LMFDB - Embedded newform 2740.1.cd.a.1187.1

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			1187.1
Root			$0.873622 + 0.486604i$ of defining polynomial
Character	$\chi$	$=$	2740.1187
Dual form			2740.1.cd.a.2463.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.850217 + 0.526432i) q^{2} +(0.445738 + 0.895163i) q^{4} +(-0.638847 - 0.769334i) q^{5} +(-0.0922684 + 0.995734i) q^{8} +(0.0461835 + 0.998933i) q^{9} +O(q^{10})$	\(q+(0.850217 + 0.526432i) q^{2} +(0.445738 + 0.895163i) q^{4} +(-0.638847 - 0.769334i) q^{5} +(-0.0922684 + 0.995734i) q^{8} +(0.0461835 + 0.998933i) q^{9} +(-0.138156 - 0.990410i) q^{10} +(-0.135507 - 0.0285848i) q^{13} +(-0.602635 + 0.798017i) q^{16} +(1.53210 - 0.141970i) q^{17} +(-0.486604 + 0.873622i) q^{18} +(0.403921 - 0.914794i) q^{20} +(-0.183750 + 0.982973i) q^{25} +(-0.100162 - 0.0956383i) q^{26} +(0.848980 + 1.44467i) q^{29} +(-0.932472 + 0.361242i) q^{32} +(1.37736 + 0.685843i) q^{34} +(-0.873622 + 0.486604i) q^{36} +1.94688i q^{37} +(0.824997 - 0.565136i) q^{40} +(0.475221 - 1.14729i) q^{41} +(0.739009 - 0.673696i) q^{45} +(0.932472 - 0.361242i) q^{49} +(-0.673696 + 0.739009i) q^{50} +(-0.0348125 - 0.134042i) q^{52} +(-1.09854 - 1.38689i) q^{53} +(-0.0387043 + 1.67521i) q^{58} +(-1.59433 - 0.0737104i) q^{61} +(-0.982973 - 0.183750i) q^{64} +(0.0645767 + 0.122511i) q^{65} +(0.810004 + 1.30820i) q^{68} +(-0.998933 - 0.0461835i) q^{72} +(0.0762025 - 0.0521999i) q^{73} +(-1.02490 + 1.65527i) q^{74} +(0.998933 - 0.0461835i) q^{80} +(-0.995734 + 0.0922684i) q^{81} +(1.00801 - 0.725270i) q^{82} +(-1.08800 - 1.08800i) q^{85} +(1.17416 + 0.844817i) q^{89} +(0.982973 - 0.183750i) q^{90} +(-0.127947 - 1.84332i) q^{97} +(0.982973 + 0.183750i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2740\mathbb{Z}\right)^\times$.

$n$	$1097$	$1371$	$1921$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{67}{136}\right)$

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 $

$2$	0.850217	+	0.526432i	0.850217	+	0.526432i
$2$	0.850217	+	0.526432i	0.850217	+	0.526432i
$3$		0			0		−0.723251	−	0.690585i	$-0.757353\pi$
$3$		0			0		0.723251	+	0.690585i	$0.242647\pi$
$4$	0.445738	+	0.895163i	0.445738	+	0.895163i
$5$	−0.638847	−	0.769334i	−0.638847	−	0.769334i
$5$	−0.638847	−	0.769334i	−0.638847	−	0.769334i
$6$		0			0
$7$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$7$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$8$	−0.0922684	+	0.995734i	−0.0922684	+	0.995734i
$9$	0.0461835	+	0.998933i	0.0461835	+	0.998933i
$10$	−0.138156	−	0.990410i	−0.138156	−	0.990410i
$11$		0			0		−0.948161	−	0.317791i	$-0.897059\pi$
$11$		0			0		0.948161	+	0.317791i	$0.102941\pi$
$12$		0			0
$13$	−0.135507	−	0.0285848i	−0.135507	−	0.0285848i	0.138156	−	0.990410i	$-0.455882\pi$
$13$	−0.135507	−	0.0285848i	−0.135507	−	0.0285848i	−0.273663	+	0.961826i	$0.588235\pi$
$14$		0			0
$15$		0			0
$16$	−0.602635	+	0.798017i	−0.602635	+	0.798017i
$17$	1.53210	−	0.141970i	1.53210	−	0.141970i	0.707107	−	0.707107i	$-0.250000\pi$
$17$	1.53210	−	0.141970i	1.53210	−	0.141970i	0.824997	+	0.565136i	$0.191176\pi$
$18$	−0.486604	+	0.873622i	−0.486604	+	0.873622i
$19$		0			0		−0.873622	−	0.486604i	$-0.838235\pi$
$19$		0			0		0.873622	+	0.486604i	$0.161765\pi$
$20$	0.403921	−	0.914794i	0.403921	−	0.914794i
$21$		0			0
$22$		0			0
$23$		0			0		−0.506653	−	0.862150i	$-0.669118\pi$
$23$		0			0		0.506653	+	0.862150i	$0.330882\pi$
$24$		0			0
$25$	−0.183750	+	0.982973i	−0.183750	+	0.982973i
$26$	−0.100162	−	0.0956383i	−0.100162	−	0.0956383i
$27$		0			0
$28$		0			0
$29$	0.848980	+	1.44467i	0.848980	+	1.44467i	0.895163	+	0.445738i	$0.147059\pi$
$29$	0.848980	+	1.44467i	0.848980	+	1.44467i	−0.0461835	+	0.998933i	$0.514706\pi$
$30$		0			0
$31$		0			0		0.993337	−	0.115243i	$-0.0367647\pi$
$31$		0			0		−0.993337	+	0.115243i	$0.963235\pi$
$32$	−0.932472	+	0.361242i	−0.932472	+	0.361242i
$33$		0			0
$34$	1.37736	+	0.685843i	1.37736	+	0.685843i
$35$		0			0
$36$	−0.873622	+	0.486604i	−0.873622	+	0.486604i
$37$			1.94688i			1.94688i	0.228951	+	0.973438i	$0.426471\pi$
$37$			1.94688i			1.94688i	−0.228951	+	0.973438i	$0.573529\pi$
$38$		0			0
$39$		0			0
$40$	0.824997	−	0.565136i	0.824997	−	0.565136i
$41$	0.475221	−	1.14729i	0.475221	−	1.14729i	−0.486604	−	0.873622i	$-0.661765\pi$
$41$	0.475221	−	1.14729i	0.475221	−	1.14729i	0.961826	−	0.273663i	$-0.0882353\pi$
$42$		0			0
$43$		0			0		0.115243	−	0.993337i	$-0.463235\pi$
$43$		0			0		−0.115243	+	0.993337i	$0.536765\pi$
$44$		0			0
$45$	0.739009	−	0.673696i	0.739009	−	0.673696i
$46$		0			0
$47$		0			0		0.339607	−	0.940567i	$-0.389706\pi$
$47$		0			0		−0.339607	+	0.940567i	$0.610294\pi$
$48$		0			0
$49$	0.932472	−	0.361242i	0.932472	−	0.361242i
$50$	−0.673696	+	0.739009i	−0.673696	+	0.739009i
$51$		0			0
$52$	−0.0348125	−	0.134042i	−0.0348125	−	0.134042i
$53$	−1.09854	−	1.38689i	−1.09854	−	1.38689i	−0.914794	−	0.403921i	$-0.867647\pi$
$53$	−1.09854	−	1.38689i	−1.09854	−	1.38689i	−0.183750	−	0.982973i	$-0.558824\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−0.0387043	+	1.67521i	−0.0387043	+	1.67521i
$59$		0			0		0.673696	−	0.739009i	$-0.264706\pi$
$59$		0			0		−0.673696	+	0.739009i	$0.735294\pi$
$60$		0			0
$61$	−1.59433	−	0.0737104i	−1.59433	−	0.0737104i	−0.769334	−	0.638847i	$-0.779412\pi$
$61$	−1.59433	−	0.0737104i	−1.59433	−	0.0737104i	−0.824997	+	0.565136i	$0.808824\pi$
$62$		0			0
$63$		0			0
$64$	−0.982973	−	0.183750i	−0.982973	−	0.183750i
$65$	0.0645767	+	0.122511i	0.0645767	+	0.122511i
$66$		0			0
$67$		0			0		−0.545930	−	0.837831i	$-0.683824\pi$
$67$		0			0		0.545930	+	0.837831i	$0.316176\pi$
$68$	0.810004	+	1.30820i	0.810004	+	1.30820i
$69$		0			0
