LMFDB - Embedded newform 676.1.t.a.367.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [676,1,Mod(3,676)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(676, base_ring=CyclotomicField(78)) chi = DirichletCharacter(H, H._module([39, 62])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			367.1
Root			$-0.632445 - 0.774605i$ of defining polynomial
Character	$\chi$	$=$	676.367
Dual form			676.1.t.a.35.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.692724 + 0.721202i) q^{2} +(-0.0402659 + 0.999189i) q^{4} +(0.316091 + 0.457937i) q^{5} +(-0.748511 + 0.663123i) q^{8} +(0.278217 - 0.960518i) q^{9} +(-0.111301 + 0.545190i) q^{10} +(-0.200026 + 0.979791i) q^{13} +(-0.996757 - 0.0804666i) q^{16} +(0.0161084 + 0.0789044i) q^{17} +(0.885456 - 0.464723i) q^{18} +(-0.470293 + 0.297395i) q^{20} +(0.244812 - 0.645517i) q^{25} +(-0.845190 + 0.534466i) q^{26} +(-1.27458 - 1.32698i) q^{29} +(-0.632445 - 0.774605i) q^{32} +(-0.0457473 + 0.0662764i) q^{34} +(0.948536 + 0.316668i) q^{36} +(-0.542249 + 0.664135i) q^{37} +(-0.540266 - 0.133164i) q^{40} +(1.10759 - 0.832298i) q^{41} +(0.527799 - 0.176205i) q^{45} +(-0.919979 + 0.391967i) q^{49} +(0.635136 - 0.270606i) q^{50} +(-0.970942 - 0.239316i) q^{52} +(0.299443 - 0.265283i) q^{53} +(0.0740877 - 1.83847i) q^{58} +(1.51660 - 0.506316i) q^{61} +(0.120537 - 0.992709i) q^{64} +(-0.511909 + 0.218104i) q^{65} +(-0.0794890 + 0.0129182i) q^{68} +(0.428693 + 0.903450i) q^{72} +(0.970942 + 0.239316i) q^{73} +(-0.854605 + 0.0689908i) q^{74} +(-0.278217 - 0.481887i) q^{80} +(-0.845190 - 0.534466i) q^{81} +(1.36751 + 0.222242i) q^{82} +(-0.0310415 + 0.0323176i) q^{85} +(-0.568065 - 0.983917i) q^{89} +(0.492699 + 0.258588i) q^{90} +(-0.304033 - 0.640736i) q^{97} +(-0.919979 - 0.391967i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/676\mathbb{Z}\right)^\times$.

$n$	$339$	$509$
$\chi(n)$	$-1$	$e\left(\frac{10}{39}\right)$

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 $

$2$	0.692724	+	0.721202i	0.692724	+	0.721202i
$2$	0.692724	+	0.721202i	0.692724	+	0.721202i
$3$		0			0		0.799443	−	0.600742i	$-0.205128\pi$
$3$		0			0		−0.799443	+	0.600742i	$0.794872\pi$
$4$	−0.0402659	+	0.999189i	−0.0402659	+	0.999189i
$5$	0.316091	+	0.457937i	0.316091	+	0.457937i	0.948536	−	0.316668i	$-0.102564\pi$
$5$	0.316091	+	0.457937i	0.316091	+	0.457937i	−0.632445	+	0.774605i	$0.717949\pi$
$6$		0			0
$7$		0			0		−0.200026	−	0.979791i	$-0.564103\pi$
$7$		0			0		0.200026	+	0.979791i	$0.435897\pi$
$8$	−0.748511	+	0.663123i	−0.748511	+	0.663123i
$9$	0.278217	−	0.960518i	0.278217	−	0.960518i
$10$	−0.111301	+	0.545190i	−0.111301	+	0.545190i
$11$		0			0		−0.278217	−	0.960518i	$-0.589744\pi$
$11$		0			0		0.278217	+	0.960518i	$0.410256\pi$
$12$		0			0
$13$	−0.200026	+	0.979791i	−0.200026	+	0.979791i
$13$	−0.200026	+	0.979791i	−0.200026	+	0.979791i
$14$		0			0
$15$		0			0
$16$	−0.996757	−	0.0804666i	−0.996757	−	0.0804666i
$17$	0.0161084	+	0.0789044i	0.0161084	+	0.0789044i	0.987050	−	0.160411i	$-0.0512821\pi$
$17$	0.0161084	+	0.0789044i	0.0161084	+	0.0789044i	−0.970942	+	0.239316i	$0.923077\pi$
$18$	0.885456	−	0.464723i	0.885456	−	0.464723i
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$	−0.470293	+	0.297395i	−0.470293	+	0.297395i
$21$		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
$25$	0.244812	−	0.645517i	0.244812	−	0.645517i
$26$	−0.845190	+	0.534466i	−0.845190	+	0.534466i
$27$		0			0
$28$		0			0
$29$	−1.27458	−	1.32698i	−1.27458	−	1.32698i	−0.919979	−	0.391967i	$-0.871795\pi$
$29$	−1.27458	−	1.32698i	−1.27458	−	1.32698i	−0.354605	−	0.935016i	$-0.615385\pi$
$30$		0			0
$31$		0			0		−0.354605	−	0.935016i	$-0.615385\pi$
$31$		0			0		0.354605	+	0.935016i	$0.384615\pi$
$32$	−0.632445	−	0.774605i	−0.632445	−	0.774605i
$33$		0			0
$34$	−0.0457473	+	0.0662764i	−0.0457473	+	0.0662764i
$35$		0			0
$36$	0.948536	+	0.316668i	0.948536	+	0.316668i
$37$	−0.542249	+	0.664135i	−0.542249	+	0.664135i	−0.970942	−	0.239316i	$-0.923077\pi$
$37$	−0.542249	+	0.664135i	−0.542249	+	0.664135i	0.428693	+	0.903450i	$0.358974\pi$
$38$		0			0
$39$		0			0
$40$	−0.540266	−	0.133164i	−0.540266	−	0.133164i
$41$	1.10759	−	0.832298i	1.10759	−	0.832298i	0.120537	−	0.992709i	$-0.461538\pi$
$41$	1.10759	−	0.832298i	1.10759	−	0.832298i	0.987050	+	0.160411i	$0.0512821\pi$
$42$		0			0
$43$		0			0		−0.632445	−	0.774605i	$-0.717949\pi$
$43$		0			0		0.632445	+	0.774605i	$0.282051\pi$
$44$		0			0
$45$	0.527799	−	0.176205i	0.527799	−	0.176205i
$46$		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
$49$	−0.919979	+	0.391967i	−0.919979	+	0.391967i
$50$	0.635136	−	0.270606i	0.635136	−	0.270606i
$51$		0			0
$52$	−0.970942	−	0.239316i	−0.970942	−	0.239316i
$53$	0.299443	−	0.265283i	0.299443	−	0.265283i	−0.500000	−	0.866025i	$-0.666667\pi$
$53$	0.299443	−	0.265283i	0.299443	−	0.265283i	0.799443	+	0.600742i	$0.205128\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	0.0740877	−	1.83847i	0.0740877	−	1.83847i
$59$		0			0		0.996757	−	0.0804666i	$-0.0256410\pi$
$59$		0			0		−0.996757	+	0.0804666i	$0.974359\pi$
$60$		0			0
$61$	1.51660	−	0.506316i	1.51660	−	0.506316i	0.568065	−	0.822984i	$-0.307692\pi$
$61$	1.51660	−	0.506316i	1.51660	−	0.506316i	0.948536	+	0.316668i	$0.102564\pi$
$62$		0			0
$63$		0			0
$64$	0.120537	−	0.992709i	0.120537	−	0.992709i
$65$	−0.511909	+	0.218104i	−0.511909	+	0.218104i
$66$		0			0
$67$		0			0		−0.0402659	−	0.999189i	$-0.512821\pi$
$67$		0			0		0.0402659	+	0.999189i	$0.487179\pi$
$68$	−0.0794890	+	0.0129182i	−0.0794890	+	0.0129182i
$69$		0			0
$70$		0			0
