LMFDB - Embedded newform 676.1.t.a.575.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [676,1,Mod(3,676)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(676, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([39, 62]))

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

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

chi := DirichletCharacter("676.3");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 676 = 2^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	676.t (of order $78$, degree $24$, 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:	$0.337367948540$
Analytic rank:	$0$
Dimension:	$24$
Coefficient field:	$\Q(\zeta_{39})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{24} - x^{23} + x^{21} - x^{20} + x^{18} - x^{17} + x^{15} - x^{14} + x^{12} - x^{10} + x^{9} + \cdots + 1 $ x^24 - x^23 + x^21 - x^20 + x^18 - x^17 + x^15 - x^14 + x^12 - x^10 + x^9 - x^7 + x^6 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{39}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{39} - \cdots)$

Embedding invariants

Embedding label			575.1
Root			$0.692724 - 0.721202i$ of defining polynomial
Character	$\chi$	$=$	676.575
Dual form			676.1.t.a.87.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.987050 - 0.160411i) q^{2} +(0.948536 - 0.316668i) q^{4} +(-0.152466 + 1.25567i) q^{5} +(0.885456 - 0.464723i) q^{8} +(-0.632445 - 0.774605i) q^{9} +(0.0509320 + 1.26386i) q^{10} +(-0.0402659 - 0.999189i) q^{13} +(0.799443 - 0.600742i) q^{16} +(-0.0763874 + 1.89553i) q^{17} +(-0.748511 - 0.663123i) q^{18} +(0.253011 + 1.23933i) q^{20} +(-0.582515 - 0.143577i) q^{25} +(-0.200026 - 0.979791i) q^{26} +(-1.96770 + 0.319782i) q^{29} +(0.692724 - 0.721202i) q^{32} +(0.228667 + 1.88324i) q^{34} +(-0.845190 - 0.534466i) q^{36} +(-1.27458 - 1.32698i) q^{37} +(0.448536 + 1.18269i) q^{40} +(0.846282 - 1.78350i) q^{41} +(1.06907 - 0.676041i) q^{45} +(-0.996757 - 0.0804666i) q^{49} +(-0.598003 - 0.0482758i) q^{50} +(-0.354605 - 0.935016i) q^{52} +(-0.0713074 + 0.0374250i) q^{53} +(-1.89092 + 0.631282i) q^{58} +(-0.724653 + 0.458243i) q^{61} +(0.568065 - 0.822984i) q^{64} +(1.26079 + 0.101781i) q^{65} +(0.527799 + 1.82217i) q^{68} +(-0.919979 - 0.391967i) q^{72} +(0.354605 + 0.935016i) q^{73} +(-1.47094 - 1.10534i) q^{74} +(0.632445 + 1.09543i) q^{80} +(-0.200026 + 0.979791i) q^{81} +(0.549229 - 1.89616i) q^{82} +(-2.36852 - 0.384921i) q^{85} +(-0.120537 - 0.208776i) q^{89} +(0.946784 - 0.838778i) q^{90} +(1.78649 + 0.761154i) q^{97} +(-0.996757 + 0.0804666i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} + q^{4} + 2 q^{5} - 2 q^{8} + q^{9} - q^{10} + q^{13} + q^{16} - q^{17} - 2 q^{18} - q^{20} + q^{26} - q^{29} + q^{32} + 2 q^{34} + q^{36} - q^{37} - 11 q^{40} - q^{41} - q^{45}+ \cdots + q^{98}+O(q^{100}) $ 24 * q + q^2 + q^4 + 2 * q^5 - 2 * q^8 + q^9 - q^10 + q^13 + q^16 - q^17 - 2 * q^18 - q^20 + q^26 - q^29 + q^32 + 2 * q^34 + q^36 - q^37 - 11 * q^40 - q^41 - q^45 + q^49 - 2 * q^52 - 11 * q^53 - q^58 - q^61 - 2 * q^64 - q^65 - q^68 + q^72 + 2 * q^73 - 14 * q^74 - q^80 + q^81 - q^82 - 12 * q^85 + 2 * q^89 + 2 * q^90 + 2 * q^97 + q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/676\mathbb{Z}\right)^\times$.

$n$	$339$	$509$
$\chi(n)$	$-1$	$e\left(\frac{37}{39}\right)$

Coefficient data

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

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

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

$2$	0.987050	−	0.160411i	0.987050	−	0.160411i
$2$	0.987050	−	0.160411i	0.987050	−	0.160411i
$3$		0			0		0.428693	−	0.903450i	$-0.358974\pi$
$3$		0			0		−0.428693	+	0.903450i	$0.641026\pi$
$4$	0.948536	−	0.316668i	0.948536	−	0.316668i
$5$	−0.152466	+	1.25567i	−0.152466	+	1.25567i	0.692724	+	0.721202i	$0.256410\pi$
$5$	−0.152466	+	1.25567i	−0.152466	+	1.25567i	−0.845190	+	0.534466i	$0.820513\pi$
$6$		0			0
$7$		0			0		0.0402659	−	0.999189i	$-0.487179\pi$
$7$		0			0		−0.0402659	+	0.999189i	$0.512821\pi$
$8$	0.885456	−	0.464723i	0.885456	−	0.464723i
$9$	−0.632445	−	0.774605i	−0.632445	−	0.774605i
$10$	0.0509320	+	1.26386i	0.0509320	+	1.26386i
$11$		0			0		0.632445	−	0.774605i	$-0.282051\pi$
$11$		0			0		−0.632445	+	0.774605i	$0.717949\pi$
$12$		0			0
$13$	−0.0402659	−	0.999189i	−0.0402659	−	0.999189i
$13$	−0.0402659	−	0.999189i	−0.0402659	−	0.999189i
$14$		0			0
$15$		0			0
$16$	0.799443	−	0.600742i	0.799443	−	0.600742i
$17$	−0.0763874	+	1.89553i	−0.0763874	+	1.89553i	0.278217	+	0.960518i	$0.410256\pi$
$17$	−0.0763874	+	1.89553i	−0.0763874	+	1.89553i	−0.354605	+	0.935016i	$0.615385\pi$
$18$	−0.748511	−	0.663123i	−0.748511	−	0.663123i
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$	0.253011	+	1.23933i	0.253011	+	1.23933i
$21$		0			0
$22$		0			0
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$		0			0
$25$	−0.582515	−	0.143577i	−0.582515	−	0.143577i
$26$	−0.200026	−	0.979791i	−0.200026	−	0.979791i
$27$		0			0
$28$		0			0
$29$	−1.96770	+	0.319782i	−1.96770	+	0.319782i	−0.970942	+	0.239316i	$0.923077\pi$
$29$	−1.96770	+	0.319782i	−1.96770	+	0.319782i	−0.996757	+	0.0804666i	$0.974359\pi$
$30$		0			0
$31$		0			0		0.970942	−	0.239316i	$-0.0769231\pi$
$31$		0			0		−0.970942	+	0.239316i	$0.923077\pi$
$32$	0.692724	−	0.721202i	0.692724	−	0.721202i
$33$		0			0
$34$	0.228667	+	1.88324i	0.228667	+	1.88324i
$35$		0			0
$36$	−0.845190	−	0.534466i	−0.845190	−	0.534466i
$37$	−1.27458	−	1.32698i	−1.27458	−	1.32698i	−0.919979	−	0.391967i	$-0.871795\pi$
$37$	−1.27458	−	1.32698i	−1.27458	−	1.32698i	−0.354605	−	0.935016i	$-0.615385\pi$
$38$		0			0
$39$		0			0
$40$	0.448536	+	1.18269i	0.448536	+	1.18269i
$41$	0.846282	−	1.78350i	0.846282	−	1.78350i	0.278217	−	0.960518i	$-0.410256\pi$
$41$	0.846282	−	1.78350i	0.846282	−	1.78350i	0.568065	−	0.822984i	$-0.307692\pi$
$42$		0			0
