LMFDB - Embedded newform 1156.1.o.a.1007.1

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			1007.1
Root			$0.961826 - 0.273663i$ of defining polynomial
Character	$\chi$	$=$	1156.1007
Dual form			1156.1.o.a.931.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.526432 + 0.850217i) q^{2} +(-0.445738 - 0.895163i) q^{4} +(0.982973 + 0.816250i) q^{5} +(0.995734 + 0.0922684i) q^{8} +(0.361242 - 0.932472i) q^{9} +O(q^{10})$	\(q+(-0.526432 + 0.850217i) q^{2} +(-0.445738 - 0.895163i) q^{4} +(0.982973 + 0.816250i) q^{5} +(0.995734 + 0.0922684i) q^{8} +(0.361242 - 0.932472i) q^{9} +(-1.21146 + 0.406040i) q^{10} +(-0.0666624 + 0.719401i) q^{13} +(-0.602635 + 0.798017i) q^{16} +(0.602635 - 0.798017i) q^{17} +(0.602635 + 0.798017i) q^{18} +(0.292529 - 1.24376i) q^{20} +(0.116222 + 0.621731i) q^{25} +(-0.576554 - 0.435393i) q^{26} +(0.765964 + 0.256725i) q^{29} +(-0.361242 - 0.932472i) q^{32} +(0.361242 + 0.932472i) q^{34} +(-0.995734 + 0.0922684i) q^{36} +(0.222817 + 0.400033i) q^{37} +(0.903466 + 0.903466i) q^{40} +(-0.869557 - 1.26940i) q^{41} +(1.11622 - 0.621731i) q^{45} +(-0.673696 + 0.739009i) q^{49} +(-0.589790 - 0.228486i) q^{50} +(0.673696 - 0.260991i) q^{52} +(-0.486734 + 1.25640i) q^{53} +(-0.621500 + 0.516087i) q^{58} +(0.0521999 + 1.12907i) q^{61} +(0.982973 + 0.183750i) q^{64} +(-0.652739 + 0.652739i) q^{65} +(-0.982973 - 0.183750i) q^{68} +(0.445738 - 0.895163i) q^{72} +(0.252769 + 1.81204i) q^{73} +(-0.457413 - 0.0211475i) q^{74} +(-1.24376 + 0.292529i) q^{80} +(-0.739009 - 0.673696i) q^{81} +(1.53703 - 0.0710610i) q^{82} +(1.24376 - 0.292529i) q^{85} +(-0.0971461 - 1.04837i) q^{89} +(-0.0590083 + 1.27633i) q^{90} +(0.581427 - 0.256725i) q^{97} +(-0.273663 - 0.961826i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1156\mathbb{Z}\right)^\times$.

$n$	$579$	$581$
$\chi(n)$	$-1$	$e\left(\frac{55}{68}\right)$

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 $

$2$	−0.526432	+	0.850217i	−0.526432	+	0.850217i
$2$	−0.526432	+	0.850217i	−0.526432	+	0.850217i
$3$		0			0		0.824997	−	0.565136i	$-0.191176\pi$
$3$		0			0		−0.824997	+	0.565136i	$0.808824\pi$
$4$	−0.445738	−	0.895163i	−0.445738	−	0.895163i
$5$	0.982973	+	0.816250i	0.982973	+	0.816250i	0.982973	−	0.183750i	$-0.0588235\pi$
$5$	0.982973	+	0.816250i	0.982973	+	0.816250i			1.00000i	$0.5\pi$
$6$		0			0
$7$		0			0		−0.403921	−	0.914794i	$-0.632353\pi$
$7$		0			0		0.403921	+	0.914794i	$0.367647\pi$
$8$	0.995734	+	0.0922684i	0.995734	+	0.0922684i
$9$	0.361242	−	0.932472i	0.361242	−	0.932472i
$10$	−1.21146	+	0.406040i	−1.21146	+	0.406040i
$11$		0			0		0.317791	−	0.948161i	$-0.397059\pi$
$11$		0			0		−0.317791	+	0.948161i	$0.602941\pi$
$12$		0			0
$13$	−0.0666624	+	0.719401i	−0.0666624	+	0.719401i	0.895163	+	0.445738i	$0.147059\pi$
$13$	−0.0666624	+	0.719401i	−0.0666624	+	0.719401i	−0.961826	+	0.273663i	$0.911765\pi$
$14$		0			0
$15$		0			0
$16$	−0.602635	+	0.798017i	−0.602635	+	0.798017i
$17$	0.602635	−	0.798017i	0.602635	−	0.798017i
$17$	0.602635	−	0.798017i	0.602635	−	0.798017i
$18$	0.602635	+	0.798017i	0.602635	+	0.798017i
$19$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$19$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$20$	0.292529	−	1.24376i	0.292529	−	1.24376i
$21$		0			0
$22$		0			0
$23$		0			0		−0.403921	−	0.914794i	$-0.632353\pi$
$23$		0			0		0.403921	+	0.914794i	$0.367647\pi$
$24$		0			0
$25$	0.116222	+	0.621731i	0.116222	+	0.621731i
$26$	−0.576554	−	0.435393i	−0.576554	−	0.435393i
$27$		0			0
$28$		0			0
$29$	0.765964	+	0.256725i	0.765964	+	0.256725i	0.673696	−	0.739009i	$-0.264706\pi$
$29$	0.765964	+	0.256725i	0.765964	+	0.256725i	0.0922684	+	0.995734i	$0.470588\pi$
$30$		0			0
$31$		0			0		−0.638847	−	0.769334i	$-0.720588\pi$
$31$		0			0		0.638847	+	0.769334i	$0.279412\pi$
$32$	−0.361242	−	0.932472i	−0.361242	−	0.932472i
$33$		0			0
$34$	0.361242	+	0.932472i	0.361242	+	0.932472i
$35$		0			0
$36$	−0.995734	+	0.0922684i	−0.995734	+	0.0922684i
$37$	0.222817	+	0.400033i	0.222817	+	0.400033i	0.961826	−	0.273663i	$-0.0882353\pi$
$37$	0.222817	+	0.400033i	0.222817	+	0.400033i	−0.739009	+	0.673696i	$0.764706\pi$
$38$		0			0
$39$		0			0
$40$	0.903466	+	0.903466i	0.903466	+	0.903466i
$41$	−0.869557	−	1.26940i	−0.869557	−	1.26940i	−0.961826	−	0.273663i	$-0.911765\pi$
$41$	−0.869557	−	1.26940i	−0.869557	−	1.26940i	0.0922684	−	0.995734i	$-0.470588\pi$
$42$		0			0
$43$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$43$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$44$		0			0
$45$	1.11622	−	0.621731i	1.11622	−	0.621731i
$46$		0			0
$47$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$47$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$48$		0			0
$49$	−0.673696	+	0.739009i	−0.673696	+	0.739009i
$50$	−0.589790	−	0.228486i	−0.589790	−	0.228486i
$51$		0			0
$52$	0.673696	−	0.260991i	0.673696	−	0.260991i
$53$	−0.486734	+	1.25640i	−0.486734	+	1.25640i	0.445738	+	0.895163i	$0.352941\pi$
$53$	−0.486734	+	1.25640i	−0.486734	+	1.25640i	−0.932472	+	0.361242i	$0.882353\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−0.621500	+	0.516087i	−0.621500	+	0.516087i
$59$		0			0		−0.673696	−	0.739009i	$-0.735294\pi$
$59$		0			0		0.673696	+	0.739009i	$0.264706\pi$
$60$		0			0
$61$	0.0521999	+	1.12907i	0.0521999	+	1.12907i	0.850217	+	0.526432i	$0.176471\pi$
$61$	0.0521999	+	1.12907i	0.0521999	+	1.12907i	−0.798017	+	0.602635i	$0.794118\pi$
$62$		0			0
$63$		0			0
$64$	0.982973	+	0.183750i	0.982973	+	0.183750i
$65$	−0.652739	+	0.652739i	−0.652739	+	0.652739i
$66$		0			0