$71$		0			0		−0.919979	−	0.391967i	$-0.871795\pi$
$71$		0			0		0.919979	+	0.391967i	$0.128205\pi$
$72$	0.428693	+	0.903450i	0.428693	+	0.903450i
$73$	0.970942	+	0.239316i	0.970942	+	0.239316i	0.692724	−	0.721202i	$-0.256410\pi$
$73$	0.970942	+	0.239316i	0.970942	+	0.239316i	0.278217	+	0.960518i	$0.410256\pi$
$74$	−0.854605	+	0.0689908i	−0.854605	+	0.0689908i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.885456	−	0.464723i	$-0.846154\pi$
$79$		0			0		0.885456	+	0.464723i	$0.153846\pi$
$80$	−0.278217	−	0.481887i	−0.278217	−	0.481887i
$81$	−0.845190	−	0.534466i	−0.845190	−	0.534466i
$82$	1.36751	+	0.222242i	1.36751	+	0.222242i
$83$		0			0		0.120537	−	0.992709i	$-0.461538\pi$
$83$		0			0		−0.120537	+	0.992709i	$0.538462\pi$
$84$		0			0
$85$	−0.0310415	+	0.0323176i	−0.0310415	+	0.0323176i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.568065	−	0.983917i	−0.568065	−	0.983917i	−0.996757	−	0.0804666i	$-0.974359\pi$
$89$	−0.568065	−	0.983917i	−0.568065	−	0.983917i	0.428693	−	0.903450i	$-0.358974\pi$
$90$	0.492699	+	0.258588i	0.492699	+	0.258588i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−0.304033	−	0.640736i	−0.304033	−	0.640736i	0.692724	−	0.721202i	$-0.256410\pi$
$97$	−0.304033	−	0.640736i	−0.304033	−	0.640736i	−0.996757	+	0.0804666i	$0.974359\pi$
$98$	−0.919979	−	0.391967i	−0.919979	−	0.391967i
$99$		0			0
$100$	0.635136	+	0.270606i	0.635136	+	0.270606i
$101$	−1.24851	+	0.202903i	−1.24851	+	0.202903i	−0.748511	−	0.663123i	$-0.769231\pi$
$101$	−1.24851	+	0.202903i	−1.24851	+	0.202903i	−0.500000	+	0.866025i	$0.666667\pi$
$102$		0			0
$103$		0			0		−0.120537	−	0.992709i	$-0.538462\pi$
$103$		0			0		0.120537	+	0.992709i	$0.461538\pi$
$104$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$105$		0			0
$106$	0.398754	+	0.0321908i	0.398754	+	0.0321908i
$107$		0			0		0.428693	−	0.903450i	$-0.358974\pi$
$107$		0			0		−0.428693	+	0.903450i	$0.641026\pi$
$108$		0			0
$109$	−0.627974	+	1.65583i	−0.627974	+	1.65583i	0.120537	+	0.992709i	$0.461538\pi$
$109$	−0.627974	+	1.65583i	−0.627974	+	1.65583i	−0.748511	+	0.663123i	$0.769231\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.59370	−	1.19759i	−1.59370	−	1.19759i	−0.845190	−	0.534466i	$-0.820513\pi$
$113$	−1.59370	−	1.19759i	−1.59370	−	1.19759i	−0.748511	−	0.663123i	$-0.769231\pi$
$114$		0			0
$115$		0			0
$116$	1.37723	−	1.22012i	1.37723	−	1.22012i
$117$	0.885456	+	0.464723i	0.885456	+	0.464723i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.845190	+	0.534466i	−0.845190	+	0.534466i
$122$	1.41574	+	0.743039i	1.41574	+	0.743039i
$123$		0			0
$124$		0			0
$125$	0.913255	−	0.225097i	0.913255	−	0.225097i
$126$		0			0
$127$		0			0		−0.0402659	−	0.999189i	$-0.512821\pi$
$127$		0			0		0.0402659	+	0.999189i	$0.487179\pi$
$128$	0.799443	−	0.600742i	0.799443	−	0.600742i
$129$		0			0
$130$	−0.511909	−	0.218104i	−0.511909	−	0.218104i
$131$		0			0		0.970942	−	0.239316i	$-0.0769231\pi$
$131$		0			0		−0.970942	+	0.239316i	$0.923077\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−0.0643806	−	0.0483789i	−0.0643806	−	0.0483789i
$137$	1.26079	+	1.54419i	1.26079	+	1.54419i	0.692724	+	0.721202i	$0.256410\pi$
$137$	1.26079	+	1.54419i	1.26079	+	1.54419i	0.568065	+	0.822984i	$0.307692\pi$
$138$		0			0
$139$		0			0		−0.428693	−	0.903450i	$-0.641026\pi$
$139$		0			0		0.428693	+	0.903450i	$0.358974\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.354605	+	0.935016i	−0.354605	+	0.935016i
$145$	0.204790	−	1.00313i	0.204790	−	1.00313i
$146$	0.500000	+	0.866025i	0.500000	+	0.866025i
$147$		0			0
$148$	−0.641762	−	0.568552i	−0.641762	−	0.568552i
$149$	−1.66849	+	1.05509i	−1.66849	+	1.05509i	−0.748511	+	0.663123i	$0.769231\pi$
$149$	−1.66849	+	1.05509i	−1.66849	+	1.05509i	−0.919979	+	0.391967i	$0.871795\pi$
$150$		0			0
$151$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$151$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$152$		0			0
$153$	0.0802707	+	0.00648012i	0.0802707	+	0.00648012i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	1.12142	+	1.62465i	1.12142	+	1.62465i	0.692724	+	0.721202i	$0.256410\pi$
$157$	1.12142	+	1.62465i	1.12142	+	1.62465i	0.428693	+	0.903450i	$0.358974\pi$
$158$		0			0
$159$		0			0
$160$	0.154810	−	0.534466i	0.154810	−	0.534466i
$161$		0			0
$162$	−0.200026	−	0.979791i	−0.200026	−	0.979791i
$163$		0			0		−0.987050	−	0.160411i	$-0.948718\pi$
$163$		0			0		0.987050	+	0.160411i	$0.0512821\pi$
$164$	0.787025	+	1.14020i	0.787025	+	1.14020i
$165$		0			0
$166$		0			0
$167$		0			0		−0.692724	−	0.721202i	$-0.743590\pi$
$167$		0			0		0.692724	+	0.721202i	$0.256410\pi$
$168$		0			0
$169$	−0.919979	−	0.391967i	−0.919979	−	0.391967i
$170$	−0.0448108			−0.0448108
$171$		0			0
$172$		0			0
$173$	−0.00970705	+	0.240878i	−0.00970705	+	0.240878i	0.987050	+	0.160411i	$0.0512821\pi$
$173$	−0.00970705	+	0.240878i	−0.00970705	+	0.240878i	−0.996757	+	0.0804666i	$0.974359\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	0.316091	−	1.09127i	0.316091	−	1.09127i
$179$		0			0		0.200026	−	0.979791i	$-0.435897\pi$
$179$		0			0		−0.200026	+	0.979791i	$0.564103\pi$
$180$	0.154810	+	0.534466i	0.154810	+	0.534466i
$181$	1.07766	+	1.56126i	1.07766	+	1.56126i	0.799443	+	0.600742i	$0.205128\pi$
$181$	1.07766	+	1.56126i	1.07766	+	1.56126i	0.278217	+	0.960518i	$0.410256\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.475532	−	0.0383889i	−0.475532	−	0.0383889i
$186$		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
$193$	−0.394871	+	1.93421i	−0.394871	+	1.93421i	−0.0402659	+	0.999189i	$0.512821\pi$
$193$	−0.394871	+	1.93421i	−0.394871	+	1.93421i	−0.354605	+	0.935016i	$0.615385\pi$
