LMFDB - Embedded newform 1156.1.o.a.659.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1156,1,Mod(47,1156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1156, base_ring=CyclotomicField(68))

chi = DirichletCharacter(H, H._module([34, 25]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("1156.47");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1156 = 2^{2} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1156.o (of order $68$, degree $32$, 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:	$0.576919154604$
Analytic rank:	$0$
Dimension:	$32$
Coefficient field:	$\Q(\zeta_{68})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{32} - x^{30} + x^{28} - x^{26} + x^{24} - x^{22} + x^{20} - x^{18} + x^{16} - x^{14} + x^{12} + \cdots + 1 $ x^32 - x^30 + x^28 - x^26 + x^24 - x^22 + x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{68}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{68} - \cdots)$

Embedding invariants

Embedding label			659.1
Root			$0.895163 - 0.445738i$ of defining polynomial
Character	$\chi$	$=$	1156.659
Dual form			1156.1.o.a.735.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.798017 - 0.602635i) q^{2} +(0.273663 - 0.961826i) q^{4} +(-0.739009 - 1.67370i) q^{5} +(-0.361242 - 0.932472i) q^{8} +(0.995734 + 0.0922684i) q^{9} +O(q^{10})$	\(q+(0.798017 - 0.602635i) q^{2} +(0.273663 - 0.961826i) q^{4} +(-0.739009 - 1.67370i) q^{5} +(-0.361242 - 0.932472i) q^{8} +(0.995734 + 0.0922684i) q^{9} +(-1.59837 - 0.890286i) q^{10} +(-1.85699 + 0.719401i) q^{13} +(-0.850217 - 0.526432i) q^{16} +(0.850217 + 0.526432i) q^{17} +(0.850217 - 0.526432i) q^{18} +(-1.81204 + 0.252769i) q^{20} +(-1.58143 + 1.73474i) q^{25} +(-1.04837 + 1.69318i) q^{26} +(1.11622 - 0.621731i) q^{29} +(-0.995734 + 0.0922684i) q^{32} +(0.995734 - 0.0922684i) q^{34} +(0.361242 - 0.932472i) q^{36} +(1.87814 - 0.629488i) q^{37} +(-1.29371 + 1.29371i) q^{40} +(0.0373089 - 0.806980i) q^{41} +(-0.581427 - 1.73474i) q^{45} +(-0.183750 + 0.982973i) q^{49} +(-0.216590 + 2.33738i) q^{50} +(0.183750 + 1.98297i) q^{52} +(-0.365931 - 0.0339085i) q^{53} +(0.516087 - 1.16883i) q^{58} +(0.0762025 - 0.0521999i) q^{61} +(-0.739009 + 0.673696i) q^{64} +(2.57639 + 2.57639i) q^{65} +(0.739009 - 0.673696i) q^{68} +(-0.273663 - 0.961826i) q^{72} +(-0.352279 - 1.49780i) q^{73} +(1.11943 - 1.63417i) q^{74} +(-0.252769 + 1.81204i) q^{80} +(0.982973 + 0.183750i) q^{81} +(-0.456541 - 0.666468i) q^{82} +(0.252769 - 1.81204i) q^{85} +(1.48826 + 0.576554i) q^{89} +(-1.50941 - 1.03397i) q^{90} +(-0.748723 + 0.621731i) q^{97} +(0.445738 + 0.895163i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{4} + 2 q^{5}+O(q^{10}) $ 32 * q + 2 * q^4 + 2 * q^5	$ 32 q + 2 q^{4} + 2 q^{5} - 2 q^{10} - 2 q^{16} + 2 q^{17} + 2 q^{18} - 2 q^{20} - 34 q^{25} - 2 q^{29} + 2 q^{37} + 2 q^{40} - 2 q^{41} - 2 q^{45} + 2 q^{50} + 2 q^{58} + 2 q^{61} + 2 q^{64} - 2 q^{68} - 2 q^{72} - 2 q^{73} - 2 q^{74} + 2 q^{80} + 2 q^{81} - 2 q^{82} - 2 q^{85} - 2 q^{90} + 2 q^{97} - 2 q^{98}+O(q^{100}) $ 32 * q + 2 * q^4 + 2 * q^5 - 2 * q^10 - 2 * q^16 + 2 * q^17 + 2 * q^18 - 2 * q^20 - 34 * q^25 - 2 * q^29 + 2 * q^37 + 2 * q^40 - 2 * q^41 - 2 * q^45 + 2 * q^50 + 2 * q^58 + 2 * q^61 + 2 * q^64 - 2 * q^68 - 2 * q^72 - 2 * q^73 - 2 * q^74 + 2 * q^80 + 2 * q^81 - 2 * q^82 - 2 * q^85 - 2 * q^90 + 2 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1156\mathbb{Z}\right)^\times$.

$n$	$579$	$581$
$\chi(n)$	$-1$	$e\left(\frac{1}{68}\right)$

Coefficient data

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

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

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

$2$	0.798017	−	0.602635i	0.798017	−	0.602635i
$2$	0.798017	−	0.602635i	0.798017	−	0.602635i
$3$		0			0		−0.998933	−	0.0461835i	$-0.985294\pi$
$3$		0			0		0.998933	+	0.0461835i	$0.0147059\pi$
$4$	0.273663	−	0.961826i	0.273663	−	0.961826i
$5$	−0.739009	−	1.67370i	−0.739009	−	1.67370i	−0.739009	−	0.673696i	$-0.764706\pi$
$5$	−0.739009	−	1.67370i	−0.739009	−	1.67370i		−	1.00000i	$-0.5\pi$
$6$		0			0
$7$		0			0		−0.638847	−	0.769334i	$-0.720588\pi$
$7$		0			0		0.638847	+	0.769334i	$0.279412\pi$
$8$	−0.361242	−	0.932472i	−0.361242	−	0.932472i
$9$	0.995734	+	0.0922684i	0.995734	+	0.0922684i
$10$	−1.59837	−	0.890286i	−1.59837	−	0.890286i
$11$		0			0		−0.486604	−	0.873622i	$-0.661765\pi$
$11$		0			0		0.486604	+	0.873622i	$0.338235\pi$
$12$		0			0
$13$	−1.85699	+	0.719401i	−1.85699	+	0.719401i	−0.895163	+	0.445738i	$0.852941\pi$
$13$	−1.85699	+	0.719401i	−1.85699	+	0.719401i	−0.961826	+	0.273663i	$0.911765\pi$
$14$		0			0
$15$		0			0
$16$	−0.850217	−	0.526432i	−0.850217	−	0.526432i
$17$	0.850217	+	0.526432i	0.850217	+	0.526432i
$17$	0.850217	+	0.526432i	0.850217	+	0.526432i
$18$	0.850217	−	0.526432i	0.850217	−	0.526432i
$19$		0			0		−0.798017	−	0.602635i	$-0.794118\pi$
$19$		0			0		0.798017	+	0.602635i	$0.205882\pi$
$20$	−1.81204	+	0.252769i	−1.81204	+	0.252769i
$21$		0			0
$22$		0			0
$23$		0			0		−0.638847	−	0.769334i	$-0.720588\pi$
$23$		0			0		0.638847	+	0.769334i	$0.279412\pi$
$24$		0			0
$25$	−1.58143	+	1.73474i	−1.58143	+	1.73474i
$26$	−1.04837	+	1.69318i	−1.04837	+	1.69318i
$27$		0			0
$28$		0			0
$29$	1.11622	−	0.621731i	1.11622	−	0.621731i	0.183750	−	0.982973i	$-0.441176\pi$
$29$	1.11622	−	0.621731i	1.11622	−	0.621731i	0.932472	+	0.361242i	$0.117647\pi$
$30$		0			0
$31$		0			0		−0.914794	−	0.403921i	$-0.867647\pi$
$31$		0			0		0.914794	+	0.403921i	$0.132353\pi$
$32$	−0.995734	+	0.0922684i	−0.995734	+	0.0922684i
$33$		0			0
$34$	0.995734	−	0.0922684i	0.995734	−	0.0922684i
$35$		0			0
$36$	0.361242	−	0.932472i	0.361242	−	0.932472i
$37$	1.87814	−	0.629488i	1.87814	−	0.629488i	0.895163	−	0.445738i	$-0.147059\pi$
$37$	1.87814	−	0.629488i	1.87814	−	0.629488i	0.982973	−	0.183750i	$-0.0588235\pi$
$38$		0			0
$39$		0			0
