LMFDB - Embedded newform 628.1.o.a.415.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [628,1,Mod(39,628)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(628, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([13, 18]))

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

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

chi := DirichletCharacter("628.39");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 628 = 2^{2} \cdot 157 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	628.o (of order $26$, degree $12$, 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:	$0.313412827934$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\Q(\zeta_{26})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ 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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{13}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{13} - \cdots)$

Embedding invariants

Embedding label			415.1
Root			$-0.120537 + 0.992709i$ of defining polynomial
Character	$\chi$	$=$	628.415
Dual form			628.1.o.a.171.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.568065 - 0.822984i) q^{2} +(-0.354605 - 0.935016i) q^{4} +(-1.32555 - 0.695701i) q^{5} +(-0.970942 - 0.239316i) q^{8} +(-0.748511 - 0.663123i) q^{9} +O(q^{10})$	\(q+(0.568065 - 0.822984i) q^{2} +(-0.354605 - 0.935016i) q^{4} +(-1.32555 - 0.695701i) q^{5} +(-0.970942 - 0.239316i) q^{8} +(-0.748511 - 0.663123i) q^{9} +(-1.32555 + 0.695701i) q^{10} +1.77091 q^{13} +(-0.748511 + 0.663123i) q^{16} +(-1.32555 - 0.695701i) q^{17} +(-0.970942 + 0.239316i) q^{18} +(-0.180446 + 1.48611i) q^{20} +(0.705010 + 1.02138i) q^{25} +(1.00599 - 1.45743i) q^{26} +(1.00599 - 0.527986i) q^{29} +(0.120537 + 0.992709i) q^{32} +(-1.32555 + 0.695701i) q^{34} +(-0.354605 + 0.935016i) q^{36} +(1.56806 - 0.822984i) q^{37} +(1.12054 + 0.992709i) q^{40} +(1.12054 + 0.992709i) q^{41} +(0.530851 + 1.39974i) q^{45} +(-0.748511 - 0.663123i) q^{49} +1.24107 q^{50} +(-0.627974 - 1.65583i) q^{52} +(0.688601 + 0.169725i) q^{53} +(0.136945 - 1.12785i) q^{58} +(-0.234068 - 0.0576926i) q^{61} +(0.885456 + 0.464723i) q^{64} +(-2.34743 - 1.23202i) q^{65} +(-0.180446 + 1.48611i) q^{68} +(0.568065 + 0.822984i) q^{72} +(-0.402877 + 1.06230i) q^{73} +(0.213460 - 1.75800i) q^{74} +(1.45352 - 0.358261i) q^{80} +(0.120537 + 0.992709i) q^{81} +(1.45352 - 0.358261i) q^{82} +(1.27307 + 1.84437i) q^{85} +(-0.234068 + 1.92773i) q^{89} +(1.45352 + 0.358261i) q^{90} +(-1.71945 - 0.902438i) q^{97} +(-0.970942 + 0.239316i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} - q^{4} - 2 q^{5} - q^{8} - q^{9}+O(q^{10}) $ 12 * q - q^2 - q^4 - 2 * q^5 - q^8 - q^9	$ 12 q - q^{2} - q^{4} - 2 q^{5} - q^{8} - q^{9} - 2 q^{10} - 2 q^{13} - q^{16} - 2 q^{17} - q^{18} - 2 q^{20} - 3 q^{25} - 2 q^{26} - 2 q^{29} - q^{32} - 2 q^{34} - q^{36} + 11 q^{37} + 11 q^{40} + 11 q^{41} - 2 q^{45} - q^{49} + 10 q^{50} - 2 q^{52} - 2 q^{53} - 2 q^{58} - 2 q^{61} - q^{64} - 4 q^{65} - 2 q^{68} - q^{72} - 2 q^{73} - 2 q^{74} - 2 q^{80} - q^{81} - 2 q^{82} - 4 q^{85} - 2 q^{89} - 2 q^{90} - 2 q^{97} - q^{98}+O(q^{100}) $ 12 * q - q^2 - q^4 - 2 * q^5 - q^8 - q^9 - 2 * q^10 - 2 * q^13 - q^16 - 2 * q^17 - q^18 - 2 * q^20 - 3 * q^25 - 2 * q^26 - 2 * q^29 - q^32 - 2 * q^34 - q^36 + 11 * q^37 + 11 * q^40 + 11 * q^41 - 2 * q^45 - q^49 + 10 * q^50 - 2 * q^52 - 2 * q^53 - 2 * q^58 - 2 * q^61 - q^64 - 4 * q^65 - 2 * q^68 - q^72 - 2 * q^73 - 2 * q^74 - 2 * q^80 - q^81 - 2 * q^82 - 4 * q^85 - 2 * q^89 - 2 * q^90 - 2 * q^97 - q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/628\mathbb{Z}\right)^\times$.

$n$	$5$	$315$
$\chi(n)$	$e\left(\frac{2}{13}\right)$	$-1$

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 $

$2$	0.568065	−	0.822984i	0.568065	−	0.822984i
$2$	0.568065	−	0.822984i	0.568065	−	0.822984i
$3$		0			0		0.354605	−	0.935016i	$-0.384615\pi$
$3$		0			0		−0.354605	+	0.935016i	$0.615385\pi$
$4$	−0.354605	−	0.935016i	−0.354605	−	0.935016i
$5$	−1.32555	−	0.695701i	−1.32555	−	0.695701i	−0.354605	−	0.935016i	$-0.615385\pi$
$5$	−1.32555	−	0.695701i	−1.32555	−	0.695701i	−0.970942	+	0.239316i	$0.923077\pi$
$6$		0			0
$7$		0			0		0.354605	−	0.935016i	$-0.384615\pi$
$7$		0			0		−0.354605	+	0.935016i	$0.615385\pi$
$8$	−0.970942	−	0.239316i	−0.970942	−	0.239316i
$9$	−0.748511	−	0.663123i	−0.748511	−	0.663123i
$10$	−1.32555	+	0.695701i	−1.32555	+	0.695701i
$11$		0			0		−0.568065	−	0.822984i	$-0.692308\pi$
$11$		0			0		0.568065	+	0.822984i	$0.307692\pi$
$12$		0			0
$13$	1.77091			1.77091			0.885456	−	0.464723i	$-0.153846\pi$
$13$	1.77091			1.77091			0.885456	+	0.464723i	$0.153846\pi$
$14$		0			0
$15$		0			0
$16$	−0.748511	+	0.663123i	−0.748511	+	0.663123i
$17$	−1.32555	−	0.695701i	−1.32555	−	0.695701i	−0.354605	−	0.935016i	$-0.615385\pi$
$17$	−1.32555	−	0.695701i	−1.32555	−	0.695701i	−0.970942	+	0.239316i	$0.923077\pi$
$18$	−0.970942	+	0.239316i	−0.970942	+	0.239316i
$19$		0			0		−0.970942	−	0.239316i	$-0.923077\pi$
$19$		0			0		0.970942	+	0.239316i	$0.0769231\pi$
$20$	−0.180446	+	1.48611i	−0.180446	+	1.48611i
$21$		0			0
$22$		0			0
$23$		0			0		0.748511	−	0.663123i	$-0.230769\pi$
$23$		0			0		−0.748511	+	0.663123i	$0.769231\pi$
$24$		0			0
$25$	0.705010	+	1.02138i	0.705010	+	1.02138i
$26$	1.00599	−	1.45743i	1.00599	−	1.45743i
$27$		0			0
$28$		0			0
$29$	1.00599	−	0.527986i	1.00599	−	0.527986i	0.120537	−	0.992709i	$-0.461538\pi$
$29$	1.00599	−	0.527986i	1.00599	−	0.527986i	0.885456	+	0.464723i	$0.153846\pi$
$30$		0			0
$31$		0			0		0.120537	−	0.992709i	$-0.461538\pi$
$31$		0			0		−0.120537	+	0.992709i	$0.538462\pi$
$32$	0.120537	+	0.992709i	0.120537	+	0.992709i
$33$		0			0
$34$	−1.32555	+	0.695701i	−1.32555	+	0.695701i
$35$		0			0
$36$	−0.354605	+	0.935016i	−0.354605	+	0.935016i