$194$	0.251489	−	0.663123i	0.251489	−	0.663123i
$195$		0			0
$196$	−0.354605	−	0.935016i	−0.354605	−	0.935016i
$197$	0.237952	−	0.0386709i	0.237952	−	0.0386709i	−0.0402659	−	0.999189i	$-0.512821\pi$
$197$	0.237952	−	0.0386709i	0.237952	−	0.0386709i	0.278217	+	0.960518i	$0.410256\pi$
$198$		0			0
$199$		0			0		−0.428693	−	0.903450i	$-0.641026\pi$
$199$		0			0		0.428693	+	0.903450i	$0.358974\pi$
$200$	0.244812	+	0.645517i	0.244812	+	0.645517i
$201$		0			0
$202$	−1.01121	−	0.759873i	−1.01121	−	0.759873i
$203$		0			0
$204$		0			0
$205$	0.731238	+	0.244123i	0.731238	+	0.244123i
$206$		0			0
$207$		0			0
$208$	0.278217	−	0.960518i	0.278217	−	0.960518i
$209$		0			0
$210$		0			0
$211$		0			0		−0.0402659	−	0.999189i	$-0.512821\pi$
$211$		0			0		0.0402659	+	0.999189i	$0.487179\pi$
$212$	0.253011	+	0.309882i	0.253011	+	0.309882i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−1.62920	+	0.694138i	−1.62920	+	0.694138i
$219$		0			0
$220$		0			0
$221$	−0.0805319			−0.0805319
$222$		0			0
$223$		0			0		0.428693	−	0.903450i	$-0.358974\pi$
$223$		0			0		−0.428693	+	0.903450i	$0.641026\pi$
$224$		0			0
$225$	−0.551919	−	0.414741i	−0.551919	−	0.414741i
$226$	−0.240292	−	1.97898i	−0.240292	−	1.97898i
$227$		0			0		0.0402659	−	0.999189i	$-0.487179\pi$
$227$		0			0		−0.0402659	+	0.999189i	$0.512821\pi$
$228$		0			0
$229$	0.530851	−	1.39974i	0.530851	−	1.39974i	−0.354605	−	0.935016i	$-0.615385\pi$
$229$	0.530851	−	1.39974i	0.530851	−	1.39974i	0.885456	−	0.464723i	$-0.153846\pi$
$230$		0			0
$231$		0			0
$232$	1.83399	+	0.148055i	1.83399	+	0.148055i
$233$	−0.0854858	+	0.704039i	−0.0854858	+	0.704039i	0.885456	+	0.464723i	$0.153846\pi$
$233$	−0.0854858	+	0.704039i	−0.0854858	+	0.704039i	−0.970942	+	0.239316i	$0.923077\pi$
$234$	0.278217	+	0.960518i	0.278217	+	0.960518i
$235$		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
$241$	0.685430	+	1.44451i	0.685430	+	1.44451i	0.885456	+	0.464723i	$0.153846\pi$
$241$	0.685430	+	1.44451i	0.685430	+	1.44451i	−0.200026	+	0.979791i	$0.564103\pi$
$242$	−0.970942	−	0.239316i	−0.970942	−	0.239316i
$243$		0			0
$244$	0.444838	+	1.53576i	0.444838	+	1.53576i
$245$	−0.470293	−	0.297395i	−0.470293	−	0.297395i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	0.794974	+	0.502711i	0.794974	+	0.502711i
$251$		0			0		−0.987050	−	0.160411i	$-0.948718\pi$
$251$		0			0		0.987050	+	0.160411i	$0.0512821\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.987050	+	0.160411i	0.987050	+	0.160411i
$257$	−1.60339	−	1.01392i	−1.60339	−	1.01392i	−0.970942	−	0.239316i	$-0.923077\pi$
$257$	−1.60339	−	1.01392i	−1.60339	−	1.01392i	−0.632445	−	0.774605i	$-0.717949\pi$
$258$		0			0
$259$		0			0
$260$	−0.197315	−	0.520276i	−0.197315	−	0.520276i
$261$	−1.62920	+	0.855072i	−1.62920	+	0.855072i
$262$		0			0
$263$		0			0		−0.278217	−	0.960518i	$-0.589744\pi$
$263$		0			0		0.278217	+	0.960518i	$0.410256\pi$
$264$		0			0
$265$	0.216134	+	0.0532723i	0.216134	+	0.0532723i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.04522	−	0.445325i	−1.04522	−	0.445325i	−0.200026	−	0.979791i	$-0.564103\pi$
$269$	−1.04522	−	0.445325i	−1.04522	−	0.445325i	−0.845190	+	0.534466i	$0.820513\pi$
$270$		0			0
$271$		0			0		−0.0402659	−	0.999189i	$-0.512821\pi$
$271$		0			0		0.0402659	+	0.999189i	$0.487179\pi$
$272$	−0.00970705	−	0.0799447i	−0.00970705	−	0.0799447i
$273$		0			0
$274$	−0.240292	+	1.97898i	−0.240292	+	1.97898i
$275$		0			0
$276$		0			0
$277$	−0.948536	+	0.316668i	−0.948536	+	0.316668i	−0.748511	−	0.663123i	$-0.769231\pi$
$277$	−0.948536	+	0.316668i	−0.948536	+	0.316668i	−0.200026	+	0.979791i	$0.564103\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.0482209	−	0.397135i	−0.0482209	−	0.397135i	−0.996757	−	0.0804666i	$-0.974359\pi$
$281$	−0.0482209	−	0.397135i	−0.0482209	−	0.397135i	0.948536	−	0.316668i	$-0.102564\pi$
$282$		0			0
$283$		0			0		0.632445	−	0.774605i	$-0.282051\pi$
$283$		0			0		−0.632445	+	0.774605i	$0.717949\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.919979	+	0.391967i	−0.919979	+	0.391967i
$289$	0.914013	−	0.389425i	0.914013	−	0.389425i
$290$	0.865320	−	0.547195i	0.865320	−	0.547195i
$291$		0			0
$292$	−0.278217	+	0.960518i	−0.278217	+	0.960518i
$293$	−1.19979	+	0.400550i	−1.19979	+	0.400550i	−0.845190	−	0.534466i	$-0.820513\pi$
$293$	−1.19979	+	0.400550i	−1.19979	+	0.400550i	−0.354605	+	0.935016i	$0.615385\pi$
$294$		0			0
$295$		0			0
$296$	−0.0345234	−	0.856690i	−0.0345234	−	0.856690i
$297$		0			0
$298$	−1.91674	−	0.472433i	−1.91674	−	0.472433i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.711245	+	0.534466i	0.711245	+	0.534466i
$306$	0.0509320	+	0.0623804i	0.0509320	+	0.0623804i
$307$		0			0		−0.354605	−	0.935016i	$-0.615385\pi$
$307$		0			0		0.354605	+	0.935016i	$0.384615\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.354605	−	0.935016i	$-0.615385\pi$
$311$		0			0		0.354605	+	0.935016i	$0.384615\pi$
$312$		0			0
$313$	0.688601	−	1.81569i	0.688601	−	1.81569i	0.120537	−	0.992709i	$-0.461538\pi$
$313$	0.688601	−	1.81569i	0.688601	−	1.81569i	0.568065	−	0.822984i	$-0.307692\pi$
$314$	−0.394871	+	1.93421i	−0.394871	+	1.93421i
$315$		0			0
$316$		0			0
$317$	0.299443	+	0.265283i	0.299443	+	0.265283i	0.799443	−	0.600742i	$-0.205128\pi$
$317$	0.299443	+	0.265283i	0.299443	+	0.265283i	−0.500000	+	0.866025i	$0.666667\pi$
$318$		0			0
$319$		0			0
$320$	0.492699	−	0.258588i	0.492699	−	0.258588i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.568065	−	0.822984i	0.568065	−	0.822984i
$325$	0.583502	+	0.368985i	0.583502	+	0.368985i