$70$		0			0
$71$		0			0		−0.997600	−	0.0692444i	$-0.977941\pi$
$71$		0			0		0.997600	+	0.0692444i	$0.0220588\pi$
$72$	−0.998933	−	0.0461835i	−0.998933	−	0.0461835i
$73$	0.0762025	−	0.0521999i	0.0762025	−	0.0521999i	−0.526432	−	0.850217i	$-0.676471\pi$
$73$	0.0762025	−	0.0521999i	0.0762025	−	0.0521999i	0.602635	+	0.798017i	$0.294118\pi$
$74$	−1.02490	+	1.65527i	−1.02490	+	1.65527i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.723251	−	0.690585i	$-0.242647\pi$
$79$		0			0		−0.723251	+	0.690585i	$0.757353\pi$
$80$	0.998933	−	0.0461835i	0.998933	−	0.0461835i
$81$	−0.995734	+	0.0922684i	−0.995734	+	0.0922684i
$82$	1.00801	−	0.725270i	1.00801	−	0.725270i
$83$		0			0		0.466296	−	0.884629i	$-0.345588\pi$
$83$		0			0		−0.466296	+	0.884629i	$0.654412\pi$
$84$		0			0
$85$	−1.08800	−	1.08800i	−1.08800	−	1.08800i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.17416	+	0.844817i	1.17416	+	0.844817i	0.990410	−	0.138156i	$-0.0441176\pi$
$89$	1.17416	+	0.844817i	1.17416	+	0.844817i	0.183750	+	0.982973i	$0.441176\pi$
$90$	0.982973	−	0.183750i	0.982973	−	0.183750i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−0.127947	−	1.84332i	−0.127947	−	1.84332i	−0.445738	−	0.895163i	$-0.647059\pi$
$97$	−0.127947	−	1.84332i	−0.127947	−	1.84332i	0.317791	−	0.948161i	$-0.397059\pi$
$98$	0.982973	+	0.183750i	0.982973	+	0.183750i
$99$		0			0
$100$	−0.961826	+	0.273663i	−0.961826	+	0.273663i
$101$	0.907490	+	1.62926i	0.907490	+	1.62926i	0.769334	+	0.638847i	$0.220588\pi$
$101$	0.907490	+	1.62926i	0.907490	+	1.62926i	0.138156	+	0.990410i	$0.455882\pi$
$102$		0			0
$103$		0			0		0.948161	−	0.317791i	$-0.102941\pi$
$103$		0			0		−0.948161	+	0.317791i	$0.897059\pi$
$104$	0.0409658	−	0.132291i	0.0409658	−	0.132291i
$105$		0			0
$106$	−0.203895	−	1.75747i	−0.203895	−	1.75747i
$107$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$107$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$108$		0			0
$109$	0.252769	−	1.81204i	0.252769	−	1.81204i	−0.273663	−	0.961826i	$-0.588235\pi$
$109$	0.252769	−	1.81204i	0.252769	−	1.81204i	0.526432	−	0.850217i	$-0.323529\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.125363	−	1.80609i	0.125363	−	1.80609i	−0.361242	−	0.932472i	$-0.617647\pi$
$113$	0.125363	−	1.80609i	0.125363	−	1.80609i	0.486604	−	0.873622i	$-0.338235\pi$
$114$		0			0
$115$		0			0
$116$	−0.914794	+	1.40392i	−0.914794	+	1.40392i
$117$	0.0222961	−	0.136682i	0.0222961	−	0.136682i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.798017	+	0.602635i	0.798017	+	0.602635i
$122$	−1.31672	−	0.901977i	−1.31672	−	0.901977i
$123$		0			0
$124$		0			0
$125$	0.873622	−	0.486604i	0.873622	−	0.486604i
$126$		0			0
$127$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$127$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$128$	−0.739009	−	0.673696i	−0.739009	−	0.673696i
$129$		0			0
$130$	−0.00958957	+	0.138156i	−0.00958957	+	0.138156i
$131$		0			0		0.967890	−	0.251374i	$-0.0808824\pi$
$131$		0			0		−0.967890	+	0.251374i	$0.919118\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$			1.53867i			1.53867i
$137$	0.183750	−	0.982973i	0.183750	−	0.982973i
$137$	0.183750	−	0.982973i	0.183750	−	0.982973i
$138$		0			0
$139$		0			0		−0.228951	−	0.973438i	$-0.573529\pi$
$139$		0			0		0.228951	+	0.973438i	$0.426471\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.824997	−	0.565136i	−0.824997	−	0.565136i
$145$	0.569067	−	1.57607i	0.569067	−	1.57607i
$146$	0.0922684	−	0.00426582i	0.0922684	−	0.00426582i
$147$		0			0
$148$	−1.74277	+	0.867797i	−1.74277	+	0.867797i
$149$	−1.74618	+	0.920426i	−1.74618	+	0.920426i	−0.798017	+	0.602635i	$0.794118\pi$
$149$	−1.74618	+	0.920426i	−1.74618	+	0.920426i	−0.948161	+	0.317791i	$0.897059\pi$
$150$		0			0
$151$		0			0		0.361242	−	0.932472i	$-0.382353\pi$
$151$		0			0		−0.361242	+	0.932472i	$0.617647\pi$
$152$		0			0
$153$	0.212577	+	1.52391i	0.212577	+	1.52391i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−1.60227	−	0.261368i	−1.60227	−	0.261368i	−0.707107	−	0.707107i	$-0.750000\pi$
$157$	−1.60227	−	0.261368i	−1.60227	−	0.261368i	−0.895163	+	0.445738i	$0.852941\pi$
$158$		0			0
$159$		0			0
$160$	0.873622	+	0.486604i	0.873622	+	0.486604i
$161$		0			0
$162$	−0.895163	−	0.445738i	−0.895163	−	0.445738i
$163$		0			0		0.999733	−	0.0230979i	$-0.00735294\pi$
$163$		0			0		−0.999733	+	0.0230979i	$0.992647\pi$
$164$	1.23883	−	0.0859886i	1.23883	−	0.0859886i
$165$		0			0
$166$		0			0
$167$		0			0		0.361242	−	0.932472i	$-0.382353\pi$
$167$		0			0		−0.361242	+	0.932472i	$0.617647\pi$
$168$		0			0
$169$	−0.897249	−	0.396174i	−0.897249	−	0.396174i
$170$	−0.352279	−	1.49780i	−0.352279	−	1.49780i
$171$		0			0
$172$		0			0
$173$	0.538007	−	1.89090i	0.538007	−	1.89090i	0.0922684	−	0.995734i	$-0.470588\pi$
$173$	0.538007	−	1.89090i	0.538007	−	1.89090i	0.445738	−	0.895163i	$-0.352941\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	0.553552	+	1.33639i	0.553552	+	1.33639i
$179$		0			0		0.339607	−	0.940567i	$-0.389706\pi$
$179$		0			0		−0.339607	+	0.940567i	$0.610294\pi$
$180$	0.932472	+	0.361242i	0.932472	+	0.361242i
$181$	−1.11943	+	0.156154i	−1.11943	+	0.156154i	−0.673696	−	0.739009i	$-0.735294\pi$
$181$	−1.11943	+	0.156154i	−1.11943	+	0.156154i	−0.445738	+	0.895163i	$0.647059\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.49780	−	1.24376i	1.49780	−	1.24376i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.295806	−	0.955248i	$-0.595588\pi$
$191$		0			0		0.295806	+	0.955248i	$0.404412\pi$
$192$		0			0
$193$	−1.03659	−	0.860777i	−1.03659	−	0.860777i	−0.0461835	−	0.998933i	$-0.514706\pi$
$193$	−1.03659	−	0.860777i	−1.03659	−	0.860777i	−0.990410	+	0.138156i	$0.955882\pi$
