LMFDB - Embedded newform 1725.1.bg.a.182.2

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			182.2
Root			$0.977147 - 0.212565i$ of defining polynomial
Character	$\chi$	$=$	1725.182
Dual form			1725.1.bg.a.218.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.278125 - 0.0605024i) q^{2} +(0.599278 - 0.800541i) q^{3} +(-0.835939 + 0.381761i) q^{4} +(0.118239 - 0.258908i) q^{6} +(-0.437256 + 0.327326i) q^{8} +(-0.281733 - 0.959493i) q^{9} +(-0.195345 + 0.897984i) q^{12} +(0.500000 - 0.577031i) q^{16} +(1.70456 - 0.635768i) q^{17} +(-0.136408 - 0.249813i) q^{18} +(-0.627899 - 1.37491i) q^{19} +(0.977147 + 0.212565i) q^{23} +0.546200i q^{24} +(-0.936950 - 0.349464i) q^{27} +(0.186393 - 1.29639i) q^{31} +(0.365917 - 0.670126i) q^{32} +(0.435615 - 0.279953i) q^{34} +(0.601808 + 0.694523i) q^{36} +(-0.257820 - 0.344407i) q^{38} +0.284630 q^{46} +(-1.18971 + 1.18971i) q^{47} +(-0.162298 - 0.746072i) q^{48} +(0.989821 - 0.142315i) q^{49} +(0.512546 - 1.74557i) q^{51} +(0.0771377 + 1.07853i) q^{53} +(-0.281733 - 0.0405070i) q^{54} +(-1.47696 - 0.321292i) q^{57} +(-1.07028 - 0.153882i) q^{61} +(-0.0265942 - 0.371836i) q^{62} +(-0.153882 + 0.524075i) q^{64} +(-1.18220 + 1.18220i) q^{68} +(0.755750 - 0.654861i) q^{69} +(0.437256 + 0.327326i) q^{72} +(1.04977 + 0.909632i) q^{76} +(0.368991 + 0.425839i) q^{79} +(-0.841254 + 0.540641i) q^{81} +(-0.948742 + 1.73749i) q^{83} +(-0.897984 + 0.195345i) q^{92} +(-0.926113 - 0.926113i) q^{93} +(-0.258908 + 0.402869i) q^{94} +(-0.317178 - 0.694523i) q^{96} +(0.266684 - 0.0994679i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1725\mathbb{Z}\right)^\times$.

$n$	$277$	$1151$	$1201$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	0.278125	−	0.0605024i	0.278125	−	0.0605024i	−0.0713392	−	0.997452i	$-0.522727\pi$
$2$	0.278125	−	0.0605024i	0.278125	−	0.0605024i	0.349464	+	0.936950i	$0.386364\pi$
$3$	0.599278	−	0.800541i	0.599278	−	0.800541i
$3$	0.599278	−	0.800541i	0.599278	−	0.800541i
$4$	−0.835939	+	0.381761i	−0.835939	+	0.381761i
$5$		0			0
$5$		0			0
$6$	0.118239	−	0.258908i	0.118239	−	0.258908i
$7$		0			0		0.997452	−	0.0713392i	$-0.0227273\pi$
$7$		0			0		−0.997452	+	0.0713392i	$0.977273\pi$
$8$	−0.437256	+	0.327326i	−0.437256	+	0.327326i
$9$	−0.281733	−	0.959493i	−0.281733	−	0.959493i
$10$		0			0
$11$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$11$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$12$	−0.195345	+	0.897984i	−0.195345	+	0.897984i
$13$		0			0		0.0713392	−	0.997452i	$-0.477273\pi$
$13$		0			0		−0.0713392	+	0.997452i	$0.522727\pi$
$14$		0			0
$15$		0			0
$16$	0.500000	−	0.577031i	0.500000	−	0.577031i
$17$	1.70456	−	0.635768i	1.70456	−	0.635768i	0.707107	−	0.707107i	$-0.250000\pi$
$17$	1.70456	−	0.635768i	1.70456	−	0.635768i	0.997452	+	0.0713392i	$0.0227273\pi$
$18$	−0.136408	−	0.249813i	−0.136408	−	0.249813i
$19$	−0.627899	−	1.37491i	−0.627899	−	1.37491i	−0.909632	−	0.415415i	$-0.863636\pi$
$19$	−0.627899	−	1.37491i	−0.627899	−	1.37491i	0.281733	−	0.959493i	$-0.409091\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.977147	+	0.212565i	0.977147	+	0.212565i
$23$	0.977147	+	0.212565i	0.977147	+	0.212565i
$24$			0.546200i			0.546200i
$25$		0			0
$26$		0			0
$27$	−0.936950	−	0.349464i	−0.936950	−	0.349464i
$28$		0			0
$29$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$29$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$30$		0			0
$31$	0.186393	−	1.29639i	0.186393	−	1.29639i	−0.654861	−	0.755750i	$-0.727273\pi$
$31$	0.186393	−	1.29639i	0.186393	−	1.29639i	0.841254	−	0.540641i	$-0.181818\pi$
$32$	0.365917	−	0.670126i	0.365917	−	0.670126i
$33$		0			0
$34$	0.435615	−	0.279953i	0.435615	−	0.279953i
$35$		0			0
$36$	0.601808	+	0.694523i	0.601808	+	0.694523i
$37$		0			0		−0.877679	−	0.479249i	$-0.840909\pi$
$37$		0			0		0.877679	+	0.479249i	$0.159091\pi$
$38$	−0.257820	−	0.344407i	−0.257820	−	0.344407i
$39$		0			0
$40$		0			0
$41$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$41$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$42$		0			0
$43$		0			0		−0.800541	−	0.599278i	$-0.795455\pi$
$43$		0			0		0.800541	+	0.599278i	$0.204545\pi$
$44$		0			0
$45$		0			0
$46$	0.284630			0.284630
$47$	−1.18971	+	1.18971i	−1.18971	+	1.18971i	−0.212565	+	0.977147i	$0.568182\pi$
$47$	−1.18971	+	1.18971i	−1.18971	+	1.18971i	−0.977147	+	0.212565i	$0.931818\pi$
$48$	−0.162298	−	0.746072i	−0.162298	−	0.746072i
$49$	0.989821	−	0.142315i	0.989821	−	0.142315i
$50$		0			0
$51$	0.512546	−	1.74557i	0.512546	−	1.74557i
$52$		0			0
$53$	0.0771377	+	1.07853i	0.0771377	+	1.07853i	0.877679	+	0.479249i	$0.159091\pi$
$53$	0.0771377	+	1.07853i	0.0771377	+	1.07853i	−0.800541	+	0.599278i	$0.795455\pi$
$54$	−0.281733	−	0.0405070i	−0.281733	−	0.0405070i
$55$		0			0
$56$		0			0
$57$	−1.47696	−	0.321292i	−1.47696	−	0.321292i
$58$		0			0
$59$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$59$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$60$		0			0
$61$	−1.07028	−	0.153882i	−1.07028	−	0.153882i	−0.415415	−	0.909632i	$-0.636364\pi$
$61$	−1.07028	−	0.153882i	−1.07028	−	0.153882i	−0.654861	+	0.755750i	$0.727273\pi$
$62$	−0.0265942	−	0.371836i	−0.0265942	−	0.371836i
$63$		0			0
$64$	−0.153882	+	0.524075i	−0.153882	+	0.524075i
$65$		0			0
$66$		0			0
$67$		0			0		−0.212565	−	0.977147i	$-0.568182\pi$
$67$		0			0		0.212565	+	0.977147i	$0.431818\pi$
$68$	−1.18220	+	1.18220i	−1.18220	+	1.18220i
$69$	0.755750	−	0.654861i	0.755750	−	0.654861i
$70$		0			0
$71$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$71$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$72$	0.437256	+	0.327326i	0.437256	+	0.327326i
