LMFDB - Embedded newform 1725.1.bg.a.557.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1725,1,Mod(107,1725)] 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("1725.107"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1725, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([22, 11, 34])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 1725 = 3 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1725.bg (of order $44$, degree $20$, 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:	$0.860887146792$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$2$ over $\Q(\zeta_{44})$
Coefficient field:	$\Q(\zeta_{88})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{40} - x^{36} + x^{32} - x^{28} + x^{24} - x^{20} + x^{16} - x^{12} + x^{8} - x^{4} + 1 $ x^40 - x^36 + x^32 - x^28 + x^24 - x^20 + x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{22}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{22} - \cdots)$

Embedding invariants

Embedding label			557.2
Root			$0.877679 - 0.479249i$ of defining polynomial
Character	$\chi$	$=$	1725.557
Dual form			1725.1.bg.a.1118.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.14952 - 0.627683i) q^{2} +(0.997452 - 0.0713392i) q^{3} +(0.386758 - 0.601808i) q^{4} +(1.10181 - 0.708089i) q^{6} +(-0.0265942 + 0.371836i) q^{8} +(0.989821 - 0.142315i) q^{9} +(0.342841 - 0.627866i) q^{12} +(0.500000 + 1.09485i) q^{16} +(-1.05657 - 0.229843i) q^{17} +(1.04849 - 0.784887i) q^{18} +(-1.53046 - 0.983568i) q^{19} +(0.877679 + 0.479249i) q^{23} +0.372786i q^{24} +(0.977147 - 0.212565i) q^{27} +(-0.544078 - 0.627899i) q^{31} +(0.963544 + 0.721300i) q^{32} +(-1.35881 + 0.398983i) q^{34} +(0.297176 - 0.650724i) q^{36} +(-2.37666 - 0.169982i) q^{38} +1.30972 q^{46} +(-1.35693 + 1.35693i) q^{47} +(0.576832 + 1.05639i) q^{48} +(-0.755750 - 0.654861i) q^{49} +(-1.07028 - 0.153882i) q^{51} +(0.527938 + 0.196911i) q^{53} +(0.989821 - 0.857685i) q^{54} +(-1.59673 - 0.871880i) q^{57} +(-0.425839 + 0.368991i) q^{61} +(-1.01955 - 0.380272i) q^{62} +(0.368991 + 0.0530529i) q^{64} +(-0.546959 + 0.546959i) q^{68} +(0.909632 + 0.415415i) q^{69} +(0.0265942 + 0.371836i) q^{72} +(-1.18384 + 0.540641i) q^{76} +(0.822373 - 1.80075i) q^{79} +(0.959493 - 0.281733i) q^{81} +(-1.21002 - 0.905808i) q^{83} +(0.627866 - 0.342841i) q^{92} +(-0.587486 - 0.587486i) q^{93} +(-0.708089 + 2.41153i) q^{94} +(1.01255 + 0.650724i) q^{96} +(-1.27979 - 0.278401i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{6} + 20 q^{16} - 8 q^{31} - 12 q^{36} + 8 q^{46} - 44 q^{76} + 4 q^{81} + 20 q^{96}+O(q^{100}) $ 40 * q + 8 * q^6 + 20 * q^16 - 8 * q^31 - 12 * q^36 + 8 * q^46 - 44 * q^76 + 4 * q^81 + 20 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1725\mathbb{Z}\right)^\times$.

$n$	$277$	$1151$	$1201$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{22}\right)$

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 $

$2$	1.14952	−	0.627683i	1.14952	−	0.627683i	0.212565	−	0.977147i	$-0.431818\pi$
$2$	1.14952	−	0.627683i	1.14952	−	0.627683i	0.936950	+	0.349464i	$0.113636\pi$
$3$	0.997452	−	0.0713392i	0.997452	−	0.0713392i
$3$	0.997452	−	0.0713392i	0.997452	−	0.0713392i
$4$	0.386758	−	0.601808i	0.386758	−	0.601808i
$5$		0			0
$5$		0			0
$6$	1.10181	−	0.708089i	1.10181	−	0.708089i
$7$		0			0		0.349464	−	0.936950i	$-0.386364\pi$
$7$		0			0		−0.349464	+	0.936950i	$0.613636\pi$
$8$	−0.0265942	+	0.371836i	−0.0265942	+	0.371836i
$9$	0.989821	−	0.142315i	0.989821	−	0.142315i
$10$		0			0
$11$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$11$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$12$	0.342841	−	0.627866i	0.342841	−	0.627866i
$13$		0			0		0.936950	−	0.349464i	$-0.113636\pi$
$13$		0			0		−0.936950	+	0.349464i	$0.886364\pi$
$14$		0			0
$15$		0			0
$16$	0.500000	+	1.09485i	0.500000	+	1.09485i
$17$	−1.05657	−	0.229843i	−1.05657	−	0.229843i	−0.349464	−	0.936950i	$-0.613636\pi$
$17$	−1.05657	−	0.229843i	−1.05657	−	0.229843i	−0.707107	+	0.707107i	$0.750000\pi$
$18$	1.04849	−	0.784887i	1.04849	−	0.784887i
$19$	−1.53046	−	0.983568i	−1.53046	−	0.983568i	−0.989821	−	0.142315i	$-0.954545\pi$
$19$	−1.53046	−	0.983568i	−1.53046	−	0.983568i	−0.540641	−	0.841254i	$-0.681818\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.877679	+	0.479249i	0.877679	+	0.479249i
$23$	0.877679	+	0.479249i	0.877679	+	0.479249i
$24$			0.372786i			0.372786i
$25$		0			0
$26$		0			0
$27$	0.977147	−	0.212565i	0.977147	−	0.212565i
$28$		0			0
$29$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$29$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$30$		0			0
$31$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	0.415415	−	0.909632i	$-0.363636\pi$
$31$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	−0.959493	+	0.281733i	$0.909091\pi$
$32$	0.963544	+	0.721300i	0.963544	+	0.721300i
$33$		0			0
$34$	−1.35881	+	0.398983i	−1.35881	+	0.398983i
$35$		0			0
$36$	0.297176	−	0.650724i	0.297176	−	0.650724i
$37$		0			0		0.599278	−	0.800541i	$-0.295455\pi$
$37$		0			0		−0.599278	+	0.800541i	$0.704545\pi$
$38$	−2.37666	−	0.169982i	−2.37666	−	0.169982i
$39$		0			0
$40$		0			0
$41$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$41$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$42$		0			0
$43$		0			0		−0.0713392	−	0.997452i	$-0.522727\pi$
$43$		0			0		0.0713392	+	0.997452i	$0.477273\pi$
$44$		0			0
$45$		0			0
$46$	1.30972			1.30972
$47$	−1.35693	+	1.35693i	−1.35693	+	1.35693i	−0.479249	+	0.877679i	$0.659091\pi$
$47$	−1.35693	+	1.35693i	−1.35693	+	1.35693i	−0.877679	+	0.479249i	$0.840909\pi$
$48$	0.576832	+	1.05639i	0.576832	+	1.05639i
$49$	−0.755750	−	0.654861i	−0.755750	−	0.654861i
$50$		0			0
$51$	−1.07028	−	0.153882i	−1.07028	−	0.153882i
$52$		0			0
$53$	0.527938	+	0.196911i	0.527938	+	0.196911i	0.599278	−	0.800541i	$-0.295455\pi$
