350	−	0.622413i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			35.3538i			1.40965i
$630$		0			0
$631$	15.4643			0.615623			0.307812	−	0.951447i	$-0.400403\pi$
$631$	15.4643			0.615623			0.307812	+	0.951447i	$0.400403\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.04135	+	0.601225i	−0.0413248	+	0.0238589i
$636$		0			0
$637$	21.3192	+	12.3086i	0.844697	+	0.487686i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	12.3638	−	21.4147i	0.488340	−	0.845829i	−0.511570	−	0.859241i	$-0.670936\pi$
$641$	12.3638	−	21.4147i	0.488340	−	0.845829i	0.999910	+	0.0134123i	$0.00426940\pi$
$642$		0			0
$643$	−40.0176	+	23.1042i	−1.57814	+	0.911141i	−0.583023	+	0.812456i	$0.698130\pi$
$643$	−40.0176	+	23.1042i	−1.57814	+	0.911141i	−0.995119	+	0.0986850i	$0.968536\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−6.36971			−0.250419			−0.125210	−	0.992130i	$-0.539960\pi$
$647$	−6.36971			−0.250419			−0.125210	+	0.992130i	$0.539960\pi$
$648$		0			0
$649$	−14.6135			−0.573630
$650$		0			0
$651$		0			0
$652$		0			0
$653$	31.8848	−	18.4087i	1.24775	−	0.720389i	0.277090	−	0.960844i	$-0.410630\pi$
$653$	31.8848	−	18.4087i	1.24775	−	0.720389i	0.970660	+	0.240455i	$0.0772968\pi$
$654$		0			0
$655$	2.31058	−	4.00205i	0.0902820	−	0.156373i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−6.46565	−	3.73294i	−0.251866	−	0.145415i	0.368752	−	0.929528i	$-0.379785\pi$
$659$	−6.46565	−	3.73294i	−0.251866	−	0.145415i	−0.620618	+	0.784113i	$0.713118\pi$
$660$		0			0
$661$	−2.51984	+	1.45483i	−0.0980102	+	0.0565862i	−0.548204	−	0.836345i	$-0.684688\pi$
$661$	−2.51984	+	1.45483i	−0.0980102	+	0.0565862i	0.450194	+	0.892931i	$0.351355\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	1.06622			0.0413461
$666$		0			0
$667$			21.6505i			0.838310i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	12.5525	+	21.7415i	0.484582	+	0.839321i
$672$		0			0
$673$	21.0527	−	36.4643i	0.811522	−	1.40560i	−0.100277	−	0.994960i	$-0.531973\pi$
$673$	21.0527	−	36.4643i	0.811522	−	1.40560i	0.911799	−	0.410637i	$-0.134694\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	32.9941	+	19.0492i	1.26807	+	0.732119i	0.974622	−	0.223858i	$-0.0718650\pi$
$677$	32.9941	+	19.0492i	1.26807	+	0.732119i	0.293445	+	0.955976i	$0.405198\pi$
$678$		0			0
$679$	−1.98507	−	3.43825i	−0.0761801	−	0.131948i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			47.0728i			1.80119i	0.434659	+	0.900595i	$0.356869\pi$
$683$			47.0728i			1.80119i	−0.434659	+	0.900595i	$0.643131\pi$
$684$		0			0
$685$		−	2.52421i		−	0.0964450i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−6.99676	−	12.1187i	−0.266555	−	0.461687i
$690$		0			0
$691$	3.38522	+	1.95446i	0.128780	+	0.0743512i	0.563006	−	0.826453i	$-0.309645\pi$
$691$	3.38522	+	1.95446i	0.128780	+	0.0743512i	−0.434226	+	0.900804i	$0.642978\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−6.02468	+	10.4350i	−0.228529	+	0.395824i
$696$		0			0
$697$	5.26678	+	9.12234i	0.199494	+	0.345533i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			16.4480i			0.621231i	0.950536	+	0.310615i	$0.100535\pi$