$73$		0			0		0.349464	−	0.936950i	$-0.386364\pi$
$73$		0			0		−0.349464	+	0.936950i	$0.613636\pi$
$74$		0			0
$75$		0			0
$76$	1.04977	+	0.909632i	1.04977	+	0.909632i
$77$		0			0
$78$		0			0
$79$	0.368991	+	0.425839i	0.368991	+	0.425839i	0.909632	−	0.415415i	$-0.136364\pi$
$79$	0.368991	+	0.425839i	0.368991	+	0.425839i	−0.540641	+	0.841254i	$0.681818\pi$
$80$		0			0
$81$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$82$		0			0
$83$	−0.948742	+	1.73749i	−0.948742	+	1.73749i	−0.349464	+	0.936950i	$0.613636\pi$
$83$	−0.948742	+	1.73749i	−0.948742	+	1.73749i	−0.599278	+	0.800541i	$0.704545\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$89$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$90$		0			0
$91$		0			0
$92$	−0.897984	+	0.195345i	−0.897984	+	0.195345i
$93$	−0.926113	−	0.926113i	−0.926113	−	0.926113i
$94$	−0.258908	+	0.402869i	−0.258908	+	0.402869i
$95$		0			0
$96$	−0.317178	−	0.694523i	−0.317178	−	0.694523i
$97$		0			0		−0.479249	−	0.877679i	$-0.659091\pi$
$97$		0			0		0.479249	+	0.877679i	$0.340909\pi$
$98$	0.266684	−	0.0994679i	0.266684	−	0.0994679i
$99$		0			0
$100$		0			0
$101$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$101$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$102$	0.0369406	−	0.516497i	0.0369406	−	0.516497i
$103$		0			0		0.212565	−	0.977147i	$-0.431818\pi$
$103$		0			0		−0.212565	+	0.977147i	$0.568182\pi$
$104$		0			0
$105$		0			0
$106$	0.0867074	+	0.295298i	0.0867074	+	0.295298i
$107$	0.451077	−	0.337672i	0.451077	−	0.337672i	−0.349464	−	0.936950i	$-0.613636\pi$
$107$	0.451077	−	0.337672i	0.451077	−	0.337672i	0.800541	+	0.599278i	$0.204545\pi$
$108$	0.916644	−	0.0655597i	0.916644	−	0.0655597i
$109$	−0.234072	+	0.512546i	−0.234072	+	0.512546i	−0.989821	−	0.142315i	$-0.954545\pi$
$109$	−0.234072	+	0.512546i	−0.234072	+	0.512546i	0.755750	+	0.654861i	$0.227273\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.93440	−	0.420803i	1.93440	−	0.420803i	0.936950	−	0.349464i	$-0.113636\pi$
$113$	1.93440	−	0.420803i	1.93440	−	0.420803i	0.997452	−	0.0713392i	$-0.0227273\pi$
$114$	−0.430218			−0.430218
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$122$	−0.306981	+	0.0219557i	−0.306981	+	0.0219557i
$123$		0			0
$124$	0.339098	+	1.15486i	0.339098	+	1.15486i
$125$		0			0
$126$		0			0
$127$		0			0		0.212565	−	0.977147i	$-0.431818\pi$
$127$		0			0		−0.212565	+	0.977147i	$0.568182\pi$
$128$	−0.0655597	+	0.916644i	−0.0655597	+	0.916644i
$129$		0			0
$130$		0			0
$131$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$131$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−0.537225	+	0.835939i	−0.537225	+	0.835939i
$137$	0.398430	+	0.398430i	0.398430	+	0.398430i	0.877679	−	0.479249i	$-0.159091\pi$
$137$	0.398430	+	0.398430i	0.398430	+	0.398430i	−0.479249	+	0.877679i	$0.659091\pi$
$138$	0.170572	−	0.227858i	0.170572	−	0.227858i
$139$		−	1.68251i		−	1.68251i	−0.540641	−	0.841254i	$-0.681818\pi$
$139$		−	1.68251i		−	1.68251i	0.540641	−	0.841254i	$-0.318182\pi$
$140$		0			0
$141$	0.239446	+	1.66538i	0.239446	+	1.66538i
$142$		0			0
$143$		0			0
$144$	−0.694523	−	0.317178i	−0.694523	−	0.317178i
$145$		0			0
$146$		0			0
$147$	0.479249	−	0.877679i	0.479249	−	0.877679i
$148$		0			0
$149$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$149$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$150$		0			0
$151$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	0.415415	−	0.909632i	$-0.363636\pi$
$151$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	−0.959493	+	0.281733i	$0.909091\pi$
$152$	0.724595	+	0.395659i	0.724595	+	0.395659i
$153$	−1.09024	−	1.45640i	−1.09024	−	1.45640i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.349464	−	0.936950i	$-0.386364\pi$
$157$		0			0		−0.349464	+	0.936950i	$0.613636\pi$
$158$	0.128390	+	0.0961115i	0.128390	+	0.0961115i
$159$	0.909632	+	0.584585i	0.909632	+	0.584585i
$160$		0			0
$161$		0			0
$162$	−0.201264	+	0.201264i	−0.201264	+	0.201264i
$163$		0			0		−0.212565	−	0.977147i	$-0.568182\pi$
$163$		0			0		0.212565	+	0.977147i	$0.431818\pi$
$164$		0			0
$165$		0			0
$166$	−0.158746	+	0.540641i	−0.158746	+	0.540641i
$167$	0.670617	+	1.79799i	0.670617	+	1.79799i	0.599278	+	0.800541i	$0.295455\pi$
$167$	0.670617	+	1.79799i	0.670617	+	1.79799i	0.0713392	+	0.997452i	$0.477273\pi$
$168$		0			0
$169$	−0.989821	−	0.142315i	−0.989821	−	0.142315i
$170$		0			0
$171$	−1.14231	+	0.989821i	−1.14231	+	0.989821i
$172$		0			0
$173$	−1.64406	−	0.357643i	−1.64406	−	0.357643i	−0.707107	−	0.707107i	$-0.750000\pi$
$173$	−1.64406	−	0.357643i	−1.64406	−	0.357643i	−0.936950	+	0.349464i	$0.886364\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$179$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$180$		0			0
$181$	−1.80075	+	0.258908i	−1.80075	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$181$	−1.80075	+	0.258908i	−1.80075	+	0.258908i	−0.841254	+	0.540641i	$0.818182\pi$
$182$		0			0
$183$	−0.764582	+	0.764582i	−0.764582	+	0.764582i
$184$	−0.496841	+	0.226900i	−0.496841	+	0.226900i
$185$		0			0
$186$	−0.313607	−	0.201543i	−0.313607	−	0.201543i
$187$		0			0
$188$	0.540342	−	1.44871i	0.540342	−	1.44871i
$189$		0			0
$190$		0			0
$191$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$191$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$192$	0.327326	+	0.437256i	0.327326	+	0.437256i
$193$		0			0		−0.877679	−	0.479249i	$-0.840909\pi$
$193$		0			0		0.877679	+	0.479249i	$0.159091\pi$
$194$		0			0
$195$		0			0
$196$	−0.773100	+	0.496841i	−0.773100	+	0.496841i
$197$	1.91410	+	0.136899i	1.91410	+	0.136899i	0.977147	−	0.212565i	$-0.0681818\pi$
$197$	1.91410	+	0.136899i	1.91410	+	0.136899i	0.936950	+	0.349464i	$0.113636\pi$