$40$	−1.29371	+	1.29371i	−1.29371	+	1.29371i
$41$	0.0373089	−	0.806980i	0.0373089	−	0.806980i	−0.895163	−	0.445738i	$-0.852941\pi$
$41$	0.0373089	−	0.806980i	0.0373089	−	0.806980i	0.932472	−	0.361242i	$-0.117647\pi$
$42$		0			0
$43$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$43$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$44$		0			0
$45$	−0.581427	−	1.73474i	−0.581427	−	1.73474i
$46$		0			0
$47$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$47$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$48$		0			0
$49$	−0.183750	+	0.982973i	−0.183750	+	0.982973i
$50$	−0.216590	+	2.33738i	−0.216590	+	2.33738i
$51$		0			0
$52$	0.183750	+	1.98297i	0.183750	+	1.98297i
$53$	−0.365931	−	0.0339085i	−0.365931	−	0.0339085i	−0.0922684	−	0.995734i	$-0.529412\pi$
$53$	−0.365931	−	0.0339085i	−0.365931	−	0.0339085i	−0.273663	+	0.961826i	$0.588235\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	0.516087	−	1.16883i	0.516087	−	1.16883i
$59$		0			0		−0.183750	−	0.982973i	$-0.558824\pi$
$59$		0			0		0.183750	+	0.982973i	$0.441176\pi$
$60$		0			0
$61$	0.0762025	−	0.0521999i	0.0762025	−	0.0521999i	−0.526432	−	0.850217i	$-0.676471\pi$
$61$	0.0762025	−	0.0521999i	0.0762025	−	0.0521999i	0.602635	+	0.798017i	$0.294118\pi$
$62$		0			0
$63$		0			0
$64$	−0.739009	+	0.673696i	−0.739009	+	0.673696i
$65$	2.57639	+	2.57639i	2.57639	+	2.57639i
$66$		0			0
$67$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$67$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$68$	0.739009	−	0.673696i	0.739009	−	0.673696i
$69$		0			0
$70$		0			0
$71$		0			0		0.769334	−	0.638847i	$-0.220588\pi$
$71$		0			0		−0.769334	+	0.638847i	$0.779412\pi$
$72$	−0.273663	−	0.961826i	−0.273663	−	0.961826i
$73$	−0.352279	−	1.49780i	−0.352279	−	1.49780i	−0.798017	−	0.602635i	$-0.794118\pi$
$73$	−0.352279	−	1.49780i	−0.352279	−	1.49780i	0.445738	−	0.895163i	$-0.352941\pi$
$74$	1.11943	−	1.63417i	1.11943	−	1.63417i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.138156	−	0.990410i	$-0.544118\pi$
$79$		0			0		0.138156	+	0.990410i	$0.455882\pi$
$80$	−0.252769	+	1.81204i	−0.252769	+	1.81204i
$81$	0.982973	+	0.183750i	0.982973	+	0.183750i
$82$	−0.456541	−	0.666468i	−0.456541	−	0.666468i
$83$		0			0		0.673696	−	0.739009i	$-0.264706\pi$
$83$		0			0		−0.673696	+	0.739009i	$0.735294\pi$
$84$		0			0
$85$	0.252769	−	1.81204i	0.252769	−	1.81204i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.48826	+	0.576554i	1.48826	+	0.576554i	0.961826	−	0.273663i	$-0.0882353\pi$
$89$	1.48826	+	0.576554i	1.48826	+	0.576554i	0.526432	+	0.850217i	$0.323529\pi$
$90$	−1.50941	−	1.03397i	−1.50941	−	1.03397i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−0.748723	+	0.621731i	−0.748723	+	0.621731i	−0.932472	−	0.361242i	$-0.882353\pi$
$97$	−0.748723	+	0.621731i	−0.748723	+	0.621731i	0.183750	+	0.982973i	$0.441176\pi$
$98$	0.445738	+	0.895163i	0.445738	+	0.895163i
$99$		0			0
$100$	1.23574	+	1.99579i	1.23574	+	1.99579i
$101$	1.03494	+	0.193463i	1.03494	+	0.193463i	0.673696	−	0.739009i	$-0.264706\pi$
$101$	1.03494	+	0.193463i	1.03494	+	0.193463i	0.361242	+	0.932472i	$0.382353\pi$
$102$		0			0
$103$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$103$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$104$	1.34164	+	1.47171i	1.34164	+	1.47171i
$105$		0			0
$106$	−0.312454	+	0.193463i	−0.312454	+	0.193463i
$107$		0			0		0.990410	−	0.138156i	$-0.0441176\pi$
$107$		0			0		−0.990410	+	0.138156i	$0.955882\pi$
$108$		0			0
$109$	−0.276018	+	0.0127611i	−0.276018	+	0.0127611i	−0.183750	−	0.982973i	$-0.558824\pi$
$109$	−0.276018	+	0.0127611i	−0.276018	+	0.0127611i	−0.0922684	+	0.995734i	$0.529412\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.0653133	+	1.41270i	−0.0653133	+	1.41270i	0.673696	+	0.739009i	$0.264706\pi$
$113$	−0.0653133	+	1.41270i	−0.0653133	+	1.41270i	−0.739009	+	0.673696i	$0.764706\pi$
$114$		0			0
$115$		0			0
$116$	−0.292529	−	1.24376i	−0.292529	−	1.24376i
$117$	−1.91545	+	0.544991i	−1.91545	+	0.544991i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.526432	+	0.850217i	−0.526432	+	0.850217i
$122$	0.0293534	−	0.0875787i	0.0293534	−	0.0875787i
$123$		0			0
$124$		0			0
$125$	2.33738	+	0.783410i	2.33738	+	0.783410i
$126$		0			0
$127$		0			0		0.895163	−	0.445738i	$-0.147059\pi$
$127$		0			0		−0.895163	+	0.445738i	$0.852941\pi$
$128$	−0.183750	+	0.982973i	−0.183750	+	0.982973i
$129$		0			0
$130$	3.60863	+	0.503382i	3.60863	+	0.503382i
$131$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$131$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.183750	−	0.982973i	0.183750	−	0.982973i
$137$	−0.197717	+	0.694903i	−0.197717	+	0.694903i	0.798017	+	0.602635i	$0.205882\pi$
$137$	−0.197717	+	0.694903i	−0.197717	+	0.694903i	−0.995734	+	0.0922684i	$0.970588\pi$
$138$		0			0
$139$		0			0		0.138156	−	0.990410i	$-0.455882\pi$
$139$		0			0		−0.138156	+	0.990410i	$0.544118\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.798017	−	0.602635i	−0.798017	−	0.602635i
$145$	−1.86549	−	1.40875i	−1.86549	−	1.40875i
$146$	−1.18375	−	0.982973i	−1.18375	−	0.982973i
$147$		0			0
$148$	−0.0914812	−	1.97871i	−0.0914812	−	1.97871i
$149$	0.136374	+	0.124322i	0.136374	+	0.124322i	0.739009	−	0.673696i	$-0.235294\pi$
$149$	0.136374	+	0.124322i	0.136374	+	0.124322i	−0.602635	+	0.798017i	$0.705882\pi$
$150$		0			0
$151$		0			0		−0.961826	−	0.273663i	$-0.911765\pi$
$151$		0			0		0.961826	+	0.273663i	$0.0882353\pi$
$152$		0			0
$153$	0.798017	+	0.602635i	0.798017	+	0.602635i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−1.83319	+	0.342683i	−1.83319	+	0.342683i	−0.982973	−	0.183750i	$-0.941176\pi$
$157$	−1.83319	+	0.342683i	−1.83319	+	0.342683i	−0.850217	+	0.526432i	$0.823529\pi$
$158$		0			0
$159$		0			0
$160$	0.890286	+	1.59837i	0.890286	+	1.59837i
$161$		0			0
$162$	0.895163	−	0.445738i	0.895163	−	0.445738i
$163$		0			0		−0.948161	−	0.317791i	$-0.897059\pi$