$43$		0			0		0.692724	−	0.721202i	$-0.256410\pi$
$43$		0			0		−0.692724	+	0.721202i	$0.743590\pi$
$44$		0			0
$45$	1.06907	−	0.676041i	1.06907	−	0.676041i
$46$		0			0
$47$		0			0		0.748511	−	0.663123i	$-0.230769\pi$
$47$		0			0		−0.748511	+	0.663123i	$0.769231\pi$
$48$		0			0
$49$	−0.996757	−	0.0804666i	−0.996757	−	0.0804666i
$50$	−0.598003	−	0.0482758i	−0.598003	−	0.0482758i
$51$		0			0
$52$	−0.354605	−	0.935016i	−0.354605	−	0.935016i
$53$	−0.0713074	+	0.0374250i	−0.0713074	+	0.0374250i	−0.500000	−	0.866025i	$-0.666667\pi$
$53$	−0.0713074	+	0.0374250i	−0.0713074	+	0.0374250i	0.428693	+	0.903450i	$0.358974\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−1.89092	+	0.631282i	−1.89092	+	0.631282i
$59$		0			0		−0.799443	−	0.600742i	$-0.794872\pi$
$59$		0			0		0.799443	+	0.600742i	$0.205128\pi$
$60$		0			0
$61$	−0.724653	+	0.458243i	−0.724653	+	0.458243i	−0.845190	−	0.534466i	$-0.820513\pi$
$61$	−0.724653	+	0.458243i	−0.724653	+	0.458243i	0.120537	+	0.992709i	$0.461538\pi$
$62$		0			0
$63$		0			0
$64$	0.568065	−	0.822984i	0.568065	−	0.822984i
$65$	1.26079	+	0.101781i	1.26079	+	0.101781i
$66$		0			0
$67$		0			0		−0.948536	−	0.316668i	$-0.897436\pi$
$67$		0			0		0.948536	+	0.316668i	$0.102564\pi$
$68$	0.527799	+	1.82217i	0.527799	+	1.82217i
$69$		0			0
$70$		0			0
$71$		0			0		0.996757	−	0.0804666i	$-0.0256410\pi$
$71$		0			0		−0.996757	+	0.0804666i	$0.974359\pi$
$72$	−0.919979	−	0.391967i	−0.919979	−	0.391967i
$73$	0.354605	+	0.935016i	0.354605	+	0.935016i	0.987050	+	0.160411i	$0.0512821\pi$
$73$	0.354605	+	0.935016i	0.354605	+	0.935016i	−0.632445	+	0.774605i	$0.717949\pi$
$74$	−1.47094	−	1.10534i	−1.47094	−	1.10534i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.748511	−	0.663123i	$-0.230769\pi$
$79$		0			0		−0.748511	+	0.663123i	$0.769231\pi$
$80$	0.632445	+	1.09543i	0.632445	+	1.09543i
$81$	−0.200026	+	0.979791i	−0.200026	+	0.979791i
$82$	0.549229	−	1.89616i	0.549229	−	1.89616i
$83$		0			0		0.568065	−	0.822984i	$-0.307692\pi$
$83$		0			0		−0.568065	+	0.822984i	$0.692308\pi$
$84$		0			0
$85$	−2.36852	−	0.384921i	−2.36852	−	0.384921i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.120537	−	0.208776i	−0.120537	−	0.208776i	0.799443	−	0.600742i	$-0.205128\pi$
$89$	−0.120537	−	0.208776i	−0.120537	−	0.208776i	−0.919979	+	0.391967i	$0.871795\pi$
$90$	0.946784	−	0.838778i	0.946784	−	0.838778i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	1.78649	+	0.761154i	1.78649	+	0.761154i	0.987050	+	0.160411i	$0.0512821\pi$
$97$	1.78649	+	0.761154i	1.78649	+	0.761154i	0.799443	+	0.600742i	$0.205128\pi$
$98$	−0.996757	+	0.0804666i	−0.996757	+	0.0804666i
$99$		0			0
$100$	−0.598003	+	0.0482758i	−0.598003	+	0.0482758i
$101$	0.385456	+	1.33075i	0.385456	+	1.33075i	0.885456	+	0.464723i	$0.153846\pi$
$101$	0.385456	+	1.33075i	0.385456	+	1.33075i	−0.500000	+	0.866025i	$0.666667\pi$
$102$		0			0
$103$		0			0		−0.568065	−	0.822984i	$-0.692308\pi$
$103$		0			0		0.568065	+	0.822984i	$0.307692\pi$
$104$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$105$		0			0
$106$	−0.0643806	+	0.0483789i	−0.0643806	+	0.0483789i
$107$		0			0		0.919979	−	0.391967i	$-0.128205\pi$
$107$		0			0		−0.919979	+	0.391967i	$0.871795\pi$
$108$		0			0
$109$	1.45352	+	0.358261i	1.45352	+	0.358261i	0.885456	−	0.464723i	$-0.153846\pi$
$109$	1.45352	+	0.358261i	1.45352	+	0.358261i	0.568065	+	0.822984i	$0.307692\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.685430	+	1.44451i	0.685430	+	1.44451i	0.885456	+	0.464723i	$0.153846\pi$
$113$	0.685430	+	1.44451i	0.685430	+	1.44451i	−0.200026	+	0.979791i	$0.564103\pi$
$114$		0			0
$115$		0			0
$116$	−1.76517	+	0.926432i	−1.76517	+	0.926432i
$117$	−0.748511	+	0.663123i	−0.748511	+	0.663123i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.200026	−	0.979791i	−0.200026	−	0.979791i
$122$	−0.641762	+	0.568552i	−0.641762	+	0.568552i
$123$		0			0
$124$		0			0
$125$	−0.179438	+	0.473138i	−0.179438	+	0.473138i
$126$		0			0
$127$		0			0		−0.948536	−	0.316668i	$-0.897436\pi$
$127$		0			0		0.948536	+	0.316668i	$0.102564\pi$
$128$	0.428693	−	0.903450i	0.428693	−	0.903450i
$129$		0			0
$130$	1.26079	−	0.101781i	1.26079	−	0.101781i
$131$		0			0		0.354605	−	0.935016i	$-0.384615\pi$
$131$		0			0		−0.354605	+	0.935016i	$0.615385\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.813261	+	1.71391i	0.813261	+	1.71391i
$137$	1.10759	−	1.15312i	1.10759	−	1.15312i	0.120537	−	0.992709i	$-0.461538\pi$
$137$	1.10759	−	1.15312i	1.10759	−	1.15312i	0.987050	−	0.160411i	$-0.0512821\pi$
$138$		0			0
$139$		0			0		−0.919979	−	0.391967i	$-0.871795\pi$
$139$		0			0		0.919979	+	0.391967i	$0.128205\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.970942	−	0.239316i	−0.970942	−	0.239316i
$145$	−0.101534	−	2.51953i	−0.101534	−	2.51953i
$146$	0.500000	+	0.866025i	0.500000	+	0.866025i
$147$		0			0
$148$	−1.62920	−	0.855072i	−1.62920	−	0.855072i
$149$	−0.111301	−	0.545190i	−0.111301	−	0.545190i	−0.996757	−	0.0804666i	$-0.974359\pi$
$149$	−0.111301	−	0.545190i	−0.111301	−	0.545190i	0.885456	−	0.464723i	$-0.153846\pi$
$150$		0			0
$151$		0			0		−0.748511	−	0.663123i	$-0.769231\pi$
$151$		0			0		0.748511	+	0.663123i	$0.230769\pi$
$152$		0			0
$153$	1.51660	−	1.13965i	1.51660	−	1.13965i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.0670708	−	0.552378i	0.0670708	−	0.552378i	−0.919979	−	0.391967i	$-0.871795\pi$
$157$	0.0670708	−	0.552378i	0.0670708	−	0.552378i	0.987050	−	0.160411i	$-0.0512821\pi$
$158$		0			0
$159$		0			0
$160$	0.799974	+	0.979791i	0.799974	+	0.979791i
$161$		0			0
$162$	−0.0402659	+	0.999189i	−0.0402659	+	0.999189i
$163$		0			0		0.278217	−	0.960518i	$-0.410256\pi$
$163$		0			0		−0.278217	+	0.960518i	$0.589744\pi$
$164$	0.237952	−	1.95971i	0.237952	−	1.95971i
$165$		0			0
$166$		0			0
$167$		0			0		0.987050	−	0.160411i	$-0.0512821\pi$