$198$		0			0
$199$	−0.281733	+	1.95949i	−0.281733	+	1.95949i			1.00000i	$0.5\pi$
$199$	−0.281733	+	1.95949i	−0.281733	+	1.95949i	−0.281733	+	0.959493i	$0.590909\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$	0.237933	+	1.65486i	0.237933	+	1.65486i
$205$		0			0
$206$		0			0
$207$	−0.0713392	−	0.997452i	−0.0713392	−	0.997452i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.345139	−	0.755750i	−0.345139	−	0.755750i	0.654861	−	0.755750i	$-0.272727\pi$
$211$	−0.345139	−	0.755750i	−0.345139	−	0.755750i	−1.00000			$\pi$
$212$	−0.476221	−	0.872134i	−0.476221	−	0.872134i
$213$		0			0
$214$	0.105026	−	0.121206i	0.105026	−	0.121206i
$215$		0			0
$216$	0.524075	−	0.153882i	0.524075	−	0.153882i
$217$		0			0
$218$	−0.0340910	+	0.156714i	−0.0340910	+	0.156714i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.997452	−	0.0713392i	$-0.0227273\pi$
$223$		0			0		−0.997452	+	0.0713392i	$0.977273\pi$
$224$		0			0
$225$		0			0
$226$	0.512546	−	0.234072i	0.512546	−	0.234072i
$227$	−0.647988	+	0.865611i	−0.647988	+	0.865611i	−0.997452	−	0.0713392i	$-0.977273\pi$
$227$	−0.647988	+	0.865611i	−0.647988	+	0.865611i	0.349464	+	0.936950i	$0.386364\pi$
$228$	1.35730	−	0.295263i	1.35730	−	0.295263i
$229$	1.97964			1.97964			0.989821	−	0.142315i	$-0.0454545\pi$
$229$	1.97964			1.97964			0.989821	+	0.142315i	$0.0454545\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.15001	−	1.53623i	1.15001	−	1.53623i	0.349464	−	0.936950i	$-0.386364\pi$
$233$	1.15001	−	1.53623i	1.15001	−	1.53623i	0.800541	−	0.599278i	$-0.204545\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.562029	−	0.0401971i	0.562029	−	0.0401971i
$238$		0			0
$239$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$239$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$240$		0			0
$241$	0.983568	+	1.53046i	0.983568	+	1.53046i	0.841254	+	0.540641i	$0.181818\pi$
$241$	0.983568	+	1.53046i	0.983568	+	1.53046i	0.142315	+	0.989821i	$0.454545\pi$
$242$	−0.0605024	+	0.278125i	−0.0605024	+	0.278125i
$243$	−0.0713392	+	0.997452i	−0.0713392	+	0.997452i
$244$	0.953431	−	0.279953i	0.953431	−	0.279953i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	0.342841	+	0.627866i	0.342841	+	0.627866i
$249$	0.822373	+	1.80075i	0.822373	+	1.80075i
$250$		0			0
$251$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$251$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i
$257$	−0.778446	−	0.290345i	−0.778446	−	0.290345i	−0.0713392	−	0.997452i	$-0.522727\pi$
$257$	−0.778446	−	0.290345i	−0.778446	−	0.290345i	−0.707107	+	0.707107i	$0.750000\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1.50765	+	0.107829i	1.50765	+	0.107829i	0.800541	−	0.599278i	$-0.204545\pi$
$263$	1.50765	+	0.107829i	1.50765	+	0.107829i	0.707107	+	0.707107i	$0.250000\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$269$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$270$		0			0
$271$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.654861	−	0.755750i	$-0.727273\pi$
$271$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.959493	+	0.281733i	$0.909091\pi$
$272$	0.485422	−	1.30147i	0.485422	−	1.30147i
$273$		0			0
$274$	0.134919	+	0.0867074i	0.134919	+	0.0867074i
$275$		0			0
$276$	−0.381761	+	0.835939i	−0.381761	+	0.835939i
$277$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$277$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$278$	−0.101796	−	0.467947i	−0.101796	−	0.467947i
$279$	−1.29639	+	0.186393i	−1.29639	+	0.186393i
$280$		0			0
$281$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$281$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$282$	0.167355	+	0.448697i	0.167355	+	0.448697i
$283$		0			0		−0.0713392	−	0.997452i	$-0.522727\pi$
$283$		0			0		0.0713392	+	0.997452i	$0.477273\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.746072	−	0.162298i	−0.746072	−	0.162298i
$289$	1.74557	−	1.51255i	1.74557	−	1.51255i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.691814	+	1.85483i	0.691814	+	1.85483i	0.479249	+	0.877679i	$0.340909\pi$
$293$	0.691814	+	1.85483i	0.691814	+	1.85483i	0.212565	+	0.977147i	$0.431818\pi$
$294$	0.0801894	−	0.273100i	0.0801894	−	0.273100i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$	−0.189311	−	0.141717i	−0.189311	−	0.141717i
$303$		0			0
$304$	−1.10731	−	0.325137i	−1.10731	−	0.325137i
$305$		0			0
$306$	−0.391340	−	0.339098i	−0.391340	−	0.339098i
$307$		0			0		−0.599278	−	0.800541i	$-0.704545\pi$
$307$		0			0		0.599278	+	0.800541i	$0.295455\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$311$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$312$		0			0
$313$		0			0		0.479249	−	0.877679i	$-0.340909\pi$
$313$		0			0		−0.479249	+	0.877679i	$0.659091\pi$
$314$		0			0
$315$		0			0
$316$	−0.471022	−	0.215109i	−0.471022	−	0.215109i
$317$	−0.729202	+	0.398174i	−0.729202	+	0.398174i	−0.800541	−	0.599278i	$-0.795455\pi$
$317$	−0.729202	+	0.398174i	−0.729202	+	0.398174i	0.0713392	+	0.997452i	$0.477273\pi$
$318$	0.288360	+	0.107553i	0.288360	+	0.107553i
$319$		0			0
$320$		0			0
$321$		−	0.563465i		−	0.563465i
$322$		0			0
$323$	−1.94441	−	1.94441i	−1.94441	−	1.94441i
$324$	0.496841	−	0.773100i	0.496841	−	0.773100i
$325$		0			0
$326$		0			0
$327$	0.270040	+	0.494541i	0.270040	+	0.494541i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	−0.142315	−	0.989821i	$-0.545455\pi$
$331$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	0.415415	+	0.909632i	$0.363636\pi$
$332$	0.129785	−	1.81463i	0.129785	−	1.81463i
$333$		0			0
$334$	0.295298	+	0.459493i	0.295298	+	0.459493i
$335$		0			0
$336$		0			0
$337$		0			0		0.800541	−	0.599278i	$-0.204545\pi$