$701$			16.4480i			0.621231i	−0.950536	+	0.310615i	$0.899465\pi$
$702$		0			0
$703$	−6.02598			−0.227274
$704$		0			0
$705$		0			0
$706$		0			0
$707$	13.0730	−	7.54772i	0.491662	−	0.283861i
$708$		0			0
$709$	6.84805	+	3.95372i	0.257184	+	0.148485i	0.623049	−	0.782183i	$-0.285894\pi$
$709$	6.84805	+	3.95372i	0.257184	+	0.148485i	−0.365865	+	0.930668i	$0.619227\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−24.3251	+	42.1324i	−0.910984	+	1.57787i
$714$		0			0
$715$	9.09037	−	5.24833i	0.339961	−	0.196276i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−37.0556			−1.38194			−0.690970	−	0.722884i	$-0.742816\pi$
$719$	−37.0556			−1.38194			−0.690970	+	0.722884i	$0.742816\pi$
$720$		0			0
$721$	23.4455			0.873156
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−12.8727	+	7.43204i	−0.478079	+	0.276019i
$726$		0			0
$727$	−2.83467	+	4.90979i	−0.105132	+	0.182094i	−0.913792	−	0.406182i	$-0.866860\pi$
$727$	−2.83467	+	4.90979i	−0.105132	+	0.182094i	0.808660	+	0.588276i	$0.200193\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−16.9461	−	9.78381i	−0.626773	−	0.361867i
$732$		0			0
$733$	−10.8544	+	6.26677i	−0.400915	+	0.231469i	−0.686879	−	0.726772i	$-0.741020\pi$
$733$	−10.8544	+	6.26677i	−0.400915	+	0.231469i	0.285964	+	0.958240i	$0.407686\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−18.8443			−0.694139
$738$		0			0
$739$			1.83358i			0.0674492i	0.999431	+	0.0337246i	$0.0107369\pi$
$739$			1.83358i			0.0674492i	−0.999431	+	0.0337246i	$0.989263\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−15.6588	−	27.1219i	−0.574467	−	0.995006i	−0.996099	−	0.0882391i	$-0.971876\pi$
$743$	−15.6588	−	27.1219i	−0.574467	−	0.995006i	0.421632	−	0.906767i	$-0.361457\pi$
$744$		0			0
$745$	7.52491	−	13.0335i	0.275691	−	0.477511i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−10.7879	−	6.22841i	−0.394182	−	0.227581i
$750$		0			0
$751$	−3.64466	−	6.31274i	−0.132996	−	0.230355i	0.791834	−	0.610736i	$-0.209126\pi$
$751$	−3.64466	−	6.31274i	−0.132996	−	0.230355i	−0.924830	+	0.380381i	$0.875793\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			8.84005i			0.321722i
$756$		0			0
$757$		−	12.8156i		−	0.465792i	−0.972502	−	0.232896i	$-0.925180\pi$
$757$		−	12.8156i		−	0.465792i	0.972502	−	0.232896i	$-0.0748202\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−12.5800	−	21.7892i	−0.456025	−	0.789859i	0.542721	−	0.839913i	$-0.317394\pi$
$761$	−12.5800	−	21.7892i	−0.456025	−	0.789859i	−0.998747	+	0.0500541i	$0.984061\pi$
$762$		0			0
$763$	0.333807	+	0.192724i	0.0120846	+	0.00697706i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	14.6854	−	25.4359i	0.530261	−	0.918439i
$768$		0			0
$769$	−10.7318	−	18.5880i	−0.386998	−	0.670300i	0.605046	−	0.796190i	$-0.293155\pi$
$769$	−10.7318	−	18.5880i	−0.386998	−	0.670300i	−0.992044	+	0.125890i	$0.959821\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	20.2122i		−	0.726981i	−0.931598	−	0.363491i	$-0.881585\pi$