$194$	0.861602	−	1.63458i	0.861602	−	1.63458i
$195$		0			0
$196$	0.739009	+	0.673696i	0.739009	+	0.673696i
$197$	−0.0998157	+	0.715555i	−0.0998157	+	0.715555i	0.873622	+	0.486604i	$0.161765\pi$
$197$	−0.0998157	+	0.715555i	−0.0998157	+	0.715555i	−0.973438	+	0.228951i	$0.926471\pi$
$198$		0			0
$199$		0			0		−0.339607	−	0.940567i	$-0.610294\pi$
$199$		0			0		0.339607	+	0.940567i	$0.389706\pi$
$200$	−0.961826	−	0.273663i	−0.961826	−	0.273663i
$201$		0			0
$202$	−0.0861296	+	1.86295i	−0.0861296	+	1.86295i
$203$		0			0
$204$		0			0
$205$	−1.18624	+	0.367336i	−1.18624	+	0.367336i
$206$		0			0
$207$		0			0
$208$	0.104472	−	0.0909104i	0.104472	−	0.0909104i
$209$		0			0
$210$		0			0
$211$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$211$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$212$	0.751834	−	1.60157i	0.751834	−	1.60157i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	1.16883	−	1.40756i	1.16883	−	1.40756i
$219$		0			0
$220$		0			0
$221$	−0.211668	−	0.0245569i	−0.211668	−	0.0245569i
$222$		0			0
$223$		0			0		−0.115243	−	0.993337i	$-0.536765\pi$
$223$		0			0		0.115243	+	0.993337i	$0.463235\pi$
$224$		0			0
$225$	−0.990410	−	0.138156i	−0.990410	−	0.138156i
$226$	1.05737	−	1.46958i	1.05737	−	1.46958i
$227$		0			0		−0.940567	−	0.339607i	$-0.889706\pi$
$227$		0			0		0.940567	+	0.339607i	$0.110294\pi$
$228$		0			0
$229$	−0.225523	+	0.0475735i	−0.225523	+	0.0475735i	−0.317791	−	0.948161i	$-0.602941\pi$
$229$	−0.225523	+	0.0475735i	−0.225523	+	0.0475735i	0.0922684	+	0.995734i	$0.470588\pi$
$230$		0			0
$231$		0			0
$232$	−1.51684	+	0.712061i	−1.51684	+	0.712061i
$233$	1.76507	−	0.731115i	1.76507	−	0.731115i	0.769334	−	0.638847i	$-0.220588\pi$
$233$	1.76507	−	0.731115i	1.76507	−	0.731115i	0.995734	−	0.0922684i	$-0.0294118\pi$
$234$	0.0909104	−	0.104472i	0.0909104	−	0.104472i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.424943	−	0.905220i	$-0.360294\pi$
$239$		0			0		−0.424943	+	0.905220i	$0.639706\pi$
$240$		0			0
$241$	−1.79695	−	0.556451i	−1.79695	−	0.556451i	−0.798017	−	0.602635i	$-0.794118\pi$
$241$	−1.79695	−	0.556451i	−1.79695	−	0.556451i	−0.998933	+	0.0461835i	$0.985294\pi$
$242$	0.361242	+	0.932472i	0.361242	+	0.932472i
$243$		0			0
$244$	−0.644672	−	1.46004i	−0.644672	−	1.46004i
$245$	−0.873622	−	0.486604i	−0.873622	−	0.486604i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	0.998933	+	0.0461835i	0.998933	+	0.0461835i
$251$		0			0		−0.967890	−	0.251374i	$-0.919118\pi$
$251$		0			0		0.967890	+	0.251374i	$0.0808824\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.273663	−	0.961826i	−0.273663	−	0.961826i
$257$	0.0586442	+	0.632872i	0.0586442	+	0.632872i	0.973438	+	0.228951i	$0.0735294\pi$
$257$	0.0586442	+	0.632872i	0.0586442	+	0.632872i	−0.914794	+	0.403921i	$0.867647\pi$
$258$		0			0
$259$		0			0
$260$	−0.0808832	+	0.112415i	−0.0808832	+	0.112415i
$261$	−1.40392	+	0.914794i	−1.40392	+	0.914794i
$262$		0			0
$263$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$263$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$264$		0			0
$265$	−0.365184	+	1.73116i	−0.365184	+	1.73116i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	0.838799	−	0.136828i	0.838799	−	0.136828i	0.273663	−	0.961826i	$-0.411765\pi$
$269$	0.838799	−	0.136828i	0.838799	−	0.136828i	0.565136	+	0.824997i	$0.308824\pi$
$270$		0			0
$271$		0			0		0.999733	−	0.0230979i	$-0.00735294\pi$
$271$		0			0		−0.999733	+	0.0230979i	$0.992647\pi$
$272$	−0.810004	+	1.30820i	−0.810004	+	1.30820i
$273$		0			0
$274$	0.673696	−	0.739009i	0.673696	−	0.739009i
$275$		0			0
$276$		0			0
$277$	0.528551	−	0.553552i	0.528551	−	0.553552i	−0.403921	−	0.914794i	$-0.632353\pi$
$277$	0.528551	−	0.553552i	0.528551	−	0.553552i	0.932472	+	0.361242i	$0.117647\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.258777	+	0.377767i	−0.258777	+	0.377767i	−0.932472	−	0.361242i	$-0.882353\pi$
$281$	−0.258777	+	0.377767i	−0.258777	+	0.377767i	0.673696	+	0.739009i	$0.264706\pi$
$282$		0			0
$283$		0			0		0.673696	−	0.739009i	$-0.264706\pi$
$283$		0			0		−0.673696	+	0.739009i	$0.735294\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.403921	−	0.914794i	−0.403921	−	0.914794i
$289$	1.34421	−	0.251277i	1.34421	−	0.251277i
$290$	1.31353	−	1.04043i	1.31353	−	1.04043i
$291$		0			0
$292$	0.0806938	+	0.0449462i	0.0806938	+	0.0449462i
$293$	−0.518953	−	1.82393i	−0.518953	−	1.82393i	−0.565136	−	0.824997i	$-0.691176\pi$
$293$	−0.518953	−	1.82393i	−0.518953	−	1.82393i	0.0461835	−	0.998933i	$-0.485294\pi$
$294$		0			0
$295$		0			0
$296$	−1.93857	−	0.179635i	−1.93857	−	0.179635i
$297$		0			0
$298$	−1.96917	−	0.136682i	−1.96917	−	0.136682i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.961826	+	1.27366i	0.961826	+	1.27366i
$306$	−0.621500	+	1.40756i	−0.621500	+	1.40756i
$307$		0			0		0.884629	−	0.466296i	$-0.154412\pi$
$307$		0			0		−0.884629	+	0.466296i	$0.845588\pi$
$308$		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
$313$	0.0507723	−	0.271608i	0.0507723	−	0.271608i	−0.948161	−	0.317791i	$-0.897059\pi$
$313$	0.0507723	−	0.271608i	0.0507723	−	0.271608i	0.998933	+	0.0461835i	$0.0147059\pi$
$314$	−1.22468	−	1.06571i	−1.22468	−	1.06571i
$315$		0			0
$316$		0			0
$317$	1.55732	+	0.180675i	1.55732	+	0.180675i	0.850217	−	0.526432i	$-0.176471\pi$
$317$	1.55732	+	0.180675i	1.55732	+	0.180675i	0.707107	+	0.707107i	$0.250000\pi$
$318$		0			0
$319$		0			0
$320$	0.486604	+	0.873622i	0.486604	+	0.873622i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.526432	−	0.850217i	−0.526432	−	0.850217i
$325$	0.0529974	−	0.127947i	0.0529974	−	0.127947i
$326$		0			0
$327$		0			0
$328$	1.09854	+	0.579052i	1.09854	+	0.579052i
$329$		0			0