$337$		0			0		−0.800541	+	0.599278i	$0.795455\pi$
$338$	−0.283904	+	0.0203052i	−0.283904	+	0.0203052i
$339$	0.822373	−	1.80075i	0.822373	−	1.80075i
$340$		0			0
$341$		0			0
$342$	−0.257820	+	0.344407i	−0.257820	+	0.344407i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.478891			−0.478891
$347$	−1.27979	+	0.278401i	−1.27979	+	0.278401i	−0.800541	−	0.599278i	$-0.795455\pi$
$347$	−1.27979	+	0.278401i	−1.27979	+	0.278401i	−0.479249	+	0.877679i	$0.659091\pi$
$348$		0			0
$349$	0.258908	−	0.118239i	0.258908	−	0.118239i	−0.281733	−	0.959493i	$-0.590909\pi$
$349$	0.258908	−	0.118239i	0.258908	−	0.118239i	0.540641	+	0.841254i	$0.318182\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.04849	+	0.784887i	−1.04849	+	0.784887i	−0.977147	−	0.212565i	$-0.931818\pi$
$353$	−1.04849	+	0.784887i	−1.04849	+	0.784887i	−0.0713392	+	0.997452i	$0.522727\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$359$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$360$		0			0
$361$	−0.841254	+	0.970858i	−0.841254	+	0.970858i
$362$	−0.485168	+	0.180958i	−0.485168	+	0.180958i
$363$	0.479249	+	0.877679i	0.479249	+	0.877679i
$364$		0			0
$365$		0			0
$366$	−0.166390	+	0.258908i	−0.166390	+	0.258908i
$367$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$367$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$368$	0.611230	−	0.457561i	0.611230	−	0.457561i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	1.12773	+	0.420621i	1.12773	+	0.420621i
$373$		0			0		0.877679	−	0.479249i	$-0.159091\pi$
$373$		0			0		−0.877679	+	0.479249i	$0.840909\pi$
$374$		0			0
$375$		0			0
$376$	0.130785	−	0.909632i	0.130785	−	0.909632i
$377$		0			0
$378$		0			0
$379$	−1.66538	+	1.07028i	−1.66538	+	1.07028i	−0.755750	+	0.654861i	$0.772727\pi$
$379$	−1.66538	+	1.07028i	−1.66538	+	1.07028i	−0.909632	+	0.415415i	$0.863636\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.18636	−	1.58479i	−1.18636	−	1.58479i	−0.707107	−	0.707107i	$-0.750000\pi$
$383$	−1.18636	−	1.58479i	−1.18636	−	1.58479i	−0.479249	−	0.877679i	$-0.659091\pi$
$384$	0.694523	+	0.601808i	0.694523	+	0.601808i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$389$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$390$		0			0
$391$	1.80075	−	0.258908i	1.80075	−	0.258908i
$392$	−0.386222	+	0.386222i	−0.386222	+	0.386222i
$393$		0			0
$394$	0.540641	−	0.0777324i	0.540641	−	0.0777324i
$395$		0			0
$396$		0			0
$397$		0			0		−0.349464	−	0.936950i	$-0.613636\pi$
$397$		0			0		0.349464	+	0.936950i	$0.386364\pi$
$398$	0.0401971	+	0.562029i	0.0401971	+	0.562029i
$399$		0			0
$400$		0			0
$401$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$401$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.347256	+	0.931031i	0.347256	+	0.931031i
$409$	−0.234072	+	0.797176i	−0.234072	+	0.797176i	0.755750	+	0.654861i	$0.227273\pi$
$409$	−0.234072	+	0.797176i	−0.234072	+	0.797176i	−0.989821	+	0.142315i	$0.954545\pi$
$410$		0			0
$411$	0.557730	−	0.0801894i	0.557730	−	0.0801894i
$412$		0			0
$413$		0			0
$414$	−0.0801894	−	0.273100i	−0.0801894	−	0.273100i
$415$		0			0
$416$		0			0
$417$	−1.34692	−	1.00829i	−1.34692	−	1.00829i
$418$		0			0
$419$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$419$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$420$		0			0
$421$	1.14231	+	0.989821i	1.14231	+	0.989821i	1.00000			$0$
$421$	1.14231	+	0.989821i	1.14231	+	0.989821i	0.142315	+	0.989821i	$0.454545\pi$
$422$	−0.141717	−	0.189311i	−0.141717	−	0.189311i
$423$	1.47670	+	0.806340i	1.47670	+	0.806340i
$424$	−0.386758	−	0.446343i	−0.386758	−	0.446343i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.248163	+	0.454477i	−0.248163	+	0.454477i
$429$		0			0
$430$		0			0
$431$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$431$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$432$	−0.670126	+	0.365917i	−0.670126	+	0.365917i
$433$		0			0		−0.936950	−	0.349464i	$-0.886364\pi$
$433$		0			0		0.936950	+	0.349464i	$0.113636\pi$
$434$		0			0
$435$		0			0
$436$		−	0.517817i		−	0.517817i
$437$	−0.321292	−	1.47696i	−0.321292	−	1.47696i
$438$		0			0
$439$	0.153882	−	0.239446i	0.153882	−	0.239446i	−0.755750	−	0.654861i	$-0.772727\pi$
$439$	0.153882	−	0.239446i	0.153882	−	0.239446i	0.909632	+	0.415415i	$0.136364\pi$
$440$		0			0
$441$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$442$		0			0
$443$	0.778446	−	0.290345i	0.778446	−	0.290345i	0.0713392	−	0.997452i	$-0.477273\pi$
$443$	0.778446	−	0.290345i	0.778446	−	0.290345i	0.707107	+	0.707107i	$0.250000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$449$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$450$		0			0
$451$		0			0
$452$	−1.45640	+	1.09024i	−1.45640	+	1.09024i
$453$	−0.828713	+	0.0592707i	−0.828713	+	0.0592707i
$454$	−0.127850	+	0.279953i	−0.127850	+	0.279953i
$455$		0			0
$456$	0.750975	−	0.342959i	0.750975	−	0.342959i
$457$		0			0		0.599278	−	0.800541i	$-0.295455\pi$
$457$		0			0		−0.599278	+	0.800541i	$0.704545\pi$
$458$	0.550588	−	0.119773i	0.550588	−	0.119773i
$459$	−1.81926			−1.81926
$460$		0			0
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$		0			0		0.599278	−	0.800541i	$-0.295455\pi$
$463$		0			0		−0.599278	+	0.800541i	$0.704545\pi$
$464$		0			0
$465$		0			0
$466$	0.226900	−	0.496841i	0.226900	−	0.496841i
$467$	1.81463	−	0.129785i	1.81463	−	0.129785i	0.877679	−	0.479249i	$-0.159091\pi$
$467$	1.81463	−	0.129785i	1.81463	−	0.129785i	0.936950	+	0.349464i	$0.113636\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$	0.153882	−	0.0451840i	0.153882	−	0.0451840i
$475$		0			0
$476$		0			0
$477$	1.01311	−	0.377869i	1.01311	−	0.377869i
$478$		0			0