$53$	0.527938	+	0.196911i	0.527938	+	0.196911i	−0.0713392	+	0.997452i	$0.522727\pi$
$54$	0.989821	−	0.857685i	0.989821	−	0.857685i
$55$		0			0
$56$		0			0
$57$	−1.59673	−	0.871880i	−1.59673	−	0.871880i
$58$		0			0
$59$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$59$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$60$		0			0
$61$	−0.425839	+	0.368991i	−0.425839	+	0.368991i	−0.841254	−	0.540641i	$-0.818182\pi$
$61$	−0.425839	+	0.368991i	−0.425839	+	0.368991i	0.415415	+	0.909632i	$0.363636\pi$
$62$	−1.01955	−	0.380272i	−1.01955	−	0.380272i
$63$		0			0
$64$	0.368991	+	0.0530529i	0.368991	+	0.0530529i
$65$		0			0
$66$		0			0
$67$		0			0		−0.479249	−	0.877679i	$-0.659091\pi$
$67$		0			0		0.479249	+	0.877679i	$0.340909\pi$
$68$	−0.546959	+	0.546959i	−0.546959	+	0.546959i
$69$	0.909632	+	0.415415i	0.909632	+	0.415415i
$70$		0			0
$71$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$71$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$72$	0.0265942	+	0.371836i	0.0265942	+	0.371836i
$73$		0			0		−0.212565	−	0.977147i	$-0.568182\pi$
$73$		0			0		0.212565	+	0.977147i	$0.431818\pi$
$74$		0			0
$75$		0			0
$76$	−1.18384	+	0.540641i	−1.18384	+	0.540641i
$77$		0			0
$78$		0			0
$79$	0.822373	−	1.80075i	0.822373	−	1.80075i	0.281733	−	0.959493i	$-0.409091\pi$
$79$	0.822373	−	1.80075i	0.822373	−	1.80075i	0.540641	−	0.841254i	$-0.318182\pi$
$80$		0			0
$81$	0.959493	−	0.281733i	0.959493	−	0.281733i
$82$		0			0
$83$	−1.21002	−	0.905808i	−1.21002	−	0.905808i	−0.212565	−	0.977147i	$-0.568182\pi$
$83$	−1.21002	−	0.905808i	−1.21002	−	0.905808i	−0.997452	+	0.0713392i	$0.977273\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$89$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$90$		0			0
$91$		0			0
$92$	0.627866	−	0.342841i	0.627866	−	0.342841i
$93$	−0.587486	−	0.587486i	−0.587486	−	0.587486i
$94$	−0.708089	+	2.41153i	−0.708089	+	2.41153i
$95$		0			0
$96$	1.01255	+	0.650724i	1.01255	+	0.650724i
$97$		0			0		0.800541	−	0.599278i	$-0.204545\pi$
$97$		0			0		−0.800541	+	0.599278i	$0.795455\pi$
$98$	−1.27979	−	0.278401i	−1.27979	−	0.278401i
$99$		0			0
$100$		0			0
$101$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$101$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$102$	−1.32689	+	0.494903i	−1.32689	+	0.494903i
$103$		0			0		0.479249	−	0.877679i	$-0.340909\pi$
$103$		0			0		−0.479249	+	0.877679i	$0.659091\pi$
$104$		0			0
$105$		0			0
$106$	0.730471	−	0.105026i	0.730471	−	0.105026i
$107$	−0.141226	+	1.97460i	−0.141226	+	1.97460i	0.0713392	+	0.997452i	$0.477273\pi$
$107$	−0.141226	+	1.97460i	−0.141226	+	1.97460i	−0.212565	+	0.977147i	$0.568182\pi$
$108$	0.249996	−	0.670266i	0.249996	−	0.670266i
$109$	1.66538	−	1.07028i	1.66538	−	1.07028i	0.755750	−	0.654861i	$-0.227273\pi$
$109$	1.66538	−	1.07028i	1.66538	−	1.07028i	0.909632	−	0.415415i	$-0.136364\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.32661	+	0.724384i	−1.32661	+	0.724384i	−0.977147	−	0.212565i	$-0.931818\pi$
$113$	−1.32661	+	0.724384i	−1.32661	+	0.724384i	−0.349464	+	0.936950i	$0.613636\pi$
$114$	−2.38273			−2.38273
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$122$	−0.257898	+	0.691452i	−0.257898	+	0.691452i
$123$		0			0
$124$	−0.588302	+	0.0845850i	−0.588302	+	0.0845850i
$125$		0			0
$126$		0			0
$127$		0			0		0.479249	−	0.877679i	$-0.340909\pi$
$127$		0			0		−0.479249	+	0.877679i	$0.659091\pi$
$128$	−0.670266	+	0.249996i	−0.670266	+	0.249996i
$129$		0			0
$130$		0			0
$131$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$131$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.113563	−	0.386758i	0.113563	−	0.386758i
$137$	1.39982	+	1.39982i	1.39982	+	1.39982i	0.800541	+	0.599278i	$0.204545\pi$
$137$	1.39982	+	1.39982i	1.39982	+	1.39982i	0.599278	+	0.800541i	$0.295455\pi$
$138$	1.30638	−	0.0934345i	1.30638	−	0.0934345i
$139$			1.91899i			1.91899i	0.281733	+	0.959493i	$0.409091\pi$
$139$			1.91899i			1.91899i	−0.281733	+	0.959493i	$0.590909\pi$
$140$		0			0
$141$	−1.25667	+	1.45027i	−1.25667	+	1.45027i
$142$		0			0
$143$		0			0
$144$	0.650724	+	1.01255i	0.650724	+	1.01255i
$145$		0			0
$146$		0			0
$147$	−0.800541	−	0.599278i	−0.800541	−	0.599278i
$148$		0			0
$149$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$149$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$150$		0			0
$151$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$151$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$152$	0.406427	−	0.542923i	0.406427	−	0.542923i
$153$	−1.07853	−	0.0771377i	−1.07853	−	0.0771377i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.212565	−	0.977147i	$-0.568182\pi$
$157$		0			0		0.212565	+	0.977147i	$0.431818\pi$
$158$	−0.184967	−	2.58617i	−0.184967	−	2.58617i
$159$	0.540641	+	0.158746i	0.540641	+	0.158746i
$160$		0			0
$161$		0			0
$162$	0.926113	−	0.926113i	0.926113	−	0.926113i
$163$		0			0		−0.479249	−	0.877679i	$-0.659091\pi$
$163$		0			0		0.479249	+	0.877679i	$0.340909\pi$
$164$		0			0
$165$		0			0
$166$	−1.95949	−	0.281733i	−1.95949	−	0.281733i
$167$	0.0605024	−	0.278125i	0.0605024	−	0.278125i	−0.936950	−	0.349464i	$-0.886364\pi$
$167$	0.0605024	−	0.278125i	0.0605024	−	0.278125i	0.997452	+	0.0713392i	$0.0227273\pi$
$168$		0			0
$169$	0.755750	−	0.654861i	0.755750	−	0.654861i
$170$		0			0
$171$	−1.65486	−	0.755750i	−1.65486	−	0.755750i
$172$		0			0
$173$	1.68425	+	0.919672i	1.68425	+	0.919672i	0.977147	+	0.212565i	$0.0681818\pi$
$173$	1.68425	+	0.919672i	1.68425	+	0.919672i	0.707107	+	0.707107i	$0.250000\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$179$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$180$		0			0
$181$	0.817178	+	0.708089i	0.817178	+	0.708089i	0.959493	−	0.281733i	$-0.0909091\pi$
$181$	0.817178	+	0.708089i	0.817178	+	0.708089i	−0.142315	+	0.989821i	$0.545455\pi$