$37$	1.56806	−	0.822984i	1.56806	−	0.822984i	0.568065	−	0.822984i	$-0.307692\pi$
$37$	1.56806	−	0.822984i	1.56806	−	0.822984i	1.00000			$0$
$38$		0			0
$39$		0			0
$40$	1.12054	+	0.992709i	1.12054	+	0.992709i
$41$	1.12054	+	0.992709i	1.12054	+	0.992709i	1.00000			$0$
$41$	1.12054	+	0.992709i	1.12054	+	0.992709i	0.120537	+	0.992709i	$0.461538\pi$
$42$		0			0
$43$		0			0		−0.354605	−	0.935016i	$-0.615385\pi$
$43$		0			0		0.354605	+	0.935016i	$0.384615\pi$
$44$		0			0
$45$	0.530851	+	1.39974i	0.530851	+	1.39974i
$46$		0			0
$47$		0			0		−0.885456	−	0.464723i	$-0.846154\pi$
$47$		0			0		0.885456	+	0.464723i	$0.153846\pi$
$48$		0			0
$49$	−0.748511	−	0.663123i	−0.748511	−	0.663123i
$50$	1.24107			1.24107
$51$		0			0
$52$	−0.627974	−	1.65583i	−0.627974	−	1.65583i
$53$	0.688601	+	0.169725i	0.688601	+	0.169725i	0.568065	−	0.822984i	$-0.307692\pi$
$53$	0.688601	+	0.169725i	0.688601	+	0.169725i	0.120537	+	0.992709i	$0.461538\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	0.136945	−	1.12785i	0.136945	−	1.12785i
$59$		0			0		0.970942	−	0.239316i	$-0.0769231\pi$
$59$		0			0		−0.970942	+	0.239316i	$0.923077\pi$
$60$		0			0
$61$	−0.234068	−	0.0576926i	−0.234068	−	0.0576926i	0.120537	−	0.992709i	$-0.461538\pi$
$61$	−0.234068	−	0.0576926i	−0.234068	−	0.0576926i	−0.354605	+	0.935016i	$0.615385\pi$
$62$		0			0
$63$		0			0
$64$	0.885456	+	0.464723i	0.885456	+	0.464723i
$65$	−2.34743	−	1.23202i	−2.34743	−	1.23202i
$66$		0			0
$67$		0			0		−0.970942	−	0.239316i	$-0.923077\pi$
$67$		0			0		0.970942	+	0.239316i	$0.0769231\pi$
$68$	−0.180446	+	1.48611i	−0.180446	+	1.48611i
$69$		0			0
$70$		0			0
$71$		0			0		−0.970942	−	0.239316i	$-0.923077\pi$
$71$		0			0		0.970942	+	0.239316i	$0.0769231\pi$
$72$	0.568065	+	0.822984i	0.568065	+	0.822984i
$73$	−0.402877	+	1.06230i	−0.402877	+	1.06230i	0.568065	+	0.822984i	$0.307692\pi$
$73$	−0.402877	+	1.06230i	−0.402877	+	1.06230i	−0.970942	+	0.239316i	$0.923077\pi$
$74$	0.213460	−	1.75800i	0.213460	−	1.75800i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.568065	−	0.822984i	$-0.692308\pi$
$79$		0			0		0.568065	+	0.822984i	$0.307692\pi$
$80$	1.45352	−	0.358261i	1.45352	−	0.358261i
$81$	0.120537	+	0.992709i	0.120537	+	0.992709i
$82$	1.45352	−	0.358261i	1.45352	−	0.358261i
$83$		0			0		0.120537	−	0.992709i	$-0.461538\pi$
$83$		0			0		−0.120537	+	0.992709i	$0.538462\pi$
$84$		0			0
$85$	1.27307	+	1.84437i	1.27307	+	1.84437i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.234068	+	1.92773i	−0.234068	+	1.92773i	0.120537	+	0.992709i	$0.461538\pi$
$89$	−0.234068	+	1.92773i	−0.234068	+	1.92773i	−0.354605	+	0.935016i	$0.615385\pi$
$90$	1.45352	+	0.358261i	1.45352	+	0.358261i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−1.71945	−	0.902438i	−1.71945	−	0.902438i	−0.970942	−	0.239316i	$-0.923077\pi$
$97$	−1.71945	−	0.902438i	−1.71945	−	0.902438i	−0.748511	−	0.663123i	$-0.769231\pi$
$98$	−0.970942	+	0.239316i	−0.970942	+	0.239316i
$99$		0			0
$100$	0.705010	−	1.02138i	0.705010	−	1.02138i
$101$	1.00599	−	1.45743i	1.00599	−	1.45743i	0.120537	−	0.992709i	$-0.461538\pi$
$101$	1.00599	−	1.45743i	1.00599	−	1.45743i	0.885456	−	0.464723i	$-0.153846\pi$
$102$		0			0
$103$		0			0		0.120537	−	0.992709i	$-0.461538\pi$
$103$		0			0		−0.120537	+	0.992709i	$0.538462\pi$
$104$	−1.71945	−	0.423807i	−1.71945	−	0.423807i
$105$		0			0
$106$	0.530851	−	0.470293i	0.530851	−	0.470293i
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$		0			0
$109$	−0.402877	−	1.06230i	−0.402877	−	1.06230i	−0.970942	−	0.239316i	$-0.923077\pi$
$109$	−0.402877	−	1.06230i	−0.402877	−	1.06230i	0.568065	−	0.822984i	$-0.307692\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.402877	+	0.583668i	−0.402877	+	0.583668i	−0.970942	−	0.239316i	$-0.923077\pi$
$113$	−0.402877	+	0.583668i	−0.402877	+	0.583668i	0.568065	+	0.822984i	$0.307692\pi$
$114$		0			0
$115$		0			0
$116$	−0.850405	−	0.753393i	−0.850405	−	0.753393i
$117$	−1.32555	−	1.17433i	−1.32555	−	1.17433i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.354605	+	0.935016i	−0.354605	+	0.935016i
$122$	−0.180446	+	0.159861i	−0.180446	+	0.159861i
$123$		0			0
$124$		0			0
$125$	−0.0435007	−	0.358261i	−0.0435007	−	0.358261i
$126$		0			0
$127$		0			0		−0.120537	−	0.992709i	$-0.538462\pi$
$127$		0			0		0.120537	+	0.992709i	$0.461538\pi$
$128$	0.885456	−	0.464723i	0.885456	−	0.464723i
$129$		0			0
$130$	−2.34743	+	1.23202i	−2.34743	+	1.23202i
$131$		0			0		0.568065	−	0.822984i	$-0.307692\pi$
$131$		0			0		−0.568065	+	0.822984i	$0.692308\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	1.12054	+	0.992709i	1.12054	+	0.992709i
$137$	0.213460	−	1.75800i	0.213460	−	1.75800i	−0.354605	−	0.935016i	$-0.615385\pi$
$137$	0.213460	−	1.75800i	0.213460	−	1.75800i	0.568065	−	0.822984i	$-0.307692\pi$
$138$		0			0
$139$		0			0		0.970942	−	0.239316i	$-0.0769231\pi$
$139$		0			0		−0.970942	+	0.239316i	$0.923077\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	1.00000			1.00000
$145$	−1.70081			−1.70081
$146$	0.645395	+	0.935016i	0.645395	+	0.935016i
$147$		0			0
$148$	−1.32555	−	1.17433i	−1.32555	−	1.17433i
$149$	0.688601	+	0.169725i	0.688601	+	0.169725i	0.568065	−	0.822984i	$-0.307692\pi$
$149$	0.688601	+	0.169725i	0.688601	+	0.169725i	0.120537	+	0.992709i	$0.461538\pi$
$150$		0			0
$151$		0			0		−0.568065	−	0.822984i	$-0.692308\pi$
$151$		0			0		0.568065	+	0.822984i	$0.307692\pi$
$152$		0			0
$153$	0.530851	+	1.39974i	0.530851	+	1.39974i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	1.00000			1.00000
$157$	1.00000			1.00000
$158$		0			0
$159$		0			0
$160$	0.530851	−	1.39974i	0.530851	−	1.39974i
$161$		0			0
$162$	0.885456	+	0.464723i	0.885456	+	0.464723i
$163$		0			0		−0.568065	−	0.822984i	$-0.692308\pi$
$163$		0			0		0.568065	+	0.822984i	$0.307692\pi$
$164$	0.530851	−	1.39974i	0.530851	−	1.39974i
