LMFDB - Embedded newform 959.1.t.a.944.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [959,1,Mod(34,959)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(959, base_ring=CyclotomicField(34))

chi = DirichletCharacter(H, H._module([17, 12]))

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

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

chi := DirichletCharacter("959.34");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 959 = 7 \cdot 137 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	959.t (of order $34$, degree $16$, 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:	$0.478603347115$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\Q(\zeta_{34})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + x^{14} - x^{13} + x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + \cdots + 1 $ x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{17}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{17} - \cdots)$

Embedding invariants

Embedding label			944.1
Root			$-0.445738 - 0.895163i$ of defining polynomial
Character	$\chi$	$=$	959.944
Dual form			959.1.t.a.895.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.510366 + 1.79375i) q^{2} +(-2.10685 - 1.30451i) q^{4} +(0.0922684 + 0.995734i) q^{7} +(2.03702 - 1.85699i) q^{8} +(0.932472 + 0.361242i) q^{9} +O(q^{10})$	\(q+(-0.510366 + 1.79375i) q^{2} +(-2.10685 - 1.30451i) q^{4} +(0.0922684 + 0.995734i) q^{7} +(2.03702 - 1.85699i) q^{8} +(0.932472 + 0.361242i) q^{9} +(0.465346 + 0.288130i) q^{11} +(-1.83319 - 0.342683i) q^{14} +(1.18680 + 2.38342i) q^{16} +(-1.12388 + 1.48826i) q^{18} +(-0.754330 + 0.687663i) q^{22} +(0.397365 + 0.798017i) q^{23} +(-0.850217 + 0.526432i) q^{25} +(1.10455 - 2.21823i) q^{28} +(-0.243964 - 0.489946i) q^{29} +(-2.17148 + 0.405920i) q^{32} +(-1.49334 - 1.97750i) q^{36} -1.70043 q^{37} +(-0.537235 + 0.711414i) q^{43} +(-0.604548 - 1.21410i) q^{44} +(-1.63425 + 0.305494i) q^{46} +(-0.982973 + 0.183750i) q^{49} +(-0.510366 - 1.79375i) q^{50} +(1.18475 - 1.56886i) q^{53} +(2.03702 + 1.85699i) q^{56} +(1.00335 - 0.187559i) q^{58} +(-0.273663 + 0.961826i) q^{63} +(0.134461 - 1.45107i) q^{64} +(0.172075 + 1.85699i) q^{67} +(1.44574 - 0.895163i) q^{71} +(2.57029 - 0.995734i) q^{72} +(0.867844 - 3.05016i) q^{74} +(-0.243964 + 0.489946i) q^{77} +(1.18475 - 0.221468i) q^{79} +(0.739009 + 0.673696i) q^{81} +(-1.00191 - 1.32675i) q^{86} +(1.48297 - 0.277216i) q^{88} +(0.203830 - 2.19967i) q^{92} +(0.172075 - 1.85699i) q^{98} +(0.329838 + 0.436776i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 3 q^{4} - q^{7} - 4 q^{8} - q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 - 3 * q^4 - q^7 - 4 * q^8 - q^9	$ 16 q - 2 q^{2} - 3 q^{4} - q^{7} - 4 q^{8} - q^{9} - 2 q^{11} - 2 q^{14} - 5 q^{16} - 2 q^{18} - 4 q^{22} + 15 q^{23} - q^{25} - 3 q^{28} - 2 q^{29} - 6 q^{32} - 3 q^{36} - 2 q^{37} - 2 q^{43} + 11 q^{44} - 4 q^{46} - q^{49} - 2 q^{50} - 2 q^{53} - 4 q^{56} - 4 q^{58} - q^{63} + 10 q^{64} - 2 q^{67} + 15 q^{71} + 13 q^{72} - 4 q^{74} - 2 q^{77} - 2 q^{79} - q^{81} - 4 q^{86} + 9 q^{88} - 6 q^{92} - 2 q^{98} - 2 q^{99}+O(q^{100}) $ 16 * q - 2 * q^2 - 3 * q^4 - q^7 - 4 * q^8 - q^9 - 2 * q^11 - 2 * q^14 - 5 * q^16 - 2 * q^18 - 4 * q^22 + 15 * q^23 - q^25 - 3 * q^28 - 2 * q^29 - 6 * q^32 - 3 * q^36 - 2 * q^37 - 2 * q^43 + 11 * q^44 - 4 * q^46 - q^49 - 2 * q^50 - 2 * q^53 - 4 * q^56 - 4 * q^58 - q^63 + 10 * q^64 - 2 * q^67 + 15 * q^71 + 13 * q^72 - 4 * q^74 - 2 * q^77 - 2 * q^79 - q^81 - 4 * q^86 + 9 * q^88 - 6 * q^92 - 2 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/959\mathbb{Z}\right)^\times$.