$182$		0			0
$183$	−0.398430	+	0.398430i	−0.398430	+	0.398430i
$184$	−0.201543	+	0.313607i	−0.201543	+	0.313607i
$185$		0			0
$186$	−1.04408	−	0.306569i	−1.04408	−	0.306569i
$187$		0			0
$188$	0.291807	+	1.34141i	0.291807	+	1.34141i
$189$		0			0
$190$		0			0
$191$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$191$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$192$	0.371836	+	0.0265942i	0.371836	+	0.0265942i
$193$		0			0		0.599278	−	0.800541i	$-0.295455\pi$
$193$		0			0		−0.599278	+	0.800541i	$0.704545\pi$
$194$		0			0
$195$		0			0
$196$	−0.686393	+	0.201543i	−0.686393	+	0.201543i
$197$	−0.0994679	−	0.266684i	−0.0994679	−	0.266684i	0.877679	−	0.479249i	$-0.159091\pi$
$197$	−0.0994679	−	0.266684i	−0.0994679	−	0.266684i	−0.977147	+	0.212565i	$0.931818\pi$
$198$		0			0
$199$	0.989821	+	1.14231i	0.989821	+	1.14231i	0.989821	+	0.142315i	$0.0454545\pi$
$199$	0.989821	+	1.14231i	0.989821	+	1.14231i			1.00000i	$0.500000\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$	−0.506546	+	0.584585i	−0.506546	+	0.584585i
$205$		0			0
$206$		0			0
$207$	0.936950	+	0.349464i	0.936950	+	0.349464i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−1.41542	−	0.909632i	−1.41542	−	0.909632i	−0.415415	−	0.909632i	$-0.636364\pi$
$211$	−1.41542	−	0.909632i	−1.41542	−	0.909632i	−1.00000			$\pi$
$212$	0.322687	−	0.241561i	0.322687	−	0.241561i
$213$		0			0
$214$	1.07708	+	2.35848i	1.07708	+	2.35848i
$215$		0			0
$216$	0.0530529	+	0.368991i	0.0530529	+	0.368991i
$217$		0			0
$218$	1.24259	−	2.27563i	1.24259	−	2.27563i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.349464	−	0.936950i	$-0.386364\pi$
$223$		0			0		−0.349464	+	0.936950i	$0.613636\pi$
$224$		0			0
$225$		0			0
$226$	−1.07028	+	1.66538i	−1.07028	+	1.66538i
$227$	0.562029	−	0.0401971i	0.562029	−	0.0401971i	0.212565	−	0.977147i	$-0.431818\pi$
$227$	0.562029	−	0.0401971i	0.562029	−	0.0401971i	0.349464	+	0.936950i	$0.386364\pi$
$228$	−1.14225	+	0.623717i	−1.14225	+	0.623717i
$229$	−1.51150			−1.51150			−0.755750	−	0.654861i	$-0.772727\pi$
$229$	−1.51150			−1.51150			−0.755750	+	0.654861i	$0.772727\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.283904	−	0.0203052i	0.283904	−	0.0203052i	0.0713392	−	0.997452i	$-0.477273\pi$
$233$	0.283904	−	0.0203052i	0.283904	−	0.0203052i	0.212565	+	0.977147i	$0.431818\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.691814	−	1.85483i	0.691814	−	1.85483i
$238$		0			0
$239$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$239$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$240$		0			0
$241$	−0.304632	−	1.03748i	−0.304632	−	1.03748i	−0.959493	−	0.281733i	$-0.909091\pi$
$241$	−0.304632	−	1.03748i	−0.304632	−	1.03748i	0.654861	−	0.755750i	$-0.272727\pi$
$242$	−0.627683	+	1.14952i	−0.627683	+	1.14952i
$243$	0.936950	−	0.349464i	0.936950	−	0.349464i
$244$	0.0573652	+	0.398983i	0.0573652	+	0.398983i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	0.247945	−	0.185609i	0.247945	−	0.185609i
$249$	−1.27155	−	0.817178i	−1.27155	−	0.817178i
$250$		0			0
$251$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$251$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.857685	+	0.989821i	−0.857685	+	0.989821i
$257$	1.64406	−	0.357643i	1.64406	−	0.357643i	0.707107	−	0.707107i	$-0.250000\pi$
$257$	1.64406	−	0.357643i	1.64406	−	0.357643i	0.936950	+	0.349464i	$0.113636\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.635768	−	1.70456i	−0.635768	−	1.70456i	−0.707107	−	0.707107i	$-0.750000\pi$
$263$	−0.635768	−	1.70456i	−0.635768	−	1.70456i	0.0713392	−	0.997452i	$-0.477273\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$269$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$270$		0			0
$271$	0.273100	−	1.89945i	0.273100	−	1.89945i	−0.142315	−	0.989821i	$-0.545455\pi$
$271$	0.273100	−	1.89945i	0.273100	−	1.89945i	0.415415	−	0.909632i	$-0.363636\pi$
$272$	−0.276643	−	1.27171i	−0.276643	−	1.27171i
$273$		0			0
$274$	2.48775	+	0.730471i	2.48775	+	0.730471i
$275$		0			0
$276$	0.601808	−	0.386758i	0.601808	−	0.386758i
$277$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$277$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$278$	1.20451	+	2.20590i	1.20451	+	2.20590i
$279$	−0.627899	−	0.544078i	−0.627899	−	0.544078i
$280$		0			0
$281$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$281$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$282$	−0.534248	+	2.45590i	−0.534248	+	2.45590i
$283$		0			0		−0.936950	−	0.349464i	$-0.886364\pi$
$283$		0			0		0.936950	+	0.349464i	$0.113636\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	1.05639	+	0.576832i	1.05639	+	0.576832i
$289$	0.153882	+	0.0702757i	0.153882	+	0.0702757i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.321292	+	1.47696i	−0.321292	+	1.47696i	0.479249	+	0.877679i	$0.340909\pi$
$293$	−0.321292	+	1.47696i	−0.321292	+	1.47696i	−0.800541	+	0.599278i	$0.795455\pi$
$294$	−1.29639	−	0.186393i	−1.29639	−	0.186393i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$	−0.157204	−	2.19800i	−0.157204	−	2.19800i
$303$		0			0
$304$	0.311626	−	2.16741i	0.311626	−	2.16741i
$305$		0			0
$306$	−1.28820	+	0.588302i	−1.28820	+	0.588302i
$307$		0			0		−0.997452	−	0.0713392i	$-0.977273\pi$
$307$		0			0		0.997452	+	0.0713392i	$0.0227273\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$311$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$312$		0			0
$313$		0			0		−0.800541	−	0.599278i	$-0.795455\pi$
$313$		0			0		0.800541	+	0.599278i	$0.204545\pi$
$314$		0			0
$315$		0			0
$316$	−0.765644	−	1.19136i	−0.765644	−	1.19136i
$317$	−1.00829	−	1.34692i	−1.00829	−	1.34692i	−0.936950	−	0.349464i	$-0.886364\pi$
$317$	−1.00829	−	1.34692i	−1.00829	−	1.34692i	−0.0713392	−	0.997452i	$-0.522727\pi$
$318$	0.721117	−	0.156869i	0.721117	−	0.156869i
$319$		0			0