$479$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$479$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$480$		0			0
$481$		0			0
$482$	0.366152	+	0.366152i	0.366152	+	0.366152i
$483$		0			0
$484$		−	0.918986i		−	0.918986i
$485$		0			0
$486$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$487$		0			0		−0.936950	−	0.349464i	$-0.886364\pi$
$487$		0			0		0.936950	+	0.349464i	$0.113636\pi$
$488$	0.518354	−	0.283043i	0.518354	−	0.283043i
$489$		0			0
$490$		0			0
$491$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$491$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$497$		0			0
$498$	0.337672	+	0.451077i	0.337672	+	0.451077i
$499$	−1.45027	−	1.25667i	−1.45027	−	1.25667i	−0.909632	−	0.415415i	$-0.863636\pi$
$499$	−1.45027	−	1.25667i	−1.45027	−	1.25667i	−0.540641	−	0.841254i	$-0.681818\pi$
$500$		0			0
$501$	1.84125	+	0.540641i	1.84125	+	0.540641i
$502$		0			0
$503$	−1.21002	−	0.905808i	−1.21002	−	0.905808i	−0.212565	−	0.977147i	$-0.568182\pi$
$503$	−1.21002	−	0.905808i	−1.21002	−	0.905808i	−0.997452	+	0.0713392i	$0.977273\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$508$		0			0
$509$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$509$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$510$		0			0
$511$		0			0
$512$	−0.349464	−	0.936950i	−0.349464	−	0.936950i
$513$	0.107829	+	1.50765i	0.107829	+	1.50765i
$514$	−0.234072	−	0.0336545i	−0.234072	−	0.0336545i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−1.27155	+	1.10181i	−1.27155	+	1.10181i
$520$		0			0
$521$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$521$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$522$		0			0
$523$		0			0		−0.349464	−	0.936950i	$-0.613636\pi$
$523$		0			0		0.349464	+	0.936950i	$0.386364\pi$
$524$		0			0
$525$		0			0
$526$	0.425839	−	0.0612263i	0.425839	−	0.0612263i
$527$	−0.506486	−	2.32828i	−0.506486	−	2.32828i
$528$		0			0
$529$	0.909632	+	0.415415i	0.909632	+	0.415415i
$530$		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
$541$	1.10181	−	0.708089i	1.10181	−	0.708089i	0.142315	−	0.989821i	$-0.454545\pi$
$541$	1.10181	−	0.708089i	1.10181	−	0.708089i	0.959493	+	0.281733i	$0.0909091\pi$
$542$	−0.477671	−	0.0341637i	−0.477671	−	0.0341637i
$543$	−0.871880	+	1.59673i	−0.871880	+	1.59673i
$544$	0.197682	−	1.37491i	0.197682	−	1.37491i
$545$		0			0
$546$		0			0
$547$		0			0		0.877679	−	0.479249i	$-0.159091\pi$
$547$		0			0		−0.877679	+	0.479249i	$0.840909\pi$
$548$	−0.485168	−	0.180958i	−0.485168	−	0.180958i
$549$	0.153882	+	1.07028i	0.153882	+	1.07028i
$550$		0			0
$551$		0			0
$552$	−0.116103	+	0.533718i	−0.116103	+	0.533718i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.642315	+	1.40647i	0.642315	+	1.40647i
$557$	0.724384	+	1.32661i	0.724384	+	1.32661i	0.936950	+	0.349464i	$0.113636\pi$
$557$	0.724384	+	1.32661i	0.724384	+	1.32661i	−0.212565	+	0.977147i	$0.568182\pi$
$558$	−0.349281	+	0.130275i	−0.349281	+	0.130275i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.229843	−	1.05657i	0.229843	−	1.05657i	−0.707107	−	0.707107i	$-0.750000\pi$
$563$	0.229843	−	1.05657i	0.229843	−	1.05657i	0.936950	−	0.349464i	$-0.113636\pi$
$564$	−0.835939	−	1.30075i	−0.835939	−	1.30075i
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$569$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$570$		0			0
$571$	−0.983568	+	0.449181i	−0.983568	+	0.449181i	−0.841254	−	0.540641i	$-0.818182\pi$
$571$	−0.983568	+	0.449181i	−0.983568	+	0.449181i	−0.142315	+	0.989821i	$0.545455\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.546200			0.546200
$577$		0			0		0.977147	−	0.212565i	$-0.0681818\pi$
$577$		0			0		−0.977147	+	0.212565i	$0.931818\pi$
$578$	0.393974	−	0.526288i	0.393974	−	0.526288i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	0.304632	+	0.474017i	0.304632	+	0.474017i
$587$	−0.278401	+	1.27979i	−0.278401	+	1.27979i	0.599278	+	0.800541i	$0.295455\pi$
$587$	−0.278401	+	1.27979i	−0.278401	+	1.27979i	−0.877679	+	0.479249i	$0.840909\pi$
$588$	−0.0655597	+	0.916644i	−0.0655597	+	0.916644i
$589$	−1.89945	+	0.557730i	−1.89945	+	0.557730i
$590$		0			0
$591$	1.25667	−	1.45027i	1.25667	−	1.45027i
$592$		0			0
$593$	−0.627683	−	1.14952i	−0.627683	−	1.14952i	−0.977147	−	0.212565i	$-0.931818\pi$
$593$	−0.627683	−	1.14952i	−0.627683	−	1.14952i	0.349464	−	0.936950i	$-0.386364\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.39982	+	1.39982i	1.39982	+	1.39982i
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	−0.273100	−	1.89945i	−0.273100	−	1.89945i	−0.415415	−	0.909632i	$-0.636364\pi$
$601$	−0.273100	−	1.89945i	−0.273100	−	1.89945i	0.142315	−	0.989821i	$-0.454545\pi$
$602$		0			0
$603$		0			0
$604$	0.694523	+	0.317178i	0.694523	+	0.317178i
$605$		0			0
$606$		0			0
$607$		0			0		0.479249	−	0.877679i	$-0.340909\pi$
$607$		0			0		−0.479249	+	0.877679i	$0.659091\pi$
$608$	−1.15112	−	0.0823298i	−1.15112	−	0.0823298i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	1.46737	+	0.801246i	1.46737	+	0.801246i
$613$		0			0		−0.599278	−	0.800541i	$-0.704545\pi$
$613$		0			0		0.599278	+	0.800541i	$0.295455\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.377869	+	1.01311i	−0.377869	+	1.01311i	0.599278	+	0.800541i	$0.295455\pi$
$617$	−0.377869	+	1.01311i	−0.377869	+	1.01311i	−0.977147	+	0.212565i	$0.931818\pi$
$618$		0			0
$619$	−0.474017	−	0.304632i	−0.474017	−	0.304632i	0.281733	−	0.959493i	$-0.409091\pi$
$619$	−0.474017	−	0.304632i	−0.474017	−	0.304632i	−0.755750	+	0.654861i	$0.772727\pi$
$620$		0			0
$621$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$622$		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