$330$		0			0
$331$		0			0		−0.884629	−	0.466296i	$-0.845588\pi$
$331$		0			0		0.884629	+	0.466296i	$0.154412\pi$
$332$		0			0
$333$	−1.94480	+	0.0899135i	−1.94480	+	0.0899135i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.867797	−	0.204104i	0.867797	−	0.204104i	0.228951	−	0.973438i	$-0.426471\pi$
$337$	0.867797	−	0.204104i	0.867797	−	0.204104i	0.638847	+	0.769334i	$0.279412\pi$
$338$	−0.554298	−	0.809175i	−0.554298	−	0.809175i
$339$		0			0
$340$	0.488975	−	1.45890i	0.488975	−	1.45890i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	1.45285	−	1.32445i	1.45285	−	1.32445i
$347$		0			0		−0.565136	−	0.824997i	$-0.691176\pi$
$347$		0			0		0.565136	+	0.824997i	$0.308824\pi$
$348$		0			0
$349$	−0.877165	+	0.316715i	−0.877165	+	0.316715i	−0.739009	−	0.673696i	$-0.764706\pi$
$349$	−0.877165	+	0.316715i	−0.877165	+	0.316715i	−0.138156	+	0.990410i	$0.544118\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.679033	+	0.0156884i	0.679033	+	0.0156884i	0.361242	−	0.932472i	$-0.382353\pi$
$353$	0.679033	+	0.0156884i	0.679033	+	0.0156884i	0.317791	+	0.948161i	$0.397059\pi$
$354$		0			0
$355$		0			0
$356$	−0.232881	+	1.42763i	−0.232881	+	1.42763i
$357$		0			0
$358$		0			0
$359$		0			0		−0.862150	−	0.506653i	$-0.830882\pi$
$359$		0			0		0.862150	+	0.506653i	$0.169118\pi$
$360$	0.602635	+	0.798017i	0.602635	+	0.798017i
$361$	0.526432	+	0.850217i	0.526432	+	0.850217i
$362$	−1.03397	−	0.456541i	−1.03397	−	0.456541i
$363$		0			0
$364$		0			0
$365$	−0.0888409	−	0.0252774i	−0.0888409	−	0.0252774i
$366$		0			0
$367$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$367$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$368$		0			0
$369$	1.16801	+	0.421728i	1.16801	+	0.421728i
$370$	1.92821	−	0.268973i	1.92821	−	0.268973i
$371$		0			0
$372$		0			0
$373$	1.56407	−	0.871181i	1.56407	−	0.871181i	0.565136	−	0.824997i	$-0.308824\pi$
$373$	1.56407	−	0.871181i	1.56407	−	0.871181i	0.998933	−	0.0461835i	$-0.0147059\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.0737468	−	0.220030i	−0.0737468	−	0.220030i
$378$		0			0
$379$		0			0		0.403921	−	0.914794i	$-0.367647\pi$
$379$		0			0		−0.403921	+	0.914794i	$0.632353\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$383$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$384$		0			0
$385$		0			0
$386$	−0.428189	−	1.27754i	−0.428189	−	1.27754i
$387$		0			0
$388$	1.59305	−	0.936174i	1.59305	−	0.936174i
$389$	1.98934	+	0.184340i	1.98934	+	0.184340i	0.998933	+	0.0461835i	$0.0147059\pi$
$389$	1.98934	+	0.184340i	1.98934	+	0.184340i	0.990410	+	0.138156i	$0.0441176\pi$
$390$		0			0
$391$		0			0
$392$	0.273663	+	0.961826i	0.273663	+	0.961826i
$393$		0			0
$394$	−0.461556	+	0.555831i	−0.461556	+	0.555831i
$395$		0			0
$396$		0			0
$397$	0.425274	+	0.963154i	0.425274	+	0.963154i	0.990410	+	0.138156i	$0.0441176\pi$
$397$	0.425274	+	0.963154i	0.425274	+	0.963154i	−0.565136	+	0.824997i	$0.691176\pi$
$398$		0			0
$399$		0			0
$400$	−0.673696	−	0.739009i	−0.673696	−	0.739009i
$401$	−0.157976	−	0.381387i	−0.157976	−	0.381387i	0.824997	−	0.565136i	$-0.191176\pi$
$401$	−0.157976	−	0.381387i	−0.157976	−	0.381387i	−0.982973	+	0.183750i	$0.941176\pi$
$402$		0			0
$403$		0			0
$404$	−1.05395	+	1.53857i	−1.05395	+	1.53857i
$405$	0.707107	+	0.707107i	0.707107	+	0.707107i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−1.87256	+	0.440421i	−1.87256	+	0.440421i	−0.998933	−	0.0461835i	$-0.985294\pi$
$409$	−1.87256	+	0.440421i	−1.87256	+	0.440421i	−0.873622	+	0.486604i	$0.838235\pi$
$410$	−1.20194	−	0.312159i	−1.20194	−	0.312159i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	0.136682	−	0.0222961i	0.136682	−	0.0222961i
$417$		0			0
$418$		0			0
$419$		0			0		−0.638847	−	0.769334i	$-0.720588\pi$
$419$		0			0		0.638847	+	0.769334i	$0.279412\pi$
$420$		0			0
$421$	−0.0426793	+	0.0176784i	−0.0426793	+	0.0176784i	−0.403921	−	0.914794i	$-0.632353\pi$
$421$	−0.0426793	+	0.0176784i	−0.0426793	+	0.0176784i	0.361242	+	0.932472i	$0.382353\pi$
$422$		0			0
$423$		0			0
$424$	1.48234	−	0.965891i	1.48234	−	0.965891i
$425$	−0.141970	+	1.53210i	−0.141970	+	1.53210i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.811724	−	0.584041i	$-0.198529\pi$
$431$		0			0		−0.811724	+	0.584041i	$0.801471\pi$
$432$		0			0
$433$	−0.621500	+	0.516087i	−0.621500	+	0.516087i	−0.895163	−	0.445738i	$-0.852941\pi$
$433$	−0.621500	+	0.516087i	−0.621500	+	0.516087i	0.273663	+	0.961826i	$0.411765\pi$
$434$		0			0
$435$		0			0
$436$	1.73474	−	0.581427i	1.73474	−	0.581427i
$437$		0			0
$438$		0			0
$439$		0			0		−0.990410	−	0.138156i	$-0.955882\pi$
$439$		0			0		0.990410	+	0.138156i	$0.0441176\pi$
$440$		0			0
$441$	0.403921	+	0.914794i	0.403921	+	0.914794i
$442$	−0.167037	−	0.132308i	−0.167037	−	0.132308i
$443$		0			0		−0.361242	−	0.932472i	$-0.617647\pi$
$443$		0			0		0.361242	+	0.932472i	$0.382353\pi$
$444$		0			0
$445$	−0.100162	−	1.44303i	−0.100162	−	1.44303i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	1.58701	+	0.451543i	1.58701	+	0.451543i	0.948161	−	0.317791i	$-0.102941\pi$
$449$	1.58701	+	0.451543i	1.58701	+	0.451543i	0.638847	+	0.769334i	$0.279412\pi$
$450$	−0.769334	−	0.638847i	−0.769334	−	0.638847i
$451$		0			0
$452$	1.67263	−	0.692825i	1.67263	−	0.692825i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.44612	+	1.38080i	−1.44612	+	1.38080i	−0.707107	+	0.707107i	$0.750000\pi$
$457$	−1.44612	+	1.38080i	−1.44612	+	1.38080i	−0.739009	+	0.673696i	$0.764706\pi$
$458$	−0.216788	−	0.0782748i	−0.216788	−	0.0782748i
$459$		0			0
$460$		0			0
$461$	1.25664	−	0.778076i	1.25664	−	0.778076i	0.273663	−	0.961826i	$-0.411765\pi$
$461$	1.25664	−	0.778076i	1.25664	−	0.778076i	0.982973	+	0.183750i	$0.0588235\pi$
