LMFDB - Embedded newform 2740.1.bw.a.1343.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2740,1,Mod(143,2740)]

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, 11]))

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

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

chi := DirichletCharacter("2740.143");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2740 = 2^{2} \cdot 5 \cdot 137 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2740.bw (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:	$\Z[a_1, \ldots, a_{9}]$
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			1343.1
Root			$-0.0461835 + 0.998933i$ of defining polynomial
Character	$\chi$	$=$	2740.1343
Dual form			2740.1.bw.a.1167.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.995734 + 0.0922684i) q^{2} +(0.982973 - 0.183750i) q^{4} +(0.895163 + 0.445738i) q^{5} +(-0.961826 + 0.273663i) q^{8} +(0.138156 - 0.990410i) q^{9} +O(q^{10})$	\(q+(-0.995734 + 0.0922684i) q^{2} +(0.982973 - 0.183750i) q^{4} +(0.895163 + 0.445738i) q^{5} +(-0.961826 + 0.273663i) q^{8} +(0.138156 - 0.990410i) q^{9} +(-0.932472 - 0.361242i) q^{10} +(0.241098 + 0.335088i) q^{13} +(0.932472 - 0.361242i) q^{16} +(-0.266331 + 0.936057i) q^{17} +(-0.0461835 + 0.998933i) q^{18} +(0.961826 + 0.273663i) q^{20} +(0.602635 + 0.798017i) q^{25} +(-0.270988 - 0.311413i) q^{26} +(-0.321906 - 0.00743733i) q^{29} +(-0.895163 + 0.445738i) q^{32} +(0.178827 - 0.956638i) q^{34} +(-0.0461835 - 0.998933i) q^{36} +1.53867 q^{37} +(-0.982973 - 0.183750i) q^{40} +(1.67263 + 0.692825i) q^{41} +(0.565136 - 0.824997i) q^{45} +(-0.445738 - 0.895163i) q^{49} +(-0.673696 - 0.739009i) q^{50} +(0.298565 + 0.285081i) q^{52} +(-0.0979435 + 0.208641i) q^{53} +(0.321219 - 0.0222961i) q^{58} +(0.715555 - 0.0998157i) q^{61} +(0.850217 - 0.526432i) q^{64} +(0.0664607 + 0.407425i) q^{65} +(-0.0897964 + 0.969057i) q^{68} +(0.138156 + 0.990410i) q^{72} +(0.268973 + 0.0632619i) q^{73} +(-1.53210 + 0.141970i) q^{74} +(0.995734 + 0.0922684i) q^{80} +(-0.961826 - 0.273663i) q^{81} +(-1.72942 - 0.535539i) q^{82} +(-0.655647 + 0.719210i) q^{85} +(-0.388362 - 1.25414i) q^{89} +(-0.486604 + 0.873622i) q^{90} +(-0.748886 - 0.157976i) q^{97} +(0.526432 + 0.850217i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{4}+O(q^{10}) $ 64 * q + 4 * q^4	$ 64 q + 4 q^{4} + 4 q^{10} - 4 q^{16} + 4 q^{25} + 4 q^{26} - 4 q^{40} + 4 q^{49} + 4 q^{53} - 4 q^{58} + 4 q^{64} + 4 q^{65} + 4 q^{73} + 4 q^{82}+O(q^{100}) $ 64 * q + 4 * q^4 + 4 * q^10 - 4 * q^16 + 4 * q^25 + 4 * q^26 - 4 * q^40 + 4 * q^49 + 4 * q^53 - 4 * q^58 + 4 * q^64 + 4 * q^65 + 4 * q^73 + 4 * q^82

Display 100 coefficients 10 coefficients

Character values

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

$n$	$1097$	$1371$	$1921$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{71}{136}\right)$

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 $

$2$	−0.995734	+	0.0922684i	−0.995734	+	0.0922684i
$2$	−0.995734	+	0.0922684i	−0.995734	+	0.0922684i
$3$		0			0		0.754373	−	0.656446i	$-0.227941\pi$
$3$		0			0		−0.754373	+	0.656446i	$0.772059\pi$
$4$	0.982973	−	0.183750i	0.982973	−	0.183750i
$5$	0.895163	+	0.445738i	0.895163	+	0.445738i
$5$	0.895163	+	0.445738i	0.895163	+	0.445738i
$6$		0			0
$7$		0			0		0.526432	−	0.850217i	$-0.323529\pi$
$7$		0			0		−0.526432	+	0.850217i	$0.676471\pi$
$8$	−0.961826	+	0.273663i	−0.961826	+	0.273663i
$9$	0.138156	−	0.990410i	0.138156	−	0.990410i
$10$	−0.932472	−	0.361242i	−0.932472	−	0.361242i
$11$		0			0		0.565136	−	0.824997i	$-0.308824\pi$
$11$		0			0		−0.565136	+	0.824997i	$0.691176\pi$
$12$		0			0
$13$	0.241098	+	0.335088i	0.241098	+	0.335088i	0.914794	−	0.403921i	$-0.132353\pi$
$13$	0.241098	+	0.335088i	0.241098	+	0.335088i	−0.673696	+	0.739009i	$0.735294\pi$
$14$		0			0
$15$		0			0
$16$	0.932472	−	0.361242i	0.932472	−	0.361242i
$17$	−0.266331	+	0.936057i	−0.266331	+	0.936057i	0.707107	+	0.707107i	$0.250000\pi$
$17$	−0.266331	+	0.936057i	−0.266331	+	0.936057i	−0.973438	+	0.228951i	$0.926471\pi$
$18$	−0.0461835	+	0.998933i	−0.0461835	+	0.998933i
$19$		0			0		0.0461835	−	0.998933i	$-0.485294\pi$
$19$		0			0		−0.0461835	+	0.998933i	$0.514706\pi$
$20$	0.961826	+	0.273663i	0.961826	+	0.273663i
$21$		0			0
$22$		0			0
$23$		0			0		0.0230979	−	0.999733i	$-0.492647\pi$
$23$		0			0		−0.0230979	+	0.999733i	$0.507353\pi$
$24$		0			0
$25$	0.602635	+	0.798017i	0.602635	+	0.798017i
$26$	−0.270988	−	0.311413i	−0.270988	−	0.311413i
$27$		0			0
$28$		0			0
$29$	−0.321906	−	0.00743733i	−0.321906	−	0.00743733i	−0.138156	−	0.990410i	$-0.544118\pi$
$29$	−0.321906	−	0.00743733i	−0.321906	−	0.00743733i	−0.183750	+	0.982973i	$0.558824\pi$
$30$		0			0
$31$		0			0		−0.940567	−	0.339607i	$-0.889706\pi$
$31$		0			0		0.940567	+	0.339607i	$0.110294\pi$
$32$	−0.895163	+	0.445738i	−0.895163	+	0.445738i
$33$		0			0
$34$	0.178827	−	0.956638i	0.178827	−	0.956638i
$35$		0			0
$36$	−0.0461835	−	0.998933i	−0.0461835	−	0.998933i
$37$	1.53867			1.53867			0.769334	−	0.638847i	$-0.220588\pi$
$37$	1.53867			1.53867			0.769334	+	0.638847i	$0.220588\pi$
$38$		0			0
$39$		0			0
$40$	−0.982973	−	0.183750i	−0.982973	−	0.183750i
$41$	1.67263	+	0.692825i	1.67263	+	0.692825i	0.998933	−	0.0461835i	$-0.0147059\pi$
$41$	1.67263	+	0.692825i	1.67263	+	0.692825i	0.673696	+	0.739009i	$0.264706\pi$
$42$		0			0
$43$		0			0		0.940567	−	0.339607i	$-0.110294\pi$
$43$		0			0		−0.940567	+	0.339607i	$0.889706\pi$
$44$		0			0
$45$	0.565136	−	0.824997i	0.565136	−	0.824997i
$46$		0			0
$47$		0			0		0.506653	−	0.862150i	$-0.330882\pi$
$47$		0			0		−0.506653	+	0.862150i	$0.669118\pi$
$48$		0			0
$49$	−0.445738	−	0.895163i	−0.445738	−	0.895163i
$50$	−0.673696	−	0.739009i	−0.673696	−	0.739009i
$51$		0			0
$52$	0.298565	+	0.285081i	0.298565	+	0.285081i
$53$	−0.0979435	+	0.208641i	−0.0979435	+	0.208641i	−0.948161	−	0.317791i	$-0.897059\pi$