$165$		0			0
$166$		0			0
$167$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$167$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$168$		0			0
$169$	2.13613			2.13613
$170$	2.24107			2.24107
$171$		0			0
$172$		0			0
$173$	−1.49702	+	1.32625i	−1.49702	+	1.32625i	−0.748511	+	0.663123i	$0.769231\pi$
$173$	−1.49702	+	1.32625i	−1.49702	+	1.32625i	−0.748511	+	0.663123i	$0.769231\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	1.45352	+	1.28771i	1.45352	+	1.28771i
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$	1.12054	−	0.992709i	1.12054	−	0.992709i
$181$	−1.10312	+	1.59814i	−1.10312	+	1.59814i	−0.354605	+	0.935016i	$0.615385\pi$
$181$	−1.10312	+	1.59814i	−1.10312	+	1.59814i	−0.748511	+	0.663123i	$0.769231\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.65109			−2.65109
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$191$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$192$		0			0
$193$	0.688601	−	1.81569i	0.688601	−	1.81569i	0.120537	−	0.992709i	$-0.461538\pi$
$193$	0.688601	−	1.81569i	0.688601	−	1.81569i	0.568065	−	0.822984i	$-0.307692\pi$
$194$	−1.71945	+	0.902438i	−1.71945	+	0.902438i
$195$		0			0
$196$	−0.354605	+	0.935016i	−0.354605	+	0.935016i
$197$	0.530851	+	0.470293i	0.530851	+	0.470293i	0.885456	−	0.464723i	$-0.153846\pi$
$197$	0.530851	+	0.470293i	0.530851	+	0.470293i	−0.354605	+	0.935016i	$0.615385\pi$
$198$		0			0
$199$		0			0		0.970942	−	0.239316i	$-0.0769231\pi$
$199$		0			0		−0.970942	+	0.239316i	$0.923077\pi$
$200$	−0.440091	−	1.16042i	−0.440091	−	1.16042i
$201$		0			0
$202$	−0.627974	−	1.65583i	−0.627974	−	1.65583i
$203$		0			0
$204$		0			0
$205$	−0.794696	−	2.09544i	−0.794696	−	2.09544i
$206$		0			0
$207$		0			0
$208$	−1.32555	+	1.17433i	−1.32555	+	1.17433i
$209$		0			0
$210$		0			0
$211$		0			0		0.120537	−	0.992709i	$-0.461538\pi$
$211$		0			0		−0.120537	+	0.992709i	$0.538462\pi$
$212$	−0.0854858	−	0.704039i	−0.0854858	−	0.704039i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−1.10312	−	0.271894i	−1.10312	−	0.271894i
$219$		0			0
$220$		0			0
$221$	−2.34743	−	1.23202i	−2.34743	−	1.23202i
$222$		0			0
$223$		0			0		0.354605	−	0.935016i	$-0.384615\pi$
$223$		0			0		−0.354605	+	0.935016i	$0.615385\pi$
$224$		0			0
$225$	0.149595	−	1.23202i	0.149595	−	1.23202i
$226$	0.251489	+	0.663123i	0.251489	+	0.663123i
$227$		0			0		−0.120537	−	0.992709i	$-0.538462\pi$
$227$		0			0		0.120537	+	0.992709i	$0.461538\pi$
$228$		0			0
$229$	1.00599	+	1.45743i	1.00599	+	1.45743i	0.885456	+	0.464723i	$0.153846\pi$
$229$	1.00599	+	1.45743i	1.00599	+	1.45743i	0.120537	+	0.992709i	$0.461538\pi$
$230$		0			0
$231$		0			0
$232$	−1.10312	+	0.271894i	−1.10312	+	0.271894i
$233$	−0.0854858	−	0.704039i	−0.0854858	−	0.704039i	−0.970942	−	0.239316i	$-0.923077\pi$
$233$	−0.0854858	−	0.704039i	−0.0854858	−	0.704039i	0.885456	−	0.464723i	$-0.153846\pi$
$234$	−1.71945	+	0.423807i	−1.71945	+	0.423807i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.970942	−	0.239316i	$-0.0769231\pi$
$239$		0			0		−0.970942	+	0.239316i	$0.923077\pi$
$240$		0			0
$241$	−0.402877	+	1.06230i	−0.402877	+	1.06230i	0.568065	+	0.822984i	$0.307692\pi$
$241$	−0.402877	+	1.06230i	−0.402877	+	1.06230i	−0.970942	+	0.239316i	$0.923077\pi$
$242$	0.568065	+	0.822984i	0.568065	+	0.822984i
$243$		0			0
$244$	0.0290582	+	0.239316i	0.0290582	+	0.239316i
$245$	0.530851	+	1.39974i	0.530851	+	1.39974i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	−0.319554	−	0.167715i	−0.319554	−	0.167715i
$251$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$251$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.120537	−	0.992709i	0.120537	−	0.992709i
$257$	0.645395	−	0.935016i	0.645395	−	0.935016i	−0.354605	−	0.935016i	$-0.615385\pi$
$257$	0.645395	−	0.935016i	0.645395	−	0.935016i	1.00000			$0$
$258$		0			0
$259$		0			0
$260$	−0.319554	+	2.63176i	−0.319554	+	2.63176i
$261$	−1.10312	−	0.271894i	−1.10312	−	0.271894i
$262$		0			0
$263$		0			0		0.748511	−	0.663123i	$-0.230769\pi$
$263$		0			0		−0.748511	+	0.663123i	$0.769231\pi$
$264$		0			0
$265$	−0.794696	−	0.704039i	−0.794696	−	0.704039i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	0.688601	+	1.81569i	0.688601	+	1.81569i	0.568065	+	0.822984i	$0.307692\pi$
$269$	0.688601	+	1.81569i	0.688601	+	1.81569i	0.120537	+	0.992709i	$0.461538\pi$
$270$		0			0
$271$		0			0		−0.354605	−	0.935016i	$-0.615385\pi$
$271$		0			0		0.354605	+	0.935016i	$0.384615\pi$
$272$	1.45352	−	0.358261i	1.45352	−	0.358261i
$273$		0			0
$274$	−1.32555	−	1.17433i	−1.32555	−	1.17433i
$275$		0			0
$276$		0			0
$277$	−1.71945	+	0.902438i	−1.71945	+	0.902438i	−0.748511	+	0.663123i	$0.769231\pi$
$277$	−1.71945	+	0.902438i	−1.71945	+	0.902438i	−0.970942	+	0.239316i	$0.923077\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.88546	−	0.464723i	1.88546	−	0.464723i	0.885456	−	0.464723i	$-0.153846\pi$
$281$	1.88546	−	0.464723i	1.88546	−	0.464723i	1.00000			$0$
$282$		0			0
$283$		0			0		0.120537	−	0.992709i	$-0.461538\pi$
$283$		0			0		−0.120537	+	0.992709i	$0.538462\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.568065	−	0.822984i	0.568065	−	0.822984i
$289$	0.705010	+	1.02138i	0.705010	+	1.02138i
$290$	−0.966170	+	1.39974i	−0.966170	+	1.39974i
$291$		0			0
$292$	1.13613			1.13613
$293$	−1.49702	−	1.32625i	−1.49702	−	1.32625i	−0.748511	−	0.663123i	$-0.769231\pi$
$293$	−1.49702	−	1.32625i	−1.49702	−	1.32625i	−0.748511	−	0.663123i	$-0.769231\pi$
$294$		0			0
$295$		0			0
$296$	−1.71945	+	0.423807i	−1.71945	+	0.423807i
$297$		0			0
$298$	0.530851	−	0.470293i	0.530851	−	0.470293i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.270132	+	0.239316i	0.270132	+	0.239316i
$306$	1.45352	+	0.358261i	1.45352	+	0.358261i
$307$		0			0		0.354605	−	0.935016i	$-0.384615\pi$