$163$		0			0		0.948161	+	0.317791i	$0.102941\pi$
$164$	−0.765964	−	0.256725i	−0.765964	−	0.256725i
$165$		0			0
$166$		0			0
$167$		0			0		0.317791	−	0.948161i	$-0.397059\pi$
$167$		0			0		−0.317791	+	0.948161i	$0.602941\pi$
$168$		0			0
$169$	2.19186	−	1.99815i	2.19186	−	1.99815i
$170$	−0.890286	−	1.59837i	−0.890286	−	1.59837i
$171$		0			0
$172$		0			0
$173$	0.377767	+	1.60617i	0.377767	+	1.60617i	0.739009	+	0.673696i	$0.235294\pi$
$173$	0.377767	+	1.60617i	0.377767	+	1.60617i	−0.361242	+	0.932472i	$0.617647\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	1.53511	−	0.436776i	1.53511	−	0.436776i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	−1.82764	+	0.0844967i	−1.82764	+	0.0844967i
$181$	−0.806980	+	1.82764i	−0.806980	+	1.82764i	−0.361242	+	0.932472i	$0.617647\pi$
$181$	−0.806980	+	1.82764i	−0.806980	+	1.82764i	−0.445738	+	0.895163i	$0.647059\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.44153	−	2.67823i	−2.44153	−	2.67823i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$191$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$192$		0			0
$193$	−1.12907	+	0.0521999i	−1.12907	+	0.0521999i	−0.602635	−	0.798017i	$-0.705882\pi$
$193$	−1.12907	+	0.0521999i	−1.12907	+	0.0521999i	−0.526432	+	0.850217i	$0.676471\pi$
$194$	−0.222817	+	0.947359i	−0.222817	+	0.947359i
$195$		0			0
$196$	0.895163	+	0.445738i	0.895163	+	0.445738i
$197$	−1.78099	+	0.786384i	−1.78099	+	0.786384i	−0.798017	+	0.602635i	$0.794118\pi$
$197$	−1.78099	+	0.786384i	−1.78099	+	0.786384i	−0.982973	+	0.183750i	$0.941176\pi$
$198$		0			0
$199$		0			0		−0.824997	−	0.565136i	$-0.808824\pi$
$199$		0			0		0.824997	+	0.565136i	$0.191176\pi$
$200$	2.18888	+	0.847976i	2.18888	+	0.847976i
$201$		0			0
$202$	0.942485	−	0.469302i	0.942485	−	0.469302i
$203$		0			0
$204$		0			0
$205$	−1.37821	+	0.533922i	−1.37821	+	0.533922i
$206$		0			0
$207$		0			0
$208$	1.95756	+	0.365931i	1.95756	+	0.365931i
$209$		0			0
$210$		0			0
$211$		0			0		0.565136	−	0.824997i	$-0.308824\pi$
$211$		0			0		−0.565136	+	0.824997i	$0.691176\pi$
$212$	−0.132756	+	0.342683i	−0.132756	+	0.342683i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−0.212577	+	0.176521i	−0.212577	+	0.176521i
$219$		0			0
$220$		0			0
$221$	−1.95756	−	0.365931i	−1.95756	−	0.365931i
$222$		0			0
$223$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$223$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$224$		0			0
$225$	−1.73474	+	1.58143i	−1.73474	+	1.58143i
$226$	0.799224	+	1.16672i	0.799224	+	1.16672i
$227$		0			0		0.973438	−	0.228951i	$-0.0735294\pi$
$227$		0			0		−0.973438	+	0.228951i	$0.926471\pi$
$228$		0			0
$229$	0.887674	−	0.0822551i	0.887674	−	0.0822551i	0.361242	−	0.932472i	$-0.382353\pi$
$229$	0.887674	−	0.0822551i	0.887674	−	0.0822551i	0.526432	+	0.850217i	$0.323529\pi$
$230$		0			0
$231$		0			0
$232$	−0.982973	−	0.816250i	−0.982973	−	0.816250i
$233$	0.947359	−	1.70083i	0.947359	−	1.70083i	0.273663	−	0.961826i	$-0.411765\pi$
$233$	0.947359	−	1.70083i	0.947359	−	1.70083i	0.673696	−	0.739009i	$-0.264706\pi$
$234$	−1.20013	+	1.58923i	−1.20013	+	1.58923i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$239$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$240$		0			0
$241$	−1.64823	−	1.12907i	−1.64823	−	1.12907i	−0.850217	−	0.526432i	$-0.823529\pi$
$241$	−1.64823	−	1.12907i	−1.64823	−	1.12907i	−0.798017	−	0.602635i	$-0.794118\pi$
$242$	0.0922684	+	0.995734i	0.0922684	+	0.995734i
$243$		0			0
$244$	−0.0293534	−	0.0875787i	−0.0293534	−	0.0875787i
$245$	1.78099	−	0.418885i	1.78099	−	0.418885i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	2.33738	−	0.783410i	2.33738	−	0.783410i
$251$		0			0		1.00000			$0$
$251$		0			0		−1.00000			$\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.445738	+	0.895163i	0.445738	+	0.895163i
$257$	1.20013	−	0.111208i	1.20013	−	0.111208i	0.526432	−	0.850217i	$-0.323529\pi$
$257$	1.20013	−	0.111208i	1.20013	−	0.111208i	0.673696	+	0.739009i	$0.264706\pi$
$258$		0			0
$259$		0			0
$260$	3.18310	−	1.77298i	3.18310	−	1.77298i
$261$	1.16883	−	0.516087i	1.16883	−	0.516087i
$262$		0			0
$263$		0			0		0.526432	−	0.850217i	$-0.323529\pi$
$263$		0			0		−0.526432	+	0.850217i	$0.676471\pi$
$264$		0			0
$265$	0.213674	+	0.637516i	0.213674	+	0.637516i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.453510	+	0.0632619i	−0.453510	+	0.0632619i	−0.361242	−	0.932472i	$-0.617647\pi$
$269$	−0.453510	+	0.0632619i	−0.453510	+	0.0632619i	−0.0922684	+	0.995734i	$0.529412\pi$
$270$		0			0
$271$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$271$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$272$	−0.445738	−	0.895163i	−0.445738	−	0.895163i
$273$		0			0
$274$	0.260991	+	0.673696i	0.260991	+	0.673696i
$275$		0			0
$276$		0			0
$277$	0.524354	−	1.56446i	0.524354	−	1.56446i	−0.273663	−	0.961826i	$-0.588235\pi$
$277$	0.524354	−	1.56446i	0.524354	−	1.56446i	0.798017	−	0.602635i	$-0.205882\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.694903	−	1.79375i	−0.694903	−	1.79375i	−0.602635	−	0.798017i	$-0.705882\pi$
$281$	−0.694903	−	1.79375i	−0.694903	−	1.79375i	−0.0922684	−	0.995734i	$-0.529412\pi$
$282$		0			0
$283$		0			0		0.824997	−	0.565136i	$-0.191176\pi$
$283$		0			0		−0.824997	+	0.565136i	$0.808824\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−1.00000			−1.00000
$289$	0.445738	+	0.895163i	0.445738	+	0.895163i
$290$	−2.33765			−2.33765
$291$		0			0
$292$	−1.53703	−	0.0710610i	−1.53703	−	0.0710610i
$293$	−0.329838	+	1.15926i	−0.329838	+	1.15926i	0.602635	+	0.798017i	$0.294118\pi$
$293$	−0.329838	+	1.15926i	−0.329838	+	1.15926i	−0.932472	+	0.361242i	$0.882353\pi$
$294$		0			0
$295$		0			0
$296$	−1.26544	−	1.52391i	−1.26544	−	1.52391i
$297$		0			0
$298$	0.183750	+	0.0170269i	0.183750	+	0.0170269i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.143681	−	0.0889636i	−0.143681	−	0.0889636i