$326$		0			0
$327$		0			0
$328$	−0.277125	+	1.35745i	−0.277125	+	1.35745i
$329$		0			0
$330$		0			0
$331$		0			0		−0.200026	−	0.979791i	$-0.564103\pi$
$331$		0			0		0.200026	+	0.979791i	$0.435897\pi$
$332$		0			0
$333$	0.487050	+	0.705614i	0.487050	+	0.705614i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.26489			−1.26489			−0.632445	−	0.774605i	$-0.717949\pi$
$337$	−1.26489			−1.26489			−0.632445	+	0.774605i	$0.717949\pi$
$338$	−0.354605	−	0.935016i	−0.354605	−	0.935016i
$339$		0			0
$340$	−0.0310415	−	0.0323176i	−0.0310415	−	0.0323176i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.180446	+	0.159861i	−0.180446	+	0.159861i
$347$		0			0		0.278217	−	0.960518i	$-0.410256\pi$
$347$		0			0		−0.278217	+	0.960518i	$0.589744\pi$
$348$		0			0
$349$	0.316091	+	1.09127i	0.316091	+	1.09127i	0.948536	+	0.316668i	$0.102564\pi$
$349$	0.316091	+	1.09127i	0.316091	+	1.09127i	−0.632445	+	0.774605i	$0.717949\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.79944	+	0.600742i	1.79944	+	0.600742i	1.00000			$0$
$353$	1.79944	+	0.600742i	1.79944	+	0.600742i	0.799443	+	0.600742i	$0.205128\pi$
$354$		0			0
$355$		0			0
$356$	1.00599	−	0.527986i	1.00599	−	0.527986i
$357$		0			0
$358$		0			0
$359$		0			0		−0.748511	−	0.663123i	$-0.769231\pi$
$359$		0			0		0.748511	+	0.663123i	$0.230769\pi$
$360$	−0.278217	+	0.481887i	−0.278217	+	0.481887i
$361$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$362$	−0.379463	+	1.85873i	−0.379463	+	1.85873i
$363$		0			0
$364$		0			0
$365$	0.197315	+	0.520276i	0.197315	+	0.520276i
$366$		0			0
$367$		0			0		−0.692724	−	0.721202i	$-0.743590\pi$
$367$		0			0		0.692724	+	0.721202i	$0.256410\pi$
$368$		0			0
$369$	−0.491287	−	1.29542i	−0.491287	−	1.29542i
$370$	−0.301726	−	0.369548i	−0.301726	−	0.369548i
$371$		0			0
$372$		0			0
$373$	0.959734	−	0.999189i	0.959734	−	0.999189i	−0.0402659	−	0.999189i	$-0.512821\pi$
$373$	0.959734	−	0.999189i	0.959734	−	0.999189i	1.00000			$0$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.55512	−	0.983395i	1.55512	−	0.983395i
$378$		0			0
$379$		0			0		0.799443	−	0.600742i	$-0.205128\pi$
$379$		0			0		−0.799443	+	0.600742i	$0.794872\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.948536	−	0.316668i	$-0.102564\pi$
$383$		0			0		−0.948536	+	0.316668i	$0.897436\pi$
$384$		0			0
$385$		0			0
$386$	−1.66849	+	1.05509i	−1.66849	+	1.05509i
$387$		0			0
$388$	0.652458	−	0.277987i	0.652458	−	0.277987i
$389$	−0.641762	−	0.568552i	−0.641762	−	0.568552i	0.278217	−	0.960518i	$-0.410256\pi$
$389$	−0.641762	−	0.568552i	−0.641762	−	0.568552i	−0.919979	+	0.391967i	$0.871795\pi$
$390$		0			0
$391$		0			0
$392$	0.428693	−	0.903450i	0.428693	−	0.903450i
$393$		0			0
$394$	0.192724	+	0.144823i	0.192724	+	0.144823i
$395$		0			0
$396$		0			0
$397$	1.93559	−	0.156257i	1.93559	−	0.156257i	0.948536	−	0.316668i	$-0.102564\pi$
$397$	1.93559	−	0.156257i	1.93559	−	0.156257i	0.987050	+	0.160411i	$0.0512821\pi$
$398$		0			0
$399$		0			0
$400$	−0.295961	+	0.623724i	−0.295961	+	0.623724i
$401$	1.26079	+	0.101781i	1.26079	+	0.101781i	0.692724	−	0.721202i	$-0.256410\pi$
$401$	1.26079	+	0.101781i	1.26079	+	0.101781i	0.568065	+	0.822984i	$0.307692\pi$
$402$		0			0
$403$		0			0
$404$	−0.152466	−	1.25567i	−0.152466	−	1.25567i
$405$	−0.0224054	−	0.555984i	−0.0224054	−	0.555984i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	0.919979	+	0.391967i	0.919979	+	0.391967i	0.799443	−	0.600742i	$-0.205128\pi$
$409$	0.919979	+	0.391967i	0.919979	+	0.391967i	0.120537	+	0.992709i	$0.461538\pi$
$410$	0.330484	+	0.696481i	0.330484	+	0.696481i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	0.885456	−	0.464723i	0.885456	−	0.464723i
$417$		0			0
$418$		0			0
$419$		0			0		−0.845190	−	0.534466i	$-0.820513\pi$
$419$		0			0		0.845190	+	0.534466i	$0.179487\pi$
$420$		0			0
$421$	0.192724	−	1.58723i	0.192724	−	1.58723i	−0.500000	−	0.866025i	$-0.666667\pi$
$421$	0.192724	−	1.58723i	0.192724	−	1.58723i	0.692724	−	0.721202i	$-0.256410\pi$
$422$		0			0
$423$		0			0
$424$	−0.0482209	+	0.397135i	−0.0482209	+	0.397135i
$425$	0.0548776	+	0.00891848i	0.0548776	+	0.00891848i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.845190	−	0.534466i	$-0.820513\pi$
$431$		0			0		0.845190	+	0.534466i	$0.179487\pi$
$432$		0			0
$433$	−0.854605	+	0.0689908i	−0.854605	+	0.0689908i	−0.500000	−	0.866025i	$-0.666667\pi$
$433$	−0.854605	+	0.0689908i	−0.854605	+	0.0689908i	−0.354605	+	0.935016i	$0.615385\pi$
$434$		0			0
$435$		0			0
$436$	−1.62920	−	0.694138i	−1.62920	−	0.694138i
$437$		0			0
$438$		0			0
$439$		0			0		0.987050	−	0.160411i	$-0.0512821\pi$
$439$		0			0		−0.987050	+	0.160411i	$0.948718\pi$
$440$		0			0
$441$	0.120537	+	0.992709i	0.120537	+	0.992709i
$442$	−0.0557864	−	0.0580798i	−0.0557864	−	0.0580798i
$443$		0			0		0.120537	−	0.992709i	$-0.461538\pi$
$443$		0			0		−0.120537	+	0.992709i	$0.538462\pi$
$444$		0			0
$445$	0.271012	−	0.571145i	0.271012	−	0.571145i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.0781918	−	1.94031i	0.0781918	−	1.94031i	−0.200026	−	0.979791i	$-0.564103\pi$
$449$	0.0781918	−	1.94031i	0.0781918	−	1.94031i	0.278217	−	0.960518i	$-0.410256\pi$
$450$	−0.0832161	−	0.685347i	−0.0832161	−	0.685347i
$451$		0			0
$452$	1.26079	−	1.54419i	1.26079	−	1.54419i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.368039	−	0.156807i	0.368039	−	0.156807i	−0.200026	−	0.979791i	$-0.564103\pi$
$457$	0.368039	−	0.156807i	0.368039	−	0.156807i	0.568065	+	0.822984i	$0.307692\pi$
$458$	1.37723	−	0.586782i	1.37723	−	0.586782i
$459$		0			0
$460$		0			0