$n$	$414$	$549$
$\chi(n)$	$e\left(\frac{1}{17}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.510366	+	1.79375i	−0.510366	+	1.79375i	0.0922684	+	0.995734i	$0.470588\pi$
$2$	−0.510366	+	1.79375i	−0.510366	+	1.79375i	−0.602635	+	0.798017i	$0.705882\pi$
$3$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$3$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$4$	−2.10685	−	1.30451i	−2.10685	−	1.30451i
$5$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$5$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$6$		0			0
$7$	0.0922684	+	0.995734i	0.0922684	+	0.995734i
$7$	0.0922684	+	0.995734i	0.0922684	+	0.995734i
$8$	2.03702	−	1.85699i	2.03702	−	1.85699i
$9$	0.932472	+	0.361242i	0.932472	+	0.361242i
$10$		0			0
$11$	0.465346	+	0.288130i	0.465346	+	0.288130i	0.739009	−	0.673696i	$-0.235294\pi$
$11$	0.465346	+	0.288130i	0.465346	+	0.288130i	−0.273663	+	0.961826i	$0.588235\pi$
$12$		0			0
$13$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$13$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$14$	−1.83319	−	0.342683i	−1.83319	−	0.342683i
$15$		0			0
$16$	1.18680	+	2.38342i	1.18680	+	2.38342i
$17$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$17$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$18$	−1.12388	+	1.48826i	−1.12388	+	1.48826i
$19$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$19$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$20$		0			0
$21$		0			0
$22$	−0.754330	+	0.687663i	−0.754330	+	0.687663i
$23$	0.397365	+	0.798017i	0.397365	+	0.798017i	1.00000			$0$
$23$	0.397365	+	0.798017i	0.397365	+	0.798017i	−0.602635	+	0.798017i	$0.705882\pi$
$24$		0			0
$25$	−0.850217	+	0.526432i	−0.850217	+	0.526432i
$26$		0			0
$27$		0			0
$28$	1.10455	−	2.21823i	1.10455	−	2.21823i
$29$	−0.243964	−	0.489946i	−0.243964	−	0.489946i	0.739009	−	0.673696i	$-0.235294\pi$
$29$	−0.243964	−	0.489946i	−0.243964	−	0.489946i	−0.982973	+	0.183750i	$0.941176\pi$
$30$		0			0
$31$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$31$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$32$	−2.17148	+	0.405920i	−2.17148	+	0.405920i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−1.49334	−	1.97750i	−1.49334	−	1.97750i
$37$	−1.70043			−1.70043			−0.850217	−	0.526432i	$-0.823529\pi$
$37$	−1.70043			−1.70043			−0.850217	+	0.526432i	$0.823529\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$		0			0
$43$	−0.537235	+	0.711414i	−0.537235	+	0.711414i	−0.982973	−	0.183750i	$-0.941176\pi$
$43$	−0.537235	+	0.711414i	−0.537235	+	0.711414i	0.445738	+	0.895163i	$0.352941\pi$
$44$	−0.604548	−	1.21410i	−0.604548	−	1.21410i
$45$		0			0
$46$	−1.63425	+	0.305494i	−1.63425	+	0.305494i
$47$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$47$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$48$		0			0
$49$	−0.982973	+	0.183750i	−0.982973	+	0.183750i
$50$	−0.510366	−	1.79375i	−0.510366	−	1.79375i
$51$		0			0
$52$		0			0
$53$	1.18475	−	1.56886i	1.18475	−	1.56886i	0.445738	−	0.895163i	$-0.352941\pi$
$53$	1.18475	−	1.56886i	1.18475	−	1.56886i	0.739009	−	0.673696i	$-0.235294\pi$
$54$		0			0
$55$		0			0
$56$	2.03702	+	1.85699i	2.03702	+	1.85699i
$57$		0			0
$58$	1.00335	−	0.187559i	1.00335	−	0.187559i
$59$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$59$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$60$		0			0
$61$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$61$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$62$		0			0
$63$	−0.273663	+	0.961826i	−0.273663	+	0.961826i
$64$	0.134461	−	1.45107i	0.134461	−	1.45107i
$65$		0			0
$66$		0			0
$67$	0.172075	+	1.85699i	0.172075	+	1.85699i	0.445738	+	0.895163i	$0.352941\pi$
$67$	0.172075	+	1.85699i	0.172075	+	1.85699i	−0.273663	+	0.961826i	$0.588235\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.44574	−	0.895163i	1.44574	−	0.895163i	0.445738	−	0.895163i	$-0.352941\pi$
$71$	1.44574	−	0.895163i	1.44574	−	0.895163i	1.00000			$0$
$72$	2.57029	−	0.995734i	2.57029	−	0.995734i
$73$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$73$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$74$	0.867844	−	3.05016i	0.867844	−	3.05016i
$75$		0			0
$76$		0			0
$77$	−0.243964	+	0.489946i	−0.243964	+	0.489946i
$78$		0			0
$79$	1.18475	−	0.221468i	1.18475	−	0.221468i	0.445738	−	0.895163i	$-0.352941\pi$
$79$	1.18475	−	0.221468i	1.18475	−	0.221468i	0.739009	+	0.673696i	$0.235294\pi$
$80$		0			0
$81$	0.739009	+	0.673696i	0.739009	+	0.673696i
$82$		0			0
$83$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$83$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$84$		0			0
$85$		0			0
$86$	−1.00191	−	1.32675i	−1.00191	−	1.32675i
$87$		0			0
$88$	1.48297	−	0.277216i	1.48297	−	0.277216i
$89$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$89$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$90$		0			0
$91$		0			0
$92$	0.203830	−	2.19967i	0.203830	−	2.19967i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$97$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$98$	0.172075	−	1.85699i	0.172075	−	1.85699i
$99$	0.329838	+	0.436776i	0.329838	+	0.436776i
$100$	2.47802			2.47802
$101$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$101$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$102$		0			0
$103$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$103$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$104$		0			0
$105$		0			0
$106$	2.20949	+	2.92583i	2.20949	+	2.92583i
$107$	−0.876298	−	0.163808i	−0.876298	−	0.163808i	−0.273663	−	0.961826i	$-0.588235\pi$
$107$	−0.876298	−	0.163808i	−0.876298	−	0.163808i	−0.602635	+	0.798017i	$0.705882\pi$
$108$		0			0
$109$	0.831277	−	1.66943i	0.831277	−	1.66943i	0.0922684	−	0.995734i	$-0.470588\pi$
$109$	0.831277	−	1.66943i	0.831277	−	1.66943i	0.739009	−	0.673696i	$-0.235294\pi$
$110$		0			0
$111$		0			0
$112$	−2.26375	+	1.40165i	−2.26375	+	1.40165i
$113$	−0.156896	+	0.0971461i	−0.156896	+	0.0971461i	−0.602635	−	0.798017i	$-0.705882\pi$
$113$	−0.156896	+	0.0971461i	−0.156896	+	0.0971461i	0.445738	+	0.895163i	$0.352941\pi$
$114$		0			0
$115$		0			0