$67$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$67$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$68$	−0.982973	−	0.183750i	−0.982973	−	0.183750i
$69$		0			0
$70$		0			0
$71$		0			0		0.914794	−	0.403921i	$-0.132353\pi$
$71$		0			0		−0.914794	+	0.403921i	$0.867647\pi$
$72$	0.445738	−	0.895163i	0.445738	−	0.895163i
$73$	0.252769	+	1.81204i	0.252769	+	1.81204i	0.526432	+	0.850217i	$0.323529\pi$
$73$	0.252769	+	1.81204i	0.252769	+	1.81204i	−0.273663	+	0.961826i	$0.588235\pi$
$74$	−0.457413	−	0.0211475i	−0.457413	−	0.0211475i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.973438	−	0.228951i	$-0.926471\pi$
$79$		0			0		0.973438	+	0.228951i	$0.0735294\pi$
$80$	−1.24376	+	0.292529i	−1.24376	+	0.292529i
$81$	−0.739009	−	0.673696i	−0.739009	−	0.673696i
$82$	1.53703	−	0.0710610i	1.53703	−	0.0710610i
$83$		0			0		−0.183750	−	0.982973i	$-0.558824\pi$
$83$		0			0		0.183750	+	0.982973i	$0.441176\pi$
$84$		0			0
$85$	1.24376	−	0.292529i	1.24376	−	0.292529i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.0971461	−	1.04837i	−0.0971461	−	1.04837i	−0.895163	−	0.445738i	$-0.852941\pi$
$89$	−0.0971461	−	1.04837i	−0.0971461	−	1.04837i	0.798017	−	0.602635i	$-0.205882\pi$
$90$	−0.0590083	+	1.27633i	−0.0590083	+	1.27633i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.581427	−	0.256725i	0.581427	−	0.256725i	−0.0922684	−	0.995734i	$-0.529412\pi$
$97$	0.581427	−	0.256725i	0.581427	−	0.256725i	0.673696	+	0.739009i	$0.264706\pi$
$98$	−0.273663	−	0.961826i	−0.273663	−	0.961826i
$99$		0			0
$100$	0.504747	−	0.381167i	0.504747	−	0.381167i
$101$	−1.17948	−	1.07524i	−1.17948	−	1.07524i	−0.995734	−	0.0922684i	$-0.970588\pi$
$101$	−1.17948	−	1.07524i	−1.17948	−	1.07524i	−0.183750	−	0.982973i	$-0.558824\pi$
$102$		0			0
$103$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$103$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$104$	−0.132756	+	0.710182i	−0.132756	+	0.710182i
$105$		0			0
$106$	−0.811985	−	1.07524i	−0.811985	−	1.07524i
$107$		0			0		0.228951	−	0.973438i	$-0.426471\pi$
$107$		0			0		−0.228951	+	0.973438i	$0.573529\pi$
$108$		0			0
$109$	−1.60617	−	1.10025i	−1.60617	−	1.10025i	−0.932472	−	0.361242i	$-0.882353\pi$
$109$	−1.60617	−	1.10025i	−1.60617	−	1.10025i	−0.673696	−	0.739009i	$-0.735294\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.799224	+	1.16672i	0.799224	+	1.16672i	0.982973	+	0.183750i	$0.0588235\pi$
$113$	0.799224	+	1.16672i	0.799224	+	1.16672i	−0.183750	+	0.982973i	$0.558824\pi$
$114$		0			0
$115$		0			0
$116$	−0.111609	−	0.800095i	−0.111609	−	0.800095i
$117$	0.646741	+	0.322039i	0.646741	+	0.322039i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.798017	−	0.602635i	−0.798017	−	0.602635i
$122$	−0.987432	−	0.549996i	−0.987432	−	0.549996i
$123$		0			0
$124$		0			0
$125$	0.228486	−	0.410210i	0.228486	−	0.410210i
$126$		0			0
$127$		0			0		0.961826	−	0.273663i	$-0.0882353\pi$
$127$		0			0		−0.961826	+	0.273663i	$0.911765\pi$
$128$	−0.673696	+	0.739009i	−0.673696	+	0.739009i
$129$		0			0
$130$	−0.211347	−	0.898593i	−0.211347	−	0.898593i
$131$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$131$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.673696	−	0.739009i	0.673696	−	0.739009i
$137$	−0.887674	−	1.78269i	−0.887674	−	1.78269i	−0.526432	−	0.850217i	$-0.676471\pi$
$137$	−0.887674	−	1.78269i	−0.887674	−	1.78269i	−0.361242	−	0.932472i	$-0.617647\pi$
$138$		0			0
$139$		0			0		0.973438	−	0.228951i	$-0.0735294\pi$
$139$		0			0		−0.973438	+	0.228951i	$0.926471\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.526432	+	0.850217i	0.526432	+	0.850217i
$145$	0.543370	+	0.877573i	0.543370	+	0.877573i
$146$	−1.67370	−	0.739009i	−1.67370	−	0.739009i
$147$		0			0
$148$	0.258777	−	0.377767i	0.258777	−	0.377767i
$149$	−1.83319	+	0.342683i	−1.83319	+	0.342683i	−0.982973	−	0.183750i	$-0.941176\pi$
$149$	−1.83319	+	0.342683i	−1.83319	+	0.342683i	−0.850217	+	0.526432i	$0.823529\pi$
$150$		0			0
$151$		0			0		0.895163	−	0.445738i	$-0.147059\pi$
$151$		0			0		−0.895163	+	0.445738i	$0.852941\pi$
$152$		0			0
$153$	−0.526432	−	0.850217i	−0.526432	−	0.850217i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.136374	−	0.124322i	0.136374	−	0.124322i	−0.602635	−	0.798017i	$-0.705882\pi$
$157$	0.136374	−	0.124322i	0.136374	−	0.124322i	0.739009	+	0.673696i	$0.235294\pi$
$158$		0			0
$159$		0			0
$160$	0.406040	−	1.21146i	0.406040	−	1.21146i
$161$		0			0
$162$	0.961826	−	0.273663i	0.961826	−	0.273663i
$163$		0			0		0.486604	−	0.873622i	$-0.338235\pi$
$163$		0			0		−0.486604	+	0.873622i	$0.661765\pi$
$164$	−0.748723	+	1.34421i	−0.748723	+	1.34421i
$165$		0			0
$166$		0			0
$167$		0			0		−0.873622	−	0.486604i	$-0.838235\pi$
$167$		0			0		0.873622	+	0.486604i	$0.161765\pi$
$168$		0			0
$169$	0.469879	+	0.0878355i	0.469879	+	0.0878355i
$170$	−0.406040	+	1.21146i	−0.406040	+	1.21146i
$171$		0			0
$172$		0			0
$173$	0.0127611	+	0.0914812i	0.0127611	+	0.0914812i	0.995734	−	0.0922684i	$-0.0294118\pi$
$173$	0.0127611	+	0.0914812i	0.0127611	+	0.0914812i	−0.982973	+	0.183750i	$0.941176\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	0.942485	+	0.469302i	0.942485	+	0.469302i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	−1.05409	−	0.722071i	−1.05409	−	0.722071i
$181$	1.26940	−	1.05409i	1.26940	−	1.05409i	0.273663	−	0.961826i	$-0.411765\pi$
$181$	1.26940	−	1.05409i	1.26940	−	1.05409i	0.995734	−	0.0922684i	$-0.0294118\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.107504	+	0.575096i	−0.107504	+	0.575096i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$191$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$192$		0			0