$320$		0			0
$321$			1.97964i			1.97964i
$322$		0			0
$323$	1.39098	+	1.39098i	1.39098	+	1.39098i
$324$	0.201543	−	0.686393i	0.201543	−	0.686393i
$325$		0			0
$326$		0			0
$327$	1.58479	−	1.18636i	1.58479	−	1.18636i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.186393	+	1.29639i	0.186393	+	1.29639i	0.841254	+	0.540641i	$0.181818\pi$
$331$	0.186393	+	1.29639i	0.186393	+	1.29639i	−0.654861	+	0.755750i	$0.727273\pi$
$332$	−1.01311	+	0.377869i	−1.01311	+	0.377869i
$333$		0			0
$334$	−0.105026	−	0.357685i	−0.105026	−	0.357685i
$335$		0			0
$336$		0			0
$337$		0			0		0.0713392	−	0.997452i	$-0.477273\pi$
$337$		0			0		−0.0713392	+	0.997452i	$0.522727\pi$
$338$	0.457701	−	1.22714i	0.457701	−	1.22714i
$339$	−1.27155	+	0.817178i	−1.27155	+	0.817178i
$340$		0			0
$341$		0			0
$342$	−2.37666	+	0.169982i	−2.37666	+	0.169982i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	2.51334			2.51334
$347$	0.729202	−	0.398174i	0.729202	−	0.398174i	−0.0713392	−	0.997452i	$-0.522727\pi$
$347$	0.729202	−	0.398174i	0.729202	−	0.398174i	0.800541	+	0.599278i	$0.204545\pi$
$348$		0			0
$349$	0.708089	−	1.10181i	0.708089	−	1.10181i	−0.281733	−	0.959493i	$-0.590909\pi$
$349$	0.708089	−	1.10181i	0.708089	−	1.10181i	0.989821	−	0.142315i	$-0.0454545\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.0592707	−	0.828713i	0.0592707	−	0.828713i	−0.877679	−	0.479249i	$-0.840909\pi$
$353$	0.0592707	−	0.828713i	0.0592707	−	0.828713i	0.936950	−	0.349464i	$-0.113636\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$359$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$360$		0			0
$361$	0.959493	+	2.10100i	0.959493	+	2.10100i
$362$	1.38381	+	0.301030i	1.38381	+	0.301030i
$363$	−0.800541	+	0.599278i	−0.800541	+	0.599278i
$364$		0			0
$365$		0			0
$366$	−0.207914	+	0.708089i	−0.207914	+	0.708089i
$367$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$367$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$368$	−0.0858650	+	1.20055i	−0.0858650	+	1.20055i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	−0.580768	+	0.126338i	−0.580768	+	0.126338i
$373$		0			0		−0.599278	−	0.800541i	$-0.704545\pi$
$373$		0			0		0.599278	+	0.800541i	$0.295455\pi$
$374$		0			0
$375$		0			0
$376$	−0.468468	−	0.540641i	−0.468468	−	0.540641i
$377$		0			0
$378$		0			0
$379$	−1.45027	+	0.425839i	−1.45027	+	0.425839i	−0.909632	−	0.415415i	$-0.863636\pi$
$379$	−1.45027	+	0.425839i	−1.45027	+	0.425839i	−0.540641	+	0.841254i	$0.681818\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.50765	+	0.107829i	1.50765	+	0.107829i	0.800541	−	0.599278i	$-0.204545\pi$
$383$	1.50765	+	0.107829i	1.50765	+	0.107829i	0.707107	+	0.707107i	$0.250000\pi$
$384$	−0.650724	+	0.297176i	−0.650724	+	0.297176i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$389$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$390$		0			0
$391$	−0.817178	−	0.708089i	−0.817178	−	0.708089i
$392$	0.263599	−	0.263599i	0.263599	−	0.263599i
$393$		0			0
$394$	−0.281733	−	0.244123i	−0.281733	−	0.244123i
$395$		0			0
$396$		0			0
$397$		0			0		0.212565	−	0.977147i	$-0.431818\pi$
$397$		0			0		−0.212565	+	0.977147i	$0.568182\pi$
$398$	1.85483	+	0.691814i	1.85483	+	0.691814i
$399$		0			0
$400$		0			0
$401$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$401$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.0856821	−	0.393874i	0.0856821	−	0.393874i
$409$	1.66538	+	0.239446i	1.66538	+	0.239446i	0.909632	−	0.415415i	$-0.136364\pi$
$409$	1.66538	+	0.239446i	1.66538	+	0.239446i	0.755750	+	0.654861i	$0.227273\pi$
$410$		0			0
$411$	1.49611	+	1.29639i	1.49611	+	1.29639i
$412$		0			0
$413$		0			0
$414$	1.29639	−	0.186393i	1.29639	−	0.186393i
$415$		0			0
$416$		0			0
$417$	0.136899	+	1.91410i	0.136899	+	1.91410i
$418$		0			0
$419$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$419$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$420$		0			0
$421$	1.65486	−	0.755750i	1.65486	−	0.755750i	0.654861	−	0.755750i	$-0.272727\pi$
$421$	1.65486	−	0.755750i	1.65486	−	0.755750i	1.00000			$0$
$422$	−2.19800	−	0.157204i	−2.19800	−	0.157204i
$423$	−1.15001	+	1.53623i	−1.15001	+	1.53623i
$424$	−0.0872586	+	0.191070i	−0.0872586	+	0.191070i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	1.13371	+	0.848684i	1.13371	+	0.848684i
$429$		0			0
$430$		0			0
$431$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$431$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$432$	0.721300	+	0.963544i	0.721300	+	0.963544i
$433$		0			0		0.977147	−	0.212565i	$-0.0681818\pi$
$433$		0			0		−0.977147	+	0.212565i	$0.931818\pi$
$434$		0			0
$435$		0			0
$436$		−	1.41618i		−	1.41618i
$437$	−0.871880	−	1.59673i	−0.871880	−	1.59673i
$438$		0			0
$439$	−0.368991	+	1.25667i	−0.368991	+	1.25667i	0.540641	+	0.841254i	$0.318182\pi$
$439$	−0.368991	+	1.25667i	−0.368991	+	1.25667i	−0.909632	+	0.415415i	$0.863636\pi$
$440$		0			0
$441$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$442$		0			0
$443$	−1.64406	−	0.357643i	−1.64406	−	0.357643i	−0.707107	−	0.707107i	$-0.750000\pi$
$443$	−1.64406	−	0.357643i	−1.64406	−	0.357643i	−0.936950	+	0.349464i	$0.886364\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$449$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$450$		0			0
$451$		0			0
$452$	−0.0771377	+	1.07853i	−0.0771377	+	1.07853i
$453$	0.587976	−	1.57642i	0.587976	−	1.57642i
$454$	0.620830	−	0.398983i	0.620830	−	0.398983i
$455$		0			0
$456$	0.366660	−	0.570534i	0.366660	−	0.570534i
$457$		0			0		0.997452	−	0.0713392i	$-0.0227273\pi$
$457$		0			0		−0.997452	+	0.0713392i	$0.977273\pi$
$458$	−1.73749	+	0.948742i	−1.73749	+	0.948742i
$459$	−1.08128			−1.08128
$460$		0			0
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$		0			0		0.997452	−	0.0713392i	$-0.0227273\pi$
$463$		0			0		−0.997452	+	0.0713392i	$0.977273\pi$