$462$		0			0
$463$		0			0		0.967890	−	0.251374i	$-0.0808824\pi$
$463$		0			0		−0.967890	+	0.251374i	$0.919118\pi$
$464$	−1.66450	−	0.193108i	−1.66450	−	0.193108i
$465$		0			0
$466$	1.88557	+	0.307582i	1.88557	+	0.307582i
$467$		0			0		0.638847	−	0.769334i	$-0.279412\pi$
$467$		0			0		−0.638847	+	0.769334i	$0.720588\pi$
$468$	0.132291	−	0.0409658i	0.132291	−	0.0409658i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.33468	−	1.16142i	1.33468	−	1.16142i
$478$		0			0
$479$		0			0		−0.973438	−	0.228951i	$-0.926471\pi$
$479$		0			0		0.973438	+	0.228951i	$0.0735294\pi$
$480$		0			0
$481$	0.0556510	−	0.263815i	0.0556510	−	0.263815i
$482$	−1.23486	−	1.41908i	−1.23486	−	1.41908i
$483$		0			0
$484$	−0.183750	+	0.982973i	−0.183750	+	0.982973i
$485$	−1.33639	+	1.27604i	−1.33639	+	1.27604i
$486$		0			0
$487$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$487$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$488$	0.220502	−	1.58073i	0.220502	−	1.58073i
$489$		0			0
$490$	−0.486604	−	0.873622i	−0.486604	−	0.873622i
$491$		0			0		0.466296	−	0.884629i	$-0.345588\pi$
$491$		0			0		−0.466296	+	0.884629i	$0.654412\pi$
$492$		0			0
$493$	1.50583	+	2.09286i	1.50583	+	2.09286i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		−0.361242	−	0.932472i	$-0.617647\pi$
$499$		0			0		0.361242	+	0.932472i	$0.382353\pi$
$500$	0.824997	+	0.565136i	0.824997	+	0.565136i
$501$		0			0
$502$		0			0
$503$		0			0		−0.837831	−	0.545930i	$-0.816176\pi$
$503$		0			0		0.837831	+	0.545930i	$0.183824\pi$
$504$		0			0
$505$	0.673696	−	1.73901i	0.673696	−	1.73901i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	1.40285	−	0.960977i	1.40285	−	0.960977i	0.403921	−	0.914794i	$-0.367647\pi$
$509$	1.40285	−	0.960977i	1.40285	−	0.960977i	0.998933	−	0.0461835i	$-0.0147059\pi$
$510$		0			0
$511$		0			0
$512$	0.273663	−	0.961826i	0.273663	−	0.961826i
$513$		0			0
$514$	−0.283304	+	0.568950i	−0.283304	+	0.568950i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−0.127947	+	0.0529974i	−0.127947	+	0.0529974i
$521$	−1.95224	+	0.135507i	−1.95224	+	0.135507i	−0.990410	−	0.138156i	$-0.955882\pi$
$521$	−1.95224	+	0.135507i	−1.95224	+	0.135507i	−0.961826	+	0.273663i	$0.911765\pi$
$522$	−1.67521	+	0.0387043i	−1.67521	+	0.0387043i
$523$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$523$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−0.486604	+	0.873622i	−0.486604	+	0.873622i
$530$	−1.22182	+	1.27962i	−1.22182	+	1.27962i
$531$		0			0
$532$		0			0
$533$	−0.0971905	+	0.141881i	−0.0971905	+	0.141881i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	0.785192	+	0.325237i	0.785192	+	0.325237i
$539$		0			0
$540$		0			0
$541$	0.451543	+	0.309314i	0.451543	+	0.309314i	0.769334	−	0.638847i	$-0.220588\pi$
$541$	0.451543	+	0.309314i	0.451543	+	0.309314i	−0.317791	+	0.948161i	$0.602941\pi$
$542$		0			0
$543$		0			0
$544$	−1.37736	+	0.685843i	−1.37736	+	0.685843i
$545$	−1.55555	+	0.963154i	−1.55555	+	0.963154i
$546$		0			0
$547$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$547$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$548$	0.961826	−	0.273663i	0.961826	−	0.273663i
$549$		−	1.59603i		−	1.59603i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	0.740791	−	0.192393i	0.740791	−	0.192393i
$555$		0			0
$556$		0			0
$557$	−1.47171	−	1.34164i	−1.47171	−	1.34164i	−0.798017	−	0.602635i	$-0.794118\pi$
$557$	−1.47171	−	1.34164i	−1.47171	−	1.34164i	−0.673696	−	0.739009i	$-0.735294\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−0.418885	+	0.184956i	−0.418885	+	0.184956i
$563$		0			0		−0.824997	−	0.565136i	$-0.808824\pi$
$563$		0			0		0.824997	+	0.565136i	$0.191176\pi$
$564$		0			0
$565$	−1.46958	+	1.05737i	−1.46958	+	1.05737i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−1.08459	+	1.66450i	−1.08459	+	1.66450i	−0.445738	+	0.895163i	$0.647059\pi$
$569$	−1.08459	+	1.66450i	−1.08459	+	1.66450i	−0.638847	+	0.769334i	$0.720588\pi$
$570$		0			0
$571$		0			0		0.251374	−	0.967890i	$-0.419118\pi$
$571$		0			0		−0.251374	+	0.967890i	$0.580882\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.138156	−	0.990410i	0.138156	−	0.990410i
$577$	0.311653	+	0.0809403i	0.311653	+	0.0809403i	0.403921	−	0.914794i	$-0.367647\pi$
$577$	0.311653	+	0.0809403i	0.311653	+	0.0809403i	−0.0922684	+	0.995734i	$0.529412\pi$
$578$	1.27515	+	0.493998i	1.27515	+	0.493998i
$579$		0			0
$580$	1.66450	−	0.193108i	1.66450	−	0.193108i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	0.0449462	+	0.0806938i	0.0449462	+	0.0806938i
$585$	−0.119398	+	0.0701658i	−0.119398	+	0.0701658i
$586$	0.518953	−	1.82393i	0.518953	−	1.82393i
$587$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$587$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−1.55364	−	1.17325i	−1.55364	−	1.17325i
$593$	−0.596079	+	0.914794i	−0.596079	+	0.914794i	0.403921	+	0.914794i	$0.367647\pi$
$593$	−0.596079	+	0.914794i	−0.596079	+	0.914794i	−1.00000			$\pi$
$594$		0			0
$595$		0			0
$596$	−1.60227	−	1.15285i	−1.60227	−	1.15285i
$597$		0			0
$598$		0			0
$599$		0			0		0.620906	−	0.783885i	$-0.286765\pi$
$599$		0			0		−0.620906	+	0.783885i	$0.713235\pi$
$600$		0			0
$601$	−0.230425	+	1.98614i	−0.230425	+	1.98614i	−0.0922684	+	0.995734i	$0.529412\pi$
$601$	−0.230425	+	1.98614i	−0.230425	+	1.98614i	−0.138156	+	0.990410i	$0.544118\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.0461835	−	0.998933i	−0.0461835	−	0.998933i
$606$		0			0
$607$		0			0		−0.0461835	−	0.998933i	$-0.514706\pi$
$607$		0			0		0.0461835	+	0.998933i	$0.485294\pi$
$608$		0			0
$609$		0			0
$610$	0.147263	+	1.58923i	0.147263	+	1.58923i
$611$		0			0
$612$	−1.26940	+	0.869557i	−1.26940	+	0.869557i