$116$	−0.125142	+	1.35050i	−0.125142	+	1.35050i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.312210	−	0.627003i	−0.312210	−	0.627003i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−1.58561	−	0.981767i	−1.58561	−	0.981767i
$127$	1.86494			1.86494			0.932472	−	0.361242i	$-0.117647\pi$
$127$	1.86494			1.86494			0.932472	+	0.361242i	$0.117647\pi$
$128$	0.474312	+	0.183750i	0.474312	+	0.183750i
$129$		0			0
$130$		0			0
$131$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$131$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$132$		0			0
$133$		0			0
$134$	−3.41880	−	0.639084i	−3.41880	−	0.639084i
$135$		0			0
$136$		0			0
$137$	1.00000			1.00000
$137$	1.00000			1.00000
$138$		0			0
$139$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$139$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$140$		0			0
$141$		0			0
$142$	0.867844	+	3.05016i	0.867844	+	3.05016i
$143$		0			0
$144$	0.245670	+	2.65120i	0.245670	+	2.65120i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	3.58257	+	2.21823i	3.58257	+	2.21823i
$149$	−1.45285	−	1.32445i	−1.45285	−	1.32445i	−0.850217	−	0.526432i	$-0.823529\pi$
$149$	−1.45285	−	1.32445i	−1.45285	−	1.32445i	−0.602635	−	0.798017i	$-0.705882\pi$
$150$		0			0
$151$	−1.96595	−	0.367499i	−1.96595	−	0.367499i	−0.982973	−	0.183750i	$-0.941176\pi$
$151$	−1.96595	−	0.367499i	−1.96595	−	0.367499i	−0.982973	−	0.183750i	$-0.941176\pi$
$152$		0			0
$153$		0			0
$154$	−0.754330	−	0.687663i	−0.754330	−	0.687663i
$155$		0			0
$156$		0			0
$157$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$157$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$158$	−0.207397	+	2.23817i	−0.207397	+	2.23817i
$159$		0			0
$160$		0			0
$161$	−0.757949	+	0.469302i	−0.757949	+	0.469302i
$162$	−1.58561	+	0.981767i	−1.58561	+	0.981767i
$163$	−1.45285	−	0.271585i	−1.45285	−	0.271585i	−0.602635	−	0.798017i	$-0.705882\pi$
$163$	−1.45285	−	0.271585i	−1.45285	−	0.271585i	−0.850217	+	0.526432i	$0.823529\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$167$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$168$		0			0
$169$	−0.982973	+	0.183750i	−0.982973	+	0.183750i
$170$		0			0
$171$		0			0
$172$	2.05992	−	0.798017i	2.05992	−	0.798017i
$173$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$173$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$174$		0			0
$175$	−0.602635	−	0.798017i	−0.602635	−	0.798017i
$176$	−0.134461	+	1.45107i	−0.134461	+	1.45107i
$177$		0			0
$178$		0			0
$179$	1.86494	+	0.722483i	1.86494	+	0.722483i	0.932472	+	0.361242i	$0.117647\pi$
$179$	1.86494	+	0.722483i	1.86494	+	0.722483i	0.932472	+	0.361242i	$0.117647\pi$
$180$		0			0
$181$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$181$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$182$		0			0
$183$		0			0
$184$	2.29135	+	0.887674i	2.29135	+	0.887674i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.37821	−	1.25640i	1.37821	−	1.25640i	0.445738	−	0.895163i	$-0.352941\pi$
$191$	1.37821	−	1.25640i	1.37821	−	1.25640i	0.932472	−	0.361242i	$-0.117647\pi$
$192$		0			0
$193$	1.37821	+	1.25640i	1.37821	+	1.25640i	0.932472	+	0.361242i	$0.117647\pi$
$193$	1.37821	+	1.25640i	1.37821	+	1.25640i	0.445738	+	0.895163i	$0.352941\pi$
$194$		0			0
$195$		0			0
$196$	2.31068	+	0.895163i	2.31068	+	0.895163i
$197$	0.658809	−	1.32307i	0.658809	−	1.32307i	−0.273663	−	0.961826i	$-0.588235\pi$
$197$	0.658809	−	1.32307i	0.658809	−	1.32307i	0.932472	−	0.361242i	$-0.117647\pi$
$198$	−0.951805	+	0.368731i	−0.951805	+	0.368731i
$199$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$199$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$200$	−0.754330	+	2.65120i	−0.754330	+	2.65120i
$201$		0			0
$202$		0			0
$203$	0.465346	−	0.288130i	0.465346	−	0.288130i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.0822551	+	0.887674i	0.0822551	+	0.887674i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.538007	−	1.89090i	0.538007	−	1.89090i	0.0922684	−	0.995734i	$-0.470588\pi$
$211$	0.538007	−	1.89090i	0.538007	−	1.89090i	0.445738	−	0.895163i	$-0.352941\pi$
$212$	−4.54268	+	1.75984i	−4.54268	+	1.75984i
$213$		0			0
$214$	0.741064	−	1.48826i	0.741064	−	1.48826i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	2.57029	+	2.34313i	2.57029	+	2.34313i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$223$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$224$	−0.604548	−	2.12476i	−0.604548	−	2.12476i
$225$	−0.982973	+	0.183750i	−0.982973	+	0.183750i
$226$	−0.0941813	−	0.331013i	−0.0941813	−	0.331013i
$227$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$227$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$228$		0			0
$229$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$229$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$230$		0			0
$231$		0			0
$232$	−1.40678	−	0.544991i	−1.40678	−	0.544991i
$233$	−1.20527			−1.20527			−0.602635	−	0.798017i	$-0.705882\pi$
$233$	−1.20527			−1.20527			−0.602635	+	0.798017i	$0.705882\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.12388	+	0.435393i	−1.12388	+	0.435393i	−0.850217	−	0.526432i	$-0.823529\pi$
$239$	−1.12388	+	0.435393i	−1.12388	+	0.435393i	−0.273663	+	0.961826i	$0.588235\pi$
$240$		0			0
$241$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$241$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$242$	1.28403	−	0.240027i	1.28403	−	0.240027i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$251$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$252$	1.83128	−	1.66943i	1.83128	−	1.66943i
$253$	−0.0450203	+	0.485847i	−0.0450203	+	0.485847i
$254$	−0.951805	+	3.34525i	−0.951805	+	3.34525i
$255$		0			0
$256$	0.306537	−	0.405920i	0.306537	−	0.405920i
$257$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$257$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$258$		0			0
$259$	−0.156896	−	1.69318i	−0.156896	−	1.69318i
$260$		0			0
$261$	−0.0505009	−	0.544991i	−0.0505009	−	0.544991i
$262$		0			0
$263$	1.02474	+	0.634493i	1.02474	+	0.634493i	0.932472	−	0.361242i	$-0.117647\pi$