$53$	−0.0979435	+	0.208641i	−0.0979435	+	0.208641i	0.850217	+	0.526432i	$0.176471\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	0.321219	−	0.0222961i	0.321219	−	0.0222961i
$59$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$59$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$60$		0			0
$61$	0.715555	−	0.0998157i	0.715555	−	0.0998157i	0.228951	−	0.973438i	$-0.426471\pi$
$61$	0.715555	−	0.0998157i	0.715555	−	0.0998157i	0.486604	+	0.873622i	$0.338235\pi$
$62$		0			0
$63$		0			0
$64$	0.850217	−	0.526432i	0.850217	−	0.526432i
$65$	0.0664607	+	0.407425i	0.0664607	+	0.407425i
$66$		0			0
$67$		0			0		0.160996	−	0.986955i	$-0.448529\pi$
$67$		0			0		−0.160996	+	0.986955i	$0.551471\pi$
$68$	−0.0897964	+	0.969057i	−0.0897964	+	0.969057i
$69$		0			0
$70$		0			0
$71$		0			0		0.978467	−	0.206405i	$-0.0661765\pi$
$71$		0			0		−0.978467	+	0.206405i	$0.933824\pi$
$72$	0.138156	+	0.990410i	0.138156	+	0.990410i
$73$	0.268973	+	0.0632619i	0.268973	+	0.0632619i	0.361242	−	0.932472i	$-0.382353\pi$
$73$	0.268973	+	0.0632619i	0.268973	+	0.0632619i	−0.0922684	+	0.995734i	$0.529412\pi$
$74$	−1.53210	+	0.141970i	−1.53210	+	0.141970i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.656446	−	0.754373i	$-0.272059\pi$
$79$		0			0		−0.656446	+	0.754373i	$0.727941\pi$
$80$	0.995734	+	0.0922684i	0.995734	+	0.0922684i
$81$	−0.961826	−	0.273663i	−0.961826	−	0.273663i
$82$	−1.72942	−	0.535539i	−1.72942	−	0.535539i
$83$		0			0		0.115243	−	0.993337i	$-0.463235\pi$
$83$		0			0		−0.115243	+	0.993337i	$0.536765\pi$
$84$		0			0
$85$	−0.655647	+	0.719210i	−0.655647	+	0.719210i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.388362	−	1.25414i	−0.388362	−	1.25414i	−0.914794	−	0.403921i	$-0.867647\pi$
$89$	−0.388362	−	1.25414i	−0.388362	−	1.25414i	0.526432	−	0.850217i	$-0.323529\pi$
$90$	−0.486604	+	0.873622i	−0.486604	+	0.873622i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−0.748886	−	0.157976i	−0.748886	−	0.157976i	−0.183750	−	0.982973i	$-0.558824\pi$
$97$	−0.748886	−	0.157976i	−0.748886	−	0.157976i	−0.565136	+	0.824997i	$0.691176\pi$
$98$	0.526432	+	0.850217i	0.526432	+	0.850217i
$99$		0			0
$100$	0.739009	+	0.673696i	0.739009	+	0.673696i
$101$	−0.890525	+	0.0411715i	−0.890525	+	0.0411715i	−0.486604	−	0.873622i	$-0.661765\pi$
$101$	−0.890525	+	0.0411715i	−0.890525	+	0.0411715i	−0.403921	+	0.914794i	$0.632353\pi$
$102$		0			0
$103$		0			0		0.824997	−	0.565136i	$-0.191176\pi$
$103$		0			0		−0.824997	+	0.565136i	$0.808824\pi$
$104$	−0.323596	−	0.256316i	−0.323596	−	0.256316i
$105$		0			0
$106$	0.0782748	−	0.216788i	0.0782748	−	0.216788i
$107$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$107$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$108$		0			0
$109$	0.256725	+	0.581427i	0.256725	+	0.581427i	0.995734	−	0.0922684i	$-0.0294118\pi$
$109$	0.256725	+	0.581427i	0.256725	+	0.581427i	−0.739009	+	0.673696i	$0.764706\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.491922	−	0.103770i	0.491922	−	0.103770i	0.0461835	−	0.998933i	$-0.485294\pi$
$113$	0.491922	−	0.103770i	0.491922	−	0.103770i	0.445738	+	0.895163i	$0.352941\pi$
$114$		0			0
$115$		0			0
$116$	−0.317791	+	0.0518394i	−0.317791	+	0.0518394i
$117$	0.365184	−	0.192492i	0.365184	−	0.192492i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.361242	−	0.932472i	−0.361242	−	0.932472i
$122$	−0.703293	+	0.165413i	−0.703293	+	0.165413i
$123$		0			0
$124$		0			0
$125$	0.183750	+	0.982973i	0.183750	+	0.982973i
$126$		0			0
$127$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$127$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$128$	−0.798017	+	0.602635i	−0.798017	+	0.602635i
$129$		0			0
$130$	−0.103770	−	0.399555i	−0.103770	−	0.399555i
$131$		0			0		−0.723251	−	0.690585i	$-0.757353\pi$
$131$		0			0		0.723251	+	0.690585i	$0.242647\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		−	0.973209i		−	0.973209i
$137$	−0.850217	+	0.526432i	−0.850217	+	0.526432i
$137$	−0.850217	+	0.526432i	−0.850217	+	0.526432i
$138$		0			0
$139$		0			0		0.638847	−	0.769334i	$-0.279412\pi$
$139$		0			0		−0.638847	+	0.769334i	$0.720588\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.228951	−	0.973438i	−0.228951	−	0.973438i
$145$	−0.284843	−	0.150143i	−0.284843	−	0.150143i
$146$	−0.273663	−	0.0381744i	−0.273663	−	0.0381744i
$147$		0			0
$148$	1.51247	−	0.282729i	1.51247	−	0.282729i
$149$	0.203895	+	1.75747i	0.203895	+	1.75747i	0.565136	+	0.824997i	$0.308824\pi$
$149$	0.203895	+	1.75747i	0.203895	+	1.75747i	−0.361242	+	0.932472i	$0.617647\pi$
$150$		0			0
$151$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$151$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$152$		0			0
$153$	0.890286	+	0.393100i	0.890286	+	0.393100i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.275866	−	0.523357i	−0.275866	−	0.523357i	0.707107	−	0.707107i	$-0.250000\pi$
$157$	−0.275866	−	0.523357i	−0.275866	−	0.523357i	−0.982973	+	0.183750i	$0.941176\pi$
$158$		0			0
$159$		0			0
$160$	−1.00000			−1.00000
$161$		0			0
$162$	0.982973	+	0.183750i	0.982973	+	0.183750i
$163$		0			0		0.0692444	−	0.997600i	$-0.477941\pi$
$163$		0			0		−0.0692444	+	0.997600i	$0.522059\pi$
$164$	1.77146	+	0.373684i	1.77146	+	0.373684i
$165$		0			0
$166$		0			0
$167$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$167$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$168$		0			0
$169$	0.263636	−	0.786582i	0.263636	−	0.786582i
$170$	0.586489	−	0.776638i	0.586489	−	0.776638i
$171$		0			0
$172$		0			0
$173$	1.14558	−	1.25664i	1.14558	−	1.25664i	0.183750	−	0.982973i	$-0.441176\pi$
$173$	1.14558	−	1.25664i	1.14558	−	1.25664i	0.961826	−	0.273663i	$-0.0882353\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	0.502422	+	1.21295i	0.502422	+	1.21295i
$179$		0			0		−0.862150	−	0.506653i	$-0.830882\pi$
$179$		0			0		0.862150	+	0.506653i	$0.169118\pi$