$306$	1.00000			1.00000
$307$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$307$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.914794	−	0.403921i	$-0.867647\pi$
$311$		0			0		0.914794	+	0.403921i	$0.132353\pi$
$312$		0			0
$313$	0.145517	+	0.434164i	0.145517	+	0.434164i	0.995734	−	0.0922684i	$-0.0294118\pi$
$313$	0.145517	+	0.434164i	0.145517	+	0.434164i	−0.850217	+	0.526432i	$0.823529\pi$
$314$	−1.25640	+	1.37821i	−1.25640	+	1.37821i
$315$		0			0
$316$		0			0
$317$	−0.418885	+	0.184956i	−0.418885	+	0.184956i	−0.602635	−	0.798017i	$-0.705882\pi$
$317$	−0.418885	+	0.184956i	−0.418885	+	0.184956i	0.183750	+	0.982973i	$0.441176\pi$
$318$		0			0
$319$		0			0
$320$	1.67370	+	0.739009i	1.67370	+	0.739009i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.445738	−	0.895163i	0.445738	−	0.895163i
$325$	1.68872	−	4.35908i	1.68872	−	4.35908i
$326$		0			0
$327$		0			0
$328$	−0.765964	+	0.256725i	−0.765964	+	0.256725i
$329$		0			0
$330$		0			0
$331$		0			0		−0.961826	−	0.273663i	$-0.911765\pi$
$331$		0			0		0.961826	+	0.273663i	$0.0882353\pi$
$332$		0			0
$333$	1.92821	−	0.453510i	1.92821	−	0.453510i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.524354	+	0.359191i	0.524354	+	0.359191i	0.798017	−	0.602635i	$-0.205882\pi$
$337$	0.524354	+	0.359191i	0.524354	+	0.359191i	−0.273663	+	0.961826i	$0.588235\pi$
$338$	0.544991	−	2.91545i	0.544991	−	2.91545i
$339$		0			0
$340$	−1.67370	−	0.739009i	−1.67370	−	0.739009i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	1.26940	+	1.05409i	1.26940	+	1.05409i
$347$		0			0		0.403921	−	0.914794i	$-0.367647\pi$
$347$		0			0		−0.403921	+	0.914794i	$0.632353\pi$
$348$		0			0
$349$	1.78269	−	0.165190i	1.78269	−	0.165190i	0.850217	−	0.526432i	$-0.176471\pi$
$349$	1.78269	−	0.165190i	1.78269	−	0.165190i	0.932472	+	0.361242i	$0.117647\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.25664	−	1.14558i	1.25664	−	1.14558i	0.273663	−	0.961826i	$-0.411765\pi$
$353$	1.25664	−	1.14558i	1.25664	−	1.14558i	0.982973	−	0.183750i	$-0.0588235\pi$
$354$		0			0
$355$		0			0
$356$	0.961826	−	1.27366i	0.961826	−	1.27366i
$357$		0			0
$358$		0			0
$359$		0			0		−0.183750	−	0.982973i	$-0.558824\pi$
$359$		0			0		0.183750	+	0.982973i	$0.441176\pi$
$360$	−1.40756	+	1.16883i	−1.40756	+	1.16883i
$361$	0.273663	+	0.961826i	0.273663	+	0.961826i
$362$	0.457413	+	1.94480i	0.457413	+	1.94480i
$363$		0			0
$364$		0			0
$365$	−2.24652	+	1.69649i	−2.24652	+	1.69649i
$366$		0			0
$367$		0			0		0.565136	−	0.824997i	$-0.308824\pi$
$367$		0			0		−0.565136	+	0.824997i	$0.691176\pi$
$368$		0			0
$369$	0.111609	−	0.800095i	0.111609	−	0.800095i
$370$	−3.56238	−	0.665924i	−3.56238	−	0.665924i
$371$		0			0
$372$		0			0
$373$	−1.66943	+	0.646741i	−1.66943	+	0.646741i	−0.995734	−	0.0922684i	$-0.970588\pi$
$373$	−1.66943	+	0.646741i	−1.66943	+	0.646741i	−0.673696	+	0.739009i	$0.735294\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.62554	+	1.95756i	−1.62554	+	1.95756i
$378$		0			0
$379$		0			0		−0.824997	−	0.565136i	$-0.808824\pi$
$379$		0			0		0.824997	+	0.565136i	$0.191176\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.673696	−	0.739009i	$-0.735294\pi$
$383$		0			0		0.673696	+	0.739009i	$0.264706\pi$
$384$		0			0
$385$		0			0
$386$	−0.869557	+	0.722071i	−0.869557	+	0.722071i
$387$		0			0
$388$	0.393100	+	0.890286i	0.393100	+	0.890286i
$389$	−1.03494	−	1.67148i	−1.03494	−	1.67148i	−0.673696	−	0.739009i	$-0.735294\pi$
$389$	−1.03494	−	1.67148i	−1.03494	−	1.67148i	−0.361242	−	0.932472i	$-0.617647\pi$
$390$		0			0
$391$		0			0
$392$	0.982973	−	0.183750i	0.982973	−	0.183750i
$393$		0			0
$394$	−0.947359	+	1.70083i	−0.947359	+	1.70083i
$395$		0			0
$396$		0			0
$397$	−0.111609	+	0.252769i	−0.111609	+	0.252769i	−0.961826	−	0.273663i	$-0.911765\pi$
$397$	−0.111609	+	0.252769i	−0.111609	+	0.252769i	0.850217	+	0.526432i	$0.176471\pi$
$398$		0			0
$399$		0			0
$400$	2.25778	−	0.642394i	2.25778	−	0.642394i
$401$	−0.227957	−	1.63417i	−0.227957	−	1.63417i	−0.673696	−	0.739009i	$-0.735294\pi$
$401$	−0.227957	−	1.63417i	−0.227957	−	1.63417i	0.445738	−	0.895163i	$-0.352941\pi$
$402$		0			0
$403$		0			0
$404$	0.469302	−	0.942485i	0.469302	−	0.942485i
$405$	−0.418885	−	1.78099i	−0.418885	−	1.78099i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−1.09227	+	0.995734i	−1.09227	+	0.995734i	−0.0922684	+	0.995734i	$0.529412\pi$
$409$	−1.09227	+	0.995734i	−1.09227	+	0.995734i	−1.00000			$1.00000\pi$
$410$	−0.778076	+	1.25664i	−0.778076	+	1.25664i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	1.78269	−	0.887674i	1.78269	−	0.887674i
$417$		0			0
$418$		0			0
$419$		0			0		−0.990410	−	0.138156i	$-0.955882\pi$
$419$		0			0		0.990410	+	0.138156i	$0.0441176\pi$
$420$		0			0
$421$	1.03494	−	0.193463i	1.03494	−	0.193463i	0.361242	−	0.932472i	$-0.382353\pi$
$421$	1.03494	−	0.193463i	1.03494	−	0.193463i	0.673696	+	0.739009i	$0.264706\pi$
$422$		0			0
$423$		0			0
$424$	0.100571	+	0.353470i	0.100571	+	0.353470i
$425$	−2.25778	+	0.642394i	−2.25778	+	0.642394i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.228951	−	0.973438i	$-0.426471\pi$
$431$		0			0		−0.228951	+	0.973438i	$0.573529\pi$
$432$		0			0
$433$	−1.48826	−	1.12388i	−1.48826	−	1.12388i	−0.961826	−	0.273663i	$-0.911765\pi$
$433$	−1.48826	−	1.12388i	−1.48826	−	1.12388i	−0.526432	−	0.850217i	$-0.676471\pi$
$434$		0			0
$435$		0			0
$436$	−0.0632619	+	0.268973i	−0.0632619	+	0.268973i
$437$		0			0
$438$		0			0
$439$		0			0		0.138156	−	0.990410i	$-0.455882\pi$
$439$		0			0		−0.138156	+	0.990410i	$0.544118\pi$
$440$		0			0
$441$	−0.273663	+	0.961826i	−0.273663	+	0.961826i
$442$	−1.78269	+	0.887674i	−1.78269	+	0.887674i
$443$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$443$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$444$		0			0