$263$	1.02474	+	0.634493i	1.02474	+	0.634493i	0.0922684	+	0.995734i	$0.470588\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	2.05992	−	4.13688i	2.05992	−	4.13688i
$269$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$269$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$270$		0			0
$271$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$271$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$272$		0			0
$273$		0			0
$274$	−0.510366	+	1.79375i	−0.510366	+	1.79375i
$275$	−0.547326			−0.547326
$276$		0			0
$277$	0.538007	+	0.100571i	0.538007	+	0.100571i	0.445738	−	0.895163i	$-0.352941\pi$
$277$	0.538007	+	0.100571i	0.538007	+	0.100571i	0.0922684	+	0.995734i	$0.470588\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.181395	−	1.95756i	−0.181395	−	1.95756i	−0.273663	−	0.961826i	$-0.588235\pi$
$281$	−0.181395	−	1.95756i	−0.181395	−	1.95756i	0.0922684	−	0.995734i	$-0.470588\pi$
$282$		0			0
$283$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$283$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$284$	−4.21371			−4.21371
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−2.17148	−	0.405920i	−2.17148	−	0.405920i
$289$	0.0922684	+	0.995734i	0.0922684	+	0.995734i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$293$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$294$		0			0
$295$		0			0
$296$	−3.46382	+	3.15769i	−3.46382	+	3.15769i
$297$		0			0
$298$	3.11722	−	1.93010i	3.11722	−	1.93010i
$299$		0			0
$300$		0			0
$301$	−0.757949	−	0.469302i	−0.757949	−	0.469302i
$302$	1.66255	−	3.33886i	1.66255	−	3.33886i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$307$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$308$	1.15314	−	0.713991i	1.15314	−	0.713991i
$309$		0			0
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$		0			0
$313$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$313$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$314$		0			0
$315$		0			0
$316$	−2.78499	−	1.07891i	−2.78499	−	1.07891i
$317$	1.02474	−	1.35698i	1.02474	−	1.35698i	0.0922684	−	0.995734i	$-0.470588\pi$
$317$	1.02474	−	1.35698i	1.02474	−	1.35698i	0.932472	−	0.361242i	$-0.117647\pi$
$318$		0			0
$319$	0.0276404	−	0.298288i	0.0276404	−	0.298288i
$320$		0			0
$321$		0			0
$322$	−0.454980	−	1.59909i	−0.454980	−	1.59909i
$323$		0			0
$324$	−0.678142	−	2.38342i	−0.678142	−	2.38342i
$325$		0			0
$326$	1.22864	−	2.46745i	1.22864	−	2.46745i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.25664	+	1.14558i	−1.25664	+	1.14558i	−0.273663	+	0.961826i	$0.588235\pi$
$331$	−1.25664	+	1.14558i	−1.25664	+	1.14558i	−0.982973	+	0.183750i	$0.941176\pi$
$332$		0			0
$333$	−1.58561	−	0.614268i	−1.58561	−	0.614268i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.149783	−	0.526432i	0.149783	−	0.526432i	−0.850217	−	0.526432i	$-0.823529\pi$
$337$	0.149783	−	0.526432i	0.149783	−	0.526432i	1.00000			$0$
$338$	0.172075	−	1.85699i	0.172075	−	1.85699i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.273663	−	0.961826i	−0.273663	−	0.961826i
$344$	0.226730	+	2.44680i	0.226730	+	2.44680i
$345$		0			0
$346$		0			0
$347$	0.0170269	−	0.183750i	0.0170269	−	0.183750i	−0.982973	−	0.183750i	$-0.941176\pi$
$347$	0.0170269	−	0.183750i	0.0170269	−	0.183750i	1.00000			$0$
$348$		0			0
$349$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$349$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$350$	1.73901	−	0.673696i	1.73901	−	0.673696i
$351$		0			0
$352$	−1.12745	−	0.436776i	−1.12745	−	0.436776i
$353$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$353$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−2.24776	+	2.97652i	−2.24776	+	2.97652i
$359$	−0.243964	+	0.489946i	−0.243964	+	0.489946i	−0.982973	−	0.183750i	$-0.941176\pi$
$359$	−0.243964	+	0.489946i	−0.243964	+	0.489946i	0.739009	+	0.673696i	$0.235294\pi$
$360$		0			0
$361$	−0.273663	−	0.961826i	−0.273663	−	0.961826i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$367$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$368$	−1.43042	+	1.89418i	−1.43042	+	1.89418i
$369$		0			0
$370$		0			0
$371$	1.67148	+	1.03494i	1.67148	+	1.03494i
$372$		0			0
$373$	−0.111208	−	0.147263i	−0.111208	−	0.147263i	0.739009	−	0.673696i	$-0.235294\pi$
$373$	−0.111208	−	0.147263i	−0.111208	−	0.147263i	−0.850217	+	0.526432i	$0.823529\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.93247	−	0.361242i	1.93247	−	0.361242i	0.932472	−	0.361242i	$-0.117647\pi$
$379$	1.93247	−	0.361242i	1.93247	−	0.361242i	1.00000			$0$
$380$		0			0
$381$		0			0
$382$	1.55029	+	3.11339i	1.55029	+	3.11339i
$383$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$383$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$384$		0			0
$385$		0			0
$386$	−2.95707	+	1.83094i	−2.95707	+	1.83094i
$387$	−0.757949	+	0.469302i	−0.757949	+	0.469302i
$388$		0			0
$389$	0.136374	−	0.124322i	0.136374	−	0.124322i	−0.602635	−	0.798017i	$-0.705882\pi$
$389$	0.136374	−	0.124322i	0.136374	−	0.124322i	0.739009	+	0.673696i	$0.235294\pi$
$390$		0			0
$391$		0			0
$392$	−1.66111	+	2.19967i	−1.66111	+	2.19967i
$393$		0			0
$394$	2.03702	+	1.85699i	2.03702	+	1.85699i
$395$		0			0
$396$	−0.125142	−	1.35050i	−0.125142	−	1.35050i
$397$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$397$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$398$		0			0
$399$		0			0
$400$	−2.26375	−	1.40165i	−2.26375	−	1.40165i
$401$	0.184537			0.184537			0.0922684	−	0.995734i	$-0.470588\pi$
$401$	0.184537			0.184537			0.0922684	+	0.995734i	$0.470588\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	0.279337	+	0.981767i	0.279337	+	0.981767i
$407$	−0.791290	−	0.489946i	−0.791290	−	0.489946i
$408$		0			0
$409$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$409$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−1.63425	−	0.305494i	−1.63425	−	0.305494i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$419$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$420$		0			0
$421$	−1.70043			−1.70043			−0.850217	−	0.526432i	$-0.823529\pi$
$421$	−1.70043			−1.70043			−0.850217	+	0.526432i	$0.823529\pi$