$180$	0.403921	−	0.914794i	0.403921	−	0.914794i
$181$	1.78099	+	0.786384i	1.78099	+	0.786384i	0.982973	+	0.183750i	$0.0588235\pi$
$181$	1.78099	+	0.786384i	1.78099	+	0.786384i	0.798017	+	0.602635i	$0.205882\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.37736	+	0.685843i	1.37736	+	0.685843i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.783885	−	0.620906i	$-0.213235\pi$
$191$		0			0		−0.783885	+	0.620906i	$0.786765\pi$
$192$		0			0
$193$	1.39433	−	0.776638i	1.39433	−	0.776638i	0.403921	−	0.914794i	$-0.367647\pi$
$193$	1.39433	−	0.776638i	1.39433	−	0.776638i	0.990410	+	0.138156i	$0.0441176\pi$
$194$	0.760267	+	0.0882033i	0.760267	+	0.0882033i
$195$		0			0
$196$	−0.602635	−	0.798017i	−0.602635	−	0.798017i
$197$	−1.63778	+	0.723151i	−1.63778	+	0.723151i	−0.998933	−	0.0461835i	$-0.985294\pi$
$197$	−1.63778	+	0.723151i	−1.63778	+	0.723151i	−0.638847	+	0.769334i	$0.720588\pi$
$198$		0			0
$199$		0			0		0.862150	−	0.506653i	$-0.169118\pi$
$199$		0			0		−0.862150	+	0.506653i	$0.830882\pi$
$200$	−0.798017	−	0.602635i	−0.798017	−	0.602635i
$201$		0			0
$202$	0.882928	−	0.123163i	0.882928	−	0.123163i
$203$		0			0
$204$		0			0
$205$	1.18846	+	1.36575i	1.18846	+	1.36575i
$206$		0			0
$207$		0			0
$208$	0.345865	+	0.225365i	0.345865	+	0.225365i
$209$		0			0
$210$		0			0
$211$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$211$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$212$	−0.0579382	+	0.223085i	−0.0579382	+	0.223085i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−0.309277	−	0.555259i	−0.309277	−	0.555259i
$219$		0			0
$220$		0			0
$221$	−0.377873	+	0.136437i	−0.377873	+	0.136437i
$222$		0			0
$223$		0			0		−0.940567	−	0.339607i	$-0.889706\pi$
$223$		0			0		0.940567	+	0.339607i	$0.110294\pi$
$224$		0			0
$225$	0.873622	−	0.486604i	0.873622	−	0.486604i
$226$	−0.480249	+	0.148716i	−0.480249	+	0.148716i
$227$		0			0		−0.862150	−	0.506653i	$-0.830882\pi$
$227$		0			0		0.862150	+	0.506653i	$0.169118\pi$
$228$		0			0
$229$	−0.551334	−	0.396689i	−0.551334	−	0.396689i	0.273663	−	0.961826i	$-0.411765\pi$
$229$	−0.551334	−	0.396689i	−0.551334	−	0.396689i	−0.824997	+	0.565136i	$0.808824\pi$
$230$		0			0
$231$		0			0
$232$	0.311653	−	0.0809403i	0.311653	−	0.0809403i
$233$	−1.14729	+	0.475221i	−1.14729	+	0.475221i	−0.873622	−	0.486604i	$-0.838235\pi$
$233$	−1.14729	+	0.475221i	−1.14729	+	0.475221i	−0.273663	+	0.961826i	$0.588235\pi$
$234$	−0.345865	+	0.225365i	−0.345865	+	0.225365i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.967890	−	0.251374i	$-0.919118\pi$
$239$		0			0		0.967890	+	0.251374i	$0.0808824\pi$
$240$		0			0
$241$	−0.629169	+	0.794316i	−0.629169	+	0.794316i	−0.990410	−	0.138156i	$-0.955882\pi$
$241$	−0.629169	+	0.794316i	−0.629169	+	0.794316i	0.361242	+	0.932472i	$0.382353\pi$
$242$	0.445738	+	0.895163i	0.445738	+	0.895163i
$243$		0			0
$244$	0.685030	−	0.229599i	0.685030	−	0.229599i
$245$		−	1.00000i		−	1.00000i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	−0.273663	−	0.961826i	−0.273663	−	0.961826i
$251$		0			0		0.723251	−	0.690585i	$-0.242647\pi$
$251$		0			0		−0.723251	+	0.690585i	$0.757353\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.739009	−	0.673696i	0.739009	−	0.673696i
$257$	−1.58701	−	0.451543i	−1.58701	−	0.451543i	−0.638847	−	0.769334i	$-0.720588\pi$
$257$	−1.58701	−	0.451543i	−1.58701	−	0.451543i	−0.948161	+	0.317791i	$0.897059\pi$
$258$		0			0
$259$		0			0
$260$	0.140193	+	0.388276i	0.140193	+	0.388276i
$261$	−0.0518394	+	0.317791i	−0.0518394	+	0.317791i
$262$		0			0
$263$		0			0		−0.183750	−	0.982973i	$-0.558824\pi$
$263$		0			0		0.183750	+	0.982973i	$0.441176\pi$
$264$		0			0
$265$	−0.180675	+	0.143110i	−0.180675	+	0.143110i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.71245	+	0.902646i	1.71245	+	0.902646i	0.973438	+	0.228951i	$0.0735294\pi$
$269$	1.71245	+	0.902646i	1.71245	+	0.902646i	0.739009	+	0.673696i	$0.235294\pi$
$270$		0			0
$271$		0			0		−0.997600	−	0.0692444i	$-0.977941\pi$
$271$		0			0		0.997600	+	0.0692444i	$0.0220588\pi$
$272$	0.0897964	+	0.969057i	0.0897964	+	0.969057i
$273$		0			0
$274$	0.798017	−	0.602635i	0.798017	−	0.602635i
$275$		0			0
$276$		0			0
$277$	−1.21295	−	1.39390i	−1.21295	−	1.39390i	−0.895163	−	0.445738i	$-0.852941\pi$
$277$	−1.21295	−	1.39390i	−1.21295	−	1.39390i	−0.317791	−	0.948161i	$-0.602941\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.24376	+	0.292529i	−1.24376	+	0.292529i	−0.798017	−	0.602635i	$-0.794118\pi$
$281$	−1.24376	+	0.292529i	−1.24376	+	0.292529i	−0.445738	+	0.895163i	$0.647059\pi$
$282$		0			0
$283$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$283$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.317791	+	0.948161i	0.317791	+	0.948161i
$289$	0.0449462	+	0.0278295i	0.0449462	+	0.0278295i
$290$	0.297482	+	0.123221i	0.297482	+	0.123221i
$291$		0			0
$292$	0.276018	+	0.0127611i	0.276018	+	0.0127611i
$293$	0.761460	+	0.835282i	0.761460	+	0.835282i	0.990410	−	0.138156i	$-0.0441176\pi$
$293$	0.761460	+	0.835282i	0.761460	+	0.835282i	−0.228951	+	0.973438i	$0.573529\pi$
$294$		0			0
$295$		0			0
$296$	−1.47993	+	0.421076i	−1.47993	+	0.421076i
$297$		0			0
$298$	−0.365184	−	1.73116i	−0.365184	−	1.73116i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.685030	+	0.229599i	0.685030	+	0.229599i
$306$	−0.922758	−	0.309277i	−0.922758	−	0.309277i
$307$		0			0		0.993337	−	0.115243i	$-0.0367647\pi$
$307$		0			0		−0.993337	+	0.115243i	$0.963235\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$311$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$312$		0			0
$313$	−0.686841	+	0.425274i	−0.686841	+	0.425274i	−0.824997	−	0.565136i	$-0.808824\pi$
$313$	−0.686841	+	0.425274i	−0.686841	+	0.425274i	0.138156	+	0.990410i	$0.455882\pi$
$314$	0.322979	+	0.495671i	0.322979	+	0.495671i
$315$		0			0
$316$		0			0
