LMFDB - Embedded newform 2740.1.cd.a.583.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2740,1,Mod(3,2740)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2740, base_ring=CyclotomicField(136))

chi = DirichletCharacter(H, H._module([68, 102, 1]))

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

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

chi := DirichletCharacter("2740.3");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2740 = 2^{2} \cdot 5 \cdot 137 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2740.cd (of order $136$, degree $64$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.36743813461$
Analytic rank:	$0$
Dimension:	$64$
Coefficient field:	$\Q(\zeta_{136})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{64} - x^{60} + x^{56} - x^{52} + x^{48} - x^{44} + x^{40} - x^{36} + x^{32} - x^{28} + x^{24} + \cdots + 1 $ x^64 - x^60 + x^56 - x^52 + x^48 - x^44 + x^40 - x^36 + x^32 - x^28 + x^24 - x^20 + x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{136}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{136} - \cdots)$

Embedding invariants

Embedding label			583.1
Root			$0.973438 + 0.228951i$ of defining polynomial
Character	$\chi$	$=$	2740.583
Dual form			2740.1.cd.a.47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.445738 - 0.895163i) q^{2} +(-0.602635 + 0.798017i) q^{4} +(-0.565136 - 0.824997i) q^{5} +(0.982973 + 0.183750i) q^{8} +(0.769334 + 0.638847i) q^{9} +O(q^{10})$	\(q+(-0.445738 - 0.895163i) q^{2} +(-0.602635 + 0.798017i) q^{4} +(-0.565136 - 0.824997i) q^{5} +(0.982973 + 0.183750i) q^{8} +(0.769334 + 0.638847i) q^{9} +(-0.486604 + 0.873622i) q^{10} +(-0.363613 + 0.347190i) q^{13} +(-0.273663 - 0.961826i) q^{16} +(0.303186 + 1.62190i) q^{17} +(0.228951 - 0.973438i) q^{18} +(0.998933 + 0.0461835i) q^{20} +(-0.361242 + 0.932472i) q^{25} +(0.472868 + 0.170737i) q^{26} +(-1.56735 + 1.24148i) q^{29} +(-0.739009 + 0.673696i) q^{32} +(1.31672 - 0.994344i) q^{34} +(-0.973438 + 0.228951i) q^{36} -0.635583i q^{37} +(-0.403921 - 0.914794i) q^{40} +(0.755383 + 1.82366i) q^{41} +(0.0922684 - 0.995734i) q^{45} +(0.739009 - 0.673696i) q^{49} +(0.995734 - 0.0922684i) q^{50} +(-0.0579382 - 0.499398i) q^{52} +(-0.407425 + 0.0664607i) q^{53} +(1.80996 + 0.849659i) q^{58} +(1.22892 + 1.47993i) q^{61} +(0.932472 + 0.361242i) q^{64} +(0.491922 + 0.103770i) q^{65} +(-1.47701 - 0.735466i) q^{68} +(0.638847 + 0.769334i) q^{72} +(-0.621500 - 1.40756i) q^{73} +(-0.568950 + 0.283304i) q^{74} +(-0.638847 + 0.769334i) q^{80} +(0.183750 + 0.982973i) q^{81} +(1.29577 - 1.48906i) q^{82} +(1.16672 - 1.16672i) q^{85} +(1.23486 + 1.41908i) q^{89} +(-0.932472 + 0.361242i) q^{90} +(0.464478 - 1.78843i) q^{97} +(-0.932472 - 0.361242i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{2} - 4 q^{4} + 4 q^{8}+O(q^{10}) $ 64 * q + 4 * q^2 - 4 * q^4 + 4 * q^8	$ 64 q + 4 q^{2} - 4 q^{4} + 4 q^{8} - 4 q^{13} - 4 q^{16} + 4 q^{26} + 4 q^{32} - 4 q^{45} - 4 q^{49} - 4 q^{52} - 4 q^{64} - 4 q^{65} + 4 q^{73} + 4 q^{85} + 4 q^{90} + 4 q^{97} + 4 q^{98}+O(q^{100}) $ 64 * q + 4 * q^2 - 4 * q^4 + 4 * q^8 - 4 * q^13 - 4 * q^16 + 4 * q^26 + 4 * q^32 - 4 * q^45 - 4 * q^49 - 4 * q^52 - 4 * q^64 - 4 * q^65 + 4 * q^73 + 4 * q^85 + 4 * q^90 + 4 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2740\mathbb{Z}\right)^\times$.

$n$	$1097$	$1371$	$1921$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{117}{136}\right)$

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 $

$2$	−0.445738	−	0.895163i	−0.445738	−	0.895163i
$2$	−0.445738	−	0.895163i	−0.445738	−	0.895163i
$3$		0			0		−0.940567	−	0.339607i	$-0.889706\pi$
$3$		0			0		0.940567	+	0.339607i	$0.110294\pi$
$4$	−0.602635	+	0.798017i	−0.602635	+	0.798017i
$5$	−0.565136	−	0.824997i	−0.565136	−	0.824997i
$5$	−0.565136	−	0.824997i	−0.565136	−	0.824997i
$6$		0			0
$7$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$7$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$8$	0.982973	+	0.183750i	0.982973	+	0.183750i
$9$	0.769334	+	0.638847i	0.769334	+	0.638847i
$10$	−0.486604	+	0.873622i	−0.486604	+	0.873622i
$11$		0			0		0.990410	−	0.138156i	$-0.0441176\pi$
$11$		0			0		−0.990410	+	0.138156i	$0.955882\pi$
$12$		0			0
$13$	−0.363613	+	0.347190i	−0.363613	+	0.347190i	−0.850217	−	0.526432i	$-0.823529\pi$
$13$	−0.363613	+	0.347190i	−0.363613	+	0.347190i	0.486604	+	0.873622i	$0.338235\pi$
$14$		0			0
$15$		0			0
$16$	−0.273663	−	0.961826i	−0.273663	−	0.961826i
$17$	0.303186	+	1.62190i	0.303186	+	1.62190i	0.707107	+	0.707107i	$0.250000\pi$
$17$	0.303186	+	1.62190i	0.303186	+	1.62190i	−0.403921	+	0.914794i	$0.632353\pi$
$18$	0.228951	−	0.973438i	0.228951	−	0.973438i
$19$		0			0		−0.973438	−	0.228951i	$-0.926471\pi$
$19$		0			0		0.973438	+	0.228951i	$0.0735294\pi$
$20$	0.998933	+	0.0461835i	0.998933	+	0.0461835i
$21$		0			0
$22$		0			0
$23$		0			0		0.783885	−	0.620906i	$-0.213235\pi$
$23$		0			0		−0.783885	+	0.620906i	$0.786765\pi$
$24$		0			0
$25$	−0.361242	+	0.932472i	−0.361242	+	0.932472i
$26$	0.472868	+	0.170737i	0.472868	+	0.170737i
$27$		0			0
$28$		0			0
$29$	−1.56735	+	1.24148i	−1.56735	+	1.24148i	−0.769334	+	0.638847i	$0.779412\pi$
$29$	−1.56735	+	1.24148i	−1.56735	+	1.24148i	−0.798017	+	0.602635i	$0.794118\pi$
$30$		0			0
$31$		0			0		0.811724	−	0.584041i	$-0.198529\pi$
$31$		0			0		−0.811724	+	0.584041i	$0.801471\pi$
$32$	−0.739009	+	0.673696i	−0.739009	+	0.673696i
$33$		0			0
$34$	1.31672	−	0.994344i	1.31672	−	0.994344i
$35$		0			0
$36$	−0.973438	+	0.228951i	−0.973438	+	0.228951i
$37$		−	0.635583i		−	0.635583i	−0.948161	−	0.317791i	$-0.897059\pi$
$37$		−	0.635583i		−	0.635583i	0.948161	−	0.317791i	$-0.102941\pi$
$38$		0			0
$39$		0			0
$40$	−0.403921	−	0.914794i	−0.403921	−	0.914794i
$41$	0.755383	+	1.82366i	0.755383	+	1.82366i	0.526432	+	0.850217i	$0.323529\pi$
$41$	0.755383	+	1.82366i	0.755383	+	1.82366i	0.228951	+	0.973438i	$0.426471\pi$
$42$		0			0