$461$	−0.554631	+	1.91481i	−0.554631	+	1.91481i	−0.200026	+	0.979791i	$0.564103\pi$
$461$	−0.554631	+	1.91481i	−0.554631	+	1.91481i	−0.354605	+	0.935016i	$0.615385\pi$
$462$		0			0
$463$		0			0		0.970942	−	0.239316i	$-0.0769231\pi$
$463$		0			0		−0.970942	+	0.239316i	$0.923077\pi$
$464$	1.16367	+	1.42524i	1.16367	+	1.42524i
$465$		0			0
$466$	−0.566973	+	0.426052i	−0.566973	+	0.426052i
$467$		0			0		−0.970942	−	0.239316i	$-0.923077\pi$
$467$		0			0		0.970942	+	0.239316i	$0.0769231\pi$
$468$	−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
$477$	−0.171499	−	0.361427i	−0.171499	−	0.361427i
$478$		0			0
$479$		0			0		0.987050	−	0.160411i	$-0.0512821\pi$
$479$		0			0		−0.987050	+	0.160411i	$0.948718\pi$
$480$		0			0
$481$	−0.542249	−	0.664135i	−0.542249	−	0.664135i
$482$	−0.566973	+	1.49498i	−0.566973	+	1.49498i
$483$		0			0
$484$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$485$	0.197315	−	0.341759i	0.197315	−	0.341759i
$486$		0			0
$487$		0			0		0.845190	−	0.534466i	$-0.179487\pi$
$487$		0			0		−0.845190	+	0.534466i	$0.820513\pi$
$488$	−0.799443	+	1.38468i	−0.799443	+	1.38468i
$489$		0			0
$490$	−0.111301	−	0.545190i	−0.111301	−	0.545190i
$491$		0			0		−0.996757	−	0.0804666i	$-0.974359\pi$
$491$		0			0		0.996757	+	0.0804666i	$0.0256410\pi$
$492$		0			0
$493$	0.0841732	−	0.121946i	0.0841732	−	0.121946i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		0.748511	−	0.663123i	$-0.230769\pi$
$499$		0			0		−0.748511	+	0.663123i	$0.769231\pi$
$500$	0.188141	+	0.921578i	0.188141	+	0.921578i
$501$		0			0
$502$		0			0
$503$		0			0		0.0402659	−	0.999189i	$-0.487179\pi$
$503$		0			0		−0.0402659	+	0.999189i	$0.512821\pi$
$504$		0			0
$505$	−0.487560	−	0.507603i	−0.487560	−	0.507603i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1.27458	−	1.32698i	−1.27458	−	1.32698i	−0.919979	−	0.391967i	$-0.871795\pi$
$509$	−1.27458	−	1.32698i	−1.27458	−	1.32698i	−0.354605	−	0.935016i	$-0.615385\pi$
$510$		0			0
$511$		0			0
$512$	0.568065	+	0.822984i	0.568065	+	0.822984i
$513$		0			0
$514$	−0.379463	−	1.85873i	−0.379463	−	1.85873i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	0.238540	−	0.502711i	0.238540	−	0.502711i
$521$	0.787025	−	1.14020i	0.787025	−	1.14020i	−0.200026	−	0.979791i	$-0.564103\pi$
$521$	0.787025	−	1.14020i	0.787025	−	1.14020i	0.987050	−	0.160411i	$-0.0512821\pi$
$522$	−1.74527	−	0.582656i	−1.74527	−	0.582656i
$523$		0			0		−0.996757	−	0.0804666i	$-0.974359\pi$
$523$		0			0		0.996757	+	0.0804666i	$0.0256410\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$530$	0.111301	+	0.192779i	0.111301	+	0.192779i
$531$		0			0
$532$		0			0
$533$	0.593932	+	1.25168i	0.593932	+	1.25168i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−0.402877	−	1.06230i	−0.402877	−	1.06230i
$539$		0			0
$540$		0			0
$541$	1.07766	−	1.56126i	1.07766	−	1.56126i	0.278217	−	0.960518i	$-0.410256\pi$
$541$	1.07766	−	1.56126i	1.07766	−	1.56126i	0.799443	−	0.600742i	$-0.205128\pi$
$542$		0			0
$543$		0			0
$544$	0.0509320	−	0.0623804i	0.0509320	−	0.0623804i
$545$	−0.956763	+	0.235821i	−0.956763	+	0.235821i
$546$		0			0
$547$		0			0		−0.970942	−	0.239316i	$-0.923077\pi$
$547$		0			0		0.970942	+	0.239316i	$0.0769231\pi$
$548$	−1.59370	+	1.19759i	−1.59370	+	1.19759i
$549$	−0.0643806	−	1.59759i	−0.0643806	−	1.59759i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−0.885456	−	0.464723i	−0.885456	−	0.464723i
$555$		0			0
$556$		0			0
$557$	0.919979	−	0.391967i	0.919979	−	0.391967i	0.120537	−	0.992709i	$-0.461538\pi$
$557$	0.919979	−	0.391967i	0.919979	−	0.391967i	0.799443	+	0.600742i	$0.205128\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.253011	−	0.309882i	0.253011	−	0.309882i
$563$		0			0		−0.799443	−	0.600742i	$-0.794872\pi$
$563$		0			0		0.799443	+	0.600742i	$0.205128\pi$
$564$		0			0
$565$	0.0446654	−	1.10836i	0.0446654	−	1.10836i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	0.759177	−	1.59993i	0.759177	−	1.59993i	−0.0402659	−	0.999189i	$-0.512821\pi$
$569$	0.759177	−	1.59993i	0.759177	−	1.59993i	0.799443	−	0.600742i	$-0.205128\pi$
$570$		0			0
$571$		0			0		0.120537	−	0.992709i	$-0.461538\pi$
$571$		0			0		−0.120537	+	0.992709i	$0.538462\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.919979	−	0.391967i	−0.919979	−	0.391967i
$577$	−1.69038			−1.69038			−0.845190	−	0.534466i	$-0.820513\pi$
$577$	−1.69038			−1.69038			−0.845190	+	0.534466i	$0.820513\pi$
$578$	0.914013	+	0.389425i	0.914013	+	0.389425i
$579$		0			0
$580$	0.994067	+	0.245016i	0.994067	+	0.245016i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−0.885456	+	0.464723i	−0.885456	+	0.464723i
$585$	0.0670708	+	0.552378i	0.0670708	+	0.552378i
$586$	−1.12001	−	0.587824i	−1.12001	−	0.587824i
$587$		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
$592$	0.593932	−	0.618348i	0.593932	−	0.618348i
$593$	−0.203753	+	1.67806i	−0.203753	+	1.67806i	0.428693	+	0.903450i	$0.358974\pi$
$593$	−0.203753	+	1.67806i	−0.203753	+	1.67806i	−0.632445	+	0.774605i	$0.717949\pi$
$594$		0			0
$595$		0			0
$596$	−0.987050	−	1.70962i	−0.987050	−	1.70962i
$597$		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
$601$	0.444838	+	1.53576i	0.444838	+	1.53576i	0.799443	+	0.600742i	$0.205128\pi$
$601$	0.444838	+	1.53576i	0.444838	+	1.53576i	−0.354605	+	0.935016i	$0.615385\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.511909	−	0.218104i	−0.511909	−	0.218104i
$606$		0			0
$607$		0			0		−0.919979	−	0.391967i	$-0.871795\pi$
$607$		0			0		0.919979	+	0.391967i	$0.128205\pi$
$608$		0			0
$609$		0			0
$610$	0.107239	+	0.883189i	0.107239	+	0.883189i
$611$		0			0