$167$		0			0		−0.987050	+	0.160411i	$0.948718\pi$
$168$		0			0
$169$	−0.996757	+	0.0804666i	−0.996757	+	0.0804666i
$170$	−2.39959			−2.39959
$171$		0			0
$172$		0			0
$173$	1.07766	−	0.359776i	1.07766	−	0.359776i	0.278217	−	0.960518i	$-0.410256\pi$
$173$	1.07766	−	0.359776i	1.07766	−	0.359776i	0.799443	+	0.600742i	$0.205128\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−0.152466	−	0.186737i	−0.152466	−	0.186737i
$179$		0			0		−0.0402659	−	0.999189i	$-0.512821\pi$
$179$		0			0		0.0402659	+	0.999189i	$0.487179\pi$
$180$	0.799974	−	0.979791i	0.799974	−	0.979791i
$181$	−0.203753	+	1.67806i	−0.203753	+	1.67806i	0.428693	+	0.903450i	$0.358974\pi$
$181$	−0.203753	+	1.67806i	−0.203753	+	1.67806i	−0.632445	+	0.774605i	$0.717949\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.86058	−	1.39814i	1.86058	−	1.39814i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$191$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$192$		0			0
$193$	−0.0224054	−	0.555984i	−0.0224054	−	0.555984i	−0.970942	−	0.239316i	$-0.923077\pi$
$193$	−0.0224054	−	0.555984i	−0.0224054	−	0.555984i	0.948536	−	0.316668i	$-0.102564\pi$
$194$	1.88546	+	0.464723i	1.88546	+	0.464723i
$195$		0			0
$196$	−0.970942	+	0.239316i	−0.970942	+	0.239316i
$197$	0.316091	+	1.09127i	0.316091	+	1.09127i	0.948536	+	0.316668i	$0.102564\pi$
$197$	0.316091	+	1.09127i	0.316091	+	1.09127i	−0.632445	+	0.774605i	$0.717949\pi$
$198$		0			0
$199$		0			0		−0.919979	−	0.391967i	$-0.871795\pi$
$199$		0			0		0.919979	+	0.391967i	$0.128205\pi$
$200$	−0.582515	+	0.143577i	−0.582515	+	0.143577i
$201$		0			0
$202$	0.593932	+	1.25168i	0.593932	+	1.25168i
$203$		0			0
$204$		0			0
$205$	2.11046	+	1.33457i	2.11046	+	1.33457i
$206$		0			0
$207$		0			0
$208$	−0.632445	−	0.774605i	−0.632445	−	0.774605i
$209$		0			0
$210$		0			0
$211$		0			0		−0.948536	−	0.316668i	$-0.897436\pi$
$211$		0			0		0.948536	+	0.316668i	$0.102564\pi$
$212$	−0.0557864	+	0.0580798i	−0.0557864	+	0.0580798i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	1.49217	+	0.120460i	1.49217	+	0.120460i
$219$		0			0
$220$		0			0
$221$	1.89707			1.89707
$222$		0			0
$223$		0			0		0.919979	−	0.391967i	$-0.128205\pi$
$223$		0			0		−0.919979	+	0.391967i	$0.871795\pi$
$224$		0			0
$225$	0.257194	+	0.542024i	0.257194	+	0.542024i
$226$	0.908271	+	1.31586i	0.908271	+	1.31586i
$227$		0			0		0.948536	−	0.316668i	$-0.102564\pi$
$227$		0			0		−0.948536	+	0.316668i	$0.897436\pi$
$228$		0			0
$229$	−1.71945	−	0.423807i	−1.71945	−	0.423807i	−0.748511	−	0.663123i	$-0.769231\pi$
$229$	−1.71945	−	0.423807i	−1.71945	−	0.423807i	−0.970942	+	0.239316i	$0.923077\pi$
$230$		0			0
$231$		0			0
$232$	−1.59370	+	1.19759i	−1.59370	+	1.19759i
$233$	−1.10312	+	1.59814i	−1.10312	+	1.59814i	−0.354605	+	0.935016i	$0.615385\pi$
$233$	−1.10312	+	1.59814i	−1.10312	+	1.59814i	−0.748511	+	0.663123i	$0.769231\pi$
$234$	−0.632445	+	0.774605i	−0.632445	+	0.774605i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$		0			0
$241$	−0.788777	−	0.336066i	−0.788777	−	0.336066i	−0.0402659	−	0.999189i	$-0.512821\pi$
$241$	−0.788777	−	0.336066i	−0.788777	−	0.336066i	−0.748511	+	0.663123i	$0.769231\pi$
$242$	−0.354605	−	0.935016i	−0.354605	−	0.935016i
$243$		0			0
$244$	−0.542249	+	0.664135i	−0.542249	+	0.664135i
$245$	0.253011	−	1.23933i	0.253011	−	1.23933i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	−0.101217	+	0.495795i	−0.101217	+	0.495795i
$251$		0			0		0.278217	−	0.960518i	$-0.410256\pi$
$251$		0			0		−0.278217	+	0.960518i	$0.589744\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.278217	−	0.960518i	0.278217	−	0.960518i
$257$	0.338119	−	1.65622i	0.338119	−	1.65622i	−0.354605	−	0.935016i	$-0.615385\pi$
$257$	0.338119	−	1.65622i	0.338119	−	1.65622i	0.692724	−	0.721202i	$-0.256410\pi$
$258$		0			0
$259$		0			0
$260$	1.22814	−	0.302708i	1.22814	−	0.302708i
$261$	1.49217	+	1.32194i	1.49217	+	1.32194i
$262$		0			0
$263$		0			0		0.632445	−	0.774605i	$-0.282051\pi$
$263$		0			0		−0.632445	+	0.774605i	$0.717949\pi$
$264$		0			0
$265$	−0.0361215	−	0.0952445i	−0.0361215	−	0.0952445i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.240292	+	0.0193983i	−0.240292	+	0.0193983i	−0.200026	−	0.979791i	$-0.564103\pi$
$269$	−0.240292	+	0.0193983i	−0.240292	+	0.0193983i	−0.0402659	+	0.999189i	$0.512821\pi$
$270$		0			0
$271$		0			0		−0.948536	−	0.316668i	$-0.897436\pi$
$271$		0			0		0.948536	+	0.316668i	$0.102564\pi$
$272$	1.07766	+	1.56126i	1.07766	+	1.56126i
$273$		0			0
$274$	0.908271	−	1.31586i	0.908271	−	1.31586i
$275$		0			0
$276$		0			0
$277$	0.845190	−	0.534466i	0.845190	−	0.534466i	−0.0402659	−	0.999189i	$-0.512821\pi$
$277$	0.845190	−	0.534466i	0.845190	−	0.534466i	0.885456	+	0.464723i	$0.153846\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.0457473	−	0.0662764i	−0.0457473	−	0.0662764i	0.799443	−	0.600742i	$-0.205128\pi$
$281$	−0.0457473	−	0.0662764i	−0.0457473	−	0.0662764i	−0.845190	+	0.534466i	$0.820513\pi$
$282$		0			0
$283$		0			0		−0.692724	−	0.721202i	$-0.743590\pi$
$283$		0			0		0.692724	+	0.721202i	$0.256410\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.996757	−	0.0804666i	−0.996757	−	0.0804666i
$289$	−2.59046	−	0.209123i	−2.59046	−	0.209123i
$290$	−0.504380	−	2.47062i	−0.504380	−	2.47062i
$291$		0			0
$292$	0.632445	+	0.774605i	0.632445	+	0.774605i
$293$	−1.17097	+	0.740475i	−1.17097	+	0.740475i	−0.970942	−	0.239316i	$-0.923077\pi$
$293$	−1.17097	+	0.740475i	−1.17097	+	0.740475i	−0.200026	+	0.979791i	$0.564103\pi$
$294$		0			0
$295$		0			0
$296$	−1.74527	−	0.582656i	−1.74527	−	0.582656i
$297$		0			0
$298$	−0.197315	−	0.520276i	−0.197315	−	0.520276i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.464916	−	0.979791i	−0.464916	−	0.979791i
$306$	1.31415	−	1.36817i	1.31415	−	1.36817i
$307$		0			0		0.970942	−	0.239316i	$-0.0769231\pi$