$43$		0			0		0.584041	−	0.811724i	$-0.301471\pi$
$43$		0			0		−0.584041	+	0.811724i	$0.698529\pi$
$44$		0			0
$45$	0.0922684	−	0.995734i	0.0922684	−	0.995734i
$46$		0			0
$47$		0			0		−0.955248	−	0.295806i	$-0.904412\pi$
$47$		0			0		0.955248	+	0.295806i	$0.0955882\pi$
$48$		0			0
$49$	0.739009	−	0.673696i	0.739009	−	0.673696i
$50$	0.995734	−	0.0922684i	0.995734	−	0.0922684i
$51$		0			0
$52$	−0.0579382	−	0.499398i	−0.0579382	−	0.499398i
$53$	−0.407425	+	0.0664607i	−0.407425	+	0.0664607i	−0.361242	−	0.932472i	$-0.617647\pi$
$53$	−0.407425	+	0.0664607i	−0.407425	+	0.0664607i	−0.0461835	+	0.998933i	$0.514706\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	1.80996	+	0.849659i	1.80996	+	0.849659i
$59$		0			0		0.995734	−	0.0922684i	$-0.0294118\pi$
$59$		0			0		−0.995734	+	0.0922684i	$0.970588\pi$
$60$		0			0
$61$	1.22892	+	1.47993i	1.22892	+	1.47993i	0.824997	+	0.565136i	$0.191176\pi$
$61$	1.22892	+	1.47993i	1.22892	+	1.47993i	0.403921	+	0.914794i	$0.367647\pi$
$62$		0			0
$63$		0			0
$64$	0.932472	+	0.361242i	0.932472	+	0.361242i
$65$	0.491922	+	0.103770i	0.491922	+	0.103770i
$66$		0			0
$67$		0			0		0.0230979	−	0.999733i	$-0.492647\pi$
$67$		0			0		−0.0230979	+	0.999733i	$0.507353\pi$
$68$	−1.47701	−	0.735466i	−1.47701	−	0.735466i
$69$		0			0
$70$		0			0
$71$		0			0		0.967890	−	0.251374i	$-0.0808824\pi$
$71$		0			0		−0.967890	+	0.251374i	$0.919118\pi$
$72$	0.638847	+	0.769334i	0.638847	+	0.769334i
$73$	−0.621500	−	1.40756i	−0.621500	−	1.40756i	−0.895163	−	0.445738i	$-0.852941\pi$
$73$	−0.621500	−	1.40756i	−0.621500	−	1.40756i	0.273663	−	0.961826i	$-0.411765\pi$
$74$	−0.568950	+	0.283304i	−0.568950	+	0.283304i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.940567	−	0.339607i	$-0.110294\pi$
$79$		0			0		−0.940567	+	0.339607i	$0.889706\pi$
$80$	−0.638847	+	0.769334i	−0.638847	+	0.769334i
$81$	0.183750	+	0.982973i	0.183750	+	0.982973i
$82$	1.29577	−	1.48906i	1.29577	−	1.48906i
$83$		0			0		0.978467	−	0.206405i	$-0.0661765\pi$
$83$		0			0		−0.978467	+	0.206405i	$0.933824\pi$
$84$		0			0
$85$	1.16672	−	1.16672i	1.16672	−	1.16672i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.23486	+	1.41908i	1.23486	+	1.41908i	0.873622	+	0.486604i	$0.161765\pi$
$89$	1.23486	+	1.41908i	1.23486	+	1.41908i	0.361242	+	0.932472i	$0.382353\pi$
$90$	−0.932472	+	0.361242i	−0.932472	+	0.361242i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.464478	−	1.78843i	0.464478	−	1.78843i	−0.138156	−	0.990410i	$-0.544118\pi$
$97$	0.464478	−	1.78843i	0.464478	−	1.78843i	0.602635	−	0.798017i	$-0.294118\pi$
$98$	−0.932472	−	0.361242i	−0.932472	−	0.361242i
$99$		0			0
$100$	−0.526432	−	0.850217i	−0.526432	−	0.850217i
$101$	−0.338393	−	1.43876i	−0.338393	−	1.43876i	−0.824997	−	0.565136i	$-0.808824\pi$
$101$	−0.338393	−	1.43876i	−0.338393	−	1.43876i	0.486604	−	0.873622i	$-0.338235\pi$
$102$		0			0
$103$		0			0		−0.990410	−	0.138156i	$-0.955882\pi$
$103$		0			0		0.990410	+	0.138156i	$0.0441176\pi$
$104$	−0.421217	+	0.274465i	−0.421217	+	0.274465i
$105$		0			0
$106$	0.241098	+	0.335088i	0.241098	+	0.335088i
$107$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$107$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$108$		0			0
$109$	0.0449462	+	0.0806938i	0.0449462	+	0.0806938i	0.895163	−	0.445738i	$-0.147059\pi$
$109$	0.0449462	+	0.0806938i	0.0449462	+	0.0806938i	−0.850217	+	0.526432i	$0.823529\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.444745	+	1.71245i	0.444745	+	1.71245i	0.673696	+	0.739009i	$0.264706\pi$
$113$	0.444745	+	1.71245i	0.444745	+	1.71245i	−0.228951	+	0.973438i	$0.573529\pi$
$114$		0			0
$115$		0			0
$116$	−0.0461835	−	1.99893i	−0.0461835	−	1.99893i
$117$	−0.501541	+	0.0348125i	−0.501541	+	0.0348125i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.961826	−	0.273663i	0.961826	−	0.273663i
$122$	0.777003	−	1.75974i	0.777003	−	1.75974i
$123$		0			0
$124$		0			0
$125$	0.973438	−	0.228951i	0.973438	−	0.228951i
$126$		0			0
$127$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$127$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$128$	−0.0922684	−	0.995734i	−0.0922684	−	0.995734i
$129$		0			0
$130$	−0.126378	−	0.486604i	−0.126378	−	0.486604i
$131$		0			0		0.993337	−	0.115243i	$-0.0367647\pi$
$131$		0			0		−0.993337	+	0.115243i	$0.963235\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$			1.64999i			1.64999i
$137$	0.361242	−	0.932472i	0.361242	−	0.932472i
$137$	0.361242	−	0.932472i	0.361242	−	0.932472i
$138$		0			0
$139$		0			0		−0.948161	−	0.317791i	$-0.897059\pi$
$139$		0			0		0.948161	+	0.317791i	$0.102941\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.403921	−	0.914794i	0.403921	−	0.914794i
$145$	1.90999	+	0.591454i	1.90999	+	0.591454i
$146$	−0.982973	+	1.18375i	−0.982973	+	1.18375i
$147$		0			0
$148$	0.507206	+	0.383024i	0.507206	+	0.383024i
$149$	0.0285848	−	0.135507i	0.0285848	−	0.135507i	−0.961826	−	0.273663i	$-0.911765\pi$
$149$	0.0285848	−	0.135507i	0.0285848	−	0.135507i	0.990410	+	0.138156i	$0.0441176\pi$
$150$		0			0
$151$		0			0		0.673696	−	0.739009i	$-0.264706\pi$
$151$		0			0		−0.673696	+	0.739009i	$0.735294\pi$
$152$		0			0
$153$	−0.802895	+	1.44147i	−0.802895	+	1.44147i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.0909104	+	1.30974i	0.0909104	+	1.30974i	0.798017	+	0.602635i	$0.205882\pi$
$157$	0.0909104	+	1.30974i	0.0909104	+	1.30974i	−0.707107	+	0.707107i	$0.750000\pi$
$158$		0			0
$159$		0			0
$160$	0.973438	+	0.228951i	0.973438	+	0.228951i
$161$		0			0
$162$	0.798017	−	0.602635i	0.798017	−	0.602635i
$163$		0			0		−0.424943	−	0.905220i	$-0.639706\pi$
$163$		0			0		0.424943	+	0.905220i	$0.360294\pi$
$164$	−1.91053	−	0.496189i	−1.91053	−	0.496189i
$165$		0			0
$166$		0			0
$167$		0			0		0.673696	−	0.739009i	$-0.264706\pi$
$167$		0			0		−0.673696	+	0.739009i	$0.735294\pi$
$168$		0			0
$169$	−0.0345103	+	0.746447i	−0.0345103	+	0.746447i
$170$	−1.56446	−	0.524354i	−1.56446	−	0.524354i
$171$		0			0
$172$		0			0