$631$	1.37491	−	1.19136i	1.37491	−	1.19136i	0.415415	−	0.909632i	$-0.363636\pi$
$631$	1.37491	−	1.19136i	1.37491	−	1.19136i	0.959493	−	0.281733i	$-0.0909091\pi$
$632$	−0.300731	−	0.0654201i	−0.300731	−	0.0654201i
$633$	−0.811843	−	0.176606i	−0.811843	−	0.176606i
$634$	−0.178719	+	0.154861i	−0.178719	+	0.154861i
$635$		0			0
$636$	−0.983568	−	0.141416i	−0.983568	−	0.141416i
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$641$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$642$	−0.0340910	−	0.156714i	−0.0340910	−	0.156714i
$643$		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
$646$	−0.658432	−	0.423148i	−0.658432	−	0.423148i
$647$	−0.665114	−	0.497898i	−0.665114	−	0.497898i	0.212565	−	0.977147i	$-0.431818\pi$
$647$	−0.665114	−	0.497898i	−0.665114	−	0.497898i	−0.877679	+	0.479249i	$0.840909\pi$
$648$	0.190877	−	0.511762i	0.190877	−	0.511762i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.68425	+	0.919672i	1.68425	+	0.919672i	0.977147	+	0.212565i	$0.0681818\pi$
$653$	1.68425	+	0.919672i	1.68425	+	0.919672i	0.707107	+	0.707107i	$0.250000\pi$
$654$	0.105026	+	0.121206i	0.105026	+	0.121206i
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$659$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$660$		0			0
$661$	1.37491	+	0.627899i	1.37491	+	0.627899i	0.959493	−	0.281733i	$-0.0909091\pi$
$661$	1.37491	+	0.627899i	1.37491	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$662$	0.0711043	−	0.0388259i	0.0711043	−	0.0388259i
$663$		0			0
$664$	−0.153882	−	1.07028i	−0.153882	−	1.07028i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−1.24700	−	1.24700i	−1.24700	−	1.24700i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.936950	−	0.349464i	$-0.113636\pi$
$673$		0			0		−0.936950	+	0.349464i	$0.886364\pi$
$674$		0			0
$675$		0			0
$676$	0.881761	−	0.258908i	0.881761	−	0.258908i
$677$	0.0401971	−	0.562029i	0.0401971	−	0.562029i	−0.936950	−	0.349464i	$-0.886364\pi$
$677$	0.0401971	−	0.562029i	0.0401971	−	0.562029i	0.977147	−	0.212565i	$-0.0681818\pi$
$678$	0.119773	−	0.550588i	0.119773	−	0.550588i
$679$		0			0
$680$		0			0
$681$	0.304632	+	1.03748i	0.304632	+	1.03748i
$682$		0			0
$683$	1.67822	−	0.120029i	1.67822	−	0.120029i	0.800541	−	0.599278i	$-0.204545\pi$
$683$	1.67822	−	0.120029i	1.67822	−	0.120029i	0.877679	+	0.479249i	$0.159091\pi$
$684$	0.577031	−	1.26352i	0.577031	−	1.26352i
$685$		0			0
$686$		0			0
$687$	1.18636	−	1.58479i	1.18636	−	1.58479i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$691$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$692$	1.51086	−	0.328669i	1.51086	−	0.328669i
$693$		0			0
$694$	−0.339098	+	0.154861i	−0.339098	+	0.154861i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	0.0648551	−	0.0485499i	0.0648551	−	0.0485499i
$699$	−0.540641	−	1.84125i	−0.540641	−	1.84125i
$700$		0			0
$701$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$701$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−0.244123	+	0.281733i	−0.244123	+	0.281733i
$707$		0			0
$708$		0			0
$709$	−0.755750	−	1.65486i	−0.755750	−	1.65486i	−0.755750	−	0.654861i	$-0.772727\pi$
$709$	−0.755750	−	1.65486i	−0.755750	−	1.65486i		−	1.00000i	$-0.5\pi$
$710$		0			0
$711$	0.304632	−	0.474017i	0.304632	−	0.474017i
$712$		0			0
$713$	0.457701	−	1.22714i	0.457701	−	1.22714i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$719$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$720$		0			0
$721$		0			0
$722$	−0.175234	+	0.320918i	−0.175234	+	0.320918i
$723$	1.81463	+	0.129785i	1.81463	+	0.129785i
$724$	1.40647	−	0.903886i	1.40647	−	0.903886i
$725$		0			0
$726$	0.186393	+	0.215109i	0.186393	+	0.215109i
$727$		0			0		−0.877679	−	0.479249i	$-0.840909\pi$
$727$		0			0		0.877679	+	0.479249i	$0.159091\pi$
$728$		0			0
$729$	0.755750	+	0.654861i	0.755750	+	0.654861i
$730$		0			0
$731$		0			0
$732$	0.347256	−	0.931031i	0.347256	−	0.931031i
$733$		0			0		−0.800541	−	0.599278i	$-0.795455\pi$
$733$		0			0		0.800541	+	0.599278i	$0.204545\pi$
$734$		0			0
$735$		0			0
$736$	0.500000	−	0.577031i	0.500000	−	0.577031i
$737$		0			0
$738$		0			0
$739$	0.281733	−	0.0405070i	0.281733	−	0.0405070i		−	1.00000i	$-0.5\pi$
$739$	0.281733	−	0.0405070i	0.281733	−	0.0405070i	0.281733	+	0.959493i	$0.409091\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.141226	−	1.97460i	−0.141226	−	1.97460i	−0.212565	−	0.977147i	$-0.568182\pi$
$743$	−0.141226	−	1.97460i	−0.141226	−	1.97460i	0.0713392	−	0.997452i	$-0.477273\pi$
$744$	0.708089	+	0.101808i	0.708089	+	0.101808i
$745$		0			0
$746$		0			0
$747$	1.93440	+	0.420803i	1.93440	+	0.420803i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	1.80075	+	0.258908i	1.80075	+	0.258908i	0.959493	−	0.281733i	$-0.0909091\pi$
$751$	1.80075	+	0.258908i	1.80075	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$752$	0.0916444	+	1.28136i	0.0916444	+	1.28136i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.212565	−	0.977147i	$-0.568182\pi$
$757$		0			0		0.212565	+	0.977147i	$0.431818\pi$
$758$	−0.398430	+	0.398430i	−0.398430	+	0.398430i
$759$		0			0
$760$		0			0
$761$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$761$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−0.425839	−	0.368991i	−0.425839	−	0.368991i
$767$		0			0
$768$	−0.249813	−	0.136408i	−0.249813	−	0.136408i
$769$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$769$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$770$		0			0
$771$	−0.698939	+	0.449181i	−0.698939	+	0.449181i
$772$		0			0
$773$	−0.724384	+	1.32661i	−0.724384	+	1.32661i	0.212565	+	0.977147i	$0.431818\pi$
$773$	−0.724384	+	1.32661i	−0.724384	+	1.32661i	−0.936950	+	0.349464i	$0.886364\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	0.485168	−	0.180958i	0.485168	−	0.180958i