$307$		0			0		−0.970942	+	0.239316i	$0.923077\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.970942	−	0.239316i	$-0.0769231\pi$
$311$		0			0		−0.970942	+	0.239316i	$0.923077\pi$
$312$		0			0
$313$	0.688601	+	0.169725i	0.688601	+	0.169725i	0.568065	−	0.822984i	$-0.307692\pi$
$313$	0.688601	+	0.169725i	0.688601	+	0.169725i	0.120537	+	0.992709i	$0.461538\pi$
$314$	−0.0224054	−	0.555984i	−0.0224054	−	0.555984i
$315$		0			0
$316$		0			0
$317$	−0.0713074	−	0.0374250i	−0.0713074	−	0.0374250i	0.428693	−	0.903450i	$-0.358974\pi$
$317$	−0.0713074	−	0.0374250i	−0.0713074	−	0.0374250i	−0.500000	+	0.866025i	$0.666667\pi$
$318$		0			0
$319$		0			0
$320$	0.946784	+	0.838778i	0.946784	+	0.838778i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.120537	+	0.992709i	0.120537	+	0.992709i
$325$	−0.120005	+	0.587824i	−0.120005	+	0.587824i
$326$		0			0
$327$		0			0
$328$	−0.0794890	−	1.97250i	−0.0794890	−	1.97250i
$329$		0			0
$330$		0			0
$331$		0			0		0.0402659	−	0.999189i	$-0.487179\pi$
$331$		0			0		−0.0402659	+	0.999189i	$0.512821\pi$
$332$		0			0
$333$	−0.221783	+	1.82654i	−0.221783	+	1.82654i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.38545			1.38545			0.692724	−	0.721202i	$-0.256410\pi$
$337$	1.38545			1.38545			0.692724	+	0.721202i	$0.256410\pi$
$338$	−0.970942	+	0.239316i	−0.970942	+	0.239316i
$339$		0			0
$340$	−2.36852	+	0.384921i	−2.36852	+	0.384921i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	1.00599	−	0.527986i	1.00599	−	0.527986i
$347$		0			0		−0.632445	−	0.774605i	$-0.717949\pi$
$347$		0			0		0.632445	+	0.774605i	$0.282051\pi$
$348$		0			0
$349$	−0.152466	+	0.186737i	−0.152466	+	0.186737i	−0.845190	−	0.534466i	$-0.820513\pi$
$349$	−0.152466	+	0.186737i	−0.152466	+	0.186737i	0.692724	+	0.721202i	$0.256410\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.42869	+	0.903450i	1.42869	+	0.903450i	1.00000			$0$
$353$	1.42869	+	0.903450i	1.42869	+	0.903450i	0.428693	+	0.903450i	$0.358974\pi$
$354$		0			0
$355$		0			0
$356$	−0.180446	−	0.159861i	−0.180446	−	0.159861i
$357$		0			0
$358$		0			0
$359$		0			0		−0.885456	−	0.464723i	$-0.846154\pi$
$359$		0			0		0.885456	+	0.464723i	$0.153846\pi$
$360$	0.632445	−	1.09543i	0.632445	−	1.09543i
$361$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$362$	0.0680647	+	1.68901i	0.0680647	+	1.68901i
$363$		0			0
$364$		0			0
$365$	−1.22814	+	0.302708i	−1.22814	+	0.302708i
$366$		0			0
$367$		0			0		0.987050	−	0.160411i	$-0.0512821\pi$
$367$		0			0		−0.987050	+	0.160411i	$0.948718\pi$
$368$		0			0
$369$	−1.91674	+	0.472433i	−1.91674	+	0.472433i
$370$	1.61221	−	1.67849i	1.61221	−	1.67849i
$371$		0			0
$372$		0			0
$373$	1.94854	+	0.316668i	1.94854	+	0.316668i	1.00000			$0$
$373$	1.94854	+	0.316668i	1.94854	+	0.316668i	0.948536	+	0.316668i	$0.102564\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.398754	+	1.95323i	0.398754	+	1.95323i
$378$		0			0
$379$		0			0		0.428693	−	0.903450i	$-0.358974\pi$
$379$		0			0		−0.428693	+	0.903450i	$0.641026\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.845190	−	0.534466i	$-0.179487\pi$
$383$		0			0		−0.845190	+	0.534466i	$0.820513\pi$
$384$		0			0
$385$		0			0
$386$	−0.111301	−	0.545190i	−0.111301	−	0.545190i
$387$		0			0
$388$	1.93559	+	0.156257i	1.93559	+	0.156257i
$389$	−1.62920	−	0.855072i	−1.62920	−	0.855072i	−0.996757	−	0.0804666i	$-0.974359\pi$
$389$	−1.62920	−	0.855072i	−1.62920	−	0.855072i	−0.632445	−	0.774605i	$-0.717949\pi$
$390$		0			0
$391$		0			0
$392$	−0.919979	+	0.391967i	−0.919979	+	0.391967i
$393$		0			0
$394$	0.487050	+	1.02644i	0.487050	+	1.02644i
$395$		0			0
$396$		0			0
$397$	−0.566973	−	0.426052i	−0.566973	−	0.426052i	0.278217	−	0.960518i	$-0.410256\pi$
$397$	−0.566973	−	0.426052i	−0.566973	−	0.426052i	−0.845190	+	0.534466i	$0.820513\pi$
$398$		0			0
$399$		0			0
$400$	−0.551940	+	0.235160i	−0.551940	+	0.235160i
$401$	1.10759	−	0.832298i	1.10759	−	0.832298i	0.120537	−	0.992709i	$-0.461538\pi$
$401$	1.10759	−	0.832298i	1.10759	−	0.832298i	0.987050	+	0.160411i	$0.0512821\pi$
$402$		0			0
$403$		0			0
$404$	0.787025	+	1.14020i	0.787025	+	1.14020i
$405$	−1.19979	−	0.400550i	−1.19979	−	0.400550i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	0.996757	−	0.0804666i	0.996757	−	0.0804666i	0.428693	−	0.903450i	$-0.358974\pi$
$409$	0.996757	−	0.0804666i	0.996757	−	0.0804666i	0.568065	+	0.822984i	$0.307692\pi$
$410$	2.29721	+	0.978749i	2.29721	+	0.978749i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−0.748511	−	0.663123i	−0.748511	−	0.663123i
$417$		0			0
$418$		0			0
$419$		0			0		0.200026	−	0.979791i	$-0.435897\pi$
$419$		0			0		−0.200026	+	0.979791i	$0.564103\pi$
$420$		0			0
$421$	0.487050	−	0.705614i	0.487050	−	0.705614i	−0.500000	−	0.866025i	$-0.666667\pi$
$421$	0.487050	−	0.705614i	0.487050	−	0.705614i	0.987050	+	0.160411i	$0.0512821\pi$
$422$		0			0
$423$		0			0
$424$	−0.0457473	+	0.0662764i	−0.0457473	+	0.0662764i
$425$	0.316652	−	1.09321i	0.316652	−	1.09321i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.200026	−	0.979791i	$-0.435897\pi$
$431$		0			0		−0.200026	+	0.979791i	$0.564103\pi$
$432$		0			0
$433$	−1.47094	−	1.10534i	−1.47094	−	1.10534i	−0.970942	−	0.239316i	$-0.923077\pi$
$433$	−1.47094	−	1.10534i	−1.47094	−	1.10534i	−0.500000	−	0.866025i	$-0.666667\pi$
$434$		0			0
$435$		0			0
$436$	1.49217	−	0.120460i	1.49217	−	0.120460i
$437$		0			0
$438$		0			0
$439$		0			0		−0.278217	−	0.960518i	$-0.589744\pi$
$439$		0			0		0.278217	+	0.960518i	$0.410256\pi$
$440$		0			0
$441$	0.568065	+	0.822984i	0.568065	+	0.822984i
$442$	1.87251	−	0.304312i	1.87251	−	0.304312i
$443$		0			0		0.568065	−	0.822984i	$-0.307692\pi$
$443$		0			0		−0.568065	+	0.822984i	$0.692308\pi$
$444$		0			0
$445$	0.280531	−	0.119523i	0.280531	−	0.119523i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.672711	+	0.224584i	−0.672711	+	0.224584i	−0.632445	−	0.774605i	$-0.717949\pi$