$612$	−0.00970705	+	0.0799447i	−0.00970705	+	0.0799447i
$613$	−1.59370	−	0.128657i	−1.59370	−	0.128657i	−0.748511	−	0.663123i	$-0.769231\pi$
$613$	−1.59370	−	0.128657i	−1.59370	−	0.128657i	−0.845190	+	0.534466i	$0.820513\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.83399	−	0.148055i	1.83399	−	0.148055i	0.885456	−	0.464723i	$-0.153846\pi$
$617$	1.83399	−	0.148055i	1.83399	−	0.148055i	0.948536	+	0.316668i	$0.102564\pi$
$618$		0			0
$619$		0			0		−0.120537	−	0.992709i	$-0.538462\pi$
$619$		0			0		0.120537	+	0.992709i	$0.461538\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.125005	−	0.110745i	−0.125005	−	0.110745i
$626$	1.78649	−	0.761154i	1.78649	−	0.761154i
$627$		0			0
$628$	−1.66849	+	1.05509i	−1.66849	+	1.05509i
$629$	−0.0611379	−	0.0320877i	−0.0611379	−	0.0320877i
$630$		0			0
$631$		0			0		0.948536	−	0.316668i	$-0.102564\pi$
$631$		0			0		−0.948536	+	0.316668i	$0.897436\pi$
$632$		0			0
$633$		0			0
$634$	0.0161084	+	0.399727i	0.0161084	+	0.399727i
$635$		0			0
$636$		0			0
$637$	−0.200026	−	0.979791i	−0.200026	−	0.979791i
$638$		0			0
$639$		0			0
$640$	0.527799	+	0.176205i	0.527799	+	0.176205i
$641$	−0.692724	+	0.721202i	−0.692724	+	0.721202i	−0.970942	−	0.239316i	$-0.923077\pi$
$641$	−0.692724	+	0.721202i	−0.692724	+	0.721202i	0.278217	+	0.960518i	$0.410256\pi$
$642$		0			0
$643$		0			0		−0.799443	−	0.600742i	$-0.794872\pi$
$643$		0			0		0.799443	+	0.600742i	$0.205128\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.692724	−	0.721202i	$-0.743590\pi$
$647$		0			0		0.692724	+	0.721202i	$0.256410\pi$
$648$	0.987050	−	0.160411i	0.987050	−	0.160411i
$649$		0			0
$650$	0.138094	+	0.676428i	0.138094	+	0.676428i
$651$		0			0
$652$		0			0
$653$	0.748511	+	1.29646i	0.748511	+	1.29646i	0.948536	+	0.316668i	$0.102564\pi$
$653$	0.748511	+	1.29646i	0.748511	+	1.29646i	−0.200026	+	0.979791i	$0.564103\pi$
$654$		0			0
$655$		0			0
$656$	−1.17097	+	0.740475i	−1.17097	+	0.740475i
$657$	0.500000	−	0.866025i	0.500000	−	0.866025i
$658$		0			0
$659$		0			0		−0.200026	−	0.979791i	$-0.564103\pi$
$659$		0			0		0.200026	+	0.979791i	$0.435897\pi$
$660$		0			0
$661$	−1.60339	−	0.535289i	−1.60339	−	0.535289i	−0.632445	−	0.774605i	$-0.717949\pi$
$661$	−1.60339	−	0.535289i	−1.60339	−	0.535289i	−0.970942	+	0.239316i	$0.923077\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−0.171499	+	0.840058i	−0.171499	+	0.840058i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.51660	−	1.13965i	1.51660	−	1.13965i	0.568065	−	0.822984i	$-0.307692\pi$
$673$	1.51660	−	1.13965i	1.51660	−	1.13965i	0.948536	−	0.316668i	$-0.102564\pi$
$674$	−0.876221	−	0.912242i	−0.876221	−	0.912242i
$675$		0			0
$676$	0.428693	−	0.903450i	0.428693	−	0.903450i
$677$	1.77091			1.77091			0.885456	−	0.464723i	$-0.153846\pi$
$677$	1.77091			1.77091			0.885456	+	0.464723i	$0.153846\pi$
$678$		0			0
$679$		0			0
$680$	0.00180435	−	0.0447744i	0.00180435	−	0.0447744i
$681$		0			0
$682$		0			0
$683$		0			0		−0.200026	−	0.979791i	$-0.564103\pi$
$683$		0			0		0.200026	+	0.979791i	$0.435897\pi$
$684$		0			0
$685$	−0.308616	+	1.06547i	−0.308616	+	1.06547i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.200026	+	0.346455i	0.200026	+	0.346455i
$690$		0			0
$691$		0			0		−0.948536	−	0.316668i	$-0.897436\pi$
$691$		0			0		0.948536	+	0.316668i	$0.102564\pi$
$692$	−0.240292	−	0.0193983i	−0.240292	−	0.0193983i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	0.0835134	+	0.0739864i	0.0835134	+	0.0739864i
$698$	−0.568065	+	0.983917i	−0.568065	+	0.983917i
$699$		0			0
$700$		0			0
$701$	0.530851	−	1.39974i	0.530851	−	1.39974i	−0.354605	−	0.935016i	$-0.615385\pi$
$701$	0.530851	−	1.39974i	0.530851	−	1.39974i	0.885456	−	0.464723i	$-0.153846\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	0.813261	+	1.71391i	0.813261	+	1.71391i
$707$		0			0
$708$		0			0
$709$	−1.35136	−	1.01548i	−1.35136	−	1.01548i	−0.996757	−	0.0804666i	$-0.974359\pi$
$709$	−1.35136	−	1.01548i	−1.35136	−	1.01548i	−0.354605	−	0.935016i	$-0.615385\pi$
$710$		0			0
$711$		0			0
$712$	1.07766	+	0.359776i	1.07766	+	0.359776i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.632445	−	0.774605i	$-0.717949\pi$
$719$		0			0		0.632445	+	0.774605i	$0.282051\pi$
$720$	−0.540266	+	0.133164i	−0.540266	+	0.133164i
$721$		0			0
$722$	0.278217	−	0.960518i	0.278217	−	0.960518i
$723$		0			0
$724$	−1.60339	+	1.01392i	−1.60339	+	1.01392i
$725$	−1.16862	+	0.497904i	−1.16862	+	0.497904i
$726$		0			0
$727$		0			0		−0.748511	−	0.663123i	$-0.769231\pi$
$727$		0			0		0.748511	+	0.663123i	$0.230769\pi$
$728$		0			0
$729$	−0.748511	+	0.663123i	−0.748511	+	0.663123i
$730$	−0.238540	+	0.502711i	−0.238540	+	0.502711i
$731$		0			0
$732$		0			0
$733$	0.237952	+	1.95971i	0.237952	+	1.95971i	0.278217	+	0.960518i	$0.410256\pi$
$733$	0.237952	+	1.95971i	0.237952	+	1.95971i	−0.0402659	+	0.999189i	$0.512821\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	0.593932	−	1.25168i	0.593932	−	1.25168i
$739$		0			0		−0.996757	−	0.0804666i	$-0.974359\pi$
$739$		0			0		0.996757	+	0.0804666i	$0.0256410\pi$
$740$	0.0575055	−	0.473601i	0.0575055	−	0.473601i
$741$		0			0
$742$		0			0
$743$		0			0		−0.0402659	−	0.999189i	$-0.512821\pi$
$743$		0			0		0.0402659	+	0.999189i	$0.487179\pi$
$744$		0			0
$745$	−1.01056	−	0.430559i	−1.01056	−	0.430559i
$746$	1.38545			1.38545
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.278217	−	0.960518i	$-0.589744\pi$
$751$		0			0		0.278217	+	0.960518i	$0.410256\pi$
$752$		0			0
$753$		0			0
$754$	1.78649	+	0.440331i	1.78649	+	0.440331i
$755$		0			0
$756$		0			0