$464$		0			0
$465$		0			0
$466$	0.313607	−	0.201543i	0.313607	−	0.201543i
$467$	−0.377869	+	1.01311i	−0.377869	+	1.01311i	0.599278	+	0.800541i	$0.295455\pi$
$467$	−0.377869	+	1.01311i	−0.377869	+	1.01311i	−0.977147	+	0.212565i	$0.931818\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$	−0.368991	−	2.56639i	−0.368991	−	2.56639i
$475$		0			0
$476$		0			0
$477$	0.550588	+	0.119773i	0.550588	+	0.119773i
$478$		0			0
$479$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$479$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$480$		0			0
$481$		0			0
$482$	−1.00139	−	1.00139i	−1.00139	−	1.00139i
$483$		0			0
$484$			0.715370i			0.715370i
$485$		0			0
$486$	0.857685	−	0.989821i	0.857685	−	0.989821i
$487$		0			0		0.977147	−	0.212565i	$-0.0681818\pi$
$487$		0			0		−0.977147	+	0.212565i	$0.931818\pi$
$488$	−0.125879	−	0.168155i	−0.125879	−	0.168155i
$489$		0			0
$490$		0			0
$491$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$491$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.415415	−	0.909632i	0.415415	−	0.909632i
$497$		0			0
$498$	−1.97460	−	0.141226i	−1.97460	−	0.141226i
$499$	−0.258908	+	0.118239i	−0.258908	+	0.118239i	−0.540641	−	0.841254i	$-0.681818\pi$
$499$	−0.258908	+	0.118239i	−0.258908	+	0.118239i	0.281733	+	0.959493i	$0.409091\pi$
$500$		0			0
$501$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$502$		0			0
$503$	−0.129785	−	1.81463i	−0.129785	−	1.81463i	−0.479249	−	0.877679i	$-0.659091\pi$
$503$	−0.129785	−	1.81463i	−0.129785	−	1.81463i	0.349464	−	0.936950i	$-0.386364\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.707107	−	0.707107i	0.707107	−	0.707107i
$508$		0			0
$509$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$509$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$510$		0			0
$511$		0			0
$512$	−0.212565	+	0.977147i	−0.212565	+	0.977147i
$513$	−1.70456	−	0.635768i	−1.70456	−	0.635768i
$514$	1.66538	−	1.44306i	1.66538	−	1.44306i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	1.74557	+	0.797176i	1.74557	+	0.797176i
$520$		0			0
$521$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$521$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$522$		0			0
$523$		0			0		0.212565	−	0.977147i	$-0.431818\pi$
$523$		0			0		−0.212565	+	0.977147i	$0.568182\pi$
$524$		0			0
$525$		0			0
$526$	−1.80075	−	1.56036i	−1.80075	−	1.56036i
$527$	0.430539	+	0.788473i	0.430539	+	0.788473i
$528$		0			0
$529$	0.540641	+	0.841254i	0.540641	+	0.841254i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	0.797176	−	0.234072i	0.797176	−	0.234072i	0.142315	−	0.989821i	$-0.454545\pi$
$541$	0.797176	−	0.234072i	0.797176	−	0.234072i	0.654861	+	0.755750i	$0.272727\pi$
$542$	−0.878321	−	2.35487i	−0.878321	−	2.35487i
$543$	0.865611	+	0.647988i	0.865611	+	0.647988i
$544$	−0.852267	−	0.983568i	−0.852267	−	0.983568i
$545$		0			0
$546$		0			0
$547$		0			0		−0.599278	−	0.800541i	$-0.704545\pi$
$547$		0			0		0.599278	+	0.800541i	$0.295455\pi$
$548$	1.38381	−	0.301030i	1.38381	−	0.301030i
$549$	−0.368991	+	0.425839i	−0.368991	+	0.425839i
$550$		0			0
$551$		0			0
$552$	−0.178657	+	0.327186i	−0.178657	+	0.327186i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.15486	+	0.742184i	1.15486	+	0.742184i
$557$	−1.45640	+	1.09024i	−1.45640	+	1.09024i	−0.479249	+	0.877679i	$0.659091\pi$
$557$	−1.45640	+	1.09024i	−1.45640	+	1.09024i	−0.977147	+	0.212565i	$0.931818\pi$
$558$	−1.06329	−	0.231304i	−1.06329	−	0.231304i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−0.270040	+	0.494541i	−0.270040	+	0.494541i	−0.977147	−	0.212565i	$-0.931818\pi$
$563$	−0.270040	+	0.494541i	−0.270040	+	0.494541i	0.707107	+	0.707107i	$0.250000\pi$
$564$	0.386758	+	1.31718i	0.386758	+	1.31718i
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$569$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$570$		0			0
$571$	0.304632	−	0.474017i	0.304632	−	0.474017i	−0.654861	−	0.755750i	$-0.727273\pi$
$571$	0.304632	−	0.474017i	0.304632	−	0.474017i	0.959493	+	0.281733i	$0.0909091\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.372786			0.372786
$577$		0			0		0.877679	−	0.479249i	$-0.159091\pi$
$577$		0			0		−0.877679	+	0.479249i	$0.840909\pi$
$578$	0.221001	−	0.0158063i	0.221001	−	0.0158063i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	0.557730	+	1.89945i	0.557730	+	1.89945i
$587$	0.398174	−	0.729202i	0.398174	−	0.729202i	−0.599278	−	0.800541i	$-0.704545\pi$
$587$	0.398174	−	0.729202i	0.398174	−	0.729202i	0.997452	+	0.0713392i	$0.0227273\pi$
$588$	−0.670266	+	0.249996i	−0.670266	+	0.249996i
$589$	0.215109	+	1.49611i	0.215109	+	1.49611i
$590$		0			0
$591$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$592$		0			0
$593$	−0.665114	+	0.497898i	−0.665114	+	0.497898i	−0.877679	−	0.479249i	$-0.840909\pi$
$593$	−0.665114	+	0.497898i	−0.665114	+	0.497898i	0.212565	+	0.977147i	$0.431818\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.06879	+	1.06879i	1.06879	+	1.06879i
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	−0.186393	+	0.215109i	−0.186393	+	0.215109i	−0.841254	−	0.540641i	$-0.818182\pi$
$601$	−0.186393	+	0.215109i	−0.186393	+	0.215109i	0.654861	+	0.755750i	$0.272727\pi$
$602$		0			0
$603$		0			0
$604$	−0.650724	−	1.01255i	−0.650724	−	1.01255i
$605$		0			0
$606$		0			0
$607$		0			0		−0.800541	−	0.599278i	$-0.795455\pi$
$607$		0			0		0.800541	+	0.599278i	$0.204545\pi$
$608$	−0.765220	−	2.05163i	−0.765220	−	2.05163i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.463551	+	0.619232i	−0.463551	+	0.619232i
$613$		0			0		−0.997452	−	0.0713392i	$-0.977273\pi$
$613$		0			0		0.997452	+	0.0713392i	$0.0227273\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.119773	+	0.550588i	0.119773	+	0.550588i	0.997452	+	0.0713392i	$0.0227273\pi$
$617$	0.119773	+	0.550588i	0.119773	+	0.550588i	−0.877679	+	0.479249i	$0.840909\pi$