$783$		0			0
$784$	0.412791	−	0.642315i	0.412791	−	0.642315i
$785$		0			0
$786$		0			0
$787$		0			0		−0.479249	−	0.877679i	$-0.659091\pi$
$787$		0			0		0.479249	+	0.877679i	$0.340909\pi$
$788$	−1.65233	+	0.616287i	−1.65233	+	0.616287i
$789$	0.989821	−	1.14231i	0.989821	−	1.14231i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−0.512546	−	1.74557i	−0.512546	−	1.74557i
$797$	−1.21002	+	0.905808i	−1.21002	+	0.905808i	−0.997452	−	0.0713392i	$-0.977273\pi$
$797$	−1.21002	+	0.905808i	−1.21002	+	0.905808i	−0.212565	+	0.977147i	$0.568182\pi$
$798$		0			0
$799$	−1.27155	+	2.78431i	−1.27155	+	2.78431i
$800$		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		0.909632	−	0.415415i	$-0.136364\pi$
$809$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$810$		0			0
$811$	0.797176	−	1.74557i	0.797176	−	1.74557i	0.142315	−	0.989821i	$-0.454545\pi$
$811$	0.797176	−	1.74557i	0.797176	−	1.74557i	0.654861	−	0.755750i	$-0.272727\pi$
$812$		0			0
$813$	−1.34692	+	1.00829i	−1.34692	+	1.00829i
$814$		0			0
$815$		0			0
$816$	−0.750975	−	1.16854i	−0.750975	−	1.16854i
$817$		0			0
$818$	−0.0168702	+	0.235876i	−0.0168702	+	0.235876i
$819$		0			0
$820$		0			0
$821$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$821$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$822$	0.150267	−	0.0560467i	0.150267	−	0.0560467i
$823$		0			0		−0.479249	−	0.877679i	$-0.659091\pi$
$823$		0			0		0.479249	+	0.877679i	$0.340909\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.06879	+	1.06879i	1.06879	+	1.06879i	0.997452	+	0.0713392i	$0.0227273\pi$
$827$	1.06879	+	1.06879i	1.06879	+	1.06879i	0.0713392	+	0.997452i	$0.477273\pi$
$828$	0.440423	+	0.806575i	0.440423	+	0.806575i
$829$			1.91899i			1.91899i	0.281733	+	0.959493i	$0.409091\pi$
$829$			1.91899i			1.91899i	−0.281733	+	0.959493i	$0.590909\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.59673	−	0.871880i	1.59673	−	0.871880i
$834$	−0.435615	−	0.198939i	−0.435615	−	0.198939i
$835$		0			0
$836$		0			0
$837$	−0.627683	+	1.14952i	−0.627683	+	1.14952i
$838$		0			0
$839$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$839$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$840$		0			0
$841$	0.654861	+	0.755750i	0.654861	+	0.755750i
$842$	0.377593	+	0.206181i	0.377593	+	0.206181i
$843$		0			0
$844$	0.577031	+	0.500000i	0.577031	+	0.500000i
$845$		0			0
$846$	0.459493	+	0.134919i	0.459493	+	0.134919i
$847$		0			0
$848$	0.660912	+	0.494752i	0.660912	+	0.494752i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.212565	−	0.977147i	$-0.568182\pi$
$853$		0			0		0.212565	+	0.977147i	$0.431818\pi$
$854$		0			0
$855$		0			0
$856$	−0.0867074	+	0.295298i	−0.0867074	+	0.295298i
$857$	−0.457701	−	1.22714i	−0.457701	−	1.22714i	−0.936950	−	0.349464i	$-0.886364\pi$
$857$	−0.457701	−	1.22714i	−0.457701	−	1.22714i	0.479249	−	0.877679i	$-0.340909\pi$
$858$		0			0
$859$	0.822373	+	0.118239i	0.822373	+	0.118239i	0.540641	−	0.841254i	$-0.318182\pi$
$859$	0.822373	+	0.118239i	0.822373	+	0.118239i	0.281733	+	0.959493i	$0.409091\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.87513	−	0.407910i	−1.87513	−	0.407910i	−0.877679	−	0.479249i	$-0.840909\pi$
$863$	−1.87513	−	0.407910i	−1.87513	−	0.407910i	−0.997452	+	0.0713392i	$0.977273\pi$
$864$	−0.577031	+	0.500000i	−0.577031	+	0.500000i
$865$		0			0
$866$		0			0
$867$	−0.164774	−	2.30384i	−0.164774	−	2.30384i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.0654201	−	0.300731i	−0.0654201	−	0.300731i
$873$		0			0
$874$	−0.178719	−	0.391340i	−0.178719	−	0.391340i
$875$		0			0
$876$		0			0
$877$		0			0		−0.800541	−	0.599278i	$-0.795455\pi$
$877$		0			0		0.800541	+	0.599278i	$0.204545\pi$
$878$	0.0283115	−	0.0759061i	0.0283115	−	0.0759061i
$879$	1.89945	+	0.557730i	1.89945	+	0.557730i
$880$		0			0
$881$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$881$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$882$	−0.170572	−	0.227858i	−0.170572	−	0.227858i
$883$		0			0		−0.877679	−	0.479249i	$-0.840909\pi$
$883$		0			0		0.877679	+	0.479249i	$0.159091\pi$
$884$		0			0
$885$		0			0
$886$	0.198939	−	0.127850i	0.198939	−	0.127850i
$887$	−0.828713	−	0.0592707i	−0.828713	−	0.0592707i	−0.349464	−	0.936950i	$-0.613636\pi$
$887$	−0.828713	−	0.0592707i	−0.828713	−	0.0592707i	−0.479249	+	0.877679i	$0.659091\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	2.38276	+	0.888725i	2.38276	+	0.888725i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	0.817178	+	1.78937i	0.817178	+	1.78937i
$902$		0			0
$903$		0			0
$904$	−0.708089	+	0.817178i	−0.708089	+	0.817178i
$905$		0			0
$906$	−0.226900	+	0.0666238i	−0.226900	+	0.0666238i
$907$		0			0		0.0713392	−	0.997452i	$-0.477273\pi$
$907$		0			0		−0.0713392	+	0.997452i	$0.522727\pi$
$908$	0.211222	−	0.970974i	0.211222	−	0.970974i
$909$		0			0
$910$		0			0
$911$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$911$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$912$	−0.923874	+	0.691603i	−0.923874	+	0.691603i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−1.65486	+	0.755750i	−1.65486	+	0.755750i
$917$		0			0
$918$	−0.505983	+	0.110070i	−0.505983	+	0.110070i
$919$	1.81926			1.81926			0.909632	−	0.415415i	$-0.136364\pi$
$919$	1.81926			1.81926			0.909632	+	0.415415i	$0.136364\pi$
$920$		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		−0.281733	−	0.959493i	$-0.590909\pi$
$929$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$930$		0			0
$931$	−0.817178	−	1.27155i	−0.817178	−	1.27155i
$932$	−0.374863	+	1.72322i	−0.374863	+	1.72322i
$933$		0			0