$757$	−0.203753	−	0.128845i	−0.203753	−	0.128845i	0.428693	−	0.903450i	$-0.358974\pi$
$757$	−0.203753	−	0.128845i	−0.203753	−	0.128845i	−0.632445	+	0.774605i	$0.717949\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−1.03702	+	1.07966i	−1.03702	+	1.07966i	−0.0402659	+	0.999189i	$0.512821\pi$
$761$	−1.03702	+	1.07966i	−1.03702	+	1.07966i	−0.996757	+	0.0804666i	$0.974359\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.0224054	+	0.0388072i	0.0224054	+	0.0388072i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−0.203753	−	0.128845i	−0.203753	−	0.128845i	0.428693	−	0.903450i	$-0.358974\pi$
$769$	−0.203753	−	0.128845i	−0.203753	−	0.128845i	−0.632445	+	0.774605i	$0.717949\pi$
$770$		0			0
$771$		0			0
$772$	−1.91674	−	0.472433i	−1.91674	−	0.472433i
$773$	0.759177	+	1.59993i	0.759177	+	1.59993i	0.799443	+	0.600742i	$0.205128\pi$
$773$	0.759177	+	1.59993i	0.759177	+	1.59993i	−0.0402659	+	0.999189i	$0.512821\pi$
$774$		0			0
$775$		0			0
$776$	0.652458	+	0.277987i	0.652458	+	0.277987i
$777$		0			0
$778$	−0.0345234	−	0.856690i	−0.0345234	−	0.856690i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.948536	−	0.316668i	0.948536	−	0.316668i
$785$	−0.389519	+	1.02708i	−0.389519	+	1.02708i
$786$		0			0
$787$		0			0		0.0402659	−	0.999189i	$-0.487179\pi$
$787$		0			0		−0.0402659	+	0.999189i	$0.512821\pi$
$788$	0.0290582	+	0.239316i	0.0290582	+	0.239316i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	0.192724	+	1.58723i	0.192724	+	1.58723i
$794$	1.45352	+	1.28771i	1.45352	+	1.28771i
$795$		0			0
$796$		0			0
$797$	1.64126	−	1.03787i	1.64126	−	1.03787i	0.692724	−	0.721202i	$-0.256410\pi$
$797$	1.64126	−	1.03787i	1.64126	−	1.03787i	0.948536	−	0.316668i	$-0.102564\pi$
$798$		0			0
$799$		0			0
$800$	−0.654851	+	0.218621i	−0.654851	+	0.218621i
$801$	−1.10312	+	0.271894i	−1.10312	+	0.271894i
$802$	0.799974	+	0.979791i	0.799974	+	0.979791i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	0.799974	−	0.979791i	0.799974	−	0.979791i
$809$	1.87251	+	0.625134i	1.87251	+	0.625134i	0.987050	+	0.160411i	$0.0512821\pi$
$809$	1.87251	+	0.625134i	1.87251	+	0.625134i	0.885456	+	0.464723i	$0.153846\pi$
$810$	0.385456	−	0.401302i	0.385456	−	0.401302i
$811$		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
$818$	0.354605	+	0.935016i	0.354605	+	0.935016i
$819$		0			0
$820$	−0.273369	+	0.720815i	−0.273369	+	0.720815i
$821$	0.141860	−	0.694877i	0.141860	−	0.694877i	−0.845190	−	0.534466i	$-0.820513\pi$
$821$	0.141860	−	0.694877i	0.141860	−	0.694877i	0.987050	−	0.160411i	$-0.0512821\pi$
$822$		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		0.885456	−	0.464723i	$-0.153846\pi$
$827$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$828$		0			0
$829$	0.398754	+	0.0321908i	0.398754	+	0.0321908i	0.278217	−	0.960518i	$-0.410256\pi$
$829$	0.398754	+	0.0321908i	0.398754	+	0.0321908i	0.120537	+	0.992709i	$0.461538\pi$
$830$		0			0
$831$		0			0
$832$	0.948536	+	0.316668i	0.948536	+	0.316668i
$833$	−0.0457473	−	0.0662764i	−0.0457473	−	0.0662764i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.987050	−	0.160411i	$-0.948718\pi$
$839$		0			0		0.987050	+	0.160411i	$0.0512821\pi$
$840$		0			0
$841$	−0.0960523	+	2.38351i	−0.0960523	+	2.38351i
$842$	1.27822	−	0.960518i	1.27822	−	0.960518i
$843$		0			0
$844$		0			0
$845$	−0.111301	−	0.545190i	−0.111301	−	0.545190i
$846$		0			0
$847$		0			0
$848$	−0.319818	+	0.240328i	−0.319818	+	0.240328i
$849$		0			0
$850$	0.0315830	+	0.0457559i	0.0315830	+	0.0457559i
$851$		0			0
$852$		0			0
$853$	0.0602790	−	0.0534025i	0.0602790	−	0.0534025i	−0.632445	−	0.774605i	$-0.717949\pi$
$853$	0.0602790	−	0.0534025i	0.0602790	−	0.0534025i	0.692724	+	0.721202i	$0.256410\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.908271	+	1.31586i	0.908271	+	1.31586i	0.948536	+	0.316668i	$0.102564\pi$
$857$	0.908271	+	1.31586i	0.908271	+	1.31586i	−0.0402659	+	0.999189i	$0.512821\pi$
$858$		0			0
$859$		0			0		0.568065	−	0.822984i	$-0.307692\pi$
$859$		0			0		−0.568065	+	0.822984i	$0.692308\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$863$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$864$		0			0
$865$	−0.113375	+	0.0716941i	−0.113375	+	0.0716941i
$866$	−0.641762	−	0.568552i	−0.641762	−	0.568552i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.627974	−	1.65583i	−0.627974	−	1.65583i
$873$	−0.700026	+	0.113765i	−0.700026	+	0.113765i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.876221	−	1.07318i	−0.876221	−	1.07318i	−0.996757	−	0.0804666i	$-0.974359\pi$
$877$	−0.876221	−	1.07318i	−0.876221	−	1.07318i	0.120537	−	0.992709i	$-0.461538\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.31415	+	0.438727i	1.31415	+	0.438727i	0.885456	−	0.464723i	$-0.153846\pi$
$881$	1.31415	+	0.438727i	1.31415	+	0.438727i	0.428693	+	0.903450i	$0.358974\pi$
$882$	−0.632445	+	0.774605i	−0.632445	+	0.774605i
$883$		0			0		0.970942	−	0.239316i	$-0.0769231\pi$
$883$		0			0		−0.970942	+	0.239316i	$0.923077\pi$
$884$	0.00324269	−	0.0804666i	0.00324269	−	0.0804666i
$885$		0			0
$886$		0			0
$887$		0			0		−0.0402659	−	0.999189i	$-0.512821\pi$
$887$		0			0		0.0402659	+	0.999189i	$0.487179\pi$
$888$		0			0
$889$		0			0
$890$	0.599648	−	0.200192i	0.599648	−	0.200192i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	1.45352	−	1.28771i	1.45352	−	1.28771i
$899$		0			0
$900$	0.436628	−	0.534772i	0.436628	−	0.534772i
$901$	0.0257556	+	0.0193540i	0.0257556	+	0.0193540i
$902$		0			0
$903$		0			0
$904$	1.98705	−	0.160411i	1.98705	−	0.160411i
$905$	−0.374320	+	0.987001i	−0.374320	+	0.987001i
$906$		0			0
$907$		0			0		0.428693	−	0.903450i	$-0.358974\pi$