$193$	−1.64823	−	1.12907i	−1.64823	−	1.12907i	−0.850217	−	0.526432i	$-0.823529\pi$
$193$	−1.64823	−	1.12907i	−1.64823	−	1.12907i	−0.798017	−	0.602635i	$-0.794118\pi$
$194$	−0.0878098	+	0.629488i	−0.0878098	+	0.629488i
$195$		0			0
$196$	0.961826	+	0.273663i	0.961826	+	0.273663i
$197$	1.26544	−	1.52391i	1.26544	−	1.52391i	0.526432	−	0.850217i	$-0.323529\pi$
$197$	1.26544	−	1.52391i	1.26544	−	1.52391i	0.739009	−	0.673696i	$-0.235294\pi$
$198$		0			0
$199$		0			0		0.0461835	−	0.998933i	$-0.485294\pi$
$199$		0			0		−0.0461835	+	0.998933i	$0.514706\pi$
$200$	0.0583598	+	0.629803i	0.0583598	+	0.629803i
$201$		0			0
$202$	1.53511	−	0.436776i	1.53511	−	0.436776i
$203$		0			0
$204$		0			0
$205$	0.181395	−	1.95756i	0.181395	−	1.95756i
$206$		0			0
$207$		0			0
$208$	−0.533922	−	0.486734i	−0.533922	−	0.486734i
$209$		0			0
$210$		0			0
$211$		0			0		−0.998933	−	0.0461835i	$-0.985294\pi$
$211$		0			0		0.998933	+	0.0461835i	$0.0147059\pi$
$212$	1.34164	−	0.124322i	1.34164	−	0.124322i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	1.78099	−	0.786384i	1.78099	−	0.786384i
$219$		0			0
$220$		0			0
$221$	0.533922	+	0.486734i	0.533922	+	0.486734i
$222$		0			0
$223$		0			0		−0.961826	−	0.273663i	$-0.911765\pi$
$223$		0			0		0.961826	+	0.273663i	$0.0882353\pi$
$224$		0			0
$225$	0.621731	+	0.116222i	0.621731	+	0.116222i
$226$	−1.41270	+	0.0653133i	−1.41270	+	0.0653133i
$227$		0			0		0.990410	−	0.138156i	$-0.0441176\pi$
$227$		0			0		−0.990410	+	0.138156i	$0.955882\pi$
$228$		0			0
$229$	−0.197717	−	0.510366i	−0.197717	−	0.510366i	0.798017	−	0.602635i	$-0.205882\pi$
$229$	−0.197717	−	0.510366i	−0.197717	−	0.510366i	−0.995734	+	0.0922684i	$0.970588\pi$
$230$		0			0
$231$		0			0
$232$	0.739009	+	0.326304i	0.739009	+	0.326304i
$233$	−0.629488	−	1.87814i	−0.629488	−	1.87814i	−0.445738	−	0.895163i	$-0.647059\pi$
$233$	−0.629488	−	1.87814i	−0.629488	−	1.87814i	−0.183750	−	0.982973i	$-0.558824\pi$
$234$	−0.614268	+	0.380338i	−0.614268	+	0.380338i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$239$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$240$		0			0
$241$	−0.0762025	+	1.64823i	−0.0762025	+	1.64823i	0.526432	+	0.850217i	$0.323529\pi$
$241$	−0.0762025	+	1.64823i	−0.0762025	+	1.64823i	−0.602635	+	0.798017i	$0.705882\pi$
$242$	0.932472	−	0.361242i	0.932472	−	0.361242i
$243$		0			0
$244$	0.987432	−	0.549996i	0.987432	−	0.549996i
$245$	−1.26544	+	0.176521i	−1.26544	+	0.176521i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	0.228486	+	0.410210i	0.228486	+	0.410210i
$251$		0			0		1.00000			$0$
$251$		0			0		−1.00000			$\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.273663	−	0.961826i	−0.273663	−	0.961826i
$257$	0.614268	+	1.58561i	0.614268	+	1.58561i	0.798017	+	0.602635i	$0.205882\pi$
$257$	0.614268	+	1.58561i	0.614268	+	1.58561i	−0.183750	+	0.982973i	$0.558824\pi$
$258$		0			0
$259$		0			0
$260$	0.875259	+	0.293357i	0.875259	+	0.293357i
$261$	0.516087	−	0.621500i	0.516087	−	0.621500i
$262$		0			0
$263$		0			0		−0.798017	−	0.602635i	$-0.794118\pi$
$263$		0			0		0.798017	+	0.602635i	$0.205882\pi$
$264$		0			0
$265$	−1.50399	+	0.837716i	−1.50399	+	0.837716i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	0.0632619	−	0.268973i	0.0632619	−	0.268973i	−0.932472	−	0.361242i	$-0.882353\pi$
$269$	0.0632619	−	0.268973i	0.0632619	−	0.268973i	0.995734	+	0.0922684i	$0.0294118\pi$
$270$		0			0
$271$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$271$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$272$	0.273663	+	0.961826i	0.273663	+	0.961826i
$273$		0			0
$274$	1.98297	+	0.183750i	1.98297	+	0.183750i
$275$		0			0
$276$		0			0
$277$	−0.0806938	−	0.0449462i	−0.0806938	−	0.0449462i	0.445738	−	0.895163i	$-0.352941\pi$
$277$	−0.0806938	−	0.0449462i	−0.0806938	−	0.0449462i	−0.526432	+	0.850217i	$0.676471\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.78269	−	0.165190i	−1.78269	−	0.165190i	−0.850217	−	0.526432i	$-0.823529\pi$
$281$	−1.78269	−	0.165190i	−1.78269	−	0.165190i	−0.932472	+	0.361242i	$0.882353\pi$
$282$		0			0
$283$		0			0		−0.0461835	−	0.998933i	$-0.514706\pi$
$283$		0			0		0.0461835	+	0.998933i	$0.485294\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−1.00000			−1.00000
$289$	−0.273663	−	0.961826i	−0.273663	−	0.961826i
$290$	−1.03217			−1.03217
$291$		0			0
$292$	1.50941	−	1.03397i	1.50941	−	1.03397i
$293$	0.757949	+	1.52217i	0.757949	+	1.52217i	0.850217	+	0.526432i	$0.176471\pi$
$293$	0.757949	+	1.52217i	0.757949	+	1.52217i	−0.0922684	+	0.995734i	$0.529412\pi$
$294$		0			0
$295$		0			0
$296$	0.184956	+	0.418885i	0.184956	+	0.418885i
$297$		0			0
$298$	0.673696	−	1.73901i	0.673696	−	1.73901i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.870290	+	1.15245i	−0.870290	+	1.15245i
$306$	1.00000			1.00000
$307$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$307$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.638847	−	0.769334i	$-0.720588\pi$
$311$		0			0		0.638847	+	0.769334i	$0.279412\pi$
$312$		0			0
$313$	−0.241393	+	0.134455i	−0.241393	+	0.134455i	−0.602635	−	0.798017i	$-0.705882\pi$
$313$	−0.241393	+	0.134455i	−0.241393	+	0.134455i	0.361242	+	0.932472i	$0.382353\pi$
$314$	0.0339085	+	0.181395i	0.0339085	+	0.181395i
$315$		0			0
$316$		0			0
$317$	−0.176521	+	0.212577i	−0.176521	+	0.212577i	−0.850217	−	0.526432i	$-0.823529\pi$
$317$	−0.176521	+	0.212577i	−0.176521	+	0.212577i	0.673696	+	0.739009i	$0.264706\pi$
$318$		0			0
$319$		0			0
$320$	0.816250	+	0.982973i	0.816250	+	0.982973i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.273663	+	0.961826i	−0.273663	+	0.961826i