$773$		−	20.2122i		−	0.726981i	0.931598	−	0.363491i	$-0.118415\pi$
$774$		0			0
$775$	−33.4007			−1.19979
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.55488	+	0.897712i	−0.0557095	+	0.0321639i
$780$		0			0
$781$	−8.73811	−	5.04495i	−0.312674	−	0.180523i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−6.07957	+	10.5301i	−0.216989	+	0.375836i
$786$		0			0
$787$	17.5726	−	10.1455i	0.626395	−	0.361649i	−0.152960	−	0.988232i	$-0.548880\pi$
$787$	17.5726	−	10.1455i	0.626395	−	0.361649i	0.779355	+	0.626583i	$0.215547\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	13.8274			0.491646
$792$		0			0
$793$	−50.4570			−1.79178
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−28.8758	+	16.6715i	−1.02283	+	0.590533i	−0.914924	−	0.403627i	$-0.867749\pi$
$797$	−28.8758	+	16.6715i	−1.02283	+	0.590533i	−0.107910	+	0.994161i	$0.534416\pi$
$798$		0			0
$799$	21.7970	−	37.7535i	0.771122	−	1.33562i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−6.71815	−	3.87873i	−0.237078	−	0.136877i
$804$		0			0
$805$	6.30432	−	3.63980i	0.222198	−	0.128286i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−30.6920			−1.07907			−0.539536	−	0.841962i	$-0.681400\pi$
$809$	−30.6920			−1.07907			−0.539536	+	0.841962i	$0.681400\pi$
$810$		0			0
$811$		−	49.5457i		−	1.73978i	−0.493241	−	0.869892i	$-0.664188\pi$
$811$		−	49.5457i		−	1.73978i	0.493241	−	0.869892i	$-0.335812\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−2.98168	−	5.16443i	−0.104444	−	0.180902i
$816$		0			0
$817$	1.66763	−	2.88842i	0.0583430	−	0.101053i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−32.9739	−	19.0375i	−1.15080	−	0.664414i	−0.201716	−	0.979444i	$-0.564652\pi$
$821$	−32.9739	−	19.0375i	−1.15080	−	0.664414i	−0.949082	+	0.315030i	$0.897985\pi$
$822$		0			0
$823$	−11.2626	−	19.5074i	−0.392589	−	0.679984i	0.600201	−	0.799849i	$-0.295087\pi$
$823$	−11.2626	−	19.5074i	−0.392589	−	0.679984i	−0.992790	+	0.119865i	$0.961754\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	33.5317i		−	1.16601i	−0.812468	−	0.583006i	$-0.801876\pi$
$827$		−	33.5317i		−	1.16601i	0.812468	−	0.583006i	$-0.198124\pi$
$828$		0			0
$829$			37.7559i			1.31132i	0.755058	+	0.655658i	$0.227609\pi$
$829$			37.7559i			1.31132i	−0.755058	+	0.655658i	$0.772391\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	12.6359	+	21.8860i	0.437807	+	0.758304i
$834$		0			0
$835$	7.20378	+	4.15910i	0.249297	+	0.143932i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−9.90604	+	17.1578i	−0.341994	+	0.592352i	−0.984803	−	0.173675i	$-0.944436\pi$
$839$	−9.90604	+	17.1578i	−0.341994	+	0.592352i	0.642809	+	0.766027i	$0.277769\pi$
$840$		0			0
$841$	−9.08210	−	15.7307i	−0.313176	−	0.542436i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			12.0481i			0.414466i
$846$		0			0
$847$	5.56028			0.191053
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−35.6304	+	20.5712i	−1.22140	+	0.705173i
$852$		0			0
$853$	5.95424	+	3.43768i	0.203869	+	0.117704i	0.598459	−	0.801153i	$-0.295780\pi$