$445$	−0.134860	−	2.91697i	−0.134860	−	2.91697i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.549996	+	0.987432i	0.549996	+	0.987432i	0.995734	+	0.0922684i	$0.0294118\pi$
$449$	0.549996	+	0.987432i	0.549996	+	0.987432i	−0.445738	+	0.895163i	$0.647059\pi$
$450$	−0.431332	+	2.30742i	−0.431332	+	2.30742i
$451$		0			0
$452$	1.34090	+	0.449425i	1.34090	+	0.449425i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.895163	+	1.44574i	−0.895163	+	1.44574i			1.00000i	$0.5\pi$
$457$	−0.895163	+	1.44574i	−0.895163	+	1.44574i	−0.895163	+	0.445738i	$0.852941\pi$
$458$	0.658809	−	0.600584i	0.658809	−	0.600584i
$459$		0			0
$460$		0			0
$461$	−1.85022	+	0.526432i	−1.85022	+	0.526432i	−0.850217	+	0.526432i	$0.823529\pi$
$461$	−1.85022	+	0.526432i	−1.85022	+	0.526432i	−1.00000			$\pi$
$462$		0			0
$463$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$463$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$464$	−1.27633	−	0.0590083i	−1.27633	−	0.0590083i
$465$		0			0
$466$	−0.268973	−	1.92821i	−0.268973	−	1.92821i
$467$		0			0		0.961826	−	0.273663i	$-0.0882353\pi$
$467$		0			0		−0.961826	+	0.273663i	$0.911765\pi$
$468$			1.99147i			1.99147i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.361242	−	0.0675278i	−0.361242	−	0.0675278i
$478$		0			0
$479$		0			0		−0.403921	−	0.914794i	$-0.632353\pi$
$479$		0			0		0.403921	+	0.914794i	$0.367647\pi$
$480$		0			0
$481$	−3.03482	+	2.52009i	−3.03482	+	2.52009i
$482$	−1.99573	+	0.0922684i	−1.99573	+	0.0922684i
$483$		0			0
$484$	0.673696	+	0.739009i	0.673696	+	0.739009i
$485$	1.59390	+	0.793669i	1.59390	+	0.793669i
$486$		0			0
$487$		0			0		−0.873622	−	0.486604i	$-0.838235\pi$
$487$		0			0		0.873622	+	0.486604i	$0.161765\pi$
$488$	−0.0762025	−	0.0521999i	−0.0762025	−	0.0521999i
$489$		0			0
$490$	1.16883	−	1.40756i	1.16883	−	1.40756i
$491$		0			0		0.895163	−	0.445738i	$-0.147059\pi$
$491$		0			0		−0.895163	+	0.445738i	$0.852941\pi$
$492$		0			0
$493$	1.27633	+	0.0590083i	1.27633	+	0.0590083i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		−0.138156	−	0.990410i	$-0.544118\pi$
$499$		0			0		0.138156	+	0.990410i	$0.455882\pi$
$500$	1.39316	−	2.03376i	1.39316	−	2.03376i
$501$		0			0
$502$		0			0
$503$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$503$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$504$		0			0
$505$	−0.441029	−	1.87514i	−0.441029	−	1.87514i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1.18475	−	1.56886i	−1.18475	−	1.56886i	−0.739009	−	0.673696i	$-0.764706\pi$
$509$	−1.18475	−	1.56886i	−1.18475	−	1.56886i	−0.445738	−	0.895163i	$-0.647059\pi$
$510$		0			0
$511$		0			0
$512$	0.895163	+	0.445738i	0.895163	+	0.445738i
$513$		0			0
$514$	0.890705	−	0.811985i	0.890705	−	0.811985i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	1.47171	−	3.33311i	1.47171	−	3.33311i
$521$	1.08800	+	0.903466i	1.08800	+	0.903466i	0.995734	−	0.0922684i	$-0.0294118\pi$
$521$	1.08800	+	0.903466i	1.08800	+	0.903466i	0.0922684	+	0.995734i	$0.470588\pi$
$522$	0.621731	−	1.11622i	0.621731	−	1.11622i
$523$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$523$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−0.183750	+	0.982973i	−0.183750	+	0.982973i
$530$	0.554705	+	0.379982i	0.554705	+	0.379982i
$531$		0			0
$532$		0			0
$533$	0.511260	+	1.52539i	0.511260	+	1.52539i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−0.323785	+	0.323785i	−0.323785	+	0.323785i
$539$		0			0
$540$		0			0
$541$	−1.89430	+	0.634905i	−1.89430	+	0.634905i	−0.932472	+	0.361242i	$0.882353\pi$
$541$	−1.89430	+	0.634905i	−1.89430	+	0.634905i	−0.961826	+	0.273663i	$0.911765\pi$
$542$		0			0
$543$		0			0
$544$	−0.895163	−	0.445738i	−0.895163	−	0.445738i
$545$	0.225338	+	0.452539i	0.225338	+	0.452539i
$546$		0			0
$547$		0			0		−0.914794	−	0.403921i	$-0.867647\pi$
$547$		0			0		0.914794	+	0.403921i	$0.132353\pi$
$548$	0.614268	+	0.380338i	0.614268	+	0.380338i
$549$	0.0806938	−	0.0449462i	0.0806938	−	0.0449462i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−0.524354	−	1.56446i	−0.524354	−	1.56446i
$555$		0			0
$556$		0			0
$557$	0.961826	+	1.27366i	0.961826	+	1.27366i	0.961826	+	0.273663i	$0.0882353\pi$
$557$	0.961826	+	1.27366i	0.961826	+	1.27366i			1.00000i	$0.5\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−1.63552	−	1.01267i	−1.63552	−	1.01267i
$563$		0			0		−0.361242	−	0.932472i	$-0.617647\pi$
$563$		0			0		0.361242	+	0.932472i	$0.382353\pi$
$564$		0			0
$565$	2.41270	−	0.934687i	2.41270	−	0.934687i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$569$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$570$		0			0
$571$		0			0		−0.638847	−	0.769334i	$-0.720588\pi$
$571$		0			0		0.638847	+	0.769334i	$0.279412\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.798017	+	0.602635i	−0.798017	+	0.602635i
$577$	1.79033			1.79033			0.895163	−	0.445738i	$-0.147059\pi$
$577$	1.79033			1.79033			0.895163	+	0.445738i	$0.147059\pi$
$578$	0.895163	+	0.445738i	0.895163	+	0.445738i
$579$		0			0
$580$	−1.86549	+	1.40875i	−1.86549	+	1.40875i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−1.26940	+	0.869557i	−1.26940	+	0.869557i
$585$	2.32768	+	2.80312i	2.32768	+	2.80312i
$586$	0.435393	+	1.12388i	0.435393	+	1.12388i
$587$		0			0		−0.995734	−	0.0922684i	$-0.970588\pi$
$587$		0			0		0.995734	+	0.0922684i	$0.0294118\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−1.92821	−	0.453510i	−1.92821	−	0.453510i
$593$	0.260991	+	0.673696i	0.260991	+	0.673696i	1.00000			$0$
$593$	0.260991	+	0.673696i	0.260991	+	0.673696i	−0.739009	+	0.673696i	$0.764706\pi$
$594$		0			0
$595$		0			0
$596$	0.156896	−	0.0971461i	0.156896	−	0.0971461i
$597$		0			0
$598$		0			0
$599$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$599$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$600$		0			0
$601$	−0.982973	−	1.18375i	−0.982973	−	1.18375i	−0.982973	−	0.183750i	$-0.941176\pi$