$325$	−0.455022	+	0.0421640i	−0.455022	+	0.0421640i
$326$		0			0
$327$		0			0
$328$	−0.748723	−	1.34421i	−0.748723	−	1.34421i
$329$		0			0
$330$		0			0
$331$		0			0		0.895163	−	0.445738i	$-0.147059\pi$
$331$		0			0		−0.895163	+	0.445738i	$0.852941\pi$
$332$		0			0
$333$	0.453510	−	0.0632619i	0.453510	−	0.0632619i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.0806938	+	1.74538i	−0.0806938	+	1.74538i	0.445738	+	0.895163i	$0.352941\pi$
$337$	−0.0806938	+	1.74538i	−0.0806938	+	1.74538i	−0.526432	+	0.850217i	$0.676471\pi$
$338$	−0.322039	+	0.353259i	−0.322039	+	0.353259i
$339$		0			0
$340$	−0.816250	−	0.982973i	−0.816250	−	0.982973i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.0844967	−	0.0373089i	−0.0844967	−	0.0373089i
$347$		0			0		0.769334	−	0.638847i	$-0.220588\pi$
$347$		0			0		−0.769334	+	0.638847i	$0.779412\pi$
$348$		0			0
$349$	0.694903	+	1.79375i	0.694903	+	1.79375i	0.602635	+	0.798017i	$0.294118\pi$
$349$	0.694903	+	1.79375i	0.694903	+	1.79375i	0.0922684	+	0.995734i	$0.470588\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.18475	−	0.221468i	−1.18475	−	0.221468i	−0.445738	−	0.895163i	$-0.647059\pi$
$353$	−1.18475	−	0.221468i	−1.18475	−	0.221468i	−0.739009	+	0.673696i	$0.764706\pi$
$354$		0			0
$355$		0			0
$356$	−0.895163	+	0.554262i	−0.895163	+	0.554262i
$357$		0			0
$358$		0			0
$359$		0			0		−0.673696	−	0.739009i	$-0.735294\pi$
$359$		0			0		0.673696	+	0.739009i	$0.264706\pi$
$360$	1.16883	−	0.516087i	1.16883	−	0.516087i
$361$	−0.445738	+	0.895163i	−0.445738	+	0.895163i
$362$	0.227957	+	1.63417i	0.227957	+	1.63417i
$363$		0			0
$364$		0			0
$365$	−1.23062	+	1.98751i	−1.23062	+	1.98751i
$366$		0			0
$367$		0			0		−0.998933	−	0.0461835i	$-0.985294\pi$
$367$		0			0		0.998933	+	0.0461835i	$0.0147059\pi$
$368$		0			0
$369$	−1.49780	+	0.352279i	−1.49780	+	0.352279i
$370$	−0.432363	−	0.394151i	−0.432363	−	0.394151i
$371$		0			0
$372$		0			0
$373$	−0.177492	+	1.91545i	−0.177492	+	1.91545i	0.183750	+	0.982973i	$0.441176\pi$
$373$	−0.177492	+	1.91545i	−0.177492	+	1.91545i	−0.361242	+	0.932472i	$0.617647\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.235749	+	0.533922i	−0.235749	+	0.533922i
$378$		0			0
$379$		0			0		0.0461835	−	0.998933i	$-0.485294\pi$
$379$		0			0		−0.0461835	+	0.998933i	$0.514706\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.183750	−	0.982973i	$-0.441176\pi$
$383$		0			0		−0.183750	+	0.982973i	$0.558824\pi$
$384$		0			0
$385$		0			0
$386$	1.82764	−	0.806980i	1.82764	−	0.806980i
$387$		0			0
$388$	−0.488975	−	0.406040i	−0.488975	−	0.406040i
$389$	1.17948	−	0.890705i	1.17948	−	0.890705i	0.183750	−	0.982973i	$-0.441176\pi$
$389$	1.17948	−	0.890705i	1.17948	−	0.890705i	0.995734	+	0.0922684i	$0.0294118\pi$
$390$		0			0
$391$		0			0
$392$	−0.739009	+	0.673696i	−0.739009	+	0.673696i
$393$		0			0
$394$	0.629488	+	1.87814i	0.629488	+	1.87814i
$395$		0			0
$396$		0			0
$397$	1.49780	−	1.24376i	1.49780	−	1.24376i	0.602635	−	0.798017i	$-0.294118\pi$
$397$	1.49780	−	1.24376i	1.49780	−	1.24376i	0.895163	−	0.445738i	$-0.147059\pi$
$398$		0			0
$399$		0			0
$400$	−0.566192	−	0.281930i	−0.566192	−	0.281930i
$401$	−0.0899135	−	0.0211475i	−0.0899135	−	0.0211475i	0.183750	−	0.982973i	$-0.441176\pi$
$401$	−0.0899135	−	0.0211475i	−0.0899135	−	0.0211475i	−0.273663	+	0.961826i	$0.588235\pi$
$402$		0			0
$403$		0			0
$404$	−0.436776	+	1.53511i	−0.436776	+	1.53511i
$405$	−0.176521	−	1.26544i	−0.176521	−	1.26544i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−1.93247	−	0.361242i	−1.93247	−	0.361242i	−0.932472	−	0.361242i	$-0.882353\pi$
$409$	−1.93247	−	0.361242i	−1.93247	−	0.361242i	−1.00000			$\pi$
$410$	1.56886	+	1.18475i	1.56886	+	1.18475i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	0.694903	−	0.197717i	0.694903	−	0.197717i
$417$		0			0
$418$		0			0
$419$		0			0		−0.228951	−	0.973438i	$-0.573529\pi$
$419$		0			0		0.228951	+	0.973438i	$0.426471\pi$
$420$		0			0
$421$	−1.17948	+	1.07524i	−1.17948	+	1.07524i	−0.183750	+	0.982973i	$0.558824\pi$
$421$	−1.17948	+	1.07524i	−1.17948	+	1.07524i	−0.995734	+	0.0922684i	$0.970588\pi$
$422$		0			0
$423$		0			0
$424$	−0.600584	+	1.20614i	−0.600584	+	1.20614i
$425$	0.566192	+	0.281930i	0.566192	+	0.281930i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.138156	−	0.990410i	$-0.455882\pi$
$431$		0			0		−0.138156	+	0.990410i	$0.544118\pi$
$432$		0			0
$433$	0.0971461	+	0.156896i	0.0971461	+	0.156896i	0.895163	−	0.445738i	$-0.147059\pi$
$433$	0.0971461	+	0.156896i	0.0971461	+	0.156896i	−0.798017	+	0.602635i	$0.794118\pi$
$434$		0			0
$435$		0			0
$436$	−0.268973	+	1.92821i	−0.268973	+	1.92821i
$437$		0			0
$438$		0			0
$439$		0			0		0.973438	−	0.228951i	$-0.0735294\pi$
$439$		0			0		−0.973438	+	0.228951i	$0.926471\pi$
$440$		0			0
$441$	0.445738	+	0.895163i	0.445738	+	0.895163i
$442$	−0.694903	+	0.197717i	−0.694903	+	0.197717i
$443$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$443$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$444$		0			0
$445$	0.760243	−	1.10982i	0.760243	−	1.10982i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.634905	−	1.89430i	0.634905	−	1.89430i	0.273663	−	0.961826i	$-0.411765\pi$
$449$	0.634905	−	1.89430i	0.634905	−	1.89430i	0.361242	−	0.932472i	$-0.382353\pi$
$450$	−0.426113	+	0.467424i	−0.426113	+	0.467424i
$451$		0			0
$452$	0.688163	−	1.23549i	0.688163	−	1.23549i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.961826	−	0.726337i	−0.961826	−	0.726337i		−	1.00000i	$-0.5\pi$
$457$	−0.961826	−	0.726337i	−0.961826	−	0.726337i	−0.961826	+	0.273663i	$0.911765\pi$
$458$	0.538007	+	0.100571i	0.538007	+	0.100571i