$618$		0			0
$619$	−1.89945	−	0.557730i	−1.89945	−	0.557730i	−0.989821	−	0.142315i	$-0.954545\pi$
$619$	−1.89945	−	0.557730i	−1.89945	−	0.557730i	−0.909632	−	0.415415i	$-0.863636\pi$
$620$		0			0
$621$	0.959493	+	0.281733i	0.959493	+	0.281733i
$622$		0			0
$623$		0			0
$624$		0			0
$625$		0			0
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.983568	+	0.449181i	0.983568	+	0.449181i	0.841254	−	0.540641i	$-0.181818\pi$
$631$	0.983568	+	0.449181i	0.983568	+	0.449181i	0.142315	+	0.989821i	$0.454545\pi$
$632$	0.647712	+	0.353677i	0.647712	+	0.353677i
$633$	−1.47670	−	0.806340i	−1.47670	−	0.806340i
$634$	−2.00448	−	0.915415i	−2.00448	−	0.915415i
$635$		0			0
$636$	0.304632	−	0.263965i	0.304632	−	0.263965i
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$641$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$642$	1.24259	+	2.27563i	1.24259	+	2.27563i
$643$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$643$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$644$		0			0
$645$		0			0
$646$	2.47204	+	0.725856i	2.47204	+	0.725856i
$647$	−0.120029	−	1.67822i	−0.120029	−	1.67822i	−0.599278	−	0.800541i	$-0.704545\pi$
$647$	−0.120029	−	1.67822i	−0.120029	−	1.67822i	0.479249	−	0.877679i	$-0.340909\pi$
$648$	0.0792413	+	0.364266i	0.0792413	+	0.364266i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.170572	−	0.227858i	0.170572	−	0.227858i	−0.707107	−	0.707107i	$-0.750000\pi$
$653$	0.170572	−	0.227858i	0.170572	−	0.227858i	0.877679	+	0.479249i	$0.159091\pi$
$654$	1.07708	−	2.35848i	1.07708	−	2.35848i
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$659$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$660$		0			0
$661$	0.983568	+	1.53046i	0.983568	+	1.53046i	0.841254	+	0.540641i	$0.181818\pi$
$661$	0.983568	+	1.53046i	0.983568	+	1.53046i	0.142315	+	0.989821i	$0.454545\pi$
$662$	1.02798	+	1.37322i	1.02798	+	1.37322i
$663$		0			0
$664$	0.368991	−	0.425839i	0.368991	−	0.425839i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−0.143978	−	0.143978i	−0.143978	−	0.143978i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.977147	−	0.212565i	$-0.931818\pi$
$673$		0			0		0.977147	+	0.212565i	$0.0681818\pi$
$674$		0			0
$675$		0			0
$676$	−0.101808	−	0.708089i	−0.101808	−	0.708089i
$677$	1.85483	−	0.691814i	1.85483	−	0.691814i	0.877679	−	0.479249i	$-0.159091\pi$
$677$	1.85483	−	0.691814i	1.85483	−	0.691814i	0.977147	−	0.212565i	$-0.0681818\pi$
$678$	−0.948742	+	1.73749i	−0.948742	+	1.73749i
$679$		0			0
$680$		0			0
$681$	0.557730	−	0.0801894i	0.557730	−	0.0801894i
$682$		0			0
$683$	0.670617	−	1.79799i	0.670617	−	1.79799i	0.0713392	−	0.997452i	$-0.477273\pi$
$683$	0.670617	−	1.79799i	0.670617	−	1.79799i	0.599278	−	0.800541i	$-0.295455\pi$
$684$	−1.09485	+	0.703616i	−1.09485	+	0.703616i
$685$		0			0
$686$		0			0
$687$	−1.50765	+	0.107829i	−1.50765	+	0.107829i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$691$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$692$	1.20487	−	0.657906i	1.20487	−	0.657906i
$693$		0			0
$694$	0.588302	−	0.915415i	0.588302	−	0.915415i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	0.122373	−	1.71100i	0.122373	−	1.71100i
$699$	0.281733	−	0.0405070i	0.281733	−	0.0405070i
$700$		0			0
$701$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$701$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−0.452036	−	0.989821i	−0.452036	−	0.989821i
$707$		0			0
$708$		0			0
$709$	−0.909632	−	0.584585i	−0.909632	−	0.584585i		−	1.00000i	$-0.5\pi$
$709$	−0.909632	−	0.584585i	−0.909632	−	0.584585i	−0.909632	+	0.415415i	$0.863636\pi$
$710$		0			0
$711$	0.557730	−	1.89945i	0.557730	−	1.89945i
$712$		0			0
$713$	−0.176606	−	0.811843i	−0.176606	−	0.811843i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$719$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$720$		0			0
$721$		0			0
$722$	2.42171	+	1.81287i	2.42171	+	1.81287i
$723$	−0.377869	−	1.01311i	−0.377869	−	1.01311i
$724$	0.742184	−	0.217925i	0.742184	−	0.217925i
$725$		0			0
$726$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$727$		0			0		0.599278	−	0.800541i	$-0.295455\pi$
$727$		0			0		−0.599278	+	0.800541i	$0.704545\pi$
$728$		0			0
$729$	0.909632	−	0.415415i	0.909632	−	0.415415i
$730$		0			0
$731$		0			0
$732$	0.0856821	+	0.393874i	0.0856821	+	0.393874i
$733$		0			0		−0.0713392	−	0.997452i	$-0.522727\pi$
$733$		0			0		0.0713392	+	0.997452i	$0.477273\pi$
$734$		0			0
$735$		0			0
$736$	0.500000	+	1.09485i	0.500000	+	1.09485i
$737$		0			0
$738$		0			0
$739$	−0.989821	−	0.857685i	−0.989821	−	0.857685i		−	1.00000i	$-0.5\pi$
$739$	−0.989821	−	0.857685i	−0.989821	−	0.857685i	−0.989821	+	0.142315i	$0.954545\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.41620	−	0.528215i	−1.41620	−	0.528215i	−0.479249	−	0.877679i	$-0.659091\pi$
$743$	−1.41620	−	0.528215i	−1.41620	−	0.528215i	−0.936950	+	0.349464i	$0.886364\pi$
$744$	0.234072	−	0.202824i	0.234072	−	0.202824i
$745$		0			0
$746$		0			0
$747$	−1.32661	−	0.724384i	−1.32661	−	0.724384i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−0.817178	+	0.708089i	−0.817178	+	0.708089i	−0.959493	−	0.281733i	$-0.909091\pi$
$751$	−0.817178	+	0.708089i	−0.817178	+	0.708089i	0.142315	+	0.989821i	$0.454545\pi$
$752$	−2.16409	−	0.807165i	−2.16409	−	0.807165i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.479249	−	0.877679i	$-0.659091\pi$
$757$		0			0		0.479249	+	0.877679i	$0.340909\pi$
$758$	−1.39982	+	1.39982i	−1.39982	+	1.39982i
$759$		0			0
$760$		0			0
$761$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$761$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	1.80075	−	0.822373i	1.80075	−	0.822373i
$767$		0			0
$768$	−0.784887	+	1.04849i	−0.784887	+	1.04849i
$769$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$769$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$770$		0			0