$317$	0.288627	+	0.799375i	0.288627	+	0.799375i	0.995734	+	0.0922684i	$0.0294118\pi$
$317$	0.288627	+	0.799375i	0.288627	+	0.799375i	−0.707107	+	0.707107i	$0.750000\pi$
$318$		0			0
$319$		0			0
$320$	0.995734	−	0.0922684i	0.995734	−	0.0922684i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.995734	−	0.0922684i	−0.995734	−	0.0922684i
$325$	−0.122112	+	0.394336i	−0.122112	+	0.394336i
$326$		0			0
$327$		0			0
$328$	−1.79838	−	0.208641i	−1.79838	−	0.208641i
$329$		0			0
$330$		0			0
$331$		0			0		0.115243	−	0.993337i	$-0.463235\pi$
$331$		0			0		−0.115243	+	0.993337i	$0.536765\pi$
$332$		0			0
$333$	0.212577	−	1.52391i	0.212577	−	1.52391i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.25594	+	1.51247i	−1.25594	+	1.51247i	−0.486604	+	0.873622i	$0.661765\pi$
$337$	−1.25594	+	1.51247i	−1.25594	+	1.51247i	−0.769334	+	0.638847i	$0.779412\pi$
$338$	−0.189935	+	0.807552i	−0.189935	+	0.807552i
$339$		0			0
$340$	−0.512328	+	0.827439i	−0.512328	+	0.827439i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−1.02474	+	1.35698i	−1.02474	+	1.35698i
$347$		0			0		0.228951	−	0.973438i	$-0.426471\pi$
$347$		0			0		−0.228951	+	0.973438i	$0.573529\pi$
$348$		0			0
$349$	−1.00656	−	1.71281i	−1.00656	−	1.71281i	−0.602635	−	0.798017i	$-0.705882\pi$
$349$	−1.00656	−	1.71281i	−1.00656	−	1.71281i	−0.403921	−	0.914794i	$-0.632353\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.119398	−	1.72016i	−0.119398	−	1.72016i	−0.565136	−	0.824997i	$-0.691176\pi$
$353$	−0.119398	−	1.72016i	−0.119398	−	1.72016i	0.445738	−	0.895163i	$-0.352941\pi$
$354$		0			0
$355$		0			0
$356$	−0.612196	−	1.16142i	−0.612196	−	1.16142i
$357$		0			0
$358$		0			0
$359$		0			0		−0.0230979	−	0.999733i	$-0.507353\pi$
$359$		0			0		0.0230979	+	0.999733i	$0.492647\pi$
$360$	−0.317791	+	0.948161i	−0.317791	+	0.948161i
$361$	−0.995734	−	0.0922684i	−0.995734	−	0.0922684i
$362$	−1.84595	−	0.618701i	−1.84595	−	0.618701i
$363$		0			0
$364$		0			0
$365$	0.212577	+	0.176521i	0.212577	+	0.176521i
$366$		0			0
$367$		0			0		−0.361242	−	0.932472i	$-0.617647\pi$
$367$		0			0		0.361242	+	0.932472i	$0.382353\pi$
$368$		0			0
$369$	0.917266	−	1.56087i	0.917266	−	1.56087i
$370$	−1.43477	−	0.555831i	−1.43477	−	0.555831i
$371$		0			0
$372$		0			0
$373$	−0.367107	+	0.0169724i	−0.367107	+	0.0169724i	−0.228951	−	0.973438i	$-0.573529\pi$
$373$	−0.367107	+	0.0169724i	−0.367107	+	0.0169724i	−0.138156	+	0.990410i	$0.544118\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.0751188	−	0.109660i	−0.0751188	−	0.109660i
$378$		0			0
$379$		0			0		−0.948161	−	0.317791i	$-0.897059\pi$
$379$		0			0		0.948161	+	0.317791i	$0.102941\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$383$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$384$		0			0
$385$		0			0
$386$	−1.31672	+	0.901977i	−1.31672	+	0.901977i
$387$		0			0
$388$	−0.765163	−	0.0176784i	−0.765163	−	0.0176784i
$389$	−1.90520	+	0.542077i	−1.90520	+	0.542077i	−0.914794	+	0.403921i	$0.867647\pi$
$389$	−1.90520	+	0.542077i	−1.90520	+	0.542077i	−0.990410	+	0.138156i	$0.955882\pi$
$390$		0			0
$391$		0			0
$392$	0.673696	+	0.739009i	0.673696	+	0.739009i
$393$		0			0
$394$	1.56407	−	0.871181i	1.56407	−	0.871181i
$395$		0			0
$396$		0			0
$397$	−0.632872	−	1.88823i	−0.632872	−	1.88823i	−0.403921	−	0.914794i	$-0.632353\pi$
$397$	−0.632872	−	1.88823i	−0.632872	−	1.88823i	−0.228951	−	0.973438i	$-0.573529\pi$
$398$		0			0
$399$		0			0
$400$	0.850217	+	0.526432i	0.850217	+	0.526432i
$401$	−1.07917	+	0.447006i	−1.07917	+	0.447006i	−0.850217	−	0.526432i	$-0.823529\pi$
$401$	−1.07917	+	0.447006i	−1.07917	+	0.447006i	−0.228951	+	0.973438i	$0.573529\pi$
$402$		0			0
$403$		0			0
$404$	−0.867797	+	0.204104i	−0.867797	+	0.204104i
$405$	−0.739009	−	0.673696i	−0.739009	−	0.673696i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	1.03659	+	0.860777i	1.03659	+	0.860777i	0.990410	−	0.138156i	$-0.0441176\pi$
$409$	1.03659	+	0.860777i	1.03659	+	0.860777i	0.0461835	+	0.998933i	$0.485294\pi$
$410$	−1.30940	−	1.25026i	−1.30940	−	1.25026i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−0.365184	−	0.192492i	−0.365184	−	0.192492i
$417$		0			0
$418$		0			0
$419$		0			0		−0.873622	−	0.486604i	$-0.838235\pi$
$419$		0			0		0.873622	+	0.486604i	$0.161765\pi$
$420$		0			0
$421$	0.0529974	+	0.127947i	0.0529974	+	0.127947i	0.948161	−	0.317791i	$-0.102941\pi$
$421$	0.0529974	+	0.127947i	0.0529974	+	0.127947i	−0.895163	+	0.445738i	$0.852941\pi$
$422$		0			0
$423$		0			0
$424$	0.0371073	−	0.227480i	0.0371073	−	0.227480i
$425$	−0.907490	+	0.351564i	−0.907490	+	0.351564i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.295806	−	0.955248i	$-0.404412\pi$
$431$		0			0		−0.295806	+	0.955248i	$0.595588\pi$
$432$		0			0
$433$	−1.65667	−	0.922758i	−1.65667	−	0.922758i	−0.982973	−	0.183750i	$-0.941176\pi$
$433$	−1.65667	−	0.922758i	−1.65667	−	0.922758i	−0.673696	−	0.739009i	$-0.735294\pi$
$434$		0			0
$435$		0			0
$436$	0.359191	+	0.524354i	0.359191	+	0.524354i
$437$		0			0
$438$		0			0
$439$		0			0		0.914794	−	0.403921i	$-0.132353\pi$
$439$		0			0		−0.914794	+	0.403921i	$0.867647\pi$
$440$		0			0
$441$	−0.948161	+	0.317791i	−0.948161	+	0.317791i
$442$	0.363673	−	0.170721i	0.363673	−	0.170721i
$443$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$443$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$444$		0			0
$445$	0.211370	−	1.29577i	0.211370	−	1.29577i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.308486	−	0.338393i	0.308486	−	0.338393i	−0.565136	−	0.824997i	$-0.691176\pi$
$449$	0.308486	−	0.338393i	0.308486	−	0.338393i	0.873622	+	0.486604i	$0.161765\pi$
$450$	−0.824997	+	0.565136i	−0.824997	+	0.565136i
$451$		0			0
$452$	0.464478	−	0.192393i	0.464478	−	0.192393i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.50512	−	1.30974i	−1.50512	−	1.30974i	−0.798017	−	0.602635i	$-0.794118\pi$
$457$	−1.50512	−	1.30974i	−1.50512	−	1.30974i	−0.707107	−	0.707107i	$-0.750000\pi$