$907$		0			0		−0.428693	+	0.903450i	$0.641026\pi$
$908$		0			0
$909$	−0.152466	+	1.25567i	−0.152466	+	1.25567i
$910$		0			0
$911$		0			0		−0.120537	−	0.992709i	$-0.538462\pi$
$911$		0			0		0.120537	+	0.992709i	$0.461538\pi$
$912$		0			0
$913$		0			0
$914$	0.368039	+	0.156807i	0.368039	+	0.156807i
$915$		0			0
$916$	1.37723	+	0.586782i	1.37723	+	0.586782i
$917$		0			0
$918$		0			0
$919$		0			0		0.996757	−	0.0804666i	$-0.0256410\pi$
$919$		0			0		−0.996757	+	0.0804666i	$0.974359\pi$
$920$		0			0
$921$		0			0
$922$	−1.76517	+	0.926432i	−1.76517	+	0.926432i
$923$		0			0
$924$		0			0
$925$	0.295961	+	0.512619i	0.295961	+	0.512619i
$926$		0			0
$927$		0			0
$928$	−0.221783	+	1.82654i	−0.221783	+	1.82654i
$929$	−0.0557864	+	0.0580798i	−0.0557864	+	0.0580798i	−0.748511	−	0.663123i	$-0.769231\pi$
$929$	−0.0557864	+	0.0580798i	−0.0557864	+	0.0580798i	0.692724	+	0.721202i	$0.256410\pi$
$930$		0			0
$931$		0			0
$932$	−0.700026	−	0.113765i	−0.700026	−	0.113765i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−0.970942	+	0.239316i	−0.970942	+	0.239316i
$937$	−0.885456	+	0.464723i	−0.885456	+	0.464723i	−0.845190	−	0.534466i	$-0.820513\pi$
$937$	−0.885456	+	0.464723i	−0.885456	+	0.464723i	−0.0402659	+	0.999189i	$0.512821\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.234068	−	0.0576926i	−0.234068	−	0.0576926i	0.120537	−	0.992709i	$-0.461538\pi$
$941$	−0.234068	−	0.0576926i	−0.234068	−	0.0576926i	−0.354605	+	0.935016i	$0.615385\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.0402659	−	0.999189i	$-0.512821\pi$
$947$		0			0		0.0402659	+	0.999189i	$0.487179\pi$
$948$		0			0
$949$	−0.428693	+	0.903450i	−0.428693	+	0.903450i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.228667	−	0.0763402i	0.228667	−	0.0763402i	−0.200026	−	0.979791i	$-0.564103\pi$
$953$	0.228667	−	0.0763402i	0.228667	−	0.0763402i	0.428693	+	0.903450i	$0.358974\pi$
$954$	0.141860	−	0.374055i	0.141860	−	0.374055i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.748511	+	0.663123i	−0.748511	+	0.663123i
$962$	0.103346	−	0.851134i	0.103346	−	0.851134i
$963$		0			0
$964$	−1.47094	+	0.626710i	−1.47094	+	0.626710i
$965$	−1.01056	+	0.430559i	−1.01056	+	0.430559i
$966$		0			0
$967$		0			0		−0.885456	−	0.464723i	$-0.846154\pi$
$967$		0			0		0.885456	+	0.464723i	$0.153846\pi$
$968$	0.278217	−	0.960518i	0.278217	−	0.960518i
$969$		0			0
$970$	0.383162	−	0.0944409i	0.383162	−	0.0944409i
$971$		0			0		−0.632445	−	0.774605i	$-0.717949\pi$
$971$		0			0		0.632445	+	0.774605i	$0.282051\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−1.55242	+	0.382638i	−1.55242	+	0.382638i
$977$	−1.24851	+	1.52915i	−1.24851	+	1.52915i	−0.500000	+	0.866025i	$0.666667\pi$
$977$	−1.24851	+	1.52915i	−1.24851	+	1.52915i	−0.748511	+	0.663123i	$0.769231\pi$
$978$		0			0
$979$		0			0
$980$	0.316091	−	0.457937i	0.316091	−	0.457937i
$981$	1.41574	+	1.06386i	1.41574	+	1.06386i
$982$		0			0
$983$		0			0		−0.354605	−	0.935016i	$-0.615385\pi$
$983$		0			0		0.354605	+	0.935016i	$0.384615\pi$
$984$		0			0
$985$	0.0929232	+	0.0967433i	0.0929232	+	0.0967433i
$986$	0.146257	−	0.0237690i	0.146257	−	0.0237690i
$987$		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
$997$	0.398754	+	1.95323i	0.398754	+	1.95323i	0.278217	+	0.960518i	$0.410256\pi$
$997$	0.398754	+	1.95323i	0.398754	+	1.95323i	0.120537	+	0.992709i	$0.461538\pi$
$998$		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.367.1	yes	24
4.3	odd	2	CM	676.1.t.a.367.1	yes	24
169.35	even	39	inner	676.1.t.a.35.1	✓	24
676.35	odd	78	inner	676.1.t.a.35.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
676.1.t.a.35.1	✓	24	169.35	even	39	inner
676.1.t.a.35.1	✓	24	676.35	odd	78	inner
676.1.t.a.367.1	yes	24	1.1	even	1	trivial
676.1.t.a.367.1	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	676.t (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.692724 + 0.721202i) q^{2} +(-0.0402659 + 0.999189i) q^{4} +(0.316091 + 0.457937i) q^{5} +(-0.748511 + 0.663123i) q^{8} +(0.278217 - 0.960518i) q^{9} +(-0.111301 + 0.545190i) q^{10} +(-0.200026 + 0.979791i) q^{13} +(-0.996757 - 0.0804666i) q^{16} +(0.0161084 + 0.0789044i) q^{17} +(0.885456 - 0.464723i) q^{18} +(-0.470293 + 0.297395i) q^{20} +(0.244812 - 0.645517i) q^{25} +(-0.845190 + 0.534466i) q^{26} +(-1.27458 - 1.32698i) q^{29} +(-0.632445 - 0.774605i) q^{32} +(-0.0457473 + 0.0662764i) q^{34} +(0.948536 + 0.316668i) q^{36} +(-0.542249 + 0.664135i) q^{37} +(-0.540266 - 0.133164i) q^{40} +(1.10759 - 0.832298i) q^{41} +(0.527799 - 0.176205i) q^{45} +(-0.919979 + 0.391967i) q^{49} +(0.635136 - 0.270606i) q^{50} +(-0.970942 - 0.239316i) q^{52} +(0.299443 - 0.265283i) q^{53} +(0.0740877 - 1.83847i) q^{58} +(1.51660 - 0.506316i) q^{61} +(0.120537 - 0.992709i) q^{64} +(-0.511909 + 0.218104i) q^{65} +(-0.0794890 + 0.0129182i) q^{68} +(0.428693 + 0.903450i) q^{72} +(0.970942 + 0.239316i) q^{73} +(-0.854605 + 0.0689908i) q^{74} +(-0.278217 - 0.481887i) q^{80} +(-0.845190 - 0.534466i) q^{81} +(1.36751 + 0.222242i) q^{82} +(-0.0310415 + 0.0323176i) q^{85} +(-0.568065 - 0.983917i) q^{89} +(0.492699 + 0.258588i) q^{90} +(-0.304033 - 0.640736i) q^{97} +(-0.919979 - 0.391967i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} + q^{4} + 2 q^{5} - 2 q^{8} + q^{9} - q^{10} + q^{13} + q^{16} - q^{17} - 2 q^{18} - q^{20} + q^{26} - q^{29} + q^{32} + 2 q^{34} + q^{36} - q^{37} - 11 q^{40} - q^{41} - q^{45}+ \cdots + q^{98}+O(q^{100}) \) 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

Introduction

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