$613$	−1.74538	−	0.0806938i	−1.74538	−	0.0806938i	−0.850217	−	0.526432i	$-0.823529\pi$
$613$	−1.74538	−	0.0806938i	−1.74538	−	0.0806938i	−0.895163	+	0.445738i	$0.852941\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.0971461	+	0.156896i	0.0971461	+	0.156896i	0.895163	−	0.445738i	$-0.147059\pi$
$617$	0.0971461	+	0.156896i	0.0971461	+	0.156896i	−0.798017	+	0.602635i	$0.794118\pi$
$618$		0			0
$619$		0			0		0.0692444	−	0.997600i	$-0.477941\pi$
$619$		0			0		−0.0692444	+	0.997600i	$0.522059\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.932472	−	0.361242i	−0.932472	−	0.361242i
$626$	0.186151	−	0.204198i	0.186151	−	0.204198i
$627$		0			0
$628$	−0.480226	−	1.55080i	−0.480226	−	1.55080i
$629$	0.276399	+	2.98282i	0.276399	+	2.98282i
$630$		0			0
$631$		0			0		0.955248	−	0.295806i	$-0.0955882\pi$
$631$		0			0		−0.955248	+	0.295806i	$0.904412\pi$
$632$		0			0
$633$		0			0
$634$	1.22895	+	0.973438i	1.22895	+	0.973438i
$635$		0			0
$636$		0			0
$637$	−0.136682	+	0.0222961i	−0.136682	+	0.0222961i
$638$		0			0
$639$		0			0
$640$	−0.0461835	+	0.998933i	−0.0461835	+	0.998933i
$641$	0.176521	+	1.26544i	0.176521	+	1.26544i	0.850217	+	0.526432i	$0.176471\pi$
$641$	0.176521	+	1.26544i	0.176521	+	1.26544i	−0.673696	+	0.739009i	$0.735294\pi$
$642$		0			0
$643$		0			0		−0.424943	−	0.905220i	$-0.639706\pi$
$643$		0			0		0.424943	+	0.905220i	$0.360294\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.486604	−	0.873622i	$-0.661765\pi$
$647$		0			0		0.486604	+	0.873622i	$0.338235\pi$
$648$		−	1.00000i		−	1.00000i
$649$		0			0
$650$	0.112415	−	0.0808832i	0.112415	−	0.0808832i
$651$		0			0
$652$		0			0
$653$	−1.86295	+	0.721712i	−1.86295	+	0.721712i	−0.914794	+	0.403921i	$0.867647\pi$
$653$	−1.86295	+	0.721712i	−1.86295	+	0.721712i	−0.948161	+	0.317791i	$0.897059\pi$
$654$		0			0
$655$		0			0
$656$	0.629169	+	1.07063i	0.629169	+	1.07063i
$657$	0.0556635	+	0.0737104i	0.0556635	+	0.0737104i
$658$		0			0
$659$		0			0		−0.723251	−	0.690585i	$-0.757353\pi$
$659$		0			0		0.723251	+	0.690585i	$0.242647\pi$
$660$		0			0
$661$	0.823669	−	0.716747i	0.823669	−	0.716747i	−0.138156	−	0.990410i	$-0.544118\pi$
$661$	0.823669	−	0.716747i	0.823669	−	0.716747i	0.961826	+	0.273663i	$0.0882353\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−1.70083	−	0.947359i	−1.70083	−	0.947359i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.275866	−	0.890856i	0.275866	−	0.890856i	−0.707107	−	0.707107i	$-0.750000\pi$
$673$	0.275866	−	0.890856i	0.275866	−	0.890856i	0.982973	−	0.183750i	$-0.0588235\pi$
$674$	0.845263	+	0.283304i	0.845263	+	0.283304i
$675$		0			0
$676$	−0.0452977	−	0.979774i	−0.0452977	−	0.979774i
$677$	−0.156896	+	1.69318i	−0.156896	+	1.69318i	0.445738	+	0.895163i	$0.352941\pi$
$677$	−0.156896	+	1.69318i	−0.156896	+	1.69318i	−0.602635	+	0.798017i	$0.705882\pi$
$678$		0			0
$679$		0			0
$680$	1.18375	−	0.982973i	1.18375	−	0.982973i
$681$		0			0
$682$		0			0
$683$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$683$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$684$		0			0
$685$	−0.873622	+	0.486604i	−0.873622	+	0.486604i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.109216	+	0.219335i	0.109216	+	0.219335i
$690$		0			0
$691$		0			0		−0.251374	−	0.967890i	$-0.580882\pi$
$691$		0			0		0.251374	+	0.967890i	$0.419118\pi$
$692$	1.93247	−	0.361242i	1.93247	−	0.361242i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	0.565208	−	1.82523i	0.565208	−	1.82523i
$698$	−0.912510	−	0.192492i	−0.912510	−	0.192492i
$699$		0			0
$700$		0			0
$701$	−0.537235	+	0.711414i	−0.537235	+	0.711414i	−0.982973	−	0.183750i	$-0.941176\pi$
$701$	−0.537235	+	0.711414i	−0.537235	+	0.711414i	0.445738	+	0.895163i	$0.352941\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	0.569067	+	0.370803i	0.569067	+	0.370803i
$707$		0			0
$708$		0			0
$709$	0.512381	−	0.445868i	0.512381	−	0.445868i	−0.361242	−	0.932472i	$-0.617647\pi$
$709$	0.512381	−	0.445868i	0.512381	−	0.445868i	0.873622	+	0.486604i	$0.161765\pi$
$710$		0			0
$711$		0			0
$712$	−0.949551	+	1.09120i	−0.949551	+	1.09120i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$719$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$720$	0.0922684	+	0.995734i	0.0922684	+	0.995734i
$721$		0			0
$722$			1.00000i			1.00000i
$723$		0			0
$724$	−0.638758	−	0.932472i	−0.638758	−	0.932472i
$725$	−1.57607	+	0.569067i	−1.57607	+	0.569067i
$726$		0			0
$727$		0			0		−0.424943	−	0.905220i	$-0.639706\pi$
$727$		0			0		0.424943	+	0.905220i	$0.360294\pi$
$728$		0			0
$729$	−0.138156	−	0.990410i	−0.138156	−	0.990410i
$730$	−0.0622272	−	0.0682600i	−0.0622272	−	0.0682600i
$731$		0			0
$732$		0			0
$733$	1.48906	−	0.242902i	1.48906	−	0.242902i	0.638847	−	0.769334i	$-0.279412\pi$
$733$	1.48906	−	0.242902i	1.48906	−	0.242902i	0.850217	+	0.526432i	$0.176471\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	0.771049	+	0.973438i	0.771049	+	0.973438i
$739$		0			0		0.955248	−	0.295806i	$-0.0955882\pi$
$739$		0			0		−0.955248	+	0.295806i	$0.904412\pi$
$740$	1.78099	+	0.786384i	1.78099	+	0.786384i
$741$		0			0
$742$		0			0
$743$		0			0		0.0230979	−	0.999733i	$-0.492647\pi$
$743$		0			0		−0.0230979	+	0.999733i	$0.507353\pi$
$744$		0			0
$745$	1.82366	+	0.755383i	1.82366	+	0.755383i
$746$	1.78842	+	0.0826835i	1.78842	+	0.0826835i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.0692444	−	0.997600i	$-0.477941\pi$
$751$		0			0		−0.0692444	+	0.997600i	$0.522059\pi$
$752$		0			0
$753$		0			0
$754$	0.0531303	−	0.225896i	0.0531303	−	0.225896i
$755$		0			0
$756$		0			0
$757$	−1.69862	−	0.0785319i	−1.69862	−	0.0785319i	−0.824997	−	0.565136i	$-0.808824\pi$