$449$	−0.672711	+	0.224584i	−0.672711	+	0.224584i	−0.0402659	+	0.999189i	$0.512821\pi$
$450$	0.340810	+	0.493748i	0.340810	+	0.493748i
$451$		0			0
$452$	1.10759	+	1.15312i	1.10759	+	1.15312i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.0802707	+	0.00648012i	0.0802707	+	0.00648012i	0.120537	−	0.992709i	$-0.461538\pi$
$457$	0.0802707	+	0.00648012i	0.0802707	+	0.00648012i	−0.0402659	+	0.999189i	$0.512821\pi$
$458$	−1.76517	−	0.142499i	−1.76517	−	0.142499i
$459$		0			0
$460$		0			0
$461$	−1.01121	−	1.23850i	−1.01121	−	1.23850i	−0.970942	−	0.239316i	$-0.923077\pi$
$461$	−1.01121	−	1.23850i	−1.01121	−	1.23850i	−0.0402659	−	0.999189i	$-0.512821\pi$
$462$		0			0
$463$		0			0		0.354605	−	0.935016i	$-0.384615\pi$
$463$		0			0		−0.354605	+	0.935016i	$0.615385\pi$
$464$	−1.38096	+	1.43773i	−1.38096	+	1.43773i
$465$		0			0
$466$	−0.832471	+	1.75440i	−0.832471	+	1.75440i
$467$		0			0		−0.354605	−	0.935016i	$-0.615385\pi$
$467$		0			0		0.354605	+	0.935016i	$0.384615\pi$
$468$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.0740877	+	0.0315658i	0.0740877	+	0.0315658i
$478$		0			0
$479$		0			0		−0.278217	−	0.960518i	$-0.589744\pi$
$479$		0			0		0.278217	+	0.960518i	$0.410256\pi$
$480$		0			0
$481$	−1.27458	+	1.32698i	−1.27458	+	1.32698i
$482$	−0.832471	−	0.205186i	−0.832471	−	0.205186i
$483$		0			0
$484$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$485$	−1.22814	+	2.12719i	−1.22814	+	2.12719i
$486$		0			0
$487$		0			0		−0.200026	−	0.979791i	$-0.564103\pi$
$487$		0			0		0.200026	+	0.979791i	$0.435897\pi$
$488$	−0.428693	+	0.742517i	−0.428693	+	0.742517i
$489$		0			0
$490$	0.0509320	−	1.26386i	0.0509320	−	1.26386i
$491$		0			0		0.799443	−	0.600742i	$-0.205128\pi$
$491$		0			0		−0.799443	+	0.600742i	$0.794872\pi$
$492$		0			0
$493$	−0.455851	−	3.75427i	−0.455851	−	3.75427i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$499$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$500$	−0.0203754	+	0.505611i	−0.0203754	+	0.505611i
$501$		0			0
$502$		0			0
$503$		0			0		0.948536	−	0.316668i	$-0.102564\pi$
$503$		0			0		−0.948536	+	0.316668i	$0.897436\pi$
$504$		0			0
$505$	−1.72975	+	0.281111i	−1.72975	+	0.281111i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1.96770	+	0.319782i	−1.96770	+	0.319782i	−0.970942	+	0.239316i	$0.923077\pi$
$509$	−1.96770	+	0.319782i	−1.96770	+	0.319782i	−0.996757	+	0.0804666i	$0.974359\pi$
$510$		0			0
$511$		0			0
$512$	0.120537	−	0.992709i	0.120537	−	0.992709i
$513$		0			0
$514$	0.0680647	−	1.68901i	0.0680647	−	1.68901i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	1.16367	−	0.495795i	1.16367	−	0.495795i
$521$	0.237952	+	1.95971i	0.237952	+	1.95971i	0.278217	+	0.960518i	$0.410256\pi$
$521$	0.237952	+	1.95971i	0.237952	+	1.95971i	−0.0402659	+	0.999189i	$0.512821\pi$
$522$	1.68490	+	1.06547i	1.68490	+	1.06547i
$523$		0			0		0.799443	−	0.600742i	$-0.205128\pi$
$523$		0			0		−0.799443	+	0.600742i	$0.794872\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$530$	−0.0509320	−	0.0882168i	−0.0509320	−	0.0882168i
$531$		0			0
$532$		0			0
$533$	−1.81613	−	0.773781i	−1.81613	−	0.773781i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−0.234068	+	0.0576926i	−0.234068	+	0.0576926i
$539$		0			0
$540$		0			0
$541$	−0.203753	−	1.67806i	−0.203753	−	1.67806i	−0.632445	−	0.774605i	$-0.717949\pi$
$541$	−0.203753	−	1.67806i	−0.203753	−	1.67806i	0.428693	−	0.903450i	$-0.358974\pi$
$542$		0			0
$543$		0			0
$544$	1.31415	+	1.36817i	1.31415	+	1.36817i
$545$	−0.671469	+	1.77052i	−0.671469	+	1.77052i
$546$		0			0
$547$		0			0		−0.354605	−	0.935016i	$-0.615385\pi$
$547$		0			0		0.354605	+	0.935016i	$0.384615\pi$
$548$	0.685430	−	1.44451i	0.685430	−	1.44451i
$549$	0.813261	+	0.271506i	0.813261	+	0.271506i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	0.748511	−	0.663123i	0.748511	−	0.663123i
$555$		0			0
$556$		0			0
$557$	0.996757	+	0.0804666i	0.996757	+	0.0804666i	0.568065	−	0.822984i	$-0.307692\pi$
$557$	0.996757	+	0.0804666i	0.996757	+	0.0804666i	0.428693	+	0.903450i	$0.358974\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−0.0557864	−	0.0580798i	−0.0557864	−	0.0580798i
$563$		0			0		−0.428693	−	0.903450i	$-0.641026\pi$
$563$		0			0		0.428693	+	0.903450i	$0.358974\pi$
$564$		0			0
$565$	−1.91833	+	0.640434i	−1.91833	+	0.640434i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.37723	−	0.586782i	1.37723	−	0.586782i	0.428693	−	0.903450i	$-0.358974\pi$
$569$	1.37723	−	0.586782i	1.37723	−	0.586782i	0.948536	+	0.316668i	$0.102564\pi$
$570$		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
$576$	−0.996757	+	0.0804666i	−0.996757	+	0.0804666i
$577$	−0.400051			−0.400051			−0.200026	−	0.979791i	$-0.564103\pi$
$577$	−0.400051			−0.400051			−0.200026	+	0.979791i	$0.564103\pi$
$578$	−2.59046	+	0.209123i	−2.59046	+	0.209123i
$579$		0			0
$580$	−0.894164	−	2.35772i	−0.894164	−	2.35772i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	0.748511	+	0.663123i	0.748511	+	0.663123i
$585$	−0.718540	−	1.04098i	−0.718540	−	1.04098i
$586$	−1.03702	+	0.918722i	−1.03702	+	0.918722i
$587$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$587$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−1.81613	−	0.295150i	−1.81613	−	0.295150i
$593$	−0.227255	+	0.329236i	−0.227255	+	0.329236i	−0.919979	−	0.391967i	$-0.871795\pi$
$593$	−0.227255	+	0.329236i	−0.227255	+	0.329236i	0.692724	+	0.721202i	$0.256410\pi$
$594$		0			0
$595$		0			0
$596$	−0.278217	−	0.481887i	−0.278217	−	0.481887i
$597$		0			0
$598$		0			0
$599$		0			0		−0.748511	−	0.663123i	$-0.769231\pi$
$599$		0			0		0.748511	+	0.663123i	$0.230769\pi$
$600$		0			0
$601$	−0.542249	+	0.664135i	−0.542249	+	0.664135i	−0.970942	−	0.239316i	$-0.923077\pi$