$771$	1.61435	−	0.474017i	1.61435	−	0.474017i
$772$		0			0
$773$	1.45640	+	1.09024i	1.45640	+	1.09024i	0.977147	+	0.212565i	$0.0681818\pi$
$773$	1.45640	+	1.09024i	1.45640	+	1.09024i	0.479249	+	0.877679i	$0.340909\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−1.38381	−	0.301030i	−1.38381	−	0.301030i
$783$		0			0
$784$	0.339098	−	1.15486i	0.339098	−	1.15486i
$785$		0			0
$786$		0			0
$787$		0			0		0.800541	−	0.599278i	$-0.204545\pi$
$787$		0			0		−0.800541	+	0.599278i	$0.795455\pi$
$788$	−0.198962	−	0.0432816i	−0.198962	−	0.0432816i
$789$	−0.755750	−	1.65486i	−0.755750	−	1.65486i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	1.07028	−	0.153882i	1.07028	−	0.153882i
$797$	−0.129785	+	1.81463i	−0.129785	+	1.81463i	0.349464	+	0.936950i	$0.386364\pi$
$797$	−0.129785	+	1.81463i	−0.129785	+	1.81463i	−0.479249	+	0.877679i	$0.659091\pi$
$798$		0			0
$799$	1.74557	−	1.12181i	1.74557	−	1.12181i
$800$		0			0
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$809$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$810$		0			0
$811$	0.239446	−	0.153882i	0.239446	−	0.153882i	−0.415415	−	0.909632i	$-0.636364\pi$
$811$	0.239446	−	0.153882i	0.239446	−	0.153882i	0.654861	+	0.755750i	$0.272727\pi$
$812$		0			0
$813$	0.136899	−	1.91410i	0.136899	−	1.91410i
$814$		0			0
$815$		0			0
$816$	−0.366660	−	1.24873i	−0.366660	−	1.24873i
$817$		0			0
$818$	2.06468	−	0.770085i	2.06468	−	0.770085i
$819$		0			0
$820$		0			0
$821$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$821$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$822$	2.53353	+	0.551135i	2.53353	+	0.551135i
$823$		0			0		0.800541	−	0.599278i	$-0.204545\pi$
$823$		0			0		−0.800541	+	0.599278i	$0.795455\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.28641	−	1.28641i	−1.28641	−	1.28641i	−0.936950	−	0.349464i	$-0.886364\pi$
$827$	−1.28641	−	1.28641i	−1.28641	−	1.28641i	−0.349464	−	0.936950i	$-0.613636\pi$
$828$	0.572683	−	0.428705i	0.572683	−	0.428705i
$829$			0.284630i			0.284630i	0.989821	+	0.142315i	$0.0454545\pi$
$829$			0.284630i			0.284630i	−0.989821	+	0.142315i	$0.954545\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.647988	+	0.865611i	0.647988	+	0.865611i
$834$	1.35881	+	2.11435i	1.35881	+	2.11435i
$835$		0			0
$836$		0			0
$837$	−0.665114	−	0.497898i	−0.665114	−	0.497898i
$838$		0			0
$839$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$839$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$840$		0			0
$841$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$842$	1.42792	−	1.90747i	1.42792	−	1.90747i
$843$		0			0
$844$	−1.09485	+	0.500000i	−1.09485	+	0.500000i
$845$		0			0
$846$	−0.357685	+	2.48775i	−0.357685	+	2.48775i
$847$		0			0
$848$	0.0483819	+	0.676467i	0.0483819	+	0.676467i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.479249	−	0.877679i	$-0.659091\pi$
$853$		0			0		0.479249	+	0.877679i	$0.340909\pi$
$854$		0			0
$855$		0			0
$856$	−0.730471	−	0.105026i	−0.730471	−	0.105026i
$857$	0.176606	−	0.811843i	0.176606	−	0.811843i	−0.800541	−	0.599278i	$-0.795455\pi$
$857$	0.176606	−	0.811843i	0.176606	−	0.811843i	0.977147	−	0.212565i	$-0.0681818\pi$
$858$		0			0
$859$	−1.27155	+	1.10181i	−1.27155	+	1.10181i	−0.281733	+	0.959493i	$0.590909\pi$
$859$	−1.27155	+	1.10181i	−1.27155	+	1.10181i	−0.989821	+	0.142315i	$0.954545\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.249813	−	0.136408i	−0.249813	−	0.136408i	0.349464	−	0.936950i	$-0.386364\pi$
$863$	−0.249813	−	0.136408i	−0.249813	−	0.136408i	−0.599278	+	0.800541i	$0.704545\pi$
$864$	1.09485	+	0.500000i	1.09485	+	0.500000i
$865$		0			0
$866$		0			0
$867$	0.158504	+	0.0591188i	0.158504	+	0.0591188i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.353677	+	0.647712i	0.353677	+	0.647712i
$873$		0			0
$874$	−2.00448	−	1.28820i	−2.00448	−	1.28820i
$875$		0			0
$876$		0			0
$877$		0			0		−0.0713392	−	0.997452i	$-0.522727\pi$
$877$		0			0		0.0713392	+	0.997452i	$0.477273\pi$
$878$	0.364628	+	1.67617i	0.364628	+	1.67617i
$879$	−0.215109	+	1.49611i	−0.215109	+	1.49611i
$880$		0			0
$881$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$881$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$882$	−1.30638	−	0.0934345i	−1.30638	−	0.0934345i
$883$		0			0		0.599278	−	0.800541i	$-0.295455\pi$
$883$		0			0		−0.599278	+	0.800541i	$0.704545\pi$
$884$		0			0
$885$		0			0
$886$	−2.11435	+	0.620830i	−2.11435	+	0.620830i
$887$	0.587976	+	1.57642i	0.587976	+	1.57642i	0.800541	+	0.599278i	$0.204545\pi$
$887$	0.587976	+	1.57642i	0.587976	+	1.57642i	−0.212565	+	0.977147i	$0.568182\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	3.41136	−	0.742096i	3.41136	−	0.742096i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	−0.512546	−	0.329393i	−0.512546	−	0.329393i
$902$		0			0
$903$		0			0
$904$	−0.234072	−	0.512546i	−0.234072	−	0.512546i
$905$		0			0
$906$	−0.313607	−	2.18119i	−0.313607	−	2.18119i
$907$		0			0		0.936950	−	0.349464i	$-0.113636\pi$
$907$		0			0		−0.936950	+	0.349464i	$0.886364\pi$
$908$	0.193179	−	0.353780i	0.193179	−	0.353780i
$909$		0			0
$910$		0			0
$911$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$911$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$912$	0.156211	−	2.18412i	0.156211	−	2.18412i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−0.584585	+	0.909632i	−0.584585	+	0.909632i
$917$		0			0
$918$	−1.24295	+	0.678702i	−1.24295	+	0.678702i
$919$	1.08128			1.08128			0.540641	−	0.841254i	$-0.318182\pi$
$919$	1.08128			1.08128			0.540641	+	0.841254i	$0.318182\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$929$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$930$		0			0
$931$	0.512546	+	1.74557i	0.512546	+	1.74557i
$932$	0.0975826	−	0.178709i	0.0975826	−	0.178709i
$933$		0			0