$173$	−1.58561	−	0.981767i	−1.58561	−	0.981767i	−0.982973	−	0.183750i	$-0.941176\pi$
$173$	−1.58561	−	0.981767i	−1.58561	−	0.981767i	−0.602635	−	0.798017i	$-0.705882\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	0.719879	−	1.73794i	0.719879	−	1.73794i
$179$		0			0		−0.955248	−	0.295806i	$-0.904412\pi$
$179$		0			0		0.955248	+	0.295806i	$0.0955882\pi$
$180$	0.739009	+	0.673696i	0.739009	+	0.673696i
$181$	1.59837	+	0.890286i	1.59837	+	0.890286i	0.995734	+	0.0922684i	$0.0294118\pi$
$181$	1.59837	+	0.890286i	1.59837	+	0.890286i	0.602635	+	0.798017i	$0.294118\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.524354	+	0.359191i	−0.524354	+	0.359191i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.837831	−	0.545930i	$-0.816176\pi$
$191$		0			0		0.837831	+	0.545930i	$0.183824\pi$
$192$		0			0
$193$	−1.64296	−	1.12545i	−1.64296	−	1.12545i	−0.873622	−	0.486604i	$-0.838235\pi$
$193$	−1.64296	−	1.12545i	−1.64296	−	1.12545i	−0.769334	−	0.638847i	$-0.779412\pi$
$194$	−1.80797	+	0.381387i	−1.80797	+	0.381387i
$195$		0			0
$196$	0.0922684	+	0.995734i	0.0922684	+	0.995734i
$197$	0.655647	+	1.17711i	0.655647	+	1.17711i	0.973438	+	0.228951i	$0.0735294\pi$
$197$	0.655647	+	1.17711i	0.655647	+	1.17711i	−0.317791	+	0.948161i	$0.602941\pi$
$198$		0			0
$199$		0			0		0.955248	−	0.295806i	$-0.0955882\pi$
$199$		0			0		−0.955248	+	0.295806i	$0.904412\pi$
$200$	−0.526432	+	0.850217i	−0.526432	+	0.850217i
$201$		0			0
$202$	−1.13709	+	0.944227i	−1.13709	+	0.944227i
$203$		0			0
$204$		0			0
$205$	1.07762	−	1.65380i	1.07762	−	1.65380i
$206$		0			0
$207$		0			0
$208$	0.433444	+	0.254719i	0.433444	+	0.254719i
$209$		0			0
$210$		0			0
$211$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$211$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$212$	0.192492	−	0.365184i	0.192492	−	0.365184i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	0.0521999	−	0.0762025i	0.0521999	−	0.0762025i
$219$		0			0
$220$		0			0
$221$	−0.673350	−	0.484480i	−0.673350	−	0.484480i
$222$		0			0
$223$		0			0		−0.584041	−	0.811724i	$-0.698529\pi$
$223$		0			0		0.584041	+	0.811724i	$0.301471\pi$
$224$		0			0
$225$	−0.873622	+	0.486604i	−0.873622	+	0.486604i
$226$	1.33468	−	1.16142i	1.33468	−	1.16142i
$227$		0			0		0.295806	−	0.955248i	$-0.404412\pi$
$227$		0			0		−0.295806	+	0.955248i	$0.595588\pi$
$228$		0			0
$229$	−0.844817	−	0.806661i	−0.844817	−	0.806661i	0.138156	−	0.990410i	$-0.455882\pi$
$229$	−0.844817	−	0.806661i	−0.844817	−	0.806661i	−0.982973	+	0.183750i	$0.941176\pi$
$230$		0			0
$231$		0			0
$232$	−1.76879	+	0.932343i	−1.76879	+	0.932343i
$233$	−1.00875	−	0.417837i	−1.00875	−	0.417837i	−0.183750	−	0.982973i	$-0.558824\pi$
$233$	−1.00875	−	0.417837i	−1.00875	−	0.417837i	−0.824997	+	0.565136i	$0.808824\pi$
$234$	0.254719	+	0.433444i	0.254719	+	0.433444i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.466296	−	0.884629i	$-0.345588\pi$
$239$		0			0		−0.466296	+	0.884629i	$0.654412\pi$
$240$		0			0
$241$	−0.322979	−	0.495671i	−0.322979	−	0.495671i	0.638847	−	0.769334i	$-0.279412\pi$
$241$	−0.322979	−	0.495671i	−0.322979	−	0.495671i	−0.961826	+	0.273663i	$0.911765\pi$
$242$	−0.673696	−	0.739009i	−0.673696	−	0.739009i
$243$		0			0
$244$	−1.92160	+	0.0888409i	−1.92160	+	0.0888409i
$245$	−0.973438	−	0.228951i	−0.973438	−	0.228951i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	−0.638847	−	0.769334i	−0.638847	−	0.769334i
$251$		0			0		−0.993337	−	0.115243i	$-0.963235\pi$
$251$		0			0		0.993337	+	0.115243i	$0.0367647\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.850217	+	0.526432i	−0.850217	+	0.526432i
$257$	0.271608	−	0.0507723i	0.271608	−	0.0507723i	−0.0461835	−	0.998933i	$-0.514706\pi$
$257$	0.271608	−	0.0507723i	0.271608	−	0.0507723i	0.317791	+	0.948161i	$0.397059\pi$
$258$		0			0
$259$		0			0
$260$	−0.379259	+	0.330027i	−0.379259	+	0.330027i
$261$	−1.99893	−	0.0461835i	−1.99893	−	0.0461835i
$262$		0			0
$263$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$263$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$264$		0			0
$265$	0.285081	+	0.298565i	0.285081	+	0.298565i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.0645767	+	0.930353i	−0.0645767	+	0.930353i	0.850217	+	0.526432i	$0.176471\pi$
$269$	−0.0645767	+	0.930353i	−0.0645767	+	0.930353i	−0.914794	+	0.403921i	$0.867647\pi$
$270$		0			0
$271$		0			0		−0.424943	−	0.905220i	$-0.639706\pi$
$271$		0			0		0.424943	+	0.905220i	$0.360294\pi$
$272$	1.47701	−	0.735466i	1.47701	−	0.735466i
$273$		0			0
$274$	−0.995734	+	0.0922684i	−0.995734	+	0.0922684i
$275$		0			0
$276$		0			0
$277$	−0.259924	+	0.719879i	−0.259924	+	0.719879i	0.739009	+	0.673696i	$0.235294\pi$
$277$	−0.259924	+	0.719879i	−0.259924	+	0.719879i	−0.998933	+	0.0461835i	$0.985294\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.73474	−	0.765964i	−1.73474	−	0.765964i	−0.995734	−	0.0922684i	$-0.970588\pi$
$281$	−1.73474	−	0.765964i	−1.73474	−	0.765964i	−0.739009	−	0.673696i	$-0.764706\pi$
$282$		0			0
$283$		0			0		0.995734	−	0.0922684i	$-0.0294118\pi$
$283$		0			0		−0.995734	+	0.0922684i	$0.970588\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.998933	+	0.0461835i	−0.998933	+	0.0461835i
$289$	−1.60617	+	0.622233i	−1.60617	+	0.622233i
$290$	−0.321906	−	1.97338i	−0.321906	−	1.97338i
$291$		0			0
$292$	1.49780	+	0.352279i	1.49780	+	0.352279i
$293$	1.68413	−	1.04277i	1.68413	−	1.04277i	0.769334	−	0.638847i	$-0.220588\pi$
$293$	1.68413	−	1.04277i	1.68413	−	1.04277i	0.914794	−	0.403921i	$-0.132353\pi$
$294$		0			0
$295$		0			0
$296$	0.116788	−	0.624761i	0.116788	−	0.624761i
$297$		0			0
$298$	−0.134042	+	0.0348125i	−0.134042	+	0.0348125i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.526432	−	1.85022i	0.526432	−	1.85022i
$306$	1.64823	+	0.0762025i	1.64823	+	0.0762025i
$307$		0			0		0.206405	−	0.978467i	$-0.433824\pi$
$307$		0			0		−0.206405	+	0.978467i	$0.566176\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$311$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$312$		0			0