$853$	5.95424	+	3.43768i	0.203869	+	0.117704i	−0.394590	+	0.918857i	$0.629113\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	3.87316	−	6.70851i	0.132305	−	0.229158i	−0.792260	−	0.610184i	$-0.791096\pi$
$857$	3.87316	−	6.70851i	0.132305	−	0.229158i	0.924565	+	0.381025i	$0.124429\pi$
$858$		0			0
$859$	0.594592	−	0.343288i	0.0202872	−	0.0117128i	−0.489822	−	0.871822i	$-0.662938\pi$
$859$	0.594592	−	0.343288i	0.0202872	−	0.0117128i	0.510109	+	0.860110i	$0.329605\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−42.9194			−1.46099			−0.730496	−	0.682917i	$-0.760711\pi$
$863$	−42.9194			−1.46099			−0.730496	+	0.682917i	$0.760711\pi$
$864$		0			0
$865$	−9.07991			−0.308726
$866$		0			0
$867$		0			0
$868$		0			0
$869$	13.6578	−	7.88535i	0.463310	−	0.267492i
$870$		0			0
$871$	18.9371	−	32.8000i	0.641658	−	1.11138i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	9.12082	+	5.26591i	0.308340	+	0.178020i
$876$		0			0
$877$	−14.7508	+	8.51640i	−0.498100	+	0.287578i	−0.727929	−	0.685653i	$-0.759517\pi$
$877$	−14.7508	+	8.51640i	−0.498100	+	0.287578i	0.229828	+	0.973231i	$0.426183\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	7.90546			0.266342			0.133171	−	0.991093i	$-0.457484\pi$
$881$	7.90546			0.266342			0.133171	+	0.991093i	$0.457484\pi$
$882$		0			0
$883$		−	7.53298i		−	0.253505i	−0.991934	−	0.126752i	$-0.959545\pi$
$883$		−	7.53298i		−	0.253505i	0.991934	−	0.126752i	$-0.0404554\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	7.02719	+	12.1715i	0.235950	+	0.408677i	0.959548	−	0.281544i	$-0.0908465\pi$
$887$	7.02719	+	12.1715i	0.235950	+	0.408677i	−0.723598	+	0.690221i	$0.757513\pi$
$888$		0			0
$889$	−1.37351	+	2.37899i	−0.0460660	+	0.0797886i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	6.43501	+	3.71525i	0.215339	+	0.124326i
$894$		0			0
$895$	1.15500	+	2.00052i	0.0386075	+	0.0668701i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			24.3489i			0.812081i
$900$		0			0
$901$		−	14.3655i		−	0.478585i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−5.19001	−	8.98936i	−0.172522	−	0.298816i
$906$		0			0
$907$	39.7958	+	22.9761i	1.32140	+	0.762910i	0.983952	−	0.178435i	$-0.0571034\pi$
$907$	39.7958	+	22.9761i	1.32140	+	0.762910i	0.337447	+	0.941345i	$0.390437\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	25.7911	−	44.6715i	0.854497	−	1.48003i	−0.0226136	−	0.999744i	$-0.507199\pi$
$911$	25.7911	−	44.6715i	0.854497	−	1.48003i	0.877111	−	0.480288i	$-0.159468\pi$
$912$		0			0
$913$	−9.09302	−	15.7496i	−0.300935	−	0.521235i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	10.5571i		−	0.348627i
$918$		0			0
$919$	21.2048			0.699481			0.349741	−	0.936847i	$-0.386270\pi$
$919$	21.2048			0.699481			0.349741	+	0.936847i	$0.386270\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	17.5623	−	10.1396i	0.578069	−	0.333748i
$924$		0			0
$925$	−24.4620	−	14.1231i	−0.804305	−	0.464366i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.70516	+	2.95343i	−0.0559446	+	0.0968989i	−0.892641	−	0.450767i	$-0.851150\pi$