$307$		0			0		−0.354605	+	0.935016i	$0.615385\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.354605	−	0.935016i	$-0.384615\pi$
$311$		0			0		−0.354605	+	0.935016i	$0.615385\pi$
$312$		0			0
$313$	0.241073			0.241073			0.120537	−	0.992709i	$-0.461538\pi$
$313$	0.241073			0.241073			0.120537	+	0.992709i	$0.461538\pi$
$314$	0.568065	−	0.822984i	0.568065	−	0.822984i
$315$		0			0
$316$		0			0
$317$	−0.0854858	+	0.225408i	−0.0854858	+	0.225408i	−0.970942	−	0.239316i	$-0.923077\pi$
$317$	−0.0854858	+	0.225408i	−0.0854858	+	0.225408i	0.885456	+	0.464723i	$0.153846\pi$
$318$		0			0
$319$		0			0
$320$	−0.850405	−	1.23202i	−0.850405	−	1.23202i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.885456	−	0.464723i	0.885456	−	0.464723i
$325$	1.24851	+	1.80878i	1.24851	+	1.80878i
$326$		0			0
$327$		0			0
$328$	−0.850405	−	1.23202i	−0.850405	−	1.23202i
$329$		0			0
$330$		0			0
$331$		0			0		−0.885456	−	0.464723i	$-0.846154\pi$
$331$		0			0		0.885456	+	0.464723i	$0.153846\pi$
$332$		0			0
$333$	−1.71945	−	0.423807i	−1.71945	−	0.423807i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.32555	+	1.17433i	−1.32555	+	1.17433i	−0.354605	+	0.935016i	$0.615385\pi$
$337$	−1.32555	+	1.17433i	−1.32555	+	1.17433i	−0.970942	+	0.239316i	$0.923077\pi$
$338$	1.21346	−	1.75800i	1.21346	−	1.75800i
$339$		0			0
$340$	1.27307	−	1.84437i	1.27307	−	1.84437i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	0.241073	+	1.98542i	0.241073	+	1.98542i
$347$		0			0		0.970942	−	0.239316i	$-0.0769231\pi$
$347$		0			0		−0.970942	+	0.239316i	$0.923077\pi$
$348$		0			0
$349$	1.12054	−	0.992709i	1.12054	−	0.992709i	0.120537	−	0.992709i	$-0.461538\pi$
$349$	1.12054	−	0.992709i	1.12054	−	0.992709i	1.00000			$0$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.251489	−	0.663123i	0.251489	−	0.663123i	−0.748511	−	0.663123i	$-0.769231\pi$
$353$	0.251489	−	0.663123i	0.251489	−	0.663123i	1.00000			$0$
$354$		0			0
$355$		0			0
$356$	1.88546	−	0.464723i	1.88546	−	0.464723i
$357$		0			0
$358$		0			0
$359$		0			0		−0.354605	−	0.935016i	$-0.615385\pi$
$359$		0			0		0.354605	+	0.935016i	$0.384615\pi$
$360$	−0.180446	−	1.48611i	−0.180446	−	1.48611i
$361$	0.885456	+	0.464723i	0.885456	+	0.464723i
$362$	0.688601	+	1.81569i	0.688601	+	1.81569i
$363$		0			0
$364$		0			0
$365$	1.27307	−	1.12785i	1.27307	−	1.12785i
$366$		0			0
$367$		0			0		−0.970942	−	0.239316i	$-0.923077\pi$
$367$		0			0		0.970942	+	0.239316i	$0.0769231\pi$
$368$		0			0
$369$	−0.180446	−	1.48611i	−0.180446	−	1.48611i
$370$	−1.50599	+	2.18181i	−1.50599	+	2.18181i
$371$		0			0
$372$		0			0
$373$	−0.234068	+	0.0576926i	−0.234068	+	0.0576926i	−0.354605	−	0.935016i	$-0.615385\pi$
$373$	−0.234068	+	0.0576926i	−0.234068	+	0.0576926i	0.120537	+	0.992709i	$0.461538\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.78152	−	0.935016i	1.78152	−	0.935016i
$378$		0			0
$379$		0			0		−0.885456	−	0.464723i	$-0.846154\pi$
$379$		0			0		0.885456	+	0.464723i	$0.153846\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.354605	−	0.935016i	$-0.615385\pi$
$383$		0			0		0.354605	+	0.935016i	$0.384615\pi$
$384$		0			0
$385$		0			0
$386$	−1.10312	−	1.59814i	−1.10312	−	1.59814i
$387$		0			0
$388$	−0.234068	+	1.92773i	−0.234068	+	1.92773i
$389$	0.688601	−	0.169725i	0.688601	−	0.169725i	0.120537	−	0.992709i	$-0.461538\pi$
$389$	0.688601	−	0.169725i	0.688601	−	0.169725i	0.568065	+	0.822984i	$0.307692\pi$
$390$		0			0
$391$		0			0
$392$	0.568065	+	0.822984i	0.568065	+	0.822984i
$393$		0			0
$394$	0.688601	−	0.169725i	0.688601	−	0.169725i
$395$		0			0
$396$		0			0
$397$	−0.0854858	+	0.704039i	−0.0854858	+	0.704039i	0.885456	+	0.464723i	$0.153846\pi$
$397$	−0.0854858	+	0.704039i	−0.0854858	+	0.704039i	−0.970942	+	0.239316i	$0.923077\pi$
$398$		0			0
$399$		0			0
$400$	−1.20501	−	0.297008i	−1.20501	−	0.297008i
$401$	0.136945	+	1.12785i	0.136945	+	1.12785i	0.885456	+	0.464723i	$0.153846\pi$
$401$	0.136945	+	1.12785i	0.136945	+	1.12785i	−0.748511	+	0.663123i	$0.769231\pi$
$402$		0			0
$403$		0			0
$404$	−1.71945	−	0.423807i	−1.71945	−	0.423807i
$405$	0.530851	−	1.39974i	0.530851	−	1.39974i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	1.45352	+	1.28771i	1.45352	+	1.28771i	0.885456	+	0.464723i	$0.153846\pi$
$409$	1.45352	+	1.28771i	1.45352	+	1.28771i	0.568065	+	0.822984i	$0.307692\pi$
$410$	−2.17595	−	0.536324i	−2.17595	−	0.536324i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	0.213460	+	1.75800i	0.213460	+	1.75800i
$417$		0			0
$418$		0			0
$419$		0			0		−0.354605	−	0.935016i	$-0.615385\pi$
$419$		0			0		0.354605	+	0.935016i	$0.384615\pi$
$420$		0			0
$421$	1.13613			1.13613			0.568065	−	0.822984i	$-0.307692\pi$
$421$	1.13613			1.13613			0.568065	+	0.822984i	$0.307692\pi$
$422$		0			0
$423$		0			0
$424$	−0.627974	−	0.329586i	−0.627974	−	0.329586i
$425$	−0.223947	−	1.84437i	−0.223947	−	1.84437i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.748511	−	0.663123i	$-0.769231\pi$
$431$		0			0		0.748511	+	0.663123i	$0.230769\pi$
$432$		0			0
$433$	−0.180446	+	0.159861i	−0.180446	+	0.159861i	−0.748511	−	0.663123i	$-0.769231\pi$
$433$	−0.180446	+	0.159861i	−0.180446	+	0.159861i	0.568065	+	0.822984i	$0.307692\pi$
$434$		0			0
$435$		0			0
$436$	−0.850405	+	0.753393i	−0.850405	+	0.753393i
$437$		0			0
$438$		0			0
$439$		0			0		−0.120537	−	0.992709i	$-0.538462\pi$
$439$		0			0		0.120537	+	0.992709i	$0.461538\pi$
$440$		0			0
$441$	0.120537	+	0.992709i	0.120537	+	0.992709i
$442$	−2.34743	+	1.23202i	−2.34743	+	1.23202i
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$		0			0
$445$	1.65139	−	2.39245i	1.65139	−	2.39245i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	1.77091			1.77091			0.885456	−	0.464723i	$-0.153846\pi$
$449$	1.77091			1.77091			0.885456	+	0.464723i	$0.153846\pi$
$450$	−0.928957	−	0.822984i	−0.928957	−	0.822984i