$422$	3.11722	+	1.93010i	3.11722	+	1.93010i
$423$		0			0
$424$	−0.500000	−	5.39586i	−0.500000	−	5.39586i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	1.63254	+	1.48826i	1.63254	+	1.48826i
$429$		0			0
$430$		0			0
$431$	−0.510366	+	1.79375i	−0.510366	+	1.79375i	0.0922684	+	0.995734i	$0.470588\pi$
$431$	−0.510366	+	1.79375i	−0.510366	+	1.79375i	−0.602635	+	0.798017i	$0.705882\pi$
$432$		0			0
$433$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$433$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$434$		0			0
$435$		0			0
$436$	−3.92916	+	2.43284i	−3.92916	+	2.43284i
$437$		0			0
$438$		0			0
$439$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$439$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$440$		0			0
$441$	−0.982973	−	0.183750i	−0.982973	−	0.183750i
$442$		0			0
$443$	−0.181395	+	0.0339085i	−0.181395	+	0.0339085i	−0.273663	−	0.961826i	$-0.588235\pi$
$443$	−0.181395	+	0.0339085i	−0.181395	+	0.0339085i	0.0922684	+	0.995734i	$0.470588\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	1.45729			1.45729
$449$	1.18475	+	1.56886i	1.18475	+	1.56886i	0.739009	+	0.673696i	$0.235294\pi$
$449$	1.18475	+	1.56886i	1.18475	+	1.56886i	0.445738	+	0.895163i	$0.352941\pi$
$450$	0.172075	−	1.85699i	0.172075	−	1.85699i
$451$		0			0
$452$	0.457285			0.457285
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.96595	+	0.367499i	−1.96595	+	0.367499i	−0.982973	+	0.183750i	$0.941176\pi$
$457$	−1.96595	+	0.367499i	−1.96595	+	0.367499i	−0.982973	+	0.183750i	$0.941176\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$461$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$462$		0			0
$463$	0.658809	−	1.32307i	0.658809	−	1.32307i	−0.273663	−	0.961826i	$-0.588235\pi$
$463$	0.658809	−	1.32307i	0.658809	−	1.32307i	0.932472	−	0.361242i	$-0.117647\pi$
$464$	0.878211	−	1.16294i	0.878211	−	1.16294i
$465$		0			0
$466$	0.615129	−	2.16195i	0.615129	−	2.16195i
$467$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$467$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$468$		0			0
$469$	−1.83319	+	0.342683i	−1.83319	+	0.342683i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.454980	+	0.176260i	−0.454980	+	0.176260i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.67148	−	1.03494i	1.67148	−	1.03494i
$478$	−0.207397	−	2.23817i	−0.207397	−	2.23817i
$479$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$479$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.160149	+	1.72828i	−0.160149	+	1.72828i
$485$		0			0
$486$		0			0
$487$	−1.12388	+	0.435393i	−1.12388	+	0.435393i	−0.850217	−	0.526432i	$-0.823529\pi$
$487$	−1.12388	+	0.435393i	−1.12388	+	0.435393i	−0.273663	+	0.961826i	$0.588235\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−0.404479	+	0.368731i	−0.404479	+	0.368731i	−0.850217	−	0.526432i	$-0.823529\pi$
$491$	−0.404479	+	0.368731i	−0.404479	+	0.368731i	0.445738	+	0.895163i	$0.352941\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.02474	+	1.35698i	1.02474	+	1.35698i
$498$		0			0
$499$	1.93247	−	0.361242i	1.93247	−	0.361242i	0.932472	−	0.361242i	$-0.117647\pi$
$499$	1.93247	−	0.361242i	1.93247	−	0.361242i	1.00000			$0$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$503$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$504$	1.22864	+	2.46745i	1.22864	+	2.46745i
$505$		0			0
$506$	−0.848512	−	0.328715i	−0.848512	−	0.328715i
$507$		0			0
$508$	−3.92916	−	2.43284i	−3.92916	−	2.43284i
$509$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$509$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$510$		0			0
$511$		0			0
$512$	0.878211	+	1.16294i	0.878211	+	1.16294i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	3.11722	+	0.582709i	3.11722	+	0.582709i
$519$		0			0
$520$		0			0
$521$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$521$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$522$	1.00335	+	0.187559i	1.00335	+	0.187559i
$523$		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
$526$	−1.66111	+	1.51431i	−1.66111	+	1.51431i
$527$		0			0
$528$		0			0
$529$	0.123702	−	0.163808i	0.123702	−	0.163808i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	3.79893	+	3.46318i	3.79893	+	3.46318i
$537$		0			0
$538$		0			0
$539$	−0.510366	−	0.197717i	−0.510366	−	0.197717i
$540$		0			0
$541$	0.136374	+	1.47171i	0.136374	+	1.47171i	0.739009	+	0.673696i	$0.235294\pi$
$541$	0.136374	+	1.47171i	0.136374	+	1.47171i	−0.602635	+	0.798017i	$0.705882\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.20527			−1.20527			−0.602635	−	0.798017i	$-0.705882\pi$
$547$	−1.20527			−1.20527			−0.602635	+	0.798017i	$0.705882\pi$
$548$	−2.10685	−	1.30451i	−2.10685	−	1.30451i
$549$		0			0
$550$	0.279337	−	0.981767i	0.279337	−	0.981767i
$551$		0			0
$552$		0			0
$553$	0.329838	+	1.15926i	0.329838	+	1.15926i
$554$	−0.454980	+	0.913722i	−0.454980	+	0.913722i
$555$		0			0
$556$		0			0
$557$	−1.12388	−	0.435393i	−1.12388	−	0.435393i	−0.273663	−	0.961826i	$-0.588235\pi$
$557$	−1.12388	−	0.435393i	−1.12388	−	0.435393i	−0.850217	+	0.526432i	$0.823529\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	3.60395	+	0.673696i	3.60395	+	0.673696i
$563$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$563$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.602635	+	0.798017i	−0.602635	+	0.798017i
$568$	1.28269	−	4.50819i	1.28269	−	4.50819i
$569$	0.0170269	−	0.183750i	0.0170269	−	0.183750i	−0.982973	−	0.183750i	$-0.941176\pi$
$569$	0.0170269	−	0.183750i	0.0170269	−	0.183750i	1.00000			$0$
$570$		0			0
$571$	−0.537235	−	1.07891i	−0.537235	−	1.07891i	−0.982973	−	0.183750i	$-0.941176\pi$
$571$	−0.537235	−	1.07891i	−0.537235	−	1.07891i	0.445738	−	0.895163i	$-0.352941\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.757949	−	0.469302i	−0.757949	−	0.469302i
$576$	0.649568	−	1.30451i	0.649568	−	1.30451i
$577$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$577$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$578$	−1.83319	−	0.342683i	−1.83319	−	0.342683i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	1.00335	−	0.388701i	1.00335	−	0.388701i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$587$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−2.01808	−	4.05285i	−2.01808	−	4.05285i