$929$	−1.70516	+	2.95343i	−0.0559446	+	0.0968989i	0.836697	+	0.547666i	$0.184484\pi$
$930$		0			0
$931$	−3.73042	+	2.15376i	−0.122259	+	0.0705865i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	10.7757			0.352403
$936$		0			0
$937$	29.4448			0.961919			0.480959	−	0.876743i	$-0.340288\pi$
$937$	29.4448			0.961919			0.480959	+	0.876743i	$0.340288\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−40.5880	+	23.4335i	−1.32313	+	0.763910i	−0.984227	−	0.176911i	$-0.943389\pi$
$941$	−40.5880	+	23.4335i	−1.32313	+	0.763910i	−0.338904	+	0.940821i	$0.610056\pi$
$942$		0			0
$943$	−6.12914	+	10.6160i	−0.199592	+	0.345704i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	31.5821	+	18.2340i	1.02628	+	0.592524i	0.915917	−	0.401367i	$-0.131465\pi$
$947$	31.5821	+	18.2340i	1.02628	+	0.592524i	0.110365	+	0.993891i	$0.464798\pi$
$948$		0			0
$949$	13.5024	−	7.79564i	0.438308	−	0.253057i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−38.0590			−1.23285			−0.616426	−	0.787413i	$-0.711420\pi$
$953$	−38.0590			−1.23285			−0.616426	+	0.787413i	$0.711420\pi$
$954$		0			0
$955$			5.09344i			0.164820i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−2.88330	−	4.99401i	−0.0931065	−	0.161265i
$960$		0			0
$961$	−11.8569	+	20.5368i	−0.382481	+	0.662477i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	12.3397	+	7.12430i	0.397228	+	0.229339i
$966$		0			0
$967$	−11.4864	−	19.8951i	−0.369378	−	0.639782i	0.620090	−	0.784531i	$-0.287096\pi$
$967$	−11.4864	−	19.8951i	−0.369378	−	0.639782i	−0.989468	+	0.144749i	$0.953763\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			53.8829i			1.72919i	0.502474	+	0.864593i	$0.332423\pi$
$971$			53.8829i			1.72919i	−0.502474	+	0.864593i	$0.667577\pi$
$972$		0			0
$973$			27.5269i			0.882473i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−19.1024	−	33.0863i	−0.611140	−	1.05853i	−0.991049	−	0.133501i	$-0.957378\pi$
$977$	−19.1024	−	33.0863i	−0.611140	−	1.05853i	0.379909	−	0.925024i	$-0.375955\pi$
$978$		0			0
$979$	−7.08585	−	4.09102i	−0.226465	−	0.130749i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−24.3307	+	42.1420i	−0.776028	+	1.34412i	0.158186	+	0.987409i	$0.449435\pi$
$983$	−24.3307	+	42.1420i	−0.776028	+	1.34412i	−0.934215	+	0.356711i	$0.883898\pi$
$984$		0			0
$985$	−7.14968	−	12.3836i	−0.227808	−	0.394574i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	22.7715i		−	0.724093i
$990$		0			0
$991$	12.7822			0.406040			0.203020	−	0.979175i	$-0.434924\pi$
$991$	12.7822			0.406040			0.203020	+	0.979175i	$0.434924\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.17905	−	0.680723i	0.0373783	−	0.0215804i
$996$		0			0
$997$	−21.1161	−	12.1914i	−0.668752	−	0.386104i	0.126851	−	0.991922i	$-0.459513\pi$
$997$	−21.1161	−	12.1914i	−0.668752	−	0.386104i	−0.795604	+	0.605817i	$0.792846\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.r.b.721.4		16
3.2	odd	2		288.2.r.b.241.7		16
4.3	odd	2		216.2.n.b.181.2		16
8.3	odd	2		216.2.n.b.181.8		16