$313$	0.351564	−	0.907490i	0.351564	−	0.907490i	−0.638847	−	0.769334i	$-0.720588\pi$
$313$	0.351564	−	0.907490i	0.351564	−	0.907490i	0.990410	−	0.138156i	$-0.0441176\pi$
$314$	1.13191	−	0.665182i	1.13191	−	0.665182i
$315$		0			0
$316$		0			0
$317$	0.261368	+	0.188057i	0.261368	+	0.188057i	0.707107	−	0.707107i	$-0.250000\pi$
$317$	0.261368	+	0.188057i	0.261368	+	0.188057i	−0.445738	+	0.895163i	$0.647059\pi$
$318$		0			0
$319$		0			0
$320$	−0.228951	−	0.973438i	−0.228951	−	0.973438i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.895163	−	0.445738i	−0.895163	−	0.445738i
$325$	−0.192393	−	0.464478i	−0.192393	−	0.464478i
$326$		0			0
$327$		0			0
$328$	0.407425	+	1.93141i	0.407425	+	1.93141i
$329$		0			0
$330$		0			0
$331$		0			0		−0.206405	−	0.978467i	$-0.566176\pi$
$331$		0			0		0.206405	+	0.978467i	$0.433824\pi$
$332$		0			0
$333$	0.406040	−	0.488975i	0.406040	−	0.488975i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.383024	+	1.14279i	−0.383024	+	1.14279i	0.565136	+	0.824997i	$0.308824\pi$
$337$	−0.383024	+	1.14279i	−0.383024	+	1.14279i	−0.948161	+	0.317791i	$0.897059\pi$
$338$	0.683575	−	0.301828i	0.683575	−	0.301828i
$339$		0			0
$340$	0.227957	+	1.63417i	0.227957	+	1.63417i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.172075	+	1.85699i	−0.172075	+	1.85699i
$347$		0			0		0.914794	−	0.403921i	$-0.132353\pi$
$347$		0			0		−0.914794	+	0.403921i	$0.867647\pi$
$348$		0			0
$349$	−0.578873	−	1.86936i	−0.578873	−	1.86936i	−0.486604	−	0.873622i	$-0.661765\pi$
$349$	−0.578873	−	1.86936i	−0.578873	−	1.86936i	−0.0922684	−	0.995734i	$-0.529412\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.811852	+	1.72942i	−0.811852	+	1.72942i	−0.138156	+	0.990410i	$0.544118\pi$
$353$	−0.811852	+	1.72942i	−0.811852	+	1.72942i	−0.673696	+	0.739009i	$0.735294\pi$
$354$		0			0
$355$		0			0
$356$	−1.87662	+	0.130258i	−1.87662	+	0.130258i
$357$		0			0
$358$		0			0
$359$		0			0		0.620906	−	0.783885i	$-0.286765\pi$
$359$		0			0		−0.620906	+	0.783885i	$0.713235\pi$
$360$	0.273663	−	0.961826i	0.273663	−	0.961826i
$361$	0.895163	+	0.445738i	0.895163	+	0.445738i
$362$	0.0844967	−	1.82764i	0.0844967	−	1.82764i
$363$		0			0
$364$		0			0
$365$	−0.810004	+	1.30820i	−0.810004	+	1.30820i
$366$		0			0
$367$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$367$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$368$		0			0
$369$	−0.583895	+	1.88557i	−0.583895	+	1.88557i
$370$	0.555259	+	0.309277i	0.555259	+	0.309277i
$371$		0			0
$372$		0			0
$373$	−1.55364	+	0.365413i	−1.55364	+	0.365413i	−0.914794	−	0.403921i	$-0.867647\pi$
$373$	−1.55364	+	0.365413i	−1.55364	+	0.365413i	−0.638847	+	0.769334i	$0.720588\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.138879	−	0.995587i	0.138879	−	0.995587i
$378$		0			0
$379$		0			0		−0.998933	−	0.0461835i	$-0.985294\pi$
$379$		0			0		0.998933	+	0.0461835i	$0.0147059\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.961826	−	0.273663i	$-0.911765\pi$
$383$		0			0		0.961826	+	0.273663i	$0.0882353\pi$
$384$		0			0
$385$		0			0
$386$	−0.275134	+	1.97237i	−0.275134	+	1.97237i
$387$		0			0
$388$	1.14729	+	1.44843i	1.14729	+	1.44843i
$389$	0.234776	−	1.25594i	0.234776	−	1.25594i	−0.638847	−	0.769334i	$-0.720588\pi$
$389$	0.234776	−	1.25594i	0.234776	−	1.25594i	0.873622	−	0.486604i	$-0.161765\pi$
$390$		0			0
$391$		0			0
$392$	0.850217	−	0.526432i	0.850217	−	0.526432i
$393$		0			0
$394$	0.761460	−	1.11159i	0.761460	−	1.11159i
$395$		0			0
$396$		0			0
$397$	1.78842	−	0.0826835i	1.78842	−	0.0826835i	0.873622	−	0.486604i	$-0.161765\pi$
$397$	1.78842	−	0.0826835i	1.78842	−	0.0826835i	0.914794	+	0.403921i	$0.132353\pi$
$398$		0			0
$399$		0			0
$400$	0.995734	+	0.0922684i	0.995734	+	0.0922684i
$401$	0.528551	−	1.27604i	0.528551	−	1.27604i	−0.403921	−	0.914794i	$-0.632353\pi$
$401$	0.528551	−	1.27604i	0.528551	−	1.27604i	0.932472	−	0.361242i	$-0.117647\pi$
$402$		0			0
$403$		0			0
$404$	1.35208	+	0.597002i	1.35208	+	0.597002i
$405$	0.707107	−	0.707107i	0.707107	−	0.707107i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−0.334591	+	0.998285i	−0.334591	+	0.998285i	0.638847	+	0.769334i	$0.279412\pi$
$409$	−0.334591	+	0.998285i	−0.334591	+	0.998285i	−0.973438	+	0.228951i	$0.926471\pi$
$410$	−1.96076	−	0.227480i	−1.96076	−	0.227480i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	0.0348125	−	0.501541i	0.0348125	−	0.501541i
$417$		0			0
$418$		0			0
$419$		0			0		−0.565136	−	0.824997i	$-0.691176\pi$
$419$		0			0		0.565136	+	0.824997i	$0.308824\pi$
$420$		0			0
$421$	−1.67263	−	0.692825i	−1.67263	−	0.692825i	−0.673696	−	0.739009i	$-0.735294\pi$
$421$	−1.67263	−	0.692825i	−1.67263	−	0.692825i	−0.998933	+	0.0461835i	$0.985294\pi$
$422$		0			0
$423$		0			0
$424$	−0.412700	−	0.00953505i	−0.412700	−	0.00953505i
$425$	−1.62190	−	0.303186i	−1.62190	−	0.303186i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.656446	−	0.754373i	$-0.272059\pi$
$431$		0			0		−0.656446	+	0.754373i	$0.727941\pi$
$432$		0			0
$433$	1.64823	−	1.12907i	1.64823	−	1.12907i	0.798017	−	0.602635i	$-0.205882\pi$
$433$	1.64823	−	1.12907i	1.64823	−	1.12907i	0.850217	−	0.526432i	$-0.176471\pi$
$434$		0			0
$435$		0			0
$436$	−0.0914812	−	0.0127611i	−0.0914812	−	0.0127611i
$437$		0			0
$438$		0			0
$439$		0			0		0.873622	−	0.486604i	$-0.161765\pi$
$439$		0			0		−0.873622	+	0.486604i	$0.838235\pi$
$440$		0			0
$441$	0.998933	−	0.0461835i	0.998933	−	0.0461835i
$442$	−0.133551	+	0.818710i	−0.133551	+	0.818710i
$443$		0			0		−0.673696	−	0.739009i	$-0.735294\pi$
$443$		0			0		0.673696	+	0.739009i	$0.264706\pi$
$444$		0			0
$445$	0.472868	−	1.82073i	0.472868	−	1.82073i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.425274	+	0.686841i	−0.425274	+	0.686841i	−0.990410	−	0.138156i	$-0.955882\pi$
$449$	−0.425274	+	0.686841i	−0.425274	+	0.686841i	0.565136	+	0.824997i	$0.308824\pi$
$450$	0.824997	+	0.565136i	0.824997	+	0.565136i
$451$		0			0