$593$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$593$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$594$		0			0
$595$		0			0
$596$	1.33319	+	4.68568i	1.33319	+	4.68568i
$597$		0			0
$598$		0			0
$599$	1.18475	+	1.56886i	1.18475	+	1.56886i	0.739009	+	0.673696i	$0.235294\pi$
$599$	1.18475	+	1.56886i	1.18475	+	1.56886i	0.445738	+	0.895163i	$0.352941\pi$
$600$		0			0
$601$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$601$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$602$	1.22864	−	1.12006i	1.22864	−	1.12006i
$603$	−0.510366	+	1.79375i	−0.510366	+	1.79375i
$604$	3.66255	+	3.33886i	3.66255	+	3.33886i
$605$		0			0
$606$		0			0
$607$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$607$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.831277	−	0.322039i	0.831277	−	0.322039i	0.0922684	−	0.995734i	$-0.470588\pi$
$613$	0.831277	−	0.322039i	0.831277	−	0.322039i	0.739009	+	0.673696i	$0.235294\pi$
$614$		0			0
$615$		0			0
$616$	0.412865	+	1.45107i	0.412865	+	1.45107i
$617$	0.329838	+	1.15926i	0.329838	+	1.15926i	0.932472	+	0.361242i	$0.117647\pi$
$617$	0.329838	+	1.15926i	0.329838	+	1.15926i	−0.602635	+	0.798017i	$0.705882\pi$
$618$		0			0
$619$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$619$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.445738	−	0.895163i	0.445738	−	0.895163i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−1.25664	+	1.14558i	−1.25664	+	1.14558i	−0.273663	+	0.961826i	$0.588235\pi$
$631$	−1.25664	+	1.14558i	−1.25664	+	1.14558i	−0.982973	+	0.183750i	$0.941176\pi$
$632$	2.00209	−	2.65120i	2.00209	−	2.65120i
$633$		0			0
$634$	1.91108	+	2.53068i	1.91108	+	2.53068i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	0.520947	+	0.201816i	0.520947	+	0.201816i
$639$	1.67148	−	0.312454i	1.67148	−	0.312454i
$640$		0			0
$641$	−0.876298	−	1.75984i	−0.876298	−	1.75984i	−0.602635	−	0.798017i	$-0.705882\pi$
$641$	−0.876298	−	1.75984i	−0.876298	−	1.75984i	−0.273663	−	0.961826i	$-0.588235\pi$
$642$		0			0
$643$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$643$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$644$	2.20910			2.20910
$645$		0			0
$646$		0			0
$647$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$647$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$648$	2.75642			2.75642
$649$		0			0
$650$		0			0
$651$		0			0
$652$	2.70666	+	2.46745i	2.70666	+	2.46745i
$653$	1.93247	−	0.361242i	1.93247	−	0.361242i	0.932472	−	0.361242i	$-0.117647\pi$
$653$	1.93247	−	0.361242i	1.93247	−	0.361242i	1.00000			$0$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.45285	−	0.271585i	−1.45285	−	0.271585i	−0.602635	−	0.798017i	$-0.705882\pi$
$659$	−1.45285	−	0.271585i	−1.45285	−	0.271585i	−0.850217	+	0.526432i	$0.823529\pi$
$660$		0			0
$661$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$661$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$662$	−1.41353	−	2.83876i	−1.41353	−	2.83876i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	1.91108	−	2.53068i	1.91108	−	2.53068i
$667$	0.294043	−	0.389375i	0.294043	−	0.389375i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.404479	−	0.368731i	−0.404479	−	0.368731i	0.445738	−	0.895163i	$-0.352941\pi$
$673$	−0.404479	−	0.368731i	−0.404479	−	0.368731i	−0.850217	+	0.526432i	$0.823529\pi$
$674$	0.867844	+	0.537346i	0.867844	+	0.537346i
$675$		0			0
$676$	2.31068	+	0.895163i	2.31068	+	0.895163i
$677$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$677$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.243964	+	0.857445i	−0.243964	+	0.857445i	0.739009	+	0.673696i	$0.235294\pi$
$683$	−0.243964	+	0.857445i	−0.243964	+	0.857445i	−0.982973	+	0.183750i	$0.941176\pi$
$684$		0			0
$685$		0			0
$686$	1.86494			1.86494
$687$		0			0
$688$	−2.33319	−	0.436149i	−2.33319	−	0.436149i
$689$		0			0
$690$		0			0
$691$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$691$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$692$		0			0
$693$	−0.404479	+	0.368731i	−0.404479	+	0.368731i
$694$	0.320911	+	0.124322i	0.320911	+	0.124322i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	0.228643	+	2.46745i	0.228643	+	2.46745i
$701$	−0.757949	−	1.52217i	−0.757949	−	1.52217i	−0.850217	−	0.526432i	$-0.823529\pi$
$701$	−0.757949	−	1.52217i	−0.757949	−	1.52217i	0.0922684	−	0.995734i	$-0.470588\pi$
$702$		0			0
$703$		0			0
$704$	0.480667	−	0.636507i	0.480667	−	0.636507i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.465346	−	0.288130i	0.465346	−	0.288130i	−0.273663	−	0.961826i	$-0.588235\pi$
$709$	0.465346	−	0.288130i	0.465346	−	0.288130i	0.739009	+	0.673696i	$0.235294\pi$
$710$		0			0
$711$	1.18475	+	0.221468i	1.18475	+	0.221468i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−2.98668	−	3.95500i	−2.98668	−	3.95500i
$717$		0			0
$718$	−0.754330	−	0.687663i	−0.754330	−	0.687663i
$719$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$719$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$720$		0			0
$721$		0			0
$722$	1.86494			1.86494
$723$		0			0
$724$		0			0
$725$	0.465346	+	0.288130i	0.465346	+	0.288130i
$726$		0			0
$727$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$727$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$728$		0			0
$729$	0.445738	+	0.895163i	0.445738	+	0.895163i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$733$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$734$		0			0
$735$		0			0
$736$	−1.18680	−	1.57158i	−1.18680	−	1.57158i
$737$	−0.454980	+	0.913722i	−0.454980	+	0.913722i
$738$		0			0
$739$	−0.890705	+	0.811985i	−0.890705	+	0.811985i	−0.982973	−	0.183750i	$-0.941176\pi$
$739$	−0.890705	+	0.811985i	−0.890705	+	0.811985i	0.0922684	+	0.995734i	$0.470588\pi$
$740$		0			0
$741$		0			0
$742$	−2.70949	+	2.47002i	−2.70949	+	2.47002i
$743$	−1.45285	+	0.271585i	−1.45285	+	0.271585i	−0.850217	−	0.526432i	$-0.823529\pi$