$601$	−0.982973	−	1.18375i	−0.982973	−	1.18375i		−	1.00000i	$-0.5\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.81204	+	0.252769i	1.81204	+	0.252769i
$606$		0			0
$607$		0			0		0.873622	−	0.486604i	$-0.161765\pi$
$607$		0			0		−0.873622	+	0.486604i	$0.838235\pi$
$608$		0			0
$609$		0			0
$610$	−0.168272	+	0.0155927i	−0.168272	+	0.0155927i
$611$		0			0
$612$	0.798017	−	0.602635i	0.798017	−	0.602635i
$613$	−0.243964	+	0.489946i	−0.243964	+	0.489946i	−0.982973	−	0.183750i	$-0.941176\pi$
$613$	−0.243964	+	0.489946i	−0.243964	+	0.489946i	0.739009	+	0.673696i	$0.235294\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.45890	+	0.488975i	−1.45890	+	0.488975i	−0.932472	−	0.361242i	$-0.882353\pi$
$617$	−1.45890	+	0.488975i	−1.45890	+	0.488975i	−0.526432	+	0.850217i	$0.676471\pi$
$618$		0			0
$619$		0			0		0.0461835	−	0.998933i	$-0.485294\pi$
$619$		0			0		−0.0461835	+	0.998933i	$0.514706\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.199563	−	2.15363i	−0.199563	−	2.15363i
$626$	0.377767	+	0.258777i	0.377767	+	0.258777i
$627$		0			0
$628$	−0.172075	+	1.85699i	−0.172075	+	1.85699i
$629$	1.92821	+	0.453510i	1.92821	+	0.453510i
$630$		0			0
$631$		0			0		−0.995734	−	0.0922684i	$-0.970588\pi$
$631$		0			0		0.995734	+	0.0922684i	$0.0294118\pi$
$632$		0			0
$633$		0			0
$634$	−0.222817	+	0.400033i	−0.222817	+	0.400033i
$635$		0			0
$636$		0			0
$637$	−0.365931	−	1.95756i	−0.365931	−	1.95756i
$638$		0			0
$639$		0			0
$640$	1.78099	−	0.418885i	1.78099	−	0.418885i
$641$	−0.359191	−	0.524354i	−0.359191	−	0.524354i	0.602635	−	0.798017i	$-0.294118\pi$
$641$	−0.359191	−	0.524354i	−0.359191	−	0.524354i	−0.961826	+	0.273663i	$0.911765\pi$
$642$		0			0
$643$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$643$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$647$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$648$	−0.183750	−	0.982973i	−0.183750	−	0.982973i
$649$		0			0
$650$	−1.27931	−	4.49630i	−1.27931	−	4.49630i
$651$		0			0
$652$		0			0
$653$	1.34090	−	1.34090i	1.34090	−	1.34090i	0.445738	−	0.895163i	$-0.352941\pi$
$653$	1.34090	−	1.34090i	1.34090	−	1.34090i	0.895163	−	0.445738i	$-0.147059\pi$
$654$		0			0
$655$		0			0
$656$	−0.456541	+	0.666468i	−0.456541	+	0.666468i
$657$	−0.212577	−	1.52391i	−0.212577	−	1.52391i
$658$		0			0
$659$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$659$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$660$		0			0
$661$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$661$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	1.26544	−	1.52391i	1.26544	−	1.52391i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.400033	+	1.70083i	−0.400033	+	1.70083i	0.273663	+	0.961826i	$0.411765\pi$
$673$	−0.400033	+	1.70083i	−0.400033	+	1.70083i	−0.673696	+	0.739009i	$0.735294\pi$
$674$	0.634905	−	0.0293534i	0.634905	−	0.0293534i
$675$		0			0
$676$	−1.32204	−	2.65501i	−1.32204	−	2.65501i
$677$	−0.705749	−	1.59837i	−0.705749	−	1.59837i	−0.798017	−	0.602635i	$-0.794118\pi$
$677$	−0.705749	−	1.59837i	−0.705749	−	1.59837i	0.0922684	−	0.995734i	$-0.470588\pi$
$678$		0			0
$679$		0			0
$680$	−1.78099	+	0.418885i	−1.78099	+	0.418885i
$681$		0			0
$682$		0			0
$683$		0			0		0.486604	−	0.873622i	$-0.338235\pi$
$683$		0			0		−0.486604	+	0.873622i	$0.661765\pi$
$684$		0			0
$685$	1.30917	−	0.182622i	1.30917	−	0.182622i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.703924	−	0.200284i	0.703924	−	0.200284i
$690$		0			0
$691$		0			0		0.0461835	−	0.998933i	$-0.485294\pi$
$691$		0			0		−0.0461835	+	0.998933i	$0.514706\pi$
$692$	1.64823	+	0.0762025i	1.64823	+	0.0762025i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	0.456541	−	0.666468i	0.456541	−	0.666468i
$698$	1.32307	−	1.20614i	1.32307	−	1.20614i
$699$		0			0
$700$		0			0
$701$	−0.0971461	+	1.04837i	−0.0971461	+	1.04837i	0.798017	+	0.602635i	$0.205882\pi$
$701$	−0.0971461	+	1.04837i	−0.0971461	+	1.04837i	−0.895163	+	0.445738i	$0.852941\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	0.312454	−	1.67148i	0.312454	−	1.67148i
$707$		0			0
$708$		0			0
$709$	1.34090	+	1.34090i	1.34090	+	1.34090i	0.895163	+	0.445738i	$0.147059\pi$
$709$	1.34090	+	1.34090i	1.34090	+	1.34090i	0.445738	+	0.895163i	$0.352941\pi$
$710$		0			0
$711$		0			0
$712$		−	1.59603i		−	1.59603i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.0461835	−	0.998933i	$-0.514706\pi$
$719$		0			0		0.0461835	+	0.998933i	$0.485294\pi$
$720$	−0.418885	+	1.78099i	−0.418885	+	1.78099i
$721$		0			0
$722$	0.798017	+	0.602635i	0.798017	+	0.602635i
$723$		0			0
$724$	1.53703	+	1.27633i	1.53703	+	1.27633i
$725$	−0.686679	+	2.91958i	−0.686679	+	2.91958i
$726$		0			0
$727$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$727$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$728$		0			0
$729$	0.961826	+	0.273663i	0.961826	+	0.273663i
$730$	−0.770396	+	2.70766i	−0.770396	+	2.70766i
$731$		0			0
$732$		0			0
$733$		−	0.722483i		−	0.722483i	−0.932472	−	0.361242i	$-0.882353\pi$
$733$		−	0.722483i		−	0.722483i	0.932472	−	0.361242i	$-0.117647\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	−0.393100	−	0.705749i	−0.393100	−	0.705749i
$739$		0			0		0.183750	−	0.982973i	$-0.441176\pi$
$739$		0			0		−0.183750	+	0.982973i	$0.558824\pi$
$740$	−3.24415	+	1.61539i	−3.24415	+	1.61539i
$741$		0			0
$742$		0			0
$743$		0			0		0.638847	−	0.769334i	$-0.279412\pi$
$743$		0			0		−0.638847	+	0.769334i	$0.720588\pi$
$744$		0			0
$745$	0.107295	−	0.320124i	0.107295	−	0.320124i
$746$	−0.942485	+	1.52217i	−0.942485	+	1.52217i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.228951	−	0.973438i	$-0.573529\pi$
$751$		0			0		0.228951	+	0.973438i	$0.426471\pi$
$752$		0			0
$753$		0			0
$754$	−0.117513	+	2.54177i	−0.117513	+	2.54177i
$755$		0			0
$756$		0			0
$757$			0.547326i			0.547326i	0.961826	+	0.273663i	$0.0882353\pi$