$452$	−1.63458	−	0.677066i	−1.63458	−	0.677066i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.799375	+	0.288627i	−0.799375	+	0.288627i	−0.707107	−	0.707107i	$-0.750000\pi$
$457$	−0.799375	+	0.288627i	−0.799375	+	0.288627i	−0.0922684	+	0.995734i	$0.529412\pi$
$458$	−0.345526	+	1.11581i	−0.345526	+	1.11581i
$459$		0			0
$460$		0			0
$461$	−0.0822551	+	0.165190i	−0.0822551	+	0.165190i	−0.932472	−	0.361242i	$-0.882353\pi$
$461$	−0.0822551	+	0.165190i	−0.0822551	+	0.165190i	0.850217	+	0.526432i	$0.176471\pi$
$462$		0			0
$463$		0			0		0.993337	−	0.115243i	$-0.0367647\pi$
$463$		0			0		−0.993337	+	0.115243i	$0.963235\pi$
$464$	1.62301	+	1.16777i	1.62301	+	1.16777i
$465$		0			0
$466$	0.0756052	+	1.08924i	0.0756052	+	1.08924i
$467$		0			0		0.565136	−	0.824997i	$-0.308824\pi$
$467$		0			0		−0.565136	+	0.824997i	$0.691176\pi$
$468$	0.274465	−	0.421217i	0.274465	−	0.421217i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.355904	−	0.209152i	−0.355904	−	0.209152i
$478$		0			0
$479$		0			0		−0.317791	−	0.948161i	$-0.602941\pi$
$479$		0			0		0.317791	+	0.948161i	$0.397059\pi$
$480$		0			0
$481$	0.220668	+	0.231106i	0.220668	+	0.231106i
$482$	−0.299742	+	0.510058i	−0.299742	+	0.510058i
$483$		0			0
$484$	−0.361242	+	0.932472i	−0.361242	+	0.932472i
$485$	−1.73794	+	0.627512i	−1.73794	+	0.627512i
$486$		0			0
$487$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$487$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$488$	0.936057	+	1.68054i	0.936057	+	1.68054i
$489$		0			0
$490$	0.228951	+	0.973438i	0.228951	+	0.973438i
$491$		0			0		0.978467	−	0.206405i	$-0.0661765\pi$
$491$		0			0		−0.978467	+	0.206405i	$0.933824\pi$
$492$		0			0
$493$	−2.48876	−	2.16569i	−2.48876	−	2.16569i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		−0.673696	−	0.739009i	$-0.735294\pi$
$499$		0			0		0.673696	+	0.739009i	$0.264706\pi$
$500$	−0.403921	+	0.914794i	−0.403921	+	0.914794i
$501$		0			0
$502$		0			0
$503$		0			0		0.999733	−	0.0230979i	$-0.00735294\pi$
$503$		0			0		−0.999733	+	0.0230979i	$0.992647\pi$
$504$		0			0
$505$	−0.995734	+	1.09227i	−0.995734	+	1.09227i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	0.360086	+	0.815517i	0.360086	+	0.815517i	0.998933	+	0.0461835i	$0.0147059\pi$
$509$	0.360086	+	0.815517i	0.360086	+	0.815517i	−0.638847	+	0.769334i	$0.720588\pi$
$510$		0			0
$511$		0			0
$512$	0.850217	+	0.526432i	0.850217	+	0.526432i
$513$		0			0
$514$	−0.166516	−	0.220502i	−0.166516	−	0.220502i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	0.464478	+	0.192393i	0.464478	+	0.192393i
$521$	−1.40005	−	0.363613i	−1.40005	−	0.363613i	−0.526432	−	0.850217i	$-0.676471\pi$
$521$	−1.40005	−	0.363613i	−1.40005	−	0.363613i	−0.873622	+	0.486604i	$0.838235\pi$
$522$	0.849659	+	1.80996i	0.849659	+	1.80996i
$523$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$523$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	0.228951	−	0.973438i	0.228951	−	0.973438i
$530$	0.140193	−	0.388276i	0.140193	−	0.388276i
$531$		0			0
$532$		0			0
$533$	−0.907822	−	0.400843i	−0.907822	−	0.400843i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	0.861602	−	0.356887i	0.861602	−	0.356887i
$539$		0			0
$540$		0			0
$541$	−0.686841	+	1.55555i	−0.686841	+	1.55555i	0.138156	+	0.990410i	$0.455882\pi$
$541$	−0.686841	+	1.55555i	−0.686841	+	1.55555i	−0.824997	+	0.565136i	$0.808824\pi$
$542$		0			0
$543$		0			0
$544$	−1.31672	−	0.994344i	−1.31672	−	0.994344i
$545$	0.0411715	−	0.0826835i	0.0411715	−	0.0826835i
$546$		0			0
$547$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$547$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$548$	0.526432	+	0.850217i	0.526432	+	0.850217i
$549$			1.92365i			1.92365i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	0.760267	−	0.0882033i	0.760267	−	0.0882033i
$555$		0			0
$556$		0			0
$557$	0.0339085	+	0.365931i	0.0339085	+	0.365931i	0.995734	+	0.0922684i	$0.0294118\pi$
$557$	0.0339085	+	0.365931i	0.0339085	+	0.365931i	−0.961826	+	0.273663i	$0.911765\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.0875787	+	1.89430i	0.0875787	+	1.89430i
$563$		0			0		0.403921	−	0.914794i	$-0.367647\pi$
$563$		0			0		−0.403921	+	0.914794i	$0.632353\pi$
$564$		0			0
$565$	1.16142	−	1.33468i	1.16142	−	1.33468i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	0.0374982	+	1.62301i	0.0374982	+	1.62301i	0.602635	+	0.798017i	$0.294118\pi$
$569$	0.0374982	+	1.62301i	0.0374982	+	1.62301i	−0.565136	+	0.824997i	$0.691176\pi$
$570$		0			0
$571$		0			0		0.115243	−	0.993337i	$-0.463235\pi$
$571$		0			0		−0.115243	+	0.993337i	$0.536765\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.486604	+	0.873622i	0.486604	+	0.873622i
$577$	1.98191	+	0.229933i	1.98191	+	0.229933i	0.998933	+	0.0461835i	$0.0147059\pi$
$577$	1.98191	+	0.229933i	1.98191	+	0.229933i	0.982973	+	0.183750i	$0.0588235\pi$
$578$	1.27293	+	1.16043i	1.27293	+	1.16043i
$579$		0			0
$580$	−1.62301	+	1.16777i	−1.62301	+	1.16777i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−0.352279	−	1.49780i	−0.352279	−	1.49780i
$585$	0.312159	+	0.394096i	0.312159	+	0.394096i
$586$	−1.68413	−	1.04277i	−1.68413	−	1.04277i
$587$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$587$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.611320	+	0.173936i	−0.611320	+	0.173936i
$593$	−0.00106703	−	0.0461835i	−0.00106703	−	0.0461835i	0.998933	−	0.0461835i	$-0.0147059\pi$
$593$	−0.00106703	−	0.0461835i	−0.00106703	−	0.0461835i	−1.00000			$\pi$
$594$		0			0
$595$		0			0
$596$	0.0909104	+	0.104472i	0.0909104	+	0.104472i
$597$		0			0
$598$		0			0
$599$		0			0		−0.986955	−	0.160996i	$-0.948529\pi$
$599$		0			0		0.986955	+	0.160996i	$0.0514706\pi$
$600$		0			0
$601$	0.496369	−	0.689873i	0.496369	−	0.689873i	−0.486604	−	0.873622i	$-0.661765\pi$
$601$	0.496369	−	0.689873i	0.496369	−	0.689873i	0.982973	+	0.183750i	$0.0588235\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.769334	−	0.638847i	−0.769334	−	0.638847i