$451$		0			0
$452$	0.688601	+	0.169725i	0.688601	+	0.169725i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.10312	−	1.59814i	−1.10312	−	1.59814i	−0.748511	−	0.663123i	$-0.769231\pi$
$457$	−1.10312	−	1.59814i	−1.10312	−	1.59814i	−0.354605	−	0.935016i	$-0.615385\pi$
$458$	1.77091			1.77091
$459$		0			0
$460$		0			0
$461$	1.00599	−	0.527986i	1.00599	−	0.527986i	0.120537	−	0.992709i	$-0.461538\pi$
$461$	1.00599	−	0.527986i	1.00599	−	0.527986i	0.885456	+	0.464723i	$0.153846\pi$
$462$		0			0
$463$		0			0		−0.970942	−	0.239316i	$-0.923077\pi$
$463$		0			0		0.970942	+	0.239316i	$0.0769231\pi$
$464$	−0.402877	+	1.06230i	−0.402877	+	1.06230i
$465$		0			0
$466$	−0.627974	−	0.329586i	−0.627974	−	0.329586i
$467$		0			0		−0.354605	−	0.935016i	$-0.615385\pi$
$467$		0			0		0.354605	+	0.935016i	$0.384615\pi$
$468$	−0.627974	+	1.65583i	−0.627974	+	1.65583i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.402877	−	0.583668i	−0.402877	−	0.583668i
$478$		0			0
$479$		0			0		−0.970942	−	0.239316i	$-0.923077\pi$
$479$		0			0		0.970942	+	0.239316i	$0.0769231\pi$
$480$		0			0
$481$	2.77690	−	1.45743i	2.77690	−	1.45743i
$482$	0.645395	+	0.935016i	0.645395	+	0.935016i
$483$		0			0
$484$	1.00000			1.00000
$485$	1.65139	+	2.39245i	1.65139	+	2.39245i
$486$		0			0
$487$		0			0		0.748511	−	0.663123i	$-0.230769\pi$
$487$		0			0		−0.748511	+	0.663123i	$0.769231\pi$
$488$	0.213460	+	0.112032i	0.213460	+	0.112032i
$489$		0			0
$490$	1.45352	+	0.358261i	1.45352	+	0.358261i
$491$		0			0		0.120537	−	0.992709i	$-0.461538\pi$
$491$		0			0		−0.120537	+	0.992709i	$0.538462\pi$
$492$		0			0
$493$	−1.70081			−1.70081
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$	−0.319554	+	0.167715i	−0.319554	+	0.167715i
$501$		0			0
$502$		0			0
$503$		0			0		−0.120537	−	0.992709i	$-0.538462\pi$
$503$		0			0		0.120537	+	0.992709i	$0.461538\pi$
$504$		0			0
$505$	−2.34743	+	1.23202i	−2.34743	+	1.23202i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−0.180446	+	0.159861i	−0.180446	+	0.159861i	−0.748511	−	0.663123i	$-0.769231\pi$
$509$	−0.180446	+	0.159861i	−0.180446	+	0.159861i	0.568065	+	0.822984i	$0.307692\pi$
$510$		0			0
$511$		0			0
$512$	−0.748511	−	0.663123i	−0.748511	−	0.663123i
$513$		0			0
$514$	−0.402877	−	1.06230i	−0.402877	−	1.06230i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	1.98437	+	1.75800i	1.98437	+	1.75800i
$521$	−0.709210			−0.709210			−0.354605	−	0.935016i	$-0.615385\pi$
$521$	−0.709210			−0.709210			−0.354605	+	0.935016i	$0.615385\pi$
$522$	−0.850405	+	0.753393i	−0.850405	+	0.753393i
$523$		0			0		−0.354605	−	0.935016i	$-0.615385\pi$
$523$		0			0		0.354605	+	0.935016i	$0.384615\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	0.120537	−	0.992709i	0.120537	−	0.992709i
$530$	−1.03085	+	0.254082i	−1.03085	+	0.254082i
$531$		0			0
$532$		0			0
$533$	1.98437	+	1.75800i	1.98437	+	1.75800i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	1.88546	+	0.464723i	1.88546	+	0.464723i
$539$		0			0
$540$		0			0
$541$	0.0290582	+	0.239316i	0.0290582	+	0.239316i	1.00000			$0$
$541$	0.0290582	+	0.239316i	0.0290582	+	0.239316i	−0.970942	+	0.239316i	$0.923077\pi$
$542$		0			0
$543$		0			0
$544$	0.530851	−	1.39974i	0.530851	−	1.39974i
$545$	−0.205010	+	1.68841i	−0.205010	+	1.68841i
$546$		0			0
$547$		0			0		−0.120537	−	0.992709i	$-0.538462\pi$
$547$		0			0		0.120537	+	0.992709i	$0.461538\pi$
$548$	−1.71945	+	0.423807i	−1.71945	+	0.423807i
$549$	0.136945	+	0.198399i	0.136945	+	0.198399i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−0.234068	+	1.92773i	−0.234068	+	1.92773i
$555$		0			0
$556$		0			0
$557$	1.45352	+	0.358261i	1.45352	+	0.358261i	0.885456	−	0.464723i	$-0.153846\pi$
$557$	1.45352	+	0.358261i	1.45352	+	0.358261i	0.568065	+	0.822984i	$0.307692\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.688601	−	1.81569i	0.688601	−	1.81569i
$563$		0			0		−0.885456	−	0.464723i	$-0.846154\pi$
$563$		0			0		0.885456	+	0.464723i	$0.153846\pi$
$564$		0			0
$565$	0.940091	−	0.493398i	0.940091	−	0.493398i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−1.94188	+	0.478631i	−1.94188	+	0.478631i	−0.970942	+	0.239316i	$0.923077\pi$
$569$	−1.94188	+	0.478631i	−1.94188	+	0.478631i	−0.970942	+	0.239316i	$0.923077\pi$
$570$		0			0
$571$		0			0		0.568065	−	0.822984i	$-0.307692\pi$
$571$		0			0		−0.568065	+	0.822984i	$0.692308\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.354605	−	0.935016i	−0.354605	−	0.935016i
$577$	−1.49702	+	1.32625i	−1.49702	+	1.32625i	−0.748511	+	0.663123i	$0.769231\pi$
$577$	−1.49702	+	1.32625i	−1.49702	+	1.32625i	−0.748511	+	0.663123i	$0.769231\pi$
$578$	1.24107			1.24107
$579$		0			0
$580$	0.603116	+	1.59029i	0.603116	+	1.59029i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	0.645395	−	0.935016i	0.645395	−	0.935016i
$585$	0.940091	+	2.47882i	0.940091	+	2.47882i
$586$	−1.94188	+	0.478631i	−1.94188	+	0.478631i
$587$		0			0		−0.748511	−	0.663123i	$-0.769231\pi$
$587$		0			0		0.748511	+	0.663123i	$0.230769\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.627974	+	1.65583i	−0.627974	+	1.65583i
$593$	0.530851	−	0.470293i	0.530851	−	0.470293i	−0.354605	−	0.935016i	$-0.615385\pi$
$593$	0.530851	−	0.470293i	0.530851	−	0.470293i	0.885456	+	0.464723i	$0.153846\pi$
$594$		0			0
$595$		0			0
$596$	−0.0854858	−	0.704039i	−0.0854858	−	0.704039i
$597$		0			0
$598$		0			0
$599$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$599$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$600$		0			0
$601$	−0.627974	+	0.329586i	−0.627974	+	0.329586i	−0.748511	−	0.663123i	$-0.769231\pi$
$601$	−0.627974	+	0.329586i	−0.627974	+	0.329586i	0.120537	+	0.992709i	$0.461538\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.12054	−	0.992709i	1.12054	−	0.992709i
$606$		0			0
$607$		0			0		−0.748511	−	0.663123i	$-0.769231\pi$