$458$	0.585584	+	0.344126i	0.585584	+	0.344126i
$459$		0			0
$460$		0			0
$461$	0.111208	−	1.20013i	0.111208	−	1.20013i	−0.739009	−	0.673696i	$-0.764706\pi$
$461$	0.111208	−	1.20013i	0.111208	−	1.20013i	0.850217	−	0.526432i	$-0.176471\pi$
$462$		0			0
$463$		0			0		0.690585	−	0.723251i	$-0.257353\pi$
$463$		0			0		−0.690585	+	0.723251i	$0.742647\pi$
$464$	−0.302855	+	0.109351i	−0.302855	+	0.109351i
$465$		0			0
$466$	1.09854	−	0.579052i	1.09854	−	0.579052i
$467$		0			0		−0.486604	−	0.873622i	$-0.661765\pi$
$467$		0			0		0.486604	+	0.873622i	$0.338235\pi$
$468$	0.323596	−	0.256316i	0.323596	−	0.256316i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.193108	+	0.125829i	0.193108	+	0.125829i
$478$		0			0
$479$		0			0		0.769334	−	0.638847i	$-0.220588\pi$
$479$		0			0		−0.769334	+	0.638847i	$0.779412\pi$
$480$		0			0
$481$	0.370970	+	0.515589i	0.370970	+	0.515589i
$482$	0.553195	−	0.848980i	0.553195	−	0.848980i
$483$		0			0
$484$	−0.526432	−	0.850217i	−0.526432	−	0.850217i
$485$	−0.599959	−	0.475221i	−0.599959	−	0.475221i
$486$		0			0
$487$		0			0		−0.798017	−	0.602635i	$-0.794118\pi$
$487$		0			0		0.798017	+	0.602635i	$0.205882\pi$
$488$	−0.660923	+	0.291826i	−0.660923	+	0.291826i
$489$		0			0
$490$	0.0922684	+	0.995734i	0.0922684	+	0.995734i
$491$		0			0		−0.993337	−	0.115243i	$-0.963235\pi$
$491$		0			0		0.993337	+	0.115243i	$0.0367647\pi$
$492$		0			0
$493$	0.0926954	−	0.299342i	0.0926954	−	0.299342i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		0.895163	−	0.445738i	$-0.147059\pi$
$499$		0			0		−0.895163	+	0.445738i	$0.852941\pi$
$500$	0.361242	+	0.932472i	0.361242	+	0.932472i
$501$		0			0
$502$		0			0
$503$		0			0		0.986955	−	0.160996i	$-0.0514706\pi$
$503$		0			0		−0.986955	+	0.160996i	$0.948529\pi$
$504$		0			0
$505$	−0.815517	−	0.360086i	−0.815517	−	0.360086i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−0.0422498	+	0.179635i	−0.0422498	+	0.179635i	−0.990410	−	0.138156i	$-0.955882\pi$
$509$	−0.0422498	+	0.179635i	−0.0422498	+	0.179635i	0.948161	+	0.317791i	$0.102941\pi$
$510$		0			0
$511$		0			0
$512$	−0.673696	+	0.739009i	−0.673696	+	0.739009i
$513$		0			0
$514$	1.62190	+	0.303186i	1.62190	+	0.303186i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−0.175421	−	0.373684i	−0.175421	−	0.373684i
$521$	−1.58849	−	0.335088i	−1.58849	−	0.335088i	−0.673696	−	0.739009i	$-0.735294\pi$
$521$	−1.58849	−	0.335088i	−1.58849	−	0.335088i	−0.914794	+	0.403921i	$0.867647\pi$
$522$	0.0222961	−	0.321219i	0.0222961	−	0.321219i
$523$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$523$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−0.998933	−	0.0461835i	−0.998933	−	0.0461835i
$530$	0.166699	−	0.159170i	0.166699	−	0.159170i
$531$		0			0
$532$		0			0
$533$	0.171110	+	0.727517i	0.171110	+	0.727517i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−1.78843	−	0.740791i	−1.78843	−	0.740791i
$539$		0			0
$540$		0			0
$541$	0.338393	+	1.43876i	0.338393	+	1.43876i	0.824997	+	0.565136i	$0.191176\pi$
$541$	0.338393	+	1.43876i	0.338393	+	1.43876i	−0.486604	+	0.873622i	$0.661765\pi$
$542$		0			0
$543$		0			0
$544$	−0.178827	−	0.956638i	−0.178827	−	0.956638i
$545$	−0.0293534	+	0.634905i	−0.0293534	+	0.634905i
$546$		0			0
$547$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$547$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$548$	−0.739009	+	0.673696i	−0.739009	+	0.673696i
$549$		−	0.722483i		−	0.722483i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	1.33639	+	1.27604i	1.33639	+	1.27604i
$555$		0			0
$556$		0			0
$557$	1.53511	−	1.15926i	1.53511	−	1.15926i	0.602635	−	0.798017i	$-0.294118\pi$
$557$	1.53511	−	1.15926i	1.53511	−	1.15926i	0.932472	−	0.361242i	$-0.117647\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	1.21146	−	0.406040i	1.21146	−	0.406040i
$563$		0			0		0.973438	−	0.228951i	$-0.0735294\pi$
$563$		0			0		−0.973438	+	0.228951i	$0.926471\pi$
$564$		0			0
$565$	0.486604	+	0.126378i	0.486604	+	0.126378i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−1.85660	+	0.302855i	−1.85660	+	0.302855i	−0.982973	−	0.183750i	$-0.941176\pi$
$569$	−1.85660	+	0.302855i	−1.85660	+	0.302855i	−0.873622	+	0.486604i	$0.838235\pi$
$570$		0			0
$571$		0			0		−0.690585	−	0.723251i	$-0.742647\pi$
$571$		0			0		0.690585	+	0.723251i	$0.257353\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.403921	−	0.914794i	−0.403921	−	0.914794i
$577$	0.644034	+	0.674498i	0.644034	+	0.674498i	0.961826	−	0.273663i	$-0.0882353\pi$
$577$	0.644034	+	0.674498i	0.644034	+	0.674498i	−0.317791	+	0.948161i	$0.602941\pi$
$578$	−0.0473222	−	0.0235637i	−0.0473222	−	0.0235637i
$579$		0			0
$580$	−0.307582	−	0.0952471i	−0.307582	−	0.0952471i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−0.276018	+	0.0127611i	−0.276018	+	0.0127611i
$585$	0.412700	−	0.00953505i	0.412700	−	0.00953505i
$586$	−0.835282	−	0.761460i	−0.835282	−	0.761460i
$587$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$587$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	1.43477	−	0.555831i	1.43477	−	0.555831i
$593$	−0.317791	−	1.94816i	−0.317791	−	1.94816i	−0.317791	−	0.948161i	$-0.602941\pi$
$593$	−0.317791	−	1.94816i	−0.317791	−	1.94816i		−	1.00000i	$-0.5\pi$
$594$		0			0
$595$		0			0
$596$	0.523357	+	1.69008i	0.523357	+	1.69008i
$597$		0			0
$598$		0			0
$599$		0			0		0.905220	−	0.424943i	$-0.139706\pi$
$599$		0			0		−0.905220	+	0.424943i	$0.860294\pi$
$600$		0			0
$601$	0.677584	+	1.87662i	0.677584	+	1.87662i	0.403921	+	0.914794i	$0.367647\pi$
$601$	0.677584	+	1.87662i	0.677584	+	1.87662i	0.273663	+	0.961826i	$0.411765\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.0922684	−	0.995734i	0.0922684	−	0.995734i
$606$		0			0
$607$		0			0		−0.990410	−	0.138156i	$-0.955882\pi$
$607$		0			0		0.990410	+	0.138156i	$0.0441176\pi$
$608$		0			0
$609$		0			0