$606$		0			0
$607$		0			0		−0.769334	−	0.638847i	$-0.779412\pi$
$607$		0			0		0.769334	+	0.638847i	$0.220588\pi$
$608$		0			0
$609$		0			0
$610$	−1.89090	+	0.353470i	−1.89090	+	0.353470i
$611$		0			0
$612$	−0.666468	−	1.50941i	−0.666468	−	1.50941i
$613$	1.24376	+	1.49780i	1.24376	+	1.49780i	0.798017	+	0.602635i	$0.205882\pi$
$613$	1.24376	+	1.49780i	1.24376	+	1.49780i	0.445738	+	0.895163i	$0.352941\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.75984	−	0.876298i	−1.75984	−	0.876298i	−0.961826	−	0.273663i	$-0.911765\pi$
$617$	−1.75984	−	0.876298i	−1.75984	−	0.876298i	−0.798017	−	0.602635i	$-0.794118\pi$
$618$		0			0
$619$		0			0		−0.251374	−	0.967890i	$-0.580882\pi$
$619$		0			0		0.251374	+	0.967890i	$0.419118\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.739009	−	0.673696i	−0.739009	−	0.673696i
$626$	−0.969057	+	0.0897964i	−0.969057	+	0.0897964i
$627$		0			0
$628$	−1.09998	−	0.716747i	−1.09998	−	0.716747i
$629$	1.03085	−	0.192700i	1.03085	−	0.192700i
$630$		0			0
$631$		0			0		0.545930	−	0.837831i	$-0.316176\pi$
$631$		0			0		−0.545930	+	0.837831i	$0.683824\pi$
$632$		0			0
$633$		0			0
$634$	0.0518394	−	0.317791i	0.0518394	−	0.317791i
$635$		0			0
$636$		0			0
$637$	−0.0348125	+	0.501541i	−0.0348125	+	0.501541i
$638$		0			0
$639$		0			0
$640$	−0.769334	+	0.638847i	−0.769334	+	0.638847i
$641$	0.549996	−	0.987432i	0.549996	−	0.987432i	−0.445738	−	0.895163i	$-0.647059\pi$
$641$	0.549996	−	0.987432i	0.549996	−	0.987432i	0.995734	−	0.0922684i	$-0.0294118\pi$
$642$		0			0
$643$		0			0		−0.466296	−	0.884629i	$-0.654412\pi$
$643$		0			0		0.466296	+	0.884629i	$0.345588\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.228951	−	0.973438i	$-0.573529\pi$
$647$		0			0		0.228951	+	0.973438i	$0.426471\pi$
$648$			1.00000i			1.00000i
$649$		0			0
$650$	−0.330027	+	0.379259i	−0.330027	+	0.379259i
$651$		0			0
$652$		0			0
$653$	0.944227	−	0.860777i	0.944227	−	0.860777i	−0.0461835	−	0.998933i	$-0.514706\pi$
$653$	0.944227	−	0.860777i	0.944227	−	0.860777i	0.990410	+	0.138156i	$0.0441176\pi$
$654$		0			0
$655$		0			0
$656$	1.54732	−	1.22561i	1.54732	−	1.22561i
$657$	0.421076	−	1.47993i	0.421076	−	1.47993i
$658$		0			0
$659$		0			0		−0.940567	−	0.339607i	$-0.889706\pi$
$659$		0			0		0.940567	+	0.339607i	$0.110294\pi$
$660$		0			0
$661$	0.0398277	+	0.0234053i	0.0398277	+	0.0234053i	0.526432	−	0.850217i	$-0.323529\pi$
$661$	0.0398277	+	0.0234053i	0.0398277	+	0.0234053i	−0.486604	+	0.873622i	$0.661765\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−0.618701	−	0.145517i	−0.618701	−	0.145517i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−1.63958	+	1.06835i	−1.63958	+	1.06835i	−0.707107	+	0.707107i	$0.750000\pi$
$673$	−1.63958	+	1.06835i	−1.63958	+	1.06835i	−0.932472	+	0.361242i	$0.882353\pi$
$674$	1.19371	−	0.166516i	1.19371	−	0.166516i
$675$		0			0
$676$	−0.574881	−	0.477375i	−0.574881	−	0.477375i
$677$	−0.876298	−	0.163808i	−0.876298	−	0.163808i	−0.273663	−	0.961826i	$-0.588235\pi$
$677$	−0.876298	−	0.163808i	−0.876298	−	0.163808i	−0.602635	+	0.798017i	$0.705882\pi$
$678$		0			0
$679$		0			0
$680$	1.36124	−	0.932472i	1.36124	−	0.932472i
$681$		0			0
$682$		0			0
$683$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$683$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$684$		0			0
$685$	−0.973438	+	0.228951i	−0.973438	+	0.228951i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.125070	−	0.165620i	0.125070	−	0.165620i
$690$		0			0
$691$		0			0		−0.115243	−	0.993337i	$-0.536765\pi$
$691$		0			0		0.115243	+	0.993337i	$0.463235\pi$
$692$	1.73901	−	0.673696i	1.73901	−	0.673696i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−2.72877	+	1.77806i	−2.72877	+	1.77806i
$698$	−1.41535	+	1.35143i	−1.41535	+	1.35143i
$699$		0			0
$700$		0			0
$701$	0.329838	+	1.15926i	0.329838	+	1.15926i	0.932472	+	0.361242i	$0.117647\pi$
$701$	0.329838	+	1.15926i	0.329838	+	1.15926i	−0.602635	+	0.798017i	$0.705882\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	1.90999	−	0.0441284i	1.90999	−	0.0441284i
$707$		0			0
$708$		0			0
$709$	1.64713	+	0.967959i	1.64713	+	0.967959i	0.973438	+	0.228951i	$0.0735294\pi$
$709$	1.64713	+	0.967959i	1.64713	+	0.967959i	0.673696	+	0.739009i	$0.264706\pi$
$710$		0			0
$711$		0			0
$712$	0.953083	+	1.62182i	0.953083	+	1.62182i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$719$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$720$	−0.982973	+	0.183750i	−0.982973	+	0.183750i
$721$		0			0
$722$		−	1.00000i		−	1.00000i
$723$		0			0
$724$	−1.67370	+	0.739009i	−1.67370	+	0.739009i
$725$	−0.591454	−	1.90999i	−0.591454	−	1.90999i
$726$		0			0
$727$		0			0		−0.466296	−	0.884629i	$-0.654412\pi$
$727$		0			0		0.466296	+	0.884629i	$0.345588\pi$
$728$		0			0
$729$	−0.486604	+	0.873622i	−0.486604	+	0.873622i
$730$	1.53210	+	0.141970i	1.53210	+	0.141970i
$731$		0			0
$732$		0			0
$733$	0.119398	−	1.72016i	0.119398	−	1.72016i	−0.445738	−	0.895163i	$-0.647059\pi$
$733$	0.119398	−	1.72016i	0.119398	−	1.72016i	0.565136	−	0.824997i	$-0.308824\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	1.94816	−	0.317791i	1.94816	−	0.317791i
$739$		0			0		0.545930	−	0.837831i	$-0.316176\pi$
$739$		0			0		−0.545930	+	0.837831i	$0.683824\pi$
$740$	0.0293534	−	0.634905i	0.0293534	−	0.634905i
$741$		0			0
$742$		0			0
$743$		0			0		−0.905220	−	0.424943i	$-0.860294\pi$
$743$		0			0		0.905220	+	0.424943i	$0.139706\pi$
$744$		0			0
$745$	−0.127947	+	0.0529974i	−0.127947	+	0.0529974i
$746$	1.01962	+	1.22788i	1.01962	+	1.22788i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.251374	−	0.967890i	$-0.580882\pi$
$751$		0			0		0.251374	+	0.967890i	$0.419118\pi$
$752$		0			0
$753$		0			0
$754$	−0.953117	+	0.319453i	−0.953117	+	0.319453i
$755$		0			0
$756$		0			0
$757$	−0.569517	−	0.685843i	−0.569517	−	0.685843i	0.403921	−	0.914794i	$-0.367647\pi$