$459$		0			0
$460$		0			0
$461$	−1.60263	−	0.798017i	−1.60263	−	0.798017i	−0.602635	−	0.798017i	$-0.705882\pi$
$461$	−1.60263	−	0.798017i	−1.60263	−	0.798017i	−1.00000			$\pi$
$462$		0			0
$463$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$463$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$464$	−0.666468	+	0.456541i	−0.666468	+	0.456541i
$465$		0			0
$466$	1.92821	+	0.453510i	1.92821	+	0.453510i
$467$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$467$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$468$		−	0.722483i		−	0.722483i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.995734	+	0.907732i	0.995734	+	0.907732i
$478$		0			0
$479$		0			0		−0.769334	−	0.638847i	$-0.779412\pi$
$479$		0			0		0.769334	+	0.638847i	$0.220588\pi$
$480$		0			0
$481$	−0.302638	+	0.133628i	−0.302638	+	0.133628i
$482$	−1.36124	−	0.932472i	−1.36124	−	0.932472i
$483$		0			0
$484$	−0.183750	+	0.982973i	−0.183750	+	0.982973i
$485$	0.781079	+	0.222236i	0.781079	+	0.222236i
$486$		0			0
$487$		0			0		0.948161	−	0.317791i	$-0.102941\pi$
$487$		0			0		−0.948161	+	0.317791i	$0.897059\pi$
$488$	−0.0521999	+	1.12907i	−0.0521999	+	1.12907i
$489$		0			0
$490$	0.516087	−	1.16883i	0.516087	−	1.16883i
$491$		0			0		0.961826	−	0.273663i	$-0.0882353\pi$
$491$		0			0		−0.961826	+	0.273663i	$0.911765\pi$
$492$		0			0
$493$	0.666468	−	0.456541i	0.666468	−	0.456541i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		−0.973438	−	0.228951i	$-0.926471\pi$
$499$		0			0		0.973438	+	0.228951i	$0.0735294\pi$
$500$	−0.469050	−	0.0216855i	−0.469050	−	0.0216855i
$501$		0			0
$502$		0			0
$503$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$503$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$504$		0			0
$505$	−0.281734	−	2.01969i	−0.281734	−	2.01969i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	1.25664	+	0.778076i	1.25664	+	0.778076i	0.982973	−	0.183750i	$-0.0588235\pi$
$509$	1.25664	+	0.778076i	1.25664	+	0.778076i	0.273663	+	0.961826i	$0.411765\pi$
$510$		0			0
$511$		0			0
$512$	0.961826	+	0.273663i	0.961826	+	0.273663i
$513$		0			0
$514$	−1.67148	−	0.312454i	−1.67148	−	0.312454i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−0.710182	+	0.589727i	−0.710182	+	0.589727i
$521$	1.29371	+	0.571231i	1.29371	+	0.571231i	0.932472	−	0.361242i	$-0.117647\pi$
$521$	1.29371	+	0.571231i	1.29371	+	0.571231i	0.361242	+	0.932472i	$0.382353\pi$
$522$	0.256725	+	0.765964i	0.256725	+	0.765964i
$523$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$523$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−0.673696	+	0.739009i	−0.673696	+	0.739009i
$530$	0.0795073	−	1.71972i	0.0795073	−	1.71972i
$531$		0			0
$532$		0			0
$533$	0.971173	−	0.540940i	0.971173	−	0.540940i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	0.195383	+	0.195383i	0.195383	+	0.195383i
$539$		0			0
$540$		0			0
$541$	0.802895	+	1.44147i	0.802895	+	1.44147i	0.895163	+	0.445738i	$0.147059\pi$
$541$	0.802895	+	1.44147i	0.802895	+	1.44147i	−0.0922684	+	0.995734i	$0.529412\pi$
$542$		0			0
$543$		0			0
$544$	−0.961826	−	0.273663i	−0.961826	−	0.273663i
$545$	−0.680740	−	2.39255i	−0.680740	−	2.39255i
$546$		0			0
$547$		0			0		−0.638847	−	0.769334i	$-0.720588\pi$
$547$		0			0		0.638847	+	0.769334i	$0.279412\pi$
$548$	−1.20013	+	1.58923i	−1.20013	+	1.58923i
$549$	1.07168	+	0.359191i	1.07168	+	0.359191i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	0.0806938	−	0.0449462i	0.0806938	−	0.0449462i
$555$		0			0
$556$		0			0
$557$	−0.895163	−	0.554262i	−0.895163	−	0.554262i		−	1.00000i	$-0.5\pi$
$557$	−0.895163	−	0.554262i	−0.895163	−	0.554262i	−0.895163	+	0.445738i	$0.852941\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	1.07891	−	1.42871i	1.07891	−	1.42871i
$563$		0			0		−0.995734	−	0.0922684i	$-0.970588\pi$
$563$		0			0		0.995734	+	0.0922684i	$0.0294118\pi$
$564$		0			0
$565$	−0.166723	+	1.79922i	−0.166723	+	1.79922i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$569$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$570$		0			0
$571$		0			0		−0.403921	−	0.914794i	$-0.632353\pi$
$571$		0			0		0.403921	+	0.914794i	$0.367647\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.526432	−	0.850217i	0.526432	−	0.850217i
$577$	1.92365			1.92365			0.961826	−	0.273663i	$-0.0882353\pi$
$577$	1.92365			1.92365			0.961826	+	0.273663i	$0.0882353\pi$
$578$	0.961826	+	0.273663i	0.961826	+	0.273663i
$579$		0			0
$580$	0.543370	−	0.877573i	0.543370	−	0.877573i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	0.0844967	+	1.82764i	0.0844967	+	1.82764i
$585$	0.372864	+	0.844458i	0.372864	+	0.844458i
$586$	−1.69318	−	0.156896i	−1.69318	−	0.156896i
$587$		0			0		0.361242	−	0.932472i	$-0.382353\pi$
$587$		0			0		−0.361242	+	0.932472i	$0.617647\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.453510	−	0.0632619i	−0.453510	−	0.0632619i
$593$	1.98297	+	0.183750i	1.98297	+	0.183750i	1.00000			$0$
$593$	1.98297	+	0.183750i	1.98297	+	0.183750i	0.982973	+	0.183750i	$0.0588235\pi$
$594$		0			0
$595$		0			0
$596$	1.12388	+	1.48826i	1.12388	+	1.48826i
$597$		0			0
$598$		0			0
$599$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$599$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$600$		0			0
$601$	0.739009	+	1.67370i	0.739009	+	1.67370i	0.739009	+	0.673696i	$0.235294\pi$
$601$	0.739009	+	1.67370i	0.739009	+	1.67370i			1.00000i	$0.5\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.292529	−	1.24376i	−0.292529	−	1.24376i
$606$		0			0
$607$		0			0		−0.948161	−	0.317791i	$-0.897059\pi$
$607$		0			0		0.948161	+	0.317791i	$0.102941\pi$