$601$	−0.542249	+	0.664135i	−0.542249	+	0.664135i	0.428693	+	0.903450i	$0.358974\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.26079	−	0.101781i	1.26079	−	0.101781i
$606$		0			0
$607$		0			0		0.996757	−	0.0804666i	$-0.0256410\pi$
$607$		0			0		−0.996757	+	0.0804666i	$0.974359\pi$
$608$		0			0
$609$		0			0
$610$	−0.616065	−	0.892525i	−0.616065	−	0.892525i
$611$		0			0
$612$	1.07766	−	1.56126i	1.07766	−	1.56126i
$613$	0.685430	−	0.515067i	0.685430	−	0.515067i	−0.200026	−	0.979791i	$-0.564103\pi$
$613$	0.685430	−	0.515067i	0.685430	−	0.515067i	0.885456	+	0.464723i	$0.153846\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.59370	−	1.19759i	−1.59370	−	1.19759i	−0.845190	−	0.534466i	$-0.820513\pi$
$617$	−1.59370	−	1.19759i	−1.59370	−	1.19759i	−0.748511	−	0.663123i	$-0.769231\pi$
$618$		0			0
$619$		0			0		−0.568065	−	0.822984i	$-0.692308\pi$
$619$		0			0		0.568065	+	0.822984i	$0.307692\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−1.09797	−	0.576262i	−1.09797	−	0.576262i
$626$	0.706910	+	0.0570677i	0.706910	+	0.0570677i
$627$		0			0
$628$	−0.111301	−	0.545190i	−0.111301	−	0.545190i
$629$	2.61270	−	2.31465i	2.61270	−	2.31465i
$630$		0			0
$631$		0			0		0.845190	−	0.534466i	$-0.179487\pi$
$631$		0			0		−0.845190	+	0.534466i	$0.820513\pi$
$632$		0			0
$633$		0			0
$634$	−0.0763874	−	0.0255019i	−0.0763874	−	0.0255019i
$635$		0			0
$636$		0			0
$637$	−0.0402659	+	0.999189i	−0.0402659	+	0.999189i
$638$		0			0
$639$		0			0
$640$	1.06907	+	0.676041i	1.06907	+	0.676041i
$641$	−0.987050	−	0.160411i	−0.987050	−	0.160411i	−0.354605	−	0.935016i	$-0.615385\pi$
$641$	−0.987050	−	0.160411i	−0.987050	−	0.160411i	−0.632445	+	0.774605i	$0.717949\pi$
$642$		0			0
$643$		0			0		−0.428693	−	0.903450i	$-0.641026\pi$
$643$		0			0		0.428693	+	0.903450i	$0.358974\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.987050	−	0.160411i	$-0.0512821\pi$
$647$		0			0		−0.987050	+	0.160411i	$0.948718\pi$
$648$	0.278217	+	0.960518i	0.278217	+	0.960518i
$649$		0			0
$650$	−0.0241575	+	0.599462i	−0.0241575	+	0.599462i
$651$		0			0
$652$		0			0
$653$	−0.885456	−	1.53365i	−0.885456	−	1.53365i	−0.845190	−	0.534466i	$-0.820513\pi$
$653$	−0.885456	−	1.53365i	−0.885456	−	1.53365i	−0.0402659	−	0.999189i	$-0.512821\pi$
$654$		0			0
$655$		0			0
$656$	−0.394871	−	1.93421i	−0.394871	−	1.93421i
$657$	0.500000	−	0.866025i	0.500000	−	0.866025i
$658$		0			0
$659$		0			0		0.0402659	−	0.999189i	$-0.487179\pi$
$659$		0			0		−0.0402659	+	0.999189i	$0.512821\pi$
$660$		0			0
$661$	0.338119	+	0.213814i	0.338119	+	0.213814i	0.692724	−	0.721202i	$-0.256410\pi$
$661$	0.338119	+	0.213814i	0.338119	+	0.213814i	−0.354605	+	0.935016i	$0.615385\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	0.0740877	+	1.83847i	0.0740877	+	1.83847i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.724653	+	1.52717i	−0.724653	+	1.52717i	0.120537	+	0.992709i	$0.461538\pi$
$673$	−0.724653	+	1.52717i	−0.724653	+	1.52717i	−0.845190	+	0.534466i	$0.820513\pi$
$674$	1.36751	−	0.222242i	1.36751	−	0.222242i
$675$		0			0
$676$	−0.919979	+	0.391967i	−0.919979	+	0.391967i
$677$	−1.49702			−1.49702			−0.748511	−	0.663123i	$-0.769231\pi$
$677$	−1.49702			−1.49702			−0.748511	+	0.663123i	$0.769231\pi$
$678$		0			0
$679$		0			0
$680$	−2.27610	+	0.759873i	−2.27610	+	0.759873i
$681$		0			0
$682$		0			0
$683$		0			0		0.0402659	−	0.999189i	$-0.487179\pi$
$683$		0			0		−0.0402659	+	0.999189i	$0.512821\pi$
$684$		0			0
$685$	1.27907	+	1.56657i	1.27907	+	1.56657i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.0402659	+	0.0697427i	0.0402659	+	0.0697427i
$690$		0			0
$691$		0			0		−0.845190	−	0.534466i	$-0.820513\pi$
$691$		0			0		0.845190	+	0.534466i	$0.179487\pi$
$692$	0.908271	−	0.682521i	0.908271	−	0.682521i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	3.31604	+	1.74039i	3.31604	+	1.74039i
$698$	−0.120537	+	0.208776i	−0.120537	+	0.208776i
$699$		0			0
$700$		0			0
$701$	−1.71945	−	0.423807i	−1.71945	−	0.423807i	−0.748511	−	0.663123i	$-0.769231\pi$
$701$	−1.71945	−	0.423807i	−1.71945	−	0.423807i	−0.970942	+	0.239316i	$0.923077\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	1.55512	+	0.662573i	1.55512	+	0.662573i
$707$		0			0
$708$		0			0
$709$	−0.171499	−	0.361427i	−0.171499	−	0.361427i	0.799443	−	0.600742i	$-0.205128\pi$
$709$	−0.171499	−	0.361427i	−0.171499	−	0.361427i	−0.970942	+	0.239316i	$0.923077\pi$
$710$		0			0
$711$		0			0
$712$	−0.203753	−	0.128845i	−0.203753	−	0.128845i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.692724	−	0.721202i	$-0.256410\pi$
$719$		0			0		−0.692724	+	0.721202i	$0.743590\pi$
$720$	0.448536	−	1.18269i	0.448536	−	1.18269i
$721$		0			0
$722$	−0.632445	−	0.774605i	−0.632445	−	0.774605i
$723$		0			0
$724$	0.338119	+	1.65622i	0.338119	+	1.65622i
$725$	1.19213	+	0.0962385i	1.19213	+	0.0962385i
$726$		0			0
$727$		0			0		−0.885456	−	0.464723i	$-0.846154\pi$
$727$		0			0		0.885456	+	0.464723i	$0.153846\pi$
$728$		0			0
$729$	0.885456	−	0.464723i	0.885456	−	0.464723i
$730$	−1.16367	+	0.495795i	−1.16367	+	0.495795i
$731$		0			0
$732$		0			0
$733$	0.316091	+	0.457937i	0.316091	+	0.457937i	0.948536	−	0.316668i	$-0.102564\pi$
$733$	0.316091	+	0.457937i	0.316091	+	0.457937i	−0.632445	+	0.774605i	$0.717949\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	−1.81613	+	0.773781i	−1.81613	+	0.773781i
$739$		0			0		0.799443	−	0.600742i	$-0.205128\pi$
$739$		0			0		−0.799443	+	0.600742i	$0.794872\pi$
$740$	1.32208	−	1.91537i	1.32208	−	1.91537i
$741$		0			0
$742$		0			0
$743$		0			0		−0.948536	−	0.316668i	$-0.897436\pi$
$743$		0			0		0.948536	+	0.316668i	$0.102564\pi$
$744$		0			0
$745$	0.701547	−	0.0566347i	0.701547	−	0.0566347i
$746$	1.97410			1.97410
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.632445	−	0.774605i	$-0.282051\pi$
$751$		0			0		−0.632445	+	0.774605i	$0.717949\pi$
$752$		0			0
$753$		0			0
$754$	0.706910	+	1.86397i	0.706910	+	1.86397i