$757$	−0.569517	−	0.685843i	−0.569517	−	0.685843i	−0.973438	+	0.228951i	$0.926471\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.49780	−	1.24376i	1.49780	−	1.24376i	0.602635	−	0.798017i	$-0.294118\pi$
$761$	1.49780	−	1.24376i	1.49780	−	1.24376i	0.895163	−	0.445738i	$-0.147059\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	1.64296	−	0.152242i	1.64296	−	0.152242i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	1.13058	−	1.57132i	1.13058	−	1.57132i	0.361242	−	0.932472i	$-0.382353\pi$
$769$	1.13058	−	1.57132i	1.13058	−	1.57132i	0.769334	−	0.638847i	$-0.220588\pi$
$770$		0			0
$771$		0			0
$772$	1.88823	−	0.632872i	1.88823	−	0.632872i
$773$	1.94480	+	0.0899135i	1.94480	+	0.0899135i	0.982973	−	0.183750i	$-0.0588235\pi$
$773$	1.94480	+	0.0899135i	1.94480	+	0.0899135i	0.961826	+	0.273663i	$0.0882353\pi$
$774$		0			0
$775$		0			0
$776$	0.785192	−	1.67263i	0.785192	−	1.67263i
$777$		0			0
$778$	−1.22892	+	0.349657i	−1.22892	+	0.349657i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.850217	−	0.526432i	−0.850217	−	0.526432i
$785$	1.02916	−	0.815183i	1.02916	−	0.815183i
$786$		0			0
$787$		0			0		0.955248	−	0.295806i	$-0.0955882\pi$
$787$		0			0		−0.955248	+	0.295806i	$0.904412\pi$
$788$	−1.33447	−	0.186151i	−1.33447	−	0.186151i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−0.960668	−	0.111453i	−0.960668	−	0.111453i
$794$	−0.871181	−	1.56407i	−0.871181	−	1.56407i
$795$		0			0
$796$		0			0
$797$	1.02474	+	1.35698i	1.02474	+	1.35698i	0.932472	+	0.361242i	$0.117647\pi$
$797$	1.02474	+	1.35698i	1.02474	+	1.35698i	0.0922684	+	0.995734i	$0.470588\pi$
$798$		0			0
$799$		0			0
$800$	−0.361242	−	0.932472i	−0.361242	−	0.932472i
$801$	0.0434502	+	1.88063i	0.0434502	+	1.88063i
$802$	−1.37786	+	0.0956383i	−1.37786	+	0.0956383i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−0.0682600	−	1.47644i	−0.0682600	−	1.47644i
$809$	−0.00743733	+	0.321906i	−0.00743733	+	0.321906i	0.982973	+	0.183750i	$0.0588235\pi$
$809$	−0.00743733	+	0.321906i	−0.00743733	+	0.321906i	−0.990410	+	0.138156i	$0.955882\pi$
$810$	−0.948161	−	0.317791i	−0.948161	−	0.317791i
$811$		0			0		−0.138156	−	0.990410i	$-0.544118\pi$
$811$		0			0		0.138156	+	0.990410i	$0.455882\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	1.04277	−	0.145460i	1.04277	−	0.145460i
$819$		0			0
$820$	0.670354	+	1.85660i	0.670354	+	1.85660i
$821$		−	1.98082i		−	1.98082i	−0.138156	−	0.990410i	$-0.544118\pi$
$821$		−	1.98082i		−	1.98082i	0.138156	−	0.990410i	$-0.455882\pi$
$822$		0			0
$823$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$823$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.656446	−	0.754373i	$-0.727941\pi$
$827$		0			0		0.656446	+	0.754373i	$0.272059\pi$
$828$		0			0
$829$	0.393100	−	0.890286i	0.393100	−	0.890286i	−0.602635	−	0.798017i	$-0.705882\pi$
$829$	0.393100	−	0.890286i	0.393100	−	0.890286i	0.995734	−	0.0922684i	$-0.0294118\pi$
$830$		0			0
$831$		0			0
$832$	−0.464478	+	0.192393i	−0.464478	+	0.192393i
$833$	1.31672	+	0.994344i	1.31672	+	0.994344i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.824997	−	0.565136i	$-0.808824\pi$
$839$		0			0		0.824997	+	0.565136i	$0.191176\pi$
$840$		0			0
$841$	0.686363	−	2.91824i	0.686363	−	2.91824i
$842$	0.125363	+	1.80609i	0.125363	+	1.80609i
$843$		0			0
$844$		0			0
$845$	0.635320	−	0.393374i	0.635320	−	0.393374i
$846$		0			0
$847$		0			0
$848$	0.175421	+	0.373684i	0.175421	+	0.373684i
$849$		0			0
$850$	0.451543	+	1.58701i	0.451543	+	1.58701i
$851$		0			0
$852$		0			0
$853$	1.78682	+	0.291473i	1.78682	+	0.291473i	0.961826	−	0.273663i	$-0.0882353\pi$
$853$	1.78682	+	0.291473i	1.78682	+	0.291473i	0.824997	+	0.565136i	$0.191176\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.408559	+	1.31936i	0.408559	+	1.31936i	0.895163	+	0.445738i	$0.147059\pi$
$857$	0.408559	+	1.31936i	0.408559	+	1.31936i	−0.486604	+	0.873622i	$0.661765\pi$
$858$		0			0
$859$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$859$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$863$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$864$		0			0
$865$	0.0861296	+	1.86295i	0.0861296	+	1.86295i
$866$	−1.74538	−	0.972171i	−1.74538	−	0.972171i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.0293534	+	0.0875787i	0.0293534	+	0.0875787i
$873$	1.49987	−	1.07917i	1.49987	−	1.07917i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.703522	−	0.612196i	−0.703522	−	0.612196i	0.228951	−	0.973438i	$-0.426471\pi$
$877$	−0.703522	−	0.612196i	−0.703522	−	0.612196i	−0.932472	+	0.361242i	$0.882353\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.156896	−	1.69318i	−0.156896	−	1.69318i	−0.602635	−	0.798017i	$-0.705882\pi$
$881$	−0.156896	−	1.69318i	−0.156896	−	1.69318i	0.445738	−	0.895163i	$-0.352941\pi$
$882$	−0.486604	−	0.873622i	−0.486604	−	0.873622i
$883$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$883$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$884$	0.792408	−	0.245380i	0.792408	−	0.245380i
$885$		0			0
$886$		0			0
$887$		0			0		0.769334	−	0.638847i	$-0.220588\pi$
$887$		0			0		−0.769334	+	0.638847i	$0.779412\pi$
$888$		0			0
$889$		0			0
$890$	−1.84063	+	0.388276i	−1.84063	+	0.388276i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.804396	+	0.0745383i	0.804396	+	0.0745383i
$899$		0			0
$900$	0.138156	−	0.990410i	0.138156	−	0.990410i
$901$	−0.231318	−	0.640653i	−0.231318	−	0.640653i
$902$		0			0
$903$		0			0
$904$	0.122511	+	1.76501i	0.122511	+	1.76501i
$905$	−0.168813	−	1.82178i	−0.168813	−	1.82178i
$906$		0			0
$907$		0			0		0.993337	−	0.115243i	$-0.0367647\pi$
$907$		0			0		−0.993337	+	0.115243i	$0.963235\pi$
$908$		0			0
$909$	0.658809	−	1.32307i	0.658809	−	1.32307i
$910$		0			0
$911$		0			0		0.754373	−	0.656446i	$-0.227941\pi$
$911$		0			0		−0.754373	+	0.656446i	$0.772059\pi$
$912$		0			0
$913$		0			0
$914$	0.614681	+	0.586919i	0.614681	+	0.586919i
$915$		0			0
$916$	1.15285	−	0.188057i	1.15285	−	0.188057i
$917$		0			0
$918$		0			0
$919$		0			0		−0.506653	−	0.862150i	$-0.669118\pi$