$934$	0.496841	−	0.145886i	0.496841	−	0.145886i
$935$		0			0
$936$		0			0
$937$		0			0		0.936950	−	0.349464i	$-0.113636\pi$
$937$		0			0		−0.936950	+	0.349464i	$0.886364\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$941$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.57642	−	0.587976i	−1.57642	−	0.587976i	−0.599278	−	0.800541i	$-0.704545\pi$
$947$	−1.57642	−	0.587976i	−1.57642	−	0.587976i	−0.977147	+	0.212565i	$0.931818\pi$
$948$	−0.454477	+	0.248163i	−0.454477	+	0.248163i
$949$		0			0
$950$		0			0
$951$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$952$		0			0
$953$	1.07853	+	0.0771377i	1.07853	+	0.0771377i	0.599278	−	0.800541i	$-0.295455\pi$
$953$	1.07853	+	0.0771377i	1.07853	+	0.0771377i	0.479249	+	0.877679i	$0.340909\pi$
$954$	0.258908	−	0.166390i	0.258908	−	0.166390i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.686393	−	0.201543i	−0.686393	−	0.201543i
$962$		0			0
$963$	−0.451077	−	0.337672i	−0.451077	−	0.337672i
$964$	−1.40647	−	0.903886i	−1.40647	−	0.903886i
$965$		0			0
$966$		0			0
$967$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$967$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$968$	−0.116103	−	0.533718i	−0.116103	−	0.533718i
$969$	−2.72183	+	0.391340i	−2.72183	+	0.391340i
$970$		0			0
$971$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$971$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$972$	−0.321153	−	0.861044i	−0.321153	−	0.861044i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−0.623933	+	0.540641i	−0.623933	+	0.540641i
$977$	−0.550588	−	0.119773i	−0.550588	−	0.119773i	−0.0713392	−	0.997452i	$-0.522727\pi$
$977$	−0.550588	−	0.119773i	−0.550588	−	0.119773i	−0.479249	+	0.877679i	$0.659091\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.557730	+	0.0801894i	0.557730	+	0.0801894i
$982$		0			0
$983$	0.196911	+	0.527938i	0.196911	+	0.527938i	0.997452	−	0.0713392i	$-0.0227273\pi$
$983$	0.196911	+	0.527938i	0.196911	+	0.527938i	−0.800541	+	0.599278i	$0.795455\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	1.61435	+	1.03748i	1.61435	+	1.03748i	0.959493	+	0.281733i	$0.0909091\pi$
$991$	1.61435	+	1.03748i	1.61435	+	1.03748i	0.654861	+	0.755750i	$0.272727\pi$
$992$	−0.800541	−	0.599278i	−0.800541	−	0.599278i
$993$	0.0994679	−	0.266684i	0.0994679	−	0.266684i
$994$		0			0
$995$		0			0
$996$	−1.37491	−	1.19136i	−1.37491	−	1.19136i
$997$		0			0		−0.599278	−	0.800541i	$-0.704545\pi$
$997$		0			0		0.599278	+	0.800541i	$0.295455\pi$
$998$	−0.479389	−	0.261766i	−0.479389	−	0.261766i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1725.1.bg.a.182.2	yes	40
3.2	odd	2	inner	1725.1.bg.a.182.1	✓	40
5.2	odd	4	inner	1725.1.bg.a.1493.2	yes	40
5.3	odd	4	inner	1725.1.bg.a.1493.1	yes	40
5.4	even	2	inner	1725.1.bg.a.182.1	✓	40
15.2	even	4	inner	1725.1.bg.a.1493.1	yes	40
15.8	even	4	inner	1725.1.bg.a.1493.2	yes	40
15.14	odd	2	CM	1725.1.bg.a.182.2	yes	40
23.11	odd	22	inner	1725.1.bg.a.632.2	yes	40
69.11	even	22	inner	1725.1.bg.a.632.1	yes	40
115.34	odd	22	inner	1725.1.bg.a.632.1	yes	40
115.57	even	44	inner	1725.1.bg.a.218.2	yes	40
115.103	even	44	inner	1725.1.bg.a.218.1	yes	40
345.149	even	22	inner	1725.1.bg.a.632.2	yes	40
345.218	odd	44	inner	1725.1.bg.a.218.2	yes	40
345.287	odd	44	inner	1725.1.bg.a.218.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1725.1.bg.a.182.1	✓	40	3.2	odd	2	inner
1725.1.bg.a.182.1	✓	40	5.4	even	2	inner
1725.1.bg.a.182.2	yes	40	1.1	even	1	trivial
1725.1.bg.a.182.2	yes	40	15.14	odd	2	CM
1725.1.bg.a.218.1	yes	40	115.103	even	44	inner
1725.1.bg.a.218.1	yes	40	345.287	odd	44	inner
1725.1.bg.a.218.2	yes	40	115.57	even	44	inner
1725.1.bg.a.218.2	yes	40	345.218	odd	44	inner
1725.1.bg.a.632.1	yes	40	69.11	even	22	inner
1725.1.bg.a.632.1	yes	40	115.34	odd	22	inner
1725.1.bg.a.632.2	yes	40	23.11	odd	22	inner
1725.1.bg.a.632.2	yes	40	345.149	even	22	inner
1725.1.bg.a.1493.1	yes	40	5.3	odd	4	inner
1725.1.bg.a.1493.1	yes	40	15.2	even	4	inner
1725.1.bg.a.1493.2	yes	40	5.2	odd	4	inner
1725.1.bg.a.1493.2	yes	40	15.8	even	4	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)

\(f(q)\)	\(=\)	\(q+(0.278125 - 0.0605024i) q^{2} +(0.599278 - 0.800541i) q^{3} +(-0.835939 + 0.381761i) q^{4} +(0.118239 - 0.258908i) q^{6} +(-0.437256 + 0.327326i) q^{8} +(-0.281733 - 0.959493i) q^{9} +(-0.195345 + 0.897984i) q^{12} +(0.500000 - 0.577031i) q^{16} +(1.70456 - 0.635768i) q^{17} +(-0.136408 - 0.249813i) q^{18} +(-0.627899 - 1.37491i) q^{19} +(0.977147 + 0.212565i) q^{23} +0.546200i q^{24} +(-0.936950 - 0.349464i) q^{27} +(0.186393 - 1.29639i) q^{31} +(0.365917 - 0.670126i) q^{32} +(0.435615 - 0.279953i) q^{34} +(0.601808 + 0.694523i) q^{36} +(-0.257820 - 0.344407i) q^{38} +0.284630 q^{46} +(-1.18971 + 1.18971i) q^{47} +(-0.162298 - 0.746072i) q^{48} +(0.989821 - 0.142315i) q^{49} +(0.512546 - 1.74557i) q^{51} +(0.0771377 + 1.07853i) q^{53} +(-0.281733 - 0.0405070i) q^{54} +(-1.47696 - 0.321292i) q^{57} +(-1.07028 - 0.153882i) q^{61} +(-0.0265942 - 0.371836i) q^{62} +(-0.153882 + 0.524075i) q^{64} +(-1.18220 + 1.18220i) q^{68} +(0.755750 - 0.654861i) q^{69} +(0.437256 + 0.327326i) q^{72} +(1.04977 + 0.909632i) q^{76} +(0.368991 + 0.425839i) q^{79} +(-0.841254 + 0.540641i) q^{81} +(-0.948742 + 1.73749i) q^{83} +(-0.897984 + 0.195345i) q^{92} +(-0.926113 - 0.926113i) q^{93} +(-0.258908 + 0.402869i) q^{94} +(-0.317178 - 0.694523i) q^{96} +(0.266684 - 0.0994679i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{6} + 20 q^{16} - 8 q^{31} - 12 q^{36} + 8 q^{46} - 44 q^{76} + 4 q^{81} + 20 q^{96}+O(q^{100}) \) 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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