$755$		0			0
$756$		0			0
$757$	−0.227255	+	1.11317i	−0.227255	+	1.11317i	0.692724	+	0.721202i	$0.256410\pi$
$757$	−0.227255	+	1.11317i	−0.227255	+	1.11317i	−0.919979	+	0.391967i	$0.871795\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.74798	+	0.284074i	1.74798	+	0.284074i	0.948536	−	0.316668i	$-0.102564\pi$
$761$	1.74798	+	0.284074i	1.74798	+	0.284074i	0.799443	+	0.600742i	$0.205128\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	1.19979	+	2.07811i	1.19979	+	2.07811i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−0.227255	+	1.11317i	−0.227255	+	1.11317i	0.692724	+	0.721202i	$0.256410\pi$
$769$	−0.227255	+	1.11317i	−0.227255	+	1.11317i	−0.919979	+	0.391967i	$0.871795\pi$
$770$		0			0
$771$		0			0
$772$	−0.197315	−	0.520276i	−0.197315	−	0.520276i
$773$	1.37723	+	0.586782i	1.37723	+	0.586782i	0.948536	−	0.316668i	$-0.102564\pi$
$773$	1.37723	+	0.586782i	1.37723	+	0.586782i	0.428693	+	0.903450i	$0.358974\pi$
$774$		0			0
$775$		0			0
$776$	1.93559	−	0.156257i	1.93559	−	0.156257i
$777$		0			0
$778$	−1.74527	−	0.582656i	−1.74527	−	0.582656i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.845190	+	0.534466i	−0.845190	+	0.534466i
$785$	0.683377	+	0.168437i	0.683377	+	0.168437i
$786$		0			0
$787$		0			0		0.948536	−	0.316668i	$-0.102564\pi$
$787$		0			0		−0.948536	+	0.316668i	$0.897436\pi$
$788$	0.645395	+	0.935016i	0.645395	+	0.935016i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	0.487050	+	0.705614i	0.487050	+	0.705614i
$794$	−0.627974	−	0.329586i	−0.627974	−	0.329586i
$795$		0			0
$796$		0			0
$797$	0.141860	+	0.694877i	0.141860	+	0.694877i	0.987050	+	0.160411i	$0.0512821\pi$
$797$	0.141860	+	0.694877i	0.141860	+	0.694877i	−0.845190	+	0.534466i	$0.820513\pi$
$798$		0			0
$799$		0			0
$800$	−0.507071	+	0.320652i	−0.507071	+	0.320652i
$801$	−0.0854858	+	0.225408i	−0.0854858	+	0.225408i
$802$	0.959734	−	0.999189i	0.959734	−	0.999189i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	0.959734	+	0.999189i	0.959734	+	0.999189i
$809$	−0.470293	−	0.297395i	−0.470293	−	0.297395i	0.278217	−	0.960518i	$-0.410256\pi$
$809$	−0.470293	−	0.297395i	−0.470293	−	0.297395i	−0.748511	+	0.663123i	$0.769231\pi$
$810$	−1.24851	−	0.202903i	−1.24851	−	0.202903i
$811$		0			0		−0.120537	−	0.992709i	$-0.538462\pi$
$811$		0			0		0.120537	+	0.992709i	$0.461538\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	0.970942	−	0.239316i	0.970942	−	0.239316i
$819$		0			0
$820$	2.42446	+	0.597576i	2.42446	+	0.597576i
$821$	0.0781918	+	1.94031i	0.0781918	+	1.94031i	0.278217	+	0.960518i	$0.410256\pi$
$821$	0.0781918	+	1.94031i	0.0781918	+	1.94031i	−0.200026	+	0.979791i	$0.564103\pi$
$822$		0			0
$823$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$823$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.748511	−	0.663123i	$-0.769231\pi$
$827$		0			0		0.748511	+	0.663123i	$0.230769\pi$
$828$		0			0
$829$	−0.0643806	+	0.0483789i	−0.0643806	+	0.0483789i	−0.632445	−	0.774605i	$-0.717949\pi$
$829$	−0.0643806	+	0.0483789i	−0.0643806	+	0.0483789i	0.568065	+	0.822984i	$0.307692\pi$
$830$		0			0
$831$		0			0
$832$	−0.845190	−	0.534466i	−0.845190	−	0.534466i
$833$	0.228667	−	1.88324i	0.228667	−	1.88324i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.278217	−	0.960518i	$-0.410256\pi$
$839$		0			0		−0.278217	+	0.960518i	$0.589744\pi$
$840$		0			0
$841$	2.82104	−	0.941802i	2.82104	−	0.941802i
$842$	0.367555	−	0.774605i	0.367555	−	0.774605i
$843$		0			0
$844$		0			0
$845$	0.0509320	−	1.26386i	0.0509320	−	1.26386i
$846$		0			0
$847$		0			0
$848$	−0.0345234	+	0.0727566i	−0.0345234	+	0.0727566i
$849$		0			0
$850$	0.137188	−	1.12985i	0.137188	−	1.12985i
$851$		0			0
$852$		0			0
$853$	1.67977	−	0.881614i	1.67977	−	0.881614i	0.692724	−	0.721202i	$-0.256410\pi$
$853$	1.67977	−	0.881614i	1.67977	−	0.881614i	0.987050	−	0.160411i	$-0.0512821\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.103346	−	0.851134i	0.103346	−	0.851134i	−0.845190	−	0.534466i	$-0.820513\pi$
$857$	0.103346	−	0.851134i	0.103346	−	0.851134i	0.948536	−	0.316668i	$-0.102564\pi$
$858$		0			0
$859$		0			0		−0.120537	−	0.992709i	$-0.538462\pi$
$859$		0			0		0.120537	+	0.992709i	$0.461538\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.748511	−	0.663123i	$-0.769231\pi$
$863$		0			0		0.748511	+	0.663123i	$0.230769\pi$
$864$		0			0
$865$	0.287453	+	1.40804i	0.287453	+	1.40804i
$866$	−1.62920	−	0.855072i	−1.62920	−	0.855072i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	1.45352	−	0.358261i	1.45352	−	0.358261i
$873$	−0.540266	−	1.86521i	−0.540266	−	1.86521i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.36751	−	1.42373i	1.36751	−	1.42373i	0.568065	−	0.822984i	$-0.307692\pi$
$877$	1.36751	−	1.42373i	1.36751	−	1.42373i	0.799443	−	0.600742i	$-0.205128\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.66849	−	1.05509i	−1.66849	−	1.05509i	−0.919979	−	0.391967i	$-0.871795\pi$
$881$	−1.66849	−	1.05509i	−1.66849	−	1.05509i	−0.748511	−	0.663123i	$-0.769231\pi$
$882$	0.692724	+	0.721202i	0.692724	+	0.721202i
$883$		0			0		0.354605	−	0.935016i	$-0.384615\pi$
$883$		0			0		−0.354605	+	0.935016i	$0.615385\pi$
$884$	1.79944	−	0.600742i	1.79944	−	0.600742i
$885$		0			0
$886$		0			0
$887$		0			0		−0.948536	−	0.316668i	$-0.897436\pi$
$887$		0			0		0.948536	+	0.316668i	$0.102564\pi$
$888$		0			0
$889$		0			0
$890$	0.257725	−	0.162975i	0.257725	−	0.162975i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.627974	+	0.329586i	−0.627974	+	0.329586i
$899$		0			0
$900$	0.415599	+	0.432684i	0.415599	+	0.432684i
$901$	−0.0654934	−	0.138025i	−0.0654934	−	0.138025i
$902$		0			0
$903$		0			0
$904$	1.27822	+	0.960518i	1.27822	+	0.960518i
$905$	−2.07602	−	0.511692i	−2.07602	−	0.511692i
$906$		0			0
$907$		0			0		0.919979	−	0.391967i	$-0.128205\pi$
$907$		0			0		−0.919979	+	0.391967i	$0.871795\pi$