$934$	0.201543	+	1.40176i	0.201543	+	1.40176i
$935$		0			0
$936$		0			0
$937$		0			0		−0.977147	−	0.212565i	$-0.931818\pi$
$937$		0			0		0.977147	+	0.212565i	$0.0681818\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$941$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.87513	+	0.407910i	−1.87513	+	0.407910i	−0.997452	−	0.0713392i	$-0.977273\pi$
$947$	−1.87513	+	0.407910i	−1.87513	+	0.407910i	−0.877679	+	0.479249i	$0.840909\pi$
$948$	−0.848684	−	1.13371i	−0.848684	−	1.13371i
$949$		0			0
$950$		0			0
$951$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$952$		0			0
$953$	0.196911	+	0.527938i	0.196911	+	0.527938i	0.997452	−	0.0713392i	$-0.0227273\pi$
$953$	0.196911	+	0.527938i	0.196911	+	0.527938i	−0.800541	+	0.599278i	$0.795455\pi$
$954$	0.708089	−	0.207914i	0.708089	−	0.207914i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.0440780	−	0.306569i	0.0440780	−	0.306569i
$962$		0			0
$963$	0.141226	+	1.97460i	0.141226	+	1.97460i
$964$	−0.742184	−	0.217925i	−0.742184	−	0.217925i
$965$		0			0
$966$		0			0
$967$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$967$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$968$	−0.178657	−	0.327186i	−0.178657	−	0.327186i
$969$	1.48666	+	1.28820i	1.48666	+	1.28820i
$970$		0			0
$971$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$971$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$972$	0.152063	−	0.699022i	0.152063	−	0.699022i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−0.616908	−	0.281733i	−0.616908	−	0.281733i
$977$	1.73749	+	0.948742i	1.73749	+	0.948742i	0.936950	+	0.349464i	$0.113636\pi$
$977$	1.73749	+	0.948742i	1.73749	+	0.948742i	0.800541	+	0.599278i	$0.204545\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	1.49611	−	1.29639i	1.49611	−	1.29639i
$982$		0			0
$983$	−0.420803	+	1.93440i	−0.420803	+	1.93440i	−0.0713392	+	0.997452i	$0.522727\pi$
$983$	−0.420803	+	1.93440i	−0.420803	+	1.93440i	−0.349464	+	0.936950i	$0.613636\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−0.273100	−	0.0801894i	−0.273100	−	0.0801894i	0.142315	−	0.989821i	$-0.454545\pi$
$991$	−0.273100	−	0.0801894i	−0.273100	−	0.0801894i	−0.415415	+	0.909632i	$0.636364\pi$
$992$	−0.0713392	−	0.997452i	−0.0713392	−	0.997452i
$993$	0.278401	+	1.27979i	0.278401	+	1.27979i
$994$		0			0
$995$		0			0
$996$	−0.983568	+	0.449181i	−0.983568	+	0.449181i
$997$		0			0		−0.997452	−	0.0713392i	$-0.977273\pi$
$997$		0			0		0.997452	+	0.0713392i	$0.0227273\pi$
$998$	−0.223402	+	0.298430i	−0.223402	+	0.298430i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1725.1.bg.a.557.2	yes	40
3.2	odd	2	inner	1725.1.bg.a.557.1	yes	40
5.2	odd	4	inner	1725.1.bg.a.143.2	yes	40
5.3	odd	4	inner	1725.1.bg.a.143.1	✓	40
5.4	even	2	inner	1725.1.bg.a.557.1	yes	40
15.2	even	4	inner	1725.1.bg.a.143.1	✓	40
15.8	even	4	inner	1725.1.bg.a.143.2	yes	40
15.14	odd	2	CM	1725.1.bg.a.557.2	yes	40
23.14	odd	22	inner	1725.1.bg.a.1532.2	yes	40
69.14	even	22	inner	1725.1.bg.a.1532.1	yes	40
115.14	odd	22	inner	1725.1.bg.a.1532.1	yes	40
115.37	even	44	inner	1725.1.bg.a.1118.2	yes	40
115.83	even	44	inner	1725.1.bg.a.1118.1	yes	40
345.14	even	22	inner	1725.1.bg.a.1532.2	yes	40
345.83	odd	44	inner	1725.1.bg.a.1118.2	yes	40
345.152	odd	44	inner	1725.1.bg.a.1118.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1725.1.bg.a.143.1	✓	40	5.3	odd	4	inner
1725.1.bg.a.143.1	✓	40	15.2	even	4	inner
1725.1.bg.a.143.2	yes	40	5.2	odd	4	inner
1725.1.bg.a.143.2	yes	40	15.8	even	4	inner
1725.1.bg.a.557.1	yes	40	3.2	odd	2	inner
1725.1.bg.a.557.1	yes	40	5.4	even	2	inner
1725.1.bg.a.557.2	yes	40	1.1	even	1	trivial
1725.1.bg.a.557.2	yes	40	15.14	odd	2	CM
1725.1.bg.a.1118.1	yes	40	115.83	even	44	inner
1725.1.bg.a.1118.1	yes	40	345.152	odd	44	inner
1725.1.bg.a.1118.2	yes	40	115.37	even	44	inner
1725.1.bg.a.1118.2	yes	40	345.83	odd	44	inner
1725.1.bg.a.1532.1	yes	40	69.14	even	22	inner
1725.1.bg.a.1532.1	yes	40	115.14	odd	22	inner
1725.1.bg.a.1532.2	yes	40	23.14	odd	22	inner
1725.1.bg.a.1532.2	yes	40	345.14	even	22	inner

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:	\( N \)	\(=\)	\( 1725 = 3 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1725.bg (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(1.14952 - 0.627683i) q^{2} +(0.997452 - 0.0713392i) q^{3} +(0.386758 - 0.601808i) q^{4} +(1.10181 - 0.708089i) q^{6} +(-0.0265942 + 0.371836i) q^{8} +(0.989821 - 0.142315i) q^{9} +(0.342841 - 0.627866i) q^{12} +(0.500000 + 1.09485i) q^{16} +(-1.05657 - 0.229843i) q^{17} +(1.04849 - 0.784887i) q^{18} +(-1.53046 - 0.983568i) q^{19} +(0.877679 + 0.479249i) q^{23} +0.372786i q^{24} +(0.977147 - 0.212565i) q^{27} +(-0.544078 - 0.627899i) q^{31} +(0.963544 + 0.721300i) q^{32} +(-1.35881 + 0.398983i) q^{34} +(0.297176 - 0.650724i) q^{36} +(-2.37666 - 0.169982i) q^{38} +1.30972 q^{46} +(-1.35693 + 1.35693i) q^{47} +(0.576832 + 1.05639i) q^{48} +(-0.755750 - 0.654861i) q^{49} +(-1.07028 - 0.153882i) q^{51} +(0.527938 + 0.196911i) q^{53} +(0.989821 - 0.857685i) q^{54} +(-1.59673 - 0.871880i) q^{57} +(-0.425839 + 0.368991i) q^{61} +(-1.01955 - 0.380272i) q^{62} +(0.368991 + 0.0530529i) q^{64} +(-0.546959 + 0.546959i) q^{68} +(0.909632 + 0.415415i) q^{69} +(0.0265942 + 0.371836i) q^{72} +(-1.18384 + 0.540641i) q^{76} +(0.822373 - 1.80075i) q^{79} +(0.959493 - 0.281733i) q^{81} +(-1.21002 - 0.905808i) q^{83} +(0.627866 - 0.342841i) q^{92} +(-0.587486 - 0.587486i) q^{93} +(-0.708089 + 2.41153i) q^{94} +(1.01255 + 0.650724i) q^{96} +(-1.27979 - 0.278401i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{6} + 20 q^{16} - 8 q^{31} - 12 q^{36} + 8 q^{46} - 44 q^{76} + 4 q^{81} + 20 q^{96}+O(q^{100}) \) 40 * q + 8 * q^6 + 20 * q^16 - 8 * q^31 - 12 * q^36 + 8 * q^46 - 44 * q^76 + 4 * q^81 + 20 * q^96

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