$608$		0			0
$609$		0			0
$610$	−0.521684	−	1.34662i	−0.521684	−	1.34662i
$611$		0			0
$612$	−0.526432	+	0.850217i	−0.526432	+	0.850217i
$613$	−0.243964	+	0.857445i	−0.243964	+	0.857445i	0.739009	+	0.673696i	$0.235294\pi$
$613$	−0.243964	+	0.857445i	−0.243964	+	0.857445i	−0.982973	+	0.183750i	$0.941176\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.890286	−	1.59837i	−0.890286	−	1.59837i	−0.798017	−	0.602635i	$-0.794118\pi$
$617$	−0.890286	−	1.59837i	−0.890286	−	1.59837i	−0.0922684	−	0.995734i	$-0.529412\pi$
$618$		0			0
$619$		0			0		−0.565136	−	0.824997i	$-0.691176\pi$
$619$		0			0		0.565136	+	0.824997i	$0.308824\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	1.14922	−	0.445210i	1.14922	−	0.445210i
$626$	0.0127611	−	0.276018i	0.0127611	−	0.276018i
$627$		0			0
$628$	−0.172075	−	0.0666624i	−0.172075	−	0.0666624i
$629$	0.453510	+	0.0632619i	0.453510	+	0.0632619i
$630$		0			0
$631$		0			0		0.361242	−	0.932472i	$-0.382353\pi$
$631$		0			0		−0.361242	+	0.932472i	$0.617647\pi$
$632$		0			0
$633$		0			0
$634$	−0.0878098	−	0.261989i	−0.0878098	−	0.261989i
$635$		0			0
$636$		0			0
$637$	−0.486734	−	0.533922i	−0.486734	−	0.533922i
$638$		0			0
$639$		0			0
$640$	−1.26544	+	0.176521i	−1.26544	+	0.176521i
$641$	1.74538	−	0.0806938i	1.74538	−	0.0806938i	0.850217	−	0.526432i	$-0.176471\pi$
$641$	1.74538	−	0.0806938i	1.74538	−	0.0806938i	0.895163	+	0.445738i	$0.147059\pi$
$642$		0			0
$643$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$643$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$647$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$648$	−0.673696	−	0.739009i	−0.673696	−	0.739009i
$649$		0			0
$650$	0.203690	−	0.409064i	0.203690	−	0.409064i
$651$		0			0
$652$		0			0
$653$	0.688163	+	0.688163i	0.688163	+	0.688163i	0.961826	−	0.273663i	$-0.0882353\pi$
$653$	0.688163	+	0.688163i	0.688163	+	0.688163i	−0.273663	+	0.961826i	$0.588235\pi$
$654$		0			0
$655$		0			0
$656$	1.53703	+	0.0710610i	1.53703	+	0.0710610i
$657$	1.78099	+	0.418885i	1.78099	+	0.418885i
$658$		0			0
$659$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$659$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$660$		0			0
$661$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$661$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−0.184956	+	0.418885i	−0.184956	+	0.418885i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.261989	+	1.87814i	−0.261989	+	1.87814i	0.183750	+	0.982973i	$0.441176\pi$
$673$	−0.261989	+	1.87814i	−0.261989	+	1.87814i	−0.445738	+	0.895163i	$0.647059\pi$
$674$	−1.44147	−	0.987432i	−1.44147	−	0.987432i
$675$		0			0
$676$	−0.130816	−	0.459770i	−0.130816	−	0.459770i
$677$	1.45890	+	1.21146i	1.45890	+	1.21146i	0.932472	+	0.361242i	$0.117647\pi$
$677$	1.45890	+	1.21146i	1.45890	+	1.21146i	0.526432	+	0.850217i	$0.323529\pi$
$678$		0			0
$679$		0			0
$680$	1.26544	−	0.176521i	1.26544	−	0.176521i
$681$		0			0
$682$		0			0
$683$		0			0		−0.317791	−	0.948161i	$-0.602941\pi$
$683$		0			0		0.317791	+	0.948161i	$0.397059\pi$
$684$		0			0
$685$	0.582562	−	2.47690i	0.582562	−	2.47690i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.871413	−	0.433912i	−0.871413	−	0.433912i
$690$		0			0
$691$		0			0		−0.565136	−	0.824997i	$-0.691176\pi$
$691$		0			0		0.565136	+	0.824997i	$0.308824\pi$
$692$	0.0762025	−	0.0521999i	0.0762025	−	0.0521999i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−1.53703	−	0.0710610i	−1.53703	−	0.0710610i
$698$	−1.89090	−	0.353470i	−1.89090	−	0.353470i
$699$		0			0
$700$		0			0
$701$	−1.48826	−	0.576554i	−1.48826	−	0.576554i	−0.526432	−	0.850217i	$-0.676471\pi$
$701$	−1.48826	−	0.576554i	−1.48826	−	0.576554i	−0.961826	+	0.273663i	$0.911765\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	0.811985	−	0.890705i	0.811985	−	0.890705i
$707$		0			0
$708$		0			0
$709$	0.688163	−	0.688163i	0.688163	−	0.688163i	−0.273663	−	0.961826i	$-0.588235\pi$
$709$	0.688163	−	0.688163i	0.688163	−	0.688163i	0.961826	+	0.273663i	$0.0882353\pi$
$710$		0			0
$711$		0			0
$712$		−	1.05286i		−	1.05286i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.565136	−	0.824997i	$-0.308824\pi$
$719$		0			0		−0.565136	+	0.824997i	$0.691176\pi$
$720$	−0.176521	+	1.26544i	−0.176521	+	1.26544i
$721$		0			0
$722$	−0.526432	−	0.850217i	−0.526432	−	0.850217i
$723$		0			0
$724$	−1.50941	−	0.666468i	−1.50941	−	0.666468i
$725$	−0.0705925	+	0.506061i	−0.0705925	+	0.506061i
$726$		0			0
$727$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$727$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$728$		0			0
$729$	−0.895163	+	0.445738i	−0.895163	+	0.445738i
$730$	−1.04198	−	2.09258i	−1.04198	−	2.09258i
$731$		0			0
$732$		0			0
$733$		−	1.99147i		−	1.99147i	−0.0922684	−	0.995734i	$-0.529412\pi$
$733$		−	1.99147i		−	1.99147i	0.0922684	−	0.995734i	$-0.470588\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	0.488975	−	1.45890i	0.488975	−	1.45890i
$739$		0			0		0.673696	−	0.739009i	$-0.264706\pi$
$739$		0			0		−0.673696	+	0.739009i	$0.735294\pi$
$740$	0.562723	−	0.160109i	0.562723	−	0.160109i
$741$		0			0
$742$		0			0
$743$		0			0		0.403921	−	0.914794i	$-0.367647\pi$
$743$		0			0		−0.403921	+	0.914794i	$0.632353\pi$
$744$		0			0
$745$	−2.08169	−	1.15949i	−2.08169	−	1.15949i
$746$	−1.53511	−	1.15926i	−1.53511	−	1.15926i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.138156	−	0.990410i	$-0.544118\pi$
$751$		0			0		0.138156	+	0.990410i	$0.455882\pi$
$752$		0			0
$753$		0			0
$754$	−0.329843	−	0.481512i	−0.329843	−	0.481512i
$755$		0			0
$756$		0			0
$757$			0.891477i			0.891477i	0.895163	+	0.445738i	$0.147059\pi$