$908$		0			0
$909$	0.787025	−	1.14020i	0.787025	−	1.14020i
$910$		0			0
$911$		0			0		−0.568065	−	0.822984i	$-0.692308\pi$
$911$		0			0		0.568065	+	0.822984i	$0.307692\pi$
$912$		0			0
$913$		0			0
$914$	0.0802707	−	0.00648012i	0.0802707	−	0.00648012i
$915$		0			0
$916$	−1.76517	+	0.142499i	−1.76517	+	0.142499i
$917$		0			0
$918$		0			0
$919$		0			0		−0.799443	−	0.600742i	$-0.794872\pi$
$919$		0			0		0.799443	+	0.600742i	$0.205128\pi$
$920$		0			0
$921$		0			0
$922$	−1.19678	−	1.06026i	−1.19678	−	1.06026i
$923$		0			0
$924$		0			0
$925$	0.551940	+	0.955989i	0.551940	+	0.955989i
$926$		0			0
$927$		0			0
$928$	−1.13245	+	1.64063i	−1.13245	+	1.64063i
$929$	1.87251	+	0.304312i	1.87251	+	0.304312i	0.987050	−	0.160411i	$-0.0512821\pi$
$929$	1.87251	+	0.304312i	1.87251	+	0.304312i	0.885456	+	0.464723i	$0.153846\pi$
$930$		0			0
$931$		0			0
$932$	−0.540266	+	1.86521i	−0.540266	+	1.86521i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−0.354605	+	0.935016i	−0.354605	+	0.935016i
$937$	0.748511	+	0.663123i	0.748511	+	0.663123i	0.948536	−	0.316668i	$-0.102564\pi$
$937$	0.748511	+	0.663123i	0.748511	+	0.663123i	−0.200026	+	0.979791i	$0.564103\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.402877	−	1.06230i	−0.402877	−	1.06230i	−0.970942	−	0.239316i	$-0.923077\pi$
$941$	−0.402877	−	1.06230i	−0.402877	−	1.06230i	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		−0.948536	−	0.316668i	$-0.897436\pi$
$947$		0			0		0.948536	+	0.316668i	$0.102564\pi$
$948$		0			0
$949$	0.919979	−	0.391967i	0.919979	−	0.391967i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.960245	+	0.607222i	−0.960245	+	0.607222i	−0.919979	−	0.391967i	$-0.871795\pi$
$953$	−0.960245	+	0.607222i	−0.960245	+	0.607222i	−0.0402659	+	0.999189i	$0.512821\pi$
$954$	0.0781918	+	0.0192725i	0.0781918	+	0.0192725i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.885456	−	0.464723i	0.885456	−	0.464723i
$962$	−1.04522	+	1.51426i	−1.04522	+	1.51426i
$963$		0			0
$964$	−0.854605	−	0.0689908i	−0.854605	−	0.0689908i
$965$	0.701547	+	0.0566347i	0.701547	+	0.0566347i
$966$		0			0
$967$		0			0		0.748511	−	0.663123i	$-0.230769\pi$
$967$		0			0		−0.748511	+	0.663123i	$0.769231\pi$
$968$	−0.632445	−	0.774605i	−0.632445	−	0.774605i
$969$		0			0
$970$	−0.871006	+	2.29665i	−0.871006	+	2.29665i
$971$		0			0		0.692724	−	0.721202i	$-0.256410\pi$
$971$		0			0		−0.692724	+	0.721202i	$0.743590\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−0.304033	+	0.801669i	−0.304033	+	0.801669i
$977$	0.385456	+	0.401302i	0.385456	+	0.401302i	0.885456	−	0.464723i	$-0.153846\pi$
$977$	0.385456	+	0.401302i	0.385456	+	0.401302i	−0.500000	+	0.866025i	$0.666667\pi$
$978$		0			0
$979$		0			0
$980$	−0.152466	−	1.25567i	−0.152466	−	1.25567i
$981$	−0.641762	−	1.35248i	−0.641762	−	1.35248i
$982$		0			0
$983$		0			0		0.970942	−	0.239316i	$-0.0769231\pi$
$983$		0			0		−0.970942	+	0.239316i	$0.923077\pi$
$984$		0			0
$985$	−1.41847	+	0.230524i	−1.41847	+	0.230524i
$986$	−1.05217	−	3.63253i	−1.05217	−	3.63253i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$991$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−0.0643806	+	1.59759i	−0.0643806	+	1.59759i	0.568065	+	0.822984i	$0.307692\pi$
$997$	−0.0643806	+	1.59759i	−0.0643806	+	1.59759i	−0.632445	+	0.774605i	$0.717949\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	676.1.t.a.575.1	yes	24
4.3	odd	2	CM	676.1.t.a.575.1	yes	24
169.87	even	39	inner	676.1.t.a.87.1	✓	24
676.87	odd	78	inner	676.1.t.a.87.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
676.1.t.a.87.1	✓	24	169.87	even	39	inner
676.1.t.a.87.1	✓	24	676.87	odd	78	inner
676.1.t.a.575.1	yes	24	1.1	even	1	trivial
676.1.t.a.575.1	yes	24	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:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	676.t (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.987050 - 0.160411i) q^{2} +(0.948536 - 0.316668i) q^{4} +(-0.152466 + 1.25567i) q^{5} +(0.885456 - 0.464723i) q^{8} +(-0.632445 - 0.774605i) q^{9} +(0.0509320 + 1.26386i) q^{10} +(-0.0402659 - 0.999189i) q^{13} +(0.799443 - 0.600742i) q^{16} +(-0.0763874 + 1.89553i) q^{17} +(-0.748511 - 0.663123i) q^{18} +(0.253011 + 1.23933i) q^{20} +(-0.582515 - 0.143577i) q^{25} +(-0.200026 - 0.979791i) q^{26} +(-1.96770 + 0.319782i) q^{29} +(0.692724 - 0.721202i) q^{32} +(0.228667 + 1.88324i) q^{34} +(-0.845190 - 0.534466i) q^{36} +(-1.27458 - 1.32698i) q^{37} +(0.448536 + 1.18269i) q^{40} +(0.846282 - 1.78350i) q^{41} +(1.06907 - 0.676041i) q^{45} +(-0.996757 - 0.0804666i) q^{49} +(-0.598003 - 0.0482758i) q^{50} +(-0.354605 - 0.935016i) q^{52} +(-0.0713074 + 0.0374250i) q^{53} +(-1.89092 + 0.631282i) q^{58} +(-0.724653 + 0.458243i) q^{61} +(0.568065 - 0.822984i) q^{64} +(1.26079 + 0.101781i) q^{65} +(0.527799 + 1.82217i) q^{68} +(-0.919979 - 0.391967i) q^{72} +(0.354605 + 0.935016i) q^{73} +(-1.47094 - 1.10534i) q^{74} +(0.632445 + 1.09543i) q^{80} +(-0.200026 + 0.979791i) q^{81} +(0.549229 - 1.89616i) q^{82} +(-2.36852 - 0.384921i) q^{85} +(-0.120537 - 0.208776i) q^{89} +(0.946784 - 0.838778i) q^{90} +(1.78649 + 0.761154i) q^{97} +(-0.996757 + 0.0804666i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} + q^{4} + 2 q^{5} - 2 q^{8} + q^{9} - q^{10} + q^{13} + q^{16} - q^{17} - 2 q^{18} - q^{20} + q^{26} - q^{29} + q^{32} + 2 q^{34} + q^{36} - q^{37} - 11 q^{40} - q^{41} - q^{45}+ \cdots + q^{98}+O(q^{100}) \) 24 * q + q^2 + q^4 + 2 * q^5 - 2 * q^8 + q^9 - q^10 + q^13 + q^16 - q^17 - 2 * q^18 - q^20 + q^26 - q^29 + q^32 + 2 * q^34 + q^36 - q^37 - 11 * q^40 - q^41 - q^45 + q^49 - 2 * q^52 - 11 * q^53 - q^58 - q^61 - 2 * q^64 - q^65 - q^68 + q^72 + 2 * q^73 - 14 * q^74 - q^80 + q^81 - q^82 - 12 * q^85 + 2 * q^89 + 2 * q^90 + 2 * q^97 + q^98

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