$607$		0			0		0.748511	+	0.663123i	$0.230769\pi$
$608$		0			0
$609$		0			0
$610$	0.350405	−	0.0863671i	0.350405	−	0.0863671i
$611$		0			0
$612$	1.12054	−	0.992709i	1.12054	−	0.992709i
$613$	1.12054	−	0.992709i	1.12054	−	0.992709i	0.120537	−	0.992709i	$-0.461538\pi$
$613$	1.12054	−	0.992709i	1.12054	−	0.992709i	1.00000			$0$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.136945	+	0.198399i	0.136945	+	0.198399i	0.885456	−	0.464723i	$-0.153846\pi$
$617$	0.136945	+	0.198399i	0.136945	+	0.198399i	−0.748511	+	0.663123i	$0.769231\pi$
$618$		0			0
$619$		0			0		−0.748511	−	0.663123i	$-0.769231\pi$
$619$		0			0		0.748511	+	0.663123i	$0.230769\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.248511	−	0.655269i	0.248511	−	0.655269i
$626$	0.136945	−	0.198399i	0.136945	−	0.198399i
$627$		0			0
$628$	−0.354605	−	0.935016i	−0.354605	−	0.935016i
$629$	−2.65109			−2.65109
$630$		0			0
$631$		0			0		0.354605	−	0.935016i	$-0.384615\pi$
$631$		0			0		−0.354605	+	0.935016i	$0.615385\pi$
$632$		0			0
$633$		0			0
$634$	0.136945	+	0.198399i	0.136945	+	0.198399i
$635$		0			0
$636$		0			0
$637$	−1.32555	−	1.17433i	−1.32555	−	1.17433i
$638$		0			0
$639$		0			0
$640$	−1.49702			−1.49702
$641$	−1.94188			−1.94188			−0.970942	−	0.239316i	$-0.923077\pi$
$641$	−1.94188			−1.94188			−0.970942	+	0.239316i	$0.923077\pi$
$642$		0			0
$643$		0			0		0.748511	−	0.663123i	$-0.230769\pi$
$643$		0			0		−0.748511	+	0.663123i	$0.769231\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.970942	−	0.239316i	$-0.923077\pi$
$647$		0			0		0.970942	+	0.239316i	$0.0769231\pi$
$648$	0.120537	−	0.992709i	0.120537	−	0.992709i
$649$		0			0
$650$	2.19783			2.19783
$651$		0			0
$652$		0			0
$653$	0.645395	+	0.935016i	0.645395	+	0.935016i	1.00000			$0$
$653$	0.645395	+	0.935016i	0.645395	+	0.935016i	−0.354605	+	0.935016i	$0.615385\pi$
$654$		0			0
$655$		0			0
$656$	−1.49702			−1.49702
$657$	1.00599	−	0.527986i	1.00599	−	0.527986i
$658$		0			0
$659$		0			0		0.120537	−	0.992709i	$-0.461538\pi$
$659$		0			0		−0.120537	+	0.992709i	$0.538462\pi$
$660$		0			0
$661$	−1.10312	+	0.271894i	−1.10312	+	0.271894i	−0.748511	−	0.663123i	$-0.769231\pi$
$661$	−1.10312	+	0.271894i	−1.10312	+	0.271894i	−0.354605	+	0.935016i	$0.615385\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−1.32555	+	1.17433i	−1.32555	+	1.17433i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.251489	+	0.663123i	0.251489	+	0.663123i	1.00000			$0$
$673$	0.251489	+	0.663123i	0.251489	+	0.663123i	−0.748511	+	0.663123i	$0.769231\pi$
$674$	0.213460	+	1.75800i	0.213460	+	1.75800i
$675$		0			0
$676$	−0.757482	−	1.99732i	−0.757482	−	1.99732i
$677$	−1.32555	−	1.17433i	−1.32555	−	1.17433i	−0.970942	−	0.239316i	$-0.923077\pi$
$677$	−1.32555	−	1.17433i	−1.32555	−	1.17433i	−0.354605	−	0.935016i	$-0.615385\pi$
$678$		0			0
$679$		0			0
$680$	−0.794696	−	2.09544i	−0.794696	−	2.09544i
$681$		0			0
$682$		0			0
$683$		0			0		−0.120537	−	0.992709i	$-0.538462\pi$
$683$		0			0		0.120537	+	0.992709i	$0.461538\pi$
$684$		0			0
$685$	−1.50599	+	2.18181i	−1.50599	+	2.18181i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.21945	+	0.300568i	1.21945	+	0.300568i
$690$		0			0
$691$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$691$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$692$	1.77091	+	0.929446i	1.77091	+	0.929446i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−0.794696	−	2.09544i	−0.794696	−	2.09544i
$698$	−0.180446	−	1.48611i	−0.180446	−	1.48611i
$699$		0			0
$700$		0			0
$701$	−0.627974	+	1.65583i	−0.627974	+	1.65583i	0.120537	+	0.992709i	$0.461538\pi$
$701$	−0.627974	+	1.65583i	−0.627974	+	1.65583i	−0.748511	+	0.663123i	$0.769231\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−0.402877	−	0.583668i	−0.402877	−	0.583668i
$707$		0			0
$708$		0			0
$709$	−0.180446	−	1.48611i	−0.180446	−	1.48611i	−0.748511	−	0.663123i	$-0.769231\pi$
$709$	−0.180446	−	1.48611i	−0.180446	−	1.48611i	0.568065	−	0.822984i	$-0.307692\pi$
$710$		0			0
$711$		0			0
$712$	0.688601	−	1.81569i	0.688601	−	1.81569i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.354605	−	0.935016i	$-0.384615\pi$
$719$		0			0		−0.354605	+	0.935016i	$0.615385\pi$
$720$	−1.32555	−	0.695701i	−1.32555	−	0.695701i
$721$		0			0
$722$	0.885456	−	0.464723i	0.885456	−	0.464723i
$723$		0			0
$724$	1.88546	+	0.464723i	1.88546	+	0.464723i
$725$	1.24851	+	0.655269i	1.24851	+	0.655269i
$726$		0			0
$727$		0			0		0.120537	−	0.992709i	$-0.461538\pi$
$727$		0			0		−0.120537	+	0.992709i	$0.538462\pi$
$728$		0			0
$729$	0.568065	−	0.822984i	0.568065	−	0.822984i
$730$	−0.205010	−	1.68841i	−0.205010	−	1.68841i
$731$		0			0
$732$		0			0
$733$	−0.402877	−	1.06230i	−0.402877	−	1.06230i	−0.970942	−	0.239316i	$-0.923077\pi$
$733$	−0.402877	−	1.06230i	−0.402877	−	1.06230i	0.568065	−	0.822984i	$-0.307692\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	−1.32555	−	0.695701i	−1.32555	−	0.695701i
$739$		0			0		−0.120537	−	0.992709i	$-0.538462\pi$
$739$		0			0		0.120537	+	0.992709i	$0.461538\pi$
$740$	0.940091	+	2.47882i	0.940091	+	2.47882i
$741$		0			0
$742$		0			0
$743$		0			0		0.970942	−	0.239316i	$-0.0769231\pi$
$743$		0			0		−0.970942	+	0.239316i	$0.923077\pi$
$744$		0			0
$745$	−0.794696	−	0.704039i	−0.794696	−	0.704039i
$746$	−0.0854858	+	0.225408i	−0.0854858	+	0.225408i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$751$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$752$		0			0
$753$		0			0
$754$	0.242518	−	1.99732i	0.242518	−	1.99732i
$755$		0			0
$756$		0			0
$757$	−1.49702			−1.49702			−0.748511	−	0.663123i	$-0.769231\pi$
$757$	−1.49702			−1.49702			−0.748511	+	0.663123i	$0.769231\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.850405	+	1.23202i	−0.850405	+	1.23202i	0.120537	+	0.992709i	$0.461538\pi$