$757$			0.891477i			0.891477i	−0.895163	+	0.445738i	$0.852941\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−1.20013	−	1.58923i	−1.20013	−	1.58923i	−0.673696	−	0.739009i	$-0.735294\pi$
$761$	−1.20013	−	1.58923i	−1.20013	−	1.58923i	−0.526432	−	0.850217i	$-0.676471\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.176521	−	1.26544i	0.176521	−	1.26544i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−0.288130	−	1.01267i	−0.288130	−	1.01267i	−0.961826	−	0.273663i	$-0.911765\pi$
$769$	−0.288130	−	1.01267i	−0.288130	−	1.01267i	0.673696	−	0.739009i	$-0.264706\pi$
$770$		0			0
$771$		0			0
$772$	−0.276018	+	1.97871i	−0.276018	+	1.97871i
$773$	−0.0339085	+	0.181395i	−0.0339085	+	0.181395i	−0.995734	−	0.0922684i	$-0.970588\pi$
$773$	−0.0339085	+	0.181395i	−0.0339085	+	0.181395i	0.961826	+	0.273663i	$0.0882353\pi$
$774$		0			0
$775$		0			0
$776$	0.602635	−	0.201983i	0.602635	−	0.201983i
$777$		0			0
$778$	0.136374	+	1.47171i	0.136374	+	1.47171i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.183750	−	0.982973i	−0.183750	−	0.982973i
$785$	0.235530	−	0.0108892i	0.235530	−	0.0108892i
$786$		0			0
$787$		0			0		0.973438	−	0.228951i	$-0.0735294\pi$
$787$		0			0		−0.973438	+	0.228951i	$0.926471\pi$
$788$	−1.92821	−	0.453510i	−1.92821	−	0.453510i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−0.815732	−	0.0377136i	−0.815732	−	0.0377136i
$794$	0.268973	+	1.92821i	0.268973	+	1.92821i
$795$		0			0
$796$		0			0
$797$	−0.907732	−	0.995734i	−0.907732	−	0.995734i	0.0922684	−	0.995734i	$-0.470588\pi$
$797$	−0.907732	−	0.995734i	−0.907732	−	0.995734i	−1.00000			$\pi$
$798$		0			0
$799$		0			0
$800$	0.537763	−	0.332969i	0.537763	−	0.332969i
$801$	−1.01267	−	0.288130i	−1.01267	−	0.288130i
$802$	0.0653133	−	0.0653133i	0.0653133	−	0.0653133i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−1.07524	−	1.17948i	−1.07524	−	1.17948i
$809$	1.52391	−	1.26544i	1.52391	−	1.26544i	0.673696	−	0.739009i	$-0.264706\pi$
$809$	1.52391	−	1.26544i	1.52391	−	1.26544i	0.850217	−	0.526432i	$-0.176471\pi$
$810$	1.16883	+	0.516087i	1.16883	+	0.516087i
$811$		0			0		−0.317791	−	0.948161i	$-0.602941\pi$
$811$		0			0		0.317791	+	0.948161i	$0.397059\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	1.32445	−	1.45285i	1.32445	−	1.45285i
$819$		0			0
$820$	−1.83319	+	0.710182i	−1.83319	+	0.710182i
$821$	1.11943	+	0.156154i	1.11943	+	0.156154i	0.673696	−	0.739009i	$-0.264706\pi$
$821$	1.11943	+	0.156154i	1.11943	+	0.156154i	0.445738	+	0.895163i	$0.352941\pi$
$822$		0			0
$823$		0			0		0.990410	−	0.138156i	$-0.0441176\pi$
$823$		0			0		−0.990410	+	0.138156i	$0.955882\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$827$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$828$		0			0
$829$	1.86494			1.86494			0.932472	−	0.361242i	$-0.117647\pi$
$829$	1.86494			1.86494			0.932472	+	0.361242i	$0.117647\pi$
$830$		0			0
$831$		0			0
$832$	−0.197717	+	0.694903i	−0.197717	+	0.694903i
$833$	0.183750	+	0.982973i	0.183750	+	0.982973i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.638847	−	0.769334i	$-0.279412\pi$
$839$		0			0		−0.638847	+	0.769334i	$0.720588\pi$
$840$		0			0
$841$	−0.277224	−	0.209350i	−0.277224	−	0.209350i
$842$	−0.293271	−	1.56886i	−0.293271	−	1.56886i
$843$		0			0
$844$		0			0
$845$	0.390182	+	0.469879i	0.390182	+	0.469879i
$846$		0			0
$847$		0			0
$848$	−0.709310	−	1.14558i	−0.709310	−	1.14558i
$849$		0			0
$850$	−0.537763	+	0.332969i	−0.537763	+	0.332969i
$851$		0			0
$852$		0			0
$853$	−1.73049	−	0.241393i	−1.73049	−	0.241393i	−0.798017	−	0.602635i	$-0.794118\pi$
$853$	−1.73049	−	0.241393i	−1.73049	−	0.241393i	−0.932472	+	0.361242i	$0.882353\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.922758	−	0.309277i	0.922758	−	0.309277i	0.183750	−	0.982973i	$-0.441176\pi$
$857$	0.922758	−	0.309277i	0.922758	−	0.309277i	0.739009	+	0.673696i	$0.235294\pi$
$858$		0			0
$859$		0			0		−0.995734	−	0.0922684i	$-0.970588\pi$
$859$		0			0		0.995734	+	0.0922684i	$0.0294118\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$863$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$864$		0			0
$865$	−0.0621277	+	0.100340i	−0.0621277	+	0.100340i
$866$	−0.184537			−0.184537
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−1.49780	−	1.24376i	−1.49780	−	1.24376i
$873$	−0.0293534	−	0.634905i	−0.0293534	−	0.634905i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.73474	+	0.581427i	−1.73474	+	0.581427i	−0.995734	−	0.0922684i	$-0.970588\pi$
$877$	−1.73474	+	0.581427i	−1.73474	+	0.581427i	−0.739009	+	0.673696i	$0.764706\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.629488	+	0.0878098i	0.629488	+	0.0878098i	0.445738	−	0.895163i	$-0.352941\pi$
$881$	0.629488	+	0.0878098i	0.629488	+	0.0878098i	0.183750	+	0.982973i	$0.441176\pi$
$882$	−0.995734	−	0.0922684i	−0.995734	−	0.0922684i
$883$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$883$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$884$	0.197717	−	0.694903i	0.197717	−	0.694903i
$885$		0			0
$886$		0			0
$887$		0			0		0.228951	−	0.973438i	$-0.426471\pi$
$887$		0			0		−0.228951	+	0.973438i	$0.573529\pi$
$888$		0			0
$889$		0			0
$890$	0.543370	+	1.23062i	0.543370	+	1.23062i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	1.27633	+	1.53703i	1.27633	+	1.53703i
$899$		0			0
$900$	−0.173092	−	0.608356i	−0.173092	−	0.608356i
$901$	0.709310	+	1.14558i	0.709310	+	1.14558i
$902$		0			0
$903$		0			0
$904$	0.688163	+	1.23549i	0.688163	+	1.23549i
$905$	2.10819			2.10819
$906$		0			0
$907$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$907$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$908$		0			0