$743$	−1.45285	+	0.271585i	−1.45285	+	0.271585i	−0.602635	+	0.798017i	$0.705882\pi$
$744$		0			0
$745$		0			0
$746$	0.320911	−	0.124322i	0.320911	−	0.124322i
$747$		0			0
$748$		0			0
$749$	0.0822551	−	0.887674i	0.0822551	−	0.887674i
$750$		0			0
$751$	−0.156896	+	0.0971461i	−0.156896	+	0.0971461i	−0.602635	−	0.798017i	$-0.705882\pi$
$751$	−0.156896	+	0.0971461i	−0.156896	+	0.0971461i	0.445738	+	0.895163i	$0.352941\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.58561	+	0.614268i	−1.58561	+	0.614268i	−0.982973	−	0.183750i	$-0.941176\pi$
$757$	−1.58561	+	0.614268i	−1.58561	+	0.614268i	−0.602635	+	0.798017i	$0.705882\pi$
$758$	−0.338291	+	3.65074i	−0.338291	+	3.65074i
$759$		0			0
$760$		0			0
$761$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$761$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$762$		0			0
$763$	1.73901	+	0.673696i	1.73901	+	0.673696i
$764$	−4.54268	+	0.849174i	−4.54268	+	0.849174i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$769$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$770$		0			0
$771$		0			0
$772$	−1.26470	−	4.44495i	−1.26470	−	4.44495i
$773$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$773$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$774$	−0.454980	−	1.59909i	−0.454980	−	1.59909i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	0.153401	+	0.308071i	0.153401	+	0.308071i
$779$		0			0
$780$		0			0
$781$	0.930692			0.930692
$782$		0			0
$783$		0			0
$784$	−1.60455	−	2.12476i	−1.60455	−	2.12476i
$785$		0			0
$786$		0			0
$787$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$787$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$788$	−3.11397	+	1.92809i	−3.11397	+	1.92809i
$789$		0			0
$790$		0			0
$791$	−0.111208	−	0.147263i	−0.111208	−	0.147263i
$792$	1.48297	+	0.277216i	1.48297	+	0.277216i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$797$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$798$		0			0
$799$		0			0
$800$	1.63254	−	1.48826i	1.63254	−	1.48826i
$801$		0			0
$802$	−0.0941813	+	0.331013i	−0.0941813	+	0.331013i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.136374	+	1.47171i	0.136374	+	1.47171i	0.739009	+	0.673696i	$0.235294\pi$
$809$	0.136374	+	1.47171i	0.136374	+	1.47171i	−0.602635	+	0.798017i	$0.705882\pi$
$810$		0			0
$811$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$811$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$812$	−1.35628			−1.35628
$813$		0			0
$814$	1.28269	−	1.16933i	1.28269	−	1.16933i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.96595			−1.96595			−0.982973	−	0.183750i	$-0.941176\pi$
$821$	−1.96595			−1.96595			−0.982973	+	0.183750i	$0.941176\pi$
$822$		0			0
$823$	−1.96595			−1.96595			−0.982973	−	0.183750i	$-0.941176\pi$
$823$	−1.96595			−1.96595			−0.982973	+	0.183750i	$0.941176\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.243964	−	0.857445i	−0.243964	−	0.857445i	−0.982973	−	0.183750i	$-0.941176\pi$
$827$	−0.243964	−	0.857445i	−0.243964	−	0.857445i	0.739009	−	0.673696i	$-0.235294\pi$
$828$	0.984678	−	1.97750i	0.984678	−	1.97750i
$829$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$829$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$839$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$840$		0			0
$841$	0.422106	−	0.558959i	0.422106	−	0.558959i
$842$	0.867844	−	3.05016i	0.867844	−	3.05016i
$843$		0			0
$844$	−3.60019	+	3.28201i	−3.60019	+	3.28201i
$845$		0			0
$846$		0			0
$847$	0.595521	−	0.368731i	0.595521	−	0.368731i
$848$	5.14531	+	0.961826i	5.14531	+	0.961826i
$849$		0			0
$850$		0			0
$851$	−0.675694	−	1.35698i	−0.675694	−	1.35698i
$852$		0			0
$853$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$853$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$854$		0			0
$855$		0			0
$856$	−2.08923	+	1.29359i	−2.08923	+	1.29359i
$857$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$857$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$858$		0			0
$859$		0			0		1.00000			$0$
$859$		0			0		−1.00000			$\pi$
$860$		0			0
$861$		0			0
$862$	−2.95707	−	1.83094i	−2.95707	−	1.83094i
$863$	−1.20527			−1.20527			−0.602635	−	0.798017i	$-0.705882\pi$
$863$	−1.20527			−1.20527			−0.602635	+	0.798017i	$0.705882\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.615129	+	0.238302i	0.615129	+	0.238302i
$870$		0			0
$871$		0			0
$872$	−1.40678	−	4.94433i	−1.40678	−	4.94433i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.547326	+	1.92365i	−0.547326	+	1.92365i	−0.273663	+	0.961826i	$0.588235\pi$
$877$	−0.547326	+	1.92365i	−0.547326	+	1.92365i	−0.273663	+	0.961826i	$0.588235\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$881$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$882$	0.831277	−	1.66943i	0.831277	−	1.66943i
$883$	0.831277	−	0.322039i	0.831277	−	0.322039i	0.0922684	−	0.995734i	$-0.470588\pi$
$883$	0.831277	−	0.322039i	0.831277	−	0.322039i	0.739009	+	0.673696i	$0.235294\pi$
$884$		0			0
$885$		0			0
$886$	0.0317542	−	0.342683i	0.0317542	−	0.342683i
$887$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$887$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$888$		0			0
$889$	0.172075	+	1.85699i	0.172075	+	1.85699i
$890$		0			0
$891$	0.149783	+	0.526432i	0.149783	+	0.526432i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−0.139202	+	0.489243i	−0.139202	+	0.489243i
$897$		0			0
$898$	−3.41880	+	1.32445i	−3.41880	+	1.32445i
$899$		0			0
$900$	2.31068	+	0.895163i	2.31068	+	0.895163i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−0.139202	+	0.489243i	−0.139202	+	0.489243i
$905$		0			0
$906$		0			0
$907$	0.0822551	−	0.165190i	0.0822551	−	0.165190i	−0.850217	−	0.526432i	$-0.823529\pi$
$907$	0.0822551	−	0.165190i	0.0822551	−	0.165190i	0.932472	+	0.361242i	$0.117647\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	0.538007	+	1.89090i	0.538007	+	1.89090i	0.445738	+	0.895163i	$0.352941\pi$
$911$	0.538007	+	1.89090i	0.538007	+	1.89090i	0.0922684	+	0.995734i	$0.470588\pi$
$912$		0			0
$913$		0			0
$914$	0.344151	−	3.71398i	0.344151	−	3.71398i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−1.25664	−	0.778076i	−1.25664	−	0.778076i	−0.273663	−	0.961826i	$-0.588235\pi$