8.5	even	2	inner	864.2.r.b.721.5		16
9.2	odd	6		2592.2.d.j.1297.5		8
9.4	even	3	inner	864.2.r.b.145.5		16
9.5	odd	6		288.2.r.b.49.2		16
9.7	even	3		2592.2.d.k.1297.4		8
12.11	even	2		72.2.n.b.61.7	yes	16
24.5	odd	2		288.2.r.b.241.2		16
24.11	even	2		72.2.n.b.61.1	yes	16
36.7	odd	6		648.2.d.k.325.4		8
36.11	even	6		648.2.d.j.325.5		8
36.23	even	6		72.2.n.b.13.1	✓	16
36.31	odd	6		216.2.n.b.37.8		16
72.5	odd	6		288.2.r.b.49.7		16
72.11	even	6		648.2.d.j.325.6		8
72.13	even	6	inner	864.2.r.b.145.4		16
72.29	odd	6		2592.2.d.j.1297.4		8
72.43	odd	6		648.2.d.k.325.3		8
72.59	even	6		72.2.n.b.13.7	yes	16
72.61	even	6		2592.2.d.k.1297.5		8
72.67	odd	6		216.2.n.b.37.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.n.b.13.1	✓	16	36.23	even	6
72.2.n.b.13.7	yes	16	72.59	even	6
72.2.n.b.61.1	yes	16	24.11	even	2
72.2.n.b.61.7	yes	16	12.11	even	2
216.2.n.b.37.2		16	72.67	odd	6
216.2.n.b.37.8		16	36.31	odd	6
216.2.n.b.181.2		16	4.3	odd	2
216.2.n.b.181.8		16	8.3	odd	2
288.2.r.b.49.2		16	9.5	odd	6
288.2.r.b.49.7		16	72.5	odd	6
288.2.r.b.241.2		16	24.5	odd	2
288.2.r.b.241.7		16	3.2	odd	2
648.2.d.j.325.5		8	36.11	even	6
648.2.d.j.325.6		8	72.11	even	6
648.2.d.k.325.3		8	72.43	odd	6
648.2.d.k.325.4		8	36.7	odd	6
864.2.r.b.145.4		16	72.13	even	6	inner
864.2.r.b.145.5		16	9.4	even	3	inner
864.2.r.b.721.4		16	1.1	even	1	trivial
864.2.r.b.721.5		16	8.5	even	2	inner
2592.2.d.j.1297.4		8	72.29	odd	6
2592.2.d.j.1297.5		8	9.2	odd	6
2592.2.d.k.1297.4		8	9.7	even	3
2592.2.d.k.1297.5		8	72.61	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.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.602794 + 0.348023i) q^{5} +(-0.795065 + 1.37709i) q^{7} +O(q^{10})\)	\(q+(-0.602794 + 0.348023i) q^{5} +(-0.795065 + 1.37709i) q^{7} +(-2.37222 - 1.36960i) q^{11} +(4.76780 - 2.75269i) q^{13} +5.65175 q^{17} +0.963328i q^{19} +(3.28857 + 5.69597i) q^{23} +(-2.25776 + 3.91055i) q^{25} +(2.85076 + 1.64589i) q^{29} +(3.69844 + 6.40589i) q^{31} -1.10680i q^{35} +6.25538i q^{37} +(0.931886 + 1.61407i) q^{41} +(-2.99838 - 1.73111i) q^{43} +(3.85668 - 6.67997i) q^{47} +(2.23574 + 3.87242i) q^{49} -2.54179i q^{53} +1.90662 q^{55} +(4.62019 - 2.66747i) q^{59} +(-7.93715 - 4.58252i) q^{61} +(-1.91600 + 3.31861i) q^{65} +(5.95780 - 3.43974i) q^{67} +3.68351 q^{71} +2.83201 q^{73} +(3.77214 - 2.17785i) q^{77} +(-2.87870 + 4.98605i) q^{79} +(5.74968 + 3.31958i) q^{83} +(-3.40684 + 1.96694i) q^{85} +2.98701 q^{89} +8.75427i q^{91} +(-0.335261 - 0.580689i) q^{95} +(-1.24837 + 2.16224i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{7}+O(q^{10}) \) 16 * q - 6 * q^7	\( 16 q - 6 q^{7} + 28 q^{17} - 10 q^{23} + 2 q^{25} + 10 q^{31} + 8 q^{41} + 6 q^{47} + 18 q^{49} + 4 q^{55} + 14 q^{65} + 72 q^{71} - 44 q^{73} + 30 q^{79} - 64 q^{89} + 44 q^{95}+O(q^{100}) \) 16 * q - 6 * q^7 + 28 * q^17 - 10 * q^23 + 2 * q^25 + 10 * q^31 + 8 * q^41 + 6 * q^47 + 18 * q^49 + 4 * q^55 + 14 * q^65 + 72 * q^71 - 44 * q^73 + 30 * q^79 - 64 * q^89 + 44 * q^95

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