$909$	−1.42871	+	0.711414i	−1.42871	+	0.711414i
$910$		0			0
$911$		0			0		0.990410	−	0.138156i	$-0.0441176\pi$
$911$		0			0		−0.990410	+	0.138156i	$0.955882\pi$
$912$		0			0
$913$		0			0
$914$	1.12388	−	0.435393i	1.12388	−	0.435393i
$915$		0			0
$916$	−0.368731	+	0.404479i	−0.368731	+	0.404479i
$917$		0			0
$918$		0			0
$919$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$919$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$920$		0			0
$921$		0			0
$922$	1.52217	−	0.942485i	1.52217	−	0.942485i
$923$		0			0
$924$		0			0
$925$	−0.222817	+	0.185025i	−0.222817	+	0.185025i
$926$		0			0
$927$		0			0
$928$	−0.0373089	−	0.806980i	−0.0373089	−	0.806980i
$929$	−1.87814	+	0.261989i	−1.87814	+	0.261989i	−0.982973	−	0.183750i	$-0.941176\pi$
$929$	−1.87814	+	0.261989i	−1.87814	+	0.261989i	−0.895163	+	0.445738i	$0.852941\pi$
$930$		0			0
$931$		0			0
$932$	−1.40065	+	1.40065i	−1.40065	+	1.40065i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	0.614268	+	0.380338i	0.614268	+	0.380338i
$937$	1.20614	+	1.32307i	1.20614	+	1.32307i	0.932472	+	0.361242i	$0.117647\pi$
$937$	1.20614	+	1.32307i	1.20614	+	1.32307i	0.273663	+	0.961826i	$0.411765\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.89430	+	0.0875787i	1.89430	+	0.0875787i	0.961826	−	0.273663i	$-0.0882353\pi$
$941$	1.89430	+	0.0875787i	1.89430	+	0.0875787i	0.932472	+	0.361242i	$0.117647\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.973438	−	0.228951i	$-0.0735294\pi$
$947$		0			0		−0.973438	+	0.228951i	$0.926471\pi$
$948$		0			0
$949$	−1.32044	+	0.0610474i	−1.32044	+	0.0610474i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.0971461	+	1.04837i	0.0971461	+	1.04837i	0.895163	+	0.445738i	$0.147059\pi$
$953$	0.0971461	+	1.04837i	0.0971461	+	1.04837i	−0.798017	+	0.602635i	$0.794118\pi$
$954$	−1.29596	+	0.368731i	−1.29596	+	0.368731i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.183750	+	0.982973i	−0.183750	+	0.982973i
$962$	0.0457057	−	0.327653i	0.0457057	−	0.327653i
$963$		0			0
$964$	1.50941	−	0.666468i	1.50941	−	0.666468i
$965$	−0.698569	−	2.45521i	−0.698569	−	2.45521i
$966$		0			0
$967$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$967$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$968$	−0.739009	−	0.673696i	−0.739009	−	0.673696i
$969$		0			0
$970$	−0.600134	+	0.547095i	−0.600134	+	0.547095i
$971$		0			0		0.183750	−	0.982973i	$-0.441176\pi$
$971$		0			0		−0.183750	+	0.982973i	$0.558824\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−0.932472	−	0.638758i	−0.932472	−	0.638758i
$977$			1.92365i			1.92365i	0.273663	+	0.961826i	$0.411765\pi$
$977$			1.92365i			1.92365i	−0.273663	+	0.961826i	$0.588235\pi$
$978$		0			0
$979$		0			0
$980$	0.722071	+	1.05409i	0.722071	+	1.05409i
$981$	−1.60617	+	1.10025i	−1.60617	+	1.10025i
$982$		0			0
$983$		0			0		−0.138156	−	0.990410i	$-0.544118\pi$
$983$		0			0		0.138156	+	0.990410i	$0.455882\pi$
$984$		0			0
$985$	2.48779	−	0.465048i	2.48779	−	0.465048i
$986$	0.0373089	+	0.806980i	0.0373089	+	0.806980i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.403921	−	0.914794i	$-0.367647\pi$
$991$		0			0		−0.403921	+	0.914794i	$0.632353\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−0.457413	−	1.94480i	−0.457413	−	1.94480i	−0.273663	−	0.961826i	$-0.588235\pi$
$997$	−0.457413	−	1.94480i	−0.457413	−	1.94480i	−0.183750	−	0.982973i	$-0.558824\pi$
$998$		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.1007.1	yes	32
4.3	odd	2	CM	1156.1.o.a.1007.1	yes	32
289.64	even	68	inner	1156.1.o.a.931.1	✓	32
1156.931	odd	68	inner	1156.1.o.a.931.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1156.1.o.a.931.1	✓	32	289.64	even	68	inner
1156.1.o.a.931.1	✓	32	1156.931	odd	68	inner
1156.1.o.a.1007.1	yes	32	1.1	even	1	trivial
1156.1.o.a.1007.1	yes	32	4.3	odd	2	CM

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)

\(f(q)\)	\(=\)	\(q+(-0.526432 + 0.850217i) q^{2} +(-0.445738 - 0.895163i) q^{4} +(0.982973 + 0.816250i) q^{5} +(0.995734 + 0.0922684i) q^{8} +(0.361242 - 0.932472i) q^{9} +O(q^{10})\)	\(q+(-0.526432 + 0.850217i) q^{2} +(-0.445738 - 0.895163i) q^{4} +(0.982973 + 0.816250i) q^{5} +(0.995734 + 0.0922684i) q^{8} +(0.361242 - 0.932472i) q^{9} +(-1.21146 + 0.406040i) q^{10} +(-0.0666624 + 0.719401i) q^{13} +(-0.602635 + 0.798017i) q^{16} +(0.602635 - 0.798017i) q^{17} +(0.602635 + 0.798017i) q^{18} +(0.292529 - 1.24376i) q^{20} +(0.116222 + 0.621731i) q^{25} +(-0.576554 - 0.435393i) q^{26} +(0.765964 + 0.256725i) q^{29} +(-0.361242 - 0.932472i) q^{32} +(0.361242 + 0.932472i) q^{34} +(-0.995734 + 0.0922684i) q^{36} +(0.222817 + 0.400033i) q^{37} +(0.903466 + 0.903466i) q^{40} +(-0.869557 - 1.26940i) q^{41} +(1.11622 - 0.621731i) q^{45} +(-0.673696 + 0.739009i) q^{49} +(-0.589790 - 0.228486i) q^{50} +(0.673696 - 0.260991i) q^{52} +(-0.486734 + 1.25640i) q^{53} +(-0.621500 + 0.516087i) q^{58} +(0.0521999 + 1.12907i) q^{61} +(0.982973 + 0.183750i) q^{64} +(-0.652739 + 0.652739i) q^{65} +(-0.982973 - 0.183750i) q^{68} +(0.445738 - 0.895163i) q^{72} +(0.252769 + 1.81204i) q^{73} +(-0.457413 - 0.0211475i) q^{74} +(-1.24376 + 0.292529i) q^{80} +(-0.739009 - 0.673696i) q^{81} +(1.53703 - 0.0710610i) q^{82} +(1.24376 - 0.292529i) q^{85} +(-0.0971461 - 1.04837i) q^{89} +(-0.0590083 + 1.27633i) q^{90} +(0.581427 - 0.256725i) q^{97} +(-0.273663 - 0.961826i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{4} + 2 q^{5}+O(q^{10}) \) 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

Introduction

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