$610$	−0.703293	−	0.165413i	−0.703293	−	0.165413i
$611$		0			0
$612$	0.947359	+	0.222817i	0.947359	+	0.222817i
$613$	−0.0127611	−	0.0914812i	−0.0127611	−	0.0914812i	0.982973	−	0.183750i	$-0.0588235\pi$
$613$	−0.0127611	−	0.0914812i	−0.0127611	−	0.0914812i	−0.995734	+	0.0922684i	$0.970588\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.0505009	−	0.544991i	0.0505009	−	0.544991i	−0.932472	−	0.361242i	$-0.882353\pi$
$617$	0.0505009	−	0.544991i	0.0505009	−	0.544991i	0.982973	−	0.183750i	$-0.0588235\pi$
$618$		0			0
$619$		0			0		−0.206405	−	0.978467i	$-0.566176\pi$
$619$		0			0		0.206405	+	0.978467i	$0.433824\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.273663	+	0.961826i	−0.273663	+	0.961826i
$626$	0.644672	−	0.486834i	0.644672	−	0.486834i
$627$		0			0
$628$	−0.367336	−	0.463756i	−0.367336	−	0.463756i
$629$	−0.409795	+	1.44028i	−0.409795	+	1.44028i
$630$		0			0
$631$		0			0		−0.620906	−	0.783885i	$-0.713235\pi$
$631$		0			0		0.620906	+	0.783885i	$0.286765\pi$
$632$		0			0
$633$		0			0
$634$	−0.361153	−	0.769334i	−0.361153	−	0.769334i
$635$		0			0
$636$		0			0
$637$	0.192492	−	0.365184i	0.192492	−	0.365184i
$638$		0			0
$639$		0			0
$640$	−0.982973	+	0.183750i	−0.982973	+	0.183750i
$641$	0.705749	−	1.59837i	0.705749	−	1.59837i	−0.0922684	−	0.995734i	$-0.529412\pi$
$641$	0.705749	−	1.59837i	0.705749	−	1.59837i	0.798017	−	0.602635i	$-0.205882\pi$
$642$		0			0
$643$		0			0		−0.251374	−	0.967890i	$-0.580882\pi$
$643$		0			0		0.251374	+	0.967890i	$0.419118\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.0461835	−	0.998933i	$-0.514706\pi$
$647$		0			0		0.0461835	+	0.998933i	$0.485294\pi$
$648$	1.00000			1.00000
$649$		0			0
$650$	0.0852061	−	0.403921i	0.0852061	−	0.403921i
$651$		0			0
$652$		0			0
$653$	1.77316	−	0.882928i	1.77316	−	0.882928i	0.824997	−	0.565136i	$-0.191176\pi$
$653$	1.77316	−	0.882928i	1.77316	−	0.882928i	0.948161	−	0.317791i	$-0.102941\pi$
$654$		0			0
$655$		0			0
$656$	1.80996	+	0.0418174i	1.80996	+	0.0418174i
$657$	0.0998157	−	0.257654i	0.0998157	−	0.257654i
$658$		0			0
$659$		0			0		−0.656446	−	0.754373i	$-0.727941\pi$
$659$		0			0		0.656446	+	0.754373i	$0.272059\pi$
$660$		0			0
$661$	1.07762	−	1.65380i	1.07762	−	1.65380i	0.403921	−	0.914794i	$-0.367647\pi$
$661$	1.07762	−	1.65380i	1.07762	−	1.65380i	0.673696	−	0.739009i	$-0.264706\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−0.0710610	+	1.53703i	−0.0710610	+	1.53703i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−1.23354	+	1.55732i	−1.23354	+	1.55732i	−0.526432	+	0.850217i	$0.676471\pi$
$673$	−1.23354	+	1.55732i	−1.23354	+	1.55732i	−0.707107	+	0.707107i	$0.750000\pi$
$674$	1.11103	−	1.62190i	1.11103	−	1.62190i
$675$		0			0
$676$	0.114613	−	0.821632i	0.114613	−	0.821632i
$677$	−0.177492	+	0.0505009i	−0.177492	+	0.0505009i	−0.361242	−	0.932472i	$-0.617647\pi$
$677$	−0.177492	+	0.0505009i	−0.177492	+	0.0505009i	0.183750	+	0.982973i	$0.441176\pi$
$678$		0			0
$679$		0			0
$680$	0.433797	−	0.871181i	0.433797	−	0.871181i
$681$		0			0
$682$		0			0
$683$		0			0		0.995734	−	0.0922684i	$-0.0294118\pi$
$683$		0			0		−0.995734	+	0.0922684i	$0.970588\pi$
$684$		0			0
$685$	−0.995734	+	0.0922684i	−0.995734	+	0.0922684i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.0935270	+	0.0174832i	−0.0935270	+	0.0174832i
$690$		0			0
$691$		0			0		0.690585	−	0.723251i	$-0.257353\pi$
$691$		0			0		−0.690585	+	0.723251i	$0.742647\pi$
$692$	0.895163	−	1.44574i	0.895163	−	1.44574i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−1.09400	+	1.38116i	−1.09400	+	1.38116i
$698$	1.16030	+	1.61263i	1.16030	+	1.61263i
$699$		0			0
$700$		0			0
$701$	−1.83319	+	0.710182i	−1.83319	+	0.710182i	−0.850217	+	0.526432i	$0.823529\pi$
$701$	−1.83319	+	0.710182i	−1.83319	+	0.710182i	−0.982973	+	0.183750i	$0.941176\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	0.277605	+	1.70181i	0.277605	+	1.70181i
$707$		0			0
$708$		0			0
$709$	−0.941347	+	1.44467i	−0.941347	+	1.44467i	−0.0461835	+	0.998933i	$0.514706\pi$
$709$	−0.941347	+	1.44467i	−0.941347	+	1.44467i	−0.895163	+	0.445738i	$0.852941\pi$
$710$		0			0
$711$		0			0
$712$	0.716747	+	1.09998i	0.716747	+	1.09998i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.183750	−	0.982973i	$-0.441176\pi$
$719$		0			0		−0.183750	+	0.982973i	$0.558824\pi$
$720$	0.228951	−	0.973438i	0.228951	−	0.973438i
$721$		0			0
$722$	1.00000			1.00000
$723$		0			0
$724$	1.89516	+	0.445738i	1.89516	+	0.445738i
$725$	−0.188057	−	0.261368i	−0.188057	−	0.261368i
$726$		0			0
$727$		0			0		−0.251374	−	0.967890i	$-0.580882\pi$
$727$		0			0		0.251374	+	0.967890i	$0.419118\pi$
$728$		0			0
$729$	−0.403921	+	0.914794i	−0.403921	+	0.914794i
$730$	−0.227957	−	0.156154i	−0.227957	−	0.156154i
$731$		0			0
$732$		0			0
$733$	0.509130	−	0.965891i	0.509130	−	0.965891i	−0.486604	−	0.873622i	$-0.661765\pi$
$733$	0.509130	−	0.965891i	0.509130	−	0.965891i	0.995734	−	0.0922684i	$-0.0294118\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	−0.769334	+	1.63885i	−0.769334	+	1.63885i
$739$		0			0		−0.620906	−	0.783885i	$-0.713235\pi$
$739$		0			0		0.620906	+	0.783885i	$0.286765\pi$
$740$	1.47993	+	0.421076i	1.47993	+	0.421076i
$741$		0			0
$742$		0			0
$743$		0			0		0.997600	−	0.0692444i	$-0.0220588\pi$
$743$		0			0		−0.997600	+	0.0692444i	$0.977941\pi$
$744$		0			0
$745$	−0.600853	+	1.66411i	−0.600853	+	1.66411i
$746$	0.363975	−	0.0507723i	0.363975	−	0.0507723i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.206405	−	0.978467i	$-0.566176\pi$
$751$		0			0		0.206405	+	0.978467i	$0.433824\pi$
$752$		0			0
$753$		0			0
$754$	0.0849165	+	0.102261i	0.0849165	+	0.102261i
$755$		0			0
$756$		0			0
$757$	−0.0254949	−	0.182767i	−0.0254949	−	0.182767i	0.973438	−	0.228951i	$-0.0735294\pi$
$757$	−0.0254949	−	0.182767i	−0.0254949	−	0.182767i	−0.998933	+	0.0461835i	$0.985294\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.0127611	−	0.0914812i	−0.0127611	−	0.0914812i	0.982973	−	0.183750i	$-0.0588235\pi$