$919$	−1.25664	−	0.778076i	−1.25664	−	0.778076i	−0.982973	+	0.183750i	$0.941176\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	1.44574	−	0.895163i	1.44574	−	0.895163i
$926$	2.03702	+	1.85699i	2.03702	+	1.85699i
$927$		0			0
$928$	0.728643	+	0.964879i	0.728643	+	0.964879i
$929$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$929$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$930$		0			0
$931$		0			0
$932$	2.53933	+	1.57228i	2.53933	+	1.57228i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$937$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$938$	0.320911	−	3.46318i	0.320911	−	3.46318i
$939$		0			0
$940$		0			0
$941$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$941$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−0.0839605	−	0.906078i	−0.0839605	−	0.906078i
$947$	0.658809	+	0.600584i	0.658809	+	0.600584i	0.932472	−	0.361242i	$-0.117647\pi$
$947$	0.658809	+	0.600584i	0.658809	+	0.600584i	−0.273663	+	0.961826i	$0.588235\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.891477	−	1.79033i	0.891477	−	1.79033i	0.445738	−	0.895163i	$-0.352941\pi$
$953$	0.891477	−	1.79033i	0.891477	−	1.79033i	0.445738	−	0.895163i	$-0.352941\pi$
$954$	1.00335	+	3.52642i	1.00335	+	3.52642i
$955$		0			0
$956$	2.93582	+	0.548801i	2.93582	+	0.548801i
$957$		0			0
$958$		0			0
$959$	0.0922684	+	0.995734i	0.0922684	+	0.995734i
$960$		0			0
$961$	−0.273663	+	0.961826i	−0.273663	+	0.961826i
$962$		0			0
$963$	−0.757949	−	0.469302i	−0.757949	−	0.469302i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.658809	−	0.600584i	0.658809	−	0.600584i	−0.273663	−	0.961826i	$-0.588235\pi$
$967$	0.658809	−	0.600584i	0.658809	−	0.600584i	0.932472	+	0.361242i	$0.117647\pi$
$968$	−1.80032	−	0.697446i	−1.80032	−	0.697446i
$969$		0			0
$970$		0			0
$971$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$971$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$972$		0			0
$973$		0			0
$974$	−0.207397	−	2.23817i	−0.207397	−	2.23817i
$975$		0			0
$976$		0			0
$977$	−0.890705	+	1.17948i	−0.890705	+	1.17948i	0.0922684	+	0.995734i	$0.470588\pi$
$977$	−0.890705	+	1.17948i	−0.890705	+	1.17948i	−0.982973	+	0.183750i	$0.941176\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	1.37821	−	1.25640i	1.37821	−	1.25640i
$982$	−0.454980	−	0.913722i	−0.454980	−	0.913722i
$983$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$983$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.781199	−	0.146031i	−0.781199	−	0.146031i
$990$		0			0
$991$	−0.876298	+	0.163808i	−0.876298	+	0.163808i	−0.602635	−	0.798017i	$-0.705882\pi$
$991$	−0.876298	+	0.163808i	−0.876298	+	0.163808i	−0.273663	+	0.961826i	$0.588235\pi$
$992$		0			0
$993$		0			0
$994$	−2.95707	+	1.14558i	−2.95707	+	1.14558i
$995$		0			0
$996$		0			0
$997$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$997$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$998$	−0.338291	+	3.65074i	−0.338291	+	3.65074i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	959.1.t.a.944.1	yes	16
7.6	odd	2	CM	959.1.t.a.944.1	yes	16
137.73	even	17	inner	959.1.t.a.895.1	✓	16
959.895	odd	34	inner	959.1.t.a.895.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
959.1.t.a.895.1	✓	16	137.73	even	17	inner
959.1.t.a.895.1	✓	16	959.895	odd	34	inner
959.1.t.a.944.1	yes	16	1.1	even	1	trivial
959.1.t.a.944.1	yes	16	7.6	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:	\( N \)	\(=\)	\( 959 = 7 \cdot 137 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	959.t (of order \(34\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.510366 + 1.79375i) q^{2} +(-2.10685 - 1.30451i) q^{4} +(0.0922684 + 0.995734i) q^{7} +(2.03702 - 1.85699i) q^{8} +(0.932472 + 0.361242i) q^{9} +O(q^{10})\)	\(q+(-0.510366 + 1.79375i) q^{2} +(-2.10685 - 1.30451i) q^{4} +(0.0922684 + 0.995734i) q^{7} +(2.03702 - 1.85699i) q^{8} +(0.932472 + 0.361242i) q^{9} +(0.465346 + 0.288130i) q^{11} +(-1.83319 - 0.342683i) q^{14} +(1.18680 + 2.38342i) q^{16} +(-1.12388 + 1.48826i) q^{18} +(-0.754330 + 0.687663i) q^{22} +(0.397365 + 0.798017i) q^{23} +(-0.850217 + 0.526432i) q^{25} +(1.10455 - 2.21823i) q^{28} +(-0.243964 - 0.489946i) q^{29} +(-2.17148 + 0.405920i) q^{32} +(-1.49334 - 1.97750i) q^{36} -1.70043 q^{37} +(-0.537235 + 0.711414i) q^{43} +(-0.604548 - 1.21410i) q^{44} +(-1.63425 + 0.305494i) q^{46} +(-0.982973 + 0.183750i) q^{49} +(-0.510366 - 1.79375i) q^{50} +(1.18475 - 1.56886i) q^{53} +(2.03702 + 1.85699i) q^{56} +(1.00335 - 0.187559i) q^{58} +(-0.273663 + 0.961826i) q^{63} +(0.134461 - 1.45107i) q^{64} +(0.172075 + 1.85699i) q^{67} +(1.44574 - 0.895163i) q^{71} +(2.57029 - 0.995734i) q^{72} +(0.867844 - 3.05016i) q^{74} +(-0.243964 + 0.489946i) q^{77} +(1.18475 - 0.221468i) q^{79} +(0.739009 + 0.673696i) q^{81} +(-1.00191 - 1.32675i) q^{86} +(1.48297 - 0.277216i) q^{88} +(0.203830 - 2.19967i) q^{92} +(0.172075 - 1.85699i) q^{98} +(0.329838 + 0.436776i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 3 q^{4} - q^{7} - 4 q^{8} - q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 - 3 * q^4 - q^7 - 4 * q^8 - q^9	\( 16 q - 2 q^{2} - 3 q^{4} - q^{7} - 4 q^{8} - q^{9} - 2 q^{11} - 2 q^{14} - 5 q^{16} - 2 q^{18} - 4 q^{22} + 15 q^{23} - q^{25} - 3 q^{28} - 2 q^{29} - 6 q^{32} - 3 q^{36} - 2 q^{37} - 2 q^{43} + 11 q^{44} - 4 q^{46} - q^{49} - 2 q^{50} - 2 q^{53} - 4 q^{56} - 4 q^{58} - q^{63} + 10 q^{64} - 2 q^{67} + 15 q^{71} + 13 q^{72} - 4 q^{74} - 2 q^{77} - 2 q^{79} - q^{81} - 4 q^{86} + 9 q^{88} - 6 q^{92} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 - 3 * q^4 - q^7 - 4 * q^8 - q^9 - 2 * q^11 - 2 * q^14 - 5 * q^16 - 2 * q^18 - 4 * q^22 + 15 * q^23 - q^25 - 3 * q^28 - 2 * q^29 - 6 * q^32 - 3 * q^36 - 2 * q^37 - 2 * q^43 + 11 * q^44 - 4 * q^46 - q^49 - 2 * q^50 - 2 * q^53 - 4 * q^56 - 4 * q^58 - q^63 + 10 * q^64 - 2 * q^67 + 15 * q^71 + 13 * q^72 - 4 * q^74 - 2 * q^77 - 2 * q^79 - q^81 - 4 * q^86 + 9 * q^88 - 6 * q^92 - 2 * q^98 - 2 * q^99

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