$757$	−1.69862	−	0.0785319i	−1.69862	−	0.0785319i	−0.873622	+	0.486604i	$0.838235\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.0806938	−	1.74538i	0.0806938	−	1.74538i	−0.445738	−	0.895163i	$-0.647059\pi$
$761$	0.0806938	−	1.74538i	0.0806938	−	1.74538i	0.526432	−	0.850217i	$-0.323529\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	1.03659	−	1.13709i	1.03659	−	1.13709i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	0.229933	−	1.98191i	0.229933	−	1.98191i	0.0461835	−	0.998933i	$-0.485294\pi$
$769$	0.229933	−	1.98191i	0.229933	−	1.98191i	0.183750	−	0.982973i	$-0.441176\pi$
$770$		0			0
$771$		0			0
$772$	0.308486	−	1.31160i	0.308486	−	1.31160i
$773$	0.705749	−	1.59837i	0.705749	−	1.59837i	−0.0922684	−	0.995734i	$-0.529412\pi$
$773$	0.705749	−	1.59837i	0.705749	−	1.59837i	0.798017	−	0.602635i	$-0.205882\pi$
$774$		0			0
$775$		0			0
$776$	1.84727	+	0.0426793i	1.84727	+	0.0426793i
$777$		0			0
$778$	1.59433	+	1.20398i	1.59433	+	1.20398i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.273663	+	0.961826i	−0.273663	+	0.961826i
$785$	0.822526	+	1.39966i	0.822526	+	1.39966i
$786$		0			0
$787$		0			0		−0.339607	−	0.940567i	$-0.610294\pi$
$787$		0			0		0.339607	+	0.940567i	$0.389706\pi$
$788$	−0.685030	+	0.229599i	−0.685030	+	0.229599i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	0.213935	+	0.0555619i	0.213935	+	0.0555619i
$794$	−0.145460	+	1.04277i	−0.145460	+	1.04277i
$795$		0			0
$796$		0			0
$797$	−0.243964	+	0.489946i	−0.243964	+	0.489946i	−0.982973	−	0.183750i	$-0.941176\pi$
$797$	−0.243964	+	0.489946i	−0.243964	+	0.489946i	0.739009	+	0.673696i	$0.235294\pi$
$798$		0			0
$799$		0			0
$800$	−0.183750	−	0.982973i	−0.183750	−	0.982973i
$801$	−0.789689	+	1.21192i	−0.789689	+	1.21192i
$802$	0.0664607	−	0.407425i	0.0664607	−	0.407425i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−1.70604	+	0.753290i	−1.70604	+	0.753290i
$809$	0.855892	+	1.31353i	0.855892	+	1.31353i	0.948161	+	0.317791i	$0.102941\pi$
$809$	0.855892	+	1.31353i	0.855892	+	1.31353i	−0.0922684	+	0.995734i	$0.529412\pi$
$810$	0.228951	+	0.973438i	0.228951	+	0.973438i
$811$		0			0		0.317791	−	0.948161i	$-0.397059\pi$
$811$		0			0		−0.317791	+	0.948161i	$0.602941\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−1.82393	−	0.611320i	−1.82393	−	0.611320i
$819$		0			0
$820$	−0.857578	−	0.898142i	−0.857578	−	0.898142i
$821$		−	1.89632i		−	1.89632i	−0.317791	−	0.948161i	$-0.602941\pi$
$821$		−	1.89632i		−	1.89632i	0.317791	−	0.948161i	$-0.397059\pi$
$822$		0			0
$823$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$823$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.811724	−	0.584041i	$-0.801471\pi$
$827$		0			0		0.811724	+	0.584041i	$0.198529\pi$
$828$		0			0
$829$	−0.227957	−	0.156154i	−0.227957	−	0.156154i	0.445738	−	0.895163i	$-0.352941\pi$
$829$	−0.227957	−	0.156154i	−0.227957	−	0.156154i	−0.673696	+	0.739009i	$0.735294\pi$
$830$		0			0
$831$		0			0
$832$	0.127947	+	0.0529974i	0.127947	+	0.0529974i
$833$	1.37736	−	0.685843i	1.37736	−	0.685843i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.769334	−	0.638847i	$-0.779412\pi$
$839$		0			0		0.769334	+	0.638847i	$0.220588\pi$
$840$		0			0
$841$	−0.879704	+	1.57937i	−0.879704	+	1.57937i
$842$	−0.0455932	−	0.00743733i	−0.0455932	−	0.00743733i
$843$		0			0
$844$		0			0
$845$	0.268414	+	0.943379i	0.268414	+	0.943379i
$846$		0			0
$847$		0			0
$848$	1.76879	−	0.0408661i	1.76879	−	0.0408661i
$849$		0			0
$850$	−0.927255	+	1.22788i	−0.927255	+	1.22788i
$851$		0			0
$852$		0			0
$853$	0.0286833	−	0.0362122i	0.0286833	−	0.0362122i	−0.769334	−	0.638847i	$-0.779412\pi$
$853$	0.0286833	−	0.0362122i	0.0286833	−	0.0362122i	0.798017	+	0.602635i	$0.205882\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.388276	−	0.140193i	0.388276	−	0.140193i	−0.138156	−	0.990410i	$-0.544118\pi$
$857$	0.388276	−	0.140193i	0.388276	−	0.140193i	0.526432	+	0.850217i	$0.323529\pi$
$858$		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
$865$	−1.79844	+	0.794087i	−1.79844	+	0.794087i
$866$	−0.800095	+	0.111609i	−0.800095	+	0.111609i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	1.78099	+	0.418885i	1.78099	+	0.418885i
$873$	1.83545	−	0.212941i	1.83545	−	0.212941i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.496369	+	0.689873i	0.496369	+	0.689873i	0.982973	−	0.183750i	$-0.0588235\pi$
$877$	0.496369	+	0.689873i	0.496369	+	0.689873i	−0.486604	+	0.873622i	$0.661765\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.404479	−	0.368731i	−0.404479	−	0.368731i	0.445738	−	0.895163i	$-0.352941\pi$
$881$	−0.404479	−	0.368731i	−0.404479	−	0.368731i	−0.850217	+	0.526432i	$0.823529\pi$
$882$	−0.138156	+	0.990410i	−0.138156	+	0.990410i
$883$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$883$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$884$	−0.0723663	−	0.200424i	−0.0723663	−	0.200424i
$885$		0			0
$886$		0			0
$887$		0			0		0.0461835	−	0.998933i	$-0.485294\pi$
$887$		0			0		−0.0461835	+	0.998933i	$0.514706\pi$
$888$		0			0
$889$		0			0
$890$	0.674498	−	1.27962i	0.674498	−	1.27962i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	1.11159	+	1.21936i	1.11159	+	1.21936i
$899$		0			0
$900$	−0.317791	−	0.948161i	−0.317791	−	0.948161i
$901$	−1.87998	−	1.96891i	−1.87998	−	1.96891i
$902$		0			0
$903$		0			0
$904$	1.78682	+	0.291473i	1.78682	+	0.291473i
$905$	0.835282	+	0.761460i	0.835282	+	0.761460i
$906$		0			0
$907$		0			0		0.967890	−	0.251374i	$-0.0808824\pi$
$907$		0			0		−0.967890	+	0.251374i	$0.919118\pi$
$908$		0			0
$909$	−1.58561	+	0.981767i	−1.58561	+	0.981767i
$910$		0			0
$911$		0			0		0.584041	−	0.811724i	$-0.301471\pi$
$911$		0			0		−0.584041	+	0.811724i	$0.698529\pi$