$761$	−0.0127611	−	0.0914812i	−0.0127611	−	0.0914812i	−0.995734	+	0.0922684i	$0.970588\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.621731	+	0.748723i	0.621731	+	0.748723i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	0.664589	+	1.84063i	0.664589	+	1.84063i	0.526432	+	0.850217i	$0.323529\pi$
$769$	0.664589	+	1.84063i	0.664589	+	1.84063i	0.138156	+	0.990410i	$0.455882\pi$
$770$		0			0
$771$		0			0
$772$	1.22788	−	1.01962i	1.22788	−	1.01962i
$773$	0.0293534	−	0.0875787i	0.0293534	−	0.0875787i	−0.932472	−	0.361242i	$-0.882353\pi$
$773$	0.0293534	−	0.0875787i	0.0293534	−	0.0875787i	0.961826	+	0.273663i	$0.0882353\pi$
$774$		0			0
$775$		0			0
$776$	0.763530	−	0.0529974i	0.763530	−	0.0529974i
$777$		0			0
$778$	1.84706	−	0.715555i	1.84706	−	0.715555i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.739009	−	0.673696i	−0.739009	−	0.673696i
$785$	−0.0136650	−	0.591454i	−0.0136650	−	0.591454i
$786$		0			0
$787$		0			0		−0.506653	−	0.862150i	$-0.669118\pi$
$787$		0			0		0.506653	+	0.862150i	$0.330882\pi$
$788$	−1.47701	+	1.01178i	−1.47701	+	1.01178i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	0.205966	+	0.215708i	0.205966	+	0.215708i
$794$	0.804396	+	1.82178i	0.804396	+	1.82178i
$795$		0			0
$796$		0			0
$797$	−0.271585	+	1.45285i	−0.271585	+	1.45285i	0.526432	+	0.850217i	$0.323529\pi$
$797$	−0.271585	+	1.45285i	−0.271585	+	1.45285i	−0.798017	+	0.602635i	$0.794118\pi$
$798$		0			0
$799$		0			0
$800$	−0.895163	−	0.445738i	−0.895163	−	0.445738i
$801$	−1.29577	+	0.211370i	−1.29577	+	0.211370i
$802$	1.03332	−	0.544672i	1.03332	−	0.544672i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	0.845263	−	0.283304i	0.845263	−	0.283304i
$809$	−0.838799	−	0.136828i	−0.838799	−	0.136828i	−0.273663	−	0.961826i	$-0.588235\pi$
$809$	−0.838799	−	0.136828i	−0.838799	−	0.136828i	−0.565136	+	0.824997i	$0.691176\pi$
$810$	0.798017	+	0.602635i	0.798017	+	0.602635i
$811$		0			0		−0.824997	−	0.565136i	$-0.808824\pi$
$811$		0			0		0.824997	+	0.565136i	$0.191176\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−1.11159	−	0.761460i	−1.11159	−	0.761460i
$819$		0			0
$820$	1.41918	+	1.12411i	1.41918	+	1.12411i
$821$		−	1.13027i		−	1.13027i	−0.824997	−	0.565136i	$-0.808824\pi$
$821$		−	1.13027i		−	1.13027i	0.824997	−	0.565136i	$-0.191176\pi$
$822$		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		0.955248	−	0.295806i	$-0.0955882\pi$
$827$		0			0		−0.955248	+	0.295806i	$0.904412\pi$
$828$		0			0
$829$	0.184956	+	0.786384i	0.184956	+	0.786384i	0.982973	+	0.183750i	$0.0588235\pi$
$829$	0.184956	+	0.786384i	0.184956	+	0.786384i	−0.798017	+	0.602635i	$0.794118\pi$
$830$		0			0
$831$		0			0
$832$	0.381387	+	0.157976i	0.381387	+	0.157976i
$833$	0.956638	−	0.178827i	0.956638	−	0.178827i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.486604	−	0.873622i	$-0.661765\pi$
$839$		0			0		0.486604	+	0.873622i	$0.338235\pi$
$840$		0			0
$841$	−0.895365	−	0.0413952i	−0.895365	−	0.0413952i
$842$	−0.0645767	−	0.122511i	−0.0645767	−	0.122511i
$843$		0			0
$844$		0			0
$845$	0.586607	−	0.586607i	0.586607	−	0.586607i
$846$		0			0
$847$		0			0
$848$	−0.0159599	+	0.229933i	−0.0159599	+	0.229933i
$849$		0			0
$850$	0.871181	−	0.433797i	0.871181	−	0.433797i
$851$		0			0
$852$		0			0
$853$	0.0588498	+	0.125363i	0.0588498	+	0.125363i	0.932472	−	0.361242i	$-0.117647\pi$
$853$	0.0588498	+	0.125363i	0.0588498	+	0.125363i	−0.873622	+	0.486604i	$0.838235\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.00706	+	0.591813i	−1.00706	+	0.591813i	−0.914794	−	0.403921i	$-0.867647\pi$
$857$	−1.00706	+	0.591813i	−1.00706	+	0.591813i	−0.0922684	+	0.995734i	$0.529412\pi$
$858$		0			0
$859$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$859$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$863$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$864$		0			0
$865$	1.58561	−	0.614268i	1.58561	−	0.614268i
$866$	1.73474	+	0.765964i	1.73474	+	0.765964i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.406040	−	0.488975i	−0.406040	−	0.488975i
$873$	−0.259924	+	0.719879i	−0.259924	+	0.719879i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.572616	−	1.84915i	0.572616	−	1.84915i	0.0461835	−	0.998933i	$-0.485294\pi$
$877$	0.572616	−	1.84915i	0.572616	−	1.84915i	0.526432	−	0.850217i	$-0.323529\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.890705	−	1.17948i	−0.890705	−	1.17948i	−0.982973	−	0.183750i	$-0.941176\pi$
$881$	−0.890705	−	1.17948i	−0.890705	−	1.17948i	0.0922684	−	0.995734i	$-0.470588\pi$
$882$	0.914794	−	0.403921i	0.914794	−	0.403921i
$883$		0			0		−0.798017	−	0.602635i	$-0.794118\pi$
$883$		0			0		0.798017	+	0.602635i	$0.205882\pi$
$884$	−0.346369	+	0.203548i	−0.346369	+	0.203548i
$885$		0			0
$886$		0			0
$887$		0			0		0.990410	−	0.138156i	$-0.0441176\pi$
$887$		0			0		−0.990410	+	0.138156i	$0.955882\pi$
$888$		0			0
$889$		0			0
$890$	−0.0909104	+	1.30974i	−0.0909104	+	1.30974i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.275947	+	0.365413i	−0.275947	+	0.365413i
$899$		0			0
$900$	0.769334	−	0.638847i	0.769334	−	0.638847i
$901$	−0.169214	−	0.147248i	−0.169214	−	0.147248i
$902$		0			0
$903$		0			0
$904$	−0.444745	+	0.234429i	−0.444745	+	0.234429i
$905$	1.24376	+	1.49780i	1.24376	+	1.49780i
$906$		0			0
$907$		0			0		0.690585	−	0.723251i	$-0.257353\pi$
$907$		0			0		−0.690585	+	0.723251i	$0.742647\pi$
$908$		0			0
$909$	−0.0822551	+	0.887674i	−0.0822551	+	0.887674i
$910$		0			0
$911$		0			0		0.955248	−	0.295806i	$-0.0955882\pi$
$911$		0			0		−0.955248	+	0.295806i	$0.904412\pi$
$912$		0			0
$913$		0			0
$914$	1.61955	+	1.16528i	1.61955	+	1.16528i
$915$		0			0
$916$	−0.614838	−	0.288627i	−0.614838	−	0.288627i
$917$		0			0
$918$		0			0
$919$		0			0		0.837831	−	0.545930i	$-0.183824\pi$