$761$	−0.850405	+	1.23202i	−0.850405	+	1.23202i	−0.970942	+	0.239316i	$0.923077\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.270132	−	2.22473i	0.270132	−	2.22473i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−0.180446	+	0.159861i	−0.180446	+	0.159861i	−0.748511	−	0.663123i	$-0.769231\pi$
$769$	−0.180446	+	0.159861i	−0.180446	+	0.159861i	0.568065	+	0.822984i	$0.307692\pi$
$770$		0			0
$771$		0			0
$772$	−1.94188			−1.94188
$773$	1.13613			1.13613			0.568065	−	0.822984i	$-0.307692\pi$
$773$	1.13613			1.13613			0.568065	+	0.822984i	$0.307692\pi$
$774$		0			0
$775$		0			0
$776$	1.45352	+	1.28771i	1.45352	+	1.28771i
$777$		0			0
$778$	0.251489	−	0.663123i	0.251489	−	0.663123i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	1.00000			1.00000
$785$	−1.32555	−	0.695701i	−1.32555	−	0.695701i
$786$		0			0
$787$		0			0		0.568065	−	0.822984i	$-0.307692\pi$
$787$		0			0		−0.568065	+	0.822984i	$0.692308\pi$
$788$	0.251489	−	0.663123i	0.251489	−	0.663123i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−0.414514	−	0.102169i	−0.414514	−	0.102169i
$794$	0.530851	+	0.470293i	0.530851	+	0.470293i
$795$		0			0
$796$		0			0
$797$	−1.94188			−1.94188			−0.970942	−	0.239316i	$-0.923077\pi$
$797$	−1.94188			−1.94188			−0.970942	+	0.239316i	$0.923077\pi$
$798$		0			0
$799$		0			0
$800$	−0.928957	+	0.822984i	−0.928957	+	0.822984i
$801$	1.45352	−	1.28771i	1.45352	−	1.28771i
$802$	1.00599	+	0.527986i	1.00599	+	0.527986i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−1.32555	+	1.17433i	−1.32555	+	1.17433i
$809$	−1.10312	+	1.59814i	−1.10312	+	1.59814i	−0.354605	+	0.935016i	$0.615385\pi$
$809$	−1.10312	+	1.59814i	−1.10312	+	1.59814i	−0.748511	+	0.663123i	$0.769231\pi$
$810$	−0.850405	−	1.23202i	−0.850405	−	1.23202i
$811$		0			0		0.568065	−	0.822984i	$-0.307692\pi$
$811$		0			0		−0.568065	+	0.822984i	$0.692308\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	1.88546	−	0.464723i	1.88546	−	0.464723i
$819$		0			0
$820$	−1.67747	+	1.48611i	−1.67747	+	1.48611i
$821$	−0.0854858	+	0.225408i	−0.0854858	+	0.225408i	−0.970942	−	0.239316i	$-0.923077\pi$
$821$	−0.0854858	+	0.225408i	−0.0854858	+	0.225408i	0.885456	+	0.464723i	$0.153846\pi$
$822$		0			0
$823$		0			0		0.748511	−	0.663123i	$-0.230769\pi$
$823$		0			0		−0.748511	+	0.663123i	$0.769231\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.970942	−	0.239316i	$-0.0769231\pi$
$827$		0			0		−0.970942	+	0.239316i	$0.923077\pi$
$828$		0			0
$829$	0.136945	−	0.198399i	0.136945	−	0.198399i	−0.748511	−	0.663123i	$-0.769231\pi$
$829$	0.136945	−	0.198399i	0.136945	−	0.198399i	0.885456	+	0.464723i	$0.153846\pi$
$830$		0			0
$831$		0			0
$832$	1.56806	+	0.822984i	1.56806	+	0.822984i
$833$	0.530851	+	1.39974i	0.530851	+	1.39974i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.120537	−	0.992709i	$-0.461538\pi$
$839$		0			0		−0.120537	+	0.992709i	$0.538462\pi$
$840$		0			0
$841$	0.165188	−	0.239316i	0.165188	−	0.239316i
$842$	0.645395	−	0.935016i	0.645395	−	0.935016i
$843$		0			0
$844$		0			0
$845$	−2.83154	−	1.48611i	−2.83154	−	1.48611i
$846$		0			0
$847$		0			0
$848$	−0.627974	+	0.329586i	−0.627974	+	0.329586i
$849$		0			0
$850$	−1.64510	−	0.863415i	−1.64510	−	0.863415i
$851$		0			0
$852$		0			0
$853$	0.213460	−	1.75800i	0.213460	−	1.75800i	−0.354605	−	0.935016i	$-0.615385\pi$
$853$	0.213460	−	1.75800i	0.213460	−	1.75800i	0.568065	−	0.822984i	$-0.307692\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.850405	−	1.23202i	−0.850405	−	1.23202i	−0.970942	−	0.239316i	$-0.923077\pi$
$857$	−0.850405	−	1.23202i	−0.850405	−	1.23202i	0.120537	−	0.992709i	$-0.461538\pi$
$858$		0			0
$859$		0			0		0.120537	−	0.992709i	$-0.461538\pi$
$859$		0			0		−0.120537	+	0.992709i	$0.538462\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.568065	−	0.822984i	$-0.692308\pi$
$863$		0			0		0.568065	+	0.822984i	$0.307692\pi$
$864$		0			0
$865$	2.90704	−	0.716521i	2.90704	−	0.716521i
$866$	0.0290582	+	0.239316i	0.0290582	+	0.239316i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.136945	+	1.12785i	0.136945	+	1.12785i
$873$	0.688601	+	1.81569i	0.688601	+	1.81569i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.00599	+	0.527986i	1.00599	+	0.527986i	0.885456	−	0.464723i	$-0.153846\pi$
$877$	1.00599	+	0.527986i	1.00599	+	0.527986i	0.120537	+	0.992709i	$0.461538\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.10312	−	0.271894i	−1.10312	−	0.271894i	−0.354605	−	0.935016i	$-0.615385\pi$
$881$	−1.10312	−	0.271894i	−1.10312	−	0.271894i	−0.748511	+	0.663123i	$0.769231\pi$
$882$	0.885456	+	0.464723i	0.885456	+	0.464723i
$883$		0			0		0.970942	−	0.239316i	$-0.0769231\pi$
$883$		0			0		−0.970942	+	0.239316i	$0.923077\pi$
$884$	−0.319554	+	2.63176i	−0.319554	+	2.63176i
$885$		0			0
$886$		0			0
$887$		0			0		−0.120537	−	0.992709i	$-0.538462\pi$
$887$		0			0		0.120537	+	0.992709i	$0.461538\pi$
$888$		0			0
$889$		0			0
$890$	−1.03085	−	2.71813i	−1.03085	−	2.71813i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	1.00599	−	1.45743i	1.00599	−	1.45743i
$899$		0			0
$900$	−1.20501	+	0.297008i	−1.20501	+	0.297008i
$901$	−0.794696	−	0.704039i	−0.794696	−	0.704039i
$902$		0			0
$903$		0			0
$904$	0.530851	−	0.470293i	0.530851	−	0.470293i
$905$	2.57406	−	1.35097i	2.57406	−	1.35097i
$906$		0			0
$907$		0			0		0.748511	−	0.663123i	$-0.230769\pi$
$907$		0			0		−0.748511	+	0.663123i	$0.769231\pi$
$908$		0			0
$909$	−1.71945	+	0.423807i	−1.71945	+	0.423807i
$910$		0			0
$911$		0			0		0.120537	−	0.992709i	$-0.461538\pi$
$911$		0			0		−0.120537	+	0.992709i	$0.538462\pi$
$912$		0			0
$913$		0			0
$914$	−1.94188			−1.94188
$915$		0			0
$916$	1.00599	−	1.45743i	1.00599	−	1.45743i
$917$		0			0
$918$		0			0
$919$		0			0		0.748511	−	0.663123i	$-0.230769\pi$
$919$		0			0		−0.748511	+	0.663123i	$0.769231\pi$
$920$		0			0