$757$			0.547326i			0.547326i	−0.961826	+	0.273663i	$0.911765\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.614268	−	0.380338i	0.614268	−	0.380338i	−0.183750	−	0.982973i	$-0.558824\pi$
$761$	0.614268	−	0.380338i	0.614268	−	0.380338i	0.798017	+	0.602635i	$0.205882\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.418885	−	1.78099i	0.418885	−	1.78099i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−0.711414	−	1.42871i	−0.711414	−	1.42871i	−0.895163	−	0.445738i	$-0.852941\pi$
$769$	−0.711414	−	1.42871i	−0.711414	−	1.42871i	0.183750	−	0.982973i	$-0.441176\pi$
$770$		0			0
$771$		0			0
$772$	−0.258777	+	1.10025i	−0.258777	+	1.10025i
$773$	1.25640	+	1.37821i	1.25640	+	1.37821i	0.895163	+	0.445738i	$0.147059\pi$
$773$	1.25640	+	1.37821i	1.25640	+	1.37821i	0.361242	+	0.932472i	$0.382353\pi$
$774$		0			0
$775$		0			0
$776$	0.850217	+	0.473568i	0.850217	+	0.473568i
$777$		0			0
$778$	−1.83319	−	0.710182i	−1.83319	−	0.710182i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.673696	−	0.739009i	0.673696	−	0.739009i
$785$	1.92829	+	2.81496i	1.92829	+	2.81496i
$786$		0			0
$787$		0			0		0.138156	−	0.990410i	$-0.455882\pi$
$787$		0			0		−0.138156	+	0.990410i	$0.544118\pi$
$788$	0.268973	+	1.92821i	0.268973	+	1.92821i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−0.103954	+	0.151755i	−0.103954	+	0.151755i
$794$	0.0632619	+	0.268973i	0.0632619	+	0.268973i
$795$		0			0
$796$		0			0
$797$	−0.0675278	−	0.361242i	−0.0675278	−	0.361242i	0.932472	−	0.361242i	$-0.117647\pi$
$797$	−0.0675278	−	0.361242i	−0.0675278	−	0.361242i	−1.00000			$\pi$
$798$		0			0
$799$		0			0
$800$	1.41462	−	1.87326i	1.41462	−	1.87326i
$801$	1.42871	+	0.711414i	1.42871	+	0.711414i
$802$	−1.16672	−	1.16672i	−1.16672	−	1.16672i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−0.193463	−	1.03494i	−0.193463	−	1.03494i
$809$	0.786384	−	1.78099i	0.786384	−	1.78099i	0.183750	−	0.982973i	$-0.441176\pi$
$809$	0.786384	−	1.78099i	0.786384	−	1.78099i	0.602635	−	0.798017i	$-0.294118\pi$
$810$	−1.40756	−	1.16883i	−1.40756	−	1.16883i
$811$		0			0		0.486604	−	0.873622i	$-0.338235\pi$
$811$		0			0		−0.486604	+	0.873622i	$0.661765\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−0.271585	+	1.45285i	−0.271585	+	1.45285i
$819$		0			0
$820$	0.136374	+	1.47171i	0.136374	+	1.47171i
$821$	−0.0899135	−	0.0211475i	−0.0899135	−	0.0211475i	0.183750	−	0.982973i	$-0.441176\pi$
$821$	−0.0899135	−	0.0211475i	−0.0899135	−	0.0211475i	−0.273663	+	0.961826i	$0.588235\pi$
$822$		0			0
$823$		0			0		0.973438	−	0.228951i	$-0.0735294\pi$
$823$		0			0		−0.973438	+	0.228951i	$0.926471\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$827$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$828$		0			0
$829$	0.184537			0.184537			0.0922684	−	0.995734i	$-0.470588\pi$
$829$	0.184537			0.184537			0.0922684	+	0.995734i	$0.470588\pi$
$830$		0			0
$831$		0			0
$832$	0.887674	−	1.78269i	0.887674	−	1.78269i
$833$	−0.673696	+	0.739009i	−0.673696	+	0.739009i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.914794	−	0.403921i	$-0.132353\pi$
$839$		0			0		−0.914794	+	0.403921i	$0.867647\pi$
$840$		0			0
$841$	0.332969	−	0.537763i	0.332969	−	0.537763i
$842$	0.709310	−	0.778076i	0.709310	−	0.778076i
$843$		0			0
$844$		0			0
$845$	−4.96409	−	2.19186i	−4.96409	−	2.19186i
$846$		0			0
$847$		0			0
$848$	0.293271	+	0.221468i	0.293271	+	0.221468i
$849$		0			0
$850$	−1.41462	+	1.87326i	−1.41462	+	1.87326i
$851$		0			0
$852$		0			0
$853$	−0.618701	−	0.145517i	−0.618701	−	0.145517i	−0.0922684	−	0.995734i	$-0.529412\pi$
$853$	−0.618701	−	0.145517i	−0.618701	−	0.145517i	−0.526432	+	0.850217i	$0.676471\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.65667	−	0.922758i	−1.65667	−	0.922758i	−0.982973	−	0.183750i	$-0.941176\pi$
$857$	−1.65667	−	0.922758i	−1.65667	−	0.922758i	−0.673696	−	0.739009i	$-0.735294\pi$
$858$		0			0
$859$		0			0		−0.361242	−	0.932472i	$-0.617647\pi$
$859$		0			0		0.361242	+	0.932472i	$0.382353\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$863$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$864$		0			0
$865$	2.40906	−	1.81924i	2.40906	−	1.81924i
$866$	−1.86494			−1.86494
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.111609	+	0.252769i	0.111609	+	0.252769i
$873$	−0.802895	+	0.549996i	−0.802895	+	0.549996i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.34421	+	0.748723i	1.34421	+	0.748723i	0.982973	−	0.183750i	$-0.0588235\pi$
$877$	1.34421	+	0.748723i	1.34421	+	0.748723i	0.361242	+	0.932472i	$0.382353\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.947359	−	0.222817i	−0.947359	−	0.222817i	−0.273663	−	0.961826i	$-0.588235\pi$
$881$	−0.947359	−	0.222817i	−0.947359	−	0.222817i	−0.673696	+	0.739009i	$0.735294\pi$
$882$	0.361242	+	0.932472i	0.361242	+	0.932472i
$883$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$883$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$884$	−0.887674	+	1.78269i	−0.887674	+	1.78269i
$885$		0			0
$886$		0			0
$887$		0			0		0.990410	−	0.138156i	$-0.0441176\pi$
$887$		0			0		−0.990410	+	0.138156i	$0.955882\pi$
$888$		0			0
$889$		0			0
$890$	−1.86549	−	2.24652i	−1.86549	−	2.24652i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	1.03397	+	0.456541i	1.03397	+	0.456541i
$899$		0			0
$900$	1.04632	+	2.10130i	1.04632	+	2.10130i
$901$	−0.293271	−	0.221468i	−0.293271	−	0.221468i
$902$		0			0
$903$		0			0
$904$	1.34090	−	0.449425i	1.34090	−	0.449425i
$905$	3.65527			3.65527
$906$		0			0
$907$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$907$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$908$		0			0
$909$	1.01267	+	0.288130i	1.01267	+	0.288130i
$910$		0			0
$911$		0			0		0.973438	−	0.228951i	$-0.0735294\pi$
$911$		0			0		−0.973438	+	0.228951i	$0.926471\pi$
$912$		0			0
$913$		0			0
$914$	0.156896	+	1.69318i	0.156896	+	1.69318i
$915$		0			0
$916$	0.163808	−	0.876298i	0.163808	−	0.876298i
$917$		0			0
$918$		0			0