$919$		0			0		−0.837831	+	0.545930i	$0.816176\pi$
$920$		0			0
$921$		0			0
$922$			1.20527i			1.20527i
$923$		0			0
$924$		0			0
$925$	0.927255	+	1.22788i	0.927255	+	1.22788i
$926$		0			0
$927$		0			0
$928$	0.291473	−	0.136828i	0.291473	−	0.136828i
$929$	1.56446	−	0.524354i	1.56446	−	0.524354i	0.602635	−	0.798017i	$-0.294118\pi$
$929$	1.56446	−	0.524354i	1.56446	−	0.524354i	0.961826	+	0.273663i	$0.0882353\pi$
$930$		0			0
$931$		0			0
$932$	−1.04043	+	0.677943i	−1.04043	+	0.677943i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−0.298565	+	0.285081i	−0.298565	+	0.285081i
$937$	−0.919806	−	0.512328i	−0.919806	−	0.512328i	−0.0461835	−	0.998933i	$-0.514706\pi$
$937$	−0.919806	−	0.512328i	−0.919806	−	0.512328i	−0.873622	+	0.486604i	$0.838235\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.29123	−	1.17711i	1.29123	−	1.17711i	0.317791	−	0.948161i	$-0.397059\pi$
$941$	1.29123	−	1.17711i	1.29123	−	1.17711i	0.973438	−	0.228951i	$-0.0735294\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.783885	−	0.620906i	$-0.786765\pi$
$947$		0			0		0.783885	+	0.620906i	$0.213235\pi$
$948$		0			0
$949$	0.0436507	+	0.105382i	0.0436507	+	0.105382i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.0215409	−	0.932343i	−0.0215409	−	0.932343i	−0.895163	−	0.445738i	$-0.852941\pi$
$953$	−0.0215409	−	0.932343i	−0.0215409	−	0.932343i	0.873622	−	0.486604i	$-0.161765\pi$
$954$	−0.203895	−	0.107475i	−0.203895	−	0.107475i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.769334	+	0.638847i	0.769334	+	0.638847i
$962$	−0.416960	−	0.479161i	−0.416960	−	0.479161i
$963$		0			0
$964$	−0.472501	+	0.896401i	−0.472501	+	0.896401i
$965$	1.59433	−	0.0737104i	1.59433	−	0.0737104i
$966$		0			0
$967$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$967$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$968$	0.602635	+	0.798017i	0.602635	+	0.798017i
$969$		0			0
$970$	0.641248	+	0.417837i	0.641248	+	0.417837i
$971$		0			0		0.993337	−	0.115243i	$-0.0367647\pi$
$971$		0			0		−0.993337	+	0.115243i	$0.963235\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.631178	−	0.351564i	0.631178	−	0.351564i
$977$	1.05174	+	0.0486249i	1.05174	+	0.0486249i	0.565136	−	0.824997i	$-0.308824\pi$
$977$	1.05174	+	0.0486249i	1.05174	+	0.0486249i	0.486604	+	0.873622i	$0.338235\pi$
$978$		0			0
$979$		0			0
$980$	−0.183750	−	0.982973i	−0.183750	−	0.982973i
$981$	0.611320	−	0.173936i	0.611320	−	0.173936i
$982$		0			0
$983$		0			0		−0.206405	−	0.978467i	$-0.566176\pi$
$983$		0			0		0.206405	+	0.978467i	$0.433824\pi$
$984$		0			0
$985$	−1.78842	−	0.0826835i	−1.78842	−	0.0826835i
$986$	−0.0646802	+	0.306617i	−0.0646802	+	0.306617i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.948161	−	0.317791i	$-0.897059\pi$
$991$		0			0		0.948161	+	0.317791i	$0.102941\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	0.546742	−	0.0252774i	0.546742	−	0.0252774i	0.228951	−	0.973438i	$-0.426471\pi$
$997$	0.546742	−	0.0252774i	0.546742	−	0.0252774i	0.317791	+	0.948161i	$0.397059\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2740.1.bw.a.1343.1	yes	64
4.3	odd	2	CM	2740.1.bw.a.1343.1	yes	64
5.2	odd	4		2740.1.cd.a.247.1	yes	64
20.7	even	4		2740.1.cd.a.247.1	yes	64
137.71	odd	136		2740.1.cd.a.2263.1	yes	64
548.71	even	136		2740.1.cd.a.2263.1	yes	64
685.482	even	136	inner	2740.1.bw.a.1167.1	✓	64
2740.1167	odd	136	inner	2740.1.bw.a.1167.1	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2740.1.bw.a.1167.1	✓	64	685.482	even	136	inner
2740.1.bw.a.1167.1	✓	64	2740.1167	odd	136	inner
2740.1.bw.a.1343.1	yes	64	1.1	even	1	trivial
2740.1.bw.a.1343.1	yes	64	4.3	odd	2	CM
2740.1.cd.a.247.1	yes	64	5.2	odd	4
2740.1.cd.a.247.1	yes	64	20.7	even	4
2740.1.cd.a.2263.1	yes	64	137.71	odd	136
2740.1.cd.a.2263.1	yes	64	548.71	even	136

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.bw (of order \(136\), degree \(64\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.995734 + 0.0922684i) q^{2} +(0.982973 - 0.183750i) q^{4} +(0.895163 + 0.445738i) q^{5} +(-0.961826 + 0.273663i) q^{8} +(0.138156 - 0.990410i) q^{9} +O(q^{10})\)	\(q+(-0.995734 + 0.0922684i) q^{2} +(0.982973 - 0.183750i) q^{4} +(0.895163 + 0.445738i) q^{5} +(-0.961826 + 0.273663i) q^{8} +(0.138156 - 0.990410i) q^{9} +(-0.932472 - 0.361242i) q^{10} +(0.241098 + 0.335088i) q^{13} +(0.932472 - 0.361242i) q^{16} +(-0.266331 + 0.936057i) q^{17} +(-0.0461835 + 0.998933i) q^{18} +(0.961826 + 0.273663i) q^{20} +(0.602635 + 0.798017i) q^{25} +(-0.270988 - 0.311413i) q^{26} +(-0.321906 - 0.00743733i) q^{29} +(-0.895163 + 0.445738i) q^{32} +(0.178827 - 0.956638i) q^{34} +(-0.0461835 - 0.998933i) q^{36} +1.53867 q^{37} +(-0.982973 - 0.183750i) q^{40} +(1.67263 + 0.692825i) q^{41} +(0.565136 - 0.824997i) q^{45} +(-0.445738 - 0.895163i) q^{49} +(-0.673696 - 0.739009i) q^{50} +(0.298565 + 0.285081i) q^{52} +(-0.0979435 + 0.208641i) q^{53} +(0.321219 - 0.0222961i) q^{58} +(0.715555 - 0.0998157i) q^{61} +(0.850217 - 0.526432i) q^{64} +(0.0664607 + 0.407425i) q^{65} +(-0.0897964 + 0.969057i) q^{68} +(0.138156 + 0.990410i) q^{72} +(0.268973 + 0.0632619i) q^{73} +(-1.53210 + 0.141970i) q^{74} +(0.995734 + 0.0922684i) q^{80} +(-0.961826 - 0.273663i) q^{81} +(-1.72942 - 0.535539i) q^{82} +(-0.655647 + 0.719210i) q^{85} +(-0.388362 - 1.25414i) q^{89} +(-0.486604 + 0.873622i) q^{90} +(-0.748886 - 0.157976i) q^{97} +(0.526432 + 0.850217i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{4}+O(q^{10}) \) 64 * q + 4 * q^4	\( 64 q + 4 q^{4} + 4 q^{10} - 4 q^{16} + 4 q^{25} + 4 q^{26} - 4 q^{40} + 4 q^{49} + 4 q^{53} - 4 q^{58} + 4 q^{64} + 4 q^{65} + 4 q^{73} + 4 q^{82}+O(q^{100}) \) 64 * q + 4 * q^4 + 4 * q^10 - 4 * q^16 + 4 * q^25 + 4 * q^26 - 4 * q^40 + 4 * q^49 + 4 * q^53 - 4 * q^58 + 4 * q^64 + 4 * q^65 + 4 * q^73 + 4 * q^82

Introduction

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