$912$		0			0
$913$		0			0
$914$	−1.95641	+	0.412700i	−1.95641	+	0.412700i
$915$		0			0
$916$	−0.143110	−	0.180675i	−0.143110	−	0.180675i
$917$		0			0
$918$		0			0
$919$		0			0		0.656446	−	0.754373i	$-0.272059\pi$
$919$		0			0		−0.656446	+	0.754373i	$0.727941\pi$
$920$		0			0
$921$		0			0
$922$	1.47802			1.47802
$923$		0			0
$924$		0			0
$925$	−1.91373	−	0.357738i	−1.91373	−	0.357738i
$926$		0			0
$927$		0			0
$928$	−1.31353	−	1.04043i	−1.31353	−	1.04043i
$929$	−0.256725	−	0.581427i	−0.256725	−	0.581427i	0.739009	−	0.673696i	$-0.235294\pi$
$929$	−0.256725	−	0.581427i	−0.256725	−	0.581427i	−0.995734	+	0.0922684i	$0.970588\pi$
$930$		0			0
$931$		0			0
$932$	1.44123	+	1.25414i	1.44123	+	1.25414i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	0.134042	+	0.0348125i	0.134042	+	0.0348125i
$937$	0.282729	−	0.234776i	0.282729	−	0.234776i	−0.486604	−	0.873622i	$-0.661765\pi$
$937$	0.282729	−	0.234776i	0.282729	−	0.234776i	0.769334	+	0.638847i	$0.220588\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	0.349657	+	1.22892i	0.349657	+	1.22892i	0.914794	+	0.403921i	$0.132353\pi$
$941$	0.349657	+	1.22892i	0.349657	+	1.22892i	−0.565136	+	0.824997i	$0.691176\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.955248	−	0.295806i	$-0.904412\pi$
$947$		0			0		0.955248	+	0.295806i	$0.0955882\pi$
$948$		0			0
$949$	−0.0118181	+	0.00489520i	−0.0118181	+	0.00489520i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.163138	+	0.277605i	−0.163138	+	0.277605i	−0.932472	−	0.361242i	$-0.882353\pi$
$953$	−0.163138	+	0.277605i	−0.163138	+	0.277605i	0.769334	+	0.638847i	$0.220588\pi$
$954$	1.74618	−	0.284843i	1.74618	−	0.284843i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.973438	−	0.228951i	0.973438	−	0.228951i
$962$	0.186196	−	0.195003i	0.186196	−	0.195003i
$963$		0			0
$964$	−0.302855	−	1.85660i	−0.302855	−	1.85660i
$965$			1.34739i			1.34739i
$966$		0			0
$967$		0			0		−0.995734	−	0.0922684i	$-0.970588\pi$
$967$		0			0		0.995734	+	0.0922684i	$0.0294118\pi$
$968$	−0.673696	+	0.739009i	−0.673696	+	0.739009i
$969$		0			0
$970$	−1.80797	+	0.381387i	−1.80797	+	0.381387i
$971$		0			0		−0.466296	−	0.884629i	$-0.654412\pi$
$971$		0			0		0.466296	+	0.884629i	$0.345588\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	1.01962	−	1.22788i	1.01962	−	1.22788i
$977$	0.321055	+	0.178827i	0.321055	+	0.178827i	0.638847	−	0.769334i	$-0.279412\pi$
$977$	0.321055	+	0.178827i	0.321055	+	0.178827i	−0.317791	+	0.948161i	$0.602941\pi$
$978$		0			0
$979$		0			0
$980$	0.0461835	−	0.998933i	0.0461835	−	0.998933i
$981$	1.82178	+	0.168813i	1.82178	+	0.168813i
$982$		0			0
$983$		0			0		−0.997600	−	0.0692444i	$-0.977941\pi$
$983$		0			0		0.997600	+	0.0692444i	$0.0220588\pi$
$984$		0			0
$985$	0.614268	−	0.380338i	0.614268	−	0.380338i
$986$	0.178532	+	2.57210i	0.178532	+	2.57210i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.403921	−	0.914794i	$-0.367647\pi$
$991$		0			0		−0.403921	+	0.914794i	$0.632353\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−0.161215	+	0.0897964i	−0.161215	+	0.0897964i	−0.565136	−	0.824997i	$-0.691176\pi$
$997$	−0.161215	+	0.0897964i	−0.161215	+	0.0897964i	0.403921	+	0.914794i	$0.367647\pi$
$998$		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.1187.1	yes	64
4.3	odd	2	CM	2740.1.cd.a.1187.1	yes	64
5.3	odd	4		2740.1.bw.a.2283.1	yes	64
20.3	even	4		2740.1.bw.a.2283.1	yes	64
137.134	odd	136		2740.1.bw.a.1367.1	✓	64
548.271	even	136		2740.1.bw.a.1367.1	✓	64
685.408	even	136	inner	2740.1.cd.a.2463.1	yes	64
2740.2463	odd	136	inner	2740.1.cd.a.2463.1	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2740.1.bw.a.1367.1	✓	64	137.134	odd	136
2740.1.bw.a.1367.1	✓	64	548.271	even	136
2740.1.bw.a.2283.1	yes	64	5.3	odd	4
2740.1.bw.a.2283.1	yes	64	20.3	even	4
2740.1.cd.a.1187.1	yes	64	1.1	even	1	trivial
2740.1.cd.a.1187.1	yes	64	4.3	odd	2	CM
2740.1.cd.a.2463.1	yes	64	685.408	even	136	inner
2740.1.cd.a.2463.1	yes	64	2740.2463	odd	136	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.850217 + 0.526432i) q^{2} +(0.445738 + 0.895163i) q^{4} +(-0.638847 - 0.769334i) q^{5} +(-0.0922684 + 0.995734i) q^{8} +(0.0461835 + 0.998933i) q^{9} +O(q^{10})\)	\(q+(0.850217 + 0.526432i) q^{2} +(0.445738 + 0.895163i) q^{4} +(-0.638847 - 0.769334i) q^{5} +(-0.0922684 + 0.995734i) q^{8} +(0.0461835 + 0.998933i) q^{9} +(-0.138156 - 0.990410i) q^{10} +(-0.135507 - 0.0285848i) q^{13} +(-0.602635 + 0.798017i) q^{16} +(1.53210 - 0.141970i) q^{17} +(-0.486604 + 0.873622i) q^{18} +(0.403921 - 0.914794i) q^{20} +(-0.183750 + 0.982973i) q^{25} +(-0.100162 - 0.0956383i) q^{26} +(0.848980 + 1.44467i) q^{29} +(-0.932472 + 0.361242i) q^{32} +(1.37736 + 0.685843i) q^{34} +(-0.873622 + 0.486604i) q^{36} +1.94688i q^{37} +(0.824997 - 0.565136i) q^{40} +(0.475221 - 1.14729i) q^{41} +(0.739009 - 0.673696i) q^{45} +(0.932472 - 0.361242i) q^{49} +(-0.673696 + 0.739009i) q^{50} +(-0.0348125 - 0.134042i) q^{52} +(-1.09854 - 1.38689i) q^{53} +(-0.0387043 + 1.67521i) q^{58} +(-1.59433 - 0.0737104i) q^{61} +(-0.982973 - 0.183750i) q^{64} +(0.0645767 + 0.122511i) q^{65} +(0.810004 + 1.30820i) q^{68} +(-0.998933 - 0.0461835i) q^{72} +(0.0762025 - 0.0521999i) q^{73} +(-1.02490 + 1.65527i) q^{74} +(0.998933 - 0.0461835i) q^{80} +(-0.995734 + 0.0922684i) q^{81} +(1.00801 - 0.725270i) q^{82} +(-1.08800 - 1.08800i) q^{85} +(1.17416 + 0.844817i) q^{89} +(0.982973 - 0.183750i) q^{90} +(-0.127947 - 1.84332i) q^{97} +(0.982973 + 0.183750i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} - 4 q^{4} + 4 q^{8}+O(q^{10}) \) 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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