$919$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$919$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$920$		0			0
$921$		0			0
$922$	−1.15926	+	1.53511i	−1.15926	+	1.53511i
$923$		0			0
$924$		0			0
$925$	−1.87814	+	4.25357i	−1.87814	+	4.25357i
$926$		0			0
$927$		0			0
$928$	−1.05409	+	0.722071i	−1.05409	+	0.722071i
$929$	1.70083	−	0.400033i	1.70083	−	0.400033i	0.739009	−	0.673696i	$-0.235294\pi$
$929$	1.70083	−	0.400033i	1.70083	−	0.400033i	0.961826	+	0.273663i	$0.0882353\pi$
$930$		0			0
$931$		0			0
$932$	−1.37665	−	1.37665i	−1.37665	−	1.37665i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	1.20013	+	1.58923i	1.20013	+	1.58923i
$937$	−0.353470	−	1.89090i	−0.353470	−	1.89090i	−0.445738	−	0.895163i	$-0.647059\pi$
$937$	−0.353470	−	1.89090i	−0.353470	−	1.89090i	0.0922684	−	0.995734i	$-0.470588\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	0.987432	−	1.44147i	0.987432	−	1.44147i	0.0922684	−	0.995734i	$-0.470588\pi$
$941$	0.987432	−	1.44147i	0.987432	−	1.44147i	0.895163	−	0.445738i	$-0.147059\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.138156	−	0.990410i	$-0.455882\pi$
$947$		0			0		−0.138156	+	0.990410i	$0.544118\pi$
$948$		0			0
$949$	1.73170	+	2.52796i	1.73170	+	2.52796i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1.48826	−	0.576554i	−1.48826	−	0.576554i	−0.526432	−	0.850217i	$-0.676471\pi$
$953$	−1.48826	−	0.576554i	−1.48826	−	0.576554i	−0.961826	+	0.273663i	$0.911765\pi$
$954$	−0.328972	+	0.163808i	−0.328972	+	0.163808i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.673696	+	0.739009i	0.673696	+	0.739009i
$962$	−0.903151	+	3.83996i	−0.903151	+	3.83996i
$963$		0			0
$964$	−1.53703	+	1.27633i	−1.53703	+	1.27633i
$965$	0.921757	+	1.85114i	0.921757	+	1.85114i
$966$		0			0
$967$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$967$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$968$	0.982973	+	0.183750i	0.982973	+	0.183750i
$969$		0			0
$970$	1.75025	−	0.327179i	1.75025	−	0.327179i
$971$		0			0		−0.673696	−	0.739009i	$-0.735294\pi$
$971$		0			0		0.673696	+	0.739009i	$0.264706\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−0.0922684	+	0.00426582i	−0.0922684	+	0.00426582i
$977$		−	1.79033i		−	1.79033i	−0.445738	−	0.895163i	$-0.647059\pi$
$977$		−	1.79033i		−	1.79033i	0.445738	−	0.895163i	$-0.352941\pi$
$978$		0			0
$979$		0			0
$980$	0.0844967	−	1.82764i	0.0844967	−	1.82764i
$981$	−0.276018	−	0.0127611i	−0.276018	−	0.0127611i
$982$		0			0
$983$		0			0		−0.228951	−	0.973438i	$-0.573529\pi$
$983$		0			0		0.228951	+	0.973438i	$0.426471\pi$
$984$		0			0
$985$	2.63234	+	2.39969i	2.63234	+	2.39969i
$986$	1.05409	−	0.722071i	1.05409	−	0.722071i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.638847	−	0.769334i	$-0.279412\pi$
$991$		0			0		−0.638847	+	0.769334i	$0.720588\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	1.11943	+	0.156154i	1.11943	+	0.156154i	0.673696	−	0.739009i	$-0.264706\pi$
$997$	1.11943	+	0.156154i	1.11943	+	0.156154i	0.445738	+	0.895163i	$0.352941\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1156.1.o.a.659.1	✓	32
4.3	odd	2	CM	1156.1.o.a.659.1	✓	32
289.157	even	68	inner	1156.1.o.a.735.1	yes	32
1156.735	odd	68	inner	1156.1.o.a.735.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1156.1.o.a.659.1	✓	32	1.1	even	1	trivial
1156.1.o.a.659.1	✓	32	4.3	odd	2	CM
1156.1.o.a.735.1	yes	32	289.157	even	68	inner
1156.1.o.a.735.1	yes	32	1156.735	odd	68	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1156 = 2^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1156.o (of order \(68\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(0.798017 - 0.602635i) q^{2} +(0.273663 - 0.961826i) q^{4} +(-0.739009 - 1.67370i) q^{5} +(-0.361242 - 0.932472i) q^{8} +(0.995734 + 0.0922684i) q^{9} +O(q^{10})\)	\(q+(0.798017 - 0.602635i) q^{2} +(0.273663 - 0.961826i) q^{4} +(-0.739009 - 1.67370i) q^{5} +(-0.361242 - 0.932472i) q^{8} +(0.995734 + 0.0922684i) q^{9} +(-1.59837 - 0.890286i) q^{10} +(-1.85699 + 0.719401i) q^{13} +(-0.850217 - 0.526432i) q^{16} +(0.850217 + 0.526432i) q^{17} +(0.850217 - 0.526432i) q^{18} +(-1.81204 + 0.252769i) q^{20} +(-1.58143 + 1.73474i) q^{25} +(-1.04837 + 1.69318i) q^{26} +(1.11622 - 0.621731i) q^{29} +(-0.995734 + 0.0922684i) q^{32} +(0.995734 - 0.0922684i) q^{34} +(0.361242 - 0.932472i) q^{36} +(1.87814 - 0.629488i) q^{37} +(-1.29371 + 1.29371i) q^{40} +(0.0373089 - 0.806980i) q^{41} +(-0.581427 - 1.73474i) q^{45} +(-0.183750 + 0.982973i) q^{49} +(-0.216590 + 2.33738i) q^{50} +(0.183750 + 1.98297i) q^{52} +(-0.365931 - 0.0339085i) q^{53} +(0.516087 - 1.16883i) q^{58} +(0.0762025 - 0.0521999i) q^{61} +(-0.739009 + 0.673696i) q^{64} +(2.57639 + 2.57639i) q^{65} +(0.739009 - 0.673696i) q^{68} +(-0.273663 - 0.961826i) q^{72} +(-0.352279 - 1.49780i) q^{73} +(1.11943 - 1.63417i) q^{74} +(-0.252769 + 1.81204i) q^{80} +(0.982973 + 0.183750i) q^{81} +(-0.456541 - 0.666468i) q^{82} +(0.252769 - 1.81204i) q^{85} +(1.48826 + 0.576554i) q^{89} +(-1.50941 - 1.03397i) q^{90} +(-0.748723 + 0.621731i) q^{97} +(0.445738 + 0.895163i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{4} + 2 q^{5}+O(q^{10}) \) 32 * q + 2 * q^4 + 2 * q^5	\( 32 q + 2 q^{4} + 2 q^{5} - 2 q^{10} - 2 q^{16} + 2 q^{17} + 2 q^{18} - 2 q^{20} - 34 q^{25} - 2 q^{29} + 2 q^{37} + 2 q^{40} - 2 q^{41} - 2 q^{45} + 2 q^{50} + 2 q^{58} + 2 q^{61} + 2 q^{64} - 2 q^{68} - 2 q^{72} - 2 q^{73} - 2 q^{74} + 2 q^{80} + 2 q^{81} - 2 q^{82} - 2 q^{85} - 2 q^{90} + 2 q^{97} - 2 q^{98}+O(q^{100}) \) 32 * q + 2 * q^4 + 2 * q^5 - 2 * q^10 - 2 * q^16 + 2 * q^17 + 2 * q^18 - 2 * q^20 - 34 * q^25 - 2 * q^29 + 2 * q^37 + 2 * q^40 - 2 * q^41 - 2 * q^45 + 2 * q^50 + 2 * q^58 + 2 * q^61 + 2 * q^64 - 2 * q^68 - 2 * q^72 - 2 * q^73 - 2 * q^74 + 2 * q^80 + 2 * q^81 - 2 * q^82 - 2 * q^85 - 2 * q^90 + 2 * q^97 - 2 * q^98

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