$919$		0			0		0.506653	+	0.862150i	$0.330882\pi$
$920$		0			0
$921$		0			0
$922$	0.184537			0.184537
$923$		0			0
$924$		0			0
$925$	0.592663	+	0.229599i	0.592663	+	0.229599i
$926$		0			0
$927$		0			0
$928$	0.321906	−	1.97338i	0.321906	−	1.97338i
$929$	0.276018	−	0.0127611i	0.276018	−	0.0127611i	0.0922684	−	0.995734i	$-0.470588\pi$
$929$	0.276018	−	0.0127611i	0.276018	−	0.0127611i	0.183750	+	0.982973i	$0.441176\pi$
$930$		0			0
$931$		0			0
$932$	0.941347	−	0.553195i	0.941347	−	0.553195i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−0.499398	−	0.0579382i	−0.499398	−	0.0579382i
$937$	−0.596047	+	0.408302i	−0.596047	+	0.408302i	−0.824997	−	0.565136i	$-0.808824\pi$
$937$	−0.596047	+	0.408302i	−0.596047	+	0.408302i	0.228951	+	0.973438i	$0.426471\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	0.960977	−	0.595012i	0.960977	−	0.595012i	0.0461835	−	0.998933i	$-0.485294\pi$
$941$	0.960977	−	0.595012i	0.960977	−	0.595012i	0.914794	+	0.403921i	$0.132353\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.545930	−	0.837831i	$-0.683824\pi$
$947$		0			0		0.545930	+	0.837831i	$0.316176\pi$
$948$		0			0
$949$	0.714678	+	0.296029i	0.714678	+	0.296029i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1.56401	−	1.23883i	−1.56401	−	1.23883i	−0.824997	−	0.565136i	$-0.808824\pi$
$953$	−1.56401	−	1.23883i	−1.56401	−	1.23883i	−0.739009	−	0.673696i	$-0.764706\pi$
$954$	−0.0285848	+	0.411819i	−0.0285848	+	0.411819i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.317791	−	0.948161i	0.317791	−	0.948161i
$962$	0.108517	−	0.300547i	0.108517	−	0.300547i
$963$		0			0
$964$	0.590192	+	0.0409658i	0.590192	+	0.0409658i
$965$			1.99147i			1.99147i
$966$		0			0
$967$		0			0		0.183750	−	0.982973i	$-0.441176\pi$
$967$		0			0		−0.183750	+	0.982973i	$0.558824\pi$
$968$	0.995734	−	0.0922684i	0.995734	−	0.0922684i
$969$		0			0
$970$	1.33639	+	1.27604i	1.33639	+	1.27604i
$971$		0			0		−0.978467	−	0.206405i	$-0.933824\pi$
$971$		0			0		0.978467	+	0.206405i	$0.0661765\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	1.08713	−	1.58701i	1.08713	−	1.58701i
$977$	0.703293	+	0.165413i	0.703293	+	0.165413i	0.565136	−	0.824997i	$-0.308824\pi$
$977$	0.703293	+	0.165413i	0.703293	+	0.165413i	0.138156	+	0.990410i	$0.455882\pi$
$978$		0			0
$979$		0			0
$980$	0.769334	−	0.638847i	0.769334	−	0.638847i
$981$	−0.0169724	+	0.0907942i	−0.0169724	+	0.0907942i
$982$		0			0
$983$		0			0		0.967890	−	0.251374i	$-0.0808824\pi$
$983$		0			0		−0.967890	+	0.251374i	$0.919118\pi$
$984$		0			0
$985$	0.600584	−	1.20614i	0.600584	−	1.20614i
$986$	−0.829310	+	3.19318i	−0.829310	+	3.19318i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.998933	−	0.0461835i	$-0.985294\pi$
$991$		0			0		0.998933	+	0.0461835i	$0.0147059\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	1.91373	−	0.450104i	1.91373	−	0.450104i	0.914794	−	0.403921i	$-0.132353\pi$
$997$	1.91373	−	0.450104i	1.91373	−	0.450104i	0.998933	−	0.0461835i	$-0.0147059\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2740.1.cd.a.583.1	yes	64
4.3	odd	2	CM	2740.1.cd.a.583.1	yes	64
5.2	odd	4		2740.1.bw.a.2227.1	yes	64
20.7	even	4		2740.1.bw.a.2227.1	yes	64
137.47	odd	136		2740.1.bw.a.1143.1	✓	64
548.47	even	136		2740.1.bw.a.1143.1	✓	64
685.47	even	136	inner	2740.1.cd.a.47.1	yes	64
2740.47	odd	136	inner	2740.1.cd.a.47.1	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2740.1.bw.a.1143.1	✓	64	137.47	odd	136
2740.1.bw.a.1143.1	✓	64	548.47	even	136
2740.1.bw.a.2227.1	yes	64	5.2	odd	4
2740.1.bw.a.2227.1	yes	64	20.7	even	4
2740.1.cd.a.47.1	yes	64	685.47	even	136	inner
2740.1.cd.a.47.1	yes	64	2740.47	odd	136	inner
2740.1.cd.a.583.1	yes	64	1.1	even	1	trivial
2740.1.cd.a.583.1	yes	64	4.3	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2740 = 2^{2} \cdot 5 \cdot 137 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2740.cd (of order \(136\), degree \(64\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.445738 - 0.895163i) q^{2} +(-0.602635 + 0.798017i) q^{4} +(-0.565136 - 0.824997i) q^{5} +(0.982973 + 0.183750i) q^{8} +(0.769334 + 0.638847i) q^{9} +O(q^{10})\)	\(q+(-0.445738 - 0.895163i) q^{2} +(-0.602635 + 0.798017i) q^{4} +(-0.565136 - 0.824997i) q^{5} +(0.982973 + 0.183750i) q^{8} +(0.769334 + 0.638847i) q^{9} +(-0.486604 + 0.873622i) q^{10} +(-0.363613 + 0.347190i) q^{13} +(-0.273663 - 0.961826i) q^{16} +(0.303186 + 1.62190i) q^{17} +(0.228951 - 0.973438i) q^{18} +(0.998933 + 0.0461835i) q^{20} +(-0.361242 + 0.932472i) q^{25} +(0.472868 + 0.170737i) q^{26} +(-1.56735 + 1.24148i) q^{29} +(-0.739009 + 0.673696i) q^{32} +(1.31672 - 0.994344i) q^{34} +(-0.973438 + 0.228951i) q^{36} -0.635583i q^{37} +(-0.403921 - 0.914794i) q^{40} +(0.755383 + 1.82366i) q^{41} +(0.0922684 - 0.995734i) q^{45} +(0.739009 - 0.673696i) q^{49} +(0.995734 - 0.0922684i) q^{50} +(-0.0579382 - 0.499398i) q^{52} +(-0.407425 + 0.0664607i) q^{53} +(1.80996 + 0.849659i) q^{58} +(1.22892 + 1.47993i) q^{61} +(0.932472 + 0.361242i) q^{64} +(0.491922 + 0.103770i) q^{65} +(-1.47701 - 0.735466i) q^{68} +(0.638847 + 0.769334i) q^{72} +(-0.621500 - 1.40756i) q^{73} +(-0.568950 + 0.283304i) q^{74} +(-0.638847 + 0.769334i) q^{80} +(0.183750 + 0.982973i) q^{81} +(1.29577 - 1.48906i) q^{82} +(1.16672 - 1.16672i) q^{85} +(1.23486 + 1.41908i) q^{89} +(-0.932472 + 0.361242i) q^{90} +(0.464478 - 1.78843i) q^{97} +(-0.932472 - 0.361242i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} - 4 q^{4} + 4 q^{8}+O(q^{10}) \) 64 * q + 4 * q^2 - 4 * q^4 + 4 * q^8	\( 64 q + 4 q^{2} - 4 q^{4} + 4 q^{8} - 4 q^{13} - 4 q^{16} + 4 q^{26} + 4 q^{32} - 4 q^{45} - 4 q^{49} - 4 q^{52} - 4 q^{64} - 4 q^{65} + 4 q^{73} + 4 q^{85} + 4 q^{90} + 4 q^{97} + 4 q^{98}+O(q^{100}) \) 64 * q + 4 * q^2 - 4 * q^4 + 4 * q^8 - 4 * q^13 - 4 * q^16 + 4 * q^26 + 4 * q^32 - 4 * q^45 - 4 * q^49 - 4 * q^52 - 4 * q^64 - 4 * q^65 + 4 * q^73 + 4 * q^85 + 4 * q^90 + 4 * q^97 + 4 * q^98

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