$921$		0			0
$922$	0.136945	−	1.12785i	0.136945	−	1.12785i
$923$		0			0
$924$		0			0
$925$	1.94608	+	1.02138i	1.94608	+	1.02138i
$926$		0			0
$927$		0			0
$928$	0.645395	+	0.935016i	0.645395	+	0.935016i
$929$	−1.49702			−1.49702			−0.748511	−	0.663123i	$-0.769231\pi$
$929$	−1.49702			−1.49702			−0.748511	+	0.663123i	$0.769231\pi$
$930$		0			0
$931$		0			0
$932$	−0.627974	+	0.329586i	−0.627974	+	0.329586i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	1.00599	+	1.45743i	1.00599	+	1.45743i
$937$	0.213460	+	0.112032i	0.213460	+	0.112032i	0.568065	−	0.822984i	$-0.307692\pi$
$937$	0.213460	+	0.112032i	0.213460	+	0.112032i	−0.354605	+	0.935016i	$0.615385\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.13613			1.13613			0.568065	−	0.822984i	$-0.307692\pi$
$941$	1.13613			1.13613			0.568065	+	0.822984i	$0.307692\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.885456	−	0.464723i	$-0.846154\pi$
$947$		0			0		0.885456	+	0.464723i	$0.153846\pi$
$948$		0			0
$949$	−0.713460	+	1.88124i	−0.713460	+	1.88124i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.645395	+	0.935016i	0.645395	+	0.935016i	1.00000			$0$
$953$	0.645395	+	0.935016i	0.645395	+	0.935016i	−0.354605	+	0.935016i	$0.615385\pi$
$954$	−0.709210			−0.709210
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.970942	−	0.239316i	−0.970942	−	0.239316i
$962$	0.378019	−	3.11326i	0.378019	−	3.11326i
$963$		0			0
$964$	1.13613			1.13613
$965$	−2.17595	+	1.92773i	−2.17595	+	1.92773i
$966$		0			0
$967$		0			0		−0.568065	−	0.822984i	$-0.692308\pi$
$967$		0			0		0.568065	+	0.822984i	$0.307692\pi$
$968$	0.568065	−	0.822984i	0.568065	−	0.822984i
$969$		0			0
$970$	2.90704			2.90704
$971$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$971$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.213460	−	0.112032i	0.213460	−	0.112032i
$977$	−1.32555	+	1.17433i	−1.32555	+	1.17433i	−0.354605	+	0.935016i	$0.615385\pi$
$977$	−1.32555	+	1.17433i	−1.32555	+	1.17433i	−0.970942	+	0.239316i	$0.923077\pi$
$978$		0			0
$979$		0			0
$980$	1.12054	−	0.992709i	1.12054	−	0.992709i
$981$	−0.402877	+	1.06230i	−0.402877	+	1.06230i
$982$		0			0
$983$		0			0		−0.748511	−	0.663123i	$-0.769231\pi$
$983$		0			0		0.748511	+	0.663123i	$0.230769\pi$
$984$		0			0
$985$	−0.376485	−	0.992709i	−0.376485	−	0.992709i
$986$	−0.966170	+	1.39974i	−0.966170	+	1.39974i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.748511	−	0.663123i	$-0.769231\pi$
$991$		0			0		0.748511	+	0.663123i	$0.230769\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−0.0854858	−	0.704039i	−0.0854858	−	0.704039i	−0.970942	−	0.239316i	$-0.923077\pi$
$997$	−0.0854858	−	0.704039i	−0.0854858	−	0.704039i	0.885456	−	0.464723i	$-0.153846\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	628.1.o.a.415.1	yes	12
4.3	odd	2	CM	628.1.o.a.415.1	yes	12
157.14	even	13	inner	628.1.o.a.171.1	✓	12
628.171	odd	26	inner	628.1.o.a.171.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
628.1.o.a.171.1	✓	12	157.14	even	13	inner
628.1.o.a.171.1	✓	12	628.171	odd	26	inner
628.1.o.a.415.1	yes	12	1.1	even	1	trivial
628.1.o.a.415.1	yes	12	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:	\( N \)	\(=\)	\( 628 = 2^{2} \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	628.o (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.568065 - 0.822984i) q^{2} +(-0.354605 - 0.935016i) q^{4} +(-1.32555 - 0.695701i) q^{5} +(-0.970942 - 0.239316i) q^{8} +(-0.748511 - 0.663123i) q^{9} +O(q^{10})\)	\(q+(0.568065 - 0.822984i) q^{2} +(-0.354605 - 0.935016i) q^{4} +(-1.32555 - 0.695701i) q^{5} +(-0.970942 - 0.239316i) q^{8} +(-0.748511 - 0.663123i) q^{9} +(-1.32555 + 0.695701i) q^{10} +1.77091 q^{13} +(-0.748511 + 0.663123i) q^{16} +(-1.32555 - 0.695701i) q^{17} +(-0.970942 + 0.239316i) q^{18} +(-0.180446 + 1.48611i) q^{20} +(0.705010 + 1.02138i) q^{25} +(1.00599 - 1.45743i) q^{26} +(1.00599 - 0.527986i) q^{29} +(0.120537 + 0.992709i) q^{32} +(-1.32555 + 0.695701i) q^{34} +(-0.354605 + 0.935016i) q^{36} +(1.56806 - 0.822984i) q^{37} +(1.12054 + 0.992709i) q^{40} +(1.12054 + 0.992709i) q^{41} +(0.530851 + 1.39974i) q^{45} +(-0.748511 - 0.663123i) q^{49} +1.24107 q^{50} +(-0.627974 - 1.65583i) q^{52} +(0.688601 + 0.169725i) q^{53} +(0.136945 - 1.12785i) q^{58} +(-0.234068 - 0.0576926i) q^{61} +(0.885456 + 0.464723i) q^{64} +(-2.34743 - 1.23202i) q^{65} +(-0.180446 + 1.48611i) q^{68} +(0.568065 + 0.822984i) q^{72} +(-0.402877 + 1.06230i) q^{73} +(0.213460 - 1.75800i) q^{74} +(1.45352 - 0.358261i) q^{80} +(0.120537 + 0.992709i) q^{81} +(1.45352 - 0.358261i) q^{82} +(1.27307 + 1.84437i) q^{85} +(-0.234068 + 1.92773i) q^{89} +(1.45352 + 0.358261i) q^{90} +(-1.71945 - 0.902438i) q^{97} +(-0.970942 + 0.239316i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} - q^{4} - 2 q^{5} - q^{8} - q^{9}+O(q^{10}) \) 12 * q - q^2 - q^4 - 2 * q^5 - q^8 - q^9	\( 12 q - q^{2} - q^{4} - 2 q^{5} - q^{8} - q^{9} - 2 q^{10} - 2 q^{13} - q^{16} - 2 q^{17} - q^{18} - 2 q^{20} - 3 q^{25} - 2 q^{26} - 2 q^{29} - q^{32} - 2 q^{34} - q^{36} + 11 q^{37} + 11 q^{40} + 11 q^{41} - 2 q^{45} - q^{49} + 10 q^{50} - 2 q^{52} - 2 q^{53} - 2 q^{58} - 2 q^{61} - q^{64} - 4 q^{65} - 2 q^{68} - q^{72} - 2 q^{73} - 2 q^{74} - 2 q^{80} - q^{81} - 2 q^{82} - 4 q^{85} - 2 q^{89} - 2 q^{90} - 2 q^{97} - q^{98}+O(q^{100}) \) 12 * q - q^2 - q^4 - 2 * q^5 - q^8 - q^9 - 2 * q^10 - 2 * q^13 - q^16 - 2 * q^17 - q^18 - 2 * q^20 - 3 * q^25 - 2 * q^26 - 2 * q^29 - q^32 - 2 * q^34 - q^36 + 11 * q^37 + 11 * q^40 + 11 * q^41 - 2 * q^45 - q^49 + 10 * q^50 - 2 * q^52 - 2 * q^53 - 2 * q^58 - 2 * q^61 - q^64 - 4 * q^65 - 2 * q^68 - q^72 - 2 * q^73 - 2 * q^74 - 2 * q^80 - q^81 - 2 * q^82 - 4 * q^85 - 2 * q^89 - 2 * q^90 - 2 * q^97 - q^98

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